LMFDB - Embedded newform 1875.2.b.e.1249.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1875,2,Mod(1249,1875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1875, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1875.1249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1875 = 3 \cdot 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1875.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:	$14.9719503790$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 23x^{10} + 199x^{8} + 794x^{6} + 1399x^{4} + 783x^{2} + 81 $ x^12 + 23x^10 + 199x^8 + 794x^6 + 1399x^4 + 783*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1249.10
Root			$2.13324i$ of defining polynomial
Character	$\chi$	$=$	1875.1249
Dual form			1875.2.b.e.1249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.13324i q^{2} +1.00000i q^{3} -2.55073 q^{4} -2.13324 q^{6} -2.16876i q^{7} -1.17484i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+2.13324i q^{2} +1.00000i q^{3} -2.55073 q^{4} -2.13324 q^{6} -2.16876i q^{7} -1.17484i q^{8} -1.00000 q^{9} -2.50913 q^{11} -2.55073i q^{12} -4.33379i q^{13} +4.62650 q^{14} -2.59524 q^{16} +6.77562i q^{17} -2.13324i q^{18} -6.83602 q^{19} +2.16876 q^{21} -5.35259i q^{22} -1.67843i q^{23} +1.17484 q^{24} +9.24504 q^{26} -1.00000i q^{27} +5.53193i q^{28} -4.44927 q^{29} +6.56295 q^{31} -7.88596i q^{32} -2.50913i q^{33} -14.4541 q^{34} +2.55073 q^{36} -7.97720i q^{37} -14.5829i q^{38} +4.33379 q^{39} +11.2249 q^{41} +4.62650i q^{42} -4.25487i q^{43} +6.40012 q^{44} +3.58050 q^{46} -4.98652i q^{47} -2.59524i q^{48} +2.29646 q^{49} -6.77562 q^{51} +11.0543i q^{52} -8.21338i q^{53} +2.13324 q^{54} -2.54795 q^{56} -6.83602i q^{57} -9.49138i q^{58} -3.67416 q^{59} +4.93960 q^{61} +14.0004i q^{62} +2.16876i q^{63} +11.6322 q^{64} +5.35259 q^{66} -11.5812i q^{67} -17.2828i q^{68} +1.67843 q^{69} -2.30251 q^{71} +1.17484i q^{72} -1.11599i q^{73} +17.0173 q^{74} +17.4368 q^{76} +5.44172i q^{77} +9.24504i q^{78} -7.78306 q^{79} +1.00000 q^{81} +23.9454i q^{82} +9.87708i q^{83} -5.53193 q^{84} +9.07667 q^{86} -4.44927i q^{87} +2.94783i q^{88} +1.24025 q^{89} -9.39897 q^{91} +4.28122i q^{92} +6.56295i q^{93} +10.6375 q^{94} +7.88596 q^{96} -15.0488i q^{97} +4.89892i q^{98} +2.50913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9	$ 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9} + 8 q^{14} + 34 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{24} + 74 q^{26} - 62 q^{29} - 4 q^{31} - 74 q^{34} + 22 q^{36} + 66 q^{41} + 22 q^{44} - 24 q^{46} - 8 q^{49} - 4 q^{51} + 2 q^{54} - 60 q^{56} + 16 q^{59} + 68 q^{61} - 24 q^{64} - 18 q^{66} - 2 q^{69} - 6 q^{71} - 72 q^{74} + 54 q^{76} - 50 q^{79} + 12 q^{81} - 88 q^{84} - 60 q^{86} - 36 q^{89} + 56 q^{91} + 100 q^{94} - 66 q^{96}+O(q^{100}) $ 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9 + 8 * q^14 + 34 * q^16 + 4 * q^19 + 4 * q^21 + 12 * q^24 + 74 * q^26 - 62 * q^29 - 4 * q^31 - 74 * q^34 + 22 * q^36 + 66 * q^41 + 22 * q^44 - 24 * q^46 - 8 * q^49 - 4 * q^51 + 2 * q^54 - 60 * q^56 + 16 * q^59 + 68 * q^61 - 24 * q^64 - 18 * q^66 - 2 * q^69 - 6 * q^71 - 72 * q^74 + 54 * q^76 - 50 * q^79 + 12 * q^81 - 88 * q^84 - 60 * q^86 - 36 * q^89 + 56 * q^91 + 100 * q^94 - 66 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times$.

$n$	$626$	$1252$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.13324i	1.50843i	0.656627	+	0.754216i	$0.271983\pi$
$2$	2.13324i	1.50843i	−0.656627	+	0.754216i	$0.728017\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−2.55073	−1.27536
$5$	0	0
$5$	0	0
$6$	−2.13324	−0.870893
$7$	− 2.16876i	− 0.819716i	−0.912149	−	0.409858i	$-0.865578\pi$
$7$	− 2.16876i	− 0.819716i	0.912149	−	0.409858i	$-0.134422\pi$
$8$	− 1.17484i	− 0.415369i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−2.50913	−0.756532	−0.378266	−	0.925697i	$-0.623480\pi$
$11$	−2.50913	−0.756532	−0.378266	+	0.925697i	$0.623480\pi$
$12$	− 2.55073i	− 0.736332i
$13$	− 4.33379i	− 1.20198i	−0.799257	−	0.600989i	$-0.794774\pi$
$13$	− 4.33379i	− 1.20198i	0.799257	−	0.600989i	$-0.205226\pi$
$14$	4.62650	1.23648
$15$	0	0
$16$	−2.59524	−0.648810
$17$	6.77562i	1.64333i	0.569971	+	0.821665i	$0.306954\pi$
$17$	6.77562i	1.64333i	−0.569971	+	0.821665i	$0.693046\pi$
$18$	− 2.13324i	− 0.502810i
$19$	−6.83602	−1.56829	−0.784145	−	0.620578i	$-0.786898\pi$
$19$	−6.83602	−1.56829	−0.784145	+	0.620578i	$0.786898\pi$
$20$	0	0
$21$	2.16876	0.473263
$22$	− 5.35259i	− 1.14118i
$23$	− 1.67843i	− 0.349977i	−0.984570	−	0.174989i	$-0.944011\pi$
$23$	− 1.67843i	− 0.349977i	0.984570	−	0.174989i	$-0.0559888\pi$
$24$	1.17484	0.239813
$25$	0	0
$26$	9.24504	1.81310
$27$	− 1.00000i	− 0.192450i
$28$	5.53193i	1.04544i
$29$	−4.44927	−0.826209	−0.413104	−	0.910684i	$-0.635556\pi$
$29$	−4.44927	−0.826209	−0.413104	+	0.910684i	$0.635556\pi$
$30$	0	0
$31$	6.56295	1.17874	0.589371	−	0.807863i	$-0.299376\pi$
$31$	6.56295	1.17874	0.589371	+	0.807863i	$0.299376\pi$
$32$	− 7.88596i	− 1.39405i
$33$	− 2.50913i	− 0.436784i
$34$	−14.4541	−2.47885
$35$	0	0
$36$	2.55073	0.425122
$37$	− 7.97720i	− 1.31144i	−0.755002	−	0.655722i	$-0.772364\pi$
$37$	− 7.97720i	− 1.31144i	0.755002	−	0.655722i	$-0.227636\pi$
$38$	− 14.5829i	− 2.36566i
$39$	4.33379	0.693962
$40$	0	0
$41$	11.2249	1.75303	0.876517	−	0.481371i	$-0.159861\pi$
$41$	11.2249	1.75303	0.876517	+	0.481371i	$0.159861\pi$
$42$	4.62650i	0.713885i
$43$	− 4.25487i	− 0.648861i	−0.945909	−	0.324431i	$-0.894827\pi$
$43$	− 4.25487i	− 0.648861i	0.945909	−	0.324431i	$-0.105173\pi$
$44$	6.40012	0.964854
$45$	0	0
$46$	3.58050	0.527916
$47$	− 4.98652i	− 0.727358i	−0.931524	−	0.363679i	$-0.881521\pi$
$47$	− 4.98652i	− 0.727358i	0.931524	−	0.363679i	$-0.118479\pi$
