LMFDB - Embedded newform 5610.2.a.cb.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5610,2,Mod(1,5610)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5610.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5610, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-3,3,3,3,-3,3,-3,3,-3,-3,3,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	yes
Analytic conductor:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.2089.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 13x - 4 $ x^3 - 13*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.309984$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +0.690016 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} -0.690016 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.00000 q^{20} +0.690016 q^{21} +1.00000 q^{22} -8.90391 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +0.690016 q^{28} -0.690016 q^{29} -1.00000 q^{30} +1.30998 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +0.690016 q^{35} +1.00000 q^{36} +9.59393 q^{37} +4.00000 q^{39} -1.00000 q^{40} -7.59393 q^{41} -0.690016 q^{42} +7.30998 q^{43} -1.00000 q^{44} +1.00000 q^{45} +8.90391 q^{46} +7.59393 q^{47} +1.00000 q^{48} -6.52388 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} +6.97396 q^{53} -1.00000 q^{54} -1.00000 q^{55} -0.690016 q^{56} +0.690016 q^{58} +9.59393 q^{59} +1.00000 q^{60} +2.00000 q^{61} -1.30998 q^{62} +0.690016 q^{63} +1.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} -8.21389 q^{67} +1.00000 q^{68} -8.90391 q^{69} -0.690016 q^{70} +14.8339 q^{71} -1.00000 q^{72} +10.2139 q^{73} -9.59393 q^{74} +1.00000 q^{75} -0.690016 q^{77} -4.00000 q^{78} +15.1879 q^{79} +1.00000 q^{80} +1.00000 q^{81} +7.59393 q^{82} -15.1879 q^{83} +0.690016 q^{84} +1.00000 q^{85} -7.30998 q^{86} -0.690016 q^{87} +1.00000 q^{88} -7.38003 q^{89} -1.00000 q^{90} +2.76007 q^{91} -8.90391 q^{92} +1.30998 q^{93} -7.59393 q^{94} -1.00000 q^{96} -19.1178 q^{97} +6.52388 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 3 q^{20} + 3 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 - q^23 - 3 * q^24 + 3 * q^25 - 12 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 3 * q^31 - 3 * q^32 - 3 * q^33 - 3 * q^34 + 3 * q^35 + 3 * q^36 + 4 * q^37 + 12 * q^39 - 3 * q^40 + 2 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 + q^46 - 2 * q^47 + 3 * q^48 + 8 * q^49 - 3 * q^50 + 3 * q^51 + 12 * q^52 - 2 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 + 3 * q^58 + 4 * q^59 + 3 * q^60 + 6 * q^61 - 3 * q^62 + 3 * q^63 + 3 * q^64 + 12 * q^65 + 3 * q^66 + 2 * q^67 + 3 * q^68 - q^69 - 3 * q^70 + 16 * q^71 - 3 * q^72 + 4 * q^73 - 4 * q^74 + 3 * q^75 - 3 * q^77 - 12 * q^78 - 4 * q^79 + 3 * q^80 + 3 * q^81 - 2 * q^82 + 4 * q^83 + 3 * q^84 + 3 * q^85 - 21 * q^86 - 3 * q^87 + 3 * q^88 - 24 * q^89 - 3 * q^90 + 12 * q^91 - q^92 + 3 * q^93 + 2 * q^94 - 3 * q^96 - 5 * q^97 - 8 * q^98 - 3 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	0.690016	0.260802	0.130401	−	0.991461i	$-0.458374\pi$
$7$	0.690016	0.260802	0.130401	+	0.991461i	$0.458374\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	−0.690016	−0.184415
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	1.00000	0.223607
$21$	0.690016	0.150574
$22$	1.00000	0.213201
$23$	−8.90391	−1.85659	−0.928297	−	0.371840i	$-0.878727\pi$
$23$	−8.90391	−1.85659	−0.928297	+	0.371840i	$0.878727\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.00000	−0.784465
$27$	1.00000	0.192450
$28$	0.690016	0.130401
$29$	−0.690016	−0.128133	−0.0640664	−	0.997946i	$-0.520407\pi$
$29$	−0.690016	−0.128133	−0.0640664	+	0.997946i	$0.520407\pi$
$30$	−1.00000	−0.182574
$31$	1.30998	0.235280	0.117640	−	0.993056i	$-0.462467\pi$
$31$	1.30998	0.235280	0.117640	+	0.993056i	$0.462467\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	0.690016	0.116634
$36$	1.00000	0.166667
$37$	9.59393	1.57723	0.788616	−	0.614886i	$-0.210798\pi$
$37$	9.59393	1.57723	0.788616	+	0.614886i	$0.210798\pi$
$38$	0	0
$39$	4.00000	0.640513
$40$	−1.00000	−0.158114
$41$	−7.59393	−1.18597	−0.592986	−	0.805213i	$-0.702051\pi$
$41$	−7.59393	−1.18597	−0.592986	+	0.805213i	$0.702051\pi$
$42$	−0.690016	−0.106472
$43$	7.30998	1.11476	0.557381	−	0.830257i	$-0.311806\pi$
$43$	7.30998	1.11476	0.557381	+	0.830257i	$0.311806\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	8.90391	1.31281
$47$	7.59393	1.10769	0.553844	−	0.832620i	$-0.313160\pi$
$47$	7.59393	1.10769	0.553844	+	0.832620i	$0.313160\pi$
$48$	1.00000	0.144338
$49$	−6.52388	−0.931982
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	4.00000	0.554700
$53$	6.97396	0.957947	0.478974	−	0.877829i	$-0.341009\pi$
$53$	6.97396	0.957947	0.478974	+	0.877829i	$0.341009\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	−0.690016	−0.0922073
$57$	0	0
$58$	0.690016	0.0906036
$59$	9.59393	1.24902	0.624511	−	0.781016i	$-0.285298\pi$
$59$	9.59393	1.24902	0.624511	+	0.781016i	$0.285298\pi$
$60$	1.00000	0.129099
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−1.30998	−0.166368
$63$	0.690016	0.0869339
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	1.00000	0.123091
$67$	−8.21389	−1.00349	−0.501743	−	0.865016i	$-0.667308\pi$
$67$	−8.21389	−1.00349	−0.501743	+	0.865016i	$0.667308\pi$
$68$	1.00000	0.121268
$69$	−8.90391	−1.07190
$70$	−0.690016	−0.0824727
$71$	14.8339	1.76046	0.880228	−	0.474552i	$-0.157390\pi$
$71$	14.8339	1.76046	0.880228	+	0.474552i	$0.157390\pi$
$72$	−1.00000	−0.117851
$73$	10.2139	1.19545	0.597723	−	0.801703i	$-0.296072\pi$
