LMFDB - Embedded newform 1925.2.b.n.1849.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1849,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, 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("1925.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.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:	$15.3712023891$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 385)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.3
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	1925.1849
Dual form			1925.2.b.n.1849.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21432i q^{2} -0.688892i q^{3} +0.525428 q^{4} -0.836535 q^{6} +1.00000i q^{7} -3.06668i q^{8} +2.52543 q^{9} +O(q^{10})$	\(q-1.21432i q^{2} -0.688892i q^{3} +0.525428 q^{4} -0.836535 q^{6} +1.00000i q^{7} -3.06668i q^{8} +2.52543 q^{9} -1.00000 q^{11} -0.361963i q^{12} -3.73975i q^{13} +1.21432 q^{14} -2.67307 q^{16} -0.0666765i q^{17} -3.06668i q^{18} -6.42864 q^{19} +0.688892 q^{21} +1.21432i q^{22} -1.09679i q^{23} -2.11261 q^{24} -4.54125 q^{26} -3.80642i q^{27} +0.525428i q^{28} +7.80642 q^{29} -5.59210 q^{31} -2.88739i q^{32} +0.688892i q^{33} -0.0809666 q^{34} +1.32693 q^{36} -1.33185i q^{37} +7.80642i q^{38} -2.57628 q^{39} +6.64296 q^{41} -0.836535i q^{42} -11.7605i q^{43} -0.525428 q^{44} -1.33185 q^{46} +2.26025i q^{47} +1.84146i q^{48} -1.00000 q^{49} -0.0459330 q^{51} -1.96497i q^{52} -1.71900i q^{53} -4.62222 q^{54} +3.06668 q^{56} +4.42864i q^{57} -9.47949i q^{58} -2.54125 q^{59} +14.4494 q^{61} +6.79060i q^{62} +2.52543i q^{63} -8.85236 q^{64} +0.836535 q^{66} -10.3827i q^{67} -0.0350337i q^{68} -0.755569 q^{69} -12.5620 q^{71} -7.74467i q^{72} +1.17775i q^{73} -1.61729 q^{74} -3.37778 q^{76} -1.00000i q^{77} +3.12843i q^{78} +8.51606 q^{79} +4.95407 q^{81} -8.06668i q^{82} -12.1017i q^{83} +0.361963 q^{84} -14.2810 q^{86} -5.37778i q^{87} +3.06668i q^{88} -15.6128 q^{89} +3.73975 q^{91} -0.576283i q^{92} +3.85236i q^{93} +2.74467 q^{94} -1.98910 q^{96} +13.4193i q^{97} +1.21432i q^{98} -2.52543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 8 * q^6 + 2 * q^9	$ 6 q - 10 q^{4} + 8 q^{6} + 2 q^{9} - 6 q^{11} - 6 q^{14} + 10 q^{16} - 12 q^{19} + 4 q^{21} - 52 q^{24} - 40 q^{26} + 20 q^{29} - 20 q^{31} + 12 q^{34} + 34 q^{36} + 24 q^{39} + 10 q^{44} + 32 q^{46} - 6 q^{49} - 40 q^{51} - 28 q^{54} + 18 q^{56} - 28 q^{59} + 20 q^{61} - 66 q^{64} - 8 q^{66} - 4 q^{69} - 48 q^{71} - 76 q^{74} - 20 q^{76} - 16 q^{79} - 10 q^{81} - 24 q^{84} - 72 q^{86} - 40 q^{89} - 4 q^{91} - 76 q^{94} + 80 q^{96} - 2 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 8 * q^6 + 2 * q^9 - 6 * q^11 - 6 * q^14 + 10 * q^16 - 12 * q^19 + 4 * q^21 - 52 * q^24 - 40 * q^26 + 20 * q^29 - 20 * q^31 + 12 * q^34 + 34 * q^36 + 24 * q^39 + 10 * q^44 + 32 * q^46 - 6 * q^49 - 40 * q^51 - 28 * q^54 + 18 * q^56 - 28 * q^59 + 20 * q^61 - 66 * q^64 - 8 * q^66 - 4 * q^69 - 48 * q^71 - 76 * q^74 - 20 * q^76 - 16 * q^79 - 10 * q^81 - 24 * q^84 - 72 * q^86 - 40 * q^89 - 4 * q^91 - 76 * q^94 + 80 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1925\mathbb{Z}\right)^\times$.

$n$	$276$	$1002$	$1751$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	− 1.21432i	− 0.858654i	−0.903149	−	0.429327i	$-0.858751\pi$
$2$	− 1.21432i	− 0.858654i	0.903149	−	0.429327i	$-0.141249\pi$
$3$	− 0.688892i	− 0.397732i	−0.980027	−	0.198866i	$-0.936274\pi$
$3$	− 0.688892i	− 0.397732i	0.980027	−	0.198866i	$-0.0637259\pi$
$4$	0.525428	0.262714
$5$	0	0
$5$	0	0
$6$	−0.836535	−0.341514
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 3.06668i	− 1.08423i
$9$	2.52543	0.841809
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	− 0.361963i	− 0.104490i
$13$	− 3.73975i	− 1.03722i	−0.855011	−	0.518610i	$-0.826450\pi$
$13$	− 3.73975i	− 1.03722i	0.855011	−	0.518610i	$-0.173550\pi$
$14$	1.21432	0.324541
$15$	0	0
$16$	−2.67307	−0.668268
$17$	− 0.0666765i	− 0.0161714i	−0.999967	−	0.00808572i	$-0.997426\pi$
$17$	− 0.0666765i	− 0.0161714i	0.999967	−	0.00808572i	$-0.00257379\pi$
$18$	− 3.06668i	− 0.722823i
$19$	−6.42864	−1.47483	−0.737416	−	0.675439i	$-0.763954\pi$
$19$	−6.42864	−1.47483	−0.737416	+	0.675439i	$0.763954\pi$
$20$	0	0
$21$	0.688892	0.150329
$22$	1.21432i	0.258894i
$23$	− 1.09679i	− 0.228696i	−0.993441	−	0.114348i	$-0.963522\pi$
$23$	− 1.09679i	− 0.228696i	0.993441	−	0.114348i	$-0.0364779\pi$
$24$	−2.11261	−0.431235
$25$	0	0
$26$	−4.54125	−0.890612
$27$	− 3.80642i	− 0.732547i
$28$	0.525428i	0.0992965i
$29$	7.80642	1.44962	0.724808	−	0.688951i	$-0.241928\pi$
$29$	7.80642	1.44962	0.724808	+	0.688951i	$0.241928\pi$
$30$	0	0
$31$	−5.59210	−1.00437	−0.502186	−	0.864760i	$-0.667471\pi$
$31$	−5.59210	−1.00437	−0.502186	+	0.864760i	$0.667471\pi$
$32$	− 2.88739i	− 0.510423i
$33$	0.688892i	0.119921i
$34$	−0.0809666	−0.0138857
$35$	0	0
$36$	1.32693	0.221155
$37$	− 1.33185i	− 0.218955i	−0.993989	−	0.109478i	$-0.965082\pi$
$37$	− 1.33185i	− 0.218955i	0.993989	−	0.109478i	$-0.0349178\pi$
$38$	7.80642i	1.26637i
$39$	−2.57628	−0.412535
$40$	0	0
$41$	6.64296	1.03746	0.518728	−	0.854939i	$-0.326406\pi$
$41$	6.64296	1.03746	0.518728	+	0.854939i	$0.326406\pi$
$42$	− 0.836535i	− 0.129080i
$43$	− 11.7605i	− 1.79346i	−0.442580	−	0.896729i	$-0.645937\pi$
$43$	− 11.7605i	− 1.79346i	0.442580	−	0.896729i	$-0.354063\pi$
$44$	−0.525428	−0.0792112
$45$	0	0
$46$	−1.33185	−0.196371
$47$	2.26025i	0.329692i	0.986319	+	0.164846i	$0.0527127\pi$
$47$	2.26025i	0.329692i	−0.986319	+	0.164846i	$0.947287\pi$
$48$	1.84146i	0.265792i
$49$	−1.00000	−0.142857
$50$	0	0
$51$	−0.0459330	−0.00643190
$52$	− 1.96497i	− 0.272492i
$53$	− 1.71900i	− 0.236123i	−0.993006	−	0.118062i	$-0.962332\pi$
$53$	− 1.71900i	− 0.236123i	0.993006	−	0.118062i	$-0.0376680\pi$
