LMFDB - Embedded newform 403.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(1,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("403.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.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:	$3.21797120146$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 7x^{6} + 19x^{5} + 21x^{4} - 31x^{3} - 29x^{2} - x + 1 $ x^8 - 3x^7 - 7x^6 + 19x^5 + 21x^4 - 31x^3 - 29x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.39479$ of defining polynomial
Character	$\chi$	$=$	403.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.39479 q^{2} -1.21460 q^{3} -0.0545724 q^{4} -0.0316546 q^{5} -1.69410 q^{6} -2.20383 q^{7} -2.86569 q^{8} -1.52475 q^{9} +O(q^{10})$	\(q+1.39479 q^{2} -1.21460 q^{3} -0.0545724 q^{4} -0.0316546 q^{5} -1.69410 q^{6} -2.20383 q^{7} -2.86569 q^{8} -1.52475 q^{9} -0.0441514 q^{10} -2.27170 q^{11} +0.0662835 q^{12} -1.00000 q^{13} -3.07387 q^{14} +0.0384476 q^{15} -3.88788 q^{16} -0.756127 q^{17} -2.12670 q^{18} +6.64611 q^{19} +0.00172747 q^{20} +2.67676 q^{21} -3.16854 q^{22} -2.39365 q^{23} +3.48066 q^{24} -4.99900 q^{25} -1.39479 q^{26} +5.49575 q^{27} +0.120268 q^{28} -2.98187 q^{29} +0.0536261 q^{30} -1.00000 q^{31} +0.308621 q^{32} +2.75920 q^{33} -1.05464 q^{34} +0.0697612 q^{35} +0.0832095 q^{36} -7.31998 q^{37} +9.26989 q^{38} +1.21460 q^{39} +0.0907122 q^{40} +1.75026 q^{41} +3.73351 q^{42} +11.3218 q^{43} +0.123972 q^{44} +0.0482654 q^{45} -3.33862 q^{46} -11.2715 q^{47} +4.72220 q^{48} -2.14314 q^{49} -6.97253 q^{50} +0.918390 q^{51} +0.0545724 q^{52} +4.81177 q^{53} +7.66540 q^{54} +0.0719098 q^{55} +6.31548 q^{56} -8.07234 q^{57} -4.15907 q^{58} +9.24725 q^{59} -0.00209818 q^{60} -7.71307 q^{61} -1.39479 q^{62} +3.36029 q^{63} +8.20621 q^{64} +0.0316546 q^{65} +3.84850 q^{66} -3.49410 q^{67} +0.0412637 q^{68} +2.90732 q^{69} +0.0973020 q^{70} +6.25252 q^{71} +4.36947 q^{72} -1.71625 q^{73} -10.2098 q^{74} +6.07177 q^{75} -0.362694 q^{76} +5.00644 q^{77} +1.69410 q^{78} +14.3323 q^{79} +0.123069 q^{80} -2.10086 q^{81} +2.44123 q^{82} -4.36742 q^{83} -0.146077 q^{84} +0.0239349 q^{85} +15.7914 q^{86} +3.62177 q^{87} +6.50999 q^{88} +0.704382 q^{89} +0.0673199 q^{90} +2.20383 q^{91} +0.130627 q^{92} +1.21460 q^{93} -15.7213 q^{94} -0.210380 q^{95} -0.374850 q^{96} +1.02821 q^{97} -2.98923 q^{98} +3.46379 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 3 q^{3} + 9 q^{4} - 15 q^{5} - 4 q^{7} - 15 q^{8} + 9 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 3 * q^3 + 9 * q^4 - 15 * q^5 - 4 * q^7 - 15 * q^8 + 9 * q^9	\( 8 q - 5 q^{2} - 3 q^{3} + 9 q^{4} - 15 q^{5} - 4 q^{7} - 15 q^{8} + 9 q^{9} + 9 q^{10} - 5 q^{11} - 9 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 3 q^{16} - 11 q^{17} - 30 q^{18} - 9 q^{19} - 31 q^{20} - 16 q^{21} - 2 q^{22} + 13 q^{24} + 19 q^{25} + 5 q^{26} - 9 q^{27} + 16 q^{28} - 12 q^{29} - 7 q^{30} - 8 q^{31} - 25 q^{32} - 14 q^{33} + 22 q^{34} + 7 q^{35} + 37 q^{36} - 9 q^{37} - 9 q^{38} + 3 q^{39} + 55 q^{40} - 25 q^{41} - 3 q^{42} + 7 q^{43} - 26 q^{44} - 45 q^{45} + 5 q^{46} - 17 q^{47} - 9 q^{48} - 11 q^{50} - 10 q^{51} - 9 q^{52} - 15 q^{53} + 54 q^{54} + 7 q^{55} - 14 q^{56} - 7 q^{57} - 5 q^{58} - 15 q^{59} + 61 q^{60} + 11 q^{61} + 5 q^{62} - 21 q^{63} + 47 q^{64} + 15 q^{65} + 83 q^{66} + 18 q^{67} - 16 q^{68} - 15 q^{69} - 24 q^{70} - 7 q^{71} - 21 q^{72} + 24 q^{73} + 48 q^{74} - 17 q^{75} - 3 q^{76} - 49 q^{77} + 33 q^{79} - 16 q^{80} + 20 q^{81} - q^{82} - 13 q^{83} - 6 q^{84} + q^{85} + 19 q^{86} + 18 q^{87} + 37 q^{88} - 23 q^{89} + 117 q^{90} + 4 q^{91} + 22 q^{92} + 3 q^{93} + 10 q^{94} + 43 q^{95} + 46 q^{96} - 17 q^{97} + 52 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 3 * q^3 + 9 * q^4 - 15 * q^5 - 4 * q^7 - 15 * q^8 + 9 * q^9 + 9 * q^10 - 5 * q^11 - 9 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 3 * q^16 - 11 * q^17 - 30 * q^18 - 9 * q^19 - 31 * q^20 - 16 * q^21 - 2 * q^22 + 13 * q^24 + 19 * q^25 + 5 * q^26 - 9 * q^27 + 16 * q^28 - 12 * q^29 - 7 * q^30 - 8 * q^31 - 25 * q^32 - 14 * q^33 + 22 * q^34 + 7 * q^35 + 37 * q^36 - 9 * q^37 - 9 * q^38 + 3 * q^39 + 55 * q^40 - 25 * q^41 - 3 * q^42 + 7 * q^43 - 26 * q^44 - 45 * q^45 + 5 * q^46 - 17 * q^47 - 9 * q^48 - 11 * q^50 - 10 * q^51 - 9 * q^52 - 15 * q^53 + 54 * q^54 + 7 * q^55 - 14 * q^56 - 7 * q^57 - 5 * q^58 - 15 * q^59 + 61 * q^60 + 11 * q^61 + 5 * q^62 - 21 * q^63 + 47 * q^64 + 15 * q^65 + 83 * q^66 + 18 * q^67 - 16 * q^68 - 15 * q^69 - 24 * q^70 - 7 * q^71 - 21 * q^72 + 24 * q^73 + 48 * q^74 - 17 * q^75 - 3 * q^76 - 49 * q^77 + 33 * q^79 - 16 * q^80 + 20 * q^81 - q^82 - 13 * q^83 - 6 * q^84 + q^85 + 19 * q^86 + 18 * q^87 + 37 * q^88 - 23 * q^89 + 117 * q^90 + 4 * q^91 + 22 * q^92 + 3 * q^93 + 10 * q^94 + 43 * q^95 + 46 * q^96 - 17 * q^97 + 52 * q^98 + 51 * 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 $

$2$	1.39479	0.986263	0.493131	−	0.869955i	$-0.335852\pi$
$2$	1.39479	0.986263	0.493131	+	0.869955i	$0.335852\pi$
$3$	−1.21460	−0.701248	−0.350624	−	0.936516i	$-0.614030\pi$
$3$	−1.21460	−0.701248	−0.350624	+	0.936516i	$0.614030\pi$
$4$	−0.0545724	−0.0272862
$5$	−0.0316546	−0.0141564	−0.00707818	−	0.999975i	$-0.502253\pi$
$5$	−0.0316546	−0.0141564	−0.00707818	+	0.999975i	$0.502253\pi$
$6$	−1.69410	−0.691615
$7$	−2.20383	−0.832969	−0.416484	−	0.909143i	$-0.636738\pi$
$7$	−2.20383	−0.832969	−0.416484	+	0.909143i	$0.636738\pi$
$8$	−2.86569	−1.01317
$9$	−1.52475	−0.508251
$10$	−0.0441514	−0.0139619
$11$	−2.27170	−0.684944	−0.342472	−	0.939528i	$-0.611264\pi$
$11$	−2.27170	−0.684944	−0.342472	+	0.939528i	$0.611264\pi$
$12$	0.0662835	0.0191344
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.07387	−0.821526
$15$	0.0384476	0.00992712
$16$	−3.88788	−0.971969
$17$	−0.756127	−0.183388	−0.0916939	−	0.995787i	$-0.529228\pi$
$17$	−0.756127	−0.183388	−0.0916939	+	0.995787i	$0.529228\pi$
$18$	−2.12670	−0.501269
$19$	6.64611	1.52472	0.762361	−	0.647153i	$-0.224040\pi$
$19$	6.64611	1.52472	0.762361	+	0.647153i	$0.224040\pi$
$20$	0.00172747	0.000386273 0
$21$	2.67676	0.584118
$22$	−3.16854	−0.675534
$23$	−2.39365	−0.499110	−0.249555	−	0.968361i	$-0.580284\pi$
$23$	−2.39365	−0.499110	−0.249555	+	0.968361i	$0.580284\pi$
$24$	3.48066	0.710486
$25$	−4.99900	−0.999800
$26$	−1.39479	−0.273540
$27$	5.49575	1.05766
$28$	0.120268	0.0227285
