LMFDB - Embedded newform 8015.2.a.k.1.15

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:	$49$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.36146 q^{2} -0.153831 q^{3} -0.146418 q^{4} -1.00000 q^{5} +0.209435 q^{6} -1.00000 q^{7} +2.92227 q^{8} -2.97634 q^{9} +O(q^{10})$	\(q-1.36146 q^{2} -0.153831 q^{3} -0.146418 q^{4} -1.00000 q^{5} +0.209435 q^{6} -1.00000 q^{7} +2.92227 q^{8} -2.97634 q^{9} +1.36146 q^{10} +0.539369 q^{11} +0.0225236 q^{12} -6.23902 q^{13} +1.36146 q^{14} +0.153831 q^{15} -3.68573 q^{16} +5.23207 q^{17} +4.05217 q^{18} -6.12872 q^{19} +0.146418 q^{20} +0.153831 q^{21} -0.734332 q^{22} -0.273786 q^{23} -0.449535 q^{24} +1.00000 q^{25} +8.49419 q^{26} +0.919345 q^{27} +0.146418 q^{28} -4.67518 q^{29} -0.209435 q^{30} +5.78759 q^{31} -0.826557 q^{32} -0.0829717 q^{33} -7.12327 q^{34} +1.00000 q^{35} +0.435789 q^{36} +7.61970 q^{37} +8.34403 q^{38} +0.959753 q^{39} -2.92227 q^{40} -2.28907 q^{41} -0.209435 q^{42} +12.2124 q^{43} -0.0789733 q^{44} +2.97634 q^{45} +0.372749 q^{46} +4.38055 q^{47} +0.566978 q^{48} +1.00000 q^{49} -1.36146 q^{50} -0.804854 q^{51} +0.913503 q^{52} +2.31259 q^{53} -1.25165 q^{54} -0.539369 q^{55} -2.92227 q^{56} +0.942787 q^{57} +6.36509 q^{58} -1.21547 q^{59} -0.0225236 q^{60} +2.25406 q^{61} -7.87960 q^{62} +2.97634 q^{63} +8.49678 q^{64} +6.23902 q^{65} +0.112963 q^{66} -0.417929 q^{67} -0.766069 q^{68} +0.0421167 q^{69} -1.36146 q^{70} +0.240115 q^{71} -8.69765 q^{72} -7.01702 q^{73} -10.3739 q^{74} -0.153831 q^{75} +0.897355 q^{76} -0.539369 q^{77} -1.30667 q^{78} +7.37195 q^{79} +3.68573 q^{80} +8.78758 q^{81} +3.11649 q^{82} -9.96293 q^{83} -0.0225236 q^{84} -5.23207 q^{85} -16.6268 q^{86} +0.719187 q^{87} +1.57618 q^{88} -13.4289 q^{89} -4.05217 q^{90} +6.23902 q^{91} +0.0400871 q^{92} -0.890310 q^{93} -5.96396 q^{94} +6.12872 q^{95} +0.127150 q^{96} +6.28472 q^{97} -1.36146 q^{98} -1.60534 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) $ 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * 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 $

$2$	−1.36146	−0.962700	−0.481350	−	0.876529i	$-0.659853\pi$
$2$	−1.36146	−0.962700	−0.481350	+	0.876529i	$0.659853\pi$
$3$	−0.153831	−0.0888143	−0.0444071	−	0.999014i	$-0.514140\pi$
$3$	−0.153831	−0.0888143	−0.0444071	+	0.999014i	$0.514140\pi$
$4$	−0.146418	−0.0732089
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.209435	0.0855015
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.92227	1.03318
$9$	−2.97634	−0.992112
$10$	1.36146	0.430532
$11$	0.539369	0.162626	0.0813130	−	0.996689i	$-0.474089\pi$
$11$	0.539369	0.162626	0.0813130	+	0.996689i	$0.474089\pi$
$12$	0.0225236	0.00650200
$13$	−6.23902	−1.73039	−0.865196	−	0.501434i	$-0.832806\pi$
$13$	−6.23902	−1.73039	−0.865196	+	0.501434i	$0.832806\pi$
$14$	1.36146	0.363866
$15$	0.153831	0.0397190
$16$	−3.68573	−0.921432
$17$	5.23207	1.26896	0.634482	−	0.772938i	$-0.281213\pi$
$17$	5.23207	1.26896	0.634482	+	0.772938i	$0.281213\pi$
$18$	4.05217	0.955106
$19$	−6.12872	−1.40603	−0.703013	−	0.711177i	$-0.748162\pi$
$19$	−6.12872	−1.40603	−0.703013	+	0.711177i	$0.748162\pi$
$20$	0.146418	0.0327400
$21$	0.153831	0.0335686
$22$	−0.734332	−0.156560
$23$	−0.273786	−0.0570883	−0.0285441	−	0.999593i	$-0.509087\pi$
$23$	−0.273786	−0.0570883	−0.0285441	+	0.999593i	$0.509087\pi$
$24$	−0.449535	−0.0917610
$25$	1.00000	0.200000
$26$	8.49419	1.66585
$27$	0.919345	0.176928
$28$	0.146418	0.0276704
$29$	−4.67518	−0.868160	−0.434080	−	0.900874i	$-0.642926\pi$
$29$	−4.67518	−0.868160	−0.434080	+	0.900874i	$0.642926\pi$
$30$	−0.209435	−0.0382374
