LMFDB - Embedded newform 8015.2.a.i.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41331 q^{2} +0.0185355 q^{3} -0.00254977 q^{4} +1.00000 q^{5} -0.0261965 q^{6} -1.00000 q^{7} +2.83023 q^{8} -2.99966 q^{9} +O(q^{10})$	\(q-1.41331 q^{2} +0.0185355 q^{3} -0.00254977 q^{4} +1.00000 q^{5} -0.0261965 q^{6} -1.00000 q^{7} +2.83023 q^{8} -2.99966 q^{9} -1.41331 q^{10} +3.03566 q^{11} -4.72613e-5 q^{12} +1.05041 q^{13} +1.41331 q^{14} +0.0185355 q^{15} -3.99489 q^{16} +5.76651 q^{17} +4.23945 q^{18} +3.18063 q^{19} -0.00254977 q^{20} -0.0185355 q^{21} -4.29034 q^{22} +3.83060 q^{23} +0.0524597 q^{24} +1.00000 q^{25} -1.48455 q^{26} -0.111207 q^{27} +0.00254977 q^{28} -5.07348 q^{29} -0.0261965 q^{30} -0.904966 q^{31} -0.0144237 q^{32} +0.0562676 q^{33} -8.14987 q^{34} -1.00000 q^{35} +0.00764844 q^{36} -7.63155 q^{37} -4.49523 q^{38} +0.0194699 q^{39} +2.83023 q^{40} -5.89029 q^{41} +0.0261965 q^{42} -10.1236 q^{43} -0.00774024 q^{44} -2.99966 q^{45} -5.41383 q^{46} -10.9148 q^{47} -0.0740474 q^{48} +1.00000 q^{49} -1.41331 q^{50} +0.106885 q^{51} -0.00267830 q^{52} -12.8070 q^{53} +0.157170 q^{54} +3.03566 q^{55} -2.83023 q^{56} +0.0589547 q^{57} +7.17040 q^{58} +2.08270 q^{59} -4.72613e-5 q^{60} -5.33239 q^{61} +1.27900 q^{62} +2.99966 q^{63} +8.01017 q^{64} +1.05041 q^{65} -0.0795236 q^{66} -8.57004 q^{67} -0.0147033 q^{68} +0.0710022 q^{69} +1.41331 q^{70} -0.609889 q^{71} -8.48971 q^{72} +12.4592 q^{73} +10.7858 q^{74} +0.0185355 q^{75} -0.00810989 q^{76} -3.03566 q^{77} -0.0275170 q^{78} +14.0049 q^{79} -3.99489 q^{80} +8.99691 q^{81} +8.32482 q^{82} +8.88995 q^{83} +4.72613e-5 q^{84} +5.76651 q^{85} +14.3077 q^{86} -0.0940395 q^{87} +8.59161 q^{88} +0.421426 q^{89} +4.23945 q^{90} -1.05041 q^{91} -0.00976715 q^{92} -0.0167740 q^{93} +15.4260 q^{94} +3.18063 q^{95} -0.000267350 q^{96} +12.0292 q^{97} -1.41331 q^{98} -9.10594 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.41331	−0.999362	−0.499681	−	0.866209i	$-0.666549\pi$
$2$	−1.41331	−0.999362	−0.499681	+	0.866209i	$0.666549\pi$
$3$	0.0185355	0.0107015	0.00535074	−	0.999986i	$-0.498297\pi$
$3$	0.0185355	0.0107015	0.00535074	+	0.999986i	$0.498297\pi$
$4$	−0.00254977	−0.00127489
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.0261965	−0.0106947
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.83023	1.00064
$9$	−2.99966	−0.999885
$10$	−1.41331	−0.446928
$11$	3.03566	0.915286	0.457643	−	0.889136i	$-0.348694\pi$
$11$	3.03566	0.915286	0.457643	+	0.889136i	$0.348694\pi$
$12$	−4.72613e−5 0	−1.36432e−5 0
$13$	1.05041	0.291331	0.145665	−	0.989334i	$-0.453468\pi$
$13$	1.05041	0.291331	0.145665	+	0.989334i	$0.453468\pi$
$14$	1.41331	0.377723
$15$	0.0185355	0.00478585
$16$	−3.99489	−0.998723
$17$	5.76651	1.39858	0.699292	−	0.714836i	$-0.253499\pi$
$17$	5.76651	1.39858	0.699292	+	0.714836i	$0.253499\pi$
$18$	4.23945	0.999248
$19$	3.18063	0.729688	0.364844	−	0.931069i	$-0.381122\pi$
$19$	3.18063	0.729688	0.364844	+	0.931069i	$0.381122\pi$
$20$	−0.00254977	−0.000570146 0
$21$	−0.0185355	−0.00404478
$22$	−4.29034	−0.914703
$23$	3.83060	0.798736	0.399368	−	0.916791i	$-0.369230\pi$
$23$	3.83060	0.798736	0.399368	+	0.916791i	$0.369230\pi$
$24$	0.0524597	0.0107083
$25$	1.00000	0.200000
$26$	−1.48455	−0.291145
$27$	−0.111207	−0.0214017
$28$	0.00254977	0.000481861 0
$29$	−5.07348	−0.942121	−0.471060	−	0.882101i	$-0.656129\pi$
$29$	−5.07348	−0.942121	−0.471060	+	0.882101i	$0.656129\pi$
$30$	−0.0261965	−0.00478280
$31$	−0.904966	−0.162537	−0.0812684	−	0.996692i	$-0.525897\pi$
$31$	−0.904966	−0.162537	−0.0812684	+	0.996692i	$0.525897\pi$
$32$	−0.0144237	−0.00254977
$33$	0.0562676	0.00979492
$34$	−8.14987	−1.39769
$35$	−1.00000	−0.169031
$36$	0.00764844	0.00127474
$37$	−7.63155	−1.25462	−0.627310	−	0.778770i	$-0.715844\pi$
$37$	−7.63155	−1.25462	−0.627310	+	0.778770i	$0.715844\pi$
$38$	−4.49523	−0.729222
$39$	0.0194699	0.00311767
$40$	2.83023	0.447498
$41$	−5.89029	−0.919909	−0.459955	−	0.887942i	$-0.652134\pi$
$41$	−5.89029	−0.919909	−0.459955	+	0.887942i	$0.652134\pi$
$42$	0.0261965	0.00404220
$43$	−10.1236	−1.54383	−0.771914	−	0.635727i	$-0.780700\pi$
$43$	−10.1236	−1.54383	−0.771914	+	0.635727i	$0.780700\pi$
$44$	−0.00774024	−0.00116689
$45$	−2.99966	−0.447162
$46$	−5.41383	−0.798226
$47$	−10.9148	−1.59209	−0.796044	−	0.605239i	$-0.793078\pi$
$47$	−10.9148	−1.59209	−0.796044	+	0.605239i	$0.793078\pi$
$48$	−0.0740474	−0.0106878
$49$	1.00000	0.142857
$50$	−1.41331	−0.199872
$51$	0.106885	0.0149669
$52$	−0.00267830	−0.000371413 0
$53$	−12.8070	−1.75918	−0.879590	−	0.475732i	$-0.842183\pi$
$53$	−12.8070	−1.75918	−0.879590	+	0.475732i	$0.842183\pi$
$54$	0.157170	0.0213881
$55$	3.03566	0.409329
$56$	−2.83023	−0.378205
$57$	0.0589547	0.00780874
$58$	7.17040	0.941520
$59$	2.08270	0.271145	0.135572	−	0.990767i	$-0.456713\pi$
$59$	2.08270	0.271145	0.135572	+	0.990767i	$0.456713\pi$
$60$	−4.72613e−5 0	−6.10141e−6 0
$61$	−5.33239	−0.682743	−0.341372	−	0.939928i	$-0.610891\pi$
$61$	−5.33239	−0.682743	−0.341372	+	0.939928i	$0.610891\pi$
$62$	1.27900	0.162433
$63$	2.99966	0.377921
$64$	8.01017	1.00127
$65$	1.05041	0.130287
$66$	−0.0795236	−0.00978868
$67$	−8.57004	−1.04700	−0.523498	−	0.852027i	$-0.675373\pi$
$67$	−8.57004	−1.04700	−0.523498	+	0.852027i	$0.675373\pi$
$68$	−0.0147033	−0.00178303
$69$	0.0710022	0.00854766
$70$	1.41331	0.168923
$71$	−0.609889	−0.0723805	−0.0361902	−	0.999345i	$-0.511522\pi$
$71$	−0.609889	−0.0723805	−0.0361902	+	0.999345i	$0.511522\pi$
$72$	−8.48971	−1.00052
$73$	12.4592	1.45824	0.729121	−	0.684384i	$-0.239929\pi$
$73$	12.4592	1.45824	0.729121	+	0.684384i	$0.239929\pi$
$74$	10.7858	1.25382
$75$	0.0185355	0.00214030
$76$	−0.00810989	−0.000930268 0
$77$	−3.03566	−0.345946
$78$	−0.0275170	−0.00311568
