LMFDB - Embedded newform 38.7.d.a.27.8

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			27.8
Root			$5.69488i$ of defining polynomial
Character	$\chi$	$=$	38.27
Dual form			38.7.d.a.31.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(-5.20717 - 3.00636i) q^{3} +(16.0000 + 27.7128i) q^{4} +(116.624 - 201.999i) q^{5} +(-17.0065 - 29.4562i) q^{6} -326.637 q^{7} +181.019i q^{8} +(-346.424 - 600.023i) q^{9} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(-5.20717 - 3.00636i) q^{3} +(16.0000 + 27.7128i) q^{4} +(116.624 - 201.999i) q^{5} +(-17.0065 - 29.4562i) q^{6} -326.637 q^{7} +181.019i q^{8} +(-346.424 - 600.023i) q^{9} +(1142.68 - 659.725i) q^{10} +1873.68 q^{11} -192.407i q^{12} +(2626.92 - 1516.65i) q^{13} +(-1600.19 - 923.870i) q^{14} +(-1214.56 + 701.227i) q^{15} +(-512.000 + 886.810i) q^{16} +(841.664 - 1457.80i) q^{17} -3919.34i q^{18} +(-6803.00 + 874.672i) q^{19} +7463.93 q^{20} +(1700.85 + 981.989i) q^{21} +(9179.12 + 5299.56i) q^{22} +(8854.81 + 15337.0i) q^{23} +(544.209 - 942.598i) q^{24} +(-19389.8 - 33584.1i) q^{25} +17158.9 q^{26} +8549.17i q^{27} +(-5226.20 - 9052.04i) q^{28} +(-25665.4 + 14817.9i) q^{29} -7933.48 q^{30} -12621.8i q^{31} +(-5016.55 + 2896.31i) q^{32} +(-9756.56 - 5632.95i) q^{33} +(8246.59 - 4761.17i) q^{34} +(-38093.7 + 65980.3i) q^{35} +(11085.6 - 19200.7i) q^{36} +30325.0i q^{37} +(-35801.7 - 14956.8i) q^{38} -18238.4 q^{39} +(36565.7 + 21111.2i) q^{40} +(99771.8 + 57603.3i) q^{41} +(5554.97 + 9621.49i) q^{42} +(-9215.51 + 15961.7i) q^{43} +(29978.9 + 51924.9i) q^{44} -161605. q^{45} +100181. i q^{46} +(-61585.4 - 106669. i) q^{47} +(5332.14 - 3078.51i) q^{48} -10957.1 q^{49} -219371. i q^{50} +(-8765.37 + 5060.69i) q^{51} +(84061.3 + 48532.8i) q^{52} +(43811.3 - 25294.5i) q^{53} +(-24180.7 + 41882.2i) q^{54} +(218516. - 378481. i) q^{55} -59127.7i q^{56} +(38053.9 + 15897.7i) q^{57} -167646. q^{58} +(263957. + 152396. i) q^{59} +(-38865.9 - 22439.3i) q^{60} +(144542. + 250354. i) q^{61} +(35699.9 - 61834.0i) q^{62} +(113155. + 195990. i) q^{63} -32768.0 q^{64} -707511. i q^{65} +(-31864.8 - 55191.4i) q^{66} +(66100.7 - 38163.3i) q^{67} +53866.5 q^{68} -106483. i q^{69} +(-373241. + 215491. i) q^{70} +(-62477.6 - 36071.4i) q^{71} +(108616. - 62709.4i) q^{72} +(-105504. + 182739. i) q^{73} +(-85772.1 + 148562. i) q^{74} +233171. i q^{75} +(-133088. - 174536. i) q^{76} -612013. q^{77} +(-89349.5 - 51585.9i) q^{78} +(441185. + 254718. i) q^{79} +(119423. + 206847. i) q^{80} +(-226841. + 392900. i) q^{81} +(325853. + 564394. i) q^{82} +267139. q^{83} +62847.3i q^{84} +(-196316. - 340030. i) q^{85} +(-90293.2 + 52130.8i) q^{86} +178192. q^{87} +339172. i q^{88} +(878847. - 507403. i) q^{89} +(-791701. - 457089. i) q^{90} +(-858049. + 495395. i) q^{91} +(-283354. + 490784. i) q^{92} +(-37945.7 + 65723.9i) q^{93} -696760. i q^{94} +(-616711. + 1.47620e6i) q^{95} +34829.4 q^{96} +(154893. + 89427.6i) q^{97} +(-53678.6 - 30991.4i) q^{98} +(-649087. - 1.12425e6i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$3$	−5.20717	−	3.00636i	−0.192858	−	0.111347i	0.400462	−	0.916313i	$-0.368850\pi$
$3$	−5.20717	−	3.00636i	−0.192858	−	0.111347i	−0.593320	+	0.804967i	$0.702183\pi$
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	116.624	−	201.999i	0.932992	−	1.61599i	0.154815	−	0.987943i	$-0.450522\pi$
$5$	116.624	−	201.999i	0.932992	−	1.61599i	0.778176	−	0.628046i	$-0.216145\pi$
$6$	−17.0065	−	29.4562i	−0.0787339	−	0.136371i
$7$	−326.637			−0.952295			−0.476148	−	0.879365i	$-0.657967\pi$
$7$	−326.637			−0.952295			−0.476148	+	0.879365i	$0.657967\pi$
$8$			181.019i			0.353553i
$9$	−346.424	−	600.023i	−0.475204	−	0.823077i
$10$	1142.68	−	659.725i	1.14268	−	0.659725i
$11$	1873.68			1.40772			0.703861	−	0.710337i	$-0.251458\pi$
$11$	1873.68			1.40772			0.703861	+	0.710337i	$0.251458\pi$
$12$		−	192.407i		−	0.111347i
$13$	2626.92	−	1516.65i	1.19568	−	0.690328i	0.236093	−	0.971730i	$-0.424133\pi$
$13$	2626.92	−	1516.65i	1.19568	−	0.690328i	0.959590	+	0.281402i	$0.0907995\pi$
$14$	−1600.19	−	923.870i	−0.583159	−	0.336687i
$15$	−1214.56	+	701.227i	−0.359870	+	0.207771i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	841.664	−	1457.80i	0.171314	−	0.296724i	−0.767566	−	0.640970i	$-0.778532\pi$
$17$	841.664	−	1457.80i	0.171314	−	0.296724i	0.938879	+	0.344246i	$0.111866\pi$
$18$		−	3919.34i		−	0.672040i
$19$	−6803.00	+	874.672i	−0.991836	+	0.127522i
$19$	−6803.00	+	874.672i	−0.991836	+	0.127522i
$20$	7463.93			0.932992
$21$	1700.85	+	981.989i	0.183658	+	0.106035i
$22$	9179.12	+	5299.56i	0.862051	+	0.497705i
$23$	8854.81	+	15337.0i	0.727773	+	1.26054i	0.957822	+	0.287361i	$0.0927779\pi$
$23$	8854.81	+	15337.0i	0.727773	+	1.26054i	−0.230049	+	0.973179i	$0.573889\pi$
$24$	544.209	−	942.598i	0.0393670	−	0.0681856i
$25$	−19389.8	−	33584.1i	−1.24095	−	2.14938i
$26$	17158.9			0.976271
$27$			8549.17i			0.434343i
$28$	−5226.20	−	9052.04i	−0.238074	−	0.412356i
$29$	−25665.4	+	14817.9i	−1.05234	+	0.607566i	−0.923302	−	0.384074i	$-0.874521\pi$
$29$	−25665.4	+	14817.9i	−1.05234	+	0.607566i	−0.129033	+	0.991640i	$0.541187\pi$
$30$	−7933.48			−0.293833
$31$		−	12621.8i		−	0.423679i	−0.977304	−	0.211839i	$-0.932055\pi$
$31$		−	12621.8i		−	0.423679i	0.977304	−	0.211839i	$-0.0679454\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$	−9756.56	−	5632.95i	−0.271491	−	0.156745i
$34$	8246.59	−	4761.17i	0.209816	−	0.121137i
$35$	−38093.7	+	65980.3i	−0.888484	+	1.53890i
$36$	11085.6	−	19200.7i	0.237602	−	0.411539i
$37$			30325.0i			0.598682i	0.954146	+	0.299341i	$0.0967667\pi$
$37$			30325.0i			0.598682i	−0.954146	+	0.299341i	$0.903233\pi$
$38$	−35801.7	−	14956.8i	−0.652459	−	0.272576i
$39$	−18238.4			−0.307463
$40$	36565.7	+	21111.2i	0.571338	+	0.329862i
$41$	99771.8	+	57603.3i	1.44763	+	0.835787i	0.998340	−	0.0576012i	$-0.0183452\pi$
$41$	99771.8	+	57603.3i	1.44763	+	0.835787i	0.449286	+	0.893388i	$0.351679\pi$
$42$	5554.97	+	9621.49i	0.0749780	+	0.129866i
$43$	−9215.51	+	15961.7i	−0.115908	+	0.200759i	−0.918142	−	0.396251i	$-0.870311\pi$
$43$	−9215.51	+	15961.7i	−0.115908	+	0.200759i	0.802234	+	0.597009i	$0.203644\pi$
$44$	29978.9	+	51924.9i	0.351931	+	0.609562i
$45$	−161605.			−1.77345
$46$			100181.i			1.02923i
$47$	−61585.4	−	106669.i	−0.593177	−	1.02741i	−0.993801	−	0.111171i	$-0.964540\pi$
$47$	−61585.4	−	106669.i	−0.593177	−	1.02741i	0.400624	−	0.916243i	$-0.368793\pi$
$48$	5332.14	−	3078.51i	0.0482145	−	0.0278367i
$49$	−10957.1			−0.0931338
$50$		−	219371.i		−	1.75496i
$51$	−8765.37	+	5060.69i	−0.0660784	+	0.0381504i
$52$	84061.3	+	48532.8i	0.597842	+	0.345164i
$53$	43811.3	−	25294.5i	0.294279	−	0.169902i	−0.345591	−	0.938385i	$-0.612322\pi$
$53$	43811.3	−	25294.5i	0.294279	−	0.169902i	0.639870	+	0.768483i	$0.278988\pi$
$54$	−24180.7	+	41882.2i	−0.153563	+	0.265979i
$55$	218516.	−	378481.i	1.31339	−	2.27486i
$56$		−	59127.7i		−	0.336687i
$57$	38053.9	+	15897.7i	0.205483	+	0.0858440i
$58$	−167646.			−0.859229
$59$	263957.	+	152396.i	1.28522	+	0.742021i	0.977798	−	0.209552i	$-0.0672005\pi$
$59$	263957.	+	152396.i	1.28522	+	0.742021i	0.307421	+	0.951573i	$0.400534\pi$
$60$	−38865.9	−	22439.3i	−0.179935	−	0.103885i
$61$	144542.	+	250354.i	0.636801	+	1.10297i	0.986130	+	0.165972i	$0.0530762\pi$
$61$	144542.	+	250354.i	0.636801	+	1.10297i	−0.349329	+	0.937000i	$0.613590\pi$
$62$	35699.9	−	61834.0i	0.149793	−	0.259449i
$63$	113155.	+	195990.i	0.452534	+	0.783813i
$64$	−32768.0			−0.125000
$65$		−	707511.i		−	2.57628i
$66$	−31864.8	−	55191.4i	−0.110836	−	0.191973i
$67$	66100.7	−	38163.3i	0.219777	−	0.126888i	−0.386070	−	0.922469i	$-0.626168\pi$
$67$	66100.7	−	38163.3i	0.219777	−	0.126888i	0.605847	+	0.795581i	$0.292834\pi$
$68$	53866.5			0.171314
$69$		−	106483.i		−	0.324140i
$70$	−373241.	+	215491.i	−1.08817	+	0.628253i
$71$	−62477.6	−	36071.4i	−0.174562	−	0.100783i	0.410173	−	0.912008i	$-0.365468\pi$
$71$	−62477.6	−	36071.4i	−0.174562	−	0.100783i	−0.584735	+	0.811224i	$0.698802\pi$
$72$	108616.	−	62709.4i	0.291002	−	0.168010i
$73$	−105504.	+	182739.i	−0.271208	+	0.469745i	−0.969171	−	0.246388i	$-0.920756\pi$
$73$	−105504.	+	182739.i	−0.271208	+	0.469745i	0.697964	+	0.716133i	$0.254090\pi$
$74$	−85772.1	+	148562.i	−0.211666	+	0.366616i
$75$			233171.i			0.552701i
$76$	−133088.	−	174536.i	−0.303177	−	0.397597i
$77$	−612013.			−1.34057
$78$	−89349.5	−	51585.9i	−0.188282	−	0.108705i
$79$	441185.	+	254718.i	0.894828	+	0.516629i	0.875519	−	0.483184i	$-0.160520\pi$
$79$	441185.	+	254718.i	0.894828	+	0.516629i	0.0193096	+	0.999814i	$0.493853\pi$
$80$	119423.	+	206847.i	0.233248	+	0.403997i
$81$	−226841.	+	392900.i	−0.426841	+	0.739311i
$82$	325853.	+	564394.i	0.590991	+	1.02363i
$83$	267139.			0.467200			0.233600	−	0.972333i	$-0.424949\pi$
$83$	267139.			0.467200			0.233600	+	0.972333i	$0.424949\pi$
