LMFDB - Embedded newform 7935.2.a.bv.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] 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("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,11,25,31,-25,11,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.404849 q^{2} +1.00000 q^{3} -1.83610 q^{4} -1.00000 q^{5} -0.404849 q^{6} -1.25801 q^{7} +1.55304 q^{8} +1.00000 q^{9} +0.404849 q^{10} +6.20063 q^{11} -1.83610 q^{12} +1.55628 q^{13} +0.509303 q^{14} -1.00000 q^{15} +3.04345 q^{16} +6.17082 q^{17} -0.404849 q^{18} +1.68250 q^{19} +1.83610 q^{20} -1.25801 q^{21} -2.51032 q^{22} +1.55304 q^{24} +1.00000 q^{25} -0.630056 q^{26} +1.00000 q^{27} +2.30982 q^{28} +3.06021 q^{29} +0.404849 q^{30} +4.23529 q^{31} -4.33822 q^{32} +6.20063 q^{33} -2.49825 q^{34} +1.25801 q^{35} -1.83610 q^{36} +11.6860 q^{37} -0.681158 q^{38} +1.55628 q^{39} -1.55304 q^{40} +1.76233 q^{41} +0.509303 q^{42} +1.68894 q^{43} -11.3850 q^{44} -1.00000 q^{45} -0.384512 q^{47} +3.04345 q^{48} -5.41742 q^{49} -0.404849 q^{50} +6.17082 q^{51} -2.85747 q^{52} -12.5823 q^{53} -0.404849 q^{54} -6.20063 q^{55} -1.95374 q^{56} +1.68250 q^{57} -1.23892 q^{58} +11.6263 q^{59} +1.83610 q^{60} -10.1814 q^{61} -1.71465 q^{62} -1.25801 q^{63} -4.33058 q^{64} -1.55628 q^{65} -2.51032 q^{66} +0.978510 q^{67} -11.3302 q^{68} -0.509303 q^{70} -2.85381 q^{71} +1.55304 q^{72} +4.48175 q^{73} -4.73105 q^{74} +1.00000 q^{75} -3.08923 q^{76} -7.80044 q^{77} -0.630056 q^{78} +13.5753 q^{79} -3.04345 q^{80} +1.00000 q^{81} -0.713476 q^{82} -12.8951 q^{83} +2.30982 q^{84} -6.17082 q^{85} -0.683764 q^{86} +3.06021 q^{87} +9.62982 q^{88} -16.3408 q^{89} +0.404849 q^{90} -1.95781 q^{91} +4.23529 q^{93} +0.155669 q^{94} -1.68250 q^{95} -4.33822 q^{96} +2.59885 q^{97} +2.19323 q^{98} +6.20063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} - 25 q^{5} + 11 q^{6} - 7 q^{7} + 33 q^{8} + 25 q^{9} - 11 q^{10} - 9 q^{11} + 31 q^{12} + 18 q^{13} - 11 q^{14} - 25 q^{15} + 39 q^{16} + 8 q^{17} + 11 q^{18} - 11 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) $ 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 - 25 * q^5 + 11 * q^6 - 7 * q^7 + 33 * q^8 + 25 * q^9 - 11 * q^10 - 9 * q^11 + 31 * q^12 + 18 * q^13 - 11 * q^14 - 25 * q^15 + 39 * q^16 + 8 * q^17 + 11 * q^18 - 11 * q^19 - 31 * q^20 - 7 * q^21 - 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 + 5 * q^28 + 33 * q^29 - 11 * q^30 + 14 * q^31 + 77 * q^32 - 9 * q^33 - 13 * q^34 + 7 * q^35 + 31 * q^36 - 4 * q^37 + 23 * q^38 + 18 * q^39 - 33 * q^40 + 56 * q^41 - 11 * q^42 + 4 * q^43 + 18 * q^44 - 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 + 8 * q^51 + 49 * q^52 - 2 * q^53 + 11 * q^54 + 9 * q^55 - 33 * q^56 - 11 * q^57 + 26 * q^58 + 61 * q^59 - 31 * q^60 - 21 * q^61 + 51 * q^62 - 7 * q^63 + 71 * q^64 - 18 * q^65 - 9 * q^66 - 2 * q^67 + 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 + 47 * q^74 + 25 * q^75 + 8 * q^76 + 49 * q^77 + 35 * q^78 - 35 * q^79 - 39 * q^80 + 25 * q^81 + 35 * q^82 + 26 * q^83 + 5 * q^84 - 8 * q^85 + 33 * q^86 + 33 * q^87 - 9 * q^88 + 7 * q^89 - 11 * q^90 - 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 + 54 * q^97 + 88 * q^98 - 9 * 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 $

$2$	−0.404849	−0.286271	−0.143136	−	0.989703i	$-0.545719\pi$
$2$	−0.404849	−0.286271	−0.143136	+	0.989703i	$0.545719\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.83610	−0.918049
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.404849	−0.165279
$7$	−1.25801	−0.475482	−0.237741	−	0.971329i	$-0.576407\pi$
$7$	−1.25801	−0.475482	−0.237741	+	0.971329i	$0.576407\pi$
$8$	1.55304	0.549082
$9$	1.00000	0.333333
$10$	0.404849	0.128024
$11$	6.20063	1.86956	0.934780	−	0.355227i	$-0.115597\pi$
$11$	6.20063	1.86956	0.934780	+	0.355227i	$0.115597\pi$
$12$	−1.83610	−0.530036
$13$	1.55628	0.431633	0.215817	−	0.976434i	$-0.430759\pi$
$13$	1.55628	0.431633	0.215817	+	0.976434i	$0.430759\pi$
$14$	0.509303	0.136117
$15$	−1.00000	−0.258199
$16$	3.04345	0.760862
$17$	6.17082	1.49664	0.748322	−	0.663335i	$-0.230860\pi$
$17$	6.17082	1.49664	0.748322	+	0.663335i	$0.230860\pi$
$18$	−0.404849	−0.0954238
$19$	1.68250	0.385992	0.192996	−	0.981200i	$-0.438180\pi$
$19$	1.68250	0.385992	0.192996	+	0.981200i	$0.438180\pi$
$20$	1.83610	0.410564
$21$	−1.25801	−0.274520
$22$	−2.51032	−0.535201
$23$	0	0
$23$	0	0
$24$	1.55304	0.317013
$25$	1.00000	0.200000
$26$	−0.630056	−0.123564
$27$	1.00000	0.192450
$28$	2.30982	0.436516
$29$	3.06021	0.568267	0.284134	−	0.958785i	$-0.408294\pi$
$29$	3.06021	0.568267	0.284134	+	0.958785i	$0.408294\pi$
$30$	0.404849	0.0739149
$31$	4.23529	0.760680	0.380340	−	0.924847i	$-0.375807\pi$
$31$	4.23529	0.760680	0.380340	+	0.924847i	$0.375807\pi$
$32$	−4.33822	−0.766895
$33$	6.20063	1.07939
$34$	−2.49825	−0.428446
$35$	1.25801	0.212642
$36$	−1.83610	−0.306016
$37$	11.6860	1.92116	0.960580	−	0.278005i	$-0.0896731\pi$
$37$	11.6860	1.92116	0.960580	+	0.278005i	$0.0896731\pi$
$38$	−0.681158	−0.110498
$39$	1.55628	0.249204
$40$	−1.55304	−0.245557
$41$	1.76233	0.275229	0.137615	−	0.990486i	$-0.456056\pi$
$41$	1.76233	0.275229	0.137615	+	0.990486i	$0.456056\pi$
$42$	0.509303	0.0785871
$43$	1.68894	0.257561	0.128780	−	0.991673i	$-0.458894\pi$
$43$	1.68894	0.257561	0.128780	+	0.991673i	$0.458894\pi$
$44$	−11.3850	−1.71635
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−0.384512	−0.0560869	−0.0280435	−	0.999607i	$-0.508928\pi$
$47$	−0.384512	−0.0560869	−0.0280435	+	0.999607i	$0.508928\pi$
$48$	3.04345	0.439284
$49$	−5.41742	−0.773917
$50$	−0.404849	−0.0572543
$51$	6.17082	0.864088
$52$	−2.85747	−0.396260
$53$	−12.5823	−1.72831	−0.864155	−	0.503226i	$-0.832146\pi$
$53$	−12.5823	−1.72831	−0.864155	+	0.503226i	$0.832146\pi$
$54$	−0.404849	−0.0550929
$55$	−6.20063	−0.836093
