LMFDB - Embedded newform 425.2.b.f.324.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(324,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, 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("425.324"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,0,0,-22,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.229451239931904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{7} + 64x^{6} - 30x^{5} + 2x^{4} + 136x^{3} + 324x^{2} + 180x + 50 $ x^10 - 2x^7 + 64x^6 - 30x^5 + 2x^4 + 136x^3 + 324x^2 + 180*x + 50
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			324.5
Root			$1.70454 - 1.70454i$ of defining polynomial
Character	$\chi$	$=$	425.324
Dual form			425.2.b.f.324.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.150980i q^{2} -1.96189i q^{3} +1.97720 q^{4} -0.296207 q^{6} +1.54475i q^{7} -0.600480i q^{8} -0.849020 q^{9} +4.56006 q^{11} -3.87906i q^{12} -1.09756i q^{13} +0.233227 q^{14} +3.86375 q^{16} -1.00000i q^{17} +0.128185i q^{18} -4.67524 q^{19} +3.03063 q^{21} -0.688480i q^{22} +0.529434i q^{23} -1.17808 q^{24} -0.165710 q^{26} -4.21999i q^{27} +3.05428i q^{28} -8.06670 q^{29} -4.78005 q^{31} -1.78431i q^{32} -8.94634i q^{33} -0.150980 q^{34} -1.67869 q^{36} +5.27917i q^{37} +0.705870i q^{38} -2.15329 q^{39} -0.751460 q^{41} -0.457565i q^{42} +9.49340i q^{43} +9.01617 q^{44} +0.0799341 q^{46} -10.7419i q^{47} -7.58026i q^{48} +4.61376 q^{49} -1.96189 q^{51} -2.17010i q^{52} +0.0227951i q^{53} -0.637136 q^{54} +0.927590 q^{56} +9.17232i q^{57} +1.21791i q^{58} +3.56962 q^{59} +3.92378 q^{61} +0.721694i q^{62} -1.31152i q^{63} +7.45810 q^{64} -1.35072 q^{66} +9.75929i q^{67} -1.97720i q^{68} +1.03869 q^{69} +1.21216 q^{71} +0.509819i q^{72} +10.1135i q^{73} +0.797051 q^{74} -9.24392 q^{76} +7.04414i q^{77} +0.325105i q^{78} -14.4151 q^{79} -10.8262 q^{81} +0.113456i q^{82} -5.08949i q^{83} +5.99217 q^{84} +1.43332 q^{86} +15.8260i q^{87} -2.73822i q^{88} +17.6123 q^{89} +1.69545 q^{91} +1.04680i q^{92} +9.37794i q^{93} -1.62182 q^{94} -3.50062 q^{96} +6.78753i q^{97} -0.696587i q^{98} -3.87158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 22 q^{4} + 6 q^{6} - 12 q^{9} + 8 q^{11} + 14 q^{14} + 54 q^{16} - 12 q^{19} - 10 q^{21} + 38 q^{24} - 10 q^{26} - 4 q^{29} + 42 q^{31} + 2 q^{34} + 44 q^{36} - 46 q^{39} - 16 q^{41} + 8 q^{44} - 12 q^{46}+ \cdots + 28 q^{99}+O(q^{100}) $ 10 * q - 22 * q^4 + 6 * q^6 - 12 * q^9 + 8 * q^11 + 14 * q^14 + 54 * q^16 - 12 * q^19 - 10 * q^21 + 38 * q^24 - 10 * q^26 - 4 * q^29 + 42 * q^31 + 2 * q^34 + 44 * q^36 - 46 * q^39 - 16 * q^41 + 8 * q^44 - 12 * q^46 - 20 * q^49 + 2 * q^51 + 50 * q^54 - 58 * q^56 - 24 * q^59 - 4 * q^61 - 86 * q^64 - 56 * q^66 + 42 * q^71 + 100 * q^74 - 28 * q^76 - 82 * q^79 - 70 * q^81 + 142 * q^84 - 72 * q^86 + 20 * q^89 + 26 * q^91 + 20 * q^94 - 170 * q^96 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 0.150980i	− 0.106759i	−0.998574	−	0.0533796i	$-0.983001\pi$
$2$	− 0.150980i	− 0.106759i	0.998574	−	0.0533796i	$-0.0169993\pi$
$3$	− 1.96189i	− 1.13270i	−0.824165	−	0.566349i	$-0.808355\pi$
$3$	− 1.96189i	− 1.13270i	0.824165	−	0.566349i	$-0.191645\pi$
$4$	1.97720	0.988602
$5$	0	0
$5$	0	0
$6$	−0.296207	−0.120926
$7$	1.54475i	0.583859i	0.956440	+	0.291930i	$0.0942973\pi$
$7$	1.54475i	0.583859i	−0.956440	+	0.291930i	$0.905703\pi$
$8$	− 0.600480i	− 0.212302i
$9$	−0.849020	−0.283007
$10$	0	0
$11$	4.56006	1.37491	0.687455	−	0.726227i	$-0.258728\pi$
$11$	4.56006	1.37491	0.687455	+	0.726227i	$0.258728\pi$
$12$	− 3.87906i	− 1.11979i
$13$	− 1.09756i	− 0.304408i	−0.988349	−	0.152204i	$-0.951363\pi$
$13$	− 1.09756i	− 0.304408i	0.988349	−	0.152204i	$-0.0486371\pi$
$14$	0.233227	0.0623324
$15$	0	0
$16$	3.86375	0.965937
$17$	− 1.00000i	− 0.242536i
$17$	− 1.00000i	− 0.242536i
$18$	0.128185i	0.0302136i
$19$	−4.67524	−1.07257	−0.536287	−	0.844036i	$-0.680174\pi$
$19$	−4.67524	−1.07257	−0.536287	+	0.844036i	$0.680174\pi$
$20$	0	0
$21$	3.03063	0.661337
$22$	− 0.688480i	− 0.146784i
$23$	0.529434i	0.110395i	0.998475	+	0.0551973i	$0.0175788\pi$
$23$	0.529434i	0.110395i	−0.998475	+	0.0551973i	$0.982421\pi$
$24$	−1.17808	−0.240474
$25$	0	0
$26$	−0.165710	−0.0324984
$27$	− 4.21999i	− 0.812138i
$28$	3.05428i	0.577205i
$29$	−8.06670	−1.49795	−0.748974	−	0.662599i	$-0.769453\pi$
$29$	−8.06670	−1.49795	−0.748974	+	0.662599i	$0.769453\pi$
$30$	0	0
$31$	−4.78005	−0.858522	−0.429261	−	0.903180i	$-0.641226\pi$
$31$	−4.78005	−0.858522	−0.429261	+	0.903180i	$0.641226\pi$
$32$	− 1.78431i	− 0.315425i
$33$	− 8.94634i	− 1.55736i
$34$	−0.150980	−0.0258929
$35$	0	0
$36$	−1.67869	−0.279781
$37$	5.27917i	0.867889i	0.900939	+	0.433945i	$0.142879\pi$
$37$	5.27917i	0.867889i	−0.900939	+	0.433945i	$0.857121\pi$
$38$	0.705870i	0.114507i
$39$	−2.15329	−0.344803
$40$	0	0
$41$	−0.751460	−0.117358	−0.0586792	−	0.998277i	$-0.518689\pi$
$41$	−0.751460	−0.117358	−0.0586792	+	0.998277i	$0.518689\pi$
$42$	− 0.457565i	− 0.0706038i
$43$	9.49340i	1.44773i	0.689941	+	0.723865i	$0.257636\pi$
$43$	9.49340i	1.44773i	−0.689941	+	0.723865i	$0.742364\pi$
$44$	9.01617	1.35924
$45$	0	0
$46$	0.0799341	0.0117856
$47$	− 10.7419i	− 1.56687i	−0.621472	−	0.783437i	$-0.713465\pi$
$47$	− 10.7419i	− 1.56687i	0.621472	−	0.783437i	$-0.286535\pi$
$48$	− 7.58026i	− 1.09412i
$49$	4.61376	0.659108
$50$	0	0
$51$	−1.96189	−0.274720
$52$	− 2.17010i	− 0.300939i
$53$	0.0227951i	0.00313115i	0.999999	+	0.00156557i	$0.000498337\pi$
$53$	0.0227951i	0.00313115i	−0.999999	+	0.00156557i	$0.999502\pi$
$54$	−0.637136	−0.0867032
$55$	0	0
$56$	0.927590	0.123954
$57$	9.17232i	1.21490i
$58$	1.21791i	0.159920i
$59$	3.56962	0.464725	0.232362	−	0.972629i	$-0.425354\pi$
