LMFDB - Embedded newform 230.4.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("230.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 60x^{2} - 45x + 108 $ x^4 - 2x^3 - 60x^2 - 45*x + 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-6.12571$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} +10.1257 q^{3} +4.00000 q^{4} +5.00000 q^{5} +20.2514 q^{6} -24.6431 q^{7} +8.00000 q^{8} +75.5301 q^{9} +10.0000 q^{10} -17.3867 q^{11} +40.5029 q^{12} +4.00699 q^{13} -49.2862 q^{14} +50.6286 q^{15} +16.0000 q^{16} +48.2740 q^{17} +151.060 q^{18} +79.3172 q^{19} +20.0000 q^{20} -249.529 q^{21} -34.7734 q^{22} -23.0000 q^{23} +81.0057 q^{24} +25.0000 q^{25} +8.01398 q^{26} +491.402 q^{27} -98.5723 q^{28} -254.267 q^{29} +101.257 q^{30} -220.696 q^{31} +32.0000 q^{32} -176.053 q^{33} +96.5480 q^{34} -123.215 q^{35} +302.120 q^{36} -422.904 q^{37} +158.634 q^{38} +40.5736 q^{39} +40.0000 q^{40} -170.251 q^{41} -499.058 q^{42} -228.920 q^{43} -69.5468 q^{44} +377.650 q^{45} -46.0000 q^{46} +580.087 q^{47} +162.011 q^{48} +264.282 q^{49} +50.0000 q^{50} +488.809 q^{51} +16.0280 q^{52} -260.354 q^{53} +982.803 q^{54} -86.9335 q^{55} -197.145 q^{56} +803.144 q^{57} -508.535 q^{58} +353.130 q^{59} +202.514 q^{60} -80.6108 q^{61} -441.392 q^{62} -1861.29 q^{63} +64.0000 q^{64} +20.0349 q^{65} -352.106 q^{66} -820.011 q^{67} +193.096 q^{68} -232.891 q^{69} -246.431 q^{70} +614.845 q^{71} +604.241 q^{72} +511.586 q^{73} -845.808 q^{74} +253.143 q^{75} +317.269 q^{76} +428.462 q^{77} +81.1472 q^{78} +160.464 q^{79} +80.0000 q^{80} +2936.48 q^{81} -340.502 q^{82} -32.5646 q^{83} -998.115 q^{84} +241.370 q^{85} -457.840 q^{86} -2574.64 q^{87} -139.094 q^{88} -25.0375 q^{89} +755.301 q^{90} -98.7445 q^{91} -92.0000 q^{92} -2234.70 q^{93} +1160.17 q^{94} +396.586 q^{95} +324.023 q^{96} -249.798 q^{97} +528.563 q^{98} -1313.22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9} + 40 q^{10} + 21 q^{11} + 56 q^{12} + 70 q^{13} + 16 q^{14} + 70 q^{15} + 64 q^{16} + 56 q^{17} + 128 q^{18} + 173 q^{19}+ \cdots - 2745 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9 + 40 * q^10 + 21 * q^11 + 56 * q^12 + 70 * q^13 + 16 * q^14 + 70 * q^15 + 64 * q^16 + 56 * q^17 + 128 * q^18 + 173 * q^19 + 80 * q^20 - 120 * q^21 + 42 * q^22 - 92 * q^23 + 112 * q^24 + 100 * q^25 + 140 * q^26 + 389 * q^27 + 32 * q^28 - 118 * q^29 + 140 * q^30 + 17 * q^31 + 128 * q^32 - 89 * q^33 + 112 * q^34 + 40 * q^35 + 256 * q^36 - 343 * q^37 + 346 * q^38 - 221 * q^39 + 160 * q^40 + 139 * q^41 - 240 * q^42 - 50 * q^43 + 84 * q^44 + 320 * q^45 - 184 * q^46 + 367 * q^47 + 224 * q^48 - 124 * q^49 + 200 * q^50 + 439 * q^51 + 280 * q^52 - 353 * q^53 + 778 * q^54 + 105 * q^55 + 64 * q^56 - 238 * q^57 - 236 * q^58 - 453 * q^59 + 280 * q^60 - 327 * q^61 + 34 * q^62 - 1723 * q^63 + 256 * q^64 + 350 * q^65 - 178 * q^66 - 455 * q^67 + 224 * q^68 - 322 * q^69 + 80 * q^70 + 195 * q^71 + 512 * q^72 - 633 * q^73 - 686 * q^74 + 350 * q^75 + 692 * q^76 - 2 * q^77 - 442 * q^78 - 1140 * q^79 + 320 * q^80 + 1456 * q^81 + 278 * q^82 - 1199 * q^83 - 480 * q^84 + 280 * q^85 - 100 * q^86 - 1775 * q^87 + 168 * q^88 - 2170 * q^89 + 640 * q^90 + 557 * q^91 - 368 * q^92 - 3241 * q^93 + 734 * q^94 + 865 * q^95 + 448 * q^96 - 703 * q^97 - 248 * q^98 - 2745 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	10.1257	1.94869	0.974347	−	0.225050i	$-0.0722546\pi$
$3$	10.1257	1.94869	0.974347	+	0.225050i	$0.0722546\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	20.2514	1.37794
$7$	−24.6431	−1.33060	−0.665301	−	0.746575i	$-0.731697\pi$
$7$	−24.6431	−1.33060	−0.665301	+	0.746575i	$0.731697\pi$
$8$	8.00000	0.353553
$9$	75.5301	2.79741
$10$	10.0000	0.316228
$11$	−17.3867	−0.476572	−0.238286	−	0.971195i	$-0.576586\pi$
$11$	−17.3867	−0.476572	−0.238286	+	0.971195i	$0.576586\pi$
$12$	40.5029	0.974347
$13$	4.00699	0.0854876	0.0427438	−	0.999086i	$-0.486390\pi$
$13$	4.00699	0.0854876	0.0427438	+	0.999086i	$0.486390\pi$
$14$	−49.2862	−0.940877
$15$	50.6286	0.871483
$16$	16.0000	0.250000
$17$	48.2740	0.688716	0.344358	−	0.938838i	$-0.388097\pi$
$17$	48.2740	0.688716	0.344358	+	0.938838i	$0.388097\pi$
$18$	151.060	1.97807
$19$	79.3172	0.957717	0.478859	−	0.877892i	$-0.341051\pi$
$19$	79.3172	0.957717	0.478859	+	0.877892i	$0.341051\pi$
$20$	20.0000	0.223607
$21$	−249.529	−2.59294
$22$	−34.7734	−0.336987
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	81.0057	0.688968
$25$	25.0000	0.200000
$26$	8.01398	0.0604488
$27$	491.402	3.50260
$28$	−98.5723	−0.665301
$29$	−254.267	−1.62815	−0.814074	−	0.580761i	$-0.802755\pi$
$29$	−254.267	−1.62815	−0.814074	+	0.580761i	$0.802755\pi$
$30$	101.257	0.616231
$31$	−220.696	−1.27865	−0.639325	−	0.768937i	$-0.720786\pi$
$31$	−220.696	−1.27865	−0.639325	+	0.768937i	$0.720786\pi$
$32$	32.0000	0.176777
$33$	−176.053	−0.928693
$34$	96.5480	0.486996
$35$	−123.215	−0.595063
$36$	302.120	1.39870
$37$	−422.904	−1.87905	−0.939527	−	0.342476i	$-0.888735\pi$
$37$	−422.904	−1.87905	−0.939527	+	0.342476i	$0.888735\pi$
$38$	158.634	0.677208
$39$	40.5736	0.166589
$40$	40.0000	0.158114
$41$	−170.251	−0.648505	−0.324252	−	0.945971i	$-0.605113\pi$
$41$	−170.251	−0.648505	−0.324252	+	0.945971i	$0.605113\pi$
$42$	−499.058	−1.83348
$43$	−228.920	−0.811860	−0.405930	−	0.913904i	$-0.633052\pi$
$43$	−228.920	−0.811860	−0.405930	+	0.913904i	$0.633052\pi$
$44$	−69.5468	−0.238286
$45$	377.650	1.25104
$46$	−46.0000	−0.147442
$47$	580.087	1.80031	0.900154	−	0.435572i	$-0.143454\pi$
$47$	580.087	1.80031	0.900154	+	0.435572i	$0.143454\pi$
$48$	162.011	0.487174
$49$	264.282	0.770500
$50$	50.0000	0.141421
$51$	488.809	1.34210
$52$	16.0280	0.0427438
$53$	−260.354	−0.674762	−0.337381	−	0.941368i	$-0.609541\pi$
$53$	−260.354	−0.674762	−0.337381	+	0.941368i	$0.609541\pi$
$54$	982.803	2.47671
$55$	−86.9335	−0.213129
$56$	−197.145	−0.470439
$57$	803.144	1.86630
$58$	−508.535	−1.15127
