LMFDB - Embedded newform 1850.2.b.j.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(149,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.b (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:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.4
Root			$1.61803i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.j.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} -1.61803 q^{6} -3.23607i q^{7} -1.00000i q^{8} +0.381966 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} -1.61803 q^{6} -3.23607i q^{7} -1.00000i q^{8} +0.381966 q^{9} -1.38197 q^{11} -1.61803i q^{12} +2.85410i q^{13} +3.23607 q^{14} +1.00000 q^{16} -4.47214i q^{17} +0.381966i q^{18} -4.47214 q^{19} +5.23607 q^{21} -1.38197i q^{22} -2.85410i q^{23} +1.61803 q^{24} -2.85410 q^{26} +5.47214i q^{27} +3.23607i q^{28} +9.32624 q^{29} +7.38197 q^{31} +1.00000i q^{32} -2.23607i q^{33} +4.47214 q^{34} -0.381966 q^{36} -1.00000i q^{37} -4.47214i q^{38} -4.61803 q^{39} +9.61803 q^{41} +5.23607i q^{42} +5.23607i q^{43} +1.38197 q^{44} +2.85410 q^{46} -1.23607i q^{47} +1.61803i q^{48} -3.47214 q^{49} +7.23607 q^{51} -2.85410i q^{52} -0.472136i q^{53} -5.47214 q^{54} -3.23607 q^{56} -7.23607i q^{57} +9.32624i q^{58} +4.76393 q^{59} +10.6180 q^{61} +7.38197i q^{62} -1.23607i q^{63} -1.00000 q^{64} +2.23607 q^{66} +1.09017i q^{67} +4.47214i q^{68} +4.61803 q^{69} +2.94427 q^{71} -0.381966i q^{72} -7.09017i q^{73} +1.00000 q^{74} +4.47214 q^{76} +4.47214i q^{77} -4.61803i q^{78} +8.56231 q^{79} -7.70820 q^{81} +9.61803i q^{82} +14.4721i q^{83} -5.23607 q^{84} -5.23607 q^{86} +15.0902i q^{87} +1.38197i q^{88} +1.52786 q^{89} +9.23607 q^{91} +2.85410i q^{92} +11.9443i q^{93} +1.23607 q^{94} -1.61803 q^{96} -0.472136i q^{97} -3.47214i q^{98} -0.527864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9	$ 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9} - 10 q^{11} + 4 q^{14} + 4 q^{16} + 12 q^{21} + 2 q^{24} + 2 q^{26} + 6 q^{29} + 34 q^{31} - 6 q^{36} - 14 q^{39} + 34 q^{41} + 10 q^{44} - 2 q^{46} + 4 q^{49} + 20 q^{51} - 4 q^{54} - 4 q^{56} + 28 q^{59} + 38 q^{61} - 4 q^{64} + 14 q^{69} - 24 q^{71} + 4 q^{74} - 6 q^{79} - 4 q^{81} - 12 q^{84} - 12 q^{86} + 24 q^{89} + 28 q^{91} - 4 q^{94} - 2 q^{96} - 20 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9 - 10 * q^11 + 4 * q^14 + 4 * q^16 + 12 * q^21 + 2 * q^24 + 2 * q^26 + 6 * q^29 + 34 * q^31 - 6 * q^36 - 14 * q^39 + 34 * q^41 + 10 * q^44 - 2 * q^46 + 4 * q^49 + 20 * q^51 - 4 * q^54 - 4 * q^56 + 28 * q^59 + 38 * q^61 - 4 * q^64 + 14 * q^69 - 24 * q^71 + 4 * q^74 - 6 * q^79 - 4 * q^81 - 12 * q^84 - 12 * q^86 + 24 * q^89 + 28 * q^91 - 4 * q^94 - 2 * q^96 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.61803i	0.934172i	0.884212	+	0.467086i	$0.154696\pi$
$3$	1.61803i	0.934172i	−0.884212	+	0.467086i	$0.845304\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.61803	−0.660560
$7$	− 3.23607i	− 1.22312i	−0.791199	−	0.611559i	$-0.790543\pi$
$7$	− 3.23607i	− 1.22312i	0.791199	−	0.611559i	$-0.209457\pi$
$8$	− 1.00000i	− 0.353553i
$9$	0.381966	0.127322
$10$	0	0
$11$	−1.38197	−0.416678	−0.208339	−	0.978057i	$-0.566806\pi$
$11$	−1.38197	−0.416678	−0.208339	+	0.978057i	$0.566806\pi$
$12$	− 1.61803i	− 0.467086i
$13$	2.85410i	0.791585i	0.918340	+	0.395793i	$0.129530\pi$
$13$	2.85410i	0.791585i	−0.918340	+	0.395793i	$0.870470\pi$
$14$	3.23607	0.864876
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.47214i	− 1.08465i	−0.840168	−	0.542326i	$-0.817544\pi$
$17$	− 4.47214i	− 1.08465i	0.840168	−	0.542326i	$-0.182456\pi$
$18$	0.381966i	0.0900303i
$19$	−4.47214	−1.02598	−0.512989	−	0.858395i	$-0.671462\pi$
$19$	−4.47214	−1.02598	−0.512989	+	0.858395i	$0.671462\pi$
$20$	0	0
$21$	5.23607	1.14260
$22$	− 1.38197i	− 0.294636i
$23$	− 2.85410i	− 0.595121i	−0.954703	−	0.297561i	$-0.903827\pi$
$23$	− 2.85410i	− 0.595121i	0.954703	−	0.297561i	$-0.0961731\pi$
$24$	1.61803	0.330280
$25$	0	0
$26$	−2.85410	−0.559735
$27$	5.47214i	1.05311i
$28$	3.23607i	0.611559i
$29$	9.32624	1.73184	0.865919	−	0.500183i	$-0.166734\pi$
$29$	9.32624	1.73184	0.865919	+	0.500183i	$0.166734\pi$
$30$	0	0
$31$	7.38197	1.32584	0.662920	−	0.748690i	$-0.269317\pi$
$31$	7.38197	1.32584	0.662920	+	0.748690i	$0.269317\pi$
$32$	1.00000i	0.176777i
$33$	− 2.23607i	− 0.389249i
$34$	4.47214	0.766965
$35$	0	0
$36$	−0.381966	−0.0636610
$37$	− 1.00000i	− 0.164399i
$37$	− 1.00000i	− 0.164399i
$38$	− 4.47214i	− 0.725476i
$39$	−4.61803	−0.739477
$40$	0	0
$41$	9.61803	1.50208	0.751042	−	0.660254i	$-0.229551\pi$
$41$	9.61803	1.50208	0.751042	+	0.660254i	$0.229551\pi$
$42$	5.23607i	0.807943i
$43$	5.23607i	0.798493i	0.916844	+	0.399246i	$0.130728\pi$
$43$	5.23607i	0.798493i	−0.916844	+	0.399246i	$0.869272\pi$
$44$	1.38197	0.208339
$45$	0	0
$46$	2.85410	0.420814
$47$	− 1.23607i	− 0.180299i	−0.995928	−	0.0901495i	$-0.971266\pi$
$47$	− 1.23607i	− 0.180299i	0.995928	−	0.0901495i	$-0.0287345\pi$
$48$	1.61803i	0.233543i
$49$	−3.47214	−0.496019
$50$	0	0
$51$	7.23607	1.01325
$52$	− 2.85410i	− 0.395793i
$53$	− 0.472136i	− 0.0648529i	−0.999474	−	0.0324264i	$-0.989677\pi$
$53$	− 0.472136i	− 0.0648529i	0.999474	−	0.0324264i	$-0.0103235\pi$
$54$	−5.47214	−0.744663
$55$	0	0
$56$	−3.23607	−0.432438
$57$	− 7.23607i	− 0.958441i
$58$	9.32624i	1.22460i
$59$	4.76393	0.620211	0.310106	−	0.950702i	$-0.399636\pi$
$59$	4.76393	0.620211	0.310106	+	0.950702i	$0.399636\pi$
$60$	0	0
$61$	10.6180	1.35950	0.679750	−	0.733444i	$-0.262088\pi$
$61$	10.6180	1.35950	0.679750	+	0.733444i	$0.262088\pi$
$62$	7.38197i	0.937511i
$63$	− 1.23607i	− 0.155730i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	2.23607	0.275241