$56$	−1.95374	−0.261079
$57$	1.68250	0.222853
$58$	−1.23892	−0.162679
$59$	11.6263	1.51361	0.756807	−	0.653639i	$-0.226758\pi$
$59$	11.6263	1.51361	0.756807	+	0.653639i	$0.226758\pi$
$60$	1.83610	0.237039
$61$	−10.1814	−1.30360	−0.651800	−	0.758391i	$-0.725986\pi$
$61$	−10.1814	−1.30360	−0.651800	+	0.758391i	$0.725986\pi$
$62$	−1.71465	−0.217761
$63$	−1.25801	−0.158494
$64$	−4.33058	−0.541322
$65$	−1.55628	−0.193032
$66$	−2.51032	−0.308999
$67$	0.978510	0.119544	0.0597720	−	0.998212i	$-0.480963\pi$
$67$	0.978510	0.119544	0.0597720	+	0.998212i	$0.480963\pi$
$68$	−11.3302	−1.37399
$69$	0	0
$70$	−0.509303	−0.0608733
$71$	−2.85381	−0.338685	−0.169343	−	0.985557i	$-0.554164\pi$
$71$	−2.85381	−0.338685	−0.169343	+	0.985557i	$0.554164\pi$
$72$	1.55304	0.183027
$73$	4.48175	0.524549	0.262275	−	0.964993i	$-0.415527\pi$
$73$	4.48175	0.524549	0.262275	+	0.964993i	$0.415527\pi$
$74$	−4.73105	−0.549973
$75$	1.00000	0.115470
$76$	−3.08923	−0.354359
$77$	−7.80044	−0.888942
$78$	−0.630056	−0.0713398
$79$	13.5753	1.52734	0.763672	−	0.645605i	$-0.223395\pi$
$79$	13.5753	1.52734	0.763672	+	0.645605i	$0.223395\pi$
$80$	−3.04345	−0.340268
$81$	1.00000	0.111111
$82$	−0.713476	−0.0787902
$83$	−12.8951	−1.41542	−0.707711	−	0.706503i	$-0.750272\pi$
$83$	−12.8951	−1.41542	−0.707711	+	0.706503i	$0.750272\pi$
$84$	2.30982	0.252023
$85$	−6.17082	−0.669320
$86$	−0.683764	−0.0737322
$87$	3.06021	0.328089
$88$	9.62982	1.02654
$89$	−16.3408	−1.73212	−0.866061	−	0.499938i	$-0.833356\pi$
$89$	−16.3408	−1.73212	−0.866061	+	0.499938i	$0.833356\pi$
$90$	0.404849	0.0426748
$91$	−1.95781	−0.205234
$92$	0	0
$93$	4.23529	0.439179
$94$	0.155669	0.0160561
$95$	−1.68250	−0.172621
$96$	−4.33822	−0.442767
$97$	2.59885	0.263873	0.131937	−	0.991258i	$-0.457880\pi$
$97$	2.59885	0.263873	0.131937	+	0.991258i	$0.457880\pi$
$98$	2.19323	0.221550
$99$	6.20063	0.623187
$100$	−1.83610	−0.183610
$101$	6.22931	0.619840	0.309920	−	0.950763i	$-0.399698\pi$
$101$	6.22931	0.619840	0.309920	+	0.950763i	$0.399698\pi$
$102$	−2.49825	−0.247364
$103$	9.23285	0.909740	0.454870	−	0.890558i	$-0.349686\pi$
$103$	9.23285	0.909740	0.454870	+	0.890558i	$0.349686\pi$
$104$	2.41696	0.237002
$105$	1.25801	0.122769
$106$	5.09392	0.494765
$107$	−2.98090	−0.288174	−0.144087	−	0.989565i	$-0.546025\pi$
$107$	−2.98090	−0.288174	−0.144087	+	0.989565i	$0.546025\pi$
$108$	−1.83610	−0.176679
$109$	−15.3168	−1.46708	−0.733540	−	0.679646i	$-0.762133\pi$
$109$	−15.3168	−1.46708	−0.733540	+	0.679646i	$0.762133\pi$
$110$	2.51032	0.239349
$111$	11.6860	1.10918
$112$	−3.82868	−0.361776
$113$	5.69752	0.535977	0.267989	−	0.963422i	$-0.413641\pi$
$113$	5.69752	0.535977	0.267989	+	0.963422i	$0.413641\pi$
$114$	−0.681158	−0.0637963
$115$	0	0
$116$	−5.61885	−0.521697
$117$	1.55628	0.143878
$118$	−4.70689	−0.433304
$119$	−7.76294	−0.711628
$120$	−1.55304	−0.141772
$121$	27.4478	2.49525
$122$	4.12194	0.373183
$123$	1.76233	0.158904
$124$	−7.77640	−0.698341
$125$	−1.00000	−0.0894427
$126$	0.509303	0.0453723
$127$	17.9861	1.59601	0.798005	−	0.602651i	$-0.205889\pi$
$127$	17.9861	1.59601	0.798005	+	0.602651i	$0.205889\pi$
$128$	10.4297	0.921860
$129$	1.68894	0.148703
$130$	0.630056	0.0552596
$131$	6.80202	0.594295	0.297148	−	0.954832i	$-0.403965\pi$
$131$	6.80202	0.594295	0.297148	+	0.954832i	$0.403965\pi$
$132$	−11.3850	−0.990933
$133$	−2.11660	−0.183532
$134$	−0.396149	−0.0342220
$135$	−1.00000	−0.0860663
$136$	9.58353	0.821781
$137$	−8.48431	−0.724864	−0.362432	−	0.932010i	$-0.618053\pi$
$137$	−8.48431	−0.724864	−0.362432	+	0.932010i	$0.618053\pi$
$138$	0	0
$139$	−22.3368	−1.89459	−0.947293	−	0.320368i	$-0.896194\pi$
$139$	−22.3368	−1.89459	−0.947293	+	0.320368i	$0.896194\pi$
$140$	−2.30982	−0.195216
$141$	−0.384512	−0.0323818
$142$	1.15536	0.0969559
$143$	9.64989	0.806964
$144$	3.04345	0.253621
$145$	−3.06021	−0.254137
$146$	−1.81443	−0.150163
$147$	−5.41742	−0.446821
$148$	−21.4566	−1.76372
$149$	5.60316	0.459029	0.229514	−	0.973305i	$-0.426286\pi$
$149$	5.60316	0.459029	0.229514	+	0.973305i	$0.426286\pi$
$150$	−0.404849	−0.0330558
$151$	−4.21632	−0.343119	−0.171560	−	0.985174i	$-0.554881\pi$
$151$	−4.21632	−0.343119	−0.171560	+	0.985174i	$0.554881\pi$
$152$	2.61299	0.211941
$153$	6.17082	0.498881
$154$	3.15800	0.254479
$155$	−4.23529	−0.340186
$156$	−2.85747	−0.228781
$157$	−4.37560	−0.349211	−0.174606	−	0.984638i	$-0.555865\pi$
$157$	−4.37560	−0.349211	−0.174606	+	0.984638i	$0.555865\pi$
$158$	−5.49596	−0.437235
$159$	−12.5823	−0.997840
$160$	4.33822	0.342966
$161$	0	0
$162$	−0.404849	−0.0318079
$163$	−0.235266	−0.0184275	−0.00921374	−	0.999958i	$-0.502933\pi$
$163$	−0.235266	−0.0184275	−0.00921374	+	0.999958i	$0.502933\pi$
$164$	−3.23580	−0.252674
$165$	−6.20063	−0.482718
$166$	5.22057	0.405194
$167$	14.1799	1.09727	0.548635	−	0.836062i	$-0.315147\pi$
$167$	14.1799	1.09727	0.548635	+	0.836062i	$0.315147\pi$
$168$	−1.95374	−0.150734
$169$	−10.5780	−0.813693
$170$	2.49825	0.191607
$171$	1.68250	0.128664
$172$	−3.10105	−0.236453
$173$	−3.26962	−0.248584	−0.124292	−	0.992246i	$-0.539666\pi$
$173$	−3.26962	−0.248584	−0.124292	+	0.992246i	$0.539666\pi$
$174$	−1.23892	−0.0939226
$175$	−1.25801	−0.0950964
$176$	18.8713	1.42248
$177$	11.6263	0.873885
$178$	6.61556	0.495857
$179$	9.64101	0.720603	0.360302	−	0.932836i	$-0.382674\pi$
$179$	9.64101	0.720603	0.360302	+	0.932836i	$0.382674\pi$
$180$	1.83610	0.136855
$181$	2.38167	0.177028	0.0885142	−	0.996075i	$-0.471788\pi$
$181$	2.38167	0.177028	0.0885142	+	0.996075i	$0.471788\pi$
$182$	0.792616	0.0587526
$183$	−10.1814	−0.752634
$184$	0	0
$185$	−11.6860	−0.859169
$186$	−1.71465	−0.125724
$187$	38.2630	2.79807
$188$	0.706002	0.0514905
$189$	−1.25801	−0.0915066
$190$	0.681158	0.0494164
$191$	−20.0297	−1.44930	−0.724648	−	0.689119i	$-0.757998\pi$
$191$	−20.0297	−1.44930	−0.724648	+	0.689119i	$0.757998\pi$
