LMFDB - Embedded newform 1850.2.b.n.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1850.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$6$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.2
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1850.149
Dual form			1850.2.b.n.149.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.53919i q^{3} -1.00000 q^{4} -1.53919 q^{6} -2.87936i q^{7} +1.00000i q^{8} +0.630898 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.53919i q^{3} -1.00000 q^{4} -1.53919 q^{6} -2.87936i q^{7} +1.00000i q^{8} +0.630898 q^{9} -1.09171 q^{11} +1.53919i q^{12} -4.53919i q^{13} -2.87936 q^{14} +1.00000 q^{16} +2.80098i q^{17} -0.630898i q^{18} +5.04945 q^{19} -4.43188 q^{21} +1.09171i q^{22} -7.41855i q^{23} +1.53919 q^{24} -4.53919 q^{26} -5.58864i q^{27} +2.87936i q^{28} -6.68035 q^{29} +3.51026 q^{31} -1.00000i q^{32} +1.68035i q^{33} +2.80098 q^{34} -0.630898 q^{36} +1.00000i q^{37} -5.04945i q^{38} -6.98667 q^{39} -8.07838 q^{41} +4.43188i q^{42} -10.2329i q^{43} +1.09171 q^{44} -7.41855 q^{46} +8.68035i q^{47} -1.53919i q^{48} -1.29072 q^{49} +4.31124 q^{51} +4.53919i q^{52} +10.0989i q^{53} -5.58864 q^{54} +2.87936 q^{56} -7.77205i q^{57} +6.68035i q^{58} -10.2329 q^{59} +6.29791 q^{61} -3.51026i q^{62} -1.81658i q^{63} -1.00000 q^{64} +1.68035 q^{66} +13.2979i q^{67} -2.80098i q^{68} -11.4186 q^{69} +6.29791 q^{71} +0.630898i q^{72} -12.7093i q^{73} +1.00000 q^{74} -5.04945 q^{76} +3.14342i q^{77} +6.98667i q^{78} -2.58145 q^{79} -6.70928 q^{81} +8.07838i q^{82} -8.48360i q^{83} +4.43188 q^{84} -10.2329 q^{86} +10.2823i q^{87} -1.09171i q^{88} +6.51026 q^{89} -13.0700 q^{91} +7.41855i q^{92} -5.40295i q^{93} +8.68035 q^{94} -1.53919 q^{96} +3.07838i q^{97} +1.29072i q^{98} -0.688756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 4 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{11} + 8 q^{14} + 6 q^{16} - 6 q^{19} + 6 q^{24} - 24 q^{26} + 4 q^{29} - 12 q^{31} - 2 q^{34} + 4 q^{36} - 40 q^{39} - 42 q^{41} + 2 q^{44} - 16 q^{46} - 22 q^{49} - 26 q^{51} + 6 q^{54} - 8 q^{56} - 16 q^{59} - 16 q^{61} - 6 q^{64} - 34 q^{66} - 40 q^{69} - 16 q^{71} + 6 q^{74} + 6 q^{76} - 44 q^{79} - 26 q^{81} - 16 q^{86} + 6 q^{89} + 24 q^{91} + 8 q^{94} - 6 q^{96} - 56 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^11 + 8 * q^14 + 6 * q^16 - 6 * q^19 + 6 * q^24 - 24 * q^26 + 4 * q^29 - 12 * q^31 - 2 * q^34 + 4 * q^36 - 40 * q^39 - 42 * q^41 + 2 * q^44 - 16 * q^46 - 22 * q^49 - 26 * q^51 + 6 * q^54 - 8 * q^56 - 16 * q^59 - 16 * q^61 - 6 * q^64 - 34 * q^66 - 40 * q^69 - 16 * q^71 + 6 * q^74 + 6 * q^76 - 44 * q^79 - 26 * q^81 - 16 * q^86 + 6 * q^89 + 24 * q^91 + 8 * q^94 - 6 * q^96 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 1.53919i	− 0.888651i	−0.895865	−	0.444326i	$-0.853443\pi$
$3$	− 1.53919i	− 0.888651i	0.895865	−	0.444326i	$-0.146557\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.53919	−0.628371
$7$	− 2.87936i	− 1.08830i	−0.838989	−	0.544148i	$-0.816853\pi$
$7$	− 2.87936i	− 1.08830i	0.838989	−	0.544148i	$-0.183147\pi$
$8$	1.00000i	0.353553i
$9$	0.630898	0.210299
$10$	0	0
$11$	−1.09171	−0.329163	−0.164581	−	0.986364i	$-0.552627\pi$
$11$	−1.09171	−0.329163	−0.164581	+	0.986364i	$0.552627\pi$
$12$	1.53919i	0.444326i
$13$	− 4.53919i	− 1.25894i	−0.777023	−	0.629472i	$-0.783271\pi$
$13$	− 4.53919i	− 1.25894i	0.777023	−	0.629472i	$-0.216729\pi$
$14$	−2.87936	−0.769542
$15$	0	0
$16$	1.00000	0.250000
$17$	2.80098i	0.679338i	0.940545	+	0.339669i	$0.110315\pi$
$17$	2.80098i	0.679338i	−0.940545	+	0.339669i	$0.889685\pi$
$18$	− 0.630898i	− 0.148704i
$19$	5.04945	1.15842	0.579211	−	0.815177i	$-0.303361\pi$
$19$	5.04945	1.15842	0.579211	+	0.815177i	$0.303361\pi$
$20$	0	0
$21$	−4.43188	−0.967116
$22$	1.09171i	0.232753i
$23$	− 7.41855i	− 1.54687i	−0.633873	−	0.773437i	$-0.718536\pi$
$23$	− 7.41855i	− 1.54687i	0.633873	−	0.773437i	$-0.281464\pi$
$24$	1.53919	0.314186
$25$	0	0
$26$	−4.53919	−0.890208
$27$	− 5.58864i	− 1.07553i
$28$	2.87936i	0.544148i
$29$	−6.68035	−1.24051	−0.620255	−	0.784401i	$-0.712971\pi$
$29$	−6.68035	−1.24051	−0.620255	+	0.784401i	$0.712971\pi$
$30$	0	0
$31$	3.51026	0.630461	0.315231	−	0.949015i	$-0.397918\pi$
$31$	3.51026	0.630461	0.315231	+	0.949015i	$0.397918\pi$
$32$	− 1.00000i	− 0.176777i
$33$	1.68035i	0.292511i
$34$	2.80098	0.480365
$35$	0	0
$36$	−0.630898	−0.105150
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	− 5.04945i	− 0.819129i
$39$	−6.98667	−1.11876
$40$	0	0
$41$	−8.07838	−1.26163	−0.630815	−	0.775933i	$-0.717279\pi$
$41$	−8.07838	−1.26163	−0.630815	+	0.775933i	$0.717279\pi$
$42$	4.43188i	0.683854i
$43$	− 10.2329i	− 1.56050i	−0.625469	−	0.780249i	$-0.715092\pi$
$43$	− 10.2329i	− 1.56050i	0.625469	−	0.780249i	$-0.284908\pi$
$44$	1.09171	0.164581
$45$	0	0
$46$	−7.41855	−1.09381
$47$	8.68035i	1.26616i	0.774087	+	0.633079i	$0.218209\pi$
$47$	8.68035i	1.26616i	−0.774087	+	0.633079i	$0.781791\pi$
$48$	− 1.53919i	− 0.222163i
$49$	−1.29072	−0.184389
$50$	0	0
$51$	4.31124	0.603695
$52$	4.53919i	0.629472i
$53$	10.0989i	1.38719i	0.720365	+	0.693595i	$0.243974\pi$
$53$	10.0989i	1.38719i	−0.720365	+	0.693595i	$0.756026\pi$
$54$	−5.58864	−0.760517
$55$	0	0
$56$	2.87936	0.384771
$57$	− 7.77205i	− 1.02943i
$58$	6.68035i	0.877172i
$59$	−10.2329	−1.33221	−0.666103	−	0.745860i	$-0.732039\pi$
$59$	−10.2329	−1.33221	−0.666103	+	0.745860i	$0.732039\pi$
$60$	0	0
$61$	6.29791	0.806365	0.403183	−	0.915120i	$-0.367904\pi$
$61$	6.29791	0.806365	0.403183	+	0.915120i	$0.367904\pi$
$62$	− 3.51026i	− 0.445803i
