LMFDB - Embedded newform 925.2.b.g.149.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(149,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.149"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-12,0,-4,0,0,-4,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

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

Embedding invariants

Embedding label			149.5
Root			$-1.21974 + 1.21974i$ of defining polynomial
Character	$\chi$	$=$	925.149
Dual form			925.2.b.g.149.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.180152i q^{2} -3.06709i q^{3} +1.96755 q^{4} -0.552543 q^{6} -4.41500i q^{7} -0.714762i q^{8} -6.40702 q^{9} +4.27171 q^{11} -6.03463i q^{12} -2.79978i q^{13} -0.795373 q^{14} +3.80632 q^{16} +4.43948i q^{17} +1.15424i q^{18} -2.43507 q^{19} -13.5412 q^{21} -0.769559i q^{22} +5.77387i q^{23} -2.19224 q^{24} -0.504387 q^{26} +10.4496i q^{27} -8.68672i q^{28} -0.409254 q^{29} +7.79180 q^{31} -2.11524i q^{32} -13.1017i q^{33} +0.799782 q^{34} -12.6061 q^{36} +1.00000i q^{37} +0.438683i q^{38} -8.58717 q^{39} +0.757374 q^{41} +2.43948i q^{42} +2.19908i q^{43} +8.40479 q^{44} +1.04018 q^{46} +4.26487i q^{47} -11.6743i q^{48} -12.4922 q^{49} +13.6163 q^{51} -5.50870i q^{52} -0.137540i q^{53} +1.88253 q^{54} -3.15568 q^{56} +7.46857i q^{57} +0.0737281i q^{58} +3.07119 q^{59} -3.02909 q^{61} -1.40371i q^{62} +28.2870i q^{63} +7.23158 q^{64} -2.36030 q^{66} +11.4482i q^{67} +8.73487i q^{68} +17.7090 q^{69} -10.7144 q^{71} +4.57950i q^{72} +8.20680i q^{73} +0.180152 q^{74} -4.79111 q^{76} -18.8596i q^{77} +1.54700i q^{78} -7.11193 q^{79} +12.8289 q^{81} -0.136443i q^{82} -11.3625i q^{83} -26.6429 q^{84} +0.396170 q^{86} +1.25522i q^{87} -3.05326i q^{88} +16.2305 q^{89} -12.3610 q^{91} +11.3603i q^{92} -23.8981i q^{93} +0.768326 q^{94} -6.48763 q^{96} -18.3399i q^{97} +2.25051i q^{98} -27.3690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9} + 14 q^{11} - 8 q^{14} + 16 q^{16} - 28 q^{19} - 18 q^{21} - 24 q^{24} - 40 q^{26} - 4 q^{29} + 16 q^{31} - 24 q^{34} - 72 q^{36} - 24 q^{39} - 18 q^{41} - 36 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) $ 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9 + 14 * q^11 - 8 * q^14 + 16 * q^16 - 28 * q^19 - 18 * q^21 - 24 * q^24 - 40 * q^26 - 4 * q^29 + 16 * q^31 - 24 * q^34 - 72 * q^36 - 24 * q^39 - 18 * q^41 - 36 * q^44 - 56 * q^46 - 4 * q^49 + 20 * q^51 + 24 * q^54 - 28 * q^56 - 24 * q^59 + 24 * q^61 - 24 * q^64 - 20 * q^66 + 60 * q^69 + 26 * q^71 + 36 * q^76 - 72 * q^79 + 42 * q^81 - 60 * q^84 - 16 * q^86 + 32 * q^89 - 8 * q^91 - 40 * q^94 - 36 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	− 0.180152i	− 0.127387i	−0.997970	−	0.0636934i	$-0.979712\pi$
$2$	− 0.180152i	− 0.127387i	0.997970	−	0.0636934i	$-0.0202880\pi$
$3$	− 3.06709i	− 1.77078i	−0.464846	−	0.885392i	$-0.653890\pi$
$3$	− 3.06709i	− 1.77078i	0.464846	−	0.885392i	$-0.346110\pi$
$4$	1.96755	0.983773
$5$	0	0
$5$	0	0
$6$	−0.552543	−0.225575
$7$	− 4.41500i	− 1.66871i	−0.551224	−	0.834357i	$-0.685839\pi$
$7$	− 4.41500i	− 1.66871i	0.551224	−	0.834357i	$-0.314161\pi$
$8$	− 0.714762i	− 0.252707i
$9$	−6.40702	−2.13567
$10$	0	0
$11$	4.27171	1.28797	0.643985	−	0.765038i	$-0.277280\pi$
$11$	4.27171	1.28797	0.643985	+	0.765038i	$0.277280\pi$
$12$	− 6.03463i	− 1.74205i
$13$	− 2.79978i	− 0.776520i	−0.921550	−	0.388260i	$-0.873076\pi$
$13$	− 2.79978i	− 0.776520i	0.921550	−	0.388260i	$-0.126924\pi$
$14$	−0.795373	−0.212572
$15$	0	0
$16$	3.80632	0.951581
$17$	4.43948i	1.07673i	0.842711	+	0.538366i	$0.180958\pi$
$17$	4.43948i	1.07673i	−0.842711	+	0.538366i	$0.819042\pi$
$18$	1.15424i	0.272057i
$19$	−2.43507	−0.558643	−0.279321	−	0.960198i	$-0.590110\pi$
$19$	−2.43507	−0.558643	−0.279321	+	0.960198i	$0.590110\pi$
$20$	0	0
$21$	−13.5412	−2.95493
$22$	− 0.769559i	− 0.164071i
$23$	5.77387i	1.20393i	0.798521	+	0.601967i	$0.205616\pi$
$23$	5.77387i	1.20393i	−0.798521	+	0.601967i	$0.794384\pi$
$24$	−2.19224	−0.447489
$25$	0	0
$26$	−0.504387	−0.0989184
$27$	10.4496i	2.01103i
$28$	− 8.68672i	− 1.64164i
$29$	−0.409254	−0.0759967	−0.0379983	−	0.999278i	$-0.512098\pi$
$29$	−0.409254	−0.0759967	−0.0379983	+	0.999278i	$0.512098\pi$
$30$	0	0
$31$	7.79180	1.39945	0.699724	−	0.714413i	$-0.253306\pi$
$31$	7.79180	1.39945	0.699724	+	0.714413i	$0.253306\pi$
$32$	− 2.11524i	− 0.373926i
$33$	− 13.1017i	− 2.28072i
$34$	0.799782	0.137161
$35$	0	0
$36$	−12.6061	−2.10102
$37$	1.00000i	0.164399i
$37$	1.00000i	0.164399i
$38$	0.438683i	0.0711638i
$39$	−8.58717	−1.37505
$40$	0	0
$41$	0.757374	0.118282	0.0591410	−	0.998250i	$-0.481164\pi$
$41$	0.757374	0.118282	0.0591410	+	0.998250i	$0.481164\pi$
$42$	2.43948i	0.376420i
$43$	2.19908i	0.335357i	0.985842	+	0.167679i	$0.0536271\pi$
$43$	2.19908i	0.335357i	−0.985842	+	0.167679i	$0.946373\pi$
$44$	8.40479	1.26707
$45$	0	0
$46$	1.04018	0.153366
$47$	4.26487i	0.622095i	0.950394	+	0.311048i	$0.100680\pi$
$47$	4.26487i	0.622095i	−0.950394	+	0.311048i	$0.899320\pi$
$48$	− 11.6743i	− 1.68504i
$49$	−12.4922	−1.78461
$50$	0	0
$51$	13.6163	1.90666
$52$	− 5.50870i	− 0.763919i
$53$	− 0.137540i	− 0.0188926i	−0.999955	−	0.00944630i	$-0.996993\pi$
$53$	− 0.137540i	− 0.0188926i	0.999955	−	0.00944630i	$-0.00300690\pi$
$54$	1.88253	0.256179
$55$	0	0
$56$	−3.15568	−0.421695
$57$	7.46857i	0.989236i
$58$	0.0737281i	0.00968098i
$59$	3.07119	0.399835	0.199918	−	0.979813i	$-0.435933\pi$
$59$	3.07119	0.399835	0.199918	+	0.979813i	$0.435933\pi$
$60$	0	0
$61$	−3.02909	−0.387835	−0.193918	−	0.981018i	$-0.562119\pi$
$61$	−3.02909	−0.387835	−0.193918	+	0.981018i	$0.562119\pi$