$31$	5.78759	1.03948	0.519741	−	0.854324i	$-0.326028\pi$
$31$	5.78759	1.03948	0.519741	+	0.854324i	$0.326028\pi$
$32$	−0.826557	−0.146116
$33$	−0.0829717	−0.0144435
$34$	−7.12327	−1.22163
$35$	1.00000	0.169031
$36$	0.435789	0.0726315
$37$	7.61970	1.25267	0.626336	−	0.779553i	$-0.284554\pi$
$37$	7.61970	1.25267	0.626336	+	0.779553i	$0.284554\pi$
$38$	8.34403	1.35358
$39$	0.959753	0.153683
$40$	−2.92227	−0.462051
$41$	−2.28907	−0.357493	−0.178747	−	0.983895i	$-0.557204\pi$
$41$	−2.28907	−0.357493	−0.178747	+	0.983895i	$0.557204\pi$
$42$	−0.209435	−0.0323165
$43$	12.2124	1.86238	0.931190	−	0.364533i	$-0.118771\pi$
$43$	12.2124	1.86238	0.931190	+	0.364533i	$0.118771\pi$
$44$	−0.0789733	−0.0119057
$45$	2.97634	0.443686
$46$	0.372749	0.0549589
$47$	4.38055	0.638969	0.319485	−	0.947591i	$-0.396490\pi$
$47$	4.38055	0.638969	0.319485	+	0.947591i	$0.396490\pi$
$48$	0.566978	0.0818363
$49$	1.00000	0.142857
$50$	−1.36146	−0.192540
$51$	−0.804854	−0.112702
$52$	0.913503	0.126680
$53$	2.31259	0.317659	0.158829	−	0.987306i	$-0.449228\pi$
$53$	2.31259	0.317659	0.158829	+	0.987306i	$0.449228\pi$
$54$	−1.25165	−0.170329
$55$	−0.539369	−0.0727286
$56$	−2.92227	−0.390505
$57$	0.942787	0.124875
$58$	6.36509	0.835777
$59$	−1.21547	−0.158241	−0.0791203	−	0.996865i	$-0.525211\pi$
$59$	−1.21547	−0.158241	−0.0791203	+	0.996865i	$0.525211\pi$
$60$	−0.0225236	−0.00290778
$61$	2.25406	0.288602	0.144301	−	0.989534i	$-0.453907\pi$
$61$	2.25406	0.288602	0.144301	+	0.989534i	$0.453907\pi$
$62$	−7.87960	−1.00071
$63$	2.97634	0.374983
$64$	8.49678	1.06210
$65$	6.23902	0.773855
$66$	0.112963	0.0139048
$67$	−0.417929	−0.0510582	−0.0255291	−	0.999674i	$-0.508127\pi$
$67$	−0.417929	−0.0510582	−0.0255291	+	0.999674i	$0.508127\pi$
$68$	−0.766069	−0.0928995
$69$	0.0421167	0.00507025
$70$	−1.36146	−0.162726
$71$	0.240115	0.0284964	0.0142482	−	0.999898i	$-0.495465\pi$
$71$	0.240115	0.0284964	0.0142482	+	0.999898i	$0.495465\pi$
$72$	−8.69765	−1.02503
$73$	−7.01702	−0.821280	−0.410640	−	0.911798i	$-0.634695\pi$
$73$	−7.01702	−0.821280	−0.410640	+	0.911798i	$0.634695\pi$
$74$	−10.3739	−1.20595
$75$	−0.153831	−0.0177629
$76$	0.897355	0.102934
$77$	−0.539369	−0.0614669
$78$	−1.30667	−0.147951
$79$	7.37195	0.829409	0.414705	−	0.909956i	$-0.363885\pi$
$79$	7.37195	0.829409	0.414705	+	0.909956i	$0.363885\pi$
$80$	3.68573	0.412077
$81$	8.78758	0.976398
$82$	3.11649	0.344159
$83$	−9.96293	−1.09357	−0.546787	−	0.837272i	$-0.684149\pi$
$83$	−9.96293	−1.09357	−0.546787	+	0.837272i	$0.684149\pi$
$84$	−0.0225236	−0.00245752
$85$	−5.23207	−0.567498
$86$	−16.6268	−1.79291
$87$	0.719187	0.0771050
$88$	1.57618	0.168022
$89$	−13.4289	−1.42346	−0.711730	−	0.702453i	$-0.752088\pi$
$89$	−13.4289	−1.42346	−0.711730	+	0.702453i	$0.752088\pi$
$90$	−4.05217	−0.427136
$91$	6.23902	0.654027
$92$	0.0400871	0.00417937
$93$	−0.890310	−0.0923209
$94$	−5.96396	−0.615136
$95$	6.12872	0.628794
$96$	0.127150	0.0129772
$97$	6.28472	0.638117	0.319058	−	0.947735i	$-0.396633\pi$
$97$	6.28472	0.638117	0.319058	+	0.947735i	$0.396633\pi$
$98$	−1.36146	−0.137529
$99$	−1.60534	−0.161343
$100$	−0.146418	−0.0146418
$101$	11.8294	1.17707	0.588533	−	0.808473i	$-0.299706\pi$
$101$	11.8294	1.17707	0.588533	+	0.808473i	$0.299706\pi$
$102$	1.09578	0.108498
$103$	−3.21569	−0.316851	−0.158426	−	0.987371i	$-0.550642\pi$
$103$	−3.21569	−0.316851	−0.158426	+	0.987371i	$0.550642\pi$
$104$	−18.2321	−1.78780
$105$	−0.153831	−0.0150124
$106$	−3.14851	−0.305810
$107$	−0.378638	−0.0366043	−0.0183022	−	0.999833i	$-0.505826\pi$
$107$	−0.378638	−0.0366043	−0.0183022	+	0.999833i	$0.505826\pi$
$108$	−0.134608	−0.0129527
