LMFDB - Embedded newform 605.2.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.27433728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} + 15x^{2} - 3 $ x^6 - 9x^4 + 15x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.37268$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.37268 q^{2} +3.26180 q^{3} -0.115749 q^{4} +1.00000 q^{5} +4.47741 q^{6} -1.37268 q^{7} -2.90425 q^{8} +7.63935 q^{9} +O(q^{10})$	\(q+1.37268 q^{2} +3.26180 q^{3} -0.115749 q^{4} +1.00000 q^{5} +4.47741 q^{6} -1.37268 q^{7} -2.90425 q^{8} +7.63935 q^{9} +1.37268 q^{10} -0.377552 q^{12} -1.93253 q^{13} -1.88425 q^{14} +3.26180 q^{15} -3.75510 q^{16} +6.20946 q^{17} +10.4864 q^{18} +0.812826 q^{19} -0.115749 q^{20} -4.47741 q^{21} -3.63935 q^{23} -9.47308 q^{24} +1.00000 q^{25} -2.65275 q^{26} +15.1327 q^{27} +0.158887 q^{28} -7.83511 q^{29} +4.47741 q^{30} -3.40786 q^{31} +0.653939 q^{32} +8.52360 q^{34} -1.37268 q^{35} -0.884251 q^{36} -4.52360 q^{37} +1.11575 q^{38} -6.30355 q^{39} -2.90425 q^{40} +1.82613 q^{41} -6.14605 q^{42} -6.46243 q^{43} +7.63935 q^{45} -4.99567 q^{46} +4.73820 q^{47} -12.2484 q^{48} -5.11575 q^{49} +1.37268 q^{50} +20.2540 q^{51} +0.223690 q^{52} -8.39446 q^{53} +20.7723 q^{54} +3.98660 q^{56} +2.65128 q^{57} -10.7551 q^{58} +1.11575 q^{59} -0.377552 q^{60} -2.54488 q^{61} -4.67789 q^{62} -10.4864 q^{63} +8.40786 q^{64} -1.93253 q^{65} +2.73820 q^{67} -0.718741 q^{68} -11.8709 q^{69} -1.88425 q^{70} -1.11575 q^{71} -22.1866 q^{72} -12.4189 q^{73} -6.20946 q^{74} +3.26180 q^{75} -0.0940841 q^{76} -8.65275 q^{78} +5.80849 q^{79} -3.75510 q^{80} +26.4417 q^{81} +2.50670 q^{82} +15.9771 q^{83} +0.518258 q^{84} +6.20946 q^{85} -8.87085 q^{86} -25.5566 q^{87} -2.70789 q^{89} +10.4864 q^{90} +2.65275 q^{91} +0.421253 q^{92} -11.1157 q^{93} +6.50403 q^{94} +0.812826 q^{95} +2.13302 q^{96} +14.1630 q^{97} -7.02229 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{3} + 6 q^{4} + 6 q^{5} + 12 q^{9}+O(q^{10}) $ 6 * q + 6 * q^3 + 6 * q^4 + 6 * q^5 + 12 * q^9	$ 6 q + 6 q^{3} + 6 q^{4} + 6 q^{5} + 12 q^{9} + 18 q^{12} - 18 q^{14} + 6 q^{15} + 18 q^{16} + 6 q^{20} + 12 q^{23} + 6 q^{25} - 36 q^{26} + 30 q^{27} + 24 q^{34} - 12 q^{36} - 30 q^{42} + 12 q^{45} + 42 q^{47} - 6 q^{48} - 24 q^{49} + 24 q^{53} - 30 q^{56} - 24 q^{58} + 18 q^{60} + 30 q^{64} + 30 q^{67} - 24 q^{69} - 18 q^{70} + 6 q^{75} - 72 q^{78} + 18 q^{80} + 30 q^{81} + 42 q^{82} - 6 q^{86} - 30 q^{89} + 36 q^{91} + 36 q^{92} - 60 q^{93} + 24 q^{97}+O(q^{100}) $ 6 * q + 6 * q^3 + 6 * q^4 + 6 * q^5 + 12 * q^9 + 18 * q^12 - 18 * q^14 + 6 * q^15 + 18 * q^16 + 6 * q^20 + 12 * q^23 + 6 * q^25 - 36 * q^26 + 30 * q^27 + 24 * q^34 - 12 * q^36 - 30 * q^42 + 12 * q^45 + 42 * q^47 - 6 * q^48 - 24 * q^49 + 24 * q^53 - 30 * q^56 - 24 * q^58 + 18 * q^60 + 30 * q^64 + 30 * q^67 - 24 * q^69 - 18 * q^70 + 6 * q^75 - 72 * q^78 + 18 * q^80 + 30 * q^81 + 42 * q^82 - 6 * q^86 - 30 * q^89 + 36 * q^91 + 36 * q^92 - 60 * q^93 + 24 * q^97

Display 100 coefficients 10 coefficients

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 $

$2$	1.37268	0.970631	0.485316	−	0.874339i	$-0.338705\pi$
$2$	1.37268	0.970631	0.485316	+	0.874339i	$0.338705\pi$
$3$	3.26180	1.88320	0.941601	−	0.336730i	$-0.109321\pi$
$3$	3.26180	1.88320	0.941601	+	0.336730i	$0.109321\pi$
$4$	−0.115749	−0.0578747
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.47741	1.82790
$7$	−1.37268	−0.518824	−0.259412	−	0.965767i	$-0.583529\pi$
$7$	−1.37268	−0.518824	−0.259412	+	0.965767i	$0.583529\pi$
$8$	−2.90425	−1.02681
$9$	7.63935	2.54645
$10$	1.37268	0.434080
$11$	0	0
$11$	0	0
$12$	−0.377552	−0.108990
$13$	−1.93253	−0.535989	−0.267994	−	0.963420i	$-0.586361\pi$
$13$	−1.93253	−0.535989	−0.267994	+	0.963420i	$0.586361\pi$
$14$	−1.88425	−0.503587
$15$	3.26180	0.842194
$16$	−3.75510	−0.938776
$17$	6.20946	1.50602	0.753008	−	0.658012i	$-0.228602\pi$
$17$	6.20946	1.50602	0.753008	+	0.658012i	$0.228602\pi$
$18$	10.4864	2.47167
$19$	0.812826	0.186475	0.0932375	−	0.995644i	$-0.470278\pi$
$19$	0.812826	0.186475	0.0932375	+	0.995644i	$0.470278\pi$
$20$	−0.115749	−0.0258824
$21$	−4.47741	−0.977051
$22$	0	0
$23$	−3.63935	−0.758858	−0.379429	−	0.925221i	$-0.623880\pi$
$23$	−3.63935	−0.758858	−0.379429	+	0.925221i	$0.623880\pi$
$24$	−9.47308	−1.93368
$25$	1.00000	0.200000
$26$	−2.65275	−0.520247
$27$	15.1327	2.91228
$28$	0.158887	0.0300268
$29$	−7.83511	−1.45494	−0.727472	−	0.686137i	$-0.759305\pi$
$29$	−7.83511	−1.45494	−0.727472	+	0.686137i	$0.759305\pi$
$30$	4.47741	0.817460
$31$	−3.40786	−0.612069	−0.306034	−	0.952020i	$-0.599002\pi$
$31$	−3.40786	−0.612069	−0.306034	+	0.952020i	$0.599002\pi$
$32$	0.653939	0.115601
$33$	0	0
$34$	8.52360	1.46179
$35$	−1.37268	−0.232025
$36$	−0.884251	−0.147375
$37$	−4.52360	−0.743676	−0.371838	−	0.928298i	$-0.621272\pi$
$37$	−4.52360	−0.743676	−0.371838	+	0.928298i	$0.621272\pi$
$38$	1.11575	0.180998
$39$	−6.30355	−1.00938
$40$	−2.90425	−0.459202
$41$	1.82613	0.285194	0.142597	−	0.989781i	$-0.454455\pi$
$41$	1.82613	0.285194	0.142597	+	0.989781i	$0.454455\pi$
$42$	−6.14605	−0.948357
$43$	−6.46243	−0.985512	−0.492756	−	0.870168i	$-0.664010\pi$
$43$	−6.46243	−0.985512	−0.492756	+	0.870168i	$0.664010\pi$
$44$	0	0
$45$	7.63935	1.13881
$46$	−4.99567	−0.736571
$47$	4.73820	0.691137	0.345569	−	0.938393i	$-0.387686\pi$
$47$	4.73820	0.691137	0.345569	+	0.938393i	$0.387686\pi$
$48$	−12.2484	−1.76790
$49$	−5.11575	−0.730821
$50$	1.37268	0.194126
$51$	20.2540	2.83613
$52$	0.223690	0.0310202
$53$	−8.39446	−1.15307	−0.576534	−	0.817073i	$-0.695595\pi$
$53$	−8.39446	−1.15307	−0.576534	+	0.817073i	$0.695595\pi$
$54$	20.7723	2.82675
$55$	0	0
$56$	3.98660	0.532732
$57$	2.65128	0.351170
$58$	−10.7551	−1.41221
$59$	1.11575	0.145258	0.0726291	−	0.997359i	$-0.476861\pi$