$62$	− 1.40371i	− 0.178271i
$63$	28.2870i	3.56383i
$64$	7.23158	0.903948
$65$	0	0
$66$	−2.36030	−0.290533
$67$	11.4482i	1.39862i	0.714819	+	0.699310i	$0.246509\pi$
$67$	11.4482i	1.39862i	−0.714819	+	0.699310i	$0.753491\pi$
$68$	8.73487i	1.05926i
$69$	17.7090	2.13191
$70$	0	0
$71$	−10.7144	−1.27156	−0.635781	−	0.771870i	$-0.719322\pi$
$71$	−10.7144	−1.27156	−0.635781	+	0.771870i	$0.719322\pi$
$72$	4.57950i	0.539699i
$73$	8.20680i	0.960534i	0.877122	+	0.480267i	$0.159460\pi$
$73$	8.20680i	0.960534i	−0.877122	+	0.480267i	$0.840540\pi$
$74$	0.180152	0.0209423
$75$	0	0
$76$	−4.79111	−0.549578
$77$	− 18.8596i	− 2.14925i
$78$	1.54700i	0.175163i
$79$	−7.11193	−0.800155	−0.400077	−	0.916481i	$-0.631017\pi$
$79$	−7.11193	−0.800155	−0.400077	+	0.916481i	$0.631017\pi$
$80$	0	0
$81$	12.8289	1.42543
$82$	− 0.136443i	− 0.0150676i
$83$	− 11.3625i	− 1.24719i	−0.781746	−	0.623597i	$-0.785671\pi$
$83$	− 11.3625i	− 1.24719i	0.781746	−	0.623597i	$-0.214329\pi$
$84$	−26.6429	−2.90698
$85$	0	0
$86$	0.396170	0.0427201
$87$	1.25522i	0.134574i
$88$	− 3.05326i	− 0.325479i
$89$	16.2305	1.72043	0.860214	−	0.509933i	$-0.170330\pi$
$89$	16.2305	1.72043	0.860214	+	0.509933i	$0.170330\pi$
$90$	0	0
$91$	−12.3610	−1.29579
$92$	11.3603i	1.18440i
$93$	− 23.8981i	− 2.47812i
$94$	0.768326	0.0792468
$95$	0	0
$96$	−6.48763	−0.662141
$97$	− 18.3399i	− 1.86213i	−0.364850	−	0.931066i	$-0.618880\pi$
$97$	− 18.3399i	− 1.86213i	0.364850	−	0.931066i	$-0.381120\pi$
$98$	2.25051i	0.227336i
$99$	−27.3690	−2.75068
$100$	0	0
$101$	−11.1319	−1.10767	−0.553835	−	0.832627i	$-0.686836\pi$
$101$	−11.1319	−1.10767	−0.553835	+	0.832627i	$0.686836\pi$
$102$	− 2.45300i	− 0.242883i
$103$	6.78105i	0.668157i	0.942545	+	0.334079i	$0.108425\pi$
$103$	6.78105i	0.668157i	−0.942545	+	0.334079i	$0.891575\pi$
$104$	−2.00118	−0.196232
$105$	0	0
$106$	−0.0247782	−0.00240667
$107$	− 0.536583i	− 0.0518734i	−0.999664	−	0.0259367i	$-0.991743\pi$
$107$	− 0.536583i	− 0.0518734i	0.999664	−	0.0259367i	$-0.00825684\pi$
$108$	20.5601i	1.97840i
$109$	−9.53465	−0.913254	−0.456627	−	0.889658i	$-0.650943\pi$
$109$	−9.53465	−0.913254	−0.456627	+	0.889658i	$0.650943\pi$
$110$	0	0
$111$	3.06709	0.291115
$112$	− 16.8049i	− 1.58792i
$113$	9.16830i	0.862481i	0.902237	+	0.431240i	$0.141924\pi$
$113$	9.16830i	0.862481i	−0.902237	+	0.431240i	$0.858076\pi$
$114$	1.34548	0.126016
$115$	0	0
$116$	−0.805227	−0.0747634
$117$	17.9383i	1.65839i
$118$	− 0.553282i	− 0.0509338i
$119$	19.6003	1.79676
$120$	0	0
$121$	7.24754	0.658867
$122$	0.545697i	0.0494051i
$123$	− 2.32293i	− 0.209452i
$124$	15.3307	1.37674
$125$	0	0
$126$	5.09597	0.453985
$127$	− 9.32621i	− 0.827567i	−0.910375	−	0.413784i	$-0.864207\pi$
$127$	− 9.32621i	− 0.827567i	0.910375	−	0.413784i	$-0.135793\pi$
$128$	− 5.53327i	− 0.489077i
$129$	6.74478	0.593845
$130$	0	0
$131$	15.6006	1.36303	0.681515	−	0.731804i	$-0.261321\pi$
$131$	15.6006	1.36303	0.681515	+	0.731804i	$0.261321\pi$
$132$	− 25.7782i	− 2.24371i
$133$	10.7508i	0.932215i
$134$	2.06242	0.178166
$135$	0	0
$136$	3.17317	0.272097
$137$	1.01986i	0.0871326i	0.999051	+	0.0435663i	$0.0138720\pi$
$137$	1.01986i	0.0871326i	−0.999051	+	0.0435663i	$0.986128\pi$
$138$	− 3.19031i	− 0.271577i
$139$	−7.08913	−0.601292	−0.300646	−	0.953736i	$-0.597202\pi$
$139$	−7.08913	−0.601292	−0.300646	+	0.953736i	$0.597202\pi$
$140$	0	0
$141$	13.0807	1.10160
$142$	1.93022i	0.161980i
$143$	− 11.9599i	− 1.00013i
$144$	−24.3872	−2.03227
$145$	0	0
$146$	1.47847	0.122359
$147$	38.3148i	3.16015i
$148$	1.96755i	0.161731i
$149$	15.5572	1.27449	0.637246	−	0.770660i	$-0.280074\pi$
$149$	15.5572	1.27449	0.637246	+	0.770660i	$0.280074\pi$
$150$	0	0
$151$	−4.00882	−0.326233	−0.163117	−	0.986607i	$-0.552155\pi$
$151$	−4.00882	−0.326233	−0.163117	+	0.986607i	$0.552155\pi$
$152$	1.74049i	0.141173i
$153$	− 28.4438i	− 2.29955i
$154$	−3.39761	−0.273787
$155$	0	0
$156$	−16.8957	−1.35273
$157$	− 3.06585i	− 0.244682i	−0.992488	−	0.122341i	$-0.960960\pi$
$157$	− 3.06585i	− 0.244682i	0.992488	−	0.122341i	$-0.0390401\pi$
$158$	1.28123i	0.101929i
$159$	−0.421848	−0.0334547
$160$	0	0
$161$	25.4916	2.00902
$162$	− 2.31115i	− 0.181581i
$163$	2.90600i	0.227616i	0.993503	+	0.113808i	$0.0363048\pi$
$163$	2.90600i	0.227616i	−0.993503	+	0.113808i	$0.963695\pi$
$164$	1.49017	0.116363
$165$	0	0
$166$	−2.04698	−0.158876
$167$	23.5324i	1.82099i	0.413519	+	0.910495i	$0.364299\pi$
$167$	23.5324i	1.82099i	−0.413519	+	0.910495i	$0.635701\pi$
$168$	9.67874i	0.746731i
$169$	5.16122	0.397017
$170$	0	0
$171$	15.6015	1.19308
$172$	4.32680i	0.329915i
$173$	− 18.6902i	− 1.42099i	−0.703703	−	0.710495i	$-0.748471\pi$
$173$	− 18.6902i	− 1.42099i	0.703703	−	0.710495i	$-0.251529\pi$
$174$	0.226131	0.0171429
$175$	0	0
$176$	16.2595	1.22561
$177$	− 9.41962i	− 0.708022i
$178$	− 2.92396i	− 0.219160i
$179$	1.22059	0.0912310	0.0456155	−	0.998959i	$-0.485475\pi$
$179$	1.22059	0.0912310	0.0456155	+	0.998959i	$0.485475\pi$
$180$	0	0
$181$	−23.8124	−1.76996	−0.884982	−	0.465626i	$-0.845829\pi$
$181$	−23.8124	−1.76996	−0.884982	+	0.465626i	$0.845829\pi$
$182$	2.22687i	0.165067i
$183$	9.29048i	0.686772i
$184$	4.12694	0.304242
$185$	0	0
$186$	−4.30530	−0.315680
$187$	18.9642i	1.38680i
$188$	8.39132i	0.612000i
$189$	46.1352	3.35584
$190$	0	0
$191$	14.9462	1.08147	0.540736	−	0.841192i	$-0.318146\pi$
$191$	14.9462	1.08147	0.540736	+	0.841192i	$0.318146\pi$
$192$	− 22.1799i	− 1.60070i
$193$	− 18.9075i	− 1.36099i	−0.732753	−	0.680495i	$-0.761765\pi$
$193$	− 18.9075i	− 1.36099i	0.732753	−	0.680495i	$-0.238235\pi$
$194$	−3.30397	−0.237211
$195$	0	0