$192$	−4.33058	−0.312532
$193$	0.879190	0.0632855	0.0316427	−	0.999499i	$-0.489926\pi$
$193$	0.879190	0.0632855	0.0316427	+	0.999499i	$0.489926\pi$
$194$	−1.05214	−0.0755394
$195$	−1.55628	−0.111447
$196$	9.94691	0.710493
$197$	−3.25186	−0.231686	−0.115843	−	0.993268i	$-0.536957\pi$
$197$	−3.25186	−0.231686	−0.115843	+	0.993268i	$0.536957\pi$
$198$	−2.51032	−0.178400
$199$	−15.7748	−1.11825	−0.559123	−	0.829085i	$-0.688862\pi$
$199$	−15.7748	−1.11825	−0.559123	+	0.829085i	$0.688862\pi$
$200$	1.55304	0.109816
$201$	0.978510	0.0690188
$202$	−2.52193	−0.177442
$203$	−3.84977	−0.270201
$204$	−11.3302	−0.793275
$205$	−1.76233	−0.123086
$206$	−3.73791	−0.260432
$207$	0	0
$208$	4.73644	0.328413
$209$	10.4326	0.721635
$210$	−0.509303	−0.0351452
$211$	−2.13121	−0.146718	−0.0733591	−	0.997306i	$-0.523372\pi$
$211$	−2.13121	−0.146718	−0.0733591	+	0.997306i	$0.523372\pi$
$212$	23.1023	1.58667
$213$	−2.85381	−0.195540
$214$	1.20681	0.0824960
$215$	−1.68894	−0.115185
$216$	1.55304	0.105671
$217$	−5.32802	−0.361690
$218$	6.20097	0.419983
$219$	4.48175	0.302849
$220$	11.3850	0.767574
$221$	9.60350	0.646001
$222$	−4.73105	−0.317527
$223$	17.1539	1.14871	0.574357	−	0.818605i	$-0.305252\pi$
$223$	17.1539	1.14871	0.574357	+	0.818605i	$0.305252\pi$
$224$	5.45751	0.364645
$225$	1.00000	0.0666667
$226$	−2.30663	−0.153435
$227$	−0.754485	−0.0500769	−0.0250385	−	0.999686i	$-0.507971\pi$
$227$	−0.754485	−0.0500769	−0.0250385	+	0.999686i	$0.507971\pi$
$228$	−3.08923	−0.204589
$229$	−8.06603	−0.533019	−0.266509	−	0.963832i	$-0.585870\pi$
$229$	−8.06603	−0.533019	−0.266509	+	0.963832i	$0.585870\pi$
$230$	0	0
$231$	−7.80044	−0.513231
$232$	4.75263	0.312026
$233$	3.67716	0.240899	0.120449	−	0.992719i	$-0.461566\pi$
$233$	3.67716	0.240899	0.120449	+	0.992719i	$0.461566\pi$
$234$	−0.630056	−0.0411881
$235$	0.384512	0.0250828
$236$	−21.3470	−1.38957
$237$	13.5753	0.881812
$238$	3.14282	0.203719
$239$	−20.0397	−1.29626	−0.648131	−	0.761529i	$-0.724449\pi$
$239$	−20.0397	−1.29626	−0.648131	+	0.761529i	$0.724449\pi$
$240$	−3.04345	−0.196454
$241$	25.1865	1.62241	0.811204	−	0.584763i	$-0.198813\pi$
$241$	25.1865	1.62241	0.811204	+	0.584763i	$0.198813\pi$
$242$	−11.1122	−0.714320
$243$	1.00000	0.0641500
$244$	18.6941	1.19677
$245$	5.41742	0.346106
$246$	−0.713476	−0.0454895
$247$	2.61843	0.166607
$248$	6.57757	0.417676
$249$	−12.8951	−0.817194
$250$	0.404849	0.0256049
$251$	15.0920	0.952602	0.476301	−	0.879282i	$-0.341977\pi$
$251$	15.0920	0.952602	0.476301	+	0.879282i	$0.341977\pi$
$252$	2.30982	0.145505
$253$	0	0
$254$	−7.28166	−0.456892
$255$	−6.17082	−0.386432
$256$	4.43872	0.277420
$257$	4.43381	0.276573	0.138287	−	0.990392i	$-0.455840\pi$
$257$	4.43381	0.276573	0.138287	+	0.990392i	$0.455840\pi$
$258$	−0.683764	−0.0425693
$259$	−14.7010	−0.913477
$260$	2.85747	0.177213
$261$	3.06021	0.189422
$262$	−2.75379	−0.170130
$263$	−11.7411	−0.723986	−0.361993	−	0.932181i	$-0.617904\pi$
$263$	−11.7411	−0.723986	−0.361993	+	0.932181i	$0.617904\pi$
$264$	9.62982	0.592675
$265$	12.5823	0.772923
$266$	0.856902	0.0525400
$267$	−16.3408	−1.00004
$268$	−1.79664	−0.109747
$269$	11.9300	0.727387	0.363693	−	0.931519i	$-0.381516\pi$
$269$	11.9300	0.727387	0.363693	+	0.931519i	$0.381516\pi$
$270$	0.404849	0.0246383
$271$	1.59814	0.0970802	0.0485401	−	0.998821i	$-0.484543\pi$
$271$	1.59814	0.0970802	0.0485401	+	0.998821i	$0.484543\pi$
$272$	18.7806	1.13874
$273$	−1.95781	−0.118492
$274$	3.43486	0.207508
$275$	6.20063	0.373912
$276$	0	0
$277$	0.510864	0.0306948	0.0153474	−	0.999882i	$-0.495115\pi$
$277$	0.510864	0.0306948	0.0153474	+	0.999882i	$0.495115\pi$
$278$	9.04305	0.542366
$279$	4.23529	0.253560
$280$	1.95374	0.116758
$281$	6.74118	0.402145	0.201073	−	0.979576i	$-0.435557\pi$
$281$	6.74118	0.402145	0.201073	+	0.979576i	$0.435557\pi$
$282$	0.155669	0.00926998
$283$	−17.5453	−1.04296	−0.521481	−	0.853263i	$-0.674620\pi$
$283$	−17.5453	−1.04296	−0.521481	+	0.853263i	$0.674620\pi$
$284$	5.23988	0.310930
$285$	−1.68250	−0.0996627
$286$	−3.90675	−0.231011
$287$	−2.21702	−0.130867
$288$	−4.33822	−0.255632
$289$	21.0791	1.23994
$290$	1.23892	0.0727521
$291$	2.59885	0.152347
$292$	−8.22893	−0.481562
$293$	−10.9886	−0.641962	−0.320981	−	0.947086i	$-0.604013\pi$
$293$	−10.9886	−0.641962	−0.320981	+	0.947086i	$0.604013\pi$
$294$	2.19323	0.127912
$295$	−11.6263	−0.676909
$296$	18.1488	1.05487
$297$	6.20063	0.359797
$298$	−2.26843	−0.131407
$299$	0	0
$300$	−1.83610	−0.106007
$301$	−2.12470	−0.122465
$302$	1.70697	0.0982252
$303$	6.22931	0.357865
$304$	5.12060	0.293687
$305$	10.1814	0.582988
$306$	−2.49825	−0.142815
$307$	−10.0070	−0.571129	−0.285565	−	0.958359i	$-0.592181\pi$
$307$	−10.0070	−0.571129	−0.285565	+	0.958359i	$0.592181\pi$
$308$	14.3224	0.816092
$309$	9.23285	0.525238
$310$	1.71465	0.0973856
$311$	−0.331383	−0.0187910	−0.00939551	−	0.999956i	$-0.502991\pi$
$311$	−0.331383	−0.0187910	−0.00939551	+	0.999956i	$0.502991\pi$
$312$	2.41696	0.136833
$313$	26.0095	1.47014	0.735072	−	0.677989i	$-0.237148\pi$
$313$	26.0095	1.47014	0.735072	+	0.677989i	$0.237148\pi$
$314$	1.77146	0.0999691
$315$	1.25801	0.0708807
$316$	−24.9256	−1.40218
$317$	28.5506	1.60356	0.801780	−	0.597620i	$-0.203887\pi$
$317$	28.5506	1.60356	0.801780	+	0.597620i	$0.203887\pi$
$318$	5.09392	0.285653
$319$	18.9752	1.06241
$320$	4.33058	0.242087
$321$	−2.98090	−0.166377
$322$	0	0
$323$	10.3824	0.577693
$324$	−1.83610	−0.102005
$325$	1.55628	0.0863266
$326$	0.0952473	0.00527526
$327$	−15.3168	−0.847019
$328$	2.73696	0.151123
$329$	0.483720	0.0266683
$330$	2.51032	0.138188
$331$	−13.4175	−0.737490	−0.368745	−	0.929531i	$-0.620212\pi$
$331$	−13.4175	−0.737490	−0.368745	+	0.929531i	$0.620212\pi$
$332$	23.6767	1.29943
$333$	11.6860	0.640386
$334$	−5.74070	−0.314117
$335$	−0.978510	−0.0534617
