LMFDB - Embedded newform 435.4.a.i.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,4,Mod(1,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("435.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$25.6658308525$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 $ x^7 - 2x^6 - 37x^5 + 55x^4 + 336x^3 - 227x^2 - 824x - 166
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-4.88324$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.88324 q^{2} -3.00000 q^{3} +15.8460 q^{4} +5.00000 q^{5} -14.6497 q^{6} +5.48750 q^{7} +38.3141 q^{8} +9.00000 q^{9} +24.4162 q^{10} +50.1324 q^{11} -47.5381 q^{12} -20.7349 q^{13} +26.7968 q^{14} -15.0000 q^{15} +60.3288 q^{16} -18.8027 q^{17} +43.9492 q^{18} +78.8346 q^{19} +79.2302 q^{20} -16.4625 q^{21} +244.809 q^{22} -6.33763 q^{23} -114.942 q^{24} +25.0000 q^{25} -101.254 q^{26} -27.0000 q^{27} +86.9552 q^{28} +29.0000 q^{29} -73.2486 q^{30} +310.950 q^{31} -11.9130 q^{32} -150.397 q^{33} -91.8182 q^{34} +27.4375 q^{35} +142.614 q^{36} -338.745 q^{37} +384.969 q^{38} +62.2047 q^{39} +191.571 q^{40} +353.526 q^{41} -80.3904 q^{42} +507.609 q^{43} +794.400 q^{44} +45.0000 q^{45} -30.9482 q^{46} -112.771 q^{47} -180.986 q^{48} -312.887 q^{49} +122.081 q^{50} +56.4081 q^{51} -328.566 q^{52} -144.849 q^{53} -131.848 q^{54} +250.662 q^{55} +210.249 q^{56} -236.504 q^{57} +141.614 q^{58} -342.739 q^{59} -237.691 q^{60} +357.486 q^{61} +1518.44 q^{62} +49.3875 q^{63} -540.804 q^{64} -103.675 q^{65} -734.426 q^{66} -183.087 q^{67} -297.949 q^{68} +19.0129 q^{69} +133.984 q^{70} -594.034 q^{71} +344.827 q^{72} -622.609 q^{73} -1654.17 q^{74} -75.0000 q^{75} +1249.22 q^{76} +275.102 q^{77} +303.761 q^{78} -1275.18 q^{79} +301.644 q^{80} +81.0000 q^{81} +1726.35 q^{82} -739.108 q^{83} -260.866 q^{84} -94.0136 q^{85} +2478.78 q^{86} -87.0000 q^{87} +1920.78 q^{88} +906.113 q^{89} +219.746 q^{90} -113.783 q^{91} -100.426 q^{92} -932.849 q^{93} -550.688 q^{94} +394.173 q^{95} +35.7390 q^{96} +76.0665 q^{97} -1527.90 q^{98} +451.192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19}+ \cdots + 684 q^{99}+O(q^{100}) $ 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * q^99

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 $

$2$	4.88324	1.72649	0.863243	−	0.504788i	$-0.168429\pi$
$2$	4.88324	1.72649	0.863243	+	0.504788i	$0.168429\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	15.8460	1.98076
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−14.6497	−0.996787
$7$	5.48750	0.296297	0.148149	−	0.988965i	$-0.452669\pi$
$7$	5.48750	0.296297	0.148149	+	0.988965i	$0.452669\pi$
$8$	38.3141	1.69326
$9$	9.00000	0.333333
$10$	24.4162	0.772108
$11$	50.1324	1.37413	0.687067	−	0.726594i	$-0.258898\pi$
$11$	50.1324	1.37413	0.687067	+	0.726594i	$0.258898\pi$
$12$	−47.5381	−1.14359
$13$	−20.7349	−0.442371	−0.221186	−	0.975232i	$-0.570993\pi$
$13$	−20.7349	−0.442371	−0.221186	+	0.975232i	$0.570993\pi$
$14$	26.7968	0.511553
$15$	−15.0000	−0.258199
$16$	60.3288	0.942637
$17$	−18.8027	−0.268255	−0.134127	−	0.990964i	$-0.542823\pi$
$17$	−18.8027	−0.268255	−0.134127	+	0.990964i	$0.542823\pi$
$18$	43.9492	0.575496
$19$	78.8346	0.951890	0.475945	−	0.879475i	$-0.342106\pi$
$19$	78.8346	0.951890	0.475945	+	0.879475i	$0.342106\pi$
$20$	79.2302	0.885821
$21$	−16.4625	−0.171067
$22$	244.809	2.37243
$23$	−6.33763	−0.0574559	−0.0287280	−	0.999587i	$-0.509146\pi$
$23$	−6.33763	−0.0574559	−0.0287280	+	0.999587i	$0.509146\pi$
$24$	−114.942	−0.977605
$25$	25.0000	0.200000
$26$	−101.254	−0.763748
$27$	−27.0000	−0.192450
$28$	86.9552	0.586892
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−73.2486	−0.445777
$31$	310.950	1.80156	0.900778	−	0.434280i	$-0.142997\pi$
$31$	310.950	1.80156	0.900778	+	0.434280i	$0.142997\pi$
$32$	−11.9130	−0.0658106
$33$	−150.397	−0.793357
$34$	−91.8182	−0.463138
$35$	27.4375	0.132508
$36$	142.614	0.660252
$37$	−338.745	−1.50512	−0.752558	−	0.658525i	$-0.771180\pi$
$37$	−338.745	−1.50512	−0.752558	+	0.658525i	$0.771180\pi$
$38$	384.969	1.64343
$39$	62.2047	0.255403
$40$	191.571	0.757250
$41$	353.526	1.34662	0.673312	−	0.739359i	$-0.264871\pi$
$41$	353.526	1.34662	0.673312	+	0.739359i	$0.264871\pi$
$42$	−80.3904	−0.295345
$43$	507.609	1.80022	0.900112	−	0.435658i	$-0.143484\pi$
$43$	507.609	1.80022	0.900112	+	0.435658i	$0.143484\pi$
$44$	794.400	2.72183
$45$	45.0000	0.149071
$46$	−30.9482	−0.0991969
$47$	−112.771	−0.349986	−0.174993	−	0.984570i	$-0.555990\pi$
$47$	−112.771	−0.349986	−0.174993	+	0.984570i	$0.555990\pi$
$48$	−180.986	−0.544232
$49$	−312.887	−0.912208
$50$	122.081	0.345297
$51$	56.4081	0.154877
$52$	−328.566	−0.876230
$53$	−144.849	−0.375406	−0.187703	−	0.982226i	$-0.560104\pi$
$53$	−144.849	−0.375406	−0.187703	+	0.982226i	$0.560104\pi$
$54$	−131.848	−0.332262
$55$	250.662	0.614532
$56$	210.249	0.501709
$57$	−236.504	−0.549574
$58$	141.614	0.320600
$59$	−342.739	−0.756285	−0.378142	−	0.925747i	$-0.623437\pi$
$59$	−342.739	−0.756285	−0.378142	+	0.925747i	$0.623437\pi$
$60$	−237.691	−0.511429
$61$	357.486	0.750350	0.375175	−	0.926954i	$-0.377583\pi$
$61$	357.486	0.750350	0.375175	+	0.926954i	$0.377583\pi$
$62$	1518.44	3.11036
$63$	49.3875	0.0987657
$64$	−540.804	−1.05626
$65$	−103.675	−0.197834
$66$	−734.426	−1.36972
$67$	−183.087	−0.333844	−0.166922	−	0.985970i	$-0.553383\pi$
$67$	−183.087	−0.333844	−0.166922	+	0.985970i	$0.553383\pi$
$68$	−297.949	−0.531347
$69$	19.0129	0.0331722
$70$	133.984	0.228773
$71$	−594.034	−0.992942	−0.496471	−	0.868053i	$-0.665371\pi$
$71$	−594.034	−0.992942	−0.496471	+	0.868053i	$0.665371\pi$