$59$	353.130	0.779215	0.389607	−	0.920981i	$-0.372611\pi$
$59$	353.130	0.779215	0.389607	+	0.920981i	$0.372611\pi$
$60$	202.514	0.435741
$61$	−80.6108	−0.169199	−0.0845996	−	0.996415i	$-0.526961\pi$
$61$	−80.6108	−0.169199	−0.0845996	+	0.996415i	$0.526961\pi$
$62$	−441.392	−0.904142
$63$	−1861.29	−3.72224
$64$	64.0000	0.125000
$65$	20.0349	0.0382312
$66$	−352.106	−0.656685
$67$	−820.011	−1.49523	−0.747614	−	0.664133i	$-0.768801\pi$
$67$	−820.011	−1.49523	−0.747614	+	0.664133i	$0.768801\pi$
$68$	193.096	0.344358
$69$	−232.891	−0.406331
$70$	−246.431	−0.420773
$71$	614.845	1.02773	0.513864	−	0.857872i	$-0.328214\pi$
$71$	614.845	1.02773	0.513864	+	0.857872i	$0.328214\pi$
$72$	604.241	0.989034
$73$	511.586	0.820228	0.410114	−	0.912034i	$-0.365489\pi$
$73$	511.586	0.820228	0.410114	+	0.912034i	$0.365489\pi$
$74$	−845.808	−1.32869
$75$	253.143	0.389739
$76$	317.269	0.478859
$77$	428.462	0.634127
$78$	81.1472	0.117796
$79$	160.464	0.228526	0.114263	−	0.993451i	$-0.463549\pi$
$79$	160.464	0.228526	0.114263	+	0.993451i	$0.463549\pi$
$80$	80.0000	0.111803
$81$	2936.48	4.02809
$82$	−340.502	−0.458562
$83$	−32.5646	−0.0430654	−0.0215327	−	0.999768i	$-0.506855\pi$
$83$	−32.5646	−0.0430654	−0.0215327	+	0.999768i	$0.506855\pi$
$84$	−998.115	−1.29647
$85$	241.370	0.308003
$86$	−457.840	−0.574072
$87$	−2574.64	−3.17276
$88$	−139.094	−0.168494
$89$	−25.0375	−0.0298199	−0.0149100	−	0.999889i	$-0.504746\pi$
$89$	−25.0375	−0.0298199	−0.0149100	+	0.999889i	$0.504746\pi$
$90$	755.301	0.884619
$91$	−98.7445	−0.113750
$92$	−92.0000	−0.104257
$93$	−2234.70	−2.49170
$94$	1160.17	1.27301
$95$	396.586	0.428304
$96$	324.023	0.344484
$97$	−249.798	−0.261476	−0.130738	−	0.991417i	$-0.541735\pi$
$97$	−249.798	−0.261476	−0.130738	+	0.991417i	$0.541735\pi$
$98$	528.563	0.544826
$99$	−1313.22	−1.33317
$100$	100.000	0.100000
$101$	620.493	0.611300	0.305650	−	0.952144i	$-0.401126\pi$
$101$	620.493	0.611300	0.305650	+	0.952144i	$0.401126\pi$
$102$	977.618	0.949006
$103$	1473.24	1.40935	0.704673	−	0.709532i	$-0.251094\pi$
$103$	1473.24	1.40935	0.704673	+	0.709532i	$0.251094\pi$
$104$	32.0559	0.0302244
$105$	−1247.64	−1.15960
$106$	−520.708	−0.477129
$107$	−940.141	−0.849410	−0.424705	−	0.905332i	$-0.639622\pi$
$107$	−940.141	−0.849410	−0.424705	+	0.905332i	$0.639622\pi$
$108$	1965.61	1.75130
$109$	−636.264	−0.559111	−0.279555	−	0.960130i	$-0.590187\pi$
$109$	−636.264	−0.559111	−0.279555	+	0.960130i	$0.590187\pi$
$110$	−173.867	−0.150705
$111$	−4282.20	−3.66170
$112$	−394.289	−0.332650
$113$	832.451	0.693013	0.346506	−	0.938048i	$-0.387368\pi$
$113$	832.451	0.693013	0.346506	+	0.938048i	$0.387368\pi$
$114$	1606.29	1.31967
$115$	−115.000	−0.0932505
$116$	−1017.07	−0.814074
$117$	302.648	0.239144
$118$	706.261	0.550988
$119$	−1189.62	−0.916406
$120$	405.029	0.308116
$121$	−1028.70	−0.772879
$122$	−161.222	−0.119642
$123$	−1723.91	−1.26374
$124$	−882.783	−0.639325
$125$	125.000	0.0894427
$126$	−3722.59	−2.63202
$127$	1614.60	1.12813	0.564067	−	0.825729i	$-0.309236\pi$
$127$	1614.60	1.12813	0.564067	+	0.825729i	$0.309236\pi$
$128$	128.000	0.0883883
$129$	−2317.98	−1.58207
$130$	40.0699	0.0270335
$131$	−1974.56	−1.31693	−0.658464	−	0.752612i	$-0.728794\pi$
$131$	−1974.56	−1.31693	−0.658464	+	0.752612i	$0.728794\pi$
$132$	−704.211	−0.464346
$133$	−1954.62	−1.27434
$134$	−1640.02	−1.05729
$135$	2457.01	1.56641
$136$	386.192	0.243498
$137$	753.805	0.470087	0.235044	−	0.971985i	$-0.424477\pi$
$137$	753.805	0.470087	0.235044	+	0.971985i	$0.424477\pi$
$138$	−465.783	−0.287319
$139$	1014.10	0.618810	0.309405	−	0.950930i	$-0.399870\pi$
$139$	1014.10	0.618810	0.309405	+	0.950930i	$0.399870\pi$
$140$	−492.862	−0.297532
$141$	5873.80	3.50825
$142$	1229.69	0.726714
$143$	−69.6683	−0.0407410
$144$	1208.48	0.699352
$145$	−1271.34	−0.728130
$146$	1023.17	0.579989
$147$	2676.04	1.50147
$148$	−1691.62	−0.939527
$149$	−2771.80	−1.52399	−0.761995	−	0.647583i	$-0.775780\pi$
$149$	−2771.80	−1.52399	−0.761995	+	0.647583i	$0.775780\pi$
$150$	506.286	0.275587
$151$	3108.62	1.67534	0.837668	−	0.546180i	$-0.183918\pi$
$151$	3108.62	1.67534	0.837668	+	0.546180i	$0.183918\pi$
$152$	634.538	0.338604
$153$	3646.14	1.92662
$154$	856.924	0.448396
$155$	−1103.48	−0.571830
$156$	162.294	0.0832946
$157$	3712.87	1.88739	0.943693	−	0.330822i	$-0.107326\pi$
$157$	3712.87	1.88739	0.943693	+	0.330822i	$0.107326\pi$
$158$	320.928	0.161593
$159$	−2636.27	−1.31490
$160$	160.000	0.0790569
$161$	566.791	0.277450
$162$	5872.96	2.84829
$163$	915.791	0.440063	0.220032	−	0.975493i	$-0.429384\pi$
$163$	915.791	0.440063	0.220032	+	0.975493i	$0.429384\pi$
$164$	−681.003	−0.324252
$165$	−880.264	−0.415324
$166$	−65.1292	−0.0304518
$167$	1432.32	0.663688	0.331844	−	0.943334i	$-0.392329\pi$
$167$	1432.32	0.663688	0.331844	+	0.943334i	$0.392329\pi$
$168$	−1996.23	−0.916741
$169$	−2180.94	−0.992692
$170$	482.740	0.217791
$171$	5990.84	2.67913
$172$	−915.680	−0.405930
$173$	−3479.54	−1.52916	−0.764580	−	0.644529i	$-0.777054\pi$
$173$	−3479.54	−1.52916	−0.764580	+	0.644529i	$0.777054\pi$
$174$	−5149.28	−2.24348
$175$	−616.077	−0.266120
$176$	−278.187	−0.119143
$177$	3575.70	1.51845
$178$	−50.0751	−0.0210859
$179$	3642.71	1.52105	0.760527	−	0.649307i	$-0.224941\pi$
$179$	3642.71	1.52105	0.760527	+	0.649307i	$0.224941\pi$
$180$	1510.60	0.625520
$181$	2409.15	0.989342	0.494671	−	0.869080i	$-0.335289\pi$
$181$	2409.15	0.989342	0.494671	+	0.869080i	$0.335289\pi$
$182$	−197.489	−0.0804333
$183$	−816.241	−0.329717
$184$	−184.000	−0.0737210
$185$	−2114.52	−0.840338
$186$	−4469.41	−1.76190
$187$	−839.326	−0.328223
$188$	2320.35	0.900154
$189$	−12109.6	−4.66057
$190$	793.172	0.302857
$191$	−189.608	−0.0718299	−0.0359150	−	0.999355i	$-0.511435\pi$
$191$	−189.608	−0.0718299	−0.0359150	+	0.999355i	$0.511435\pi$
$192$	648.046	0.243587
$193$	−1855.45	−0.692012	−0.346006	−	0.938232i	$-0.612462\pi$
$193$	−1855.45	−0.692012	−0.346006	+	0.938232i	$0.612462\pi$
