LMFDB - Embedded newform 100.4.e.f.7.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,4,Mod(7,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("100.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	100.e (of order $4$, 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:	$5.90019100057$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.9
Character	$\chi$	$=$	100.7
Dual form			100.4.e.f.43.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.75332 + 2.21943i) q^{2} +(6.14790 + 6.14790i) q^{3} +(-1.85174 + 7.78274i) q^{4} +(-2.86560 + 24.4241i) q^{6} +(16.4522 - 16.4522i) q^{7} +(-20.5199 + 9.53582i) q^{8} +48.5934i q^{9} +O(q^{10})$	\(q+(1.75332 + 2.21943i) q^{2} +(6.14790 + 6.14790i) q^{3} +(-1.85174 + 7.78274i) q^{4} +(-2.86560 + 24.4241i) q^{6} +(16.4522 - 16.4522i) q^{7} +(-20.5199 + 9.53582i) q^{8} +48.5934i q^{9} -44.6211i q^{11} +(-59.2319 + 36.4632i) q^{12} +(-0.849478 + 0.849478i) q^{13} +(65.3604 + 7.66854i) q^{14} +(-57.1421 - 28.8233i) q^{16} +(-58.2897 - 58.2897i) q^{17} +(-107.850 + 85.1997i) q^{18} +23.7025 q^{19} +202.293 q^{21} +(99.0334 - 78.2350i) q^{22} +(-10.9325 - 10.9325i) q^{23} +(-184.780 - 67.5294i) q^{24} +(-3.37476 - 0.395951i) q^{26} +(-132.754 + 132.754i) q^{27} +(97.5778 + 158.508i) q^{28} +127.106i q^{29} +253.779i q^{31} +(-36.2171 - 177.359i) q^{32} +(274.326 - 274.326i) q^{33} +(27.1695 - 231.571i) q^{34} +(-378.190 - 89.9824i) q^{36} +(92.9341 + 92.9341i) q^{37} +(41.5581 + 52.6061i) q^{38} -10.4450 q^{39} +98.0252 q^{41} +(354.684 + 448.975i) q^{42} +(-235.212 - 235.212i) q^{43} +(347.274 + 82.6268i) q^{44} +(5.09576 - 43.4321i) q^{46} +(250.419 - 250.419i) q^{47} +(-174.101 - 528.507i) q^{48} -198.348i q^{49} -716.719i q^{51} +(-5.03825 - 8.18428i) q^{52} +(149.126 - 149.126i) q^{53} +(-527.398 - 61.8781i) q^{54} +(-180.713 + 494.483i) q^{56} +(145.721 + 145.721i) q^{57} +(-282.103 + 222.857i) q^{58} +12.5393 q^{59} -332.505 q^{61} +(-563.246 + 444.956i) q^{62} +(799.467 + 799.467i) q^{63} +(330.136 - 391.349i) q^{64} +(1089.83 + 127.866i) q^{66} +(199.472 - 199.472i) q^{67} +(561.592 - 345.716i) q^{68} -134.424i q^{69} +664.410i q^{71} +(-463.378 - 997.134i) q^{72} +(-699.484 + 699.484i) q^{73} +(-43.3176 + 369.204i) q^{74} +(-43.8910 + 184.471i) q^{76} +(-734.114 - 734.114i) q^{77} +(-18.3135 - 23.1820i) q^{78} -703.490 q^{79} -320.295 q^{81} +(171.869 + 217.560i) q^{82} +(-940.531 - 940.531i) q^{83} +(-374.594 + 1574.39i) q^{84} +(109.635 - 934.437i) q^{86} +(-781.435 + 781.435i) q^{87} +(425.499 + 915.623i) q^{88} -386.574i q^{89} +27.9515i q^{91} +(105.329 - 64.8407i) q^{92} +(-1560.21 + 1560.21i) q^{93} +(994.852 + 116.723i) q^{94} +(867.728 - 1313.05i) q^{96} +(1064.76 + 1064.76i) q^{97} +(440.220 - 347.768i) q^{98} +2168.29 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 36 q^{6}+O(q^{10}) $ 24 * q + 36 * q^6	$ 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) $ 24 * q + 36 * q^6 - 676 * q^16 + 512 * q^21 + 2072 * q^26 - 4600 * q^36 - 392 * q^41 + 5016 * q^46 - 8224 * q^56 + 1088 * q^61 + 11140 * q^66 - 6700 * q^76 - 2424 * q^81 + 5216 * q^86 + 796 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.75332	+	2.21943i	0.619892	+	0.784687i
$2$	1.75332	+	2.21943i	0.619892	+	0.784687i
$3$	6.14790	+	6.14790i	1.18316	+	1.18316i	0.978920	+	0.204244i	$0.0654737\pi$
$3$	6.14790	+	6.14790i	1.18316	+	1.18316i	0.204244	+	0.978920i	$0.434526\pi$
$4$	−1.85174	+	7.78274i	−0.231468	+	0.972843i
$5$		0			0
$5$		0			0
$6$	−2.86560	+	24.4241i	−0.194980	+	1.66185i
$7$	16.4522	−	16.4522i	0.888334	−	0.888334i	−0.106029	−	0.994363i	$-0.533814\pi$
$7$	16.4522	−	16.4522i	0.888334	−	0.888334i	0.994363	+	0.106029i	$0.0338136\pi$
$8$	−20.5199	+	9.53582i	−0.906862	+	0.421427i
$9$			48.5934i			1.79975i
$10$		0			0
$11$		−	44.6211i		−	1.22307i	−0.791217	−	0.611535i	$-0.790552\pi$
$11$		−	44.6211i		−	1.22307i	0.791217	−	0.611535i	$-0.209448\pi$
$12$	−59.2319	+	36.4632i	−1.42490	+	0.877168i
$13$	−0.849478	+	0.849478i	−0.0181233	+	0.0181233i	−0.716110	−	0.697987i	$-0.754079\pi$
$13$	−0.849478	+	0.849478i	−0.0181233	+	0.0181233i	0.697987	+	0.716110i	$0.254079\pi$
$14$	65.3604	+	7.66854i	1.24774	+	0.146393i
$15$		0			0
$16$	−57.1421	−	28.8233i	−0.892845	−	0.450364i
$17$	−58.2897	−	58.2897i	−0.831608	−	0.831608i	0.156128	−	0.987737i	$-0.450099\pi$
$17$	−58.2897	−	58.2897i	−0.831608	−	0.831608i	−0.987737	+	0.156128i	$0.950099\pi$
$18$	−107.850	+	85.1997i	−1.41224	+	1.11565i
$19$	23.7025			0.286197			0.143098	−	0.989708i	$-0.454293\pi$
$19$	23.7025			0.286197			0.143098	+	0.989708i	$0.454293\pi$
$20$		0			0
$21$	202.293			2.10209
$22$	99.0334	−	78.2350i	0.959727	−	0.758171i
$23$	−10.9325	−	10.9325i	−0.0991124	−	0.0991124i	0.655812	−	0.754924i	$-0.272326\pi$
$23$	−10.9325	−	10.9325i	−0.0991124	−	0.0991124i	−0.754924	+	0.655812i	$0.772326\pi$
$24$	−184.780	−	67.5294i	−1.57158	−	0.574349i
$25$		0			0
$26$	−3.37476	−	0.395951i	−0.0254556	−	0.00298663i
$27$	−132.754	+	132.754i	−0.946241	+	0.946241i
$28$	97.5778	+	158.508i	0.658588	+	1.06983i
$29$			127.106i			0.813896i	0.913451	+	0.406948i	$0.133407\pi$
$29$			127.106i			0.813896i	−0.913451	+	0.406948i	$0.866593\pi$
$30$		0			0
$31$			253.779i			1.47033i	0.677890	+	0.735163i	$0.262894\pi$
$31$			253.779i			1.47033i	−0.677890	+	0.735163i	$0.737106\pi$
$32$	−36.2171	−	177.359i	−0.200073	−	0.979781i
$33$	274.326	−	274.326i	1.44709	−	1.44709i
$34$	27.1695	−	231.571i	0.137045	−	1.16806i
$35$		0			0
$36$	−378.190	−	89.9824i	−1.75088	−	0.416585i
$37$	92.9341	+	92.9341i	0.412926	+	0.412926i	0.882757	−	0.469830i	$-0.155685\pi$
$37$	92.9341	+	92.9341i	0.412926	+	0.412926i	−0.469830	+	0.882757i	$0.655685\pi$
$38$	41.5581	+	52.6061i	0.177411	+	0.224575i
$39$	−10.4450			−0.0428857
$40$		0			0
$41$	98.0252			0.373389			0.186695	−	0.982418i	$-0.440222\pi$
$41$	98.0252			0.373389			0.186695	+	0.982418i	$0.440222\pi$
$42$	354.684	+	448.975i	1.30307	+	1.64948i
$43$	−235.212	−	235.212i	−0.834173	−	0.834173i	0.153911	−	0.988085i	$-0.450813\pi$
$43$	−235.212	−	235.212i	−0.834173	−	0.834173i	−0.988085	+	0.153911i	$0.950813\pi$
$44$	347.274	+	82.6268i	1.18985	+	0.283101i
$45$		0			0
$46$	5.09576	−	43.4321i	0.0163332	−	0.139211i
$47$	250.419	−	250.419i	0.777178	−	0.777178i	−0.202172	−	0.979350i	$-0.564800\pi$
$47$	250.419	−	250.419i	0.777178	−	0.777178i	0.979350	+	0.202172i	$0.0648000\pi$
$48$	−174.101	−	528.507i	−0.523529	−	1.58924i
$49$		−	198.348i		−	0.578275i
$50$		0			0
$51$		−	716.719i		−	1.96786i
$52$	−5.03825	−	8.18428i	−0.0134362	−	0.0218261i
$53$	149.126	−	149.126i	0.386491	−	0.386491i	−0.486943	−	0.873434i	$-0.661888\pi$
$53$	149.126	−	149.126i	0.386491	−	0.386491i	0.873434	+	0.486943i	$0.161888\pi$
$54$	−527.398	−	61.8781i	−1.32907	−	0.155936i
$55$		0			0
$56$	−180.713	+	494.483i	−0.431228	+	1.17996i
$57$	145.721	+	145.721i	0.338618	+	0.338618i
$58$	−282.103	+	222.857i	−0.638654	+	0.504528i
$59$	12.5393			0.0276690			0.0138345	−	0.999904i	$-0.495596\pi$
$59$	12.5393			0.0276690			0.0138345	+	0.999904i	$0.495596\pi$
$60$		0			0
$61$	−332.505			−0.697916			−0.348958	−	0.937138i	$-0.613464\pi$
$61$	−332.505			−0.697916			−0.348958	+	0.937138i	$0.613464\pi$
$62$	−563.246	+	444.956i	−1.15375	+	0.911444i
$63$	799.467	+	799.467i	1.59878	+	1.59878i
$64$	330.136	−	391.349i	0.644798	−	0.764353i
$65$		0			0
$66$	1089.83	+	127.866i	2.03256	+	0.238474i
$67$	199.472	−	199.472i	0.363723	−	0.363723i	−0.501459	−	0.865182i	$-0.667203\pi$
$67$	199.472	−	199.472i	0.363723	−	0.363723i	0.865182	+	0.501459i	$0.167203\pi$
$68$	561.592	−	345.716i	1.00151	−	0.616533i
$69$		−	134.424i		−	0.234532i
$70$		0			0
$71$			664.410i			1.11058i	0.831658	+	0.555288i	$0.187392\pi$
$71$			664.410i			1.11058i	−0.831658	+	0.555288i	$0.812608\pi$
$72$	−463.378	−	997.134i	−0.758466	−	1.63213i