$72$	344.827	0.564421
$73$	−622.609	−0.998231	−0.499115	−	0.866536i	$-0.666342\pi$
$73$	−622.609	−0.998231	−0.499115	+	0.866536i	$0.666342\pi$
$74$	−1654.17	−2.59856
$75$	−75.0000	−0.115470
$76$	1249.22	1.88546
$77$	275.102	0.407152
$78$	303.761	0.440950
$79$	−1275.18	−1.81607	−0.908034	−	0.418897i	$-0.862417\pi$
$79$	−1275.18	−1.81607	−0.908034	+	0.418897i	$0.862417\pi$
$80$	301.644	0.421560
$81$	81.0000	0.111111
$82$	1726.35	2.32493
$83$	−739.108	−0.977441	−0.488720	−	0.872440i	$-0.662536\pi$
$83$	−739.108	−0.977441	−0.488720	+	0.872440i	$0.662536\pi$
$84$	−260.866	−0.338842
$85$	−94.0136	−0.119967
$86$	2478.78	3.10806
$87$	−87.0000	−0.107211
$88$	1920.78	2.32677
$89$	906.113	1.07919	0.539594	−	0.841925i	$-0.318578\pi$
$89$	906.113	1.07919	0.539594	+	0.841925i	$0.318578\pi$
$90$	219.746	0.257369
$91$	−113.783	−0.131073
$92$	−100.426	−0.113806
$93$	−932.849	−1.04013
$94$	−550.688	−0.604246
$95$	394.173	0.425698
$96$	35.7390	0.0379958
$97$	76.0665	0.0796225	0.0398112	−	0.999207i	$-0.487324\pi$
$97$	76.0665	0.0796225	0.0398112	+	0.999207i	$0.487324\pi$
$98$	−1527.90	−1.57491
$99$	451.192	0.458045
$100$	396.151	0.396151
$101$	653.553	0.643871	0.321935	−	0.946762i	$-0.395667\pi$
$101$	653.553	0.643871	0.321935	+	0.946762i	$0.395667\pi$
$102$	275.455	0.267393
$103$	969.801	0.927741	0.463871	−	0.885903i	$-0.346460\pi$
$103$	969.801	0.927741	0.463871	+	0.885903i	$0.346460\pi$
$104$	−794.440	−0.749050
$105$	−82.3125	−0.0765036
$106$	−707.332	−0.648133
$107$	−1267.53	−1.14520	−0.572601	−	0.819835i	$-0.694065\pi$
$107$	−1267.53	−1.14520	−0.572601	+	0.819835i	$0.694065\pi$
$108$	−427.843	−0.381197
$109$	−808.142	−0.710146	−0.355073	−	0.934838i	$-0.615544\pi$
$109$	−808.142	−0.710146	−0.355073	+	0.934838i	$0.615544\pi$
$110$	1224.04	1.06098
$111$	1016.23	0.868980
$112$	331.054	0.279301
$113$	−1220.10	−1.01572	−0.507862	−	0.861438i	$-0.669564\pi$
$113$	−1220.10	−1.01572	−0.507862	+	0.861438i	$0.669564\pi$
$114$	−1154.91	−0.948832
$115$	−31.6881	−0.0256951
$116$	459.535	0.367817
$117$	−186.614	−0.147457
$118$	−1673.68	−1.30572
$119$	−103.180	−0.0794831
$120$	−574.712	−0.437198
$121$	1182.26	0.888247
$122$	1745.69	1.29547
$123$	−1060.58	−0.777473
$124$	4927.32	3.56844
$125$	125.000	0.0894427
$126$	241.171	0.170518
$127$	814.733	0.569258	0.284629	−	0.958638i	$-0.408130\pi$
$127$	814.733	0.569258	0.284629	+	0.958638i	$0.408130\pi$
$128$	−2545.57	−1.75781
$129$	−1522.83	−1.03936
$130$	−506.268	−0.341559
$131$	−1493.91	−0.996363	−0.498181	−	0.867073i	$-0.665999\pi$
$131$	−1493.91	−0.996363	−0.498181	+	0.867073i	$0.665999\pi$
$132$	−2383.20	−1.57145
$133$	432.605	0.282042
$134$	−894.056	−0.576378
$135$	−135.000	−0.0860663
$136$	−720.410	−0.454225
$137$	−1608.72	−1.00323	−0.501615	−	0.865091i	$-0.667261\pi$
$137$	−1608.72	−1.00323	−0.501615	+	0.865091i	$0.667261\pi$
$138$	92.8445	0.0572714
$139$	51.5725	0.0314700	0.0157350	−	0.999876i	$-0.494991\pi$
$139$	51.5725	0.0314700	0.0157350	+	0.999876i	$0.494991\pi$
$140$	434.776	0.262466
$141$	338.313	0.202064
$142$	−2900.81	−1.71430
$143$	−1039.49	−0.607878
$144$	542.959	0.314212
$145$	145.000	0.0830455
$146$	−3040.35	−1.72343
$147$	938.662	0.526664
$148$	−5367.77	−2.98127
$149$	−608.330	−0.334472	−0.167236	−	0.985917i	$-0.553484\pi$
$149$	−608.330	−0.334472	−0.167236	+	0.985917i	$0.553484\pi$
$150$	−366.243	−0.199357
$151$	−341.568	−0.184082	−0.0920412	−	0.995755i	$-0.529339\pi$
$151$	−341.568	−0.184082	−0.0920412	+	0.995755i	$0.529339\pi$
$152$	3020.48	1.61180
$153$	−169.224	−0.0894182
$154$	1343.39	0.702943
$155$	1554.75	0.805680
$156$	985.699	0.505891
$157$	−358.378	−0.182176	−0.0910882	−	0.995843i	$-0.529035\pi$
$157$	−358.378	−0.182176	−0.0910882	+	0.995843i	$0.529035\pi$
$158$	−6227.03	−3.13542
$159$	434.547	0.216741
$160$	−59.5650	−0.0294314
$161$	−34.7777	−0.0170240
$162$	395.543	0.191832
$163$	−1667.36	−0.801213	−0.400606	−	0.916250i	$-0.631201\pi$
$163$	−1667.36	−0.801213	−0.400606	+	0.916250i	$0.631201\pi$
$164$	5602.00	2.66733
$165$	−751.986	−0.354800
$166$	−3609.24	−1.68754
$167$	−1832.30	−0.849029	−0.424514	−	0.905421i	$-0.639555\pi$
$167$	−1832.30	−0.849029	−0.424514	+	0.905421i	$0.639555\pi$
$168$	−630.746	−0.289662
$169$	−1767.06	−0.804308
$170$	−459.091	−0.207122
$171$	709.512	0.317297
$172$	8043.60	3.56580
$173$	2034.77	0.894224	0.447112	−	0.894478i	$-0.352453\pi$
$173$	2034.77	0.894224	0.447112	+	0.894478i	$0.352453\pi$
$174$	−424.842	−0.185099
$175$	137.188	0.0592594
$176$	3024.43	1.29531
$177$	1028.22	0.436641
$178$	4424.77	1.86320
$179$	−332.198	−0.138713	−0.0693566	−	0.997592i	$-0.522095\pi$
$179$	−332.198	−0.138713	−0.0693566	+	0.997592i	$0.522095\pi$
$180$	713.072	0.295274
$181$	−843.391	−0.346347	−0.173173	−	0.984891i	$-0.555402\pi$
$181$	−843.391	−0.346347	−0.173173	+	0.984891i	$0.555402\pi$
$182$	−555.629	−0.226296
$183$	−1072.46	−0.433215
$184$	−242.821	−0.0972879
$185$	−1693.72	−0.673109
$186$	−4555.33	−1.79577
$187$	−942.625	−0.368618
$188$	−1786.97	−0.693236
$189$	−148.163	−0.0570224
$190$	1924.84	0.734962
$191$	2438.81	0.923908	0.461954	−	0.886904i	$-0.347148\pi$
$191$	2438.81	0.923908	0.461954	+	0.886904i	$0.347148\pi$
$192$	1622.41	0.609831
$193$	4095.03	1.52729	0.763645	−	0.645637i	$-0.223408\pi$
$193$	4095.03	1.52729	0.763645	+	0.645637i	$0.223408\pi$
$194$	371.451	0.137467
$195$	311.024	0.114220
$196$	−4958.03	−1.80686
$197$	3226.76	1.16699	0.583495	−	0.812117i	$-0.301685\pi$
$197$	3226.76	1.16699	0.583495	+	0.812117i	$0.301685\pi$
$198$	2203.28	0.790809
$199$	−4218.74	−1.50281	−0.751404	−	0.659842i	$-0.770623\pi$