$54$	−4.62222	−0.629004
$55$	0	0
$56$	3.06668	0.409802
$57$	4.42864i	0.586588i
$58$	− 9.47949i	− 1.24472i
$59$	−2.54125	−0.330842	−0.165421	−	0.986223i	$-0.552898\pi$
$59$	−2.54125	−0.330842	−0.165421	+	0.986223i	$0.552898\pi$
$60$	0	0
$61$	14.4494	1.85005	0.925027	−	0.379901i	$-0.124042\pi$
$61$	14.4494	1.85005	0.925027	+	0.379901i	$0.124042\pi$
$62$	6.79060i	0.862407i
$63$	2.52543i	0.318174i
$64$	−8.85236	−1.10654
$65$	0	0
$66$	0.836535	0.102970
$67$	− 10.3827i	− 1.26845i	−0.773149	−	0.634225i	$-0.781319\pi$
$67$	− 10.3827i	− 1.26845i	0.773149	−	0.634225i	$-0.218681\pi$
$68$	− 0.0350337i	− 0.00424846i
$69$	−0.755569	−0.0909598
$70$	0	0
$71$	−12.5620	−1.49083	−0.745417	−	0.666598i	$-0.767750\pi$
$71$	−12.5620	−1.49083	−0.745417	+	0.666598i	$0.767750\pi$
$72$	− 7.74467i	− 0.912718i
$73$	1.17775i	0.137846i	0.997622	+	0.0689229i	$0.0219562\pi$
$73$	1.17775i	0.137846i	−0.997622	+	0.0689229i	$0.978044\pi$
$74$	−1.61729	−0.188007
$75$	0	0
$76$	−3.37778	−0.387458
$77$	− 1.00000i	− 0.113961i
$78$	3.12843i	0.354225i
$79$	8.51606	0.958132	0.479066	−	0.877779i	$-0.340976\pi$
$79$	8.51606	0.958132	0.479066	+	0.877779i	$0.340976\pi$
$80$	0	0
$81$	4.95407	0.550452
$82$	− 8.06668i	− 0.890815i
$83$	− 12.1017i	− 1.32834i	−0.747584	−	0.664168i	$-0.768786\pi$
$83$	− 12.1017i	− 1.32834i	0.747584	−	0.664168i	$-0.231214\pi$
$84$	0.361963	0.0394934
$85$	0	0
$86$	−14.2810	−1.53996
$87$	− 5.37778i	− 0.576559i
$88$	3.06668i	0.326909i
$89$	−15.6128	−1.65496	−0.827479	−	0.561496i	$-0.810226\pi$
$89$	−15.6128	−1.65496	−0.827479	+	0.561496i	$0.810226\pi$
$90$	0	0
$91$	3.73975	0.392032
$92$	− 0.576283i	− 0.0600816i
$93$	3.85236i	0.399471i
$94$	2.74467	0.283091
$95$	0	0
$96$	−1.98910	−0.203012
$97$	13.4193i	1.36252i	0.732041	+	0.681260i	$0.238568\pi$
$97$	13.4193i	1.36252i	−0.732041	+	0.681260i	$0.761432\pi$
$98$	1.21432i	0.122665i
$99$	−2.52543	−0.253815
$100$	0	0
$101$	−8.44938	−0.840745	−0.420373	−	0.907352i	$-0.638101\pi$
$101$	−8.44938	−0.840745	−0.420373	+	0.907352i	$0.638101\pi$
$102$	0.0557773i	0.00552277i
$103$	− 9.54617i	− 0.940612i	−0.882503	−	0.470306i	$-0.844144\pi$
$103$	− 9.54617i	− 0.940612i	0.882503	−	0.470306i	$-0.155856\pi$
$104$	−11.4686	−1.12459
$105$	0	0
$106$	−2.08742	−0.202748
$107$	8.56199i	0.827719i	0.910341	+	0.413860i	$0.135820\pi$
$107$	8.56199i	0.827719i	−0.910341	+	0.413860i	$0.864180\pi$
$108$	− 2.00000i	− 0.192450i
$109$	6.99063	0.669581	0.334791	−	0.942293i	$-0.391334\pi$
$109$	6.99063	0.669581	0.334791	+	0.942293i	$0.391334\pi$
$110$	0	0
$111$	−0.917502	−0.0870854
$112$	− 2.67307i	− 0.252581i
$113$	− 1.57136i	− 0.147821i	−0.997265	−	0.0739106i	$-0.976452\pi$
$113$	− 1.57136i	− 0.147821i	0.997265	−	0.0739106i	$-0.0235479\pi$
$114$	5.37778	0.503676
$115$	0	0
$116$	4.10171	0.380834
$117$	− 9.44446i	− 0.873141i
$118$	3.08589i	0.284079i
$119$	0.0666765	0.00611223
$120$	0	0
$121$	1.00000	0.0909091
$122$	− 17.5462i	− 1.58856i
$123$	− 4.57628i	− 0.412630i
$124$	−2.93825	−0.263862
$125$	0	0
$126$	3.06668	0.273201
$127$	13.3778i	1.18709i	0.804802	+	0.593543i	$0.202271\pi$
$127$	13.3778i	1.18709i	−0.804802	+	0.593543i	$0.797729\pi$
$128$	4.97481i	0.439715i
$129$	−8.10171	−0.713316
$130$	0	0
$131$	−2.75557	−0.240755	−0.120378	−	0.992728i	$-0.538411\pi$
$131$	−2.75557	−0.240755	−0.120378	+	0.992728i	$0.538411\pi$
$132$	0.361963i	0.0315048i
$133$	− 6.42864i	− 0.557434i
$134$	−12.6079	−1.08916
$135$	0	0
$136$	−0.204475	−0.0175336
$137$	17.8938i	1.52877i	0.644758	+	0.764387i	$0.276958\pi$
$137$	17.8938i	1.52877i	−0.644758	+	0.764387i	$0.723042\pi$
$138$	0.917502i	0.0781030i
$139$	3.86665	0.327965	0.163982	−	0.986463i	$-0.447566\pi$
$139$	3.86665	0.327965	0.163982	+	0.986463i	$0.447566\pi$
$140$	0	0
$141$	1.55707	0.131129
$142$	15.2543i	1.28011i
$143$	3.73975i	0.312733i
$144$	−6.75065	−0.562554
$145$	0	0
$146$	1.43017	0.118362
$147$	0.688892i	0.0568189i
$148$	− 0.699791i	− 0.0575225i
$149$	−4.88892	−0.400516	−0.200258	−	0.979743i	$-0.564178\pi$
$149$	−4.88892	−0.400516	−0.200258	+	0.979743i	$0.564178\pi$
$150$	0	0
$151$	22.1891	1.80573	0.902863	−	0.429929i	$-0.141461\pi$
$151$	22.1891	1.80573	0.902863	+	0.429929i	$0.141461\pi$
$152$	19.7146i	1.59906i
$153$	− 0.168387i	− 0.0136133i
$154$	−1.21432	−0.0978527
$155$	0	0
$156$	−1.35365	−0.108379
$157$	4.81579i	0.384342i	0.981361	+	0.192171i	$0.0615528\pi$
$157$	4.81579i	0.384342i	−0.981361	+	0.192171i	$0.938447\pi$
$158$	− 10.3412i	− 0.822703i
$159$	−1.18421	−0.0939138
$160$	0	0
$161$	1.09679	0.0864390
$162$	− 6.01582i	− 0.472648i
$163$	6.08742i	0.476804i	0.971167	+	0.238402i	$0.0766235\pi$
$163$	6.08742i	0.476804i	−0.971167	+	0.238402i	$0.923376\pi$
$164$	3.49039	0.272554
$165$	0	0
$166$	−14.6953	−1.14058
$167$	3.67307i	0.284231i	0.989850	+	0.142115i	$0.0453904\pi$
$167$	3.67307i	0.284231i	−0.989850	+	0.142115i	$0.954610\pi$
$168$	− 2.11261i	− 0.162991i
$169$	−0.985710	−0.0758238
$170$	0	0
$171$	−16.2351	−1.24153
$172$	− 6.17929i	− 0.471166i
$173$	− 0.628669i	− 0.0477968i	−0.999714	−	0.0238984i	$-0.992392\pi$
$173$	− 0.628669i	− 0.0477968i	0.999714	−	0.0238984i	$-0.00760783\pi$
$174$	−6.53035	−0.495065
$175$	0	0
$176$	2.67307	0.201490
$177$	1.75065i	0.131587i
$178$	18.9590i	1.42104i
$179$	7.70471	0.575877	0.287939	−	0.957649i	$-0.407030\pi$
$179$	7.70471	0.575877	0.287939	+	0.957649i	$0.407030\pi$
$180$	0	0
$181$	10.9175	0.811492	0.405746	−	0.913986i	$-0.367012\pi$
$181$	10.9175	0.811492	0.405746	+	0.913986i	$0.367012\pi$
$182$	− 4.54125i	− 0.336620i
$183$	− 9.95407i	− 0.735826i
$184$	−3.36349	−0.247960
$185$	0	0
$186$	4.67799	0.343007
$187$	0.0666765i	0.00487587i
$188$	1.18760i	0.0866146i
$189$	3.80642	0.276877
$190$	0	0
$191$	−10.9175	−0.789963	−0.394981	−	0.918689i	$-0.629249\pi$