$109$	7.82200	0.749211	0.374606	−	0.927184i	$-0.377778\pi$
$109$	7.82200	0.749211	0.374606	+	0.927184i	$0.377778\pi$
$110$	0.734332	0.0700158
$111$	−1.17215	−0.111255
$112$	3.68573	0.348268
$113$	15.1886	1.42882	0.714412	−	0.699726i	$-0.246694\pi$
$113$	15.1886	1.42882	0.714412	+	0.699726i	$0.246694\pi$
$114$	−1.28357	−0.120217
$115$	0.273786	0.0255306
$116$	0.684530	0.0635570
$117$	18.5694	1.71674
$118$	1.65482	0.152338
$119$	−5.23207	−0.479623
$120$	0.449535	0.0410368
$121$	−10.7091	−0.973553
$122$	−3.06882	−0.277837
$123$	0.352130	0.0317505
$124$	−0.847407	−0.0760994
$125$	−1.00000	−0.0894427
$126$	−4.05217	−0.360996
$127$	−14.5962	−1.29520	−0.647602	−	0.761979i	$-0.724228\pi$
$127$	−14.5962	−1.29520	−0.647602	+	0.761979i	$0.724228\pi$
$128$	−9.91494	−0.876365
$129$	−1.87865	−0.165406
$130$	−8.49419	−0.744990
$131$	−0.781948	−0.0683191	−0.0341595	−	0.999416i	$-0.510875\pi$
$131$	−0.781948	−0.0683191	−0.0341595	+	0.999416i	$0.510875\pi$
$132$	0.0121485	0.00105739
$133$	6.12872	0.531428
$134$	0.568995	0.0491537
$135$	−0.919345	−0.0791246
$136$	15.2895	1.31107
$137$	−12.4279	−1.06179	−0.530893	−	0.847439i	$-0.678143\pi$
$137$	−12.4279	−1.06179	−0.530893	+	0.847439i	$0.678143\pi$
$138$	−0.0573403	−0.00488113
$139$	−2.90277	−0.246210	−0.123105	−	0.992394i	$-0.539285\pi$
$139$	−2.90277	−0.246210	−0.123105	+	0.992394i	$0.539285\pi$
$140$	−0.146418	−0.0123746
$141$	−0.673864	−0.0567496
$142$	−0.326907	−0.0274334
$143$	−3.36513	−0.281407
$144$	10.9700	0.914163
$145$	4.67518	0.388253
$146$	9.55342	0.790646
$147$	−0.153831	−0.0126878
$148$	−1.11566	−0.0917067
$149$	8.08313	0.662196	0.331098	−	0.943596i	$-0.392581\pi$
$149$	8.08313	0.662196	0.331098	+	0.943596i	$0.392581\pi$
$150$	0.209435	0.0171003
$151$	3.60142	0.293080	0.146540	−	0.989205i	$-0.453186\pi$
$151$	3.60142	0.293080	0.146540	+	0.989205i	$0.453186\pi$
$152$	−17.9098	−1.45268
$153$	−15.5724	−1.25895
$154$	0.734332	0.0591741
$155$	−5.78759	−0.464871
$156$	−0.140525	−0.0112510
$157$	10.2462	0.817737	0.408868	−	0.912593i	$-0.365924\pi$
$157$	10.2462	0.817737	0.408868	+	0.912593i	$0.365924\pi$
$158$	−10.0366	−0.798472
$159$	−0.355748	−0.0282127
$160$	0.826557	0.0653451
$161$	0.273786	0.0215773
$162$	−11.9640	−0.939979
$163$	−2.25444	−0.176582	−0.0882908	−	0.996095i	$-0.528140\pi$
$163$	−2.25444	−0.176582	−0.0882908	+	0.996095i	$0.528140\pi$
$164$	0.335161	0.0261717
$165$	0.0829717	0.00645933
$166$	13.5642	1.05278
$167$	8.90372	0.688991	0.344495	−	0.938788i	$-0.388050\pi$
$167$	8.90372	0.688991	0.344495	+	0.938788i	$0.388050\pi$
$168$	0.449535	0.0346824
$169$	25.9253	1.99426
$170$	7.12327	0.546330
$171$	18.2411	1.39494
$172$	−1.78812	−0.136343
$173$	5.36776	0.408103	0.204052	−	0.978960i	$-0.434589\pi$
$173$	5.36776	0.408103	0.204052	+	0.978960i	$0.434589\pi$
$174$	−0.979147	−0.0742290
$175$	−1.00000	−0.0755929
$176$	−1.98797	−0.149849
$177$	0.186977	0.0140540
$178$	18.2830	1.37037
$179$	1.17149	0.0875613	0.0437806	−	0.999041i	$-0.486060\pi$
$179$	1.17149	0.0875613	0.0437806	+	0.999041i	$0.486060\pi$
$180$	−0.435789	−0.0324818
$181$	−10.5920	−0.787294	−0.393647	−	0.919262i	$-0.628787\pi$
$181$	−10.5920	−0.787294	−0.393647	+	0.919262i	$0.628787\pi$
$182$	−8.49419	−0.629631
$183$	−0.346743	−0.0256320
$184$	−0.800075	−0.0589823
$185$	−7.61970	−0.560212
$186$	1.21212	0.0888773
$187$	2.82202	0.206367
$188$	−0.641391	−0.0467783
$189$	−0.919345	−0.0668725
$190$	−8.34403	−0.605340
$191$	8.47686	0.613364	0.306682	−	0.951812i	$-0.400781\pi$
$191$	8.47686	0.613364	0.306682	+	0.951812i	$0.400781\pi$
$192$	−1.30707	−0.0943294
$193$	16.0633	1.15626	0.578130	−	0.815944i	$-0.303782\pi$
