LMFDB - Embedded newform 38.7.d.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,7,Mod(27,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("38.27");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	38.d (of order $6$, degree $2$, 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:	$8.74205517755$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 9440 x^{18} + 37579488 x^{16} + 83109028728 x^{14} + 112838424559344 x^{12} + \cdots + 83\!\cdots\!96 $ x^20 + 9440x^18 + 37579488x^16 + 83109028728x^14 + 112838424559344x^12 + 97808951849137728x^10 + 54352282696688610576x^8 + 18825433555812367062720x^6 + 3765133606401310416173376x^4 + 360077534420960567854418432*x^2 + 8303121574870947536327197696
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.7
Root			$-19.6100i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.7.d.a.27.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 - 2.82843i) q^{2} +(-17.2580 + 9.96392i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-17.0310 - 29.4985i) q^{5} +(-56.3644 + 97.6261i) q^{6} -265.741 q^{7} -181.019i q^{8} +(-165.941 + 287.418i) q^{9} +O(q^{10})$	\(q+(4.89898 - 2.82843i) q^{2} +(-17.2580 + 9.96392i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-17.0310 - 29.4985i) q^{5} +(-56.3644 + 97.6261i) q^{6} -265.741 q^{7} -181.019i q^{8} +(-165.941 + 287.418i) q^{9} +(-166.869 - 96.3417i) q^{10} -1457.94 q^{11} +637.691i q^{12} +(-2784.56 - 1607.67i) q^{13} +(-1301.86 + 751.629i) q^{14} +(587.842 + 339.390i) q^{15} +(-512.000 - 886.810i) q^{16} +(41.0838 + 71.1592i) q^{17} +1877.40i q^{18} +(3013.25 + 6161.67i) q^{19} -1089.98 q^{20} +(4586.16 - 2647.82i) q^{21} +(-7142.44 + 4123.69i) q^{22} +(-1509.00 + 2613.67i) q^{23} +(1803.66 + 3124.03i) q^{24} +(7232.39 - 12526.9i) q^{25} -18188.7 q^{26} -21141.1i q^{27} +(-4251.86 + 7364.43i) q^{28} +(4959.81 + 2863.55i) q^{29} +3839.76 q^{30} -956.786i q^{31} +(-5016.55 - 2896.31i) q^{32} +(25161.2 - 14526.8i) q^{33} +(402.537 + 232.405i) q^{34} +(4525.83 + 7838.97i) q^{35} +(5310.10 + 9197.37i) q^{36} +5520.55i q^{37} +(32189.7 + 21663.2i) q^{38} +64074.7 q^{39} +(-5339.80 + 3082.94i) q^{40} +(95072.3 - 54890.0i) q^{41} +(14978.3 - 25943.3i) q^{42} +(2926.12 + 5068.20i) q^{43} +(-23327.1 + 40403.7i) q^{44} +11304.5 q^{45} +17072.4i q^{46} +(-51666.4 + 89488.9i) q^{47} +(17672.2 + 10203.1i) q^{48} -47030.7 q^{49} -81825.2i q^{50} +(-1418.05 - 818.710i) q^{51} +(-89106.0 + 51445.4i) q^{52} +(-181296. - 104671. i) q^{53} +(-59796.0 - 103570. i) q^{54} +(24830.2 + 43007.2i) q^{55} +48104.3i q^{56} +(-113397. - 76314.5i) q^{57} +32397.3 q^{58} +(-225853. + 130396. i) q^{59} +(18810.9 - 10860.5i) q^{60} +(-70385.4 + 121911. i) q^{61} +(-2706.20 - 4687.28i) q^{62} +(44097.3 - 76378.7i) q^{63} -32768.0 q^{64} +109521. i q^{65} +(82176.2 - 142333. i) q^{66} +(114412. + 66056.0i) q^{67} +2629.36 q^{68} -60142.4i q^{69} +(44343.9 + 25602.0i) q^{70} +(-314256. + 181436. i) q^{71} +(52028.2 + 30038.5i) q^{72} +(-163387. - 282994. i) q^{73} +(15614.5 + 27045.1i) q^{74} +288252. i q^{75} +(218969. + 15081.3i) q^{76} +387436. q^{77} +(313900. - 181231. i) q^{78} +(52388.3 - 30246.4i) q^{79} +(-17439.7 + 30206.5i) q^{80} +(89677.1 + 155325. i) q^{81} +(310505. - 537810. i) q^{82} +259525. q^{83} -169461. i q^{84} +(1399.39 - 2423.82i) q^{85} +(28670.0 + 16552.7i) q^{86} -114129. q^{87} +263916. i q^{88} +(-423488. - 244501. i) q^{89} +(55380.6 - 31974.0i) q^{90} +(739973. + 427223. i) q^{91} +(48288.1 + 83637.5i) q^{92} +(9533.34 + 16512.2i) q^{93} +584539. i q^{94} +(130442. - 193826. i) q^{95} +115434. q^{96} +(342904. - 197975. i) q^{97} +(-230402. + 133023. i) q^{98} +(241932. - 419039. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) $ 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$2$	4.89898	−	2.82843i	0.612372	−	0.353553i
$3$	−17.2580	+	9.96392i	−0.639186	+	0.369034i	−0.784301	−	0.620381i	$-0.786978\pi$
$3$	−17.2580	+	9.96392i	−0.639186	+	0.369034i	0.145115	+	0.989415i	$0.453645\pi$
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	−17.0310	−	29.4985i	−0.136248	−	0.235988i	0.789826	−	0.613331i	$-0.210171\pi$
$5$	−17.0310	−	29.4985i	−0.136248	−	0.235988i	−0.926073	+	0.377343i	$0.876838\pi$
$6$	−56.3644	+	97.6261i	−0.260946	+	0.451972i
$7$	−265.741			−0.774755			−0.387378	−	0.921921i	$-0.626619\pi$
$7$	−265.741			−0.774755			−0.387378	+	0.921921i	$0.626619\pi$
$8$		−	181.019i		−	0.353553i
$9$	−165.941	+	287.418i	−0.227628	+	0.394263i
$10$	−166.869	−	96.3417i	−0.166869	−	0.0963417i
$11$	−1457.94			−1.09538			−0.547688	−	0.836683i	$-0.684492\pi$
$11$	−1457.94			−1.09538			−0.547688	+	0.836683i	$0.684492\pi$
$12$			637.691i			0.369034i
$13$	−2784.56	−	1607.67i	−1.26744	−	0.731756i	−0.292936	−	0.956132i	$-0.594632\pi$
$13$	−2784.56	−	1607.67i	−1.26744	−	0.731756i	−0.974503	+	0.224376i	$0.927965\pi$
$14$	−1301.86	+	751.629i	−0.474439	+	0.273917i
$15$	587.842	+	339.390i	0.174175	+	0.100560i
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$	41.0838	+	71.1592i	0.00836226	+	0.0144839i	0.870176	−	0.492741i	$-0.164005\pi$
$17$	41.0838	+	71.1592i	0.00836226	+	0.0144839i	−0.861814	+	0.507224i	$0.830672\pi$
$18$			1877.40i			0.321914i
$19$	3013.25	+	6161.67i	0.439313	+	0.898334i
$19$	3013.25	+	6161.67i	0.439313	+	0.898334i
$20$	−1089.98			−0.136248
$21$	4586.16	−	2647.82i	0.495213	−	0.285911i
$22$	−7142.44	+	4123.69i	−0.670778	+	0.387274i
$23$	−1509.00	+	2613.67i	−0.124024	+	0.214816i	−0.921351	−	0.388731i	$-0.872913\pi$
$23$	−1509.00	+	2613.67i	−0.124024	+	0.214816i	0.797327	+	0.603548i	$0.206247\pi$
$24$	1803.66	+	3124.03i	0.130473	+	0.225986i
$25$	7232.39	−	12526.9i	0.462873	−	0.801720i
$26$	−18188.7			−1.03486
$27$		−	21141.1i		−	1.07408i
$28$	−4251.86	+	7364.43i	−0.193689	+	0.335479i
$29$	4959.81	+	2863.55i	0.203362	+	0.117411i	0.598223	−	0.801330i	$-0.295874\pi$
$29$	4959.81	+	2863.55i	0.203362	+	0.117411i	−0.394860	+	0.918741i	$0.629207\pi$
$30$	3839.76			0.142214
$31$		−	956.786i		−	0.0321166i	−0.999871	−	0.0160583i	$-0.994888\pi$
$31$		−	956.786i		−	0.0321166i	0.999871	−	0.0160583i	$-0.00511174\pi$
$32$	−5016.55	−	2896.31i	−0.153093	−	0.0883883i
$33$	25161.2	−	14526.8i	0.700148	−	0.404231i
$34$	402.537	+	232.405i	0.0102416	+	0.00591301i
$35$	4525.83	+	7838.97i	0.105559	+	0.182833i
$36$	5310.10	+	9197.37i	0.113814	+	0.197131i
$37$			5520.55i			0.108988i	0.998514	+	0.0544938i	$0.0173545\pi$
$37$			5520.55i			0.108988i	−0.998514	+	0.0544938i	$0.982645\pi$
$38$	32189.7	+	21663.2i	0.586632	+	0.394795i
$39$	64074.7			1.08017
$40$	−5339.80	+	3082.94i	−0.0834344	+	0.0481709i
$41$	95072.3	−	54890.0i	1.37944	−	0.796419i	0.387346	−	0.921934i	$-0.373392\pi$
$41$	95072.3	−	54890.0i	1.37944	−	0.796419i	0.992092	+	0.125515i	$0.0400584\pi$
$42$	14978.3	−	25943.3i	0.202170	−	0.350168i
$43$	2926.12	+	5068.20i	0.0368034	+	0.0637453i	0.883840	−	0.467789i	$-0.154949\pi$
$43$	2926.12	+	5068.20i	0.0368034	+	0.0637453i	−0.847037	+	0.531534i	$0.821616\pi$
$44$	−23327.1	+	40403.7i	−0.273844	+	0.474311i
$45$	11304.5			0.124055
$46$			17072.4i			0.175397i
$47$	−51666.4	+	89488.9i	−0.497639	+	0.861937i	−0.999996	−	0.00272364i	$-0.999133\pi$
$47$	−51666.4	+	89488.9i	−0.497639	+	0.861937i	0.502357	+	0.864660i	$0.332466\pi$
$48$	17672.2	+	10203.1i	0.159796	+	0.0922585i
$49$	−47030.7			−0.399754
$50$		−	81825.2i		−	0.654601i
$51$	−1418.05	−	818.710i	−0.0106901	−	0.00617191i
$52$	−89106.0	+	51445.4i	−0.633719	+	0.365878i
$53$	−181296.	−	104671.i	−1.21776	−	0.703073i	−0.253320	−	0.967382i	$-0.581523\pi$
$53$	−181296.	−	104671.i	−1.21776	−	0.703073i	−0.964438	+	0.264309i	$0.914856\pi$
$54$	−59796.0	−	103570.i	−0.379744	−	0.657736i
$55$	24830.2	+	43007.2i	0.149242	+	0.258496i
$56$			48104.3i			0.273917i
$57$	−113397.	−	76314.5i	−0.612318	−	0.412081i
$58$	32397.3			0.166045
$59$	−225853.	+	130396.i	−1.09969	+	0.634906i	−0.936139	−	0.351629i	$-0.885628\pi$
$59$	−225853.	+	130396.i	−1.09969	+	0.634906i	−0.163550	+	0.986535i	$0.552295\pi$
$60$	18810.9	−	10860.5i	0.0870876	−	0.0502801i
$61$	−70385.4	+	121911.i	−0.310094	+	0.537098i	−0.978382	−	0.206804i	$-0.933694\pi$
$61$	−70385.4	+	121911.i	−0.310094	+	0.537098i	0.668289	+	0.743902i	$0.267027\pi$
$62$	−2706.20	−	4687.28i	−0.0113549	−	0.0196673i
$63$	44097.3	−	76378.7i	0.176356	−	0.305457i
$64$	−32768.0			−0.125000
$65$			109521.i			0.398800i
$66$	82176.2	−	142333.i	0.285834	−	0.495079i
$67$	114412.	+	66056.0i	0.380407	+	0.219628i	0.677995	−	0.735066i	$-0.262849\pi$
$67$	114412.	+	66056.0i	0.380407	+	0.219628i	−0.297588	+	0.954694i	$0.596182\pi$
$68$	2629.36			0.00836226
$69$		−	60142.4i		−	0.183077i
$70$	44343.9	+	25602.0i	0.129283	+	0.0746413i
$71$	−314256.	+	181436.i	−0.878027	+	0.506929i	−0.870008	−	0.493038i	$-0.835886\pi$
$71$	−314256.	+	181436.i	−0.878027	+	0.506929i	−0.00801994	+	0.999968i	$0.502553\pi$
$72$	52028.2	+	30038.5i	0.139393	+	0.0804786i
$73$	−163387.	−	282994.i	−0.419999	−	0.727459i	0.575940	−	0.817492i	$-0.304636\pi$
$73$	−163387.	−	282994.i	−0.419999	−	0.727459i	−0.995939	+	0.0900329i	$0.971303\pi$
$74$	15614.5	+	27045.1i	0.0385330	+	0.0667411i
$75$			288252.i			0.683264i
$76$	218969.	+	15081.3i	0.498818	+	0.0343556i
$77$	387436.			0.848648
$78$	313900.	−	181231.i	0.661467	−	0.381898i
