LMFDB - Embedded newform 4235.2.a.bo.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + \cdots - 176 $ x^18 - 2x^17 - 28x^16 + 54x^15 + 317x^14 - 580x^13 - 1874x^12 + 3158x^11 + 6290x^10 - 9228x^9 - 12411x^8 + 14224x^7 + 14618x^6 - 10744x^5 - 9817x^4 + 3146x^3 + 3048x^2 - 16*x - 176
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-1.95691$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.95691 q^{2} +0.270998 q^{3} +1.82949 q^{4} +1.00000 q^{5} +0.530318 q^{6} -1.00000 q^{7} -0.333679 q^{8} -2.92656 q^{9} +O(q^{10})$	\(q+1.95691 q^{2} +0.270998 q^{3} +1.82949 q^{4} +1.00000 q^{5} +0.530318 q^{6} -1.00000 q^{7} -0.333679 q^{8} -2.92656 q^{9} +1.95691 q^{10} +0.495788 q^{12} +0.690259 q^{13} -1.95691 q^{14} +0.270998 q^{15} -4.31195 q^{16} +3.49086 q^{17} -5.72701 q^{18} +6.97577 q^{19} +1.82949 q^{20} -0.270998 q^{21} +7.74463 q^{23} -0.0904264 q^{24} +1.00000 q^{25} +1.35077 q^{26} -1.60609 q^{27} -1.82949 q^{28} +4.56021 q^{29} +0.530318 q^{30} +1.84701 q^{31} -7.77073 q^{32} +6.83129 q^{34} -1.00000 q^{35} -5.35410 q^{36} -9.07844 q^{37} +13.6509 q^{38} +0.187059 q^{39} -0.333679 q^{40} +9.13482 q^{41} -0.530318 q^{42} -1.88323 q^{43} -2.92656 q^{45} +15.1555 q^{46} +6.83067 q^{47} -1.16853 q^{48} +1.00000 q^{49} +1.95691 q^{50} +0.946017 q^{51} +1.26282 q^{52} -3.36668 q^{53} -3.14296 q^{54} +0.333679 q^{56} +1.89042 q^{57} +8.92390 q^{58} +9.61424 q^{59} +0.495788 q^{60} -4.07459 q^{61} +3.61443 q^{62} +2.92656 q^{63} -6.58270 q^{64} +0.690259 q^{65} +8.79817 q^{67} +6.38648 q^{68} +2.09878 q^{69} -1.95691 q^{70} +14.9006 q^{71} +0.976531 q^{72} -7.61343 q^{73} -17.7657 q^{74} +0.270998 q^{75} +12.7621 q^{76} +0.366057 q^{78} -14.2969 q^{79} -4.31195 q^{80} +8.34443 q^{81} +17.8760 q^{82} +0.222730 q^{83} -0.495788 q^{84} +3.49086 q^{85} -3.68530 q^{86} +1.23581 q^{87} +10.4852 q^{89} -5.72701 q^{90} -0.690259 q^{91} +14.1687 q^{92} +0.500537 q^{93} +13.3670 q^{94} +6.97577 q^{95} -2.10585 q^{96} -12.6526 q^{97} +1.95691 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9}+O(q^{10}) $ 18 * q - 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 + q^6 - 18 * q^7 - 6 * q^8 + 37 * q^9	\( 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9} - 2 q^{10} + 15 q^{12} - 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} + 5 q^{17} - 2 q^{18} - 15 q^{19} + 24 q^{20} - 5 q^{21} + 4 q^{23} - 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} - 24 q^{28} + 6 q^{29} + q^{30} + 22 q^{31} + 6 q^{32} + 44 q^{34} - 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} + 38 q^{39} - 6 q^{40} - 7 q^{41} - q^{42} - 10 q^{43} + 37 q^{45} + 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} - 2 q^{50} + 11 q^{51} - 18 q^{52} + 23 q^{53} - 13 q^{54} + 6 q^{56} + 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} - 17 q^{61} - 57 q^{62} - 37 q^{63} + 64 q^{64} - 8 q^{65} + 29 q^{67} + 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} + 77 q^{72} - 3 q^{73} + 48 q^{74} + 5 q^{75} - 47 q^{76} + 10 q^{78} + 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} - 9 q^{83} - 15 q^{84} + 5 q^{85} + 25 q^{86} - 23 q^{87} + 59 q^{89} - 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} + 19 q^{94} - 15 q^{95} - 14 q^{96} + 30 q^{97} - 2 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 + q^6 - 18 * q^7 - 6 * q^8 + 37 * q^9 - 2 * q^10 + 15 * q^12 - 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 + 5 * q^17 - 2 * q^18 - 15 * q^19 + 24 * q^20 - 5 * q^21 + 4 * q^23 - 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 - 24 * q^28 + 6 * q^29 + q^30 + 22 * q^31 + 6 * q^32 + 44 * q^34 - 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 + 38 * q^39 - 6 * q^40 - 7 * q^41 - q^42 - 10 * q^43 + 37 * q^45 + 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 - 2 * q^50 + 11 * q^51 - 18 * q^52 + 23 * q^53 - 13 * q^54 + 6 * q^56 + 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 - 17 * q^61 - 57 * q^62 - 37 * q^63 + 64 * q^64 - 8 * q^65 + 29 * q^67 + 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 + 77 * q^72 - 3 * q^73 + 48 * q^74 + 5 * q^75 - 47 * q^76 + 10 * q^78 + 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 - 9 * q^83 - 15 * q^84 + 5 * q^85 + 25 * q^86 - 23 * q^87 + 59 * q^89 - 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 + 19 * q^94 - 15 * q^95 - 14 * q^96 + 30 * q^97 - 2 * q^98

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 $

$2$	1.95691	1.38374	0.691871	−	0.722021i	$-0.256787\pi$
$2$	1.95691	1.38374	0.691871	+	0.722021i	$0.256787\pi$
$3$	0.270998	0.156461	0.0782305	−	0.996935i	$-0.475073\pi$
$3$	0.270998	0.156461	0.0782305	+	0.996935i	$0.475073\pi$
$4$	1.82949	0.914743
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.530318	0.216502
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.333679	−0.117973
$9$	−2.92656	−0.975520
$10$	1.95691	0.618828
$11$	0	0
$11$	0	0
$12$	0.495788	0.143122
$13$	0.690259	0.191443	0.0957217	−	0.995408i	$-0.469484\pi$
$13$	0.690259	0.191443	0.0957217	+	0.995408i	$0.469484\pi$
$14$	−1.95691	−0.523006
$15$	0.270998	0.0699714
$16$	−4.31195	−1.07799
$17$	3.49086	0.846658	0.423329	−	0.905976i	$-0.360861\pi$
$17$	3.49086	0.846658	0.423329	+	0.905976i	$0.360861\pi$
$18$	−5.72701	−1.34987
$19$	6.97577	1.60035	0.800176	−	0.599765i	$-0.204739\pi$
$19$	6.97577	1.60035	0.800176	+	0.599765i	$0.204739\pi$
$20$	1.82949	0.409086
$21$	−0.270998	−0.0591367
$22$	0	0
$23$	7.74463	1.61487	0.807433	−	0.589959i	$-0.200856\pi$
$23$	7.74463	1.61487	0.807433	+	0.589959i	$0.200856\pi$
$24$	−0.0904264	−0.0184582
$25$	1.00000	0.200000
$26$	1.35077	0.264908
$27$	−1.60609	−0.309092
$28$	−1.82949	−0.345740
$29$	4.56021	0.846809	0.423404	−	0.905941i	$-0.360835\pi$
$29$	4.56021	0.846809	0.423404	+	0.905941i	$0.360835\pi$
$30$	0.530318	0.0968225
$31$	1.84701	0.331733	0.165867	−	0.986148i	$-0.446958\pi$
$31$	1.84701	0.331733	0.165867	+	0.986148i	$0.446958\pi$
$32$	−7.77073	−1.37368
$33$	0	0
$34$	6.83129	1.17156
$35$	−1.00000	−0.169031
$36$	−5.35410	−0.892350
