LMFDB - Embedded newform 1875.2.b.e.1249.3

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

$q$-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	$-0.728017\pi$
$2$	− 2.13324i	− 1.50843i	0.656627	−	0.754216i	$-0.271983\pi$
$3$	− 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	$0.134422\pi$
$7$	2.16876i	0.819716i	−0.912149	+	0.409858i	$0.865578\pi$
$8$	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	$0.205226\pi$
$13$	4.33379i	1.20198i	−0.799257	+	0.600989i	$0.794774\pi$
$14$	4.62650	1.23648
$15$	0	0
$16$	−2.59524	−0.648810
$17$	− 6.77562i	− 1.64333i	−0.569971	−	0.821665i	$-0.693046\pi$
$17$	− 6.77562i	− 1.64333i	0.569971	−	0.821665i	$-0.306954\pi$
$18$	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	$0.0559888\pi$
$23$	1.67843i	0.349977i	−0.984570	+	0.174989i	$0.944011\pi$
$24$	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	$0.227636\pi$
$37$	7.97720i	1.31144i	−0.755002	+	0.655722i	$0.772364\pi$
$38$	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	$0.105173\pi$
$43$	4.25487i	0.648861i	−0.945909	+	0.324431i	$0.894827\pi$
$44$	6.40012	0.964854
$45$	0	0
$46$	3.58050	0.527916
$47$	4.98652i	0.727358i	0.931524	+	0.363679i	$0.118479\pi$
$47$	4.98652i	0.727358i	−0.931524	+	0.363679i	$0.881521\pi$
$48$	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	$0.190776\pi$
$53$	8.21338i	1.12820i	−0.825708	+	0.564098i	$0.809224\pi$
$54$	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	$0.250148\pi$
$67$	11.5812i	1.41487i	−0.706778	+	0.707436i	$0.749852\pi$
$68$	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	$0.0208031\pi$
$73$	1.11599i	0.130617i	−0.997865	+	0.0653084i	$0.979197\pi$
$74$	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	$-0.817639\pi$
$83$	− 9.87708i	− 1.08415i	0.840330	−	0.542075i	$-0.182361\pi$
$84$	−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	$0.276760\pi$
$97$	15.0488i	1.52797i	−0.645234	+	0.763985i	$0.723240\pi$
$98$	− 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	$-0.834473\pi$
$103$	− 10.0859i	− 0.993793i	0.867810	−	0.496897i	$-0.165527\pi$
$104$	−5.09151	−0.499264
$105$	0	0
$106$	17.5212	1.70180
$107$	5.67218i	0.548351i	0.961680	+	0.274175i	$0.0884049\pi$
$107$	5.67218i	0.548351i	−0.961680	+	0.274175i	$0.911595\pi$
$108$	− 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	$0.245566\pi$
$113$	14.8224i	1.39438i	−0.716888	+	0.697188i	$0.754434\pi$
$114$	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	$-0.992908\pi$
$127$	− 0.502113i	− 0.0445553i	0.999752	−	0.0222777i	$-0.00709179\pi$
$128$	− 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	$-0.973589\pi$
$137$	− 1.94014i	− 0.165757i	0.996560	−	0.0828786i	$-0.0264114\pi$
$138$	− 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	$-0.729974\pi$
$157$	− 18.7991i	− 1.50033i	0.661250	−	0.750165i	$-0.270026\pi$
$158$	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	$0.0922826\pi$
$163$	7.29949i	0.571740i	−0.958268	+	0.285870i	$0.907717\pi$
$164$	−28.6317	−2.23576
$165$	0	0
$166$	−21.0702	−1.63537
$167$	14.7991i	1.14519i	0.819839	+	0.572594i	$0.194063\pi$
$167$	14.7991i	1.14519i	−0.819839	+	0.572594i	$0.805937\pi$
$168$	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	$-0.972199\pi$
$173$	− 2.29460i	− 0.174455i	0.996188	−	0.0872276i	$-0.0278007\pi$
