LMFDB - Embedded Newform 4017.2.a.j.1.19

Newspace parameters

Level:	$ N $	=	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	4017.a (trivial)

Newform invariants

Self dual:	Yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	=	4017.1

$q$-expansion

$f(q)$	$=$	$q+1.86177 q^{2} -1.00000 q^{3} +1.46619 q^{4} -1.56946 q^{5} -1.86177 q^{6} +2.25881 q^{7} -0.993826 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.86177 q^{2} -1.00000 q^{3} +1.46619 q^{4} -1.56946 q^{5} -1.86177 q^{6} +2.25881 q^{7} -0.993826 q^{8} +1.00000 q^{9} -2.92198 q^{10} +6.29697 q^{11} -1.46619 q^{12} +1.00000 q^{13} +4.20539 q^{14} +1.56946 q^{15} -4.78266 q^{16} -4.10223 q^{17} +1.86177 q^{18} +8.25707 q^{19} -2.30113 q^{20} -2.25881 q^{21} +11.7235 q^{22} -2.99206 q^{23} +0.993826 q^{24} -2.53680 q^{25} +1.86177 q^{26} -1.00000 q^{27} +3.31186 q^{28} -0.0882376 q^{29} +2.92198 q^{30} -7.72751 q^{31} -6.91658 q^{32} -6.29697 q^{33} -7.63742 q^{34} -3.54512 q^{35} +1.46619 q^{36} +7.34373 q^{37} +15.3728 q^{38} -1.00000 q^{39} +1.55977 q^{40} +5.08697 q^{41} -4.20539 q^{42} -1.50267 q^{43} +9.23258 q^{44} -1.56946 q^{45} -5.57053 q^{46} +11.9728 q^{47} +4.78266 q^{48} -1.89776 q^{49} -4.72293 q^{50} +4.10223 q^{51} +1.46619 q^{52} +10.8404 q^{53} -1.86177 q^{54} -9.88285 q^{55} -2.24487 q^{56} -8.25707 q^{57} -0.164278 q^{58} +6.81304 q^{59} +2.30113 q^{60} +6.84133 q^{61} -14.3869 q^{62} +2.25881 q^{63} -3.31176 q^{64} -1.56946 q^{65} -11.7235 q^{66} +4.62221 q^{67} -6.01466 q^{68} +2.99206 q^{69} -6.60020 q^{70} +4.74962 q^{71} -0.993826 q^{72} -0.130293 q^{73} +13.6723 q^{74} +2.53680 q^{75} +12.1065 q^{76} +14.2237 q^{77} -1.86177 q^{78} -10.1097 q^{79} +7.50620 q^{80} +1.00000 q^{81} +9.47078 q^{82} -17.1480 q^{83} -3.31186 q^{84} +6.43829 q^{85} -2.79763 q^{86} +0.0882376 q^{87} -6.25809 q^{88} -6.49793 q^{89} -2.92198 q^{90} +2.25881 q^{91} -4.38694 q^{92} +7.72751 q^{93} +22.2906 q^{94} -12.9591 q^{95} +6.91658 q^{96} -10.0318 q^{97} -3.53320 q^{98} +6.29697 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) $	\( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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 $

$2$	1.86177	1.31647	0.658236	−	0.752812i	$-0.271303\pi$
$2$	1.86177	1.31647	0.658236	+	0.752812i	$0.271303\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.46619	0.733097
$5$	−1.56946	−0.701884	−0.350942	−	0.936397i	$-0.614139\pi$
$5$	−1.56946	−0.701884	−0.350942	+	0.936397i	$0.614139\pi$
$6$	−1.86177	−0.760065
$7$	2.25881	0.853751	0.426876	−	0.904310i	$-0.359614\pi$
$7$	2.25881	0.853751	0.426876	+	0.904310i	$0.359614\pi$
$8$	−0.993826	−0.351370
$9$	1.00000	0.333333
$10$	−2.92198	−0.924010
$11$	6.29697	1.89861	0.949304	−	0.314358i	$-0.101789\pi$
$11$	6.29697	1.89861	0.949304	+	0.314358i	$0.101789\pi$
$12$	−1.46619	−0.423254
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.20539	1.12394
$15$	1.56946	0.405233
$16$	−4.78266	−1.19567
$17$	−4.10223	−0.994937	−0.497468	−	0.867482i	$-0.665737\pi$
$17$	−4.10223	−0.994937	−0.497468	+	0.867482i	$0.665737\pi$
$18$	1.86177	0.438824
$19$	8.25707	1.89430	0.947151	−	0.320787i	$-0.103948\pi$
$19$	8.25707	1.89430	0.947151	+	0.320787i	$0.103948\pi$
$20$	−2.30113	−0.514549
$21$	−2.25881	−0.492913
$22$	11.7235	2.49946
$23$	−2.99206	−0.623887	−0.311944	−	0.950101i	$-0.600980\pi$
$23$	−2.99206	−0.623887	−0.311944	+	0.950101i	$0.600980\pi$
$24$	0.993826	0.202864
$25$	−2.53680	−0.507359
$26$	1.86177	0.365123
$27$	−1.00000	−0.192450
$28$	3.31186	0.625882
$29$	−0.0882376	−0.0163853	−0.00819265	−	0.999966i	$-0.502608\pi$
$29$	−0.0882376	−0.0163853	−0.00819265	+	0.999966i	$0.502608\pi$
$30$	2.92198	0.533477
$31$	−7.72751	−1.38790	−0.693951	−	0.720022i	$-0.744132\pi$
$31$	−7.72751	−1.38790	−0.693951	+	0.720022i	$0.744132\pi$
$32$	−6.91658	−1.22269
$33$	−6.29697	−1.09616
$34$	−7.63742	−1.30981
$35$	−3.54512	−0.599234
$36$	1.46619	0.244366
$37$	7.34373	1.20730	0.603651	−	0.797249i	$-0.293712\pi$
$37$	7.34373	1.20730	0.603651	+	0.797249i	$0.293712\pi$
$38$	15.3728	2.49379
$39$	−1.00000	−0.160128
$40$	1.55977	0.246621
$41$	5.08697	0.794451	0.397226	−	0.917721i	$-0.369973\pi$
$41$	5.08697	0.794451	0.397226	+	0.917721i	$0.369973\pi$
$42$	−4.20539	−0.648906
$43$	−1.50267	−0.229155	−0.114578	−	0.993414i	$-0.536551\pi$
$43$	−1.50267	−0.229155	−0.114578	+	0.993414i	$0.536551\pi$
$44$	9.23258	1.39186
$45$	−1.56946	−0.233961
$46$	−5.57053	−0.821330
$47$	11.9728	1.74641	0.873205	−	0.487353i	$-0.162037\pi$
$47$	11.9728	1.74641	0.873205	+	0.487353i	$0.162037\pi$
$48$	4.78266	0.690318
$49$	−1.89776	−0.271109
$50$	−4.72293	−0.667924
$51$	4.10223	0.574427
$52$	1.46619	0.203324
$53$	10.8404	1.48905	0.744523	−	0.667597i	$-0.232677\pi$
$53$	10.8404	1.48905	0.744523	+	0.667597i	$0.232677\pi$
$54$	−1.86177	−0.253355
$55$	−9.88285	−1.33260
$56$	−2.24487	−0.299983
$57$	−8.25707	−1.09368
$58$	−0.164278	−0.0215708
$59$	6.81304	0.886982	0.443491	−	0.896279i	$-0.353740\pi$
$59$	6.81304	0.886982	0.443491	+	0.896279i	$0.353740\pi$
$60$	2.30113	0.297075
$61$	6.84133	0.875942	0.437971	−	0.898989i	$-0.355697\pi$
$61$	6.84133	0.875942	0.437971	+	0.898989i	$0.355697\pi$
$62$	−14.3869	−1.82713
$63$	2.25881	0.284584
$64$	−3.31176	−0.413970
$65$	−1.56946	−0.194668
$66$	−11.7235	−1.44307
$67$	4.62221	0.564693	0.282346	−	0.959313i	$-0.408887\pi$
$67$	4.62221	0.564693	0.282346	+	0.959313i	$0.408887\pi$
$68$	−6.01466	−0.729385
$69$	2.99206	0.360201
$70$	−6.60020	−0.788875
$71$	4.74962	0.563677	0.281838	−	0.959462i	$-0.409056\pi$
$71$	4.74962	0.563677	0.281838	+	0.959462i	$0.409056\pi$
$72$	−0.993826	−0.117123