$191$	−10.9175	−0.789963	−0.394981	+	0.918689i	$0.629249\pi$
$192$	6.09832i	0.440108i
$193$	11.7003i	0.842204i	0.907013	+	0.421102i	$0.138357\pi$
$193$	11.7003i	0.842204i	−0.907013	+	0.421102i	$0.861643\pi$
$194$	16.2953	1.16993
$195$	0	0
$196$	−0.525428	−0.0375305
$197$	− 10.8430i	− 0.772531i	−0.922388	−	0.386265i	$-0.873765\pi$
$197$	− 10.8430i	− 0.772531i	0.922388	−	0.386265i	$-0.126235\pi$
$198$	3.06668i	0.217939i
$199$	−2.08097	−0.147516	−0.0737579	−	0.997276i	$-0.523499\pi$
$199$	−2.08097	−0.147516	−0.0737579	+	0.997276i	$0.523499\pi$
$200$	0	0
$201$	−7.15257	−0.504503
$202$	10.2603i	0.721909i
$203$	7.80642i	0.547904i
$204$	−0.0241344	−0.00168975
$205$	0	0
$206$	−11.5921	−0.807660
$207$	− 2.76986i	− 0.192518i
$208$	9.99661i	0.693140i
$209$	6.42864	0.444678
$210$	0	0
$211$	23.0923	1.58974	0.794871	−	0.606778i	$-0.207538\pi$
$211$	23.0923	1.58974	0.794871	+	0.606778i	$0.207538\pi$
$212$	− 0.903212i	− 0.0620328i
$213$	8.65386i	0.592953i
$214$	10.3970	0.710724
$215$	0	0
$216$	−11.6731	−0.794252
$217$	− 5.59210i	− 0.379617i
$218$	− 8.48886i	− 0.574938i
$219$	0.811346	0.0548257
$220$	0	0
$221$	−0.249353	−0.0167733
$222$	1.11414i	0.0747762i
$223$	− 21.5462i	− 1.44284i	−0.692499	−	0.721419i	$-0.743490\pi$
$223$	− 21.5462i	− 1.44284i	0.692499	−	0.721419i	$-0.256510\pi$
$224$	2.88739	0.192922
$225$	0	0
$226$	−1.90813	−0.126927
$227$	27.2257i	1.80703i	0.428553	+	0.903516i	$0.359023\pi$
$227$	27.2257i	1.80703i	−0.428553	+	0.903516i	$0.640977\pi$
$228$	2.32693i	0.154105i
$229$	−25.0005	−1.65208	−0.826039	−	0.563613i	$-0.809411\pi$
$229$	−25.0005	−1.65208	−0.826039	+	0.563613i	$0.809411\pi$
$230$	0	0
$231$	−0.688892	−0.0453258
$232$	− 23.9398i	− 1.57172i
$233$	− 3.65878i	− 0.239695i	−0.992792	−	0.119847i	$-0.961759\pi$
$233$	− 3.65878i	− 0.239695i	0.992792	−	0.119847i	$-0.0382405\pi$
$234$	−11.4686	−0.749726
$235$	0	0
$236$	−1.33524	−0.0869169
$237$	− 5.86665i	− 0.381080i
$238$	− 0.0809666i	− 0.00524829i
$239$	−14.7052	−0.951200	−0.475600	−	0.879662i	$-0.657769\pi$
$239$	−14.7052	−0.951200	−0.475600	+	0.879662i	$0.657769\pi$
$240$	0	0
$241$	13.6938	0.882096	0.441048	−	0.897483i	$-0.354607\pi$
$241$	13.6938	0.882096	0.441048	+	0.897483i	$0.354607\pi$
$242$	− 1.21432i	− 0.0780594i
$243$	− 14.8321i	− 0.951479i
$244$	7.59210	0.486035
$245$	0	0
$246$	−5.55707	−0.354306
$247$	24.0415i	1.52972i
$248$	17.1492i	1.08897i
$249$	−8.33677	−0.528322
$250$	0	0
$251$	−11.0114	−0.695032	−0.347516	−	0.937674i	$-0.612975\pi$
$251$	−11.0114	−0.695032	−0.347516	+	0.937674i	$0.612975\pi$
$252$	1.32693i	0.0835887i
$253$	1.09679i	0.0689545i
$254$	16.2449	1.01930
$255$	0	0
$256$	−11.6637	−0.728981
$257$	15.9496i	0.994910i	0.867490	+	0.497455i	$0.165732\pi$
$257$	15.9496i	0.994910i	−0.867490	+	0.497455i	$0.834268\pi$
$258$	9.83807i	0.612491i
$259$	1.33185	0.0827572
$260$	0	0
$261$	19.7146	1.22030
$262$	3.34614i	0.206725i
$263$	− 5.11108i	− 0.315163i	−0.987506	−	0.157581i	$-0.949630\pi$
$263$	− 5.11108i	− 0.315163i	0.987506	−	0.157581i	$-0.0503696\pi$
$264$	2.11261	0.130022
$265$	0	0
$266$	−7.80642	−0.478643
$267$	10.7556i	0.658230i
$268$	− 5.45536i	− 0.333239i
$269$	18.2351	1.11181	0.555906	−	0.831245i	$-0.312372\pi$
$269$	18.2351	1.11181	0.555906	+	0.831245i	$0.312372\pi$
$270$	0	0
$271$	6.23506	0.378753	0.189377	−	0.981905i	$-0.439353\pi$
$271$	6.23506	0.378753	0.189377	+	0.981905i	$0.439353\pi$
$272$	0.178231i	0.0108068i
$273$	− 2.57628i	− 0.155924i
$274$	21.7288	1.31269
$275$	0	0
$276$	−0.396997	−0.0238964
$277$	− 6.32248i	− 0.379881i	−0.981796	−	0.189941i	$-0.939170\pi$
$277$	− 6.32248i	− 0.379881i	0.981796	−	0.189941i	$-0.0608295\pi$
$278$	− 4.69535i	− 0.281608i
$279$	−14.1225	−0.845489
$280$	0	0
$281$	−25.2257	−1.50484	−0.752419	−	0.658684i	$-0.771113\pi$
$281$	−25.2257	−1.50484	−0.752419	+	0.658684i	$0.771113\pi$
$282$	− 1.89078i	− 0.112594i
$283$	13.4193i	0.797693i	0.917018	+	0.398846i	$0.130589\pi$
$283$	13.4193i	0.797693i	−0.917018	+	0.398846i	$0.869411\pi$
$284$	−6.60042	−0.391663
$285$	0	0
$286$	4.54125	0.268530
$287$	6.64296i	0.392121i
$288$	− 7.29190i	− 0.429679i
$289$	16.9956	0.999738
$290$	0	0
$291$	9.24443	0.541918
$292$	0.618825i	0.0362140i
$293$	17.6064i	1.02858i	0.857617	+	0.514288i	$0.171944\pi$
$293$	17.6064i	1.02858i	−0.857617	+	0.514288i	$0.828056\pi$
$294$	0.836535	0.0487877
$295$	0	0
$296$	−4.08436	−0.237398
$297$	3.80642i	0.220871i
$298$	5.93671i	0.343905i
$299$	−4.10171	−0.237208
$300$	0	0
$301$	11.7605	0.677863
$302$	− 26.9447i	− 1.55049i
$303$	5.82071i	0.334391i
$304$	17.1842	0.985582
$305$	0	0
$306$	−0.204475	−0.0116891
$307$	− 26.3368i	− 1.50312i	−0.659665	−	0.751560i	$-0.729302\pi$
$307$	− 26.3368i	− 1.50312i	0.659665	−	0.751560i	$-0.270698\pi$
$308$	− 0.525428i	− 0.0299390i
$309$	−6.57628	−0.374112
$310$	0	0
$311$	5.96052	0.337990	0.168995	−	0.985617i	$-0.445948\pi$
$311$	5.96052	0.337990	0.168995	+	0.985617i	$0.445948\pi$
$312$	7.90063i	0.447285i
$313$	− 5.52098i	− 0.312064i	−0.987752	−	0.156032i	$-0.950130\pi$
$313$	− 5.52098i	− 0.312064i	0.987752	−	0.156032i	$-0.0498704\pi$
$314$	5.84791	0.330017
$315$	0	0
$316$	4.47457	0.251714
$317$	15.7146i	0.882618i	0.897355	+	0.441309i	$0.145486\pi$
$317$	15.7146i	0.882618i	−0.897355	+	0.441309i	$0.854514\pi$
$318$	1.43801i	0.0806395i
$319$	−7.80642	−0.437076
$320$	0	0
$321$	5.89829	0.329210
$322$	− 1.33185i	− 0.0742212i
$323$	0.428639i	0.0238501i
$324$	2.60300	0.144611
$325$	0	0
$326$	7.39207	0.409409
$327$	− 4.81579i	− 0.266314i
$328$	− 20.3718i	− 1.12484i
$329$	−2.26025	−0.124612
$330$	0	0
$331$	18.2351	1.00229	0.501145	−	0.865363i	$-0.332912\pi$
$331$	18.2351	1.00229	0.501145	+	0.865363i	$0.332912\pi$
$332$	− 6.35857i	− 0.348972i
$333$	− 3.36349i	− 0.184318i