$194$	−499.597	−0.184891
$195$	202.868	0.0745009
$196$	1057.13	0.385250
$197$	2429.85	0.878779	0.439390	−	0.898297i	$-0.355195\pi$
$197$	2429.85	0.878779	0.439390	+	0.898297i	$0.355195\pi$
$198$	−2626.44	−0.942691
$199$	4333.49	1.54368	0.771842	−	0.635815i	$-0.219336\pi$
$199$	4333.49	1.54368	0.771842	+	0.635815i	$0.219336\pi$
$200$	200.000	0.0707107
$201$	−8303.20	−2.91374
$202$	1240.99	0.432255
$203$	6265.94	2.16642
$204$	1955.24	0.671048
$205$	−851.254	−0.290020
$206$	2946.48	0.996558
$207$	−1737.19	−0.583300
$208$	64.1118	0.0213719
$209$	−1379.07	−0.456421
$210$	−2495.29	−0.819958
$211$	−816.788	−0.266493	−0.133247	−	0.991083i	$-0.542540\pi$
$211$	−816.788	−0.266493	−0.133247	+	0.991083i	$0.542540\pi$
$212$	−1041.42	−0.337381
$213$	6225.75	2.00273
$214$	−1880.28	−0.600624
$215$	−1144.60	−0.363075
$216$	3931.21	1.23836
$217$	5438.63	1.70137
$218$	−1272.53	−0.395351
$219$	5180.18	1.59837
$220$	−347.734	−0.106565
$221$	193.433	0.0588767
$222$	−8564.41	−2.58921
$223$	−4513.80	−1.35546	−0.677728	−	0.735313i	$-0.737035\pi$
$223$	−4513.80	−1.35546	−0.677728	+	0.735313i	$0.737035\pi$
$224$	−788.579	−0.235219
$225$	1888.25	0.559482
$226$	1664.90	0.490034
$227$	2792.85	0.816599	0.408300	−	0.912848i	$-0.366122\pi$
$227$	2792.85	0.816599	0.408300	+	0.912848i	$0.366122\pi$
$228$	3212.57	0.933149
$229$	1404.50	0.405292	0.202646	−	0.979252i	$-0.435046\pi$
$229$	1404.50	0.405292	0.202646	+	0.979252i	$0.435046\pi$
$230$	−230.000	−0.0659380
$231$	4338.48	1.23572
$232$	−2034.14	−0.575637
$233$	1073.79	0.301916	0.150958	−	0.988540i	$-0.451764\pi$
$233$	1073.79	0.301916	0.150958	+	0.988540i	$0.451764\pi$
$234$	605.296	0.169100
$235$	2900.44	0.805122
$236$	1412.52	0.389607
$237$	1624.81	0.445328
$238$	−2379.24	−0.647997
$239$	−2573.18	−0.696423	−0.348212	−	0.937416i	$-0.613211\pi$
$239$	−2573.18	−0.696423	−0.348212	+	0.937416i	$0.613211\pi$
$240$	810.057	0.217871
$241$	−696.127	−0.186064	−0.0930321	−	0.995663i	$-0.529656\pi$
$241$	−696.127	−0.186064	−0.0930321	+	0.995663i	$0.529656\pi$
$242$	−2057.40	−0.546508
$243$	16466.1	4.34692
$244$	−322.443	−0.0845996
$245$	1321.41	0.344578
$246$	−3447.82	−0.893598
$247$	317.823	0.0818729
$248$	−1765.57	−0.452071
$249$	−329.740	−0.0839213
$250$	250.000	0.0632456
$251$	6467.81	1.62647	0.813236	−	0.581934i	$-0.197704\pi$
$251$	6467.81	1.62647	0.813236	+	0.581934i	$0.197704\pi$
$252$	−7445.18	−1.86112
$253$	399.894	0.0993721
$254$	3229.21	0.797711
$255$	2444.04	0.600204
$256$	256.000	0.0625000
$257$	5332.72	1.29434	0.647172	−	0.762344i	$-0.275952\pi$
$257$	5332.72	1.29434	0.647172	+	0.762344i	$0.275952\pi$
$258$	−4635.96	−1.11869
$259$	10421.7	2.50027
$260$	80.1398	0.0191156
$261$	−19204.8	−4.55460
$262$	−3949.11	−0.931209
$263$	−6872.85	−1.61140	−0.805699	−	0.592325i	$-0.798210\pi$
$263$	−6872.85	−1.61140	−0.805699	+	0.592325i	$0.798210\pi$
$264$	−1408.42	−0.328342
$265$	−1301.77	−0.301763
$266$	−3909.24	−0.901094
$267$	−253.523	−0.0581099
$268$	−3280.04	−0.747614
$269$	−1926.13	−0.436572	−0.218286	−	0.975885i	$-0.570047\pi$
$269$	−1926.13	−0.436572	−0.218286	+	0.975885i	$0.570047\pi$
$270$	4914.02	1.10762
$271$	−3653.06	−0.818847	−0.409423	−	0.912344i	$-0.634270\pi$
$271$	−3653.06	−0.818847	−0.409423	+	0.912344i	$0.634270\pi$
$272$	772.384	0.172179
$273$	−999.859	−0.221664
$274$	1507.61	0.332402
$275$	−434.668	−0.0953144
$276$	−931.566	−0.203165
$277$	−1047.37	−0.227185	−0.113592	−	0.993527i	$-0.536236\pi$
$277$	−1047.37	−0.227185	−0.113592	+	0.993527i	$0.536236\pi$
$278$	2028.19	0.437565
$279$	−16669.2	−3.57691
$280$	−985.723	−0.210387
$281$	−2758.90	−0.585701	−0.292851	−	0.956158i	$-0.594604\pi$
$281$	−2758.90	−0.585701	−0.292851	+	0.956158i	$0.594604\pi$
$282$	11747.6	2.48071
$283$	3355.58	0.704837	0.352418	−	0.935843i	$-0.385359\pi$
$283$	3355.58	0.704837	0.352418	+	0.935843i	$0.385359\pi$
$284$	2459.38	0.513864
$285$	4015.72	0.834634
$286$	−139.337	−0.0288082
$287$	4195.50	0.862902
$288$	2416.96	0.494517
$289$	−2582.62	−0.525670
$290$	−2542.67	−0.514866
$291$	−2529.39	−0.509537
$292$	2046.35	0.410114
$293$	419.625	0.0836681	0.0418341	−	0.999125i	$-0.486680\pi$
$293$	419.625	0.0836681	0.0418341	+	0.999125i	$0.486680\pi$
$294$	5352.08	1.06170
$295$	1765.65	0.348475
$296$	−3383.23	−0.664346
$297$	−8543.85	−1.66924
$298$	−5543.59	−1.07762
$299$	−92.1607	−0.0178254
$300$	1012.57	0.194869
$301$	5641.30	1.08026
$302$	6217.24	1.18464
$303$	6282.93	1.19124
$304$	1269.08	0.239429
$305$	−403.054	−0.0756682
$306$	7292.28	1.36233
$307$	−4133.41	−0.768425	−0.384212	−	0.923245i	$-0.625527\pi$
$307$	−4133.41	−0.768425	−0.384212	+	0.923245i	$0.625527\pi$
$308$	1713.85	0.317064
$309$	14917.6	2.74639
$310$	−2206.96	−0.404345
$311$	−6991.03	−1.27468	−0.637339	−	0.770584i	$-0.719965\pi$
$311$	−6991.03	−1.27468	−0.637339	+	0.770584i	$0.719965\pi$
$312$	324.589	0.0588982
$313$	9380.53	1.69399	0.846996	−	0.531600i	$-0.178409\pi$
$313$	9380.53	1.69399	0.846996	+	0.531600i	$0.178409\pi$
$314$	7425.75	1.33458
$315$	−9306.47	−1.66464
$316$	641.855	0.114263
$317$	−7995.35	−1.41660	−0.708302	−	0.705910i	$-0.750538\pi$
$317$	−7995.35	−1.41660	−0.708302	+	0.705910i	$0.750538\pi$
$318$	−5272.54	−0.929778
$319$	4420.87	0.775929
$320$	320.000	0.0559017
$321$	−9519.60	−1.65524
$322$	1133.58	0.196186
$323$	3828.96	0.659595
$324$	11745.9	2.01405
$325$	100.175	0.0170975
$326$	1831.58	0.311172
$327$	−6442.63	−1.08954
$328$	−1362.01	−0.229281
$329$	−14295.1	−2.39549
$330$	−1760.53	−0.293678
$331$	−4798.86	−0.796886	−0.398443	−	0.917193i	$-0.630449\pi$
$331$	−4798.86	−0.796886	−0.398443	+	0.917193i	$0.630449\pi$
$332$	−130.258	−0.0215327
$333$	−31942.0	−5.25648
$334$	2864.63	0.469298
$335$	−4100.06	−0.668687
$336$	−3992.46	−0.648234
$337$	6895.51	1.11461	0.557303	−	0.830309i	$-0.311836\pi$
$337$	6895.51	1.11461	0.557303	+	0.830309i	$0.311836\pi$
$338$	−4361.89	−0.701939
$339$	8429.16	1.35047