$59$	1.11575	0.145258	0.0726291	+	0.997359i	$0.476861\pi$
$60$	−0.377552	−0.0487417
$61$	−2.54488	−0.325838	−0.162919	−	0.986639i	$-0.552091\pi$
$61$	−2.54488	−0.325838	−0.162919	+	0.986639i	$0.552091\pi$
$62$	−4.67789	−0.594093
$63$	−10.4864	−1.32116
$64$	8.40786	1.05098
$65$	−1.93253	−0.239701
$66$	0	0
$67$	2.73820	0.334524	0.167262	−	0.985912i	$-0.446507\pi$
$67$	2.73820	0.334524	0.167262	+	0.985912i	$0.446507\pi$
$68$	−0.718741	−0.0871602
$69$	−11.8709	−1.42908
$70$	−1.88425	−0.225211
$71$	−1.11575	−0.132415	−0.0662075	−	0.997806i	$-0.521090\pi$
$71$	−1.11575	−0.132415	−0.0662075	+	0.997806i	$0.521090\pi$
$72$	−22.1866	−2.61471
$73$	−12.4189	−1.45353	−0.726763	−	0.686889i	$-0.758976\pi$
$73$	−12.4189	−1.45353	−0.726763	+	0.686889i	$0.758976\pi$
$74$	−6.20946	−0.721835
$75$	3.26180	0.376640
$76$	−0.0940841	−0.0107922
$77$	0	0
$78$	−8.65275	−0.979731
$79$	5.80849	0.653507	0.326753	−	0.945110i	$-0.394045\pi$
$79$	5.80849	0.653507	0.326753	+	0.945110i	$0.394045\pi$
$80$	−3.75510	−0.419833
$81$	26.4417	2.93796
$82$	2.50670	0.276819
$83$	15.9771	1.75372	0.876858	−	0.480750i	$-0.159635\pi$
$83$	15.9771	1.75372	0.876858	+	0.480750i	$0.159635\pi$
$84$	0.518258	0.0565465
$85$	6.20946	0.673511
$86$	−8.87085	−0.956569
$87$	−25.5566	−2.73995
$88$	0	0
$89$	−2.70789	−0.287036	−0.143518	−	0.989648i	$-0.545842\pi$
$89$	−2.70789	−0.287036	−0.143518	+	0.989648i	$0.545842\pi$
$90$	10.4864	1.10536
$91$	2.65275	0.278084
$92$	0.421253	0.0439187
$93$	−11.1157	−1.15265
$94$	6.50403	0.670839
$95$	0.812826	0.0833941
$96$	2.13302	0.217700
$97$	14.1630	1.43803	0.719015	−	0.694994i	$-0.244593\pi$
$97$	14.1630	1.43803	0.719015	+	0.694994i	$0.244593\pi$
$98$	−7.02229	−0.709358
$99$	0	0
$100$	−0.115749	−0.0115749
$101$	11.4056	1.13490	0.567451	−	0.823408i	$-0.307930\pi$
$101$	11.4056	1.13490	0.567451	+	0.823408i	$0.307930\pi$
$102$	27.8023	2.75284
$103$	13.8709	1.36674	0.683368	−	0.730074i	$-0.260515\pi$
$103$	13.8709	1.36674	0.683368	+	0.730074i	$0.260515\pi$
$104$	5.61256	0.550357
$105$	−4.47741	−0.436951
$106$	−11.5229	−1.11920
$107$	−1.06580	−0.103034	−0.0515172	−	0.998672i	$-0.516406\pi$
$107$	−1.06580	−0.103034	−0.0515172	+	0.998672i	$0.516406\pi$
$108$	−1.75160	−0.168547
$109$	11.3115	1.08345	0.541724	−	0.840556i	$-0.317772\pi$
$109$	11.3115	1.08345	0.541724	+	0.840556i	$0.317772\pi$
$110$	0	0
$111$	−14.7551	−1.40049
$112$	5.15456	0.487060
$113$	−3.76850	−0.354511	−0.177255	−	0.984165i	$-0.556722\pi$
$113$	−3.76850	−0.354511	−0.177255	+	0.984165i	$0.556722\pi$
$114$	3.63935	0.340857
$115$	−3.63935	−0.339371
$116$	0.906910	0.0842044
$117$	−14.7633	−1.36487
$118$	1.53157	0.140992
$119$	−8.52360	−0.781358
$120$	−9.47308	−0.864770
$121$	0	0
$122$	−3.49330	−0.316269
$123$	5.95649	0.537079
$124$	0.394457	0.0354233
$125$	1.00000	0.0894427
$126$	−14.3945	−1.28236
$127$	−1.67956	−0.149037	−0.0745186	−	0.997220i	$-0.523742\pi$
$127$	−1.67956	−0.149037	−0.0745186	+	0.997220i	$0.523742\pi$
$128$	10.2334	0.904515
$129$	−21.0792	−1.85592
$130$	−2.65275	−0.232662
$131$	11.7943	1.03047	0.515235	−	0.857049i	$-0.327705\pi$
$131$	11.7943	1.03047	0.515235	+	0.857049i	$0.327705\pi$
$132$	0	0
$133$	−1.11575	−0.0967477
$134$	3.75867	0.324700
$135$	15.1327	1.30241
$136$	−18.0338	−1.54639
$137$	−7.40786	−0.632896	−0.316448	−	0.948610i	$-0.602490\pi$
$137$	−7.40786	−0.632896	−0.316448	+	0.948610i	$0.602490\pi$
$138$	−16.2949	−1.38711
$139$	−2.65128	−0.224878	−0.112439	−	0.993659i	$-0.535866\pi$
$139$	−2.65128	−0.224878	−0.112439	+	0.993659i	$0.535866\pi$
$140$	0.158887	0.0134284
$141$	15.4551	1.30155
$142$	−1.53157	−0.128526
$143$	0	0
$144$	−28.6866	−2.39055
$145$	−7.83511	−0.650671
$146$	−17.0472	−1.41084
$147$	−16.6866	−1.37628
$148$	0.523604	0.0430400
$149$	8.35337	0.684335	0.342167	−	0.939639i	$-0.388839\pi$
$149$	8.35337	0.684335	0.342167	+	0.939639i	$0.388839\pi$
$150$	4.47741	0.365579
$151$	7.42325	0.604096	0.302048	−	0.953293i	$-0.402330\pi$
$151$	7.42325	0.604096	0.302048	+	0.953293i	$0.402330\pi$
$152$	−2.36065	−0.191474
$153$	47.4363	3.83500
$154$	0	0
$155$	−3.40786	−0.273726
$156$	0.729632	0.0584173
$157$	−8.58421	−0.685095	−0.342547	−	0.939501i	$-0.611290\pi$
$157$	−8.58421	−0.685095	−0.342547	+	0.939501i	$0.611290\pi$
$158$	7.97320	0.634314
$159$	−27.3811	−2.17146
$160$	0.653939	0.0516984
$161$	4.99567	0.393714
$162$	36.2959	2.85168
$163$	16.3776	1.28279	0.641394	−	0.767211i	$-0.278356\pi$
$163$	16.3776	1.28279	0.641394	+	0.767211i	$0.278356\pi$
$164$	−0.211374	−0.0165055
$165$	0	0
$166$	21.9315	1.70221
$167$	21.4385	1.65896	0.829482	−	0.558533i	$-0.188636\pi$
$167$	21.4385	1.65896	0.829482	+	0.558533i	$0.188636\pi$
$168$	13.0035	1.00324
$169$	−9.26531	−0.712716
$170$	8.52360	0.653731
$171$	6.20946	0.474849
$172$	0.748023	0.0570362
$173$	13.7377	1.04446	0.522229	−	0.852806i	$-0.325101\pi$
$173$	13.7377	1.04446	0.522229	+	0.852806i	$0.325101\pi$
$174$	−35.0810	−2.65949
$175$	−1.37268	−0.103765
$176$	0	0
$177$	3.63935	0.273551
$178$	−3.71707	−0.278606
$179$	−3.76850	−0.281671	−0.140836	−	0.990033i	$-0.544979\pi$
$179$	−3.76850	−0.281671	−0.140836	+	0.990033i	$0.544979\pi$
$180$	−0.884251	−0.0659081
$181$	−0.0133979	−0.000995860 0	−0.000497930	−	1.00000i	$-0.500158\pi$
$181$	−0.0133979	−0.000995860 0	−0.000497930		1.00000i	$0.500158\pi$
$182$	3.64138	0.269917
$183$	−8.30088	−0.613619
$184$	10.5696	0.779200
$185$	−4.52360	−0.332582
$186$	−15.2584	−1.11880
$187$	0	0
$188$	−0.548444	−0.0399994
$189$	−20.7723	−1.51096
$190$	1.11575	0.0809450
$191$	−16.6260	−1.20301	−0.601506	−	0.798868i	$-0.705432\pi$
$191$	−16.6260	−1.20301	−0.601506	+	0.798868i	$0.705432\pi$
$192$	27.4248	1.97921
$193$	−26.7813	−1.92776	−0.963879	−	0.266340i	$-0.914186\pi$
$193$	−26.7813	−1.92776	−0.963879	+	0.266340i	$0.914186\pi$
$194$	19.4412	1.39580