$334$	4.46028	0.244056
$335$	0	0
$336$	−1.84146	−0.100460
$337$	− 32.2908i	− 1.75899i	−0.475904	−	0.879497i	$-0.657879\pi$
$337$	− 32.2908i	− 1.75899i	0.475904	−	0.879497i	$-0.342121\pi$
$338$	1.19697i	0.0651064i
$339$	−1.08250	−0.0587932
$340$	0	0
$341$	5.59210	0.302829
$342$	19.7146i	1.06604i
$343$	− 1.00000i	− 0.0539949i
$344$	−36.0656	−1.94453
$345$	0	0
$346$	−0.763405	−0.0410409
$347$	− 22.6909i	− 1.21811i	−0.793127	−	0.609056i	$-0.791549\pi$
$347$	− 22.6909i	− 1.21811i	0.793127	−	0.609056i	$-0.208451\pi$
$348$	− 2.82564i	− 0.151470i
$349$	−16.9097	−0.905154	−0.452577	−	0.891725i	$-0.649495\pi$
$349$	−16.9097	−0.905154	−0.452577	+	0.891725i	$0.649495\pi$
$350$	0	0
$351$	−14.2351	−0.759811
$352$	2.88739i	0.153898i
$353$	24.3970i	1.29852i	0.760566	+	0.649261i	$0.224922\pi$
$353$	24.3970i	1.29852i	−0.760566	+	0.649261i	$0.775078\pi$
$354$	2.12584	0.112987
$355$	0	0
$356$	−8.20342	−0.434780
$357$	− 0.0459330i	− 0.00243103i
$358$	− 9.35599i	− 0.494479i
$359$	32.8113	1.73172	0.865858	−	0.500289i	$-0.166773\pi$
$359$	32.8113	1.73172	0.865858	+	0.500289i	$0.166773\pi$
$360$	0	0
$361$	22.3274	1.17513
$362$	− 13.2573i	− 0.696790i
$363$	− 0.688892i	− 0.0361575i
$364$	1.96497	0.102992
$365$	0	0
$366$	−12.0874	−0.631820
$367$	6.94269i	0.362406i	0.983446	+	0.181203i	$0.0579990\pi$
$367$	6.94269i	0.362406i	−0.983446	+	0.181203i	$0.942001\pi$
$368$	2.93179i	0.152830i
$369$	16.7763	0.873340
$370$	0	0
$371$	1.71900	0.0892462
$372$	2.02413i	0.104946i
$373$	36.9733i	1.91440i	0.289421	+	0.957202i	$0.406537\pi$
$373$	36.9733i	1.91440i	−0.289421	+	0.957202i	$0.593463\pi$
$374$	0.0809666	0.00418669
$375$	0	0
$376$	6.93146	0.357463
$377$	− 29.1941i	− 1.50357i
$378$	− 4.62222i	− 0.237741i
$379$	23.6414	1.21438	0.607189	−	0.794557i	$-0.292297\pi$
$379$	23.6414	1.21438	0.607189	+	0.794557i	$0.292297\pi$
$380$	0	0
$381$	9.21585	0.472142
$382$	13.2573i	0.678304i
$383$	13.7210i	0.701111i	0.936542	+	0.350555i	$0.114007\pi$
$383$	13.7210i	0.701111i	−0.936542	+	0.350555i	$0.885993\pi$
$384$	3.42711	0.174889
$385$	0	0
$386$	14.2079	0.723161
$387$	− 29.7003i	− 1.50975i
$388$	7.05086i	0.357953i
$389$	15.5526	0.788549	0.394275	−	0.918993i	$-0.370996\pi$
$389$	15.5526	0.788549	0.394275	+	0.918993i	$0.370996\pi$
$390$	0	0
$391$	−0.0731300	−0.00369835
$392$	3.06668i	0.154891i
$393$	1.89829i	0.0957561i
$394$	−13.1669	−0.663337
$395$	0	0
$396$	−1.32693	−0.0666807
$397$	0.253799i	0.0127378i	0.999980	+	0.00636891i	$0.00202730\pi$
$397$	0.253799i	0.0127378i	−0.999980	+	0.00636891i	$0.997973\pi$
$398$	2.52696i	0.126665i
$399$	−4.42864	−0.221709
$400$	0	0
$401$	20.3684	1.01715	0.508575	−	0.861018i	$-0.330172\pi$
$401$	20.3684	1.01715	0.508575	+	0.861018i	$0.330172\pi$
$402$	8.68550i	0.433193i
$403$	20.9131i	1.04175i
$404$	−4.43954	−0.220875
$405$	0	0
$406$	9.47949	0.470459
$407$	1.33185i	0.0660174i
$408$	0.140862i	0.00697368i
$409$	−12.1225	−0.599417	−0.299708	−	0.954031i	$-0.596889\pi$
$409$	−12.1225	−0.599417	−0.299708	+	0.954031i	$0.596889\pi$
$410$	0	0
$411$	12.3269	0.608043
$412$	− 5.01582i	− 0.247112i
$413$	− 2.54125i	− 0.125047i
$414$	−3.36349	−0.165307
$415$	0	0
$416$	−10.7981	−0.529421
$417$	− 2.66370i	− 0.130442i
$418$	− 7.80642i	− 0.381825i
$419$	21.4400	1.04741	0.523707	−	0.851899i	$-0.324549\pi$
$419$	21.4400	1.04741	0.523707	+	0.851899i	$0.324549\pi$
$420$	0	0
$421$	29.8622	1.45539	0.727697	−	0.685898i	$-0.240591\pi$
$421$	29.8622	1.45539	0.727697	+	0.685898i	$0.240591\pi$
$422$	− 28.0415i	− 1.36504i
$423$	5.70810i	0.277538i
$424$	−5.27163	−0.256013
$425$	0	0
$426$	10.5086	0.509141
$427$	14.4494i	0.699255i
$428$	4.49871i	0.217453i
$429$	2.57628	0.124384
$430$	0	0
$431$	−19.6588	−0.946930	−0.473465	−	0.880813i	$-0.656997\pi$
$431$	−19.6588	−0.946930	−0.473465	+	0.880813i	$0.656997\pi$
$432$	10.1748i	0.489537i
$433$	− 32.9719i	− 1.58453i	−0.610178	−	0.792264i	$-0.708902\pi$
$433$	− 32.9719i	− 1.58453i	0.610178	−	0.792264i	$-0.291098\pi$
$434$	−6.79060	−0.325959
$435$	0	0
$436$	3.67307	0.175908
$437$	7.05086i	0.337288i
$438$	− 0.985233i	− 0.0470763i
$439$	0.815792	0.0389356	0.0194678	−	0.999810i	$-0.493803\pi$
$439$	0.815792	0.0389356	0.0194678	+	0.999810i	$0.493803\pi$
$440$	0	0
$441$	−2.52543	−0.120258
$442$	0.302795i	0.0144025i
$443$	24.9763i	1.18666i	0.804959	+	0.593331i	$0.202187\pi$
$443$	24.9763i	1.18666i	−0.804959	+	0.593331i	$0.797813\pi$
$444$	−0.482081	−0.0228785
$445$	0	0
$446$	−26.1639	−1.23890
$447$	3.36794i	0.159298i
$448$	− 8.85236i	− 0.418235i
$449$	−0.414349	−0.0195544	−0.00977718	−	0.999952i	$-0.503112\pi$
$449$	−0.414349	−0.0195544	−0.00977718	+	0.999952i	$0.503112\pi$
$450$	0	0
$451$	−6.64296	−0.312805
$452$	− 0.825636i	− 0.0388347i
$453$	− 15.2859i	− 0.718195i
$454$	33.0607	1.55162
$455$	0	0
$456$	13.5812	0.635998
$457$	− 9.33185i	− 0.436526i	−0.975890	−	0.218263i	$-0.929961\pi$
$457$	− 9.33185i	− 0.436526i	0.975890	−	0.218263i	$-0.0700390\pi$
$458$	30.3586i	1.41856i
$459$	−0.253799	−0.0118463
$460$	0	0
$461$	29.9891	1.39673	0.698366	−	0.715741i	$-0.253911\pi$
$461$	29.9891	1.39673	0.698366	+	0.715741i	$0.253911\pi$
$462$	0.836535i	0.0389191i
$463$	− 31.5353i	− 1.46557i	−0.680461	−	0.732784i	$-0.738220\pi$
$463$	− 31.5353i	− 1.46557i	0.680461	−	0.732784i	$-0.261780\pi$
$464$	−20.8671	−0.968732
$465$	0	0
$466$	−4.44293	−0.205815
$467$	5.67952i	0.262817i	0.991328	+	0.131409i	$0.0419500\pi$
$467$	5.67952i	0.262817i	−0.991328	+	0.131409i	$0.958050\pi$
$468$	− 4.96238i	− 0.229386i
$469$	10.3827	0.479429
$470$	0	0
$471$	3.31756	0.152865
$472$	7.79319i	0.358711i
$473$	11.7605i	0.540748i
$474$	−7.12399	−0.327215
$475$	0	0
$476$	0.0350337	0.00160577
$477$	− 4.34122i	− 0.198771i
$478$	17.8568i	0.816751i
$479$	39.4608	1.80301	0.901504	−	0.432771i	$-0.142464\pi$