$63$	− 1.81658i	− 0.228868i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	1.68035	0.206836
$67$	13.2979i	1.62460i	0.583241	+	0.812299i	$0.301784\pi$
$67$	13.2979i	1.62460i	−0.583241	+	0.812299i	$0.698216\pi$
$68$	− 2.80098i	− 0.339669i
$69$	−11.4186	−1.37463
$70$	0	0
$71$	6.29791	0.747425	0.373712	−	0.927545i	$-0.378085\pi$
$71$	6.29791	0.747425	0.373712	+	0.927545i	$0.378085\pi$
$72$	0.630898i	0.0743520i
$73$	− 12.7093i	− 1.48751i	−0.668453	−	0.743754i	$-0.733043\pi$
$73$	− 12.7093i	− 1.48751i	0.668453	−	0.743754i	$-0.266957\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−5.04945	−0.579211
$77$	3.14342i	0.358226i
$78$	6.98667i	0.791084i
$79$	−2.58145	−0.290436	−0.145218	−	0.989400i	$-0.546388\pi$
$79$	−2.58145	−0.290436	−0.145218	+	0.989400i	$0.546388\pi$
$80$	0	0
$81$	−6.70928	−0.745475
$82$	8.07838i	0.892108i
$83$	− 8.48360i	− 0.931196i	−0.884996	−	0.465598i	$-0.845839\pi$
$83$	− 8.48360i	− 0.931196i	0.884996	−	0.465598i	$-0.154161\pi$
$84$	4.43188	0.483558
$85$	0	0
$86$	−10.2329	−1.10344
$87$	10.2823i	1.10238i
$88$	− 1.09171i	− 0.116377i
$89$	6.51026	0.690086	0.345043	−	0.938587i	$-0.387864\pi$
$89$	6.51026	0.690086	0.345043	+	0.938587i	$0.387864\pi$
$90$	0	0
$91$	−13.0700	−1.37010
$92$	7.41855i	0.773437i
$93$	− 5.40295i	− 0.560260i
$94$	8.68035	0.895309
$95$	0	0
$96$	−1.53919	−0.157093
$97$	3.07838i	0.312562i	0.987713	+	0.156281i	$0.0499505\pi$
$97$	3.07838i	0.312562i	−0.987713	+	0.156281i	$0.950049\pi$
$98$	1.29072i	0.130383i
$99$	−0.688756	−0.0692226
$100$	0	0
$101$	−15.9155	−1.58365	−0.791825	−	0.610748i	$-0.790869\pi$
$101$	−15.9155	−1.58365	−0.791825	+	0.610748i	$0.790869\pi$
$102$	− 4.31124i	− 0.426877i
$103$	10.5886i	1.04333i	0.853151	+	0.521665i	$0.174689\pi$
$103$	10.5886i	1.04333i	−0.853151	+	0.521665i	$0.825311\pi$
$104$	4.53919	0.445104
$105$	0	0
$106$	10.0989	0.980892
$107$	− 4.03612i	− 0.390186i	−0.980785	−	0.195093i	$-0.937499\pi$
$107$	− 4.03612i	− 0.390186i	0.980785	−	0.195093i	$-0.0625009\pi$
$108$	5.58864i	0.537767i
$109$	4.49693	0.430728	0.215364	−	0.976534i	$-0.430906\pi$
$109$	4.49693	0.430728	0.215364	+	0.976534i	$0.430906\pi$
$110$	0	0
$111$	1.53919	0.146093
$112$	− 2.87936i	− 0.272074i
$113$	− 3.58864i	− 0.337591i	−0.985651	−	0.168795i	$-0.946012\pi$
$113$	− 3.58864i	− 0.337591i	0.985651	−	0.168795i	$-0.0539877\pi$
$114$	−7.77205	−0.727920
$115$	0	0
$116$	6.68035	0.620255
$117$	− 2.86376i	− 0.264755i
$118$	10.2329i	0.942012i
$119$	8.06505	0.739322
$120$	0	0
$121$	−9.80817	−0.891652
$122$	− 6.29791i	− 0.570186i
$123$	12.4341i	1.12115i
$124$	−3.51026	−0.315231
$125$	0	0
$126$	−1.81658	−0.161834
$127$	8.14116i	0.722411i	0.932486	+	0.361205i	$0.117635\pi$
$127$	8.14116i	0.722411i	−0.932486	+	0.361205i	$0.882365\pi$
$128$	1.00000i	0.0883883i
$129$	−15.7503	−1.38674
$130$	0	0
$131$	−1.46800	−0.128260	−0.0641298	−	0.997942i	$-0.520427\pi$
$131$	−1.46800	−0.128260	−0.0641298	+	0.997942i	$0.520427\pi$
$132$	− 1.68035i	− 0.146255i
$133$	− 14.5392i	− 1.26071i
$134$	13.2979	1.14876
$135$	0	0
$136$	−2.80098	−0.240182
$137$	− 6.17727i	− 0.527760i	−0.964555	−	0.263880i	$-0.914998\pi$
$137$	− 6.17727i	− 0.527760i	0.964555	−	0.263880i	$-0.0850023\pi$
$138$	11.4186i	0.972012i
$139$	−13.0338	−1.10552	−0.552758	−	0.833342i	$-0.686425\pi$
$139$	−13.0338	−1.10552	−0.552758	+	0.833342i	$0.686425\pi$
$140$	0	0
$141$	13.3607	1.12517
$142$	− 6.29791i	− 0.528509i
$143$	4.95547i	0.414397i
$144$	0.630898	0.0525748
$145$	0	0
$146$	−12.7093	−1.05183
$147$	1.98667i	0.163858i
$148$	− 1.00000i	− 0.0821995i
$149$	4.40522	0.360890	0.180445	−	0.983585i	$-0.442246\pi$
$149$	4.40522	0.360890	0.180445	+	0.983585i	$0.442246\pi$
$150$	0	0
$151$	2.92162	0.237758	0.118879	−	0.992909i	$-0.462070\pi$
$151$	2.92162	0.237758	0.118879	+	0.992909i	$0.462070\pi$
$152$	5.04945i	0.409564i
$153$	1.76713i	0.142864i
$154$	3.14342	0.253304
$155$	0	0
$156$	6.98667	0.559381
$157$	22.1906i	1.77100i	0.464636	+	0.885502i	$0.346185\pi$
$157$	22.1906i	1.77100i	−0.464636	+	0.885502i	$0.653815\pi$
$158$	2.58145i	0.205369i
$159$	15.5441	1.23273
$160$	0	0
$161$	−21.3607	−1.68346
$162$	6.70928i	0.527130i
$163$	14.6248i	1.14550i	0.819730	+	0.572750i	$0.194123\pi$
$163$	14.6248i	1.14550i	−0.819730	+	0.572750i	$0.805877\pi$
$164$	8.07838	0.630815
$165$	0	0
$166$	−8.48360	−0.658455
$167$	− 6.34736i	− 0.491174i	−0.969375	−	0.245587i	$-0.921019\pi$
$167$	− 6.34736i	− 0.491174i	0.969375	−	0.245587i	$-0.0789806\pi$
$168$	− 4.43188i	− 0.341927i
$169$	−7.60424	−0.584941
$170$	0	0
$171$	3.18568	0.243615
$172$	10.2329i	0.780249i
$173$	1.23513i	0.0939054i	0.998897	+	0.0469527i	$0.0149510\pi$
$173$	1.23513i	0.0939054i	−0.998897	+	0.0469527i	$0.985049\pi$
$174$	10.2823	0.779500
$175$	0	0
$176$	−1.09171	−0.0822906
$177$	15.7503i	1.18387i
$178$	− 6.51026i	− 0.487965i
$179$	−1.76487	−0.131912	−0.0659562	−	0.997823i	$-0.521010\pi$
$179$	−1.76487	−0.131912	−0.0659562	+	0.997823i	$0.521010\pi$
$180$	0	0
$181$	6.49693	0.482913	0.241456	−	0.970412i	$-0.422375\pi$
$181$	6.49693	0.482913	0.241456	+	0.970412i	$0.422375\pi$
$182$	13.0700i	0.968810i
$183$	− 9.69368i	− 0.716577i
$184$	7.41855	0.546903
$185$	0	0
$186$	−5.40295	−0.396164
$187$	− 3.05786i	− 0.223613i
$188$	− 8.68035i	− 0.633079i
$189$	−16.0917	−1.17050
$190$	0	0
$191$	21.2039	1.53426	0.767131	−	0.641490i	$-0.221683\pi$
$191$	21.2039	1.53426	0.767131	+	0.641490i	$0.221683\pi$
$192$	1.53919i	0.111081i
$193$	− 8.14342i	− 0.586177i	−0.956085	−	0.293088i	$-0.905317\pi$
$193$	− 8.14342i	− 0.586177i	0.956085	−	0.293088i	$-0.0946830\pi$
$194$	3.07838	0.221015
$195$	0	0
$196$	1.29072	0.0921946