$37$	−9.07844	−1.49249	−0.746243	−	0.665674i	$-0.768144\pi$
$37$	−9.07844	−1.49249	−0.746243	+	0.665674i	$0.768144\pi$
$38$	13.6509	2.21448
$39$	0.187059	0.0299534
$40$	−0.333679	−0.0527593
$41$	9.13482	1.42662	0.713310	−	0.700849i	$-0.247195\pi$
$41$	9.13482	1.42662	0.713310	+	0.700849i	$0.247195\pi$
$42$	−0.530318	−0.0818299
$43$	−1.88323	−0.287189	−0.143595	−	0.989637i	$-0.545866\pi$
$43$	−1.88323	−0.287189	−0.143595	+	0.989637i	$0.545866\pi$
$44$	0	0
$45$	−2.92656	−0.436266
$46$	15.1555	2.23456
$47$	6.83067	0.996356	0.498178	−	0.867075i	$-0.334003\pi$
$47$	6.83067	0.996356	0.498178	+	0.867075i	$0.334003\pi$
$48$	−1.16853	−0.168663
$49$	1.00000	0.142857
$50$	1.95691	0.276749
$51$	0.946017	0.132469
$52$	1.26282	0.175122
$53$	−3.36668	−0.462448	−0.231224	−	0.972900i	$-0.574273\pi$
$53$	−3.36668	−0.462448	−0.231224	+	0.972900i	$0.574273\pi$
$54$	−3.14296	−0.427703
$55$	0	0
$56$	0.333679	0.0445897
$57$	1.89042	0.250393
$58$	8.92390	1.17177
$59$	9.61424	1.25167	0.625834	−	0.779956i	$-0.284759\pi$
$59$	9.61424	1.25167	0.625834	+	0.779956i	$0.284759\pi$
$60$	0.495788	0.0640059
$61$	−4.07459	−0.521697	−0.260849	−	0.965380i	$-0.584002\pi$
$61$	−4.07459	−0.521697	−0.260849	+	0.965380i	$0.584002\pi$
$62$	3.61443	0.459033
$63$	2.92656	0.368712
$64$	−6.58270	−0.822838
$65$	0.690259	0.0856161
$66$	0	0
$67$	8.79817	1.07487	0.537434	−	0.843306i	$-0.319394\pi$
$67$	8.79817	1.07487	0.537434	+	0.843306i	$0.319394\pi$
$68$	6.38648	0.774474
$69$	2.09878	0.252663
$70$	−1.95691	−0.233895
$71$	14.9006	1.76838	0.884189	−	0.467129i	$-0.154712\pi$
$71$	14.9006	1.76838	0.884189	+	0.467129i	$0.154712\pi$
$72$	0.976531	0.115085
$73$	−7.61343	−0.891084	−0.445542	−	0.895261i	$-0.646989\pi$
$73$	−7.61343	−0.891084	−0.445542	+	0.895261i	$0.646989\pi$
$74$	−17.7657	−2.06522
$75$	0.270998	0.0312922
$76$	12.7621	1.46391
$77$	0	0
$78$	0.366057	0.0414478
$79$	−14.2969	−1.60853	−0.804264	−	0.594272i	$-0.797440\pi$
$79$	−14.2969	−1.60853	−0.804264	+	0.594272i	$0.797440\pi$
$80$	−4.31195	−0.482091
$81$	8.34443	0.927159
$82$	17.8760	1.97407
$83$	0.222730	0.0244478	0.0122239	−	0.999925i	$-0.496109\pi$
$83$	0.222730	0.0244478	0.0122239	+	0.999925i	$0.496109\pi$
$84$	−0.495788	−0.0540949
$85$	3.49086	0.378637
$86$	−3.68530	−0.397396
$87$	1.23581	0.132492
$88$	0	0
$89$	10.4852	1.11143	0.555717	−	0.831372i	$-0.312444\pi$
$89$	10.4852	1.11143	0.555717	+	0.831372i	$0.312444\pi$
$90$	−5.72701	−0.603680
$91$	−0.690259	−0.0723588
$92$	14.1687	1.47719
$93$	0.500537	0.0519033
$94$	13.3670	1.37870
$95$	6.97577	0.715699
$96$	−2.10585	−0.214928
$97$	−12.6526	−1.28467	−0.642337	−	0.766423i	$-0.722035\pi$
$97$	−12.6526	−1.28467	−0.642337	+	0.766423i	$0.722035\pi$
$98$	1.95691	0.197678
$99$	0	0
$100$	1.82949	0.182949
$101$	4.87420	0.485001	0.242501	−	0.970151i	$-0.422032\pi$
$101$	4.87420	0.485001	0.242501	+	0.970151i	$0.422032\pi$
$102$	1.85127	0.183303
$103$	12.6214	1.24362	0.621811	−	0.783167i	$-0.286397\pi$
$103$	12.6214	1.24362	0.621811	+	0.783167i	$0.286397\pi$
$104$	−0.230325	−0.0225852
$105$	−0.270998	−0.0264467
$106$	−6.58827	−0.639910
$107$	10.2588	0.991759	0.495879	−	0.868391i	$-0.334846\pi$
$107$	10.2588	0.991759	0.495879	+	0.868391i	$0.334846\pi$
$108$	−2.93832	−0.282740
$109$	−3.94667	−0.378022	−0.189011	−	0.981975i	$-0.560528\pi$
$109$	−3.94667	−0.378022	−0.189011	+	0.981975i	$0.560528\pi$
$110$	0	0
$111$	−2.46024	−0.233516
$112$	4.31195	0.407441
$113$	−10.8083	−1.01675	−0.508377	−	0.861134i	$-0.669754\pi$
$113$	−10.8083	−1.01675	−0.508377	+	0.861134i	$0.669754\pi$
$114$	3.69938	0.346479
$115$	7.74463	0.722190
$116$	8.34284	0.774613
$117$	−2.02009	−0.186757
$118$	18.8142	1.73199
$119$	−3.49086	−0.320007
$120$	−0.0904264	−0.00825476
$121$	0	0
$122$	−7.97359	−0.721895
$123$	2.47552	0.223210
$124$	3.37908	0.303451
$125$	1.00000	0.0894427
$126$	5.72701	0.510202
$127$	7.80577	0.692650	0.346325	−	0.938115i	$-0.387430\pi$
$127$	7.80577	0.692650	0.346325	+	0.938115i	$0.387430\pi$
$128$	2.65973	0.235089
$129$	−0.510351	−0.0449339
$130$	1.35077	0.118471
$131$	−11.5221	−1.00669	−0.503344	−	0.864086i	$-0.667897\pi$
$131$	−11.5221	−1.00669	−0.503344	+	0.864086i	$0.667897\pi$
$132$	0	0
$133$	−6.97577	−0.604876
$134$	17.2172	1.48734
$135$	−1.60609	−0.138230
$136$	−1.16483	−0.0998830
$137$	9.42765	0.805458	0.402729	−	0.915319i	$-0.368062\pi$
$137$	9.42765	0.805458	0.402729	+	0.915319i	$0.368062\pi$
$138$	4.10712	0.349621
$139$	−17.4083	−1.47655	−0.738277	−	0.674498i	$-0.764360\pi$
$139$	−17.4083	−1.47655	−0.738277	+	0.674498i	$0.764360\pi$
$140$	−1.82949	−0.154620
$141$	1.85110	0.155891
$142$	29.1591	2.44698
$143$	0	0
$144$	12.6192	1.05160
$145$	4.56021	0.378704
$146$	−14.8988	−1.23303
$147$	0.270998	0.0223516
$148$	−16.6089	−1.36524
$149$	12.4852	1.02283	0.511413	−	0.859335i	$-0.329122\pi$
$149$	12.4852	1.02283	0.511413	+	0.859335i	$0.329122\pi$
$150$	0.530318	0.0433003
$151$	−8.99731	−0.732191	−0.366095	−	0.930577i	$-0.619306\pi$
$151$	−8.99731	−0.732191	−0.366095	+	0.930577i	$0.619306\pi$
$152$	−2.32767	−0.188799
$153$	−10.2162	−0.825932
$154$	0	0
$155$	1.84701	0.148356
$156$	0.342222	0.0273997
$157$	18.8322	1.50298	0.751488	−	0.659747i	$-0.229337\pi$
$157$	18.8322	1.50298	0.751488	+	0.659747i	$0.229337\pi$
$158$	−27.9777	−2.22579
$159$	−0.912363	−0.0723551
$160$	−7.77073	−0.614330
$161$	−7.74463	−0.610362
$162$	16.3293	1.28295
$163$	−0.286944	−0.0224752	−0.0112376	−	0.999937i	$-0.503577\pi$
$163$	−0.286944	−0.0224752	−0.0112376	+	0.999937i	$0.503577\pi$
$164$	16.7120	1.30499
$165$	0	0
$166$	0.435862	0.0338295
$167$	0.408093	0.0315792	0.0157896	−	0.999875i	$-0.494974\pi$
$167$	0.408093	0.0315792	0.0157896	+	0.999875i	$0.494974\pi$
$168$	0.0904264	0.00697655
$169$	−12.5235	−0.963349
$170$	6.83129	0.523936
$171$	−20.4150	−1.56118
$172$	−3.44534	−0.262705
$173$	−22.8940	−1.74060	−0.870300	−	0.492522i	$-0.836075\pi$
$173$	−22.8940	−1.74060	−0.870300	+	0.492522i	$0.836075\pi$
$174$	2.41836	0.183335
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	2.60544	0.195837