$73$	10.2139	1.19545	0.597723	+	0.801703i	$0.296072\pi$
$74$	−9.59393	−1.11527
$75$	1.00000	0.115470
$76$	0	0
$77$	−0.690016	−0.0786347
$78$	−4.00000	−0.452911
$79$	15.1879	1.70877	0.854383	−	0.519643i	$-0.173935\pi$
$79$	15.1879	1.70877	0.854383	+	0.519643i	$0.173935\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	7.59393	0.838609
$83$	−15.1879	−1.66708	−0.833542	−	0.552456i	$-0.813691\pi$
$83$	−15.1879	−1.66708	−0.833542	+	0.552456i	$0.813691\pi$
$84$	0.690016	0.0752870
$85$	1.00000	0.108465
$86$	−7.30998	−0.788256
$87$	−0.690016	−0.0739775
$88$	1.00000	0.106600
$89$	−7.38003	−0.782282	−0.391141	−	0.920331i	$-0.627920\pi$
$89$	−7.38003	−0.782282	−0.391141	+	0.920331i	$0.627920\pi$
$90$	−1.00000	−0.105409
$91$	2.76007	0.289334
$92$	−8.90391	−0.928297
$93$	1.30998	0.135839
$94$	−7.59393	−0.783254
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−19.1178	−1.94112	−0.970559	−	0.240862i	$-0.922570\pi$
$97$	−19.1178	−1.94112	−0.970559	+	0.240862i	$0.922570\pi$
$98$	6.52388	0.659011
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	6.21389	0.618306	0.309153	−	0.951012i	$-0.399955\pi$
$101$	6.21389	0.618306	0.309153	+	0.951012i	$0.399955\pi$
$102$	−1.00000	−0.0990148
$103$	−2.28394	−0.225044	−0.112522	−	0.993649i	$-0.535893\pi$
$103$	−2.28394	−0.225044	−0.112522	+	0.993649i	$0.535893\pi$
$104$	−4.00000	−0.392232
$105$	0.690016	0.0673387
$106$	−6.97396	−0.677371
$107$	10.2839	0.994186	0.497093	−	0.867697i	$-0.334401\pi$
$107$	10.2839	0.994186	0.497093	+	0.867697i	$0.334401\pi$
$108$	1.00000	0.0962250
$109$	−4.61997	−0.442513	−0.221256	−	0.975216i	$-0.571016\pi$
$109$	−4.61997	−0.442513	−0.221256	+	0.975216i	$0.571016\pi$
$110$	1.00000	0.0953463
$111$	9.59393	0.910615
$112$	0.690016	0.0652004
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	0	0
$115$	−8.90391	−0.830294
$116$	−0.690016	−0.0640664
$117$	4.00000	0.369800
$118$	−9.59393	−0.883193
$119$	0.690016	0.0632537
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	−7.59393	−0.684721
$124$	1.30998	0.117640
$125$	1.00000	0.0894427
$126$	−0.690016	−0.0614716
$127$	16.9740	1.50620	0.753098	−	0.657909i	$-0.228559\pi$
$127$	16.9740	1.50620	0.753098	+	0.657909i	$0.228559\pi$
$128$	−1.00000	−0.0883883
$129$	7.30998	0.643608
$130$	−4.00000	−0.350823
$131$	5.23993	0.457815	0.228908	−	0.973448i	$-0.426485\pi$
$131$	5.23993	0.457815	0.228908	+	0.973448i	$0.426485\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	8.21389	0.709572
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	5.66398	0.483906	0.241953	−	0.970288i	$-0.422212\pi$
$137$	5.66398	0.483906	0.241953	+	0.970288i	$0.422212\pi$
$138$	8.90391	0.757951
$139$	18.1438	1.53894	0.769470	−	0.638682i	$-0.220520\pi$
$139$	18.1438	1.53894	0.769470	+	0.638682i	$0.220520\pi$
$140$	0.690016	0.0583170
$141$	7.59393	0.639524
$142$	−14.8339	−1.24483
$143$	−4.00000	−0.334497
$144$	1.00000	0.0833333
$145$	−0.690016	−0.0573027
$146$	−10.2139	−0.845308
$147$	−6.52388	−0.538080
$148$	9.59393	0.788616
$149$	−3.59393	−0.294426	−0.147213	−	0.989105i	$-0.547030\pi$
$149$	−3.59393	−0.294426	−0.147213	+	0.989105i	$0.547030\pi$
$150$	−1.00000	−0.0816497
$151$	0.406073	0.0330458	0.0165229	−	0.999863i	$-0.494740\pi$
$151$	0.406073	0.0330458	0.0165229	+	0.999863i	$0.494740\pi$
$152$	0	0
$153$	1.00000	0.0808452
$154$	0.690016	0.0556031
$155$	1.30998	0.105220
$156$	4.00000	0.320256
$157$	−12.9740	−1.03543	−0.517717	−	0.855552i	$-0.673218\pi$
$157$	−12.9740	−1.03543	−0.517717	+	0.855552i	$0.673218\pi$
$158$	−15.1879	−1.20828
$159$	6.97396	0.553071
$160$	−1.00000	−0.0790569
$161$	−6.14384	−0.484203
$162$	−1.00000	−0.0785674
$163$	11.5239	0.902620	0.451310	−	0.892367i	$-0.350957\pi$
$163$	11.5239	0.902620	0.451310	+	0.892367i	$0.350957\pi$
$164$	−7.59393	−0.592986
$165$	−1.00000	−0.0778499
$166$	15.1879	1.17881
$167$	−4.97396	−0.384897	−0.192448	−	0.981307i	$-0.561643\pi$
$167$	−4.97396	−0.384897	−0.192448	+	0.981307i	$0.561643\pi$
$168$	−0.690016	−0.0532359
$169$	3.00000	0.230769
$170$	−1.00000	−0.0766965
$171$	0	0
$172$	7.30998	0.557381
$173$	−10.8339	−0.823683	−0.411842	−	0.911255i	$-0.635114\pi$
$173$	−10.8339	−0.823683	−0.411842	+	0.911255i	$0.635114\pi$
$174$	0.690016	0.0523100
$175$	0.690016	0.0521603
$176$	−1.00000	−0.0753778
$177$	9.59393	0.721124
$178$	7.38003	0.553157
$179$	13.5939	1.01606	0.508029	−	0.861340i	$-0.330374\pi$
$179$	13.5939	1.01606	0.508029	+	0.861340i	$0.330374\pi$
$180$	1.00000	0.0745356
$181$	−21.2579	−1.58009	−0.790044	−	0.613050i	$-0.789942\pi$
$181$	−21.2579	−1.58009	−0.790044	+	0.613050i	$0.789942\pi$
$182$	−2.76007	−0.204590
$183$	2.00000	0.147844
$184$	8.90391	0.656405
$185$	9.59393	0.705360
$186$	−1.30998	−0.0960527
$187$	−1.00000	−0.0731272
$188$	7.59393	0.553844
$189$	0.690016	0.0501913
$190$	0	0
$191$	12.4978	0.904312	0.452156	−	0.891939i	$-0.350655\pi$
$191$	12.4978	0.904312	0.452156	+	0.891939i	$0.350655\pi$
$192$	1.00000	0.0721688
$193$	19.4538	1.40032	0.700159	−	0.713987i	$-0.253113\pi$
$193$	19.4538	1.40032	0.700159	+	0.713987i	$0.253113\pi$
$194$	19.1178	1.37258
$195$	4.00000	0.286446
$196$	−6.52388	−0.465991
$197$	−10.9740	−0.781862	−0.390931	−	0.920420i	$-0.627847\pi$
$197$	−10.9740	−0.781862	−0.390931	+	0.920420i	$0.627847\pi$
$198$	1.00000	0.0710669
$199$	−10.3540	−0.733975	−0.366988	−	0.930226i	$-0.619611\pi$
$199$	−10.3540	−0.733975	−0.366988	+	0.930226i	$0.619611\pi$
$200$	−1.00000	−0.0707107
$201$	−8.21389	−0.579363
$202$	−6.21389	−0.437208
$203$	−0.476123	−0.0334173
$204$	1.00000	0.0700140
$205$	−7.59393	−0.530383
