LMFDB - Embedded newform 3850.2.c.ba.1849.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1849,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("3850.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.c (of order $2$, degree $1$, not 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:	$30.7424047782$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 770)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.4
Root			$1.40680 - 0.144584i$ of defining polynomial
Character	$\chi$	$=$	3850.1849
Dual form			3850.2.c.ba.1849.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -3.10278i q^{3} -1.00000 q^{4} +3.10278 q^{6} -1.00000i q^{7} -1.00000i q^{8} -6.62721 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -3.10278i q^{3} -1.00000 q^{4} +3.10278 q^{6} -1.00000i q^{7} -1.00000i q^{8} -6.62721 q^{9} +1.00000 q^{11} +3.10278i q^{12} +3.62721i q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.20555i q^{17} -6.62721i q^{18} +8.15165 q^{19} -3.10278 q^{21} +1.00000i q^{22} -0.897225i q^{23} -3.10278 q^{24} -3.62721 q^{26} +11.2544i q^{27} +1.00000i q^{28} +7.30833 q^{29} -3.42166 q^{31} +1.00000i q^{32} -3.10278i q^{33} +4.20555 q^{34} +6.62721 q^{36} -1.10278i q^{37} +8.15165i q^{38} +11.2544 q^{39} +12.3572 q^{41} -3.10278i q^{42} -10.6761i q^{43} -1.00000 q^{44} +0.897225 q^{46} -1.15667i q^{47} -3.10278i q^{48} -1.00000 q^{49} -13.0489 q^{51} -3.62721i q^{52} -11.3083i q^{53} -11.2544 q^{54} -1.00000 q^{56} -25.2927i q^{57} +7.30833i q^{58} -7.25443 q^{59} -3.15667 q^{61} -3.42166i q^{62} +6.62721i q^{63} -1.00000 q^{64} +3.10278 q^{66} -8.41110i q^{67} +4.20555i q^{68} -2.78389 q^{69} -13.0489 q^{71} +6.62721i q^{72} -0.205550i q^{73} +1.10278 q^{74} -8.15165 q^{76} -1.00000i q^{77} +11.2544i q^{78} -12.1517 q^{79} +15.0383 q^{81} +12.3572i q^{82} -2.20555i q^{83} +3.10278 q^{84} +10.6761 q^{86} -22.6761i q^{87} -1.00000i q^{88} +7.45998 q^{89} +3.62721 q^{91} +0.897225i q^{92} +10.6167i q^{93} +1.15667 q^{94} +3.10278 q^{96} +2.25945i q^{97} -1.00000i q^{98} -6.62721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 4 q^{6} - 14 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 4 * q^6 - 14 * q^9	$ 6 q - 6 q^{4} + 4 q^{6} - 14 q^{9} + 6 q^{11} + 6 q^{14} + 6 q^{16} + 12 q^{19} - 4 q^{21} - 4 q^{24} + 4 q^{26} - 24 q^{31} - 4 q^{34} + 14 q^{36} + 16 q^{39} + 8 q^{41} - 6 q^{44} + 20 q^{46} - 6 q^{49} - 56 q^{51} - 16 q^{54} - 6 q^{56} + 8 q^{59} - 12 q^{61} - 6 q^{64} + 4 q^{66} + 16 q^{69} - 56 q^{71} - 8 q^{74} - 12 q^{76} - 36 q^{79} + 6 q^{81} + 4 q^{84} + 16 q^{86} - 36 q^{89} - 4 q^{91} + 4 q^{96} - 14 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 4 * q^6 - 14 * q^9 + 6 * q^11 + 6 * q^14 + 6 * q^16 + 12 * q^19 - 4 * q^21 - 4 * q^24 + 4 * q^26 - 24 * q^31 - 4 * q^34 + 14 * q^36 + 16 * q^39 + 8 * q^41 - 6 * q^44 + 20 * q^46 - 6 * q^49 - 56 * q^51 - 16 * q^54 - 6 * q^56 + 8 * q^59 - 12 * q^61 - 6 * q^64 + 4 * q^66 + 16 * q^69 - 56 * q^71 - 8 * q^74 - 12 * q^76 - 36 * q^79 + 6 * q^81 + 4 * q^84 + 16 * q^86 - 36 * q^89 - 4 * q^91 + 4 * q^96 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times$.

$n$	$1751$	$2201$	$2927$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	− 3.10278i	− 1.79139i	−0.444671	−	0.895694i	$-0.646679\pi$
$3$	− 3.10278i	− 1.79139i	0.444671	−	0.895694i	$-0.353321\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	3.10278	1.26670
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	−6.62721	−2.20907
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.10278i	0.895694i
$13$	3.62721i	1.00601i	0.864284	+	0.503004i	$0.167772\pi$
$13$	3.62721i	1.00601i	−0.864284	+	0.503004i	$0.832228\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.20555i	− 1.02000i	−0.860176	−	0.509998i	$-0.829646\pi$
$17$	− 4.20555i	− 1.02000i	0.860176	−	0.509998i	$-0.170354\pi$
$18$	− 6.62721i	− 1.56205i
$19$	8.15165	1.87012	0.935058	−	0.354493i	$-0.115347\pi$
$19$	8.15165	1.87012	0.935058	+	0.354493i	$0.115347\pi$
$20$	0	0
$21$	−3.10278	−0.677081
$22$	1.00000i	0.213201i
$23$	− 0.897225i	− 0.187084i	−0.995615	−	0.0935422i	$-0.970181\pi$
$23$	− 0.897225i	− 0.187084i	0.995615	−	0.0935422i	$-0.0298190\pi$
$24$	−3.10278	−0.633351
$25$	0	0
$26$	−3.62721	−0.711355
$27$	11.2544i	2.16592i
$28$	1.00000i	0.188982i
$29$	7.30833	1.35712	0.678561	−	0.734544i	$-0.262604\pi$
$29$	7.30833	1.35712	0.678561	+	0.734544i	$0.262604\pi$
$30$	0	0
$31$	−3.42166	−0.614549	−0.307274	−	0.951621i	$-0.599417\pi$
$31$	−3.42166	−0.614549	−0.307274	+	0.951621i	$0.599417\pi$
$32$	1.00000i	0.176777i
$33$	− 3.10278i	− 0.540124i
$34$	4.20555	0.721246
$35$	0	0
$36$	6.62721	1.10454
$37$	− 1.10278i	− 0.181295i	−0.995883	−	0.0906476i	$-0.971106\pi$
$37$	− 1.10278i	− 0.181295i	0.995883	−	0.0906476i	$-0.0288937\pi$
$38$	8.15165i	1.32237i
$39$	11.2544	1.80215
$40$	0	0
$41$	12.3572	1.92987	0.964935	−	0.262488i	$-0.0845430\pi$
$41$	12.3572	1.92987	0.964935	+	0.262488i	$0.0845430\pi$
$42$	− 3.10278i	− 0.478769i
$43$	− 10.6761i	− 1.62809i	−0.580803	−	0.814044i	$-0.697261\pi$
$43$	− 10.6761i	− 1.62809i	0.580803	−	0.814044i	$-0.302739\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	0.897225	0.132289
$47$	− 1.15667i	− 0.168718i	−0.996435	−	0.0843591i	$-0.973116\pi$
$47$	− 1.15667i	− 0.168718i	0.996435	−	0.0843591i	$-0.0268843\pi$
$48$	− 3.10278i	− 0.447847i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	−13.0489	−1.82721
$52$	− 3.62721i	− 0.503004i
$53$	− 11.3083i	− 1.55332i	−0.629921	−	0.776659i	$-0.716913\pi$
$53$	− 11.3083i	− 1.55332i	0.629921	−	0.776659i	$-0.283087\pi$
$54$	−11.2544	−1.53153
$55$	0	0
$56$	−1.00000	−0.133631
$57$	− 25.2927i	− 3.35011i
$58$	7.30833i	0.959630i