$340$	965.480	0.154002
$341$	3837.17	0.609368
$342$	11981.7	1.89443
$343$	1939.86	0.305372
$344$	−1831.36	−0.287036
$345$	−1164.46	−0.181717
$346$	−6959.08	−1.08128
$347$	−8744.17	−1.35277	−0.676386	−	0.736548i	$-0.736455\pi$
$347$	−8744.17	−1.35277	−0.676386	+	0.736548i	$0.736455\pi$
$348$	−10298.6	−1.58638
$349$	−6387.08	−0.979635	−0.489818	−	0.871825i	$-0.662937\pi$
$349$	−6387.08	−0.979635	−0.489818	+	0.871825i	$0.662937\pi$
$350$	−1232.15	−0.188175
$351$	1969.04	0.299429
$352$	−556.375	−0.0842468
$353$	−589.384	−0.0888661	−0.0444331	−	0.999012i	$-0.514148\pi$
$353$	−589.384	−0.0888661	−0.0444331	+	0.999012i	$0.514148\pi$
$354$	7151.39	1.07371
$355$	3074.23	0.459614
$356$	−100.150	−0.0149100
$357$	−12045.8	−1.78580
$358$	7285.41	1.07555
$359$	7214.13	1.06058	0.530289	−	0.847817i	$-0.322083\pi$
$359$	7214.13	1.06058	0.530289	+	0.847817i	$0.322083\pi$
$360$	3021.20	0.442309
$361$	−567.774	−0.0827780
$362$	4818.30	0.699570
$363$	−10416.3	−1.50611
$364$	−394.978	−0.0568749
$365$	2557.93	0.366817
$366$	−1632.48	−0.233145
$367$	12356.4	1.75750	0.878748	−	0.477286i	$-0.158379\pi$
$367$	12356.4	1.75750	0.878748	+	0.477286i	$0.158379\pi$
$368$	−368.000	−0.0521286
$369$	−12859.1	−1.81413
$370$	−4229.04	−0.594209
$371$	6415.92	0.897839
$372$	−8938.81	−1.24585
$373$	7145.98	0.991969	0.495985	−	0.868331i	$-0.334807\pi$
$373$	7145.98	0.991969	0.495985	+	0.868331i	$0.334807\pi$
$374$	−1678.65	−0.232088
$375$	1265.71	0.174297
$376$	4640.70	0.636505
$377$	−1018.85	−0.139186
$378$	−24219.3	−3.29552
$379$	2170.69	0.294197	0.147099	−	0.989122i	$-0.453007\pi$
$379$	2170.69	0.294197	0.147099	+	0.989122i	$0.453007\pi$
$380$	1586.34	0.214152
$381$	16349.0	2.19839
$382$	−379.215	−0.0507914
$383$	−7967.21	−1.06294	−0.531469	−	0.847078i	$-0.678360\pi$
$383$	−7967.21	−1.06294	−0.531469	+	0.847078i	$0.678360\pi$
$384$	1296.09	0.172242
$385$	2142.31	0.283590
$386$	−3710.90	−0.489326
$387$	−17290.3	−2.27111
$388$	−999.193	−0.130738
$389$	−568.951	−0.0741567	−0.0370783	−	0.999312i	$-0.511805\pi$
$389$	−568.951	−0.0741567	−0.0370783	+	0.999312i	$0.511805\pi$
$390$	405.736	0.0526801
$391$	−1110.30	−0.143607
$392$	2114.25	0.272413
$393$	−19993.8	−2.56629
$394$	4859.70	0.621391
$395$	802.319	0.102200
$396$	−5252.88	−0.666583
$397$	8564.88	1.08277	0.541384	−	0.840775i	$-0.317900\pi$
$397$	8564.88	1.08277	0.541384	+	0.840775i	$0.317900\pi$
$398$	8666.98	1.09155
$399$	−19791.9	−2.48330
$400$	400.000	0.0500000
$401$	−12455.6	−1.55113	−0.775563	−	0.631270i	$-0.782534\pi$
$401$	−12455.6	−1.55113	−0.775563	+	0.631270i	$0.782534\pi$
$402$	−16606.4	−2.06033
$403$	−884.325	−0.109309
$404$	2481.97	0.305650
$405$	14682.4	1.80142
$406$	12531.9	1.53189
$407$	7352.91	0.895504
$408$	3910.47	0.474503
$409$	11838.9	1.43129	0.715645	−	0.698465i	$-0.246133\pi$
$409$	11838.9	1.43129	0.715645	+	0.698465i	$0.246133\pi$
$410$	−1702.51	−0.205075
$411$	7632.82	0.916056
$412$	5892.96	0.704673
$413$	−8702.22	−1.03682
$414$	−3474.38	−0.412456
$415$	−162.823	−0.0192594
$416$	128.224	0.0151122
$417$	10268.5	1.20587
$418$	−2758.13	−0.322738
$419$	−1531.77	−0.178596	−0.0892981	−	0.996005i	$-0.528462\pi$
$419$	−1531.77	−0.178596	−0.0892981	+	0.996005i	$0.528462\pi$
$420$	−4990.58	−0.579798
$421$	−9985.06	−1.15592	−0.577959	−	0.816066i	$-0.696151\pi$
$421$	−9985.06	−1.15592	−0.577959	+	0.816066i	$0.696151\pi$
$422$	−1633.58	−0.188439
$423$	43814.0	5.03620
$424$	−2082.83	−0.238564
$425$	1206.85	0.137743
$426$	12451.5	1.41614
$427$	1986.50	0.225137
$428$	−3760.56	−0.424705
$429$	−705.441	−0.0793917
$430$	−2289.20	−0.256733
$431$	−13786.7	−1.54079	−0.770396	−	0.637566i	$-0.779941\pi$
$431$	−13786.7	−1.54079	−0.770396	+	0.637566i	$0.779941\pi$
$432$	7862.42	0.875651
$433$	−2621.92	−0.290996	−0.145498	−	0.989359i	$-0.546478\pi$
$433$	−2621.92	−0.290996	−0.145498	+	0.989359i	$0.546478\pi$
$434$	10877.3	1.20305
$435$	−12873.2	−1.41890
$436$	−2545.06	−0.279555
$437$	−1824.30	−0.199698
$438$	10360.4	1.13022
$439$	12062.7	1.31143	0.655717	−	0.755007i	$-0.272367\pi$
$439$	12062.7	1.31143	0.655717	+	0.755007i	$0.272367\pi$
$440$	−695.468	−0.0753526
$441$	19961.2	2.15541
$442$	386.867	0.0416321
$443$	3659.26	0.392453	0.196227	−	0.980559i	$-0.437131\pi$
$443$	3659.26	0.392453	0.196227	+	0.980559i	$0.437131\pi$
$444$	−17128.8	−1.83085
$445$	−125.188	−0.0133359
$446$	−9027.60	−0.958452
$447$	−28066.4	−2.96979
$448$	−1577.16	−0.166325
$449$	−10529.6	−1.10674	−0.553368	−	0.832937i	$-0.686658\pi$
$449$	−10529.6	−1.10674	−0.553368	+	0.832937i	$0.686658\pi$
$450$	3776.50	0.395613
$451$	2960.10	0.309059
$452$	3329.81	0.346506
$453$	31477.0	3.26472
$454$	5585.70	0.577423
$455$	−493.723	−0.0508705
$456$	6425.15	0.659836
$457$	6443.23	0.659522	0.329761	−	0.944064i	$-0.393032\pi$
$457$	6443.23	0.659522	0.329761	+	0.944064i	$0.393032\pi$
$458$	2809.00	0.286585
$459$	23721.9	2.41230
$460$	−460.000	−0.0466252
$461$	−3263.86	−0.329747	−0.164873	−	0.986315i	$-0.552722\pi$
$461$	−3263.86	−0.329747	−0.164873	+	0.986315i	$0.552722\pi$
$462$	8676.97	0.873786
$463$	9518.12	0.955388	0.477694	−	0.878526i	$-0.341473\pi$
$463$	9518.12	0.955388	0.477694	+	0.878526i	$0.341473\pi$
$464$	−4068.28	−0.407037
$465$	−11173.5	−1.11432
$466$	2147.59	0.213487
$467$	19092.6	1.89187	0.945934	−	0.324360i	$-0.105149\pi$
$467$	19092.6	1.89187	0.945934	+	0.324360i	$0.105149\pi$
$468$	1210.59	0.119572
$469$	20207.6	1.98955
$470$	5800.87	0.569307
$471$	37595.5	3.67794
$472$	2825.04	0.275494
$473$	3980.17	0.386910
$474$	3249.62	0.314895
$475$	1982.93	0.191543
$476$	−4758.48	−0.458203
$477$	−19664.6	−1.88758
$478$	−5146.36	−0.492446
$479$	−6324.81	−0.603315	−0.301658	−	0.953416i	$-0.597540\pi$
$479$	−6324.81	−0.603315	−0.301658	+	0.953416i	$0.597540\pi$
$480$	1620.11	0.154058
$481$	−1694.57	−0.160636
$482$	−1392.25	−0.131567
$483$	5739.16	0.540664
$484$	−4114.81	−0.386440
$485$	−1248.99	−0.116936
$486$	32932.2	3.07373