$29$	−2.98187	−0.553720	−0.276860	−	0.960910i	$-0.589294\pi$
$29$	−2.98187	−0.553720	−0.276860	+	0.960910i	$0.589294\pi$
$30$	0.0536261	0.00979074
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	0.308621	0.0545570
$33$	2.75920	0.480315
$34$	−1.05464	−0.180868
$35$	0.0697612	0.0117918
$36$	0.0832095	0.0138682
$37$	−7.31998	−1.20340	−0.601699	−	0.798723i	$-0.705509\pi$
$37$	−7.31998	−1.20340	−0.601699	+	0.798723i	$0.705509\pi$
$38$	9.26989	1.50378
$39$	1.21460	0.194491
$40$	0.0907122	0.0143429
$41$	1.75026	0.273344	0.136672	−	0.990616i	$-0.456359\pi$
$41$	1.75026	0.273344	0.136672	+	0.990616i	$0.456359\pi$
$42$	3.73351	0.576093
$43$	11.3218	1.72655	0.863277	−	0.504731i	$-0.168408\pi$
$43$	11.3218	1.72655	0.863277	+	0.504731i	$0.168408\pi$
$44$	0.123972	0.0186895
$45$	0.0482654	0.00719499
$46$	−3.33862	−0.492253
$47$	−11.2715	−1.64412	−0.822059	−	0.569402i	$-0.807175\pi$
$47$	−11.2715	−1.64412	−0.822059	+	0.569402i	$0.807175\pi$
$48$	4.72220	0.681592
$49$	−2.14314	−0.306163
$50$	−6.97253	−0.986065
$51$	0.918390	0.128600
$52$	0.0545724	0.00756783
$53$	4.81177	0.660947	0.330473	−	0.943815i	$-0.392792\pi$
$53$	4.81177	0.660947	0.330473	+	0.943815i	$0.392792\pi$
$54$	7.66540	1.04313
$55$	0.0719098	0.00969631
$56$	6.31548	0.843942
$57$	−8.07234	−1.06921
$58$	−4.15907	−0.546113
$59$	9.24725	1.20389	0.601945	−	0.798538i	$-0.294393\pi$
$59$	9.24725	1.20389	0.601945	+	0.798538i	$0.294393\pi$
$60$	−0.00209818	−0.000270873 0
$61$	−7.71307	−0.987557	−0.493779	−	0.869588i	$-0.664385\pi$
$61$	−7.71307	−0.987557	−0.493779	+	0.869588i	$0.664385\pi$
$62$	−1.39479	−0.177138
$63$	3.36029	0.423357
$64$	8.20621	1.02578
$65$	0.0316546	0.00392627
$66$	3.84850	0.473717
$67$	−3.49410	−0.426872	−0.213436	−	0.976957i	$-0.568465\pi$
$67$	−3.49410	−0.426872	−0.213436	+	0.976957i	$0.568465\pi$
$68$	0.0412637	0.00500395
$69$	2.90732	0.350000
$70$	0.0973020	0.0116298
$71$	6.25252	0.742037	0.371019	−	0.928625i	$-0.379009\pi$
$71$	6.25252	0.742037	0.371019	+	0.928625i	$0.379009\pi$
$72$	4.36947	0.514947
$73$	−1.71625	−0.200872	−0.100436	−	0.994944i	$-0.532024\pi$
$73$	−1.71625	−0.200872	−0.100436	+	0.994944i	$0.532024\pi$
$74$	−10.2098	−1.18687
$75$	6.07177	0.701107
$76$	−0.362694	−0.0416038
$77$	5.00644	0.570537
$78$	1.69410	0.191819
$79$	14.3323	1.61251	0.806257	−	0.591566i	$-0.201490\pi$
$79$	14.3323	1.61251	0.806257	+	0.591566i	$0.201490\pi$
$80$	0.123069	0.0137595
$81$	−2.10086	−0.233429
$82$	2.44123	0.269589
$83$	−4.36742	−0.479387	−0.239693	−	0.970849i	$-0.577047\pi$
$83$	−4.36742	−0.479387	−0.239693	+	0.970849i	$0.577047\pi$
$84$	−0.146077	−0.0159383
$85$	0.0239349	0.00259610
$86$	15.7914	1.70283
$87$	3.62177	0.388295
$88$	6.50999	0.693967
$89$	0.704382	0.0746643	0.0373322	−	0.999303i	$-0.488114\pi$
$89$	0.704382	0.0746643	0.0373322	+	0.999303i	$0.488114\pi$
$90$	0.0673199	0.00709615
$91$	2.20383	0.231024
$92$	0.130627	0.0136188
$93$	1.21460	0.125948
$94$	−15.7213	−1.62153
$95$	−0.210380	−0.0215845
$96$	−0.374850	−0.0382580
$97$	1.02821	0.104399	0.0521993	−	0.998637i	$-0.483377\pi$
$97$	1.02821	0.104399	0.0521993	+	0.998637i	$0.483377\pi$
$98$	−2.98923	−0.301957
$99$	3.46379	0.348124
$100$	0.272807	0.0272807
$101$	−19.7267	−1.96288	−0.981439	−	0.191773i	$-0.938576\pi$
$101$	−19.7267	−1.96288	−0.981439	+	0.191773i	$0.938576\pi$
$102$	1.28096	0.126834
$103$	−17.6768	−1.74175	−0.870876	−	0.491503i	$-0.836448\pi$
$103$	−17.6768	−1.74175	−0.870876	+	0.491503i	$0.836448\pi$
$104$	2.86569	0.281004
$105$	−0.0847318	−0.00826898
$106$	6.71138	0.651867
$107$	−17.2842	−1.67093	−0.835464	−	0.549545i	$-0.814801\pi$
$107$	−17.2842	−1.67093	−0.835464	+	0.549545i	$0.814801\pi$
$108$	−0.299916	−0.0288595
$109$	−5.50489	−0.527273	−0.263636	−	0.964622i	$-0.584922\pi$
$109$	−5.50489	−0.527273	−0.263636	+	0.964622i	$0.584922\pi$
$110$	0.100299	0.00956311
$111$	8.89083	0.843880
$112$	8.56821	0.809620
$113$	4.61051	0.433720	0.216860	−	0.976203i	$-0.430418\pi$
$113$	4.61051	0.433720	0.216860	+	0.976203i	$0.430418\pi$
$114$	−11.2592	−1.05452
$115$	0.0757699	0.00706558
$116$	0.162728	0.0151089
$117$	1.52475	0.140964
$118$	12.8979	1.18735
$119$	1.66637	0.152756
$120$	−0.110179	−0.0100579
$121$	−5.83937	−0.530852
$122$	−10.7581	−0.973991
$123$	−2.12586	−0.191682
$124$	0.0545724	0.00490075
$125$	0.316514	0.0283099
$126$	4.68689	0.417541
$127$	16.6838	1.48045	0.740224	−	0.672360i	$-0.234719\pi$
$127$	16.6838	1.48045	0.740224	+	0.672360i	$0.234719\pi$
$128$	10.8287	0.957128
$129$	−13.7514	−1.21074
$130$	0.0441514	0.00387233
$131$	−10.1165	−0.883883	−0.441941	−	0.897044i	$-0.645710\pi$
$131$	−10.1165	−0.883883	−0.441941	+	0.897044i	$0.645710\pi$
$132$	−0.150576	−0.0131060
$133$	−14.6469	−1.27004
$134$	−4.87352	−0.421008
$135$	−0.173966	−0.0149726
$136$	2.16682	0.185804
$137$	−6.69867	−0.572306	−0.286153	−	0.958184i	$-0.592377\pi$
$137$	−6.69867	−0.572306	−0.286153	+	0.958184i	$0.592377\pi$
$138$	4.05508	0.345192
$139$	−19.1673	−1.62575	−0.812874	−	0.582440i	$-0.802098\pi$
$139$	−19.1673	−1.62575	−0.812874	+	0.582440i	$0.802098\pi$
$140$	−0.00380704	−0.000321753 0
$141$	13.6903	1.15293
$142$	8.72092	0.731844
$143$	2.27170	0.189969
$144$	5.92806	0.494005
$145$	0.0943899	0.00783865
$146$	−2.39380	−0.198112
$147$	2.60306	0.214696
$148$	0.399469	0.0328362
$149$	−8.89720	−0.728887	−0.364444	−	0.931225i	$-0.618741\pi$
$149$	−8.89720	−0.728887	−0.364444	+	0.931225i	$0.618741\pi$
$150$	8.46882	0.691476
$151$	−5.21134	−0.424093	−0.212047	−	0.977260i	$-0.568013\pi$
$151$	−5.21134	−0.424093	−0.212047	+	0.977260i	$0.568013\pi$
$152$	−19.0457	−1.54481
$153$	1.15291	0.0932070
$154$	6.98291	0.562699
$155$	0.0316546	0.00254256
$156$	−0.0662835	−0.00530693
$157$	7.65264	0.610747	0.305374	−	0.952233i	$-0.401219\pi$
$157$	7.65264	0.610747	0.305374	+	0.952233i	$0.401219\pi$
$158$	19.9905	1.59036
$159$	−5.84436	−0.463488
$160$	−0.00976927	−0.000772329 0
$161$	5.27518	0.415743
$162$	−2.93026	−0.230223
$163$	−7.99672	−0.626351	−0.313176	−	0.949695i	$-0.601393\pi$
$163$	−7.99672	−0.626351	−0.313176	+	0.949695i	$0.601393\pi$
$164$	−0.0955156	−0.00745852
$165$	−0.0873414	−0.00679952
$166$	−6.09162	−0.472801
$167$	−15.3590	−1.18852	−0.594259	−	0.804274i	$-0.702555\pi$
$167$	−15.3590	−1.18852	−0.594259	+	0.804274i	$0.702555\pi$
$168$	−7.67077	−0.591813
$169$	1.00000	0.0769231
$170$	0.0333840	0.00256044
$171$	−10.1337	−0.774941