$336$	−3.82868	−0.208872
$337$	31.4815	1.71491	0.857453	−	0.514563i	$-0.172046\pi$
$337$	31.4815	1.71491	0.857453	+	0.514563i	$0.172046\pi$
$338$	4.28249	0.232937
$339$	5.69752	0.309447
$340$	11.3302	0.614468
$341$	26.2614	1.42214
$342$	−0.681158	−0.0368328
$343$	15.6212	0.843466
$344$	2.62299	0.141422
$345$	0	0
$346$	1.32370	0.0711626
$347$	11.4206	0.613088	0.306544	−	0.951857i	$-0.400827\pi$
$347$	11.4206	0.613088	0.306544	+	0.951857i	$0.400827\pi$
$348$	−5.61885	−0.301202
$349$	25.0655	1.34172	0.670862	−	0.741583i	$-0.265924\pi$
$349$	25.0655	1.34172	0.670862	+	0.741583i	$0.265924\pi$
$350$	0.509303	0.0272234
$351$	1.55628	0.0830678
$352$	−26.8997	−1.43376
$353$	−6.12737	−0.326127	−0.163063	−	0.986616i	$-0.552138\pi$
$353$	−6.12737	−0.326127	−0.163063	+	0.986616i	$0.552138\pi$
$354$	−4.70689	−0.250168
$355$	2.85381	0.151465
$356$	30.0033	1.59017
$357$	−7.76294	−0.410858
$358$	−3.90315	−0.206288
$359$	9.90608	0.522823	0.261411	−	0.965227i	$-0.415812\pi$
$359$	9.90608	0.522823	0.261411	+	0.965227i	$0.415812\pi$
$360$	−1.55304	−0.0818524
$361$	−16.1692	−0.851010
$362$	−0.964218	−0.0506782
$363$	27.4478	1.44064
$364$	3.59472	0.188415
$365$	−4.48175	−0.234586
$366$	4.12194	0.215458
$367$	−5.45507	−0.284752	−0.142376	−	0.989813i	$-0.545474\pi$
$367$	−5.45507	−0.284752	−0.142376	+	0.989813i	$0.545474\pi$
$368$	0	0
$369$	1.76233	0.0917430
$370$	4.73105	0.245955
$371$	15.8286	0.821780
$372$	−7.77640	−0.403188
$373$	−31.3914	−1.62538	−0.812692	−	0.582693i	$-0.801999\pi$
$373$	−31.3914	−1.62538	−0.812692	+	0.582693i	$0.801999\pi$
$374$	−15.4907	−0.801006
$375$	−1.00000	−0.0516398
$376$	−0.597163	−0.0307963
$377$	4.76254	0.245283
$378$	0.509303	0.0261957
$379$	−30.6164	−1.57266	−0.786330	−	0.617807i	$-0.788021\pi$
$379$	−30.6164	−1.57266	−0.786330	+	0.617807i	$0.788021\pi$
$380$	3.08923	0.158474
$381$	17.9861	0.921457
$382$	8.10899	0.414892
$383$	23.4443	1.19795	0.598973	−	0.800769i	$-0.295576\pi$
$383$	23.4443	1.19795	0.598973	+	0.800769i	$0.295576\pi$
$384$	10.4297	0.532236
$385$	7.80044	0.397547
$386$	−0.355939	−0.0181168
$387$	1.68894	0.0858535
$388$	−4.77174	−0.242249
$389$	−28.1376	−1.42663	−0.713316	−	0.700843i	$-0.752808\pi$
$389$	−28.1376	−1.42663	−0.713316	+	0.700843i	$0.752808\pi$
$390$	0.630056	0.0319041
$391$	0	0
$392$	−8.41346	−0.424944
$393$	6.80202	0.343117
$394$	1.31651	0.0663250
$395$	−13.5753	−0.683049
$396$	−11.3850	−0.572116
$397$	−34.8555	−1.74935	−0.874673	−	0.484714i	$-0.838924\pi$
$397$	−34.8555	−1.74935	−0.874673	+	0.484714i	$0.838924\pi$
$398$	6.38641	0.320122
$399$	−2.11660	−0.105962
$400$	3.04345	0.152172
$401$	31.4740	1.57173	0.785867	−	0.618395i	$-0.212217\pi$
$401$	31.4740	1.57173	0.785867	+	0.618395i	$0.212217\pi$
$402$	−0.396149	−0.0197581
$403$	6.59127	0.328335
$404$	−11.4376	−0.569043
$405$	−1.00000	−0.0496904
$406$	1.55858	0.0773508
$407$	72.4603	3.59172
$408$	9.58353	0.474456
$409$	20.5970	1.01846	0.509228	−	0.860632i	$-0.329931\pi$
$409$	20.5970	1.01846	0.509228	+	0.860632i	$0.329931\pi$
$410$	0.713476	0.0352360
$411$	−8.48431	−0.418500
$412$	−16.9524	−0.835185
$413$	−14.6260	−0.719696
$414$	0	0
$415$	12.8951	0.632996
$416$	−6.75146	−0.331018
$417$	−22.3368	−1.09384
$418$	−4.22361	−0.206583
$419$	16.5329	0.807686	0.403843	−	0.914828i	$-0.367674\pi$
$419$	16.5329	0.807686	0.403843	+	0.914828i	$0.367674\pi$
$420$	−2.30982	−0.112708
$421$	11.4014	0.555671	0.277835	−	0.960629i	$-0.410383\pi$
$421$	11.4014	0.555671	0.277835	+	0.960629i	$0.410383\pi$
$422$	0.862816	0.0420012
$423$	−0.384512	−0.0186956
$424$	−19.5408	−0.948984
$425$	6.17082	0.299329
$426$	1.15536	0.0559775
$427$	12.8083	0.619839
$428$	5.47321	0.264558
$429$	9.64989	0.465901
$430$	0.683764	0.0329740
$431$	−13.3572	−0.643393	−0.321697	−	0.946843i	$-0.604253\pi$
$431$	−13.3572	−0.643393	−0.321697	+	0.946843i	$0.604253\pi$
$432$	3.04345	0.146428
$433$	−31.4711	−1.51240	−0.756202	−	0.654339i	$-0.772947\pi$
$433$	−31.4711	−1.51240	−0.756202	+	0.654339i	$0.772947\pi$
$434$	2.15704	0.103541
$435$	−3.06021	−0.146726
$436$	28.1231	1.34685
$437$	0	0
$438$	−1.81443	−0.0866969
$439$	−27.0996	−1.29339	−0.646697	−	0.762747i	$-0.723850\pi$
$439$	−27.0996	−1.29339	−0.646697	+	0.762747i	$0.723850\pi$
$440$	−9.62982	−0.459084
$441$	−5.41742	−0.257972
$442$	−3.88797	−0.184932
$443$	12.0908	0.574452	0.287226	−	0.957863i	$-0.407267\pi$
$443$	12.0908	0.574452	0.287226	+	0.957863i	$0.407267\pi$
$444$	−21.4566	−1.01828
$445$	16.3408	0.774629
$446$	−6.94475	−0.328844
$447$	5.60316	0.265020
$448$	5.44790	0.257389
$449$	7.91531	0.373547	0.186773	−	0.982403i	$-0.440197\pi$
$449$	7.91531	0.373547	0.186773	+	0.982403i	$0.440197\pi$
$450$	−0.404849	−0.0190848
$451$	10.9275	0.514557
$452$	−10.4612	−0.492053
$453$	−4.21632	−0.198100
$454$	0.305452	0.0143356
$455$	1.95781	0.0917834
$456$	2.61299	0.122364
$457$	−25.9180	−1.21239	−0.606197	−	0.795315i	$-0.707306\pi$
$457$	−25.9180	−1.21239	−0.606197	+	0.795315i	$0.707306\pi$
$458$	3.26552	0.152588
$459$	6.17082	0.288029
$460$	0	0
$461$	15.7472	0.733419	0.366709	−	0.930336i	$-0.380484\pi$
$461$	15.7472	0.733419	0.366709	+	0.930336i	$0.380484\pi$
$462$	3.15800	0.146923
$463$	10.6271	0.493882	0.246941	−	0.969031i	$-0.420575\pi$
$463$	10.6271	0.493882	0.246941	+	0.969031i	$0.420575\pi$
$464$	9.31360	0.432373
$465$	−4.23529	−0.196407
$466$	−1.48869	−0.0689624
$467$	31.9120	1.47671	0.738356	−	0.674411i	$-0.235602\pi$
$467$	31.9120	1.47671	0.738356	+	0.674411i	$0.235602\pi$
$468$	−2.85747	−0.132087
$469$	−1.23097	−0.0568411
$470$	−0.155669	−0.00718049
$471$	−4.37560	−0.201617
$472$	18.0561	0.831099
$473$	10.4725	0.481525
$474$	−5.49596	−0.252438
$475$	1.68250	0.0771984
$476$	14.2535	0.653309
$477$	−12.5823	−0.576103
$478$	8.11306	0.371083
$479$	−28.4982	−1.30211	−0.651057	−	0.759028i	$-0.725674\pi$
$479$	−28.4982	−1.30211	−0.651057	+	0.759028i	$0.725674\pi$
