LMFDB - Embedded newform 525.4.d.m.274.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.4
Root			$2.56155i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.m.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.56155i q^{2} +3.00000i q^{3} -4.68466 q^{4} -10.6847 q^{6} -7.00000i q^{7} +11.8078i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+3.56155i q^{2} +3.00000i q^{3} -4.68466 q^{4} -10.6847 q^{6} -7.00000i q^{7} +11.8078i q^{8} -9.00000 q^{9} -5.19224 q^{11} -14.0540i q^{12} -54.5464i q^{13} +24.9309 q^{14} -79.5312 q^{16} +16.1619i q^{17} -32.0540i q^{18} -87.4470 q^{19} +21.0000 q^{21} -18.4924i q^{22} -176.477i q^{23} -35.4233 q^{24} +194.270 q^{26} -27.0000i q^{27} +32.7926i q^{28} -142.170 q^{29} -94.3002 q^{31} -188.793i q^{32} -15.5767i q^{33} -57.5616 q^{34} +42.1619 q^{36} +17.3305i q^{37} -311.447i q^{38} +163.639 q^{39} +210.270 q^{41} +74.7926i q^{42} -521.570i q^{43} +24.3239 q^{44} +628.533 q^{46} -105.417i q^{47} -238.594i q^{48} -49.0000 q^{49} -48.4858 q^{51} +255.531i q^{52} +108.978i q^{53} +96.1619 q^{54} +82.6543 q^{56} -262.341i q^{57} -506.348i q^{58} -210.365 q^{59} -674.304 q^{61} -335.855i q^{62} +63.0000i q^{63} +36.1449 q^{64} +55.4773 q^{66} +324.929i q^{67} -75.7131i q^{68} +529.432 q^{69} +793.965 q^{71} -106.270i q^{72} -315.417i q^{73} -61.7235 q^{74} +409.659 q^{76} +36.3457i q^{77} +582.810i q^{78} +425.840 q^{79} +81.0000 q^{81} +748.887i q^{82} +283.029i q^{83} -98.3778 q^{84} +1857.60 q^{86} -426.511i q^{87} -61.3087i q^{88} +843.131 q^{89} -381.825 q^{91} +826.736i q^{92} -282.901i q^{93} +375.447 q^{94} +566.378 q^{96} +1537.33i q^{97} -174.516i q^{98} +46.7301 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4} - 18 q^{6} - 36 q^{9}+O(q^{10}) $ 4 * q + 6 * q^4 - 18 * q^6 - 36 * q^9	$ 4 q + 6 q^{4} - 18 q^{6} - 36 q^{9} - 62 q^{11} + 42 q^{14} - 46 q^{16} + 112 q^{19} + 84 q^{21} - 18 q^{24} + 406 q^{26} + 124 q^{29} - 270 q^{31} - 222 q^{34} - 54 q^{36} + 234 q^{39} + 470 q^{41} - 348 q^{44} + 1170 q^{46} - 196 q^{49} + 474 q^{51} + 162 q^{54} + 42 q^{56} + 882 q^{59} - 446 q^{61} + 862 q^{64} + 24 q^{66} + 1524 q^{69} + 1238 q^{71} - 16 q^{74} + 3024 q^{76} + 854 q^{79} + 324 q^{81} + 126 q^{84} + 3398 q^{86} - 932 q^{89} - 546 q^{91} + 1040 q^{94} + 1746 q^{96} + 558 q^{99}+O(q^{100}) $ 4 * q + 6 * q^4 - 18 * q^6 - 36 * q^9 - 62 * q^11 + 42 * q^14 - 46 * q^16 + 112 * q^19 + 84 * q^21 - 18 * q^24 + 406 * q^26 + 124 * q^29 - 270 * q^31 - 222 * q^34 - 54 * q^36 + 234 * q^39 + 470 * q^41 - 348 * q^44 + 1170 * q^46 - 196 * q^49 + 474 * q^51 + 162 * q^54 + 42 * q^56 + 882 * q^59 - 446 * q^61 + 862 * q^64 + 24 * q^66 + 1524 * q^69 + 1238 * q^71 - 16 * q^74 + 3024 * q^76 + 854 * q^79 + 324 * q^81 + 126 * q^84 + 3398 * q^86 - 932 * q^89 - 546 * q^91 + 1040 * q^94 + 1746 * q^96 + 558 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	3.56155i	1.25920i	0.776920	+	0.629600i	$0.216781\pi$
$2$	3.56155i	1.25920i	−0.776920	+	0.629600i	$0.783219\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−4.68466	−0.585582
$5$	0	0
$5$	0	0
$6$	−10.6847	−0.726999
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	11.8078i	0.521834i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−5.19224	−0.142320	−0.0711599	−	0.997465i	$-0.522670\pi$
$11$	−5.19224	−0.142320	−0.0711599	+	0.997465i	$0.522670\pi$
$12$	− 14.0540i	− 0.338086i
$13$	− 54.5464i	− 1.16373i	−0.813287	−	0.581863i	$-0.802324\pi$
$13$	− 54.5464i	− 1.16373i	0.813287	−	0.581863i	$-0.197676\pi$
$14$	24.9309	0.475933
$15$	0	0
$16$	−79.5312	−1.24268
$17$	16.1619i	0.230579i	0.993332	+	0.115289i	$0.0367796\pi$
$17$	16.1619i	0.230579i	−0.993332	+	0.115289i	$0.963220\pi$
$18$	− 32.0540i	− 0.419733i
$19$	−87.4470	−1.05588	−0.527940	−	0.849282i	$-0.677035\pi$
$19$	−87.4470	−1.05588	−0.527940	+	0.849282i	$0.677035\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	− 18.4924i	− 0.179209i
$23$	− 176.477i	− 1.59992i	−0.600056	−	0.799958i	$-0.704855\pi$
$23$	− 176.477i	− 1.59992i	0.600056	−	0.799958i	$-0.295145\pi$
$24$	−35.4233	−0.301281
$25$	0	0
$26$	194.270	1.46536
$27$	− 27.0000i	− 0.192450i
$28$	32.7926i	0.221329i
$29$	−142.170	−0.910358	−0.455179	−	0.890400i	$-0.650425\pi$
$29$	−142.170	−0.910358	−0.455179	+	0.890400i	$0.650425\pi$
$30$	0	0
$31$	−94.3002	−0.546349	−0.273174	−	0.961965i	$-0.588074\pi$
$31$	−94.3002	−0.546349	−0.273174	+	0.961965i	$0.588074\pi$
$32$	− 188.793i	− 1.04294i
$33$	− 15.5767i	− 0.0821684i
$34$	−57.5616	−0.290345
$35$	0	0
$36$	42.1619	0.195194
$37$	17.3305i	0.0770031i	0.999259	+	0.0385016i	$0.0122585\pi$
$37$	17.3305i	0.0770031i	−0.999259	+	0.0385016i	$0.987742\pi$
$38$	− 311.447i	− 1.32956i
$39$	163.639	0.671878
$40$	0	0
$41$	210.270	0.800942	0.400471	−	0.916309i	$-0.368846\pi$
$41$	210.270	0.800942	0.400471	+	0.916309i	$0.368846\pi$
$42$	74.7926i	0.274780i
$43$	− 521.570i	− 1.84974i	−0.380287	−	0.924868i	$-0.624175\pi$
$43$	− 521.570i	− 1.84974i	0.380287	−	0.924868i	$-0.375825\pi$
$44$	24.3239	0.0833400
$45$	0	0
$46$	628.533	2.01461
$47$	− 105.417i	− 0.327162i	−0.986530	−	0.163581i	$-0.947696\pi$
$47$	− 105.417i	− 0.327162i	0.986530	−	0.163581i	$-0.0523045\pi$
$48$	− 238.594i	− 0.717459i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	−48.4858	−0.133125
$52$	255.531i	0.681458i
$53$	108.978i	0.282440i	0.989978	+	0.141220i	$0.0451025\pi$
$53$	108.978i	0.282440i	−0.989978	+	0.141220i	$0.954898\pi$
$54$	96.1619	0.242333
$55$	0	0
$56$	82.6543	0.197235
$57$	− 262.341i	− 0.609612i
$58$	− 506.348i	− 1.14632i
$59$	−210.365	−0.464189	−0.232094	−	0.972693i	$-0.574558\pi$
$59$	−210.365	−0.464189	−0.232094	+	0.972693i	$0.574558\pi$
$60$	0	0