$172$	−0.617856	−0.0471111
$173$	2.49732	0.189868	0.0949339	−	0.995484i	$-0.469736\pi$
$173$	2.49732	0.189868	0.0949339	+	0.995484i	$0.469736\pi$
$174$	5.05160	0.382961
$175$	11.0169	0.832802
$176$	8.83210	0.665744
$177$	−11.2317	−0.844225
$178$	0.982462	0.0736386
$179$	24.1117	1.80219	0.901095	−	0.433621i	$-0.142764\pi$
$179$	24.1117	1.80219	0.901095	+	0.433621i	$0.142764\pi$
$180$	−0.00263396	−0.000196324 0
$181$	8.91500	0.662647	0.331324	−	0.943517i	$-0.392505\pi$
$181$	8.91500	0.662647	0.331324	+	0.943517i	$0.392505\pi$
$182$	3.07387	0.227850
$183$	9.36827	0.692523
$184$	6.85944	0.505685
$185$	0.231711	0.0170357
$186$	1.69410	0.124218
$187$	1.71769	0.125610
$188$	0.615113	0.0448617
$189$	−12.1117	−0.880996
$190$	−0.293435	−0.0212880
$191$	10.3738	0.750619	0.375309	−	0.926900i	$-0.377536\pi$
$191$	10.3738	0.750619	0.375309	+	0.926900i	$0.377536\pi$
$192$	−9.96724	−0.719324
$193$	11.3467	0.816751	0.408376	−	0.912814i	$-0.366095\pi$
$193$	11.3467	0.816751	0.408376	+	0.912814i	$0.366095\pi$
$194$	1.43413	0.102964
$195$	−0.0384476	−0.00275329
$196$	0.116956	0.00835403
$197$	−21.2974	−1.51738	−0.758688	−	0.651454i	$-0.774159\pi$
$197$	−21.2974	−1.51738	−0.758688	+	0.651454i	$0.774159\pi$
$198$	4.83124	0.343341
$199$	18.4900	1.31072	0.655362	−	0.755315i	$-0.272516\pi$
$199$	18.4900	1.31072	0.655362	+	0.755315i	$0.272516\pi$
$200$	14.3256	1.01297
$201$	4.24392	0.299343
$202$	−27.5145	−1.93591
$203$	6.57153	0.461231
$204$	−0.0501187	−0.00350901
$205$	−0.0554036	−0.00386956
$206$	−24.6554	−1.71782
$207$	3.64972	0.253673
$208$	3.88788	0.269576
$209$	−15.0980	−1.04435
$210$	−0.118183	−0.00815538
$211$	2.42016	0.166611	0.0833053	−	0.996524i	$-0.473452\pi$
$211$	2.42016	0.166611	0.0833053	+	0.996524i	$0.473452\pi$
$212$	−0.262590	−0.0180347
$213$	−7.59429	−0.520352
$214$	−24.1078	−1.64797
$215$	−0.358386	−0.0244417
$216$	−15.7491	−1.07159
$217$	2.20383	0.149606
$218$	−7.67815	−0.520030
$219$	2.08455	0.140861
$220$	−0.00392429	−0.000264575 0
$221$	0.756127	0.0508626
$222$	12.4008	0.832288
$223$	17.1048	1.14542	0.572710	−	0.819758i	$-0.305892\pi$
$223$	17.1048	1.14542	0.572710	+	0.819758i	$0.305892\pi$
$224$	−0.680148	−0.0454443
$225$	7.62224	0.508149
$226$	6.43067	0.427762
$227$	−19.7883	−1.31340	−0.656698	−	0.754153i	$-0.728048\pi$
$227$	−19.7883	−1.31340	−0.656698	+	0.754153i	$0.728048\pi$
$228$	0.440527	0.0291746
$229$	26.8254	1.77267	0.886336	−	0.463042i	$-0.153242\pi$
$229$	26.8254	1.77267	0.886336	+	0.463042i	$0.153242\pi$
$230$	0.105683	0.00696851
$231$	−6.08081	−0.400088
$232$	8.54511	0.561014
$233$	−6.79532	−0.445177	−0.222588	−	0.974913i	$-0.571451\pi$
$233$	−6.79532	−0.445177	−0.222588	+	0.974913i	$0.571451\pi$
$234$	2.12670	0.139027
$235$	0.356795	0.0232747
$236$	−0.504645	−0.0328496
$237$	−17.4080	−1.13077
$238$	2.32423	0.150658
$239$	−13.1704	−0.851921	−0.425960	−	0.904742i	$-0.640064\pi$
$239$	−13.1704	−0.851921	−0.425960	+	0.904742i	$0.640064\pi$
$240$	−0.149479	−0.00964885
$241$	8.58679	0.553124	0.276562	−	0.960996i	$-0.410805\pi$
$241$	8.58679	0.553124	0.276562	+	0.960996i	$0.410805\pi$
$242$	−8.14467	−0.523559
$243$	−13.9356	−0.893966
$244$	0.420921	0.0269467
$245$	0.0678403	0.00433416
$246$	−2.96511	−0.189049
$247$	−6.64611	−0.422882
$248$	2.86569	0.181971
$249$	5.30466	0.336169
$250$	0.441469	0.0279210
$251$	12.8929	0.813791	0.406896	−	0.913475i	$-0.366611\pi$
$251$	12.8929	0.813791	0.406896	+	0.913475i	$0.366611\pi$
$252$	−0.183379	−0.0115518
$253$	5.43765	0.341862
$254$	23.2703	1.46011
$255$	−0.0290712	−0.00182051
$256$	−1.30875	−0.0817971
$257$	−12.7681	−0.796453	−0.398226	−	0.917287i	$-0.630374\pi$
$257$	−12.7681	−0.796453	−0.398226	+	0.917287i	$0.630374\pi$
$258$	−19.1802	−1.19411
$259$	16.1320	1.00239
$260$	−0.00172747	−0.000107133 0
$261$	4.54662	0.281429
$262$	−14.1104	−0.871740
$263$	−2.69818	−0.166377	−0.0831884	−	0.996534i	$-0.526510\pi$
$263$	−2.69818	−0.166377	−0.0831884	+	0.996534i	$0.526510\pi$
$264$	−7.90701	−0.486643
$265$	−0.152314	−0.00935660
$266$	−20.4292	−1.25260
$267$	−0.855540	−0.0523582
$268$	0.190681	0.0116477
$269$	−2.02436	−0.123427	−0.0617136	−	0.998094i	$-0.519657\pi$
$269$	−2.02436	−0.123427	−0.0617136	+	0.998094i	$0.519657\pi$
$270$	−0.242645	−0.0147669
$271$	−6.48950	−0.394209	−0.197104	−	0.980382i	$-0.563154\pi$
$271$	−6.48950	−0.394209	−0.197104	+	0.980382i	$0.563154\pi$
$272$	2.93973	0.178247
$273$	−2.67676	−0.162005
$274$	−9.34321	−0.564444
$275$	11.3562	0.684807
$276$	−0.158659	−0.00955016
$277$	−5.10361	−0.306646	−0.153323	−	0.988176i	$-0.548997\pi$
$277$	−5.10361	−0.306646	−0.153323	+	0.988176i	$0.548997\pi$
$278$	−26.7342	−1.60341
$279$	1.52475	0.0912846
$280$	−0.199914	−0.0119471
$281$	11.0668	0.660190	0.330095	−	0.943948i	$-0.392919\pi$
$281$	11.0668	0.660190	0.330095	+	0.943948i	$0.392919\pi$
$282$	19.0951	1.13710
$283$	−8.08319	−0.480496	−0.240248	−	0.970712i	$-0.577229\pi$
$283$	−8.08319	−0.480496	−0.240248	+	0.970712i	$0.577229\pi$
$284$	−0.341215	−0.0202474
$285$	0.255527	0.0151361
$286$	3.16854	0.187360
$287$	−3.85726	−0.227687
$288$	−0.470571	−0.0277287
$289$	−16.4283	−0.966369
$290$	0.131654	0.00773097
$291$	−1.24886	−0.0732093
$292$	0.0936599	0.00548103
$293$	−3.90725	−0.228264	−0.114132	−	0.993466i	$-0.536409\pi$
$293$	−3.90725	−0.228264	−0.114132	+	0.993466i	$0.536409\pi$
$294$	3.63070	0.211747
$295$	−0.292718	−0.0170427
$296$	20.9768	1.21925
$297$	−12.4847	−0.724436
$298$	−12.4097	−0.718874
$299$	2.39365	0.138428
$300$	−0.331351	−0.0191306
$301$	−24.9512	−1.43816
$302$	−7.26871	−0.418267
$303$	23.9600	1.37646
$304$	−25.8392	−1.48198
$305$	0.244154	0.0139802
$306$	1.60806	0.0919266
$307$	3.49247	0.199326	0.0996628	−	0.995021i	$-0.468224\pi$
$307$	3.49247	0.199326	0.0996628	+	0.995021i	$0.468224\pi$
$308$	−0.273213	−0.0155678
$309$	21.4702	1.22140
$310$	0.0441514	0.00250763
$311$	4.99252	0.283100	0.141550	−	0.989931i	$-0.454791\pi$
$311$	4.99252	0.283100	0.141550	+	0.989931i	$0.454791\pi$
$312$	−3.48066	−0.197053
$313$	7.87023	0.444852	0.222426	−	0.974950i	$-0.428602\pi$
$313$	7.87023	0.444852	0.222426	+	0.974950i	$0.428602\pi$
$314$	10.6738	0.602357
$315$	−0.106369	−0.00599320
$316$	−0.782150	−0.0439994
$317$	−35.2297	−1.97870	−0.989349	−	0.145563i	$-0.953501\pi$
$317$	−35.2297	−1.97870	−0.989349	+	0.145563i	$0.953501\pi$
$318$	−8.15163	−0.457121
$319$	6.77392	0.379267