$73$	−0.130293	−0.0152497	−0.00762483	−	0.999971i	$-0.502427\pi$
$73$	−0.130293	−0.0152497	−0.00762483	+	0.999971i	$0.502427\pi$
$74$	13.6723	1.58938
$75$	2.53680	0.292924
$76$	12.1065	1.38871
$77$	14.2237	1.62094
$78$	−1.86177	−0.210804
$79$	−10.1097	−1.13743	−0.568715	−	0.822535i	$-0.692559\pi$
$79$	−10.1097	−1.13743	−0.568715	+	0.822535i	$0.692559\pi$
$80$	7.50620	0.839219
$81$	1.00000	0.111111
$82$	9.47078	1.04587
$83$	−17.1480	−1.88224	−0.941118	−	0.338079i	$-0.890223\pi$
$83$	−17.1480	−1.88224	−0.941118	+	0.338079i	$0.890223\pi$
$84$	−3.31186	−0.361353
$85$	6.43829	0.698330
$86$	−2.79763	−0.301676
$87$	0.0882376	0.00946006
$88$	−6.25809	−0.667115
$89$	−6.49793	−0.688780	−0.344390	−	0.938827i	$-0.611914\pi$
$89$	−6.49793	−0.688780	−0.344390	+	0.938827i	$0.611914\pi$
$90$	−2.92198	−0.308003
$91$	2.25881	0.236788
$92$	−4.38694	−0.457370
$93$	7.72751	0.801305
$94$	22.2906	2.29910
$95$	−12.9591	−1.32958
$96$	6.91658	0.705920
$97$	−10.0318	−1.01858	−0.509288	−	0.860596i	$-0.670091\pi$
$97$	−10.0318	−1.01858	−0.509288	+	0.860596i	$0.670091\pi$
$98$	−3.53320	−0.356907
$99$	6.29697	0.632870
$100$	−3.71943	−0.371943
$101$	14.3062	1.42352	0.711762	−	0.702421i	$-0.247897\pi$
$101$	14.3062	1.42352	0.711762	+	0.702421i	$0.247897\pi$
$102$	7.63742	0.756217
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−0.993826	−0.0974526
$105$	3.54512	0.345968
$106$	20.1824	1.96029
$107$	14.1867	1.37148	0.685739	−	0.727848i	$-0.259479\pi$
$107$	14.1867	1.37148	0.685739	+	0.727848i	$0.259479\pi$
$108$	−1.46619	−0.141085
$109$	0.400719	0.0383819	0.0191909	−	0.999816i	$-0.493891\pi$
$109$	0.400719	0.0383819	0.0191909	+	0.999816i	$0.493891\pi$
$110$	−18.3996	−1.75433
$111$	−7.34373	−0.697036
$112$	−10.8031	−1.02080
$113$	10.7347	1.00984	0.504918	−	0.863167i	$-0.331523\pi$
$113$	10.7347	1.00984	0.504918	+	0.863167i	$0.331523\pi$
$114$	−15.3728	−1.43979
$115$	4.69591	0.437896
$116$	−0.129373	−0.0120120
$117$	1.00000	0.0924500
$118$	12.6843	1.16769
$119$	−9.26617	−0.849428
$120$	−1.55977	−0.142387
$121$	28.6519	2.60472
$122$	12.7370	1.15315
$123$	−5.08697	−0.458677
$124$	−11.3300	−1.01747
$125$	11.8287	1.05799
$126$	4.20539	0.374646
$127$	2.42583	0.215258	0.107629	−	0.994191i	$-0.465674\pi$
$127$	2.42583	0.215258	0.107629	+	0.994191i	$0.465674\pi$
$128$	7.66741	0.677710
$129$	1.50267	0.132303
$130$	−2.92198	−0.256274
$131$	−6.31062	−0.551361	−0.275681	−	0.961249i	$-0.588903\pi$
$131$	−6.31062	−0.551361	−0.275681	+	0.961249i	$0.588903\pi$
$132$	−9.23258	−0.803593
$133$	18.6512	1.61726
$134$	8.60550	0.743402
$135$	1.56946	0.135078
$136$	4.07690	0.349591
$137$	21.7361	1.85704	0.928521	−	0.371279i	$-0.121081\pi$
$137$	21.7361	1.85704	0.928521	+	0.371279i	$0.121081\pi$
$138$	5.57053	0.474195
$139$	17.1967	1.45861	0.729304	−	0.684190i	$-0.239844\pi$
$139$	17.1967	1.45861	0.729304	+	0.684190i	$0.239844\pi$
$140$	−5.19783	−0.439297
$141$	−11.9728	−1.00829
$142$	8.84272	0.742064
$143$	6.29697	0.526579
$144$	−4.78266	−0.398555
$145$	0.138485	0.0115006
$146$	−0.242576	−0.0200757
$147$	1.89776	0.156525
$148$	10.7673	0.885069
$149$	2.90495	0.237983	0.118992	−	0.992895i	$-0.462034\pi$
$149$	2.90495	0.237983	0.118992	+	0.992895i	$0.462034\pi$
$150$	4.72293	0.385626
$151$	−12.0229	−0.978411	−0.489205	−	0.872169i	$-0.662713\pi$
$151$	−12.0229	−0.978411	−0.489205	+	0.872169i	$0.662713\pi$
$152$	−8.20609	−0.665602
$153$	−4.10223	−0.331646
$154$	26.4813	2.13392
$155$	12.1280	0.974146
$156$	−1.46619	−0.117389
$157$	3.12910	0.249730	0.124865	−	0.992174i	$-0.460150\pi$
$157$	3.12910	0.249730	0.124865	+	0.992174i	$0.460150\pi$
$158$	−18.8219	−1.49739
$159$	−10.8404	−0.859701
$160$	10.8553	0.858186
$161$	−6.75850	−0.532644
$162$	1.86177	0.146275
$163$	18.7831	1.47120	0.735602	−	0.677414i	$-0.236899\pi$
$163$	18.7831	1.47120	0.735602	+	0.677414i	$0.236899\pi$
$164$	7.45848	0.582410
$165$	9.88285	0.769379
$166$	−31.9256	−2.47791
$167$	9.35561	0.723959	0.361979	−	0.932186i	$-0.382101\pi$
$167$	9.35561	0.723959	0.361979	+	0.932186i	$0.382101\pi$
$168$	2.24487	0.173195
$169$	1.00000	0.0769231
$170$	11.9866	0.919332
$171$	8.25707	0.631434
$172$	−2.20321	−0.167993
$173$	9.69810	0.737333	0.368666	−	0.929562i	$-0.379814\pi$
$173$	9.69810	0.737333	0.368666	+	0.929562i	$0.379814\pi$
$174$	0.164278	0.0124539
$175$	−5.73015	−0.433158
$176$	−30.1163	−2.27010
$177$	−6.81304	−0.512099
$178$	−12.0977	−0.906759
$179$	2.84544	0.212678	0.106339	−	0.994330i	$-0.466087\pi$
$179$	2.84544	0.212678	0.106339	+	0.994330i	$0.466087\pi$
$180$	−2.30113	−0.171516
$181$	−4.83800	−0.359606	−0.179803	−	0.983703i	$-0.557546\pi$
$181$	−4.83800	−0.359606	−0.179803	+	0.983703i	$0.557546\pi$
$182$	4.20539	0.311725
$183$	−6.84133	−0.505725
$184$	2.97358	0.219215
$185$	−11.5257	−0.847385
$186$	14.3869	1.05490
$187$	−25.8316	−1.88900
$188$	17.5544	1.28029
$189$	−2.25881	−0.164304
$190$	−24.1270	−1.75035
$191$	−13.8101	−0.999261	−0.499631	−	0.866239i	$-0.666531\pi$
$191$	−13.8101	−0.999261	−0.499631	+	0.866239i	$0.666531\pi$
$192$	3.31176	0.239006
$193$	−7.34299	−0.528560	−0.264280	−	0.964446i	$-0.585134\pi$
$193$	−7.34299	−0.528560	−0.264280	+	0.964446i	$0.585134\pi$
$194$	−18.6769	−1.34093
$195$	1.56946	0.112391
$196$	−2.78249	−0.198749
$197$	7.11104	0.506641	0.253320	−	0.967382i	$-0.418477\pi$
$197$	7.11104	0.506641	0.253320	+	0.967382i	$0.418477\pi$
$198$	11.7235	0.833155
$199$	2.75212	0.195093	0.0975463	−	0.995231i	$-0.468901\pi$
$199$	2.75212	0.195093	0.0975463	+	0.995231i	$0.468901\pi$
$200$	2.52113	0.178271
$201$	−4.62221	−0.326026
$202$	26.6349	1.87403
$203$	−0.199312	−0.0139890
$204$	6.01466	0.421111
