LMFDB - Embedded newform 5239.2.a.r.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.80367 q^{2} -1.10798 q^{3} +1.25322 q^{4} -0.771735 q^{5} -1.99844 q^{6} -4.39563 q^{7} -1.34694 q^{8} -1.77237 q^{9} +O(q^{10})$	\(q+1.80367 q^{2} -1.10798 q^{3} +1.25322 q^{4} -0.771735 q^{5} -1.99844 q^{6} -4.39563 q^{7} -1.34694 q^{8} -1.77237 q^{9} -1.39195 q^{10} +5.43090 q^{11} -1.38855 q^{12} -7.92826 q^{14} +0.855069 q^{15} -4.93588 q^{16} -1.17127 q^{17} -3.19678 q^{18} -6.05291 q^{19} -0.967157 q^{20} +4.87028 q^{21} +9.79556 q^{22} -1.15047 q^{23} +1.49238 q^{24} -4.40443 q^{25} +5.28771 q^{27} -5.50871 q^{28} +4.82434 q^{29} +1.54226 q^{30} -1.00000 q^{31} -6.20882 q^{32} -6.01735 q^{33} -2.11258 q^{34} +3.39226 q^{35} -2.22118 q^{36} -6.37694 q^{37} -10.9175 q^{38} +1.03948 q^{40} +11.7350 q^{41} +8.78438 q^{42} -5.64848 q^{43} +6.80614 q^{44} +1.36780 q^{45} -2.07508 q^{46} -4.06481 q^{47} +5.46887 q^{48} +12.3215 q^{49} -7.94413 q^{50} +1.29774 q^{51} +1.26335 q^{53} +9.53728 q^{54} -4.19122 q^{55} +5.92063 q^{56} +6.70652 q^{57} +8.70152 q^{58} +8.62832 q^{59} +1.07159 q^{60} +0.975562 q^{61} -1.80367 q^{62} +7.79069 q^{63} -1.32691 q^{64} -10.8533 q^{66} +8.48686 q^{67} -1.46786 q^{68} +1.27471 q^{69} +6.11851 q^{70} -3.84007 q^{71} +2.38727 q^{72} +4.37422 q^{73} -11.5019 q^{74} +4.88003 q^{75} -7.58565 q^{76} -23.8722 q^{77} +8.38024 q^{79} +3.80919 q^{80} -0.541573 q^{81} +21.1661 q^{82} +12.8430 q^{83} +6.10355 q^{84} +0.903906 q^{85} -10.1880 q^{86} -5.34529 q^{87} -7.31508 q^{88} -10.8208 q^{89} +2.46706 q^{90} -1.44180 q^{92} +1.10798 q^{93} -7.33158 q^{94} +4.67124 q^{95} +6.87927 q^{96} +0.0691975 q^{97} +22.2240 q^{98} -9.62559 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q + 8 * q^2 + 32 * q^4 + 16 * q^5 + 12 * q^6 + 8 * q^7 + 24 * q^8 + 34 * q^9	\( 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9} + 8 q^{10} + 26 q^{11} + 8 q^{12} - 4 q^{14} + 16 q^{15} + 36 q^{16} - 6 q^{17} + 64 q^{18} + 4 q^{19} + 40 q^{20} + 32 q^{21} + 20 q^{22} - 8 q^{23} - 16 q^{24} + 36 q^{25} - 6 q^{27} + 24 q^{28} + 32 q^{30} - 34 q^{31} + 36 q^{32} + 40 q^{33} + 16 q^{34} - 30 q^{35} + 40 q^{36} + 2 q^{37} + 18 q^{38} + 4 q^{40} + 80 q^{41} + 16 q^{42} + 12 q^{43} + 108 q^{44} + 12 q^{45} + 48 q^{46} + 24 q^{47} + 46 q^{48} + 22 q^{49} - 44 q^{50} - 28 q^{51} + 10 q^{53} + 48 q^{54} + 6 q^{55} - 2 q^{56} + 66 q^{57} - 44 q^{58} + 64 q^{59} + 48 q^{60} - 6 q^{61} - 8 q^{62} - 52 q^{63} - 12 q^{64} + 4 q^{66} + 16 q^{67} - 58 q^{68} - 28 q^{69} + 72 q^{70} + 52 q^{71} + 152 q^{72} + 42 q^{73} - 8 q^{74} - 4 q^{75} - 48 q^{76} + 10 q^{77} + 8 q^{79} + 48 q^{80} + 58 q^{81} - 42 q^{82} + 44 q^{83} - 8 q^{84} + 96 q^{85} + 16 q^{86} + 20 q^{87} + 64 q^{88} + 74 q^{89} - 26 q^{90} + 24 q^{92} - 8 q^{94} - 32 q^{95} + 50 q^{96} + 40 q^{97} + 72 q^{98} + 74 q^{99}+O(q^{100}) \) 34 * q + 8 * q^2 + 32 * q^4 + 16 * q^5 + 12 * q^6 + 8 * q^7 + 24 * q^8 + 34 * q^9 + 8 * q^10 + 26 * q^11 + 8 * q^12 - 4 * q^14 + 16 * q^15 + 36 * q^16 - 6 * q^17 + 64 * q^18 + 4 * q^19 + 40 * q^20 + 32 * q^21 + 20 * q^22 - 8 * q^23 - 16 * q^24 + 36 * q^25 - 6 * q^27 + 24 * q^28 + 32 * q^30 - 34 * q^31 + 36 * q^32 + 40 * q^33 + 16 * q^34 - 30 * q^35 + 40 * q^36 + 2 * q^37 + 18 * q^38 + 4 * q^40 + 80 * q^41 + 16 * q^42 + 12 * q^43 + 108 * q^44 + 12 * q^45 + 48 * q^46 + 24 * q^47 + 46 * q^48 + 22 * q^49 - 44 * q^50 - 28 * q^51 + 10 * q^53 + 48 * q^54 + 6 * q^55 - 2 * q^56 + 66 * q^57 - 44 * q^58 + 64 * q^59 + 48 * q^60 - 6 * q^61 - 8 * q^62 - 52 * q^63 - 12 * q^64 + 4 * q^66 + 16 * q^67 - 58 * q^68 - 28 * q^69 + 72 * q^70 + 52 * q^71 + 152 * q^72 + 42 * q^73 - 8 * q^74 - 4 * q^75 - 48 * q^76 + 10 * q^77 + 8 * q^79 + 48 * q^80 + 58 * q^81 - 42 * q^82 + 44 * q^83 - 8 * q^84 + 96 * q^85 + 16 * q^86 + 20 * q^87 + 64 * q^88 + 74 * q^89 - 26 * q^90 + 24 * q^92 - 8 * q^94 - 32 * q^95 + 50 * q^96 + 40 * q^97 + 72 * q^98 + 74 * q^99

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 $

$2$	1.80367	1.27539	0.637694	−	0.770290i	$-0.279889\pi$
$2$	1.80367	1.27539	0.637694	+	0.770290i	$0.279889\pi$
$3$	−1.10798	−0.639694	−0.319847	−	0.947469i	$-0.603632\pi$
$3$	−1.10798	−0.639694	−0.319847	+	0.947469i	$0.603632\pi$
$4$	1.25322	0.626612
$5$	−0.771735	−0.345130	−0.172565	−	0.984998i	$-0.555206\pi$
$5$	−0.771735	−0.345130	−0.172565	+	0.984998i	$0.555206\pi$
$6$	−1.99844	−0.815858
$7$	−4.39563	−1.66139	−0.830695	−	0.556727i	$-0.812057\pi$
$7$	−4.39563	−1.66139	−0.830695	+	0.556727i	$0.812057\pi$
$8$	−1.34694	−0.476214
$9$	−1.77237	−0.590791
$10$	−1.39195	−0.440175
$11$	5.43090	1.63748	0.818740	−	0.574165i	$-0.194673\pi$
$11$	5.43090	1.63748	0.818740	+	0.574165i	$0.194673\pi$
$12$	−1.38855	−0.400840
$13$	0	0
$13$	0	0
$14$	−7.92826	−2.11892
$15$	0.855069	0.220778
$16$	−4.93588	−1.23397
$17$	−1.17127	−0.284074	−0.142037	−	0.989861i	$-0.545365\pi$
$17$	−1.17127	−0.284074	−0.142037	+	0.989861i	$0.545365\pi$
$18$	−3.19678	−0.753487
$19$	−6.05291	−1.38863	−0.694316	−	0.719670i	$-0.744293\pi$
$19$	−6.05291	−1.38863	−0.694316	+	0.719670i	$0.744293\pi$
$20$	−0.967157	−0.216263
$21$	4.87028	1.06278
$22$	9.79556	2.08842
$23$	−1.15047	−0.239891	−0.119945	−	0.992781i	$-0.538272\pi$
$23$	−1.15047	−0.239891	−0.119945	+	0.992781i	$0.538272\pi$
$24$	1.49238	0.304631
$25$	−4.40443	−0.880885
$26$	0	0
$27$	5.28771	1.01762
$28$	−5.50871	−1.04105
$29$	4.82434	0.895858	0.447929	−	0.894069i	$-0.352162\pi$
$29$	4.82434	0.895858	0.447929	+	0.894069i	$0.352162\pi$
$30$	1.54226	0.281577
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−6.20882	−1.09757
$33$	−6.01735	−1.04749
$34$	−2.11258	−0.362304
$35$	3.39226	0.573396
$36$	−2.22118	−0.370197
$37$	−6.37694	−1.04836	−0.524181	−	0.851607i	$-0.675629\pi$
$37$	−6.37694	−1.04836	−0.524181	+	0.851607i	$0.675629\pi$
$38$	−10.9175	−1.77104
$39$	0	0
$40$	1.03948	0.164356
$41$	11.7350	1.83270	0.916350	−	0.400377i	$-0.131121\pi$
