LMFDB - Embedded newform 435.4.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,4,Mod(1,435)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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:	yes
Analytic conductor:	$25.6658308525$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 31x^{4} + 9x^{3} + 230x^{2} + 32x - 128 $ x^6 - x^5 - 31x^4 + 9x^3 + 230x^2 + 32x - 128
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.98965$ 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)

$f(q)$	$=$	\(q-4.98965 q^{2} -3.00000 q^{3} +16.8966 q^{4} +5.00000 q^{5} +14.9690 q^{6} +22.5076 q^{7} -44.3911 q^{8} +9.00000 q^{9} -24.9483 q^{10} -32.8384 q^{11} -50.6899 q^{12} +31.3437 q^{13} -112.305 q^{14} -15.0000 q^{15} +86.3230 q^{16} -66.5556 q^{17} -44.9069 q^{18} -103.349 q^{19} +84.4831 q^{20} -67.5228 q^{21} +163.852 q^{22} +5.86439 q^{23} +133.173 q^{24} +25.0000 q^{25} -156.394 q^{26} -27.0000 q^{27} +380.302 q^{28} -29.0000 q^{29} +74.8448 q^{30} -26.9324 q^{31} -75.5933 q^{32} +98.5153 q^{33} +332.089 q^{34} +112.538 q^{35} +152.070 q^{36} -18.2548 q^{37} +515.675 q^{38} -94.0312 q^{39} -221.955 q^{40} -115.564 q^{41} +336.915 q^{42} +415.780 q^{43} -554.859 q^{44} +45.0000 q^{45} -29.2613 q^{46} +11.7223 q^{47} -258.969 q^{48} +163.592 q^{49} -124.741 q^{50} +199.667 q^{51} +529.604 q^{52} -275.059 q^{53} +134.721 q^{54} -164.192 q^{55} -999.136 q^{56} +310.046 q^{57} +144.700 q^{58} +212.467 q^{59} -253.449 q^{60} -766.954 q^{61} +134.383 q^{62} +202.568 q^{63} -313.400 q^{64} +156.719 q^{65} -491.557 q^{66} +256.113 q^{67} -1124.57 q^{68} -17.5932 q^{69} -561.525 q^{70} -711.750 q^{71} -399.520 q^{72} +45.4465 q^{73} +91.0850 q^{74} -75.0000 q^{75} -1746.25 q^{76} -739.114 q^{77} +469.183 q^{78} +329.147 q^{79} +431.615 q^{80} +81.0000 q^{81} +576.623 q^{82} -283.281 q^{83} -1140.91 q^{84} -332.778 q^{85} -2074.60 q^{86} +87.0000 q^{87} +1457.73 q^{88} -802.821 q^{89} -224.534 q^{90} +705.472 q^{91} +99.0885 q^{92} +80.7973 q^{93} -58.4903 q^{94} -516.744 q^{95} +226.780 q^{96} +389.532 q^{97} -816.265 q^{98} -295.546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 18 q^{3} + 15 q^{4} + 30 q^{5} + 3 q^{6} + 23 q^{7} - 51 q^{8} + 54 q^{9} - 5 q^{10} - 111 q^{11} - 45 q^{12} - 83 q^{13} - 102 q^{14} - 90 q^{15} - 37 q^{16} - 35 q^{17} - 9 q^{18} - 76 q^{19}+ \cdots - 999 q^{99}+O(q^{100}) $ 6 * q - q^2 - 18 * q^3 + 15 * q^4 + 30 * q^5 + 3 * q^6 + 23 * q^7 - 51 * q^8 + 54 * q^9 - 5 * q^10 - 111 * q^11 - 45 * q^12 - 83 * q^13 - 102 * q^14 - 90 * q^15 - 37 * q^16 - 35 * q^17 - 9 * q^18 - 76 * q^19 + 75 * q^20 - 69 * q^21 + 66 * q^22 + 166 * q^23 + 153 * q^24 + 150 * q^25 - 282 * q^26 - 162 * q^27 + 368 * q^28 - 174 * q^29 + 15 * q^30 - 164 * q^31 - 259 * q^32 + 333 * q^33 + 512 * q^34 + 115 * q^35 + 135 * q^36 - 538 * q^37 + 6 * q^38 + 249 * q^39 - 255 * q^40 - 1250 * q^41 + 306 * q^42 - 80 * q^43 - 1004 * q^44 + 270 * q^45 - 1190 * q^46 - 491 * q^47 + 111 * q^48 - 969 * q^49 - 25 * q^50 + 105 * q^51 - 336 * q^52 - 356 * q^53 + 27 * q^54 - 555 * q^55 - 1260 * q^56 + 228 * q^57 + 29 * q^58 - 646 * q^59 - 225 * q^60 - 1476 * q^61 - 4 * q^62 + 207 * q^63 - 845 * q^64 - 415 * q^65 - 198 * q^66 + 87 * q^67 - 558 * q^68 - 498 * q^69 - 510 * q^70 - 1312 * q^71 - 459 * q^72 - 1142 * q^73 - 2270 * q^74 - 450 * q^75 - 1594 * q^76 - 2561 * q^77 + 846 * q^78 - 142 * q^79 - 185 * q^80 + 486 * q^81 - 1544 * q^82 + 346 * q^83 - 1104 * q^84 - 175 * q^85 - 2056 * q^86 + 522 * q^87 + 1400 * q^88 - 2827 * q^89 - 45 * q^90 + 1379 * q^91 - 1434 * q^92 + 492 * q^93 + 978 * q^94 - 380 * q^95 + 777 * q^96 - 4 * q^97 - 1903 * q^98 - 999 * 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 $

$2$	−4.98965	−1.76411	−0.882054	−	0.471148i	$-0.843840\pi$
$2$	−4.98965	−1.76411	−0.882054	+	0.471148i	$0.843840\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	16.8966	2.11208
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	14.9690	1.01851
$7$	22.5076	1.21530	0.607648	−	0.794207i	$-0.292113\pi$
$7$	22.5076	1.21530	0.607648	+	0.794207i	$0.292113\pi$
$8$	−44.3911	−1.96183
$9$	9.00000	0.333333
$10$	−24.9483	−0.788933
$11$	−32.8384	−0.900106	−0.450053	−	0.893002i	$-0.648595\pi$
$11$	−32.8384	−0.900106	−0.450053	+	0.893002i	$0.648595\pi$
$12$	−50.6899	−1.21941
$13$	31.3437	0.668707	0.334353	−	0.942448i	$-0.391482\pi$
$13$	31.3437	0.668707	0.334353	+	0.942448i	$0.391482\pi$
$14$	−112.305	−2.14391
$15$	−15.0000	−0.258199
$16$	86.3230	1.34880
$17$	−66.5556	−0.949536	−0.474768	−	0.880111i	$-0.657468\pi$
$17$	−66.5556	−0.949536	−0.474768	+	0.880111i	$0.657468\pi$
$18$	−44.9069	−0.588036
$19$	−103.349	−1.24789	−0.623943	−	0.781470i	$-0.714470\pi$
$19$	−103.349	−1.24789	−0.623943	+	0.781470i	$0.714470\pi$
$20$	84.4831	0.944550
$21$	−67.5228	−0.701651
$22$	163.852	1.58788
$23$	5.86439	0.0531657	0.0265828	−	0.999647i	$-0.491537\pi$
$23$	5.86439	0.0531657	0.0265828	+	0.999647i	$0.491537\pi$
$24$	133.173	1.13266
$25$	25.0000	0.200000
$26$	−156.394	−1.17967
$27$	−27.0000	−0.192450
$28$	380.302	2.56680
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	74.8448	0.455491
$31$	−26.9324	−0.156039	−0.0780195	−	0.996952i	$-0.524860\pi$
$31$	−26.9324	−0.156039	−0.0780195	+	0.996952i	$0.524860\pi$
$32$	−75.5933	−0.417598
$33$	98.5153	0.519676
$34$	332.089	1.67508
$35$	112.538	0.543497
$36$	152.070	0.704026
$37$	−18.2548	−0.0811099	−0.0405550	−	0.999177i	$-0.512913\pi$
$37$	−18.2548	−0.0811099	−0.0405550	+	0.999177i	$0.512913\pi$
$38$	515.675	2.20141
$39$	−94.0312	−0.386078
$40$	−221.955	−0.877356
$41$	−115.564	−0.440196	−0.220098	−	0.975478i	$-0.570638\pi$
$41$	−115.564	−0.440196	−0.220098	+	0.975478i	$0.570638\pi$
$42$	336.915	1.23779
$43$	415.780	1.47455	0.737277	−	0.675591i	$-0.236111\pi$
$43$	415.780	1.47455	0.737277	+	0.675591i	$0.236111\pi$
$44$	−554.859	−1.90109
$45$	45.0000	0.149071
$46$	−29.2613	−0.0937900
$47$	11.7223	0.0363804	0.0181902	−	0.999835i	$-0.494210\pi$
