LMFDB - Embedded newform 435.4.a.h.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:	$0$
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} - 49x^{4} + 27x^{3} + 692x^{2} - 82x - 2588 $ x^6 - x^5 - 49x^4 + 27x^3 + 692x^2 - 82x - 2588
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-5.05047$ 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)

$f(q)$	$=$	\(q-5.05047 q^{2} +3.00000 q^{3} +17.5072 q^{4} -5.00000 q^{5} -15.1514 q^{6} +19.3889 q^{7} -48.0160 q^{8} +9.00000 q^{9} +25.2523 q^{10} +6.81451 q^{11} +52.5217 q^{12} +36.9473 q^{13} -97.9229 q^{14} -15.0000 q^{15} +102.445 q^{16} -71.5529 q^{17} -45.4542 q^{18} +88.3064 q^{19} -87.5361 q^{20} +58.1666 q^{21} -34.4164 q^{22} +185.418 q^{23} -144.048 q^{24} +25.0000 q^{25} -186.601 q^{26} +27.0000 q^{27} +339.446 q^{28} +29.0000 q^{29} +75.7570 q^{30} -120.393 q^{31} -133.269 q^{32} +20.4435 q^{33} +361.376 q^{34} -96.9444 q^{35} +157.565 q^{36} -117.351 q^{37} -445.989 q^{38} +110.842 q^{39} +240.080 q^{40} -229.591 q^{41} -293.769 q^{42} +66.8319 q^{43} +119.303 q^{44} -45.0000 q^{45} -936.448 q^{46} -42.0170 q^{47} +307.336 q^{48} +32.9286 q^{49} -126.262 q^{50} -214.659 q^{51} +646.845 q^{52} +9.42394 q^{53} -136.363 q^{54} -34.0725 q^{55} -930.976 q^{56} +264.919 q^{57} -146.464 q^{58} -232.484 q^{59} -262.608 q^{60} -546.541 q^{61} +608.042 q^{62} +174.500 q^{63} -146.492 q^{64} -184.737 q^{65} -103.249 q^{66} +953.049 q^{67} -1252.69 q^{68} +556.254 q^{69} +489.615 q^{70} +429.898 q^{71} -432.144 q^{72} +554.903 q^{73} +592.675 q^{74} +75.0000 q^{75} +1546.00 q^{76} +132.126 q^{77} -559.804 q^{78} +965.168 q^{79} -512.226 q^{80} +81.0000 q^{81} +1159.54 q^{82} +625.186 q^{83} +1018.34 q^{84} +357.765 q^{85} -337.532 q^{86} +87.0000 q^{87} -327.205 q^{88} -271.169 q^{89} +227.271 q^{90} +716.367 q^{91} +3246.16 q^{92} -361.180 q^{93} +212.206 q^{94} -441.532 q^{95} -399.806 q^{96} +1167.66 q^{97} -166.305 q^{98} +61.3305 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} + 18 q^{3} + 51 q^{4} - 30 q^{5} + 3 q^{6} + 47 q^{7} + 51 q^{8} + 54 q^{9} - 5 q^{10} + 81 q^{11} + 153 q^{12} + 169 q^{13} - 30 q^{14} - 90 q^{15} + 131 q^{16} - q^{17} + 9 q^{18} + 116 q^{19}+ \cdots + 729 q^{99}+O(q^{100}) $ 6 * q + q^2 + 18 * q^3 + 51 * q^4 - 30 * q^5 + 3 * q^6 + 47 * q^7 + 51 * q^8 + 54 * q^9 - 5 * q^10 + 81 * q^11 + 153 * q^12 + 169 * q^13 - 30 * q^14 - 90 * q^15 + 131 * q^16 - q^17 + 9 * q^18 + 116 * q^19 - 255 * q^20 + 141 * q^21 + 90 * q^22 - 52 * q^23 + 153 * q^24 + 150 * q^25 + 294 * q^26 + 162 * q^27 + 344 * q^28 + 174 * q^29 - 15 * q^30 + 340 * q^31 + 499 * q^32 + 243 * q^33 + 920 * q^34 - 235 * q^35 + 459 * q^36 + 332 * q^37 - 378 * q^38 + 507 * q^39 - 255 * q^40 - 616 * q^41 - 90 * q^42 + 334 * q^43 - 52 * q^44 - 270 * q^45 - 158 * q^46 - 85 * q^47 + 393 * q^48 + 879 * q^49 + 25 * q^50 - 3 * q^51 + 2220 * q^52 - 850 * q^53 + 27 * q^54 - 405 * q^55 - 624 * q^56 + 348 * q^57 + 29 * q^58 - 758 * q^59 - 765 * q^60 - 36 * q^61 - 152 * q^62 + 423 * q^63 + 1795 * q^64 - 845 * q^65 + 270 * q^66 + 939 * q^67 - 186 * q^68 - 156 * q^69 + 150 * q^70 - 1388 * q^71 + 459 * q^72 + 1708 * q^73 - 814 * q^74 + 450 * q^75 + 566 * q^76 + 2585 * q^77 + 882 * q^78 + 1250 * q^79 - 655 * q^80 + 486 * q^81 + 1372 * q^82 - 748 * q^83 + 1032 * q^84 + 5 * q^85 - 800 * q^86 + 522 * q^87 + 536 * q^88 + 1099 * q^89 - 45 * q^90 + 539 * q^91 + 1698 * q^92 + 1020 * q^93 - 4542 * q^94 - 580 * q^95 + 1497 * q^96 - 22 * q^97 - 1433 * q^98 + 729 * 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 $

$2$	−5.05047	−1.78561	−0.892805	−	0.450443i	$-0.851266\pi$
$2$	−5.05047	−1.78561	−0.892805	+	0.450443i	$0.851266\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	17.5072	2.18840
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−15.1514	−1.03092
$7$	19.3889	1.04690	0.523451	−	0.852056i	$-0.324644\pi$
$7$	19.3889	1.04690	0.523451	+	0.852056i	$0.324644\pi$
$8$	−48.0160	−2.12203
$9$	9.00000	0.333333
$10$	25.2523	0.798549
$11$	6.81451	0.186786	0.0933932	−	0.995629i	$-0.470229\pi$
$11$	6.81451	0.186786	0.0933932	+	0.995629i	$0.470229\pi$
$12$	52.5217	1.26348
$13$	36.9473	0.788257	0.394128	−	0.919055i	$-0.371046\pi$
$13$	36.9473	0.788257	0.394128	+	0.919055i	$0.371046\pi$
$14$	−97.9229	−1.86936
$15$	−15.0000	−0.258199
$16$	102.445	1.60071
$17$	−71.5529	−1.02083	−0.510416	−	0.859928i	$-0.670508\pi$
$17$	−71.5529	−1.02083	−0.510416	+	0.859928i	$0.670508\pi$
$18$	−45.4542	−0.595203
$19$	88.3064	1.06626	0.533129	−	0.846034i	$-0.321016\pi$
$19$	88.3064	1.06626	0.533129	+	0.846034i	$0.321016\pi$
$20$	−87.5361	−0.978684
$21$	58.1666	0.604429
$22$	−34.4164	−0.333528
$23$	185.418	1.68097	0.840486	−	0.541834i	$-0.182270\pi$
$23$	185.418	1.68097	0.840486	+	0.541834i	$0.182270\pi$
$24$	−144.048	−1.22515
$25$	25.0000	0.200000
$26$	−186.601	−1.40752
$27$	27.0000	0.192450
$28$	339.446	2.29104
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	75.7570	0.461043
$31$	−120.393	−0.697524	−0.348762	−	0.937211i	$-0.613398\pi$
$31$	−120.393	−0.697524	−0.348762	+	0.937211i	$0.613398\pi$
$32$	−133.269	−0.736213
$33$	20.4435	0.107841
$34$	361.376	1.82281
$35$	−96.9444	−0.468188
$36$	157.565	0.729468
$37$	−117.351	−0.521414	−0.260707	−	0.965418i	$-0.583956\pi$
$37$	−117.351	−0.521414	−0.260707	+	0.965418i	$0.583956\pi$
$38$	−445.989	−1.90392
$39$	110.842	0.455100
$40$	240.080	0.948999
$41$	−229.591	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$41$	−229.591	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$42$	−293.769	−1.07927
$43$	66.8319	0.237018	0.118509	−	0.992953i	$-0.462189\pi$
$43$	66.8319	0.237018	0.118509	+	0.992953i	$0.462189\pi$
$44$	119.303	0.408764
$45$	−45.0000	−0.149071
$46$	−936.448	−3.00156
$47$	−42.0170	−0.130400	−0.0652001	−	0.997872i	$-0.520769\pi$
$47$	−42.0170	−0.130400	−0.0652001	+	0.997872i	$0.520769\pi$
$48$	307.336	0.924168
