LMFDB - Embedded newform 396.3.s.a.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,3,Mod(91,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("396.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	396.s (of order $10$, degree $4$, 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:	$10.7902184687$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			235.1
Character	$\chi$	$=$	396.235
Dual form			396.3.s.a.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98526 - 0.242393i) q^{2} +(3.88249 + 0.962424i) q^{4} +(-0.605291 + 0.439770i) q^{5} +(-3.68852 + 1.19847i) q^{7} +(-7.47446 - 2.85175i) q^{8} +O(q^{10})$	\(q+(-1.98526 - 0.242393i) q^{2} +(3.88249 + 0.962424i) q^{4} +(-0.605291 + 0.439770i) q^{5} +(-3.68852 + 1.19847i) q^{7} +(-7.47446 - 2.85175i) q^{8} +(1.30826 - 0.726338i) q^{10} +(10.4619 - 3.39827i) q^{11} +(-2.78472 - 2.02322i) q^{13} +(7.61316 - 1.48521i) q^{14} +(14.1475 + 7.47320i) q^{16} +(-6.28791 + 4.56843i) q^{17} +(18.2467 + 5.92872i) q^{19} +(-2.77328 + 1.12486i) q^{20} +(-21.5933 + 4.21055i) q^{22} +15.0061i q^{23} +(-7.55245 + 23.2440i) q^{25} +(5.03798 + 4.69161i) q^{26} +(-15.4741 + 1.10314i) q^{28} +(-4.31911 - 13.2929i) q^{29} +(32.6981 - 45.0051i) q^{31} +(-26.2749 - 18.2655i) q^{32} +(13.5905 - 7.54537i) q^{34} +(1.70557 - 2.34752i) q^{35} +(11.3339 + 34.8823i) q^{37} +(-34.7874 - 16.1929i) q^{38} +(5.77833 - 1.56090i) q^{40} +(-17.0545 + 52.4884i) q^{41} +43.0444i q^{43} +(43.8889 - 3.12496i) q^{44} +(3.63738 - 29.7910i) q^{46} +(46.1847 + 15.0063i) q^{47} +(-27.4730 + 19.9603i) q^{49} +(20.6277 - 44.3147i) q^{50} +(-8.86447 - 10.5352i) q^{52} +(74.7736 + 54.3262i) q^{53} +(-4.83805 + 6.65778i) q^{55} +(30.9874 + 1.56078i) q^{56} +(5.35245 + 27.4367i) q^{58} +(76.2995 - 24.7912i) q^{59} +(62.8898 - 45.6921i) q^{61} +(-75.8230 + 81.4209i) q^{62} +(47.7351 + 42.6305i) q^{64} +2.57532 q^{65} +57.7376i q^{67} +(-28.8095 + 11.6853i) q^{68} +(-3.95503 + 4.24702i) q^{70} +(57.7740 + 79.5191i) q^{71} +(23.1219 + 71.1618i) q^{73} +(-14.0456 - 71.9975i) q^{74} +(65.1368 + 40.5793i) q^{76} +(-34.5162 + 25.0729i) q^{77} +(44.4641 - 61.1996i) q^{79} +(-11.8498 + 1.69817i) q^{80} +(46.5804 - 100.069i) q^{82} +(-38.8192 - 53.4301i) q^{83} +(1.79696 - 5.53046i) q^{85} +(10.4337 - 85.4543i) q^{86} +(-87.8882 - 4.43450i) q^{88} -46.7420 q^{89} +(12.6963 + 4.12527i) q^{91} +(-14.4423 + 58.2612i) q^{92} +(-88.0511 - 40.9862i) q^{94} +(-13.6519 + 4.43576i) q^{95} +(-86.8069 - 63.0689i) q^{97} +(59.3792 - 32.9671i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - 9 q^{4} + 6 q^{5} - 7 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 - 9 * q^4 + 6 * q^5 - 7 * q^8	$ 40 q + 5 q^{2} - 9 q^{4} + 6 q^{5} - 7 q^{8} - 8 q^{10} - 6 q^{13} + 36 q^{14} - 65 q^{16} + 30 q^{17} - 34 q^{20} + 25 q^{22} - 156 q^{26} + 130 q^{28} + 38 q^{29} - 20 q^{32} + 258 q^{34} - 150 q^{37} - 80 q^{38} + 112 q^{40} + 150 q^{41} - 4 q^{44} + 40 q^{46} + 132 q^{49} + 177 q^{50} - 314 q^{52} - 290 q^{53} + 856 q^{56} - 476 q^{58} + 42 q^{61} + 364 q^{62} + 303 q^{64} - 164 q^{65} - 14 q^{68} + 576 q^{70} + 186 q^{73} - 588 q^{74} + 366 q^{76} - 190 q^{77} - 1100 q^{80} + 365 q^{82} + 286 q^{85} + 501 q^{86} + 47 q^{88} + 88 q^{89} + 702 q^{92} - 678 q^{94} - 130 q^{97} + 652 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 - 9 * q^4 + 6 * q^5 - 7 * q^8 - 8 * q^10 - 6 * q^13 + 36 * q^14 - 65 * q^16 + 30 * q^17 - 34 * q^20 + 25 * q^22 - 156 * q^26 + 130 * q^28 + 38 * q^29 - 20 * q^32 + 258 * q^34 - 150 * q^37 - 80 * q^38 + 112 * q^40 + 150 * q^41 - 4 * q^44 + 40 * q^46 + 132 * q^49 + 177 * q^50 - 314 * q^52 - 290 * q^53 + 856 * q^56 - 476 * q^58 + 42 * q^61 + 364 * q^62 + 303 * q^64 - 164 * q^65 - 14 * q^68 + 576 * q^70 + 186 * q^73 - 588 * q^74 + 366 * q^76 - 190 * q^77 - 1100 * q^80 + 365 * q^82 + 286 * q^85 + 501 * q^86 + 47 * q^88 + 88 * q^89 + 702 * q^92 - 678 * q^94 - 130 * q^97 + 652 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$1$

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 $

$2$	−1.98526	−	0.242393i	−0.992629	−	0.121196i
$2$	−1.98526	−	0.242393i	−0.992629	−	0.121196i
$3$		0			0
$3$		0			0
$4$	3.88249	+	0.962424i	0.970623	+	0.240606i
$5$	−0.605291	+	0.439770i	−0.121058	+	0.0879539i	−0.646667	−	0.762773i	$-0.723838\pi$
$5$	−0.605291	+	0.439770i	−0.121058	+	0.0879539i	0.525609	+	0.850726i	$0.323838\pi$
$6$		0			0
$7$	−3.68852	+	1.19847i	−0.526931	+	0.171210i	−0.560389	−	0.828230i	$-0.689348\pi$
$7$	−3.68852	+	1.19847i	−0.526931	+	0.171210i	0.0334574	+	0.999440i	$0.489348\pi$
$8$	−7.47446	−	2.85175i	−0.934307	−	0.356468i
$9$		0			0
$10$	1.30826	−	0.726338i	0.130826	−	0.0726338i
$11$	10.4619	−	3.39827i	0.951084	−	0.308934i
$11$	10.4619	−	3.39827i	0.951084	−	0.308934i
$12$		0			0
$13$	−2.78472	−	2.02322i	−0.214210	−	0.155632i	0.475507	−	0.879712i	$-0.342265\pi$
$13$	−2.78472	−	2.02322i	−0.214210	−	0.155632i	−0.689716	+	0.724080i	$0.742265\pi$
$14$	7.61316	−	1.48521i	0.543797	−	0.106086i
$15$		0			0
$16$	14.1475	+	7.47320i	0.884218	+	0.467075i
$17$	−6.28791	+	4.56843i	−0.369877	+	0.268731i	−0.757160	−	0.653230i	$-0.773414\pi$
$17$	−6.28791	+	4.56843i	−0.369877	+	0.268731i	0.387283	+	0.921961i	$0.373414\pi$
$18$		0			0
$19$	18.2467	+	5.92872i	0.960354	+	0.312038i	0.746916	−	0.664919i	$-0.231534\pi$
$19$	18.2467	+	5.92872i	0.960354	+	0.312038i	0.213438	+	0.976957i	$0.431534\pi$
$20$	−2.77328	+	1.12486i	−0.138664	+	0.0562428i
$21$		0			0
$22$	−21.5933	+	4.21055i	−0.981514	+	0.191389i
$23$			15.0061i			0.652441i	0.945294	+	0.326220i	$0.105775\pi$
$23$			15.0061i			0.652441i	−0.945294	+	0.326220i	$0.894225\pi$
$24$		0			0
$25$	−7.55245	+	23.2440i	−0.302098	+	0.929761i
$26$	5.03798	+	4.69161i	0.193768	+	0.180447i
$27$		0			0
$28$	−15.4741	+	1.10314i	−0.552646	+	0.0393979i
$29$	−4.31911	−	13.2929i	−0.148935	−	0.458374i	0.848561	−	0.529097i	$-0.177469\pi$
$29$	−4.31911	−	13.2929i	−0.148935	−	0.458374i	−0.997496	+	0.0707231i	$0.977469\pi$
$30$		0			0
$31$	32.6981	−	45.0051i	1.05478	−	1.45178i	0.170185	−	0.985412i	$-0.445564\pi$
$31$	32.6981	−	45.0051i	1.05478	−	1.45178i	0.884593	−	0.466364i	$-0.154436\pi$
$32$	−26.2749	−	18.2655i	−0.821092	−	0.570796i
$33$		0			0
$34$	13.5905	−	7.54537i	0.399720	−	0.221923i
$35$	1.70557	−	2.34752i	0.0487307	−	0.0670721i
$36$		0			0
$37$	11.3339	+	34.8823i	0.306323	+	0.942764i	0.979180	+	0.202992i	$0.0650666\pi$
$37$	11.3339	+	34.8823i	0.306323	+	0.942764i	−0.672858	+	0.739772i	$0.734933\pi$
$38$	−34.7874	−	16.1929i	−0.915457	−	0.426129i
$39$		0			0
$40$	5.77833	−	1.56090i	0.144458	−	0.0390226i
$41$	−17.0545	+	52.4884i	−0.415964	+	1.28020i	0.495422	+	0.868652i	$0.335013\pi$
$41$	−17.0545	+	52.4884i	−0.415964	+	1.28020i	−0.911386	+	0.411553i	$0.864987\pi$
$42$		0			0
$43$			43.0444i			1.00103i	0.865727	+	0.500517i	$0.166857\pi$
$43$			43.0444i			1.00103i	−0.865727	+	0.500517i	$0.833143\pi$
$44$	43.8889	−	3.12496i	0.997475	−	0.0710218i
$45$		0			0
$46$	3.63738	−	29.7910i	0.0790734	−	0.647631i
$47$	46.1847	+	15.0063i	0.982653	+	0.319283i	0.755913	−	0.654672i	$-0.227193\pi$
$47$	46.1847	+	15.0063i	0.982653	+	0.319283i	0.226740	+	0.973955i	$0.427193\pi$
$48$		0			0
$49$	−27.4730	+	19.9603i	−0.560674	+	0.407353i
$50$	20.6277	−	44.3147i	0.412555	−	0.886295i
$51$		0			0
$52$	−8.86447	−	10.5352i	−0.170471	−	0.202600i
$53$	74.7736	+	54.3262i	1.41082	+	1.02502i	0.993202	+	0.116402i	$0.0371361\pi$
$53$	74.7736	+	54.3262i	1.41082	+	1.02502i	0.417621	+	0.908621i	$0.362864\pi$
$54$		0			0
$55$	−4.83805	+	6.65778i	−0.0879645	+	0.121050i
$56$	30.9874	+	1.56078i	0.553347	+	0.0278712i
$57$		0			0
$58$	5.35245	+	27.4367i	0.0922837	+	0.473046i
$59$	76.2995	−	24.7912i	1.29321	−	0.420190i	0.419997	−	0.907525i	$-0.362031\pi$
$59$	76.2995	−	24.7912i	1.29321	−	0.420190i	0.873215	+	0.487335i	$0.162031\pi$
$60$		0			0
$61$	62.8898	−	45.6921i	1.03098	−	0.749052i	0.0624763	−	0.998046i	$-0.480100\pi$