$61$	−674.304	−1.41534	−0.707670	−	0.706543i	$-0.750254\pi$
$61$	−674.304	−1.41534	−0.707670	+	0.706543i	$0.750254\pi$
$62$	− 335.855i	− 0.687962i
$63$	63.0000i	0.125988i
$64$	36.1449	0.0705955
$65$	0	0
$66$	55.4773	0.103466
$67$	324.929i	0.592484i	0.955113	+	0.296242i	$0.0957334\pi$
$67$	324.929i	0.592484i	−0.955113	+	0.296242i	$0.904267\pi$
$68$	− 75.7131i	− 0.135023i
$69$	529.432	0.923712
$70$	0	0
$71$	793.965	1.32713	0.663565	−	0.748118i	$-0.269042\pi$
$71$	793.965	1.32713	0.663565	+	0.748118i	$0.269042\pi$
$72$	− 106.270i	− 0.173945i
$73$	− 315.417i	− 0.505709i	−0.967504	−	0.252854i	$-0.918631\pi$
$73$	− 315.417i	− 0.505709i	0.967504	−	0.252854i	$-0.0813693\pi$
$74$	−61.7235	−0.0969623
$75$	0	0
$76$	409.659	0.618304
$77$	36.3457i	0.0537918i
$78$	582.810i	0.846028i
$79$	425.840	0.606465	0.303233	−	0.952917i	$-0.401934\pi$
$79$	425.840	0.606465	0.303233	+	0.952917i	$0.401934\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	748.887i	1.00855i
$83$	283.029i	0.374295i	0.982332	+	0.187148i	$0.0599243\pi$
$83$	283.029i	0.374295i	−0.982332	+	0.187148i	$0.940076\pi$
$84$	−98.3778	−0.127785
$85$	0	0
$86$	1857.60	2.32919
$87$	− 426.511i	− 0.525596i
$88$	− 61.3087i	− 0.0742674i
$89$	843.131	1.00418	0.502088	−	0.864817i	$-0.332565\pi$
$89$	843.131	1.00418	0.502088	+	0.864817i	$0.332565\pi$
$90$	0	0
$91$	−381.825	−0.439847
$92$	826.736i	0.936882i
$93$	− 282.901i	− 0.315435i
$94$	375.447	0.411962
$95$	0	0
$96$	566.378	0.602143
$97$	1537.33i	1.60920i	0.593816	+	0.804601i	$0.297621\pi$
$97$	1537.33i	1.60920i	−0.593816	+	0.804601i	$0.702379\pi$
$98$	− 174.516i	− 0.179886i
$99$	46.7301	0.0474399
$100$	0	0
$101$	−1589.99	−1.56644	−0.783219	−	0.621745i	$-0.786424\pi$
$101$	−1589.99	−1.56644	−0.783219	+	0.621745i	$0.786424\pi$
$102$	− 172.685i	− 0.167631i
$103$	164.793i	0.157646i	0.996889	+	0.0788228i	$0.0251161\pi$
$103$	164.793i	0.157646i	−0.996889	+	0.0788228i	$0.974884\pi$
$104$	644.071	0.607273
$105$	0	0
$106$	−388.132	−0.355648
$107$	1184.08i	1.06981i	0.844913	+	0.534904i	$0.179652\pi$
$107$	1184.08i	1.06981i	−0.844913	+	0.534904i	$0.820348\pi$
$108$	126.486i	0.112695i
$109$	−333.247	−0.292837	−0.146419	−	0.989223i	$-0.546775\pi$
$109$	−333.247	−0.292837	−0.146419	+	0.989223i	$0.546775\pi$
$110$	0	0
$111$	−51.9915	−0.0444578
$112$	556.719i	0.469687i
$113$	− 1881.49i	− 1.56634i	−0.621810	−	0.783168i	$-0.713602\pi$
$113$	− 1881.49i	− 1.56634i	0.621810	−	0.783168i	$-0.286398\pi$
$114$	934.341	0.767623
$115$	0	0
$116$	666.020	0.533090
$117$	490.918i	0.387909i
$118$	− 749.224i	− 0.584506i
$119$	113.133	0.0871507
$120$	0	0
$121$	−1304.04	−0.979745
$122$	− 2401.57i	− 1.78220i
$123$	630.810i	0.462424i
$124$	441.764	0.319932
$125$	0	0
$126$	−224.378	−0.158644
$127$	1638.79i	1.14503i	0.819893	+	0.572516i	$0.194033\pi$
$127$	1638.79i	1.14503i	−0.819893	+	0.572516i	$0.805967\pi$
$128$	− 1381.61i	− 0.954048i
$129$	1564.71	1.06795
$130$	0	0
$131$	−598.142	−0.398931	−0.199465	−	0.979905i	$-0.563921\pi$
$131$	−598.142	−0.398931	−0.199465	+	0.979905i	$0.563921\pi$
$132$	72.9716i	0.0481164i
$133$	612.129i	0.399085i
$134$	−1157.25	−0.746055
$135$	0	0
$136$	−190.836	−0.120324
$137$	− 1005.25i	− 0.626894i	−0.949606	−	0.313447i	$-0.898516\pi$
$137$	− 1005.25i	− 0.626894i	0.949606	−	0.313447i	$-0.101484\pi$
$138$	1885.60i	1.16314i
$139$	1875.01	1.14414	0.572072	−	0.820204i	$-0.306140\pi$
$139$	1875.01	1.14414	0.572072	+	0.820204i	$0.306140\pi$
$140$	0	0
$141$	316.250	0.188887
$142$	2827.75i	1.67112i
$143$	283.218i	0.165621i
$144$	715.781	0.414225
$145$	0	0
$146$	1123.37	0.636788
$147$	− 147.000i	− 0.0824786i
$148$	− 81.1875i	− 0.0450917i
$149$	1051.80	0.578299	0.289150	−	0.957284i	$-0.406627\pi$
$149$	1051.80	0.578299	0.289150	+	0.957284i	$0.406627\pi$
$150$	0	0
$151$	−750.383	−0.404406	−0.202203	−	0.979344i	$-0.564810\pi$
$151$	−750.383	−0.404406	−0.202203	+	0.979344i	$0.564810\pi$
$152$	− 1032.55i	− 0.550994i
$153$	− 145.457i	− 0.0768597i
$154$	−129.447	−0.0677346
$155$	0	0
$156$	−766.594	−0.393440
$157$	− 1453.90i	− 0.739067i	−0.929217	−	0.369533i	$-0.879518\pi$
$157$	− 1453.90i	− 0.739067i	0.929217	−	0.369533i	$-0.120482\pi$
$158$	1516.65i	0.763660i
$159$	−326.935	−0.163067
$160$	0	0
$161$	−1235.34	−0.604711
$162$	288.486i	0.139911i
$163$	− 1300.49i	− 0.624921i	−0.949931	−	0.312461i	$-0.898847\pi$
$163$	− 1300.49i	− 0.624921i	0.949931	−	0.312461i	$-0.101153\pi$
$164$	−985.043	−0.469018
$165$	0	0
$166$	−1008.02	−0.471312
$167$	− 2111.46i	− 0.978381i	−0.872177	−	0.489191i	$-0.837292\pi$
$167$	− 2111.46i	− 0.978381i	0.872177	−	0.489191i	$-0.162708\pi$
$168$	247.963i	0.113874i
$169$	−778.310	−0.354260
$170$	0	0
$171$	787.023	0.351960
$172$	2443.38i	1.08317i
$173$	− 335.292i	− 0.147351i	−0.997282	−	0.0736756i	$-0.976527\pi$
$173$	− 335.292i	− 0.147351i	0.997282	−	0.0736756i	$-0.0234729\pi$
$174$	1519.04	0.661829
$175$	0	0
$176$	412.945	0.176857
$177$	− 631.094i	− 0.267999i
$178$	3002.85i	1.26446i
$179$	−2322.23	−0.969672	−0.484836	−	0.874605i	$-0.661121\pi$
$179$	−2322.23	−0.969672	−0.484836	+	0.874605i	$0.661121\pi$
$180$	0	0
$181$	−1525.59	−0.626500	−0.313250	−	0.949671i	$-0.601418\pi$
$181$	−1525.59	−0.626500	−0.313250	+	0.949671i	$0.601418\pi$
$182$	− 1359.89i	− 0.553855i
$183$	− 2022.91i	− 0.817147i
$184$	2083.80	0.834891
$185$	0	0
$186$	1007.57	0.397195
$187$	− 83.9165i	− 0.0328160i
$188$	493.841i	0.191580i
$189$	−189.000	−0.0727393
$190$	0	0
$191$	293.912	0.111344	0.0556721	−	0.998449i	$-0.482270\pi$
$191$	293.912	0.111344	0.0556721	+	0.998449i	$0.482270\pi$
$192$	108.435i	0.0407583i
$193$	3664.91i	1.36687i	0.730012	+	0.683435i	$0.239515\pi$
$193$	3664.91i	1.36687i	−0.730012	+	0.683435i	$0.760485\pi$