$174$	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	$-0.820307\pi$
$193$	− 14.8653i	− 1.07002i	0.844844	−	0.535012i	$-0.179693\pi$
$194$	32.1027	2.30484
$195$	0	0
$196$	−5.85766	−0.418404
$197$	− 22.8292i	− 1.62651i	−0.581906	−	0.813256i	$-0.697693\pi$
$197$	− 22.8292i	− 1.62651i	0.581906	−	0.813256i	$-0.302307\pi$
$198$	− 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	$-0.964644\pi$
$223$	− 3.31060i	− 0.221694i	0.993837	−	0.110847i	$-0.0353563\pi$
$224$	−17.1028	−1.14273
$225$	0	0
$226$	31.6198	2.10332
$227$	2.70185i	0.179328i	0.995972	+	0.0896641i	$0.0285793\pi$
$227$	2.70185i	0.179328i	−0.995972	+	0.0896641i	$0.971421\pi$
$228$	− 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	$0.100998\pi$
$233$	9.52491i	0.623998i	−0.950083	+	0.311999i	$0.899002\pi$
$234$	−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	$0.205473\pi$
$257$	19.2890i	1.20322i	−0.798791	+	0.601608i	$0.794527\pi$
$258$	− 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	$-0.759459\pi$
$263$	− 22.2432i	− 1.37157i	0.727803	−	0.685786i	$-0.240541\pi$
$264$	−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	$-0.804754\pi$
$277$	− 19.1611i	− 1.15128i	0.817704	−	0.575638i	$-0.195246\pi$
$278$	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	$-0.734676\pi$
$283$	− 24.9081i	− 1.48063i	0.672258	−	0.740317i	$-0.265324\pi$
$284$	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	$-0.870314\pi$
$293$	− 13.5651i	− 0.792484i	0.918146	−	0.396242i	$-0.129686\pi$
$294$	−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	$0.110936\pi$
$307$	11.9672i	0.683007i	−0.939880	+	0.341504i	$0.889064\pi$
$308$	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	$0.267863\pi$
$313$	26.3840i	1.49131i	−0.666332	+	0.745655i	$0.732137\pi$
$314$	−40.1030	−2.26315
$315$	0	0
$316$	19.8525	1.11679
$317$	10.8880i	0.611529i	0.952107	+	0.305765i	$0.0989121\pi$
$317$	10.8880i	0.611529i	−0.952107	+	0.305765i	$0.901088\pi$
$318$	− 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	$0.0301437\pi$
$337$	3.47169i	0.189115i	−0.995519	+	0.0945576i	$0.969856\pi$
$338$	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	$0.0952305\pi$
$347$	10.9805i	0.589465i	−0.955580	+	0.294733i	$0.904769\pi$
$348$	− 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	$-0.856551\pi$
$353$	− 16.3668i	− 0.871119i	0.900160	−	0.435559i	$-0.143449\pi$
$354$	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	$-0.930529\pi$
$367$	− 8.29594i	− 0.433044i	0.976278	−	0.216522i	$-0.0694714\pi$
$368$	− 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	$-0.835079\pi$
$373$	− 19.1295i	− 0.990486i	0.868755	−	0.495243i	$-0.164921\pi$
$374$	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	$0.168852\pi$
$383$	19.8026i	1.01187i	−0.862573	+	0.505933i	$0.831148\pi$
$384$	−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	$0.172691\pi$
$397$	20.5745i	1.03260i	−0.856407	+	0.516301i	$0.827309\pi$
$398$	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	$0.106819\pi$
$433$	13.7054i	0.658640i	−0.944218	+	0.329320i	$0.893181\pi$
$434$	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	$0.0890938\pi$
$443$	11.6290i	0.552512i	−0.961084	+	0.276256i	$0.910906\pi$
$444$	−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	$0.183494\pi$
$457$	23.3042i	1.09013i	−0.838395	+	0.545063i	$0.816506\pi$
