LMFDB - Embedded newform 4027.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44690 q^{2} +2.58463 q^{3} +3.98731 q^{4} +2.27529 q^{5} -6.32432 q^{6} +3.46377 q^{7} -4.86273 q^{8} +3.68031 q^{9} +O(q^{10})$	\(q-2.44690 q^{2} +2.58463 q^{3} +3.98731 q^{4} +2.27529 q^{5} -6.32432 q^{6} +3.46377 q^{7} -4.86273 q^{8} +3.68031 q^{9} -5.56739 q^{10} -5.05005 q^{11} +10.3057 q^{12} +1.28353 q^{13} -8.47548 q^{14} +5.88077 q^{15} +3.92400 q^{16} +6.50258 q^{17} -9.00533 q^{18} -3.10416 q^{19} +9.07226 q^{20} +8.95255 q^{21} +12.3569 q^{22} +7.38988 q^{23} -12.5684 q^{24} +0.176928 q^{25} -3.14066 q^{26} +1.75834 q^{27} +13.8111 q^{28} +2.98380 q^{29} -14.3896 q^{30} +0.537779 q^{31} +0.123849 q^{32} -13.0525 q^{33} -15.9111 q^{34} +7.88106 q^{35} +14.6745 q^{36} +3.82076 q^{37} +7.59557 q^{38} +3.31744 q^{39} -11.0641 q^{40} +2.50067 q^{41} -21.9060 q^{42} -4.72015 q^{43} -20.1361 q^{44} +8.37375 q^{45} -18.0823 q^{46} -6.16795 q^{47} +10.1421 q^{48} +4.99768 q^{49} -0.432925 q^{50} +16.8067 q^{51} +5.11781 q^{52} -10.0020 q^{53} -4.30248 q^{54} -11.4903 q^{55} -16.8434 q^{56} -8.02311 q^{57} -7.30104 q^{58} +10.5242 q^{59} +23.4484 q^{60} -4.18841 q^{61} -1.31589 q^{62} +12.7477 q^{63} -8.15104 q^{64} +2.92039 q^{65} +31.9381 q^{66} +11.3522 q^{67} +25.9278 q^{68} +19.1001 q^{69} -19.2841 q^{70} +12.0832 q^{71} -17.8964 q^{72} -10.5570 q^{73} -9.34900 q^{74} +0.457293 q^{75} -12.3773 q^{76} -17.4922 q^{77} -8.11744 q^{78} -0.598593 q^{79} +8.92822 q^{80} -6.49626 q^{81} -6.11889 q^{82} +14.0315 q^{83} +35.6966 q^{84} +14.7952 q^{85} +11.5497 q^{86} +7.71201 q^{87} +24.5570 q^{88} -3.96737 q^{89} -20.4897 q^{90} +4.44584 q^{91} +29.4657 q^{92} +1.38996 q^{93} +15.0923 q^{94} -7.06286 q^{95} +0.320105 q^{96} +4.46761 q^{97} -12.2288 q^{98} -18.5857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) $ 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * 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 $

$2$	−2.44690	−1.73022	−0.865109	−	0.501584i	$-0.832751\pi$
$2$	−2.44690	−1.73022	−0.865109	+	0.501584i	$0.832751\pi$
$3$	2.58463	1.49224	0.746118	−	0.665814i	$-0.231915\pi$
$3$	2.58463	1.49224	0.746118	+	0.665814i	$0.231915\pi$
$4$	3.98731	1.99365
$5$	2.27529	1.01754	0.508769	−	0.860903i	$-0.330101\pi$
$5$	2.27529	1.01754	0.508769	+	0.860903i	$0.330101\pi$
$6$	−6.32432	−2.58189
$7$	3.46377	1.30918	0.654590	−	0.755984i	$-0.272841\pi$
$7$	3.46377	1.30918	0.654590	+	0.755984i	$0.272841\pi$
$8$	−4.86273	−1.71924
$9$	3.68031	1.22677
$10$	−5.56739	−1.76056
$11$	−5.05005	−1.52265	−0.761323	−	0.648372i	$-0.775450\pi$
$11$	−5.05005	−1.52265	−0.761323	+	0.648372i	$0.775450\pi$
$12$	10.3057	2.97500
$13$	1.28353	0.355986	0.177993	−	0.984032i	$-0.443040\pi$
$13$	1.28353	0.355986	0.177993	+	0.984032i	$0.443040\pi$
$14$	−8.47548	−2.26517
$15$	5.88077	1.51841
$16$	3.92400	0.980999
$17$	6.50258	1.57711	0.788553	−	0.614967i	$-0.210830\pi$
$17$	6.50258	1.57711	0.788553	+	0.614967i	$0.210830\pi$
$18$	−9.00533	−2.12258
$19$	−3.10416	−0.712144	−0.356072	−	0.934458i	$-0.615884\pi$
$19$	−3.10416	−0.712144	−0.356072	+	0.934458i	$0.615884\pi$
$20$	9.07226	2.02862
$21$	8.95255	1.95361
$22$	12.3569	2.63451
$23$	7.38988	1.54090	0.770449	−	0.637502i	$-0.220032\pi$
$23$	7.38988	1.54090	0.770449	+	0.637502i	$0.220032\pi$
$24$	−12.5684	−2.56551
$25$	0.176928	0.0353856
$26$	−3.14066	−0.615934
$27$	1.75834	0.338393
$28$	13.8111	2.61005
$29$	2.98380	0.554077	0.277039	−	0.960859i	$-0.410647\pi$
$29$	2.98380	0.554077	0.277039	+	0.960859i	$0.410647\pi$
$30$	−14.3896	−2.62718
$31$	0.537779	0.0965879	0.0482940	−	0.998833i	$-0.484622\pi$
$31$	0.537779	0.0965879	0.0482940	+	0.998833i	$0.484622\pi$
$32$	0.123849	0.0218937
$33$	−13.0525	−2.27215
$34$	−15.9111	−2.72874
$35$	7.88106	1.33214
$36$	14.6745	2.44575
$37$	3.82076	0.628128	0.314064	−	0.949402i	$-0.398309\pi$
$37$	3.82076	0.628128	0.314064	+	0.949402i	$0.398309\pi$
$38$	7.59557	1.23216
$39$	3.31744	0.531216
$40$	−11.0641	−1.74939
$41$	2.50067	0.390539	0.195270	−	0.980750i	$-0.437442\pi$
$41$	2.50067	0.390539	0.195270	+	0.980750i	$0.437442\pi$
$42$	−21.9060	−3.38017
$43$	−4.72015	−0.719817	−0.359908	−	0.932988i	$-0.617192\pi$
$43$	−4.72015	−0.719817	−0.359908	+	0.932988i	$0.617192\pi$
$44$	−20.1361	−3.03563
$45$	8.37375	1.24829
$46$	−18.0823	−2.66609
$47$	−6.16795	−0.899688	−0.449844	−	0.893107i	$-0.648520\pi$
$47$	−6.16795	−0.899688	−0.449844	+	0.893107i	$0.648520\pi$
$48$	10.1421	1.46388
$49$	4.99768	0.713955
$50$	−0.432925	−0.0612248
$51$	16.8067	2.35342
$52$	5.11781	0.709713
$53$	−10.0020	−1.37387	−0.686937	−	0.726717i	$-0.741045\pi$
$53$	−10.0020	−1.37387	−0.686937	+	0.726717i	$0.741045\pi$
$54$	−4.30248	−0.585493
$55$	−11.4903	−1.54935
$56$	−16.8434	−2.25079
$57$	−8.02311	−1.06269
$58$	−7.30104	−0.958674
$59$	10.5242	1.37013	0.685066	−	0.728481i	$-0.259773\pi$
$59$	10.5242	1.37013	0.685066	+	0.728481i	$0.259773\pi$
$60$	23.4484	3.02718
$61$	−4.18841	−0.536271	−0.268135	−	0.963381i	$-0.586407\pi$
$61$	−4.18841	−0.536271	−0.268135	+	0.963381i	$0.586407\pi$
$62$	−1.31589	−0.167118
$63$	12.7477	1.60606
$64$	−8.15104	−1.01888
$65$	2.92039	0.362230
$66$	31.9381	3.93131
$67$	11.3522	1.38689	0.693446	−	0.720509i	$-0.256092\pi$
$67$	11.3522	1.38689	0.693446	+	0.720509i	$0.256092\pi$
$68$	25.9278	3.14420
$69$	19.1001	2.29938
$70$	−19.2841	−2.30490
$71$	12.0832	1.43401	0.717004	−	0.697069i	$-0.245513\pi$
$71$	12.0832	1.43401	0.717004	+	0.697069i	$0.245513\pi$
$72$	−17.8964	−2.10911