$61$	62.8898	−	45.6921i	1.03098	−	0.749052i	0.968505	+	0.248995i	$0.0801002\pi$
$62$	−75.8230	+	81.4209i	−1.22295	+	1.31324i
$63$		0			0
$64$	47.7351	+	42.6305i	0.745861	+	0.666102i
$65$	2.57532			0.0396203
$66$		0			0
$67$			57.7376i			0.861755i	0.902411	+	0.430877i	$0.141796\pi$
$67$			57.7376i			0.861755i	−0.902411	+	0.430877i	$0.858204\pi$
$68$	−28.8095	+	11.6853i	−0.423669	+	0.171842i
$69$		0			0
$70$	−3.95503	+	4.24702i	−0.0565004	+	0.0606717i
$71$	57.7740	+	79.5191i	0.813719	+	1.11999i	0.990739	+	0.135780i	$0.0433541\pi$
$71$	57.7740	+	79.5191i	0.813719	+	1.11999i	−0.177020	+	0.984207i	$0.556646\pi$
$72$		0			0
$73$	23.1219	+	71.1618i	0.316738	+	0.974820i	0.975033	+	0.222060i	$0.0712780\pi$
$73$	23.1219	+	71.1618i	0.316738	+	0.974820i	−0.658295	+	0.752760i	$0.728722\pi$
$74$	−14.0456	−	71.9975i	−0.189805	−	0.972939i
$75$		0			0
$76$	65.1368	+	40.5793i	0.857064	+	0.533938i
$77$	−34.5162	+	25.0729i	−0.448263	+	0.325622i
$78$		0			0
$79$	44.4641	−	61.1996i	0.562837	−	0.774678i	−0.428847	−	0.903377i	$-0.641080\pi$
$79$	44.4641	−	61.1996i	0.562837	−	0.774678i	0.991684	+	0.128699i	$0.0410801\pi$
$80$	−11.8498	+	1.69817i	−0.148123	+	0.0212271i
$81$		0			0
$82$	46.5804	−	100.069i	0.568054	−	1.22035i
$83$	−38.8192	−	53.4301i	−0.467701	−	0.643736i	0.508382	−	0.861132i	$-0.330244\pi$
$83$	−38.8192	−	53.4301i	−0.467701	−	0.643736i	−0.976084	+	0.217396i	$0.930244\pi$
$84$		0			0
$85$	1.79696	−	5.53046i	0.0211407	−	0.0650643i
$86$	10.4337	−	85.4543i	0.121322	−	0.993654i
$87$		0			0
$88$	−87.8882	−	4.43450i	−0.998730	−	0.0503920i
$89$	−46.7420			−0.525191			−0.262596	−	0.964906i	$-0.584579\pi$
$89$	−46.7420			−0.525191			−0.262596	+	0.964906i	$0.584579\pi$
$90$		0			0
$91$	12.6963	+	4.12527i	0.139520	+	0.0453327i
$92$	−14.4423	+	58.2612i	−0.156981	+	0.633274i
$93$		0			0
$94$	−88.0511	−	40.9862i	−0.936713	−	0.436024i
$95$	−13.6519	+	4.43576i	−0.143704	+	0.0466922i
$96$		0			0
$97$	−86.8069	−	63.0689i	−0.894916	−	0.650195i	0.0422389	−	0.999108i	$-0.486551\pi$
$97$	−86.8069	−	63.0689i	−0.894916	−	0.650195i	−0.937155	+	0.348913i	$0.886551\pi$
$98$	59.3792	−	32.9671i	0.605910	−	0.336399i
$99$		0			0
$100$	−51.6929	+	82.9761i	−0.516929	+	0.829761i
$101$	−58.6040	−	42.5783i	−0.580238	−	0.421568i	0.258572	−	0.965992i	$-0.416748\pi$
$101$	−58.6040	−	42.5783i	−0.580238	−	0.421568i	−0.838810	+	0.544424i	$0.816748\pi$
$102$		0			0
$103$	19.9403	−	6.47899i	0.193595	−	0.0629029i	−0.210615	−	0.977569i	$-0.567547\pi$
$103$	19.9403	−	6.47899i	0.193595	−	0.0629029i	0.404210	+	0.914666i	$0.367547\pi$
$104$	15.0446	+	23.0638i	0.144660	+	0.221767i
$105$		0			0
$106$	−135.277	−	125.976i	−1.27619	−	1.18845i
$107$	−24.9694	−	8.11306i	−0.233359	−	0.0758230i	0.190003	−	0.981783i	$-0.439150\pi$
$107$	−24.9694	−	8.11306i	−0.233359	−	0.0758230i	−0.423362	+	0.905961i	$0.639150\pi$
$108$		0			0
$109$	−79.3568			−0.728044			−0.364022	−	0.931390i	$-0.618597\pi$
$109$	−79.3568			−0.728044			−0.364022	+	0.931390i	$0.618597\pi$
$110$	11.2186	−	12.0447i	0.101987	−	0.109497i
$111$		0			0
$112$	−61.1397	−	10.6097i	−0.545890	−	0.0947293i
$113$	7.02958	−	21.6348i	0.0622087	−	0.191459i	−0.915122	−	0.403177i	$-0.867906\pi$
$113$	7.02958	−	21.6348i	0.0622087	−	0.191459i	0.977331	+	0.211718i	$0.0679059\pi$
$114$		0			0
$115$	−6.59924	−	9.08308i	−0.0573847	−	0.0789833i
$116$	−3.97555	−	55.7662i	−0.0342720	−	0.480743i
$117$		0			0
$118$	−157.483	+	30.7225i	−1.33460	+	0.260360i
$119$	17.7179	−	24.3866i	0.148890	−	0.204930i
$120$		0			0
$121$	97.9035	−	71.1049i	0.809120	−	0.587644i
$122$	−135.928	+	75.4666i	−1.11416	+	0.618579i
$123$		0			0
$124$	170.264	−	143.262i	1.37310	−	1.15534i
$125$	−11.4306	−	35.1798i	−0.0914449	−	0.281438i
$126$		0			0
$127$	52.1961	+	71.8418i	0.410993	+	0.565683i	0.963460	−	0.267851i	$-0.0863136\pi$
$127$	52.1961	+	71.8418i	0.410993	+	0.565683i	−0.552467	+	0.833535i	$0.686314\pi$
$128$	−84.4331	−	96.2032i	−0.659634	−	0.751587i
$129$		0			0
$130$	−5.11267	−	0.624239i	−0.0393282	−	0.00480184i
$131$			170.654i			1.30271i	0.758775	+	0.651353i	$0.225798\pi$
$131$			170.654i			1.30271i	−0.758775	+	0.651353i	$0.774202\pi$
$132$		0			0
$133$	−74.4088			−0.559465
$134$	13.9952	−	114.624i	0.104442	−	0.855402i
$135$		0			0
$136$	60.0267	−	16.2151i	0.441373	−	0.119228i
$137$	72.1395	−	52.4124i	0.526565	−	0.382572i	−0.292506	−	0.956264i	$-0.594489\pi$
$137$	72.1395	−	52.4124i	0.526565	−	0.382572i	0.819071	+	0.573692i	$0.194489\pi$
$138$		0			0
$139$	−170.380	+	55.3599i	−1.22576	+	0.398273i	−0.849176	−	0.528111i	$-0.822901\pi$
$139$	−170.380	+	55.3599i	−1.22576	+	0.398273i	−0.376582	+	0.926383i	$0.622901\pi$
$140$	8.88119	−	7.47275i	0.0634371	−	0.0533768i
$141$		0			0
$142$	−95.4214	−	171.870i	−0.671982	−	1.21035i
$143$	−36.0090	−	11.7035i	−0.251811	−	0.0818428i
$144$		0			0
$145$	8.46011	+	6.14663i	0.0583456	+	0.0423906i
$146$	−28.6538	−	146.879i	−0.196259	−	1.00602i
$147$		0			0
$148$	10.4324	+	146.338i	0.0704891	+	0.988771i
$149$	−95.8450	+	69.6355i	−0.643255	+	0.467352i	−0.860967	−	0.508661i	$-0.830141\pi$
$149$	−95.8450	+	69.6355i	−0.643255	+	0.467352i	0.217712	+	0.976013i	$0.430141\pi$
$150$		0			0
$151$	−138.124	−	44.8793i	−0.914731	−	0.297214i	−0.186427	−	0.982469i	$-0.559691\pi$
$151$	−138.124	−	44.8793i	−0.914731	−	0.297214i	−0.728303	+	0.685255i	$0.759691\pi$
$152$	−119.477	−	96.3490i	−0.786034	−	0.633875i
$153$		0			0
$154$	74.6011	−	41.4097i	0.484423	−	0.268894i
$155$			41.6208i			0.268521i
$156$		0			0
$157$	27.4296	−	84.4196i	0.174711	−	0.537705i	−0.824909	−	0.565265i	$-0.808774\pi$
$157$	27.4296	−	84.4196i	0.174711	−	0.537705i	0.999620	+	0.0275605i	$0.00877388\pi$
$158$	−103.107	+	110.719i	−0.652576	+	0.700754i
$159$		0			0
$160$	23.9366	−	0.498992i	0.149604	−	0.00311870i
$161$	−17.9844	−	55.3504i	−0.111705	−	0.343791i
$162$		0			0
$163$	13.3585	−	18.3864i	0.0819539	−	0.112800i	−0.766072	−	0.642755i	$-0.777791\pi$
$163$	13.3585	−	18.3864i	0.0819539	−	0.112800i	0.848026	+	0.529955i	$0.177791\pi$
$164$	−116.730	+	187.372i	−0.711769	+	1.14251i
$165$		0			0
$166$	64.1151	+	115.482i	0.386235	+	0.695674i
$167$	175.977	−	242.212i	1.05376	−	1.45037i	0.168247	−	0.985745i	$-0.446189\pi$
$167$	175.977	−	242.212i	1.05376	−	1.45037i	0.885508	−	0.464624i	$-0.153811\pi$
$168$		0			0
$169$	−48.5626	−	149.460i	−0.287353	−	0.884381i
$170$	−4.90796	+	10.5438i	−0.0288704	+	0.0620225i
$171$		0			0
$172$	−41.4270	+	167.120i	−0.240855	+	0.971626i
$173$	14.5428	−	44.7583i	0.0840627	−	0.258718i	−0.900187	−	0.435504i	$-0.856570\pi$
$173$	14.5428	−	44.7583i	0.0840627	−	0.258718i	0.984249	+	0.176786i	$0.0565700\pi$
$174$		0			0
$175$		−	94.7874i		−	0.541642i
$176$	173.406	+	30.1071i	0.985260	+	0.171063i
$177$		0			0
$178$	92.7949	+	11.3299i	0.521320	+	0.0636513i
$179$	−86.7866	−	28.1987i	−0.484842	−	0.157535i	0.0563889	−	0.998409i	$-0.482041\pi$
$179$	−86.7866	−	28.1987i	−0.484842	−	0.157535i	−0.541230	+	0.840874i	$0.682041\pi$
$180$		0			0
$181$	16.1873	−	11.7607i	0.0894324	−	0.0649764i	−0.542171	−	0.840268i	$-0.682397\pi$
$181$	16.1873	−	11.7607i	0.0894324	−	0.0649764i	0.631603	+	0.775292i	$0.282397\pi$
$182$	−24.2054	−	11.2672i	−0.132997	−	0.0619077i
$183$		0			0
$184$	42.7937	−	112.163i	0.232574	−	0.609580i
$185$	−22.2005	−	16.1296i	−0.120003	−	0.0871870i
$186$		0			0
$187$	−50.2588	+	69.1626i	−0.268764	+	0.369854i
$188$	164.869	+	102.711i	0.876964	+	0.546336i
$189$		0			0
$190$	28.1776	−	5.49701i	0.148303	−	0.0289316i
$191$	−208.998	+	67.9075i	−1.09423	+	0.355537i	−0.799879	−	0.600161i	$-0.795103\pi$
$191$	−208.998	+	67.9075i	−1.09423	+	0.355537i	−0.294350	+	0.955698i	$0.595103\pi$
$192$		0			0
$193$	−72.6595	+	52.7902i	−0.376474	+	0.273524i	−0.759890	−	0.650051i	$-0.774747\pi$
$193$	−72.6595	+	52.7902i	−0.376474	+	0.273524i	0.383416	+	0.923576i	$0.374747\pi$
$194$	157.047	+	146.249i	0.809518	+	0.753862i
$195$		0			0
$196$	−125.874	+	51.0551i	−0.642214	+	0.260485i
