LMFDB - Embedded newform 925.2.b.g.149.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(149,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, 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("925.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.8689006034944.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} + 10x^{7} + 26x^{6} - 4x^{5} + 6x^{4} + 22x^{3} + 25x^{2} + 10x + 2 $ x^10 - 2x^9 + 2x^8 + 10x^7 + 26x^6 - 4x^5 + 6x^4 + 22x^3 + 25x^2 + 10*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.8
Root			$2.14978 + 2.14978i$ of defining polynomial
Character	$\chi$	$=$	925.149
Dual form			925.2.b.g.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.46516i q^{2} -0.744131i q^{3} -0.146703 q^{4} +1.09027 q^{6} +3.94357i q^{7} +2.71538i q^{8} +2.44627 q^{9} +O(q^{10})$	\(q+1.46516i q^{2} -0.744131i q^{3} -0.146703 q^{4} +1.09027 q^{6} +3.94357i q^{7} +2.71538i q^{8} +2.44627 q^{9} -4.52210 q^{11} +0.109166i q^{12} -1.36924i q^{13} -5.77797 q^{14} -4.27188 q^{16} +2.29957i q^{17} +3.58418i q^{18} -4.84765 q^{19} +2.93453 q^{21} -6.62562i q^{22} +4.41859i q^{23} +2.02060 q^{24} +2.00616 q^{26} -4.05274i q^{27} -0.578534i q^{28} +9.55595 q^{29} -4.75908 q^{31} -0.828243i q^{32} +3.36504i q^{33} -3.36924 q^{34} -0.358875 q^{36} -1.00000i q^{37} -7.10259i q^{38} -1.01889 q^{39} +5.21439 q^{41} +4.29957i q^{42} +1.19485i q^{43} +0.663407 q^{44} -6.47395 q^{46} +5.34785i q^{47} +3.17884i q^{48} -8.55174 q^{49} +1.71118 q^{51} +0.200872i q^{52} -1.03384i q^{53} +5.93792 q^{54} -10.7083 q^{56} +3.60728i q^{57} +14.0010i q^{58} -14.6197 q^{59} +1.30772 q^{61} -6.97283i q^{62} +9.64703i q^{63} -7.33026 q^{64} -4.93033 q^{66} +7.23975i q^{67} -0.337354i q^{68} +3.28801 q^{69} +15.1787 q^{71} +6.64256i q^{72} +4.81551i q^{73} +1.46516 q^{74} +0.711165 q^{76} -17.8332i q^{77} -1.49285i q^{78} -4.64520 q^{79} +4.32304 q^{81} +7.63993i q^{82} +5.89279i q^{83} -0.430505 q^{84} -1.75066 q^{86} -7.11087i q^{87} -12.2792i q^{88} +10.3435 q^{89} +5.39969 q^{91} -0.648221i q^{92} +3.54138i q^{93} -7.83547 q^{94} -0.616321 q^{96} +6.37000i q^{97} -12.5297i q^{98} -11.0623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) $ 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9	$ 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9} + 14 q^{11} - 8 q^{14} + 16 q^{16} - 28 q^{19} - 18 q^{21} - 24 q^{24} - 40 q^{26} - 4 q^{29} + 16 q^{31} - 24 q^{34} - 72 q^{36} - 24 q^{39} - 18 q^{41} - 36 q^{44} - 56 q^{46} - 4 q^{49} + 20 q^{51} + 24 q^{54} - 28 q^{56} - 24 q^{59} + 24 q^{61} - 24 q^{64} - 20 q^{66} + 60 q^{69} + 26 q^{71} + 36 q^{76} - 72 q^{79} + 42 q^{81} - 60 q^{84} - 16 q^{86} + 32 q^{89} - 8 q^{91} - 40 q^{94} - 36 q^{99}+O(q^{100}) $ 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9 + 14 * q^11 - 8 * q^14 + 16 * q^16 - 28 * q^19 - 18 * q^21 - 24 * q^24 - 40 * q^26 - 4 * q^29 + 16 * q^31 - 24 * q^34 - 72 * q^36 - 24 * q^39 - 18 * q^41 - 36 * q^44 - 56 * q^46 - 4 * q^49 + 20 * q^51 + 24 * q^54 - 28 * q^56 - 24 * q^59 + 24 * q^61 - 24 * q^64 - 20 * q^66 + 60 * q^69 + 26 * q^71 + 36 * q^76 - 72 * q^79 + 42 * q^81 - 60 * q^84 - 16 * q^86 + 32 * q^89 - 8 * q^91 - 40 * q^94 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.46516i	1.03603i	0.855372	+	0.518013i	$0.173328\pi$
$2$	1.46516i	1.03603i	−0.855372	+	0.518013i	$0.826672\pi$
$3$	− 0.744131i	− 0.429624i	−0.976655	−	0.214812i	$-0.931086\pi$
$3$	− 0.744131i	− 0.429624i	0.976655	−	0.214812i	$-0.0689139\pi$
$4$	−0.146703	−0.0733516
$5$	0	0
$5$	0	0
$6$	1.09027	0.445102
$7$	3.94357i	1.49053i	0.666769	+	0.745265i	$0.267677\pi$
$7$	3.94357i	1.49053i	−0.666769	+	0.745265i	$0.732323\pi$
$8$	2.71538i	0.960033i
$9$	2.44627	0.815423
$10$	0	0
$11$	−4.52210	−1.36347	−0.681733	−	0.731601i	$-0.738773\pi$
$11$	−4.52210	−1.36347	−0.681733	+	0.731601i	$0.738773\pi$
$12$	0.109166i	0.0315136i
$13$	− 1.36924i	− 0.379759i	−0.981807	−	0.189879i	$-0.939190\pi$
$13$	− 1.36924i	− 0.379759i	0.981807	−	0.189879i	$-0.0608097\pi$
$14$	−5.77797	−1.54423
$15$	0	0
$16$	−4.27188	−1.06797
$17$	2.29957i	0.557727i	0.960331	+	0.278863i	$0.0899577\pi$
$17$	2.29957i	0.557727i	−0.960331	+	0.278863i	$0.910042\pi$
$18$	3.58418i	0.844800i
$19$	−4.84765	−1.11213	−0.556063	−	0.831140i	$-0.687689\pi$
$19$	−4.84765	−1.11213	−0.556063	+	0.831140i	$0.687689\pi$
$20$	0	0
$21$	2.93453	0.640367
$22$	− 6.62562i	− 1.41259i
$23$	4.41859i	0.921339i	0.887572	+	0.460670i	$0.152391\pi$
$23$	4.41859i	0.921339i	−0.887572	+	0.460670i	$0.847609\pi$
$24$	2.02060	0.412453
$25$	0	0
$26$	2.00616	0.393440
$27$	− 4.05274i	− 0.779949i
$28$	− 0.578534i	− 0.109333i
$29$	9.55595	1.77449	0.887247	−	0.461294i	$-0.152615\pi$
$29$	9.55595	1.77449	0.887247	+	0.461294i	$0.152615\pi$
$30$	0	0
$31$	−4.75908	−0.854756	−0.427378	−	0.904073i	$-0.640563\pi$
$31$	−4.75908	−0.854756	−0.427378	+	0.904073i	$0.640563\pi$
$32$	− 0.828243i	− 0.146414i
$33$	3.36504i	0.585778i
$34$	−3.36924	−0.577820
$35$	0	0
$36$	−0.358875	−0.0598126
$37$	− 1.00000i	− 0.164399i
$37$	− 1.00000i	− 0.164399i
$38$	− 7.10259i	− 1.15219i
$39$	−1.01889	−0.163154
$40$	0	0
$41$	5.21439	0.814351	0.407175	−	0.913350i	$-0.366514\pi$
$41$	5.21439	0.814351	0.407175	+	0.913350i	$0.366514\pi$
$42$	4.29957i	0.663438i
$43$	1.19485i	0.182214i	0.995841	+	0.0911068i	$0.0290405\pi$
$43$	1.19485i	0.182214i	−0.995841	+	0.0911068i	$0.970960\pi$
$44$	0.663407	0.100012
$45$	0	0
$46$	−6.47395	−0.954532
$47$	5.34785i	0.780064i	0.920801	+	0.390032i	$0.127536\pi$
$47$	5.34785i	0.780064i	−0.920801	+	0.390032i	$0.872464\pi$
$48$	3.17884i	0.458826i
$49$	−8.55174	−1.22168
$50$	0	0
$51$	1.71118	0.239613
$52$	0.200872i	0.0278559i
$53$	− 1.03384i	− 0.142009i	−0.997476	−	0.0710046i	$-0.977380\pi$