$84$			62847.3i			0.106035i
$85$	−196316.	−	340030.i	−0.319669	−	0.553682i
$86$	−90293.2	+	52130.8i	−0.141958	+	0.0819594i
$87$	178192.			0.270602
$88$			339172.i			0.497705i
$89$	878847.	−	507403.i	1.24665	−	0.719752i	0.276207	−	0.961098i	$-0.410922\pi$
$89$	878847.	−	507403.i	1.24665	−	0.719752i	0.970439	+	0.241347i	$0.0775890\pi$
$90$	−791701.	−	457089.i	−1.08601	−	0.627008i
$91$	−858049.	+	495395.i	−1.13864	+	0.657396i
$92$	−283354.	+	490784.i	−0.363886	+	0.630270i
$93$	−37945.7	+	65723.9i	−0.0471752	+	0.0817099i
$94$		−	696760.i		−	0.838879i
$95$	−616711.	+	1.47620e6i	−0.719301	+	1.72177i
$96$	34829.4			0.0393670
$97$	154893.	+	89427.6i	0.169714	+	0.0979843i	0.582451	−	0.812866i	$-0.302094\pi$
$97$	154893.	+	89427.6i	0.169714	+	0.0979843i	−0.412737	+	0.910850i	$0.635427\pi$
$98$	−53678.6	−	30991.4i	−0.0570326	−	0.0329278i
$99$	−649087.	−	1.12425e6i	−0.668955	−	1.15866i
$100$	620474.	−	1.07469e6i	0.620474	−	1.07469i
$101$	−229275.	−	397117.i	−0.222533	−	0.385438i	0.733044	−	0.680181i	$-0.238099\pi$
$101$	−229275.	−	397117.i	−0.222533	−	0.385438i	−0.955576	+	0.294744i	$0.904766\pi$
$102$	−57255.2			−0.0539528
$103$			389239.i			0.356209i	0.984012	+	0.178104i	$0.0569965\pi$
$103$			389239.i			0.356209i	−0.984012	+	0.178104i	$0.943003\pi$
$104$	274543.	+	475523.i	0.244068	+	0.422738i
$105$	396721.	−	229047.i	0.342702	−	0.197859i
$106$	286174.			0.240278
$107$			779465.i			0.636276i	0.948044	+	0.318138i	$0.103057\pi$
$107$			779465.i			0.636276i	−0.948044	+	0.318138i	$0.896943\pi$
$108$	−236921.	+	136787.i	−0.188076	+	0.108586i
$109$	−809716.	−	467490.i	−0.625250	−	0.360988i	0.153660	−	0.988124i	$-0.450894\pi$
$109$	−809716.	−	467490.i	−0.625250	−	0.360988i	−0.778910	+	0.627136i	$0.784227\pi$
$110$	2.14101e6	−	1.23611e6i	1.60857	−	0.928710i
$111$	91167.9	−	157907.i	0.0666612	−	0.115461i
$112$	167238.	−	289665.i	0.119037	−	0.206178i
$113$		−	906516.i		−	0.628261i	−0.949380	−	0.314131i	$-0.898287\pi$
$113$		−	906516.i		−	0.628261i	0.949380	−	0.314131i	$-0.101713\pi$
$114$	141460.	+	185515.i	0.0954814	+	0.125218i
$115$	4.13073e6			2.71602
$116$	−821293.	−	474174.i	−0.526168	−	0.303783i
$117$	−1.82005e6	−	1.05081e6i	−1.13639	−	0.656093i
$118$	862080.	+	1.49317e6i	0.524688	+	0.908787i
$119$	−274919.	+	476173.i	−0.163141	+	0.282569i
$120$	−126936.	−	219859.i	−0.0734581	−	0.127233i
$121$	1.73911e6			0.981684
$122$			1.63530e6i			0.900573i
$123$	−346352.	−	599900.i	−0.186124	−	0.322376i
$124$	349786.	−	201949.i	0.183458	−	0.105920i
$125$	−5.40076e6			−2.76519
$126$			1.28020e6i			0.639980i
$127$	−915288.	+	528442.i	−0.446834	+	0.257980i	−0.706492	−	0.707721i	$-0.749723\pi$
$127$	−915288.	+	528442.i	−0.446834	+	0.257980i	0.259658	+	0.965701i	$0.416390\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$	95973.4	−	55410.3i	0.0447076	−	0.0258120i
$130$	2.00114e6	−	3.46608e6i	0.910853	−	1.57764i
$131$	−501394.	+	868440.i	−0.223031	+	0.386301i	−0.955727	−	0.294255i	$-0.904928\pi$
$131$	−501394.	+	868440.i	−0.223031	+	0.386301i	0.732696	+	0.680556i	$0.238262\pi$
$132$		−	360509.i		−	0.156745i
$133$	2.22211e6	−	285700.i	0.944520	−	0.121438i
$134$	431768.			0.179447
$135$	1.72692e6	+	997038.i	0.701893	+	0.405238i
$136$	263891.	+	152357.i	0.104908	+	0.0605685i
$137$	−1.51478e6	−	2.62367e6i	−0.589098	−	1.02035i	−0.994351	−	0.106143i	$-0.966150\pi$
$137$	−1.51478e6	−	2.62367e6i	−0.589098	−	1.02035i	0.405253	−	0.914205i	$-0.367184\pi$
$138$	301179.	−	521658.i	0.114601	−	0.198495i
$139$	78300.9	+	135621.i	0.0291556	+	0.0504990i	0.880235	−	0.474538i	$-0.157385\pi$
$139$	78300.9	+	135621.i	0.0291556	+	0.0504990i	−0.851079	+	0.525037i	$0.824051\pi$
$140$	−2.43800e6			−0.888484
$141$			740592.i			0.264193i
$142$	−204051.	−	353426.i	−0.0712645	−	0.123434i
$143$	4.92200e6	−	2.84172e6i	1.68319	−	0.971791i
$144$	709476.			0.237602
$145$			6.91251e6i			2.26742i
$146$	−1.03373e6	+	596823.i	−0.332160	+	0.191773i
$147$	57055.4	+	32941.0i	0.0179616	+	0.0103701i
$148$	−840392.	+	485200.i	−0.259237	+	0.149670i
$149$	−954478.	+	1.65320e6i	−0.288541	+	0.499767i	−0.973462	−	0.228850i	$-0.926503\pi$
$149$	−954478.	+	1.65320e6i	−0.288541	+	0.499767i	0.684921	+	0.728617i	$0.259837\pi$
$150$	−659507.	+	1.14230e6i	−0.195409	+	0.338459i
$151$		−	923037.i		−	0.268095i	−0.990975	−	0.134047i	$-0.957203\pi$
$151$		−	923037.i		−	0.268095i	0.990975	−	0.134047i	$-0.0427974\pi$
$152$	−158333.	−	1.23147e6i	−0.0450858	−	0.350667i
$153$	−1.16629e6			−0.325636
$154$	−2.99824e6	−	1.73104e6i	−0.820927	−	0.473962i
$155$	−2.54959e6	−	1.47201e6i	−0.684661	−	0.395289i
$156$	−291814.	−	505437.i	−0.0768657	−	0.133135i
$157$	−128042.	+	221776.i	−0.0330868	+	0.0573080i	−0.882095	−	0.471072i	$-0.843867\pi$
$157$	−128042.	+	221776.i	−0.0330868	+	0.0573080i	0.849008	+	0.528380i	$0.177200\pi$
$158$	1.44090e6	+	2.49572e6i	0.365312	+	0.632739i
$159$	−304177.			−0.0756720
$160$			1.35112e6i			0.329862i
$161$	−2.89231e6	−	5.00963e6i	−0.693055	−	1.20041i
$162$	−2.22258e6	+	1.28321e6i	−0.522772	+	0.301822i
$163$	793580.			0.183243			0.0916216	−	0.995794i	$-0.470795\pi$
$163$	793580.			0.183243			0.0916216	+	0.995794i	$0.470795\pi$
$164$			3.68661e6i			0.835787i
$165$	−2.27570e6	+	1.31387e6i	−0.506597	+	0.292484i
$166$	1.30871e6	+	755583.i	0.286101	+	0.165180i
$167$	−4.08967e6	+	2.36117e6i	−0.878090	+	0.506965i	−0.870028	−	0.493002i	$-0.835899\pi$
$167$	−4.08967e6	+	2.36117e6i	−0.878090	+	0.506965i	−0.00806166	+	0.999968i	$0.502566\pi$
$168$	−177759.	+	307888.i	−0.0374890	+	0.0649328i
$169$	2.18705e6	−	3.78809e6i	0.453106	−	0.784802i
$170$		−	2.22107e6i		−	0.452080i
$171$	2.88154e6	+	3.77895e6i	0.576284	+	0.755759i
$172$	−589793.			−0.115908
$173$	−1.09335e6	−	631246.i	−0.211164	−	0.121916i	0.390688	−	0.920523i	$-0.372237\pi$
$173$	−1.09335e6	−	631246.i	−0.211164	−	0.121916i	−0.601852	+	0.798607i	$0.705570\pi$
$174$	872960.	+	504003.i	0.165709	+	0.0956722i
$175$	6.33343e6	+	1.09698e7i	1.18175	+	2.04685i
$176$	−959324.	+	1.66160e6i	−0.175965	+	0.304781i
$177$	−916312.	−	1.58710e6i	−0.165243	−	0.286210i
$178$	5.74060e6			1.01788
$179$		−	995599.i		−	0.173590i	−0.996226	−	0.0867951i	$-0.972337\pi$
$179$		−	995599.i		−	0.173590i	0.996226	−	0.0867951i	$-0.0276625\pi$
$180$	−2.58568e6	−	4.47853e6i	−0.443361	−	0.767924i
$181$	8.17517e6	−	4.71994e6i	1.37867	−	0.795977i	0.386673	−	0.922217i	$-0.373624\pi$
$181$	8.17517e6	−	4.71994e6i	1.37867	−	0.795977i	0.992000	+	0.126240i	$0.0402909\pi$
$182$	−5.60475e6			−0.929698
$183$		−	1.73818e6i		−	0.283623i
$184$	−2.77629e6	+	1.60289e6i	−0.445668	+	0.257307i
$185$	6.12561e6	+	3.53662e6i	0.967463	+	0.558565i
$186$	−371791.	+	214653.i	−0.0577776	+	0.0333579i
$187$	1.57701e6	−	2.73146e6i	0.241162	−	0.417705i
$188$	1.97073e6	−	3.41341e6i	0.296589	−	0.513707i
$189$		−	2.79248e6i		−	0.413622i
$190$	−7.19659e6	+	5.48758e6i	−1.04922	+	0.800055i
$191$	−7.04374e6			−1.01089			−0.505444	−	0.862859i	$-0.668671\pi$
$191$	−7.04374e6			−1.01089			−0.505444	+	0.862859i	$0.668671\pi$
$192$	170628.	+	98512.4i	0.0241072	+	0.0139183i
$193$	−5.14388e6	−	2.96982e6i	−0.715516	−	0.413103i	0.0975843	−	0.995227i	$-0.468888\pi$
$193$	−5.14388e6	−	2.96982e6i	−0.715516	−	0.413103i	−0.813100	+	0.582124i	$0.802222\pi$
$194$	505879.	+	876208.i	0.0692854	+	0.120006i
$195$	−2.12703e6	+	3.68413e6i	−0.286860	+	0.496857i
$196$	−175314.	−	303652.i	−0.0232835	−	0.0403281i
$197$	1.10256e6			0.144213			0.0721063	−	0.997397i	$-0.477028\pi$
$197$	1.10256e6			0.144213			0.0721063	+	0.997397i	$0.477028\pi$
$198$		−	7.34358e6i		−	0.946046i
$199$	1.73434e6	+	3.00397e6i	0.220077	+	0.381185i	0.954831	−	0.297149i	$-0.0960357\pi$
$199$	1.73434e6	+	3.00397e6i	0.220077	+	0.381185i	−0.734754	+	0.678334i	$0.762702\pi$
$200$	6.07938e6	−	3.50993e6i	0.759922	−	0.438741i
$201$	−458930.			−0.0565143
$202$		−	2.59396e6i		−	0.314708i
$203$	8.38328e6	−	4.84009e6i	1.00213	−	0.578583i
$204$	−280492.	−	161942.i	−0.0330392	−	0.0190752i
$205$	2.32716e7	−	1.34358e7i	2.70125	−	1.55956i
$206$	−1.10093e6	+	1.90687e6i	−0.125939	+	0.218133i
$207$	6.13503e6	−	1.06262e7i	0.691681	−	1.19803i
$208$			3.10610e6i			0.345164i
$209$	−1.27466e7	+	1.63885e6i	−1.39623	+	0.179515i
$210$	2.59137e6			0.279815
$211$	−4.04111e6	−	2.33314e6i	−0.430183	−	0.248366i	0.269241	−	0.963073i	$-0.413227\pi$
$211$	−4.04111e6	−	2.33314e6i	−0.430183	−	0.248366i	−0.699425	+	0.714706i	$0.746560\pi$
$212$	1.40196e6	+	809423.i	0.147139	+	0.0849509i
$213$	216887.	+	375660.i	0.0224438	+	0.0388737i
$214$	−2.20466e6	+	3.81858e6i	−0.224957	+	0.389638i
$215$	2.14950e6	+	3.72304e6i	0.216283	+	0.374613i
$216$	−1.54756e6			−0.153563
$217$			4.12276e6i			0.403467i
$218$	−2.64452e6	−	4.58045e6i	−0.255257	−	0.442118i
$219$	1.09876e6	−	634368.i	0.104609	−	0.0603961i
$220$	1.39850e7			1.31339
$221$		−	5.10604e6i		−	0.473051i
