LMFDB - Embedded newform 196.6.d.b.195.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,6,Mod(195,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("196.195");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	196.d (of order $2$, degree $1$, 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:	$31.4352286833$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			195.25
Character	$\chi$	$=$	196.195
Dual form			196.6.d.b.195.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.73498 - 4.24852i) q^{2} -22.1401 q^{3} +(-4.09980 - 31.7363i) q^{4} +2.56629i q^{5} +(-82.6927 + 94.0624i) q^{6} +(-150.145 - 101.116i) q^{8} +247.182 q^{9} +(10.9029 + 9.58505i) q^{10} +80.3962i q^{11} +(90.7697 + 702.643i) q^{12} +980.594i q^{13} -56.8178i q^{15} +(-990.383 + 260.225i) q^{16} +601.293i q^{17} +(923.221 - 1050.16i) q^{18} -1157.66 q^{19} +(81.4445 - 10.5213i) q^{20} +(341.565 + 300.278i) q^{22} -3963.02i q^{23} +(3324.21 + 2238.72i) q^{24} +3118.41 q^{25} +(4166.07 + 3662.50i) q^{26} -92.5894 q^{27} -2352.14 q^{29} +(-241.391 - 212.214i) q^{30} +5927.57 q^{31} +(-2593.50 + 5179.60i) q^{32} -1779.98i q^{33} +(2554.60 + 2245.82i) q^{34} +(-1013.40 - 7844.64i) q^{36} +14095.5 q^{37} +(-4323.85 + 4918.34i) q^{38} -21710.4i q^{39} +(259.494 - 385.315i) q^{40} -14300.9i q^{41} +6888.99i q^{43} +(2551.48 - 329.608i) q^{44} +634.341i q^{45} +(-16837.0 - 14801.8i) q^{46} -18211.4 q^{47} +(21927.1 - 5761.39i) q^{48} +(11647.2 - 13248.6i) q^{50} -13312.7i q^{51} +(31120.4 - 4020.24i) q^{52} +19698.0 q^{53} +(-345.820 + 393.368i) q^{54} -206.320 q^{55} +25630.7 q^{57} +(-8785.20 + 9993.11i) q^{58} +25432.6 q^{59} +(-1803.19 + 232.941i) q^{60} -13406.0i q^{61} +(22139.4 - 25183.4i) q^{62} +(12318.9 + 30364.2i) q^{64} -2516.49 q^{65} +(-7562.26 - 6648.18i) q^{66} +5663.55i q^{67} +(19082.8 - 2465.18i) q^{68} +87741.5i q^{69} +24339.4i q^{71} +(-37113.1 - 24994.2i) q^{72} -42720.1i q^{73} +(52646.4 - 59884.9i) q^{74} -69041.9 q^{75} +(4746.18 + 36739.9i) q^{76} +(-92237.0 - 81088.0i) q^{78} +39976.1i q^{79} +(-667.812 - 2541.61i) q^{80} -58015.3 q^{81} +(-60757.5 - 53413.5i) q^{82} +42246.6 q^{83} -1543.09 q^{85} +(29268.0 + 25730.3i) q^{86} +52076.5 q^{87} +(8129.38 - 12071.1i) q^{88} +92505.4i q^{89} +(2695.01 + 2369.25i) q^{90} +(-125772. + 16247.6i) q^{92} -131237. q^{93} +(-68019.4 + 77371.5i) q^{94} -2970.90i q^{95} +(57420.2 - 114677. i) q^{96} +35315.4i q^{97} +19872.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50}+ \cdots + 330324 q^{93}+O(q^{100}) $ 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$-1$

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 $

$2$	3.73498	−	4.24852i	0.660258	−	0.751039i
$2$	3.73498	−	4.24852i	0.660258	−	0.751039i
$3$	−22.1401			−1.42029			−0.710143	−	0.704058i	$-0.751370\pi$
$3$	−22.1401			−1.42029			−0.710143	+	0.704058i	$0.751370\pi$
$4$	−4.09980	−	31.7363i	−0.128119	−	0.991759i
$5$			2.56629i			0.0459072i	0.999737	+	0.0229536i	$0.00730700\pi$
$5$			2.56629i			0.0459072i	−0.999737	+	0.0229536i	$0.992693\pi$
$6$	−82.6927	+	94.0624i	−0.937755	+	1.06669i
$7$		0			0
$7$		0			0
$8$	−150.145	−	101.116i	−0.829441	−	0.558595i
$9$	247.182			1.01721
$10$	10.9029	+	9.58505i	0.0344781	+	0.0303106i
$11$			80.3962i			0.200334i	0.994971	+	0.100167i	$0.0319376\pi$
$11$			80.3962i			0.200334i	−0.994971	+	0.100167i	$0.968062\pi$
$12$	90.7697	+	702.643i	0.181965	+	1.40858i
$13$			980.594i			1.60928i	0.593765	+	0.804639i	$0.297641\pi$
$13$			980.594i			1.60928i	−0.593765	+	0.804639i	$0.702359\pi$
$14$		0			0
$15$		−	56.8178i		−	0.0652013i
$16$	−990.383	+	260.225i	−0.967171	+	0.254126i
$17$			601.293i			0.504619i	0.967647	+	0.252310i	$0.0811902\pi$
$17$			601.293i			0.504619i	−0.967647	+	0.252310i	$0.918810\pi$
$18$	923.221	−	1050.16i	0.671621	−	0.763964i
$19$	−1157.66			−0.735695			−0.367847	−	0.929886i	$-0.619905\pi$
$19$	−1157.66			−0.735695			−0.367847	+	0.929886i	$0.619905\pi$
$20$	81.4445	−	10.5213i	0.0455289	−	0.00588157i
$21$		0			0
$22$	341.565	+	300.278i	0.150458	+	0.132272i
$23$		−	3963.02i		−	1.56209i	−0.624473	−	0.781047i	$-0.714686\pi$
$23$		−	3963.02i		−	1.56209i	0.624473	−	0.781047i	$-0.285314\pi$
$24$	3324.21	+	2238.72i	1.17804	+	0.793364i
$25$	3118.41			0.997893
$26$	4166.07	+	3662.50i	1.20863	+	1.06254i
$27$	−92.5894			−0.0244429
$28$		0			0
$29$	−2352.14			−0.519360			−0.259680	−	0.965695i	$-0.583617\pi$
$29$	−2352.14			−0.519360			−0.259680	+	0.965695i	$0.583617\pi$
$30$	−241.391	−	212.214i	−0.0489687	−	0.0430497i
$31$	5927.57			1.10783			0.553914	−	0.832574i	$-0.313134\pi$
$31$	5927.57			1.10783			0.553914	+	0.832574i	$0.313134\pi$
$32$	−2593.50	+	5179.60i	−0.447724	+	0.894172i
$33$		−	1779.98i		−	0.284531i
$34$	2554.60	+	2245.82i	0.378989	+	0.333179i
$35$		0			0
$36$	−1013.40	−	7844.64i	−0.130324	−	1.00883i
$37$	14095.5			1.69268			0.846342	−	0.532640i	$-0.178800\pi$
$37$	14095.5			1.69268			0.846342	+	0.532640i	$0.178800\pi$
$38$	−4323.85	+	4918.34i	−0.485748	+	0.552535i
$39$		−	21710.4i		−	2.28563i
$40$	259.494	−	385.315i	0.0256435	−	0.0380773i
$41$		−	14300.9i		−	1.32863i	−0.747455	−	0.664313i	$-0.768724\pi$
$41$		−	14300.9i		−	1.32863i	0.747455	−	0.664313i	$-0.231276\pi$
$42$		0			0
$43$			6888.99i			0.568178i	0.958798	+	0.284089i	$0.0916911\pi$
$43$			6888.99i			0.568178i	−0.958798	+	0.284089i	$0.908309\pi$
$44$	2551.48	−	329.608i	0.198683	−	0.0256665i
$45$			634.341i			0.0466972i
$46$	−16837.0	−	14801.8i	−1.17319	−	1.03138i
$47$	−18211.4			−1.20254			−0.601270	−	0.799046i	$-0.705338\pi$
$47$	−18211.4			−1.20254			−0.601270	+	0.799046i	$0.705338\pi$
$48$	21927.1	−	5761.39i	1.37366	−	0.360931i
$49$		0			0
$50$	11647.2	−	13248.6i	0.658867	−	0.749456i
$51$		−	13312.7i		−	0.716703i
$52$	31120.4	−	4020.24i	1.59602	−	0.206178i
$53$	19698.0			0.963234			0.481617	−	0.876382i	$-0.340050\pi$
$53$	19698.0			0.963234			0.481617	+	0.876382i	$0.340050\pi$
$54$	−345.820	+	393.368i	−0.0161386	+	0.0183575i
$55$	−206.320			−0.00919675
$56$		0			0
$57$	25630.7			1.04490
$58$	−8785.20	+	9993.11i	−0.342911	+	0.390059i
$59$	25432.6			0.951174			0.475587	−	0.879669i	$-0.342236\pi$
$59$	25432.6			0.951174			0.475587	+	0.879669i	$0.342236\pi$
$60$	−1803.19	+	232.941i	−0.0646640	+	0.00835350i
$61$		−	13406.0i		−	0.461290i	−0.973038	−	0.230645i	$-0.925916\pi$
$61$		−	13406.0i		−	0.461290i	0.973038	−	0.230645i	$-0.0740836\pi$
$62$	22139.4	−	25183.4i	0.731452	−	0.832022i
$63$		0			0
$64$	12318.9	+	30364.2i	0.375944	+	0.926642i
$65$	−2516.49			−0.0738774
$66$	−7562.26	−	6648.18i	−0.213694	−	0.187864i
$67$			5663.55i			0.154135i	0.997026	+	0.0770676i	$0.0245557\pi$
$67$			5663.55i			0.154135i	−0.997026	+	0.0770676i	$0.975444\pi$
$68$	19082.8	−	2465.18i	0.500461	−	0.0646511i
$69$			87741.5i			2.21862i
$70$		0			0
$71$			24339.4i			0.573012i	0.958078	+	0.286506i	$0.0924938\pi$
$71$			24339.4i			0.573012i	−0.958078	+	0.286506i	$0.907506\pi$
$72$	−37113.1	−	24994.2i	−0.843715	−	0.568208i
$73$		−	42720.1i		−	0.938263i	−0.883128	−	0.469132i	$-0.844567\pi$
$73$		−	42720.1i		−	0.938263i	0.883128	−	0.469132i	$-0.155433\pi$
$74$	52646.4	−	59884.9i	1.11761	−	1.27127i
$75$	−69041.9			−1.41729
$76$	4746.18	+	36739.9i	0.0942562	+	0.729632i
$77$		0			0
$78$	−92237.0	−	81088.0i	−1.71660	−	1.50911i
$79$			39976.1i			0.720663i	0.932824	+	0.360331i	$0.117336\pi$
$79$			39976.1i			0.720663i	−0.932824	+	0.360331i	$0.882664\pi$
$80$	−667.812	−	2541.61i	−0.0116662	−	0.0444001i