$59$	3.56962	0.464725	0.232362	+	0.972629i	$0.425354\pi$
$60$	0	0
$61$	3.92378	0.502389	0.251195	−	0.967937i	$-0.419177\pi$
$61$	3.92378	0.502389	0.251195	+	0.967937i	$0.419177\pi$
$62$	0.721694i	0.0916552i
$63$	− 1.31152i	− 0.165236i
$64$	7.45810	0.932263
$65$	0	0
$66$	−1.35072	−0.166262
$67$	9.75929i	1.19229i	0.802878	+	0.596144i	$0.203301\pi$
$67$	9.75929i	1.19229i	−0.802878	+	0.596144i	$0.796699\pi$
$68$	− 1.97720i	− 0.239771i
$69$	1.03869	0.125044
$70$	0	0
$71$	1.21216	0.143857	0.0719285	−	0.997410i	$-0.477085\pi$
$71$	1.21216	0.143857	0.0719285	+	0.997410i	$0.477085\pi$
$72$	0.509819i	0.0600828i
$73$	10.1135i	1.18369i	0.806052	+	0.591845i	$0.201600\pi$
$73$	10.1135i	1.18369i	−0.806052	+	0.591845i	$0.798400\pi$
$74$	0.797051	0.0926552
$75$	0	0
$76$	−9.24392	−1.06035
$77$	7.04414i	0.802754i
$78$	0.325105i	0.0368109i
$79$	−14.4151	−1.62183	−0.810913	−	0.585166i	$-0.801029\pi$
$79$	−14.4151	−1.62183	−0.810913	+	0.585166i	$0.801029\pi$
$80$	0	0
$81$	−10.8262	−1.20291
$82$	0.113456i	0.0125291i
$83$	− 5.08949i	− 0.558644i	−0.960197	−	0.279322i	$-0.909890\pi$
$83$	− 5.08949i	− 0.558644i	0.960197	−	0.279322i	$-0.0901098\pi$
$84$	5.99217	0.653799
$85$	0	0
$86$	1.43332	0.154559
$87$	15.8260i	1.69672i
$88$	− 2.73822i	− 0.291896i
$89$	17.6123	1.86690	0.933450	−	0.358707i	$-0.116782\pi$
$89$	17.6123	1.86690	0.933450	+	0.358707i	$0.116782\pi$
$90$	0	0
$91$	1.69545	0.177732
$92$	1.04680i	0.109136i
$93$	9.37794i	0.972447i
$94$	−1.62182	−0.167278
$95$	0	0
$96$	−3.50062	−0.357281
$97$	6.78753i	0.689170i	0.938755	+	0.344585i	$0.111980\pi$
$97$	6.78753i	0.689170i	−0.938755	+	0.344585i	$0.888020\pi$
$98$	− 0.696587i	− 0.0703659i
$99$	−3.87158	−0.389108
$100$	0	0
$101$	−8.21768	−0.817690	−0.408845	−	0.912604i	$-0.634068\pi$
$101$	−8.21768	−0.817690	−0.408845	+	0.912604i	$0.634068\pi$
$102$	0.296207i	0.0293289i
$103$	17.2696i	1.70163i	0.525466	+	0.850814i	$0.323891\pi$
$103$	17.2696i	1.70163i	−0.525466	+	0.850814i	$0.676109\pi$
$104$	−0.659062	−0.0646264
$105$	0	0
$106$	0.00344161	0.000334279 0
$107$	− 15.3869i	− 1.48750i	−0.668455	−	0.743752i	$-0.733044\pi$
$107$	− 15.3869i	− 1.48750i	0.668455	−	0.743752i	$-0.266956\pi$
$108$	− 8.34379i	− 0.802881i
$109$	−17.2221	−1.64957	−0.824787	−	0.565443i	$-0.808705\pi$
$109$	−17.2221	−1.64957	−0.824787	+	0.565443i	$0.808705\pi$
$110$	0	0
$111$	10.3572	0.983057
$112$	5.96851i	0.563972i
$113$	18.9562i	1.78325i	0.452777	+	0.891624i	$0.350433\pi$
$113$	18.9562i	1.78325i	−0.452777	+	0.891624i	$0.649567\pi$
$114$	1.38484	0.129702
$115$	0	0
$116$	−15.9495	−1.48088
$117$	0.931849i	0.0861495i
$118$	− 0.538943i	− 0.0496137i
$119$	1.54475	0.141607
$120$	0	0
$121$	9.79415	0.890377
$122$	− 0.592414i	− 0.0536347i
$123$	1.47428i	0.132932i
$124$	−9.45114	−0.848737
$125$	0	0
$126$	−0.198014	−0.0176405
$127$	− 15.6123i	− 1.38537i	−0.721241	−	0.692684i	$-0.756428\pi$
$127$	− 15.6123i	− 1.38537i	0.721241	−	0.692684i	$-0.243572\pi$
$128$	− 4.69465i	− 0.414952i
$129$	18.6250	1.63984
$130$	0	0
$131$	−4.79329	−0.418791	−0.209396	−	0.977831i	$-0.567150\pi$
$131$	−4.79329	−0.418791	−0.209396	+	0.977831i	$0.567150\pi$
$132$	− 17.6888i	− 1.53961i
$133$	− 7.22207i	− 0.626233i
$134$	1.47346	0.127288
$135$	0	0
$136$	−0.600480	−0.0514907
$137$	15.6750i	1.33921i	0.742719	+	0.669603i	$0.233536\pi$
$137$	15.6750i	1.33921i	−0.742719	+	0.669603i	$0.766464\pi$
$138$	− 0.156822i	− 0.0133496i
$139$	−8.33055	−0.706588	−0.353294	−	0.935512i	$-0.614938\pi$
$139$	−8.33055	−0.706588	−0.353294	+	0.935512i	$0.614938\pi$
$140$	0	0
$141$	−21.0745	−1.77480
$142$	− 0.183012i	− 0.0153581i
$143$	− 5.00494i	− 0.418534i
$144$	−3.28040	−0.273367
$145$	0	0
$146$	1.52693	0.126370
$147$	− 9.05169i	− 0.746571i
$148$	10.4380i	0.857998i
$149$	3.10739	0.254568	0.127284	−	0.991866i	$-0.459374\pi$
$149$	3.10739	0.254568	0.127284	+	0.991866i	$0.459374\pi$
$150$	0	0
$151$	10.4088	0.847056	0.423528	−	0.905883i	$-0.360791\pi$
$151$	10.4088	0.847056	0.423528	+	0.905883i	$0.360791\pi$
$152$	2.80739i	0.227709i
$153$	0.849020i	0.0686392i
$154$	1.06353	0.0857014
$155$	0	0
$156$	−4.25750	−0.340873
$157$	0.661967i	0.0528307i	0.999651	+	0.0264154i	$0.00840925\pi$
$157$	0.661967i	0.0528307i	−0.999651	+	0.0264154i	$0.991591\pi$
$158$	2.17640i	0.173145i
$159$	0.0447215	0.00354664
$160$	0	0
$161$	−0.817841	−0.0644549
$162$	1.63455i	0.128422i
$163$	− 16.2543i	− 1.27314i	−0.771220	−	0.636569i	$-0.780353\pi$
$163$	− 16.2543i	− 1.27314i	0.771220	−	0.636569i	$-0.219647\pi$
$164$	−1.48579	−0.116021
$165$	0	0
$166$	−0.768414	−0.0596405
$167$	− 19.9527i	− 1.54398i	−0.635632	−	0.771992i	$-0.719260\pi$
$167$	− 19.9527i	− 1.54398i	0.635632	−	0.771992i	$-0.280740\pi$
$168$	− 1.81983i	− 0.140403i
$169$	11.7954	0.907336
$170$	0	0
$171$	3.96937	0.303546
$172$	18.7704i	1.43123i
$173$	3.91717i	0.297817i	0.988851	+	0.148908i	$0.0475760\pi$
$173$	3.91717i	0.297817i	−0.988851	+	0.148908i	$0.952424\pi$
$174$	2.38941	0.181141
$175$	0	0
$176$	17.6189	1.32808
$177$	− 7.00321i	− 0.526393i
$178$	− 2.65911i	− 0.199309i
$179$	−3.14170	−0.234821	−0.117411	−	0.993083i	$-0.537459\pi$
$179$	−3.14170	−0.234821	−0.117411	+	0.993083i	$0.537459\pi$
$180$	0	0
$181$	0.782087	0.0581320	0.0290660	−	0.999577i	$-0.490747\pi$
$181$	0.782087	0.0581320	0.0290660	+	0.999577i	$0.490747\pi$
$182$	− 0.255980i	− 0.0189745i
$183$	− 7.69804i	− 0.569055i
$184$	0.317914	0.0234370
$185$	0	0
$186$	1.41589	0.103818
$187$	− 4.56006i	− 0.333465i
$188$	− 21.2390i	− 1.54901i
$189$	6.51882	0.474174
$190$	0	0
$191$	12.4154	0.898348	0.449174	−	0.893444i	$-0.351718\pi$
$191$	12.4154	0.898348	0.449174	+	0.893444i	$0.351718\pi$
$192$	− 14.6320i	− 1.05597i
$193$	1.70465i	0.122704i	0.998116	+	0.0613518i	$0.0195412\pi$