$178$	20.5186	1.53794
$179$	1.11958	0.0836815	0.0418408	−	0.999124i	$-0.486678\pi$
$179$	1.11958	0.0836815	0.0418408	+	0.999124i	$0.486678\pi$
$180$	−5.35410	−0.399071
$181$	14.3312	1.06523	0.532614	−	0.846358i	$-0.321210\pi$
$181$	14.3312	1.06523	0.532614	+	0.846358i	$0.321210\pi$
$182$	−1.35077	−0.100126
$183$	−1.10421	−0.0816252
$184$	−2.58422	−0.190511
$185$	−9.07844	−0.667460
$186$	0.979504	0.0718208
$187$	0	0
$188$	12.4966	0.911410
$189$	1.60609	0.116826
$190$	13.6509	0.990343
$191$	−19.0676	−1.37968	−0.689842	−	0.723960i	$-0.742320\pi$
$191$	−19.0676	−1.37968	−0.689842	+	0.723960i	$0.742320\pi$
$192$	−1.78390	−0.128742
$193$	−11.3892	−0.819813	−0.409907	−	0.912127i	$-0.634439\pi$
$193$	−11.3892	−0.819813	−0.409907	+	0.912127i	$0.634439\pi$
$194$	−24.7599	−1.77766
$195$	0.187059	0.0133956
$196$	1.82949	0.130678
$197$	9.21509	0.656548	0.328274	−	0.944583i	$-0.393533\pi$
$197$	9.21509	0.656548	0.328274	+	0.944583i	$0.393533\pi$
$198$	0	0
$199$	−26.5142	−1.87954	−0.939770	−	0.341807i	$-0.888961\pi$
$199$	−26.5142	−1.87954	−0.939770	+	0.341807i	$0.888961\pi$
$200$	−0.333679	−0.0235947
$201$	2.38429	0.168175
$202$	9.53836	0.671117
$203$	−4.56021	−0.320064
$204$	1.73072	0.121175
$205$	9.13482	0.638004
$206$	24.6989	1.72085
$207$	−22.6651	−1.57533
$208$	−2.97636	−0.206374
$209$	0	0
$210$	−0.530318	−0.0365954
$211$	−13.5661	−0.933929	−0.466965	−	0.884276i	$-0.654652\pi$
$211$	−13.5661	−0.933929	−0.466965	+	0.884276i	$0.654652\pi$
$212$	−6.15929	−0.423022
$213$	4.03804	0.276682
$214$	20.0756	1.37234
$215$	−1.88323	−0.128435
$216$	0.535917	0.0364646
$217$	−1.84701	−0.125383
$218$	−7.72327	−0.523086
$219$	−2.06323	−0.139420
$220$	0	0
$221$	2.40960	0.162087
$222$	−4.81446	−0.323126
$223$	−15.7550	−1.05503	−0.527517	−	0.849545i	$-0.676877\pi$
$223$	−15.7550	−1.05503	−0.527517	+	0.849545i	$0.676877\pi$
$224$	7.77073	0.519204
$225$	−2.92656	−0.195104
$226$	−21.1507	−1.40693
$227$	7.49135	0.497218	0.248609	−	0.968604i	$-0.420027\pi$
$227$	7.49135	0.497218	0.248609	+	0.968604i	$0.420027\pi$
$228$	3.45850	0.229045
$229$	15.3136	1.01195	0.505976	−	0.862548i	$-0.331133\pi$
$229$	15.3136	1.01195	0.505976	+	0.862548i	$0.331133\pi$
$230$	15.1555	0.999325
$231$	0	0
$232$	−1.52164	−0.0999008
$233$	11.3301	0.742257	0.371129	−	0.928581i	$-0.378971\pi$
$233$	11.3301	0.742257	0.371129	+	0.928581i	$0.378971\pi$
$234$	−3.95312	−0.258424
$235$	6.83067	0.445584
$236$	17.5891	1.14495
$237$	−3.87444	−0.251672
$238$	−6.83129	−0.442807
$239$	−1.37872	−0.0891817	−0.0445908	−	0.999005i	$-0.514198\pi$
$239$	−1.37872	−0.0891817	−0.0445908	+	0.999005i	$0.514198\pi$
$240$	−1.16853	−0.0754284
$241$	−10.5864	−0.681927	−0.340964	−	0.940076i	$-0.610753\pi$
$241$	−10.5864	−0.681927	−0.340964	+	0.940076i	$0.610753\pi$
$242$	0	0
$243$	7.07959	0.454156
$244$	−7.45440	−0.477219
$245$	1.00000	0.0638877
$246$	4.84436	0.308865
$247$	4.81509	0.306377
$248$	−0.616309	−0.0391356
$249$	0.0603595	0.00382512
$250$	1.95691	0.123766
$251$	12.1269	0.765441	0.382721	−	0.923864i	$-0.374987\pi$
$251$	12.1269	0.765441	0.382721	+	0.923864i	$0.374987\pi$
$252$	5.35410	0.337277
$253$	0	0
$254$	15.2752	0.958449
$255$	0.946017	0.0592419
$256$	18.3702	1.14814
$257$	−25.8821	−1.61448	−0.807242	−	0.590221i	$-0.799041\pi$
$257$	−25.8821	−1.61448	−0.807242	+	0.590221i	$0.799041\pi$
$258$	−0.998710	−0.0621770
$259$	9.07844	0.564107
$260$	1.26282	0.0783168
$261$	−13.3457	−0.826079
$262$	−22.5476	−1.39300
$263$	−5.75078	−0.354609	−0.177304	−	0.984156i	$-0.556738\pi$
$263$	−5.75078	−0.354609	−0.177304	+	0.984156i	$0.556738\pi$
$264$	0	0
$265$	−3.36668	−0.206813
$266$	−13.6509	−0.836993
$267$	2.84148	0.173896
$268$	16.0961	0.983228
$269$	−6.41450	−0.391099	−0.195550	−	0.980694i	$-0.562649\pi$
$269$	−6.41450	−0.391099	−0.195550	+	0.980694i	$0.562649\pi$
$270$	−3.14296	−0.191275
$271$	22.1740	1.34697	0.673486	−	0.739200i	$-0.264796\pi$
$271$	22.1740	1.34697	0.673486	+	0.739200i	$0.264796\pi$
$272$	−15.0524	−0.912687
$273$	−0.187059	−0.0113213
$274$	18.4490	1.11455
$275$	0	0
$276$	3.83969	0.231122
$277$	0.516004	0.0310037	0.0155018	−	0.999880i	$-0.495065\pi$
$277$	0.516004	0.0310037	0.0155018	+	0.999880i	$0.495065\pi$
$278$	−34.0664	−2.04317
$279$	−5.40539	−0.323612
$280$	0.333679	0.0199411
$281$	4.30303	0.256697	0.128349	−	0.991729i	$-0.459032\pi$
$281$	4.30303	0.256697	0.128349	+	0.991729i	$0.459032\pi$
$282$	3.62243	0.215713
$283$	−23.6322	−1.40479	−0.702394	−	0.711788i	$-0.747885\pi$
$283$	−23.6322	−1.40479	−0.702394	+	0.711788i	$0.747885\pi$
$284$	27.2605	1.61761
$285$	1.89042	0.111979
$286$	0	0
$287$	−9.13482	−0.539211
$288$	22.7415	1.34006
$289$	−4.81390	−0.283171
$290$	8.92390	0.524029
$291$	−3.42882	−0.201001
$292$	−13.9287	−0.815113
$293$	−2.95546	−0.172660	−0.0863298	−	0.996267i	$-0.527514\pi$
$293$	−2.95546	−0.172660	−0.0863298	+	0.996267i	$0.527514\pi$
$294$	0.530318	0.0309288
$295$	9.61424	0.559763
$296$	3.02928	0.176073
$297$	0	0
$298$	24.4323	1.41533
$299$	5.34580	0.309156
$300$	0.495788	0.0286243
$301$	1.88323	0.108547
$302$	−17.6069	−1.01316
$303$	1.32090	0.0758837
$304$	−30.0792	−1.72516
$305$	−4.07459	−0.233310
$306$	−19.9922	−1.14288
$307$	9.80557	0.559634	0.279817	−	0.960053i	$-0.409726\pi$
$307$	9.80557	0.559634	0.279817	+	0.960053i	$0.409726\pi$
$308$	0	0
$309$	3.42037	0.194578
$310$	3.61443	0.205286
$311$	−18.2920	−1.03725	−0.518623	−	0.855003i	$-0.673555\pi$
$311$	−18.2920	−1.03725	−0.518623	+	0.855003i	$0.673555\pi$
$312$	−0.0624177	−0.00353370
$313$	18.6547	1.05443	0.527214	−	0.849732i	$-0.323236\pi$
$313$	18.6547	1.05443	0.527214	+	0.849732i	$0.323236\pi$
$314$	36.8529	2.07973
$315$	2.92656	0.164893
$316$	−26.1560	−1.47139
$317$	12.1975	0.685081	0.342541	−	0.939503i	$-0.388713\pi$
$317$	12.1975	0.685081	0.342541	+	0.939503i	$0.388713\pi$
$318$	−1.78541	−0.100121
$319$	0	0
$320$	−6.58270	−0.367984
$321$	2.78013	0.155172
$322$	−15.1555	−0.844584
$323$	24.3514	1.35495
$324$	15.2660	0.848113
$325$	0.690259	0.0382887
$326$	−0.561522	−0.0310998
$327$	−1.06954	−0.0591457