$206$	2.28394	0.159130
$207$	−8.90391	−0.618865
$208$	4.00000	0.277350
$209$	0	0
$210$	−0.690016	−0.0476157
$211$	0.336024	0.0231328	0.0115664	−	0.999933i	$-0.496318\pi$
$211$	0.336024	0.0231328	0.0115664	+	0.999933i	$0.496318\pi$
$212$	6.97396	0.478974
$213$	14.8339	1.01640
$214$	−10.2839	−0.702996
$215$	7.30998	0.498537
$216$	−1.00000	−0.0680414
$217$	0.903910	0.0613614
$218$	4.61997	0.312904
$219$	10.2139	0.690191
$220$	−1.00000	−0.0674200
$221$	4.00000	0.269069
$222$	−9.59393	−0.643902
$223$	20.9039	1.39983	0.699915	−	0.714226i	$-0.253221\pi$
$223$	20.9039	1.39983	0.699915	+	0.714226i	$0.253221\pi$
$224$	−0.690016	−0.0461037
$225$	1.00000	0.0666667
$226$	−2.00000	−0.133038
$227$	−10.4240	−0.691868	−0.345934	−	0.938259i	$-0.612438\pi$
$227$	−10.4240	−0.691868	−0.345934	+	0.938259i	$0.612438\pi$
$228$	0	0
$229$	11.3800	0.752014	0.376007	−	0.926617i	$-0.377297\pi$
$229$	11.3800	0.752014	0.376007	+	0.926617i	$0.377297\pi$
$230$	8.90391	0.587106
$231$	−0.690016	−0.0453997
$232$	0.690016	0.0453018
$233$	0.283943	0.0186017	0.00930086	−	0.999957i	$-0.497039\pi$
$233$	0.283943	0.0186017	0.00930086	+	0.999957i	$0.497039\pi$
$234$	−4.00000	−0.261488
$235$	7.59393	0.495373
$236$	9.59393	0.624511
$237$	15.1879	0.986557
$238$	−0.690016	−0.0447271
$239$	28.5679	1.84790	0.923951	−	0.382510i	$-0.124940\pi$
$239$	28.5679	1.84790	0.923951	+	0.382510i	$0.124940\pi$
$240$	1.00000	0.0645497
$241$	−0.283943	−0.0182904	−0.00914519	−	0.999958i	$-0.502911\pi$
$241$	−0.283943	−0.0182904	−0.00914519	+	0.999958i	$0.502911\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	−6.52388	−0.416795
$246$	7.59393	0.484171
$247$	0	0
$248$	−1.30998	−0.0831840
$249$	−15.1879	−0.962491
$250$	−1.00000	−0.0632456
$251$	−23.4017	−1.47711	−0.738553	−	0.674196i	$-0.764490\pi$
$251$	−23.4017	−1.47711	−0.738553	+	0.674196i	$0.764490\pi$
$252$	0.690016	0.0434670
$253$	8.90391	0.559784
$254$	−16.9740	−1.06504
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−21.6640	−1.35136	−0.675681	−	0.737194i	$-0.736150\pi$
$257$	−21.6640	−1.35136	−0.675681	+	0.737194i	$0.736150\pi$
$258$	−7.30998	−0.455100
$259$	6.61997	0.411345
$260$	4.00000	0.248069
$261$	−0.690016	−0.0427109
$262$	−5.23993	−0.323724
$263$	11.5239	0.710593	0.355296	−	0.934754i	$-0.384380\pi$
$263$	11.5239	0.710593	0.355296	+	0.934754i	$0.384380\pi$
$264$	1.00000	0.0615457
$265$	6.97396	0.428407
$266$	0	0
$267$	−7.38003	−0.451651
$268$	−8.21389	−0.501743
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	−1.00000	−0.0608581
$271$	29.7378	1.80644	0.903220	−	0.429177i	$-0.141196\pi$
$271$	29.7378	1.80644	0.903220	+	0.429177i	$0.141196\pi$
$272$	1.00000	0.0606339
$273$	2.76007	0.167047
$274$	−5.66398	−0.342173
$275$	−1.00000	−0.0603023
$276$	−8.90391	−0.535952
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−18.1438	−1.08820
$279$	1.30998	0.0784267
$280$	−0.690016	−0.0412364
$281$	−5.52388	−0.329527	−0.164763	−	0.986333i	$-0.552686\pi$
$281$	−5.52388	−0.329527	−0.164763	+	0.986333i	$0.552686\pi$
$282$	−7.59393	−0.452212
$283$	−19.0478	−1.13227	−0.566136	−	0.824312i	$-0.691562\pi$
$283$	−19.0478	−1.13227	−0.566136	+	0.824312i	$0.691562\pi$
$284$	14.8339	0.880228
$285$	0	0
$286$	4.00000	0.236525
$287$	−5.23993	−0.309304
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	0.690016	0.0405192
$291$	−19.1178	−1.12071
$292$	10.2139	0.597723
$293$	−20.1438	−1.17682	−0.588408	−	0.808564i	$-0.700245\pi$
$293$	−20.1438	−1.17682	−0.588408	+	0.808564i	$0.700245\pi$
$294$	6.52388	0.380480
$295$	9.59393	0.558580
$296$	−9.59393	−0.557636
$297$	−1.00000	−0.0580259
$298$	3.59393	0.208191
$299$	−35.6156	−2.05971
$300$	1.00000	0.0577350
$301$	5.04401	0.290732
$302$	−0.406073	−0.0233669
$303$	6.21389	0.356979
$304$	0	0
$305$	2.00000	0.114520
$306$	−1.00000	−0.0571662
$307$	15.4017	0.879024	0.439512	−	0.898237i	$-0.355151\pi$
$307$	15.4017	0.879024	0.439512	+	0.898237i	$0.355151\pi$
$308$	−0.690016	−0.0393173
$309$	−2.28394	−0.129929
$310$	−1.30998	−0.0744021
$311$	−14.9740	−0.849095	−0.424548	−	0.905406i	$-0.639567\pi$
$311$	−14.9740	−0.849095	−0.424548	+	0.905406i	$0.639567\pi$
$312$	−4.00000	−0.226455
$313$	18.3057	1.03470	0.517348	−	0.855775i	$-0.326919\pi$
$313$	18.3057	1.03470	0.517348	+	0.855775i	$0.326919\pi$
$314$	12.9740	0.732163
$315$	0.690016	0.0388780
$316$	15.1879	0.854383
$317$	0.283943	0.0159478	0.00797392	−	0.999968i	$-0.497462\pi$
$317$	0.283943	0.0159478	0.00797392	+	0.999968i	$0.497462\pi$
$318$	−6.97396	−0.391080
$319$	0.690016	0.0386335
$320$	1.00000	0.0559017
$321$	10.2839	0.573994
$322$	6.14384	0.342383
$323$	0	0
$324$	1.00000	0.0555556
$325$	4.00000	0.221880
$326$	−11.5239	−0.638249
$327$	−4.61997	−0.255485
$328$	7.59393	0.419304
$329$	5.23993	0.288887
$330$	1.00000	0.0550482
$331$	−3.52388	−0.193690	−0.0968449	−	0.995299i	$-0.530875\pi$
$331$	−3.52388	−0.193690	−0.0968449	+	0.995299i	$0.530875\pi$
$332$	−15.1879	−0.833542
$333$	9.59393	0.525744
$334$	4.97396	0.272163
$335$	−8.21389	−0.448773
$336$	0.690016	0.0376435
$337$	−15.4538	−0.841824	−0.420912	−	0.907102i	$-0.638290\pi$
$337$	−15.4538	−0.841824	−0.420912	+	0.907102i	$0.638290\pi$
$338$	−3.00000	−0.163178
$339$	2.00000	0.108625
$340$	1.00000	0.0542326
$341$	−1.30998	−0.0709396
$342$	0	0
$343$	−9.33170	−0.503864
$344$	−7.30998	−0.394128
$345$	−8.90391	−0.479370
$346$	10.8339	0.582432
$347$	−21.6677	−1.16318	−0.581592	−	0.813481i	$-0.697570\pi$
$347$	−21.6677	−1.16318	−0.581592	+	0.813481i	$0.697570\pi$
$348$	−0.690016	−0.0369888
$349$	18.8339	1.00815	0.504077	−	0.863659i	$-0.331833\pi$