$81$	−58015.3			−0.982494
$82$	−60757.5	−	53413.5i	−0.997849	−	0.877236i
$83$	42246.6			0.673126			0.336563	−	0.941661i	$-0.390735\pi$
$83$	42246.6			0.673126			0.336563	+	0.941661i	$0.390735\pi$
$84$		0			0
$85$	−1543.09			−0.0231657
$86$	29268.0	+	25730.3i	0.426724	+	0.375144i
$87$	52076.5			0.737639
$88$	8129.38	−	12071.1i	0.111905	−	0.166165i
$89$			92505.4i			1.23792i	0.785423	+	0.618959i	$0.212445\pi$
$89$			92505.4i			1.23792i	−0.785423	+	0.618959i	$0.787555\pi$
$90$	2695.01	+	2369.25i	0.0350714	+	0.0308322i
$91$		0			0
$92$	−125772.	+	16247.6i	−1.54922	+	0.200133i
$93$	−131237.			−1.57343
$94$	−68019.4	+	77371.5i	−0.793986	+	0.903153i
$95$		−	2970.90i		−	0.0337737i
$96$	57420.2	−	114677.i	0.635896	−	1.26998i
$97$			35315.4i			0.381096i	0.981678	+	0.190548i	$0.0610265\pi$
$97$			35315.4i			0.381096i	−0.981678	+	0.190548i	$0.938973\pi$
$98$		0			0
$99$			19872.5i			0.203781i
$100$	−12784.9	−	98966.9i	−0.127849	−	0.989669i
$101$			69159.9i			0.674607i	0.941396	+	0.337303i	$0.109515\pi$
$101$			69159.9i			0.674607i	−0.941396	+	0.337303i	$0.890485\pi$
$102$	−56559.1	−	49722.6i	−0.538272	−	0.473209i
$103$	95325.3			0.885350			0.442675	−	0.896682i	$-0.354029\pi$
$103$	95325.3			0.885350			0.442675	+	0.896682i	$0.354029\pi$
$104$	99154.2	−	147231.i	0.898934	−	1.33480i
$105$		0			0
$106$	73571.6	−	83687.2i	0.635983	−	0.723426i
$107$			86797.8i			0.732908i	0.930436	+	0.366454i	$0.119428\pi$
$107$			86797.8i			0.732908i	−0.930436	+	0.366454i	$0.880572\pi$
$108$	379.598	+	2938.44i	0.00313159	+	0.0242414i
$109$	101542.			0.818615			0.409308	−	0.912396i	$-0.365770\pi$
$109$	101542.			0.818615			0.409308	+	0.912396i	$0.365770\pi$
$110$	−770.602	+	876.554i	−0.00607223	+	0.00690712i
$111$	−312075.			−2.40409
$112$		0			0
$113$	180243.			1.32789			0.663945	−	0.747782i	$-0.268881\pi$
$113$	180243.			1.32789			0.663945	+	0.747782i	$0.268881\pi$
$114$	95730.2	−	108892.i	0.689901	−	0.784758i
$115$	10170.3			0.0717113
$116$	9643.30	+	74648.2i	0.0665396	+	0.515080i
$117$			242385.i			1.63697i
$118$	94990.2	−	108051.i	0.628020	−	0.714369i
$119$		0			0
$120$	−5745.21	+	8530.90i	−0.0364211	+	0.0540806i
$121$	154587.			0.959866
$122$	−56955.6	−	50071.1i	−0.346447	−	0.304571i
$123$			316622.i			1.88703i
$124$	−24301.8	−	188119.i	−0.141933	−	1.09870i
$125$			16022.4i			0.0917176i
$126$		0			0
$127$			300092.i			1.65099i	0.564409	+	0.825495i	$0.309104\pi$
$127$			300092.i			1.65099i	−0.564409	+	0.825495i	$0.690896\pi$
$128$	175014.	+	61072.7i	0.944164	+	0.329475i
$129$		−	152523.i		−	0.806975i
$130$	−9399.05	+	10691.3i	−0.0487782	+	0.0554848i
$131$	−40149.1			−0.204408			−0.102204	−	0.994763i	$-0.532589\pi$
$131$	−40149.1			−0.204408			−0.102204	+	0.994763i	$0.532589\pi$
$132$	−56489.8	+	7297.54i	−0.282186	+	0.0364537i
$133$		0			0
$134$	24061.7	+	21153.3i	0.115762	+	0.101769i
$135$		−	237.611i		−	0.00112210i
$136$	60800.6	−	90281.0i	0.281878	−	0.418552i
$137$	−64514.0			−0.293665			−0.146833	−	0.989161i	$-0.546908\pi$
$137$	−64514.0			−0.293665			−0.146833	+	0.989161i	$0.546908\pi$
$138$	372771.	+	327713.i	1.66627	+	1.46486i
$139$	−94558.1			−0.415109			−0.207554	−	0.978223i	$-0.566550\pi$
$139$	−94558.1			−0.415109			−0.207554	+	0.978223i	$0.566550\pi$
$140$		0			0
$141$	403202.			1.70795
$142$	103406.	+	90907.2i	0.430354	+	0.378336i
$143$	−78836.0			−0.322392
$144$	−244805.	+	64322.8i	−0.983816	+	0.258499i
$145$		−	6036.27i		−	0.0238423i
$146$	−181497.	−	159559.i	−0.704672	−	0.619496i
$147$		0			0
$148$	−57788.6	−	447338.i	−0.216864	−	1.67873i
$149$	438429.			1.61783			0.808916	−	0.587924i	$-0.200055\pi$
$149$	438429.			1.61783			0.808916	+	0.587924i	$0.200055\pi$
$150$	−257870.	+	293326.i	−0.935778	+	1.06444i
$151$		−	167155.i		−	0.596592i	−0.954473	−	0.298296i	$-0.903582\pi$
$151$		−	167155.i		−	0.596592i	0.954473	−	0.298296i	$-0.0964183\pi$
$152$	173817.	+	117059.i	0.610215	+	0.410955i
$153$			148629.i			0.513304i
$154$		0			0
$155$			15211.9i			0.0508573i
$156$	−689008.	+	89008.3i	−2.26680	+	0.292832i
$157$		−	74018.0i		−	0.239656i	−0.992795	−	0.119828i	$-0.961766\pi$
$157$		−	74018.0i		−	0.239656i	0.992795	−	0.119828i	$-0.0382343\pi$
$158$	169839.	+	149310.i	0.541246	+	0.475824i
$159$	−436114.			−1.36807
$160$	−13292.3	−	6655.67i	−0.0410489	−	0.0205538i
$161$		0			0
$162$	−216686.	+	246479.i	−0.648700	+	0.737891i
$163$		−	186639.i		−	0.550217i	−0.961413	−	0.275108i	$-0.911286\pi$
$163$		−	186639.i		−	0.550217i	0.961413	−	0.275108i	$-0.0887137\pi$
$164$	−453856.	+	58630.6i	−1.31768	+	0.170222i
$165$	4567.93			0.0130620
$166$	157790.	−	179485.i	0.444437	−	0.505544i
$167$	−396668.			−1.10062			−0.550309	−	0.834961i	$-0.685490\pi$
$167$	−396668.			−1.10062			−0.550309	+	0.834961i	$0.685490\pi$
$168$		0			0
$169$	−590272.			−1.58977
$170$	−5763.42	+	6555.85i	−0.0152953	+	0.0173983i
$171$	−286153.			−0.748356
$172$	218631.	−	28243.4i	0.563495	−	0.0727942i
$173$		−	450638.i		−	1.14475i	−0.819991	−	0.572377i	$-0.806021\pi$
$173$		−	450638.i		−	1.14475i	0.819991	−	0.572377i	$-0.193979\pi$
$174$	194505.	−	221248.i	0.487032	−	0.553995i
$175$		0			0
$176$	−20921.1	−	79623.0i	−0.0509099	−	0.193757i
$177$	−563078.			−1.35094
$178$	393011.	+	345506.i	0.929725	+	0.817345i
$179$			546080.i			1.27387i	0.770919	+	0.636933i	$0.219797\pi$
$179$			546080.i			1.27387i	−0.770919	+	0.636933i	$0.780203\pi$
$180$	20131.6	−	2600.67i	0.0463124	−	0.00598279i
$181$			198083.i			0.449418i	0.974426	+	0.224709i	$0.0721431\pi$
$181$			198083.i			0.449418i	−0.974426	+	0.224709i	$0.927857\pi$
$182$		0			0
$183$			296809.i			0.655164i
$184$	−400727.	+	595027.i	−0.872577	+	1.29566i
$185$			36173.1i			0.0777064i
$186$	−490167.	+	557561.i	−1.03887	+	1.18171i
$187$	−48341.7			−0.101092
$188$	74663.1	+	577963.i	0.154068	+	1.19263i
$189$		0			0
$190$	−12621.9	−	11096.2i	−0.0253653	−	0.0222993i
$191$		−	111585.i		−	0.221321i	−0.993858	−	0.110661i	$-0.964703\pi$
$191$		−	111585.i		−	0.221321i	0.993858	−	0.110661i	$-0.0352967\pi$
$192$	−272742.	−	672265.i	−0.533948	−	1.31610i
$193$	779369.			1.50609			0.753043	−	0.657971i	$-0.228585\pi$
$193$	779369.			1.50609			0.753043	+	0.657971i	$0.228585\pi$
$194$	150038.	+	131902.i	0.286218	+	0.251622i
$195$	55715.2			0.104927
$196$		0			0
$197$	−350276.			−0.643049			−0.321525	−	0.946901i	$-0.604195\pi$
$197$	−350276.			−0.643049			−0.321525	+	0.946901i	$0.604195\pi$
$198$	84428.6	+	74223.4i	0.153048	+	0.134548i
$199$	−14954.4			−0.0267692			−0.0133846	−	0.999910i	$-0.504261\pi$
$199$	−14954.4			−0.0267692			−0.0133846	+	0.999910i	$0.504261\pi$
$200$	−468214.	−	315323.i	−0.827693	−	0.557417i
$201$		−	125391.i		−	0.218916i
$202$	293827.	+	258311.i	0.506656	+	0.445415i
$203$		0			0
$204$	−422494.	+	54579.2i	−0.710797	+	0.0918230i
$205$	36700.2			0.0609935
$206$	356039.	−	404991.i	0.584560	−	0.664933i
$207$		−	979588.i		−	1.58898i
$208$	−255175.	−	971164.i	−0.408959	−	1.55645i
$209$		−	93071.6i		−	0.147384i
$210$		0			0
$211$		−	17195.2i		−	0.0265890i	−0.999912	−	0.0132945i	$-0.995768\pi$
$211$		−	17195.2i		−	0.0265890i	0.999912	−	0.0132945i	$-0.00423190\pi$
$212$	−80757.7	−	625140.i	−0.123408	−	0.955296i
$213$		−	538875.i		−	0.813840i
$214$	368762.	+	324188.i	0.550442	+	0.483908i
$215$	−17679.1			−0.0260835
$216$	13901.8	+	9362.32i	0.0202739	+	0.0136537i
$217$		0			0
$218$	379258.	−	431403.i	0.540497	−	0.614812i
$219$			945824.i			1.33260i
$220$	845.870	+	6547.83i	0.00117828	+	0.00912096i
$221$	−589624.			−0.812073