$194$	−5475.29	−2.02630
$195$	0	0
$196$	229.548	0.0836546
$197$	− 5101.89i	− 1.84515i	−0.385816	−	0.922576i	$-0.626080\pi$
$197$	− 5101.89i	− 1.84515i	0.385816	−	0.922576i	$-0.373920\pi$
$198$	166.432i	0.0597363i
$199$	−5025.86	−1.79032	−0.895161	−	0.445743i	$-0.852939\pi$
$199$	−5025.86	−1.79032	−0.895161	+	0.445743i	$0.852939\pi$
$200$	0	0
$201$	−974.787	−0.342071
$202$	− 5662.85i	− 1.97246i
$203$	995.193i	0.344083i
$204$	227.139	0.0779556
$205$	0	0
$206$	−586.918	−0.198507
$207$	1588.30i	0.533305i
$208$	4338.14i	1.44614i
$209$	454.045	0.150273
$210$	0	0
$211$	−3267.98	−1.06624	−0.533122	−	0.846039i	$-0.678981\pi$
$211$	−3267.98	−1.06624	−0.533122	+	0.846039i	$0.678981\pi$
$212$	− 510.526i	− 0.165392i
$213$	2381.89i	0.766219i
$214$	−4217.17	−1.34710
$215$	0	0
$216$	318.810	0.100427
$217$	660.101i	0.206500i
$218$	− 1186.88i	− 0.368741i
$219$	946.250	0.291971
$220$	0	0
$221$	881.575	0.268331
$222$	− 185.170i	− 0.0559812i
$223$	− 5457.65i	− 1.63888i	−0.573162	−	0.819442i	$-0.694283\pi$
$223$	− 5457.65i	− 1.63888i	0.573162	−	0.819442i	$-0.305717\pi$
$224$	−1321.55	−0.394195
$225$	0	0
$226$	6701.04	1.97233
$227$	281.023i	0.0821682i	0.999156	+	0.0410841i	$0.0130812\pi$
$227$	281.023i	0.0821682i	−0.999156	+	0.0410841i	$0.986919\pi$
$228$	1228.98i	0.356978i
$229$	−2776.64	−0.801248	−0.400624	−	0.916243i	$-0.631207\pi$
$229$	−2776.64	−0.801248	−0.400624	+	0.916243i	$0.631207\pi$
$230$	0	0
$231$	−109.037	−0.0310567
$232$	− 1678.71i	− 0.475056i
$233$	− 5781.09i	− 1.62546i	−0.582642	−	0.812729i	$-0.697981\pi$
$233$	− 5781.09i	− 1.62546i	0.582642	−	0.812729i	$-0.302019\pi$
$234$	−1748.43	−0.488455
$235$	0	0
$236$	985.486	0.271821
$237$	1277.52i	0.350143i
$238$	402.931i	0.109740i
$239$	−1588.17	−0.429833	−0.214916	−	0.976632i	$-0.568948\pi$
$239$	−1588.17	−0.429833	−0.214916	+	0.976632i	$0.568948\pi$
$240$	0	0
$241$	−4330.01	−1.15735	−0.578673	−	0.815560i	$-0.696429\pi$
$241$	−4330.01	−1.15735	−0.578673	+	0.815560i	$0.696429\pi$
$242$	− 4644.41i	− 1.23369i
$243$	243.000i	0.0641500i
$244$	3158.88	0.828798
$245$	0	0
$246$	−2246.66	−0.582284
$247$	4769.92i	1.22876i
$248$	− 1113.47i	− 0.285104i
$249$	−849.088	−0.216099
$250$	0	0
$251$	1400.53	0.352195	0.176097	−	0.984373i	$-0.443653\pi$
$251$	1400.53	0.352195	0.176097	+	0.984373i	$0.443653\pi$
$252$	− 295.133i	− 0.0737764i
$253$	916.312i	0.227700i
$254$	−5836.64	−1.44182
$255$	0	0
$256$	5209.83	1.27193
$257$	4304.86i	1.04486i	0.852681	+	0.522431i	$0.174975\pi$
$257$	4304.86i	1.04486i	−0.852681	+	0.522431i	$0.825025\pi$
$258$	5572.80i	1.34476i
$259$	121.313	0.0291045
$260$	0	0
$261$	1279.53	0.303453
$262$	− 2130.31i	− 0.502333i
$263$	1724.69i	0.404369i	0.979347	+	0.202184i	$0.0648041\pi$
$263$	1724.69i	0.404369i	−0.979347	+	0.202184i	$0.935196\pi$
$264$	183.926	0.0428783
$265$	0	0
$266$	−2180.13	−0.502527
$267$	2529.39i	0.579761i
$268$	− 1522.18i	− 0.346948i
$269$	−8004.82	−1.81436	−0.907180	−	0.420744i	$-0.861769\pi$
$269$	−8004.82	−1.81436	−0.907180	+	0.420744i	$0.861769\pi$
$270$	0	0
$271$	−1963.65	−0.440160	−0.220080	−	0.975482i	$-0.570632\pi$
$271$	−1963.65	−0.440160	−0.220080	+	0.975482i	$0.570632\pi$
$272$	− 1285.38i	− 0.286535i
$273$	− 1145.47i	− 0.253946i
$274$	3580.26	0.789384
$275$	0	0
$276$	−2480.21	−0.540909
$277$	− 3278.33i	− 0.711104i	−0.934656	−	0.355552i	$-0.884293\pi$
$277$	− 3278.33i	− 0.711104i	0.934656	−	0.355552i	$-0.115707\pi$
$278$	6677.93i	1.44070i
$279$	848.702	0.182116
$280$	0	0
$281$	2859.04	0.606961	0.303480	−	0.952838i	$-0.401851\pi$
$281$	2859.04	0.606961	0.303480	+	0.952838i	$0.401851\pi$
$282$	1126.34i	0.237846i
$283$	5433.66i	1.14134i	0.821181	+	0.570668i	$0.193315\pi$
$283$	5433.66i	1.14134i	−0.821181	+	0.570668i	$0.806685\pi$
$284$	−3719.45	−0.777144
$285$	0	0
$286$	−1008.70	−0.208550
$287$	− 1471.89i	− 0.302728i
$288$	1699.13i	0.347647i
$289$	4651.79	0.946833
$290$	0	0
$291$	−4612.00	−0.929073
$292$	1477.62i	0.296134i
$293$	− 8583.43i	− 1.71143i	−0.517447	−	0.855715i	$-0.673117\pi$
$293$	− 8583.43i	− 1.71143i	0.517447	−	0.855715i	$-0.326883\pi$
$294$	523.548	0.103857
$295$	0	0
$296$	−204.634	−0.0401829
$297$	140.190i	0.0273895i
$298$	3746.03i	0.728194i
$299$	−9626.20	−1.86186
$300$	0	0
$301$	−3650.99	−0.699135
$302$	− 2672.53i	− 0.509228i
$303$	− 4769.98i	− 0.904384i
$304$	6954.77	1.31212
$305$	0	0
$306$	518.054	0.0967816
$307$	− 5269.83i	− 0.979691i	−0.871809	−	0.489846i	$-0.837053\pi$
$307$	− 5269.83i	− 0.979691i	0.871809	−	0.489846i	$-0.162947\pi$
$308$	− 170.267i	− 0.0314995i
$309$	−494.378	−0.0910167
$310$	0	0
$311$	−4761.43	−0.868154	−0.434077	−	0.900876i	$-0.642925\pi$
$311$	−4761.43	−0.868154	−0.434077	+	0.900876i	$0.642925\pi$
$312$	1932.21i	0.350609i
$313$	7602.95i	1.37298i	0.727137	+	0.686492i	$0.240850\pi$
$313$	7602.95i	1.37298i	−0.727137	+	0.686492i	$0.759150\pi$
$314$	5178.13	0.930632
$315$	0	0
$316$	−1994.91	−0.355135
$317$	8064.55i	1.42886i	0.699704	+	0.714432i	$0.253315\pi$
$317$	8064.55i	1.42886i	−0.699704	+	0.714432i	$0.746685\pi$
$318$	− 1164.39i	− 0.205333i
$319$	738.182	0.129562
$320$	0	0
$321$	−3552.24	−0.617654
$322$	− 4399.73i	− 0.761452i
$323$	− 1413.31i	− 0.243464i
$324$	−379.457	−0.0650647
$325$	0	0
$326$	4631.76	0.786901
$327$	− 999.741i	− 0.169070i
$328$	2482.82i	0.417959i
$329$	−737.917	−0.123655
$330$	0	0
$331$	6960.79	1.15589	0.577945	−	0.816076i	$-0.303855\pi$
$331$	6960.79	1.15589	0.577945	+	0.816076i	$0.303855\pi$
$332$	− 1325.90i	− 0.219181i
$333$	− 155.974i	− 0.0256677i
$334$	7520.08	1.23198
$335$	0	0
$336$	−1670.16	−0.271174
$337$	4731.61i	0.764828i	0.923991	+	0.382414i	$0.124907\pi$
$337$	4731.61i	0.764828i	−0.923991	+	0.382414i	$0.875093\pi$