$79$	52388.3	−	30246.4i	0.106256	−	0.0613469i	−0.445930	−	0.895068i	$-0.647127\pi$
$79$	52388.3	−	30246.4i	0.106256	−	0.0613469i	0.552186	+	0.833721i	$0.313794\pi$
$80$	−17439.7	+	30206.5i	−0.0340619	+	0.0589970i
$81$	89677.1	+	155325.i	0.168743	+	0.292272i
$82$	310505.	−	537810.i	0.563153	−	0.975410i
$83$	259525.			0.453883			0.226942	−	0.973908i	$-0.427127\pi$
$83$	259525.			0.453883			0.226942	+	0.973908i	$0.427127\pi$
$84$		−	169461.i		−	0.285911i
$85$	1399.39	−	2423.82i	0.00227868	−	0.00394679i
$86$	28670.0	+	16552.7i	0.0450747	+	0.0260239i
$87$	−114129.			−0.173315
$88$			263916.i			0.387274i
$89$	−423488.	−	244501.i	−0.600719	−	0.346825i	0.168605	−	0.985684i	$-0.446074\pi$
$89$	−423488.	−	244501.i	−0.600719	−	0.346825i	−0.769324	+	0.638858i	$0.779407\pi$
$90$	55380.6	−	31974.0i	0.0759680	−	0.0438601i
$91$	739973.	+	427223.i	0.981955	+	0.566932i
$92$	48288.1	+	83637.5i	0.0620122	+	0.107408i
$93$	9533.34	+	16512.2i	0.0118521	+	0.0205285i
$94$			584539.i			0.703768i
$95$	130442.	−	193826.i	0.152141	−	0.226069i
$96$	115434.			0.130473
$97$	342904.	−	197975.i	0.375713	−	0.216918i	−0.300238	−	0.953864i	$-0.597066\pi$
$97$	342904.	−	197975.i	0.375713	−	0.216918i	0.675952	+	0.736946i	$0.263733\pi$
$98$	−230402.	+	133023.i	−0.244798	+	0.141334i
$99$	241932.	−	419039.i	0.249338	−	0.431866i
$100$	−231437.	−	400860.i	−0.231437	−	0.400860i
$101$	722124.	−	1.25076e6i	0.700886	−	1.21397i	−0.267269	−	0.963622i	$-0.586121\pi$
$101$	722124.	−	1.25076e6i	0.700886	−	1.21397i	0.968156	−	0.250349i	$-0.0805453\pi$
$102$	−9262.65			−0.00872840
$103$			1.66516e6i			1.52386i	0.647659	+	0.761930i	$0.275748\pi$
$103$			1.66516e6i			1.52386i	−0.647659	+	0.761930i	$0.724252\pi$
$104$	−291019.	+	504059.i	−0.258715	+	0.448107i
$105$	−156214.	−	90190.0i	−0.134943	−	0.0779095i
$106$	−1.18422e6			−0.994295
$107$		−	1.78323e6i		−	1.45565i	−0.685764	−	0.727824i	$-0.740532\pi$
$107$		−	1.78323e6i		−	1.45565i	0.685764	−	0.727824i	$-0.259468\pi$
$108$	−585879.	−	338257.i	−0.465089	−	0.268519i
$109$	−1.81047e6	+	1.04527e6i	−1.39801	+	0.807143i	−0.994184	−	0.107692i	$-0.965654\pi$
$109$	−1.81047e6	+	1.04527e6i	−1.39801	+	0.807143i	−0.403828	+	0.914835i	$0.632321\pi$
$110$	243285.	+	140461.i	0.182784	+	0.105530i
$111$	−55006.3	−	95273.8i	−0.0402202	−	0.0696634i
$112$	136059.	+	235662.i	0.0968444	+	0.167739i
$113$		−	274375.i		−	0.190156i	−0.995470	−	0.0950779i	$-0.969690\pi$
$113$		−	274375.i		−	0.190156i	0.995470	−	0.0950779i	$-0.0303100\pi$
$114$	−771380.	−	53128.0i	−0.520659	−	0.0358599i
$115$	102799.			0.0675922
$116$	158714.	−	91633.5i	0.101681	−	0.0587057i
$117$	924144.	−	533555.i	0.577008	−	0.333136i
$118$	−737633.	+	1.27762e6i	−0.448946	+	0.777598i
$119$	−10917.6	−	18909.9i	−0.00647870	−	0.0112214i
$120$	61436.2	−	106411.i	0.0355534	−	0.0615803i
$121$	354041.			0.199847
$122$			796320.i			0.438539i
$123$	−1.09384e6	+	1.89458e6i	−0.587811	+	1.01812i
$124$	−26515.2	−	15308.6i	−0.0139069	−	0.00802916i
$125$	−1.02492e6			−0.524757
$126$		−	498904.i		−	0.249405i
$127$	415263.	+	239752.i	0.202727	+	0.117045i	0.597927	−	0.801551i	$-0.295991\pi$
$127$	415263.	+	239752.i	0.202727	+	0.117045i	−0.395200	+	0.918595i	$0.629325\pi$
$128$	−160530.	+	92681.9i	−0.0765466	+	0.0441942i
$129$	−100998.	−	58311.3i	−0.0470484	−	0.0271634i
$130$	309771.	+	536539.i	0.140997	+	0.244214i
$131$	135990.	+	235541.i	0.0604912	+	0.104774i	0.894685	−	0.446697i	$-0.147400\pi$
$131$	135990.	+	235541.i	0.0604912	+	0.104774i	−0.834194	+	0.551471i	$0.814067\pi$
$132$		−	929718.i		−	0.404231i
$133$	−800743.	−	1.63741e6i	−0.340360	−	0.695989i
$134$	747338.			0.310601
$135$	−623630.	+	360053.i	−0.253470	+	0.146341i
$136$	12881.2	−	7436.96i	0.00512081	−	0.00295650i
$137$	2.18068e6	−	3.77705e6i	0.848068	−	1.46890i	−0.0348615	−	0.999392i	$-0.511099\pi$
$137$	2.18068e6	−	3.77705e6i	0.848068	−	1.46890i	0.882930	−	0.469505i	$-0.155568\pi$
$138$	−170108.	−	294636.i	−0.0647274	−	0.112111i
$139$	−1.83479e6	+	3.17795e6i	−0.683191	+	1.18332i	0.290811	+	0.956781i	$0.406075\pi$
$139$	−1.83479e6	+	3.17795e6i	−0.683191	+	1.18332i	−0.974002	+	0.226541i	$0.927258\pi$
$140$	289653.			0.105559
$141$		−	2.05920e6i		−	0.734583i
$142$	−1.02635e6	+	1.77770e6i	−0.358453	+	0.620859i
$143$	4.05974e6	+	2.34389e6i	1.38832	+	0.801547i
$144$	339847.			0.113814
$145$		−	195076.i		−	0.0639882i
$146$	−1.60086e6	−	924254.i	−0.514391	−	0.296984i
$147$	811656.	−	468610.i	0.255517	−	0.147523i
$148$	152990.	+	88328.9i	0.0471931	+	0.0272469i
$149$	−1.64920e6	−	2.85650e6i	−0.498557	−	0.863526i	0.501442	−	0.865191i	$-0.332803\pi$
$149$	−1.64920e6	−	2.85650e6i	−0.498557	−	0.863526i	−0.999999	+	0.00166575i	$0.999470\pi$
$150$	815299.	+	1.41214e6i	0.241570	+	0.418412i
$151$			3.42018e6i			0.993385i	0.867927	+	0.496692i	$0.165452\pi$
$151$			3.42018e6i			0.993385i	−0.867927	+	0.496692i	$0.834548\pi$
$152$	1.11538e6	−	545456.i	0.317609	−	0.155320i
$153$	−27269.9			−0.00761393
$154$	1.89804e6	−	1.09583e6i	0.519689	−	0.300042i
$155$	−28223.8	+	16295.0i	−0.00757914	+	0.00437582i
$156$	1.02519e6	−	1.77569e6i	0.270043	−	0.467728i
$157$	−822606.	−	1.42480e6i	−0.212566	−	0.368174i	0.739951	−	0.672661i	$-0.234849\pi$
$157$	−822606.	−	1.42480e6i	−0.212566	−	0.368174i	−0.952517	+	0.304486i	$0.901515\pi$
$158$	171099.	−	296353.i	0.0433788	−	0.0751343i
$159$	4.17175e6			1.03783
$160$			197308.i			0.0481709i
$161$	401004.	−	694560.i	0.0960885	−	0.166430i
$162$	878653.	+	507290.i	0.206668	+	0.119320i
$163$	−6.62645e6			−1.53009			−0.765047	−	0.643974i	$-0.777284\pi$
$163$	−6.62645e6			−1.53009			−0.765047	+	0.643974i	$0.777284\pi$
$164$		−	3.51296e6i		−	0.796419i
$165$	−857040.	−	494812.i	−0.190787	−	0.110151i
$166$	1.27141e6	−	734046.i	0.277946	−	0.160472i
$167$	5.66491e6	+	3.27064e6i	1.21631	+	0.702236i	0.964126	−	0.265444i	$-0.0855187\pi$
$167$	5.66491e6	+	3.27064e6i	1.21631	+	0.702236i	0.252181	+	0.967680i	$0.418852\pi$
$168$	−479307.	−	830184.i	−0.101085	−	0.175084i
$169$	2.75578e6	+	4.77316e6i	0.570933	+	0.988885i
$170$		−	15832.3i		−	0.00322254i
$171$	−2.27099e6	−	156412.i	−0.454180	−	0.0312812i
$172$	187272.			0.0368034
$173$	−1.58787e6	+	916760.i	−0.306675	+	0.177059i	−0.645437	−	0.763813i	$-0.723325\pi$
$173$	−1.58787e6	+	916760.i	−0.306675	+	0.177059i	0.338763	+	0.940872i	$0.389992\pi$
$174$	−559113.	+	322804.i	−0.106133	+	0.0612762i
$175$	−1.92194e6	+	3.32890e6i	−0.358613	+	0.621137i
$176$	746468.	+	1.29292e6i	0.136922	+	0.237156i
$177$	2.59852e6	−	4.50076e6i	0.468604	−	0.811646i
$178$	−2.76621e6			−0.490485
$179$		−	7.03017e6i		−	1.22576i	−0.790175	−	0.612881i	$-0.790010\pi$
$179$		−	7.03017e6i		−	1.22576i	0.790175	−	0.612881i	$-0.209990\pi$
$180$	180872.	−	313280.i	0.0310138	−	0.0537175i
$181$	8.42093e6	+	4.86182e6i	1.42012	+	0.819905i	0.996308	−	0.0858469i	$-0.0273596\pi$
$181$	8.42093e6	+	4.86182e6i	1.42012	+	0.819905i	0.423809	+	0.905752i	$0.360693\pi$
$182$	4.83348e6			0.801763
$183$		−	2.80526e6i		−	0.457741i
$184$	473125.	+	273159.i	0.0759491	+	0.0438492i
$185$	162848.	−	94020.4i	0.0257198	−	0.0148493i
$186$	93407.3	+	53928.7i	0.0145158	+	0.00838072i
$187$	−59897.8	−	103746.i	−0.00915981	−	0.0158653i
$188$	1.65333e6	+	2.86364e6i	0.248820	+	0.430968i
$189$			5.61805e6i			0.832148i
$190$	90809.8	−	1.31849e6i	0.0132395	−	0.192228i
$191$	−7.07960e6			−1.01604			−0.508018	−	0.861347i	$-0.669622\pi$
$191$	−7.07960e6			−1.01604			−0.508018	+	0.861347i	$0.669622\pi$
$192$	565511.	−	326498.i	0.0798982	−	0.0461292i
$193$	−1.06261e7	+	6.13499e6i	−1.47810	+	0.853379i	−0.999693	−	0.0247613i	$-0.992117\pi$
$193$	−1.06261e7	+	6.13499e6i	−1.47810	+	0.853379i	−0.478403	+	0.878141i	$0.658784\pi$
$194$	1.11992e6	−	1.93976e6i	0.153384	−	0.265670i
$195$	−1.09125e6	−	1.89011e6i	−0.147171	−	0.254907i
$196$	−752490.	+	1.30335e6i	−0.0999385	+	0.173099i
$197$	−9.46237e6			−1.23766			−0.618830	−	0.785525i	$-0.712393\pi$
$197$	−9.46237e6			−1.23766			−0.618830	+	0.785525i	$0.712393\pi$
$198$		−	2.73715e6i		−	0.352617i
$199$	−4.03923e6	+	6.99615e6i	−0.512554	+	0.887769i	0.487340	+	0.873212i	$0.337967\pi$
$199$	−4.03923e6	+	6.99615e6i	−0.512554	+	0.887769i	−0.999894	+	0.0145569i	$0.995366\pi$
$200$	−2.26761e6	−	1.30920e6i	−0.283451	−	0.163650i
$201$	−2.63271e6			−0.324201
$202$		−	8.16990e6i		−	0.991203i
$203$	−1.31802e6	−	760962.i	−0.157556	−	0.0909651i
$204$	−45377.5	+	26198.7i	−0.00534503	+	0.00308596i
$205$	−3.23835e6	−	1.86966e6i	−0.375891	−	0.217021i
$206$	4.70979e6	+	8.15760e6i	0.538766	+	0.933170i
$207$	−500810.	−	867429.i	−0.0564628	−	0.0977964i
$208$			3.29250e6i			0.365878i
$209$	−4.39314e6	−	8.98338e6i	−0.481212	−	0.984013i
$210$	−1.02038e6			−0.110181
$211$	−3.85106e6	+	2.22341e6i	−0.409952	+	0.236686i	−0.690769	−	0.723075i	$-0.742728\pi$
$211$	−3.85106e6	+	2.22341e6i	−0.409952	+	0.236686i	0.280817	+	0.959761i	$0.409395\pi$
$212$	−5.80148e6	+	3.34949e6i	−0.608879	+	0.351537i
$213$	3.61562e6	−	6.26244e6i	0.374148	−	0.648044i
$214$	−5.04374e6	−	8.73601e6i	−0.514649	−	0.891398i
$215$	99669.5	−	172633.i	0.0100288	−	0.0173703i
$216$	−3.82694e6			−0.379744
$217$			254258.i			0.0248825i
$218$	−5.91296e6	+	1.02415e7i	−0.570736	+	0.988544i
$219$	5.63946e6	+	3.25594e6i	0.536914	+	0.309988i
$220$	1.58913e6			0.149242
$221$		−	264196.i		−	0.0244765i
$222$	−538950.	−	311163.i	−0.0492594	−	0.0284400i