$222$	−1.16559e6	+	1.32586e6i	−1.58732	+	1.80557i
$223$	368195.			0.495811			0.247905	−	0.968784i	$-0.420258\pi$
$223$	368195.			0.495811			0.247905	+	0.968784i	$0.420258\pi$
$224$		0			0
$225$	770816.			1.01507
$226$	673204.	−	765765.i	0.876750	−	0.997297i
$227$	594493.			0.765742			0.382871	−	0.923802i	$-0.374935\pi$
$227$	594493.			0.765742			0.382871	+	0.923802i	$0.374935\pi$
$228$	−105081.	−	813423.i	−0.133871	−	1.03628i
$229$			423922.i			0.534192i	0.963670	+	0.267096i	$0.0860641\pi$
$229$			423922.i			0.534192i	−0.963670	+	0.267096i	$0.913936\pi$
$230$	37985.8	−	43208.5i	0.0473480	−	0.0538580i
$231$		0			0
$232$	353162.	+	237840.i	0.430778	+	0.290112i
$233$	117716.			0.142052			0.0710259	−	0.997474i	$-0.477373\pi$
$233$	117716.			0.142052			0.0710259	+	0.997474i	$0.477373\pi$
$234$	1.02978e6	+	905305.i	1.22943	+	1.08082i
$235$		−	46735.8i		−	0.0552052i
$236$	−104268.	−	807135.i	−0.121863	−	0.943335i
$237$		−	885072.i		−	1.02355i
$238$		0			0
$239$		−	782169.i		−	0.885739i	−0.896586	−	0.442870i	$-0.853960\pi$
$239$		−	782169.i		−	0.885739i	0.896586	−	0.442870i	$-0.146040\pi$
$240$	14785.4	+	56271.4i	0.0165693	+	0.0630608i
$241$			1.23348e6i			1.36801i	0.729478	+	0.684004i	$0.239763\pi$
$241$			1.23348e6i			1.36801i	−0.729478	+	0.684004i	$0.760237\pi$
$242$	577382.	−	656767.i	0.633760	−	0.720897i
$243$	1.30696e6			1.41986
$244$	−425456.	+	54961.8i	−0.457489	+	0.0590999i
$245$		0			0
$246$	1.34517e6	+	1.18258e6i	1.41723	+	1.24592i
$247$		−	1.13520e6i		−	1.18394i
$248$	−889994.	−	599375.i	−0.918878	−	0.618827i
$249$	−935342.			−0.956031
$250$	68071.5	+	59843.4i	0.0688835	+	0.0605573i
$251$	1.78168e6			1.78503			0.892515	−	0.451018i	$-0.148939\pi$
$251$	1.78168e6			1.78503			0.892515	+	0.451018i	$0.148939\pi$
$252$		0			0
$253$	318612.			0.312940
$254$	1.27494e6	+	1.12084e6i	1.23996	+	1.09008i
$255$	34164.1			0.0329018
$256$	913142.	−	515444.i	0.870840	−	0.491566i
$257$			180436.i			0.170408i	0.996364	+	0.0852040i	$0.0271542\pi$
$257$			180436.i			0.170408i	−0.996364	+	0.0852040i	$0.972846\pi$
$258$	−647995.	−	569669.i	−0.606069	−	0.532811i
$259$		0			0
$260$	10317.1	+	79864.0i	0.00946507	+	0.0732686i
$261$	−581407.			−0.528298
$262$	−149956.	+	170574.i	−0.134962	+	0.153518i
$263$		−	94099.1i		−	0.0838873i	−0.999120	−	0.0419436i	$-0.986645\pi$
$263$		−	94099.1i		−	0.0838873i	0.999120	−	0.0419436i	$-0.0133550\pi$
$264$	−179985.	+	267254.i	−0.158937	+	0.236001i
$265$			50550.7i			0.0442194i
$266$		0			0
$267$		−	2.04807e6i		−	1.75820i
$268$	179740.	−	23219.4i	0.152865	−	0.0197476i
$269$			100381.i			0.0845803i	0.999105	+	0.0422901i	$0.0134654\pi$
$269$			100381.i			0.0845803i	−0.999105	+	0.0422901i	$0.986535\pi$
$270$	−1009.50	−	887.475i	−0.000842743	−	0.000740878i
$271$	−985074.			−0.814790			−0.407395	−	0.913252i	$-0.633563\pi$
$271$	−985074.			−0.814790			−0.407395	+	0.913252i	$0.633563\pi$
$272$	−156471.	−	595511.i	−0.128237	−	0.488053i
$273$		0			0
$274$	−240959.	+	274089.i	−0.193895	+	0.220554i
$275$			250709.i			0.199911i
$276$	2.78459e6	−	359722.i	2.20033	−	0.284246i
$277$	−698702.			−0.547132			−0.273566	−	0.961853i	$-0.588203\pi$
$277$	−698702.			−0.547132			−0.273566	+	0.961853i	$0.588203\pi$
$278$	−353173.	+	401732.i	−0.274079	+	0.311763i
$279$	1.46519e6			1.12689
$280$		0			0
$281$	−1.28297e6			−0.969285			−0.484642	−	0.874712i	$-0.661050\pi$
$281$	−1.28297e6			−0.969285			−0.484642	+	0.874712i	$0.661050\pi$
$282$	1.50595e6	−	1.71301e6i	1.12769	−	1.28274i
$283$	1.91015e6			1.41776			0.708879	−	0.705330i	$-0.249201\pi$
$283$	1.91015e6			1.41776			0.708879	+	0.705330i	$0.249201\pi$
$284$	772441.	−	99786.5i	0.568290	−	0.0734135i
$285$			65775.8i			0.0479682i
$286$	−294451.	+	334936.i	−0.212862	+	0.242129i
$287$		0			0
$288$	−641066.	+	1.28030e6i	−0.455430	+	0.909560i
$289$	1.05830e6			0.745359
$290$	−25645.2	−	22545.4i	−0.0179065	−	0.0157421i
$291$		−	781885.i		−	0.541265i
$292$	−1.35578e6	+	175144.i	−0.930531	+	0.120209i
$293$		−	149810.i		−	0.101946i	−0.998700	−	0.0509732i	$-0.983768\pi$
$293$		−	149810.i		−	0.101946i	0.998700	−	0.0509732i	$-0.0162323\pi$
$294$		0			0
$295$			65267.3i			0.0436657i
$296$	−2.11636e6	−	1.42529e6i	−1.40398	−	0.945524i
$297$		−	7443.84i		−	0.00489673i
$298$	1.63752e6	−	1.86267e6i	1.06819	−	1.21506i
$299$	3.88612e6			2.51384
$300$	283058.	+	2.19113e6i	0.181581	+	1.40561i
$301$		0			0
$302$	−710162.	−	624322.i	−0.448064	−	0.393905i
$303$		−	1.53120e6i		−	0.958134i
$304$	1.14653e6	−	301252.i	0.711543	−	0.186959i
$305$	34403.7			0.0211765
$306$	631452.	+	555126.i	0.385511	+	0.338913i
$307$	−26748.9			−0.0161979			−0.00809897	−	0.999967i	$-0.502578\pi$
$307$	−26748.9			−0.0161979			−0.00809897	+	0.999967i	$0.502578\pi$
$308$		0			0
$309$	−2.11051e6			−1.25745
$310$	64627.9	+	56816.1i	0.0381958	+	0.0335789i
$311$	−1.62563e6			−0.953059			−0.476529	−	0.879159i	$-0.658105\pi$
$311$	−1.62563e6			−0.953059			−0.476529	+	0.879159i	$0.658105\pi$
$312$	−2.19528e6	+	3.25971e6i	−1.27674	+	1.89580i
$313$		−	1.81341e6i		−	1.04625i	−0.852257	−	0.523124i	$-0.824767\pi$
$313$		−	1.81341e6i		−	1.04625i	0.852257	−	0.523124i	$-0.175233\pi$
$314$	−314467.	−	276456.i	−0.179991	−	0.158235i
$315$		0			0
$316$	1.26869e6	−	163894.i	0.714724	−	0.0923304i
$317$	−2.35582e6			−1.31672			−0.658360	−	0.752703i	$-0.728750\pi$
$317$	−2.35582e6			−1.31672			−0.658360	+	0.752703i	$0.728750\pi$
$318$	−1.62888e6	+	1.85284e6i	−0.903277	+	1.02747i
$319$		−	189103.i		−	0.104045i
$320$	−77923.4	+	31614.0i	−0.0425396	+	0.0172585i
$321$		−	1.92171e6i		−	1.04094i
$322$		0			0
$323$		−	696094.i		−	0.371246i
$324$	237851.	+	1.84119e6i	0.125876	+	0.974397i
$325$			3.05790e6i			1.60589i
$326$	−792939.	−	697094.i	−0.413234	−	0.363285i
$327$	−2.24815e6			−1.16267
$328$	−1.44605e6	+	2.14720e6i	−0.742163	+	1.10202i
$329$		0			0
$330$	17061.2	−	19406.9i	0.00862430	−	0.00981008i
$331$			3.46449e6i			1.73808i	0.494742	+	0.869040i	$0.335262\pi$
$331$			3.46449e6i			1.73808i	−0.494742	+	0.869040i	$0.664738\pi$
$332$	−173202.	−	1.34075e6i	−0.0862400	−	0.667579i
$333$	3.48415e6			1.72181
$334$	−1.48155e6	+	1.68525e6i	−0.726692	+	0.826607i
$335$	−14534.3			−0.00707591
$336$		0			0
$337$	−942106.			−0.451882			−0.225941	−	0.974141i	$-0.572546\pi$
$337$	−942106.			−0.451882			−0.225941	+	0.974141i	$0.572546\pi$
$338$	−2.20466e6	+	2.50778e6i	−1.04966	+	1.19398i
$339$	−3.99059e6			−1.88598
$340$	6326.36	+	48972.0i	0.00296795	+	0.0229747i
$341$			476554.i			0.221935i
$342$	−1.06878e6	+	1.21573e6i	−0.494108	+	0.562044i
$343$		0			0
$344$	696590.	−	1.03435e6i	0.317381	−	0.471270i
$345$	−225170.			−0.101851
$346$	−1.91454e6	−	1.68312e6i	−0.859755	−	0.755833i
$347$		−	523643.i		−	0.233460i	−0.993164	−	0.116730i	$-0.962759\pi$
$347$		−	523643.i		−	0.233460i	0.993164	−	0.116730i	$-0.0372412\pi$
$348$	−213503.	−	1.65271e6i	−0.0945053	−	0.731560i
$349$			1.24188e6i			0.545778i	0.962045	+	0.272889i	$0.0879792\pi$
$349$			1.24188e6i			0.545778i	−0.962045	+	0.272889i	$0.912021\pi$
$350$		0			0
$351$		−	90792.7i		−	0.0393354i
$352$	−416420.	−	208507.i	−0.179133	−	0.0896942i
$353$		−	2.22945e6i		−	0.952273i	−0.879371	−	0.476136i	$-0.842037\pi$
$353$		−	2.22945e6i		−	0.952273i	0.879371	−	0.476136i	$-0.157963\pi$
$354$	−2.10309e6	+	2.39225e6i	−0.891968	+	1.01461i
$355$	−62461.9			−0.0263054
$356$	2.93578e6	−	379253.i	1.22772	−	0.158600i
$357$		0			0
$358$	2.32003e6	+	2.03960e6i	0.956723	+	0.841080i