$199$	−4218.74	−1.50281	−0.751404	+	0.659842i	$0.770623\pi$
$200$	957.853	0.338652
$201$	549.260	0.192745
$202$	3191.46	1.11163
$203$	159.138	0.0550210
$204$	893.846	0.306773
$205$	1767.63	0.602228
$206$	4735.77	1.60173
$207$	−57.0387	−0.0191520
$208$	−1250.91	−0.416996
$209$	3952.17	1.30803
$210$	−401.952	−0.132082
$211$	−2798.33	−0.913010	−0.456505	−	0.889721i	$-0.650899\pi$
$211$	−2798.33	−0.913010	−0.456505	+	0.889721i	$0.650899\pi$
$212$	−2295.28	−0.743588
$213$	1782.10	0.573276
$214$	−6189.64	−1.97717
$215$	2538.05	0.805085
$216$	−1034.48	−0.325868
$217$	1706.34	0.533796
$218$	−3946.35	−1.22606
$219$	1867.83	0.576329
$220$	3972.00	1.21724
$221$	389.872	0.118668
$222$	4962.52	1.50028
$223$	2496.01	0.749529	0.374764	−	0.927120i	$-0.377724\pi$
$223$	2496.01	0.749529	0.374764	+	0.927120i	$0.377724\pi$
$224$	−65.3725	−0.0194995
$225$	225.000	0.0666667
$226$	−5958.02	−1.75364
$227$	3409.57	0.996920	0.498460	−	0.866913i	$-0.333899\pi$
$227$	3409.57	0.996920	0.498460	+	0.866913i	$0.333899\pi$
$228$	−3747.65	−1.08857
$229$	4794.47	1.38353	0.691763	−	0.722125i	$-0.256834\pi$
$229$	4794.47	1.38353	0.691763	+	0.722125i	$0.256834\pi$
$230$	−154.741	−0.0443622
$231$	−825.305	−0.235069
$232$	1111.11	0.314431
$233$	1989.36	0.559345	0.279672	−	0.960095i	$-0.409774\pi$
$233$	1989.36	0.559345	0.279672	+	0.960095i	$0.409774\pi$
$234$	−911.282	−0.254583
$235$	−563.855	−0.156518
$236$	−5431.06	−1.49802
$237$	3825.55	1.04851
$238$	−503.852	−0.137226
$239$	2574.69	0.696832	0.348416	−	0.937340i	$-0.386720\pi$
$239$	2574.69	0.696832	0.348416	+	0.937340i	$0.386720\pi$
$240$	−904.932	−0.243388
$241$	−3683.44	−0.984528	−0.492264	−	0.870446i	$-0.663831\pi$
$241$	−3683.44	−0.984528	−0.492264	+	0.870446i	$0.663831\pi$
$242$	5773.24	1.53355
$243$	−243.000	−0.0641500
$244$	5664.73	1.48626
$245$	−1564.44	−0.407952
$246$	−5179.06	−1.34230
$247$	−1634.63	−0.421089
$248$	11913.8	3.05050
$249$	2217.32	0.564326
$250$	610.405	0.154422
$251$	4631.27	1.16463	0.582317	−	0.812962i	$-0.302146\pi$
$251$	4631.27	1.16463	0.582317	+	0.812962i	$0.302146\pi$
$252$	782.597	0.195631
$253$	−317.720	−0.0789522
$254$	3978.54	0.982817
$255$	282.041	0.0692630
$256$	−8104.22	−1.97857
$257$	−1609.98	−0.390770	−0.195385	−	0.980727i	$-0.562596\pi$
$257$	−1609.98	−0.390770	−0.195385	+	0.980727i	$0.562596\pi$
$258$	−7436.33	−1.79444
$259$	−1858.86	−0.445962
$260$	−1642.83	−0.391862
$261$	261.000	0.0618984
$262$	−7295.12	−1.72021
$263$	−2868.22	−0.672479	−0.336239	−	0.941777i	$-0.609155\pi$
$263$	−2868.22	−0.672479	−0.336239	+	0.941777i	$0.609155\pi$
$264$	−5762.34	−1.34336
$265$	−724.244	−0.167887
$266$	2112.52	0.486942
$267$	−2718.34	−0.623070
$268$	−2901.20	−0.661264
$269$	−554.047	−0.125579	−0.0627896	−	0.998027i	$-0.520000\pi$
$269$	−554.047	−0.125579	−0.0627896	+	0.998027i	$0.520000\pi$
$270$	−659.238	−0.148592
$271$	−1826.02	−0.409309	−0.204655	−	0.978834i	$-0.565607\pi$
$271$	−1826.02	−0.409309	−0.204655	+	0.978834i	$0.565607\pi$
$272$	−1134.35	−0.252867
$273$	341.348	0.0756752
$274$	−7855.79	−1.73206
$275$	1253.31	0.274827
$276$	301.279	0.0657060
$277$	1470.00	0.318859	0.159429	−	0.987209i	$-0.449035\pi$
$277$	1470.00	0.318859	0.159429	+	0.987209i	$0.449035\pi$
$278$	251.841	0.0543325
$279$	2798.55	0.600519
$280$	1051.24	0.224371
$281$	7826.43	1.66151	0.830757	−	0.556635i	$-0.187908\pi$
$281$	7826.43	1.66151	0.830757	+	0.556635i	$0.187908\pi$
$282$	1652.06	0.348861
$283$	−6796.87	−1.42767	−0.713837	−	0.700312i	$-0.753044\pi$
$283$	−6796.87	−1.42767	−0.713837	+	0.700312i	$0.753044\pi$
$284$	−9413.10	−1.96678
$285$	−1182.52	−0.245777
$286$	−5076.08	−1.04949
$287$	1939.98	0.399001
$288$	−107.217	−0.0219369
$289$	−4559.46	−0.928039
$290$	708.070	0.143377
$291$	−228.199	−0.0459701
$292$	−9865.89	−1.97725
$293$	3631.49	0.724074	0.362037	−	0.932164i	$-0.382081\pi$
$293$	3631.49	0.724074	0.362037	+	0.932164i	$0.382081\pi$
$294$	4583.71	0.909277
$295$	−1713.69	−0.338221
$296$	−12978.7	−2.54856
$297$	−1353.57	−0.264452
$298$	−2970.62	−0.577461
$299$	131.410	0.0254169
$300$	−1188.45	−0.228718
$301$	2785.50	0.533401
$302$	−1667.96	−0.317816
$303$	−1960.66	−0.371739
$304$	4756.00	0.897287
$305$	1787.43	0.335567
$306$	−826.364	−0.154379
$307$	−9080.77	−1.68817	−0.844083	−	0.536213i	$-0.819854\pi$
$307$	−9080.77	−1.68817	−0.844083	+	0.536213i	$0.819854\pi$
$308$	4359.27	0.806469
$309$	−2909.40	−0.535632
$310$	7592.21	1.39100
$311$	2657.69	0.484577	0.242289	−	0.970204i	$-0.422102\pi$
$311$	2657.69	0.484577	0.242289	+	0.970204i	$0.422102\pi$
$312$	2383.32	0.432464
$313$	−530.474	−0.0957960	−0.0478980	−	0.998852i	$-0.515252\pi$
$313$	−530.474	−0.0957960	−0.0478980	+	0.998852i	$0.515252\pi$
$314$	−1750.05	−0.314525
$315$	246.938	0.0441694
$316$	−20206.6	−3.59719
$317$	2393.66	0.424106	0.212053	−	0.977258i	$-0.431985\pi$
$317$	2393.66	0.424106	0.212053	+	0.977258i	$0.431985\pi$
$318$	2122.00	0.374200
$319$	1453.84	0.255170
$320$	−2704.02	−0.472373
$321$	3802.58	0.661182
$322$	−169.828	−0.0293918
$323$	−1482.31	−0.255349
$324$	1283.53	0.220084
$325$	−518.373	−0.0884743
$326$	−8142.12	−1.38328
$327$	2424.43	0.410003
$328$	13545.1	2.28019
$329$	−618.830	−0.103700
$330$	−3672.13	−0.612558
$331$	−7984.54	−1.32589	−0.662945	−	0.748668i	$-0.730694\pi$
$331$	−7984.54	−1.32589	−0.662945	+	0.748668i	$0.730694\pi$
$332$	−11711.9	−1.93607
$333$	−3048.70	−0.501706
$334$	−8947.57	−1.46584
$335$	−915.433	−0.149300
$336$	−993.163	−0.161254
$337$	9704.45	1.56865	0.784325	−	0.620350i	$-0.213010\pi$
$337$	9704.45	1.56865	0.784325	+	0.620350i	$0.213010\pi$
$338$	−8629.00	−1.38863
$339$	3660.29	0.586429
