LMFDB - Embedded newform 4598.2.a.cc.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 $ x^10 - 2x^9 - 19x^8 + 36x^7 + 118x^6 - 220x^5 - 270x^4 + 512x^3 + 176x^2 - 392*x + 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.12868$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +2.12868 q^{3} +1.00000 q^{4} -0.444747 q^{5} -2.12868 q^{6} +0.813941 q^{7} -1.00000 q^{8} +1.53127 q^{9} +0.444747 q^{10} +2.12868 q^{12} +0.531472 q^{13} -0.813941 q^{14} -0.946723 q^{15} +1.00000 q^{16} -5.88116 q^{17} -1.53127 q^{18} -1.00000 q^{19} -0.444747 q^{20} +1.73262 q^{21} +6.69536 q^{23} -2.12868 q^{24} -4.80220 q^{25} -0.531472 q^{26} -3.12645 q^{27} +0.813941 q^{28} -4.16686 q^{29} +0.946723 q^{30} -5.80088 q^{31} -1.00000 q^{32} +5.88116 q^{34} -0.361998 q^{35} +1.53127 q^{36} +2.37532 q^{37} +1.00000 q^{38} +1.13133 q^{39} +0.444747 q^{40} -10.2569 q^{41} -1.73262 q^{42} -10.2461 q^{43} -0.681029 q^{45} -6.69536 q^{46} +6.33722 q^{47} +2.12868 q^{48} -6.33750 q^{49} +4.80220 q^{50} -12.5191 q^{51} +0.531472 q^{52} +9.31823 q^{53} +3.12645 q^{54} -0.813941 q^{56} -2.12868 q^{57} +4.16686 q^{58} +3.37870 q^{59} -0.946723 q^{60} -4.76838 q^{61} +5.80088 q^{62} +1.24637 q^{63} +1.00000 q^{64} -0.236370 q^{65} -1.23043 q^{67} -5.88116 q^{68} +14.2523 q^{69} +0.361998 q^{70} -11.5841 q^{71} -1.53127 q^{72} +12.3402 q^{73} -2.37532 q^{74} -10.2223 q^{75} -1.00000 q^{76} -1.13133 q^{78} -3.46996 q^{79} -0.444747 q^{80} -11.2490 q^{81} +10.2569 q^{82} -12.8659 q^{83} +1.73262 q^{84} +2.61563 q^{85} +10.2461 q^{86} -8.86991 q^{87} +7.40160 q^{89} +0.681029 q^{90} +0.432587 q^{91} +6.69536 q^{92} -12.3482 q^{93} -6.33722 q^{94} +0.444747 q^{95} -2.12868 q^{96} -14.2295 q^{97} +6.33750 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9} + 3 q^{10} + 2 q^{12} - 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 10 q^{19} - 3 q^{20}+ \cdots + 3 q^{98}+O(q^{100}) $ 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 - 2 * q^6 - 11 * q^7 - 10 * q^8 + 12 * q^9 + 3 * q^10 + 2 * q^12 - 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 10 * q^19 - 3 * q^20 + q^21 + 14 * q^23 - 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 - 11 * q^28 - 16 * q^29 - q^30 + 12 * q^31 - 10 * q^32 + 12 * q^34 + 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 - 11 * q^39 + 3 * q^40 + 5 * q^41 - q^42 - 22 * q^43 - 2 * q^45 - 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 - 5 * q^50 - 8 * q^51 - 11 * q^52 + 2 * q^53 - 2 * q^54 + 11 * q^56 - 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 - 35 * q^61 - 12 * q^62 - 38 * q^63 + 10 * q^64 - 4 * q^65 + 9 * q^67 - 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 - 12 * q^72 - 5 * q^73 + q^74 - 15 * q^75 - 10 * q^76 + 11 * q^78 - 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 - 7 * q^83 + q^84 - 35 * q^85 + 22 * q^86 - 8 * q^87 + 22 * q^89 + 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 - 8 * q^94 + 3 * q^95 - 2 * q^96 + 32 * q^97 + 3 * q^98

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.12868	1.22899	0.614497	−	0.788919i	$-0.289359\pi$
$3$	2.12868	1.22899	0.614497	+	0.788919i	$0.289359\pi$
$4$	1.00000	0.500000
$5$	−0.444747	−0.198897	−0.0994485	−	0.995043i	$-0.531708\pi$
$5$	−0.444747	−0.198897	−0.0994485	+	0.995043i	$0.531708\pi$
$6$	−2.12868	−0.869029
$7$	0.813941	0.307641	0.153820	−	0.988099i	$-0.450842\pi$
$7$	0.813941	0.307641	0.153820	+	0.988099i	$0.450842\pi$
$8$	−1.00000	−0.353553
$9$	1.53127	0.510424
$10$	0.444747	0.140641
$11$	0	0
$11$	0	0
$12$	2.12868	0.614497
$13$	0.531472	0.147404	0.0737019	−	0.997280i	$-0.476519\pi$
$13$	0.531472	0.147404	0.0737019	+	0.997280i	$0.476519\pi$
$14$	−0.813941	−0.217535
$15$	−0.946723	−0.244443
$16$	1.00000	0.250000
$17$	−5.88116	−1.42639	−0.713196	−	0.700965i	$-0.752753\pi$
$17$	−5.88116	−1.42639	−0.713196	+	0.700965i	$0.752753\pi$
$18$	−1.53127	−0.360924
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.444747	−0.0994485
$21$	1.73262	0.378089
$22$	0	0
$23$	6.69536	1.39608	0.698040	−	0.716059i	$-0.254056\pi$
$23$	6.69536	1.39608	0.698040	+	0.716059i	$0.254056\pi$
$24$	−2.12868	−0.434515
$25$	−4.80220	−0.960440
$26$	−0.531472	−0.104230
$27$	−3.12645	−0.601685
$28$	0.813941	0.153820
$29$	−4.16686	−0.773767	−0.386883	−	0.922129i	$-0.626448\pi$
$29$	−4.16686	−0.773767	−0.386883	+	0.922129i	$0.626448\pi$
$30$	0.946723	0.172847
$31$	−5.80088	−1.04187	−0.520934	−	0.853597i	$-0.674416\pi$
$31$	−5.80088	−1.04187	−0.520934	+	0.853597i	$0.674416\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	5.88116	1.00861
$35$	−0.361998	−0.0611888
$36$	1.53127	0.255212
$37$	2.37532	0.390500	0.195250	−	0.980754i	$-0.437448\pi$
$37$	2.37532	0.390500	0.195250	+	0.980754i	$0.437448\pi$
$38$	1.00000	0.162221
$39$	1.13133	0.181158
$40$	0.444747	0.0703207
$41$	−10.2569	−1.60186	−0.800932	−	0.598755i	$-0.795662\pi$
$41$	−10.2569	−1.60186	−0.800932	+	0.598755i	$0.795662\pi$
$42$	−1.73262	−0.267349
$43$	−10.2461	−1.56252	−0.781258	−	0.624208i	$-0.785422\pi$
$43$	−10.2461	−1.56252	−0.781258	+	0.624208i	$0.785422\pi$
$44$	0	0
$45$	−0.681029	−0.101522
$46$	−6.69536	−0.987177
$47$	6.33722	0.924379	0.462189	−	0.886781i	$-0.347064\pi$
$47$	6.33722	0.924379	0.462189	+	0.886781i	$0.347064\pi$
$48$	2.12868	0.307248
$49$	−6.33750	−0.905357
$50$	4.80220	0.679134
$51$	−12.5191	−1.75302
$52$	0.531472	0.0737019
$53$	9.31823	1.27996	0.639979	−	0.768392i	$-0.278943\pi$
$53$	9.31823	1.27996	0.639979	+	0.768392i	$0.278943\pi$
$54$	3.12645	0.425456
$55$	0	0
$56$	−0.813941	−0.108768
$57$	−2.12868	−0.281950
$58$	4.16686	0.547136
$59$	3.37870	0.439869	0.219935	−	0.975515i	$-0.429416\pi$
$59$	3.37870	0.439869	0.219935	+	0.975515i	$0.429416\pi$