$479$	39.4608	1.80301	0.901504	+	0.432771i	$0.142464\pi$
$480$	0	0
$481$	−4.98079	−0.227104
$482$	− 16.6287i	− 0.757415i
$483$	− 0.755569i	− 0.0343796i
$484$	0.525428	0.0238831
$485$	0	0
$486$	−18.0109	−0.816991
$487$	3.19850i	0.144938i	0.997371	+	0.0724689i	$0.0230878\pi$
$487$	3.19850i	0.144938i	−0.997371	+	0.0724689i	$0.976912\pi$
$488$	− 44.3116i	− 2.00589i
$489$	4.19358	0.189640
$490$	0	0
$491$	26.3511	1.18921	0.594603	−	0.804019i	$-0.297309\pi$
$491$	26.3511	1.18921	0.594603	+	0.804019i	$0.297309\pi$
$492$	− 2.40451i	− 0.108403i
$493$	− 0.520505i	− 0.0234424i
$494$	29.1941	1.31350
$495$	0	0
$496$	14.9481	0.671189
$497$	− 12.5620i	− 0.563482i
$498$	10.1235i	0.453645i
$499$	−3.52987	−0.158019	−0.0790094	−	0.996874i	$-0.525176\pi$
$499$	−3.52987	−0.158019	−0.0790094	+	0.996874i	$0.525176\pi$
$500$	0	0
$501$	2.53035	0.113048
$502$	13.3713i	0.596792i
$503$	22.7368i	1.01379i	0.862009	+	0.506893i	$0.169206\pi$
$503$	22.7368i	1.01379i	−0.862009	+	0.506893i	$0.830794\pi$
$504$	7.74467	0.344975
$505$	0	0
$506$	1.33185	0.0592080
$507$	0.679048i	0.0301576i
$508$	7.02906i	0.311864i
$509$	36.2351	1.60609	0.803045	−	0.595918i	$-0.203212\pi$
$509$	36.2351	1.60609	0.803045	+	0.595918i	$0.203212\pi$
$510$	0	0
$511$	−1.17775	−0.0521008
$512$	24.1131i	1.06566i
$513$	24.4701i	1.08038i
$514$	19.3679	0.854283
$515$	0	0
$516$	−4.25686	−0.187398
$517$	− 2.26025i	− 0.0994058i
$518$	− 1.61729i	− 0.0710598i
$519$	−0.433085	−0.0190103
$520$	0	0
$521$	−6.79706	−0.297784	−0.148892	−	0.988853i	$-0.547571\pi$
$521$	−6.79706	−0.297784	−0.148892	+	0.988853i	$0.547571\pi$
$522$	− 23.9398i	− 1.04782i
$523$	34.0701i	1.48978i	0.667187	+	0.744890i	$0.267498\pi$
$523$	34.0701i	1.48978i	−0.667187	+	0.744890i	$0.732502\pi$
$524$	−1.44785	−0.0632497
$525$	0	0
$526$	−6.20648	−0.270616
$527$	0.372862i	0.0162421i
$528$	− 1.84146i	− 0.0801392i
$529$	21.7971	0.947698
$530$	0	0
$531$	−6.41774	−0.278506
$532$	− 3.37778i	− 0.146446i
$533$	− 24.8430i	− 1.07607i
$534$	13.0607	0.565192
$535$	0	0
$536$	−31.8404	−1.37530
$537$	− 5.30772i	− 0.229045i
$538$	− 22.1432i	− 0.954661i
$539$	1.00000	0.0430730
$540$	0	0
$541$	−27.1941	−1.16916	−0.584582	−	0.811335i	$-0.698741\pi$
$541$	−27.1941	−1.16916	−0.584582	+	0.811335i	$0.698741\pi$
$542$	− 7.57136i	− 0.325218i
$543$	− 7.52098i	− 0.322756i
$544$	−0.192521	−0.00825428
$545$	0	0
$546$	−3.12843	−0.133884
$547$	40.2449i	1.72075i	0.509663	+	0.860374i	$0.329770\pi$
$547$	40.2449i	1.72075i	−0.509663	+	0.860374i	$0.670230\pi$
$548$	9.40192i	0.401630i
$549$	36.4909	1.55739
$550$	0	0
$551$	−50.1847	−2.13794
$552$	2.31708i	0.0986217i
$553$	8.51606i	0.362140i
$554$	−7.67752	−0.326186
$555$	0	0
$556$	2.03164	0.0861608
$557$	7.09679i	0.300701i	0.988633	+	0.150350i	$0.0480401\pi$
$557$	7.09679i	0.300701i	−0.988633	+	0.150350i	$0.951960\pi$
$558$	17.1492i	0.725982i
$559$	−43.9813	−1.86021
$560$	0	0
$561$	0.0459330	0.00193929
$562$	30.6321i	1.29214i
$563$	− 18.7971i	− 0.792201i	−0.918207	−	0.396101i	$-0.870363\pi$
$563$	− 18.7971i	− 0.792201i	0.918207	−	0.396101i	$-0.129637\pi$
$564$	0.818128	0.0344494
$565$	0	0
$566$	16.2953	0.684942
$567$	4.95407i	0.208051i
$568$	38.5236i	1.61641i
$569$	0.0316429	0.00132654	0.000663269	−	1.00000i	$-0.499789\pi$
$569$	0.0316429	0.00132654	0.000663269		1.00000i	$0.499789\pi$
$570$	0	0
$571$	0.0503787	0.00210828	0.00105414	−	0.999999i	$-0.499664\pi$
$571$	0.0503787	0.00210828	0.00105414	+	0.999999i	$0.499664\pi$
$572$	1.96497i	0.0821594i
$573$	7.52098i	0.314194i
$574$	8.06668	0.336697
$575$	0	0
$576$	−22.3560	−0.931499
$577$	13.6316i	0.567490i	0.958900	+	0.283745i	$0.0915770\pi$
$577$	13.6316i	0.567490i	−0.958900	+	0.283745i	$0.908423\pi$
$578$	− 20.6380i	− 0.858429i
$579$	8.06022	0.334971
$580$	0	0
$581$	12.1017	0.502064
$582$	− 11.2257i	− 0.465320i
$583$	1.71900i	0.0711939i
$584$	3.61179	0.149457
$585$	0	0
$586$	21.3798	0.883191
$587$	− 1.63804i	− 0.0676090i	−0.999428	−	0.0338045i	$-0.989238\pi$
$587$	− 1.63804i	− 0.0676090i	0.999428	−	0.0338045i	$-0.0107624\pi$
$588$	0.361963i	0.0149271i
$589$	35.9496	1.48128
$590$	0	0
$591$	−7.46965	−0.307260
$592$	3.56013i	0.146321i
$593$	8.46367i	0.347561i	0.984784	+	0.173781i	$0.0555984\pi$
$593$	8.46367i	0.347561i	−0.984784	+	0.173781i	$0.944402\pi$
$594$	4.62222	0.189652
$595$	0	0
$596$	−2.56877	−0.105221
$597$	1.43356i	0.0586718i
$598$	4.98079i	0.203680i
$599$	26.9590	1.10151	0.550757	−	0.834665i	$-0.314339\pi$
$599$	26.9590	1.10151	0.550757	+	0.834665i	$0.314339\pi$
$600$	0	0
$601$	−16.4909	−0.672677	−0.336338	−	0.941741i	$-0.609189\pi$
$601$	−16.4909	−0.672677	−0.336338	+	0.941741i	$0.609189\pi$
$602$	− 14.2810i	− 0.582050i
$603$	− 26.2208i	− 1.06779i
$604$	11.6588	0.474389
$605$	0	0
$606$	7.06821	0.287126
$607$	− 19.5526i	− 0.793617i	−0.917902	−	0.396808i	$-0.870118\pi$
$607$	− 19.5526i	− 0.793617i	0.917902	−	0.396808i	$-0.129882\pi$
$608$	18.5620i	0.752788i
$609$	5.37778	0.217919
$610$	0	0
$611$	8.45277	0.341963
$612$	− 0.0884751i	− 0.00357639i
$613$	− 39.5955i	− 1.59925i	−0.600502	−	0.799623i	$-0.705032\pi$
$613$	− 39.5955i	− 1.59925i	0.600502	−	0.799623i	$-0.294968\pi$
$614$	−31.9813	−1.29066
$615$	0	0
$616$	−3.06668	−0.123560
$617$	− 23.1669i	− 0.932662i	−0.884610	−	0.466331i	$-0.845575\pi$
$617$	− 23.1669i	− 0.932662i	0.884610	−	0.466331i	$-0.154425\pi$
$618$	7.98571i	0.321232i
$619$	−3.43017	−0.137870	−0.0689351	−	0.997621i	$-0.521960\pi$
$619$	−3.43017	−0.137870	−0.0689351	+	0.997621i	$0.521960\pi$
$620$	0	0
$621$	−4.17484	−0.167531
$622$	− 7.23798i	− 0.290216i
$623$	− 15.6128i	− 0.625516i
$624$	6.88659	0.275684
$625$	0	0
$626$	−6.70424	−0.267955
$627$	− 4.42864i	− 0.176863i
$628$	2.53035i	0.100972i
$629$	−0.0888033	−0.00354082
$630$	0	0