$349$	18.8339	1.00815	0.504077	+	0.863659i	$0.331833\pi$
$350$	−0.690016	−0.0368829
$351$	4.00000	0.213504
$352$	1.00000	0.0533002
$353$	14.9039	0.793255	0.396628	−	0.917980i	$-0.370180\pi$
$353$	14.9039	0.793255	0.396628	+	0.917980i	$0.370180\pi$
$354$	−9.59393	−0.509911
$355$	14.8339	0.787300
$356$	−7.38003	−0.391141
$357$	0.690016	0.0365195
$358$	−13.5939	−0.718461
$359$	−21.8078	−1.15097	−0.575486	−	0.817811i	$-0.695187\pi$
$359$	−21.8078	−1.15097	−0.575486	+	0.817811i	$0.695187\pi$
$360$	−1.00000	−0.0527046
$361$	−19.0000	−1.00000
$362$	21.2579	1.11729
$363$	1.00000	0.0524864
$364$	2.76007	0.144667
$365$	10.2139	0.534620
$366$	−2.00000	−0.104542
$367$	24.3757	1.27240	0.636201	−	0.771524i	$-0.280505\pi$
$367$	24.3757	1.27240	0.636201	+	0.771524i	$0.280505\pi$
$368$	−8.90391	−0.464148
$369$	−7.59393	−0.395324
$370$	−9.59393	−0.498764
$371$	4.81215	0.249834
$372$	1.30998	0.0679195
$373$	0.140099	0.00725403	0.00362702	−	0.999993i	$-0.498845\pi$
$373$	0.140099	0.00725403	0.00362702	+	0.999993i	$0.498845\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	−7.59393	−0.391627
$377$	−2.76007	−0.142151
$378$	−0.690016	−0.0354906
$379$	−16.7080	−0.858232	−0.429116	−	0.903250i	$-0.641175\pi$
$379$	−16.7080	−0.858232	−0.429116	+	0.903250i	$0.641175\pi$
$380$	0	0
$381$	16.9740	0.869602
$382$	−12.4978	−0.639445
$383$	5.64601	0.288498	0.144249	−	0.989541i	$-0.453923\pi$
$383$	5.64601	0.288498	0.144249	+	0.989541i	$0.453923\pi$
$384$	−1.00000	−0.0510310
$385$	−0.690016	−0.0351665
$386$	−19.4538	−0.990174
$387$	7.30998	0.371587
$388$	−19.1178	−0.970559
$389$	−15.0478	−0.762951	−0.381476	−	0.924379i	$-0.624584\pi$
$389$	−15.0478	−0.762951	−0.381476	+	0.924379i	$0.624584\pi$
$390$	−4.00000	−0.202548
$391$	−8.90391	−0.450290
$392$	6.52388	0.329506
$393$	5.23993	0.264320
$394$	10.9740	0.552860
$395$	15.1879	0.764184
$396$	−1.00000	−0.0502519
$397$	−26.8339	−1.34675	−0.673376	−	0.739300i	$-0.735157\pi$
$397$	−26.8339	−1.34675	−0.673376	+	0.739300i	$0.735157\pi$
$398$	10.3540	0.518999
$399$	0	0
$400$	1.00000	0.0500000
$401$	−2.12213	−0.105974	−0.0529871	−	0.998595i	$-0.516874\pi$
$401$	−2.12213	−0.105974	−0.0529871	+	0.998595i	$0.516874\pi$
$402$	8.21389	0.409672
$403$	5.23993	0.261020
$404$	6.21389	0.309153
$405$	1.00000	0.0496904
$406$	0.476123	0.0236296
$407$	−9.59393	−0.475553
$408$	−1.00000	−0.0495074
$409$	4.19218	0.207290	0.103645	−	0.994614i	$-0.466949\pi$
$409$	4.19218	0.207290	0.103645	+	0.994614i	$0.466949\pi$
$410$	7.59393	0.375037
$411$	5.66398	0.279383
$412$	−2.28394	−0.112522
$413$	6.61997	0.325747
$414$	8.90391	0.437603
$415$	−15.1879	−0.745542
$416$	−4.00000	−0.196116
$417$	18.1438	0.888508
$418$	0	0
$419$	24.0918	1.17696	0.588480	−	0.808512i	$-0.299727\pi$
$419$	24.0918	1.17696	0.588480	+	0.808512i	$0.299727\pi$
$420$	0.690016	0.0336694
$421$	13.8599	0.675490	0.337745	−	0.941238i	$-0.390336\pi$
$421$	13.8599	0.675490	0.337745	+	0.941238i	$0.390336\pi$
$422$	−0.336024	−0.0163574
$423$	7.59393	0.369229
$424$	−6.97396	−0.338685
$425$	1.00000	0.0485071
$426$	−14.8339	−0.718703
$427$	1.38003	0.0667845
$428$	10.2839	0.497093
$429$	−4.00000	−0.193122
$430$	−7.30998	−0.352519
$431$	26.2319	1.26354	0.631772	−	0.775154i	$-0.282328\pi$
$431$	26.2319	1.26354	0.631772	+	0.775154i	$0.282328\pi$
$432$	1.00000	0.0481125
$433$	−3.80782	−0.182992	−0.0914961	−	0.995805i	$-0.529165\pi$
$433$	−3.80782	−0.182992	−0.0914961	+	0.995805i	$0.529165\pi$
$434$	−0.903910	−0.0433891
$435$	−0.690016	−0.0330838
$436$	−4.61997	−0.221256
$437$	0	0
$438$	−10.2139	−0.488039
$439$	−1.80782	−0.0862826	−0.0431413	−	0.999069i	$-0.513737\pi$
$439$	−1.80782	−0.0862826	−0.0431413	+	0.999069i	$0.513737\pi$
$440$	1.00000	0.0476731
$441$	−6.52388	−0.310661
$442$	−4.00000	−0.190261
$443$	19.9517	0.947932	0.473966	−	0.880543i	$-0.342822\pi$
$443$	19.9517	0.947932	0.473966	+	0.880543i	$0.342822\pi$
$444$	9.59393	0.455308
$445$	−7.38003	−0.349847
$446$	−20.9039	−0.989829
$447$	−3.59393	−0.169987
$448$	0.690016	0.0326002
$449$	34.4458	1.62560	0.812798	−	0.582546i	$-0.197943\pi$
$449$	34.4458	1.62560	0.812798	+	0.582546i	$0.197943\pi$
$450$	−1.00000	−0.0471405
$451$	7.59393	0.357584
$452$	2.00000	0.0940721
$453$	0.406073	0.0190790
$454$	10.4240	0.489225
$455$	2.76007	0.129394
$456$	0	0
$457$	31.6677	1.48135	0.740677	−	0.671862i	$-0.234505\pi$
$457$	31.6677	1.48135	0.740677	+	0.671862i	$0.234505\pi$
$458$	−11.3800	−0.531754
$459$	1.00000	0.0466760
$460$	−8.90391	−0.415147
$461$	23.4538	1.09235	0.546177	−	0.837670i	$-0.316083\pi$
$461$	23.4538	1.09235	0.546177	+	0.837670i	$0.316083\pi$
$462$	0.690016	0.0321025
$463$	−13.9479	−0.648215	−0.324107	−	0.946020i	$-0.605064\pi$
$463$	−13.9479	−0.648215	−0.324107	+	0.946020i	$0.605064\pi$
$464$	−0.690016	−0.0320332
$465$	1.30998	0.0607490
$466$	−0.283943	−0.0131534
$467$	−35.6156	−1.64810	−0.824048	−	0.566520i	$-0.808289\pi$
$467$	−35.6156	−1.64810	−0.824048	+	0.566520i	$0.808289\pi$
$468$	4.00000	0.184900
$469$	−5.66772	−0.261711
$470$	−7.59393	−0.350282
$471$	−12.9740	−0.597808
$472$	−9.59393	−0.441596
$473$	−7.30998	−0.336113
$474$	−15.1879	−0.697601
$475$	0	0
$476$	0.690016	0.0316269
$477$	6.97396	0.319316
$478$	−28.5679	−1.30666
$479$	9.66398	0.441558	0.220779	−	0.975324i	$-0.429140\pi$
$479$	9.66398	0.441558	0.220779	+	0.975324i	$0.429140\pi$
$480$	−1.00000	−0.0456435
$481$	38.3757	1.74978
$482$	0.283943	0.0129333
$483$	−6.14384	−0.279555
$484$	1.00000	0.0454545
$485$	−19.1178	−0.868095
$486$	−1.00000	−0.0453609