$328$	−3.04810	−0.168303
$329$	−6.83067	−0.376587
$330$	0	0
$331$	32.2293	1.77148	0.885740	−	0.464182i	$-0.153652\pi$
$331$	32.2293	1.77148	0.885740	+	0.464182i	$0.153652\pi$
$332$	0.407482	0.0223635
$333$	26.5686	1.45595
$334$	0.798601	0.0436975
$335$	8.79817	0.480696
$336$	1.16853	0.0637486
$337$	10.0358	0.546684	0.273342	−	0.961917i	$-0.411871\pi$
$337$	10.0358	0.546684	0.273342	+	0.961917i	$0.411871\pi$
$338$	−24.5074	−1.33303
$339$	−2.92902	−0.159082
$340$	6.38648	0.346356
$341$	0	0
$342$	−39.9503	−2.16026
$343$	−1.00000	−0.0539949
$344$	0.628393	0.0338807
$345$	2.09878	0.112995
$346$	−44.8015	−2.40854
$347$	−34.1152	−1.83140	−0.915700	−	0.401863i	$-0.868363\pi$
$347$	−34.1152	−1.83140	−0.915700	+	0.401863i	$0.868363\pi$
$348$	2.26089	0.121197
$349$	−19.3382	−1.03515	−0.517576	−	0.855637i	$-0.673166\pi$
$349$	−19.3382	−1.03515	−0.517576	+	0.855637i	$0.673166\pi$
$350$	−1.95691	−0.104601
$351$	−1.10862	−0.0591736
$352$	0	0
$353$	−15.2975	−0.814201	−0.407101	−	0.913383i	$-0.633460\pi$
$353$	−15.2975	−0.814201	−0.407101	+	0.913383i	$0.633460\pi$
$354$	5.09861	0.270988
$355$	14.9006	0.790843
$356$	19.1826	1.01668
$357$	−0.946017	−0.0500685
$358$	2.19092	0.115794
$359$	−6.72779	−0.355079	−0.177540	−	0.984114i	$-0.556814\pi$
$359$	−6.72779	−0.355079	−0.177540	+	0.984114i	$0.556814\pi$
$360$	0.976531	0.0514677
$361$	29.6614	1.56113
$362$	28.0448	1.47400
$363$	0	0
$364$	−1.26282	−0.0661898
$365$	−7.61343	−0.398505
$366$	−2.16083	−0.112948
$367$	28.6442	1.49521	0.747607	−	0.664141i	$-0.231203\pi$
$367$	28.6442	1.49521	0.747607	+	0.664141i	$0.231203\pi$
$368$	−33.3945	−1.74081
$369$	−26.7336	−1.39170
$370$	−17.7657	−0.923593
$371$	3.36668	0.174789
$372$	0.915726	0.0474782
$373$	−0.425780	−0.0220461	−0.0110230	−	0.999939i	$-0.503509\pi$
$373$	−0.425780	−0.0220461	−0.0110230	+	0.999939i	$0.503509\pi$
$374$	0	0
$375$	0.270998	0.0139943
$376$	−2.27925	−0.117543
$377$	3.14772	0.162116
$378$	3.14296	0.161657
$379$	−15.9181	−0.817656	−0.408828	−	0.912612i	$-0.634062\pi$
$379$	−15.9181	−0.817656	−0.408828	+	0.912612i	$0.634062\pi$
$380$	12.7621	0.654681
$381$	2.11535	0.108373
$382$	−37.3135	−1.90913
$383$	−9.16735	−0.468430	−0.234215	−	0.972185i	$-0.575252\pi$
$383$	−9.16735	−0.468430	−0.234215	+	0.972185i	$0.575252\pi$
$384$	0.720782	0.0367823
$385$	0	0
$386$	−22.2876	−1.13441
$387$	5.51138	0.280159
$388$	−23.1477	−1.17515
$389$	9.38008	0.475589	0.237794	−	0.971315i	$-0.423576\pi$
$389$	9.38008	0.475589	0.237794	+	0.971315i	$0.423576\pi$
$390$	0.366057	0.0185360
$391$	27.0354	1.36724
$392$	−0.333679	−0.0168533
$393$	−3.12246	−0.157507
$394$	18.0331	0.908493
$395$	−14.2969	−0.719356
$396$	0	0
$397$	−14.1721	−0.711280	−0.355640	−	0.934623i	$-0.615737\pi$
$397$	−14.1721	−0.711280	−0.355640	+	0.934623i	$0.615737\pi$
$398$	−51.8858	−2.60080
$399$	−1.89042	−0.0946395
$400$	−4.31195	−0.215598
$401$	15.4577	0.771923	0.385961	−	0.922515i	$-0.373870\pi$
$401$	15.4577	0.771923	0.385961	+	0.922515i	$0.373870\pi$
$402$	4.66583	0.232711
$403$	1.27492	0.0635081
$404$	8.91729	0.443652
$405$	8.34443	0.414638
$406$	−8.92390	−0.442886
$407$	0	0
$408$	−0.315666	−0.0156278
$409$	−26.6037	−1.31547	−0.657734	−	0.753250i	$-0.728485\pi$
$409$	−26.6037	−1.31547	−0.657734	+	0.753250i	$0.728485\pi$
$410$	17.8760	0.882833
$411$	2.55488	0.126023
$412$	23.0907	1.13760
$413$	−9.61424	−0.473086
$414$	−44.3535	−2.17986
$415$	0.222730	0.0109334
$416$	−5.36382	−0.262983
$417$	−4.71762	−0.231023
$418$	0	0
$419$	20.1927	0.986477	0.493239	−	0.869894i	$-0.335813\pi$
$419$	20.1927	0.986477	0.493239	+	0.869894i	$0.335813\pi$
$420$	−0.495788	−0.0241920
$421$	5.62890	0.274336	0.137168	−	0.990548i	$-0.456200\pi$
$421$	5.62890	0.274336	0.137168	+	0.990548i	$0.456200\pi$
$422$	−26.5476	−1.29232
$423$	−19.9904	−0.971965
$424$	1.12339	0.0545566
$425$	3.49086	0.169332
$426$	7.90207	0.382857
$427$	4.07459	0.197183
$428$	18.7684	0.907205
$429$	0	0
$430$	−3.68530	−0.177721
$431$	7.11837	0.342880	0.171440	−	0.985195i	$-0.445158\pi$
$431$	7.11837	0.342880	0.171440	+	0.985195i	$0.445158\pi$
$432$	6.92537	0.333197
$433$	−16.2721	−0.781985	−0.390992	−	0.920394i	$-0.627868\pi$
$433$	−16.2721	−0.781985	−0.390992	+	0.920394i	$0.627868\pi$
$434$	−3.61443	−0.173498
$435$	1.23581	0.0592524
$436$	−7.22038	−0.345793
$437$	54.0248	2.58435
$438$	−4.03754	−0.192921
$439$	−18.0043	−0.859300	−0.429650	−	0.902996i	$-0.641363\pi$
$439$	−18.0043	−0.859300	−0.429650	+	0.902996i	$0.641363\pi$
$440$	0	0
$441$	−2.92656	−0.139360
$442$	4.71536	0.224287
$443$	−9.64033	−0.458026	−0.229013	−	0.973423i	$-0.573550\pi$
$443$	−9.64033	−0.458026	−0.229013	+	0.973423i	$0.573550\pi$
$444$	−4.50098	−0.213607
$445$	10.4852	0.497048
$446$	−30.8311	−1.45989
$447$	3.38346	0.160032
$448$	6.58270	0.311003
$449$	17.1921	0.811344	0.405672	−	0.914019i	$-0.367038\pi$
$449$	17.1921	0.811344	0.405672	+	0.914019i	$0.367038\pi$
$450$	−5.72701	−0.269974
$451$	0	0
$452$	−19.7735	−0.930070
$453$	−2.43825	−0.114559
$454$	14.6599	0.688022
$455$	−0.690259	−0.0323599
$456$	−0.630794	−0.0295396
$457$	8.19755	0.383465	0.191733	−	0.981447i	$-0.438589\pi$
$457$	8.19755	0.383465	0.191733	+	0.981447i	$0.438589\pi$
$458$	29.9673	1.40028
$459$	−5.60662	−0.261695
$460$	14.1687	0.660619
$461$	−13.5177	−0.629581	−0.314791	−	0.949161i	$-0.601934\pi$
$461$	−13.5177	−0.629581	−0.314791	+	0.949161i	$0.601934\pi$
$462$	0	0
$463$	−1.62055	−0.0753136	−0.0376568	−	0.999291i	$-0.511989\pi$
$463$	−1.62055	−0.0753136	−0.0376568	+	0.999291i	$0.511989\pi$
$464$	−19.6634	−0.912850
$465$	0.500537	0.0232118
$466$	22.1719	1.02709
$467$	−0.241272	−0.0111647	−0.00558237	−	0.999984i	$-0.501777\pi$
$467$	−0.241272	−0.0111647	−0.00558237	+	0.999984i	$0.501777\pi$
$468$	−3.69572	−0.170835
$469$	−8.79817	−0.406262
$470$	13.3670	0.616573
$471$	5.10350	0.235157
$472$	−3.20807	−0.147663
$473$	0	0
$474$	−7.58191	−0.348249
$475$	6.97577	0.320070
$476$	−6.38648	−0.292724
$477$	9.85278	0.451128
$478$	−2.69802	−0.123404
$479$	−0.429644	−0.0196309	−0.00981546	−	0.999952i	$-0.503124\pi$