$67$	1.09017i	0.133185i	0.997780	+	0.0665927i	$0.0212128\pi$
$67$	1.09017i	0.133185i	−0.997780	+	0.0665927i	$0.978787\pi$
$68$	4.47214i	0.542326i
$69$	4.61803	0.555946
$70$	0	0
$71$	2.94427	0.349421	0.174710	−	0.984620i	$-0.444101\pi$
$71$	2.94427	0.349421	0.174710	+	0.984620i	$0.444101\pi$
$72$	− 0.381966i	− 0.0450151i
$73$	− 7.09017i	− 0.829842i	−0.909858	−	0.414921i	$-0.863809\pi$
$73$	− 7.09017i	− 0.829842i	0.909858	−	0.414921i	$-0.136191\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	4.47214	0.512989
$77$	4.47214i	0.509647i
$78$	− 4.61803i	− 0.522889i
$79$	8.56231	0.963335	0.481667	−	0.876354i	$-0.340031\pi$
$79$	8.56231	0.963335	0.481667	+	0.876354i	$0.340031\pi$
$80$	0	0
$81$	−7.70820	−0.856467
$82$	9.61803i	1.06213i
$83$	14.4721i	1.58852i	0.607576	+	0.794262i	$0.292142\pi$
$83$	14.4721i	1.58852i	−0.607576	+	0.794262i	$0.707858\pi$
$84$	−5.23607	−0.571302
$85$	0	0
$86$	−5.23607	−0.564620
$87$	15.0902i	1.61784i
$88$	1.38197i	0.147318i
$89$	1.52786	0.161953	0.0809766	−	0.996716i	$-0.474196\pi$
$89$	1.52786	0.161953	0.0809766	+	0.996716i	$0.474196\pi$
$90$	0	0
$91$	9.23607	0.968203
$92$	2.85410i	0.297561i
$93$	11.9443i	1.23856i
$94$	1.23607	0.127491
$95$	0	0
$96$	−1.61803	−0.165140
$97$	− 0.472136i	− 0.0479381i	−0.999713	−	0.0239691i	$-0.992370\pi$
$97$	− 0.472136i	− 0.0479381i	0.999713	−	0.0239691i	$-0.00763032\pi$
$98$	− 3.47214i	− 0.350739i
$99$	−0.527864	−0.0530523
$100$	0	0
$101$	3.52786	0.351036	0.175518	−	0.984476i	$-0.443840\pi$
$101$	3.52786	0.351036	0.175518	+	0.984476i	$0.443840\pi$
$102$	7.23607i	0.716477i
$103$	− 17.2705i	− 1.70171i	−0.525397	−	0.850857i	$-0.676083\pi$
$103$	− 17.2705i	− 1.70171i	0.525397	−	0.850857i	$-0.323917\pi$
$104$	2.85410	0.279868
$105$	0	0
$106$	0.472136	0.0458579
$107$	− 7.32624i	− 0.708254i	−0.935197	−	0.354127i	$-0.884778\pi$
$107$	− 7.32624i	− 0.708254i	0.935197	−	0.354127i	$-0.115222\pi$
$108$	− 5.47214i	− 0.526557i
$109$	−2.94427	−0.282010	−0.141005	−	0.990009i	$-0.545033\pi$
$109$	−2.94427	−0.282010	−0.141005	+	0.990009i	$0.545033\pi$
$110$	0	0
$111$	1.61803	0.153577
$112$	− 3.23607i	− 0.305780i
$113$	6.94427i	0.653262i	0.945152	+	0.326631i	$0.105913\pi$
$113$	6.94427i	0.653262i	−0.945152	+	0.326631i	$0.894087\pi$
$114$	7.23607	0.677720
$115$	0	0
$116$	−9.32624	−0.865919
$117$	1.09017i	0.100786i
$118$	4.76393i	0.438555i
$119$	−14.4721	−1.32666
$120$	0	0
$121$	−9.09017	−0.826379
$122$	10.6180i	0.961312i
$123$	15.5623i	1.40321i
$124$	−7.38197	−0.662920
$125$	0	0
$126$	1.23607	0.110118
$127$	− 8.47214i	− 0.751780i	−0.926664	−	0.375890i	$-0.877337\pi$
$127$	− 8.47214i	− 0.751780i	0.926664	−	0.375890i	$-0.122663\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−8.47214	−0.745930
$130$	0	0
$131$	−22.6525	−1.97916	−0.989578	−	0.143998i	$-0.954004\pi$
$131$	−22.6525	−1.97916	−0.989578	+	0.143998i	$0.954004\pi$
$132$	2.23607i	0.194625i
$133$	14.4721i	1.25489i
$134$	−1.09017	−0.0941763
$135$	0	0
$136$	−4.47214	−0.383482
$137$	3.67376i	0.313871i	0.987609	+	0.156935i	$0.0501614\pi$
$137$	3.67376i	0.313871i	−0.987609	+	0.156935i	$0.949839\pi$
$138$	4.61803i	0.393113i
$139$	−4.85410	−0.411720	−0.205860	−	0.978581i	$-0.565999\pi$
$139$	−4.85410	−0.411720	−0.205860	+	0.978581i	$0.565999\pi$
$140$	0	0
$141$	2.00000	0.168430
$142$	2.94427i	0.247078i
$143$	− 3.94427i	− 0.329837i
$144$	0.381966	0.0318305
$145$	0	0
$146$	7.09017	0.586787
$147$	− 5.61803i	− 0.463368i
$148$	1.00000i	0.0821995i
$149$	−16.1803	−1.32555	−0.662773	−	0.748821i	$-0.730620\pi$
$149$	−16.1803	−1.32555	−0.662773	+	0.748821i	$0.730620\pi$
$150$	0	0
$151$	4.29180	0.349261	0.174631	−	0.984634i	$-0.444127\pi$
$151$	4.29180	0.349261	0.174631	+	0.984634i	$0.444127\pi$
$152$	4.47214i	0.362738i
$153$	− 1.70820i	− 0.138100i
$154$	−4.47214	−0.360375
$155$	0	0
$156$	4.61803	0.369739
$157$	− 16.4721i	− 1.31462i	−0.753620	−	0.657310i	$-0.771694\pi$
$157$	− 16.4721i	− 1.31462i	0.753620	−	0.657310i	$-0.228306\pi$
$158$	8.56231i	0.681180i
$159$	0.763932	0.0605838
$160$	0	0
$161$	−9.23607	−0.727904
$162$	− 7.70820i	− 0.605614i
$163$	3.52786i	0.276324i	0.990410	+	0.138162i	$0.0441194\pi$
$163$	3.52786i	0.276324i	−0.990410	+	0.138162i	$0.955881\pi$
$164$	−9.61803	−0.751042
$165$	0	0
$166$	−14.4721	−1.12326
$167$	13.8541i	1.07206i	0.844198	+	0.536031i	$0.180077\pi$
$167$	13.8541i	1.07206i	−0.844198	+	0.536031i	$0.819923\pi$
$168$	− 5.23607i	− 0.403971i
$169$	4.85410	0.373392
$170$	0	0
$171$	−1.70820	−0.130630
$172$	− 5.23607i	− 0.399246i
$173$	0.472136i	0.0358958i	0.999839	+	0.0179479i	$0.00571331\pi$
$173$	0.472136i	0.0358958i	−0.999839	+	0.0179479i	$0.994287\pi$
$174$	−15.0902	−1.14398
$175$	0	0
$176$	−1.38197	−0.104170
$177$	7.70820i	0.579384i
$178$	1.52786i	0.114518i
$179$	12.6525	0.945690	0.472845	−	0.881146i	$-0.343227\pi$
$179$	12.6525	0.945690	0.472845	+	0.881146i	$0.343227\pi$
$180$	0	0
$181$	14.4721	1.07571	0.537853	−	0.843039i	$-0.319236\pi$
$181$	14.4721	1.07571	0.537853	+	0.843039i	$0.319236\pi$
$182$	9.23607i	0.684623i
$183$	17.1803i	1.27001i
$184$	−2.85410	−0.210407
$185$	0	0
$186$	−11.9443	−0.875797
$187$	6.18034i	0.451951i
$188$	1.23607i	0.0901495i
$189$	17.7082	1.28808
$190$	0	0
$191$	−7.09017	−0.513027	−0.256513	−	0.966541i	$-0.582574\pi$
$191$	−7.09017	−0.513027	−0.256513	+	0.966541i	$0.582574\pi$
$192$	− 1.61803i	− 0.116772i
$193$	− 4.00000i	− 0.287926i	−0.989583	−	0.143963i	$-0.954015\pi$
$193$	− 4.00000i	− 0.287926i	0.989583	−	0.143963i	$-0.0459847\pi$
$194$	0.472136	0.0338974
$195$	0	0
$196$	3.47214	0.248010
$197$	− 7.52786i	− 0.536338i	−0.963372	−	0.268169i	$-0.913581\pi$
$197$	− 7.52786i	− 0.536338i	0.963372	−	0.268169i	$-0.0864186\pi$