$79$	14.0049	1.57568	0.787839	−	0.615882i	$-0.211200\pi$
$79$	14.0049	1.57568	0.787839	+	0.615882i	$0.211200\pi$
$80$	−3.99489	−0.446643
$81$	8.99691	0.999656
$82$	8.32482	0.919323
$83$	8.88995	0.975799	0.487900	−	0.872900i	$-0.337763\pi$
$83$	8.88995	0.975799	0.487900	+	0.872900i	$0.337763\pi$
$84$	4.72613e−5 0	5.15663e−6 0
$85$	5.76651	0.625466
$86$	14.3077	1.54284
$87$	−0.0940395	−0.0100821
$88$	8.59161	0.915869
$89$	0.421426	0.0446710	0.0223355	−	0.999751i	$-0.492890\pi$
$89$	0.421426	0.0446710	0.0223355	+	0.999751i	$0.492890\pi$
$90$	4.23945	0.446877
$91$	−1.05041	−0.110113
$92$	−0.00976715	−0.00101830
$93$	−0.0167740	−0.00173938
$94$	15.4260	1.59107
$95$	3.18063	0.326326
$96$	−0.000267350 0	−2.72863e−5 0
$97$	12.0292	1.22138	0.610691	−	0.791869i	$-0.290892\pi$
$97$	12.0292	1.22138	0.610691	+	0.791869i	$0.290892\pi$
$98$	−1.41331	−0.142766
$99$	−9.10594	−0.915182
$100$	−0.00254977	−0.000254977 0
$101$	5.84751	0.581849	0.290925	−	0.956746i	$-0.406037\pi$
$101$	5.84751	0.581849	0.290925	+	0.956746i	$0.406037\pi$
$102$	−0.151062	−0.0149574
$103$	−2.76216	−0.272163	−0.136082	−	0.990698i	$-0.543451\pi$
$103$	−2.76216	−0.272163	−0.136082	+	0.990698i	$0.543451\pi$
$104$	2.97289	0.291516
$105$	−0.0185355	−0.00180888
$106$	18.1003	1.75806
$107$	1.45347	0.140512	0.0702561	−	0.997529i	$-0.477618\pi$
$107$	1.45347	0.140512	0.0702561	+	0.997529i	$0.477618\pi$
$108$	0.000283552 0	2.72848e−5 0
$109$	−9.37064	−0.897544	−0.448772	−	0.893646i	$-0.648138\pi$
$109$	−9.37064	−0.897544	−0.448772	+	0.893646i	$0.648138\pi$
$110$	−4.29034	−0.409068
$111$	−0.141455	−0.0134263
$112$	3.99489	0.377482
$113$	2.29812	0.216189	0.108095	−	0.994141i	$-0.465525\pi$
$113$	2.29812	0.216189	0.108095	+	0.994141i	$0.465525\pi$
$114$	−0.0833214	−0.00780376
$115$	3.83060	0.357205
$116$	0.0129362	0.00120110
$117$	−3.15086	−0.291297
$118$	−2.94351	−0.270972
$119$	−5.76651	−0.528615
$120$	0.0524597	0.00478890
$121$	−1.78476	−0.162251
$122$	7.53634	0.682308
$123$	−0.109180	−0.00984440
$124$	0.00230746	0.000207216 0
$125$	1.00000	0.0894427
$126$	−4.23945	−0.377680
$127$	−15.9473	−1.41509	−0.707547	−	0.706666i	$-0.750198\pi$
$127$	−15.9473	−1.41509	−0.707547	+	0.706666i	$0.750198\pi$
$128$	−11.2920	−0.998083
$129$	−0.187645	−0.0165213
$130$	−1.48455	−0.130204
$131$	−14.4012	−1.25824	−0.629121	−	0.777307i	$-0.716585\pi$
$131$	−14.4012	−1.25824	−0.629121	+	0.777307i	$0.716585\pi$
$132$	−0.000143469 0	−1.24874e−5 0
$133$	−3.18063	−0.275796
$134$	12.1121	1.04633
$135$	−0.111207	−0.00957115
$136$	16.3205	1.39947
$137$	−11.6104	−0.991939	−0.495970	−	0.868340i	$-0.665187\pi$
$137$	−11.6104	−0.991939	−0.495970	+	0.868340i	$0.665187\pi$
$138$	−0.100348	−0.00854221
$139$	0.675760	0.0573172	0.0286586	−	0.999589i	$-0.490876\pi$
$139$	0.675760	0.0573172	0.0286586	+	0.999589i	$0.490876\pi$
$140$	0.00254977	0.000215495 0
$141$	−0.202312	−0.0170377
$142$	0.861963	0.0723343
$143$	3.18868	0.266651
$144$	11.9833	0.998609
$145$	−5.07348	−0.421329
$146$	−17.6088	−1.45731
$147$	0.0185355	0.00152878
$148$	0.0194587	0.00159950
$149$	20.7189	1.69736	0.848679	−	0.528908i	$-0.177398\pi$
$149$	20.7189	1.69736	0.848679	+	0.528908i	$0.177398\pi$
$150$	−0.0261965	−0.00213893
$151$	3.03681	0.247132	0.123566	−	0.992336i	$-0.460567\pi$
$151$	3.03681	0.247132	0.123566	+	0.992336i	$0.460567\pi$
$152$	9.00192	0.730152
$153$	−17.2975	−1.39842
$154$	4.29034	0.345725
$155$	−0.904966	−0.0726886
$156$	−4.96437e−5 0	−3.97467e−6 0
$157$	18.2623	1.45749	0.728747	−	0.684783i	$-0.240103\pi$
$157$	18.2623	1.45749	0.728747	+	0.684783i	$0.240103\pi$
$158$	−19.7933	−1.57467
$159$	−0.237385	−0.0188258
$160$	−0.0144237	−0.00114029
$161$	−3.83060	−0.301894
$162$	−12.7154	−0.999019
$163$	−1.14688	−0.0898308	−0.0449154	−	0.998991i	$-0.514302\pi$
$163$	−1.14688	−0.0898308	−0.0449154	+	0.998991i	$0.514302\pi$
$164$	0.0150189	0.00117278
$165$	0.0562676	0.00438042
$166$	−12.5643	−0.975177
$167$	−17.7012	−1.36976	−0.684881	−	0.728655i	$-0.740146\pi$
$167$	−17.7012	−1.36976	−0.684881	+	0.728655i	$0.740146\pi$
$168$	−0.0524597	−0.00404736
$169$	−11.8966	−0.915126
$170$	−8.14987	−0.625067
$171$	−9.54081	−0.729604
$172$	0.0258127	0.00196820
$173$	10.0675	0.765421	0.382711	−	0.923868i	$-0.374991\pi$
$173$	10.0675	0.765421	0.382711	+	0.923868i	$0.374991\pi$
$174$	0.132907	0.0100757
$175$	−1.00000	−0.0755929
$176$	−12.1271	−0.914118
$177$	0.0386040	0.00290165
$178$	−0.595606	−0.0446426
$179$	−13.5560	−1.01322	−0.506612	−	0.862174i	$-0.669102\pi$
$179$	−13.5560	−1.01322	−0.506612	+	0.862174i	$0.669102\pi$
$180$	0.00764844	0.000570081 0
$181$	1.03101	0.0766345	0.0383172	−	0.999266i	$-0.487800\pi$
$181$	1.03101	0.0766345	0.0383172	+	0.999266i	$0.487800\pi$
$182$	1.48455	0.110042
$183$	−0.0988387	−0.00730637
$184$	10.8415	0.799244
$185$	−7.63155	−0.561083
$186$	0.0237069	0.00173828
$187$	17.5052	1.28010
$188$	0.0278303	0.00202973
$189$	0.111207	0.00808910
$190$	−4.49523	−0.326118
$191$	−9.26502	−0.670394	−0.335197	−	0.942148i	$-0.608803\pi$
$191$	−9.26502	−0.670394	−0.335197	+	0.942148i	$0.608803\pi$
$192$	0.148473	0.0107151
$193$	5.79275	0.416972	0.208486	−	0.978025i	$-0.433146\pi$
$193$	5.79275	0.416972	0.208486	+	0.978025i	$0.433146\pi$
$194$	−17.0010	−1.22060
$195$	0.0194699	0.00139427
$196$	−0.00254977	−0.000182126 0
$197$	14.0713	1.00254	0.501269	−	0.865291i	$-0.332867\pi$
$197$	14.0713	1.00254	0.501269	+	0.865291i	$0.332867\pi$
$198$	12.8695	0.914598
$199$	15.9377	1.12979	0.564897	−	0.825162i	$-0.308916\pi$
$199$	15.9377	1.12979	0.564897	+	0.825162i	$0.308916\pi$
$200$	2.83023	0.200127
$201$	−0.158850	−0.0112044
$202$	−8.26436	−0.581478
$203$	5.07348	0.356088
$204$	−0.000272533 0	−1.90811e−5 0
$205$	−5.89029	−0.411396
$206$	3.90379	0.271990
$207$	−11.4905	−0.798644