$73$	−699.484	+	699.484i	−1.12149	+	1.12149i	−0.129967	+	0.991518i	$0.541487\pi$
$73$	−699.484	+	699.484i	−1.12149	+	1.12149i	−0.991518	+	0.129967i	$0.958513\pi$
$74$	−43.3176	+	369.204i	−0.0680482	+	0.579987i
$75$		0			0
$76$	−43.8910	+	184.471i	−0.0662453	+	0.278424i
$77$	−734.114	−	734.114i	−1.08649	−	1.08649i
$78$	−18.3135	−	23.1820i	−0.0265845	−	0.0336518i
$79$	−703.490			−1.00188			−0.500942	−	0.865481i	$-0.667013\pi$
$79$	−703.490			−1.00188			−0.500942	+	0.865481i	$0.667013\pi$
$80$		0			0
$81$	−320.295			−0.439363
$82$	171.869	+	217.560i	0.231461	+	0.292994i
$83$	−940.531	−	940.531i	−1.24382	−	1.24382i	−0.958406	−	0.285410i	$-0.907870\pi$
$83$	−940.531	−	940.531i	−1.24382	−	1.24382i	−0.285410	−	0.958406i	$-0.592130\pi$
$84$	−374.594	+	1574.39i	−0.486566	+	2.04500i
$85$		0			0
$86$	109.635	−	934.437i	0.137468	−	1.17166i
$87$	−781.435	+	781.435i	−0.962973	+	0.962973i
$88$	425.499	+	915.623i	0.515435	+	1.10916i
$89$		−	386.574i		−	0.460413i	−0.973142	−	0.230206i	$-0.926060\pi$
$89$		−	386.574i		−	0.460413i	0.973142	−	0.230206i	$-0.0739401\pi$
$90$		0			0
$91$			27.9515i			0.0321991i
$92$	105.329	−	64.8407i	0.119362	−	0.0734794i
$93$	−1560.21	+	1560.21i	−1.73964	+	1.73964i
$94$	994.852	+	116.723i	1.09161	+	0.128075i
$95$		0			0
$96$	867.728	−	1313.05i	0.922522	−	1.39596i
$97$	1064.76	+	1064.76i	1.11453	+	1.11453i	0.992530	+	0.122005i	$0.0389323\pi$
$97$	1064.76	+	1064.76i	1.11453	+	1.11453i	0.122005	+	0.992530i	$0.461068\pi$
$98$	440.220	−	347.768i	0.453765	−	0.358468i
$99$	2168.29			2.20123
$100$		0			0
$101$	−1263.35			−1.24463			−0.622316	−	0.782766i	$-0.713808\pi$
$101$	−1263.35			−1.24463			−0.622316	+	0.782766i	$0.713808\pi$
$102$	1590.71	−	1256.64i	1.54415	−	1.21986i
$103$	228.987	+	228.987i	0.219056	+	0.219056i	0.808101	−	0.589045i	$-0.200496\pi$
$103$	228.987	+	228.987i	0.219056	+	0.219056i	−0.589045	+	0.808101i	$0.700496\pi$
$104$	9.33078	−	25.5317i	0.00879768	−	0.0240730i
$105$		0			0
$106$	592.440	+	69.5092i	0.542857	+	0.0636918i
$107$	−413.024	+	413.024i	−0.373164	+	0.373164i	−0.868628	−	0.495464i	$-0.834998\pi$
$107$	−413.024	+	413.024i	−0.373164	+	0.373164i	0.495464	+	0.868628i	$0.334998\pi$
$108$	−787.364	−	1279.02i	−0.701519	−	1.13957i
$109$			1424.06i			1.25138i	0.780071	+	0.625691i	$0.215183\pi$
$109$			1424.06i			1.25138i	−0.780071	+	0.625691i	$0.784817\pi$
$110$		0			0
$111$			1142.70i			0.977119i
$112$	−1414.32	+	465.907i	−1.19322	+	0.393072i
$113$	910.839	−	910.839i	0.758270	−	0.758270i	−0.217737	−	0.976007i	$-0.569868\pi$
$113$	910.839	−	910.839i	0.758270	−	0.758270i	0.976007	+	0.217737i	$0.0698677\pi$
$114$	−67.9221	+	578.912i	−0.0558025	+	0.475615i
$115$		0			0
$116$	−989.233	−	235.368i	−0.791793	−	0.188391i
$117$	−41.2790	−	41.2790i	−0.0326175	−	0.0326175i
$118$	21.9853	+	27.8300i	0.0171518	+	0.0217115i
$119$	−1917.99			−1.47749
$120$		0			0
$121$	−660.042			−0.495900
$122$	−582.987	−	737.971i	−0.432632	−	0.547646i
$123$	602.649	+	602.649i	0.441781	+	0.441781i
$124$	−1975.10	−	469.934i	−1.43040	−	0.340333i
$125$		0			0
$126$	−372.640	+	3176.08i	−0.263472	+	2.24562i
$127$	1439.87	−	1439.87i	1.00604	−	1.00604i	0.00606278	−	0.999982i	$-0.498070\pi$
$127$	1439.87	−	1439.87i	1.00604	−	1.00604i	0.999982	−	0.00606278i	$-0.00192986\pi$
$128$	1447.41	+	46.5554i	0.999483	+	0.0321481i
$129$		−	2892.12i		−	1.97393i
$130$		0			0
$131$		−	1327.53i		−	0.885393i	−0.896672	−	0.442696i	$-0.854022\pi$
$131$		−	1327.53i		−	0.885393i	0.896672	−	0.442696i	$-0.145978\pi$
$132$	1627.03	+	2642.99i	1.07284	+	1.74275i
$133$	389.958	−	389.958i	0.254238	−	0.254238i
$134$	792.454	+	92.9763i	0.510878	+	0.0599398i
$135$		0			0
$136$	1751.94	+	640.262i	1.10462	+	0.403691i
$137$	−1009.78	−	1009.78i	−0.629715	−	0.629715i	0.318281	−	0.947996i	$-0.396894\pi$
$137$	−1009.78	−	1009.78i	−0.629715	−	0.629715i	−0.947996	+	0.318281i	$0.896894\pi$
$138$	298.344	−	235.688i	0.184035	−	0.145385i
$139$	−1282.81			−0.782782			−0.391391	−	0.920224i	$-0.628006\pi$
$139$	−1282.81			−0.782782			−0.391391	+	0.920224i	$0.628006\pi$
$140$		0			0
$141$	3079.10			1.83906
$142$	−1474.61	+	1164.92i	−0.871455	+	0.688437i
$143$	37.9047	+	37.9047i	0.0221661	+	0.0221661i
$144$	1400.62	−	2776.73i	0.810544	−	1.60690i
$145$		0			0
$146$	−2778.88	−	326.037i	−1.57521	−	0.184815i
$147$	1219.43	−	1219.43i	0.684194	−	0.684194i
$148$	−895.372	+	551.192i	−0.497291	+	0.306133i
$149$		−	94.5789i		−	0.0520014i	−0.999662	−	0.0260007i	$-0.991723\pi$
$149$		−	94.5789i		−	0.0520014i	0.999662	−	0.0260007i	$-0.00827721\pi$
$150$		0			0
$151$		−	2723.98i		−	1.46804i	−0.679128	−	0.734020i	$-0.737642\pi$
$151$		−	2723.98i		−	1.46804i	0.679128	−	0.734020i	$-0.262358\pi$
$152$	−486.375	+	226.023i	−0.259541	+	0.120611i
$153$	2832.50	−	2832.50i	1.49669	−	1.49669i
$154$	342.179	−	2916.45i	0.179049	−	1.52607i
$155$		0			0
$156$	19.3415	−	81.2909i	0.00992665	−	0.0417210i
$157$	1201.75	+	1201.75i	0.610894	+	0.610894i	0.943179	−	0.332285i	$-0.107820\pi$
$157$	1201.75	+	1201.75i	0.610894	+	0.610894i	−0.332285	+	0.943179i	$0.607820\pi$
$158$	−1233.44	−	1561.35i	−0.621060	−	0.786166i
$159$	1833.62			0.914564
$160$		0			0
$161$	−359.727			−0.176090
$162$	−561.580	−	710.873i	−0.272357	−	0.344762i
$163$	−336.009	−	336.009i	−0.161462	−	0.161462i	0.621752	−	0.783214i	$-0.286421\pi$
$163$	−336.009	−	336.009i	−0.161462	−	0.161462i	−0.783214	+	0.621752i	$0.786421\pi$
$164$	−181.517	+	762.905i	−0.0864276	+	0.363249i
$165$		0			0
$166$	438.392	−	3736.49i	0.204975	−	1.74704i
$167$	−1362.82	+	1362.82i	−0.631488	+	0.631488i	−0.948441	−	0.316953i	$-0.897340\pi$
$167$	−1362.82	+	1362.82i	−0.631488	+	0.631488i	0.316953	+	0.948441i	$0.397340\pi$
$168$	−4151.04	+	1929.03i	−1.90631	+	0.885879i
$169$			2195.56i			0.999343i
$170$		0			0
$171$			1151.79i			0.515084i
$172$	2266.14	−	1395.04i	1.00460	−	0.618435i
$173$	−648.186	+	648.186i	−0.284859	+	0.284859i	−0.835043	−	0.550184i	$-0.814558\pi$
$173$	−648.186	+	648.186i	−0.284859	+	0.284859i	0.550184	+	0.835043i	$0.314558\pi$
$174$	−3104.45	−	364.235i	−1.35257	−	0.158693i
$175$		0			0
$176$	−1286.13	+	2549.74i	−0.550826	+	1.09201i
$177$	77.0902	+	77.0902i	0.0327370	+	0.0327370i
$178$	857.973	−	677.787i	0.361280	−	0.285406i
$179$	96.1861			0.0401636			0.0200818	−	0.999798i	$-0.493607\pi$
$179$	96.1861			0.0401636			0.0200818	+	0.999798i	$0.493607\pi$
$180$		0			0
$181$	2470.64			1.01459			0.507297	−	0.861771i	$-0.330645\pi$
$181$	2470.64			1.01459			0.507297	+	0.861771i	$0.330645\pi$
$182$	−62.0365	+	49.0080i	−0.0252662	+	0.0199600i
$183$	−2044.21	−	2044.21i	−0.825749	−	0.825749i
$184$	328.585	+	120.084i	0.131650	+	0.0481126i
$185$		0			0
$186$	−6198.33	−	727.231i	−2.44346	−	0.286684i
$187$	−2600.95	+	2600.95i	−1.01711	+	1.01711i
$188$	1485.24	+	2412.66i	0.576180	+	0.935964i
$189$			4368.18i			1.68116i
$190$		0			0
$191$			3314.57i			1.25567i	0.778345	+	0.627837i	$0.216060\pi$
$191$			3314.57i			1.25567i	−0.778345	+	0.627837i	$0.783940\pi$
$192$	4435.62	−	376.328i	1.66726	−	0.141454i
$193$	2491.16	−	2491.16i	0.929106	−	0.929106i	−0.0685419	−	0.997648i	$-0.521835\pi$
$193$	2491.16	−	2491.16i	0.929106	−	0.929106i	0.997648	+	0.0685419i	$0.0218347\pi$
$194$	−496.296	+	4230.02i	−0.183670	+	1.56545i
$195$		0			0
$196$	1543.69	+	367.290i	0.562571	+	0.133852i
$197$	−3419.89	−	3419.89i	−1.23684	−	1.23684i	−0.961287	−	0.275550i	$-0.911140\pi$
$197$	−3419.89	−	3419.89i	−1.23684	−	1.23684i	−0.275550	−	0.961287i	$-0.588860\pi$
$198$	3801.70	+	4812.37i	1.36452	+	1.72727i
$199$	3891.88			1.38637			0.693185	−	0.720759i	$-0.256207\pi$
$199$	3891.88			1.38637			0.693185	+	0.720759i	$0.256207\pi$
$200$		0			0
$201$	2452.67			0.860688
$202$	−2215.05	−	2803.91i	−0.771537	−	0.976646i
$203$	2091.17	+	2091.17i	0.723012	+	0.723012i
$204$	5578.04	+	1327.18i	1.91442	+	0.455496i
$205$		0			0