$205$	−7.98380	−0.557613
$206$	−1.86177	−0.129716
$207$	−2.99206	−0.207962
$208$	−4.78266	−0.331618
$209$	51.9946	3.59654
$210$	6.60020	0.455457
$211$	−7.77779	−0.535445	−0.267723	−	0.963496i	$-0.586271\pi$
$211$	−7.77779	−0.535445	−0.267723	+	0.963496i	$0.586271\pi$
$212$	15.8941	1.09161
$213$	−4.74962	−0.325439
$214$	26.4123	1.80551
$215$	2.35838	0.160840
$216$	0.993826	0.0676213
$217$	−17.4550	−1.18492
$218$	0.746047	0.0505286
$219$	0.130293	0.00880439
$220$	−14.4902	−0.976927
$221$	−4.10223	−0.275946
$222$	−13.6723	−0.917627
$223$	−14.4522	−0.967791	−0.483896	−	0.875126i	$-0.660779\pi$
$223$	−14.4522	−0.967791	−0.483896	+	0.875126i	$0.660779\pi$
$224$	−15.6233	−1.04387
$225$	−2.53680	−0.169120
$226$	19.9856	1.32942
$227$	−3.65605	−0.242661	−0.121330	−	0.992612i	$-0.538716\pi$
$227$	−3.65605	−0.242661	−0.121330	+	0.992612i	$0.538716\pi$
$228$	−12.1065	−0.801770
$229$	−7.00073	−0.462621	−0.231311	−	0.972880i	$-0.574301\pi$
$229$	−7.00073	−0.462621	−0.231311	+	0.972880i	$0.574301\pi$
$230$	8.74272	0.576478
$231$	−14.2237	−0.935850
$232$	0.0876928	0.00575731
$233$	−0.911437	−0.0597102	−0.0298551	−	0.999554i	$-0.509505\pi$
$233$	−0.911437	−0.0597102	−0.0298551	+	0.999554i	$0.509505\pi$
$234$	1.86177	0.121708
$235$	−18.7908	−1.22578
$236$	9.98923	0.650244
$237$	10.1097	0.656695
$238$	−17.2515	−1.11825
$239$	−5.55401	−0.359259	−0.179630	−	0.983734i	$-0.557490\pi$
$239$	−5.55401	−0.359259	−0.179630	+	0.983734i	$0.557490\pi$
$240$	−7.50620	−0.484523
$241$	−11.5522	−0.744141	−0.372071	−	0.928204i	$-0.621352\pi$
$241$	−11.5522	−0.744141	−0.372071	+	0.928204i	$0.621352\pi$
$242$	53.3432	3.42903
$243$	−1.00000	−0.0641500
$244$	10.0307	0.642150
$245$	2.97846	0.190287
$246$	−9.47078	−0.603835
$247$	8.25707	0.525385
$248$	7.67980	0.487668
$249$	17.1480	1.08671
$250$	22.0223	1.39281
$251$	−17.2837	−1.09094	−0.545468	−	0.838132i	$-0.683648\pi$
$251$	−17.2837	−1.09094	−0.545468	+	0.838132i	$0.683648\pi$
$252$	3.31186	0.208627
$253$	−18.8409	−1.18452
$254$	4.51635	0.283381
$255$	−6.43829	−0.403181
$256$	20.8985	1.30616
$257$	−9.43669	−0.588645	−0.294322	−	0.955706i	$-0.595094\pi$
$257$	−9.43669	−0.588645	−0.294322	+	0.955706i	$0.595094\pi$
$258$	2.79763	0.174173
$259$	16.5881	1.03073
$260$	−2.30113	−0.142710
$261$	−0.0882376	−0.00546177
$262$	−11.7489	−0.725851
$263$	25.6603	1.58228	0.791142	−	0.611632i	$-0.209487\pi$
$263$	25.6603	1.58228	0.791142	+	0.611632i	$0.209487\pi$
$264$	6.25809	0.385159
$265$	−17.0136	−1.04514
$266$	34.7242	2.12908
$267$	6.49793	0.397667
$268$	6.77706	0.413975
$269$	30.8547	1.88124	0.940621	−	0.339458i	$-0.110244\pi$
$269$	30.8547	1.88124	0.940621	+	0.339458i	$0.110244\pi$
$270$	2.92198	0.177826
$271$	−27.8837	−1.69381	−0.846906	−	0.531743i	$-0.821537\pi$
$271$	−27.8837	−1.69381	−0.846906	+	0.531743i	$0.821537\pi$
$272$	19.6196	1.18961
$273$	−2.25881	−0.136710
$274$	40.4677	2.44474
$275$	−15.9741	−0.963276
$276$	4.38694	0.264063
$277$	1.10800	0.0665733	0.0332866	−	0.999446i	$-0.489403\pi$
$277$	1.10800	0.0665733	0.0332866	+	0.999446i	$0.489403\pi$
$278$	32.0164	1.92022
$279$	−7.72751	−0.462634
$280$	3.52323	0.210553
$281$	−24.6142	−1.46836	−0.734181	−	0.678954i	$-0.762433\pi$
$281$	−24.6142	−1.46836	−0.734181	+	0.678954i	$0.762433\pi$
$282$	−22.2906	−1.32739
$283$	−13.9248	−0.827746	−0.413873	−	0.910335i	$-0.635824\pi$
$283$	−13.9248	−0.827746	−0.413873	+	0.910335i	$0.635824\pi$
$284$	6.96387	0.413230
$285$	12.9591	0.767634
$286$	11.7235	0.693227
$287$	11.4905	0.678264
$288$	−6.91658	−0.407563
$289$	−0.171710	−0.0101006
$290$	0.257828	0.0151402
$291$	10.0318	0.588075
$292$	−0.191035	−0.0111795
$293$	2.79845	0.163487	0.0817435	−	0.996653i	$-0.473951\pi$
$293$	2.79845	0.163487	0.0817435	+	0.996653i	$0.473951\pi$
$294$	3.53320	0.206060
$295$	−10.6928	−0.622558
$296$	−7.29838	−0.424210
$297$	−6.29697	−0.365387
$298$	5.40836	0.313298
$299$	−2.99206	−0.173035
$300$	3.71943	0.214742
$301$	−3.39425	−0.195641
$302$	−22.3839	−1.28805
$303$	−14.3062	−0.821872
$304$	−39.4908	−2.26495
$305$	−10.7372	−0.614810
$306$	−7.63742	−0.436602
$307$	8.30771	0.474146	0.237073	−	0.971492i	$-0.423812\pi$
$307$	8.30771	0.474146	0.237073	+	0.971492i	$0.423812\pi$
$308$	20.8547	1.18831
$309$	1.00000	0.0568880
$310$	22.5796	1.28244
$311$	−21.6061	−1.22517	−0.612586	−	0.790404i	$-0.709871\pi$
$311$	−21.6061	−1.22517	−0.612586	+	0.790404i	$0.709871\pi$
$312$	0.993826	0.0562643
$313$	5.64234	0.318924	0.159462	−	0.987204i	$-0.449024\pi$
$313$	5.64234	0.318924	0.159462	+	0.987204i	$0.449024\pi$
$314$	5.82567	0.328762
$315$	−3.54512	−0.199745
$316$	−14.8228	−0.833846
$317$	−12.4310	−0.698193	−0.349097	−	0.937087i	$-0.613511\pi$
$317$	−12.4310	−0.698193	−0.349097	+	0.937087i	$0.613511\pi$
$318$	−20.1824	−1.13177
$319$	−0.555630	−0.0311093
$320$	5.19767	0.290559
$321$	−14.1867	−0.791823
$322$	−12.5828	−0.701211
$323$	−33.8724	−1.88471
$324$	1.46619	0.0814552
$325$	−2.53680	−0.140716
$326$	34.9698	1.93680
$327$	−0.400719	−0.0221598
$328$	−5.05556	−0.279147
$329$	27.0443	1.49100
$330$	18.3996	1.01286
$331$	18.9862	1.04357	0.521787	−	0.853076i	$-0.325266\pi$
$331$	18.9862	1.04357	0.521787	+	0.853076i	$0.325266\pi$
$332$	−25.1423	−1.37986
$333$	7.34373	0.402434
$334$	17.4180	0.953071
$335$	−7.25437	−0.396349
$336$	10.8031	0.589360
$337$	−33.6146	−1.83110	−0.915551	−	0.402201i	$-0.868245\pi$
$337$	−33.6146	−1.83110	−0.915551	+	0.402201i	$0.868245\pi$
$338$	1.86177	0.101267
$339$	−10.7347	−0.583029
$340$	9.43977	0.511944
$341$	−48.6599	−2.63508
$342$	15.3728	0.831265
$343$	−20.0984	−1.08521
$344$	1.49339	0.0805183
$345$	−4.69591	−0.252820