$208$	−4.19627	−0.290959
$209$	9.65533	0.667873
$210$	0.0261965	0.00180773
$211$	−5.12157	−0.352583	−0.176292	−	0.984338i	$-0.556410\pi$
$211$	−5.12157	−0.352583	−0.176292	+	0.984338i	$0.556410\pi$
$212$	0.0326550	0.00224275
$213$	−0.0113046	−0.000774579 0
$214$	−2.05421	−0.140423
$215$	−10.1236	−0.690421
$216$	−0.314740	−0.0214154
$217$	0.904966	0.0614331
$218$	13.2436	0.896972
$219$	0.230938	0.0156054
$220$	−0.00774024	−0.000521847 0
$221$	6.05718	0.407450
$222$	0.199920	0.0134177
$223$	19.5381	1.30837	0.654186	−	0.756334i	$-0.273012\pi$
$223$	19.5381	1.30837	0.654186	+	0.756334i	$0.273012\pi$
$224$	0.0144237	0.000963722 0
$225$	−2.99966	−0.199977
$226$	−3.24796	−0.216051
$227$	−3.43241	−0.227817	−0.113908	−	0.993491i	$-0.536337\pi$
$227$	−3.43241	−0.227817	−0.113908	+	0.993491i	$0.536337\pi$
$228$	−0.000150321 0	−9.95525e−6 0
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−5.41383	−0.356978
$231$	−0.0562676	−0.00370213
$232$	−14.3591	−0.942720
$233$	−16.3489	−1.07105	−0.535525	−	0.844520i	$-0.679886\pi$
$233$	−16.3489	−1.07105	−0.535525	+	0.844520i	$0.679886\pi$
$234$	4.45315	0.291112
$235$	−10.9148	−0.712003
$236$	−0.00531041	−0.000345678 0
$237$	0.259589	0.0168621
$238$	8.14987	0.528278
$239$	−25.1379	−1.62604	−0.813018	−	0.582238i	$-0.802177\pi$
$239$	−25.1379	−1.62604	−0.813018	+	0.582238i	$0.802177\pi$
$240$	−0.0740474	−0.00477974
$241$	−5.50557	−0.354645	−0.177323	−	0.984153i	$-0.556744\pi$
$241$	−5.50557	−0.354645	−0.177323	+	0.984153i	$0.556744\pi$
$242$	2.52242	0.162147
$243$	0.500383	0.0320996
$244$	0.0135964	0.000870419 0
$245$	1.00000	0.0638877
$246$	0.154305	0.00983812
$247$	3.34096	0.212580
$248$	−2.56126	−0.162640
$249$	0.164780	0.0104425
$250$	−1.41331	−0.0893857
$251$	−20.6176	−1.30137	−0.650685	−	0.759348i	$-0.725518\pi$
$251$	−20.6176	−1.30137	−0.650685	+	0.759348i	$0.725518\pi$
$252$	−0.00764844	−0.000481806 0
$253$	11.6284	0.731072
$254$	22.5385	1.41419
$255$	0.106885	0.00669341
$256$	−0.0611944	−0.00382465
$257$	−8.21791	−0.512619	−0.256310	−	0.966595i	$-0.582507\pi$
$257$	−8.21791	−0.512619	−0.256310	+	0.966595i	$0.582507\pi$
$258$	0.265201	0.0165107
$259$	7.63155	0.474201
$260$	−0.00267830	−0.000166101 0
$261$	15.2187	0.942013
$262$	20.3534	1.25744
$263$	6.39180	0.394136	0.197068	−	0.980390i	$-0.436858\pi$
$263$	6.39180	0.394136	0.197068	+	0.980390i	$0.436858\pi$
$264$	0.159250	0.00980116
$265$	−12.8070	−0.786729
$266$	4.49523	0.275620
$267$	0.00781134	0.000478046 0
$268$	0.0218516	0.00133480
$269$	−1.25589	−0.0765727	−0.0382864	−	0.999267i	$-0.512190\pi$
$269$	−1.25589	−0.0765727	−0.0382864	+	0.999267i	$0.512190\pi$
$270$	0.157170	0.00956505
$271$	−29.0067	−1.76203	−0.881015	−	0.473088i	$-0.843139\pi$
$271$	−29.0067	−1.76203	−0.881015	+	0.473088i	$0.843139\pi$
$272$	−23.0366	−1.39680
$273$	−0.0194699	−0.00117837
$274$	16.4090	0.991307
$275$	3.03566	0.183057
$276$	−0.000181039 0	−1.08973e−5 0
$277$	−22.4082	−1.34638	−0.673190	−	0.739470i	$-0.735076\pi$
$277$	−22.4082	−1.34638	−0.673190	+	0.739470i	$0.735076\pi$
$278$	−0.955060	−0.0572807
$279$	2.71459	0.162518
$280$	−2.83023	−0.169138
$281$	−31.8245	−1.89849	−0.949246	−	0.314536i	$-0.898151\pi$
$281$	−31.8245	−1.89849	−0.949246	+	0.314536i	$0.898151\pi$
$282$	0.285929	0.0170268
$283$	20.1722	1.19911	0.599556	−	0.800333i	$-0.295344\pi$
$283$	20.1722	1.19911	0.599556	+	0.800333i	$0.295344\pi$
$284$	0.00155508	9.22768e−5 0
$285$	0.0589547	0.00349218
$286$	−4.50660	−0.266481
$287$	5.89029	0.347693
$288$	0.0432661	0.00254948
$289$	16.2526	0.956036
$290$	7.17040	0.421061
$291$	0.222968	0.0130706
$292$	−0.0317682	−0.00185909
$293$	−26.1125	−1.52551	−0.762755	−	0.646687i	$-0.776154\pi$
$293$	−26.1125	−1.52551	−0.762755	+	0.646687i	$0.776154\pi$
$294$	−0.0261965	−0.00152781
$295$	2.08270	0.121260
$296$	−21.5990	−1.25542
$297$	−0.337586	−0.0195887
$298$	−29.2823	−1.69628
$299$	4.02369	0.232696
$300$	−4.72613e−5 0	−2.72863e−6 0
$301$	10.1236	0.583512
$302$	−4.29196	−0.246974
$303$	0.108387	0.00622665
$304$	−12.7063	−0.728756
$305$	−5.33239	−0.305332
$306$	24.4468	1.39753
$307$	−2.46427	−0.140643	−0.0703216	−	0.997524i	$-0.522403\pi$
$307$	−2.46427	−0.140643	−0.0703216	+	0.997524i	$0.522403\pi$
$308$	0.00774024	0.000441041 0
$309$	−0.0511980	−0.00291255
$310$	1.27900	0.0726423
$311$	20.5624	1.16599	0.582995	−	0.812476i	$-0.301881\pi$
$311$	20.5624	1.16599	0.582995	+	0.812476i	$0.301881\pi$
$312$	0.0551041	0.00311966
$313$	28.1635	1.59189	0.795946	−	0.605367i	$-0.206974\pi$
$313$	28.1635	1.59189	0.795946	+	0.605367i	$0.206974\pi$
$314$	−25.8104	−1.45656
$315$	2.99966	0.169011
$316$	−0.0357093	−0.00200881
$317$	2.94967	0.165670	0.0828349	−	0.996563i	$-0.473603\pi$
$317$	2.94967	0.165670	0.0828349	+	0.996563i	$0.473603\pi$
$318$	0.335499	0.0188138
$319$	−15.4014	−0.862310
$320$	8.01017	0.447782
$321$	0.0269408	0.00150369
$322$	5.41383	0.301701
$323$	18.3412	1.02053
$324$	−0.0229400	−0.00127445
$325$	1.05041	0.0582661
$326$	1.62090	0.0897735
$327$	−0.173690	−0.00960506
$328$	−16.6709	−0.920495
$329$	10.9148	0.601753
$330$	−0.0795236	−0.00437763
$331$	12.1221	0.666289	0.333144	−	0.942876i	$-0.391890\pi$
$331$	12.1221	0.666289	0.333144	+	0.942876i	$0.391890\pi$
$332$	−0.0226673	−0.00124403
$333$	22.8920	1.25448
$334$	25.0174	1.36889
$335$	−8.57004	−0.468231
$336$	0.0740474	0.00403962
$337$	−9.05235	−0.493113	−0.246556	−	0.969128i	$-0.579299\pi$
$337$	−9.05235	−0.493113	−0.246556	+	0.969128i	$0.579299\pi$
$338$	16.8137	0.914543
$339$	0.0425969	0.00231355
$340$	−0.0147033	−0.000797397 0
$341$	−2.74717	−0.148768
$342$	13.4841	0.729139
$343$	−1.00000	−0.0539949
$344$	−28.6520	−1.54481
$345$	0.0710022	0.00382263
$346$	−14.2286	−0.764933
$347$	13.4506	0.722066	0.361033	−	0.932553i	$-0.382424\pi$