$49$	32.9286	0.0960018
$50$	−126.262	−0.357122
$51$	−214.659	−0.589377
$52$	646.845	1.72502
$53$	9.42394	0.0244241	0.0122121	−	0.999925i	$-0.496113\pi$
$53$	9.42394	0.0244241	0.0122121	+	0.999925i	$0.496113\pi$
$54$	−136.363	−0.343641
$55$	−34.0725	−0.0835334
$56$	−930.976	−2.22155
$57$	264.919	0.615604
$58$	−146.464	−0.331579
$59$	−232.484	−0.512996	−0.256498	−	0.966545i	$-0.582569\pi$
$59$	−232.484	−0.512996	−0.256498	+	0.966545i	$0.582569\pi$
$60$	−262.608	−0.565043
$61$	−546.541	−1.14717	−0.573586	−	0.819146i	$-0.694448\pi$
$61$	−546.541	−1.14717	−0.573586	+	0.819146i	$0.694448\pi$
$62$	608.042	1.24551
$63$	174.500	0.348967
$64$	−146.492	−0.286118
$65$	−184.737	−0.352519
$66$	−103.249	−0.192562
$67$	953.049	1.73781	0.868907	−	0.494976i	$-0.164823\pi$
$67$	953.049	1.73781	0.868907	+	0.494976i	$0.164823\pi$
$68$	−1252.69	−2.23399
$69$	556.254	0.970509
$70$	489.615	0.836002
$71$	429.898	0.718584	0.359292	−	0.933225i	$-0.383018\pi$
$71$	429.898	0.718584	0.359292	+	0.933225i	$0.383018\pi$
$72$	−432.144	−0.707342
$73$	554.903	0.889678	0.444839	−	0.895611i	$-0.353261\pi$
$73$	554.903	0.889678	0.444839	+	0.895611i	$0.353261\pi$
$74$	592.675	0.931041
$75$	75.0000	0.115470
$76$	1546.00	2.33340
$77$	132.126	0.195547
$78$	−559.804	−0.812632
$79$	965.168	1.37456	0.687278	−	0.726395i	$-0.258805\pi$
$79$	965.168	1.37456	0.687278	+	0.726395i	$0.258805\pi$
$80$	−512.226	−0.715858
$81$	81.0000	0.111111
$82$	1159.54	1.56158
$83$	625.186	0.826784	0.413392	−	0.910553i	$-0.364344\pi$
$83$	625.186	0.826784	0.413392	+	0.910553i	$0.364344\pi$
$84$	1018.34	1.32273
$85$	357.765	0.456530
$86$	−337.532	−0.423222
$87$	87.0000	0.107211
$88$	−327.205	−0.396366
$89$	−271.169	−0.322964	−0.161482	−	0.986876i	$-0.551627\pi$
$89$	−271.169	−0.322964	−0.161482	+	0.986876i	$0.551627\pi$
$90$	227.271	0.266183
$91$	716.367	0.825227
$92$	3246.16	3.67864
$93$	−361.180	−0.402716
$94$	212.206	0.232844
$95$	−441.532	−0.476845
$96$	−399.806	−0.425053
$97$	1167.66	1.22225	0.611125	−	0.791534i	$-0.290717\pi$
$97$	1167.66	1.22225	0.611125	+	0.791534i	$0.290717\pi$
$98$	−166.305	−0.171422
$99$	61.3305	0.0622621
$100$	437.681	0.437681
$101$	1004.86	0.989977	0.494989	−	0.868899i	$-0.335172\pi$
$101$	1004.86	0.989977	0.494989	+	0.868899i	$0.335172\pi$
$102$	1084.13	1.05240
$103$	704.225	0.673683	0.336842	−	0.941561i	$-0.390641\pi$
$103$	704.225	0.673683	0.336842	+	0.941561i	$0.390641\pi$
$104$	−1774.06	−1.67270
$105$	−290.833	−0.270309
$106$	−47.5953	−0.0436119
$107$	1116.49	1.00874	0.504371	−	0.863487i	$-0.331724\pi$
$107$	1116.49	1.00874	0.504371	+	0.863487i	$0.331724\pi$
$108$	472.695	0.421158
$109$	−1306.48	−1.14806	−0.574029	−	0.818835i	$-0.694621\pi$
$109$	−1306.48	−1.14806	−0.574029	+	0.818835i	$0.694621\pi$
$110$	172.082	0.149158
$111$	−352.052	−0.301038
$112$	1986.30	1.67578
$113$	256.295	0.213364	0.106682	−	0.994293i	$-0.465977\pi$
$113$	256.295	0.213364	0.106682	+	0.994293i	$0.465977\pi$
$114$	−1337.97	−1.09923
$115$	−927.090	−0.751753
$116$	507.710	0.406376
$117$	332.526	0.262752
$118$	1174.15	0.916011
$119$	−1387.33	−1.06871
$120$	720.239	0.547905
$121$	−1284.56	−0.965111
$122$	2760.29	2.04840
$123$	−688.773	−0.504915
$124$	−2107.75	−1.52646
$125$	−125.000	−0.0894427
$126$	−881.306	−0.623119
$127$	−1201.30	−0.839355	−0.419677	−	0.907673i	$-0.637857\pi$
$127$	−1201.30	−0.839355	−0.419677	+	0.907673i	$0.637857\pi$
$128$	1806.01	1.24711
$129$	200.496	0.136842
$130$	933.006	0.629462
$131$	1049.57	0.700008	0.350004	−	0.936748i	$-0.386180\pi$
$131$	1049.57	0.700008	0.350004	+	0.936748i	$0.386180\pi$
$132$	357.909	0.236000
$133$	1712.16	1.11627
$134$	−4813.34	−3.10306
$135$	−135.000	−0.0860663
$136$	3435.68	2.16623
$137$	2881.21	1.79678	0.898388	−	0.439202i	$-0.144739\pi$
$137$	2881.21	1.79678	0.898388	+	0.439202i	$0.144739\pi$
$138$	−2809.34	−1.73295
$139$	2584.43	1.57704	0.788521	−	0.615008i	$-0.210847\pi$
$139$	2584.43	1.57704	0.788521	+	0.615008i	$0.210847\pi$
$140$	−1697.23	−1.02459
$141$	−126.051	−0.0752866
$142$	−2171.18	−1.28311
$143$	251.778	0.147236
$144$	922.007	0.533569
$145$	−145.000	−0.0830455
$146$	−2802.52	−1.58862
$147$	98.7858	0.0554267
$148$	−2054.48	−1.14106
$149$	−1449.23	−0.796813	−0.398407	−	0.917209i	$-0.630437\pi$
$149$	−1449.23	−0.796813	−0.398407	+	0.917209i	$0.630437\pi$
$150$	−378.785	−0.206184
$151$	2760.46	1.48770	0.743851	−	0.668345i	$-0.232997\pi$
$151$	2760.46	1.48770	0.743851	+	0.668345i	$0.232997\pi$
$152$	−4240.12	−2.26262
$153$	−643.976	−0.340277
$154$	−667.296	−0.349171
$155$	601.966	0.311942
$156$	1940.54	0.995943
$157$	766.465	0.389621	0.194811	−	0.980841i	$-0.437591\pi$
$157$	766.465	0.389621	0.194811	+	0.980841i	$0.437591\pi$
$158$	−4874.55	−2.45442
$159$	28.2718	0.0141013
$160$	666.344	0.329244
$161$	3595.05	1.75981
$162$	−409.088	−0.198401
$163$	−1871.11	−0.899119	−0.449560	−	0.893250i	$-0.648419\pi$
$163$	−1871.11	−0.899119	−0.449560	+	0.893250i	$0.648419\pi$
$164$	−4019.50	−1.91384
$165$	−102.218	−0.0482280
$166$	−3157.48	−1.47631
$167$	2343.62	1.08596	0.542978	−	0.839747i	$-0.317297\pi$
$167$	2343.62	1.08596	0.542978	+	0.839747i	$0.317297\pi$
$168$	−2792.93	−1.28261
$169$	−831.896	−0.378651
$170$	−1806.88	−0.815184
$171$	794.758	0.355419
$172$	1170.04	0.518691
$173$	−1485.73	−0.652935	−0.326468	−	0.945208i	$-0.605858\pi$
$173$	−1485.73	−0.652935	−0.326468	+	0.945208i	$0.605858\pi$
$174$	−439.391	−0.191438
$175$	484.722	0.209380
$176$	698.114	0.298990
$177$	−697.451	−0.296179
$178$	1369.53	0.576689
$179$	71.4418	0.0298314	0.0149157	−	0.999889i	$-0.495252\pi$
$179$	71.4418	0.0298314	0.0149157	+	0.999889i	$0.495252\pi$
$180$	−787.825	−0.326228
$181$	−1696.31	−0.696607	−0.348304	−	0.937382i	$-0.613242\pi$
$181$	−1696.31	−0.696607	−0.348304	+	0.937382i	$0.613242\pi$
$182$	−3617.99	−1.47353
$183$	−1639.62	−0.662320
$184$	−8903.03	−3.56706
$185$	586.753	0.233183
$186$	1824.13	0.719093
$187$	−487.598	−0.190677