$193$	1.70465i	0.122704i	−0.998116	+	0.0613518i	$0.980459\pi$
$194$	1.02478	0.0735752
$195$	0	0
$196$	9.12234	0.651596
$197$	16.2755i	1.15958i	0.814766	+	0.579790i	$0.196866\pi$
$197$	16.2755i	1.15958i	−0.814766	+	0.579790i	$0.803134\pi$
$198$	0.584533i	0.0415409i
$199$	−17.1946	−1.21889	−0.609447	−	0.792827i	$-0.708608\pi$
$199$	−17.1946	−1.21889	−0.609447	+	0.792827i	$0.708608\pi$
$200$	0	0
$201$	19.1467	1.35050
$202$	1.24071i	0.0872959i
$203$	− 12.4610i	− 0.874591i
$204$	−3.87906	−0.271589
$205$	0	0
$206$	2.60738	0.181665
$207$	− 0.449500i	− 0.0312424i
$208$	− 4.24069i	− 0.294039i
$209$	−21.3194	−1.47469
$210$	0	0
$211$	2.01038	0.138400	0.0692000	−	0.997603i	$-0.477955\pi$
$211$	2.01038	0.138400	0.0692000	+	0.997603i	$0.477955\pi$
$212$	0.0450706i	0.00309546i
$213$	− 2.37813i	− 0.162947i
$214$	−2.32312	−0.158805
$215$	0	0
$216$	−2.53402	−0.172418
$217$	− 7.38397i	− 0.501256i
$218$	2.60019i	0.176107i
$219$	19.8415	1.34076
$220$	0	0
$221$	−1.09756	−0.0738298
$222$	− 1.56373i	− 0.104950i
$223$	− 14.1074i	− 0.944701i	−0.881411	−	0.472351i	$-0.843406\pi$
$223$	− 14.1074i	− 0.944701i	0.881411	−	0.472351i	$-0.156594\pi$
$224$	2.75631	0.184164
$225$	0	0
$226$	2.86201	0.190378
$227$	15.7117i	1.04282i	0.853306	+	0.521410i	$0.174594\pi$
$227$	15.7117i	1.04282i	−0.853306	+	0.521410i	$0.825406\pi$
$228$	18.1356i	1.20106i
$229$	−16.5921	−1.09644	−0.548219	−	0.836335i	$-0.684694\pi$
$229$	−16.5921	−1.09644	−0.548219	+	0.836335i	$0.684694\pi$
$230$	0	0
$231$	13.8198	0.909279
$232$	4.84389i	0.318017i
$233$	6.56378i	0.430007i	0.976613	+	0.215004i	$0.0689764\pi$
$233$	6.56378i	0.430007i	−0.976613	+	0.215004i	$0.931024\pi$
$234$	0.140691	0.00919726
$235$	0	0
$236$	7.05787	0.459428
$237$	28.2809i	1.83704i
$238$	− 0.233227i	− 0.0151178i
$239$	7.62182	0.493015	0.246507	−	0.969141i	$-0.420717\pi$
$239$	7.62182	0.493015	0.246507	+	0.969141i	$0.420717\pi$
$240$	0	0
$241$	6.89554	0.444181	0.222090	−	0.975026i	$-0.428712\pi$
$241$	6.89554	0.444181	0.222090	+	0.975026i	$0.428712\pi$
$242$	− 1.47872i	− 0.0950560i
$243$	8.57991i	0.550401i
$244$	7.75812	0.496663
$245$	0	0
$246$	0.222588	0.0141917
$247$	5.13136i	0.326500i
$248$	2.87032i	0.182266i
$249$	−9.98504	−0.632776
$250$	0	0
$251$	−25.8326	−1.63054	−0.815270	−	0.579081i	$-0.803411\pi$
$251$	−25.8326	−1.63054	−0.815270	+	0.579081i	$0.803411\pi$
$252$	− 2.59314i	− 0.163353i
$253$	2.41425i	0.151783i
$254$	−2.35715	−0.147901
$255$	0	0
$256$	14.2074	0.887963
$257$	− 17.8491i	− 1.11340i	−0.830715	−	0.556698i	$-0.812068\pi$
$257$	− 17.8491i	− 1.11340i	0.830715	−	0.556698i	$-0.187932\pi$
$258$	− 2.81201i	− 0.175068i
$259$	−8.15497	−0.506725
$260$	0	0
$261$	6.84879	0.423929
$262$	0.723692i	0.0447099i
$263$	− 14.3446i	− 0.884529i	−0.896885	−	0.442264i	$-0.854175\pi$
$263$	− 14.3446i	− 0.884529i	0.896885	−	0.442264i	$-0.145825\pi$
$264$	−5.37210	−0.330630
$265$	0	0
$266$	−1.09039	−0.0668562
$267$	− 34.5534i	− 2.11464i
$268$	19.2961i	1.17870i
$269$	3.91172	0.238502	0.119251	−	0.992864i	$-0.461951\pi$
$269$	3.91172	0.238502	0.119251	+	0.992864i	$0.461951\pi$
$270$	0	0
$271$	28.4490	1.72816	0.864078	−	0.503358i	$-0.167902\pi$
$271$	28.4490	1.72816	0.864078	+	0.503358i	$0.167902\pi$
$272$	− 3.86375i	− 0.234274i
$273$	− 3.32629i	− 0.201316i
$274$	2.36662	0.142973
$275$	0	0
$276$	2.05371	0.123619
$277$	− 25.6839i	− 1.54320i	−0.636111	−	0.771598i	$-0.719458\pi$
$277$	− 25.6839i	− 1.54320i	0.636111	−	0.771598i	$-0.280542\pi$
$278$	1.25775i	0.0754348i
$279$	4.05836	0.242967
$280$	0	0
$281$	−20.7667	−1.23884	−0.619420	−	0.785060i	$-0.712632\pi$
$281$	−20.7667	−1.23884	−0.619420	+	0.785060i	$0.712632\pi$
$282$	3.18184i	0.189476i
$283$	− 24.4689i	− 1.45452i	−0.686360	−	0.727262i	$-0.740793\pi$
$283$	− 24.4689i	− 1.45452i	0.686360	−	0.727262i	$-0.259207\pi$
$284$	2.39669	0.142217
$285$	0	0
$286$	−0.755647	−0.0446824
$287$	− 1.16082i	− 0.0685208i
$288$	1.51491i	0.0892672i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	13.3164	0.780621
$292$	19.9964i	1.17020i
$293$	− 28.1952i	− 1.64718i	−0.567185	−	0.823591i	$-0.691967\pi$
$293$	− 28.1952i	− 1.64718i	0.567185	−	0.823591i	$-0.308033\pi$
$294$	−1.36663	−0.0797034
$295$	0	0
$296$	3.17003	0.184254
$297$	− 19.2434i	− 1.11662i
$298$	− 0.469156i	− 0.0271775i
$299$	0.581085	0.0336050
$300$	0	0
$301$	−14.6649	−0.845271
$302$	− 1.57153i	− 0.0904311i
$303$	16.1222i	0.926196i
$304$	−18.0640	−1.03604
$305$	0	0
$306$	0.128185	0.00732787
$307$	0.0120595i	0 0.000688275i	1.00000		0.000344137i	$0.000109542\pi$
$307$	0.0120595i	0 0.000688275i	−1.00000		0.000344137i	$0.999890\pi$
$308$	13.9277i	0.793605i
$309$	33.8812	1.92743
$310$	0	0
$311$	−28.5605	−1.61951	−0.809757	−	0.586765i	$-0.800401\pi$
$311$	−28.5605	−1.61951	−0.809757	+	0.586765i	$0.800401\pi$
$312$	1.29301i	0.0732022i
$313$	− 4.11691i	− 0.232702i	−0.993208	−	0.116351i	$-0.962880\pi$
$313$	− 4.11691i	− 0.232702i	0.993208	−	0.116351i	$-0.0371197\pi$
$314$	0.0999440	0.00564017
$315$	0	0
$316$	−28.5016	−1.60334
$317$	− 20.6297i	− 1.15868i	−0.815087	−	0.579338i	$-0.803311\pi$
$317$	− 20.6297i	− 1.15868i	0.815087	−	0.579338i	$-0.196689\pi$
$318$	− 0.00675207i	0 0.000378637i
$319$	−36.7846	−2.05954
$320$	0	0
$321$	−30.1874	−1.68489
$322$	0.123478i	0.00688116i
$323$	4.67524i	0.260138i
$324$	−21.4057	−1.18920
$325$	0	0
$326$	−2.45409	−0.135919
$327$	33.7878i	1.86847i
$328$	0.451237i	0.0249154i
$329$	16.5936	0.914834
$330$	0	0
$331$	−0.971759	−0.0534127	−0.0267063	−	0.999643i	$-0.508502\pi$
$331$	−0.971759	−0.0534127	−0.0267063	+	0.999643i	$0.508502\pi$
$332$	− 10.0630i	− 0.552277i
$333$	− 4.48212i	− 0.245618i
$334$	−3.01246	−0.164835
$335$	0	0
$336$	11.7096	0.638810
