LMFDB - Embedded newform 43.7.f.a.2.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,7,Mod(2,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([9]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	43.f (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.89232559565$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$21$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			2.13
Character	$\chi$	$=$	43.2
Dual form			43.7.f.a.22.13

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11483 + 2.31496i) q^{2} +(18.6979 - 38.8265i) q^{3} +(35.7871 - 44.8756i) q^{4} +(137.550 + 31.3949i) q^{5} +110.727 q^{6} +167.161i q^{7} +(304.102 + 69.4092i) q^{8} +(-703.365 - 881.992i) q^{9} +O(q^{10})$	\(q+(1.11483 + 2.31496i) q^{2} +(18.6979 - 38.8265i) q^{3} +(35.7871 - 44.8756i) q^{4} +(137.550 + 31.3949i) q^{5} +110.727 q^{6} +167.161i q^{7} +(304.102 + 69.4092i) q^{8} +(-703.365 - 881.992i) q^{9} +(80.6666 + 353.424i) q^{10} +(-449.994 - 564.275i) q^{11} +(-1073.22 - 2228.57i) q^{12} +(-269.644 + 1181.39i) q^{13} +(-386.972 + 186.356i) q^{14} +(3790.85 - 4753.58i) q^{15} +(-639.085 - 2800.01i) q^{16} +(1343.57 + 5886.55i) q^{17} +(1257.65 - 2611.53i) q^{18} +(-1791.70 - 1428.83i) q^{19} +(6331.40 - 5049.12i) q^{20} +(6490.28 + 3125.56i) q^{21} +(804.610 - 1670.79i) q^{22} +(1018.14 + 1276.70i) q^{23} +(8380.97 - 10509.4i) q^{24} +(3856.78 + 1857.33i) q^{25} +(-3035.48 + 692.828i) q^{26} +(-16768.1 + 3827.21i) q^{27} +(7501.46 + 5982.22i) q^{28} +(-12111.5 - 25149.8i) q^{29} +(15230.5 + 3476.26i) q^{30} +(-35994.9 + 17334.3i) q^{31} +(21377.2 - 17047.7i) q^{32} +(-30322.8 + 6920.98i) q^{33} +(-12129.3 + 9672.79i) q^{34} +(-5248.01 + 22993.0i) q^{35} -64751.4 q^{36} +57675.0i q^{37} +(1310.26 - 5740.62i) q^{38} +(40827.5 + 32558.8i) q^{39} +(39650.1 + 19094.5i) q^{40} +(38489.8 - 18535.7i) q^{41} +18509.2i q^{42} +(64855.7 + 45990.2i) q^{43} -41426.2 q^{44} +(-69058.0 - 143400. i) q^{45} +(-1820.47 + 3780.25i) q^{46} +(-71242.4 + 89335.2i) q^{47} +(-120664. - 27540.9i) q^{48} +89706.2 q^{49} +10998.9i q^{50} +(253676. + 57899.9i) q^{51} +(43365.8 + 54379.0i) q^{52} +(43839.1 + 192072. i) q^{53} +(-27553.4 - 34550.9i) q^{54} +(-44181.4 - 91743.7i) q^{55} +(-11602.5 + 50833.9i) q^{56} +(-88977.6 + 42849.4i) q^{57} +(44718.7 - 56075.5i) q^{58} +(-87202.5 - 382059. i) q^{59} +(-77656.2 - 340234. i) q^{60} +(-131089. + 272210. i) q^{61} +(-80256.3 - 64002.3i) q^{62} +(147435. - 117575. i) q^{63} +(-102310. - 49269.8i) q^{64} +(-74179.2 + 154035. i) q^{65} +(-49826.5 - 62480.4i) q^{66} +(224291. - 281252. i) q^{67} +(312245. + 150369. i) q^{68} +(68606.9 - 15659.1i) q^{69} +(-59078.6 + 13484.3i) q^{70} +(-91052.3 - 72611.8i) q^{71} +(-152676. - 317035. i) q^{72} +(350082. + 79903.8i) q^{73} +(-133516. + 64297.7i) q^{74} +(144227. - 115017. i) q^{75} +(-128240. + 29269.9i) q^{76} +(94324.8 - 75221.5i) q^{77} +(-29856.9 + 130811. i) q^{78} +648492. q^{79} -405207. i q^{80} +(18068.8 - 79164.6i) q^{81} +(85819.0 + 68438.3i) q^{82} +(285499. + 137489. i) q^{83} +(372530. - 179401. i) q^{84} +851877. i q^{85} +(-34162.7 + 201410. i) q^{86} -1.20294e6 q^{87} +(-97678.1 - 202831. i) q^{88} +(-531436. + 1.10354e6i) q^{89} +(254979. - 319733. i) q^{90} +(-197482. - 45074.0i) q^{91} +93729.0 q^{92} +1.72167e6i q^{93} +(-286231. - 65330.2i) q^{94} +(-201591. - 252787. i) q^{95} +(-262196. - 1.14876e6i) q^{96} +(-1.05002e6 - 1.31668e6i) q^{97} +(100007. + 207666. i) q^{98} +(-181176. + 793783. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) $ 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.11483	+	2.31496i	0.139353	+	0.289370i	0.958952	−	0.283567i	$-0.0915180\pi$
$2$	1.11483	+	2.31496i	0.139353	+	0.289370i	−0.819599	+	0.572938i	$0.805804\pi$
$3$	18.6979	−	38.8265i	0.692514	−	1.43802i	−0.196670	−	0.980470i	$-0.563013\pi$
$3$	18.6979	−	38.8265i	0.692514	−	1.43802i	0.889184	−	0.457550i	$-0.151273\pi$
$4$	35.7871	−	44.8756i	0.559174	−	0.701182i
$5$	137.550	+	31.3949i	1.10040	+	0.251159i	0.733900	−	0.679258i	$-0.237698\pi$
$5$	137.550	+	31.3949i	1.10040	+	0.251159i	0.366502	+	0.930417i	$0.380555\pi$
$6$	110.727			0.512624
$7$			167.161i			0.487350i	0.969857	+	0.243675i	$0.0783530\pi$
$7$			167.161i			0.487350i	−0.969857	+	0.243675i	$0.921647\pi$
$8$	304.102	+	69.4092i	0.593948	+	0.135565i
$9$	−703.365	−	881.992i	−0.964836	−	1.20987i
$10$	80.6666	+	353.424i	0.0806666	+	0.353424i
$11$	−449.994	−	564.275i	−0.338087	−	0.423948i	0.583504	−	0.812111i	$-0.301681\pi$
$11$	−449.994	−	564.275i	−0.338087	−	0.423948i	−0.921591	+	0.388162i	$0.873110\pi$
$12$	−1073.22	−	2228.57i	−0.621078	−	1.28968i
$13$	−269.644	+	1181.39i	−0.122733	+	0.537728i	0.875755	+	0.482756i	$0.160364\pi$
$13$	−269.644	+	1181.39i	−0.122733	+	0.537728i	−0.998488	+	0.0549722i	$0.982493\pi$
$14$	−386.972	+	186.356i	−0.141025	+	0.0679139i
$15$	3790.85	−	4753.58i	1.12322	−	1.40847i
$16$	−639.085	−	2800.01i	−0.156027	−	0.683597i
$17$	1343.57	+	5886.55i	0.273472	+	1.19816i	0.905884	+	0.423526i	$0.139208\pi$
$17$	1343.57	+	5886.55i	0.273472	+	1.19816i	−0.632412	+	0.774632i	$0.717935\pi$
$18$	1257.65	−	2611.53i	0.215646	−	0.447794i
$19$	−1791.70	−	1428.83i	−0.261219	−	0.208315i	0.484119	−	0.875002i	$-0.339140\pi$
$19$	−1791.70	−	1428.83i	−0.261219	−	0.208315i	−0.745338	+	0.666687i	$0.767712\pi$
$20$	6331.40	−	5049.12i	0.791424	−	0.631140i
$21$	6490.28	+	3125.56i	0.700819	+	0.337497i
$22$	804.610	−	1670.79i	0.0755644	−	0.156911i
$23$	1018.14	+	1276.70i	0.0836801	+	0.104931i	0.821909	−	0.569619i	$-0.192909\pi$
$23$	1018.14	+	1276.70i	0.0836801	+	0.104931i	−0.738229	+	0.674550i	$0.764338\pi$
$24$	8380.97	−	10509.4i	0.606262	−	0.760229i
$25$	3856.78	+	1857.33i	0.246834	+	0.118869i
$26$	−3035.48	+	692.828i	−0.172706	+	0.0394190i
$27$	−16768.1	+	3827.21i	−0.851909	+	0.194443i
$28$	7501.46	+	5982.22i	0.341721	+	0.272513i
$29$	−12111.5	−	25149.8i	−0.496598	−	1.03120i	−0.987152	−	0.159785i	$-0.948920\pi$
$29$	−12111.5	−	25149.8i	−0.496598	−	1.03120i	0.490554	−	0.871411i	$-0.336794\pi$
$30$	15230.5	+	3476.26i	0.564093	+	0.128750i
$31$	−35994.9	+	17334.3i	−1.20825	+	0.581862i	−0.926016	−	0.377484i	$-0.876789\pi$
$31$	−35994.9	+	17334.3i	−1.20825	+	0.581862i	−0.282233	+	0.959346i	$0.591075\pi$
$32$	21377.2	−	17047.7i	0.652379	−	0.520255i
$33$	−30322.8	+	6920.98i	−0.843776	+	0.192586i
$34$	−12129.3	+	9672.79i	−0.308602	+	0.246102i
$35$	−5248.01	+	22993.0i	−0.122403	+	0.536281i
$36$	−64751.4			−1.38785
$37$			57675.0i			1.13863i	0.822119	+	0.569315i	$0.192792\pi$
$37$			57675.0i			1.13863i	−0.822119	+	0.569315i	$0.807208\pi$
$38$	1310.26	−	5740.62i	0.0238785	−	0.104618i
$39$	40827.5	+	32558.8i	0.688269	+	0.548877i
$40$	39650.1	+	19094.5i	0.619533	+	0.298352i
$41$	38489.8	−	18535.7i	0.558463	−	0.268941i	−0.133289	−	0.991077i	$-0.542554\pi$
$41$	38489.8	−	18535.7i	0.558463	−	0.268941i	0.691751	+	0.722136i	$0.256839\pi$
$42$			18509.2i			0.249828i
$43$	64855.7	+	45990.2i	0.815723	+	0.578442i
$43$	64855.7	+	45990.2i	0.815723	+	0.578442i
$44$	−41426.2			−0.486315
$45$	−69058.0	−	143400.i	−0.757838	−	1.57367i
$46$	−1820.47	+	3780.25i	−0.0187030	+	0.0388371i
$47$	−71242.4	+	89335.2i	−0.686191	+	0.860456i	−0.995908	−	0.0903725i	$-0.971194\pi$
$47$	−71242.4	+	89335.2i	−0.686191	+	0.860456i	0.309717	+	0.950829i	$0.399766\pi$
$48$	−120664.	−	27540.9i	−1.09108	−	0.249031i
$49$	89706.2			0.762490
$50$			10998.9i			0.0879911i
$51$	253676.	+	57899.9i	1.91236	+	0.436483i
$52$	43365.8	+	54379.0i	0.308416	+	0.386742i
$53$	43839.1	+	192072.i	0.294465	+	1.29014i	0.878240	+	0.478221i	$0.158718\pi$
$53$	43839.1	+	192072.i	0.294465	+	1.29014i	−0.583774	+	0.811916i	$0.698425\pi$
$54$	−27553.4	−	34550.9i	−0.174982	−	0.219421i
$55$	−44181.4	−	91743.7i	−0.265553	−	0.551427i
$56$	−11602.5	+	50833.9i	−0.0660675	+	0.289461i
$57$	−88977.6	+	42849.4i	−0.480459	+	0.231377i
$58$	44718.7	−	56075.5i	0.229195	−	0.287401i
$59$	−87202.5	−	382059.i	−0.424593	−	1.86026i	−0.504424	−	0.863456i	$-0.668295\pi$
$59$	−87202.5	−	382059.i	−0.424593	−	1.86026i	0.0798304	−	0.996808i	$-0.474562\pi$
$60$	−77656.2	−	340234.i	−0.359519	−	1.57516i
$61$	−131089.	+	272210.i	−0.577535	+	1.19926i	0.383681	+	0.923466i	$0.374656\pi$
$61$	−131089.	+	272210.i	−0.577535	+	1.19926i	−0.961216	+	0.275797i	$0.911058\pi$
$62$	−80256.3	−	64002.3i	−0.336747	−	0.268547i
$63$	147435.	−	117575.i	0.589628	−	0.470213i
$64$	−102310.	−	49269.8i	−0.390281	−	0.187949i
$65$	−74179.2	+	154035.i	−0.270111	+	0.560891i
$66$	−49826.5	−	62480.4i	−0.173312	−	0.217326i
$67$	224291.	−	281252.i	0.745741	−	0.935129i	−0.253743	−	0.967272i	$-0.581662\pi$
$67$	224291.	−	281252.i	0.745741	−	0.935129i	0.999483	+	0.0321425i	$0.0102331\pi$
$68$	312245.	+	150369.i	0.993045	+	0.478225i
$69$	68606.9	−	15659.1i	0.208843	−	0.0476671i
$70$	−59078.6	+	13484.3i	−0.172241	+	0.0393129i
$71$	−91052.3	−	72611.8i	−0.254399	−	0.202877i	0.487983	−	0.872853i	$-0.337733\pi$
$71$	−91052.3	−	72611.8i	−0.254399	−	0.202877i	−0.742382	+	0.669976i	$0.766304\pi$
$72$	−152676.	−	317035.i	−0.409047	−	0.849396i
$73$	350082.	+	79903.8i	0.899913	+	0.205399i	0.647361	−	0.762184i	$-0.275873\pi$
$73$	350082.	+	79903.8i	0.899913	+	0.205399i	0.252553	+	0.967583i	$0.418730\pi$
$74$	−133516.	+	64297.7i	−0.329486	+	0.158672i
$75$	144227.	−	115017.i	0.341872	−	0.272633i
$76$	−128240.	+	29269.9i	−0.292134	+	0.0666776i
$77$	94324.8	−	75221.5i	0.206611	−	0.164767i
$78$	−29856.9	+	130811.i	−0.0629159	+	0.275653i
$79$	648492.			1.31530			0.657648	−	0.753326i	$-0.271552\pi$
$79$	648492.			1.31530			0.657648	+	0.753326i	$0.271552\pi$
$80$		−	405207.i		−	0.791419i
$81$	18068.8	−	79164.6i	0.0339996	−	0.148962i