$206$	−106.733	+	909.708i	−0.0360994	+	0.307681i
$207$	531.247	−	531.247i	0.178378	−	0.178378i
$208$	73.0257	−	24.0562i	0.0243434	−	0.00801923i
$209$		−	1057.63i		−	0.350038i
$210$		0			0
$211$			5180.09i			1.69010i	0.534684	+	0.845052i	$0.320431\pi$
$211$			5180.09i			1.69010i	−0.534684	+	0.845052i	$0.679569\pi$
$212$	884.465	+	1436.75i	0.286534	+	0.465455i
$213$	−4084.73	+	4084.73i	−1.31399	+	1.31399i
$214$	−1640.84	−	192.515i	−0.524138	−	0.0614956i
$215$		0			0
$216$	1458.19	−	3990.02i	0.459338	−	1.25688i
$217$	4175.22	+	4175.22i	1.30614	+	1.30614i
$218$	−3160.61	+	2496.84i	−0.981944	+	0.775722i
$219$	−8600.72			−2.65380
$220$		0			0
$221$	99.0318			0.0301430
$222$	−2536.14	+	2003.52i	−0.766733	+	0.605708i
$223$	−1451.70	−	1451.70i	−0.435933	−	0.435933i	0.454707	−	0.890641i	$-0.349744\pi$
$223$	−1451.70	−	1451.70i	−0.435933	−	0.435933i	−0.890641	+	0.454707i	$0.849744\pi$
$224$	−3513.80	−	2322.10i	−1.04810	−	0.692641i
$225$		0			0
$226$	3618.53	+	424.552i	1.06505	+	0.124959i
$227$	1418.20	−	1418.20i	0.414667	−	0.414667i	−0.468694	−	0.883361i	$-0.655275\pi$
$227$	1418.20	−	1418.20i	0.414667	−	0.414667i	0.883361	+	0.468694i	$0.155275\pi$
$228$	−1403.95	+	864.270i	−0.407801	+	0.251042i
$229$			6354.57i			1.83372i	0.399208	+	0.916860i	$0.369285\pi$
$229$			6354.57i			1.83372i	−0.399208	+	0.916860i	$0.630715\pi$
$230$		0			0
$231$		−	9026.52i		−	2.57100i
$232$	−1212.06	−	2608.21i	−0.342998	−	0.738092i
$233$	−732.523	+	732.523i	−0.205962	+	0.205962i	−0.802549	−	0.596587i	$-0.796523\pi$
$233$	−732.523	+	732.523i	−0.205962	+	0.205962i	0.596587	+	0.802549i	$0.296523\pi$
$234$	19.2406	−	163.991i	0.00537520	−	0.0458139i
$235$		0			0
$236$	−23.2195	+	97.5899i	−0.00640449	+	0.0269176i
$237$	−4324.99	−	4324.99i	−1.18539	−	1.18539i
$238$	−3362.84	−	4256.84i	−0.915885	−	1.15937i
$239$	7017.11			1.89916			0.949580	−	0.313525i	$-0.101510\pi$
$239$	7017.11			1.89916			0.949580	+	0.313525i	$0.101510\pi$
$240$		0			0
$241$	−2758.67			−0.737351			−0.368675	−	0.929558i	$-0.620189\pi$
$241$	−2758.67			−0.737351			−0.368675	+	0.929558i	$0.620189\pi$
$242$	−1157.27	−	1464.92i	−0.307404	−	0.389126i
$243$	1615.21	+	1615.21i	0.426403	+	0.426403i
$244$	615.713	−	2587.80i	0.161545	−	0.678962i
$245$		0			0
$246$	−280.901	+	2394.17i	−0.0728033	+	0.620516i
$247$	−20.1348	+	20.1348i	−0.00518683	+	0.00518683i
$248$	−2419.99	−	5207.54i	−0.619636	−	1.33338i
$249$		−	11564.6i		−	2.94328i
$250$		0			0
$251$		−	4312.99i		−	1.08460i	−0.840186	−	0.542298i	$-0.817554\pi$
$251$		−	4312.99i		−	1.08460i	0.840186	−	0.542298i	$-0.182446\pi$
$252$	−7702.45	+	4741.64i	−1.92543	+	1.18530i
$253$	−487.820	+	487.820i	−0.121221	+	0.121221i
$254$	5720.24	+	671.138i	1.41307	+	0.165791i
$255$		0			0
$256$	2434.44	+	3294.04i	0.594345	+	0.804210i
$257$	−178.554	−	178.554i	−0.0433382	−	0.0433382i	0.685106	−	0.728444i	$-0.259756\pi$
$257$	−178.554	−	178.554i	−0.0433382	−	0.0433382i	−0.728444	+	0.685106i	$0.759756\pi$
$258$	6418.85	−	5070.80i	1.54892	−	1.22362i
$259$	3057.94			0.733633
$260$		0			0
$261$	−6176.51			−1.46481
$262$	2946.35	−	2327.58i	0.694756	−	0.548848i
$263$	950.128	+	950.128i	0.222766	+	0.222766i	0.809662	−	0.586896i	$-0.199650\pi$
$263$	950.128	+	950.128i	0.222766	+	0.222766i	−0.586896	+	0.809662i	$0.699650\pi$
$264$	−3013.23	+	8245.08i	−0.702469	+	1.92216i
$265$		0			0
$266$	1549.21	+	181.764i	0.357098	+	0.0418972i
$267$	2376.62	−	2376.62i	0.544744	−	0.544744i
$268$	1183.07	+	1921.81i	0.269655	+	0.438035i
$269$		−	5698.67i		−	1.29165i	−0.763485	−	0.645826i	$-0.776513\pi$
$269$		−	5698.67i		−	1.29165i	0.763485	−	0.645826i	$-0.223487\pi$
$270$		0			0
$271$		−	1588.26i		−	0.356014i	−0.984029	−	0.178007i	$-0.943035\pi$
$271$		−	1588.26i		−	0.356014i	0.984029	−	0.178007i	$-0.0569649\pi$
$272$	1650.70	+	5010.90i	0.367972	+	1.11702i
$273$	−171.843	+	171.843i	−0.0380968	+	0.0380968i
$274$	470.668	−	4011.59i	0.103774	−	0.884484i
$275$		0			0
$276$	1046.19	+	248.918i	0.228163	+	0.0542867i
$277$	2260.64	+	2260.64i	0.490355	+	0.490355i	0.908418	−	0.418063i	$-0.137291\pi$
$277$	2260.64	+	2260.64i	0.490355	+	0.490355i	−0.418063	+	0.908418i	$0.637291\pi$
$278$	−2249.18	−	2847.11i	−0.485240	−	0.614239i
$279$	−12332.0			−2.64623
$280$		0			0
$281$	252.556			0.0536165			0.0268082	−	0.999641i	$-0.491466\pi$
$281$	252.556			0.0536165			0.0268082	+	0.999641i	$0.491466\pi$
$282$	5398.65	+	6833.86i	1.14002	+	1.44309i
$283$	4366.71	+	4366.71i	0.917223	+	0.917223i	0.996827	−	0.0796034i	$-0.0253654\pi$
$283$	4366.71	+	4366.71i	0.917223	+	0.917223i	−0.0796034	+	0.996827i	$0.525365\pi$
$284$	−5170.93	−	1230.32i	−1.08042	−	0.257063i
$285$		0			0
$286$	−17.6678	+	150.586i	−0.00365286	+	0.0311340i
$287$	1612.73	−	1612.73i	0.331694	−	0.331694i
$288$	8618.49	−	1759.91i	1.76337	−	0.360083i
$289$			1882.39i			0.383145i
$290$		0			0
$291$			13092.1i			2.63735i
$292$	−4148.64	−	6739.17i	−0.831441	−	1.35062i
$293$	−1484.31	+	1484.31i	−0.295954	+	0.295954i	−0.839427	−	0.543473i	$-0.817109\pi$
$293$	−1484.31	+	1484.31i	−0.295954	+	0.295954i	0.543473	+	0.839427i	$0.317109\pi$
$294$	4844.47	+	568.388i	0.961005	+	0.112752i
$295$		0			0
$296$	−2793.20	−	1020.80i	−0.548486	−	0.200449i
$297$	5923.63	+	5923.63i	1.15732	+	1.15732i
$298$	209.911	−	165.827i	0.0408048	−	0.0322352i
$299$	18.5738			0.00359249
$300$		0			0
$301$	−7739.49			−1.48205
$302$	6045.67	−	4776.00i	1.15195	−	0.910026i
$303$	−7766.93	−	7766.93i	−1.47260	−	1.47260i
$304$	−1354.41	−	683.184i	−0.255529	−	0.128892i
$305$		0			0
$306$	11252.8	+	1320.26i	2.10222	+	0.246647i
$307$	1130.20	−	1130.20i	0.210110	−	0.210110i	−0.594204	−	0.804314i	$-0.702533\pi$
$307$	1130.20	−	1130.20i	0.210110	−	0.210110i	0.804314	+	0.594204i	$0.202533\pi$
$308$	7072.81	−	4354.03i	1.30848	−	0.805500i
$309$			2815.58i			0.518358i
$310$		0			0
$311$			2093.83i			0.381769i	0.981612	+	0.190885i	$0.0611356\pi$
$311$			2093.83i			0.381769i	−0.981612	+	0.190885i	$0.938864\pi$
$312$	214.331	−	99.6018i	0.0388914	−	0.0180732i
$313$	2420.68	−	2420.68i	0.437140	−	0.437140i	−0.453908	−	0.891048i	$-0.649971\pi$
$313$	2420.68	−	2420.68i	0.437140	−	0.437140i	0.891048	+	0.453908i	$0.149971\pi$
$314$	−560.151	+	4774.27i	−0.100672	+	0.858049i
$315$		0			0
$316$	1302.68	−	5475.08i	0.231904	−	0.974675i
$317$	4280.20	+	4280.20i	0.758360	+	0.758360i	0.976024	−	0.217664i	$-0.0698438\pi$
$317$	4280.20	+	4280.20i	0.758360	+	0.758360i	−0.217664	+	0.976024i	$0.569844\pi$
$318$	3214.92	+	4069.60i	0.566931	+	0.717646i
$319$	5671.61			0.995452
$320$		0			0
$321$	−5078.46			−0.883028
$322$	−630.716	−	798.389i	−0.109157	−	0.138175i
$323$	−1381.61	−	1381.61i	−0.238003	−	0.238003i
$324$	593.105	−	2492.78i	0.101698	−	0.427431i
$325$		0			0
$326$	156.617	−	1334.88i	0.0266081	−	0.226786i
$327$	−8755.01	+	8755.01i	−1.48059	+	1.48059i
$328$	−2011.47	+	934.750i	−0.338613	+	0.157357i
$329$		−	8239.88i		−	1.38079i
$330$		0			0
$331$		−	2409.27i		−	0.400077i	−0.979788	−	0.200038i	$-0.935893\pi$
$331$		−	2409.27i		−	0.400077i	0.979788	−	0.200038i	$-0.0641067\pi$
$332$	9061.53	−	5578.29i	1.49794	−	0.922133i
$333$	−4515.98	+	4515.98i	−0.743166	+	0.743166i
$334$	−5414.16	−	635.227i	−0.886974	−	0.104066i
$335$		0			0
$336$	−11559.4	−	5830.74i	−1.87684	−	0.946705i
$337$	−3683.97	−	3683.97i	−0.595486	−	0.595486i	0.343622	−	0.939108i	$-0.388346\pi$
$337$	−3683.97	−	3683.97i	−0.595486	−	0.595486i	−0.939108	+	0.343622i	$0.888346\pi$
$338$	−4872.89	+	3849.51i	−0.784172	+	0.619485i
$339$	11199.5			1.79432
$340$		0			0
$341$	11323.9			1.79831
$342$	−2556.31	+	2019.45i	−0.404180	+	0.319296i
$343$	2379.83	+	2379.83i	0.374633	+	0.374633i
$344$	7069.47	+	2583.60i	1.10802	+	0.404937i
$345$		0			0
$346$	−2575.08	−	302.127i	−0.400107	−	0.0469434i
$347$	−6739.78	+	6739.78i	−1.04268	+	1.04268i	−0.0436336	+	0.999048i	$0.513893\pi$