$53$	− 1.03384i	− 0.142009i	0.997476	−	0.0710046i	$-0.0226205\pi$
$54$	5.93792	0.808048
$55$	0	0
$56$	−10.7083	−1.43096
$57$	3.60728i	0.477796i
$58$	14.0010i	1.83842i
$59$	−14.6197	−1.90333	−0.951664	−	0.307143i	$-0.900627\pi$
$59$	−14.6197	−1.90333	−0.951664	+	0.307143i	$0.900627\pi$
$60$	0	0
$61$	1.30772	0.167436	0.0837179	−	0.996489i	$-0.473321\pi$
$61$	1.30772	0.167436	0.0837179	+	0.996489i	$0.473321\pi$
$62$	− 6.97283i	− 0.885550i
$63$	9.64703i	1.21541i
$64$	−7.33026	−0.916282
$65$	0	0
$66$	−4.93033	−0.606881
$67$	7.23975i	0.884476i	0.896898	+	0.442238i	$0.145815\pi$
$67$	7.23975i	0.884476i	−0.896898	+	0.442238i	$0.854185\pi$
$68$	− 0.337354i	− 0.0409101i
$69$	3.28801	0.395829
$70$	0	0
$71$	15.1787	1.80138	0.900692	−	0.434458i	$-0.143060\pi$
$71$	15.1787	1.80138	0.900692	+	0.434458i	$0.143060\pi$
$72$	6.64256i	0.782833i
$73$	4.81551i	0.563613i	0.959471	+	0.281806i	$0.0909336\pi$
$73$	4.81551i	0.563613i	−0.959471	+	0.281806i	$0.909066\pi$
$74$	1.46516	0.170322
$75$	0	0
$76$	0.711165	0.0815762
$77$	− 17.8332i	− 2.03229i
$78$	− 1.49285i	− 0.169031i
$79$	−4.64520	−0.522626	−0.261313	−	0.965254i	$-0.584155\pi$
$79$	−4.64520	−0.522626	−0.261313	+	0.965254i	$0.584155\pi$
$80$	0	0
$81$	4.32304	0.480338
$82$	7.63993i	0.843689i
$83$	5.89279i	0.646818i	0.946259	+	0.323409i	$0.104829\pi$
$83$	5.89279i	0.646818i	−0.946259	+	0.323409i	$0.895171\pi$
$84$	−0.430505	−0.0469719
$85$	0	0
$86$	−1.75066	−0.188778
$87$	− 7.11087i	− 0.762365i
$88$	− 12.2792i	− 1.30897i
$89$	10.3435	1.09641	0.548205	−	0.836344i	$-0.315311\pi$
$89$	10.3435	1.09641	0.548205	+	0.836344i	$0.315311\pi$
$90$	0	0
$91$	5.39969	0.566042
$92$	− 0.648221i	− 0.0675817i
$93$	3.54138i	0.367224i
$94$	−7.83547	−0.808167
$95$	0	0
$96$	−0.616321	−0.0629030
$97$	6.37000i	0.646776i	0.946267	+	0.323388i	$0.104822\pi$
$97$	6.37000i	0.646776i	−0.946267	+	0.323388i	$0.895178\pi$
$98$	− 12.5297i	− 1.26569i
$99$	−11.0623	−1.11180
$100$	0	0
$101$	−4.62142	−0.459848	−0.229924	−	0.973209i	$-0.573848\pi$
$101$	−4.62142	−0.459848	−0.229924	+	0.973209i	$0.573848\pi$
$102$	2.50715i	0.248245i
$103$	− 18.3734i	− 1.81039i	−0.425001	−	0.905193i	$-0.639726\pi$
$103$	− 18.3734i	− 1.81039i	0.425001	−	0.905193i	$-0.360274\pi$
$104$	3.71801	0.364581
$105$	0	0
$106$	1.51475	0.147125
$107$	− 17.8700i	− 1.72755i	−0.503875	−	0.863777i	$-0.668093\pi$
$107$	− 17.8700i	− 1.72755i	0.503875	−	0.863777i	$-0.331907\pi$
$108$	0.594549i	0.0572105i
$109$	3.03189	0.290402	0.145201	−	0.989402i	$-0.453617\pi$
$109$	3.03189	0.290402	0.145201	+	0.989402i	$0.453617\pi$
$110$	0	0
$111$	−0.744131	−0.0706298
$112$	− 16.8465i	− 1.59184i
$113$	20.1901i	1.89933i	0.313273	+	0.949663i	$0.398575\pi$
$113$	20.1901i	1.89933i	−0.313273	+	0.949663i	$0.601425\pi$
$114$	−5.28526	−0.495010
$115$	0	0
$116$	−1.40189	−0.130162
$117$	− 3.34953i	− 0.309664i
$118$	− 21.4203i	− 1.97190i
$119$	−9.06850	−0.831308
$120$	0	0
$121$	9.44942	0.859038
$122$	1.91602i	0.173468i
$123$	− 3.88019i	− 0.349865i
$124$	0.698172	0.0626977
$125$	0	0
$126$	−14.1345	−1.25920
$127$	− 13.5915i	− 1.20605i	−0.797722	−	0.603025i	$-0.793962\pi$
$127$	− 13.5915i	− 1.20605i	0.797722	−	0.603025i	$-0.206038\pi$
$128$	− 12.3965i	− 1.09571i
$129$	0.889128	0.0782834
$130$	0	0
$131$	21.1799	1.85049	0.925246	−	0.379367i	$-0.123858\pi$
$131$	21.1799	1.85049	0.925246	+	0.379367i	$0.123858\pi$
$132$	− 0.493661i	− 0.0429677i
$133$	− 19.1170i	− 1.65766i
$134$	−10.6074	−0.916341
$135$	0	0
$136$	−6.24420	−0.535436
$137$	7.17856i	0.613305i	0.951821	+	0.306653i	$0.0992090\pi$
$137$	7.17856i	0.613305i	−0.951821	+	0.306653i	$0.900791\pi$
$138$	4.81747i	0.410090i
$139$	12.9602	1.09927	0.549636	−	0.835404i	$-0.314766\pi$
$139$	12.9602	1.09927	0.549636	+	0.835404i	$0.314766\pi$
$140$	0	0
$141$	3.97950	0.335134
$142$	22.2393i	1.86628i
$143$	6.19185i	0.517788i
$144$	−10.4502	−0.870848
$145$	0	0
$146$	−7.05551	−0.583918
$147$	6.36361i	0.524862i
$148$	0.146703i	0.0120589i
$149$	15.8451	1.29809	0.649043	−	0.760752i	$-0.275170\pi$
$149$	15.8451	1.29809	0.649043	+	0.760752i	$0.275170\pi$
$150$	0	0
$151$	14.2944	1.16326	0.581632	−	0.813452i	$-0.302414\pi$
$151$	14.2944	1.16326	0.581632	+	0.813452i	$0.302414\pi$
$152$	− 13.1632i	− 1.06768i
$153$	5.62536i	0.454783i
$154$	26.1286	2.10550
$155$	0	0
$156$	0.149475	0.0119676
$157$	− 1.95398i	− 0.155945i	−0.996956	−	0.0779723i	$-0.975155\pi$
$157$	− 1.95398i	− 0.155945i	0.996956	−	0.0779723i	$-0.0248446\pi$
$158$	− 6.80597i	− 0.541454i
$159$	−0.769314	−0.0610105
$160$	0	0
$161$	−17.4250	−1.37328
$162$	6.33397i	0.497643i
$163$	− 3.01431i	− 0.236099i	−0.993008	−	0.118049i	$-0.962336\pi$
$163$	− 3.01431i	− 0.236099i	0.993008	−	0.118049i	$-0.0376641\pi$
$164$	−0.764967	−0.0597339
$165$	0	0
$166$	−8.63390	−0.670120
$167$	4.16008i	0.321916i	0.986961	+	0.160958i	$0.0514584\pi$
$167$	4.16008i	0.321916i	−0.986961	+	0.160958i	$0.948542\pi$
$168$	7.96837i	0.614773i
$169$	11.1252	0.855783
$170$	0	0
$171$	−11.8587	−0.906854
$172$	− 0.175289i	− 0.0133657i
$173$	3.79279i	0.288361i	0.989551	+	0.144180i	$0.0460545\pi$
$173$	3.79279i	0.288361i	−0.989551	+	0.144180i	$0.953945\pi$
$174$	10.4186	0.789831
$175$	0	0
$176$	19.3179	1.45614
$177$	10.8790i	0.817715i
$178$	15.1549i	1.13591i
$179$	13.0017	0.971793	0.485897	−	0.874016i	$-0.338493\pi$
$179$	13.0017	0.971793	0.485897	+	0.874016i	$0.338493\pi$
$180$	0	0
$181$	−16.6739	−1.23936	−0.619681	−	0.784854i	$-0.712738\pi$
$181$	−16.6739	−1.23936	−0.619681	+	0.784854i	$0.712738\pi$
$182$	7.91143i	0.586434i
$183$	− 0.973111i	− 0.0719345i
$184$	−11.9982	−0.884516
$185$	0	0
$186$	−5.18869	−0.380454
$187$	− 10.3989i	− 0.760441i
$188$	− 0.784546i	− 0.0572189i
$189$	15.9822	1.16254
$190$	0	0
$191$	8.73937	0.632359	0.316179	−	0.948699i	$-0.397600\pi$