$197$	113.348			0.575370			0.287685	−	0.957725i	$-0.407114\pi$
$197$	113.348			0.575370			0.287685	+	0.957725i	$0.407114\pi$
$198$		0			0
$199$			128.213i			0.644289i	0.946691	+	0.322144i	$0.104404\pi$
$199$			128.213i			0.644289i	−0.946691	+	0.322144i	$0.895596\pi$
$200$	122.737	−	152.199i	0.613683	−	0.760995i
$201$		0			0
$202$	106.023	+	98.7341i	0.524868	+	0.488783i
$203$	31.8622	+	43.8546i	0.156957	+	0.216032i
$204$		0			0
$205$	−12.7599	−	39.2708i	−0.0622432	−	0.191565i
$206$	−41.1571	+	8.02909i	−0.199792	+	0.0389762i
$207$		0			0
$208$	−24.2769	−	49.4343i	−0.116716	−	0.237665i
$209$	211.043	+	0.0184845i	1.00978	+	8.84427e-5i
$210$		0			0
$211$	169.233	−	232.929i	0.802053	−	1.10393i	−0.190449	−	0.981697i	$-0.560994\pi$
$211$	169.233	−	232.929i	0.802053	−	1.10393i	0.992501	−	0.122234i	$-0.0390058\pi$
$212$	238.023	+	282.885i	1.12275	+	1.33436i
$213$		0			0
$214$	47.6042	+	22.1589i	0.222449	+	0.103546i
$215$	−18.9296	−	26.0544i	−0.0880448	−	0.121183i
$216$		0			0
$217$	−66.6702	+	205.190i	−0.307236	+	0.945575i
$218$	157.544	+	19.2355i	0.722677	+	0.0882363i
$219$		0			0
$220$	−25.1913	+	21.1925i	−0.114506	+	0.0963296i
$221$	26.7530			0.121055
$222$		0			0
$223$	146.310	+	47.5389i	0.656097	+	0.213179i	0.618101	−	0.786099i	$-0.287902\pi$
$223$	146.310	+	47.5389i	0.656097	+	0.213179i	0.0379966	+	0.999278i	$0.487902\pi$
$224$	118.806	+	35.8828i	0.530385	+	0.160191i
$225$		0			0
$226$	−19.1996	+	41.2468i	−0.0849542	+	0.182508i
$227$	−307.232	+	99.8258i	−1.35345	+	0.439761i	−0.893850	−	0.448367i	$-0.852006\pi$
$227$	−307.232	+	99.8258i	−1.35345	+	0.439761i	−0.459596	+	0.888128i	$0.652006\pi$
$228$		0			0
$229$	230.677	+	167.597i	1.00732	+	0.731864i	0.963646	−	0.267181i	$-0.0860922\pi$
$229$	230.677	+	167.597i	1.00732	+	0.731864i	0.0436787	+	0.999046i	$0.486092\pi$
$230$	10.8995	+	19.6319i	0.0473892	+	0.0853559i
$231$		0			0
$232$	−5.62483	+	111.674i	−0.0242450	+	0.481353i
$233$	−157.782	−	114.636i	−0.677178	−	0.491999i	0.195242	−	0.980755i	$-0.437451\pi$
$233$	−157.782	−	114.636i	−0.677178	−	0.491999i	−0.872420	+	0.488756i	$0.837451\pi$
$234$		0			0
$235$	−34.5545	+	11.2274i	−0.147040	+	0.0477763i
$236$	320.092	−	22.8192i	1.35632	−	0.0966916i
$237$		0			0
$238$	−41.0858	+	44.1190i	−0.172629	+	0.185374i
$239$	−200.985	−	65.3040i	−0.840941	−	0.273238i	−0.143294	−	0.989680i	$-0.545770\pi$
$239$	−200.985	−	65.3040i	−0.840941	−	0.273238i	−0.697647	+	0.716442i	$0.745770\pi$
$240$		0			0
$241$	328.286			1.36218			0.681092	−	0.732198i	$-0.261505\pi$
$241$	328.286			1.36218			0.681092	+	0.732198i	$0.261505\pi$
$242$	−211.599	+	117.430i	−0.874376	+	0.485249i
$243$		0			0
$244$	288.145	−	116.873i	1.18092	−	0.478986i
$245$	7.85123	−	24.1636i	0.0320458	−	0.0986269i
$246$		0			0
$247$	−38.8170	−	53.4270i	−0.157154	−	0.216304i
$248$	−372.744	+	243.142i	−1.50300	+	0.980411i
$249$		0			0
$250$	14.1654	+	72.6116i	0.0566615	+	0.290447i
$251$	49.3072	−	67.8655i	0.196443	−	0.270380i	−0.699420	−	0.714711i	$-0.746558\pi$
$251$	49.3072	−	67.8655i	0.196443	−	0.270380i	0.895863	+	0.444330i	$0.146558\pi$
$252$		0			0
$253$	50.9949	+	156.993i	0.201561	+	0.620526i
$254$	−86.2088	−	155.276i	−0.339405	−	0.611324i
$255$		0			0
$256$	144.302	+	211.454i	0.563681	+	0.825992i
$257$	50.0346	+	153.991i	0.194687	+	0.599185i	0.999980	+	0.00630817i	$0.00200797\pi$
$257$	50.0346	+	153.991i	0.194687	+	0.599185i	−0.805293	+	0.592877i	$0.797992\pi$
$258$		0			0
$259$	−83.6108	−	115.080i	−0.322822	−	0.444326i
$260$	9.99866	+	2.47855i	0.0384564	+	0.00953288i
$261$		0			0
$262$	41.3654	−	338.793i	0.157883	−	1.29310i
$263$		−	399.263i		−	1.51811i	−0.651027	−	0.759055i	$-0.725661\pi$
$263$		−	399.263i		−	1.51811i	0.651027	−	0.759055i	$-0.274339\pi$
$264$		0			0
$265$	−69.1508			−0.260947
$266$	147.721	+	18.0362i	0.555341	+	0.0678051i
$267$		0			0
$268$	−55.5680	+	224.166i	−0.207343	+	0.836439i
$269$	−51.6076	+	37.4951i	−0.191850	+	0.139387i	−0.679564	−	0.733617i	$-0.737831\pi$
$269$	−51.6076	+	37.4951i	−0.191850	+	0.139387i	0.487714	+	0.873003i	$0.337831\pi$
$270$		0			0
$271$	162.436	−	52.7786i	0.599394	−	0.194755i	0.00642369	−	0.999979i	$-0.497955\pi$
$271$	162.436	−	52.7786i	0.599394	−	0.194755i	0.592970	+	0.805225i	$0.297955\pi$
$272$	−123.099	+	17.6410i	−0.452570	+	0.0648566i
$273$		0			0
$274$	−155.920	+	86.5660i	−0.569050	+	0.315934i
$275$	−0.0235469	+	268.842i	−8.56253e−5	+	0.977609i
$276$		0			0
$277$	−261.885	−	190.270i	−0.945432	−	0.686897i	0.00428992	−	0.999991i	$-0.498634\pi$
$277$	−261.885	−	190.270i	−0.945432	−	0.686897i	−0.949722	+	0.313094i	$0.898634\pi$
$278$	351.667	−	68.6047i	1.26499	−	0.246780i
$279$		0			0
$280$	−19.4428	+	12.6826i	−0.0694385	+	0.0452950i
$281$	309.396	−	224.789i	1.10105	−	0.799961i	0.119821	−	0.992796i	$-0.461768\pi$
$281$	309.396	−	224.789i	1.10105	−	0.799961i	0.981231	+	0.192834i	$0.0617680\pi$
$282$		0			0
$283$	−419.260	−	136.226i	−1.48148	−	0.481364i	−0.546928	−	0.837179i	$-0.684203\pi$
$283$	−419.260	−	136.226i	−1.48148	−	0.481364i	−0.934556	+	0.355816i	$0.884203\pi$
$284$	147.776	+	364.335i	0.520338	+	1.28287i
$285$		0			0
$286$	68.6503	+	31.9628i	0.240036	+	0.111758i
$287$		−	214.044i		−	0.745797i
$288$		0			0
$289$	−70.6387	+	217.404i	−0.244425	+	0.752261i
$290$	−15.3056	−	14.2533i	−0.0527779	−	0.0491493i
$291$		0			0
$292$	21.2827	+	298.538i	0.0728859	+	1.02239i
$293$	161.544	+	497.182i	0.551345	+	1.69687i	0.705404	+	0.708805i	$0.250765\pi$
$293$	161.544	+	497.182i	0.551345	+	1.69687i	−0.154059	+	0.988062i	$0.549235\pi$
$294$		0			0
$295$	−35.2810	+	48.5601i	−0.119597	+	0.164611i
$296$	14.7603	−	293.048i	0.0498659	−	0.990026i
$297$		0			0
$298$	207.156	−	115.012i	0.695155	−	0.385947i
$299$	30.3607	−	41.7880i	0.101541	−	0.139759i
$300$		0			0
$301$	−51.5875	−	158.770i	−0.171387	−	0.527476i
$302$	263.334	+	122.577i	0.871966	+	0.405885i
$303$		0			0
$304$	213.839	+	220.238i	0.703417	+	0.724467i
$305$	−17.9726	+	55.3141i	−0.0589267	+	0.181358i
$306$		0			0
$307$			528.080i			1.72013i	0.510183	+	0.860066i	$0.329578\pi$
$307$			528.080i			1.72013i	−0.510183	+	0.860066i	$0.670422\pi$
$308$	−158.140	+	64.1261i	−0.513441	+	0.208202i
$309$		0			0
$310$	10.0886	−	82.6280i	0.0325438	−	0.266542i
$311$	303.245	+	98.5302i	0.975064	+	0.316817i	0.752859	−	0.658182i	$-0.228674\pi$
$311$	303.245	+	98.5302i	0.975064	+	0.316817i	0.222205	+	0.975000i	$0.428674\pi$
$312$		0			0
$313$	260.815	−	189.493i	0.833274	−	0.605409i	−0.0872100	−	0.996190i	$-0.527795\pi$
$313$	260.815	−	189.493i	0.833274	−	0.605409i	0.920484	+	0.390781i	$0.127795\pi$
$314$	−74.9175	+	160.946i	−0.238591	+	0.512567i
$315$		0			0
$316$	231.531	−	194.814i	0.732694	−	0.616499i
$317$	−293.298	−	213.093i	−0.925230	−	0.672219i	0.0195904	−	0.999808i	$-0.493764\pi$
$317$	−293.298	−	213.093i	−0.925230	−	0.672219i	−0.944820	+	0.327589i	$0.893764\pi$
$318$		0			0
$319$	−90.3589	−	124.391i	−0.283257	−	0.389941i
$320$	−47.6412	−	4.81143i	−0.148879	−	0.0150357i
$321$		0			0
$322$	22.2872	+	114.244i	0.0692149	+	0.354795i
$323$	−141.819	+	46.0797i	−0.439067	+	0.142662i
$324$		0			0
$325$	68.0593	−	49.4480i	0.209413	−	0.152148i
$326$	−30.9767	+	33.2637i	−0.0950207	+	0.102036i
$327$		0			0
$328$	277.157	−	343.687i	0.844990	−	1.04783i
$329$	−188.338			−0.572455
$330$		0			0
$331$		−	88.0333i		−	0.265962i	−0.991119	−	0.132981i	$-0.957545\pi$
$331$		−	88.0333i		−	0.265962i	0.991119	−	0.132981i	$-0.0424549\pi$
$332$	−99.2929	−	244.802i	−0.299075	−	0.737356i
$333$		0			0
$334$	−408.070	+	438.197i	−1.22177	+	1.31197i
$335$	−25.3912	−	34.9480i	−0.0757947	−	0.104322i
$336$		0			0
$337$	−3.58012	−	11.0185i	−0.0106235	−	0.0326957i	0.945604	−	0.325319i	$-0.105472\pi$
$337$	−3.58012	−	11.0185i	−0.0106235	−	0.0326957i	−0.956228	+	0.292623i	$0.905472\pi$
$338$	60.1812	+	308.488i	0.178051	+	0.912688i
$339$		0			0
$340$	12.2993	−	19.7425i	0.0361745	−	0.0580663i
$341$	189.145	−	581.956i	0.554679	−	1.70662i
$342$		0			0
$343$	189.115	−	260.294i	0.551355	−	0.758875i