$479$	−0.429644	−0.0196309	−0.00981546	+	0.999952i	$0.503124\pi$
$480$	−2.10585	−0.0961187
$481$	−6.26647	−0.285727
$482$	−20.7165	−0.943612
$483$	−2.09878	−0.0954978
$484$	0	0
$485$	−12.6526	−0.574523
$486$	13.8541	0.628435
$487$	27.7381	1.25693	0.628466	−	0.777837i	$-0.283683\pi$
$487$	27.7381	1.25693	0.628466	+	0.777837i	$0.283683\pi$
$488$	1.35960	0.0615464
$489$	−0.0777612	−0.00351648
$490$	1.95691	0.0884041
$491$	26.1024	1.17798	0.588992	−	0.808139i	$-0.299525\pi$
$491$	26.1024	1.17798	0.588992	+	0.808139i	$0.299525\pi$
$492$	4.52893	0.204180
$493$	15.9190	0.716957
$494$	9.42269	0.423947
$495$	0	0
$496$	−7.96423	−0.357604
$497$	−14.9006	−0.668384
$498$	0.118118	0.00529299
$499$	−8.12782	−0.363851	−0.181926	−	0.983312i	$-0.558233\pi$
$499$	−8.12782	−0.363851	−0.181926	+	0.983312i	$0.558233\pi$
$500$	1.82949	0.0818171
$501$	0.110593	0.00494091
$502$	23.7312	1.05917
$503$	14.7714	0.658623	0.329312	−	0.944221i	$-0.393183\pi$
$503$	14.7714	0.658623	0.329312	+	0.944221i	$0.393183\pi$
$504$	−0.976531	−0.0434982
$505$	4.87420	0.216899
$506$	0	0
$507$	−3.39386	−0.150727
$508$	14.2805	0.633597
$509$	42.6444	1.89018	0.945090	−	0.326811i	$-0.105974\pi$
$509$	42.6444	1.89018	0.945090	+	0.326811i	$0.105974\pi$
$510$	1.85127	0.0819755
$511$	7.61343	0.336798
$512$	30.6294	1.35364
$513$	−11.2037	−0.494655
$514$	−50.6490	−2.23403
$515$	12.6214	0.556165
$516$	−0.933681	−0.0411030
$517$	0	0
$518$	17.7657	0.780578
$519$	−6.20424	−0.272336
$520$	−0.230325	−0.0101004
$521$	17.7203	0.776340	0.388170	−	0.921588i	$-0.373107\pi$
$521$	17.7203	0.776340	0.388170	+	0.921588i	$0.373107\pi$
$522$	−26.1163	−1.14308
$523$	−16.9433	−0.740878	−0.370439	−	0.928857i	$-0.620793\pi$
$523$	−16.9433	−0.740878	−0.370439	+	0.928857i	$0.620793\pi$
$524$	−21.0795	−0.920860
$525$	−0.270998	−0.0118273
$526$	−11.2538	−0.490687
$527$	6.44766	0.280864
$528$	0	0
$529$	36.9793	1.60779
$530$	−6.58827	−0.286176
$531$	−28.1367	−1.22103
$532$	−12.7621	−0.553306
$533$	6.30539	0.273117
$534$	5.56052	0.240627
$535$	10.2588	0.443528
$536$	−2.93576	−0.126806
$537$	0.303405	0.0130929
$538$	−12.5526	−0.541180
$539$	0	0
$540$	−2.93832	−0.126445
$541$	1.49736	0.0643765	0.0321883	−	0.999482i	$-0.489752\pi$
$541$	1.49736	0.0643765	0.0321883	+	0.999482i	$0.489752\pi$
$542$	43.3924	1.86386
$543$	3.88372	0.166666
$544$	−27.1265	−1.16304
$545$	−3.94667	−0.169057
$546$	−0.366057	−0.0156658
$547$	−32.0609	−1.37083	−0.685413	−	0.728154i	$-0.740378\pi$
$547$	−32.0609	−1.37083	−0.685413	+	0.728154i	$0.740378\pi$
$548$	17.2478	0.736787
$549$	11.9245	0.508926
$550$	0	0
$551$	31.8110	1.35519
$552$	−0.700319	−0.0298075
$553$	14.2969	0.607966
$554$	1.00977	0.0429011
$555$	−2.46024	−0.104431
$556$	−31.8483	−1.35067
$557$	44.3749	1.88023	0.940113	−	0.340864i	$-0.110719\pi$
$557$	44.3749	1.88023	0.940113	+	0.340864i	$0.110719\pi$
$558$	−10.5778	−0.447796
$559$	−1.29991	−0.0549805
$560$	4.31195	0.182213
$561$	0	0
$562$	8.42063	0.355203
$563$	−42.4549	−1.78926	−0.894630	−	0.446808i	$-0.852561\pi$
$563$	−42.4549	−1.78926	−0.894630	+	0.446808i	$0.852561\pi$
$564$	3.38656	0.142600
$565$	−10.8083	−0.454707
$566$	−46.2460	−1.94386
$567$	−8.34443	−0.350433
$568$	−4.97202	−0.208621
$569$	−25.6121	−1.07372	−0.536858	−	0.843673i	$-0.680389\pi$
$569$	−25.6121	−1.07372	−0.536858	+	0.843673i	$0.680389\pi$
$570$	3.69938	0.154950
$571$	2.36080	0.0987965	0.0493983	−	0.998779i	$-0.484270\pi$
$571$	2.36080	0.0987965	0.0493983	+	0.998779i	$0.484270\pi$
$572$	0	0
$573$	−5.16729	−0.215866
$574$	−17.8760	−0.746130
$575$	7.74463	0.322973
$576$	19.2647	0.802695
$577$	30.7782	1.28131	0.640656	−	0.767828i	$-0.278663\pi$
$577$	30.7782	1.28131	0.640656	+	0.767828i	$0.278663\pi$
$578$	−9.42036	−0.391835
$579$	−3.08646	−0.128269
$580$	8.34284	0.346417
$581$	−0.222730	−0.00924040
$582$	−6.70989	−0.278134
$583$	0	0
$584$	2.54044	0.105124
$585$	−2.02009	−0.0835202
$586$	−5.78356	−0.238917
$587$	−35.1967	−1.45272	−0.726362	−	0.687312i	$-0.758790\pi$
$587$	−35.1967	−1.45272	−0.726362	+	0.687312i	$0.758790\pi$
$588$	0.495788	0.0204459
$589$	12.8843	0.530890
$590$	18.8142	0.774568
$591$	2.49727	0.102724
$592$	39.1458	1.60888
$593$	8.00440	0.328701	0.164351	−	0.986402i	$-0.447447\pi$
$593$	8.00440	0.328701	0.164351	+	0.986402i	$0.447447\pi$
$594$	0	0
$595$	−3.49086	−0.143111
$596$	22.8415	0.935623
$597$	−7.18530	−0.294075
$598$	10.4612	0.427792
$599$	11.2996	0.461689	0.230844	−	0.972991i	$-0.425851\pi$
$599$	11.2996	0.461689	0.230844	+	0.972991i	$0.425851\pi$
$600$	−0.0904264	−0.00369164
$601$	−6.88528	−0.280856	−0.140428	−	0.990091i	$-0.544848\pi$
$601$	−6.88528	−0.280856	−0.140428	+	0.990091i	$0.544848\pi$
$602$	3.68530	0.150202
$603$	−25.7484	−1.04856
$604$	−16.4605	−0.669766
$605$	0	0
$606$	2.58488	0.105004
$607$	7.17990	0.291423	0.145712	−	0.989327i	$-0.453453\pi$
$607$	7.17990	0.291423	0.145712	+	0.989327i	$0.453453\pi$
$608$	−54.2069	−2.19838
$609$	−1.23581	−0.0500775
$610$	−7.97359	−0.322841
$611$	4.71493	0.190746
$612$	−18.6904	−0.755515
$613$	−16.4513	−0.664460	−0.332230	−	0.943198i	$-0.607801\pi$
$613$	−16.4513	−0.664460	−0.332230	+	0.943198i	$0.607801\pi$
$614$	19.1886	0.774389
$615$	2.47552	0.0998226
$616$	0	0
$617$	−18.1124	−0.729178	−0.364589	−	0.931168i	$-0.618791\pi$
$617$	−18.1124	−0.729178	−0.364589	+	0.931168i	$0.618791\pi$
$618$	6.69336	0.269246
$619$	20.5389	0.825528	0.412764	−	0.910838i	$-0.364563\pi$
$619$	20.5389	0.825528	0.412764	+	0.910838i	$0.364563\pi$
$620$	3.37908	0.135707
$621$	−12.4385	−0.499142
$622$	−35.7958	−1.43528
$623$	−10.4852	−0.420082
$624$	−0.806590	−0.0322894
$625$	1.00000	0.0400000
$626$	36.5056	1.45906
$627$	0	0
$628$	34.4533	1.37484
$629$	−31.6915	−1.26362
$630$	5.72701	0.228169
$631$	19.4535	0.774430	0.387215	−	0.921989i	$-0.373437\pi$
$631$	19.4535	0.774430	0.387215	+	0.921989i	$0.373437\pi$
$632$	4.77058	0.189763
$633$	−3.67639	−0.146123
$634$	23.8694	0.947976
$635$	7.80577	0.309762
$636$	−1.66916	−0.0661864
$637$	0.690259	0.0273491
$638$	0	0
$639$	−43.6075	−1.72509