$340$	−1489.74	−0.237626
$341$	15588.7	2.47558
$342$	3464.72	0.547808
$343$	−3599.18	−0.566582
$344$	19448.6	3.04825
$345$	95.0644	0.0148351
$346$	9936.27	1.54387
$347$	5514.04	0.853053	0.426526	−	0.904475i	$-0.359737\pi$
$347$	5514.04	0.853053	0.426526	+	0.904475i	$0.359737\pi$
$348$	−1378.61	−0.212359
$349$	2521.06	0.386674	0.193337	−	0.981132i	$-0.438069\pi$
$349$	2521.06	0.386674	0.193337	+	0.981132i	$0.438069\pi$
$350$	669.920	0.102311
$351$	559.842	0.0851344
$352$	−597.227	−0.0904326
$353$	5721.03	0.862606	0.431303	−	0.902207i	$-0.358054\pi$
$353$	5721.03	0.862606	0.431303	+	0.902207i	$0.358054\pi$
$354$	5021.03	0.753855
$355$	−2970.17	−0.444057
$356$	14358.3	2.13761
$357$	309.540	0.0458896
$358$	−1622.20	−0.239486
$359$	6403.95	0.941470	0.470735	−	0.882275i	$-0.343989\pi$
$359$	6403.95	0.941470	0.470735	+	0.882275i	$0.343989\pi$
$360$	1724.14	0.252417
$361$	−644.098	−0.0939055
$362$	−4118.48	−0.597963
$363$	−3546.77	−0.512830
$364$	−1803.01	−0.259624
$365$	−3113.04	−0.446422
$366$	−5237.06	−0.747939
$367$	13350.7	1.89891	0.949456	−	0.313899i	$-0.101635\pi$
$367$	13350.7	1.89891	0.949456	+	0.313899i	$0.101635\pi$
$368$	−382.341	−0.0541601
$369$	3181.74	0.448874
$370$	−8270.87	−1.16211
$371$	−794.858	−0.111232
$372$	−14782.0	−2.06024
$373$	−1367.05	−0.189767	−0.0948837	−	0.995488i	$-0.530248\pi$
$373$	−1367.05	−0.189767	−0.0948837	+	0.995488i	$0.530248\pi$
$374$	−4603.07	−0.636414
$375$	−375.000	−0.0516398
$376$	−4320.72	−0.592617
$377$	−601.312	−0.0821463
$378$	−723.513	−0.0984484
$379$	9882.96	1.33945	0.669727	−	0.742607i	$-0.266411\pi$
$379$	9882.96	1.33945	0.669727	+	0.742607i	$0.266411\pi$
$380$	6246.09	0.843204
$381$	−2444.20	−0.328662
$382$	11909.3	1.59511
$383$	13225.8	1.76450	0.882252	−	0.470777i	$-0.156026\pi$
$383$	13225.8	1.76450	0.882252	+	0.470777i	$0.156026\pi$
$384$	7636.72	1.01487
$385$	1375.51	0.182084
$386$	19997.0	2.63684
$387$	4568.48	0.600075
$388$	1205.35	0.157713
$389$	−8442.16	−1.10035	−0.550173	−	0.835051i	$-0.685438\pi$
$389$	−8442.16	−1.10035	−0.550173	+	0.835051i	$0.685438\pi$
$390$	1518.80	0.197199
$391$	119.165	0.0154128
$392$	−11988.0	−1.54461
$393$	4481.73	0.575250
$394$	15757.0	2.01479
$395$	−6375.92	−0.812170
$396$	7149.60	0.907275
$397$	−2268.55	−0.286789	−0.143394	−	0.989666i	$-0.545802\pi$
$397$	−2268.55	−0.286789	−0.143394	+	0.989666i	$0.545802\pi$
$398$	−20601.1	−2.59458
$399$	−1297.82	−0.162837
$400$	1508.22	0.188527
$401$	8294.00	1.03287	0.516437	−	0.856325i	$-0.327258\pi$
$401$	8294.00	1.03287	0.516437	+	0.856325i	$0.327258\pi$
$402$	2682.17	0.332772
$403$	−6447.51	−0.796957
$404$	10356.2	1.27535
$405$	405.000	0.0496904
$406$	777.107	0.0949930
$407$	−16982.1	−2.06823
$408$	2161.23	0.262247
$409$	9913.01	1.19845	0.599226	−	0.800580i	$-0.295475\pi$
$409$	9913.01	1.19845	0.599226	+	0.800580i	$0.295475\pi$
$410$	8631.77	1.03974
$411$	4826.17	0.579216
$412$	15367.5	1.83763
$413$	−1880.78	−0.224085
$414$	−278.534	−0.0330656
$415$	−3695.54	−0.437125
$416$	247.015	0.0291127
$417$	−154.718	−0.0181692
$418$	19299.4	2.25829
$419$	−13332.1	−1.55446	−0.777228	−	0.629219i	$-0.783375\pi$
$419$	−13332.1	−1.55446	−0.777228	+	0.629219i	$0.783375\pi$
$420$	−1304.33	−0.151535
$421$	−2848.13	−0.329714	−0.164857	−	0.986317i	$-0.552716\pi$
$421$	−2848.13	−0.329714	−0.164857	+	0.986317i	$0.552716\pi$
$422$	−13664.9	−1.57630
$423$	−1014.94	−0.116662
$424$	−5549.76	−0.635661
$425$	−470.068	−0.0536509
$426$	8702.44	0.989752
$427$	1961.70	0.222326
$428$	−20085.3	−2.26836
$429$	3118.47	0.350958
$430$	12393.9	1.38997
$431$	12669.7	1.41595	0.707977	−	0.706235i	$-0.249608\pi$
$431$	12669.7	1.41595	0.707977	+	0.706235i	$0.249608\pi$
$432$	−1628.88	−0.181411
$433$	−14545.6	−1.61436	−0.807178	−	0.590308i	$-0.799006\pi$
$433$	−14545.6	−1.61436	−0.807178	+	0.590308i	$0.799006\pi$
$434$	8332.45	0.921591
$435$	−435.000	−0.0479463
$436$	−12805.9	−1.40663
$437$	−499.625	−0.0546917
$438$	9121.05	0.995024
$439$	11489.4	1.24911	0.624557	−	0.780979i	$-0.285280\pi$
$439$	11489.4	1.24911	0.624557	+	0.780979i	$0.285280\pi$
$440$	9603.90	1.04056
$441$	−2815.99	−0.304069
$442$	1903.84	0.204879
$443$	−11125.7	−1.19322	−0.596611	−	0.802531i	$-0.703486\pi$
$443$	−11125.7	−1.19322	−0.596611	+	0.802531i	$0.703486\pi$
$444$	16103.3	1.72124
$445$	4530.57	0.482628
$446$	12188.6	1.29405
$447$	1824.99	0.193107
$448$	−2967.66	−0.312966
$449$	−6676.79	−0.701776	−0.350888	−	0.936418i	$-0.614120\pi$
$449$	−6676.79	−0.701776	−0.350888	+	0.936418i	$0.614120\pi$
$450$	1098.73	0.115099
$451$	17723.1	1.85044
$452$	−19333.7	−2.01190
$453$	1024.70	0.106280
$454$	16649.7	1.72117
$455$	−568.914	−0.0586178
$456$	−9061.44	−0.930572
$457$	−10826.9	−1.10823	−0.554114	−	0.832441i	$-0.686943\pi$
$457$	−10826.9	−1.10823	−0.554114	+	0.832441i	$0.686943\pi$
$458$	23412.6	2.38864
$459$	507.673	0.0516256
$460$	−502.132	−0.0508957
$461$	−4114.21	−0.415657	−0.207829	−	0.978165i	$-0.566640\pi$
$461$	−4114.21	−0.415657	−0.207829	+	0.978165i	$0.566640\pi$
$462$	−4030.16	−0.405844
$463$	−6107.19	−0.613014	−0.306507	−	0.951868i	$-0.599160\pi$
$463$	−6107.19	−0.613014	−0.306507	+	0.951868i	$0.599160\pi$
$464$	1749.54	0.175043
$465$	−4664.25	−0.465160
$466$	9714.53	0.965701
$467$	−1409.31	−0.139647	−0.0698235	−	0.997559i	$-0.522244\pi$
$467$	−1409.31	−0.139647	−0.0698235	+	0.997559i	$0.522244\pi$
$468$	−2957.10	−0.292077
$469$	−1004.69	−0.0989172
$470$	−2753.44	−0.270227
$471$	1075.13	0.105180
$472$	−13131.7	−1.28059
$473$	25447.7	2.47375
$474$	18681.1	1.81023
$475$	1970.87	0.190378
$476$	−1634.99	−0.157437
$477$	−1303.64	−0.125135