$59$	−7.25443	−0.944446	−0.472223	−	0.881479i	$-0.656548\pi$
$59$	−7.25443	−0.944446	−0.472223	+	0.881479i	$0.656548\pi$
$60$	0	0
$61$	−3.15667	−0.404171	−0.202085	−	0.979368i	$-0.564772\pi$
$61$	−3.15667	−0.404171	−0.202085	+	0.979368i	$0.564772\pi$
$62$	− 3.42166i	− 0.434552i
$63$	6.62721i	0.834950i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	3.10278	0.381925
$67$	− 8.41110i	− 1.02758i	−0.857916	−	0.513790i	$-0.828241\pi$
$67$	− 8.41110i	− 1.02758i	0.857916	−	0.513790i	$-0.171759\pi$
$68$	4.20555i	0.509998i
$69$	−2.78389	−0.335141
$70$	0	0
$71$	−13.0489	−1.54862	−0.774308	−	0.632809i	$-0.781902\pi$
$71$	−13.0489	−1.54862	−0.774308	+	0.632809i	$0.781902\pi$
$72$	6.62721i	0.781025i
$73$	− 0.205550i	− 0.0240578i	−0.999928	−	0.0120289i	$-0.996171\pi$
$73$	− 0.205550i	− 0.0240578i	0.999928	−	0.0120289i	$-0.00382901\pi$
$74$	1.10278	0.128195
$75$	0	0
$76$	−8.15165	−0.935058
$77$	− 1.00000i	− 0.113961i
$78$	11.2544i	1.27431i
$79$	−12.1517	−1.36717	−0.683584	−	0.729872i	$-0.739580\pi$
$79$	−12.1517	−1.36717	−0.683584	+	0.729872i	$0.739580\pi$
$80$	0	0
$81$	15.0383	1.67092
$82$	12.3572i	1.36462i
$83$	− 2.20555i	− 0.242091i	−0.992647	−	0.121045i	$-0.961375\pi$
$83$	− 2.20555i	− 0.242091i	0.992647	−	0.121045i	$-0.0386246\pi$
$84$	3.10278	0.338541
$85$	0	0
$86$	10.6761	1.15123
$87$	− 22.6761i	− 2.43113i
$88$	− 1.00000i	− 0.106600i
$89$	7.45998	0.790756	0.395378	−	0.918519i	$-0.370614\pi$
$89$	7.45998	0.790756	0.395378	+	0.918519i	$0.370614\pi$
$90$	0	0
$91$	3.62721	0.380235
$92$	0.897225i	0.0935422i
$93$	10.6167i	1.10090i
$94$	1.15667	0.119302
$95$	0	0
$96$	3.10278	0.316676
$97$	2.25945i	0.229412i	0.993399	+	0.114706i	$0.0365926\pi$
$97$	2.25945i	0.229412i	−0.993399	+	0.114706i	$0.963407\pi$
$98$	− 1.00000i	− 0.101015i
$99$	−6.62721	−0.666060
$100$	0	0
$101$	13.6655	1.35977	0.679885	−	0.733318i	$-0.262030\pi$
$101$	13.6655	1.35977	0.679885	+	0.733318i	$0.262030\pi$
$102$	− 13.0489i	− 1.29203i
$103$	5.04888i	0.497481i	0.968570	+	0.248740i	$0.0800166\pi$
$103$	5.04888i	0.497481i	−0.968570	+	0.248740i	$0.919983\pi$
$104$	3.62721	0.355677
$105$	0	0
$106$	11.3083	1.09836
$107$	12.9894i	1.25574i	0.778320	+	0.627868i	$0.216072\pi$
$107$	12.9894i	1.25574i	−0.778320	+	0.627868i	$0.783928\pi$
$108$	− 11.2544i	− 1.08296i
$109$	−5.10278	−0.488757	−0.244379	−	0.969680i	$-0.578584\pi$
$109$	−5.10278	−0.488757	−0.244379	+	0.969680i	$0.578584\pi$
$110$	0	0
$111$	−3.42166	−0.324770
$112$	− 1.00000i	− 0.0944911i
$113$	10.4111i	0.979394i	0.871893	+	0.489697i	$0.162893\pi$
$113$	10.4111i	0.979394i	−0.871893	+	0.489697i	$0.837107\pi$
$114$	25.2927	2.36888
$115$	0	0
$116$	−7.30833	−0.678561
$117$	− 24.0383i	− 2.22234i
$118$	− 7.25443i	− 0.667824i
$119$	−4.20555	−0.385522
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 3.15667i	− 0.285792i
$123$	− 38.3416i	− 3.45715i
$124$	3.42166	0.307274
$125$	0	0
$126$	−6.62721	−0.590399
$127$	3.25443i	0.288784i	0.989521	+	0.144392i	$0.0461226\pi$
$127$	3.25443i	0.288784i	−0.989521	+	0.144392i	$0.953877\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−33.1255	−2.91654
$130$	0	0
$131$	−17.3083	−1.51224	−0.756118	−	0.654436i	$-0.772906\pi$
$131$	−17.3083	−1.51224	−0.756118	+	0.654436i	$0.772906\pi$
$132$	3.10278i	0.270062i
$133$	− 8.15165i	− 0.706838i
$134$	8.41110	0.726608
$135$	0	0
$136$	−4.20555	−0.360623
$137$	10.0000i	0.854358i	0.904167	+	0.427179i	$0.140493\pi$
$137$	10.0000i	0.854358i	−0.904167	+	0.427179i	$0.859507\pi$
$138$	− 2.78389i	− 0.236980i
$139$	−13.2005	−1.11965	−0.559827	−	0.828609i	$-0.689132\pi$
$139$	−13.2005	−1.11965	−0.559827	+	0.828609i	$0.689132\pi$
$140$	0	0
$141$	−3.58890	−0.302240
$142$	− 13.0489i	− 1.09504i
$143$	3.62721i	0.303323i
$144$	−6.62721	−0.552268
$145$	0	0
$146$	0.205550	0.0170114
$147$	3.10278i	0.255913i
$148$	1.10278i	0.0906476i
$149$	23.6116	1.93434	0.967170	−	0.254131i	$-0.0817893\pi$
$149$	23.6116	1.93434	0.967170	+	0.254131i	$0.0817893\pi$
$150$	0	0
$151$	11.5139	0.936986	0.468493	−	0.883467i	$-0.344797\pi$
$151$	11.5139	0.936986	0.468493	+	0.883467i	$0.344797\pi$
$152$	− 8.15165i	− 0.661186i
$153$	27.8711i	2.25324i
$154$	1.00000	0.0805823
$155$	0	0
$156$	−11.2544	−0.901075
$157$	− 16.2056i	− 1.29334i	−0.762768	−	0.646672i	$-0.776160\pi$
$157$	− 16.2056i	− 1.29334i	0.762768	−	0.646672i	$-0.223840\pi$
$158$	− 12.1517i	− 0.966733i
$159$	−35.0872	−2.78260
$160$	0	0
$161$	−0.897225	−0.0707112
$162$	15.0383i	1.18152i
$163$	− 6.31335i	− 0.494500i	−0.968952	−	0.247250i	$-0.920473\pi$
$163$	− 6.31335i	− 0.494500i	0.968952	−	0.247250i	$-0.0795268\pi$
$164$	−12.3572	−0.964935
$165$	0	0
$166$	2.20555	0.171184
$167$	− 8.00000i	− 0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$	− 8.00000i	− 0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$	3.10278i	0.239384i
$169$	−0.156674	−0.0120519
$170$	0	0
$171$	−54.0227	−4.13122
$172$	10.6761i	0.814044i
$173$	− 9.25443i	− 0.703601i	−0.936075	−	0.351800i	$-0.885570\pi$
$173$	− 9.25443i	− 0.703601i	0.936075	−	0.351800i	$-0.114430\pi$
$174$	22.6761	1.71907
$175$	0	0
$176$	1.00000	0.0753778
$177$	22.5089i	1.69187i
$178$	7.45998i	0.559149i
$179$	−4.98944	−0.372928	−0.186464	−	0.982462i	$-0.559703\pi$
$179$	−4.98944	−0.372928	−0.186464	+	0.982462i	$0.559703\pi$
$180$	0	0
$181$	−9.66553	−0.718433	−0.359216	−	0.933254i	$-0.616956\pi$
$181$	−9.66553	−0.718433	−0.359216	+	0.933254i	$0.616956\pi$
$182$	3.62721i	0.268867i
$183$	9.79445i	0.724027i
$184$	−0.897225	−0.0661443
$185$	0	0
$186$	−10.6167	−0.778451
$187$	− 4.20555i	− 0.307540i
$188$	1.15667i	0.0843591i
$189$	11.2544	0.818639
$190$	0	0
$191$	−9.15667	−0.662554	−0.331277	−	0.943534i	$-0.607479\pi$
$191$	−9.15667	−0.662554	−0.331277	+	0.943534i	$0.607479\pi$
