LMFDB - Embedded newform 446.2.a.e.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [446,2,Mod(1,446)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(446, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("446.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 446 = 2 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	446.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,7,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$3.56132793015$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 14x^{5} + 12x^{4} + 50x^{3} - 36x^{2} - 38x + 18 $ x^7 - x^6 - 14x^5 + 12x^4 + 50x^3 - 36x^2 - 38*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$2.08198$ of defining polynomial
Character	$\chi$	$=$	446.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.08198 q^{3} +1.00000 q^{4} -3.23274 q^{5} +2.08198 q^{6} +4.23794 q^{7} +1.00000 q^{8} +1.33463 q^{9} -3.23274 q^{10} +1.62710 q^{11} +2.08198 q^{12} +0.843989 q^{13} +4.23794 q^{14} -6.73050 q^{15} +1.00000 q^{16} -0.942042 q^{17} +1.33463 q^{18} -4.16396 q^{19} -3.23274 q^{20} +8.82331 q^{21} +1.62710 q^{22} -1.50859 q^{23} +2.08198 q^{24} +5.45063 q^{25} +0.843989 q^{26} -3.46725 q^{27} +4.23794 q^{28} +9.60642 q^{29} -6.73050 q^{30} -3.22967 q^{31} +1.00000 q^{32} +3.38759 q^{33} -0.942042 q^{34} -13.7002 q^{35} +1.33463 q^{36} -0.461265 q^{37} -4.16396 q^{38} +1.75717 q^{39} -3.23274 q^{40} -12.3855 q^{41} +8.82331 q^{42} +2.06612 q^{43} +1.62710 q^{44} -4.31453 q^{45} -1.50859 q^{46} -8.12310 q^{47} +2.08198 q^{48} +10.9602 q^{49} +5.45063 q^{50} -1.96131 q^{51} +0.843989 q^{52} -7.87624 q^{53} -3.46725 q^{54} -5.26001 q^{55} +4.23794 q^{56} -8.66927 q^{57} +9.60642 q^{58} -3.22499 q^{59} -6.73050 q^{60} -1.92513 q^{61} -3.22967 q^{62} +5.65611 q^{63} +1.00000 q^{64} -2.72840 q^{65} +3.38759 q^{66} +3.16991 q^{67} -0.942042 q^{68} -3.14085 q^{69} -13.7002 q^{70} -6.48629 q^{71} +1.33463 q^{72} +5.90009 q^{73} -0.461265 q^{74} +11.3481 q^{75} -4.16396 q^{76} +6.89557 q^{77} +1.75717 q^{78} +5.22096 q^{79} -3.23274 q^{80} -11.2227 q^{81} -12.3855 q^{82} +9.91652 q^{83} +8.82331 q^{84} +3.04538 q^{85} +2.06612 q^{86} +20.0004 q^{87} +1.62710 q^{88} -18.3369 q^{89} -4.31453 q^{90} +3.57678 q^{91} -1.50859 q^{92} -6.72411 q^{93} -8.12310 q^{94} +13.4610 q^{95} +2.08198 q^{96} +14.2978 q^{97} +10.9602 q^{98} +2.17159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + q^{3} + 7 q^{4} + 2 q^{5} + q^{6} + 6 q^{7} + 7 q^{8} + 8 q^{9} + 2 q^{10} + 9 q^{11} + q^{12} - 2 q^{13} + 6 q^{14} + 6 q^{15} + 7 q^{16} - 7 q^{17} + 8 q^{18} - 2 q^{19} + 2 q^{20}+ \cdots + 10 q^{99}+O(q^{100}) $ 7 * q + 7 * q^2 + q^3 + 7 * q^4 + 2 * q^5 + q^6 + 6 * q^7 + 7 * q^8 + 8 * q^9 + 2 * q^10 + 9 * q^11 + q^12 - 2 * q^13 + 6 * q^14 + 6 * q^15 + 7 * q^16 - 7 * q^17 + 8 * q^18 - 2 * q^19 + 2 * q^20 - 2 * q^21 + 9 * q^22 + 15 * q^23 + q^24 + 13 * q^25 - 2 * q^26 + q^27 + 6 * q^28 + 9 * q^29 + 6 * q^30 - 2 * q^31 + 7 * q^32 - 25 * q^33 - 7 * q^34 - 4 * q^35 + 8 * q^36 + 5 * q^37 - 2 * q^38 - 20 * q^39 + 2 * q^40 - 33 * q^41 - 2 * q^42 + 20 * q^43 + 9 * q^44 - 34 * q^45 + 15 * q^46 - 2 * q^47 + q^48 + 3 * q^49 + 13 * q^50 - 9 * q^51 - 2 * q^52 - 13 * q^53 + q^54 - 18 * q^55 + 6 * q^56 - 58 * q^57 + 9 * q^58 + 9 * q^59 + 6 * q^60 + 8 * q^61 - 2 * q^62 - 16 * q^63 + 7 * q^64 - 44 * q^65 - 25 * q^66 + 29 * q^67 - 7 * q^68 + 23 * q^69 - 4 * q^70 + 8 * q^72 - 37 * q^73 + 5 * q^74 - 11 * q^75 - 2 * q^76 - 18 * q^77 - 20 * q^78 + 32 * q^79 + 2 * q^80 + 3 * q^81 - 33 * q^82 - 6 * q^83 - 2 * q^84 - 4 * q^85 + 20 * q^86 - 3 * q^87 + 9 * q^88 - 17 * q^89 - 34 * q^90 - 4 * q^91 + 15 * q^92 - 12 * q^93 - 2 * q^94 - 12 * q^95 + q^96 + 12 * q^97 + 3 * q^98 + 10 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.08198	1.20203	0.601015	−	0.799237i	$-0.294763\pi$
$3$	2.08198	1.20203	0.601015	+	0.799237i	$0.294763\pi$
$4$	1.00000	0.500000
$5$	−3.23274	−1.44573	−0.722863	−	0.690991i	$-0.757174\pi$
$5$	−3.23274	−1.44573	−0.722863	+	0.690991i	$0.757174\pi$
$6$	2.08198	0.849964
$7$	4.23794	1.60179	0.800896	−	0.598803i	$-0.204357\pi$
$7$	4.23794	1.60179	0.800896	+	0.598803i	$0.204357\pi$
$8$	1.00000	0.353553
$9$	1.33463	0.444878
$10$	−3.23274	−1.02228
$11$	1.62710	0.490590	0.245295	−	0.969448i	$-0.421115\pi$
$11$	1.62710	0.490590	0.245295	+	0.969448i	$0.421115\pi$
$12$	2.08198	0.601015
$13$	0.843989	0.234080	0.117040	−	0.993127i	$-0.462659\pi$
$13$	0.843989	0.234080	0.117040	+	0.993127i	$0.462659\pi$
$14$	4.23794	1.13264
$15$	−6.73050	−1.73781
$16$	1.00000	0.250000
$17$	−0.942042	−0.228479	−0.114239	−	0.993453i	$-0.536443\pi$
$17$	−0.942042	−0.228479	−0.114239	+	0.993453i	$0.536443\pi$
$18$	1.33463	0.314576
$19$	−4.16396	−0.955277	−0.477639	−	0.878556i	$-0.658507\pi$
$19$	−4.16396	−0.955277	−0.477639	+	0.878556i	$0.658507\pi$
$20$	−3.23274	−0.722863
$21$	8.82331	1.92540
$22$	1.62710	0.346900
$23$	−1.50859	−0.314562	−0.157281	−	0.987554i	$-0.550273\pi$
$23$	−1.50859	−0.314562	−0.157281	+	0.987554i	$0.550273\pi$
$24$	2.08198	0.424982
$25$	5.45063	1.09013
$26$	0.843989	0.165520
$27$	−3.46725	−0.667273
$28$	4.23794	0.800896
$29$	9.60642	1.78387	0.891934	−	0.452165i	$-0.149348\pi$
$29$	9.60642	1.78387	0.891934	+	0.452165i	$0.149348\pi$
$30$	−6.73050	−1.22882
$31$	−3.22967	−0.580066	−0.290033	−	0.957017i	$-0.593666\pi$
$31$	−3.22967	−0.580066	−0.290033	+	0.957017i	$0.593666\pi$
$32$	1.00000	0.176777
$33$	3.38759	0.589705
$34$	−0.942042	−0.161559
$35$	−13.7002	−2.31575
$36$	1.33463	0.222439
$37$	−0.461265	−0.0758315	−0.0379158	−	0.999281i	$-0.512072\pi$
$37$	−0.461265	−0.0758315	−0.0379158	+	0.999281i	$0.512072\pi$
$38$	−4.16396	−0.675483
$39$	1.75717	0.281372
$40$	−3.23274	−0.511142
$41$	−12.3855	−1.93428	−0.967142	−	0.254235i	$-0.918176\pi$
$41$	−12.3855	−1.93428	−0.967142	+	0.254235i	$0.918176\pi$
$42$	8.82331	1.36147
$43$	2.06612	0.315080	0.157540	−	0.987513i	$-0.449644\pi$
$43$	2.06612	0.315080	0.157540	+	0.987513i	$0.449644\pi$