$344$	122.752	−	321.734i	0.356837	−	0.935273i
$345$		0			0
$346$	−39.7204	+	85.3316i	−0.114799	+	0.246623i
$347$	15.5579	+	21.4136i	0.0448355	+	0.0617108i	0.830846	−	0.556502i	$-0.187857\pi$
$347$	15.5579	+	21.4136i	0.0448355	+	0.0617108i	−0.786011	+	0.618213i	$0.787857\pi$
$348$		0			0
$349$	−89.5402	+	275.576i	−0.256562	+	0.789617i	0.736956	+	0.675941i	$0.236263\pi$
$349$	−89.5402	+	275.576i	−0.256562	+	0.789617i	−0.993518	+	0.113676i	$0.963737\pi$
$350$	−22.9758	+	188.177i	−0.0656451	+	0.537650i
$351$		0			0
$352$	−336.957	−	101.803i	−0.957265	−	0.289212i
$353$	−217.033			−0.614825			−0.307413	−	0.951576i	$-0.599463\pi$
$353$	−217.033			−0.614825			−0.307413	+	0.951576i	$0.599463\pi$
$354$		0			0
$355$	−69.9402	−	22.7249i	−0.197015	−	0.0640139i
$356$	−181.476	−	44.9856i	−0.509763	−	0.126364i
$357$		0			0
$358$	165.459	+	77.0181i	0.462175	+	0.215134i
$359$	−222.876	+	72.4169i	−0.620825	+	0.201718i	−0.602507	−	0.798114i	$-0.705831\pi$
$359$	−222.876	+	72.4169i	−0.620825	+	0.201718i	−0.0183184	+	0.999832i	$0.505831\pi$
$360$		0			0
$361$	5.73832	+	4.16913i	0.0158956	+	0.0115488i
$362$	−34.9866	+	19.4244i	−0.0966480	+	0.0536586i
$363$		0			0
$364$	45.3229	+	28.2355i	0.124514	+	0.0775701i
$365$	−45.2903	−	32.9053i	−0.124083	−	0.0901516i
$366$		0			0
$367$	269.892	−	87.6932i	0.735400	−	0.238946i	0.0827128	−	0.996573i	$-0.473642\pi$
$367$	269.892	−	87.6932i	0.735400	−	0.238946i	0.652687	+	0.757627i	$0.273642\pi$
$368$	−112.144	+	212.299i	−0.304739	+	0.576900i
$369$		0			0
$370$	40.1640	+	37.4026i	0.108551	+	0.101088i
$371$	−340.912	−	110.769i	−0.918901	−	0.298569i
$372$		0			0
$373$	377.208			1.01128			0.505640	−	0.862744i	$-0.331256\pi$
$373$	377.208			1.01128			0.505640	+	0.862744i	$0.331256\pi$
$374$	116.541	−	125.123i	0.311608	−	0.334554i
$375$		0			0
$376$	−302.411	−	243.871i	−0.804286	−	0.648593i
$377$	−14.8668	+	45.7554i	−0.0394346	+	0.121367i
$378$		0			0
$379$	237.957	+	327.520i	0.627855	+	0.864168i	0.997895	−	0.0648476i	$-0.0206561\pi$
$379$	237.957	+	327.520i	0.627855	+	0.864168i	−0.370040	+	0.929016i	$0.620656\pi$
$380$	−57.2723	+	4.08292i	−0.150717	+	0.0107445i
$381$		0			0
$382$	431.375	−	84.1544i	1.12925	−	0.220299i
$383$	−106.026	+	145.932i	−0.276830	+	0.381023i	−0.924681	−	0.380744i	$-0.875668\pi$
$383$	−106.026	+	145.932i	−0.276830	+	0.381023i	0.647851	+	0.761767i	$0.275668\pi$
$384$		0			0
$385$	9.86607	−	30.3556i	0.0256262	−	0.0788457i
$386$	157.044	−	87.1900i	0.406849	−	0.225881i
$387$		0			0
$388$	−276.328	−	328.409i	−0.712186	−	0.846416i
$389$	−65.7531	−	202.367i	−0.169031	−	0.520224i	0.830280	−	0.557347i	$-0.188181\pi$
$389$	−65.7531	−	202.367i	−0.169031	−	0.520224i	−0.999311	+	0.0371228i	$0.988181\pi$
$390$		0			0
$391$	−68.5545	−	94.3572i	−0.175331	−	0.241323i
$392$	262.268	−	70.8465i	0.669050	−	0.180731i
$393$		0			0
$394$	−225.025	−	27.4747i	−0.571128	−	0.0697327i
$395$			56.5975i			0.143285i
$396$		0			0
$397$	−510.883			−1.28686			−0.643430	−	0.765505i	$-0.722489\pi$
$397$	−510.883			−1.28686			−0.643430	+	0.765505i	$0.722489\pi$
$398$	31.0780	−	254.537i	0.0780855	−	0.639539i
$399$		0			0
$400$	−280.555	+	272.404i	−0.701389	+	0.681009i
$401$	−22.1925	+	16.1238i	−0.0553429	+	0.0402090i	−0.615113	−	0.788439i	$-0.710890\pi$
$401$	−22.1925	+	16.1238i	−0.0553429	+	0.0402090i	0.559770	+	0.828648i	$0.310890\pi$
$402$		0			0
$403$	−182.110	+	59.1713i	−0.451887	+	0.146827i
$404$	−186.551	−	221.712i	−0.461761	−	0.548792i
$405$		0			0
$406$	−52.6247	−	94.7858i	−0.129617	−	0.233463i
$407$	237.114	+	326.420i	0.582590	+	0.802014i
$408$		0			0
$409$	−107.946	−	78.4274i	−0.263927	−	0.191754i	0.447950	−	0.894059i	$-0.352154\pi$
$409$	−107.946	−	78.4274i	−0.263927	−	0.191754i	−0.711876	+	0.702305i	$0.752154\pi$
$410$	15.8126	+	81.0556i	0.0385674	+	0.197696i
$411$		0			0
$412$	83.6536	−	5.96363i	0.203043	−	0.0144748i
$413$	−251.721	+	182.886i	−0.609493	+	0.442822i
$414$		0			0
$415$	46.9938	+	15.2692i	0.113238	+	0.0367933i
$416$	36.2134	+	104.024i	0.0870514	+	0.250058i
$417$		0			0
$418$	−418.971	−	51.1920i	−1.00232	−	0.122469i
$419$		−	302.402i		−	0.721723i	−0.932619	−	0.360861i	$-0.882483\pi$
$419$		−	302.402i		−	0.721723i	0.932619	−	0.360861i	$-0.117517\pi$
$420$		0			0
$421$	−32.1608	+	98.9806i	−0.0763914	+	0.235108i	−0.981959	−	0.189093i	$-0.939445\pi$
$421$	−32.1608	+	98.9806i	−0.0763914	+	0.235108i	0.905568	+	0.424202i	$0.139445\pi$
$422$	−392.432	+	421.404i	−0.929933	+	0.998588i
$423$		0			0
$424$	−403.968	−	619.295i	−0.952755	−	1.46060i
$425$	−58.6997	−	180.659i	−0.138117	−	0.425081i
$426$		0			0
$427$	−177.210	+	243.908i	−0.415011	+	0.571213i
$428$	−89.1354	−	55.5300i	−0.208260	−	0.129743i
$429$		0			0
$430$	31.2648	+	56.3131i	0.0727088	+	0.130961i
$431$	197.345	−	271.622i	0.457876	−	0.630213i	−0.516190	−	0.856474i	$-0.672650\pi$
$431$	197.345	−	271.622i	0.457876	−	0.630213i	0.974067	+	0.226261i	$0.0726503\pi$
$432$		0			0
$433$	−197.554	−	608.008i	−0.456244	−	1.40418i	−0.869668	−	0.493637i	$-0.835667\pi$
$433$	−197.554	−	608.008i	−0.456244	−	1.40418i	0.413424	−	0.910539i	$-0.364333\pi$
$434$	182.094	−	391.194i	0.419571	−	0.901369i
$435$		0			0
$436$	−308.102	−	76.3748i	−0.706656	−	0.175172i
$437$	−88.9672	+	273.813i	−0.203586	+	0.626574i
$438$		0			0
$439$		−	419.823i		−	0.956317i	−0.878273	−	0.478159i	$-0.841304\pi$
$439$		−	419.823i		−	0.956317i	0.878273	−	0.478159i	$-0.158696\pi$
$440$	55.1481	−	35.9664i	0.125337	−	0.0817418i
$441$		0			0
$442$	−53.1117	−	6.48474i	−0.120162	−	0.0146714i
$443$	238.218	+	77.4017i	0.537738	+	0.174722i	0.565280	−	0.824899i	$-0.308768\pi$
$443$	238.218	+	77.4017i	0.537738	+	0.174722i	−0.0275424	+	0.999621i	$0.508768\pi$
$444$		0			0
$445$	28.2925	−	20.5557i	0.0635787	−	0.0461926i
$446$	−278.939	−	129.841i	−0.625424	−	0.291124i
$447$		0			0
$448$	−227.163	−	100.034i	−0.507061	−	0.223291i
$449$	88.8032	+	64.5193i	0.197780	+	0.143695i	0.682268	−	0.731103i	$-0.260994\pi$
$449$	88.8032	+	64.5193i	0.197780	+	0.143695i	−0.484488	+	0.874798i	$0.660994\pi$
$450$		0			0
$451$	−0.0531724	+	607.085i	−0.000117899	+	1.34609i
$452$	48.1141	−	77.2316i	0.106447	−	0.170866i
$453$		0			0
$454$	634.132	−	123.709i	1.39677	−	0.272487i
$455$	−9.49911	+	3.08645i	−0.0208772	+	0.00678340i
$456$		0			0
$457$	−258.376	+	187.721i	−0.565375	+	0.410769i	−0.833422	−	0.552637i	$-0.813622\pi$
$457$	−258.376	+	187.721i	−0.565375	+	0.410769i	0.268047	+	0.963406i	$0.413622\pi$
$458$	−417.330	−	388.638i	−0.911200	−	0.848554i
$459$		0			0
$460$	−16.8797	−	41.6162i	−0.0366951	−	0.0904701i
$461$	635.144			1.37775			0.688876	−	0.724879i	$-0.258104\pi$
$461$	635.144			1.37775			0.688876	+	0.724879i	$0.258104\pi$
$462$		0			0
$463$		−	735.608i		−	1.58879i	−0.607404	−	0.794393i	$-0.707789\pi$
$463$		−	735.608i		−	1.58879i	0.607404	−	0.794393i	$-0.292211\pi$
$464$	38.2357	−	220.338i	0.0824045	−	0.474866i
$465$		0			0
$466$	285.452	+	265.827i	0.612558	+	0.570443i
$467$	172.418	+	237.313i	0.369204	+	0.508166i	0.952684	−	0.303962i	$-0.0983094\pi$
$467$	172.418	+	237.313i	0.369204	+	0.508166i	−0.583480	+	0.812127i	$0.698309\pi$
$468$		0			0
$469$	−69.1969	−	212.966i	−0.147541	−	0.454085i
$470$	71.3210	−	13.9136i	0.151747	−	0.0296034i
$471$		0			0
$472$	−640.996	−	32.2859i	−1.35804	−	0.0684023i
$473$	146.277	+	450.327i	0.309253	+	0.952066i
$474$		0			0
$475$	−275.615	+	379.351i	−0.580242	+	0.798634i
$476$	92.2600	−	77.6287i	0.193823	−	0.163086i
$477$		0			0
$478$	383.178	+	178.363i	0.801627	+	0.373143i
$479$	59.1076	+	81.3546i	0.123398	+	0.169843i	0.866247	−	0.499617i	$-0.166526\pi$
$479$	59.1076	+	81.3546i	0.123398	+	0.169843i	−0.742849	+	0.669459i	$0.766526\pi$
$480$		0			0
$481$	39.0126	−	120.069i	0.0811074	−	0.249623i
$482$	−651.733	−	79.5742i	−1.35214	−	0.165092i
$483$		0			0
$484$	448.543	−	181.839i	0.926741	−	0.375701i
$485$	80.2792			0.165524
$486$		0			0
$487$	113.789	+	36.9723i	0.233653	+	0.0759186i	0.423503	−	0.905895i	$-0.360800\pi$