$82$	85819.0	+	68438.3i	0.155647	+	0.124125i
$83$	285499.	+	137489.i	0.499311	+	0.240455i	0.666549	−	0.745461i	$-0.267771\pi$
$83$	285499.	+	137489.i	0.499311	+	0.240455i	−0.167238	+	0.985916i	$0.553485\pi$
$84$	372530.	−	179401.i	0.628526	−	0.302682i
$85$			851877.i			1.38714i
$86$	−34162.7	+	201410.i	−0.0537102	+	0.316654i
$87$	−1.20294e6			−1.82678
$88$	−97678.1	−	202831.i	−0.143334	−	0.297636i
$89$	−531436.	+	1.10354e6i	−0.753843	+	1.56537i	0.0693387	+	0.997593i	$0.477911\pi$
$89$	−531436.	+	1.10354e6i	−0.753843	+	1.56537i	−0.823182	+	0.567778i	$0.807803\pi$
$90$	254979.	−	319733.i	0.349765	−	0.438591i
$91$	−197482.	−	45074.0i	−0.262062	−	0.0598139i
$92$	93729.0			0.120368
$93$			1.72167e6i			2.14043i
$94$	−286231.	−	65330.2i	−0.344614	−	0.0786558i
$95$	−201591.	−	252787.i	−0.235125	−	0.294838i
$96$	−262196.	−	1.14876e6i	−0.296356	−	1.29842i
$97$	−1.05002e6	−	1.31668e6i	−1.15049	−	1.44267i	−0.876803	−	0.480849i	$-0.840328\pi$
$97$	−1.05002e6	−	1.31668e6i	−1.15049	−	1.44267i	−0.273686	−	0.961819i	$-0.588243\pi$
$98$	100007.	+	207666.i	0.106256	+	0.220642i
$99$	−181176.	+	793783.i	−0.186722	+	0.818081i
$100$	221372.	−	106607.i	0.221372	−	0.106607i
$101$	−227553.	+	285342.i	−0.220861	+	0.276950i	−0.879901	−	0.475157i	$-0.842391\pi$
$101$	−227553.	+	285342.i	−0.220861	+	0.276950i	0.659040	+	0.752108i	$0.270963\pi$
$102$	148769.	+	651799.i	0.140188	+	0.614205i
$103$	−95257.7	−	417351.i	−0.0871743	−	0.381935i	0.912455	−	0.409178i	$-0.134184\pi$
$103$	−95257.7	−	417351.i	−0.0871743	−	0.381935i	−0.999629	+	0.0272426i	$0.991327\pi$
$104$	−163998.	+	340546.i	−0.145794	+	0.302744i
$105$	794613.	+	633683.i	0.686417	+	0.547399i
$106$	−395766.	+	315613.i	−0.332293	+	0.264995i
$107$	−827423.	−	398466.i	−0.675423	−	0.325267i	0.0645389	−	0.997915i	$-0.479442\pi$
$107$	−827423.	−	398466.i	−0.675423	−	0.325267i	−0.739962	+	0.672648i	$0.765157\pi$
$108$	−428334.	+	889445.i	−0.340026	+	0.706070i
$109$	441478.	+	553596.i	0.340902	+	0.427478i	0.922499	−	0.385999i	$-0.126143\pi$
$109$	441478.	+	553596.i	0.340902	+	0.427478i	−0.581597	+	0.813477i	$0.697572\pi$
$110$	163129.	−	204557.i	0.122561	−	0.153686i
$111$	2.23932e6	+	1.07840e6i	1.63737	+	0.788517i
$112$	468053.	−	106830.i	0.333151	−	0.0760396i
$113$	925178.	−	211166.i	0.641195	−	0.146349i	0.110452	−	0.993881i	$-0.464770\pi$
$113$	925178.	−	211166.i	0.641195	−	0.146349i	0.530743	+	0.847533i	$0.321913\pi$
$114$	−198389.	−	158210.i	−0.133907	−	0.106787i
$115$	99962.8	+	207575.i	0.0657271	+	0.136484i
$116$	−1.56205e6	−	356528.i	−1.00074	−	0.228413i
$117$	1.23163e6	−	593124.i	0.768996	−	0.370329i
$118$	787237.	−	627801.i	0.479137	−	0.382099i
$119$	−984002.	+	224592.i	−0.583922	+	0.133276i
$120$	1.48275e6	−	1.18245e6i	0.858071	−	0.684289i
$121$	278298.	−	1.21930e6i	0.157092	−	0.688265i
$122$	−776298.			−0.427513
$123$		−	1.84100e6i		−	0.989326i
$124$	−510270.	+	2.23564e6i	−0.267630	+	1.17256i
$125$	−1.25135e6	−	997920.i	−0.640692	−	0.510935i
$126$	436547.	+	210230.i	0.218232	+	0.105095i
$127$	−386070.	+	185922.i	−0.188476	+	0.0907651i	−0.525742	−	0.850644i	$-0.676212\pi$
$127$	−386070.	+	185922.i	−0.188476	+	0.0907651i	0.337266	+	0.941409i	$0.390498\pi$
$128$		−	2.04169e6i		−	0.973552i
$129$	2.99830e6	−	1.65820e6i	1.39671	−	0.772447i
$130$	−439282.			−0.199946
$131$	−799625.	−	1.66044e6i	−0.355690	−	0.738599i	0.643959	−	0.765060i	$-0.277291\pi$
$131$	−799625.	−	1.66044e6i	−0.355690	−	0.738599i	−0.999650	+	0.0264608i	$0.991576\pi$
$132$	−774582.	+	1.60844e6i	−0.336780	+	0.699330i
$133$	238845.	−	299502.i	0.101522	−	0.127305i
$134$	901134.	+	205678.i	0.374520	+	0.0854818i
$135$	−2.42661e6			−0.986278
$136$			1.88337e6i			0.748717i
$137$	−3.72565e6	−	850355.i	−1.44891	−	0.330703i	−0.575542	−	0.817772i	$-0.695209\pi$
$137$	−3.72565e6	−	850355.i	−1.44891	−	0.330703i	−0.873363	+	0.487069i	$0.838066\pi$
$138$	112735.	+	141365.i	0.0428964	+	0.0537904i
$139$	−543691.	−	2.38207e6i	−0.202445	−	0.886971i	−0.969442	−	0.245320i	$-0.921107\pi$
$139$	−543691.	−	2.38207e6i	−0.202445	−	0.886971i	0.766997	−	0.641651i	$-0.221750\pi$
$140$	844016.	+	1.05836e6i	0.307586	+	0.385701i
$141$	2.13649e6	+	4.43647e6i	0.762156	+	1.58263i
$142$	66586.0	−	291732.i	0.0232551	−	0.101887i
$143$	787967.	−	379465.i	0.269463	−	0.129767i
$144$	−2.02008e6	+	2.53310e6i	−0.676521	+	0.848330i
$145$	−876365.	−	3.83961e6i	−0.287462	−	1.25945i
$146$	205306.	+	899505.i	0.0659695	+	0.289031i
$147$	1.67731e6	−	3.48298e6i	0.528035	−	1.09648i
$148$	2.58820e6	+	2.06402e6i	0.798387	+	0.636692i
$149$	−2.01620e6	+	1.60787e6i	−0.609502	+	0.486061i	−0.878925	−	0.476960i	$-0.841738\pi$
$149$	−2.01620e6	+	1.60787e6i	−0.609502	+	0.486061i	0.269423	+	0.963022i	$0.413167\pi$
$150$	427049.	+	205656.i	0.126533	+	0.0609351i
$151$	1.80835e6	−	3.75508e6i	0.525233	−	1.09066i	−0.454574	−	0.890709i	$-0.650208\pi$
$151$	1.80835e6	−	3.75508e6i	0.525233	−	1.09066i	0.979807	−	0.199948i	$-0.0640773\pi$
$152$	−445685.	−	558871.i	−0.126910	−	0.159140i
$153$	4.24687e6	−	5.32541e6i	1.18576	−	1.48689i
$154$	279291.	+	134499.i	0.0764706	+	0.0368263i
$155$	−5.49532e6	+	1.25427e6i	−1.47570	+	0.336819i
$156$	2.92220e6	−	666972.i	0.769725	−	0.175685i
$157$	1.42290e6	+	1.13472e6i	0.367684	+	0.293218i	0.789850	−	0.613300i	$-0.210158\pi$
$157$	1.42290e6	+	1.13472e6i	0.367684	+	0.293218i	−0.422165	+	0.906519i	$0.638730\pi$
$158$	722957.	+	1.50123e6i	0.183291	+	0.380607i
$159$	8.27718e6	+	1.88921e6i	2.05916	+	0.469991i
$160$	3.47565e6	−	1.67378e6i	0.848546	−	0.408638i
$161$	−213415.	+	170193.i	−0.0511384	+	0.0407815i
$162$	203407.	−	46426.2i	0.0478432	−	0.0109199i
$163$	−5.28616e6	+	4.21557e6i	−1.22061	+	0.973404i	−0.999998	−	0.00195709i	$-0.999377\pi$
$163$	−5.28616e6	+	4.21557e6i	−1.22061	+	0.973404i	−0.220612	+	0.975362i	$0.570806\pi$
$164$	545638.	−	2.39060e6i	0.123701	−	0.541969i
$165$	−4.38819e6			−0.976862
$166$			814197.i			0.177994i
$167$	−377824.	+	1.65535e6i	−0.0811223	+	0.355420i	−0.999156	−	0.0410830i	$-0.986919\pi$
$167$	−377824.	+	1.65535e6i	−0.0811223	+	0.355420i	0.918033	+	0.396503i	$0.129776\pi$
$168$	1.75676e6	+	1.40097e6i	0.370498	+	0.295462i
$169$	3.02583e6	+	1.45716e6i	0.626881	+	0.301890i
$170$	−1.97206e6	+	949696.i	−0.401397	+	0.193303i
$171$			2.58526e6i			0.517030i
$172$	4.38484e6	−	1.26458e6i	0.861725	−	0.248521i
$173$	−8.87572e6			−1.71421			−0.857107	−	0.515138i	$-0.827741\pi$
$173$	−8.87572e6			−1.71421			−0.857107	+	0.515138i	$0.827741\pi$
$174$	−1.34107e6	−	2.78476e6i	−0.254568	−	0.528616i
$175$	−310473.	+	644703.i	−0.0579307	+	0.120294i
$176$	−1.29239e6	+	1.62061e6i	−0.237059	+	0.297263i
$177$	−1.64645e7	−	3.75792e6i	−2.96913	−	0.677686i
$178$	−3.14711e6			−0.558023
$179$			2.32107e6i			0.404696i	0.979314	+	0.202348i	$0.0648572\pi$
$179$			2.32107e6i			0.404696i	−0.979314	+	0.202348i	$0.935143\pi$
$180$	−8.90657e6	−	2.03287e6i	−1.52719	−	0.348571i
$181$	110800.	+	138939.i	0.0186855	+	0.0234309i	0.791086	−	0.611704i	$-0.209516\pi$
$181$	110800.	+	138939.i	0.0186855	+	0.0234309i	−0.772401	+	0.635135i	$0.780944\pi$
$182$	−115814.	−	507414.i	−0.0192108	−	0.0841682i
$183$	8.11787e6	+	1.01795e7i	1.32461	+	1.66101i
$184$	221002.	+	458915.i	0.0354766	+	0.0736680i
$185$	−1.81070e6	+	7.93321e6i	−0.285978	+	1.25295i
$186$	−3.98561e6	+	1.91937e6i	−0.619378	+	0.298277i
$187$	2.71704e6	−	3.40706e6i	0.415500	−	0.521020i
$188$	1.45941e6	+	6.39410e6i	0.219636	+	0.962290i
$189$	−639761.	−	2.80298e6i	−0.0947616	−	0.415178i
$190$	360453.	−	748488.i	0.0525518	−	0.109125i
$191$	2.68022e6	+	2.13740e6i	0.384654	+	0.306751i	0.796657	−	0.604431i	$-0.206600\pi$
$191$	2.68022e6	+	2.13740e6i	0.384654	+	0.306751i	−0.412004	+	0.911182i	$0.635171\pi$
$192$	−3.82595e6	+	3.05110e6i	−0.540550	+	0.431074i
$193$	1.04338e7	+	5.02466e6i	1.45135	+	0.698931i	0.982828	−	0.184523i	$-0.0590739\pi$
$193$	1.04338e7	+	5.02466e6i	1.45135	+	0.698931i	0.468518	+	0.883454i	$0.344788\pi$
$194$	1.87748e6	−	3.89863e6i	0.257141	−	0.533958i
$195$	4.59364e6	+	5.76025e6i	0.619517	+	0.776850i
$196$	3.21033e6	−	4.02562e6i	0.426365	−	0.534644i
$197$	−1.01547e7	−	4.89025e6i	−1.32822	−	0.639635i	−0.370898	−	0.928673i	$-0.620950\pi$
$197$	−1.01547e7	−	4.89025e6i	−1.32822	−	0.639635i	−0.957317	+	0.289038i	$0.906664\pi$
$198$	−2.03956e6	+	465516.i	−0.262749	+	0.0599707i
$199$	6.95516e6	−	1.58747e6i	0.882568	−	0.201440i	0.242863	−	0.970061i	$-0.421914\pi$
$199$	6.95516e6	−	1.58747e6i	0.882568	−	0.201440i	0.639705	+	0.768620i	$0.279056\pi$
$200$	1.04394e6	+	832511.i	0.130492	+	0.104064i
$201$	−6.72628e6	−	1.39673e7i	−0.828299	−	1.71998i
$202$	−914239.	−	208669.i	−0.110919	−	0.0253165i
$203$	4.20407e6	−	2.02458e6i	0.502553	−	0.242017i
$204$	1.16766e7	−	9.31181e6i	1.37540	−	1.09684i
$205$	5.87621e6	−	1.34121e6i	0.682080	−	0.155680i
$206$	859956.	−	685792.i	0.0983727	−	0.0784496i
$207$	409920.	−	1.79597e6i	0.0462155	−	0.202483i
$208$	3.48023e6			0.386739
$209$			1.65398e6i			0.181172i
$210$	−581096.	+	2.54595e6i	−0.0627466	+	0.274911i
$211$	−3.09604e6	−	2.46901e6i	−0.329578	−	0.262830i	0.444694	−	0.895683i	$-0.353312\pi$
$211$	−3.09604e6	−	2.46901e6i	−0.329578	−	0.262830i	−0.774272	+	0.632853i	$0.781884\pi$
$212$	1.01882e7	+	4.90639e6i	1.06928	+	0.514937i
$213$	−4.52175e6	+	2.17756e6i	−0.467916	+	0.225336i
$214$		−	2.35967e6i		−	0.240774i
$215$	7.47706e6	+	8.36210e6i	0.752342	+	0.841395i
$216$	−5.36486e6			−0.532349
$217$	−2.89761e6	−	6.01695e6i	−0.283570	−	0.588840i
$218$	−789383.	+	1.63917e6i	−0.0761936	+	0.158218i
$219$	9.64817e6	−	1.20984e7i	0.918571	−	1.15185i
$220$	−5.69818e6	−	1.30057e6i	−0.535141	−	0.122143i
$221$	−7.31659e6			−0.677847
$222$			6.38618e6i			0.583690i