$60$	−0.946723	−0.122221
$61$	−4.76838	−0.610529	−0.305264	−	0.952268i	$-0.598745\pi$
$61$	−4.76838	−0.610529	−0.305264	+	0.952268i	$0.598745\pi$
$62$	5.80088	0.736712
$63$	1.24637	0.157027
$64$	1.00000	0.125000
$65$	−0.236370	−0.0293181
$66$	0	0
$67$	−1.23043	−0.150321	−0.0751604	−	0.997171i	$-0.523947\pi$
$67$	−1.23043	−0.150321	−0.0751604	+	0.997171i	$0.523947\pi$
$68$	−5.88116	−0.713196
$69$	14.2523	1.71577
$70$	0.361998	0.0432670
$71$	−11.5841	−1.37479	−0.687393	−	0.726286i	$-0.741245\pi$
$71$	−11.5841	−1.37479	−0.687393	+	0.726286i	$0.741245\pi$
$72$	−1.53127	−0.180462
$73$	12.3402	1.44431	0.722155	−	0.691731i	$-0.243152\pi$
$73$	12.3402	1.44431	0.722155	+	0.691731i	$0.243152\pi$
$74$	−2.37532	−0.276125
$75$	−10.2223	−1.18037
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−1.13133	−0.128098
$79$	−3.46996	−0.390401	−0.195200	−	0.980763i	$-0.562536\pi$
$79$	−3.46996	−0.390401	−0.195200	+	0.980763i	$0.562536\pi$
$80$	−0.444747	−0.0497242
$81$	−11.2490	−1.24989
$82$	10.2569	1.13269
$83$	−12.8659	−1.41222	−0.706110	−	0.708102i	$-0.749551\pi$
$83$	−12.8659	−1.41222	−0.706110	+	0.708102i	$0.749551\pi$
$84$	1.73262	0.189044
$85$	2.61563	0.283705
$86$	10.2461	1.10487
$87$	−8.86991	−0.950954
$88$	0	0
$89$	7.40160	0.784568	0.392284	−	0.919844i	$-0.371685\pi$
$89$	7.40160	0.784568	0.392284	+	0.919844i	$0.371685\pi$
$90$	0.681029	0.0717867
$91$	0.432587	0.0453474
$92$	6.69536	0.698040
$93$	−12.3482	−1.28045
$94$	−6.33722	−0.653635
$95$	0.444747	0.0456301
$96$	−2.12868	−0.217257
$97$	−14.2295	−1.44479	−0.722395	−	0.691481i	$-0.756959\pi$
$97$	−14.2295	−1.44479	−0.722395	+	0.691481i	$0.756959\pi$
$98$	6.33750	0.640184
$99$	0	0
$100$	−4.80220	−0.480220
$101$	3.50507	0.348767	0.174384	−	0.984678i	$-0.444207\pi$
$101$	3.50507	0.348767	0.174384	+	0.984678i	$0.444207\pi$
$102$	12.5191	1.23958
$103$	0.694123	0.0683939	0.0341970	−	0.999415i	$-0.489113\pi$
$103$	0.694123	0.0683939	0.0341970	+	0.999415i	$0.489113\pi$
$104$	−0.531472	−0.0521151
$105$	−0.770577	−0.0752007
$106$	−9.31823	−0.905067
$107$	8.63080	0.834371	0.417185	−	0.908821i	$-0.363017\pi$
$107$	8.63080	0.834371	0.417185	+	0.908821i	$0.363017\pi$
$108$	−3.12645	−0.300843
$109$	8.10360	0.776184	0.388092	−	0.921621i	$-0.373134\pi$
$109$	8.10360	0.776184	0.388092	+	0.921621i	$0.373134\pi$
$110$	0	0
$111$	5.05629	0.479922
$112$	0.813941	0.0769102
$113$	4.66260	0.438620	0.219310	−	0.975655i	$-0.429619\pi$
$113$	4.66260	0.438620	0.219310	+	0.975655i	$0.429619\pi$
$114$	2.12868	0.199369
$115$	−2.97774	−0.277676
$116$	−4.16686	−0.386883
$117$	0.813828	0.0752384
$118$	−3.37870	−0.311034
$119$	−4.78692	−0.438816
$120$	0.946723	0.0864236
$121$	0	0
$122$	4.76838	0.431709
$123$	−21.8337	−1.96868
$124$	−5.80088	−0.520934
$125$	4.35950	0.389925
$126$	−1.24637	−0.111035
$127$	5.75512	0.510684	0.255342	−	0.966851i	$-0.417812\pi$
$127$	5.75512	0.510684	0.255342	+	0.966851i	$0.417812\pi$
$128$	−1.00000	−0.0883883
$129$	−21.8107	−1.92032
$130$	0.236370	0.0207311
$131$	−0.970302	−0.0847756	−0.0423878	−	0.999101i	$-0.513497\pi$
$131$	−0.970302	−0.0847756	−0.0423878	+	0.999101i	$0.513497\pi$
$132$	0	0
$133$	−0.813941	−0.0705777
$134$	1.23043	0.106293
$135$	1.39048	0.119673
$136$	5.88116	0.504305
$137$	2.14682	0.183415	0.0917077	−	0.995786i	$-0.470767\pi$
$137$	2.14682	0.183415	0.0917077	+	0.995786i	$0.470767\pi$
$138$	−14.2523	−1.21323
$139$	−9.78816	−0.830221	−0.415110	−	0.909771i	$-0.636257\pi$
$139$	−9.78816	−0.830221	−0.415110	+	0.909771i	$0.636257\pi$
$140$	−0.361998	−0.0305944
$141$	13.4899	1.13606
$142$	11.5841	0.972120
$143$	0	0
$144$	1.53127	0.127606
$145$	1.85320	0.153900
$146$	−12.3402	−1.02128
$147$	−13.4905	−1.11268
$148$	2.37532	0.195250
$149$	1.24923	0.102341	0.0511703	−	0.998690i	$-0.483705\pi$
$149$	1.24923	0.102341	0.0511703	+	0.998690i	$0.483705\pi$
$150$	10.2223	0.834651
$151$	−13.8527	−1.12732	−0.563659	−	0.826008i	$-0.690607\pi$
$151$	−13.8527	−1.12732	−0.563659	+	0.826008i	$0.690607\pi$
$152$	1.00000	0.0811107
$153$	−9.00566	−0.728065
$154$	0	0
$155$	2.57992	0.207224
$156$	1.13133	0.0905791
$157$	17.3097	1.38146	0.690731	−	0.723112i	$-0.257289\pi$
$157$	17.3097	1.38146	0.690731	+	0.723112i	$0.257289\pi$
$158$	3.46996	0.276055
$159$	19.8355	1.57306
$160$	0.444747	0.0351603
$161$	5.44963	0.429491
$162$	11.2490	0.883807
$163$	−9.97325	−0.781165	−0.390583	−	0.920568i	$-0.627726\pi$
$163$	−9.97325	−0.781165	−0.390583	+	0.920568i	$0.627726\pi$
$164$	−10.2569	−0.800932
$165$	0	0
$166$	12.8659	0.998590
$167$	22.8982	1.77191	0.885957	−	0.463768i	$-0.153503\pi$
$167$	22.8982	1.77191	0.885957	+	0.463768i	$0.153503\pi$
$168$	−1.73262	−0.133675
$169$	−12.7175	−0.978272
$170$	−2.61563	−0.200610
$171$	−1.53127	−0.117099
$172$	−10.2461	−0.781258
$173$	−7.74923	−0.589163	−0.294581	−	0.955626i	$-0.595180\pi$
$173$	−7.74923	−0.589163	−0.294581	+	0.955626i	$0.595180\pi$
$174$	8.86991	0.672426
$175$	−3.90871	−0.295471
$176$	0	0
$177$	7.19216	0.540596
$178$	−7.40160	−0.554773
$179$	13.1788	0.985032	0.492516	−	0.870303i	$-0.336077\pi$
$179$	13.1788	0.985032	0.492516	+	0.870303i	$0.336077\pi$
$180$	−0.681029	−0.0507609
$181$	−9.16172	−0.680985	−0.340493	−	0.940247i	$-0.610594\pi$
$181$	−9.16172	−0.680985	−0.340493	+	0.940247i	$0.610594\pi$
$182$	−0.432587	−0.0320655
$183$	−10.1503	−0.750335
$184$	−6.69536	−0.493589
$185$	−1.05642	−0.0776692
$186$	12.3482	0.905414
$187$	0	0
$188$	6.33722	0.462189
$189$	−2.54475	−0.185103
$190$	−0.444747	−0.0322653
$191$	−14.5629	−1.05373	−0.526865	−	0.849949i	$-0.676633\pi$
$191$	−14.5629	−1.05373	−0.526865	+	0.849949i	$0.676633\pi$
$192$	2.12868	0.153624
$193$	−2.43059	−0.174958	−0.0874789	−	0.996166i	$-0.527881\pi$