$41$	11.7350	1.83270	0.916350	+	0.400377i	$0.131121\pi$
$42$	8.78438	1.35546
$43$	−5.64848	−0.861385	−0.430692	−	0.902499i	$-0.641731\pi$
$43$	−5.64848	−0.861385	−0.430692	+	0.902499i	$0.641731\pi$
$44$	6.80614	1.02606
$45$	1.36780	0.203900
$46$	−2.07508	−0.305953
$47$	−4.06481	−0.592914	−0.296457	−	0.955046i	$-0.595805\pi$
$47$	−4.06481	−0.592914	−0.296457	+	0.955046i	$0.595805\pi$
$48$	5.46887	0.789363
$49$	12.3215	1.76022
$50$	−7.94413	−1.12347
$51$	1.29774	0.181720
$52$	0	0
$53$	1.26335	0.173535	0.0867674	−	0.996229i	$-0.472346\pi$
$53$	1.26335	0.173535	0.0867674	+	0.996229i	$0.472346\pi$
$54$	9.53728	1.29786
$55$	−4.19122	−0.565143
$56$	5.92063	0.791177
$57$	6.70652	0.888301
$58$	8.70152	1.14257
$59$	8.62832	1.12331	0.561656	−	0.827371i	$-0.310165\pi$
$59$	8.62832	1.12331	0.561656	+	0.827371i	$0.310165\pi$
$60$	1.07159	0.138342
$61$	0.975562	0.124908	0.0624540	−	0.998048i	$-0.480107\pi$
$61$	0.975562	0.124908	0.0624540	+	0.998048i	$0.480107\pi$
$62$	−1.80367	−0.229066
$63$	7.79069	0.981535
$64$	−1.32691	−0.165863
$65$	0	0
$66$	−10.8533	−1.33595
$67$	8.48686	1.03683	0.518417	−	0.855128i	$-0.326521\pi$
$67$	8.48686	1.03683	0.518417	+	0.855128i	$0.326521\pi$
$68$	−1.46786	−0.178004
$69$	1.27471	0.153457
$70$	6.11851	0.731302
$71$	−3.84007	−0.455732	−0.227866	−	0.973693i	$-0.573175\pi$
$71$	−3.84007	−0.455732	−0.227866	+	0.973693i	$0.573175\pi$
$72$	2.38727	0.281343
$73$	4.37422	0.511964	0.255982	−	0.966682i	$-0.417601\pi$
$73$	4.37422	0.511964	0.255982	+	0.966682i	$0.417601\pi$
$74$	−11.5019	−1.33707
$75$	4.88003	0.563497
$76$	−7.58565	−0.870134
$77$	−23.8722	−2.72049
$78$	0	0
$79$	8.38024	0.942851	0.471425	−	0.881906i	$-0.343740\pi$
$79$	8.38024	0.942851	0.471425	+	0.881906i	$0.343740\pi$
$80$	3.80919	0.425880
$81$	−0.541573	−0.0601748
$82$	21.1661	2.33740
$83$	12.8430	1.40971	0.704853	−	0.709353i	$-0.251013\pi$
$83$	12.8430	1.40971	0.704853	+	0.709353i	$0.251013\pi$
$84$	6.10355	0.665952
$85$	0.903906	0.0980424
$86$	−10.1880	−1.09860
$87$	−5.34529	−0.573076
$88$	−7.31508	−0.779790
$89$	−10.8208	−1.14700	−0.573499	−	0.819206i	$-0.694414\pi$
$89$	−10.8208	−1.14700	−0.573499	+	0.819206i	$0.694414\pi$
$90$	2.46706	0.260051
$91$	0	0
$92$	−1.44180	−0.150318
$93$	1.10798	0.114893
$94$	−7.33158	−0.756195
$95$	4.67124	0.479259
$96$	6.87927	0.702112
$97$	0.0691975	0.00702595	0.00351297	−	0.999994i	$-0.498882\pi$
$97$	0.0691975	0.00702595	0.00351297	+	0.999994i	$0.498882\pi$
$98$	22.2240	2.24496
$99$	−9.62559	−0.967408
$100$	−5.51973	−0.551973
$101$	1.54300	0.153534	0.0767670	−	0.997049i	$-0.475540\pi$
$101$	1.54300	0.153534	0.0767670	+	0.997049i	$0.475540\pi$
$102$	2.34070	0.231764
$103$	4.80271	0.473225	0.236612	−	0.971604i	$-0.423963\pi$
$103$	4.80271	0.473225	0.236612	+	0.971604i	$0.423963\pi$
$104$	0	0
$105$	−3.75856	−0.366798
$106$	2.27867	0.221324
$107$	−12.3706	−1.19591	−0.597957	−	0.801528i	$-0.704021\pi$
$107$	−12.3706	−1.19591	−0.597957	+	0.801528i	$0.704021\pi$
$108$	6.62669	0.637653
$109$	6.83808	0.654970	0.327485	−	0.944856i	$-0.393799\pi$
$109$	6.83808	0.654970	0.327485	+	0.944856i	$0.393799\pi$
$110$	−7.55957	−0.720777
$111$	7.06554	0.670632
$112$	21.6963	2.05011
$113$	−6.97786	−0.656422	−0.328211	−	0.944604i	$-0.606446\pi$
$113$	−6.97786	−0.656422	−0.328211	+	0.944604i	$0.606446\pi$
$114$	12.0964	1.13293
$115$	0.887861	0.0827935
$116$	6.04599	0.561356
$117$	0	0
$118$	15.5626	1.43266
$119$	5.14844	0.471957
$120$	−1.15172	−0.105137
$121$	18.4947	1.68134
$122$	1.75959	0.159306
$123$	−13.0022	−1.17237
$124$	−1.25322	−0.112543
$125$	7.25772	0.649150
$126$	14.0518	1.25184
$127$	−14.7534	−1.30915	−0.654577	−	0.755995i	$-0.727153\pi$
$127$	−14.7534	−1.30915	−0.654577	+	0.755995i	$0.727153\pi$
$128$	10.0243	0.886035
$129$	6.25842	0.551023
$130$	0	0
$131$	−17.3028	−1.51175	−0.755875	−	0.654716i	$-0.772788\pi$
$131$	−17.3028	−1.51175	−0.755875	+	0.654716i	$0.772788\pi$
$132$	−7.54109	−0.656368
$133$	26.6063	2.30706
$134$	15.3075	1.32237
$135$	−4.08071	−0.351211
$136$	1.57762	0.135280
$137$	−1.54150	−0.131699	−0.0658495	−	0.997830i	$-0.520976\pi$
$137$	−1.54150	−0.131699	−0.0658495	+	0.997830i	$0.520976\pi$
$138$	2.29915	0.195717
$139$	16.9217	1.43528	0.717638	−	0.696416i	$-0.245223\pi$
$139$	16.9217	1.43528	0.717638	+	0.696416i	$0.245223\pi$
$140$	4.25126	0.359297
$141$	4.50375	0.379284
$142$	−6.92621	−0.581235
$143$	0	0
$144$	8.74822	0.729018
$145$	−3.72311	−0.309188
$146$	7.88966	0.652953
$147$	−13.6520	−1.12600
$148$	−7.99174	−0.656917
$149$	9.23408	0.756486	0.378243	−	0.925706i	$-0.376528\pi$
$149$	9.23408	0.756486	0.378243	+	0.925706i	$0.376528\pi$
$150$	8.80196	0.718677
$151$	21.7043	1.76627	0.883135	−	0.469119i	$-0.155429\pi$
$151$	21.7043	1.76627	0.883135	+	0.469119i	$0.155429\pi$
$152$	8.15288	0.661286
$153$	2.07592	0.167828
$154$	−43.0576	−3.46968
$155$	0.771735	0.0619872
$156$	0	0
$157$	22.7044	1.81201	0.906003	−	0.423272i	$-0.139119\pi$
$157$	22.7044	1.81201	0.906003	+	0.423272i	$0.139119\pi$
$158$	15.1152	1.20250
$159$	−1.39977	−0.111009
$160$	4.79156	0.378806
$161$	5.05706	0.398552
$162$	−0.976819	−0.0767462
$163$	3.65029	0.285913	0.142956	−	0.989729i	$-0.454339\pi$
$163$	3.65029	0.285913	0.142956	+	0.989729i	$0.454339\pi$
$164$	14.7066	1.14839
$165$	4.64380	0.361519
$166$	23.1646	1.79792
$167$	−20.8732	−1.61521	−0.807607	−	0.589721i	$-0.799238\pi$
$167$	−20.8732	−1.61521	−0.807607	+	0.589721i	$0.799238\pi$
$168$	−6.55996	−0.506112
$169$	0	0
$170$	1.63035	0.125042
$171$	10.7280	0.820392
$172$	−7.07881	−0.539754
$173$	−8.11798	−0.617198	−0.308599	−	0.951192i	$-0.599860\pi$
$173$	−8.11798	−0.617198	−0.308599	+	0.951192i	$0.599860\pi$
$174$	−9.64114	−0.730893
$175$	19.3602	1.46349
$176$	−26.8063	−2.02060
$177$	−9.56003	−0.718576
$178$	−19.5171	−1.46287
$179$	23.1226	1.72826	0.864132	−	0.503266i	$-0.167868\pi$
$179$	23.1226	1.72826	0.864132	+	0.503266i	$0.167868\pi$
$180$	1.71416	0.127766
$181$	8.27560	0.615120	0.307560	−	0.951529i	$-0.400487\pi$