$222$	893259.	−	515723.i	0.0816429	−	0.0471366i
$223$	−1.56975e7	−	9.06296e6i	−1.41552	−	0.817251i	−0.419619	−	0.907700i	$-0.637836\pi$
$223$	−1.56975e7	−	9.06296e6i	−1.41552	−	0.817251i	−0.995901	+	0.0904493i	$0.971170\pi$
$224$	1.63859e6	−	946043.i	0.145790	−	0.0841718i
$225$	−1.34342e7	+	2.32687e7i	−1.17941	+	2.04279i
$226$	2.56402e6	−	4.44100e6i	0.222124	−	0.384730i
$227$		−	1.58093e6i		−	0.135156i	−0.997714	−	0.0675778i	$-0.978473\pi$
$227$		−	1.58093e6i		−	0.135156i	0.997714	−	0.0675778i	$-0.0215271\pi$
$228$	168293.	+	1.30894e6i	0.0141991	+	0.110438i
$229$	1.86092e6			0.154961			0.0774803	−	0.996994i	$-0.475313\pi$
$229$	1.86092e6			0.154961			0.0774803	+	0.996994i	$0.475313\pi$
$230$	2.02364e7	+	1.16835e7i	1.66322	+	0.960260i
$231$	3.18686e6	+	1.83993e6i	0.258539	+	0.149268i
$232$	−2.68233e6	−	4.64594e6i	−0.214807	−	0.372057i
$233$	−6.91739e6	+	1.19813e7i	−0.546858	+	0.947186i	0.451629	+	0.892206i	$0.350843\pi$
$233$	−6.91739e6	+	1.19813e7i	−0.546858	+	0.947186i	−0.998487	+	0.0549802i	$0.982490\pi$
$234$	−5.94426e6	−	1.02958e7i	−0.463928	−	0.803547i
$235$	−2.87294e7			−2.21372
$236$			9.75332e6i			0.742021i
$237$	−1.53155e6	−	2.65272e6i	−0.115050	−	0.199272i
$238$	−2.69364e6	+	1.55518e6i	−0.199806	+	0.115358i
$239$	−1.11799e6			−0.0818927			−0.0409464	−	0.999161i	$-0.513037\pi$
$239$	−1.11799e6			−0.0818927			−0.0409464	+	0.999161i	$0.513037\pi$
$240$		−	1.43611e6i		−	0.103885i
$241$	−4.41772e6	+	2.55057e6i	−0.315607	+	0.182216i	−0.649433	−	0.760419i	$-0.724994\pi$
$241$	−4.41772e6	+	2.55057e6i	−0.315607	+	0.182216i	0.333826	+	0.942635i	$0.391660\pi$
$242$	8.51988e6	+	4.91895e6i	0.601156	+	0.347078i
$243$	7.75976e6	−	4.48010e6i	0.540791	−	0.312226i
$244$	−4.62534e6	+	8.01132e6i	−0.318401	+	0.551486i
$245$	−1.27786e6	+	2.21332e6i	−0.0868931	+	0.150503i
$246$		−	3.91853e6i		−	0.263219i
$247$	−1.65443e7	+	1.26155e7i	−1.09789	+	0.837168i
$248$	2.28479e6			0.149793
$249$	−1.39104e6	−	803116.i	−0.0901033	−	0.0520212i
$250$	−2.64582e7	−	1.52757e7i	−1.69333	−	0.977643i
$251$	1.48395e7	+	2.57028e7i	0.938422	+	1.62539i	0.768415	+	0.639952i	$0.221046\pi$
$251$	1.48395e7	+	2.57028e7i	0.938422	+	1.62539i	0.170007	+	0.985443i	$0.445621\pi$
$252$	−3.62096e6	+	6.27168e6i	−0.226267	+	0.391906i
$253$	1.65911e7	+	2.87366e7i	1.02450	+	1.77449i
$254$	−5.97863e6			−0.364839
$255$			2.36079e6i			0.142376i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.48785e7	+	8.59011e6i	−0.876517	+	0.506057i	−0.869508	−	0.493918i	$-0.835564\pi$
$257$	−1.48785e7	+	8.59011e6i	−0.876517	+	0.506057i	−0.00700825	+	0.999975i	$0.502231\pi$
$258$	626895.			0.0365036
$259$		−	9.90528e6i		−	0.570122i
$260$	1.96071e7	−	1.13202e7i	1.11556	−	0.644070i
$261$	1.77822e7	+	1.02666e7i	1.00015	+	0.577436i
$262$	−4.91264e6	+	2.83631e6i	−0.273156	+	0.157707i
$263$	1.71224e7	−	2.96569e7i	0.941236	−	1.63027i	0.178117	−	0.984009i	$-0.442999\pi$
$263$	1.71224e7	−	2.96569e7i	0.941236	−	1.63027i	0.763118	−	0.646259i	$-0.223667\pi$
$264$	1.01967e6	−	1.76613e6i	0.0554178	−	0.0959864i
$265$		−	1.17998e7i		−	0.634068i
$266$	1.16942e7	+	4.88545e6i	0.621333	+	0.259573i
$267$	−6.10174e6			−0.320568
$268$	2.11522e6	+	1.22122e6i	0.109888	+	0.0634441i
$269$	−1.15758e7	−	6.68330e6i	−0.594695	−	0.343347i	0.172257	−	0.985052i	$-0.444894\pi$
$269$	−1.15758e7	−	6.68330e6i	−0.594695	−	0.343347i	−0.766952	+	0.641705i	$0.778228\pi$
$270$	5.64010e6	+	9.76893e6i	0.286547	+	0.496313i
$271$	−3.90299e6	+	6.76018e6i	−0.196105	+	0.339664i	−0.947262	−	0.320459i	$-0.896163\pi$
$271$	−3.90299e6	+	6.76018e6i	−0.196105	+	0.339664i	0.751157	+	0.660124i	$0.229496\pi$
$272$	861864.	+	1.49279e6i	0.0428284	+	0.0741810i
$273$	5.95734e6			0.292795
$274$		−	1.71378e7i		−	0.833111i
$275$	−3.63303e7	−	6.29259e7i	−1.74691	−	3.02574i
$276$	2.95094e6	−	1.70373e6i	0.140357	−	0.0810351i
$277$	4.78394e6			0.225085			0.112542	−	0.993647i	$-0.464101\pi$
$277$	4.78394e6			0.225085			0.112542	+	0.993647i	$0.464101\pi$
$278$			885873.i			0.0412323i
$279$	−7.57339e6	+	4.37250e6i	−0.348720	+	0.201334i
$280$	−1.19437e7	−	6.89570e6i	−0.544083	−	0.314126i
$281$	1.80441e7	−	1.04177e7i	0.813234	−	0.469521i	−0.0348438	−	0.999393i	$-0.511093\pi$
$281$	1.80441e7	−	1.04177e7i	0.813234	−	0.469521i	0.848078	+	0.529872i	$0.177760\pi$
$282$	−2.09471e6	+	3.62814e6i	−0.0934064	+	0.161785i
$283$	−1.47334e7	+	2.55190e7i	−0.650045	+	1.12591i	0.333067	+	0.942903i	$0.391917\pi$
$283$	−1.47334e7	+	2.55190e7i	−0.650045	+	1.12591i	−0.983112	+	0.183007i	$0.941417\pi$
$284$		−	2.30857e6i		−	0.100783i
$285$	7.64932e6	−	5.83279e6i	0.330436	−	0.251966i
$286$	3.21504e7			1.37432
$287$	−3.25892e7	−	1.88154e7i	−1.37857	−	0.795916i
$288$	3.47571e6	+	2.00670e6i	0.145501	+	0.0840050i
$289$	1.06520e7	+	1.84498e7i	0.441303	+	0.764360i
$290$	−1.95515e7	+	3.38642e7i	−0.801653	+	1.38850i
$291$	−537703.	−	931329.i	−0.0218204	−	0.0377941i
$292$	−6.75228e6			−0.271208
$293$		−	1.56557e7i		−	0.622401i	−0.950344	−	0.311201i	$-0.899269\pi$
$293$		−	1.56557e7i		−	0.622401i	0.950344	−	0.311201i	$-0.100731\pi$
$294$	186342.	+	322754.i	0.00733279	+	0.0127008i
$295$	6.15674e7	−	3.55460e7i	2.39820	−	1.38460i
$296$	−5.48941e6			−0.211666
$297$			1.60184e7i			0.611434i
$298$	−9.35194e6	+	5.39934e6i	−0.353389	+	0.204029i
$299$	4.65217e7	+	2.68593e7i	1.74037	+	1.00480i
$300$	−6.46182e6	+	3.73073e6i	−0.239327	+	0.138175i
$301$	3.01013e6	−	5.21370e6i	0.110379	−	0.191182i
$302$	2.61074e6	−	4.52194e6i	0.0947858	−	0.164174i
$303$			2.75714e6i			0.0991130i
$304$	2.70747e6	−	6.48080e6i	0.0963702	−	0.230679i
$305$	6.74282e7			2.37652
$306$	−5.71363e6	−	3.29876e6i	−0.199410	−	0.115130i
$307$	−3.75862e7	−	2.17004e7i	−1.29901	−	0.749985i	−0.318779	−	0.947829i	$-0.603273\pi$
$307$	−3.75862e7	−	2.17004e7i	−1.29901	−	0.749985i	−0.980233	+	0.197844i	$0.936606\pi$
$308$	−9.79221e6	−	1.69606e7i	−0.335142	−	0.580483i
$309$	1.17019e6	−	2.02683e6i	0.0396627	−	0.0686978i
$310$	−8.32693e6	−	1.44227e7i	−0.279512	−	0.484128i
$311$	−5.53187e6			−0.183904			−0.0919520	−	0.995763i	$-0.529311\pi$
$311$	−5.53187e6			−0.183904			−0.0919520	+	0.995763i	$0.529311\pi$
$312$		−	3.30150e6i		−	0.108705i
$313$	1.71262e7	+	2.96634e7i	0.558506	+	0.967360i	0.997622	+	0.0689296i	$0.0219584\pi$
$313$	1.71262e7	+	2.96634e7i	0.558506	+	0.967360i	−0.439116	+	0.898430i	$0.644708\pi$
$314$	−1.25455e6	+	724317.i	−0.0405229	+	0.0233959i
$315$	5.27863e7			1.68884
$316$			1.63020e7i			0.516629i
$317$	1.46088e7	−	8.43437e6i	0.458601	−	0.264774i	−0.252855	−	0.967504i	$-0.581369\pi$
$317$	1.46088e7	−	8.43437e6i	0.458601	−	0.264774i	0.711456	+	0.702731i	$0.248036\pi$
$318$	−1.49016e6	−	860343.i	−0.0463394	−	0.0267541i
$319$	−4.80888e7	+	2.77641e7i	−1.48140	+	0.855285i
$320$	−3.82153e6	+	6.61909e6i	−0.116624	+	0.201999i
$321$	2.34335e6	−	4.05880e6i	0.0708471	−	0.122711i
$322$		−	3.27228e7i		−	0.980127i
$323$	−4.45074e6	+	1.06536e7i	−0.132076	+	0.316148i
$324$	−1.45178e7			−0.426841
$325$	−1.01871e8	−	5.88151e7i	−2.96756	−	1.71332i
$326$	3.88773e6	+	2.24458e6i	0.112213	+	0.0647863i
$327$	2.81088e6	+	4.86860e6i	0.0803896	+	0.139239i
$328$	−1.04273e7	+	1.80606e7i	−0.295495	+	0.511813i
$329$	2.01161e7	+	3.48421e7i	0.564880	+	0.978401i
$330$	−1.48648e7			−0.413635
$331$			3.12540e7i			0.861830i	0.902393	+	0.430915i	$0.141809\pi$
$331$			3.12540e7i			0.861830i	−0.902393	+	0.430915i	$0.858191\pi$
$332$	4.27422e6	+	7.40317e6i	0.116800	+	0.202304i
$333$	1.81957e7	−	1.05053e7i	0.492761	−	0.284496i
$334$	−2.67136e7			−0.716957
$335$		−	1.78030e7i		−	0.473542i
$336$	−1.74167e6	+	1.00556e6i	−0.0459144	+	0.0265087i
$337$	−582358.	−	336224.i	−0.0152160	−	0.00878496i	0.492373	−	0.870384i	$-0.336130\pi$
$337$	−582358.	−	336224.i	−0.0152160	−	0.00878496i	−0.507589	+	0.861600i	$0.669463\pi$
$338$	2.14287e7	−	1.23718e7i	0.554939	−	0.320394i
$339$	−2.72531e6	+	4.72038e6i	−0.0699548	+	0.121165i
$340$	6.28213e6	−	1.08810e7i	0.159834	−	0.276841i
$341$		−	2.36492e7i		−	0.596423i
$342$	3.42813e6	+	2.66632e7i	0.0856997	+	0.666553i
$343$	4.20075e7			1.04099
$344$	−2.88938e6	−	1.66819e6i	−0.0709790	−	0.0409797i
$345$	−2.15094e7	−	1.24185e7i	−0.523807	−	0.302420i
$346$	−3.57087e6	−	6.18492e6i	−0.0862075	−	0.149316i
$347$	−6.93857e6	+	1.20180e7i	−0.166066	+	0.287635i	−0.937033	−	0.349240i	$-0.886440\pi$
$347$	−6.93857e6	+	1.20180e7i	−0.166066	+	0.287635i	0.770967	+	0.636875i	$0.219773\pi$
$348$	2.85107e6	+	4.93820e6i	0.0676505	+	0.117174i
$349$	−6.80606e6			−0.160110			−0.0800552	−	0.996790i	$-0.525510\pi$
$349$	−6.80606e6			−0.160110			−0.0800552	+	0.996790i	$0.525510\pi$
$350$			7.16546e7i			1.67124i
$351$	1.29661e7	+	2.24579e7i	0.299839	+	0.519336i
$352$	−9.39941e6	+	5.42675e6i	−0.215513	+	0.124426i
$353$	−4.89192e7			−1.11213			−0.556065	−	0.831139i	$-0.687689\pi$
$353$	−4.89192e7			−1.11213			−0.556065	+	0.831139i	$0.687689\pi$
$354$		−	1.03669e7i		−	0.233689i