$337$	6.01450i	0.327630i	0.986491	+	0.163815i	$0.0523801\pi$
$337$	6.01450i	0.327630i	−0.986491	+	0.163815i	$0.947620\pi$
$338$	− 1.78087i	− 0.0968665i
$339$	37.1900	2.01988
$340$	0	0
$341$	−21.7973	−1.18039
$342$	− 0.599298i	− 0.0324063i
$343$	17.9403i	0.968686i
$344$	5.70060	0.307356
$345$	0	0
$346$	0.591416	0.0317947
$347$	5.33466i	0.286380i	0.989695	+	0.143190i	$0.0457360\pi$
$347$	5.33466i	0.286380i	−0.989695	+	0.143190i	$0.954264\pi$
$348$	31.2912i	1.67739i
$349$	20.7601	1.11126	0.555632	−	0.831429i	$-0.312476\pi$
$349$	20.7601	1.11126	0.555632	+	0.831429i	$0.312476\pi$
$350$	0	0
$351$	−4.63169	−0.247221
$352$	− 8.13656i	− 0.433680i
$353$	15.0618i	0.801659i	0.916153	+	0.400829i	$0.131278\pi$
$353$	15.0618i	0.801659i	−0.916153	+	0.400829i	$0.868722\pi$
$354$	−1.05735	−0.0561974
$355$	0	0
$356$	34.8231	1.84562
$357$	− 3.03063i	− 0.160398i
$358$	0.474335i	0.0250694i
$359$	9.72949	0.513503	0.256751	−	0.966477i	$-0.417348\pi$
$359$	9.72949	0.513503	0.256751	+	0.966477i	$0.417348\pi$
$360$	0	0
$361$	2.85791	0.150416
$362$	− 0.118080i	− 0.00620613i
$363$	− 19.2151i	− 1.00853i
$364$	3.35225	0.175706
$365$	0	0
$366$	−1.16225	−0.0607519
$367$	8.62563i	0.450254i	0.974329	+	0.225127i	$0.0722797\pi$
$367$	8.62563i	0.450254i	−0.974329	+	0.225127i	$0.927720\pi$
$368$	2.04560i	0.106634i
$369$	0.638005	0.0332132
$370$	0	0
$371$	−0.0352126	−0.00182815
$372$	18.5421i	0.961364i
$373$	15.0922i	0.781444i	0.920509	+	0.390722i	$0.127775\pi$
$373$	15.0922i	0.781444i	−0.920509	+	0.390722i	$0.872225\pi$
$374$	−0.688480	−0.0356004
$375$	0	0
$376$	−6.45032	−0.332650
$377$	8.85368i	0.455988i
$378$	− 0.984214i	− 0.0506225i
$379$	10.7124	0.550261	0.275131	−	0.961407i	$-0.411279\pi$
$379$	10.7124	0.550261	0.275131	+	0.961407i	$0.411279\pi$
$380$	0	0
$381$	−30.6297	−1.56920
$382$	− 1.87448i	− 0.0959070i
$383$	− 15.8670i	− 0.810764i	−0.914147	−	0.405382i	$-0.867139\pi$
$383$	− 15.8670i	− 0.810764i	0.914147	−	0.405382i	$-0.132861\pi$
$384$	−9.21039	−0.470016
$385$	0	0
$386$	0.257369	0.0130997
$387$	− 8.06009i	− 0.409717i
$388$	13.4203i	0.681315i
$389$	−22.3496	−1.13317	−0.566585	−	0.824003i	$-0.691736\pi$
$389$	−22.3496	−1.13317	−0.566585	+	0.824003i	$0.691736\pi$
$390$	0	0
$391$	0.529434	0.0267746
$392$	− 2.77047i	− 0.139930i
$393$	9.40391i	0.474364i
$394$	2.45728	0.123796
$395$	0	0
$396$	−7.65491	−0.384674
$397$	31.3003i	1.57092i	0.618915	+	0.785458i	$0.287572\pi$
$397$	31.3003i	1.57092i	−0.618915	+	0.785458i	$0.712428\pi$
$398$	2.59605i	0.130128i
$399$	−14.1689	−0.709333
$400$	0	0
$401$	32.0373	1.59987	0.799934	−	0.600088i	$-0.204868\pi$
$401$	32.0373	1.59987	0.799934	+	0.600088i	$0.204868\pi$
$402$	− 2.89077i	− 0.144179i
$403$	5.24639i	0.261341i
$404$	−16.2480	−0.808370
$405$	0	0
$406$	−1.88137	−0.0933707
$407$	24.0733i	1.19327i
$408$	1.17808i	0.0583235i
$409$	21.5037	1.06329	0.531645	−	0.846968i	$-0.321574\pi$
$409$	21.5037	1.06329	0.531645	+	0.846968i	$0.321574\pi$
$410$	0	0
$411$	30.7527	1.51692
$412$	34.1456i	1.68223i
$413$	5.51416i	0.271334i
$414$	−0.0678656	−0.00333541
$415$	0	0
$416$	−1.95839	−0.0960178
$417$	16.3436i	0.800352i
$418$	3.21881i	0.157437i
$419$	16.7246	0.817048	0.408524	−	0.912748i	$-0.366044\pi$
$419$	16.7246	0.817048	0.408524	+	0.912748i	$0.366044\pi$
$420$	0	0
$421$	−16.9873	−0.827908	−0.413954	−	0.910298i	$-0.635853\pi$
$421$	−16.9873	−0.827908	−0.413954	+	0.910298i	$0.635853\pi$
$422$	− 0.303528i	− 0.0147755i
$423$	9.12012i	0.443435i
$424$	0.0136880	0.000664748 0
$425$	0	0
$426$	−0.359051	−0.0173961
$427$	6.06125i	0.293325i
$428$	− 30.4230i	− 1.47055i
$429$	−9.81914	−0.474073
$430$	0	0
$431$	−17.0941	−0.823392	−0.411696	−	0.911321i	$-0.635064\pi$
$431$	−17.0941	−0.823392	−0.411696	+	0.911321i	$0.635064\pi$
$432$	− 16.3050i	− 0.784474i
$433$	− 9.95242i	− 0.478283i	−0.970985	−	0.239141i	$-0.923134\pi$
$433$	− 9.95242i	− 0.478283i	0.970985	−	0.239141i	$-0.0768659\pi$
$434$	−1.11483	−0.0535138
$435$	0	0
$436$	−34.0516	−1.63077
$437$	− 2.47523i	− 0.118406i
$438$	− 2.99568i	− 0.143139i
$439$	−2.92877	−0.139782	−0.0698912	−	0.997555i	$-0.522265\pi$
$439$	−2.92877	−0.139782	−0.0698912	+	0.997555i	$0.522265\pi$
$440$	0	0
$441$	−3.91717	−0.186532
$442$	0.165710i	0.00788202i
$443$	0.778484i	0.0369869i	0.999829	+	0.0184934i	$0.00588698\pi$
$443$	0.778484i	0.0369869i	−0.999829	+	0.0184934i	$0.994113\pi$
$444$	20.4782	0.971853
$445$	0	0
$446$	−2.12994	−0.100856
$447$	− 6.09637i	− 0.288349i
$448$	11.5209i	0.544310i
$449$	31.2804	1.47621	0.738107	−	0.674684i	$-0.235720\pi$
$449$	31.2804	1.47621	0.738107	+	0.674684i	$0.235720\pi$
$450$	0	0
$451$	−3.42670	−0.161357
$452$	37.4803i	1.76292i
$453$	− 20.4209i	− 0.959460i
$454$	2.37215	0.111331
$455$	0	0
$456$	5.50780	0.257926
$457$	− 3.59265i	− 0.168057i	−0.996463	−	0.0840285i	$-0.973221\pi$
$457$	− 3.59265i	− 0.168057i	0.996463	−	0.0840285i	$-0.0267787\pi$
$458$	2.50509i	0.117055i
$459$	−4.21999	−0.196972
$460$	0	0
$461$	−6.60392	−0.307575	−0.153788	−	0.988104i	$-0.549147\pi$
$461$	−6.60392	−0.307575	−0.153788	+	0.988104i	$0.549147\pi$
$462$	− 2.08652i	− 0.0970739i
$463$	− 10.9502i	− 0.508898i	−0.967086	−	0.254449i	$-0.918106\pi$
$463$	− 10.9502i	− 0.508898i	0.967086	−	0.254449i	$-0.0818941\pi$
$464$	−31.1677	−1.44692
$465$	0	0
$466$	0.991002	0.0459073
$467$	10.1288i	0.468704i	0.972152	+	0.234352i	$0.0752968\pi$
$467$	10.1288i	0.468704i	−0.972152	+	0.234352i	$0.924703\pi$
$468$	1.84246i	0.0851676i
$469$	−15.0756	−0.696128
$470$	0	0
$471$	1.29871	0.0598413
$472$	− 2.14349i	− 0.0986619i
$473$	43.2905i	1.99050i
$474$	4.26986	0.196121
$475$	0	0
$476$	3.05428	0.139993
$477$	− 0.0193535i	0 0.000886135i
$478$	− 1.15075i	− 0.0526339i