$191$	8.73937	0.632359	0.316179	+	0.948699i	$0.397600\pi$
$192$	5.45467i	0.393657i
$193$	− 21.6457i	− 1.55809i	−0.626966	−	0.779047i	$-0.715703\pi$
$193$	− 21.6457i	− 1.55809i	0.626966	−	0.779047i	$-0.284297\pi$
$194$	−9.33309	−0.670077
$195$	0	0
$196$	1.25457	0.0896119
$197$	− 2.60609i	− 0.185676i	−0.995681	−	0.0928380i	$-0.970406\pi$
$197$	− 2.60609i	− 0.185676i	0.995681	−	0.0928380i	$-0.0295939\pi$
$198$	− 16.2081i	− 1.15186i
$199$	6.57573	0.466141	0.233071	−	0.972460i	$-0.425123\pi$
$199$	6.57573	0.466141	0.233071	+	0.972460i	$0.425123\pi$
$200$	0	0
$201$	5.38732	0.379992
$202$	− 6.77113i	− 0.476415i
$203$	37.6845i	2.64494i
$204$	−0.251035	−0.0175760
$205$	0	0
$206$	26.9200	1.87561
$207$	10.8091i	0.751281i
$208$	5.84924i	0.405572i
$209$	21.9216	1.51635
$210$	0	0
$211$	−2.00196	−0.137820	−0.0689102	−	0.997623i	$-0.521952\pi$
$211$	−2.00196	−0.137820	−0.0689102	+	0.997623i	$0.521952\pi$
$212$	0.151668i	0.0104166i
$213$	− 11.2950i	− 0.773918i
$214$	26.1824	1.78979
$215$	0	0
$216$	11.0047	0.748777
$217$	− 18.7678i	− 1.27404i
$218$	4.44221i	0.300864i
$219$	3.58337	0.242142
$220$	0	0
$221$	3.14866	0.211802
$222$	− 1.09027i	− 0.0731743i
$223$	7.43402i	0.497819i	0.968527	+	0.248910i	$0.0800722\pi$
$223$	7.43402i	0.497819i	−0.968527	+	0.248910i	$0.919928\pi$
$224$	3.26623	0.218234
$225$	0	0
$226$	−29.5818	−1.96775
$227$	− 0.633009i	− 0.0420143i	−0.999779	−	0.0210071i	$-0.993313\pi$
$227$	− 0.633009i	− 0.0420143i	0.999779	−	0.0210071i	$-0.00668727\pi$
$228$	− 0.529200i	− 0.0350471i
$229$	−15.9122	−1.05151	−0.525754	−	0.850636i	$-0.676217\pi$
$229$	−15.9122	−1.05151	−0.525754	+	0.850636i	$0.676217\pi$
$230$	0	0
$231$	−13.2703	−0.873119
$232$	25.9480i	1.70357i
$233$	8.89467i	0.582709i	0.956615	+	0.291355i	$0.0941060\pi$
$233$	8.89467i	0.582709i	−0.956615	+	0.291355i	$0.905894\pi$
$234$	4.90761	0.320820
$235$	0	0
$236$	2.14476	0.139612
$237$	3.45663i	0.224533i
$238$	− 13.2868i	− 0.861257i
$239$	0.0826797	0.00534810	0.00267405	−	0.999996i	$-0.499149\pi$
$239$	0.0826797	0.00534810	0.00267405	+	0.999996i	$0.499149\pi$
$240$	0	0
$241$	−19.6320	−1.26461	−0.632305	−	0.774719i	$-0.717891\pi$
$241$	−19.6320	−1.26461	−0.632305	+	0.774719i	$0.717891\pi$
$242$	13.8449i	0.889987i
$243$	− 15.3751i	− 0.986314i
$244$	−0.191846	−0.0122817
$245$	0	0
$246$	5.68511	0.362469
$247$	6.63759i	0.422340i
$248$	− 12.9227i	− 0.820594i
$249$	4.38501	0.277888
$250$	0	0
$251$	−3.16254	−0.199618	−0.0998089	−	0.995007i	$-0.531823\pi$
$251$	−3.16254	−0.199618	−0.0998089	+	0.995007i	$0.531823\pi$
$252$	− 1.41525i	− 0.0891524i
$253$	− 19.9813i	− 1.25621i
$254$	19.9138	1.24950
$255$	0	0
$256$	3.50239	0.218900
$257$	− 11.7279i	− 0.731569i	−0.930700	−	0.365784i	$-0.880801\pi$
$257$	− 11.7279i	− 0.731569i	0.930700	−	0.365784i	$-0.119199\pi$
$258$	1.30272i	0.0811037i
$259$	3.94357	0.245041
$260$	0	0
$261$	23.3764	1.44696
$262$	31.0320i	1.91716i
$263$	− 0.755431i	− 0.0465819i	−0.999729	−	0.0232909i	$-0.992586\pi$
$263$	− 0.755431i	− 0.0465819i	0.999729	−	0.0232909i	$-0.00741441\pi$
$264$	−9.13736	−0.562366
$265$	0	0
$266$	28.0096	1.71738
$267$	− 7.69693i	− 0.471044i
$268$	− 1.06209i	− 0.0648777i
$269$	−13.4542	−0.820320	−0.410160	−	0.912014i	$-0.634527\pi$
$269$	−13.4542	−0.820320	−0.410160	+	0.912014i	$0.634527\pi$
$270$	0	0
$271$	7.94268	0.482483	0.241242	−	0.970465i	$-0.422445\pi$
$271$	7.94268	0.482483	0.241242	+	0.970465i	$0.422445\pi$
$272$	− 9.82348i	− 0.595636i
$273$	− 4.01808i	− 0.243185i
$274$	−10.5178	−0.635401
$275$	0	0
$276$	−0.482361	−0.0290347
$277$	6.88638i	0.413762i	0.978366	+	0.206881i	$0.0663314\pi$
$277$	6.88638i	0.413762i	−0.978366	+	0.206881i	$0.933669\pi$
$278$	18.9888i	1.13888i
$279$	−11.6420	−0.696988
$280$	0	0
$281$	16.0874	0.959693	0.479847	−	0.877352i	$-0.340692\pi$
$281$	16.0874	0.959693	0.479847	+	0.877352i	$0.340692\pi$
$282$	5.83061i	0.347208i
$283$	− 24.9263i	− 1.48172i	−0.671661	−	0.740859i	$-0.734419\pi$
$283$	− 24.9263i	− 1.48172i	0.671661	−	0.740859i	$-0.265581\pi$
$284$	−2.22677	−0.132134
$285$	0	0
$286$	−9.07206	−0.536442
$287$	20.5633i	1.21381i
$288$	− 2.02611i	− 0.119389i
$289$	11.7120	0.688941
$290$	0	0
$291$	4.74011	0.277870
$292$	− 0.706450i	− 0.0413419i
$293$	− 26.0732i	− 1.52321i	−0.648039	−	0.761607i	$-0.724411\pi$
$293$	− 26.0732i	− 1.52321i	0.648039	−	0.761607i	$-0.275589\pi$
$294$	−9.32373	−0.543771
$295$	0	0
$296$	2.71538	0.157828
$297$	18.3269i	1.06343i
$298$	23.2157i	1.34485i
$299$	6.05011	0.349887
$300$	0	0
$301$	−4.71199	−0.271595
$302$	20.9437i	1.20517i
$303$	3.43894i	0.197562i
$304$	20.7086	1.18772
$305$	0	0
$306$	−8.24207	−0.471168
$307$	− 18.2979i	− 1.04432i	−0.852849	−	0.522158i	$-0.825127\pi$
$307$	− 18.2979i	− 1.04432i	0.852849	−	0.522158i	$-0.174873\pi$
$308$	2.61619i	0.149071i
$309$	−13.6722	−0.777785
$310$	0	0
$311$	−1.44118	−0.0817216	−0.0408608	−	0.999165i	$-0.513010\pi$
$311$	−1.44118	−0.0817216	−0.0408608	+	0.999165i	$0.513010\pi$
$312$	− 2.76669i	− 0.156633i
$313$	18.5015i	1.04576i	0.852405	+	0.522882i	$0.175143\pi$
$313$	18.5015i	1.04576i	−0.852405	+	0.522882i	$0.824857\pi$
$314$	2.86290	0.161563
$315$	0	0
$316$	0.681465	0.0383354
$317$	− 24.1703i	− 1.35754i	−0.734352	−	0.678769i	$-0.762514\pi$
$317$	− 24.1703i	− 1.35754i	0.734352	−	0.678769i	$-0.237486\pi$
$318$	− 1.12717i	− 0.0632086i
$319$	−43.2130	−2.41946
$320$	0	0
$321$	−13.2976	−0.742198
$322$	− 25.5305i	− 1.42276i
$323$	− 11.1475i	− 0.620263i
$324$	−0.634204	−0.0352336
$325$	0	0
$326$	4.41646	0.244605
$327$	− 2.25612i	− 0.124764i
$328$	14.1591i	0.781803i
$329$	−21.0896	−1.16271
$330$	0	0
$331$	−0.308401	−0.0169513	−0.00847563	−	0.999964i	$-0.502698\pi$
$331$	−0.308401	−0.0169513	−0.00847563	+	0.999964i	$0.502698\pi$