$192$	3.10278i	0.223924i
$193$	− 1.52946i	− 0.110093i	−0.998484	−	0.0550465i	$-0.982469\pi$
$193$	− 1.52946i	− 0.110093i	0.998484	−	0.0550465i	$-0.0175307\pi$
$194$	−2.25945	−0.162219
$195$	0	0
$196$	1.00000	0.0714286
$197$	14.3033i	1.01907i	0.860451	+	0.509534i	$0.170182\pi$
$197$	14.3033i	1.01907i	−0.860451	+	0.509534i	$0.829818\pi$
$198$	− 6.62721i	− 0.470976i
$199$	10.0978	0.715811	0.357905	−	0.933758i	$-0.383491\pi$
$199$	10.0978	0.715811	0.357905	+	0.933758i	$0.383491\pi$
$200$	0	0
$201$	−26.0978	−1.84079
$202$	13.6655i	0.961503i
$203$	− 7.30833i	− 0.512944i
$204$	13.0489	0.913604
$205$	0	0
$206$	−5.04888	−0.351772
$207$	5.94610i	0.413283i
$208$	3.62721i	0.251502i
$209$	8.15165	0.563861
$210$	0	0
$211$	10.8433	0.746485	0.373243	−	0.927734i	$-0.378246\pi$
$211$	10.8433	0.746485	0.373243	+	0.927734i	$0.378246\pi$
$212$	11.3083i	0.776659i
$213$	40.4877i	2.77417i
$214$	−12.9894	−0.887940
$215$	0	0
$216$	11.2544	0.765767
$217$	3.42166i	0.232278i
$218$	− 5.10278i	− 0.345604i
$219$	−0.637776	−0.0430969
$220$	0	0
$221$	15.2544	1.02612
$222$	− 3.42166i	− 0.229647i
$223$	9.45998i	0.633487i	0.948511	+	0.316743i	$0.102589\pi$
$223$	9.45998i	0.633487i	−0.948511	+	0.316743i	$0.897411\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−10.4111	−0.692536
$227$	− 17.5678i	− 1.16601i	−0.812467	−	0.583007i	$-0.801876\pi$
$227$	− 17.5678i	− 1.16601i	0.812467	−	0.583007i	$-0.198124\pi$
$228$	25.2927i	1.67505i
$229$	−25.7250	−1.69995	−0.849977	−	0.526820i	$-0.823384\pi$
$229$	−25.7250	−1.69995	−0.849977	+	0.526820i	$0.823384\pi$
$230$	0	0
$231$	−3.10278	−0.204148
$232$	− 7.30833i	− 0.479815i
$233$	− 19.1567i	− 1.25500i	−0.778618	−	0.627498i	$-0.784079\pi$
$233$	− 19.1567i	− 1.25500i	0.778618	−	0.627498i	$-0.215921\pi$
$234$	24.0383	1.57143
$235$	0	0
$236$	7.25443	0.472223
$237$	37.7038i	2.44913i
$238$	− 4.20555i	− 0.272605i
$239$	18.0539	1.16781	0.583905	−	0.811822i	$-0.301524\pi$
$239$	18.0539	1.16781	0.583905	+	0.811822i	$0.301524\pi$
$240$	0	0
$241$	6.15165	0.396263	0.198131	−	0.980175i	$-0.436513\pi$
$241$	6.15165	0.396263	0.198131	+	0.980175i	$0.436513\pi$
$242$	1.00000i	0.0642824i
$243$	− 12.8972i	− 0.827357i
$244$	3.15667	0.202085
$245$	0	0
$246$	38.3416	2.44457
$247$	29.5678i	1.88135i
$248$	3.42166i	0.217276i
$249$	−6.84333	−0.433678
$250$	0	0
$251$	−29.9789	−1.89225	−0.946125	−	0.323802i	$-0.895039\pi$
$251$	−29.9789	−1.89225	−0.946125	+	0.323802i	$0.895039\pi$
$252$	− 6.62721i	− 0.417475i
$253$	− 0.897225i	− 0.0564080i
$254$	−3.25443	−0.204201
$255$	0	0
$256$	1.00000	0.0625000
$257$	4.05390i	0.252875i	0.991975	+	0.126438i	$0.0403544\pi$
$257$	4.05390i	0.252875i	−0.991975	+	0.126438i	$0.959646\pi$
$258$	− 33.1255i	− 2.06230i
$259$	−1.10278	−0.0685231
$260$	0	0
$261$	−48.4338	−2.99798
$262$	− 17.3083i	− 1.06931i
$263$	14.5089i	0.894654i	0.894370	+	0.447327i	$0.147624\pi$
$263$	14.5089i	0.894654i	−0.894370	+	0.447327i	$0.852376\pi$
$264$	−3.10278	−0.190963
$265$	0	0
$266$	8.15165	0.499810
$267$	− 23.1466i	− 1.41655i
$268$	8.41110i	0.513790i
$269$	−4.37279	−0.266614	−0.133307	−	0.991075i	$-0.542560\pi$
$269$	−4.37279	−0.266614	−0.133307	+	0.991075i	$0.542560\pi$
$270$	0	0
$271$	−10.6167	−0.644916	−0.322458	−	0.946584i	$-0.604509\pi$
$271$	−10.6167	−0.644916	−0.322458	+	0.946584i	$0.604509\pi$
$272$	− 4.20555i	− 0.254999i
$273$	− 11.2544i	− 0.681149i
$274$	−10.0000	−0.604122
$275$	0	0
$276$	2.78389	0.167570
$277$	− 19.7633i	− 1.18746i	−0.804664	−	0.593730i	$-0.797655\pi$
$277$	− 19.7633i	− 1.18746i	0.804664	−	0.593730i	$-0.202345\pi$
$278$	− 13.2005i	− 0.791715i
$279$	22.6761	1.35758
$280$	0	0
$281$	−27.0489	−1.61360	−0.806800	−	0.590824i	$-0.798803\pi$
$281$	−27.0489	−1.61360	−0.806800	+	0.590824i	$0.798803\pi$
$282$	− 3.58890i	− 0.213716i
$283$	− 27.6655i	− 1.64454i	−0.569094	−	0.822272i	$-0.692706\pi$
$283$	− 27.6655i	− 1.64454i	0.569094	−	0.822272i	$-0.307294\pi$
$284$	13.0489	0.774308
$285$	0	0
$286$	−3.62721	−0.214482
$287$	− 12.3572i	− 0.729423i
$288$	− 6.62721i	− 0.390512i
$289$	−0.686652	−0.0403913
$290$	0	0
$291$	7.01056	0.410966
$292$	0.205550i	0.0120289i
$293$	8.37279i	0.489143i	0.969631	+	0.244572i	$0.0786474\pi$
$293$	8.37279i	0.489143i	−0.969631	+	0.244572i	$0.921353\pi$
$294$	−3.10278	−0.180958
$295$	0	0
$296$	−1.10278	−0.0640975
$297$	11.2544i	0.653048i
$298$	23.6116i	1.36778i
$299$	3.25443	0.188208
$300$	0	0
$301$	−10.6761	−0.615360
$302$	11.5139i	0.662549i
$303$	− 42.4011i	− 2.43588i
$304$	8.15165	0.467529
$305$	0	0
$306$	−27.8711	−1.59328
$307$	− 10.2056i	− 0.582462i	−0.956653	−	0.291231i	$-0.905935\pi$
$307$	− 10.2056i	− 0.582462i	0.956653	−	0.291231i	$-0.0940647\pi$
$308$	1.00000i	0.0569803i
$309$	15.6655	0.891181
$310$	0	0
$311$	−8.16724	−0.463122	−0.231561	−	0.972820i	$-0.574383\pi$
$311$	−8.16724	−0.463122	−0.231561	+	0.972820i	$0.574383\pi$
$312$	− 11.2544i	− 0.637156i
$313$	− 34.5628i	− 1.95360i	−0.214149	−	0.976801i	$-0.568698\pi$
$313$	− 34.5628i	− 1.95360i	0.214149	−	0.976801i	$-0.431302\pi$
$314$	16.2056	0.914532
$315$	0	0
$316$	12.1517	0.683584
$317$	9.21057i	0.517317i	0.965969	+	0.258659i	$0.0832805\pi$
$317$	9.21057i	0.517317i	−0.965969	+	0.258659i	$0.916720\pi$
$318$	− 35.0872i	− 1.96759i
$319$	7.30833	0.409188
$320$	0	0
$321$	40.3033	2.24951
$322$	− 0.897225i	− 0.0500004i
$323$	− 34.2822i	− 1.90751i
$324$	−15.0383	−0.835462
$325$	0	0
$326$	6.31335	0.349664
$327$	15.8328i	0.875554i
$328$	− 12.3572i	− 0.682312i
$329$	−1.15667	−0.0637695
$330$	0	0
$331$	16.2439	0.892843	0.446422	−	0.894823i	$-0.352698\pi$
$331$	16.2439	0.892843	0.446422	+	0.894823i	$0.352698\pi$
$332$	2.20555i	0.121045i
$333$	7.30833i	0.400494i
$334$	8.00000	0.437741