$193$	16.0633	1.15626	0.578130	+	0.815944i	$0.303782\pi$
$194$	−8.55641	−0.614315
$195$	−0.959753	−0.0687293
$196$	−0.146418	−0.0104584
$197$	−15.9371	−1.13547	−0.567736	−	0.823211i	$-0.692180\pi$
$197$	−15.9371	−1.13547	−0.567736	+	0.823211i	$0.692180\pi$
$198$	2.18562	0.155325
$199$	6.06685	0.430068	0.215034	−	0.976607i	$-0.431014\pi$
$199$	6.06685	0.430068	0.215034	+	0.976607i	$0.431014\pi$
$200$	2.92227	0.206636
$201$	0.0642904	0.00453469
$202$	−16.1052	−1.13316
$203$	4.67518	0.328134
$204$	0.117845	0.00825080
$205$	2.28907	0.159876
$206$	4.37805	0.305033
$207$	0.814878	0.0566380
$208$	22.9953	1.59444
$209$	−3.30565	−0.228656
$210$	0.209435	0.0144524
$211$	−0.356723	−0.0245579	−0.0122789	−	0.999925i	$-0.503909\pi$
$211$	−0.356723	−0.0245579	−0.0122789	+	0.999925i	$0.503909\pi$
$212$	−0.338605	−0.0232555
$213$	−0.0369370	−0.00253088
$214$	0.515502	0.0352390
$215$	−12.2124	−0.832882
$216$	2.68657	0.182798
$217$	−5.78759	−0.392887
$218$	−10.6494	−0.721266
$219$	1.07943	0.0729414
$220$	0.0789733	0.00532438
$221$	−32.6430	−2.19580
$222$	1.59583	0.107105
$223$	−12.0919	−0.809735	−0.404868	−	0.914375i	$-0.632682\pi$
$223$	−12.0919	−0.809735	−0.404868	+	0.914375i	$0.632682\pi$
$224$	0.826557	0.0552267
$225$	−2.97634	−0.198422
$226$	−20.6787	−1.37553
$227$	0.264007	0.0175228	0.00876139	−	0.999962i	$-0.497211\pi$
$227$	0.264007	0.0175228	0.00876139	+	0.999962i	$0.497211\pi$
$228$	−0.138041	−0.00914198
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−0.372749	−0.0245784
$231$	0.0829717	0.00545913
$232$	−13.6621	−0.896964
$233$	−10.0637	−0.659295	−0.329648	−	0.944104i	$-0.606930\pi$
$233$	−10.0637	−0.659295	−0.329648	+	0.944104i	$0.606930\pi$
$234$	−25.2816	−1.65271
$235$	−4.38055	−0.285756
$236$	0.177966	0.0115846
$237$	−1.13403	−0.0736634
$238$	7.12327	0.461733
$239$	−18.9275	−1.22432	−0.612158	−	0.790735i	$-0.709699\pi$
$239$	−18.9275	−1.22432	−0.612158	+	0.790735i	$0.709699\pi$
$240$	−0.566978	−0.0365983
$241$	12.1390	0.781942	0.390971	−	0.920403i	$-0.372139\pi$
$241$	12.1390	0.781942	0.390971	+	0.920403i	$0.372139\pi$
$242$	14.5800	0.937239
$243$	−4.10984	−0.263646
$244$	−0.330034	−0.0211283
$245$	−1.00000	−0.0638877
$246$	−0.479412	−0.0305662
$247$	38.2372	2.43298
$248$	16.9129	1.07397
$249$	1.53261	0.0971250
$250$	1.36146	0.0861065
$251$	3.82840	0.241647	0.120823	−	0.992674i	$-0.461447\pi$
$251$	3.82840	0.241647	0.120823	+	0.992674i	$0.461447\pi$
$252$	−0.435789	−0.0274521
$253$	−0.147672	−0.00928404
$254$	19.8722	1.24689
$255$	0.804854	0.0504019
$256$	−3.49474	−0.218421
$257$	12.0776	0.753380	0.376690	−	0.926339i	$-0.377062\pi$
$257$	12.0776	0.753380	0.376690	+	0.926339i	$0.377062\pi$
$258$	2.55771	0.159236
$259$	−7.61970	−0.473465
$260$	−0.913503	−0.0566531
$261$	13.9149	0.861312
$262$	1.06459	0.0657708
$263$	−26.5112	−1.63475	−0.817374	−	0.576107i	$-0.804571\pi$
$263$	−26.5112	−1.63475	−0.817374	+	0.576107i	$0.804571\pi$
$264$	−0.242465	−0.0149227
$265$	−2.31259	−0.142061
$266$	−8.34403	−0.511605
$267$	2.06578	0.126424
$268$	0.0611923	0.00373791
$269$	29.6698	1.80900	0.904500	−	0.426473i	$-0.140244\pi$
$269$	29.6698	1.80900	0.904500	+	0.426473i	$0.140244\pi$
$270$	1.25165	0.0761732
$271$	−21.5382	−1.30835	−0.654176	−	0.756342i	$-0.726985\pi$
$271$	−21.5382	−1.30835	−0.654176	+	0.756342i	$0.726985\pi$
$272$	−19.2840	−1.16926
$273$	−0.959753	−0.0580869
$274$	16.9201	1.02218
$275$	0.539369	0.0325252
$276$	−0.00616663	−0.000371188 0
$277$	14.5802	0.876042	0.438021	−	0.898965i	$-0.355680\pi$
$277$	14.5802	0.876042	0.438021	+	0.898965i	$0.355680\pi$
$278$	3.95201	0.237026
$279$	−17.2258	−1.03128
$280$	2.92227	0.174639