$223$	7.21514e6	+	1.64681e6i	0.650624	+	0.148501i	0.535080	−	0.844802i	$-0.320282\pi$
$223$	7.21514e6	+	1.64681e6i	0.650624	+	0.148501i	0.115544	+	0.993302i	$0.463139\pi$
$224$	2.84972e6	+	3.57343e6i	0.253546	+	0.317937i
$225$	−1.07458e6	−	4.70803e6i	−0.0943386	−	0.413325i
$226$	1.52026e6	+	1.90634e6i	0.131702	+	0.165149i
$227$	1.78822e6	+	3.71327e6i	0.152877	+	0.317453i	0.963316	−	0.268371i	$-0.0864853\pi$
$227$	1.78822e6	+	3.71327e6i	0.152877	+	0.317453i	−0.810438	+	0.585824i	$0.800771\pi$
$228$	−1.26136e6	+	5.52638e6i	−0.106423	+	0.466269i
$229$	−1.87278e7	+	9.01884e6i	−1.55948	+	0.751007i	−0.997117	−	0.0758812i	$-0.975823\pi$
$229$	−1.87278e7	+	9.01884e6i	−1.55948	+	0.751007i	−0.562366	+	0.826889i	$0.690109\pi$
$230$	−369087.	+	462820.i	−0.0303351	+	0.0380390i
$231$	−1.15692e6	−	5.06879e6i	−0.0938570	−	0.411214i
$232$	−1.93750e6	−	8.48876e6i	−0.155160	−	0.679798i
$233$	9.06845e6	−	1.88308e7i	0.716911	−	1.48868i	−0.149187	−	0.988809i	$-0.547666\pi$
$233$	9.06845e6	−	1.88308e7i	0.716911	−	1.48868i	0.866099	−	0.499873i	$-0.166620\pi$
$234$	2.74612e6	+	2.18996e6i	0.214324	+	0.170918i
$235$	−1.26041e7	+	1.00514e7i	−0.971197	+	0.774504i
$236$	−2.02659e7	−	9.75954e6i	−1.54181	−	0.742494i
$237$	1.21254e7	−	2.51787e7i	0.910860	−	1.89142i
$238$	−1.61691e6	−	2.02755e6i	−0.119938	−	0.150397i
$239$	−939586.	+	1.17820e6i	−0.0688245	+	0.0863032i	−0.815052	−	0.579388i	$-0.803292\pi$
$239$	−939586.	+	1.17820e6i	−0.0688245	+	0.0863032i	0.746228	+	0.665691i	$0.231863\pi$
$240$	−1.57328e7	−	7.57650e6i	−1.13808	−	0.548069i
$241$	−4.12433e6	+	941352.i	−0.294647	+	0.0672514i	−0.367289	−	0.930107i	$-0.619714\pi$
$241$	−4.12433e6	+	941352.i	−0.294647	+	0.0672514i	0.0726419	+	0.997358i	$0.476857\pi$
$242$	3.13290e6	−	715063.i	0.221055	−	0.0504543i
$243$	−1.25387e7	−	9.99927e6i	−0.873843	−	0.696867i
$244$	7.52428e6	+	1.56243e7i	0.517959	+	1.07555i
$245$	1.23391e7	+	2.81632e6i	0.839045	+	0.191507i
$246$	4.26186e6	−	2.05240e6i	0.286282	−	0.137866i
$247$	2.17113e6	−	1.73142e6i	0.144077	−	0.114898i
$248$	−1.21493e7	+	2.77299e6i	−0.796517	+	0.181800i
$249$	1.06765e7	−	8.51419e6i	0.691559	−	0.551500i
$250$	915106.	−	4.00934e6i	0.0585668	−	0.256598i
$251$	2.26024e7			1.42933			0.714667	−	0.699465i	$-0.246578\pi$
$251$	2.26024e7			1.42933			0.714667	+	0.699465i	$0.246578\pi$
$252$		−	1.08239e7i		−	0.676367i
$253$	262256.	−	1.14902e6i	0.0161943	−	0.0709520i
$254$	−860803.	−	686468.i	−0.0525294	−	0.0418908i
$255$	3.30754e7	+	1.59283e7i	1.99474	+	0.960614i
$256$	−1.82140e6	+	877141.i	−0.108564	+	0.0522817i
$257$			151968.i			0.00895269i	0.999990	+	0.00447634i	$0.00142487\pi$
$257$			151968.i			0.00895269i	−0.999990	+	0.00447634i	$0.998575\pi$
$258$	7.18127e6	+	5.09235e6i	0.418160	+	0.296524i
$259$	−9.64102e6			−0.554912
$260$	4.25775e6	+	8.84131e6i	0.242248	+	0.503033i
$261$	−1.36631e7	+	2.83718e7i	−0.768473	+	1.59575i
$262$	2.95241e6	−	3.70220e6i	0.164162	−	0.205853i
$263$	−3.07645e7	−	7.02180e6i	−1.69115	−	0.385994i	−0.734817	−	0.678266i	$-0.762732\pi$
$263$	−3.07645e7	−	7.02180e6i	−1.69115	−	0.385994i	−0.956335	+	0.292271i	$0.905589\pi$
$264$	−9.70158e6			−0.527267
$265$			2.77958e7i			1.49363i
$266$	959608.	+	219024.i	0.0509858	+	0.0116372i
$267$	3.29098e7	+	4.12676e7i	1.72899	+	2.16808i
$268$	−4.59464e6	−	2.01304e7i	−0.238697	−	1.04580i
$269$	−9.03422e6	−	1.13285e7i	−0.464124	−	0.581993i	0.493598	−	0.869690i	$-0.335682\pi$
$269$	−9.03422e6	−	1.13285e7i	−0.464124	−	0.581993i	−0.957721	+	0.287698i	$0.907110\pi$
$270$	−2.70525e6	−	5.61752e6i	−0.137441	−	0.285400i
$271$	−6.54341e6	+	2.86685e7i	−0.328773	+	1.44045i	0.492699	+	0.870200i	$0.336010\pi$
$271$	−6.54341e6	+	2.86685e7i	−0.328773	+	1.44045i	−0.821472	+	0.570248i	$0.806847\pi$
$272$	1.56238e7	−	7.52401e6i	0.776389	−	0.373889i
$273$	−5.44256e6	+	6.82476e6i	−0.267495	+	0.335428i
$274$	−2.18491e6	−	9.57273e6i	−0.106214	−	0.465355i
$275$	−687485.	−	3.01207e6i	−0.0330571	−	0.144833i
$276$	1.75253e6	−	3.63917e6i	0.0833564	−	0.173091i
$277$	−8.91938e6	−	7.11297e6i	−0.419658	−	0.334666i	0.390787	−	0.920481i	$-0.372203\pi$
$277$	−8.91938e6	−	7.11297e6i	−0.419658	−	0.334666i	−0.810445	+	0.585815i	$0.800774\pi$
$278$	4.90827e6	−	3.91422e6i	0.228452	−	0.182184i
$279$	4.06063e7	+	1.95549e7i	1.86974	+	0.900418i
$280$	−3.19186e6	+	6.62796e6i	−0.145402	+	0.301930i
$281$	4.80602e6	+	6.02655e6i	0.216604	+	0.271613i	0.878248	−	0.478205i	$-0.158712\pi$
$281$	4.80602e6	+	6.02655e6i	0.216604	+	0.271613i	−0.661644	+	0.749818i	$0.730141\pi$
$282$	−7.88845e6	+	9.89180e6i	−0.351758	+	0.441091i
$283$	95465.3	+	45973.6i	0.00421198	+	0.00202838i	0.435989	−	0.899952i	$-0.356399\pi$
$283$	95465.3	+	45973.6i	0.00421198	+	0.00202838i	−0.431777	+	0.901981i	$0.642113\pi$
$284$	−6.51700e6	+	1.48746e6i	−0.284507	+	0.0649368i
$285$	−1.35841e7	+	3.10049e6i	−0.586810	+	0.133936i
$286$	1.75689e6	+	1.40108e6i	0.0751013	+	0.0598913i
$287$	3.09845e6	+	6.43400e6i	0.131069	+	0.272167i
$288$	−3.00719e7	−	6.86372e6i	−1.25888	−	0.287331i
$289$	−1.10991e7	+	5.34505e6i	−0.459827	+	0.221441i
$290$	7.91155e6	−	6.30925e6i	0.324390	−	0.258692i
$291$	−7.07554e7	+	1.61495e7i	−2.87132	+	0.655359i
$292$	1.61142e7	−	1.28506e7i	0.647230	−	0.516149i
$293$	4.59394e6	−	2.01274e7i	0.182635	−	0.800174i	−0.797735	−	0.603008i	$-0.793969\pi$
$293$	4.59394e6	−	2.01274e7i	0.182635	−	0.800174i	0.980370	−	0.197167i	$-0.0631740\pi$
$294$	9.93289e6			0.390871
$295$		−	5.52901e7i		−	2.15368i
$296$	−4.00318e6	+	1.75391e7i	−0.154358	+	0.676288i
$297$	9.70516e6	+	7.73961e6i	0.370453	+	0.295427i
$298$	−5.96987e6	−	2.87494e6i	−0.225588	−	0.108637i
$299$	−1.78282e6	+	858558.i	−0.0666949	+	0.0321186i
$300$		−	1.05884e7i		−	0.392164i
$301$	−7.68777e6	+	1.08413e7i	−0.281904	+	0.397543i
$302$	1.07089e7			0.388797
$303$	6.82410e6	+	1.41704e7i	0.245311	+	0.509394i
$304$	−2.85570e6	+	5.92993e6i	−0.101647	+	0.211071i
$305$	−2.65774e7	+	3.33270e7i	−0.936726	+	1.17462i
$306$	1.70627e7	+	3.89444e6i	0.595501	+	0.135919i
$307$	2.45041e7			0.846882			0.423441	−	0.905924i	$-0.360822\pi$
$307$	2.45041e7			0.846882			0.423441	+	0.905924i	$0.360822\pi$
$308$		−	6.92485e6i		−	0.237005i
$309$	−1.79854e7	−	4.10505e6i	−0.609600	−	0.139137i
$310$	−9.02992e6	−	1.13232e7i	−0.303109	−	0.380087i
$311$	−5.44112e6	−	2.38391e7i	−0.180887	−	0.792517i	−0.981209	−	0.192947i	$-0.938195\pi$
$311$	−5.44112e6	−	2.38391e7i	−0.180887	−	0.792517i	0.800322	−	0.599570i	$-0.204662\pi$
$312$	1.01558e7	+	1.27350e7i	0.334388	+	0.419309i
$313$	1.08818e7	+	2.25963e7i	0.354868	+	0.736892i	0.999622	−	0.0274989i	$-0.00875426\pi$
$313$	1.08818e7	+	2.25963e7i	0.354868	+	0.736892i	−0.644753	+	0.764391i	$0.723040\pi$
$314$	−1.04056e6	+	4.55898e6i	−0.0336107	+	0.147258i
$315$	2.39709e7	−	1.15438e7i	0.766926	−	0.369332i
$316$	2.32077e7	−	2.91015e7i	0.735479	−	0.922262i
$317$	−6.30357e6	−	2.76177e7i	−0.197883	−	0.866982i	−0.972194	−	0.234177i	$-0.924761\pi$
$317$	−6.30357e6	−	2.76177e7i	−0.197883	−	0.866982i	0.774311	−	0.632805i	$-0.218097\pi$
$318$	4.85417e6	+	2.12675e7i	0.150950	+	0.661356i
$319$	−8.74131e6	+	1.81515e7i	−0.269280	+	0.559166i
$320$	−1.25259e7	−	9.98908e6i	−0.382261	−	0.304843i
$321$	−3.09421e7	+	2.46755e7i	−0.935480	+	0.746020i
$322$	−631910.	−	304312.i	−0.0189273	−	0.00911489i
$323$	6.00363e6	−	1.24667e7i	0.178158	−	0.369950i
$324$	−2.90593e6	−	3.64392e6i	−0.0854379	−	0.107136i
$325$	−3.23418e6	+	4.05554e6i	−0.0942138	+	0.118140i
$326$	−1.56520e7	−	7.53762e6i	−0.451771	−	0.217561i
$327$	2.97489e7	−	6.79000e6i	0.850802	−	0.194190i
$328$	1.29914e7	−	2.96519e6i	0.368157	−	0.0840294i
$329$	−1.49334e7	−	1.19090e7i	−0.419343	−	0.334415i
$330$	−4.89207e6	−	1.01585e7i	−0.136129	−	0.282675i
$331$	−3.41709e7	−	7.79930e6i	−0.942265	−	0.215066i	−0.276319	−	0.961066i	$-0.589115\pi$
$331$	−3.41709e7	−	7.79930e6i	−0.942265	−	0.215066i	−0.665946	+	0.746000i	$0.731972\pi$
$332$	1.63871e7	−	7.89162e6i	0.447804	−	0.215651i
$333$	5.08689e7	−	4.05666e7i	1.37759	−	1.09859i
$334$	−4.25329e6	+	970786.i	−0.114153	+	0.0260546i
$335$	3.96812e7	−	3.16447e7i	1.05548	−	0.841718i
$336$	4.60376e6	−	2.01704e7i	0.121365	−	0.531736i
$337$	2.57339e7			0.672382			0.336191	−	0.941794i	$-0.390861\pi$
$337$	2.57339e7			0.672382			0.336191	+	0.941794i	$0.390861\pi$
$338$			8.62918e6i			0.223470i
$339$	9.10003e6	−	3.98698e7i	0.233584	−	1.02340i
$340$	3.82286e7	+	3.04863e7i	0.972638	+	0.775653i
$341$	2.59788e7	+	1.25107e7i	0.655173	+	0.315515i
$342$	−5.98477e6	+	2.88211e6i	−0.149613	+	0.0720498i
$343$			3.46617e7i			0.858949i
$344$	1.65306e7	+	1.84873e7i	0.406081	+	0.454148i
$345$	9.92850e6			0.241783
$346$	−9.89489e6	−	2.05470e7i	−0.238882	−	0.496043i
$347$	2.79371e7	−	5.80119e7i	0.668640	−	1.38844i	−0.239962	−	0.970782i	$-0.577135\pi$
$347$	2.79371e7	−	5.80119e7i	0.668640	−	1.38844i	0.908602	−	0.417663i	$-0.137151\pi$
$348$	−4.30498e7	+	5.39828e7i	−1.02149	+	1.28091i
$349$	−3.74345e7	−	8.54417e6i	−0.880634	−	0.200999i	−0.241784	−	0.970330i	$-0.577732\pi$
$349$	−3.74345e7	−	8.54417e6i	−0.880634	−	0.200999i	−0.638850	+	0.769331i	$0.720590\pi$
$350$	−1.83859e6			−0.0428825
$351$		−	2.08417e7i		−	0.481960i
$352$	−1.92392e7	−	4.39122e6i	−0.441123	−	0.100683i
$353$	−6.14961e6	−	7.71137e6i	−0.139805	−	0.175310i	0.707000	−	0.707214i	$-0.250048\pi$
$353$	−6.14961e6	−	7.71137e6i	−0.139805	−	0.175310i	−0.846805	+	0.531904i	$0.821477\pi$
$354$	−9.65567e6	−	4.23042e7i	−0.217657	−	0.953617i
$355$	−1.02446e7	−	1.28463e7i	−0.228987	−	0.287141i
$356$	3.05034e7	+	6.33410e7i	0.676081	+	1.40390i
$357$	−9.67861e6	+	4.24048e7i	−0.212720	+	0.931988i
$358$	−5.37319e6	+	2.58759e6i	−0.117107	+	0.0563958i
$359$	1.85206e7	−	2.32241e7i	0.400288	−	0.501945i	−0.540311	−	0.841465i	$-0.681693\pi$