$197$	− 24.8443i	− 1.77008i	−0.465513	−	0.885041i	$-0.654130\pi$
$197$	− 24.8443i	− 1.77008i	0.465513	−	0.885041i	$-0.345870\pi$
$198$	0.688756i	0.0489478i
$199$	8.47027	0.600441	0.300221	−	0.953870i	$-0.402940\pi$
$199$	8.47027	0.600441	0.300221	+	0.953870i	$0.402940\pi$
$200$	0	0
$201$	20.4680	1.44370
$202$	15.9155i	1.11981i
$203$	19.2351i	1.35004i
$204$	−4.31124	−0.301847
$205$	0	0
$206$	10.5886	0.737745
$207$	− 4.68035i	− 0.325307i
$208$	− 4.53919i	− 0.314736i
$209$	−5.51253	−0.381309
$210$	0	0
$211$	21.7370	1.49644	0.748218	−	0.663453i	$-0.230910\pi$
$211$	21.7370	1.49644	0.748218	+	0.663453i	$0.230910\pi$
$212$	− 10.0989i	− 0.693595i
$213$	− 9.69368i	− 0.664200i
$214$	−4.03612	−0.275903
$215$	0	0
$216$	5.58864	0.380259
$217$	− 10.1073i	− 0.686129i
$218$	− 4.49693i	− 0.304570i
$219$	−19.5620	−1.32188
$220$	0	0
$221$	12.7142	0.855249
$222$	− 1.53919i	− 0.103304i
$223$	− 16.6537i	− 1.11521i	−0.830105	−	0.557607i	$-0.811720\pi$
$223$	− 16.6537i	− 1.11521i	0.830105	−	0.557607i	$-0.188280\pi$
$224$	−2.87936	−0.192385
$225$	0	0
$226$	−3.58864	−0.238713
$227$	− 11.2123i	− 0.744190i	−0.928195	−	0.372095i	$-0.878640\pi$
$227$	− 11.2123i	− 0.744190i	0.928195	−	0.372095i	$-0.121360\pi$
$228$	7.77205i	0.514717i
$229$	7.62863	0.504114	0.252057	−	0.967712i	$-0.418893\pi$
$229$	7.62863	0.504114	0.252057	+	0.967712i	$0.418893\pi$
$230$	0	0
$231$	4.83832	0.318338
$232$	− 6.68035i	− 0.438586i
$233$	0.0494483i	0.00323947i	0.999999	+	0.00161973i	$0.000515578\pi$
$233$	0.0494483i	0.00323947i	−0.999999	+	0.00161973i	$0.999484\pi$
$234$	−2.86376	−0.187210
$235$	0	0
$236$	10.2329	0.666103
$237$	3.97334i	0.258096i
$238$	− 8.06505i	− 0.522779i
$239$	14.7070	0.951317	0.475659	−	0.879630i	$-0.342210\pi$
$239$	14.7070	0.951317	0.475659	+	0.879630i	$0.342210\pi$
$240$	0	0
$241$	−14.8999	−0.959786	−0.479893	−	0.877327i	$-0.659324\pi$
$241$	−14.8999	−0.959786	−0.479893	+	0.877327i	$0.659324\pi$
$242$	9.80817i	0.630493i
$243$	− 6.43907i	− 0.413067i
$244$	−6.29791	−0.403183
$245$	0	0
$246$	12.4341	0.792772
$247$	− 22.9204i	− 1.45839i
$248$	3.51026i	0.222902i
$249$	−13.0579	−0.827508
$250$	0	0
$251$	6.23513	0.393558	0.196779	−	0.980448i	$-0.436952\pi$
$251$	6.23513	0.393558	0.196779	+	0.980448i	$0.436952\pi$
$252$	1.81658i	0.114434i
$253$	8.09890i	0.509173i
$254$	8.14116	0.510822
$255$	0	0
$256$	1.00000	0.0625000
$257$	16.1568i	1.00783i	0.863753	+	0.503915i	$0.168108\pi$
$257$	16.1568i	1.00783i	−0.863753	+	0.503915i	$0.831892\pi$
$258$	15.7503i	0.980572i
$259$	2.87936	0.178915
$260$	0	0
$261$	−4.21461	−0.260878
$262$	1.46800i	0.0906933i
$263$	18.6537i	1.15024i	0.818071	+	0.575118i	$0.195044\pi$
$263$	18.6537i	1.15024i	−0.818071	+	0.575118i	$0.804956\pi$
$264$	−1.68035	−0.103418
$265$	0	0
$266$	−14.5392	−0.891455
$267$	− 10.0205i	− 0.613246i
$268$	− 13.2979i	− 0.812299i
$269$	−21.8310	−1.33106	−0.665529	−	0.746372i	$-0.731794\pi$
$269$	−21.8310	−1.33106	−0.665529	+	0.746372i	$0.731794\pi$
$270$	0	0
$271$	24.9783	1.51732	0.758661	−	0.651486i	$-0.225854\pi$
$271$	24.9783	1.51732	0.758661	+	0.651486i	$0.225854\pi$
$272$	2.80098i	0.169835i
$273$	20.1171i	1.21755i
$274$	−6.17727	−0.373183
$275$	0	0
$276$	11.4186	0.687316
$277$	− 0.822726i	− 0.0494328i	−0.999695	−	0.0247164i	$-0.992132\pi$
$277$	− 0.822726i	− 0.0494328i	0.999695	−	0.0247164i	$-0.00786827\pi$
$278$	13.0338i	0.781718i
$279$	2.21461	0.132585
$280$	0	0
$281$	−1.65142	−0.0985153	−0.0492576	−	0.998786i	$-0.515686\pi$
$281$	−1.65142	−0.0985153	−0.0492576	+	0.998786i	$0.515686\pi$
$282$	− 13.3607i	− 0.795618i
$283$	− 15.1340i	− 0.899621i	−0.893124	−	0.449811i	$-0.851492\pi$
$283$	− 15.1340i	− 0.899621i	0.893124	−	0.449811i	$-0.148508\pi$
$284$	−6.29791	−0.373712
$285$	0	0
$286$	4.95547	0.293023
$287$	23.2606i	1.37303i
$288$	− 0.630898i	− 0.0371760i
$289$	9.15449	0.538499
$290$	0	0
$291$	4.73820	0.277758
$292$	12.7093i	0.743754i
$293$	25.4524i	1.48695i	0.668766	+	0.743473i	$0.266823\pi$
$293$	25.4524i	1.48695i	−0.668766	+	0.743473i	$0.733177\pi$
$294$	1.98667	0.115865
$295$	0	0
$296$	−1.00000	−0.0581238
$297$	6.10116i	0.354025i
$298$	− 4.40522i	− 0.255188i
$299$	−33.6742	−1.94743
$300$	0	0
$301$	−29.4641	−1.69828
$302$	− 2.92162i	− 0.168120i
$303$	24.4969i	1.40731i
$304$	5.04945	0.289606
$305$	0	0
$306$	1.76713	0.101020
$307$	− 27.8176i	− 1.58764i	−0.608155	−	0.793818i	$-0.708090\pi$
$307$	− 27.8176i	− 1.58764i	0.608155	−	0.793818i	$-0.291910\pi$
$308$	− 3.14342i	− 0.179113i
$309$	16.2979	0.927156
$310$	0	0
$311$	0.0650468	0.00368846	0.00184423	−	0.999998i	$-0.499413\pi$
$311$	0.0650468	0.00368846	0.00184423	+	0.999998i	$0.499413\pi$
$312$	− 6.98667i	− 0.395542i
$313$	− 22.5464i	− 1.27440i	−0.770700	−	0.637198i	$-0.780093\pi$
$313$	− 22.5464i	− 1.27440i	0.770700	−	0.637198i	$-0.219907\pi$
$314$	22.1906	1.25229
$315$	0	0
$316$	2.58145	0.145218
$317$	− 24.4775i	− 1.37479i	−0.726283	−	0.687395i	$-0.758754\pi$
$317$	− 24.4775i	− 1.37479i	0.726283	−	0.687395i	$-0.241246\pi$
$318$	− 15.5441i	− 0.871670i
$319$	7.29299	0.408329
$320$	0	0
$321$	−6.21235	−0.346739
$322$	21.3607i	1.19038i
$323$	14.1434i	0.786961i
$324$	6.70928	0.372738
$325$	0	0
$326$	14.6248	0.809990
$327$	− 6.92162i	− 0.382767i
$328$	− 8.07838i	− 0.446054i
$329$	24.9939	1.37796
$330$	0	0
$331$	−1.91321	−0.105160	−0.0525798	−	0.998617i	$-0.516744\pi$
$331$	−1.91321	−0.105160	−0.0525798	+	0.998617i	$0.516744\pi$
$332$	8.48360i	0.465598i
$333$	0.630898i	0.0345730i
$334$	−6.34736	−0.347312
$335$	0	0
$336$	−4.43188	−0.241779
$337$	− 12.6286i	− 0.687925i	−0.938983	−	0.343963i	$-0.888231\pi$