$346$	18.0556	0.970677
$347$	25.5823	1.37333	0.686664	−	0.726975i	$-0.259074\pi$
$347$	25.5823	1.37333	0.686664	+	0.726975i	$0.259074\pi$
$348$	0.129373	0.00693514
$349$	−30.0749	−1.60987	−0.804936	−	0.593361i	$-0.797801\pi$
$349$	−30.0749	−1.60987	−0.804936	+	0.593361i	$0.797801\pi$
$350$	−10.6682	−0.570241
$351$	−1.00000	−0.0533761
$352$	−43.5535	−2.32141
$353$	−16.6497	−0.886174	−0.443087	−	0.896479i	$-0.646117\pi$
$353$	−16.6497	−0.886174	−0.443087	+	0.896479i	$0.646117\pi$
$354$	−12.6843	−0.674164
$355$	−7.45435	−0.395636
$356$	−9.52723	−0.504942
$357$	9.26617	0.490418
$358$	5.29755	0.279984
$359$	−14.6032	−0.770727	−0.385363	−	0.922765i	$-0.625924\pi$
$359$	−14.6032	−0.770727	−0.385363	+	0.922765i	$0.625924\pi$
$360$	1.55977	0.0822071
$361$	49.1793	2.58838
$362$	−9.00725	−0.473410
$363$	−28.6519	−1.50383
$364$	3.31186	0.173589
$365$	0.204490	0.0107035
$366$	−12.7370	−0.665773
$367$	26.8928	1.40379	0.701896	−	0.712279i	$-0.252337\pi$
$367$	26.8928	1.40379	0.701896	+	0.712279i	$0.252337\pi$
$368$	14.3100	0.745961
$369$	5.08697	0.264817
$370$	−21.4582	−1.11556
$371$	24.4865	1.27127
$372$	11.3300	0.587434
$373$	−16.4048	−0.849408	−0.424704	−	0.905332i	$-0.639622\pi$
$373$	−16.4048	−0.849408	−0.424704	+	0.905332i	$0.639622\pi$
$374$	−48.0926	−2.48681
$375$	−11.8287	−0.610831
$376$	−11.8989	−0.613637
$377$	−0.0882376	−0.00454447
$378$	−4.20539	−0.216302
$379$	21.9502	1.12751	0.563753	−	0.825944i	$-0.309357\pi$
$379$	21.9502	1.12751	0.563753	+	0.825944i	$0.309357\pi$
$380$	−19.0006	−0.974711
$381$	−2.42583	−0.124279
$382$	−25.7112	−1.31550
$383$	−13.3214	−0.680691	−0.340345	−	0.940300i	$-0.610544\pi$
$383$	−13.3214	−0.680691	−0.340345	+	0.940300i	$0.610544\pi$
$384$	−7.66741	−0.391276
$385$	−22.3235	−1.13771
$386$	−13.6710	−0.695834
$387$	−1.50267	−0.0763851
$388$	−14.7086	−0.746715
$389$	8.48281	0.430096	0.215048	−	0.976604i	$-0.431009\pi$
$389$	8.48281	0.430096	0.215048	+	0.976604i	$0.431009\pi$
$390$	2.92198	0.147960
$391$	12.2741	0.620728
$392$	1.88605	0.0952597
$393$	6.31062	0.318328
$394$	13.2391	0.666978
$395$	15.8668	0.798343
$396$	9.23258	0.463955
$397$	−26.8086	−1.34549	−0.672743	−	0.739876i	$-0.734884\pi$
$397$	−26.8086	−1.34549	−0.672743	+	0.739876i	$0.734884\pi$
$398$	5.12382	0.256834
$399$	−18.6512	−0.933727
$400$	12.1326	0.606632
$401$	−35.4638	−1.77098	−0.885489	−	0.464661i	$-0.846176\pi$
$401$	−35.4638	−1.77098	−0.885489	+	0.464661i	$0.846176\pi$
$402$	−8.60550	−0.429203
$403$	−7.72751	−0.384935
$404$	20.9757	1.04358
$405$	−1.56946	−0.0779871
$406$	−0.371074	−0.0184161
$407$	46.2432	2.29219
$408$	−4.07690	−0.201837
$409$	−10.7234	−0.530237	−0.265118	−	0.964216i	$-0.585411\pi$
$409$	−10.7234	−0.530237	−0.265118	+	0.964216i	$0.585411\pi$
$410$	−14.8640	−0.734081
$411$	−21.7361	−1.07216
$412$	−1.46619	−0.0722342
$413$	15.3894	0.757262
$414$	−5.57053	−0.273777
$415$	26.9131	1.32111
$416$	−6.91658	−0.339113
$417$	−17.1967	−0.842128
$418$	96.8020	4.73474
$419$	−14.3837	−0.702689	−0.351344	−	0.936246i	$-0.614275\pi$
$419$	−14.3837	−0.702689	−0.351344	+	0.936246i	$0.614275\pi$
$420$	5.19783	0.253628
$421$	2.64706	0.129010	0.0645048	−	0.997917i	$-0.479453\pi$
$421$	2.64706	0.129010	0.0645048	+	0.997917i	$0.479453\pi$
$422$	−14.4805	−0.704899
$423$	11.9728	0.582137
$424$	−10.7735	−0.523207
$425$	10.4065	0.504790
$426$	−8.84272	−0.428431
$427$	15.4533	0.747836
$428$	20.8004	1.00543
$429$	−6.29697	−0.304021
$430$	4.39077	0.211742
$431$	1.86512	0.0898397	0.0449199	−	0.998991i	$-0.485697\pi$
$431$	1.86512	0.0898397	0.0449199	+	0.998991i	$0.485697\pi$
$432$	4.78266	0.230106
$433$	40.8079	1.96110	0.980550	−	0.196267i	$-0.0628820\pi$
$433$	40.8079	1.96110	0.980550	+	0.196267i	$0.0628820\pi$
$434$	−32.4972	−1.55992
$435$	−0.138485	−0.00663986
$436$	0.587531	0.0281376
$437$	−24.7056	−1.18183
$438$	0.242576	0.0115907
$439$	−21.3173	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$439$	−21.3173	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$440$	9.82183	0.468237
$441$	−1.89776	−0.0903697
$442$	−7.63742	−0.363275
$443$	−19.0780	−0.906425	−0.453212	−	0.891403i	$-0.649722\pi$
$443$	−19.0780	−0.906425	−0.453212	+	0.891403i	$0.649722\pi$
$444$	−10.7673	−0.510995
$445$	10.1982	0.483443
$446$	−26.9067	−1.27407
$447$	−2.90495	−0.137400
$448$	−7.48064	−0.353427
$449$	17.6287	0.831949	0.415974	−	0.909376i	$-0.363441\pi$
$449$	17.6287	0.831949	0.415974	+	0.909376i	$0.363441\pi$
$450$	−4.72293	−0.222641
$451$	32.0325	1.50835
$452$	15.7391	0.740307
$453$	12.0229	0.564886
$454$	−6.80674	−0.319456
$455$	−3.54512	−0.166198
$456$	8.20609	0.384285
$457$	30.3878	1.42148	0.710742	−	0.703453i	$-0.248359\pi$
$457$	30.3878	1.42148	0.710742	+	0.703453i	$0.248359\pi$
$458$	−13.0338	−0.609028
$459$	4.10223	0.191476
$460$	6.88512	0.321020
$461$	−18.4832	−0.860850	−0.430425	−	0.902626i	$-0.641636\pi$
$461$	−18.4832	−0.860850	−0.430425	+	0.902626i	$0.641636\pi$
$462$	−26.4813	−1.23202
$463$	−1.43876	−0.0668649	−0.0334325	−	0.999441i	$-0.510644\pi$
$463$	−1.43876	−0.0668649	−0.0334325	+	0.999441i	$0.510644\pi$
$464$	0.422011	0.0195914
$465$	−12.1280	−0.562423
$466$	−1.69689	−0.0786068
$467$	4.30295	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$467$	4.30295	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$468$	1.46619	0.0677748
$469$	10.4407	0.482107
$470$	−34.9842	−1.61370
$471$	−3.12910	−0.144181
$472$	−6.77097	−0.311659
$473$	−9.46228	−0.435076
$474$	18.8219	0.864520
$475$	−20.9465	−0.961091
$476$	−13.5860	−0.622713
$477$	10.8404	0.496348
$478$	−10.3403	−0.472955
$479$	−37.4876	−1.71285	−0.856427	−	0.516269i	$-0.827321\pi$