$281$	18.0044	1.07405	0.537027	−	0.843565i	$-0.319547\pi$
$281$	18.0044	1.07405	0.537027	+	0.843565i	$0.319547\pi$
$282$	0.917441	0.0546328
$283$	−2.69622	−0.160273	−0.0801367	−	0.996784i	$-0.525536\pi$
$283$	−2.69622	−0.160273	−0.0801367	+	0.996784i	$0.525536\pi$
$284$	−0.0351571	−0.00208619
$285$	−0.942787	−0.0558459
$286$	4.58151	0.270910
$287$	2.28907	0.135120
$288$	2.46011	0.144964
$289$	10.3746	0.610269
$290$	−6.36509	−0.373771
$291$	−0.966784	−0.0566739
$292$	1.02742	0.0601250
$293$	−19.2708	−1.12581	−0.562905	−	0.826522i	$-0.690316\pi$
$293$	−19.2708	−1.12581	−0.562905	+	0.826522i	$0.690316\pi$
$294$	0.209435	0.0122145
$295$	1.21547	0.0707674
$296$	22.2668	1.29423
$297$	0.495866	0.0287731
$298$	−11.0049	−0.637496
$299$	1.70815	0.0987851
$300$	0.0225236	0.00130040
$301$	−12.2124	−0.703914
$302$	−4.90321	−0.282148
$303$	−1.81972	−0.104540
$304$	22.5888	1.29556
$305$	−2.25406	−0.129067
$306$	21.2013	1.21200
$307$	19.0638	1.08803	0.544014	−	0.839076i	$-0.316904\pi$
$307$	19.0638	1.08803	0.544014	+	0.839076i	$0.316904\pi$
$308$	0.0789733	0.00449992
$309$	0.494672	0.0281409
$310$	7.87960	0.447531
$311$	−13.6889	−0.776229	−0.388114	−	0.921611i	$-0.626873\pi$
$311$	−13.6889	−0.776229	−0.388114	+	0.921611i	$0.626873\pi$
$312$	2.80466	0.158782
$313$	−2.43895	−0.137858	−0.0689288	−	0.997622i	$-0.521958\pi$
$313$	−2.43895	−0.137858	−0.0689288	+	0.997622i	$0.521958\pi$
$314$	−13.9498	−0.787235
$315$	−2.97634	−0.167698
$316$	−1.07938	−0.0607201
$317$	−20.3305	−1.14187	−0.570937	−	0.820994i	$-0.693420\pi$
$317$	−20.3305	−1.14187	−0.570937	+	0.820994i	$0.693420\pi$
$318$	0.484338	0.0271603
$319$	−2.52165	−0.141185
$320$	−8.49678	−0.474984
$321$	0.0582462	0.00325099
$322$	−0.372749	−0.0207725
$323$	−32.0659	−1.78420
$324$	−1.28666	−0.0714811
$325$	−6.23902	−0.346078
$326$	3.06934	0.169995
$327$	−1.20326	−0.0665407
$328$	−6.68929	−0.369354
$329$	−4.38055	−0.241508
$330$	−0.112963	−0.00621840
$331$	28.6316	1.57373	0.786866	−	0.617123i	$-0.211702\pi$
$331$	28.6316	1.57373	0.786866	+	0.617123i	$0.211702\pi$
$332$	1.45875	0.0800594
$333$	−22.6788	−1.24279
$334$	−12.1221	−0.663291
$335$	0.417929	0.0228339
$336$	−0.566978	−0.0309312
$337$	7.45405	0.406048	0.203024	−	0.979174i	$-0.434923\pi$
$337$	7.45405	0.406048	0.203024	+	0.979174i	$0.434923\pi$
$338$	−35.2964	−1.91987
$339$	−2.33648	−0.126900
$340$	0.766069	0.0415459
$341$	3.12165	0.169047
$342$	−24.8346	−1.34290
$343$	−1.00000	−0.0539949
$344$	35.6881	1.92417
$345$	−0.0421167	−0.00226749
$346$	−7.30801	−0.392881
$347$	21.5519	1.15697	0.578483	−	0.815695i	$-0.303645\pi$
$347$	21.5519	1.15697	0.578483	+	0.815695i	$0.303645\pi$
$348$	−0.105302	−0.00564477
$349$	−30.5084	−1.63308	−0.816539	−	0.577291i	$-0.804110\pi$
$349$	−30.5084	−1.63308	−0.816539	+	0.577291i	$0.804110\pi$
$350$	1.36146	0.0727733
$351$	−5.73581	−0.306155
$352$	−0.445820	−0.0237623
$353$	−7.15195	−0.380660	−0.190330	−	0.981720i	$-0.560956\pi$
$353$	−7.15195	−0.380660	−0.190330	+	0.981720i	$0.560956\pi$
$354$	−0.254562	−0.0135298
$355$	−0.240115	−0.0127440
$356$	1.96623	0.104210
$357$	0.804854	0.0425974
$358$	−1.59494	−0.0842952
$359$	28.0378	1.47978	0.739890	−	0.672728i	$-0.234878\pi$
$359$	28.0378	1.47978	0.739890	+	0.672728i	$0.234878\pi$
$360$	8.69765	0.458407
$361$	18.5613	0.976909
$362$	14.4206	0.757928
$363$	1.64739	0.0864654
$364$	−0.913503	−0.0478806
$365$	7.01702	0.367288
$366$	0.472078	0.0246759
$367$	−13.7003	−0.715151	−0.357576	−	0.933884i	$-0.616397\pi$
$367$	−13.7003	−0.715151	−0.357576	+	0.933884i	$0.616397\pi$
$368$	1.00910	0.0526029
$369$	6.81305	0.354673
$370$	10.3739	0.539316
$371$	−2.31259	−0.120064
$372$	0.130357	0.00675871