$347$	13.4506	0.722066	0.361033	+	0.932553i	$0.382424\pi$
$348$	0.000239779 0	1.28535e−5 0
$349$	23.2873	1.24654	0.623271	−	0.782006i	$-0.285803\pi$
$349$	23.2873	1.24654	0.623271	+	0.782006i	$0.285803\pi$
$350$	1.41331	0.0755447
$351$	−0.116812	−0.00623499
$352$	−0.0437854	−0.00233377
$353$	−0.433619	−0.0230792	−0.0115396	−	0.999933i	$-0.503673\pi$
$353$	−0.433619	−0.0230792	−0.0115396	+	0.999933i	$0.503673\pi$
$354$	−0.0545594	−0.00289980
$355$	−0.609889	−0.0323695
$356$	−0.00107454	−5.69504e−5 0
$357$	−0.106885	−0.00565696
$358$	19.1589	1.01258
$359$	−0.123616	−0.00652422	−0.00326211	−	0.999995i	$-0.501038\pi$
$359$	−0.123616	−0.00652422	−0.00326211	+	0.999995i	$0.501038\pi$
$360$	−8.48971	−0.447447
$361$	−8.88357	−0.467556
$362$	−1.45714	−0.0765856
$363$	−0.0330814	−0.00173632
$364$	0.00267830	0.000140381 0
$365$	12.4592	0.652146
$366$	0.139690	0.00730171
$367$	−31.2417	−1.63080	−0.815402	−	0.578895i	$-0.803484\pi$
$367$	−31.2417	−1.63080	−0.815402	+	0.578895i	$0.803484\pi$
$368$	−15.3028	−0.797716
$369$	17.6689	0.919804
$370$	10.7858	0.560725
$371$	12.8070	0.664908
$372$	4.27699e−5 0	2.21752e−6 0
$373$	33.2231	1.72023	0.860115	−	0.510101i	$-0.170392\pi$
$373$	33.2231	1.72023	0.860115	+	0.510101i	$0.170392\pi$
$374$	−24.7403	−1.27929
$375$	0.0185355	0.000957170 0
$376$	−30.8914	−1.59310
$377$	−5.32922	−0.274469
$378$	−0.157170	−0.00808394
$379$	−32.1555	−1.65172	−0.825859	−	0.563877i	$-0.809309\pi$
$379$	−32.1555	−1.65172	−0.825859	+	0.563877i	$0.809309\pi$
$380$	−0.00810989	−0.000416028 0
$381$	−0.295591	−0.0151436
$382$	13.0944	0.669966
$383$	17.7069	0.904779	0.452389	−	0.891821i	$-0.350572\pi$
$383$	17.7069	0.904779	0.452389	+	0.891821i	$0.350572\pi$
$384$	−0.209304	−0.0106810
$385$	−3.03566	−0.154712
$386$	−8.18697	−0.416706
$387$	30.3672	1.54365
$388$	−0.0306718	−0.00155712
$389$	−0.305961	−0.0155128	−0.00775642	−	0.999970i	$-0.502469\pi$
$389$	−0.305961	−0.0155128	−0.00775642	+	0.999970i	$0.502469\pi$
$390$	−0.0275170	−0.00139338
$391$	22.0892	1.11710
$392$	2.83023	0.142948
$393$	−0.266934	−0.0134651
$394$	−19.8871	−1.00190
$395$	14.0049	0.704664
$396$	0.0232181	0.00116675
$397$	20.0196	1.00475	0.502377	−	0.864649i	$-0.332459\pi$
$397$	20.0196	1.00475	0.502377	+	0.864649i	$0.332459\pi$
$398$	−22.5249	−1.12907
$399$	−0.0589547	−0.00295143
$400$	−3.99489	−0.199745
$401$	0.462072	0.0230748	0.0115374	−	0.999933i	$-0.496327\pi$
$401$	0.462072	0.0230748	0.0115374	+	0.999933i	$0.496327\pi$
$402$	0.224505	0.0111973
$403$	−0.950584	−0.0473519
$404$	−0.0149098	−0.000741791 0
$405$	8.99691	0.447060
$406$	−7.17040	−0.355861
$407$	−23.1668	−1.14834
$408$	0.302509	0.0149764
$409$	−38.1051	−1.88417	−0.942087	−	0.335369i	$-0.891139\pi$
$409$	−38.1051	−1.88417	−0.942087	+	0.335369i	$0.891139\pi$
$410$	8.32482	0.411134
$411$	−0.215204	−0.0106152
$412$	0.00704287	0.000346977 0
$413$	−2.08270	−0.102483
$414$	16.2396	0.798135
$415$	8.88995	0.436391
$416$	−0.0151507	−0.000742826 0
$417$	0.0125256	0.000613380 0
$418$	−13.6460	−0.667447
$419$	−27.8953	−1.36278	−0.681388	−	0.731922i	$-0.738623\pi$
$419$	−27.8953	−1.36278	−0.681388	+	0.731922i	$0.738623\pi$
$420$	4.72613e−5 0	2.30612e−6 0
$421$	−13.8562	−0.675309	−0.337655	−	0.941270i	$-0.609634\pi$
$421$	−13.8562	−0.675309	−0.337655	+	0.941270i	$0.609634\pi$
$422$	7.23837	0.352358
$423$	32.7407	1.59191
$424$	−36.2468	−1.76030
$425$	5.76651	0.279717
$426$	0.0159769	0.000774085 0
$427$	5.33239	0.258053
$428$	−0.00370601	−0.000179137 0
$429$	0.0591039	0.00285356
$430$	14.3077	0.689981
$431$	−36.4803	−1.75719	−0.878596	−	0.477565i	$-0.841519\pi$
$431$	−36.4803	−1.75719	−0.878596	+	0.477565i	$0.841519\pi$
$432$	0.444259	0.0213744
$433$	−32.9899	−1.58539	−0.792696	−	0.609618i	$-0.791323\pi$
$433$	−32.9899	−1.58539	−0.792696	+	0.609618i	$0.791323\pi$
$434$	−1.27900	−0.0613939
$435$	−0.0940395	−0.00450885
$436$	0.0238930	0.00114427
$437$	12.1837	0.582827
$438$	−0.326388	−0.0155954
$439$	−6.38295	−0.304642	−0.152321	−	0.988331i	$-0.548675\pi$
$439$	−6.38295	−0.304642	−0.152321	+	0.988331i	$0.548675\pi$
$440$	8.59161	0.409589
$441$	−2.99966	−0.142841
$442$	−8.56069	−0.407191
$443$	−8.96137	−0.425767	−0.212884	−	0.977078i	$-0.568286\pi$
$443$	−8.96137	−0.425767	−0.212884	+	0.977078i	$0.568286\pi$
$444$	0.000360677 0	1.71170e−5 0
$445$	0.421426	0.0199775
$446$	−27.6135	−1.30754
$447$	0.384036	0.0181643
$448$	−8.01017	−0.378445
$449$	−19.4886	−0.919726	−0.459863	−	0.887990i	$-0.652101\pi$
$449$	−19.4886	−0.919726	−0.459863	+	0.887990i	$0.652101\pi$
$450$	4.23945	0.199850
$451$	−17.8809	−0.841980
$452$	−0.00585969	−0.000275616 0
$453$	0.0562888	0.00264468
$454$	4.85106	0.227672
$455$	−1.05041	−0.0492439
$456$	0.166855	0.00781371
$457$	−8.98712	−0.420400	−0.210200	−	0.977658i	$-0.567411\pi$
$457$	−8.98712	−0.420400	−0.210200	+	0.977658i	$0.567411\pi$
$458$	−1.41331	−0.0660397
$459$	−0.641274	−0.0299321
$460$	−0.00976715	−0.000455396 0
$461$	−1.71958	−0.0800886	−0.0400443	−	0.999198i	$-0.512750\pi$
$461$	−1.71958	−0.0800886	−0.0400443	+	0.999198i	$0.512750\pi$
$462$	0.0795236	0.00369977
$463$	18.7034	0.869219	0.434610	−	0.900619i	$-0.356886\pi$
$463$	18.7034	0.869219	0.434610	+	0.900619i	$0.356886\pi$
$464$	20.2680	0.940918
$465$	−0.0167740	−0.000777877 0
$466$	23.1060	1.07037
$467$	0.756812	0.0350211	0.0175105	−	0.999847i	$-0.494426\pi$
$467$	0.756812	0.0350211	0.0175105	+	0.999847i	$0.494426\pi$
$468$	0.00803398	0.000371371 0
$469$	8.57004	0.395728
$470$	15.4260	0.711549
$471$	0.338502	0.0155974
$472$	5.89452	0.271317
$473$	−30.7317	−1.41304
$474$	−0.366880	−0.0168513
$475$	3.18063	0.145938
$476$	0.0147033	0.000673923 0
$477$	38.4167	1.75898
$478$	35.5277	1.62500
$479$	13.0062	0.594267	0.297134	−	0.954836i	$-0.403969\pi$
$479$	13.0062	0.594267	0.297134	+	0.954836i	$0.403969\pi$