$359$		−	4.46801e6i		−	1.82969i	−0.403803	−	0.914846i	$-0.632312\pi$
$359$		−	4.46801e6i		−	1.82969i	0.403803	−	0.914846i	$-0.367688\pi$
$360$	64142.3	−	95243.0i	0.0260848	−	0.0387326i
$361$	−1.13592e6			−0.458753
$362$	841558.	+	739836.i	0.337530	+	0.296732i
$363$	−3.42257e6			−1.36328
$364$		0			0
$365$	109632.			0.0430730
$366$	1.26100e6	+	1.10858e6i	0.492053	+	0.432577i
$367$	1.18761e6			0.460266			0.230133	−	0.973159i	$-0.426084\pi$
$367$	1.18761e6			0.460266			0.230133	+	0.973159i	$0.426084\pi$
$368$	1.03128e6	+	3.92491e6i	0.396968	+	1.51081i
$369$		−	3.53492e6i		−	1.35149i
$370$	153682.	+	135106.i	0.0583605	+	0.0513063i
$371$		0			0
$372$	538044.	+	4.16496e6i	0.201586	+	1.56046i
$373$	3.48885e6			1.29840			0.649202	−	0.760616i	$-0.275103\pi$
$373$	3.48885e6			1.29840			0.649202	+	0.760616i	$0.275103\pi$
$374$	−180555.	+	205380.i	−0.0667469	+	0.0759242i
$375$		−	354737.i		−	0.130265i
$376$	2.73435e6	+	1.84147e6i	0.997435	+	0.671732i
$377$		−	2.30650e6i		−	0.835794i
$378$		0			0
$379$			1.83482e6i			0.656137i	0.944654	+	0.328068i	$0.106398\pi$
$379$			1.83482e6i			0.656137i	−0.944654	+	0.328068i	$0.893602\pi$
$380$	−94285.2	+	12180.1i	−0.0334953	+	0.00432704i
$381$		−	6.64404e6i		−	2.34488i
$382$	−474071.	−	416769.i	−0.166221	−	0.146129i
$383$	−1.69541e6			−0.590578			−0.295289	−	0.955408i	$-0.595416\pi$
$383$	−1.69541e6			−0.590578			−0.295289	+	0.955408i	$0.595416\pi$
$384$	−3.87482e6	−	1.35215e6i	−1.34098	−	0.467948i
$385$		0			0
$386$	2.91093e6	−	3.31116e6i	0.994406	−	1.13113i
$387$			1.70283e6i			0.577956i
$388$	1.12078e6	−	144786.i	0.377956	−	0.0488255i
$389$	−3.59849e6			−1.20572			−0.602861	−	0.797847i	$-0.705972\pi$
$389$	−3.59849e6			−1.20572			−0.602861	+	0.797847i	$0.705972\pi$
$390$	208095.	−	236707.i	0.0692789	−	0.0788042i
$391$	2.38294e6			0.788262
$392$		0			0
$393$	888902.			0.290317
$394$	−1.30827e6	+	1.48815e6i	−0.424578	+	0.482955i
$395$	−102590.			−0.0330836
$396$	630679.	−	81473.1i	0.202102	−	0.0261082i
$397$		−	2.21756e6i		−	0.706152i	−0.935595	−	0.353076i	$-0.885136\pi$
$397$		−	2.21756e6i		−	0.706152i	0.935595	−	0.353076i	$-0.114864\pi$
$398$	−55854.3	+	63533.9i	−0.0176746	+	0.0201047i
$399$		0			0
$400$	−3.08843e6	+	811488.i	−0.965133	+	0.253590i
$401$	819017.			0.254350			0.127175	−	0.991880i	$-0.459409\pi$
$401$	819017.			0.254350			0.127175	+	0.991880i	$0.459409\pi$
$402$	−532727.	−	468335.i	−0.164414	−	0.144541i
$403$			5.81254e6i			1.78280i
$404$	2.19488e6	−	283541.i	0.669047	−	0.0864297i
$405$		−	148884.i		−	0.0451035i
$406$		0			0
$407$			1.13322e6i			0.339101i
$408$	−1.34613e6	+	1.99883e6i	−0.400347	+	0.594463i
$409$			3.52880e6i			1.04308i	0.853226	+	0.521541i	$0.174643\pi$
$409$			3.52880e6i			1.04308i	−0.853226	+	0.521541i	$0.825357\pi$
$410$	137074.	−	155921.i	0.0402714	−	0.0458085i
$411$	1.42834e6			0.417088
$412$	−390814.	−	3.02527e6i	−0.113430	−	0.878054i
$413$		0			0
$414$	−4.16180e6	−	3.65874e6i	−1.19338	−	1.04913i
$415$			108417.i			0.0309013i
$416$	−5.07908e6	−	2.54317e6i	−1.43897	−	0.720513i
$417$	2.09352e6			0.589573
$418$	−395416.	−	347621.i	−0.110691	−	0.0973117i
$419$	2.07589e6			0.577656			0.288828	−	0.957381i	$-0.406734\pi$
$419$	2.07589e6			0.577656			0.288828	+	0.957381i	$0.406734\pi$
$420$		0			0
$421$	4.12936e6			1.13547			0.567737	−	0.823210i	$-0.307819\pi$
$421$	4.12936e6			1.13547			0.567737	+	0.823210i	$0.307819\pi$
$422$	−73054.3	−	64223.9i	−0.0199694	−	0.0175556i
$423$	−4.50154e6			−1.22323
$424$	−2.95755e6	−	1.99179e6i	−0.798946	−	0.538058i
$425$			1.87508e6i			0.503556i
$426$	−2.28942e6	−	2.01269e6i	−0.611226	−	0.537345i
$427$		0			0
$428$	2.75464e6	−	355853.i	0.726868	−	0.0938992i
$429$	1.74543e6			0.457889
$430$	−66031.3	+	75110.1i	−0.0172218	+	0.0195897i
$431$			464413.i			0.120423i	0.998186	+	0.0602117i	$0.0191776\pi$
$431$			464413.i			0.120423i	−0.998186	+	0.0602117i	$0.980822\pi$
$432$	91699.0	−	24094.1i	0.0236404	−	0.00621156i
$433$		−	963586.i		−	0.246985i	−0.992345	−	0.123493i	$-0.960590\pi$
$433$		−	963586.i		−	0.246985i	0.992345	−	0.123493i	$-0.0394095\pi$
$434$		0			0
$435$			133643.i			0.0338629i
$436$	−416302.	−	3.22257e6i	−0.104880	−	0.811869i
$437$			4.58784e6i			1.14922i
$438$	4.01835e6	+	3.53264e6i	1.00084	+	0.879861i
$439$	−2.72777e6			−0.675532			−0.337766	−	0.941230i	$-0.609671\pi$
$439$	−2.72777e6			−0.675532			−0.337766	+	0.941230i	$0.609671\pi$
$440$	30977.9	+	20862.3i	0.00762816	+	0.00513726i
$441$		0			0
$442$	−2.20224e6	+	2.50503e6i	−0.536177	+	0.609898i
$443$			1.79763e6i			0.435201i	0.976038	+	0.217601i	$0.0698230\pi$
$443$			1.79763e6i			0.435201i	−0.976038	+	0.217601i	$0.930177\pi$
$444$	1.27944e6	+	9.90410e6i	0.308009	+	2.38428i
$445$	−237396.			−0.0568293
$446$	1.37520e6	−	1.56428e6i	0.327363	−	0.372373i
$447$	−9.70684e6			−2.29778
$448$		0			0
$449$	−4.42590e6			−1.03606			−0.518031	−	0.855362i	$-0.673335\pi$
$449$	−4.42590e6			−1.03606			−0.518031	+	0.855362i	$0.673335\pi$
$450$	2.87898e6	−	3.27482e6i	0.670206	−	0.762354i
$451$	1.14973e6			0.266168
$452$	−738959.	−	5.72024e6i	−0.170127	−	1.31695i
$453$			3.70082e6i			0.847331i
$454$	2.22042e6	−	2.52572e6i	0.505587	−	0.575102i
$455$		0			0
$456$	−3.84831e6	−	2.59168e6i	−0.866679	−	0.583673i
$457$	−7.00990e6			−1.57008			−0.785040	−	0.619446i	$-0.787357\pi$
$457$	−7.00990e6			−1.57008			−0.785040	+	0.619446i	$0.787357\pi$
$458$	1.80104e6	+	1.58334e6i	0.401199	+	0.352705i
$459$		−	55673.4i		−	0.0123343i
$460$	−41696.0	−	322766.i	−0.00918756	−	0.0711203i
$461$			8.59109e6i			1.88276i	0.337341	+	0.941382i	$0.390472\pi$
$461$			8.59109e6i			1.88276i	−0.337341	+	0.941382i	$0.609528\pi$
$462$		0			0
$463$			877840.i			0.190311i	0.995462	+	0.0951553i	$0.0303348\pi$
$463$			877840.i			0.190311i	−0.995462	+	0.0951553i	$0.969665\pi$
$464$	2.32952e6	−	612085.i	0.502310	−	0.131983i
$465$		−	336791.i		−	0.0722318i
$466$	439668.	−	500119.i	0.0937908	−	0.106686i
$467$	7.15954e6			1.51912			0.759561	−	0.650436i	$-0.225414\pi$
$467$	7.15954e6			1.51912			0.759561	+	0.650436i	$0.225414\pi$
$468$	7.69241e6	−	993730.i	1.62348	−	0.209727i
$469$		0			0
$470$	−198558.	−	174557.i	−0.0414612	−	0.0364497i
$471$			1.63876e6i			0.340380i
$472$	−3.81857e6	−	2.57165e6i	−0.788942	−	0.531321i
$473$	−553848.			−0.113825
$474$	−3.76024e6	−	3.30573e6i	−0.768723	−	0.675805i
$475$	−3.61007e6			−0.734144
$476$		0			0
$477$	4.86898e6			0.979811
$478$	−3.32306e6	−	2.92139e6i	−0.665225	−	0.584817i
$479$	4.90745e6			0.977276			0.488638	−	0.872487i	$-0.337494\pi$
$479$	4.90745e6			0.977276			0.488638	+	0.872487i	$0.337494\pi$
$480$	294293.	+	147357.i	0.0583012	+	0.0291922i
$481$			1.38220e7i			2.72400i
$482$	5.24045e6	+	4.60702e6i	1.02743	+	0.903239i
$483$		0			0
$484$	−633777.	−	4.90603e6i	−0.122977	−	0.951956i
$485$	−90629.5			−0.0174951
$486$	4.88148e6	−	5.55265e6i	0.937477	−	1.06637i
$487$		−	1.13898e6i		−	0.217617i	−0.994063	−	0.108808i	$-0.965296\pi$
$487$		−	1.13898e6i		−	0.217617i	0.994063	−	0.108808i	$-0.0347035\pi$
$488$	−1.35557e6	+	2.01284e6i	−0.257674	+	0.382613i
$489$			4.13220e6i			0.781464i
$490$		0			0
$491$		−	2.85826e6i		−	0.535055i	−0.963550	−	0.267528i	$-0.913793\pi$
$491$		−	2.85826e6i		−	0.535055i	0.963550	−	0.267528i	$-0.0862066\pi$
$492$	1.00484e7	−	1.29808e6i	1.87148	−	0.241763i
$493$		−	1.41433e6i		−	0.262079i
$494$	−4.82290e6	−	4.23994e6i	−0.889183	−	0.781704i
$495$	−50998.6			−0.00935503
$496$	−5.87057e6	+	1.54250e6i	−1.07146	+	0.281527i
$497$		0			0