$487$	−7873.07	−0.732573	−0.366286	−	0.930502i	$-0.619371\pi$
$487$	−7873.07	−0.732573	−0.366286	+	0.930502i	$0.619371\pi$
$488$	−644.886	−0.0598209
$489$	9273.04	0.857549
$490$	2642.82	0.243654
$491$	−3556.82	−0.326918	−0.163459	−	0.986550i	$-0.552265\pi$
$491$	−3556.82	−0.326918	−0.163459	+	0.986550i	$0.552265\pi$
$492$	−6895.64	−0.631869
$493$	−12274.5	−1.12133
$494$	635.646	0.0578929
$495$	−6566.10	−0.596210
$496$	−3531.13	−0.319662
$497$	−15151.7	−1.36750
$498$	−659.479	−0.0593413
$499$	−1933.37	−0.173446	−0.0867231	−	0.996232i	$-0.527640\pi$
$499$	−1933.37	−0.173446	−0.0867231	+	0.996232i	$0.527640\pi$
$500$	500.000	0.0447214
$501$	14503.2	1.29332
$502$	12935.6	1.15009
$503$	2114.36	0.187425	0.0937123	−	0.995599i	$-0.470127\pi$
$503$	2114.36	0.187425	0.0937123	+	0.995599i	$0.470127\pi$
$504$	−14890.4	−1.31601
$505$	3102.46	0.273382
$506$	799.789	0.0702667
$507$	−22083.6	−1.93445
$508$	6458.42	0.564067
$509$	−316.452	−0.0275570	−0.0137785	−	0.999905i	$-0.504386\pi$
$509$	−316.452	−0.0275570	−0.0137785	+	0.999905i	$0.504386\pi$
$510$	4888.09	0.424408
$511$	−12607.1	−1.09140
$512$	512.000	0.0441942
$513$	38976.6	3.35450
$514$	10665.4	0.915239
$515$	7366.20	0.630279
$516$	−9271.92	−0.791034
$517$	−10085.8	−0.857976
$518$	20843.3	1.76796
$519$	−35232.8	−2.97987
$520$	160.280	0.0135168
$521$	−309.041	−0.0259872	−0.0129936	−	0.999916i	$-0.504136\pi$
$521$	−309.041	−0.0259872	−0.0129936	+	0.999916i	$0.504136\pi$
$522$	−38409.7	−3.22059
$523$	−5892.46	−0.492656	−0.246328	−	0.969186i	$-0.579224\pi$
$523$	−5892.46	−0.492656	−0.246328	+	0.969186i	$0.579224\pi$
$524$	−7898.22	−0.658464
$525$	−6238.22	−0.518587
$526$	−13745.7	−1.13943
$527$	−10653.9	−0.880626
$528$	−2816.84	−0.232173
$529$	529.000	0.0434783
$530$	−2603.54	−0.213378
$531$	26672.0	2.17978
$532$	−7818.49	−0.637170
$533$	−682.193	−0.0554391
$534$	−507.046	−0.0410899
$535$	−4700.71	−0.379868
$536$	−6560.09	−0.528643
$537$	36885.0	2.96407
$538$	−3852.25	−0.308703
$539$	−4594.99	−0.367199
$540$	9828.03	0.783206
$541$	1560.55	0.124017	0.0620085	−	0.998076i	$-0.480249\pi$
$541$	1560.55	0.124017	0.0620085	+	0.998076i	$0.480249\pi$
$542$	−7306.12	−0.579012
$543$	24394.4	1.92792
$544$	1544.77	0.121749
$545$	−3181.32	−0.250042
$546$	−1999.72	−0.156740
$547$	17756.3	1.38795	0.693973	−	0.720001i	$-0.255859\pi$
$547$	17756.3	1.38795	0.693973	+	0.720001i	$0.255859\pi$
$548$	3015.22	0.235044
$549$	−6088.54	−0.473319
$550$	−869.335	−0.0673974
$551$	−20167.8	−1.55930
$552$	−1863.13	−0.143660
$553$	−3954.32	−0.304078
$554$	−2094.73	−0.160644
$555$	−21411.0	−1.63756
$556$	4056.39	0.309405
$557$	1212.77	0.0922559	0.0461280	−	0.998936i	$-0.485312\pi$
$557$	1212.77	0.0922559	0.0461280	+	0.998936i	$0.485312\pi$
$558$	−33338.3	−2.52926
$559$	−917.280	−0.0694040
$560$	−1971.45	−0.148766
$561$	−8498.78	−0.639605
$562$	−5517.80	−0.414153
$563$	12558.2	0.940078	0.470039	−	0.882646i	$-0.344240\pi$
$563$	12558.2	0.940078	0.470039	+	0.882646i	$0.344240\pi$
$564$	23495.2	1.75412
$565$	4162.26	0.309925
$566$	6711.17	0.498395
$567$	−72363.9	−5.35978
$568$	4918.76	0.363357
$569$	9776.72	0.720319	0.360159	−	0.932891i	$-0.382722\pi$
$569$	9776.72	0.720319	0.360159	+	0.932891i	$0.382722\pi$
$570$	8031.44	0.590175
$571$	−18733.9	−1.37301	−0.686505	−	0.727125i	$-0.740856\pi$
$571$	−18733.9	−1.37301	−0.686505	+	0.727125i	$0.740856\pi$
$572$	−278.673	−0.0203705
$573$	−1919.91	−0.139975
$574$	8391.01	0.610164
$575$	−575.000	−0.0417029
$576$	4833.92	0.349676
$577$	5113.58	0.368944	0.184472	−	0.982838i	$-0.440942\pi$
$577$	5113.58	0.368944	0.184472	+	0.982838i	$0.440942\pi$
$578$	−5165.24	−0.371705
$579$	−18787.8	−1.34852
$580$	−5085.35	−0.364065
$581$	802.492	0.0573029
$582$	−5058.77	−0.360297
$583$	4526.70	0.321572
$584$	4092.69	0.289995
$585$	1513.24	0.106948
$586$	839.250	0.0591623
$587$	−5379.95	−0.378287	−0.189143	−	0.981949i	$-0.560571\pi$
$587$	−5379.95	−0.378287	−0.189143	+	0.981949i	$0.560571\pi$
$588$	10704.2	0.750735
$589$	−17505.0	−1.22458
$590$	3531.30	0.246409
$591$	24603.9	1.71247
$592$	−6766.46	−0.469763
$593$	−15060.3	−1.04292	−0.521461	−	0.853275i	$-0.674613\pi$
$593$	−15060.3	−1.04292	−0.521461	+	0.853275i	$0.674613\pi$
$594$	−17087.7	−1.18033
$595$	−5948.10	−0.409829
$596$	−11087.2	−0.761995
$597$	43879.7	3.00817
$598$	−184.321	−0.0126045
$599$	−3772.04	−0.257298	−0.128649	−	0.991690i	$-0.541064\pi$
$599$	−3772.04	−0.257298	−0.128649	+	0.991690i	$0.541064\pi$
$600$	2025.14	0.137794
$601$	−14663.9	−0.995261	−0.497631	−	0.867389i	$-0.665796\pi$
$601$	−14663.9	−0.995261	−0.497631	+	0.867389i	$0.665796\pi$
$602$	11282.6	0.763861
$603$	−61935.5	−4.18277
$604$	12434.5	0.837668
$605$	−5143.51	−0.345642
$606$	12565.9	0.842332
$607$	−24514.5	−1.63923	−0.819614	−	0.572915i	$-0.805812\pi$
$607$	−24514.5	−1.63923	−0.819614	+	0.572915i	$0.805812\pi$
$608$	2538.15	0.169302
$609$	63447.1	4.22168
$610$	−806.108	−0.0535055
$611$	2324.40	0.153904
$612$	14584.6	0.963310
$613$	14451.2	0.952167	0.476084	−	0.879400i	$-0.342056\pi$
$613$	14451.2	0.952167	0.476084	+	0.879400i	$0.342056\pi$
$614$	−8266.83	−0.543358
$615$	−8619.55	−0.565161
$616$	3427.70	0.224198
$617$	3292.19	0.214811	0.107406	−	0.994215i	$-0.465746\pi$
$617$	3292.19	0.214811	0.107406	+	0.994215i	$0.465746\pi$
$618$	29835.2	1.94199
$619$	−12595.5	−0.817858	−0.408929	−	0.912566i	$-0.634098\pi$
$619$	−12595.5	−0.817858	−0.408929	+	0.912566i	$0.634098\pi$
$620$	−4413.92	−0.285915
$621$	−11302.2	−0.730343
$622$	−13982.1	−0.901333
$623$	617.002	0.0396785
$624$	649.178	0.0416473
$625$	625.000	0.0400000
$626$	18761.1	1.19783
$627$	−13964.0	−0.889425
$628$	14851.5	0.943693
$629$	−20415.3	−1.29413
$630$	−18612.9	−1.17707
$631$	19889.3	1.25480	0.627401	−	0.778697i	$-0.284119\pi$
$631$	19889.3	1.25480	0.627401	+	0.778697i	$0.284119\pi$
$632$	1283.71	0.0807963
$633$	−8270.56	−0.519313
$634$	−15990.7	−1.00169
$635$	8073.02	0.504517
$636$	−10545.1	−0.657452