$480$	−0.000267350 0	−1.22028e−5 0
$481$	−8.01624	−0.365509
$482$	7.78109	0.354419
$483$	−0.0710022	−0.00323071
$484$	0.00455072	0.000206851 0
$485$	12.0292	0.546219
$486$	−0.707197	−0.0320791
$487$	−4.99113	−0.226170	−0.113085	−	0.993585i	$-0.536073\pi$
$487$	−4.99113	−0.226170	−0.113085	+	0.993585i	$0.536073\pi$
$488$	−15.0919	−0.683178
$489$	−0.0212581	−0.000961323 0
$490$	−1.41331	−0.0638469
$491$	36.3538	1.64063	0.820313	−	0.571915i	$-0.193799\pi$
$491$	36.3538	1.64063	0.820313	+	0.571915i	$0.193799\pi$
$492$	0.000278383 0	1.25505e−5 0
$493$	−29.2562	−1.31763
$494$	−4.72182	−0.212445
$495$	−9.10594	−0.409282
$496$	3.61524	0.162329
$497$	0.609889	0.0273572
$498$	−0.232885	−0.0104358
$499$	−11.2755	−0.504763	−0.252381	−	0.967628i	$-0.581214\pi$
$499$	−11.2755	−0.504763	−0.252381	+	0.967628i	$0.581214\pi$
$500$	−0.00254977	−0.000114029 0
$501$	−0.328102	−0.0146585
$502$	29.1391	1.30054
$503$	32.2016	1.43580	0.717898	−	0.696148i	$-0.245104\pi$
$503$	32.2016	1.43580	0.717898	+	0.696148i	$0.245104\pi$
$504$	8.48971	0.378162
$505$	5.84751	0.260211
$506$	−16.4346	−0.730606
$507$	−0.220510	−0.00979321
$508$	0.0406620	0.00180408
$509$	31.7377	1.40675	0.703374	−	0.710820i	$-0.251676\pi$
$509$	31.7377	1.40675	0.703374	+	0.710820i	$0.251676\pi$
$510$	−0.151062	−0.00668914
$511$	−12.4592	−0.551164
$512$	22.6705	1.00191
$513$	−0.353708	−0.0156166
$514$	11.6145	0.512293
$515$	−2.76216	−0.121715
$516$	0.000478453 0	2.10627e−5 0
$517$	−33.1337	−1.45722
$518$	−10.7858	−0.473899
$519$	0.186607	0.00819114
$520$	2.97289	0.130370
$521$	−29.8600	−1.30819	−0.654095	−	0.756413i	$-0.726950\pi$
$521$	−29.8600	−1.30819	−0.654095	+	0.756413i	$0.726950\pi$
$522$	−21.5087	−0.941412
$523$	17.3925	0.760522	0.380261	−	0.924879i	$-0.375834\pi$
$523$	17.3925	0.760522	0.380261	+	0.924879i	$0.375834\pi$
$524$	0.0367199	0.00160411
$525$	−0.0185355	−0.000808956 0
$526$	−9.03361	−0.393884
$527$	−5.21850	−0.227321
$528$	−0.224783	−0.00978242
$529$	−8.32649	−0.362021
$530$	18.1003	0.786228
$531$	−6.24739	−0.271114
$532$	0.00810989	0.000351608 0
$533$	−6.18721	−0.267998
$534$	−0.0110399	−0.000477742 0
$535$	1.45347	0.0628390
$536$	−24.2552	−1.04766
$537$	−0.251268	−0.0108430
$538$	1.77496	0.0765239
$539$	3.03566	0.130755
$540$	0.000283552 0	1.22021e−5 0
$541$	−34.5996	−1.48755	−0.743777	−	0.668427i	$-0.766968\pi$
$541$	−34.5996	−1.48755	−0.743777	+	0.668427i	$0.766968\pi$
$542$	40.9955	1.76091
$543$	0.0191103	0.000820103 0
$544$	−0.0831742	−0.00356606
$545$	−9.37064	−0.401394
$546$	0.0275170	0.00117762
$547$	−18.4494	−0.788841	−0.394421	−	0.918930i	$-0.629055\pi$
$547$	−18.4494	−0.788841	−0.394421	+	0.918930i	$0.629055\pi$
$548$	0.0296037	0.00126461
$549$	15.9954	0.682665
$550$	−4.29034	−0.182941
$551$	−16.1369	−0.687454
$552$	0.200952	0.00855310
$553$	−14.0049	−0.595550
$554$	31.6698	1.34552
$555$	−0.141455	−0.00600442
$556$	−0.00172303	−7.30729e−5 0
$557$	−40.2313	−1.70466	−0.852328	−	0.523008i	$-0.824810\pi$
$557$	−40.2313	−1.70466	−0.852328	+	0.523008i	$0.824810\pi$
$558$	−3.83656	−0.162415
$559$	−10.6339	−0.449765
$560$	3.99489	0.168815
$561$	0.324467	0.0136990
$562$	44.9780	1.89728
$563$	−20.3235	−0.856534	−0.428267	−	0.903652i	$-0.640876\pi$
$563$	−20.3235	−0.856534	−0.428267	+	0.903652i	$0.640876\pi$
$564$	0.000515848 0	2.17211e−5 0
$565$	2.29812	0.0966827
$566$	−28.5096	−1.19835
$567$	−8.99691	−0.377835
$568$	−1.72612	−0.0724265
$569$	−8.73843	−0.366334	−0.183167	−	0.983082i	$-0.558635\pi$
$569$	−8.73843	−0.366334	−0.183167	+	0.983082i	$0.558635\pi$
$570$	−0.0833214	−0.00348995
$571$	−6.80623	−0.284832	−0.142416	−	0.989807i	$-0.545487\pi$
$571$	−6.80623	−0.284832	−0.142416	+	0.989807i	$0.545487\pi$
$572$	−0.00813041	−0.000339949 0
$573$	−0.171732	−0.00717421
$574$	−8.32482	−0.347471
$575$	3.83060	0.159747
$576$	−24.0278	−1.00116
$577$	−44.5694	−1.85545	−0.927724	−	0.373267i	$-0.878237\pi$
$577$	−44.5694	−1.85545	−0.927724	+	0.373267i	$0.878237\pi$
$578$	−22.9700	−0.955426
$579$	0.107372	0.00446222
$580$	0.0129362	0.000537146 0
$581$	−8.88995	−0.368817
$582$	−0.315123	−0.0130623
$583$	−38.8778	−1.61015
$584$	35.2625	1.45917
$585$	−3.15086	−0.130272
$586$	36.9052	1.52454
$587$	17.9731	0.741831	0.370916	−	0.928667i	$-0.379044\pi$
$587$	17.9731	0.741831	0.370916	+	0.928667i	$0.379044\pi$
$588$	−4.72613e−5 0	−1.94902e−6 0
$589$	−2.87837	−0.118601
$590$	−2.94351	−0.121182
$591$	0.260819	0.0107287
$592$	30.4872	1.25302
$593$	15.6688	0.643441	0.321721	−	0.946835i	$-0.395739\pi$
$593$	15.6688	0.643441	0.321721	+	0.946835i	$0.395739\pi$
$594$	0.477114	0.0195762
$595$	−5.76651	−0.236404
$596$	−0.0528285	−0.00216394
$597$	0.295414	0.0120905
$598$	−5.68673	−0.232548
$599$	25.1065	1.02582	0.512912	−	0.858441i	$-0.328567\pi$
$599$	25.1065	1.02582	0.512912	+	0.858441i	$0.328567\pi$
$600$	0.0524597	0.00214166
$601$	−11.4851	−0.468487	−0.234244	−	0.972178i	$-0.575261\pi$
$601$	−11.4851	−0.468487	−0.234244	+	0.972178i	$0.575261\pi$
$602$	−14.3077	−0.583140
$603$	25.7072	1.04688
$604$	−0.00774317	−0.000315065 0
$605$	−1.78476	−0.0725607
$606$	−0.153184	−0.00622268
$607$	−1.66065	−0.0674038	−0.0337019	−	0.999432i	$-0.510730\pi$
$607$	−1.66065	−0.0674038	−0.0337019	+	0.999432i	$0.510730\pi$
$608$	−0.0458764	−0.00186053
$609$	0.0940395	0.00381067
$610$	7.53634	0.305137
$611$	−11.4650	−0.463824
$612$	0.0441048	0.00178283
$613$	15.2614	0.616402	0.308201	−	0.951321i	$-0.400273\pi$
$613$	15.2614	0.616402	0.308201	+	0.951321i	$0.400273\pi$
$614$	3.48278	0.140554
$615$	−0.109180	−0.00440255
$616$	−8.59161	−0.346166
$617$	46.9388	1.88968	0.944842	−	0.327527i	$-0.106215\pi$
$617$	46.9388	1.88968	0.944842	+	0.327527i	$0.106215\pi$
$618$	0.0723587	0.00291070
$619$	23.8131	0.957131	0.478565	−	0.878052i	$-0.341157\pi$