$498$	−3.49349e6	+	3.97382e6i	−0.631227	+	0.718016i
$499$		−	1.19215e6i		−	0.214329i	−0.994241	−	0.107165i	$-0.965823\pi$
$499$		−	1.19215e6i		−	0.214329i	0.994241	−	0.107165i	$-0.0341772\pi$
$500$	508492.	−	65688.6i	0.0909618	−	0.0117507i
$501$	8.78226e6			1.56319
$502$	6.65454e6	−	7.56950e6i	1.17858	−	1.34063i
$503$	3.90095e6			0.687465			0.343732	−	0.939068i	$-0.388309\pi$
$503$	3.90095e6			0.687465			0.343732	+	0.939068i	$0.388309\pi$
$504$		0			0
$505$	−177484.			−0.0309693
$506$	1.19001e6	−	1.35363e6i	0.206621	−	0.235030i
$507$	1.30687e7			2.25793
$508$	9.52379e6	−	1.23031e6i	1.63738	−	0.211523i
$509$			6.72650e6i			1.15079i	0.817877	+	0.575393i	$0.195151\pi$
$509$			6.72650e6i			1.15079i	−0.817877	+	0.575393i	$0.804849\pi$
$510$	127603.	−	145147.i	0.0217237	−	0.0247106i
$511$		0			0
$512$	1.22070e6	−	5.80468e6i	0.205794	−	0.978595i
$513$	107187.			0.0179825
$514$	766585.	+	673925.i	0.127983	+	0.112513i
$515$			244632.i			0.0406440i
$516$	−4.84050e6	+	625311.i	−0.800324	+	0.103388i
$517$		−	1.46413e6i		−	0.240909i
$518$		0			0
$519$			9.97714e6i			1.62588i
$520$	377838.	+	254458.i	0.0612769	+	0.0412675i
$521$		−	3.03652e6i		−	0.490097i	−0.969511	−	0.245049i	$-0.921196\pi$
$521$		−	3.03652e6i		−	0.490097i	0.969511	−	0.245049i	$-0.0788040\pi$
$522$	−2.17154e6	+	2.47012e6i	−0.348813	+	0.396772i
$523$	−1.10904e7			−1.77294			−0.886471	−	0.462785i	$-0.846850\pi$
$523$	−1.10904e7			−1.77294			−0.886471	+	0.462785i	$0.846850\pi$
$524$	164603.	+	1.27418e6i	0.0261884	+	0.202723i
$525$		0			0
$526$	−399782.	−	351459.i	−0.0630026	−	0.0553872i
$527$			3.56421e6i			0.559031i
$528$	463193.	+	1.76286e6i	0.0723065	+	0.275190i
$529$	−9.26921e6			−1.44014
$530$	214766.	+	188806.i	0.0332105	+	0.0291962i
$531$	6.28647e6			0.967544
$532$		0			0
$533$	1.40233e7			2.13813
$534$	−8.70128e6	−	7.64952e6i	−1.32047	−	1.16086i
$535$	−222748.			−0.0336457
$536$	572678.	−	850353.i	0.0860991	−	0.127846i
$537$		−	1.20902e7i		−	1.80925i
$538$	426469.	+	374920.i	0.0635231	+	0.0558448i
$539$		0			0
$540$	−7540.90	+	974.158i	−0.00111286	+	0.000143762i
$541$	880519.			0.129344			0.0646719	−	0.997907i	$-0.479400\pi$
$541$	880519.			0.129344			0.0646719	+	0.997907i	$0.479400\pi$
$542$	−3.67924e6	+	4.18510e6i	−0.537972	+	0.611939i
$543$		−	4.38556e6i		−	0.638302i
$544$	−3.11445e6	−	1.55945e6i	−0.451216	−	0.225930i
$545$			260586.i			0.0375803i
$546$		0			0
$547$			6.56436e6i			0.938047i	0.883186	+	0.469023i	$0.155394\pi$
$547$			6.56436e6i			0.938047i	−0.883186	+	0.469023i	$0.844606\pi$
$548$	264494.	+	2.04743e6i	0.0376240	+	0.291245i
$549$		−	3.31372e6i		−	0.469229i
$550$	1.06514e6	+	936392.i	0.150141	+	0.131993i
$551$	2.72298e6			0.382090
$552$	8.87211e6	−	1.31739e7i	1.23931	−	1.84021i
$553$		0			0
$554$	−2.60964e6	+	2.96845e6i	−0.361248	+	0.410918i
$555$		−	800875.i		−	0.110365i
$556$	387669.	+	3.00092e6i	0.0531832	+	0.411688i
$557$	−1.05590e6			−0.144206			−0.0721031	−	0.997397i	$-0.522971\pi$
$557$	−1.05590e6			−0.144206			−0.0721031	+	0.997397i	$0.522971\pi$
$558$	5.47245e6	−	6.22488e6i	0.744041	−	0.846341i
$559$	−6.75530e6			−0.914356
$560$		0			0
$561$	1.07029e6			0.143580
$562$	−4.79188e6	+	5.45073e6i	−0.639978	+	0.727971i
$563$	−6.57110e6			−0.873709			−0.436855	−	0.899532i	$-0.643908\pi$
$563$	−6.57110e6			−0.873709			−0.436855	+	0.899532i	$0.643908\pi$
$564$	−1.65305e6	−	1.27961e7i	−0.218820	−	1.69387i
$565$			462556.i			0.0609597i
$566$	7.13439e6	−	8.11532e6i	0.936086	−	1.06479i
$567$		0			0
$568$	2.46111e6	−	3.65443e6i	0.320081	−	0.475279i
$569$	4.52467e6			0.585877			0.292938	−	0.956131i	$-0.405367\pi$
$569$	4.52467e6			0.585877			0.292938	+	0.956131i	$0.405367\pi$
$570$	279450.	+	245671.i	0.0360260	+	0.0316714i
$571$		−	590361.i		−	0.0757753i	−0.999282	−	0.0378876i	$-0.987937\pi$
$571$		−	590361.i		−	0.0757753i	0.999282	−	0.0378876i	$-0.0120629\pi$
$572$	323212.	+	2.50196e6i	0.0413045	+	0.319735i
$573$			2.47050e6i			0.314339i
$574$		0			0
$575$		−	1.23583e7i		−	1.55880i
$576$	3.04502e6	+	7.50549e6i	0.382414	+	0.942590i
$577$			451460.i			0.0564521i	0.999602	+	0.0282260i	$0.00898582\pi$
$577$			451460.i			0.0564521i	−0.999602	+	0.0282260i	$0.991014\pi$
$578$	3.95275e6	−	4.49622e6i	0.492130	−	0.559794i
$579$	−1.72553e7			−2.13907
$580$	−191569.	+	24747.5i	−0.0236459	+	0.00305465i
$581$		0			0
$582$	−3.32185e6	−	2.92033e6i	−0.406511	−	0.357375i
$583$			1.58364e6i			0.192968i
$584$	−4.31970e6	+	6.41420e6i	−0.524109	+	0.778234i
$585$	−622031.			−0.0751488
$586$	−636470.	−	559538.i	−0.0765657	−	0.0673109i
$587$	6.87565e6			0.823604			0.411802	−	0.911273i	$-0.364900\pi$
$587$	6.87565e6			0.823604			0.411802	+	0.911273i	$0.364900\pi$
$588$		0			0
$589$	−6.86212e6			−0.815023
$590$	277289.	+	243772.i	0.0327947	+	0.0288306i
$591$	7.75512e6			0.913313
$592$	−1.39599e7	+	3.66799e6i	−1.63712	+	0.430154i
$593$		−	1.53361e7i		−	1.79093i	−0.445129	−	0.895466i	$-0.646842\pi$
$593$		−	1.53361e7i		−	1.79093i	0.445129	−	0.895466i	$-0.353158\pi$
$594$	−31625.3	−	27802.6i	−0.00367763	−	0.00323310i
$595$		0			0
$596$	−1.79747e6	−	1.39141e7i	−0.207274	−	1.60450i
$597$	331091.			0.0380199
$598$	1.45146e7	−	1.65102e7i	1.65978	−	1.88799i
$599$		−	4.12329e6i		−	0.469544i	−0.972050	−	0.234772i	$-0.924566\pi$
$599$		−	4.12329e6i		−	0.469544i	0.972050	−	0.234772i	$-0.0754344\pi$
$600$	1.03663e7	+	6.98127e6i	1.17556	+	0.791692i
$601$		−	1.79015e6i		−	0.202164i	−0.994878	−	0.101082i	$-0.967770\pi$
$601$		−	1.79015e6i		−	0.202164i	0.994878	−	0.101082i	$-0.0322305\pi$
$602$		0			0
$603$			1.39993e6i			0.156788i
$604$	−5.30488e6	+	685302.i	−0.591675	+	0.0764346i
$605$			396716.i			0.0440648i
$606$	−6.50534e6	−	5.71902e6i	−0.719596	−	0.632616i
$607$	−1.32087e6			−0.145508			−0.0727540	−	0.997350i	$-0.523179\pi$
$607$	−1.32087e6			−0.145508			−0.0727540	+	0.997350i	$0.523179\pi$
$608$	3.00239e6	−	5.99622e6i	0.329388	−	0.657837i
$609$		0			0
$610$	128497.	−	146165.i	0.0139820	−	0.0159044i
$611$		−	1.78580e7i		−	1.93522i
$612$	4.71693e6	−	609348.i	0.509073	−	0.0657638i
$613$	6.48815e6			0.697380			0.348690	−	0.937238i	$-0.386627\pi$
$613$	6.48815e6			0.697380			0.348690	+	0.937238i	$0.386627\pi$
$614$	−99906.7	+	113643.i	−0.0106948	+	0.0121653i
$615$	−812543.			−0.0866281
$616$		0			0
$617$	−7.26297e6			−0.768071			−0.384035	−	0.923318i	$-0.625466\pi$
$617$	−7.26297e6			−0.768071			−0.384035	+	0.923318i	$0.625466\pi$
$618$	−7.88271e6	+	8.96653e6i	−0.830242	+	0.944394i
$619$	−9.61329e6			−1.00843			−0.504214	−	0.863578i	$-0.668218\pi$
$619$	−9.61329e6			−1.00843			−0.504214	+	0.863578i	$0.668218\pi$
$620$	482768.	−	62365.5i	0.0504382	−	0.00651576i
$621$			366934.i			0.0381820i
$622$	−6.07169e6	+	6.90650e6i	−0.629265	+	0.715784i
$623$		0			0
$624$	5.64958e6	+	2.15016e7i	0.580838	+	2.21060i
$625$	9.70393e6			0.993682
$626$	−7.70429e6	−	6.77304e6i	−0.785772	−	0.690793i
$627$			2.06061e6i			0.209328i
$628$	−2.34906e6	+	303459.i	−0.237681	+	0.0307044i
$629$			8.47552e6i			0.854161i
$630$		0			0
$631$			1.70616e7i			1.70587i	0.522017	+	0.852935i	$0.325180\pi$
$631$			1.70616e7i			1.70587i	−0.522017	+	0.852935i	$0.674820\pi$
$632$	4.04224e6	−	6.00220e6i	0.402559	−	0.597747i
$633$			380703.i			0.0377640i
$634$	−8.79894e6	+	1.00087e7i	−0.869375	+	0.988908i
$635$	−770122.			−0.0757923
$636$	1.78798e6	+	1.38406e7i	0.175275	+	1.35679i
$637$		0			0
$638$	−803408.	−	706297.i	−0.0781420	−	0.0686967i
$639$			6.01626e6i			0.582873i
$640$	−156730.	+	449136.i	−0.0151253	+	0.0433439i