$487$	113.789	+	36.9723i	0.233653	+	0.0759186i	−0.189850	+	0.981813i	$0.560800\pi$
$488$	−600.370	+	162.178i	−1.23027	+	0.332332i
$489$		0			0
$490$	−21.4438	+	46.0679i	−0.0437628	+	0.0940160i
$491$	265.485	−	86.2615i	0.540704	−	0.175685i	−0.0259170	−	0.999664i	$-0.508251\pi$
$491$	265.485	−	86.2615i	0.540704	−	0.175685i	0.566621	+	0.823979i	$0.308251\pi$
$492$		0			0
$493$	87.8857	+	63.8527i	0.178267	+	0.129519i
$494$	64.1114	+	115.475i	0.129780	+	0.233756i
$495$		0			0
$496$	798.928	−	392.349i	1.61074	−	0.791026i
$497$	−308.402	−	224.067i	−0.620527	−	0.450839i
$498$		0			0
$499$	−160.821	+	52.2540i	−0.322287	+	0.104717i	−0.465693	−	0.884947i	$-0.654195\pi$
$499$	−160.821	+	52.2540i	−0.322287	+	0.104717i	0.143405	+	0.989664i	$0.454195\pi$
$500$	−10.5214	−	147.586i	−0.0210427	−	0.295173i
$501$		0			0
$502$	−114.337	+	122.779i	−0.227764	+	0.244579i
$503$	591.543	+	192.204i	1.17603	+	0.382115i	0.830890	−	0.556436i	$-0.187832\pi$
$503$	591.543	+	192.204i	1.17603	+	0.382115i	0.345139	+	0.938552i	$0.387832\pi$
$504$		0			0
$505$	54.1971			0.107321
$506$	−63.1841	−	324.032i	−0.124870	−	0.640380i
$507$		0			0
$508$	133.509	+	329.160i	0.262812	+	0.647953i
$509$	−97.9151	+	301.352i	−0.192367	+	0.592046i	0.807630	+	0.589690i	$0.200750\pi$
$509$	−97.9151	+	301.352i	−0.192367	+	0.592046i	−0.999997	+	0.00235633i	$0.999250\pi$
$510$		0			0
$511$	−170.571	−	234.771i	−0.333798	−	0.459434i
$512$	−235.223	−	454.768i	−0.459419	−	0.888220i
$513$		0			0
$514$	−62.0053	−	317.839i	−0.120633	−	0.618364i
$515$	−9.22042	+	12.6908i	−0.0179037	+	0.0246424i
$516$		0			0
$517$	534.176	+	0.0467866i	1.03322	+	9.04962e-5i
$518$	138.094	+	248.731i	0.266591	+	0.480176i
$519$		0			0
$520$	−19.2491	−	7.34416i	−0.0370175	−	0.0141234i
$521$	108.271	+	333.223i	0.207814	+	0.639584i	0.999586	+	0.0287683i	$0.00915850\pi$
$521$	108.271	+	333.223i	0.207814	+	0.639584i	−0.791773	+	0.610816i	$0.790842\pi$
$522$		0			0
$523$	397.190	+	546.685i	0.759445	+	1.04529i	0.997260	+	0.0739759i	$0.0235688\pi$
$523$	397.190	+	546.685i	0.759445	+	1.04529i	−0.237815	+	0.971310i	$0.576431\pi$
$524$	−164.242	+	662.565i	−0.313439	+	1.26444i
$525$		0			0
$526$	−96.7784	+	792.640i	−0.183989	+	1.50692i
$527$			432.367i			0.820431i
$528$		0			0
$529$	303.816			0.574321
$530$	137.282	+	16.7617i	0.259023	+	0.0316258i
$531$		0			0
$532$	−288.892	−	71.6128i	−0.543029	−	0.134611i
$533$	153.688	−	111.661i	0.288345	−	0.209495i
$534$		0			0
$535$	18.6816	−	6.07003i	0.0349190	−	0.0113459i
$536$	164.653	−	431.557i	0.307188	−	0.805144i
$537$		0			0
$538$	111.543	−	61.9281i	0.207329	−	0.115108i
$539$	−219.590	+	302.184i	−0.407402	+	0.560638i
$540$		0			0
$541$	−307.422	−	223.355i	−0.568247	−	0.412856i	0.266221	−	0.963912i	$-0.414225\pi$
$541$	−307.422	−	223.355i	−0.568247	−	0.412856i	−0.834468	+	0.551056i	$0.814225\pi$
$542$	−335.270	+	65.4058i	−0.618579	+	0.120675i
$543$		0			0
$544$	248.659	−	5.18365i	0.457094	−	0.00952877i
$545$	48.0339	−	34.8987i	0.0881357	−	0.0640343i
$546$		0			0
$547$	−222.878	−	72.4175i	−0.407455	−	0.132390i	0.0981162	−	0.995175i	$-0.468718\pi$
$547$	−222.878	−	72.4175i	−0.407455	−	0.132390i	−0.505571	+	0.862785i	$0.668718\pi$
$548$	330.524	−	134.062i	0.603146	−	0.244639i
$549$		0			0
$550$	65.2122	−	533.716i	0.118568	−	0.970392i
$551$		−	268.158i		−	0.486675i
$552$		0			0
$553$	−90.6606	+	279.025i	−0.163943	+	0.504566i
$554$	473.788	+	441.215i	0.855214	+	0.796416i
$555$		0			0
$556$	−714.780	+	50.9564i	−1.28557	+	0.0916481i
$557$	15.6464	+	48.1548i	0.0280906	+	0.0864539i	0.964119	−	0.265471i	$-0.0855274\pi$
$557$	15.6464	+	48.1548i	0.0280906	+	0.0864539i	−0.936028	+	0.351925i	$0.885527\pi$
$558$		0			0
$559$	87.0884	−	119.867i	0.155793	−	0.214431i
$560$	41.6731	−	20.4654i	0.0744163	−	0.0365454i
$561$		0			0
$562$	−668.717	+	371.269i	−1.18989	+	0.660621i
$563$	306.745	−	422.198i	0.544840	−	0.749908i	−0.444460	−	0.895798i	$-0.646605\pi$
$563$	306.745	−	422.198i	0.544840	−	0.749908i	0.989301	+	0.145890i	$0.0466046\pi$
$564$		0			0
$565$	5.25940	+	16.1868i	0.00930866	+	0.0286491i
$566$	799.319	+	372.069i	1.41222	+	0.657366i
$567$		0			0
$568$	−205.061	−	759.119i	−0.361023	−	1.33648i
$569$	−87.5395	+	269.419i	−0.153848	+	0.473495i	−0.998042	−	0.0625419i	$-0.980079\pi$
$569$	−87.5395	+	269.419i	−0.153848	+	0.473495i	0.844194	+	0.536037i	$0.180079\pi$
$570$		0			0
$571$			187.846i			0.328977i	0.986379	+	0.164488i	$0.0525973\pi$
$571$			187.846i			0.328977i	−0.986379	+	0.164488i	$0.947403\pi$
$572$	−128.541	−	80.0948i	−0.224722	−	0.140026i
$573$		0			0
$574$	−51.8826	+	424.932i	−0.0903879	+	0.740299i
$575$	−348.803	−	113.333i	−0.606614	−	0.197101i
$576$		0			0
$577$	−762.773	+	554.187i	−1.32196	+	0.960463i	−0.322058	+	0.946720i	$0.604374\pi$
$577$	−762.773	+	554.187i	−1.32196	+	0.960463i	−0.999906	+	0.0137424i	$0.995626\pi$
$578$	192.933	−	414.480i	0.333794	−	0.717093i
$579$		0			0
$580$	26.9306	+	32.0065i	0.0464322	+	0.0551835i
$581$	207.220	+	150.554i	0.356661	+	0.259129i
$582$		0			0
$583$	966.891	+	314.256i	1.65848	+	0.539032i
$584$	30.1119	−	597.834i	0.0515615	−	1.02369i
$585$		0			0
$586$	−200.194	−	1026.19i	−0.341627	−	1.75118i
$587$	29.3693	−	9.54266i	0.0500329	−	0.0162567i	−0.283894	−	0.958856i	$-0.591626\pi$
$587$	29.3693	−	9.54266i	0.0500329	−	0.0162567i	0.333927	+	0.942599i	$0.391626\pi$
$588$		0			0
$589$	863.456	−	627.337i	1.46597	−	1.06509i
$590$	81.8124	−	87.8524i	0.138665	−	0.148902i
$591$		0			0
$592$	−100.336	+	578.197i	−0.169486	+	0.976684i
$593$	313.027			0.527870			0.263935	−	0.964540i	$-0.414980\pi$
$593$	313.027			0.527870			0.263935	+	0.964540i	$0.414980\pi$
$594$		0			0
$595$			22.5528i			0.0379039i
$596$	−439.136	+	178.116i	−0.736806	+	0.298852i
$597$		0			0
$598$	−70.4030	+	75.6006i	−0.117731	+	0.126422i
$599$	533.190	+	733.872i	0.890133	+	1.22516i	0.973510	+	0.228645i	$0.0734294\pi$
$599$	533.190	+	733.872i	0.890133	+	1.22516i	−0.0833771	+	0.996518i	$0.526571\pi$
$600$		0			0
$601$	320.006	+	984.877i	0.532456	+	1.63873i	0.749083	+	0.662477i	$0.230495\pi$
$601$	320.006	+	984.877i	0.532456	+	1.63873i	−0.216627	+	0.976255i	$0.569505\pi$
$602$	63.9298	+	327.704i	0.106196	+	0.544359i
$603$		0			0
$604$	−493.074	−	307.178i	−0.816347	−	0.508572i
$605$	−27.9904	+	86.0941i	−0.0462650	+	0.142304i
$606$		0			0
$607$	290.604	−	399.983i	0.478755	−	0.658950i	−0.499510	−	0.866308i	$-0.666487\pi$
$607$	290.604	−	399.983i	0.478755	−	0.658950i	0.978265	+	0.207358i	$0.0664866\pi$
$608$	−371.141	−	489.062i	−0.610429	−	0.804378i
$609$		0			0
$610$	49.0880	−	105.456i	0.0804722	−	0.172879i
$611$	−98.2505	−	135.230i	−0.160803	−	0.221326i
$612$		0			0
$613$	−252.174	+	776.112i	−0.411377	+	1.26609i	0.504075	+	0.863660i	$0.331834\pi$
$613$	−252.174	+	776.112i	−0.411377	+	1.26609i	−0.915452	+	0.402428i	$0.868166\pi$
$614$	128.003	−	1048.38i	0.208474	−	1.70745i
$615$		0			0
$616$	329.492	−	88.9748i	0.534889	−	0.144440i
$617$	−965.796			−1.56531			−0.782654	−	0.622457i	$-0.786135\pi$
$617$	−965.796			−1.56531			−0.782654	+	0.622457i	$0.786135\pi$
$618$		0			0
$619$	1.84967	+	0.600994i	0.00298816	+	0.000970911i	0.310511	−	0.950570i	$-0.399500\pi$
$619$	1.84967	+	0.600994i	0.00298816	+	0.000970911i	−0.307523	+	0.951541i	$0.599500\pi$
$620$	−40.0568	+	161.592i	−0.0646078	+	0.260633i
$621$		0			0
$622$	−578.136	−	269.112i	−0.929479	−	0.432656i
$623$	172.409	−	56.0190i	0.276740	−	0.0899182i
$624$		0			0
$625$	−471.924	−	342.873i	−0.755079	−	0.548597i
$626$	−563.716	+	312.973i	−0.900504	+	0.499956i
$627$		0			0
$628$	187.743	−	301.360i	0.298953	−	0.479872i
$629$	−230.624	−	167.558i	−0.366652	−	0.266388i
$630$		0			0
$631$	408.093	−	132.598i	0.646740	−	0.210139i	0.0327641	−	0.999463i	$-0.489569\pi$
$631$	408.093	−	132.598i	0.646740	−	0.210139i	0.613976	+	0.789324i	$0.289569\pi$
$632$	−506.871	+	330.633i	−0.802011	+	0.523154i
$633$		0			0
$634$	530.619	+	494.138i	0.836939	+	0.779398i