$479$	−37.4876	−1.71285	−0.856427	+	0.516269i	$0.827321\pi$
$480$	−10.8553	−0.495474
$481$	7.34373	0.334845
$482$	−21.5075	−0.979640
$483$	6.75850	0.307522
$484$	42.0092	1.90951
$485$	15.7445	0.714922
$486$	−1.86177	−0.0844517
$487$	−11.7948	−0.534476	−0.267238	−	0.963631i	$-0.586111\pi$
$487$	−11.7948	−0.534476	−0.267238	+	0.963631i	$0.586111\pi$
$488$	−6.79908	−0.307780
$489$	−18.7831	−0.849400
$490$	5.54522	0.250507
$491$	−23.3888	−1.05552	−0.527761	−	0.849393i	$-0.676968\pi$
$491$	−23.3888	−1.05552	−0.527761	+	0.849393i	$0.676968\pi$
$492$	−7.45848	−0.336254
$493$	0.361971	0.0163023
$494$	15.3728	0.691654
$495$	−9.88285	−0.444201
$496$	36.9581	1.65947
$497$	10.7285	0.481240
$498$	31.9256	1.43062
$499$	−16.9072	−0.756871	−0.378435	−	0.925628i	$-0.623538\pi$
$499$	−16.9072	−0.756871	−0.378435	+	0.925628i	$0.623538\pi$
$500$	17.3432	0.775610
$501$	−9.35561	−0.417978
$502$	−32.1782	−1.43618
$503$	−7.62989	−0.340200	−0.170100	−	0.985427i	$-0.554409\pi$
$503$	−7.62989	−0.340200	−0.170100	+	0.985427i	$0.554409\pi$
$504$	−2.24487	−0.0999943
$505$	−22.4531	−0.999148
$506$	−35.0775	−1.55938
$507$	−1.00000	−0.0444116
$508$	3.55674	0.157805
$509$	22.1165	0.980295	0.490148	−	0.871639i	$-0.336943\pi$
$509$	22.1165	0.980295	0.490148	+	0.871639i	$0.336943\pi$
$510$	−11.9866	−0.530776
$511$	−0.294308	−0.0130194
$512$	23.5734	1.04181
$513$	−8.25707	−0.364559
$514$	−17.5690	−0.774934
$515$	1.56946	0.0691587
$516$	2.20321	0.0969908
$517$	75.3923	3.31575
$518$	30.8833	1.35693
$519$	−9.69810	−0.425699
$520$	1.55977	0.0684004
$521$	−11.3798	−0.498557	−0.249278	−	0.968432i	$-0.580193\pi$
$521$	−11.3798	−0.498557	−0.249278	+	0.968432i	$0.580193\pi$
$522$	−0.164278	−0.00719026
$523$	27.0292	1.18190	0.590951	−	0.806707i	$-0.298753\pi$
$523$	27.0292	1.18190	0.590951	+	0.806707i	$0.298753\pi$
$524$	−9.25258	−0.404201
$525$	5.73015	0.250084
$526$	47.7737	2.08303
$527$	31.7000	1.38087
$528$	30.1163	1.31064
$529$	−14.0476	−0.610765
$530$	−31.6754	−1.37589
$531$	6.81304	0.295661
$532$	27.3462	1.18561
$533$	5.08697	0.220341
$534$	12.0977	0.523517
$535$	−22.2654	−0.962618
$536$	−4.59367	−0.198416
$537$	−2.84544	−0.122790
$538$	57.4444	2.47660
$539$	−11.9502	−0.514730
$540$	2.30113	0.0990250
$541$	25.5420	1.09814	0.549069	−	0.835777i	$-0.314982\pi$
$541$	25.5420	1.09814	0.549069	+	0.835777i	$0.314982\pi$
$542$	−51.9130	−2.22985
$543$	4.83800	0.207618
$544$	28.3734	1.21650
$545$	−0.628912	−0.0269396
$546$	−4.20539	−0.179974
$547$	−4.95564	−0.211888	−0.105944	−	0.994372i	$-0.533786\pi$
$547$	−4.95564	−0.211888	−0.105944	+	0.994372i	$0.533786\pi$
$548$	31.8694	1.36139
$549$	6.84133	0.291981
$550$	−29.7402	−1.26813
$551$	−0.728584	−0.0310387
$552$	−2.97358	−0.126564
$553$	−22.8359	−0.971081
$554$	2.06284	0.0876418
$555$	11.5257	0.489238
$556$	25.2137	1.06930
$557$	24.0526	1.01914	0.509571	−	0.860429i	$-0.329804\pi$
$557$	24.0526	1.01914	0.509571	+	0.860429i	$0.329804\pi$
$558$	−14.3869	−0.609044
$559$	−1.50267	−0.0635562
$560$	16.9551	0.716484
$561$	25.8316	1.09061
$562$	−45.8261	−1.93306
$563$	−6.38648	−0.269158	−0.134579	−	0.990903i	$-0.542968\pi$
$563$	−6.38648	−0.269158	−0.134579	+	0.990903i	$0.542968\pi$
$564$	−17.5544	−0.739174
$565$	−16.8477	−0.708787
$566$	−25.9249	−1.08970
$567$	2.25881	0.0948612
$568$	−4.72030	−0.198059
$569$	14.4713	0.606668	0.303334	−	0.952884i	$-0.401900\pi$
$569$	14.4713	0.606668	0.303334	+	0.952884i	$0.401900\pi$
$570$	24.1270	1.01057
$571$	−43.1996	−1.80785	−0.903924	−	0.427693i	$-0.859326\pi$
$571$	−43.1996	−1.80785	−0.903924	+	0.427693i	$0.859326\pi$
$572$	9.23258	0.386034
$573$	13.8101	0.576924
$574$	21.3927	0.892915
$575$	7.59024	0.316535
$576$	−3.31176	−0.137990
$577$	1.30090	0.0541572	0.0270786	−	0.999633i	$-0.491380\pi$
$577$	1.30090	0.0541572	0.0270786	+	0.999633i	$0.491380\pi$
$578$	−0.319686	−0.0132972
$579$	7.34299	0.305164
$580$	0.203046	0.00843104
$581$	−38.7341	−1.60696
$582$	18.6769	0.774184
$583$	68.2618	2.82711
$584$	0.129489	0.00535828
$585$	−1.56946	−0.0648892
$586$	5.21007	0.215226
$587$	−17.4285	−0.719352	−0.359676	−	0.933077i	$-0.617113\pi$
$587$	−17.4285	−0.719352	−0.359676	+	0.933077i	$0.617113\pi$
$588$	2.78249	0.114748
$589$	−63.8066	−2.62911
$590$	−19.9075	−0.819580
$591$	−7.11104	−0.292509
$592$	−35.1226	−1.44353
$593$	16.3440	0.671166	0.335583	−	0.942011i	$-0.391067\pi$
$593$	16.3440	0.671166	0.335583	+	0.942011i	$0.391067\pi$
$594$	−11.7235	−0.481022
$595$	14.5429	0.596200
$596$	4.25922	0.174465
$597$	−2.75212	−0.112637
$598$	−5.57053	−0.227796
$599$	6.85876	0.280242	0.140121	−	0.990134i	$-0.455251\pi$
$599$	6.85876	0.280242	0.140121	+	0.990134i	$0.455251\pi$
$600$	−2.52113	−0.102925
$601$	−25.9055	−1.05671	−0.528354	−	0.849024i	$-0.677191\pi$
$601$	−25.9055	−1.05671	−0.528354	+	0.849024i	$0.677191\pi$
$602$	−6.31932	−0.257556
$603$	4.62221	0.188231
$604$	−17.6279	−0.717270
$605$	−44.9680	−1.82821
$606$	−26.6349	−1.08197
$607$	−29.5102	−1.19778	−0.598892	−	0.800830i	$-0.704392\pi$
$607$	−29.5102	−1.19778	−0.598892	+	0.800830i	$0.704392\pi$
$608$	−57.1107	−2.31614
$609$	0.199312	0.00807654
$610$	−19.9902	−0.809379
$611$	11.9728	0.484367
$612$	−6.01466	−0.243128
$613$	21.8619	0.882996	0.441498	−	0.897262i	$-0.354447\pi$
$613$	21.8619	0.882996	0.441498	+	0.897262i	$0.354447\pi$
$614$	15.4671	0.624200
$615$	7.98380	0.321938
$616$	−14.1359	−0.569550
$617$	36.7047	1.47767	0.738837	−	0.673884i	$-0.235375\pi$
$617$	36.7047	1.47767	0.738837	+	0.673884i	$0.235375\pi$
$618$	1.86177	0.0748914
$619$	−15.4592	−0.621357	−0.310679	−	0.950515i	$-0.600556\pi$
$619$	−15.4592	−0.621357	−0.310679	+	0.950515i	$0.600556\pi$