$73$	−10.5570	−1.23560	−0.617800	−	0.786335i	$-0.711976\pi$
$73$	−10.5570	−1.23560	−0.617800	+	0.786335i	$0.711976\pi$
$74$	−9.34900	−1.08680
$75$	0.457293	0.0528037
$76$	−12.3773	−1.41977
$77$	−17.4922	−1.99342
$78$	−8.11744	−0.919119
$79$	−0.598593	−0.0673470	−0.0336735	−	0.999433i	$-0.510721\pi$
$79$	−0.598593	−0.0673470	−0.0336735	+	0.999433i	$0.510721\pi$
$80$	8.92822	0.998205
$81$	−6.49626	−0.721807
$82$	−6.11889	−0.675718
$83$	14.0315	1.54016	0.770080	−	0.637948i	$-0.220216\pi$
$83$	14.0315	1.54016	0.770080	+	0.637948i	$0.220216\pi$
$84$	35.6966	3.89481
$85$	14.7952	1.60477
$86$	11.5497	1.24544
$87$	7.71201	0.826814
$88$	24.5570	2.61779
$89$	−3.96737	−0.420540	−0.210270	−	0.977643i	$-0.567434\pi$
$89$	−3.96737	−0.420540	−0.210270	+	0.977643i	$0.567434\pi$
$90$	−20.4897	−2.15981
$91$	4.44584	0.466050
$92$	29.4657	3.07201
$93$	1.38996	0.144132
$94$	15.0923	1.55666
$95$	−7.06286	−0.724635
$96$	0.320105	0.0326705
$97$	4.46761	0.453617	0.226809	−	0.973939i	$-0.427171\pi$
$97$	4.46761	0.453617	0.226809	+	0.973939i	$0.427171\pi$
$98$	−12.2288	−1.23530
$99$	−18.5857	−1.86794
$100$	0.705466	0.0705466
$101$	19.2251	1.91297	0.956485	−	0.291781i	$-0.0942479\pi$
$101$	19.2251	1.91297	0.956485	+	0.291781i	$0.0942479\pi$
$102$	−41.1244	−4.07192
$103$	−15.1074	−1.48858	−0.744290	−	0.667856i	$-0.767212\pi$
$103$	−15.1074	−1.48858	−0.744290	+	0.667856i	$0.767212\pi$
$104$	−6.24145	−0.612024
$105$	20.3696	1.98787
$106$	24.4738	2.37710
$107$	−17.6161	−1.70302	−0.851508	−	0.524342i	$-0.824311\pi$
$107$	−17.6161	−1.70302	−0.851508	+	0.524342i	$0.824311\pi$
$108$	7.01105	0.674638
$109$	−1.22833	−0.117653	−0.0588264	−	0.998268i	$-0.518736\pi$
$109$	−1.22833	−0.117653	−0.0588264	+	0.998268i	$0.518736\pi$
$110$	28.1156	2.68072
$111$	9.87524	0.937316
$112$	13.5918	1.28431
$113$	5.87389	0.552569	0.276284	−	0.961076i	$-0.410897\pi$
$113$	5.87389	0.552569	0.276284	+	0.961076i	$0.410897\pi$
$114$	19.6317	1.83868
$115$	16.8141	1.56792
$116$	11.8973	1.10464
$117$	4.72377	0.436713
$118$	−25.7516	−2.37063
$119$	22.5234	2.06472
$120$	−28.5966	−2.61050
$121$	14.5030	1.31845
$122$	10.2486	0.927866
$123$	6.46331	0.582777
$124$	2.14429	0.192563
$125$	−10.9739	−0.981533
$126$	−31.1924	−2.77884
$127$	9.37822	0.832182	0.416091	−	0.909323i	$-0.363400\pi$
$127$	9.37822	0.832182	0.416091	+	0.909323i	$0.363400\pi$
$128$	19.6971	1.74099
$129$	−12.1998	−1.07414
$130$	−7.14590	−0.626737
$131$	13.3994	1.17072	0.585358	−	0.810775i	$-0.300954\pi$
$131$	13.3994	1.17072	0.585358	+	0.810775i	$0.300954\pi$
$132$	−52.0443	−4.52988
$133$	−10.7521	−0.932326
$134$	−27.7777	−2.39962
$135$	4.00073	0.344328
$136$	−31.6203	−2.71142
$137$	−1.41973	−0.121296	−0.0606478	−	0.998159i	$-0.519317\pi$
$137$	−1.41973	−0.121296	−0.0606478	+	0.998159i	$0.519317\pi$
$138$	−46.7360	−3.97843
$139$	−2.56273	−0.217368	−0.108684	−	0.994076i	$-0.534664\pi$
$139$	−2.56273	−0.217368	−0.108684	+	0.994076i	$0.534664\pi$
$140$	31.4242	2.65583
$141$	−15.9419	−1.34255
$142$	−29.5663	−2.48115
$143$	−6.48187	−0.542041
$144$	14.4415	1.20346
$145$	6.78899	0.563795
$146$	25.8318	2.13786
$147$	12.9172	1.06539
$148$	15.2345	1.25227
$149$	16.9613	1.38952	0.694762	−	0.719239i	$-0.255510\pi$
$149$	16.9613	1.38952	0.694762	+	0.719239i	$0.255510\pi$
$150$	−1.11895	−0.0913619
$151$	−3.48483	−0.283592	−0.141796	−	0.989896i	$-0.545288\pi$
$151$	−3.48483	−0.283592	−0.141796	+	0.989896i	$0.545288\pi$
$152$	15.0947	1.22434
$153$	23.9315	1.93475
$154$	42.8016	3.44905
$155$	1.22360	0.0982820
$156$	13.2277	1.05906
$157$	−6.86734	−0.548073	−0.274037	−	0.961719i	$-0.588359\pi$
$157$	−6.86734	−0.548073	−0.274037	+	0.961719i	$0.588359\pi$
$158$	1.46470	0.116525
$159$	−25.8513	−2.05014
$160$	0.281793	0.0222777
$161$	25.5968	2.01731
$162$	15.8957	1.24888
$163$	−20.9875	−1.64387	−0.821935	−	0.569582i	$-0.807105\pi$
$163$	−20.9875	−1.64387	−0.821935	+	0.569582i	$0.807105\pi$
$164$	9.97094	0.778600
$165$	−29.6982	−2.31200
$166$	−34.3337	−2.66481
$167$	−18.5803	−1.43779	−0.718894	−	0.695119i	$-0.755352\pi$
$167$	−18.5803	−1.43779	−0.718894	+	0.695119i	$0.755352\pi$
$168$	−43.5339	−3.35871
$169$	−11.3526	−0.873274
$170$	−36.2024	−2.77660
$171$	−11.4243	−0.873637
$172$	−18.8207	−1.43506
$173$	19.7209	1.49935	0.749674	−	0.661807i	$-0.230210\pi$
$173$	19.7209	1.49935	0.749674	+	0.661807i	$0.230210\pi$
$174$	−18.8705	−1.43057
$175$	0.612837	0.0463262
$176$	−19.8164	−1.49372
$177$	27.2011	2.04456
$178$	9.70773	0.727625
$179$	7.40159	0.553221	0.276610	−	0.960982i	$-0.410789\pi$
$179$	7.40159	0.553221	0.276610	+	0.960982i	$0.410789\pi$
$180$	33.3887	2.48865
$181$	16.2079	1.20472	0.602362	−	0.798223i	$-0.294226\pi$
$181$	16.2079	1.20472	0.602362	+	0.798223i	$0.294226\pi$
$182$	−10.8785	−0.806369
$183$	−10.8255	−0.800243
$184$	−35.9350	−2.64917
$185$	8.69331	0.639145
$186$	−3.40109	−0.249380
$187$	−32.8383	−2.40138
$188$	−24.5935	−1.79367
$189$	6.09049	0.443018
$190$	17.2821	1.25378
$191$	−2.03586	−0.147309	−0.0736547	−	0.997284i	$-0.523466\pi$
$191$	−2.03586	−0.147309	−0.0736547	+	0.997284i	$0.523466\pi$
$192$	−21.0674	−1.52041
$193$	12.1649	0.875650	0.437825	−	0.899060i	$-0.355749\pi$
$193$	12.1649	0.875650	0.437825	+	0.899060i	$0.355749\pi$
$194$	−10.9318	−0.784857
$195$	7.54813	0.540533
$196$	19.9273	1.42338
$197$	0.963613	0.0686546	0.0343273	−	0.999411i	$-0.489071\pi$
$197$	0.963613	0.0686546	0.0343273	+	0.999411i	$0.489071\pi$
$198$	45.4774	3.23194
$199$	13.2795	0.941359	0.470680	−	0.882304i	$-0.344009\pi$
$199$	13.2795	0.941359	0.470680	+	0.882304i	$0.344009\pi$