$47$	11.7223	0.0363804	0.0181902	+	0.999835i	$0.494210\pi$
$48$	−258.969	−0.778729
$49$	163.592	0.476943
$50$	−124.741	−0.352822
$51$	199.667	0.548215
$52$	529.604	1.41236
$53$	−275.059	−0.712872	−0.356436	−	0.934320i	$-0.616008\pi$
$53$	−275.059	−0.712872	−0.356436	+	0.934320i	$0.616008\pi$
$54$	134.721	0.339503
$55$	−164.192	−0.402540
$56$	−999.136	−2.38420
$57$	310.046	0.720467
$58$	144.700	0.327587
$59$	212.467	0.468829	0.234414	−	0.972137i	$-0.424683\pi$
$59$	212.467	0.468829	0.234414	+	0.972137i	$0.424683\pi$
$60$	−253.449	−0.545336
$61$	−766.954	−1.60981	−0.804905	−	0.593403i	$-0.797784\pi$
$61$	−766.954	−1.60981	−0.804905	+	0.593403i	$0.797784\pi$
$62$	134.383	0.275270
$63$	202.568	0.405099
$64$	−313.400	−0.612110
$65$	156.719	0.299055
$66$	−491.557	−0.916765
$67$	256.113	0.467003	0.233501	−	0.972356i	$-0.424982\pi$
$67$	256.113	0.467003	0.233501	+	0.972356i	$0.424982\pi$
$68$	−1124.57	−2.00549
$69$	−17.5932	−0.0306952
$70$	−561.525	−0.958787
$71$	−711.750	−1.18971	−0.594854	−	0.803834i	$-0.702790\pi$
$71$	−711.750	−1.18971	−0.594854	+	0.803834i	$0.702790\pi$
$72$	−399.520	−0.653942
$73$	45.4465	0.0728646	0.0364323	−	0.999336i	$-0.488401\pi$
$73$	45.4465	0.0728646	0.0364323	+	0.999336i	$0.488401\pi$
$74$	91.0850	0.143087
$75$	−75.0000	−0.115470
$76$	−1746.25	−2.63563
$77$	−739.114	−1.09389
$78$	469.183	0.681084
$79$	329.147	0.468759	0.234380	−	0.972145i	$-0.424694\pi$
$79$	329.147	0.468759	0.234380	+	0.972145i	$0.424694\pi$
$80$	431.615	0.603201
$81$	81.0000	0.111111
$82$	576.623	0.776553
$83$	−283.281	−0.374628	−0.187314	−	0.982300i	$-0.559978\pi$
$83$	−283.281	−0.374628	−0.187314	+	0.982300i	$0.559978\pi$
$84$	−1140.91	−1.48194
$85$	−332.778	−0.424645
$86$	−2074.60	−2.60127
$87$	87.0000	0.107211
$88$	1457.73	1.76585
$89$	−802.821	−0.956167	−0.478083	−	0.878314i	$-0.658668\pi$
$89$	−802.821	−0.956167	−0.478083	+	0.878314i	$0.658668\pi$
$90$	−224.534	−0.262978
$91$	705.472	0.812677
$92$	99.0885	0.112290
$93$	80.7973	0.0900891
$94$	−58.4903	−0.0641789
$95$	−516.744	−0.558072
$96$	226.780	0.241100
$97$	389.532	0.407742	0.203871	−	0.978998i	$-0.434648\pi$
$97$	389.532	0.407742	0.203871	+	0.978998i	$0.434648\pi$
$98$	−816.265	−0.841379
$99$	−295.546	−0.300035
$100$	422.416	0.422416
$101$	274.559	0.270492	0.135246	−	0.990812i	$-0.456818\pi$
$101$	274.559	0.270492	0.135246	+	0.990812i	$0.456818\pi$
$102$	−996.268	−0.967110
$103$	−841.113	−0.804635	−0.402317	−	0.915500i	$-0.631795\pi$
$103$	−841.113	−0.804635	−0.402317	+	0.915500i	$0.631795\pi$
$104$	−1391.38	−1.31189
$105$	−337.614	−0.313788
$106$	1372.45	1.25758
$107$	−1489.04	−1.34534	−0.672670	−	0.739943i	$-0.734853\pi$
$107$	−1489.04	−1.34534	−0.672670	+	0.739943i	$0.734853\pi$
$108$	−456.209	−0.406470
$109$	−987.120	−0.867422	−0.433711	−	0.901052i	$-0.642796\pi$
$109$	−987.120	−0.867422	−0.433711	+	0.901052i	$0.642796\pi$
$110$	819.262	0.710123
$111$	54.7643	0.0468288
$112$	1942.92	1.63919
$113$	135.446	0.112758	0.0563791	−	0.998409i	$-0.482044\pi$
$113$	135.446	0.112758	0.0563791	+	0.998409i	$0.482044\pi$
$114$	−1547.02	−1.27098
$115$	29.3220	0.0237764
$116$	−490.002	−0.392203
$117$	282.094	0.222902
$118$	−1060.14	−0.827065
$119$	−1498.01	−1.15397
$120$	665.866	0.506542
$121$	−252.636	−0.189809
$122$	3826.84	2.83988
$123$	346.691	0.254147
$124$	−455.067	−0.329567
$125$	125.000	0.0894427
$126$	−1010.75	−0.714638
$127$	1539.42	1.07560	0.537802	−	0.843071i	$-0.319255\pi$
$127$	1539.42	1.07560	0.537802	+	0.843071i	$0.319255\pi$
$128$	2168.50	1.49743
$129$	−1247.34	−0.851334
$130$	−781.972	−0.527565
$131$	1625.05	1.08383	0.541914	−	0.840434i	$-0.317700\pi$
$131$	1625.05	1.08383	0.541914	+	0.840434i	$0.317700\pi$
$132$	1664.58	1.09760
$133$	−2326.13	−1.51655
$134$	−1277.91	−0.823843
$135$	−135.000	−0.0860663
$136$	2954.48	1.86282
$137$	−925.116	−0.576920	−0.288460	−	0.957492i	$-0.593143\pi$
$137$	−925.116	−0.576920	−0.288460	+	0.957492i	$0.593143\pi$
$138$	87.7839	0.0541497
$139$	−3232.14	−1.97228	−0.986138	−	0.165928i	$-0.946938\pi$
$139$	−3232.14	−1.97228	−0.986138	+	0.165928i	$0.946938\pi$
$140$	1901.51	1.14791
$141$	−35.1670	−0.0210042
$142$	3551.39	2.09877
$143$	−1029.28	−0.601907
$144$	776.907	0.449599
$145$	−145.000	−0.0830455
$146$	−226.762	−0.128541
$147$	−490.775	−0.275363
$148$	−308.444	−0.171311
$149$	764.349	0.420255	0.210127	−	0.977674i	$-0.432612\pi$
$149$	764.349	0.420255	0.210127	+	0.977674i	$0.432612\pi$
$150$	374.224	0.203702
$151$	2721.64	1.46678	0.733390	−	0.679808i	$-0.237937\pi$
$151$	2721.64	1.46678	0.733390	+	0.679808i	$0.237937\pi$
$152$	4587.76	2.44814
$153$	−599.000	−0.316512
$154$	3687.92	1.92975
$155$	−134.662	−0.0697827
$156$	−1588.81	−0.815427
$157$	1760.38	0.894862	0.447431	−	0.894319i	$-0.352339\pi$
$157$	1760.38	0.894862	0.447431	+	0.894319i	$0.352339\pi$
$158$	−1642.33	−0.826942
$159$	825.176	0.411577
$160$	−377.966	−0.186755
$161$	131.993	0.0646120
$162$	−404.162	−0.196012
$163$	−3566.14	−1.71363	−0.856816	−	0.515622i	$-0.827561\pi$
$163$	−3566.14	−1.71363	−0.856816	+	0.515622i	$0.827561\pi$
$164$	−1952.64	−0.929728
$165$	492.577	0.232406
$166$	1413.47	0.660885
$167$	−1976.07	−0.915647	−0.457824	−	0.889043i	$-0.651371\pi$
$167$	−1976.07	−0.915647	−0.457824	+	0.889043i	$0.651371\pi$
$168$	2997.41	1.37652
$169$	−1214.57	−0.552831
$170$	1660.45	0.749120
$171$	−930.139	−0.415962
$172$	7025.28	3.11437
$173$	−1836.14	−0.806934	−0.403467	−	0.914994i	$-0.632195\pi$
$173$	−1836.14	−0.806934	−0.403467	+	0.914994i	$0.632195\pi$
$174$	−434.100	−0.189132
$175$	562.690	0.243059
$176$	−2834.71	−1.21406
$177$	−637.402	−0.270678
$178$	4005.80	1.68678
$179$	2241.87	0.936117	0.468058	−	0.883698i	$-0.344954\pi$
$179$	2241.87	0.936117	0.468058	+	0.883698i	$0.344954\pi$
$180$	760.348	0.314850
$181$	2084.75	0.856122	0.428061	−	0.903750i	$-0.359197\pi$
$181$	2084.75	0.856122	0.428061	+	0.903750i	$0.359197\pi$
$182$	−3520.06	−1.43365
$183$	2300.86	0.929425