$193$	−2.43059	−0.174958	−0.0874789	+	0.996166i	$0.527881\pi$
$194$	14.2295	1.02162
$195$	−0.503157	−0.0360318
$196$	−6.33750	−0.452679
$197$	−10.9047	−0.776928	−0.388464	−	0.921464i	$-0.626994\pi$
$197$	−10.9047	−0.776928	−0.388464	+	0.921464i	$0.626994\pi$
$198$	0	0
$199$	−15.3004	−1.08461	−0.542307	−	0.840180i	$-0.682449\pi$
$199$	−15.3004	−1.08461	−0.542307	+	0.840180i	$0.682449\pi$
$200$	4.80220	0.339567
$201$	−2.61919	−0.184743
$202$	−3.50507	−0.246616
$203$	−3.39158	−0.238042
$204$	−12.5191	−0.876512
$205$	4.56174	0.318606
$206$	−0.694123	−0.0483618
$207$	10.2524	0.712593
$208$	0.531472	0.0368509
$209$	0	0
$210$	0.770577	0.0531749
$211$	−5.61110	−0.386284	−0.193142	−	0.981171i	$-0.561868\pi$
$211$	−5.61110	−0.386284	−0.193142	+	0.981171i	$0.561868\pi$
$212$	9.31823	0.639979
$213$	−24.6589	−1.68960
$214$	−8.63080	−0.589989
$215$	4.55693	0.310780
$216$	3.12645	0.212728
$217$	−4.72157	−0.320521
$218$	−8.10360	−0.548845
$219$	26.2683	1.77505
$220$	0	0
$221$	−3.12567	−0.210255
$222$	−5.05629	−0.339356
$223$	−23.9862	−1.60624	−0.803118	−	0.595821i	$-0.796827\pi$
$223$	−23.9862	−1.60624	−0.803118	+	0.595821i	$0.796827\pi$
$224$	−0.813941	−0.0543838
$225$	−7.35348	−0.490232
$226$	−4.66260	−0.310151
$227$	−3.52771	−0.234142	−0.117071	−	0.993124i	$-0.537351\pi$
$227$	−3.52771	−0.234142	−0.117071	+	0.993124i	$0.537351\pi$
$228$	−2.12868	−0.140975
$229$	−19.5717	−1.29334	−0.646669	−	0.762771i	$-0.723838\pi$
$229$	−19.5717	−1.29334	−0.646669	+	0.762771i	$0.723838\pi$
$230$	2.97774	0.196347
$231$	0	0
$232$	4.16686	0.273568
$233$	19.2019	1.25796	0.628980	−	0.777422i	$-0.283473\pi$
$233$	19.2019	1.25796	0.628980	+	0.777422i	$0.283473\pi$
$234$	−0.813828	−0.0532016
$235$	−2.81846	−0.183856
$236$	3.37870	0.219935
$237$	−7.38643	−0.479800
$238$	4.78692	0.310290
$239$	−19.3799	−1.25358	−0.626790	−	0.779188i	$-0.715632\pi$
$239$	−19.3799	−1.25358	−0.626790	+	0.779188i	$0.715632\pi$
$240$	−0.946723	−0.0611107
$241$	5.20964	0.335582	0.167791	−	0.985823i	$-0.446337\pi$
$241$	5.20964	0.335582	0.167791	+	0.985823i	$0.446337\pi$
$242$	0	0
$243$	−14.5662	−0.934423
$244$	−4.76838	−0.305264
$245$	2.81858	0.180073
$246$	21.8337	1.39207
$247$	−0.531472	−0.0338167
$248$	5.80088	0.368356
$249$	−27.3874	−1.73561
$250$	−4.35950	−0.275719
$251$	13.5993	0.858382	0.429191	−	0.903214i	$-0.358799\pi$
$251$	13.5993	0.858382	0.429191	+	0.903214i	$0.358799\pi$
$252$	1.24637	0.0785137
$253$	0	0
$254$	−5.75512	−0.361108
$255$	5.56783	0.348671
$256$	1.00000	0.0625000
$257$	−10.9529	−0.683224	−0.341612	−	0.939841i	$-0.610973\pi$
$257$	−10.9529	−0.683224	−0.341612	+	0.939841i	$0.610973\pi$
$258$	21.8107	1.35787
$259$	1.93337	0.120134
$260$	−0.236370	−0.0146591
$261$	−6.38060	−0.394949
$262$	0.970302	0.0599454
$263$	27.8602	1.71793	0.858966	−	0.512032i	$-0.171107\pi$
$263$	27.8602	1.71793	0.858966	+	0.512032i	$0.171107\pi$
$264$	0	0
$265$	−4.14426	−0.254580
$266$	0.813941	0.0499060
$267$	15.7556	0.964228
$268$	−1.23043	−0.0751604
$269$	12.9191	0.787693	0.393847	−	0.919176i	$-0.371144\pi$
$269$	12.9191	0.787693	0.393847	+	0.919176i	$0.371144\pi$
$270$	−1.39048	−0.0846218
$271$	8.10604	0.492407	0.246203	−	0.969218i	$-0.420817\pi$
$271$	8.10604	0.492407	0.246203	+	0.969218i	$0.420817\pi$
$272$	−5.88116	−0.356598
$273$	0.920838	0.0557317
$274$	−2.14682	−0.129694
$275$	0	0
$276$	14.2523	0.857886
$277$	23.4635	1.40979	0.704893	−	0.709313i	$-0.250995\pi$
$277$	23.4635	1.40979	0.704893	+	0.709313i	$0.250995\pi$
$278$	9.78816	0.587055
$279$	−8.88272	−0.531795
$280$	0.361998	0.0216335
$281$	−14.3704	−0.857269	−0.428634	−	0.903478i	$-0.641005\pi$
$281$	−14.3704	−0.857269	−0.428634	+	0.903478i	$0.641005\pi$
$282$	−13.4899	−0.803312
$283$	−11.6889	−0.694833	−0.347416	−	0.937711i	$-0.612941\pi$
$283$	−11.6889	−0.694833	−0.347416	+	0.937711i	$0.612941\pi$
$284$	−11.5841	−0.687393
$285$	0.946723	0.0560791
$286$	0	0
$287$	−8.34854	−0.492799
$288$	−1.53127	−0.0902311
$289$	17.5881	1.03459
$290$	−1.85320	−0.108824
$291$	−30.2901	−1.77564
$292$	12.3402	0.722155
$293$	24.6851	1.44212	0.721059	−	0.692874i	$-0.243656\pi$
$293$	24.6851	1.44212	0.721059	+	0.692874i	$0.243656\pi$
$294$	13.4905	0.786782
$295$	−1.50267	−0.0874886
$296$	−2.37532	−0.138063
$297$	0	0
$298$	−1.24923	−0.0723657
$299$	3.55839	0.205787
$300$	−10.2223	−0.590187
$301$	−8.33973	−0.480694
$302$	13.8527	0.797134
$303$	7.46117	0.428633
$304$	−1.00000	−0.0573539
$305$	2.12072	0.121432
$306$	9.00566	0.514819
$307$	−11.2527	−0.642226	−0.321113	−	0.947041i	$-0.604057\pi$
$307$	−11.2527	−0.642226	−0.321113	+	0.947041i	$0.604057\pi$
$308$	0	0
$309$	1.47756	0.0840557
$310$	−2.57992	−0.146530
$311$	3.40711	0.193199	0.0965996	−	0.995323i	$-0.469203\pi$
$311$	3.40711	0.193199	0.0965996	+	0.995323i	$0.469203\pi$
$312$	−1.13133	−0.0640491
$313$	20.6424	1.16678	0.583388	−	0.812194i	$-0.301727\pi$
$313$	20.6424	1.16678	0.583388	+	0.812194i	$0.301727\pi$
$314$	−17.3097	−0.976840
$315$	−0.554318	−0.0312323
$316$	−3.46996	−0.195200
$317$	−26.2022	−1.47166	−0.735832	−	0.677165i	$-0.763209\pi$
$317$	−26.2022	−1.47166	−0.735832	+	0.677165i	$0.763209\pi$
$318$	−19.8355	−1.11232
$319$	0	0
$320$	−0.444747	−0.0248621
$321$	18.3722	1.02544
$322$	−5.44963	−0.303696
$323$	5.88116	0.327237
$324$	−11.2490	−0.624946
$325$	−2.55223	−0.141572
$326$	9.97325	0.552367
$327$	17.2500	0.953925
$328$	10.2569	0.566344
$329$	5.15813	0.284377
$330$	0	0
$331$	22.7831	1.25227	0.626137	−	0.779713i	$-0.284635\pi$
$331$	22.7831	1.25227	0.626137	+	0.779713i	$0.284635\pi$
$332$	−12.8659	−0.706110
$333$	3.63726	0.199321
$334$	−22.8982	−1.25293
$335$	0.547230	0.0298984
$336$	1.73262	0.0945222
$337$	−16.6810	−0.908670	−0.454335	−	0.890831i	$-0.650123\pi$