$373$	13.8721	0.718268	0.359134	−	0.933286i	$-0.383072\pi$
$373$	13.8721	0.718268	0.359134	+	0.933286i	$0.383072\pi$
$374$	−3.84208	−0.198669
$375$	0.153831	0.00794379
$376$	12.8012	0.660169
$377$	29.1685	1.50226
$378$	1.25165	0.0643781
$379$	−11.6901	−0.600479	−0.300240	−	0.953864i	$-0.597067\pi$
$379$	−11.6901	−0.600479	−0.300240	+	0.953864i	$0.597067\pi$
$380$	−0.897355	−0.0460333
$381$	2.24535	0.115033
$382$	−11.5409	−0.590486
$383$	−26.1492	−1.33616	−0.668080	−	0.744090i	$-0.732884\pi$
$383$	−26.1492	−1.33616	−0.668080	+	0.744090i	$0.732884\pi$
$384$	1.52522	0.0778337
$385$	0.539369	0.0274888
$386$	−21.8696	−1.11313
$387$	−36.3484	−1.84769
$388$	−0.920195	−0.0467158
$389$	−17.8708	−0.906087	−0.453044	−	0.891488i	$-0.649662\pi$
$389$	−17.8708	−0.906087	−0.453044	+	0.891488i	$0.649662\pi$
$390$	1.30667	0.0661657
$391$	−1.43247	−0.0724429
$392$	2.92227	0.147597
$393$	0.120288	0.00606771
$394$	21.6978	1.09312
$395$	−7.37195	−0.370923
$396$	0.235051	0.0118118
$397$	−18.4783	−0.927398	−0.463699	−	0.885993i	$-0.653478\pi$
$397$	−18.4783	−0.927398	−0.463699	+	0.885993i	$0.653478\pi$
$398$	−8.25980	−0.414026
$399$	−0.942787	−0.0471984
$400$	−3.68573	−0.184286
$401$	26.5702	1.32685	0.663426	−	0.748242i	$-0.269102\pi$
$401$	26.5702	1.32685	0.663426	+	0.748242i	$0.269102\pi$
$402$	−0.0875290	−0.00436555
$403$	−36.1089	−1.79871
$404$	−1.73203	−0.0861717
$405$	−8.78758	−0.436659
$406$	−6.36509	−0.315894
$407$	4.10984	0.203717
$408$	−2.35200	−0.116441
$409$	−12.7224	−0.629082	−0.314541	−	0.949244i	$-0.601851\pi$
$409$	−12.7224	−0.629082	−0.314541	+	0.949244i	$0.601851\pi$
$410$	−3.11649	−0.153912
$411$	1.91179	0.0943018
$412$	0.470835	0.0231964
$413$	1.21547	0.0598093
$414$	−1.10943	−0.0545254
$415$	9.96293	0.489061
$416$	5.15691	0.252838
$417$	0.446535	0.0218669
$418$	4.50052	0.220127
$419$	11.0684	0.540727	0.270364	−	0.962758i	$-0.412856\pi$
$419$	11.0684	0.540727	0.270364	+	0.962758i	$0.412856\pi$
$420$	0.0225236	0.00109904
$421$	−16.4609	−0.802253	−0.401127	−	0.916023i	$-0.631381\pi$
$421$	−16.4609	−0.802253	−0.401127	+	0.916023i	$0.631381\pi$
$422$	0.485666	0.0236418
$423$	−13.0380	−0.633929
$424$	6.75802	0.328198
$425$	5.23207	0.253793
$426$	0.0502884	0.00243648
$427$	−2.25406	−0.109081
$428$	0.0554394	0.00267976
$429$	0.517661	0.0249929
$430$	16.6268	0.801815
$431$	−10.0032	−0.481838	−0.240919	−	0.970545i	$-0.577449\pi$
$431$	−10.0032	−0.481838	−0.240919	+	0.970545i	$0.577449\pi$
$432$	−3.38845	−0.163027
$433$	−11.7762	−0.565930	−0.282965	−	0.959130i	$-0.591318\pi$
$433$	−11.7762	−0.565930	−0.282965	+	0.959130i	$0.591318\pi$
$434$	7.87960	0.378233
$435$	−0.719187	−0.0344824
$436$	−1.14528	−0.0548490
$437$	1.67796	0.0802676
$438$	−1.46961	−0.0702207
$439$	15.8981	0.758773	0.379386	−	0.925238i	$-0.376135\pi$
$439$	15.8981	0.758773	0.379386	+	0.925238i	$0.376135\pi$
$440$	−1.57618	−0.0751416
$441$	−2.97634	−0.141730
$442$	44.4422	2.11390
$443$	−2.03032	−0.0964636	−0.0482318	−	0.998836i	$-0.515359\pi$
$443$	−2.03032	−0.0964636	−0.0482318	+	0.998836i	$0.515359\pi$
$444$	0.171623	0.00814487
$445$	13.4289	0.636591
$446$	16.4627	0.779532
$447$	−1.24343	−0.0588124
$448$	−8.49678	−0.401435
$449$	−31.7143	−1.49669	−0.748346	−	0.663309i	$-0.769152\pi$
$449$	−31.7143	−1.49669	−0.748346	+	0.663309i	$0.769152\pi$
$450$	4.05217	0.191021
$451$	−1.23466	−0.0581377
$452$	−2.22388	−0.104603
$453$	−0.554010	−0.0260297
$454$	−0.359436	−0.0168692
$455$	−6.23902	−0.292490
$456$	2.75508	0.129018
$457$	5.77297	0.270048	0.135024	−	0.990842i	$-0.456889\pi$
$457$	5.77297	0.270048	0.135024	+	0.990842i	$0.456889\pi$
$458$	1.36146	0.0636170