$48$	− 2.59524i	− 0.374590i
$49$	2.29646	0.328066
$50$	0	0
$51$	−6.77562	−0.948777
$52$	11.0543i	1.53296i
$53$	− 8.21338i	− 1.12820i	−0.825708	−	0.564098i	$-0.809224\pi$
$53$	− 8.21338i	− 1.12820i	0.825708	−	0.564098i	$-0.190776\pi$
$54$	2.13324	0.290298
$55$	0	0
$56$	−2.54795	−0.340484
$57$	− 6.83602i	− 0.905453i
$58$	− 9.49138i	− 1.24628i
$59$	−3.67416	−0.478335	−0.239168	−	0.970978i	$-0.576875\pi$
$59$	−3.67416	−0.478335	−0.239168	+	0.970978i	$0.576875\pi$
$60$	0	0
$61$	4.93960	0.632451	0.316226	−	0.948684i	$-0.397584\pi$
$61$	4.93960	0.632451	0.316226	+	0.948684i	$0.397584\pi$
$62$	14.0004i	1.77805i
$63$	2.16876i	0.273239i
$64$	11.6322	1.45402
$65$	0	0
$66$	5.35259	0.658859
$67$	− 11.5812i	− 1.41487i	−0.706778	−	0.707436i	$-0.749852\pi$
$67$	− 11.5812i	− 1.41487i	0.706778	−	0.707436i	$-0.250148\pi$
$68$	− 17.2828i	− 2.09584i
$69$	1.67843	0.202059
$70$	0	0
$71$	−2.30251	−0.273257	−0.136629	−	0.990622i	$-0.543627\pi$
$71$	−2.30251	−0.273257	−0.136629	+	0.990622i	$0.543627\pi$
$72$	1.17484i	0.138456i
$73$	− 1.11599i	− 0.130617i	−0.997865	−	0.0653084i	$-0.979197\pi$
$73$	− 1.11599i	− 0.130617i	0.997865	−	0.0653084i	$-0.0208031\pi$
$74$	17.0173	1.97822
$75$	0	0
$76$	17.4368	2.00014
$77$	5.44172i	0.620141i
$78$	9.24504i	1.04679i
$79$	−7.78306	−0.875663	−0.437831	−	0.899057i	$-0.644253\pi$
$79$	−7.78306	−0.875663	−0.437831	+	0.899057i	$0.644253\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	23.9454i	2.64433i
$83$	9.87708i	1.08415i	0.840330	+	0.542075i	$0.182361\pi$
$83$	9.87708i	1.08415i	−0.840330	+	0.542075i	$0.817639\pi$
$84$	−5.53193	−0.603583
$85$	0	0
$86$	9.07667	0.978763
$87$	− 4.44927i	− 0.477012i
$88$	2.94783i	0.314240i
$89$	1.24025	0.131466	0.0657329	−	0.997837i	$-0.479061\pi$
$89$	1.24025	0.131466	0.0657329	+	0.997837i	$0.479061\pi$
$90$	0	0
$91$	−9.39897	−0.985280
$92$	4.28122i	0.446348i
$93$	6.56295i	0.680546i
$94$	10.6375	1.09717
$95$	0	0
$96$	7.88596	0.804857
$97$	− 15.0488i	− 1.52797i	−0.645234	−	0.763985i	$-0.723240\pi$
$97$	− 15.0488i	− 1.52797i	0.645234	−	0.763985i	$-0.276760\pi$
$98$	4.89892i	0.494866i
$99$	2.50913	0.252177
$100$	0	0
$101$	−17.0211	−1.69366	−0.846830	−	0.531864i	$-0.821492\pi$
$101$	−17.0211	−1.69366	−0.846830	+	0.531864i	$0.821492\pi$
$102$	− 14.4541i	− 1.43116i
$103$	10.0859i	0.993793i	0.867810	+	0.496897i	$0.165527\pi$
$103$	10.0859i	0.993793i	−0.867810	+	0.496897i	$0.834473\pi$
$104$	−5.09151	−0.499264
$105$	0	0
$106$	17.5212	1.70180
$107$	− 5.67218i	− 0.548351i	−0.961680	−	0.274175i	$-0.911595\pi$
$107$	− 5.67218i	− 0.548351i	0.961680	−	0.274175i	$-0.0884049\pi$
$108$	2.55073i	0.245444i
$109$	−8.34557	−0.799361	−0.399680	−	0.916655i	$-0.630879\pi$
$109$	−8.34557	−0.799361	−0.399680	+	0.916655i	$0.630879\pi$
$110$	0	0
$111$	7.97720	0.757163
$112$	5.62846i	0.531839i
$113$	− 14.8224i	− 1.39438i	−0.716888	−	0.697188i	$-0.754434\pi$
$113$	− 14.8224i	− 1.39438i	0.716888	−	0.697188i	$-0.245566\pi$
$114$	14.5829	1.36581
$115$	0	0
$116$	11.3489	1.05372
$117$	4.33379i	0.400659i
$118$	− 7.83788i	− 0.721536i
$119$	14.6947	1.34706
$120$	0	0
$121$	−4.70425	−0.427659
$122$	10.5374i	0.954009i
$123$	11.2249i	1.01211i
$124$	−16.7403	−1.50332
$125$	0	0
$126$	−4.62650	−0.412162
$127$	0.502113i	0.0445553i	0.999752	+	0.0222777i	$0.00709179\pi$
$127$	0.502113i	0.0445553i	−0.999752	+	0.0222777i	$0.992908\pi$
$128$	9.04239i	0.799242i
$129$	4.25487	0.374620
$130$	0	0
$131$	6.05788	0.529280	0.264640	−	0.964347i	$-0.414747\pi$
$131$	6.05788	0.529280	0.264640	+	0.964347i	$0.414747\pi$
$132$	6.40012i	0.557059i
$133$	14.8257i	1.28555i
$134$	24.7056	2.13424
$135$	0	0
$136$	7.96027	0.682588
$137$	1.94014i	0.165757i	0.996560	+	0.0828786i	$0.0264114\pi$
$137$	1.94014i	0.165757i	−0.996560	+	0.0828786i	$0.973589\pi$
$138$	3.58050i	0.304793i
$139$	−19.2023	−1.62872	−0.814358	−	0.580363i	$-0.802911\pi$
$139$	−19.2023	−1.62872	−0.814358	+	0.580363i	$0.802911\pi$
$140$	0	0
$141$	4.98652	0.419940
$142$	− 4.91181i	− 0.412190i
$143$	10.8741i	0.909335i
$144$	2.59524	0.216270
$145$	0	0
$146$	2.38068	0.197026
$147$	2.29646i	0.189409i
$148$	20.3477i	1.67257i
$149$	−9.49138	−0.777564	−0.388782	−	0.921330i	$-0.627104\pi$
$149$	−9.49138	−0.777564	−0.388782	+	0.921330i	$0.627104\pi$
$150$	0	0
$151$	−12.5747	−1.02332	−0.511659	−	0.859189i	$-0.670969\pi$
$151$	−12.5747	−1.02332	−0.511659	+	0.859189i	$0.670969\pi$
$152$	8.03123i	0.651419i
$153$	− 6.77562i	− 0.547776i
$154$	−11.6085	−0.935440
$155$	0	0
$156$	−11.0543	−0.885055
$157$	18.7991i	1.50033i	0.661250	+	0.750165i	$0.270026\pi$
$157$	18.7991i	1.50033i	−0.661250	+	0.750165i	$0.729974\pi$
$158$	− 16.6032i	− 1.32088i
$159$	8.21338	0.651364
$160$	0	0
$161$	−3.64012	−0.286882
$162$	2.13324i	0.167603i
$163$	− 7.29949i	− 0.571740i	−0.958268	−	0.285870i	$-0.907717\pi$
$163$	− 7.29949i	− 0.571740i	0.958268	−	0.285870i	$-0.0922826\pi$
$164$	−28.6317	−2.23576
$165$	0	0
$166$	−21.0702	−1.63537
$167$	− 14.7991i	− 1.14519i	−0.819839	−	0.572594i	$-0.805937\pi$
$167$	− 14.7991i	− 1.14519i	0.819839	−	0.572594i	$-0.194063\pi$
$168$	− 2.54795i	− 0.196579i
$169$	−5.78176	−0.444750
$170$	0	0
$171$	6.83602	0.522763
$172$	10.8530i	0.827535i
$173$	2.29460i	0.174455i	0.996188	+	0.0872276i	$0.0278007\pi$
$173$	2.29460i	0.174455i	−0.996188	+	0.0872276i	$0.972199\pi$
$174$	9.49138	0.719540
$175$	0	0
$176$	6.51180	0.490845
$177$	− 3.67416i	− 0.276167i
$178$	2.64575i	0.198307i
$179$	−13.6637	−1.02127	−0.510636	−	0.859797i	$-0.670590\pi$
$179$	−13.6637	−1.02127	−0.510636	+	0.859797i	$0.670590\pi$
$180$	0	0
$181$	8.71878	0.648062	0.324031	−	0.946046i	$-0.394962\pi$
$181$	8.71878	0.648062	0.324031	+	0.946046i	$0.394962\pi$
$182$	− 20.0503i	− 1.48623i
$183$	4.93960i	0.365146i