$337$	−16.6810	−0.908670	−0.454335	+	0.890831i	$0.650123\pi$
$338$	12.7175	0.691743
$339$	9.92517	0.539061
$340$	2.61563	0.141852
$341$	0	0
$342$	1.53127	0.0828017
$343$	−10.8559	−0.586166
$344$	10.2461	0.552433
$345$	−6.33866	−0.341262
$346$	7.74923	0.416601
$347$	24.8615	1.33463	0.667317	−	0.744774i	$-0.267443\pi$
$347$	24.8615	1.33463	0.667317	+	0.744774i	$0.267443\pi$
$348$	−8.86991	−0.475477
$349$	19.5583	1.04693	0.523467	−	0.852046i	$-0.324638\pi$
$349$	19.5583	1.04693	0.523467	+	0.852046i	$0.324638\pi$
$350$	3.90871	0.208929
$351$	−1.66162	−0.0886907
$352$	0	0
$353$	−17.1793	−0.914360	−0.457180	−	0.889374i	$-0.651141\pi$
$353$	−17.1793	−0.914360	−0.457180	+	0.889374i	$0.651141\pi$
$354$	−7.19216	−0.382259
$355$	5.15201	0.273441
$356$	7.40160	0.392284
$357$	−10.1898	−0.539302
$358$	−13.1788	−0.696523
$359$	19.0190	1.00379	0.501893	−	0.864930i	$-0.332637\pi$
$359$	19.0190	1.00379	0.501893	+	0.864930i	$0.332637\pi$
$360$	0.681029	0.0358934
$361$	1.00000	0.0526316
$362$	9.16172	0.481529
$363$	0	0
$364$	0.432587	0.0226737
$365$	−5.48827	−0.287269
$366$	10.1503	0.530567
$367$	4.19576	0.219017	0.109509	−	0.993986i	$-0.465072\pi$
$367$	4.19576	0.219017	0.109509	+	0.993986i	$0.465072\pi$
$368$	6.69536	0.349020
$369$	−15.7062	−0.817630
$370$	1.05642	0.0549204
$371$	7.58450	0.393767
$372$	−12.3482	−0.640225
$373$	−30.5753	−1.58313	−0.791564	−	0.611086i	$-0.790733\pi$
$373$	−30.5753	−1.58313	−0.791564	+	0.611086i	$0.790733\pi$
$374$	0	0
$375$	9.27997	0.479216
$376$	−6.33722	−0.326817
$377$	−2.21457	−0.114056
$378$	2.54475	0.130888
$379$	27.9152	1.43391	0.716954	−	0.697121i	$-0.245536\pi$
$379$	27.9152	1.43391	0.716954	+	0.697121i	$0.245536\pi$
$380$	0.444747	0.0228150
$381$	12.2508	0.627627
$382$	14.5629	0.745100
$383$	−13.3334	−0.681304	−0.340652	−	0.940189i	$-0.610648\pi$
$383$	−13.3334	−0.681304	−0.340652	+	0.940189i	$0.610648\pi$
$384$	−2.12868	−0.108629
$385$	0	0
$386$	2.43059	0.123714
$387$	−15.6896	−0.797546
$388$	−14.2295	−0.722395
$389$	−6.00531	−0.304481	−0.152241	−	0.988343i	$-0.548649\pi$
$389$	−6.00531	−0.304481	−0.152241	+	0.988343i	$0.548649\pi$
$390$	0.503157	0.0254783
$391$	−39.3765	−1.99136
$392$	6.33750	0.320092
$393$	−2.06546	−0.104189
$394$	10.9047	0.549371
$395$	1.54325	0.0776495
$396$	0	0
$397$	−27.7223	−1.39134	−0.695671	−	0.718360i	$-0.744893\pi$
$397$	−27.7223	−1.39134	−0.695671	+	0.718360i	$0.744893\pi$
$398$	15.3004	0.766938
$399$	−1.73262	−0.0867395
$400$	−4.80220	−0.240110
$401$	29.1632	1.45634	0.728170	−	0.685396i	$-0.240371\pi$
$401$	29.1632	1.45634	0.728170	+	0.685396i	$0.240371\pi$
$402$	2.61919	0.130633
$403$	−3.08300	−0.153575
$404$	3.50507	0.174384
$405$	5.00297	0.248600
$406$	3.39158	0.168321
$407$	0	0
$408$	12.5191	0.619788
$409$	11.2326	0.555415	0.277708	−	0.960666i	$-0.410425\pi$
$409$	11.2326	0.555415	0.277708	+	0.960666i	$0.410425\pi$
$410$	−4.56174	−0.225288
$411$	4.56990	0.225416
$412$	0.694123	0.0341970
$413$	2.75006	0.135322
$414$	−10.2524	−0.503879
$415$	5.72208	0.280886
$416$	−0.531472	−0.0260575
$417$	−20.8358	−1.02034
$418$	0	0
$419$	−20.2013	−0.986897	−0.493449	−	0.869775i	$-0.664264\pi$
$419$	−20.2013	−0.986897	−0.493449	+	0.869775i	$0.664264\pi$
$420$	−0.770577	−0.0376003
$421$	−12.7072	−0.619311	−0.309656	−	0.950849i	$-0.600214\pi$
$421$	−12.7072	−0.619311	−0.309656	+	0.950849i	$0.600214\pi$
$422$	5.61110	0.273144
$423$	9.70401	0.471825
$424$	−9.31823	−0.452533
$425$	28.2425	1.36996
$426$	24.6589	1.19473
$427$	−3.88118	−0.187824
$428$	8.63080	0.417185
$429$	0	0
$430$	−4.55693	−0.219754
$431$	−31.5802	−1.52117	−0.760583	−	0.649240i	$-0.775087\pi$
$431$	−31.5802	−1.52117	−0.760583	+	0.649240i	$0.775087\pi$
$432$	−3.12645	−0.150421
$433$	21.2373	1.02060	0.510299	−	0.859997i	$-0.329535\pi$
$433$	21.2373	1.02060	0.510299	+	0.859997i	$0.329535\pi$
$434$	4.72157	0.226643
$435$	3.94487	0.189142
$436$	8.10360	0.388092
$437$	−6.69536	−0.320283
$438$	−26.2683	−1.25515
$439$	23.1919	1.10689	0.553445	−	0.832886i	$-0.313313\pi$
$439$	23.1919	1.10689	0.553445	+	0.832886i	$0.313313\pi$
$440$	0	0
$441$	−9.70444	−0.462116
$442$	3.12567	0.148673
$443$	−16.6453	−0.790843	−0.395421	−	0.918500i	$-0.629401\pi$
$443$	−16.6453	−0.790843	−0.395421	+	0.918500i	$0.629401\pi$
$444$	5.05629	0.239961
$445$	−3.29184	−0.156048
$446$	23.9862	1.13578
$447$	2.65920	0.125776
$448$	0.813941	0.0384551
$449$	−2.23355	−0.105408	−0.0527038	−	0.998610i	$-0.516784\pi$
$449$	−2.23355	−0.105408	−0.0527038	+	0.998610i	$0.516784\pi$
$450$	7.35348	0.346646
$451$	0	0
$452$	4.66260	0.219310
$453$	−29.4880	−1.38547
$454$	3.52771	0.165564
$455$	−0.192392	−0.00901946
$456$	2.12868	0.0996845
$457$	12.4265	0.581288	0.290644	−	0.956831i	$-0.406131\pi$
$457$	12.4265	0.581288	0.290644	+	0.956831i	$0.406131\pi$
$458$	19.5717	0.914527
$459$	18.3871	0.858239
$460$	−2.97774	−0.138838
$461$	31.8148	1.48176	0.740881	−	0.671636i	$-0.234408\pi$
$461$	31.8148	1.48176	0.740881	+	0.671636i	$0.234408\pi$
$462$	0	0
$463$	−0.0722953	−0.00335985	−0.00167992	−	0.999999i	$-0.500535\pi$
$463$	−0.0722953	−0.00335985	−0.00167992	+	0.999999i	$0.500535\pi$
$464$	−4.16686	−0.193442
$465$	5.49183	0.254677
$466$	−19.2019	−0.889511
$467$	−33.8105	−1.56456	−0.782281	−	0.622925i	$-0.785944\pi$
$467$	−33.8105	−1.56456	−0.782281	+	0.622925i	$0.785944\pi$
$468$	0.813828	0.0376192
$469$	−1.00150	−0.0462449
$470$	2.81846	0.130006
$471$	36.8467	1.69781
$472$	−3.37870	−0.155517
$473$	0	0
$474$	7.38643	0.339270
$475$	4.80220	0.220340
$476$	−4.78692	−0.219408
$477$	14.2688	0.653321
$478$	19.3799	0.886415
$479$	−7.68378	−0.351081	−0.175540	−	0.984472i	$-0.556167\pi$
$479$	−7.68378	−0.351081	−0.175540	+	0.984472i	$0.556167\pi$