$320$	−0.259764	−0.0145213
$321$	20.9934	1.17173
$322$	7.35775	0.410031
$323$	−5.02530	−0.279615
$324$	0.114649	0.00636940
$325$	4.99900	0.277295
$326$	−11.1537	−0.617747
$327$	6.68623	0.369749
$328$	−5.01569	−0.276945
$329$	24.8405	1.36950
$330$	−0.121823	−0.00670611
$331$	3.82141	0.210044	0.105022	−	0.994470i	$-0.466509\pi$
$331$	3.82141	0.210044	0.105022	+	0.994470i	$0.466509\pi$
$332$	0.238341	0.0130806
$333$	11.1612	0.611629
$334$	−21.4226	−1.17219
$335$	0.110604	0.00604295
$336$	−10.4069	−0.567744
$337$	36.0258	1.96245	0.981226	−	0.192864i	$-0.0617776\pi$
$337$	36.0258	1.96245	0.981226	+	0.192864i	$0.0617776\pi$
$338$	1.39479	0.0758663
$339$	−5.59991	−0.304145
$340$	−0.00130618	−7.08378e−5 0
$341$	2.27170	0.123020
$342$	−14.1343	−0.764296
$343$	20.1499	1.08799
$344$	−32.4447	−1.74930
$345$	−0.0920299	−0.00495472
$346$	3.48323	0.187259
$347$	35.8546	1.92477	0.962387	−	0.271681i	$-0.0875795\pi$
$347$	35.8546	1.92477	0.962387	+	0.271681i	$0.0875795\pi$
$348$	−0.197649	−0.0105951
$349$	−16.3834	−0.876985	−0.438493	−	0.898735i	$-0.644487\pi$
$349$	−16.3834	−0.876985	−0.438493	+	0.898735i	$0.644487\pi$
$350$	15.3663	0.821361
$351$	−5.49575	−0.293342
$352$	−0.701095	−0.0373685
$353$	−16.9567	−0.902515	−0.451258	−	0.892394i	$-0.649024\pi$
$353$	−16.9567	−0.902515	−0.451258	+	0.892394i	$0.649024\pi$
$354$	−15.6658	−0.832628
$355$	−0.197921	−0.0105045
$356$	−0.0384398	−0.00203730
$357$	−2.02397	−0.107120
$358$	33.6306	1.77743
$359$	−10.8892	−0.574708	−0.287354	−	0.957824i	$-0.592776\pi$
$359$	−10.8892	−0.574708	−0.287354	+	0.957824i	$0.592776\pi$
$360$	−0.138314	−0.00728977
$361$	25.1707	1.32477
$362$	12.4345	0.653544
$363$	7.09248	0.372259
$364$	−0.120268	−0.00630376
$365$	0.0543272	0.00284361
$366$	13.0667	0.683009
$367$	−11.1037	−0.579607	−0.289804	−	0.957086i	$-0.593590\pi$
$367$	−11.1037	−0.579607	−0.289804	+	0.957086i	$0.593590\pi$
$368$	9.30620	0.485119
$369$	−2.66871	−0.138927
$370$	0.323187	0.0168017
$371$	−10.6043	−0.550548
$372$	−0.0662835	−0.00343664
$373$	30.7074	1.58997	0.794983	−	0.606631i	$-0.207480\pi$
$373$	30.7074	1.58997	0.794983	+	0.606631i	$0.207480\pi$
$374$	2.39582	0.123885
$375$	−0.384437	−0.0198522
$376$	32.3006	1.66578
$377$	2.98187	0.153574
$378$	−16.8932	−0.868893
$379$	16.1617	0.830170	0.415085	−	0.909783i	$-0.363752\pi$
$379$	16.1617	0.830170	0.415085	+	0.909783i	$0.363752\pi$
$380$	0.0114809	0.000588959 0
$381$	−20.2641	−1.03816
$382$	14.4692	0.740307
$383$	19.5554	0.999232	0.499616	−	0.866247i	$-0.333474\pi$
$383$	19.5554	0.999232	0.499616	+	0.866247i	$0.333474\pi$
$384$	−13.1525	−0.671184
$385$	−0.158477	−0.00807672
$386$	15.8262	0.805531
$387$	−17.2629	−0.877523
$388$	−0.0561117	−0.00284864
$389$	−23.2955	−1.18113	−0.590565	−	0.806990i	$-0.701095\pi$
$389$	−23.2955	−1.18113	−0.590565	+	0.806990i	$0.701095\pi$
$390$	−0.0536261	−0.00271546
$391$	1.80990	0.0915306
$392$	6.14158	0.310197
$393$	12.2875	0.619821
$394$	−29.7053	−1.49653
$395$	−0.453684	−0.0228273
$396$	−0.189027	−0.00949897
$397$	−15.9749	−0.801759	−0.400879	−	0.916131i	$-0.631295\pi$
$397$	−15.9749	−0.801759	−0.400879	+	0.916131i	$0.631295\pi$
$398$	25.7897	1.29272
$399$	17.7900	0.890616
$400$	19.4355	0.971774
$401$	4.86023	0.242708	0.121354	−	0.992609i	$-0.461276\pi$
$401$	4.86023	0.242708	0.121354	+	0.992609i	$0.461276\pi$
$402$	5.91936	0.295231
$403$	1.00000	0.0498135
$404$	1.07653	0.0535595
$405$	0.0665020	0.00330451
$406$	9.16588	0.454895
$407$	16.6288	0.824260
$408$	−2.63182	−0.130294
$409$	11.4228	0.564823	0.282411	−	0.959293i	$-0.408866\pi$
$409$	11.4228	0.564823	0.282411	+	0.959293i	$0.408866\pi$
$410$	−0.0772762	−0.00381640
$411$	8.13619	0.401329
$412$	0.964668	0.0475258
$413$	−20.3793	−1.00280
$414$	5.09058	0.250188
$415$	0.138249	0.00678637
$416$	−0.308621	−0.0151314
$417$	23.2805	1.14005
$418$	−21.0584	−1.03000
$419$	29.3359	1.43315	0.716576	−	0.697509i	$-0.245708\pi$
$419$	29.3359	1.43315	0.716576	+	0.697509i	$0.245708\pi$
$420$	0.00462402	0.000225629 0
$421$	21.8419	1.06451	0.532253	−	0.846585i	$-0.321345\pi$
$421$	21.8419	1.06451	0.532253	+	0.846585i	$0.321345\pi$
$422$	3.37560	0.164322
$423$	17.1863	0.835625
$424$	−13.7890	−0.669654
$425$	3.77988	0.183351
$426$	−10.5924	−0.513204
$427$	16.9983	0.822604
$428$	0.943241	0.0455933
$429$	−2.75920	−0.133216
$430$	−0.499871	−0.0241059
$431$	−34.9584	−1.68389	−0.841945	−	0.539564i	$-0.818589\pi$
$431$	−34.9584	−1.68389	−0.841945	+	0.539564i	$0.818589\pi$
$432$	−21.3668	−1.02801
$433$	18.5460	0.891264	0.445632	−	0.895216i	$-0.352979\pi$
$433$	18.5460	0.891264	0.445632	+	0.895216i	$0.352979\pi$
$434$	3.07387	0.147550
$435$	−0.114646	−0.00549684
$436$	0.300415	0.0143873
$437$	−15.9084	−0.761003
$438$	2.90750	0.138926
$439$	22.9879	1.09715	0.548577	−	0.836100i	$-0.315170\pi$
$439$	22.9879	1.09715	0.548577	+	0.836100i	$0.315170\pi$
$440$	−0.206071	−0.00982405
$441$	3.26776	0.155608
$442$	1.05464	0.0501639
$443$	−3.28965	−0.156296	−0.0781479	−	0.996942i	$-0.524901\pi$
$443$	−3.28965	−0.156296	−0.0781479	+	0.996942i	$0.524901\pi$
$444$	−0.485194	−0.0230263
$445$	−0.0222969	−0.00105697
$446$	23.8575	1.12968
$447$	10.8065	0.511131
$448$	−18.0851	−0.854440
$449$	−11.0551	−0.521721	−0.260860	−	0.965377i	$-0.584006\pi$
$449$	−11.0551	−0.521721	−0.260860	+	0.965377i	$0.584006\pi$
$450$	10.6314	0.501169
$451$	−3.97606	−0.187225
$452$	−0.251607	−0.0118346
$453$	6.32968	0.297395
$454$	−27.6005	−1.29535
$455$	−0.0697612	−0.00327046
$456$	23.1328	1.08329
$457$	−1.12847	−0.0527878	−0.0263939	−	0.999652i	$-0.508402\pi$
$457$	−1.12847	−0.0527878	−0.0263939	+	0.999652i	$0.508402\pi$
$458$	37.4157	1.74832
$459$	−4.15549	−0.193962
$460$	−0.00413494	−0.000192793 0
$461$	12.5596	0.584958	0.292479	−	0.956272i	$-0.405520\pi$
$461$	12.5596	0.584958	0.292479	+	0.956272i	$0.405520\pi$
$462$	−8.48142	−0.394592
$463$	6.60396	0.306912	0.153456	−	0.988155i	$-0.450960\pi$
$463$	6.60396	0.306912	0.153456	+	0.988155i	$0.450960\pi$
$464$	11.5931	0.538198
$465$	−0.0384476	−0.00178296
$466$	−9.47802	−0.439061
$467$	12.4783	0.577429	0.288714	−	0.957415i	$-0.406772\pi$
$467$	12.4783	0.577429	0.288714	+	0.957415i	$0.406772\pi$
$468$	−0.0832095	−0.00384636
$469$	7.70039	0.355571
$470$	0.497652	0.0229550
$471$	−9.29488	−0.428285
$472$	−26.4997	−1.21975
$473$	−25.7197	−1.18259
$474$	−24.2805	−1.11524
$475$	−33.2239	−1.52442