$332$	− 0.864491i	− 0.0474451i
$333$	− 2.44627i	− 0.134055i
$334$	−6.09519	−0.333514
$335$	0	0
$336$	−12.5360	−0.683894
$337$	− 17.7374i	− 0.966219i	−0.875560	−	0.483110i	$-0.839507\pi$
$337$	− 17.7374i	− 0.966219i	0.875560	−	0.483110i	$-0.160493\pi$
$338$	16.3002i	0.886614i
$339$	15.0241	0.815996
$340$	0	0
$341$	21.5211	1.16543
$342$	− 17.3749i	− 0.939525i
$343$	− 6.11940i	− 0.330417i
$344$	−3.24449	−0.174931
$345$	0	0
$346$	−5.55706	−0.298749
$347$	13.4103i	0.719902i	0.932971	+	0.359951i	$0.117207\pi$
$347$	13.4103i	0.719902i	−0.932971	+	0.359951i	$0.882793\pi$
$348$	1.04319i	0.0559207i
$349$	18.0187	0.964521	0.482261	−	0.876028i	$-0.339816\pi$
$349$	18.0187	0.964521	0.482261	+	0.876028i	$0.339816\pi$
$350$	0	0
$351$	−5.54917	−0.296193
$352$	3.74540i	0.199631i
$353$	16.5967i	0.883355i	0.897174	+	0.441678i	$0.145617\pi$
$353$	16.5967i	0.883355i	−0.897174	+	0.441678i	$0.854383\pi$
$354$	−15.9395	−0.847175
$355$	0	0
$356$	−1.51743	−0.0804234
$357$	6.74815i	0.357150i
$358$	19.0496i	1.00680i
$359$	−0.294342	−0.0155348	−0.00776739	−	0.999970i	$-0.502472\pi$
$359$	−0.294342	−0.0155348	−0.00776739	+	0.999970i	$0.502472\pi$
$360$	0	0
$361$	4.49968	0.236825
$362$	− 24.4300i	− 1.28401i
$363$	− 7.03160i	− 0.369063i
$364$	−0.792152	−0.0415200
$365$	0	0
$366$	1.42577	0.0745260
$367$	23.2638i	1.21436i	0.794563	+	0.607181i	$0.207700\pi$
$367$	23.2638i	1.21436i	−0.794563	+	0.607181i	$0.792300\pi$
$368$	− 18.8757i	− 0.983964i
$369$	12.7558	0.664040
$370$	0	0
$371$	4.07703	0.211669
$372$	− 0.519531i	− 0.0269364i
$373$	37.2311i	1.92776i	0.266345	+	0.963878i	$0.414184\pi$
$373$	37.2311i	1.92776i	−0.266345	+	0.963878i	$0.585816\pi$
$374$	15.2361	0.787838
$375$	0	0
$376$	−14.5215	−0.748887
$377$	− 13.0844i	− 0.673880i
$378$	23.4166i	1.20442i
$379$	23.0305	1.18300	0.591498	−	0.806306i	$-0.298537\pi$
$379$	23.0305	1.18300	0.591498	+	0.806306i	$0.298537\pi$
$380$	0	0
$381$	−10.1138	−0.518148
$382$	12.8046i	0.655140i
$383$	12.8637i	0.657302i	0.944451	+	0.328651i	$0.106594\pi$
$383$	12.8637i	0.657302i	−0.944451	+	0.328651i	$0.893406\pi$
$384$	−9.22462	−0.470742
$385$	0	0
$386$	31.7145	1.61423
$387$	2.92294i	0.148581i
$388$	− 0.934499i	− 0.0474420i
$389$	16.1194	0.817287	0.408644	−	0.912694i	$-0.366002\pi$
$389$	16.1194	0.817287	0.408644	+	0.912694i	$0.366002\pi$
$390$	0	0
$391$	−10.1608	−0.513856
$392$	− 23.2212i	− 1.17285i
$393$	− 15.7606i	− 0.795016i
$394$	3.81834	0.192365
$395$	0	0
$396$	1.62287	0.0815524
$397$	− 12.9491i	− 0.649897i	−0.945732	−	0.324948i	$-0.894653\pi$
$397$	− 12.9491i	− 0.649897i	0.945732	−	0.324948i	$-0.105347\pi$
$398$	9.63452i	0.482935i
$399$	−14.2256	−0.712169
$400$	0	0
$401$	−17.2452	−0.861185	−0.430593	−	0.902546i	$-0.641695\pi$
$401$	−17.2452	−0.861185	−0.430593	+	0.902546i	$0.641695\pi$
$402$	7.89330i	0.393682i
$403$	6.51632i	0.324601i
$404$	0.677976	0.0337306
$405$	0	0
$406$	−55.2140	−2.74022
$407$	4.52210i	0.224152i
$408$	4.64650i	0.230036i
$409$	−31.2920	−1.54729	−0.773644	−	0.633621i	$-0.781568\pi$
$409$	−31.2920	−1.54729	−0.773644	+	0.633621i	$0.781568\pi$
$410$	0	0
$411$	5.34178	0.263491
$412$	2.69544i	0.132795i
$413$	− 57.6539i	− 2.83696i
$414$	−15.8370	−0.778348
$415$	0	0
$416$	−1.13406	−0.0556020
$417$	− 9.64410i	− 0.472274i
$418$	32.1187i	1.57098i
$419$	11.8203	0.577459	0.288730	−	0.957411i	$-0.406767\pi$
$419$	11.8203	0.577459	0.288730	+	0.957411i	$0.406767\pi$
$420$	0	0
$421$	19.1673	0.934155	0.467077	−	0.884216i	$-0.345307\pi$
$421$	19.1673	0.934155	0.467077	+	0.884216i	$0.345307\pi$
$422$	− 2.93319i	− 0.142786i
$423$	13.0823i	0.636082i
$424$	2.80728	0.136333
$425$	0	0
$426$	16.5490	0.801800
$427$	5.15707i	0.249568i
$428$	2.62158i	0.126719i
$429$	4.60754	0.222454
$430$	0	0
$431$	9.78469	0.471312	0.235656	−	0.971837i	$-0.424276\pi$
$431$	9.78469	0.471312	0.235656	+	0.971837i	$0.424276\pi$
$432$	17.3128i	0.832963i
$433$	− 35.2661i	− 1.69478i	−0.530969	−	0.847391i	$-0.678172\pi$
$433$	− 35.2661i	− 1.69478i	0.530969	−	0.847391i	$-0.321828\pi$
$434$	27.4978	1.31994
$435$	0	0
$436$	−0.444787	−0.0213014
$437$	− 21.4198i	− 1.02465i
$438$	5.25022i	0.250865i
$439$	−24.4934	−1.16901	−0.584503	−	0.811392i	$-0.698710\pi$
$439$	−24.4934	−1.16901	−0.584503	+	0.811392i	$0.698710\pi$
$440$	0	0
$441$	−20.9199	−0.996184
$442$	4.61330i	0.219432i
$443$	26.1850i	1.24409i	0.782982	+	0.622044i	$0.213698\pi$
$443$	26.1850i	1.24409i	−0.782982	+	0.622044i	$0.786302\pi$
$444$	0.109166	0.00518080
$445$	0	0
$446$	−10.8921	−0.515754
$447$	− 11.7909i	− 0.557689i
$448$	− 28.9074i	− 1.36575i
$449$	−39.6969	−1.87341	−0.936705	−	0.350119i	$-0.886141\pi$
$449$	−39.6969	−1.87341	−0.936705	+	0.350119i	$0.886141\pi$
$450$	0	0
$451$	−23.5800	−1.11034
$452$	− 2.96195i	− 0.139319i
$453$	− 10.6369i	− 0.499766i
$454$	0.927461	0.0435279
$455$	0	0
$456$	−9.79515	−0.458700
$457$	20.6802i	0.967380i	0.875239	+	0.483690i	$0.160704\pi$
$457$	20.6802i	0.967380i	−0.875239	+	0.483690i	$0.839296\pi$
$458$	− 23.3140i	− 1.08939i
$459$	9.31954	0.434999
$460$	0	0
$461$	−5.51764	−0.256982	−0.128491	−	0.991711i	$-0.541013\pi$
$461$	−5.51764	−0.256982	−0.128491	+	0.991711i	$0.541013\pi$
$462$	− 19.4431i	− 0.904574i
$463$	− 20.9783i	− 0.974944i	−0.873139	−	0.487472i	$-0.837919\pi$
$463$	− 20.9783i	− 0.974944i	0.873139	−	0.487472i	$-0.162081\pi$
$464$	−40.8219	−1.89511
$465$	0	0
$466$	−13.0321	−0.603702
$467$	− 7.62261i	− 0.352732i	−0.984325	−	0.176366i	$-0.943566\pi$
$467$	− 7.62261i	− 0.352732i	0.984325	−	0.176366i	$-0.0564343\pi$
$468$	0.491387i	0.0227144i
$469$	−28.5504	−1.31834
$470$	0	0
$471$	−1.45402	−0.0669976
$472$	− 39.6982i	− 1.82726i
$473$	− 5.40326i	− 0.248442i
$474$	−5.06453	−0.232622
$475$	0	0
$476$	1.33038	0.0609777
$477$	− 2.52906i	− 0.115798i
$478$	0.121139i	0.00554078i