$631$	10.9590	0.436270	0.218135	−	0.975919i	$-0.430003\pi$
$631$	10.9590	0.436270	0.218135	+	0.975919i	$0.430003\pi$
$632$	− 26.1160i	− 1.03884i
$633$	− 15.9081i	− 0.632292i
$634$	19.0825	0.757863
$635$	0	0
$636$	−0.622216	−0.0246725
$637$	3.73975i	0.148174i
$638$	9.47949i	0.375297i
$639$	−31.7244	−1.25500
$640$	0	0
$641$	−14.9862	−0.591919	−0.295959	−	0.955201i	$-0.595639\pi$
$641$	−14.9862	−0.591919	−0.295959	+	0.955201i	$0.595639\pi$
$642$	− 7.16241i	− 0.282678i
$643$	− 14.4222i	− 0.568755i	−0.958712	−	0.284378i	$-0.908213\pi$
$643$	− 14.4222i	− 0.568755i	0.958712	−	0.284378i	$-0.0917870\pi$
$644$	0.576283	0.0227087
$645$	0	0
$646$	0.520505	0.0204790
$647$	33.7309i	1.32610i	0.748577	+	0.663048i	$0.230738\pi$
$647$	33.7309i	1.32610i	−0.748577	+	0.663048i	$0.769262\pi$
$648$	− 15.1925i	− 0.596819i
$649$	2.54125	0.0997527
$650$	0	0
$651$	−3.85236	−0.150986
$652$	3.19850i	0.125263i
$653$	36.7971i	1.43998i	0.693984	+	0.719990i	$0.255854\pi$
$653$	36.7971i	1.43998i	−0.693984	+	0.719990i	$0.744146\pi$
$654$	−5.84791	−0.228671
$655$	0	0
$656$	−17.7571	−0.693298
$657$	2.97433i	0.116040i
$658$	2.74467i	0.106998i
$659$	−3.79213	−0.147721	−0.0738603	−	0.997269i	$-0.523532\pi$
$659$	−3.79213	−0.147721	−0.0738603	+	0.997269i	$0.523532\pi$
$660$	0	0
$661$	−35.2543	−1.37123	−0.685616	−	0.727963i	$-0.740467\pi$
$661$	−35.2543	−1.37123	−0.685616	+	0.727963i	$0.740467\pi$
$662$	− 22.1432i	− 0.860620i
$663$	0.171778i	0.00667129i
$664$	−37.1120	−1.44023
$665$	0	0
$666$	−4.08436	−0.158266
$667$	− 8.56199i	− 0.331522i
$668$	1.92993i	0.0746713i
$669$	−14.8430	−0.573863
$670$	0	0
$671$	−14.4494	−0.557812
$672$	− 1.98910i	− 0.0767312i
$673$	− 35.1383i	− 1.35448i	−0.735762	−	0.677240i	$-0.763176\pi$
$673$	− 35.1383i	− 1.35448i	0.735762	−	0.677240i	$-0.236824\pi$
$674$	−39.2114	−1.51037
$675$	0	0
$676$	−0.517919	−0.0199200
$677$	− 23.1907i	− 0.891290i	−0.895210	−	0.445645i	$-0.852974\pi$
$677$	− 23.1907i	− 0.891290i	0.895210	−	0.445645i	$-0.147026\pi$
$678$	1.31450i	0.0504830i
$679$	−13.4193	−0.514984
$680$	0	0
$681$	18.7556	0.718715
$682$	− 6.79060i	− 0.260026i
$683$	− 7.74758i	− 0.296453i	−0.988953	−	0.148227i	$-0.952644\pi$
$683$	− 7.74758i	− 0.296453i	0.988953	−	0.148227i	$-0.0473565\pi$
$684$	−8.53035	−0.326166
$685$	0	0
$686$	−1.21432	−0.0463629
$687$	17.2226i	0.657084i
$688$	31.4366i	1.19851i
$689$	−6.42864	−0.244912
$690$	0	0
$691$	−14.7763	−0.562117	−0.281059	−	0.959691i	$-0.590686\pi$
$691$	−14.7763	−0.562117	−0.281059	+	0.959691i	$0.590686\pi$
$692$	− 0.330320i	− 0.0125569i
$693$	− 2.52543i	− 0.0959331i
$694$	−27.5540	−1.04594
$695$	0	0
$696$	−16.4919	−0.625125
$697$	− 0.442930i	− 0.0167772i
$698$	20.5337i	0.777214i
$699$	−2.52051	−0.0953343
$700$	0	0
$701$	−19.8765	−0.750725	−0.375362	−	0.926878i	$-0.622482\pi$
$701$	−19.8765	−0.750725	−0.375362	+	0.926878i	$0.622482\pi$
$702$	17.2859i	0.652415i
$703$	8.56199i	0.322922i
$704$	8.85236	0.333636
$705$	0	0
$706$	29.6258	1.11498
$707$	− 8.44938i	− 0.317772i
$708$	0.919838i	0.0345696i
$709$	−0.368416	−0.0138362	−0.00691808	−	0.999976i	$-0.502202\pi$
$709$	−0.368416	−0.0138362	−0.00691808	+	0.999976i	$0.502202\pi$
$710$	0	0
$711$	21.5067	0.806564
$712$	47.8796i	1.79436i
$713$	6.13335i	0.229696i
$714$	−0.0557773	−0.00208741
$715$	0	0
$716$	4.04827	0.151291
$717$	10.1303i	0.378323i
$718$	− 39.8435i	− 1.48694i
$719$	5.86865	0.218864	0.109432	−	0.993994i	$-0.465097\pi$
$719$	5.86865	0.218864	0.109432	+	0.993994i	$0.465097\pi$
$720$	0	0
$721$	9.54617	0.355518
$722$	− 27.1126i	− 1.00903i
$723$	− 9.43356i	− 0.350838i
$724$	5.73636	0.213190
$725$	0	0
$726$	−0.836535	−0.0310467
$727$	− 1.19066i	− 0.0441592i	−0.999756	−	0.0220796i	$-0.992971\pi$
$727$	− 1.19066i	− 0.0441592i	0.999756	−	0.0220796i	$-0.00702873\pi$
$728$	− 11.4686i	− 0.425054i
$729$	4.64449	0.172018
$730$	0	0
$731$	−0.784149	−0.0290028
$732$	− 5.23014i	− 0.193312i
$733$	19.6795i	0.726880i	0.931618	+	0.363440i	$0.118398\pi$
$733$	19.6795i	0.726880i	−0.931618	+	0.363440i	$0.881602\pi$
$734$	8.43065	0.311181
$735$	0	0
$736$	−3.16686	−0.116732
$737$	10.3827i	0.382452i
$738$	− 20.3718i	− 0.749897i
$739$	−27.1427	−0.998461	−0.499231	−	0.866469i	$-0.666384\pi$
$739$	−27.1427	−0.998461	−0.499231	+	0.866469i	$0.666384\pi$
$740$	0	0
$741$	16.5620	0.608420
$742$	− 2.08742i	− 0.0766316i
$743$	− 31.0509i	− 1.13915i	−0.821941	−	0.569573i	$-0.807109\pi$
$743$	− 31.0509i	− 1.13915i	0.821941	−	0.569573i	$-0.192891\pi$
$744$	11.8139	0.433120
$745$	0	0
$746$	44.8974	1.64381
$747$	− 30.5620i	− 1.11820i
$748$	0.0350337i	0.00128096i
$749$	−8.56199	−0.312848
$750$	0	0
$751$	−35.8292	−1.30743	−0.653713	−	0.756743i	$-0.726789\pi$
$751$	−35.8292	−1.30743	−0.653713	+	0.756743i	$0.726789\pi$
$752$	− 6.04182i	− 0.220322i
$753$	7.58565i	0.276436i
$754$	−35.4509	−1.29105
$755$	0	0
$756$	2.00000	0.0727393
$757$	1.15563i	0.0420020i	0.999779	+	0.0210010i	$0.00668532\pi$
$757$	1.15563i	0.0420020i	−0.999779	+	0.0210010i	$0.993315\pi$
$758$	− 28.7083i	− 1.04273i
$759$	0.755569	0.0274254
$760$	0	0
$761$	36.5640	1.32544	0.662722	−	0.748866i	$-0.269401\pi$
$761$	36.5640	1.32544	0.662722	+	0.748866i	$0.269401\pi$
$762$	− 11.1910i	− 0.405407i
$763$	6.99063i	0.253078i
$764$	−5.73636	−0.207534
$765$	0	0
$766$	16.6617	0.602012
$767$	9.50363i	0.343156i
$768$	8.03503i	0.289939i
$769$	38.7545	1.39752	0.698762	−	0.715354i	$-0.253735\pi$
$769$	38.7545	1.39752	0.698762	+	0.715354i	$0.253735\pi$
$770$	0	0
$771$	10.9876	0.395708
$772$	6.14764i	0.221259i
$773$	55.3372i	1.99034i	0.0981537	+	0.995171i	$0.468706\pi$
$773$	55.3372i	1.99034i	−0.0981537	+	0.995171i	$0.531294\pi$
$774$	−36.0656	−1.29635
$775$	0	0
$776$	41.1526	1.47729
$777$	− 0.917502i	− 0.0329152i
$778$	− 18.8859i	− 0.677091i