$198$	− 0.527864i	− 0.0375137i
$199$	−3.05573	−0.216615	−0.108307	−	0.994117i	$-0.534543\pi$
$199$	−3.05573	−0.216615	−0.108307	+	0.994117i	$0.534543\pi$
$200$	0	0
$201$	−1.76393	−0.124418
$202$	3.52786i	0.248220i
$203$	− 30.1803i	− 2.11824i
$204$	−7.23607	−0.506626
$205$	0	0
$206$	17.2705	1.20329
$207$	− 1.09017i	− 0.0757720i
$208$	2.85410i	0.197896i
$209$	6.18034	0.427503
$210$	0	0
$211$	11.2705	0.775894	0.387947	−	0.921682i	$-0.373184\pi$
$211$	11.2705	0.775894	0.387947	+	0.921682i	$0.373184\pi$
$212$	0.472136i	0.0324264i
$213$	4.76393i	0.326419i
$214$	7.32624	0.500811
$215$	0	0
$216$	5.47214	0.372332
$217$	− 23.8885i	− 1.62166i
$218$	− 2.94427i	− 0.199411i
$219$	11.4721	0.775215
$220$	0	0
$221$	12.7639	0.858595
$222$	1.61803i	0.108595i
$223$	− 14.1803i	− 0.949586i	−0.880098	−	0.474793i	$-0.842523\pi$
$223$	− 14.1803i	− 0.949586i	0.880098	−	0.474793i	$-0.157477\pi$
$224$	3.23607	0.216219
$225$	0	0
$226$	−6.94427	−0.461926
$227$	− 4.29180i	− 0.284857i	−0.989805	−	0.142428i	$-0.954509\pi$
$227$	− 4.29180i	− 0.284857i	0.989805	−	0.142428i	$-0.0454910\pi$
$228$	7.23607i	0.479220i
$229$	23.1246	1.52812	0.764059	−	0.645147i	$-0.223204\pi$
$229$	23.1246	1.52812	0.764059	+	0.645147i	$0.223204\pi$
$230$	0	0
$231$	−7.23607	−0.476098
$232$	− 9.32624i	− 0.612298i
$233$	6.56231i	0.429911i	0.976624	+	0.214955i	$0.0689606\pi$
$233$	6.56231i	0.429911i	−0.976624	+	0.214955i	$0.931039\pi$
$234$	−1.09017	−0.0712666
$235$	0	0
$236$	−4.76393	−0.310106
$237$	13.8541i	0.899921i
$238$	− 14.4721i	− 0.938089i
$239$	−9.85410	−0.637409	−0.318704	−	0.947854i	$-0.603248\pi$
$239$	−9.85410	−0.637409	−0.318704	+	0.947854i	$0.603248\pi$
$240$	0	0
$241$	−1.52786	−0.0984184	−0.0492092	−	0.998788i	$-0.515670\pi$
$241$	−1.52786	−0.0984184	−0.0492092	+	0.998788i	$0.515670\pi$
$242$	− 9.09017i	− 0.584338i
$243$	3.94427i	0.253025i
$244$	−10.6180	−0.679750
$245$	0	0
$246$	−15.5623	−0.992216
$247$	− 12.7639i	− 0.812150i
$248$	− 7.38197i	− 0.468755i
$249$	−23.4164	−1.48395
$250$	0	0
$251$	−20.9443	−1.32199	−0.660995	−	0.750390i	$-0.729866\pi$
$251$	−20.9443	−1.32199	−0.660995	+	0.750390i	$0.729866\pi$
$252$	1.23607i	0.0778650i
$253$	3.94427i	0.247974i
$254$	8.47214	0.531589
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 1.05573i	− 0.0658545i	−0.999458	−	0.0329273i	$-0.989517\pi$
$257$	− 1.05573i	− 0.0658545i	0.999458	−	0.0329273i	$-0.0104830\pi$
$258$	− 8.47214i	− 0.527452i
$259$	−3.23607	−0.201079
$260$	0	0
$261$	3.56231	0.220501
$262$	− 22.6525i	− 1.39947i
$263$	13.2361i	0.816171i	0.912944	+	0.408085i	$0.133803\pi$
$263$	13.2361i	0.816171i	−0.912944	+	0.408085i	$0.866197\pi$
$264$	−2.23607	−0.137620
$265$	0	0
$266$	−14.4721	−0.887344
$267$	2.47214i	0.151292i
$268$	− 1.09017i	− 0.0665927i
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	0	0
$271$	12.9443	0.786309	0.393154	−	0.919473i	$-0.371384\pi$
$271$	12.9443	0.786309	0.393154	+	0.919473i	$0.371384\pi$
$272$	− 4.47214i	− 0.271163i
$273$	14.9443i	0.904468i
$274$	−3.67376	−0.221940
$275$	0	0
$276$	−4.61803	−0.277973
$277$	16.7984i	1.00932i	0.863319	+	0.504658i	$0.168381\pi$
$277$	16.7984i	1.00932i	−0.863319	+	0.504658i	$0.831619\pi$
$278$	− 4.85410i	− 0.291130i
$279$	2.81966	0.168809
$280$	0	0
$281$	29.8885	1.78300	0.891501	−	0.453020i	$-0.149653\pi$
$281$	29.8885	1.78300	0.891501	+	0.453020i	$0.149653\pi$
$282$	2.00000i	0.119098i
$283$	− 6.76393i	− 0.402074i	−0.979584	−	0.201037i	$-0.935569\pi$
$283$	− 6.76393i	− 0.402074i	0.979584	−	0.201037i	$-0.0644312\pi$
$284$	−2.94427	−0.174710
$285$	0	0
$286$	3.94427	0.233230
$287$	− 31.1246i	− 1.83723i
$288$	0.381966i	0.0225076i
$289$	−3.00000	−0.176471
$290$	0	0
$291$	0.763932	0.0447825
$292$	7.09017i	0.414921i
$293$	12.6525i	0.739166i	0.929198	+	0.369583i	$0.120499\pi$
$293$	12.6525i	0.739166i	−0.929198	+	0.369583i	$0.879501\pi$
$294$	5.61803	0.327650
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	− 7.56231i	− 0.438809i
$298$	− 16.1803i	− 0.937302i
$299$	8.14590	0.471089
$300$	0	0
$301$	16.9443	0.976652
$302$	4.29180i	0.246965i
$303$	5.70820i	0.327928i
$304$	−4.47214	−0.256495
$305$	0	0
$306$	1.70820	0.0976515
$307$	− 12.8541i	− 0.733622i	−0.930295	−	0.366811i	$-0.880450\pi$
$307$	− 12.8541i	− 0.733622i	0.930295	−	0.366811i	$-0.119550\pi$
$308$	− 4.47214i	− 0.254824i
$309$	27.9443	1.58969
$310$	0	0
$311$	−27.0344	−1.53298	−0.766491	−	0.642255i	$-0.777999\pi$
$311$	−27.0344	−1.53298	−0.766491	+	0.642255i	$0.777999\pi$
$312$	4.61803i	0.261445i
$313$	− 28.1803i	− 1.59285i	−0.604739	−	0.796423i	$-0.706723\pi$
$313$	− 28.1803i	− 1.59285i	0.604739	−	0.796423i	$-0.293277\pi$
$314$	16.4721	0.929576
$315$	0	0
$316$	−8.56231	−0.481667
$317$	20.9443i	1.17635i	0.808735	+	0.588174i	$0.200153\pi$
$317$	20.9443i	1.17635i	−0.808735	+	0.588174i	$0.799847\pi$
$318$	0.763932i	0.0428392i
$319$	−12.8885	−0.721620
$320$	0	0
$321$	11.8541	0.661631
$322$	− 9.23607i	− 0.514706i
$323$	20.0000i	1.11283i
$324$	7.70820	0.428234
$325$	0	0
$326$	−3.52786	−0.195390
$327$	− 4.76393i	− 0.263446i
$328$	− 9.61803i	− 0.531067i
$329$	−4.00000	−0.220527
$330$	0	0
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	− 14.4721i	− 0.794262i
$333$	− 0.381966i	− 0.0209316i
$334$	−13.8541	−0.758063
$335$	0	0
$336$	5.23607	0.285651
$337$	12.0344i	0.655558i	0.944754	+	0.327779i	$0.106300\pi$
$337$	12.0344i	0.655558i	−0.944754	+	0.327779i	$0.893700\pi$
$338$	4.85410i	0.264028i
$339$	−11.2361	−0.610259
$340$	0	0
$341$	−10.2016	−0.552449
$342$	− 1.70820i	− 0.0923691i
$343$	− 11.4164i	− 0.616428i
$344$	5.23607	0.282310
$345$	0	0
$346$	−0.472136	−0.0253822
$347$	17.2361i	0.925281i	0.886546	+	0.462640i	$0.153098\pi$