$188$	−735.601	−0.285368
$189$	523.500	0.201476
$190$	2229.94	0.851459
$191$	−3657.80	−1.38570	−0.692852	−	0.721080i	$-0.743646\pi$
$191$	−3657.80	−1.38570	−0.692852	+	0.721080i	$0.743646\pi$
$192$	−439.477	−0.165190
$193$	−3156.73	−1.17734	−0.588669	−	0.808374i	$-0.700348\pi$
$193$	−3156.73	−1.17734	−0.588669	+	0.808374i	$0.700348\pi$
$194$	−5897.25	−2.18246
$195$	−554.210	−0.203527
$196$	576.489	0.210091
$197$	−969.523	−0.350638	−0.175319	−	0.984512i	$-0.556096\pi$
$197$	−969.523	−0.350638	−0.175319	+	0.984512i	$0.556096\pi$
$198$	−309.748	−0.111176
$199$	5423.02	1.93180	0.965898	−	0.258921i	$-0.0833670\pi$
$199$	5423.02	1.93180	0.965898	+	0.258921i	$0.0833670\pi$
$200$	−1200.40	−0.424405
$201$	2859.15	1.00333
$202$	−5075.03	−1.76771
$203$	562.277	0.194405
$204$	−3758.08	−1.28980
$205$	1147.95	0.391106
$206$	−3556.67	−1.20294
$207$	1668.76	0.560324
$208$	3785.08	1.26177
$209$	601.765	0.199162
$210$	1468.84	0.482666
$211$	−2848.51	−0.929382	−0.464691	−	0.885473i	$-0.653835\pi$
$211$	−2848.51	−0.929382	−0.464691	+	0.885473i	$0.653835\pi$
$212$	164.987	0.0534498
$213$	1289.69	0.414875
$214$	−5638.81	−1.80122
$215$	−334.160	−0.105998
$216$	−1296.43	−0.408384
$217$	−2334.29	−0.730239
$218$	6598.35	2.04999
$219$	1664.71	0.513656
$220$	−596.516	−0.182805
$221$	−2643.69	−0.804678
$222$	1778.02	0.537537
$223$	502.488	0.150893	0.0754465	−	0.997150i	$-0.475962\pi$
$223$	502.488	0.150893	0.0754465	+	0.997150i	$0.475962\pi$
$224$	−2583.93	−0.770742
$225$	225.000	0.0666667
$226$	−1294.41	−0.380985
$227$	1336.83	0.390876	0.195438	−	0.980716i	$-0.437387\pi$
$227$	1336.83	0.390876	0.195438	+	0.980716i	$0.437387\pi$
$228$	4638.00	1.34719
$229$	−1131.26	−0.326445	−0.163223	−	0.986589i	$-0.552189\pi$
$229$	−1131.26	−0.326445	−0.163223	+	0.986589i	$0.552189\pi$
$230$	4682.24	1.34234
$231$	396.377	0.112899
$232$	−1392.46	−0.394050
$233$	1271.63	0.357541	0.178770	−	0.983891i	$-0.442788\pi$
$233$	1271.63	0.357541	0.178770	+	0.983891i	$0.442788\pi$
$234$	−1679.41	−0.469173
$235$	210.085	0.0583168
$236$	−4070.14	−1.12264
$237$	2895.50	0.793600
$238$	7006.67	1.90830
$239$	1507.40	0.407973	0.203987	−	0.978974i	$-0.434610\pi$
$239$	1507.40	0.407973	0.203987	+	0.978974i	$0.434610\pi$
$240$	−1536.68	−0.413301
$241$	4251.32	1.13631	0.568156	−	0.822921i	$-0.307657\pi$
$241$	4251.32	1.13631	0.568156	+	0.822921i	$0.307657\pi$
$242$	6487.64	1.72331
$243$	243.000	0.0641500
$244$	−9568.42	−2.51047
$245$	−164.643	−0.0429333
$246$	3478.63	0.901582
$247$	3262.69	0.840485
$248$	5780.79	1.48016
$249$	1875.56	0.477344
$250$	631.309	0.159710
$251$	7219.41	1.81548	0.907739	−	0.419535i	$-0.137807\pi$
$251$	7219.41	1.81548	0.907739	+	0.419535i	$0.137807\pi$
$252$	3055.01	0.763681
$253$	1263.53	0.313983
$254$	6067.12	1.49876
$255$	1073.29	0.263578
$256$	−7949.23	−1.94073
$257$	3436.04	0.833986	0.416993	−	0.908910i	$-0.363084\pi$
$257$	3436.04	0.833986	0.416993	+	0.908910i	$0.363084\pi$
$258$	−1012.60	−0.244347
$259$	−2275.29	−0.545868
$260$	−3234.23	−0.771454
$261$	261.000	0.0618984
$262$	−5300.80	−1.24994
$263$	1494.14	0.350314	0.175157	−	0.984540i	$-0.443957\pi$
$263$	1494.14	0.350314	0.175157	+	0.984540i	$0.443957\pi$
$264$	−981.615	−0.228842
$265$	−47.1197	−0.0109228
$266$	−8647.22	−1.99322
$267$	−813.506	−0.186464
$268$	16685.2	3.80304
$269$	−1692.06	−0.383520	−0.191760	−	0.981442i	$-0.561419\pi$
$269$	−1692.06	−0.383520	−0.191760	+	0.981442i	$0.561419\pi$
$270$	681.813	0.153681
$271$	3147.75	0.705581	0.352790	−	0.935702i	$-0.385233\pi$
$271$	3147.75	0.705581	0.352790	+	0.935702i	$0.385233\pi$
$272$	−7330.26	−1.63405
$273$	2149.10	0.476445
$274$	−14551.5	−3.20834
$275$	170.363	0.0373573
$276$	9738.47	2.12387
$277$	−3873.16	−0.840129	−0.420065	−	0.907494i	$-0.637993\pi$
$277$	−3873.16	−0.840129	−0.420065	+	0.907494i	$0.637993\pi$
$278$	−13052.6	−2.81598
$279$	−1083.54	−0.232508
$280$	4654.88	0.993508
$281$	−4951.42	−1.05116	−0.525582	−	0.850743i	$-0.676152\pi$
$281$	−4951.42	−1.05116	−0.525582	+	0.850743i	$0.676152\pi$
$282$	636.617	0.134433
$283$	−4895.30	−1.02825	−0.514126	−	0.857715i	$-0.671884\pi$
$283$	−4895.30	−1.02825	−0.514126	+	0.857715i	$0.671884\pi$
$284$	7526.32	1.57255
$285$	−1324.60	−0.275306
$286$	−1271.60	−0.262906
$287$	−4451.51	−0.915555
$288$	−1199.42	−0.245404
$289$	206.822	0.0420969
$290$	732.318	0.148287
$291$	3502.99	0.705667
$292$	9714.82	1.94697
$293$	−8978.98	−1.79030	−0.895150	−	0.445766i	$-0.852932\pi$
$293$	−8978.98	−1.79030	−0.895150	+	0.445766i	$0.852932\pi$
$294$	−498.915	−0.0989704
$295$	1162.42	0.229419
$296$	5634.70	1.10645
$297$	183.992	0.0359471
$298$	7319.27	1.42280
$299$	6850.70	1.32504
$300$	1313.04	0.252695
$301$	1295.80	0.248134
$302$	−13941.6	−2.65646
$303$	3014.59	0.571564
$304$	9046.57	1.70676
$305$	2732.71	0.513031
$306$	3252.38	0.607602
$307$	7282.96	1.35394	0.676972	−	0.736009i	$-0.263292\pi$
$307$	7282.96	1.35394	0.676972	+	0.736009i	$0.263292\pi$
$308$	2313.15	0.427936
$309$	2112.68	0.388951
$310$	−3040.21	−0.557007
$311$	−2424.98	−0.442149	−0.221074	−	0.975257i	$-0.570956\pi$
$311$	−2424.98	−0.442149	−0.221074	+	0.975257i	$0.570956\pi$
$312$	−5322.18	−0.965735
$313$	−6511.66	−1.17591	−0.587957	−	0.808892i	$-0.700068\pi$
$313$	−6511.66	−1.17591	−0.587957	+	0.808892i	$0.700068\pi$
$314$	−3871.01	−0.695712
$315$	−872.500	−0.156063
$316$	16897.4	3.00808
$317$	6634.14	1.17543	0.587713	−	0.809069i	$-0.300028\pi$
$317$	6634.14	1.17543	0.587713	+	0.809069i	$0.300028\pi$
$318$	−142.786	−0.0251794
$319$	197.621	0.0346854
$320$	732.462	0.127956
$321$	3349.48	0.582398
$322$	−18156.7	−3.14234
$323$	−6318.58	−1.08847
$324$	1418.09	0.243156
$325$	923.683	0.157651
$326$	9449.97	1.60548
$327$	−3919.45	−0.662832
$328$	11024.0	1.85579
$329$	−814.663	−0.136516
$330$	516.247	0.0861165
$331$	−6727.98	−1.11723	−0.558615	−	0.829427i	$-0.688667\pi$
$331$	−6727.98	−1.11723	−0.558615	+	0.829427i	$0.688667\pi$