$635$	−63.1877	−	20.5309i	−0.0995081	−	0.0323322i
$636$		0			0
$637$	116.889			0.183499
$638$	149.234	+	268.851i	0.233909	+	0.421396i
$639$		0			0
$640$	93.4138	+	21.0998i	0.145959	+	0.0329684i
$641$	86.8750	−	267.374i	0.135530	−	0.417120i	−0.860142	−	0.510055i	$-0.829625\pi$
$641$	86.8750	−	267.374i	0.135530	−	0.417120i	0.995672	+	0.0929354i	$0.0296250\pi$
$642$		0			0
$643$	−367.425	−	505.717i	−0.571422	−	0.786495i	0.421300	−	0.906921i	$-0.361574\pi$
$643$	−367.425	−	505.717i	−0.571422	−	0.786495i	−0.992722	+	0.120426i	$0.961574\pi$
$644$	−16.5539	−	232.206i	−0.0257048	−	0.360569i
$645$		0			0
$646$	292.716	−	57.1042i	0.453121	−	0.0883967i
$647$	−4.40525	+	6.06331i	−0.00680874	+	0.00937142i	−0.812408	−	0.583090i	$-0.801844\pi$
$647$	−4.40525	+	6.06331i	−0.00680874	+	0.00937142i	0.805599	+	0.592461i	$0.201844\pi$
$648$		0			0
$649$	713.992	−	518.650i	1.10014	−	0.799153i
$650$	−147.101	+	81.6699i	−0.226309	+	0.125646i
$651$		0			0
$652$	69.5597	−	58.5284i	0.106687	−	0.0897675i
$653$	−338.138	−	1040.68i	−0.517823	−	1.59369i	−0.778087	−	0.628157i	$-0.783810\pi$
$653$	−338.138	−	1040.68i	−0.517823	−	1.59369i	0.260264	−	0.965538i	$-0.416190\pi$
$654$		0			0
$655$	−75.0487	−	103.296i	−0.114578	−	0.157703i
$656$	−633.535	+	615.127i	−0.965754	+	0.937693i
$657$		0			0
$658$	373.899	+	45.6517i	0.568235	+	0.0693795i
$659$			690.561i			1.04789i	0.851752	+	0.523946i	$0.175541\pi$
$659$			690.561i			1.04789i	−0.851752	+	0.523946i	$0.824459\pi$
$660$		0			0
$661$	−981.006			−1.48412			−0.742062	−	0.670331i	$-0.766152\pi$
$661$	−981.006			−1.48412			−0.742062	+	0.670331i	$0.766152\pi$
$662$	−21.3386	+	174.769i	−0.0322336	+	0.264001i
$663$		0			0
$664$	137.784	+	510.063i	0.207506	+	0.768168i
$665$	45.0390	−	32.7227i	0.0677278	−	0.0492071i
$666$		0			0
$667$	199.474	−	64.8132i	0.299062	−	0.0971711i
$668$	916.340	−	771.020i	1.37177	−	1.15422i
$669$		0			0
$670$	41.9370	+	75.5355i	0.0625925	+	0.112739i
$671$	502.674	−	691.744i	0.749142	−	1.03092i
$672$		0			0
$673$	173.221	+	125.852i	0.257386	+	0.187002i	0.708994	−	0.705214i	$-0.249149\pi$
$673$	173.221	+	125.852i	0.257386	+	0.187002i	−0.451608	+	0.892217i	$0.649149\pi$
$674$	4.43666	+	22.7423i	0.00658258	+	0.0337423i
$675$		0			0
$676$	−44.6997	−	627.016i	−0.0661239	−	0.927539i
$677$	−909.036	+	660.454i	−1.34274	+	0.975559i	−0.343404	+	0.939188i	$0.611580\pi$
$677$	−909.036	+	660.454i	−1.34274	+	0.975559i	−0.999338	+	0.0363712i	$0.988420\pi$
$678$		0			0
$679$	395.775	+	128.595i	0.582879	+	0.189389i
$680$	−29.2028	+	36.2128i	−0.0429452	+	0.0532541i
$681$		0			0
$682$	−516.564	+	1109.49i	−0.757426	+	1.62681i
$683$			87.6213i			0.128289i	0.997941	+	0.0641445i	$0.0204318\pi$
$683$			87.6213i			0.128289i	−0.997941	+	0.0641445i	$0.979568\pi$
$684$		0			0
$685$	−20.6160	+	63.4495i	−0.0300963	+	0.0926270i
$686$	−438.535	+	470.910i	−0.639263	+	0.686458i
$687$		0			0
$688$	−321.680	+	608.970i	−0.467558	+	0.885131i
$689$	−98.3100	−	302.567i	−0.142685	−	0.439140i
$690$		0			0
$691$	−316.481	+	435.598i	−0.458004	+	0.630388i	−0.974093	−	0.226147i	$-0.927387\pi$
$691$	−316.481	+	435.598i	−0.458004	+	0.630388i	0.516090	+	0.856535i	$0.327387\pi$
$692$	99.5389	−	159.777i	0.143842	−	0.230892i
$693$		0			0
$694$	−25.6960	−	46.2827i	−0.0370259	−	0.0666898i
$695$	78.7840	−	108.437i	0.113358	−	0.156024i
$696$		0			0
$697$	−132.553	−	407.955i	−0.190176	−	0.585301i
$698$	244.558	−	525.386i	0.350370	−	0.752702i
$699$		0			0
$700$	91.2257	−	368.011i	0.130322	−	0.525731i
$701$	−253.827	+	781.200i	−0.362093	+	1.11441i	0.589688	+	0.807631i	$0.299251\pi$
$701$	−253.827	+	781.200i	−0.362093	+	1.11441i	−0.951781	+	0.306777i	$0.900749\pi$
$702$		0			0
$703$			703.683i			1.00097i
$704$	644.271	+	283.780i	0.915157	+	0.403097i
$705$		0			0
$706$	430.867	+	52.6073i	0.610293	+	0.0745146i
$707$	267.191	+	86.8156i	0.377922	+	0.122794i
$708$		0			0
$709$	−574.514	+	417.409i	−0.810315	+	0.588729i	−0.913922	−	0.405890i	$-0.866962\pi$
$709$	−574.514	+	417.409i	−0.810315	+	0.588729i	0.103607	+	0.994618i	$0.466962\pi$
$710$	133.341	+	62.0678i	0.187804	+	0.0874195i
$711$		0			0
$712$	349.371	+	133.296i	0.490690	+	0.187214i
$713$	675.352	+	490.672i	0.947198	+	0.688180i
$714$		0			0
$715$	26.9428	−	8.75163i	0.0376822	−	0.0122400i
$716$	−309.809	−	193.007i	−0.432695	−	0.269562i
$717$		0			0
$718$	460.020	−	89.7425i	0.640696	−	0.124990i
$719$	878.206	−	285.347i	1.22143	−	0.396866i	0.373826	−	0.927499i	$-0.378046\pi$
$719$	878.206	−	285.347i	1.22143	−	0.396866i	0.847602	+	0.530633i	$0.178046\pi$
$720$		0			0
$721$	−65.7852	+	47.7958i	−0.0912417	+	0.0662909i
$722$	−10.3815	−	9.66772i	−0.0143788	−	0.0133902i
$723$		0			0
$724$	74.1657	−	30.0819i	0.102439	−	0.0415497i
$725$	341.599			0.471172
$726$		0			0
$727$		−	824.285i		−	1.13382i	−0.823781	−	0.566909i	$-0.808139\pi$
$727$		−	824.285i		−	1.13382i	0.823781	−	0.566909i	$-0.191861\pi$
$728$	−83.1336	−	67.0407i	−0.114195	−	0.0920889i
$729$		0			0
$730$	81.9369	+	76.3036i	0.112242	+	0.104525i
$731$	−196.646	−	270.659i	−0.269009	−	0.370259i
$732$		0			0
$733$	−0.267616	−	0.823639i	−0.000365098	−	0.00112365i	0.950874	−	0.309579i	$-0.100188\pi$
$733$	−0.267616	−	0.823639i	−0.000365098	−	0.00112365i	−0.951239	+	0.308455i	$0.900188\pi$
$734$	−557.061	+	108.674i	−0.758938	+	0.148057i
$735$		0			0
$736$	274.094	−	394.285i	0.372411	−	0.535714i
$737$	196.208	+	604.046i	0.266225	+	0.819601i
$738$		0			0
$739$	−247.106	+	340.112i	−0.334378	+	0.460232i	−0.942789	−	0.333390i	$-0.891807\pi$
$739$	−247.106	+	340.112i	−0.334378	+	0.460232i	0.608411	+	0.793622i	$0.291807\pi$
$740$	−70.6697	−	83.9893i	−0.0954996	−	0.113499i
$741$		0			0
$742$	649.949	+	302.540i	0.875942	+	0.407736i
$743$	−814.385	−	1120.90i	−1.09608	−	1.50862i	−0.840485	−	0.541835i	$-0.817730\pi$
$743$	−814.385	−	1120.90i	−1.09608	−	1.50862i	−0.255591	−	0.966785i	$-0.582270\pi$
$744$		0			0
$745$	27.3905	−	84.2994i	0.0367658	−	0.113154i
$746$	−748.854	−	91.4324i	−1.00383	−	0.122563i
$747$		0			0
$748$	−261.693	+	220.153i	−0.349857	+	0.294322i
$749$	101.823			0.135946
$750$		0			0
$751$	−1243.83	−	404.146i	−1.65624	−	0.538144i	−0.676159	−	0.736756i	$-0.736357\pi$
$751$	−1243.83	−	404.146i	−1.65624	−	0.538144i	−0.980078	+	0.198612i	$0.936357\pi$
$752$	541.252	+	557.449i	0.719750	+	0.741289i
$753$		0			0
$754$	40.6053	−	87.2327i	0.0538532	−	0.115693i
$755$	103.342	−	33.5778i	0.136877	−	0.0444740i
$756$		0			0
$757$	27.1049	+	19.6929i	0.0358057	+	0.0260143i	0.605544	−	0.795812i	$-0.292956\pi$
$757$	27.1049	+	19.6929i	0.0358057	+	0.0260143i	−0.569738	+	0.821826i	$0.692956\pi$
$758$	−393.017	−	707.890i	−0.518493	−	0.933892i
$759$		0			0
$760$	114.690	+	5.77674i	0.150908	+	0.00760097i
$761$	53.4377	+	38.8247i	0.0702203	+	0.0510181i	0.622342	−	0.782746i	$-0.286181\pi$
$761$	53.4377	+	38.8247i	0.0702203	+	0.0510181i	−0.552121	+	0.833764i	$0.686181\pi$
$762$		0			0
$763$	292.709	−	95.1069i	0.383629	−	0.124649i
$764$	−876.788	+	62.5059i	−1.14763	+	0.0818140i
$765$		0			0
$766$	245.861	−	264.013i	0.320968	−	0.344664i
$767$	−262.631	−	85.3341i	−0.342414	−	0.111257i
$768$		0			0
$769$	1115.14			1.45012			0.725062	−	0.688684i	$-0.241811\pi$
$769$	1115.14			1.45012			0.725062	+	0.688684i	$0.241811\pi$
$770$	−26.9447	+	57.8722i	−0.0349931	+	0.0751587i
$771$		0			0
$772$	−332.907	+	135.028i	−0.431226	+	0.174907i
$773$	52.6568	−	162.061i	0.0681200	−	0.209652i	−0.911202	−	0.411960i	$-0.864844\pi$
$773$	52.6568	−	162.061i	0.0681200	−	0.209652i	0.979322	+	0.202308i	$0.0648443\pi$
$774$		0			0
$775$	799.149	+	1099.93i	1.03116	+	1.41927i
$776$	468.978	+	718.957i	0.604353	+	0.926491i
$777$		0			0
$778$	81.4845	+	417.689i	0.104736	+	0.536875i
$779$	−622.378	+	856.630i	−0.798945	+	1.09965i
$780$		0			0
$781$	874.655	+	635.591i	1.11992	+	0.813817i
$782$	113.227	+	203.940i	0.144791	+	0.260793i
$783$		0			0
$784$	−537.841	+	77.0767i	−0.686022	+	0.0983121i