$479$	7.73039	0.353211	0.176605	−	0.984282i	$-0.443488\pi$
$479$	7.73039	0.353211	0.176605	+	0.984282i	$0.443488\pi$
$480$	0	0
$481$	5.79420	0.264193
$482$	− 1.04109i	− 0.0474204i
$483$	1.60452i	0.0730080i
$484$	19.3650	0.880229
$485$	0	0
$486$	1.29540	0.0587605
$487$	− 13.5925i	− 0.615933i	−0.951397	−	0.307966i	$-0.900352\pi$
$487$	− 13.5925i	− 0.615933i	0.951397	−	0.307966i	$-0.0996485\pi$
$488$	− 2.35615i	− 0.106658i
$489$	−31.8892	−1.44208
$490$	0	0
$491$	38.8592	1.75369	0.876846	−	0.480772i	$-0.159643\pi$
$491$	38.8592	1.75369	0.876846	+	0.480772i	$0.159643\pi$
$492$	2.91496i	0.131417i
$493$	8.06670i	0.363306i
$494$	0.774734	0.0348569
$495$	0	0
$496$	−18.4689	−0.829279
$497$	1.87248i	0.0839922i
$498$	1.50754i	0.0675547i
$499$	26.6894	1.19478	0.597391	−	0.801950i	$-0.296204\pi$
$499$	26.6894	1.19478	0.597391	+	0.801950i	$0.296204\pi$
$500$	0	0
$501$	−39.1450	−1.74887
$502$	3.90022i	0.174075i
$503$	− 0.591853i	− 0.0263894i	−0.999913	−	0.0131947i	$-0.995800\pi$
$503$	− 0.591853i	− 0.0263894i	0.999913	−	0.0131947i	$-0.00420013\pi$
$504$	−0.787542	−0.0350799
$505$	0	0
$506$	0.364504	0.0162042
$507$	− 23.1412i	− 1.02774i
$508$	− 30.8687i	− 1.36958i
$509$	−11.6397	−0.515922	−0.257961	−	0.966155i	$-0.583051\pi$
$509$	−11.6397	−0.515922	−0.257961	+	0.966155i	$0.583051\pi$
$510$	0	0
$511$	−15.6227	−0.691109
$512$	− 11.5343i	− 0.509750i
$513$	19.7295i	0.871078i
$514$	−2.69486	−0.118865
$515$	0	0
$516$	36.8255	1.62115
$517$	− 48.9839i	− 2.15431i
$518$	1.23124i	0.0540976i
$519$	7.68506	0.337337
$520$	0	0
$521$	−11.5584	−0.506382	−0.253191	−	0.967416i	$-0.581480\pi$
$521$	−11.5584	−0.506382	−0.253191	+	0.967416i	$0.581480\pi$
$522$	− 1.03403i	− 0.0452584i
$523$	14.5087i	0.634420i	0.948355	+	0.317210i	$0.102746\pi$
$523$	14.5087i	0.634420i	−0.948355	+	0.317210i	$0.897254\pi$
$524$	−9.47731	−0.414018
$525$	0	0
$526$	−2.16576	−0.0944316
$527$	4.78005i	0.208222i
$528$	− 34.5664i	− 1.50431i
$529$	22.7197	0.987813
$530$	0	0
$531$	−3.03068	−0.131520
$532$	− 14.2795i	− 0.619095i
$533$	0.824772i	0.0357249i
$534$	−5.21689	−0.225757
$535$	0	0
$536$	5.86026	0.253125
$537$	6.16367i	0.265982i
$538$	− 0.590594i	− 0.0254623i
$539$	21.0390	0.906214
$540$	0	0
$541$	−3.23241	−0.138972	−0.0694860	−	0.997583i	$-0.522136\pi$
$541$	−3.23241	−0.138972	−0.0694860	+	0.997583i	$0.522136\pi$
$542$	− 4.29525i	− 0.184497i
$543$	− 1.53437i	− 0.0658461i
$544$	−1.78431	−0.0765017
$545$	0	0
$546$	−0.502205	−0.0214924
$547$	− 38.7154i	− 1.65535i	−0.561206	−	0.827676i	$-0.689662\pi$
$547$	− 38.7154i	− 1.65535i	0.561206	−	0.827676i	$-0.310338\pi$
$548$	30.9927i	1.32394i
$549$	−3.33137	−0.142179
$550$	0	0
$551$	37.7138	1.60666
$552$	− 0.623714i	− 0.0265470i
$553$	− 22.2677i	− 0.946919i
$554$	−3.87777	−0.164750
$555$	0	0
$556$	−16.4712	−0.698535
$557$	− 0.669168i	− 0.0283536i	−0.999900	−	0.0141768i	$-0.995487\pi$
$557$	− 0.669168i	− 0.0283536i	0.999900	−	0.0141768i	$-0.00451276\pi$
$558$	− 0.612732i	− 0.0259390i
$559$	10.4196	0.440701
$560$	0	0
$561$	−8.94634	−0.377715
$562$	3.13537i	0.132258i
$563$	− 42.4772i	− 1.79020i	−0.445864	−	0.895101i	$-0.647104\pi$
$563$	− 42.4772i	− 1.79020i	0.445864	−	0.895101i	$-0.352896\pi$
$564$	−41.6687	−1.75457
$565$	0	0
$566$	−3.69432	−0.155284
$567$	− 16.7238i	− 0.702333i
$568$	− 0.727878i	− 0.0305411i
$569$	−36.3706	−1.52474	−0.762368	−	0.647143i	$-0.775964\pi$
$569$	−36.3706	−1.52474	−0.762368	+	0.647143i	$0.775964\pi$
$570$	0	0
$571$	26.5970	1.11305	0.556525	−	0.830831i	$-0.312134\pi$
$571$	26.5970	1.11305	0.556525	+	0.830831i	$0.312134\pi$
$572$	− 9.89578i	− 0.413763i
$573$	− 24.3577i	− 1.01756i
$574$	−0.175260	−0.00731523
$575$	0	0
$576$	−6.33207	−0.263836
$577$	2.30741i	0.0960586i	0.998846	+	0.0480293i	$0.0152941\pi$
$577$	2.30741i	0.0960586i	−0.998846	+	0.0480293i	$0.984706\pi$
$578$	0.150980i	0.00627996i
$579$	3.34434	0.138986
$580$	0	0
$581$	7.86198	0.326170
$582$	− 2.01052i	− 0.0833386i
$583$	0.103947i	0.00430504i
$584$	6.07293	0.251300
$585$	0	0
$586$	−4.25692	−0.175852
$587$	− 25.8915i	− 1.06866i	−0.845277	−	0.534329i	$-0.820564\pi$
$587$	− 25.8915i	− 1.06866i	0.845277	−	0.534329i	$-0.179436\pi$
$588$	− 17.8971i	− 0.738062i
$589$	22.3479	0.920829
$590$	0	0
$591$	31.9308	1.31346
$592$	20.3974i	0.838327i
$593$	42.0620i	1.72728i	0.504109	+	0.863640i	$0.331821\pi$
$593$	42.0620i	1.72728i	−0.504109	+	0.863640i	$0.668179\pi$
$594$	−2.90538	−0.119209
$595$	0	0
$596$	6.14396	0.251666
$597$	33.7340i	1.38064i
$598$	− 0.0877324i	− 0.00358765i
$599$	−23.6399	−0.965902	−0.482951	−	0.875647i	$-0.660435\pi$
$599$	−23.6399	−0.965902	−0.482951	+	0.875647i	$0.660435\pi$
$600$	0	0
$601$	−9.89731	−0.403720	−0.201860	−	0.979414i	$-0.564699\pi$
$601$	−9.89731	−0.403720	−0.201860	+	0.979414i	$0.564699\pi$
$602$	2.21411i	0.0902405i
$603$	− 8.28583i	− 0.337425i
$604$	20.5803	0.837402
$605$	0	0
$606$	2.43414	0.0988800
$607$	− 29.5988i	− 1.20138i	−0.799483	−	0.600688i	$-0.794893\pi$
$607$	− 29.5988i	− 1.20138i	0.799483	−	0.600688i	$-0.205107\pi$
$608$	8.34209i	0.338316i
$609$	−24.4471	−0.990648
$610$	0	0
$611$	−11.7899	−0.476969
$612$	1.67869i	0.0678568i
$613$	13.6657i	0.551953i	0.961164	+	0.275977i	$0.0890013\pi$
$613$	13.6657i	0.551953i	−0.961164	+	0.275977i	$0.910999\pi$
$614$	0.00182076	7.34797e−5 0
$615$	0	0
$616$	4.22986	0.170426
$617$	− 41.8255i	− 1.68383i	−0.539609	−	0.841916i	$-0.681428\pi$
$617$	− 41.8255i	− 1.68383i	0.539609	−	0.841916i	$-0.318572\pi$
$618$	− 5.11539i	− 0.205771i
$619$	−17.8194	−0.716221	−0.358110	−	0.933679i	$-0.616579\pi$
$619$	−17.8194	−0.716221	−0.358110	+	0.933679i	$0.616579\pi$
$620$	0	0
$621$	2.23421	0.0896556
$622$	4.31207i	0.172898i
$623$	27.2066i	1.09001i
$624$	−8.31978	−0.333058
