LMFDB - Embedded newform 38.7.d.a.31.2

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			31.2
Root			$-22.2621i$ of defining polynomial
Character	$\chi$	$=$	38.31
Dual form			38.7.d.a.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 + 2.82843i) q^{2} +(-22.0043 + 12.7042i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-85.1965 - 147.565i) q^{5} +(71.8656 - 124.475i) q^{6} +473.710 q^{7} +181.019i q^{8} +(-41.7080 + 72.2405i) q^{9} +O(q^{10})$	\(q+(-4.89898 + 2.82843i) q^{2} +(-22.0043 + 12.7042i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-85.1965 - 147.565i) q^{5} +(71.8656 - 124.475i) q^{6} +473.710 q^{7} +181.019i q^{8} +(-41.7080 + 72.2405i) q^{9} +(834.752 + 481.944i) q^{10} -2118.68 q^{11} +813.067i q^{12} +(2401.07 + 1386.26i) q^{13} +(-2320.70 + 1339.85i) q^{14} +(3749.37 + 2164.70i) q^{15} +(-512.000 - 886.810i) q^{16} +(4199.48 + 7273.71i) q^{17} -471.873i q^{18} +(6819.60 - 734.105i) q^{19} -5452.58 q^{20} +(-10423.6 + 6018.09i) q^{21} +(10379.4 - 5992.52i) q^{22} +(3495.35 - 6054.13i) q^{23} +(-2299.70 - 3983.20i) q^{24} +(-6704.40 + 11612.4i) q^{25} -15683.7 q^{26} -20642.1i q^{27} +(7579.36 - 13127.8i) q^{28} +(25424.0 + 14678.6i) q^{29} -24490.8 q^{30} +38548.2i q^{31} +(5016.55 + 2896.31i) q^{32} +(46620.0 - 26916.0i) q^{33} +(-41146.3 - 23755.8i) q^{34} +(-40358.4 - 69902.9i) q^{35} +(1334.66 + 2311.69i) q^{36} -49167.4i q^{37} +(-31332.7 + 22885.1i) q^{38} -70445.1 q^{39} +(26712.1 - 15422.2i) q^{40} +(39559.5 - 22839.7i) q^{41} +(34043.5 - 58965.0i) q^{42} +(34060.1 + 58993.9i) q^{43} +(-33898.8 + 58714.5i) q^{44} +14213.5 q^{45} +39545.4i q^{46} +(-79086.9 + 136983. i) q^{47} +(22532.4 + 13009.1i) q^{48} +106752. q^{49} -75851.6i q^{50} +(-184813. - 106702. i) q^{51} +(76834.3 - 44360.3i) q^{52} +(60725.2 + 35059.7i) q^{53} +(58384.8 + 101125. i) q^{54} +(180504. + 312642. i) q^{55} +85750.7i q^{56} +(-140734. + 102791. i) q^{57} -166069. q^{58} +(214108. - 123615. i) q^{59} +(119980. - 69270.5i) q^{60} +(25917.8 - 44891.0i) q^{61} +(-109031. - 188847. i) q^{62} +(-19757.5 + 34221.0i) q^{63} -32768.0 q^{64} -472418. i q^{65} +(-152260. + 263722. i) q^{66} +(-144770. - 83583.2i) q^{67} +268767. q^{68} +177622. i q^{69} +(395430. + 228302. i) q^{70} +(2281.45 - 1317.20i) q^{71} +(-13076.9 - 7549.96i) q^{72} +(115884. + 200716. i) q^{73} +(139066. + 240870. i) q^{74} -340695. i q^{75} +(88769.5 - 200736. i) q^{76} -1.00364e6 q^{77} +(345109. - 199249. i) q^{78} +(-376948. + 217631. i) q^{79} +(-87241.2 + 151106. i) q^{80} +(231836. + 401552. i) q^{81} +(-129201. + 223782. i) q^{82} -553204. q^{83} +385158. i q^{84} +(715562. - 1.23939e6i) q^{85} +(-333720. - 192673. i) q^{86} -745917. q^{87} -383522. i q^{88} +(324464. + 187330. i) q^{89} +(-69631.8 + 40201.9i) q^{90} +(1.13741e6 + 656685. i) q^{91} +(-111851. - 193732. i) q^{92} +(-489723. - 848225. i) q^{93} -894766. i q^{94} +(-689334. - 943789. i) q^{95} -147181. q^{96} +(274550. - 158512. i) q^{97} +(-522976. + 301940. i) q^{98} +(88365.9 - 153054. 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
$3$	−22.0043	+	12.7042i	−0.814973	+	0.470525i	−0.848680	−	0.528907i	$-0.822602\pi$
$3$	−22.0043	+	12.7042i	−0.814973	+	0.470525i	0.0337069	+	0.999432i	$0.489269\pi$
$4$	16.0000	−	27.7128i	0.250000	−	0.433013i
$5$	−85.1965	−	147.565i	−0.681572	−	1.18052i	−0.974501	−	0.224383i	$-0.927963\pi$
$5$	−85.1965	−	147.565i	−0.681572	−	1.18052i	0.292929	−	0.956134i	$-0.405370\pi$
$6$	71.8656	−	124.475i	0.332711	−	0.576273i
$7$	473.710			1.38108			0.690539	−	0.723295i	$-0.257373\pi$
$7$	473.710			1.38108			0.690539	+	0.723295i	$0.257373\pi$
$8$			181.019i			0.353553i
$9$	−41.7080	+	72.2405i	−0.0572127	+	0.0990953i
$10$	834.752	+	481.944i	0.834752	+	0.481944i
$11$	−2118.68			−1.59179			−0.795897	−	0.605432i	$-0.793000\pi$
$11$	−2118.68			−1.59179			−0.795897	+	0.605432i	$0.793000\pi$
$12$			813.067i			0.470525i
$13$	2401.07	+	1386.26i	1.09289	+	0.630978i	0.934344	−	0.356374i	$-0.115987\pi$
$13$	2401.07	+	1386.26i	1.09289	+	0.630978i	0.158543	+	0.987352i	$0.449320\pi$
$14$	−2320.70	+	1339.85i	−0.845734	+	0.488285i
$15$	3749.37	+	2164.70i	1.11093	+	0.641393i
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$	4199.48	+	7273.71i	0.854769	+	1.48050i	0.876859	+	0.480747i	$0.159635\pi$
$17$	4199.48	+	7273.71i	0.854769	+	1.48050i	−0.0220902	+	0.999756i	$0.507032\pi$
$18$		−	471.873i		−	0.0809110i
$19$	6819.60	−	734.105i	0.994256	−	0.107028i
$19$	6819.60	−	734.105i	0.994256	−	0.107028i
$20$	−5452.58			−0.681572
$21$	−10423.6	+	6018.09i	−1.12554	+	0.649832i
$22$	10379.4	−	5992.52i	0.974771	−	0.562784i
$23$	3495.35	−	6054.13i	0.287282	−	0.497586i	−0.685878	−	0.727716i	$-0.740582\pi$
$23$	3495.35	−	6054.13i	0.287282	−	0.497586i	0.973160	+	0.230130i	$0.0739151\pi$
$24$	−2299.70	−	3983.20i	−0.166356	−	0.288136i
$25$	−6704.40	+	11612.4i	−0.429081	+	0.743191i
$26$	−15683.7			−0.892338
$27$		−	20642.1i		−	1.04873i
$28$	7579.36	−	13127.8i	0.345270	−	0.598025i
$29$	25424.0	+	14678.6i	1.04244	+	0.601853i	0.920523	−	0.390688i	$-0.127763\pi$
$29$	25424.0	+	14678.6i	1.04244	+	0.601853i	0.121916	+	0.992540i	$0.461096\pi$
$30$	−24490.8			−0.907067
$31$			38548.2i			1.29395i	0.762509	+	0.646977i	$0.223967\pi$
$31$			38548.2i			1.29395i	−0.762509	+	0.646977i	$0.776033\pi$
$32$	5016.55	+	2896.31i	0.153093	+	0.0883883i
$33$	46620.0	−	26916.0i	1.29727	−	0.748979i
$34$	−41146.3	−	23755.8i	−1.04687	−	0.604413i
$35$	−40358.4	−	69902.9i	−0.941305	−	1.63039i
$36$	1334.66	+	2311.69i	0.0286063	+	0.0495476i
$37$		−	49167.4i		−	0.970671i	−0.874328	−	0.485335i	$-0.838698\pi$
$37$		−	49167.4i		−	0.970671i	0.874328	−	0.485335i	$-0.161302\pi$
$38$	−31332.7	+	22885.1i	−0.571015	+	0.417064i
$39$	−70445.1			−1.18756
$40$	26712.1	−	15422.2i	0.417376	−	0.240972i
$41$	39559.5	−	22839.7i	0.573983	−	0.331389i	−0.184756	−	0.982785i	$-0.559149\pi$
$41$	39559.5	−	22839.7i	0.573983	−	0.331389i	0.758739	+	0.651395i	$0.225816\pi$
$42$	34043.5	−	58965.0i	0.459500	−	0.795878i
$43$	34060.1	+	58993.9i	0.428392	+	0.741996i	0.996730	−	0.0807986i	$-0.0257471\pi$
$43$	34060.1	+	58993.9i	0.428392	+	0.741996i	−0.568339	+	0.822795i	$0.692414\pi$
$44$	−33898.8	+	58714.5i	−0.397948	+	0.689267i
$45$	14213.5			0.155978
$46$			39545.4i			0.406277i
$47$	−79086.9	+	136983.i	−0.761748	+	1.31939i	0.180201	+	0.983630i	$0.442325\pi$
$47$	−79086.9	+	136983.i	−0.761748	+	1.31939i	−0.941949	+	0.335756i	$0.891008\pi$
$48$	22532.4	+	13009.1i	0.203743	+	0.117631i
$49$	106752.			0.907378
$50$		−	75851.6i		−	0.606813i
$51$	−184813.	−	106702.i	−1.39323	−	0.804380i
$52$	76834.3	−	44360.3i	0.546443	−	0.315489i
$53$	60725.2	+	35059.7i	0.407888	+	0.235494i	0.689882	−	0.723922i	$-0.257662\pi$
$53$	60725.2	+	35059.7i	0.407888	+	0.235494i	−0.281994	+	0.959416i	$0.590996\pi$
$54$	58384.8	+	101125.i	0.370782	+	0.642213i
$55$	180504.	+	312642.i	1.08492	+	1.87914i
$56$			85750.7i			0.488285i
$57$	−140734.	+	102791.i	−0.759932	+	0.555047i
$58$	−166069.			−0.851148
$59$	214108.	−	123615.i	1.04250	−	0.601887i	0.121959	−	0.992535i	$-0.461082\pi$
$59$	214108.	−	123615.i	1.04250	−	0.601887i	0.920540	+	0.390648i	$0.127749\pi$
$60$	119980.	−	69270.5i	0.555463	−	0.320697i
$61$	25917.8	−	44891.0i	0.114185	−	0.197774i	−0.803269	−	0.595617i	$-0.796908\pi$
$61$	25917.8	−	44891.0i	0.114185	−	0.197774i	0.917454	+	0.397843i	$0.130241\pi$
$62$	−109031.	−	188847.i	−0.457482	−	0.792382i
$63$	−19757.5	+	34221.0i	−0.0790152	+	0.136858i
$64$	−32768.0			−0.125000
$65$		−	472418.i		−	1.72023i
$66$	−152260.	+	263722.i	−0.529608	+	0.917308i
$67$	−144770.	−	83583.2i	−0.481344	−	0.277904i	0.239633	−	0.970864i	$-0.422973\pi$
$67$	−144770.	−	83583.2i	−0.481344	−	0.277904i	−0.720976	+	0.692960i	$0.756306\pi$
$68$	268767.			0.854769
$69$			177622.i			0.540692i
$70$	395430.	+	228302.i	1.15286	+	0.665603i
$71$	2281.45	−	1317.20i	0.00637435	−	0.00368023i	−0.496809	−	0.867860i	$-0.665495\pi$
$71$	2281.45	−	1317.20i	0.00637435	−	0.00368023i	0.503184	+	0.864179i	$0.332162\pi$
$72$	−13076.9	−	7549.96i	−0.0350355	−	0.0202277i
$73$	115884.	+	200716.i	0.297889	+	0.515958i	0.975653	−	0.219321i	$-0.0703843\pi$
$73$	115884.	+	200716.i	0.297889	+	0.515958i	−0.677764	+	0.735279i	$0.737051\pi$
$74$	139066.	+	240870.i	0.343184	+	0.594412i
$75$		−	340695.i		−	0.807574i
$76$	88769.5	−	200736.i	0.202220	−	0.457282i
$77$	−1.00364e6			−2.19839
$78$	345109.	−	199249.i	0.727231	−	0.419867i
$79$	−376948.	+	217631.i	−0.764540	+	0.441408i	−0.830924	−	0.556387i	$-0.812187\pi$
$79$	−376948.	+	217631.i	−0.764540	+	0.441408i	0.0663831	+	0.997794i	$0.478854\pi$
$80$	−87241.2	+	151106.i	−0.170393	+	0.295129i
$81$	231836.	+	401552.i	0.436241	+	0.755591i
$82$	−129201.	+	223782.i	−0.234328	+	0.405867i
$83$	−553204.			−0.967500			−0.483750	−	0.875206i	$-0.660726\pi$