$619$	23.8131	0.957131	0.478565	+	0.878052i	$0.341157\pi$
$620$	0.00230746	9.26697e−5 0
$621$	−0.425989	−0.0170943
$622$	−29.0611	−1.16525
$623$	−0.421426	−0.0168841
$624$	−0.0777800	−0.00311369
$625$	1.00000	0.0400000
$626$	−39.8037	−1.59088
$627$	0.178967	0.00714723
$628$	−0.0465648	−0.00185814
$629$	−44.0074	−1.75469
$630$	−4.23945	−0.168904
$631$	2.74571	0.109305	0.0546525	−	0.998505i	$-0.482595\pi$
$631$	2.74571	0.109305	0.0546525	+	0.998505i	$0.482595\pi$
$632$	39.6371	1.57668
$633$	−0.0949309	−0.00377316
$634$	−4.16880	−0.165564
$635$	−15.9473	−0.632849
$636$	0.000605277 0	2.40008e−5 0
$637$	1.05041	0.0416187
$638$	21.7669	0.861761
$639$	1.82946	0.0723722
$640$	−11.2920	−0.446356
$641$	32.8995	1.29945	0.649727	−	0.760168i	$-0.274883\pi$
$641$	32.8995	1.29945	0.649727	+	0.760168i	$0.274883\pi$
$642$	−0.0380758	−0.00150273
$643$	−27.8928	−1.09998	−0.549992	−	0.835170i	$-0.685369\pi$
$643$	−27.8928	−1.09998	−0.549992	+	0.835170i	$0.685369\pi$
$644$	0.00976715	0.000384880 0
$645$	−0.187645	−0.00738853
$646$	−25.9218	−1.01988
$647$	31.5507	1.24039	0.620193	−	0.784449i	$-0.287054\pi$
$647$	31.5507	1.24039	0.620193	+	0.784449i	$0.287054\pi$
$648$	25.4633	1.00029
$649$	6.32238	0.248175
$650$	−1.48455	−0.0582290
$651$	0.0167740	0.000657426 0
$652$	0.00292429	0.000114524 0
$653$	−19.0396	−0.745078	−0.372539	−	0.928017i	$-0.621513\pi$
$653$	−19.0396	−0.745078	−0.372539	+	0.928017i	$0.621513\pi$
$654$	0.245478	0.00959893
$655$	−14.4012	−0.562703
$656$	23.5311	0.918735
$657$	−37.3734	−1.45808
$658$	−15.4260	−0.601369
$659$	−28.5218	−1.11105	−0.555525	−	0.831500i	$-0.687483\pi$
$659$	−28.5218	−1.11105	−0.555525	+	0.831500i	$0.687483\pi$
$660$	−0.000143469 0	−5.58454e−6 0
$661$	10.5001	0.408408	0.204204	−	0.978928i	$-0.434539\pi$
$661$	10.5001	0.408408	0.204204	+	0.978928i	$0.434539\pi$
$662$	−17.1323	−0.665864
$663$	0.112273	0.00436032
$664$	25.1606	0.976420
$665$	−3.18063	−0.123340
$666$	−32.3536	−1.25368
$667$	−19.4345	−0.752506
$668$	0.0451341	0.00174629
$669$	0.362150	0.0140015
$670$	12.1121	0.467933
$671$	−16.1873	−0.624905
$672$	0.000267350 0	1.03133e−5 0
$673$	−42.0557	−1.62113	−0.810564	−	0.585650i	$-0.800839\pi$
$673$	−42.0557	−1.62113	−0.810564	+	0.585650i	$0.800839\pi$
$674$	12.7938	0.492798
$675$	−0.111207	−0.00428035
$676$	0.0303337	0.00116668
$677$	6.78123	0.260624	0.130312	−	0.991473i	$-0.458402\pi$
$677$	6.78123	0.260624	0.130312	+	0.991473i	$0.458402\pi$
$678$	−0.0602027	−0.00231207
$679$	−12.0292	−0.461639
$680$	16.3205	0.625864
$681$	−0.0636215	−0.00243798
$682$	3.88261	0.148673
$683$	11.0623	0.423285	0.211643	−	0.977347i	$-0.432119\pi$
$683$	11.0623	0.423285	0.211643	+	0.977347i	$0.432119\pi$
$684$	0.0243269	0.000930161 0
$685$	−11.6104	−0.443609
$686$	1.41331	0.0539605
$687$	0.0185355	0.000707174 0
$688$	40.4425	1.54186
$689$	−13.4526	−0.512503
$690$	−0.100348	−0.00382019
$691$	−28.6251	−1.08895	−0.544475	−	0.838777i	$-0.683271\pi$
$691$	−28.6251	−1.08895	−0.544475	+	0.838777i	$0.683271\pi$
$692$	−0.0256699	−0.000975824 0
$693$	9.10594	0.345906
$694$	−19.0099	−0.721606
$695$	0.675760	0.0256331
$696$	−0.266153	−0.0100885
$697$	−33.9664	−1.28657
$698$	−32.9122	−1.24575
$699$	−0.303035	−0.0114618
$700$	0.00254977	9.63723e−5 0
$701$	14.0901	0.532174	0.266087	−	0.963949i	$-0.414269\pi$
$701$	14.0901	0.532174	0.266087	+	0.963949i	$0.414269\pi$
$702$	0.165092	0.00623101
$703$	−24.2732	−0.915480
$704$	24.3162	0.916450
$705$	−0.202312	−0.00761950
$706$	0.612840	0.0230645
$707$	−5.84751	−0.219918
$708$	−9.84313e−5 0	−3.69927e−6 0
$709$	24.7743	0.930418	0.465209	−	0.885201i	$-0.345979\pi$
$709$	24.7743	0.930418	0.465209	+	0.885201i	$0.345979\pi$
$710$	0.861963	0.0323489
$711$	−42.0100	−1.57550
$712$	1.19273	0.0446995
$713$	−3.46657	−0.129824
$714$	0.151062	0.00565336
$715$	3.18868	0.119250
$716$	0.0345647	0.00129174
$717$	−0.465944	−0.0174010
$718$	0.174708	0.00652006
$719$	−10.6611	−0.397593	−0.198797	−	0.980041i	$-0.563703\pi$
$719$	−10.6611	−0.397593	−0.198797	+	0.980041i	$0.563703\pi$
$720$	11.9833	0.446592
$721$	2.76216	0.102868
$722$	12.5552	0.467258
$723$	−0.102049	−0.00379523
$724$	−0.00262884	−9.77002e−5 0
$725$	−5.07348	−0.188424
$726$	0.0467544	0.00173522
$727$	3.41068	0.126495	0.0632476	−	0.997998i	$-0.479854\pi$
$727$	3.41068	0.126495	0.0632476	+	0.997998i	$0.479854\pi$
$728$	−2.97289	−0.110183
$729$	−26.9814	−0.999313
$730$	−17.6088	−0.651730
$731$	−58.3776	−2.15917
$732$	0.000252016 0	9.31478e−6 0
$733$	19.2252	0.710099	0.355050	−	0.934847i	$-0.384464\pi$
$733$	19.2252	0.710099	0.355050	+	0.934847i	$0.384464\pi$
$734$	44.1543	1.62976
$735$	0.0185355	0.000683693 0
$736$	−0.0552513	−0.00203659
$737$	−26.0157	−0.958302
$738$	−24.9716	−0.919217
$739$	−36.4751	−1.34176	−0.670880	−	0.741566i	$-0.734083\pi$
$739$	−36.4751	−1.34176	−0.670880	+	0.741566i	$0.734083\pi$
$740$	0.0194587	0.000715316 0
$741$	0.0619265	0.00227493
$742$	−18.1003	−0.664484
$743$	3.69209	0.135450	0.0677249	−	0.997704i	$-0.478426\pi$
$743$	3.69209	0.135450	0.0677249	+	0.997704i	$0.478426\pi$
$744$	−0.0474743	−0.00174049
$745$	20.7189	0.759082
$746$	−46.9547	−1.71913
$747$	−26.6668	−0.975687
$748$	−0.0446342	−0.00163199
$749$	−1.45347	−0.0531086
$750$	−0.0261965	−0.000956560 0
$751$	49.4211	1.80340	0.901700	−	0.432361i	$-0.142320\pi$
$751$	49.4211	1.80340	0.901700	+	0.432361i	$0.142320\pi$
$752$	43.6035	1.59006
$753$	−0.382157	−0.0139266
$754$	7.53185	0.274294
$755$	3.03681	0.110521
$756$	−0.000283552 0	−1.03127e−5 0
$757$	−27.7857	−1.00989	−0.504944	−	0.863152i	$-0.668487\pi$
$757$	−27.7857	−1.00989	−0.504944	+	0.863152i	$0.668487\pi$
$758$	45.4457	1.65066
$759$	0.215539	0.00782356
$760$	9.00192	0.326534
$761$	51.4775	1.86606	0.933030	−	0.359799i	$-0.117155\pi$
$761$	51.4775	1.86606	0.933030	+	0.359799i	$0.117155\pi$