$196$	−24.5791	−1.75565
$197$	− 3.72602i	− 0.265468i	−0.991152	−	0.132734i	$-0.957624\pi$
$197$	− 3.72602i	− 0.265468i	0.991152	−	0.132734i	$-0.0423756\pi$
$198$	4.93058i	0.350401i
$199$	18.7237	1.32729	0.663645	−	0.748048i	$-0.269009\pi$
$199$	18.7237	1.32729	0.663645	+	0.748048i	$0.269009\pi$
$200$	0	0
$201$	35.1126	2.47665
$202$	2.00544i	0.141103i
$203$	1.80686i	0.126817i
$204$	26.7906	1.87572
$205$	0	0
$206$	1.22162	0.0851145
$207$	− 36.9933i	− 2.57121i
$208$	− 10.6569i	− 0.738922i
$209$	−10.4019	−0.719516
$210$	0	0
$211$	−13.3971	−0.922295	−0.461148	−	0.887323i	$-0.652562\pi$
$211$	−13.3971	−0.922295	−0.461148	+	0.887323i	$0.652562\pi$
$212$	− 0.270617i	− 0.0185860i
$213$	32.8619i	2.25166i
$214$	−0.0966666	−0.00660800
$215$	0	0
$216$	7.46900	0.508201
$217$	− 34.4008i	− 2.33528i
$218$	1.71769i	0.116337i
$219$	25.1710	1.70090
$220$	0	0
$221$	12.4296	0.836103
$222$	− 0.552543i	− 0.0370842i
$223$	− 17.4471i	− 1.16834i	−0.811630	−	0.584172i	$-0.801419\pi$
$223$	− 17.4471i	− 1.16834i	0.811630	−	0.584172i	$-0.198581\pi$
$224$	−9.33880	−0.623975
$225$	0	0
$226$	1.65169	0.109869
$227$	− 20.4988i	− 1.36056i	−0.732954	−	0.680278i	$-0.761859\pi$
$227$	− 20.4988i	− 1.36056i	0.732954	−	0.680278i	$-0.238141\pi$
$228$	14.6947i	0.973183i
$229$	14.0698	0.929756	0.464878	−	0.885375i	$-0.346098\pi$
$229$	14.0698	0.929756	0.464878	+	0.885375i	$0.346098\pi$
$230$	0	0
$231$	−57.8441	−3.80586
$232$	0.292520i	0.0192049i
$233$	15.1114i	0.989983i	0.868898	+	0.494992i	$0.164829\pi$
$233$	15.1114i	0.989983i	−0.868898	+	0.494992i	$0.835171\pi$
$234$	3.23162	0.211258
$235$	0	0
$236$	6.04271	0.393347
$237$	21.8129i	1.41690i
$238$	− 3.53104i	− 0.228883i
$239$	−0.0747636	−0.00483606	−0.00241803	−	0.999997i	$-0.500770\pi$
$239$	−0.0747636	−0.00483606	−0.00241803	+	0.999997i	$0.500770\pi$
$240$	0	0
$241$	20.4873	1.31971	0.659853	−	0.751395i	$-0.270619\pi$
$241$	20.4873	1.31971	0.659853	+	0.751395i	$0.270619\pi$
$242$	− 1.30566i	− 0.0839311i
$243$	− 7.99836i	− 0.513095i
$244$	−5.95987	−0.381541
$245$	0	0
$246$	−0.418482	−0.0266814
$247$	6.81766i	0.433797i
$248$	− 5.56929i	− 0.353650i
$249$	−34.8497	−2.20851
$250$	0	0
$251$	−6.85355	−0.432592	−0.216296	−	0.976328i	$-0.569398\pi$
$251$	−6.85355	−0.432592	−0.216296	+	0.976328i	$0.569398\pi$
$252$	55.6560i	3.50600i
$253$	24.6643i	1.55063i
$254$	−1.68014	−0.105421
$255$	0	0
$256$	13.4663	0.841646
$257$	10.4751i	0.653422i	0.945124	+	0.326711i	$0.105940\pi$
$257$	10.4751i	0.653422i	−0.945124	+	0.326711i	$0.894060\pi$
$258$	− 1.21509i	− 0.0756481i
$259$	4.41500	0.274335
$260$	0	0
$261$	2.62210	0.162304
$262$	− 2.81048i	− 0.173632i
$263$	5.99787i	0.369844i	0.982753	+	0.184922i	$0.0592033\pi$
$263$	5.99787i	0.369844i	−0.982753	+	0.184922i	$0.940797\pi$
$264$	−9.36461	−0.576352
$265$	0	0
$266$	1.93679	0.118752
$267$	− 49.7803i	− 3.04651i
$268$	22.5248i	1.37592i
$269$	2.32781	0.141929	0.0709646	−	0.997479i	$-0.477392\pi$
$269$	2.32781	0.141929	0.0709646	+	0.997479i	$0.477392\pi$
$270$	0	0
$271$	−6.13081	−0.372420	−0.186210	−	0.982510i	$-0.559620\pi$
$271$	−6.13081	−0.372420	−0.186210	+	0.982510i	$0.559620\pi$
$272$	16.8981i	1.02460i
$273$	37.9124i	2.29456i
$274$	0.183730	0.0110996
$275$	0	0
$276$	34.8432	2.09731
$277$	8.30966i	0.499279i	0.968339	+	0.249639i	$0.0803121\pi$
$277$	8.30966i	0.499279i	−0.968339	+	0.249639i	$0.919688\pi$
$278$	1.27712i	0.0765967i
$279$	−49.9223	−2.98877
$280$	0	0
$281$	−5.01313	−0.299058	−0.149529	−	0.988757i	$-0.547776\pi$
$281$	−5.01313	−0.299058	−0.149529	+	0.988757i	$0.547776\pi$
$282$	− 2.35652i	− 0.140329i
$283$	12.5308i	0.744876i	0.928057	+	0.372438i	$0.121478\pi$
$283$	12.5308i	0.744876i	−0.928057	+	0.372438i	$0.878522\pi$
$284$	−21.0810	−1.25093
$285$	0	0
$286$	−2.15460	−0.127404
$287$	− 3.34381i	− 0.197379i
$288$	13.5524i	0.798583i
$289$	−2.70896	−0.159351
$290$	0	0
$291$	−56.2500	−3.29743
$292$	16.1473i	0.944947i
$293$	− 6.13130i	− 0.358194i	−0.983831	−	0.179097i	$-0.942682\pi$
$293$	− 6.13130i	− 0.358194i	0.983831	−	0.179097i	$-0.0573176\pi$
$294$	6.90250	0.402562
$295$	0	0
$296$	0.714762	0.0415447
$297$	44.6379i	2.59015i
$298$	− 2.80266i	− 0.162354i
$299$	16.1656	0.934879
$300$	0	0
$301$	9.70896	0.559615
$302$	0.722198i	0.0415578i
$303$	34.1426i	1.96144i
$304$	−9.26866	−0.531594
$305$	0	0
$306$	−5.12422	−0.292932
$307$	− 12.6426i	− 0.721552i	−0.932652	−	0.360776i	$-0.882512\pi$
$307$	− 12.6426i	− 0.721552i	0.932652	−	0.360776i	$-0.117488\pi$
$308$	− 37.1072i	− 2.11438i
$309$	20.7981	1.18316
$310$	0	0
$311$	8.05133	0.456549	0.228275	−	0.973597i	$-0.426692\pi$
$311$	8.05133	0.456549	0.228275	+	0.973597i	$0.426692\pi$
$312$	6.13779i	0.347484i
$313$	− 2.99549i	− 0.169315i	−0.996410	−	0.0846576i	$-0.973020\pi$
$313$	− 2.99549i	− 0.169315i	0.996410	−	0.0846576i	$-0.0269796\pi$
$314$	−0.552321	−0.0311693
$315$	0	0
$316$	−13.9930	−0.787170
$317$	− 2.24377i	− 0.126023i	−0.998013	−	0.0630113i	$-0.979930\pi$
$317$	− 2.24377i	− 0.126023i	0.998013	−	0.0630113i	$-0.0200704\pi$
$318$	0.0759969i	0.00426169i
$319$	−1.74822	−0.0978814
$320$	0	0
$321$	−1.64575	−0.0918566
$322$	− 4.59238i	− 0.255923i
$323$	− 10.8104i	− 0.601508i
$324$	25.2414	1.40230
$325$	0	0
$326$	0.523523	0.0289952
$327$	29.2436i	1.61718i
$328$	− 0.541343i	− 0.0298906i
$329$	18.8294	1.03810
$330$	0	0
$331$	1.73477	0.0953518	0.0476759	−	0.998863i	$-0.484819\pi$
$331$	1.73477	0.0953518	0.0476759	+	0.998863i	$0.484819\pi$
$332$	− 22.3562i	− 1.22696i
$333$	− 6.40702i	− 0.351103i
$334$	4.23941	0.231970
$335$	0	0
$336$	−51.5422	−2.81186
$337$	29.9565i	1.63183i	0.578169	+	0.815917i	$0.303768\pi$