$641$	1.51865e7			1.45987			0.729933	−	0.683518i	$-0.239551\pi$
$641$	1.51865e7			1.45987			0.729933	+	0.683518i	$0.239551\pi$
$642$	−8.16441e6	−	7.17755e6i	−0.781785	−	0.687288i
$643$	−1.16456e7			−1.11079			−0.555396	−	0.831586i	$-0.687433\pi$
$643$	−1.16456e7			−1.11079			−0.555396	+	0.831586i	$0.687433\pi$
$644$		0			0
$645$	391417.			0.0370459
$646$	−2.95737e6	−	2.59990e6i	−0.278820	−	0.245118i
$647$	5.90941e6			0.554988			0.277494	−	0.960727i	$-0.410496\pi$
$647$	5.90941e6			0.554988			0.277494	+	0.960727i	$0.410496\pi$
$648$	8.71069e6	+	5.86630e6i	0.814921	+	0.548816i
$649$			2.04468e6i			0.190552i
$650$	1.29915e7	+	1.14212e7i	1.20608	+	1.06030i
$651$		0			0
$652$	−5.92323e6	+	765182.i	−0.545682	+	0.0704930i
$653$	−4.77946e6			−0.438628			−0.219314	−	0.975654i	$-0.570382\pi$
$653$	−4.77946e6			−0.438628			−0.219314	+	0.975654i	$0.570382\pi$
$654$	−8.39679e6	+	9.55129e6i	−0.767660	+	0.873208i
$655$		−	103034.i		−	0.00938378i
$656$	3.72144e6	+	1.41633e7i	0.337638	+	1.28501i
$657$		−	1.05596e7i		−	0.954411i
$658$		0			0
$659$		−	5.36654e6i		−	0.481372i	−0.970603	−	0.240686i	$-0.922628\pi$
$659$		−	5.36654e6i		−	0.481372i	0.970603	−	0.240686i	$-0.0773723\pi$
$660$	−18727.6	−	144969.i	−0.00167349	−	0.0129544i
$661$		−	1.54071e7i		−	1.37157i	−0.727804	−	0.685786i	$-0.759459\pi$
$661$		−	1.54071e7i		−	1.37157i	0.727804	−	0.685786i	$-0.240541\pi$
$662$	1.47190e7	+	1.29398e7i	1.30537	+	1.14758i
$663$	1.30543e7			1.15337
$664$	−6.34311e6	−	4.27182e6i	−0.558318	−	0.376005i
$665$		0			0
$666$	1.30132e7	−	1.48025e7i	1.13684	−	1.29315i
$667$			9.32158e6i			0.811288i
$668$	1.62626e6	+	1.25888e7i	0.141010	+	1.09155i
$669$	−8.15186e6			−0.704193
$670$	−54285.4	+	61749.3i	−0.00467193	+	0.00531429i
$671$	1.07779e6			0.0924119
$672$		0			0
$673$	−3.09611e6			−0.263499			−0.131750	−	0.991283i	$-0.542059\pi$
$673$	−3.09611e6			−0.263499			−0.131750	+	0.991283i	$0.542059\pi$
$674$	−3.51875e6	+	4.00256e6i	−0.298359	+	0.339381i
$675$	−288732.			−0.0243914
$676$	2.42000e6	+	1.87330e7i	0.203680	+	1.57667i
$677$			9.95794e6i			0.835022i	0.908672	+	0.417511i	$0.137098\pi$
$677$			9.95794e6i			0.835022i	−0.908672	+	0.417511i	$0.862902\pi$
$678$	−1.49048e7	+	1.69541e7i	−1.24523	+	1.41645i
$679$		0			0
$680$	231687.	+	156032.i	0.0192145	+	0.0129402i
$681$	−1.31621e7			−1.08757
$682$	2.02465e6	+	1.77992e6i	0.166682	+	0.146534i
$683$		−	1.13131e7i		−	0.927958i	−0.885846	−	0.463979i	$-0.846421\pi$
$683$		−	1.13131e7i		−	0.927958i	0.885846	−	0.463979i	$-0.153579\pi$
$684$	1.17317e6	+	9.08143e6i	0.0958783	+	0.742188i
$685$		−	165562.i		−	0.0134813i
$686$		0			0
$687$		−	9.38566e6i		−	0.758705i
$688$	−1.79268e6	−	6.82274e6i	−0.144389	−	0.549525i
$689$			1.93157e7i			1.55011i
$690$	−841007.	+	956640.i	−0.0672476	+	0.0764937i
$691$	3.06789e6			0.244424			0.122212	−	0.992504i	$-0.461001\pi$
$691$	3.06789e6			0.244424			0.122212	+	0.992504i	$0.461001\pi$
$692$	−1.43016e7	+	1.84752e6i	−1.13532	+	0.146664i
$693$		0			0
$694$	−2.22471e6	−	1.95580e6i	−0.175337	−	0.154144i
$695$		−	242664.i		−	0.0190565i
$696$	−7.81902e6	−	5.26579e6i	−0.611828	−	0.412041i
$697$	8.59901e6			0.670450
$698$	5.27615e6	+	4.63840e6i	0.409901	+	0.360354i
$699$	−2.60624e6			−0.201754
$700$		0			0
$701$	33900.5			0.00260562			0.00130281	−	0.999999i	$-0.499585\pi$
$701$	33900.5			0.00260562			0.00130281	+	0.999999i	$0.499585\pi$
$702$	−385734.	−	339109.i	−0.0295424	−	0.0259715i
$703$	−1.63178e7			−1.24530
$704$	−2.44117e6	+	990395.i	−0.185638	+	0.0753142i
$705$			1.03473e6i			0.0784071i
$706$	−9.47186e6	−	8.32697e6i	−0.715194	−	0.628746i
$707$		0			0
$708$	2.30851e6	+	1.78700e7i	0.173080	+	1.33980i
$709$	8.08213e6			0.603824			0.301912	−	0.953336i	$-0.402375\pi$
$709$	8.08213e6			0.603824			0.301912	+	0.953336i	$0.402375\pi$
$710$	−233294.	+	265371.i	−0.0173683	+	0.0197564i
$711$			9.88136e6i			0.733065i
$712$	9.35381e6	−	1.38892e7i	0.691494	−	1.02678i
$713$		−	2.34911e7i		−	1.73053i
$714$		0			0
$715$		−	202316.i		−	0.0148001i
$716$	1.73305e7	−	2.23882e6i	1.26337	−	0.163206i
$717$			1.73173e7i			1.25800i
$718$	−1.89824e7	−	1.66879e7i	−1.37417	−	1.20807i
$719$	1.40670e7			1.01480			0.507398	−	0.861712i	$-0.330607\pi$
$719$	1.40670e7			1.01480			0.507398	+	0.861712i	$0.330607\pi$
$720$	−165071.	−	628240.i	−0.0118670	−	0.0451642i
$721$		0			0
$722$	−4.24264e6	+	4.82597e6i	−0.302896	+	0.344542i
$723$		−	2.73093e7i		−	1.94296i
$724$	6.28641e6	−	812099.i	0.445714	−	0.0575788i
$725$	−7.33495e6			−0.518265
$726$	−1.27833e7	+	1.45409e7i	−0.900119	+	1.02388i
$727$	1.08183e7			0.759145			0.379572	−	0.925162i	$-0.376071\pi$
$727$	1.08183e7			0.759145			0.379572	+	0.925162i	$0.376071\pi$
$728$		0			0
$729$	−1.48385e7			−1.03412
$730$	409474.	−	465774.i	0.0284393	−	0.0323495i
$731$	−4.14230e6			−0.286714
$732$	9.41962e6	−	1.21686e6i	0.649764	−	0.0839387i
$733$			8.58482e6i			0.590162i	0.955472	+	0.295081i	$0.0953466\pi$
$733$			8.58482e6i			0.590162i	−0.955472	+	0.295081i	$0.904653\pi$
$734$	4.43570e6	−	5.04558e6i	0.303894	−	0.345677i
$735$		0			0
$736$	2.05269e7	+	1.02781e7i	1.39678	+	0.699387i
$737$	−455328.			−0.0308785
$738$	−1.50181e7	−	1.32028e7i	−1.01502	−	0.892333i
$739$			1.35460e7i			0.912432i	0.889869	+	0.456216i	$0.150796\pi$
$739$			1.35460e7i			0.912432i	−0.889869	+	0.456216i	$0.849204\pi$
$740$	1.14800e6	−	148302.i	0.0770660	−	0.00995563i
$741$			2.51333e7i			1.68153i
$742$		0			0
$743$		−	2.57238e7i		−	1.70948i	−0.519057	−	0.854740i	$-0.673717\pi$
$743$		−	2.57238e7i		−	1.70948i	0.519057	−	0.854740i	$-0.326283\pi$
$744$	1.97045e7	+	1.32702e7i	1.30507	+	0.878911i
$745$			1.12514e6i			0.0742702i
$746$	1.30308e7	−	1.48224e7i	0.857281	−	0.975151i
$747$	1.04426e7			0.684710
$748$	198191.	+	1.53418e6i	0.0129518	+	0.100259i
$749$		0			0
$750$	−1.50711e6	−	1.32494e6i	−0.0978342	−	0.0860086i
$751$			2.54858e7i			1.64892i	0.565924	+	0.824458i	$0.308520\pi$
$751$			2.54858e7i			1.64892i	−0.565924	+	0.824458i	$0.691480\pi$
$752$	1.80363e7	−	4.73906e6i	1.16306	−	0.305596i
$753$	−3.94465e7			−2.53525
$754$	−9.79918e6	−	8.61472e6i	−0.627714	−	0.551840i
$755$	428969.			0.0273879
$756$		0			0
$757$	2.84880e6			0.180685			0.0903425	−	0.995911i	$-0.471204\pi$
$757$	2.84880e6			0.180685			0.0903425	+	0.995911i	$0.471204\pi$
$758$	7.79524e6	+	6.85300e6i	0.492784	+	0.433220i
$759$	−7.05408e6			−0.444464
$760$	−300406.	+	446065.i	−0.0188658	+	0.0280133i
$761$		−	2.36887e7i		−	1.48279i	−0.671070	−	0.741394i	$-0.734165\pi$
$761$		−	2.36887e7i		−	1.48279i	0.671070	−	0.741394i	$-0.265835\pi$
$762$	−2.82273e7	−	2.48154e7i	−1.76109	−	1.54822i
$763$		0			0
$764$	−3.54130e6	+	457476.i	−0.219497	+	0.0283554i
$765$	−381425.			−0.0235643
$766$	−6.33232e6	+	7.20296e6i	−0.389934	+	0.443547i
$767$			2.49390e7i			1.53070i
$768$	−2.02170e7	+	1.14120e7i	−1.23684	+	0.698164i
$769$		−	2.67208e7i		−	1.62942i	−0.579866	−	0.814712i	$-0.696895\pi$
$769$		−	2.67208e7i		−	1.62942i	0.579866	−	0.814712i	$-0.303105\pi$
$770$		0			0
$771$		−	3.99486e6i		−	0.242028i
$772$	−3.19525e6	−	2.47343e7i	−0.192958	−	1.49367i
$773$		−	2.97686e7i		−	1.79189i	−0.444169	−	0.895943i	$-0.646501\pi$
$773$		−	2.97686e7i		−	1.79189i	0.444169	−	0.895943i	$-0.353499\pi$
$774$	7.23452e6	+	6.36006e6i	0.434067	+	0.381600i
$775$	1.84846e7			1.10549
$776$	3.57097e6	−	5.30242e6i	0.212878	−	0.316097i
$777$		0			0
$778$	−1.34403e7	+	1.52883e7i	−0.796087	+	0.905543i
$779$			1.65556e7i			0.977463i
$780$	−228421.	−	1.76819e6i	−0.0134431	−	0.104062i