$359$	1.85206e7	−	2.32241e7i	0.400288	−	0.501945i	0.940599	+	0.339520i	$0.110265\pi$
$360$	−1.10473e7	−	4.84015e7i	−0.236783	−	1.03741i
$361$	−9.30007e6	−	4.07463e7i	−0.197681	−	0.866096i
$362$	−198116.	+	411392.i	−0.00417632	+	0.00867221i
$363$	−4.21377e7	−	3.36037e7i	−0.880950	−	0.702534i
$364$	−9.09005e6	+	7.24907e6i	−0.188479	+	0.150307i
$365$	4.56452e7	+	2.19816e7i	0.938678	+	0.452043i
$366$	−1.45151e7	+	3.01410e7i	−0.296058	+	0.614772i
$367$	2.98942e7	+	3.74861e7i	0.604768	+	0.758355i	0.986113	−	0.166078i	$-0.0531104\pi$
$367$	2.98942e7	+	3.74861e7i	0.604768	+	0.758355i	−0.381345	+	0.924433i	$0.624539\pi$
$368$	2.92411e6	−	3.66671e6i	0.0586746	−	0.0735756i
$369$	−4.34208e7	−	2.09103e7i	−0.864208	−	0.416181i
$370$	−2.03837e7	+	4.65245e6i	−0.402419	+	0.0918495i
$371$	−3.21069e7	+	7.32819e6i	−0.628748	+	0.143508i
$372$	7.72612e7	+	6.16137e7i	1.50083	+	1.19687i
$373$	2.42834e7	+	5.04250e7i	0.467932	+	0.971671i	0.992721	+	0.120438i	$0.0384300\pi$
$373$	2.42834e7	+	5.04250e7i	0.467932	+	0.971671i	−0.524789	+	0.851232i	$0.675856\pi$
$374$	1.09162e7	+	2.49156e6i	0.208669	+	0.0476273i
$375$	−6.21434e7	+	2.99267e7i	−1.17842	+	0.567499i
$376$	−2.78656e7	+	2.22221e7i	−0.524210	+	0.418043i
$377$	3.29775e7	−	7.52691e6i	0.615452	−	0.140473i
$378$	5.77556e6	−	4.60586e6i	0.106935	−	0.0852776i
$379$	313743.	−	1.37460e6i	0.00576310	−	0.0252498i	−0.971965	−	0.235127i	$-0.924449\pi$
$379$	313743.	−	1.37460e6i	0.00576310	−	0.0252498i	0.977728	+	0.209877i	$0.0673065\pi$
$380$	−1.85583e7			−0.338211
$381$			1.84661e7i			0.333888i
$382$	−1.96003e6	+	8.58744e6i	−0.0351619	+	0.154054i
$383$	2.53181e7	+	2.01905e7i	0.450645	+	0.359378i	0.822358	−	0.568970i	$-0.192658\pi$
$383$	2.53181e7	+	2.01905e7i	0.450645	+	0.359378i	−0.371713	+	0.928348i	$0.621229\pi$
$384$	−7.92716e7	−	3.81752e7i	−1.39999	−	0.674198i
$385$	1.53360e7	−	7.38541e6i	0.268738	−	0.129417i
$386$			2.97555e7i			0.517375i
$387$	−5.05425e6	−	8.95502e7i	−0.0872015	−	1.54502i
$388$	−9.66643e7			−1.65490
$389$	−1.25559e7	−	2.60725e7i	−0.213303	−	0.442929i	0.766674	−	0.642036i	$-0.221910\pi$
$389$	−1.25559e7	−	2.60725e7i	−0.213303	−	0.442929i	−0.979978	+	0.199107i	$0.936196\pi$
$390$	−8.21364e6	+	1.70558e7i	−0.138466	+	0.287527i
$391$	−6.14743e6	+	7.70864e6i	−0.102840	+	0.128958i
$392$	2.72798e7	+	6.22643e6i	0.452880	+	0.103367i
$393$	−7.94203e7			−1.30844
$394$		−	2.89595e7i		−	0.473482i
$395$	8.92002e7	+	2.03594e7i	1.44735	+	0.330349i
$396$	2.91378e7	+	3.65376e7i	0.469214	+	0.588375i
$397$	1.39207e7	+	6.09904e7i	0.222479	+	0.974743i	0.955605	+	0.294651i	$0.0952033\pi$
$397$	1.39207e7	+	6.09904e7i	0.222479	+	0.974743i	−0.733126	+	0.680093i	$0.761940\pi$
$398$	1.14287e7	+	1.43312e7i	0.181280	+	0.227318i
$399$	−7.16274e6	−	1.48736e7i	−0.112761	−	0.234152i
$400$	2.73573e6	−	1.19860e7i	0.0427458	−	0.187282i
$401$	−1.42001e7	+	6.83841e6i	−0.220221	+	0.106053i	−0.540742	−	0.841189i	$-0.681856\pi$
$401$	−1.42001e7	+	6.83841e6i	−0.220221	+	0.106053i	0.320521	+	0.947241i	$0.396142\pi$
$402$	2.48351e7	−	3.11422e7i	0.382285	−	0.479370i
$403$	−1.07727e7	−	4.71981e7i	−0.164592	−	0.721123i
$404$	4.66146e6	+	2.04232e7i	0.0706932	+	0.309727i
$405$	4.97073e6	−	1.03218e7i	0.0748265	−	0.155379i
$406$	9.37363e6	+	7.47522e6i	0.140065	+	0.111698i
$407$	3.25446e7	−	2.59534e7i	0.482720	−	0.384957i
$408$	7.31245e7	+	3.52149e7i	1.07667	+	0.518497i
$409$	1.96643e7	−	4.08332e7i	0.287414	−	0.596821i	−0.706409	−	0.707804i	$-0.749686\pi$
$409$	1.96643e7	−	4.08332e7i	0.287414	−	0.596821i	0.993822	+	0.110984i	$0.0354001\pi$
$410$	9.65580e6	+	1.21080e7i	0.140100	+	0.175679i
$411$	−1.02678e8	+	1.28754e8i	−1.47894	+	1.85454i
$412$	−2.21379e7	−	1.06611e7i	−0.316552	−	0.152443i
$413$	6.38654e7	−	1.45769e7i	0.906600	−	0.206926i
$414$	4.61460e6	−	1.05325e6i	0.0650330	−	0.0148433i
$415$	3.49540e7	+	2.78749e7i	0.489050	+	0.390004i
$416$	1.43758e7	+	2.98516e7i	0.199687	+	0.414655i
$417$	−1.02653e8	−	2.34299e7i	−1.41568	−	0.323119i
$418$	−3.82890e6	+	1.84390e6i	−0.0524258	+	0.0252469i
$419$	−3.51568e7	+	2.80366e7i	−0.477933	+	0.381139i	−0.832619	−	0.553847i	$-0.813159\pi$
$419$	−3.51568e7	+	2.80366e7i	−0.477933	+	0.381139i	0.354685	+	0.934986i	$0.384588\pi$
$420$	5.68739e7	−	1.29811e7i	0.767653	−	0.175212i
$421$	−6.54843e7	+	5.22220e7i	−0.877588	+	0.699853i	−0.954828	−	0.297159i	$-0.903961\pi$
$421$	−6.54843e7	+	5.22220e7i	−0.877588	+	0.699853i	0.0772396	+	0.997013i	$0.475389\pi$
$422$	2.26411e6	−	9.91973e6i	0.0301273	−	0.131996i
$423$	1.28902e8			1.70310
$424$			6.14521e7i			0.806194i
$425$	−5.75141e6	+	2.51986e7i	−0.0749216	+	0.328253i
$426$	−1.00819e7	−	8.04008e6i	−0.130411	−	0.104000i
$427$	−4.55029e7	−	2.19130e7i	−0.584461	−	0.281461i
$428$	−4.74925e7	+	2.28712e7i	−0.605750	+	0.291714i
$429$		−	3.76892e7i		−	0.477359i
$430$	−1.10223e7	+	2.66314e7i	−0.138633	+	0.334957i
$431$	9.03965e7			1.12907			0.564533	−	0.825410i	$-0.309056\pi$
$431$	9.03965e7			1.12907			0.564533	+	0.825410i	$0.309056\pi$
$432$	2.14325e7	+	4.45051e7i	0.265841	+	0.552024i
$433$	3.83419e7	−	7.96179e7i	0.472292	−	0.980724i	−0.519691	−	0.854354i	$-0.673953\pi$
$433$	3.83419e7	−	7.96179e7i	0.472292	−	0.980724i	0.991983	−	0.126370i	$-0.0403327\pi$
$434$	1.06987e7	−	1.34157e7i	0.130876	−	0.164114i
$435$	−1.65465e8	−	3.77663e7i	−2.01019	−	0.458813i
$436$	4.06422e7			0.490364
$437$		−	3.74221e6i		−	0.0448419i
$438$	3.87634e7	+	8.84750e6i	0.461318	+	0.105293i
$439$	−5.74825e7	−	7.20808e7i	−0.679426	−	0.851973i	0.315875	−	0.948801i	$-0.397702\pi$
$439$	−5.74825e7	−	7.20808e7i	−0.679426	−	0.851973i	−0.995301	+	0.0968277i	$0.969130\pi$
$440$	−7.06779e6	−	3.09660e7i	−0.0829708	−	0.363519i
$441$	−6.30962e7	−	7.91202e7i	−0.735678	−	0.922511i
$442$	−8.15673e6	−	1.69376e7i	−0.0944603	−	0.196149i
$443$	−8.02732e6	+	3.51700e7i	−0.0923336	+	0.404540i	−0.999881	−	0.0154092i	$-0.995095\pi$
$443$	−8.02732e6	+	3.51700e7i	−0.0923336	+	0.404540i	0.907548	+	0.419949i	$0.137952\pi$
$444$	1.28533e8	−	6.18982e7i	1.46847	−	0.707178i
$445$	−1.07745e8	+	1.35107e8i	−1.22269	+	1.53320i
$446$	4.23133e6	+	1.85387e7i	0.0476950	+	0.208965i
$447$	2.47292e7	+	1.08346e8i	0.276878	+	1.21308i
$448$	8.23599e6	−	1.71022e7i	0.0915972	−	0.190203i
$449$	3.14751e7	+	2.51006e7i	0.347719	+	0.277297i	0.781738	−	0.623607i	$-0.214333\pi$
$449$	3.14751e7	+	2.51006e7i	0.347719	+	0.277297i	−0.434019	+	0.900904i	$0.642905\pi$
$450$	9.70094e6	−	7.73624e6i	0.106457	−	0.0848970i
$451$	−2.77794e7	−	1.33779e7i	−0.302826	−	0.145834i
$452$	2.36333e7	−	4.90750e7i	0.255923	−	0.531429i
$453$	−1.11984e8	−	1.40424e8i	−1.20466	−	1.51059i
$454$	−6.60253e6	+	8.27932e6i	−0.0705575	+	0.0884763i
$455$	−2.57486e7	−	1.23999e7i	−0.273350	−	0.131639i
$456$	−3.00324e7	+	6.85469e6i	−0.316734	+	0.0722925i
$457$	1.03605e8	−	2.36472e7i	1.08551	−	0.247760i	0.357904	−	0.933758i	$-0.383491\pi$
$457$	1.03605e8	−	2.36472e7i	1.08551	−	0.247760i	0.727603	+	0.685998i	$0.240634\pi$
$458$	−4.17565e7	−	3.32997e7i	−0.434638	−	0.346613i
$459$	−4.50582e7	−	9.35643e7i	−0.465946	−	0.967547i
$460$	1.28924e7	+	2.94261e6i	0.132453	+	0.0302315i
$461$	−2.79946e7	+	1.34815e7i	−0.285740	+	0.137605i	−0.571264	−	0.820767i	$-0.693547\pi$
$461$	−2.79946e7	+	1.34815e7i	−0.285740	+	0.137605i	0.285524	+	0.958372i	$0.407832\pi$
$462$	1.04443e7	−	8.32904e6i	0.105914	−	0.0844635i
$463$	1.35607e8	−	3.09513e7i	1.36627	−	0.311843i	0.524379	−	0.851485i	$-0.324298\pi$
$463$	1.35607e8	−	3.09513e7i	1.36627	−	0.311843i	0.841895	+	0.539642i	$0.181440\pi$
$464$	−6.26796e7	+	4.99853e7i	−0.627440	+	0.500367i
$465$	−5.40518e7	+	2.36816e8i	−0.537590	+	2.35534i
$466$	5.37024e7			0.530684
$467$			8.82488e7i			0.866479i	0.901279	+	0.433240i	$0.142630\pi$
$467$			8.82488e7i			0.866479i	−0.901279	+	0.433240i	$0.857370\pi$
$468$	1.74598e7	−	7.64966e7i	0.170335	−	0.746285i
$469$	4.70144e7	+	3.74928e7i	0.455735	+	0.363437i
$470$	−3.73200e7	−	1.79724e7i	−0.359458	−	0.173106i
$471$	7.06626e7	−	3.40293e7i	0.676281	−	0.325680i
$472$		−	1.22237e8i		−	1.16246i
$473$	−3.23358e6	−	5.72918e7i	−0.0305562	−	0.541388i
$474$	7.18055e7			0.674253
$475$	−4.25638e6	−	8.83846e6i	−0.0397154	−	0.0824700i
$476$	−2.51359e7	+	5.21952e7i	−0.233063	+	0.483961i
$477$	1.38571e8	−	1.73762e8i	1.27678	−	1.60103i
$478$	−3.77497e6	−	861613.i	−0.0345645	−	0.00788912i
$479$	1.62441e8			1.47805			0.739025	−	0.673678i	$-0.235286\pi$
$479$	1.62441e8			1.47805			0.739025	+	0.673678i	$0.235286\pi$
$480$		−	1.66243e8i		−	1.50321i
$481$	−6.81366e7	−	1.55517e7i	−0.612274	−	0.139747i
$482$	−6.77712e6	−	8.49823e6i	−0.0605207	−	0.0758905i
$483$	2.61759e6	+	1.14684e7i	0.0232306	+	0.101780i
$484$	−4.47575e7	−	5.61242e7i	−0.394757	−	0.495010i
$485$	−1.03093e8	−	2.14076e8i	−0.903661	−	1.87647i
$486$	9.16947e6	−	4.01741e7i	0.0798795	−	0.349975i
$487$	−6.26685e7	+	3.01795e7i	−0.542578	+	0.261292i	−0.685036	−	0.728509i	$-0.740214\pi$
$487$	−6.26685e7	+	3.01795e7i	−0.542578	+	0.261292i	0.142458	+	0.989801i	$0.454499\pi$
$488$	−5.87584e7	+	7.36806e7i	−0.505604	+	0.634007i
$489$	6.48360e7	+	2.84065e8i	0.554485	+	2.42936i
$490$	7.23629e6	+	3.17043e7i	0.0615075	+	0.269482i
$491$	−644307.	+	1.33792e6i	−0.00544312	+	0.0113028i	−0.903673	−	0.428224i	$-0.859139\pi$
$491$	−644307.	+	1.33792e6i	−0.00544312	+	0.0113028i	0.898230	+	0.439527i	$0.144854\pi$
$492$	−8.26163e7	−	6.58843e7i	−0.693698	−	0.553205i
$493$	1.31773e8	−	1.05086e8i	1.09973	−	0.877006i
$494$	6.42860e6	+	3.09585e6i	0.0533256	+	0.0256802i
$495$	−4.98415e7	+	1.03497e8i	−0.410938	+	0.853321i
$496$	7.15400e7	+	8.97083e7i	0.586278	+	0.735170i
$497$	1.21379e7	−	1.52204e7i	0.0988719	−	0.123981i
$498$	3.16124e7	+	1.52238e7i	0.255959	+	0.123263i