$223$	1.06572e7	−	6.15294e6i	0.961012	−	0.554840i	0.0645274	−	0.997916i	$-0.479446\pi$
$223$	1.06572e7	−	6.15294e6i	0.961012	−	0.554840i	0.896484	+	0.443076i	$0.146113\pi$
$224$	1.33310e6	+	769669.i	0.118610	+	0.0684794i
$225$	2.40030e6	+	4.15743e6i	0.210726	+	0.364987i
$226$	−776050.	−	1.34416e6i	−0.0672302	−	0.116446i
$227$		−	1.30141e7i		−	1.11259i	−0.830985	−	0.556295i	$-0.812223\pi$
$227$		−	1.30141e7i		−	1.11259i	0.830985	−	0.556295i	$-0.187777\pi$
$228$	−3.92924e6	+	1.92152e6i	−0.331516	+	0.162121i
$229$	1.52500e7			1.26988			0.634941	−	0.772561i	$-0.281025\pi$
$229$	1.52500e7			1.26988			0.634941	+	0.772561i	$0.281025\pi$
$230$	503611.	−	290760.i	0.0413916	−	0.0238974i
$231$	−6.68637e6	+	3.86038e6i	−0.542444	+	0.313180i
$232$	518357.	−	897821.i	0.0415112	−	0.0718995i
$233$	1.38922e6	+	2.40619e6i	0.109825	+	0.190223i	0.915699	−	0.401864i	$-0.131638\pi$
$233$	1.38922e6	+	2.40619e6i	0.109825	+	0.190223i	−0.805874	+	0.592087i	$0.798304\pi$
$234$	3.01824e6	−	5.22775e6i	0.235563	−	0.408006i
$235$	3.51972e6			0.271209
$236$			8.34537e6i			0.634906i
$237$	−602745.	+	1.04399e6i	−0.0452782	+	0.0784241i
$238$	−106971.	−	61759.5i	−0.00793476	−	0.00458114i
$239$	1.68368e7			1.23329			0.616646	−	0.787241i	$-0.288491\pi$
$239$	1.68368e7			1.23329			0.616646	+	0.787241i	$0.288491\pi$
$240$		−	695072.i		−	0.0502801i
$241$	2.23527e7	+	1.29053e7i	1.59690	+	0.921971i	0.992080	+	0.125610i	$0.0400890\pi$
$241$	2.23527e7	+	1.29053e7i	1.59690	+	0.921971i	0.604822	+	0.796361i	$0.293244\pi$
$242$	1.73444e6	−	1.00138e6i	0.122381	−	0.0706566i
$243$	1.02517e7	+	5.91885e6i	0.714462	+	0.412495i
$244$	2.25233e6	+	3.90115e6i	0.155047	+	0.268549i
$245$	800978.	+	1.38733e6i	0.0544656	+	0.0943372i
$246$			1.23754e7i			0.831291i
$247$	1.51536e6	−	2.20019e7i	0.100560	−	1.46005i
$248$	−173197.			−0.0113549
$249$	−4.47888e6	+	2.58588e6i	−0.290116	+	0.167498i
$250$	−5.02105e6	+	2.89890e6i	−0.321347	+	0.185530i
$251$	9.85691e6	−	1.70727e7i	0.623332	−	1.07964i	−0.365529	−	0.930800i	$-0.619112\pi$
$251$	9.85691e6	−	1.70727e7i	0.623332	−	1.07964i	0.988861	−	0.148843i	$-0.0475548\pi$
$252$	−1.41111e6	−	2.44412e6i	−0.0881779	−	0.152729i
$253$	2.20004e6	−	3.81059e6i	0.135853	−	0.235305i
$254$	2.71249e6			0.165526
$255$			55773.7i			0.00336364i
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	1.81604e7	+	1.04849e7i	1.06986	+	0.617682i	0.928142	−	0.372226i	$-0.121405\pi$
$257$	1.81604e7	+	1.04849e7i	1.06986	+	0.617682i	0.141714	+	0.989908i	$0.454739\pi$
$258$	−659717.			−0.0384148
$259$		−	1.46704e6i		−	0.0844388i
$260$	3.03512e6	+	1.75233e6i	0.172686	+	0.0997001i
$261$	−1.64607e6	+	950358.i	−0.0925819	+	0.0534522i
$262$	1.33242e6	+	769274.i	0.0740863	+	0.0427738i
$263$	−1.05119e7	−	1.82071e7i	−0.577848	−	1.00086i	−0.995726	−	0.0923588i	$-0.970559\pi$
$263$	−1.05119e7	−	1.82071e7i	−0.577848	−	1.00086i	0.417878	−	0.908503i	$-0.362774\pi$
$264$	−2.62964e6	−	4.55467e6i	−0.142917	−	0.247540i
$265$			7.13062e6i			0.383169i
$266$	−8.55412e6	−	5.75680e6i	−0.454496	−	0.305869i
$267$	9.74476e6			0.511961
$268$	3.66119e6	−	2.11379e6i	0.190203	−	0.109814i
$269$	−2.97934e7	+	1.72012e7i	−1.53060	+	0.883695i	−0.531270	+	0.847203i	$0.678285\pi$
$269$	−2.97934e7	+	1.72012e7i	−1.53060	+	0.883695i	−0.999334	+	0.0364920i	$0.988382\pi$
$270$	−2.03677e6	+	3.52778e6i	−0.103479	+	0.179230i
$271$	−1.55929e7	−	2.70076e7i	−0.783462	−	1.35700i	−0.929914	−	0.367778i	$-0.880119\pi$
$271$	−1.55929e7	−	2.70076e7i	−0.783462	−	1.35700i	0.146452	−	0.989218i	$-0.453215\pi$
$272$	42069.8	−	72867.0i	0.00209056	−	0.00362096i
$273$	−1.70273e7			−0.836868
$274$		−	2.46716e7i		−	1.19935i
$275$	−1.05444e7	+	1.82635e7i	−0.507020	+	0.878184i
$276$	−1.66671e6	−	962278.i	−0.0792746	−	0.0457692i
$277$	−1.32845e7			−0.625040			−0.312520	−	0.949911i	$-0.601173\pi$
$277$	−1.32845e7			−0.625040			−0.312520	+	0.949911i	$0.601173\pi$
$278$			2.07583e7i			0.966178i
$279$	274997.	+	158770.i	0.0126624	+	0.00731064i
$280$	1.41900e6	−	819263.i	0.0646413	−	0.0373206i
$281$	1.15703e7	+	6.68012e6i	0.521466	+	0.301069i	0.737534	−	0.675310i	$-0.235990\pi$
$281$	1.15703e7	+	6.68012e6i	0.521466	+	0.301069i	−0.216068	+	0.976378i	$0.569323\pi$
$282$	−5.82430e6	−	1.00880e7i	−0.259714	−	0.449839i
$283$	−9.86365e6	−	1.70843e7i	−0.435189	−	0.753770i	0.562122	−	0.827054i	$-0.309985\pi$
$283$	−9.86365e6	−	1.70843e7i	−0.435189	−	0.753770i	−0.997311	+	0.0732845i	$0.976652\pi$
$284$			1.16119e7i			0.506929i
$285$	−319903.	+	4.64475e6i	−0.0138192	+	0.200645i
$286$	2.65181e7			1.13356
$287$	−2.52646e7	+	1.45865e7i	−1.06873	+	0.617030i
$288$	1.66490e6	−	961231.i	0.0696965	−	0.0402393i
$289$	1.20654e7	−	2.08979e7i	0.499860	−	0.865783i
$290$	−551758.	−	955673.i	−0.0226232	−	0.0391846i
$291$	−3.94522e6	+	6.83333e6i	−0.160100	+	0.277302i
$292$	−1.04567e7			−0.419999
$293$			9.68341e6i			0.384969i	0.981300	+	0.192484i	$0.0616545\pi$
$293$			9.68341e6i			0.384969i	−0.981300	+	0.192484i	$0.938346\pi$
$294$	2.65086e6	−	4.59142e6i	0.104314	−	0.180678i
$295$	7.69300e6	+	4.44155e6i	0.299661	+	0.173009i
$296$	999327.			0.0385330
$297$			3.08225e7i			1.17652i
$298$	−1.61588e7	−	9.32929e6i	−0.610605	−	0.352533i
$299$	8.40383e6	−	4.85195e6i	0.314386	−	0.181511i
$300$	7.98827e6	+	4.61203e6i	0.295862	+	0.170816i
$301$	−777592.	−	1.34683e6i	−0.0285136	−	0.0493870i
$302$	9.67372e6	+	1.67554e7i	0.351215	+	0.608321i
$303$			2.87807e7i			1.03460i
$304$	3.92145e6	−	5.82695e6i	0.139581	−	0.207406i
$305$	4.79493e6			0.168998
$306$	−133595.	+	77130.8i	−0.00466256	+	0.00269193i
$307$	−1.72174e6	+	994047.i	−0.0595048	+	0.0343551i	−0.529457	−	0.848337i	$-0.677604\pi$
$307$	−1.72174e6	+	994047.i	−0.0595048	+	0.0343551i	0.469952	+	0.882692i	$0.344271\pi$
$308$	6.19897e6	−	1.07369e7i	0.212162	−	0.367475i
$309$	−1.65916e7	−	2.87374e7i	−0.562356	−	0.974030i
$310$	−92178.5	+	159658.i	−0.00309417	+	0.00535926i
$311$	−3.96645e7			−1.31862			−0.659312	−	0.751870i	$-0.729152\pi$
$311$	−3.96645e7			−1.31862			−0.659312	+	0.751870i	$0.729152\pi$
$312$		−	1.15988e7i		−	0.381898i
$313$	−4.93260e6	+	8.54351e6i	−0.160858	+	0.278614i	−0.935177	−	0.354182i	$-0.884759\pi$
$313$	−4.93260e6	+	8.54351e6i	−0.160858	+	0.278614i	0.774319	+	0.632796i	$0.218093\pi$
$314$	−8.05986e6	−	4.65336e6i	−0.260339	−	0.150307i
$315$	−3.00408e6			−0.0961124
$316$		−	1.93577e6i		−	0.0613469i
$317$	−5.26380e6	−	3.03906e6i	−0.165242	−	0.0954028i	0.415098	−	0.909777i	$-0.363747\pi$
$317$	−5.26380e6	−	3.03906e6i	−0.165242	−	0.0954028i	−0.580341	+	0.814374i	$0.697081\pi$
$318$	2.04373e7	−	1.17995e7i	0.635539	−	0.366929i
$319$	−7.23112e6	−	4.17489e6i	−0.222758	−	0.128610i
$320$	558071.	+	966607.i	0.0170310	+	0.0294985i
$321$	1.77680e7	+	3.07750e7i	0.537183	+	0.930429i
$322$		−	4.53685e6i		−	0.135890i
$323$	−314664.	+	467565.i	−0.00933769	+	0.0138750i
$324$	5.73934e6			0.168743
$325$	−4.02781e7	+	2.32546e7i	−1.17333	+	0.677420i
$326$	−3.24629e7	+	1.87424e7i	−0.936988	+	0.540970i
$327$	2.08300e7	−	3.60787e7i	0.595726	−	1.03183i
$328$	−9.93615e6	−	1.72099e7i	−0.281577	−	0.487705i
$329$	1.37299e7	−	2.37809e7i	0.385549	−	0.667790i
$330$	−5.59816e6			−0.155777
$331$			3.96077e7i			1.09218i	0.837725	+	0.546092i	$0.183885\pi$
$331$			3.96077e7i			1.09218i	−0.837725	+	0.546092i	$0.816115\pi$
$332$	4.15239e6	−	7.19216e6i	0.113471	−	0.196537i
$333$	−1.58670e6	−	916084.i	−0.0429698	−	0.0248086i
$334$	3.70030e7			0.993111
$335$		−	4.49999e6i		−	0.119695i
$336$	−4.69623e6	−	2.71137e6i	−0.123803	−	0.0714778i
$337$	4.78445e7	−	2.76231e7i	1.25009	−	0.721742i	0.278966	−	0.960301i	$-0.410008\pi$
$337$	4.78445e7	−	2.76231e7i	1.25009	−	0.721742i	0.971128	+	0.238559i	$0.0766751\pi$
$338$	2.70011e7	+	1.55891e7i	0.699247	+	0.403710i
$339$	2.73385e6	+	4.73517e6i	0.0701739	+	0.121545i
$340$	−44780.6	−	77562.2i	−0.00113934	−	0.00197339i
$341$			1.39494e6i			0.0351798i
$342$	−1.15680e7	+	5.65708e6i	−0.289187	+	0.141421i
$343$	4.37622e7			1.08447
$344$	917441.	−	529685.i	0.0225374	−	0.0130120i
$345$	−1.77411e6	+	1.02428e6i	−0.0432039	+	0.0249438i
$346$	−5.18598e6	+	8.98237e6i	−0.125199	+	0.216852i
$347$	−3.78199e7	−	6.55060e7i	−0.905175	−	1.56781i	−0.820683	−	0.571384i	$-0.806407\pi$
$347$	−3.78199e7	−	6.55060e7i	−0.905175	−	1.56781i	−0.0844917	−	0.996424i	$-0.526927\pi$
$348$	−1.82606e6	+	3.16282e6i	−0.0433288	+	0.0750477i
$349$	2.44073e7			0.574174			0.287087	−	0.957904i	$-0.407313\pi$
$349$	2.44073e7			0.574174			0.287087	+	0.957904i	$0.407313\pi$
$350$			2.17443e7i			0.507156i
$351$	−3.39878e7	+	5.88686e7i	−0.785962	+	1.36133i
$352$	7.31386e6	+	4.22266e6i	0.167694	+	0.0968184i
$353$	4.42355e7			1.00565			0.502824	−	0.864389i	$-0.332294\pi$
$353$	4.42355e7			1.00565			0.502824	+	0.864389i	$0.332294\pi$
$354$		−	2.93989e7i		−	0.662706i
$355$	1.07042e7	+	6.18005e6i	0.239259	+	0.138136i
$356$	−1.35516e7	+	7.82404e6i	−0.300360	+	0.173413i
$357$	376834.	+	217565.i	0.00828219	+	0.00478172i
$358$	−1.98843e7	−	3.44406e7i	−0.433373	−	0.750623i
$359$	−4.29609e6	−	7.44105e6i	−0.0928518	−	0.160824i	0.815858	−	0.578252i	$-0.196265\pi$
$359$	−4.29609e6	−	7.44105e6i	−0.0928518	−	0.160824i	−0.908710	+	0.417428i	$0.862932\pi$
$360$		−	2.04634e6i		−	0.0438601i
$361$	−2.88866e7	+	3.71333e7i	−0.614009	+	0.789299i
$362$	5.50053e7			1.15952
$363$	−6.11004e6	+	3.52764e6i	−0.127739	+	0.0737503i