$620$	17.7820	0.714143
$621$	2.99206	0.120067
$622$	−40.2257	−1.61290
$623$	−14.6776	−0.588046
$624$	4.78266	0.191460
$625$	−5.88069	−0.235228
$626$	10.5047	0.419854
$627$	−51.9946	−2.07646
$628$	4.58787	0.183076
$629$	−30.1257	−1.20119
$630$	−6.60020	−0.262958
$631$	28.8182	1.14724	0.573618	−	0.819123i	$-0.305539\pi$
$631$	28.8182	1.14724	0.573618	+	0.819123i	$0.305539\pi$
$632$	10.0473	0.399659
$633$	7.77779	0.309140
$634$	−23.1436	−0.919151
$635$	−3.80725	−0.151086
$636$	−15.8941	−0.630244
$637$	−1.89776	−0.0751921
$638$	−1.03446	−0.0409545
$639$	4.74962	0.187892
$640$	−12.0337	−0.475674
$641$	13.6517	0.539212	0.269606	−	0.962971i	$-0.413107\pi$
$641$	13.6517	0.539212	0.269606	+	0.962971i	$0.413107\pi$
$642$	−26.4123	−1.04241
$643$	42.1100	1.66066	0.830329	−	0.557274i	$-0.188153\pi$
$643$	42.1100	1.66066	0.830329	+	0.557274i	$0.188153\pi$
$644$	−9.90927	−0.390480
$645$	−2.35838	−0.0928612
$646$	−63.0627	−2.48117
$647$	38.2621	1.50424	0.752120	−	0.659026i	$-0.229031\pi$
$647$	38.2621	1.50424	0.752120	+	0.659026i	$0.229031\pi$
$648$	−0.993826	−0.0390412
$649$	42.9015	1.68403
$650$	−4.72293	−0.185249
$651$	17.4550	0.684115
$652$	27.5396	1.07853
$653$	−13.9046	−0.544130	−0.272065	−	0.962279i	$-0.587707\pi$
$653$	−13.9046	−0.544130	−0.272065	+	0.962279i	$0.587707\pi$
$654$	−0.746047	−0.0291727
$655$	9.90426	0.386991
$656$	−24.3293	−0.949898
$657$	−0.130293	−0.00508322
$658$	50.3503	1.96286
$659$	−44.7137	−1.74180	−0.870899	−	0.491462i	$-0.836463\pi$
$659$	−44.7137	−1.74180	−0.870899	+	0.491462i	$0.836463\pi$
$660$	14.4902	0.564029
$661$	−48.5856	−1.88976	−0.944880	−	0.327417i	$-0.893822\pi$
$661$	−48.5856	−1.88976	−0.944880	+	0.327417i	$0.893822\pi$
$662$	35.3479	1.37384
$663$	4.10223	0.159317
$664$	17.0421	0.661362
$665$	−29.2723	−1.13513
$666$	13.6723	0.529792
$667$	0.264012	0.0102226
$668$	13.7171	0.530732
$669$	14.4522	0.558755
$670$	−13.5060	−0.521782
$671$	43.0796	1.66307
$672$	15.6233	0.602680
$673$	−31.2441	−1.20437	−0.602187	−	0.798355i	$-0.705704\pi$
$673$	−31.2441	−1.20437	−0.602187	+	0.798355i	$0.705704\pi$
$674$	−62.5827	−2.41059
$675$	2.53680	0.0976413
$676$	1.46619	0.0563921
$677$	−5.43786	−0.208994	−0.104497	−	0.994525i	$-0.533323\pi$
$677$	−5.43786	−0.208994	−0.104497	+	0.994525i	$0.533323\pi$
$678$	−19.9856	−0.767541
$679$	−22.6600	−0.869610
$680$	−6.39853	−0.245373
$681$	3.65605	0.140100
$682$	−90.5937	−3.46901
$683$	−15.9902	−0.611848	−0.305924	−	0.952056i	$-0.598965\pi$
$683$	−15.9902	−0.611848	−0.305924	+	0.952056i	$0.598965\pi$
$684$	12.1065	0.462902
$685$	−34.1140	−1.30343
$686$	−37.4186	−1.42865
$687$	7.00073	0.267095
$688$	7.18677	0.273993
$689$	10.8404	0.412987
$690$	−8.74272	−0.332830
$691$	1.91968	0.0730280	0.0365140	−	0.999333i	$-0.488375\pi$
$691$	1.91968	0.0730280	0.0365140	+	0.999333i	$0.488375\pi$
$692$	14.2193	0.540536
$693$	14.2237	0.540313
$694$	47.6283	1.80795
$695$	−26.9896	−1.02377
$696$	−0.0876928	−0.00332399
$697$	−20.8679	−0.790429
$698$	−55.9926	−2.11935
$699$	0.911437	0.0344737
$700$	−8.40150	−0.317547
$701$	7.69884	0.290781	0.145391	−	0.989374i	$-0.453556\pi$
$701$	7.69884	0.290781	0.145391	+	0.989374i	$0.453556\pi$
$702$	−1.86177	−0.0702680
$703$	60.6377	2.28699
$704$	−20.8541	−0.785967
$705$	18.7908	0.707703
$706$	−30.9979	−1.16662
$707$	32.3151	1.21534
$708$	−9.98923	−0.375418
$709$	41.3316	1.55224	0.776120	−	0.630586i	$-0.217185\pi$
$709$	41.3316	1.55224	0.776120	+	0.630586i	$0.217185\pi$
$710$	−13.8783	−0.520843
$711$	−10.1097	−0.379143
$712$	6.45781	0.242017
$713$	23.1212	0.865894
$714$	17.2515	0.645621
$715$	−9.88285	−0.369598
$716$	4.17196	0.155913
$717$	5.55401	0.207418
$718$	−27.1878	−1.01464
$719$	16.2299	0.605272	0.302636	−	0.953106i	$-0.402133\pi$
$719$	16.2299	0.605272	0.302636	+	0.953106i	$0.402133\pi$
$720$	7.50620	0.279740
$721$	−2.25881	−0.0841226
$722$	91.5605	3.40753
$723$	11.5522	0.429630
$724$	−7.09344	−0.263626
$725$	0.223841	0.00831323
$726$	−53.3432	−1.97975
$727$	−14.9840	−0.555728	−0.277864	−	0.960620i	$-0.589626\pi$
$727$	−14.9840	−0.555728	−0.277864	+	0.960620i	$0.589626\pi$
$728$	−2.24487	−0.0832003
$729$	1.00000	0.0370370
$730$	0.380713	0.0140908
$731$	6.16430	0.227995
$732$	−10.0307	−0.370746
$733$	4.13745	0.152820	0.0764101	−	0.997076i	$-0.475654\pi$
$733$	4.13745	0.152820	0.0764101	+	0.997076i	$0.475654\pi$
$734$	50.0682	1.84805
$735$	−2.97846	−0.109862
$736$	20.6948	0.762820
$737$	29.1059	1.07213
$738$	9.47078	0.348624
$739$	41.1580	1.51402	0.757011	−	0.653402i	$-0.226659\pi$
$739$	41.1580	1.51402	0.757011	+	0.653402i	$0.226659\pi$
$740$	−16.8989	−0.621215
$741$	−8.25707	−0.303331
$742$	45.5882	1.67360
$743$	49.6684	1.82216	0.911079	−	0.412232i	$-0.135251\pi$
$743$	49.6684	1.82216	0.911079	+	0.412232i	$0.135251\pi$
$744$	−7.67980	−0.281555
$745$	−4.55921	−0.167036
$746$	−30.5420	−1.11822
$747$	−17.1480	−0.627412
$748$	−37.8742	−1.38482
$749$	32.0450	1.17090
$750$	−22.0223	−0.804142
$751$	27.8496	1.01625	0.508123	−	0.861284i	$-0.330339\pi$
$751$	27.8496	1.01625	0.508123	+	0.861284i	$0.330339\pi$
$752$	−57.2618	−2.08812
$753$	17.2837	0.629852
$754$	−0.164278	−0.00598266
$755$	18.8695	0.686731
$756$	−3.31186	−0.120451
$757$	14.8108	0.538307	0.269154	−	0.963097i	$-0.413256\pi$
$757$	14.8108	0.538307	0.269154	+	0.963097i	$0.413256\pi$
$758$	40.8662	1.48433
$759$	18.8409	0.683882
$760$	12.8791	0.467175
$761$	−31.3382	−1.13601	−0.568004	−	0.823026i	$-0.692284\pi$
$761$	−31.3382	−1.13601	−0.568004	+	0.823026i	$0.692284\pi$
$762$	−4.51635	−0.163610
$763$	0.905149	0.0327686
$764$	−20.2482	−0.732555
$765$	6.43829	0.232777