$83$	−553204.			−0.967500			−0.483750	+	0.875206i	$0.660726\pi$
$84$			385158.i			0.649832i
$85$	715562.	−	1.23939e6i	1.16517	−	2.01814i
$86$	−333720.	−	192673.i	−0.524670	−	0.302919i
$87$	−745917.			−1.13275
$88$		−	383522.i		−	0.562784i
$89$	324464.	+	187330.i	0.460254	+	0.265727i	0.712151	−	0.702026i	$-0.247721\pi$
$89$	324464.	+	187330.i	0.460254	+	0.265727i	−0.251897	+	0.967754i	$0.581055\pi$
$90$	−69631.8	+	40201.9i	−0.0955168	+	0.0551467i
$91$	1.13741e6	+	656685.i	1.50936	+	0.871431i
$92$	−111851.	−	193732.i	−0.143641	−	0.248793i
$93$	−489723.	−	848225.i	−0.608838	−	1.05454i
$94$		−	894766.i		−	1.07727i
$95$	−689334.	−	943789.i	−0.804006	−	1.10079i
$96$	−147181.			−0.166356
$97$	274550.	−	158512.i	0.300820	−	0.173678i	−0.341991	−	0.939703i	$-0.611101\pi$
$97$	274550.	−	158512.i	0.300820	−	0.173678i	0.642811	+	0.766025i	$0.277768\pi$
$98$	−522976.	+	301940.i	−0.555653	+	0.320806i
$99$	88365.9	−	153054.i	0.0910708	−	0.157739i
$100$	214541.	+	371595.i	0.214541	+	0.371595i
$101$	56161.6	−	97274.8i	0.0545099	−	0.0944139i	−0.837483	−	0.546464i	$-0.815974\pi$
$101$	56161.6	−	97274.8i	0.0545099	−	0.0944139i	0.891993	+	0.452050i	$0.149307\pi$
$102$	1.20719e6			1.13757
$103$		−	736462.i		−	0.673967i	−0.941511	−	0.336983i	$-0.890593\pi$
$103$		−	736462.i		−	0.673967i	0.941511	−	0.336983i	$-0.109407\pi$
$104$	−250940.	+	434640.i	−0.223085	+	0.386394i
$105$	1.77612e6	+	1.02544e6i	1.53428	+	0.885815i
$106$	−396655.			−0.333039
$107$			110276.i			0.0900184i	0.998987	+	0.0450092i	$0.0143317\pi$
$107$			110276.i			0.0900184i	−0.998987	+	0.0450092i	$0.985668\pi$
$108$	−572052.	−	330274.i	−0.454113	−	0.262182i
$109$	−628454.	+	362838.i	−0.485282	+	0.280177i	−0.722615	−	0.691251i	$-0.757060\pi$
$109$	−628454.	+	362838.i	−0.485282	+	0.280177i	0.237333	+	0.971428i	$0.423727\pi$
$110$	−1.76857e6	−	1.02108e6i	−1.32875	−	0.767156i
$111$	624631.	+	1.08189e6i	0.456725	+	0.791070i
$112$	−242539.	−	420091.i	−0.172635	−	0.299012i
$113$			1.72474e6i			1.19533i	0.801746	+	0.597665i	$0.203905\pi$
$113$			1.72474e6i			1.19533i	−0.801746	+	0.597665i	$0.796095\pi$
$114$	398717.	−	901627.i	0.269123	−	0.608572i
$115$	−1.19117e6			−0.783212
$116$	813570.	−	469715.i	0.521220	−	0.300926i
$117$	−200288.	+	115636.i	−0.125054	+	0.0721999i
$118$	−699272.	+	1.21118e6i	−0.425599	+	0.737159i
$119$	1.98934e6	+	3.44563e6i	1.18050	+	2.04469i
$120$	−391853.	+	678709.i	−0.226767	+	0.392772i
$121$	2.71723e6			1.53381
$122$			293227.i			0.161482i
$123$	−580318.	+	1.00514e6i	−0.311854	+	0.540147i
$124$	1.06828e6	+	616771.i	0.560299	+	0.323489i
$125$	−377626.			−0.193345
$126$		−	223531.i		−	0.111744i
$127$	1.48410e6	+	856846.i	0.724523	+	0.418304i	0.816415	−	0.577465i	$-0.195958\pi$
$127$	1.48410e6	+	856846.i	0.724523	+	0.418304i	−0.0918919	+	0.995769i	$0.529291\pi$
$128$	160530.	−	92681.9i	0.0765466	−	0.0441942i
$129$	−1.49894e6	−	865411.i	−0.698255	−	0.403138i
$130$	1.33620e6	+	2.31437e6i	0.608193	+	1.05342i
$131$	−363251.	−	629170.i	−0.161582	−	0.279868i	0.773854	−	0.633364i	$-0.218326\pi$
$131$	−363251.	−	629170.i	−0.161582	−	0.279868i	−0.935436	+	0.353495i	$0.884993\pi$
$132$		−	1.72263e6i		−	0.748979i
$133$	3.23051e6	−	347753.i	1.37315	−	0.147814i
$134$	945636.			0.393015
$135$	−3.04605e6	+	1.75864e6i	−1.23804	+	0.714785i
$136$	−1.31668e6	+	760187.i	−0.523437	+	0.302206i
$137$	1.24733e6	−	2.16044e6i	0.485088	−	0.840197i	−0.514765	−	0.857331i	$-0.672121\pi$
$137$	1.24733e6	−	2.16044e6i	0.485088	−	0.840197i	0.999853	+	0.0171344i	$0.00545433\pi$
$138$	−502392.	−	870168.i	−0.191164	−	0.331105i
$139$	76133.2	−	131867.i	0.0283485	−	0.0491010i	−0.851503	−	0.524350i	$-0.824309\pi$
$139$	76133.2	−	131867.i	0.0283485	−	0.0491010i	0.879852	+	0.475249i	$0.157642\pi$
$140$	−2.58294e6			−0.941305
$141$		−	4.01894e6i		−	1.43368i
$142$	−7451.18	+	12905.8i	−0.00260232	+	0.00450734i
$143$	−5.08710e6	−	2.93704e6i	−1.73965	−	1.00439i
$144$	85418.1			0.0286063
$145$		−	5.00226e6i		−	1.64082i
$146$	−1.13542e6	−	655537.i	−0.364837	−	0.210639i
$147$	−2.34900e6	+	1.35620e6i	−0.739488	+	0.426944i
$148$	−1.36257e6	−	786678.i	−0.420313	−	0.242668i
$149$	2.11509e6	+	3.66345e6i	0.639397	+	1.10747i	0.985565	+	0.169295i	$0.0541491\pi$
$149$	2.11509e6	+	3.66345e6i	0.639397	+	1.10747i	−0.346169	+	0.938172i	$0.612518\pi$
$150$	963632.	+	1.66906e6i	0.285520	+	0.494536i
$151$			1.23909e6i			0.359891i	0.983677	+	0.179946i	$0.0575922\pi$
$151$			1.23909e6i			0.359891i	−0.983677	+	0.179946i	$0.942408\pi$
$152$	132887.	+	1.23448e6i	0.0378401	+	0.351523i
$153$	−700608.			−0.195615
$154$	4.91680e6	−	2.83872e6i	1.34623	−	0.777249i
$155$	5.68835e6	−	3.28417e6i	1.52754	−	0.881923i
$156$	−1.12712e6	+	1.95223e6i	−0.296891	+	0.514230i
$157$	2.26593e6	+	3.92470e6i	0.585527	+	1.01416i	0.994809	+	0.101755i	$0.0324458\pi$
$157$	2.26593e6	+	3.92470e6i	0.585527	+	1.01416i	−0.409282	+	0.912408i	$0.634221\pi$
$158$	1.23111e6	−	2.13234e6i	0.312122	−	0.540612i
$159$	−1.78162e6			−0.443224
$160$		−	987022.i		−	0.240972i
$161$	1.65578e6	−	2.86790e6i	0.396758	−	0.687206i
$162$	−2.27152e6	−	1.31146e6i	−0.534284	−	0.308469i
$163$	−3.81695e6			−0.881361			−0.440681	−	0.897664i	$-0.645263\pi$
$163$	−3.81695e6			−0.881361			−0.440681	+	0.897664i	$0.645263\pi$
$164$		−	1.46174e6i		−	0.331389i
$165$	−7.94372e6	−	4.58631e6i	−1.76836	−	1.02097i
$166$	2.71013e6	−	1.56470e6i	0.592470	−	0.342063i
$167$	−4.57438e6	−	2.64102e6i	−0.982161	−	0.567051i	−0.0792390	−	0.996856i	$-0.525249\pi$
$167$	−4.57438e6	−	2.64102e6i	−0.982161	−	0.567051i	−0.902922	+	0.429805i	$0.858582\pi$
$168$	−1.08939e6	−	1.88688e6i	−0.229750	−	0.397939i
$169$	1.43003e6	+	2.47688e6i	0.296267	+	0.513150i
$170$			8.09566e6i			1.64780i
$171$	−231400.	+	523269.i	−0.0462781	+	0.104649i
$172$	2.17985e6			0.428392
$173$	3.18607e6	−	1.83948e6i	0.615342	−	0.355268i	−0.159711	−	0.987164i	$-0.551056\pi$
$173$	3.18607e6	−	1.83948e6i	0.615342	−	0.355268i	0.775053	+	0.631896i	$0.217723\pi$
$174$	3.65423e6	−	2.10977e6i	0.693663	−	0.400486i
$175$	−3.17594e6	+	5.50089e6i	−0.592595	+	1.02640i
$176$	1.08476e6	+	1.87886e6i	0.198974	+	0.344633i
$177$	−3.14085e6	+	5.44012e6i	−0.566406	+	0.981044i
$178$	−2.11939e6			−0.375795
$179$			580056.i			0.101137i	0.998721	+	0.0505686i	$0.0161033\pi$
$179$			580056.i			0.101137i	−0.998721	+	0.0505686i	$0.983897\pi$
$180$	227416.	−	393897.i	0.0389946	−	0.0675406i
$181$	7.93034e6	+	4.57858e6i	1.33738	+	0.772139i	0.986419	−	0.164250i	$-0.0525204\pi$
$181$	7.93034e6	+	4.57858e6i	1.33738	+	0.772139i	0.350965	+	0.936389i	$0.385854\pi$
$182$	−7.42954e6			−1.23239
$183$			1.31706e6i			0.214907i
$184$	1.09591e6	+	632727.i	0.175923	+	0.101569i
$185$	−7.25537e6	+	4.18889e6i	−1.14589	+	0.661582i
$186$	4.79828e6	+	2.77029e6i	0.745671	+	0.430513i
$187$	−8.89734e6	−	1.54107e7i	−1.36062	−	2.35666i
$188$	2.53078e6	+	4.38344e6i	0.380874	+	0.659693i
$189$		−	9.77839e6i		−	1.44838i
$190$	6.04647e6	+	2.67387e6i	0.881539	+	0.389834i
$191$	2.51336e6			0.360706			0.180353	−	0.983602i	$-0.442276\pi$
$191$	2.51336e6			0.360706			0.180353	+	0.983602i	$0.442276\pi$
$192$	721036.	−	416290.i	0.101872	−	0.0588156i
$193$	5.97892e6	−	3.45193e6i	0.831670	−	0.480165i	−0.0227540	−	0.999741i	$-0.507243\pi$
$193$	5.97892e6	−	3.45193e6i	0.831670	−	0.480165i	0.854424	+	0.519576i	$0.173910\pi$
$194$	−896677.	+	1.55309e6i	−0.122809	+	0.212712i
$195$	6.00168e6	+	1.03952e7i	0.809411	+	1.40194i
$196$	1.70803e6	−	2.95840e6i	0.226844	−	0.392906i
$197$	9.83753e6			1.28673			0.643365	−	0.765560i	$-0.277538\pi$
$197$	9.83753e6			1.28673			0.643365	+	0.765560i	$0.277538\pi$
$198$			999746.i			0.128794i
$199$	−747801.	+	1.29523e6i	−0.0948914	+	0.164357i	−0.909563	−	0.415565i	$-0.863584\pi$
$199$	−747801.	+	1.29523e6i	−0.0948914	+	0.164357i	0.814672	+	0.579922i	$0.196917\pi$
$200$	−2.10206e6	−	1.21363e6i	−0.262758	−	0.151703i
$201$	4.24742e6			0.523043
$202$			635396.i			0.0770887i
$203$	1.20436e7	+	6.95339e6i	1.43969	+	0.831206i
$204$	−5.91402e6	+	3.41446e6i	−0.696614	+	0.402190i
$205$	−6.74066e6	−	3.89172e6i	−0.782422	−	0.451731i
$206$	2.08303e6	+	3.60791e6i	0.238283	+	0.412719i
$207$	291569.	+	505012.i	0.0328723	+	0.0569365i
$208$		−	2.83906e6i		−	0.315489i
$209$	−1.44485e7	+	1.55533e6i	−1.58265	+	0.170366i
$210$	−1.16015e7			−1.25273
$211$	−1.21782e6	+	703106.i	−0.129639	+	0.0748469i	−0.563417	−	0.826173i	$-0.690513\pi$
$211$	−1.21782e6	+	703106.i	−0.129639	+	0.0748469i	0.433778	+	0.901020i	$0.357180\pi$
$212$	1.94321e6	−	1.12191e6i	0.203944	−	0.117747i
$213$	−33467.8	+	57967.8i	−0.00346328	+	0.00599858i
$214$	−311909.	−	540242.i	−0.0318263	−	0.0551248i
$215$	5.80361e6	−	1.00521e7i	0.583960	−	1.01145i
$216$	3.73663e6			0.370782
$217$			1.82607e7i			1.78705i
$218$	2.05252e6	−	3.55507e6i	0.198115	−	0.343146i
$219$	−5.09987e6	−	2.94441e6i	−0.485542	−	0.280328i
$220$	1.15523e7			1.08492