$337$	29.9565i	1.63183i	−0.578169	+	0.815917i	$0.696232\pi$
$338$	− 0.929806i	− 0.0505748i
$339$	28.1200	1.52727
$340$	0	0
$341$	33.2844	1.80245
$342$	− 2.81065i	− 0.151983i
$343$	24.2483i	1.30928i
$344$	1.57182	0.0847470
$345$	0	0
$346$	−3.36708	−0.181015
$347$	14.9978i	0.805123i	0.915393	+	0.402561i	$0.131880\pi$
$347$	14.9978i	0.805123i	−0.915393	+	0.402561i	$0.868120\pi$
$348$	2.46970i	0.132390i
$349$	7.29913	0.390714	0.195357	−	0.980732i	$-0.437414\pi$
$349$	7.29913	0.390714	0.195357	+	0.980732i	$0.437414\pi$
$350$	0	0
$351$	29.2567	1.56161
$352$	− 9.03571i	− 0.481605i
$353$	− 12.6061i	− 0.670957i	−0.942048	−	0.335479i	$-0.891102\pi$
$353$	− 12.6061i	− 0.670957i	0.942048	−	0.335479i	$-0.108898\pi$
$354$	−1.69697	−0.0901927
$355$	0	0
$356$	31.9342	1.69251
$357$	− 60.1158i	− 3.18167i
$358$	− 0.219892i	− 0.0116216i
$359$	−21.5358	−1.13661	−0.568307	−	0.822817i	$-0.692401\pi$
$359$	−21.5358	−1.13661	−0.568307	+	0.822817i	$0.692401\pi$
$360$	0	0
$361$	−13.0704	−0.687918
$362$	4.28986i	0.225470i
$363$	− 22.2288i	− 1.16671i
$364$	−24.3209	−1.27476
$365$	0	0
$366$	1.67370	0.0874857
$367$	− 20.1463i	− 1.05163i	−0.850600	−	0.525814i	$-0.823761\pi$
$367$	− 20.1463i	− 1.05163i	0.850600	−	0.525814i	$-0.176239\pi$
$368$	21.9772i	1.14564i
$369$	−4.85251	−0.252612
$370$	0	0
$371$	−0.607241	−0.0315264
$372$	− 47.0207i	− 2.43791i
$373$	9.88395i	0.511772i	0.966707	+	0.255886i	$0.0823671\pi$
$373$	9.88395i	0.511772i	−0.966707	+	0.255886i	$0.917633\pi$
$374$	3.41644	0.176660
$375$	0	0
$376$	3.04837	0.157208
$377$	1.14582i	0.0590129i
$378$	− 8.31135i	− 0.427490i
$379$	−26.5438	−1.36346	−0.681732	−	0.731602i	$-0.738773\pi$
$379$	−26.5438	−1.36346	−0.681732	+	0.731602i	$0.738773\pi$
$380$	0	0
$381$	−28.6043	−1.46544
$382$	− 2.69260i	− 0.137765i
$383$	1.43834i	0.0734959i	0.999325	+	0.0367479i	$0.0116999\pi$
$383$	1.43834i	0.0734959i	−0.999325	+	0.0367479i	$0.988300\pi$
$384$	−16.9710	−0.866049
$385$	0	0
$386$	−3.40623	−0.173372
$387$	− 14.0896i	− 0.716214i
$388$	− 36.0845i	− 1.83192i
$389$	−28.7600	−1.45819	−0.729094	−	0.684414i	$-0.760058\pi$
$389$	−28.7600	−1.45819	−0.729094	+	0.684414i	$0.760058\pi$
$390$	0	0
$391$	−25.6330	−1.29631
$392$	8.92899i	0.450982i
$393$	− 47.8484i	− 2.41363i
$394$	−0.671250	−0.0338171
$395$	0	0
$396$	−53.8497	−2.70605
$397$	− 33.8486i	− 1.69881i	−0.527740	−	0.849406i	$-0.676960\pi$
$397$	− 33.8486i	− 1.69881i	0.527740	−	0.849406i	$-0.323040\pi$
$398$	− 3.37312i	− 0.169079i
$399$	32.9737	1.65075
$400$	0	0
$401$	−20.7788	−1.03764	−0.518822	−	0.854883i	$-0.673629\pi$
$401$	−20.7788	−1.03764	−0.518822	+	0.854883i	$0.673629\pi$
$402$	− 6.32562i	− 0.315493i
$403$	− 21.8153i	− 1.08670i
$404$	−21.9026	−1.08970
$405$	0	0
$406$	0.325510	0.0161548
$407$	4.27171i	0.211741i
$408$	− 9.73239i	− 0.481825i
$409$	3.46191	0.171180	0.0855902	−	0.996330i	$-0.472722\pi$
$409$	3.46191	0.171180	0.0855902	+	0.996330i	$0.472722\pi$
$410$	0	0
$411$	3.12800	0.154293
$412$	13.3420i	0.657315i
$413$	− 13.5593i	− 0.667211i
$414$	−6.66443	−0.327539
$415$	0	0
$416$	−5.92222	−0.290361
$417$	21.7430i	1.06476i
$418$	1.87393i	0.0916569i
$419$	18.7259	0.914818	0.457409	−	0.889256i	$-0.348777\pi$
$419$	18.7259	0.914818	0.457409	+	0.889256i	$0.348777\pi$
$420$	0	0
$421$	1.91518	0.0933404	0.0466702	−	0.998910i	$-0.485139\pi$
$421$	1.91518	0.0933404	0.0466702	+	0.998910i	$0.485139\pi$
$422$	2.41352i	0.117488i
$423$	− 27.3251i	− 1.32859i
$424$	−0.0983086	−0.00477429
$425$	0	0
$426$	5.92015	0.286832
$427$	13.3734i	0.647186i
$428$	− 1.05575i	− 0.0510317i
$429$	−36.6820	−1.77102
$430$	0	0
$431$	6.17915	0.297639	0.148820	−	0.988864i	$-0.452453\pi$
$431$	6.17915	0.297639	0.148820	+	0.988864i	$0.452453\pi$
$432$	39.7747i	1.91366i
$433$	− 11.7275i	− 0.563588i	−0.959475	−	0.281794i	$-0.909071\pi$
$433$	− 11.7275i	− 0.563588i	0.959475	−	0.281794i	$-0.0909294\pi$
$434$	−6.19739	−0.297484
$435$	0	0
$436$	−18.7599	−0.898434
$437$	− 14.0598i	− 0.672570i
$438$	− 4.53461i	− 0.216672i
$439$	18.4724	0.881640	0.440820	−	0.897595i	$-0.354688\pi$
$439$	18.4724	0.881640	0.440820	+	0.897595i	$0.354688\pi$
$440$	0	0
$441$	80.0381	3.81134
$442$	− 2.23922i	− 0.106509i
$443$	3.81261i	0.181142i	0.995890	+	0.0905712i	$0.0288693\pi$
$443$	3.81261i	0.181142i	−0.995890	+	0.0905712i	$0.971131\pi$
$444$	6.03463	0.286391
$445$	0	0
$446$	−3.14313	−0.148832
$447$	− 47.7152i	− 2.25685i
$448$	− 31.9275i	− 1.50843i
$449$	4.81563	0.227264	0.113632	−	0.993523i	$-0.463752\pi$
$449$	4.81563	0.227264	0.113632	+	0.993523i	$0.463752\pi$
$450$	0	0
$451$	3.23529	0.152344
$452$	18.0390i	0.848485i
$453$	12.2954i	0.577688i
$454$	−3.69291	−0.173317
$455$	0	0
$456$	5.33825	0.249986
$457$	27.2012i	1.27242i	0.771516	+	0.636210i	$0.219499\pi$
$457$	27.2012i	1.27242i	−0.771516	+	0.636210i	$0.780501\pi$
$458$	− 2.53470i	− 0.118439i
$459$	−46.3909	−2.16534
$460$	0	0
$461$	−40.8432	−1.90226	−0.951128	−	0.308796i	$-0.900074\pi$
$461$	−40.8432	−1.90226	−0.951128	+	0.308796i	$0.900074\pi$
$462$	10.4208i	0.484817i
$463$	34.8233i	1.61837i	0.587551	+	0.809187i	$0.300092\pi$
$463$	34.8233i	1.61837i	−0.587551	+	0.809187i	$0.699908\pi$
$464$	−1.55776	−0.0723170
$465$	0	0
$466$	2.72236	0.126111
$467$	9.38939i	0.434489i	0.976117	+	0.217245i	$0.0697069\pi$
$467$	9.38939i	0.434489i	−0.976117	+	0.217245i	$0.930293\pi$
$468$	35.2943i	1.63148i
$469$	50.5438	2.33390
$470$	0	0
$471$	−9.40324	−0.433278
$472$	− 2.19517i	− 0.101041i
$473$	9.39386i	0.431930i
$474$	3.92965	0.180495
$475$	0	0
$476$	38.5645	1.76760
$477$	0.881224i	0.0403485i
$478$	0.0134688i	0 0.000616050i