$195$	−6.30355	−0.451406
$196$	0.592145	0.0422961
$197$	−2.55719	−0.182192	−0.0910962	−	0.995842i	$-0.529037\pi$
$197$	−2.55719	−0.182192	−0.0910962	+	0.995842i	$0.529037\pi$
$198$	0	0
$199$	−21.8629	−1.54982	−0.774911	−	0.632071i	$-0.782205\pi$
$199$	−21.8629	−1.54982	−0.774911	+	0.632071i	$0.782205\pi$
$200$	−2.90425	−0.205361
$201$	8.93146	0.629977
$202$	15.6563	1.10157
$203$	10.7551	0.754860
$204$	−2.34439	−0.164140
$205$	1.82613	0.127543
$206$	19.0402	1.32660
$207$	−27.8023	−1.93239
$208$	7.25687	0.503173
$209$	0	0
$210$	−6.14605	−0.424118
$211$	−12.8308	−0.883307	−0.441654	−	0.897186i	$-0.645608\pi$
$211$	−12.8308	−0.883307	−0.441654	+	0.897186i	$0.645608\pi$
$212$	0.971653	0.0667334
$213$	−3.63935	−0.249364
$214$	−1.46300	−0.100008
$215$	−6.46243	−0.440734
$216$	−43.9490	−2.99035
$217$	4.67789	0.317556
$218$	15.5271	1.05163
$219$	−40.5081	−2.73728
$220$	0	0
$221$	−12.0000	−0.807207
$222$	−20.2540	−1.35936
$223$	−7.36415	−0.493140	−0.246570	−	0.969125i	$-0.579304\pi$
$223$	−7.36415	−0.493140	−0.246570	+	0.969125i	$0.579304\pi$
$224$	−0.897649	−0.0599767
$225$	7.63935	0.509290
$226$	−5.17295	−0.344099
$227$	−1.37268	−0.0911080	−0.0455540	−	0.998962i	$-0.514505\pi$
$227$	−1.37268	−0.0911080	−0.0455540	+	0.998962i	$0.514505\pi$
$228$	−0.306884	−0.0203239
$229$	29.4968	1.94920	0.974602	−	0.223944i	$-0.0718933\pi$
$229$	29.4968	1.94920	0.974602	+	0.223944i	$0.0718933\pi$
$230$	−4.99567	−0.329405
$231$	0	0
$232$	22.7551	1.49395
$233$	−21.9984	−1.44116	−0.720582	−	0.693370i	$-0.756125\pi$
$233$	−21.9984	−1.44116	−0.720582	+	0.693370i	$0.756125\pi$
$234$	−20.2653	−1.32478
$235$	4.73820	0.309086
$236$	−0.129147	−0.00840677
$237$	18.9462	1.23069
$238$	−11.7002	−0.758410
$239$	−18.7225	−1.21106	−0.605528	−	0.795824i	$-0.707038\pi$
$239$	−18.7225	−1.21106	−0.605528	+	0.795824i	$0.707038\pi$
$240$	−12.2484	−0.790631
$241$	26.2630	1.69175	0.845875	−	0.533382i	$-0.179079\pi$
$241$	26.2630	1.69175	0.845875	+	0.533382i	$0.179079\pi$
$242$	0	0
$243$	40.8495	2.62050
$244$	0.294568	0.0188578
$245$	−5.11575	−0.326833
$246$	8.17636	0.521305
$247$	−1.57081	−0.0999485
$248$	9.89725	0.628476
$249$	52.1142	3.30260
$250$	1.37268	0.0868159
$251$	−22.6260	−1.42814	−0.714069	−	0.700075i	$-0.753150\pi$
$251$	−22.6260	−1.42814	−0.714069	+	0.700075i	$0.753150\pi$
$252$	1.21379	0.0764618
$253$	0	0
$254$	−2.30550	−0.144660
$255$	20.2540	1.26836
$256$	−2.76850	−0.173031
$257$	17.2102	1.07354	0.536770	−	0.843728i	$-0.319644\pi$
$257$	17.2102	1.07354	0.536770	+	0.843728i	$0.319644\pi$
$258$	−28.9350	−1.80141
$259$	6.20946	0.385837
$260$	0.223690	0.0138726
$261$	−59.8552	−3.70494
$262$	16.1898	1.00021
$263$	−5.71441	−0.352366	−0.176183	−	0.984357i	$-0.556375\pi$
$263$	−5.71441	−0.352366	−0.176183	+	0.984357i	$0.556375\pi$
$264$	0	0
$265$	−8.39446	−0.515667
$266$	−1.53157	−0.0939064
$267$	−8.83262	−0.540547
$268$	−0.316945	−0.0193605
$269$	−2.87085	−0.175039	−0.0875195	−	0.996163i	$-0.527894\pi$
$269$	−2.87085	−0.175039	−0.0875195	+	0.996163i	$0.527894\pi$
$270$	20.7723	1.26416
$271$	7.64694	0.464519	0.232259	−	0.972654i	$-0.425388\pi$
$271$	7.64694	0.464519	0.232259	+	0.972654i	$0.425388\pi$
$272$	−23.3172	−1.41381
$273$	8.65275	0.523688
$274$	−10.1686	−0.614309
$275$	0	0
$276$	1.37404	0.0827077
$277$	29.3970	1.76630	0.883148	−	0.469094i	$-0.155420\pi$
$277$	29.3970	1.76630	0.883148	+	0.469094i	$0.155420\pi$
$278$	−3.63935	−0.218274
$279$	−26.0338	−1.55860
$280$	3.98660	0.238245
$281$	−24.2241	−1.44509	−0.722544	−	0.691325i	$-0.757027\pi$
$281$	−24.2241	−1.44509	−0.722544	+	0.691325i	$0.757027\pi$
$282$	21.2149	1.26333
$283$	−5.11903	−0.304295	−0.152147	−	0.988358i	$-0.548619\pi$
$283$	−5.11903	−0.304295	−0.152147	+	0.988358i	$0.548619\pi$
$284$	0.129147	0.00766348
$285$	2.65128	0.157048
$286$	0	0
$287$	−2.50670	−0.147966
$288$	4.99567	0.294373
$289$	21.5574	1.26808
$290$	−10.7551	−0.631561
$291$	46.1968	2.70810
$292$	1.43748	0.0841223
$293$	−10.9923	−0.642179	−0.321089	−	0.947049i	$-0.604049\pi$
$293$	−10.9923	−0.642179	−0.321089	+	0.947049i	$0.604049\pi$
$294$	−22.9053	−1.33586
$295$	1.11575	0.0649614
$296$	13.1377	0.763611
$297$	0	0
$298$	11.4665	0.664237
$299$	7.03318	0.406739
$300$	−0.377552	−0.0217980
$301$	8.87085	0.511307
$302$	10.1898	0.586354
$303$	37.2029	2.13725
$304$	−3.05224	−0.175058
$305$	−2.54488	−0.145719
$306$	65.1148	3.72237
$307$	14.3515	0.819081	0.409540	−	0.912292i	$-0.365689\pi$
$307$	14.3515	0.819081	0.409540	+	0.912292i	$0.365689\pi$
$308$	0	0
$309$	45.2440	2.57384
$310$	−4.67789	−0.265687
$311$	27.3811	1.55264	0.776319	−	0.630341i	$-0.217085\pi$
$311$	27.3811	1.55264	0.776319	+	0.630341i	$0.217085\pi$
$312$	18.3071	1.03643
$313$	3.87085	0.218794	0.109397	−	0.993998i	$-0.465108\pi$
$313$	3.87085	0.218794	0.109397	+	0.993998i	$0.465108\pi$
$314$	−11.7834	−0.664974
$315$	−10.4864	−0.590841
$316$	−0.672330	−0.0378215
$317$	−15.5102	−0.871140	−0.435570	−	0.900155i	$-0.643453\pi$
$317$	−15.5102	−0.871140	−0.435570	+	0.900155i	$0.643453\pi$
$318$	−37.5854	−2.10769
$319$	0	0
$320$	8.40786	0.470013
$321$	−3.47642	−0.194035
$322$	6.85745	0.382151
$323$	5.04721	0.280834
$324$	−3.06061	−0.170034
$325$	−1.93253	−0.107198
$326$	22.4811	1.24512
$327$	36.8960	2.04035
$328$	−5.30355	−0.292839
$329$	−6.50403	−0.358579
$330$	0	0
$331$	26.8575	1.47622	0.738110	−	0.674681i	$-0.235719\pi$
$331$	26.8575	1.47622	0.738110	+	0.674681i	$0.235719\pi$
$332$	−1.84934	−0.101496
$333$	−34.5574	−1.89373
$334$	29.4283	1.61024
$335$	2.73820	0.149604
$336$	16.8131	0.917232
$337$	1.93253	0.105272	0.0526359	−	0.998614i	$-0.483238\pi$
$337$	1.93253	0.105272	0.0526359	+	0.998614i	$0.483238\pi$
$338$	−12.7183	−0.691785
$339$	−12.2921	−0.667616
$340$	−0.718741	−0.0389792
$341$	0	0
$342$	8.52360	0.460904
$343$	16.6310	0.897992