$221$			2.32863e7i			2.15736i
$222$	−6.12011e6	−	3.53345e6i	−0.559371	−	0.322953i
$223$	−6.31963e6	+	3.64864e6i	−0.569872	+	0.329016i	−0.757098	−	0.653301i	$-0.773384\pi$
$223$	−6.31963e6	+	3.64864e6i	−0.569872	+	0.329016i	0.187226	+	0.982317i	$0.440050\pi$
$224$	2.37639e6	+	1.37201e6i	0.211434	+	0.122071i
$225$	−559255.	−	968657.i	−0.0490978	−	0.0850399i
$226$	−4.87829e6	−	8.44945e6i	−0.422613	−	0.731987i
$227$		−	9.97093e6i		−	0.852429i	−0.904622	−	0.426214i	$-0.859847\pi$
$227$		−	9.97093e6i		−	0.852429i	0.904622	−	0.426214i	$-0.140153\pi$
$228$	596876.	+	5.54479e6i	0.0503593	+	0.467822i
$229$	−1.78273e7			−1.48450			−0.742250	−	0.670123i	$-0.766241\pi$
$229$	−1.78273e7			−1.48450			−0.742250	+	0.670123i	$0.766241\pi$
$230$	5.83551e6	−	3.36913e6i	0.479618	−	0.276907i
$231$	2.20843e7	−	1.27504e7i	1.79163	−	1.03440i
$232$	−2.65711e6	+	4.60224e6i	−0.212787	+	0.368558i
$233$	−4.52526e6	−	7.83799e6i	−0.357747	−	0.619636i	0.629837	−	0.776727i	$-0.283122\pi$
$233$	−4.52526e6	−	7.83799e6i	−0.357747	−	0.619636i	−0.987584	+	0.157091i	$0.949788\pi$
$234$	654138.	−	1.13300e6i	0.0510531	−	0.0884265i
$235$	2.69517e7			2.07674
$236$		−	7.91136e6i		−	0.601887i
$237$	5.52965e6	−	9.57763e6i	0.415387	−	0.719471i
$238$	−1.94914e7	−	1.12534e7i	−1.44582	−	0.834742i
$239$	−1.07087e7			−0.784407			−0.392204	−	0.919878i	$-0.628287\pi$
$239$	−1.07087e7			−0.784407			−0.392204	+	0.919878i	$0.628287\pi$
$240$		−	4.43331e6i		−	0.320697i
$241$	−1.09983e6	−	634985.i	−0.0785730	−	0.0453641i	0.460199	−	0.887816i	$-0.347778\pi$
$241$	−1.09983e6	−	634985.i	−0.0785730	−	0.0453641i	−0.538772	+	0.842452i	$0.681111\pi$
$242$	−1.33117e7	+	7.68550e6i	−0.939261	+	0.542283i
$243$	2.82929e6	+	1.63349e6i	0.197178	+	0.113841i
$244$	−829370.	−	1.43651e6i	−0.0570925	−	0.0988871i
$245$	−9.09491e6	−	1.57528e7i	−0.618443	−	1.07118i
$246$		−	6.56555e6i		−	0.441028i
$247$	1.73920e7	+	7.69110e6i	1.15414	+	0.510385i
$248$	−6.97797e6			−0.457482
$249$	1.21728e7	−	7.02800e6i	0.788486	−	0.455233i
$250$	1.84998e6	−	1.06809e6i	0.118399	−	0.0683577i
$251$	−7.66607e6	+	1.32780e7i	−0.484788	+	0.839677i	−0.999847	−	0.0174776i	$-0.994436\pi$
$251$	−7.66607e6	+	1.32780e7i	−0.484788	+	0.839677i	0.515060	+	0.857154i	$0.327770\pi$
$252$	632241.	+	1.09507e6i	0.0395076	+	0.0684292i
$253$	−7.40553e6	+	1.28268e7i	−0.457293	+	0.792055i
$254$	−9.69411e6			−0.591571
$255$			3.63625e7i			2.19297i
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	−6.98740e6	−	4.03418e6i	−0.411639	−	0.237660i	0.279855	−	0.960042i	$-0.409714\pi$
$257$	−6.98740e6	−	4.03418e6i	−0.411639	−	0.237660i	−0.691494	+	0.722383i	$0.743047\pi$
$258$	9.79101e6			0.570123
$259$		−	2.32911e7i		−	1.34057i
$260$	−1.30920e7	−	7.55869e6i	−0.744881	−	0.430057i
$261$	−2.12077e6	+	1.22443e6i	−0.119281	+	0.0688672i
$262$	3.55912e6	+	2.05486e6i	0.197897	+	0.114256i
$263$	319023.	+	552564.i	0.0175370	+	0.0303749i	0.874661	−	0.484736i	$-0.161084\pi$
$263$	319023.	+	552564.i	0.0175370	+	0.0303749i	−0.857124	+	0.515111i	$0.827751\pi$
$264$	4.87232e6	+	8.43911e6i	0.264804	+	0.458654i
$265$		−	1.19479e7i		−	0.642026i
$266$	−1.48426e7	+	1.08409e7i	−0.788616	+	0.575997i
$267$	−9.51947e6			−0.500126
$268$	−4.63265e6	+	2.67466e6i	−0.240672	+	0.138952i
$269$	2.20327e7	−	1.27206e7i	1.13191	−	0.653507i	0.187493	−	0.982266i	$-0.439964\pi$
$269$	2.20327e7	−	1.27206e7i	1.13191	−	0.653507i	0.944414	+	0.328759i	$0.106630\pi$
$270$	9.94837e6	−	1.72311e7i	0.505429	−	0.875429i
$271$	3.57904e6	+	6.19908e6i	0.179829	+	0.311472i	0.941822	−	0.336113i	$-0.109112\pi$
$271$	3.57904e6	+	6.19908e6i	0.179829	+	0.311472i	−0.761993	+	0.647585i	$0.775779\pi$
$272$	4.30027e6	−	7.44828e6i	0.213692	−	0.370126i
$273$	−3.33705e7			−1.64012
$274$			1.41119e7i			0.686018i
$275$	1.42045e7	−	2.46028e7i	0.683009	−	1.18301i
$276$	4.92241e6	+	2.84196e6i	0.234127	+	0.135173i
$277$	−2.13300e7			−1.00358			−0.501788	−	0.864990i	$-0.667324\pi$
$277$	−2.13300e7			−1.00358			−0.501788	+	0.864990i	$0.667324\pi$
$278$			861349.i			0.0400908i
$279$	−2.78474e6	−	1.60777e6i	−0.128225	−	0.0740306i
$280$	1.26538e7	−	7.30566e6i	0.576429	−	0.332801i
$281$	8.37820e6	+	4.83716e6i	0.377600	+	0.218007i	0.676773	−	0.736191i	$-0.263378\pi$
$281$	8.37820e6	+	4.83716e6i	0.377600	+	0.218007i	−0.299174	+	0.954199i	$0.596711\pi$
$282$	1.13673e7	+	1.96887e7i	0.506884	+	0.877949i
$283$	−3.92776e6	−	6.80308e6i	−0.173295	−	0.300155i	0.766275	−	0.642513i	$-0.222108\pi$
$283$	−3.92776e6	−	6.80308e6i	−0.173295	−	0.300155i	−0.939570	+	0.342357i	$0.888775\pi$
$284$		−	84300.5i		−	0.00368023i
$285$	2.71584e7	+	1.20100e7i	1.17319	+	0.518809i
$286$	3.32288e7			1.42042
$287$	1.87397e7	−	1.08194e7i	0.792716	−	0.457675i
$288$	−418461.	+	241599.i	−0.0175177	+	0.0101139i
$289$	−2.32025e7	+	4.01879e7i	−0.961260	+	1.66495i
$290$	1.41485e7	+	2.45060e7i	0.580119	+	1.00480i
$291$	−4.02752e6	+	6.97587e6i	−0.163440	+	0.283087i
$292$	7.41656e6			0.297889
$293$		−	4.56689e7i		−	1.81559i	−0.419415	−	0.907795i	$-0.637765\pi$
$293$		−	4.56689e7i		−	1.81559i	0.419415	−	0.907795i	$-0.362235\pi$
$294$	7.67181e6	−	1.32880e7i	0.301895	−	0.522897i
$295$	−3.64824e7	−	2.10631e7i	−1.42108	−	0.820460i
$296$	8.90025e6			0.343184
$297$			4.37341e7i			1.66936i
$298$	−2.07236e7	−	1.19648e7i	−0.783098	−	0.452122i
$299$	1.67852e7	−	9.69094e6i	0.627932	−	0.362537i
$300$	−9.44162e6	−	5.45112e6i	−0.349690	−	0.201893i
$301$	1.61346e7	+	2.79460e7i	0.591642	+	1.02475i
$302$	−3.50467e6	−	6.07027e6i	−0.127241	−	0.220388i
$303$			2.85395e6i			0.102593i
$304$	−4.14265e6	−	5.67183e6i	−0.147454	−	0.201884i
$305$	−8.83243e6			−0.311301
$306$	3.43227e6	−	1.98162e6i	0.119789	−	0.0691602i
$307$	−3.95527e7	+	2.28357e7i	−1.36698	+	0.789223i	−0.990541	−	0.137220i	$-0.956183\pi$
$307$	−3.95527e7	+	2.28357e7i	−1.36698	+	0.789223i	−0.376435	+	0.926443i	$0.622850\pi$
$308$	−1.60582e7	+	2.78136e7i	−0.549598	+	0.951932i
$309$	9.35614e6	+	1.62053e7i	0.317118	+	0.549265i
$310$	−1.85781e7	+	3.21782e7i	−0.623614	+	1.08013i
$311$	5.28277e7			1.75623			0.878113	−	0.478453i	$-0.158802\pi$
$311$	5.28277e7			1.75623			0.878113	+	0.478453i	$0.158802\pi$
$312$		−	1.27519e7i		−	0.419867i
$313$	1.97271e7	−	3.41683e7i	0.643324	−	1.11427i	−0.341361	−	0.939932i	$-0.610888\pi$
$313$	1.97271e7	−	3.41683e7i	0.643324	−	1.11427i	0.984686	−	0.174338i	$-0.0557787\pi$
$314$	−2.22015e7	−	1.28180e7i	−0.717121	−	0.414030i
$315$	6.73309e6			0.215418
$316$			1.39284e7i			0.441408i
$317$	2.25973e7	+	1.30466e7i	0.709381	+	0.409561i	0.810832	−	0.585279i	$-0.199015\pi$
$317$	2.25973e7	+	1.30466e7i	0.709381	+	0.409561i	−0.101451	+	0.994841i	$0.532348\pi$
$318$	8.72811e6	−	5.03918e6i	0.271418	−	0.156703i
$319$	−5.38654e7	−	3.10992e7i	−1.65935	−	0.958025i
$320$	2.79172e6	+	4.83540e6i	0.0851965	+	0.147565i
$321$	−1.40097e6	−	2.42655e6i	−0.0423559	−	0.0733626i
$322$			1.87331e7i			0.561101i
$323$	3.39784e7	+	4.65210e7i	1.00831	+	1.38052i
$324$	1.48375e7			0.436241
$325$	−3.21955e7	+	1.85881e7i	−0.937875	+	0.541482i
$326$	1.86992e7	−	1.07960e7i	0.539721	−	0.311608i
$327$	9.21911e6	−	1.59680e7i	0.263661	−	0.456674i
$328$	4.13442e6	+	7.16103e6i	0.117164	+	0.202934i
$329$	−3.74643e7	+	6.48900e7i	−1.05203	+	1.82218i
$330$	5.18881e7			1.44386
$331$		−	2.71670e7i		−	0.749130i	−0.927201	−	0.374565i	$-0.877792\pi$
$331$		−	2.71670e7i		−	0.749130i	0.927201	−	0.374565i	$-0.122208\pi$
$332$	−8.85126e6	+	1.53308e7i	−0.241875	+	0.418940i
$333$	3.55187e6	+	2.05068e6i	0.0961889	+	0.0555347i
$334$	2.98797e7			0.801931
$335$			2.84840e7i			0.757646i
$336$	1.06738e7	+	6.16253e6i	0.281385	+	0.162458i
$337$	−774580.	+	447204.i	−0.0202384	+	0.0116847i	−0.510085	−	0.860124i	$-0.670386\pi$
$337$	−774580.	+	447204.i	−0.0202384	+	0.0116847i	0.489847	+	0.871809i	$0.337053\pi$
$338$	−1.40113e7	−	8.08945e6i	−0.362852	−	0.209493i
$339$	−2.19114e7	−	3.79516e7i	−0.562432	−	0.974161i
$340$	−2.28980e7	−	3.96605e7i	−0.582587	−	1.00907i
$341$		−	8.16712e7i		−	2.05971i
$342$	−346404.	−	3.21798e6i	−0.00865973	−	0.0804462i
$343$	−5.16198e6			−0.127919
$344$	−1.06790e7	+	6.16554e6i	−0.262335	+	0.151459i
$345$	2.62108e7	−	1.51328e7i	0.638297	−	0.368521i
$346$	−1.04056e7	+	1.80231e7i	−0.251212	+	0.435112i
$347$	−1.55261e6	−	2.68920e6i	−0.0371599	−	0.0643628i	0.846847	−	0.531836i	$-0.178498\pi$
$347$	−1.55261e6	−	2.68920e6i	−0.0371599	−	0.0643628i	−0.884007	+	0.467473i	$0.845164\pi$
$348$	−1.19347e7	+	2.06715e7i	−0.283187	+	0.490494i
$349$	−5.85298e7			−1.37690			−0.688448	−	0.725286i	$-0.741708\pi$
$349$	−5.85298e7			−1.37690			−0.688448	+	0.725286i	$0.741708\pi$
$350$		−	3.59316e7i		−	0.838056i
$351$	2.86154e7	−	4.95633e7i	0.661726	−	1.14614i
$352$	−1.06285e7	−	6.13635e6i	−0.243693	−	0.140696i
$353$	−1.20882e7			−0.274814			−0.137407	−	0.990515i	$-0.543877\pi$
$353$	−1.20882e7			−0.274814			−0.137407	+	0.990515i	$0.543877\pi$