$762$	0.417763	0.0151340
$763$	9.37064	0.339240
$764$	0.0236237	0.000854675 0
$765$	−17.2975	−0.625394
$766$	−25.0253	−0.904202
$767$	2.18769	0.0789928
$768$	−0.00113427	−4.09294e−5 0
$769$	−48.0907	−1.73419	−0.867097	−	0.498139i	$-0.834017\pi$
$769$	−48.0907	−1.73419	−0.867097	+	0.498139i	$0.834017\pi$
$770$	4.29034	0.154613
$771$	−0.152323	−0.00548579
$772$	−0.0147702	−0.000531591 0
$773$	−13.6971	−0.492649	−0.246325	−	0.969187i	$-0.579223\pi$
$773$	−13.6971	−0.492649	−0.246325	+	0.969187i	$0.579223\pi$
$774$	−42.9183	−1.54267
$775$	−0.904966	−0.0325074
$776$	34.0454	1.22216
$777$	0.141455	0.00507466
$778$	0.432418	0.0155030
$779$	−18.7349	−0.671246
$780$	−4.96437e−5 0	−1.77753e−6 0
$781$	−1.85142	−0.0662489
$782$	−31.2189	−1.11639
$783$	0.564205	0.0201630
$784$	−3.99489	−0.142675
$785$	18.2623	0.651811
$786$	0.377262	0.0134565
$787$	38.8184	1.38373	0.691864	−	0.722028i	$-0.256790\pi$
$787$	38.8184	1.38373	0.691864	+	0.722028i	$0.256790\pi$
$788$	−0.0358786	−0.00127812
$789$	0.118475	0.00421784
$790$	−19.7933	−0.704215
$791$	−2.29812	−0.0817118
$792$	−25.7719	−0.915764
$793$	−5.60119	−0.198904
$794$	−28.2939	−1.00411
$795$	−0.237385	−0.00841917
$796$	−0.0406375	−0.00144036
$797$	3.74477	0.132647	0.0663233	−	0.997798i	$-0.478873\pi$
$797$	3.74477	0.132647	0.0663233	+	0.997798i	$0.478873\pi$
$798$	0.0833214	0.00294954
$799$	−62.9403	−2.22667
$800$	−0.0144237	−0.000509954 0
$801$	−1.26413	−0.0446659
$802$	−0.653052	−0.0230601
$803$	37.8220	1.33471
$804$	0.000405031 0	1.42843e−5 0
$805$	−3.83060	−0.135011
$806$	1.34347	0.0473218
$807$	−0.0232785	−0.000819442 0
$808$	16.5498	0.582220
$809$	0.373166	0.0131198	0.00655991	−	0.999978i	$-0.497912\pi$
$809$	0.373166	0.0131198	0.00655991	+	0.999978i	$0.497912\pi$
$810$	−12.7154	−0.446775
$811$	19.4643	0.683485	0.341742	−	0.939794i	$-0.388983\pi$
$811$	19.4643	0.683485	0.341742	+	0.939794i	$0.388983\pi$
$812$	−0.0129362	−0.000453972 0
$813$	−0.537654	−0.0188563
$814$	32.7419	1.14760
$815$	−1.14688	−0.0401736
$816$	−0.426995	−0.0149478
$817$	−32.1993	−1.12651
$818$	53.8543	1.88297
$819$	3.15086	0.110100
$820$	0.0150189	0.000524483 0
$821$	30.5341	1.06565	0.532823	−	0.846227i	$-0.321131\pi$
$821$	30.5341	1.06565	0.532823	+	0.846227i	$0.321131\pi$
$822$	0.304150	0.0106085
$823$	36.7717	1.28178	0.640891	−	0.767632i	$-0.278565\pi$
$823$	36.7717	1.28178	0.640891	+	0.767632i	$0.278565\pi$
$824$	−7.81753	−0.272337
$825$	0.0562676	0.00195898
$826$	2.94351	0.102418
$827$	−30.7727	−1.07007	−0.535036	−	0.844829i	$-0.679702\pi$
$827$	−30.7727	−1.07007	−0.535036	+	0.844829i	$0.679702\pi$
$828$	0.0292981	0.00101818
$829$	23.7145	0.823637	0.411819	−	0.911266i	$-0.364894\pi$
$829$	23.7145	0.823637	0.411819	+	0.911266i	$0.364894\pi$
$830$	−12.5643	−0.436112
$831$	−0.415348	−0.0144083
$832$	8.41395	0.291701
$833$	5.76651	0.199798
$834$	−0.0177025	−0.000612989 0
$835$	−17.7012	−0.612577
$836$	−0.0246189	−0.000851462 0
$837$	0.100638	0.00347857
$838$	39.4248	1.36191
$839$	31.8647	1.10009	0.550046	−	0.835135i	$-0.314610\pi$
$839$	31.8647	1.10009	0.550046	+	0.835135i	$0.314610\pi$
$840$	−0.0524597	−0.00181003
$841$	−3.25984	−0.112408
$842$	19.5831	0.674879
$843$	−0.589884	−0.0203167
$844$	0.0130588	0.000449503 0
$845$	−11.8966	−0.409257
$846$	−46.2728	−1.59089
$847$	1.78476	0.0613250
$848$	51.1627	1.75693
$849$	0.373902	0.0128323
$850$	−8.14987	−0.279538
$851$	−29.2334	−1.00211
$852$	2.88241e−5 0	9.87499e−7 0
$853$	−4.76912	−0.163291	−0.0816457	−	0.996661i	$-0.526018\pi$
$853$	−4.76912	−0.163291	−0.0816457	+	0.996661i	$0.526018\pi$
$854$	−7.53634	−0.257888
$855$	−9.54081	−0.326289
$856$	4.11365	0.140602
$857$	−18.9535	−0.647441	−0.323720	−	0.946153i	$-0.604934\pi$
$857$	−18.9535	−0.647441	−0.323720	+	0.946153i	$0.604934\pi$
$858$	−0.0835322	−0.00285174
$859$	19.4630	0.664068	0.332034	−	0.943267i	$-0.392265\pi$
$859$	19.4630	0.664068	0.332034	+	0.943267i	$0.392265\pi$
$860$	0.0258127	0.000880207 0
$861$	0.109180	0.00372083
$862$	51.5580	1.75607
$863$	17.1272	0.583015	0.291508	−	0.956568i	$-0.405843\pi$
$863$	17.1272	0.583015	0.291508	+	0.956568i	$0.405843\pi$
$864$	0.00160401	5.45695e−5 0
$865$	10.0675	0.342307
$866$	46.6250	1.58438
$867$	0.301251	0.0102310
$868$	−0.00230746	−7.83202e−5 0
$869$	42.5142	1.44220
$870$	0.132907	0.00450597
$871$	−9.00203	−0.305022
$872$	−26.5210	−0.898115
$873$	−36.0835	−1.22124
$874$	−17.2194	−0.582456
$875$	−1.00000	−0.0338062
$876$	−0.000588840 0	−1.98951e−5 0
$877$	−35.4017	−1.19543	−0.597715	−	0.801708i	$-0.703925\pi$
$877$	−35.4017	−1.19543	−0.597715	+	0.801708i	$0.703925\pi$
$878$	9.02110	0.304447
$879$	−0.484009	−0.0163252
$880$	−12.1271	−0.408806
$881$	−33.9985	−1.14544	−0.572719	−	0.819752i	$-0.694111\pi$
$881$	−33.9985	−1.14544	−0.572719	+	0.819752i	$0.694111\pi$
$882$	4.23945	0.142750
$883$	8.83163	0.297208	0.148604	−	0.988897i	$-0.452522\pi$
$883$	8.83163	0.297208	0.148604	+	0.988897i	$0.452522\pi$
$884$	−0.0154444	−0.000519452 0
$885$	0.0386040	0.00129766
$886$	12.6652	0.425496
$887$	18.9221	0.635340	0.317670	−	0.948201i	$-0.397100\pi$
$887$	18.9221	0.635340	0.317670	+	0.948201i	$0.397100\pi$
$888$	−0.400349	−0.0134348
$889$	15.9473	0.534855
$890$	−0.595606	−0.0199648
$891$	27.3116	0.914972
$892$	−0.0498178	−0.00166802
$893$	−34.7160	−1.16173
$894$	−0.542762	−0.0181527
$895$	−13.5560	−0.453127
$896$	11.2920	0.377240
$897$	0.0745813	0.00249020
$898$	27.5435	0.919139
$899$	4.59132	0.153129
$900$	0.00764844	0.000254948 0
$901$	−73.8518	−2.46036
$902$	25.2713	0.841444
$903$	0.187645	0.00624445
$904$	6.50421	0.216327
$905$	1.03101	0.0342720
$906$	−0.0795537	−0.00264299
$907$	9.86419	0.327535	0.163768	−	0.986499i	$-0.447635\pi$
$907$	9.86419	0.327535	0.163768	+	0.986499i	$0.447635\pi$