$480$	4.33822	0.198012
$481$	18.1866	0.829236
$482$	−10.1967	−0.464449
$483$	0	0
$484$	−50.3968	−2.29076
$485$	−2.59885	−0.118008
$486$	−0.404849	−0.0183643
$487$	−6.86340	−0.311010	−0.155505	−	0.987835i	$-0.549701\pi$
$487$	−6.86340	−0.311010	−0.155505	+	0.987835i	$0.549701\pi$
$488$	−15.8122	−0.715784
$489$	−0.235266	−0.0106391
$490$	−2.19323	−0.0990803
$491$	43.0510	1.94286	0.971432	−	0.237316i	$-0.0762677\pi$
$491$	43.0510	1.94286	0.971432	+	0.237316i	$0.0762677\pi$
$492$	−3.23580	−0.145881
$493$	18.8840	0.850494
$494$	−1.06007	−0.0476948
$495$	−6.20063	−0.278698
$496$	12.8899	0.578773
$497$	3.59012	0.161039
$498$	5.22057	0.233939
$499$	20.8436	0.933087	0.466543	−	0.884498i	$-0.345499\pi$
$499$	20.8436	0.933087	0.466543	+	0.884498i	$0.345499\pi$
$500$	1.83610	0.0821128
$501$	14.1799	0.633510
$502$	−6.11000	−0.272703
$503$	−24.4968	−1.09226	−0.546129	−	0.837701i	$-0.683899\pi$
$503$	−24.4968	−1.09226	−0.546129	+	0.837701i	$0.683899\pi$
$504$	−1.95374	−0.0870263
$505$	−6.22931	−0.277201
$506$	0	0
$507$	−10.5780	−0.469786
$508$	−33.0243	−1.46521
$509$	28.7448	1.27409	0.637045	−	0.770827i	$-0.280157\pi$
$509$	28.7448	1.27409	0.637045	+	0.770827i	$0.280157\pi$
$510$	2.49825	0.110624
$511$	−5.63808	−0.249414
$512$	−22.6563	−1.00128
$513$	1.68250	0.0742842
$514$	−1.79502	−0.0791750
$515$	−9.23285	−0.406848
$516$	−3.10105	−0.136516
$517$	−2.38422	−0.104858
$518$	5.95169	0.261502
$519$	−3.26962	−0.143520
$520$	−2.41696	−0.105991
$521$	−15.7839	−0.691507	−0.345754	−	0.938325i	$-0.612377\pi$
$521$	−15.7839	−0.691507	−0.345754	+	0.938325i	$0.612377\pi$
$522$	−1.23892	−0.0542262
$523$	−23.8069	−1.04100	−0.520501	−	0.853861i	$-0.674255\pi$
$523$	−23.8069	−1.04100	−0.520501	+	0.853861i	$0.674255\pi$
$524$	−12.4892	−0.545592
$525$	−1.25801	−0.0549040
$526$	4.75336	0.207257
$527$	26.1352	1.13847
$528$	18.8713	0.821268
$529$	0	0
$530$	−5.09392	−0.221266
$531$	11.6263	0.504538
$532$	3.88628	0.168492
$533$	2.74266	0.118798
$534$	6.61556	0.286283
$535$	2.98090	0.128875
$536$	1.51967	0.0656395
$537$	9.64101	0.416040
$538$	−4.82986	−0.208230
$539$	−33.5914	−1.44688
$540$	1.83610	0.0790131
$541$	−8.71420	−0.374653	−0.187326	−	0.982298i	$-0.559982\pi$
$541$	−8.71420	−0.374653	−0.187326	+	0.982298i	$0.559982\pi$
$542$	−0.647006	−0.0277913
$543$	2.38167	0.102207
$544$	−26.7704	−1.14777
$545$	15.3168	0.656098
$546$	0.792616	0.0339208
$547$	−10.3075	−0.440717	−0.220359	−	0.975419i	$-0.570723\pi$
$547$	−10.3075	−0.440717	−0.220359	+	0.975419i	$0.570723\pi$
$548$	15.5780	0.665460
$549$	−10.1814	−0.434533
$550$	−2.51032	−0.107040
$551$	5.14881	0.219347
$552$	0	0
$553$	−17.0779	−0.726225
$554$	−0.206822	−0.00878705
$555$	−11.6860	−0.496041
$556$	41.0126	1.73932
$557$	−40.5257	−1.71713	−0.858565	−	0.512705i	$-0.828644\pi$
$557$	−40.5257	−1.71713	−0.858565	+	0.512705i	$0.828644\pi$
$558$	−1.71465	−0.0725870
$559$	2.62845	0.111172
$560$	3.82868	0.161791
$561$	38.2630	1.61546
$562$	−2.72916	−0.115123
$563$	23.1422	0.975329	0.487664	−	0.873031i	$-0.337849\pi$
$563$	23.1422	0.975329	0.487664	+	0.873031i	$0.337849\pi$
$564$	0.706002	0.0297281
$565$	−5.69752	−0.239696
$566$	7.10321	0.298570
$567$	−1.25801	−0.0528314
$568$	−4.43209	−0.185966
$569$	−35.1537	−1.47372	−0.736860	−	0.676045i	$-0.763692\pi$
$569$	−35.1537	−1.47372	−0.736860	+	0.676045i	$0.763692\pi$
$570$	0.681158	0.0285306
$571$	12.3446	0.516607	0.258303	−	0.966064i	$-0.416837\pi$
$571$	12.3446	0.516607	0.258303	+	0.966064i	$0.416837\pi$
$572$	−17.7181	−0.740832
$573$	−20.0297	−0.836752
$574$	0.897558	0.0374633
$575$	0	0
$576$	−4.33058	−0.180441
$577$	22.0999	0.920032	0.460016	−	0.887911i	$-0.347844\pi$
$577$	22.0999	0.920032	0.460016	+	0.887911i	$0.347844\pi$
$578$	−8.53383	−0.354961
$579$	0.879190	0.0365379
$580$	5.61885	0.233310
$581$	16.2221	0.673007
$582$	−1.05214	−0.0436127
$583$	−78.0180	−3.23118
$584$	6.96034	0.288021
$585$	−1.55628	−0.0643441
$586$	4.44873	0.183775
$587$	−24.6098	−1.01575	−0.507877	−	0.861430i	$-0.669569\pi$
$587$	−24.6098	−1.01575	−0.507877	+	0.861430i	$0.669569\pi$
$588$	9.94691	0.410203
$589$	7.12587	0.293616
$590$	4.70689	0.193780
$591$	−3.25186	−0.133764
$592$	35.5656	1.46174
$593$	−31.9753	−1.31307	−0.656533	−	0.754297i	$-0.727978\pi$
$593$	−31.9753	−1.31307	−0.656533	+	0.754297i	$0.727978\pi$
$594$	−2.51032	−0.103000
$595$	7.76294	0.318250
$596$	−10.2879	−0.421411
$597$	−15.7748	−0.645619
$598$	0	0
$599$	9.89067	0.404122	0.202061	−	0.979373i	$-0.435236\pi$
$599$	9.89067	0.404122	0.202061	+	0.979373i	$0.435236\pi$
$600$	1.55304	0.0634026
$601$	28.9710	1.18175	0.590875	−	0.806763i	$-0.298783\pi$
$601$	28.9710	1.18175	0.590875	+	0.806763i	$0.298783\pi$
$602$	0.860181	0.0350583
$603$	0.978510	0.0398480
$604$	7.74157	0.315000
$605$	−27.4478	−1.11591
$606$	−2.52193	−0.102446
$607$	0.907479	0.0368334	0.0184167	−	0.999830i	$-0.494137\pi$
$607$	0.907479	0.0368334	0.0184167	+	0.999830i	$0.494137\pi$
$608$	−7.29905	−0.296015
$609$	−3.84977	−0.156001
$610$	−4.12194	−0.166893
$611$	−0.598407	−0.0242090
$612$	−11.3302	−0.457997
$613$	5.20925	0.210400	0.105200	−	0.994451i	$-0.466452\pi$
$613$	5.20925	0.210400	0.105200	+	0.994451i	$0.466452\pi$
$614$	4.05132	0.163498
$615$	−1.76233	−0.0710638
$616$	−12.1144	−0.488103
$617$	11.0161	0.443492	0.221746	−	0.975104i	$-0.428824\pi$
$617$	11.0161	0.443492	0.221746	+	0.975104i	$0.428824\pi$
$618$	−3.73791	−0.150361
$619$	34.6911	1.39435	0.697176	−	0.716900i	$-0.254440\pi$
$619$	34.6911	1.39435	0.697176	+	0.716900i	$0.254440\pi$
$620$	7.77640	0.312308
$621$	0	0
$622$	0.134160	0.00537933
$623$	20.5569	0.823593
$624$	4.73644	0.189610
$625$	1.00000	0.0400000
$626$	−10.5299	−0.420860
$627$	10.4326	0.416636
$628$	8.03403	0.320593
$629$	72.1120	2.87529
$630$	−0.509303	−0.0202911
$631$	−21.0390	−0.837550	−0.418775	−	0.908090i	$-0.637540\pi$