$184$	−260.327	−0.104302
$185$	−91.2739	−0.0362735
$186$	−403.150	−0.158927
$187$	2185.58	0.854682
$188$	198.068	0.0768382
$189$	−607.705	−0.233884
$190$	2578.37	0.984499
$191$	4206.24	1.59347	0.796735	−	0.604328i	$-0.206558\pi$
$191$	4206.24	1.59347	0.796735	+	0.604328i	$0.206558\pi$
$192$	940.201	0.353402
$193$	−2047.28	−0.763558	−0.381779	−	0.924254i	$-0.624688\pi$
$193$	−2047.28	−0.763558	−0.381779	+	0.924254i	$0.624688\pi$
$194$	−1943.63	−0.719301
$195$	−470.156	−0.172659
$196$	2764.15	1.00734
$197$	4461.88	1.61369	0.806843	−	0.590766i	$-0.201174\pi$
$197$	4461.88	1.61369	0.806843	+	0.590766i	$0.201174\pi$
$198$	1474.67	0.529295
$199$	−1926.80	−0.686367	−0.343183	−	0.939268i	$-0.611505\pi$
$199$	−1926.80	−0.686367	−0.343183	+	0.939268i	$0.611505\pi$
$200$	−1109.78	−0.392365
$201$	−768.339	−0.269624
$202$	−1369.95	−0.477177
$203$	−652.720	−0.225675
$204$	3373.70	1.15787
$205$	−577.819	−0.196862
$206$	4196.86	1.41946
$207$	52.7796	0.0177219
$208$	2705.69	0.901950
$209$	3393.81	1.12323
$210$	1684.58	0.553556
$211$	−4487.22	−1.46404	−0.732021	−	0.681282i	$-0.761423\pi$
$211$	−4487.22	−1.46404	−0.732021	+	0.681282i	$0.761423\pi$
$212$	−4647.57	−1.50564
$213$	2135.25	0.686878
$214$	7429.81	2.37332
$215$	2078.90	0.659441
$216$	1198.56	0.377554
$217$	−606.184	−0.189633
$218$	4925.39	1.53023
$219$	−136.340	−0.0420684
$220$	−2774.30	−0.850195
$221$	−2086.10	−0.634961
$222$	−273.255	−0.0826111
$223$	−5113.28	−1.53547	−0.767737	−	0.640765i	$-0.778617\pi$
$223$	−5113.28	−1.53547	−0.767737	+	0.640765i	$0.778617\pi$
$224$	−1701.42	−0.507505
$225$	225.000	0.0666667
$226$	−675.827	−0.198918
$227$	−5258.42	−1.53751	−0.768753	−	0.639546i	$-0.779122\pi$
$227$	−5258.42	−1.53751	−0.768753	+	0.639546i	$0.779122\pi$
$228$	5238.74	1.52168
$229$	−5242.30	−1.51276	−0.756378	−	0.654135i	$-0.773033\pi$
$229$	−5242.30	−1.51276	−0.756378	+	0.654135i	$0.773033\pi$
$230$	−146.306	−0.0419442
$231$	2217.34	0.631560
$232$	1287.34	0.364302
$233$	−6046.86	−1.70018	−0.850092	−	0.526635i	$-0.823453\pi$
$233$	−6046.86	−1.70018	−0.850092	+	0.526635i	$0.823453\pi$
$234$	−1407.55	−0.393224
$235$	58.6116	0.0162698
$236$	3589.98	0.990203
$237$	−987.442	−0.270638
$238$	7474.53	2.03572
$239$	−212.645	−0.0575518	−0.0287759	−	0.999586i	$-0.509161\pi$
$239$	−212.645	−0.0575518	−0.0287759	+	0.999586i	$0.509161\pi$
$240$	−1294.85	−0.348258
$241$	−5857.59	−1.56565	−0.782823	−	0.622245i	$-0.786221\pi$
$241$	−5857.59	−1.56565	−0.782823	+	0.622245i	$0.786221\pi$
$242$	1260.57	0.334844
$243$	−243.000	−0.0641500
$244$	−12958.9	−3.40005
$245$	817.958	0.213295
$246$	−1729.87	−0.448343
$247$	−3239.34	−0.834470
$248$	1195.56	0.306121
$249$	849.844	0.216292
$250$	−623.707	−0.157787
$251$	−3510.70	−0.882842	−0.441421	−	0.897300i	$-0.645525\pi$
$251$	−3510.70	−0.882842	−0.441421	+	0.897300i	$0.645525\pi$
$252$	3422.72	0.855600
$253$	−192.578	−0.0478547
$254$	−7681.18	−1.89748
$255$	998.334	0.245169
$256$	−8312.88	−2.02951
$257$	2682.10	0.650990	0.325495	−	0.945544i	$-0.394469\pi$
$257$	2682.10	0.650990	0.325495	+	0.945544i	$0.394469\pi$
$258$	6223.79	1.50185
$259$	−410.871	−0.0985725
$260$	2648.02	0.631627
$261$	−261.000	−0.0618984
$262$	−8108.45	−1.91199
$263$	4147.94	0.972521	0.486261	−	0.873814i	$-0.338361\pi$
$263$	4147.94	0.972521	0.486261	+	0.873814i	$0.338361\pi$
$264$	−4373.20	−1.01952
$265$	−1375.29	−0.318806
$266$	11606.6	2.67536
$267$	2408.46	0.552043
$268$	4327.45	0.986346
$269$	−7462.57	−1.69145	−0.845726	−	0.533617i	$-0.820832\pi$
$269$	−7462.57	−1.69145	−0.845726	+	0.533617i	$0.820832\pi$
$270$	673.603	0.151830
$271$	6848.81	1.53519	0.767594	−	0.640937i	$-0.221454\pi$
$271$	6848.81	1.53519	0.767594	+	0.640937i	$0.221454\pi$
$272$	−5745.28	−1.28073
$273$	−2116.42	−0.469199
$274$	4616.01	1.01775
$275$	−820.961	−0.180021
$276$	−297.266	−0.0648307
$277$	−100.396	−0.0217769	−0.0108884	−	0.999941i	$-0.503466\pi$
$277$	−100.396	−0.0217769	−0.0108884	+	0.999941i	$0.503466\pi$
$278$	16127.2	3.47931
$279$	−242.392	−0.0520130
$280$	−4995.68	−1.06625
$281$	3619.61	0.768426	0.384213	−	0.923244i	$-0.374473\pi$
$281$	3619.61	0.768426	0.384213	+	0.923244i	$0.374473\pi$
$282$	175.471	0.0370537
$283$	−3692.84	−0.775677	−0.387839	−	0.921727i	$-0.626778\pi$
$283$	−3692.84	−0.775677	−0.387839	+	0.921727i	$0.626778\pi$
$284$	−12026.2	−2.51276
$285$	1550.23	0.322203
$286$	5135.75	1.06183
$287$	−2601.06	−0.534968
$288$	−680.339	−0.139199
$289$	−483.352	−0.0983823
$290$	723.500	0.146501
$291$	−1168.60	−0.235410
$292$	767.893	0.153896
$293$	−1172.85	−0.233851	−0.116926	−	0.993141i	$-0.537304\pi$
$293$	−1172.85	−0.233851	−0.116926	+	0.993141i	$0.537304\pi$
$294$	2448.79	0.485771
$295$	1062.34	0.209667
$296$	810.349	0.159124
$297$	886.638	0.173225
$298$	−3813.84	−0.741375
$299$	183.812	0.0355523
$300$	−1267.25	−0.243882
$301$	9358.20	1.79202
$302$	−13580.0	−2.58756
$303$	−823.678	−0.156168
$304$	−8921.38	−1.68315
$305$	−3834.77	−0.719929
$306$	2988.80	0.558361
$307$	−4625.08	−0.859829	−0.429915	−	0.902870i	$-0.641456\pi$
$307$	−4625.08	−0.859829	−0.429915	+	0.902870i	$0.641456\pi$
$308$	−12488.5	−2.31039
$309$	2523.34	0.464556
$310$	671.917	0.123104
$311$	5757.91	1.04984	0.524921	−	0.851151i	$-0.324095\pi$
$311$	5757.91	1.04984	0.524921	+	0.851151i	$0.324095\pi$
$312$	4174.15	0.757419
$313$	−7518.69	−1.35777	−0.678884	−	0.734246i	$-0.737536\pi$
$313$	−7518.69	−1.35777	−0.678884	+	0.734246i	$0.737536\pi$
$314$	−8783.66	−1.57863
$315$	1012.84	0.181166
$316$	5561.48	0.990056
$317$	695.769	0.123275	0.0616376	−	0.998099i	$-0.480368\pi$
$317$	695.769	0.123275	0.0616376	+	0.998099i	$0.480368\pi$
$318$	−4117.34	−0.726066
$319$	952.315	0.167145
$320$	−1567.00	−0.273744
$321$	4467.13	0.776732
$322$	−658.601	−0.113983
$323$	6878.44	1.18491
$324$	1368.63	0.234675
$325$	783.594	0.133741
$326$	17793.8	3.02303
$327$	2961.36	0.500806
$328$	5130.00	0.863588
$329$	263.841	0.0442129
$330$	−2457.79	−0.409990