$338$	− 2771.99i	− 0.446084i
$339$	5644.48	0.904325
$340$	0	0
$341$	489.629	0.0777563
$342$	2803.02i	0.443187i
$343$	343.000i	0.0539949i
$344$	6158.58	0.965256
$345$	0	0
$346$	1194.16	0.185544
$347$	9796.67i	1.51560i	0.652487	+	0.757800i	$0.273726\pi$
$347$	9796.67i	1.51560i	−0.652487	+	0.757800i	$0.726274\pi$
$348$	1998.06i	0.307779i
$349$	−12702.4	−1.94827	−0.974134	−	0.225971i	$-0.927445\pi$
$349$	−12702.4	−1.94827	−0.974134	+	0.225971i	$0.927445\pi$
$350$	0	0
$351$	−1472.75	−0.223959
$352$	980.256i	0.148431i
$353$	9970.21i	1.50329i	0.659569	+	0.751644i	$0.270739\pi$
$353$	9970.21i	1.50329i	−0.659569	+	0.751644i	$0.729261\pi$
$354$	2247.67	0.337465
$355$	0	0
$356$	−3949.78	−0.588028
$357$	339.400i	0.0503165i
$358$	− 8270.73i	− 1.22101i
$359$	−4388.21	−0.645128	−0.322564	−	0.946548i	$-0.604545\pi$
$359$	−4388.21	−0.645128	−0.322564	+	0.946548i	$0.604545\pi$
$360$	0	0
$361$	787.970	0.114881
$362$	− 5433.49i	− 0.788889i
$363$	− 3912.12i	− 0.565656i
$364$	1788.72	0.257567
$365$	0	0
$366$	7204.71	1.02895
$367$	− 9441.30i	− 1.34287i	−0.741065	−	0.671433i	$-0.765679\pi$
$367$	− 9441.30i	− 1.34287i	0.741065	−	0.671433i	$-0.234321\pi$
$368$	14035.5i	1.98818i
$369$	−1892.43	−0.266981
$370$	0	0
$371$	762.847	0.106752
$372$	1325.29i	0.184713i
$373$	3219.40i	0.446901i	0.974715	+	0.223451i	$0.0717322\pi$
$373$	3219.40i	0.446901i	−0.974715	+	0.223451i	$0.928268\pi$
$374$	298.873	0.0413218
$375$	0	0
$376$	1244.73	0.170724
$377$	7754.89i	1.05941i
$378$	− 673.133i	− 0.0915933i
$379$	14011.4	1.89899	0.949495	−	0.313783i	$-0.101597\pi$
$379$	14011.4	1.89899	0.949495	+	0.313783i	$0.101597\pi$
$380$	0	0
$381$	−4916.37	−0.661085
$382$	1046.78i	0.140204i
$383$	− 5322.87i	− 0.710147i	−0.934838	−	0.355073i	$-0.884456\pi$
$383$	− 5322.87i	− 0.710147i	0.934838	−	0.355073i	$-0.115544\pi$
$384$	4144.83	0.550820
$385$	0	0
$386$	−13052.8	−1.72116
$387$	4694.13i	0.616579i
$388$	− 7201.88i	− 0.942320i
$389$	3844.51	0.501091	0.250545	−	0.968105i	$-0.419390\pi$
$389$	3844.51	0.501091	0.250545	+	0.968105i	$0.419390\pi$
$390$	0	0
$391$	2852.21	0.368907
$392$	− 578.580i	− 0.0745478i
$393$	− 1794.43i	− 0.230323i
$394$	18170.7	2.32341
$395$	0	0
$396$	−218.915	−0.0277800
$397$	− 8046.40i	− 1.01722i	−0.860996	−	0.508611i	$-0.830159\pi$
$397$	− 8046.40i	− 1.01722i	0.860996	−	0.508611i	$-0.169841\pi$
$398$	− 17899.9i	− 2.25437i
$399$	−1836.39	−0.230412
$400$	0	0
$401$	7741.38	0.964055	0.482027	−	0.876156i	$-0.339901\pi$
$401$	7741.38	0.964055	0.482027	+	0.876156i	$0.339901\pi$
$402$	− 3471.76i	− 0.430735i
$403$	5143.74i	0.635801i
$404$	7448.58	0.917279
$405$	0	0
$406$	−3544.43	−0.433269
$407$	− 89.9840i	− 0.0109591i
$408$	− 572.509i	− 0.0694691i
$409$	8966.94	1.08407	0.542037	−	0.840354i	$-0.317653\pi$
$409$	8966.94	1.08407	0.542037	+	0.840354i	$0.317653\pi$
$410$	0	0
$411$	3015.76	0.361937
$412$	− 771.997i	− 0.0923145i
$413$	1472.55i	0.175447i
$414$	−5656.80	−0.671537
$415$	0	0
$416$	−10298.0	−1.21370
$417$	5625.02i	0.660571i
$418$	1617.11i	0.189223i
$419$	12413.6	1.44736	0.723681	−	0.690135i	$-0.242449\pi$
$419$	12413.6	1.44736	0.723681	+	0.690135i	$0.242449\pi$
$420$	0	0
$421$	−1672.14	−0.193575	−0.0967875	−	0.995305i	$-0.530857\pi$
$421$	−1672.14	−0.193575	−0.0967875	+	0.995305i	$0.530857\pi$
$422$	− 11639.1i	− 1.34261i
$423$	948.750i	0.109054i
$424$	−1286.79	−0.147387
$425$	0	0
$426$	−8483.24	−0.964823
$427$	4720.13i	0.534948i
$428$	− 5547.02i	− 0.626461i
$429$	−849.653	−0.0956216
$430$	0	0
$431$	16021.8	1.79059	0.895296	−	0.445472i	$-0.146964\pi$
$431$	16021.8	1.79059	0.895296	+	0.445472i	$0.146964\pi$
$432$	2147.34i	0.239153i
$433$	− 10882.7i	− 1.20782i	−0.797051	−	0.603912i	$-0.793608\pi$
$433$	− 10882.7i	− 1.20782i	0.797051	−	0.603912i	$-0.206392\pi$
$434$	−2350.99	−0.260025
$435$	0	0
$436$	1561.15	0.171480
$437$	15432.4i	1.68932i
$438$	3370.12i	0.367650i
$439$	−7738.40	−0.841307	−0.420653	−	0.907221i	$-0.638199\pi$
$439$	−7738.40	−0.841307	−0.420653	+	0.907221i	$0.638199\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	3139.78i	0.337882i
$443$	− 8766.56i	− 0.940207i	−0.882611	−	0.470103i	$-0.844217\pi$
$443$	− 8766.56i	− 0.940207i	0.882611	−	0.470103i	$-0.155783\pi$
$444$	243.562	0.0260337
$445$	0	0
$446$	19437.7	2.06368
$447$	3155.39i	0.333881i
$448$	− 253.014i	− 0.0266826i
$449$	−3099.58	−0.325786	−0.162893	−	0.986644i	$-0.552083\pi$
$449$	−3099.58	−0.325786	−0.162893	+	0.986644i	$0.552083\pi$
$450$	0	0
$451$	−1091.77	−0.113990
$452$	8814.15i	0.917219i
$453$	− 2251.15i	− 0.233484i
$454$	−1000.88	−0.103466
$455$	0	0
$456$	3097.66	0.318117
$457$	− 6122.94i	− 0.626737i	−0.949632	−	0.313369i	$-0.898542\pi$
$457$	− 6122.94i	− 0.626737i	0.949632	−	0.313369i	$-0.101458\pi$
$458$	− 9889.16i	− 1.00893i
$459$	436.372	0.0443749
$460$	0	0
$461$	−10412.2	−1.05194	−0.525970	−	0.850503i	$-0.676297\pi$
$461$	−10412.2	−1.05194	−0.525970	+	0.850503i	$0.676297\pi$
$462$	− 388.341i	− 0.0391066i
$463$	11278.5i	1.13209i	0.824376	+	0.566043i	$0.191526\pi$
$463$	11278.5i	1.13209i	−0.824376	+	0.566043i	$0.808474\pi$
$464$	11307.0	1.13128
$465$	0	0
$466$	20589.6	2.04677
$467$	14923.2i	1.47872i	0.673311	+	0.739359i	$0.264872\pi$
$467$	14923.2i	1.47872i	−0.673311	+	0.739359i	$0.735128\pi$
$468$	− 2299.78i	− 0.227153i
$469$	2274.50	0.223938
$470$	0	0
$471$	4361.69	0.426701
$472$	− 2483.93i	− 0.242230i
$473$	2708.11i	0.263254i
$474$	−4549.95	−0.440899
$475$	0	0
$476$	−529.992	−0.0510339
$477$	− 980.804i	− 0.0941466i
$478$	− 5656.34i	− 0.541245i
$479$	4674.21	0.445867	0.222933	−	0.974834i	$-0.428437\pi$
$479$	4674.21	0.445867	0.222933	+	0.974834i	$0.428437\pi$
$480$	0	0
$481$	945.316	0.0896106