$337$	− 12.6286i	− 0.687925i	0.938983	−	0.343963i	$-0.111769\pi$
$338$	7.60424i	0.413616i
$339$	−5.52359	−0.300000
$340$	0	0
$341$	−3.83218	−0.207524
$342$	− 3.18568i	− 0.172262i
$343$	− 16.4391i	− 0.887626i
$344$	10.2329	0.551719
$345$	0	0
$346$	1.23513	0.0664012
$347$	− 8.33403i	− 0.447394i	−0.974659	−	0.223697i	$-0.928187\pi$
$347$	− 8.33403i	− 0.447394i	0.974659	−	0.223697i	$-0.0718126\pi$
$348$	− 10.2823i	− 0.551190i
$349$	−2.11837	−0.113394	−0.0566969	−	0.998391i	$-0.518057\pi$
$349$	−2.11837	−0.113394	−0.0566969	+	0.998391i	$0.518057\pi$
$350$	0	0
$351$	−25.3679	−1.35404
$352$	1.09171i	0.0581883i
$353$	− 28.4534i	− 1.51442i	−0.653169	−	0.757212i	$-0.726561\pi$
$353$	− 28.4534i	− 1.51442i	0.653169	−	0.757212i	$-0.273439\pi$
$354$	15.7503	0.837120
$355$	0	0
$356$	−6.51026	−0.345043
$357$	− 12.4136i	− 0.656999i
$358$	1.76487i	0.0932761i
$359$	−2.65368	−0.140056	−0.0700280	−	0.997545i	$-0.522309\pi$
$359$	−2.65368	−0.140056	−0.0700280	+	0.997545i	$0.522309\pi$
$360$	0	0
$361$	6.49693	0.341944
$362$	− 6.49693i	− 0.341471i
$363$	15.0966i	0.792368i
$364$	13.0700	0.685052
$365$	0	0
$366$	−9.69368	−0.506697
$367$	− 31.7575i	− 1.65773i	−0.559450	−	0.828864i	$-0.688988\pi$
$367$	− 31.7575i	− 1.65773i	0.559450	−	0.828864i	$-0.311012\pi$
$368$	− 7.41855i	− 0.386719i
$369$	−5.09663	−0.265320
$370$	0	0
$371$	29.0784	1.50967
$372$	5.40295i	0.280130i
$373$	− 25.1122i	− 1.30026i	−0.759822	−	0.650131i	$-0.774714\pi$
$373$	− 25.1122i	− 1.30026i	0.759822	−	0.650131i	$-0.225286\pi$
$374$	−3.05786	−0.158118
$375$	0	0
$376$	−8.68035	−0.447655
$377$	30.3234i	1.56173i
$378$	16.0917i	0.827668i
$379$	−22.5330	−1.15744	−0.578722	−	0.815525i	$-0.696449\pi$
$379$	−22.5330	−1.15744	−0.578722	+	0.815525i	$0.696449\pi$
$380$	0	0
$381$	12.5308	0.641971
$382$	− 21.2039i	− 1.08489i
$383$	12.5886i	0.643249i	0.946867	+	0.321625i	$0.104229\pi$
$383$	12.5886i	0.643249i	−0.946867	+	0.321625i	$0.895771\pi$
$384$	1.53919	0.0785464
$385$	0	0
$386$	−8.14342	−0.414489
$387$	− 6.45589i	− 0.328171i
$388$	− 3.07838i	− 0.156281i
$389$	0.879362	0.0445854	0.0222927	−	0.999751i	$-0.492903\pi$
$389$	0.879362	0.0445854	0.0222927	+	0.999751i	$0.492903\pi$
$390$	0	0
$391$	20.7792	1.05085
$392$	− 1.29072i	− 0.0651914i
$393$	2.25953i	0.113978i
$394$	−24.8443	−1.25164
$395$	0	0
$396$	0.688756	0.0346113
$397$	− 29.6814i	− 1.48967i	−0.667251	−	0.744833i	$-0.732529\pi$
$397$	− 29.6814i	− 1.48967i	0.667251	−	0.744833i	$-0.267471\pi$
$398$	− 8.47027i	− 0.424576i
$399$	−22.3786	−1.12033
$400$	0	0
$401$	−13.9867	−0.698461	−0.349230	−	0.937037i	$-0.613557\pi$
$401$	−13.9867	−0.698461	−0.349230	+	0.937037i	$0.613557\pi$
$402$	− 20.4680i	− 1.02085i
$403$	− 15.9337i	− 0.793716i
$404$	15.9155	0.791825
$405$	0	0
$406$	19.2351	0.954624
$407$	− 1.09171i	− 0.0541140i
$408$	4.31124i	0.213438i
$409$	21.9060	1.08318	0.541592	−	0.840642i	$-0.317822\pi$
$409$	21.9060	1.08318	0.541592	+	0.840642i	$0.317822\pi$
$410$	0	0
$411$	−9.50799	−0.468995
$412$	− 10.5886i	− 0.521665i
$413$	29.4641i	1.44983i
$414$	−4.68035	−0.230026
$415$	0	0
$416$	−4.53919	−0.222552
$417$	20.0616i	0.982419i
$418$	5.51253i	0.269627i
$419$	34.8648	1.70326	0.851629	−	0.524146i	$-0.175615\pi$
$419$	34.8648	1.70326	0.851629	+	0.524146i	$0.175615\pi$
$420$	0	0
$421$	−4.76487	−0.232225	−0.116113	−	0.993236i	$-0.537043\pi$
$421$	−4.76487	−0.232225	−0.116113	+	0.993236i	$0.537043\pi$
$422$	− 21.7370i	− 1.05814i
$423$	5.47641i	0.266272i
$424$	−10.0989	−0.490446
$425$	0	0
$426$	−9.69368	−0.469660
$427$	− 18.1340i	− 0.877564i
$428$	4.03612i	0.195093i
$429$	7.62741	0.368255
$430$	0	0
$431$	2.66597	0.128415	0.0642076	−	0.997937i	$-0.479548\pi$
$431$	2.66597	0.128415	0.0642076	+	0.997937i	$0.479548\pi$
$432$	− 5.58864i	− 0.268883i
$433$	− 32.3074i	− 1.55259i	−0.630368	−	0.776297i	$-0.717096\pi$
$433$	− 32.3074i	− 1.55259i	0.630368	−	0.776297i	$-0.282904\pi$
$434$	−10.1073	−0.485166
$435$	0	0
$436$	−4.49693	−0.215364
$437$	− 37.4596i	− 1.79194i
$438$	19.5620i	0.934707i
$439$	22.1568	1.05748	0.528742	−	0.848783i	$-0.322664\pi$
$439$	22.1568	1.05748	0.528742	+	0.848783i	$0.322664\pi$
$440$	0	0
$441$	−0.814315	−0.0387769
$442$	− 12.7142i	− 0.604753i
$443$	− 39.1061i	− 1.85799i	−0.370097	−	0.928993i	$-0.620676\pi$
$443$	− 39.1061i	− 1.85799i	0.370097	−	0.928993i	$-0.379324\pi$
$444$	−1.53919	−0.0730467
$445$	0	0
$446$	−16.6537	−0.788575
$447$	− 6.78047i	− 0.320705i
$448$	2.87936i	0.136037i
$449$	−30.8915	−1.45786	−0.728929	−	0.684589i	$-0.759982\pi$
$449$	−30.8915	−1.45786	−0.728929	+	0.684589i	$0.759982\pi$
$450$	0	0
$451$	8.81924	0.415282
$452$	3.58864i	0.168795i
$453$	− 4.49693i	− 0.211284i
$454$	−11.2123	−0.526222
$455$	0	0
$456$	7.77205	0.363960
$457$	− 0.438025i	− 0.0204899i	−0.999948	−	0.0102450i	$-0.996739\pi$
$457$	− 0.438025i	− 0.0204899i	0.999948	−	0.0102450i	$-0.00326113\pi$
$458$	− 7.62863i	− 0.356462i
$459$	15.6537	0.730651
$460$	0	0
$461$	0.523590	0.0243860	0.0121930	−	0.999926i	$-0.496119\pi$
$461$	0.523590	0.0243860	0.0121930	+	0.999926i	$0.496119\pi$
$462$	− 4.83832i	− 0.225099i
$463$	29.1845i	1.35632i	0.734916	+	0.678158i	$0.237222\pi$
$463$	29.1845i	1.35632i	−0.734916	+	0.678158i	$0.762778\pi$
$464$	−6.68035	−0.310127
$465$	0	0
$466$	0.0494483	0.00229065
$467$	9.49079i	0.439181i	0.975592	+	0.219591i	$0.0704722\pi$
$467$	9.49079i	0.439181i	−0.975592	+	0.219591i	$0.929528\pi$
$468$	2.86376i	0.132378i
$469$	38.2895	1.76804
$470$	0	0
$471$	34.1555	1.57380
$472$	− 10.2329i	− 0.471006i
$473$	11.1713i	0.513657i
$474$	3.97334	0.182501
$475$	0	0
$476$	−8.06505	−0.369661
$477$	6.37137i	0.291725i
$478$	− 14.7070i	− 0.672683i