$332$	10945.3	1.80934
$333$	−1056.15	−0.173805
$334$	−11836.4	−1.93909
$335$	−4765.25	−0.777174
$336$	5958.89	0.967513
$337$	−7683.33	−1.24195	−0.620976	−	0.783830i	$-0.713264\pi$
$337$	−7683.33	−1.24195	−0.620976	+	0.783830i	$0.713264\pi$
$338$	4201.46	0.676123
$339$	768.884	0.123186
$340$	6263.47	0.999071
$341$	−820.420	−0.130288
$342$	−4013.90	−0.634640
$343$	−6011.94	−0.946397
$344$	−3209.00	−0.502958
$345$	−2781.27	−0.434025
$346$	7503.62	1.16589
$347$	1401.55	0.216827	0.108413	−	0.994106i	$-0.465423\pi$
$347$	1401.55	0.216827	0.108413	+	0.994106i	$0.465423\pi$
$348$	1523.13	0.234621
$349$	−10253.9	−1.57272	−0.786362	−	0.617766i	$-0.788038\pi$
$349$	−10253.9	−1.57272	−0.786362	+	0.617766i	$0.788038\pi$
$350$	−2448.07	−0.373871
$351$	997.577	0.151700
$352$	−908.160	−0.137515
$353$	−3309.99	−0.499074	−0.249537	−	0.968365i	$-0.580278\pi$
$353$	−3309.99	−0.499074	−0.249537	+	0.968365i	$0.580278\pi$
$354$	3522.45	0.528859
$355$	−2149.49	−0.321361
$356$	−4747.41	−0.706777
$357$	−4161.99	−0.617020
$358$	−360.815	−0.0532672
$359$	10427.4	1.53297	0.766483	−	0.642264i	$-0.222005\pi$
$359$	10427.4	1.53297	0.766483	+	0.642264i	$0.222005\pi$
$360$	2160.72	0.316333
$361$	939.026	0.136904
$362$	8567.17	1.24387
$363$	−3853.69	−0.557207
$364$	12541.6	1.80593
$365$	−2774.52	−0.397876
$366$	8280.87	1.18264
$367$	−6667.61	−0.948356	−0.474178	−	0.880429i	$-0.657255\pi$
$367$	−6667.61	−0.948356	−0.474178	+	0.880429i	$0.657255\pi$
$368$	18995.2	2.69074
$369$	−2066.32	−0.291513
$370$	−2963.37	−0.416374
$371$	182.720	0.0255696
$372$	−6323.25	−0.881305
$373$	6100.55	0.846849	0.423424	−	0.905931i	$-0.360828\pi$
$373$	6100.55	0.846849	0.423424	+	0.905931i	$0.360828\pi$
$374$	2462.60	0.340476
$375$	−375.000	−0.0516398
$376$	2017.49	0.276713
$377$	1071.47	0.146376
$378$	−2643.92	−0.359758
$379$	6291.88	0.852750	0.426375	−	0.904546i	$-0.359790\pi$
$379$	6291.88	0.852750	0.426375	+	0.904546i	$0.359790\pi$
$380$	−7730.00	−1.04353
$381$	−3603.90	−0.484602
$382$	18473.6	2.47433
$383$	10349.3	1.38074	0.690369	−	0.723457i	$-0.257448\pi$
$383$	10349.3	1.38074	0.690369	+	0.723457i	$0.257448\pi$
$384$	5418.02	0.720018
$385$	−660.628	−0.0874512
$386$	15943.0	2.10227
$387$	601.487	0.0790060
$388$	20442.6	2.67478
$389$	−2361.08	−0.307742	−0.153871	−	0.988091i	$-0.549174\pi$
$389$	−2361.08	−0.307742	−0.153871	+	0.988091i	$0.549174\pi$
$390$	2799.02	0.363420
$391$	−13267.2	−1.71599
$392$	−1581.10	−0.203718
$393$	3148.70	0.404150
$394$	4896.55	0.626103
$395$	−4825.84	−0.614720
$396$	1073.73	0.136255
$397$	6963.12	0.880274	0.440137	−	0.897931i	$-0.354930\pi$
$397$	6963.12	0.880274	0.440137	+	0.897931i	$0.354930\pi$
$398$	−27388.8	−3.44944
$399$	5136.49	0.644476
$400$	2561.13	0.320141
$401$	−1419.32	−0.176752	−0.0883759	−	0.996087i	$-0.528168\pi$
$401$	−1419.32	−0.176752	−0.0883759	+	0.996087i	$0.528168\pi$
$402$	−14440.0	−1.79155
$403$	−4448.20	−0.549828
$404$	17592.4	2.16647
$405$	−405.000	−0.0496904
$406$	−2839.76	−0.347131
$407$	−799.686	−0.0973930
$408$	10307.0	1.25067
$409$	−5199.93	−0.628655	−0.314327	−	0.949315i	$-0.601779\pi$
$409$	−5199.93	−0.628655	−0.314327	+	0.949315i	$0.601779\pi$
$410$	−5797.71	−0.698362
$411$	8643.63	1.03737
$412$	12329.0	1.47429
$413$	−4507.60	−0.537056
$414$	−8428.03	−1.00052
$415$	−3125.93	−0.369749
$416$	−4923.92	−0.580325
$417$	7753.30	0.910506
$418$	−3039.19	−0.355626
$419$	4476.06	0.521885	0.260943	−	0.965354i	$-0.415967\pi$
$419$	4476.06	0.521885	0.260943	+	0.965354i	$0.415967\pi$
$420$	−5091.68	−0.591544
$421$	2924.54	0.338558	0.169279	−	0.985568i	$-0.445856\pi$
$421$	2924.54	0.338558	0.169279	+	0.985568i	$0.445856\pi$
$422$	14386.3	1.65951
$423$	−378.153	−0.0434667
$424$	−452.499	−0.0518286
$425$	−1788.82	−0.204166
$426$	−6513.55	−0.740804
$427$	−10596.8	−1.20097
$428$	19546.7	2.20754
$429$	755.333	0.0850066
$430$	1687.66	0.189270
$431$	1488.98	0.166408	0.0832039	−	0.996533i	$-0.473485\pi$
$431$	1488.98	0.166408	0.0832039	+	0.996533i	$0.473485\pi$
$432$	2766.02	0.308056
$433$	−8411.84	−0.933597	−0.466798	−	0.884364i	$-0.654593\pi$
$433$	−8411.84	−0.933597	−0.466798	+	0.884364i	$0.654593\pi$
$434$	11789.3	1.30392
$435$	−435.000	−0.0479463
$436$	−22872.9	−2.51242
$437$	16373.6	1.79235
$438$	−8407.56	−0.917189
$439$	−10584.7	−1.15076	−0.575378	−	0.817887i	$-0.695145\pi$
$439$	−10584.7	−1.15076	−0.575378	+	0.817887i	$0.695145\pi$
$440$	1636.02	0.177260
$441$	296.358	0.0320006
$442$	13351.9	1.43684
$443$	−10335.6	−1.10848	−0.554242	−	0.832356i	$-0.686992\pi$
$443$	−10335.6	−1.10848	−0.554242	+	0.832356i	$0.686992\pi$
$444$	−6163.45	−0.658793
$445$	1355.84	0.144434
$446$	−2537.80	−0.269436
$447$	−4347.68	−0.460040
$448$	−2840.32	−0.299537
$449$	16626.7	1.74758	0.873788	−	0.486306i	$-0.161656\pi$
$449$	16626.7	1.74758	0.873788	+	0.486306i	$0.161656\pi$
$450$	−1136.36	−0.119041
$451$	−1564.55	−0.163352
$452$	4487.01	0.466927
$453$	8281.38	0.858925
$454$	−6751.63	−0.697951
$455$	−3581.83	−0.369053
$456$	−12720.4	−1.30633
$457$	−9008.26	−0.922076	−0.461038	−	0.887380i	$-0.652523\pi$
$457$	−9008.26	−0.922076	−0.461038	+	0.887380i	$0.652523\pi$
$458$	5713.41	0.582904
$459$	−1931.93	−0.196459
$460$	−16230.8	−1.64514
$461$	−8097.37	−0.818074	−0.409037	−	0.912518i	$-0.634135\pi$
$461$	−8097.37	−0.818074	−0.409037	+	0.912518i	$0.634135\pi$
$462$	−2001.89	−0.201594
$463$	4897.89	0.491629	0.245815	−	0.969317i	$-0.420945\pi$
$463$	4897.89	0.491629	0.245815	+	0.969317i	$0.420945\pi$
$464$	2970.91	0.297244
$465$	1805.90	0.180100
$466$	−6422.31	−0.638429
$467$	−3331.22	−0.330087	−0.165043	−	0.986286i	$-0.552776\pi$
$467$	−3331.22	−0.330087	−0.165043	+	0.986286i	$0.552776\pi$
$468$	5821.61	0.575008
$469$	18478.6	1.81932
$470$	−1061.03	−0.104131
$471$	2299.39	0.224948
$472$	11162.9	1.08859
$473$	455.426	0.0442717
$474$	−14623.7	−1.41706
$475$	2207.66	0.213251
$476$	−24288.3	−2.33877
$477$	84.8154	0.00814137