$347$	17.2361i	0.925281i	−0.886546	+	0.462640i	$0.846902\pi$
$348$	− 15.0902i	− 0.808918i
$349$	10.1803	0.544941	0.272471	−	0.962164i	$-0.412159\pi$
$349$	10.1803	0.544941	0.272471	+	0.962164i	$0.412159\pi$
$350$	0	0
$351$	−15.6180	−0.833629
$352$	− 1.38197i	− 0.0736590i
$353$	− 16.2918i	− 0.867125i	−0.901124	−	0.433562i	$-0.857256\pi$
$353$	− 16.2918i	− 0.867125i	0.901124	−	0.433562i	$-0.142744\pi$
$354$	−7.70820	−0.409686
$355$	0	0
$356$	−1.52786	−0.0809766
$357$	− 23.4164i	− 1.23933i
$358$	12.6525i	0.668704i
$359$	4.47214	0.236030	0.118015	−	0.993012i	$-0.462347\pi$
$359$	4.47214	0.236030	0.118015	+	0.993012i	$0.462347\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	14.4721i	0.760639i
$363$	− 14.7082i	− 0.771980i
$364$	−9.23607	−0.484102
$365$	0	0
$366$	−17.1803	−0.898031
$367$	13.1246i	0.685099i	0.939500	+	0.342550i	$0.111290\pi$
$367$	13.1246i	0.685099i	−0.939500	+	0.342550i	$0.888710\pi$
$368$	− 2.85410i	− 0.148780i
$369$	3.67376	0.191248
$370$	0	0
$371$	−1.52786	−0.0793227
$372$	− 11.9443i	− 0.619282i
$373$	− 27.7082i	− 1.43468i	−0.696725	−	0.717338i	$-0.745360\pi$
$373$	− 27.7082i	− 1.43468i	0.696725	−	0.717338i	$-0.254640\pi$
$374$	−6.18034	−0.319578
$375$	0	0
$376$	−1.23607	−0.0637453
$377$	26.6180i	1.37090i
$378$	17.7082i	0.910812i
$379$	−28.0902	−1.44290	−0.721448	−	0.692469i	$-0.756523\pi$
$379$	−28.0902	−1.44290	−0.721448	+	0.692469i	$0.756523\pi$
$380$	0	0
$381$	13.7082	0.702293
$382$	− 7.09017i	− 0.362765i
$383$	− 17.8885i	− 0.914062i	−0.889451	−	0.457031i	$-0.848913\pi$
$383$	− 17.8885i	− 0.914062i	0.889451	−	0.457031i	$-0.151087\pi$
$384$	1.61803	0.0825700
$385$	0	0
$386$	4.00000	0.203595
$387$	2.00000i	0.101666i
$388$	0.472136i	0.0239691i
$389$	6.85410	0.347517	0.173758	−	0.984788i	$-0.444409\pi$
$389$	6.85410	0.347517	0.173758	+	0.984788i	$0.444409\pi$
$390$	0	0
$391$	−12.7639	−0.645500
$392$	3.47214i	0.175369i
$393$	− 36.6525i	− 1.84887i
$394$	7.52786	0.379248
$395$	0	0
$396$	0.527864	0.0265262
$397$	20.6525i	1.03652i	0.855224	+	0.518259i	$0.173420\pi$
$397$	20.6525i	1.03652i	−0.855224	+	0.518259i	$0.826580\pi$
$398$	− 3.05573i	− 0.153170i
$399$	−23.4164	−1.17229
$400$	0	0
$401$	−4.76393	−0.237899	−0.118950	−	0.992900i	$-0.537953\pi$
$401$	−4.76393	−0.237899	−0.118950	+	0.992900i	$0.537953\pi$
$402$	− 1.76393i	− 0.0879769i
$403$	21.0689i	1.04952i
$404$	−3.52786	−0.175518
$405$	0	0
$406$	30.1803	1.49783
$407$	1.38197i	0.0685015i
$408$	− 7.23607i	− 0.358239i
$409$	26.1803	1.29453	0.647267	−	0.762263i	$-0.275912\pi$
$409$	26.1803	1.29453	0.647267	+	0.762263i	$0.275912\pi$
$410$	0	0
$411$	−5.94427	−0.293209
$412$	17.2705i	0.850857i
$413$	− 15.4164i	− 0.758592i
$414$	1.09017	0.0535789
$415$	0	0
$416$	−2.85410	−0.139934
$417$	− 7.85410i	− 0.384617i
$418$	6.18034i	0.302290i
$419$	10.5623	0.516002	0.258001	−	0.966145i	$-0.416936\pi$
$419$	10.5623	0.516002	0.258001	+	0.966145i	$0.416936\pi$
$420$	0	0
$421$	−31.0344	−1.51253	−0.756263	−	0.654268i	$-0.772977\pi$
$421$	−31.0344	−1.51253	−0.756263	+	0.654268i	$0.772977\pi$
$422$	11.2705i	0.548640i
$423$	− 0.472136i	− 0.0229560i
$424$	−0.472136	−0.0229289
$425$	0	0
$426$	−4.76393	−0.230813
$427$	− 34.3607i	− 1.66283i
$428$	7.32624i	0.354127i
$429$	6.38197	0.308124
$430$	0	0
$431$	12.3607	0.595393	0.297696	−	0.954661i	$-0.403782\pi$
$431$	12.3607	0.595393	0.297696	+	0.954661i	$0.403782\pi$
$432$	5.47214i	0.263278i
$433$	20.6738i	0.993518i	0.867889	+	0.496759i	$0.165477\pi$
$433$	20.6738i	0.993518i	−0.867889	+	0.496759i	$0.834523\pi$
$434$	23.8885	1.14669
$435$	0	0
$436$	2.94427	0.141005
$437$	12.7639i	0.610582i
$438$	11.4721i	0.548160i
$439$	−7.79837	−0.372196	−0.186098	−	0.982531i	$-0.559584\pi$
$439$	−7.79837	−0.372196	−0.186098	+	0.982531i	$0.559584\pi$
$440$	0	0
$441$	−1.32624	−0.0631542
$442$	12.7639i	0.607118i
$443$	− 15.2705i	− 0.725524i	−0.931882	−	0.362762i	$-0.881834\pi$
$443$	− 15.2705i	− 0.725524i	0.931882	−	0.362762i	$-0.118166\pi$
$444$	−1.61803	−0.0767885
$445$	0	0
$446$	14.1803	0.671459
$447$	− 26.1803i	− 1.23829i
$448$	3.23607i	0.152890i
$449$	28.4721	1.34368	0.671842	−	0.740695i	$-0.265504\pi$
$449$	28.4721	1.34368	0.671842	+	0.740695i	$0.265504\pi$
$450$	0	0
$451$	−13.2918	−0.625886
$452$	− 6.94427i	− 0.326631i
$453$	6.94427i	0.326270i
$454$	4.29180	0.201424
$455$	0	0
$456$	−7.23607	−0.338860
$457$	− 24.7639i	− 1.15841i	−0.815183	−	0.579204i	$-0.803363\pi$
$457$	− 24.7639i	− 1.15841i	0.815183	−	0.579204i	$-0.196637\pi$
$458$	23.1246i	1.08054i
$459$	24.4721	1.14226
$460$	0	0
$461$	−38.9443	−1.81382	−0.906908	−	0.421329i	$-0.861564\pi$
$461$	−38.9443	−1.81382	−0.906908	+	0.421329i	$0.861564\pi$
$462$	− 7.23607i	− 0.336652i
$463$	4.56231i	0.212028i	0.994365	+	0.106014i	$0.0338089\pi$
$463$	4.56231i	0.212028i	−0.994365	+	0.106014i	$0.966191\pi$
$464$	9.32624	0.432960
$465$	0	0
$466$	−6.56231	−0.303993
$467$	− 24.3607i	− 1.12728i	−0.826021	−	0.563639i	$-0.809401\pi$
$467$	− 24.3607i	− 1.12728i	0.826021	−	0.563639i	$-0.190599\pi$
$468$	− 1.09017i	− 0.0503931i
$469$	3.52786	0.162902
$470$	0	0
$471$	26.6525	1.22808
$472$	− 4.76393i	− 0.219278i
$473$	− 7.23607i	− 0.332715i
$474$	−13.8541	−0.636340
$475$	0	0
$476$	14.4721	0.663329
$477$	− 0.180340i	− 0.00825720i
$478$	− 9.85410i	− 0.450716i
$479$	−36.5623	−1.67057	−0.835287	−	0.549814i	$-0.814699\pi$
$479$	−36.5623	−1.67057	−0.835287	+	0.549814i	$0.814699\pi$
$480$	0	0
$481$	2.85410	0.130136
$482$	− 1.52786i	− 0.0695923i
$483$	− 14.9443i	− 0.679988i
$484$	9.09017	0.413190
$485$	0	0
$486$	−3.94427	−0.178916
$487$	37.3050i	1.69045i	0.534412	+	0.845224i	$0.320533\pi$
$487$	37.3050i	1.69045i	−0.534412	+	0.845224i	$0.679467\pi$