$479$	−32.7445	−1.49613	−0.748067	−	0.663623i	$-0.769018\pi$
$479$	−32.7445	−1.49613	−0.748067	+	0.663623i	$0.769018\pi$
$480$	0	0
$481$	−1.36924	−0.0624320
$482$	− 28.7641i	− 1.31017i
$483$	12.9665i	0.589995i
$484$	−1.38626	−0.0630118
$485$	0	0
$486$	22.5271	1.02185
$487$	− 24.3487i	− 1.10335i	−0.834061	−	0.551673i	$-0.813990\pi$
$487$	− 24.3487i	− 1.10335i	0.834061	−	0.551673i	$-0.186010\pi$
$488$	3.55095i	0.160744i
$489$	−2.24304	−0.101434
$490$	0	0
$491$	9.88214	0.445975	0.222987	−	0.974821i	$-0.428419\pi$
$491$	9.88214	0.445975	0.222987	+	0.974821i	$0.428419\pi$
$492$	0.569235i	0.0256631i
$493$	21.9745i	0.989683i
$494$	−9.72516	−0.437555
$495$	0	0
$496$	20.3302	0.912855
$497$	59.8584i	2.68502i
$498$	6.42475i	0.287900i
$499$	−38.4155	−1.71971	−0.859857	−	0.510535i	$-0.829447\pi$
$499$	−38.4155	−1.71971	−0.859857	+	0.510535i	$0.829447\pi$
$500$	0	0
$501$	3.09564	0.138303
$502$	− 4.63364i	− 0.206809i
$503$	14.2482i	0.635297i	0.948209	+	0.317649i	$0.102893\pi$
$503$	14.2482i	0.635297i	−0.948209	+	0.317649i	$0.897107\pi$
$504$	−26.1954	−1.16684
$505$	0	0
$506$	29.2759	1.30147
$507$	− 8.27859i	− 0.367665i
$508$	1.99391i	0.0884657i
$509$	−28.0410	−1.24290	−0.621448	−	0.783455i	$-0.713455\pi$
$509$	−28.0410	−1.24290	−0.621448	+	0.783455i	$0.713455\pi$
$510$	0	0
$511$	−18.9903	−0.840081
$512$	− 19.6614i	− 0.868921i
$513$	19.6462i	0.867402i
$514$	17.1833	0.757925
$515$	0	0
$516$	−0.130438	−0.00574221
$517$	− 24.1835i	− 1.06359i
$518$	5.77797i	0.253870i
$519$	2.82233	0.123887
$520$	0	0
$521$	31.3715	1.37441	0.687204	−	0.726464i	$-0.258838\pi$
$521$	31.3715	1.37441	0.687204	+	0.726464i	$0.258838\pi$
$522$	34.2503i	1.49909i
$523$	37.1439i	1.62419i	0.583525	+	0.812095i	$0.301673\pi$
$523$	37.1439i	1.62419i	−0.583525	+	0.812095i	$0.698327\pi$
$524$	−3.10715	−0.135737
$525$	0	0
$526$	1.10683	0.0482601
$527$	− 10.9438i	− 0.476720i
$528$	− 14.3750i	− 0.625593i
$529$	3.47608	0.151134
$530$	0	0
$531$	−35.7638	−1.55202
$532$	2.80453i	0.121592i
$533$	− 7.13975i	− 0.309257i
$534$	11.2773	0.488014
$535$	0	0
$536$	−19.6587	−0.849126
$537$	− 9.67497i	− 0.417506i
$538$	− 19.7127i	− 0.849873i
$539$	38.6719	1.66571
$540$	0	0
$541$	−4.01732	−0.172718	−0.0863590	−	0.996264i	$-0.527523\pi$
$541$	−4.01732	−0.172718	−0.0863590	+	0.996264i	$0.527523\pi$
$542$	11.6373i	0.499866i
$543$	12.4076i	0.532460i
$544$	1.90460	0.0816591
$545$	0	0
$546$	5.88714	0.251946
$547$	− 40.4991i	− 1.73162i	−0.500375	−	0.865809i	$-0.666805\pi$
$547$	− 40.4991i	− 1.73162i	0.500375	−	0.865809i	$-0.333195\pi$
$548$	− 1.05312i	− 0.0449869i
$549$	3.19903	0.136531
$550$	0	0
$551$	−46.3238	−1.97346
$552$	8.92819i	0.380009i
$553$	− 18.3187i	− 0.778989i
$554$	−10.0897	−0.428669
$555$	0	0
$556$	−1.90131	−0.0806333
$557$	41.5078i	1.75874i	0.476139	+	0.879370i	$0.342036\pi$
$557$	41.5078i	1.75874i	−0.476139	+	0.879370i	$0.657964\pi$
$558$	− 17.0574i	− 0.722098i
$559$	1.63604	0.0691973
$560$	0	0
$561$	−7.73812	−0.326704
$562$	23.5707i	0.994268i
$563$	− 8.82377i	− 0.371877i	−0.982561	−	0.185939i	$-0.940467\pi$
$563$	− 8.82377i	− 0.371877i	0.982561	−	0.185939i	$-0.0595326\pi$
$564$	−0.583805	−0.0245826
$565$	0	0
$566$	36.5212	1.53510
$567$	17.0482i	0.715958i
$568$	41.2161i	1.72939i
$569$	1.06707	0.0447338	0.0223669	−	0.999750i	$-0.492880\pi$
$569$	1.06707	0.0447338	0.0223669	+	0.999750i	$0.492880\pi$
$570$	0	0
$571$	3.43435	0.143723	0.0718616	−	0.997415i	$-0.477106\pi$
$571$	3.43435	0.143723	0.0718616	+	0.997415i	$0.477106\pi$
$572$	− 0.908363i	− 0.0379806i
$573$	− 6.50323i	− 0.271676i
$574$	−30.1286	−1.25754
$575$	0	0
$576$	−17.9318	−0.747158
$577$	30.2801i	1.26058i	0.776361	+	0.630289i	$0.217064\pi$
$577$	30.2801i	1.26058i	−0.776361	+	0.630289i	$0.782936\pi$
$578$	17.1600i	0.713761i
$579$	−16.1073	−0.669395
$580$	0	0
$581$	−23.2386	−0.964101
$582$	6.94504i	0.287881i
$583$	4.67514i	0.193625i
$584$	−13.0760	−0.541087
$585$	0	0
$586$	38.2015	1.57809
$587$	− 10.4265i	− 0.430347i	−0.976576	−	0.215173i	$-0.930968\pi$
$587$	− 10.4265i	− 0.430347i	0.976576	−	0.215173i	$-0.0690317\pi$
$588$	− 0.933562i	− 0.0384994i
$589$	23.0703	0.950597
$590$	0	0
$591$	−1.93927	−0.0797709
$592$	4.27188i	0.175573i
$593$	− 19.5382i	− 0.802337i	−0.916004	−	0.401169i	$-0.868604\pi$
$593$	− 19.5382i	− 0.802337i	0.916004	−	0.401169i	$-0.131396\pi$
$594$	−26.8519	−1.10175
$595$	0	0
$596$	−2.32453	−0.0952166
$597$	− 4.89320i	− 0.200265i
$598$	8.86439i	0.362492i
$599$	9.95917	0.406921	0.203460	−	0.979083i	$-0.434781\pi$
$599$	9.95917	0.406921	0.203460	+	0.979083i	$0.434781\pi$
$600$	0	0
$601$	0.201892	0.00823534	0.00411767	−	0.999992i	$-0.498689\pi$
$601$	0.201892	0.00823534	0.00411767	+	0.999992i	$0.498689\pi$
$602$	− 6.90384i	− 0.281380i
$603$	17.7104i	0.721222i
$604$	−2.09704	−0.0853272
$605$	0	0
$606$	−5.03860	−0.204679
$607$	33.5993i	1.36375i	0.731468	+	0.681876i	$0.238836\pi$
$607$	33.5993i	1.36375i	−0.731468	+	0.681876i	$0.761164\pi$
$608$	4.01503i	0.162831i
$609$	28.0422	1.13633
$610$	0	0
$611$	7.32249	0.296236
$612$	− 0.825258i	− 0.0333591i
$613$	− 8.63736i	− 0.348859i	−0.984670	−	0.174430i	$-0.944192\pi$
$613$	− 8.63736i	− 0.348859i	0.984670	−	0.174430i	$-0.0558082\pi$
$614$	26.8094	1.08194
$615$	0	0
$616$	48.4240	1.95106
$617$	8.37257i	0.337067i	0.985696	+	0.168533i	$0.0539031\pi$
$617$	8.37257i	0.337067i	−0.985696	+	0.168533i	$0.946097\pi$
$618$	− 20.0320i	− 0.805806i
$619$	0.670360	0.0269441	0.0134720	−	0.999909i	$-0.495712\pi$
$619$	0.670360	0.0269441	0.0134720	+	0.999909i	$0.495712\pi$
$620$	0	0
$621$	17.9074	0.718598
$622$	− 2.11156i	− 0.0846657i
$623$	40.7904i	1.63423i
$624$	4.35260	0.174243
$625$	0	0
$626$	−27.1077	−1.08344
$627$	− 16.3125i	− 0.651459i
$628$	0.286655i	0.0114388i