$331$	−7536.11	−1.25143	−0.625713	−	0.780053i	$-0.715192\pi$
$331$	−7536.11	−1.25143	−0.625713	+	0.780053i	$0.715192\pi$
$332$	−4786.50	−0.791245
$333$	−164.293	−0.0270366
$334$	9859.92	1.61530
$335$	1280.56	0.208850
$336$	−5828.77	−0.946385
$337$	6481.09	1.04762	0.523809	−	0.851836i	$-0.324511\pi$
$337$	6481.09	1.04762	0.523809	+	0.851836i	$0.324511\pi$
$338$	6060.28	0.975254
$339$	−406.337	−0.0651009
$340$	−5622.83	−0.896884
$341$	884.419	0.140452
$342$	4641.07	0.733802
$343$	−4038.05	−0.635669
$344$	−18456.9	−2.89282
$345$	−87.9659	−0.0137273
$346$	9161.72	1.42352
$347$	−1154.45	−0.178600	−0.0893000	−	0.996005i	$-0.528463\pi$
$347$	−1154.45	−0.178600	−0.0893000	+	0.996005i	$0.528463\pi$
$348$	1470.01	0.226439
$349$	7656.69	1.17436	0.587182	−	0.809455i	$-0.300237\pi$
$349$	7656.69	1.17436	0.587182	+	0.809455i	$0.300237\pi$
$350$	−2807.63	−0.428783
$351$	−846.281	−0.128693
$352$	2482.37	0.375882
$353$	1112.90	0.167801	0.0839003	−	0.996474i	$-0.473262\pi$
$353$	1112.90	0.167801	0.0839003	+	0.996474i	$0.473262\pi$
$354$	3180.41	0.477506
$355$	−3558.75	−0.532053
$356$	−13565.0	−2.01950
$357$	4494.02	0.666243
$358$	−11186.1	−1.65141
$359$	12401.6	1.82321	0.911604	−	0.411068i	$-0.134844\pi$
$359$	12401.6	1.82321	0.911604	+	0.411068i	$0.134844\pi$
$360$	−1997.60	−0.292452
$361$	3821.97	0.557220
$362$	−10402.2	−1.51029
$363$	757.909	0.109587
$364$	11920.1	1.71644
$365$	227.233	0.0325860
$366$	−11480.5	−1.63961
$367$	11259.8	1.60152	0.800759	−	0.598987i	$-0.204430\pi$
$367$	11259.8	1.60152	0.800759	+	0.598987i	$0.204430\pi$
$368$	506.232	0.0717097
$369$	−1040.07	−0.146732
$370$	455.425	0.0639903
$371$	−6190.91	−0.866350
$372$	1365.20	0.190275
$373$	−8049.64	−1.11741	−0.558706	−	0.829366i	$-0.688702\pi$
$373$	−8049.64	−1.11741	−0.558706	+	0.829366i	$0.688702\pi$
$374$	−10905.3	−1.50775
$375$	−375.000	−0.0516398
$376$	−520.367	−0.0713720
$377$	−908.969	−0.124176
$378$	3032.24	0.412596
$379$	9811.51	1.32977	0.664886	−	0.746945i	$-0.268480\pi$
$379$	9811.51	1.32977	0.664886	+	0.746945i	$0.268480\pi$
$380$	−8731.23	−1.17869
$381$	−4618.27	−0.621000
$382$	−20987.7	−2.81106
$383$	6660.10	0.888551	0.444276	−	0.895890i	$-0.353461\pi$
$383$	6660.10	0.888551	0.444276	+	0.895890i	$0.353461\pi$
$384$	−6505.51	−0.864539
$385$	−3695.57	−0.489205
$386$	10215.2	1.34700
$387$	3742.02	0.491518
$388$	6581.78	0.861183
$389$	−15036.0	−1.95979	−0.979894	−	0.199521i	$-0.936061\pi$
$389$	−15036.0	−1.95979	−0.979894	+	0.199521i	$0.936061\pi$
$390$	2345.92	0.304590
$391$	−390.308	−0.0504827
$392$	−7262.00	−0.935680
$393$	−4875.16	−0.625749
$394$	−22263.2	−2.84672
$395$	1645.74	0.209636
$396$	−4993.73	−0.633698
$397$	−2227.56	−0.281607	−0.140804	−	0.990038i	$-0.544969\pi$
$397$	−2227.56	−0.281607	−0.140804	+	0.990038i	$0.544969\pi$
$398$	9614.05	1.21083
$399$	6978.40	0.875581
$400$	2158.08	0.269759
$401$	−7601.22	−0.946600	−0.473300	−	0.880901i	$-0.656937\pi$
$401$	−7601.22	−0.946600	−0.473300	+	0.880901i	$0.656937\pi$
$402$	3833.74	0.475646
$403$	−844.163	−0.104344
$404$	4639.13	0.571300
$405$	405.000	0.0496904
$406$	3256.85	0.398115
$407$	599.458	0.0730075
$408$	−8863.43	−1.07550
$409$	−13097.7	−1.58347	−0.791733	−	0.610867i	$-0.790821\pi$
$409$	−13097.7	−1.58347	−0.791733	+	0.610867i	$0.790821\pi$
$410$	2883.12	0.347285
$411$	2775.35	0.333085
$412$	−14212.0	−1.69945
$413$	4782.13	0.569765
$414$	−263.352	−0.0312633
$415$	−1416.41	−0.167539
$416$	−2369.38	−0.279251
$417$	9696.41	1.13869
$418$	−16934.0	−1.98150
$419$	10997.7	1.28227	0.641135	−	0.767428i	$-0.278464\pi$
$419$	10997.7	1.28227	0.641135	+	0.767428i	$0.278464\pi$
$420$	−5704.54	−0.662745
$421$	−13032.2	−1.50867	−0.754333	−	0.656492i	$-0.772040\pi$
$421$	−13032.2	−1.50867	−0.754333	+	0.656492i	$0.772040\pi$
$422$	22389.7	2.58273
$423$	105.501	0.0121268
$424$	12210.2	1.39853
$425$	−1663.89	−0.189907
$426$	−10654.2	−1.21173
$427$	−17262.3	−1.95640
$428$	−25159.8	−2.84146
$429$	3087.84	0.347511
$430$	−10373.0	−1.16332
$431$	−781.858	−0.0873800	−0.0436900	−	0.999045i	$-0.513911\pi$
$431$	−781.858	−0.0873800	−0.0436900	+	0.999045i	$0.513911\pi$
$432$	−2330.72	−0.259576
$433$	9159.83	1.01661	0.508306	−	0.861176i	$-0.330272\pi$
$433$	9159.83	1.01661	0.508306	+	0.861176i	$0.330272\pi$
$434$	3024.65	0.334534
$435$	435.000	0.0479463
$436$	−16679.0	−1.83206
$437$	−606.078	−0.0663447
$438$	680.287	0.0742132
$439$	−4048.62	−0.440160	−0.220080	−	0.975482i	$-0.570632\pi$
$439$	−4048.62	−0.440160	−0.220080	+	0.975482i	$0.570632\pi$
$440$	7288.67	0.789713
$441$	1472.32	0.158981
$442$	10408.9	1.12014
$443$	−6522.28	−0.699510	−0.349755	−	0.936841i	$-0.613735\pi$
$443$	−6522.28	−0.699510	−0.349755	+	0.936841i	$0.613735\pi$
$444$	925.332	0.0989062
$445$	−4014.10	−0.427611
$446$	25513.5	2.70874
$447$	−2293.05	−0.242634
$448$	−7053.88	−0.743894
$449$	−4946.78	−0.519940	−0.259970	−	0.965617i	$-0.583713\pi$
$449$	−4946.78	−0.519940	−0.259970	+	0.965617i	$0.583713\pi$
$450$	−1122.67	−0.117607
$451$	3794.94	0.396223
$452$	2288.58	0.238154
$453$	−8164.91	−0.846846
$454$	26237.7	2.71233
$455$	3527.36	0.363440
$456$	−13763.3	−1.41343
$457$	16111.7	1.64918	0.824590	−	0.565731i	$-0.191406\pi$
$457$	16111.7	1.64918	0.824590	+	0.565731i	$0.191406\pi$
$458$	26157.3	2.66866
$459$	1797.00	0.182738
$460$	495.443	0.0502177
$461$	3232.48	0.326576	0.163288	−	0.986578i	$-0.447790\pi$
$461$	3232.48	0.326576	0.163288	+	0.986578i	$0.447790\pi$
$462$	−11063.8	−1.11414
$463$	6763.53	0.678894	0.339447	−	0.940625i	$-0.389760\pi$
$463$	6763.53	0.678894	0.339447	+	0.940625i	$0.389760\pi$
$464$	−2503.37	−0.250465
$465$	403.986	0.0402891
$466$	30171.7	2.99931
$467$	2459.52	0.243711	0.121855	−	0.992548i	$-0.461116\pi$
$467$	2459.52	0.243711	0.121855	+	0.992548i	$0.461116\pi$
$468$	4766.43	0.470787
$469$	5764.48	0.567546
$470$	−292.452	−0.0287017
$471$	−5281.13	−0.516649
$472$	−9431.66	−0.919761
$473$	−13653.6	−1.32725
$474$	4926.99	0.477435
$475$	−2583.72	−0.249577