$355$	−1.45728e7	+	8.41359e6i	−0.325729	+	0.188060i
$356$	2.81231e7	+	1.62369e7i	0.623323	+	0.359876i
$357$	2.86310e6	−	1.65301e6i	0.0629262	−	0.0363304i
$358$	2.81598e6	−	4.87742e6i	0.0613734	−	0.106302i
$359$	−2.44749e7	+	4.23917e7i	−0.528978	+	0.916216i	0.470451	+	0.882426i	$0.344091\pi$
$359$	−2.44749e7	+	4.23917e7i	−0.528978	+	0.916216i	−0.999429	+	0.0337901i	$0.989242\pi$
$360$		−	2.92537e7i		−	0.627008i
$361$	4.55158e7	−	1.19008e7i	0.967476	−	0.252961i
$362$	5.34000e7			1.12568
$363$	−9.05585e6	−	5.22840e6i	−0.189326	−	0.109307i
$364$	−2.74576e7	−	1.58526e7i	−0.569322	−	0.328698i
$365$	2.46087e7	+	4.26235e7i	0.506069	+	0.876537i
$366$	4.91631e6	−	8.51530e6i	0.100276	−	0.173683i
$367$	−4.12766e7	−	7.14932e7i	−0.835037	−	1.44633i	−0.894000	−	0.448067i	$-0.852113\pi$
$367$	−4.12766e7	−	7.14932e7i	−0.835037	−	1.44633i	0.0589631	−	0.998260i	$-0.481221\pi$
$368$	−1.81347e7			−0.363886
$369$		−	7.98205e7i		−	1.58868i
$370$	2.00062e7	+	3.46517e7i	0.394965	+	0.684100i
$371$	−1.43104e7	+	8.26212e6i	−0.280240	+	0.161797i
$372$	−2.42853e6			−0.0471752
$373$			4.93413e7i			0.950788i	0.879773	+	0.475394i	$0.157695\pi$
$373$			4.93413e7i			0.950788i	−0.879773	+	0.475394i	$0.842305\pi$
$374$	1.54515e7	−	8.92091e6i	0.295362	−	0.170527i
$375$	2.81227e7	+	1.62366e7i	0.533289	+	0.307895i
$376$	1.93092e7	−	1.11482e7i	0.363245	−	0.209720i
$377$	−4.49473e7	+	7.78509e7i	−0.838840	+	1.45291i
$378$	7.89831e6	−	1.36803e7i	0.146238	−	0.253291i
$379$		−	1.42830e6i		−	0.0262362i	−0.999914	−	0.0131181i	$-0.995824\pi$
$379$		−	1.42830e6i		−	0.0262362i	0.999914	−	0.0131181i	$-0.00417574\pi$
$380$	−5.07772e7	+	6.52849e6i	−0.925375	+	0.118977i
$381$	6.35474e6			0.114901
$382$	−3.45071e7	−	1.99227e7i	−0.619040	−	0.357403i
$383$	−8.47011e7	−	4.89022e7i	−1.50762	−	0.870426i	−0.999961	−	0.00886976i	$-0.997177\pi$
$383$	−8.47011e7	−	4.89022e7i	−1.50762	−	0.870426i	−0.507662	−	0.861556i	$-0.669490\pi$
$384$	557270.	+	965220.i	0.00984174	+	0.0170464i
$385$	−7.13754e7	+	1.23626e8i	−1.25074	+	2.16634i
$386$	−1.67998e7	−	2.90982e7i	−0.292108	−	0.505946i
$387$	1.27699e7			0.220320
$388$			5.72337e6i			0.0979843i
$389$	−4.20917e7	−	7.29050e7i	−0.715069	−	1.23854i	−0.962933	−	0.269741i	$-0.913062\pi$
$389$	−4.20917e7	−	7.29050e7i	−0.715069	−	1.23854i	0.247863	−	0.968795i	$-0.420272\pi$
$390$	−2.08406e7	+	1.20323e7i	−0.351331	+	0.202841i
$391$	2.98111e7			0.498710
$392$		−	1.98345e6i		−	0.0329278i
$393$	5.22169e6	−	3.01474e6i	0.0860267	−	0.0496675i
$394$	5.40142e6	+	3.11851e6i	0.0883118	+	0.0509869i
$395$	1.02906e8	−	5.94125e7i	1.66973	−	0.964022i
$396$	2.07708e7	−	3.59760e7i	0.334478	−	0.579332i
$397$	1.36076e7	−	2.35691e7i	0.217475	−	0.376679i	−0.736560	−	0.676372i	$-0.763551\pi$
$397$	1.36076e7	−	2.35691e7i	0.217475	−	0.376679i	0.954036	+	0.299694i	$0.0968844\pi$
$398$			1.96218e7i			0.311236i
$399$	−1.24298e7	−	5.19278e6i	−0.195680	−	0.0817488i
$400$	3.97103e7			0.620474
$401$	8.71643e7	+	5.03243e7i	1.35178	+	0.780450i	0.988499	−	0.151230i	$-0.0483235\pi$
$401$	8.71643e7	+	5.03243e7i	1.35178	+	0.780450i	0.363280	+	0.931680i	$0.381657\pi$
$402$	−2.24829e6	−	1.29805e6i	−0.0346078	−	0.0199808i
$403$	−1.91429e7	−	3.31565e7i	−0.292477	−	0.506586i
$404$	7.33681e6	−	1.27077e7i	0.111266	−	0.192719i
$405$	5.29102e7	+	9.16431e7i	0.796479	+	1.37954i
$406$	5.47594e7			0.818239
$407$			5.68194e7i			0.842778i
$408$	−916082.	−	1.58670e6i	−0.0134882	−	0.0233623i
$409$	7.68869e7	−	4.43907e7i	1.12378	−	0.648817i	0.181419	−	0.983406i	$-0.441931\pi$
$409$	7.68869e7	−	4.43907e7i	1.12378	−	0.648817i	0.942364	+	0.334589i	$0.108598\pi$
$410$	1.52009e8			2.20556
$411$			1.82159e7i			0.262376i
$412$	−1.07869e7	+	6.22783e6i	−0.154243	+	0.0890522i
$413$	−8.62182e7	−	4.97781e7i	−1.22391	−	0.706624i
$414$	6.01108e7	−	3.47050e7i	0.847133	−	0.489092i
$415$	3.11548e7	−	5.39617e7i	0.435894	−	0.754991i
$416$	−8.78538e6	+	1.52167e7i	−0.122034	+	0.211369i
$417$		−	941602.i		−	0.0129855i
$418$	−6.70809e7	−	2.80242e7i	−0.918481	−	0.383712i
$419$	−1.18948e8			−1.61702			−0.808508	−	0.588485i	$-0.799725\pi$
$419$	−1.18948e8			−1.61702			−0.808508	+	0.588485i	$0.799725\pi$
$420$	1.26951e7	+	7.32950e6i	0.171351	+	0.0989296i
$421$	5.05130e7	+	2.91637e7i	0.676951	+	0.390838i	0.798705	−	0.601723i	$-0.205519\pi$
$421$	5.05130e7	+	2.91637e7i	0.676951	+	0.390838i	−0.121754	+	0.992560i	$0.538852\pi$
$422$	−1.31982e7	−	2.28600e7i	−0.175622	−	0.304186i
$423$	−4.26693e7	+	7.39054e7i	−0.563760	+	0.976461i
$424$	4.57879e6	+	7.93070e6i	0.0600694	+	0.104043i
$425$	−6.52788e7			−0.850365
$426$			2.45380e6i			0.0317403i
$427$	−4.72127e7	−	8.17749e7i	−0.606423	−	1.05036i
$428$	−2.16012e7	+	1.24714e7i	−0.275515	+	0.159069i
$429$	−3.41729e7			−0.432822
$430$			2.43188e7i			0.305870i
$431$	1.37096e8	−	7.91526e7i	1.71236	−	0.988629i	0.780991	−	0.624542i	$-0.214714\pi$
$431$	1.37096e8	−	7.91526e7i	1.71236	−	0.988629i	0.931365	−	0.364087i	$-0.118619\pi$
$432$	−7.58149e6	−	4.37717e6i	−0.0940379	−	0.0542928i
$433$	−7.46005e7	+	4.30706e7i	−0.918921	+	0.530539i	−0.883291	−	0.468826i	$-0.844677\pi$
$433$	−7.46005e7	+	4.30706e7i	−0.918921	+	0.530539i	−0.0356301	+	0.999365i	$0.511344\pi$
$434$	−1.16609e7	+	2.01973e7i	−0.142647	+	0.247072i
$435$	2.07815e7	−	3.59946e7i	0.252469	−	0.437290i
$436$		−	2.99194e7i		−	0.360988i
$437$	−7.36541e7	−	9.65925e7i	−0.882578	−	1.15744i
$438$	7.17706e6			0.0854130
$439$	7.75854e7	+	4.47940e7i	0.917036	+	0.529451i	0.882688	−	0.469959i	$-0.155731\pi$
$439$	7.75854e7	+	4.47940e7i	0.917036	+	0.529451i	0.0343480	+	0.999410i	$0.489065\pi$
$440$	6.85123e7	+	3.95556e7i	0.804286	+	0.464355i
$441$	3.79580e6	+	6.57452e6i	0.0442576	+	0.0766563i
$442$	1.44421e7	−	2.50144e7i	0.167249	−	0.289683i
$443$	−345055.	−	597653.i	−0.00396896	−	0.00687444i	0.864034	−	0.503433i	$-0.167930\pi$
$443$	−345055.	−	597653.i	−0.00396896	−	0.00687444i	−0.868003	+	0.496559i	$0.834597\pi$
$444$	5.83474e6			0.0666612
$445$		−	2.36701e8i		−	2.68609i
$446$	−5.12678e7	−	8.87985e7i	−0.577884	−	1.00092i
$447$	9.94025e6	−	5.73901e6i	0.111295	−	0.0642561i
$448$	1.07032e7			0.119037
$449$		−	1.12574e8i		−	1.24365i	−0.783156	−	0.621825i	$-0.786391\pi$
$449$		−	1.12574e8i		−	1.24365i	0.783156	−	0.621825i	$-0.213609\pi$
$450$	−1.31627e8	+	7.59951e7i	−1.44447	+	0.833966i
$451$	1.86940e8	+	1.07930e8i	2.03786	+	1.17656i
$452$	2.51221e7	−	1.45043e7i	0.272045	−	0.157065i
$453$	−2.77498e6	+	4.80641e6i	−0.0298515	+	0.0517042i
$454$	4.47153e6	−	7.74493e6i	0.0477847	−	0.0827656i
$455$			2.31100e8i			2.45338i
$456$	−2.87779e6	+	6.88850e6i	−0.0303504	+	0.0726491i
$457$	−5.85255e7			−0.613192			−0.306596	−	0.951840i	$-0.599190\pi$
$457$	−5.85255e7			−0.613192			−0.306596	+	0.951840i	$0.599190\pi$
$458$	9.11661e6	+	5.26348e6i	0.0948936	+	0.0547868i
$459$	1.24630e7	+	7.19553e6i	0.128880	+	0.0744088i
$460$	6.60917e7	+	1.14474e8i	0.679006	+	1.17607i
$461$	3.60055e7	−	6.23633e7i	0.367507	−	0.636541i	−0.621668	−	0.783281i	$-0.713545\pi$
$461$	3.60055e7	−	6.23633e7i	0.367507	−	0.636541i	0.989175	+	0.146740i	$0.0468780\pi$
$462$	1.04082e7	+	1.80276e7i	0.105548	+	0.182815i
$463$	−3.65045e7			−0.367793			−0.183896	−	0.982946i	$-0.558871\pi$
$463$	−3.65045e7			−0.367793			−0.183896	+	0.982946i	$0.558871\pi$
$464$		−	3.03471e7i		−	0.303783i
$465$	8.85076e6	+	1.53300e7i	0.0880282	+	0.152469i
$466$	−6.77763e7	+	3.91307e7i	−0.669762	+	0.386687i
$467$	−1.41558e8			−1.38990			−0.694949	−	0.719059i	$-0.744573\pi$
$467$	−1.41558e8			−1.38990			−0.694949	+	0.719059i	$0.744573\pi$
$468$		−	6.72517e7i		−	0.656093i
$469$	−2.15910e7	+	1.24655e7i	−0.209292	+	0.120835i
$470$	−1.40745e8	−	8.12589e7i	−1.35562	−	0.782668i
$471$	1.33348e6	−	769882.i	0.0127621	−	0.00736820i
$472$	−2.75866e7	+	4.77813e7i	−0.262344	+	0.454394i
$473$	−1.72669e7	+	2.99072e7i	−0.163167	+	0.282613i
$474$		−	1.73275e7i		−	0.162705i
$475$	1.61284e8	+	2.11513e8i	1.50491	+	1.97359i
$476$	−1.75948e7			−0.163141
$477$	−3.03546e7	−	1.75252e7i	−0.279685	−	0.161476i
$478$	−5.47703e6	−	3.16216e6i	−0.0501489	−	0.0289535i
$479$	7.17564e7	+	1.24286e8i	0.652911	+	1.13088i	0.982413	+	0.186721i	$0.0597859\pi$
$479$	7.17564e7	+	1.24286e8i	0.652911	+	1.13088i	−0.329502	+	0.944155i	$0.606881\pi$
$480$	4.06194e6	−	7.03549e6i	0.0367291	−	0.0636166i
$481$	4.59925e7	+	7.96613e7i	0.413287	+	0.715834i
$482$	−2.88564e7			−0.257692
$483$			3.47813e7i			0.308677i
$484$	2.78258e7	+	4.81957e7i	0.245421	+	0.425081i
$485$	3.61285e7	−	2.08588e7i	0.316683	−	0.182837i
$486$	5.06866e7			0.441554
$487$		−	1.01843e8i		−	0.881744i	−0.897570	−	0.440872i	$-0.854669\pi$
$487$		−	1.01843e8i		−	0.881744i	0.897570	−	0.440872i	$-0.145331\pi$
$488$	−4.53189e7	+	2.61649e7i	−0.389960	+	0.225143i
$489$	−4.13230e6	−	2.38579e6i	−0.0353399	−	0.0204035i
$490$	−1.25204e7	+	7.22867e6i	−0.106422	+	0.0614427i