$335$	0	0
$336$	−3.10278	−0.169270
$337$	− 1.25443i	− 0.0683329i	−0.999416	−	0.0341665i	$-0.989122\pi$
$337$	− 1.25443i	− 0.0683329i	0.999416	−	0.0341665i	$-0.0108776\pi$
$338$	− 0.156674i	− 0.00852195i
$339$	32.3033	1.75447
$340$	0	0
$341$	−3.42166	−0.185293
$342$	− 54.0227i	− 2.92121i
$343$	1.00000i	0.0539949i
$344$	−10.6761	−0.575616
$345$	0	0
$346$	9.25443	0.497521
$347$	7.42166i	0.398416i	0.979957	+	0.199208i	$0.0638369\pi$
$347$	7.42166i	0.398416i	−0.979957	+	0.199208i	$0.936163\pi$
$348$	22.6761i	1.21557i
$349$	18.3033	0.979753	0.489877	−	0.871792i	$-0.337042\pi$
$349$	18.3033	0.979753	0.489877	+	0.871792i	$0.337042\pi$
$350$	0	0
$351$	−40.8222	−2.17893
$352$	1.00000i	0.0533002i
$353$	− 28.8761i	− 1.53692i	−0.639898	−	0.768460i	$-0.721023\pi$
$353$	− 28.8761i	− 1.53692i	0.639898	−	0.768460i	$-0.278977\pi$
$354$	−22.5089	−1.19633
$355$	0	0
$356$	−7.45998	−0.395378
$357$	13.0489i	0.690620i
$358$	− 4.98944i	− 0.263700i
$359$	−4.15165	−0.219116	−0.109558	−	0.993980i	$-0.534943\pi$
$359$	−4.15165	−0.219116	−0.109558	+	0.993980i	$0.534943\pi$
$360$	0	0
$361$	47.4494	2.49734
$362$	− 9.66553i	− 0.508009i
$363$	− 3.10278i	− 0.162853i
$364$	−3.62721	−0.190118
$365$	0	0
$366$	−9.79445	−0.511964
$367$	− 5.26447i	− 0.274803i	−0.990515	−	0.137402i	$-0.956125\pi$
$367$	− 5.26447i	− 0.274803i	0.990515	−	0.137402i	$-0.0438751\pi$
$368$	− 0.897225i	− 0.0467711i
$369$	−81.8938	−4.26322
$370$	0	0
$371$	−11.3083	−0.587099
$372$	− 10.6167i	− 0.550448i
$373$	− 35.8711i	− 1.85733i	−0.370915	−	0.928667i	$-0.620956\pi$
$373$	− 35.8711i	− 1.85733i	0.370915	−	0.928667i	$-0.379044\pi$
$374$	4.20555	0.217464
$375$	0	0
$376$	−1.15667	−0.0596509
$377$	26.5089i	1.36528i
$378$	11.2544i	0.578865i
$379$	33.0177	1.69601	0.848003	−	0.529992i	$-0.177805\pi$
$379$	33.0177	1.69601	0.848003	+	0.529992i	$0.177805\pi$
$380$	0	0
$381$	10.0978	0.517323
$382$	− 9.15667i	− 0.468496i
$383$	− 2.95112i	− 0.150795i	−0.997154	−	0.0753977i	$-0.975977\pi$
$383$	− 2.95112i	− 0.150795i	0.997154	−	0.0753977i	$-0.0240226\pi$
$384$	−3.10278	−0.158338
$385$	0	0
$386$	1.52946	0.0778475
$387$	70.7527i	3.59656i
$388$	− 2.25945i	− 0.114706i
$389$	−1.89220	−0.0959384	−0.0479692	−	0.998849i	$-0.515275\pi$
$389$	−1.89220	−0.0959384	−0.0479692	+	0.998849i	$0.515275\pi$
$390$	0	0
$391$	−3.77332	−0.190825
$392$	1.00000i	0.0505076i
$393$	53.7038i	2.70900i
$394$	−14.3033	−0.720590
$395$	0	0
$396$	6.62721	0.333030
$397$	5.36222i	0.269122i	0.990905	+	0.134561i	$0.0429625\pi$
$397$	5.36222i	0.269122i	−0.990905	+	0.134561i	$0.957038\pi$
$398$	10.0978i	0.506155i
$399$	−25.2927	−1.26622
$400$	0	0
$401$	23.7038	1.18371	0.591857	−	0.806043i	$-0.298395\pi$
$401$	23.7038	1.18371	0.591857	+	0.806043i	$0.298395\pi$
$402$	− 26.0978i	− 1.30164i
$403$	− 12.4111i	− 0.618241i
$404$	−13.6655	−0.679885
$405$	0	0
$406$	7.30833	0.362706
$407$	− 1.10278i	− 0.0546625i
$408$	13.0489i	0.646016i
$409$	−27.0816	−1.33910	−0.669551	−	0.742766i	$-0.733513\pi$
$409$	−27.0816	−1.33910	−0.669551	+	0.742766i	$0.733513\pi$
$410$	0	0
$411$	31.0278	1.53049
$412$	− 5.04888i	− 0.248740i
$413$	7.25443i	0.356967i
$414$	−5.94610	−0.292235
$415$	0	0
$416$	−3.62721	−0.177839
$417$	40.9583i	2.00573i
$418$	8.15165i	0.398710i
$419$	3.05892	0.149438	0.0747191	−	0.997205i	$-0.476194\pi$
$419$	3.05892	0.149438	0.0747191	+	0.997205i	$0.476194\pi$
$420$	0	0
$421$	21.6655	1.05591	0.527957	−	0.849271i	$-0.322958\pi$
$421$	21.6655	1.05591	0.527957	+	0.849271i	$0.322958\pi$
$422$	10.8433i	0.527845i
$423$	7.66553i	0.372711i
$424$	−11.3083	−0.549181
$425$	0	0
$426$	−40.4877	−1.96164
$427$	3.15667i	0.152762i
$428$	− 12.9894i	− 0.627868i
$429$	11.2544	0.543369
$430$	0	0
$431$	−34.3260	−1.65343	−0.826713	−	0.562623i	$-0.809792\pi$
$431$	−34.3260	−1.65343	−0.826713	+	0.562623i	$0.809792\pi$
$432$	11.2544i	0.541479i
$433$	0.0538991i	0.00259023i	0.999999	+	0.00129511i	$0.000412248\pi$
$433$	0.0538991i	0.00259023i	−0.999999	+	0.00129511i	$0.999588\pi$
$434$	−3.42166	−0.164245
$435$	0	0
$436$	5.10278	0.244379
$437$	− 7.31386i	− 0.349870i
$438$	− 0.637776i	− 0.0304741i
$439$	7.14663	0.341090	0.170545	−	0.985350i	$-0.445447\pi$
$439$	7.14663	0.341090	0.170545	+	0.985350i	$0.445447\pi$
$440$	0	0
$441$	6.62721	0.315582
$442$	15.2544i	0.725579i
$443$	− 8.74557i	− 0.415515i	−0.978180	−	0.207757i	$-0.933384\pi$
$443$	− 8.74557i	− 0.415515i	0.978180	−	0.207757i	$-0.0666165\pi$
$444$	3.42166	0.162385
$445$	0	0
$446$	−9.45998	−0.447943
$447$	− 73.2616i	− 3.46515i
$448$	1.00000i	0.0472456i
$449$	−39.7038	−1.87374	−0.936870	−	0.349678i	$-0.886291\pi$
$449$	−39.7038	−1.87374	−0.936870	+	0.349678i	$0.886291\pi$
$450$	0	0
$451$	12.3572	0.581878
$452$	− 10.4111i	− 0.489697i
$453$	− 35.7250i	− 1.67851i
$454$	17.5678	0.824497
$455$	0	0
$456$	−25.2927	−1.18444
$457$	12.3133i	0.575994i	0.957631	+	0.287997i	$0.0929893\pi$
$457$	12.3133i	0.575994i	−0.957631	+	0.287997i	$0.907011\pi$
$458$	− 25.7250i	− 1.20205i
$459$	47.3311	2.20922
$460$	0	0
$461$	−15.0489	−0.700896	−0.350448	−	0.936582i	$-0.613971\pi$
$461$	−15.0489	−0.700896	−0.350448	+	0.936582i	$0.613971\pi$
$462$	− 3.10278i	− 0.144354i
$463$	− 31.4061i	− 1.45956i	−0.683680	−	0.729782i	$-0.739622\pi$
$463$	− 31.4061i	− 1.45956i	0.683680	−	0.729782i	$-0.260378\pi$
$464$	7.30833	0.339280
$465$	0	0
$466$	19.1567	0.887416
$467$	− 19.0716i	− 0.882529i	−0.897377	−	0.441264i	$-0.854530\pi$
$467$	− 19.0716i	− 0.882529i	0.897377	−	0.441264i	$-0.145470\pi$
$468$	24.0383i	1.11117i
$469$	−8.41110	−0.388389
$470$	0	0
$471$	−50.2822	−2.31688
$472$	7.25443i	0.333912i
$473$	− 10.6761i	− 0.490887i
$474$	−37.7038	−1.73179
$475$	0	0
$476$	4.20555	0.192761
$477$	74.9427i	3.43139i
$478$	18.0539i	0.825766i