$476$	−25311.3	−2.43727
$477$	−2475.53	−0.237624
$478$	1061.03	0.101528
$479$	3207.84	0.305991	0.152996	−	0.988227i	$-0.451108\pi$
$479$	3207.84	0.305991	0.152996	+	0.988227i	$0.451108\pi$
$480$	1133.90	0.107823
$481$	−572.173	−0.0542388
$482$	29227.3	2.76197
$483$	−395.980	−0.0373038
$484$	−4268.70	−0.400892
$485$	1947.66	0.182348
$486$	1212.49	0.113168
$487$	12362.0	1.15026	0.575130	−	0.818062i	$-0.304952\pi$
$487$	12362.0	1.15026	0.575130	+	0.818062i	$0.304952\pi$
$488$	34045.9	3.15817
$489$	10698.4	0.989366
$490$	−4081.32	−0.376276
$491$	18430.3	1.69399	0.846993	−	0.531604i	$-0.178410\pi$
$491$	18430.3	1.69399	0.846993	+	0.531604i	$0.178410\pi$
$492$	5857.92	0.536779
$493$	1930.11	0.176324
$494$	16163.2	1.47210
$495$	−1477.73	−0.134180
$496$	−2324.89	−0.210465
$497$	−16019.8	−1.44585
$498$	−4240.42	−0.381562
$499$	9338.78	0.837798	0.418899	−	0.908033i	$-0.362416\pi$
$499$	9338.78	0.837798	0.418899	+	0.908033i	$0.362416\pi$
$500$	2112.08	0.188910
$501$	5928.22	0.528649
$502$	17517.2	1.55743
$503$	19444.6	1.72364	0.861819	−	0.507216i	$-0.169326\pi$
$503$	19444.6	1.72364	0.861819	+	0.507216i	$0.169326\pi$
$504$	−8992.23	−0.794733
$505$	1372.80	0.120968
$506$	960.895	0.0844210
$507$	3643.71	0.319177
$508$	26011.0	2.27176
$509$	11959.2	1.04142	0.520711	−	0.853733i	$-0.325667\pi$
$509$	11959.2	1.04142	0.520711	+	0.853733i	$0.325667\pi$
$510$	−4981.34	−0.432505
$511$	1022.89	0.0885520
$512$	24130.3	2.08285
$513$	2790.42	0.240156
$514$	−13382.7	−1.14842
$515$	−4205.57	−0.359844
$516$	−21075.8	−1.79808
$517$	−384.943	−0.0327462
$518$	2050.10	0.173893
$519$	5508.43	0.465883
$520$	−6956.91	−0.586694
$521$	−2757.67	−0.231892	−0.115946	−	0.993256i	$-0.536990\pi$
$521$	−2757.67	−0.231892	−0.115946	+	0.993256i	$0.536990\pi$
$522$	1302.30	0.109196
$523$	3886.64	0.324954	0.162477	−	0.986712i	$-0.448052\pi$
$523$	3886.64	0.324954	0.162477	+	0.986712i	$0.448052\pi$
$524$	27457.9	2.28913
$525$	−1688.07	−0.140330
$526$	−20696.8	−1.71563
$527$	1792.50	0.148165
$528$	8504.14	0.700938
$529$	−12132.6	−0.997173
$530$	6862.24	0.562409
$531$	1912.21	0.156276
$532$	−39303.8	−3.20307
$533$	−3622.20	−0.294362
$534$	−12017.4	−0.973864
$535$	−7445.22	−0.601654
$536$	−11369.1	−0.916178
$537$	−6725.60	−0.540467
$538$	37235.6	2.98390
$539$	−5372.09	−0.429299
$540$	−2281.04	−0.181779
$541$	−11307.5	−0.898610	−0.449305	−	0.893379i	$-0.648328\pi$
$541$	−11307.5	−0.898610	−0.449305	+	0.893379i	$0.648328\pi$
$542$	−34173.2	−2.70824
$543$	−6254.24	−0.494282
$544$	5031.15	0.396524
$545$	−4935.60	−0.387923
$546$	10560.2	0.827718
$547$	9195.12	0.718748	0.359374	−	0.933194i	$-0.382990\pi$
$547$	9195.12	0.718748	0.359374	+	0.933194i	$0.382990\pi$
$548$	−15631.3	−1.21850
$549$	−6902.59	−0.536604
$550$	4096.31	0.317577
$551$	2997.11	0.231727
$552$	780.981	0.0602187
$553$	7408.32	0.569681
$554$	500.940	0.0384168
$555$	273.822	0.0209425
$556$	−54612.2	−4.16560
$557$	12391.1	0.942596	0.471298	−	0.881974i	$-0.343786\pi$
$557$	12391.1	0.942596	0.471298	+	0.881974i	$0.343786\pi$
$558$	1209.45	0.0917565
$559$	13032.1	0.986045
$560$	9714.62	0.733067
$561$	−6556.75	−0.493451
$562$	−18060.6	−1.35559
$563$	9161.81	0.685834	0.342917	−	0.939366i	$-0.388585\pi$
$563$	9161.81	0.685834	0.342917	+	0.939366i	$0.388585\pi$
$564$	−594.203	−0.0443625
$565$	677.229	0.0504270
$566$	18426.0	1.36838
$567$	1823.11	0.135033
$568$	31595.4	2.33400
$569$	−15614.8	−1.15045	−0.575226	−	0.817994i	$-0.695086\pi$
$569$	−15614.8	−1.15045	−0.575226	+	0.817994i	$0.695086\pi$
$570$	−7735.12	−0.568401
$571$	13526.3	0.991345	0.495673	−	0.868509i	$-0.334922\pi$
$571$	13526.3	0.991345	0.495673	+	0.868509i	$0.334922\pi$
$572$	−17391.4	−1.27128
$573$	−12618.7	−0.919991
$574$	12978.4	0.943742
$575$	146.610	0.0106331
$576$	−2820.60	−0.204037
$577$	21208.3	1.53018	0.765090	−	0.643923i	$-0.222694\pi$
$577$	21208.3	1.53018	0.765090	+	0.643923i	$0.222694\pi$
$578$	2411.76	0.173557
$579$	6141.85	0.440841
$580$	−2450.01	−0.175399
$581$	−6375.98	−0.455284
$582$	5830.89	0.415289
$583$	9032.50	0.641660
$584$	−2017.42	−0.142948
$585$	1410.47	0.0996850
$586$	5852.09	0.412539
$587$	7975.12	0.560764	0.280382	−	0.959888i	$-0.409539\pi$
$587$	7975.12	0.560764	0.280382	+	0.959888i	$0.409539\pi$
$588$	−8292.44	−0.581589
$589$	2783.43	0.194719
$590$	−5300.69	−0.369875
$591$	−13385.7	−0.931662
$592$	−1575.81	−0.109401
$593$	−6169.18	−0.427214	−0.213607	−	0.976920i	$-0.568521\pi$
$593$	−6169.18	−0.427214	−0.213607	+	0.976920i	$0.568521\pi$
$594$	−4424.02	−0.305588
$595$	−7490.03	−0.516069
$596$	12914.9	0.887611
$597$	5780.39	0.396274
$598$	−917.158	−0.0627181
$599$	10909.8	0.744180	0.372090	−	0.928197i	$-0.378641\pi$
$599$	10909.8	0.744180	0.372090	+	0.928197i	$0.378641\pi$
$600$	3329.33	0.226532
$601$	−11926.7	−0.809483	−0.404741	−	0.914431i	$-0.632638\pi$
$601$	−11926.7	−0.809483	−0.404741	+	0.914431i	$0.632638\pi$
$602$	−46694.2	−3.16132
$603$	2305.02	0.155668
$604$	45986.5	3.09795
$605$	−1263.18	−0.0848853
$606$	4109.86	0.275498
$607$	−12043.2	−0.805301	−0.402650	−	0.915354i	$-0.631911\pi$
$607$	−12043.2	−0.805301	−0.402650	+	0.915354i	$0.631911\pi$
$608$	7812.47	0.521114
$609$	1958.16	0.130293
$610$	19134.2	1.27003
$611$	367.422	0.0243278
$612$	−10121.1	−0.668498
$613$	11777.4	0.775992	0.387996	−	0.921661i	$-0.373168\pi$
$613$	11777.4	0.775992	0.387996	+	0.921661i	$0.373168\pi$
$614$	23077.6	1.51683
$615$	1733.46	0.113658
$616$	32810.1	2.14603
$617$	−2907.19	−0.189691	−0.0948454	−	0.995492i	$-0.530236\pi$
$617$	−2907.19	−0.189691	−0.0948454	+	0.995492i	$0.530236\pi$
$618$	−12590.6	−0.819527
$619$	−839.647	−0.0545206	−0.0272603	−	0.999628i	$-0.508678\pi$
$619$	−839.647	−0.0545206	−0.0272603	+	0.999628i	$0.508678\pi$
$620$	−2275.34	−0.147387
$621$	−158.339	−0.0102317
$622$	−28730.0	−1.85204
$623$	−18069.6	−1.16203
$624$	−8117.06	−0.520741
$625$	625.000	0.0400000
$626$	37515.6	2.39525
$627$	−10181.4	−0.648497
$628$	29744.4	1.89002
$629$	1214.96	0.0770167