$908$	0.00875185	0.000290440 0
$909$	−17.5405	−0.581783
$910$	1.48455	0.0492125
$911$	−7.92783	−0.262661	−0.131330	−	0.991339i	$-0.541925\pi$
$911$	−7.92783	−0.262661	−0.131330	+	0.991339i	$0.541925\pi$
$912$	−0.235518	−0.00779877
$913$	26.9869	0.893136
$914$	12.7016	0.420132
$915$	−0.0988387	−0.00326751
$916$	−0.00254977	−8.42468e−5 0
$917$	14.4012	0.475571
$918$	0.906321	0.0299130
$919$	29.1789	0.962523	0.481262	−	0.876577i	$-0.340179\pi$
$919$	29.1789	0.962523	0.481262	+	0.876577i	$0.340179\pi$
$920$	10.8415	0.357433
$921$	−0.0456765	−0.00150509
$922$	2.43030	0.0800376
$923$	−0.640632	−0.0210867
$924$	0.000143469 0	4.71980e−6 0
$925$	−7.63155	−0.250924
$926$	−26.4337	−0.868665
$927$	8.28552	0.272132
$928$	0.0731781	0.00240219
$929$	−36.7880	−1.20697	−0.603487	−	0.797372i	$-0.706223\pi$
$929$	−36.7880	−1.20697	−0.603487	+	0.797372i	$0.706223\pi$
$930$	0.0237069	0.000777381 0
$931$	3.18063	0.104241
$932$	0.0416858	0.00136546
$933$	0.381136	0.0124778
$934$	−1.06961	−0.0349988
$935$	17.5052	0.572480
$936$	−8.91766	−0.291483
$937$	4.27269	0.139583	0.0697913	−	0.997562i	$-0.477767\pi$
$937$	4.27269	0.139583	0.0697913	+	0.997562i	$0.477767\pi$
$938$	−12.1121	−0.395475
$939$	0.522024	0.0170356
$940$	0.0278303	0.000907723 0
$941$	−4.41762	−0.144010	−0.0720052	−	0.997404i	$-0.522940\pi$
$941$	−4.41762	−0.144010	−0.0720052	+	0.997404i	$0.522940\pi$
$942$	−0.478409	−0.0155874
$943$	−22.5634	−0.734764
$944$	−8.32018	−0.270799
$945$	0.111207	0.00361756
$946$	43.4335	1.41214
$947$	−17.9584	−0.583568	−0.291784	−	0.956484i	$-0.594249\pi$
$947$	−17.9584	−0.583568	−0.291784	+	0.956484i	$0.594249\pi$
$948$	−0.000661891 0	−2.14972e−5 0
$949$	13.0873	0.424831
$950$	−4.49523	−0.145844
$951$	0.0546736	0.00177291
$952$	−16.3205	−0.528951
$953$	23.0969	0.748181	0.374091	−	0.927392i	$-0.377955\pi$
$953$	23.0969	0.748181	0.374091	+	0.927392i	$0.377955\pi$
$954$	−54.2947	−1.75786
$955$	−9.26502	−0.299809
$956$	0.0640959	0.00207301
$957$	−0.285472	−0.00922800
$958$	−18.3818	−0.593888
$959$	11.6104	0.374918
$960$	0.148473	0.00479194
$961$	−30.1810	−0.973582
$962$	11.3294	0.365276
$963$	−4.35991	−0.140496
$964$	0.0140380	0.000452132 0
$965$	5.79275	0.186475
$966$	0.100348	0.00322865
$967$	−45.5440	−1.46460	−0.732298	−	0.680984i	$-0.761552\pi$
$967$	−45.5440	−1.46460	−0.732298	+	0.680984i	$0.761552\pi$
$968$	−5.05127	−0.162354
$969$	0.339963	0.0109212
$970$	−17.0010	−0.545870
$971$	−36.5472	−1.17286	−0.586428	−	0.810002i	$-0.699466\pi$
$971$	−36.5472	−1.17286	−0.586428	+	0.810002i	$0.699466\pi$
$972$	−0.00127586	−4.09232e−5 0
$973$	−0.675760	−0.0216639
$974$	7.05402	0.226025
$975$	0.0194699	0.000623534 0
$976$	21.3023	0.681872
$977$	30.2496	0.967770	0.483885	−	0.875131i	$-0.339225\pi$
$977$	30.2496	0.967770	0.483885	+	0.875131i	$0.339225\pi$
$978$	0.0300443	0.000960710 0
$979$	1.27931	0.0408868
$980$	−0.00254977	−8.14494e−5 0
$981$	28.1087	0.897441
$982$	−51.3793	−1.63958
$983$	37.3398	1.19096	0.595478	−	0.803372i	$-0.296963\pi$
$983$	37.3398	1.19096	0.595478	+	0.803372i	$0.296963\pi$
$984$	−0.309003	−0.00985066
$985$	14.0713	0.448349
$986$	41.3482	1.31679
$987$	0.202312	0.00643965
$988$	−0.00851869	−0.000271016 0
$989$	−38.7793	−1.23311
$990$	12.8695	0.409021
$991$	−20.3080	−0.645106	−0.322553	−	0.946551i	$-0.604541\pi$
$991$	−20.3080	−0.645106	−0.322553	+	0.946551i	$0.604541\pi$
$992$	0.0130529	0.000414431 0
$993$	0.224689	0.00713028
$994$	−0.861963	−0.0273398
$995$	15.9377	0.505259
$996$	−0.000420151 0	−1.33130e−5 0
$997$	−15.6866	−0.496801	−0.248401	−	0.968657i	$-0.579905\pi$
$997$	−15.6866	−0.496801	−0.248401	+	0.968657i	$0.579905\pi$
$998$	15.9359	0.504441
$999$	0.848680	0.0268510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.12	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.12	✓	44	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.41331 q^{2} +0.0185355 q^{3} -0.00254977 q^{4} +1.00000 q^{5} -0.0261965 q^{6} -1.00000 q^{7} +2.83023 q^{8} -2.99966 q^{9} +O(q^{10})\)	\(q-1.41331 q^{2} +0.0185355 q^{3} -0.00254977 q^{4} +1.00000 q^{5} -0.0261965 q^{6} -1.00000 q^{7} +2.83023 q^{8} -2.99966 q^{9} -1.41331 q^{10} +3.03566 q^{11} -4.72613e-5 q^{12} +1.05041 q^{13} +1.41331 q^{14} +0.0185355 q^{15} -3.99489 q^{16} +5.76651 q^{17} +4.23945 q^{18} +3.18063 q^{19} -0.00254977 q^{20} -0.0185355 q^{21} -4.29034 q^{22} +3.83060 q^{23} +0.0524597 q^{24} +1.00000 q^{25} -1.48455 q^{26} -0.111207 q^{27} +0.00254977 q^{28} -5.07348 q^{29} -0.0261965 q^{30} -0.904966 q^{31} -0.0144237 q^{32} +0.0562676 q^{33} -8.14987 q^{34} -1.00000 q^{35} +0.00764844 q^{36} -7.63155 q^{37} -4.49523 q^{38} +0.0194699 q^{39} +2.83023 q^{40} -5.89029 q^{41} +0.0261965 q^{42} -10.1236 q^{43} -0.00774024 q^{44} -2.99966 q^{45} -5.41383 q^{46} -10.9148 q^{47} -0.0740474 q^{48} +1.00000 q^{49} -1.41331 q^{50} +0.106885 q^{51} -0.00267830 q^{52} -12.8070 q^{53} +0.157170 q^{54} +3.03566 q^{55} -2.83023 q^{56} +0.0589547 q^{57} +7.17040 q^{58} +2.08270 q^{59} -4.72613e-5 q^{60} -5.33239 q^{61} +1.27900 q^{62} +2.99966 q^{63} +8.01017 q^{64} +1.05041 q^{65} -0.0795236 q^{66} -8.57004 q^{67} -0.0147033 q^{68} +0.0710022 q^{69} +1.41331 q^{70} -0.609889 q^{71} -8.48971 q^{72} +12.4592 q^{73} +10.7858 q^{74} +0.0185355 q^{75} -0.00810989 q^{76} -3.03566 q^{77} -0.0275170 q^{78} +14.0049 q^{79} -3.99489 q^{80} +8.99691 q^{81} +8.32482 q^{82} +8.88995 q^{83} +4.72613e-5 q^{84} +5.76651 q^{85} +14.3077 q^{86} -0.0940395 q^{87} +8.59161 q^{88} +0.421426 q^{89} +4.23945 q^{90} -1.05041 q^{91} -0.00976715 q^{92} -0.0167740 q^{93} +15.4260 q^{94} +3.18063 q^{95} -0.000267350 q^{96} +12.0292 q^{97} -1.41331 q^{98} -9.10594 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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