$344$	18.7685	1.01193
$345$	−11.8709	−0.639105
$346$	18.8575	1.01378
$347$	3.80027	0.204009	0.102004	−	0.994784i	$-0.467474\pi$
$347$	3.80027	0.204009	0.102004	+	0.994784i	$0.467474\pi$
$348$	2.95816	0.158574
$349$	17.1909	0.920208	0.460104	−	0.887865i	$-0.347812\pi$
$349$	17.1909	0.920208	0.460104	+	0.887865i	$0.347812\pi$
$350$	−1.88425	−0.100717
$351$	−29.2444	−1.56095
$352$	0	0
$353$	−1.99207	−0.106027	−0.0530135	−	0.998594i	$-0.516883\pi$
$353$	−1.99207	−0.106027	−0.0530135	+	0.998594i	$0.516883\pi$
$354$	4.99567	0.265517
$355$	−1.11575	−0.0592178
$356$	0.313437	0.0166121
$357$	−27.8023	−1.47145
$358$	−5.17295	−0.273399
$359$	−15.5761	−0.822077	−0.411039	−	0.911618i	$-0.634834\pi$
$359$	−15.5761	−0.822077	−0.411039	+	0.911618i	$0.634834\pi$
$360$	−22.1866	−1.16933
$361$	−18.3393	−0.965227
$362$	−0.0183911	−0.000966613 0
$363$	0	0
$364$	−0.307054	−0.0160940
$365$	−12.4189	−0.650036
$366$	−11.3945	−0.595598
$367$	18.7720	0.979891	0.489945	−	0.871753i	$-0.337017\pi$
$367$	18.7720	0.979891	0.489945	+	0.871753i	$0.337017\pi$
$368$	13.6661	0.712397
$369$	13.9505	0.726234
$370$	−6.20946	−0.322815
$371$	11.5229	0.598239
$372$	1.28664	0.0667092
$373$	−2.62664	−0.136003	−0.0680013	−	0.997685i	$-0.521662\pi$
$373$	−2.62664	−0.136003	−0.0680013	+	0.997685i	$0.521662\pi$
$374$	0	0
$375$	3.26180	0.168439
$376$	−13.7609	−0.709664
$377$	15.1416	0.779833
$378$	−28.5137	−1.46659
$379$	2.66069	0.136670	0.0683351	−	0.997662i	$-0.478231\pi$
$379$	2.66069	0.136670	0.0683351	+	0.997662i	$0.478231\pi$
$380$	−0.0940841	−0.00482641
$381$	−5.47840	−0.280667
$382$	−22.8221	−1.16768
$383$	21.9315	1.12065	0.560323	−	0.828274i	$-0.310677\pi$
$383$	21.9315	1.12065	0.560323	+	0.828274i	$0.310677\pi$
$384$	33.3794	1.70338
$385$	0	0
$386$	−36.7621	−1.87114
$387$	−49.3688	−2.50956
$388$	−1.63935	−0.0832256
$389$	−3.42125	−0.173464	−0.0867322	−	0.996232i	$-0.527642\pi$
$389$	−3.42125	−0.173464	−0.0867322	+	0.996232i	$0.527642\pi$
$390$	−8.65275	−0.438149
$391$	−22.5984	−1.14285
$392$	14.8574	0.750412
$393$	38.4706	1.94058
$394$	−3.51021	−0.176842
$395$	5.80849	0.292257
$396$	0	0
$397$	5.51021	0.276549	0.138275	−	0.990394i	$-0.455844\pi$
$397$	5.51021	0.276549	0.138275	+	0.990394i	$0.455844\pi$
$398$	−30.0108	−1.50431
$399$	−3.63935	−0.182196
$400$	−3.75510	−0.187755
$401$	−17.9260	−0.895181	−0.447591	−	0.894239i	$-0.647718\pi$
$401$	−17.9260	−0.895181	−0.447591	+	0.894239i	$0.647718\pi$
$402$	12.2600	0.611475
$403$	6.58580	0.328062
$404$	−1.32019	−0.0656821
$405$	26.4417	1.31390
$406$	14.7633	0.732691
$407$	0	0
$408$	−58.8227	−2.91216
$409$	−29.3261	−1.45008	−0.725042	−	0.688704i	$-0.758180\pi$
$409$	−29.3261	−1.45008	−0.725042	+	0.688704i	$0.758180\pi$
$410$	2.50670	0.123797
$411$	−24.1630	−1.19187
$412$	−1.60554	−0.0790994
$413$	−1.53157	−0.0753635
$414$	−38.1637	−1.87564
$415$	15.9771	0.784285
$416$	−1.26376	−0.0619609
$417$	−8.64794	−0.423491
$418$	0	0
$419$	2.65275	0.129595	0.0647977	−	0.997898i	$-0.479360\pi$
$419$	2.65275	0.129595	0.0647977	+	0.997898i	$0.479360\pi$
$420$	0.518258	0.0252884
$421$	−11.1630	−0.544049	−0.272025	−	0.962290i	$-0.587693\pi$
$421$	−11.1630	−0.544049	−0.272025	+	0.962290i	$0.587693\pi$
$422$	−17.6126	−0.857366
$423$	36.1968	1.75995
$424$	24.3796	1.18398
$425$	6.20946	0.301203
$426$	−4.99567	−0.242041
$427$	3.49330	0.169053
$428$	0.123365	0.00596309
$429$	0	0
$430$	−8.87085	−0.427791
$431$	−4.55918	−0.219608	−0.109804	−	0.993953i	$-0.535022\pi$
$431$	−4.55918	−0.219608	−0.109804	+	0.993953i	$0.535022\pi$
$432$	−56.8247	−2.73398
$433$	20.1630	0.968970	0.484485	−	0.874800i	$-0.339007\pi$
$433$	20.1630	0.968970	0.484485	+	0.874800i	$0.339007\pi$
$434$	6.42125	0.308230
$435$	−25.5566	−1.22534
$436$	−1.30930	−0.0627042
$437$	−2.95816	−0.141508
$438$	−55.6046	−2.65689
$439$	34.4868	1.64596	0.822982	−	0.568067i	$-0.192309\pi$
$439$	34.4868	1.64596	0.822982	+	0.568067i	$0.192309\pi$
$440$	0	0
$441$	−39.0810	−1.86100
$442$	−16.4722	−0.783501
$443$	31.4586	1.49464	0.747321	−	0.664463i	$-0.231340\pi$
$443$	31.4586	1.49464	0.747321	+	0.664463i	$0.231340\pi$
$444$	1.70789	0.0810531
$445$	−2.70789	−0.128367
$446$	−10.1086	−0.478657
$447$	27.2470	1.28874
$448$	−11.5413	−0.545275
$449$	−4.77643	−0.225414	−0.112707	−	0.993628i	$-0.535952\pi$
$449$	−4.77643	−0.225414	−0.112707	+	0.993628i	$0.535952\pi$
$450$	10.4864	0.494333
$451$	0	0
$452$	0.436202	0.0205172
$453$	24.2132	1.13763
$454$	−1.88425	−0.0884323
$455$	2.65275	0.124363
$456$	−7.69996	−0.360584
$457$	−1.53157	−0.0716437	−0.0358218	−	0.999358i	$-0.511405\pi$
$457$	−1.53157	−0.0716437	−0.0358218	+	0.999358i	$0.511405\pi$
$458$	40.4897	1.89196
$459$	93.9656	4.38594
$460$	0.421253	0.0196410
$461$	−18.5220	−0.862655	−0.431327	−	0.902195i	$-0.641955\pi$
$461$	−18.5220	−0.862655	−0.431327	+	0.902195i	$0.641955\pi$
$462$	0	0
$463$	9.68306	0.450010	0.225005	−	0.974358i	$-0.427760\pi$
$463$	9.68306	0.450010	0.225005	+	0.974358i	$0.427760\pi$
$464$	29.4217	1.36587
$465$	−11.1157	−0.515481
$466$	−30.1968	−1.39884
$467$	−31.6980	−1.46681	−0.733404	−	0.679793i	$-0.762070\pi$
$467$	−31.6980	−1.46681	−0.733404	+	0.679793i	$0.762070\pi$
$468$	1.70884	0.0789914
$469$	−3.75867	−0.173559
$470$	6.50403	0.300009
$471$	−28.0000	−1.29017
$472$	−3.24041	−0.149152
$473$	0	0
$474$	26.0070	1.19454
$475$	0.812826	0.0372950
$476$	0.986602	0.0452208
$477$	−64.1282	−2.93623
$478$	−25.7000	−1.17549
$479$	−30.8345	−1.40886	−0.704432	−	0.709771i	$-0.748798\pi$
$479$	−30.8345	−1.40886	−0.704432	+	0.709771i	$0.748798\pi$
$480$	2.13302	0.0973585
$481$	8.74202	0.398602
$482$	36.0507	1.64207
$483$	16.2949	0.741443
$484$	0	0
$485$	14.1630	0.643107
$486$	56.0733	2.54354
$487$	29.9921	1.35907	0.679535	−	0.733643i	$-0.262182\pi$
$487$	29.9921	1.35907	0.679535	+	0.733643i	$0.262182\pi$