$479$	−21.0154	−0.960217	−0.480109	−	0.877209i	$-0.659403\pi$
$479$	−21.0154	−0.960217	−0.480109	+	0.877209i	$0.659403\pi$
$480$	0	0
$481$	2.79978	0.127659
$482$	− 3.69084i	− 0.168113i
$483$	− 78.1851i	− 3.55755i
$484$	14.2599	0.648176
$485$	0	0
$486$	−1.44092	−0.0653616
$487$	35.7633i	1.62059i	0.586023	+	0.810294i	$0.300693\pi$
$487$	35.7633i	1.62059i	−0.586023	+	0.810294i	$0.699307\pi$
$488$	2.16508i	0.0980085i
$489$	8.91296	0.403058
$490$	0	0
$491$	15.0742	0.680288	0.340144	−	0.940373i	$-0.389524\pi$
$491$	15.0742	0.680288	0.340144	+	0.940373i	$0.389524\pi$
$492$	− 4.57048i	− 0.206053i
$493$	− 1.81688i	− 0.0818280i
$494$	1.22822	0.0552601
$495$	0	0
$496$	29.6581	1.33169
$497$	47.3040i	2.12187i
$498$	6.27826i	0.281335i
$499$	−32.9424	−1.47470	−0.737352	−	0.675509i	$-0.763924\pi$
$499$	−32.9424	−1.47470	−0.737352	+	0.675509i	$0.763924\pi$
$500$	0	0
$501$	72.1759	3.22458
$502$	1.23468i	0.0551066i
$503$	− 8.61983i	− 0.384339i	−0.981362	−	0.192170i	$-0.938448\pi$
$503$	− 8.61983i	− 0.384339i	0.981362	−	0.192170i	$-0.0615524\pi$
$504$	20.2185	0.900603
$505$	0	0
$506$	4.44333	0.197530
$507$	− 15.8299i	− 0.703031i
$508$	− 18.3497i	− 0.814138i
$509$	−37.3100	−1.65374	−0.826869	−	0.562395i	$-0.809880\pi$
$509$	−37.3100	−1.65374	−0.826869	+	0.562395i	$0.809880\pi$
$510$	0	0
$511$	36.2331	1.60286
$512$	− 13.4925i	− 0.596291i
$513$	− 25.4456i	− 1.12345i
$514$	1.88712	0.0832374
$515$	0	0
$516$	13.2707	0.584208
$517$	18.2183i	0.801240i
$518$	− 0.795373i	− 0.0349467i
$519$	−57.3245	−2.51626
$520$	0	0
$521$	−18.6417	−0.816710	−0.408355	−	0.912823i	$-0.633897\pi$
$521$	−18.6417	−0.816710	−0.408355	+	0.912823i	$0.633897\pi$
$522$	− 0.472378i	− 0.0206754i
$523$	6.56533i	0.287082i	0.989644	+	0.143541i	$0.0458489\pi$
$523$	6.56533i	0.287082i	−0.989644	+	0.143541i	$0.954151\pi$
$524$	30.6949	1.34091
$525$	0	0
$526$	1.08053	0.0471133
$527$	34.5915i	1.50683i
$528$	− 49.8694i	− 2.17029i
$529$	−10.3376	−0.449459
$530$	0	0
$531$	−19.6772	−0.853918
$532$	21.1527i	0.917088i
$533$	− 2.12048i	− 0.0918483i
$534$	−8.96804	−0.388085
$535$	0	0
$536$	8.18274	0.353441
$537$	− 3.74365i	− 0.161550i
$538$	− 0.419361i	− 0.0180799i
$539$	−53.3633	−2.29852
$540$	0	0
$541$	5.25295	0.225842	0.112921	−	0.993604i	$-0.463979\pi$
$541$	5.25295	0.225842	0.112921	+	0.993604i	$0.463979\pi$
$542$	1.10448i	0.0474414i
$543$	73.0348i	3.13422i
$544$	9.39057	0.402617
$545$	0	0
$546$	6.83000	0.292297
$547$	− 37.4845i	− 1.60272i	−0.598181	−	0.801361i	$-0.704110\pi$
$547$	− 37.4845i	− 1.60272i	0.598181	−	0.801361i	$-0.295890\pi$
$548$	2.00662i	0.0857187i
$549$	19.4074	0.828289
$550$	0	0
$551$	0.996563	0.0424550
$552$	− 12.6577i	− 0.538747i
$553$	31.3992i	1.33523i
$554$	1.49700	0.0636016
$555$	0	0
$556$	−13.9482	−0.591534
$557$	− 12.2789i	− 0.520275i	−0.965572	−	0.260138i	$-0.916232\pi$
$557$	− 12.2789i	− 0.520275i	0.965572	−	0.260138i	$-0.0837679\pi$
$558$	8.99361i	0.380730i
$559$	6.15695	0.260411
$560$	0	0
$561$	58.1648	2.45572
$562$	0.903127i	0.0380961i
$563$	20.4994i	0.863948i	0.901886	+	0.431974i	$0.142183\pi$
$563$	20.4994i	0.863948i	−0.901886	+	0.431974i	$0.857817\pi$
$564$	25.7369	1.08372
$565$	0	0
$566$	2.25744	0.0948874
$567$	− 56.6395i	− 2.37864i
$568$	7.65823i	0.321332i
$569$	−1.60123	−0.0671269	−0.0335634	−	0.999437i	$-0.510686\pi$
$569$	−1.60123	−0.0671269	−0.0335634	+	0.999437i	$0.510686\pi$
$570$	0	0
$571$	−41.8238	−1.75027	−0.875136	−	0.483877i	$-0.839228\pi$
$571$	−41.8238	−1.75027	−0.875136	+	0.483877i	$0.839228\pi$
$572$	− 23.5316i	− 0.983905i
$573$	− 45.8414i	− 1.91505i
$574$	−0.602395	−0.0251435
$575$	0	0
$576$	−46.3329	−1.93054
$577$	14.9405i	0.621981i	0.950413	+	0.310991i	$0.100661\pi$
$577$	14.9405i	0.621981i	−0.950413	+	0.310991i	$0.899339\pi$
$578$	0.488025i	0.0202992i
$579$	−57.9909	−2.41002
$580$	0	0
$581$	−50.1654	−2.08121
$582$	10.1336i	0.420050i
$583$	− 0.587533i	− 0.0243331i
$584$	5.86591	0.242733
$585$	0	0
$586$	−1.10457	−0.0456293
$587$	32.8499i	1.35586i	0.735126	+	0.677930i	$0.237123\pi$
$587$	32.8499i	1.35586i	−0.735126	+	0.677930i	$0.762877\pi$
$588$	75.3861i	3.10887i
$589$	−18.9736	−0.781792
$590$	0	0
$591$	−11.4280	−0.470086
$592$	3.80632i	0.156439i
$593$	39.7259i	1.63135i	0.578512	+	0.815674i	$0.303634\pi$
$593$	39.7259i	1.63135i	−0.578512	+	0.815674i	$0.696366\pi$
$594$	8.04161	0.329951
$595$	0	0
$596$	30.6094	1.25381
$597$	− 57.4273i	− 2.35034i
$598$	− 2.91227i	− 0.119091i
$599$	10.4669	0.427668	0.213834	−	0.976870i	$-0.431405\pi$
$599$	10.4669	0.427668	0.213834	+	0.976870i	$0.431405\pi$
$600$	0	0
$601$	−8.56503	−0.349375	−0.174687	−	0.984624i	$-0.555891\pi$
$601$	−8.56503	−0.349375	−0.174687	+	0.984624i	$0.555891\pi$
$602$	− 1.74909i	− 0.0712876i
$603$	− 73.3489i	− 2.98700i
$604$	−7.88753	−0.320939
$605$	0	0
$606$	6.15087	0.249862
$607$	− 8.90888i	− 0.361600i	−0.983520	−	0.180800i	$-0.942131\pi$
$607$	− 8.90888i	− 0.361600i	0.983520	−	0.180800i	$-0.0578687\pi$
$608$	5.15076i	0.208891i
$609$	5.54180	0.224565
$610$	0	0
$611$	11.9407	0.483069
$612$	− 55.9645i	− 2.26223i
$613$	− 10.5868i	− 0.427598i	−0.976878	−	0.213799i	$-0.931416\pi$
$613$	− 10.5868i	− 0.427598i	0.976878	−	0.213799i	$-0.0685837\pi$
$614$	−2.27760	−0.0919163
$615$	0	0
$616$	−13.4802	−0.543131
$617$	6.83972i	0.275357i	0.990477	+	0.137678i	$0.0439641\pi$
$617$	6.83972i	0.275357i	−0.990477	+	0.137678i	$0.956036\pi$
$618$	− 3.74682i	− 0.150719i
$619$	15.5577	0.625318	0.312659	−	0.949865i	$-0.398780\pi$
$619$	15.5577	0.625318	0.312659	+	0.949865i	$0.398780\pi$
$620$	0	0
$621$	−60.3348	−2.42115
$622$	− 1.45047i	− 0.0581584i
$623$	− 71.6576i	− 2.87090i
$624$	−32.6856	−1.30847