$631$	−21.0390	−0.837550	−0.418775	+	0.908090i	$0.637540\pi$
$632$	21.0830	0.838638
$633$	−2.13121	−0.0847078
$634$	−11.5587	−0.459053
$635$	−17.9861	−0.713757
$636$	23.1023	0.916066
$637$	−8.43099	−0.334048
$638$	−7.68211	−0.304138
$639$	−2.85381	−0.112895
$640$	−10.4297	−0.412269
$641$	−4.46867	−0.176502	−0.0882508	−	0.996098i	$-0.528128\pi$
$641$	−4.46867	−0.176502	−0.0882508	+	0.996098i	$0.528128\pi$
$642$	1.20681	0.0476291
$643$	−1.97280	−0.0777995	−0.0388998	−	0.999243i	$-0.512385\pi$
$643$	−1.97280	−0.0777995	−0.0388998	+	0.999243i	$0.512385\pi$
$644$	0	0
$645$	−1.68894	−0.0665018
$646$	−4.20331	−0.165377
$647$	16.8790	0.663584	0.331792	−	0.943353i	$-0.392347\pi$
$647$	16.8790	0.663584	0.331792	+	0.943353i	$0.392347\pi$
$648$	1.55304	0.0610092
$649$	72.0903	2.82979
$650$	−0.630056	−0.0247128
$651$	−5.32802	−0.208822
$652$	0.431972	0.0169173
$653$	41.7866	1.63524	0.817618	−	0.575760i	$-0.195294\pi$
$653$	41.7866	1.63524	0.817618	+	0.575760i	$0.195294\pi$
$654$	6.20097	0.242477
$655$	−6.80202	−0.265777
$656$	5.36355	0.209411
$657$	4.48175	0.174850
$658$	−0.195833	−0.00763438
$659$	21.7254	0.846301	0.423151	−	0.906059i	$-0.360924\pi$
$659$	21.7254	0.846301	0.423151	+	0.906059i	$0.360924\pi$
$660$	11.3850	0.443159
$661$	−22.1373	−0.861041	−0.430521	−	0.902581i	$-0.641670\pi$
$661$	−22.1373	−0.861041	−0.430521	+	0.902581i	$0.641670\pi$
$662$	5.43204	0.211122
$663$	9.60350	0.372969
$664$	−20.0266	−0.777183
$665$	2.11660	0.0820781
$666$	−4.73105	−0.183324
$667$	0	0
$668$	−26.0356	−1.00735
$669$	17.1539	0.663210
$670$	0.396149	0.0153046
$671$	−63.1313	−2.43716
$672$	5.45751	0.210528
$673$	26.4168	1.01829	0.509146	−	0.860680i	$-0.329961\pi$
$673$	26.4168	1.01829	0.509146	+	0.860680i	$0.329961\pi$
$674$	−12.7452	−0.490928
$675$	1.00000	0.0384900
$676$	19.4223	0.747010
$677$	1.84707	0.0709885	0.0354943	−	0.999370i	$-0.488699\pi$
$677$	1.84707	0.0709885	0.0354943	+	0.999370i	$0.488699\pi$
$678$	−2.30663	−0.0885857
$679$	−3.26937	−0.125467
$680$	−9.58353	−0.367512
$681$	−0.754485	−0.0289119
$682$	−10.6319	−0.407117
$683$	−33.8516	−1.29530	−0.647648	−	0.761940i	$-0.724247\pi$
$683$	−33.8516	−1.29530	−0.647648	+	0.761940i	$0.724247\pi$
$684$	−3.08923	−0.118120
$685$	8.48431	0.324169
$686$	−6.32423	−0.241460
$687$	−8.06603	−0.307738
$688$	5.14019	0.195968
$689$	−19.5815	−0.745996
$690$	0	0
$691$	−15.9102	−0.605253	−0.302627	−	0.953109i	$-0.597863\pi$
$691$	−15.9102	−0.605253	−0.302627	+	0.953109i	$0.597863\pi$
$692$	6.00333	0.228213
$693$	−7.80044	−0.296314
$694$	−4.62360	−0.175510
$695$	22.3368	0.847285
$696$	4.75263	0.180148
$697$	10.8750	0.411920
$698$	−10.1477	−0.384097
$699$	3.67716	0.139083
$700$	2.30982	0.0873032
$701$	10.7430	0.405756	0.202878	−	0.979204i	$-0.434971\pi$
$701$	10.7430	0.405756	0.202878	+	0.979204i	$0.434971\pi$
$702$	−0.630056	−0.0237799
$703$	19.6616	0.741552
$704$	−26.8523	−1.01203
$705$	0.384512	0.0144816
$706$	2.48066	0.0933608
$707$	−7.83652	−0.294723
$708$	−21.3470	−0.802269
$709$	−47.6647	−1.79009	−0.895043	−	0.445980i	$-0.852855\pi$
$709$	−47.6647	−1.79009	−0.895043	+	0.445980i	$0.852855\pi$
$710$	−1.15536	−0.0433600
$711$	13.5753	0.509115
$712$	−25.3779	−0.951078
$713$	0	0
$714$	3.14282	0.117617
$715$	−9.64989	−0.360885
$716$	−17.7018	−0.661549
$717$	−20.0397	−0.748397
$718$	−4.01046	−0.149669
$719$	−7.67207	−0.286120	−0.143060	−	0.989714i	$-0.545694\pi$
$719$	−7.67207	−0.286120	−0.143060	+	0.989714i	$0.545694\pi$
$720$	−3.04345	−0.113423
$721$	−11.6150	−0.432565
$722$	6.54608	0.243620
$723$	25.1865	0.936698
$724$	−4.37299	−0.162521
$725$	3.06021	0.113653
$726$	−11.1122	−0.412413
$727$	−0.575517	−0.0213448	−0.0106724	−	0.999943i	$-0.503397\pi$
$727$	−0.575517	−0.0213448	−0.0106724	+	0.999943i	$0.503397\pi$
$728$	−3.04055	−0.112690
$729$	1.00000	0.0370370
$730$	1.81443	0.0671551
$731$	10.4221	0.385477
$732$	18.6941	0.690955
$733$	25.3573	0.936593	0.468296	−	0.883571i	$-0.344868\pi$
$733$	25.3573	0.936593	0.468296	+	0.883571i	$0.344868\pi$
$734$	2.20848	0.0815165
$735$	5.41742	0.199824
$736$	0	0
$737$	6.06738	0.223495
$738$	−0.713476	−0.0262634
$739$	−13.9292	−0.512394	−0.256197	−	0.966625i	$-0.582470\pi$
$739$	−13.9292	−0.512394	−0.256197	+	0.966625i	$0.582470\pi$
$740$	21.4566	0.788759
$741$	2.61843	0.0961906
$742$	−6.40819	−0.235252
$743$	0.0934609	0.00342875	0.00171437	−	0.999999i	$-0.499454\pi$
$743$	0.0934609	0.00342875	0.00171437	+	0.999999i	$0.499454\pi$
$744$	6.57757	0.241145
$745$	−5.60316	−0.205284
$746$	12.7088	0.465301
$747$	−12.8951	−0.471807
$748$	−70.2546	−2.56876
$749$	3.74999	0.137022
$750$	0.404849	0.0147830
$751$	−3.88058	−0.141604	−0.0708022	−	0.997490i	$-0.522556\pi$
$751$	−3.88058	−0.141604	−0.0708022	+	0.997490i	$0.522556\pi$
$752$	−1.17024	−0.0426744
$753$	15.0920	0.549985
$754$	−1.92811	−0.0702175
$755$	4.21632	0.153448
$756$	2.30982	0.0840075
$757$	9.48006	0.344559	0.172279	−	0.985048i	$-0.444887\pi$
$757$	9.48006	0.344559	0.172279	+	0.985048i	$0.444887\pi$
$758$	12.3950	0.450207
$759$	0	0
$760$	−2.61299	−0.0947831
$761$	−4.05543	−0.147009	−0.0735046	−	0.997295i	$-0.523418\pi$
$761$	−4.05543	−0.147009	−0.0735046	+	0.997295i	$0.523418\pi$
$762$	−7.28166	−0.263787
$763$	19.2686	0.697570
$764$	36.7764	1.33052
$765$	−6.17082	−0.223107
$766$	−9.49138	−0.342938
$767$	18.0937	0.653326
$768$	4.43872	0.160168
$769$	−31.1032	−1.12161	−0.560805	−	0.827948i	$-0.689508\pi$
$769$	−31.1032	−1.12161	−0.560805	+	0.827948i	$0.689508\pi$
$770$	−3.15800	−0.113806
$771$	4.43381	0.159680
$772$	−1.61428	−0.0580992
$773$	−45.5010	−1.63656	−0.818279	−	0.574821i	$-0.805072\pi$
$773$	−45.5010	−1.63656	−0.818279	+	0.574821i	$0.805072\pi$
$774$	−0.683764	−0.0245774
$775$	4.23529	0.152136
$776$	4.03612	0.144888
$777$	−14.7010	−0.527396
$778$	11.3915	0.408404
$779$	2.96511	0.106236