$200$	−0.860354	−0.0608362
$201$	29.3412	2.06957
$202$	−47.0419	−3.30985
$203$	10.3352	0.725387
$204$	67.0136	4.69189
$205$	5.68974	0.397389
$206$	36.9664	2.57557
$207$	27.1970	1.89033
$208$	5.03656	0.349222
$209$	15.6762	1.08434
$210$	−49.8424	−3.43945
$211$	13.2964	0.915359	0.457679	−	0.889117i	$-0.348681\pi$
$211$	13.2964	0.915359	0.457679	+	0.889117i	$0.348681\pi$
$212$	−39.8809	−2.73903
$213$	31.2305	2.13988
$214$	43.1048	2.94659
$215$	−10.7397	−0.732441
$216$	−8.55035	−0.581777
$217$	1.86274	0.126451
$218$	3.00560	0.203565
$219$	−27.2859	−1.84381
$220$	−45.8154	−3.08887
$221$	8.34623	0.561428
$222$	−24.1637	−1.62176
$223$	−0.166662	−0.0111605	−0.00558025	−	0.999984i	$-0.501776\pi$
$223$	−0.166662	−0.0111605	−0.00558025	+	0.999984i	$0.501776\pi$
$224$	0.428985	0.0286628
$225$	0.651149	0.0434100
$226$	−14.3728	−0.956064
$227$	−16.0863	−1.06769	−0.533843	−	0.845583i	$-0.679253\pi$
$227$	−16.0863	−1.06769	−0.533843	+	0.845583i	$0.679253\pi$
$228$	−31.9906	−2.11863
$229$	−27.5327	−1.81941	−0.909706	−	0.415253i	$-0.863693\pi$
$229$	−27.5327	−1.81941	−0.909706	+	0.415253i	$0.863693\pi$
$230$	−41.1424	−2.71285
$231$	−45.2108	−2.97465
$232$	−14.5094	−0.952589
$233$	19.8860	1.30277	0.651386	−	0.758746i	$-0.274188\pi$
$233$	19.8860	1.30277	0.651386	+	0.758746i	$0.274188\pi$
$234$	−11.5586	−0.755608
$235$	−14.0339	−0.915468
$236$	41.9631	2.73157
$237$	−1.54714	−0.100498
$238$	−55.1125	−3.57241
$239$	−16.9003	−1.09319	−0.546594	−	0.837398i	$-0.684076\pi$
$239$	−16.9003	−1.09319	−0.546594	+	0.837398i	$0.684076\pi$
$240$	23.0761	1.48956
$241$	−27.3417	−1.76124	−0.880618	−	0.473826i	$-0.842872\pi$
$241$	−27.3417	−1.76124	−0.880618	+	0.473826i	$0.842872\pi$
$242$	−35.4873	−2.28121
$243$	−22.0654	−1.41550
$244$	−16.7005	−1.06914
$245$	11.3712	0.726477
$246$	−15.8150	−1.00833
$247$	−3.98428	−0.253514
$248$	−2.61507	−0.166057
$249$	36.2663	2.29828
$250$	26.8519	1.69827
$251$	−23.4935	−1.48290	−0.741449	−	0.671010i	$-0.765861\pi$
$251$	−23.4935	−1.48290	−0.741449	+	0.671010i	$0.765861\pi$
$252$	50.8291	3.20193
$253$	−37.3193	−2.34624
$254$	−22.9475	−1.43986
$255$	38.2402	2.39469
$256$	−31.8946	−1.99341
$257$	5.45624	0.340351	0.170175	−	0.985414i	$-0.445567\pi$
$257$	5.45624	0.340351	0.170175	+	0.985414i	$0.445567\pi$
$258$	29.8518	1.85849
$259$	13.2342	0.822334
$260$	11.6445	0.722161
$261$	10.9813	0.679725
$262$	−32.7871	−2.02559
$263$	3.53650	0.218070	0.109035	−	0.994038i	$-0.465224\pi$
$263$	3.53650	0.218070	0.109035	+	0.994038i	$0.465224\pi$
$264$	63.4708	3.90636
$265$	−22.7573	−1.39797
$266$	26.3093	1.61313
$267$	−10.2542	−0.627545
$268$	45.2647	2.76498
$269$	−17.3328	−1.05680	−0.528399	−	0.848996i	$-0.677208\pi$
$269$	−17.3328	−1.05680	−0.528399	+	0.848996i	$0.677208\pi$
$270$	−9.78938	−0.595762
$271$	11.7276	0.712400	0.356200	−	0.934410i	$-0.384072\pi$
$271$	11.7276	0.712400	0.356200	+	0.934410i	$0.384072\pi$
$272$	25.5161	1.54714
$273$	11.4908	0.695457
$274$	3.47393	0.209868
$275$	−0.893495	−0.0538798
$276$	76.1580	4.58417
$277$	1.53326	0.0921245	0.0460622	−	0.998939i	$-0.485333\pi$
$277$	1.53326	0.0921245	0.0460622	+	0.998939i	$0.485333\pi$
$278$	6.27075	0.376095
$279$	1.97919	0.118491
$280$	−38.3235	−2.29027
$281$	−22.3751	−1.33479	−0.667394	−	0.744705i	$-0.732590\pi$
$281$	−22.3751	−1.33479	−0.667394	+	0.744705i	$0.732590\pi$
$282$	39.0081	2.32290
$283$	−6.17147	−0.366856	−0.183428	−	0.983033i	$-0.558719\pi$
$283$	−6.17147	−0.366856	−0.183428	+	0.983033i	$0.558719\pi$
$284$	48.1793	2.85892
$285$	−18.2549	−1.08133
$286$	15.8605	0.937849
$287$	8.66174	0.511286
$288$	0.455803	0.0268585
$289$	25.2835	1.48726
$290$	−16.6120	−0.975488
$291$	11.5471	0.676904
$292$	−42.0939	−2.46336
$293$	−6.69813	−0.391309	−0.195655	−	0.980673i	$-0.562683\pi$
$293$	−6.69813	−0.391309	−0.195655	+	0.980673i	$0.562683\pi$
$294$	−31.6070	−1.84335
$295$	23.9455	1.39416
$296$	−18.5793	−1.07990
$297$	−8.87971	−0.515253
$298$	−41.5026	−2.40418
$299$	9.48511	0.548538
$300$	1.82337	0.105272
$301$	−16.3495	−0.942370
$302$	8.52703	0.490676
$303$	49.6898	2.85460
$304$	−12.1807	−0.698613
$305$	−9.52983	−0.545677
$306$	−58.5579	−3.34753
$307$	−5.87528	−0.335320	−0.167660	−	0.985845i	$-0.553621\pi$
$307$	−5.87528	−0.335320	−0.167660	+	0.985845i	$0.553621\pi$
$308$	−69.7467	−3.97419
$309$	−39.0471	−2.22131
$310$	−2.99402	−0.170049
$311$	−16.7451	−0.949529	−0.474764	−	0.880113i	$-0.657467\pi$
$311$	−16.7451	−0.949529	−0.474764	+	0.880113i	$0.657467\pi$
$312$	−16.1318	−0.913285
$313$	21.0823	1.19164	0.595820	−	0.803118i	$-0.296827\pi$
$313$	21.0823	1.19164	0.595820	+	0.803118i	$0.296827\pi$
$314$	16.8037	0.948286
$315$	29.0047	1.63423
$316$	−2.38677	−0.134266
$317$	−26.1986	−1.47146	−0.735730	−	0.677275i	$-0.763161\pi$
$317$	−26.1986	−1.47146	−0.735730	+	0.677275i	$0.763161\pi$
$318$	63.2556	3.54720
$319$	−15.0683	−0.843664
$320$	−18.5460	−1.03675
$321$	−45.5311	−2.54130
$322$	−62.6328	−3.49039
$323$	−20.1851	−1.12313
$324$	−25.9026	−1.43903
$325$	0.227092	0.0125968
$326$	51.3543	2.84425
$327$	−3.17478	−0.175566
$328$	−12.1601	−0.671429
$329$	−21.3644	−1.17785
$330$	72.6684	4.00026
$331$	−4.35410	−0.239323	−0.119662	−	0.992815i	$-0.538181\pi$
$331$	−4.35410	−0.239323	−0.119662	+	0.992815i	$0.538181\pi$
$332$	55.9480	3.07054
$333$	14.0616	0.770568
$334$	45.4642	2.48769
$335$	25.8295	1.41122
$336$	35.1298	1.91649
$337$	−3.99045	−0.217374	−0.108687	−	0.994076i	$-0.534665\pi$
$337$	−3.99045	−0.217374	−0.108687	+	0.994076i	$0.534665\pi$
$338$	27.7785	1.51095