$354$		−	3.55347e7i		−	0.801019i
$355$	−388743.	−	224441.i	−0.00868916	−	0.00501669i
$356$	1.03829e7	−	5.99455e6i	0.230127	−	0.132864i
$357$	−8.75477e7	−	5.05457e7i	−1.92416	−	1.11091i
$358$	−1.64065e6	−	2.84168e6i	−0.0357574	−	0.0619336i
$359$	−1.11371e7	−	1.92901e7i	−0.240708	−	0.416918i	0.720208	−	0.693758i	$-0.244046\pi$
$359$	−1.11371e7	−	1.92901e7i	−0.240708	−	0.416918i	−0.960916	+	0.276840i	$0.910713\pi$
$360$			2.57292e6i			0.0551467i
$361$	4.59681e7	−	1.00126e7i	0.977090	−	0.212826i
$362$	−5.18007e7			−1.09197
$363$	−5.97907e7	+	3.45202e7i	−1.25001	+	0.721694i
$364$	3.63972e7	−	2.10139e7i	0.754681	−	0.435715i
$365$	1.97458e7	−	3.42007e7i	0.406065	−	0.703325i
$366$	−3.72520e6	−	6.45224e6i	−0.0759813	−	0.131603i
$367$	4.10044e7	−	7.10217e7i	0.829530	−	1.43679i	−0.0688770	−	0.997625i	$-0.521942\pi$
$367$	4.10044e7	−	7.10217e7i	0.829530	−	1.43679i	0.898407	−	0.439163i	$-0.144725\pi$
$368$	−7.15849e6			−0.143641
$369$			3.81039e6i			0.0758387i
$370$	2.36959e7	−	4.10426e7i	0.467809	−	0.810269i
$371$	2.87661e7	+	1.66081e7i	0.563326	+	0.325236i
$372$	−3.13423e7			−0.608838
$373$		−	3.36821e7i		−	0.649041i	−0.945879	−	0.324521i	$-0.894797\pi$
$373$		−	3.36821e7i		−	0.649041i	0.945879	−	0.324521i	$-0.105203\pi$
$374$	8.71758e7	+	5.03310e7i	1.66641	+	0.962101i
$375$	8.30939e6	−	4.79743e6i	0.157571	−	0.0909735i
$376$	−2.47965e7	−	1.43163e7i	−0.466473	−	0.269318i
$377$	4.06966e7	+	7.04887e7i	0.759512	+	1.31551i
$378$	2.76575e7	+	4.79041e7i	0.512079	+	0.886947i
$379$			6.05239e6i			0.111175i	0.998454	+	0.0555877i	$0.0177033\pi$
$379$			6.05239e6i			0.111175i	−0.998454	+	0.0555877i	$0.982297\pi$
$380$	−3.71844e7	+	4.00276e6i	−0.677657	+	0.0729473i
$381$	−4.35421e7			−0.787289
$382$	−1.23129e7	+	7.10885e6i	−0.220887	+	0.127529i
$383$	−6.43303e6	+	3.71411e6i	−0.114504	+	0.0661087i	−0.556158	−	0.831077i	$-0.687725\pi$
$383$	−6.43303e6	+	3.71411e6i	−0.114504	+	0.0661087i	0.441654	+	0.897185i	$0.354392\pi$
$384$	−2.35489e6	+	4.07880e6i	−0.0415889	+	0.0720341i
$385$	8.55065e7	+	1.48102e8i	1.49836	+	2.59524i
$386$	−1.95271e7	+	3.38219e7i	−0.339528	+	0.588080i
$387$	−5.68233e6			−0.0980377
$388$		−	1.01447e7i		−	0.173678i
$389$	−3.11660e7	+	5.39811e7i	−0.529459	+	0.917049i	0.469951	+	0.882693i	$0.344272\pi$
$389$	−3.11660e7	+	5.39811e7i	−0.529459	+	0.917049i	−0.999410	+	0.0343568i	$0.989062\pi$
$390$	−5.88042e7	−	3.39506e7i	−0.991322	−	0.572340i
$391$	5.87147e7			0.982237
$392$			1.93242e7i			0.320806i
$393$	1.59862e7	+	9.22961e6i	0.263370	+	0.152057i
$394$	−4.81938e7	+	2.78247e7i	−0.787958	+	0.454928i
$395$	6.42294e7	+	3.70828e7i	1.04218	+	0.601702i
$396$	−2.82771e6	−	4.89774e6i	−0.0455354	−	0.0788696i
$397$	−5.89353e7	−	1.02079e8i	−0.941898	−	1.63141i	−0.761846	−	0.647758i	$-0.775707\pi$
$397$	−5.89353e7	−	1.02079e8i	−0.941898	−	1.63141i	−0.180051	−	0.983657i	$-0.557626\pi$
$398$		−	8.46040e6i		−	0.134197i
$399$	−6.66672e7	+	4.86930e7i	−1.04953	+	0.766564i
$400$	1.37306e7			0.214541
$401$	1.07712e8	−	6.21876e7i	1.67044	−	0.964430i	0.703052	−	0.711138i	$-0.251820\pi$
$401$	1.07712e8	−	6.21876e7i	1.67044	−	0.964430i	0.967390	−	0.253292i	$-0.0815134\pi$
$402$	−2.08080e7	+	1.20135e7i	−0.320297	+	0.184923i
$403$	−5.34378e7	+	9.25570e7i	−0.816457	+	1.41415i
$404$	−1.79717e6	−	3.11279e6i	−0.0272550	−	0.0472070i
$405$	3.95033e7	−	6.84217e7i	0.594659	−	1.02998i
$406$	−7.86686e7			−1.17550
$407$			1.04170e8i			1.54511i
$408$	1.93151e7	−	3.34547e7i	0.284391	−	0.492580i
$409$	−2.42654e6	−	1.40096e6i	−0.0354664	−	0.0204765i	0.482162	−	0.876082i	$-0.339852\pi$
$409$	−2.42654e6	−	1.40096e6i	−0.0354664	−	0.0204765i	−0.517628	+	0.855606i	$0.673185\pi$
$410$	4.40298e7			0.638845
$411$			6.33853e7i			0.912983i
$412$	−2.04094e7	−	1.17834e7i	−0.291836	−	0.168492i
$413$	1.01425e8	−	5.85577e7i	1.43977	−	0.831254i
$414$	−2.85678e6	−	1.64936e6i	−0.0402602	−	0.0232442i
$415$	4.71310e7	+	8.16334e7i	0.659421	+	1.14215i
$416$	8.03007e6	+	1.39085e7i	0.111542	+	0.193197i
$417$			3.86884e6i			0.0533546i
$418$	6.63839e7	−	4.84862e7i	0.908938	−	0.663879i
$419$	−7.84560e7			−1.06656			−0.533278	−	0.845940i	$-0.679040\pi$
$419$	−7.84560e7			−1.06656			−0.533278	+	0.845940i	$0.679040\pi$
$420$	5.68357e7	−	3.28141e7i	0.767138	−	0.442907i
$421$	−3.89553e7	+	2.24909e7i	−0.522060	+	0.301412i	−0.737777	−	0.675044i	$-0.764125\pi$
$421$	−3.89553e7	+	2.24909e7i	−0.522060	+	0.301412i	0.215717	+	0.976456i	$0.430791\pi$
$422$	3.97737e6	−	6.88901e6i	0.0529247	−	0.0916683i
$423$	−6.59712e6	−	1.14266e7i	−0.0871633	−	0.150971i
$424$	−6.34648e6	+	1.09924e7i	−0.0832599	+	0.144210i
$425$	−1.12620e8			−1.46706
$426$		−	378644.i		−	0.00489782i
$427$	1.22775e7	−	2.12653e7i	0.157698	−	0.273142i
$428$	3.05607e6	+	1.76442e6i	0.0389791	+	0.0225046i
$429$	1.49250e8			1.89036
$430$			6.56603e7i			0.825844i
$431$	−2.65195e7	−	1.53110e7i	−0.331233	−	0.191237i	0.325155	−	0.945661i	$-0.394583\pi$
$431$	−2.65195e7	−	1.53110e7i	−0.331233	−	0.191237i	−0.656388	+	0.754423i	$0.727917\pi$
$432$	−1.83057e7	+	1.05688e7i	−0.227057	+	0.131091i
$433$	5.86645e7	+	3.38700e7i	0.722623	+	0.417207i	0.815717	−	0.578451i	$-0.196342\pi$
$433$	5.86645e7	+	3.38700e7i	0.722623	+	0.417207i	−0.0930943	+	0.995657i	$0.529676\pi$
$434$	−5.16489e7	−	8.94586e7i	−0.631818	−	1.09434i
$435$	6.35495e7	+	1.10071e8i	0.772048	+	1.33723i
$436$			2.32216e7i			0.280177i
$437$	1.93926e7	−	4.38527e7i	0.232376	−	0.525475i
$438$	3.33122e7			0.396444
$439$	1.04174e7	−	6.01448e6i	0.123130	−	0.0710893i	−0.437170	−	0.899379i	$-0.644019\pi$
$439$	1.04174e7	−	6.01448e6i	0.123130	−	0.0710893i	0.560300	+	0.828290i	$0.310686\pi$
$440$	−5.65943e7	+	3.26747e7i	−0.664377	+	0.383578i
$441$	−4.45242e6	+	7.71182e6i	−0.0519135	+	0.0899168i
$442$	−6.58635e7	−	1.14079e8i	−0.762743	−	1.32111i
$443$	4.34937e7	−	7.53334e7i	0.500283	−	0.866515i	−0.499717	−	0.866189i	$-0.666563\pi$
$443$	4.34937e7	−	7.53334e7i	0.500283	−	0.866515i	1.00000		0.000326534i	$-0.000103939\pi$
$444$	3.99764e7			0.456725
$445$		−	6.38393e7i		−	0.724450i
$446$	2.06398e7	−	3.57492e7i	0.232649	−	0.402960i
$447$	−9.30821e7	−	5.37410e7i	−1.04218	−	0.601704i
$448$	−1.55225e7			−0.172635
$449$			1.35990e8i			1.50234i	0.660109	+	0.751170i	$0.270510\pi$
$449$			1.35990e8i			1.50234i	−0.660109	+	0.751170i	$0.729490\pi$
$450$	5.47955e6	+	3.16362e6i	0.0601323	+	0.0347174i
$451$	−8.38138e7	+	4.83899e7i	−0.913663	+	0.527503i
$452$	4.77973e7	+	2.75958e7i	0.517593	+	0.298832i
$453$	−1.57416e7	−	2.72652e7i	−0.169338	−	0.293302i
$454$	2.82020e7	+	4.88474e7i	0.301379	+	0.522004i
$455$		−	2.23789e8i		−	2.37577i
$456$	−1.86071e7	−	2.54756e7i	−0.196239	−	0.268677i
$457$	−1.41239e8			−1.47981			−0.739907	−	0.672709i	$-0.765131\pi$
$457$	−1.41239e8			−1.47981			−0.739907	+	0.672709i	$0.765131\pi$
$458$	8.73358e7	−	5.04233e7i	0.909067	−	0.524850i
$459$	1.50145e8	−	8.66863e7i	1.55265	−	0.896422i
$460$	−1.90587e7	+	3.30106e7i	−0.195803	+	0.339141i
$461$	2.15628e7	+	3.73479e7i	0.220091	+	0.381209i	0.954835	−	0.297135i	$-0.0960312\pi$
$461$	2.15628e7	+	3.73479e7i	0.220091	+	0.381209i	−0.734744	+	0.678344i	$0.762698\pi$
$462$	−7.21271e7	+	1.24928e8i	−0.731430	+	1.26687i
$463$	1.48353e8			1.49470			0.747350	−	0.664431i	$-0.231326\pi$
$463$	1.48353e8			1.49470			0.747350	+	0.664431i	$0.231326\pi$
$464$		−	3.00617e7i		−	0.300926i
$465$	−8.34454e7	+	1.44532e8i	−0.829934	+	1.43749i
$466$	4.43383e7	+	2.55988e7i	0.438149	+	0.252965i
$467$	−1.76094e8			−1.72900			−0.864500	−	0.502634i	$-0.832364\pi$
$467$	−1.76094e8			−1.72900			−0.864500	+	0.502634i	$0.832364\pi$
$468$			7.40073e6i			0.0721999i
$469$	−6.85791e7	−	3.95942e7i	−0.664773	−	0.383807i
$470$	−1.32036e8	+	7.62310e7i	−1.27174	+	0.734240i
$471$	−9.97202e7	−	5.75735e7i	−0.954378	−	0.551010i
$472$	2.23767e7	+	3.87576e7i	0.212799	+	0.368579i
$473$	−7.21624e7	−	1.24989e8i	−0.681911	−	1.18110i
$474$			6.25608e7i			0.587445i
$475$	−3.71966e7	+	8.41134e7i	−0.347075	+	0.784846i
$476$	1.27317e8			1.18050
$477$	−5.06546e6	+	2.92454e6i	−0.0466728	+	0.0269465i
$478$	5.24615e7	−	3.02887e7i	0.480349	−	0.277330i
$479$	5.49533e7	−	9.51819e7i	0.500020	−	0.866060i	−0.499980	−	0.866037i	$-0.666659\pi$
$479$	5.49533e7	−	9.51819e7i	0.500020	−	0.866060i	1.00000		2.30769e-5i	$-7.34560e-6\pi$
$480$	1.25393e7	+	2.17187e7i	0.113383	+	0.196386i
$481$	6.81587e7	−	1.18054e8i	0.612472	−	1.06083i
$482$	7.18404e6			0.0641546
$483$			8.41414e7i			0.746739i
$484$	4.34757e7	−	7.53022e7i	0.383452	−	0.664158i
$485$	−4.67815e7	−	2.70093e7i	−0.410061	−	0.236749i
$486$	−1.84808e7			−0.160995
$487$		−	1.17186e8i		−	1.01458i	−0.861775	−	0.507291i	$-0.830647\pi$
$487$		−	1.17186e8i		−	1.01458i	0.861775	−	0.507291i	$-0.169353\pi$
$488$	8.12614e6	+	4.69163e6i	0.0699237	+	0.0403705i
$489$	8.39893e7	−	4.84912e7i	0.718286	−	0.414702i
$490$	8.91115e7	+	5.14486e7i	0.757435	+	0.437306i