$625$	0	0
$626$	−0.539645	−0.0215685
$627$	31.9036i	1.27411i
$628$	− 6.03221i	− 0.240711i
$629$	−4.43948	−0.177014
$630$	0	0
$631$	12.0975	0.481596	0.240798	−	0.970575i	$-0.422591\pi$
$631$	12.0975	0.481596	0.240798	+	0.970575i	$0.422591\pi$
$632$	5.08334i	0.202204i
$633$	41.0901i	1.63319i
$634$	−0.404220	−0.0160536
$635$	0	0
$636$	−0.830005	−0.0329118
$637$	34.9756i	1.38578i
$638$	0.314946i	0.0124688i
$639$	68.6472	2.71564
$640$	0	0
$641$	−39.4179	−1.55691	−0.778457	−	0.627698i	$-0.783997\pi$
$641$	−39.4179	−1.55691	−0.778457	+	0.627698i	$0.783997\pi$
$642$	0.296485i	0.0117013i
$643$	− 2.80810i	− 0.110741i	−0.998466	−	0.0553704i	$-0.982366\pi$
$643$	− 2.80810i	− 0.110741i	0.998466	−	0.0553704i	$-0.0176340\pi$
$644$	50.1560	1.97642
$645$	0	0
$646$	−1.94752	−0.0766243
$647$	47.0232i	1.84867i	0.381577	+	0.924337i	$0.375381\pi$
$647$	47.0232i	1.84867i	−0.381577	+	0.924337i	$0.624619\pi$
$648$	− 9.16959i	− 0.360216i
$649$	13.1193	0.514976
$650$	0	0
$651$	−105.510	−4.13528
$652$	5.71769i	0.223922i
$653$	21.7426i	0.850852i	0.904993	+	0.425426i	$0.139876\pi$
$653$	21.7426i	0.850852i	−0.904993	+	0.425426i	$0.860124\pi$
$654$	5.26830	0.206007
$655$	0	0
$656$	2.88281	0.112555
$657$	− 52.5812i	− 2.05139i
$658$	− 3.39216i	− 0.132240i
$659$	26.3436	1.02620	0.513100	−	0.858329i	$-0.328497\pi$
$659$	26.3436	1.02620	0.513100	+	0.858329i	$0.328497\pi$
$660$	0	0
$661$	20.5259	0.798364	0.399182	−	0.916872i	$-0.369294\pi$
$661$	20.5259	0.798364	0.399182	+	0.916872i	$0.369294\pi$
$662$	− 0.312523i	− 0.0121466i
$663$	− 38.1226i	− 1.48056i
$664$	−8.12147	−0.315174
$665$	0	0
$666$	−1.15424	−0.0447259
$667$	− 2.36298i	− 0.0914950i
$668$	46.3010i	1.79144i
$669$	−53.5118	−2.06888
$670$	0	0
$671$	−12.9394	−0.499520
$672$	28.6429i	1.10492i
$673$	− 5.66357i	− 0.218315i	−0.994024	−	0.109157i	$-0.965185\pi$
$673$	− 5.66357i	− 0.218315i	0.994024	−	0.109157i	$-0.0348152\pi$
$674$	5.39673	0.207874
$675$	0	0
$676$	10.1549	0.390574
$677$	− 6.93823i	− 0.266658i	−0.991072	−	0.133329i	$-0.957433\pi$
$677$	− 6.93823i	− 0.266658i	0.991072	−	0.133329i	$-0.0425667\pi$
$678$	− 5.06588i	− 0.194554i
$679$	−80.9706	−3.10737
$680$	0	0
$681$	−62.8717	−2.40925
$682$	− 5.99625i	− 0.229608i
$683$	19.4849i	0.745570i	0.927918	+	0.372785i	$0.121597\pi$
$683$	19.4849i	0.745570i	−0.927918	+	0.372785i	$0.878403\pi$
$684$	30.6967	1.17372
$685$	0	0
$686$	4.36838	0.166786
$687$	− 43.1532i	− 1.64640i
$688$	8.37043i	0.319119i
$689$	−0.385083	−0.0146705
$690$	0	0
$691$	−19.9927	−0.760557	−0.380278	−	0.924872i	$-0.624172\pi$
$691$	−19.9927	−0.760557	−0.380278	+	0.924872i	$0.624172\pi$
$692$	− 36.7738i	− 1.39793i
$693$	120.834i	4.59011i
$694$	2.70188	0.102562
$695$	0	0
$696$	0.897183	0.0340076
$697$	3.36235i	0.127358i
$698$	− 1.31496i	− 0.0497718i
$699$	46.3481	1.75305
$700$	0	0
$701$	−25.5726	−0.965863	−0.482932	−	0.875658i	$-0.660428\pi$
$701$	−25.5726	−0.965863	−0.482932	+	0.875658i	$0.660428\pi$
$702$	− 5.27066i	− 0.198928i
$703$	− 2.43507i	− 0.0918403i
$704$	30.8913	1.16426
$705$	0	0
$706$	−2.27103	−0.0854712
$707$	49.1476i	1.84838i
$708$	− 18.5335i	− 0.696532i
$709$	36.7156	1.37888	0.689441	−	0.724342i	$-0.257856\pi$
$709$	36.7156	1.37888	0.689441	+	0.724342i	$0.257856\pi$
$710$	0	0
$711$	45.5663	1.70887
$712$	− 11.6009i	− 0.434764i
$713$	44.9888i	1.68485i
$714$	−10.8300	−0.405303
$715$	0	0
$716$	2.40156	0.0897505
$717$	0.229307i	0.00856361i
$718$	3.87971i	0.144790i
$719$	−4.11485	−0.153458	−0.0767290	−	0.997052i	$-0.524448\pi$
$719$	−4.11485	−0.153458	−0.0767290	+	0.997052i	$0.524448\pi$
$720$	0	0
$721$	29.9384	1.11496
$722$	2.35467i	0.0876317i
$723$	− 62.8364i	− 2.33691i
$724$	−46.8520	−1.74124
$725$	0	0
$726$	−4.00458	−0.148624
$727$	− 27.2507i	− 1.01067i	−0.862923	−	0.505336i	$-0.831369\pi$
$727$	− 27.2507i	− 1.01067i	0.862923	−	0.505336i	$-0.168631\pi$
$728$	8.83521i	0.327455i
$729$	13.9550	0.516850
$730$	0	0
$731$	−9.76278	−0.361090
$732$	18.2794i	0.675627i
$733$	27.7634i	1.02546i	0.858549	+	0.512732i	$0.171366\pi$
$733$	27.7634i	1.02546i	−0.858549	+	0.512732i	$0.828634\pi$
$734$	−3.62940	−0.133964
$735$	0	0
$736$	12.2131	0.450182
$737$	48.9034i	1.80138i
$738$	0.874192i	0.0321794i
$739$	41.6263	1.53125	0.765624	−	0.643288i	$-0.222430\pi$
$739$	41.6263	1.53125	0.765624	+	0.643288i	$0.222430\pi$
$740$	0	0
$741$	20.9104	0.768161
$742$	0.109396i	0.00401605i
$743$	− 48.9645i	− 1.79633i	−0.439657	−	0.898166i	$-0.644900\pi$
$743$	− 48.9645i	− 1.79633i	0.439657	−	0.898166i	$-0.355100\pi$
$744$	−17.0815	−0.626238
$745$	0	0
$746$	1.78062	0.0651930
$747$	72.7997i	2.66360i
$748$	37.3129i	1.36429i
$749$	−2.36902	−0.0865619
$750$	0	0
$751$	7.34688	0.268091	0.134046	−	0.990975i	$-0.457203\pi$
$751$	7.34688	0.268091	0.134046	+	0.990975i	$0.457203\pi$
$752$	16.2335i	0.591974i
$753$	21.0204i	0.766027i
$754$	0.206423	0.00751747
$755$	0	0
$756$	90.7730	3.30138
$757$	4.47852i	0.162775i	0.996683	+	0.0813873i	$0.0259351\pi$
$757$	4.47852i	0.162775i	−0.996683	+	0.0813873i	$0.974065\pi$
$758$	4.78193i	0.173687i
$759$	75.6476	2.74583
$760$	0	0
$761$	33.7349	1.22289	0.611445	−	0.791287i	$-0.290589\pi$
$761$	33.7349	1.22289	0.611445	+	0.791287i	$0.290589\pi$
$762$	5.15313i	0.186678i
$763$	42.0955i	1.52396i
$764$	29.4074	1.06392
$765$	0	0
$766$	0.259121	0.00936241
$767$	− 8.59867i	− 0.310480i
$768$	− 41.3024i	− 1.49037i
$769$	−25.1523	−0.907014	−0.453507	−	0.891253i	$-0.649827\pi$
$769$	−25.1523	−0.907014	−0.453507	+	0.891253i	$0.649827\pi$
$770$	0	0
$771$	32.1282	1.15707
$772$	− 37.2013i	− 1.33890i
$773$	13.1660i	0.473549i	0.971565	+	0.236774i	$0.0760902\pi$