$364$	2.36791e7	−	1.36711e7i	0.490977	−	0.283466i
$365$	−5.56527e6	+	9.63932e6i	−0.114448	+	0.198229i
$366$	−7.93446e6	−	1.37429e7i	−0.161836	−	0.280308i
$367$	3.68807e7	−	6.38793e7i	0.746108	−	1.29230i	−0.203568	−	0.979061i	$-0.565254\pi$
$367$	3.68807e7	−	6.38793e7i	0.746108	−	1.29230i	0.949676	−	0.313235i	$-0.101413\pi$
$368$	3.09044e6			0.0620122
$369$			3.64339e7i			0.725148i
$370$	531860.	−	921208.i	0.0105001	−	0.0181866i
$371$	4.81779e7	+	2.78155e7i	0.943465	+	0.544710i
$372$	610134.			0.0118521
$373$		−	6.31631e7i		−	1.21713i	−0.793504	−	0.608565i	$-0.791745\pi$
$373$		−	6.31631e7i		−	1.21713i	0.793504	−	0.608565i	$-0.208255\pi$
$374$	−586877.	−	338833.i	−0.0112184	−	0.00647696i
$375$	1.76880e7	−	1.02122e7i	0.335417	−	0.193653i
$376$	1.61992e7	+	9.35262e6i	0.304741	+	0.175942i
$377$	−9.20726e6	−	1.59474e7i	−0.171833	−	0.297623i
$378$	1.58902e7	+	2.75227e7i	0.294209	+	0.509584i
$379$		−	4.75697e6i		−	0.0873802i	−0.999045	−	0.0436901i	$-0.986089\pi$
$379$		−	4.75697e6i		−	0.0873802i	0.999045	−	0.0436901i	$-0.0139114\pi$
$380$	−3.28438e6	−	6.71612e6i	−0.0598554	−	0.122396i
$381$	−9.55549e6			−0.172774
$382$	−3.46828e7	+	2.00241e7i	−0.622192	+	0.359223i
$383$	2.28018e6	−	1.31646e6i	0.0405857	−	0.0234322i	−0.479570	−	0.877504i	$-0.659207\pi$
$383$	2.28018e6	−	1.31646e6i	0.0405857	−	0.0234322i	0.520156	+	0.854072i	$0.325874\pi$
$384$	1.84695e6	−	3.19901e6i	0.0326183	−	0.0564966i
$385$	−6.59841e6	−	1.14288e7i	−0.115626	−	0.200271i
$386$	−3.47048e7	+	6.01104e7i	−0.603430	+	1.04517i
$387$	−1.94225e6			−0.0335099
$388$		−	1.26704e7i		−	0.216918i
$389$	−1.08433e7	+	1.87811e7i	−0.184209	+	0.319060i	−0.943310	−	0.331913i	$-0.892306\pi$
$389$	−1.08433e7	+	1.87811e7i	−0.184209	+	0.319060i	0.759100	+	0.650974i	$0.225639\pi$
$390$	−1.06921e7	−	6.17306e6i	−0.180247	−	0.104066i
$391$	−247982.			−0.00414849
$392$			8.51346e6i			0.141334i
$393$	−4.69383e6	−	2.70998e6i	−0.0773303	−	0.0446466i
$394$	−4.63559e7	+	2.67636e7i	−0.757909	+	0.437579i
$395$	−1.78445e6	−	1.03025e6i	−0.0289543	−	0.0167167i
$396$	−7.74183e6	−	1.34092e7i	−0.124669	−	0.215933i
$397$	−4.10066e7	−	7.10255e7i	−0.655364	−	1.13512i	−0.981802	−	0.189905i	$-0.939182\pi$
$397$	−4.10066e7	−	7.10255e7i	−0.655364	−	1.13512i	0.326439	−	0.945218i	$-0.394151\pi$
$398$			4.56987e7i			0.724860i
$399$	3.01343e7	+	2.02799e7i	0.474397	+	0.319262i
$400$	−1.48119e7			−0.231437
$401$	1.68242e6	−	971348.i	0.0260917	−	0.0150641i	−0.486897	−	0.873459i	$-0.661871\pi$
$401$	1.68242e6	−	971348.i	0.0260917	−	0.0150641i	0.512989	+	0.858395i	$0.328538\pi$
$402$	−1.28976e7	+	7.44642e6i	−0.198532	+	0.114622i
$403$	−1.53819e6	+	2.66423e6i	−0.0235015	+	0.0407058i
$404$	−2.31080e7	−	4.00242e7i	−0.350443	−	0.606985i
$405$	3.05458e6	−	5.29068e6i	0.0459818	−	0.0796428i
$406$	−8.60930e6			−0.128644
$407$		−	8.04866e6i		−	0.119382i
$408$	−148202.	+	256694.i	−0.00218210	+	0.00377951i
$409$	5.09847e7	+	2.94360e7i	0.745195	+	0.430239i	0.823955	−	0.566655i	$-0.191763\pi$
$409$	5.09847e7	+	2.94360e7i	0.745195	+	0.430239i	−0.0787600	+	0.996894i	$0.525096\pi$
$410$	−2.11528e7			−0.306914
$411$			8.69126e7i			1.25186i
$412$	4.61464e7	+	2.66426e7i	0.659851	+	0.380965i
$413$	6.00185e7	−	3.46517e7i	0.851991	−	0.491897i
$414$	−4.90692e6	−	2.83301e6i	−0.0691525	−	0.0399252i
$415$	−4.41996e6	−	7.65559e6i	−0.0618406	−	0.107111i
$416$	9.31260e6	+	1.61299e7i	0.129357	+	0.224054i
$417$		−	7.31268e7i		−	1.00848i
$418$	−4.69308e7	−	3.15837e7i	−0.642582	−	0.432448i
$419$	3.91192e6			0.0531800			0.0265900	−	0.999646i	$-0.491535\pi$
$419$	3.91192e6			0.0531800			0.0265900	+	0.999646i	$0.491535\pi$
$420$	−4.99884e6	+	2.88608e6i	−0.0674716	+	0.0389548i
$421$	−1.17020e8	+	6.75617e7i	−1.56825	+	0.905428i	−0.571875	+	0.820341i	$0.693784\pi$
$421$	−1.17020e8	+	6.75617e7i	−1.56825	+	0.905428i	−0.996373	+	0.0850873i	$0.972883\pi$
$422$	−1.25775e7	+	2.17849e7i	−0.167362	+	0.289880i
$423$	−1.71471e7	−	2.96997e7i	−0.226553	−	0.392402i
$424$	−1.89475e7	+	3.28181e7i	−0.248574	+	0.430543i
$425$	1.18854e6			0.0154827
$426$		−	4.09061e7i		−	0.529126i
$427$	1.87043e7	−	3.23968e7i	0.240247	−	0.416120i
$428$	−4.94183e7	−	2.85317e7i	−0.630314	−	0.363912i
$429$	−9.34173e7			−1.18319
$430$		−	1.12763e6i		−	0.0141828i
$431$	−2.32828e7	−	1.34423e7i	−0.290806	−	0.167897i	0.347500	−	0.937680i	$-0.387031\pi$
$431$	−2.32828e7	−	1.34423e7i	−0.290806	−	0.167897i	−0.638305	+	0.769784i	$0.720364\pi$
$432$	−1.87481e7	+	1.08242e7i	−0.232545	+	0.134260i
$433$	1.31409e8	+	7.58690e7i	1.61868	+	0.934546i	0.987262	+	0.159105i	$0.0508609\pi$
$433$	1.31409e8	+	7.58690e7i	1.61868	+	0.934546i	0.631420	+	0.775441i	$0.282472\pi$
$434$	719149.	+	1.24560e6i	0.00879730	+	0.0152374i
$435$	1.94372e6	+	3.36662e6i	0.0236138	+	0.0409003i
$436$			6.68975e7i			0.807143i
$437$	−2.06516e7	−	1.42236e6i	−0.247462	−	0.0170437i
$438$	3.68368e7			0.438389
$439$	−7.44601e7	+	4.29896e7i	−0.880096	+	0.508124i	−0.870690	−	0.491832i	$-0.836327\pi$
$439$	−7.44601e7	+	4.29896e7i	−0.880096	+	0.508124i	−0.00940592	+	0.999956i	$0.502994\pi$
$440$	7.78513e6	−	4.49475e6i	0.0913920	−	0.0527652i
$441$	7.80430e6	−	1.35174e7i	0.0909951	−	0.157608i
$442$	−747259.	−	1.29429e6i	−0.00865375	−	0.0149887i
$443$	3.84135e7	−	6.65342e7i	0.441848	−	0.765303i	−0.555979	−	0.831197i	$-0.687656\pi$
$443$	3.84135e7	−	6.65342e7i	0.441848	−	0.765303i	0.997827	+	0.0658932i	$0.0209897\pi$
$444$	−3.52041e6			−0.0402202
$445$			1.66564e7i			0.189017i
$446$	3.48063e7	−	6.02862e7i	0.392331	−	0.679538i
$447$	5.69238e7	+	3.28650e7i	0.637341	+	0.367969i
$448$	8.70781e6			0.0968444
$449$		−	6.34172e7i		−	0.700596i	−0.936638	−	0.350298i	$-0.886080\pi$
$449$		−	6.34172e7i		−	0.700596i	0.936638	−	0.350298i	$-0.113920\pi$
$450$	2.35180e7	+	1.35781e7i	0.258085	+	0.149005i
$451$	−1.38610e8	+	8.00266e7i	−1.51100	+	0.872378i
$452$	−7.60371e6	−	4.39000e6i	−0.0823398	−	0.0475389i
$453$	−3.40783e7	−	5.90254e7i	−0.366593	−	0.634957i
$454$	−3.68093e7	−	6.37556e7i	−0.393360	−	0.681319i
$455$		−	2.91041e7i		−	0.308973i
$456$	−1.38144e7	+	2.05271e7i	−0.145693	+	0.216487i
$457$	−3.63007e7			−0.380335			−0.190168	−	0.981752i	$-0.560903\pi$
$457$	−3.63007e7			−0.380335			−0.190168	+	0.981752i	$0.560903\pi$
$458$	7.47094e7	−	4.31335e7i	0.777640	−	0.448971i
$459$	1.50438e6	−	868555.i	0.0155568	−	0.00898171i
$460$	1.64479e6	−	2.84886e6i	0.0168980	−	0.0292683i
$461$	1.21126e7	+	2.09797e7i	0.123633	+	0.214139i	0.921198	−	0.389094i	$-0.127212\pi$
$461$	1.21126e7	+	2.09797e7i	0.123633	+	0.214139i	−0.797565	+	0.603234i	$0.793879\pi$
$462$	−2.18376e7	+	3.78238e7i	−0.221452	+	0.383566i
$463$	−1.17751e7			−0.118638			−0.0593189	−	0.998239i	$-0.518893\pi$
$463$	−1.17751e7			−0.118638			−0.0593189	+	0.998239i	$0.518893\pi$
$464$		−	5.86454e6i		−	0.0587057i
$465$	324724.	−	562439.i	0.00322965	−	0.00559392i
$466$	1.36115e7	+	7.85859e6i	0.134508	+	0.0776581i
$467$	3.10624e7			0.304989			0.152495	−	0.988304i	$-0.451269\pi$
$467$	3.10624e7			0.304989			0.152495	+	0.988304i	$0.451269\pi$
$468$		−	3.41475e7i		−	0.333136i
$469$	−3.04041e7	−	1.75538e7i	−0.294722	−	0.170158i
$470$	1.72430e7	−	9.95526e6i	0.166081	−	0.0958869i
$471$	2.83931e7	+	1.63928e7i	0.271738	+	0.156888i
$472$	2.36043e7	+	4.08838e7i	0.224473	+	0.388799i
$473$	−4.26613e6	−	7.38915e6i	−0.0403135	−	0.0698250i
$474$			6.81928e6i			0.0640330i
$475$	9.89795e7	+	6.81711e6i	0.923558	+	0.0636091i
$476$	−698729.			−0.00647870
$477$	6.01688e7	−	3.47385e7i	0.554391	−	0.320078i
$478$	8.24831e7	−	4.76217e7i	0.755234	−	0.436034i
$479$	−1.62077e7	+	2.80726e7i	−0.147474	+	0.255432i	−0.930293	−	0.366817i	$-0.880448\pi$
$479$	−1.62077e7	+	2.80726e7i	−0.147474	+	0.255432i	0.782819	+	0.622249i	$0.213781\pi$
$480$	−1.96596e6	−	3.40514e6i	−0.0177767	−	0.0307901i
$481$	8.87521e6	−	1.53723e7i	0.0797524	−	0.138135i
$482$	1.46007e8			1.30386
$483$			1.59823e7i			0.141840i
$484$	5.66466e6	−	9.81147e6i	0.0499617	−	0.0865363i
$485$	−1.16800e7	−	6.74343e6i	−0.102380	−	0.0591093i
$486$	6.69641e7			0.583356
$487$			9.44269e6i			0.0817539i	0.999164	+	0.0408770i	$0.0130152\pi$
$487$			9.44269e6i			0.0817539i	−0.999164	+	0.0408770i	$0.986985\pi$
$488$	2.20683e7	+	1.27411e7i	0.189893	+	0.109635i
$489$	1.14359e8	−	6.60254e7i	0.978014	−	0.564657i
$490$	7.84795e6	+	4.53101e6i	0.0667065	+	0.0385130i
$491$	1.10539e8	+	1.91460e8i	0.933841	+	1.61746i	0.776688	+	0.629885i	$0.216898\pi$
$491$	1.10539e8	+	1.91460e8i	0.933841	+	1.61746i	0.157152	+	0.987574i	$0.449769\pi$
$492$	3.50028e7	+	6.06267e7i	0.293906	+	0.509060i
$493$			470581.i			0.00392730i
$494$	−5.48070e7	−	1.12073e8i	−0.454627	−	0.929649i
$495$	−1.64814e7			−0.135887
$496$	−848488.	+	489875.i	−0.00695345	+	0.00401458i
$497$	8.35107e7	−	4.82149e7i	0.680257	−	0.392746i
$498$	−1.46280e7	+	2.53364e7i	−0.118439	+	0.205143i
$499$	1.08681e8	+	1.88241e8i	0.874684	+	1.51500i	0.857099	+	0.515151i	$0.172264\pi$
$499$	1.08681e8	+	1.88241e8i	0.874684	+	1.51500i	0.0175843	+	0.999845i	$0.494402\pi$
$500$	−1.63987e7	+	2.84033e7i	−0.131189	+	0.227227i
$501$	−1.30353e8			−1.03660
$502$		−	1.11518e8i		−	0.881525i
$503$	−8.36891e7	+	1.44954e8i	−0.657605	+	1.13900i	0.323629	+	0.946184i	$0.395097\pi$
$503$	−8.36891e7	+	1.44954e8i	−0.657605	+	1.13900i	−0.981234	+	0.192821i	$0.938236\pi$
$504$	−1.38260e7	−	7.98246e6i	−0.107995	−	0.0623512i