$459$	4.81008	0.224515
$460$	−0.0400871	−0.00186907
$461$	−7.12270	−0.331737	−0.165869	−	0.986148i	$-0.553043\pi$
$461$	−7.12270	−0.331737	−0.165869	+	0.986148i	$0.553043\pi$
$462$	−0.112963	−0.00525551
$463$	−14.8708	−0.691106	−0.345553	−	0.938399i	$-0.612309\pi$
$463$	−14.8708	−0.691106	−0.345553	+	0.938399i	$0.612309\pi$
$464$	17.2314	0.799950
$465$	0.890310	0.0412872
$466$	13.7014	0.634704
$467$	12.6856	0.587018	0.293509	−	0.955956i	$-0.405177\pi$
$467$	12.6856	0.587018	0.293509	+	0.955956i	$0.405177\pi$
$468$	−2.71889	−0.125681
$469$	0.417929	0.0192982
$470$	5.96396	0.275097
$471$	−1.57618	−0.0726267
$472$	−3.55193	−0.163491
$473$	6.58702	0.302872
$474$	1.54394	0.0709157
$475$	−6.12872	−0.281205
$476$	0.766069	0.0351127
$477$	−6.88305	−0.315153
$478$	25.7691	1.17865
$479$	−12.3494	−0.564257	−0.282129	−	0.959377i	$-0.591041\pi$
$479$	−12.3494	−0.564257	−0.282129	+	0.959377i	$0.591041\pi$
$480$	−0.127150	−0.00580358
$481$	−47.5395	−2.16761
$482$	−16.5268	−0.752775
$483$	−0.0421167	−0.00191638
$484$	1.56800	0.0712728
$485$	−6.28472	−0.285374
$486$	5.59539	0.253812
$487$	−11.5561	−0.523656	−0.261828	−	0.965115i	$-0.584325\pi$
$487$	−11.5561	−0.523656	−0.261828	+	0.965115i	$0.584325\pi$
$488$	6.58696	0.298178
$489$	0.346803	0.0156830
$490$	1.36146	0.0615046
$491$	7.83668	0.353664	0.176832	−	0.984241i	$-0.443415\pi$
$491$	7.83668	0.353664	0.176832	+	0.984241i	$0.443415\pi$
$492$	−0.0515581	−0.00232442
$493$	−24.4609	−1.10166
$494$	−52.0586	−2.34223
$495$	1.60534	0.0721549
$496$	−21.3315	−0.957812
$497$	−0.240115	−0.0107706
$498$	−2.08659	−0.0935022
$499$	−36.9295	−1.65319	−0.826595	−	0.562797i	$-0.809725\pi$
$499$	−36.9295	−1.65319	−0.826595	+	0.562797i	$0.809725\pi$
$500$	0.146418	0.00654801
$501$	−1.36967	−0.0611922
$502$	−5.21223	−0.232633
$503$	0.825579	0.0368108	0.0184054	−	0.999831i	$-0.494141\pi$
$503$	0.825579	0.0368108	0.0184054	+	0.999831i	$0.494141\pi$
$504$	8.69765	0.387424
$505$	−11.8294	−0.526400
$506$	0.201050	0.00893774
$507$	−3.98811	−0.177118
$508$	2.13715	0.0948205
$509$	5.66776	0.251219	0.125610	−	0.992080i	$-0.459911\pi$
$509$	5.66776	0.251219	0.125610	+	0.992080i	$0.459911\pi$
$510$	−1.09578	−0.0485219
$511$	7.01702	0.310415
$512$	24.5878	1.08664
$513$	−5.63441	−0.248765
$514$	−16.4432	−0.725279
$515$	3.21569	0.141700
$516$	0.275068	0.0121092
$517$	2.36274	0.103913
$518$	10.3739	0.455805
$519$	−0.825727	−0.0362454
$520$	18.2321	0.799530
$521$	−26.4702	−1.15968	−0.579839	−	0.814731i	$-0.696885\pi$
$521$	−26.4702	−1.15968	−0.579839	+	0.814731i	$0.696885\pi$
$522$	−18.9446	−0.829185
$523$	13.2702	0.580264	0.290132	−	0.956987i	$-0.406301\pi$
$523$	13.2702	0.580264	0.290132	+	0.956987i	$0.406301\pi$
$524$	0.114491	0.00500157
$525$	0.153831	0.00671373
$526$	36.0940	1.57377
$527$	30.2811	1.31907
$528$	0.305811	0.0133087
$529$	−22.9250	−0.996741
$530$	3.14851	0.136763
$531$	3.61765	0.156992
$532$	−0.897355	−0.0389053
$533$	14.2816	0.618603
$534$	−2.81248	−0.121708
$535$	0.378638	0.0163700
$536$	−1.22130	−0.0527522
$537$	−0.180211	−0.00777669
$538$	−40.3944	−1.74152
$539$	0.539369	0.0232323
$540$	0.134608	0.00579263
$541$	−5.34229	−0.229683	−0.114841	−	0.993384i	$-0.536636\pi$
$541$	−5.34229	−0.229683	−0.114841	+	0.993384i	$0.536636\pi$
$542$	29.3235	1.25955
$543$	1.62937	0.0699229
$544$	−4.32461	−0.185416
$545$	−7.82200	−0.335058
$546$	1.30667	0.0559203
$547$	21.8898	0.935941	0.467970	−	0.883744i	$-0.344985\pi$
$547$	21.8898	0.935941	0.467970	+	0.883744i	$0.344985\pi$
$548$	1.81967	0.0777323
$549$	−6.70883	−0.286326
$550$	−0.734332	−0.0313120
$551$	28.6529	1.22066
$552$	0.123076	0.00523847