$339$	15.1818	0.824563
$340$	58.9931	3.19935
$341$	−2.71581	−0.147069
$342$	27.9540	1.51158
$343$	−6.93556	−0.374485
$344$	22.9528	1.23753
$345$	43.4582	2.33971
$346$	−48.2549	−2.59420
$347$	32.3995	1.73930	0.869648	−	0.493673i	$-0.164346\pi$
$347$	32.3995	1.73930	0.869648	+	0.493673i	$0.164346\pi$
$348$	30.7501	1.64838
$349$	22.3808	1.19802	0.599009	−	0.800742i	$-0.295561\pi$
$349$	22.3808	1.19802	0.599009	+	0.800742i	$0.295561\pi$
$350$	−1.49955	−0.0801543
$351$	2.25688	0.120463
$352$	−0.625445	−0.0333363
$353$	−11.5164	−0.612955	−0.306478	−	0.951878i	$-0.599150\pi$
$353$	−11.5164	−0.612955	−0.306478	+	0.951878i	$0.599150\pi$
$354$	−66.5583	−3.53754
$355$	27.4927	1.45916
$356$	−15.8191	−0.838411
$357$	58.2147	3.08105
$358$	−18.1109	−0.957192
$359$	−28.0748	−1.48173	−0.740866	−	0.671653i	$-0.765584\pi$
$359$	−28.0748	−1.48173	−0.740866	+	0.671653i	$0.765584\pi$
$360$	−40.7193	−2.14610
$361$	−9.36416	−0.492851
$362$	−39.6591	−2.08444
$363$	37.4848	1.96744
$364$	17.7269	0.929143
$365$	−24.0201	−1.25727
$366$	26.4889	1.38459
$367$	−26.8245	−1.40023	−0.700113	−	0.714032i	$-0.746867\pi$
$367$	−26.8245	−1.40023	−0.700113	+	0.714032i	$0.746867\pi$
$368$	28.9979	1.51162
$369$	9.20324	0.479101
$370$	−21.2716	−1.10586
$371$	−34.6444	−1.79865
$372$	5.54219	0.287349
$373$	34.0368	1.76236	0.881180	−	0.472781i	$-0.156750\pi$
$373$	34.0368	1.76236	0.881180	+	0.472781i	$0.156750\pi$
$374$	80.3520	4.15490
$375$	−28.3634	−1.46468
$376$	29.9931	1.54678
$377$	3.82978	0.197244
$378$	−14.9028	−0.766517
$379$	24.9932	1.28382	0.641908	−	0.766782i	$-0.278143\pi$
$379$	24.9932	1.28382	0.641908	+	0.766782i	$0.278143\pi$
$380$	−28.1618	−1.44467
$381$	24.2392	1.24181
$382$	4.98153	0.254877
$383$	−11.4755	−0.586373	−0.293186	−	0.956055i	$-0.594716\pi$
$383$	−11.4755	−0.586373	−0.293186	+	0.956055i	$0.594716\pi$
$384$	50.9096	2.59797
$385$	−39.7997	−2.02838
$386$	−29.7663	−1.51507
$387$	−17.3716	−0.883049
$388$	17.8137	0.904356
$389$	−22.7641	−1.15418	−0.577092	−	0.816679i	$-0.695813\pi$
$389$	−22.7641	−1.15418	−0.577092	+	0.816679i	$0.695813\pi$
$390$	−18.4695	−0.935239
$391$	48.0533	2.43016
$392$	−24.3024	−1.22746
$393$	34.6326	1.74698
$394$	−2.35786	−0.118787
$395$	−1.36197	−0.0685282
$396$	−74.1070	−3.72402
$397$	15.5371	0.779783	0.389891	−	0.920861i	$-0.372513\pi$
$397$	15.5371	0.779783	0.389891	+	0.920861i	$0.372513\pi$
$398$	−32.4936	−1.62876
$399$	−27.7902	−1.39125
$400$	0.694265	0.0347133
$401$	26.9833	1.34748	0.673740	−	0.738969i	$-0.264687\pi$
$401$	26.9833	1.34748	0.673740	+	0.738969i	$0.264687\pi$
$402$	−71.7949	−3.58081
$403$	0.690253	0.0343840
$404$	76.6564	3.81380
$405$	−14.7809	−0.734467
$406$	−25.2891	−1.25508
$407$	−19.2950	−0.956418
$408$	−81.7267	−4.04608
$409$	12.6047	0.623265	0.311632	−	0.950203i	$-0.399124\pi$
$409$	12.6047	0.623265	0.311632	+	0.950203i	$0.399124\pi$
$410$	−13.9222	−0.687569
$411$	−3.66947	−0.181002
$412$	−60.2380	−2.96771
$413$	36.4533	1.79375
$414$	−66.5484	−3.27067
$415$	31.9257	1.56717
$416$	0.158964	0.00779385
$417$	−6.62372	−0.324365
$418$	−38.3580	−1.87615
$419$	7.57424	0.370026	0.185013	−	0.982736i	$-0.440767\pi$
$419$	7.57424	0.370026	0.185013	+	0.982736i	$0.440767\pi$
$420$	81.2199	3.96313
$421$	−16.7439	−0.816049	−0.408024	−	0.912971i	$-0.633782\pi$
$421$	−16.7439	−0.816049	−0.408024	+	0.912971i	$0.633782\pi$
$422$	−32.5348	−1.58377
$423$	−22.7000	−1.10371
$424$	48.6368	2.36201
$425$	1.15049	0.0558069
$426$	−76.4178	−3.70246
$427$	−14.5077	−0.702076
$428$	−70.2409	−3.39522
$429$	−16.7532	−0.808854
$430$	26.2789	1.26728
$431$	−35.5158	−1.71073	−0.855367	−	0.518023i	$-0.826668\pi$
$431$	−35.5158	−1.71073	−0.855367	+	0.518023i	$0.826668\pi$
$432$	6.89973	0.331963
$433$	13.5539	0.651357	0.325678	−	0.945481i	$-0.394407\pi$
$433$	13.5539	0.651357	0.325678	+	0.945481i	$0.394407\pi$
$434$	−4.55793	−0.218788
$435$	17.5470	0.841316
$436$	−4.89773	−0.234559
$437$	−22.9394	−1.09734
$438$	66.7657	3.19019
$439$	−16.9332	−0.808177	−0.404088	−	0.914720i	$-0.632411\pi$
$439$	−16.9332	−0.808177	−0.404088	+	0.914720i	$0.632411\pi$
$440$	55.8743	2.66370
$441$	18.3930	0.875857
$442$	−20.4224	−0.971393
$443$	−9.69482	−0.460615	−0.230307	−	0.973118i	$-0.573973\pi$
$443$	−9.69482	−0.460615	−0.230307	+	0.973118i	$0.573973\pi$
$444$	39.3756	1.86868
$445$	−9.02689	−0.427916
$446$	0.407804	0.0193101
$447$	43.8387	2.07350
$448$	−28.2333	−1.33390
$449$	14.4209	0.680563	0.340281	−	0.940324i	$-0.389478\pi$
$449$	14.4209	0.680563	0.340281	+	0.940324i	$0.389478\pi$
$450$	−1.59330	−0.0751087
$451$	−12.6285	−0.594653
$452$	23.4210	1.10163
$453$	−9.00700	−0.423186
$454$	39.3616	1.84733
$455$	10.1156	0.474224
$456$	39.0143	1.82701
$457$	12.2362	0.572383	0.286192	−	0.958172i	$-0.407611\pi$
$457$	12.2362	0.572383	0.286192	+	0.958172i	$0.407611\pi$
$458$	67.3697	3.14798
$459$	11.4337	0.533682
$460$	67.0430	3.12589
$461$	3.28422	0.152961	0.0764807	−	0.997071i	$-0.475632\pi$
$461$	3.28422	0.152961	0.0764807	+	0.997071i	$0.475632\pi$
$462$	110.626	5.14680
$463$	−22.8529	−1.06206	−0.531031	−	0.847352i	$-0.678195\pi$
$463$	−22.8529	−1.06206	−0.531031	+	0.847352i	$0.678195\pi$
$464$	11.7084	0.543549
$465$	3.16255	0.146660
$466$	−48.6589	−2.25408
$467$	8.98539	0.415794	0.207897	−	0.978151i	$-0.433338\pi$
$467$	8.98539	0.415794	0.207897	+	0.978151i	$0.433338\pi$
$468$	18.8351	0.870654
$469$	39.3214	1.81569
$470$	34.3394	1.58396
$471$	−17.7495	−0.817854
$472$	−51.1763	−2.35558
$473$	23.8370	1.09603
$474$	3.78569	0.173883
$475$	−0.549214	−0.0251997