$487$	−32.3757	−1.46708	−0.733542	−	0.679644i	$-0.762134\pi$
$487$	−32.3757	−1.46708	−0.733542	+	0.679644i	$0.762134\pi$
$488$	−2.00000	−0.0905357
$489$	11.5239	0.521128
$490$	6.52388	0.294719
$491$	27.4017	1.23662	0.618312	−	0.785933i	$-0.287817\pi$
$491$	27.4017	1.23662	0.618312	+	0.785933i	$0.287817\pi$
$492$	−7.59393	−0.342361
$493$	−0.690016	−0.0310768
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	1.30998	0.0588200
$497$	10.2356	0.459130
$498$	15.1879	0.680584
$499$	1.52013	0.0680504	0.0340252	−	0.999421i	$-0.489167\pi$
$499$	1.52013	0.0680504	0.0340252	+	0.999421i	$0.489167\pi$
$500$	1.00000	0.0447214
$501$	−4.97396	−0.222220
$502$	23.4017	1.04447
$503$	21.5418	0.960503	0.480252	−	0.877131i	$-0.340545\pi$
$503$	21.5418	0.960503	0.480252	+	0.877131i	$0.340545\pi$
$504$	−0.690016	−0.0307358
$505$	6.21389	0.276515
$506$	−8.90391	−0.395827
$507$	3.00000	0.133235
$508$	16.9740	0.753098
$509$	−15.0478	−0.666980	−0.333490	−	0.942754i	$-0.608226\pi$
$509$	−15.0478	−0.666980	−0.333490	+	0.942754i	$0.608226\pi$
$510$	−1.00000	−0.0442807
$511$	7.04775	0.311774
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	21.6640	0.955557
$515$	−2.28394	−0.100643
$516$	7.30998	0.321804
$517$	−7.59393	−0.333981
$518$	−6.61997	−0.290865
$519$	−10.8339	−0.475554
$520$	−4.00000	−0.175412
$521$	−5.78611	−0.253494	−0.126747	−	0.991935i	$-0.540454\pi$
$521$	−5.78611	−0.253494	−0.126747	+	0.991935i	$0.540454\pi$
$522$	0.690016	0.0302012
$523$	−9.92995	−0.434206	−0.217103	−	0.976149i	$-0.569661\pi$
$523$	−9.92995	−0.434206	−0.217103	+	0.976149i	$0.569661\pi$
$524$	5.23993	0.228908
$525$	0.690016	0.0301148
$526$	−11.5239	−0.502465
$527$	1.30998	0.0570638
$528$	−1.00000	−0.0435194
$529$	56.2796	2.44694
$530$	−6.97396	−0.302929
$531$	9.59393	0.416341
$532$	0	0
$533$	−30.3757	−1.31572
$534$	7.38003	0.319365
$535$	10.2839	0.444614
$536$	8.21389	0.354786
$537$	13.5939	0.586621
$538$	10.0000	0.431131
$539$	6.52388	0.281003
$540$	1.00000	0.0430331
$541$	15.3800	0.661239	0.330620	−	0.943764i	$-0.392742\pi$
$541$	15.3800	0.661239	0.330620	+	0.943764i	$0.392742\pi$
$542$	−29.7378	−1.27735
$543$	−21.2579	−0.912264
$544$	−1.00000	−0.0428746
$545$	−4.61997	−0.197898
$546$	−2.76007	−0.118120
$547$	37.8078	1.61655	0.808273	−	0.588808i	$-0.200403\pi$
$547$	37.8078	1.61655	0.808273	+	0.588808i	$0.200403\pi$
$548$	5.66398	0.241953
$549$	2.00000	0.0853579
$550$	1.00000	0.0426401
$551$	0	0
$552$	8.90391	0.378976
$553$	10.4799	0.445649
$554$	2.00000	0.0849719
$555$	9.59393	0.407240
$556$	18.1438	0.769470
$557$	4.14384	0.175580	0.0877902	−	0.996139i	$-0.472020\pi$
$557$	4.14384	0.175580	0.0877902	+	0.996139i	$0.472020\pi$
$558$	−1.30998	−0.0554560
$559$	29.2399	1.23672
$560$	0.690016	0.0291585
$561$	−1.00000	−0.0422200
$562$	5.52388	0.233011
$563$	1.94792	0.0820950	0.0410475	−	0.999157i	$-0.486931\pi$
$563$	1.94792	0.0820950	0.0410475	+	0.999157i	$0.486931\pi$
$564$	7.59393	0.319762
$565$	2.00000	0.0841406
$566$	19.0478	0.800637
$567$	0.690016	0.0289780
$568$	−14.8339	−0.622415
$569$	43.6677	1.83065	0.915323	−	0.402720i	$-0.131935\pi$
$569$	43.6677	1.83065	0.915323	+	0.402720i	$0.131935\pi$
$570$	0	0
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	−4.00000	−0.167248
$573$	12.4978	0.522105
$574$	5.23993	0.218711
$575$	−8.90391	−0.371319
$576$	1.00000	0.0416667
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−1.00000	−0.0415945
$579$	19.4538	0.808474
$580$	−0.690016	−0.0286514
$581$	−10.4799	−0.434778
$582$	19.1178	0.792458
$583$	−6.97396	−0.288832
$584$	−10.2139	−0.422654
$585$	4.00000	0.165380
$586$	20.1438	0.832135
$587$	−33.4718	−1.38153	−0.690764	−	0.723080i	$-0.742726\pi$
$587$	−33.4718	−1.38153	−0.690764	+	0.723080i	$0.742726\pi$
$588$	−6.52388	−0.269040
$589$	0	0
$590$	−9.59393	−0.394976
$591$	−10.9740	−0.451408
$592$	9.59393	0.394308
$593$	−27.1358	−1.11433	−0.557166	−	0.830401i	$-0.688111\pi$
$593$	−27.1358	−1.11433	−0.557166	+	0.830401i	$0.688111\pi$
$594$	1.00000	0.0410305
$595$	0.690016	0.0282879
$596$	−3.59393	−0.147213
$597$	−10.3540	−0.423761
$598$	35.6156	1.45643
$599$	−2.83012	−0.115635	−0.0578177	−	0.998327i	$-0.518414\pi$
$599$	−2.83012	−0.115635	−0.0578177	+	0.998327i	$0.518414\pi$
$600$	−1.00000	−0.0408248
$601$	35.6677	1.45492	0.727458	−	0.686152i	$-0.240701\pi$
$601$	35.6677	1.45492	0.727458	+	0.686152i	$0.240701\pi$
$602$	−5.04401	−0.205578
$603$	−8.21389	−0.334496
$604$	0.406073	0.0165229
$605$	1.00000	0.0406558
$606$	−6.21389	−0.252422
$607$	−13.4538	−0.546074	−0.273037	−	0.962004i	$-0.588028\pi$
$607$	−13.4538	−0.546074	−0.273037	+	0.962004i	$0.588028\pi$
$608$	0	0
$609$	−0.476123	−0.0192935
$610$	−2.00000	−0.0809776
$611$	30.3757	1.22887
$612$	1.00000	0.0404226
$613$	8.14010	0.328775	0.164388	−	0.986396i	$-0.447435\pi$
$613$	8.14010	0.328775	0.164388	+	0.986396i	$0.447435\pi$
$614$	−15.4017	−0.621564
$615$	−7.59393	−0.306217
$616$	0.690016	0.0278016
$617$	−16.3757	−0.659261	−0.329631	−	0.944110i	$-0.606924\pi$
$617$	−16.3757	−0.659261	−0.329631	+	0.944110i	$0.606924\pi$
$618$	2.28394	0.0918737
$619$	−0.567886	−0.0228253	−0.0114126	−	0.999935i	$-0.503633\pi$
$619$	−0.567886	−0.0228253	−0.0114126	+	0.999935i	$0.503633\pi$
$620$	1.30998	0.0526102
$621$	−8.90391	−0.357302
$622$	14.9740	0.600401
$623$	−5.09234	−0.204020
$624$	4.00000	0.160128
$625$	1.00000	0.0400000
$626$	−18.3057	−0.731641
$627$	0	0
$628$	−12.9740	−0.517717
$629$	9.59393	0.382535
$630$	−0.690016	−0.0274909
$631$	−43.7557	−1.74189	−0.870944	−	0.491382i	$-0.836492\pi$