$480$	0.946723	0.0432118
$481$	1.26241	0.0575611
$482$	−5.20964	−0.237293
$483$	11.6005	0.527842
$484$	0	0
$485$	6.32854	0.287364
$486$	14.5662	0.660737
$487$	−30.3683	−1.37612	−0.688059	−	0.725654i	$-0.741537\pi$
$487$	−30.3683	−1.37612	−0.688059	+	0.725654i	$0.741537\pi$
$488$	4.76838	0.215854
$489$	−21.2298	−0.960047
$490$	−2.81858	−0.127331
$491$	10.1148	0.456473	0.228236	−	0.973606i	$-0.426704\pi$
$491$	10.1148	0.456473	0.228236	+	0.973606i	$0.426704\pi$
$492$	−21.8337	−0.984340
$493$	24.5060	1.10369
$494$	0.531472	0.0239120
$495$	0	0
$496$	−5.80088	−0.260467
$497$	−9.42882	−0.422940
$498$	27.3874	1.22726
$499$	−18.6624	−0.835445	−0.417723	−	0.908575i	$-0.637172\pi$
$499$	−18.6624	−0.835445	−0.417723	+	0.908575i	$0.637172\pi$
$500$	4.35950	0.194963
$501$	48.7428	2.17767
$502$	−13.5993	−0.606968
$503$	−13.3397	−0.594790	−0.297395	−	0.954755i	$-0.596118\pi$
$503$	−13.3397	−0.594790	−0.297395	+	0.954755i	$0.596118\pi$
$504$	−1.24637	−0.0555176
$505$	−1.55887	−0.0693688
$506$	0	0
$507$	−27.0716	−1.20229
$508$	5.75512	0.255342
$509$	35.1855	1.55957	0.779784	−	0.626048i	$-0.215329\pi$
$509$	35.1855	1.55957	0.779784	+	0.626048i	$0.215329\pi$
$510$	−5.56783	−0.246548
$511$	10.0442	0.444329
$512$	−1.00000	−0.0441942
$513$	3.12645	0.138036
$514$	10.9529	0.483113
$515$	−0.308709	−0.0136033
$516$	−21.8107	−0.960161
$517$	0	0
$518$	−1.93337	−0.0849474
$519$	−16.4956	−0.724077
$520$	0.236370	0.0103655
$521$	−27.1020	−1.18736	−0.593679	−	0.804702i	$-0.702325\pi$
$521$	−27.1020	−1.18736	−0.593679	+	0.804702i	$0.702325\pi$
$522$	6.38060	0.279271
$523$	12.2389	0.535169	0.267584	−	0.963534i	$-0.413775\pi$
$523$	12.2389	0.535169	0.267584	+	0.963534i	$0.413775\pi$
$524$	−0.970302	−0.0423878
$525$	−8.32039	−0.363131
$526$	−27.8602	−1.21476
$527$	34.1159	1.48611
$528$	0	0
$529$	21.8279	0.949038
$530$	4.14426	0.180015
$531$	5.17371	0.224520
$532$	−0.813941	−0.0352888
$533$	−5.45127	−0.236121
$534$	−15.7556	−0.681812
$535$	−3.83852	−0.165954
$536$	1.23043	0.0531464
$537$	28.0535	1.21060
$538$	−12.9191	−0.556983
$539$	0	0
$540$	1.39048	0.0598367
$541$	44.6953	1.92160	0.960801	−	0.277238i	$-0.0894189\pi$
$541$	44.6953	1.92160	0.960801	+	0.277238i	$0.0894189\pi$
$542$	−8.10604	−0.348184
$543$	−19.5024	−0.836926
$544$	5.88116	0.252153
$545$	−3.60405	−0.154381
$546$	−0.920838	−0.0394082
$547$	−2.84216	−0.121522	−0.0607610	−	0.998152i	$-0.519353\pi$
$547$	−2.84216	−0.121522	−0.0607610	+	0.998152i	$0.519353\pi$
$548$	2.14682	0.0917077
$549$	−7.30169	−0.311629
$550$	0	0
$551$	4.16686	0.177514
$552$	−14.2523	−0.606617
$553$	−2.82434	−0.120103
$554$	−23.4635	−0.996870
$555$	−2.24877	−0.0954550
$556$	−9.78816	−0.415110
$557$	−31.6341	−1.34038	−0.670189	−	0.742190i	$-0.733787\pi$
$557$	−31.6341	−1.34038	−0.670189	+	0.742190i	$0.733787\pi$
$558$	8.88272	0.376036
$559$	−5.44551	−0.230321
$560$	−0.361998	−0.0152972
$561$	0	0
$562$	14.3704	0.606180
$563$	−4.38903	−0.184976	−0.0924878	−	0.995714i	$-0.529482\pi$
$563$	−4.38903	−0.184976	−0.0924878	+	0.995714i	$0.529482\pi$
$564$	13.4899	0.568028
$565$	−2.07368	−0.0872402
$566$	11.6889	0.491321
$567$	−9.15605	−0.384518
$568$	11.5841	0.486060
$569$	−38.8116	−1.62707	−0.813534	−	0.581517i	$-0.802459\pi$
$569$	−38.8116	−1.62707	−0.813534	+	0.581517i	$0.802459\pi$
$570$	−0.946723	−0.0396539
$571$	−22.3077	−0.933547	−0.466774	−	0.884377i	$-0.654584\pi$
$571$	−22.3077	−0.933547	−0.466774	+	0.884377i	$0.654584\pi$
$572$	0	0
$573$	−30.9996	−1.29503
$574$	8.34854	0.348462
$575$	−32.1525	−1.34085
$576$	1.53127	0.0638030
$577$	19.6493	0.818009	0.409005	−	0.912532i	$-0.365876\pi$
$577$	19.6493	0.818009	0.409005	+	0.912532i	$0.365876\pi$
$578$	−17.5881	−0.731567
$579$	−5.17395	−0.215022
$580$	1.85320	0.0769499
$581$	−10.4721	−0.434457
$582$	30.2901	1.25556
$583$	0	0
$584$	−12.3402	−0.510641
$585$	−0.361948	−0.0149647
$586$	−24.6851	−1.01973
$587$	40.5186	1.67238	0.836191	−	0.548439i	$-0.184778\pi$
$587$	40.5186	1.67238	0.836191	+	0.548439i	$0.184778\pi$
$588$	−13.4905	−0.556339
$589$	5.80088	0.239021
$590$	1.50267	0.0618638
$591$	−23.2126	−0.954840
$592$	2.37532	0.0976250
$593$	−11.8720	−0.487525	−0.243762	−	0.969835i	$-0.578382\pi$
$593$	−11.8720	−0.487525	−0.243762	+	0.969835i	$0.578382\pi$
$594$	0	0
$595$	2.12897	0.0872792
$596$	1.24923	0.0511703
$597$	−32.5696	−1.33298
$598$	−3.55839	−0.145514
$599$	−37.2135	−1.52050	−0.760250	−	0.649630i	$-0.774924\pi$
$599$	−37.2135	−1.52050	−0.760250	+	0.649630i	$0.774924\pi$
$600$	10.2223	0.417325
$601$	−17.3215	−0.706559	−0.353280	−	0.935518i	$-0.614934\pi$
$601$	−17.3215	−0.706559	−0.353280	+	0.935518i	$0.614934\pi$
$602$	8.33973	0.339902
$603$	−1.88412	−0.0767274
$604$	−13.8527	−0.563659
$605$	0	0
$606$	−7.46117	−0.303089
$607$	0.942834	0.0382685	0.0191342	−	0.999817i	$-0.493909\pi$
$607$	0.942834	0.0382685	0.0191342	+	0.999817i	$0.493909\pi$
$608$	1.00000	0.0405554
$609$	−7.21959	−0.292552
$610$	−2.12072	−0.0858656
$611$	3.36805	0.136257
$612$	−9.00566	−0.364032
$613$	−34.0246	−1.37424	−0.687121	−	0.726543i	$-0.741126\pi$
$613$	−34.0246	−1.37424	−0.687121	+	0.726543i	$0.741126\pi$
$614$	11.2527	0.454122
$615$	9.71048	0.391564
$616$	0	0
$617$	−12.4983	−0.503162	−0.251581	−	0.967836i	$-0.580950\pi$
$617$	−12.4983	−0.503162	−0.251581	+	0.967836i	$0.580950\pi$
$618$	−1.47756	−0.0594363
$619$	−29.4196	−1.18247	−0.591237	−	0.806498i	$-0.701360\pi$
$619$	−29.4196	−1.18247	−0.591237	+	0.806498i	$0.701360\pi$
$620$	2.57992	0.103612
$621$	−20.9327	−0.840001
$622$	−3.40711	−0.136613
$623$	6.02447	0.241365
$624$	1.13133	0.0452895
$625$	22.0721	0.882885
$626$	−20.6424	−0.825035
$627$	0	0
$628$	17.3097	0.690731
$629$	−13.9696	−0.557006
$630$	0.554318	0.0220845