$44$	1.62710	0.245295
$45$	−4.31453	−0.643173
$46$	−1.50859	−0.222429
$47$	−8.12310	−1.18488	−0.592438	−	0.805616i	$-0.701834\pi$
$47$	−8.12310	−1.18488	−0.592438	+	0.805616i	$0.701834\pi$
$48$	2.08198	0.300508
$49$	10.9602	1.56574
$50$	5.45063	0.770836
$51$	−1.96131	−0.274639
$52$	0.843989	0.117040
$53$	−7.87624	−1.08188	−0.540942	−	0.841060i	$-0.681932\pi$
$53$	−7.87624	−1.08188	−0.540942	+	0.841060i	$0.681932\pi$
$54$	−3.46725	−0.471834
$55$	−5.26001	−0.709259
$56$	4.23794	0.566319
$57$	−8.66927	−1.14827
$58$	9.60642	1.26139
$59$	−3.22499	−0.419858	−0.209929	−	0.977717i	$-0.567323\pi$
$59$	−3.22499	−0.419858	−0.209929	+	0.977717i	$0.567323\pi$
$60$	−6.73050	−0.868904
$61$	−1.92513	−0.246488	−0.123244	−	0.992376i	$-0.539330\pi$
$61$	−1.92513	−0.246488	−0.123244	+	0.992376i	$0.539330\pi$
$62$	−3.22967	−0.410169
$63$	5.65611	0.712603
$64$	1.00000	0.125000
$65$	−2.72840	−0.338416
$66$	3.38759	0.416984
$67$	3.16991	0.387266	0.193633	−	0.981074i	$-0.437973\pi$
$67$	3.16991	0.387266	0.193633	+	0.981074i	$0.437973\pi$
$68$	−0.942042	−0.114239
$69$	−3.14085	−0.378114
$70$	−13.7002	−1.63749
$71$	−6.48629	−0.769781	−0.384891	−	0.922962i	$-0.625761\pi$
$71$	−6.48629	−0.769781	−0.384891	+	0.922962i	$0.625761\pi$
$72$	1.33463	0.157288
$73$	5.90009	0.690553	0.345277	−	0.938501i	$-0.387785\pi$
$73$	5.90009	0.690553	0.345277	+	0.938501i	$0.387785\pi$
$74$	−0.461265	−0.0536210
$75$	11.3481	1.31037
$76$	−4.16396	−0.477639
$77$	6.89557	0.785824
$78$	1.75717	0.198960
$79$	5.22096	0.587404	0.293702	−	0.955897i	$-0.405113\pi$
$79$	5.22096	0.587404	0.293702	+	0.955897i	$0.405113\pi$
$80$	−3.23274	−0.361432
$81$	−11.2227	−1.24696
$82$	−12.3855	−1.36775
$83$	9.91652	1.08848	0.544240	−	0.838930i	$-0.316818\pi$
$83$	9.91652	1.08848	0.544240	+	0.838930i	$0.316818\pi$
$84$	8.82331	0.962702
$85$	3.04538	0.330318
$86$	2.06612	0.222796
$87$	20.0004	2.14426
$88$	1.62710	0.173450
$89$	−18.3369	−1.94371	−0.971855	−	0.235579i	$-0.924301\pi$
$89$	−18.3369	−1.94371	−0.971855	+	0.235579i	$0.924301\pi$
$90$	−4.31453	−0.454792
$91$	3.57678	0.374948
$92$	−1.50859	−0.157281
$93$	−6.72411	−0.697257
$94$	−8.12310	−0.837833
$95$	13.4610	1.38107
$96$	2.08198	0.212491
$97$	14.2978	1.45172	0.725859	−	0.687843i	$-0.241442\pi$
$97$	14.2978	1.45172	0.725859	+	0.687843i	$0.241442\pi$
$98$	10.9602	1.10714
$99$	2.17159	0.218253
$100$	5.45063	0.545063
$101$	17.1309	1.70459	0.852294	−	0.523062i	$-0.175211\pi$
$101$	17.1309	1.70459	0.852294	+	0.523062i	$0.175211\pi$
$102$	−1.96131	−0.194199
$103$	9.53416	0.939429	0.469714	−	0.882818i	$-0.344357\pi$
$103$	9.53416	0.939429	0.469714	+	0.882818i	$0.344357\pi$
$104$	0.843989	0.0827600
$105$	−28.5235	−2.78361
$106$	−7.87624	−0.765008
$107$	−7.46425	−0.721596	−0.360798	−	0.932644i	$-0.617496\pi$
$107$	−7.46425	−0.721596	−0.360798	+	0.932644i	$0.617496\pi$
$108$	−3.46725	−0.333637
$109$	12.6731	1.21386	0.606931	−	0.794754i	$-0.292400\pi$
$109$	12.6731	1.21386	0.606931	+	0.794754i	$0.292400\pi$
$110$	−5.26001	−0.501522
$111$	−0.960344	−0.0911519
$112$	4.23794	0.400448
$113$	−3.37605	−0.317592	−0.158796	−	0.987311i	$-0.550761\pi$
$113$	−3.37605	−0.317592	−0.158796	+	0.987311i	$0.550761\pi$
$114$	−8.66927	−0.811952
$115$	4.87688	0.454771
$116$	9.60642	0.891934
$117$	1.12642	0.104137
$118$	−3.22499	−0.296884
$119$	−3.99232	−0.365976
$120$	−6.73050	−0.614408
$121$	−8.35253	−0.759321
$122$	−1.92513	−0.174294
$123$	−25.7863	−2.32507
$124$	−3.22967	−0.290033
$125$	−1.45677	−0.130298
$126$	5.65611	0.503886
$127$	−1.35204	−0.119974	−0.0599872	−	0.998199i	$-0.519106\pi$
$127$	−1.35204	−0.119974	−0.0599872	+	0.998199i	$0.519106\pi$
$128$	1.00000	0.0883883
$129$	4.30162	0.378736
$130$	−2.72840	−0.239297
$131$	−8.34957	−0.729505	−0.364753	−	0.931104i	$-0.618846\pi$
$131$	−8.34957	−0.729505	−0.364753	+	0.931104i	$0.618846\pi$
$132$	3.38759	0.294852
$133$	−17.6466	−1.53016
$134$	3.16991	0.273839
$135$	11.2087	0.964695
$136$	−0.942042	−0.0807795
$137$	−18.8099	−1.60704	−0.803521	−	0.595276i	$-0.797043\pi$
$137$	−18.8099	−1.60704	−0.803521	+	0.595276i	$0.797043\pi$
$138$	−3.14085	−0.267367
$139$	−12.6716	−1.07479	−0.537394	−	0.843331i	$-0.680591\pi$
$139$	−12.6716	−1.07479	−0.537394	+	0.843331i	$0.680591\pi$
$140$	−13.7002	−1.15788
$141$	−16.9121	−1.42426
$142$	−6.48629	−0.544317
$143$	1.37326	0.114838
$144$	1.33463	0.111220
$145$	−31.0551	−2.57899
$146$	5.90009	0.488295
$147$	22.8188	1.88207
$148$	−0.461265	−0.0379158
$149$	19.2109	1.57382	0.786909	−	0.617069i	$-0.211680\pi$
$149$	19.2109	1.57382	0.786909	+	0.617069i	$0.211680\pi$
$150$	11.3481	0.926568
$151$	−6.95537	−0.566020	−0.283010	−	0.959117i	$-0.591333\pi$
$151$	−6.95537	−0.566020	−0.283010	+	0.959117i	$0.591333\pi$
$152$	−4.16396	−0.337742
$153$	−1.25728	−0.101645
$154$	6.89557	0.555661
$155$	10.4407	0.838617
$156$	1.75717	0.140686
$157$	12.6050	1.00599	0.502995	−	0.864289i	$-0.332231\pi$
$157$	12.6050	1.00599	0.502995	+	0.864289i	$0.332231\pi$
$158$	5.22096	0.415357
$159$	−16.3982	−1.30046
$160$	−3.23274	−0.255571
$161$	−6.39331	−0.503864
$162$	−11.2227	−0.881735
$163$	19.6244	1.53710	0.768550	−	0.639790i	$-0.220979\pi$
$163$	19.6244	1.53710	0.768550	+	0.639790i	$0.220979\pi$
$164$	−12.3855	−0.967142
$165$	−10.9512	−0.852552
$166$	9.91652	0.769672
$167$	12.1817	0.942647	0.471323	−	0.881960i	$-0.343776\pi$
$167$	12.1817	0.942647	0.471323	+	0.881960i	$0.343776\pi$
$168$	8.82331	0.680733
$169$	−12.2877	−0.945206
$170$	3.04538	0.233570
$171$	−5.55736	−0.424982
$172$	2.06612	0.157540
$173$	24.7449	1.88132	0.940660	−	0.339350i	$-0.110207\pi$
$173$	24.7449	1.88132	0.940660	+	0.339350i	$0.110207\pi$
$174$	20.0004	1.51622
$175$	23.0995	1.74616
$176$	1.62710	0.122648
$177$	−6.71435	−0.504682
$178$	−18.3369	−1.37441
$179$	22.0363	1.64707	0.823534	−	0.567267i	$-0.191999\pi$
$179$	22.0363	1.64707	0.823534	+	0.567267i	$0.191999\pi$
$180$	−4.31453	−0.321586
$181$	3.97416	0.295397	0.147699	−	0.989032i	$-0.452813\pi$