$631$	−43.7557	−1.74189	−0.870944	+	0.491382i	$0.836492\pi$
$632$	−15.1879	−0.604140
$633$	0.336024	0.0133558
$634$	−0.283943	−0.0112768
$635$	16.9740	0.673591
$636$	6.97396	0.276535
$637$	−26.0955	−1.03394
$638$	−0.690016	−0.0273180
$639$	14.8339	0.586818
$640$	−1.00000	−0.0395285
$641$	−16.3577	−0.646092	−0.323046	−	0.946383i	$-0.604707\pi$
$641$	−16.3577	−0.646092	−0.323046	+	0.946383i	$0.604707\pi$
$642$	−10.2839	−0.405875
$643$	−4.33602	−0.170996	−0.0854980	−	0.996338i	$-0.527248\pi$
$643$	−4.33602	−0.170996	−0.0854980	+	0.996338i	$0.527248\pi$
$644$	−6.14384	−0.242101
$645$	7.30998	0.287830
$646$	0	0
$647$	−27.8816	−1.09614	−0.548070	−	0.836433i	$-0.684637\pi$
$647$	−27.8816	−1.09614	−0.548070	+	0.836433i	$0.684637\pi$
$648$	−1.00000	−0.0392837
$649$	−9.59393	−0.376595
$650$	−4.00000	−0.156893
$651$	0.903910	0.0354270
$652$	11.5239	0.451310
$653$	−23.3317	−0.913040	−0.456520	−	0.889713i	$-0.650904\pi$
$653$	−23.3317	−0.913040	−0.456520	+	0.889713i	$0.650904\pi$
$654$	4.61997	0.180655
$655$	5.23993	0.204741
$656$	−7.59393	−0.296493
$657$	10.2139	0.398482
$658$	−5.23993	−0.204274
$659$	11.4501	0.446032	0.223016	−	0.974815i	$-0.428410\pi$
$659$	11.4501	0.446032	0.223016	+	0.974815i	$0.428410\pi$
$660$	−1.00000	−0.0389249
$661$	28.6200	1.11319	0.556594	−	0.830785i	$-0.312108\pi$
$661$	28.6200	1.11319	0.556594	+	0.830785i	$0.312108\pi$
$662$	3.52388	0.136959
$663$	4.00000	0.155347
$664$	15.1879	0.589403
$665$	0	0
$666$	−9.59393	−0.371757
$667$	6.14384	0.237891
$668$	−4.97396	−0.192448
$669$	20.9039	0.808192
$670$	8.21389	0.317330
$671$	−2.00000	−0.0772091
$672$	−0.690016	−0.0266180
$673$	7.16614	0.276234	0.138117	−	0.990416i	$-0.455895\pi$
$673$	7.16614	0.276234	0.138117	+	0.990416i	$0.455895\pi$
$674$	15.4538	0.595259
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	−14.4061	−0.553670	−0.276835	−	0.960917i	$-0.589286\pi$
$677$	−14.4061	−0.553670	−0.276835	+	0.960917i	$0.589286\pi$
$678$	−2.00000	−0.0768095
$679$	−13.1916	−0.506247
$680$	−1.00000	−0.0383482
$681$	−10.4240	−0.399450
$682$	1.30998	0.0501619
$683$	6.76007	0.258667	0.129333	−	0.991601i	$-0.458716\pi$
$683$	6.76007	0.258667	0.129333	+	0.991601i	$0.458716\pi$
$684$	0	0
$685$	5.66398	0.216409
$686$	9.33170	0.356286
$687$	11.3800	0.434175
$688$	7.30998	0.278691
$689$	27.8958	1.06275
$690$	8.90391	0.338966
$691$	5.66772	0.215610	0.107805	−	0.994172i	$-0.465618\pi$
$691$	5.66772	0.215610	0.107805	+	0.994172i	$0.465618\pi$
$692$	−10.8339	−0.411842
$693$	−0.690016	−0.0262116
$694$	21.6677	0.822495
$695$	18.1438	0.688235
$696$	0.690016	0.0261550
$697$	−7.59393	−0.287640
$698$	−18.8339	−0.712872
$699$	0.283943	0.0107397
$700$	0.690016	0.0260802
$701$	−17.4017	−0.657255	−0.328627	−	0.944460i	$-0.606586\pi$
$701$	−17.4017	−0.657255	−0.328627	+	0.944460i	$0.606586\pi$
$702$	−4.00000	−0.150970
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	7.59393	0.286004
$706$	−14.9039	−0.560916
$707$	4.28769	0.161255
$708$	9.59393	0.360562
$709$	−16.0738	−0.603664	−0.301832	−	0.953361i	$-0.597598\pi$
$709$	−16.0738	−0.603664	−0.301832	+	0.953361i	$0.597598\pi$
$710$	−14.8339	−0.556705
$711$	15.1879	0.569589
$712$	7.38003	0.276578
$713$	−11.6640	−0.436819
$714$	−0.690016	−0.0258232
$715$	−4.00000	−0.149592
$716$	13.5939	0.508029
$717$	28.5679	1.06689
$718$	21.8078	0.813861
$719$	−31.5418	−1.17631	−0.588156	−	0.808747i	$-0.700146\pi$
$719$	−31.5418	−1.17631	−0.588156	+	0.808747i	$0.700146\pi$
$720$	1.00000	0.0372678
$721$	−1.57596	−0.0586918
$722$	19.0000	0.707107
$723$	−0.283943	−0.0105600
$724$	−21.2579	−0.790044
$725$	−0.690016	−0.0256266
$726$	−1.00000	−0.0371135
$727$	31.3838	1.16396	0.581980	−	0.813203i	$-0.302278\pi$
$727$	31.3838	1.16396	0.581980	+	0.813203i	$0.302278\pi$
$728$	−2.76007	−0.102295
$729$	1.00000	0.0370370
$730$	−10.2139	−0.378033
$731$	7.30998	0.270370
$732$	2.00000	0.0739221
$733$	−49.6677	−1.83452	−0.917260	−	0.398290i	$-0.869604\pi$
$733$	−49.6677	−1.83452	−0.917260	+	0.398290i	$0.869604\pi$
$734$	−24.3757	−0.899724
$735$	−6.52388	−0.240637
$736$	8.90391	0.328202
$737$	8.21389	0.302563
$738$	7.59393	0.279536
$739$	40.5679	1.49231	0.746157	−	0.665770i	$-0.231897\pi$
$739$	40.5679	1.49231	0.746157	+	0.665770i	$0.231897\pi$
$740$	9.59393	0.352680
$741$	0	0
$742$	−4.81215	−0.176659
$743$	7.87412	0.288874	0.144437	−	0.989514i	$-0.453863\pi$
$743$	7.87412	0.288874	0.144437	+	0.989514i	$0.453863\pi$
$744$	−1.30998	−0.0480263
$745$	−3.59393	−0.131671
$746$	−0.140099	−0.00512938
$747$	−15.1879	−0.555694
$748$	−1.00000	−0.0365636
$749$	7.09609	0.259285
$750$	−1.00000	−0.0365148
$751$	7.11780	0.259732	0.129866	−	0.991532i	$-0.458545\pi$
$751$	7.11780	0.259732	0.129866	+	0.991532i	$0.458545\pi$
$752$	7.59393	0.276922
$753$	−23.4017	−0.852807
$754$	2.76007	0.100516
$755$	0.406073	0.0147785
$756$	0.690016	0.0250957
$757$	−25.4501	−0.924999	−0.462499	−	0.886620i	$-0.653047\pi$
$757$	−25.4501	−0.924999	−0.462499	+	0.886620i	$0.653047\pi$
$758$	16.7080	0.606861
$759$	8.90391	0.323191
$760$	0	0
$761$	−43.3317	−1.57077	−0.785386	−	0.619006i	$-0.787536\pi$
$761$	−43.3317	−1.57077	−0.785386	+	0.619006i	$0.787536\pi$
$762$	−16.9740	−0.614902
$763$	−3.18785	−0.115408
$764$	12.4978	0.452156
$765$	1.00000	0.0361551
$766$	−5.64601	−0.203999
$767$	38.3757	1.38567
$768$	1.00000	0.0360844
$769$	41.6156	1.50070	0.750349	−	0.661042i	$-0.229885\pi$
$769$	41.6156	1.50070	0.750349	+	0.661042i	$0.229885\pi$
$770$	0.690016	0.0248665
$771$	−21.6640	−0.780209
$772$	19.4538	0.700159
$773$	30.1618	1.08485	0.542423	−	0.840106i	$-0.317507\pi$