$491$	−1.07773e7	+	1.86668e7i	−0.0910469	+	0.157698i	−0.907952	−	0.419074i	$-0.862355\pi$
$491$	−1.07773e7	+	1.86668e7i	−0.0910469	+	0.157698i	0.816905	+	0.576772i	$0.195688\pi$
$492$	1.10833e7	−	1.91968e7i	0.0930620	−	0.161188i
$493$			4.98869e7i			0.416338i
$494$	−1.16732e8	+	1.50084e7i	−0.968301	+	0.124496i
$495$	−3.02796e8			−2.49652
$496$	1.11932e7	+	6.46237e6i	0.0917292	+	0.0529599i
$497$	2.04075e7	+	1.17823e7i	0.166234	+	0.0959754i
$498$	−4.54311e6	−	7.86889e6i	−0.0367845	−	0.0637127i
$499$	2.85945e7	−	4.95271e7i	0.230134	−	0.398604i	−0.727713	−	0.685881i	$-0.759417\pi$
$499$	2.85945e7	−	4.95271e7i	0.230134	−	0.398604i	0.957847	+	0.287278i	$0.0927503\pi$
$500$	−8.64122e7	−	1.49670e8i	−0.691298	−	1.19736i
$501$	2.83941e7			0.225796
$502$			1.67890e8i			1.32713i
$503$	2.47810e7	+	4.29220e7i	0.194722	+	0.337269i	0.946809	−	0.321795i	$-0.104286\pi$
$503$	2.47810e7	+	4.29220e7i	0.194722	+	0.337269i	−0.752087	+	0.659064i	$0.770953\pi$
$504$	−3.54780e7	+	2.04832e7i	−0.277120	+	0.159995i
$505$	−1.06956e8			−0.830484
$506$			1.87707e8i			1.44887i
$507$	−2.27767e7	+	1.31501e7i	−0.174770	+	0.100904i
$508$	−2.92892e7	−	1.69101e7i	−0.223417	−	0.128990i
$509$	6.87736e7	−	3.97065e7i	0.521517	−	0.301098i	−0.216038	−	0.976385i	$-0.569314\pi$
$509$	6.87736e7	−	3.97065e7i	0.521517	−	0.301098i	0.737555	+	0.675287i	$0.235980\pi$
$510$	−6.67732e6	+	1.15655e7i	−0.0503375	+	0.0871872i
$511$	3.44617e7	−	5.96894e7i	0.258270	−	0.447336i
$512$		−	5.93164e6i		−	0.0441942i
$513$	−7.47772e6	−	5.81600e7i	−0.0553881	−	0.430797i
$514$	−9.71860e7			−0.715673
$515$	7.86258e7	+	4.53946e7i	0.575630	+	0.332340i
$516$	3.07115e6	+	1.77313e6i	0.0223538	+	0.0129060i
$517$	−1.15391e8	−	1.99864e8i	−0.835029	−	1.44631i
$518$	2.80164e7	−	4.85258e7i	0.201568	−	0.349127i
$519$	3.79550e6	+	6.57400e6i	0.0271498	+	0.0470249i
$520$	1.28073e8			0.910853
$521$		−	1.95472e6i		−	0.0138220i	−0.999976	−	0.00691101i	$-0.997800\pi$
$521$		−	1.95472e6i		−	0.0138220i	0.999976	−	0.00691101i	$-0.00219986\pi$
$522$	5.80765e7	+	1.00591e8i	0.408309	+	0.707211i
$523$	1.86719e8	−	1.07802e8i	1.30522	−	0.753568i	0.323924	−	0.946083i	$-0.394998\pi$
$523$	1.86719e8	−	1.07802e8i	1.30522	−	0.753568i	0.981294	+	0.192516i	$0.0616646\pi$
$524$	−3.20892e7			−0.223031
$525$		−	7.61623e7i		−	0.526335i
$526$	1.67765e8	−	9.68591e7i	1.15277	−	0.665554i
$527$	−1.84002e7	−	1.06233e7i	−0.125716	−	0.0725820i
$528$	9.99072e6	−	5.76814e6i	0.0678727	−	0.0391863i
$529$	−8.27975e7	+	1.43409e8i	−0.559307	+	0.968748i
$530$	3.33748e7	−	5.78068e7i	0.224177	−	0.388286i
$531$		−	2.11174e8i		−	1.41045i
$532$	4.34714e7	+	5.70098e7i	0.288714	+	0.378630i
$533$	3.49456e8			2.30787
$534$	−2.98923e7	−	1.72583e7i	−0.196307	−	0.113338i
$535$	1.57451e8	+	9.09043e7i	1.02821	+	0.593640i
$536$	6.90829e6	+	1.19655e7i	0.0448617	+	0.0777028i
$537$	−2.99313e6	+	5.18425e6i	−0.0193287	+	0.0334783i
$538$	−3.78064e7	−	6.54827e7i	−0.242783	−	0.420513i
$539$	−2.05301e7			−0.131107
$540$			6.38104e7i			0.405238i
$541$	4.53879e7	+	7.86142e7i	0.286648	+	0.496488i	0.973007	−	0.230774i	$-0.0741257\pi$
$541$	4.53879e7	+	7.86142e7i	0.286648	+	0.496488i	−0.686360	+	0.727262i	$0.740792\pi$
$542$	−3.82413e7	+	2.20786e7i	−0.240179	+	0.138667i
$543$	−5.67593e7			−0.354517
$544$			9.75088e6i			0.0605685i
$545$	−1.88865e8	+	1.09041e8i	−1.16671	+	0.673598i
$546$	2.91849e7	+	1.68499e7i	0.179300	+	0.103519i
$547$	−1.17955e8	+	6.81014e7i	−0.720701	+	0.416097i	−0.815010	−	0.579446i	$-0.803269\pi$
$547$	−1.17955e8	+	6.81014e7i	−0.720701	+	0.416097i	0.0943099	+	0.995543i	$0.469936\pi$
$548$	4.84729e7	−	8.39576e7i	0.294549	−	0.510174i
$549$	1.00145e8	−	1.73457e8i	0.605221	−	1.04827i
$550$		−	4.11030e8i		−	2.47050i
$551$	1.61641e8	−	1.23255e8i	0.966266	−	0.736802i
$552$	1.92755e7			0.114601
$553$	−1.44108e8	−	8.32005e7i	−0.852141	−	0.491984i
$554$	2.34364e7	+	1.35310e7i	0.137836	+	0.0795795i
$555$	−2.12647e7	−	3.68316e7i	−0.124389	−	0.215447i
$556$	−2.50563e6	+	4.33988e6i	−0.0145778	+	0.0252495i
$557$	9.62188e6	+	1.66656e7i	0.0556794	+	0.0964395i	0.892522	−	0.451005i	$-0.148934\pi$
$557$	9.62188e6	+	1.66656e7i	0.0556794	+	0.0964395i	−0.836842	+	0.547444i	$0.815601\pi$
$558$	−4.94691e7			−0.284729
$559$			5.59068e7i			0.320059i
$560$	−3.90080e7	−	6.75638e7i	−0.222121	−	0.384725i
$561$	−1.64235e7	+	9.48211e6i	−0.0930201	+	0.0537052i
$562$	1.17863e8			0.664003
$563$			1.49403e8i			0.837210i	0.908168	+	0.418605i	$0.137481\pi$
$563$			1.49403e8i			0.837210i	−0.908168	+	0.418605i	$0.862519\pi$
$564$	−2.05239e7	+	1.18495e7i	−0.114399	+	0.0660483i
$565$	−1.83115e8	−	1.05722e8i	−1.01526	−	0.586163i
$566$	−1.44357e8	+	8.33446e7i	−0.796139	+	0.459651i
$567$	7.40947e7	−	1.28336e8i	0.406479	−	0.704042i
$568$	6.52963e6	−	1.13096e7i	0.0356323	−	0.0617169i
$569$			2.62262e8i			1.42364i	0.702364	+	0.711818i	$0.252128\pi$
$569$			2.62262e8i			1.42364i	−0.702364	+	0.711818i	$0.747872\pi$
$570$	5.39715e7	−	6.93919e6i	0.291434	−	0.0374700i
$571$	−1.63644e8			−0.879006			−0.439503	−	0.898241i	$-0.644845\pi$
$571$	−1.63644e8			−0.879006			−0.439503	+	0.898241i	$0.644845\pi$
$572$	1.57504e8	+	9.09349e7i	0.841595	+	0.485895i
$573$	3.66779e7	+	2.11760e7i	0.194958	+	0.112559i
$574$	−1.06436e8	−	1.84352e8i	−0.562798	−	0.974794i
$575$	3.43386e8	−	5.94762e8i	1.80626	−	3.12853i
$576$	1.13516e7	+	1.96616e7i	0.0594005	+	0.102885i
$577$	3.25910e8			1.69657			0.848283	−	0.529544i	$-0.177637\pi$
$577$	3.25910e8			1.69657			0.848283	+	0.529544i	$0.177637\pi$
$578$			1.20513e8i			0.624097i
$579$	1.78567e7	+	3.09287e7i	0.0919953	+	0.159340i
$580$	−1.91565e8	+	1.10600e8i	−0.981821	+	0.566854i
$581$	−8.72576e7			−0.444913
$582$		−	6.08341e6i		−	0.0308588i
$583$	8.20884e7	−	4.73937e7i	0.414263	−	0.239175i
$584$	−3.30793e7	−	1.90983e7i	−0.166080	−	0.0958864i
$585$	−4.24523e8	+	2.45099e8i	−2.12048	+	1.22426i
$586$	4.42811e7	−	7.66971e7i	0.220052	−	0.381141i
$587$	−1.24835e8	+	2.16221e8i	−0.617195	+	1.06901i	0.372800	+	0.927912i	$0.378398\pi$
$587$	−1.24835e8	+	2.16221e8i	−0.617195	+	1.06901i	−0.989995	+	0.141101i	$0.954936\pi$
$588$			2.10822e6i			0.0103701i
$589$	1.10400e7	+	8.58663e7i	0.0540283	+	0.420220i
$590$	4.02157e8			1.95812
$591$	−5.74121e6	−	3.31469e6i	−0.0278126	−	0.0160576i
$592$	−2.68925e7	−	1.55264e7i	−0.129618	−	0.0748352i
$593$	7.96286e7	+	1.37921e8i	0.381861	+	0.661402i	0.991328	−	0.131409i	$-0.0419500\pi$
$593$	7.96286e7	+	1.37921e8i	0.381861	+	0.661402i	−0.609467	+	0.792811i	$0.708617\pi$
$594$	−4.53069e7	+	7.84738e7i	−0.216175	+	0.374425i
$595$	6.41243e7	+	1.11066e8i	0.304419	+	0.527269i
$596$	−6.10866e7			−0.288541
$597$		−	2.08562e7i		−	0.0980195i
$598$	1.51939e8	+	2.63167e8i	0.710504	+	1.23063i
$599$	−2.65226e8	+	1.53128e8i	−1.23406	+	0.712483i	−0.967873	−	0.251439i	$-0.919096\pi$
$599$	−2.65226e8	+	1.53128e8i	−1.23406	+	0.712483i	−0.266184	+	0.963922i	$0.585763\pi$
$600$	−4.22084e7			−0.195409
$601$			3.87730e8i			1.78610i	0.449955	+	0.893051i	$0.351440\pi$
$601$			3.87730e8i			1.78610i	−0.449955	+	0.893051i	$0.648560\pi$
$602$	2.94931e7	−	1.70279e7i	0.135186	−	0.0780496i
$603$	−4.57977e7	−	2.64413e7i	−0.208877	−	0.120595i
$604$	2.55800e7	−	1.47686e7i	0.116088	−	0.0670237i
$605$	2.02822e8	−	3.51298e8i	0.915903	−	1.58639i
$606$	−7.79836e6	+	1.35072e7i	−0.0350417	+	0.0606940i
$607$			1.37181e8i			0.613377i	0.951810	+	0.306689i	$0.0992211\pi$
$607$			1.37181e8i			0.613377i	−0.951810	+	0.306689i	$0.900779\pi$
$608$	3.15943e7	−	2.40914e7i	0.140572	−	0.107189i
$609$	−5.82042e7			−0.257693
$610$	3.30329e8	+	1.90716e8i	1.45532	+	0.840227i
$611$	−3.23560e8	−	1.86807e8i	−1.41850	−	0.818974i
$612$	−1.86606e7	−	3.23212e7i	−0.0814089	−	0.141004i
$613$	1.85666e8	−	3.21582e8i	0.806027	−	1.39608i	−0.109568	−	0.993979i	$-0.534947\pi$
$613$	1.85666e8	−	3.21582e8i	0.806027	−	1.39608i	0.915595	−	0.402101i	$-0.131720\pi$
$614$	−1.22756e8	−	2.12620e8i	−0.530319	−	0.918540i
$615$	−1.61572e8			−0.694609
$616$		−	1.10786e8i		−	0.473962i
$617$	−1.68276e8	−	2.91462e8i	−0.716418	−	1.24087i	−0.962410	−	0.271600i	$-0.912447\pi$
$617$	−1.68276e8	−	2.91462e8i	−0.716418	−	1.24087i	0.245992	−	0.969272i	$-0.420886\pi$
$618$	1.14655e7	−	6.61961e6i	0.0485766	−	0.0280457i
$619$	−2.51175e7			−0.105902			−0.0529511	−	0.998597i	$-0.516863\pi$
$619$	−2.51175e7			−0.105902			−0.0529511	+	0.998597i	$0.516863\pi$
$620$		−	9.42084e7i		−	0.395289i
$621$	−1.31118e8	+	7.57013e7i	−0.547506	+	0.316103i
$622$	−2.71005e7	−	1.56465e7i	−0.112618	−	0.0650199i
$623$	−2.87064e8	+	1.65737e8i	−1.18718	+	0.685416i
$624$	9.33805e6	−	1.61740e7i	0.0384328	−	0.0665676i
$625$	−3.26893e8	+	5.66195e8i	−1.33895	+	2.31914i
$626$			1.93761e8i			0.789846i
$627$	7.13009e7	+	2.97872e7i	0.289263	+	0.120845i
$628$	−8.19471e6			−0.0330868
$629$	4.42080e7	+	2.55235e7i	0.177643	+	0.102562i
$630$	2.58599e8	+	1.49302e8i	1.03420	+	0.597096i