$476$	89.8077	4.11633
$477$	−36.8103	−1.68543
$478$	41.3533	1.89145
$479$	31.7769	1.45192	0.725961	−	0.687736i	$-0.241395\pi$
$479$	31.7769	1.45192	0.725961	+	0.687736i	$0.241395\pi$
$480$	0.728329	0.0332435
$481$	4.90404	0.223605
$482$	66.9024	3.04732
$483$	66.1583	3.01031
$484$	57.8278	2.62854
$485$	10.1651	0.461573
$486$	53.9919	2.44912
$487$	−28.0077	−1.26915	−0.634576	−	0.772860i	$-0.718825\pi$
$487$	−28.0077	−1.26915	−0.634576	+	0.772860i	$0.718825\pi$
$488$	20.3671	0.921976
$489$	−54.2450	−2.45304
$490$	−27.8241	−1.25696
$491$	25.7443	1.16183	0.580913	−	0.813966i	$-0.302696\pi$
$491$	25.7443	1.16183	0.580913	+	0.813966i	$0.302696\pi$
$492$	25.7712	1.16185
$493$	19.4024	0.873839
$494$	9.74912	0.438634
$495$	−42.2878	−1.90070
$496$	2.11024	0.0947527
$497$	41.8533	1.87738
$498$	−88.7398	−3.97653
$499$	4.59216	0.205573	0.102787	−	0.994703i	$-0.467224\pi$
$499$	4.59216	0.205573	0.102787	+	0.994703i	$0.467224\pi$
$500$	−43.7562	−1.95684
$501$	−48.0233	−2.14552
$502$	57.4862	2.56573
$503$	9.18899	0.409717	0.204858	−	0.978792i	$-0.434327\pi$
$503$	9.18899	0.409717	0.204858	+	0.978792i	$0.434327\pi$
$504$	−61.9888	−2.76120
$505$	43.7426	1.94652
$506$	91.3164	4.05951
$507$	−29.3422	−1.30313
$508$	37.3938	1.65908
$509$	−23.5588	−1.04423	−0.522114	−	0.852876i	$-0.674856\pi$
$509$	−23.5588	−1.04423	−0.522114	+	0.852876i	$0.674856\pi$
$510$	−93.5697	−4.14334
$511$	−36.5669	−1.61762
$512$	38.6487	1.70805
$513$	−5.45818	−0.240985
$514$	−13.3509	−0.588881
$515$	−34.3738	−1.51469
$516$	−48.6445	−2.14146
$517$	31.1485	1.36991
$518$	−32.3827	−1.42282
$519$	50.9711	2.23738
$520$	−14.2011	−0.622759
$521$	34.5888	1.51536	0.757682	−	0.652623i	$-0.226332\pi$
$521$	34.5888	1.51536	0.757682	+	0.652623i	$0.226332\pi$
$522$	−26.8701	−1.17607
$523$	−9.00917	−0.393943	−0.196972	−	0.980409i	$-0.563111\pi$
$523$	−9.00917	−0.393943	−0.196972	+	0.980409i	$0.563111\pi$
$524$	53.4277	2.33400
$525$	1.58396	0.0691296
$526$	−8.65344	−0.377308
$527$	3.49695	0.152329
$528$	−51.2180	−2.22898
$529$	31.6104	1.37436
$530$	55.6848	2.41879
$531$	38.7322	1.68084
$532$	−42.8719	−1.85873
$533$	3.20968	0.139027
$534$	25.0909	1.08579
$535$	−40.0817	−1.73288
$536$	−55.2027	−2.38439
$537$	19.1304	0.825536
$538$	42.4116	1.82849
$539$	−25.2385	−1.08710
$540$	15.9521	0.686471
$541$	−14.5556	−0.625794	−0.312897	−	0.949787i	$-0.601300\pi$
$541$	−14.5556	−0.625794	−0.312897	+	0.949787i	$0.601300\pi$
$542$	−28.6962	−1.23261
$543$	41.8914	1.79773
$544$	0.805340	0.0345286
$545$	−2.79480	−0.119716
$546$	−28.1169	−1.20329
$547$	9.34392	0.399517	0.199759	−	0.979845i	$-0.435984\pi$
$547$	9.34392	0.399517	0.199759	+	0.979845i	$0.435984\pi$
$548$	−5.66089	−0.241821
$549$	−15.4146	−0.657881
$550$	2.18629	0.0932237
$551$	−9.26220	−0.394583
$552$	−92.8787	−3.95318
$553$	−2.07339	−0.0881694
$554$	−3.75172	−0.159395
$555$	22.4690	0.953756
$556$	−10.2184	−0.433357
$557$	−10.5078	−0.445230	−0.222615	−	0.974906i	$-0.571459\pi$
$557$	−10.5078	−0.445230	−0.222615	+	0.974906i	$0.571459\pi$
$558$	−4.84288	−0.205015
$559$	−6.05844	−0.256245
$560$	30.9253	1.30683
$561$	−84.8749	−3.58342
$562$	54.7496	2.30947
$563$	10.7242	0.451972	0.225986	−	0.974131i	$-0.427440\pi$
$563$	10.7242	0.451972	0.225986	+	0.974131i	$0.427440\pi$
$564$	−63.5651	−2.67657
$565$	13.3648	0.562260
$566$	15.1010	0.634740
$567$	−22.5015	−0.944976
$568$	−58.7572	−2.46540
$569$	28.9531	1.21378	0.606889	−	0.794787i	$-0.292417\pi$
$569$	28.9531	1.21378	0.606889	+	0.794787i	$0.292417\pi$
$570$	44.6678	1.87093
$571$	14.4583	0.605060	0.302530	−	0.953140i	$-0.402169\pi$
$571$	14.4583	0.605060	0.302530	+	0.953140i	$0.402169\pi$
$572$	−25.8452	−1.08064
$573$	−5.26193	−0.219820
$574$	−21.1944	−0.884637
$575$	1.30748	0.0545256
$576$	−29.9983	−1.24993
$577$	−26.2575	−1.09312	−0.546558	−	0.837421i	$-0.684062\pi$
$577$	−26.2575	−1.09312	−0.546558	+	0.837421i	$0.684062\pi$
$578$	−61.8661	−2.57329
$579$	31.4418	1.30668
$580$	27.0698	1.12401
$581$	48.6019	2.01635
$582$	−28.2546	−1.17119
$583$	50.5103	2.09192
$584$	51.3357	2.12429
$585$	10.7479	0.444372
$586$	16.3896	0.677050
$587$	37.9410	1.56599	0.782996	−	0.622027i	$-0.213691\pi$
$587$	37.9410	1.56599	0.782996	+	0.622027i	$0.213691\pi$
$588$	51.5047	2.12402
$589$	−1.66935	−0.0687845
$590$	−58.5923	−2.41221
$591$	2.49058	0.102449
$592$	14.9926	0.616194
$593$	−0.768202	−0.0315463	−0.0157731	−	0.999876i	$-0.505021\pi$
$593$	−0.768202	−0.0315463	−0.0157731	+	0.999876i	$0.505021\pi$
$594$	21.7277	0.891500
$595$	51.2472	2.10093
$596$	67.6299	2.77023
$597$	34.3226	1.40473
$598$	−23.2091	−0.949091
$599$	−26.3726	−1.07756	−0.538778	−	0.842448i	$-0.681114\pi$
$599$	−26.3726	−1.07756	−0.538778	+	0.842448i	$0.681114\pi$
$600$	−2.22370	−0.0907820
$601$	−31.2533	−1.27485	−0.637424	−	0.770513i	$-0.720000\pi$
$601$	−31.2533	−1.27485	−0.637424	+	0.770513i	$0.720000\pi$
$602$	40.0056	1.63051
$603$	41.7796	1.70140
$604$	−13.8951	−0.565384
$605$	32.9984	1.34158
$606$	−121.586	−4.93909
$607$	−5.62229	−0.228202	−0.114101	−	0.993469i	$-0.536399\pi$
$607$	−5.62229	−0.228202	−0.114101	+	0.993469i	$0.536399\pi$
$608$	−0.384449	−0.0155915
$609$	26.7126	1.08245
$610$	23.3185	0.944139
$611$	−7.91673	−0.320277
$612$	95.4221	3.85721
$613$	−26.1491	−1.05615	−0.528077	−	0.849197i	$-0.677087\pi$
$613$	−26.1491	−1.05615	−0.528077	+	0.849197i	$0.677087\pi$
$614$	14.3762	0.580177
$615$	14.7059	0.592998
$616$	85.0599	3.42716
$617$	6.62152	0.266573	0.133286	−	0.991078i	$-0.457447\pi$
$617$	6.62152	0.266573	0.133286	+	0.991078i	$0.457447\pi$