$488$	− 10.6180i	− 0.480656i
$489$	−5.70820	−0.258134
$490$	0	0
$491$	−28.4508	−1.28397	−0.641984	−	0.766718i	$-0.721889\pi$
$491$	−28.4508	−1.28397	−0.641984	+	0.766718i	$0.721889\pi$
$492$	− 15.5623i	− 0.701603i
$493$	− 41.7082i	− 1.87844i
$494$	12.7639	0.574276
$495$	0	0
$496$	7.38197	0.331460
$497$	− 9.52786i	− 0.427383i
$498$	− 23.4164i	− 1.04931i
$499$	−10.2918	−0.460724	−0.230362	−	0.973105i	$-0.573991\pi$
$499$	−10.2918	−0.460724	−0.230362	+	0.973105i	$0.573991\pi$
$500$	0	0
$501$	−22.4164	−1.00149
$502$	− 20.9443i	− 0.934789i
$503$	− 19.0902i	− 0.851189i	−0.904914	−	0.425594i	$-0.860065\pi$
$503$	− 19.0902i	− 0.851189i	0.904914	−	0.425594i	$-0.139935\pi$
$504$	−1.23607	−0.0550588
$505$	0	0
$506$	−3.94427	−0.175344
$507$	7.85410i	0.348813i
$508$	8.47214i	0.375890i
$509$	17.7082	0.784902	0.392451	−	0.919773i	$-0.371627\pi$
$509$	17.7082	0.784902	0.392451	+	0.919773i	$0.371627\pi$
$510$	0	0
$511$	−22.9443	−1.01499
$512$	1.00000i	0.0441942i
$513$	− 24.4721i	− 1.08047i
$514$	1.05573	0.0465662
$515$	0	0
$516$	8.47214	0.372965
$517$	1.70820i	0.0751267i
$518$	− 3.23607i	− 0.142185i
$519$	−0.763932	−0.0335329
$520$	0	0
$521$	−1.41641	−0.0620540	−0.0310270	−	0.999519i	$-0.509878\pi$
$521$	−1.41641	−0.0620540	−0.0310270	+	0.999519i	$0.509878\pi$
$522$	3.56231i	0.155918i
$523$	− 11.8197i	− 0.516838i	−0.966033	−	0.258419i	$-0.916799\pi$
$523$	− 11.8197i	− 0.516838i	0.966033	−	0.258419i	$-0.0832015\pi$
$524$	22.6525	0.989578
$525$	0	0
$526$	−13.2361	−0.577120
$527$	− 33.0132i	− 1.43808i
$528$	− 2.23607i	− 0.0973124i
$529$	14.8541	0.645831
$530$	0	0
$531$	1.81966	0.0789665
$532$	− 14.4721i	− 0.627447i
$533$	27.4508i	1.18903i
$534$	−2.47214	−0.106980
$535$	0	0
$536$	1.09017	0.0470882
$537$	20.4721i	0.883438i
$538$	− 4.00000i	− 0.172452i
$539$	4.79837	0.206681
$540$	0	0
$541$	−10.3262	−0.443960	−0.221980	−	0.975051i	$-0.571252\pi$
$541$	−10.3262	−0.443960	−0.221980	+	0.975051i	$0.571252\pi$
$542$	12.9443i	0.556004i
$543$	23.4164i	1.00489i
$544$	4.47214	0.191741
$545$	0	0
$546$	−14.9443	−0.639556
$547$	− 16.0689i	− 0.687056i	−0.939142	−	0.343528i	$-0.888378\pi$
$547$	− 16.0689i	− 0.687056i	0.939142	−	0.343528i	$-0.111622\pi$
$548$	− 3.67376i	− 0.156935i
$549$	4.05573	0.173094
$550$	0	0
$551$	−41.7082	−1.77683
$552$	− 4.61803i	− 0.196557i
$553$	− 27.7082i	− 1.17827i
$554$	−16.7984	−0.713695
$555$	0	0
$556$	4.85410	0.205860
$557$	19.5623i	0.828882i	0.910076	+	0.414441i	$0.136023\pi$
$557$	19.5623i	0.828882i	−0.910076	+	0.414441i	$0.863977\pi$
$558$	2.81966i	0.119366i
$559$	−14.9443	−0.632075
$560$	0	0
$561$	−10.0000	−0.422200
$562$	29.8885i	1.26077i
$563$	− 7.88854i	− 0.332462i	−0.986087	−	0.166231i	$-0.946840\pi$
$563$	− 7.88854i	− 0.332462i	0.986087	−	0.166231i	$-0.0531598\pi$
$564$	−2.00000	−0.0842152
$565$	0	0
$566$	6.76393	0.284309
$567$	24.9443i	1.04756i
$568$	− 2.94427i	− 0.123539i
$569$	−13.8885	−0.582238	−0.291119	−	0.956687i	$-0.594028\pi$
$569$	−13.8885	−0.582238	−0.291119	+	0.956687i	$0.594028\pi$
$570$	0	0
$571$	−10.5623	−0.442019	−0.221009	−	0.975272i	$-0.570935\pi$
$571$	−10.5623	−0.442019	−0.221009	+	0.975272i	$0.570935\pi$
$572$	3.94427i	0.164918i
$573$	− 11.4721i	− 0.479255i
$574$	31.1246	1.29912
$575$	0	0
$576$	−0.381966	−0.0159153
$577$	10.6525i	0.443468i	0.975107	+	0.221734i	$0.0711717\pi$
$577$	10.6525i	0.443468i	−0.975107	+	0.221734i	$0.928828\pi$
$578$	− 3.00000i	− 0.124784i
$579$	6.47214	0.268973
$580$	0	0
$581$	46.8328	1.94295
$582$	0.763932i	0.0316660i
$583$	0.652476i	0.0270228i
$584$	−7.09017	−0.293393
$585$	0	0
$586$	−12.6525	−0.522669
$587$	− 13.0557i	− 0.538868i	−0.963019	−	0.269434i	$-0.913163\pi$
$587$	− 13.0557i	− 0.538868i	0.963019	−	0.269434i	$-0.0868365\pi$
$588$	5.61803i	0.231684i
$589$	−33.0132	−1.36028
$590$	0	0
$591$	12.1803	0.501032
$592$	− 1.00000i	− 0.0410997i
$593$	− 17.5623i	− 0.721197i	−0.932721	−	0.360599i	$-0.882572\pi$
$593$	− 17.5623i	− 0.721197i	0.932721	−	0.360599i	$-0.117428\pi$
$594$	7.56231	0.310285
$595$	0	0
$596$	16.1803	0.662773
$597$	− 4.94427i	− 0.202356i
$598$	8.14590i	0.333111i
$599$	6.36068	0.259890	0.129945	−	0.991521i	$-0.458520\pi$
$599$	6.36068	0.259890	0.129945	+	0.991521i	$0.458520\pi$
$600$	0	0
$601$	−24.6869	−1.00700	−0.503500	−	0.863995i	$-0.667955\pi$
$601$	−24.6869	−1.00700	−0.503500	+	0.863995i	$0.667955\pi$
$602$	16.9443i	0.690597i
$603$	0.416408i	0.0169574i
$604$	−4.29180	−0.174631
$605$	0	0
$606$	−5.70820	−0.231880
$607$	35.0344i	1.42200i	0.703190	+	0.711002i	$0.251758\pi$
$607$	35.0344i	1.42200i	−0.703190	+	0.711002i	$0.748242\pi$
$608$	− 4.47214i	− 0.181369i
$609$	48.8328	1.97881
$610$	0	0
$611$	3.52786	0.142722
$612$	1.70820i	0.0690501i
$613$	13.8197i	0.558171i	0.960266	+	0.279085i	$0.0900313\pi$
$613$	13.8197i	0.558171i	−0.960266	+	0.279085i	$0.909969\pi$
$614$	12.8541	0.518749
$615$	0	0
$616$	4.47214	0.180187
$617$	0.0901699i	0.00363011i	0.999998	+	0.00181505i	$0.000577750\pi$
$617$	0.0901699i	0.00363011i	−0.999998	+	0.00181505i	$0.999422\pi$
$618$	27.9443i	1.12408i
$619$	15.2705	0.613774	0.306887	−	0.951746i	$-0.400713\pi$
$619$	15.2705	0.613774	0.306887	+	0.951746i	$0.400713\pi$
$620$	0	0
$621$	15.6180	0.626730
$622$	− 27.0344i	− 1.08398i
$623$	− 4.94427i	− 0.198088i
$624$	−4.61803	−0.184869
$625$	0	0
$626$	28.1803	1.12631
$627$	10.0000i	0.399362i
$628$	16.4721i	0.657310i
$629$	−4.47214	−0.178316
$630$	0	0
$631$	−47.3951	−1.88677	−0.943385	−	0.331700i	$-0.892378\pi$
$631$	−47.3951	−1.88677	−0.943385	+	0.331700i	$0.892378\pi$
$632$	− 8.56231i	− 0.340590i
$633$	18.2361i	0.724819i
$634$	−20.9443	−0.831803
$635$	0	0
$636$	−0.763932	−0.0302919