$629$	2.29957	0.0916897
$630$	0	0
$631$	15.0416	0.598798	0.299399	−	0.954128i	$-0.403214\pi$
$631$	15.0416	0.598798	0.299399	+	0.954128i	$0.403214\pi$
$632$	− 12.6135i	− 0.501738i
$633$	1.48972i	0.0592109i
$634$	35.4134	1.40645
$635$	0	0
$636$	0.112861	0.00447522
$637$	11.7094i	0.463943i
$638$	− 63.3141i	− 2.50663i
$639$	37.1313	1.46889
$640$	0	0
$641$	18.9440	0.748241	0.374121	−	0.927380i	$-0.377945\pi$
$641$	18.9440	0.748241	0.374121	+	0.927380i	$0.377945\pi$
$642$	− 19.4831i	− 0.768937i
$643$	27.9869i	1.10369i	0.833945	+	0.551847i	$0.186077\pi$
$643$	27.9869i	1.10369i	−0.833945	+	0.551847i	$0.813923\pi$
$644$	2.55630	0.100732
$645$	0	0
$646$	16.3329	0.642609
$647$	20.3334i	0.799387i	0.916649	+	0.399694i	$0.130883\pi$
$647$	20.3334i	0.799387i	−0.916649	+	0.399694i	$0.869117\pi$
$648$	11.7387i	0.461140i
$649$	66.1119	2.59512
$650$	0	0
$651$	−13.9657	−0.547358
$652$	0.442209i	0.0173182i
$653$	12.5212i	0.489991i	0.969524	+	0.244996i	$0.0787865\pi$
$653$	12.5212i	0.489991i	−0.969524	+	0.244996i	$0.921213\pi$
$654$	3.30558	0.129259
$655$	0	0
$656$	−22.2753	−0.869703
$657$	11.7800i	0.459583i
$658$	− 30.8997i	− 1.20460i
$659$	10.5140	0.409565	0.204783	−	0.978807i	$-0.434351\pi$
$659$	10.5140	0.409565	0.204783	+	0.978807i	$0.434351\pi$
$660$	0	0
$661$	12.9804	0.504880	0.252440	−	0.967613i	$-0.418767\pi$
$661$	12.9804	0.504880	0.252440	+	0.967613i	$0.418767\pi$
$662$	− 0.451858i	− 0.0175620i
$663$	− 2.34301i	− 0.0909951i
$664$	−16.0012	−0.620966
$665$	0	0
$666$	3.58418	0.138884
$667$	42.2238i	1.63491i
$668$	− 0.610296i	− 0.0236131i
$669$	5.53188	0.213875
$670$	0	0
$671$	−5.91363	−0.228293
$672$	− 2.43050i	− 0.0937588i
$673$	− 2.47979i	− 0.0955890i	−0.998857	−	0.0477945i	$-0.984781\pi$
$673$	− 2.47979i	− 0.0955890i	0.998857	−	0.0477945i	$-0.0152193\pi$
$674$	25.9882	1.00103
$675$	0	0
$676$	−1.63210	−0.0627730
$677$	− 23.8883i	− 0.918103i	−0.888410	−	0.459052i	$-0.848189\pi$
$677$	− 23.8883i	− 0.918103i	0.888410	−	0.459052i	$-0.151811\pi$
$678$	22.0127i	0.845394i
$679$	−25.1205	−0.964038
$680$	0	0
$681$	−0.471041	−0.0180503
$682$	31.5319i	1.20742i
$683$	36.3338i	1.39028i	0.718876	+	0.695138i	$0.244657\pi$
$683$	36.3338i	1.39028i	−0.718876	+	0.695138i	$0.755343\pi$
$684$	1.73970	0.0665191
$685$	0	0
$686$	8.96592	0.342320
$687$	11.8408i	0.451753i
$688$	− 5.10428i	− 0.194599i
$689$	−1.41558	−0.0539292
$690$	0	0
$691$	2.36561	0.0899922	0.0449961	−	0.998987i	$-0.485672\pi$
$691$	2.36561	0.0899922	0.0449961	+	0.998987i	$0.485672\pi$
$692$	− 0.556414i	− 0.0211517i
$693$	− 43.6249i	− 1.65717i
$694$	−19.6483	−0.745838
$695$	0	0
$696$	19.3087	0.731896
$697$	11.9908i	0.454185i
$698$	26.4004i	0.999270i
$699$	6.61880	0.250346
$700$	0	0
$701$	−36.1238	−1.36438	−0.682189	−	0.731176i	$-0.738972\pi$
$701$	−36.1238	−1.36438	−0.682189	+	0.731176i	$0.738972\pi$
$702$	− 8.13044i	− 0.306864i
$703$	4.84765i	0.182832i
$704$	33.1482	1.24932
$705$	0	0
$706$	−24.3169	−0.915180
$707$	− 18.2249i	− 0.685417i
$708$	− 1.59598i	− 0.0599807i
$709$	−24.4167	−0.916989	−0.458495	−	0.888697i	$-0.651611\pi$
$709$	−24.4167	−0.916989	−0.458495	+	0.888697i	$0.651611\pi$
$710$	0	0
$711$	−11.3634	−0.426161
$712$	28.0866i	1.05259i
$713$	− 21.0284i	− 0.787520i
$714$	−9.88714	−0.370017
$715$	0	0
$716$	−1.90739	−0.0712825
$717$	− 0.0615245i	− 0.00229767i
$718$	− 0.431259i	− 0.0160944i
$719$	26.7224	0.996576	0.498288	−	0.867012i	$-0.333962\pi$
$719$	26.7224	0.996576	0.498288	+	0.867012i	$0.333962\pi$
$720$	0	0
$721$	72.4568	2.69843
$722$	6.59276i	0.245357i
$723$	14.6088i	0.543307i
$724$	2.44612	0.0909092
$725$	0	0
$726$	10.3024	0.382360
$727$	2.85449i	0.105867i	0.998598	+	0.0529336i	$0.0168572\pi$
$727$	2.85449i	0.105867i	−0.998598	+	0.0529336i	$0.983143\pi$
$728$	14.6622i	0.543419i
$729$	1.52804	0.0565940
$730$	0	0
$731$	−2.74765	−0.101625
$732$	0.142758i	0.00527650i
$733$	23.9471i	0.884507i	0.896890	+	0.442253i	$0.145821\pi$
$733$	23.9471i	0.884507i	−0.896890	+	0.442253i	$0.854179\pi$
$734$	−34.0853	−1.25811
$735$	0	0
$736$	3.65966	0.134897
$737$	− 32.7389i	− 1.20595i
$738$	18.6893i	0.687964i
$739$	−27.0438	−0.994823	−0.497411	−	0.867515i	$-0.665716\pi$
$739$	−27.0438	−0.994823	−0.497411	+	0.867515i	$0.665716\pi$
$740$	0	0
$741$	4.93924	0.181447
$742$	5.97351i	0.219295i
$743$	− 38.5442i	− 1.41405i	−0.707188	−	0.707026i	$-0.750037\pi$
$743$	− 38.5442i	− 1.41405i	0.707188	−	0.707026i	$-0.249963\pi$
$744$	−9.61619	−0.352547
$745$	0	0
$746$	−54.5497	−1.99721
$747$	14.4154i	0.527430i
$748$	1.52555i	0.0557796i
$749$	70.4714	2.57497
$750$	0	0
$751$	−42.9011	−1.56548	−0.782741	−	0.622348i	$-0.786179\pi$
$751$	−42.9011	−1.56548	−0.782741	+	0.622348i	$0.786179\pi$
$752$	− 22.8454i	− 0.833086i
$753$	2.35334i	0.0857606i
$754$	19.1708	0.698158
$755$	0	0
$756$	−2.34465	−0.0852739
$757$	17.3376i	0.630146i	0.949067	+	0.315073i	$0.102029\pi$
$757$	17.3376i	0.630146i	−0.949067	+	0.315073i	$0.897971\pi$
$758$	33.7434i	1.22562i
$759$	−14.8687	−0.539700
$760$	0	0
$761$	41.5752	1.50710	0.753550	−	0.657390i	$-0.228340\pi$
$761$	41.5752	1.50710	0.753550	+	0.657390i	$0.228340\pi$
$762$	− 14.8184i	− 0.536815i
$763$	11.9565i	0.432853i
$764$	−1.28209	−0.0463845
$765$	0	0
$766$	−18.8474	−0.680983
$767$	20.0179i	0.722805i
$768$	− 2.60624i	− 0.0940445i
$769$	10.1940	0.367603	0.183802	−	0.982963i	$-0.441160\pi$
$769$	10.1940	0.367603	0.183802	+	0.982963i	$0.441160\pi$
$770$	0	0
$771$	−8.72712	−0.314300
$772$	3.17550i	0.114289i
$773$	1.79833i	0.0646816i	0.999477	+	0.0323408i	$0.0102962\pi$
$773$	1.79833i	0.0646816i	−0.999477	+	0.0323408i	$0.989704\pi$
$774$	−4.28258	−0.153934
$775$	0	0
$776$	−17.2970	−0.620926
$777$	− 2.93453i	− 0.105276i
$778$	23.6176i	0.846732i
$779$	−25.2775	−0.905661
$780$	0	0
$781$	−68.6398	−2.45613