$482$	− 15421.6i	− 1.45733i
$483$	− 3706.02i	− 0.349130i
$484$	6108.99	0.573721
$485$	0	0
$486$	−865.457	−0.0807777
$487$	17081.7i	1.58941i	0.606994	+	0.794706i	$0.292375\pi$
$487$	17081.7i	1.58941i	−0.606994	+	0.794706i	$0.707625\pi$
$488$	− 7962.02i	− 0.738573i
$489$	3901.47	0.360799
$490$	0	0
$491$	18203.9	1.67318	0.836588	−	0.547832i	$-0.184547\pi$
$491$	18203.9	1.67318	0.836588	+	0.547832i	$0.184547\pi$
$492$	− 2955.13i	− 0.270787i
$493$	− 2297.75i	− 0.209909i
$494$	−16988.3	−1.54725
$495$	0	0
$496$	7499.81	0.678934
$497$	− 5557.75i	− 0.501608i
$498$	− 3024.07i	− 0.272112i
$499$	−7109.47	−0.637803	−0.318901	−	0.947788i	$-0.603314\pi$
$499$	−7109.47	−0.637803	−0.318901	+	0.947788i	$0.603314\pi$
$500$	0	0
$501$	6334.38	0.564869
$502$	4988.07i	0.443483i
$503$	15402.0i	1.36529i	0.730748	+	0.682647i	$0.239171\pi$
$503$	15402.0i	1.36529i	−0.730748	+	0.682647i	$0.760829\pi$
$504$	−743.889	−0.0657450
$505$	0	0
$506$	−3263.49	−0.286719
$507$	− 2334.93i	− 0.204532i
$508$	− 7677.17i	− 0.670511i
$509$	−6404.72	−0.557730	−0.278865	−	0.960330i	$-0.589958\pi$
$509$	−6404.72	−0.557730	−0.278865	+	0.960330i	$0.589958\pi$
$510$	0	0
$511$	−2207.92	−0.191140
$512$	7502.22i	0.647567i
$513$	2361.07i	0.203204i
$514$	−15332.0	−1.31569
$515$	0	0
$516$	−7330.13	−0.625370
$517$	547.348i	0.0465616i
$518$	432.064i	0.0366483i
$519$	1005.88	0.0850732
$520$	0	0
$521$	−8916.72	−0.749806	−0.374903	−	0.927064i	$-0.622324\pi$
$521$	−8916.72	−0.749806	−0.374903	+	0.927064i	$0.622324\pi$
$522$	4557.13i	0.382107i
$523$	6929.40i	0.579353i	0.957125	+	0.289677i	$0.0935478\pi$
$523$	6929.40i	0.579353i	−0.957125	+	0.289677i	$0.906452\pi$
$524$	2802.09	0.233607
$525$	0	0
$526$	−6142.58	−0.509181
$527$	− 1524.07i	− 0.125977i
$528$	1238.83i	0.102109i
$529$	−18977.2	−1.55973
$530$	0	0
$531$	1893.28	0.154730
$532$	− 2867.61i	− 0.233697i
$533$	− 11469.5i	− 0.932078i
$534$	−9008.56	−0.730035
$535$	0	0
$536$	−3836.69	−0.309178
$537$	− 6966.68i	− 0.559840i
$538$	− 28509.6i	− 2.28464i
$539$	254.420	0.0203314
$540$	0	0
$541$	−6929.23	−0.550667	−0.275334	−	0.961349i	$-0.588788\pi$
$541$	−6929.23	−0.550667	−0.275334	+	0.961349i	$0.588788\pi$
$542$	− 6993.65i	− 0.554249i
$543$	− 4576.78i	− 0.361710i
$544$	3051.25	0.240480
$545$	0	0
$546$	4079.67	0.319769
$547$	− 8509.95i	− 0.665190i	−0.943070	−	0.332595i	$-0.892076\pi$
$547$	− 8509.95i	− 0.665190i	0.943070	−	0.332595i	$-0.107924\pi$
$548$	4709.26i	0.367098i
$549$	6068.74	0.471780
$550$	0	0
$551$	12432.4	0.961228
$552$	6251.41i	0.482024i
$553$	− 2980.88i	− 0.229222i
$554$	11676.0	0.895422
$555$	0	0
$556$	−8783.76	−0.669990
$557$	− 4043.94i	− 0.307625i	−0.988100	−	0.153813i	$-0.950845\pi$
$557$	− 4043.94i	− 0.307625i	0.988100	−	0.153813i	$-0.0491552\pi$
$558$	3022.70i	0.229321i
$559$	−28449.8	−2.15259
$560$	0	0
$561$	251.750	0.0189463
$562$	10182.6i	0.764285i
$563$	− 15878.9i	− 1.18866i	−0.804221	−	0.594331i	$-0.797417\pi$
$563$	− 15878.9i	− 1.18866i	0.804221	−	0.594331i	$-0.202583\pi$
$564$	−1481.52	−0.110609
$565$	0	0
$566$	−19352.3	−1.43717
$567$	− 567.000i	− 0.0419961i
$568$	9374.95i	0.692543i
$569$	−11611.6	−0.855510	−0.427755	−	0.903895i	$-0.640695\pi$
$569$	−11611.6	−0.855510	−0.427755	+	0.903895i	$0.640695\pi$
$570$	0	0
$571$	17395.7	1.27493	0.637466	−	0.770478i	$-0.279982\pi$
$571$	17395.7	1.27493	0.637466	+	0.770478i	$0.279982\pi$
$572$	− 1326.78i	− 0.0969850i
$573$	881.736i	0.0642846i
$574$	5242.21	0.381195
$575$	0	0
$576$	−325.304	−0.0235318
$577$	− 11474.0i	− 0.827848i	−0.910311	−	0.413924i	$-0.864158\pi$
$577$	− 11474.0i	− 0.827848i	0.910311	−	0.413924i	$-0.135842\pi$
$578$	16567.6i	1.19225i
$579$	−10994.7	−0.789162
$580$	0	0
$581$	1981.20	0.141470
$582$	− 16425.9i	− 1.16989i
$583$	− 565.841i	− 0.0401968i
$584$	3724.37	0.263896
$585$	0	0
$586$	30570.3	2.15503
$587$	11870.4i	0.834659i	0.908755	+	0.417330i	$0.137034\pi$
$587$	11870.4i	0.834659i	−0.908755	+	0.417330i	$0.862966\pi$
$588$	688.645i	0.0482980i
$589$	8246.26	0.576878
$590$	0	0
$591$	15305.7	1.06530
$592$	− 1378.32i	− 0.0956899i
$593$	5760.65i	0.398923i	0.979906	+	0.199462i	$0.0639193\pi$
$593$	5760.65i	0.398923i	−0.979906	+	0.199462i	$0.936081\pi$
$594$	−499.295	−0.0344888
$595$	0	0
$596$	−4927.31	−0.338642
$597$	− 15077.6i	− 1.03364i
$598$	− 34284.2i	− 2.34446i
$599$	21696.5	1.47996	0.739978	−	0.672631i	$-0.234836\pi$
$599$	21696.5	1.47996	0.739978	+	0.672631i	$0.234836\pi$
$600$	0	0
$601$	−12403.0	−0.841812	−0.420906	−	0.907104i	$-0.638288\pi$
$601$	−12403.0	−0.841812	−0.420906	+	0.907104i	$0.638288\pi$
$602$	− 13003.2i	− 0.880350i
$603$	− 2924.36i	− 0.197495i
$604$	3515.29	0.236813
$605$	0	0
$606$	16988.5	1.13880
$607$	17066.5i	1.14120i	0.821228	+	0.570600i	$0.193289\pi$
$607$	17066.5i	1.14120i	−0.821228	+	0.570600i	$0.806711\pi$
$608$	16509.3i	1.10122i
$609$	−2985.58	−0.198656
$610$	0	0
$611$	−5750.10	−0.380727
$612$	681.418i	0.0450077i
$613$	− 2707.50i	− 0.178393i	−0.996014	−	0.0891965i	$-0.971570\pi$
$613$	− 2707.50i	− 0.178393i	0.996014	−	0.0891965i	$-0.0284299\pi$
$614$	18768.8	1.23363
$615$	0	0
$616$	−429.161	−0.0280704
$617$	− 23226.3i	− 1.51549i	−0.652553	−	0.757743i	$-0.726302\pi$
$617$	− 23226.3i	− 1.51549i	0.652553	−	0.757743i	$-0.273698\pi$
$618$	− 1760.75i	− 0.114608i
$619$	2298.43	0.149243	0.0746216	−	0.997212i	$-0.476225\pi$
$619$	2298.43	0.149243	0.0746216	+	0.997212i	$0.476225\pi$
$620$	0	0
$621$	−4764.89	−0.307904
$622$	− 16958.1i	− 1.09318i
$623$	− 5901.91i	− 0.379543i
$624$	−13014.4	−0.834926
$625$	0	0
$626$	−27078.3	−1.72886
$627$	1362.14i	0.0867599i
$628$	6811.01i	0.432785i
$629$	−280.094	−0.0177553
$630$	0	0
$631$	−663.913	−0.0418858	−0.0209429	−	0.999781i	$-0.506667\pi$