$499$	1.89469e8	−	4.32450e7i	1.52488	−	0.348044i	0.623761	−	0.781615i	$-0.285604\pi$
$499$	1.89469e8	−	4.32450e7i	1.52488	−	0.348044i	0.901119	+	0.433571i	$0.142747\pi$
$500$	−8.95646e7	+	2.04425e7i	−0.716517	+	0.163540i
$501$	5.72072e7	+	4.56212e7i	0.454922	+	0.362789i
$502$	2.51978e7	+	5.23237e7i	0.199182	+	0.413607i
$503$	1.16097e8	+	2.64984e7i	0.912259	+	0.208217i	0.652794	−	0.757535i	$-0.273597\pi$
$503$	1.16097e8	+	2.64984e7i	0.912259	+	0.208217i	0.259465	+	0.965753i	$0.416454\pi$
$504$	5.29959e7	−	2.55215e7i	0.413953	−	0.199349i
$505$	−4.02583e7	+	3.21049e7i	−0.312594	+	0.249285i
$506$	2.95230e6	−	673843.i	0.0227881	−	0.00520125i
$507$	1.13153e8	−	9.02367e7i	0.868247	−	0.692404i
$508$	−5.47300e6	+	2.39788e7i	−0.0417478	+	0.182909i
$509$	−6.94648e7			−0.526758			−0.263379	−	0.964692i	$-0.584837\pi$
$509$	−6.94648e7			−0.526758			−0.263379	+	0.964692i	$0.584837\pi$
$510$			9.43257e7i			0.711082i
$511$	−1.33568e7	+	5.85200e7i	−0.100101	+	0.438573i
$512$	−1.06221e8	−	8.47087e7i	−0.791411	−	0.631129i
$513$	3.55119e7	+	1.71016e7i	0.263040	+	0.126673i
$514$	−351801.	+	169418.i	−0.00259064	+	0.00124759i
$515$		−	6.03973e7i		−	0.442177i
$516$	3.28878e7	−	1.93893e8i	0.239379	−	1.41128i
$517$	8.24683e7			0.596781
$518$	−1.07481e7	−	2.23186e7i	−0.0773288	−	0.160575i
$519$	−1.65957e8	+	3.44613e8i	−1.18712	+	2.46507i
$520$	−3.32495e7	+	4.16935e7i	−0.236469	+	0.296523i
$521$	−1.67092e8	−	3.81377e7i	−1.18153	−	0.269676i	−0.413748	−	0.910391i	$-0.635781\pi$
$521$	−1.67092e8	−	3.81377e7i	−1.18153	−	0.269676i	−0.767778	+	0.640716i	$0.778638\pi$
$522$	−8.09117e7			−0.568853
$523$		−	1.42743e8i		−	0.997812i	−0.866656	−	0.498906i	$-0.833735\pi$
$523$		−	1.42743e8i		−	0.997812i	0.866656	−	0.498906i	$-0.166265\pi$
$524$	−1.03129e8	−	2.35386e7i	−0.716785	−	0.163602i
$525$	1.92264e7	+	2.41091e7i	0.132868	+	0.166611i
$526$	−1.80419e7	−	7.90468e7i	−0.123972	−	0.543159i
$527$	−1.50401e8	−	1.88596e8i	−1.02758	−	1.28855i
$528$	3.87577e7	+	8.04811e7i	0.263303	+	0.546754i
$529$	3.23477e7	−	1.41725e8i	0.218513	−	0.957367i
$530$	−6.43463e7	+	3.09875e7i	−0.432211	+	0.208142i
$531$	−2.75638e8	+	3.45639e8i	−1.84101	+	2.30855i
$532$	−4.89278e6	−	2.14367e7i	−0.0324953	−	0.142371i
$533$	1.15193e7	+	5.04695e7i	0.0760756	+	0.333309i
$534$	−5.88442e7	+	1.22191e8i	−0.386438	+	0.802448i
$535$	−1.01302e8	−	8.07859e7i	−0.661543	−	0.527563i
$536$	8.77288e7	−	6.99614e7i	0.569702	−	0.454322i
$537$	9.01191e7	+	4.33991e7i	0.581961	+	0.280258i
$538$	1.61536e7	−	3.35433e7i	0.103734	−	0.215406i
$539$	−4.03673e7	−	5.06190e7i	−0.257788	−	0.323256i
$540$	−8.68415e7	+	1.08896e8i	−0.551501	+	0.691560i
$541$	−5.90872e7	−	2.84549e7i	−0.373166	−	0.179707i	0.237895	−	0.971291i	$-0.423543\pi$
$541$	−5.90872e7	−	2.84549e7i	−0.373166	−	0.179707i	−0.611061	+	0.791584i	$0.709257\pi$
$542$	−7.36614e7	+	1.68127e7i	−0.462639	+	0.105594i
$543$	7.46626e6	−	1.70412e6i	0.0466341	−	0.0106439i
$544$	1.29074e8	+	1.02933e8i	0.801755	+	0.639379i
$545$	4.33453e7	+	9.00075e7i	0.267764	+	0.556018i
$546$	−2.18666e7	−	4.99091e6i	−0.134339	−	0.0306621i
$547$	−1.90258e8	+	9.16234e7i	−1.16247	+	0.559815i	−0.912756	−	0.408506i	$-0.866050\pi$
$547$	−1.90258e8	+	9.16234e7i	−1.16247	+	0.559815i	−0.249711	+	0.968320i	$0.580336\pi$
$548$	−1.71490e8	+	1.36759e8i	−1.04207	+	0.831026i
$549$	3.32291e8	−	7.58432e7i	2.00817	−	0.458352i
$550$	6.20640e6	−	4.94944e6i	0.0373037	−	0.0297487i
$551$	−1.42347e7	+	6.23663e7i	−0.0850930	+	0.372817i
$552$	2.19503e7			0.130504
$553$			1.08403e8i			0.641009i
$554$	6.52269e6	−	2.85778e7i	0.0383617	−	0.168073i
$555$	2.74163e8	+	2.18638e8i	1.60372	+	1.27893i
$556$	−1.26354e8	−	6.08488e7i	−0.735130	−	0.354020i
$557$	3.96140e7	−	1.90771e7i	0.229236	−	0.110394i	−0.315740	−	0.948846i	$-0.602253\pi$
$557$	3.96140e7	−	1.90771e7i	0.229236	−	0.110394i	0.544977	+	0.838451i	$0.316539\pi$
$558$			1.15802e8i			0.666523i
$559$	−7.18203e7	+	6.42188e7i	−0.411161	+	0.367643i
$560$	6.77347e7			0.385698
$561$	−8.14814e7	−	1.69198e8i	−0.461498	−	0.958310i
$562$	−8.59337e6	+	1.78443e7i	−0.0484122	+	0.100529i
$563$	−9.72526e7	+	1.21951e8i	−0.544974	+	0.683376i	−0.975701	−	0.219106i	$-0.929686\pi$
$563$	−9.72526e7	+	1.21951e8i	−0.544974	+	0.683376i	0.430727	+	0.902482i	$0.358257\pi$
$564$	2.75549e8	+	6.28922e7i	1.53589	+	0.350557i
$565$	1.33888e8			0.742329
$566$			272251.i			0.00150148i
$567$	1.32332e7	+	3.02040e6i	0.0725967	+	0.0165697i
$568$	−2.26492e7	−	2.84012e7i	−0.123597	−	0.154986i
$569$	−2.46653e6	−	1.08066e7i	−0.0133890	−	0.0586612i	0.967792	−	0.251751i	$-0.0810063\pi$
$569$	−2.46653e6	−	1.08066e7i	−0.0133890	−	0.0586612i	−0.981181	+	0.193090i	$0.938149\pi$
$570$	−2.23215e7	−	2.79903e7i	−0.120531	−	0.151141i
$571$	7.10753e7	+	1.47589e8i	0.381777	+	0.792769i	0.999977	+	0.00674783i	$0.00214792\pi$
$571$	7.10753e7	+	1.47589e8i	0.381777	+	0.792769i	−0.618200	+	0.786021i	$0.712138\pi$
$572$	1.11703e7	−	4.89405e7i	0.0596868	−	0.261505i
$573$	1.33102e8	−	6.40987e7i	0.707492	−	0.340710i
$574$	−1.14402e7	+	1.43456e7i	−0.0604921	+	0.0758547i
$575$	1.55547e6	+	6.81496e6i	0.00818198	+	0.0358476i
$576$	2.85056e7	+	1.24891e8i	0.149164	+	0.653528i
$577$	−1.38774e7	+	2.88167e7i	−0.0722405	+	0.150009i	−0.933962	−	0.357373i	$-0.883672\pi$
$577$	−1.38774e7	+	2.88167e7i	−0.0722405	+	0.150009i	0.861721	+	0.507382i	$0.169387\pi$
$578$	−2.47472e7	−	1.97352e7i	−0.128157	−	0.102202i
$579$	3.90180e8	−	3.11158e8i	2.01015	−	1.60304i
$580$	−2.03667e8	−	9.80810e7i	−1.04385	−	0.502691i
$581$	−2.29828e7	+	4.77244e7i	−0.117186	+	0.243339i
$582$	−1.16266e8	−	1.45792e8i	−0.589769	−	0.739547i
$583$	8.86539e7	−	1.11168e8i	0.447396	−	0.561017i
$584$	1.00914e8	+	4.85978e7i	0.506657	+	0.243993i
$585$	1.88033e8	−	4.29172e7i	0.939216	−	0.214370i
$586$	5.17156e7	−	1.18037e7i	0.256997	−	0.0586580i
$587$	1.94939e7	+	1.55458e7i	0.0963793	+	0.0768599i	0.670494	−	0.741915i	$-0.266082\pi$
$587$	1.94939e7	+	1.55458e7i	0.0963793	+	0.0768599i	−0.574115	+	0.818775i	$0.694654\pi$
$588$	−9.62747e7	−	1.99916e8i	−0.473566	−	0.983369i
$589$	8.92599e7	+	2.03730e7i	0.436828	+	0.0997031i
$590$	1.27994e8	−	6.16389e7i	0.623211	−	0.300122i
$591$	−3.79743e8	+	3.02835e8i	−1.83962	+	1.46704i
$592$	1.61491e8	−	3.68593e7i	0.778365	−	0.177657i
$593$	5.67469e7	−	4.52541e7i	0.272131	−	0.217017i	−0.477910	−	0.878409i	$-0.658605\pi$
$593$	5.67469e7	−	4.52541e7i	0.272131	−	0.217017i	0.750041	+	0.661392i	$0.230034\pi$
$594$	−7.09732e6	+	3.10954e7i	−0.0338638	+	0.148367i
$595$	−1.42401e8			−0.676023
$596$			1.48019e8i			0.699165i
$597$	6.84108e7	−	2.99727e8i	0.321515	−	1.40865i
$598$	−3.97506e6	−	3.17001e6i	−0.0185883	−	0.0148237i
$599$	−6.10598e7	−	2.94048e7i	−0.284102	−	0.136816i	0.286406	−	0.958108i	$-0.407539\pi$
$599$	−6.10598e7	−	2.94048e7i	−0.284102	−	0.136816i	−0.570508	+	0.821292i	$0.693254\pi$
$600$	5.18429e7	−	2.49662e7i	0.240014	−	0.115584i
$601$			3.01079e8i			1.38694i	0.720487	+	0.693469i	$0.243918\pi$
$601$			3.01079e8i			1.38694i	−0.720487	+	0.693469i	$0.756082\pi$
$602$	−3.36679e7	−	5.71067e6i	−0.154321	−	0.0261757i
$603$	−4.05821e8			−1.85090
$604$	−1.03796e8	−	2.15534e8i	−0.471053	−	0.978151i
$605$	7.65599e7	−	1.58978e8i	0.345728	−	0.717913i
$606$	−2.51962e7	+	3.15951e7i	−0.113219	+	0.141972i
$607$	6.61479e7	+	1.50978e7i	0.295767	+	0.0675070i	0.367830	−	0.929893i	$-0.380101\pi$
$607$	6.61479e7	+	1.50978e7i	0.295767	+	0.0675070i	−0.0720624	+	0.997400i	$0.522958\pi$
$608$	−6.26598e7			−0.278791
$609$		−	2.01085e8i		−	0.890282i
$610$	−1.06780e8	−	2.43718e7i	−0.470435	−	0.107374i
$611$	−8.63294e7	−	1.08254e8i	−0.378473	−	0.474591i
$612$	−8.69978e7	−	3.81162e8i	−0.379537	−	1.66286i
$613$	2.29564e8	+	2.87864e8i	0.996604	+	1.24970i	0.968219	+	0.250105i	$0.0804652\pi$
$613$	2.29564e8	+	2.87864e8i	0.996604	+	1.24970i	0.0283857	+	0.999597i	$0.490963\pi$
$614$	2.73178e7	+	5.67260e7i	0.118016	+	0.245063i
$615$	5.77982e7	−	2.53231e8i	0.248479	−	1.08866i
$616$	3.39054e7	−	1.63280e7i	0.145053	−	0.0698538i
$617$	−1.55524e8	+	1.95020e8i	−0.662126	+	0.830280i	−0.993573	−	0.113194i	$-0.963892\pi$
$617$	−1.55524e8	+	1.95020e8i	−0.662126	+	0.830280i	0.331447	+	0.943474i	$0.392463\pi$
$618$	−1.05476e7	−	4.62120e7i	−0.0446877	−	0.195789i
$619$	4.25153e7	+	1.86272e8i	0.179256	+	0.785371i	0.981975	+	0.189013i	$0.0605289\pi$
$619$	4.25153e7	+	1.86272e8i	0.179256	+	0.785371i	−0.802719	+	0.596358i	$0.796614\pi$
$620$	−1.40376e8	+	2.91493e8i	−0.589001	+	1.22307i
$621$	−2.19584e7	−	1.75113e7i	−0.0916909	−	0.0731211i
$622$	4.91207e7	−	3.91725e7i	0.204124	−	0.162783i
$623$	−1.84469e8	−	8.88354e7i	−0.762884	−	0.367385i
$624$	6.50729e7	−	1.35125e8i	0.267822	−	0.556138i
$625$	−1.82497e8	−	2.28844e8i	−0.747507	−	0.937344i
$626$	−4.01782e7	+	5.03819e7i	−0.163782	+	0.205377i
$627$	6.42182e7	+	3.09259e7i	0.260529	+	0.125464i
$628$	1.01843e8	−	2.32450e7i	0.411199	−	0.0938535i
$629$	−3.39507e8	+	7.74903e7i	−1.36426	+	0.311383i
$630$	5.34469e7	+	4.26225e7i	0.213748	+	0.170458i
$631$	−1.07889e8	−	2.24034e8i	−0.429427	−	0.891715i	−0.997629	−	0.0688254i	$-0.978075\pi$
$631$	−1.07889e8	−	2.24034e8i	−0.429427	−	0.891715i	0.568202	−	0.822889i	$-0.307639\pi$
$632$	1.97207e8	+	4.50113e7i	0.781218	+	0.178308i
$633$	−1.53752e8	+	7.40432e7i	−0.606192	+	0.291927i
$634$	5.69066e7	−	4.53815e7i	0.223303	−	0.178078i
$635$	−5.89410e7	+	1.34529e7i	−0.230195	+	0.0525406i
$636$	3.80996e8	−	3.03834e8i	1.48098	−	1.18104i
$637$	−2.41888e7	+	1.05978e8i	−0.0935826	+	0.410012i
$638$	−5.17651e7			−0.199331
$639$			1.31380e8i			0.503532i
$640$	6.40986e7	−	2.80834e8i	0.244517	−	1.07130i
$641$	3.97450e8	+	3.16956e8i	1.50907	+	1.20344i	0.917850	+	0.396927i	$0.129923\pi$