$766$	−24.8014	−0.896110
$767$	6.81304	0.246005
$768$	−20.8985	−0.754109
$769$	−32.7375	−1.18055	−0.590273	−	0.807204i	$-0.700980\pi$
$769$	−32.7375	−1.18055	−0.590273	+	0.807204i	$0.700980\pi$
$770$	−41.5613	−1.49776
$771$	9.43669	0.339854
$772$	−10.7662	−0.387486
$773$	31.6059	1.13679	0.568393	−	0.822757i	$-0.307565\pi$
$773$	31.6059	1.13679	0.568393	+	0.822757i	$0.307565\pi$
$774$	−2.79763	−0.100559
$775$	19.6031	0.704164
$776$	9.96987	0.357897
$777$	−16.5881	−0.595095
$778$	15.7931	0.566209
$779$	42.0035	1.50493
$780$	2.30113	0.0823938
$781$	29.9083	1.07020
$782$	22.8516	0.817171
$783$	0.0882376	0.00315335
$784$	9.07636	0.324156
$785$	−4.91100	−0.175281
$786$	11.7489	0.419070
$787$	−16.4804	−0.587463	−0.293732	−	0.955888i	$-0.594897\pi$
$787$	−16.4804	−0.587463	−0.293732	+	0.955888i	$0.594897\pi$
$788$	10.4262	0.371417
$789$	−25.6603	−0.913533
$790$	29.5403	1.05100
$791$	24.2477	0.862148
$792$	−6.25809	−0.222372
$793$	6.84133	0.242943
$794$	−49.9115	−1.77129
$795$	17.0136	0.603410
$796$	4.03514	0.143022
$797$	−17.5556	−0.621851	−0.310925	−	0.950434i	$-0.600639\pi$
$797$	−17.5556	−0.621851	−0.310925	+	0.950434i	$0.600639\pi$
$798$	−34.7242	−1.22923
$799$	−49.1151	−1.73757
$800$	17.5459	0.620343
$801$	−6.49793	−0.229593
$802$	−66.0255	−2.33144
$803$	−0.820452	−0.0289531
$804$	−6.77706	−0.239008
$805$	10.6072	0.373854
$806$	−14.3869	−0.506755
$807$	−30.8547	−1.08614
$808$	−14.2179	−0.500184
$809$	−26.0745	−0.916732	−0.458366	−	0.888764i	$-0.651565\pi$
$809$	−26.0745	−0.916732	−0.458366	+	0.888764i	$0.651565\pi$
$810$	−2.92198	−0.102668
$811$	−43.6580	−1.53304	−0.766521	−	0.642220i	$-0.778014\pi$
$811$	−43.6580	−1.53304	−0.766521	+	0.642220i	$0.778014\pi$
$812$	−0.292230	−0.0102553
$813$	27.8837	0.977922
$814$	86.0944	3.01761
$815$	−29.4793	−1.03261
$816$	−19.6196	−0.686823
$817$	−12.4077	−0.434089
$818$	−19.9645	−0.698041
$819$	2.25881	0.0789293
$820$	−11.7058	−0.408784
$821$	35.9072	1.25317	0.626585	−	0.779353i	$-0.284452\pi$
$821$	35.9072	1.25317	0.626585	+	0.779353i	$0.284452\pi$
$822$	−40.4677	−1.41147
$823$	−21.9078	−0.763657	−0.381828	−	0.924233i	$-0.624705\pi$
$823$	−21.9078	−0.763657	−0.381828	+	0.924233i	$0.624705\pi$
$824$	0.993826	0.0346216
$825$	15.9741	0.556148
$826$	28.6515	0.996914
$827$	−8.38794	−0.291677	−0.145839	−	0.989308i	$-0.546588\pi$
$827$	−8.38794	−0.291677	−0.145839	+	0.989308i	$0.546588\pi$
$828$	−4.38694	−0.152457
$829$	−43.2560	−1.50234	−0.751171	−	0.660108i	$-0.770510\pi$
$829$	−43.2560	−1.50234	−0.751171	+	0.660108i	$0.770510\pi$
$830$	50.1060	1.73920
$831$	−1.10800	−0.0384361
$832$	−3.31176	−0.114815
$833$	7.78506	0.269736
$834$	−32.0164	−1.10864
$835$	−14.6833	−0.508135
$836$	76.2341	2.63661
$837$	7.72751	0.267102
$838$	−26.7791	−0.925070
$839$	53.5221	1.84779	0.923894	−	0.382648i	$-0.124988\pi$
$839$	53.5221	1.84779	0.923894	+	0.382648i	$0.124988\pi$
$840$	−3.52323	−0.121563
$841$	−28.9922	−0.999732
$842$	4.92821	0.169837
$843$	24.6142	0.847759
$844$	−11.4038	−0.392533
$845$	−1.56946	−0.0539911
$846$	22.2906	0.766366
$847$	64.7192	2.22378
$848$	−51.8461	−1.78040
$849$	13.9248	0.477900
$850$	19.3746	0.664542
$851$	−21.9729	−0.753220
$852$	−6.96387	−0.238578
$853$	−24.2736	−0.831113	−0.415557	−	0.909567i	$-0.636413\pi$
$853$	−24.2736	−0.831113	−0.415557	+	0.909567i	$0.636413\pi$
$854$	28.7705	0.984505
$855$	−12.9591	−0.443193
$856$	−14.0991	−0.481897
$857$	−50.6639	−1.73065	−0.865323	−	0.501214i	$-0.832887\pi$
$857$	−50.6639	−1.73065	−0.865323	+	0.501214i	$0.832887\pi$
$858$	−11.7235	−0.400235
$859$	−11.3242	−0.386377	−0.193188	−	0.981162i	$-0.561883\pi$
$859$	−11.3242	−0.386377	−0.193188	+	0.981162i	$0.561883\pi$
$860$	3.45784	0.117912
$861$	−11.4905	−0.391596
$862$	3.47243	0.118271
$863$	34.7110	1.18158	0.590788	−	0.806827i	$-0.298817\pi$
$863$	34.7110	1.18158	0.590788	+	0.806827i	$0.298817\pi$
$864$	6.91658	0.235307
$865$	−15.2208	−0.517522
$866$	75.9749	2.58173
$867$	0.171710	0.00583159
$868$	−25.5924	−0.868663
$869$	−63.6605	−2.15953
$870$	−0.257828	−0.00874119
$871$	4.62221	0.156618
$872$	−0.398244	−0.0134863
$873$	−10.0318	−0.339525
$874$	−45.9963	−1.55585
$875$	26.7188	0.903261
$876$	0.191035	0.00645447
$877$	−11.2275	−0.379127	−0.189564	−	0.981868i	$-0.560707\pi$
$877$	−11.2275	−0.379127	−0.189564	+	0.981868i	$0.560707\pi$
$878$	−39.6880	−1.33940
$879$	−2.79845	−0.0943892
$880$	47.2663	1.59335
$881$	−48.5663	−1.63624	−0.818120	−	0.575047i	$-0.804984\pi$
$881$	−48.5663	−1.63624	−0.818120	+	0.575047i	$0.804984\pi$
$882$	−3.53320	−0.118969
$883$	10.5796	0.356033	0.178016	−	0.984028i	$-0.443032\pi$
$883$	10.5796	0.356033	0.178016	+	0.984028i	$0.443032\pi$
$884$	−6.01466	−0.202295
$885$	10.6928	0.359434
$886$	−35.5189	−1.19328
$887$	9.40046	0.315637	0.157818	−	0.987468i	$-0.449554\pi$
$887$	9.40046	0.315637	0.157818	+	0.987468i	$0.449554\pi$
$888$	7.29838	0.244918
$889$	5.47950	0.183777
$890$	18.9868	0.636439
$891$	6.29697	0.210957
$892$	−21.1897	−0.709485
$893$	98.8602	3.30823
$894$	−5.40836	−0.180883
$895$	−4.46580	−0.149275
$896$	17.3193	0.578596
$897$	2.99206	0.0999019
$898$	32.8206	1.09524
$899$	0.681857	0.0227412
$900$	−3.71943	−0.123981
$901$	−44.4699	−1.48151
$902$	59.6372	1.98570
$903$	3.39425	0.112954
$904$	−10.6684	−0.354826
$905$	7.59304	0.252401
$906$	22.3839	0.743656
$907$	48.2415	1.60183	0.800917	−	0.598775i	$-0.204346\pi$
$907$	48.2415	1.60183	0.800917	+	0.598775i	$0.204346\pi$
$908$	−5.36048	−0.177894
$909$	14.3062	0.474508
$910$	−6.60020	−0.218794
$911$	−5.40615	−0.179114	−0.0895569	−	0.995982i	$-0.528545\pi$
$911$	−5.40615	−0.179114	−0.0895569	+	0.995982i	$0.528545\pi$