$625$	0	0
$626$	−0.621573	−0.0248431
$627$	41.8263i	1.67038i
$628$	1.30884i	0.0522286i
$629$	5.27917	0.210494
$630$	0	0
$631$	32.6557	1.30000	0.650001	−	0.759934i	$-0.274769\pi$
$631$	32.6557	1.30000	0.650001	+	0.759934i	$0.274769\pi$
$632$	8.65599i	0.344317i
$633$	− 3.94414i	− 0.156766i
$634$	−3.11467	−0.123699
$635$	0	0
$636$	0.0884235	0.00350622
$637$	− 5.06387i	− 0.200638i
$638$	5.55376i	0.219875i
$639$	−1.02915	−0.0407124
$640$	0	0
$641$	25.0356	0.988845	0.494422	−	0.869222i	$-0.335380\pi$
$641$	25.0356	0.988845	0.494422	+	0.869222i	$0.335380\pi$
$642$	4.55770i	0.179878i
$643$	− 12.4048i	− 0.489196i	−0.969625	−	0.244598i	$-0.921344\pi$
$643$	− 12.4048i	− 0.489196i	0.969625	−	0.244598i	$-0.0786560\pi$
$644$	−1.61704	−0.0637203
$645$	0	0
$646$	0.705870	0.0277721
$647$	37.9570i	1.49224i	0.665811	+	0.746121i	$0.268086\pi$
$647$	37.9570i	1.49224i	−0.665811	+	0.746121i	$0.731914\pi$
$648$	6.50093i	0.255381i
$649$	16.2777	0.638955
$650$	0	0
$651$	−14.4865	−0.567773
$652$	− 32.1382i	− 1.25863i
$653$	− 36.9847i	− 1.44732i	−0.690155	−	0.723662i	$-0.742457\pi$
$653$	− 36.9847i	− 1.44732i	0.690155	−	0.723662i	$-0.257543\pi$
$654$	5.10130	0.199477
$655$	0	0
$656$	−2.90345	−0.113361
$657$	− 8.58652i	− 0.334992i
$658$	− 2.50531i	− 0.0976670i
$659$	−29.0956	−1.13341	−0.566703	−	0.823922i	$-0.691781\pi$
$659$	−29.0956	−1.13341	−0.566703	+	0.823922i	$0.691781\pi$
$660$	0	0
$661$	33.6207	1.30769	0.653847	−	0.756627i	$-0.273154\pi$
$661$	33.6207	1.30769	0.653847	+	0.756627i	$0.273154\pi$
$662$	0.146717i	0.00570230i
$663$	2.15329i	0.0836269i
$664$	−3.05614	−0.118601
$665$	0	0
$666$	−0.676712	−0.0262220
$667$	− 4.27078i	− 0.165365i
$668$	− 39.4505i	− 1.52639i
$669$	−27.6772	−1.07006
$670$	0	0
$671$	17.8927	0.690740
$672$	− 5.40758i	− 0.208602i
$673$	13.1865i	0.508304i	0.967164	+	0.254152i	$0.0817964\pi$
$673$	13.1865i	0.508304i	−0.967164	+	0.254152i	$0.918204\pi$
$674$	0.908071	0.0349776
$675$	0	0
$676$	23.3219	0.896994
$677$	1.37696i	0.0529208i	0.999650	+	0.0264604i	$0.00842360\pi$
$677$	1.37696i	0.0529208i	−0.999650	+	0.0264604i	$0.991576\pi$
$678$	− 5.61496i	− 0.215641i
$679$	−10.4850	−0.402378
$680$	0	0
$681$	30.8246	1.18120
$682$	3.29097i	0.126018i
$683$	− 10.4181i	− 0.398637i	−0.979935	−	0.199319i	$-0.936127\pi$
$683$	− 10.4181i	− 0.398637i	0.979935	−	0.199319i	$-0.0638729\pi$
$684$	7.84827	0.300086
$685$	0	0
$686$	2.70864	0.103416
$687$	32.5520i	1.24193i
$688$	36.6801i	1.39842i
$689$	0.0250190	0.000953146 0
$690$	0	0
$691$	4.39455	0.167177	0.0835883	−	0.996500i	$-0.473362\pi$
$691$	4.39455	0.167177	0.0835883	+	0.996500i	$0.473362\pi$
$692$	7.74505i	0.294423i
$693$	− 5.98061i	− 0.227185i
$694$	0.805430	0.0305737
$695$	0	0
$696$	9.50319	0.360218
$697$	0.751460i	0.0284636i
$698$	− 3.13437i	− 0.118638i
$699$	12.8774	0.487069
$700$	0	0
$701$	−1.18383	−0.0447127	−0.0223563	−	0.999750i	$-0.507117\pi$
$701$	−1.18383	−0.0447127	−0.0223563	+	0.999750i	$0.507117\pi$
$702$	0.699294i	0.0263932i
$703$	− 24.6814i	− 0.930876i
$704$	34.0094	1.28178
$705$	0	0
$706$	2.27404	0.0855845
$707$	− 12.6942i	− 0.477416i
$708$	− 13.8468i	− 0.520394i
$709$	13.3650	0.501932	0.250966	−	0.967996i	$-0.419252\pi$
$709$	13.3650	0.501932	0.250966	+	0.967996i	$0.419252\pi$
$710$	0	0
$711$	12.2387	0.458987
$712$	− 10.5758i	− 0.396346i
$713$	− 2.53072i	− 0.0947762i
$714$	−0.457565	−0.0171239
$715$	0	0
$716$	−6.21178	−0.232145
$717$	− 14.9532i	− 0.558437i
$718$	− 1.46896i	− 0.0548212i
$719$	−14.1925	−0.529292	−0.264646	−	0.964346i	$-0.585255\pi$
$719$	−14.1925	−0.529292	−0.264646	+	0.964346i	$0.585255\pi$
$720$	0	0
$721$	−26.6772	−0.993512
$722$	− 0.431488i	− 0.0160583i
$723$	− 13.5283i	− 0.503123i
$724$	1.54635	0.0574695
$725$	0	0
$726$	−2.90110	−0.107670
$727$	33.0852i	1.22706i	0.789671	+	0.613530i	$0.210251\pi$
$727$	33.0852i	1.22706i	−0.789671	+	0.613530i	$0.789749\pi$
$728$	− 1.01808i	− 0.0377327i
$729$	−15.6458	−0.579475
$730$	0	0
$731$	9.49340	0.351126
$732$	− 15.2206i	− 0.562570i
$733$	− 14.0451i	− 0.518767i	−0.965774	−	0.259383i	$-0.916481\pi$
$733$	− 14.0451i	− 0.518767i	0.965774	−	0.259383i	$-0.0835193\pi$
$734$	1.30230	0.0480688
$735$	0	0
$736$	0.944674	0.0348212
$737$	44.5030i	1.63929i
$738$	− 0.0963262i	− 0.00354582i
$739$	5.14831	0.189384	0.0946918	−	0.995507i	$-0.469813\pi$
$739$	5.14831	0.189384	0.0946918	+	0.995507i	$0.469813\pi$
$740$	0	0
$741$	10.0672	0.369827
$742$	0.00531642i	0 0.000195172i
$743$	26.8978i	0.986784i	0.869807	+	0.493392i	$0.164243\pi$
$743$	26.8978i	0.986784i	−0.869807	+	0.493392i	$0.835757\pi$
$744$	5.63127	0.206452
$745$	0	0
$746$	2.27863	0.0834264
$747$	4.32108i	0.158100i
$748$	− 9.01617i	− 0.329664i
$749$	23.7688	0.868494
$750$	0	0
$751$	13.5733	0.495295	0.247648	−	0.968850i	$-0.420343\pi$
$751$	13.5733	0.495295	0.247648	+	0.968850i	$0.420343\pi$
$752$	− 41.5042i	− 1.51350i
$753$	50.6808i	1.84691i
$754$	1.33673	0.0486809
$755$	0	0
$756$	12.8890	0.468770
$757$	9.44665i	0.343344i	0.985154	+	0.171672i	$0.0549170\pi$
$757$	9.44665i	0.343344i	−0.985154	+	0.171672i	$0.945083\pi$
$758$	− 1.61737i	− 0.0587455i
$759$	4.73650	0.171924
$760$	0	0
$761$	−26.6325	−0.965427	−0.482713	−	0.875778i	$-0.660349\pi$
$761$	−26.6325	−0.965427	−0.482713	+	0.875778i	$0.660349\pi$
$762$	4.62448i	0.167527i
$763$	− 26.6037i	− 0.963120i
$764$	24.5478	0.888109
$765$	0	0
$766$	−2.39560	−0.0865565
$767$	− 3.91787i	− 0.141466i
$768$	− 27.8734i	− 1.00579i
$769$	17.9587	0.647609	0.323805	−	0.946124i	$-0.395038\pi$
$769$	17.9587	0.647609	0.323805	+	0.946124i	$0.395038\pi$
$770$	0	0
$771$	−35.0180	−1.26114
$772$	3.37045i	0.121305i
$773$	− 17.0705i	− 0.613984i	−0.951712	−	0.306992i	$-0.900677\pi$