$478$	−7613.08	−0.728482
$479$	−13606.3	−1.29788	−0.648942	−	0.760838i	$-0.724788\pi$
$479$	−13606.3	−1.29788	−0.648942	+	0.760838i	$0.724788\pi$
$480$	1999.03	0.190089
$481$	−4335.79	−0.411008
$482$	−21471.1	−2.02901
$483$	10785.1	1.01603
$484$	−22489.1	−2.11205
$485$	−5838.32	−0.546607
$486$	−1227.26	−0.114547
$487$	−15460.9	−1.43861	−0.719304	−	0.694696i	$-0.755539\pi$
$487$	−15460.9	−1.43861	−0.719304	+	0.694696i	$0.755539\pi$
$488$	26242.7	2.43433
$489$	−5613.32	−0.519107
$490$	831.525	0.0766621
$491$	−19016.4	−1.74785	−0.873927	−	0.486057i	$-0.838435\pi$
$491$	−19016.4	−1.74785	−0.873927	+	0.486057i	$0.838435\pi$
$492$	−12058.5	−1.10496
$493$	−2075.03	−0.189564
$494$	−16478.1	−1.50078
$495$	−306.653	−0.0278445
$496$	−12333.7	−1.11653
$497$	8335.23	0.752286
$498$	−9472.44	−0.852350
$499$	−13675.0	−1.22681	−0.613406	−	0.789768i	$-0.710201\pi$
$499$	−13675.0	−1.22681	−0.613406	+	0.789768i	$0.710201\pi$
$500$	−2188.40	−0.195737
$501$	7030.85	0.626977
$502$	−36461.4	−3.24174
$503$	−1456.45	−0.129105	−0.0645525	−	0.997914i	$-0.520562\pi$
$503$	−1456.45	−0.129105	−0.0645525	+	0.997914i	$0.520562\pi$
$504$	−8378.78	−0.740517
$505$	−5024.32	−0.442731
$506$	−6381.43	−0.560651
$507$	−2495.69	−0.218614
$508$	−21031.4	−1.83685
$509$	15219.7	1.32535	0.662674	−	0.748908i	$-0.269422\pi$
$509$	15219.7	1.32535	0.662674	+	0.748908i	$0.269422\pi$
$510$	−5420.64	−0.470647
$511$	10758.9	0.931405
$512$	25699.3	2.21828
$513$	2384.27	0.205201
$514$	−17353.6	−1.48917
$515$	−3521.13	−0.301280
$516$	3510.12	0.299466
$517$	−286.325	−0.0243570
$518$	11491.3	0.974708
$519$	−4457.18	−0.376972
$520$	8870.30	0.748055
$521$	19988.9	1.68086	0.840432	−	0.541917i	$-0.182301\pi$
$521$	19988.9	1.68086	0.840432	+	0.541917i	$0.182301\pi$
$522$	−1318.17	−0.110526
$523$	9728.36	0.813368	0.406684	−	0.913569i	$-0.366685\pi$
$523$	9728.36	0.813368	0.406684	+	0.913569i	$0.366685\pi$
$524$	18375.0	1.53190
$525$	1454.17	0.120886
$526$	−7546.11	−0.625525
$527$	8614.48	0.712055
$528$	2094.34	0.172622
$529$	22212.9	1.82566
$530$	237.976	0.0195038
$531$	−2092.35	−0.170999
$532$	29975.2	2.44284
$533$	−8482.77	−0.689361
$534$	4108.59	0.332951
$535$	−5582.47	−0.451123
$536$	−45761.6	−3.68768
$537$	214.325	0.0172231
$538$	8545.70	0.684817
$539$	224.392	0.0179318
$540$	−2363.48	−0.188348
$541$	15290.2	1.21511	0.607556	−	0.794277i	$-0.292150\pi$
$541$	15290.2	1.21511	0.607556	+	0.794277i	$0.292150\pi$
$542$	−15897.6	−1.25989
$543$	−5088.94	−0.402186
$544$	9535.77	0.751549
$545$	6532.42	0.513428
$546$	−10854.0	−0.850745
$547$	−9101.20	−0.711406	−0.355703	−	0.934599i	$-0.615759\pi$
$547$	−9101.20	−0.711406	−0.355703	+	0.934599i	$0.615759\pi$
$548$	50442.0	3.93207
$549$	−4918.87	−0.382390
$550$	−860.411	−0.0667055
$551$	2560.89	0.197999
$552$	−26709.1	−2.05945
$553$	18713.5	1.43902
$554$	19561.3	1.50014
$555$	1760.26	0.134628
$556$	45246.3	3.45120
$557$	−3752.41	−0.285448	−0.142724	−	0.989763i	$-0.545586\pi$
$557$	−3752.41	−0.285448	−0.142724	+	0.989763i	$0.545586\pi$
$558$	5472.38	0.415169
$559$	2469.26	0.186831
$560$	−9931.49	−0.749432
$561$	−1462.79	−0.110088
$562$	25007.0	1.87697
$563$	18097.1	1.35471	0.677356	−	0.735656i	$-0.263126\pi$
$563$	18097.1	1.35471	0.677356	+	0.735656i	$0.263126\pi$
$564$	−2206.80	−0.164757
$565$	−1281.47	−0.0954194
$566$	24723.6	1.83606
$567$	1570.50	0.116322
$568$	−20641.9	−1.52485
$569$	−14101.9	−1.03898	−0.519492	−	0.854475i	$-0.673879\pi$
$569$	−14101.9	−1.03898	−0.519492	+	0.854475i	$0.673879\pi$
$570$	6689.83	0.491590
$571$	2874.72	0.210689	0.105344	−	0.994436i	$-0.466406\pi$
$571$	2874.72	0.210689	0.105344	+	0.994436i	$0.466406\pi$
$572$	4407.93	0.322211
$573$	−10973.4	−0.800036
$574$	22482.2	1.63482
$575$	4635.45	0.336194
$576$	−1318.43	−0.0953727
$577$	11659.8	0.841256	0.420628	−	0.907233i	$-0.361810\pi$
$577$	11659.8	0.841256	0.420628	+	0.907233i	$0.361810\pi$
$578$	−1044.55	−0.0751686
$579$	−9470.18	−0.679736
$580$	−2538.55	−0.181737
$581$	12121.6	0.865561
$582$	−17691.7	−1.26005
$583$	64.2195	0.00456209
$584$	−26644.2	−1.88792
$585$	−1662.63	−0.117506
$586$	45348.1	3.19678
$587$	−14565.9	−1.02419	−0.512095	−	0.858929i	$-0.671130\pi$
$587$	−14565.9	−1.02419	−0.512095	+	0.858929i	$0.671130\pi$
$588$	1729.47	0.121296
$589$	−10631.5	−0.743740
$590$	−5870.75	−0.409653
$591$	−2908.57	−0.202441
$592$	−12022.0	−0.834630
$593$	−18632.6	−1.29030	−0.645152	−	0.764054i	$-0.723206\pi$
$593$	−18632.6	−1.29030	−0.645152	+	0.764054i	$0.723206\pi$
$594$	−929.244	−0.0641874
$595$	6936.66	0.477941
$596$	−25371.9	−1.74375
$597$	16269.1	1.11532
$598$	−34599.2	−2.36600
$599$	−11080.2	−0.755802	−0.377901	−	0.925846i	$-0.623354\pi$
$599$	−11080.2	−0.755802	−0.377901	+	0.925846i	$0.623354\pi$
$600$	−3601.20	−0.245030
$601$	−26806.7	−1.81941	−0.909706	−	0.415254i	$-0.863693\pi$
$601$	−26806.7	−1.81941	−0.909706	+	0.415254i	$0.863693\pi$
$602$	−6544.38	−0.443071
$603$	8577.44	0.579271
$604$	48328.0	3.25569
$605$	6422.81	0.431611
$606$	−15225.1	−1.02059
$607$	2408.52	0.161052	0.0805262	−	0.996752i	$-0.474340\pi$
$607$	2408.52	0.161052	0.0805262	+	0.996752i	$0.474340\pi$
$608$	−11768.5	−0.784992
$609$	1686.83	0.112240
$610$	−13801.4	−0.916073
$611$	−1552.42	−0.102789
$612$	−11274.2	−0.744664
$613$	24558.8	1.61814	0.809071	−	0.587710i	$-0.199971\pi$
$613$	24558.8	1.61814	0.809071	+	0.587710i	$0.199971\pi$
$614$	−36782.4	−2.41762
$615$	3443.86	0.225805
$616$	−6344.14	−0.414956
$617$	−6367.34	−0.415461	−0.207731	−	0.978186i	$-0.566608\pi$
$617$	−6367.34	−0.415461	−0.207731	+	0.978186i	$0.566608\pi$
$618$	−10670.0	−0.694515
$619$	25893.6	1.68134	0.840671	−	0.541546i	$-0.182161\pi$
$619$	25893.6	1.68134	0.840671	+	0.541546i	$0.182161\pi$
$620$	10538.8	0.682656
$621$	5006.29	0.323503
$622$	12247.3	0.789505
$623$	−5257.66	−0.338112
$624$	11355.2	0.728482
$625$	625.000	0.0400000
$626$	32887.0	2.09972
$627$	1805.29	0.114986