$637$	− 9.90983i	− 0.392642i
$638$	− 12.8885i	− 0.510262i
$639$	1.12461	0.0444890
$640$	0	0
$641$	15.5066	0.612473	0.306236	−	0.951955i	$-0.400930\pi$
$641$	15.5066	0.612473	0.306236	+	0.951955i	$0.400930\pi$
$642$	11.8541i	0.467844i
$643$	28.7639i	1.13434i	0.823601	+	0.567169i	$0.191962\pi$
$643$	28.7639i	1.13434i	−0.823601	+	0.567169i	$0.808038\pi$
$644$	9.23607	0.363952
$645$	0	0
$646$	−20.0000	−0.786889
$647$	30.0902i	1.18297i	0.806317	+	0.591483i	$0.201457\pi$
$647$	30.0902i	1.18297i	−0.806317	+	0.591483i	$0.798543\pi$
$648$	7.70820i	0.302807i
$649$	−6.58359	−0.258429
$650$	0	0
$651$	38.6525	1.51491
$652$	− 3.52786i	− 0.138162i
$653$	38.2705i	1.49764i	0.662773	+	0.748820i	$0.269379\pi$
$653$	38.2705i	1.49764i	−0.662773	+	0.748820i	$0.730621\pi$
$654$	4.76393	0.186284
$655$	0	0
$656$	9.61803	0.375521
$657$	− 2.70820i	− 0.105657i
$658$	− 4.00000i	− 0.155936i
$659$	−40.4508	−1.57574	−0.787871	−	0.615841i	$-0.788816\pi$
$659$	−40.4508	−1.57574	−0.787871	+	0.615841i	$0.788816\pi$
$660$	0	0
$661$	17.3262	0.673913	0.336956	−	0.941520i	$-0.390603\pi$
$661$	17.3262	0.673913	0.336956	+	0.941520i	$0.390603\pi$
$662$	28.0000i	1.08825i
$663$	20.6525i	0.802076i
$664$	14.4721	0.561628
$665$	0	0
$666$	0.381966	0.0148009
$667$	− 26.6180i	− 1.03065i
$668$	− 13.8541i	− 0.536031i
$669$	22.9443	0.887077
$670$	0	0
$671$	−14.6738	−0.566474
$672$	5.23607i	0.201986i
$673$	− 11.1459i	− 0.429643i	−0.976653	−	0.214821i	$-0.931083\pi$
$673$	− 11.1459i	− 0.429643i	0.976653	−	0.214821i	$-0.0689169\pi$
$674$	−12.0344	−0.463549
$675$	0	0
$676$	−4.85410	−0.186696
$677$	34.6525i	1.33180i	0.746040	+	0.665901i	$0.231953\pi$
$677$	34.6525i	1.33180i	−0.746040	+	0.665901i	$0.768047\pi$
$678$	− 11.2361i	− 0.431519i
$679$	−1.52786	−0.0586340
$680$	0	0
$681$	6.94427	0.266105
$682$	− 10.2016i	− 0.390640i
$683$	8.58359i	0.328442i	0.986424	+	0.164221i	$0.0525110\pi$
$683$	8.58359i	0.328442i	−0.986424	+	0.164221i	$0.947489\pi$
$684$	1.70820	0.0653148
$685$	0	0
$686$	11.4164	0.435880
$687$	37.4164i	1.42752i
$688$	5.23607i	0.199623i
$689$	1.34752	0.0513366
$690$	0	0
$691$	35.7771	1.36102	0.680512	−	0.732737i	$-0.261757\pi$
$691$	35.7771	1.36102	0.680512	+	0.732737i	$0.261757\pi$
$692$	− 0.472136i	− 0.0179479i
$693$	1.70820i	0.0648893i
$694$	−17.2361	−0.654272
$695$	0	0
$696$	15.0902	0.571991
$697$	− 43.0132i	− 1.62924i
$698$	10.1803i	0.385332i
$699$	−10.6180	−0.401611
$700$	0	0
$701$	−42.9787	−1.62328	−0.811642	−	0.584155i	$-0.801426\pi$
$701$	−42.9787	−1.62328	−0.811642	+	0.584155i	$0.801426\pi$
$702$	− 15.6180i	− 0.589465i
$703$	4.47214i	0.168670i
$704$	1.38197	0.0520848
$705$	0	0
$706$	16.2918	0.613150
$707$	− 11.4164i	− 0.429358i
$708$	− 7.70820i	− 0.289692i
$709$	8.21478	0.308513	0.154256	−	0.988031i	$-0.450702\pi$
$709$	8.21478	0.308513	0.154256	+	0.988031i	$0.450702\pi$
$710$	0	0
$711$	3.27051	0.122654
$712$	− 1.52786i	− 0.0572591i
$713$	− 21.0689i	− 0.789036i
$714$	23.4164	0.876337
$715$	0	0
$716$	−12.6525	−0.472845
$717$	− 15.9443i	− 0.595450i
$718$	4.47214i	0.166899i
$719$	−27.4164	−1.02246	−0.511230	−	0.859444i	$-0.670810\pi$
$719$	−27.4164	−1.02246	−0.511230	+	0.859444i	$0.670810\pi$
$720$	0	0
$721$	−55.8885	−2.08140
$722$	1.00000i	0.0372161i
$723$	− 2.47214i	− 0.0919397i
$724$	−14.4721	−0.537853
$725$	0	0
$726$	14.7082	0.545873
$727$	− 29.8541i	− 1.10723i	−0.832774	−	0.553614i	$-0.813248\pi$
$727$	− 29.8541i	− 1.10723i	0.832774	−	0.553614i	$-0.186752\pi$
$728$	− 9.23607i	− 0.342311i
$729$	−29.5066	−1.09284
$730$	0	0
$731$	23.4164	0.866087
$732$	− 17.1803i	− 0.635004i
$733$	− 27.5279i	− 1.01676i	−0.861131	−	0.508382i	$-0.830244\pi$
$733$	− 27.5279i	− 1.01676i	0.861131	−	0.508382i	$-0.169756\pi$
$734$	−13.1246	−0.484438
$735$	0	0
$736$	2.85410	0.105204
$737$	− 1.50658i	− 0.0554955i
$738$	3.67376i	0.135233i
$739$	10.9098	0.401325	0.200662	−	0.979660i	$-0.435691\pi$
$739$	10.9098	0.401325	0.200662	+	0.979660i	$0.435691\pi$
$740$	0	0
$741$	20.6525	0.758688
$742$	− 1.52786i	− 0.0560897i
$743$	48.0689i	1.76348i	0.471739	+	0.881738i	$0.343626\pi$
$743$	48.0689i	1.76348i	−0.471739	+	0.881738i	$0.656374\pi$
$744$	11.9443	0.437898
$745$	0	0
$746$	27.7082	1.01447
$747$	5.52786i	0.202254i
$748$	− 6.18034i	− 0.225976i
$749$	−23.7082	−0.866279
$750$	0	0
$751$	−1.05573	−0.0385241	−0.0192620	−	0.999814i	$-0.506132\pi$
$751$	−1.05573	−0.0385241	−0.0192620	+	0.999814i	$0.506132\pi$
$752$	− 1.23607i	− 0.0450748i
$753$	− 33.8885i	− 1.23497i
$754$	−26.6180	−0.969372
$755$	0	0
$756$	−17.7082	−0.644041
$757$	− 4.14590i	− 0.150685i	−0.997158	−	0.0753426i	$-0.975995\pi$
$757$	− 4.14590i	− 0.150685i	0.997158	−	0.0753426i	$-0.0240050\pi$
$758$	− 28.0902i	− 1.02028i
$759$	−6.38197	−0.231651
$760$	0	0
$761$	−19.1459	−0.694038	−0.347019	−	0.937858i	$-0.612806\pi$
$761$	−19.1459	−0.694038	−0.347019	+	0.937858i	$0.612806\pi$
$762$	13.7082i	0.496596i
$763$	9.52786i	0.344932i
$764$	7.09017	0.256513
$765$	0	0
$766$	17.8885	0.646339
$767$	13.5967i	0.490950i
$768$	1.61803i	0.0583858i
$769$	−23.8885	−0.861443	−0.430721	−	0.902485i	$-0.641741\pi$
$769$	−23.8885	−0.861443	−0.430721	+	0.902485i	$0.641741\pi$
$770$	0	0
$771$	1.70820	0.0615195
$772$	4.00000i	0.143963i
$773$	24.0000i	0.863220i	0.902060	+	0.431610i	$0.142054\pi$
$773$	24.0000i	0.863220i	−0.902060	+	0.431610i	$0.857946\pi$
$774$	−2.00000	−0.0718885
$775$	0	0
$776$	−0.472136	−0.0169487
$777$	− 5.23607i	− 0.187843i
$778$	6.85410i	0.245731i
$779$	−43.0132	−1.54111
$780$	0	0
$781$	−4.06888	−0.145596
$782$	− 12.7639i	− 0.456437i
$783$	51.0344i	1.82382i
$784$	−3.47214	−0.124005
$785$	0	0
$786$	36.6525	1.30735
$787$	− 25.5279i	− 0.909970i	−0.890499	−	0.454985i	$-0.849645\pi$