$476$	−0.0909380	−0.00416814
$477$	−7.33676	−0.335927
$478$	−18.3699	−0.840218
$479$	3.41780	0.156163	0.0780816	−	0.996947i	$-0.475121\pi$
$479$	3.41780	0.156163	0.0780816	+	0.996947i	$0.475121\pi$
$480$	0.0118657	0.000541594 0
$481$	7.31998	0.333763
$482$	11.9767	0.545525
$483$	−6.40722	−0.291539
$484$	0.318668	0.0144849
$485$	−0.0325474	−0.00147790
$486$	−19.4371	−0.881685
$487$	−13.0700	−0.592260	−0.296130	−	0.955148i	$-0.595696\pi$
$487$	−13.0700	−0.592260	−0.296130	+	0.955148i	$0.595696\pi$
$488$	22.1033	1.00057
$489$	9.71279	0.439227
$490$	0.0946227	0.00427462
$491$	−10.5239	−0.474937	−0.237468	−	0.971395i	$-0.576318\pi$
$491$	−10.5239	−0.474937	−0.237468	+	0.971395i	$0.576318\pi$
$492$	0.116013	0.00523027
$493$	2.25467	0.101545
$494$	−9.26989	−0.417072
$495$	−0.109645	−0.00492816
$496$	3.88788	0.174571
$497$	−13.7795	−0.618094
$498$	7.39886	0.331551
$499$	27.9910	1.25305	0.626524	−	0.779403i	$-0.284477\pi$
$499$	27.9910	1.25305	0.626524	+	0.779403i	$0.284477\pi$
$500$	−0.0172729	−0.000772469 0
$501$	18.6550	0.833446
$502$	17.9828	0.802612
$503$	−9.91828	−0.442234	−0.221117	−	0.975247i	$-0.570970\pi$
$503$	−9.91828	−0.442234	−0.221117	+	0.975247i	$0.570970\pi$
$504$	−9.62956	−0.428935
$505$	0.624440	0.0277872
$506$	7.58436	0.337166
$507$	−1.21460	−0.0539422
$508$	−0.910475	−0.0403958
$509$	−16.8627	−0.747427	−0.373713	−	0.927544i	$-0.621916\pi$
$509$	−16.8627	−0.747427	−0.373713	+	0.927544i	$0.621916\pi$
$510$	−0.0405481	−0.00179550
$511$	3.78232	0.167320
$512$	−23.4828	−1.03780
$513$	36.5254	1.61263
$514$	−17.8088	−0.785512
$515$	0.559553	0.0246569
$516$	0.750446	0.0330365
$517$	25.6055	1.12613
$518$	22.5007	0.988622
$519$	−3.03324	−0.133144
$520$	−0.0907122	−0.00397799
$521$	−4.96787	−0.217646	−0.108823	−	0.994061i	$-0.534708\pi$
$521$	−4.96787	−0.217646	−0.108823	+	0.994061i	$0.534708\pi$
$522$	6.34156	0.277563
$523$	14.2867	0.624715	0.312357	−	0.949965i	$-0.398881\pi$
$523$	14.2867	0.624715	0.312357	+	0.949965i	$0.398881\pi$
$524$	0.552082	0.0241178
$525$	−13.3811	−0.584001
$526$	−3.76338	−0.164091
$527$	0.756127	0.0329374
$528$	−10.7274	−0.466852
$529$	−17.2705	−0.750889
$530$	−0.212446	−0.00922807
$531$	−14.0998	−0.611878
$532$	0.799315	0.0346547
$533$	−1.75026	−0.0758120
$534$	−1.19330	−0.0516389
$535$	0.547124	0.0236543
$536$	10.0130	0.432495
$537$	−29.2860	−1.26378
$538$	−2.82354	−0.121732
$539$	4.86858	0.209705
$540$	0.00949373	0.000408545 0
$541$	20.7488	0.892062	0.446031	−	0.895018i	$-0.352837\pi$
$541$	20.7488	0.892062	0.446031	+	0.895018i	$0.352837\pi$
$542$	−9.05146	−0.388793
$543$	−10.8281	−0.464680
$544$	−0.233357	−0.0100051
$545$	0.174255	0.00746427
$546$	−3.73351	−0.159780
$547$	−39.2872	−1.67980	−0.839900	−	0.542742i	$-0.817386\pi$
$547$	−39.2872	−1.67980	−0.839900	+	0.542742i	$0.817386\pi$
$548$	0.365563	0.0156161
$549$	11.7605	0.501927
$550$	15.8395	0.675399
$551$	−19.8178	−0.844268
$552$	−8.33146	−0.354611
$553$	−31.5860	−1.34317
$554$	−7.11844	−0.302433
$555$	−0.281436	−0.0119463
$556$	1.04600	0.0443605
$557$	−38.0814	−1.61356	−0.806781	−	0.590851i	$-0.798792\pi$
$557$	−38.0814	−1.61356	−0.806781	+	0.590851i	$0.798792\pi$
$558$	2.12670	0.0900306
$559$	−11.3218	−0.478860
$560$	−0.271223	−0.0114613
$561$	−2.08631	−0.0880840
$562$	15.4358	0.651120
$563$	−39.0178	−1.64440	−0.822201	−	0.569197i	$-0.807254\pi$
$563$	−39.0178	−1.64440	−0.822201	+	0.569197i	$0.807254\pi$
$564$	−0.747115	−0.0314592
$565$	−0.145944	−0.00613990
$566$	−11.2743	−0.473895
$567$	4.62994	0.194439
$568$	−17.9178	−0.751813
$569$	13.1012	0.549233	0.274616	−	0.961554i	$-0.411449\pi$
$569$	13.1012	0.549233	0.274616	+	0.961554i	$0.411449\pi$
$570$	0.356405	0.0149282
$571$	−0.656872	−0.0274892	−0.0137446	−	0.999906i	$-0.504375\pi$
$571$	−0.656872	−0.0274892	−0.0137446	+	0.999906i	$0.504375\pi$
$572$	−0.123972	−0.00518354
$573$	−12.5999	−0.526370
$574$	−5.38006	−0.224559
$575$	11.9658	0.499010
$576$	−12.5125	−0.521352
$577$	−7.36710	−0.306696	−0.153348	−	0.988172i	$-0.549006\pi$
$577$	−7.36710	−0.306696	−0.153348	+	0.988172i	$0.549006\pi$
$578$	−22.9139	−0.953093
$579$	−13.7816	−0.572745
$580$	−0.00515108	−0.000213887 0
$581$	9.62505	0.399314
$582$	−1.74189	−0.0722036
$583$	−10.9309	−0.452712
$584$	4.91824	0.203518
$585$	−0.0482654	−0.00199553
$586$	−5.44978	−0.225128
$587$	−42.5180	−1.75490	−0.877452	−	0.479665i	$-0.840758\pi$
$587$	−42.5180	−1.75490	−0.877452	+	0.479665i	$0.840758\pi$
$588$	−0.142055	−0.00585825
$589$	−6.64611	−0.273848
$590$	−0.408279	−0.0168086
$591$	25.8677	1.06406
$592$	28.4592	1.16967
$593$	−3.31087	−0.135961	−0.0679805	−	0.997687i	$-0.521656\pi$
$593$	−3.31087	−0.135961	−0.0679805	+	0.997687i	$0.521656\pi$
$594$	−17.4135	−0.714484
$595$	−0.0527484	−0.00216247
$596$	0.485542	0.0198886
$597$	−22.4580	−0.919143
$598$	3.33862	0.136526
$599$	−0.831399	−0.0339700	−0.0169850	−	0.999856i	$-0.505407\pi$
$599$	−0.831399	−0.0339700	−0.0169850	+	0.999856i	$0.505407\pi$
$600$	−17.3998	−0.710344
$601$	−7.91975	−0.323053	−0.161527	−	0.986868i	$-0.551642\pi$
$601$	−7.91975	−0.323053	−0.161527	+	0.986868i	$0.551642\pi$
$602$	−34.8016	−1.41841
$603$	5.32764	0.216958
$604$	0.284396	0.0115719
$605$	0.184843	0.00751493
$606$	33.4190	1.35756
$607$	33.9726	1.37891	0.689453	−	0.724330i	$-0.257851\pi$
$607$	33.9726	1.37891	0.689453	+	0.724330i	$0.257851\pi$
$608$	2.05113	0.0831842
$609$	−7.98176	−0.323437
$610$	0.340543	0.0137882
$611$	11.2715	0.455996
$612$	−0.0629169	−0.00254327
$613$	−9.49348	−0.383438	−0.191719	−	0.981450i	$-0.561406\pi$
$613$	−9.49348	−0.383438	−0.191719	+	0.981450i	$0.561406\pi$
$614$	4.87125	0.196587
$615$	0.0672931	0.00271352
$616$	−14.3469	−0.578053
$617$	−2.27920	−0.0917573	−0.0458787	−	0.998947i	$-0.514609\pi$
$617$	−2.27920	−0.0917573	−0.0458787	+	0.998947i	$0.514609\pi$
$618$	29.9464	1.20462
$619$	−11.1954	−0.449981	−0.224991	−	0.974361i	$-0.572235\pi$
$619$	−11.1954	−0.449981	−0.224991	+	0.974361i	$0.572235\pi$
$620$	−0.00172747	−6.93767e−5 0
$621$	−13.1549	−0.527887
$622$	6.96349	0.279211
$623$	−1.55234	−0.0621930
$624$	−4.72220	−0.189039
$625$	24.9850	0.999399
$626$	10.9773	0.438741
$627$	18.3379	0.732347
$628$	−0.417623	−0.0166650
$629$	5.53484	0.220688
$630$	−0.148362	−0.00591087
$631$	2.37499	0.0945470	0.0472735	−	0.998882i	$-0.484947\pi$
$631$	2.37499	0.0945470	0.0472735	+	0.998882i	$0.484947\pi$
$632$	−41.0720	−1.63376