$184$	−1.97189	−0.145370
$185$	0	0
$186$	−14.0004	−1.02656
$187$	− 17.0009i	− 1.24323i
$188$	12.7193i	0.927647i
$189$	−2.16876	−0.157754
$190$	0	0
$191$	11.6080	0.839925	0.419963	−	0.907541i	$-0.362043\pi$
$191$	11.6080	0.839925	0.419963	+	0.907541i	$0.362043\pi$
$192$	11.6322i	0.839481i
$193$	14.8653i	1.07002i	0.844844	+	0.535012i	$0.179693\pi$
$193$	14.8653i	1.07002i	−0.844844	+	0.535012i	$0.820307\pi$
$194$	32.1027	2.30484
$195$	0	0
$196$	−5.85766	−0.418404
$197$	22.8292i	1.62651i	0.581906	+	0.813256i	$0.302307\pi$
$197$	22.8292i	1.62651i	−0.581906	+	0.813256i	$0.697693\pi$
$198$	5.35259i	0.380392i
$199$	−5.87697	−0.416607	−0.208304	−	0.978064i	$-0.566794\pi$
$199$	−5.87697	−0.416607	−0.208304	+	0.978064i	$0.566794\pi$
$200$	0	0
$201$	11.5812	0.816876
$202$	− 36.3101i	− 2.55477i
$203$	9.64942i	0.677256i
$204$	17.2828	1.21004
$205$	0	0
$206$	−21.5157	−1.49907
$207$	1.67843i	0.116659i
$208$	11.2472i	0.779855i
$209$	17.1525	1.18646
$210$	0	0
$211$	−24.6884	−1.69962	−0.849810	−	0.527090i	$-0.823283\pi$
$211$	−24.6884	−1.69962	−0.849810	+	0.527090i	$0.823283\pi$
$212$	20.9501i	1.43886i
$213$	− 2.30251i	− 0.157765i
$214$	12.1002	0.827149
$215$	0	0
$216$	−1.17484	−0.0799378
$217$	− 14.2335i	− 0.966232i
$218$	− 17.8031i	− 1.20578i
$219$	1.11599	0.0754116
$220$	0	0
$221$	29.3641	1.97525
$222$	17.0173i	1.14213i
$223$	3.31060i	0.221694i	0.993837	+	0.110847i	$0.0353563\pi$
$223$	3.31060i	0.221694i	−0.993837	+	0.110847i	$0.964644\pi$
$224$	−17.1028	−1.14273
$225$	0	0
$226$	31.6198	2.10332
$227$	− 2.70185i	− 0.179328i	−0.995972	−	0.0896641i	$-0.971421\pi$
$227$	− 2.70185i	− 0.179328i	0.995972	−	0.0896641i	$-0.0285793\pi$
$228$	17.4368i	1.15478i
$229$	9.33473	0.616856	0.308428	−	0.951248i	$-0.400197\pi$
$229$	9.33473	0.616856	0.308428	+	0.951248i	$0.400197\pi$
$230$	0	0
$231$	−5.44172	−0.358039
$232$	5.22718i	0.343181i
$233$	− 9.52491i	− 0.623998i	−0.950083	−	0.311999i	$-0.899002\pi$
$233$	− 9.52491i	− 0.623998i	0.950083	−	0.311999i	$-0.100998\pi$
$234$	−9.24504	−0.604367
$235$	0	0
$236$	9.37179	0.610052
$237$	− 7.78306i	− 0.505564i
$238$	31.3474i	2.03195i
$239$	−7.84648	−0.507546	−0.253773	−	0.967264i	$-0.581672\pi$
$239$	−7.84648	−0.507546	−0.253773	+	0.967264i	$0.581672\pi$
$240$	0	0
$241$	1.42783	0.0919747	0.0459874	−	0.998942i	$-0.485357\pi$
$241$	1.42783	0.0919747	0.0459874	+	0.998942i	$0.485357\pi$
$242$	− 10.0353i	− 0.645095i
$243$	1.00000i	0.0641500i
$244$	−12.5996	−0.806606
$245$	0	0
$246$	−23.9454	−1.52670
$247$	29.6259i	1.88505i
$248$	− 7.71042i	− 0.489612i
$249$	−9.87708	−0.625935
$250$	0	0
$251$	−17.5762	−1.10940	−0.554701	−	0.832050i	$-0.687167\pi$
$251$	−17.5762	−1.10940	−0.554701	+	0.832050i	$0.687167\pi$
$252$	− 5.53193i	− 0.348479i
$253$	4.21141i	0.264769i
$254$	−1.07113	−0.0672087
$255$	0	0
$256$	3.97476	0.248423
$257$	− 19.2890i	− 1.20322i	−0.798791	−	0.601608i	$-0.794527\pi$
$257$	− 19.2890i	− 1.20322i	0.798791	−	0.601608i	$-0.205473\pi$
$258$	9.07667i	0.565089i
$259$	−17.3007	−1.07501
$260$	0	0
$261$	4.44927	0.275403
$262$	12.9229i	0.798382i
$263$	22.2432i	1.37157i	0.727803	+	0.685786i	$0.240541\pi$
$263$	22.2432i	1.37157i	−0.727803	+	0.685786i	$0.759459\pi$
$264$	−2.94783	−0.181426
$265$	0	0
$266$	−31.6268	−1.93917
$267$	1.24025i	0.0759018i
$268$	29.5406i	1.80448i
$269$	−25.1785	−1.53516	−0.767581	−	0.640951i	$-0.778540\pi$
$269$	−25.1785	−1.53516	−0.767581	+	0.640951i	$0.778540\pi$
$270$	0	0
$271$	−5.70091	−0.346306	−0.173153	−	0.984895i	$-0.555395\pi$
$271$	−5.70091	−0.346306	−0.173153	+	0.984895i	$0.555395\pi$
$272$	− 17.5843i	− 1.06621i
$273$	− 9.39897i	− 0.568852i
$274$	−4.13879	−0.250033
$275$	0	0
$276$	−4.28122	−0.257699
$277$	19.1611i	1.15128i	0.817704	+	0.575638i	$0.195246\pi$
$277$	19.1611i	1.15128i	−0.817704	+	0.575638i	$0.804754\pi$
$278$	− 40.9631i	− 2.45681i
$279$	−6.56295	−0.392914
$280$	0	0
$281$	4.36015	0.260105	0.130052	−	0.991507i	$-0.458485\pi$
$281$	4.36015	0.260105	0.130052	+	0.991507i	$0.458485\pi$
$282$	10.6375i	0.633451i
$283$	24.9081i	1.48063i	0.672258	+	0.740317i	$0.265324\pi$
$283$	24.9081i	1.48063i	−0.672258	+	0.740317i	$0.734676\pi$
$284$	5.87307	0.348503
$285$	0	0
$286$	−23.1970	−1.37167
$287$	− 24.3441i	− 1.43699i
$288$	7.88596i	0.464684i
$289$	−28.9090	−1.70053
$290$	0	0
$291$	15.0488	0.882174
$292$	2.84659i	0.166584i
$293$	13.5651i	0.792484i	0.918146	+	0.396242i	$0.129686\pi$
$293$	13.5651i	0.792484i	−0.918146	+	0.396242i	$0.870314\pi$
$294$	−4.89892	−0.285711
$295$	0	0
$296$	−9.37194	−0.544733
$297$	2.50913i	0.145595i
$298$	− 20.2474i	− 1.17290i
$299$	−7.27397	−0.420665
$300$	0	0
$301$	−9.22780	−0.531882
$302$	− 26.8250i	− 1.54360i
$303$	− 17.0211i	− 0.977835i
$304$	17.7411	1.01752
$305$	0	0
$306$	14.4541	0.826283
$307$	− 11.9672i	− 0.683007i	−0.939880	−	0.341504i	$-0.889064\pi$
$307$	− 11.9672i	− 0.683007i	0.939880	−	0.341504i	$-0.110936\pi$
$308$	− 13.8803i	− 0.790906i
$309$	−10.0859	−0.573767
$310$	0	0
$311$	7.66452	0.434615	0.217308	−	0.976103i	$-0.430273\pi$
$311$	7.66452	0.434615	0.217308	+	0.976103i	$0.430273\pi$
$312$	− 5.09151i	− 0.288250i
$313$	− 26.3840i	− 1.49131i	−0.666332	−	0.745655i	$-0.732137\pi$
$313$	− 26.3840i	− 1.49131i	0.666332	−	0.745655i	$-0.267863\pi$
$314$	−40.1030	−2.26315
$315$	0	0
$316$	19.8525	1.11679
$317$	− 10.8880i	− 0.611529i	−0.952107	−	0.305765i	$-0.901088\pi$
$317$	− 10.8880i	− 0.611529i	0.952107	−	0.305765i	$-0.0989121\pi$
$318$	17.5212i	0.982537i
$319$	11.1638	0.625053
$320$	0	0
$321$	5.67218	0.316590
$322$	− 7.76526i	− 0.432741i
$323$	− 46.3183i	− 2.57722i
$324$	−2.55073	−0.141707
$325$	0	0
$326$	15.5716	0.862431
$327$	− 8.34557i	− 0.461511i
$328$	− 13.1875i	− 0.728155i
$329$	−10.8146	−0.596227