$773$	30.1618	1.08485	0.542423	+	0.840106i	$0.317507\pi$
$774$	−7.30998	−0.262752
$775$	1.30998	0.0470560
$776$	19.1178	0.686289
$777$	6.61997	0.237490
$778$	15.0478	0.539488
$779$	0	0
$780$	4.00000	0.143223
$781$	−14.8339	−0.530797
$782$	8.90391	0.318403
$783$	−0.690016	−0.0246592
$784$	−6.52388	−0.232996
$785$	−12.9740	−0.463060
$786$	−5.23993	−0.186902
$787$	−34.8035	−1.24061	−0.620305	−	0.784360i	$-0.712991\pi$
$787$	−34.8035	−1.24061	−0.620305	+	0.784360i	$0.712991\pi$
$788$	−10.9740	−0.390931
$789$	11.5239	0.410261
$790$	−15.1879	−0.540360
$791$	1.38003	0.0490683
$792$	1.00000	0.0355335
$793$	8.00000	0.284088
$794$	26.8339	0.952298
$795$	6.97396	0.247341
$796$	−10.3540	−0.366988
$797$	−1.73403	−0.0614223	−0.0307112	−	0.999528i	$-0.509777\pi$
$797$	−1.73403	−0.0614223	−0.0307112	+	0.999528i	$0.509777\pi$
$798$	0	0
$799$	7.59393	0.268654
$800$	−1.00000	−0.0353553
$801$	−7.38003	−0.260761
$802$	2.12213	0.0749350
$803$	−10.2139	−0.360440
$804$	−8.21389	−0.289682
$805$	−6.14384	−0.216542
$806$	−5.23993	−0.184569
$807$	−10.0000	−0.352017
$808$	−6.21389	−0.218604
$809$	20.6938	0.727554	0.363777	−	0.931486i	$-0.381487\pi$
$809$	20.6938	0.727554	0.363777	+	0.931486i	$0.381487\pi$
$810$	−1.00000	−0.0351364
$811$	−6.76007	−0.237378	−0.118689	−	0.992931i	$-0.537869\pi$
$811$	−6.76007	−0.237378	−0.118689	+	0.992931i	$0.537869\pi$
$812$	−0.476123	−0.0167086
$813$	29.7378	1.04295
$814$	9.59393	0.336267
$815$	11.5239	0.403664
$816$	1.00000	0.0350070
$817$	0	0
$818$	−4.19218	−0.146576
$819$	2.76007	0.0964445
$820$	−7.59393	−0.265191
$821$	29.1178	1.01622	0.508109	−	0.861293i	$-0.330345\pi$
$821$	29.1178	1.01622	0.508109	+	0.861293i	$0.330345\pi$
$822$	−5.66398	−0.197554
$823$	−11.5201	−0.401567	−0.200783	−	0.979636i	$-0.564349\pi$
$823$	−11.5201	−0.401567	−0.200783	+	0.979636i	$0.564349\pi$
$824$	2.28394	0.0795649
$825$	−1.00000	−0.0348155
$826$	−6.61997	−0.230338
$827$	−35.0961	−1.22041	−0.610205	−	0.792243i	$-0.708913\pi$
$827$	−35.0961	−1.22041	−0.610205	+	0.792243i	$0.708913\pi$
$828$	−8.90391	−0.309432
$829$	35.9479	1.24852	0.624261	−	0.781216i	$-0.285400\pi$
$829$	35.9479	1.24852	0.624261	+	0.781216i	$0.285400\pi$
$830$	15.1879	0.527178
$831$	−2.00000	−0.0693792
$832$	4.00000	0.138675
$833$	−6.52388	−0.226039
$834$	−18.1438	−0.628270
$835$	−4.97396	−0.172131
$836$	0	0
$837$	1.30998	0.0452797
$838$	−24.0918	−0.832236
$839$	3.11406	0.107509	0.0537546	−	0.998554i	$-0.482881\pi$
$839$	3.11406	0.107509	0.0537546	+	0.998554i	$0.482881\pi$
$840$	−0.690016	−0.0238078
$841$	−28.5239	−0.983582
$842$	−13.8599	−0.477644
$843$	−5.52388	−0.190252
$844$	0.336024	0.0115664
$845$	3.00000	0.103203
$846$	−7.59393	−0.261085
$847$	0.690016	0.0237092
$848$	6.97396	0.239487
$849$	−19.0478	−0.653717
$850$	−1.00000	−0.0342997
$851$	−85.4235	−2.92828
$852$	14.8339	0.508200
$853$	−10.9039	−0.373343	−0.186671	−	0.982422i	$-0.559770\pi$
$853$	−10.9039	−0.373343	−0.186671	+	0.982422i	$0.559770\pi$
$854$	−1.38003	−0.0472238
$855$	0	0
$856$	−10.2839	−0.351498
$857$	36.0397	1.23109	0.615546	−	0.788101i	$-0.288936\pi$
$857$	36.0397	1.23109	0.615546	+	0.788101i	$0.288936\pi$
$858$	4.00000	0.136558
$859$	33.0440	1.12745	0.563724	−	0.825964i	$-0.309368\pi$
$859$	33.0440	1.12745	0.563724	+	0.825964i	$0.309368\pi$
$860$	7.30998	0.249268
$861$	−5.23993	−0.178576
$862$	−26.2319	−0.893461
$863$	−10.3540	−0.352454	−0.176227	−	0.984350i	$-0.556389\pi$
$863$	−10.3540	−0.352454	−0.176227	+	0.984350i	$0.556389\pi$
$864$	−1.00000	−0.0340207
$865$	−10.8339	−0.368362
$866$	3.80782	0.129395
$867$	1.00000	0.0339618
$868$	0.903910	0.0306807
$869$	−15.1879	−0.515213
$870$	0.690016	0.0233937
$871$	−32.8556	−1.11327
$872$	4.61997	0.156452
$873$	−19.1178	−0.647040
$874$	0	0
$875$	0.690016	0.0233268
$876$	10.2139	0.345095
$877$	−48.4675	−1.63663	−0.818315	−	0.574770i	$-0.805092\pi$
$877$	−48.4675	−1.63663	−0.818315	+	0.574770i	$0.805092\pi$
$878$	1.80782	0.0610110
$879$	−20.1438	−0.679435
$880$	−1.00000	−0.0337100
$881$	45.8779	1.54566	0.772832	−	0.634610i	$-0.218839\pi$
$881$	45.8779	1.54566	0.772832	+	0.634610i	$0.218839\pi$
$882$	6.52388	0.219670
$883$	46.5896	1.56786	0.783932	−	0.620846i	$-0.213211\pi$
$883$	46.5896	1.56786	0.783932	+	0.620846i	$0.213211\pi$
$884$	4.00000	0.134535
$885$	9.59393	0.322496
$886$	−19.9517	−0.670289
$887$	31.2096	1.04791	0.523957	−	0.851744i	$-0.324455\pi$
$887$	31.2096	1.04791	0.523957	+	0.851744i	$0.324455\pi$
$888$	−9.59393	−0.321951
$889$	11.7123	0.392818
$890$	7.38003	0.247379
$891$	−1.00000	−0.0335013
$892$	20.9039	0.699915
$893$	0	0
$894$	3.59393	0.120199
$895$	13.5939	0.454395
$896$	−0.690016	−0.0230518
$897$	−35.6156	−1.18917
$898$	−34.4458	−1.14947
$899$	−0.903910	−0.0301471
$900$	1.00000	0.0333333
$901$	6.97396	0.232336
$902$	−7.59393	−0.252850
$903$	5.04401	0.167854
$904$	−2.00000	−0.0665190
$905$	−21.2579	−0.706637
$906$	−0.406073	−0.0134909
$907$	−35.5239	−1.17955	−0.589775	−	0.807567i	$-0.700784\pi$
$907$	−35.5239	−1.17955	−0.589775	+	0.807567i	$0.700784\pi$
$908$	−10.4240	−0.345934
$909$	6.21389	0.206102
$910$	−2.76007	−0.0914953
$911$	−45.4538	−1.50595	−0.752976	−	0.658048i	$-0.771383\pi$
$911$	−45.4538	−1.50595	−0.752976	+	0.658048i	$0.771383\pi$
$912$	0	0
$913$	15.1879	0.502645
$914$	−31.6677	−1.04748
$915$	2.00000	0.0661180
$916$	11.3800	0.376007
$917$	3.61564	0.119399
$918$	−1.00000	−0.0330049
$919$	25.4501	0.839521	0.419760	−	0.907635i	$-0.362114\pi$
$919$	25.4501	0.839521	0.419760	+	0.907635i	$0.362114\pi$
$920$	8.90391	0.293553
$921$	15.4017	0.507505