$633$	−2.93952	−0.116835
$634$	−49.1379	−1.95152
$635$	−0.528119	−0.0209578
$636$	0.318941	0.0126468
$637$	2.14314	0.0849144
$638$	9.44817	0.374057
$639$	−9.53355	−0.377141
$640$	−0.342777	−0.0135494
$641$	−18.1313	−0.716143	−0.358071	−	0.933694i	$-0.616566\pi$
$641$	−18.1313	−0.716143	−0.358071	+	0.933694i	$0.616566\pi$
$642$	29.2812	1.15564
$643$	−49.0841	−1.93569	−0.967844	−	0.251551i	$-0.919059\pi$
$643$	−49.0841	−1.93569	−0.967844	+	0.251551i	$0.919059\pi$
$644$	−0.287879	−0.0113440
$645$	0.435294	0.0171397
$646$	−7.00922	−0.275774
$647$	−6.49432	−0.255318	−0.127659	−	0.991818i	$-0.540746\pi$
$647$	−6.49432	−0.255318	−0.127659	+	0.991818i	$0.540746\pi$
$648$	6.02042	0.236505
$649$	−21.0070	−0.824597
$650$	6.97253	0.273485
$651$	−2.67676	−0.104911
$652$	0.436400	0.0170907
$653$	8.57348	0.335506	0.167753	−	0.985829i	$-0.446349\pi$
$653$	8.57348	0.335506	0.167753	+	0.985829i	$0.446349\pi$
$654$	9.32585	0.364670
$655$	0.320234	0.0125126
$656$	−6.80478	−0.265682
$657$	2.61686	0.102093
$658$	34.6471	1.35069
$659$	41.2876	1.60834	0.804168	−	0.594402i	$-0.202611\pi$
$659$	41.2876	1.60834	0.804168	+	0.594402i	$0.202611\pi$
$660$	0.00476643	0.000185533 0
$661$	−32.1572	−1.25077	−0.625384	−	0.780317i	$-0.715058\pi$
$661$	−32.1572	−1.25077	−0.625384	+	0.780317i	$0.715058\pi$
$662$	5.33005	0.207158
$663$	−0.918390	−0.0356673
$664$	12.5157	0.485702
$665$	0.463641	0.0179792
$666$	15.5674	0.603226
$667$	7.13754	0.276367
$668$	0.838180	0.0324301
$669$	−20.7754	−0.803223
$670$	0.154269	0.00595993
$671$	17.5218	0.676421
$672$	0.826106	0.0318677
$673$	−1.31640	−0.0507435	−0.0253718	−	0.999678i	$-0.508077\pi$
$673$	−1.31640	−0.0507435	−0.0253718	+	0.999678i	$0.508077\pi$
$674$	50.2483	1.93549
$675$	−27.4733	−1.05745
$676$	−0.0545724	−0.00209894
$677$	8.14750	0.313134	0.156567	−	0.987667i	$-0.449957\pi$
$677$	8.14750	0.313134	0.156567	+	0.987667i	$0.449957\pi$
$678$	−7.81068	−0.299967
$679$	−2.26599	−0.0869607
$680$	−0.0685899	−0.00263030
$681$	24.0348	0.921017
$682$	3.16854	0.121330
$683$	15.5720	0.595846	0.297923	−	0.954590i	$-0.403706\pi$
$683$	15.5720	0.595846	0.297923	+	0.954590i	$0.403706\pi$
$684$	0.553019	0.0211452
$685$	0.212044	0.00810177
$686$	28.1048	1.07305
$687$	−32.5821	−1.24308
$688$	−44.0176	−1.67816
$689$	−4.81177	−0.183314
$690$	−0.128362	−0.00488666
$691$	26.8685	1.02213	0.511064	−	0.859543i	$-0.329252\pi$
$691$	26.8685	1.02213	0.511064	+	0.859543i	$0.329252\pi$
$692$	−0.136285	−0.00518077
$693$	−7.63359	−0.289976
$694$	50.0095	1.89833
$695$	0.606732	0.0230147
$696$	−10.3789	−0.393410
$697$	−1.32342	−0.0501279
$698$	−22.8514	−0.864938
$699$	8.25358	0.312179
$700$	−0.601220	−0.0227240
$701$	51.2668	1.93632	0.968161	−	0.250329i	$-0.0805389\pi$
$701$	51.2668	1.93632	0.968161	+	0.250329i	$0.0805389\pi$
$702$	−7.66540	−0.289312
$703$	−48.6494	−1.83485
$704$	−18.6421	−0.702599
$705$	−0.433362	−0.0163214
$706$	−23.6510	−0.890117
$707$	43.4742	1.63502
$708$	0.612940	0.0230357
$709$	−40.3934	−1.51701	−0.758503	−	0.651669i	$-0.774069\pi$
$709$	−40.3934	−1.51701	−0.758503	+	0.651669i	$0.774069\pi$
$710$	−0.276057	−0.0103602
$711$	−21.8533	−0.819562
$712$	−2.01854	−0.0756479
$713$	2.39365	0.0896428
$714$	−2.82301	−0.105648
$715$	−0.0719098	−0.00268927
$716$	−1.31583	−0.0491749
$717$	15.9967	0.597408
$718$	−15.1881	−0.566813
$719$	4.87825	0.181928	0.0909640	−	0.995854i	$-0.471005\pi$
$719$	4.87825	0.181928	0.0909640	+	0.995854i	$0.471005\pi$
$720$	−0.187650	−0.00699331
$721$	38.9567	1.45082
$722$	35.1078	1.30658
$723$	−10.4295	−0.387877
$724$	−0.486513	−0.0180811
$725$	14.9064	0.553609
$726$	9.89250	0.367145
$727$	−28.8654	−1.07056	−0.535279	−	0.844676i	$-0.679793\pi$
$727$	−28.8654	−1.07056	−0.535279	+	0.844676i	$0.679793\pi$
$728$	−6.31548	−0.234067
$729$	23.2287	0.860321
$730$	0.0757748	0.00280455
$731$	−8.56069	−0.316629
$732$	−0.511249	−0.0188963
$733$	−40.0267	−1.47842	−0.739209	−	0.673476i	$-0.764801\pi$
$733$	−40.0267	−1.47842	−0.739209	+	0.673476i	$0.764801\pi$
$734$	−15.4873	−0.571645
$735$	−0.0823986	−0.00303932
$736$	−0.738730	−0.0272299
$737$	7.93754	0.292383
$738$	−3.72228	−0.137019
$739$	26.6433	0.980091	0.490046	−	0.871697i	$-0.336980\pi$
$739$	26.6433	0.980091	0.490046	+	0.871697i	$0.336980\pi$
$740$	−0.0126450	−0.000464840 0
$741$	8.07234	0.296545
$742$	−14.7907	−0.542985
$743$	20.5314	0.753225	0.376613	−	0.926371i	$-0.377089\pi$
$743$	20.5314	0.753225	0.376613	+	0.926371i	$0.377089\pi$
$744$	−3.48066	−0.127607
$745$	0.281637	0.0103184
$746$	42.8302	1.56812
$747$	6.65924	0.243649
$748$	−0.0937387	−0.00342743
$749$	38.0914	1.39183
$750$	−0.536207	−0.0195795
$751$	8.57769	0.313004	0.156502	−	0.987678i	$-0.449978\pi$
$751$	8.57769	0.313004	0.156502	+	0.987678i	$0.449978\pi$
$752$	43.8222	1.59803
$753$	−15.6597	−0.570670
$754$	4.15907	0.151464
$755$	0.164963	0.00600362
$756$	0.660964	0.0240390
$757$	25.4945	0.926613	0.463306	−	0.886198i	$-0.346663\pi$
$757$	25.4945	0.926613	0.463306	+	0.886198i	$0.346663\pi$
$758$	22.5421	0.818766
$759$	−6.60455	−0.239730
$760$	0.602883	0.0218688
$761$	−16.1795	−0.586505	−0.293252	−	0.956035i	$-0.594738\pi$
$761$	−16.1795	−0.586505	−0.293252	+	0.956035i	$0.594738\pi$
$762$	−28.2641	−1.02390
$763$	12.1318	0.439202
$764$	−0.566121	−0.0204815
$765$	−0.0364948	−0.00131947
$766$	27.2755	0.985505
$767$	−9.24725	−0.333899
$768$	1.58961	0.0573600
$769$	−6.70484	−0.241783	−0.120891	−	0.992666i	$-0.538575\pi$
$769$	−6.70484	−0.241783	−0.120891	+	0.992666i	$0.538575\pi$
$770$	−0.221041	−0.00796577
$771$	15.5081	0.558511
$772$	−0.619215	−0.0222860
$773$	−29.8222	−1.07263	−0.536316	−	0.844017i	$-0.680184\pi$
$773$	−29.8222	−1.07263	−0.536316	+	0.844017i	$0.680184\pi$
$774$	−24.0781	−0.865468
$775$	4.99900	0.179569
$776$	−2.94652	−0.105774
$777$	−19.5939	−0.702926
$778$	−32.4923	−1.16490
$779$	11.6324	0.416773
$780$	0.00209818	7.51267e−5 0
$781$	−14.2039	−0.508254
$782$	2.52442	0.0902732
$783$	−16.3876	−0.585646
$784$	8.33228	0.297581
$785$	−0.242241	−0.00864596
$786$	17.1384	0.611306
$787$	−50.0339	−1.78352	−0.891758	−	0.452512i	$-0.850528\pi$
$787$	−50.0339	−1.78352	−0.891758	+	0.452512i	$0.850528\pi$
$788$	1.16225	0.0414034
$789$	3.27720	0.116671
$790$	−0.632792	−0.0225137
$791$	−10.1608	−0.361275
$792$	−9.92613	−0.352710
$793$	7.71307	0.273899
$794$	−22.2816	−0.790744
$795$	0.185001	0.00656130