$773$	13.1660i	0.473549i	−0.971565	+	0.236774i	$0.923910\pi$
$774$	−2.53827	−0.0912362
$775$	0	0
$776$	−13.1087	−0.470573
$777$	− 13.5412i	− 0.485788i
$778$	5.18117i	0.185754i
$779$	−1.84426	−0.0660774
$780$	0	0
$781$	−45.7687	−1.63773
$782$	4.61784i	0.165134i
$783$	− 4.27656i	− 0.152832i
$784$	−47.5495	−1.69820
$785$	0	0
$786$	−8.62000	−0.307465
$787$	− 19.5552i	− 0.697066i	−0.937296	−	0.348533i	$-0.886680\pi$
$787$	− 19.5552i	− 0.697066i	0.937296	−	0.348533i	$-0.113320\pi$
$788$	− 7.33111i	− 0.261160i
$789$	18.3960	0.654914
$790$	0	0
$791$	40.4781	1.43923
$792$	19.5623i	0.695116i
$793$	8.48079i	0.301162i
$794$	−6.09790	−0.216406
$795$	0	0
$796$	36.8398	1.30575
$797$	− 51.4656i	− 1.82300i	−0.411295	−	0.911502i	$-0.634923\pi$
$797$	− 51.4656i	− 1.82300i	0.411295	−	0.911502i	$-0.365077\pi$
$798$	− 5.94029i	− 0.210284i
$799$	−18.9338	−0.669829
$800$	0	0
$801$	−103.989	−3.67427
$802$	3.74335i	0.132182i
$803$	35.0571i	1.23714i
$804$	69.0857	2.43646
$805$	0	0
$806$	−3.93008	−0.138431
$807$	− 7.13960i	− 0.251326i
$808$	7.95669i	0.279915i
$809$	−42.6242	−1.49859	−0.749293	−	0.662238i	$-0.769607\pi$
$809$	−42.6242	−1.49859	−0.749293	+	0.662238i	$0.769607\pi$
$810$	0	0
$811$	−26.7451	−0.939147	−0.469574	−	0.882893i	$-0.655592\pi$
$811$	−26.7451	−0.939147	−0.469574	+	0.882893i	$0.655592\pi$
$812$	3.55508i	0.124759i
$813$	18.8037i	0.659475i
$814$	0.769559	0.0269730
$815$	0	0
$816$	51.8279	1.81434
$817$	− 5.35492i	− 0.187345i
$818$	− 0.623671i	− 0.0218061i
$819$	79.1975	2.76738
$820$	0	0
$821$	43.8050	1.52880	0.764402	−	0.644740i	$-0.223034\pi$
$821$	43.8050	1.52880	0.764402	+	0.644740i	$0.223034\pi$
$822$	− 0.563517i	− 0.0196549i
$823$	− 5.72621i	− 0.199603i	−0.995007	−	0.0998016i	$-0.968179\pi$
$823$	− 5.72621i	− 0.199603i	0.995007	−	0.0998016i	$-0.0318208\pi$
$824$	4.84684	0.168848
$825$	0	0
$826$	−2.44274	−0.0849939
$827$	35.4306i	1.23204i	0.787730	+	0.616021i	$0.211256\pi$
$827$	35.4306i	1.23204i	−0.787730	+	0.616021i	$0.788744\pi$
$828$	− 72.7860i	− 2.52949i
$829$	20.7040	0.719081	0.359541	−	0.933129i	$-0.382933\pi$
$829$	20.7040	0.719081	0.359541	+	0.933129i	$0.382933\pi$
$830$	0	0
$831$	25.4864	0.884115
$832$	− 20.2469i	− 0.701933i
$833$	− 55.4590i	− 1.92154i
$834$	3.91704	0.135636
$835$	0	0
$836$	−20.4662	−0.707840
$837$	81.4215i	2.81434i
$838$	− 3.37351i	− 0.116536i
$839$	−10.9086	−0.376607	−0.188303	−	0.982111i	$-0.560299\pi$
$839$	−10.9086	−0.376607	−0.188303	+	0.982111i	$0.560299\pi$
$840$	0	0
$841$	−28.8325	−0.994225
$842$	− 0.345025i	− 0.0118903i
$843$	15.3757i	0.529567i
$844$	−26.3594	−0.907329
$845$	0	0
$846$	−4.92268	−0.169245
$847$	− 31.9979i	− 1.09946i
$848$	− 0.523523i	− 0.0179778i
$849$	38.4329	1.31901
$850$	0	0
$851$	−5.77387	−0.197926
$852$	64.6573i	2.21512i
$853$	− 38.8833i	− 1.33134i	−0.746247	−	0.665670i	$-0.768146\pi$
$853$	− 38.8833i	− 1.33134i	0.746247	−	0.665670i	$-0.231854\pi$
$854$	2.40925	0.0824430
$855$	0	0
$856$	−0.383529	−0.0131088
$857$	− 40.6975i	− 1.39020i	−0.718913	−	0.695100i	$-0.755360\pi$
$857$	− 40.6975i	− 1.39020i	0.718913	−	0.695100i	$-0.244640\pi$
$858$	6.60834i	0.225605i
$859$	−28.1532	−0.960574	−0.480287	−	0.877111i	$-0.659467\pi$
$859$	−28.1532	−0.960574	−0.480287	+	0.877111i	$0.659467\pi$
$860$	0	0
$861$	−10.2558	−0.349515
$862$	− 1.11319i	− 0.0379154i
$863$	18.5236i	0.630552i	0.949000	+	0.315276i	$0.102097\pi$
$863$	18.5236i	0.630552i	−0.949000	+	0.315276i	$0.897903\pi$
$864$	22.1035	0.751977
$865$	0	0
$866$	−2.11274	−0.0717937
$867$	8.30862i	0.282175i
$868$	− 67.6852i	− 2.29738i
$869$	−30.3801	−1.03058
$870$	0	0
$871$	32.0525	1.08606
$872$	6.81501i	0.230785i
$873$	117.504i	3.97691i
$874$	−2.53290	−0.0856766
$875$	0	0
$876$	49.5250	1.67330
$877$	− 14.0422i	− 0.474172i	−0.971489	−	0.237086i	$-0.923808\pi$
$877$	− 14.0422i	− 0.474172i	0.971489	−	0.237086i	$-0.0761923\pi$
$878$	− 3.32785i	− 0.112309i
$879$	−18.8052	−0.634285
$880$	0	0
$881$	7.68268	0.258836	0.129418	−	0.991590i	$-0.458689\pi$
$881$	7.68268	0.258836	0.129418	+	0.991590i	$0.458689\pi$
$882$	− 14.4190i	− 0.485515i
$883$	35.0479i	1.17945i	0.807602	+	0.589727i	$0.200765\pi$
$883$	35.0479i	1.17945i	−0.807602	+	0.589727i	$0.799235\pi$
$884$	24.4557	0.822535
$885$	0	0
$886$	0.686850	0.0230752
$887$	9.30606i	0.312467i	0.987720	+	0.156233i	$0.0499352\pi$
$887$	9.30606i	0.312467i	−0.987720	+	0.156233i	$0.950065\pi$
$888$	− 2.19224i	− 0.0735667i
$889$	−41.1752	−1.38097
$890$	0	0
$891$	54.8013	1.83591
$892$	− 34.3280i	− 1.14938i
$893$	− 10.3852i	− 0.347529i
$894$	−8.59599	−0.287493
$895$	0	0
$896$	−24.4294	−0.816129
$897$	− 49.5812i	− 1.65547i
$898$	− 0.867547i	− 0.0289504i
$899$	−3.18883	−0.106353
$900$	0	0
$901$	0.610607	0.0203423
$902$	− 0.582844i	− 0.0194066i
$903$	− 29.7782i	− 0.990957i
$904$	6.55315	0.217955
$905$	0	0
$906$	2.21504	0.0735899
$907$	4.56415i	0.151550i	0.997125	+	0.0757751i	$0.0241431\pi$
$907$	4.56415i	0.151550i	−0.997125	+	0.0757751i	$0.975857\pi$
$908$	− 40.3324i	− 1.33848i
$909$	71.3226	2.36562
$910$	0	0
$911$	−0.294602	−0.00976060	−0.00488030	−	0.999988i	$-0.501553\pi$
$911$	−0.294602	−0.00976060	−0.00488030	+	0.999988i	$0.501553\pi$
$912$	28.4278i	0.941338i
$913$	− 48.5373i	− 1.60635i
$914$	4.90036	0.162090
$915$	0	0
$916$	27.6829	0.914668
$917$	− 68.8767i	− 2.27451i
$918$	8.35743i	0.275836i
$919$	−33.9110	−1.11862	−0.559311	−	0.828958i	$-0.688934\pi$
$919$	−33.9110	−1.11862	−0.559311	+	0.828958i	$0.688934\pi$
$920$	0	0
$921$	−38.7760	−1.27771
$922$	7.35799i	0.242323i
$923$	29.9979i	0.987393i
$924$	−113.811	−3.74410
$925$	0	0
$926$	6.27349	0.206160
$927$	− 43.4464i	− 1.42697i