$787$	− 25.5279i	− 0.909970i	0.890499	−	0.454985i	$-0.150355\pi$
$788$	7.52786i	0.268169i
$789$	−21.4164	−0.762444
$790$	0	0
$791$	22.4721	0.799017
$792$	0.527864i	0.0187568i
$793$	30.3050i	1.07616i
$794$	−20.6525	−0.732929
$795$	0	0
$796$	3.05573	0.108307
$797$	46.2705i	1.63899i	0.573090	+	0.819493i	$0.305745\pi$
$797$	46.2705i	1.63899i	−0.573090	+	0.819493i	$0.694255\pi$
$798$	− 23.4164i	− 0.828932i
$799$	−5.52786	−0.195562
$800$	0	0
$801$	0.583592	0.0206202
$802$	− 4.76393i	− 0.168220i
$803$	9.79837i	0.345777i
$804$	1.76393	0.0622091
$805$	0	0
$806$	−21.0689	−0.742120
$807$	− 6.47214i	− 0.227830i
$808$	− 3.52786i	− 0.124110i
$809$	13.1246	0.461437	0.230718	−	0.973021i	$-0.425892\pi$
$809$	13.1246	0.461437	0.230718	+	0.973021i	$0.425892\pi$
$810$	0	0
$811$	−34.1033	−1.19753	−0.598765	−	0.800925i	$-0.704342\pi$
$811$	−34.1033	−1.19753	−0.598765	+	0.800925i	$0.704342\pi$
$812$	30.1803i	1.05912i
$813$	20.9443i	0.734548i
$814$	−1.38197	−0.0484379
$815$	0	0
$816$	7.23607	0.253313
$817$	− 23.4164i	− 0.819236i
$818$	26.1803i	0.915374i
$819$	3.52786	0.123274
$820$	0	0
$821$	−5.41641	−0.189034	−0.0945170	−	0.995523i	$-0.530131\pi$
$821$	−5.41641	−0.189034	−0.0945170	+	0.995523i	$0.530131\pi$
$822$	− 5.94427i	− 0.207330i
$823$	− 1.88854i	− 0.0658305i	−0.999458	−	0.0329152i	$-0.989521\pi$
$823$	− 1.88854i	− 0.0658305i	0.999458	−	0.0329152i	$-0.0104791\pi$
$824$	−17.2705	−0.601647
$825$	0	0
$826$	15.4164	0.536405
$827$	− 2.06888i	− 0.0719421i	−0.999353	−	0.0359711i	$-0.988548\pi$
$827$	− 2.06888i	− 0.0719421i	0.999353	−	0.0359711i	$-0.0114524\pi$
$828$	1.09017i	0.0378860i
$829$	−55.7984	−1.93796	−0.968979	−	0.247144i	$-0.920508\pi$
$829$	−55.7984	−1.93796	−0.968979	+	0.247144i	$0.920508\pi$
$830$	0	0
$831$	−27.1803	−0.942876
$832$	− 2.85410i	− 0.0989482i
$833$	15.5279i	0.538009i
$834$	7.85410	0.271965
$835$	0	0
$836$	−6.18034	−0.213752
$837$	40.3951i	1.39626i
$838$	10.5623i	0.364869i
$839$	36.6525	1.26538	0.632692	−	0.774404i	$-0.281950\pi$
$839$	36.6525	1.26538	0.632692	+	0.774404i	$0.281950\pi$
$840$	0	0
$841$	57.9787	1.99927
$842$	− 31.0344i	− 1.06952i
$843$	48.3607i	1.66563i
$844$	−11.2705	−0.387947
$845$	0	0
$846$	0.472136	0.0162324
$847$	29.4164i	1.01076i
$848$	− 0.472136i	− 0.0162132i
$849$	10.9443	0.375606
$850$	0	0
$851$	−2.85410	−0.0978374
$852$	− 4.76393i	− 0.163210i
$853$	− 29.7426i	− 1.01837i	−0.860657	−	0.509184i	$-0.829947\pi$
$853$	− 29.7426i	− 1.01837i	0.860657	−	0.509184i	$-0.170053\pi$
$854$	34.3607	1.17580
$855$	0	0
$856$	−7.32624	−0.250406
$857$	− 9.05573i	− 0.309338i	−0.987966	−	0.154669i	$-0.950569\pi$
$857$	− 9.05573i	− 0.309338i	0.987966	−	0.154669i	$-0.0494311\pi$
$858$	6.38197i	0.217877i
$859$	−53.4164	−1.82254	−0.911272	−	0.411805i	$-0.864899\pi$
$859$	−53.4164	−1.82254	−0.911272	+	0.411805i	$0.864899\pi$
$860$	0	0
$861$	50.3607	1.71629
$862$	12.3607i	0.421006i
$863$	− 19.4164i	− 0.660942i	−0.943816	−	0.330471i	$-0.892792\pi$
$863$	− 19.4164i	− 0.660942i	0.943816	−	0.330471i	$-0.107208\pi$
$864$	−5.47214	−0.186166
$865$	0	0
$866$	−20.6738	−0.702523
$867$	− 4.85410i	− 0.164854i
$868$	23.8885i	0.810830i
$869$	−11.8328	−0.401401
$870$	0	0
$871$	−3.11146	−0.105428
$872$	2.94427i	0.0997056i
$873$	− 0.180340i	− 0.00610358i
$874$	−12.7639	−0.431746
$875$	0	0
$876$	−11.4721	−0.387608
$877$	− 16.8328i	− 0.568404i	−0.958764	−	0.284202i	$-0.908271\pi$
$877$	− 16.8328i	− 0.568404i	0.958764	−	0.284202i	$-0.0917286\pi$
$878$	− 7.79837i	− 0.263182i
$879$	−20.4721	−0.690508
$880$	0	0
$881$	19.7426	0.665147	0.332573	−	0.943077i	$-0.392083\pi$
$881$	19.7426	0.665147	0.332573	+	0.943077i	$0.392083\pi$
$882$	− 1.32624i	− 0.0446568i
$883$	33.3050i	1.12080i	0.828222	+	0.560400i	$0.189353\pi$
$883$	33.3050i	1.12080i	−0.828222	+	0.560400i	$0.810647\pi$
$884$	−12.7639	−0.429297
$885$	0	0
$886$	15.2705	0.513023
$887$	27.8885i	0.936406i	0.883621	+	0.468203i	$0.155098\pi$
$887$	27.8885i	0.936406i	−0.883621	+	0.468203i	$0.844902\pi$
$888$	− 1.61803i	− 0.0542977i
$889$	−27.4164	−0.919517
$890$	0	0
$891$	10.6525	0.356871
$892$	14.1803i	0.474793i
$893$	5.52786i	0.184983i
$894$	26.1803	0.875602
$895$	0	0
$896$	−3.23607	−0.108109
$897$	13.1803i	0.440079i
$898$	28.4721i	0.950127i
$899$	68.8460	2.29614
$900$	0	0
$901$	−2.11146	−0.0703428
$902$	− 13.2918i	− 0.442568i
$903$	27.4164i	0.912361i
$904$	6.94427	0.230963
$905$	0	0
$906$	−6.94427	−0.230708
$907$	− 55.8885i	− 1.85575i	−0.372893	−	0.927874i	$-0.621634\pi$
$907$	− 55.8885i	− 1.85575i	0.372893	−	0.927874i	$-0.378366\pi$
$908$	4.29180i	0.142428i
$909$	1.34752	0.0446946
$910$	0	0
$911$	13.8885	0.460148	0.230074	−	0.973173i	$-0.426103\pi$
$911$	13.8885	0.460148	0.230074	+	0.973173i	$0.426103\pi$
$912$	− 7.23607i	− 0.239610i
$913$	− 20.0000i	− 0.661903i
$914$	24.7639	0.819118
$915$	0	0
$916$	−23.1246	−0.764059
$917$	73.3050i	2.42074i
$918$	24.4721i	0.807701i
$919$	5.88854	0.194245	0.0971226	−	0.995272i	$-0.469036\pi$
$919$	5.88854	0.194245	0.0971226	+	0.995272i	$0.469036\pi$
$920$	0	0
$921$	20.7984	0.685330
$922$	− 38.9443i	− 1.28256i
$923$	8.40325i	0.276596i
$924$	7.23607	0.238049
$925$	0	0
$926$	−4.56231	−0.149927
$927$	− 6.59675i	− 0.216666i
$928$	9.32624i	0.306149i
$929$	27.4508	0.900633	0.450317	−	0.892869i	$-0.351311\pi$
$929$	27.4508	0.900633	0.450317	+	0.892869i	$0.351311\pi$
$930$	0	0
$931$	15.5279	0.508905
$932$	− 6.56231i	− 0.214955i
$933$	− 43.7426i	− 1.43207i
$934$	24.3607	0.797106
$935$	0	0
$936$	1.09017	0.0356333
$937$	− 48.0476i	− 1.56965i	−0.619720	−	0.784823i	$-0.712754\pi$
$937$	− 48.0476i	− 1.56965i	0.619720	−	0.784823i	$-0.287246\pi$
$938$	3.52786i	0.115189i
$939$	45.5967	1.48799