$347$	−6739.78	+	6739.78i	−1.04268	+	1.04268i	−0.999048	+	0.0436336i	$0.986107\pi$
$348$	−4634.69	−	7528.72i	−0.713924	−	1.15972i
$349$			1241.79i			0.190463i	0.995455	+	0.0952313i	$0.0303591\pi$
$349$			1241.79i			0.190463i	−0.995455	+	0.0952313i	$0.969641\pi$
$350$		0			0
$351$		−	225.543i		−	0.0342980i
$352$	−7913.97	+	1616.05i	−1.19834	+	0.244703i
$353$	1393.38	−	1393.38i	0.210090	−	0.210090i	−0.594215	−	0.804306i	$-0.702537\pi$
$353$	1393.38	−	1393.38i	0.210090	−	0.210090i	0.804306	+	0.594215i	$0.202537\pi$
$354$	−35.9326	+	306.260i	−0.00539490	+	0.0459817i
$355$		0			0
$356$	3008.60	+	715.835i	0.447909	+	0.106571i
$357$	−11791.6	−	11791.6i	−1.74812	−	1.74812i
$358$	168.645	+	213.478i	0.0248971	+	0.0315159i
$359$	−7760.71			−1.14093			−0.570466	−	0.821321i	$-0.693237\pi$
$359$	−7760.71			−1.14093			−0.570466	+	0.821321i	$0.693237\pi$
$360$		0			0
$361$	−6297.19			−0.918092
$362$	4331.83	+	5483.42i	0.628939	+	0.796139i
$363$	−4057.88	−	4057.88i	−0.586731	−	0.586731i
$364$	−217.540	−	51.7591i	−0.0313246	−	0.00745305i
$365$		0			0
$366$	952.827	−	8121.12i	0.136079	−	1.15983i
$367$	4508.13	−	4508.13i	0.641206	−	0.641206i	−0.309646	−	0.950852i	$-0.600211\pi$
$367$	4508.13	−	4508.13i	0.641206	−	0.641206i	0.950852	+	0.309646i	$0.100211\pi$
$368$	309.596	+	939.817i	0.0438554	+	0.133129i
$369$			4763.38i			0.672009i
$370$		0			0
$371$		−	4906.89i		−	0.686666i
$372$	−9253.60	−	15031.8i	−1.28972	−	2.09506i
$373$	−5363.66	+	5363.66i	−0.744557	+	0.744557i	−0.973451	−	0.228894i	$-0.926489\pi$
$373$	−5363.66	+	5363.66i	−0.744557	+	0.744557i	0.228894	+	0.973451i	$0.426489\pi$
$374$	−10332.9	−	1212.33i	−1.42862	−	0.167616i
$375$		0			0
$376$	−2750.64	+	7526.54i	−0.377269	+	1.03232i
$377$	−107.974	−	107.974i	−0.0147505	−	0.0147505i
$378$	−9694.88	+	7658.82i	−1.31918	+	1.04214i
$379$	−8526.74			−1.15564			−0.577822	−	0.816163i	$-0.696097\pi$
$379$	−8526.74			−1.15564			−0.577822	+	0.816163i	$0.696097\pi$
$380$		0			0
$381$	17704.3			2.38063
$382$	−7356.46	+	5811.50i	−0.985312	+	0.778383i
$383$	7645.72	+	7645.72i	1.02005	+	1.02005i	0.999795	+	0.0202520i	$0.00644685\pi$
$383$	7645.72	+	7645.72i	1.02005	+	1.02005i	0.0202520	+	0.999795i	$0.493553\pi$
$384$	8612.29	+	9184.73i	1.14452	+	1.22059i
$385$		0			0
$386$	9896.75	+	1161.16i	1.30500	+	0.153112i
$387$	11429.7	−	11429.7i	1.50131	−	1.50131i
$388$	−10258.4	+	6315.08i	−1.34225	+	0.826287i
$389$			10831.8i			1.41181i	0.708304	+	0.705907i	$0.249460\pi$
$389$			10831.8i			1.41181i	−0.708304	+	0.705907i	$0.750540\pi$
$390$		0			0
$391$			1274.51i			0.164845i
$392$	1891.41	+	4070.10i	0.243701	+	0.524416i
$393$	8161.50	−	8161.50i	1.04756	−	1.04756i
$394$	1594.05	−	13586.4i	0.203825	−	1.73723i
$395$		0			0
$396$	−4015.12	+	16875.2i	−0.509513	+	2.14145i
$397$	7632.28	+	7632.28i	0.964870	+	0.964870i	0.999404	−	0.0345340i	$-0.0109947\pi$
$397$	7632.28	+	7632.28i	0.964870	+	0.964870i	−0.0345340	+	0.999404i	$0.510995\pi$
$398$	6823.70	+	8637.75i	0.859400	+	1.08787i
$399$	4794.85			0.601611
$400$		0			0
$401$	7809.85			0.972582			0.486291	−	0.873797i	$-0.338350\pi$
$401$	7809.85			0.972582			0.486291	+	0.873797i	$0.338350\pi$
$402$	4300.32	+	5443.54i	0.533534	+	0.675371i
$403$	−215.580	−	215.580i	−0.0266472	−	0.0266472i
$404$	2339.39	−	9832.30i	0.288092	−	1.21083i
$405$		0			0
$406$	−974.718	+	8307.70i	−0.119149	+	1.01553i
$407$	4146.82	−	4146.82i	0.505038	−	0.505038i
$408$	6834.50	+	14707.0i	0.829310	+	1.78458i
$409$			11561.3i			1.39772i	0.715259	+	0.698860i	$0.246309\pi$
$409$			11561.3i			1.39772i	−0.715259	+	0.698860i	$0.753691\pi$
$410$		0			0
$411$		−	12416.0i		−	1.49011i
$412$	−2206.17	+	1358.12i	−0.263811	+	0.162403i
$413$	206.298	−	206.298i	0.0245794	−	0.0245794i
$414$	2110.51	+	247.620i	0.250546	+	0.0293958i
$415$		0			0
$416$	181.429	+	119.897i	0.0213828	+	0.0141309i
$417$	−7886.60	−	7886.60i	−0.926160	−	0.926160i
$418$	2347.34	−	1854.37i	0.274671	−	0.216986i
$419$	−223.257			−0.0260306			−0.0130153	−	0.999915i	$-0.504143\pi$
$419$	−223.257			−0.0260306			−0.0130153	+	0.999915i	$0.504143\pi$
$420$		0			0
$421$	−9330.20			−1.08011			−0.540055	−	0.841630i	$-0.681597\pi$
$421$	−9330.20			−1.08011			−0.540055	+	0.841630i	$0.681597\pi$
$422$	−11496.8	+	9082.35i	−1.32620	+	1.04768i
$423$	12168.7	+	12168.7i	1.39873	+	1.39873i
$424$	−1638.02	+	4482.09i	−0.187616	+	0.513372i
$425$		0			0
$426$	−16227.6	−	1903.94i	−1.84561	−	0.216540i
$427$	−5470.43	+	5470.43i	−0.619982	+	0.619982i
$428$	−2449.64	−	3979.27i	−0.276654	−	0.449405i
$429$			466.068i			0.0524522i
$430$		0			0
$431$			4319.11i			0.482701i	0.970438	+	0.241350i	$0.0775903\pi$
$431$			4319.11i			0.482701i	−0.970438	+	0.241350i	$0.922410\pi$
$432$	11412.2	−	3759.44i	1.27100	−	0.418695i
$433$	3860.89	−	3860.89i	0.428505	−	0.428505i	−0.459614	−	0.888119i	$-0.652012\pi$
$433$	3860.89	−	3860.89i	0.428505	−	0.428505i	0.888119	+	0.459614i	$0.152012\pi$
$434$	−1946.12	+	16587.1i	−0.215246	+	1.83458i
$435$		0			0
$436$	−11083.1	−	2637.00i	−1.21740	−	0.289655i
$437$	−259.128	−	259.128i	−0.0283656	−	0.0283656i
$438$	−15079.8	−	19088.7i	−1.64507	−	2.08240i
$439$	−2790.65			−0.303395			−0.151697	−	0.988427i	$-0.548474\pi$
$439$	−2790.65			−0.303395			−0.151697	+	0.988427i	$0.548474\pi$
$440$		0			0
$441$	9638.42			1.04075
$442$	173.634	+	219.794i	0.0186854	+	0.0236528i
$443$	−12801.3	−	12801.3i	−1.37293	−	1.37293i	−0.856077	−	0.516849i	$-0.827105\pi$
$443$	−12801.3	−	12801.3i	−1.37293	−	1.37293i	−0.516849	−	0.856077i	$-0.672895\pi$
$444$	−8893.33	−	2115.98i	−0.950583	−	0.226172i
$445$		0			0
$446$	676.654	−	5767.25i	0.0718397	−	0.612303i
$447$	581.462	−	581.462i	0.0615262	−	0.0615262i
$448$	−1007.08	−	11870.0i	−0.106205	−	1.25180i
$449$		−	2245.42i		−	0.236008i	−0.993013	−	0.118004i	$-0.962350\pi$
$449$		−	2245.42i		−	0.236008i	0.993013	−	0.118004i	$-0.0376496\pi$
$450$		0			0
$451$		−	4373.99i		−	0.456681i
$452$	5402.18	+	8775.46i	0.562162	+	0.913192i
$453$	16746.7	−	16746.7i	1.73693	−	1.73693i
$454$	5634.16	+	661.040i	0.582433	+	0.0683351i
$455$		0			0
$456$	−4379.75	−	1600.62i	−0.449782	−	0.164377i
$457$	1560.21	+	1560.21i	0.159701	+	0.159701i	0.782434	−	0.622733i	$-0.213978\pi$
$457$	1560.21	+	1560.21i	0.159701	+	0.159701i	−0.622733	+	0.782434i	$0.713978\pi$
$458$	−14103.5	+	11141.6i	−1.43890	+	1.13671i
$459$	15476.4			1.57380
$460$		0			0
$461$	2633.09			0.266020			0.133010	−	0.991115i	$-0.457536\pi$
$461$	2633.09			0.266020			0.133010	+	0.991115i	$0.457536\pi$
$462$	20033.7	−	15826.4i	2.01743	−	1.59374i
$463$	−7629.96	−	7629.96i	−0.765862	−	0.765862i	0.211513	−	0.977375i	$-0.432161\pi$
$463$	−7629.96	−	7629.96i	−0.765862	−	0.765862i	−0.977375	+	0.211513i	$0.932161\pi$
$464$	3663.61	−	7263.10i	0.366549	−	0.726683i
$465$		0			0
$466$	−2910.13	−	341.437i	−0.289290	−	0.0339416i
$467$	−5048.30	+	5048.30i	−0.500230	+	0.500230i	−0.911509	−	0.411280i	$-0.865082\pi$
$467$	−5048.30	+	5048.30i	−0.500230	+	0.500230i	0.411280	+	0.911509i	$0.365082\pi$
$468$	397.702	−	244.826i	0.0392816	−	0.0241818i
$469$		−	6563.51i		−	0.646215i
$470$		0			0
$471$			14776.5i			1.44558i
$472$	−257.305	+	119.572i	−0.0250920	+	0.0116605i
$473$	−10495.4	+	10495.4i	−1.02025	+	1.02025i
$474$	2015.93	−	17182.1i	0.195347	−	1.66498i
$475$		0			0
$476$	3551.62	−	14927.2i	0.341992	−	1.43737i
$477$	7246.53	+	7246.53i	0.695588	+	0.695588i
$478$	12303.2	+	15574.0i	1.17727	+	1.49025i
$479$	2483.78			0.236924			0.118462	−	0.992959i	$-0.462204\pi$
$479$	2483.78			0.236924			0.118462	+	0.992959i	$0.462204\pi$
$480$		0			0
$481$	−157.891			−0.0149672
$482$	−4836.83	−	6122.67i	−0.457078	−	0.578590i
$483$	−2211.57	−	2211.57i	−0.208343	−	0.208343i
$484$	1222.23	−	5136.94i	0.114785	−	0.482432i
$485$		0			0
$486$	−752.869	+	6416.84i	−0.0702692	+	0.598917i
$487$	−3898.10	+	3898.10i	−0.362710	+	0.362710i	−0.864810	−	0.502099i	$-0.832561\pi$