$631$	−1.29882e8	−	2.24962e8i	−0.516965	−	0.895409i	−0.999806	−	0.0197010i	$-0.993729\pi$
$631$	−1.29882e8	−	2.24962e8i	−0.516965	−	0.895409i	0.482841	−	0.875708i	$-0.339605\pi$
$632$	−4.61090e7	+	7.98631e7i	−0.182656	+	0.316370i
$633$	1.40285e7	+	2.42981e7i	0.0553095	+	0.0957989i
$634$	9.54240e7			0.374447
$635$			2.46516e8i			0.962772i
$636$	−4.86683e6	−	8.42960e6i	−0.0189180	−	0.0327669i
$637$	−2.87834e7	+	1.66181e7i	−0.111359	+	0.0642929i
$638$	−3.14114e8			−1.20956
$639$			4.99840e7i			0.191570i
$640$	−3.74432e7	+	2.16179e7i	−0.142835	+	0.0824656i
$641$	−1.12149e8	−	6.47495e7i	−0.425817	−	0.245846i	0.271746	−	0.962369i	$-0.412399\pi$
$641$	−1.12149e8	−	6.47495e7i	−0.425817	−	0.245846i	−0.697563	+	0.716523i	$0.745732\pi$
$642$	2.29601e7	−	1.32560e7i	0.0867697	−	0.0500965i
$643$	9.07232e7	−	1.57137e8i	0.341260	−	0.591080i	−0.643407	−	0.765524i	$-0.722480\pi$
$643$	9.07232e7	−	1.57137e8i	0.341260	−	0.591080i	0.984667	+	0.174445i	$0.0558130\pi$
$644$	9.25540e7	−	1.60308e8i	0.346527	−	0.600203i
$645$		−	2.58487e7i		−	0.0963294i
$646$	−5.19371e7	+	3.96033e7i	−0.192655	+	0.146904i
$647$	−3.15145e8			−1.16358			−0.581791	−	0.813338i	$-0.697648\pi$
$647$	−3.15145e8			−1.16358			−0.581791	+	0.813338i	$0.697648\pi$
$648$	−7.11225e7	−	4.10626e7i	−0.261386	−	0.150911i
$649$	4.94571e8	+	2.85541e8i	1.80923	+	1.04456i
$650$	−3.32709e8	−	5.76268e8i	−1.21150	−	2.09838i
$651$	1.23945e7	−	2.14679e7i	0.0449247	−	0.0778119i
$652$	1.26973e7	+	2.19923e7i	0.0458108	+	0.0793467i
$653$	1.74874e8			0.628039			0.314020	−	0.949417i	$-0.398324\pi$
$653$	1.74874e8			0.628039			0.314020	+	0.949417i	$0.398324\pi$
$654$			3.18015e7i			0.113688i
$655$	1.16949e8	+	2.02562e8i	0.416172	+	0.720832i
$656$	−1.02166e8	+	5.89857e7i	−0.361906	+	0.208947i
$657$	1.46197e8			0.515516
$658$			2.27588e8i			0.798861i
$659$	2.03039e8	−	1.17225e8i	0.709453	−	0.409603i	−0.101405	−	0.994845i	$-0.532334\pi$
$659$	2.03039e8	−	1.17225e8i	0.709453	−	0.409603i	0.810859	+	0.585242i	$0.199001\pi$
$660$	−7.28223e7	−	4.20440e7i	−0.253299	−	0.146242i
$661$	4.59662e8	−	2.65386e8i	1.59160	−	0.918912i	0.598569	−	0.801071i	$-0.295736\pi$
$661$	4.59662e8	−	2.65386e8i	1.59160	−	0.918912i	0.993033	−	0.117840i	$-0.0375971\pi$
$662$	−8.83996e7	+	1.53113e8i	−0.304703	+	0.527761i
$663$	−1.53506e7	+	2.65880e7i	−0.0526726	+	0.0912316i
$664$			4.83573e7i			0.165180i
$665$	2.01441e8	−	4.82184e8i	0.684987	−	1.63964i
$666$	1.18854e8			0.402338
$667$	−4.54525e8	−	2.62420e8i	−1.53172	−	0.884341i
$668$	−1.30869e8	−	7.55575e7i	−0.439045	−	0.253483i
$669$	5.44930e7	+	9.43847e7i	0.181996	+	0.315227i
$670$	5.03545e7	−	8.72165e7i	0.167423	−	0.289984i
$671$	2.70825e8	+	4.69083e8i	0.896440	+	1.55268i
$672$	−1.13766e7			−0.0374890
$673$		−	3.03663e8i		−	0.996199i	−0.867120	−	0.498100i	$-0.834031\pi$
$673$		−	3.03663e8i		−	0.996199i	0.867120	−	0.498100i	$-0.165969\pi$
$674$	−1.90197e6	−	3.29431e6i	−0.00621190	−	0.0107593i
$675$	2.87116e8	−	1.65767e8i	0.933569	−	0.538996i
$676$	1.39971e8			0.453106
$677$			5.98000e7i			0.192724i	0.995346	+	0.0963618i	$0.0307206\pi$
$677$			5.98000e7i			0.192724i	−0.995346	+	0.0963618i	$0.969279\pi$
$678$	−2.67025e7	+	1.54167e7i	−0.0856767	+	0.0494655i
$679$	−5.05939e7	−	2.92104e7i	−0.161618	−	0.0933100i
$680$	6.15520e7	−	3.55371e7i	0.195756	−	0.113020i
$681$	−4.75283e6	+	8.23215e6i	−0.0150491	+	0.0260658i
$682$	6.68901e7	−	1.15857e8i	0.210867	−	0.365233i
$683$			4.37224e8i			1.37228i	0.727471	+	0.686139i	$0.240696\pi$
$683$			4.37224e8i			1.37228i	−0.727471	+	0.686139i	$0.759304\pi$
$684$	−5.86207e7	+	1.40319e8i	−0.183182	+	0.438478i
$685$	−7.06638e8			−2.19849
$686$	2.05794e8	+	1.18815e8i	0.637471	+	0.368044i
$687$	−9.69012e6	−	5.59459e6i	−0.0298854	−	0.0172543i
$688$	−9.43668e6	−	1.63448e7i	−0.0289770	−	0.0501897i
$689$	7.67258e7	−	1.32893e8i	0.234576	−	0.406298i
$690$	−7.02495e7	−	1.21676e8i	−0.213843	−	0.370388i
$691$	−9.60933e7			−0.291245			−0.145623	−	0.989340i	$-0.546519\pi$
$691$	−9.60933e7			−0.291245			−0.145623	+	0.989340i	$0.546519\pi$
$692$		−	4.03997e7i		−	0.121916i
$693$	2.12016e8	+	3.67222e8i	0.637043	+	1.10339i
$694$	−6.79838e7	+	3.92505e7i	−0.203389	+	0.117427i
$695$	3.65270e7			0.108808
$696$			3.22562e7i			0.0956722i
$697$	1.67949e8	−	9.69652e7i	0.495996	−	0.286363i
$698$	−3.33427e7	−	1.92504e7i	−0.0980472	−	0.0566076i
$699$	7.20400e7	−	4.15923e7i	0.210932	−	0.121782i
$700$	−2.02670e8	+	3.51034e8i	−0.590874	+	1.02342i
$701$	−2.25825e8	+	3.91140e8i	−0.655568	+	1.13548i	0.326183	+	0.945307i	$0.394237\pi$
$701$	−2.25825e8	+	3.91140e8i	−0.655568	+	1.13548i	−0.981751	+	0.190171i	$0.939096\pi$
$702$			1.46695e8i			0.424036i
$703$	−2.65244e7	−	2.06301e8i	−0.0763449	−	0.593794i
$704$	−6.13967e7			−0.175965
$705$	1.49599e8	+	8.63707e7i	0.426933	+	0.246490i
$706$	−2.39654e8	−	1.38365e8i	−0.681038	−	0.393197i
$707$	7.48899e7	+	1.29713e8i	0.211917	+	0.367050i
$708$	2.93220e7	−	5.07872e7i	0.0826216	−	0.143105i
$709$	−1.57684e8	−	2.73117e8i	−0.442434	−	0.766319i	0.555435	−	0.831560i	$-0.312552\pi$
$709$	−1.57684e8	−	2.73117e8i	−0.442434	−	0.766319i	−0.997870	+	0.0652412i	$0.979218\pi$
$710$	−9.51889e7			−0.265957
$711$		−	3.52962e8i		−	0.982017i
$712$	9.18497e7	+	1.59088e8i	0.254471	+	0.440756i
$713$	1.93581e8	−	1.11764e8i	0.534064	−	0.308342i
$714$	1.87017e7			0.0513790
$715$		−	1.32565e9i		−	3.62669i
$716$	2.75908e7	−	1.59296e7i	0.0751668	−	0.0433975i
$717$	5.82158e6	+	3.36109e6i	0.0157937	+	0.00911848i
$718$	−2.39804e8	+	1.38451e8i	−0.647863	+	0.374044i
$719$	−1.63976e8	+	2.84014e8i	−0.441157	+	0.764106i	−0.997776	−	0.0666619i	$-0.978765\pi$
$719$	−1.63976e8	+	2.84014e8i	−0.441157	+	0.764106i	0.556619	+	0.830768i	$0.312098\pi$
$720$	8.27419e7	−	1.43313e8i	0.221681	−	0.383962i
$721$		−	1.27140e8i		−	0.339216i
$722$	2.56641e8	+	7.04363e7i	0.681891	+	0.187148i
$723$	3.06717e7			0.0811565
$724$	2.61606e8	+	1.51038e8i	0.689336	+	0.397989i
$725$	9.95295e8	+	5.74634e8i	2.61179	+	1.50792i
$726$	−2.95763e7	−	5.12276e7i	−0.0772918	−	0.133873i
$727$	1.00522e8	−	1.74110e8i	0.261613	−	0.453128i	−0.705057	−	0.709150i	$-0.749079\pi$
$727$	1.00522e8	−	1.74110e8i	0.261613	−	0.453128i	0.966671	+	0.256023i	$0.0824122\pi$
$728$	−8.96760e7	−	1.55323e8i	−0.232425	−	0.402571i
$729$	2.76859e8			0.714621
$730$			2.78415e8i			0.715690i
$731$	1.55127e7	+	2.68688e7i	0.0397133	+	0.0687855i
$732$	4.81698e7	−	2.78109e7i	0.122812	−	0.0709057i
$733$	−2.89256e8			−0.734463			−0.367232	−	0.930130i	$-0.619694\pi$
$733$	−2.89256e8			−0.734463			−0.367232	+	0.930130i	$0.619694\pi$
$734$		−	4.66991e8i		−	1.18092i
$735$	1.33081e7	−	7.68342e6i	0.0335161	−	0.0193505i
$736$	−8.88413e7	−	5.12926e7i	−0.222834	−	0.128653i
$737$	1.23852e8	−	7.15057e7i	0.309385	−	0.178623i
$738$	2.25767e8	−	3.91039e8i	0.561682	−	0.972862i
$739$	2.76811e8	−	4.79452e8i	0.685884	−	1.18799i	−0.287274	−	0.957848i	$-0.592749\pi$
$739$	2.76811e8	−	4.79452e8i	0.685884	−	1.18799i	0.973158	−	0.230138i	$-0.0739177\pi$
$740$			2.26344e8i			0.558565i
$741$	1.24076e8	−	1.59526e7i	0.304953	−	0.0392082i
$742$	−9.34752e7			−0.228815
$743$	1.98541e8	+	1.14628e8i	0.484043	+	0.279462i	0.722100	−	0.691789i	$-0.243177\pi$
$743$	1.98541e8	+	1.14628e8i	0.484043	+	0.279462i	−0.238057	+	0.971251i	$0.576511\pi$
$744$	−1.18973e7	−	6.86891e6i	−0.0288888	−	0.0166790i
$745$	2.22630e8	+	3.85607e8i	0.538412	+	0.932558i
$746$	−1.39558e8	+	2.41722e8i	−0.336154	+	0.582237i
$747$	−9.25433e7	−	1.60290e8i	−0.222015	−	0.384542i
$748$	1.00929e8			0.241162
$749$		−	2.54602e8i		−	0.605922i
$750$	9.18483e7	+	1.59086e8i	0.217714	+	0.377092i
$751$	−6.92035e8	+	3.99547e8i	−1.63384	+	0.943296i	−0.650941	+	0.759128i	$0.725626\pi$
$751$	−6.92035e8	+	3.99547e8i	−1.63384	+	0.943296i	−0.982895	+	0.184168i	$0.941041\pi$
$752$	1.26127e8			0.296589
$753$		−	1.78451e8i		−	0.417961i
$754$	−4.40391e8	+	2.54260e8i	−1.02737	+	0.593150i
$755$	−1.86452e8	−	1.07648e8i	−0.433238	−	0.250130i
$756$	7.73874e7	−	4.46796e7i	0.179104	−	0.103406i
$757$	−8.85773e7	+	1.53420e8i	−0.204190	+	0.353668i	−0.949874	−	0.312632i	$-0.898789\pi$
$757$	−8.85773e7	+	1.53420e8i	−0.204190	+	0.353668i	0.745684	+	0.666299i	$0.232123\pi$
$758$	4.03983e6	−	6.99719e6i	0.00927589	−	0.0160663i
$759$		−	1.99515e8i		−	0.456300i
$760$	−2.67222e8	−	1.11637e8i	−0.608739	−	0.254311i
$761$	−6.01790e8			−1.36550			−0.682749	−	0.730653i	$-0.739216\pi$
$761$	−6.01790e8			−1.36550			−0.682749	+	0.730653i	$0.739216\pi$
$762$	3.11317e7	+	1.79739e7i	0.0703620	+	0.0406235i
$763$	2.64484e8	+	1.52700e8i	0.595422	+	0.343767i
$764$	−1.12700e8	−	1.95202e8i	−0.252722	−	0.437727i
$765$	−1.36017e8	+	2.35589e8i	−0.303815	+	0.526224i
$766$	−2.76633e8	−	4.79142e8i	−0.615484	−	1.06605i
$767$	9.24524e8			2.04895
$768$			6.30479e6i			0.0139183i
$769$	2.73169e8	+	4.73142e8i	0.600692	+	1.04043i	0.992717	+	0.120474i	$0.0384414\pi$