$940$	0	0
$941$	−26.1803	−0.853455	−0.426727	−	0.904380i	$-0.640334\pi$
$941$	−26.1803	−0.853455	−0.426727	+	0.904380i	$0.640334\pi$
$942$	26.6525i	0.868385i
$943$	− 27.4508i	− 0.893923i
$944$	4.76393	0.155053
$945$	0	0
$946$	7.23607	0.235265
$947$	18.8328i	0.611984i	0.952034	+	0.305992i	$0.0989881\pi$
$947$	18.8328i	0.611984i	−0.952034	+	0.305992i	$0.901012\pi$
$948$	− 13.8541i	− 0.449960i
$949$	20.2361	0.656891
$950$	0	0
$951$	−33.8885	−1.09891
$952$	14.4721i	0.469045i
$953$	− 11.4508i	− 0.370929i	−0.982651	−	0.185465i	$-0.940621\pi$
$953$	− 11.4508i	− 0.370929i	0.982651	−	0.185465i	$-0.0593790\pi$
$954$	0.180340	0.00583872
$955$	0	0
$956$	9.85410	0.318704
$957$	− 20.8541i	− 0.674117i
$958$	− 36.5623i	− 1.18127i
$959$	11.8885	0.383901
$960$	0	0
$961$	23.4934	0.757852
$962$	2.85410i	0.0920199i
$963$	− 2.79837i	− 0.0901763i
$964$	1.52786	0.0492092
$965$	0	0
$966$	14.9443	0.480824
$967$	45.2705i	1.45580i	0.685683	+	0.727901i	$0.259504\pi$
$967$	45.2705i	1.45580i	−0.685683	+	0.727901i	$0.740496\pi$
$968$	9.09017i	0.292169i
$969$	−32.3607	−1.03957
$970$	0	0
$971$	42.3262	1.35831	0.679157	−	0.733993i	$-0.262346\pi$
$971$	42.3262	1.35831	0.679157	+	0.733993i	$0.262346\pi$
$972$	− 3.94427i	− 0.126513i
$973$	15.7082i	0.503582i
$974$	−37.3050	−1.19533
$975$	0	0
$976$	10.6180	0.339875
$977$	43.5279i	1.39258i	0.717761	+	0.696290i	$0.245167\pi$
$977$	43.5279i	1.39258i	−0.717761	+	0.696290i	$0.754833\pi$
$978$	− 5.70820i	− 0.182528i
$979$	−2.11146	−0.0674824
$980$	0	0
$981$	−1.12461	−0.0359061
$982$	− 28.4508i	− 0.907903i
$983$	31.7771i	1.01353i	0.862084	+	0.506766i	$0.169159\pi$
$983$	31.7771i	1.01353i	−0.862084	+	0.506766i	$0.830841\pi$
$984$	15.5623	0.496108
$985$	0	0
$986$	41.7082	1.32826
$987$	− 6.47214i	− 0.206010i
$988$	12.7639i	0.406075i
$989$	14.9443	0.475200
$990$	0	0
$991$	33.1033	1.05156	0.525781	−	0.850620i	$-0.323773\pi$
$991$	33.1033	1.05156	0.525781	+	0.850620i	$0.323773\pi$
$992$	7.38197i	0.234378i
$993$	45.3050i	1.43771i
$994$	9.52786	0.302205
$995$	0	0
$996$	23.4164	0.741977
$997$	− 17.7771i	− 0.563006i	−0.959560	−	0.281503i	$-0.909167\pi$
$997$	− 17.7771i	− 0.563006i	0.959560	−	0.281503i	$-0.0908329\pi$
$998$	− 10.2918i	− 0.325781i
$999$	5.47214	0.173131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.j.149.4		4
5.2	odd	4		1850.2.a.t.1.2		2
5.3	odd	4		74.2.a.b.1.1	✓	2
5.4	even	2	inner	1850.2.b.j.149.1		4
15.8	even	4		666.2.a.i.1.1		2
20.3	even	4		592.2.a.g.1.2		2
35.13	even	4		3626.2.a.s.1.2		2
40.3	even	4		2368.2.a.u.1.1		2
40.13	odd	4		2368.2.a.y.1.2		2
55.43	even	4		8954.2.a.j.1.1		2
60.23	odd	4		5328.2.a.bc.1.1		2
185.73	odd	4		2738.2.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.a.b.1.1	✓	2	5.3	odd	4
592.2.a.g.1.2		2	20.3	even	4
666.2.a.i.1.1		2	15.8	even	4
1850.2.a.t.1.2		2	5.2	odd	4
1850.2.b.j.149.1		4	5.4	even	2	inner
1850.2.b.j.149.4		4	1.1	even	1	trivial
2368.2.a.u.1.1		2	40.3	even	4
2368.2.a.y.1.2		2	40.13	odd	4
2738.2.a.g.1.1		2	185.73	odd	4
3626.2.a.s.1.2		2	35.13	even	4
5328.2.a.bc.1.1		2	60.23	odd	4
8954.2.a.j.1.1		2	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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} -1.61803 q^{6} -3.23607i q^{7} -1.00000i q^{8} +0.381966 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.61803i q^{3} -1.00000 q^{4} -1.61803 q^{6} -3.23607i q^{7} -1.00000i q^{8} +0.381966 q^{9} -1.38197 q^{11} -1.61803i q^{12} +2.85410i q^{13} +3.23607 q^{14} +1.00000 q^{16} -4.47214i q^{17} +0.381966i q^{18} -4.47214 q^{19} +5.23607 q^{21} -1.38197i q^{22} -2.85410i q^{23} +1.61803 q^{24} -2.85410 q^{26} +5.47214i q^{27} +3.23607i q^{28} +9.32624 q^{29} +7.38197 q^{31} +1.00000i q^{32} -2.23607i q^{33} +4.47214 q^{34} -0.381966 q^{36} -1.00000i q^{37} -4.47214i q^{38} -4.61803 q^{39} +9.61803 q^{41} +5.23607i q^{42} +5.23607i q^{43} +1.38197 q^{44} +2.85410 q^{46} -1.23607i q^{47} +1.61803i q^{48} -3.47214 q^{49} +7.23607 q^{51} -2.85410i q^{52} -0.472136i q^{53} -5.47214 q^{54} -3.23607 q^{56} -7.23607i q^{57} +9.32624i q^{58} +4.76393 q^{59} +10.6180 q^{61} +7.38197i q^{62} -1.23607i q^{63} -1.00000 q^{64} +2.23607 q^{66} +1.09017i q^{67} +4.47214i q^{68} +4.61803 q^{69} +2.94427 q^{71} -0.381966i q^{72} -7.09017i q^{73} +1.00000 q^{74} +4.47214 q^{76} +4.47214i q^{77} -4.61803i q^{78} +8.56231 q^{79} -7.70820 q^{81} +9.61803i q^{82} +14.4721i q^{83} -5.23607 q^{84} -5.23607 q^{86} +15.0902i q^{87} +1.38197i q^{88} +1.52786 q^{89} +9.23607 q^{91} +2.85410i q^{92} +11.9443i q^{93} +1.23607 q^{94} -1.61803 q^{96} -0.472136i q^{97} -3.47214i q^{98} -0.527864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9	\( 4 q - 4 q^{4} - 2 q^{6} + 6 q^{9} - 10 q^{11} + 4 q^{14} + 4 q^{16} + 12 q^{21} + 2 q^{24} + 2 q^{26} + 6 q^{29} + 34 q^{31} - 6 q^{36} - 14 q^{39} + 34 q^{41} + 10 q^{44} - 2 q^{46} + 4 q^{49} + 20 q^{51} - 4 q^{54} - 4 q^{56} + 28 q^{59} + 38 q^{61} - 4 q^{64} + 14 q^{69} - 24 q^{71} + 4 q^{74} - 6 q^{79} - 4 q^{81} - 12 q^{84} - 12 q^{86} + 24 q^{89} + 28 q^{91} - 4 q^{94} - 2 q^{96} - 20 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 + 6 * q^9 - 10 * q^11 + 4 * q^14 + 4 * q^16 + 12 * q^21 + 2 * q^24 + 2 * q^26 + 6 * q^29 + 34 * q^31 - 6 * q^36 - 14 * q^39 + 34 * q^41 + 10 * q^44 - 2 * q^46 + 4 * q^49 + 20 * q^51 - 4 * q^54 - 4 * q^56 + 28 * q^59 + 38 * q^61 - 4 * q^64 + 14 * q^69 - 24 * q^71 + 4 * q^74 - 6 * q^79 - 4 * q^81 - 12 * q^84 - 12 * q^86 + 24 * q^89 + 28 * q^91 - 4 * q^94 - 2 * q^96 - 20 * q^99

Introduction

L-functions

Modular forms

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Database

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