$181$	3.97416	0.295397	0.147699	+	0.989032i	$0.452813\pi$
$182$	3.57678	0.265129
$183$	−4.00809	−0.296287
$184$	−1.50859	−0.111215
$185$	1.49115	0.109632
$186$	−6.72411	−0.493035
$187$	−1.53280	−0.112089
$188$	−8.12310	−0.592438
$189$	−14.6940	−1.06883
$190$	13.4610	0.976564
$191$	19.4735	1.40906	0.704528	−	0.709677i	$-0.251159\pi$
$191$	19.4735	1.40906	0.704528	+	0.709677i	$0.251159\pi$
$192$	2.08198	0.150254
$193$	16.5416	1.19069	0.595344	−	0.803471i	$-0.297016\pi$
$193$	16.5416	1.19069	0.595344	+	0.803471i	$0.297016\pi$
$194$	14.2978	1.02652
$195$	−5.68047	−0.406787
$196$	10.9602	0.782870
$197$	−7.38564	−0.526205	−0.263103	−	0.964768i	$-0.584746\pi$
$197$	−7.38564	−0.526205	−0.263103	+	0.964768i	$0.584746\pi$
$198$	2.17159	0.154328
$199$	−18.9590	−1.34396	−0.671982	−	0.740567i	$-0.734557\pi$
$199$	−18.9590	−1.34396	−0.671982	+	0.740567i	$0.734557\pi$
$200$	5.45063	0.385418
$201$	6.59969	0.465506
$202$	17.1309	1.20533
$203$	40.7115	2.85739
$204$	−1.96131	−0.137319
$205$	40.0390	2.79645
$206$	9.53416	0.664276
$207$	−2.01341	−0.139942
$208$	0.843989	0.0585201
$209$	−6.77519	−0.468650
$210$	−28.5235	−1.96831
$211$	−17.1052	−1.17757	−0.588787	−	0.808288i	$-0.700394\pi$
$211$	−17.1052	−1.17757	−0.588787	+	0.808288i	$0.700394\pi$
$212$	−7.87624	−0.540942
$213$	−13.5043	−0.925301
$214$	−7.46425	−0.510246
$215$	−6.67924	−0.455520
$216$	−3.46725	−0.235917
$217$	−13.6872	−0.929146
$218$	12.6731	0.858330
$219$	12.2839	0.830066
$220$	−5.26001	−0.354630
$221$	−0.795074	−0.0534824
$222$	−0.960344	−0.0644541
$223$	−1.00000	−0.0669650
$223$	−1.00000	−0.0669650
$224$	4.23794	0.283160
$225$	7.27460	0.484973
$226$	−3.37605	−0.224571
$227$	4.46715	0.296495	0.148248	−	0.988950i	$-0.452637\pi$
$227$	4.46715	0.296495	0.148248	+	0.988950i	$0.452637\pi$
$228$	−8.66927	−0.574136
$229$	−12.5863	−0.831726	−0.415863	−	0.909427i	$-0.636520\pi$
$229$	−12.5863	−0.831726	−0.415863	+	0.909427i	$0.636520\pi$
$230$	4.87688	0.321572
$231$	14.3564	0.944584
$232$	9.60642	0.630693
$233$	−3.20498	−0.209965	−0.104982	−	0.994474i	$-0.533479\pi$
$233$	−3.20498	−0.209965	−0.104982	+	0.994474i	$0.533479\pi$
$234$	1.12642	0.0736362
$235$	26.2599	1.71301
$236$	−3.22499	−0.209929
$237$	10.8699	0.706077
$238$	−3.99232	−0.258784
$239$	3.91975	0.253547	0.126774	−	0.991932i	$-0.459538\pi$
$239$	3.91975	0.253547	0.126774	+	0.991932i	$0.459538\pi$
$240$	−6.73050	−0.434452
$241$	16.9198	1.08990	0.544950	−	0.838469i	$-0.316549\pi$
$241$	16.9198	1.08990	0.544950	+	0.838469i	$0.316549\pi$
$242$	−8.35253	−0.536921
$243$	−12.9636	−0.831613
$244$	−1.92513	−0.123244
$245$	−35.4314	−2.26363
$246$	−25.7863	−1.64407
$247$	−3.51433	−0.223612
$248$	−3.22967	−0.205084
$249$	20.6460	1.30839
$250$	−1.45677	−0.0921344
$251$	−12.1186	−0.764916	−0.382458	−	0.923973i	$-0.624922\pi$
$251$	−12.1186	−0.764916	−0.382458	+	0.923973i	$0.624922\pi$
$252$	5.65611	0.356301
$253$	−2.45463	−0.154321
$254$	−1.35204	−0.0848348
$255$	6.34042	0.397052
$256$	1.00000	0.0625000
$257$	−18.3212	−1.14284	−0.571422	−	0.820656i	$-0.693608\pi$
$257$	−18.3212	−1.14284	−0.571422	+	0.820656i	$0.693608\pi$
$258$	4.30162	0.267807
$259$	−1.95482	−0.121466
$260$	−2.72840	−0.169208
$261$	12.8211	0.793604
$262$	−8.34957	−0.515838
$263$	22.4825	1.38633	0.693165	−	0.720779i	$-0.256216\pi$
$263$	22.4825	1.38633	0.693165	+	0.720779i	$0.256216\pi$
$264$	3.38759	0.208492
$265$	25.4619	1.56411
$266$	−17.6466	−1.08198
$267$	−38.1771	−2.33640
$268$	3.16991	0.193633
$269$	31.5427	1.92319	0.961597	−	0.274466i	$-0.0885011\pi$
$269$	31.5427	1.92319	0.961597	+	0.274466i	$0.0885011\pi$
$270$	11.2087	0.682142
$271$	21.4428	1.30256	0.651280	−	0.758837i	$-0.274232\pi$
$271$	21.4428	1.30256	0.651280	+	0.758837i	$0.274232\pi$
$272$	−0.942042	−0.0571197
$273$	7.44678	0.450700
$274$	−18.8099	−1.13635
$275$	8.86874	0.534805
$276$	−3.14085	−0.189057
$277$	3.53182	0.212207	0.106103	−	0.994355i	$-0.466163\pi$
$277$	3.53182	0.212207	0.106103	+	0.994355i	$0.466163\pi$
$278$	−12.6716	−0.759990
$279$	−4.31043	−0.258059
$280$	−13.7002	−0.818743
$281$	16.2985	0.972288	0.486144	−	0.873879i	$-0.338403\pi$
$281$	16.2985	0.972288	0.486144	+	0.873879i	$0.338403\pi$
$282$	−16.9121	−1.00710
$283$	19.2174	1.14236	0.571179	−	0.820826i	$-0.306486\pi$
$283$	19.2174	1.14236	0.571179	+	0.820826i	$0.306486\pi$
$284$	−6.48629	−0.384891
$285$	28.0255	1.66009
$286$	1.37326	0.0812024
$287$	−52.4889	−3.09832
$288$	1.33463	0.0786441
$289$	−16.1126	−0.947797
$290$	−31.0551	−1.82362
$291$	29.7676	1.74501
$292$	5.90009	0.345277
$293$	−28.4149	−1.66002	−0.830008	−	0.557751i	$-0.811664\pi$
$293$	−28.4149	−1.66002	−0.830008	+	0.557751i	$0.811664\pi$
$294$	22.8188	1.33082
$295$	10.4256	0.606999
$296$	−0.461265	−0.0268105
$297$	−5.64158	−0.327358
$298$	19.2109	1.11286
$299$	−1.27323	−0.0736329
$300$	11.3481	0.655183
$301$	8.75611	0.504694
$302$	−6.95537	−0.400236
$303$	35.6662	2.04897
$304$	−4.16396	−0.238819
$305$	6.22347	0.356355
$306$	−1.25728	−0.0718741
$307$	−17.8204	−1.01706	−0.508531	−	0.861044i	$-0.669811\pi$
$307$	−17.8204	−1.01706	−0.508531	+	0.861044i	$0.669811\pi$
$308$	6.89557	0.392912
$309$	19.8499	1.12922
$310$	10.4407	0.592992
$311$	−25.7600	−1.46071	−0.730357	−	0.683065i	$-0.760646\pi$
$311$	−25.7600	−1.46071	−0.730357	+	0.683065i	$0.760646\pi$
$312$	1.75717	0.0994800
$313$	−18.5999	−1.05133	−0.525665	−	0.850692i	$-0.676184\pi$
$313$	−18.5999	−1.05133	−0.525665	+	0.850692i	$0.676184\pi$
$314$	12.6050	0.711342
$315$	−18.2847	−1.03023
$316$	5.22096	0.293702
$317$	−21.6706	−1.21714	−0.608570	−	0.793500i	$-0.708257\pi$
$317$	−21.6706	−1.21714	−0.608570	+	0.793500i	$0.708257\pi$
$318$	−16.3982	−0.919563
$319$	15.6306	0.875148
$320$	−3.23274	−0.180716
$321$	−15.5404	−0.867381
$322$	−6.39331	−0.356285
$323$	3.92262	0.218261
$324$	−11.2227	−0.623481
$325$	4.60027	0.255177
$326$	19.6244	1.08689
$327$	26.3851	1.45910
$328$	−12.3855	−0.683873
$329$	−34.4252	−1.89792
$330$	−10.9512	−0.602845