$330$	0	0
$331$	−32.2137	−1.77062	−0.885312	−	0.464998i	$-0.846055\pi$
$331$	−32.2137	−1.77062	−0.885312	+	0.464998i	$0.846055\pi$
$332$	− 25.1938i	− 1.38269i
$333$	7.97720i	0.437148i
$334$	31.5701	1.72744
$335$	0	0
$336$	−5.62846	−0.307058
$337$	− 3.47169i	− 0.189115i	−0.995519	−	0.0945576i	$-0.969856\pi$
$337$	− 3.47169i	− 0.189115i	0.995519	−	0.0945576i	$-0.0301437\pi$
$338$	− 12.3339i	− 0.670875i
$339$	14.8224	0.805043
$340$	0	0
$341$	−16.4673	−0.891755
$342$	14.5829i	0.788553i
$343$	− 20.1618i	− 1.08864i
$344$	−4.99879	−0.269517
$345$	0	0
$346$	−4.89494	−0.263154
$347$	− 10.9805i	− 0.589465i	−0.955580	−	0.294733i	$-0.904769\pi$
$347$	− 10.9805i	− 0.589465i	0.955580	−	0.294733i	$-0.0952305\pi$
$348$	11.3489i	0.608364i
$349$	26.3158	1.40865	0.704325	−	0.709878i	$-0.251250\pi$
$349$	26.3158	1.40865	0.704325	+	0.709878i	$0.251250\pi$
$350$	0	0
$351$	−4.33379	−0.231321
$352$	19.7869i	1.05465i
$353$	16.3668i	0.871119i	0.900160	+	0.435559i	$0.143449\pi$
$353$	16.3668i	0.871119i	−0.900160	+	0.435559i	$0.856551\pi$
$354$	7.83788	0.416579
$355$	0	0
$356$	−3.16353	−0.167667
$357$	14.6947i	0.777727i
$358$	− 29.1480i	− 1.54052i
$359$	17.4871	0.922934	0.461467	−	0.887157i	$-0.347323\pi$
$359$	17.4871	0.922934	0.461467	+	0.887157i	$0.347323\pi$
$360$	0	0
$361$	27.7311	1.45953
$362$	18.5993i	0.977557i
$363$	− 4.70425i	− 0.246909i
$364$	23.9742	1.25659
$365$	0	0
$366$	−10.5374	−0.550798
$367$	8.29594i	0.433044i	0.976278	+	0.216522i	$0.0694714\pi$
$367$	8.29594i	0.433044i	−0.976278	+	0.216522i	$0.930529\pi$
$368$	4.35593i	0.227068i
$369$	−11.2249	−0.584345
$370$	0	0
$371$	−17.8129	−0.924799
$372$	− 16.7403i	− 0.867945i
$373$	19.1295i	0.990486i	0.868755	+	0.495243i	$0.164921\pi$
$373$	19.1295i	0.990486i	−0.868755	+	0.495243i	$0.835079\pi$
$374$	36.2671	1.87533
$375$	0	0
$376$	−5.85836	−0.302122
$377$	19.2822i	0.993085i
$378$	− 4.62650i	− 0.237962i
$379$	27.0952	1.39179	0.695894	−	0.718145i	$-0.255008\pi$
$379$	27.0952	1.39179	0.695894	+	0.718145i	$0.255008\pi$
$380$	0	0
$381$	−0.502113	−0.0257240
$382$	24.7627i	1.26697i
$383$	− 19.8026i	− 1.01187i	−0.862573	−	0.505933i	$-0.831148\pi$
$383$	− 19.8026i	− 1.01187i	0.862573	−	0.505933i	$-0.168852\pi$
$384$	−9.04239	−0.461443
$385$	0	0
$386$	−31.7112	−1.61406
$387$	4.25487i	0.216287i
$388$	38.3853i	1.94872i
$389$	23.0130	1.16680	0.583402	−	0.812183i	$-0.301721\pi$
$389$	23.0130	1.16680	0.583402	+	0.812183i	$0.301721\pi$
$390$	0	0
$391$	11.3724	0.575128
$392$	− 2.69798i	− 0.136269i
$393$	6.05788i	0.305580i
$394$	−48.7002	−2.45348
$395$	0	0
$396$	−6.40012	−0.321618
$397$	− 20.5745i	− 1.03260i	−0.856407	−	0.516301i	$-0.827309\pi$
$397$	− 20.5745i	− 1.03260i	0.856407	−	0.516301i	$-0.172691\pi$
$398$	− 12.5370i	− 0.628423i
$399$	−14.8257	−0.742214
$400$	0	0
$401$	−13.1542	−0.656889	−0.328444	−	0.944523i	$-0.606524\pi$
$401$	−13.1542	−0.656889	−0.328444	+	0.944523i	$0.606524\pi$
$402$	24.7056i	1.23220i
$403$	− 28.4425i	− 1.41682i
$404$	43.4161	2.16003
$405$	0	0
$406$	−20.5846	−1.02159
$407$	20.0159i	0.992150i
$408$	7.96027i	0.394092i
$409$	−2.76531	−0.136736	−0.0683679	−	0.997660i	$-0.521779\pi$
$409$	−2.76531	−0.136736	−0.0683679	+	0.997660i	$0.521779\pi$
$410$	0	0
$411$	−1.94014	−0.0956999
$412$	− 25.7264i	− 1.26745i
$413$	7.96839i	0.392099i
$414$	−3.58050	−0.175972
$415$	0	0
$416$	−34.1761	−1.67562
$417$	− 19.2023i	− 0.940340i
$418$	36.5904i	1.78970i
$419$	9.70852	0.474292	0.237146	−	0.971474i	$-0.423788\pi$
$419$	9.70852	0.474292	0.237146	+	0.971474i	$0.423788\pi$
$420$	0	0
$421$	−4.21745	−0.205546	−0.102773	−	0.994705i	$-0.532772\pi$
$421$	−4.21745	−0.205546	−0.102773	+	0.994705i	$0.532772\pi$
$422$	− 52.6664i	− 2.56376i
$423$	4.98652i	0.242453i
$424$	−9.64942	−0.468617
$425$	0	0
$426$	4.91181	0.237978
$427$	− 10.7128i	− 0.518430i
$428$	14.4682i	0.699347i
$429$	−10.8741	−0.525005
$430$	0	0
$431$	18.9785	0.914164	0.457082	−	0.889425i	$-0.348895\pi$
$431$	18.9785	0.914164	0.457082	+	0.889425i	$0.348895\pi$
$432$	2.59524i	0.124863i
$433$	− 13.7054i	− 0.658640i	−0.944218	−	0.329320i	$-0.893181\pi$
$433$	− 13.7054i	− 0.658640i	0.944218	−	0.329320i	$-0.106819\pi$
$434$	30.3635	1.45750
$435$	0	0
$436$	21.2873	1.01948
$437$	11.4738i	0.548866i
$438$	2.38068i	0.113753i
$439$	33.3843	1.59335	0.796673	−	0.604410i	$-0.206591\pi$
$439$	33.3843	1.59335	0.796673	+	0.604410i	$0.206591\pi$
$440$	0	0
$441$	−2.29646	−0.109355
$442$	62.6409i	2.97952i
$443$	− 11.6290i	− 0.552512i	−0.961084	−	0.276256i	$-0.910906\pi$
$443$	− 11.6290i	− 0.552512i	0.961084	−	0.276256i	$-0.0890938\pi$
$444$	−20.3477	−0.965659
$445$	0	0
$446$	−7.06231	−0.334410
$447$	− 9.49138i	− 0.448927i
$448$	− 25.2275i	− 1.19189i
$449$	13.3509	0.630069	0.315034	−	0.949080i	$-0.397984\pi$
$449$	13.3509	0.630069	0.315034	+	0.949080i	$0.397984\pi$
$450$	0	0
$451$	−28.1647	−1.32623
$452$	37.8080i	1.77834i
$453$	− 12.5747i	− 0.590813i
$454$	5.76371	0.270504
$455$	0	0
$456$	−8.03123	−0.376097
$457$	− 23.3042i	− 1.09013i	−0.838395	−	0.545063i	$-0.816506\pi$
$457$	− 23.3042i	− 1.09013i	0.838395	−	0.545063i	$-0.183494\pi$
$458$	19.9132i	0.930485i
$459$	6.77562	0.316259
$460$	0	0
$461$	5.03269	0.234396	0.117198	−	0.993109i	$-0.462609\pi$
$461$	5.03269	0.234396	0.117198	+	0.993109i	$0.462609\pi$
$462$	− 11.6085i	− 0.540077i
$463$	12.7759i	0.593746i	0.954917	+	0.296873i	$0.0959438\pi$
$463$	12.7759i	0.593746i	−0.954917	+	0.296873i	$0.904056\pi$
$464$	11.5469	0.536052
$465$	0	0
$466$	20.3190	0.941257
$467$	4.86284i	0.225025i	0.993650	+	0.112513i	$0.0358899\pi$
$467$	4.86284i	0.225025i	−0.993650	+	0.112513i	$0.964110\pi$
$468$	− 11.0543i	− 0.510987i
$469$	−25.1169	−1.15979
$470$	0	0
$471$	−18.7991	−0.866216
$472$	4.31655i	0.198685i