$641$	3.97450e8	+	3.16956e8i	1.50907	+	1.20344i	0.591216	+	0.806513i	$0.298648\pi$
$642$	−9.16179e7	−	4.41209e7i	−0.346239	−	0.166740i
$643$	−3.87635e7	+	1.86675e7i	−0.145811	+	0.0702188i	−0.505366	−	0.862905i	$-0.668643\pi$
$643$	−3.87635e7	+	1.86675e7i	−0.145811	+	0.0702188i	0.359555	+	0.933124i	$0.382928\pi$
$644$			1.56678e7i			0.0586612i
$645$	4.64477e8	−	1.33955e8i	1.73095	−	0.499205i
$646$	3.55529e7			0.131879
$647$	−1.46519e8	−	3.04250e8i	−0.540981	−	1.12336i	−0.974949	−	0.222429i	$-0.928601\pi$
$647$	−1.46519e8	−	3.04250e8i	−0.540981	−	1.12336i	0.433968	−	0.900928i	$-0.357113\pi$
$648$	1.09895e7	−	2.28199e7i	0.0403881	−	0.0838667i
$649$	−1.76346e8	+	2.21131e8i	−0.645106	+	0.808938i
$650$	−1.29940e7	−	2.96579e6i	−0.0473153	−	0.0107994i
$651$	−2.87797e8			−1.04314
$652$			3.88083e8i			1.40017i
$653$	2.72619e8	+	6.22234e7i	0.979075	+	0.223468i	0.681972	−	0.731378i	$-0.261122\pi$
$653$	2.72619e8	+	6.22234e7i	0.979075	+	0.223468i	0.297103	+	0.954845i	$0.403980\pi$
$654$	4.88835e7	+	6.12980e7i	0.174755	+	0.219136i
$655$	−5.78592e7	−	2.53498e8i	−0.205896	−	0.902090i
$656$	−7.64985e7	−	9.59261e7i	−0.270983	−	0.339802i
$657$	−1.75761e8	−	3.64971e8i	−0.619763	−	1.28695i
$658$	1.09207e7	−	4.78466e7i	0.0383329	−	0.167947i
$659$	4.11363e8	−	1.98102e8i	1.43737	−	0.692202i	0.457019	−	0.889457i	$-0.348917\pi$
$659$	4.11363e8	−	1.98102e8i	1.43737	−	0.692202i	0.980352	+	0.197255i	$0.0632027\pi$
$660$	−1.57041e8	+	1.96923e8i	−0.546236	+	0.684958i
$661$	4.66643e7	+	2.04450e8i	0.161577	+	0.707916i	0.989193	+	0.146621i	$0.0468397\pi$
$661$	4.66643e7	+	2.04450e8i	0.161577	+	0.707916i	−0.827616	+	0.561295i	$0.810303\pi$
$662$	−2.00396e7	−	8.77993e7i	−0.0690742	−	0.302634i
$663$	−1.36805e8	+	2.84078e8i	−0.469419	+	0.974758i
$664$	7.72778e7	+	6.16270e7i	0.263967	+	0.210507i
$665$	4.22561e7	−	3.36981e7i	0.143689	−	0.114588i
$666$	1.50620e8	+	7.25349e7i	0.509872	+	0.245541i
$667$	1.97777e7	−	4.10687e7i	0.0666496	−	0.138399i
$668$	6.07639e7	+	7.61955e7i	0.203853	+	0.255623i
$669$	1.98848e8	−	2.49347e8i	0.664113	−	0.832771i
$670$	1.17494e8	+	5.65821e7i	0.390653	+	0.188129i
$671$	2.12591e8	−	4.85224e7i	0.703683	−	0.160611i
$672$	1.92028e8	−	4.38290e7i	0.632784	−	0.144429i
$673$	2.47633e8	+	1.97481e8i	0.812389	+	0.647858i	0.938932	−	0.344103i	$-0.111817\pi$
$673$	2.47633e8	+	1.97481e8i	0.812389	+	0.647858i	−0.126543	+	0.991961i	$0.540388\pi$
$674$	2.86889e7	+	5.95731e7i	0.0936988	+	0.194567i
$675$	−7.17793e7	−	1.63832e7i	−0.233393	−	0.0532704i
$676$	1.73677e8	−	8.36385e7i	0.562215	−	0.270749i
$677$	−7.10731e7	+	5.66789e7i	−0.229055	+	0.182665i	−0.731291	−	0.682065i	$-0.761082\pi$
$677$	−7.10731e7	+	5.66789e7i	−0.229055	+	0.182665i	0.502237	+	0.864730i	$0.332511\pi$
$678$	1.02442e8	−	2.33817e7i	0.328692	−	0.0750219i
$679$	2.20098e8	−	1.75523e8i	0.703084	−	0.560691i
$680$	−5.91281e7	+	2.59057e8i	−0.188047	+	0.823890i
$681$	1.77609e8			0.562373
$682$			7.40873e7i			0.233556i
$683$	7.91327e7	−	3.46703e8i	0.248367	−	1.08817i	−0.684802	−	0.728729i	$-0.740111\pi$
$683$	7.91327e7	−	3.46703e8i	0.248367	−	1.08817i	0.933169	−	0.359438i	$-0.117032\pi$
$684$	1.16015e8	+	9.25189e7i	0.362532	+	0.289109i
$685$	−4.85767e8	−	2.33933e8i	−1.51132	−	0.727813i
$686$	−8.02406e7	+	3.86418e7i	−0.248555	+	0.119698i
$687$			8.95769e8i			2.76265i
$688$	8.73249e7	−	2.10989e8i	0.268147	−	0.647879i
$689$	−2.38732e8			−0.729883
$690$	1.10686e7	+	2.29841e7i	0.0336933	+	0.0699649i
$691$	−7.05184e7	+	1.46433e8i	−0.213732	+	0.443818i	−0.980079	−	0.198608i	$-0.936358\pi$
$691$	−7.05184e7	+	1.46433e8i	−0.213732	+	0.443818i	0.766347	+	0.642426i	$0.222072\pi$
$692$	−3.17636e8	+	3.98303e8i	−0.958544	+	1.20198i
$693$	−1.32690e8	−	3.02855e7i	−0.398692	−	0.0909988i
$694$	1.65440e8			0.494952
$695$		−	3.44723e8i		−	1.02687i
$696$	−3.65816e8	−	8.34952e7i	−1.08501	−	0.247647i
$697$	1.60825e8	+	2.01668e8i	0.474958	+	0.595579i
$698$	−2.19535e7	−	9.61847e7i	−0.0645562	−	0.282839i
$699$	−5.61575e8	−	7.04193e8i	−1.64428	−	2.06187i
$700$	1.78205e7	+	3.70047e7i	0.0519549	+	0.107885i
$701$	−7.31303e7	+	3.20405e8i	−0.212297	+	0.930133i	0.750705	+	0.660638i	$0.229714\pi$
$701$	−7.31303e7	+	3.20405e8i	−0.212297	+	0.930133i	−0.963002	+	0.269495i	$0.913143\pi$
$702$	4.82477e7	−	2.32348e7i	0.139465	−	0.0671627i
$703$	8.24080e7	−	1.03336e8i	0.237194	−	0.297432i
$704$	1.82371e7	+	7.99020e7i	0.0522683	+	0.229002i
$705$	1.54592e8	+	6.77313e8i	0.441185	+	1.93296i
$706$	1.09958e7	−	2.28330e7i	0.0312473	−	0.0648856i
$707$	−4.76981e7	−	3.80380e7i	−0.134972	−	0.107636i
$708$	−7.57858e8	+	6.04372e8i	−2.13544	+	1.70296i
$709$	4.34945e7	+	2.09458e7i	0.122038	+	0.0587704i	0.493907	−	0.869515i	$-0.335568\pi$
$709$	4.34945e7	+	2.09458e7i	0.122038	+	0.0587704i	−0.371869	+	0.928285i	$0.621283\pi$
$710$	1.83178e7	−	3.80374e7i	0.0511799	−	0.106276i
$711$	−4.56127e8	−	5.71965e8i	−1.26904	−	1.59133i
$712$	−2.38206e8	+	2.98701e8i	−0.659953	+	0.827555i
$713$	−5.87784e7	−	2.83062e7i	−0.162162	−	0.0780931i
$714$	−1.08955e8	+	2.48684e7i	−0.299333	+	0.0683208i
$715$	1.20298e8	−	2.74573e7i	0.329110	−	0.0751172i
$716$	1.04159e8	+	8.30644e7i	0.283766	+	0.226296i
$717$	2.81773e7	+	5.85108e7i	0.0764438	+	0.158737i
$718$	7.44103e7	+	1.69837e7i	0.201029	+	0.0458837i
$719$	−2.64429e8	+	1.27342e8i	−0.711415	+	0.342599i	−0.754344	−	0.656479i	$-0.772045\pi$
$719$	−2.64429e8	+	1.27342e8i	−0.711415	+	0.342599i	0.0429297	+	0.999078i	$0.486331\pi$
$720$	−3.57389e8	+	2.85008e8i	−0.957511	+	0.763589i
$721$	6.97649e7	−	1.59234e7i	0.186136	−	0.0424844i
$722$	8.39581e7	−	6.69544e7i	0.223075	−	0.177896i
$723$	−4.05668e7	+	1.77735e8i	−0.107339	+	0.470281i
$724$	1.02002e7			0.0268778
$725$		−	1.19492e8i		−	0.313564i
$726$	3.08151e7	−	1.35010e8i	0.0805292	−	0.352821i
$727$	−1.83616e8	−	1.46429e8i	−0.477868	−	0.381087i	0.354726	−	0.934970i	$-0.384574\pi$
$727$	−1.83616e8	−	1.46429e8i	−0.477868	−	0.381087i	−0.832595	+	0.553883i	$0.813146\pi$
$728$	−5.69261e7	−	2.74142e7i	−0.147543	−	0.0710527i
$729$	−5.69351e8	+	2.74185e8i	−1.46959	+	0.707720i
$730$			1.30173e8i			0.334619i
$731$	−1.83586e8	+	4.43567e8i	−0.469988	+	1.13555i
$732$	7.47327e8			1.90536
$733$	4.91867e7	+	1.02137e8i	0.124892	+	0.259342i	0.954035	−	0.299696i	$-0.0968851\pi$
$733$	4.91867e7	+	1.02137e8i	0.124892	+	0.259342i	−0.829143	+	0.559037i	$0.811171\pi$
$734$	−5.34521e7	+	1.10994e8i	−0.135169	+	0.280681i
$735$	3.40063e8	−	4.26425e8i	0.856441	−	1.07394i
$736$	4.35297e7	+	9.93537e6i	0.109182	+	0.0249202i
$737$	−2.59633e8			−0.648572
$738$		−	1.23829e8i		−	0.308072i
$739$	4.26101e8	+	9.72547e7i	1.05579	+	0.240978i	0.714974	−	0.699151i	$-0.246438\pi$
$739$	4.26101e8	+	9.72547e7i	1.05579	+	0.240978i	0.340819	+	0.940129i	$0.389296\pi$
$740$	2.91208e8	+	3.65164e8i	0.718635	+	0.901140i
$741$	−2.66294e7	−	1.16671e8i	−0.0654497	−	0.286754i
$742$	−5.27581e7	−	6.61566e7i	−0.129145	−	0.161943i
$743$	−3.70903e7	−	7.70188e7i	−0.0904261	−	0.187772i	0.850851	−	0.525407i	$-0.176087\pi$
$743$	−3.70903e7	−	7.70188e7i	−0.0904261	−	0.187772i	−0.941277	+	0.337636i	$0.890373\pi$
$744$	−1.19500e8	+	5.23563e8i	−0.290167	+	1.27131i
$745$	−3.27808e8	+	1.57864e8i	−0.792776	+	0.381781i
$746$	−8.96601e7	+	1.12430e8i	−0.215965	+	0.270811i
$747$	−7.95459e7	−	3.48513e8i	−0.190834	−	0.836099i
$748$	−5.56589e7	−	2.43858e8i	−0.132993	−	0.582682i
$749$	6.66079e7	−	1.38313e8i	0.158519	−	0.329168i
$750$	−1.38558e8	−	1.10497e8i	−0.328435	−	0.261918i
$751$	5.54273e8	−	4.42018e8i	1.30859	−	1.04357i	0.313002	−	0.949752i	$-0.398665\pi$
$751$	5.54273e8	−	4.42018e8i	1.30859	−	1.04357i	0.995590	−	0.0938150i	$-0.0299062\pi$
$752$	2.95670e8	+	1.42387e8i	0.695270	+	0.334824i
$753$	4.22617e8	−	8.77573e8i	0.989833	−	2.05541i
$754$	5.41888e7	+	6.79506e7i	0.126414	+	0.158518i
$755$	3.66629e8	−	4.59739e8i	0.851896	−	1.06824i
$756$	−1.48681e8	−	7.16008e7i	−0.344103	−	0.165711i
$757$	−5.23916e6	+	1.19580e6i	−0.0120774	+	0.00275659i	−0.228555	−	0.973531i	$-0.573400\pi$
$757$	−5.23916e6	+	1.19580e6i	−0.0120774	+	0.00275659i	0.216478	+	0.976288i	$0.430543\pi$
$758$	3.53191e6	−	806135.i	0.00810964	−	0.00185097i
$759$	−3.97087e7	−	3.16666e7i	−0.0908156	−	0.0724230i
$760$	−4.37583e7	−	9.08650e7i	−0.0996826	−	0.206993i
$761$	−3.27102e8	−	7.46590e7i	−0.742215	−	0.169406i	−0.165338	−	0.986237i	$-0.552872\pi$
$761$	−3.27102e8	−	7.46590e7i	−0.742215	−	0.169406i	−0.576877	+	0.816831i	$0.695729\pi$
$762$	−4.27484e7	+	2.05865e7i	−0.0966172	+	0.0465284i
$763$	−9.25398e7	+	7.37980e7i	−0.208331	+	0.166139i
$764$	1.91835e8	−	4.37850e7i	0.430177	−	0.0981850i
$765$	7.51349e8	−	5.99181e8i	1.67825	−	1.33836i
$766$	−1.85150e7	+	8.11194e7i	−0.0411943	+	0.180484i
$767$	4.74874e8			1.05243
$768$			8.71194e7i			0.192323i
$769$	−1.94230e8	+	8.50979e8i	−0.427108	+	1.87128i	0.0604133	+	0.998173i	$0.480758\pi$
$769$	−1.94230e8	+	8.50979e8i	−0.427108	+	1.87128i	−0.487522	+	0.873111i	$0.662099\pi$
$770$	3.41939e7	+	2.72687e7i	0.0748991	+	0.0597301i
$771$	5.90040e6	+	2.84148e6i	0.0128741	+	0.00619986i
$772$	5.98881e8	−	2.88406e8i	1.30163	−	0.626833i
$773$		−	5.86512e8i		−	1.26981i	−0.772591	−	0.634905i	$-0.781039\pi$
$773$		−	5.86512e8i		−	1.26981i	0.772591	−	0.634905i	$-0.218961\pi$
$774$	2.01671e8	−	1.11533e8i	0.434930	−	0.240537i
$775$	−1.71020e8			−0.367402
$776$	−2.27923e8	−	4.73287e8i	−0.487756	−	1.01284i
$777$	−1.80267e8	+	3.74327e8i	−0.384284	+	0.797974i
$778$	4.63593e7	−	5.81327e7i	0.0984459	−	0.123447i
$779$	−9.54466e7	−	2.17851e7i	−0.201906	−	0.0460836i
$780$	4.22888e8			0.891131
$781$			8.40534e7i			0.176442i
$782$	−2.46985e7	−	5.63728e6i	−0.0516477	−	0.0117883i
$783$	2.99341e8	+	3.75362e8i	0.623564	+	0.781925i
$784$	−5.73299e7	−	2.51179e8i	−0.118969	−	0.521236i