$631$	7.76186	0.308995	0.154497	−	0.987993i	$-0.450624\pi$
$631$	7.76186	0.308995	0.154497	+	0.987993i	$0.450624\pi$
$632$	3.46996	0.138028
$633$	−11.9442	−0.474740
$634$	26.2022	1.04062
$635$	−2.55957	−0.101573
$636$	19.8355	0.786530
$637$	−3.36820	−0.133453
$638$	0	0
$639$	−17.7385	−0.701724
$640$	0.444747	0.0175802
$641$	19.5247	0.771180	0.385590	−	0.922670i	$-0.373998\pi$
$641$	19.5247	0.771180	0.385590	+	0.922670i	$0.373998\pi$
$642$	−18.3722	−0.725093
$643$	−48.4409	−1.91032	−0.955162	−	0.296083i	$-0.904319\pi$
$643$	−48.4409	−1.91032	−0.955162	+	0.296083i	$0.904319\pi$
$644$	5.44963	0.214746
$645$	9.70023	0.381946
$646$	−5.88116	−0.231391
$647$	32.0388	1.25958	0.629788	−	0.776767i	$-0.283142\pi$
$647$	32.0388	1.25958	0.629788	+	0.776767i	$0.283142\pi$
$648$	11.2490	0.441903
$649$	0	0
$650$	2.55223	0.100107
$651$	−10.0507	−0.393919
$652$	−9.97325	−0.390583
$653$	−36.7648	−1.43872	−0.719359	−	0.694638i	$-0.755565\pi$
$653$	−36.7648	−1.43872	−0.719359	+	0.694638i	$0.755565\pi$
$654$	−17.2500	−0.674527
$655$	0.431539	0.0168616
$656$	−10.2569	−0.400466
$657$	18.8962	0.737211
$658$	−5.15813	−0.201085
$659$	−1.92517	−0.0749940	−0.0374970	−	0.999297i	$-0.511938\pi$
$659$	−1.92517	−0.0749940	−0.0374970	+	0.999297i	$0.511938\pi$
$660$	0	0
$661$	−0.375942	−0.0146225	−0.00731123	−	0.999973i	$-0.502327\pi$
$661$	−0.375942	−0.0146225	−0.00731123	+	0.999973i	$0.502327\pi$
$662$	−22.7831	−0.885491
$663$	−6.65355	−0.258402
$664$	12.8659	0.499295
$665$	0.361998	0.0140377
$666$	−3.63726	−0.140941
$667$	−27.8986	−1.08024
$668$	22.8982	0.885957
$669$	−51.0589	−1.97405
$670$	−0.547230	−0.0211413
$671$	0	0
$672$	−1.73262	−0.0668373
$673$	−13.5595	−0.522681	−0.261340	−	0.965247i	$-0.584165\pi$
$673$	−13.5595	−0.522681	−0.261340	+	0.965247i	$0.584165\pi$
$674$	16.6810	0.642526
$675$	15.0138	0.577883
$676$	−12.7175	−0.489136
$677$	46.1646	1.77425	0.887125	−	0.461530i	$-0.152699\pi$
$677$	46.1646	1.77425	0.887125	+	0.461530i	$0.152699\pi$
$678$	−9.92517	−0.381174
$679$	−11.5820	−0.444476
$680$	−2.61563	−0.100305
$681$	−7.50937	−0.287759
$682$	0	0
$683$	13.2284	0.506170	0.253085	−	0.967444i	$-0.418555\pi$
$683$	13.2284	0.506170	0.253085	+	0.967444i	$0.418555\pi$
$684$	−1.53127	−0.0585497
$685$	−0.954793	−0.0364808
$686$	10.8559	0.414482
$687$	−41.6619	−1.58950
$688$	−10.2461	−0.390629
$689$	4.95238	0.188671
$690$	6.33866	0.241309
$691$	30.8706	1.17437	0.587186	−	0.809452i	$-0.300236\pi$
$691$	30.8706	1.17437	0.587186	+	0.809452i	$0.300236\pi$
$692$	−7.74923	−0.294581
$693$	0	0
$694$	−24.8615	−0.943728
$695$	4.35325	0.165128
$696$	8.86991	0.336213
$697$	60.3227	2.28488
$698$	−19.5583	−0.740294
$699$	40.8747	1.54602
$700$	−3.90871	−0.147735
$701$	−48.6574	−1.83777	−0.918883	−	0.394530i	$-0.870907\pi$
$701$	−48.6574	−1.83777	−0.918883	+	0.394530i	$0.870907\pi$
$702$	1.66162	0.0627138
$703$	−2.37532	−0.0895868
$704$	0	0
$705$	−5.99960	−0.225958
$706$	17.1793	0.646551
$707$	2.85292	0.107295
$708$	7.19216	0.270298
$709$	−4.26738	−0.160265	−0.0801324	−	0.996784i	$-0.525534\pi$
$709$	−4.26738	−0.160265	−0.0801324	+	0.996784i	$0.525534\pi$
$710$	−5.15201	−0.193352
$711$	−5.31345	−0.199270
$712$	−7.40160	−0.277387
$713$	−38.8390	−1.45453
$714$	10.1898	0.381344
$715$	0	0
$716$	13.1788	0.492516
$717$	−41.2535	−1.54064
$718$	−19.0190	−0.709784
$719$	30.5349	1.13876	0.569379	−	0.822075i	$-0.307184\pi$
$719$	30.5349	1.13876	0.569379	+	0.822075i	$0.307184\pi$
$720$	−0.681029	−0.0253804
$721$	0.564975	0.0210408
$722$	−1.00000	−0.0372161
$723$	11.0897	0.412429
$724$	−9.16172	−0.340493
$725$	20.0101	0.743157
$726$	0	0
$727$	−3.87417	−0.143685	−0.0718425	−	0.997416i	$-0.522888\pi$
$727$	−3.87417	−0.143685	−0.0718425	+	0.997416i	$0.522888\pi$
$728$	−0.432587	−0.0160327
$729$	2.74030	0.101492
$730$	5.48827	0.203130
$731$	60.2590	2.22876
$732$	−10.1503	−0.375168
$733$	23.0823	0.852566	0.426283	−	0.904590i	$-0.359823\pi$
$733$	23.0823	0.852566	0.426283	+	0.904590i	$0.359823\pi$
$734$	−4.19576	−0.154868
$735$	5.99986	0.221308
$736$	−6.69536	−0.246794
$737$	0	0
$738$	15.7062	0.578152
$739$	−29.8163	−1.09681	−0.548404	−	0.836213i	$-0.684765\pi$
$739$	−29.8163	−1.09681	−0.548404	+	0.836213i	$0.684765\pi$
$740$	−1.05642	−0.0388346
$741$	−1.13133	−0.0415605
$742$	−7.58450	−0.278436
$743$	2.86361	0.105056	0.0525279	−	0.998619i	$-0.483272\pi$
$743$	2.86361	0.105056	0.0525279	+	0.998619i	$0.483272\pi$
$744$	12.3482	0.452707
$745$	−0.555589	−0.0203552
$746$	30.5753	1.11944
$747$	−19.7012	−0.720831
$748$	0	0
$749$	7.02496	0.256687
$750$	−9.27997	−0.338857
$751$	−48.3540	−1.76446	−0.882232	−	0.470815i	$-0.843960\pi$
$751$	−48.3540	−1.76446	−0.882232	+	0.470815i	$0.843960\pi$
$752$	6.33722	0.231095
$753$	28.9486	1.05495
$754$	2.21457	0.0806498
$755$	6.16095	0.224220
$756$	−2.54475	−0.0925515
$757$	22.8415	0.830188	0.415094	−	0.909778i	$-0.363749\pi$
$757$	22.8415	0.830188	0.415094	+	0.909778i	$0.363749\pi$
$758$	−27.9152	−1.01393
$759$	0	0
$760$	−0.444747	−0.0161327
$761$	23.6802	0.858408	0.429204	−	0.903208i	$-0.358794\pi$
$761$	23.6802	0.858408	0.429204	+	0.903208i	$0.358794\pi$
$762$	−12.2508	−0.443799
$763$	6.59586	0.238786
$764$	−14.5629	−0.526865
$765$	4.00524	0.144810
$766$	13.3334	0.481755
$767$	1.79568	0.0648383
$768$	2.12868	0.0768121
$769$	−49.9760	−1.80218	−0.901090	−	0.433633i	$-0.857231\pi$
$769$	−49.9760	−1.80218	−0.901090	+	0.433633i	$0.857231\pi$
$770$	0	0
$771$	−23.3152	−0.839678
$772$	−2.43059	−0.0874789
$773$	−33.4774	−1.20410	−0.602049	−	0.798459i	$-0.705649\pi$
$773$	−33.4774	−1.20410	−0.602049	+	0.798459i	$0.705649\pi$
$774$	15.6896	0.563950
$775$	27.8570	1.00065
$776$	14.2295	0.510810
$777$	4.11552	0.147644
$778$	6.00531	0.215301