$479$	6.12291	0.279763	0.139881	−	0.990168i	$-0.455328\pi$
$479$	6.12291	0.279763	0.139881	+	0.990168i	$0.455328\pi$
$480$	0	0
$481$	4.53919	0.206969
$482$	14.8999i	0.678671i
$483$	32.8781i	1.49601i
$484$	9.80817	0.445826
$485$	0	0
$486$	−6.43907	−0.292082
$487$	10.3018i	0.466819i	0.972379	+	0.233409i	$0.0749882\pi$
$487$	10.3018i	0.466819i	−0.972379	+	0.233409i	$0.925012\pi$
$488$	6.29791i	0.285093i
$489$	22.5103	1.01795
$490$	0	0
$491$	−10.5380	−0.475572	−0.237786	−	0.971318i	$-0.576422\pi$
$491$	−10.5380	−0.475572	−0.237786	+	0.971318i	$0.576422\pi$
$492$	− 12.4341i	− 0.560575i
$493$	− 18.7115i	− 0.842726i
$494$	−22.9204	−1.03124
$495$	0	0
$496$	3.51026	0.157615
$497$	− 18.1340i	− 0.813420i
$498$	13.0579i	0.585137i
$499$	31.2123	1.39726	0.698628	−	0.715485i	$-0.253794\pi$
$499$	31.2123	1.39726	0.698628	+	0.715485i	$0.253794\pi$
$500$	0	0
$501$	−9.76979	−0.436482
$502$	− 6.23513i	− 0.278288i
$503$	36.1978i	1.61398i	0.590565	+	0.806990i	$0.298905\pi$
$503$	36.1978i	1.61398i	−0.590565	+	0.806990i	$0.701095\pi$
$504$	1.81658	0.0809170
$505$	0	0
$506$	8.09890	0.360040
$507$	11.7044i	0.519809i
$508$	− 8.14116i	− 0.361205i
$509$	33.6092	1.48970	0.744850	−	0.667232i	$-0.232521\pi$
$509$	33.6092	1.48970	0.744850	+	0.667232i	$0.232521\pi$
$510$	0	0
$511$	−36.5946	−1.61885
$512$	− 1.00000i	− 0.0441942i
$513$	− 28.2195i	− 1.24592i
$514$	16.1568	0.712644
$515$	0	0
$516$	15.7503	0.693369
$517$	− 9.47641i	− 0.416772i
$518$	− 2.87936i	− 0.126512i
$519$	1.90110	0.0834492
$520$	0	0
$521$	5.42082	0.237490	0.118745	−	0.992925i	$-0.462113\pi$
$521$	5.42082	0.237490	0.118745	+	0.992925i	$0.462113\pi$
$522$	4.21461i	0.184469i
$523$	31.3545i	1.37104i	0.728054	+	0.685519i	$0.240425\pi$
$523$	31.3545i	1.37104i	−0.728054	+	0.685519i	$0.759575\pi$
$524$	1.46800	0.0641298
$525$	0	0
$526$	18.6537	0.813339
$527$	9.83218i	0.428297i
$528$	1.68035i	0.0731277i
$529$	−32.0349	−1.39282
$530$	0	0
$531$	−6.45589	−0.280162
$532$	14.5392i	0.630354i
$533$	36.6693i	1.58832i
$534$	−10.0205	−0.433630
$535$	0	0
$536$	−13.2979	−0.574382
$537$	2.71646i	0.117224i
$538$	21.8310i	0.941199i
$539$	1.40910	0.0606940
$540$	0	0
$541$	−9.98440	−0.429263	−0.214631	−	0.976695i	$-0.568855\pi$
$541$	−9.98440	−0.429263	−0.214631	+	0.976695i	$0.568855\pi$
$542$	− 24.9783i	− 1.07291i
$543$	− 10.0000i	− 0.429141i
$544$	2.80098	0.120091
$545$	0	0
$546$	20.1171	0.860934
$547$	32.9649i	1.40948i	0.709466	+	0.704739i	$0.248936\pi$
$547$	32.9649i	1.40948i	−0.709466	+	0.704739i	$0.751064\pi$
$548$	6.17727i	0.263880i
$549$	3.97334	0.169578
$550$	0	0
$551$	−33.7321	−1.43703
$552$	− 11.4186i	− 0.486006i
$553$	7.43293i	0.316080i
$554$	−0.822726	−0.0349543
$555$	0	0
$556$	13.0338	0.552758
$557$	− 21.7009i	− 0.919495i	−0.888050	−	0.459748i	$-0.847940\pi$
$557$	− 21.7009i	− 0.919495i	0.888050	−	0.459748i	$-0.152060\pi$
$558$	− 2.21461i	− 0.0937521i
$559$	−46.4489	−1.96458
$560$	0	0
$561$	−4.70662	−0.198714
$562$	1.65142i	0.0696608i
$563$	1.05559i	0.0444879i	0.999753	+	0.0222439i	$0.00708105\pi$
$563$	1.05559i	0.0444879i	−0.999753	+	0.0222439i	$0.992919\pi$
$564$	−13.3607	−0.562587
$565$	0	0
$566$	−15.1340	−0.636128
$567$	19.3184i	0.811298i
$568$	6.29791i	0.264255i
$569$	41.4196	1.73640	0.868200	−	0.496215i	$-0.165277\pi$
$569$	41.4196	1.73640	0.868200	+	0.496215i	$0.165277\pi$
$570$	0	0
$571$	21.4452	0.897454	0.448727	−	0.893669i	$-0.351878\pi$
$571$	21.4452	0.897454	0.448727	+	0.893669i	$0.351878\pi$
$572$	− 4.95547i	− 0.207199i
$573$	− 32.6369i	− 1.36342i
$574$	23.2606	0.970878
$575$	0	0
$576$	−0.630898	−0.0262874
$577$	17.2667i	0.718823i	0.933179	+	0.359411i	$0.117023\pi$
$577$	17.2667i	0.718823i	−0.933179	+	0.359411i	$0.882977\pi$
$578$	− 9.15449i	− 0.380777i
$579$	−12.5343	−0.520906
$580$	0	0
$581$	−24.4273	−1.01342
$582$	− 4.73820i	− 0.196405i
$583$	− 11.0251i	− 0.456611i
$584$	12.7093	0.525914
$585$	0	0
$586$	25.4524	1.05143
$587$	− 9.63090i	− 0.397510i	−0.980049	−	0.198755i	$-0.936310\pi$
$587$	− 9.63090i	− 0.397510i	0.980049	−	0.198755i	$-0.0636898\pi$
$588$	− 1.98667i	− 0.0819288i
$589$	17.7249	0.730341
$590$	0	0
$591$	−38.2401	−1.57299
$592$	1.00000i	0.0410997i
$593$	− 2.78992i	− 0.114568i	−0.998358	−	0.0572842i	$-0.981756\pi$
$593$	− 2.78992i	− 0.114568i	0.998358	−	0.0572842i	$-0.0182441\pi$
$594$	6.10116	0.250334
$595$	0	0
$596$	−4.40522	−0.180445
$597$	− 13.0373i	− 0.533583i
$598$	33.6742i	1.37704i
$599$	−25.2606	−1.03212	−0.516060	−	0.856553i	$-0.672602\pi$
$599$	−25.2606	−1.03212	−0.516060	+	0.856553i	$0.672602\pi$
$600$	0	0
$601$	35.4040	1.44416	0.722080	−	0.691810i	$-0.243186\pi$
$601$	35.4040	1.44416	0.722080	+	0.691810i	$0.243186\pi$
$602$	29.4641i	1.20087i
$603$	8.38962i	0.341652i
$604$	−2.92162	−0.118879
$605$	0	0
$606$	24.4969	0.995120
$607$	38.2485i	1.55246i	0.630452	+	0.776229i	$0.282870\pi$
$607$	38.2485i	1.55246i	−0.630452	+	0.776229i	$0.717130\pi$
$608$	− 5.04945i	− 0.204782i
$609$	29.6065	1.19972
$610$	0	0
$611$	39.4017	1.59402
$612$	− 1.76713i	− 0.0714322i
$613$	46.3279i	1.87117i	0.353107	+	0.935583i	$0.385125\pi$
$613$	46.3279i	1.87117i	−0.353107	+	0.935583i	$0.614875\pi$
$614$	−27.8176	−1.12263
$615$	0	0
$616$	−3.14342	−0.126652
$617$	23.7503i	0.956152i	0.878319	+	0.478076i	$0.158666\pi$
$617$	23.7503i	0.956152i	−0.878319	+	0.478076i	$0.841334\pi$
$618$	− 16.2979i	− 0.655598i
$619$	6.53797	0.262783	0.131392	−	0.991331i	$-0.458055\pi$
$619$	6.53797	0.262783	0.131392	+	0.991331i	$0.458055\pi$
$620$	0	0
$621$	−41.4596	−1.66372
$622$	− 0.0650468i	− 0.00260814i
$623$	− 18.7454i	− 0.751018i
$624$	−6.98667	−0.279691
$625$	0	0