$631$	−663.913	−0.0418858	−0.0209429	+	0.999781i	$0.506667\pi$
$632$	5028.22i	0.316474i
$633$	− 9803.95i	− 0.615596i
$634$	−28722.3	−1.79923
$635$	0	0
$636$	1531.58	0.0954890
$637$	2672.77i	0.166247i
$638$	2629.08i	0.163144i
$639$	−7145.68	−0.442377
$640$	0	0
$641$	15215.6	0.937566	0.468783	−	0.883313i	$-0.344693\pi$
$641$	15215.6	0.937566	0.468783	+	0.883313i	$0.344693\pi$
$642$	− 12651.5i	− 0.777749i
$643$	− 12904.0i	− 0.791420i	−0.918375	−	0.395710i	$-0.870498\pi$
$643$	− 12904.0i	− 0.791420i	0.918375	−	0.395710i	$-0.129502\pi$
$644$	5787.15	0.354108
$645$	0	0
$646$	5033.58	0.306569
$647$	− 9425.54i	− 0.572730i	−0.958121	−	0.286365i	$-0.907553\pi$
$647$	− 9425.54i	− 0.572730i	0.958121	−	0.286365i	$-0.0924470\pi$
$648$	956.429i	0.0579816i
$649$	1092.26	0.0660632
$650$	0	0
$651$	−1980.30	−0.119223
$652$	6092.35i	0.365943i
$653$	29894.7i	1.79153i	0.444528	+	0.895765i	$0.353372\pi$
$653$	29894.7i	1.79153i	−0.444528	+	0.895765i	$0.646628\pi$
$654$	3560.63	0.212892
$655$	0	0
$656$	−16723.0	−0.995312
$657$	2838.75i	0.168570i
$658$	− 2628.13i	− 0.155707i
$659$	11593.6	0.685313	0.342656	−	0.939461i	$-0.388673\pi$
$659$	11593.6	0.685313	0.342656	+	0.939461i	$0.388673\pi$
$660$	0	0
$661$	−17149.2	−1.00911	−0.504557	−	0.863378i	$-0.668344\pi$
$661$	−17149.2	−1.00911	−0.504557	+	0.863378i	$0.668344\pi$
$662$	24791.2i	1.45550i
$663$	2644.72i	0.154921i
$664$	−3341.94	−0.195320
$665$	0	0
$666$	555.511	0.0323208
$667$	25089.9i	1.45650i
$668$	9891.47i	0.572923i
$669$	16372.9	0.946210
$670$	0	0
$671$	3501.15	0.201431
$672$	− 3964.64i	− 0.227589i
$673$	16475.0i	0.943633i	0.881697	+	0.471817i	$0.156402\pi$
$673$	16475.0i	0.943633i	−0.881697	+	0.471817i	$0.843598\pi$
$674$	−16851.9	−0.963071
$675$	0	0
$676$	3646.11	0.207448
$677$	− 4559.89i	− 0.258864i	−0.991588	−	0.129432i	$-0.958685\pi$
$677$	− 4559.89i	− 0.258864i	0.991588	−	0.129432i	$-0.0413154\pi$
$678$	20103.1i	1.13872i
$679$	10761.3	0.608221
$680$	0	0
$681$	−843.070	−0.0474398
$682$	1743.84i	0.0979106i
$683$	27895.9i	1.56282i	0.624017	+	0.781411i	$0.285500\pi$
$683$	27895.9i	1.56282i	−0.624017	+	0.781411i	$0.714500\pi$
$684$	−3686.93	−0.206101
$685$	0	0
$686$	−1221.61	−0.0679904
$687$	− 8329.93i	− 0.462601i
$688$	41481.1i	2.29862i
$689$	5944.37	0.328683
$690$	0	0
$691$	−28178.5	−1.55132	−0.775659	−	0.631152i	$-0.782582\pi$
$691$	−28178.5	−1.55132	−0.775659	+	0.631152i	$0.782582\pi$
$692$	1570.73i	0.0862862i
$693$	− 327.111i	− 0.0179306i
$694$	−34891.4	−1.90844
$695$	0	0
$696$	5036.14	0.274274
$697$	3398.37i	0.184680i
$698$	− 45240.4i	− 2.45326i
$699$	17343.3	0.938458
$700$	0	0
$701$	3912.96	0.210828	0.105414	−	0.994428i	$-0.466383\pi$
$701$	3912.96	0.210828	0.105414	+	0.994428i	$0.466383\pi$
$702$	− 5245.29i	− 0.282009i
$703$	− 1515.50i	− 0.0813060i
$704$	−187.673	−0.0100471
$705$	0	0
$706$	−35509.4	−1.89294
$707$	11130.0i	0.592058i
$708$	2956.46i	0.156936i
$709$	7782.72	0.412251	0.206126	−	0.978526i	$-0.433914\pi$
$709$	7782.72	0.412251	0.206126	+	0.978526i	$0.433914\pi$
$710$	0	0
$711$	−3832.56	−0.202155
$712$	9955.49i	0.524014i
$713$	16641.8i	0.874112i
$714$	−1208.79	−0.0633584
$715$	0	0
$716$	10878.8	0.567823
$717$	− 4764.50i	− 0.248164i
$718$	− 15628.9i	− 0.812345i
$719$	27868.8	1.44552	0.722762	−	0.691097i	$-0.242872\pi$
$719$	27868.8	1.44552	0.722762	+	0.691097i	$0.242872\pi$
$720$	0	0
$721$	1153.55	0.0595844
$722$	2806.40i	0.144658i
$723$	− 12990.0i	− 0.668194i
$724$	7146.89	0.366868
$725$	0	0
$726$	13933.2	0.712274
$727$	− 34202.4i	− 1.74484i	−0.488759	−	0.872419i	$-0.662550\pi$
$727$	− 34202.4i	− 1.74484i	0.488759	−	0.872419i	$-0.337450\pi$
$728$	− 4508.50i	− 0.229527i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	8429.58	0.426510
$732$	9476.65i	0.478507i
$733$	12544.2i	0.632101i	0.948742	+	0.316051i	$0.102357\pi$
$733$	12544.2i	0.632101i	−0.948742	+	0.316051i	$0.897643\pi$
$734$	33625.7	1.69094
$735$	0	0
$736$	−33317.6	−1.66862
$737$	− 1687.11i	− 0.0843221i
$738$	− 6739.99i	− 0.336182i
$739$	−4563.19	−0.227144	−0.113572	−	0.993530i	$-0.536229\pi$
$739$	−4563.19	−0.227144	−0.113572	+	0.993530i	$0.536229\pi$
$740$	0	0
$741$	−14309.7	−0.709422
$742$	2716.92i	0.134422i
$743$	− 10369.7i	− 0.512017i	−0.966674	−	0.256009i	$-0.917592\pi$
$743$	− 10369.7i	− 0.512017i	0.966674	−	0.256009i	$-0.0824076\pi$
$744$	3340.42	0.164605
$745$	0	0
$746$	−11466.1	−0.562738
$747$	− 2547.26i	− 0.124765i
$748$	393.120i	0.0192164i
$749$	8288.57	0.404349
$750$	0	0
$751$	−36808.0	−1.78847	−0.894237	−	0.447595i	$-0.852281\pi$
$751$	−36808.0	−1.78847	−0.894237	+	0.447595i	$0.852281\pi$
$752$	8383.92i	0.406556i
$753$	4201.60i	0.203340i
$754$	−27619.4	−1.33401
$755$	0	0
$756$	885.400	0.0425948
$757$	− 12516.6i	− 0.600955i	−0.953789	−	0.300477i	$-0.902854\pi$
$757$	− 12516.6i	− 0.600955i	0.953789	−	0.300477i	$-0.0971460\pi$
$758$	49902.3i	2.39121i
$759$	−2748.93	−0.131462
$760$	0	0
$761$	11745.1	0.559473	0.279736	−	0.960077i	$-0.409753\pi$
$761$	11745.1	0.559473	0.279736	+	0.960077i	$0.409753\pi$
$762$	− 17509.9i	− 0.832438i
$763$	2332.73i	0.110682i
$764$	−1376.88	−0.0652011
$765$	0	0
$766$	18957.7	0.894216
$767$	11474.6i	0.540189i
$768$	15629.5i	0.734350i
$769$	−36497.1	−1.71147	−0.855735	−	0.517414i	$-0.826895\pi$
$769$	−36497.1	−1.71147	−0.855735	+	0.517414i	$0.826895\pi$
$770$	0	0
$771$	−12914.6	−0.603252
$772$	− 17168.8i	− 0.800414i
$773$	29858.1i	1.38929i	0.719353	+	0.694644i	$0.244438\pi$
$773$	29858.1i	1.38929i	−0.719353	+	0.694644i	$0.755562\pi$
$774$	−16718.4	−0.776396
$775$	0	0
$776$	−18152.5	−0.839737
$777$	363.940i	0.0168035i
$778$	13692.4i	0.630973i
$779$	−18387.5	−0.845699
$780$	0	0