$618$	95.5443	3.84336
$619$	−4.61778	−0.185604	−0.0928022	−	0.995685i	$-0.529582\pi$
$619$	−4.61778	−0.185604	−0.0928022	+	0.995685i	$0.529582\pi$
$620$	4.87887	0.195940
$621$	12.9939	0.521429
$622$	40.9736	1.64289
$623$	−13.7420	−0.550563
$624$	13.0176	0.521122
$625$	−25.8533	−1.03413
$626$	−51.5862	−2.06180
$627$	40.5171	1.61810
$628$	−27.3822	−1.09267
$629$	24.8448	0.990625
$630$	−70.9716	−2.82758
$631$	−4.29947	−0.171159	−0.0855795	−	0.996331i	$-0.527274\pi$
$631$	−4.29947	−0.171159	−0.0855795	+	0.996331i	$0.527274\pi$
$632$	2.91080	0.115785
$633$	34.3661	1.36593
$634$	64.1053	2.54595
$635$	21.3381	0.846778
$636$	−103.077	−4.08728
$637$	6.41466	0.254158
$638$	36.8706	1.45972
$639$	44.4698	1.75920
$640$	44.8165	1.77153
$641$	37.9651	1.49953	0.749766	−	0.661704i	$-0.230166\pi$
$641$	37.9651	1.49953	0.749766	+	0.661704i	$0.230166\pi$
$642$	111.410	4.39700
$643$	14.2784	0.563084	0.281542	−	0.959549i	$-0.409154\pi$
$643$	14.2784	0.563084	0.281542	+	0.959549i	$0.409154\pi$
$644$	102.062	4.02182
$645$	−27.7581	−1.09298
$646$	49.3908	1.94325
$647$	−3.45597	−0.135868	−0.0679341	−	0.997690i	$-0.521641\pi$
$647$	−3.45597	−0.135868	−0.0679341	+	0.997690i	$0.521641\pi$
$648$	31.5896	1.24096
$649$	−53.1476	−2.08623
$650$	−0.555670	−0.0217952
$651$	4.81449	0.188695
$652$	−83.6837	−3.27731
$653$	−28.6301	−1.12038	−0.560191	−	0.828364i	$-0.689272\pi$
$653$	−28.6301	−1.12038	−0.560191	+	0.828364i	$0.689272\pi$
$654$	7.76836	0.303767
$655$	30.4876	1.19125
$656$	9.81263	0.383119
$657$	−38.8529	−1.51580
$658$	52.2764	2.03795
$659$	−39.2432	−1.52870	−0.764349	−	0.644803i	$-0.776939\pi$
$659$	−39.2432	−1.52870	−0.764349	+	0.644803i	$0.776939\pi$
$660$	−118.416	−4.60933
$661$	−36.2381	−1.40950	−0.704749	−	0.709457i	$-0.748940\pi$
$661$	−36.2381	−1.40950	−0.704749	+	0.709457i	$0.748940\pi$
$662$	10.6540	0.414081
$663$	21.5719	0.837784
$664$	−68.2315	−2.64790
$665$	−24.4641	−0.948678
$666$	−34.4072	−1.33325
$667$	22.0499	0.853776
$668$	−74.0855	−2.86645
$669$	−0.430759	−0.0166541
$670$	−63.2021	−2.44171
$671$	21.1517	0.816551
$672$	1.10877	0.0427716
$673$	−30.8309	−1.18844	−0.594222	−	0.804301i	$-0.702540\pi$
$673$	−30.8309	−1.18844	−0.594222	+	0.804301i	$0.702540\pi$
$674$	9.76422	0.376104
$675$	0.311100	0.0119742
$676$	−45.2661	−1.74100
$677$	26.4451	1.01637	0.508184	−	0.861248i	$-0.330317\pi$
$677$	26.4451	1.01637	0.508184	+	0.861248i	$0.330317\pi$
$678$	−37.1484	−1.42667
$679$	15.4748	0.593867
$680$	−71.9452	−2.75897
$681$	−41.5772	−1.59324
$682$	6.64530	0.254462
$683$	−29.4645	−1.12743	−0.563714	−	0.825970i	$-0.690628\pi$
$683$	−29.4645	−1.12743	−0.563714	+	0.825970i	$0.690628\pi$
$684$	−45.5521	−1.74173
$685$	−3.23029	−0.123423
$686$	16.9706	0.647941
$687$	−71.1618	−2.71499
$688$	−18.5219	−0.706140
$689$	−12.8378	−0.489080
$690$	−106.338	−4.04821
$691$	12.5912	0.478992	0.239496	−	0.970897i	$-0.423018\pi$
$691$	12.5912	0.478992	0.239496	+	0.970897i	$0.423018\pi$
$692$	78.6331	2.98918
$693$	−64.3766	−2.44547
$694$	−79.2782	−3.00936
$695$	−5.83096	−0.221181
$696$	−37.5014	−1.42149
$697$	16.2608	0.615922
$698$	−54.7636	−2.07283
$699$	51.3978	1.94404
$700$	2.44357	0.0923583
$701$	38.3465	1.44833	0.724163	−	0.689629i	$-0.242226\pi$
$701$	38.3465	1.44833	0.724163	+	0.689629i	$0.242226\pi$
$702$	−5.52235	−0.208428
$703$	−11.8603	−0.447318
$704$	41.1631	1.55139
$705$	−36.2723	−1.36609
$706$	28.1794	1.06055
$707$	66.5913	2.50442
$708$	108.459	4.07614
$709$	39.6718	1.48991	0.744954	−	0.667116i	$-0.232472\pi$
$709$	39.6718	1.48991	0.744954	+	0.667116i	$0.232472\pi$
$710$	−67.2717	−2.52466
$711$	−2.20301	−0.0826192
$712$	19.2922	0.723007
$713$	3.97412	0.148832
$714$	−142.445	−5.33088
$715$	−14.7481	−0.551548
$716$	29.5124	1.10293
$717$	−43.6810	−1.63130
$718$	68.6961	2.56372
$719$	−25.8141	−0.962704	−0.481352	−	0.876527i	$-0.659854\pi$
$719$	−25.8141	−0.962704	−0.481352	+	0.876527i	$0.659854\pi$
$720$	32.8586	1.22457
$721$	−52.3287	−1.94882
$722$	22.9131	0.852739
$723$	−70.6683	−2.62818
$724$	64.6259	2.40180
$725$	0.527917	0.0196064
$726$	−91.7215	−3.40410
$727$	46.4268	1.72188	0.860938	−	0.508710i	$-0.169877\pi$
$727$	46.4268	1.72188	0.860938	+	0.508710i	$0.169877\pi$
$728$	−21.6189	−0.801251
$729$	−37.5422	−1.39045
$730$	58.7748	2.17535
$731$	−30.6932	−1.13523
$732$	−43.1645	−1.59541
$733$	30.8983	1.14125	0.570627	−	0.821209i	$-0.306700\pi$
$733$	30.8983	1.14125	0.570627	+	0.821209i	$0.306700\pi$
$734$	65.6368	2.42270
$735$	29.3902	1.08407
$736$	0.915232	0.0337359
$737$	−57.3291	−2.11175
$738$	−22.5194	−0.828950
$739$	−22.5809	−0.830652	−0.415326	−	0.909673i	$-0.636333\pi$
$739$	−22.5809	−0.830652	−0.415326	+	0.909673i	$0.636333\pi$
$740$	34.6629	1.27423
$741$	−10.2979	−0.378302
$742$	84.7714	3.11206
$743$	−43.4693	−1.59473	−0.797367	−	0.603495i	$-0.793774\pi$
$743$	−43.4693	−1.59473	−0.797367	+	0.603495i	$0.793774\pi$
$744$	−6.75900	−0.247797
$745$	38.5918	1.41390
$746$	−83.2846	−3.04927
$747$	51.6403	1.88942
$748$	−130.936	−4.78751
$749$	−61.0182	−2.22955
$750$	69.4023	2.53421
$751$	−7.36515	−0.268758	−0.134379	−	0.990930i	$-0.542904\pi$
$751$	−7.36515	−0.268758	−0.134379	+	0.990930i	$0.542904\pi$
$752$	−24.2030	−0.882594
$753$	−60.7220	−2.21283
$754$	−9.37109	−0.341275
$755$	−7.92900	−0.288566
$756$	24.2846	0.883223
$757$	22.4077	0.814422	0.407211	−	0.913334i	$-0.366501\pi$
$757$	22.4077	0.814422	0.407211	+	0.913334i	$0.366501\pi$
$758$	−61.1559	−2.22128
$759$	−96.4565	−3.50115
$760$	34.3448	1.24582