$779$	−42.7052	−1.53007
$780$	0	0
$781$	12.5620	0.449503
$782$	0.0888033i	0.00317560i
$783$	− 29.7146i	− 1.06191i
$784$	2.67307	0.0954668
$785$	0	0
$786$	2.30513	0.0822213
$787$	13.6731i	0.487392i	0.969852	+	0.243696i	$0.0783600\pi$
$787$	13.6731i	0.487392i	−0.969852	+	0.243696i	$0.921640\pi$
$788$	− 5.69721i	− 0.202955i
$789$	−3.52098	−0.125350
$790$	0	0
$791$	1.57136	0.0558711
$792$	7.74467i	0.275195i
$793$	− 54.0370i	− 1.91891i
$794$	0.308193	0.0109374
$795$	0	0
$796$	−1.09340	−0.0387544
$797$	− 17.8765i	− 0.633218i	−0.948556	−	0.316609i	$-0.897456\pi$
$797$	− 17.8765i	− 0.633218i	0.948556	−	0.316609i	$-0.102544\pi$
$798$	5.37778i	0.190372i
$799$	0.150706	0.00533159
$800$	0	0
$801$	−39.4291	−1.39316
$802$	− 24.7338i	− 0.873380i
$803$	− 1.17775i	− 0.0415621i
$804$	−3.75815	−0.132540
$805$	0	0
$806$	25.3951	0.894506
$807$	− 12.5620i	− 0.442203i
$808$	25.9115i	0.911564i
$809$	−14.6450	−0.514890	−0.257445	−	0.966293i	$-0.582881\pi$
$809$	−14.6450	−0.514890	−0.257445	+	0.966293i	$0.582881\pi$
$810$	0	0
$811$	30.2667	1.06281	0.531404	−	0.847119i	$-0.321665\pi$
$811$	30.2667	1.06281	0.531404	+	0.847119i	$0.321665\pi$
$812$	4.10171i	0.143942i
$813$	− 4.29529i	− 0.150642i
$814$	1.61729	0.0566861
$815$	0	0
$816$	0.122782	0.00429823
$817$	75.6040i	2.64505i
$818$	14.7205i	0.514691i
$819$	9.44446	0.330016
$820$	0	0
$821$	10.4286	0.363962	0.181981	−	0.983302i	$-0.441749\pi$
$821$	10.4286	0.363962	0.181981	+	0.983302i	$0.441749\pi$
$822$	− 14.9688i	− 0.522098i
$823$	4.28100i	0.149226i	0.997213	+	0.0746131i	$0.0237722\pi$
$823$	4.28100i	0.149226i	−0.997213	+	0.0746131i	$0.976228\pi$
$824$	−29.2750	−1.01984
$825$	0	0
$826$	−3.08589	−0.107372
$827$	13.8336i	0.481042i	0.970644	+	0.240521i	$0.0773183\pi$
$827$	13.8336i	0.481042i	−0.970644	+	0.240521i	$0.922682\pi$
$828$	− 1.45536i	− 0.0505773i
$829$	−10.8573	−0.377089	−0.188544	−	0.982065i	$-0.560377\pi$
$829$	−10.8573	−0.377089	−0.188544	+	0.982065i	$0.560377\pi$
$830$	0	0
$831$	−4.35551	−0.151091
$832$	33.1056i	1.14773i
$833$	0.0666765i	0.00231021i
$834$	−3.23459	−0.112005
$835$	0	0
$836$	3.37778	0.116823
$837$	21.2859i	0.735749i
$838$	− 26.0350i	− 0.899365i
$839$	−52.4820	−1.81188	−0.905940	−	0.423407i	$-0.860834\pi$
$839$	−52.4820	−1.81188	−0.905940	+	0.423407i	$0.860834\pi$
$840$	0	0
$841$	31.9403	1.10139
$842$	− 36.2623i	− 1.24968i
$843$	17.3778i	0.598523i
$844$	12.1334	0.417647
$845$	0	0
$846$	6.93146	0.238309
$847$	1.00000i	0.0343604i
$848$	4.59502i	0.157794i
$849$	9.24443	0.317268
$850$	0	0
$851$	−1.46076	−0.0500742
$852$	4.54698i	0.155777i
$853$	9.89184i	0.338690i	0.985557	+	0.169345i	$0.0541652\pi$
$853$	9.89184i	0.338690i	−0.985557	+	0.169345i	$0.945835\pi$
$854$	17.5462	0.600418
$855$	0	0
$856$	26.2569	0.897441
$857$	3.58766i	0.122552i	0.998121	+	0.0612760i	$0.0195170\pi$
$857$	3.58766i	0.122552i	−0.998121	+	0.0612760i	$0.980483\pi$
$858$	− 3.12843i	− 0.106803i
$859$	17.2050	0.587025	0.293513	−	0.955955i	$-0.405176\pi$
$859$	17.2050	0.587025	0.293513	+	0.955955i	$0.405176\pi$
$860$	0	0
$861$	4.57628	0.155959
$862$	23.8720i	0.813085i
$863$	15.0781i	0.513263i	0.966509	+	0.256631i	$0.0826126\pi$
$863$	15.0781i	0.513263i	−0.966509	+	0.256631i	$0.917387\pi$
$864$	−10.9906	−0.373909
$865$	0	0
$866$	−40.0384	−1.36056
$867$	− 11.7081i	− 0.397628i
$868$	− 2.93825i	− 0.0997306i
$869$	−8.51606	−0.288888
$870$	0	0
$871$	−38.8287	−1.31566
$872$	− 21.4380i	− 0.725983i
$873$	33.8894i	1.14698i
$874$	8.56199	0.289614
$875$	0	0
$876$	0.426304	0.0144035
$877$	31.4750i	1.06284i	0.847109	+	0.531418i	$0.178341\pi$
$877$	31.4750i	1.06284i	−0.847109	+	0.531418i	$0.821659\pi$
$878$	− 0.990632i	− 0.0334322i
$879$	12.1289	0.409098
$880$	0	0
$881$	−47.1209	−1.58754	−0.793772	−	0.608215i	$-0.791886\pi$
$881$	−47.1209	−1.58754	−0.793772	+	0.608215i	$0.791886\pi$
$882$	3.06668i	0.103260i
$883$	33.8118i	1.13786i	0.822386	+	0.568929i	$0.192642\pi$
$883$	33.8118i	1.13786i	−0.822386	+	0.568929i	$0.807358\pi$
$884$	−0.131017	−0.00440658
$885$	0	0
$886$	30.3293	1.01893
$887$	31.6258i	1.06189i	0.847407	+	0.530944i	$0.178163\pi$
$887$	31.6258i	1.06189i	−0.847407	+	0.530944i	$0.821837\pi$
$888$	2.81368i	0.0944210i
$889$	−13.3778	−0.448676
$890$	0	0
$891$	−4.95407	−0.165967
$892$	− 11.3210i	− 0.379054i
$893$	− 14.5303i	− 0.486240i
$894$	4.08976	0.136782
$895$	0	0
$896$	−4.97481	−0.166197
$897$	2.82564i	0.0943452i
$898$	0.503153i	0.0167904i
$899$	−43.6543	−1.45595
$900$	0	0
$901$	−0.114617	−0.00381845
$902$	8.06668i	0.268591i
$903$	− 8.10171i	− 0.269608i
$904$	−4.81885	−0.160273
$905$	0	0
$906$	−18.5620	−0.616681
$907$	46.8943i	1.55710i	0.627582	+	0.778550i	$0.284045\pi$
$907$	46.8943i	1.55710i	−0.627582	+	0.778550i	$0.715955\pi$
$908$	14.3051i	0.474732i
$909$	−21.3383	−0.707747
$910$	0	0
$911$	−28.5620	−0.946301	−0.473151	−	0.880982i	$-0.656883\pi$
$911$	−28.5620	−0.946301	−0.473151	+	0.880982i	$0.656883\pi$
$912$	− 11.8381i	− 0.391998i
$913$	12.1017i	0.400508i
$914$	−11.3319	−0.374824
$915$	0	0
$916$	−13.1359	−0.434024
$917$	− 2.75557i	− 0.0909969i
$918$	0.308193i	0.0101719i
$919$	−30.3555	−1.00134	−0.500668	−	0.865639i	$-0.666912\pi$
$919$	−30.3555	−1.00134	−0.500668	+	0.865639i	$0.666912\pi$
$920$	0	0
$921$	−18.1432	−0.597839
$922$	− 36.4164i	− 1.19931i
$923$	46.9787i	1.54632i
$924$	−0.361963	−0.0119077
$925$	0	0
$926$	−38.2939	−1.25842
$927$	− 24.1082i	− 0.791816i
$928$	− 22.5402i	− 0.739918i
$929$	−2.71408	−0.0890461	−0.0445231	−	0.999008i	$-0.514177\pi$
$929$	−2.71408	−0.0890461	−0.0445231	+	0.999008i	$0.514177\pi$
$930$	0	0
$931$	6.42864	0.210690
$932$	− 1.92242i	− 0.0629711i
$933$	− 4.10616i	− 0.134430i
$934$	6.89676	0.225669
$935$	0	0
$936$	−28.9631	−0.946689
$937$	− 13.7081i	− 0.447824i	−0.974609	−	0.223912i	$-0.928117\pi$