$773$	− 17.0705i	− 0.613984i	0.951712	−	0.306992i	$-0.0993226\pi$
$774$	−1.21691	−0.0437411
$775$	0	0
$776$	4.07578	0.146312
$777$	15.9992i	0.573967i
$778$	3.37436i	0.120976i
$779$	3.51326	0.125876
$780$	0	0
$781$	5.52752	0.197790
$782$	− 0.0799341i	− 0.00285844i
$783$	34.0414i	1.21654i
$784$	17.8264	0.636657
$785$	0	0
$786$	1.41981	0.0506428
$787$	18.3219i	0.653104i	0.945179	+	0.326552i	$0.105887\pi$
$787$	18.3219i	0.653104i	−0.945179	+	0.326552i	$0.894113\pi$
$788$	32.1800i	1.14636i
$789$	−28.1426	−1.00190
$790$	0	0
$791$	−29.2825	−1.04117
$792$	2.32481i	0.0826084i
$793$	− 4.30658i	− 0.152931i
$794$	4.72573	0.167710
$795$	0	0
$796$	−33.9973	−1.20500
$797$	− 16.4573i	− 0.582949i	−0.956579	−	0.291474i	$-0.905854\pi$
$797$	− 16.4573i	− 0.582949i	0.956579	−	0.291474i	$-0.0941458\pi$
$798$	2.13923i	0.0757279i
$799$	−10.7419	−0.380023
$800$	0	0
$801$	−14.9532	−0.528345
$802$	− 4.83701i	− 0.170801i
$803$	46.1180i	1.62747i
$804$	37.8569	1.33511
$805$	0	0
$806$	0.792102	0.0279006
$807$	− 7.67438i	− 0.270151i
$808$	4.93455i	0.173597i
$809$	−19.3869	−0.681607	−0.340804	−	0.940134i	$-0.610699\pi$
$809$	−19.3869	−0.681607	−0.340804	+	0.940134i	$0.610699\pi$
$810$	0	0
$811$	−27.4015	−0.962196	−0.481098	−	0.876667i	$-0.659762\pi$
$811$	−27.4015	−0.962196	−0.481098	+	0.876667i	$0.659762\pi$
$812$	− 24.6380i	− 0.864623i
$813$	− 55.8139i	− 1.95748i
$814$	3.63460	0.127393
$815$	0	0
$816$	−7.58026	−0.265362
$817$	− 44.3840i	− 1.55280i
$818$	− 3.24664i	− 0.113516i
$819$	−1.43947	−0.0502992
$820$	0	0
$821$	20.6646	0.721198	0.360599	−	0.932721i	$-0.382572\pi$
$821$	20.6646	0.721198	0.360599	+	0.932721i	$0.382572\pi$
$822$	− 4.64305i	− 0.161945i
$823$	0.983957i	0.0342986i	0.999853	+	0.0171493i	$0.00545906\pi$
$823$	0.983957i	0.0342986i	−0.999853	+	0.0171493i	$0.994541\pi$
$824$	10.3701	0.361259
$825$	0	0
$826$	0.832530	0.0289674
$827$	− 15.5237i	− 0.539811i	−0.962887	−	0.269906i	$-0.913008\pi$
$827$	− 15.5237i	− 0.539811i	0.962887	−	0.269906i	$-0.0869925\pi$
$828$	− 0.888753i	− 0.0308863i
$829$	41.6910	1.44799	0.723994	−	0.689806i	$-0.242304\pi$
$829$	41.6910	1.44799	0.723994	+	0.689806i	$0.242304\pi$
$830$	0	0
$831$	−50.3890	−1.74798
$832$	− 8.18571i	− 0.283788i
$833$	− 4.61376i	− 0.159857i
$834$	2.46757	0.0854449
$835$	0	0
$836$	−42.1528	−1.45789
$837$	20.1718i	0.697238i
$838$	− 2.52508i	− 0.0872274i
$839$	−11.0633	−0.381949	−0.190974	−	0.981595i	$-0.561165\pi$
$839$	−11.0633	−0.381949	−0.190974	+	0.981595i	$0.561165\pi$
$840$	0	0
$841$	36.0716	1.24385
$842$	2.56474i	0.0883869i
$843$	40.7421i	1.40323i
$844$	3.97493	0.136823
$845$	0	0
$846$	1.37696	0.0473408
$847$	15.1295i	0.519855i
$848$	0.0880745i	0.00302449i
$849$	−48.0053	−1.64754
$850$	0	0
$851$	−2.79497	−0.0958103
$852$	− 4.70204i	− 0.161089i
$853$	16.9575i	0.580615i	0.956933	+	0.290307i	$0.0937576\pi$
$853$	16.9575i	0.580615i	−0.956933	+	0.290307i	$0.906242\pi$
$854$	0.915130	0.0313151
$855$	0	0
$856$	−9.23951	−0.315800
$857$	21.7394i	0.742605i	0.928512	+	0.371302i	$0.121089\pi$
$857$	21.7394i	0.742605i	−0.928512	+	0.371302i	$0.878911\pi$
$858$	1.48250i	0.0506117i
$859$	−31.5036	−1.07489	−0.537444	−	0.843300i	$-0.680610\pi$
$859$	−31.5036	−1.07489	−0.537444	+	0.843300i	$0.680610\pi$
$860$	0	0
$861$	−2.27740	−0.0776134
$862$	2.58087i	0.0879048i
$863$	− 12.4798i	− 0.424817i	−0.977181	−	0.212408i	$-0.931869\pi$
$863$	− 12.4798i	− 0.424817i	0.977181	−	0.212408i	$-0.0681307\pi$
$864$	−7.52977	−0.256168
$865$	0	0
$866$	−1.50262	−0.0510611
$867$	1.96189i	0.0666293i
$868$	− 14.5996i	− 0.495543i
$869$	−65.7338	−2.22987
$870$	0	0
$871$	10.7114	0.362942
$872$	10.3415i	0.350208i
$873$	− 5.76275i	− 0.195039i
$874$	−0.373712	−0.0126410
$875$	0	0
$876$	39.2307	1.32548
$877$	− 14.5835i	− 0.492450i	−0.969213	−	0.246225i	$-0.920810\pi$
$877$	− 14.5835i	− 0.492450i	0.969213	−	0.246225i	$-0.0791902\pi$
$878$	0.442186i	0.0149231i
$879$	−55.3159	−1.86576
$880$	0	0
$881$	−12.4663	−0.420001	−0.210001	−	0.977701i	$-0.567347\pi$
$881$	−12.4663	−0.420001	−0.210001	+	0.977701i	$0.567347\pi$
$882$	0.591416i	0.0199140i
$883$	− 52.0737i	− 1.75242i	−0.481931	−	0.876209i	$-0.660064\pi$
$883$	− 52.0737i	− 1.75242i	0.481931	−	0.876209i	$-0.339936\pi$
$884$	−2.17010	−0.0729883
$885$	0	0
$886$	0.117536	0.00394869
$887$	46.1318i	1.54895i	0.632602	+	0.774477i	$0.281987\pi$
$887$	46.1318i	1.54895i	−0.632602	+	0.774477i	$0.718013\pi$
$888$	− 6.21926i	− 0.208705i
$889$	24.1171	0.808860
$890$	0	0
$891$	−49.3682	−1.65390
$892$	− 27.8932i	− 0.933934i
$893$	50.2212i	1.68059i
$894$	−0.920433	−0.0307839
$895$	0	0
$896$	7.25204	0.242274
$897$	− 1.14003i	− 0.0380643i
$898$	− 4.72273i	− 0.157600i
$899$	38.5592	1.28602
$900$	0	0
$901$	0.0227951	0.000759414 0
$902$	0.517365i	0.0172264i
$903$	28.7710i	0.957437i
$904$	11.3828	0.378587
$905$	0	0
$906$	−3.08316	−0.102431
$907$	− 2.91050i	− 0.0966415i	−0.998832	−	0.0483207i	$-0.984613\pi$
$907$	− 2.91050i	− 0.0966415i	0.998832	−	0.0483207i	$-0.0153870\pi$
$908$	31.0652i	1.03093i
$909$	6.97697	0.231412
$910$	0	0
$911$	−41.7029	−1.38168	−0.690839	−	0.723009i	$-0.742759\pi$
$911$	−41.7029	−1.38168	−0.690839	+	0.723009i	$0.742759\pi$
$912$	35.4396i	1.17352i
$913$	− 23.2084i	− 0.768086i
$914$	−0.542420	−0.0179416
$915$	0	0
$916$	−32.8060	−1.08394
$917$	− 7.40441i	− 0.244515i
$918$	0.637136i	0.0210286i
$919$	2.60146	0.0858144	0.0429072	−	0.999079i	$-0.486338\pi$
$919$	2.60146	0.0858144	0.0429072	+	0.999079i	$0.486338\pi$
$920$	0	0
$921$	0.0236595	0.000779608 0
$922$	0.997063i	0.0328365i
$923$	− 1.33042i	− 0.0437912i
$924$	27.3246	0.898915
$925$	0	0
$926$	−1.65326	−0.0543296
$927$	− 14.6623i	− 0.481572i
$928$	14.3935i	0.472490i
$929$	−5.89744	−0.193489	−0.0967443	−	0.995309i	$-0.530843\pi$