$479$	9.49115	0.433662	0.216831	−	0.976209i	$-0.430428\pi$
$479$	9.49115	0.433662	0.216831	+	0.976209i	$0.430428\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	6.15165i	0.280200i
$483$	2.78389i	0.126671i
$484$	−1.00000	−0.0454545
$485$	0	0
$486$	12.8972	0.585030
$487$	0.0438527i	0.00198715i	1.00000		0.000993577i	$0.000316266\pi$
$487$	0.0438527i	0.00198715i	−1.00000		0.000993577i	$0.999684\pi$
$488$	3.15667i	0.142896i
$489$	−19.5889	−0.885841
$490$	0	0
$491$	1.56777	0.0707527	0.0353763	−	0.999374i	$-0.488737\pi$
$491$	1.56777	0.0707527	0.0353763	+	0.999374i	$0.488737\pi$
$492$	38.3416i	1.72857i
$493$	− 30.7355i	− 1.38426i
$494$	−29.5678	−1.33032
$495$	0	0
$496$	−3.42166	−0.153637
$497$	13.0489i	0.585322i
$498$	− 6.84333i	− 0.306657i
$499$	42.3416	1.89547	0.947736	−	0.319057i	$-0.103366\pi$
$499$	42.3416	1.89547	0.947736	+	0.319057i	$0.103366\pi$
$500$	0	0
$501$	−24.8222	−1.10897
$502$	− 29.9789i	− 1.33802i
$503$	36.4111i	1.62349i	0.584012	+	0.811745i	$0.301482\pi$
$503$	36.4111i	1.62349i	−0.584012	+	0.811745i	$0.698518\pi$
$504$	6.62721	0.295200
$505$	0	0
$506$	0.897225	0.0398865
$507$	0.486125i	0.0215896i
$508$	− 3.25443i	− 0.144392i
$509$	30.0766	1.33312	0.666562	−	0.745450i	$-0.267765\pi$
$509$	30.0766	1.33312	0.666562	+	0.745450i	$0.267765\pi$
$510$	0	0
$511$	−0.205550	−0.00909300
$512$	1.00000i	0.0441942i
$513$	91.7422i	4.05051i
$514$	−4.05390	−0.178810
$515$	0	0
$516$	33.1255	1.45827
$517$	− 1.15667i	− 0.0508705i
$518$	− 1.10278i	− 0.0484532i
$519$	−28.7144	−1.26042
$520$	0	0
$521$	−33.2233	−1.45554	−0.727769	−	0.685823i	$-0.759443\pi$
$521$	−33.2233	−1.45554	−0.727769	+	0.685823i	$0.759443\pi$
$522$	− 48.4338i	− 2.11989i
$523$	15.5577i	0.680292i	0.940373	+	0.340146i	$0.110476\pi$
$523$	15.5577i	0.680292i	−0.940373	+	0.340146i	$0.889524\pi$
$524$	17.3083	0.756118
$525$	0	0
$526$	−14.5089	−0.632616
$527$	14.3900i	0.626837i
$528$	− 3.10278i	− 0.135031i
$529$	22.1950	0.964999
$530$	0	0
$531$	48.0766	2.08635
$532$	8.15165i	0.353419i
$533$	44.8222i	1.94147i
$534$	23.1466	1.00165
$535$	0	0
$536$	−8.41110	−0.363304
$537$	15.4811i	0.668059i
$538$	− 4.37279i	− 0.188524i
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	23.4161	1.00674	0.503369	−	0.864072i	$-0.332094\pi$
$541$	23.4161	1.00674	0.503369	+	0.864072i	$0.332094\pi$
$542$	− 10.6167i	− 0.456024i
$543$	29.9900i	1.28699i
$544$	4.20555	0.180311
$545$	0	0
$546$	11.2544	0.481645
$547$	− 8.41110i	− 0.359633i	−0.983700	−	0.179816i	$-0.942450\pi$
$547$	− 8.41110i	− 0.359633i	0.983700	−	0.179816i	$-0.0575503\pi$
$548$	− 10.0000i	− 0.427179i
$549$	20.9200	0.892842
$550$	0	0
$551$	59.5749	2.53798
$552$	2.78389i	0.118490i
$553$	12.1517i	0.516741i
$554$	19.7633	0.839661
$555$	0	0
$556$	13.2005	0.559827
$557$	37.0278i	1.56892i	0.620182	+	0.784458i	$0.287059\pi$
$557$	37.0278i	1.56892i	−0.620182	+	0.784458i	$0.712941\pi$
$558$	22.6761i	0.959955i
$559$	38.7244	1.63787
$560$	0	0
$561$	−13.0489	−0.550924
$562$	− 27.0489i	− 1.14099i
$563$	− 22.9200i	− 0.965961i	−0.875631	−	0.482980i	$-0.839554\pi$
$563$	− 22.9200i	− 0.965961i	0.875631	−	0.482980i	$-0.160446\pi$
$564$	3.58890	0.151120
$565$	0	0
$566$	27.6655	1.16287
$567$	− 15.0383i	− 0.631550i
$568$	13.0489i	0.547519i
$569$	22.0000	0.922288	0.461144	−	0.887325i	$-0.347439\pi$
$569$	22.0000	0.922288	0.461144	+	0.887325i	$0.347439\pi$
$570$	0	0
$571$	20.3033	0.849667	0.424833	−	0.905272i	$-0.360333\pi$
$571$	20.3033	0.849667	0.424833	+	0.905272i	$0.360333\pi$
$572$	− 3.62721i	− 0.151661i
$573$	28.4111i	1.18689i
$574$	12.3572	0.515780
$575$	0	0
$576$	6.62721	0.276134
$577$	16.4650i	0.685447i	0.939436	+	0.342723i	$0.111349\pi$
$577$	16.4650i	0.685447i	−0.939436	+	0.342723i	$0.888651\pi$
$578$	− 0.686652i	− 0.0285609i
$579$	−4.74557	−0.197219
$580$	0	0
$581$	−2.20555	−0.0915016
$582$	7.01056i	0.290597i
$583$	− 11.3083i	− 0.468343i
$584$	−0.205550	−0.00850572
$585$	0	0
$586$	−8.37279	−0.345877
$587$	− 30.6605i	− 1.26549i	−0.774358	−	0.632747i	$-0.781927\pi$
$587$	− 30.6605i	− 1.26549i	0.774358	−	0.632747i	$-0.218073\pi$
$588$	− 3.10278i	− 0.127956i
$589$	−27.8922	−1.14928
$590$	0	0
$591$	44.3799	1.82555
$592$	− 1.10278i	− 0.0453238i
$593$	− 18.3033i	− 0.751627i	−0.926695	−	0.375813i	$-0.877363\pi$
$593$	− 18.3033i	− 0.751627i	0.926695	−	0.375813i	$-0.122637\pi$
$594$	−11.2544	−0.461775
$595$	0	0
$596$	−23.6116	−0.967170
$597$	− 31.3311i	− 1.28229i
$598$	3.25443i	0.133083i
$599$	−29.6555	−1.21169	−0.605845	−	0.795583i	$-0.707165\pi$
$599$	−29.6555	−1.21169	−0.605845	+	0.795583i	$0.707165\pi$
$600$	0	0
$601$	18.7783	0.765985	0.382992	−	0.923751i	$-0.374894\pi$
$601$	18.7783	0.765985	0.382992	+	0.923751i	$0.374894\pi$
$602$	− 10.6761i	− 0.435125i
$603$	55.7422i	2.27000i
$604$	−11.5139	−0.468493
$605$	0	0
$606$	42.4011	1.72243
$607$	14.6761i	0.595684i	0.954615	+	0.297842i	$0.0962669\pi$
$607$	14.6761i	0.595684i	−0.954615	+	0.297842i	$0.903733\pi$
$608$	8.15165i	0.330593i
$609$	−22.6761	−0.918881
$610$	0	0
$611$	4.19550	0.169732
$612$	− 27.8711i	− 1.12662i
$613$	5.28560i	0.213483i	0.994287	+	0.106742i	$0.0340418\pi$
$613$	5.28560i	0.213483i	−0.994287	+	0.106742i	$0.965958\pi$
$614$	10.2056	0.411862
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	− 44.6933i	− 1.79928i	−0.436629	−	0.899642i	$-0.643828\pi$
$617$	− 44.6933i	− 1.79928i	0.436629	−	0.899642i	$-0.356172\pi$
$618$	15.6655i	0.630160i
$619$	17.5678	0.706108	0.353054	−	0.935603i	$-0.385143\pi$
$619$	17.5678	0.706108	0.353054	+	0.935603i	$0.385143\pi$
$620$	0	0
$621$	10.0978	0.405209
$622$	− 8.16724i	− 0.327476i
$623$	− 7.45998i	− 0.298878i
$624$	11.2544	0.450538
$625$	0	0
$626$	34.5628	1.38141
$627$	− 25.2927i	− 1.01009i