$181$	8.27560	0.615120	0.307560	+	0.951529i	$0.400487\pi$
$182$	0	0
$183$	−1.08091	−0.0799029
$184$	1.54962	0.114239
$185$	4.92131	0.361822
$186$	1.99844	0.146532
$187$	−6.36103	−0.465165
$188$	−5.09412	−0.371527
$189$	−23.2428	−1.69066
$190$	8.42537	0.611241
$191$	11.9829	0.867049	0.433524	−	0.901142i	$-0.357270\pi$
$191$	11.9829	0.867049	0.433524	+	0.901142i	$0.357270\pi$
$192$	1.47019	0.106102
$193$	6.79106	0.488831	0.244416	−	0.969671i	$-0.421404\pi$
$193$	6.79106	0.488831	0.244416	+	0.969671i	$0.421404\pi$
$194$	0.124810	0.00896080
$195$	0	0
$196$	15.4416	1.10297
$197$	−2.55648	−0.182141	−0.0910707	−	0.995844i	$-0.529029\pi$
$197$	−2.55648	−0.182141	−0.0910707	+	0.995844i	$0.529029\pi$
$198$	−17.3614	−1.23382
$199$	−5.05390	−0.358262	−0.179131	−	0.983825i	$-0.557329\pi$
$199$	−5.05390	−0.358262	−0.179131	+	0.983825i	$0.557329\pi$
$200$	5.93248	0.419490
$201$	−9.40329	−0.663257
$202$	2.78306	0.195815
$203$	−21.2060	−1.48837
$204$	1.62636	0.113868
$205$	−9.05631	−0.632520
$206$	8.66250	0.603545
$207$	2.03907	0.141725
$208$	0	0
$209$	−32.8728	−2.27386
$210$	−6.77921	−0.467810
$211$	11.5141	0.792665	0.396332	−	0.918107i	$-0.370283\pi$
$211$	11.5141	0.792665	0.396332	+	0.918107i	$0.370283\pi$
$212$	1.58326	0.108739
$213$	4.25473	0.291529
$214$	−22.3125	−1.52525
$215$	4.35912	0.297290
$216$	−7.12221	−0.484605
$217$	4.39563	0.298395
$218$	12.3336	0.835340
$219$	−4.84657	−0.327501
$220$	−5.25253	−0.354126
$221$	0	0
$222$	12.7439	0.855315
$223$	5.79039	0.387753	0.193877	−	0.981026i	$-0.437894\pi$
$223$	5.79039	0.387753	0.193877	+	0.981026i	$0.437894\pi$
$224$	27.2917	1.82350
$225$	7.80629	0.520419
$226$	−12.5858	−0.837192
$227$	11.2255	0.745064	0.372532	−	0.928019i	$-0.378490\pi$
$227$	11.2255	0.745064	0.372532	+	0.928019i	$0.378490\pi$
$228$	8.40478	0.556620
$229$	−26.0722	−1.72290	−0.861450	−	0.507842i	$-0.830444\pi$
$229$	−26.0722	−1.72290	−0.861450	+	0.507842i	$0.830444\pi$
$230$	1.60141	0.105594
$231$	26.4500	1.74028
$232$	−6.49809	−0.426620
$233$	−3.14064	−0.205750	−0.102875	−	0.994694i	$-0.532804\pi$
$233$	−3.14064	−0.205750	−0.102875	+	0.994694i	$0.532804\pi$
$234$	0	0
$235$	3.13696	0.204633
$236$	10.8132	0.703880
$237$	−9.28517	−0.603136
$238$	9.28609	0.601928
$239$	−10.9723	−0.709737	−0.354868	−	0.934916i	$-0.615474\pi$
$239$	−10.9723	−0.709737	−0.354868	+	0.934916i	$0.615474\pi$
$240$	−4.22052	−0.272433
$241$	6.64065	0.427762	0.213881	−	0.976860i	$-0.431390\pi$
$241$	6.64065	0.427762	0.213881	+	0.976860i	$0.431390\pi$
$242$	33.3584	2.14436
$243$	−15.2631	−0.979127
$244$	1.22260	0.0782688
$245$	−9.50895	−0.607505
$246$	−23.4517	−1.49522
$247$	0	0
$248$	1.34694	0.0855305
$249$	−14.2299	−0.901781
$250$	13.0905	0.827918
$251$	−12.1934	−0.769642	−0.384821	−	0.922991i	$-0.625737\pi$
$251$	−12.1934	−0.769642	−0.384821	+	0.922991i	$0.625737\pi$
$252$	9.76348	0.615042
$253$	−6.24812	−0.392816
$254$	−26.6103	−1.66968
$255$	−1.00151	−0.0627171
$256$	20.7344	1.29590
$257$	18.8733	1.17728	0.588641	−	0.808394i	$-0.299663\pi$
$257$	18.8733	1.17728	0.588641	+	0.808394i	$0.299663\pi$
$258$	11.2881	0.702767
$259$	28.0306	1.74174
$260$	0	0
$261$	−8.55054	−0.529265
$262$	−31.2085	−1.92807
$263$	−7.28401	−0.449151	−0.224576	−	0.974457i	$-0.572100\pi$
$263$	−7.28401	−0.449151	−0.224576	+	0.974457i	$0.572100\pi$
$264$	8.10499	0.498828
$265$	−0.974973	−0.0598921
$266$	47.9890	2.94240
$267$	11.9892	0.733728
$268$	10.6359	0.649693
$269$	−18.0480	−1.10041	−0.550203	−	0.835031i	$-0.685450\pi$
$269$	−18.0480	−1.10041	−0.550203	+	0.835031i	$0.685450\pi$
$270$	−7.36025	−0.447931
$271$	0.880778	0.0535034	0.0267517	−	0.999642i	$-0.491484\pi$
$271$	0.880778	0.0535034	0.0267517	+	0.999642i	$0.491484\pi$
$272$	5.78122	0.350538
$273$	0	0
$274$	−2.78035	−0.167967
$275$	−23.9200	−1.44243
$276$	1.59749	0.0961578
$277$	21.3545	1.28307	0.641534	−	0.767094i	$-0.278298\pi$
$277$	21.3545	1.28307	0.641534	+	0.767094i	$0.278298\pi$
$278$	30.5211	1.83053
$279$	1.77237	0.106109
$280$	−4.56915	−0.273059
$281$	16.9935	1.01374	0.506872	−	0.862021i	$-0.330802\pi$
$281$	16.9935	1.01374	0.506872	+	0.862021i	$0.330802\pi$
$282$	8.12327	0.483734
$283$	−20.0191	−1.19001	−0.595006	−	0.803721i	$-0.702850\pi$
$283$	−20.0191	−1.19001	−0.595006	+	0.803721i	$0.702850\pi$
$284$	−4.81246	−0.285567
$285$	−5.17566	−0.306579
$286$	0	0
$287$	−51.5827	−3.04483
$288$	11.0043	0.648437
$289$	−15.6281	−0.919302
$290$	−6.71527	−0.394334
$291$	−0.0766697	−0.00449446
$292$	5.48188	0.320803
$293$	26.7083	1.56032	0.780158	−	0.625583i	$-0.215139\pi$
$293$	26.7083	1.56032	0.780158	+	0.625583i	$0.215139\pi$
$294$	−24.6238	−1.43609
$295$	−6.65877	−0.387689
$296$	8.58933	0.499245
$297$	28.7170	1.66633
$298$	16.6552	0.964812
$299$	0	0
$300$	6.11577	0.353094
$301$	24.8286	1.43110
$302$	39.1474	2.25268
$303$	−1.70962	−0.0982148
$304$	29.8764	1.71353
$305$	−0.752875	−0.0431095
$306$	3.74427	0.214046
$307$	−26.9507	−1.53816	−0.769080	−	0.639152i	$-0.779285\pi$
$307$	−26.9507	−1.53816	−0.769080	+	0.639152i	$0.779285\pi$
$308$	−29.9173	−1.70469
$309$	−5.32132	−0.302719
$310$	1.39195	0.0790577
$311$	−17.1492	−0.972443	−0.486222	−	0.873836i	$-0.661625\pi$
$311$	−17.1492	−0.972443	−0.486222	+	0.873836i	$0.661625\pi$
$312$	0	0
$313$	−18.2964	−1.03417	−0.517087	−	0.855933i	$-0.672984\pi$
$313$	−18.2964	−1.03417	−0.517087	+	0.855933i	$0.672984\pi$
$314$	40.9512	2.31101
$315$	−6.01235	−0.338757
$316$	10.5023	0.590802
$317$	20.2800	1.13904	0.569519	−	0.821978i	$-0.307130\pi$
$317$	20.2800	1.13904	0.569519	+	0.821978i	$0.307130\pi$
$318$	−2.52473	−0.141580
$319$	26.2006	1.46695
$320$	1.02402	0.0572444
$321$	13.7065	0.765020
$322$	9.12126	0.508308
$323$	7.08956	0.394474
$324$	−0.678713	−0.0377063
$325$	0	0
$326$	6.58391	0.364649
$327$	−7.57648	−0.418980
$328$	−15.8063	−0.872758
$329$	17.8674	0.985062
$330$	8.37588	0.461077
$331$	29.8669	1.64163	0.820817	−	0.571191i	$-0.193518\pi$
$331$	29.8669	1.64163	0.820817	+	0.571191i	$0.193518\pi$