$781$	−4122.45	−0.188877
$782$	10158.3i	0.464527i
$783$	3838.60i	0.175199i
$784$	3897.03	0.177525
$785$	0	0
$786$	6390.94	0.290022
$787$	3168.00i	0.143491i	0.997423	+	0.0717453i	$0.0228569\pi$
$787$	3168.00i	0.143491i	−0.997423	+	0.0717453i	$0.977143\pi$
$788$	23900.6i	1.08049i
$789$	−5174.07	−0.233463
$790$	0	0
$791$	−13170.5	−0.592019
$792$	551.778i	0.0247558i
$793$	36780.8i	1.64707i
$794$	28657.7	1.28089
$795$	0	0
$796$	23544.5	1.04838
$797$	29317.0i	1.30296i	0.758665	+	0.651481i	$0.225852\pi$
$797$	29317.0i	1.30296i	−0.758665	+	0.651481i	$0.774148\pi$
$798$	− 6540.39i	− 0.290134i
$799$	1703.74	0.0754366
$800$	0	0
$801$	−7588.18	−0.334725
$802$	27571.3i	1.21394i
$803$	1637.72i	0.0719724i
$804$	4566.54	0.200310
$805$	0	0
$806$	−18319.7	−0.800600
$807$	− 24014.5i	− 1.04752i
$808$	− 18774.3i	− 0.817422i
$809$	−16657.3	−0.723904	−0.361952	−	0.932197i	$-0.617890\pi$
$809$	−16657.3	−0.723904	−0.361952	+	0.932197i	$0.617890\pi$
$810$	0	0
$811$	5144.55	0.222749	0.111375	−	0.993779i	$-0.464475\pi$
$811$	5144.55	0.222749	0.111375	+	0.993779i	$0.464475\pi$
$812$	− 4662.14i	− 0.201489i
$813$	− 5890.95i	− 0.254126i
$814$	320.483	0.0137997
$815$	0	0
$816$	3856.13	0.165431
$817$	45609.7i	1.95310i
$818$	31936.2i	1.36507i
$819$	3436.42	0.146616
$820$	0	0
$821$	−5217.18	−0.221779	−0.110890	−	0.993833i	$-0.535370\pi$
$821$	−5217.18	−0.221779	−0.110890	+	0.993833i	$0.535370\pi$
$822$	10740.8i	0.455751i
$823$	− 42326.5i	− 1.79272i	−0.443327	−	0.896360i	$-0.646202\pi$
$823$	− 42326.5i	− 1.79272i	0.443327	−	0.896360i	$-0.353798\pi$
$824$	−1945.83	−0.0822649
$825$	0	0
$826$	−5244.57	−0.220922
$827$	− 31675.8i	− 1.33189i	−0.746000	−	0.665946i	$-0.768028\pi$
$827$	− 31675.8i	− 1.33189i	0.746000	−	0.665946i	$-0.231972\pi$
$828$	− 7440.62i	− 0.312294i
$829$	3471.22	0.145429	0.0727144	−	0.997353i	$-0.476834\pi$
$829$	3471.22	0.145429	0.0727144	+	0.997353i	$0.476834\pi$
$830$	0	0
$831$	9835.00	0.410556
$832$	− 1971.57i	− 0.0821539i
$833$	− 791.934i	− 0.0329399i
$834$	−20033.8	−0.831791
$835$	0	0
$836$	−2127.05	−0.0879970
$837$	2546.11i	0.105145i
$838$	44211.7i	1.82252i
$839$	20964.9	0.862682	0.431341	−	0.902189i	$-0.358041\pi$
$839$	20964.9	0.862682	0.431341	+	0.902189i	$0.358041\pi$
$840$	0	0
$841$	−4176.57	−0.171248
$842$	− 5955.41i	− 0.243749i
$843$	8577.12i	0.350429i
$844$	15309.4	0.624373
$845$	0	0
$846$	−3379.02	−0.137321
$847$	9128.28i	0.370309i
$848$	− 8667.17i	− 0.350981i
$849$	−16301.0	−0.658950
$850$	0	0
$851$	3058.44	0.123199
$852$	− 11158.4i	− 0.448685i
$853$	− 1084.77i	− 0.0435426i	−0.999763	−	0.0217713i	$-0.993069\pi$
$853$	− 1084.77i	− 0.0435426i	0.999763	−	0.0217713i	$-0.00693057\pi$
$854$	−16811.0	−0.673607
$855$	0	0
$856$	−13981.4	−0.558263
$857$	− 12661.6i	− 0.504679i	−0.967639	−	0.252340i	$-0.918800\pi$
$857$	− 12661.6i	− 0.504679i	0.967639	−	0.252340i	$-0.0812001\pi$
$858$	− 3026.09i	− 0.120407i
$859$	39678.7	1.57604	0.788021	−	0.615648i	$-0.211106\pi$
$859$	39678.7	1.57604	0.788021	+	0.615648i	$0.211106\pi$
$860$	0	0
$861$	4415.67	0.174780
$862$	57062.6i	2.25471i
$863$	41614.0i	1.64143i	0.571334	+	0.820717i	$0.306426\pi$
$863$	41614.0i	1.64143i	−0.571334	+	0.820717i	$0.693574\pi$
$864$	−5097.40	−0.200714
$865$	0	0
$866$	38759.2	1.52089
$867$	13955.4i	0.546654i
$868$	− 3092.35i	− 0.120923i
$869$	−2211.06	−0.0863120
$870$	0	0
$871$	17723.7	0.689489
$872$	− 3934.90i	− 0.152813i
$873$	− 13836.0i	− 0.536400i
$874$	−54963.3	−2.12719
$875$	0	0
$876$	−4432.86	−0.170973
$877$	− 37061.0i	− 1.42698i	−0.700665	−	0.713490i	$-0.747113\pi$
$877$	− 37061.0i	− 1.42698i	0.700665	−	0.713490i	$-0.252887\pi$
$878$	− 27560.7i	− 1.05937i
$879$	25750.3	0.988095
$880$	0	0
$881$	−25468.7	−0.973962	−0.486981	−	0.873412i	$-0.661902\pi$
$881$	−25468.7	−0.973962	−0.486981	+	0.873412i	$0.661902\pi$
$882$	1570.64i	0.0599619i
$883$	− 34428.3i	− 1.31212i	−0.754707	−	0.656062i	$-0.772221\pi$
$883$	− 34428.3i	− 1.31212i	0.754707	−	0.656062i	$-0.227779\pi$
$884$	−4129.88	−0.157130
$885$	0	0
$886$	31222.6	1.18391
$887$	41295.4i	1.56321i	0.623777	+	0.781603i	$0.285597\pi$
$887$	41295.4i	1.56321i	−0.623777	+	0.781603i	$0.714403\pi$
$888$	− 613.903i	− 0.0231996i
$889$	11471.5	0.432782
$890$	0	0
$891$	−420.571	−0.0158133
$892$	25567.2i	0.959702i
$893$	9218.37i	0.345443i
$894$	−11238.1	−0.420423
$895$	0	0
$896$	−9671.26	−0.360596
$897$	− 28878.6i	− 1.07495i
$898$	− 11039.3i	− 0.410230i
$899$	13406.7	0.497373
$900$	0	0
$901$	−1761.30	−0.0651247
$902$	− 3888.40i	− 0.143536i
$903$	− 10953.0i	− 0.403646i
$904$	22216.2	0.817368
$905$	0	0
$906$	8017.59	0.294003
$907$	− 53733.8i	− 1.96715i	−0.180509	−	0.983573i	$-0.557775\pi$
$907$	− 53733.8i	− 1.96715i	0.180509	−	0.983573i	$-0.442225\pi$
$908$	− 1316.50i	− 0.0481162i
$909$	14309.9	0.522146
$910$	0	0
$911$	24296.8	0.883634	0.441817	−	0.897105i	$-0.354334\pi$
$911$	24296.8	0.883634	0.441817	+	0.897105i	$0.354334\pi$
$912$	20864.3i	0.757550i
$913$	− 1469.55i	− 0.0532696i
$914$	21807.2	0.789187
$915$	0	0
$916$	13007.6	0.469197
$917$	4186.99i	0.150782i
$918$	1554.16i	0.0558769i
$919$	−4280.46	−0.153645	−0.0768223	−	0.997045i	$-0.524477\pi$
$919$	−4280.46	−0.153645	−0.0768223	+	0.997045i	$0.524477\pi$
$920$	0	0
$921$	15809.5	0.565625
$922$	− 37083.6i	− 1.32460i
$923$	− 43307.9i	− 1.54442i
$924$	510.801	0.0181863
$925$	0	0
$926$	−40168.9	−1.42552
$927$	− 1483.13i	− 0.0525485i
$928$	26840.7i	0.949450i
$929$	31884.5	1.12604	0.563022	−	0.826442i	$-0.309639\pi$
$929$	31884.5	1.12604	0.563022	+	0.826442i	$0.309639\pi$
$930$	0	0
$931$	4284.90	0.150840
$932$	27082.4i	0.951839i
$933$	− 14284.3i	− 0.501229i
$934$	−53149.6	−1.86200
$935$	0	0
$936$	−5796.64	−0.202424