$785$	1.60095e8	+	2.00753e8i	0.330956	+	0.415006i
$786$	−8.85399e7	−	1.83855e8i	−0.182336	−	0.378624i
$787$	−9.44838e7	+	4.13960e8i	−0.193835	+	0.849248i	0.780681	+	0.624930i	$0.214873\pi$
$787$	−9.44838e7	+	4.13960e8i	−0.193835	+	0.849248i	−0.974516	+	0.224318i	$0.927985\pi$
$788$	−5.82861e8	+	2.80691e8i	−1.19120	+	0.573654i
$789$	−8.47863e8	+	1.06319e9i	−1.72621	+	2.16460i
$790$	5.23116e7	+	2.29192e8i	0.106100	+	0.464856i
$791$	3.52987e7	+	1.54654e8i	0.0713230	+	0.312486i
$792$	−1.10192e8	+	2.28815e8i	−0.221806	+	0.460585i
$793$	−2.86238e8	−	2.28267e8i	−0.573995	−	0.457746i
$794$	−1.25671e8	+	1.00220e8i	−0.251059	+	0.200213i
$795$	1.07922e9	+	5.19723e8i	2.14786	+	1.03436i
$796$	1.77667e8	−	3.68929e8i	0.352263	−	0.731481i
$797$	5.19093e7	+	6.50921e7i	0.102534	+	0.128574i	0.830451	−	0.557091i	$-0.188083\pi$
$797$	5.19093e7	+	6.50921e7i	0.102534	+	0.128574i	−0.727917	+	0.685666i	$0.759511\pi$
$798$	2.64466e7	−	3.31630e7i	0.0520428	−	0.0652597i
$799$	−6.21595e8	−	2.99344e8i	−1.21862	−	0.586855i
$800$	1.14110e8	−	2.60449e7i	0.222871	−	0.0508689i
$801$	1.34711e9	−	3.07468e8i	2.62122	−	0.598277i
$802$	−3.16613e7	−	2.52491e7i	−0.0613770	−	0.0489465i
$803$	−1.12447e8	−	2.33499e8i	−0.217171	−	0.450959i
$804$	−8.67505e8	−	1.98002e8i	−1.66918	−	0.380980i
$805$	−3.46984e7	+	1.67099e7i	−0.0665154	+	0.0320321i
$806$	9.72522e7	−	7.75560e7i	0.185735	−	0.148119i
$807$	−6.08769e8	+	1.38948e8i	−1.15833	+	0.264381i
$808$	−8.90046e7	+	7.09788e7i	−0.168725	+	0.134553i
$809$	2.23868e8	−	9.80832e8i	0.422812	−	1.85246i	−0.0928667	−	0.995679i	$-0.529603\pi$
$809$	2.23868e8	−	9.80832e8i	0.422812	−	1.85246i	0.515679	−	0.856782i	$-0.327540\pi$
$810$	2.94362e7			0.0553894
$811$		−	7.50657e8i		−	1.40728i	−0.710559	−	0.703638i	$-0.751558\pi$
$811$		−	7.50657e8i		−	1.40728i	0.710559	−	0.703638i	$-0.248442\pi$
$812$	5.95976e7	−	2.61114e8i	0.111317	−	0.487711i
$813$	9.90752e8	+	7.90098e8i	1.84371	+	1.47031i
$814$	9.63628e7	+	4.64059e7i	0.178664	+	0.0860399i
$815$	−8.59459e8	+	4.13894e8i	−1.58764	+	0.764568i
$816$		−	7.47300e8i		−	1.37539i
$817$	−5.04896e7	−	1.75069e8i	−0.0925841	−	0.321027i
$818$	1.16450e8			0.212754
$819$	9.91472e7	+	2.05881e8i	0.180480	+	0.374770i
$820$	1.50105e8	−	3.11697e8i	0.272241	−	0.565315i
$821$	4.36588e8	−	5.47464e8i	0.788937	−	0.989296i	−0.210993	−	0.977488i	$-0.567670\pi$
$821$	4.36588e8	−	5.47464e8i	0.788937	−	0.989296i	0.999930	−	0.0118085i	$-0.00375885\pi$
$822$	−4.12529e8	−	9.41571e7i	−0.742744	−	0.169527i
$823$	−1.04331e9			−1.87161			−0.935805	−	0.352519i	$-0.885325\pi$
$823$	−1.04331e9			−1.87161			−0.935805	+	0.352519i	$0.885325\pi$
$824$		−	1.33529e8i		−	0.238668i
$825$	−1.29803e8	−	2.96266e7i	−0.231165	−	0.0527619i
$826$	1.04944e8	+	1.31595e8i	0.186216	+	0.233507i
$827$	−2.39514e7	−	1.04938e8i	−0.0423462	−	0.185531i	0.949331	−	0.314277i	$-0.101762\pi$
$827$	−2.39514e7	−	1.04938e8i	−0.0423462	−	0.185531i	−0.991678	+	0.128746i	$0.958905\pi$
$828$	−6.59257e7	−	8.26682e7i	−0.116135	−	0.145629i
$829$	−4.69854e8	−	9.75661e8i	−0.824706	−	1.71252i	−0.692647	−	0.721277i	$-0.743556\pi$
$829$	−4.69854e8	−	9.75661e8i	−0.824706	−	1.71252i	−0.132059	−	0.991242i	$-0.542159\pi$
$830$	−2.55617e7	+	1.11993e8i	−0.0447049	+	0.195865i
$831$	−4.42945e8	+	2.13311e8i	−0.771875	+	0.371716i
$832$	8.57941e7	−	1.07582e8i	0.148966	−	0.186798i
$833$	1.20526e8	+	5.28060e8i	0.208519	+	0.913584i
$834$	−6.02012e7	−	2.63759e8i	−0.103778	−	0.454683i
$835$	−1.03940e8	+	2.15833e8i	−0.178534	+	0.370730i
$836$	7.42233e7	+	5.91911e7i	0.127035	+	0.101307i
$837$	5.37226e8	−	4.28423e8i	0.916179	−	0.730628i
$838$	−1.04097e8	−	5.01307e7i	−0.176892	−	0.0851867i
$839$	1.05647e7	−	2.19378e7i	0.0178884	−	0.0371456i	−0.891833	−	0.452364i	$-0.850581\pi$
$839$	1.05647e7	−	2.19378e7i	0.0178884	−	0.0371456i	0.909722	+	0.415219i	$0.136295\pi$
$840$	1.97660e8	+	2.47857e8i	0.333488	+	0.418181i
$841$	−1.14959e8	+	1.44154e8i	−0.193266	+	0.242348i
$842$	−1.93896e8	−	9.33752e7i	−0.324812	−	0.156421i
$843$	3.23853e8	−	7.39172e7i	0.540586	−	0.123385i
$844$	−2.21597e8	+	5.05780e7i	−0.368583	+	0.0841268i
$845$	3.70456e8	+	2.95429e8i	0.613998	+	0.489647i
$846$	1.43704e8	+	2.98404e8i	0.237333	+	0.492826i
$847$	2.03820e8	+	4.65206e7i	0.335426	+	0.0765588i
$848$	5.09787e8	−	2.45500e8i	0.835990	−	0.402591i
$849$	3.56999e6	−	2.84698e6i	0.00583371	−	0.00465223i
$850$	−6.47455e7	+	1.47777e7i	−0.105427	+	0.0240631i
$851$	−7.36338e7	+	5.87210e7i	−0.119478	+	0.0952807i
$852$	−6.41010e7	+	2.80845e8i	−0.103645	+	0.454096i
$853$	7.54037e8			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$853$	7.54037e8			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$854$		−	1.29767e8i		−	0.208348i
$855$	−8.11640e7	+	3.55603e8i	−0.129857	+	0.568940i
$856$	−2.23963e8	−	1.78605e8i	−0.357072	−	0.284755i
$857$	2.72207e8	+	1.31088e8i	0.432470	+	0.208267i	0.637437	−	0.770502i	$-0.279994\pi$
$857$	2.72207e8	+	1.31088e8i	0.432470	+	0.208267i	−0.204967	+	0.978769i	$0.565709\pi$
$858$	8.72491e7	−	4.20169e7i	0.138133	−	0.0665216i
$859$			1.14581e8i			0.180772i	0.995907	+	0.0903862i	$0.0288102\pi$
$859$			1.14581e8i			0.180772i	−0.995907	+	0.0903862i	$0.971190\pi$
$860$	6.42837e8	−	3.62820e7i	1.01066	−	0.0570422i
$861$	3.07744e8			0.482148
$862$	1.00776e8	+	2.09264e8i	0.157339	+	0.326718i
$863$	−7.74051e7	+	1.60733e8i	−0.120431	+	0.250077i	−0.952465	−	0.304647i	$-0.901462\pi$
$863$	−7.74051e7	+	1.60733e8i	−0.120431	+	0.250077i	0.832035	+	0.554723i	$0.187176\pi$
$864$	−2.93210e8	+	3.67673e8i	−0.454608	+	0.570060i
$865$	−1.22086e9	−	2.78653e8i	−1.88632	−	0.430541i
$866$	2.27057e8			0.349608
$867$			5.30881e8i			0.814592i
$868$	−3.73712e8	−	8.52973e7i	−0.571449	−	0.130430i
$869$	−2.91818e8	−	3.65928e8i	−0.444685	−	0.557617i
$870$	−9.70372e7	−	4.25148e8i	−0.147360	−	0.645627i
$871$	2.71789e8	+	3.40813e8i	0.411318	+	0.515777i
$872$	9.58296e7	+	1.98992e8i	0.144527	+	0.300114i
$873$	−4.22757e8	+	1.85222e9i	−0.635401	+	2.78388i
$874$	8.66308e6	−	4.17192e6i	0.0129759	−	0.00624887i
$875$	1.66813e8	−	2.09177e8i	0.249004	−	0.312241i
$876$	−1.97644e8	−	8.65936e8i	−0.294016	−	1.28817i
$877$	1.42328e8	+	6.23578e8i	0.211004	+	0.924468i	0.963886	+	0.266313i	$0.0858056\pi$
$877$	1.42328e8	+	6.23578e8i	0.211004	+	0.924468i	−0.752883	+	0.658155i	$0.771337\pi$
$878$	1.02781e8	−	2.13427e8i	0.151855	−	0.315331i
$879$	−6.95580e8	−	5.54706e8i	−1.02419	−	0.816764i
$880$	−2.28648e8	+	1.82341e8i	−0.335521	+	0.267569i
$881$	8.77970e8	+	4.22808e8i	1.28396	+	0.618323i	0.946405	−	0.322982i	$-0.104685\pi$
$881$	8.77970e8	+	4.22808e8i	1.28396	+	0.618323i	0.337557	+	0.941305i	$0.390400\pi$
$882$	1.12819e8	−	2.34271e8i	0.164428	−	0.341438i
$883$	1.85795e8	+	2.32980e8i	0.269869	+	0.338405i	0.898237	−	0.439511i	$-0.144848\pi$
$883$	1.85795e8	+	2.32980e8i	0.269869	+	0.338405i	−0.628368	+	0.777916i	$0.716277\pi$
$884$	−2.61840e8	+	3.28337e8i	−0.379035	+	0.475294i
$885$	−2.14672e9	−	1.03381e9i	−3.09703	−	1.49145i
$886$	−9.03663e7	+	2.06255e7i	−0.129929	+	0.0296554i
$887$	8.76405e8	−	2.00034e8i	1.25584	−	0.286637i	0.457698	−	0.889108i	$-0.348674\pi$
$887$	8.76405e8	−	2.00034e8i	1.25584	−	0.286637i	0.798141	+	0.602471i	$0.205817\pi$
$888$	6.06130e8	+	4.83373e8i	0.865620	+	0.690309i
$889$	−3.10789e7	−	6.45359e7i	−0.0442344	−	0.0918536i
$890$	−4.32885e8	−	9.88033e7i	−0.614049	−	0.140153i
$891$	−5.28015e7	+	2.54278e7i	−0.0746471	+	0.0359481i
$892$	3.32111e8	−	2.64849e8i	0.467938	−	0.373168i
$893$	2.55290e8	−	5.82683e7i	0.358492	−	0.0818235i
$894$	−2.23248e8	+	1.78034e8i	−0.312446	+	0.249167i
$895$	−7.28698e7	+	3.19264e8i	−0.101643	+	0.445328i
$896$	3.41290e8			0.474460
$897$			8.52737e7i			0.118151i
$898$	−2.30176e7	+	1.00847e8i	−0.0317856	+	0.139262i
$899$	8.71907e8	+	6.95323e8i	1.20003	+	0.956990i
$900$	−2.49732e8	−	1.20264e8i	−0.342567	−	0.164972i
$901$	−1.07174e9	+	5.16122e8i	−1.46526	+	0.705632i
$902$		−	7.92224e7i		−	0.107951i
$903$	2.77187e8	+	5.01200e8i	0.376452	+	0.680687i
$904$	2.96005e8			0.400676
$905$	1.08786e7	+	2.25897e7i	0.0146767	+	0.0304764i
$906$	2.00233e8	−	4.15788e8i	0.269247	−	0.559097i
$907$	−3.87709e8	+	4.86171e8i	−0.519618	+	0.651580i	−0.970528	−	0.240990i	$-0.922528\pi$
$907$	−3.87709e8	+	4.86171e8i	−0.519618	+	0.651580i	0.450910	+	0.892569i	$0.351099\pi$
$908$	2.30631e8	+	5.26400e7i	0.308077	+	0.0703166i
$909$	4.11723e8			0.548167
$910$		−	7.34308e7i		−	0.0974438i
$911$	−2.85872e8	−	6.52484e7i	−0.378108	−	0.0863008i	0.0292429	−	0.999572i	$-0.490690\pi$
$911$	−2.85872e8	−	6.52484e7i	−0.378108	−	0.0863008i	−0.407351	+	0.913272i	$0.633548\pi$
$912$	1.76843e8	+	2.21754e8i	0.233133	+	0.292339i
$913$	−5.08913e7	−	2.22970e8i	−0.0668700	−	0.292977i
$914$	1.70244e8	+	2.13480e8i	0.222964	+	0.279587i
$915$	7.97031e8	+	1.65505e9i	1.04043	+	2.16047i
$916$	−2.65488e8	+	1.16318e9i	−0.345429	+	1.51342i
$917$	2.77560e8	−	1.33666e8i	0.359956	−	0.173346i
$918$	1.66366e8	−	2.08616e8i	0.215048	−	0.269662i
$919$	−3.03658e8	−	1.33041e9i	−0.391236	−	1.71412i	−0.660308	−	0.750995i	$-0.729574\pi$
$919$	−3.03658e8	−	1.33041e9i	−0.391236	−	1.71412i	0.269072	−	0.963120i	$-0.413283\pi$
$920$	1.59912e7	+	7.00622e7i	0.0205361	+	0.0899746i
$921$	4.58174e8	−	9.51408e8i	0.586478	−	1.21783i
$922$	−6.24182e7	−	4.97768e7i	−0.0796376	−	0.0635089i
$923$	1.10334e8	−	8.79888e7i	0.140316	−	0.111898i
$924$	−2.68868e8	−	1.29480e8i	−0.340818	−	0.164130i
$925$	−1.07121e8	+	2.22440e8i	−0.135348	+	0.281052i
$926$	2.22829e8	+	2.79419e8i	0.280633	+	0.351903i
$927$	−3.01100e8	+	3.77567e8i	−0.377982	+	0.473974i
$928$	−6.87658e8	−	3.31158e8i	−0.860455	−	0.414373i
$929$	−1.13655e9	+	2.59410e8i	−1.41756	+	0.323549i	−0.861569	−	0.507640i	$-0.830518\pi$