$780$	2.85747	0.102314
$781$	−17.6954	−0.633193
$782$	0	0
$783$	3.06021	0.109363
$784$	−16.4876	−0.588844
$785$	4.37560	0.156172
$786$	−2.75379	−0.0982245
$787$	32.9901	1.17597	0.587985	−	0.808872i	$-0.299921\pi$
$787$	32.9901	1.17597	0.587985	+	0.808872i	$0.299921\pi$
$788$	5.97074	0.212699
$789$	−11.7411	−0.417994
$790$	5.49596	0.195537
$791$	−7.16752	−0.254848
$792$	9.62982	0.342181
$793$	−15.8451	−0.562677
$794$	14.1112	0.500787
$795$	12.5823	0.446248
$796$	28.9641	1.02660
$797$	−22.8611	−0.809781	−0.404890	−	0.914365i	$-0.632690\pi$
$797$	−22.8611	−0.809781	−0.404890	+	0.914365i	$0.632690\pi$
$798$	0.856902	0.0303340
$799$	−2.37276	−0.0839421
$800$	−4.33822	−0.153379
$801$	−16.3408	−0.577374
$802$	−12.7422	−0.449943
$803$	27.7897	0.980676
$804$	−1.79664	−0.0633626
$805$	0	0
$806$	−2.66847	−0.0939928
$807$	11.9300	0.419957
$808$	9.67437	0.340343
$809$	23.5468	0.827862	0.413931	−	0.910308i	$-0.364155\pi$
$809$	23.5468	0.827862	0.413931	+	0.910308i	$0.364155\pi$
$810$	0.404849	0.0142249
$811$	−7.74805	−0.272071	−0.136035	−	0.990704i	$-0.543436\pi$
$811$	−7.74805	−0.272071	−0.136035	+	0.990704i	$0.543436\pi$
$812$	7.06856	0.248058
$813$	1.59814	0.0560493
$814$	−29.3355	−1.02821
$815$	0.235266	0.00824102
$816$	18.7806	0.657452
$817$	2.84164	0.0994163
$818$	−8.33867	−0.291555
$819$	−1.95781	−0.0684113
$820$	3.23580	0.112999
$821$	−48.1540	−1.68059	−0.840293	−	0.542133i	$-0.817617\pi$
$821$	−48.1540	−1.68059	−0.840293	+	0.542133i	$0.817617\pi$
$822$	3.43486	0.119805
$823$	6.23259	0.217255	0.108627	−	0.994083i	$-0.465355\pi$
$823$	6.23259	0.217255	0.108627	+	0.994083i	$0.465355\pi$
$824$	14.3390	0.499522
$825$	6.20063	0.215878
$826$	5.92130	0.206028
$827$	44.8732	1.56039	0.780197	−	0.625534i	$-0.215119\pi$
$827$	44.8732	1.56039	0.780197	+	0.625534i	$0.215119\pi$
$828$	0	0
$829$	−1.84316	−0.0640156	−0.0320078	−	0.999488i	$-0.510190\pi$
$829$	−1.84316	−0.0640156	−0.0320078	+	0.999488i	$0.510190\pi$
$830$	−5.22057	−0.181208
$831$	0.510864	0.0177217
$832$	−6.73957	−0.233653
$833$	−33.4299	−1.15828
$834$	9.04305	0.313135
$835$	−14.1799	−0.490714
$836$	−19.1552	−0.662496
$837$	4.23529	0.146393
$838$	−6.69333	−0.231217
$839$	−33.4504	−1.15484	−0.577418	−	0.816449i	$-0.695940\pi$
$839$	−33.4504	−1.15484	−0.577418	+	0.816449i	$0.695940\pi$
$840$	1.95374	0.0674103
$841$	−19.6351	−0.677072
$842$	−4.61585	−0.159073
$843$	6.74118	0.232179
$844$	3.91310	0.134694
$845$	10.5780	0.363894
$846$	0.155669	0.00535202
$847$	−34.5295	−1.18645
$848$	−38.2935	−1.31501
$849$	−17.5453	−0.602154
$850$	−2.49825	−0.0856893
$851$	0	0
$852$	5.23988	0.179515
$853$	10.7669	0.368650	0.184325	−	0.982865i	$-0.440990\pi$
$853$	10.7669	0.368650	0.184325	+	0.982865i	$0.440990\pi$
$854$	−5.18544	−0.177442
$855$	−1.68250	−0.0575403
$856$	−4.62945	−0.158231
$857$	10.7293	0.366506	0.183253	−	0.983066i	$-0.441337\pi$
$857$	10.7293	0.366506	0.183253	+	0.983066i	$0.441337\pi$
$858$	−3.90675	−0.133374
$859$	33.7750	1.15239	0.576194	−	0.817313i	$-0.304537\pi$
$859$	33.7750	1.15239	0.576194	+	0.817313i	$0.304537\pi$
$860$	3.10105	0.105745
$861$	−2.21702	−0.0755558
$862$	5.40764	0.184185
$863$	5.82528	0.198295	0.0991475	−	0.995073i	$-0.468388\pi$
$863$	5.82528	0.198295	0.0991475	+	0.995073i	$0.468388\pi$
$864$	−4.33822	−0.147589
$865$	3.26962	0.111170
$866$	12.7410	0.432958
$867$	21.0791	0.715882
$868$	9.78277	0.332049
$869$	84.1756	2.85546
$870$	1.23892	0.0420035
$871$	1.52283	0.0515992
$872$	−23.7875	−0.805548
$873$	2.59885	0.0879578
$874$	0	0
$875$	1.25801	0.0425284
$876$	−8.22893	−0.278030
$877$	27.2559	0.920365	0.460182	−	0.887824i	$-0.347784\pi$
$877$	27.2559	0.920365	0.460182	+	0.887824i	$0.347784\pi$
$878$	10.9712	0.370262
$879$	−10.9886	−0.370637
$880$	−18.8713	−0.636151
$881$	11.0578	0.372546	0.186273	−	0.982498i	$-0.440359\pi$
$881$	11.0578	0.372546	0.186273	+	0.982498i	$0.440359\pi$
$882$	2.19323	0.0738501
$883$	−20.4221	−0.687258	−0.343629	−	0.939105i	$-0.611656\pi$
$883$	−20.4221	−0.687258	−0.343629	+	0.939105i	$0.611656\pi$
$884$	−17.6330	−0.593061
$885$	−11.6263	−0.390813
$886$	−4.89495	−0.164449
$887$	5.03758	0.169145	0.0845727	−	0.996417i	$-0.473047\pi$
$887$	5.03758	0.169145	0.0845727	+	0.996417i	$0.473047\pi$
$888$	18.1488	0.609032
$889$	−22.6267	−0.758874
$890$	−6.61556	−0.221754
$891$	6.20063	0.207729
$892$	−31.4963	−1.05457
$893$	−0.646942	−0.0216491
$894$	−2.26843	−0.0758677
$895$	−9.64101	−0.322264
$896$	−13.1206	−0.438328
$897$	0	0
$898$	−3.20451	−0.106936
$899$	12.9609	0.432270
$900$	−1.83610	−0.0612032
$901$	−77.6430	−2.58666
$902$	−4.42400	−0.147303
$903$	−2.12470	−0.0707055
$904$	8.84847	0.294296
$905$	−2.38167	−0.0791695
$906$	1.70697	0.0567104
$907$	−20.7839	−0.690117	−0.345058	−	0.938581i	$-0.612141\pi$
$907$	−20.7839	−0.690117	−0.345058	+	0.938581i	$0.612141\pi$
$908$	1.38531	0.0459731
$909$	6.22931	0.206613
$910$	−0.792616	−0.0262750
$911$	30.3596	1.00586	0.502929	−	0.864328i	$-0.332256\pi$
$911$	30.3596	1.00586	0.502929	+	0.864328i	$0.332256\pi$
$912$	5.12060	0.169560
$913$	−79.9577	−2.64621
$914$	10.4929	0.347073
$915$	10.1814	0.336588
$916$	14.8100	0.489337
$917$	−8.55700	−0.282577
$918$	−2.49825	−0.0824545
$919$	−43.7684	−1.44379	−0.721893	−	0.692004i	$-0.756728\pi$
$919$	−43.7684	−1.44379	−0.721893	+	0.692004i	$0.756728\pi$
$920$	0	0
$921$	−10.0070	−0.329742
$922$	−6.37522	−0.209957
$923$	−4.44132	−0.146188
$924$	14.3224	0.471171
$925$	11.6860	0.384232
$926$	−4.30236	−0.141384
$927$	9.23285	0.303247
$928$	−13.2759	−0.435802
$929$	−34.4775	−1.13117	−0.565585	−	0.824690i	$-0.691350\pi$
$929$	−34.4775	−1.13117	−0.565585	+	0.824690i	$0.691350\pi$
$930$	1.71465	0.0562256
$931$	−9.11480	−0.298726
$932$	−6.75162	−0.221157
$933$	−0.331383	−0.0108490
$934$	−12.9195	−0.422740
$935$	−38.2630	−1.25133
$936$	2.41696	0.0790007
$937$	−26.7699	−0.874536	−0.437268	−	0.899331i	$-0.644054\pi$