$628$	13418.7	0.852649
$629$	8396.77	0.532275
$630$	4406.53	0.278667
$631$	−1864.31	−0.117618	−0.0588089	−	0.998269i	$-0.518730\pi$
$631$	−1864.31	−0.117618	−0.0588089	+	0.998269i	$0.518730\pi$
$632$	−46343.5	−2.91684
$633$	−8545.53	−0.536579
$634$	−33505.5	−2.09885
$635$	6006.50	0.375371
$636$	494.961	0.0308593
$637$	1216.62	0.0756741
$638$	−998.077	−0.0619345
$639$	3869.08	0.239528
$640$	−9030.03	−0.557724
$641$	−25891.1	−1.59538	−0.797689	−	0.603069i	$-0.793944\pi$
$641$	−25891.1	−1.59538	−0.797689	+	0.603069i	$0.793944\pi$
$642$	−16916.4	−1.03994
$643$	−19494.1	−1.19560	−0.597801	−	0.801645i	$-0.703959\pi$
$643$	−19494.1	−1.19560	−0.597801	+	0.801645i	$0.703959\pi$
$644$	62939.3	3.85118
$645$	−1002.48	−0.0611978
$646$	31911.8	1.94358
$647$	−17987.6	−1.09299	−0.546495	−	0.837463i	$-0.684038\pi$
$647$	−17987.6	−1.09299	−0.546495	+	0.837463i	$0.684038\pi$
$648$	−3889.29	−0.235781
$649$	−1584.26	−0.0958207
$650$	−4665.03	−0.281504
$651$	−7002.87	−0.421604
$652$	−32757.9	−1.96764
$653$	2069.77	0.124037	0.0620186	−	0.998075i	$-0.480246\pi$
$653$	2069.77	0.124037	0.0620186	+	0.998075i	$0.480246\pi$
$654$	19795.1	1.18356
$655$	−5247.83	−0.313053
$656$	−23520.5	−1.39988
$657$	4994.13	0.296559
$658$	4114.43	0.243765
$659$	−15787.8	−0.933239	−0.466619	−	0.884458i	$-0.654528\pi$
$659$	−15787.8	−0.933239	−0.466619	+	0.884458i	$0.654528\pi$
$660$	−1789.55	−0.105542
$661$	32239.9	1.89711	0.948554	−	0.316615i	$-0.102546\pi$
$661$	32239.9	1.89711	0.948554	+	0.316615i	$0.102546\pi$
$662$	33979.4	1.99494
$663$	−7931.07	−0.464581
$664$	−30018.9	−1.75446
$665$	−8560.81	−0.499209
$666$	5334.07	0.310347
$667$	5377.12	0.312149
$668$	41030.2	2.37651
$669$	1507.47	0.0871181
$670$	24066.7	1.38773
$671$	−3724.41	−0.214276
$672$	−7751.79	−0.444988
$673$	1039.67	0.0595488	0.0297744	−	0.999557i	$-0.490521\pi$
$673$	1039.67	0.0595488	0.0297744	+	0.999557i	$0.490521\pi$
$674$	38804.4	2.21764
$675$	675.000	0.0384900
$676$	−14564.2	−0.828641
$677$	−12781.5	−0.725604	−0.362802	−	0.931866i	$-0.618180\pi$
$677$	−12781.5	−0.725604	−0.362802	+	0.931866i	$0.618180\pi$
$678$	−3883.22	−0.219962
$679$	22639.7	1.27958
$680$	−17178.4	−0.968768
$681$	4010.50	0.225672
$682$	4143.50	0.232644
$683$	176.490	0.00988755	0.00494378	−	0.999988i	$-0.498426\pi$
$683$	176.490	0.00988755	0.00494378	+	0.999988i	$0.498426\pi$
$684$	13914.0	0.777800
$685$	−14406.1	−0.803543
$686$	30363.1	1.68990
$687$	−3393.79	−0.188473
$688$	6846.61	0.379396
$689$	348.189	0.0192525
$690$	14046.7	0.774999
$691$	28767.9	1.58377	0.791884	−	0.610672i	$-0.209101\pi$
$691$	28767.9	1.58377	0.791884	+	0.610672i	$0.209101\pi$
$692$	−26011.0	−1.42889
$693$	1189.13	0.0651823
$694$	−7078.46	−0.387168
$695$	−12922.2	−0.705275
$696$	−4177.39	−0.227505
$697$	16427.9	0.892757
$698$	51787.2	2.80827
$699$	3814.88	0.206426
$700$	8486.14	0.458208
$701$	−27326.9	−1.47236	−0.736179	−	0.676787i	$-0.763372\pi$
$701$	−27326.9	−1.47236	−0.736179	+	0.676787i	$0.763372\pi$
$702$	−5038.23	−0.270877
$703$	−10362.8	−0.555961
$704$	−998.274	−0.0534430
$705$	630.255	0.0336692
$706$	16717.0	0.891152
$707$	19483.2	1.03641
$708$	−12210.4	−0.648158
$709$	3138.76	0.166261	0.0831303	−	0.996539i	$-0.473508\pi$
$709$	3138.76	0.166261	0.0831303	+	0.996539i	$0.473508\pi$
$710$	10855.9	0.573825
$711$	8686.51	0.458185
$712$	13020.4	0.685339
$713$	−22323.1	−1.17252
$714$	21020.0	1.10176
$715$	−1258.89	−0.0658458
$716$	1250.75	0.0652830
$717$	4522.20	0.235544
$718$	−52663.1	−2.73728
$719$	21026.6	1.09062	0.545312	−	0.838233i	$-0.316411\pi$
$719$	21026.6	1.09062	0.545312	+	0.838233i	$0.316411\pi$
$720$	−4610.04	−0.238619
$721$	13654.1	0.705280
$722$	−4742.52	−0.244458
$723$	12753.9	0.656050
$724$	−29697.7	−1.52446
$725$	725.000	0.0371391
$726$	19462.9	0.994954
$727$	4458.08	0.227429	0.113715	−	0.993513i	$-0.463725\pi$
$727$	4458.08	0.227429	0.113715	+	0.993513i	$0.463725\pi$
$728$	−34397.0	−1.75115
$729$	729.000	0.0370370
$730$	14012.6	0.710452
$731$	−4782.02	−0.241955
$732$	−28705.3	−1.44942
$733$	−28933.7	−1.45797	−0.728984	−	0.684531i	$-0.760007\pi$
$733$	−28933.7	−1.45797	−0.728984	+	0.684531i	$0.760007\pi$
$734$	33674.6	1.69339
$735$	−493.929	−0.0247876
$736$	−24710.4	−1.23755
$737$	6494.56	0.324600
$738$	10435.9	0.520528
$739$	−9135.10	−0.454723	−0.227361	−	0.973810i	$-0.573010\pi$
$739$	−9135.10	−0.454723	−0.227361	+	0.973810i	$0.573010\pi$
$740$	10272.4	0.510299
$741$	9788.06	0.485254
$742$	−922.819	−0.0456574
$743$	−26380.8	−1.30258	−0.651290	−	0.758829i	$-0.725772\pi$
$743$	−26380.8	−1.30258	−0.651290	+	0.758829i	$0.725772\pi$
$744$	17342.4	0.854573
$745$	7246.13	0.356346
$746$	−30810.6	−1.51214
$747$	5626.67	0.275595
$748$	−8536.49	−0.417279
$749$	21647.6	1.05605
$750$	1893.93	0.0922085
$751$	18205.6	0.884597	0.442298	−	0.896868i	$-0.354163\pi$
$751$	18205.6	0.884597	0.442298	+	0.896868i	$0.354163\pi$
$752$	−4304.44	−0.208733
$753$	21658.2	1.04817
$754$	−5411.44	−0.261370
$755$	−13802.3	−0.665321
$756$	9165.03	0.440911
$757$	14889.8	0.714902	0.357451	−	0.933932i	$-0.383646\pi$
$757$	14889.8	0.714902	0.357451	+	0.933932i	$0.383646\pi$
$758$	−31777.0	−1.52268
$759$	3790.60	0.181278
$760$	21200.6	1.01188
$761$	4359.81	0.207678	0.103839	−	0.994594i	$-0.466887\pi$
$761$	4359.81	0.207678	0.103839	+	0.994594i	$0.466887\pi$
$762$	18201.4	0.865310
$763$	−25331.2	−1.20190
$764$	−64038.0	−3.03248
$765$	3219.88	0.152177
$766$	−52268.7	−2.46546
$767$	−8589.64	−0.404373
$768$	−23847.7	−1.12048
$769$	−23823.7	−1.11717	−0.558585	−	0.829448i	$-0.688655\pi$
$769$	−23823.7	−1.11717	−0.558585	+	0.829448i	$0.688655\pi$
$770$	3336.48	0.156154
$771$	10308.1	0.481502
$772$	−55265.6	−2.57649
$773$	18653.0	0.867922	0.433961	−	0.900932i	$-0.357116\pi$
$773$	18653.0	0.867922	0.433961	+	0.900932i	$0.357116\pi$
$774$	−3037.79	−0.141074
$775$	−3009.83	−0.139505
$776$	−56066.5	−2.59365
$777$	−6825.88	−0.315157
$778$	11924.6	0.549508