$628$	16.2056i	0.646672i
$629$	−4.63778	−0.184920
$630$	0	0
$631$	4.74557	0.188918	0.0944592	−	0.995529i	$-0.469888\pi$
$631$	4.74557	0.188918	0.0944592	+	0.995529i	$0.469888\pi$
$632$	12.1517i	0.483367i
$633$	− 33.6444i	− 1.33724i
$634$	−9.21057	−0.365799
$635$	0	0
$636$	35.0872	1.39130
$637$	− 3.62721i	− 0.143715i
$638$	7.30833i	0.289339i
$639$	86.4777	3.42100
$640$	0	0
$641$	−2.52998	−0.0999281	−0.0499641	−	0.998751i	$-0.515911\pi$
$641$	−2.52998	−0.0999281	−0.0499641	+	0.998751i	$0.515911\pi$
$642$	40.3033i	1.59064i
$643$	0.670549i	0.0264439i	0.999913	+	0.0132219i	$0.00420880\pi$
$643$	0.670549i	0.0264439i	−0.999913	+	0.0132219i	$0.995791\pi$
$644$	0.897225	0.0353556
$645$	0	0
$646$	34.2822	1.34881
$647$	11.8922i	0.467531i	0.972293	+	0.233765i	$0.0751048\pi$
$647$	11.8922i	0.467531i	−0.972293	+	0.233765i	$0.924895\pi$
$648$	− 15.0383i	− 0.590761i
$649$	−7.25443	−0.284761
$650$	0	0
$651$	10.6167	0.416099
$652$	6.31335i	0.247250i
$653$	11.4161i	0.446747i	0.974733	+	0.223374i	$0.0717070\pi$
$653$	11.4161i	0.446747i	−0.974733	+	0.223374i	$0.928293\pi$
$654$	−15.8328	−0.619110
$655$	0	0
$656$	12.3572	0.482468
$657$	1.36222i	0.0531454i
$658$	− 1.15667i	− 0.0450919i
$659$	−1.87108	−0.0728868	−0.0364434	−	0.999336i	$-0.511603\pi$
$659$	−1.87108	−0.0728868	−0.0364434	+	0.999336i	$0.511603\pi$
$660$	0	0
$661$	33.1355	1.28882	0.644412	−	0.764679i	$-0.277102\pi$
$661$	33.1355	1.28882	0.644412	+	0.764679i	$0.277102\pi$
$662$	16.2439i	0.631336i
$663$	− 47.3311i	− 1.83819i
$664$	−2.20555	−0.0855919
$665$	0	0
$666$	−7.30833	−0.283192
$667$	− 6.55721i	− 0.253896i
$668$	8.00000i	0.309529i
$669$	29.3522	1.13482
$670$	0	0
$671$	−3.15667	−0.121862
$672$	− 3.10278i	− 0.119692i
$673$	18.1955i	0.701385i	0.936491	+	0.350693i	$0.114054\pi$
$673$	18.1955i	0.701385i	−0.936491	+	0.350693i	$0.885946\pi$
$674$	1.25443	0.0483187
$675$	0	0
$676$	0.156674	0.00602593
$677$	15.9789i	0.614118i	0.951690	+	0.307059i	$0.0993449\pi$
$677$	15.9789i	0.614118i	−0.951690	+	0.307059i	$0.900655\pi$
$678$	32.3033i	1.24060i
$679$	2.25945	0.0867097
$680$	0	0
$681$	−54.5089	−2.08878
$682$	− 3.42166i	− 0.131022i
$683$	17.8711i	0.683818i	0.939733	+	0.341909i	$0.111073\pi$
$683$	17.8711i	0.683818i	−0.939733	+	0.341909i	$0.888927\pi$
$684$	54.0227	2.06561
$685$	0	0
$686$	−1.00000	−0.0381802
$687$	79.8188i	3.04528i
$688$	− 10.6761i	− 0.407022i
$689$	41.0177	1.56265
$690$	0	0
$691$	−2.20555	−0.0839031	−0.0419515	−	0.999120i	$-0.513358\pi$
$691$	−2.20555	−0.0839031	−0.0419515	+	0.999120i	$0.513358\pi$
$692$	9.25443i	0.351800i
$693$	6.62721i	0.251747i
$694$	−7.42166	−0.281722
$695$	0	0
$696$	−22.6761	−0.859535
$697$	− 51.9688i	− 1.96846i
$698$	18.3033i	0.692790i
$699$	−59.4389	−2.24818
$700$	0	0
$701$	−25.6217	−0.967717	−0.483859	−	0.875146i	$-0.660765\pi$
$701$	−25.6217	−0.967717	−0.483859	+	0.875146i	$0.660765\pi$
$702$	− 40.8222i	− 1.54073i
$703$	− 8.98944i	− 0.339043i
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	28.8761	1.08677
$707$	− 13.6655i	− 0.513945i
$708$	− 22.5089i	− 0.845934i
$709$	−5.48110	−0.205847	−0.102924	−	0.994689i	$-0.532820\pi$
$709$	−5.48110	−0.205847	−0.102924	+	0.994689i	$0.532820\pi$
$710$	0	0
$711$	80.5316	3.02017
$712$	− 7.45998i	− 0.279574i
$713$	3.07000i	0.114972i
$714$	−13.0489	−0.488342
$715$	0	0
$716$	4.98944	0.186464
$717$	− 56.0172i	− 2.09200i
$718$	− 4.15165i	− 0.154938i
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	0	0
$721$	5.04888	0.188030
$722$	47.4494i	1.76588i
$723$	− 19.0872i	− 0.709860i
$724$	9.66553	0.359216
$725$	0	0
$726$	3.10278	0.115155
$727$	18.5855i	0.689297i	0.938732	+	0.344649i	$0.112002\pi$
$727$	18.5855i	0.689297i	−0.938732	+	0.344649i	$0.887998\pi$
$728$	− 3.62721i	− 0.134433i
$729$	5.09775	0.188806
$730$	0	0
$731$	−44.8988	−1.66064
$732$	− 9.79445i	− 0.362013i
$733$	42.0000i	1.55131i	0.631160	+	0.775653i	$0.282579\pi$
$733$	42.0000i	1.55131i	−0.631160	+	0.775653i	$0.717421\pi$
$734$	5.26447	0.194315
$735$	0	0
$736$	0.897225	0.0330722
$737$	− 8.41110i	− 0.309827i
$738$	− 81.8938i	− 3.01455i
$739$	−5.97887	−0.219936	−0.109968	−	0.993935i	$-0.535075\pi$
$739$	−5.97887	−0.219936	−0.109968	+	0.993935i	$0.535075\pi$
$740$	0	0
$741$	91.7422	3.37023
$742$	− 11.3083i	− 0.415142i
$743$	50.0978i	1.83791i	0.394364	+	0.918954i	$0.370965\pi$
$743$	50.0978i	1.83791i	−0.394364	+	0.918954i	$0.629035\pi$
$744$	10.6167	0.389225
$745$	0	0
$746$	35.8711	1.31333
$747$	14.6167i	0.534795i
$748$	4.20555i	0.153770i
$749$	12.9894	0.474624
$750$	0	0
$751$	−8.63778	−0.315197	−0.157598	−	0.987503i	$-0.550375\pi$
$751$	−8.63778	−0.315197	−0.157598	+	0.987503i	$0.550375\pi$
$752$	− 1.15667i	− 0.0421796i
$753$	93.0177i	3.38975i
$754$	−26.5089	−0.965395
$755$	0	0
$756$	−11.2544	−0.409320
$757$	25.5139i	0.927318i	0.886014	+	0.463659i	$0.153464\pi$
$757$	25.5139i	0.927318i	−0.886014	+	0.463659i	$0.846536\pi$
$758$	33.0177i	1.19926i
$759$	−2.78389	−0.101049
$760$	0	0
$761$	−32.6605	−1.18394	−0.591971	−	0.805959i	$-0.701650\pi$
$761$	−32.6605	−1.18394	−0.591971	+	0.805959i	$0.701650\pi$
$762$	10.0978i	0.365803i
$763$	5.10278i	0.184733i
$764$	9.15667	0.331277
$765$	0	0
$766$	2.95112	0.106628
$767$	− 26.3133i	− 0.950120i
$768$	− 3.10278i	− 0.111962i
$769$	−16.7683	−0.604680	−0.302340	−	0.953200i	$-0.597768\pi$
$769$	−16.7683	−0.604680	−0.302340	+	0.953200i	$0.597768\pi$
$770$	0	0
$771$	12.5783	0.452998
$772$	1.52946i	0.0550465i
$773$	2.82220i	0.101507i	0.998711	+	0.0507537i	$0.0161624\pi$
$773$	2.82220i	0.101507i	−0.998711	+	0.0507537i	$0.983838\pi$
$774$	−70.7527	−2.54315
$775$	0	0
$776$	2.25945	0.0811095
$777$	3.42166i	0.122751i
$778$	− 1.89220i	− 0.0678387i
$779$	100.732	3.60908
$780$	0	0
$781$	−13.0489	−0.466925