$782$	− 14.8873i	− 0.532368i
$783$	− 38.7277i	− 1.38402i
$784$	36.5321	1.30472
$785$	0	0
$786$	23.0918	0.823658
$787$	− 44.7062i	− 1.59360i	−0.604241	−	0.796802i	$-0.706523\pi$
$787$	− 44.7062i	− 1.59360i	0.604241	−	0.796802i	$-0.293477\pi$
$788$	0.382321i	0.0136196i
$789$	−0.562139	−0.0200127
$790$	0	0
$791$	−79.6211	−2.83100
$792$	− 30.0383i	− 1.06737i
$793$	− 1.79058i	− 0.0635852i
$794$	18.9725	0.673310
$795$	0	0
$796$	−0.964680	−0.0341922
$797$	1.95203i	0.0691444i	0.999402	+	0.0345722i	$0.0110069\pi$
$797$	1.95203i	0.0691444i	−0.999402	+	0.0345722i	$0.988993\pi$
$798$	− 20.8428i	− 0.737826i
$799$	−12.2977	−0.435062
$800$	0	0
$801$	25.3030	0.894038
$802$	− 25.2671i	− 0.892211i
$803$	− 21.7762i	− 0.768467i
$804$	−0.790336	−0.0278730
$805$	0	0
$806$	−9.54748	−0.336296
$807$	10.0117i	0.352429i
$808$	− 12.5489i	− 0.441469i
$809$	−32.1732	−1.13115	−0.565574	−	0.824698i	$-0.691345\pi$
$809$	−32.1732	−1.13115	−0.565574	+	0.824698i	$0.691345\pi$
$810$	0	0
$811$	43.5729	1.53005	0.765025	−	0.644000i	$-0.222726\pi$
$811$	43.5729	1.53005	0.765025	+	0.644000i	$0.222726\pi$
$812$	− 5.52844i	− 0.194010i
$813$	− 5.91039i	− 0.207286i
$814$	−6.62562	−0.232228
$815$	0	0
$816$	−7.30995	−0.255900
$817$	− 5.79223i	− 0.202645i
$818$	− 45.8478i	− 1.60303i
$819$	13.2091	0.461564
$820$	0	0
$821$	−42.7990	−1.49370	−0.746848	−	0.664995i	$-0.768434\pi$
$821$	−42.7990	−1.49370	−0.746848	+	0.664995i	$0.768434\pi$
$822$	7.82658i	0.272983i
$823$	− 52.9850i	− 1.84694i	−0.383670	−	0.923470i	$-0.625340\pi$
$823$	− 52.9850i	− 1.84694i	0.383670	−	0.923470i	$-0.374660\pi$
$824$	49.8908	1.73803
$825$	0	0
$826$	84.4724	2.93917
$827$	23.3945i	0.813508i	0.913538	+	0.406754i	$0.133339\pi$
$827$	23.3945i	0.813508i	−0.913538	+	0.406754i	$0.866661\pi$
$828$	− 1.58572i	− 0.0551077i
$829$	−0.375803	−0.0130522	−0.00652608	−	0.999979i	$-0.502077\pi$
$829$	−0.375803	−0.0130522	−0.00652608	+	0.999979i	$0.502077\pi$
$830$	0	0
$831$	5.12437	0.177762
$832$	10.0369i	0.347966i
$833$	− 19.6653i	− 0.681362i
$834$	14.1302	0.489288
$835$	0	0
$836$	−3.21596	−0.111226
$837$	19.2873i	0.666666i
$838$	17.3187i	0.598263i
$839$	−15.8320	−0.546583	−0.273291	−	0.961931i	$-0.588112\pi$
$839$	−15.8320	−0.546583	−0.273291	+	0.961931i	$0.588112\pi$
$840$	0	0
$841$	62.3161	2.14883
$842$	28.0832i	0.967810i
$843$	− 11.9711i	− 0.412307i
$844$	0.293693	0.0101093
$845$	0	0
$846$	−19.1677	−0.658998
$847$	37.2644i	1.28042i
$848$	4.41646i	0.151662i
$849$	−18.5485	−0.636581
$850$	0	0
$851$	4.41859	0.151467
$852$	1.65701i	0.0567681i
$853$	9.32579i	0.319309i	0.987173	+	0.159655i	$0.0510380\pi$
$853$	9.32579i	0.319309i	−0.987173	+	0.159655i	$0.948962\pi$
$854$	−7.55595	−0.258559
$855$	0	0
$856$	48.5238	1.65851
$857$	− 5.99313i	− 0.204721i	−0.994747	−	0.102361i	$-0.967360\pi$
$857$	− 5.99313i	− 0.204721i	0.994747	−	0.102361i	$-0.0326396\pi$
$858$	6.75080i	0.230469i
$859$	44.6541	1.52358	0.761788	−	0.647826i	$-0.224322\pi$
$859$	44.6541	1.52358	0.761788	+	0.647826i	$0.224322\pi$
$860$	0	0
$861$	15.3018	0.521483
$862$	14.3362i	0.488292i
$863$	21.8515i	0.743832i	0.928266	+	0.371916i	$0.121299\pi$
$863$	21.8515i	0.743832i	−0.928266	+	0.371916i	$0.878701\pi$
$864$	−3.35665	−0.114196
$865$	0	0
$866$	51.6706	1.75584
$867$	− 8.71525i	− 0.295986i
$868$	2.75329i	0.0934527i
$869$	21.0061	0.712582
$870$	0	0
$871$	9.91295	0.335888
$872$	8.23273i	0.278795i
$873$	15.5827i	0.527396i
$874$	31.3834	1.06156
$875$	0	0
$876$	−0.525691	−0.0177615
$877$	− 11.3951i	− 0.384786i	−0.981318	−	0.192393i	$-0.938375\pi$
$877$	− 11.3951i	− 0.384786i	0.981318	−	0.192393i	$-0.0616248\pi$
$878$	− 35.8868i	− 1.21112i
$879$	−19.4019	−0.654409
$880$	0	0
$881$	−48.2087	−1.62419	−0.812096	−	0.583523i	$-0.801674\pi$
$881$	−48.2087	−1.62419	−0.812096	+	0.583523i	$0.801674\pi$
$882$	− 30.6510i	− 1.03207i
$883$	36.2461i	1.21978i	0.792486	+	0.609890i	$0.208786\pi$
$883$	36.2461i	1.21978i	−0.792486	+	0.609890i	$0.791214\pi$
$884$	−0.461918	−0.0155360
$885$	0	0
$886$	−38.3653	−1.28891
$887$	− 23.8002i	− 0.799134i	−0.916704	−	0.399567i	$-0.869160\pi$
$887$	− 23.8002i	− 0.799134i	0.916704	−	0.399567i	$-0.130840\pi$
$888$	− 2.02060i	− 0.0678069i
$889$	53.5990	1.79765
$890$	0	0
$891$	−19.5493	−0.654925
$892$	− 1.09059i	− 0.0365158i
$893$	− 25.9245i	− 0.867530i
$894$	17.2755	0.577780
$895$	0	0
$896$	48.8865	1.63318
$897$	− 4.50207i	− 0.150320i
$898$	− 58.1624i	− 1.94090i
$899$	−45.4775	−1.51676
$900$	0	0
$901$	2.37739	0.0792023
$902$	− 34.5486i	− 1.15034i
$903$	3.50634i	0.116684i
$904$	−54.8239	−1.82342
$905$	0	0
$906$	15.5848	0.517771
$907$	− 9.82566i	− 0.326256i	−0.986605	−	0.163128i	$-0.947842\pi$
$907$	− 9.82566i	− 0.326256i	0.986605	−	0.163128i	$-0.0521583\pi$
$908$	0.0928643i	0.00308181i
$909$	−11.3052	−0.374971
$910$	0	0
$911$	31.2125	1.03412	0.517058	−	0.855950i	$-0.327027\pi$
$911$	31.2125	1.03412	0.517058	+	0.855950i	$0.327027\pi$
$912$	− 15.4099i	− 0.510273i
$913$	− 26.6478i	− 0.881914i
$914$	−30.2999	−1.00223
$915$	0	0
$916$	2.33437	0.0771298
$917$	83.5243i	2.75821i
$918$	13.6546i	0.450670i
$919$	−28.5950	−0.943263	−0.471631	−	0.881796i	$-0.656335\pi$
$919$	−28.5950	−0.943263	−0.471631	+	0.881796i	$0.656335\pi$
$920$	0	0
$921$	−13.6160	−0.448663
$922$	− 8.08424i	− 0.266240i
$923$	− 20.7833i	− 0.684092i
$924$	1.94679	0.0640446
$925$	0	0
$926$	30.7366	1.01007
$927$	− 44.9463i	− 1.47623i
$928$	− 7.91465i	− 0.259811i
$929$	45.3832	1.48898	0.744488	−	0.667636i	$-0.232694\pi$
$929$	45.3832	1.48898	0.744488	+	0.667636i	$0.232694\pi$
$930$	0	0
$931$	41.4558	1.35866
$932$	− 1.30488i	− 0.0427426i
$933$	1.07242i	0.0351095i
$934$	11.1684	0.365440
$935$	0	0
$936$	9.09526	0.297288
$937$	− 27.0457i	− 0.883543i	−0.897128	−	0.441772i	$-0.854350\pi$