$640$	2.65973	0.105135
$641$	−17.8174	−0.703747	−0.351873	−	0.936048i	$-0.614455\pi$
$641$	−17.8174	−0.703747	−0.351873	+	0.936048i	$0.614455\pi$
$642$	5.44045	0.214717
$643$	−15.2570	−0.601678	−0.300839	−	0.953675i	$-0.597267\pi$
$643$	−15.2570	−0.601678	−0.300839	+	0.953675i	$0.597267\pi$
$644$	−14.1687	−0.558325
$645$	−0.510351	−0.0200951
$646$	47.6535	1.87490
$647$	−14.8931	−0.585508	−0.292754	−	0.956188i	$-0.594572\pi$
$647$	−14.8931	−0.585508	−0.292754	+	0.956188i	$0.594572\pi$
$648$	−2.78436	−0.109380
$649$	0	0
$650$	1.35077	0.0529817
$651$	−0.500537	−0.0196176
$652$	−0.524959	−0.0205590
$653$	−23.5684	−0.922302	−0.461151	−	0.887322i	$-0.652563\pi$
$653$	−23.5684	−0.922302	−0.461151	+	0.887322i	$0.652563\pi$
$654$	−2.09299	−0.0818424
$655$	−11.5221	−0.450204
$656$	−39.3889	−1.53788
$657$	22.2811	0.869270
$658$	−13.3670	−0.521100
$659$	−42.5595	−1.65788	−0.828942	−	0.559334i	$-0.811057\pi$
$659$	−42.5595	−1.65788	−0.828942	+	0.559334i	$0.811057\pi$
$660$	0	0
$661$	−0.889678	−0.0346045	−0.0173022	−	0.999850i	$-0.505508\pi$
$661$	−0.889678	−0.0346045	−0.0173022	+	0.999850i	$0.505508\pi$
$662$	63.0697	2.45127
$663$	0.652997	0.0253603
$664$	−0.0743203	−0.00288419
$665$	−6.97577	−0.270509
$666$	51.9923	2.01466
$667$	35.3171	1.36748
$668$	0.746601	0.0288869
$669$	−4.26958	−0.165071
$670$	17.2172	0.665159
$671$	0	0
$672$	2.10585	0.0812351
$673$	25.7462	0.992445	0.496222	−	0.868195i	$-0.334720\pi$
$673$	25.7462	0.992445	0.496222	+	0.868195i	$0.334720\pi$
$674$	19.6391	0.756470
$675$	−1.60609	−0.0618183
$676$	−22.9117	−0.881217
$677$	21.7293	0.835123	0.417562	−	0.908649i	$-0.362885\pi$
$677$	21.7293	0.835123	0.417562	+	0.908649i	$0.362885\pi$
$678$	−5.73181	−0.220129
$679$	12.6526	0.485561
$680$	−1.16483	−0.0446690
$681$	2.03014	0.0777952
$682$	0	0
$683$	39.9842	1.52995	0.764976	−	0.644058i	$-0.222751\pi$
$683$	39.9842	1.52995	0.764976	+	0.644058i	$0.222751\pi$
$684$	−37.3490	−1.42807
$685$	9.42765	0.360212
$686$	−1.95691	−0.0747151
$687$	4.14996	0.158331
$688$	8.12038	0.309587
$689$	−2.32388	−0.0885327
$690$	4.10712	0.156355
$691$	9.44054	0.359135	0.179568	−	0.983746i	$-0.442530\pi$
$691$	9.44054	0.359135	0.179568	+	0.983746i	$0.442530\pi$
$692$	−41.8843	−1.59220
$693$	0	0
$694$	−66.7603	−2.53418
$695$	−17.4083	−0.660335
$696$	−0.412363	−0.0156306
$697$	31.8884	1.20786
$698$	−37.8431	−1.43238
$699$	3.07043	0.116134
$700$	−1.82949	−0.0691481
$701$	7.00620	0.264621	0.132310	−	0.991208i	$-0.457760\pi$
$701$	7.00620	0.264621	0.132310	+	0.991208i	$0.457760\pi$
$702$	−2.16946	−0.0818810
$703$	−63.3291	−2.38850
$704$	0	0
$705$	1.85110	0.0697165
$706$	−29.9357	−1.12665
$707$	−4.87420	−0.183313
$708$	4.76662	0.179141
$709$	−35.0073	−1.31473	−0.657363	−	0.753574i	$-0.728328\pi$
$709$	−35.0073	−1.31473	−0.657363	+	0.753574i	$0.728328\pi$
$710$	29.1591	1.09432
$711$	41.8408	1.56915
$712$	−3.49870	−0.131119
$713$	14.3044	0.535705
$714$	−1.85127	−0.0692819
$715$	0	0
$716$	2.04826	0.0765471
$717$	−0.373629	−0.0139534
$718$	−13.1657	−0.491338
$719$	−23.2024	−0.865303	−0.432652	−	0.901561i	$-0.642422\pi$
$719$	−23.2024	−0.865303	−0.432652	+	0.901561i	$0.642422\pi$
$720$	12.6192	0.470289
$721$	−12.6214	−0.470045
$722$	58.0446	2.16020
$723$	−2.86888	−0.106695
$724$	26.2187	0.974410
$725$	4.56021	0.169362
$726$	0	0
$727$	−39.5640	−1.46735	−0.733674	−	0.679502i	$-0.762196\pi$
$727$	−39.5640	−1.46735	−0.733674	+	0.679502i	$0.762196\pi$
$728$	0.230325	0.00853641
$729$	−23.1147	−0.856102
$730$	−14.8988	−0.551428
$731$	−6.57408	−0.243151
$732$	−2.02013	−0.0746661
$733$	−26.1004	−0.964038	−0.482019	−	0.876161i	$-0.660096\pi$
$733$	−26.1004	−0.964038	−0.482019	+	0.876161i	$0.660096\pi$
$734$	56.0540	2.06899
$735$	0.270998	0.00999592
$736$	−60.1814	−2.21832
$737$	0	0
$738$	−52.3152	−1.92575
$739$	37.8168	1.39111	0.695556	−	0.718472i	$-0.255158\pi$
$739$	37.8168	1.39111	0.695556	+	0.718472i	$0.255158\pi$
$740$	−16.6089	−0.610554
$741$	1.30488	0.0479360
$742$	6.58827	0.241863
$743$	−19.2200	−0.705113	−0.352557	−	0.935791i	$-0.614688\pi$
$743$	−19.2200	−0.705113	−0.352557	+	0.935791i	$0.614688\pi$
$744$	−0.167019	−0.00612320
$745$	12.4852	0.457421
$746$	−0.833213	−0.0305061
$747$	−0.651833	−0.0238493
$748$	0	0
$749$	−10.2588	−0.374850
$750$	0.530318	0.0193645
$751$	7.61510	0.277879	0.138939	−	0.990301i	$-0.455631\pi$
$751$	7.61510	0.277879	0.138939	+	0.990301i	$0.455631\pi$
$752$	−29.4535	−1.07406
$753$	3.28636	0.119762
$754$	6.15980	0.224327
$755$	−8.99731	−0.327446
$756$	2.93832	0.106865
$757$	−5.52813	−0.200923	−0.100462	−	0.994941i	$-0.532032\pi$
$757$	−5.52813	−0.200923	−0.100462	+	0.994941i	$0.532032\pi$
$758$	−31.1502	−1.13142
$759$	0	0
$760$	−2.32767	−0.0844334
$761$	−16.0742	−0.582690	−0.291345	−	0.956618i	$-0.594103\pi$
$761$	−16.0742	−0.582690	−0.291345	+	0.956618i	$0.594103\pi$
$762$	4.13954	0.149960
$763$	3.94667	0.142879
$764$	−34.8839	−1.26206
$765$	−10.2162	−0.369368
$766$	−17.9397	−0.648186
$767$	6.63632	0.239624
$768$	4.97830	0.179639
$769$	26.6920	0.962537	0.481268	−	0.876573i	$-0.340176\pi$
$769$	26.6920	0.962537	0.481268	+	0.876573i	$0.340176\pi$
$770$	0	0
$771$	−7.01402	−0.252604
$772$	−20.8364	−0.749919
$773$	−32.1400	−1.15599	−0.577997	−	0.816039i	$-0.696166\pi$
$773$	−32.1400	−1.15599	−0.577997	+	0.816039i	$0.696166\pi$
$774$	10.7853	0.387668
$775$	1.84701	0.0663466
$776$	4.22189	0.151557
$777$	2.46024	0.0882606
$778$	18.3559	0.658093
$779$	63.7224	2.28309
$780$	0.342222	0.0122535
$781$	0	0
$782$	52.9058	1.89191
$783$	−7.32409	−0.261742
$784$	−4.31195	−0.153998
$785$	18.8322	0.672151
$786$	−6.11036	−0.217949
$787$	−7.43951	−0.265190	−0.132595	−	0.991170i	$-0.542331\pi$
$787$	−7.43951	−0.265190	−0.132595	+	0.991170i	$0.542331\pi$
$788$	16.8589	0.600573
$789$	−1.55845	−0.0554824
$790$	−27.9777	−0.995403
$791$	10.8083	0.384297
$792$	0	0
$793$	−2.81252	−0.0998755
$794$	−27.7336	−0.984228
$795$	−0.912363	−0.0323582
$796$	−48.5073	−1.71930
$797$	−22.6755	−0.803207	−0.401603	−	0.915814i	$-0.631547\pi$
$797$	−22.6755	−0.803207	−0.401603	+	0.915814i	$0.631547\pi$