$331$	−28.0553	−1.54206	−0.771029	−	0.636800i	$-0.780258\pi$
$331$	−28.0553	−1.54206	−0.771029	+	0.636800i	$0.780258\pi$
$332$	9.91652	0.544240
$333$	−0.615621	−0.0337358
$334$	12.1817	0.666552
$335$	−10.2475	−0.559881
$336$	8.82331	0.481351
$337$	14.8556	0.809237	0.404618	−	0.914486i	$-0.367404\pi$
$337$	14.8556	0.809237	0.404618	+	0.914486i	$0.367404\pi$
$338$	−12.2877	−0.668362
$339$	−7.02886	−0.381755
$340$	3.04538	0.165159
$341$	−5.25501	−0.284575
$342$	−5.55736	−0.300508
$343$	16.7830	0.906197
$344$	2.06612	0.111398
$345$	10.1536	0.546649
$346$	24.7449	1.33029
$347$	12.9427	0.694798	0.347399	−	0.937717i	$-0.387065\pi$
$347$	12.9427	0.694798	0.347399	+	0.937717i	$0.387065\pi$
$348$	20.0004	1.07213
$349$	15.5050	0.829962	0.414981	−	0.909830i	$-0.363788\pi$
$349$	15.5050	0.829962	0.414981	+	0.909830i	$0.363788\pi$
$350$	23.0995	1.23472
$351$	−2.92633	−0.156196
$352$	1.62710	0.0867249
$353$	19.5212	1.03901	0.519505	−	0.854468i	$-0.326116\pi$
$353$	19.5212	1.03901	0.519505	+	0.854468i	$0.326116\pi$
$354$	−6.71435	−0.356864
$355$	20.9685	1.11289
$356$	−18.3369	−0.971855
$357$	−8.31193	−0.439914
$358$	22.0363	1.16465
$359$	15.2551	0.805134	0.402567	−	0.915390i	$-0.368118\pi$
$359$	15.2551	0.805134	0.402567	+	0.915390i	$0.368118\pi$
$360$	−4.31453	−0.227396
$361$	−1.66146	−0.0874453
$362$	3.97416	0.208877
$363$	−17.3898	−0.912728
$364$	3.57678	0.187474
$365$	−19.0735	−0.998351
$366$	−4.00809	−0.209506
$367$	3.05112	0.159267	0.0796335	−	0.996824i	$-0.474625\pi$
$367$	3.05112	0.159267	0.0796335	+	0.996824i	$0.474625\pi$
$368$	−1.50859	−0.0786406
$369$	−16.5301	−0.860521
$370$	1.49115	0.0775213
$371$	−33.3791	−1.73295
$372$	−6.72411	−0.348629
$373$	−8.80327	−0.455816	−0.227908	−	0.973683i	$-0.573189\pi$
$373$	−8.80327	−0.455816	−0.227908	+	0.973683i	$0.573189\pi$
$374$	−1.53280	−0.0792592
$375$	−3.03297	−0.156622
$376$	−8.12310	−0.418917
$377$	8.10772	0.417569
$378$	−14.6940	−0.755779
$379$	10.7931	0.554405	0.277202	−	0.960812i	$-0.410593\pi$
$379$	10.7931	0.554405	0.277202	+	0.960812i	$0.410593\pi$
$380$	13.4610	0.690535
$381$	−2.81493	−0.144213
$382$	19.4735	0.996352
$383$	3.58797	0.183336	0.0916682	−	0.995790i	$-0.470780\pi$
$383$	3.58797	0.183336	0.0916682	+	0.995790i	$0.470780\pi$
$384$	2.08198	0.106246
$385$	−22.2916	−1.13609
$386$	16.5416	0.841944
$387$	2.75752	0.140172
$388$	14.2978	0.725859
$389$	12.1818	0.617640	0.308820	−	0.951120i	$-0.400066\pi$
$389$	12.1818	0.617640	0.308820	+	0.951120i	$0.400066\pi$
$390$	−5.68047	−0.287642
$391$	1.42115	0.0718708
$392$	10.9602	0.553572
$393$	−17.3836	−0.876888
$394$	−7.38564	−0.372083
$395$	−16.8780	−0.849225
$396$	2.17159	0.109126
$397$	−37.8938	−1.90184	−0.950918	−	0.309442i	$-0.899858\pi$
$397$	−37.8938	−1.90184	−0.950918	+	0.309442i	$0.899858\pi$
$398$	−18.9590	−0.950327
$399$	−36.7399	−1.83929
$400$	5.45063	0.272532
$401$	8.08258	0.403625	0.201812	−	0.979424i	$-0.435317\pi$
$401$	8.08258	0.403625	0.201812	+	0.979424i	$0.435317\pi$
$402$	6.59969	0.329162
$403$	−2.72581	−0.135782
$404$	17.1309	0.852294
$405$	36.2800	1.80277
$406$	40.7115	2.02048
$407$	−0.750526	−0.0372022
$408$	−1.96131	−0.0970994
$409$	−3.78638	−0.187224	−0.0936122	−	0.995609i	$-0.529841\pi$
$409$	−3.78638	−0.187224	−0.0936122	+	0.995609i	$0.529841\pi$
$410$	40.0390	1.97739
$411$	−39.1619	−1.93171
$412$	9.53416	0.469714
$413$	−13.6673	−0.672525
$414$	−2.01341	−0.0989539
$415$	−32.0576	−1.57364
$416$	0.843989	0.0413800
$417$	−26.3819	−1.29193
$418$	−6.77519	−0.331385
$419$	2.72170	0.132964	0.0664819	−	0.997788i	$-0.478823\pi$
$419$	2.72170	0.132964	0.0664819	+	0.997788i	$0.478823\pi$
$420$	−28.5235	−1.39180
$421$	−25.2691	−1.23154	−0.615771	−	0.787925i	$-0.711155\pi$
$421$	−25.2691	−1.23154	−0.615771	+	0.787925i	$0.711155\pi$
$422$	−17.1052	−0.832670
$423$	−10.8414	−0.527125
$424$	−7.87624	−0.382504
$425$	−5.13472	−0.249071
$426$	−13.5043	−0.654286
$427$	−8.15862	−0.394823
$428$	−7.46425	−0.360798
$429$	2.85909	0.138038
$430$	−6.67924	−0.322101
$431$	−4.38653	−0.211292	−0.105646	−	0.994404i	$-0.533691\pi$
$431$	−4.38653	−0.211292	−0.105646	+	0.994404i	$0.533691\pi$
$432$	−3.46725	−0.166818
$433$	24.1448	1.16033	0.580163	−	0.814500i	$-0.302989\pi$
$433$	24.1448	1.16033	0.580163	+	0.814500i	$0.302989\pi$
$434$	−13.6872	−0.657005
$435$	−64.6561	−3.10002
$436$	12.6731	0.606931
$437$	6.28170	0.300494
$438$	12.2839	0.586945
$439$	−6.58706	−0.314383	−0.157192	−	0.987568i	$-0.550244\pi$
$439$	−6.58706	−0.314383	−0.157192	+	0.987568i	$0.550244\pi$
$440$	−5.26001	−0.250761
$441$	14.6278	0.696563
$442$	−0.795074	−0.0378178
$443$	−30.2193	−1.43576	−0.717881	−	0.696166i	$-0.754888\pi$
$443$	−30.2193	−1.43576	−0.717881	+	0.696166i	$0.754888\pi$
$444$	−0.960344	−0.0455759
$445$	59.2786	2.81007
$446$	−1.00000	−0.0473514
$447$	39.9967	1.89178
$448$	4.23794	0.200224
$449$	−14.9422	−0.705166	−0.352583	−	0.935781i	$-0.614696\pi$
$449$	−14.9422	−0.705166	−0.352583	+	0.935781i	$0.614696\pi$
$450$	7.27460	0.342928
$451$	−20.1524	−0.948941
$452$	−3.37605	−0.158796
$453$	−14.4809	−0.680373
$454$	4.46715	0.209654
$455$	−11.5628	−0.542073
$456$	−8.66927	−0.405976
$457$	14.6447	0.685051	0.342525	−	0.939509i	$-0.388718\pi$
$457$	14.6447	0.685051	0.342525	+	0.939509i	$0.388718\pi$
$458$	−12.5863	−0.588119
$459$	3.26630	0.152458
$460$	4.87688	0.227386
$461$	−25.3454	−1.18045	−0.590226	−	0.807238i	$-0.700962\pi$
$461$	−25.3454	−1.18045	−0.590226	+	0.807238i	$0.700962\pi$
$462$	14.3564	0.667922
$463$	−19.0759	−0.886534	−0.443267	−	0.896390i	$-0.646181\pi$
$463$	−19.0759	−0.886534	−0.443267	+	0.896390i	$0.646181\pi$
$464$	9.60642	0.445967
$465$	21.7373	1.00804
$466$	−3.20498	−0.148468
$467$	34.2858	1.58656	0.793280	−	0.608857i	$-0.208372\pi$
$467$	34.2858	1.58656	0.793280	+	0.608857i	$0.208372\pi$
$468$	1.12642	0.0520687
$469$	13.4339	0.620320
$470$	26.2599	1.21128
$471$	26.2434	1.20923
$472$	−3.22499	−0.148442
$473$	3.36179	0.154575
$474$	10.8699	0.499272
$475$	−22.6962	−1.04137