$779$	10.2569	0.367493
$780$	−0.503157	−0.0180159
$781$	0	0
$782$	39.3765	1.40810
$783$	13.0275	0.465564
$784$	−6.33750	−0.226339
$785$	−7.69842	−0.274768
$786$	2.06546	0.0736725
$787$	16.7744	0.597944	0.298972	−	0.954262i	$-0.403356\pi$
$787$	16.7744	0.597944	0.298972	+	0.954262i	$0.403356\pi$
$788$	−10.9047	−0.388464
$789$	59.3054	2.11133
$790$	−1.54325	−0.0549065
$791$	3.79508	0.134938
$792$	0	0
$793$	−2.53426	−0.0899942
$794$	27.7223	0.983828
$795$	−8.82179	−0.312877
$796$	−15.3004	−0.542307
$797$	22.0845	0.782273	0.391136	−	0.920333i	$-0.372082\pi$
$797$	22.0845	0.782273	0.391136	+	0.920333i	$0.372082\pi$
$798$	1.73262	0.0613341
$799$	−37.2702	−1.31853
$800$	4.80220	0.169783
$801$	11.3339	0.400462
$802$	−29.1632	−1.02979
$803$	0	0
$804$	−2.61919	−0.0923716
$805$	−2.42371	−0.0854245
$806$	3.08300	0.108594
$807$	27.5007	0.968070
$808$	−3.50507	−0.123308
$809$	29.1249	1.02398	0.511988	−	0.858993i	$-0.328909\pi$
$809$	29.1249	1.02398	0.511988	+	0.858993i	$0.328909\pi$
$810$	−5.00297	−0.175786
$811$	30.3451	1.06556	0.532780	−	0.846254i	$-0.321147\pi$
$811$	30.3451	1.06556	0.532780	+	0.846254i	$0.321147\pi$
$812$	−3.39158	−0.119021
$813$	17.2551	0.605164
$814$	0	0
$815$	4.43557	0.155371
$816$	−12.5191	−0.438256
$817$	10.2461	0.358466
$818$	−11.2326	−0.392738
$819$	0.662408	0.0231464
$820$	4.56174	0.159303
$821$	7.07451	0.246902	0.123451	−	0.992351i	$-0.460604\pi$
$821$	7.07451	0.246902	0.123451	+	0.992351i	$0.460604\pi$
$822$	−4.56990	−0.159393
$823$	−29.8242	−1.03961	−0.519803	−	0.854286i	$-0.673995\pi$
$823$	−29.8242	−1.03961	−0.519803	+	0.854286i	$0.673995\pi$
$824$	−0.694123	−0.0241809
$825$	0	0
$826$	−2.75006	−0.0956869
$827$	40.6914	1.41498	0.707490	−	0.706723i	$-0.249827\pi$
$827$	40.6914	1.41498	0.707490	+	0.706723i	$0.249827\pi$
$828$	10.2524	0.356296
$829$	14.0816	0.489073	0.244537	−	0.969640i	$-0.421364\pi$
$829$	14.0816	0.489073	0.244537	+	0.969640i	$0.421364\pi$
$830$	−5.72208	−0.198616
$831$	49.9463	1.73262
$832$	0.531472	0.0184255
$833$	37.2719	1.29139
$834$	20.8358	0.721486
$835$	−10.1839	−0.352428
$836$	0	0
$837$	18.1361	0.626877
$838$	20.2013	0.697842
$839$	49.4824	1.70832	0.854162	−	0.520007i	$-0.174071\pi$
$839$	49.4824	1.70832	0.854162	+	0.520007i	$0.174071\pi$
$840$	0.770577	0.0265874
$841$	−11.6373	−0.401285
$842$	12.7072	0.437919
$843$	−30.5901	−1.05358
$844$	−5.61110	−0.193142
$845$	5.65609	0.194575
$846$	−9.70401	−0.333631
$847$	0	0
$848$	9.31823	0.319989
$849$	−24.8819	−0.853945
$850$	−28.2425	−0.968710
$851$	15.9036	0.545169
$852$	−24.6589	−0.844801
$853$	23.6652	0.810280	0.405140	−	0.914255i	$-0.367223\pi$
$853$	23.6652	0.810280	0.405140	+	0.914255i	$0.367223\pi$
$854$	3.88118	0.132811
$855$	0.681029	0.0232907
$856$	−8.63080	−0.294995
$857$	−17.6097	−0.601535	−0.300768	−	0.953697i	$-0.597243\pi$
$857$	−17.6097	−0.601535	−0.300768	+	0.953697i	$0.597243\pi$
$858$	0	0
$859$	35.6398	1.21602	0.608008	−	0.793931i	$-0.291969\pi$
$859$	35.6398	1.21602	0.608008	+	0.793931i	$0.291969\pi$
$860$	4.55693	0.155390
$861$	−17.7714	−0.605647
$862$	31.5802	1.07563
$863$	32.1883	1.09570	0.547850	−	0.836576i	$-0.315446\pi$
$863$	32.1883	1.09570	0.547850	+	0.836576i	$0.315446\pi$
$864$	3.12645	0.106364
$865$	3.44645	0.117183
$866$	−21.2373	−0.721672
$867$	37.4393	1.27151
$868$	−4.72157	−0.160261
$869$	0	0
$870$	−3.94487	−0.133743
$871$	−0.653938	−0.0221578
$872$	−8.10360	−0.274423
$873$	−21.7893	−0.737455
$874$	6.69536	0.226474
$875$	3.54838	0.119957
$876$	26.2683	0.887524
$877$	29.1474	0.984238	0.492119	−	0.870528i	$-0.336222\pi$
$877$	29.1474	0.984238	0.492119	+	0.870528i	$0.336222\pi$
$878$	−23.1919	−0.782689
$879$	52.5466	1.77235
$880$	0	0
$881$	−17.4611	−0.588279	−0.294139	−	0.955763i	$-0.595033\pi$
$881$	−17.4611	−0.588279	−0.294139	+	0.955763i	$0.595033\pi$
$882$	9.70444	0.326765
$883$	10.2292	0.344239	0.172119	−	0.985076i	$-0.444939\pi$
$883$	10.2292	0.344239	0.172119	+	0.985076i	$0.444939\pi$
$884$	−3.12567	−0.105128
$885$	−3.19869	−0.107523
$886$	16.6453	0.559210
$887$	−29.5730	−0.992966	−0.496483	−	0.868047i	$-0.665375\pi$
$887$	−29.5730	−0.992966	−0.496483	+	0.868047i	$0.665375\pi$
$888$	−5.05629	−0.169678
$889$	4.68433	0.157107
$890$	3.29184	0.110343
$891$	0	0
$892$	−23.9862	−0.803118
$893$	−6.33722	−0.212067
$894$	−2.65920	−0.0889369
$895$	−5.86124	−0.195920
$896$	−0.813941	−0.0271919
$897$	7.57468	0.252911
$898$	2.23355	0.0745344
$899$	24.1715	0.806163
$900$	−7.35348	−0.245116
$901$	−54.8020	−1.82572
$902$	0	0
$903$	−17.7526	−0.590770
$904$	−4.66260	−0.155076
$905$	4.07465	0.135446
$906$	29.4880	0.979673
$907$	−11.7834	−0.391260	−0.195630	−	0.980678i	$-0.562675\pi$
$907$	−11.7834	−0.391260	−0.195630	+	0.980678i	$0.562675\pi$
$908$	−3.52771	−0.117071
$909$	5.36722	0.178019
$910$	0.192392	0.00637772
$911$	−48.6666	−1.61240	−0.806198	−	0.591646i	$-0.798478\pi$
$911$	−48.6666	−1.61240	−0.806198	+	0.591646i	$0.798478\pi$
$912$	−2.12868	−0.0704876
$913$	0	0
$914$	−12.4265	−0.411032
$915$	4.51434	0.149239
$916$	−19.5717	−0.646669
$917$	−0.789769	−0.0260805
$918$	−18.3871	−0.606866
$919$	−44.7874	−1.47740	−0.738700	−	0.674035i	$-0.764560\pi$
$919$	−44.7874	−1.47740	−0.738700	+	0.674035i	$0.764560\pi$
$920$	2.97774	0.0981733
$921$	−23.9534	−0.789291
$922$	−31.8148	−1.04776
$923$	−6.15665	−0.202648
$924$	0	0
$925$	−11.4068	−0.375052
$926$	0.0722953	0.00237577
$927$	1.06289	0.0349099
$928$	4.16686	0.136784
$929$	40.9518	1.34359	0.671793	−	0.740739i	$-0.265524\pi$
$929$	40.9518	1.34359	0.671793	+	0.740739i	$0.265524\pi$
$930$	−5.49183	−0.180084
$931$	6.33750	0.207703
$932$	19.2019	0.628980
$933$	7.25263	0.237441
$934$	33.8105	1.10631
$935$	0	0
$936$	−0.813828	−0.0266008