$796$	−1.00905	−0.0357647
$797$	18.4243	0.652624	0.326312	−	0.945262i	$-0.394194\pi$
$797$	18.4243	0.652624	0.326312	+	0.945262i	$0.394194\pi$
$798$	24.8133	0.878382
$799$	8.52269	0.301511
$800$	−1.54280	−0.0545461
$801$	−1.07401	−0.0379482
$802$	6.77898	0.239374
$803$	3.89881	0.137586
$804$	−0.231601	−0.00816793
$805$	−0.166984	−0.00588540
$806$	1.39479	0.0491292
$807$	2.45878	0.0865531
$808$	56.5305	1.98874
$809$	41.9703	1.47560	0.737799	−	0.675021i	$-0.235865\pi$
$809$	41.9703	1.47560	0.737799	+	0.675021i	$0.235865\pi$
$810$	0.0927560	0.00325912
$811$	15.3871	0.540313	0.270157	−	0.962816i	$-0.412925\pi$
$811$	15.3871	0.540313	0.270157	+	0.962816i	$0.412925\pi$
$812$	−0.358624	−0.0125852
$813$	7.88213	0.276438
$814$	23.1936	0.812937
$815$	0.253133	0.00886685
$816$	−3.57059	−0.124996
$817$	75.2457	2.63251
$818$	15.9324	0.557064
$819$	−3.36029	−0.117418
$820$	0.00302351	0.000105585 0
$821$	−38.9723	−1.36014	−0.680072	−	0.733146i	$-0.738051\pi$
$821$	−38.9723	−1.36014	−0.680072	+	0.733146i	$0.738051\pi$
$822$	11.3482	0.395815
$823$	−48.4085	−1.68741	−0.843706	−	0.536805i	$-0.819631\pi$
$823$	−48.4085	−1.68741	−0.843706	+	0.536805i	$0.819631\pi$
$824$	50.6563	1.76470
$825$	−13.7932	−0.480219
$826$	−28.4248	−0.989026
$827$	1.78815	0.0621801	0.0310900	−	0.999517i	$-0.490102\pi$
$827$	1.78815	0.0621801	0.0310900	+	0.999517i	$0.490102\pi$
$828$	−0.199174	−0.00692178
$829$	12.4239	0.431498	0.215749	−	0.976449i	$-0.430781\pi$
$829$	12.4239	0.431498	0.215749	+	0.976449i	$0.430781\pi$
$830$	0.192828	0.00669315
$831$	6.19883	0.215035
$832$	−8.20621	−0.284499
$833$	1.62049	0.0561466
$834$	32.4713	1.12439
$835$	0.486184	0.0168251
$836$	0.823932	0.0284963
$837$	−5.49575	−0.189961
$838$	40.9173	1.41346
$839$	−40.8158	−1.40912	−0.704558	−	0.709646i	$-0.748855\pi$
$839$	−40.8158	−1.40912	−0.704558	+	0.709646i	$0.748855\pi$
$840$	0.242815	0.00837791
$841$	−20.1084	−0.693395
$842$	30.4647	1.04988
$843$	−13.4417	−0.462957
$844$	−0.132074	−0.00454617
$845$	−0.0316546	−0.00108895
$846$	23.9712	0.824146
$847$	12.8690	0.442183
$848$	−18.7076	−0.642420
$849$	9.81783	0.336947
$850$	5.27212	0.180832
$851$	17.5215	0.600628
$852$	0.414439	0.0141984
$853$	−49.7034	−1.70181	−0.850906	−	0.525318i	$-0.823946\pi$
$853$	−49.7034	−1.70181	−0.850906	+	0.525318i	$0.823946\pi$
$854$	23.7090	0.811304
$855$	0.320777	0.0109703
$856$	49.5312	1.69294
$857$	9.28976	0.317332	0.158666	−	0.987332i	$-0.449281\pi$
$857$	9.28976	0.317332	0.158666	+	0.987332i	$0.449281\pi$
$858$	−3.84850	−0.131386
$859$	−36.8878	−1.25860	−0.629299	−	0.777164i	$-0.716658\pi$
$859$	−36.8878	−1.25860	−0.629299	+	0.777164i	$0.716658\pi$
$860$	0.0195580	0.000666921 0
$861$	4.68502	0.159665
$862$	−48.7596	−1.66076
$863$	−30.3508	−1.03315	−0.516576	−	0.856241i	$-0.672794\pi$
$863$	−30.3508	−1.03315	−0.516576	+	0.856241i	$0.672794\pi$
$864$	1.69611	0.0577027
$865$	−0.0790516	−0.00268784
$866$	25.8677	0.879020
$867$	19.9537	0.677664
$868$	−0.120268	−0.00408217
$869$	−32.5588	−1.10448
$870$	−0.159906	−0.00542133
$871$	3.49410	0.118393
$872$	15.7753	0.534219
$873$	−1.56776	−0.0530607
$874$	−22.1888	−0.750549
$875$	−0.697543	−0.0235812
$876$	−0.113759	−0.00384356
$877$	19.7054	0.665403	0.332701	−	0.943032i	$-0.392040\pi$
$877$	19.7054	0.665403	0.332701	+	0.943032i	$0.392040\pi$
$878$	32.0633	1.08208
$879$	4.74574	0.160070
$880$	−0.279576	−0.00942451
$881$	−0.282262	−0.00950964	−0.00475482	−	0.999989i	$-0.501514\pi$
$881$	−0.282262	−0.00950964	−0.00475482	+	0.999989i	$0.501514\pi$
$882$	4.55783	0.153470
$883$	−40.7372	−1.37092	−0.685458	−	0.728112i	$-0.740398\pi$
$883$	−40.7372	−1.37092	−0.685458	+	0.728112i	$0.740398\pi$
$884$	−0.0412637	−0.00138785
$885$	0.355534	0.0119512
$886$	−4.58835	−0.154149
$887$	21.6873	0.728189	0.364094	−	0.931362i	$-0.381379\pi$
$887$	21.6873	0.728189	0.364094	+	0.931362i	$0.381379\pi$
$888$	−25.4784	−0.854998
$889$	−36.7682	−1.23317
$890$	−0.0310994	−0.00104245
$891$	4.77254	0.159886
$892$	−0.933448	−0.0312541
$893$	−74.9116	−2.50682
$894$	15.0728	0.504109
$895$	−0.763245	−0.0255125
$896$	−23.8645	−0.797258
$897$	−2.90732	−0.0970724
$898$	−15.4195	−0.514554
$899$	2.98187	0.0994510
$900$	−0.415964	−0.0138655
$901$	−3.63831	−0.121210
$902$	−5.54575	−0.184653
$903$	30.3057	1.00851
$904$	−13.2123	−0.439434
$905$	−0.282201	−0.00938067
$906$	8.82855	0.293309
$907$	−21.6300	−0.718214	−0.359107	−	0.933296i	$-0.616919\pi$
$907$	−21.6300	−0.718214	−0.359107	+	0.933296i	$0.616919\pi$
$908$	1.07990	0.0358376
$909$	30.0783	0.997636
$910$	−0.0973020	−0.00322553
$911$	50.1337	1.66100	0.830502	−	0.557016i	$-0.188054\pi$
$911$	50.1337	1.66100	0.830502	+	0.557016i	$0.188054\pi$
$912$	31.3843	1.03924
$913$	9.92148	0.328353
$914$	−1.57398	−0.0520626
$915$	−0.296549	−0.00980360
$916$	−1.46393	−0.0483695
$917$	22.2950	0.736247
$918$	−5.79601	−0.191297
$919$	29.2452	0.964711	0.482356	−	0.875976i	$-0.339781\pi$
$919$	29.2452	0.964711	0.482356	+	0.875976i	$0.339781\pi$
$920$	−0.217133	−0.00715866
$921$	−4.24194	−0.139777
$922$	17.5179	0.576922
$923$	−6.25252	−0.205804
$924$	0.331844	0.0109169
$925$	36.5926	1.20316
$926$	9.21112	0.302696
$927$	26.9528	0.885247
$928$	−0.920268	−0.0302093
$929$	32.4295	1.06398	0.531989	−	0.846751i	$-0.321445\pi$
$929$	32.4295	1.06398	0.531989	+	0.846751i	$0.321445\pi$
$930$	−0.0536261	−0.00175847
$931$	−14.2436	−0.466814
$932$	0.370837	0.0121472
$933$	−6.06390	−0.198523
$934$	17.4046	0.569496
$935$	−0.0543729	−0.00177818
$936$	−4.36947	−0.142821
$937$	−17.9030	−0.584865	−0.292432	−	0.956286i	$-0.594465\pi$
$937$	−17.9030	−0.584865	−0.292432	+	0.956286i	$0.594465\pi$
$938$	10.7404	0.350686
$939$	−9.55916	−0.311951
$940$	−0.0194712	−0.000635079 0
$941$	−16.3313	−0.532387	−0.266193	−	0.963920i	$-0.585766\pi$
$941$	−16.3313	−0.532387	−0.266193	+	0.963920i	$0.585766\pi$
$942$	−12.9644	−0.422402
$943$	−4.18949	−0.136429
$944$	−35.9522	−1.17014
$945$	0.383391	0.0124717
$946$	−35.8734	−1.16635
$947$	−29.6209	−0.962549	−0.481274	−	0.876570i	$-0.659826\pi$
$947$	−29.6209	−0.962549	−0.481274	+	0.876570i	$0.659826\pi$
$948$	0.949997	0.0308545
$949$	1.71625	0.0557118
$950$	−46.3402	−1.50347
$951$	42.7899	1.38756
$952$	−4.77531	−0.154769
$953$	40.1153	1.29946	0.649731	−	0.760165i	$-0.274882\pi$
$953$	40.1153	1.29946	0.649731	+	0.760165i	$0.274882\pi$
$954$	−10.2332	−0.331312
$955$	−0.328377	−0.0106260