$785$	20.5223	+	63.1611i	0.0261431	+	0.0804601i
$786$		0			0
$787$	−306.107	−	421.320i	−0.388954	−	0.535350i	0.568975	−	0.822355i	$-0.307340\pi$
$787$	−306.107	−	421.320i	−0.388954	−	0.535350i	−0.957929	+	0.287005i	$0.907340\pi$
$788$	440.072	+	109.089i	0.558467	+	0.138437i
$789$		0			0
$790$	13.7188	−	112.361i	0.0173656	−	0.142229i
$791$			88.2252i			0.111536i
$792$		0			0
$793$	−267.576			−0.337423
$794$	1014.23	+	123.834i	1.27737	+	0.155963i
$795$		0			0
$796$	−123.396	+	497.788i	−0.155020	+	0.625361i
$797$	332.100	−	241.285i	0.416688	−	0.302742i	−0.359616	−	0.933100i	$-0.617092\pi$
$797$	332.100	−	241.285i	0.416688	−	0.302742i	0.776304	+	0.630359i	$0.217092\pi$
$798$		0			0
$799$	−358.960	+	116.633i	−0.449262	+	0.145974i
$800$	623.003	−	472.787i	0.778754	−	0.590983i
$801$		0			0
$802$	47.9662	−	26.6306i	0.0598082	−	0.0332052i
$803$	483.727	+	665.915i	0.602399	+	0.829284i
$804$		0			0
$805$	35.2272	+	25.5941i	0.0437606	+	0.0317939i
$806$	375.879	−	73.3279i	0.466351	−	0.0909776i
$807$		0			0
$808$	316.611	+	485.374i	0.391845	+	0.600710i
$809$	1064.09	−	773.105i	1.31531	−	0.955630i	0.315334	−	0.948981i	$-0.397883\pi$
$809$	1064.09	−	773.105i	1.31531	−	0.955630i	0.999978	−	0.00664931i	$-0.00211656\pi$
$810$		0			0
$811$	967.742	+	314.438i	1.19327	+	0.387717i	0.837281	−	0.546773i	$-0.184144\pi$
$811$	967.742	+	314.438i	1.19327	+	0.387717i	0.355989	+	0.934490i	$0.384144\pi$
$812$	81.4981	+	200.930i	0.100367	+	0.247451i
$813$		0			0
$814$	−391.611	−	705.502i	−0.481094	−	0.866710i
$815$			17.0038i			0.0208635i
$816$		0			0
$817$	−255.198	+	785.420i	−0.312360	+	0.961347i
$818$	195.290	+	181.864i	0.238741	+	0.222328i
$819$		0			0
$820$	−11.7449	−	164.749i	−0.0143230	−	0.200913i
$821$	−1.01822	−	3.13376i	−0.00124022	−	0.00381700i	0.950434	−	0.310925i	$-0.100639\pi$
$821$	−1.01822	−	3.13376i	−0.00124022	−	0.00381700i	−0.951675	+	0.307108i	$0.900639\pi$
$822$		0			0
$823$	686.883	−	945.413i	0.834608	−	1.14874i	−0.152440	−	0.988313i	$-0.548713\pi$
$823$	686.883	−	945.413i	0.834608	−	1.14874i	0.987048	−	0.160427i	$-0.0512870\pi$
$824$	−167.519	−	8.43767i	−0.203300	−	0.0102399i
$825$		0			0
$826$	544.060	−	302.060i	0.658668	−	0.365690i
$827$	−629.832	+	866.889i	−0.761586	+	1.04823i	0.235494	+	0.971876i	$0.424329\pi$
$827$	−629.832	+	866.889i	−0.761586	+	1.04823i	−0.997080	+	0.0763576i	$0.975671\pi$
$828$		0			0
$829$	74.0327	+	227.849i	0.0893036	+	0.274848i	0.985727	−	0.168350i	$-0.0538438\pi$
$829$	74.0327	+	227.849i	0.0893036	+	0.274848i	−0.896424	+	0.443198i	$0.853844\pi$
$830$	−89.5937	−	41.7043i	−0.107944	−	0.0502461i
$831$		0			0
$832$	−46.6781	−	215.293i	−0.0561035	−	0.258765i
$833$	81.5604	−	251.017i	0.0979117	−	0.301341i
$834$		0			0
$835$			223.998i			0.268261i
$836$	819.356	+	203.185i	0.980091	+	0.243044i
$837$		0			0
$838$	−73.3000	+	600.345i	−0.0874701	+	0.716402i
$839$	−826.516	−	268.551i	−0.985120	−	0.320085i	−0.228216	−	0.973611i	$-0.573289\pi$
$839$	−826.516	−	268.551i	−0.985120	−	0.320085i	−0.756904	+	0.653526i	$0.773289\pi$
$840$		0			0
$841$	522.338	−	379.501i	0.621092	−	0.451249i
$842$	87.8396	−	188.706i	0.104323	−	0.224117i
$843$		0			0
$844$	881.223	−	741.473i	1.04410	−	0.878522i
$845$	95.1226	+	69.1106i	0.112571	+	0.0817877i
$846$		0			0
$847$	−275.902	+	379.606i	−0.325740	+	0.448177i
$848$	651.868	+	1327.38i	0.768712	+	1.56530i
$849$		0			0
$850$	72.7436	+	372.883i	0.0855807	+	0.438686i
$851$	−523.448	+	170.079i	−0.615098	+	0.199857i
$852$		0			0
$853$	1053.49	−	765.403i	1.23504	−	0.897307i	0.237780	−	0.971319i	$-0.423580\pi$
$853$	1053.49	−	765.403i	1.23504	−	0.897307i	0.997257	+	0.0740115i	$0.0235802\pi$
$854$	410.928	−	441.266i	0.481180	−	0.516705i
$855$		0			0
$856$	163.497	+	131.847i	0.191001	+	0.154027i
$857$	−676.267			−0.789110			−0.394555	−	0.918872i	$-0.629101\pi$
$857$	−676.267			−0.789110			−0.394555	+	0.918872i	$0.629101\pi$
$858$		0			0
$859$		−	745.506i		−	0.867877i	−0.900943	−	0.433938i	$-0.857124\pi$
$859$		−	745.506i		−	0.867877i	0.900943	−	0.433938i	$-0.142876\pi$
$860$	−48.4188	−	119.374i	−0.0563009	−	0.138807i
$861$		0			0
$862$	−457.619	+	491.404i	−0.530881	+	0.570074i
$863$	−783.896	−	1078.94i	−0.908338	−	1.25022i	−0.967731	−	0.251986i	$-0.918916\pi$
$863$	−783.896	−	1078.94i	−0.908338	−	1.25022i	0.0593926	−	0.998235i	$-0.481084\pi$
$864$		0			0
$865$	10.8807	+	33.4873i	0.0125788	+	0.0387136i
$866$	244.818	+	1254.94i	0.282700	+	1.44912i
$867$		0			0
$868$	−456.326	+	732.483i	−0.525721	+	0.843874i
$869$	257.207	−	791.366i	0.295981	−	0.910663i
$870$		0			0
$871$	116.816	−	160.783i	0.134117	−	0.184596i
$872$	593.149	+	226.305i	0.680217	+	0.259525i
$873$		0			0
$874$	242.993	−	522.024i	0.278024	−	0.597282i
$875$	84.3240	+	116.062i	0.0963703	+	0.132642i
$876$		0			0
$877$	−122.743	+	377.764i	−0.139958	+	0.430746i	−0.996328	−	0.0856163i	$-0.972714\pi$
$877$	−122.743	+	377.764i	−0.139958	+	0.430746i	0.856370	+	0.516362i	$0.172714\pi$
$878$	−101.762	+	833.457i	−0.115902	+	0.949268i
$879$		0			0
$880$	−118.201	+	58.0351i	−0.134319	+	0.0659489i
$881$	−473.383			−0.537325			−0.268662	−	0.963234i	$-0.586582\pi$
$881$	−473.383			−0.537325			−0.268662	+	0.963234i	$0.586582\pi$
$882$		0			0
$883$	−1305.74	−	424.260i	−1.47875	−	0.480475i	−0.545011	−	0.838429i	$-0.683475\pi$
$883$	−1305.74	−	424.260i	−1.47875	−	0.480475i	−0.933739	+	0.357954i	$0.883475\pi$
$884$	103.868	+	25.7478i	0.117498	+	0.0291264i
$885$		0			0
$886$	−454.162	−	211.404i	−0.512598	−	0.238605i
$887$	−266.937	+	86.7330i	−0.300943	+	0.0977824i	−0.455597	−	0.890186i	$-0.650574\pi$
$887$	−266.937	+	86.7330i	−0.300943	+	0.0977824i	0.154653	+	0.987969i	$0.450574\pi$
$888$		0			0
$889$	−278.627	−	202.434i	−0.313416	−	0.227710i
$890$	−61.1505	+	33.9505i	−0.0687084	+	0.0381466i
$891$		0			0
$892$	522.294	+	325.381i	0.585531	+	0.364777i
$893$	753.751	+	547.632i	0.844066	+	0.613250i
$894$		0			0
$895$	64.9321	−	21.0977i	0.0725498	−	0.0235729i
$896$	426.730	+	253.656i	0.476261	+	0.283099i
$897$		0			0
$898$	−160.658	−	149.613i	−0.178907	−	0.166606i
$899$	−739.472	−	240.269i	−0.822550	−	0.267263i
$900$		0			0
$901$	−718.356			−0.797287
$902$	147.259	−	1205.21i	0.163258	−	1.33615i
$903$		0			0
$904$	−114.239	+	141.662i	−0.126371	+	0.156706i
$905$	−4.62599	+	14.2373i	−0.00511159	+	0.0157319i
$906$		0			0
$907$	−286.376	−	394.163i	−0.315740	−	0.434578i	0.621421	−	0.783477i	$-0.286556\pi$
$907$	−286.376	−	394.163i	−0.315740	−	0.434578i	−0.937160	+	0.348899i	$0.886556\pi$
$908$	−1288.90	+	91.8853i	−1.41949	+	0.101195i
$909$		0			0
$910$	19.6063	−	3.82488i	0.0215454	−	0.00420316i
$911$	627.748	−	864.021i	0.689076	−	0.948431i	−0.310922	−	0.950435i	$-0.600638\pi$
$911$	627.748	−	864.021i	0.689076	−	0.948431i	0.999998	+	0.00200421i	$0.000637960\pi$
$912$		0			0
$913$	−587.693	−	427.063i	−0.643695	−	0.467758i
$914$	558.446	−	310.047i	0.610991	−	0.339219i
$915$		0			0
$916$	734.304	+	872.703i	0.801642	+	0.952733i
$917$	−204.525	−	629.462i	−0.223037	−	0.686436i
$918$		0			0
$919$	−170.812	−	235.102i	−0.185867	−	0.255824i	0.705908	−	0.708304i	$-0.250539\pi$
$919$	−170.812	−	235.102i	−0.185867	−	0.255824i	−0.891774	+	0.452480i	$0.850539\pi$
$920$	23.4231	+	86.7105i	0.0254599	+	0.0942505i
$921$		0			0
$922$	−1260.92	−	153.954i	−1.36760	−	0.166979i
$923$		−	338.328i		−	0.366553i
$924$		0			0
$925$	−896.403			−0.969085
$926$	−178.306	+	1460.37i	−0.192555	+	1.57707i
$927$		0			0
$928$	−129.316	+	428.159i	−0.139349	+	0.461379i
$929$	−139.029	+	101.011i	−0.149655	+	0.108731i	−0.660093	−	0.751184i	$-0.729483\pi$
$929$	−139.029	+	101.011i	−0.149655	+	0.108731i	0.510438	+	0.859914i	$0.329483\pi$
$930$		0			0
$931$	−619.632	+	201.331i	−0.665555	+	0.216252i
$932$	−502.261	−	596.926i	−0.538907	−	0.640478i
$933$		0			0
$934$	−284.772	−	512.921i	−0.304895	−	0.549166i
$935$	0.00560254	−	63.9658i	5.99202e−6	−	0.0684126i
$936$		0			0
$937$	−694.695	−	504.726i	−0.741404	−	0.538661i	0.151747	−	0.988419i	$-0.451510\pi$