$928$	0.865673i	0.0284171i
$929$	−22.4955	−0.738055	−0.369028	−	0.929418i	$-0.620309\pi$
$929$	−22.4955	−0.738055	−0.369028	+	0.929418i	$0.620309\pi$
$930$	0	0
$931$	30.4195	0.996958
$932$	29.7324i	0.973918i
$933$	− 24.6941i	− 0.808450i
$934$	1.69152	0.0553482
$935$	0	0
$936$	12.8216	0.419087
$937$	− 25.4994i	− 0.833028i	−0.909129	−	0.416514i	$-0.863252\pi$
$937$	− 25.4994i	− 0.833028i	0.909129	−	0.416514i	$-0.136748\pi$
$938$	− 9.10558i	− 0.297308i
$939$	−9.18743	−0.299821
$940$	0	0
$941$	52.3734	1.70732	0.853662	−	0.520827i	$-0.174376\pi$
$941$	52.3734	1.70732	0.853662	+	0.520827i	$0.174376\pi$
$942$	1.69402i	0.0551940i
$943$	4.37298i	0.142404i
$944$	11.6900	0.380476
$945$	0	0
$946$	1.69232	0.0550222
$947$	50.7001i	1.64753i	0.566931	+	0.823766i	$0.308131\pi$
$947$	50.7001i	1.64753i	−0.566931	+	0.823766i	$0.691869\pi$
$948$	42.9179i	1.39391i
$949$	22.9773	0.745874
$950$	0	0
$951$	−6.88183	−0.223159
$952$	− 14.0096i	− 0.454052i
$953$	18.5912i	0.602228i	0.953588	+	0.301114i	$0.0973585\pi$
$953$	18.5912i	0.602228i	−0.953588	+	0.301114i	$0.902641\pi$
$954$	0.158754	0.00513986
$955$	0	0
$956$	−0.147101	−0.00475758
$957$	5.36194i	0.173327i
$958$	3.78597i	0.122319i
$959$	4.50269	0.145399
$960$	0	0
$961$	29.7122	0.958457
$962$	− 0.504387i	− 0.0162621i
$963$	3.43790i	0.110785i
$964$	40.3098	1.29829
$965$	0	0
$966$	−14.0852	−0.453185
$967$	20.5566i	0.661056i	0.943796	+	0.330528i	$0.107227\pi$
$967$	20.5566i	0.661056i	−0.943796	+	0.330528i	$0.892773\pi$
$968$	− 5.18027i	− 0.166500i
$969$	−33.1565	−1.06514
$970$	0	0
$971$	40.7627	1.30814	0.654069	−	0.756435i	$-0.273061\pi$
$971$	40.7627	1.30814	0.654069	+	0.756435i	$0.273061\pi$
$972$	− 15.7371i	− 0.504769i
$973$	31.2985i	1.00338i
$974$	6.44284	0.206442
$975$	0	0
$976$	−11.5297	−0.369056
$977$	− 5.60203i	− 0.179225i	−0.995977	−	0.0896124i	$-0.971437\pi$
$977$	− 5.60203i	− 0.179225i	0.995977	−	0.0896124i	$-0.0285628\pi$
$978$	− 1.60569i	− 0.0513443i
$979$	69.3320	2.21586
$980$	0	0
$981$	61.0887	1.95041
$982$	− 2.71565i	− 0.0866598i
$983$	16.0493i	0.511894i	0.966691	+	0.255947i	$0.0823872\pi$
$983$	16.0493i	0.511894i	−0.966691	+	0.255947i	$0.917613\pi$
$984$	−1.66034	−0.0529299
$985$	0	0
$986$	−0.327314	−0.0104238
$987$	− 57.7514i	− 1.83825i
$988$	13.4141i	0.426758i
$989$	−12.6972	−0.403748
$990$	0	0
$991$	−36.8868	−1.17175	−0.585874	−	0.810402i	$-0.699249\pi$
$991$	−36.8868	−1.17175	−0.585874	+	0.810402i	$0.699249\pi$
$992$	− 16.4816i	− 0.523290i
$993$	− 5.32070i	− 0.168847i
$994$	8.52192	0.270299
$995$	0	0
$996$	−68.5684	−2.17267
$997$	0.491984i	0.0155813i	0.999970	+	0.00779064i	$0.00247986\pi$
$997$	0.491984i	0.0155813i	−0.999970	+	0.00779064i	$0.997520\pi$
$998$	5.93465i	0.187858i
$999$	−10.4496	−0.330612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.b.g.149.5		10
5.2	odd	4		185.2.a.d.1.3	✓	5
5.3	odd	4		925.2.a.h.1.3		5
5.4	even	2	inner	925.2.b.g.149.6		10
15.2	even	4		1665.2.a.q.1.3		5
15.8	even	4		8325.2.a.cc.1.3		5
20.7	even	4		2960.2.a.ba.1.5		5
35.27	even	4		9065.2.a.j.1.3		5
185.147	odd	4		6845.2.a.g.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.d.1.3	✓	5	5.2	odd	4
925.2.a.h.1.3		5	5.3	odd	4
925.2.b.g.149.5		10	1.1	even	1	trivial
925.2.b.g.149.6		10	5.4	even	2	inner
1665.2.a.q.1.3		5	15.2	even	4
2960.2.a.ba.1.5		5	20.7	even	4
6845.2.a.g.1.3		5	185.147	odd	4
8325.2.a.cc.1.3		5	15.8	even	4
9065.2.a.j.1.3		5	35.27	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.180152i q^{2} -3.06709i q^{3} +1.96755 q^{4} -0.552543 q^{6} -4.41500i q^{7} -0.714762i q^{8} -6.40702 q^{9} +4.27171 q^{11} -6.03463i q^{12} -2.79978i q^{13} -0.795373 q^{14} +3.80632 q^{16} +4.43948i q^{17} +1.15424i q^{18} -2.43507 q^{19} -13.5412 q^{21} -0.769559i q^{22} +5.77387i q^{23} -2.19224 q^{24} -0.504387 q^{26} +10.4496i q^{27} -8.68672i q^{28} -0.409254 q^{29} +7.79180 q^{31} -2.11524i q^{32} -13.1017i q^{33} +0.799782 q^{34} -12.6061 q^{36} +1.00000i q^{37} +0.438683i q^{38} -8.58717 q^{39} +0.757374 q^{41} +2.43948i q^{42} +2.19908i q^{43} +8.40479 q^{44} +1.04018 q^{46} +4.26487i q^{47} -11.6743i q^{48} -12.4922 q^{49} +13.6163 q^{51} -5.50870i q^{52} -0.137540i q^{53} +1.88253 q^{54} -3.15568 q^{56} +7.46857i q^{57} +0.0737281i q^{58} +3.07119 q^{59} -3.02909 q^{61} -1.40371i q^{62} +28.2870i q^{63} +7.23158 q^{64} -2.36030 q^{66} +11.4482i q^{67} +8.73487i q^{68} +17.7090 q^{69} -10.7144 q^{71} +4.57950i q^{72} +8.20680i q^{73} +0.180152 q^{74} -4.79111 q^{76} -18.8596i q^{77} +1.54700i q^{78} -7.11193 q^{79} +12.8289 q^{81} -0.136443i q^{82} -11.3625i q^{83} -26.6429 q^{84} +0.396170 q^{86} +1.25522i q^{87} -3.05326i q^{88} +16.2305 q^{89} -12.3610 q^{91} +11.3603i q^{92} -23.8981i q^{93} +0.768326 q^{94} -6.48763 q^{96} -18.3399i q^{97} +2.25051i q^{98} -27.3690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{4} - 4 q^{6} - 4 q^{9} + 14 q^{11} - 8 q^{14} + 16 q^{16} - 28 q^{19} - 18 q^{21} - 24 q^{24} - 40 q^{26} - 4 q^{29} + 16 q^{31} - 24 q^{34} - 72 q^{36} - 24 q^{39} - 18 q^{41} - 36 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) \) 10 * q - 12 * q^4 - 4 * q^6 - 4 * q^9 + 14 * q^11 - 8 * q^14 + 16 * q^16 - 28 * q^19 - 18 * q^21 - 24 * q^24 - 40 * q^26 - 4 * q^29 + 16 * q^31 - 24 * q^34 - 72 * q^36 - 24 * q^39 - 18 * q^41 - 36 * q^44 - 56 * q^46 - 4 * q^49 + 20 * q^51 + 24 * q^54 - 28 * q^56 - 24 * q^59 + 24 * q^61 - 24 * q^64 - 20 * q^66 + 60 * q^69 + 26 * q^71 + 36 * q^76 - 72 * q^79 + 42 * q^81 - 60 * q^84 - 16 * q^86 + 32 * q^89 - 8 * q^91 - 40 * q^94 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more