$478$	12572.8	1.20307
$479$	12633.9	1.20513	0.602566	−	0.798069i	$-0.294145\pi$
$479$	12633.9	1.20513	0.602566	+	0.798069i	$0.294145\pi$
$480$	178.695	0.0169922
$481$	7023.84	0.665821
$482$	−17987.1	−1.69977
$483$	104.333	0.00982883
$484$	18734.1	1.75940
$485$	380.332	0.0356083
$486$	−1186.63	−0.110754
$487$	−17024.7	−1.58411	−0.792056	−	0.610449i	$-0.790989\pi$
$487$	−17024.7	−1.58411	−0.792056	+	0.610449i	$0.790989\pi$
$488$	13696.7	1.27054
$489$	5002.08	0.462580
$490$	−7639.52	−0.704323
$491$	−3792.47	−0.348578	−0.174289	−	0.984695i	$-0.555763\pi$
$491$	−3792.47	−0.348578	−0.174289	+	0.984695i	$0.555763\pi$
$492$	−16806.0	−1.53998
$493$	−545.279	−0.0498136
$494$	−7982.29	−0.727004
$495$	2255.96	0.204844
$496$	18759.2	1.69821
$497$	−3259.76	−0.294206
$498$	10827.7	0.974301
$499$	6484.19	0.581708	0.290854	−	0.956767i	$-0.406061\pi$
$499$	6484.19	0.581708	0.290854	+	0.956767i	$0.406061\pi$
$500$	1980.76	0.177164
$501$	5496.91	0.490187
$502$	22615.6	2.01073
$503$	−8781.60	−0.778434	−0.389217	−	0.921146i	$-0.627254\pi$
$503$	−8781.60	−0.778434	−0.389217	+	0.921146i	$0.627254\pi$
$504$	1892.24	0.167236
$505$	3267.76	0.287948
$506$	−1551.51	−0.136310
$507$	5301.19	0.464367
$508$	12910.3	1.12756
$509$	21343.3	1.85860	0.929299	−	0.369328i	$-0.120412\pi$
$509$	21343.3	1.85860	0.929299	+	0.369328i	$0.120412\pi$
$510$	1377.27	0.119582
$511$	−3416.57	−0.295773
$512$	−19210.3	−1.65817
$513$	−2128.54	−0.183191
$514$	−7861.93	−0.674659
$515$	4849.01	0.414898
$516$	−24130.8	−2.05872
$517$	−5653.48	−0.480928
$518$	−9077.28	−0.769947
$519$	−6104.31	−0.516280
$520$	−3972.20	−0.334985
$521$	7007.06	0.589223	0.294611	−	0.955617i	$-0.404810\pi$
$521$	7007.06	0.589223	0.294611	+	0.955617i	$0.404810\pi$
$522$	1274.53	0.106867
$523$	−5901.85	−0.493441	−0.246721	−	0.969087i	$-0.579353\pi$
$523$	−5901.85	−0.493441	−0.246721	+	0.969087i	$0.579353\pi$
$524$	−23672.6	−1.97355
$525$	−411.563	−0.0342134
$526$	−14006.2	−1.16103
$527$	−5846.70	−0.483276
$528$	−9073.28	−0.747848
$529$	−12126.8	−0.996699
$530$	−3536.66	−0.289854
$531$	−3084.65	−0.252095
$532$	6855.08	0.558657
$533$	−7330.34	−0.595707
$534$	−13274.3	−1.07572
$535$	−6337.64	−0.512149
$536$	−7014.80	−0.565286
$537$	996.595	0.0800861
$538$	−2705.54	−0.216811
$539$	−15685.8	−1.25350
$540$	−2139.22	−0.170476
$541$	7826.71	0.621990	0.310995	−	0.950412i	$-0.399338\pi$
$541$	7826.71	0.621990	0.310995	+	0.950412i	$0.399338\pi$
$542$	−8916.90	−0.706667
$543$	2530.17	0.199963
$544$	223.997	0.0176540
$545$	−4040.71	−0.317587
$546$	1666.89	0.130652
$547$	4256.78	0.332737	0.166368	−	0.986064i	$-0.446796\pi$
$547$	4256.78	0.332737	0.166368	+	0.986064i	$0.446796\pi$
$548$	−25491.9	−1.98716
$549$	3217.37	0.250117
$550$	6120.21	0.474485
$551$	2286.20	0.176762
$552$	728.462	0.0561692
$553$	−6997.57	−0.538096
$554$	7178.38	0.550506
$555$	5081.17	0.388620
$556$	817.221	0.0623343
$557$	−11138.6	−0.847324	−0.423662	−	0.905820i	$-0.639256\pi$
$557$	−11138.6	−0.847324	−0.423662	+	0.905820i	$0.639256\pi$
$558$	13666.0	1.03679
$559$	−10525.2	−0.796368
$560$	1655.27	0.124907
$561$	2827.88	0.212822
$562$	38218.3	2.86858
$563$	16458.1	1.23202	0.616009	−	0.787739i	$-0.288748\pi$
$563$	16458.1	1.23202	0.616009	+	0.787739i	$0.288748\pi$
$564$	5360.92	0.400240
$565$	−6100.48	−0.454246
$566$	−33190.7	−2.46486
$567$	444.488	0.0329219
$568$	−22759.9	−1.68131
$569$	2449.68	0.180485	0.0902423	−	0.995920i	$-0.471236\pi$
$569$	2449.68	0.180485	0.0902423	+	0.995920i	$0.471236\pi$
$570$	−5774.53	−0.424331
$571$	156.880	0.0114978	0.00574888	−	0.999983i	$-0.498170\pi$
$571$	156.880	0.0114978	0.00574888	+	0.999983i	$0.498170\pi$
$572$	−16471.8	−1.20406
$573$	−7316.44	−0.533419
$574$	9473.37	0.688869
$575$	−158.441	−0.0114912
$576$	−4867.24	−0.352086
$577$	−20318.3	−1.46597	−0.732984	−	0.680246i	$-0.761873\pi$
$577$	−20318.3	−1.46597	−0.732984	+	0.680246i	$0.761873\pi$
$578$	−22264.9	−1.60225
$579$	−12285.1	−0.881781
$580$	2297.68	0.164493
$581$	−4055.85	−0.289613
$582$	−1114.35	−0.0793667
$583$	−7261.62	−0.515859
$584$	−23854.7	−1.69027
$585$	−933.071	−0.0659448
$586$	17733.4	1.25010
$587$	−9510.91	−0.668752	−0.334376	−	0.942440i	$-0.608525\pi$
$587$	−9510.91	−0.668752	−0.334376	+	0.942440i	$0.608525\pi$
$588$	14874.1	1.04319
$589$	24513.6	1.71488
$590$	−8368.38	−0.583934
$591$	−9680.27	−0.673762
$592$	−20436.1	−1.41878
$593$	−15977.2	−1.10641	−0.553207	−	0.833044i	$-0.686596\pi$
$593$	−15977.2	−1.10641	−0.553207	+	0.833044i	$0.686596\pi$
$594$	−6609.83	−0.456574
$595$	−515.900	−0.0355459
$596$	−9639.62	−0.662507
$597$	12656.2	0.867647
$598$	641.707	0.0438819
$599$	−4002.17	−0.272995	−0.136498	−	0.990640i	$-0.543585\pi$
$599$	−4002.17	−0.272995	−0.136498	+	0.990640i	$0.543585\pi$
$600$	−2873.56	−0.195521
$601$	−1574.81	−0.106885	−0.0534425	−	0.998571i	$-0.517019\pi$
$601$	−1574.81	−0.106885	−0.0534425	+	0.998571i	$0.517019\pi$
$602$	13602.3	0.920910
$603$	−1647.78	−0.111281
$604$	−5412.51	−0.364622
$605$	5911.28	0.397236
$606$	−9574.37	−0.641802
$607$	−8803.52	−0.588672	−0.294336	−	0.955702i	$-0.595098\pi$
$607$	−8803.52	−0.588672	−0.294336	+	0.955702i	$0.595098\pi$
$608$	−939.156	−0.0626444
$609$	−477.413	−0.0317664
$610$	8728.44	0.579351
$611$	2338.29	0.154824
$612$	−2681.54	−0.177116
$613$	16874.2	1.11181	0.555907	−	0.831245i	$-0.312371\pi$
$613$	16874.2	1.11181	0.555907	+	0.831245i	$0.312371\pi$
$614$	−44343.6	−2.91460
$615$	−5302.90	−0.347697
$616$	10540.3	0.689415
$617$	4592.02	0.299624	0.149812	−	0.988715i	$-0.452133\pi$
$617$	4592.02	0.299624	0.149812	+	0.988715i	$0.452133\pi$