$782$	− 3.77332i	− 0.134934i
$783$	82.2510i	2.93941i
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	−53.7038	−1.91555
$787$	− 4.82220i	− 0.171893i	−0.996300	−	0.0859464i	$-0.972609\pi$
$787$	− 4.82220i	− 0.171893i	0.996300	−	0.0859464i	$-0.0273914\pi$
$788$	− 14.3033i	− 0.509534i
$789$	45.0177	1.60267
$790$	0	0
$791$	10.4111	0.370176
$792$	6.62721i	0.235488i
$793$	− 11.4499i	− 0.406599i
$794$	−5.36222	−0.190298
$795$	0	0
$796$	−10.0978	−0.357905
$797$	− 0.540024i	− 0.0191286i	−0.999954	−	0.00956431i	$-0.996956\pi$
$797$	− 0.540024i	− 0.0191286i	0.999954	−	0.00956431i	$-0.00304446\pi$
$798$	− 25.2927i	− 0.895353i
$799$	−4.86445	−0.172092
$800$	0	0
$801$	−49.4389	−1.74684
$802$	23.7038i	0.837012i
$803$	− 0.205550i	− 0.00725371i
$804$	26.0978	0.920397
$805$	0	0
$806$	12.4111	0.437162
$807$	13.5678i	0.477608i
$808$	− 13.6655i	− 0.480752i
$809$	17.8922	0.629056	0.314528	−	0.949248i	$-0.398154\pi$
$809$	17.8922	0.629056	0.314528	+	0.949248i	$0.398154\pi$
$810$	0	0
$811$	−12.2283	−0.429393	−0.214696	−	0.976681i	$-0.568876\pi$
$811$	−12.2283	−0.429393	−0.214696	+	0.976681i	$0.568876\pi$
$812$	7.30833i	0.256472i
$813$	32.9411i	1.15529i
$814$	1.10278	0.0386522
$815$	0	0
$816$	−13.0489	−0.456802
$817$	− 87.0278i	− 3.04472i
$818$	− 27.0816i	− 0.946888i
$819$	−24.0383	−0.839967
$820$	0	0
$821$	38.5316	1.34476	0.672381	−	0.740206i	$-0.265272\pi$
$821$	38.5316	1.34476	0.672381	+	0.740206i	$0.265272\pi$
$822$	31.0278i	1.08222i
$823$	− 21.9461i	− 0.764993i	−0.923957	−	0.382496i	$-0.875064\pi$
$823$	− 21.9461i	− 0.764993i	0.923957	−	0.382496i	$-0.124936\pi$
$824$	5.04888	0.175886
$825$	0	0
$826$	−7.25443	−0.252414
$827$	9.68665i	0.336838i	0.985716	+	0.168419i	$0.0538661\pi$
$827$	9.68665i	0.336838i	−0.985716	+	0.168419i	$0.946134\pi$
$828$	− 5.94610i	− 0.206641i
$829$	−31.0771	−1.07935	−0.539677	−	0.841872i	$-0.681454\pi$
$829$	−31.0771	−1.07935	−0.539677	+	0.841872i	$0.681454\pi$
$830$	0	0
$831$	−61.3210	−2.12720
$832$	− 3.62721i	− 0.125751i
$833$	4.20555i	0.145714i
$834$	−40.9583	−1.41827
$835$	0	0
$836$	−8.15165	−0.281931
$837$	− 38.5089i	− 1.33106i
$838$	3.05892i	0.105669i
$839$	24.7738	0.855288	0.427644	−	0.903947i	$-0.359344\pi$
$839$	24.7738	0.855288	0.427644	+	0.903947i	$0.359344\pi$
$840$	0	0
$841$	24.4116	0.841780
$842$	21.6655i	0.746643i
$843$	83.9266i	2.89058i
$844$	−10.8433	−0.373243
$845$	0	0
$846$	−7.66553	−0.263546
$847$	− 1.00000i	− 0.0343604i
$848$	− 11.3083i	− 0.388329i
$849$	−85.8399	−2.94602
$850$	0	0
$851$	−0.989437	−0.0339175
$852$	− 40.4877i	− 1.38709i
$853$	− 1.58890i	− 0.0544029i	−0.999630	−	0.0272014i	$-0.991340\pi$
$853$	− 1.58890i	− 0.0544029i	0.999630	−	0.0272014i	$-0.00865956\pi$
$854$	−3.15667	−0.108019
$855$	0	0
$856$	12.9894	0.443970
$857$	19.1255i	0.653315i	0.945143	+	0.326657i	$0.105922\pi$
$857$	19.1255i	0.653315i	−0.945143	+	0.326657i	$0.894078\pi$
$858$	11.2544i	0.384220i
$859$	−4.94108	−0.168587	−0.0842937	−	0.996441i	$-0.526863\pi$
$859$	−4.94108	−0.168587	−0.0842937	+	0.996441i	$0.526863\pi$
$860$	0	0
$861$	−38.3416	−1.30668
$862$	− 34.3260i	− 1.16915i
$863$	19.3295i	0.657982i	0.944333	+	0.328991i	$0.106709\pi$
$863$	19.3295i	0.657982i	−0.944333	+	0.328991i	$0.893291\pi$
$864$	−11.2544	−0.382883
$865$	0	0
$866$	−0.0538991	−0.00183157
$867$	2.13053i	0.0723564i
$868$	− 3.42166i	− 0.116139i
$869$	−12.1517	−0.412217
$870$	0	0
$871$	30.5089	1.03375
$872$	5.10278i	0.172802i
$873$	− 14.9739i	− 0.506788i
$874$	7.31386	0.247395
$875$	0	0
$876$	0.637776	0.0215484
$877$	16.4011i	0.553824i	0.960895	+	0.276912i	$0.0893111\pi$
$877$	16.4011i	0.553824i	−0.960895	+	0.276912i	$0.910689\pi$
$878$	7.14663i	0.241187i
$879$	25.9789	0.876246
$880$	0	0
$881$	39.5678	1.33307	0.666536	−	0.745473i	$-0.267776\pi$
$881$	39.5678	1.33307	0.666536	+	0.745473i	$0.267776\pi$
$882$	6.62721i	0.223150i
$883$	− 55.4389i	− 1.86567i	−0.360309	−	0.932833i	$-0.617329\pi$
$883$	− 55.4389i	− 1.86567i	0.360309	−	0.932833i	$-0.382671\pi$
$884$	−15.2544	−0.513062
$885$	0	0
$886$	8.74557	0.293813
$887$	44.1955i	1.48394i	0.670433	+	0.741970i	$0.266108\pi$
$887$	44.1955i	1.48394i	−0.670433	+	0.741970i	$0.733892\pi$
$888$	3.42166i	0.114823i
$889$	3.25443	0.109150
$890$	0	0
$891$	15.0383	0.503802
$892$	− 9.45998i	− 0.316743i
$893$	− 9.42880i	− 0.315523i
$894$	73.2616	2.45023
$895$	0	0
$896$	−1.00000	−0.0334077
$897$	− 10.0978i	− 0.337154i
$898$	− 39.7038i	− 1.32493i
$899$	−25.0066	−0.834018
$900$	0	0
$901$	−47.5577	−1.58438
$902$	12.3572i	0.411450i
$903$	33.1255i	1.10235i
$904$	10.4111	0.346268
$905$	0	0
$906$	35.7250	1.18688
$907$	9.26447i	0.307622i	0.988100	+	0.153811i	$0.0491547\pi$
$907$	9.26447i	0.307622i	−0.988100	+	0.153811i	$0.950845\pi$
$908$	17.5678i	0.583007i
$909$	−90.5644	−3.00383
$910$	0	0
$911$	−37.0489	−1.22748	−0.613742	−	0.789507i	$-0.710336\pi$
$911$	−37.0489	−1.22748	−0.613742	+	0.789507i	$0.710336\pi$
$912$	− 25.2927i	− 0.837526i
$913$	− 2.20555i	− 0.0729931i
$914$	−12.3133	−0.407289
$915$	0	0
$916$	25.7250	0.849977
$917$	17.3083i	0.571571i
$918$	47.3311i	1.56216i
$919$	13.9149	0.459011	0.229506	−	0.973307i	$-0.426289\pi$
$919$	13.9149	0.459011	0.229506	+	0.973307i	$0.426289\pi$
$920$	0	0
$921$	−31.6655	−1.04341
$922$	− 15.0489i	− 0.495608i
$923$	− 47.3311i	− 1.55792i
$924$	3.10278	0.102074
$925$	0	0
$926$	31.4061	1.03207
$927$	− 33.4600i	− 1.09897i
$928$	7.30833i	0.239908i
$929$	32.0666	1.05207	0.526035	−	0.850463i	$-0.323678\pi$
$929$	32.0666	1.05207	0.526035	+	0.850463i	$0.323678\pi$
$930$	0	0
$931$	−8.15165	−0.267160
$932$	19.1567i	0.627498i
$933$	25.3411i	0.829630i
$934$	19.0716	0.624042
$935$	0	0
$936$	−24.0383	−0.785717
$937$	25.4499i	0.831413i	0.909499	+	0.415706i	$0.136466\pi$