$487$	−3898.10	+	3898.10i	−0.362710	+	0.362710i	0.502099	+	0.864810i	$0.332561\pi$
$488$	6822.98	−	3170.70i	0.632913	−	0.294121i
$489$		−	4131.50i		−	0.382071i
$490$		0			0
$491$		−	9000.53i		−	0.827267i	−0.910443	−	0.413634i	$-0.864259\pi$
$491$		−	9000.53i		−	0.827267i	0.910443	−	0.413634i	$-0.135741\pi$
$492$	−5806.21	+	3574.31i	−0.532041	+	0.327525i
$493$	7408.98	−	7408.98i	0.676843	−	0.676843i
$494$	−79.9905	−	9.38505i	−0.00728531	−	0.000854764i
$495$		0			0
$496$	7314.75	−	14501.5i	0.662181	−	1.31277i
$497$	10931.0	+	10931.0i	0.986563	+	0.986563i
$498$	25666.8	−	20276.4i	2.30955	−	1.82451i
$499$	−13057.4			−1.17140			−0.585699	−	0.810528i	$-0.699180\pi$
$499$	−13057.4			−1.17140			−0.585699	+	0.810528i	$0.699180\pi$
$500$		0			0
$501$	−16757.0			−1.49431
$502$	9572.39	−	7562.06i	0.851069	−	0.672333i
$503$	−1782.55	−	1782.55i	−0.158012	−	0.158012i	0.623673	−	0.781685i	$-0.285640\pi$
$503$	−1782.55	−	1782.55i	−0.158012	−	0.158012i	−0.781685	+	0.623673i	$0.785640\pi$
$504$	−24028.6	−	8781.45i	−2.12365	−	0.776105i
$505$		0			0
$506$	−1937.99	−	227.378i	−0.170265	−	0.0199767i
$507$	−13498.1	+	13498.1i	−1.18239	+	1.18239i
$508$	8539.86	+	13872.4i	0.745856	+	1.21159i
$509$		−	6098.28i		−	0.531044i	−0.964105	−	0.265522i	$-0.914456\pi$
$509$		−	6098.28i		−	0.531044i	0.964105	−	0.265522i	$-0.0855443\pi$
$510$		0			0
$511$			23016.1i			1.99251i
$512$	−3042.55	+	11178.6i	−0.262623	+	0.964898i
$513$	−3146.61	+	3146.61i	−0.270811	+	0.270811i
$514$	83.2262	−	709.352i	0.00714193	−	0.0608720i
$515$		0			0
$516$	22508.6	+	5355.46i	1.92032	+	0.456901i
$517$	−11174.0	−	11174.0i	−0.950543	−	0.950543i
$518$	5361.54	+	6786.88i	0.454773	+	0.575672i
$519$	−7969.96			−0.674070
$520$		0			0
$521$	14621.2			1.22949			0.614746	−	0.788725i	$-0.289258\pi$
$521$	14621.2			1.22949			0.614746	+	0.788725i	$0.289258\pi$
$522$	−10829.4	−	13708.3i	−0.908026	−	1.14942i
$523$	−3175.36	−	3175.36i	−0.265486	−	0.265486i	0.561793	−	0.827278i	$-0.310112\pi$
$523$	−3175.36	−	3175.36i	−0.265486	−	0.265486i	−0.827278	+	0.561793i	$0.810112\pi$
$524$	10331.8	+	2458.24i	0.861348	+	0.204940i
$525$		0			0
$526$	−442.865	+	3774.62i	−0.0367107	+	0.312892i
$527$	14792.7	−	14792.7i	1.22274	−	1.22274i
$528$	−23582.5	+	7768.60i	−1.94375	+	0.640312i
$529$		−	11928.0i		−	0.980353i
$530$		0			0
$531$			609.325i			0.0497975i
$532$	2312.84	+	3757.05i	0.188486	+	0.306182i
$533$	−83.2703	+	83.2703i	−0.00676705	+	0.00676705i
$534$	9441.70	+	1107.77i	0.765135	+	0.0897711i
$535$		0			0
$536$	−2191.03	+	5995.30i	−0.176564	+	0.483130i
$537$	591.343	+	591.343i	0.0475202	+	0.0475202i
$538$	12647.8	−	9991.59i	1.01354	−	0.800684i
$539$	−8850.52			−0.707271
$540$		0			0
$541$	6733.34			0.535099			0.267550	−	0.963544i	$-0.413786\pi$
$541$	6733.34			0.535099			0.267550	+	0.963544i	$0.413786\pi$
$542$	3525.02	−	2784.72i	0.279359	−	0.220690i
$543$	15189.3	+	15189.3i	1.20043	+	1.20043i
$544$	−8227.14	+	12449.3i	−0.648411	+	0.981176i
$545$		0			0
$546$	−682.690	−	80.0981i	−0.0535100	−	0.00627817i
$547$	5281.02	−	5281.02i	0.412797	−	0.412797i	−0.469915	−	0.882712i	$-0.655715\pi$
$547$	5281.02	−	5281.02i	0.412797	−	0.412797i	0.882712	+	0.469915i	$0.155715\pi$
$548$	9728.67	−	5988.98i	0.758372	−	0.466855i
$549$		−	16157.5i		−	1.25608i
$550$		0			0
$551$			3012.73i			0.232934i
$552$	1281.84	+	2758.37i	0.0988384	+	0.212689i
$553$	−11573.9	+	11573.9i	−0.890008	+	0.890008i
$554$	−1053.71	+	8980.94i	−0.0808082	+	0.688743i
$555$		0			0
$556$	2375.44	−	9983.79i	0.181189	−	0.761524i
$557$	−9284.66	−	9284.66i	−0.706290	−	0.706290i	0.259463	−	0.965753i	$-0.416455\pi$
$557$	−9284.66	−	9284.66i	−0.706290	−	0.706290i	−0.965753	+	0.259463i	$0.916455\pi$
$558$	−21621.9	−	27370.0i	−1.64037	−	2.07646i
$559$	399.614			0.0302359
$560$		0			0
$561$	−31980.8			−2.40683
$562$	442.811	+	560.531i	0.0332364	+	0.0420722i
$563$	7802.12	+	7802.12i	0.584050	+	0.584050i	0.936014	−	0.351963i	$-0.114486\pi$
$563$	7802.12	+	7802.12i	0.584050	+	0.584050i	−0.351963	+	0.936014i	$0.614486\pi$
$564$	−5701.71	+	23963.9i	−0.425683	+	1.78911i
$565$		0			0
$566$	−2035.37	+	17347.9i	−0.151154	+	1.28831i
$567$	−5269.56	+	5269.56i	−0.390301	+	0.390301i
$568$	−6335.69	−	13633.7i	−0.468027	−	1.00714i
$569$			15179.2i			1.11836i	0.829046	+	0.559180i	$0.188884\pi$
$569$			15179.2i			1.11836i	−0.829046	+	0.559180i	$0.811116\pi$
$570$		0			0
$571$		−	15123.8i		−	1.10843i	−0.832375	−	0.554213i	$-0.813019\pi$
$571$		−	15123.8i		−	1.10843i	0.832375	−	0.554213i	$-0.186981\pi$
$572$	−365.192	+	224.812i	−0.0266948	+	0.0164334i
$573$	−20377.6	+	20377.6i	−1.48567	+	1.48567i
$574$	6406.96	+	751.710i	0.465891	+	0.0546616i
$575$		0			0
$576$	19017.0	+	16042.4i	1.37565	+	1.16048i
$577$	−6086.54	−	6086.54i	−0.439144	−	0.439144i	0.452580	−	0.891724i	$-0.350504\pi$
$577$	−6086.54	−	6086.54i	−0.439144	−	0.439144i	−0.891724	+	0.452580i	$0.850504\pi$
$578$	−4177.83	+	3300.43i	−0.300649	+	0.237508i
$579$	30630.8			2.19857
$580$		0			0
$581$	−30947.6			−2.20985
$582$	−29056.9	+	22954.6i	−2.06950	+	1.63487i
$583$	−6654.16	−	6654.16i	−0.472705	−	0.472705i
$584$	7683.22	−	21023.5i	0.544408	−	1.48966i
$585$		0			0
$586$	−5896.80	−	691.854i	−0.415691	−	0.0487718i
$587$	9334.98	−	9334.98i	0.656381	−	0.656381i	−0.298141	−	0.954522i	$-0.596367\pi$
$587$	9334.98	−	9334.98i	0.656381	−	0.656381i	0.954522	+	0.298141i	$0.0963665\pi$
$588$	7232.41	+	11748.5i	0.507244	+	0.823982i
$589$			6015.21i			0.420802i
$590$		0			0
$591$		−	42050.2i		−	2.92676i
$592$	−2631.78	−	7989.11i	−0.182712	−	0.554646i
$593$	801.327	−	801.327i	0.0554917	−	0.0554917i	−0.678816	−	0.734308i	$-0.737507\pi$
$593$	801.327	−	801.327i	0.0554917	−	0.0554917i	0.734308	+	0.678816i	$0.237507\pi$
$594$	−2761.07	+	23533.1i	−0.190721	+	1.62555i
$595$		0			0
$596$	736.083	+	175.136i	0.0505892	+	0.0120366i
$597$	23926.9	+	23926.9i	1.64030	+	1.64030i
$598$	32.5659	+	41.2234i	0.00222695	+	0.00281898i
$599$	−2384.18			−0.162629			−0.0813146	−	0.996688i	$-0.525912\pi$
$599$	−2384.18			−0.162629			−0.0813146	+	0.996688i	$0.525912\pi$
$600$		0			0
$601$	11760.3			0.798190			0.399095	−	0.916910i	$-0.369324\pi$
$601$	11760.3			0.798190			0.399095	+	0.916910i	$0.369324\pi$
$602$	−13569.8	−	17177.3i	−0.918710	−	1.16294i
$603$	9693.04	+	9693.04i	0.654612	+	0.654612i
$604$	21200.0	+	5044.10i	1.42817	+	0.339804i
$605$		0			0
$606$	3620.25	−	30856.1i	0.242678	−	2.06839i
$607$	4286.59	−	4286.59i	0.286635	−	0.286635i	−0.549113	−	0.835748i	$-0.685034\pi$
$607$	4286.59	−	4286.59i	0.286635	−	0.286635i	0.835748	+	0.549113i	$0.185034\pi$
$608$	−858.437	−	4203.86i	−0.0572603	−	0.280410i
$609$			25712.6i			1.71088i
$610$		0			0
$611$			425.451i			0.0281701i
$612$	16799.5	+	27289.6i	1.10961	+	1.80248i
$613$	2911.11	−	2911.11i	0.191808	−	0.191808i	−0.604669	−	0.796477i	$-0.706695\pi$
$613$	2911.11	−	2911.11i	0.191808	−	0.191808i	0.796477	+	0.604669i	$0.206695\pi$
$614$	4489.99	+	526.797i	0.295116	+	0.0346251i
$615$		0			0
$616$	22064.4	+	8063.61i	1.44318	+	0.527422i
$617$	4635.01	+	4635.01i	0.302429	+	0.302429i	0.841963	−	0.539535i	$-0.181400\pi$
$617$	4635.01	+	4635.01i	0.302429	+	0.302429i	−0.539535	+	0.841963i	$0.681400\pi$
$618$	−6248.98	+	4936.61i	−0.406749	+	0.321326i
$619$	6898.58			0.447944			0.223972	−	0.974596i	$-0.428098\pi$
$619$	6898.58			0.447944			0.223972	+	0.974596i	$0.428098\pi$
$620$		0			0
$621$	2902.67			0.187568
$622$	−4647.11	+	3671.15i	−0.299569	+	0.236656i
$623$	−6359.98	−	6359.98i	−0.409000	−	0.409000i
$624$	596.850	+	301.059i	0.0382903	+	0.0193141i
$625$		0			0
$626$	9616.75	+	1128.30i	0.613998	+	0.0720385i
$627$	6502.22	−	6502.22i	0.414153	−	0.414153i
$628$	−11578.3	+	7127.60i	−0.735706	+	0.452901i
$629$		−	10834.2i		−	0.686786i
$630$		0			0
$631$			6731.96i			0.424715i	0.977192	+	0.212357i	$0.0681141\pi$