$618$	−14207.3	−0.924761
$619$	4982.48	0.323526	0.161763	−	0.986830i	$-0.448282\pi$
$619$	4982.48	0.323526	0.161763	+	0.986830i	$0.448282\pi$
$620$	24636.6	1.59586
$621$	171.116	0.0110574
$622$	12978.1	0.836616
$623$	4972.30	0.319761
$624$	3752.74	0.240753
$625$	625.000	0.0400000
$626$	−2590.43	−0.165391
$627$	−11856.5	−0.755189
$628$	−5678.88	−0.360847
$629$	6369.32	0.403755
$630$	1205.86	0.0762578
$631$	20584.3	1.29865	0.649325	−	0.760511i	$-0.275051\pi$
$631$	20584.3	1.29865	0.649325	+	0.760511i	$0.275051\pi$
$632$	−48857.6	−3.07508
$633$	8394.99	0.527126
$634$	11688.8	0.732213
$635$	4073.66	0.254580
$636$	6885.84	0.429310
$637$	6487.69	0.403535
$638$	7099.45	0.440548
$639$	−5346.31	−0.330981
$640$	−12727.9	−0.786115
$641$	4840.03	0.298237	0.149118	−	0.988819i	$-0.452356\pi$
$641$	4840.03	0.298237	0.149118	+	0.988819i	$0.452356\pi$
$642$	18568.9	1.14152
$643$	1340.16	0.0821941	0.0410970	−	0.999155i	$-0.486915\pi$
$643$	1340.16	0.0821941	0.0410970	+	0.999155i	$0.486915\pi$
$644$	−551.090	−0.0337205
$645$	−7614.14	−0.464816
$646$	−7238.46	−0.440856
$647$	15752.3	0.957169	0.478585	−	0.878041i	$-0.341150\pi$
$647$	15752.3	0.957169	0.478585	+	0.878041i	$0.341150\pi$
$648$	3103.44	0.188140
$649$	−17182.3	−1.03924
$650$	−2531.34	−0.152750
$651$	−5119.01	−0.308187
$652$	−26421.1	−1.58701
$653$	2290.66	0.137275	0.0686373	−	0.997642i	$-0.478135\pi$
$653$	2290.66	0.137275	0.0686373	+	0.997642i	$0.478135\pi$
$654$	11839.1	0.707865
$655$	−7469.55	−0.445587
$656$	21327.8	1.26938
$657$	−5603.48	−0.332744
$658$	−3021.90	−0.179036
$659$	−3003.49	−0.177541	−0.0887704	−	0.996052i	$-0.528294\pi$
$659$	−3003.49	−0.177541	−0.0887704	+	0.996052i	$0.528294\pi$
$660$	−11916.0	−0.702772
$661$	8104.71	0.476909	0.238454	−	0.971154i	$-0.423359\pi$
$661$	8104.71	0.476909	0.238454	+	0.971154i	$0.423359\pi$
$662$	−38990.4	−2.28913
$663$	−1169.62	−0.0685131
$664$	−28318.3	−1.65506
$665$	2163.03	0.126133
$666$	−14887.6	−0.866188
$667$	−183.791	−0.0106693
$668$	−29034.7	−1.68172
$669$	−7488.02	−0.432741
$670$	−4470.28	−0.257764
$671$	17921.6	1.03108
$672$	196.118	0.0112580
$673$	5747.03	0.329170	0.164585	−	0.986363i	$-0.447371\pi$
$673$	5747.03	0.329170	0.164585	+	0.986363i	$0.447371\pi$
$674$	47389.2	2.70825
$675$	−675.000	−0.0384900
$676$	−28001.0	−1.59314
$677$	25714.2	1.45979	0.729895	−	0.683559i	$-0.239569\pi$
$677$	25714.2	1.45979	0.729895	+	0.683559i	$0.239569\pi$
$678$	17874.1	1.01246
$679$	417.415	0.0235919
$680$	−3602.05	−0.203136
$681$	−10228.7	−0.575572
$682$	76123.2	4.27406
$683$	4007.09	0.224490	0.112245	−	0.993681i	$-0.464196\pi$
$683$	4007.09	0.224490	0.112245	+	0.993681i	$0.464196\pi$
$684$	11243.0	0.628487
$685$	−8043.62	−0.448658
$686$	−17575.7	−0.978196
$687$	−14383.4	−0.798779
$688$	30623.4	1.69696
$689$	3003.43	0.166069
$690$	464.223	0.0256125
$691$	−27863.7	−1.53399	−0.766993	−	0.641655i	$-0.778248\pi$
$691$	−27863.7	−1.53399	−0.766993	+	0.641655i	$0.778248\pi$
$692$	32243.1	1.77124
$693$	2475.91	0.135717
$694$	26926.4	1.47278
$695$	257.863	0.0140738
$696$	−3333.33	−0.181537
$697$	−6647.26	−0.361238
$698$	12311.0	0.667588
$699$	−5968.08	−0.322938
$700$	2173.88	0.117378
$701$	12916.0	0.695906	0.347953	−	0.937512i	$-0.386877\pi$
$701$	12916.0	0.695906	0.347953	+	0.937512i	$0.386877\pi$
$702$	2733.85	0.146983
$703$	−26704.8	−1.43271
$704$	−27111.8	−1.45144
$705$	1691.56	0.0903659
$706$	27937.2	1.48928
$707$	3586.37	0.190777
$708$	16293.2	0.864880
$709$	−30250.8	−1.60239	−0.801193	−	0.598406i	$-0.795801\pi$
$709$	−30250.8	−1.60239	−0.801193	+	0.598406i	$0.795801\pi$
$710$	−14504.1	−0.766659
$711$	−11476.7	−0.605356
$712$	34716.9	1.82735
$713$	−1970.68	−0.103510
$714$	1511.56	0.0792277
$715$	−5197.45	−0.271851
$716$	−5264.03	−0.274757
$717$	−7724.07	−0.402316
$718$	31272.1	1.62544
$719$	6161.35	0.319582	0.159791	−	0.987151i	$-0.448918\pi$
$719$	6161.35	0.319582	0.159791	+	0.987151i	$0.448918\pi$
$720$	2714.80	0.140520
$721$	5321.78	0.274887
$722$	−3145.29	−0.162127
$723$	11050.3	0.568417
$724$	−13364.4	−0.686029
$725$	725.000	0.0371391
$726$	−17319.7	−0.885393
$727$	−35454.3	−1.80870	−0.904352	−	0.426786i	$-0.859646\pi$
$727$	−35454.3	−1.80870	−0.904352	+	0.426786i	$0.859646\pi$
$728$	−4359.49	−0.221941
$729$	729.000	0.0370370
$730$	−15201.7	−0.770742
$731$	−9544.43	−0.482919
$732$	−16994.2	−0.858092
$733$	−26681.1	−1.34446	−0.672231	−	0.740342i	$-0.734664\pi$
$733$	−26681.1	−1.34446	−0.672231	+	0.740342i	$0.734664\pi$
$734$	65194.7	3.27845
$735$	4693.31	0.235531
$736$	75.5001	0.00378121
$737$	−9178.57	−0.458747
$738$	15537.2	0.774976
$739$	−28886.6	−1.43791	−0.718953	−	0.695059i	$-0.755378\pi$
$739$	−28886.6	−1.43791	−0.718953	+	0.695059i	$0.755378\pi$
$740$	−26838.8	−1.33326
$741$	4903.89	0.243116
$742$	−3881.48	−0.192040
$743$	−16398.0	−0.809669	−0.404834	−	0.914390i	$-0.632671\pi$
$743$	−16398.0	−0.809669	−0.404834	+	0.914390i	$0.632671\pi$
$744$	−35741.3	−1.76121
$745$	−3041.65	−0.149580
$746$	−6675.64	−0.327631
$747$	−6651.97	−0.325814
$748$	−14936.9	−0.730142
$749$	−6955.56	−0.339320
$750$	−1831.22	−0.0891554
$751$	−5905.21	−0.286930	−0.143465	−	0.989655i	$-0.545824\pi$
$751$	−5905.21	−0.286930	−0.143465	+	0.989655i	$0.545824\pi$
$752$	−6803.33	−0.329910
$753$	−13893.8	−0.672402
$754$	−2936.35	−0.141824
$755$	−1707.84	−0.0823241
$756$	−2347.79	−0.112947
$757$	−12439.0	−0.597229	−0.298614	−	0.954374i	$-0.596524\pi$
$757$	−12439.0	−0.597229	−0.298614	+	0.954374i	$0.596524\pi$
$758$	48260.9	2.31255
$759$	953.161	0.0455831
$760$	15102.4	0.720818
$761$	14270.0	0.679748	0.339874	−	0.940471i	$-0.389616\pi$