$937$	−26.7699	−0.874536	−0.437268	+	0.899331i	$0.644054\pi$
$938$	0.498358	0.0162720
$939$	26.0095	0.848788
$940$	−0.706002	−0.0230273
$941$	−39.4986	−1.28762	−0.643808	−	0.765187i	$-0.722647\pi$
$941$	−39.4986	−1.28762	−0.643808	+	0.765187i	$0.722647\pi$
$942$	1.77146	0.0577172
$943$	0	0
$944$	35.3840	1.15165
$945$	1.25801	0.0409230
$946$	−4.23977	−0.137847
$947$	41.8722	1.36066	0.680331	−	0.732905i	$-0.261836\pi$
$947$	41.8722	1.36066	0.680331	+	0.732905i	$0.261836\pi$
$948$	−24.9256	−0.809547
$949$	6.97484	0.226413
$950$	−0.681158	−0.0220997
$951$	28.5506	0.925815
$952$	−12.0562	−0.390742
$953$	36.0123	1.16655	0.583277	−	0.812273i	$-0.301770\pi$
$953$	36.0123	1.16655	0.583277	+	0.812273i	$0.301770\pi$
$954$	5.09392	0.164922
$955$	20.0297	0.648145
$956$	36.7949	1.19003
$957$	18.9752	0.613383
$958$	11.5375	0.372758
$959$	10.6733	0.344660
$960$	4.33058	0.139769
$961$	−13.0623	−0.421366
$962$	−7.36281	−0.237387
$963$	−2.98090	−0.0960580
$964$	−46.2450	−1.48945
$965$	−0.879190	−0.0283021
$966$	0	0
$967$	36.7830	1.18286	0.591431	−	0.806356i	$-0.298563\pi$
$967$	36.7830	1.18286	0.591431	+	0.806356i	$0.298563\pi$
$968$	42.6275	1.37010
$969$	10.3824	0.333531
$970$	1.05214	0.0337822
$971$	−20.8225	−0.668225	−0.334112	−	0.942533i	$-0.608437\pi$
$971$	−20.8225	−0.668225	−0.334112	+	0.942533i	$0.608437\pi$
$972$	−1.83610	−0.0588929
$973$	28.0999	0.900842
$974$	2.77864	0.0890334
$975$	1.55628	0.0498407
$976$	−30.9867	−0.991860
$977$	−20.6447	−0.660482	−0.330241	−	0.943897i	$-0.607130\pi$
$977$	−20.6447	−0.660482	−0.330241	+	0.943897i	$0.607130\pi$
$978$	0.0952473	0.00304567
$979$	−101.323	−3.23831
$980$	−9.94691	−0.317742
$981$	−15.3168	−0.489027
$982$	−17.4292	−0.556187
$983$	37.5745	1.19844	0.599219	−	0.800585i	$-0.295478\pi$
$983$	37.5745	1.19844	0.599219	+	0.800585i	$0.295478\pi$
$984$	2.73696	0.0872511
$985$	3.25186	0.103613
$986$	−7.64518	−0.243472
$987$	0.483720	0.0153970
$988$	−4.80770	−0.152953
$989$	0	0
$990$	2.51032	0.0797831
$991$	−46.3137	−1.47120	−0.735601	−	0.677415i	$-0.763100\pi$
$991$	−46.3137	−1.47120	−0.735601	+	0.677415i	$0.763100\pi$
$992$	−18.3736	−0.583362
$993$	−13.4175	−0.425790
$994$	−1.45346	−0.0461008
$995$	15.7748	0.500094
$996$	23.6767	0.750224
$997$	−58.8241	−1.86298	−0.931489	−	0.363770i	$-0.881489\pi$
$997$	−58.8241	−1.86298	−0.931489	+	0.363770i	$0.881489\pi$
$998$	−8.43850	−0.267116
$999$	11.6860	0.369727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bv.1.9		25
23.2	even	11		345.2.m.c.211.2	yes	50
23.12	even	11		345.2.m.c.121.2	✓	50
23.22	odd	2		7935.2.a.bw.1.9		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.121.2	✓	50	23.12	even	11
345.2.m.c.211.2	yes	50	23.2	even	11
7935.2.a.bv.1.9		25	1.1	even	1	trivial
7935.2.a.bw.1.9		25	23.22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-0.404849 q^{2} +1.00000 q^{3} -1.83610 q^{4} -1.00000 q^{5} -0.404849 q^{6} -1.25801 q^{7} +1.55304 q^{8} +1.00000 q^{9} +0.404849 q^{10} +6.20063 q^{11} -1.83610 q^{12} +1.55628 q^{13} +0.509303 q^{14} -1.00000 q^{15} +3.04345 q^{16} +6.17082 q^{17} -0.404849 q^{18} +1.68250 q^{19} +1.83610 q^{20} -1.25801 q^{21} -2.51032 q^{22} +1.55304 q^{24} +1.00000 q^{25} -0.630056 q^{26} +1.00000 q^{27} +2.30982 q^{28} +3.06021 q^{29} +0.404849 q^{30} +4.23529 q^{31} -4.33822 q^{32} +6.20063 q^{33} -2.49825 q^{34} +1.25801 q^{35} -1.83610 q^{36} +11.6860 q^{37} -0.681158 q^{38} +1.55628 q^{39} -1.55304 q^{40} +1.76233 q^{41} +0.509303 q^{42} +1.68894 q^{43} -11.3850 q^{44} -1.00000 q^{45} -0.384512 q^{47} +3.04345 q^{48} -5.41742 q^{49} -0.404849 q^{50} +6.17082 q^{51} -2.85747 q^{52} -12.5823 q^{53} -0.404849 q^{54} -6.20063 q^{55} -1.95374 q^{56} +1.68250 q^{57} -1.23892 q^{58} +11.6263 q^{59} +1.83610 q^{60} -10.1814 q^{61} -1.71465 q^{62} -1.25801 q^{63} -4.33058 q^{64} -1.55628 q^{65} -2.51032 q^{66} +0.978510 q^{67} -11.3302 q^{68} -0.509303 q^{70} -2.85381 q^{71} +1.55304 q^{72} +4.48175 q^{73} -4.73105 q^{74} +1.00000 q^{75} -3.08923 q^{76} -7.80044 q^{77} -0.630056 q^{78} +13.5753 q^{79} -3.04345 q^{80} +1.00000 q^{81} -0.713476 q^{82} -12.8951 q^{83} +2.30982 q^{84} -6.17082 q^{85} -0.683764 q^{86} +3.06021 q^{87} +9.62982 q^{88} -16.3408 q^{89} +0.404849 q^{90} -1.95781 q^{91} +4.23529 q^{93} +0.155669 q^{94} -1.68250 q^{95} -4.33822 q^{96} +2.59885 q^{97} +2.19323 q^{98} +6.20063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} - 25 q^{5} + 11 q^{6} - 7 q^{7} + 33 q^{8} + 25 q^{9} - 11 q^{10} - 9 q^{11} + 31 q^{12} + 18 q^{13} - 11 q^{14} - 25 q^{15} + 39 q^{16} + 8 q^{17} + 11 q^{18} - 11 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) \) 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 - 25 * q^5 + 11 * q^6 - 7 * q^7 + 33 * q^8 + 25 * q^9 - 11 * q^10 - 9 * q^11 + 31 * q^12 + 18 * q^13 - 11 * q^14 - 25 * q^15 + 39 * q^16 + 8 * q^17 + 11 * q^18 - 11 * q^19 - 31 * q^20 - 7 * q^21 - 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 + 5 * q^28 + 33 * q^29 - 11 * q^30 + 14 * q^31 + 77 * q^32 - 9 * q^33 - 13 * q^34 + 7 * q^35 + 31 * q^36 - 4 * q^37 + 23 * q^38 + 18 * q^39 - 33 * q^40 + 56 * q^41 - 11 * q^42 + 4 * q^43 + 18 * q^44 - 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 + 8 * q^51 + 49 * q^52 - 2 * q^53 + 11 * q^54 + 9 * q^55 - 33 * q^56 - 11 * q^57 + 26 * q^58 + 61 * q^59 - 31 * q^60 - 21 * q^61 + 51 * q^62 - 7 * q^63 + 71 * q^64 - 18 * q^65 - 9 * q^66 - 2 * q^67 + 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 + 47 * q^74 + 25 * q^75 + 8 * q^76 + 49 * q^77 + 35 * q^78 - 35 * q^79 - 39 * q^80 + 25 * q^81 + 35 * q^82 + 26 * q^83 + 5 * q^84 - 8 * q^85 + 33 * q^86 + 33 * q^87 - 9 * q^88 + 7 * q^89 - 11 * q^90 - 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 + 54 * q^97 + 88 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more