$781$	−1.95679e6			−0.114794
$782$	8.90023e6	−	1.01240e7i	0.520457	−	0.592016i
$783$	217783.			0.0126946
$784$		0			0
$785$	189952.			0.0110019
$786$	3.32003e6	−	3.77652e6i	0.191684	−	0.218039i
$787$	−1.65056e7			−0.949939			−0.474969	−	0.880002i	$-0.657541\pi$
$787$	−1.65056e7			−0.949939			−0.474969	+	0.880002i	$0.657541\pi$
$788$	1.43606e6	+	1.11164e7i	0.0823866	+	0.637750i
$789$			2.08336e6i			0.119144i
$790$	−383173.	+	435856.i	−0.0218437	+	0.0248471i
$791$		0			0
$792$	2.00944e6	−	2.98375e6i	0.113831	−	0.169024i
$793$	1.31458e7			0.742344
$794$	−9.42133e6	−	8.28254e6i	−0.530348	−	0.466243i
$795$		−	1.11920e6i		−	0.0628041i
$796$	61309.9	+	474596.i	0.00342963	+	0.0265486i
$797$		−	1.84844e6i		−	0.103076i	−0.998671	−	0.0515381i	$-0.983588\pi$
$797$		−	1.84844e6i		−	0.103076i	0.998671	−	0.0515381i	$-0.0164124\pi$
$798$		0			0
$799$		−	1.09504e7i		−	0.606824i
$800$	−8.08760e6	+	1.61521e7i	−0.446781	+	0.892287i
$801$			2.28657e7i			1.25922i
$802$	3.05901e6	−	3.47961e6i	0.167937	−	0.191027i
$803$	3.43453e6			0.187966
$804$	−3.97945e6	+	514079.i	−0.217112	+	0.0280472i
$805$		0			0
$806$	2.46947e7	+	2.17097e7i	1.33895	+	1.17711i
$807$		−	2.22243e6i		−	0.120128i
$808$	6.99320e6	−	1.03840e7i	0.376832	−	0.559546i
$809$	7.15081e6			0.384135			0.192068	−	0.981382i	$-0.438481\pi$
$809$	7.15081e6			0.384135			0.192068	+	0.981382i	$0.438481\pi$
$810$	−632536.	−	556080.i	−0.0338745	−	0.0297800i
$811$	2.59878e7			1.38745			0.693724	−	0.720241i	$-0.255969\pi$
$811$	2.59878e7			1.38745			0.693724	+	0.720241i	$0.255969\pi$
$812$		0			0
$813$	2.18096e7			1.15723
$814$	4.81452e6	+	4.23257e6i	0.254678	+	0.223894i
$815$	478970.			0.0252589
$816$	3.46428e6	+	1.31846e7i	0.182133	+	0.693175i
$817$		−	7.97512e6i		−	0.418005i
$818$	1.49921e7	+	1.31800e7i	0.783395	+	0.688703i
$819$		0			0
$820$	−150463.	−	1.16473e6i	−0.00781440	−	0.0604908i
$821$	−2.55002e7			−1.32034			−0.660169	−	0.751117i	$-0.729515\pi$
$821$	−2.55002e7			−1.32034			−0.660169	+	0.751117i	$0.729515\pi$
$822$	5.33484e6	−	6.06834e6i	0.275386	−	0.313250i
$823$			1.36450e7i			0.702223i	0.936334	+	0.351111i	$0.114196\pi$
$823$			1.36450e7i			0.702223i	−0.936334	+	0.351111i	$0.885804\pi$
$824$	−1.43126e7	−	9.63896e6i	−0.734346	−	0.494552i
$825$		−	5.55070e6i		−	0.283931i
$826$		0			0
$827$			2.08890e7i			1.06207i	0.847349	+	0.531037i	$0.178197\pi$
$827$			2.08890e7i			1.06207i	−0.847349	+	0.531037i	$0.821803\pi$
$828$	−3.10885e7	+	4.01611e6i	−1.57588	+	0.203578i
$829$			1.04204e7i			0.526622i	0.964711	+	0.263311i	$0.0848146\pi$
$829$			1.04204e7i			0.526622i	−0.964711	+	0.263311i	$0.915185\pi$
$830$	460612.	+	404936.i	0.0232081	+	0.0204029i
$831$	1.54693e7			0.777084
$832$	−2.97750e7	+	1.20799e7i	−1.49122	+	0.604998i
$833$		0			0
$834$	7.81927e6	−	8.89437e6i	0.389270	−	0.442792i
$835$		−	1.01797e6i		−	0.0505263i
$836$	−2.95375e6	+	381574.i	−0.146170	+	0.0188827i
$837$	−548830.			−0.0270785
$838$	7.75342e6	−	8.81946e6i	0.381402	−	0.433842i
$839$	2.75943e7			1.35336			0.676682	−	0.736275i	$-0.263417\pi$
$839$	2.75943e7			1.35336			0.676682	+	0.736275i	$0.263417\pi$
$840$		0			0
$841$	−1.49786e7			−0.730266
$842$	1.54231e7	−	1.75437e7i	0.749706	−	0.852786i
$843$	2.84051e7			1.37666
$844$	−545713.	+	70497.0i	−0.0263699	+	0.00340655i
$845$		−	1.51481e6i		−	0.0729821i
$846$	−1.68132e7	+	1.91248e7i	−0.807650	+	0.918697i
$847$		0			0
$848$	−1.95085e7	+	5.12590e6i	−0.931612	+	0.244782i
$849$	−4.22909e7			−2.01362
$850$	7.96631e6	+	7.00340e6i	0.378190	+	0.332477i
$851$		−	5.58607e7i		−	2.64413i
$852$	−1.71019e7	+	2.20928e6i	−0.807133	+	0.104268i
$853$		−	2.59748e7i		−	1.22230i	−0.791514	−	0.611152i	$-0.790707\pi$
$853$		−	2.59748e7i		−	1.22230i	0.791514	−	0.611152i	$-0.209293\pi$
$854$		0			0
$855$		−	734352.i		−	0.0343549i
$856$	8.77669e6	−	1.30322e7i	0.409398	−	0.607904i
$857$		−	2.20659e7i		−	1.02629i	−0.858302	−	0.513146i	$-0.828480\pi$
$857$		−	2.20659e7i		−	1.02629i	0.858302	−	0.513146i	$-0.171520\pi$
$858$	6.51917e6	−	7.41551e6i	0.302325	−	0.343892i
$859$	−3.58149e7			−1.65608			−0.828038	−	0.560672i	$-0.810543\pi$
$859$	−3.58149e7			−1.65608			−0.828038	+	0.560672i	$0.810543\pi$
$860$	72480.9	+	561070.i	0.00334178	+	0.0258685i
$861$		0			0
$862$	1.97307e6	+	1.73457e6i	0.0904427	+	0.0795105i
$863$		−	1.15237e7i		−	0.526703i	−0.964700	−	0.263352i	$-0.915172\pi$
$863$		−	1.15237e7i		−	0.526703i	0.964700	−	0.263352i	$-0.0848280\pi$
$864$	240130.	−	479576.i	0.0109437	−	0.0218561i
$865$	1.15647e6			0.0525524
$866$	−4.09381e6	−	3.59898e6i	−0.185495	−	0.163074i
$867$	−2.34309e7			−1.05862
$868$		0			0
$869$	−3.21392e6			−0.144373
$870$	567786.	+	499156.i	0.0254324	+	0.0223583i
$871$	−5.55365e6			−0.248046
$872$	−1.52460e7	−	1.02676e7i	−0.678993	−	0.457274i
$873$			8.72933e6i			0.387655i
$874$	1.94915e7	+	1.71355e7i	0.863112	+	0.758784i
$875$		0			0
$876$	3.00170e7	−	3.87769e6i	1.32162	−	0.170731i
$877$	1.78199e7			0.782358			0.391179	−	0.920315i	$-0.372067\pi$
$877$	1.78199e7			0.782358			0.391179	+	0.920315i	$0.372067\pi$
$878$	−1.01882e7	+	1.15890e7i	−0.446025	+	0.507351i
$879$			3.31680e6i			0.144793i
$880$	204336.	−	53689.5i	0.00889483	−	0.00233713i
$881$			4.32683e7i			1.87815i	0.343716	+	0.939074i	$0.388314\pi$
$881$			4.32683e7i			1.87815i	−0.343716	+	0.939074i	$0.611686\pi$
$882$		0			0
$883$		−	2.84375e7i		−	1.22741i	−0.789536	−	0.613704i	$-0.789679\pi$
$883$		−	2.84375e7i		−	1.22741i	0.789536	−	0.613704i	$-0.210321\pi$
$884$	2.41734e6	+	1.87125e7i	0.104042	+	0.805380i
$885$		−	1.44502e6i		−	0.0620178i
$886$	7.63725e6	+	6.71410e6i	0.326853	+	0.287345i
$887$	2.69026e6			0.114812			0.0574058	−	0.998351i	$-0.481717\pi$
$887$	2.69026e6			0.114812			0.0574058	+	0.998351i	$0.481717\pi$
$888$	4.68564e7	+	3.15559e7i	1.99405	+	1.34291i
$889$		0			0
$890$	−886669.	+	1.00858e6i	−0.0375220	+	0.0426810i
$891$		−	4.66421e6i		−	0.196827i
$892$	−1.50952e6	−	1.16851e7i	−0.0635226	−	0.491725i
$893$	2.10827e7			0.884701
$894$	−3.62549e7	+	4.12397e7i	−1.51713	+	1.72572i
$895$	−1.40140e6			−0.0584796
$896$		0			0
$897$	−8.60388e7			−3.57037
$898$	−1.65307e7	+	1.88035e7i	−0.684069	+	0.778123i
$899$	−1.39425e7			−0.575361
$900$	−3.16019e6	−	2.44628e7i	−0.130049	−	1.00670i
$901$			1.18443e7i			0.486067i
$902$	4.29424e6	−	4.88467e6i	0.175740	−	0.199903i
$903$		0			0
$904$	−2.70625e7	−	1.82255e7i	−1.10141	−	0.741752i
$905$	−508338.			−0.0206315
$906$	1.57230e7	+	1.38225e7i	0.636378	+	0.559457i
$907$		−	4.62717e7i		−	1.86766i	−0.357720	−	0.933829i	$-0.616446\pi$
$907$		−	4.62717e7i		−	1.86766i	0.357720	−	0.933829i	$-0.383554\pi$
$908$	−2.43730e6	−	1.88670e7i	−0.0981058	−	0.759431i
$909$			1.70951e7i			0.686217i
$910$		0			0
$911$		−	2.10834e7i		−	0.841677i	−0.907136	−	0.420838i	$-0.861736\pi$
$911$		−	2.10834e7i		−	0.841677i	0.907136	−	0.420838i	$-0.138264\pi$
$912$	−2.53842e7	+	6.66974e6i	−1.01059	+	0.265535i
$913$			3.39646e6i			0.134850i
$914$	−2.61819e7	+	2.97817e7i	−1.03666	+	1.17919i
$915$	−761699.			−0.0300767
$916$	1.34537e7	−	1.73799e6i	0.529790	−	0.0684399i
$917$		0			0
$918$	−236529.	−	207939.i	−0.00926357	−	0.00814385i
$919$			3.34197e7i			1.30531i	0.757655	+	0.652655i	$0.226345\pi$
$919$			3.34197e7i			1.30531i	−0.757655	+	0.652655i	$0.773655\pi$
$920$	−1.52701e6	−	1.02838e6i	−0.0594803	−	0.0400576i
$921$	592222.			0.0230057
$922$	3.64994e7	+	3.20876e7i	1.41403	+	1.24311i
$923$	−2.38671e7			−0.922135
$924$		0			0
$925$	4.39556e7			1.68912