$491$	−5.26780e7	−	9.12410e7i	−0.445026	−	0.770807i	0.553028	−	0.833162i	$-0.313472\pi$
$491$	−5.26780e7	−	9.12410e7i	−0.445026	−	0.770807i	−0.998054	+	0.0623553i	$0.980139\pi$
$492$	1.85702e7	+	3.21645e7i	0.155927	+	0.270073i
$493$			2.46570e8i			2.05778i
$494$	−1.06957e8	+	1.15135e7i	−0.887213	+	0.0955051i
$495$	−3.01139e7			−0.248285
$496$	3.41849e7	−	1.97367e7i	0.280149	−	0.161744i
$497$	1.08075e6	−	623968.i	0.00880347	−	0.00508269i
$498$	−3.97564e7	+	6.88600e7i	−0.321898	+	0.557544i
$499$	−9.68864e7	−	1.67812e8i	−0.779761	−	1.35059i	−0.932080	−	0.362254i	$-0.882007\pi$
$499$	−9.68864e7	−	1.67812e8i	−0.779761	−	1.35059i	0.152319	−	0.988331i	$-0.451326\pi$
$500$	−6.04202e6	+	1.04651e7i	−0.0483362	+	0.0837207i
$501$	1.34208e8			1.06725
$502$		−	8.67317e7i		−	0.685593i
$503$	−1.02650e8	+	1.77795e8i	−0.806595	+	1.39706i	0.108614	+	0.994084i	$0.465359\pi$
$503$	−1.02650e8	+	1.77795e8i	−0.806595	+	1.39706i	−0.915209	+	0.402980i	$0.867974\pi$
$504$	−6.19467e6	−	3.57649e6i	−0.0483867	−	0.0279361i
$505$	−1.91391e7			−0.148610
$506$		−	8.37840e7i		−	0.646710i
$507$	−6.29334e7	−	3.63346e7i	−0.482900	−	0.278802i
$508$	4.74912e7	−	2.74191e7i	0.362262	−	0.209152i
$509$	4.03451e6	+	2.32933e6i	0.0305941	+	0.0176635i	0.515219	−	0.857059i	$-0.327711\pi$
$509$	4.03451e6	+	2.32933e6i	0.0305941	+	0.0176635i	−0.484625	+	0.874722i	$0.661044\pi$
$510$	−1.02849e8	−	1.78139e8i	−0.775333	−	1.34292i
$511$	5.48953e7	+	9.50814e7i	0.411407	+	0.712579i
$512$		−	5.93164e6i		−	0.0441942i
$513$	−1.51535e7	−	1.40771e8i	−0.112243	−	1.04271i
$514$	4.56415e7			0.336101
$515$	−1.08676e8	+	6.27440e7i	−0.795630	+	0.459357i
$516$	−4.79660e7	+	2.76932e7i	−0.349128	+	0.201569i
$517$	1.67560e8	−	2.90222e8i	1.21255	−	2.10019i
$518$	6.58771e7	+	1.14102e8i	0.473964	+	0.820929i
$519$	−4.67380e7	+	8.09526e7i	−0.334325	+	0.579067i
$520$	8.55168e7			0.608193
$521$			1.51264e8i			1.06960i	0.844978	+	0.534801i	$0.179613\pi$
$521$			1.51264e8i			1.06960i	−0.844978	+	0.534801i	$0.820387\pi$
$522$	6.92642e6	−	1.19969e7i	0.0486965	−	0.0843447i
$523$	1.89523e8	+	1.09421e8i	1.32482	+	0.764883i	0.984493	−	0.175425i	$-0.0561300\pi$
$523$	1.89523e8	+	1.09421e8i	1.32482	+	0.764883i	0.340324	+	0.940308i	$0.389463\pi$
$524$	−2.32481e7			−0.161582
$525$		−	1.61391e8i		−	1.11532i
$526$	−3.12577e6	−	1.80467e6i	−0.0214783	−	0.0124005i
$527$	−2.80388e8	+	1.61882e8i	−1.91570	+	1.10603i
$528$	−4.77388e7	−	2.75620e7i	−0.324317	−	0.187245i
$529$	4.95829e7	+	8.58802e7i	0.334939	+	0.580131i
$530$	3.37937e7	+	5.85323e7i	0.226990	+	0.393159i
$531$			2.06230e7i			0.137742i
$532$	4.20510e7	−	9.50906e7i	0.279281	−	0.631543i
$533$	1.26647e8			0.836398
$534$	4.66357e7	−	2.69251e7i	0.306263	−	0.176821i
$535$	1.62729e7	−	9.39517e6i	0.106268	−	0.0613540i
$536$	1.51302e7	−	2.62062e7i	0.0982538	−	0.170181i
$537$	−7.36913e6	−	1.27637e7i	−0.0475876	−	0.0824241i
$538$	−7.19585e7	+	1.24636e8i	−0.462099	+	0.800379i
$539$	−2.26173e8			−1.44436
$540$			1.12553e8i			0.714785i
$541$	6.56754e7	−	1.13753e8i	0.414773	−	0.718409i	−0.580631	−	0.814167i	$-0.697194\pi$
$541$	6.56754e7	−	1.13753e8i	0.414773	−	0.718409i	0.995405	+	0.0957581i	$0.0305275\pi$
$542$	−3.50673e7	−	2.02461e7i	−0.220244	−	0.127158i
$543$	−2.32668e8			−1.45324
$544$			4.86520e7i			0.302206i
$545$	1.07084e8	+	6.18251e7i	0.661509	+	0.381922i
$546$	1.63482e8	−	9.43862e7i	1.00436	−	0.579870i
$547$	1.10784e8	+	6.39611e7i	0.676885	+	0.390800i	0.798680	−	0.601756i	$-0.205532\pi$
$547$	1.10784e8	+	6.39611e7i	0.676885	+	0.390800i	−0.121796	+	0.992555i	$0.538865\pi$
$548$	−3.99146e7	−	6.91341e7i	−0.242544	−	0.420098i
$549$	2.16196e6	+	3.74463e6i	0.0130657	+	0.0226304i
$550$			1.60705e8i			0.965921i
$551$	1.84158e8	+	8.14382e7i	1.10087	+	0.486825i
$552$	−3.21531e7			−0.191164
$553$	−1.78564e8	+	1.03094e8i	−1.05589	+	0.609619i
$554$	1.04495e8	−	6.03302e7i	0.614563	−	0.354818i
$555$	1.06433e8	−	1.84347e8i	0.622582	−	1.07834i
$556$	−2.43626e6	−	4.21973e6i	−0.0141742	−	0.0245505i
$557$	−5.21712e7	+	9.03632e7i	−0.301902	+	0.522909i	−0.976567	−	0.215215i	$-0.930955\pi$
$557$	−5.21712e7	+	9.03632e7i	−0.301902	+	0.522909i	0.674665	+	0.738124i	$0.264288\pi$
$558$	1.81898e7			0.104695
$559$			1.88865e8i			1.08122i
$560$	−4.13270e7	+	7.15805e7i	−0.235326	+	0.407597i
$561$	3.91559e8	+	2.26067e8i	2.21773	+	1.28041i
$562$	−5.47262e7			−0.308309
$563$		−	2.08088e8i		−	1.16606i	−0.812450	−	0.583030i	$-0.801867\pi$
$563$		−	2.08088e8i		−	1.16606i	0.812450	−	0.583030i	$-0.198133\pi$
$564$	−1.11376e8	−	6.43030e7i	−0.620804	−	0.358421i
$565$	2.54510e8	−	1.46942e8i	1.41111	−	0.814704i
$566$	3.84840e7	+	2.22188e7i	0.212242	+	0.122538i
$567$	1.09823e8	+	1.90219e8i	0.602483	+	1.04353i
$568$	238438.	+	412986.i	0.00130116	+	0.00225367i
$569$		−	1.74234e8i		−	0.945792i	−0.881118	−	0.472896i	$-0.843209\pi$
$569$		−	1.74234e8i		−	0.945792i	0.881118	−	0.472896i	$-0.156791\pi$
$570$	−1.67018e8	+	1.79788e7i	−0.901857	+	0.0970815i
$571$	2.87430e8			1.54392			0.771958	−	0.635674i	$-0.219278\pi$
$571$	2.87430e8			1.54392			0.771958	+	0.635674i	$0.219278\pi$
$572$	−1.62787e8	+	9.39852e7i	−0.869825	+	0.502194i
$573$	−5.53046e7	+	3.19301e7i	−0.293966	+	0.169721i
$574$	−6.12037e7	+	1.06008e8i	−0.323625	+	0.560535i
$575$	4.68685e7	+	8.11786e7i	0.246534	+	0.427010i
$576$	1.36669e6	−	2.36718e6i	0.00715159	−	0.0123869i
$577$	−7.22861e6			−0.0376294			−0.0188147	−	0.999823i	$-0.505989\pi$
$577$	−7.22861e6			−0.0376294			−0.0188147	+	0.999823i	$0.505989\pi$
$578$		−	2.62506e8i		−	1.35943i
$579$	−8.77079e7	+	1.51915e8i	−0.451859	+	0.782643i
$580$	−1.38627e8	−	8.00361e7i	−0.710498	−	0.410206i
$581$	−2.62058e8			−1.33619
$582$		−	4.55662e7i		−	0.231139i
$583$	−1.28657e8	−	7.42802e7i	−0.649274	−	0.374859i
$584$	−3.63336e7	+	2.09772e7i	−0.182419	+	0.105319i
$585$	3.41277e7	+	1.97036e7i	0.170467	+	0.0984189i
$586$	1.29171e8	+	2.23731e8i	0.641908	+	1.11182i
$587$	2.51761e7	+	4.36062e7i	0.124473	+	0.215593i	0.921527	−	0.388315i	$-0.126943\pi$
$587$	2.51761e7	+	4.36062e7i	0.124473	+	0.215593i	−0.797054	+	0.603908i	$0.793609\pi$
$588$			8.67966e7i			0.426944i
$589$	2.82984e7	+	2.62883e8i	0.138489	+	1.28652i
$590$	2.38302e8			1.16031
$591$	−2.16468e8	+	1.24978e8i	−1.04865	+	0.605438i
$592$	−4.36021e7	+	2.51737e7i	−0.210156	+	0.121334i
$593$	−1.83196e8	+	3.17304e8i	−0.878520	+	1.52164i	−0.0255541	+	0.999673i	$0.508135\pi$
$593$	−1.83196e8	+	3.17304e8i	−0.878520	+	1.52164i	−0.852966	+	0.521967i	$0.825198\pi$
$594$	−1.23699e8	−	2.14252e8i	−0.590208	−	1.02227i
$595$	3.38969e8	−	5.87111e8i	1.60920	−	2.78721i
$596$	1.35366e8			0.639397
$597$		−	3.80008e7i		−	0.178595i
$598$	−5.48202e7	+	9.49514e7i	−0.256352	+	0.444015i
$599$	1.99548e8	+	1.15209e8i	0.928466	+	0.536050i	0.886326	−	0.463061i	$-0.153249\pi$
$599$	1.99548e8	+	1.15209e8i	0.928466	+	0.536050i	0.0421401	+	0.999112i	$0.486582\pi$
$600$	6.16724e7			0.285520
$601$		−	2.68476e8i		−	1.23675i	−0.785884	−	0.618374i	$-0.787792\pi$
$601$		−	2.68476e8i		−	1.23675i	0.785884	−	0.618374i	$-0.212208\pi$
$602$	−1.58086e8	−	9.12712e7i	−0.724611	−	0.418354i
$603$	1.20762e7	−	6.97218e6i	0.0550779	−	0.0317992i
$604$	3.43386e7	+	1.98254e7i	0.155838	+	0.0899728i
$605$	−2.31499e8	−	4.00968e8i	−1.04540	−	1.81069i
$606$	−8.07218e6	−	1.39814e7i	−0.0362721	−	0.0628252i
$607$		−	9.66029e7i		−	0.431941i	−0.976400	−	0.215970i	$-0.930709\pi$
$607$		−	9.66029e7i		−	0.431941i	0.976400	−	0.215970i	$-0.0692915\pi$
$608$	3.63371e7	+	1.60690e7i	0.161674	+	0.0714954i
$609$	−3.53348e8			−1.56441
$610$	4.32699e7	−	2.49819e7i	0.190632	−	0.110062i
$611$	−3.79787e8	+	2.19270e8i	−1.66501	+	0.961293i
$612$	−1.12097e7	+	1.94158e7i	−0.0489036	+	0.0847036i
$613$	−4.38546e7	−	7.59583e7i	−0.190385	−	0.329757i	0.754993	−	0.655733i	$-0.227640\pi$
$613$	−4.38546e7	−	7.59583e7i	−0.190385	−	0.329757i	−0.945378	+	0.325976i	$0.894307\pi$
$614$	1.29178e8	−	2.23744e8i	0.558065	−	0.966597i
$615$	1.97764e8			0.850204
$616$		−	1.81678e8i		−	0.777249i
$617$	−5.96747e7	+	1.03360e8i	−0.254059	+	0.440043i	−0.964640	−	0.263573i	$-0.915099\pi$
$617$	−5.96747e7	+	1.03360e8i	−0.254059	+	0.440043i	0.710580	+	0.703616i	$0.248432\pi$
$618$	−9.16710e7	−	5.29263e7i	−0.388389	−	0.224236i
$619$	−3.57227e7			−0.150617			−0.0753083	−	0.997160i	$-0.523994\pi$
$619$	−3.57227e7			−0.150617			−0.0753083	+	0.997160i	$0.523994\pi$
$620$		−	2.10187e8i		−	0.881923i
$621$	−1.24970e8	−	7.21516e7i	−0.521833	−	0.301281i
$622$	−2.58802e8	+	1.49419e8i	−1.07546	+	0.620920i
$623$	1.53702e8	+	8.87399e7i	0.635646	+	0.366991i
$624$	3.60679e7	+	6.24714e7i	0.148446	+	0.257115i
$625$	1.36929e8	+	2.37167e8i	0.560860	+	0.971438i
$626$			2.23187e8i			0.909798i
$627$	2.98170e8	−	2.17781e8i	1.20966	−	0.883520i
$628$	1.45019e8			0.585527
$629$	3.57629e8	−	2.06477e8i	1.43708	−	0.829699i
$630$	−3.29853e7	+	1.90440e7i	−0.131916	+	0.0761619i