$922$	−23.4538	−0.772411
$923$	59.3354	1.95305
$924$	−0.690016	−0.0226999
$925$	9.59393	0.315446
$926$	13.9479	0.458357
$927$	−2.28394	−0.0750145
$928$	0.690016	0.0226509
$929$	−51.5456	−1.69116	−0.845578	−	0.533852i	$-0.820744\pi$
$929$	−51.5456	−1.69116	−0.845578	+	0.533852i	$0.820744\pi$
$930$	−1.30998	−0.0429561
$931$	0	0
$932$	0.283943	0.00930086
$933$	−14.9740	−0.490225
$934$	35.6156	1.16538
$935$	−1.00000	−0.0327035
$936$	−4.00000	−0.130744
$937$	0.479868	0.0156766	0.00783831	−	0.999969i	$-0.497505\pi$
$937$	0.479868	0.0156766	0.00783831	+	0.999969i	$0.497505\pi$
$938$	5.66772	0.185058
$939$	18.3057	0.597383
$940$	7.59393	0.247687
$941$	24.5016	0.798729	0.399364	−	0.916792i	$-0.369231\pi$
$941$	24.5016	0.798729	0.399364	+	0.916792i	$0.369231\pi$
$942$	12.9740	0.422714
$943$	67.6156	2.20187
$944$	9.59393	0.312256
$945$	0.690016	0.0224462
$946$	7.30998	0.237668
$947$	28.1835	0.915842	0.457921	−	0.888993i	$-0.348594\pi$
$947$	28.1835	0.915842	0.457921	+	0.888993i	$0.348594\pi$
$948$	15.1879	0.493279
$949$	40.8556	1.32623
$950$	0	0
$951$	0.283943	0.00920749
$952$	−0.690016	−0.0223636
$953$	−31.9479	−1.03489	−0.517447	−	0.855715i	$-0.673118\pi$
$953$	−31.9479	−1.03489	−0.517447	+	0.855715i	$0.673118\pi$
$954$	−6.97396	−0.225790
$955$	12.4978	0.404421
$956$	28.5679	0.923951
$957$	0.690016	0.0223051
$958$	−9.66398	−0.312229
$959$	3.90824	0.126204
$960$	1.00000	0.0322749
$961$	−29.2839	−0.944643
$962$	−38.3757	−1.23728
$963$	10.2839	0.331395
$964$	−0.283943	−0.00914519
$965$	19.4538	0.626241
$966$	6.14384	0.197675
$967$	38.1097	1.22553	0.612763	−	0.790267i	$-0.290058\pi$
$967$	38.1097	1.22553	0.612763	+	0.790267i	$0.290058\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	19.1178	0.613836
$971$	−22.1618	−0.711206	−0.355603	−	0.934637i	$-0.615725\pi$
$971$	−22.1618	−0.711206	−0.355603	+	0.934637i	$0.615725\pi$
$972$	1.00000	0.0320750
$973$	12.5196	0.401358
$974$	32.3757	1.03738
$975$	4.00000	0.128103
$976$	2.00000	0.0640184
$977$	−38.7080	−1.23838	−0.619189	−	0.785242i	$-0.712539\pi$
$977$	−38.7080	−1.23838	−0.619189	+	0.785242i	$0.712539\pi$
$978$	−11.5239	−0.368493
$979$	7.38003	0.235867
$980$	−6.52388	−0.208398
$981$	−4.61997	−0.147504
$982$	−27.4017	−0.874425
$983$	−34.1438	−1.08902	−0.544510	−	0.838755i	$-0.683284\pi$
$983$	−34.1438	−1.08902	−0.544510	+	0.838755i	$0.683284\pi$
$984$	7.59393	0.242086
$985$	−10.9740	−0.349659
$986$	0.690016	0.0219746
$987$	5.23993	0.166789
$988$	0	0
$989$	−65.0874	−2.06966
$990$	1.00000	0.0317821
$991$	−31.9659	−1.01543	−0.507715	−	0.861525i	$-0.669510\pi$
$991$	−31.9659	−1.01543	−0.507715	+	0.861525i	$0.669510\pi$
$992$	−1.30998	−0.0415920
$993$	−3.52388	−0.111827
$994$	−10.2356	−0.324654
$995$	−10.3540	−0.328244
$996$	−15.1879	−0.481246
$997$	−33.5239	−1.06171	−0.530856	−	0.847462i	$-0.678129\pi$
$997$	−33.5239	−1.06171	−0.530856	+	0.847462i	$0.678129\pi$
$998$	−1.52013	−0.0481189
$999$	9.59393	0.303538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cb.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cb.1.2	✓	3	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +0.690016 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.00000 q^{13} -0.690016 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +1.00000 q^{20} +0.690016 q^{21} +1.00000 q^{22} -8.90391 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +0.690016 q^{28} -0.690016 q^{29} -1.00000 q^{30} +1.30998 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +0.690016 q^{35} +1.00000 q^{36} +9.59393 q^{37} +4.00000 q^{39} -1.00000 q^{40} -7.59393 q^{41} -0.690016 q^{42} +7.30998 q^{43} -1.00000 q^{44} +1.00000 q^{45} +8.90391 q^{46} +7.59393 q^{47} +1.00000 q^{48} -6.52388 q^{49} -1.00000 q^{50} +1.00000 q^{51} +4.00000 q^{52} +6.97396 q^{53} -1.00000 q^{54} -1.00000 q^{55} -0.690016 q^{56} +0.690016 q^{58} +9.59393 q^{59} +1.00000 q^{60} +2.00000 q^{61} -1.30998 q^{62} +0.690016 q^{63} +1.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} -8.21389 q^{67} +1.00000 q^{68} -8.90391 q^{69} -0.690016 q^{70} +14.8339 q^{71} -1.00000 q^{72} +10.2139 q^{73} -9.59393 q^{74} +1.00000 q^{75} -0.690016 q^{77} -4.00000 q^{78} +15.1879 q^{79} +1.00000 q^{80} +1.00000 q^{81} +7.59393 q^{82} -15.1879 q^{83} +0.690016 q^{84} +1.00000 q^{85} -7.30998 q^{86} -0.690016 q^{87} +1.00000 q^{88} -7.38003 q^{89} -1.00000 q^{90} +2.76007 q^{91} -8.90391 q^{92} +1.30998 q^{93} -7.59393 q^{94} -1.00000 q^{96} -19.1178 q^{97} +6.52388 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 3 q^{20} + 3 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 - q^23 - 3 * q^24 + 3 * q^25 - 12 * q^26 + 3 * q^27 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 3 * q^31 - 3 * q^32 - 3 * q^33 - 3 * q^34 + 3 * q^35 + 3 * q^36 + 4 * q^37 + 12 * q^39 - 3 * q^40 + 2 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 + q^46 - 2 * q^47 + 3 * q^48 + 8 * q^49 - 3 * q^50 + 3 * q^51 + 12 * q^52 - 2 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 + 3 * q^58 + 4 * q^59 + 3 * q^60 + 6 * q^61 - 3 * q^62 + 3 * q^63 + 3 * q^64 + 12 * q^65 + 3 * q^66 + 2 * q^67 + 3 * q^68 - q^69 - 3 * q^70 + 16 * q^71 - 3 * q^72 + 4 * q^73 - 4 * q^74 + 3 * q^75 - 3 * q^77 - 12 * q^78 - 4 * q^79 + 3 * q^80 + 3 * q^81 - 2 * q^82 + 4 * q^83 + 3 * q^84 + 3 * q^85 - 21 * q^86 - 3 * q^87 + 3 * q^88 - 24 * q^89 - 3 * q^90 + 12 * q^91 - q^92 + 3 * q^93 + 2 * q^94 - 3 * q^96 - 5 * q^97 - 8 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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