$769$	2.73169e8	+	4.73142e8i	0.600692	+	1.04043i	−0.392025	+	0.919955i	$0.628225\pi$
$770$	−6.99334e8	+	4.03760e8i	−1.53184	+	0.884406i
$771$	1.03300e8			0.225391
$772$		−	1.90069e8i		−	0.413103i
$773$	−2.39959e8	+	1.38541e8i	−0.519516	+	0.299943i	−0.736737	−	0.676180i	$-0.763634\pi$
$773$	−2.39959e8	+	1.38541e8i	−0.519516	+	0.299943i	0.217220	+	0.976123i	$0.430301\pi$
$774$	6.25594e7	+	3.61187e7i	0.134918	+	0.0778949i
$775$	−4.23893e8	+	2.44735e8i	−0.910649	+	0.525763i
$776$	−1.61881e7	+	2.80387e7i	−0.0346427	+	0.0600029i
$777$	−2.97788e7	+	5.15784e7i	−0.0634811	+	0.109953i
$778$		−	4.76214e8i		−	1.01126i
$779$	−7.29132e8	−	3.04608e8i	−1.54239	−	0.644360i
$780$	−1.36130e8			−0.286860
$781$	−1.17063e8	−	6.75863e7i	−0.245735	−	0.141875i
$782$	1.46044e8	+	8.43186e7i	0.305396	+	0.176321i
$783$	−1.26681e8	−	2.19418e8i	−0.263892	−	0.457074i
$784$	5.61004e6	−	9.71687e6i	0.0116417	−	0.0201641i
$785$	2.98656e7	+	5.17288e7i	0.0617394	+	0.106936i
$786$	3.41079e7			0.0702405
$787$		−	1.68809e8i		−	0.346316i	−0.984894	−	0.173158i	$-0.944603\pi$
$787$		−	1.68809e8i		−	0.346316i	0.984894	−	0.173158i	$-0.0553971\pi$
$788$	1.76409e7	+	3.05550e7i	0.0360532	+	0.0624459i
$789$	−1.78319e8	+	1.02952e8i	−0.363050	+	0.209607i
$790$	6.72176e8			1.36333
$791$			2.96102e8i			0.598290i
$792$	2.03511e8	−	1.17497e8i	0.409650	−	0.236511i
$793$	7.59399e8	+	4.38439e8i	1.52283	+	0.879204i
$794$	1.33327e8	−	7.69763e7i	0.266352	−	0.153778i
$795$	−3.54743e7	+	6.14434e7i	−0.0706013	+	0.122285i
$796$	−5.54989e7	+	9.61270e7i	−0.110039	+	0.190593i
$797$			7.19223e8i			1.42065i	0.703872	+	0.710327i	$0.251453\pi$
$797$			7.19223e8i			1.42065i	−0.703872	+	0.710327i	$0.748547\pi$
$798$	−4.62061e7	−	6.05962e7i	−0.0909265	−	0.119244i
$799$	−2.07337e8			−0.406477
$800$	1.94540e8	+	1.12318e8i	0.379961	+	0.219371i
$801$	−6.08907e8	−	3.51552e8i	−1.18482	−	0.684057i
$802$	2.84677e8	+	4.93076e8i	0.551861	+	0.955852i
$803$	−1.97681e8	+	3.42394e8i	−0.381785	+	0.661271i
$804$	−7.34288e6	−	1.27182e7i	−0.0141286	−	0.0244714i
$805$	−1.34925e9			−2.58646
$806$		−	2.16577e8i		−	0.413626i
$807$	4.01848e7	+	6.96021e7i	0.0764612	+	0.132435i
$808$	7.18858e7	−	4.15033e7i	0.136273	−	0.0786771i
$809$	5.20410e8			0.982879			0.491439	−	0.870912i	$-0.336471\pi$
$809$	5.20410e8			0.982879			0.491439	+	0.870912i	$0.336471\pi$
$810$			5.98610e8i			1.12639i
$811$	−5.91472e8	+	3.41487e8i	−1.10885	+	0.640194i	−0.938531	−	0.345196i	$-0.887813\pi$
$811$	−5.91472e8	+	3.41487e8i	−1.10885	+	0.640194i	−0.170317	+	0.985389i	$0.554479\pi$
$812$	2.68265e8	+	1.54883e8i	0.501067	+	0.289291i
$813$	4.06470e7	−	2.34676e7i	0.0756410	−	0.0436713i
$814$	−1.60709e8	+	2.78357e8i	−0.297967	+	0.516094i
$815$	9.25505e7	−	1.60302e8i	0.170964	−	0.296119i
$816$		−	1.03643e7i		−	0.0190752i
$817$	4.87318e7	−	1.16648e8i	0.0893607	−	0.213901i
$818$	5.02223e8			0.917565
$819$	5.94497e8	+	3.43233e8i	1.08218	+	0.624794i
$820$	7.44690e8	+	4.29947e8i	1.35062	+	0.779782i
$821$	−4.68268e8	−	8.11065e8i	−0.846185	−	1.46564i	−0.884588	−	0.466373i	$-0.845560\pi$
$821$	−4.68268e8	−	8.11065e8i	−0.846185	−	1.46564i	0.0384027	−	0.999262i	$-0.487773\pi$
$822$	−5.15223e7	+	8.92392e7i	−0.0927640	+	0.160672i
$823$	−2.58042e8	−	4.46942e8i	−0.462904	−	0.801773i	0.536200	−	0.844091i	$-0.319859\pi$
$823$	−2.58042e8	−	4.46942e8i	−0.462904	−	0.801773i	−0.999104	+	0.0423177i	$0.986526\pi$
$824$	−7.04598e7			−0.125939
$825$			4.36887e8i			0.778050i
$826$	−2.81587e8	−	4.87724e8i	−0.499658	−	0.865434i
$827$	1.69200e8	−	9.76874e7i	0.299146	−	0.172712i	−0.342913	−	0.939367i	$-0.611414\pi$
$827$	1.69200e8	−	9.76874e7i	0.299146	−	0.172712i	0.642059	+	0.766655i	$0.278080\pi$
$828$	3.92642e8			0.691681
$829$			1.16831e8i			0.205066i	0.994730	+	0.102533i	$0.0326947\pi$
$829$			1.16831e8i			0.205066i	−0.994730	+	0.102533i	$0.967305\pi$
$830$	3.05254e8	−	1.76238e8i	0.533859	−	0.308224i
$831$	−2.49108e7	−	1.43822e7i	−0.0434094	−	0.0250624i
$832$	−8.60788e7	+	4.96976e7i	−0.149460	+	0.0862910i
$833$	−9.22220e6	+	1.59733e7i	−0.0159551	+	0.0276350i
$834$	2.66325e6	−	4.61289e6i	0.00459107	−	0.00795197i
$835$			1.10148e9i			1.89198i
$836$	−2.49364e8	−	3.27024e8i	−0.426790	−	0.559706i
$837$	1.07906e8			0.184022
$838$	−5.82723e8	−	3.36435e8i	−0.990216	−	0.571702i
$839$	−6.27152e7	−	3.62086e7i	−0.106191	−	0.0613092i	0.445964	−	0.895051i	$-0.352861\pi$
$839$	−6.27152e7	−	3.62086e7i	−0.106191	−	0.0613092i	−0.552155	+	0.833742i	$0.686194\pi$
$840$	4.14619e7	+	7.18141e7i	0.0699538	+	0.121164i
$841$	1.41731e8	−	2.45485e8i	0.238274	−	0.412702i
$842$	1.64975e8	+	2.85745e8i	0.276364	+	0.478676i
$843$	−1.25278e8			−0.209118
$844$		−	1.49321e8i		−	0.248366i
$845$	−5.10126e8	−	8.83564e8i	−0.845488	−	1.46443i
$846$	−4.18072e8	+	2.41374e8i	−0.690462	+	0.398639i
$847$	−5.68059e8			−0.934853
$848$			5.18031e7i			0.0849509i
$849$	1.53438e8	−	8.85877e7i	0.250733	−	0.144761i
$850$	−3.19800e8	−	1.84636e8i	−0.520740	−	0.300649i
$851$	−4.65094e8	+	2.68522e8i	−0.754662	+	0.435704i
$852$	−6.94040e6	+	1.20211e7i	−0.0112219	+	0.0194369i
$853$	3.14832e8	−	5.45304e8i	0.507261	−	0.878601i	−0.492704	−	0.870197i	$-0.663991\pi$
$853$	3.14832e8	−	5.45304e8i	0.507261	−	0.878601i	0.999965	−	0.00840435i	$-0.00267522\pi$
$854$		−	5.34151e8i		−	0.857612i
$855$	1.09940e9	−	1.41352e8i	1.75897	−	0.226153i
$856$	−1.41098e8			−0.224957
$857$	−7.43684e8	−	4.29366e8i	−1.18153	−	0.682158i	−0.225164	−	0.974321i	$-0.572292\pi$
$857$	−7.43684e8	−	4.29366e8i	−1.18153	−	0.682158i	−0.956369	+	0.292163i	$0.905625\pi$
$858$	−1.67412e8	−	9.66555e7i	−0.265048	−	0.153026i
$859$	2.39610e8	+	4.15017e8i	0.378029	+	0.654766i	0.990775	−	0.135514i	$-0.0432685\pi$
$859$	2.39610e8	+	4.15017e8i	0.378029	+	0.654766i	−0.612746	+	0.790280i	$0.709935\pi$
$860$	−6.87840e7	+	1.19137e8i	−0.108141	+	0.187306i
$861$	1.13132e8	+	1.95950e8i	0.177245	+	0.306997i
$862$	8.95510e8			1.39813
$863$		−	3.01060e8i		−	0.468404i	−0.972188	−	0.234202i	$-0.924752\pi$
$863$		−	3.01060e8i		−	0.468404i	0.972188	−	0.234202i	$-0.0752478\pi$
$864$	−2.47610e7	−	4.28874e7i	−0.0383908	−	0.0664949i
$865$	−2.55022e8	+	1.47237e8i	−0.394029	+	0.227493i
$866$	−4.87288e8			−0.750296
$867$		−	1.28095e8i		−	0.196550i
$868$	−1.14253e8	+	6.59641e7i	−0.174707	+	0.100867i
$869$	8.26640e8	+	4.77261e8i	1.25967	+	0.727271i
$870$	2.03616e8	−	1.17558e8i	0.309210	−	0.178523i
$871$	1.15761e8	−	2.00503e8i	0.175189	−	0.303436i
$872$	8.46247e7	−	1.46574e8i	0.127629	−	0.221059i
$873$		−	1.23919e8i		−	0.186250i
$874$	−8.76253e7	−	6.81530e8i	−0.131249	−	1.02082i
$875$	1.76409e9			2.63328
$876$	3.51602e7	+	2.02998e7i	0.0523046	+	0.0301981i
$877$	−5.12910e8	−	2.96129e8i	−0.760401	−	0.439018i	0.0690387	−	0.997614i	$-0.478007\pi$
$877$	−5.12910e8	−	2.96129e8i	−0.760401	−	0.439018i	−0.829440	+	0.558596i	$0.811340\pi$
$878$	2.53393e8	+	4.38889e8i	0.374379	+	0.648443i
$879$	−4.70667e7	+	8.15220e7i	−0.0693023	+	0.120035i
$880$	2.23760e8	+	3.87564e8i	0.328348	+	0.568716i
$881$	940805.			0.00137585			0.000687926	−	1.00000i	$-0.499781\pi$
$881$	940805.			0.00137585			0.000687926		1.00000i	$0.499781\pi$
$882$			4.29446e7i			0.0625896i
$883$	1.99908e8	+	3.46251e8i	0.290368	+	0.502932i	0.973897	−	0.226992i	$-0.0728890\pi$
$883$	1.99908e8	+	3.46251e8i	0.290368	+	0.502932i	−0.683529	+	0.729923i	$0.739556\pi$
$884$	1.41503e8	−	8.16967e7i	0.204837	−	0.118263i
$885$	−4.27456e8			−0.616682
$886$		−	3.90385e6i		−	0.00561296i
$887$	8.22057e8	−	4.74615e8i	1.17796	−	0.680096i	0.222419	−	0.974951i	$-0.428605\pi$
$887$	8.22057e8	−	4.74615e8i	1.17796	−	0.680096i	0.955542	+	0.294855i	$0.0952713\pi$
$888$	2.85843e7	+	1.65031e7i	0.0408215	+	0.0235683i
$889$	2.98967e8	−	1.72609e8i	0.425518	−	0.245673i
$890$	6.69492e8	−	1.15959e9i	0.949676	−	1.64489i
$891$	−4.25027e8	+	7.36169e8i	−0.600874	+	1.04074i
$892$		−	5.80029e8i		−	0.817251i
$893$	5.12266e8	+	6.71803e8i	0.719352	+	0.943382i
$894$	6.49295e7			0.0908718
$895$	−2.01110e8	−	1.16111e8i	−0.280520	−	0.161958i
$896$	5.24350e7	+	3.02734e7i	0.0728949	+	0.0420859i
$897$	−1.61497e8	−	2.79722e8i	−0.223763	−	0.387569i
$898$	3.18407e8	−	5.51497e8i	0.439697	−	0.761577i
$899$	1.87029e8	+	3.23944e8i	0.257413	+	0.445852i
$900$	−8.59787e8			−1.17941
$901$		−	8.51578e7i		−	0.116426i
$902$	6.10545e8	+	1.05749e9i	0.831951	+	1.44098i
$903$	−3.13485e7	+	1.80991e7i	−0.0425749	+	0.0245806i
$904$	1.64097e8			0.222124
$905$		−	2.20183e9i		−	2.97056i
$906$	−2.71892e7	+	1.56977e7i	−0.0365604	+	0.0211082i
$907$	−5.51070e8	−	3.18160e8i	−0.738559	−	0.426407i	0.0829865	−	0.996551i	$-0.473554\pi$
$907$	−5.51070e8	−	3.18160e8i	−0.738559	−	0.426407i	−0.821545	+	0.570144i	$0.806888\pi$
$908$	4.38119e7	−	2.52948e7i	0.0585241	−	0.0337889i
$909$	−1.58853e8	+	2.75141e8i	−0.211497	+	0.366323i
$910$	−6.53648e8	+	1.13215e9i	−0.867401	+	1.50238i
$911$		−	6.46761e8i		−	0.855438i	−0.903912	−	0.427719i	$-0.859317\pi$