$473$	10.6760i	0.490884i
$474$	16.6032	0.762609
$475$	0	0
$476$	−37.4823	−1.71800
$477$	8.21338i	0.376065i
$478$	− 16.7385i	− 0.765599i
$479$	−4.79202	−0.218953	−0.109476	−	0.993989i	$-0.534917\pi$
$479$	−4.79202	−0.218953	−0.109476	+	0.993989i	$0.534917\pi$
$480$	0	0
$481$	−34.5715	−1.57633
$482$	3.04591i	0.138738i
$483$	− 3.64012i	− 0.165631i
$484$	11.9993	0.545421
$485$	0	0
$486$	−2.13324	−0.0967659
$487$	9.16949i	0.415509i	0.978181	+	0.207755i	$0.0666156\pi$
$487$	9.16949i	0.415509i	−0.978181	+	0.207755i	$0.933384\pi$
$488$	− 5.80325i	− 0.262701i
$489$	7.29949	0.330094
$490$	0	0
$491$	31.9054	1.43987	0.719935	−	0.694042i	$-0.244172\pi$
$491$	31.9054	1.43987	0.719935	+	0.694042i	$0.244172\pi$
$492$	− 28.6317i	− 1.29081i
$493$	− 30.1466i	− 1.35773i
$494$	−63.1992	−2.84347
$495$	0	0
$496$	−17.0324	−0.764778
$497$	4.99359i	0.223993i
$498$	− 21.0702i	− 0.944179i
$499$	−9.07297	−0.406162	−0.203081	−	0.979162i	$-0.565095\pi$
$499$	−9.07297	−0.406162	−0.203081	+	0.979162i	$0.565095\pi$
$500$	0	0
$501$	14.7991	0.661175
$502$	− 37.4944i	− 1.67346i
$503$	− 38.7485i	− 1.72771i	−0.503739	−	0.863856i	$-0.668043\pi$
$503$	− 38.7485i	− 1.72771i	0.503739	−	0.863856i	$-0.331957\pi$
$504$	2.54795	0.113495
$505$	0	0
$506$	−8.98396	−0.399386
$507$	− 5.78176i	− 0.256777i
$508$	− 1.28075i	− 0.0568243i
$509$	−32.9367	−1.45989	−0.729947	−	0.683503i	$-0.760455\pi$
$509$	−32.9367	−1.45989	−0.729947	+	0.683503i	$0.760455\pi$
$510$	0	0
$511$	−2.42032	−0.107069
$512$	26.5639i	1.17397i
$513$	6.83602i	0.301818i
$514$	41.1482	1.81497
$515$	0	0
$516$	−10.8530	−0.477777
$517$	12.5118i	0.550270i
$518$	− 36.9065i	− 1.62158i
$519$	−2.29460	−0.100722
$520$	0	0
$521$	−17.7521	−0.777735	−0.388867	−	0.921294i	$-0.627134\pi$
$521$	−17.7521	−0.777735	−0.388867	+	0.921294i	$0.627134\pi$
$522$	9.49138i	0.415426i
$523$	4.98678i	0.218056i	0.994039	+	0.109028i	$0.0347739\pi$
$523$	4.98678i	0.218056i	−0.994039	+	0.109028i	$0.965226\pi$
$524$	−15.4520	−0.675025
$525$	0	0
$526$	−47.4501	−2.06892
$527$	44.4681i	1.93706i
$528$	6.51180i	0.283390i
$529$	20.1829	0.877516
$530$	0	0
$531$	3.67416	0.159445
$532$	− 37.8164i	− 1.63955i
$533$	− 48.6463i	− 2.10711i
$534$	−2.64575	−0.114493
$535$	0	0
$536$	−13.6061	−0.587693
$537$	− 13.6637i	− 0.589632i
$538$	− 53.7120i	− 2.31569i
$539$	−5.76214	−0.248193
$540$	0	0
$541$	−3.49960	−0.150460	−0.0752298	−	0.997166i	$-0.523969\pi$
$541$	−3.49960	−0.150460	−0.0752298	+	0.997166i	$0.523969\pi$
$542$	− 12.1614i	− 0.522378i
$543$	8.71878i	0.374159i
$544$	53.4322	2.29089
$545$	0	0
$546$	20.0503	0.858073
$547$	− 17.4640i	− 0.746709i	−0.927689	−	0.373354i	$-0.878208\pi$
$547$	− 17.4640i	− 0.746709i	0.927689	−	0.373354i	$-0.121792\pi$
$548$	− 4.94877i	− 0.211401i
$549$	−4.93960	−0.210817
$550$	0	0
$551$	30.4153	1.29574
$552$	− 1.97189i	− 0.0839291i
$553$	16.8796i	0.717795i
$554$	−40.8752	−1.73662
$555$	0	0
$556$	48.9798	2.07721
$557$	6.02774i	0.255403i	0.991813	+	0.127702i	$0.0407600\pi$
$557$	6.02774i	0.255403i	−0.991813	+	0.127702i	$0.959240\pi$
$558$	− 14.0004i	− 0.592683i
$559$	−18.4397	−0.779917
$560$	0	0
$561$	17.0009	0.717780
$562$	9.30126i	0.392350i
$563$	− 9.19823i	− 0.387659i	−0.981035	−	0.193830i	$-0.937909\pi$
$563$	− 9.19823i	− 0.387659i	0.981035	−	0.193830i	$-0.0620909\pi$
$564$	−12.7193	−0.535577
$565$	0	0
$566$	−53.1351	−2.23343
$567$	− 2.16876i	− 0.0910795i
$568$	2.70508i	0.113503i
$569$	−9.06517	−0.380032	−0.190016	−	0.981781i	$-0.560854\pi$
$569$	−9.06517	−0.380032	−0.190016	+	0.981781i	$0.560854\pi$
$570$	0	0
$571$	−6.34688	−0.265609	−0.132804	−	0.991142i	$-0.542398\pi$
$571$	−6.34688	−0.265609	−0.132804	+	0.991142i	$0.542398\pi$
$572$	− 27.7368i	− 1.15973i
$573$	11.6080i	0.484931i
$574$	51.9320	2.16760
$575$	0	0
$576$	−11.6322	−0.484675
$577$	2.41418i	0.100504i	0.998737	+	0.0502519i	$0.0160024\pi$
$577$	2.41418i	0.100504i	−0.998737	+	0.0502519i	$0.983998\pi$
$578$	− 61.6700i	− 2.56513i
$579$	−14.8653	−0.617779
$580$	0	0
$581$	21.4211	0.888695
$582$	32.1027i	1.33070i
$583$	20.6085i	0.853516i
$584$	−1.31111	−0.0542541
$585$	0	0
$586$	−28.9378	−1.19541
$587$	4.50976i	0.186138i	0.995660	+	0.0930689i	$0.0296677\pi$
$587$	4.50976i	0.186138i	−0.995660	+	0.0930689i	$0.970332\pi$
$588$	− 5.85766i	− 0.241566i
$589$	−44.8645	−1.84861
$590$	0	0
$591$	−22.8292	−0.939067
$592$	20.7027i	0.850877i
$593$	33.2824i	1.36674i	0.730071	+	0.683371i	$0.239487\pi$
$593$	33.2824i	1.36674i	−0.730071	+	0.683371i	$0.760513\pi$
$594$	−5.35259	−0.219620
$595$	0	0
$596$	24.2099	0.991678
$597$	− 5.87697i	− 0.240528i
$598$	− 15.5172i	− 0.634544i
$599$	−39.1061	−1.59783	−0.798915	−	0.601444i	$-0.794592\pi$
$599$	−39.1061	−1.59783	−0.798915	+	0.601444i	$0.794592\pi$
$600$	0	0
$601$	−28.8076	−1.17509	−0.587543	−	0.809193i	$-0.699905\pi$
$601$	−28.8076	−1.17509	−0.587543	+	0.809193i	$0.699905\pi$
$602$	− 19.6852i	− 0.802307i
$603$	11.5812i	0.471624i
$604$	32.0747	1.30510
$605$	0	0
$606$	36.3101	1.47500
$607$	− 23.0933i	− 0.937327i	−0.883377	−	0.468663i	$-0.844736\pi$
$607$	− 23.0933i	− 0.937327i	0.883377	−	0.468663i	$-0.155264\pi$
$608$	53.9085i	2.18628i
$609$	−9.64942	−0.391014
$610$	0	0
$611$	−21.6105	−0.874268
$612$	17.2828i	0.698615i
$613$	18.2228i	0.736013i	0.929823	+	0.368007i	$0.119960\pi$
$613$	18.2228i	0.736013i	−0.929823	+	0.368007i	$0.880040\pi$
$614$	25.5291	1.03027
$615$	0	0
$616$	6.39315	0.257587
$617$	15.4484i	0.621930i	0.950421	+	0.310965i	$0.100652\pi$
$617$	15.4484i	0.621930i	−0.950421	+	0.310965i	$0.899348\pi$
$618$	− 21.5157i	− 0.865488i
$619$	−16.5042	−0.663359	−0.331680	−	0.943392i	$-0.607615\pi$
$619$	−16.5042	−0.663359	−0.331680	+	0.943392i	$0.607615\pi$
$620$	0	0
$621$	−1.67843	−0.0673531
$622$	16.3503i	0.655587i