$488$	7.39095	0.334573
$489$	53.4203	2.41575
$490$	−7.02229	−0.317235
$491$	−34.5114	−1.55748	−0.778739	−	0.627348i	$-0.784140\pi$
$491$	−34.5114	−1.55748	−0.778739	+	0.627348i	$0.784140\pi$
$492$	−0.689460	−0.0310833
$493$	−48.6518	−2.19117
$494$	−2.15622	−0.0970131
$495$	0	0
$496$	12.7968	0.574595
$497$	1.53157	0.0687002
$498$	71.5361	3.20561
$499$	17.8629	0.799654	0.399827	−	0.916591i	$-0.369070\pi$
$499$	17.8629	0.799654	0.399827	+	0.916591i	$0.369070\pi$
$500$	−0.115749	−0.00517647
$501$	69.9283	3.12417
$502$	−31.0582	−1.38620
$503$	−5.11903	−0.228246	−0.114123	−	0.993467i	$-0.536406\pi$
$503$	−5.11903	−0.228246	−0.114123	+	0.993467i	$0.536406\pi$
$504$	30.4551	1.35658
$505$	11.4056	0.507543
$506$	0	0
$507$	−30.2216	−1.34219
$508$	0.194408	0.00862548
$509$	−18.1078	−0.802615	−0.401307	−	0.915943i	$-0.631444\pi$
$509$	−18.1078	−0.802615	−0.401307	+	0.915943i	$0.631444\pi$
$510$	27.8023	1.23111
$511$	17.0472	0.754124
$512$	−24.2671	−1.07246
$513$	12.3002	0.543067
$514$	23.6241	1.04201
$515$	13.8709	0.611223
$516$	2.43990	0.107411
$517$	0	0
$518$	8.52360	0.374506
$519$	44.8096	1.96692
$520$	5.61256	0.246127
$521$	−34.5708	−1.51457	−0.757287	−	0.653082i	$-0.773476\pi$
$521$	−34.5708	−1.51457	−0.757287	+	0.653082i	$0.773476\pi$
$522$	−82.1620	−3.59613
$523$	−32.7917	−1.43388	−0.716940	−	0.697135i	$-0.754458\pi$
$523$	−32.7917	−1.43388	−0.716940	+	0.697135i	$0.754458\pi$
$524$	−1.36518	−0.0596381
$525$	−4.47741	−0.195410
$526$	−7.84406	−0.342017
$527$	−21.1609	−0.921785
$528$	0	0
$529$	−9.75510	−0.424135
$530$	−11.5229	−0.500523
$531$	8.52360	0.369893
$532$	0.129147	0.00559925
$533$	−3.52907	−0.152861
$534$	−12.1244	−0.524672
$535$	−1.06580	−0.0460784
$536$	−7.95240	−0.343491
$537$	−12.2921	−0.530444
$538$	−3.94076	−0.169898
$539$	0	0
$540$	−1.75160	−0.0753767
$541$	−4.37244	−0.187986	−0.0939929	−	0.995573i	$-0.529963\pi$
$541$	−4.37244	−0.187986	−0.0939929	+	0.995573i	$0.529963\pi$
$542$	10.4968	0.450877
$543$	−0.0437014	−0.00187541
$544$	4.06061	0.174097
$545$	11.3115	0.484533
$546$	11.8775	0.508308
$547$	−31.6473	−1.35314	−0.676571	−	0.736377i	$-0.736535\pi$
$547$	−31.6473	−1.35314	−0.676571	+	0.736377i	$0.736535\pi$
$548$	0.857455	0.0366287
$549$	−19.4412	−0.829731
$550$	0	0
$551$	−6.36858	−0.271311
$552$	34.4759	1.46739
$553$	−7.97320	−0.339055
$554$	40.3527	1.71442
$555$	−14.7551	−0.626319
$556$	0.306884	0.0130148
$557$	−1.52068	−0.0644331	−0.0322166	−	0.999481i	$-0.510257\pi$
$557$	−1.52068	−0.0644331	−0.0322166	+	0.999481i	$0.510257\pi$
$558$	−35.7361	−1.51283
$559$	12.4889	0.528223
$560$	5.15456	0.217820
$561$	0	0
$562$	−33.2519	−1.40265
$563$	−0.653939	−0.0275602	−0.0137801	−	0.999905i	$-0.504386\pi$
$563$	−0.653939	−0.0275602	−0.0137801	+	0.999905i	$0.504386\pi$
$564$	−1.78891	−0.0753269
$565$	−3.76850	−0.158542
$566$	−7.02680	−0.295358
$567$	−36.2959	−1.52429
$568$	3.24041	0.135965
$569$	−32.6606	−1.36921	−0.684603	−	0.728916i	$-0.740024\pi$
$569$	−32.6606	−1.36921	−0.684603	+	0.728916i	$0.740024\pi$
$570$	3.63935	0.152436
$571$	−26.1457	−1.09416	−0.547082	−	0.837079i	$-0.684262\pi$
$571$	−26.1457	−1.09416	−0.547082	+	0.837079i	$0.684262\pi$
$572$	0	0
$573$	−54.2306	−2.26552
$574$	−3.44090	−0.143620
$575$	−3.63935	−0.151772
$576$	64.2306	2.67627
$577$	5.73377	0.238700	0.119350	−	0.992852i	$-0.461919\pi$
$577$	5.73377	0.238700	0.119350	+	0.992852i	$0.461919\pi$
$578$	29.5914	1.23084
$579$	−87.3552	−3.63036
$580$	0.906910	0.0376574
$581$	−21.9315	−0.909870
$582$	63.4134	2.62857
$583$	0	0
$584$	36.0676	1.49249
$585$	−14.7633	−0.610388
$586$	−15.0890	−0.623319
$587$	43.4586	1.79373	0.896864	−	0.442307i	$-0.145840\pi$
$587$	43.4586	1.79373	0.896864	+	0.442307i	$0.145840\pi$
$588$	1.93146	0.0796521
$589$	−2.76999	−0.114136
$590$	1.53157	0.0630536
$591$	−8.34105	−0.343105
$592$	16.9866	0.698145
$593$	−9.23707	−0.379321	−0.189661	−	0.981850i	$-0.560739\pi$
$593$	−9.23707	−0.379321	−0.189661	+	0.981850i	$0.560739\pi$
$594$	0	0
$595$	−8.52360	−0.349434
$596$	−0.966898	−0.0396057
$597$	−71.3125	−2.91863
$598$	9.65430	0.394794
$599$	−36.0865	−1.47445	−0.737227	−	0.675645i	$-0.763865\pi$
$599$	−36.0865	−1.47445	−0.737227	+	0.675645i	$0.763865\pi$
$600$	−9.47308	−0.386737
$601$	23.1290	0.943452	0.471726	−	0.881745i	$-0.343631\pi$
$601$	23.1290	0.943452	0.471726	+	0.881745i	$0.343631\pi$
$602$	12.1768	0.496291
$603$	20.9181	0.851849
$604$	−0.859237	−0.0349619
$605$	0	0
$606$	51.0676	2.07448
$607$	−21.9984	−0.892888	−0.446444	−	0.894812i	$-0.647310\pi$
$607$	−21.9984	−0.892888	−0.446444	+	0.894812i	$0.647310\pi$
$608$	0.531538	0.0215567
$609$	35.0810	1.42155
$610$	−3.49330	−0.141440
$611$	−9.15673	−0.370442
$612$	−5.49072	−0.221949
$613$	−8.42425	−0.340252	−0.170126	−	0.985422i	$-0.554418\pi$
$613$	−8.42425	−0.340252	−0.170126	+	0.985422i	$0.554418\pi$
$614$	19.7000	0.795026
$615$	5.95649	0.240189
$616$	0	0
$617$	−17.8709	−0.719453	−0.359727	−	0.933058i	$-0.617130\pi$
$617$	−17.8709	−0.719453	−0.359727	+	0.933058i	$0.617130\pi$
$618$	62.1055	2.49825
$619$	29.5102	1.18612	0.593058	−	0.805160i	$-0.297921\pi$
$619$	29.5102	1.18612	0.593058	+	0.805160i	$0.297921\pi$
$620$	0.394457	0.0158418
$621$	−55.0731	−2.21001
$622$	37.5854	1.50704
$623$	3.71707	0.148921
$624$	23.6705	0.947577
$625$	1.00000	0.0400000
$626$	5.31344	0.212368
$627$	0	0
$628$	0.993617	0.0396496
$629$	−28.0891	−1.11999
$630$	−14.3945	−0.573489
$631$	23.0204	0.916428	0.458214	−	0.888842i	$-0.348489\pi$
$631$	23.0204	0.916428	0.458214	+	0.888842i	$0.348489\pi$
$632$	−16.8693	−0.671025
$633$	−41.8515	−1.66345
$634$	−21.2906	−0.845556
$635$	−1.67956	−0.0666515
$636$	3.16934	0.125673
$637$	9.88636	0.391712
$638$	0	0
$639$	−8.52360	−0.337189
$640$	10.2334	0.404511
$641$	−3.76850	−0.148847	−0.0744234	−	0.997227i	$-0.523712\pi$