$761$	14270.0	0.679748	0.339874	+	0.940471i	$0.389616\pi$
$762$	−11935.6	−0.567430
$763$	−4434.68	−0.210414
$764$	38645.6	1.83004
$765$	−846.122	−0.0399890
$766$	64584.6	3.04639
$767$	7106.66	0.334559
$768$	24312.7	1.14233
$769$	−15143.9	−0.710147	−0.355074	−	0.934838i	$-0.615544\pi$
$769$	−15143.9	−0.710147	−0.355074	+	0.934838i	$0.615544\pi$
$770$	6716.94	0.314366
$771$	4829.95	0.225611
$772$	64890.1	3.02519
$773$	−40617.2	−1.88991	−0.944955	−	0.327202i	$-0.893894\pi$
$773$	−40617.2	−1.88991	−0.944955	+	0.327202i	$0.893894\pi$
$774$	22309.0	1.03602
$775$	7773.74	0.360311
$776$	2914.42	0.134822
$777$	5576.59	0.257476
$778$	−41225.1	−1.89973
$779$	27870.1	1.28184
$780$	4928.49	0.226241
$781$	−29780.4	−1.36444
$782$	581.910	0.0266100
$783$	−783.000	−0.0357371
$784$	−18876.1	−0.859881
$785$	−1791.89	−0.0814718
$786$	21885.4	0.993162
$787$	43878.2	1.98741	0.993703	−	0.112048i	$-0.0357412\pi$
$787$	43878.2	1.98741	0.993703	+	0.112048i	$0.0357412\pi$
$788$	51131.3	2.31152
$789$	8604.66	0.388256
$790$	−31135.1	−1.40220
$791$	−6695.27	−0.300956
$792$	17287.0	0.775590
$793$	−7412.43	−0.331933
$794$	−11077.9	−0.495137
$795$	2172.73	0.0969294
$796$	−66850.4	−2.97670
$797$	14556.0	0.646925	0.323463	−	0.946241i	$-0.395153\pi$
$797$	14556.0	0.646925	0.323463	+	0.946241i	$0.395153\pi$
$798$	−6337.55	−0.281136
$799$	2120.40	0.0938853
$800$	−297.825	−0.0131621
$801$	8155.02	0.359730
$802$	40501.6	1.78324
$803$	−31212.9	−1.37170
$804$	8703.59	0.381781
$805$	−173.889	−0.00761338
$806$	−31484.8	−1.37593
$807$	1662.14	0.0725032
$808$	25040.3	1.09024
$809$	−14030.7	−0.609755	−0.304878	−	0.952392i	$-0.598616\pi$
$809$	−14030.7	−0.609755	−0.304878	+	0.952392i	$0.598616\pi$
$810$	1977.71	0.0857898
$811$	30195.7	1.30741	0.653707	−	0.756747i	$-0.273213\pi$
$811$	30195.7	1.30741	0.653707	+	0.756747i	$0.273213\pi$
$812$	2521.70	0.108983
$813$	5478.06	0.236315
$814$	−82927.7	−3.57078
$815$	−8336.80	−0.358313
$816$	3403.04	0.145993
$817$	40017.2	1.71362
$818$	48407.6	2.06911
$819$	−1024.05	−0.0436911
$820$	28010.0	1.19287
$821$	31237.5	1.32789	0.663944	−	0.747782i	$-0.268881\pi$
$821$	31237.5	1.32789	0.663944	+	0.747782i	$0.268881\pi$
$822$	23567.4	1.00001
$823$	−22306.9	−0.944798	−0.472399	−	0.881385i	$-0.656612\pi$
$823$	−22306.9	−0.944798	−0.472399	+	0.881385i	$0.656612\pi$
$824$	37157.1	1.57091
$825$	−3759.93	−0.158671
$826$	−9184.30	−0.386880
$827$	41561.9	1.74758	0.873790	−	0.486304i	$-0.161655\pi$
$827$	41561.9	1.74758	0.873790	+	0.486304i	$0.161655\pi$
$828$	−903.837	−0.0379354
$829$	42423.6	1.77736	0.888681	−	0.458527i	$-0.151623\pi$
$829$	42423.6	1.77736	0.888681	+	0.458527i	$0.151623\pi$
$830$	−18046.2	−0.754690
$831$	−4410.01	−0.184093
$832$	11213.5	0.467259
$833$	5883.13	0.244704
$834$	−755.524	−0.0313689
$835$	−9161.51	−0.379697
$836$	62626.3	2.59088
$837$	−8395.64	−0.346710
$838$	−65104.0	−2.68375
$839$	−31547.4	−1.29814	−0.649068	−	0.760730i	$-0.724841\pi$
$839$	−31547.4	−1.29814	−0.649068	+	0.760730i	$0.724841\pi$
$840$	−3153.73	−0.129541
$841$	841.000	0.0344828
$842$	−13908.1	−0.569247
$843$	−23479.3	−0.959276
$844$	−44342.5	−1.80845
$845$	−8835.32	−0.359697
$846$	−4956.19	−0.201415
$847$	6487.63	0.263185
$848$	−8738.56	−0.353872
$849$	20390.6	0.824268
$850$	−2295.45	−0.0926276
$851$	2146.84	0.0864779
$852$	28239.3	1.13552
$853$	−5030.77	−0.201935	−0.100967	−	0.994890i	$-0.532194\pi$
$853$	−5030.77	−0.201935	−0.100967	+	0.994890i	$0.532194\pi$
$854$	9579.46	0.383844
$855$	3547.56	0.141899
$856$	−48564.2	−1.93912
$857$	−16655.5	−0.663875	−0.331937	−	0.943301i	$-0.607702\pi$
$857$	−16655.5	−0.663875	−0.331937	+	0.943301i	$0.607702\pi$
$858$	15228.2	0.605925
$859$	33206.7	1.31897	0.659486	−	0.751717i	$-0.270774\pi$
$859$	33206.7	1.31897	0.659486	+	0.751717i	$0.270774\pi$
$860$	40218.0	1.59468
$861$	−5819.93	−0.230363
$862$	61869.0	2.44463
$863$	−12156.5	−0.479504	−0.239752	−	0.970834i	$-0.577066\pi$
$863$	−12156.5	−0.479504	−0.239752	+	0.970834i	$0.577066\pi$
$864$	321.651	0.0126653
$865$	10173.9	0.399909
$866$	−71029.6	−2.78716
$867$	13678.4	0.535804
$868$	27038.7	1.05732
$869$	−63928.0	−2.49552
$870$	−2124.21	−0.0827787
$871$	3796.28	0.147683
$872$	−30963.3	−1.20246
$873$	684.598	0.0265408
$874$	−2439.79	−0.0944246
$875$	685.938	0.0265016
$876$	29597.7	1.14157
$877$	10910.0	0.420075	0.210037	−	0.977693i	$-0.432641\pi$
$877$	10910.0	0.420075	0.210037	+	0.977693i	$0.432641\pi$
$878$	56105.7	2.15658
$879$	−10894.5	−0.418044
$880$	15122.1	0.579281
$881$	−10796.4	−0.412871	−0.206435	−	0.978460i	$-0.566186\pi$
$881$	−10796.4	−0.412871	−0.206435	+	0.978460i	$0.566186\pi$
$882$	−13751.1	−0.524972
$883$	−23778.3	−0.906232	−0.453116	−	0.891452i	$-0.649688\pi$
$883$	−23778.3	−0.906232	−0.453116	+	0.891452i	$0.649688\pi$
$884$	6177.94	0.235053
$885$	5141.08	0.195272
$886$	−54329.4	−2.06008
$887$	−26229.5	−0.992897	−0.496449	−	0.868066i	$-0.665363\pi$
$887$	−26229.5	−0.992897	−0.496449	+	0.868066i	$0.665363\pi$
$888$	38936.2	1.47141
$889$	4470.85	0.168670
$890$	22123.8	0.833251
$891$	4060.72	0.152682
$892$	39551.8	1.48463
$893$	−8890.26	−0.333148
$894$	8911.86	0.333397
$895$	−1660.99	−0.0620344
$896$	−13968.8	−0.520833
$897$	−394.230	−0.0146744
$898$	−32604.4	−1.21161
$899$	9017.54	0.334540
$900$	3565.36	0.132050
$901$	2723.55	0.100704
$902$	86546.3	3.19476
$903$	−8356.51	−0.307959
$904$	−46746.9	−1.71989
$905$	−4216.96	−0.154891
$906$	5003.88	0.183491
$907$	53019.1	1.94098	0.970491	−	0.241136i	$-0.0775201\pi$
$907$	53019.1	1.94098	0.970491	+	0.241136i	$0.0775201\pi$
$908$	54028.1	1.97465
$909$	5881.98	0.214624