$623$	− 2.68980i	− 0.107765i
$624$	−11.2472	−0.450249
$625$	0	0
$626$	56.2835	2.24954
$627$	17.1525i	0.685004i
$628$	− 47.9514i	− 1.91347i
$629$	54.0505	2.15513
$630$	0	0
$631$	−38.1237	−1.51768	−0.758841	−	0.651276i	$-0.774234\pi$
$631$	−38.1237	−1.51768	−0.758841	+	0.651276i	$0.774234\pi$
$632$	9.14386i	0.363723i
$633$	− 24.6884i	− 0.981276i
$634$	23.2267	0.922450
$635$	0	0
$636$	−20.9501	−0.830726
$637$	− 9.95240i	− 0.394329i
$638$	23.8151i	0.942850i
$639$	2.30251	0.0910858
$640$	0	0
$641$	38.9299	1.53764	0.768819	−	0.639466i	$-0.220845\pi$
$641$	38.9299	1.53764	0.768819	+	0.639466i	$0.220845\pi$
$642$	12.1002i	0.477555i
$643$	− 40.5346i	− 1.59853i	−0.600979	−	0.799265i	$-0.705222\pi$
$643$	− 40.5346i	− 1.59853i	0.600979	−	0.799265i	$-0.294778\pi$
$644$	9.28496	0.365879
$645$	0	0
$646$	98.8082	3.88755
$647$	31.8752i	1.25315i	0.779363	+	0.626573i	$0.215543\pi$
$647$	31.8752i	1.25315i	−0.779363	+	0.626573i	$0.784457\pi$
$648$	− 1.17484i	− 0.0461521i
$649$	9.21896	0.361876
$650$	0	0
$651$	14.2335	0.557855
$652$	18.6190i	0.729177i
$653$	19.5285i	0.764210i	0.924119	+	0.382105i	$0.124801\pi$
$653$	19.5285i	0.764210i	−0.924119	+	0.382105i	$0.875199\pi$
$654$	17.8031	0.696158
$655$	0	0
$656$	−29.1313	−1.13738
$657$	1.11599i	0.0435389i
$658$	− 23.0701i	− 0.899367i
$659$	−47.6562	−1.85642	−0.928211	−	0.372055i	$-0.878653\pi$
$659$	−47.6562	−1.85642	−0.928211	+	0.372055i	$0.878653\pi$
$660$	0	0
$661$	3.91738	0.152368	0.0761842	−	0.997094i	$-0.475726\pi$
$661$	3.91738	0.152368	0.0761842	+	0.997094i	$0.475726\pi$
$662$	− 68.7196i	− 2.67086i
$663$	29.3641i	1.14041i
$664$	11.6040	0.450322
$665$	0	0
$666$	−17.0173	−0.659408
$667$	7.46779i	0.289154i
$668$	37.7485i	1.46053i
$669$	−3.31060	−0.127995
$670$	0	0
$671$	−12.3941	−0.478470
$672$	− 17.1028i	− 0.659754i
$673$	− 28.1866i	− 1.08651i	−0.839566	−	0.543257i	$-0.817191\pi$
$673$	− 28.1866i	− 1.08651i	0.839566	−	0.543257i	$-0.182809\pi$
$674$	7.40597	0.285267
$675$	0	0
$676$	14.7477	0.567219
$677$	− 9.50611i	− 0.365350i	−0.983173	−	0.182675i	$-0.941524\pi$
$677$	− 9.50611i	− 0.365350i	0.983173	−	0.182675i	$-0.0584756\pi$
$678$	31.6198i	1.21435i
$679$	−32.6372	−1.25250
$680$	0	0
$681$	2.70185	0.103535
$682$	− 35.1288i	− 1.34515i
$683$	− 7.49565i	− 0.286813i	−0.989664	−	0.143407i	$-0.954194\pi$
$683$	− 7.49565i	− 0.286813i	0.989664	−	0.143407i	$-0.0458056\pi$
$684$	−17.4368	−0.666714
$685$	0	0
$686$	43.0101	1.64213
$687$	9.33473i	0.356142i
$688$	11.0424i	0.420987i
$689$	−35.5951	−1.35607
$690$	0	0
$691$	−0.745188	−0.0283483	−0.0141741	−	0.999900i	$-0.504512\pi$
$691$	−0.745188	−0.0283483	−0.0141741	+	0.999900i	$0.504512\pi$
$692$	− 5.85290i	− 0.222494i
$693$	− 5.44172i	− 0.206714i
$694$	23.4241	0.889167
$695$	0	0
$696$	−5.22718	−0.198136
$697$	76.0556i	2.88081i
$698$	56.1379i	2.12485i
$699$	9.52491	0.360265
$700$	0	0
$701$	31.6488	1.19536	0.597679	−	0.801735i	$-0.296090\pi$
$701$	31.6488	1.19536	0.597679	+	0.801735i	$0.296090\pi$
$702$	− 9.24504i	− 0.348931i
$703$	54.5323i	2.05672i
$704$	−29.1867	−1.10002
$705$	0	0
$706$	−34.9145	−1.31402
$707$	36.9147i	1.38832i
$708$	9.37179i	0.352214i
$709$	16.0181	0.601571	0.300785	−	0.953692i	$-0.402751\pi$
$709$	16.0181	0.601571	0.300785	+	0.953692i	$0.402751\pi$
$710$	0	0
$711$	7.78306	0.291888
$712$	− 1.45709i	− 0.0546068i
$713$	− 11.0155i	− 0.412532i
$714$	−31.3474	−1.17315
$715$	0	0
$716$	34.8524	1.30250
$717$	− 7.84648i	− 0.293032i
$718$	37.3043i	1.39218i
$719$	−14.3316	−0.534478	−0.267239	−	0.963630i	$-0.586111\pi$
$719$	−14.3316	−0.534478	−0.267239	+	0.963630i	$0.586111\pi$
$720$	0	0
$721$	21.8739	0.814628
$722$	59.1573i	2.20161i
$723$	1.42783i	0.0531016i
$724$	−22.2393	−0.826515
$725$	0	0
$726$	10.0353	0.372445
$727$	− 18.3551i	− 0.680755i	−0.940289	−	0.340377i	$-0.889445\pi$
$727$	− 18.3551i	− 0.680755i	0.940289	−	0.340377i	$-0.110555\pi$
$728$	11.0423i	0.409254i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	28.8294	1.06629
$732$	− 12.5996i	− 0.465694i
$733$	0.665145i	0.0245677i	0.999925	+	0.0122838i	$0.00391017\pi$
$733$	0.665145i	0.0245677i	−0.999925	+	0.0122838i	$0.996090\pi$
$734$	−17.6973	−0.653218
$735$	0	0
$736$	−13.2360	−0.487887
$737$	29.0588i	1.07040i
$738$	− 23.9454i	− 0.881443i
$739$	32.8332	1.20779	0.603895	−	0.797064i	$-0.293615\pi$
$739$	32.8332	1.20779	0.603895	+	0.797064i	$0.293615\pi$
$740$	0	0
$741$	−29.6259	−1.08833
$742$	− 37.9992i	− 1.39500i
$743$	− 29.6004i	− 1.08593i	−0.839754	−	0.542967i	$-0.817301\pi$
$743$	− 29.6004i	− 1.08593i	0.839754	−	0.542967i	$-0.182699\pi$
$744$	7.71042	0.282678
$745$	0	0
$746$	−40.8078	−1.49408
$747$	− 9.87708i	− 0.361383i
$748$	43.3648i	1.58557i
$749$	−12.3016	−0.449492
$750$	0	0
$751$	24.9709	0.911199	0.455600	−	0.890185i	$-0.349425\pi$
$751$	24.9709	0.911199	0.455600	+	0.890185i	$0.349425\pi$
$752$	12.9412i	0.471917i
$753$	− 17.5762i	− 0.640514i
$754$	−41.1337	−1.49800
$755$	0	0
$756$	5.53193	0.201194
$757$	11.2173i	0.407700i	0.979002	+	0.203850i	$0.0653455\pi$
$757$	11.2173i	0.407700i	−0.979002	+	0.203850i	$0.934655\pi$
$758$	57.8007i	2.09942i
$759$	−4.21141	−0.152864
$760$	0	0
$761$	19.3105	0.700004	0.350002	−	0.936749i	$-0.386181\pi$
$761$	19.3105	0.700004	0.350002	+	0.936749i	$0.386181\pi$
$762$	− 1.07113i	− 0.0388029i
$763$	18.0996i	0.655249i
$764$	−29.6089	−1.07121
$765$	0	0
$766$	42.2438	1.52633
$767$	15.9231i	0.574948i
$768$	3.97476i	0.143427i
$769$	19.3372	0.697318	0.348659	−	0.937250i	$-0.386637\pi$
$769$	19.3372	0.697318	0.348659	+	0.937250i	$0.386637\pi$
$770$	0	0
$771$	19.2890	0.694677
$772$	− 37.9172i	− 1.36467i
$773$	7.79217i	0.280265i	0.990133	+	0.140132i	$0.0447528\pi$
$773$	7.79217i	0.280265i	−0.990133	+	0.140132i	$0.955247\pi$