$779$	−20274.4	−0.932483
$780$	−9702.68	−0.445399
$781$	2929.54	0.134222
$782$	67005.6	3.06409
$783$	783.000	0.0357371
$784$	3373.38	0.153671
$785$	−3832.32	−0.174244
$786$	−15902.4	−0.721654
$787$	16426.1	0.743998	0.371999	−	0.928233i	$-0.378672\pi$
$787$	16426.1	0.743998	0.371999	+	0.928233i	$0.378672\pi$
$788$	−16973.7	−0.767337
$789$	4482.42	0.202254
$790$	24372.8	1.09765
$791$	4969.26	0.223371
$792$	−2944.84	−0.132122
$793$	−20193.2	−0.904266
$794$	−35167.0	−1.57183
$795$	−141.359	−0.00630628
$796$	94942.0	4.22755
$797$	−8480.05	−0.376887	−0.188443	−	0.982084i	$-0.560344\pi$
$797$	−8480.05	−0.376887	−0.188443	+	0.982084i	$0.560344\pi$
$798$	−25941.7	−1.15078
$799$	3006.44	0.133117
$800$	−3331.72	−0.147243
$801$	−2440.52	−0.107655
$802$	7168.23	0.315610
$803$	3781.39	0.166180
$804$	50055.7	2.19568
$805$	−17975.2	−0.787011
$806$	22465.5	0.981779
$807$	−5076.18	−0.221425
$808$	−48249.5	−2.10076
$809$	−28294.8	−1.22965	−0.614827	−	0.788662i	$-0.710774\pi$
$809$	−28294.8	−1.22965	−0.614827	+	0.788662i	$0.710774\pi$
$810$	2045.44	0.0887277
$811$	−28383.8	−1.22896	−0.614482	−	0.788931i	$-0.710635\pi$
$811$	−28383.8	−1.22896	−0.614482	+	0.788931i	$0.710635\pi$
$812$	9843.92	0.425436
$813$	9443.26	0.407367
$814$	4038.79	0.173906
$815$	9355.54	0.402098
$816$	−21990.8	−0.943420
$817$	5901.69	0.252722
$818$	26262.1	1.12253
$819$	6447.30	0.275076
$820$	20097.5	0.855897
$821$	27288.2	1.16001	0.580003	−	0.814615i	$-0.303052\pi$
$821$	27288.2	1.16001	0.580003	+	0.814615i	$0.303052\pi$
$822$	−43654.4	−1.85234
$823$	−37261.0	−1.57818	−0.789088	−	0.614281i	$-0.789446\pi$
$823$	−37261.0	−1.57818	−0.789088	+	0.614281i	$0.789446\pi$
$824$	−33814.1	−1.42957
$825$	511.088	0.0215682
$826$	22765.5	0.958973
$827$	2964.91	0.124668	0.0623338	−	0.998055i	$-0.480146\pi$
$827$	2964.91	0.124668	0.0623338	+	0.998055i	$0.480146\pi$
$828$	29215.4	1.22621
$829$	35023.4	1.46733	0.733664	−	0.679513i	$-0.237809\pi$
$829$	35023.4	1.46733	0.733664	+	0.679513i	$0.237809\pi$
$830$	15787.4	0.660227
$831$	−11619.5	−0.485049
$832$	−5412.50	−0.225535
$833$	−2356.14	−0.0980016
$834$	−39157.8	−1.62581
$835$	−11718.1	−0.485654
$836$	10535.2	0.435848
$837$	−3250.62	−0.134239
$838$	−22606.2	−0.931884
$839$	−5316.37	−0.218762	−0.109381	−	0.994000i	$-0.534887\pi$
$839$	−5316.37	−0.218762	−0.109381	+	0.994000i	$0.534887\pi$
$840$	13964.6	0.573602
$841$	841.000	0.0344828
$842$	−14770.3	−0.604533
$843$	−14854.3	−0.606889
$844$	−49869.5	−2.03386
$845$	4159.48	0.169338
$846$	1909.85	0.0776147
$847$	−24906.2	−1.01038
$848$	965.437	0.0390958
$849$	−14685.9	−0.593662
$850$	9034.39	0.364561
$851$	−21758.9	−0.876481
$852$	22579.0	0.907913
$853$	−40627.7	−1.63079	−0.815396	−	0.578904i	$-0.803481\pi$
$853$	−40627.7	−1.63079	−0.815396	+	0.578904i	$0.803481\pi$
$854$	53518.9	2.14447
$855$	−3973.79	−0.158948
$856$	−53609.5	−2.14058
$857$	22175.9	0.883914	0.441957	−	0.897036i	$-0.354284\pi$
$857$	22175.9	0.883914	0.441957	+	0.897036i	$0.354284\pi$
$858$	−3814.79	−0.151789
$859$	−39450.8	−1.56699	−0.783495	−	0.621399i	$-0.786565\pi$
$859$	−39450.8	−1.56699	−0.783495	+	0.621399i	$0.786565\pi$
$860$	−5850.21	−0.231966
$861$	−13354.5	−0.528596
$862$	−7520.06	−0.297139
$863$	5285.21	0.208471	0.104236	−	0.994553i	$-0.466760\pi$
$863$	5285.21	0.208471	0.104236	+	0.994553i	$0.466760\pi$
$864$	−3598.26	−0.141684
$865$	7428.64	0.292002
$866$	42483.7	1.66704
$867$	620.466	0.0243046
$868$	−40866.9	−1.59806
$869$	6577.14	0.256748
$870$	2196.95	0.0856135
$871$	35212.6	1.36984
$872$	62732.0	2.43621
$873$	10509.0	0.407417
$874$	−82694.4	−3.20043
$875$	−2423.61	−0.0936377
$876$	29144.4	1.12409
$877$	17785.8	0.684815	0.342407	−	0.939552i	$-0.388758\pi$
$877$	17785.8	0.684815	0.342407	+	0.939552i	$0.388758\pi$
$878$	53457.9	2.05480
$879$	−26936.9	−1.03363
$880$	−3490.57	−0.133713
$881$	19542.5	0.747338	0.373669	−	0.927562i	$-0.378100\pi$
$881$	19542.5	0.747338	0.373669	+	0.927562i	$0.378100\pi$
$882$	−1496.74	−0.0571406
$883$	−1625.38	−0.0619460	−0.0309730	−	0.999520i	$-0.509861\pi$
$883$	−1625.38	−0.0619460	−0.0309730	+	0.999520i	$0.509861\pi$
$884$	−46283.7	−1.76096
$885$	3487.25	0.132455
$886$	52199.5	1.97932
$887$	−48250.9	−1.82650	−0.913251	−	0.407396i	$-0.866437\pi$
$887$	−48250.9	−1.82650	−0.913251	+	0.407396i	$0.866437\pi$
$888$	16904.1	0.638811
$889$	−23291.8	−0.878722
$890$	−6847.65	−0.257903
$891$	551.975	0.0207540
$892$	8797.18	0.330215
$893$	−3710.37	−0.139040
$894$	21957.8	0.821453
$895$	−357.209	−0.0133410
$896$	35016.4	1.30560
$897$	20552.1	0.765011
$898$	−83972.6	−3.12049
$899$	−3491.40	−0.129527
$900$	3939.13	0.145894
$901$	−674.310	−0.0249329
$902$	7901.70	0.291683
$903$	3887.39	0.143260
$904$	−12306.2	−0.452764
$905$	8481.56	0.311532
$906$	−41824.8	−1.53371
$907$	20513.2	0.750971	0.375486	−	0.926828i	$-0.377476\pi$
$907$	20513.2	0.750971	0.375486	+	0.926828i	$0.377476\pi$
$908$	23404.2	0.855393
$909$	9043.78	0.329992
$910$	18089.9	0.658984
$911$	−33692.7	−1.22534	−0.612672	−	0.790338i	$-0.709905\pi$
$911$	−33692.7	−1.22534	−0.612672	+	0.790338i	$0.709905\pi$
$912$	27139.7	0.985401
$913$	4260.33	0.154432
$914$	45495.9	1.64647
$915$	8198.12	0.296198
$916$	−19805.3	−0.714394
$917$	20349.9	0.732839
$918$	9757.15	0.350799
$919$	36764.9	1.31966	0.659828	−	0.751417i	$-0.270629\pi$
$919$	36764.9	1.31966	0.659828	+	0.751417i	$0.270629\pi$
$920$	44515.1	1.59524
$921$	21848.9	0.781700
$922$	40895.5	1.46076
$923$	15883.6	0.566429
$924$	6939.46	0.247069
$925$	−2933.76	−0.104283
$926$	−24736.6	−0.877858
$927$	6338.03	0.224561
$928$	−3864.79	−0.136711
$929$	13533.8	0.477965	0.238982	−	0.971024i	$-0.423186\pi$
$929$	13533.8	0.477965	0.238982	+	0.971024i	$0.423186\pi$
$930$	−9120.63	−0.321588
$931$	2907.81	0.102363
$932$	22262.7	0.782444
$933$	−7274.95	−0.255275
$934$	16824.2	0.589406
$935$	2437.99	0.0852736
$936$	−15966.5	−0.557567
$937$	−54144.0	−1.88773	−0.943867	−	0.330325i	$-0.892842\pi$