$626$	−22.5464	−0.901134
$627$	8.48482i	0.338851i
$628$	− 22.1906i	− 0.885502i
$629$	−2.80098	−0.111683
$630$	0	0
$631$	27.1506	1.08085	0.540424	−	0.841393i	$-0.318264\pi$
$631$	27.1506	1.08085	0.540424	+	0.841393i	$0.318264\pi$
$632$	− 2.58145i	− 0.102685i
$633$	− 33.4573i	− 1.32981i
$634$	−24.4775	−0.972124
$635$	0	0
$636$	−15.5441	−0.616364
$637$	5.85884i	0.232136i
$638$	− 7.29299i	− 0.288732i
$639$	3.97334	0.157183
$640$	0	0
$641$	31.9877	1.26344	0.631719	−	0.775197i	$-0.282350\pi$
$641$	31.9877	1.26344	0.631719	+	0.775197i	$0.282350\pi$
$642$	6.21235i	0.245182i
$643$	− 26.2784i	− 1.03632i	−0.855284	−	0.518160i	$-0.826617\pi$
$643$	− 26.2784i	− 1.03632i	0.855284	−	0.518160i	$-0.173383\pi$
$644$	21.3607	0.841729
$645$	0	0
$646$	14.1434	0.556466
$647$	31.3679i	1.23320i	0.787277	+	0.616599i	$0.211490\pi$
$647$	31.3679i	1.23320i	−0.787277	+	0.616599i	$0.788510\pi$
$648$	− 6.70928i	− 0.263565i
$649$	11.1713	0.438512
$650$	0	0
$651$	−15.5571	−0.609729
$652$	− 14.6248i	− 0.572750i
$653$	25.3184i	0.990787i	0.868669	+	0.495393i	$0.164976\pi$
$653$	25.3184i	0.990787i	−0.868669	+	0.495393i	$0.835024\pi$
$654$	−6.92162	−0.270657
$655$	0	0
$656$	−8.07838	−0.315408
$657$	− 8.01825i	− 0.312822i
$658$	− 24.9939i	− 0.974362i
$659$	38.2072	1.48834	0.744172	−	0.667989i	$-0.232844\pi$
$659$	38.2072	1.48834	0.744172	+	0.667989i	$0.232844\pi$
$660$	0	0
$661$	13.7899	0.536366	0.268183	−	0.963368i	$-0.413577\pi$
$661$	13.7899	0.536366	0.268183	+	0.963368i	$0.413577\pi$
$662$	1.91321i	0.0743591i
$663$	− 19.5695i	− 0.760018i
$664$	8.48360	0.329227
$665$	0	0
$666$	0.630898	0.0244468
$667$	49.5585i	1.91891i
$668$	6.34736i	0.245587i
$669$	−25.6332	−0.991035
$670$	0	0
$671$	−6.87549	−0.265425
$672$	4.43188i	0.170964i
$673$	− 4.41628i	− 0.170235i	−0.996371	−	0.0851176i	$-0.972873\pi$
$673$	− 4.41628i	− 0.170235i	0.996371	−	0.0851176i	$-0.0271266\pi$
$674$	−12.6286	−0.486437
$675$	0	0
$676$	7.60424	0.292471
$677$	− 38.1399i	− 1.46584i	−0.680317	−	0.732918i	$-0.738158\pi$
$677$	− 38.1399i	− 1.46584i	0.680317	−	0.732918i	$-0.261842\pi$
$678$	5.52359i	0.212132i
$679$	8.86376	0.340160
$680$	0	0
$681$	−17.2579	−0.661325
$682$	3.83218i	0.146742i
$683$	22.6514i	0.866732i	0.901218	+	0.433366i	$0.142674\pi$
$683$	22.6514i	0.866732i	−0.901218	+	0.433366i	$0.857326\pi$
$684$	−3.18568	−0.121808
$685$	0	0
$686$	−16.4391	−0.627647
$687$	− 11.7419i	− 0.447982i
$688$	− 10.2329i	− 0.390124i
$689$	45.8408	1.74640
$690$	0	0
$691$	−15.8443	−0.602745	−0.301373	−	0.953506i	$-0.597445\pi$
$691$	−15.8443	−0.602745	−0.301373	+	0.953506i	$0.597445\pi$
$692$	− 1.23513i	− 0.0469527i
$693$	1.98318i	0.0753347i
$694$	−8.33403	−0.316355
$695$	0	0
$696$	−10.2823	−0.389750
$697$	− 22.6274i	− 0.857074i
$698$	2.11837i	0.0801815i
$699$	0.0761103	0.00287876
$700$	0	0
$701$	−2.92284	−0.110394	−0.0551972	−	0.998475i	$-0.517579\pi$
$701$	−2.92284	−0.110394	−0.0551972	+	0.998475i	$0.517579\pi$
$702$	25.3679i	0.957449i
$703$	5.04945i	0.190444i
$704$	1.09171	0.0411453
$705$	0	0
$706$	−28.4534	−1.07086
$707$	45.8264i	1.72348i
$708$	− 15.7503i	− 0.591933i
$709$	8.45136	0.317397	0.158699	−	0.987327i	$-0.449270\pi$
$709$	8.45136	0.317397	0.158699	+	0.987327i	$0.449270\pi$
$710$	0	0
$711$	−1.62863	−0.0610784
$712$	6.51026i	0.243982i
$713$	− 26.0410i	− 0.975245i
$714$	−12.4136	−0.464568
$715$	0	0
$716$	1.76487	0.0659562
$717$	− 22.6369i	− 0.845389i
$718$	2.65368i	0.0990346i
$719$	15.3763	0.573439	0.286719	−	0.958015i	$-0.407435\pi$
$719$	15.3763	0.573439	0.286719	+	0.958015i	$0.407435\pi$
$720$	0	0
$721$	30.4885	1.13545
$722$	− 6.49693i	− 0.241791i
$723$	22.9337i	0.852915i
$724$	−6.49693	−0.241456
$725$	0	0
$726$	15.0966	0.560288
$727$	− 15.7275i	− 0.583302i	−0.956525	−	0.291651i	$-0.905795\pi$
$727$	− 15.7275i	− 0.583302i	0.956525	−	0.291651i	$-0.0942045\pi$
$728$	− 13.0700i	− 0.484405i
$729$	−30.0388	−1.11255
$730$	0	0
$731$	28.6621	1.06011
$732$	9.69368i	0.358289i
$733$	− 15.7275i	− 0.580909i	−0.956889	−	0.290455i	$-0.906193\pi$
$733$	− 15.7275i	− 0.580909i	0.956889	−	0.290455i	$-0.0938066\pi$
$734$	−31.7575	−1.17219
$735$	0	0
$736$	−7.41855	−0.273451
$737$	− 14.5174i	− 0.534757i
$738$	5.09663i	0.187610i
$739$	−45.0472	−1.65709	−0.828544	−	0.559924i	$-0.810830\pi$
$739$	−45.0472	−1.65709	−0.828544	+	0.559924i	$0.810830\pi$
$740$	0	0
$741$	−35.2788	−1.29600
$742$	− 29.0784i	− 1.06750i
$743$	9.31965i	0.341905i	0.985279	+	0.170952i	$0.0546845\pi$
$743$	9.31965i	0.341905i	−0.985279	+	0.170952i	$0.945316\pi$
$744$	5.40295	0.198082
$745$	0	0
$746$	−25.1122	−0.919424
$747$	− 5.35228i	− 0.195830i
$748$	3.05786i	0.111806i
$749$	−11.6214	−0.424638
$750$	0	0
$751$	11.6020	0.423362	0.211681	−	0.977339i	$-0.432106\pi$
$751$	11.6020	0.423362	0.211681	+	0.977339i	$0.432106\pi$
$752$	8.68035i	0.316540i
$753$	− 9.59705i	− 0.349736i
$754$	30.3234	1.10431
$755$	0	0
$756$	16.0917	0.585250
$757$	38.3545i	1.39402i	0.717062	+	0.697010i	$0.245487\pi$
$757$	38.3545i	1.39402i	−0.717062	+	0.697010i	$0.754513\pi$
$758$	22.5330i	0.818437i
$759$	12.4657	0.452477
$760$	0	0
$761$	−45.3318	−1.64328	−0.821638	−	0.570010i	$-0.806939\pi$
$761$	−45.3318	−1.64328	−0.821638	+	0.570010i	$0.806939\pi$
$762$	− 12.5308i	− 0.453942i
$763$	− 12.9483i	− 0.468759i
$764$	−21.2039	−0.767131
$765$	0	0
$766$	12.5886	0.454846
$767$	46.4489i	1.67717i
$768$	− 1.53919i	− 0.0555407i
$769$	31.7454	1.14477	0.572384	−	0.819986i	$-0.306019\pi$
$769$	31.7454	1.14477	0.572384	+	0.819986i	$0.306019\pi$
$770$	0	0
$771$	24.8683	0.895610
$772$	8.14342i	0.293088i
$773$	38.0482i	1.36850i	0.729248	+	0.684250i	$0.239870\pi$