$630$	−5053.73	−0.319596
$631$	9825.37	0.619876	0.309938	−	0.950757i	$-0.399692\pi$
$631$	9825.37	0.619876	0.309938	+	0.950757i	$0.399692\pi$
$632$	−14611.2	−0.919625
$633$	13461.7	0.845265
$634$	−3471.64	−0.217471
$635$	7697.11	0.481024
$636$	13942.7	0.869283
$637$	5127.57	0.318935
$638$	−4751.72	−0.294863
$639$	−6405.75	−0.396569
$640$	10842.5	0.669669
$641$	−22040.3	−1.35810	−0.679049	−	0.734093i	$-0.737608\pi$
$641$	−22040.3	−1.35810	−0.679049	+	0.734093i	$0.737608\pi$
$642$	−22289.4	−1.37024
$643$	−21366.9	−1.31047	−0.655233	−	0.755427i	$-0.727429\pi$
$643$	−21366.9	−1.31047	−0.655233	+	0.755427i	$0.727429\pi$
$644$	2230.24	0.136466
$645$	−6236.70	−0.380728
$646$	−34321.0	−2.09031
$647$	−5826.03	−0.354011	−0.177005	−	0.984210i	$-0.556641\pi$
$647$	−5826.03	−0.354011	−0.177005	+	0.984210i	$0.556641\pi$
$648$	−3595.68	−0.217981
$649$	−6977.10	−0.421995
$650$	−3909.86	−0.235934
$651$	1818.55	0.109485
$652$	−60255.8	−3.61933
$653$	−20058.4	−1.20206	−0.601030	−	0.799227i	$-0.705243\pi$
$653$	−20058.4	−1.20206	−0.601030	+	0.799227i	$0.705243\pi$
$654$	−14776.2	−0.883477
$655$	8125.26	0.484703
$656$	−9975.82	−0.593735
$657$	409.019	0.0242882
$658$	−1316.48	−0.0779963
$659$	−28535.3	−1.68676	−0.843382	−	0.537315i	$-0.819439\pi$
$659$	−28535.3	−1.68676	−0.843382	+	0.537315i	$0.819439\pi$
$660$	8322.89	0.490860
$661$	15044.6	0.885274	0.442637	−	0.896701i	$-0.354043\pi$
$661$	15044.6	0.885274	0.442637	+	0.896701i	$0.354043\pi$
$662$	37602.6	2.20765
$663$	6258.31	0.366595
$664$	12575.2	0.734956
$665$	−11630.7	−0.678222
$666$	819.765	0.0476956
$667$	−170.067	−0.00987262
$668$	−33389.0	−1.93392
$669$	15339.8	0.886506
$670$	−6389.57	−0.368434
$671$	25185.6	1.44900
$672$	5104.27	0.293008
$673$	15511.3	0.888434	0.444217	−	0.895919i	$-0.353482\pi$
$673$	15511.3	0.888434	0.444217	+	0.895919i	$0.353482\pi$
$674$	−32338.4	−1.84811
$675$	−675.000	−0.0384900
$676$	−20522.1	−1.16762
$677$	−10695.3	−0.607170	−0.303585	−	0.952804i	$-0.598184\pi$
$677$	−10695.3	−0.607170	−0.303585	+	0.952804i	$0.598184\pi$
$678$	2027.48	0.114845
$679$	8767.43	0.495527
$680$	14772.4	0.833081
$681$	15775.3	0.887679
$682$	−4412.94	−0.247772
$683$	−11144.8	−0.624367	−0.312184	−	0.950022i	$-0.601060\pi$
$683$	−11144.8	−0.624367	−0.312184	+	0.950022i	$0.601060\pi$
$684$	−15716.2	−0.878545
$685$	−4625.58	−0.258006
$686$	20148.5	1.12139
$687$	15726.9	0.873390
$688$	35891.4	1.98887
$689$	−8621.37	−0.476703
$690$	438.919	0.0242165
$691$	−5380.30	−0.296203	−0.148102	−	0.988972i	$-0.547316\pi$
$691$	−5380.30	−0.296203	−0.148102	+	0.988972i	$0.547316\pi$
$692$	−31024.7	−1.70431
$693$	−6652.03	−0.364632
$694$	5760.31	0.315070
$695$	−16160.7	−0.882029
$696$	−3862.02	−0.210330
$697$	7691.42	0.417982
$698$	−38204.2	−2.07171
$699$	18140.6	0.981601
$700$	9507.56	0.513360
$701$	21377.2	1.15179	0.575896	−	0.817523i	$-0.304653\pi$
$701$	21377.2	1.15179	0.575896	+	0.817523i	$0.304653\pi$
$702$	4222.65	0.227028
$703$	1886.61	0.101216
$704$	10291.6	0.550964
$705$	−175.835	−0.00939337
$706$	−5552.97	−0.296018
$707$	6179.67	0.328727
$708$	−10769.9	−0.571694
$709$	−1384.02	−0.0733116	−0.0366558	−	0.999328i	$-0.511671\pi$
$709$	−1384.02	−0.0733116	−0.0366558	+	0.999328i	$0.511671\pi$
$710$	17756.9	0.938600
$711$	2962.33	0.156253
$712$	35638.1	1.87583
$713$	−157.942	−0.00829592
$714$	−22423.6	−1.17532
$715$	−5146.40	−0.269181
$716$	37880.0	1.97715
$717$	637.936	0.0332275
$718$	−61879.7	−3.21634
$719$	−10439.9	−0.541504	−0.270752	−	0.962649i	$-0.587272\pi$
$719$	−10439.9	−0.541504	−0.270752	+	0.962649i	$0.587272\pi$
$720$	3884.54	0.201067
$721$	−18931.4	−0.977869
$722$	−19070.3	−0.982996
$723$	17572.8	0.903926
$724$	35225.2	1.80820
$725$	−725.000	−0.0371391
$726$	−3781.70	−0.193322
$727$	24684.5	1.25928	0.629640	−	0.776887i	$-0.283203\pi$
$727$	24684.5	1.25928	0.629640	+	0.776887i	$0.283203\pi$
$728$	−31316.7	−1.59433
$729$	729.000	0.0370370
$730$	−1133.81	−0.0574853
$731$	−27672.5	−1.40014
$732$	38876.8	1.96302
$733$	−858.035	−0.0432363	−0.0216182	−	0.999766i	$-0.506882\pi$
$733$	−858.035	−0.0432363	−0.0216182	+	0.999766i	$0.506882\pi$
$734$	−56182.5	−2.82525
$735$	−2453.87	−0.123146
$736$	−443.309	−0.0222019
$737$	−8410.35	−0.420352
$738$	5189.61	0.258851
$739$	−10331.9	−0.514299	−0.257149	−	0.966372i	$-0.582783\pi$
$739$	−10331.9	−0.514299	−0.257149	+	0.966372i	$0.582783\pi$
$740$	−1542.22	−0.0766124
$741$	9718.01	0.481782
$742$	30890.5	1.52834
$743$	−27385.1	−1.35217	−0.676084	−	0.736824i	$-0.736324\pi$
$743$	−27385.1	−1.35217	−0.676084	+	0.736824i	$0.736324\pi$
$744$	−3586.68	−0.176739
$745$	3821.75	0.187944
$746$	40164.9	1.97123
$747$	−2549.53	−0.124876
$748$	36929.0	1.80516
$749$	−33514.8	−1.63499
$750$	1871.12	0.0910982
$751$	−40267.8	−1.95658	−0.978291	−	0.207234i	$-0.933554\pi$
$751$	−40267.8	−1.95658	−0.978291	+	0.207234i	$0.933554\pi$
$752$	1011.91	0.0490697
$753$	10532.1	0.509709
$754$	4535.44	0.219060
$755$	13608.2	0.655964
$756$	−10268.2	−0.493981
$757$	−7047.02	−0.338346	−0.169173	−	0.985586i	$-0.554110\pi$
$757$	−7047.02	−0.338346	−0.169173	+	0.985586i	$0.554110\pi$
$758$	−48956.0	−2.34586
$759$	577.733	0.0276290
$760$	22938.8	1.09484
$761$	38699.3	1.84343	0.921714	−	0.387871i	$-0.126789\pi$
$761$	38699.3	1.84343	0.921714	+	0.387871i	$0.126789\pi$
$762$	23043.5	1.09551
$763$	−22217.7	−1.05417
$764$	71071.3	3.36554
$765$	−2995.00	−0.141548
$766$	−33231.6	−1.56750
$767$	6659.52	0.313509
$768$	24938.6	1.17174
$769$	−2374.27	−0.111337	−0.0556686	−	0.998449i	$-0.517729\pi$
$769$	−2374.27	−0.111337	−0.0556686	+	0.998449i	$0.517729\pi$
$770$	18439.6	0.863010
$771$	−8046.29	−0.375850
$772$	−34592.2	−1.61270
$773$	−12947.9	−0.602464	−0.301232	−	0.953551i	$-0.597398\pi$
$773$	−12947.9	−0.602464	−0.301232	+	0.953551i	$0.597398\pi$
$774$	−18671.4	−0.867091
$775$	−673.311	−0.0312078
$776$	−17291.7	−0.799920
$777$	1232.61	0.0569109
$778$	75024.6	3.45728
$779$	11943.4	0.549314
$780$	−7944.05	−0.364670