$631$			6731.96i			0.424715i	−0.977192	+	0.212357i	$0.931886\pi$
$632$	14435.6	−	6708.35i	0.908571	−	0.422221i
$633$	−31846.7	+	31846.7i	−1.99967	+	1.99967i
$634$	−1995.05	+	17004.2i	−0.124974	+	1.06518i
$635$		0			0
$636$	−3395.40	+	14270.6i	−0.211692	+	0.889727i
$637$	168.493	+	168.493i	0.0104803	+	0.0104803i
$638$	9944.14	+	12587.7i	0.617073	+	0.781118i
$639$	−32285.9			−1.99877
$640$		0			0
$641$	−20886.3			−1.28699			−0.643495	−	0.765450i	$-0.722516\pi$
$641$	−20886.3			−1.28699			−0.643495	+	0.765450i	$0.722516\pi$
$642$	−8904.17	−	11271.3i	−0.547382	−	0.692901i
$643$	−3857.48	−	3857.48i	−0.236585	−	0.236585i	0.578849	−	0.815434i	$-0.303502\pi$
$643$	−3857.48	−	3857.48i	−0.236585	−	0.236585i	−0.815434	+	0.578849i	$0.803502\pi$
$644$	666.122	−	2799.66i	0.0407591	−	0.171308i
$645$		0			0
$646$	643.986	−	5488.81i	0.0392218	−	0.334295i
$647$	−2807.13	+	2807.13i	−0.170572	+	0.170572i	−0.787230	−	0.616659i	$-0.788486\pi$
$647$	−2807.13	+	2807.13i	−0.170572	+	0.170572i	0.616659	+	0.787230i	$0.288486\pi$
$648$	6572.44	−	3054.28i	0.398441	−	0.185160i
$649$		−	559.516i		−	0.0338412i
$650$		0			0
$651$			51337.7i			3.09076i
$652$	3237.27	−	1992.87i	0.194450	−	0.119704i
$653$	9353.51	−	9353.51i	0.560538	−	0.560538i	−0.368922	−	0.929460i	$-0.620273\pi$
$653$	9353.51	−	9353.51i	0.560538	−	0.560538i	0.929460	+	0.368922i	$0.120273\pi$
$654$	−34781.5	−	4080.81i	−2.07961	−	0.243994i
$655$		0			0
$656$	−5601.36	−	2825.41i	−0.333379	−	0.168161i
$657$	−33990.3	−	33990.3i	−2.01840	−	2.01840i
$658$	18287.8	−	14447.1i	1.08349	−	0.855939i
$659$	−18295.5			−1.08147			−0.540737	−	0.841191i	$-0.681855\pi$
$659$	−18295.5			−1.08147			−0.540737	+	0.841191i	$0.681855\pi$
$660$		0			0
$661$	27859.2			1.63933			0.819664	−	0.572845i	$-0.194160\pi$
$661$	27859.2			1.63933			0.819664	+	0.572845i	$0.194160\pi$
$662$	5347.21	−	4224.22i	0.313935	−	0.248004i
$663$	608.837	+	608.837i	0.0356641	+	0.0356641i
$664$	28268.4	+	10330.9i	1.65215	+	0.603791i
$665$		0			0
$666$	−17940.9	−	2104.95i	−1.04384	−	0.122470i
$667$	1389.59	−	1389.59i	0.0806672	−	0.0806672i
$668$	−8082.90	−	13130.1i	−0.468169	−	0.760507i
$669$		−	17849.8i		−	1.03156i
$670$		0			0
$671$			14836.7i			0.853600i
$672$	−7326.46	−	35878.5i	−0.420572	−	2.05959i
$673$	4252.85	−	4252.85i	0.243589	−	0.243589i	−0.574744	−	0.818333i	$-0.694898\pi$
$673$	4252.85	−	4252.85i	0.243589	−	0.243589i	0.818333	+	0.574744i	$0.194898\pi$
$674$	1717.14	−	14635.5i	0.0981332	−	0.836407i
$675$		0			0
$676$	−17087.4	−	4065.61i	−0.972203	−	0.231316i
$677$	3002.52	+	3002.52i	0.170453	+	0.170453i	0.787178	−	0.616726i	$-0.211541\pi$
$677$	3002.52	+	3002.52i	0.170453	+	0.170453i	−0.616726	+	0.787178i	$0.711541\pi$
$678$	19636.3	+	24856.5i	1.11228	+	1.40798i
$679$	35035.2			1.98016
$680$		0			0
$681$	17437.9			0.981238
$682$	19854.4	+	25132.6i	1.11476	+	1.41111i
$683$	3185.21	+	3185.21i	0.178446	+	0.178446i	0.790678	−	0.612232i	$-0.209728\pi$
$683$	3185.21	+	3185.21i	0.178446	+	0.178446i	−0.612232	+	0.790678i	$0.709728\pi$
$684$	−8964.05	−	2132.81i	−0.501095	−	0.119225i
$685$		0			0
$686$	−1109.27	+	9454.49i	−0.0617376	+	0.526201i
$687$	−39067.3	+	39067.3i	−2.16959	+	2.16959i
$688$	6660.92	+	20220.1i	0.369106	+	1.12047i
$689$			253.358i			0.0140090i
$690$		0			0
$691$		−	5509.61i		−	0.303322i	−0.988433	−	0.151661i	$-0.951538\pi$
$691$		−	5509.61i		−	0.303322i	0.988433	−	0.151661i	$-0.0484622\pi$
$692$	−3844.39	−	6244.93i	−0.211187	−	0.343059i
$693$	35673.1	−	35673.1i	1.95542	−	1.95542i
$694$	−26775.5	−	3141.49i	−1.46453	−	0.171829i
$695$		0			0
$696$	8583.38	−	23486.6i	0.467460	−	1.27911i
$697$	−5713.86	−	5713.86i	−0.310514	−	0.310514i
$698$	−2756.07	+	2177.25i	−0.149454	+	0.118066i
$699$	−9006.96			−0.487374
$700$		0			0
$701$	−1423.05			−0.0766731			−0.0383365	−	0.999265i	$-0.512206\pi$
$701$	−1423.05			−0.0766731			−0.0383365	+	0.999265i	$0.512206\pi$
$702$	500.578	−	395.449i	0.0269132	−	0.0212611i
$703$	2202.77	+	2202.77i	0.118178	+	0.118178i
$704$	−17462.4	−	14731.1i	−0.934857	−	0.788633i
$705$		0			0
$706$	5535.53	+	649.468i	0.295089	+	0.0346219i
$707$	−20784.8	+	20784.8i	−1.10565	+	1.10565i
$708$	−742.724	+	457.222i	−0.0394255	+	0.0242704i
$709$		−	26914.2i		−	1.42565i	−0.701343	−	0.712824i	$-0.747416\pi$
$709$		−	26914.2i		−	1.42565i	0.701343	−	0.712824i	$-0.252584\pi$
$710$		0			0
$711$		−	34185.0i		−	1.80315i
$712$	3686.29	+	7932.47i	0.194030	+	0.417531i
$713$	2774.44	−	2774.44i	0.145728	−	0.145728i
$714$	5496.19	−	46845.0i	0.288081	−	2.45537i
$715$		0			0
$716$	−178.112	+	748.592i	−0.00929659	+	0.0390729i
$717$	43140.5	+	43140.5i	2.24702	+	2.24702i
$718$	−13607.0	−	17224.4i	−0.707254	−	0.895274i
$719$	35973.4			1.86590			0.932950	−	0.360006i	$-0.117225\pi$
$719$	35973.4			1.86590			0.932950	+	0.360006i	$0.117225\pi$
$720$		0			0
$721$	7534.67			0.389190
$722$	−11041.0	−	13976.2i	−0.569118	−	0.720415i
$723$	−16960.0	−	16960.0i	−0.872407	−	0.872407i
$724$	−4575.00	+	19228.4i	−0.234846	+	0.987040i
$725$		0			0
$726$	1891.42	−	16120.9i	0.0966904	−	0.824110i
$727$	9307.24	−	9307.24i	0.474809	−	0.474809i	−0.428658	−	0.903467i	$-0.641013\pi$
$727$	9307.24	−	9307.24i	0.474809	−	0.474809i	0.903467	+	0.428658i	$0.141013\pi$
$728$	−266.541	−	573.564i	−0.0135696	−	0.0292001i
$729$			28508.3i			1.44837i
$730$		0			0
$731$			27420.9i			1.38741i
$732$	19694.9	−	12124.2i	0.994458	−	0.612189i
$733$	−7372.92	+	7372.92i	−0.371521	+	0.371521i	−0.868031	−	0.496510i	$-0.834615\pi$
$733$	−7372.92	+	7372.92i	−0.371521	+	0.371521i	0.496510	+	0.868031i	$0.334615\pi$
$734$	17909.7	+	2101.29i	0.900624	+	0.105668i
$735$		0			0
$736$	−1543.04	+	2334.92i	−0.0772787	+	0.116938i
$737$	−8900.68	−	8900.68i	−0.444859	−	0.444859i
$738$	−10572.0	+	8351.72i	−0.527317	+	0.416573i
$739$	−24540.3			−1.22156			−0.610778	−	0.791802i	$-0.709143\pi$
$739$	−24540.3			−1.22156			−0.610778	+	0.791802i	$0.709143\pi$
$740$		0			0
$741$	−247.573			−0.0122737
$742$	10890.5	−	8603.34i	0.538818	−	0.425659i
$743$	−25077.8	−	25077.8i	−1.23825	−	1.23825i	−0.960718	−	0.277528i	$-0.910485\pi$
$743$	−25077.8	−	25077.8i	−1.23825	−	1.23825i	−0.277528	−	0.960718i	$-0.589515\pi$
$744$	17137.6	−	46893.3i	0.844480	−	2.31074i
$745$		0			0
$746$	−21308.5	−	2500.06i	−1.04579	−	0.122699i
$747$	45703.6	−	45703.6i	2.23856	−	2.23856i
$748$	−15426.2	−	25058.8i	−0.754063	−	1.22492i
$749$			13590.3i			0.662989i
$750$		0			0
$751$		−	23078.2i		−	1.12135i	−0.828035	−	0.560676i	$-0.810541\pi$
$751$		−	23078.2i		−	1.12135i	0.828035	−	0.560676i	$-0.189459\pi$
$752$	−21527.4	+	7091.58i	−1.04391	+	0.343887i
$753$	26515.9	−	26515.9i	1.28326	−	1.28326i
$754$	50.3278	−	428.953i	0.00243081	−	0.0207182i
$755$		0			0
$756$	−33996.4	−	8088.75i	−1.63550	−	0.389134i
$757$	−16966.6	−	16966.6i	−0.814613	−	0.814613i	0.170708	−	0.985322i	$-0.445394\pi$
$757$	−16966.6	−	16966.6i	−0.814613	−	0.814613i	−0.985322	+	0.170708i	$0.945394\pi$
$758$	−14950.1	−	18924.5i	−0.716375	−	0.906819i
$759$	−5998.14			−0.286849
$760$		0			0
$761$	7121.15			0.339213			0.169607	−	0.985512i	$-0.445750\pi$
$761$	7121.15			0.339213			0.169607	+	0.985512i	$0.445750\pi$
$762$	31041.4	+	39293.5i	1.47573	+	1.86805i
$763$	23429.0	+	23429.0i	1.11165	+	1.11165i
$764$	−25796.4	−	6137.73i	−1.22157	−	0.290648i
$765$		0			0
$766$	−3563.75	+	30374.5i	−0.168099	+	1.43274i
$767$	−10.6518	+	10.6518i	−0.000501454	+	0.000501454i
$768$	−5284.77	+	35218.1i	−0.248304	+	1.65472i
$769$		−	10040.5i		−	0.470831i	−0.971895	−	0.235415i	$-0.924355\pi$
$769$		−	10040.5i		−	0.470831i	0.971895	−	0.235415i	$-0.0756451\pi$
$770$		0			0
$771$		−	2195.47i		−	0.102552i
$772$	14775.1	+	24001.0i	0.688816	+	1.11893i
$773$	18388.2	−	18388.2i	0.855599	−	0.855599i	−0.135217	−	0.990816i	$-0.543173\pi$
$773$	18388.2	−	18388.2i	0.855599	−	0.855599i	0.990816	+	0.135217i	$0.0431732\pi$