$937$	5.66048	0.184920	0.0924599	−	0.995716i	$-0.470527\pi$
$937$	5.66048	0.184920	0.0924599	+	0.995716i	$0.470527\pi$
$938$	1.00150	0.0327000
$939$	43.9410	1.43396
$940$	−2.81846	−0.0919281
$941$	−14.4380	−0.470664	−0.235332	−	0.971915i	$-0.575618\pi$
$941$	−14.4380	−0.470664	−0.235332	+	0.971915i	$0.575618\pi$
$942$	−36.8467	−1.20053
$943$	−68.6739	−2.23633
$944$	3.37870	0.109967
$945$	1.13177	0.0368164
$946$	0	0
$947$	6.99025	0.227153	0.113576	−	0.993529i	$-0.463769\pi$
$947$	6.99025	0.227153	0.113576	+	0.993529i	$0.463769\pi$
$948$	−7.38643	−0.239900
$949$	6.55846	0.212897
$950$	−4.80220	−0.155804
$951$	−55.7761	−1.80866
$952$	4.78692	0.155145
$953$	16.6615	0.539718	0.269859	−	0.962900i	$-0.413023\pi$
$953$	16.6615	0.539718	0.269859	+	0.962900i	$0.413023\pi$
$954$	−14.2688	−0.461968
$955$	6.47678	0.209584
$956$	−19.3799	−0.626790
$957$	0	0
$958$	7.68378	0.248252
$959$	1.74739	0.0564261
$960$	−0.946723	−0.0305554
$961$	2.65018	0.0854897
$962$	−1.26241	−0.0407019
$963$	13.2161	0.425883
$964$	5.20964	0.167791
$965$	1.08100	0.0347986
$966$	−11.6005	−0.373240
$967$	8.50933	0.273642	0.136821	−	0.990596i	$-0.456312\pi$
$967$	8.50933	0.273642	0.136821	+	0.990596i	$0.456312\pi$
$968$	0	0
$969$	12.5191	0.402172
$970$	−6.32854	−0.203197
$971$	−18.6734	−0.599257	−0.299628	−	0.954056i	$-0.596863\pi$
$971$	−18.6734	−0.599257	−0.299628	+	0.954056i	$0.596863\pi$
$972$	−14.5662	−0.467211
$973$	−7.96699	−0.255410
$974$	30.3683	0.973063
$975$	−5.43288	−0.173992
$976$	−4.76838	−0.152632
$977$	−0.303786	−0.00971897	−0.00485948	−	0.999988i	$-0.501547\pi$
$977$	−0.303786	−0.00971897	−0.00485948	+	0.999988i	$0.501547\pi$
$978$	21.2298	0.678856
$979$	0	0
$980$	2.81858	0.0900364
$981$	12.4088	0.396183
$982$	−10.1148	−0.322775
$983$	45.9811	1.46657	0.733285	−	0.679922i	$-0.237986\pi$
$983$	45.9811	1.46657	0.733285	+	0.679922i	$0.237986\pi$
$984$	21.8337	0.696033
$985$	4.84984	0.154529
$986$	−24.5060	−0.780430
$987$	10.9800	0.349497
$988$	−0.531472	−0.0169084
$989$	−68.6014	−2.18140
$990$	0	0
$991$	19.4299	0.617210	0.308605	−	0.951190i	$-0.400138\pi$
$991$	19.4299	0.617210	0.308605	+	0.951190i	$0.400138\pi$
$992$	5.80088	0.184178
$993$	48.4979	1.53904
$994$	9.42882	0.299064
$995$	6.80479	0.215726
$996$	−27.3874	−0.867804
$997$	−22.5459	−0.714035	−0.357018	−	0.934098i	$-0.616206\pi$
$997$	−22.5459	−0.714035	−0.357018	+	0.934098i	$0.616206\pi$
$998$	18.6624	0.590749
$999$	−7.42631	−0.234958

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cc.1.9		10
11.3	even	5		418.2.f.h.229.1	yes	20
11.4	even	5		418.2.f.h.115.1	✓	20
11.10	odd	2		4598.2.a.cd.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.1	✓	20	11.4	even	5
418.2.f.h.229.1	yes	20	11.3	even	5
4598.2.a.cc.1.9		10	1.1	even	1	trivial
4598.2.a.cd.1.9		10	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.12868 q^{3} +1.00000 q^{4} -0.444747 q^{5} -2.12868 q^{6} +0.813941 q^{7} -1.00000 q^{8} +1.53127 q^{9} +0.444747 q^{10} +2.12868 q^{12} +0.531472 q^{13} -0.813941 q^{14} -0.946723 q^{15} +1.00000 q^{16} -5.88116 q^{17} -1.53127 q^{18} -1.00000 q^{19} -0.444747 q^{20} +1.73262 q^{21} +6.69536 q^{23} -2.12868 q^{24} -4.80220 q^{25} -0.531472 q^{26} -3.12645 q^{27} +0.813941 q^{28} -4.16686 q^{29} +0.946723 q^{30} -5.80088 q^{31} -1.00000 q^{32} +5.88116 q^{34} -0.361998 q^{35} +1.53127 q^{36} +2.37532 q^{37} +1.00000 q^{38} +1.13133 q^{39} +0.444747 q^{40} -10.2569 q^{41} -1.73262 q^{42} -10.2461 q^{43} -0.681029 q^{45} -6.69536 q^{46} +6.33722 q^{47} +2.12868 q^{48} -6.33750 q^{49} +4.80220 q^{50} -12.5191 q^{51} +0.531472 q^{52} +9.31823 q^{53} +3.12645 q^{54} -0.813941 q^{56} -2.12868 q^{57} +4.16686 q^{58} +3.37870 q^{59} -0.946723 q^{60} -4.76838 q^{61} +5.80088 q^{62} +1.24637 q^{63} +1.00000 q^{64} -0.236370 q^{65} -1.23043 q^{67} -5.88116 q^{68} +14.2523 q^{69} +0.361998 q^{70} -11.5841 q^{71} -1.53127 q^{72} +12.3402 q^{73} -2.37532 q^{74} -10.2223 q^{75} -1.00000 q^{76} -1.13133 q^{78} -3.46996 q^{79} -0.444747 q^{80} -11.2490 q^{81} +10.2569 q^{82} -12.8659 q^{83} +1.73262 q^{84} +2.61563 q^{85} +10.2461 q^{86} -8.86991 q^{87} +7.40160 q^{89} +0.681029 q^{90} +0.432587 q^{91} +6.69536 q^{92} -12.3482 q^{93} -6.33722 q^{94} +0.444747 q^{95} -2.12868 q^{96} -14.2295 q^{97} +6.33750 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} - 2 q^{6} - 11 q^{7} - 10 q^{8} + 12 q^{9} + 3 q^{10} + 2 q^{12} - 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 10 q^{19} - 3 q^{20}+ \cdots + 3 q^{98}+O(q^{100}) \) 10 * q - 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 - 2 * q^6 - 11 * q^7 - 10 * q^8 + 12 * q^9 + 3 * q^10 + 2 * q^12 - 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 - 12 * q^17 - 12 * q^18 - 10 * q^19 - 3 * q^20 + q^21 + 14 * q^23 - 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 - 11 * q^28 - 16 * q^29 - q^30 + 12 * q^31 - 10 * q^32 + 12 * q^34 + 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 - 11 * q^39 + 3 * q^40 + 5 * q^41 - q^42 - 22 * q^43 - 2 * q^45 - 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 - 5 * q^50 - 8 * q^51 - 11 * q^52 + 2 * q^53 - 2 * q^54 + 11 * q^56 - 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 - 35 * q^61 - 12 * q^62 - 38 * q^63 + 10 * q^64 - 4 * q^65 + 9 * q^67 - 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 - 12 * q^72 - 5 * q^73 + q^74 - 15 * q^75 - 10 * q^76 + 11 * q^78 - 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 - 7 * q^83 + q^84 - 35 * q^85 + 22 * q^86 - 8 * q^87 + 22 * q^89 + 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 - 8 * q^94 + 3 * q^95 - 2 * q^96 + 32 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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