$505$	−4.91939e7			−0.381977
$506$		−	2.48907e7i		−	0.192125i
$507$	−9.51187e7	−	5.49168e7i	−0.729864	−	0.421387i
$508$	1.32884e7	−	7.67207e6i	0.101364	−	0.0585223i
$509$	−1.77203e8	−	1.02308e8i	−1.34374	−	0.775812i	−0.356390	−	0.934337i	$-0.615993\pi$
$509$	−1.77203e8	−	1.02308e8i	−1.34374	−	0.775812i	−0.987355	+	0.158526i	$0.949326\pi$
$510$	157752.	+	273234.i	0.00118923	+	0.00205980i
$511$	4.34185e7	+	7.52031e7i	0.325396	+	0.563603i
$512$			5.93164e6i			0.0441942i
$513$	1.30264e8	−	6.37032e7i	0.964881	−	0.471856i
$514$	1.18623e8			0.873534
$515$	4.91198e7	−	2.83594e7i	0.359613	−	0.207623i
$516$	−3.23194e6	+	1.86596e6i	−0.0235242	+	0.0135817i
$517$	7.53268e7	−	1.30470e8i	0.545102	−	0.944144i
$518$	−4.14941e6	−	7.18699e6i	−0.0298536	−	0.0517080i
$519$	1.82690e7	−	3.16429e7i	0.130681	−	0.226347i
$520$	1.98253e7			0.140997
$521$			8.58535e7i			0.607079i	0.952819	+	0.303539i	$0.0981684\pi$
$521$			8.58535e7i			0.607079i	−0.952819	+	0.303539i	$0.901832\pi$
$522$	−5.37603e6	+	9.31156e6i	−0.0377964	+	0.0654653i
$523$	−5.53001e7	−	3.19275e7i	−0.386564	−	0.223183i	0.294106	−	0.955773i	$-0.404978\pi$
$523$	−5.53001e7	−	3.19275e7i	−0.386564	−	0.223183i	−0.680670	+	0.732590i	$0.738311\pi$
$524$	8.70335e6			0.0604912
$525$		−	7.66004e7i		−	0.529362i
$526$	−1.02995e8	−	5.94642e7i	−0.707716	−	0.408600i
$527$	68084.1	−	39308.4i	0.000465172	−	0.000268567i
$528$	−2.57651e7	−	1.48755e7i	−0.175037	−	0.101058i
$529$	6.94638e7	+	1.20315e8i	0.469236	+	0.812740i
$530$	2.01685e7	+	3.49328e7i	0.135471	+	0.234642i
$531$		−	8.65523e7i		−	0.578089i
$532$	−5.81891e7	−	4.00772e6i	−0.386462	−	0.0266172i
$533$	−3.52979e8			−2.33114
$534$	4.77394e7	−	2.75623e7i	0.313511	−	0.181006i
$535$	−5.26026e7	+	3.03702e7i	−0.343515	+	0.198329i
$536$	1.19574e7	−	2.07108e7i	0.0776502	−	0.134494i
$537$	7.00480e7	+	1.21327e8i	0.452348	+	0.783490i
$538$	−9.73047e7	+	1.68537e8i	−0.624866	+	1.08230i
$539$	6.85681e7			0.437881
$540$			2.30434e7i			0.146341i
$541$	−5.68724e6	+	9.85059e6i	−0.0359178	+	0.0622115i	−0.883426	−	0.468572i	$-0.844769\pi$
$541$	−5.68724e6	+	9.85059e6i	−0.0359178	+	0.0622115i	0.847508	+	0.530783i	$0.178102\pi$
$542$	−1.52778e8	−	8.82065e7i	−0.959541	−	0.553991i
$543$	−1.93771e8			−1.21029
$544$		−	475965.i		−	0.00295650i
$545$	6.16680e7	+	3.56040e7i	0.380952	+	0.219943i
$546$	−8.34163e7	+	4.81604e7i	−0.512475	+	0.295878i
$547$	−2.43394e8	−	1.40524e8i	−1.48713	−	0.858594i	−0.487236	−	0.873270i	$-0.661995\pi$
$547$	−2.43394e8	−	1.40524e8i	−1.48713	−	0.858594i	−0.999892	+	0.0146760i	$0.995328\pi$
$548$	−6.97819e7	−	1.20866e8i	−0.424034	−	0.734449i
$549$	−2.33596e7	−	4.04600e7i	−0.141172	−	0.244517i
$550$			1.19297e8i			0.717034i
$551$	−2.69912e6	+	3.91893e7i	−0.0161349	+	0.234268i
$552$	−1.08869e7			−0.0647274
$553$	−1.39217e7	+	8.03771e6i	−0.0823223	+	0.0475288i
$554$	−6.50807e7	+	3.75744e7i	−0.382757	+	0.220985i
$555$	−1.87362e6	+	3.24521e6i	−0.0109598	+	0.0189830i
$556$	5.87133e7	+	1.01694e8i	0.341595	+	0.591661i
$557$	5.78260e7	−	1.00158e8i	0.334624	−	0.579587i	−0.648788	−	0.760969i	$-0.724724\pi$
$557$	5.78260e7	−	1.00158e8i	0.334624	−	0.579587i	0.983413	+	0.181382i	$0.0580572\pi$
$558$	1.79628e6			0.0103388
$559$		−	1.88169e7i		−	0.107724i
$560$	4.63445e6	−	8.02710e6i	0.0263897	−	0.0457083i
$561$	2.06744e6	+	1.19363e6i	0.0117096	+	0.00676056i
$562$	7.55770e7			0.425775
$563$			1.46624e8i			0.821634i	0.911718	+	0.410817i	$0.134757\pi$
$563$			1.46624e8i			0.821634i	−0.911718	+	0.410817i	$0.865243\pi$
$564$	−5.70662e7	−	3.29472e7i	−0.318084	−	0.183646i
$565$	−8.09366e6	+	4.67288e6i	−0.0448745	+	0.0259083i
$566$	−9.66436e7	−	5.57972e7i	−0.532996	−	0.307725i
$567$	−2.38309e7	−	4.12763e7i	−0.130735	−	0.226439i
$568$	3.28434e7	+	5.68864e7i	0.179227	+	0.310430i
$569$			2.34342e7i			0.127207i	0.997975	+	0.0636037i	$0.0202594\pi$
$569$			2.34342e7i			0.127207i	−0.997975	+	0.0636037i	$0.979741\pi$
$570$	1.15702e7	+	2.36594e7i	0.0624762	+	0.127755i
$571$	−2.55804e8			−1.37404			−0.687019	−	0.726640i	$-0.741081\pi$
$571$	−2.55804e8			−1.37404			−0.687019	+	0.726640i	$0.741081\pi$
$572$	1.29912e8	−	7.50045e7i	0.694160	−	0.400774i
$573$	1.22180e8	−	7.05406e7i	0.649435	−	0.374952i
$574$	−8.25139e7	+	1.42918e8i	−0.436306	+	0.755704i
$575$	2.18274e7	+	3.78062e7i	0.114815	+	0.198865i
$576$	5.43754e6	−	9.41810e6i	0.0284535	−	0.0492829i
$577$	3.73522e7			0.194441			0.0972207	−	0.995263i	$-0.469005\pi$
$577$	3.73522e7			0.194441			0.0972207	+	0.995263i	$0.469005\pi$
$578$		−	1.36505e8i		−	0.706909i
$579$	1.22257e8	−	2.11756e8i	0.629852	−	1.09094i
$580$	−5.40610e6	−	3.12121e6i	−0.0277077	−	0.0159970i
$581$	−6.89664e7			−0.351649
$582$			4.46351e7i			0.226416i
$583$	2.64320e8	+	1.52605e8i	1.33390	+	0.770129i
$584$	−5.12274e7	+	2.95761e7i	−0.257196	+	0.148492i
$585$	−3.14781e7	−	1.81739e7i	−0.157232	−	0.0907781i
$586$	2.73888e7	+	4.74388e7i	0.136107	+	0.235744i
$587$	7.45357e6	+	1.29100e7i	0.0368511	+	0.0638279i	0.883863	−	0.467746i	$-0.154934\pi$
$587$	7.45357e6	+	1.29100e7i	0.0368511	+	0.0638279i	−0.847012	+	0.531574i	$0.821601\pi$
$588$		−	2.99910e7i		−	0.147523i
$589$	5.89541e6	−	2.88303e6i	0.0288515	−	0.0141092i
$590$	5.02505e7			0.244672
$591$	1.63302e8	−	9.42823e7i	0.791094	−	0.456738i
$592$	4.89568e6	−	2.82652e6i	0.0235965	−	0.0136235i
$593$	−6.14241e7	+	1.06390e8i	−0.294561	+	0.510194i	−0.974883	−	0.222719i	$-0.928507\pi$
$593$	−6.14241e7	+	1.06390e8i	−0.294561	+	0.510194i	0.680322	+	0.732914i	$0.261840\pi$
$594$	8.71792e7	+	1.50999e8i	0.415962	+	0.720467i
$595$	−371876.	+	644109.i	−0.00176542	+	0.00305779i
$596$	−1.05549e8			−0.498557
$597$		−	1.60986e8i		−	0.756599i
$598$	2.74468e7	−	4.75392e7i	0.128348	−	0.222305i
$599$	1.74792e8	+	1.00916e8i	0.813280	+	0.469548i	0.848094	−	0.529846i	$-0.177750\pi$
$599$	1.74792e8	+	1.00916e8i	0.813280	+	0.469548i	−0.0348134	+	0.999394i	$0.511084\pi$
$600$	5.21792e7			0.241570
$601$			7.04506e7i			0.324535i	0.986747	+	0.162267i	$0.0518807\pi$
$601$			7.04506e7i			0.324535i	−0.986747	+	0.162267i	$0.948119\pi$
$602$	−7.61881e6	−	4.39872e6i	−0.0349219	−	0.0201622i
$603$	−3.79713e7	+	2.19228e7i	−0.173182	+	0.0999869i
$604$	9.47827e7	+	5.47228e7i	0.430148	+	0.248346i
$605$	−6.02966e6	−	1.04437e7i	−0.0272287	−	0.0471615i
$606$	8.14042e7	+	1.40996e8i	0.365788	+	0.633563i
$607$		−	2.87013e8i		−	1.28332i	−0.766988	−	0.641662i	$-0.778245\pi$
$607$		−	2.87013e8i		−	1.28332i	0.766988	−	0.641662i	$-0.221755\pi$
$608$	2.73000e6	−	3.96377e7i	0.0121465	−	0.176359i
$609$	3.03286e7			0.134277
$610$	2.34902e7	−	1.35621e7i	0.103490	−	0.0597499i
$611$	2.87737e8	−	1.66125e8i	1.26145	−	0.728301i
$612$	−436318.	+	755725.i	−0.00190348	+	0.00329693i
$613$	2.12258e8	+	3.67642e8i	0.921474	+	1.59604i	0.797137	+	0.603799i	$0.206347\pi$
$613$	2.12258e8	+	3.67642e8i	0.921474	+	1.59604i	0.124337	+	0.992240i	$0.460320\pi$
$614$	−5.62318e6	+	9.73963e6i	−0.0242928	+	0.0420763i
$615$	7.45166e7			0.320352
$616$		−	7.01334e7i		−	0.300042i
$617$	2.56216e7	−	4.43778e7i	0.109081	−	0.188934i	−0.806317	−	0.591484i	$-0.798542\pi$
$617$	2.56216e7	−	4.43778e7i	0.109081	−	0.188934i	0.915398	+	0.402549i	$0.131876\pi$
$618$	−1.62563e8	−	9.38560e7i	−0.688743	−	0.397646i
$619$	−1.98352e8			−0.836303			−0.418152	−	0.908377i	$-0.637322\pi$
$619$	−1.98352e8			−0.836303			−0.418152	+	0.908377i	$0.637322\pi$
$620$			1.04288e6i			0.00437582i
$621$	5.52558e7	+	3.19020e7i	0.230729	+	0.133212i
$622$	−1.94316e8	+	1.12188e8i	−0.807489	+	0.466204i
$623$	1.12538e8	+	6.49740e7i	0.465410	+	0.268705i
$624$	−3.28062e7	−	5.68221e7i	−0.135021	−	0.233864i
$625$	−9.55508e7	−	1.65499e8i	−0.391376	−	0.677883i
$626$			5.58060e7i			0.227488i
$627$	1.65327e8	+	1.11262e8i	0.670718	+	0.451383i
$628$	−5.26468e7			−0.212566
$629$	−392838.	+	226805.i	−0.00157856	+	0.000911383i
$630$	−1.47169e7	+	8.49681e6i	−0.0588566	+	0.0339809i
$631$	2.86470e7	−	4.96181e7i	0.114023	−	0.197493i	−0.803366	−	0.595486i	$-0.796960\pi$
$631$	2.86470e7	−	4.96181e7i	0.114023	−	0.197493i	0.917389	+	0.397993i	$0.130293\pi$
$632$	−5.47518e6	−	9.48329e6i	−0.0216894	−	0.0375671i
$633$	4.43078e7	−	7.67434e7i	0.174690	−	0.302573i
$634$	−3.43830e7			−0.134920
$635$		−	1.63329e7i		−	0.0637883i
$636$	6.67480e7	−	1.15611e8i	0.259458	−	0.449394i
$637$	1.30960e8	+	7.56096e7i	0.506663	+	0.292522i
$638$	−4.72335e7			−0.181881
$639$		−	1.20430e8i		−	0.461565i
$640$	5.46796e6	+	3.15693e6i	0.0208586	+	0.0120427i
$641$	−9.78067e7	+	5.64687e7i	−0.371359	+	0.214404i	−0.674052	−	0.738684i	$-0.735448\pi$
$641$	−9.78067e7	+	5.64687e7i	−0.371359	+	0.214404i	0.302693	+	0.953088i	$0.402114\pi$
$642$	1.74090e8	+	1.00511e8i	0.657913	+	0.379846i
$643$	−1.34380e8	−	2.32753e8i	−0.505477	−	0.875512i	−0.999980	−	0.00633613i	$-0.997983\pi$
$643$	−1.34380e8	−	2.32753e8i	−0.505477	−	0.875512i	0.494503	−	0.869176i	$-0.335350\pi$
$644$	−1.28321e7	−	2.22259e7i	−0.0480443	−	0.0832151i
$645$			3.97239e6i			0.0148038i
$646$	−219060.	+	3.18059e6i	−0.000812580	+	0.0117981i
$647$	−1.81593e8			−0.670482			−0.335241	−	0.942132i	$-0.608818\pi$
$647$	−1.81593e8			−0.670482			−0.335241	+	0.942132i	$0.608818\pi$
$648$	2.81169e7	−	1.62333e7i	0.103334	−	0.0596598i
$649$	3.29281e8	−	1.90111e8i	1.20457	−	0.695460i
$650$	−1.31548e8	+	2.27847e8i	−0.479008	+	0.829667i
$651$	−2.53340e6	−	4.38798e6i	−0.00918250	−	0.0159046i