$781$	23372.8	1.07086
$782$	1947.50	0.0890570
$783$	783.000	0.0357371
$784$	14121.7	0.643300
$785$	8801.88	0.400194
$786$	24325.3	1.10389
$787$	−15659.1	−0.709260	−0.354630	−	0.935007i	$-0.615393\pi$
$787$	−15659.1	−0.709260	−0.354630	+	0.935007i	$0.615393\pi$
$788$	75390.8	3.40823
$789$	−12443.8	−0.561485
$790$	−8211.66	−0.369820
$791$	3048.56	0.137034
$792$	13119.6	0.588617
$793$	−24039.2	−1.07649
$794$	11114.7	0.496786
$795$	4125.88	0.184063
$796$	−32556.4	−1.44966
$797$	36033.7	1.60148	0.800739	−	0.599013i	$-0.204440\pi$
$797$	36033.7	1.60148	0.800739	+	0.599013i	$0.204440\pi$
$798$	−34819.8	−1.54462
$799$	−780.186	−0.0345444
$800$	−1889.83	−0.0835195
$801$	−7225.39	−0.318722
$802$	37927.4	1.66991
$803$	−1492.39	−0.0655858
$804$	−12982.3	−0.569467
$805$	659.967	0.0288954
$806$	4212.08	0.184075
$807$	22387.7	0.976560
$808$	−12188.0	−0.530658
$809$	8941.26	0.388576	0.194288	−	0.980945i	$-0.437760\pi$
$809$	8941.26	0.388576	0.194288	+	0.980945i	$0.437760\pi$
$810$	−2020.81	−0.0876593
$811$	31988.8	1.38506	0.692528	−	0.721391i	$-0.256497\pi$
$811$	31988.8	1.38506	0.692528	+	0.721391i	$0.256497\pi$
$812$	−11028.8	−0.476643
$813$	−20546.4	−0.886341
$814$	−2991.09	−0.128793
$815$	−17830.7	−0.766359
$816$	17235.8	0.739430
$817$	−42970.3	−1.84008
$818$	65352.8	2.79341
$819$	6349.25	0.270892
$820$	−9763.19	−0.415787
$821$	−27919.3	−1.18683	−0.593417	−	0.804895i	$-0.702222\pi$
$821$	−27919.3	−1.18683	−0.593417	+	0.804895i	$0.702222\pi$
$822$	−13848.0	−0.587597
$823$	44835.5	1.89899	0.949494	−	0.313784i	$-0.101597\pi$
$823$	44835.5	1.89899	0.949494	+	0.313784i	$0.101597\pi$
$824$	37337.9	1.57855
$825$	2462.88	0.103935
$826$	−23861.2	−1.00513
$827$	−26829.4	−1.12811	−0.564056	−	0.825737i	$-0.690760\pi$
$827$	−26829.4	−1.12811	−0.564056	+	0.825737i	$0.690760\pi$
$828$	891.797	0.0374300
$829$	−34790.3	−1.45756	−0.728780	−	0.684748i	$-0.759912\pi$
$829$	−34790.3	−1.45756	−0.728780	+	0.684748i	$0.759912\pi$
$830$	7067.37	0.295557
$831$	301.187	0.0125729
$832$	−9823.14	−0.409322
$833$	−10887.9	−0.452874
$834$	−48381.7	−2.00878
$835$	−9880.36	−0.409490
$836$	57344.0	2.37235
$837$	727.176	0.0300297
$838$	−54874.6	−2.26206
$839$	23387.9	0.962383	0.481192	−	0.876615i	$-0.340204\pi$
$839$	23387.9	0.962383	0.481192	+	0.876615i	$0.340204\pi$
$840$	14987.0	0.615598
$841$	841.000	0.0344828
$842$	65025.9	2.66145
$843$	−10858.8	−0.443651
$844$	−75818.9	−3.09217
$845$	−6072.85	−0.247234
$846$	−526.413	−0.0213930
$847$	−5686.23	−0.230675
$848$	−23743.9	−0.961520
$849$	11078.5	0.447838
$850$	8302.23	0.335017
$851$	−107.053	−0.00431226
$852$	36078.5	1.45074
$853$	3915.34	0.157161	0.0785807	−	0.996908i	$-0.474961\pi$
$853$	3915.34	0.157161	0.0785807	+	0.996908i	$0.474961\pi$
$854$	86132.8	3.45129
$855$	−4650.70	−0.186024
$856$	66100.3	2.63932
$857$	31094.8	1.23942	0.619708	−	0.784833i	$-0.287251\pi$
$857$	31094.8	1.23942	0.619708	+	0.784833i	$0.287251\pi$
$858$	−15407.2	−0.613047
$859$	9069.15	0.360227	0.180114	−	0.983646i	$-0.442353\pi$
$859$	9069.15	0.360227	0.180114	+	0.983646i	$0.442353\pi$
$860$	35126.4	1.39279
$861$	7803.19	0.308864
$862$	3901.20	0.154148
$863$	−18282.8	−0.721151	−0.360576	−	0.932730i	$-0.617420\pi$
$863$	−18282.8	−0.721151	−0.360576	+	0.932730i	$0.617420\pi$
$864$	2041.02	0.0803667
$865$	−9180.72	−0.360872
$866$	−45704.3	−1.79341
$867$	1450.06	0.0568011
$868$	−10242.5	−0.400521
$869$	−10808.7	−0.421933
$870$	−2170.50	−0.0845825
$871$	8027.54	0.312288
$872$	43819.3	1.70173
$873$	3505.79	0.135914
$874$	3024.12	0.117039
$875$	2813.45	0.108699
$876$	−2303.68	−0.0888517
$877$	4534.49	0.174594	0.0872970	−	0.996182i	$-0.472177\pi$
$877$	4534.49	0.174594	0.0872970	+	0.996182i	$0.472177\pi$
$878$	20201.2	0.776490
$879$	3518.54	0.135014
$880$	−14173.6	−0.542944
$881$	27949.4	1.06883	0.534415	−	0.845223i	$-0.320532\pi$
$881$	27949.4	1.06883	0.534415	+	0.845223i	$0.320532\pi$
$882$	−7346.38	−0.280460
$883$	7755.96	0.295593	0.147797	−	0.989018i	$-0.452782\pi$
$883$	7755.96	0.295593	0.147797	+	0.989018i	$0.452782\pi$
$884$	−35248.1	−1.34109
$885$	−3187.01	−0.121051
$886$	32543.9	1.23401
$887$	28219.5	1.06823	0.534115	−	0.845412i	$-0.320645\pi$
$887$	28219.5	1.06823	0.534115	+	0.845412i	$0.320645\pi$
$888$	−2431.05	−0.0918701
$889$	34648.7	1.30718
$890$	20029.0	0.754352
$891$	−2659.91	−0.100012
$892$	−86397.2	−3.24304
$893$	−1211.49	−0.0453985
$894$	11441.5	0.428033
$895$	11209.3	0.418644
$896$	48807.8	1.81981
$897$	−551.436	−0.0205261
$898$	24682.7	0.917230
$899$	781.041	0.0289757
$900$	3801.74	0.140805
$901$	18306.7	0.676897
$902$	−18935.4	−0.698980
$903$	−28074.6	−1.03462
$904$	−6012.58	−0.221212
$905$	10423.7	0.382869
$906$	40740.1	1.49393
$907$	182.994	0.00669926	0.00334963	−	0.999994i	$-0.498934\pi$
$907$	182.994	0.00669926	0.00334963	+	0.999994i	$0.498934\pi$
$908$	−88849.6	−3.24733
$909$	2471.03	0.0901639
$910$	−17600.3	−0.641148
$911$	−15870.4	−0.577179	−0.288590	−	0.957453i	$-0.593186\pi$
$911$	−15870.4	−0.577179	−0.288590	+	0.957453i	$0.593186\pi$
$912$	26764.1	0.971765
$913$	9302.52	0.337205
$914$	−80391.9	−2.90933
$915$	11504.3	0.415651
$916$	−88577.2	−3.19506
$917$	36576.0	1.31717
$918$	−8966.41	−0.322370
$919$	−14707.3	−0.527908	−0.263954	−	0.964535i	$-0.585027\pi$
$919$	−14707.3	−0.527908	−0.263954	+	0.964535i	$0.585027\pi$
$920$	−1301.63	−0.0466452
$921$	13875.3	0.496423
$922$	−16129.0	−0.576116
$923$	−22308.9	−0.795566
$924$	37465.6	1.33391
$925$	−456.369	−0.0162220
$926$	−33747.6	−1.19764
$927$	−7570.02	−0.268212
$928$	2192.20	0.0775459
$929$	4008.12	0.141552	0.0707762	−	0.997492i	$-0.477452\pi$
$929$	4008.12	0.141552	0.0707762	+	0.997492i	$0.477452\pi$
$930$	−2015.75	−0.0710743
$931$	−16907.0	−0.595171
$932$	−102171.	−3.59092
$933$	−17273.7	−0.606127
$934$	−12272.1	−0.429932
$935$	10927.9	0.382226
$936$	−12522.4	−0.437296
$937$	17088.4	0.595788	0.297894	−	0.954599i	$-0.403716\pi$
$937$	17088.4	0.595788	0.297894	+	0.954599i	$0.403716\pi$