$956$	0.718739	0.0232457
$957$	−8.22759	−0.265960
$958$	4.76709	0.154018
$959$	14.7627	0.476713
$960$	0.315509	0.0101830
$961$	1.00000	0.0322581
$962$	10.2098	0.329178
$963$	26.3542	0.849251
$964$	−0.468601	−0.0150926
$965$	−0.359174	−0.0115622
$966$	−8.93670	−0.287534
$967$	8.06262	0.259276	0.129638	−	0.991561i	$-0.458618\pi$
$967$	8.06262	0.259276	0.129638	+	0.991561i	$0.458618\pi$
$968$	16.7338	0.537845
$969$	6.10371	0.196080
$970$	−0.0453967	−0.00145760
$971$	25.5661	0.820454	0.410227	−	0.911983i	$-0.365449\pi$
$971$	25.5661	0.820454	0.410227	+	0.911983i	$0.365449\pi$
$972$	0.760497	0.0243929
$973$	42.2414	1.35420
$974$	−18.2299	−0.584124
$975$	−6.07177	−0.194452
$976$	29.9875	0.959876
$977$	20.3145	0.649918	0.324959	−	0.945728i	$-0.394650\pi$
$977$	20.3145	0.649918	0.324959	+	0.945728i	$0.394650\pi$
$978$	13.5473	0.433194
$979$	−1.60014	−0.0511409
$980$	−0.00370221	−0.000118263 0
$981$	8.39360	0.267987
$982$	−14.6786	−0.468413
$983$	−31.7972	−1.01417	−0.507086	−	0.861895i	$-0.669277\pi$
$983$	−31.7972	−1.01417	−0.507086	+	0.861895i	$0.669277\pi$
$984$	6.09204	0.194207
$985$	0.674160	0.0214805
$986$	3.14479	0.100150
$987$	−30.1712	−0.960359
$988$	0.362694	0.0115388
$989$	−27.1003	−0.861739
$990$	−0.152931	−0.00486046
$991$	12.7029	0.403520	0.201760	−	0.979435i	$-0.435334\pi$
$991$	12.7029	0.403520	0.201760	+	0.979435i	$0.435334\pi$
$992$	−0.308621	−0.00979873
$993$	−4.64148	−0.147293
$994$	−19.2194	−0.609603
$995$	−0.585295	−0.0185551
$996$	−0.289488	−0.00917278
$997$	−52.2574	−1.65501	−0.827504	−	0.561459i	$-0.810240\pi$
$997$	−52.2574	−1.65501	−0.827504	+	0.561459i	$0.810240\pi$
$998$	39.0414	1.23583
$999$	−40.2288	−1.27278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.a.d.1.7	✓	8
3.2	odd	2		3627.2.a.q.1.2		8
4.3	odd	2		6448.2.a.bf.1.5		8
13.12	even	2		5239.2.a.j.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.a.d.1.7	✓	8	1.1	even	1	trivial
3627.2.a.q.1.2		8	3.2	odd	2
5239.2.a.j.1.2		8	13.12	even	2
6448.2.a.bf.1.5		8	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.a (trivial)

\(f(q)\)	\(=\)	\(q+1.39479 q^{2} -1.21460 q^{3} -0.0545724 q^{4} -0.0316546 q^{5} -1.69410 q^{6} -2.20383 q^{7} -2.86569 q^{8} -1.52475 q^{9} +O(q^{10})\)	\(q+1.39479 q^{2} -1.21460 q^{3} -0.0545724 q^{4} -0.0316546 q^{5} -1.69410 q^{6} -2.20383 q^{7} -2.86569 q^{8} -1.52475 q^{9} -0.0441514 q^{10} -2.27170 q^{11} +0.0662835 q^{12} -1.00000 q^{13} -3.07387 q^{14} +0.0384476 q^{15} -3.88788 q^{16} -0.756127 q^{17} -2.12670 q^{18} +6.64611 q^{19} +0.00172747 q^{20} +2.67676 q^{21} -3.16854 q^{22} -2.39365 q^{23} +3.48066 q^{24} -4.99900 q^{25} -1.39479 q^{26} +5.49575 q^{27} +0.120268 q^{28} -2.98187 q^{29} +0.0536261 q^{30} -1.00000 q^{31} +0.308621 q^{32} +2.75920 q^{33} -1.05464 q^{34} +0.0697612 q^{35} +0.0832095 q^{36} -7.31998 q^{37} +9.26989 q^{38} +1.21460 q^{39} +0.0907122 q^{40} +1.75026 q^{41} +3.73351 q^{42} +11.3218 q^{43} +0.123972 q^{44} +0.0482654 q^{45} -3.33862 q^{46} -11.2715 q^{47} +4.72220 q^{48} -2.14314 q^{49} -6.97253 q^{50} +0.918390 q^{51} +0.0545724 q^{52} +4.81177 q^{53} +7.66540 q^{54} +0.0719098 q^{55} +6.31548 q^{56} -8.07234 q^{57} -4.15907 q^{58} +9.24725 q^{59} -0.00209818 q^{60} -7.71307 q^{61} -1.39479 q^{62} +3.36029 q^{63} +8.20621 q^{64} +0.0316546 q^{65} +3.84850 q^{66} -3.49410 q^{67} +0.0412637 q^{68} +2.90732 q^{69} +0.0973020 q^{70} +6.25252 q^{71} +4.36947 q^{72} -1.71625 q^{73} -10.2098 q^{74} +6.07177 q^{75} -0.362694 q^{76} +5.00644 q^{77} +1.69410 q^{78} +14.3323 q^{79} +0.123069 q^{80} -2.10086 q^{81} +2.44123 q^{82} -4.36742 q^{83} -0.146077 q^{84} +0.0239349 q^{85} +15.7914 q^{86} +3.62177 q^{87} +6.50999 q^{88} +0.704382 q^{89} +0.0673199 q^{90} +2.20383 q^{91} +0.130627 q^{92} +1.21460 q^{93} -15.7213 q^{94} -0.210380 q^{95} -0.374850 q^{96} +1.02821 q^{97} -2.98923 q^{98} +3.46379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 3 q^{3} + 9 q^{4} - 15 q^{5} - 4 q^{7} - 15 q^{8} + 9 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 3 * q^3 + 9 * q^4 - 15 * q^5 - 4 * q^7 - 15 * q^8 + 9 * q^9	\( 8 q - 5 q^{2} - 3 q^{3} + 9 q^{4} - 15 q^{5} - 4 q^{7} - 15 q^{8} + 9 q^{9} + 9 q^{10} - 5 q^{11} - 9 q^{12} - 8 q^{13} + 2 q^{14} + 2 q^{15} + 3 q^{16} - 11 q^{17} - 30 q^{18} - 9 q^{19} - 31 q^{20} - 16 q^{21} - 2 q^{22} + 13 q^{24} + 19 q^{25} + 5 q^{26} - 9 q^{27} + 16 q^{28} - 12 q^{29} - 7 q^{30} - 8 q^{31} - 25 q^{32} - 14 q^{33} + 22 q^{34} + 7 q^{35} + 37 q^{36} - 9 q^{37} - 9 q^{38} + 3 q^{39} + 55 q^{40} - 25 q^{41} - 3 q^{42} + 7 q^{43} - 26 q^{44} - 45 q^{45} + 5 q^{46} - 17 q^{47} - 9 q^{48} - 11 q^{50} - 10 q^{51} - 9 q^{52} - 15 q^{53} + 54 q^{54} + 7 q^{55} - 14 q^{56} - 7 q^{57} - 5 q^{58} - 15 q^{59} + 61 q^{60} + 11 q^{61} + 5 q^{62} - 21 q^{63} + 47 q^{64} + 15 q^{65} + 83 q^{66} + 18 q^{67} - 16 q^{68} - 15 q^{69} - 24 q^{70} - 7 q^{71} - 21 q^{72} + 24 q^{73} + 48 q^{74} - 17 q^{75} - 3 q^{76} - 49 q^{77} + 33 q^{79} - 16 q^{80} + 20 q^{81} - q^{82} - 13 q^{83} - 6 q^{84} + q^{85} + 19 q^{86} + 18 q^{87} + 37 q^{88} - 23 q^{89} + 117 q^{90} + 4 q^{91} + 22 q^{92} + 3 q^{93} + 10 q^{94} + 43 q^{95} + 46 q^{96} - 17 q^{97} + 52 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 3 * q^3 + 9 * q^4 - 15 * q^5 - 4 * q^7 - 15 * q^8 + 9 * q^9 + 9 * q^10 - 5 * q^11 - 9 * q^12 - 8 * q^13 + 2 * q^14 + 2 * q^15 + 3 * q^16 - 11 * q^17 - 30 * q^18 - 9 * q^19 - 31 * q^20 - 16 * q^21 - 2 * q^22 + 13 * q^24 + 19 * q^25 + 5 * q^26 - 9 * q^27 + 16 * q^28 - 12 * q^29 - 7 * q^30 - 8 * q^31 - 25 * q^32 - 14 * q^33 + 22 * q^34 + 7 * q^35 + 37 * q^36 - 9 * q^37 - 9 * q^38 + 3 * q^39 + 55 * q^40 - 25 * q^41 - 3 * q^42 + 7 * q^43 - 26 * q^44 - 45 * q^45 + 5 * q^46 - 17 * q^47 - 9 * q^48 - 11 * q^50 - 10 * q^51 - 9 * q^52 - 15 * q^53 + 54 * q^54 + 7 * q^55 - 14 * q^56 - 7 * q^57 - 5 * q^58 - 15 * q^59 + 61 * q^60 + 11 * q^61 + 5 * q^62 - 21 * q^63 + 47 * q^64 + 15 * q^65 + 83 * q^66 + 18 * q^67 - 16 * q^68 - 15 * q^69 - 24 * q^70 - 7 * q^71 - 21 * q^72 + 24 * q^73 + 48 * q^74 - 17 * q^75 - 3 * q^76 - 49 * q^77 + 33 * q^79 - 16 * q^80 + 20 * q^81 - q^82 - 13 * q^83 - 6 * q^84 + q^85 + 19 * q^86 + 18 * q^87 + 37 * q^88 - 23 * q^89 + 117 * q^90 + 4 * q^91 + 22 * q^92 + 3 * q^93 + 10 * q^94 + 43 * q^95 + 46 * q^96 - 17 * q^97 + 52 * q^98 + 51 * q^99

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