$641$	−3.76850	−0.148847	−0.0744234	+	0.997227i	$0.523712\pi$
$642$	−4.77201	−0.188336
$643$	28.3011	1.11609	0.558043	−	0.829812i	$-0.311552\pi$
$643$	28.3011	1.11609	0.558043	+	0.829812i	$0.311552\pi$
$644$	−0.578246	−0.0227861
$645$	−21.0792	−0.829992
$646$	6.92820	0.272587
$647$	11.7775	0.463020	0.231510	−	0.972832i	$-0.425633\pi$
$647$	11.7775	0.463020	0.231510	+	0.972832i	$0.425633\pi$
$648$	−76.7931	−3.01672
$649$	0	0
$650$	−2.65275	−0.104049
$651$	15.2584	0.598023
$652$	−1.89569	−0.0742410
$653$	−46.1282	−1.80514	−0.902569	−	0.430546i	$-0.858321\pi$
$653$	−46.1282	−1.80514	−0.902569	+	0.430546i	$0.858321\pi$
$654$	50.6464	1.98043
$655$	11.7943	0.460840
$656$	−6.85733	−0.267734
$657$	−94.8726	−3.70133
$658$	−8.92795	−0.348048
$659$	−15.7781	−0.614626	−0.307313	−	0.951609i	$-0.599430\pi$
$659$	−15.7781	−0.614626	−0.307313	+	0.951609i	$0.599430\pi$
$660$	0	0
$661$	−38.6732	−1.50421	−0.752106	−	0.659042i	$-0.770962\pi$
$661$	−38.6732	−1.50421	−0.752106	+	0.659042i	$0.770962\pi$
$662$	36.8667	1.43286
$663$	−39.1416	−1.52013
$664$	−46.4015	−1.80073
$665$	−1.11575	−0.0432669
$666$	−47.4363	−1.83812
$667$	28.5147	1.10410
$668$	−2.48150	−0.0960121
$669$	−24.0204	−0.928683
$670$	3.75867	0.145210
$671$	0	0
$672$	−2.92795	−0.112948
$673$	44.2791	1.70683	0.853416	−	0.521230i	$-0.174527\pi$
$673$	44.2791	1.70683	0.853416	+	0.521230i	$0.174527\pi$
$674$	2.65275	0.102180
$675$	15.1327	0.582456
$676$	1.07245	0.0412482
$677$	6.74004	0.259041	0.129520	−	0.991577i	$-0.458656\pi$
$677$	6.74004	0.259041	0.129520	+	0.991577i	$0.458656\pi$
$678$	−16.8731	−0.648009
$679$	−19.4412	−0.746085
$680$	−18.0338	−0.691565
$681$	−4.47741	−0.171575
$682$	0	0
$683$	33.3303	1.27535	0.637675	−	0.770305i	$-0.279896\pi$
$683$	33.3303	1.27535	0.637675	+	0.770305i	$0.279896\pi$
$684$	−0.718741	−0.0274818
$685$	−7.40786	−0.283040
$686$	22.8291	0.871619
$687$	96.2128	3.67075
$688$	24.2671	0.925175
$689$	16.2226	0.618031
$690$	−16.2949	−0.620336
$691$	9.00546	0.342584	0.171292	−	0.985220i	$-0.445206\pi$
$691$	9.00546	0.342584	0.171292	+	0.985220i	$0.445206\pi$
$692$	−1.59013	−0.0604477
$693$	0	0
$694$	5.21655	0.198018
$695$	−2.65128	−0.100569
$696$	74.2226	2.81340
$697$	11.3393	0.429507
$698$	23.5976	0.893183
$699$	−71.7544	−2.71400
$700$	0.158887	0.00600536
$701$	45.8938	1.73339	0.866693	−	0.498842i	$-0.166241\pi$
$701$	45.8938	1.73339	0.866693	+	0.498842i	$0.166241\pi$
$702$	−40.1432	−1.51511
$703$	−3.67690	−0.138677
$704$	0	0
$705$	15.4551	0.582071
$706$	−2.73447	−0.102913
$707$	−15.6563	−0.588814
$708$	−0.421253	−0.0158317
$709$	−8.51021	−0.319608	−0.159804	−	0.987149i	$-0.551086\pi$
$709$	−8.51021	−0.319608	−0.159804	+	0.987149i	$0.551086\pi$
$710$	−1.53157	−0.0574787
$711$	44.3731	1.66412
$712$	7.86439	0.294731
$713$	12.4024	0.464473
$714$	−38.1637	−1.42824
$715$	0	0
$716$	0.436202	0.0163016
$717$	−61.0690	−2.28066
$718$	−21.3811	−0.797934
$719$	−9.60554	−0.358226	−0.179113	−	0.983828i	$-0.557323\pi$
$719$	−9.60554	−0.358226	−0.179113	+	0.983828i	$0.557323\pi$
$720$	−28.6866	−1.06909
$721$	−19.0402	−0.709096
$722$	−25.1740	−0.936880
$723$	85.6648	3.18591
$724$	0.00155080	5.76351e−5 0
$725$	−7.83511	−0.290989
$726$	0	0
$727$	32.9688	1.22274	0.611372	−	0.791343i	$-0.290618\pi$
$727$	32.9688	1.22274	0.611372	+	0.791343i	$0.290618\pi$
$728$	−7.70425	−0.285538
$729$	53.9181	1.99697
$730$	−17.0472	−0.630946
$731$	−40.1282	−1.48420
$732$	0.960822	0.0355130
$733$	−27.3704	−1.01095	−0.505475	−	0.862842i	$-0.668683\pi$
$733$	−27.3704	−1.01095	−0.505475	+	0.862842i	$0.668683\pi$
$734$	25.7680	0.951113
$735$	−16.6866	−0.615493
$736$	−2.37991	−0.0877248
$737$	0	0
$738$	19.1496	0.704905
$739$	38.5646	1.41862	0.709312	−	0.704895i	$-0.249006\pi$
$739$	38.5646	1.41862	0.709312	+	0.704895i	$0.249006\pi$
$740$	0.523604	0.0192481
$741$	−5.12368	−0.188223
$742$	15.8173	0.580670
$743$	34.1644	1.25337	0.626684	−	0.779273i	$-0.284412\pi$
$743$	34.1644	1.25337	0.626684	+	0.779273i	$0.284412\pi$
$744$	32.2829	1.18355
$745$	8.35337	0.306044
$746$	−3.60554	−0.132008
$747$	122.055	4.46575
$748$	0	0
$749$	1.46300	0.0534568
$750$	4.47741	0.163492
$751$	−45.9305	−1.67603	−0.838015	−	0.545648i	$-0.816284\pi$
$751$	−45.9305	−1.67603	−0.838015	+	0.545648i	$0.816284\pi$
$752$	−17.7924	−0.648823
$753$	−73.8014	−2.68947
$754$	20.7846	0.756931
$755$	7.42325	0.270160
$756$	2.40438	0.0874465
$757$	−30.2236	−1.09849	−0.549247	−	0.835660i	$-0.685085\pi$
$757$	−30.2236	−1.09849	−0.549247	+	0.835660i	$0.685085\pi$
$758$	3.65227	0.132656
$759$	0	0
$760$	−2.36065	−0.0856296
$761$	−13.4308	−0.486866	−0.243433	−	0.969918i	$-0.578274\pi$
$761$	−13.4308	−0.486866	−0.243433	+	0.969918i	$0.578274\pi$
$762$	−7.52010	−0.272424
$763$	−15.5271	−0.562119
$764$	1.92444	0.0696240
$765$	47.4363	1.71506
$766$	30.1049	1.08773
$767$	−2.15622	−0.0778567
$768$	−9.03030	−0.325853
$769$	10.8982	0.393001	0.196500	−	0.980504i	$-0.437042\pi$
$769$	10.8982	0.393001	0.196500	+	0.980504i	$0.437042\pi$
$770$	0	0
$771$	56.1362	2.02169
$772$	3.09992	0.111568
$773$	13.1496	0.472957	0.236478	−	0.971637i	$-0.424007\pi$
$773$	13.1496	0.472957	0.236478	+	0.971637i	$0.424007\pi$
$774$	−67.7676	−2.43586
$775$	−3.40786	−0.122414
$776$	−41.1327	−1.47658
$777$	20.2540	0.726610
$778$	−4.69629	−0.168370
$779$	1.48433	0.0531816
$780$	0.729632	0.0261250
$781$	0	0
$782$	−31.0204	−1.10929
$783$	−118.566	−4.23721
$784$	19.2102	0.686077
$785$	−8.58421	−0.306384
$786$	52.8078	1.88359
$787$	11.5413	0.411403	0.205701	−	0.978615i	$-0.434052\pi$
$787$	11.5413	0.411403	0.205701	+	0.978615i	$0.434052\pi$
$788$	0.295993	0.0105443
$789$	−18.6393	−0.663576
$790$	7.97320	0.283674
$791$	5.17295	0.183929
$792$	0	0
$793$	4.91806	0.174645
$794$	7.56375	0.268427
$795$	−27.3811	−0.971106
$796$	2.53062	0.0896954