$332$	16.0952	0.883339
$333$	11.3023	0.619363
$334$	−37.6483	−2.06002
$335$	−6.54960	−0.357843
$336$	−24.0391	−1.31144
$337$	−25.6842	−1.39911	−0.699555	−	0.714579i	$-0.746618\pi$
$337$	−25.6842	−1.39911	−0.699555	+	0.714579i	$0.746618\pi$
$338$	0	0
$339$	7.73136	0.419910
$340$	1.13280	0.0614345
$341$	−5.43090	−0.294100
$342$	19.3498	1.04632
$343$	−23.3915	−1.26302
$344$	7.60814	0.410203
$345$	−0.983735	−0.0529625
$346$	−14.6421	−0.787167
$347$	4.35012	0.233527	0.116763	−	0.993160i	$-0.462748\pi$
$347$	4.35012	0.233527	0.116763	+	0.993160i	$0.462748\pi$
$348$	−6.69885	−0.359096
$349$	4.98391	0.266782	0.133391	−	0.991063i	$-0.457413\pi$
$349$	4.98391	0.266782	0.133391	+	0.991063i	$0.457413\pi$
$350$	34.9194	1.86652
$351$	0	0
$352$	−33.7195	−1.79726
$353$	9.63154	0.512635	0.256318	−	0.966593i	$-0.417491\pi$
$353$	9.63154	0.512635	0.256318	+	0.966593i	$0.417491\pi$
$354$	−17.2431	−0.916462
$355$	2.96351	0.157287
$356$	−13.5608	−0.718723
$357$	−5.70439	−0.301908
$358$	41.7055	2.20420
$359$	−36.8886	−1.94691	−0.973453	−	0.228887i	$-0.926491\pi$
$359$	−36.8886	−1.94691	−0.973453	+	0.228887i	$0.926491\pi$
$360$	−1.84234	−0.0970999
$361$	17.6377	0.928301
$362$	14.9264	0.784516
$363$	−20.4918	−1.07554
$364$	0	0
$365$	−3.37574	−0.176694
$366$	−1.94960	−0.101907
$367$	−3.13314	−0.163549	−0.0817743	−	0.996651i	$-0.526059\pi$
$367$	−3.13314	−0.163549	−0.0817743	+	0.996651i	$0.526059\pi$
$368$	5.67860	0.296018
$369$	−20.7988	−1.08274
$370$	8.87641	0.461463
$371$	−5.55323	−0.288309
$372$	1.38855	0.0719930
$373$	−17.5456	−0.908478	−0.454239	−	0.890880i	$-0.650089\pi$
$373$	−17.5456	−0.908478	−0.454239	+	0.890880i	$0.650089\pi$
$374$	−11.4732	−0.593265
$375$	−8.04143	−0.415258
$376$	5.47505	0.282354
$377$	0	0
$378$	−41.9223	−2.15625
$379$	28.4806	1.46295	0.731476	−	0.681867i	$-0.238832\pi$
$379$	28.4806	1.46295	0.731476	+	0.681867i	$0.238832\pi$
$380$	5.85411	0.300310
$381$	16.3465	0.837459
$382$	21.6131	1.10582
$383$	−10.6706	−0.545240	−0.272620	−	0.962122i	$-0.587890\pi$
$383$	−10.6706	−0.545240	−0.272620	+	0.962122i	$0.587890\pi$
$384$	−11.1068	−0.566792
$385$	18.4230	0.938924
$386$	12.2488	0.623449
$387$	10.0112	0.508898
$388$	0.0867201	0.00440254
$389$	14.5072	0.735545	0.367773	−	0.929916i	$-0.380120\pi$
$389$	14.5072	0.735545	0.367773	+	0.929916i	$0.380120\pi$
$390$	0	0
$391$	1.34751	0.0681466
$392$	−16.5963	−0.838241
$393$	19.1712	0.967058
$394$	−4.61104	−0.232301
$395$	−6.46732	−0.325406
$396$	−12.0630	−0.606190
$397$	−30.7256	−1.54207	−0.771037	−	0.636790i	$-0.780262\pi$
$397$	−30.7256	−1.54207	−0.771037	+	0.636790i	$0.780262\pi$
$398$	−9.11557	−0.456922
$399$	−29.4794	−1.47581
$400$	21.7397	1.08699
$401$	31.0341	1.54977	0.774885	−	0.632102i	$-0.217808\pi$
$401$	31.0341	1.54977	0.774885	+	0.632102i	$0.217808\pi$
$402$	−16.9604	−0.845910
$403$	0	0
$404$	1.93372	0.0962063
$405$	0.417951	0.0207681
$406$	−38.2487	−1.89825
$407$	−34.6326	−1.71667
$408$	−1.74798	−0.0865377
$409$	1.81236	0.0896156	0.0448078	−	0.998996i	$-0.485732\pi$
$409$	1.81236	0.0896156	0.0448078	+	0.998996i	$0.485732\pi$
$410$	−16.3346	−0.806708
$411$	1.70795	0.0842471
$412$	6.01887	0.296528
$413$	−37.9269	−1.86626
$414$	3.67781	0.180755
$415$	−9.91142	−0.486532
$416$	0	0
$417$	−18.7489	−0.918139
$418$	−59.2916	−2.90005
$419$	−18.5901	−0.908187	−0.454094	−	0.890954i	$-0.650037\pi$
$419$	−18.5901	−0.908187	−0.454094	+	0.890954i	$0.650037\pi$
$420$	−4.71032	−0.229840
$421$	5.36839	0.261639	0.130820	−	0.991406i	$-0.458239\pi$
$421$	5.36839	0.261639	0.130820	+	0.991406i	$0.458239\pi$
$422$	20.7677	1.01095
$423$	7.20437	0.350288
$424$	−1.70166	−0.0826397
$425$	5.15875	0.250236
$426$	7.67413	0.371813
$427$	−4.28821	−0.207521
$428$	−15.5032	−0.749375
$429$	0	0
$430$	7.86242	0.379160
$431$	22.4260	1.08022	0.540111	−	0.841594i	$-0.318382\pi$
$431$	22.4260	1.08022	0.540111	+	0.841594i	$0.318382\pi$
$432$	−26.0995	−1.25571
$433$	−13.2953	−0.638930	−0.319465	−	0.947598i	$-0.603503\pi$
$433$	−13.2953	−0.638930	−0.319465	+	0.947598i	$0.603503\pi$
$434$	7.92826	0.380569
$435$	4.12515	0.197786
$436$	8.56965	0.410412
$437$	6.96372	0.333120
$438$	−8.74161	−0.417690
$439$	−31.6140	−1.50885	−0.754426	−	0.656385i	$-0.772085\pi$
$439$	−31.6140	−1.50885	−0.754426	+	0.656385i	$0.772085\pi$
$440$	5.64530	0.269129
$441$	−21.8384	−1.03992
$442$	0	0
$443$	26.6865	1.26791	0.633957	−	0.773368i	$-0.281430\pi$
$443$	26.6865	1.26791	0.633957	+	0.773368i	$0.281430\pi$
$444$	8.85471	0.420226
$445$	8.35075	0.395863
$446$	10.4440	0.494535
$447$	−10.2312	−0.483920
$448$	5.83258	0.275564
$449$	−19.8020	−0.934512	−0.467256	−	0.884122i	$-0.654757\pi$
$449$	−19.8020	−0.934512	−0.467256	+	0.884122i	$0.654757\pi$
$450$	14.0800	0.663736
$451$	63.7317	3.00101
$452$	−8.74483	−0.411322
$453$	−24.0480	−1.12987
$454$	20.2471	0.950246
$455$	0	0
$456$	−9.03326	−0.423021
$457$	22.2437	1.04052	0.520258	−	0.854009i	$-0.325836\pi$
$457$	22.2437	1.04052	0.520258	+	0.854009i	$0.325836\pi$
$458$	−47.0257	−2.19737
$459$	−6.19331	−0.289079
$460$	1.11269	0.0518794
$461$	5.25642	0.244816	0.122408	−	0.992480i	$-0.460938\pi$
$461$	5.25642	0.244816	0.122408	+	0.992480i	$0.460938\pi$
$462$	47.7071	2.21954
$463$	1.95426	0.0908223	0.0454112	−	0.998968i	$-0.485540\pi$
$463$	1.95426	0.0908223	0.0454112	+	0.998968i	$0.485540\pi$
$464$	−23.8124	−1.10546
$465$	−0.855069	−0.0396529
$466$	−5.66468	−0.262411
$467$	−32.8358	−1.51946	−0.759730	−	0.650239i	$-0.774669\pi$
$467$	−32.8358	−1.51946	−0.759730	+	0.650239i	$0.774669\pi$
$468$	0	0
$469$	−37.3051	−1.72259
$470$	5.65804	0.260986
$471$	−25.1561	−1.15913
$472$	−11.6218	−0.534936
$473$	−30.6763	−1.41050
$474$	−16.7474	−0.769232
$475$	26.6596	1.22323
$476$	6.45216	0.295734
$477$	−2.23913	−0.102523
$478$	−19.7903	−0.905189
$479$	−14.0568	−0.642270	−0.321135	−	0.947033i	$-0.604064\pi$
$479$	−14.0568	−0.642270	−0.321135	+	0.947033i	$0.604064\pi$
$480$	−5.30897	−0.242320
$481$	0	0