$911$		−	6.46761e8i		−	0.855438i	0.903912	−	0.427719i	$-0.140683\pi$
$912$	−3.35819e7	+	2.56070e7i	−0.0442711	+	0.0337578i
$913$	5.00533e8			0.657688
$914$	−2.86715e8	−	1.65535e8i	−0.375502	−	0.216796i
$915$	−3.51110e8	−	2.02713e8i	−0.458331	−	0.264618i
$916$	2.97747e7	+	5.15713e7i	0.0387402	+	0.0670999i
$917$	1.63774e8	−	2.83665e8i	0.212391	−	0.367873i
$918$	4.07040e7	+	7.05015e7i	0.0526150	+	0.0911318i
$919$	−3.94782e8			−0.508641			−0.254320	−	0.967120i	$-0.581852\pi$
$919$	−3.94782e8			−0.508641			−0.254320	+	0.967120i	$0.581852\pi$
$920$			7.47743e8i			0.960260i
$921$	1.30478e8	+	2.25995e8i	0.167017	+	0.289281i
$922$	3.52780e8	−	2.03678e8i	0.450103	−	0.259867i
$923$	−2.18831e8			−0.278294
$924$			1.17756e8i			0.149268i
$925$	1.01844e9	−	5.87996e8i	1.28680	−	0.742932i
$926$	−1.78835e8	−	1.03250e8i	−0.225226	−	0.130034i
$927$	2.33553e8	−	1.34842e8i	0.293188	−	0.169272i
$928$	8.58347e7	−	1.48670e8i	0.107404	−	0.186028i
$929$	−6.61103e8	+	1.14506e9i	−0.824559	+	1.42818i	0.0776968	+	0.996977i	$0.475243\pi$
$929$	−6.61103e8	+	1.14506e9i	−0.824559	+	1.42818i	−0.902256	+	0.431201i	$0.858090\pi$
$930$			1.00135e8i			0.124491i
$931$	7.45412e7	−	9.58387e6i	0.0923735	−	0.0118766i
$932$	−4.42713e8			−0.546858
$933$	2.88054e7	+	1.66308e7i	0.0354674	+	0.0204771i
$934$	−6.93488e8	−	4.00386e8i	−0.851135	−	0.491403i
$935$	−3.67834e8	−	6.37107e8i	−0.450005	−	0.779431i
$936$	1.90216e8	−	3.29465e8i	0.231964	−	0.401773i
$937$	−1.22981e8	−	2.13009e8i	−0.149492	−	0.258928i	0.781548	−	0.623845i	$-0.214431\pi$
$937$	−1.22981e8	−	2.13009e8i	−0.149492	−	0.258928i	−0.931040	+	0.364917i	$0.881097\pi$
$938$	−1.41032e8			−0.170886
$939$		−	2.05950e8i		−	0.248751i
$940$	−4.59670e8	−	7.96171e8i	−0.553430	−	0.958568i
$941$	1.08459e9	−	6.26190e8i	1.30166	−	0.751514i	0.320971	−	0.947089i	$-0.395991\pi$
$941$	1.08459e9	−	6.26190e8i	1.30166	−	0.751514i	0.980689	+	0.195575i	$0.0626574\pi$
$942$	8.71022e6			0.0104202
$943$			2.04026e9i			2.43305i
$944$	−2.70292e8	+	1.56053e8i	−0.321305	+	0.185505i
$945$	−5.64076e8	−	3.25670e8i	−0.668409	−	0.385906i
$946$	−1.69180e8	+	9.76764e7i	−0.199837	+	0.115376i
$947$	−2.22894e8	+	3.86064e8i	−0.262451	+	0.454579i	−0.966893	−	0.255183i	$-0.917864\pi$
$947$	−2.22894e8	+	3.86064e8i	−0.262451	+	0.454579i	0.704441	+	0.709762i	$0.251198\pi$
$948$	4.90096e7	−	8.48871e7i	0.0575249	−	0.0996361i
$949$			6.40053e8i			0.748889i
$950$	1.91877e8	+	1.49238e9i	0.223796	+	1.74064i
$951$	−1.01427e8			−0.117927
$952$	−8.61966e7	−	4.97656e7i	−0.0999032	−	0.0576791i
$953$	−1.30521e9	−	7.53566e8i	−1.50801	−	0.870648i	−0.999957	−	0.00931961i	$-0.997033\pi$
$953$	−1.30521e9	−	7.53566e8i	−1.50801	−	0.870648i	−0.508049	−	0.861328i	$-0.669633\pi$
$954$	−9.91376e7	−	1.71711e8i	−0.114181	−	0.197767i
$955$	−8.21469e8	+	1.42283e9i	−0.943150	+	1.63358i
$956$	−1.78879e7	−	3.09827e7i	−0.0204732	−	0.0354606i
$957$	3.33875e8			0.380932
$958$			8.11831e8i			0.923356i
$959$	4.94783e8	+	8.56990e8i	0.560995	+	0.971672i
$960$	3.97987e7	−	2.29778e7i	0.0449837	−	0.0259714i
$961$	7.28193e8			0.820496
$962$			5.20345e8i			0.584476i
$963$	4.67697e8	−	2.70025e8i	0.523704	−	0.302361i
$964$	−1.41367e8	−	8.16183e7i	−0.157804	−	0.0911080i
$965$	−1.19980e9	+	6.92705e8i	−1.33514	+	0.770844i
$966$	−9.83764e7	+	1.70393e8i	−0.109134	+	0.189025i
$967$	2.51900e8	−	4.36303e8i	0.278579	−	0.482513i	−0.692453	−	0.721463i	$-0.743470\pi$
$967$	2.51900e8	−	4.36303e8i	0.278579	−	0.482513i	0.971032	+	0.238950i	$0.0768032\pi$
$968$			3.14813e8i			0.347078i
$969$	5.52044e7	−	4.20947e7i	0.0606739	−	0.0462654i
$970$	2.35990e8			0.258571
$971$	−6.42819e8	−	3.71132e8i	−0.702152	−	0.405388i	0.105996	−	0.994367i	$-0.466197\pi$
$971$	−6.42819e8	−	3.71132e8i	−0.702152	−	0.405388i	−0.808148	+	0.588979i	$0.799530\pi$
$972$	2.48312e8	+	1.43363e8i	0.270396	+	0.156113i
$973$	−2.55760e7	−	4.42989e7i	−0.0277648	−	0.0480900i
$974$	2.88054e8	−	4.98925e8i	0.311744	−	0.539956i
$975$	3.53639e8	+	6.12520e8i	0.381545	+	0.660856i
$976$	−2.96022e8			−0.318401
$977$			1.50889e9i			1.61799i	0.587817	+	0.808994i	$0.299987\pi$
$977$			1.50889e9i			1.61799i	−0.587817	+	0.808994i	$0.700013\pi$
$978$	−1.34960e7	−	2.33758e7i	−0.0144275	−	0.0249891i
$979$	1.64668e9	−	9.50710e8i	1.75493	−	1.01321i
$980$	−8.17831e7			−0.0868931
$981$			6.47798e8i			0.686172i
$982$	−1.05595e8	+	6.09655e7i	−0.111509	+	0.0643799i
$983$	4.08670e8	+	2.35946e8i	0.430242	+	0.248400i	0.699450	−	0.714682i	$-0.253429\pi$
$983$	4.08670e8	+	2.35946e8i	0.430242	+	0.248400i	−0.269208	+	0.963082i	$0.586762\pi$
$984$	1.08593e8	−	6.26964e7i	0.113977	−	0.0658048i
$985$	1.28585e8	−	2.22715e8i	0.134549	−	0.233046i
$986$	−1.41101e8	+	2.44395e8i	−0.147198	+	0.254954i
$987$		−	2.41905e8i		−	0.251590i
$988$	−6.14320e8	−	2.56643e8i	−0.636977	−	0.266108i
$989$	−3.26406e8			−0.337419
$990$	−1.48339e9	−	8.56437e8i	−1.52880	−	0.882653i
$991$	5.94726e8	+	3.43365e8i	0.611077	+	0.352806i	0.773387	−	0.633934i	$-0.218561\pi$
$991$	5.94726e8	+	3.43365e8i	0.611077	+	0.352806i	−0.162310	+	0.986740i	$0.551894\pi$
$992$	3.65567e7	+	6.33180e7i	0.0374483	+	0.0648623i
$993$	9.39607e7	−	1.62745e8i	0.0959618	−	0.166211i
$994$	6.66506e7	+	1.15442e8i	0.0678649	+	0.117545i
$995$	8.09063e8			0.821322
$996$		−	5.13994e7i		−	0.0520212i
$997$	−7.43813e7	−	1.28832e8i	−0.0750548	−	0.129999i	0.826055	−	0.563589i	$-0.190580\pi$
$997$	−7.43813e7	−	1.28832e8i	−0.0750548	−	0.129999i	−0.901110	+	0.433590i	$0.857247\pi$
$998$	2.80168e8	−	1.61755e8i	0.281855	−	0.162729i
$999$	−2.59254e8			−0.260033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.7.d.a.27.8	✓	20
3.2	odd	2		342.7.m.a.217.1		20
19.12	odd	6	inner	38.7.d.a.31.8	yes	20
57.50	even	6		342.7.m.a.145.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.7.d.a.27.8	✓	20	1.1	even	1	trivial
38.7.d.a.31.8	yes	20	19.12	odd	6	inner
342.7.m.a.145.1		20	57.50	even	6
342.7.m.a.217.1		20	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(-5.20717 - 3.00636i) q^{3} +(16.0000 + 27.7128i) q^{4} +(116.624 - 201.999i) q^{5} +(-17.0065 - 29.4562i) q^{6} -326.637 q^{7} +181.019i q^{8} +(-346.424 - 600.023i) q^{9} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(-5.20717 - 3.00636i) q^{3} +(16.0000 + 27.7128i) q^{4} +(116.624 - 201.999i) q^{5} +(-17.0065 - 29.4562i) q^{6} -326.637 q^{7} +181.019i q^{8} +(-346.424 - 600.023i) q^{9} +(1142.68 - 659.725i) q^{10} +1873.68 q^{11} -192.407i q^{12} +(2626.92 - 1516.65i) q^{13} +(-1600.19 - 923.870i) q^{14} +(-1214.56 + 701.227i) q^{15} +(-512.000 + 886.810i) q^{16} +(841.664 - 1457.80i) q^{17} -3919.34i q^{18} +(-6803.00 + 874.672i) q^{19} +7463.93 q^{20} +(1700.85 + 981.989i) q^{21} +(9179.12 + 5299.56i) q^{22} +(8854.81 + 15337.0i) q^{23} +(544.209 - 942.598i) q^{24} +(-19389.8 - 33584.1i) q^{25} +17158.9 q^{26} +8549.17i q^{27} +(-5226.20 - 9052.04i) q^{28} +(-25665.4 + 14817.9i) q^{29} -7933.48 q^{30} -12621.8i q^{31} +(-5016.55 + 2896.31i) q^{32} +(-9756.56 - 5632.95i) q^{33} +(8246.59 - 4761.17i) q^{34} +(-38093.7 + 65980.3i) q^{35} +(11085.6 - 19200.7i) q^{36} +30325.0i q^{37} +(-35801.7 - 14956.8i) q^{38} -18238.4 q^{39} +(36565.7 + 21111.2i) q^{40} +(99771.8 + 57603.3i) q^{41} +(5554.97 + 9621.49i) q^{42} +(-9215.51 + 15961.7i) q^{43} +(29978.9 + 51924.9i) q^{44} -161605. q^{45} +100181. i q^{46} +(-61585.4 - 106669. i) q^{47} +(5332.14 - 3078.51i) q^{48} -10957.1 q^{49} -219371. i q^{50} +(-8765.37 + 5060.69i) q^{51} +(84061.3 + 48532.8i) q^{52} +(43811.3 - 25294.5i) q^{53} +(-24180.7 + 41882.2i) q^{54} +(218516. - 378481. i) q^{55} -59127.7i q^{56} +(38053.9 + 15897.7i) q^{57} -167646. q^{58} +(263957. + 152396. i) q^{59} +(-38865.9 - 22439.3i) q^{60} +(144542. + 250354. i) q^{61} +(35699.9 - 61834.0i) q^{62} +(113155. + 195990. i) q^{63} -32768.0 q^{64} -707511. i q^{65} +(-31864.8 - 55191.4i) q^{66} +(66100.7 - 38163.3i) q^{67} +53866.5 q^{68} -106483. i q^{69} +(-373241. + 215491. i) q^{70} +(-62477.6 - 36071.4i) q^{71} +(108616. - 62709.4i) q^{72} +(-105504. + 182739. i) q^{73} +(-85772.1 + 148562. i) q^{74} +233171. i q^{75} +(-133088. - 174536. i) q^{76} -612013. q^{77} +(-89349.5 - 51585.9i) q^{78} +(441185. + 254718. i) q^{79} +(119423. + 206847. i) q^{80} +(-226841. + 392900. i) q^{81} +(325853. + 564394. i) q^{82} +267139. q^{83} +62847.3i q^{84} +(-196316. - 340030. i) q^{85} +(-90293.2 + 52130.8i) q^{86} +178192. q^{87} +339172. i q^{88} +(878847. - 507403. i) q^{89} +(-791701. - 457089. i) q^{90} +(-858049. + 495395. i) q^{91} +(-283354. + 490784. i) q^{92} +(-37945.7 + 65723.9i) q^{93} -696760. i q^{94} +(-616711. + 1.47620e6i) q^{95} +34829.4 q^{96} +(154893. + 89427.6i) q^{97} +(-53678.6 - 30991.4i) q^{98} +(-649087. - 1.12425e6i) 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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