$774$	45407.5	+	5327.52i	2.10870	+	0.247408i
$775$		0			0
$776$	−32002.1	−	11695.4i	−1.48042	−	0.541033i
$777$	18799.9	+	18799.9i	0.868008	+	0.868008i
$778$	−24040.5	+	18991.7i	−1.10783	+	0.875172i
$779$	2323.45			0.106863
$780$		0			0
$781$	29646.7			1.35831
$782$	−2828.68	+	2234.62i	−0.129352	+	0.102186i
$783$	−16873.8	−	16873.8i	−0.770142	−	0.770142i
$784$	−5717.05	+	11334.0i	−0.260434	+	0.516310i
$785$		0			0
$786$	32423.6	+	3804.16i	1.47139	+	0.172634i
$787$	−12222.0	+	12222.0i	−0.553578	+	0.553578i	−0.927472	−	0.373894i	$-0.878022\pi$
$787$	−12222.0	+	12222.0i	−0.553578	+	0.553578i	0.373894	+	0.927472i	$0.378022\pi$
$788$	32948.8	−	20283.3i	1.48953	−	0.916959i
$789$			11682.6i			0.527137i
$790$		0			0
$791$		−	29970.6i		−	1.34719i
$792$	−44493.2	+	20676.4i	−1.99621	+	0.927657i
$793$	282.456	−	282.456i	0.0126485	−	0.0126485i
$794$	−3557.49	+	30321.1i	−0.159006	+	1.35524i
$795$		0			0
$796$	−7206.75	+	30289.5i	−0.320900	+	1.34872i
$797$	−3432.79	−	3432.79i	−0.152567	−	0.152567i	0.626697	−	0.779263i	$-0.284407\pi$
$797$	−3432.79	−	3432.79i	−0.152567	−	0.152567i	−0.779263	+	0.626697i	$0.784407\pi$
$798$	8406.90	+	10641.8i	0.372934	+	0.472076i
$799$	−29193.7			−1.29262
$800$		0			0
$801$	18784.9			0.828630
$802$	13693.2	+	17333.4i	0.602896	+	0.763173i
$803$	31211.7	+	31211.7i	1.37165	+	1.37165i
$804$	−4541.72	+	19088.5i	−0.199222	+	0.837314i
$805$		0			0
$806$	100.484	−	856.446i	0.00439132	−	0.0374281i
$807$	35034.9	−	35034.9i	1.52824	−	1.52824i
$808$	25923.8	−	12047.0i	1.12871	−	0.524522i
$809$			21193.7i			0.921053i	0.887646	+	0.460526i	$0.152339\pi$
$809$			21193.7i			0.921053i	−0.887646	+	0.460526i	$0.847661\pi$
$810$		0			0
$811$		−	8690.30i		−	0.376273i	−0.982143	−	0.188137i	$-0.939755\pi$
$811$		−	8690.30i		−	0.376273i	0.982143	−	0.188137i	$-0.0602448\pi$
$812$	−20147.3	+	12402.7i	−0.870730	+	0.536023i
$813$	9764.44	−	9764.44i	0.421222	−	0.421222i
$814$	16474.3	+	1932.88i	0.709365	+	0.0832277i
$815$		0			0
$816$	−20658.2	+	40954.8i	−0.886252	+	1.75699i
$817$	−5575.11	−	5575.11i	−0.238738	−	0.238738i
$818$	−25659.4	+	20270.6i	−1.09677	+	0.866435i
$819$	−1358.26			−0.0579505
$820$		0			0
$821$	−42739.3			−1.81682			−0.908411	−	0.418077i	$-0.862704\pi$
$821$	−42739.3			−1.81682			−0.908411	+	0.418077i	$0.862704\pi$
$822$	27556.4	−	21769.2i	1.16927	−	0.923709i
$823$	14335.6	+	14335.6i	0.607176	+	0.607176i	0.942207	−	0.335031i	$-0.108747\pi$
$823$	14335.6	+	14335.6i	0.607176	+	0.607176i	−0.335031	+	0.942207i	$0.608747\pi$
$824$	−6882.38	−	2515.22i	−0.290970	−	0.106337i
$825$		0			0
$826$	819.571	+	96.1579i	0.0345237	+	0.00405056i
$827$	−2890.06	+	2890.06i	−0.121520	+	0.121520i	−0.765252	−	0.643731i	$-0.777385\pi$
$827$	−2890.06	+	2890.06i	−0.121520	+	0.121520i	0.643731	+	0.765252i	$0.277385\pi$
$828$	3150.83	+	5118.29i	0.132245	+	0.214822i
$829$		−	22098.9i		−	0.925847i	−0.886398	−	0.462924i	$-0.846800\pi$
$829$		−	22098.9i		−	0.925847i	0.886398	−	0.462924i	$-0.153200\pi$
$830$		0			0
$831$			27796.3i			1.16034i
$832$	51.9986	+	612.886i	0.00216674	+	0.0255385i
$833$	−11561.7	+	11561.7i	−0.480898	+	0.480898i
$834$	3676.03	−	31331.5i	0.152627	−	1.30086i
$835$		0			0
$836$	8231.28	+	1958.46i	0.340532	+	0.0810226i
$837$	−33690.2	−	33690.2i	−1.39128	−	1.39128i
$838$	−391.441	−	495.504i	−0.0161362	−	0.0204259i
$839$	47240.3			1.94388			0.971940	−	0.235229i	$-0.0755841\pi$
$839$	47240.3			1.94388			0.971940	+	0.235229i	$0.0755841\pi$
$840$		0			0
$841$	8233.07			0.337573
$842$	−16358.8	−	20707.7i	−0.669552	−	0.847548i
$843$	1552.69	+	1552.69i	0.0634371	+	0.0634371i
$844$	−40315.3	−	9592.19i	−1.64421	−	0.391205i
$845$		0			0
$846$	−5671.97	+	48343.2i	−0.230504	+	1.96463i
$847$	−10859.1	+	10859.1i	−0.440525	+	0.440525i
$848$	−12819.7	+	4223.07i	−0.519138	+	0.171015i
$849$			53692.2i			2.17045i
$850$		0			0
$851$		−	2032.00i		−	0.0818522i
$852$	−24226.5	−	39354.2i	−0.974162	−	1.58246i
$853$	9572.36	−	9572.36i	0.384234	−	0.384234i	−0.488391	−	0.872625i	$-0.662416\pi$
$853$	9572.36	−	9572.36i	0.384234	−	0.384234i	0.872625	+	0.488391i	$0.162416\pi$
$854$	−21732.6	−	2549.83i	−0.870814	−	0.102170i
$855$		0			0
$856$	4536.71	−	12413.8i	0.181147	−	0.495670i
$857$	10468.9	+	10468.9i	0.417284	+	0.417284i	0.884266	−	0.466983i	$-0.154659\pi$
$857$	10468.9	+	10468.9i	0.417284	+	0.417284i	−0.466983	+	0.884266i	$0.654659\pi$
$858$	−1034.41	+	817.166i	−0.0411585	+	0.0325147i
$859$	2068.01			0.0821416			0.0410708	−	0.999156i	$-0.486923\pi$
$859$	2068.01			0.0821416			0.0410708	+	0.999156i	$0.486923\pi$
$860$		0			0
$861$	19829.8			0.784898
$862$	−9585.95	+	7572.77i	−0.378769	+	0.299222i
$863$	7493.32	+	7493.32i	0.295568	+	0.295568i	0.839275	−	0.543707i	$-0.182980\pi$
$863$	7493.32	+	7493.32i	0.295568	+	0.295568i	−0.543707	+	0.839275i	$0.682980\pi$
$864$	28353.1	+	18737.2i	1.11643	+	0.737792i
$865$		0			0
$866$	15338.3	+	1799.60i	0.601869	+	0.0706155i
$867$	−11572.7	+	11572.7i	−0.453323	+	0.453323i
$868$	−40226.1	+	24763.2i	−1.57300	+	0.968340i
$869$			31390.5i			1.22537i
$870$		0			0
$871$			338.895i			0.0131837i
$872$	−13579.6	−	29221.7i	−0.527367	−	1.13483i
$873$	−51740.2	+	51740.2i	−2.00589	+	2.00589i
$874$	120.782	−	1029.45i	0.00467452	−	0.0398418i
$875$		0			0
$876$	15926.3	−	66937.2i	0.614270	−	2.58173i
$877$	15683.5	+	15683.5i	0.603872	+	0.603872i	0.941338	−	0.337466i	$-0.109570\pi$
$877$	15683.5	+	15683.5i	0.603872	+	0.603872i	−0.337466	+	0.941338i	$0.609570\pi$
$878$	−4892.90	−	6193.65i	−0.188072	−	0.238070i
$879$	−18250.8			−0.700324
$880$		0			0
$881$	5393.01			0.206237			0.103119	−	0.994669i	$-0.467118\pi$
$881$	5393.01			0.206237			0.103119	+	0.994669i	$0.467118\pi$
$882$	16899.2	+	21391.8i	0.645155	+	0.816666i
$883$	−629.665	−	629.665i	−0.0239976	−	0.0239976i	0.695006	−	0.719004i	$-0.255402\pi$
$883$	−629.665	−	629.665i	−0.0239976	−	0.0239976i	−0.719004	+	0.695006i	$0.755402\pi$
$884$	−183.381	+	770.738i	−0.00697713	+	0.0293244i
$885$		0			0
$886$	5966.81	−	50856.2i	0.226251	−	1.92838i
$887$	−748.301	+	748.301i	−0.0283264	+	0.0283264i	−0.721128	−	0.692802i	$-0.756376\pi$
$887$	−748.301	+	748.301i	−0.0283264	+	0.0283264i	0.692802	+	0.721128i	$0.256376\pi$
$888$	−10896.6	−	23448.1i	−0.411785	−	0.886112i
$889$		−	47377.9i		−	1.78741i
$890$		0			0
$891$			14291.9i			0.537371i
$892$	13986.4	−	8610.04i	0.524999	−	0.323190i
$893$	5935.57	−	5935.57i	0.222426	−	0.222426i
$894$	2310.00	+	271.026i	0.0864184	+	0.0101392i
$895$		0			0
$896$	24578.9	−	23047.0i	0.916433	−	0.859317i
$897$	114.190	+	114.190i	0.00425050	+	0.00425050i
$898$	4983.54	−	3936.93i	0.185193	−	0.146300i
$899$	−32256.9			−1.19669
$900$		0			0
$901$	−17385.0			−0.642818
$902$	9707.77	−	7669.00i	0.358352	−	0.283093i
$903$	−47581.6	−	47581.6i	−1.75351	−	1.75351i
$904$	−10004.8	+	27376.0i	−0.368090	+	1.00720i
$905$		0			0
$906$	66530.6	+	7805.84i	2.43966	+	0.286238i
$907$	−28781.0	+	28781.0i	−1.05365	+	1.05365i	−0.0551706	+	0.998477i	$0.517570\pi$
$907$	−28781.0	+	28781.0i	−1.05365	+	1.05365i	−0.998477	+	0.0551706i	$0.982430\pi$
$908$	8411.36	+	13663.6i	0.307424	+	0.499388i
$909$		−	61390.3i		−	2.24003i
$910$		0			0
$911$		−	15888.2i		−	0.577828i	−0.957355	−	0.288914i	$-0.906706\pi$
$911$		−	15888.2i		−	0.577828i	0.957355	−	0.288914i	$-0.0932941\pi$
$912$	−4126.64	−	12526.9i	−0.149832	−	0.454834i
$913$	−41967.5	+	41967.5i	−1.52127	+	1.52127i
$914$	−727.229	+	6198.30i	−0.0263179	+	0.224313i
$915$		0			0
$916$	−49456.0	−	11767.0i	−1.78392	−	0.424447i
$917$	−21840.7	−	21840.7i	−0.786525	−	0.786525i
$918$	27135.1	+	34348.8i	0.975589	+	1.23494i
$919$	47850.0			1.71755			0.858773	−	0.512356i	$-0.171227\pi$
$919$	47850.0			1.71755			0.858773	+	0.512356i	$0.171227\pi$
$920$		0			0
$921$	13896.7			0.497189
$922$	4616.64	+	5843.95i	0.164903	+	0.208742i