$910$	−2778.14	−0.101203
$911$	−16886.9	−0.614147	−0.307074	−	0.951686i	$-0.599350\pi$
$911$	−16886.9	−0.614147	−0.307074	+	0.951686i	$0.599350\pi$
$912$	−14268.0	−0.518049
$913$	−37053.2	−1.34314
$914$	−52870.3	−1.91334
$915$	−5362.28	−0.193739
$916$	75973.4	2.74043
$917$	−8197.83	−0.295219
$918$	2479.09	0.0891309
$919$	−54865.8	−1.96937	−0.984687	−	0.174330i	$-0.944224\pi$
$919$	−54865.8	−1.96937	−0.984687	+	0.174330i	$0.944224\pi$
$920$	−1214.10	−0.0435085
$921$	27242.3	0.974663
$922$	−20090.7	−0.717626
$923$	12317.2	0.439249
$924$	−13077.8	−0.465615
$925$	−8468.62	−0.301023
$926$	−29822.9	−1.05836
$927$	8728.21	0.309247
$928$	−345.477	−0.0122207
$929$	27835.6	0.983053	0.491527	−	0.870863i	$-0.336439\pi$
$929$	27835.6	0.983053	0.491527	+	0.870863i	$0.336439\pi$
$930$	−22776.6	−0.803092
$931$	−24666.4	−0.868322
$932$	31523.5	1.10793
$933$	−7973.06	−0.279771
$934$	−6882.01	−0.241099
$935$	−4713.13	−0.164851
$936$	−7149.96	−0.249683
$937$	−38996.7	−1.35962	−0.679811	−	0.733387i	$-0.737938\pi$
$937$	−38996.7	−1.35962	−0.679811	+	0.733387i	$0.737938\pi$
$938$	−4906.13	−0.170779
$939$	1591.42	0.0553079
$940$	−8934.87	−0.310025
$941$	15686.8	0.543437	0.271718	−	0.962377i	$-0.412408\pi$
$941$	15686.8	0.543437	0.271718	+	0.962377i	$0.412408\pi$
$942$	5250.14	0.181591
$943$	−2240.52	−0.0773715
$944$	−20677.0	−0.712902
$945$	−740.813	−0.0255012
$946$	124267.	4.27090
$947$	−54527.1	−1.87106	−0.935530	−	0.353248i	$-0.885077\pi$
$947$	−54527.1	−1.87106	−0.935530	+	0.353248i	$0.885077\pi$
$948$	60619.8	2.07684
$949$	12909.7	0.441589
$950$	9624.22	0.328685
$951$	−7180.99	−0.244858
$952$	−3953.25	−0.134586
$953$	48998.7	1.66550	0.832752	−	0.553647i	$-0.186764\pi$
$953$	48998.7	1.66550	0.832752	+	0.553647i	$0.186764\pi$
$954$	−6365.99	−0.216044
$955$	12194.1	0.413184
$956$	40798.6	1.38025
$957$	−4361.52	−0.147323
$958$	61694.4	2.08064
$959$	−8827.88	−0.297254
$960$	8112.07	0.272725
$961$	66898.8	2.24560
$962$	34299.1	1.14953
$963$	−11407.7	−0.381734
$964$	−58368.0	−1.95011
$965$	20475.2	0.683025
$966$	509.484	0.0169693
$967$	−18866.1	−0.627395	−0.313698	−	0.949523i	$-0.601568\pi$
$967$	−18866.1	−0.627395	−0.313698	+	0.949523i	$0.601568\pi$
$968$	45297.1	1.50403
$969$	4446.92	0.147426
$970$	1857.25	0.0614772
$971$	49921.4	1.64990	0.824950	−	0.565205i	$-0.191203\pi$
$971$	49921.4	1.64990	0.824950	+	0.565205i	$0.191203\pi$
$972$	−3850.59	−0.127066
$973$	283.004	0.00932446
$974$	−83135.6	−2.73495
$975$	1555.12	0.0510806
$976$	21566.7	0.707308
$977$	−2591.52	−0.0848618	−0.0424309	−	0.999099i	$-0.513510\pi$
$977$	−2591.52	−0.0848618	−0.0424309	+	0.999099i	$0.513510\pi$
$978$	24426.4	0.798639
$979$	45425.6	1.48295
$980$	−24790.1	−0.808053
$981$	−7273.28	−0.236715
$982$	−18519.6	−0.601815
$983$	18566.6	0.602423	0.301211	−	0.953557i	$-0.402609\pi$
$983$	18566.6	0.602423	0.301211	+	0.953557i	$0.402609\pi$
$984$	−40635.2	−1.31647
$985$	16133.8	0.521894
$986$	−2662.73	−0.0860026
$987$	1856.49	0.0598711
$988$	−25902.4	−0.834074
$989$	−3217.04	−0.103434
$990$	11016.4	0.353660
$991$	−34558.3	−1.10775	−0.553875	−	0.832600i	$-0.686851\pi$
$991$	−34558.3	−1.10775	−0.553875	+	0.832600i	$0.686851\pi$
$992$	−3704.34	−0.118561
$993$	23953.6	0.765503
$994$	−15918.2	−0.507943
$995$	−21093.7	−0.672076
$996$	35135.8	1.11779
$997$	−11238.6	−0.357000	−0.178500	−	0.983940i	$-0.557124\pi$
$997$	−11238.6	−0.357000	−0.178500	+	0.983940i	$0.557124\pi$
$998$	31663.9	1.00431
$999$	9146.11	0.289660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.i.1.7	✓	7
3.2	odd	2		1305.4.a.n.1.1		7
5.4	even	2		2175.4.a.n.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.i.1.7	✓	7	1.1	even	1	trivial
1305.4.a.n.1.1		7	3.2	odd	2
2175.4.a.n.1.1		7	5.4	even	2

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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q+4.88324 q^{2} -3.00000 q^{3} +15.8460 q^{4} +5.00000 q^{5} -14.6497 q^{6} +5.48750 q^{7} +38.3141 q^{8} +9.00000 q^{9} +24.4162 q^{10} +50.1324 q^{11} -47.5381 q^{12} -20.7349 q^{13} +26.7968 q^{14} -15.0000 q^{15} +60.3288 q^{16} -18.8027 q^{17} +43.9492 q^{18} +78.8346 q^{19} +79.2302 q^{20} -16.4625 q^{21} +244.809 q^{22} -6.33763 q^{23} -114.942 q^{24} +25.0000 q^{25} -101.254 q^{26} -27.0000 q^{27} +86.9552 q^{28} +29.0000 q^{29} -73.2486 q^{30} +310.950 q^{31} -11.9130 q^{32} -150.397 q^{33} -91.8182 q^{34} +27.4375 q^{35} +142.614 q^{36} -338.745 q^{37} +384.969 q^{38} +62.2047 q^{39} +191.571 q^{40} +353.526 q^{41} -80.3904 q^{42} +507.609 q^{43} +794.400 q^{44} +45.0000 q^{45} -30.9482 q^{46} -112.771 q^{47} -180.986 q^{48} -312.887 q^{49} +122.081 q^{50} +56.4081 q^{51} -328.566 q^{52} -144.849 q^{53} -131.848 q^{54} +250.662 q^{55} +210.249 q^{56} -236.504 q^{57} +141.614 q^{58} -342.739 q^{59} -237.691 q^{60} +357.486 q^{61} +1518.44 q^{62} +49.3875 q^{63} -540.804 q^{64} -103.675 q^{65} -734.426 q^{66} -183.087 q^{67} -297.949 q^{68} +19.0129 q^{69} +133.984 q^{70} -594.034 q^{71} +344.827 q^{72} -622.609 q^{73} -1654.17 q^{74} -75.0000 q^{75} +1249.22 q^{76} +275.102 q^{77} +303.761 q^{78} -1275.18 q^{79} +301.644 q^{80} +81.0000 q^{81} +1726.35 q^{82} -739.108 q^{83} -260.866 q^{84} -94.0136 q^{85} +2478.78 q^{86} -87.0000 q^{87} +1920.78 q^{88} +906.113 q^{89} +219.746 q^{90} -113.783 q^{91} -100.426 q^{92} -932.849 q^{93} -550.688 q^{94} +394.173 q^{95} +35.7390 q^{96} +76.0665 q^{97} -1527.90 q^{98} +451.192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19}+ \cdots + 684 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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