$637$	1058.97	0.0658682
$638$	8841.75	0.548665
$639$	46439.3	2.87498
$640$	640.000	0.0395285
$641$	−19276.0	−1.18776	−0.593880	−	0.804553i	$-0.702405\pi$
$641$	−19276.0	−1.18776	−0.593880	+	0.804553i	$0.702405\pi$
$642$	−19039.2	−1.17043
$643$	−10219.2	−0.626758	−0.313379	−	0.949628i	$-0.601461\pi$
$643$	−10219.2	−0.626758	−0.313379	+	0.949628i	$0.601461\pi$
$644$	2267.16	0.138725
$645$	−11589.9	−0.707522
$646$	7657.93	0.466404
$647$	20818.4	1.26500	0.632500	−	0.774560i	$-0.282029\pi$
$647$	20818.4	1.26500	0.632500	+	0.774560i	$0.282029\pi$
$648$	23491.8	1.42415
$649$	−6139.77	−0.371352
$650$	200.349	0.0120898
$651$	55070.0	3.31546
$652$	3663.17	0.220032
$653$	−15135.3	−0.907031	−0.453516	−	0.891248i	$-0.649830\pi$
$653$	−15135.3	−0.907031	−0.453516	+	0.891248i	$0.649830\pi$
$654$	−12885.3	−0.770418
$655$	−9872.78	−0.588949
$656$	−2724.01	−0.162126
$657$	38640.2	2.29451
$658$	−28590.3	−1.69387
$659$	−13207.9	−0.780737	−0.390369	−	0.920659i	$-0.627652\pi$
$659$	−13207.9	−0.780737	−0.390369	+	0.920659i	$0.627652\pi$
$660$	−3521.06	−0.207662
$661$	6671.34	0.392564	0.196282	−	0.980547i	$-0.437113\pi$
$661$	6671.34	0.392564	0.196282	+	0.980547i	$0.437113\pi$
$662$	−9597.72	−0.563484
$663$	1958.65	0.114733
$664$	−260.517	−0.0152259
$665$	−9773.11	−0.569902
$666$	−63883.9	−3.71689
$667$	5848.15	0.339492
$668$	5729.26	0.331844
$669$	−45705.5	−2.64137
$670$	−8200.11	−0.472833
$671$	1401.56	0.0806355
$672$	−7984.92	−0.458371
$673$	−9534.41	−0.546099	−0.273049	−	0.962000i	$-0.588032\pi$
$673$	−9534.41	−0.546099	−0.273049	+	0.962000i	$0.588032\pi$
$674$	13791.0	0.788146
$675$	12285.0	0.700520
$676$	−8723.78	−0.496346
$677$	17748.4	1.00757	0.503787	−	0.863828i	$-0.331940\pi$
$677$	17748.4	1.00757	0.503787	+	0.863828i	$0.331940\pi$
$678$	16858.3	0.954927
$679$	6155.80	0.347920
$680$	1930.96	0.108896
$681$	28279.6	1.59130
$682$	7674.35	0.430888
$683$	9583.57	0.536904	0.268452	−	0.963293i	$-0.413488\pi$
$683$	9583.57	0.536904	0.268452	+	0.963293i	$0.413488\pi$
$684$	23963.3	1.33956
$685$	3769.03	0.210229
$686$	3879.73	0.215931
$687$	14221.5	0.789790
$688$	−3662.72	−0.202965
$689$	−1043.24	−0.0576837
$690$	−2328.91	−0.128493
$691$	9410.74	0.518092	0.259046	−	0.965865i	$-0.416592\pi$
$691$	9410.74	0.518092	0.259046	+	0.965865i	$0.416592\pi$
$692$	−13918.2	−0.764580
$693$	32361.8	1.77391
$694$	−17488.3	−0.956554
$695$	5070.48	0.276740
$696$	−20597.1	−1.12174
$697$	−8218.69	−0.446636
$698$	−12774.2	−0.692707
$699$	10872.9	0.588343
$700$	−2464.31	−0.133060
$701$	−19517.9	−1.05161	−0.525806	−	0.850605i	$-0.676236\pi$
$701$	−19517.9	−1.05161	−0.525806	+	0.850605i	$0.676236\pi$
$702$	3938.08	0.211728
$703$	−33543.6	−1.79960
$704$	−1112.75	−0.0595715
$705$	29369.0	1.56894
$706$	−1178.77	−0.0628378
$707$	−15290.9	−0.813397
$708$	14302.8	0.759225
$709$	−28430.7	−1.50598	−0.752990	−	0.658033i	$-0.771389\pi$
$709$	−28430.7	−1.50598	−0.752990	+	0.658033i	$0.771389\pi$
$710$	6148.45	0.324996
$711$	12119.8	0.639282
$712$	−200.300	−0.0105429
$713$	5076.00	0.266617
$714$	−24091.5	−1.26275
$715$	−348.342	−0.0182199
$716$	14570.8	0.760527
$717$	−26055.3	−1.35712
$718$	14428.3	0.749942
$719$	18716.0	0.970779	0.485390	−	0.874298i	$-0.338678\pi$
$719$	18716.0	0.970779	0.485390	+	0.874298i	$0.338678\pi$
$720$	6042.41	0.312760
$721$	−36305.2	−1.87528
$722$	−1135.55	−0.0585329
$723$	−7048.78	−0.362582
$724$	9636.61	0.494671
$725$	−6356.69	−0.325630
$726$	−20832.7	−1.06498
$727$	18419.5	0.939670	0.469835	−	0.882754i	$-0.344313\pi$
$727$	18419.5	0.939670	0.469835	+	0.882754i	$0.344313\pi$
$728$	−789.956	−0.0402167
$729$	87446.1	4.44272
$730$	5115.86	0.259379
$731$	−11050.9	−0.559141
$732$	−3264.97	−0.164859
$733$	−21548.4	−1.08582	−0.542912	−	0.839790i	$-0.682678\pi$
$733$	−21548.4	−1.08582	−0.542912	+	0.839790i	$0.682678\pi$
$734$	24712.9	1.24274
$735$	13380.2	0.671478
$736$	−736.000	−0.0368605
$737$	14257.3	0.712584
$738$	−25718.1	−1.28279
$739$	12066.4	0.600636	0.300318	−	0.953839i	$-0.402907\pi$
$739$	12066.4	0.600636	0.300318	+	0.953839i	$0.402907\pi$
$740$	−8458.08	−0.420169
$741$	3218.19	0.159545
$742$	12831.8	0.634868
$743$	−21951.0	−1.08385	−0.541926	−	0.840426i	$-0.682305\pi$
$743$	−21951.0	−1.08385	−0.541926	+	0.840426i	$0.682305\pi$
$744$	−17877.6	−0.880948
$745$	−13859.0	−0.681549
$746$	14292.0	0.701428
$747$	−2459.61	−0.120472
$748$	−3357.31	−0.164111
$749$	23168.0	1.13023
$750$	2531.43	0.123246
$751$	−3112.43	−0.151230	−0.0756152	−	0.997137i	$-0.524092\pi$
$751$	−3112.43	−0.151230	−0.0756152	+	0.997137i	$0.524092\pi$
$752$	9281.40	0.450077
$753$	65491.2	3.16950
$754$	−2037.69	−0.0984197
$755$	15543.1	0.749233
$756$	−48438.6	−2.33028
$757$	−7684.64	−0.368960	−0.184480	−	0.982836i	$-0.559060\pi$
$757$	−7684.64	−0.368960	−0.184480	+	0.982836i	$0.559060\pi$
$758$	4341.38	0.208029
$759$	4049.21	0.193646
$760$	3172.69	0.151428
$761$	−36484.6	−1.73793	−0.868965	−	0.494874i	$-0.835214\pi$
$761$	−36484.6	−1.73793	−0.868965	+	0.494874i	$0.835214\pi$
$762$	32698.0	1.55450
$763$	15679.5	0.743954
$764$	−758.430	−0.0359150
$765$	18230.7	0.861611
$766$	−15934.4	−0.751611
$767$	1414.99	0.0666132
$768$	2592.18	0.121793
$769$	2004.39	0.0939925	0.0469962	−	0.998895i	$-0.485035\pi$
$769$	2004.39	0.0939925	0.0469962	+	0.998895i	$0.485035\pi$
$770$	4284.62	0.200529
$771$	53997.6	2.52228
$772$	−7421.81	−0.346006
$773$	7716.17	0.359031	0.179516	−	0.983755i	$-0.442547\pi$
$773$	7716.17	0.359031	0.179516	+	0.983755i	$0.442547\pi$
$774$	−34580.7	−1.60591
$775$	−5517.40	−0.255730
$776$	−1998.39	−0.0924457
$777$	105527.	4.87226
$778$	−1137.90	−0.0524367
$779$	−13503.8	−0.621084
$780$	811.472	0.0372505
$781$	−10690.1	−0.489786
$782$	−2220.61	−0.101546
$783$	−124947.	−5.70275
$784$	4228.51	0.192625
$785$	18564.4	0.844065
$786$	−39987.6	−1.81464
$787$	−57.0149	−0.00258241	−0.00129121	−	0.999999i	$-0.500411\pi$
$787$	−57.0149	−0.00258241	−0.00129121	+	0.999999i	$0.500411\pi$