$761$	−21.0573	−0.763325	−0.381663	−	0.924302i	$-0.624648\pi$
$761$	−21.0573	−0.763325	−0.381663	+	0.924302i	$0.624648\pi$
$762$	−59.3109	−2.14861
$763$	−4.25465	−0.154029
$764$	−8.11758	−0.293684
$765$	54.4510	1.96868
$766$	28.0795	1.01455
$767$	13.5081	0.487748
$768$	−82.4357	−2.97464
$769$	−38.8505	−1.40098	−0.700492	−	0.713660i	$-0.747036\pi$
$769$	−38.8505	−1.40098	−0.700492	+	0.713660i	$0.747036\pi$
$770$	97.3859	3.50954
$771$	14.1024	0.507884
$772$	48.5053	1.74574
$773$	14.3652	0.516679	0.258339	−	0.966054i	$-0.416825\pi$
$773$	14.3652	0.516679	0.258339	+	0.966054i	$0.416825\pi$
$774$	42.5066	1.52787
$775$	0.0951481	0.00341782
$776$	−21.7248	−0.779875
$777$	34.2055	1.22712
$778$	55.7013	1.99699
$779$	−7.76250	−0.278120
$780$	30.0967	1.07763
$781$	−61.0206	−2.18349
$782$	−117.581	−4.20470
$783$	5.24653	0.187496
$784$	19.6109	0.700389
$785$	−15.6252	−0.557686
$786$	−84.7424	−3.02266
$787$	30.0605	1.07154	0.535770	−	0.844364i	$-0.320021\pi$
$787$	30.0605	1.07154	0.535770	+	0.844364i	$0.320021\pi$
$788$	3.84222	0.136873
$789$	9.14053	0.325412
$790$	3.33260	0.118569
$791$	20.3458	0.723413
$792$	90.3774	3.21142
$793$	−5.37594	−0.190905
$794$	−38.0176	−1.34919
$795$	−58.8192	−2.08610
$796$	52.9495	1.87674
$797$	36.7219	1.30076	0.650379	−	0.759610i	$-0.274610\pi$
$797$	36.7219	1.30076	0.650379	+	0.759610i	$0.274610\pi$
$798$	67.9998	2.40717
$799$	−40.1076	−1.41890
$800$	0.0219124	0.000774721 0
$801$	−14.6011	−0.515905
$802$	−66.0253	−2.33143
$803$	53.3132	1.88138
$804$	116.992	4.12600
$805$	58.2401	2.05270
$806$	−1.68898	−0.0594918
$807$	−44.7988	−1.57699
$808$	−93.4866	−3.28885
$809$	19.4848	0.685049	0.342524	−	0.939509i	$-0.388718\pi$
$809$	19.4848	0.685049	0.342524	+	0.939509i	$0.388718\pi$
$810$	36.1672	1.27079
$811$	−11.3326	−0.397941	−0.198970	−	0.980006i	$-0.563760\pi$
$811$	−11.3326	−0.397941	−0.198970	+	0.980006i	$0.563760\pi$
$812$	41.2095	1.44617
$813$	30.3115	1.06307
$814$	47.2129	1.65481
$815$	−47.7526	−1.67270
$816$	65.9496	2.30870
$817$	14.6521	0.512613
$818$	−30.8425	−1.07838
$819$	16.3620	0.571736
$820$	22.6867	0.792256
$821$	2.35941	0.0823441	0.0411721	−	0.999152i	$-0.486891\pi$
$821$	2.35941	0.0823441	0.0411721	+	0.999152i	$0.486891\pi$
$822$	8.97881	0.313172
$823$	−36.3475	−1.26699	−0.633497	−	0.773745i	$-0.718381\pi$
$823$	−36.3475	−1.26699	−0.633497	+	0.773745i	$0.718381\pi$
$824$	73.4635	2.55922
$825$	−2.30935	−0.0804013
$826$	−89.1975	−3.10358
$827$	−41.8150	−1.45405	−0.727024	−	0.686612i	$-0.759097\pi$
$827$	−41.8150	−1.45405	−0.727024	+	0.686612i	$0.759097\pi$
$828$	108.443	3.76865
$829$	−4.71950	−0.163915	−0.0819575	−	0.996636i	$-0.526117\pi$
$829$	−4.71950	−0.163915	−0.0819575	+	0.996636i	$0.526117\pi$
$830$	−78.1190	−2.71155
$831$	3.96290	0.137471
$832$	−10.4621	−0.362707
$833$	32.4978	1.12598
$834$	16.2076	0.561222
$835$	−42.2756	−1.46301
$836$	62.5057	2.16181
$837$	0.945599	0.0326847
$838$	−18.5334	−0.640225
$839$	20.3410	0.702249	0.351125	−	0.936329i	$-0.385799\pi$
$839$	20.3410	0.702249	0.351125	+	0.936329i	$0.385799\pi$
$840$	−99.0520	−3.41762
$841$	−20.0970	−0.692998
$842$	40.9706	1.41194
$843$	−57.8314	−1.99182
$844$	53.0166	1.82491
$845$	−25.8303	−0.888590
$846$	55.5445	1.90966
$847$	50.2349	1.72609
$848$	−39.2476	−1.34777
$849$	−15.9510	−0.547436
$850$	−2.81513	−0.0965580
$851$	28.2349	0.967881
$852$	124.526	4.26618
$853$	−19.9384	−0.682677	−0.341339	−	0.939940i	$-0.610880\pi$
$853$	−19.9384	−0.682677	−0.341339	+	0.939940i	$0.610880\pi$
$854$	35.4988	1.21474
$855$	−25.9935	−0.888959
$856$	85.6625	2.92788
$857$	−5.78930	−0.197759	−0.0988794	−	0.995099i	$-0.531526\pi$
$857$	−5.78930	−0.197759	−0.0988794	+	0.995099i	$0.531526\pi$
$858$	40.9934	1.39949
$859$	−1.54411	−0.0526844	−0.0263422	−	0.999653i	$-0.508386\pi$
$859$	−1.54411	−0.0526844	−0.0263422	+	0.999653i	$0.508386\pi$
$860$	−42.8225	−1.46023
$861$	22.3874	0.762960
$862$	86.9034	2.95994
$863$	23.6174	0.803946	0.401973	−	0.915652i	$-0.368325\pi$
$863$	23.6174	0.803946	0.401973	+	0.915652i	$0.368325\pi$
$864$	0.217769	0.00740866
$865$	44.8706	1.52565
$866$	−33.1649	−1.12699
$867$	65.3485	2.21935
$868$	7.42732	0.252100
$869$	3.02292	0.102546
$870$	−42.9358	−1.45566
$871$	14.5708	0.493714
$872$	5.97305	0.202273
$873$	16.4422	0.556484
$874$	56.1304	1.89864
$875$	−38.0109	−1.28500
$876$	−108.797	−3.67591
$877$	−37.2253	−1.25701	−0.628505	−	0.777806i	$-0.716333\pi$
$877$	−37.2253	−1.25701	−0.628505	+	0.777806i	$0.716333\pi$
$878$	41.4338	1.39832
$879$	−17.3122	−0.583925
$880$	−45.0879	−1.51991
$881$	−24.8109	−0.835900	−0.417950	−	0.908470i	$-0.637251\pi$
$881$	−24.8109	−0.835900	−0.417950	+	0.908470i	$0.637251\pi$
$882$	−45.0058	−1.51542
$883$	−7.47681	−0.251615	−0.125807	−	0.992055i	$-0.540152\pi$
$883$	−7.47681	−0.251615	−0.125807	+	0.992055i	$0.540152\pi$
$884$	33.2790	1.11929
$885$	61.8903	2.08042
$886$	23.7222	0.796964
$887$	37.4736	1.25824	0.629119	−	0.777309i	$-0.283416\pi$
$887$	37.4736	1.25824	0.629119	+	0.777309i	$0.283416\pi$
$888$	−48.0206	−1.61147
$889$	32.4840	1.08948
$890$	22.0879	0.740387
$891$	32.8064	1.09906
$892$	−0.664532	−0.0222502
$893$	19.1463	0.640708
$894$	−107.269	−3.58760
$895$	16.8407	0.562923
$896$	68.2260	2.27927
$897$	24.5155	0.818549
$898$	−35.2864	−1.17752
$899$	1.60462	0.0535172
$900$	2.59633	0.0865444
$901$	−65.0385	−2.16675
$902$	30.9007	1.02888
$903$	−42.2574	−1.40624
$904$	−28.5632	−0.949996
$905$	36.8776	1.22585
$906$	22.0392	0.732204
$907$	−42.7181	−1.41843	−0.709216	−	0.704991i	$-0.750951\pi$