$476$	−3.99232	−0.182988
$477$	−10.5119	−0.481307
$478$	3.91975	0.179285
$479$	−23.0099	−1.05135	−0.525674	−	0.850686i	$-0.676187\pi$
$479$	−23.0099	−1.05135	−0.525674	+	0.850686i	$0.676187\pi$
$480$	−6.73050	−0.307204
$481$	−0.389303	−0.0177507
$482$	16.9198	0.770676
$483$	−13.3107	−0.605660
$484$	−8.35253	−0.379661
$485$	−46.2210	−2.09879
$486$	−12.9636	−0.588039
$487$	13.9176	0.630665	0.315332	−	0.948981i	$-0.397884\pi$
$487$	13.9176	0.630665	0.315332	+	0.948981i	$0.397884\pi$
$488$	−1.92513	−0.0871468
$489$	40.8575	1.84764
$490$	−35.4314	−1.60063
$491$	29.1777	1.31677	0.658385	−	0.752681i	$-0.271240\pi$
$491$	29.1777	1.31677	0.658385	+	0.752681i	$0.271240\pi$
$492$	−25.7863	−1.16254
$493$	−9.04966	−0.407576
$494$	−3.51433	−0.158117
$495$	−7.02019	−0.315534
$496$	−3.22967	−0.145017
$497$	−27.4885	−1.23303
$498$	20.6460	0.925169
$499$	28.4731	1.27463	0.637315	−	0.770604i	$-0.280045\pi$
$499$	28.4731	1.27463	0.637315	+	0.770604i	$0.280045\pi$
$500$	−1.45677	−0.0651488
$501$	25.3620	1.13309
$502$	−12.1186	−0.540877
$503$	28.5037	1.27092	0.635458	−	0.772135i	$-0.280811\pi$
$503$	28.5037	1.27092	0.635458	+	0.772135i	$0.280811\pi$
$504$	5.65611	0.251943
$505$	−55.3798	−2.46437
$506$	−2.45463	−0.109122
$507$	−25.5827	−1.13617
$508$	−1.35204	−0.0599872
$509$	−18.3677	−0.814135	−0.407067	−	0.913398i	$-0.633449\pi$
$509$	−18.3677	−0.814135	−0.407067	+	0.913398i	$0.633449\pi$
$510$	6.34042	0.280758
$511$	25.0042	1.10612
$512$	1.00000	0.0441942
$513$	14.4375	0.637431
$514$	−18.3212	−0.808113
$515$	−30.8215	−1.35816
$516$	4.30162	0.189368
$517$	−13.2171	−0.581288
$518$	−1.95482	−0.0858897
$519$	51.5184	2.26141
$520$	−2.72840	−0.119648
$521$	−25.6718	−1.12470	−0.562352	−	0.826898i	$-0.690103\pi$
$521$	−25.6718	−1.12470	−0.562352	+	0.826898i	$0.690103\pi$
$522$	12.8211	0.561163
$523$	−12.3532	−0.540168	−0.270084	−	0.962837i	$-0.587051\pi$
$523$	−12.3532	−0.540168	−0.270084	+	0.962837i	$0.587051\pi$
$524$	−8.34957	−0.364753
$525$	48.0926	2.09893
$526$	22.4825	0.980283
$527$	3.04249	0.132533
$528$	3.38759	0.147426
$529$	−20.7242	−0.901051
$530$	25.4619	1.10599
$531$	−4.30418	−0.186786
$532$	−17.6466	−0.765078
$533$	−10.4532	−0.452778
$534$	−38.1771	−1.65208
$535$	24.1300	1.04323
$536$	3.16991	0.136919
$537$	45.8790	1.97983
$538$	31.5427	1.35990
$539$	17.8333	0.768136
$540$	11.2087	0.482348
$541$	6.81882	0.293164	0.146582	−	0.989199i	$-0.453173\pi$
$541$	6.81882	0.293164	0.146582	+	0.989199i	$0.453173\pi$
$542$	21.4428	0.921049
$543$	8.27413	0.355077
$544$	−0.942042	−0.0403897
$545$	−40.9689	−1.75491
$546$	7.44678	0.318693
$547$	−12.6106	−0.539191	−0.269595	−	0.962974i	$-0.586890\pi$
$547$	−12.6106	−0.539191	−0.269595	+	0.962974i	$0.586890\pi$
$548$	−18.8099	−0.803521
$549$	−2.56935	−0.109657
$550$	8.86874	0.378164
$551$	−40.0007	−1.70409
$552$	−3.14085	−0.133683
$553$	22.1261	0.940899
$554$	3.53182	0.150053
$555$	3.10455	0.131781
$556$	−12.6716	−0.537394
$557$	0.665650	0.0282045	0.0141022	−	0.999901i	$-0.495511\pi$
$557$	0.665650	0.0282045	0.0141022	+	0.999901i	$0.495511\pi$
$558$	−4.31043	−0.182475
$559$	1.74378	0.0737542
$560$	−13.7002	−0.578939
$561$	−3.19126	−0.134735
$562$	16.2985	0.687511
$563$	26.5159	1.11751	0.558755	−	0.829333i	$-0.311279\pi$
$563$	26.5159	1.11751	0.558755	+	0.829333i	$0.311279\pi$
$564$	−16.9121	−0.712128
$565$	10.9139	0.459151
$566$	19.2174	0.807769
$567$	−47.5610	−1.99737
$568$	−6.48629	−0.272159
$569$	42.2037	1.76927	0.884636	−	0.466283i	$-0.154407\pi$
$569$	42.2037	1.76927	0.884636	+	0.466283i	$0.154407\pi$
$570$	28.0255	1.17386
$571$	0.974618	0.0407865	0.0203932	−	0.999792i	$-0.493508\pi$
$571$	0.974618	0.0407865	0.0203932	+	0.999792i	$0.493508\pi$
$572$	1.37326	0.0574188
$573$	40.5435	1.69373
$574$	−52.4889	−2.19085
$575$	−8.22275	−0.342913
$576$	1.33463	0.0556098
$577$	−40.8701	−1.70144	−0.850722	−	0.525615i	$-0.823835\pi$
$577$	−40.8701	−1.70144	−0.850722	+	0.525615i	$0.823835\pi$
$578$	−16.1126	−0.670194
$579$	34.4392	1.43124
$580$	−31.0551	−1.28949
$581$	42.0257	1.74352
$582$	29.7676	1.23391
$583$	−12.8155	−0.530762
$584$	5.90009	0.244147
$585$	−3.64142	−0.150554
$586$	−28.4149	−1.17381
$587$	−12.3589	−0.510105	−0.255053	−	0.966927i	$-0.582093\pi$
$587$	−12.3589	−0.510105	−0.255053	+	0.966927i	$0.582093\pi$
$588$	22.8188	0.941033
$589$	13.4482	0.554124
$590$	10.4256	0.429213
$591$	−15.3767	−0.632515
$592$	−0.461265	−0.0189579
$593$	6.03062	0.247648	0.123824	−	0.992304i	$-0.460484\pi$
$593$	6.03062	0.247648	0.123824	+	0.992304i	$0.460484\pi$
$594$	−5.64158	−0.231477
$595$	12.9062	0.529101
$596$	19.2109	0.786909
$597$	−39.4721	−1.61549
$598$	−1.27323	−0.0520663
$599$	−0.932663	−0.0381076	−0.0190538	−	0.999818i	$-0.506065\pi$
$599$	−0.932663	−0.0381076	−0.0190538	+	0.999818i	$0.506065\pi$
$600$	11.3481	0.463284
$601$	14.9218	0.608674	0.304337	−	0.952564i	$-0.401565\pi$
$601$	14.9218	0.608674	0.304337	+	0.952564i	$0.401565\pi$
$602$	8.75611	0.356872
$603$	4.23067	0.172286
$604$	−6.95537	−0.283010
$605$	27.0016	1.09777
$606$	35.6662	1.44884
$607$	−13.8044	−0.560301	−0.280151	−	0.959956i	$-0.590384\pi$
$607$	−13.8044	−0.560301	−0.280151	+	0.959956i	$0.590384\pi$
$608$	−4.16396	−0.168871
$609$	84.7605	3.43467
$610$	6.22347	0.251981
$611$	−6.85580	−0.277356
$612$	−1.25728	−0.0508226
$613$	−39.9303	−1.61277	−0.806385	−	0.591391i	$-0.798579\pi$
$613$	−39.9303	−1.61277	−0.806385	+	0.591391i	$0.798579\pi$
$614$	−17.8204	−0.719172
$615$	83.3604	3.36142
$616$	6.89557	0.277831
$617$	−2.07604	−0.0835783	−0.0417892	−	0.999126i	$-0.513306\pi$
$617$	−2.07604	−0.0835783	−0.0417892	+	0.999126i	$0.513306\pi$
$618$	19.8499	0.798481
$619$	20.3472	0.817822	0.408911	−	0.912574i	$-0.365909\pi$
$619$	20.3472	0.817822	0.408911	+	0.912574i	$0.365909\pi$
$620$	10.4407	0.419309
$621$	5.23066	0.209899
$622$	−25.7600	−1.03288
$623$	−77.7109	−3.11342
$624$	1.75717	0.0703430
$625$	−22.5438	−0.901751
$626$	−18.5999	−0.743403
$627$	−14.1058	−0.563331
$628$	12.6050	0.502995