$937$	− 44523.1i	− 1.55230i	−0.630548	−	0.776151i	$-0.717170\pi$
$937$	− 44523.1i	− 1.55230i	0.630548	−	0.776151i	$-0.282830\pi$
$938$	8100.76i	0.281982i
$939$	−22808.8	−0.792693
$940$	0	0
$941$	46374.9	1.60657	0.803283	−	0.595598i	$-0.203085\pi$
$941$	46374.9	1.60657	0.803283	+	0.595598i	$0.203085\pi$
$942$	15534.4i	0.537301i
$943$	− 37107.9i	− 1.28144i
$944$	16730.6	0.576836
$945$	0	0
$946$	−9645.09	−0.331489
$947$	− 20348.2i	− 0.698234i	−0.937079	−	0.349117i	$-0.886482\pi$
$947$	− 20348.2i	− 0.698234i	0.937079	−	0.349117i	$-0.113518\pi$
$948$	− 5984.74i	− 0.205037i
$949$	−17204.8	−0.588507
$950$	0	0
$951$	−24193.6	−0.824956
$952$	1335.85i	0.0454782i
$953$	45012.9i	1.53002i	0.644018	+	0.765010i	$0.277266\pi$
$953$	45012.9i	1.53002i	−0.644018	+	0.765010i	$0.722734\pi$
$954$	3493.18	0.118549
$955$	0	0
$956$	7440.02	0.251702
$957$	2214.55i	0.0748027i
$958$	16647.4i	0.561435i
$959$	−7036.76	−0.236944
$960$	0	0
$961$	−20898.5	−0.701503
$962$	3366.79i	0.112838i
$963$	− 10656.7i	− 0.356603i
$964$	20284.6	0.677721
$965$	0	0
$966$	13199.2	0.439624
$967$	− 40305.8i	− 1.34038i	−0.742190	−	0.670190i	$-0.766213\pi$
$967$	− 40305.8i	− 1.34038i	0.742190	−	0.670190i	$-0.233787\pi$
$968$	− 15397.8i	− 0.511265i
$969$	4239.93	0.140564
$970$	0	0
$971$	33991.8	1.12343	0.561713	−	0.827332i	$-0.310142\pi$
$971$	33991.8	1.12343	0.561713	+	0.827332i	$0.310142\pi$
$972$	− 1138.37i	− 0.0375651i
$973$	− 13125.0i	− 0.432445i
$974$	−60837.2	−2.00139
$975$	0	0
$976$	53628.2	1.75881
$977$	− 18219.0i	− 0.596600i	−0.954472	−	0.298300i	$-0.903580\pi$
$977$	− 18219.0i	− 0.596600i	0.954472	−	0.298300i	$-0.0964196\pi$
$978$	13895.3i	0.454317i
$979$	−4377.73	−0.142914
$980$	0	0
$981$	2999.22	0.0976125
$982$	64834.1i	2.10686i
$983$	− 7676.89i	− 0.249089i	−0.992214	−	0.124545i	$-0.960253\pi$
$983$	− 7676.89i	− 0.249089i	0.992214	−	0.124545i	$-0.0397470\pi$
$984$	−7448.45	−0.241309
$985$	0	0
$986$	8183.55	0.264318
$987$	− 2213.75i	− 0.0713925i
$988$	− 22345.4i	− 0.719537i
$989$	−92045.3	−2.95942
$990$	0	0
$991$	50585.6	1.62150	0.810748	−	0.585395i	$-0.199061\pi$
$991$	50585.6	1.62150	0.810748	+	0.585395i	$0.199061\pi$
$992$	17803.2i	0.569810i
$993$	20882.4i	0.667354i
$994$	19794.2	0.631625
$995$	0	0
$996$	3977.69	0.126544
$997$	− 53060.5i	− 1.68550i	−0.538305	−	0.842750i	$-0.680935\pi$
$997$	− 53060.5i	− 1.68550i	0.538305	−	0.842750i	$-0.319065\pi$
$998$	− 25320.8i	− 0.803121i
$999$	467.923	0.0148193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.m.274.4		4
5.2	odd	4		525.4.a.j.1.1	✓	2
5.3	odd	4		525.4.a.m.1.2	yes	2
5.4	even	2	inner	525.4.d.m.274.1		4
15.2	even	4		1575.4.a.x.1.2		2
15.8	even	4		1575.4.a.o.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.j.1.1	✓	2	5.2	odd	4
525.4.a.m.1.2	yes	2	5.3	odd	4
525.4.d.m.274.1		4	5.4	even	2	inner
525.4.d.m.274.4		4	1.1	even	1	trivial
1575.4.a.o.1.1		2	15.8	even	4
1575.4.a.x.1.2		2	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.56155i q^{2} +3.00000i q^{3} -4.68466 q^{4} -10.6847 q^{6} -7.00000i q^{7} +11.8078i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+3.56155i q^{2} +3.00000i q^{3} -4.68466 q^{4} -10.6847 q^{6} -7.00000i q^{7} +11.8078i q^{8} -9.00000 q^{9} -5.19224 q^{11} -14.0540i q^{12} -54.5464i q^{13} +24.9309 q^{14} -79.5312 q^{16} +16.1619i q^{17} -32.0540i q^{18} -87.4470 q^{19} +21.0000 q^{21} -18.4924i q^{22} -176.477i q^{23} -35.4233 q^{24} +194.270 q^{26} -27.0000i q^{27} +32.7926i q^{28} -142.170 q^{29} -94.3002 q^{31} -188.793i q^{32} -15.5767i q^{33} -57.5616 q^{34} +42.1619 q^{36} +17.3305i q^{37} -311.447i q^{38} +163.639 q^{39} +210.270 q^{41} +74.7926i q^{42} -521.570i q^{43} +24.3239 q^{44} +628.533 q^{46} -105.417i q^{47} -238.594i q^{48} -49.0000 q^{49} -48.4858 q^{51} +255.531i q^{52} +108.978i q^{53} +96.1619 q^{54} +82.6543 q^{56} -262.341i q^{57} -506.348i q^{58} -210.365 q^{59} -674.304 q^{61} -335.855i q^{62} +63.0000i q^{63} +36.1449 q^{64} +55.4773 q^{66} +324.929i q^{67} -75.7131i q^{68} +529.432 q^{69} +793.965 q^{71} -106.270i q^{72} -315.417i q^{73} -61.7235 q^{74} +409.659 q^{76} +36.3457i q^{77} +582.810i q^{78} +425.840 q^{79} +81.0000 q^{81} +748.887i q^{82} +283.029i q^{83} -98.3778 q^{84} +1857.60 q^{86} -426.511i q^{87} -61.3087i q^{88} +843.131 q^{89} -381.825 q^{91} +826.736i q^{92} -282.901i q^{93} +375.447 q^{94} +566.378 q^{96} +1537.33i q^{97} -174.516i q^{98} +46.7301 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4} - 18 q^{6} - 36 q^{9}+O(q^{10}) \) 4 * q + 6 * q^4 - 18 * q^6 - 36 * q^9	\( 4 q + 6 q^{4} - 18 q^{6} - 36 q^{9} - 62 q^{11} + 42 q^{14} - 46 q^{16} + 112 q^{19} + 84 q^{21} - 18 q^{24} + 406 q^{26} + 124 q^{29} - 270 q^{31} - 222 q^{34} - 54 q^{36} + 234 q^{39} + 470 q^{41} - 348 q^{44} + 1170 q^{46} - 196 q^{49} + 474 q^{51} + 162 q^{54} + 42 q^{56} + 882 q^{59} - 446 q^{61} + 862 q^{64} + 24 q^{66} + 1524 q^{69} + 1238 q^{71} - 16 q^{74} + 3024 q^{76} + 854 q^{79} + 324 q^{81} + 126 q^{84} + 3398 q^{86} - 932 q^{89} - 546 q^{91} + 1040 q^{94} + 1746 q^{96} + 558 q^{99}+O(q^{100}) \) 4 * q + 6 * q^4 - 18 * q^6 - 36 * q^9 - 62 * q^11 + 42 * q^14 - 46 * q^16 + 112 * q^19 + 84 * q^21 - 18 * q^24 + 406 * q^26 + 124 * q^29 - 270 * q^31 - 222 * q^34 - 54 * q^36 + 234 * q^39 + 470 * q^41 - 348 * q^44 + 1170 * q^46 - 196 * q^49 + 474 * q^51 + 162 * q^54 + 42 * q^56 + 882 * q^59 - 446 * q^61 + 862 * q^64 + 24 * q^66 + 1524 * q^69 + 1238 * q^71 - 16 * q^74 + 3024 * q^76 + 854 * q^79 + 324 * q^81 + 126 * q^84 + 3398 * q^86 - 932 * q^89 - 546 * q^91 + 1040 * q^94 + 1746 * q^96 + 558 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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