$798$	−3.69938	−0.130957
$799$	23.8449	0.843572
$800$	−7.77073	−0.274737
$801$	−30.6857	−1.08423
$802$	30.2494	1.06814
$803$	0	0
$804$	4.36203	0.153837
$805$	−7.74463	−0.272962
$806$	2.49489	0.0878789
$807$	−1.73832	−0.0611917
$808$	−1.62642	−0.0572172
$809$	45.9770	1.61646	0.808232	−	0.588864i	$-0.200425\pi$
$809$	45.9770	1.61646	0.808232	+	0.588864i	$0.200425\pi$
$810$	16.3293	0.573753
$811$	−22.1247	−0.776904	−0.388452	−	0.921469i	$-0.626990\pi$
$811$	−22.1247	−0.776904	−0.388452	+	0.921469i	$0.626990\pi$
$812$	−8.34284	−0.292776
$813$	6.00910	0.210748
$814$	0	0
$815$	−0.286944	−0.0100512
$816$	−4.07918	−0.142800
$817$	−13.1370	−0.459604
$818$	−52.0610	−1.82027
$819$	2.02009	0.0705875
$820$	16.7120	0.583609
$821$	−15.4909	−0.540636	−0.270318	−	0.962771i	$-0.587129\pi$
$821$	−15.4909	−0.540636	−0.270318	+	0.962771i	$0.587129\pi$
$822$	4.99965	0.174383
$823$	−4.08689	−0.142460	−0.0712300	−	0.997460i	$-0.522692\pi$
$823$	−4.08689	−0.142460	−0.0712300	+	0.997460i	$0.522692\pi$
$824$	−4.21149	−0.146714
$825$	0	0
$826$	−18.8142	−0.654629
$827$	−15.1500	−0.526816	−0.263408	−	0.964684i	$-0.584847\pi$
$827$	−15.1500	−0.526816	−0.263408	+	0.964684i	$0.584847\pi$
$828$	−41.4655	−1.44103
$829$	26.6252	0.924731	0.462365	−	0.886689i	$-0.347001\pi$
$829$	26.6252	0.924731	0.462365	+	0.886689i	$0.347001\pi$
$830$	0.435862	0.0151290
$831$	0.139836	0.00485086
$832$	−4.54377	−0.157527
$833$	3.49086	0.120951
$834$	−9.23194	−0.319676
$835$	0.408093	0.0141226
$836$	0	0
$837$	−2.96646	−0.102536
$838$	39.5152	1.36503
$839$	−51.9922	−1.79497	−0.897485	−	0.441046i	$-0.854608\pi$
$839$	−51.9922	−1.79497	−0.897485	+	0.441046i	$0.854608\pi$
$840$	0.0904264	0.00312001
$841$	−8.20452	−0.282915
$842$	11.0152	0.379610
$843$	1.16611	0.0401631
$844$	−24.8190	−0.854305
$845$	−12.5235	−0.430823
$846$	−39.1193	−1.34495
$847$	0	0
$848$	14.5169	0.498514
$849$	−6.40428	−0.219794
$850$	6.83129	0.234311
$851$	−70.3091	−2.41016
$852$	7.38754	0.253093
$853$	−52.5241	−1.79839	−0.899195	−	0.437549i	$-0.855847\pi$
$853$	−52.5241	−1.79839	−0.899195	+	0.437549i	$0.855847\pi$
$854$	7.97359	0.272851
$855$	−20.4150	−0.698179
$856$	−3.42316	−0.117001
$857$	48.0342	1.64082	0.820409	−	0.571777i	$-0.193746\pi$
$857$	48.0342	1.64082	0.820409	+	0.571777i	$0.193746\pi$
$858$	0	0
$859$	33.6731	1.14891	0.574456	−	0.818535i	$-0.305214\pi$
$859$	33.6731	1.14891	0.574456	+	0.818535i	$0.305214\pi$
$860$	−3.44534	−0.117485
$861$	−2.47552	−0.0843655
$862$	13.9300	0.474458
$863$	36.9877	1.25907	0.629537	−	0.776970i	$-0.283244\pi$
$863$	36.9877	1.25907	0.629537	+	0.776970i	$0.283244\pi$
$864$	12.4805	0.424594
$865$	−22.8940	−0.778420
$866$	−31.8429	−1.08207
$867$	−1.30456	−0.0443051
$868$	−3.37908	−0.114694
$869$	0	0
$870$	2.41836	0.0819901
$871$	6.07302	0.205776
$872$	1.31692	0.0445965
$873$	37.0285	1.25322
$874$	105.721	3.57608
$875$	−1.00000	−0.0338062
$876$	−3.77464	−0.127533
$877$	0.174956	0.00590783	0.00295392	−	0.999996i	$-0.499060\pi$
$877$	0.174956	0.00590783	0.00295392	+	0.999996i	$0.499060\pi$
$878$	−35.2328	−1.18905
$879$	−0.800924	−0.0270145
$880$	0	0
$881$	−29.0125	−0.977456	−0.488728	−	0.872436i	$-0.662539\pi$
$881$	−29.0125	−0.977456	−0.488728	+	0.872436i	$0.662539\pi$
$882$	−5.72701	−0.192838
$883$	11.9787	0.403116	0.201558	−	0.979477i	$-0.435400\pi$
$883$	11.9787	0.403116	0.201558	+	0.979477i	$0.435400\pi$
$884$	4.40833	0.148268
$885$	2.60544	0.0875810
$886$	−18.8652	−0.633790
$887$	1.74320	0.0585308	0.0292654	−	0.999572i	$-0.490683\pi$
$887$	1.74320	0.0585308	0.0292654	+	0.999572i	$0.490683\pi$
$888$	0.820930	0.0275486
$889$	−7.80577	−0.261797
$890$	20.5186	0.687787
$891$	0	0
$892$	−28.8236	−0.965085
$893$	47.6492	1.59452
$894$	6.62112	0.221443
$895$	1.11958	0.0374235
$896$	−2.65973	−0.0888553
$897$	1.44870	0.0483708
$898$	33.6433	1.12269
$899$	8.42275	0.280915
$900$	−5.35410	−0.178470
$901$	−11.7526	−0.391536
$902$	0	0
$903$	0.510351	0.0169834
$904$	3.60648	0.119950
$905$	14.3312	0.476384
$906$	−4.77144	−0.158520
$907$	−39.1501	−1.29996	−0.649979	−	0.759952i	$-0.725222\pi$
$907$	−39.1501	−1.29996	−0.649979	+	0.759952i	$0.725222\pi$
$908$	13.7053	0.454827
$909$	−14.2646	−0.473128
$910$	−1.35077	−0.0447777
$911$	−22.3917	−0.741869	−0.370935	−	0.928659i	$-0.620963\pi$
$911$	−22.3917	−0.741869	−0.370935	+	0.928659i	$0.620963\pi$
$912$	−8.15141	−0.269920
$913$	0	0
$914$	16.0418	0.530617
$915$	−1.10421	−0.0365039
$916$	28.0160	0.925676
$917$	11.5221	0.380492
$918$	−10.9716	−0.362118
$919$	−50.9594	−1.68099	−0.840497	−	0.541816i	$-0.817737\pi$
$919$	−50.9594	−1.68099	−0.840497	+	0.541816i	$0.817737\pi$
$920$	−2.58422	−0.0851992
$921$	2.65729	0.0875608
$922$	−26.4529	−0.871178
$923$	10.2853	0.338544
$924$	0	0
$925$	−9.07844	−0.298497
$926$	−3.17128	−0.104215
$927$	−36.9373	−1.21318
$928$	−35.4361	−1.16325
$929$	36.7960	1.20724	0.603618	−	0.797273i	$-0.293725\pi$
$929$	36.7960	1.20724	0.603618	+	0.797273i	$0.293725\pi$
$930$	0.979504	0.0321192
$931$	6.97577	0.228622
$932$	20.7282	0.678975
$933$	−4.95711	−0.162288
$934$	−0.472147	−0.0154491
$935$	0	0
$936$	0.674060	0.0220323
$937$	−54.0477	−1.76566	−0.882831	−	0.469691i	$-0.844365\pi$
$937$	−54.0477	−1.76566	−0.882831	+	0.469691i	$0.844365\pi$
$938$	−17.2172	−0.562162
$939$	5.05540	0.164977
$940$	12.4966	0.407595
$941$	47.4467	1.54672	0.773359	−	0.633969i	$-0.218575\pi$
$941$	47.4467	1.54672	0.773359	+	0.633969i	$0.218575\pi$
$942$	9.98708	0.325397
$943$	70.7458	2.30380
$944$	−41.4562	−1.34928
$945$	1.60609	0.0522460
$946$	0	0
$947$	7.16681	0.232890	0.116445	−	0.993197i	$-0.462850\pi$
$947$	7.16681	0.232890	0.116445	+	0.993197i	$0.462850\pi$
$948$	−7.08823	−0.230215
$949$	−5.25524	−0.170592
$950$	13.6509	0.442895
$951$	3.30551	0.107188
$952$	1.16483	0.0377522
$953$	12.6450	0.409611	0.204805	−	0.978803i	$-0.434344\pi$
$953$	12.6450	0.409611	0.204805	+	0.978803i	$0.434344\pi$
$954$	19.2810	0.624245
$955$	−19.0676	−0.617013
$956$	−2.52234	−0.0815783
$957$	0	0
$958$	−0.840773	−0.0271641
$959$	−9.42765	−0.304435