$912$	39.4908	1.30767
$913$	−107.980	−3.57363
$914$	56.5752	1.87134
$915$	10.7372	0.354960
$916$	−10.2644	−0.339146
$917$	−14.2545	−0.470725
$918$	7.63742	0.252072
$919$	5.22341	0.172304	0.0861522	−	0.996282i	$-0.472543\pi$
$919$	5.22341	0.172304	0.0861522	+	0.996282i	$0.472543\pi$
$920$	−4.66692	−0.153864
$921$	−8.30771	−0.273748
$922$	−34.4115	−1.13328
$923$	4.74962	0.156336
$924$	−20.8547	−0.686068
$925$	−18.6295	−0.612535
$926$	−2.67865	−0.0880258
$927$	−1.00000	−0.0328443
$928$	0.610302	0.0200341
$929$	−26.5938	−0.872515	−0.436258	−	0.899822i	$-0.643696\pi$
$929$	−26.5938	−0.872515	−0.436258	+	0.899822i	$0.643696\pi$
$930$	−22.5796	−0.740414
$931$	−15.6700	−0.513562
$932$	−1.33634	−0.0437734
$933$	21.6061	0.707353
$934$	8.01112	0.262132
$935$	40.5417	1.32586
$936$	−0.993826	−0.0324842
$937$	35.2974	1.15311	0.576557	−	0.817057i	$-0.304396\pi$
$937$	35.2974	1.15311	0.576557	+	0.817057i	$0.304396\pi$
$938$	19.4382	0.634680
$939$	−5.64234	−0.184131
$940$	−27.5510	−0.898613
$941$	−14.9835	−0.488449	−0.244224	−	0.969719i	$-0.578533\pi$
$941$	−14.9835	−0.488449	−0.244224	+	0.969719i	$0.578533\pi$
$942$	−5.82567	−0.189811
$943$	−15.2205	−0.495648
$944$	−32.5845	−1.06053
$945$	3.54512	0.115323
$946$	−17.6166	−0.572765
$947$	39.0354	1.26848	0.634240	−	0.773137i	$-0.281313\pi$
$947$	39.0354	1.26848	0.634240	+	0.773137i	$0.281313\pi$
$948$	14.8228	0.481421
$949$	−0.130293	−0.00422949
$950$	−38.9976	−1.26525
$951$	12.4310	0.403102
$952$	9.20896	0.298464
$953$	−17.0114	−0.551053	−0.275527	−	0.961293i	$-0.588852\pi$
$953$	−17.0114	−0.551053	−0.275527	+	0.961293i	$0.588852\pi$
$954$	20.1824	0.653429
$955$	21.6743	0.701365
$956$	−8.14326	−0.263372
$957$	0.555630	0.0179610
$958$	−69.7934	−2.25492
$959$	49.0978	1.58545
$960$	−5.19767	−0.167754
$961$	28.7144	0.926271
$962$	13.6723	0.440814
$963$	14.1867	0.457159
$964$	−16.9377	−0.545527
$965$	11.5245	0.370988
$966$	12.5828	0.404844
$967$	−1.49089	−0.0479439	−0.0239720	−	0.999713i	$-0.507631\pi$
$967$	−1.49089	−0.0479439	−0.0239720	+	0.999713i	$0.507631\pi$
$968$	−28.4750	−0.915220
$969$	33.8724	1.08814
$970$	29.3127	0.941174
$971$	26.5605	0.852366	0.426183	−	0.904637i	$-0.359858\pi$
$971$	26.5605	0.852366	0.426183	+	0.904637i	$0.359858\pi$
$972$	−1.46619	−0.0470282
$973$	38.8442	1.24529
$974$	−21.9593	−0.703622
$975$	2.53680	0.0812425
$976$	−32.7198	−1.04733
$977$	4.51459	0.144434	0.0722172	−	0.997389i	$-0.476993\pi$
$977$	4.51459	0.144434	0.0722172	+	0.997389i	$0.476993\pi$
$978$	−34.9698	−1.11821
$979$	−40.9173	−1.30772
$980$	4.36700	0.139499
$981$	0.400719	0.0127940
$982$	−43.5446	−1.38956
$983$	28.9362	0.922922	0.461461	−	0.887160i	$-0.347325\pi$
$983$	28.9362	0.922922	0.461461	+	0.887160i	$0.347325\pi$
$984$	5.05556	0.161165
$985$	−11.1605	−0.355603
$986$	0.673907	0.0214616
$987$	−27.0443	−0.860829
$988$	12.1065	0.385158
$989$	4.49608	0.142967
$990$	−18.3996	−0.584778
$991$	2.53040	0.0803808	0.0401904	−	0.999192i	$-0.487204\pi$
$991$	2.53040	0.0803808	0.0401904	+	0.999192i	$0.487204\pi$
$992$	53.4479	1.69697
$993$	−18.9862	−0.602508
$994$	19.9740	0.633538
$995$	−4.31934	−0.136932
$996$	25.1423	0.796663
$997$	−11.3967	−0.360936	−0.180468	−	0.983581i	$-0.557761\pi$
$997$	−11.3967	−0.360936	−0.180468	+	0.983581i	$0.557761\pi$
$998$	−31.4774	−0.996399
$999$	−7.34373	−0.232345

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.86177 q^{2} -1.00000 q^{3} +1.46619 q^{4} -1.56946 q^{5} -1.86177 q^{6} +2.25881 q^{7} -0.993826 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.86177 q^{2} -1.00000 q^{3} +1.46619 q^{4} -1.56946 q^{5} -1.86177 q^{6} +2.25881 q^{7} -0.993826 q^{8} +1.00000 q^{9} -2.92198 q^{10} +6.29697 q^{11} -1.46619 q^{12} +1.00000 q^{13} +4.20539 q^{14} +1.56946 q^{15} -4.78266 q^{16} -4.10223 q^{17} +1.86177 q^{18} +8.25707 q^{19} -2.30113 q^{20} -2.25881 q^{21} +11.7235 q^{22} -2.99206 q^{23} +0.993826 q^{24} -2.53680 q^{25} +1.86177 q^{26} -1.00000 q^{27} +3.31186 q^{28} -0.0882376 q^{29} +2.92198 q^{30} -7.72751 q^{31} -6.91658 q^{32} -6.29697 q^{33} -7.63742 q^{34} -3.54512 q^{35} +1.46619 q^{36} +7.34373 q^{37} +15.3728 q^{38} -1.00000 q^{39} +1.55977 q^{40} +5.08697 q^{41} -4.20539 q^{42} -1.50267 q^{43} +9.23258 q^{44} -1.56946 q^{45} -5.57053 q^{46} +11.9728 q^{47} +4.78266 q^{48} -1.89776 q^{49} -4.72293 q^{50} +4.10223 q^{51} +1.46619 q^{52} +10.8404 q^{53} -1.86177 q^{54} -9.88285 q^{55} -2.24487 q^{56} -8.25707 q^{57} -0.164278 q^{58} +6.81304 q^{59} +2.30113 q^{60} +6.84133 q^{61} -14.3869 q^{62} +2.25881 q^{63} -3.31176 q^{64} -1.56946 q^{65} -11.7235 q^{66} +4.62221 q^{67} -6.01466 q^{68} +2.99206 q^{69} -6.60020 q^{70} +4.74962 q^{71} -0.993826 q^{72} -0.130293 q^{73} +13.6723 q^{74} +2.53680 q^{75} +12.1065 q^{76} +14.2237 q^{77} -1.86177 q^{78} -10.1097 q^{79} +7.50620 q^{80} +1.00000 q^{81} +9.47078 q^{82} -17.1480 q^{83} -3.31186 q^{84} +6.43829 q^{85} -2.79763 q^{86} +0.0882376 q^{87} -6.25809 q^{88} -6.49793 q^{89} -2.92198 q^{90} +2.25881 q^{91} -4.38694 q^{92} +7.72751 q^{93} +22.2906 q^{94} -12.9591 q^{95} +6.91658 q^{96} -10.0318 q^{97} -3.53320 q^{98} +6.29697 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \)	\( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$-expansion

Coefficient data

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	4017.2.a.j.1.19

Level	4017
Weight	2
Character	4017.1
Self dual	Yes
Analytic conductor	32.076
Analytic rank	0
Dimension	25
CM	No

Self dual:	Yes
Analytic conductor:	\(32.0759064919\)
Analytic rank:	\(0\)
Dimension:	\(25\)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$