$631$	−1.05749e8	+	1.83162e8i	−0.420907	+	0.729032i	−0.996028	−	0.0890356i	$-0.971621\pi$
$631$	−1.05749e8	+	1.83162e8i	−0.420907	+	0.729032i	0.575121	+	0.818068i	$0.304955\pi$
$632$	−3.93954e7	−	6.82349e7i	−0.156061	−	0.270306i
$633$	1.78648e7	−	3.09427e7i	0.0704346	−	0.121996i
$634$	−1.47605e8			−0.579207
$635$		−	2.92001e8i		−	1.14042i
$636$	−2.85059e7	+	4.93736e7i	−0.110806	+	0.191922i
$637$	2.56319e8	+	1.47986e8i	0.991661	+	0.572536i
$638$	3.51847e8			1.35485
$639$			219751.i			0.000842224i
$640$	−2.73532e7	−	1.57924e7i	−0.104344	−	0.0602430i
$641$	−1.29393e7	+	7.47051e6i	−0.0491289	+	0.0283646i	−0.524363	−	0.851495i	$-0.675697\pi$
$641$	−1.29393e7	+	7.47051e6i	−0.0491289	+	0.0283646i	0.475234	+	0.879859i	$0.342363\pi$
$642$	1.37266e7	+	7.92508e6i	0.0518752	+	0.0299501i
$643$	−9.07546e7	−	1.57192e8i	−0.341378	−	0.591284i	0.643311	−	0.765605i	$-0.277560\pi$
$643$	−9.07546e7	−	1.57192e8i	−0.341378	−	0.591284i	−0.984689	+	0.174321i	$0.944227\pi$
$644$	−5.29851e7	−	9.17729e7i	−0.198379	−	0.343603i
$645$			2.94920e8i			1.09907i
$646$	−2.98041e8	−	1.31800e8i	−1.10555	−	0.488896i
$647$	4.57321e8			1.68853			0.844265	−	0.535927i	$-0.180038\pi$
$647$	4.57321e8			1.68853			0.844265	+	0.535927i	$0.180038\pi$
$648$	−7.26887e7	+	4.19668e7i	−0.267142	+	0.154234i
$649$	−4.53625e8	+	2.61900e8i	−1.65944	+	0.958081i
$650$	1.05150e8	−	1.82125e8i	0.382886	−	0.663177i
$651$	−2.31987e8	−	4.01813e8i	−0.840853	−	1.45640i
$652$	−6.10712e7	+	1.05778e8i	−0.220340	+	0.381641i
$653$	−2.28284e8			−0.819852			−0.409926	−	0.912119i	$-0.634445\pi$
$653$	−2.28284e8			−0.819852			−0.409926	+	0.912119i	$0.634445\pi$
$654$			1.04302e8i			0.372873i
$655$	−6.18955e7	+	1.07206e8i	−0.220260	+	0.381501i
$656$	−4.05089e7	−	2.33878e7i	−0.143496	−	0.0828473i
$657$	−1.93331e7			−0.0681720
$658$		−	4.23860e8i		−	1.48780i
$659$	3.43814e8	+	1.98501e8i	1.20134	+	0.693595i	0.960854	−	0.277057i	$-0.0893589\pi$
$659$	3.43814e8	+	1.98501e8i	1.20134	+	0.693595i	0.240489	+	0.970652i	$0.422692\pi$
$660$	−2.54199e8	+	1.46762e8i	−0.884182	+	0.510483i
$661$	−1.88382e8	−	1.08763e8i	−0.652282	−	0.376595i	0.137048	−	0.990564i	$-0.456239\pi$
$661$	−1.88382e8	−	1.08763e8i	−0.652282	−	0.376595i	−0.789330	+	0.613969i	$0.789572\pi$
$662$	7.68398e7	+	1.33090e8i	0.264857	+	0.458746i
$663$	−2.95833e8	−	5.12398e8i	−1.01509	−	1.75819i
$664$		−	1.00141e8i		−	0.342063i
$665$	−3.26545e8	−	4.47082e8i	−1.11039	−	1.52028i
$666$	−2.32007e7			−0.0785379
$667$	1.77732e8	−	1.02614e8i	0.598947	−	0.345802i
$668$	−1.46380e8	+	8.45126e7i	−0.491080	+	0.283525i
$669$	9.27060e7	−	1.60571e8i	0.309620	−	0.536278i
$670$	−8.05649e7	−	1.39542e8i	−0.267868	−	0.463962i
$671$	−5.49115e7	+	9.51095e7i	−0.181759	+	0.314816i
$672$	−6.97210e7			−0.229750
$673$			3.63099e8i			1.19119i	0.803286	+	0.595593i	$0.203083\pi$
$673$			3.63099e8i			1.19119i	−0.803286	+	0.595593i	$0.796917\pi$
$674$	2.52977e6	−	4.38168e6i	0.00826230	−	0.0143107i
$675$	2.39704e8	+	1.38393e8i	0.779406	+	0.449990i
$676$	9.15217e7			0.296267
$677$			2.31011e8i			0.744504i	0.928132	+	0.372252i	$0.121414\pi$
$677$			2.31011e8i			0.744504i	−0.928132	+	0.372252i	$0.878586\pi$
$678$	2.14687e8	+	1.23949e8i	0.688836	+	0.397700i
$679$	1.30057e8	−	7.50885e7i	0.415456	−	0.239864i
$680$	2.24354e8	+	1.29531e8i	0.713520	+	0.411951i
$681$	1.26672e8	+	2.19403e8i	0.401089	+	0.694706i
$682$	2.31001e8	+	4.00105e8i	0.728217	+	1.26131i
$683$			1.93486e8i			0.607276i	0.952787	+	0.303638i	$0.0982014\pi$
$683$			1.93486e8i			0.607276i	−0.952787	+	0.303638i	$0.901799\pi$
$684$	1.07989e7	+	1.47851e7i	0.0337450	+	0.0462014i
$685$	−4.25073e8			−1.32249
$686$	2.52884e7	−	1.46003e7i	0.0783339	−	0.0452261i
$687$	3.92278e8	−	2.26482e8i	1.20983	−	0.698494i
$688$	3.48776e7	−	6.04097e7i	0.107098	−	0.185499i
$689$	9.72037e7	+	1.68362e8i	0.297184	+	0.514737i
$690$	−8.56041e7	+	1.48271e8i	−0.260584	+	0.451344i
$691$	−1.56808e8			−0.475264			−0.237632	−	0.971355i	$-0.576371\pi$
$691$	−1.56808e8			−0.475264			−0.237632	+	0.971355i	$0.576371\pi$
$692$		−	1.17726e8i		−	0.355268i
$693$	4.18598e7	−	7.25033e7i	0.125776	−	0.217850i
$694$	1.52124e7	+	8.78290e6i	0.0455114	+	0.0262760i
$695$	−2.59451e7			−0.0772861
$696$		−	1.35025e8i		−	0.400486i
$697$	3.32259e8	+	1.91830e8i	0.981246	+	0.566523i
$698$	2.86736e8	−	1.65547e8i	0.843173	−	0.486806i
$699$	1.99150e8	+	1.14979e8i	0.583108	+	0.336658i
$700$	1.01630e8	+	1.76028e8i	0.296298	+	0.513202i
$701$	−7.57926e7	−	1.31277e8i	−0.220025	−	0.381095i	0.734790	−	0.678295i	$-0.237281\pi$
$701$	−7.57926e7	−	1.31277e8i	−0.220025	−	0.381095i	−0.954815	+	0.297199i	$0.903947\pi$
$702$			3.23746e8i			0.935822i
$703$	−3.60940e7	−	3.35302e8i	−0.103889	−	0.965095i
$704$	6.94248e7			0.198974
$705$	−5.93053e8	+	3.42399e8i	−1.69249	+	0.977160i
$706$	5.92200e7	−	3.41907e7i	0.168289	−	0.0971614i
$707$	2.66043e7	−	4.60800e7i	0.0752825	−	0.130393i
$708$	1.00507e8	+	1.74084e8i	0.283203	+	0.490522i
$709$	−9.62778e7	+	1.66758e8i	−0.270139	+	0.467894i	−0.968897	−	0.247463i	$-0.920403\pi$
$709$	−9.62778e7	+	1.66758e8i	−0.270139	+	0.467894i	0.698758	+	0.715358i	$0.253736\pi$
$710$	2.53926e6			0.00709467
$711$		−	3.63079e7i		−	0.101016i
$712$	−3.39103e7	+	5.87343e7i	−0.0939489	+	0.162724i
$713$	2.33376e8	+	1.34740e8i	0.643854	+	0.371729i
$714$	5.71859e8			1.57107
$715$			1.00090e9i			2.73825i
$716$	1.60750e7	+	9.28090e6i	0.0437937	+	0.0252843i
$717$	2.35636e8	−	1.36045e8i	0.639271	−	0.369083i
$718$	1.09121e8	+	6.30012e7i	0.294806	+	0.170206i
$719$	−3.07401e8	−	5.32434e8i	−0.827024	−	1.43245i	−0.900362	−	0.435141i	$-0.856699\pi$
$719$	−3.07401e8	−	5.32434e8i	−0.827024	−	1.43245i	0.0733379	−	0.997307i	$-0.476635\pi$
$720$	−7.27732e6	−	1.26047e7i	−0.0194973	−	0.0337703i
$721$		−	3.48869e8i		−	0.930801i
$722$	−1.96877e8	+	1.79069e8i	−0.523098	+	0.475782i
$723$	3.22678e7			0.0853798
$724$	2.53771e8	−	1.46515e8i	0.668692	−	0.386069i
$725$	−3.40906e8	+	1.96822e8i	−0.894582	+	0.516487i
$726$	1.95276e8	−	3.38227e8i	0.510315	−	0.883892i
$727$	−2.88645e8	−	4.99947e8i	−0.751208	−	1.30113i	−0.947238	−	0.320532i	$-0.896138\pi$
$727$	−2.88645e8	−	4.99947e8i	−0.751208	−	1.30113i	0.196030	−	0.980598i	$-0.437195\pi$
$728$	−1.18873e8	+	2.05893e8i	−0.308097	+	0.533640i
$729$	−4.21026e8			−1.08674
$730$			2.23398e8i			0.574263i
$731$	−2.86070e8	+	4.95487e8i	−0.732352	+	1.26847i
$732$	3.64994e7	+	2.10729e7i	0.0930577	+	0.0537269i
$733$	−1.47386e7			−0.0374236			−0.0187118	−	0.999825i	$-0.505956\pi$
$733$	−1.47386e7			−0.0374236			−0.0187118	+	0.999825i	$0.505956\pi$
$734$			4.63912e8i			1.17313i
$735$	4.00254e8	+	2.31086e8i	1.00803	+	0.581986i
$736$	3.50693e7	−	2.02473e7i	0.0879616	−	0.0507847i
$737$	3.06722e8	+	1.77086e8i	0.766200	+	0.442366i
$738$	−1.07774e7	−	1.86670e7i	−0.0268130	−	0.0464415i
$739$	6.64418e7	+	1.15081e8i	0.164630	+	0.285147i	0.936524	−	0.350604i	$-0.114024\pi$
$739$	6.64418e7	+	1.15081e8i	0.164630	+	0.285147i	−0.771894	+	0.635751i	$0.780690\pi$
$740$			2.68089e8i			0.661582i
$741$	−4.80408e8	+	5.17141e7i	−1.18074	+	0.127103i
$742$	−1.87900e8			−0.459954
$743$	−3.69572e8	+	2.13372e8i	−0.901016	+	0.520202i	−0.877530	−	0.479522i	$-0.840810\pi$
$743$	−3.69572e8	+	2.13372e8i	−0.901016	+	0.520202i	−0.0234864	+	0.999724i	$0.507477\pi$
$744$	1.53545e8	−	8.86493e7i	0.372835	−	0.215257i
$745$	3.60397e8	−	6.24226e8i	0.871590	−	1.50964i
$746$	9.52673e7	+	1.65008e8i	0.229471	+	0.397455i
$747$	2.30731e7	−	3.99637e7i	0.0553533	−	0.0958747i
$748$	−5.69430e8			−1.36062
$749$			5.22390e7i			0.124322i
$750$	−2.71384e7	+	4.70050e7i	−0.0643280	+	0.111419i
$751$	7.55366e7	+	4.36111e7i	0.178335	+	0.102962i	0.586510	−	0.809942i	$-0.300501\pi$
$751$	7.55366e7	+	4.36111e7i	0.178335	+	0.102962i	−0.408175	+	0.912904i	$0.633835\pi$
$752$	1.61970e8			0.380874
$753$		−	3.89564e8i		−	0.912419i
$754$	−3.98744e8	−	2.30215e8i	−0.930208	−	0.537056i
$755$	1.82846e8	−	1.05566e8i	0.424858	−	0.245292i
$756$	−2.70987e8	−	1.56454e8i	−0.627166	−	0.362095i
$757$	−9.60655e7	−	1.66390e8i	−0.221452	−	0.383566i	0.733797	−	0.679369i	$-0.237746\pi$
$757$	−9.60655e7	−	1.66390e8i	−0.221452	−	0.383566i	−0.955249	+	0.295802i	$0.904413\pi$
$758$	−1.71187e7	−	2.96505e7i	−0.0393065	−	0.0680808i
$759$		−	3.76324e8i		−	0.860671i
$760$	1.70844e8	−	1.24783e8i	0.389188	−	0.284259i
$761$	3.89947e8			0.884814			0.442407	−	0.896814i	$-0.354125\pi$
$761$	3.89947e8			0.884814			0.442407	+	0.896814i	$0.354125\pi$
$762$	2.13312e8	−	1.23156e8i	0.482114	−	0.278349i
$763$	−2.97705e8	+	1.71880e8i	−0.670212	+	0.386947i
$764$	4.02137e7	−	6.96522e7i	0.0901766	−	0.156190i
$765$	5.96894e7	+	1.03385e8i	0.133325	+	0.230926i
$766$	2.10102e7	−	3.63907e7i	0.0467459	−	0.0809663i
$767$	6.85450e8			1.51911
$768$		−	2.66426e7i		−	0.0588156i
$769$	1.28041e8	−	2.21774e8i	0.281560	−	0.487676i	−0.690209	−	0.723610i	$-0.742482\pi$