$629$	0.434531	0.0173259
$630$	−18.2847	−0.728482
$631$	−38.0428	−1.51446	−0.757230	−	0.653149i	$-0.773448\pi$
$631$	−38.0428	−1.51446	−0.757230	+	0.653149i	$0.773448\pi$
$632$	5.22096	0.207679
$633$	−35.6128	−1.41548
$634$	−21.6706	−0.860649
$635$	4.37081	0.173450
$636$	−16.3982	−0.650229
$637$	9.25027	0.366509
$638$	15.6306	0.618823
$639$	−8.65683	−0.342459
$640$	−3.23274	−0.127785
$641$	−3.27668	−0.129421	−0.0647106	−	0.997904i	$-0.520612\pi$
$641$	−3.27668	−0.129421	−0.0647106	+	0.997904i	$0.520612\pi$
$642$	−15.5404	−0.613331
$643$	−45.1564	−1.78079	−0.890397	−	0.455185i	$-0.849573\pi$
$643$	−45.1564	−1.78079	−0.890397	+	0.455185i	$0.849573\pi$
$644$	−6.39331	−0.251932
$645$	−13.9060	−0.547549
$646$	3.92262	0.154334
$647$	28.9340	1.13751	0.568757	−	0.822505i	$-0.307424\pi$
$647$	28.9340	1.13751	0.568757	+	0.822505i	$0.307424\pi$
$648$	−11.2227	−0.440868
$649$	−5.24739	−0.205978
$650$	4.60027	0.180438
$651$	−28.4964	−1.11686
$652$	19.6244	0.768550
$653$	−0.601430	−0.0235358	−0.0117679	−	0.999931i	$-0.503746\pi$
$653$	−0.601430	−0.0235358	−0.0117679	+	0.999931i	$0.503746\pi$
$654$	26.3851	1.03174
$655$	26.9920	1.05467
$656$	−12.3855	−0.483571
$657$	7.87446	0.307212
$658$	−34.4252	−1.34204
$659$	−1.13037	−0.0440328	−0.0220164	−	0.999758i	$-0.507009\pi$
$659$	−1.13037	−0.0440328	−0.0220164	+	0.999758i	$0.507009\pi$
$660$	−10.9512	−0.426276
$661$	0.496004	0.0192923	0.00964615	−	0.999953i	$-0.496929\pi$
$661$	0.496004	0.0192923	0.00964615	+	0.999953i	$0.496929\pi$
$662$	−28.0553	−1.09040
$663$	−1.65533	−0.0642875
$664$	9.91652	0.384836
$665$	57.0470	2.21219
$666$	−0.615621	−0.0238548
$667$	−14.4921	−0.561138
$668$	12.1817	0.471323
$669$	−2.08198	−0.0804939
$670$	−10.2475	−0.395896
$671$	−3.13239	−0.120925
$672$	8.82331	0.340367
$673$	−2.19328	−0.0845448	−0.0422724	−	0.999106i	$-0.513460\pi$
$673$	−2.19328	−0.0845448	−0.0422724	+	0.999106i	$0.513460\pi$
$674$	14.8556	0.572217
$675$	−18.8987	−0.727412
$676$	−12.2877	−0.472603
$677$	−12.6302	−0.485417	−0.242708	−	0.970099i	$-0.578036\pi$
$677$	−12.6302	−0.485417	−0.242708	+	0.970099i	$0.578036\pi$
$678$	−7.02886	−0.269942
$679$	60.5931	2.32535
$680$	3.04538	0.116785
$681$	9.30052	0.356397
$682$	−5.25501	−0.201225
$683$	46.0057	1.76036	0.880179	−	0.474643i	$-0.157423\pi$
$683$	46.0057	1.76036	0.880179	+	0.474643i	$0.157423\pi$
$684$	−5.55736	−0.212491
$685$	60.8077	2.32334
$686$	16.7830	0.640778
$687$	−26.2044	−0.999760
$688$	2.06612	0.0787701
$689$	−6.64746	−0.253248
$690$	10.1536	0.386539
$691$	−40.0066	−1.52192	−0.760961	−	0.648797i	$-0.775272\pi$
$691$	−40.0066	−1.52192	−0.760961	+	0.648797i	$0.775272\pi$
$692$	24.7449	0.940660
$693$	9.20307	0.349596
$694$	12.9427	0.491296
$695$	40.9639	1.55385
$696$	20.0004	0.758112
$697$	11.6676	0.441943
$698$	15.5050	0.586872
$699$	−6.67269	−0.252384
$700$	23.0995	0.873078
$701$	−3.96354	−0.149701	−0.0748504	−	0.997195i	$-0.523848\pi$
$701$	−3.96354	−0.149701	−0.0748504	+	0.997195i	$0.523848\pi$
$702$	−2.92633	−0.110447
$703$	1.92069	0.0724402
$704$	1.62710	0.0613238
$705$	54.6725	2.05909
$706$	19.5212	0.734691
$707$	72.5998	2.73040
$708$	−6.71435	−0.252341
$709$	23.0155	0.864364	0.432182	−	0.901786i	$-0.357744\pi$
$709$	23.0155	0.864364	0.432182	+	0.901786i	$0.357744\pi$
$710$	20.9685	0.786934
$711$	6.96807	0.261323
$712$	−18.3369	−0.687205
$713$	4.87224	0.182467
$714$	−8.31193	−0.311066
$715$	−4.43939	−0.166024
$716$	22.0363	0.823534
$717$	8.16083	0.304772
$718$	15.2551	0.569316
$719$	3.11974	0.116347	0.0581734	−	0.998306i	$-0.481472\pi$
$719$	3.11974	0.116347	0.0581734	+	0.998306i	$0.481472\pi$
$720$	−4.31453	−0.160793
$721$	40.4052	1.50477
$722$	−1.66146	−0.0618331
$723$	35.2267	1.31009
$724$	3.97416	0.147699
$725$	52.3611	1.94464
$726$	−17.3898	−0.645396
$727$	−46.5659	−1.72703	−0.863517	−	0.504319i	$-0.831744\pi$
$727$	−46.5659	−1.72703	−0.863517	+	0.504319i	$0.831744\pi$
$728$	3.57678	0.132564
$729$	6.67810	0.247337
$730$	−19.0735	−0.705941
$731$	−1.94637	−0.0719892
$732$	−4.00809	−0.148143
$733$	−12.8098	−0.473140	−0.236570	−	0.971614i	$-0.576023\pi$
$733$	−12.8098	−0.473140	−0.236570	+	0.971614i	$0.576023\pi$
$734$	3.05112	0.112619
$735$	−73.7675	−2.72095
$736$	−1.50859	−0.0556073
$737$	5.15777	0.189989
$738$	−16.5301	−0.608480
$739$	−11.7528	−0.432332	−0.216166	−	0.976357i	$-0.569355\pi$
$739$	−11.7528	−0.432332	−0.216166	+	0.976357i	$0.569355\pi$
$740$	1.49115	0.0548158
$741$	−7.31677	−0.268788
$742$	−33.3791	−1.22538
$743$	8.31456	0.305032	0.152516	−	0.988301i	$-0.451262\pi$
$743$	8.31456	0.305032	0.152516	+	0.988301i	$0.451262\pi$
$744$	−6.72411	−0.246518
$745$	−62.1039	−2.27531
$746$	−8.80327	−0.322311
$747$	13.2349	0.484241
$748$	−1.53280	−0.0560447
$749$	−31.6331	−1.15585
$750$	−3.03297	−0.110748
$751$	21.5225	0.785368	0.392684	−	0.919673i	$-0.371547\pi$
$751$	21.5225	0.785368	0.392684	+	0.919673i	$0.371547\pi$
$752$	−8.12310	−0.296219
$753$	−25.2306	−0.919453
$754$	8.10772	0.295266
$755$	22.4849	0.818310
$756$	−14.6940	−0.534417
$757$	6.72567	0.244449	0.122224	−	0.992503i	$-0.460997\pi$
$757$	6.72567	0.244449	0.122224	+	0.992503i	$0.460997\pi$
$758$	10.7931	0.392023
$759$	−5.11048	−0.185499
$760$	13.4610	0.488282
$761$	−18.3748	−0.666085	−0.333042	−	0.942912i	$-0.608075\pi$
$761$	−18.3748	−0.666085	−0.333042	+	0.942912i	$0.608075\pi$
$762$	−2.81493	−0.101974
$763$	53.7079	1.94436
$764$	19.4735	0.704528
$765$	4.06447	0.146951
$766$	3.58797	0.129638
$767$	−2.72185	−0.0982805
$768$	2.08198	0.0751269
$769$	0.646091	0.0232986	0.0116493	−	0.999932i	$-0.496292\pi$
$769$	0.646091	0.0232986	0.0116493	+	0.999932i	$0.496292\pi$
$770$	−22.2916	−0.803334
$771$	−38.1443	−1.37373
$772$	16.5416	0.595344
$773$	8.31989	0.299246	0.149623	−	0.988743i	$-0.452194\pi$
$773$	8.31989	0.299246	0.149623	+	0.988743i	$0.452194\pi$
$774$	2.75752	0.0991169
$775$	−17.6037	−0.632345
$776$	14.2978	0.513260
$777$	−4.06989	−0.146006
$778$	12.1818	0.436738
$779$	51.5725	1.84778