$652$	−1.06023e8	+	1.83638e8i	−0.382524	+	0.662550i
$653$	1.01436e8			0.364296			0.182148	−	0.983271i	$-0.441695\pi$
$653$	1.01436e8			0.364296			0.182148	+	0.983271i	$0.441695\pi$
$654$		−	2.35665e8i		−	0.842484i
$655$	4.63208e6	−	8.02299e6i	0.0164836	−	0.0285504i
$656$	−9.73540e7	−	5.62074e7i	−0.344860	−	0.199105i
$657$	1.08450e8			0.382413
$658$		−	1.55336e8i		−	0.545248i
$659$	−1.37761e8	−	7.95365e7i	−0.481361	−	0.277914i	0.239623	−	0.970866i	$-0.422976\pi$
$659$	−1.37761e8	−	7.95365e7i	−0.481361	−	0.277914i	−0.720983	+	0.692952i	$0.756310\pi$
$660$	−2.74253e7	+	1.58340e7i	−0.0953936	+	0.0550755i
$661$	−4.12519e8	−	2.38168e8i	−1.42837	−	0.824668i	−0.431375	−	0.902173i	$-0.641971\pi$
$661$	−4.12519e8	−	2.38168e8i	−1.42837	−	0.824668i	−0.996992	+	0.0775046i	$0.975305\pi$
$662$	1.12028e8	+	1.94037e8i	0.386145	+	0.668823i
$663$	2.63243e6	+	4.55950e6i	0.00903267	+	0.0156450i
$664$		−	4.69790e7i		−	0.160472i
$665$	−3.46637e7	+	5.15074e7i	−0.117872	+	0.175148i
$666$	−1.03643e7			−0.0350847
$667$	−1.49687e7	+	8.64220e6i	−0.0504438	+	0.0291237i
$668$	1.81277e8	−	1.04660e8i	0.608154	−	0.351118i
$669$	−1.22615e8	+	2.12375e8i	−0.409510	+	0.709292i
$670$	−1.27279e7	−	2.20454e7i	−0.0423187	−	0.0732981i
$671$	1.02618e8	−	1.77740e8i	0.339669	−	0.588324i
$672$	−3.06757e7			−0.101085
$673$			5.96410e8i			1.95659i	0.207221	+	0.978294i	$0.433558\pi$
$673$			5.96410e8i			1.95659i	−0.207221	+	0.978294i	$0.566442\pi$
$674$	1.56260e8	−	2.70650e8i	0.510349	−	0.883950i
$675$	−2.64831e8	−	1.52900e8i	−0.861109	−	0.497162i
$676$	1.76370e8			0.570933
$677$			2.89768e8i			0.933864i	0.884293	+	0.466932i	$0.154641\pi$
$677$			2.89768e8i			0.933864i	−0.884293	+	0.466932i	$0.845359\pi$
$678$	2.67862e7	+	1.54650e7i	0.0859452	+	0.0496205i
$679$	−9.11236e7	+	5.26102e7i	−0.291086	+	0.168059i
$680$	−438758.	−	253317.i	−0.00139540	−	0.000805634i
$681$	1.29671e8	+	2.24597e8i	0.410583	+	0.711151i
$682$	3.94549e6	+	6.83379e6i	0.0124379	+	0.0215431i
$683$		−	4.84834e8i		−	1.52171i	−0.648924	−	0.760854i	$-0.724780\pi$
$683$		−	4.84834e8i		−	1.52171i	0.648924	−	0.760854i	$-0.275220\pi$
$684$	−4.06705e7	+	6.04330e7i	−0.127090	+	0.188845i
$685$	−1.48557e8			−0.462190
$686$	2.14390e8	−	1.23778e8i	0.664098	−	0.383417i
$687$	−2.63184e8	+	1.51950e8i	−0.811690	+	0.468629i
$688$	2.99635e6	−	5.18983e6i	0.00920084	−	0.0159363i
$689$	3.36554e8	+	5.82928e8i	1.02896	+	1.78220i
$690$	−5.79422e6	+	1.00359e7i	−0.0176379	+	0.0305498i
$691$	4.51536e8			1.36854			0.684272	−	0.729227i	$-0.260120\pi$
$691$	4.51536e8			1.36854			0.684272	+	0.729227i	$0.260120\pi$
$692$			5.86726e7i			0.177059i
$693$	−6.42914e7	+	1.11356e8i	−0.193176	+	0.334590i
$694$	−3.70558e8	−	2.13942e8i	−1.10861	−	0.640055i
$695$	1.24993e8			0.372333
$696$			2.06595e7i			0.0612762i
$697$	7.81185e6	+	4.51017e6i	0.0230704	+	0.0133197i
$698$	1.19571e8	−	6.90343e7i	0.351608	−	0.203001i
$699$	−4.79502e7	−	2.76841e7i	−0.140397	−	0.0810584i
$700$	6.15022e7	+	1.06525e8i	0.179307	+	0.310568i
$701$	−2.57735e8	−	4.46410e8i	−0.748203	−	1.29593i	−0.948683	−	0.316228i	$-0.897584\pi$
$701$	−2.57735e8	−	4.46410e8i	−0.748203	−	1.29593i	0.200480	−	0.979698i	$-0.435750\pi$
$702$			3.84528e8i			1.11152i
$703$	−3.40159e7	+	1.66348e7i	−0.0979074	+	0.0478797i
$704$	4.77739e7			0.136922
$705$	−6.07433e7	+	3.50702e7i	−0.173353	+	0.100085i
$706$	2.16709e8	−	1.25117e8i	0.615832	−	0.355551i
$707$	−1.91898e8	+	3.32377e8i	−0.543015	+	0.940530i
$708$	−8.31526e7	−	1.44024e8i	−0.234302	−	0.405823i
$709$	−2.26706e8	+	3.92667e8i	−0.636099	+	1.10176i	0.350182	+	0.936682i	$0.386120\pi$
$709$	−2.26706e8	+	3.92667e8i	−0.636099	+	1.10176i	−0.986281	+	0.165074i	$0.947214\pi$
$710$	6.99193e7			0.195354
$711$			2.00764e7i			0.0558570i
$712$	−4.42594e7	+	7.66596e7i	−0.122621	+	0.212386i
$713$	2.50073e6	+	1.44379e6i	0.00689918	+	0.00398324i
$714$	2.46147e6			0.00676238
$715$		−	1.59675e8i		−	0.436836i
$716$	−1.94826e8	−	1.12483e8i	−0.530771	−	0.306441i
$717$	−2.90570e8	+	1.67760e8i	−0.788302	+	0.455127i
$718$	−4.20929e7	−	2.43024e7i	−0.113720	−	0.0656561i
$719$	6.27428e7	+	1.08674e8i	0.168802	+	0.292374i	0.937999	−	0.346638i	$-0.112677\pi$
$719$	6.27428e7	+	1.08674e8i	0.168802	+	0.292374i	−0.769197	+	0.639012i	$0.779344\pi$
$720$	−5.78792e6	−	1.00250e7i	−0.0155069	−	0.0268587i
$721$		−	4.42502e8i		−	1.18062i
$722$	−3.64860e7	+	2.63619e8i	−0.0969426	+	0.700430i
$723$	−5.14350e8			−1.36096
$724$	2.69470e8	−	1.55578e8i	0.710058	−	0.409952i
$725$	7.17425e7	−	4.14206e7i	0.188262	−	0.108693i
$726$	−1.99553e7	+	3.45636e7i	−0.0521493	+	0.0903253i
$727$	−2.70507e8	−	4.68532e8i	−0.704004	−	1.21937i	−0.967050	−	0.254588i	$-0.918060\pi$
$727$	−2.70507e8	−	4.68532e8i	−0.704004	−	1.21937i	0.263045	−	0.964784i	$-0.415273\pi$
$728$	7.73357e7	−	1.33949e8i	0.200441	−	0.347173i
$729$	−3.66649e8			−0.946385
$730$			6.29638e7i			0.161854i
$731$	−240432.	+	416441.i	−0.000615518	+	0.00106611i
$732$	−7.77416e7	−	4.48841e7i	−0.198207	−	0.114435i
$733$	8.59688e7			0.218288			0.109144	−	0.994026i	$-0.465189\pi$
$733$	8.59688e7			0.218288			0.109144	+	0.994026i	$0.465189\pi$
$734$		−	4.17258e8i		−	1.05516i
$735$	−2.76466e7	−	1.59618e7i	−0.0696272	−	0.0401993i
$736$	1.51400e7	−	8.74108e6i	0.0379745	−	0.0219246i
$737$	−1.66807e8	−	9.63060e7i	−0.416688	−	0.240575i
$738$	1.03051e8	+	1.78489e8i	0.256379	+	0.444061i
$739$	−1.28928e8	−	2.23310e8i	−0.319459	−	0.553319i	0.660916	−	0.750460i	$-0.270168\pi$
$739$	−1.28928e8	−	2.23310e8i	−0.319459	−	0.553319i	−0.980375	+	0.197140i	$0.936835\pi$
$740$		−	6.01731e6i		−	0.0148493i
$741$	1.93073e8	+	3.94807e8i	0.474533	+	0.970355i
$742$	3.14696e8			0.770336
$743$	−5.76295e8	+	3.32724e8i	−1.40501	+	0.811181i	−0.994901	−	0.100857i	$-0.967841\pi$
$743$	−5.76295e8	+	3.32724e8i	−1.40501	+	0.811181i	−0.410106	+	0.912038i	$0.634508\pi$
$744$	2.98903e6	−	1.72572e6i	0.00725792	−	0.00419036i
$745$	−5.61750e7	+	9.72979e7i	−0.135855	+	0.235307i
$746$	−1.78652e8	−	3.09435e8i	−0.430320	−	0.745337i
$747$	−4.30657e7	+	7.45920e7i	−0.103316	+	0.178949i
$748$	−3.83346e6			−0.00915981
$749$			4.73878e8i			1.12777i
$750$	5.77688e7	−	1.00059e8i	0.136934	−	0.237176i
$751$	−5.70450e7	−	3.29350e7i	−0.134678	−	0.0777566i	0.431147	−	0.902282i	$-0.358109\pi$
$751$	−5.70450e7	−	3.29350e7i	−0.134678	−	0.0777566i	−0.565825	+	0.824525i	$0.691442\pi$
$752$	1.05813e8			0.248820
$753$			3.92854e8i			0.920123i
$754$	−9.02123e7	−	5.20841e7i	−0.210451	−	0.121504i
$755$	1.00890e8	−	5.82489e7i	0.234427	−	0.135346i
$756$	1.55692e8	+	8.98888e7i	0.360330	+	0.208037i
$757$	−2.03504e8	−	3.52479e8i	−0.469121	−	0.812541i	0.530256	−	0.847837i	$-0.322096\pi$
$757$	−2.03504e8	−	3.52479e8i	−0.469121	−	0.812541i	−0.999377	+	0.0352966i	$0.988762\pi$
$758$	−1.34547e7	−	2.33043e7i	−0.0308936	−	0.0535092i
$759$			8.76842e7i			0.200538i
$760$	−3.50862e7	−	2.36125e7i	−0.0799273	−	0.0537899i
$761$	5.40629e8			1.22672			0.613359	−	0.789804i	$-0.289818\pi$
$761$	5.40629e8			1.22672			0.613359	+	0.789804i	$0.289818\pi$
$762$	−4.68121e7	+	2.70270e7i	−0.105802	+	0.0610848i
$763$	4.81115e8	−	2.77772e8i	1.08312	−	0.625338i
$764$	−1.13274e8	+	1.96196e8i	−0.254009	+	0.439956i
$765$	464432.	+	804421.i	0.00103738	+	0.00179680i
$766$	7.44704e6	−	1.28986e7i	0.0165690	−	0.0286984i
$767$	8.38536e8			1.85838
$768$		−	2.08959e7i		−	0.0461292i
$769$	4.20811e8	−	7.28867e8i	0.925355	−	1.60276i	0.134367	−	0.990932i	$-0.457100\pi$
$769$	4.20811e8	−	7.28867e8i	0.925355	−	1.60276i	0.790989	−	0.611831i	$-0.209567\pi$
$770$	−6.46509e7	−	3.73262e7i	−0.141613	−	0.0817602i
$771$	−4.17882e8			−0.911782
$772$			3.92639e8i			0.853379i
$773$	−6.21205e8	−	3.58653e8i	−1.34492	−	0.776490i	−0.357396	−	0.933953i	$-0.616335\pi$
$773$	−6.21205e8	−	3.58653e8i	−1.34492	−	0.776490i	−0.987525	+	0.157463i	$0.949669\pi$
$774$	−9.51505e6	+	5.49352e6i	−0.0205205	+	0.0118475i
$775$	−1.19855e7	−	6.91985e6i	−0.0257485	−	0.0148659i
$776$	−3.58374e7	−	6.20722e7i	−0.0766922	−	0.132835i
$777$	1.46174e7	+	2.53182e7i	0.0311608	+	0.0539721i
$778$			1.22678e8i			0.260511i
$779$	6.24690e8	+	4.20407e8i	1.32146	+	0.889320i
$780$	−6.98402e7			−0.147171
$781$	4.58167e8	−	2.64523e8i	0.961770	−	0.555278i
$782$	−1.21486e6	+	701400.i	−0.00254042	+	0.00146671i
$783$	6.05384e7	−	1.04856e8i	0.126109	−	0.218427i
$784$	2.40797e7	+	4.17073e7i	0.0499692	+	0.0865493i
$785$	−2.80196e7	+	4.85313e7i	−0.0579232	+	0.100326i
$786$	−3.06599e7			−0.0631399
$787$			2.68544e6i			0.00550923i	0.999996	+	0.00275462i	$0.000876823\pi$
$787$			2.68544e6i			0.00550923i	−0.999996	+	0.00275462i	$0.999123\pi$
$788$	−1.51398e8	+	2.62229e8i	−0.309415	+	0.535922i
$789$	3.62829e8	+	2.09479e8i	0.738704	+	0.426491i
$790$	−1.16560e7			−0.0236411
$791$			7.29128e7i			0.147324i
$792$	−7.58542e7	−	4.37944e7i	−0.152688	−	0.0881543i
$793$	3.91985e8	−	2.26313e8i	0.786049	−	0.453826i
$794$	−4.01781e8	−	2.31968e8i	−0.802653	−	0.463412i
$795$	−7.10490e7	−	1.23060e8i	−0.141402	−	0.244916i
$796$	1.29255e8	+	2.23877e8i	0.256277	+	0.443885i
$797$		−	8.02506e6i		−	0.0158516i	−0.999969	−	0.00792581i	$-0.997477\pi$
$797$		−	8.02506e6i		−	0.0158516i	0.999969	−	0.00792581i	$-0.00252289\pi$
$798$	2.04987e8	+	1.41183e7i	0.403384	+	0.0277826i
$799$	−8.49060e6			−0.0166456
$800$	−7.25634e7	+	4.18945e7i	−0.141725	+	0.0818252i