$482$	11.9775	0.545562
$483$	−5.60314	−0.254951
$484$	23.1780	1.05355
$485$	−0.0534021	−0.00242487
$486$	−27.5295	−1.24877
$487$	−7.66454	−0.347313	−0.173657	−	0.984806i	$-0.555558\pi$
$487$	−7.66454	−0.347313	−0.173657	+	0.984806i	$0.555558\pi$
$488$	−1.31402	−0.0594829
$489$	−4.04446	−0.182897
$490$	−17.1510	−0.774804
$491$	−33.8981	−1.52980	−0.764901	−	0.644148i	$-0.777212\pi$
$491$	−33.8981	−1.52980	−0.764901	+	0.644148i	$0.777212\pi$
$492$	−16.2947	−0.734620
$493$	−5.65059	−0.254490
$494$	0	0
$495$	7.42840	0.333882
$496$	4.93588	0.221627
$497$	16.8795	0.757149
$498$	−25.6660	−1.15012
$499$	31.4186	1.40649	0.703245	−	0.710947i	$-0.251734\pi$
$499$	31.4186	1.40649	0.703245	+	0.710947i	$0.251734\pi$
$500$	9.09555	0.406765
$501$	23.1271	1.03324
$502$	−21.9929	−0.981591
$503$	−16.8502	−0.751311	−0.375656	−	0.926759i	$-0.622582\pi$
$503$	−16.8502	−0.751311	−0.375656	+	0.926759i	$0.622582\pi$
$504$	−10.4936	−0.467421
$505$	−1.19078	−0.0529892
$506$	−11.2695	−0.500992
$507$	0	0
$508$	−18.4893	−0.820332
$509$	−23.7192	−1.05134	−0.525668	−	0.850690i	$-0.676185\pi$
$509$	−23.7192	−1.05134	−0.525668	+	0.850690i	$0.676185\pi$
$510$	−1.80640	−0.0799886
$511$	−19.2275	−0.850573
$512$	17.3493	0.766740
$513$	−32.0060	−1.41310
$514$	34.0412	1.50149
$515$	−3.70641	−0.163324
$516$	7.84320	0.345278
$517$	−22.0756	−0.970884
$518$	50.5580	2.22139
$519$	8.99458	0.394818
$520$	0	0
$521$	8.07286	0.353678	0.176839	−	0.984240i	$-0.443413\pi$
$521$	8.07286	0.353678	0.176839	+	0.984240i	$0.443413\pi$
$522$	−15.4223	−0.675018
$523$	32.9375	1.44026	0.720128	−	0.693841i	$-0.244083\pi$
$523$	32.9375	1.44026	0.720128	+	0.693841i	$0.244083\pi$
$524$	−21.6843	−0.947281
$525$	−21.4508	−0.936189
$526$	−13.1379	−0.572841
$527$	1.17127	0.0510211
$528$	29.7009	1.29257
$529$	−21.6764	−0.942452
$530$	−1.75853	−0.0763856
$531$	−15.2926	−0.663642
$532$	33.3437	1.44563
$533$	0	0
$534$	21.6246	0.935787
$535$	9.54685	0.412746
$536$	−11.4313	−0.493755
$537$	−25.6194	−1.10556
$538$	−32.5526	−1.40344
$539$	66.9171	2.88232
$540$	−5.11404	−0.220073
$541$	−22.2562	−0.956871	−0.478435	−	0.878123i	$-0.658796\pi$
$541$	−22.2562	−0.956871	−0.478435	+	0.878123i	$0.658796\pi$
$542$	1.58863	0.0682376
$543$	−9.16922	−0.393489
$544$	7.27217	0.311792
$545$	−5.27718	−0.226050
$546$	0	0
$547$	−0.321415	−0.0137427	−0.00687136	−	0.999976i	$-0.502187\pi$
$547$	−0.321415	−0.0137427	−0.00687136	+	0.999976i	$0.502187\pi$
$548$	−1.93184	−0.0825242
$549$	−1.72906	−0.0737945
$550$	−43.1438	−1.83966
$551$	−29.2013	−1.24402
$552$	−1.71695	−0.0730782
$553$	−36.8364	−1.56644
$554$	38.5165	1.63641
$555$	−5.45272	−0.231455
$556$	21.2066	0.899362
$557$	32.8068	1.39007	0.695034	−	0.718977i	$-0.255389\pi$
$557$	32.8068	1.39007	0.695034	+	0.718977i	$0.255389\pi$
$558$	3.19678	0.135330
$559$	0	0
$560$	−16.7438	−0.707553
$561$	7.04791	0.297563
$562$	30.6506	1.29292
$563$	13.1109	0.552557	0.276278	−	0.961078i	$-0.410899\pi$
$563$	13.1109	0.552557	0.276278	+	0.961078i	$0.410899\pi$
$564$	5.64420	0.237664
$565$	5.38506	0.226551
$566$	−36.1079	−1.51773
$567$	2.38055	0.0999738
$568$	5.17232	0.217026
$569$	−7.92078	−0.332056	−0.166028	−	0.986121i	$-0.553094\pi$
$569$	−7.92078	−0.332056	−0.166028	+	0.986121i	$0.553094\pi$
$570$	−9.33517	−0.391007
$571$	25.1527	1.05261	0.526304	−	0.850297i	$-0.323578\pi$
$571$	25.1527	1.05261	0.526304	+	0.850297i	$0.323578\pi$
$572$	0	0
$573$	−13.2768	−0.554646
$574$	−93.0382	−3.88334
$575$	5.06718	0.211316
$576$	2.35177	0.0979905
$577$	8.99328	0.374395	0.187198	−	0.982322i	$-0.440060\pi$
$577$	8.99328	0.374395	0.187198	+	0.982322i	$0.440060\pi$
$578$	−28.1880	−1.17247
$579$	−7.52438	−0.312702
$580$	−4.66590	−0.193741
$581$	−56.4532	−2.34207
$582$	−0.138287	−0.00573217
$583$	6.86115	0.284160
$584$	−5.89180	−0.243804
$585$	0	0
$586$	48.1730	1.99001
$587$	5.36014	0.221237	0.110618	−	0.993863i	$-0.464717\pi$
$587$	5.36014	0.221237	0.110618	+	0.993863i	$0.464717\pi$
$588$	−17.1091	−0.705567
$589$	6.05291	0.249406
$590$	−12.0102	−0.494453
$591$	2.83253	0.116515
$592$	31.4758	1.29365
$593$	15.8227	0.649759	0.324879	−	0.945755i	$-0.394676\pi$
$593$	15.8227	0.649759	0.324879	+	0.945755i	$0.394676\pi$
$594$	51.7961	2.12522
$595$	−3.97323	−0.162887
$596$	11.5724	0.474023
$597$	5.59964	0.229178
$598$	0	0
$599$	22.5066	0.919593	0.459797	−	0.888024i	$-0.347922\pi$
$599$	22.5066	0.919593	0.459797	+	0.888024i	$0.347922\pi$
$600$	−6.57309	−0.268345
$601$	−9.23527	−0.376714	−0.188357	−	0.982101i	$-0.560316\pi$
$601$	−9.23527	−0.376714	−0.188357	+	0.982101i	$0.560316\pi$
$602$	44.7826	1.82520
$603$	−15.0419	−0.612553
$604$	27.2003	1.10677
$605$	−14.2730	−0.580280
$606$	−3.08358	−0.125262
$607$	8.22103	0.333681	0.166841	−	0.985984i	$-0.446643\pi$
$607$	8.22103	0.333681	0.166841	+	0.985984i	$0.446643\pi$
$608$	37.5814	1.52413
$609$	23.4959	0.952102
$610$	−1.35794	−0.0549813
$611$	0	0
$612$	2.60159	0.105163
$613$	−6.63476	−0.267975	−0.133988	−	0.990983i	$-0.542778\pi$
$613$	−6.63476	−0.267975	−0.133988	+	0.990983i	$0.542778\pi$
$614$	−48.6102	−1.96175
$615$	10.0342	0.404620
$616$	32.1544	1.29554
$617$	24.2825	0.977576	0.488788	−	0.872403i	$-0.337439\pi$
$617$	24.2825	0.977576	0.488788	+	0.872403i	$0.337439\pi$
$618$	−9.59790	−0.386084
$619$	6.89786	0.277248	0.138624	−	0.990345i	$-0.455732\pi$
$619$	6.89786	0.277248	0.138624	+	0.990345i	$0.455732\pi$
$620$	0.967157	0.0388419
$621$	−6.08338	−0.244118
$622$	−30.9315	−1.24024
$623$	47.5640	1.90561
$624$	0	0
$625$	16.4211	0.656844
$626$	−33.0007	−1.31897
$627$	36.4225	1.45457
$628$	28.4537	1.13542
$629$	7.46909	0.297812
$630$	−10.8443	−0.432047
$631$	8.02010	0.319275	0.159638	−	0.987176i	$-0.448967\pi$
$631$	8.02010	0.319275	0.159638	+	0.987176i	$0.448967\pi$
$632$	−11.2877	−0.448999
$633$	−12.7574	−0.507063
$634$	36.5784	1.45271
$635$	11.3857	0.451829
$636$	−1.75423	−0.0695597
$637$	0	0
$638$	47.2571	1.87093
$639$	6.80603	0.269242
$640$	−7.73613	−0.305797