$926$	3.72952e6	+	3.27872e6i	0.142931	+	0.125654i
$927$	2.35627e7			0.900587
$928$	6.10027e6	−	1.21831e7i	0.232530	−	0.464397i
$929$		−	5.10574e7i		−	1.94097i	−0.241154	−	0.970487i	$-0.577526\pi$
$929$		−	5.10574e7i		−	1.94097i	0.241154	−	0.970487i	$-0.422474\pi$
$930$	−1.43086e6	−	1.25791e6i	−0.0542489	−	0.0476916i
$931$		0			0
$932$	−482612.	−	3.73588e6i	−0.0181995	−	0.140881i
$933$	3.59914e7			1.35362
$934$	2.67408e7	−	3.04174e7i	1.00301	−	1.14092i
$935$		−	124059.i		−	0.00464086i
$936$	2.45091e7	−	3.63929e7i	0.914404	−	1.35777i
$937$		−	4.53625e6i		−	0.168790i	−0.996432	−	0.0843952i	$-0.973104\pi$
$937$		−	4.53625e6i		−	0.168790i	0.996432	−	0.0843952i	$-0.0268958\pi$
$938$		0			0
$939$			4.01489e7i			1.48597i
$940$	−1.48322e6	+	191607.i	−0.0547502	+	0.00707281i
$941$			1.83286e6i			0.0674770i	0.999431	+	0.0337385i	$0.0107413\pi$
$941$			1.83286e6i			0.0674770i	−0.999431	+	0.0337385i	$0.989259\pi$
$942$	6.96231e6	+	6.12075e6i	0.255639	+	0.224739i
$943$	−5.66746e7			−2.07544
$944$	−2.51880e7	+	6.61818e6i	−0.919948	+	0.241718i
$945$		0			0
$946$	−2.06861e6	+	2.35303e6i	−0.0751539	+	0.0854871i
$947$		−	4.98890e7i		−	1.80771i	−0.427834	−	0.903857i	$-0.640723\pi$
$947$		−	4.98890e7i		−	1.80771i	0.427834	−	0.903857i	$-0.359277\pi$
$948$	−2.80889e7	+	3.62861e6i	−1.01511	+	0.131135i
$949$	4.18910e7			1.50993
$950$	−1.34835e7	+	1.53374e7i	−0.484725	+	0.551371i
$951$	5.21579e7			1.87012
$952$		0			0
$953$	5.96814e6			0.212866			0.106433	−	0.994320i	$-0.466057\pi$
$953$	5.96814e6			0.212866			0.106433	+	0.994320i	$0.466057\pi$
$954$	1.81856e7	−	2.06860e7i	0.646928	−	0.735876i
$955$	286360.			0.0101602
$956$	−2.48231e7	+	3.20673e6i	−0.878440	+	0.113480i
$957$			4.18675e6i			0.147774i
$958$	1.83293e7	−	2.08494e7i	0.645254	−	0.733972i
$959$		0			0
$960$	1.72523e6	−	699935.i	0.0604183	−	0.0245120i
$961$	6.50692e6			0.227283
$962$	5.87228e7	+	5.16248e7i	2.04583	+	1.79854i
$963$			2.14549e7i			0.745521i
$964$	3.91460e7	−	5.05701e6i	1.35673	−	0.175267i
$965$			2.00009e6i			0.0691402i
$966$		0			0
$967$			3.04278e7i			1.04641i	0.852205	+	0.523207i	$0.175265\pi$
$967$			3.04278e7i			1.04641i	−0.852205	+	0.523207i	$0.824735\pi$
$968$	−2.32105e7	−	1.56313e7i	−0.796152	−	0.536176i
$969$			1.54116e7i			0.527275i
$970$	−338500.	+	385041.i	−0.0115513	+	0.0131395i
$971$	2.52565e7			0.859658			0.429829	−	0.902910i	$-0.358574\pi$
$971$	2.52565e7			0.859658			0.429829	+	0.902910i	$0.358574\pi$
$972$	−5.35827e6	−	4.14781e7i	−0.181911	−	1.40816i
$973$		0			0
$974$	−4.83897e6	−	4.25406e6i	−0.163439	−	0.143683i
$975$		−	6.77020e7i		−	2.28082i
$976$	3.48857e6	+	1.32771e7i	0.117226	+	0.446147i
$977$	−1.60729e7			−0.538713			−0.269357	−	0.963041i	$-0.586811\pi$
$977$	−1.60729e7			−0.538713			−0.269357	+	0.963041i	$0.586811\pi$
$978$	1.75557e7	+	1.54337e7i	0.586910	+	0.515968i
$979$	−7.43708e6			−0.247997
$980$		0			0
$981$	2.50994e7			0.832703
$982$	−1.21434e7	−	1.06756e7i	−0.401847	−	0.353274i
$983$	3.77651e7			1.24654			0.623271	−	0.782006i	$-0.285803\pi$
$983$	3.77651e7			1.24654			0.623271	+	0.782006i	$0.285803\pi$
$984$	3.20157e7	−	4.75391e7i	1.05408	−	1.56518i
$985$		−	898909.i		−	0.0295206i
$986$	−6.00879e6	−	5.28248e6i	−0.196831	−	0.173040i
$987$		0			0
$988$	−3.60269e7	+	4.65407e6i	−1.17418	+	0.151684i
$989$	2.73012e7			0.887547
$990$	−190479.	+	216668.i	−0.00617673	+	0.00702599i
$991$		−	2.24588e6i		−	0.0726444i	−0.999340	−	0.0363222i	$-0.988436\pi$
$991$		−	2.24588e6i		−	0.0726444i	0.999340	−	0.0363222i	$-0.0115643\pi$
$992$	−1.53731e7	+	3.07024e7i	−0.496002	+	0.990588i
$993$		−	7.67040e7i		−	2.46857i
$994$		0			0
$995$		−	38377.3i		−	0.00122890i
$996$	3.83471e6	+	2.96843e7i	0.122485	+	0.948152i
$997$			2.98413e7i			0.950780i	0.879775	+	0.475390i	$0.157693\pi$
$997$			2.98413e7i			0.950780i	−0.879775	+	0.475390i	$0.842307\pi$
$998$	−5.06489e6	−	4.45268e6i	−0.160970	−	0.141513i
$999$	−1.30509e6			−0.0413740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.6.d.b.195.25		36
4.3	odd	2	inner	196.6.d.b.195.28		36
7.4	even	3		28.6.f.a.19.11	yes	36
7.5	odd	6		28.6.f.a.3.1	✓	36
7.6	odd	2	inner	196.6.d.b.195.26		36
28.11	odd	6		28.6.f.a.19.1	yes	36
28.19	even	6		28.6.f.a.3.11	yes	36
28.27	even	2	inner	196.6.d.b.195.27		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.6.f.a.3.1	✓	36	7.5	odd	6
28.6.f.a.3.11	yes	36	28.19	even	6
28.6.f.a.19.1	yes	36	28.11	odd	6
28.6.f.a.19.11	yes	36	7.4	even	3
196.6.d.b.195.25		36	1.1	even	1	trivial
196.6.d.b.195.26		36	7.6	odd	2	inner
196.6.d.b.195.27		36	28.27	even	2	inner
196.6.d.b.195.28		36	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	196.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(3.73498 - 4.24852i) q^{2} -22.1401 q^{3} +(-4.09980 - 31.7363i) q^{4} +2.56629i q^{5} +(-82.6927 + 94.0624i) q^{6} +(-150.145 - 101.116i) q^{8} +247.182 q^{9} +(10.9029 + 9.58505i) q^{10} +80.3962i q^{11} +(90.7697 + 702.643i) q^{12} +980.594i q^{13} -56.8178i q^{15} +(-990.383 + 260.225i) q^{16} +601.293i q^{17} +(923.221 - 1050.16i) q^{18} -1157.66 q^{19} +(81.4445 - 10.5213i) q^{20} +(341.565 + 300.278i) q^{22} -3963.02i q^{23} +(3324.21 + 2238.72i) q^{24} +3118.41 q^{25} +(4166.07 + 3662.50i) q^{26} -92.5894 q^{27} -2352.14 q^{29} +(-241.391 - 212.214i) q^{30} +5927.57 q^{31} +(-2593.50 + 5179.60i) q^{32} -1779.98i q^{33} +(2554.60 + 2245.82i) q^{34} +(-1013.40 - 7844.64i) q^{36} +14095.5 q^{37} +(-4323.85 + 4918.34i) q^{38} -21710.4i q^{39} +(259.494 - 385.315i) q^{40} -14300.9i q^{41} +6888.99i q^{43} +(2551.48 - 329.608i) q^{44} +634.341i q^{45} +(-16837.0 - 14801.8i) q^{46} -18211.4 q^{47} +(21927.1 - 5761.39i) q^{48} +(11647.2 - 13248.6i) q^{50} -13312.7i q^{51} +(31120.4 - 4020.24i) q^{52} +19698.0 q^{53} +(-345.820 + 393.368i) q^{54} -206.320 q^{55} +25630.7 q^{57} +(-8785.20 + 9993.11i) q^{58} +25432.6 q^{59} +(-1803.19 + 232.941i) q^{60} -13406.0i q^{61} +(22139.4 - 25183.4i) q^{62} +(12318.9 + 30364.2i) q^{64} -2516.49 q^{65} +(-7562.26 - 6648.18i) q^{66} +5663.55i q^{67} +(19082.8 - 2465.18i) q^{68} +87741.5i q^{69} +24339.4i q^{71} +(-37113.1 - 24994.2i) q^{72} -42720.1i q^{73} +(52646.4 - 59884.9i) q^{74} -69041.9 q^{75} +(4746.18 + 36739.9i) q^{76} +(-92237.0 - 81088.0i) q^{78} +39976.1i q^{79} +(-667.812 - 2541.61i) q^{80} -58015.3 q^{81} +(-60757.5 - 53413.5i) q^{82} +42246.6 q^{83} -1543.09 q^{85} +(29268.0 + 25730.3i) q^{86} +52076.5 q^{87} +(8129.38 - 12071.1i) q^{88} +92505.4i q^{89} +(2695.01 + 2369.25i) q^{90} +(-125772. + 16247.6i) q^{92} -131237. q^{93} +(-68019.4 + 77371.5i) q^{94} -2970.90i q^{95} +(57420.2 - 114677. i) q^{96} +35315.4i q^{97} +19872.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 24 q^{4} - 72 q^{8} + 2272 q^{9} - 1328 q^{16} + 3560 q^{18} + 13768 q^{22} - 15224 q^{25} + 176 q^{29} + 11672 q^{30} - 2320 q^{32} - 27920 q^{36} - 23444 q^{37} - 18192 q^{44} + 2080 q^{46} - 51168 q^{50}+ \cdots + 330324 q^{93}+O(q^{100}) \) 36 * q + 24 * q^4 - 72 * q^8 + 2272 * q^9 - 1328 * q^16 + 3560 * q^18 + 13768 * q^22 - 15224 * q^25 + 176 * q^29 + 11672 * q^30 - 2320 * q^32 - 27920 * q^36 - 23444 * q^37 - 18192 * q^44 + 2080 * q^46 - 51168 * q^50 + 66972 * q^53 - 1668 * q^57 + 96872 * q^58 - 28624 * q^60 + 44544 * q^64 - 30712 * q^65 - 296128 * q^72 - 34304 * q^74 + 127704 * q^78 - 320804 * q^81 + 71212 * q^85 + 504992 * q^86 - 110536 * q^88 - 190176 * q^92 + 330324 * q^93

Introduction

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