$929$	−5.89744	−0.193489	−0.0967443	+	0.995309i	$0.530843\pi$
$930$	0	0
$931$	−21.5704	−0.706943
$932$	12.9779i	0.425106i
$933$	56.0325i	1.83442i
$934$	1.52925	0.0500385
$935$	0	0
$936$	0.559557	0.0182897
$937$	− 58.2446i	− 1.90277i	−0.308010	−	0.951383i	$-0.599663\pi$
$937$	− 58.2446i	− 1.90277i	0.308010	−	0.951383i	$-0.400337\pi$
$938$	2.27613i	0.0743181i
$939$	−8.07694	−0.263581
$940$	0	0
$941$	28.2631	0.921350	0.460675	−	0.887569i	$-0.347607\pi$
$941$	28.2631	0.921350	0.460675	+	0.887569i	$0.347607\pi$
$942$	− 0.196079i	− 0.00638861i
$943$	− 0.397848i	− 0.0129557i
$944$	13.7921	0.448895
$945$	0	0
$946$	6.53602	0.212504
$947$	31.3759i	1.01958i	0.860299	+	0.509789i	$0.170277\pi$
$947$	31.3759i	1.01958i	−0.860299	+	0.509789i	$0.829723\pi$
$948$	55.9171i	1.81610i
$949$	11.1001	0.360325
$950$	0	0
$951$	−40.4731	−1.31243
$952$	− 0.927590i	− 0.0300634i
$953$	27.2735i	0.883476i	0.897144	+	0.441738i	$0.145638\pi$
$953$	27.2735i	0.883476i	−0.897144	+	0.441738i	$0.854362\pi$
$954$	−0.00292200	−9.46031e−5 0
$955$	0	0
$956$	15.0699	0.487396
$957$	72.1675i	2.33284i
$958$	− 1.16714i	− 0.0377085i
$959$	−24.2139	−0.781908
$960$	0	0
$961$	−8.15111	−0.262939
$962$	− 0.874810i	− 0.0282050i
$963$	13.0638i	0.420974i
$964$	13.6339	0.439118
$965$	0	0
$966$	0.242250	0.00779428
$967$	1.30807i	0.0420648i	0.999779	+	0.0210324i	$0.00669531\pi$
$967$	1.30807i	0.0420648i	−0.999779	+	0.0210324i	$0.993305\pi$
$968$	− 5.88119i	− 0.189029i
$969$	9.17232	0.294657
$970$	0	0
$971$	−41.0902	−1.31865	−0.659324	−	0.751859i	$-0.729157\pi$
$971$	−41.0902	−1.31865	−0.659324	+	0.751859i	$0.729157\pi$
$972$	16.9642i	0.544128i
$973$	− 12.8686i	− 0.412548i
$974$	−2.05219	−0.0657566
$975$	0	0
$976$	15.1605	0.485276
$977$	60.7556i	1.94375i	0.235507	+	0.971873i	$0.424325\pi$
$977$	60.7556i	1.94375i	−0.235507	+	0.971873i	$0.575675\pi$
$978$	4.81465i	0.153956i
$979$	80.3132	2.56682
$980$	0	0
$981$	14.6219	0.466840
$982$	− 5.86698i	− 0.187223i
$983$	9.13830i	0.291466i	0.989324	+	0.145733i	$0.0465541\pi$
$983$	9.13830i	0.291466i	−0.989324	+	0.145733i	$0.953446\pi$
$984$	0.885278	0.0282216
$985$	0	0
$986$	1.21791	0.0387863
$987$	− 32.5548i	− 1.03623i
$988$	10.1457i	0.322779i
$989$	−5.02613	−0.159822
$990$	0	0
$991$	33.1886	1.05427	0.527135	−	0.849782i	$-0.323266\pi$
$991$	33.1886	1.05427	0.527135	+	0.849782i	$0.323266\pi$
$992$	8.52909i	0.270799i
$993$	1.90649i	0.0605005i
$994$	0.282708	0.00896695
$995$	0	0
$996$	−19.7425	−0.625564
$997$	30.0746i	0.952471i	0.879318	+	0.476235i	$0.157999\pi$
$997$	30.0746i	0.952471i	−0.879318	+	0.476235i	$0.842001\pi$
$998$	− 4.02958i	− 0.127554i
$999$	22.2780	0.704846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.b.f.324.5		10
5.2	odd	4		425.2.a.i.1.3	✓	5
5.3	odd	4		425.2.a.j.1.3	yes	5
5.4	even	2	inner	425.2.b.f.324.6		10
15.2	even	4		3825.2.a.bq.1.3		5
15.8	even	4		3825.2.a.bl.1.3		5
20.3	even	4		6800.2.a.cd.1.2		5
20.7	even	4		6800.2.a.bz.1.4		5
85.33	odd	4		7225.2.a.y.1.3		5
85.67	odd	4		7225.2.a.x.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.a.i.1.3	✓	5	5.2	odd	4
425.2.a.j.1.3	yes	5	5.3	odd	4
425.2.b.f.324.5		10	1.1	even	1	trivial
425.2.b.f.324.6		10	5.4	even	2	inner
3825.2.a.bl.1.3		5	15.8	even	4
3825.2.a.bq.1.3		5	15.2	even	4
6800.2.a.bz.1.4		5	20.7	even	4
6800.2.a.cd.1.2		5	20.3	even	4
7225.2.a.x.1.3		5	85.67	odd	4
7225.2.a.y.1.3		5	85.33	odd	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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.150980i q^{2} -1.96189i q^{3} +1.97720 q^{4} -0.296207 q^{6} +1.54475i q^{7} -0.600480i q^{8} -0.849020 q^{9} +4.56006 q^{11} -3.87906i q^{12} -1.09756i q^{13} +0.233227 q^{14} +3.86375 q^{16} -1.00000i q^{17} +0.128185i q^{18} -4.67524 q^{19} +3.03063 q^{21} -0.688480i q^{22} +0.529434i q^{23} -1.17808 q^{24} -0.165710 q^{26} -4.21999i q^{27} +3.05428i q^{28} -8.06670 q^{29} -4.78005 q^{31} -1.78431i q^{32} -8.94634i q^{33} -0.150980 q^{34} -1.67869 q^{36} +5.27917i q^{37} +0.705870i q^{38} -2.15329 q^{39} -0.751460 q^{41} -0.457565i q^{42} +9.49340i q^{43} +9.01617 q^{44} +0.0799341 q^{46} -10.7419i q^{47} -7.58026i q^{48} +4.61376 q^{49} -1.96189 q^{51} -2.17010i q^{52} +0.0227951i q^{53} -0.637136 q^{54} +0.927590 q^{56} +9.17232i q^{57} +1.21791i q^{58} +3.56962 q^{59} +3.92378 q^{61} +0.721694i q^{62} -1.31152i q^{63} +7.45810 q^{64} -1.35072 q^{66} +9.75929i q^{67} -1.97720i q^{68} +1.03869 q^{69} +1.21216 q^{71} +0.509819i q^{72} +10.1135i q^{73} +0.797051 q^{74} -9.24392 q^{76} +7.04414i q^{77} +0.325105i q^{78} -14.4151 q^{79} -10.8262 q^{81} +0.113456i q^{82} -5.08949i q^{83} +5.99217 q^{84} +1.43332 q^{86} +15.8260i q^{87} -2.73822i q^{88} +17.6123 q^{89} +1.69545 q^{91} +1.04680i q^{92} +9.37794i q^{93} -1.62182 q^{94} -3.50062 q^{96} +6.78753i q^{97} -0.696587i q^{98} -3.87158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 22 q^{4} + 6 q^{6} - 12 q^{9} + 8 q^{11} + 14 q^{14} + 54 q^{16} - 12 q^{19} - 10 q^{21} + 38 q^{24} - 10 q^{26} - 4 q^{29} + 42 q^{31} + 2 q^{34} + 44 q^{36} - 46 q^{39} - 16 q^{41} + 8 q^{44} - 12 q^{46}+ \cdots + 28 q^{99}+O(q^{100}) \) 10 * q - 22 * q^4 + 6 * q^6 - 12 * q^9 + 8 * q^11 + 14 * q^14 + 54 * q^16 - 12 * q^19 - 10 * q^21 + 38 * q^24 - 10 * q^26 - 4 * q^29 + 42 * q^31 + 2 * q^34 + 44 * q^36 - 46 * q^39 - 16 * q^41 + 8 * q^44 - 12 * q^46 - 20 * q^49 + 2 * q^51 + 50 * q^54 - 58 * q^56 - 24 * q^59 - 4 * q^61 - 86 * q^64 - 56 * q^66 + 42 * q^71 + 100 * q^74 - 28 * q^76 - 82 * q^79 - 70 * q^81 + 142 * q^84 - 72 * q^86 + 20 * q^89 + 26 * q^91 + 20 * q^94 - 170 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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