$929$	−1.13655e9	+	2.59410e8i	−1.41756	+	0.323549i	−0.555990	+	0.831189i	$0.687661\pi$
$930$	−6.08480e8	+	1.38881e8i	−0.756479	+	0.172661i
$931$	−1.60727e8	−	1.28175e8i	−0.199177	−	0.158838i
$932$	−5.20512e8	−	1.08085e9i	−0.642959	−	1.33512i
$933$	−1.02733e9	−	2.34481e8i	−1.26492	−	0.288710i
$934$	−2.04293e8	+	9.83821e7i	−0.250733	+	0.120747i
$935$	4.80693e8	−	3.83340e8i	0.588076	−	0.468975i
$936$	4.15710e8	−	9.48831e7i	0.506948	−	0.115707i
$937$	8.81650e8	−	7.03092e8i	1.07171	−	0.854660i	0.0818411	−	0.996645i	$-0.473920\pi$
$937$	8.81650e8	−	7.03092e8i	1.07171	−	0.854660i	0.989869	+	0.141985i	$0.0453486\pi$
$938$	−3.43814e7	+	1.50635e8i	−0.0416595	+	0.182522i
$939$	1.08080e9			1.30542
$940$			9.25328e8i			1.11407i
$941$	−4.87473e7	+	2.13576e8i	−0.0585035	+	0.256320i	−0.995719	−	0.0924297i	$-0.970537\pi$
$941$	−4.87473e7	+	2.13576e8i	−0.0585035	+	0.256320i	0.937216	+	0.348750i	$0.113394\pi$
$942$	1.57553e8	+	1.25644e8i	0.188484	+	0.150311i
$943$	6.28524e7	+	3.02681e7i	0.0749526	+	0.0360953i
$944$	−1.01404e9	+	4.88337e8i	−1.20542	+	0.580502i
$945$		−	4.05635e8i		−	0.480663i
$946$	1.29023e8	−	7.13561e7i	0.152404	−	0.0842864i
$947$	−6.68116e8			−0.786687			−0.393343	−	0.919392i	$-0.628682\pi$
$947$	−6.68116e8			−0.786687			−0.393343	+	0.919392i	$0.628682\pi$
$948$	−6.95976e8	−	1.44521e9i	−0.816901	−	1.69631i
$949$	−1.88795e8	+	3.92037e8i	−0.220898	+	0.458699i
$950$	1.57156e7	−	1.97067e7i	0.0183299	−	0.0229849i
$951$	−1.19016e9	−	2.71647e8i	−1.38377	−	0.315837i
$952$	−3.14825e8			−0.364887
$953$		−	7.21748e8i		−	0.833887i	−0.908932	−	0.416943i	$-0.863101\pi$
$953$		−	7.21748e8i		−	0.833887i	0.908932	−	0.416943i	$-0.136899\pi$
$954$	5.56736e8	+	1.27071e8i	0.641216	+	0.146353i
$955$	3.01561e8	+	3.78145e8i	0.346230	+	0.434159i
$956$	1.92476e7	+	8.43291e7i	0.0220294	+	0.0965170i
$957$	5.41317e8	+	6.78790e8i	0.617612	+	0.774461i
$958$	1.81094e8	+	3.76045e8i	0.205971	+	0.427704i
$959$	1.42146e8	−	6.22783e8i	0.161168	−	0.706124i
$960$	−6.22050e8	+	2.99563e8i	−0.703091	+	0.338591i
$961$	4.41810e8	−	5.54012e8i	0.497812	−	0.624237i
$962$	−3.99589e7	−	1.75071e8i	−0.0448836	−	0.196648i
$963$	2.30537e8	+	1.01005e9i	0.258144	+	1.13100i
$964$	−1.05354e8	+	2.18770e8i	−0.117604	+	0.244207i
$965$	1.27742e9	+	1.01871e9i	1.42152	+	1.13362i
$966$	−2.36307e7	+	1.88449e7i	−0.0262148	+	0.0209056i
$967$	7.02551e8	+	3.38331e8i	0.776960	+	0.374164i	0.779958	−	0.625831i	$-0.215240\pi$
$967$	7.02551e8	+	3.38331e8i	0.776960	+	0.374164i	−0.00299866	+	0.999996i	$0.500955\pi$
$968$	1.69262e8	−	3.51476e8i	0.186609	−	0.387498i
$969$	−3.71782e8	−	4.66200e8i	−0.408618	−	0.512391i
$970$	3.80646e8	−	4.77314e8i	0.417067	−	0.522985i
$971$	1.17820e9	+	5.67389e8i	1.28694	+	0.619760i	0.947165	−	0.320745i	$-0.103933\pi$
$971$	1.17820e9	+	5.67389e8i	1.28694	+	0.619760i	0.339779	+	0.940505i	$0.389648\pi$
$972$	−8.97448e8	+	2.04837e8i	−0.977261	+	0.223053i
$973$	3.98189e8	−	9.08840e7i	0.432265	−	0.0986618i
$974$	−1.39729e8	−	1.11430e8i	−0.151220	−	0.120594i
$975$	9.69901e7	+	2.01402e8i	0.104644	+	0.217295i
$976$	8.45969e8	+	1.93087e8i	0.909924	+	0.207684i
$977$	−2.54876e8	+	1.22742e8i	−0.273304	+	0.131616i	−0.565516	−	0.824737i	$-0.691323\pi$
$977$	−2.54876e8	+	1.22742e8i	−0.273304	+	0.131616i	0.292212	+	0.956353i	$0.405609\pi$
$978$	−5.85320e8	+	4.66777e8i	−0.625715	+	0.498991i
$979$	8.61842e8	−	1.96710e8i	0.918501	−	0.209642i
$980$	5.67965e8	−	4.52937e8i	0.603453	−	0.481238i
$981$	1.77747e8	−	7.78761e8i	0.188276	−	0.824892i
$982$	−3.81552e6			−0.00402920
$983$		−	1.14064e9i		−	1.20085i	−0.799682	−	0.600424i	$-0.794998\pi$
$983$		−	1.14064e9i		−	1.20085i	0.799682	−	0.600424i	$-0.205002\pi$
$984$	1.27783e8	−	5.59852e8i	0.134118	−	0.587609i
$985$	−1.24325e9	−	9.91461e8i	−1.30092	−	1.03745i
$986$	3.90174e8	+	1.87898e8i	0.407031	+	0.196016i
$987$	−7.41606e8	+	3.57138e8i	−0.771297	+	0.371437i
$988$		−	1.59393e8i		−	0.165272i
$989$	7.31613e6	+	1.29626e8i	0.00756298	+	0.133999i
$990$	−2.95156e8			−0.304191
$991$	2.74199e8	+	5.69381e8i	0.281738	+	0.585035i	0.993030	−	0.117862i	$-0.0376040\pi$
$991$	2.74199e8	+	5.69381e8i	0.281738	+	0.585035i	−0.711292	+	0.702897i	$0.751890\pi$
$992$	−4.73960e8	+	9.84189e8i	−0.485520	+	1.00819i
$993$	−9.41744e8	+	1.18091e9i	−0.961800	+	1.20606i
$994$	4.87663e7	+	1.11306e7i	0.0496547	+	0.0113334i
$995$	1.00652e9			1.02177
$996$		−	7.83812e8i		−	0.793293i
$997$	−2.43968e8	−	5.56842e7i	−0.246177	−	0.0561884i	0.0976516	−	0.995221i	$-0.468867\pi$
$997$	−2.43968e8	−	5.56842e7i	−0.246177	−	0.0561884i	−0.343829	+	0.939032i	$0.611724\pi$
$998$	3.11335e8	+	3.90402e8i	0.313211	+	0.392754i
$999$	−2.20735e8	−	9.67102e8i	−0.221398	−	0.970009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.7.f.a.2.13	✓	126
43.22	odd	14	inner	43.7.f.a.22.13	yes	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.7.f.a.2.13	✓	126	1.1	even	1	trivial
43.7.f.a.22.13	yes	126	43.22	odd	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	43.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11483 + 2.31496i) q^{2} +(18.6979 - 38.8265i) q^{3} +(35.7871 - 44.8756i) q^{4} +(137.550 + 31.3949i) q^{5} +110.727 q^{6} +167.161i q^{7} +(304.102 + 69.4092i) q^{8} +(-703.365 - 881.992i) q^{9} +O(q^{10})\)	\(q+(1.11483 + 2.31496i) q^{2} +(18.6979 - 38.8265i) q^{3} +(35.7871 - 44.8756i) q^{4} +(137.550 + 31.3949i) q^{5} +110.727 q^{6} +167.161i q^{7} +(304.102 + 69.4092i) q^{8} +(-703.365 - 881.992i) q^{9} +(80.6666 + 353.424i) q^{10} +(-449.994 - 564.275i) q^{11} +(-1073.22 - 2228.57i) q^{12} +(-269.644 + 1181.39i) q^{13} +(-386.972 + 186.356i) q^{14} +(3790.85 - 4753.58i) q^{15} +(-639.085 - 2800.01i) q^{16} +(1343.57 + 5886.55i) q^{17} +(1257.65 - 2611.53i) q^{18} +(-1791.70 - 1428.83i) q^{19} +(6331.40 - 5049.12i) q^{20} +(6490.28 + 3125.56i) q^{21} +(804.610 - 1670.79i) q^{22} +(1018.14 + 1276.70i) q^{23} +(8380.97 - 10509.4i) q^{24} +(3856.78 + 1857.33i) q^{25} +(-3035.48 + 692.828i) q^{26} +(-16768.1 + 3827.21i) q^{27} +(7501.46 + 5982.22i) q^{28} +(-12111.5 - 25149.8i) q^{29} +(15230.5 + 3476.26i) q^{30} +(-35994.9 + 17334.3i) q^{31} +(21377.2 - 17047.7i) q^{32} +(-30322.8 + 6920.98i) q^{33} +(-12129.3 + 9672.79i) q^{34} +(-5248.01 + 22993.0i) q^{35} -64751.4 q^{36} +57675.0i q^{37} +(1310.26 - 5740.62i) q^{38} +(40827.5 + 32558.8i) q^{39} +(39650.1 + 19094.5i) q^{40} +(38489.8 - 18535.7i) q^{41} +18509.2i q^{42} +(64855.7 + 45990.2i) q^{43} -41426.2 q^{44} +(-69058.0 - 143400. i) q^{45} +(-1820.47 + 3780.25i) q^{46} +(-71242.4 + 89335.2i) q^{47} +(-120664. - 27540.9i) q^{48} +89706.2 q^{49} +10998.9i q^{50} +(253676. + 57899.9i) q^{51} +(43365.8 + 54379.0i) q^{52} +(43839.1 + 192072. i) q^{53} +(-27553.4 - 34550.9i) q^{54} +(-44181.4 - 91743.7i) q^{55} +(-11602.5 + 50833.9i) q^{56} +(-88977.6 + 42849.4i) q^{57} +(44718.7 - 56075.5i) q^{58} +(-87202.5 - 382059. i) q^{59} +(-77656.2 - 340234. i) q^{60} +(-131089. + 272210. i) q^{61} +(-80256.3 - 64002.3i) q^{62} +(147435. - 117575. i) q^{63} +(-102310. - 49269.8i) q^{64} +(-74179.2 + 154035. i) q^{65} +(-49826.5 - 62480.4i) q^{66} +(224291. - 281252. i) q^{67} +(312245. + 150369. i) q^{68} +(68606.9 - 15659.1i) q^{69} +(-59078.6 + 13484.3i) q^{70} +(-91052.3 - 72611.8i) q^{71} +(-152676. - 317035. i) q^{72} +(350082. + 79903.8i) q^{73} +(-133516. + 64297.7i) q^{74} +(144227. - 115017. i) q^{75} +(-128240. + 29269.9i) q^{76} +(94324.8 - 75221.5i) q^{77} +(-29856.9 + 130811. i) q^{78} +648492. q^{79} -405207. i q^{80} +(18068.8 - 79164.6i) q^{81} +(85819.0 + 68438.3i) q^{82} +(285499. + 137489. i) q^{83} +(372530. - 179401. i) q^{84} +851877. i q^{85} +(-34162.7 + 201410. i) q^{86} -1.20294e6 q^{87} +(-97678.1 - 202831. i) q^{88} +(-531436. + 1.10354e6i) q^{89} +(254979. - 319733. i) q^{90} +(-197482. - 45074.0i) q^{91} +93729.0 q^{92} +1.72167e6i q^{93} +(-286231. - 65330.2i) q^{94} +(-201591. - 252787. i) q^{95} +(-262196. - 1.14876e6i) q^{96} +(-1.05002e6 - 1.31668e6i) q^{97} +(100007. + 207666. i) q^{98} +(-181176. + 793783. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9	\( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) 126 * q - 7 * q^2 - 7 * q^3 + 725 * q^4 - 7 * q^5 + 244 * q^6 + 2233 * q^8 + 6312 * q^9 + 1955 * q^10 - 985 * q^11 - 455 * q^12 - 4485 * q^13 - 6771 * q^14 + 5017 * q^15 - 41935 * q^16 - 10409 * q^17 - 5110 * q^18 - 33397 * q^19 - 24507 * q^20 - 5448 * q^21 + 25193 * q^22 - 29017 * q^23 - 1885 * q^24 - 2080 * q^25 + 34713 * q^26 - 7 * q^27 + 28665 * q^28 + 17353 * q^29 - 290052 * q^30 + 13547 * q^31 + 458283 * q^32 - 94801 * q^33 - 191527 * q^34 + 183008 * q^35 + 956352 * q^36 + 304607 * q^38 - 381031 * q^39 + 66419 * q^40 + 313447 * q^41 - 323228 * q^43 + 281588 * q^44 - 1237551 * q^45 + 80948 * q^46 - 180133 * q^47 - 762055 * q^48 - 1861754 * q^49 + 999215 * q^51 + 471797 * q^52 + 1030011 * q^53 - 92099 * q^54 + 324233 * q^55 - 842713 * q^56 + 331037 * q^57 + 849461 * q^58 - 369609 * q^59 + 553323 * q^60 - 594727 * q^61 - 886711 * q^62 + 1914136 * q^63 - 3250219 * q^64 + 1473521 * q^65 - 427559 * q^66 + 122535 * q^67 - 602346 * q^68 + 4320057 * q^69 - 1694994 * q^70 - 770707 * q^71 - 391202 * q^72 + 476945 * q^73 - 3943812 * q^74 + 2061367 * q^75 - 2044462 * q^76 + 3016216 * q^77 + 239350 * q^78 + 5077268 * q^79 + 2388946 * q^81 + 5820437 * q^82 - 1324235 * q^83 + 3759618 * q^84 - 4967947 * q^86 - 3537894 * q^87 - 7289555 * q^88 - 4331495 * q^89 - 12825206 * q^90 + 1802976 * q^91 - 12038260 * q^92 + 6249341 * q^94 - 5313259 * q^95 + 7069598 * q^96 + 788975 * q^97 + 4724783 * q^98 - 2216971 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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