$937$	25.4499i	0.831413i	−0.909499	+	0.415706i	$0.863534\pi$
$938$	− 8.41110i	− 0.274632i
$939$	−107.240	−3.49966
$940$	0	0
$941$	−3.49115	−0.113808	−0.0569041	−	0.998380i	$-0.518123\pi$
$941$	−3.49115	−0.113808	−0.0569041	+	0.998380i	$0.518123\pi$
$942$	− 50.2822i	− 1.63828i
$943$	− 11.0872i	− 0.361049i
$944$	−7.25443	−0.236111
$945$	0	0
$946$	10.6761	0.347110
$947$	30.6167i	0.994907i	0.867491	+	0.497454i	$0.165732\pi$
$947$	30.6167i	0.994907i	−0.867491	+	0.497454i	$0.834268\pi$
$948$	− 37.7038i	− 1.22456i
$949$	0.745574	0.0242024
$950$	0	0
$951$	28.5783	0.926716
$952$	4.20555i	0.136303i
$953$	33.9406i	1.09944i	0.835348	+	0.549721i	$0.185266\pi$
$953$	33.9406i	1.09944i	−0.835348	+	0.549721i	$0.814734\pi$
$954$	−74.9427	−2.42636
$955$	0	0
$956$	−18.0539	−0.583905
$957$	− 22.6761i	− 0.733014i
$958$	9.49115i	0.306645i
$959$	10.0000	0.322917
$960$	0	0
$961$	−19.2922	−0.622330
$962$	4.00000i	0.128965i
$963$	− 86.0838i	− 2.77401i
$964$	−6.15165	−0.198131
$965$	0	0
$966$	−2.78389	−0.0895701
$967$	− 60.8021i	− 1.95526i	−0.210323	−	0.977632i	$-0.567452\pi$
$967$	− 60.8021i	− 1.95526i	0.210323	−	0.977632i	$-0.432548\pi$
$968$	− 1.00000i	− 0.0321412i
$969$	−106.370	−3.41709
$970$	0	0
$971$	50.2933	1.61399	0.806994	−	0.590560i	$-0.201093\pi$
$971$	50.2933	1.61399	0.806994	+	0.590560i	$0.201093\pi$
$972$	12.8972i	0.413679i
$973$	13.2005i	0.423189i
$974$	−0.0438527	−0.00140513
$975$	0	0
$976$	−3.15667	−0.101043
$977$	28.0978i	0.898927i	0.893299	+	0.449463i	$0.148385\pi$
$977$	28.0978i	0.898927i	−0.893299	+	0.449463i	$0.851615\pi$
$978$	− 19.5889i	− 0.626384i
$979$	7.45998	0.238422
$980$	0	0
$981$	33.8172	1.07970
$982$	1.56777i	0.0500297i
$983$	21.0489i	0.671355i	0.941977	+	0.335677i	$0.108965\pi$
$983$	21.0489i	0.671355i	−0.941977	+	0.335677i	$0.891035\pi$
$984$	−38.3416	−1.22229
$985$	0	0
$986$	30.7355	0.978819
$987$	3.58890i	0.114236i
$988$	− 29.5678i	− 0.940676i
$989$	−9.57885	−0.304590
$990$	0	0
$991$	−44.6832	−1.41941	−0.709705	−	0.704499i	$-0.751172\pi$
$991$	−44.6832	−1.41941	−0.709705	+	0.704499i	$0.751172\pi$
$992$	− 3.42166i	− 0.108638i
$993$	− 50.4011i	− 1.59943i
$994$	−13.0489	−0.413885
$995$	0	0
$996$	6.84333	0.216839
$997$	9.47002i	0.299919i	0.988692	+	0.149959i	$0.0479143\pi$
$997$	9.47002i	0.299919i	−0.988692	+	0.149959i	$0.952086\pi$
$998$	42.3416i	1.34030i
$999$	12.4111	0.392670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.c.ba.1849.4		6
5.2	odd	4		3850.2.a.bt.1.1		3
5.3	odd	4		770.2.a.m.1.3	✓	3
5.4	even	2	inner	3850.2.c.ba.1849.3		6
15.8	even	4		6930.2.a.ce.1.1		3
20.3	even	4		6160.2.a.bf.1.1		3
35.13	even	4		5390.2.a.ca.1.1		3
55.43	even	4		8470.2.a.ci.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.m.1.3	✓	3	5.3	odd	4
3850.2.a.bt.1.1		3	5.2	odd	4
3850.2.c.ba.1849.3		6	5.4	even	2	inner
3850.2.c.ba.1849.4		6	1.1	even	1	trivial
5390.2.a.ca.1.1		3	35.13	even	4
6160.2.a.bf.1.1		3	20.3	even	4
6930.2.a.ce.1.1		3	15.8	even	4
8470.2.a.ci.1.3		3	55.43	even	4

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:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.10278i q^{3} -1.00000 q^{4} +3.10278 q^{6} -1.00000i q^{7} -1.00000i q^{8} -6.62721 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -3.10278i q^{3} -1.00000 q^{4} +3.10278 q^{6} -1.00000i q^{7} -1.00000i q^{8} -6.62721 q^{9} +1.00000 q^{11} +3.10278i q^{12} +3.62721i q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.20555i q^{17} -6.62721i q^{18} +8.15165 q^{19} -3.10278 q^{21} +1.00000i q^{22} -0.897225i q^{23} -3.10278 q^{24} -3.62721 q^{26} +11.2544i q^{27} +1.00000i q^{28} +7.30833 q^{29} -3.42166 q^{31} +1.00000i q^{32} -3.10278i q^{33} +4.20555 q^{34} +6.62721 q^{36} -1.10278i q^{37} +8.15165i q^{38} +11.2544 q^{39} +12.3572 q^{41} -3.10278i q^{42} -10.6761i q^{43} -1.00000 q^{44} +0.897225 q^{46} -1.15667i q^{47} -3.10278i q^{48} -1.00000 q^{49} -13.0489 q^{51} -3.62721i q^{52} -11.3083i q^{53} -11.2544 q^{54} -1.00000 q^{56} -25.2927i q^{57} +7.30833i q^{58} -7.25443 q^{59} -3.15667 q^{61} -3.42166i q^{62} +6.62721i q^{63} -1.00000 q^{64} +3.10278 q^{66} -8.41110i q^{67} +4.20555i q^{68} -2.78389 q^{69} -13.0489 q^{71} +6.62721i q^{72} -0.205550i q^{73} +1.10278 q^{74} -8.15165 q^{76} -1.00000i q^{77} +11.2544i q^{78} -12.1517 q^{79} +15.0383 q^{81} +12.3572i q^{82} -2.20555i q^{83} +3.10278 q^{84} +10.6761 q^{86} -22.6761i q^{87} -1.00000i q^{88} +7.45998 q^{89} +3.62721 q^{91} +0.897225i q^{92} +10.6167i q^{93} +1.15667 q^{94} +3.10278 q^{96} +2.25945i q^{97} -1.00000i q^{98} -6.62721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 4 q^{6} - 14 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 4 * q^6 - 14 * q^9	\( 6 q - 6 q^{4} + 4 q^{6} - 14 q^{9} + 6 q^{11} + 6 q^{14} + 6 q^{16} + 12 q^{19} - 4 q^{21} - 4 q^{24} + 4 q^{26} - 24 q^{31} - 4 q^{34} + 14 q^{36} + 16 q^{39} + 8 q^{41} - 6 q^{44} + 20 q^{46} - 6 q^{49} - 56 q^{51} - 16 q^{54} - 6 q^{56} + 8 q^{59} - 12 q^{61} - 6 q^{64} + 4 q^{66} + 16 q^{69} - 56 q^{71} - 8 q^{74} - 12 q^{76} - 36 q^{79} + 6 q^{81} + 4 q^{84} + 16 q^{86} - 36 q^{89} - 4 q^{91} + 4 q^{96} - 14 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 4 * q^6 - 14 * q^9 + 6 * q^11 + 6 * q^14 + 6 * q^16 + 12 * q^19 - 4 * q^21 - 4 * q^24 + 4 * q^26 - 24 * q^31 - 4 * q^34 + 14 * q^36 + 16 * q^39 + 8 * q^41 - 6 * q^44 + 20 * q^46 - 6 * q^49 - 56 * q^51 - 16 * q^54 - 6 * q^56 + 8 * q^59 - 12 * q^61 - 6 * q^64 + 4 * q^66 + 16 * q^69 - 56 * q^71 - 8 * q^74 - 12 * q^76 - 36 * q^79 + 6 * q^81 + 4 * q^84 + 16 * q^86 - 36 * q^89 - 4 * q^91 + 4 * q^96 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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