$960$	−1.78390	−0.0575751
$961$	−27.5885	−0.889953
$962$	−12.2629	−0.395372
$963$	−30.0231	−0.967481
$964$	−19.3676	−0.623789
$965$	−11.3892	−0.366632
$966$	−4.10712	−0.132144
$967$	−13.1825	−0.423921	−0.211961	−	0.977278i	$-0.567985\pi$
$967$	−13.1825	−0.423921	−0.211961	+	0.977278i	$0.567985\pi$
$968$	0	0
$969$	6.59920	0.211997
$970$	−24.7599	−0.794992
$971$	5.74467	0.184355	0.0921775	−	0.995743i	$-0.470617\pi$
$971$	5.74467	0.184355	0.0921775	+	0.995743i	$0.470617\pi$
$972$	12.9520	0.415436
$973$	17.4083	0.558085
$974$	54.2809	1.73927
$975$	0.187059	0.00599068
$976$	17.5694	0.562383
$977$	47.1799	1.50942	0.754709	−	0.656060i	$-0.227778\pi$
$977$	47.1799	1.50942	0.754709	+	0.656060i	$0.227778\pi$
$978$	−0.152171	−0.00486591
$979$	0	0
$980$	1.82949	0.0584408
$981$	11.5502	0.368768
$982$	51.0799	1.63003
$983$	−8.40771	−0.268164	−0.134082	−	0.990970i	$-0.542809\pi$
$983$	−8.40771	−0.268164	−0.134082	+	0.990970i	$0.542809\pi$
$984$	−0.826029	−0.0263328
$985$	9.21509	0.293617
$986$	31.1521	0.992084
$987$	−1.85110	−0.0589212
$988$	8.80915	0.280256
$989$	−14.5849	−0.463773
$990$	0	0
$991$	12.0899	0.384048	0.192024	−	0.981390i	$-0.438495\pi$
$991$	12.0899	0.384048	0.192024	+	0.981390i	$0.438495\pi$
$992$	−14.3526	−0.455697
$993$	8.73407	0.277167
$994$	−29.1591	−0.924871
$995$	−26.5142	−0.840556
$996$	0.110427	0.00349901
$997$	21.6166	0.684604	0.342302	−	0.939590i	$-0.388793\pi$
$997$	21.6166	0.684604	0.342302	+	0.939590i	$0.388793\pi$
$998$	−15.9054	−0.503477
$999$	14.5808	0.461315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bo.1.15		18
11.5	even	5		385.2.n.f.36.2	✓	36
11.9	even	5		385.2.n.f.246.2	yes	36
11.10	odd	2		4235.2.a.bp.1.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.2	✓	36	11.5	even	5
385.2.n.f.246.2	yes	36	11.9	even	5
4235.2.a.bo.1.15		18	1.1	even	1	trivial
4235.2.a.bp.1.4		18	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+1.95691 q^{2} +0.270998 q^{3} +1.82949 q^{4} +1.00000 q^{5} +0.530318 q^{6} -1.00000 q^{7} -0.333679 q^{8} -2.92656 q^{9} +O(q^{10})\)	\(q+1.95691 q^{2} +0.270998 q^{3} +1.82949 q^{4} +1.00000 q^{5} +0.530318 q^{6} -1.00000 q^{7} -0.333679 q^{8} -2.92656 q^{9} +1.95691 q^{10} +0.495788 q^{12} +0.690259 q^{13} -1.95691 q^{14} +0.270998 q^{15} -4.31195 q^{16} +3.49086 q^{17} -5.72701 q^{18} +6.97577 q^{19} +1.82949 q^{20} -0.270998 q^{21} +7.74463 q^{23} -0.0904264 q^{24} +1.00000 q^{25} +1.35077 q^{26} -1.60609 q^{27} -1.82949 q^{28} +4.56021 q^{29} +0.530318 q^{30} +1.84701 q^{31} -7.77073 q^{32} +6.83129 q^{34} -1.00000 q^{35} -5.35410 q^{36} -9.07844 q^{37} +13.6509 q^{38} +0.187059 q^{39} -0.333679 q^{40} +9.13482 q^{41} -0.530318 q^{42} -1.88323 q^{43} -2.92656 q^{45} +15.1555 q^{46} +6.83067 q^{47} -1.16853 q^{48} +1.00000 q^{49} +1.95691 q^{50} +0.946017 q^{51} +1.26282 q^{52} -3.36668 q^{53} -3.14296 q^{54} +0.333679 q^{56} +1.89042 q^{57} +8.92390 q^{58} +9.61424 q^{59} +0.495788 q^{60} -4.07459 q^{61} +3.61443 q^{62} +2.92656 q^{63} -6.58270 q^{64} +0.690259 q^{65} +8.79817 q^{67} +6.38648 q^{68} +2.09878 q^{69} -1.95691 q^{70} +14.9006 q^{71} +0.976531 q^{72} -7.61343 q^{73} -17.7657 q^{74} +0.270998 q^{75} +12.7621 q^{76} +0.366057 q^{78} -14.2969 q^{79} -4.31195 q^{80} +8.34443 q^{81} +17.8760 q^{82} +0.222730 q^{83} -0.495788 q^{84} +3.49086 q^{85} -3.68530 q^{86} +1.23581 q^{87} +10.4852 q^{89} -5.72701 q^{90} -0.690259 q^{91} +14.1687 q^{92} +0.500537 q^{93} +13.3670 q^{94} +6.97577 q^{95} -2.10585 q^{96} -12.6526 q^{97} +1.95691 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9}+O(q^{10}) \) 18 * q - 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 + q^6 - 18 * q^7 - 6 * q^8 + 37 * q^9	\( 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9} - 2 q^{10} + 15 q^{12} - 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} + 5 q^{17} - 2 q^{18} - 15 q^{19} + 24 q^{20} - 5 q^{21} + 4 q^{23} - 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} - 24 q^{28} + 6 q^{29} + q^{30} + 22 q^{31} + 6 q^{32} + 44 q^{34} - 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} + 38 q^{39} - 6 q^{40} - 7 q^{41} - q^{42} - 10 q^{43} + 37 q^{45} + 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} - 2 q^{50} + 11 q^{51} - 18 q^{52} + 23 q^{53} - 13 q^{54} + 6 q^{56} + 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} - 17 q^{61} - 57 q^{62} - 37 q^{63} + 64 q^{64} - 8 q^{65} + 29 q^{67} + 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} + 77 q^{72} - 3 q^{73} + 48 q^{74} + 5 q^{75} - 47 q^{76} + 10 q^{78} + 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} - 9 q^{83} - 15 q^{84} + 5 q^{85} + 25 q^{86} - 23 q^{87} + 59 q^{89} - 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} + 19 q^{94} - 15 q^{95} - 14 q^{96} + 30 q^{97} - 2 q^{98}+O(q^{100}) \) 18 * q - 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 + q^6 - 18 * q^7 - 6 * q^8 + 37 * q^9 - 2 * q^10 + 15 * q^12 - 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 + 5 * q^17 - 2 * q^18 - 15 * q^19 + 24 * q^20 - 5 * q^21 + 4 * q^23 - 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 - 24 * q^28 + 6 * q^29 + q^30 + 22 * q^31 + 6 * q^32 + 44 * q^34 - 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 + 38 * q^39 - 6 * q^40 - 7 * q^41 - q^42 - 10 * q^43 + 37 * q^45 + 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 - 2 * q^50 + 11 * q^51 - 18 * q^52 + 23 * q^53 - 13 * q^54 + 6 * q^56 + 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 - 17 * q^61 - 57 * q^62 - 37 * q^63 + 64 * q^64 - 8 * q^65 + 29 * q^67 + 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 + 77 * q^72 - 3 * q^73 + 48 * q^74 + 5 * q^75 - 47 * q^76 + 10 * q^78 + 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 - 9 * q^83 - 15 * q^84 + 5 * q^85 + 25 * q^86 - 23 * q^87 + 59 * q^89 - 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 + 19 * q^94 - 15 * q^95 - 14 * q^96 + 30 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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