$458$	− 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	$-0.904056\pi$
$463$	− 12.7759i	− 0.593746i	0.954917	−	0.296873i	$-0.0959438\pi$
$464$	11.5469	0.536052
$465$	0	0
$466$	20.3190	0.941257
$467$	− 4.86284i	− 0.225025i	−0.993650	−	0.112513i	$-0.964110\pi$
$467$	− 4.86284i	− 0.225025i	0.993650	−	0.112513i	$-0.0358899\pi$
$468$	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	$-0.933384\pi$
$487$	− 9.16949i	− 0.415509i	0.978181	−	0.207755i	$-0.0666156\pi$
$488$	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	$0.331957\pi$
$503$	38.7485i	1.72771i	−0.503739	+	0.863856i	$0.668043\pi$
$504$	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	$-0.965226\pi$
$523$	− 4.98678i	− 0.218056i	0.994039	−	0.109028i	$-0.0347739\pi$
$524$	−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	$0.121792\pi$
$547$	17.4640i	0.746709i	−0.927689	+	0.373354i	$0.878208\pi$
$548$	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	$-0.959240\pi$
$557$	− 6.02774i	− 0.255403i	0.991813	−	0.127702i	$-0.0407600\pi$
$558$	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	$0.0620909\pi$
$563$	9.19823i	0.387659i	−0.981035	+	0.193830i	$0.937909\pi$
$564$	−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	$-0.983998\pi$
$577$	− 2.41418i	− 0.100504i	0.998737	−	0.0502519i	$-0.0160024\pi$
$578$	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	$-0.970332\pi$
$587$	− 4.50976i	− 0.186138i	0.995660	−	0.0930689i	$-0.0296677\pi$
$588$	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	$-0.760513\pi$
$593$	− 33.2824i	− 1.36674i	0.730071	−	0.683371i	$-0.239487\pi$
$594$	−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	$0.155264\pi$
$607$	23.0933i	0.937327i	−0.883377	+	0.468663i	$0.844736\pi$
$608$	− 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	$-0.880040\pi$
$613$	− 18.2228i	− 0.736013i	0.929823	−	0.368007i	$-0.119960\pi$
$614$	25.5291	1.03027
$615$	0	0
$616$	6.39315	0.257587
$617$	− 15.4484i	− 0.621930i	−0.950421	−	0.310965i	$-0.899348\pi$
$617$	− 15.4484i	− 0.621930i	0.950421	−	0.310965i	$-0.100652\pi$
$618$	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	$0.294778\pi$
$643$	40.5346i	1.59853i	−0.600979	+	0.799265i	$0.705222\pi$
$644$	9.28496	0.365879
$645$	0	0
$646$	98.8082	3.88755
$647$	− 31.8752i	− 1.25315i	−0.779363	−	0.626573i	$-0.784457\pi$
$647$	− 31.8752i	− 1.25315i	0.779363	−	0.626573i	$-0.215543\pi$
$648$	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	$-0.875199\pi$
$653$	− 19.5285i	− 0.764210i	0.924119	−	0.382105i	$-0.124801\pi$
$654$	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	$0.182809\pi$
$673$	28.1866i	1.08651i	−0.839566	+	0.543257i	$0.817191\pi$
$674$	7.40597	0.285267
$675$	0	0
$676$	14.7477	0.567219
$677$	9.50611i	0.365350i	0.983173	+	0.182675i	$0.0584756\pi$
$677$	9.50611i	0.365350i	−0.983173	+	0.182675i	$0.941524\pi$
$678$	− 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	$0.0458056\pi$
$683$	7.49565i	0.286813i	−0.989664	+	0.143407i	$0.954194\pi$
$684$	−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	$0.110555\pi$
$727$	18.3551i	0.680755i	−0.940289	+	0.340377i	$0.889445\pi$
$728$	− 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	$-0.996090\pi$
$733$	− 0.665145i	− 0.0245677i	0.999925	−	0.0122838i	$-0.00391017\pi$
$734$	−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	$0.182699\pi$