$641$	−31.1453	−1.23016	−0.615082	−	0.788463i	$-0.710877\pi$
$641$	−31.1453	−1.23016	−0.615082	+	0.788463i	$0.710877\pi$
$642$	24.7219	0.975697
$643$	26.6445	1.05076	0.525378	−	0.850869i	$-0.323924\pi$
$643$	26.6445	1.05076	0.525378	+	0.850869i	$0.323924\pi$
$644$	6.33763	0.249738
$645$	−4.82984	−0.190175
$646$	12.7872	0.503107
$647$	−1.24485	−0.0489402	−0.0244701	−	0.999701i	$-0.507790\pi$
$647$	−1.24485	−0.0489402	−0.0244701	+	0.999701i	$0.507790\pi$
$648$	0.729465	0.0286561
$649$	46.8596	1.83940
$650$	0	0
$651$	−4.87028	−0.190881
$652$	4.57463	0.179156
$653$	18.3460	0.717936	0.358968	−	0.933350i	$-0.383129\pi$
$653$	18.3460	0.717936	0.358968	+	0.933350i	$0.383129\pi$
$654$	−13.6655	−0.534362
$655$	13.3531	0.521751
$656$	−57.9226	−2.26150
$657$	−7.75276	−0.302464
$658$	32.2269	1.25634
$659$	16.3726	0.637785	0.318893	−	0.947791i	$-0.396689\pi$
$659$	16.3726	0.637785	0.318893	+	0.947791i	$0.396689\pi$
$660$	5.81972	0.226532
$661$	20.7767	0.808121	0.404060	−	0.914732i	$-0.367599\pi$
$661$	20.7767	0.808121	0.404060	+	0.914732i	$0.367599\pi$
$662$	53.8701	2.09372
$663$	0	0
$664$	−17.2988	−0.671322
$665$	−20.5330	−0.796237
$666$	20.3857	0.789928
$667$	−5.55029	−0.214908
$668$	−26.1588	−1.01211
$669$	−6.41565	−0.248044
$670$	−11.8133	−0.456388
$671$	5.29818	0.204534
$672$	−30.2387	−1.16648
$673$	13.3140	0.513216	0.256608	−	0.966516i	$-0.417395\pi$
$673$	13.3140	0.513216	0.256608	+	0.966516i	$0.417395\pi$
$674$	−46.3259	−1.78441
$675$	−23.2893	−0.896406
$676$	0	0
$677$	9.58632	0.368432	0.184216	−	0.982886i	$-0.441025\pi$
$677$	9.58632	0.368432	0.184216	+	0.982886i	$0.441025\pi$
$678$	13.9448	0.535547
$679$	−0.304167	−0.0116728
$680$	−1.21750	−0.0466891
$681$	−12.4377	−0.476614
$682$	−9.79556	−0.375091
$683$	−23.3627	−0.893947	−0.446974	−	0.894547i	$-0.647498\pi$
$683$	−23.3627	−0.893947	−0.446974	+	0.894547i	$0.647498\pi$
$684$	13.4446	0.514068
$685$	1.18963	0.0454533
$686$	−42.1905	−1.61084
$687$	28.8876	1.10213
$688$	27.8802	1.06292
$689$	0	0
$690$	−1.77433	−0.0675477
$691$	−5.49572	−0.209067	−0.104534	−	0.994521i	$-0.533335\pi$
$691$	−5.49572	−0.209067	−0.104534	+	0.994521i	$0.533335\pi$
$692$	−10.1736	−0.386744
$693$	42.3105	1.60724
$694$	7.84618	0.297837
$695$	−13.0590	−0.495357
$696$	7.19977	0.272907
$697$	−13.7448	−0.520622
$698$	8.98932	0.340251
$699$	3.47977	0.131617
$700$	24.2627	0.917043
$701$	43.4482	1.64101	0.820507	−	0.571636i	$-0.193691\pi$
$701$	43.4482	1.64101	0.820507	+	0.571636i	$0.193691\pi$
$702$	0	0
$703$	38.5990	1.45579
$704$	−7.20630	−0.271598
$705$	−3.47570	−0.130902
$706$	17.3721	0.653808
$707$	−6.78244	−0.255080
$708$	−11.9809	−0.450268
$709$	2.98948	0.112272	0.0561361	−	0.998423i	$-0.482122\pi$
$709$	2.98948	0.112272	0.0561361	+	0.998423i	$0.482122\pi$
$710$	5.34520	0.200602
$711$	−14.8529	−0.557028
$712$	14.5749	0.546216
$713$	1.15047	0.0430856
$714$	−10.2888	−0.385050
$715$	0	0
$716$	28.9778	1.08295
$717$	12.1571	0.454015
$718$	−66.5348	−2.48306
$719$	−8.67861	−0.323658	−0.161829	−	0.986819i	$-0.551739\pi$
$719$	−8.67861	−0.323658	−0.161829	+	0.986819i	$0.551739\pi$
$720$	−6.75130	−0.251606
$721$	−21.1109	−0.786211
$722$	31.8126	1.18394
$723$	−7.35773	−0.273637
$724$	10.3712	0.385442
$725$	−21.2485	−0.789148
$726$	−36.9605	−1.37173
$727$	−3.15935	−0.117174	−0.0585869	−	0.998282i	$-0.518659\pi$
$727$	−3.15935	−0.117174	−0.0585869	+	0.998282i	$0.518659\pi$
$728$	0	0
$729$	18.5359	0.686517
$730$	−6.08872	−0.225354
$731$	6.61586	0.244697
$732$	−1.35462	−0.0500681
$733$	28.0004	1.03422	0.517109	−	0.855920i	$-0.327008\pi$
$733$	28.0004	1.03422	0.517109	+	0.855920i	$0.327008\pi$
$734$	−5.65115	−0.208588
$735$	10.5358	0.388617
$736$	7.14309	0.263298
$737$	46.0913	1.69779
$738$	−37.5142	−1.38092
$739$	−48.9381	−1.80022	−0.900109	−	0.435664i	$-0.856513\pi$
$739$	−48.9381	−1.80022	−0.900109	+	0.435664i	$0.856513\pi$
$740$	6.16750	0.226722
$741$	0	0
$742$	−10.0162	−0.367706
$743$	15.1832	0.557019	0.278509	−	0.960434i	$-0.410160\pi$
$743$	15.1832	0.557019	0.278509	+	0.960434i	$0.410160\pi$
$744$	−1.49238	−0.0547134
$745$	−7.12626	−0.261086
$746$	−31.6465	−1.15866
$747$	−22.7627	−0.832842
$748$	−7.97180	−0.291478
$749$	54.3767	1.98688
$750$	−14.5041	−0.529614
$751$	15.9198	0.580923	0.290462	−	0.956887i	$-0.406191\pi$
$751$	15.9198	0.580923	0.290462	+	0.956887i	$0.406191\pi$
$752$	20.0634	0.731638
$753$	13.5101	0.492335
$754$	0	0
$755$	−16.7499	−0.609593
$756$	−29.1284	−1.05939
$757$	−22.5455	−0.819431	−0.409715	−	0.912213i	$-0.634372\pi$
$757$	−22.5455	−0.819431	−0.409715	+	0.912213i	$0.634372\pi$
$758$	51.3697	1.86583
$759$	6.92281	0.251282
$760$	−6.29186	−0.228230
$761$	19.7074	0.714392	0.357196	−	0.934029i	$-0.383733\pi$
$761$	19.7074	0.714392	0.357196	+	0.934029i	$0.383733\pi$
$762$	29.4838	1.06808
$763$	−30.0577	−1.08816
$764$	15.0172	0.543303
$765$	−1.60206	−0.0579225
$766$	−19.2462	−0.695392
$767$	0	0
$768$	−22.9734	−0.828980
$769$	4.89356	0.176466	0.0882332	−	0.996100i	$-0.471878\pi$
$769$	4.89356	0.176466	0.0882332	+	0.996100i	$0.471878\pi$
$770$	33.2290	1.19749
$771$	−20.9113	−0.753101
$772$	8.51072	0.306308
$773$	39.8265	1.43246	0.716231	−	0.697864i	$-0.245866\pi$
$773$	39.8265	1.43246	0.716231	+	0.697864i	$0.245866\pi$
$774$	18.0569	0.649042
$775$	4.40443	0.158212
$776$	−0.0932047	−0.00334585
$777$	−31.0575	−1.11418
$778$	26.1662	0.938105
$779$	−71.0310	−2.54495
$780$	0	0
$781$	−20.8550	−0.746252
$782$	2.43047	0.0869133
$783$	25.5097	0.911644
$784$	−60.8176	−2.17206
$785$	−17.5217	−0.625378
$786$	34.5785	1.23337
$787$	−26.2552	−0.935896	−0.467948	−	0.883756i	$-0.655007\pi$
$787$	−26.2552	−0.935896	−0.467948	+	0.883756i	$0.655007\pi$
$788$	−3.20384	−0.114132
$789$	8.07056	0.287319
$790$	−11.6649	−0.415019
$791$	30.6721	1.09057
$792$	12.9651	0.460693
$793$	0	0
$794$	−55.4188	−1.96674
$795$	1.08025	0.0383126
$796$	−6.33367	−0.224491
$797$	−16.3967	−0.580800	−0.290400	−	0.956905i	$-0.593788\pi$