$774$	−9.07667	−0.326254
$775$	0	0
$776$	−17.6799	−0.634671
$777$	− 17.3007i	− 0.620658i
$778$	49.0923i	1.76004i
$779$	−76.7336	−2.74926
$780$	0	0
$781$	5.77730	0.206728
$782$	24.2601i	0.867540i
$783$	4.44927i	0.159004i
$784$	−5.95987	−0.212853
$785$	0	0
$786$	−12.9229	−0.460946
$787$	9.07666i	0.323548i	0.986828	+	0.161774i	$0.0517216\pi$
$787$	9.07666i	0.323548i	−0.986828	+	0.161774i	$0.948278\pi$
$788$	− 58.2311i	− 2.07440i
$789$	−22.2432	−0.791877
$790$	0	0
$791$	−32.1463	−1.14299
$792$	− 2.94783i	− 0.104747i
$793$	− 21.4072i	− 0.760192i
$794$	43.8903	1.55761
$795$	0	0
$796$	14.9906	0.531326
$797$	22.9954i	0.814541i	0.913308	+	0.407270i	$0.133519\pi$
$797$	22.9954i	0.814541i	−0.913308	+	0.407270i	$0.866481\pi$
$798$	− 31.6268i	− 1.11958i
$799$	33.7867	1.19529
$800$	0	0
$801$	−1.24025	−0.0438219
$802$	− 28.0611i	− 0.990872i
$803$	2.80017i	0.0988158i
$804$	−29.5406	−1.04182
$805$	0	0
$806$	60.6747	2.13718
$807$	− 25.1785i	− 0.886327i
$808$	19.9970i	0.703493i
$809$	50.6773	1.78172	0.890860	−	0.454278i	$-0.150103\pi$
$809$	50.6773	1.78172	0.890860	+	0.454278i	$0.150103\pi$
$810$	0	0
$811$	26.7614	0.939720	0.469860	−	0.882741i	$-0.344304\pi$
$811$	26.7614	0.939720	0.469860	+	0.882741i	$0.344304\pi$
$812$	− 24.6130i	− 0.863749i
$813$	− 5.70091i	− 0.199940i
$814$	−42.6987	−1.49659
$815$	0	0
$816$	17.5843	0.615575
$817$	29.0864i	1.01760i
$818$	− 5.89908i	− 0.206256i
$819$	9.39897	0.328427
$820$	0	0
$821$	−0.832947	−0.0290700	−0.0145350	−	0.999894i	$-0.504627\pi$
$821$	−0.832947	−0.0290700	−0.0145350	+	0.999894i	$0.504627\pi$
$822$	− 4.13879i	− 0.144357i
$823$	− 6.67034i	− 0.232514i	−0.993219	−	0.116257i	$-0.962910\pi$
$823$	− 6.67034i	− 0.232514i	0.993219	−	0.116257i	$-0.0370895\pi$
$824$	11.8493	0.412791
$825$	0	0
$826$	−16.9985	−0.591454
$827$	− 1.34470i	− 0.0467599i	−0.999727	−	0.0233799i	$-0.992557\pi$
$827$	− 1.34470i	− 0.0467599i	0.999727	−	0.0233799i	$-0.00744275\pi$
$828$	− 4.28122i	− 0.148783i
$829$	24.7770	0.860541	0.430270	−	0.902700i	$-0.358418\pi$
$829$	24.7770	0.860541	0.430270	+	0.902700i	$0.358418\pi$
$830$	0	0
$831$	−19.1611	−0.664690
$832$	− 50.4115i	− 1.74770i
$833$	15.5600i	0.539121i
$834$	40.9631	1.41844
$835$	0	0
$836$	−43.7513	−1.51317
$837$	− 6.56295i	− 0.226849i
$838$	20.7106i	0.715437i
$839$	6.72534	0.232184	0.116092	−	0.993238i	$-0.462963\pi$
$839$	6.72534	0.232184	0.116092	+	0.993238i	$0.462963\pi$
$840$	0	0
$841$	−9.20399	−0.317379
$842$	− 8.99685i	− 0.310052i
$843$	4.36015i	0.150171i
$844$	62.9734	2.16763
$845$	0	0
$846$	−10.6375	−0.365723
$847$	10.2024i	0.350559i
$848$	21.3157i	0.731984i
$849$	−24.9081	−0.854844
$850$	0	0
$851$	−13.3892	−0.458975
$852$	5.87307i	0.201208i
$853$	16.7244i	0.572632i	0.958135	+	0.286316i	$0.0924307\pi$
$853$	16.7244i	0.572632i	−0.958135	+	0.286316i	$0.907569\pi$
$854$	22.8531	0.782016
$855$	0	0
$856$	−6.66391	−0.227768
$857$	12.9930i	0.443831i	0.975066	+	0.221915i	$0.0712309\pi$
$857$	12.9930i	0.443831i	−0.975066	+	0.221915i	$0.928769\pi$
$858$	− 23.1970i	− 0.791933i
$859$	36.5682	1.24769	0.623845	−	0.781548i	$-0.285570\pi$
$859$	36.5682	1.24769	0.623845	+	0.781548i	$0.285570\pi$
$860$	0	0
$861$	24.3441	0.829646
$862$	40.4859i	1.37895i
$863$	46.3384i	1.57738i	0.614794	+	0.788688i	$0.289239\pi$
$863$	46.3384i	1.57738i	−0.614794	+	0.788688i	$0.710761\pi$
$864$	−7.88596	−0.268286
$865$	0	0
$866$	29.2370	0.993513
$867$	− 28.9090i	− 0.981802i
$868$	36.3058i	1.23230i
$869$	19.5287	0.662467
$870$	0	0
$871$	−50.1906	−1.70064
$872$	9.80472i	0.332030i
$873$	15.0488i	0.509323i
$874$	−24.4764	−0.827926
$875$	0	0
$876$	−2.84659	−0.0961773
$877$	− 44.2548i	− 1.49438i	−0.664611	−	0.747190i	$-0.731403\pi$
$877$	− 44.2548i	− 1.49438i	0.664611	−	0.747190i	$-0.268597\pi$
$878$	71.2169i	2.40345i
$879$	−13.5651	−0.457541
$880$	0	0
$881$	−42.2495	−1.42342	−0.711712	−	0.702472i	$-0.752080\pi$
$881$	−42.2495	−1.42342	−0.711712	+	0.702472i	$0.752080\pi$
$882$	− 4.89892i	− 0.164955i
$883$	− 3.49289i	− 0.117545i	−0.998271	−	0.0587726i	$-0.981281\pi$
$883$	− 3.49289i	− 0.117545i	0.998271	−	0.0587726i	$-0.0187187\pi$
$884$	−74.9000	−2.51916
$885$	0	0
$886$	24.8076	0.833427
$887$	14.7275i	0.494501i	0.968952	+	0.247250i	$0.0795270\pi$
$887$	14.7275i	0.494501i	−0.968952	+	0.247250i	$0.920473\pi$
$888$	− 9.37194i	− 0.314502i
$889$	1.08896	0.0365227
$890$	0	0
$891$	−2.50913	−0.0840591
$892$	− 8.44444i	− 0.282741i
$893$	34.0879i	1.14071i
$894$	20.2474	0.677175
$895$	0	0
$896$	19.6108	0.655151
$897$	− 7.27397i	− 0.242871i
$898$	28.4808i	0.950416i
$899$	−29.2004	−0.973886
$900$	0	0
$901$	55.6508	1.85400
$902$	− 60.0823i	− 2.00052i
$903$	− 9.22780i	− 0.307082i
$904$	−17.4140	−0.579180
$905$	0	0
$906$	26.8250	0.891200
$907$	7.33785i	0.243649i	0.992552	+	0.121825i	$0.0388746\pi$
$907$	7.33785i	0.243649i	−0.992552	+	0.121825i	$0.961125\pi$
$908$	6.89169i	0.228709i
$909$	17.0211	0.564553
$910$	0	0
$911$	−53.5731	−1.77496	−0.887479	−	0.460849i	$-0.847545\pi$
$911$	−53.5731	−1.77496	−0.887479	+	0.460849i	$0.847545\pi$
$912$	17.7411i	0.587466i
$913$	− 24.7829i	− 0.820195i
$914$	49.7136	1.64438
$915$	0	0
$916$	−23.8104	−0.786717
$917$	− 13.1381i	− 0.433859i
$918$	14.4541i	0.477055i
$919$	43.2016	1.42509	0.712545	−	0.701627i	$-0.247542\pi$
$919$	43.2016	1.42509	0.712545	+	0.701627i	$0.247542\pi$
$920$	0	0
$921$	11.9672	0.394334
$922$	10.7359i	0.353570i
$923$	9.97859i	0.328449i
$924$	13.8803	0.456630
$925$	0	0
$926$	−27.2541	−0.895625
$927$	− 10.0859i	− 0.331264i
$928$	35.0868i	1.15178i
$929$	14.8420	0.486951	0.243476	−	0.969907i	$-0.421712\pi$
$929$	14.8420	0.486951	0.243476	+	0.969907i	$0.421712\pi$
$930$	0	0
$931$	−15.6987	−0.514503
$932$	24.2955i	0.795824i
$933$	7.66452i	0.250925i