$788$	9719.39	0.439390
$789$	−69592.5	−3.14012
$790$	1604.64	0.0722664
$791$	−20514.2	−0.922124
$792$	−10505.8	−0.471346
$793$	−323.006	−0.0144644
$794$	17129.8	0.765633
$795$	−13181.3	−0.588043
$796$	17334.0	0.771842
$797$	−15184.7	−0.674870	−0.337435	−	0.941349i	$-0.609559\pi$
$797$	−15184.7	−0.674870	−0.337435	+	0.941349i	$0.609559\pi$
$798$	−39583.9	−1.75596
$799$	28003.2	1.23990
$800$	800.000	0.0353553
$801$	−1891.09	−0.0834186
$802$	−24911.1	−1.09681
$803$	−8894.80	−0.390898
$804$	−33212.8	−1.45687
$805$	2833.95	0.124079
$806$	−1768.65	−0.0772929
$807$	−19503.4	−0.850746
$808$	4963.94	0.216127
$809$	−30286.4	−1.31621	−0.658105	−	0.752926i	$-0.728642\pi$
$809$	−30286.4	−1.31621	−0.658105	+	0.752926i	$0.728642\pi$
$810$	29364.8	1.27379
$811$	−43936.2	−1.90235	−0.951176	−	0.308650i	$-0.900123\pi$
$811$	−43936.2	−1.90235	−0.951176	+	0.308650i	$0.900123\pi$
$812$	25063.7	1.08321
$813$	−36989.8	−1.59568
$814$	14705.8	0.633217
$815$	4578.96	0.196802
$816$	7820.94	0.335524
$817$	−18157.3	−0.777532
$818$	23677.9	1.01207
$819$	−7458.18	−0.318205
$820$	−3405.02	−0.145010
$821$	−5245.69	−0.222991	−0.111496	−	0.993765i	$-0.535564\pi$
$821$	−5245.69	−0.222991	−0.111496	+	0.993765i	$0.535564\pi$
$822$	15265.6	0.647750
$823$	10678.0	0.452260	0.226130	−	0.974097i	$-0.427393\pi$
$823$	10678.0	0.452260	0.226130	+	0.974097i	$0.427393\pi$
$824$	11785.9	0.498279
$825$	−4401.32	−0.185739
$826$	−17404.4	−0.733145
$827$	3393.69	0.142697	0.0713484	−	0.997451i	$-0.477270\pi$
$827$	3393.69	0.142697	0.0713484	+	0.997451i	$0.477270\pi$
$828$	−6948.77	−0.291650
$829$	9601.74	0.402270	0.201135	−	0.979564i	$-0.435537\pi$
$829$	9601.74	0.402270	0.201135	+	0.979564i	$0.435537\pi$
$830$	−325.646	−0.0136185
$831$	−10605.3	−0.442713
$832$	256.447	0.0106859
$833$	12757.9	0.530656
$834$	20536.9	0.852680
$835$	7161.58	0.296810
$836$	−5516.26	−0.228210
$837$	−108450.	−4.47860
$838$	−3063.54	−0.126287
$839$	11992.8	0.493489	0.246744	−	0.969081i	$-0.420639\pi$
$839$	11992.8	0.493489	0.246744	+	0.969081i	$0.420639\pi$
$840$	−9981.15	−0.409979
$841$	40263.0	1.65087
$842$	−19970.1	−0.817358
$843$	−27935.8	−1.14135
$844$	−3267.15	−0.133247
$845$	−10904.7	−0.443945
$846$	87628.1	3.56113
$847$	25350.4	1.02839
$848$	−4165.66	−0.168690
$849$	33977.7	1.37351
$850$	2413.70	0.0973991
$851$	9726.79	0.391810
$852$	24903.0	1.00136
$853$	−15441.5	−0.619821	−0.309911	−	0.950766i	$-0.600299\pi$
$853$	−15441.5	−0.619821	−0.309911	+	0.950766i	$0.600299\pi$
$854$	3973.00	0.159196
$855$	29954.2	1.19814
$856$	−7521.13	−0.300312
$857$	−44572.4	−1.77662	−0.888310	−	0.459244i	$-0.848120\pi$
$857$	−44572.4	−1.77662	−0.888310	+	0.459244i	$0.848120\pi$
$858$	−1410.88	−0.0561384
$859$	2519.56	0.100077	0.0500386	−	0.998747i	$-0.484066\pi$
$859$	2519.56	0.100077	0.0500386	+	0.998747i	$0.484066\pi$
$860$	−4578.40	−0.181537
$861$	42482.5	1.68153
$862$	−27573.4	−1.08950
$863$	28980.1	1.14310	0.571548	−	0.820568i	$-0.306343\pi$
$863$	28980.1	1.14310	0.571548	+	0.820568i	$0.306343\pi$
$864$	15724.8	0.619178
$865$	−17397.7	−0.683861
$866$	−5243.83	−0.205765
$867$	−26150.9	−1.02437
$868$	21754.5	0.850687
$869$	−2789.94	−0.108909
$870$	−25746.4	−1.00332
$871$	−3285.77	−0.127823
$872$	−5090.11	−0.197675
$873$	−18867.3	−0.731455
$874$	−3648.59	−0.141208
$875$	−3080.39	−0.119013
$876$	20720.7	0.799187
$877$	−7955.28	−0.306307	−0.153153	−	0.988202i	$-0.548943\pi$
$877$	−7955.28	−0.306307	−0.153153	+	0.988202i	$0.548943\pi$
$878$	24125.3	0.927323
$879$	4249.00	0.163044
$880$	−1390.94	−0.0532823
$881$	29722.0	1.13662	0.568309	−	0.822815i	$-0.307598\pi$
$881$	29722.0	1.13662	0.568309	+	0.822815i	$0.307598\pi$
$882$	39922.4	1.52410
$883$	−19379.7	−0.738596	−0.369298	−	0.929311i	$-0.620402\pi$
$883$	−19379.7	−0.738596	−0.369298	+	0.929311i	$0.620402\pi$
$884$	773.734	0.0294383
$885$	17878.5	0.679072
$886$	7318.53	0.277507
$887$	22901.7	0.866925	0.433463	−	0.901172i	$-0.357292\pi$
$887$	22901.7	0.866925	0.433463	+	0.901172i	$0.357292\pi$
$888$	−34257.6	−1.29461
$889$	−39788.8	−1.50110
$890$	−250.375	−0.00942989
$891$	−51055.7	−1.91967
$892$	−18055.2	−0.677728
$893$	46010.9	1.72419
$894$	−56132.9	−2.09996
$895$	18213.5	0.680236
$896$	−3154.31	−0.117610
$897$	−933.193	−0.0347362
$898$	−21059.3	−0.782581
$899$	56115.8	2.08183
$900$	7553.01	0.279741
$901$	−12568.3	−0.464719
$902$	5920.20	0.218538
$903$	57122.2	2.10510
$904$	6659.61	0.245017
$905$	12045.8	0.442447
$906$	62953.9	2.30850
$907$	42542.2	1.55743	0.778716	−	0.627376i	$-0.215871\pi$
$907$	42542.2	1.55743	0.778716	+	0.627376i	$0.215871\pi$
$908$	11171.4	0.408300
$909$	46865.9	1.71006
$910$	−987.445	−0.0359709
$911$	220.864	0.00803243	0.00401622	−	0.999992i	$-0.498722\pi$
$911$	220.864	0.00803243	0.00401622	+	0.999992i	$0.498722\pi$
$912$	12850.3	0.466574
$913$	566.191	0.0205237
$914$	12886.5	0.466352
$915$	−4081.21	−0.147454
$916$	5617.99	0.202646
$917$	48659.1	1.75231
$918$	47443.9	1.70575
$919$	27835.4	0.999135	0.499567	−	0.866275i	$-0.333492\pi$
$919$	27835.4	0.999135	0.499567	+	0.866275i	$0.333492\pi$
$920$	−920.000	−0.0329690
$921$	−41853.8	−1.49743
$922$	−6527.72	−0.233166
$923$	2463.68	0.0878580
$924$	17353.9	0.617860
$925$	−10572.6	−0.375811
$926$	19036.2	0.675562
$927$	111274.	3.94252
$928$	−8136.56	−0.287819
$929$	−2172.71	−0.0767323	−0.0383661	−	0.999264i	$-0.512215\pi$
$929$	−2172.71	−0.0767323	−0.0383661	+	0.999264i	$0.512215\pi$
$930$	−22347.0	−0.787944
$931$	20962.1	0.737921
$932$	4295.17	0.150958
$933$	−70789.1	−2.48396
$934$	38185.3	1.33775
$935$	−4196.63	−0.146786
$936$	2421.18	0.0845501
$937$	54906.5	1.91432	0.957160	−	0.289560i	$-0.0935090\pi$
$937$	54906.5	1.91432	0.957160	+	0.289560i	$0.0935090\pi$
$938$	40415.2	1.40683
$939$	94984.6	3.30107
$940$	11601.7	0.402561
$941$	5980.06	0.207167	0.103584	−	0.994621i	$-0.466969\pi$
$941$	5980.06	0.207167	0.103584	+	0.994621i	$0.466969\pi$
$942$	75191.0	2.60070
$943$	3915.77	0.135223