$743$	29.6004i	1.08593i	−0.839754	+	0.542967i	$0.817301\pi$
$744$	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	$-0.934655\pi$
$757$	− 11.2173i	− 0.407700i	0.979002	−	0.203850i	$-0.0653455\pi$
$758$	− 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	$-0.955247\pi$
$773$	− 7.79217i	− 0.280265i	0.990133	−	0.140132i	$-0.0447528\pi$
$774$	−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	$-0.948278\pi$
$787$	− 9.07666i	− 0.323548i	0.986828	−	0.161774i	$-0.0517216\pi$
$788$	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	$-0.866481\pi$
$797$	− 22.9954i	− 0.814541i	0.913308	−	0.407270i	$-0.133519\pi$
$798$	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	$0.0370895\pi$
$823$	6.67034i	0.232514i	−0.993219	+	0.116257i	$0.962910\pi$
$824$	11.8493	0.412791
$825$	0	0
$826$	−16.9985	−0.591454
$827$	1.34470i	0.0467599i	0.999727	+	0.0233799i	$0.00744275\pi$
$827$	1.34470i	0.0467599i	−0.999727	+	0.0233799i	$0.992557\pi$
$828$	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	$-0.907569\pi$
$853$	− 16.7244i	− 0.572632i	0.958135	−	0.286316i	$-0.0924307\pi$
$854$	22.8531	0.782016
$855$	0	0
$856$	−6.66391	−0.227768
$857$	− 12.9930i	− 0.443831i	−0.975066	−	0.221915i	$-0.928769\pi$
$857$	− 12.9930i	− 0.443831i	0.975066	−	0.221915i	$-0.0712309\pi$
$858$	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	$-0.710761\pi$
$863$	− 46.3384i	− 1.57738i	0.614794	−	0.788688i	$-0.289239\pi$
$864$	−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	$0.268597\pi$
$877$	44.2548i	1.49438i	−0.664611	+	0.747190i	$0.731403\pi$
$878$	− 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	$0.0187187\pi$
$883$	3.49289i	0.117545i	−0.998271	+	0.0587726i	$0.981281\pi$
$884$	−74.9000	−2.51916
$885$	0	0
$886$	24.8076	0.833427
$887$	− 14.7275i	− 0.494501i	−0.968952	−	0.247250i	$-0.920473\pi$
$887$	− 14.7275i	− 0.494501i	0.968952	−	0.247250i	$-0.0795270\pi$
$888$	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	$-0.961125\pi$
$907$	− 7.33785i	− 0.243649i	0.992552	−	0.121825i	$-0.0388746\pi$
$908$	− 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	$0.0195417\pi$
$937$	3.75611i	0.122707i	−0.998116	+	0.0613534i	$0.980458\pi$
$938$	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	$0.129876\pi$
$947$	24.4212i	0.793581i	−0.917909	+	0.396791i	$0.870124\pi$
$948$	− 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	$-0.797726\pi$
$953$	− 36.6466i	− 1.18710i	0.804797	−	0.593550i	$-0.202274\pi$
$954$	−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	$0.276164\pi$
$967$	47.4395i	1.52555i	−0.646663	+	0.762776i	$0.723836\pi$
$968$	− 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	$-0.988291\pi$
$977$	− 2.29901i	− 0.0735518i	0.999324	−	0.0367759i	$-0.0117088\pi$
$978$	− 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	$0.0119766\pi$
$983$	2.35879i	0.0752336i	−0.999292	+	0.0376168i	$0.988023\pi$
$984$	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	$0.0422598\pi$
$997$	8.35947i	0.264747i	−0.991200	+	0.132374i	$0.957740\pi$
$998$	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.1249.3		12
5.2	odd	4		1875.2.a.l.1.5	yes	6
5.3	odd	4		1875.2.a.i.1.2	✓	6
5.4	even	2	inner	1875.2.b.e.1249.10		12
15.2	even	4		5625.2.a.o.1.2		6
15.8	even	4		5625.2.a.r.1.5		6

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