$934$	−10.3736	−0.339435
$935$	0	0
$936$	5.09151	0.166421
$937$	− 3.75611i	− 0.122707i	−0.998116	−	0.0613534i	$-0.980458\pi$
$937$	− 3.75611i	− 0.122707i	0.998116	−	0.0613534i	$-0.0195417\pi$
$938$	− 53.5805i	− 1.74947i
$939$	26.3840	0.861008
$940$	0	0
$941$	59.9208	1.95336	0.976682	−	0.214692i	$-0.0688747\pi$
$941$	59.9208	1.95336	0.976682	+	0.214692i	$0.0688747\pi$
$942$	− 40.1030i	− 1.30663i
$943$	− 18.8402i	− 0.613521i
$944$	9.53532	0.310348
$945$	0	0
$946$	−22.7746	−0.740465
$947$	− 24.4212i	− 0.793581i	−0.917909	−	0.396791i	$-0.870124\pi$
$947$	− 24.4212i	− 0.793581i	0.917909	−	0.396791i	$-0.129876\pi$
$948$	19.8525i	0.644779i
$949$	−4.83647	−0.156998
$950$	0	0
$951$	10.8880	0.353067
$952$	− 17.2639i	− 0.559528i
$953$	36.6466i	1.18710i	0.804797	+	0.593550i	$0.202274\pi$
$953$	36.6466i	1.18710i	−0.804797	+	0.593550i	$0.797726\pi$
$954$	−17.5212	−0.567268
$955$	0	0
$956$	20.0142	0.647307
$957$	11.1638i	0.360875i
$958$	− 10.2225i	− 0.330275i
$959$	4.20770	0.135874
$960$	0	0
$961$	12.0723	0.389431
$962$	− 73.7495i	− 2.37778i
$963$	5.67218i	0.182784i
$964$	−3.64201	−0.117301
$965$	0	0
$966$	7.76526	0.249843
$967$	− 47.4395i	− 1.52555i	−0.646663	−	0.762776i	$-0.723836\pi$
$967$	− 47.4395i	− 1.52555i	0.646663	−	0.762776i	$-0.276164\pi$
$968$	5.52674i	0.177636i
$969$	46.3183	1.48796
$970$	0	0
$971$	−5.68782	−0.182531	−0.0912655	−	0.995827i	$-0.529091\pi$
$971$	−5.68782	−0.182531	−0.0912655	+	0.995827i	$0.529091\pi$
$972$	− 2.55073i	− 0.0818147i
$973$	41.6452i	1.33508i
$974$	−19.5608	−0.626767
$975$	0	0
$976$	−12.8194	−0.410340
$977$	2.29901i	0.0735518i	0.999324	+	0.0367759i	$0.0117088\pi$
$977$	2.29901i	0.0735518i	−0.999324	+	0.0367759i	$0.988291\pi$
$978$	15.5716i	0.497925i
$979$	−3.11194	−0.0994581
$980$	0	0
$981$	8.34557	0.266454
$982$	68.0620i	2.17194i
$983$	− 2.35879i	− 0.0752336i	−0.999292	−	0.0376168i	$-0.988023\pi$
$983$	− 2.35879i	− 0.0752336i	0.999292	−	0.0376168i	$-0.0119766\pi$
$984$	13.1875	0.420401
$985$	0	0
$986$	64.3100	2.04805
$987$	− 10.8146i	− 0.344232i
$988$	− 75.5676i	− 2.40413i
$989$	−7.14150	−0.227087
$990$	0	0
$991$	−7.76677	−0.246720	−0.123360	−	0.992362i	$-0.539367\pi$
$991$	−7.76677	−0.246720	−0.123360	+	0.992362i	$0.539367\pi$
$992$	− 51.7552i	− 1.64323i
$993$	− 32.2137i	− 1.02227i
$994$	−10.6526	−0.337879
$995$	0	0
$996$	25.1938	0.798295
$997$	− 8.35947i	− 0.264747i	−0.991200	−	0.132374i	$-0.957740\pi$
$997$	− 8.35947i	− 0.264747i	0.991200	−	0.132374i	$-0.0422598\pi$
$998$	− 19.3549i	− 0.612668i
$999$	−7.97720	−0.252388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1875.2.b.e.1249.10		12
5.2	odd	4		1875.2.a.i.1.2	✓	6
5.3	odd	4		1875.2.a.l.1.5	yes	6
5.4	even	2	inner	1875.2.b.e.1249.3		12
15.2	even	4		5625.2.a.r.1.5		6
15.8	even	4		5625.2.a.o.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1875.2.a.i.1.2	✓	6	5.2	odd	4
1875.2.a.l.1.5	yes	6	5.3	odd	4
1875.2.b.e.1249.3		12	5.4	even	2	inner
1875.2.b.e.1249.10		12	1.1	even	1	trivial
5625.2.a.o.1.2		6	15.8	even	4
5625.2.a.r.1.5		6	15.2	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:	\( N \)	\(=\)	\( 1875 = 3 \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1875.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.13324i q^{2} +1.00000i q^{3} -2.55073 q^{4} -2.13324 q^{6} -2.16876i q^{7} -1.17484i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+2.13324i q^{2} +1.00000i q^{3} -2.55073 q^{4} -2.13324 q^{6} -2.16876i q^{7} -1.17484i q^{8} -1.00000 q^{9} -2.50913 q^{11} -2.55073i q^{12} -4.33379i q^{13} +4.62650 q^{14} -2.59524 q^{16} +6.77562i q^{17} -2.13324i q^{18} -6.83602 q^{19} +2.16876 q^{21} -5.35259i q^{22} -1.67843i q^{23} +1.17484 q^{24} +9.24504 q^{26} -1.00000i q^{27} +5.53193i q^{28} -4.44927 q^{29} +6.56295 q^{31} -7.88596i q^{32} -2.50913i q^{33} -14.4541 q^{34} +2.55073 q^{36} -7.97720i q^{37} -14.5829i q^{38} +4.33379 q^{39} +11.2249 q^{41} +4.62650i q^{42} -4.25487i q^{43} +6.40012 q^{44} +3.58050 q^{46} -4.98652i q^{47} -2.59524i q^{48} +2.29646 q^{49} -6.77562 q^{51} +11.0543i q^{52} -8.21338i q^{53} +2.13324 q^{54} -2.54795 q^{56} -6.83602i q^{57} -9.49138i q^{58} -3.67416 q^{59} +4.93960 q^{61} +14.0004i q^{62} +2.16876i q^{63} +11.6322 q^{64} +5.35259 q^{66} -11.5812i q^{67} -17.2828i q^{68} +1.67843 q^{69} -2.30251 q^{71} +1.17484i q^{72} -1.11599i q^{73} +17.0173 q^{74} +17.4368 q^{76} +5.44172i q^{77} +9.24504i q^{78} -7.78306 q^{79} +1.00000 q^{81} +23.9454i q^{82} +9.87708i q^{83} -5.53193 q^{84} +9.07667 q^{86} -4.44927i q^{87} +2.94783i q^{88} +1.24025 q^{89} -9.39897 q^{91} +4.28122i q^{92} +6.56295i q^{93} +10.6375 q^{94} +7.88596 q^{96} -15.0488i q^{97} +4.89892i q^{98} +2.50913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9	\( 12 q - 22 q^{4} - 2 q^{6} - 12 q^{9} + 8 q^{14} + 34 q^{16} + 4 q^{19} + 4 q^{21} + 12 q^{24} + 74 q^{26} - 62 q^{29} - 4 q^{31} - 74 q^{34} + 22 q^{36} + 66 q^{41} + 22 q^{44} - 24 q^{46} - 8 q^{49} - 4 q^{51} + 2 q^{54} - 60 q^{56} + 16 q^{59} + 68 q^{61} - 24 q^{64} - 18 q^{66} - 2 q^{69} - 6 q^{71} - 72 q^{74} + 54 q^{76} - 50 q^{79} + 12 q^{81} - 88 q^{84} - 60 q^{86} - 36 q^{89} + 56 q^{91} + 100 q^{94} - 66 q^{96}+O(q^{100}) \) 12 * q - 22 * q^4 - 2 * q^6 - 12 * q^9 + 8 * q^14 + 34 * q^16 + 4 * q^19 + 4 * q^21 + 12 * q^24 + 74 * q^26 - 62 * q^29 - 4 * q^31 - 74 * q^34 + 22 * q^36 + 66 * q^41 + 22 * q^44 - 24 * q^46 - 8 * q^49 - 4 * q^51 + 2 * q^54 - 60 * q^56 + 16 * q^59 + 68 * q^61 - 24 * q^64 - 18 * q^66 - 2 * q^69 - 6 * q^71 - 72 * q^74 + 54 * q^76 - 50 * q^79 + 12 * q^81 - 88 * q^84 - 60 * q^86 - 36 * q^89 + 56 * q^91 + 100 * q^94 - 66 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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