$801$	1.40548e8	−	8.11454e7i	0.273481	−	0.157894i
$802$	5.49478e6	−	9.51723e6i	0.0106519	−	0.0184496i
$803$	2.38209e8	+	4.12589e8i	0.460056	+	0.796840i
$804$	−4.21233e7	+	7.29597e7i	−0.0810502	+	0.140383i
$805$	−2.73180e7			−0.0523674
$806$			1.74027e7i			0.0332362i
$807$	3.42783e8	−	5.93717e8i	0.652227	−	1.12969i
$808$	−2.26411e8	−	1.30718e8i	−0.429203	−	0.247801i
$809$	−3.84120e8			−0.725473			−0.362736	−	0.931892i	$-0.618157\pi$
$809$	−3.84120e8			−0.725473			−0.362736	+	0.931892i	$0.618157\pi$
$810$		−	3.45586e7i		−	0.0650281i
$811$	7.52679e8	+	4.34560e8i	1.41107	+	0.814679i	0.995489	−	0.0948785i	$-0.0302463\pi$
$811$	7.52679e8	+	4.34560e8i	1.41107	+	0.814679i	0.415577	+	0.909558i	$0.363580\pi$
$812$	−4.21768e7	+	2.43508e7i	−0.0787781	+	0.0454826i
$813$	5.38203e8	+	3.10732e8i	1.00155	+	0.578248i
$814$	−2.27650e7	−	3.94302e7i	−0.0422081	−	0.0731065i
$815$	1.12855e8	+	1.95470e8i	0.208472	+	0.361084i
$816$			1.67672e6i			0.00308596i
$817$	−2.24114e7	+	3.33015e7i	−0.0410964	+	0.0610658i
$818$	3.33031e8			0.608449
$819$	−2.45583e8	+	1.41787e8i	−0.447040	+	0.258099i
$820$	−1.03627e8	+	5.98291e7i	−0.187945	+	0.108510i
$821$	3.82922e8	−	6.63241e8i	0.691960	−	1.19851i	−0.279234	−	0.960223i	$-0.590081\pi$
$821$	3.82922e8	−	6.63241e8i	0.691960	−	1.19851i	0.971195	−	0.238288i	$-0.0765861\pi$
$822$	2.45826e8	+	4.25783e8i	0.442601	+	0.766607i
$823$	−1.18241e7	+	2.04799e7i	−0.0212113	+	0.0367390i	−0.876436	−	0.481518i	$-0.840086\pi$
$823$	−1.18241e7	+	2.04799e7i	−0.0212113	+	0.0367390i	0.855225	+	0.518257i	$0.173419\pi$
$824$	3.01427e8			0.538766
$825$		−	4.20255e8i		−	0.748430i
$826$	1.96020e8	−	3.39516e8i	0.347824	−	0.602448i
$827$	−6.26587e8	−	3.61760e8i	−1.10781	−	0.639594i	−0.169548	−	0.985522i	$-0.554231\pi$
$827$	−6.26587e8	−	3.61760e8i	−1.10781	−	0.639594i	−0.938261	+	0.345928i	$0.887564\pi$
$828$	−3.20519e7			−0.0564628
$829$			3.91627e8i			0.687399i	0.939080	+	0.343699i	$0.111680\pi$
$829$			3.91627e8i			0.687399i	−0.939080	+	0.343699i	$0.888320\pi$
$830$	−4.33065e7	−	2.50030e7i	−0.0757390	−	0.0437279i
$831$	2.29265e8	−	1.32366e8i	0.399516	−	0.230661i
$832$	9.12445e7	+	5.26800e7i	0.158430	+	0.0914695i
$833$	−1.93220e6	−	3.34666e6i	−0.00334284	−	0.00578998i
$834$	−2.06834e8	−	3.58247e8i	−0.356552	−	0.617567i
$835$		−	2.22808e8i		−	0.382712i
$836$	−3.19245e8	−	2.19877e7i	−0.546393	−	0.0376323i
$837$	−2.02275e7			−0.0344957
$838$	1.91644e7	−	1.10646e7i	0.0325660	−	0.0188020i
$839$	−2.94732e8	+	1.70164e8i	−0.499048	+	0.288125i	−0.728320	−	0.685237i	$-0.759699\pi$
$839$	−2.94732e8	+	1.70164e8i	−0.499048	+	0.288125i	0.229273	+	0.973362i	$0.426365\pi$
$840$	−1.63261e7	+	2.82777e7i	−0.0275452	+	0.0477096i
$841$	−2.81012e8	−	4.86727e8i	−0.472429	−	0.818271i
$842$	−3.82187e8	+	6.61967e8i	−0.640235	+	1.10892i
$843$	−2.66241e8			−0.444418
$844$			1.42298e8i			0.236686i
$845$	9.38674e7	−	1.62583e8i	0.155577	−	0.269467i
$846$	−1.68007e8	−	9.69988e7i	−0.277470	−	0.160197i
$847$	−9.40833e7			−0.154833
$848$			2.14367e8i			0.351537i
$849$	3.40454e8	+	1.96561e8i	0.556333	+	0.321199i
$850$	5.82261e6	−	3.36169e6i	0.00948115	−	0.00547394i
$851$	−1.44289e7	−	8.33054e6i	−0.0234123	−	0.0135171i
$852$	−1.15700e8	−	2.00398e8i	−0.187074	−	0.324022i
$853$	−9.81417e7	−	1.69986e8i	−0.158127	−	0.273884i	0.776066	−	0.630652i	$-0.217212\pi$
$853$	−9.81417e7	−	1.69986e8i	−0.158127	−	0.273884i	−0.934193	+	0.356767i	$0.883879\pi$
$854$		−	2.11615e8i		−	0.339760i
$855$	3.40633e7	+	6.96548e7i	0.0544990	+	0.111443i
$856$	−3.22799e8			−0.514649
$857$	−9.73224e8	+	5.61891e8i	−1.54622	+	0.892709i	−0.547792	+	0.836615i	$0.684531\pi$
$857$	−9.73224e8	+	5.61891e8i	−1.54622	+	0.892709i	−0.998425	+	0.0560941i	$0.982135\pi$
$858$	−4.57649e8	+	2.64224e8i	−0.724554	+	0.418322i
$859$	−1.30393e8	+	2.25847e8i	−0.205719	+	0.356316i	−0.950362	−	0.311147i	$-0.899287\pi$
$859$	−1.30393e8	+	2.25847e8i	−0.205719	+	0.356316i	0.744642	+	0.667464i	$0.232620\pi$
$860$	−3.18942e6	−	5.52424e6i	−0.00501438	−	0.00868515i
$861$	2.90678e8	−	5.03469e8i	0.455410	−	0.788793i
$862$	−1.52082e8			−0.237442
$863$			2.11782e8i			0.329502i	0.986335	+	0.164751i	$0.0526820\pi$
$863$			2.11782e8i			0.329502i	−0.986335	+	0.164751i	$0.947318\pi$
$864$	−6.12311e7	+	1.06055e8i	−0.0949359	+	0.164434i
$865$	5.40861e7	+	3.12266e7i	0.0835675	+	0.0482477i
$866$	8.58360e8			1.32165
$867$			4.80875e8i			0.737862i
$868$	7.04619e6	+	4.06812e6i	0.0107745	+	0.00622063i
$869$	−7.63792e7	+	4.40976e7i	−0.116390	+	0.0671978i
$870$	1.90445e7	+	1.09953e7i	0.0289209	+	0.0166975i
$871$	−2.12392e8	−	3.67874e8i	−0.321428	−	0.556730i
$872$	1.89215e8	+	3.27729e8i	0.285368	+	0.494272i
$873$			1.31409e8i			0.197507i
$874$	−1.05195e8	+	5.14434e7i	−0.157565	+	0.0770541i
$875$	2.72363e8			0.406559
$876$	1.80463e8	−	1.04190e8i	0.268457	−	0.154994i
$877$	5.14666e8	−	2.97143e8i	0.763004	−	0.440520i	−0.0673694	−	0.997728i	$-0.521461\pi$
$877$	5.14666e8	−	2.97143e8i	0.763004	−	0.440520i	0.830373	+	0.557208i	$0.188127\pi$
$878$	−2.43186e8	+	4.21210e8i	−0.359298	+	0.622322i
$879$	−9.64847e7	−	1.67116e8i	−0.142067	−	0.246066i
$880$	2.54261e7	−	4.40394e7i	0.0373106	−	0.0646239i
$881$	−7.56197e8			−1.10588			−0.552939	−	0.833222i	$-0.686494\pi$
$881$	−7.56197e8			−1.10588			−0.552939	+	0.833222i	$0.686494\pi$
$882$		−	8.82956e7i		−	0.128687i
$883$	−3.21433e8	+	5.56738e8i	−0.466883	+	0.808665i	−0.999284	−	0.0378269i	$-0.987956\pi$
$883$	−3.21433e8	+	5.56738e8i	−0.466883	+	0.808665i	0.532401	+	0.846492i	$0.321290\pi$
$884$	−7.32162e6	−	4.22714e6i	−0.0105986	−	0.00611913i
$885$	−1.77021e8			−0.255385
$886$		−	4.34599e8i		−	0.624868i
$887$	1.11050e8	+	6.41148e7i	0.159129	+	0.0918729i	0.577450	−	0.816426i	$-0.304048\pi$
$887$	1.11050e8	+	6.41148e7i	0.159129	+	0.0918729i	−0.418321	+	0.908299i	$0.637381\pi$
$888$	−1.72464e7	+	9.95721e6i	−0.0246297	+	0.0142200i
$889$	−1.10353e8	−	6.37121e7i	−0.157064	−	0.0906810i
$890$	4.71113e7	+	8.15992e7i	0.0668275	+	0.115749i
$891$	−1.30744e8	−	2.26456e8i	−0.184837	−	0.320148i
$892$		−	3.93788e8i		−	0.554840i
$893$	−7.07085e8	−	4.86997e7i	−0.992927	−	0.0683868i
$894$	3.71825e8			0.520386
$895$	−2.07379e8	+	1.19731e8i	−0.289265	+	0.167007i
$896$	4.26594e7	−	2.46294e7i	0.0593049	−	0.0342397i
$897$	−9.66889e7	+	1.67470e8i	−0.133967	+	0.232038i
$898$	−1.79371e8	−	3.10679e8i	−0.247698	−	0.429026i
$899$	2.73980e6	−	4.74548e6i	0.00377086	−	0.00653132i
$900$	1.53619e8			0.210726
$901$		−	1.72012e7i		−	0.0235171i
$902$	−4.52699e8	+	7.84097e8i	−0.616864	+	1.06844i
$903$	2.68394e7	+	1.54957e7i	0.0364510	+	0.0210450i
$904$	−4.96672e7			−0.0672302
$905$		−	3.31206e8i		−	0.446841i
$906$	−3.33898e8	−	1.92776e8i	−0.448983	−	0.259220i
$907$	−1.07515e8	+	6.20735e7i	−0.144094	+	0.0831926i	−0.570314	−	0.821427i	$-0.693178\pi$
$907$	−1.07515e8	+	6.20735e7i	−0.144094	+	0.0831926i	0.426220	+	0.904620i	$0.359845\pi$
$908$	−3.60656e8	−	2.08225e8i	−0.481765	−	0.278147i
$909$	2.39659e8	+	4.15102e8i	0.319082	+	0.552667i
$910$	−8.23189e7	−	1.42580e8i	−0.109238	−	0.189206i
$911$		−	9.28400e7i		−	0.122795i	−0.998113	−	0.0613974i	$-0.980444\pi$
$911$		−	9.28400e7i		−	0.122795i	0.998113	−	0.0613974i	$-0.0195557\pi$
$912$	−9.61719e6	+	1.39635e8i	−0.0126784	+	0.184081i
$913$	−3.78372e8			−0.497173
$914$	−1.77837e8	+	1.02674e8i	−0.232907	+	0.134469i
$915$	−8.27509e7	+	4.77763e7i	−0.108021	+	0.0623661i
$916$	2.44000e8	−	4.22620e8i	0.317470	−	0.549875i
$917$	−3.61381e7	−	6.25930e7i	−0.0468659	−	0.0811741i
$918$	4.91329e6	−	8.51006e6i	0.00635103	−	0.0110003i
$919$	−6.98490e8			−0.899940			−0.449970	−	0.893044i	$-0.648565\pi$
$919$	−6.98490e8			−0.899940			−0.449970	+	0.893044i	$0.648565\pi$
$920$		−	1.86086e7i		−	0.0238974i
$921$	1.98092e7	−	3.43105e7i	0.0253564	−	0.0439186i
$922$	1.18679e8	+	6.85193e7i	0.151419	+	0.0874219i
$923$	1.16675e9			1.48379
$924$			2.47064e8i			0.313180i
$925$	6.91553e7	+	3.99268e7i	0.0873776	+	0.0504475i
$926$	−5.76862e7	+	3.33051e7i	−0.0726506	+	0.0419448i
$927$	−4.78597e8	−	2.76318e8i	−0.600802	−	0.346873i
$928$	−1.65874e7	−	2.87303e7i	−0.0207556	−	0.0359497i
$929$	−2.66383e8	−	4.61389e8i	−0.332246	−	0.575466i	0.650706	−	0.759330i	$-0.274473\pi$
$929$	−2.66383e8	−	4.61389e8i	−0.332246	−	0.575466i	−0.982952	+	0.183863i	$0.941140\pi$
$930$		−	3.67383e6i		−	0.00456742i
$931$	−1.41715e8	−	2.89788e8i	−0.175617	−	0.359113i
$932$	8.89098e7			0.109825
$933$	6.84531e8	−	3.95214e8i	0.842845	−	0.486617i
$934$	1.52174e8	−	8.78577e7i	0.186767	−	0.107830i
$935$	−2.04024e6	+	3.53379e6i	−0.00249601	+	0.00432321i
$936$	−9.65837e7	−	1.67288e8i	−0.117781	−	0.204003i
$937$	−1.48238e8	+	2.56756e8i	−0.180194	+	0.312105i	−0.941947	−	0.335763i	$-0.891006\pi$
$937$	−1.48238e8	+	2.56756e8i	−0.180194	+	0.312105i	0.761752	+	0.647868i	$0.224339\pi$
$938$	−1.98599e8			−0.240640
$939$		−	1.96592e8i		−	0.237448i
$940$	5.63155e7	−	9.75413e7i	0.0678023	−	0.117437i
$941$	5.37445e7	+	3.10294e7i	0.0645008	+	0.0372396i	0.531904	−	0.846805i	$-0.321477\pi$
$941$	5.37445e7	+	3.10294e7i	0.0645008	+	0.0372396i	−0.467403	+	0.884044i	$0.654810\pi$
$942$	1.85463e8			0.221873
$943$			3.31317e8i			0.395101i
$944$	2.31274e8	+	1.33526e8i	0.274922	+	0.158727i
$945$	1.65724e8	−	9.56809e7i	0.196377	−	0.113378i
$946$	−4.17993e7	−	2.41329e7i	−0.0493737	−	0.0285059i
$947$	2.70853e8	+	4.69132e8i	0.318922	+	0.552389i	0.980263	−	0.197696i	$-0.0633459\pi$