$797$	−5.54494	−0.196412	−0.0982059	−	0.995166i	$-0.531310\pi$
$797$	−5.54494	−0.196412	−0.0982059	+	0.995166i	$0.531310\pi$
$798$	−4.99567	−0.176845
$799$	29.4217	1.04086
$800$	0.653939	0.0231202
$801$	−20.6866	−0.730924
$802$	−24.6067	−0.868891
$803$	0	0
$804$	−1.03381	−0.0364597
$805$	4.99567	0.176074
$806$	9.04019	0.318427
$807$	−9.36415	−0.329634
$808$	−33.1247	−1.16532
$809$	−18.4402	−0.648324	−0.324162	−	0.946002i	$-0.605082\pi$
$809$	−18.4402	−0.648324	−0.324162	+	0.946002i	$0.605082\pi$
$810$	36.2959	1.27531
$811$	−6.32818	−0.222212	−0.111106	−	0.993809i	$-0.535439\pi$
$811$	−6.32818	−0.222212	−0.111106	+	0.993809i	$0.535439\pi$
$812$	−1.24490	−0.0436873
$813$	24.9428	0.874783
$814$	0	0
$815$	16.3776	0.573681
$816$	−76.0560	−2.66249
$817$	−5.25283	−0.183773
$818$	−40.2554	−1.40750
$819$	20.2653	0.708127
$820$	−0.211374	−0.00738150
$821$	−7.95240	−0.277541	−0.138770	−	0.990325i	$-0.544315\pi$
$821$	−7.95240	−0.277541	−0.138770	+	0.990325i	$0.544315\pi$
$822$	−33.1680	−1.15687
$823$	1.32241	0.0460963	0.0230481	−	0.999734i	$-0.492663\pi$
$823$	1.32241	0.0460963	0.0230481	+	0.999734i	$0.492663\pi$
$824$	−40.2844	−1.40337
$825$	0	0
$826$	−2.10235	−0.0731502
$827$	4.52990	0.157520	0.0787600	−	0.996894i	$-0.474904\pi$
$827$	4.52990	0.157520	0.0787600	+	0.996894i	$0.474904\pi$
$828$	3.21810	0.111837
$829$	−37.8148	−1.31336	−0.656681	−	0.754168i	$-0.728040\pi$
$829$	−37.8148	−1.31336	−0.656681	+	0.754168i	$0.728040\pi$
$830$	21.9315	0.761252
$831$	95.8873	3.32629
$832$	−16.2485	−0.563314
$833$	−31.7661	−1.10063
$834$	−11.8709	−0.411054
$835$	21.4385	0.741912
$836$	0	0
$837$	−51.5699	−1.78252
$838$	3.64138	0.125789
$839$	−39.2519	−1.35513	−0.677563	−	0.735465i	$-0.736964\pi$
$839$	−39.2519	−1.35513	−0.677563	+	0.735465i	$0.736964\pi$
$840$	13.0035	0.448664
$841$	32.3890	1.11686
$842$	−15.3232	−0.528071
$843$	−79.0142	−2.72139
$844$	1.48516	0.0511212
$845$	−9.26531	−0.318736
$846$	49.6866	1.70826
$847$	0	0
$848$	31.5221	1.08247
$849$	−16.6973	−0.573049
$850$	8.52360	0.292357
$851$	16.4630	0.564344
$852$	0.421253	0.0144319
$853$	−33.3917	−1.14331	−0.571655	−	0.820494i	$-0.693698\pi$
$853$	−33.3917	−1.14331	−0.571655	+	0.820494i	$0.693698\pi$
$854$	4.79518	0.164088
$855$	6.20946	0.212359
$856$	3.09534	0.105796
$857$	16.9781	0.579961	0.289980	−	0.957033i	$-0.406351\pi$
$857$	16.9781	0.579961	0.289980	+	0.957033i	$0.406351\pi$
$858$	0	0
$859$	−40.8148	−1.39258	−0.696291	−	0.717759i	$-0.745168\pi$
$859$	−40.8148	−1.39258	−0.696291	+	0.717759i	$0.745168\pi$
$860$	0.748023	0.0255074
$861$	−8.17636	−0.278649
$862$	−6.25829	−0.213158
$863$	35.0303	1.19245	0.596223	−	0.802819i	$-0.296668\pi$
$863$	35.0303	1.19245	0.596223	+	0.802819i	$0.296668\pi$
$864$	9.89583	0.336663
$865$	13.7377	0.467096
$866$	27.6773	0.940513
$867$	70.3160	2.38806
$868$	−0.541464	−0.0183785
$869$	0	0
$870$	−35.0810	−1.18936
$871$	−5.29166	−0.179301
$872$	−32.8515	−1.11249
$873$	108.196	3.66187
$874$	−4.06061	−0.137352
$875$	−1.37268	−0.0464051
$876$	4.68878	0.158419
$877$	26.6626	0.900331	0.450165	−	0.892945i	$-0.351365\pi$
$877$	26.6626	0.900331	0.450165	+	0.892945i	$0.351365\pi$
$878$	47.3393	1.59762
$879$	−35.8548	−1.20935
$880$	0	0
$881$	−4.66615	−0.157207	−0.0786033	−	0.996906i	$-0.525046\pi$
$881$	−4.66615	−0.157207	−0.0786033	+	0.996906i	$0.525046\pi$
$882$	−53.6457	−1.80635
$883$	6.47093	0.217764	0.108882	−	0.994055i	$-0.465273\pi$
$883$	6.47093	0.217764	0.108882	+	0.994055i	$0.465273\pi$
$884$	1.38899	0.0467169
$885$	3.63935	0.122336
$886$	43.1826	1.45075
$887$	−18.3508	−0.616159	−0.308079	−	0.951361i	$-0.599686\pi$
$887$	−18.3508	−0.616159	−0.308079	+	0.951361i	$0.599686\pi$
$888$	42.8525	1.43803
$889$	2.30550	0.0773241
$890$	−3.71707	−0.124597
$891$	0	0
$892$	0.852396	0.0285403
$893$	3.85133	0.128880
$894$	37.4015	1.25089
$895$	−3.76850	−0.125967
$896$	−14.0472	−0.469284
$897$	22.9408	0.765972
$898$	−6.55652	−0.218794
$899$	26.7009	0.890526
$900$	−0.884251	−0.0294750
$901$	−52.1251	−1.73654
$902$	0	0
$903$	28.9350	0.962895
$904$	10.9447	0.364014
$905$	−0.0133979	−0.000445362 0
$906$	33.2370	1.10422
$907$	−29.7845	−0.988978	−0.494489	−	0.869184i	$-0.664645\pi$
$907$	−29.7845	−0.988978	−0.494489	+	0.869184i	$0.664645\pi$
$908$	0.158887	0.00527285
$909$	87.1315	2.88997
$910$	3.64138	0.120711
$911$	45.8699	1.51974	0.759869	−	0.650076i	$-0.225263\pi$
$911$	45.8699	1.51974	0.759869	+	0.650076i	$0.225263\pi$
$912$	−9.95582	−0.329670
$913$	0	0
$914$	−2.10235	−0.0695396
$915$	−8.30088	−0.274419
$916$	−3.41424	−0.112810
$917$	−16.1898	−0.534633
$918$	128.985	4.25713
$919$	58.1355	1.91771	0.958856	−	0.283893i	$-0.0916260\pi$
$919$	58.1355	1.91771	0.958856	+	0.283893i	$0.0916260\pi$
$920$	10.5696	0.348469
$921$	46.8116	1.54250
$922$	−25.4248	−0.837320
$923$	2.15622	0.0709730
$924$	0	0
$925$	−4.52360	−0.148735
$926$	13.2917	0.436794
$927$	105.964	3.48033
$928$	−5.12368	−0.168193
$929$	39.8361	1.30698	0.653490	−	0.756935i	$-0.273304\pi$
$929$	39.8361	1.30698	0.653490	+	0.756935i	$0.273304\pi$
$930$	−15.2584	−0.500342
$931$	−4.15821	−0.136280
$932$	2.54630	0.0834069
$933$	89.3116	2.92393
$934$	−43.5112	−1.42373
$935$	0	0
$936$	42.8763	1.40146
$937$	−9.67356	−0.316022	−0.158011	−	0.987437i	$-0.550508\pi$
$937$	−9.67356	−0.316022	−0.158011	+	0.987437i	$0.550508\pi$
$938$	−5.15945	−0.168462
$939$	12.6260	0.412033
$940$	−0.548444	−0.0178883
$941$	−3.97147	−0.129466	−0.0647331	−	0.997903i	$-0.520620\pi$
$941$	−3.97147	−0.129466	−0.0647331	+	0.997903i	$0.520620\pi$
$942$	−38.4350	−1.25228
$943$	−6.64595	−0.216422
$944$	−4.18975	−0.136365
$945$	−20.7723	−0.675723
$946$	0	0
$947$	2.65275	0.0862029	0.0431014	−	0.999071i	$-0.486276\pi$
$947$	2.65275	0.0862029	0.0431014	+	0.999071i	$0.486276\pi$
$948$	−2.19301	−0.0712255
$949$	24.0000	0.779073