$773$	38.0482i	1.36850i	−0.729248	+	0.684250i	$0.760130\pi$
$774$	−6.45589	−0.232052
$775$	0	0
$776$	−3.07838	−0.110507
$777$	− 4.43188i	− 0.158993i
$778$	− 0.879362i	− 0.0315266i
$779$	−40.7914	−1.46150
$780$	0	0
$781$	−6.87549	−0.246024
$782$	− 20.7792i	− 0.743064i
$783$	37.3340i	1.33421i
$784$	−1.29072	−0.0460973
$785$	0	0
$786$	2.25953	0.0805947
$787$	− 15.1506i	− 0.540061i	−0.962852	−	0.270031i	$-0.912966\pi$
$787$	− 15.1506i	− 0.540061i	0.962852	−	0.270031i	$-0.0870338\pi$
$788$	24.8443i	0.885041i
$789$	28.7115	1.02216
$790$	0	0
$791$	−10.3330	−0.367399
$792$	− 0.688756i	− 0.0244739i
$793$	− 28.5874i	− 1.01517i
$794$	−29.6814	−1.05335
$795$	0	0
$796$	−8.47027	−0.300221
$797$	43.1350i	1.52792i	0.645263	+	0.763960i	$0.276748\pi$
$797$	43.1350i	1.52792i	−0.645263	+	0.763960i	$0.723252\pi$
$798$	22.3786i	0.792192i
$799$	−24.3135	−0.860150
$800$	0	0
$801$	4.10731	0.145125
$802$	13.9867i	0.493886i
$803$	13.8748i	0.489632i
$804$	−20.4680	−0.721851
$805$	0	0
$806$	−15.9337	−0.561242
$807$	33.6020i	1.18285i
$808$	− 15.9155i	− 0.559905i
$809$	−33.3874	−1.17384	−0.586918	−	0.809646i	$-0.699659\pi$
$809$	−33.3874	−1.17384	−0.586918	+	0.809646i	$0.699659\pi$
$810$	0	0
$811$	10.9216	0.383510	0.191755	−	0.981443i	$-0.438582\pi$
$811$	10.9216	0.383510	0.191755	+	0.981443i	$0.438582\pi$
$812$	− 19.2351i	− 0.675021i
$813$	− 38.4463i	− 1.34837i
$814$	−1.09171	−0.0382644
$815$	0	0
$816$	4.31124	0.150924
$817$	− 51.6703i	− 1.80772i
$818$	− 21.9060i	− 0.765926i
$819$	−8.24581	−0.288132
$820$	0	0
$821$	−32.7910	−1.14441	−0.572206	−	0.820110i	$-0.693912\pi$
$821$	−32.7910	−1.14441	−0.572206	+	0.820110i	$0.693912\pi$
$822$	9.50799i	0.331629i
$823$	− 9.83218i	− 0.342728i	−0.985208	−	0.171364i	$-0.945183\pi$
$823$	− 9.83218i	− 0.342728i	0.985208	−	0.171364i	$-0.0548175\pi$
$824$	−10.5886	−0.368873
$825$	0	0
$826$	29.4641	1.02519
$827$	17.0228i	0.591940i	0.955197	+	0.295970i	$0.0956429\pi$
$827$	17.0228i	0.591940i	−0.955197	+	0.295970i	$0.904357\pi$
$828$	4.68035i	0.162653i
$829$	−12.8260	−0.445467	−0.222733	−	0.974879i	$-0.571498\pi$
$829$	−12.8260	−0.445467	−0.222733	+	0.974879i	$0.571498\pi$
$830$	0	0
$831$	−1.26633	−0.0439285
$832$	4.53919i	0.157368i
$833$	− 3.61530i	− 0.125263i
$834$	20.0616	0.694675
$835$	0	0
$836$	5.51253	0.190655
$837$	− 19.6176i	− 0.678082i
$838$	− 34.8648i	− 1.20438i
$839$	11.5018	0.397088	0.198544	−	0.980092i	$-0.436379\pi$
$839$	11.5018	0.397088	0.198544	+	0.980092i	$0.436379\pi$
$840$	0	0
$841$	15.6270	0.538863
$842$	4.76487i	0.164208i
$843$	2.54184i	0.0875457i
$844$	−21.7370	−0.748218
$845$	0	0
$846$	5.47641	0.188283
$847$	28.2413i	0.970382i
$848$	10.0989i	0.346798i
$849$	−23.2940	−0.799449
$850$	0	0
$851$	7.41855	0.254305
$852$	9.69368i	0.332100i
$853$	− 40.5946i	− 1.38993i	−0.719042	−	0.694966i	$-0.755419\pi$
$853$	− 40.5946i	− 1.38993i	0.719042	−	0.694966i	$-0.244581\pi$
$854$	−18.1340	−0.620532
$855$	0	0
$856$	4.03612	0.137952
$857$	38.0361i	1.29929i	0.760238	+	0.649645i	$0.225082\pi$
$857$	38.0361i	1.29929i	−0.760238	+	0.649645i	$0.774918\pi$
$858$	− 7.62741i	− 0.260395i
$859$	40.9506	1.39721	0.698607	−	0.715505i	$-0.253803\pi$
$859$	40.9506	1.39721	0.698607	+	0.715505i	$0.253803\pi$
$860$	0	0
$861$	35.8024	1.22014
$862$	− 2.66597i	− 0.0908033i
$863$	− 33.0817i	− 1.12611i	−0.826418	−	0.563057i	$-0.809625\pi$
$863$	− 33.0817i	− 1.12611i	0.826418	−	0.563057i	$-0.190375\pi$
$864$	−5.58864	−0.190129
$865$	0	0
$866$	−32.3074	−1.09785
$867$	− 14.0905i	− 0.478538i
$868$	10.1073i	0.343064i
$869$	2.81819	0.0956006
$870$	0	0
$871$	60.3617	2.04528
$872$	4.49693i	0.152285i
$873$	1.94214i	0.0657315i
$874$	−37.4596	−1.26709
$875$	0	0
$876$	19.5620	0.660938
$877$	25.5057i	0.861267i	0.902527	+	0.430634i	$0.141710\pi$
$877$	25.5057i	0.861267i	−0.902527	+	0.430634i	$0.858290\pi$
$878$	− 22.1568i	− 0.747754i
$879$	39.1761	1.32138
$880$	0	0
$881$	15.6514	0.527310	0.263655	−	0.964617i	$-0.415072\pi$
$881$	15.6514	0.527310	0.263655	+	0.964617i	$0.415072\pi$
$882$	0.814315i	0.0274194i
$883$	− 56.1071i	− 1.88816i	−0.329723	−	0.944078i	$-0.606955\pi$
$883$	− 56.1071i	− 1.88816i	0.329723	−	0.944078i	$-0.393045\pi$
$884$	−12.7142	−0.427625
$885$	0	0
$886$	−39.1061	−1.31379
$887$	− 47.5052i	− 1.59507i	−0.603275	−	0.797534i	$-0.706138\pi$
$887$	− 47.5052i	− 1.59507i	0.603275	−	0.797534i	$-0.293862\pi$
$888$	1.53919i	0.0516518i
$889$	23.4413	0.786197
$890$	0	0
$891$	7.32457	0.245382
$892$	16.6537i	0.557607i
$893$	43.8310i	1.46675i
$894$	−6.78047	−0.226773
$895$	0	0
$896$	2.87936	0.0961927
$897$	51.8310i	1.73059i
$898$	30.8915i	1.03086i
$899$	−23.4497	−0.782093
$900$	0	0
$901$	−28.2868	−0.942372
$902$	− 8.81924i	− 0.293648i
$903$	45.3509i	1.50918i
$904$	3.58864	0.119356
$905$	0	0
$906$	−4.49693	−0.149400
$907$	15.8394i	0.525938i	0.964804	+	0.262969i	$0.0847016\pi$
$907$	15.8394i	0.525938i	−0.964804	+	0.262969i	$0.915298\pi$
$908$	11.2123i	0.372095i
$909$	−10.0410	−0.333040
$910$	0	0
$911$	11.9539	0.396049	0.198025	−	0.980197i	$-0.436547\pi$
$911$	11.9539	0.396049	0.198025	+	0.980197i	$0.436547\pi$
$912$	− 7.77205i	− 0.257358i
$913$	9.26162i	0.306515i
$914$	−0.438025	−0.0144886
$915$	0	0
$916$	−7.62863	−0.252057
$917$	4.22690i	0.139585i
$918$	− 15.6537i	− 0.516649i
$919$	34.8781	1.15052	0.575262	−	0.817969i	$-0.304900\pi$
$919$	34.8781	1.15052	0.575262	+	0.817969i	$0.304900\pi$
$920$	0	0
$921$	−42.8166	−1.41085
$922$	− 0.523590i	− 0.0172435i
$923$	− 28.5874i	− 0.940966i
$924$	−4.83832	−0.159169
$925$	0	0
$926$	29.1845	0.959061
$927$	6.68035i	0.219411i
$928$	6.68035i	0.219293i
$929$	52.5439	1.72391	0.861955	−	0.506984i	$-0.169240\pi$