$923$	−564.402	−	564.402i	−0.0201273	−	0.0201273i
$924$	70251.1	+	16714.8i	2.50118	+	0.595104i
$925$		0			0
$926$	3556.41	−	30311.9i	0.126210	−	1.07571i
$927$	−11127.3	+	11127.3i	−0.394247	+	0.394247i
$928$	22543.4	−	4603.41i	0.797440	−	0.162839i
$929$			19071.0i			0.673517i	0.941591	+	0.336759i	$0.109331\pi$
$929$			19071.0i			0.673517i	−0.941591	+	0.336759i	$0.890669\pi$
$930$		0			0
$931$		−	4701.36i		−	0.165500i
$932$	−4344.59	−	7057.48i	−0.152695	−	0.248042i
$933$	−12872.7	+	12872.7i	−0.451696	+	0.451696i
$934$	−20055.6	−	2353.07i	−0.702612	−	0.0824354i
$935$		0			0
$936$	1240.67	+	453.414i	0.0433255	+	0.0158337i
$937$	−24304.0	−	24304.0i	−0.847362	−	0.847362i	0.142441	−	0.989803i	$-0.454505\pi$
$937$	−24304.0	−	24304.0i	−0.847362	−	0.847362i	−0.989803	+	0.142441i	$0.954505\pi$
$938$	14567.3	−	11507.9i	0.507077	−	0.400584i
$939$	29764.2			1.03442
$940$		0			0
$941$	−25946.3			−0.898856			−0.449428	−	0.893316i	$-0.648372\pi$
$941$	−25946.3			−0.898856			−0.449428	+	0.893316i	$0.648372\pi$
$942$	−32795.5	+	25908.0i	−1.13432	+	0.896101i
$943$	−1071.66	−	1071.66i	−0.0370075	−	0.0370075i
$944$	−716.520	−	361.423i	−0.0247042	−	0.0124611i
$945$		0			0
$946$	−41695.6	−	4892.02i	−1.43302	−	0.168133i
$947$	−29498.0	+	29498.0i	−1.01220	+	1.01220i	−0.0122772	+	0.999925i	$0.503908\pi$
$947$	−29498.0	+	29498.0i	−1.01220	+	1.01220i	−0.999925	+	0.0122772i	$0.996092\pi$
$948$	41669.0	−	25651.5i	1.42758	−	0.878821i
$949$		−	1188.39i		−	0.0406500i
$950$		0			0
$951$			52628.5i			1.79453i
$952$	39357.0	−	18289.6i	1.33988	−	0.622656i
$953$	22625.2	−	22625.2i	0.769048	−	0.769048i	−0.208891	−	0.977939i	$-0.566985\pi$
$953$	22625.2	−	22625.2i	0.769048	−	0.769048i	0.977939	+	0.208891i	$0.0669853\pi$
$954$	−3377.69	+	28788.6i	−0.114630	+	0.977009i
$955$		0			0
$956$	−12993.9	+	54612.4i	−0.439594	+	1.84758i
$957$	34868.5	+	34868.5i	1.17778	+	1.17778i
$958$	4354.86	+	5512.57i	0.146867	+	0.185911i
$959$	−33226.0			−1.11879
$960$		0			0
$961$	−34613.0			−1.16186
$962$	−276.833	−	350.428i	−0.00927803	−	0.0117445i
$963$	−20070.2	−	20070.2i	−0.671604	−	0.671604i
$964$	5108.35	−	21470.0i	0.170673	−	0.717326i
$965$		0			0
$966$	1030.84	−	8786.00i	0.0343339	−	0.292634i
$967$	19943.6	−	19943.6i	0.663230	−	0.663230i	−0.292910	−	0.956140i	$-0.594624\pi$
$967$	19943.6	−	19943.6i	0.663230	−	0.663230i	0.956140	+	0.292910i	$0.0946235\pi$
$968$	13544.0	−	6294.04i	0.449713	−	0.208986i
$969$		−	16988.1i		−	0.563194i
$970$		0			0
$971$			7147.31i			0.236218i	0.993001	+	0.118109i	$0.0376833\pi$
$971$			7147.31i			0.236218i	−0.993001	+	0.118109i	$0.962317\pi$
$972$	−15561.7	+	9579.82i	−0.513522	+	0.316124i
$973$	−21105.1	+	21105.1i	−0.695372	+	0.695372i
$974$	−15486.2	−	1816.95i	−0.509455	−	0.0597729i
$975$		0			0
$976$	19000.0	+	9583.87i	0.623131	+	0.314316i
$977$	−4019.53	−	4019.53i	−0.131623	−	0.131623i	0.638226	−	0.769849i	$-0.279669\pi$
$977$	−4019.53	−	4019.53i	−0.131623	−	0.131623i	−0.769849	+	0.638226i	$0.779669\pi$
$978$	9169.57	−	7243.84i	0.299806	−	0.236843i
$979$	−17249.3			−0.563117
$980$		0			0
$981$	−69200.1			−2.25218
$982$	19976.1	−	15780.8i	0.649146	−	0.512816i
$983$	26810.4	+	26810.4i	0.869907	+	0.869907i	0.992462	−	0.122555i	$-0.0391086\pi$
$983$	26810.4	+	26810.4i	0.869907	+	0.869907i	−0.122555	+	0.992462i	$0.539109\pi$
$984$	−18113.1	−	6619.58i	−0.586813	−	0.214456i
$985$		0			0
$986$	29434.0	+	3453.41i	0.950679	+	0.111540i
$987$	50658.0	−	50658.0i	1.63370	−	1.63370i
$988$	−119.419	−	193.988i	−0.00384538	−	0.00624655i
$989$			5142.91i			0.165354i
$990$		0			0
$991$			43289.7i			1.38763i	0.720153	+	0.693815i	$0.244072\pi$
$991$			43289.7i			1.38763i	−0.720153	+	0.693815i	$0.755928\pi$
$992$	45010.1	−	9191.16i	1.44060	−	0.294173i
$993$	14812.0	−	14812.0i	0.473357	−	0.473357i
$994$	−5095.05	+	43426.1i	−0.162581	+	1.38571i
$995$		0			0
$996$	90004.1	+	21414.6i	2.86334	+	0.681274i
$997$	31938.0	+	31938.0i	1.01453	+	1.01453i	0.999893	+	0.0146370i	$0.00465928\pi$
$997$	31938.0	+	31938.0i	1.01453	+	1.01453i	0.0146370	+	0.999893i	$0.495341\pi$
$998$	−22893.7	−	28979.9i	−0.726141	−	0.919181i
$999$	−24674.7			−0.781456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.4.e.f.7.9	yes	24
4.3	odd	2	inner	100.4.e.f.7.10	yes	24
5.2	odd	4	inner	100.4.e.f.43.3	yes	24
5.3	odd	4	inner	100.4.e.f.43.10	yes	24
5.4	even	2	inner	100.4.e.f.7.4	yes	24
20.3	even	4	inner	100.4.e.f.43.9	yes	24
20.7	even	4	inner	100.4.e.f.43.4	yes	24
20.19	odd	2	inner	100.4.e.f.7.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.e.f.7.3	✓	24	20.19	odd	2	inner
100.4.e.f.7.4	yes	24	5.4	even	2	inner
100.4.e.f.7.9	yes	24	1.1	even	1	trivial
100.4.e.f.7.10	yes	24	4.3	odd	2	inner
100.4.e.f.43.3	yes	24	5.2	odd	4	inner
100.4.e.f.43.4	yes	24	20.7	even	4	inner
100.4.e.f.43.9	yes	24	20.3	even	4	inner
100.4.e.f.43.10	yes	24	5.3	odd	4	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	100.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.75332 + 2.21943i) q^{2} +(6.14790 + 6.14790i) q^{3} +(-1.85174 + 7.78274i) q^{4} +(-2.86560 + 24.4241i) q^{6} +(16.4522 - 16.4522i) q^{7} +(-20.5199 + 9.53582i) q^{8} +48.5934i q^{9} +O(q^{10})\)	\(q+(1.75332 + 2.21943i) q^{2} +(6.14790 + 6.14790i) q^{3} +(-1.85174 + 7.78274i) q^{4} +(-2.86560 + 24.4241i) q^{6} +(16.4522 - 16.4522i) q^{7} +(-20.5199 + 9.53582i) q^{8} +48.5934i q^{9} -44.6211i q^{11} +(-59.2319 + 36.4632i) q^{12} +(-0.849478 + 0.849478i) q^{13} +(65.3604 + 7.66854i) q^{14} +(-57.1421 - 28.8233i) q^{16} +(-58.2897 - 58.2897i) q^{17} +(-107.850 + 85.1997i) q^{18} +23.7025 q^{19} +202.293 q^{21} +(99.0334 - 78.2350i) q^{22} +(-10.9325 - 10.9325i) q^{23} +(-184.780 - 67.5294i) q^{24} +(-3.37476 - 0.395951i) q^{26} +(-132.754 + 132.754i) q^{27} +(97.5778 + 158.508i) q^{28} +127.106i q^{29} +253.779i q^{31} +(-36.2171 - 177.359i) q^{32} +(274.326 - 274.326i) q^{33} +(27.1695 - 231.571i) q^{34} +(-378.190 - 89.9824i) q^{36} +(92.9341 + 92.9341i) q^{37} +(41.5581 + 52.6061i) q^{38} -10.4450 q^{39} +98.0252 q^{41} +(354.684 + 448.975i) q^{42} +(-235.212 - 235.212i) q^{43} +(347.274 + 82.6268i) q^{44} +(5.09576 - 43.4321i) q^{46} +(250.419 - 250.419i) q^{47} +(-174.101 - 528.507i) q^{48} -198.348i q^{49} -716.719i q^{51} +(-5.03825 - 8.18428i) q^{52} +(149.126 - 149.126i) q^{53} +(-527.398 - 61.8781i) q^{54} +(-180.713 + 494.483i) q^{56} +(145.721 + 145.721i) q^{57} +(-282.103 + 222.857i) q^{58} +12.5393 q^{59} -332.505 q^{61} +(-563.246 + 444.956i) q^{62} +(799.467 + 799.467i) q^{63} +(330.136 - 391.349i) q^{64} +(1089.83 + 127.866i) q^{66} +(199.472 - 199.472i) q^{67} +(561.592 - 345.716i) q^{68} -134.424i q^{69} +664.410i q^{71} +(-463.378 - 997.134i) q^{72} +(-699.484 + 699.484i) q^{73} +(-43.3176 + 369.204i) q^{74} +(-43.8910 + 184.471i) q^{76} +(-734.114 - 734.114i) q^{77} +(-18.3135 - 23.1820i) q^{78} -703.490 q^{79} -320.295 q^{81} +(171.869 + 217.560i) q^{82} +(-940.531 - 940.531i) q^{83} +(-374.594 + 1574.39i) q^{84} +(109.635 - 934.437i) q^{86} +(-781.435 + 781.435i) q^{87} +(425.499 + 915.623i) q^{88} -386.574i q^{89} +27.9515i q^{91} +(105.329 - 64.8407i) q^{92} +(-1560.21 + 1560.21i) q^{93} +(994.852 + 116.723i) q^{94} +(867.728 - 1313.05i) q^{96} +(1064.76 + 1064.76i) q^{97} +(440.220 - 347.768i) q^{98} +2168.29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 36 q^{6}+O(q^{10}) \) 24 * q + 36 * q^6	\( 24 q + 36 q^{6} - 676 q^{16} + 512 q^{21} + 2072 q^{26} - 4600 q^{36} - 392 q^{41} + 5016 q^{46} - 8224 q^{56} + 1088 q^{61} + 11140 q^{66} - 6700 q^{76} - 2424 q^{81} + 5216 q^{86} + 796 q^{96}+O(q^{100}) \) 24 * q + 36 * q^6 - 676 * q^16 + 512 * q^21 + 2072 * q^26 - 4600 * q^36 - 392 * q^41 + 5016 * q^46 - 8224 * q^56 + 1088 * q^61 + 11140 * q^66 - 6700 * q^76 - 2424 * q^81 + 5216 * q^86 + 796 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more