$780$	−5.68047	−0.203394
$781$	−10.5539	−0.377647
$782$	1.42115	0.0508204
$783$	−33.3079	−1.19033
$784$	10.9602	0.391435
$785$	−40.7488	−1.45439
$786$	−17.3836	−0.620054
$787$	−1.45675	−0.0519275	−0.0259637	−	0.999663i	$-0.508265\pi$
$787$	−1.45675	−0.0519275	−0.0259637	+	0.999663i	$0.508265\pi$
$788$	−7.38564	−0.263103
$789$	46.8081	1.66641
$790$	−16.8780	−0.600493
$791$	−14.3075	−0.508716
$792$	2.17159	0.0771641
$793$	−1.62479	−0.0576981
$794$	−37.8938	−1.34480
$795$	53.0110	1.88011
$796$	−18.9590	−0.671982
$797$	9.33351	0.330610	0.165305	−	0.986243i	$-0.447139\pi$
$797$	9.33351	0.330610	0.165305	+	0.986243i	$0.447139\pi$
$798$	−36.7399	−1.30058
$799$	7.65230	0.270719
$800$	5.45063	0.192709
$801$	−24.4731	−0.864715
$802$	8.08258	0.285406
$803$	9.60005	0.338779
$804$	6.59969	0.232753
$805$	20.6679	0.728449
$806$	−2.72581	−0.0960125
$807$	65.6713	2.31174
$808$	17.1309	0.602663
$809$	−1.15995	−0.0407816	−0.0203908	−	0.999792i	$-0.506491\pi$
$809$	−1.15995	−0.0407816	−0.0203908	+	0.999792i	$0.506491\pi$
$810$	36.2800	1.27475
$811$	19.7705	0.694237	0.347119	−	0.937821i	$-0.387160\pi$
$811$	19.7705	0.694237	0.347119	+	0.937821i	$0.387160\pi$
$812$	40.7115	1.42869
$813$	44.6435	1.56572
$814$	−0.750526	−0.0263059
$815$	−63.4406	−2.22223
$816$	−1.96131	−0.0686597
$817$	−8.60324	−0.300989
$818$	−3.78638	−0.132388
$819$	4.77369	0.166806
$820$	40.0390	1.39822
$821$	−27.5239	−0.960589	−0.480295	−	0.877107i	$-0.659470\pi$
$821$	−27.5239	−0.960589	−0.480295	+	0.877107i	$0.659470\pi$
$822$	−39.1619	−1.36593
$823$	−37.9780	−1.32383	−0.661915	−	0.749579i	$-0.730256\pi$
$823$	−37.9780	−1.32383	−0.661915	+	0.749579i	$0.730256\pi$
$824$	9.53416	0.332138
$825$	18.4645	0.642852
$826$	−13.6673	−0.475547
$827$	−37.8370	−1.31572	−0.657860	−	0.753140i	$-0.728538\pi$
$827$	−37.8370	−1.31572	−0.657860	+	0.753140i	$0.728538\pi$
$828$	−2.01341	−0.0699710
$829$	55.1825	1.91657	0.958283	−	0.285821i	$-0.0922664\pi$
$829$	55.1825	1.91657	0.958283	+	0.285821i	$0.0922664\pi$
$830$	−32.0576	−1.11273
$831$	7.35318	0.255079
$832$	0.843989	0.0292601
$833$	−10.3249	−0.357738
$834$	−26.3819	−0.913531
$835$	−39.3803	−1.36281
$836$	−6.77519	−0.234325
$837$	11.1981	0.387063
$838$	2.72170	0.0940196
$839$	32.3853	1.11807	0.559033	−	0.829146i	$-0.311173\pi$
$839$	32.3853	1.11807	0.559033	+	0.829146i	$0.311173\pi$
$840$	−28.5235	−0.984154
$841$	63.2834	2.18219
$842$	−25.2691	−0.870832
$843$	33.9332	1.16872
$844$	−17.1052	−0.588787
$845$	39.7229	1.36651
$846$	−10.8414	−0.372734
$847$	−35.3976	−1.21628
$848$	−7.87624	−0.270471
$849$	40.0103	1.37315
$850$	−5.13472	−0.176120
$851$	0.695859	0.0238537
$852$	−13.5043	−0.462650
$853$	42.6423	1.46004	0.730022	−	0.683423i	$-0.239510\pi$
$853$	42.6423	1.46004	0.730022	+	0.683423i	$0.239510\pi$
$854$	−8.15862	−0.279182
$855$	17.9655	0.614408
$856$	−7.46425	−0.255123
$857$	−52.4569	−1.79189	−0.895947	−	0.444161i	$-0.853502\pi$
$857$	−52.4569	−1.79189	−0.895947	+	0.444161i	$0.853502\pi$
$858$	2.85909	0.0976078
$859$	13.4612	0.459291	0.229645	−	0.973274i	$-0.426243\pi$
$859$	13.4612	0.459291	0.229645	+	0.973274i	$0.426243\pi$
$860$	−6.67924	−0.227760
$861$	−109.281	−3.72428
$862$	−4.38653	−0.149406
$863$	1.83135	0.0623399	0.0311700	−	0.999514i	$-0.490077\pi$
$863$	1.83135	0.0623399	0.0311700	+	0.999514i	$0.490077\pi$
$864$	−3.46725	−0.117958
$865$	−79.9939	−2.71988
$866$	24.1448	0.820474
$867$	−33.5460	−1.13928
$868$	−13.6872	−0.464573
$869$	8.49504	0.288175
$870$	−64.6561	−2.19205
$871$	2.67537	0.0906515
$872$	12.6731	0.429165
$873$	19.0823	0.645838
$874$	6.28170	0.212482
$875$	−6.17372	−0.208710
$876$	12.2839	0.415033
$877$	−16.0327	−0.541386	−0.270693	−	0.962666i	$-0.587253\pi$
$877$	−16.0327	−0.541386	−0.270693	+	0.962666i	$0.587253\pi$
$878$	−6.58706	−0.222303
$879$	−59.1592	−1.99539
$880$	−5.26001	−0.177315
$881$	37.1248	1.25077	0.625383	−	0.780318i	$-0.284943\pi$
$881$	37.1248	1.25077	0.625383	+	0.780318i	$0.284943\pi$
$882$	14.6278	0.492545
$883$	−9.66118	−0.325125	−0.162562	−	0.986698i	$-0.551976\pi$
$883$	−9.66118	−0.325125	−0.162562	+	0.986698i	$0.551976\pi$
$884$	−0.795074	−0.0267412
$885$	21.7058	0.729632
$886$	−30.2193	−1.01524
$887$	−9.43129	−0.316672	−0.158336	−	0.987385i	$-0.550613\pi$
$887$	−9.43129	−0.316672	−0.158336	+	0.987385i	$0.550613\pi$
$888$	−0.960344	−0.0322270
$889$	−5.72989	−0.192174
$890$	59.2786	1.98702
$891$	−18.2604	−0.611747
$892$	−1.00000	−0.0334825
$893$	33.8242	1.13188
$894$	39.9967	1.33769
$895$	−71.2376	−2.38121
$896$	4.23794	0.141580
$897$	−2.65084	−0.0885090
$898$	−14.9422	−0.498627
$899$	−31.0256	−1.03476
$900$	7.27460	0.242487
$901$	7.41975	0.247188
$902$	−20.1524	−0.671003
$903$	18.2300	0.606657
$904$	−3.37605	−0.112286
$905$	−12.8475	−0.427064
$906$	−14.4809	−0.481096
$907$	−7.22663	−0.239956	−0.119978	−	0.992777i	$-0.538282\pi$
$907$	−7.22663	−0.239956	−0.119978	+	0.992777i	$0.538282\pi$
$908$	4.46715	0.148248
$909$	22.8635	0.758335
$910$	−11.5628	−0.383303
$911$	3.77478	0.125064	0.0625321	−	0.998043i	$-0.480082\pi$
$911$	3.77478	0.125064	0.0625321	+	0.998043i	$0.480082\pi$
$912$	−8.66927	−0.287068
$913$	16.1352	0.533998
$914$	14.6447	0.484404
$915$	12.9571	0.428349
$916$	−12.5863	−0.415863
$917$	−35.3850	−1.16852
$918$	3.26630	0.107804
$919$	5.30434	0.174974	0.0874870	−	0.996166i	$-0.472116\pi$
$919$	5.30434	0.174974	0.0874870	+	0.996166i	$0.472116\pi$
$920$	4.87688	0.160786
$921$	−37.1016	−1.22254
$922$	−25.3454	−0.834706
$923$	−5.47436	−0.180191
$924$	14.3564	0.472292
$925$	−2.51419	−0.0826659
$926$	−19.0759	−0.626874
$927$	12.7246	0.417931
$928$	9.60642	0.315346
$929$	25.8603	0.848450	0.424225	−	0.905557i	$-0.360547\pi$
$929$	25.8603	0.848450	0.424225	+	0.905557i	$0.360547\pi$
$930$	21.7373	0.712795
$931$	−45.6377	−1.49572
$932$	−3.20498	−0.104982
$933$	−53.6317	−1.75582
$934$	34.2858	1.12187
$935$	4.95515	0.162051
$936$	1.12642	0.0368181
$937$	−14.3585	−0.469072	−0.234536	−	0.972107i	$-0.575357\pi$