$769$	1.28041e8	−	2.21774e8i	0.281560	−	0.487676i	0.971769	+	0.235934i	$0.0758149\pi$
$770$	−8.37789e8	−	4.83698e8i	−1.83511	−	1.05950i
$771$	2.05003e8			0.447299
$772$		−	2.20924e8i		−	0.480165i
$773$	−3.69690e7	−	2.13441e7i	−0.0800385	−	0.0462103i	0.459447	−	0.888205i	$-0.348048\pi$
$773$	−3.69690e7	−	2.13441e7i	−0.0800385	−	0.0462103i	−0.539485	+	0.841995i	$0.681381\pi$
$774$	2.78376e7	−	1.60720e7i	0.0600356	−	0.0346616i
$775$	−4.47635e8	−	2.58442e8i	−0.961655	−	0.555212i
$776$	2.86937e7	+	4.96989e7i	0.0614046	+	0.106356i
$777$	2.95894e8	+	5.12503e8i	0.630773	+	1.09253i
$778$		−	3.52603e8i		−	0.748768i
$779$	2.53013e8	−	1.84798e8i	0.535218	−	0.390918i
$780$	3.84107e8			0.809411
$781$	−4.83365e6	+	2.79071e6i	−0.0101466	+	0.00585817i
$782$	−2.87642e8	+	1.66070e8i	−0.601495	+	0.347273i
$783$	3.02997e8	−	5.24807e8i	0.631181	−	1.09324i
$784$	−5.46571e7	−	9.46688e7i	−0.113422	−	0.196453i
$785$	3.86098e8	−	6.68742e8i	0.798158	−	1.38245i
$786$	−1.04421e8			−0.215041
$787$		−	6.52431e8i		−	1.33847i	−0.743049	−	0.669237i	$-0.766621\pi$
$787$		−	6.52431e8i		−	1.33847i	0.743049	−	0.669237i	$-0.233379\pi$
$788$	1.57400e8	−	2.72625e8i	0.321682	−	0.557170i
$789$	−1.40397e7	−	8.10585e6i	−0.0285843	−	0.0165032i
$790$	−4.19544e8			−0.850936
$791$			8.17025e8i			1.65084i
$792$	2.77058e7	+	1.59959e7i	0.0557692	+	0.0321984i
$793$	1.24461e8	−	7.18576e7i	0.249582	−	0.144097i
$794$	5.77445e8	+	3.33388e8i	1.15358	+	0.666022i
$795$	1.51788e8	+	2.62904e8i	0.302089	+	0.523234i
$796$	2.39296e7	+	4.14473e7i	0.0474457	+	0.0821784i
$797$		−	5.56853e8i		−	1.09993i	−0.835187	−	0.549966i	$-0.814641\pi$
$797$		−	5.56853e8i		−	1.09993i	0.835187	−	0.549966i	$-0.185359\pi$
$798$	1.88876e8	−	4.27109e8i	0.371680	−	0.840486i
$799$	−1.32850e9			−2.60447
$800$	−6.72659e7	+	3.88360e7i	−0.131379	+	0.0758516i
$801$	−2.70656e7	+	1.56263e7i	−0.0526647	+	0.0304060i
$802$	−3.51786e8	+	6.09312e8i	−0.681955	+	1.18118i
$803$	−2.45520e8	−	4.25253e8i	−0.474177	−	0.821299i
$804$	6.79587e7	−	1.17708e8i	0.130761	−	0.226484i
$805$	−5.64268e8			−1.08168
$806$		−	6.04580e8i		−	1.15464i
$807$	−3.23209e8	+	5.59814e8i	−0.614982	+	1.06518i
$808$	1.76086e7	+	1.01663e7i	0.0333804	+	0.0192722i
$809$	−8.85849e8			−1.67307			−0.836535	−	0.547914i	$-0.815422\pi$
$809$	−8.85849e8			−1.67307			−0.836535	+	0.547914i	$0.815422\pi$
$810$			4.46929e8i			0.840975i
$811$	−2.91933e8	−	1.68547e8i	−0.547294	−	0.315980i	0.200736	−	0.979645i	$-0.435667\pi$
$811$	−2.91933e8	−	1.68547e8i	−0.547294	−	0.315980i	−0.748030	+	0.663665i	$0.769000\pi$
$812$	3.85396e8	−	2.22508e8i	0.719845	−	0.415603i
$813$	−1.57508e8	−	9.09375e7i	−0.293111	−	0.169228i
$814$	−2.94637e8	−	5.10326e8i	−0.546278	−	0.946181i
$815$	3.25191e8	+	5.63247e8i	0.600711	+	1.04046i
$816$			2.18525e8i			0.402190i
$817$	2.75584e8	+	3.77311e8i	0.505345	+	0.691884i
$818$	1.58501e7			0.0289582
$819$	−9.48784e7	+	5.47781e7i	−0.172709	+	0.0997138i
$820$	−2.15701e8	+	1.24535e8i	−0.391211	+	0.225866i
$821$	3.08479e8	−	5.34300e8i	0.557437	−	0.965508i	−0.440273	−	0.897864i	$-0.645118\pi$
$821$	3.08479e8	−	5.34300e8i	0.557437	−	0.965508i	0.997709	−	0.0676445i	$-0.0215484\pi$
$822$	−1.79281e8	−	3.10523e8i	−0.322788	−	0.559086i
$823$	−1.86716e8	+	3.23401e8i	−0.334951	+	0.580153i	−0.983475	−	0.181041i	$-0.942053\pi$
$823$	−1.86716e8	+	3.23401e8i	−0.334951	+	0.580153i	0.648524	+	0.761194i	$0.275387\pi$
$824$	1.33314e8			0.238283
$825$			7.21823e8i			1.28549i
$826$	−3.31252e8	+	5.73746e8i	−0.587785	+	1.01807i
$827$	2.92181e8	+	1.68691e8i	0.516577	+	0.298246i	0.735533	−	0.677489i	$-0.236932\pi$
$827$	2.92181e8	+	1.68691e8i	0.516577	+	0.298246i	−0.218956	+	0.975735i	$0.570265\pi$
$828$	1.86604e7			0.0328723
$829$			8.99748e8i			1.57927i	0.613575	+	0.789637i	$0.289731\pi$
$829$			8.99748e8i			1.57927i	−0.613575	+	0.789637i	$0.710269\pi$
$830$	−4.61788e8	−	2.66613e8i	−0.807623	−	0.466281i
$831$	4.69350e8	−	2.70979e8i	0.817888	−	0.472208i
$832$	−7.86783e7	−	4.54249e7i	−0.136611	−	0.0788723i
$833$	4.48303e8	+	7.76484e8i	0.775598	+	1.34338i
$834$	−1.09427e7	−	1.89534e7i	−0.0188637	−	0.0326729i
$835$			9.00022e8i			1.54594i
$836$	−1.88074e8	+	4.25295e8i	−0.321892	+	0.727899i
$837$	7.95717e8			1.35701
$838$	3.84354e8	−	2.21907e8i	0.653130	−	0.377085i
$839$	2.08397e8	−	1.20318e8i	0.352863	−	0.203726i	−0.313082	−	0.949726i	$-0.601362\pi$
$839$	2.08397e8	−	1.20318e8i	0.352863	−	0.203726i	0.665946	+	0.746000i	$0.268028\pi$
$840$	−1.85625e8	+	3.21511e8i	−0.313183	+	0.542448i
$841$	1.33510e8	+	2.31246e8i	0.224453	+	0.388764i
$842$	1.27228e8	−	2.20365e8i	0.213130	−	0.369152i
$843$	−2.45808e8			−0.410311
$844$			4.49988e7i			0.0748469i
$845$	2.43667e8	−	4.22043e8i	0.403855	−	0.699498i
$846$	6.46383e7	+	3.73190e7i	0.106753	+	0.0616337i
$847$	1.28718e9			2.11831
$848$		−	7.18023e7i		−	0.117747i
$849$	1.72855e8	+	9.97978e7i	0.282461	+	0.163079i
$850$	5.51723e8	−	3.18537e8i	0.898388	−	0.518685i
$851$	−2.97666e8	−	1.71857e8i	−0.482992	−	0.278856i
$852$	1.07097e6	+	1.85497e6i	0.00173164	+	0.00299929i
$853$	−4.17202e8	−	7.22615e8i	−0.672201	−	1.16429i	−0.977278	−	0.211959i	$-0.932016\pi$
$853$	−4.17202e8	−	7.22615e8i	−0.672201	−	1.16429i	0.305077	−	0.952328i	$-0.401318\pi$
$854$			1.38904e8i			0.223019i
$855$	9.69306e7	−	1.04342e7i	0.155082	−	0.0166940i
$856$	−1.99622e7			−0.0318263
$857$	−3.04172e8	+	1.75614e8i	−0.483255	+	0.279007i	−0.721772	−	0.692131i	$-0.756672\pi$
$857$	−3.04172e8	+	1.75614e8i	−0.483255	+	0.279007i	0.238517	+	0.971138i	$0.423339\pi$
$858$	−7.31175e8	+	4.22144e8i	−1.15760	+	0.668342i
$859$	4.57849e8	−	7.93018e8i	0.722342	−	1.25113i	−0.237716	−	0.971335i	$-0.576399\pi$
$859$	4.57849e8	−	7.93018e8i	0.722342	−	1.25113i	0.960059	−	0.279799i	$-0.0902678\pi$
$860$	−1.85715e8	−	3.21669e8i	−0.291980	−	0.505724i
$861$	−2.74903e8	+	4.76145e8i	−0.430695	+	0.745985i
$862$	1.73225e8			0.270451
$863$		−	1.32268e8i		−	0.205789i	−0.994692	−	0.102895i	$-0.967190\pi$
$863$		−	1.32268e8i		−	0.205789i	0.994692	−	0.102895i	$-0.0328104\pi$
$864$	5.97860e7	−	1.03552e8i	0.0926955	−	0.160553i
$865$	−5.42883e8	−	3.13434e8i	−0.838800	−	0.484281i
$866$	−3.83195e8			−0.590019
$867$		−	1.17907e9i		−	1.80919i
$868$	5.06054e8	+	2.92171e8i	0.773816	+	0.446763i
$869$	7.98632e8	−	4.61090e8i	1.21699	−	0.702630i
$870$	−6.22656e8	−	3.59490e8i	−0.945562	−	0.545921i
$871$	−2.31736e8	−	4.01378e8i	−0.350703	−	0.607435i
$872$	−6.56807e7	−	1.13762e8i	−0.0990577	−	0.171573i
$873$			2.64448e7i			0.0397464i
$874$	2.90305e7	+	2.69684e8i	0.0434830	+	0.403944i
$875$	−1.78885e8			−0.267024
$876$	−1.63196e8	+	9.42212e7i	−0.242771	+	0.140164i
$877$	−2.45547e8	+	1.41767e8i	−0.364029	+	0.210172i	−0.670847	−	0.741596i	$-0.734069\pi$
$877$	−2.45547e8	+	1.41767e8i	−0.364029	+	0.210172i	0.306818	+	0.951768i	$0.400736\pi$
$878$	−3.40230e7	+	5.89296e7i	−0.0502677	+	0.0870663i
$879$	5.80185e8	+	1.00491e9i	0.854280	+	1.47966i
$880$	1.84836e8	−	3.20145e8i	0.271231	−	0.469785i
$881$	−2.29004e8			−0.334901			−0.167450	−	0.985881i	$-0.553553\pi$
$881$	−2.29004e8			−0.334901			−0.167450	+	0.985881i	$0.553553\pi$
$882$		−	5.03734e7i		−	0.0734168i
$883$	−8.94334e7	+	1.54903e8i	−0.129902	+	0.224998i	−0.923639	−	0.383265i	$-0.874800\pi$
$883$	−8.94334e7	+	1.54903e8i	−0.129902	+	0.224998i	0.793736	+	0.608262i	$0.208133\pi$
$884$	6.45328e8	+	3.72580e8i	0.934166	+	0.539341i
$885$	1.07036e9			1.54419
$886$			4.92075e8i			0.707507i
$887$	1.25755e8	+	7.26046e7i	0.180200	+	0.104038i	0.587386	−	0.809307i	$-0.300157\pi$
$887$	1.25755e8	+	7.26046e7i	0.180200	+	0.104038i	−0.407187	+	0.913345i	$0.633490\pi$
$888$	−1.95843e8	+	1.13070e8i	−0.279686	+	0.161477i
$889$	7.03034e8	+	4.05897e8i	1.00062	+	0.577710i
$890$	1.80565e8	+	3.12748e8i	0.256132	+	0.443633i
$891$	−4.91186e8	−	8.50759e8i	−0.694405	−	1.20275i
$892$			2.33513e8i			0.329016i
$893$	−4.38782e8	+	9.92225e8i	−0.616161	+	1.39334i
$894$	6.08010e8			0.850938
$895$	8.55958e7	−	4.94188e7i	0.119394	−	0.0689323i
$896$	7.60445e7	−	4.39043e7i	0.105717	−	0.0610356i
$897$	−2.46231e8	+	4.26484e8i	−0.341165	+	0.590915i
$898$	−3.84638e8	−	6.66213e8i	−0.531158	−	0.919992i
$899$	−5.65833e8	+	9.80051e8i	−0.778770	+	1.34887i
$900$	−3.57923e7			−0.0490978
$901$			5.88930e8i			0.805173i
$902$	2.73735e8	−	4.74122e8i	0.373001	−	0.646057i
$903$	−7.10061e8	−	4.09954e8i	−0.964345	−	0.556765i
$904$	−3.12211e8			−0.422613
$905$		−	1.56032e9i		−	2.10507i
$906$	1.54235e8	+	8.90479e7i	0.207396	+	0.119740i
$907$	−1.02435e9	+	5.91408e8i	−1.37286	+	0.792621i	−0.991287	−	0.131718i	$-0.957951\pi$
$907$	−1.02435e9	+	5.91408e8i	−1.37286	+	0.792621i	−0.381573	+	0.924339i	$0.624617\pi$
$908$	−2.76322e8	−	1.59535e8i	−0.369112	−	0.213107i
$909$	4.68478e6	+	8.11428e6i	0.00623732	+	0.0108033i
$910$	6.32971e8	+	1.09634e9i	0.839962	+	1.45486i
$911$		−	1.07316e8i		−	0.141942i	−0.997478	−	0.0709708i	$-0.977390\pi$