$937$	−694.695	−	504.726i	−0.741404	−	0.538661i	−0.893150	+	0.449758i	$0.851510\pi$
$938$	85.7521	+	439.565i	0.0914202	+	0.468620i
$939$		0			0
$940$	−144.963	+	10.3344i	−0.154216	+	0.0109940i
$941$	755.437	−	548.857i	0.802802	−	0.583270i	−0.108932	−	0.994049i	$-0.534743\pi$
$941$	755.437	−	548.857i	0.802802	−	0.583270i	0.911735	+	0.410779i	$0.134743\pi$
$942$		0			0
$943$	−787.648	−	255.922i	−0.835258	−	0.271392i
$944$	1264.72	+	219.469i	1.33974	+	0.232488i
$945$		0			0
$946$	−181.241	−	929.472i	−0.191586	−	0.982528i
$947$		−	588.592i		−	0.621533i	−0.950486	−	0.310767i	$-0.899414\pi$
$947$		−	588.592i		−	0.621533i	0.950486	−	0.310767i	$-0.100586\pi$
$948$		0			0
$949$	79.5881	−	244.947i	0.0838652	−	0.258110i
$950$	639.118	−	686.303i	0.672756	−	0.722424i
$951$		0			0
$952$	−201.976	+	131.750i	−0.212160	+	0.138393i
$953$	4.59701	+	14.1481i	0.00482373	+	0.0148459i	0.953439	−	0.301585i	$-0.0975156\pi$
$953$	4.59701	+	14.1481i	0.00482373	+	0.0148459i	−0.948616	+	0.316431i	$0.897516\pi$
$954$		0			0
$955$	96.6409	−	133.015i	0.101195	−	0.139282i
$956$	−717.473	−	446.975i	−0.750494	−	0.467547i
$957$		0			0
$958$	−97.6240	−	175.837i	−0.101904	−	0.183546i
$959$	−203.273	+	279.781i	−0.211963	+	0.291743i
$960$		0			0
$961$	−659.325	−	2029.19i	−0.686083	−	2.11155i
$962$	−106.554	+	228.911i	−0.110763	+	0.237953i
$963$		0			0
$964$	1274.57	+	315.951i	1.32217	+	0.327750i
$965$	20.7646	−	63.9069i	0.0215177	−	0.0662248i
$966$		0			0
$967$			974.002i			1.00724i	0.863925	+	0.503621i	$0.167999\pi$
$967$			974.002i			1.00724i	−0.863925	+	0.503621i	$0.832001\pi$
$968$	−934.549	+	252.274i	−0.965443	+	0.260614i
$969$		0			0
$970$	−159.375	−	19.4591i	−0.164304	−	0.0200609i
$971$	−408.637	−	132.774i	−0.420841	−	0.136740i	0.0909380	−	0.995857i	$-0.471013\pi$
$971$	−408.637	−	132.774i	−0.420841	−	0.136740i	−0.511779	+	0.859117i	$0.671013\pi$
$972$		0			0
$973$	562.103	−	408.392i	0.577701	−	0.419725i
$974$	−216.939	−	100.981i	−0.222730	−	0.103677i
$975$		0			0
$976$	1231.20	−	176.440i	1.26148	−	0.180779i
$977$	−258.647	−	187.918i	−0.264736	−	0.192342i	0.447496	−	0.894286i	$-0.352316\pi$
$977$	−258.647	−	187.918i	−0.264736	−	0.192342i	−0.712232	+	0.701944i	$0.752316\pi$
$978$		0			0
$979$	−489.011	+	158.842i	−0.499501	+	0.162249i
$980$	53.7379	−	86.2587i	0.0548346	−	0.0880191i
$981$		0			0
$982$	−547.966	+	106.899i	−0.558010	+	0.108859i
$983$	281.950	−	91.6112i	0.286826	−	0.0931955i	−0.162070	−	0.986779i	$-0.551817\pi$
$983$	281.950	−	91.6112i	0.286826	−	0.0931955i	0.448897	+	0.893584i	$0.351817\pi$
$984$		0			0
$985$	−68.6084	+	49.8469i	−0.0696532	+	0.0506060i
$986$	−158.998	−	148.067i	−0.161256	−	0.150169i
$987$		0			0
$988$	−99.2873	−	244.788i	−0.100493	−	0.247762i
$989$	−645.931			−0.653115
$990$		0			0
$991$			418.812i			0.422616i	0.977420	+	0.211308i	$0.0677723\pi$
$991$			418.812i			0.422616i	−0.977420	+	0.211308i	$0.932228\pi$
$992$	−1681.18	+	585.259i	−1.69474	+	0.589979i
$993$		0			0
$994$	557.945	+	519.585i	0.561313	+	0.522722i
$995$	−56.3844	−	77.6065i	−0.0566677	−	0.0779964i
$996$		0			0
$997$	−474.883	−	1461.54i	−0.476312	−	1.46594i	−0.844180	−	0.536059i	$-0.819912\pi$
$997$	−474.883	−	1461.54i	−0.476312	−	1.46594i	0.367868	−	0.929878i	$-0.380088\pi$
$998$	331.938	−	64.7557i	0.332603	−	0.0648855i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.3.s.a.235.1		40
3.2	odd	2		44.3.h.a.15.10	yes	40
4.3	odd	2	inner	396.3.s.a.235.4		40
11.3	even	5	inner	396.3.s.a.91.4		40
12.11	even	2		44.3.h.a.15.7	yes	40
33.5	odd	10		484.3.b.j.243.4		20
33.14	odd	10		44.3.h.a.3.7	✓	40
33.17	even	10		484.3.b.k.243.17		20
44.3	odd	10	inner	396.3.s.a.91.1		40
132.47	even	10		44.3.h.a.3.10	yes	40
132.71	even	10		484.3.b.j.243.3		20
132.83	odd	10		484.3.b.k.243.18		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.3.h.a.3.7	✓	40	33.14	odd	10
44.3.h.a.3.10	yes	40	132.47	even	10
44.3.h.a.15.7	yes	40	12.11	even	2
44.3.h.a.15.10	yes	40	3.2	odd	2
396.3.s.a.91.1		40	44.3	odd	10	inner
396.3.s.a.91.4		40	11.3	even	5	inner
396.3.s.a.235.1		40	1.1	even	1	trivial
396.3.s.a.235.4		40	4.3	odd	2	inner
484.3.b.j.243.3		20	132.71	even	10
484.3.b.j.243.4		20	33.5	odd	10
484.3.b.k.243.17		20	33.17	even	10
484.3.b.k.243.18		20	132.83	odd	10

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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	396.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98526 - 0.242393i) q^{2} +(3.88249 + 0.962424i) q^{4} +(-0.605291 + 0.439770i) q^{5} +(-3.68852 + 1.19847i) q^{7} +(-7.47446 - 2.85175i) q^{8} +O(q^{10})\)	\(q+(-1.98526 - 0.242393i) q^{2} +(3.88249 + 0.962424i) q^{4} +(-0.605291 + 0.439770i) q^{5} +(-3.68852 + 1.19847i) q^{7} +(-7.47446 - 2.85175i) q^{8} +(1.30826 - 0.726338i) q^{10} +(10.4619 - 3.39827i) q^{11} +(-2.78472 - 2.02322i) q^{13} +(7.61316 - 1.48521i) q^{14} +(14.1475 + 7.47320i) q^{16} +(-6.28791 + 4.56843i) q^{17} +(18.2467 + 5.92872i) q^{19} +(-2.77328 + 1.12486i) q^{20} +(-21.5933 + 4.21055i) q^{22} +15.0061i q^{23} +(-7.55245 + 23.2440i) q^{25} +(5.03798 + 4.69161i) q^{26} +(-15.4741 + 1.10314i) q^{28} +(-4.31911 - 13.2929i) q^{29} +(32.6981 - 45.0051i) q^{31} +(-26.2749 - 18.2655i) q^{32} +(13.5905 - 7.54537i) q^{34} +(1.70557 - 2.34752i) q^{35} +(11.3339 + 34.8823i) q^{37} +(-34.7874 - 16.1929i) q^{38} +(5.77833 - 1.56090i) q^{40} +(-17.0545 + 52.4884i) q^{41} +43.0444i q^{43} +(43.8889 - 3.12496i) q^{44} +(3.63738 - 29.7910i) q^{46} +(46.1847 + 15.0063i) q^{47} +(-27.4730 + 19.9603i) q^{49} +(20.6277 - 44.3147i) q^{50} +(-8.86447 - 10.5352i) q^{52} +(74.7736 + 54.3262i) q^{53} +(-4.83805 + 6.65778i) q^{55} +(30.9874 + 1.56078i) q^{56} +(5.35245 + 27.4367i) q^{58} +(76.2995 - 24.7912i) q^{59} +(62.8898 - 45.6921i) q^{61} +(-75.8230 + 81.4209i) q^{62} +(47.7351 + 42.6305i) q^{64} +2.57532 q^{65} +57.7376i q^{67} +(-28.8095 + 11.6853i) q^{68} +(-3.95503 + 4.24702i) q^{70} +(57.7740 + 79.5191i) q^{71} +(23.1219 + 71.1618i) q^{73} +(-14.0456 - 71.9975i) q^{74} +(65.1368 + 40.5793i) q^{76} +(-34.5162 + 25.0729i) q^{77} +(44.4641 - 61.1996i) q^{79} +(-11.8498 + 1.69817i) q^{80} +(46.5804 - 100.069i) q^{82} +(-38.8192 - 53.4301i) q^{83} +(1.79696 - 5.53046i) q^{85} +(10.4337 - 85.4543i) q^{86} +(-87.8882 - 4.43450i) q^{88} -46.7420 q^{89} +(12.6963 + 4.12527i) q^{91} +(-14.4423 + 58.2612i) q^{92} +(-88.0511 - 40.9862i) q^{94} +(-13.6519 + 4.43576i) q^{95} +(-86.8069 - 63.0689i) q^{97} +(59.3792 - 32.9671i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - 9 q^{4} + 6 q^{5} - 7 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 - 9 * q^4 + 6 * q^5 - 7 * q^8	\( 40 q + 5 q^{2} - 9 q^{4} + 6 q^{5} - 7 q^{8} - 8 q^{10} - 6 q^{13} + 36 q^{14} - 65 q^{16} + 30 q^{17} - 34 q^{20} + 25 q^{22} - 156 q^{26} + 130 q^{28} + 38 q^{29} - 20 q^{32} + 258 q^{34} - 150 q^{37} - 80 q^{38} + 112 q^{40} + 150 q^{41} - 4 q^{44} + 40 q^{46} + 132 q^{49} + 177 q^{50} - 314 q^{52} - 290 q^{53} + 856 q^{56} - 476 q^{58} + 42 q^{61} + 364 q^{62} + 303 q^{64} - 164 q^{65} - 14 q^{68} + 576 q^{70} + 186 q^{73} - 588 q^{74} + 366 q^{76} - 190 q^{77} - 1100 q^{80} + 365 q^{82} + 286 q^{85} + 501 q^{86} + 47 q^{88} + 88 q^{89} + 702 q^{92} - 678 q^{94} - 130 q^{97} + 652 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 - 9 * q^4 + 6 * q^5 - 7 * q^8 - 8 * q^10 - 6 * q^13 + 36 * q^14 - 65 * q^16 + 30 * q^17 - 34 * q^20 + 25 * q^22 - 156 * q^26 + 130 * q^28 + 38 * q^29 - 20 * q^32 + 258 * q^34 - 150 * q^37 - 80 * q^38 + 112 * q^40 + 150 * q^41 - 4 * q^44 + 40 * q^46 + 132 * q^49 + 177 * q^50 - 314 * q^52 - 290 * q^53 + 856 * q^56 - 476 * q^58 + 42 * q^61 + 364 * q^62 + 303 * q^64 - 164 * q^65 - 14 * q^68 + 576 * q^70 + 186 * q^73 - 588 * q^74 + 366 * q^76 - 190 * q^77 - 1100 * q^80 + 365 * q^82 + 286 * q^85 + 501 * q^86 + 47 * q^88 + 88 * q^89 + 702 * q^92 - 678 * q^94 - 130 * q^97 + 652 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more