$797$	−16.3967	−0.580800	−0.290400	+	0.956905i	$0.593788\pi$
$798$	−53.1710	−1.88223
$799$	4.76098	0.168431
$800$	27.3463	0.966837
$801$	19.1784	0.677636
$802$	55.9753	1.97656
$803$	23.7560	0.838331
$804$	−11.7844	−0.415605
$805$	−3.90271	−0.137552
$806$	0	0
$807$	19.9969	0.703924
$808$	−2.07832	−0.0731150
$809$	−14.1592	−0.497809	−0.248905	−	0.968528i	$-0.580071\pi$
$809$	−14.1592	−0.497809	−0.248905	+	0.968528i	$0.580071\pi$
$810$	0.753845	0.0264874
$811$	20.7922	0.730114	0.365057	−	0.930985i	$-0.381049\pi$
$811$	20.7922	0.730114	0.365057	+	0.930985i	$0.381049\pi$
$812$	−26.5759	−0.932631
$813$	−0.975887	−0.0342259
$814$	−62.4657	−2.18942
$815$	−2.81705	−0.0986771
$816$	−6.40550	−0.224237
$817$	34.1897	1.19615
$818$	3.26891	0.114295
$819$	0	0
$820$	−11.3496	−0.396345
$821$	26.8337	0.936502	0.468251	−	0.883596i	$-0.344884\pi$
$821$	26.8337	0.936502	0.468251	+	0.883596i	$0.344884\pi$
$822$	3.08058	0.107448
$823$	1.19210	0.0415542	0.0207771	−	0.999784i	$-0.493386\pi$
$823$	1.19210	0.0415542	0.0207771	+	0.999784i	$0.493386\pi$
$824$	−6.46894	−0.225356
$825$	26.5030	0.922715
$826$	−68.4075	−2.38020
$827$	8.94631	0.311094	0.155547	−	0.987829i	$-0.450286\pi$
$827$	8.94631	0.311094	0.155547	+	0.987829i	$0.450286\pi$
$828$	2.55541	0.0888068
$829$	−47.7351	−1.65791	−0.828955	−	0.559315i	$-0.811064\pi$
$829$	−47.7351	−1.65791	−0.828955	+	0.559315i	$0.811064\pi$
$830$	−17.8769	−0.620517
$831$	−23.6605	−0.820772
$832$	0	0
$833$	−14.4318	−0.500032
$834$	−33.8169	−1.17098
$835$	16.1085	0.557459
$836$	−41.1970	−1.42483
$837$	−5.28771	−0.182770
$838$	−33.5304	−1.15829
$839$	49.2176	1.69918	0.849591	−	0.527442i	$-0.176849\pi$
$839$	49.2176	1.69918	0.849591	+	0.527442i	$0.176849\pi$
$840$	5.06255	0.174674
$841$	−5.72570	−0.197438
$842$	9.68281	0.333692
$843$	−18.8285	−0.648487
$844$	14.4298	0.496693
$845$	0	0
$846$	12.9943	0.446753
$847$	−81.2959	−2.79336
$848$	−6.23575	−0.214137
$849$	22.1808	0.761244
$850$	9.30468	0.319148
$851$	7.33651	0.251492
$852$	5.33213	0.182676
$853$	46.8047	1.60256	0.801281	−	0.598288i	$-0.204152\pi$
$853$	46.8047	1.60256	0.801281	+	0.598288i	$0.204152\pi$
$854$	−7.73451	−0.264669
$855$	−8.27918	−0.283142
$856$	16.6625	0.569511
$857$	−26.2083	−0.895257	−0.447629	−	0.894220i	$-0.647731\pi$
$857$	−26.2083	−0.895257	−0.447629	+	0.894220i	$0.647731\pi$
$858$	0	0
$859$	39.6143	1.35162	0.675812	−	0.737074i	$-0.263793\pi$
$859$	39.6143	1.35162	0.675812	+	0.737074i	$0.263793\pi$
$860$	5.46296	0.186285
$861$	57.1528	1.94776
$862$	40.4491	1.37770
$863$	−57.2856	−1.95003	−0.975013	−	0.222149i	$-0.928693\pi$
$863$	−57.2856	−1.95003	−0.975013	+	0.222149i	$0.928693\pi$
$864$	−32.8304	−1.11691
$865$	6.26492	0.213014
$866$	−23.9803	−0.814883
$867$	17.3157	0.588072
$868$	5.50871	0.186978
$869$	45.5123	1.54390
$870$	7.44040	0.252253
$871$	0	0
$872$	−9.21046	−0.311906
$873$	−0.122644	−0.00415087
$874$	12.5603	0.424857
$875$	−31.9022	−1.07849
$876$	−6.07384	−0.205216
$877$	48.8415	1.64926	0.824630	−	0.565672i	$-0.191383\pi$
$877$	48.8415	1.64926	0.824630	+	0.565672i	$0.191383\pi$
$878$	−57.0211	−1.92437
$879$	−29.5923	−0.998125
$880$	20.6873	0.697370
$881$	−31.1046	−1.04794	−0.523971	−	0.851736i	$-0.675550\pi$
$881$	−31.1046	−1.04794	−0.523971	+	0.851736i	$0.675550\pi$
$882$	−39.3892	−1.32630
$883$	32.2081	1.08389	0.541945	−	0.840414i	$-0.317688\pi$
$883$	32.2081	1.08389	0.541945	+	0.840414i	$0.317688\pi$
$884$	0	0
$885$	7.37780	0.248002
$886$	48.1336	1.61708
$887$	−19.7522	−0.663213	−0.331607	−	0.943418i	$-0.607591\pi$
$887$	−19.7522	−0.663213	−0.331607	+	0.943418i	$0.607591\pi$
$888$	−9.51684	−0.319364
$889$	64.8505	2.17502
$890$	15.0620	0.504879
$891$	−2.94123	−0.0985350
$892$	7.25666	0.242971
$893$	24.6040	0.823340
$894$	−18.4537	−0.617185
$895$	−17.8445	−0.596476
$896$	−44.0633	−1.47205
$897$	0	0
$898$	−35.7162	−1.19186
$899$	−4.82434	−0.160901
$900$	9.78303	0.326101
$901$	−1.47972	−0.0492966
$902$	114.951	3.82745
$903$	−27.5097	−0.915464
$904$	9.39874	0.312597
$905$	−6.38656	−0.212297
$906$	−43.3746	−1.44103
$907$	44.9806	1.49356	0.746778	−	0.665073i	$-0.231600\pi$
$907$	44.9806	1.49356	0.746778	+	0.665073i	$0.231600\pi$
$908$	14.0681	0.466866
$909$	−2.73477	−0.0907065
$910$	0	0
$911$	−24.7942	−0.821469	−0.410735	−	0.911755i	$-0.634728\pi$
$911$	−24.7942	−0.821469	−0.410735	+	0.911755i	$0.634728\pi$
$912$	−33.1026	−1.09614
$913$	69.7493	2.30836
$914$	40.1203	1.32706
$915$	0.834173	0.0275769
$916$	−32.6743	−1.07959
$917$	76.0565	2.51161
$918$	−11.1707	−0.368688
$919$	−51.7865	−1.70828	−0.854140	−	0.520044i	$-0.825916\pi$
$919$	−51.7865	−1.70828	−0.854140	+	0.520044i	$0.825916\pi$
$920$	−1.19589	−0.0394274
$921$	29.8610	0.983952
$922$	9.48084	0.312235
$923$	0	0
$924$	33.1478	1.09048
$925$	28.0868	0.923487
$926$	3.52485	0.115834
$927$	−8.51219	−0.279577
$928$	−29.9535	−0.983271
$929$	28.3489	0.930096	0.465048	−	0.885285i	$-0.346037\pi$
$929$	28.3489	0.930096	0.465048	+	0.885285i	$0.346037\pi$
$930$	−1.54226	−0.0505728
$931$	−74.5811	−2.44430
$932$	−3.93593	−0.128926
$933$	19.0010	0.622066
$934$	−59.2249	−1.93790
$935$	4.90903	0.160542
$936$	0	0
$937$	2.21095	0.0722287	0.0361143	−	0.999348i	$-0.488502\pi$
$937$	2.21095	0.0722287	0.0361143	+	0.999348i	$0.488502\pi$
$938$	−67.2860	−2.19697
$939$	20.2721	0.661555
$940$	3.93131	0.128225
$941$	22.2919	0.726694	0.363347	−	0.931654i	$-0.381634\pi$
$941$	22.2919	0.726694	0.363347	+	0.931654i	$0.381634\pi$
$942$	−45.3732	−1.47834
$943$	−13.5008	−0.439648
$944$	−42.5883	−1.38613
$945$	17.9373	0.583499
$946$	−55.3300	−1.79893
$947$	−14.2509	−0.463092	−0.231546	−	0.972824i	$-0.574378\pi$
$947$	−14.2509	−0.463092	−0.231546	+	0.972824i	$0.574378\pi$
$948$	−11.6364	−0.377933
$949$	0	0
$950$	48.0851	1.56009
$951$	−22.4699	−0.728636
$952$	−6.93463	−0.224753
$953$	39.6157	1.28328	0.641639	−	0.767007i	$-0.278255\pi$
$953$	39.6157	1.28328	0.641639	+	0.767007i	$0.278255\pi$
$954$	−4.03865	−0.130756
$955$	−9.24758	−0.299245
$956$	−13.7507	−0.444730