$929$	52.5439	1.72391	0.861955	+	0.506984i	$0.169240\pi$
$930$	0	0
$931$	−6.51745	−0.213601
$932$	− 0.0494483i	− 0.00161973i
$933$	− 0.100119i	− 0.00327776i
$934$	9.49079	0.310548
$935$	0	0
$936$	2.86376	0.0936050
$937$	− 13.3318i	− 0.435530i	−0.976001	−	0.217765i	$-0.930123\pi$
$937$	− 13.3318i	− 0.435530i	0.976001	−	0.217765i	$-0.0698766\pi$
$938$	− 38.2895i	− 1.25020i
$939$	−34.7031	−1.13249
$940$	0	0
$941$	14.5281	0.473603	0.236802	−	0.971558i	$-0.423901\pi$
$941$	14.5281	0.473603	0.236802	+	0.971558i	$0.423901\pi$
$942$	− 34.1555i	− 1.11285i
$943$	59.9299i	1.95158i
$944$	−10.2329	−0.333051
$945$	0	0
$946$	11.1713	0.363211
$947$	− 24.6803i	− 0.802003i	−0.916077	−	0.401002i	$-0.868662\pi$
$947$	− 24.6803i	− 0.802003i	0.916077	−	0.401002i	$-0.131338\pi$
$948$	− 3.97334i	− 0.129048i
$949$	−57.6898	−1.87269
$950$	0	0
$951$	−37.6754	−1.22171
$952$	8.06505i	0.261390i
$953$	40.5936i	1.31495i	0.753474	+	0.657477i	$0.228376\pi$
$953$	40.5936i	1.31495i	−0.753474	+	0.657477i	$0.771624\pi$
$954$	6.37137	0.206281
$955$	0	0
$956$	−14.7070	−0.475659
$957$	− 11.2253i	− 0.362862i
$958$	− 6.12291i	− 0.197822i
$959$	−17.7866	−0.574360
$960$	0	0
$961$	−18.6781	−0.602519
$962$	− 4.53919i	− 0.146349i
$963$	− 2.54638i	− 0.0820558i
$964$	14.8999	0.479893
$965$	0	0
$966$	32.8781	1.05784
$967$	− 1.06400i	− 0.0342160i	−0.999854	−	0.0171080i	$-0.994554\pi$
$967$	− 1.06400i	− 0.0342160i	0.999854	−	0.0171080i	$-0.00544591\pi$
$968$	− 9.80817i	− 0.315247i
$969$	21.7694	0.699334
$970$	0	0
$971$	11.9333	0.382959	0.191480	−	0.981497i	$-0.438671\pi$
$971$	11.9333	0.382959	0.191480	+	0.981497i	$0.438671\pi$
$972$	6.43907i	0.206533i
$973$	37.5292i	1.20313i
$974$	10.3018	0.330091
$975$	0	0
$976$	6.29791	0.201591
$977$	− 19.1867i	− 0.613838i	−0.951736	−	0.306919i	$-0.900702\pi$
$977$	− 19.1867i	− 0.613838i	0.951736	−	0.306919i	$-0.0992980\pi$
$978$	− 22.5103i	− 0.719799i
$979$	−7.10731	−0.227151
$980$	0	0
$981$	2.83710	0.0905817
$982$	10.5380i	0.336280i
$983$	22.9171i	0.730942i	0.930823	+	0.365471i	$0.119092\pi$
$983$	22.9171i	0.730942i	−0.930823	+	0.365471i	$0.880908\pi$
$984$	−12.4341	−0.396386
$985$	0	0
$986$	−18.7115	−0.595897
$987$	− 38.4703i	− 1.22452i
$988$	22.9204i	0.729195i
$989$	−75.9130	−2.41389
$990$	0	0
$991$	−52.2772	−1.66064	−0.830320	−	0.557287i	$-0.811842\pi$
$991$	−52.2772	−1.66064	−0.830320	+	0.557287i	$0.811842\pi$
$992$	− 3.51026i	− 0.111451i
$993$	2.94479i	0.0934502i
$994$	−18.1340	−0.575175
$995$	0	0
$996$	13.0579	0.413754
$997$	48.8892i	1.54834i	0.632980	+	0.774168i	$0.281832\pi$
$997$	48.8892i	1.54834i	−0.632980	+	0.774168i	$0.718168\pi$
$998$	− 31.2123i	− 0.988010i
$999$	5.58864	0.176817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.b.n.149.2		6
5.2	odd	4		1850.2.a.bb.1.2	yes	3
5.3	odd	4		1850.2.a.ba.1.2	✓	3
5.4	even	2	inner	1850.2.b.n.149.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.ba.1.2	✓	3	5.3	odd	4
1850.2.a.bb.1.2	yes	3	5.2	odd	4
1850.2.b.n.149.2		6	1.1	even	1	trivial
1850.2.b.n.149.5		6	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.53919i q^{3} -1.00000 q^{4} -1.53919 q^{6} -2.87936i q^{7} +1.00000i q^{8} +0.630898 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.53919i q^{3} -1.00000 q^{4} -1.53919 q^{6} -2.87936i q^{7} +1.00000i q^{8} +0.630898 q^{9} -1.09171 q^{11} +1.53919i q^{12} -4.53919i q^{13} -2.87936 q^{14} +1.00000 q^{16} +2.80098i q^{17} -0.630898i q^{18} +5.04945 q^{19} -4.43188 q^{21} +1.09171i q^{22} -7.41855i q^{23} +1.53919 q^{24} -4.53919 q^{26} -5.58864i q^{27} +2.87936i q^{28} -6.68035 q^{29} +3.51026 q^{31} -1.00000i q^{32} +1.68035i q^{33} +2.80098 q^{34} -0.630898 q^{36} +1.00000i q^{37} -5.04945i q^{38} -6.98667 q^{39} -8.07838 q^{41} +4.43188i q^{42} -10.2329i q^{43} +1.09171 q^{44} -7.41855 q^{46} +8.68035i q^{47} -1.53919i q^{48} -1.29072 q^{49} +4.31124 q^{51} +4.53919i q^{52} +10.0989i q^{53} -5.58864 q^{54} +2.87936 q^{56} -7.77205i q^{57} +6.68035i q^{58} -10.2329 q^{59} +6.29791 q^{61} -3.51026i q^{62} -1.81658i q^{63} -1.00000 q^{64} +1.68035 q^{66} +13.2979i q^{67} -2.80098i q^{68} -11.4186 q^{69} +6.29791 q^{71} +0.630898i q^{72} -12.7093i q^{73} +1.00000 q^{74} -5.04945 q^{76} +3.14342i q^{77} +6.98667i q^{78} -2.58145 q^{79} -6.70928 q^{81} +8.07838i q^{82} -8.48360i q^{83} +4.43188 q^{84} -10.2329 q^{86} +10.2823i q^{87} -1.09171i q^{88} +6.51026 q^{89} -13.0700 q^{91} +7.41855i q^{92} -5.40295i q^{93} +8.68035 q^{94} -1.53919 q^{96} +3.07838i q^{97} +1.29072i q^{98} -0.688756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 4 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 4 q^{9} - 2 q^{11} + 8 q^{14} + 6 q^{16} - 6 q^{19} + 6 q^{24} - 24 q^{26} + 4 q^{29} - 12 q^{31} - 2 q^{34} + 4 q^{36} - 40 q^{39} - 42 q^{41} + 2 q^{44} - 16 q^{46} - 22 q^{49} - 26 q^{51} + 6 q^{54} - 8 q^{56} - 16 q^{59} - 16 q^{61} - 6 q^{64} - 34 q^{66} - 40 q^{69} - 16 q^{71} + 6 q^{74} + 6 q^{76} - 44 q^{79} - 26 q^{81} - 16 q^{86} + 6 q^{89} + 24 q^{91} + 8 q^{94} - 6 q^{96} - 56 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 4 * q^9 - 2 * q^11 + 8 * q^14 + 6 * q^16 - 6 * q^19 + 6 * q^24 - 24 * q^26 + 4 * q^29 - 12 * q^31 - 2 * q^34 + 4 * q^36 - 40 * q^39 - 42 * q^41 + 2 * q^44 - 16 * q^46 - 22 * q^49 - 26 * q^51 + 6 * q^54 - 8 * q^56 - 16 * q^59 - 16 * q^61 - 6 * q^64 - 34 * q^66 - 40 * q^69 - 16 * q^71 + 6 * q^74 + 6 * q^76 - 44 * q^79 - 26 * q^81 - 16 * q^86 + 6 * q^89 + 24 * q^91 + 8 * q^94 - 6 * q^96 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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