$944$	5650.09	0.194804
$945$	−60548.2	−2.08427
$946$	7960.33	0.273586
$947$	−20268.6	−0.695504	−0.347752	−	0.937587i	$-0.613055\pi$
$947$	−20268.6	−0.695504	−0.347752	+	0.937587i	$0.613055\pi$
$948$	6499.24	0.222664
$949$	2049.92	0.0701193
$950$	3965.86	0.135442
$951$	−80958.6	−2.76053
$952$	−9516.97	−0.323999
$953$	−21797.9	−0.740925	−0.370463	−	0.928847i	$-0.620801\pi$
$953$	−21797.9	−0.740925	−0.370463	+	0.928847i	$0.620801\pi$
$954$	−39329.1	−1.33472
$955$	−948.038	−0.0321233
$956$	−10292.7	−0.348212
$957$	44764.5	1.51205
$958$	−12649.6	−0.426608
$959$	−18576.1	−0.625499
$960$	3240.23	0.108935
$961$	18915.6	0.634945
$962$	−3389.14	−0.113587
$963$	−71008.9	−2.37615
$964$	−2784.51	−0.0930321
$965$	−9277.26	−0.309477
$966$	11478.3	0.382308
$967$	48950.6	1.62786	0.813932	−	0.580960i	$-0.197323\pi$
$967$	48950.6	1.62786	0.813932	+	0.580960i	$0.197323\pi$
$968$	−8229.62	−0.273254
$969$	38771.0	1.28535
$970$	−2497.98	−0.0826860
$971$	−26426.2	−0.873386	−0.436693	−	0.899611i	$-0.643850\pi$
$971$	−26426.2	−0.873386	−0.436693	+	0.899611i	$0.643850\pi$
$972$	65864.4	2.17346
$973$	−24990.5	−0.823389
$974$	−15746.1	−0.518007
$975$	1014.34	0.0333178
$976$	−1289.77	−0.0422998
$977$	5770.09	0.188947	0.0944736	−	0.995527i	$-0.469883\pi$
$977$	5770.09	0.188947	0.0944736	+	0.995527i	$0.469883\pi$
$978$	18546.1	0.606379
$979$	435.320	0.0142113
$980$	5285.63	0.172289
$981$	−48057.1	−1.56406
$982$	−7113.64	−0.231166
$983$	−484.532	−0.0157214	−0.00786071	−	0.999969i	$-0.502502\pi$
$983$	−484.532	−0.0157214	−0.00786071	+	0.999969i	$0.502502\pi$
$984$	−13791.3	−0.446799
$985$	12149.2	0.393002
$986$	−24549.0	−0.792901
$987$	−144749.	−4.66808
$988$	1271.29	0.0409365
$989$	5265.16	0.169285
$990$	−13132.2	−0.421584
$991$	−26511.5	−0.849813	−0.424907	−	0.905237i	$-0.639693\pi$
$991$	−26511.5	−0.849813	−0.424907	+	0.905237i	$0.639693\pi$
$992$	−7062.27	−0.226035
$993$	−48591.9	−1.55289
$994$	−30303.4	−0.966966
$995$	21667.4	0.690356
$996$	−1318.96	−0.0419606
$997$	−4628.20	−0.147018	−0.0735088	−	0.997295i	$-0.523420\pi$
$997$	−4628.20	−0.147018	−0.0735088	+	0.997295i	$0.523420\pi$
$998$	−3866.74	−0.122645
$999$	−207816.	−6.58158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.a.j.1.4	✓	4
3.2	odd	2		2070.4.a.bg.1.1		4
4.3	odd	2		1840.4.a.k.1.1		4
5.2	odd	4		1150.4.b.o.599.5		8
5.3	odd	4		1150.4.b.o.599.4		8
5.4	even	2		1150.4.a.n.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.j.1.4	✓	4	1.1	even	1	trivial
1150.4.a.n.1.1		4	5.4	even	2
1150.4.b.o.599.4		8	5.3	odd	4
1150.4.b.o.599.5		8	5.2	odd	4
1840.4.a.k.1.1		4	4.3	odd	2
2070.4.a.bg.1.1		4	3.2	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +10.1257 q^{3} +4.00000 q^{4} +5.00000 q^{5} +20.2514 q^{6} -24.6431 q^{7} +8.00000 q^{8} +75.5301 q^{9} +10.0000 q^{10} -17.3867 q^{11} +40.5029 q^{12} +4.00699 q^{13} -49.2862 q^{14} +50.6286 q^{15} +16.0000 q^{16} +48.2740 q^{17} +151.060 q^{18} +79.3172 q^{19} +20.0000 q^{20} -249.529 q^{21} -34.7734 q^{22} -23.0000 q^{23} +81.0057 q^{24} +25.0000 q^{25} +8.01398 q^{26} +491.402 q^{27} -98.5723 q^{28} -254.267 q^{29} +101.257 q^{30} -220.696 q^{31} +32.0000 q^{32} -176.053 q^{33} +96.5480 q^{34} -123.215 q^{35} +302.120 q^{36} -422.904 q^{37} +158.634 q^{38} +40.5736 q^{39} +40.0000 q^{40} -170.251 q^{41} -499.058 q^{42} -228.920 q^{43} -69.5468 q^{44} +377.650 q^{45} -46.0000 q^{46} +580.087 q^{47} +162.011 q^{48} +264.282 q^{49} +50.0000 q^{50} +488.809 q^{51} +16.0280 q^{52} -260.354 q^{53} +982.803 q^{54} -86.9335 q^{55} -197.145 q^{56} +803.144 q^{57} -508.535 q^{58} +353.130 q^{59} +202.514 q^{60} -80.6108 q^{61} -441.392 q^{62} -1861.29 q^{63} +64.0000 q^{64} +20.0349 q^{65} -352.106 q^{66} -820.011 q^{67} +193.096 q^{68} -232.891 q^{69} -246.431 q^{70} +614.845 q^{71} +604.241 q^{72} +511.586 q^{73} -845.808 q^{74} +253.143 q^{75} +317.269 q^{76} +428.462 q^{77} +81.1472 q^{78} +160.464 q^{79} +80.0000 q^{80} +2936.48 q^{81} -340.502 q^{82} -32.5646 q^{83} -998.115 q^{84} +241.370 q^{85} -457.840 q^{86} -2574.64 q^{87} -139.094 q^{88} -25.0375 q^{89} +755.301 q^{90} -98.7445 q^{91} -92.0000 q^{92} -2234.70 q^{93} +1160.17 q^{94} +396.586 q^{95} +324.023 q^{96} -249.798 q^{97} +528.563 q^{98} -1313.22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} + 14 q^{3} + 16 q^{4} + 20 q^{5} + 28 q^{6} + 8 q^{7} + 32 q^{8} + 64 q^{9} + 40 q^{10} + 21 q^{11} + 56 q^{12} + 70 q^{13} + 16 q^{14} + 70 q^{15} + 64 q^{16} + 56 q^{17} + 128 q^{18} + 173 q^{19}+ \cdots - 2745 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 + 14 * q^3 + 16 * q^4 + 20 * q^5 + 28 * q^6 + 8 * q^7 + 32 * q^8 + 64 * q^9 + 40 * q^10 + 21 * q^11 + 56 * q^12 + 70 * q^13 + 16 * q^14 + 70 * q^15 + 64 * q^16 + 56 * q^17 + 128 * q^18 + 173 * q^19 + 80 * q^20 - 120 * q^21 + 42 * q^22 - 92 * q^23 + 112 * q^24 + 100 * q^25 + 140 * q^26 + 389 * q^27 + 32 * q^28 - 118 * q^29 + 140 * q^30 + 17 * q^31 + 128 * q^32 - 89 * q^33 + 112 * q^34 + 40 * q^35 + 256 * q^36 - 343 * q^37 + 346 * q^38 - 221 * q^39 + 160 * q^40 + 139 * q^41 - 240 * q^42 - 50 * q^43 + 84 * q^44 + 320 * q^45 - 184 * q^46 + 367 * q^47 + 224 * q^48 - 124 * q^49 + 200 * q^50 + 439 * q^51 + 280 * q^52 - 353 * q^53 + 778 * q^54 + 105 * q^55 + 64 * q^56 - 238 * q^57 - 236 * q^58 - 453 * q^59 + 280 * q^60 - 327 * q^61 + 34 * q^62 - 1723 * q^63 + 256 * q^64 + 350 * q^65 - 178 * q^66 - 455 * q^67 + 224 * q^68 - 322 * q^69 + 80 * q^70 + 195 * q^71 + 512 * q^72 - 633 * q^73 - 686 * q^74 + 350 * q^75 + 692 * q^76 - 2 * q^77 - 442 * q^78 - 1140 * q^79 + 320 * q^80 + 1456 * q^81 + 278 * q^82 - 1199 * q^83 - 480 * q^84 + 280 * q^85 - 100 * q^86 - 1775 * q^87 + 168 * q^88 - 2170 * q^89 + 640 * q^90 + 557 * q^91 - 368 * q^92 - 3241 * q^93 + 734 * q^94 + 865 * q^95 + 448 * q^96 - 703 * q^97 - 248 * q^98 - 2745 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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