$907$	−42.7181	−1.41843	−0.709216	+	0.704991i	$0.750951\pi$
$908$	−64.1411	−2.12860
$909$	70.7543	2.34677
$910$	−24.7517	−0.820512
$911$	−11.2091	−0.371374	−0.185687	−	0.982609i	$-0.559451\pi$
$911$	−11.2091	−0.371374	−0.185687	+	0.982609i	$0.559451\pi$
$912$	−31.4827	−1.04250
$913$	−70.8598	−2.34512
$914$	−29.9406	−0.990348
$915$	−24.6311	−0.814278
$916$	−109.781	−3.62728
$917$	46.4126	1.53268
$918$	−27.9772	−0.923385
$919$	22.1315	0.730052	0.365026	−	0.930997i	$-0.381060\pi$
$919$	22.1315	0.730052	0.365026	+	0.930997i	$0.381060\pi$
$920$	−81.7625	−2.69563
$921$	−15.1854	−0.500377
$922$	−8.03616	−0.264657
$923$	15.5091	0.510487
$924$	−180.269	−5.93043
$925$	0.675999	0.0222267
$926$	55.9186	1.83760
$927$	−55.6000	−1.82614
$928$	0.369541	0.0121308
$929$	−32.0206	−1.05056	−0.525280	−	0.850929i	$-0.676040\pi$
$929$	−32.0206	−1.05056	−0.525280	+	0.850929i	$0.676040\pi$
$930$	−7.73844	−0.253754
$931$	−15.5136	−0.508439
$932$	79.2914	2.59728
$933$	−43.2799	−1.41692
$934$	−21.9863	−0.719415
$935$	−74.7166	−2.44349
$936$	−22.9704	−0.750813
$937$	27.0541	0.883818	0.441909	−	0.897060i	$-0.354301\pi$
$937$	27.0541	0.883818	0.441909	+	0.897060i	$0.354301\pi$
$938$	−96.2153	−3.14154
$939$	54.4899	1.77821
$940$	−55.9573	−1.82513
$941$	14.7855	0.481993	0.240996	−	0.970526i	$-0.422526\pi$
$941$	14.7855	0.481993	0.240996	+	0.970526i	$0.422526\pi$
$942$	43.4312	1.41507
$943$	18.4797	0.601781
$944$	41.2969	1.34410
$945$	13.8576	0.450788
$946$	−58.3267	−1.89636
$947$	−46.3268	−1.50542	−0.752710	−	0.658352i	$-0.771254\pi$
$947$	−46.3268	−1.50542	−0.752710	+	0.658352i	$0.771254\pi$
$948$	−6.16892	−0.200357
$949$	−13.5502	−0.439857
$950$	1.34387	0.0436009
$951$	−67.7137	−2.19577
$952$	−109.525	−3.54974
$953$	−18.5298	−0.600239	−0.300120	−	0.953902i	$-0.597027\pi$
$953$	−18.5298	−0.600239	−0.300120	+	0.953902i	$0.597027\pi$
$954$	90.0709	2.91615
$955$	−4.63216	−0.149893
$956$	−67.3866	−2.17944
$957$	−38.9460	−1.25895
$958$	−77.7548	−2.51214
$959$	−4.91761	−0.158798
$960$	−47.9344	−1.54708
$961$	−30.7108	−0.990671
$962$	−11.9997	−0.386885
$963$	−64.8327	−2.08921
$964$	−109.020	−3.51129
$965$	27.6787	0.891008
$966$	−161.883	−5.20849
$967$	16.9220	0.544174	0.272087	−	0.962273i	$-0.412286\pi$
$967$	16.9220	0.544174	0.272087	+	0.962273i	$0.412286\pi$
$968$	−70.5241	−2.26673
$969$	−52.1709	−1.67597
$970$	−24.8730	−0.798622
$971$	23.3446	0.749162	0.374581	−	0.927194i	$-0.377786\pi$
$971$	23.3446	0.749162	0.374581	+	0.927194i	$0.377786\pi$
$972$	−87.9817	−2.82201
$973$	−8.87672	−0.284574
$974$	68.5321	2.19591
$975$	0.586948	0.0187974
$976$	−16.4353	−0.526081
$977$	−14.9791	−0.479224	−0.239612	−	0.970869i	$-0.577020\pi$
$977$	−14.9791	−0.479224	−0.239612	+	0.970869i	$0.577020\pi$
$978$	132.732	4.24430
$979$	20.0354	0.640334
$980$	45.3403	1.44834
$981$	−4.52063	−0.144333
$982$	−62.9937	−2.01021
$983$	−7.44793	−0.237552	−0.118776	−	0.992921i	$-0.537897\pi$
$983$	−7.44793	−0.237552	−0.118776	+	0.992921i	$0.537897\pi$
$984$	−31.4293	−1.00193
$985$	2.19250	0.0698587
$986$	−47.4756	−1.51193
$987$	−55.2189	−1.75764
$988$	−15.8865	−0.505418
$989$	−34.8814	−1.10916
$990$	103.474	3.28862
$991$	−22.7680	−0.723248	−0.361624	−	0.932324i	$-0.617778\pi$
$991$	−22.7680	−0.723248	−0.361624	+	0.932324i	$0.617778\pi$
$992$	0.0666035	0.00211466
$993$	−11.2537	−0.357127
$994$	−102.411	−3.24827
$995$	30.2147	0.957870
$996$	144.605	4.58198
$997$	1.55998	0.0494052	0.0247026	−	0.999695i	$-0.492136\pi$
$997$	1.55998	0.0494052	0.0247026	+	0.999695i	$0.492136\pi$
$998$	−11.2365	−0.355687
$999$	6.71819	0.212554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.14	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.14	✓	174	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44690 q^{2} +2.58463 q^{3} +3.98731 q^{4} +2.27529 q^{5} -6.32432 q^{6} +3.46377 q^{7} -4.86273 q^{8} +3.68031 q^{9} +O(q^{10})\)	\(q-2.44690 q^{2} +2.58463 q^{3} +3.98731 q^{4} +2.27529 q^{5} -6.32432 q^{6} +3.46377 q^{7} -4.86273 q^{8} +3.68031 q^{9} -5.56739 q^{10} -5.05005 q^{11} +10.3057 q^{12} +1.28353 q^{13} -8.47548 q^{14} +5.88077 q^{15} +3.92400 q^{16} +6.50258 q^{17} -9.00533 q^{18} -3.10416 q^{19} +9.07226 q^{20} +8.95255 q^{21} +12.3569 q^{22} +7.38988 q^{23} -12.5684 q^{24} +0.176928 q^{25} -3.14066 q^{26} +1.75834 q^{27} +13.8111 q^{28} +2.98380 q^{29} -14.3896 q^{30} +0.537779 q^{31} +0.123849 q^{32} -13.0525 q^{33} -15.9111 q^{34} +7.88106 q^{35} +14.6745 q^{36} +3.82076 q^{37} +7.59557 q^{38} +3.31744 q^{39} -11.0641 q^{40} +2.50067 q^{41} -21.9060 q^{42} -4.72015 q^{43} -20.1361 q^{44} +8.37375 q^{45} -18.0823 q^{46} -6.16795 q^{47} +10.1421 q^{48} +4.99768 q^{49} -0.432925 q^{50} +16.8067 q^{51} +5.11781 q^{52} -10.0020 q^{53} -4.30248 q^{54} -11.4903 q^{55} -16.8434 q^{56} -8.02311 q^{57} -7.30104 q^{58} +10.5242 q^{59} +23.4484 q^{60} -4.18841 q^{61} -1.31589 q^{62} +12.7477 q^{63} -8.15104 q^{64} +2.92039 q^{65} +31.9381 q^{66} +11.3522 q^{67} +25.9278 q^{68} +19.1001 q^{69} -19.2841 q^{70} +12.0832 q^{71} -17.8964 q^{72} -10.5570 q^{73} -9.34900 q^{74} +0.457293 q^{75} -12.3773 q^{76} -17.4922 q^{77} -8.11744 q^{78} -0.598593 q^{79} +8.92822 q^{80} -6.49626 q^{81} -6.11889 q^{82} +14.0315 q^{83} +35.6966 q^{84} +14.7952 q^{85} +11.5497 q^{86} +7.71201 q^{87} +24.5570 q^{88} -3.96737 q^{89} -20.4897 q^{90} +4.44584 q^{91} +29.4657 q^{92} +1.38996 q^{93} +15.0923 q^{94} -7.06286 q^{95} +0.320105 q^{96} +4.46761 q^{97} -12.2288 q^{98} -18.5857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more