$937$	− 13.7081i	− 0.447824i	0.974609	−	0.223912i	$-0.0718829\pi$
$938$	− 12.6079i	− 0.411663i
$939$	−3.80336	−0.124118
$940$	0	0
$941$	−21.1635	−0.689909	−0.344955	−	0.938619i	$-0.612106\pi$
$941$	−21.1635	−0.689909	−0.344955	+	0.938619i	$0.612106\pi$
$942$	− 4.02858i	− 0.131258i
$943$	− 7.28592i	− 0.237262i
$944$	6.79294	0.221091
$945$	0	0
$946$	14.2810	0.464315
$947$	14.8746i	0.483361i	0.970356	+	0.241680i	$0.0776985\pi$
$947$	14.8746i	0.483361i	−0.970356	+	0.241680i	$0.922301\pi$
$948$	− 3.08250i	− 0.100115i
$949$	4.40451	0.142976
$950$	0	0
$951$	10.8256	0.351045
$952$	− 0.204475i	− 0.00662709i
$953$	35.0968i	1.13690i	0.822719	+	0.568448i	$0.192456\pi$
$953$	35.0968i	1.13690i	−0.822719	+	0.568448i	$0.807544\pi$
$954$	−5.27163	−0.170675
$955$	0	0
$956$	−7.72651	−0.249893
$957$	5.37778i	0.173839i
$958$	− 47.9180i	− 1.54816i
$959$	−17.8938	−0.577822
$960$	0	0
$961$	0.271628	0.00876221
$962$	6.04827i	0.195004i
$963$	21.6227i	0.696782i
$964$	7.19511	0.231739
$965$	0	0
$966$	−0.917502	−0.0295201
$967$	53.0879i	1.70719i	0.520936	+	0.853596i	$0.325583\pi$
$967$	53.0879i	1.70719i	−0.520936	+	0.853596i	$0.674417\pi$
$968$	− 3.06668i	− 0.0985667i
$969$	0.295286	0.00948597
$970$	0	0
$971$	21.4400	0.688043	0.344021	−	0.938962i	$-0.388211\pi$
$971$	21.4400	0.688043	0.344021	+	0.938962i	$0.388211\pi$
$972$	− 7.79319i	− 0.249967i
$973$	3.86665i	0.123959i
$974$	3.88400	0.124451
$975$	0	0
$976$	−38.6242	−1.23633
$977$	54.0415i	1.72894i	0.502684	+	0.864470i	$0.332346\pi$
$977$	54.0415i	1.72894i	−0.502684	+	0.864470i	$0.667654\pi$
$978$	− 5.09234i	− 0.162835i
$979$	15.6128	0.498989
$980$	0	0
$981$	17.6543	0.563660
$982$	− 31.9986i	− 1.02112i
$983$	− 38.3432i	− 1.22296i	−0.791260	−	0.611480i	$-0.790575\pi$
$983$	− 38.3432i	− 1.22296i	0.791260	−	0.611480i	$-0.209425\pi$
$984$	−14.0340	−0.447387
$985$	0	0
$986$	−0.632060	−0.0201289
$987$	1.55707i	0.0495621i
$988$	12.6321i	0.401879i
$989$	−12.8988	−0.410157
$990$	0	0
$991$	51.6543	1.64085	0.820427	−	0.571751i	$-0.193736\pi$
$991$	51.6543	1.64085	0.820427	+	0.571751i	$0.193736\pi$
$992$	16.1466i	0.512655i
$993$	− 12.5620i	− 0.398643i
$994$	−15.2543	−0.483836
$995$	0	0
$996$	−4.38037	−0.138797
$997$	− 41.4445i	− 1.31256i	−0.754518	−	0.656280i	$-0.772129\pi$
$997$	− 41.4445i	− 1.31256i	0.754518	−	0.656280i	$-0.227871\pi$
$998$	4.28639i	0.135683i
$999$	−5.06959	−0.160395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.b.n.1849.3		6
5.2	odd	4		385.2.a.f.1.3	✓	3
5.3	odd	4		1925.2.a.v.1.1		3
5.4	even	2	inner	1925.2.b.n.1849.4		6
15.2	even	4		3465.2.a.bh.1.1		3
20.7	even	4		6160.2.a.bn.1.2		3
35.27	even	4		2695.2.a.g.1.3		3
55.32	even	4		4235.2.a.q.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.a.f.1.3	✓	3	5.2	odd	4
1925.2.a.v.1.1		3	5.3	odd	4
1925.2.b.n.1849.3		6	1.1	even	1	trivial
1925.2.b.n.1849.4		6	5.4	even	2	inner
2695.2.a.g.1.3		3	35.27	even	4
3465.2.a.bh.1.1		3	15.2	even	4
4235.2.a.q.1.1		3	55.32	even	4
6160.2.a.bn.1.2		3	20.7	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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.21432i q^{2} -0.688892i q^{3} +0.525428 q^{4} -0.836535 q^{6} +1.00000i q^{7} -3.06668i q^{8} +2.52543 q^{9} +O(q^{10})\)	\(q-1.21432i q^{2} -0.688892i q^{3} +0.525428 q^{4} -0.836535 q^{6} +1.00000i q^{7} -3.06668i q^{8} +2.52543 q^{9} -1.00000 q^{11} -0.361963i q^{12} -3.73975i q^{13} +1.21432 q^{14} -2.67307 q^{16} -0.0666765i q^{17} -3.06668i q^{18} -6.42864 q^{19} +0.688892 q^{21} +1.21432i q^{22} -1.09679i q^{23} -2.11261 q^{24} -4.54125 q^{26} -3.80642i q^{27} +0.525428i q^{28} +7.80642 q^{29} -5.59210 q^{31} -2.88739i q^{32} +0.688892i q^{33} -0.0809666 q^{34} +1.32693 q^{36} -1.33185i q^{37} +7.80642i q^{38} -2.57628 q^{39} +6.64296 q^{41} -0.836535i q^{42} -11.7605i q^{43} -0.525428 q^{44} -1.33185 q^{46} +2.26025i q^{47} +1.84146i q^{48} -1.00000 q^{49} -0.0459330 q^{51} -1.96497i q^{52} -1.71900i q^{53} -4.62222 q^{54} +3.06668 q^{56} +4.42864i q^{57} -9.47949i q^{58} -2.54125 q^{59} +14.4494 q^{61} +6.79060i q^{62} +2.52543i q^{63} -8.85236 q^{64} +0.836535 q^{66} -10.3827i q^{67} -0.0350337i q^{68} -0.755569 q^{69} -12.5620 q^{71} -7.74467i q^{72} +1.17775i q^{73} -1.61729 q^{74} -3.37778 q^{76} -1.00000i q^{77} +3.12843i q^{78} +8.51606 q^{79} +4.95407 q^{81} -8.06668i q^{82} -12.1017i q^{83} +0.361963 q^{84} -14.2810 q^{86} -5.37778i q^{87} +3.06668i q^{88} -15.6128 q^{89} +3.73975 q^{91} -0.576283i q^{92} +3.85236i q^{93} +2.74467 q^{94} -1.98910 q^{96} +13.4193i q^{97} +1.21432i q^{98} -2.52543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 8 q^{6} + 2 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 8 * q^6 + 2 * q^9	\( 6 q - 10 q^{4} + 8 q^{6} + 2 q^{9} - 6 q^{11} - 6 q^{14} + 10 q^{16} - 12 q^{19} + 4 q^{21} - 52 q^{24} - 40 q^{26} + 20 q^{29} - 20 q^{31} + 12 q^{34} + 34 q^{36} + 24 q^{39} + 10 q^{44} + 32 q^{46} - 6 q^{49} - 40 q^{51} - 28 q^{54} + 18 q^{56} - 28 q^{59} + 20 q^{61} - 66 q^{64} - 8 q^{66} - 4 q^{69} - 48 q^{71} - 76 q^{74} - 20 q^{76} - 16 q^{79} - 10 q^{81} - 24 q^{84} - 72 q^{86} - 40 q^{89} - 4 q^{91} - 76 q^{94} + 80 q^{96} - 2 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 8 * q^6 + 2 * q^9 - 6 * q^11 - 6 * q^14 + 10 * q^16 - 12 * q^19 + 4 * q^21 - 52 * q^24 - 40 * q^26 + 20 * q^29 - 20 * q^31 + 12 * q^34 + 34 * q^36 + 24 * q^39 + 10 * q^44 + 32 * q^46 - 6 * q^49 - 40 * q^51 - 28 * q^54 + 18 * q^56 - 28 * q^59 + 20 * q^61 - 66 * q^64 - 8 * q^66 - 4 * q^69 - 48 * q^71 - 76 * q^74 - 20 * q^76 - 16 * q^79 - 10 * q^81 - 24 * q^84 - 72 * q^86 - 40 * q^89 - 4 * q^91 - 76 * q^94 + 80 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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