$938$	−28762.8	−1.00121
$939$	22556.1	0.783908
$940$	990.339	0.0343631
$941$	1981.60	0.0686486	0.0343243	−	0.999411i	$-0.489072\pi$
$941$	1981.60	0.0686486	0.0343243	+	0.999411i	$0.489072\pi$
$942$	26351.0	0.911424
$943$	−677.712	−0.0234033
$944$	18340.8	0.632355
$945$	−3038.52	−0.104596
$946$	68126.5	2.34142
$947$	−19125.0	−0.656260	−0.328130	−	0.944633i	$-0.606418\pi$
$947$	−19125.0	−0.656260	−0.328130	+	0.944633i	$0.606418\pi$
$948$	−16684.4	−0.571609
$949$	1424.46	0.0487251
$950$	12891.9	0.440281
$951$	−2087.31	−0.0711730
$952$	66498.1	2.26388
$953$	10338.6	0.351416	0.175708	−	0.984442i	$-0.443778\pi$
$953$	10338.6	0.351416	0.175708	+	0.984442i	$0.443778\pi$
$954$	12352.0	0.419195
$955$	21031.2	0.712622
$956$	−3592.99	−0.121554
$957$	−2856.95	−0.0965015
$958$	−16006.0	−0.539802
$959$	−20822.1	−0.701128
$960$	4701.00	0.158046
$961$	−29065.6	−0.975652
$962$	2854.94	0.0956831
$963$	−13401.4	−0.448447
$964$	−98973.5	−3.30677
$965$	−10236.4	−0.341474
$966$	1975.80	0.0658079
$967$	−18633.6	−0.619664	−0.309832	−	0.950791i	$-0.600273\pi$
$967$	−18633.6	−0.619664	−0.309832	+	0.950791i	$0.600273\pi$
$968$	11214.8	0.372373
$969$	−20635.3	−0.684109
$970$	−9718.15	−0.321681
$971$	−39486.5	−1.30503	−0.652515	−	0.757776i	$-0.726286\pi$
$971$	−39486.5	−1.30503	−0.652515	+	0.757776i	$0.726286\pi$
$972$	−4105.88	−0.135490
$973$	−72747.6	−2.39690
$974$	−61682.1	−2.02918
$975$	−2350.78	−0.0772156
$976$	−66205.8	−2.17131
$977$	33392.3	1.09346	0.546731	−	0.837308i	$-0.315872\pi$
$977$	33392.3	1.09346	0.546731	+	0.837308i	$0.315872\pi$
$978$	−53381.5	−1.74535
$979$	26363.4	0.860651
$980$	13820.7	0.450497
$981$	−8884.08	−0.289141
$982$	−91960.7	−2.98838
$983$	20923.0	0.678880	0.339440	−	0.940628i	$-0.389762\pi$
$983$	20923.0	0.678880	0.339440	+	0.940628i	$0.389762\pi$
$984$	−15390.0	−0.498593
$985$	22309.4	0.721662
$986$	−9630.59	−0.311055
$987$	−791.524	−0.0255263
$988$	−54733.9	−1.76247
$989$	2438.30	0.0783957
$990$	7373.36	0.236708
$991$	44681.6	1.43225	0.716124	−	0.697973i	$-0.245914\pi$
$991$	44681.6	1.43225	0.716124	+	0.697973i	$0.245914\pi$
$992$	2035.91	0.0651615
$993$	22608.3	0.722512
$994$	79933.2	2.55063
$995$	−9633.98	−0.306953
$996$	14359.5	0.456825
$997$	−49844.7	−1.58335	−0.791674	−	0.610944i	$-0.790790\pi$
$997$	−49844.7	−1.58335	−0.791674	+	0.610944i	$0.790790\pi$
$998$	−46597.2	−1.47797
$999$	492.879	0.0156096

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.g.1.1	✓	6
3.2	odd	2		1305.4.a.i.1.6		6
5.4	even	2		2175.4.a.l.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.g.1.1	✓	6	1.1	even	1	trivial
1305.4.a.i.1.6		6	3.2	odd	2
2175.4.a.l.1.6		6	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-4.98965 q^{2} -3.00000 q^{3} +16.8966 q^{4} +5.00000 q^{5} +14.9690 q^{6} +22.5076 q^{7} -44.3911 q^{8} +9.00000 q^{9} -24.9483 q^{10} -32.8384 q^{11} -50.6899 q^{12} +31.3437 q^{13} -112.305 q^{14} -15.0000 q^{15} +86.3230 q^{16} -66.5556 q^{17} -44.9069 q^{18} -103.349 q^{19} +84.4831 q^{20} -67.5228 q^{21} +163.852 q^{22} +5.86439 q^{23} +133.173 q^{24} +25.0000 q^{25} -156.394 q^{26} -27.0000 q^{27} +380.302 q^{28} -29.0000 q^{29} +74.8448 q^{30} -26.9324 q^{31} -75.5933 q^{32} +98.5153 q^{33} +332.089 q^{34} +112.538 q^{35} +152.070 q^{36} -18.2548 q^{37} +515.675 q^{38} -94.0312 q^{39} -221.955 q^{40} -115.564 q^{41} +336.915 q^{42} +415.780 q^{43} -554.859 q^{44} +45.0000 q^{45} -29.2613 q^{46} +11.7223 q^{47} -258.969 q^{48} +163.592 q^{49} -124.741 q^{50} +199.667 q^{51} +529.604 q^{52} -275.059 q^{53} +134.721 q^{54} -164.192 q^{55} -999.136 q^{56} +310.046 q^{57} +144.700 q^{58} +212.467 q^{59} -253.449 q^{60} -766.954 q^{61} +134.383 q^{62} +202.568 q^{63} -313.400 q^{64} +156.719 q^{65} -491.557 q^{66} +256.113 q^{67} -1124.57 q^{68} -17.5932 q^{69} -561.525 q^{70} -711.750 q^{71} -399.520 q^{72} +45.4465 q^{73} +91.0850 q^{74} -75.0000 q^{75} -1746.25 q^{76} -739.114 q^{77} +469.183 q^{78} +329.147 q^{79} +431.615 q^{80} +81.0000 q^{81} +576.623 q^{82} -283.281 q^{83} -1140.91 q^{84} -332.778 q^{85} -2074.60 q^{86} +87.0000 q^{87} +1457.73 q^{88} -802.821 q^{89} -224.534 q^{90} +705.472 q^{91} +99.0885 q^{92} +80.7973 q^{93} -58.4903 q^{94} -516.744 q^{95} +226.780 q^{96} +389.532 q^{97} -816.265 q^{98} -295.546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 18 q^{3} + 15 q^{4} + 30 q^{5} + 3 q^{6} + 23 q^{7} - 51 q^{8} + 54 q^{9} - 5 q^{10} - 111 q^{11} - 45 q^{12} - 83 q^{13} - 102 q^{14} - 90 q^{15} - 37 q^{16} - 35 q^{17} - 9 q^{18} - 76 q^{19}+ \cdots - 999 q^{99}+O(q^{100}) \) 6 * q - q^2 - 18 * q^3 + 15 * q^4 + 30 * q^5 + 3 * q^6 + 23 * q^7 - 51 * q^8 + 54 * q^9 - 5 * q^10 - 111 * q^11 - 45 * q^12 - 83 * q^13 - 102 * q^14 - 90 * q^15 - 37 * q^16 - 35 * q^17 - 9 * q^18 - 76 * q^19 + 75 * q^20 - 69 * q^21 + 66 * q^22 + 166 * q^23 + 153 * q^24 + 150 * q^25 - 282 * q^26 - 162 * q^27 + 368 * q^28 - 174 * q^29 + 15 * q^30 - 164 * q^31 - 259 * q^32 + 333 * q^33 + 512 * q^34 + 115 * q^35 + 135 * q^36 - 538 * q^37 + 6 * q^38 + 249 * q^39 - 255 * q^40 - 1250 * q^41 + 306 * q^42 - 80 * q^43 - 1004 * q^44 + 270 * q^45 - 1190 * q^46 - 491 * q^47 + 111 * q^48 - 969 * q^49 - 25 * q^50 + 105 * q^51 - 336 * q^52 - 356 * q^53 + 27 * q^54 - 555 * q^55 - 1260 * q^56 + 228 * q^57 + 29 * q^58 - 646 * q^59 - 225 * q^60 - 1476 * q^61 - 4 * q^62 + 207 * q^63 - 845 * q^64 - 415 * q^65 - 198 * q^66 + 87 * q^67 - 558 * q^68 - 498 * q^69 - 510 * q^70 - 1312 * q^71 - 459 * q^72 - 1142 * q^73 - 2270 * q^74 - 450 * q^75 - 1594 * q^76 - 2561 * q^77 + 846 * q^78 - 142 * q^79 - 185 * q^80 + 486 * q^81 - 1544 * q^82 + 346 * q^83 - 1104 * q^84 - 175 * q^85 - 2056 * q^86 + 522 * q^87 + 1400 * q^88 - 2827 * q^89 - 45 * q^90 + 1379 * q^91 - 1434 * q^92 + 492 * q^93 + 978 * q^94 - 380 * q^95 + 777 * q^96 - 4 * q^97 - 1903 * q^98 - 999 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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