$937$	−54144.0	−1.88773	−0.943867	+	0.330325i	$0.892842\pi$
$938$	−93325.3	−3.24859
$939$	−19535.0	−0.678914
$940$	3678.01	0.127621
$941$	−8397.60	−0.290918	−0.145459	−	0.989364i	$-0.546466\pi$
$941$	−8397.60	−0.290918	−0.145459	+	0.989364i	$0.546466\pi$
$942$	−11613.0	−0.401669
$943$	−42570.3	−1.47007
$944$	−23816.8	−0.821157
$945$	−2617.50	−0.0901029
$946$	−2300.12	−0.0790521
$947$	−4931.24	−0.169212	−0.0846059	−	0.996414i	$-0.526963\pi$
$947$	−4931.24	−0.169212	−0.0846059	+	0.996414i	$0.526963\pi$
$948$	50692.3	1.73672
$949$	20502.2	0.701295
$950$	−11149.7	−0.380784
$951$	19902.4	0.678633
$952$	66614.0	2.26783
$953$	−21509.1	−0.731111	−0.365555	−	0.930790i	$-0.619121\pi$
$953$	−21509.1	−0.731111	−0.365555	+	0.930790i	$0.619121\pi$
$954$	−428.358	−0.0145373
$955$	18289.0	0.619705
$956$	26390.4	0.892811
$957$	592.862	0.0200256
$958$	68718.0	2.31751
$959$	55863.4	1.88105
$960$	2197.39	0.0738754
$961$	−15296.5	−0.513460
$962$	21897.7	0.733900
$963$	10048.4	0.336248
$964$	74428.8	2.48671
$965$	15783.6	0.526522
$966$	−54470.0	−1.81423
$967$	56174.6	1.86810	0.934051	−	0.357140i	$-0.116248\pi$
$967$	56174.6	1.86810	0.934051	+	0.357140i	$0.116248\pi$
$968$	61679.5	2.04799
$969$	−18955.8	−0.628428
$970$	29486.2	0.976027
$971$	59470.2	1.96549	0.982745	−	0.184966i	$-0.0592173\pi$
$971$	59470.2	1.96549	0.982745	+	0.184966i	$0.0592173\pi$
$972$	4254.26	0.140386
$973$	50109.3	1.65101
$974$	78084.9	2.56879
$975$	2771.05	0.0910201
$976$	−55990.5	−1.83628
$977$	−54861.4	−1.79649	−0.898245	−	0.439494i	$-0.855158\pi$
$977$	−54861.4	−1.79649	−0.898245	+	0.439494i	$0.855158\pi$
$978$	28349.9	0.926922
$979$	−1847.88	−0.0603254
$980$	−2882.44	−0.0939554
$981$	−11758.4	−0.382686
$982$	96041.5	3.12099
$983$	−20759.3	−0.673568	−0.336784	−	0.941582i	$-0.609339\pi$
$983$	−20759.3	−0.673568	−0.336784	+	0.941582i	$0.609339\pi$
$984$	33072.1	1.07144
$985$	4847.62	0.156810
$986$	10479.9	0.338487
$987$	−2443.99	−0.0788176
$988$	57120.6	1.83932
$989$	12391.8	0.398420
$990$	1548.74	0.0497194
$991$	−25662.6	−0.822603	−0.411301	−	0.911499i	$-0.634926\pi$
$991$	−25662.6	−0.822603	−0.411301	+	0.911499i	$0.634926\pi$
$992$	16044.6	0.513526
$993$	−20183.9	−0.645033
$994$	−42096.8	−1.34329
$995$	−27115.1	−0.863926
$996$	32835.8	1.04462
$997$	43697.7	1.38808	0.694042	−	0.719935i	$-0.255828\pi$
$997$	43697.7	1.38808	0.694042	+	0.719935i	$0.255828\pi$
$998$	69065.4	2.19061
$999$	−3168.46	−0.100346

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.h.1.1	✓	6	1.1	even	1	trivial
1305.4.a.h.1.6		6	3.2	odd	2
2175.4.a.k.1.6		6	5.4	even	2

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-5.05047 q^{2} +3.00000 q^{3} +17.5072 q^{4} -5.00000 q^{5} -15.1514 q^{6} +19.3889 q^{7} -48.0160 q^{8} +9.00000 q^{9} +25.2523 q^{10} +6.81451 q^{11} +52.5217 q^{12} +36.9473 q^{13} -97.9229 q^{14} -15.0000 q^{15} +102.445 q^{16} -71.5529 q^{17} -45.4542 q^{18} +88.3064 q^{19} -87.5361 q^{20} +58.1666 q^{21} -34.4164 q^{22} +185.418 q^{23} -144.048 q^{24} +25.0000 q^{25} -186.601 q^{26} +27.0000 q^{27} +339.446 q^{28} +29.0000 q^{29} +75.7570 q^{30} -120.393 q^{31} -133.269 q^{32} +20.4435 q^{33} +361.376 q^{34} -96.9444 q^{35} +157.565 q^{36} -117.351 q^{37} -445.989 q^{38} +110.842 q^{39} +240.080 q^{40} -229.591 q^{41} -293.769 q^{42} +66.8319 q^{43} +119.303 q^{44} -45.0000 q^{45} -936.448 q^{46} -42.0170 q^{47} +307.336 q^{48} +32.9286 q^{49} -126.262 q^{50} -214.659 q^{51} +646.845 q^{52} +9.42394 q^{53} -136.363 q^{54} -34.0725 q^{55} -930.976 q^{56} +264.919 q^{57} -146.464 q^{58} -232.484 q^{59} -262.608 q^{60} -546.541 q^{61} +608.042 q^{62} +174.500 q^{63} -146.492 q^{64} -184.737 q^{65} -103.249 q^{66} +953.049 q^{67} -1252.69 q^{68} +556.254 q^{69} +489.615 q^{70} +429.898 q^{71} -432.144 q^{72} +554.903 q^{73} +592.675 q^{74} +75.0000 q^{75} +1546.00 q^{76} +132.126 q^{77} -559.804 q^{78} +965.168 q^{79} -512.226 q^{80} +81.0000 q^{81} +1159.54 q^{82} +625.186 q^{83} +1018.34 q^{84} +357.765 q^{85} -337.532 q^{86} +87.0000 q^{87} -327.205 q^{88} -271.169 q^{89} +227.271 q^{90} +716.367 q^{91} +3246.16 q^{92} -361.180 q^{93} +212.206 q^{94} -441.532 q^{95} -399.806 q^{96} +1167.66 q^{97} -166.305 q^{98} +61.3305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} + 18 q^{3} + 51 q^{4} - 30 q^{5} + 3 q^{6} + 47 q^{7} + 51 q^{8} + 54 q^{9} - 5 q^{10} + 81 q^{11} + 153 q^{12} + 169 q^{13} - 30 q^{14} - 90 q^{15} + 131 q^{16} - q^{17} + 9 q^{18} + 116 q^{19}+ \cdots + 729 q^{99}+O(q^{100}) \) 6 * q + q^2 + 18 * q^3 + 51 * q^4 - 30 * q^5 + 3 * q^6 + 47 * q^7 + 51 * q^8 + 54 * q^9 - 5 * q^10 + 81 * q^11 + 153 * q^12 + 169 * q^13 - 30 * q^14 - 90 * q^15 + 131 * q^16 - q^17 + 9 * q^18 + 116 * q^19 - 255 * q^20 + 141 * q^21 + 90 * q^22 - 52 * q^23 + 153 * q^24 + 150 * q^25 + 294 * q^26 + 162 * q^27 + 344 * q^28 + 174 * q^29 - 15 * q^30 + 340 * q^31 + 499 * q^32 + 243 * q^33 + 920 * q^34 - 235 * q^35 + 459 * q^36 + 332 * q^37 - 378 * q^38 + 507 * q^39 - 255 * q^40 - 616 * q^41 - 90 * q^42 + 334 * q^43 - 52 * q^44 - 270 * q^45 - 158 * q^46 - 85 * q^47 + 393 * q^48 + 879 * q^49 + 25 * q^50 - 3 * q^51 + 2220 * q^52 - 850 * q^53 + 27 * q^54 - 405 * q^55 - 624 * q^56 + 348 * q^57 + 29 * q^58 - 758 * q^59 - 765 * q^60 - 36 * q^61 - 152 * q^62 + 423 * q^63 + 1795 * q^64 - 845 * q^65 + 270 * q^66 + 939 * q^67 - 186 * q^68 - 156 * q^69 + 150 * q^70 - 1388 * q^71 + 459 * q^72 + 1708 * q^73 - 814 * q^74 + 450 * q^75 + 566 * q^76 + 2585 * q^77 + 882 * q^78 + 1250 * q^79 - 655 * q^80 + 486 * q^81 + 1372 * q^82 - 748 * q^83 + 1032 * q^84 + 5 * q^85 - 800 * q^86 + 522 * q^87 + 536 * q^88 + 1099 * q^89 - 45 * q^90 + 539 * q^91 + 1698 * q^92 + 1020 * q^93 - 4542 * q^94 - 580 * q^95 + 1497 * q^96 - 22 * q^97 - 1433 * q^98 + 729 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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