$937$	−14.3585	−0.469072	−0.234536	+	0.972107i	$0.575357\pi$
$938$	13.4339	0.438633
$939$	−38.7247	−1.26373
$940$	26.2599	0.856503
$941$	−38.8128	−1.26526	−0.632631	−	0.774453i	$-0.718025\pi$
$941$	−38.8128	−1.26526	−0.632631	+	0.774453i	$0.718025\pi$
$942$	26.2434	0.855055
$943$	18.6846	0.608453
$944$	−3.22499	−0.104964
$945$	47.5020	1.54524
$946$	3.36179	0.109301
$947$	8.59005	0.279139	0.139570	−	0.990212i	$-0.455428\pi$
$947$	8.59005	0.279139	0.139570	+	0.990212i	$0.455428\pi$
$948$	10.8699	0.353039
$949$	4.97961	0.161645
$950$	−22.6962	−0.736362
$951$	−45.1177	−1.46304
$952$	−3.99232	−0.129392
$953$	46.4293	1.50399	0.751996	−	0.659167i	$-0.229091\pi$
$953$	46.4293	1.50399	0.751996	+	0.659167i	$0.229091\pi$
$954$	−10.5119	−0.340335
$955$	−62.9529	−2.03711
$956$	3.91975	0.126774
$957$	32.5427	1.05196
$958$	−23.0099	−0.743415
$959$	−79.7155	−2.57415
$960$	−6.73050	−0.217226
$961$	−20.5692	−0.663523
$962$	−0.389303	−0.0125516
$963$	−9.96205	−0.321022
$964$	16.9198	0.544950
$965$	−53.4747	−1.72141
$966$	−13.3107	−0.428266
$967$	−29.2131	−0.939431	−0.469716	−	0.882818i	$-0.655644\pi$
$967$	−29.2131	−0.939431	−0.469716	+	0.882818i	$0.655644\pi$
$968$	−8.35253	−0.268461
$969$	8.16682	0.262356
$970$	−46.2210	−1.48407
$971$	36.6586	1.17643	0.588216	−	0.808704i	$-0.299831\pi$
$971$	36.6586	1.17643	0.588216	+	0.808704i	$0.299831\pi$
$972$	−12.9636	−0.415806
$973$	−53.7014	−1.72159
$974$	13.9176	0.445947
$975$	9.57767	0.306731
$976$	−1.92513	−0.0616221
$977$	−54.5538	−1.74533	−0.872665	−	0.488320i	$-0.837610\pi$
$977$	−54.5538	−1.74533	−0.872665	+	0.488320i	$0.837610\pi$
$978$	40.8575	1.30648
$979$	−29.8361	−0.953565
$980$	−35.4314	−1.13182
$981$	16.9140	0.540021
$982$	29.1777	0.931097
$983$	−0.763825	−0.0243622	−0.0121811	−	0.999926i	$-0.503877\pi$
$983$	−0.763825	−0.0243622	−0.0121811	+	0.999926i	$0.503877\pi$
$984$	−25.7863	−0.822036
$985$	23.8759	0.760749
$986$	−9.04966	−0.288200
$987$	−71.6726	−2.28136
$988$	−3.51433	−0.111806
$989$	−3.11692	−0.0991124
$990$	−7.02019	−0.223116
$991$	53.0829	1.68623	0.843117	−	0.537731i	$-0.180718\pi$
$991$	53.0829	1.68623	0.843117	+	0.537731i	$0.180718\pi$
$992$	−3.22967	−0.102542
$993$	−58.4105	−1.85360
$994$	−27.4885	−0.871884
$995$	61.2894	1.94301
$996$	20.6460	0.654193
$997$	−1.97056	−0.0624083	−0.0312041	−	0.999513i	$-0.509934\pi$
$997$	−1.97056	−0.0624083	−0.0312041	+	0.999513i	$0.509934\pi$
$998$	28.4731	0.901299
$999$	1.59932	0.0506004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	446.2.a.e.1.6	✓	7
3.2	odd	2		4014.2.a.w.1.6		7
4.3	odd	2		3568.2.a.l.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
446.2.a.e.1.6	✓	7	1.1	even	1	trivial
3568.2.a.l.1.2		7	4.3	odd	2
4014.2.a.w.1.6		7	3.2	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:	\( N \)	\(=\)	\( 446 = 2 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	446.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.08198 q^{3} +1.00000 q^{4} -3.23274 q^{5} +2.08198 q^{6} +4.23794 q^{7} +1.00000 q^{8} +1.33463 q^{9} -3.23274 q^{10} +1.62710 q^{11} +2.08198 q^{12} +0.843989 q^{13} +4.23794 q^{14} -6.73050 q^{15} +1.00000 q^{16} -0.942042 q^{17} +1.33463 q^{18} -4.16396 q^{19} -3.23274 q^{20} +8.82331 q^{21} +1.62710 q^{22} -1.50859 q^{23} +2.08198 q^{24} +5.45063 q^{25} +0.843989 q^{26} -3.46725 q^{27} +4.23794 q^{28} +9.60642 q^{29} -6.73050 q^{30} -3.22967 q^{31} +1.00000 q^{32} +3.38759 q^{33} -0.942042 q^{34} -13.7002 q^{35} +1.33463 q^{36} -0.461265 q^{37} -4.16396 q^{38} +1.75717 q^{39} -3.23274 q^{40} -12.3855 q^{41} +8.82331 q^{42} +2.06612 q^{43} +1.62710 q^{44} -4.31453 q^{45} -1.50859 q^{46} -8.12310 q^{47} +2.08198 q^{48} +10.9602 q^{49} +5.45063 q^{50} -1.96131 q^{51} +0.843989 q^{52} -7.87624 q^{53} -3.46725 q^{54} -5.26001 q^{55} +4.23794 q^{56} -8.66927 q^{57} +9.60642 q^{58} -3.22499 q^{59} -6.73050 q^{60} -1.92513 q^{61} -3.22967 q^{62} +5.65611 q^{63} +1.00000 q^{64} -2.72840 q^{65} +3.38759 q^{66} +3.16991 q^{67} -0.942042 q^{68} -3.14085 q^{69} -13.7002 q^{70} -6.48629 q^{71} +1.33463 q^{72} +5.90009 q^{73} -0.461265 q^{74} +11.3481 q^{75} -4.16396 q^{76} +6.89557 q^{77} +1.75717 q^{78} +5.22096 q^{79} -3.23274 q^{80} -11.2227 q^{81} -12.3855 q^{82} +9.91652 q^{83} +8.82331 q^{84} +3.04538 q^{85} +2.06612 q^{86} +20.0004 q^{87} +1.62710 q^{88} -18.3369 q^{89} -4.31453 q^{90} +3.57678 q^{91} -1.50859 q^{92} -6.72411 q^{93} -8.12310 q^{94} +13.4610 q^{95} +2.08198 q^{96} +14.2978 q^{97} +10.9602 q^{98} +2.17159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + q^{3} + 7 q^{4} + 2 q^{5} + q^{6} + 6 q^{7} + 7 q^{8} + 8 q^{9} + 2 q^{10} + 9 q^{11} + q^{12} - 2 q^{13} + 6 q^{14} + 6 q^{15} + 7 q^{16} - 7 q^{17} + 8 q^{18} - 2 q^{19} + 2 q^{20}+ \cdots + 10 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + q^3 + 7 * q^4 + 2 * q^5 + q^6 + 6 * q^7 + 7 * q^8 + 8 * q^9 + 2 * q^10 + 9 * q^11 + q^12 - 2 * q^13 + 6 * q^14 + 6 * q^15 + 7 * q^16 - 7 * q^17 + 8 * q^18 - 2 * q^19 + 2 * q^20 - 2 * q^21 + 9 * q^22 + 15 * q^23 + q^24 + 13 * q^25 - 2 * q^26 + q^27 + 6 * q^28 + 9 * q^29 + 6 * q^30 - 2 * q^31 + 7 * q^32 - 25 * q^33 - 7 * q^34 - 4 * q^35 + 8 * q^36 + 5 * q^37 - 2 * q^38 - 20 * q^39 + 2 * q^40 - 33 * q^41 - 2 * q^42 + 20 * q^43 + 9 * q^44 - 34 * q^45 + 15 * q^46 - 2 * q^47 + q^48 + 3 * q^49 + 13 * q^50 - 9 * q^51 - 2 * q^52 - 13 * q^53 + q^54 - 18 * q^55 + 6 * q^56 - 58 * q^57 + 9 * q^58 + 9 * q^59 + 6 * q^60 + 8 * q^61 - 2 * q^62 - 16 * q^63 + 7 * q^64 - 44 * q^65 - 25 * q^66 + 29 * q^67 - 7 * q^68 + 23 * q^69 - 4 * q^70 + 8 * q^72 - 37 * q^73 + 5 * q^74 - 11 * q^75 - 2 * q^76 - 18 * q^77 - 20 * q^78 + 32 * q^79 + 2 * q^80 + 3 * q^81 - 33 * q^82 - 6 * q^83 - 2 * q^84 - 4 * q^85 + 20 * q^86 - 3 * q^87 + 9 * q^88 - 17 * q^89 - 34 * q^90 - 4 * q^91 + 15 * q^92 - 12 * q^93 - 2 * q^94 - 12 * q^95 + q^96 + 12 * q^97 + 3 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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