$950$	1.11575	0.0361997
$951$	−50.5912	−1.64053
$952$	24.7547	0.802303
$953$	20.8678	0.675974	0.337987	−	0.941151i	$-0.390254\pi$
$953$	20.8678	0.675974	0.337987	+	0.941151i	$0.390254\pi$
$954$	−88.0275	−2.85000
$955$	−16.6260	−0.538003
$956$	2.16711	0.0700895
$957$	0	0
$958$	−42.3259	−1.36749
$959$	10.1686	0.328362
$960$	27.4248	0.885130
$961$	−19.3865	−0.625372
$962$	12.0000	0.386896
$963$	−8.14200	−0.262372
$964$	−3.03993	−0.0979095
$965$	−26.7813	−0.862120
$966$	22.3677	0.719668
$967$	−58.5364	−1.88240	−0.941202	−	0.337843i	$-0.890303\pi$
$967$	−58.5364	−1.88240	−0.941202	+	0.337843i	$0.890303\pi$
$968$	0	0
$969$	16.4630	0.528868
$970$	19.4412	0.624220
$971$	−56.2653	−1.80564	−0.902820	−	0.430019i	$-0.858507\pi$
$971$	−56.2653	−1.80564	−0.902820	+	0.430019i	$0.858507\pi$
$972$	−4.72831	−0.151661
$973$	3.63935	0.116672
$974$	41.1695	1.31916
$975$	−6.30355	−0.201875
$976$	9.55627	0.305889
$977$	36.9866	1.18331	0.591653	−	0.806193i	$-0.298476\pi$
$977$	36.9866	1.18331	0.591653	+	0.806193i	$0.298476\pi$
$978$	73.3290	2.34480
$979$	0	0
$980$	0.592145	0.0189154
$981$	86.4128	2.75895
$982$	−47.3731	−1.51174
$983$	−19.6642	−0.627190	−0.313595	−	0.949557i	$-0.601533\pi$
$983$	−19.6642	−0.627190	−0.313595	+	0.949557i	$0.601533\pi$
$984$	−17.2991	−0.551476
$985$	−2.55719	−0.0814789
$986$	−66.7834	−2.12682
$987$	−21.2149	−0.675276
$988$	0.181821	0.00578449
$989$	23.5191	0.747863
$990$	0	0
$991$	18.5763	0.590095	0.295047	−	0.955483i	$-0.404665\pi$
$991$	18.5763	0.590095	0.295047	+	0.955483i	$0.404665\pi$
$992$	−2.22853	−0.0707558
$993$	87.6037	2.78002
$994$	2.10235	0.0666825
$995$	−21.8629	−0.693101
$996$	−6.03218	−0.191137
$997$	30.1049	0.953431	0.476716	−	0.879058i	$-0.341827\pi$
$997$	30.1049	0.953431	0.476716	+	0.879058i	$0.341827\pi$
$998$	24.5201	0.776169
$999$	−68.4541	−2.16579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.m.1.5	yes	6
3.2	odd	2		5445.2.a.bx.1.2		6
4.3	odd	2		9680.2.a.cw.1.2		6
5.4	even	2		3025.2.a.bg.1.2		6
11.2	odd	10		605.2.g.q.81.5		24
11.3	even	5		605.2.g.q.251.5		24
11.4	even	5		605.2.g.q.511.5		24
11.5	even	5		605.2.g.q.366.2		24
11.6	odd	10		605.2.g.q.366.5		24
11.7	odd	10		605.2.g.q.511.2		24
11.8	odd	10		605.2.g.q.251.2		24
11.9	even	5		605.2.g.q.81.2		24
11.10	odd	2	inner	605.2.a.m.1.2	✓	6
33.32	even	2		5445.2.a.bx.1.5		6
44.43	even	2		9680.2.a.cw.1.1		6
55.54	odd	2		3025.2.a.bg.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.m.1.2	✓	6	11.10	odd	2	inner
605.2.a.m.1.5	yes	6	1.1	even	1	trivial
605.2.g.q.81.2		24	11.9	even	5
605.2.g.q.81.5		24	11.2	odd	10
605.2.g.q.251.2		24	11.8	odd	10
605.2.g.q.251.5		24	11.3	even	5
605.2.g.q.366.2		24	11.5	even	5
605.2.g.q.366.5		24	11.6	odd	10
605.2.g.q.511.2		24	11.7	odd	10
605.2.g.q.511.5		24	11.4	even	5
3025.2.a.bg.1.2		6	5.4	even	2
3025.2.a.bg.1.5		6	55.54	odd	2
5445.2.a.bx.1.2		6	3.2	odd	2
5445.2.a.bx.1.5		6	33.32	even	2
9680.2.a.cw.1.1		6	44.43	even	2
9680.2.a.cw.1.2		6	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+1.37268 q^{2} +3.26180 q^{3} -0.115749 q^{4} +1.00000 q^{5} +4.47741 q^{6} -1.37268 q^{7} -2.90425 q^{8} +7.63935 q^{9} +O(q^{10})\)	\(q+1.37268 q^{2} +3.26180 q^{3} -0.115749 q^{4} +1.00000 q^{5} +4.47741 q^{6} -1.37268 q^{7} -2.90425 q^{8} +7.63935 q^{9} +1.37268 q^{10} -0.377552 q^{12} -1.93253 q^{13} -1.88425 q^{14} +3.26180 q^{15} -3.75510 q^{16} +6.20946 q^{17} +10.4864 q^{18} +0.812826 q^{19} -0.115749 q^{20} -4.47741 q^{21} -3.63935 q^{23} -9.47308 q^{24} +1.00000 q^{25} -2.65275 q^{26} +15.1327 q^{27} +0.158887 q^{28} -7.83511 q^{29} +4.47741 q^{30} -3.40786 q^{31} +0.653939 q^{32} +8.52360 q^{34} -1.37268 q^{35} -0.884251 q^{36} -4.52360 q^{37} +1.11575 q^{38} -6.30355 q^{39} -2.90425 q^{40} +1.82613 q^{41} -6.14605 q^{42} -6.46243 q^{43} +7.63935 q^{45} -4.99567 q^{46} +4.73820 q^{47} -12.2484 q^{48} -5.11575 q^{49} +1.37268 q^{50} +20.2540 q^{51} +0.223690 q^{52} -8.39446 q^{53} +20.7723 q^{54} +3.98660 q^{56} +2.65128 q^{57} -10.7551 q^{58} +1.11575 q^{59} -0.377552 q^{60} -2.54488 q^{61} -4.67789 q^{62} -10.4864 q^{63} +8.40786 q^{64} -1.93253 q^{65} +2.73820 q^{67} -0.718741 q^{68} -11.8709 q^{69} -1.88425 q^{70} -1.11575 q^{71} -22.1866 q^{72} -12.4189 q^{73} -6.20946 q^{74} +3.26180 q^{75} -0.0940841 q^{76} -8.65275 q^{78} +5.80849 q^{79} -3.75510 q^{80} +26.4417 q^{81} +2.50670 q^{82} +15.9771 q^{83} +0.518258 q^{84} +6.20946 q^{85} -8.87085 q^{86} -25.5566 q^{87} -2.70789 q^{89} +10.4864 q^{90} +2.65275 q^{91} +0.421253 q^{92} -11.1157 q^{93} +6.50403 q^{94} +0.812826 q^{95} +2.13302 q^{96} +14.1630 q^{97} -7.02229 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{3} + 6 q^{4} + 6 q^{5} + 12 q^{9}+O(q^{10}) \) 6 * q + 6 * q^3 + 6 * q^4 + 6 * q^5 + 12 * q^9	\( 6 q + 6 q^{3} + 6 q^{4} + 6 q^{5} + 12 q^{9} + 18 q^{12} - 18 q^{14} + 6 q^{15} + 18 q^{16} + 6 q^{20} + 12 q^{23} + 6 q^{25} - 36 q^{26} + 30 q^{27} + 24 q^{34} - 12 q^{36} - 30 q^{42} + 12 q^{45} + 42 q^{47} - 6 q^{48} - 24 q^{49} + 24 q^{53} - 30 q^{56} - 24 q^{58} + 18 q^{60} + 30 q^{64} + 30 q^{67} - 24 q^{69} - 18 q^{70} + 6 q^{75} - 72 q^{78} + 18 q^{80} + 30 q^{81} + 42 q^{82} - 6 q^{86} - 30 q^{89} + 36 q^{91} + 36 q^{92} - 60 q^{93} + 24 q^{97}+O(q^{100}) \) 6 * q + 6 * q^3 + 6 * q^4 + 6 * q^5 + 12 * q^9 + 18 * q^12 - 18 * q^14 + 6 * q^15 + 18 * q^16 + 6 * q^20 + 12 * q^23 + 6 * q^25 - 36 * q^26 + 30 * q^27 + 24 * q^34 - 12 * q^36 - 30 * q^42 + 12 * q^45 + 42 * q^47 - 6 * q^48 - 24 * q^49 + 24 * q^53 - 30 * q^56 - 24 * q^58 + 18 * q^60 + 30 * q^64 + 30 * q^67 - 24 * q^69 - 18 * q^70 + 6 * q^75 - 72 * q^78 + 18 * q^80 + 30 * q^81 + 42 * q^82 - 6 * q^86 - 30 * q^89 + 36 * q^91 + 36 * q^92 - 60 * q^93 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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