$937$	− 27.0457i	− 0.883543i	0.897128	−	0.441772i	$-0.145650\pi$
$938$	− 41.8311i	− 1.36583i
$939$	13.7675	0.449285
$940$	0	0
$941$	31.3367	1.02155	0.510773	−	0.859716i	$-0.329359\pi$
$941$	31.3367	1.02155	0.510773	+	0.859716i	$0.329359\pi$
$942$	− 2.13037i	− 0.0694113i
$943$	23.0402i	0.750293i
$944$	62.4538	2.03270
$945$	0	0
$946$	7.91665	0.257393
$947$	− 27.4446i	− 0.891830i	−0.895075	−	0.445915i	$-0.852878\pi$
$947$	− 27.4446i	− 0.891830i	0.895075	−	0.445915i	$-0.147122\pi$
$948$	− 0.507099i	− 0.0164698i
$949$	6.59359	0.214037
$950$	0	0
$951$	−17.9858	−0.583231
$952$	− 24.6244i	− 0.798083i
$953$	35.3324i	1.14453i	0.820069	+	0.572265i	$0.193935\pi$
$953$	35.3324i	1.14453i	−0.820069	+	0.572265i	$0.806065\pi$
$954$	3.70548	0.119969
$955$	0	0
$956$	−0.0121294	−0.000392292 0
$957$	32.1561i	1.03946i
$958$	− 47.9760i	− 1.55004i
$959$	−28.3091	−0.914150
$960$	0	0
$961$	−8.35116	−0.269392
$962$	− 2.00616i	− 0.0646812i
$963$	− 43.7147i	− 1.40869i
$964$	2.88008	0.0927612
$965$	0	0
$966$	−18.9980	−0.611251
$967$	31.4137i	1.01020i	0.863062	+	0.505098i	$0.168544\pi$
$967$	31.4137i	1.01020i	−0.863062	+	0.505098i	$0.831456\pi$
$968$	25.6588i	0.824705i
$969$	−8.29519	−0.266480
$970$	0	0
$971$	6.60982	0.212119	0.106060	−	0.994360i	$-0.466177\pi$
$971$	6.60982	0.212119	0.106060	+	0.994360i	$0.466177\pi$
$972$	2.25558i	0.0723477i
$973$	51.1095i	1.63850i
$974$	35.6748	1.14310
$975$	0	0
$976$	−5.58641	−0.178817
$977$	− 0.318781i	− 0.0101987i	−0.999987	−	0.00509935i	$-0.998377\pi$
$977$	− 0.318781i	− 0.0101987i	0.999987	−	0.00509935i	$-0.00162318\pi$
$978$	− 3.28642i	− 0.105088i
$979$	−46.7744	−1.49492
$980$	0	0
$981$	7.41681	0.236801
$982$	14.4789i	0.462042i
$983$	10.7688i	0.343473i	0.985143	+	0.171736i	$0.0549377\pi$
$983$	10.7688i	0.343473i	−0.985143	+	0.171736i	$0.945062\pi$
$984$	10.5362	0.335881
$985$	0	0
$986$	−32.1963	−1.02534
$987$	15.6934i	0.499527i
$988$	− 0.973756i	− 0.0309793i
$989$	−5.27957	−0.167881
$990$	0	0
$991$	−23.6638	−0.751706	−0.375853	−	0.926679i	$-0.622650\pi$
$991$	−23.6638	−0.751706	−0.375853	+	0.926679i	$0.622650\pi$
$992$	3.94167i	0.125148i
$993$	0.229491i	0.00728267i
$994$	−87.7023	−2.78175
$995$	0	0
$996$	−0.643294	−0.0203835
$997$	− 4.48006i	− 0.141885i	−0.997480	−	0.0709425i	$-0.977399\pi$
$997$	− 4.48006i	− 0.141885i	0.997480	−	0.0709425i	$-0.0226007\pi$
$998$	− 56.2850i	− 1.78167i
$999$	−4.05274	−0.128223

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.b.g.149.8		10
5.2	odd	4		925.2.a.h.1.2		5
5.3	odd	4		185.2.a.d.1.4	✓	5
5.4	even	2	inner	925.2.b.g.149.3		10
15.2	even	4		8325.2.a.cc.1.4		5
15.8	even	4		1665.2.a.q.1.2		5
20.3	even	4		2960.2.a.ba.1.2		5
35.13	even	4		9065.2.a.j.1.4		5
185.73	odd	4		6845.2.a.g.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.d.1.4	✓	5	5.3	odd	4
925.2.a.h.1.2		5	5.2	odd	4
925.2.b.g.149.3		10	5.4	even	2	inner
925.2.b.g.149.8		10	1.1	even	1	trivial
1665.2.a.q.1.2		5	15.8	even	4
2960.2.a.ba.1.2		5	20.3	even	4
6845.2.a.g.1.2		5	185.73	odd	4
8325.2.a.cc.1.4		5	15.2	even	4
9065.2.a.j.1.4		5	35.13	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.46516i q^{2} -0.744131i q^{3} -0.146703 q^{4} +1.09027 q^{6} +3.94357i q^{7} +2.71538i q^{8} +2.44627 q^{9} +O(q^{10})\)	\(q+1.46516i q^{2} -0.744131i q^{3} -0.146703 q^{4} +1.09027 q^{6} +3.94357i q^{7} +2.71538i q^{8} +2.44627 q^{9} -4.52210 q^{11} +0.109166i q^{12} -1.36924i q^{13} -5.77797 q^{14} -4.27188 q^{16} +2.29957i q^{17} +3.58418i q^{18} -4.84765 q^{19} +2.93453 q^{21} -6.62562i q^{22} +4.41859i q^{23} +2.02060 q^{24} +2.00616 q^{26} -4.05274i q^{27} -0.578534i q^{28} +9.55595 q^{29} -4.75908 q^{31} -0.828243i q^{32} +3.36504i q^{33} -3.36924 q^{34} -0.358875 q^{36} -1.00000i q^{37} -7.10259i q^{38} -1.01889 q^{39} +5.21439 q^{41} +4.29957i q^{42} +1.19485i q^{43} +0.663407 q^{44} -6.47395 q^{46} +5.34785i q^{47} +3.17884i q^{48} -8.55174 q^{49} +1.71118 q^{51} +0.200872i q^{52} -1.03384i q^{53} +5.93792 q^{54} -10.7083 q^{56} +3.60728i q^{57} +14.0010i q^{58} -14.6197 q^{59} +1.30772 q^{61} -6.97283i q^{62} +9.64703i q^{63} -7.33026 q^{64} -4.93033 q^{66} +7.23975i q^{67} -0.337354i q^{68} +3.28801 q^{69} +15.1787 q^{71} +6.64256i q^{72} +4.81551i q^{73} +1.46516 q^{74} +0.711165 q^{76} -17.8332i q^{77} -1.49285i q^{78} -4.64520 q^{79} +4.32304 q^{81} +7.63993i q^{82} +5.89279i q^{83} -0.430505 q^{84} -1.75066 q^{86} -7.11087i q^{87} -12.2792i q^{88} +10.3435 q^{89} +5.39969 q^{91} -0.648221i q^{92} +3.54138i q^{93} -7.83547 q^{94} -0.616321 q^{96} +6.37000i q^{97} -12.5297i q^{98} -11.0623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9}+O(q^{10}) \) 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9	\( 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9} + 14 q^{11} - 8 q^{14} + 16 q^{16} - 28 q^{19} - 18 q^{21} - 24 q^{24} - 40 q^{26} - 4 q^{29} + 16 q^{31} - 24 q^{34} - 72 q^{36} - 24 q^{39} - 18 q^{41} - 36 q^{44} - 56 q^{46} - 4 q^{49} + 20 q^{51} + 24 q^{54} - 28 q^{56} - 24 q^{59} + 24 q^{61} - 24 q^{64} - 20 q^{66} + 60 q^{69} + 26 q^{71} + 36 q^{76} - 72 q^{79} + 42 q^{81} - 60 q^{84} - 16 q^{86} + 32 q^{89} - 8 q^{91} - 40 q^{94} - 36 q^{99}+O(q^{100}) \) 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9 + 14 * q^11 - 8 * q^14 + 16 * q^16 - 28 * q^19 - 18 * q^21 - 24 * q^24 - 40 * q^26 - 4 * q^29 + 16 * q^31 - 24 * q^34 - 72 * q^36 - 24 * q^39 - 18 * q^41 - 36 * q^44 - 56 * q^46 - 4 * q^49 + 20 * q^51 + 24 * q^54 - 28 * q^56 - 24 * q^59 + 24 * q^61 - 24 * q^64 - 20 * q^66 + 60 * q^69 + 26 * q^71 + 36 * q^76 - 72 * q^79 + 42 * q^81 - 60 * q^84 - 16 * q^86 + 32 * q^89 - 8 * q^91 - 40 * q^94 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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