$957$	−29.0298	−0.938399
$958$	−25.3538	−0.819143
$959$	6.77585	0.218803
$960$	−1.13460	−0.0366189
$961$	1.00000	0.0322581
$962$	0	0
$963$	21.9254	0.706536
$964$	8.32222	0.268041
$965$	−5.24089	−0.168710
$966$	−10.1062	−0.325162
$967$	−35.4974	−1.14152	−0.570760	−	0.821117i	$-0.693351\pi$
$967$	−35.4974	−1.14152	−0.570760	+	0.821117i	$0.693351\pi$
$968$	−24.9112	−0.800677
$969$	−7.85512	−0.252343
$970$	−0.0963198	−0.00309264
$971$	−5.93044	−0.190317	−0.0951584	−	0.995462i	$-0.530336\pi$
$971$	−5.93044	−0.190317	−0.0951584	+	0.995462i	$0.530336\pi$
$972$	−19.1281	−0.613533
$973$	−74.3813	−2.38456
$974$	−13.8243	−0.442959
$975$	0	0
$976$	−4.81525	−0.154133
$977$	10.4010	0.332758	0.166379	−	0.986062i	$-0.446792\pi$
$977$	10.4010	0.332758	0.166379	+	0.986062i	$0.446792\pi$
$978$	−7.29487	−0.233264
$979$	−58.7665	−1.87818
$980$	−11.9169	−0.380670
$981$	−12.1196	−0.386950
$982$	−61.1410	−1.95109
$983$	21.6354	0.690062	0.345031	−	0.938591i	$-0.387868\pi$
$983$	21.6354	0.690062	0.345031	+	0.938591i	$0.387868\pi$
$984$	17.5131	0.558298
$985$	1.97292	0.0628625
$986$	−10.1918	−0.324573
$987$	−19.7968	−0.630139
$988$	0	0
$989$	6.49843	0.206638
$990$	13.3984	0.425828
$991$	26.4991	0.841772	0.420886	−	0.907114i	$-0.361719\pi$
$991$	26.4991	0.841772	0.420886	+	0.907114i	$0.361719\pi$
$992$	6.20882	0.197130
$993$	−33.0920	−1.05014
$994$	30.4450	0.965658
$995$	3.90027	0.123647
$996$	−17.8332	−0.565067
$997$	15.2917	0.484293	0.242147	−	0.970240i	$-0.422149\pi$
$997$	15.2917	0.484293	0.242147	+	0.970240i	$0.422149\pi$
$998$	56.6688	1.79382
$999$	−33.7194	−1.06683

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.r.1.25		34
13.6	odd	12		403.2.r.a.218.8	✓	68
13.11	odd	12		403.2.r.a.342.8	yes	68
13.12	even	2		5239.2.a.q.1.10		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.8	✓	68	13.6	odd	12
403.2.r.a.342.8	yes	68	13.11	odd	12
5239.2.a.q.1.10		34	13.12	even	2
5239.2.a.r.1.25		34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+1.80367 q^{2} -1.10798 q^{3} +1.25322 q^{4} -0.771735 q^{5} -1.99844 q^{6} -4.39563 q^{7} -1.34694 q^{8} -1.77237 q^{9} +O(q^{10})\)	\(q+1.80367 q^{2} -1.10798 q^{3} +1.25322 q^{4} -0.771735 q^{5} -1.99844 q^{6} -4.39563 q^{7} -1.34694 q^{8} -1.77237 q^{9} -1.39195 q^{10} +5.43090 q^{11} -1.38855 q^{12} -7.92826 q^{14} +0.855069 q^{15} -4.93588 q^{16} -1.17127 q^{17} -3.19678 q^{18} -6.05291 q^{19} -0.967157 q^{20} +4.87028 q^{21} +9.79556 q^{22} -1.15047 q^{23} +1.49238 q^{24} -4.40443 q^{25} +5.28771 q^{27} -5.50871 q^{28} +4.82434 q^{29} +1.54226 q^{30} -1.00000 q^{31} -6.20882 q^{32} -6.01735 q^{33} -2.11258 q^{34} +3.39226 q^{35} -2.22118 q^{36} -6.37694 q^{37} -10.9175 q^{38} +1.03948 q^{40} +11.7350 q^{41} +8.78438 q^{42} -5.64848 q^{43} +6.80614 q^{44} +1.36780 q^{45} -2.07508 q^{46} -4.06481 q^{47} +5.46887 q^{48} +12.3215 q^{49} -7.94413 q^{50} +1.29774 q^{51} +1.26335 q^{53} +9.53728 q^{54} -4.19122 q^{55} +5.92063 q^{56} +6.70652 q^{57} +8.70152 q^{58} +8.62832 q^{59} +1.07159 q^{60} +0.975562 q^{61} -1.80367 q^{62} +7.79069 q^{63} -1.32691 q^{64} -10.8533 q^{66} +8.48686 q^{67} -1.46786 q^{68} +1.27471 q^{69} +6.11851 q^{70} -3.84007 q^{71} +2.38727 q^{72} +4.37422 q^{73} -11.5019 q^{74} +4.88003 q^{75} -7.58565 q^{76} -23.8722 q^{77} +8.38024 q^{79} +3.80919 q^{80} -0.541573 q^{81} +21.1661 q^{82} +12.8430 q^{83} +6.10355 q^{84} +0.903906 q^{85} -10.1880 q^{86} -5.34529 q^{87} -7.31508 q^{88} -10.8208 q^{89} +2.46706 q^{90} -1.44180 q^{92} +1.10798 q^{93} -7.33158 q^{94} +4.67124 q^{95} +6.87927 q^{96} +0.0691975 q^{97} +22.2240 q^{98} -9.62559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q + 8 * q^2 + 32 * q^4 + 16 * q^5 + 12 * q^6 + 8 * q^7 + 24 * q^8 + 34 * q^9	\( 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9} + 8 q^{10} + 26 q^{11} + 8 q^{12} - 4 q^{14} + 16 q^{15} + 36 q^{16} - 6 q^{17} + 64 q^{18} + 4 q^{19} + 40 q^{20} + 32 q^{21} + 20 q^{22} - 8 q^{23} - 16 q^{24} + 36 q^{25} - 6 q^{27} + 24 q^{28} + 32 q^{30} - 34 q^{31} + 36 q^{32} + 40 q^{33} + 16 q^{34} - 30 q^{35} + 40 q^{36} + 2 q^{37} + 18 q^{38} + 4 q^{40} + 80 q^{41} + 16 q^{42} + 12 q^{43} + 108 q^{44} + 12 q^{45} + 48 q^{46} + 24 q^{47} + 46 q^{48} + 22 q^{49} - 44 q^{50} - 28 q^{51} + 10 q^{53} + 48 q^{54} + 6 q^{55} - 2 q^{56} + 66 q^{57} - 44 q^{58} + 64 q^{59} + 48 q^{60} - 6 q^{61} - 8 q^{62} - 52 q^{63} - 12 q^{64} + 4 q^{66} + 16 q^{67} - 58 q^{68} - 28 q^{69} + 72 q^{70} + 52 q^{71} + 152 q^{72} + 42 q^{73} - 8 q^{74} - 4 q^{75} - 48 q^{76} + 10 q^{77} + 8 q^{79} + 48 q^{80} + 58 q^{81} - 42 q^{82} + 44 q^{83} - 8 q^{84} + 96 q^{85} + 16 q^{86} + 20 q^{87} + 64 q^{88} + 74 q^{89} - 26 q^{90} + 24 q^{92} - 8 q^{94} - 32 q^{95} + 50 q^{96} + 40 q^{97} + 72 q^{98} + 74 q^{99}+O(q^{100}) \) 34 * q + 8 * q^2 + 32 * q^4 + 16 * q^5 + 12 * q^6 + 8 * q^7 + 24 * q^8 + 34 * q^9 + 8 * q^10 + 26 * q^11 + 8 * q^12 - 4 * q^14 + 16 * q^15 + 36 * q^16 - 6 * q^17 + 64 * q^18 + 4 * q^19 + 40 * q^20 + 32 * q^21 + 20 * q^22 - 8 * q^23 - 16 * q^24 + 36 * q^25 - 6 * q^27 + 24 * q^28 + 32 * q^30 - 34 * q^31 + 36 * q^32 + 40 * q^33 + 16 * q^34 - 30 * q^35 + 40 * q^36 + 2 * q^37 + 18 * q^38 + 4 * q^40 + 80 * q^41 + 16 * q^42 + 12 * q^43 + 108 * q^44 + 12 * q^45 + 48 * q^46 + 24 * q^47 + 46 * q^48 + 22 * q^49 - 44 * q^50 - 28 * q^51 + 10 * q^53 + 48 * q^54 + 6 * q^55 - 2 * q^56 + 66 * q^57 - 44 * q^58 + 64 * q^59 + 48 * q^60 - 6 * q^61 - 8 * q^62 - 52 * q^63 - 12 * q^64 + 4 * q^66 + 16 * q^67 - 58 * q^68 - 28 * q^69 + 72 * q^70 + 52 * q^71 + 152 * q^72 + 42 * q^73 - 8 * q^74 - 4 * q^75 - 48 * q^76 + 10 * q^77 + 8 * q^79 + 48 * q^80 + 58 * q^81 - 42 * q^82 + 44 * q^83 - 8 * q^84 + 96 * q^85 + 16 * q^86 + 20 * q^87 + 64 * q^88 + 74 * q^89 - 26 * q^90 + 24 * q^92 - 8 * q^94 - 32 * q^95 + 50 * q^96 + 40 * q^97 + 72 * q^98 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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