$911$		−	1.07316e8i		−	0.141942i	0.997478	−	0.0709708i	$-0.0226097\pi$
$912$	1.63212e8	+	7.21756e7i	0.215163	+	0.0951493i
$913$	1.17206e9			1.54006
$914$	6.91929e8	−	3.99485e8i	0.906198	−	0.523194i
$915$	1.94351e8	−	1.12209e8i	0.253702	−	0.146475i
$916$	−2.85237e8	+	4.94046e8i	−0.371125	+	0.642807i
$917$	−1.72076e8	−	2.98044e8i	−0.223158	−	0.386520i
$918$	−4.90372e8	+	8.49349e8i	−0.633866	+	1.09789i
$919$	8.67281e7			0.111741			0.0558706	−	0.998438i	$-0.482207\pi$
$919$	8.67281e7			0.111741			0.0558706	+	0.998438i	$0.482207\pi$
$920$		−	2.15624e8i		−	0.276907i
$921$	5.80218e8	−	1.00497e9i	0.742699	−	1.28639i
$922$	−2.11271e8	−	1.21978e8i	−0.269555	−	0.155628i
$923$	7.30390e6			0.00928859
$924$		−	8.16025e8i		−	1.03440i
$925$	5.70949e8	+	3.29638e8i	0.721393	+	0.416497i
$926$	−7.26779e8	+	4.19606e8i	−0.915313	+	0.528456i
$927$	5.32023e7	+	3.07164e7i	0.0667869	+	0.0385595i
$928$	8.50274e7	+	1.47272e8i	0.106393	+	0.184279i
$929$	−5.27852e8	−	9.14267e8i	−0.658362	−	1.14032i	−0.981039	−	0.193808i	$-0.937916\pi$
$929$	−5.27852e8	−	9.14267e8i	−0.658362	−	1.14032i	0.322677	−	0.946509i	$-0.395417\pi$
$930$		−	9.44077e8i		−	1.17370i
$931$	7.28007e8	−	7.83672e7i	0.902166	−	0.0971148i
$932$	−2.89617e8			−0.357747
$933$	−1.16243e9	+	6.71132e8i	−1.43128	+	0.826348i
$934$	8.62683e8	−	4.98070e8i	1.05879	−	0.611293i
$935$	−1.51605e9	+	2.62587e9i	−1.85472	+	3.21246i
$936$	−2.09324e7	−	3.62560e7i	−0.0255265	−	0.0442133i
$937$	3.34198e8	−	5.78847e8i	0.406242	−	0.703632i	−0.588223	−	0.808699i	$-0.700172\pi$
$937$	3.34198e8	−	5.78847e8i	0.406242	−	0.703632i	0.994465	+	0.105067i	$0.0335057\pi$
$938$	4.47957e8			0.542785
$939$			1.00247e9i			1.21080i
$940$	4.31228e8	−	7.46908e8i	0.519186	−	0.899257i
$941$	7.92814e8	+	4.57731e8i	0.951486	+	0.549341i	0.893542	−	0.448979i	$-0.148212\pi$
$941$	7.92814e8	+	4.57731e8i	0.951486	+	0.549341i	0.0579438	+	0.998320i	$0.481546\pi$
$942$	6.51369e8			0.779246
$943$		−	3.19331e8i		−	0.380808i
$944$	−2.19246e8	−	1.26582e8i	−0.260625	−	0.150472i
$945$	−1.44295e9	+	8.33085e8i	−1.70984	+	0.987174i
$946$	7.07044e8	+	4.08212e8i	0.835167	+	0.482184i
$947$	2.84686e8	+	4.93091e8i	0.335209	+	0.580600i	0.983525	−	0.180772i	$-0.0578596\pi$
$947$	2.84686e8	+	4.93091e8i	0.335209	+	0.580600i	−0.648316	+	0.761372i	$0.724526\pi$
$948$	−1.76949e8	−	3.06484e8i	−0.207693	−	0.359735i
$949$			6.42580e8i			0.751845i
$950$	−5.56830e7	−	5.17278e8i	−0.0649459	−	0.603327i
$951$	−6.62984e8			−0.770835
$952$	−6.23726e8	+	3.60108e8i	−0.722908	+	0.417371i
$953$	1.37353e9	−	7.93011e8i	1.58694	−	0.916221i	0.593134	−	0.805104i	$-0.297890\pi$
$953$	1.37353e9	−	7.93011e8i	1.58694	−	0.916221i	0.993807	−	0.111118i	$-0.0354430\pi$
$954$	1.65437e7	−	2.86546e7i	0.0190541	−	0.0330026i
$955$	−2.14129e8	−	3.70883e8i	−0.245848	−	0.425820i
$956$	−1.71339e8	+	2.96767e8i	−0.196102	+	0.339658i
$957$	1.58036e9			1.80310
$958$			6.21726e8i			0.707135i
$959$	5.90873e8	−	1.02342e9i	0.669944	−	1.16038i
$960$	−1.22860e8	−	7.09330e7i	−0.138866	−	0.0801742i
$961$	−5.98459e8			−0.674318
$962$			7.71128e8i			0.866166i
$963$	−7.96642e6	−	4.59941e6i	−0.00892040	−	0.00515019i
$964$	−3.51945e7	+	2.03195e7i	−0.0392865	+	0.0226821i
$965$	−1.01877e9	−	5.88186e8i	−1.13369	−	0.654534i
$966$	−2.37988e8	−	4.12207e8i	−0.264012	−	0.457282i
$967$	−1.43965e8	−	2.49354e8i	−0.159212	−	0.275763i	0.775373	−	0.631504i	$-0.217562\pi$
$967$	−1.43965e8	−	2.49354e8i	−0.159212	−	0.275763i	−0.934585	+	0.355740i	$0.884229\pi$
$968$			4.91872e8i			0.542283i
$969$	−1.33868e9	−	5.91992e8i	−1.47132	−	0.650646i
$970$	3.05575e8			0.334813
$971$	−1.24333e9	+	7.17834e8i	−1.35809	+	0.784091i	−0.989366	−	0.145449i	$-0.953537\pi$
$971$	−1.24333e9	+	7.17834e8i	−1.35809	+	0.784091i	−0.368720	+	0.929541i	$0.620204\pi$
$972$	9.05371e7	−	5.22716e7i	0.0985889	−	0.0569203i
$973$	3.60650e7	−	6.24665e7i	0.0391515	−	0.0678123i
$974$	3.31451e8	+	5.74090e8i	0.358709	+	0.621302i
$975$	4.72292e8	−	8.18034e8i	0.509562	−	0.882587i
$976$	−5.30797e7			−0.0570925
$977$		−	1.35543e9i		−	1.45343i	−0.686940	−	0.726715i	$-0.741046\pi$
$977$		−	1.35543e9i		−	1.45343i	0.686940	−	0.726715i	$-0.258954\pi$
$978$	−2.74308e8	+	4.75115e8i	−0.293239	+	0.507905i
$979$	−6.87436e8	−	3.96891e8i	−0.732629	−	0.422983i
$980$	−5.82074e8			−0.618443
$981$		−	6.05330e7i		−	0.0641188i
$982$	5.16137e8	+	2.97992e8i	0.545043	+	0.314681i
$983$	4.46227e8	−	2.57629e8i	0.469781	−	0.271228i	−0.246367	−	0.969177i	$-0.579237\pi$
$983$	4.46227e8	−	2.57629e8i	0.469781	−	0.271228i	0.716148	+	0.697948i	$0.245904\pi$
$984$	−1.81950e8	−	1.05049e8i	−0.190971	−	0.110257i
$985$	−8.38123e8	−	1.45167e9i	−0.876999	−	1.51901i
$986$	−6.97404e8	−	1.20794e9i	−0.727535	−	1.26013i
$987$		−	1.90381e9i		−	1.98003i
$988$	4.91414e8	−	3.58924e8i	0.509538	−	0.372162i
$989$	4.76209e8			0.492276
$990$	1.47527e8	−	8.51749e7i	0.152043	−	0.0877821i
$991$	−2.51972e8	+	1.45476e8i	−0.258900	+	0.149476i	−0.623833	−	0.781558i	$-0.714425\pi$
$991$	−2.51972e8	+	1.45476e8i	−0.258900	+	0.149476i	0.364933	+	0.931034i	$0.381092\pi$
$992$	−1.11647e8	+	1.93379e8i	−0.114370	+	0.198095i
$993$	3.45134e8	+	5.97789e8i	0.352484	+	0.610520i
$994$	−3.52970e6	+	6.11362e6i	−0.00359400	+	0.00622500i
$995$	2.54840e8			0.258701
$996$		−	4.49792e8i		−	0.455233i
$997$	−8.07050e8	+	1.39785e9i	−0.814357	+	1.41051i	0.0954314	+	0.995436i	$0.469577\pi$
$997$	−8.07050e8	+	1.39785e9i	−0.814357	+	1.41051i	−0.909789	+	0.415072i	$0.863756\pi$
$998$	9.49289e8	+	5.48072e8i	0.955008	+	0.551374i
$999$	−1.01492e9			−1.01797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.d.a.31.2	yes	20
3.2	odd	2		342.7.m.a.145.10		20
19.8	odd	6	inner	38.7.d.a.27.2	✓	20
57.8	even	6		342.7.m.a.217.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.d.a.27.2	✓	20	19.8	odd	6	inner
38.7.d.a.31.2	yes	20	1.1	even	1	trivial
342.7.m.a.145.10		20	3.2	odd	2
342.7.m.a.217.10		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)

\(f(q)\)	\(=\)	\(q+(-4.89898 + 2.82843i) q^{2} +(-22.0043 + 12.7042i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-85.1965 - 147.565i) q^{5} +(71.8656 - 124.475i) q^{6} +473.710 q^{7} +181.019i q^{8} +(-41.7080 + 72.2405i) q^{9} +O(q^{10})\)	\(q+(-4.89898 + 2.82843i) q^{2} +(-22.0043 + 12.7042i) q^{3} +(16.0000 - 27.7128i) q^{4} +(-85.1965 - 147.565i) q^{5} +(71.8656 - 124.475i) q^{6} +473.710 q^{7} +181.019i q^{8} +(-41.7080 + 72.2405i) q^{9} +(834.752 + 481.944i) q^{10} -2118.68 q^{11} +813.067i q^{12} +(2401.07 + 1386.26i) q^{13} +(-2320.70 + 1339.85i) q^{14} +(3749.37 + 2164.70i) q^{15} +(-512.000 - 886.810i) q^{16} +(4199.48 + 7273.71i) q^{17} -471.873i q^{18} +(6819.60 - 734.105i) q^{19} -5452.58 q^{20} +(-10423.6 + 6018.09i) q^{21} +(10379.4 - 5992.52i) q^{22} +(3495.35 - 6054.13i) q^{23} +(-2299.70 - 3983.20i) q^{24} +(-6704.40 + 11612.4i) q^{25} -15683.7 q^{26} -20642.1i q^{27} +(7579.36 - 13127.8i) q^{28} +(25424.0 + 14678.6i) q^{29} -24490.8 q^{30} +38548.2i q^{31} +(5016.55 + 2896.31i) q^{32} +(46620.0 - 26916.0i) q^{33} +(-41146.3 - 23755.8i) q^{34} +(-40358.4 - 69902.9i) q^{35} +(1334.66 + 2311.69i) q^{36} -49167.4i q^{37} +(-31332.7 + 22885.1i) q^{38} -70445.1 q^{39} +(26712.1 - 15422.2i) q^{40} +(39559.5 - 22839.7i) q^{41} +(34043.5 - 58965.0i) q^{42} +(34060.1 + 58993.9i) q^{43} +(-33898.8 + 58714.5i) q^{44} +14213.5 q^{45} +39545.4i q^{46} +(-79086.9 + 136983. i) q^{47} +(22532.4 + 13009.1i) q^{48} +106752. q^{49} -75851.6i q^{50} +(-184813. - 106702. i) q^{51} +(76834.3 - 44360.3i) q^{52} +(60725.2 + 35059.7i) q^{53} +(58384.8 + 101125. i) q^{54} +(180504. + 312642. i) q^{55} +85750.7i q^{56} +(-140734. + 102791. i) q^{57} -166069. q^{58} +(214108. - 123615. i) q^{59} +(119980. - 69270.5i) q^{60} +(25917.8 - 44891.0i) q^{61} +(-109031. - 188847. i) q^{62} +(-19757.5 + 34221.0i) q^{63} -32768.0 q^{64} -472418. i q^{65} +(-152260. + 263722. i) q^{66} +(-144770. - 83583.2i) q^{67} +268767. q^{68} +177622. i q^{69} +(395430. + 228302. i) q^{70} +(2281.45 - 1317.20i) q^{71} +(-13076.9 - 7549.96i) q^{72} +(115884. + 200716. i) q^{73} +(139066. + 240870. i) q^{74} -340695. i q^{75} +(88769.5 - 200736. i) q^{76} -1.00364e6 q^{77} +(345109. - 199249. i) q^{78} +(-376948. + 217631. i) q^{79} +(-87241.2 + 151106. i) q^{80} +(231836. + 401552. i) q^{81} +(-129201. + 223782. i) q^{82} -553204. q^{83} +385158. i q^{84} +(715562. - 1.23939e6i) q^{85} +(-333720. - 192673. i) q^{86} -745917. q^{87} -383522. i q^{88} +(324464. + 187330. i) q^{89} +(-69631.8 + 40201.9i) q^{90} +(1.13741e6 + 656685. i) q^{91} +(-111851. - 193732. i) q^{92} +(-489723. - 848225. i) q^{93} -894766. i q^{94} +(-689334. - 943789. i) q^{95} -147181. q^{96} +(274550. - 158512. i) q^{97} +(-522976. + 301940. i) q^{98} +(88365.9 - 153054. 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

Varieties

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