$947$	2.70853e8	+	4.69132e8i	0.318922	+	0.552389i	−0.661341	+	0.750085i	$0.730013\pi$
$948$	1.92878e7	+	3.34075e7i	0.0226391	+	0.0392120i
$949$			1.05069e9i			1.22935i
$950$	5.04180e8	−	2.46559e8i	0.588051	−	0.287575i
$951$	1.21124e8			0.140827
$952$	−3.42306e6	+	1.97630e6i	−0.00396738	+	0.00229057i
$953$	−8.83715e8	+	5.10213e8i	−1.02102	+	0.589485i	−0.914399	−	0.404815i	$-0.867336\pi$
$953$	−8.83715e8	+	5.10213e8i	−1.02102	+	0.589485i	−0.106619	+	0.994300i	$0.534003\pi$
$954$	1.96511e8	−	3.40366e8i	0.226329	−	0.392014i
$955$	1.20573e8	+	2.08838e8i	0.138433	+	0.239772i
$956$	2.69389e8	−	4.66595e8i	0.308323	−	0.534031i
$957$	1.66393e8			0.189845
$958$			1.83369e8i			0.208560i
$959$	−5.79497e8	+	1.00372e9i	−0.657046	+	1.13804i
$960$	−1.92624e7	−	1.11211e7i	−0.0217719	−	0.0125700i
$961$	8.86588e8			0.998969
$962$		−	1.00412e8i		−	0.112787i
$963$	5.12532e8	+	2.95910e8i	0.573908	+	0.331346i
$964$	7.15285e8	−	4.12970e8i	0.798451	−	0.460986i
$965$	3.61946e8	+	2.08970e8i	0.402775	+	0.232542i
$966$	4.52048e7	+	7.82970e7i	0.0501479	+	0.0868587i
$967$	5.22129e8	+	9.04353e8i	0.577428	+	1.00013i	0.995773	+	0.0918467i	$0.0292770\pi$
$967$	5.22129e8	+	9.04353e8i	0.577428	+	1.00013i	−0.418345	+	0.908288i	$0.637390\pi$
$968$		−	6.40883e7i		−	0.0706566i
$969$	771700.	−	1.12045e7i	0.000848159	−	0.0123147i
$970$	−7.62932e7			−0.0835931
$971$	9.97416e8	−	5.75858e8i	1.08948	−	0.629011i	0.156041	−	0.987751i	$-0.450127\pi$
$971$	9.97416e8	−	5.75858e8i	1.08948	−	0.629011i	0.933438	+	0.358740i	$0.116793\pi$
$972$	3.28056e8	−	1.89403e8i	0.357231	−	0.206247i
$973$	4.87579e8	−	8.44512e8i	0.529306	−	0.916785i
$974$	2.67080e7	+	4.62595e7i	0.0289044	+	0.0500639i
$975$	4.63413e8	−	8.02655e8i	0.499982	−	0.865994i
$976$	1.44149e8			0.155047
$977$		−	5.25487e8i		−	0.563480i	−0.959491	−	0.281740i	$-0.909089\pi$
$977$		−	5.25487e8i		−	0.563480i	0.959491	−	0.281740i	$-0.0909115\pi$
$978$	3.73496e8	−	6.46914e8i	0.399273	−	0.691561i
$979$	6.17423e8	+	3.56469e8i	0.658013	+	0.379904i
$980$	5.12626e7			0.0544656
$981$		−	6.93813e8i		−	0.734912i
$982$	1.08306e9	+	6.25306e8i	1.14372	+	0.660325i
$983$	3.46796e8	−	2.00223e8i	0.365102	−	0.210792i	−0.306215	−	0.951962i	$-0.599063\pi$
$983$	3.46796e8	−	2.00223e8i	0.365102	−	0.210792i	0.671316	+	0.741171i	$0.265729\pi$
$984$	3.42956e8	+	1.98006e8i	0.359959	+	0.207823i
$985$	1.61153e8	+	2.79126e8i	0.168628	+	0.292073i
$986$	1.33100e6	+	2.30537e6i	0.00138851	+	0.00240497i
$987$			5.47214e8i			0.569123i
$988$	−5.85488e8	−	3.94024e8i	−0.607081	−	0.408557i
$989$	−1.76621e7			−0.0182580
$990$	−8.07419e7	+	4.66164e7i	−0.0832134	+	0.0480433i
$991$	−1.13435e9	+	6.54916e8i	−1.16553	+	0.672922i	−0.952624	−	0.304150i	$-0.901628\pi$
$991$	−1.13435e9	+	6.54916e8i	−1.16553	+	0.672922i	−0.212910	+	0.977072i	$0.568294\pi$
$992$	−2.77115e6	+	4.79977e6i	−0.00283874	+	0.00491683i
$993$	−3.94648e8	−	6.83551e8i	−0.403053	−	0.698108i
$994$	2.72745e8	−	4.72408e8i	0.277714	−	0.481014i
$995$	2.75168e8			0.279337
$996$			1.65496e8i			0.167498i
$997$	−3.62992e8	+	6.28720e8i	−0.366278	+	0.634413i	−0.988980	−	0.148046i	$-0.952702\pi$
$997$	−3.62992e8	+	6.28720e8i	−0.366278	+	0.634413i	0.622702	+	0.782459i	$0.286035\pi$
$998$	1.06485e9	+	6.14791e8i	1.07126	+	0.618495i
$999$	1.16710e8			0.117061

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.d.a.31.7	yes	20
3.2	odd	2		342.7.m.a.145.3		20
19.8	odd	6	inner	38.7.d.a.27.7	✓	20
57.8	even	6		342.7.m.a.217.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.d.a.27.7	✓	20	19.8	odd	6	inner
38.7.d.a.31.7	yes	20	1.1	even	1	trivial
342.7.m.a.145.3		20	3.2	odd	2
342.7.m.a.217.3		20	57.8	even	6

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	38.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 - 2.82843i) q^{2} +(-17.2580 + 9.96392i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-17.0310 - 29.4985i) q^{5} +(-56.3644 + 97.6261i) q^{6} -265.741 q^{7} -181.019i q^{8} +(-165.941 + 287.418i) q^{9} +O(q^{10})\)	\(q+(4.89898 - 2.82843i) q^{2} +(-17.2580 + 9.96392i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-17.0310 - 29.4985i) q^{5} +(-56.3644 + 97.6261i) q^{6} -265.741 q^{7} -181.019i q^{8} +(-165.941 + 287.418i) q^{9} +(-166.869 - 96.3417i) q^{10} -1457.94 q^{11} +637.691i q^{12} +(-2784.56 - 1607.67i) q^{13} +(-1301.86 + 751.629i) q^{14} +(587.842 + 339.390i) q^{15} +(-512.000 - 886.810i) q^{16} +(41.0838 + 71.1592i) q^{17} +1877.40i q^{18} +(3013.25 + 6161.67i) q^{19} -1089.98 q^{20} +(4586.16 - 2647.82i) q^{21} +(-7142.44 + 4123.69i) q^{22} +(-1509.00 + 2613.67i) q^{23} +(1803.66 + 3124.03i) q^{24} +(7232.39 - 12526.9i) q^{25} -18188.7 q^{26} -21141.1i q^{27} +(-4251.86 + 7364.43i) q^{28} +(4959.81 + 2863.55i) q^{29} +3839.76 q^{30} -956.786i q^{31} +(-5016.55 - 2896.31i) q^{32} +(25161.2 - 14526.8i) q^{33} +(402.537 + 232.405i) q^{34} +(4525.83 + 7838.97i) q^{35} +(5310.10 + 9197.37i) q^{36} +5520.55i q^{37} +(32189.7 + 21663.2i) q^{38} +64074.7 q^{39} +(-5339.80 + 3082.94i) q^{40} +(95072.3 - 54890.0i) q^{41} +(14978.3 - 25943.3i) q^{42} +(2926.12 + 5068.20i) q^{43} +(-23327.1 + 40403.7i) q^{44} +11304.5 q^{45} +17072.4i q^{46} +(-51666.4 + 89488.9i) q^{47} +(17672.2 + 10203.1i) q^{48} -47030.7 q^{49} -81825.2i q^{50} +(-1418.05 - 818.710i) q^{51} +(-89106.0 + 51445.4i) q^{52} +(-181296. - 104671. i) q^{53} +(-59796.0 - 103570. i) q^{54} +(24830.2 + 43007.2i) q^{55} +48104.3i q^{56} +(-113397. - 76314.5i) q^{57} +32397.3 q^{58} +(-225853. + 130396. i) q^{59} +(18810.9 - 10860.5i) q^{60} +(-70385.4 + 121911. i) q^{61} +(-2706.20 - 4687.28i) q^{62} +(44097.3 - 76378.7i) q^{63} -32768.0 q^{64} +109521. i q^{65} +(82176.2 - 142333. i) q^{66} +(114412. + 66056.0i) q^{67} +2629.36 q^{68} -60142.4i q^{69} +(44343.9 + 25602.0i) q^{70} +(-314256. + 181436. i) q^{71} +(52028.2 + 30038.5i) q^{72} +(-163387. - 282994. i) q^{73} +(15614.5 + 27045.1i) q^{74} +288252. i q^{75} +(218969. + 15081.3i) q^{76} +387436. q^{77} +(313900. - 181231. i) q^{78} +(52388.3 - 30246.4i) q^{79} +(-17439.7 + 30206.5i) q^{80} +(89677.1 + 155325. i) q^{81} +(310505. - 537810. i) q^{82} +259525. q^{83} -169461. i q^{84} +(1399.39 - 2423.82i) q^{85} +(28670.0 + 16552.7i) q^{86} -114129. q^{87} +263916. i q^{88} +(-423488. - 244501. i) q^{89} +(55380.6 - 31974.0i) q^{90} +(739973. + 427223. i) q^{91} +(48288.1 + 83637.5i) q^{92} +(9533.34 + 16512.2i) q^{93} +584539. i q^{94} +(130442. - 193826. i) q^{95} +115434. q^{96} +(342904. - 197975. i) q^{97} +(-230402. + 133023. i) q^{98} +(241932. - 419039. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9}+O(q^{10}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9	\( 20 q - 30 q^{3} + 320 q^{4} + 112 q^{5} + 80 q^{6} - 208 q^{7} + 2200 q^{9} - 284 q^{11} + 10500 q^{13} + 1248 q^{14} + 14136 q^{15} - 10240 q^{16} - 11684 q^{17} + 12862 q^{19} + 7168 q^{20} + 2916 q^{21} + 52704 q^{22} + 8488 q^{23} - 2560 q^{24} - 63842 q^{25} - 43968 q^{26} - 3328 q^{28} + 137760 q^{29} - 94688 q^{30} - 250194 q^{33} + 70560 q^{34} - 6916 q^{35} - 70400 q^{36} - 77232 q^{38} + 9672 q^{39} + 109206 q^{41} - 92672 q^{42} + 35572 q^{43} - 4544 q^{44} + 131264 q^{45} - 361184 q^{47} + 30720 q^{48} + 259740 q^{49} - 496512 q^{51} + 336000 q^{52} - 236172 q^{53} + 375728 q^{54} + 56760 q^{55} + 314796 q^{57} - 225600 q^{58} + 1310610 q^{59} + 452352 q^{60} + 83552 q^{61} + 225792 q^{62} + 553364 q^{63} - 655360 q^{64} - 4736 q^{66} + 806646 q^{67} - 747776 q^{68} - 245664 q^{70} - 869220 q^{71} + 353280 q^{72} - 207422 q^{73} + 1460832 q^{74} - 140096 q^{76} - 3988336 q^{77} - 85008 q^{78} - 1706808 q^{79} + 114688 q^{80} + 2303170 q^{81} + 887712 q^{82} + 3527548 q^{83} - 5604 q^{85} + 195792 q^{86} - 8414832 q^{87} + 708432 q^{89} - 4483104 q^{90} - 1914384 q^{91} - 271616 q^{92} + 3537876 q^{93} - 2820356 q^{95} - 163840 q^{96} + 5113242 q^{97} - 612480 q^{98} + 603704 q^{99}+O(q^{100}) \) 20 * q - 30 * q^3 + 320 * q^4 + 112 * q^5 + 80 * q^6 - 208 * q^7 + 2200 * q^9 - 284 * q^11 + 10500 * q^13 + 1248 * q^14 + 14136 * q^15 - 10240 * q^16 - 11684 * q^17 + 12862 * q^19 + 7168 * q^20 + 2916 * q^21 + 52704 * q^22 + 8488 * q^23 - 2560 * q^24 - 63842 * q^25 - 43968 * q^26 - 3328 * q^28 + 137760 * q^29 - 94688 * q^30 - 250194 * q^33 + 70560 * q^34 - 6916 * q^35 - 70400 * q^36 - 77232 * q^38 + 9672 * q^39 + 109206 * q^41 - 92672 * q^42 + 35572 * q^43 - 4544 * q^44 + 131264 * q^45 - 361184 * q^47 + 30720 * q^48 + 259740 * q^49 - 496512 * q^51 + 336000 * q^52 - 236172 * q^53 + 375728 * q^54 + 56760 * q^55 + 314796 * q^57 - 225600 * q^58 + 1310610 * q^59 + 452352 * q^60 + 83552 * q^61 + 225792 * q^62 + 553364 * q^63 - 655360 * q^64 - 4736 * q^66 + 806646 * q^67 - 747776 * q^68 - 245664 * q^70 - 869220 * q^71 + 353280 * q^72 - 207422 * q^73 + 1460832 * q^74 - 140096 * q^76 - 3988336 * q^77 - 85008 * q^78 - 1706808 * q^79 + 114688 * q^80 + 2303170 * q^81 + 887712 * q^82 + 3527548 * q^83 - 5604 * q^85 + 195792 * q^86 - 8414832 * q^87 + 708432 * q^89 - 4483104 * q^90 - 1914384 * q^91 - 271616 * q^92 + 3537876 * q^93 - 2820356 * q^95 - 163840 * q^96 + 5113242 * q^97 - 612480 * q^98 + 603704 * q^99

Introduction

L-functions

Modular forms

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