$553$	−7.37195	−0.313487
$554$	−19.8505	−0.843365
$555$	1.17215	0.0497548
$556$	0.425017	0.0180247
$557$	2.09779	0.0888862	0.0444431	−	0.999012i	$-0.485849\pi$
$557$	2.09779	0.0888862	0.0444431	+	0.999012i	$0.485849\pi$
$558$	23.4523	0.992816
$559$	−76.1937	−3.22265
$560$	−3.68573	−0.155750
$561$	−0.434114	−0.0183283
$562$	−24.5124	−1.03399
$563$	−15.0077	−0.632498	−0.316249	−	0.948676i	$-0.602424\pi$
$563$	−15.0077	−0.632498	−0.316249	+	0.948676i	$0.602424\pi$
$564$	0.0986657	0.00415458
$565$	−15.1886	−0.638989
$566$	3.67080	0.154295
$567$	−8.78758	−0.369044
$568$	0.701680	0.0294418
$569$	−1.21095	−0.0507657	−0.0253829	−	0.999678i	$-0.508080\pi$
$569$	−1.21095	−0.0507657	−0.0253829	+	0.999678i	$0.508080\pi$
$570$	1.28357	0.0537628
$571$	−4.38934	−0.183688	−0.0918440	−	0.995773i	$-0.529276\pi$
$571$	−4.38934	−0.183688	−0.0918440	+	0.995773i	$0.529276\pi$
$572$	0.492716	0.0206015
$573$	−1.30400	−0.0544755
$574$	−3.11649	−0.130080
$575$	−0.273786	−0.0114177
$576$	−25.2893	−1.05372
$577$	−42.1216	−1.75355	−0.876773	−	0.480905i	$-0.840308\pi$
$577$	−42.1216	−1.75355	−0.876773	+	0.480905i	$0.840308\pi$
$578$	−14.1246	−0.587506
$579$	−2.47103	−0.102692
$580$	−0.684530	−0.0284236
$581$	9.96293	0.413332
$582$	1.31624	0.0545599
$583$	1.24734	0.0516596
$584$	−20.5056	−0.848529
$585$	−18.5694	−0.767751
$586$	26.2364	1.08382
$587$	39.2187	1.61873	0.809365	−	0.587306i	$-0.199811\pi$
$587$	39.2187	1.61873	0.809365	+	0.587306i	$0.199811\pi$
$588$	0.0225236	0.000928857 0
$589$	−35.4706	−1.46154
$590$	−1.65482	−0.0681277
$591$	2.45162	0.100846
$592$	−28.0841	−1.15425
$593$	14.0236	0.575879	0.287939	−	0.957649i	$-0.407030\pi$
$593$	14.0236	0.575879	0.287939	+	0.957649i	$0.407030\pi$
$594$	−0.675104	−0.0276999
$595$	5.23207	0.214494
$596$	−1.18351	−0.0484786
$597$	−0.933269	−0.0381962
$598$	−2.32559	−0.0951004
$599$	−0.197961	−0.00808849	−0.00404424	−	0.999992i	$-0.501287\pi$
$599$	−0.197961	−0.00808849	−0.00404424	+	0.999992i	$0.501287\pi$
$600$	−0.449535	−0.0183522
$601$	−22.8354	−0.931474	−0.465737	−	0.884923i	$-0.654211\pi$
$601$	−22.8354	−0.931474	−0.465737	+	0.884923i	$0.654211\pi$
$602$	16.6268	0.677658
$603$	1.24390	0.0506554
$604$	−0.527313	−0.0214561
$605$	10.7091	0.435386
$606$	2.47748	0.100641
$607$	−19.1850	−0.778694	−0.389347	−	0.921091i	$-0.627299\pi$
$607$	−19.1850	−0.778694	−0.389347	+	0.921091i	$0.627299\pi$
$608$	5.06574	0.205443
$609$	−0.719187	−0.0291429
$610$	3.06882	0.124253
$611$	−27.3303	−1.10567
$612$	2.28008	0.0921667
$613$	−15.8884	−0.641727	−0.320863	−	0.947125i	$-0.603973\pi$
$613$	−15.8884	−0.641727	−0.320863	+	0.947125i	$0.603973\pi$
$614$	−25.9547	−1.04745
$615$	−0.352130	−0.0141993
$616$	−1.57618	−0.0635062
$617$	−47.6636	−1.91887	−0.959433	−	0.281937i	$-0.909023\pi$
$617$	−47.6636	−1.91887	−0.959433	+	0.281937i	$0.909023\pi$
$618$	−0.673478	−0.0270913
$619$	5.18037	0.208217	0.104108	−	0.994566i	$-0.466801\pi$
$619$	5.18037	0.208217	0.104108	+	0.994566i	$0.466801\pi$
$620$	0.847407	0.0340327
$621$	−0.251703	−0.0101005
$622$	18.6370	0.747275
$623$	13.4289	0.538018
$624$	−3.53739	−0.141609
$625$	1.00000	0.0400000
$626$	3.32054	0.132716
$627$	0.508510	0.0203079
$628$	−1.50023	−0.0598656
$629$	39.8668	1.58960
$630$	4.05217	0.161442
$631$	33.7988	1.34551	0.672754	−	0.739866i	$-0.265111\pi$
$631$	33.7988	1.34551	0.672754	+	0.739866i	$0.265111\pi$
$632$	21.5428	0.856927
$633$	0.0548751	0.00218109
$634$	27.6792	1.09928
$635$	14.5962	0.579233
$636$	0.0520879	0.00206542
$637$	−6.23902	−0.247199
$638$	3.43314	0.135919
$639$	−0.714662	−0.0282716
$640$	9.91494	0.391922
$641$	18.7661	0.741214	0.370607	−	0.928790i	$-0.379150\pi$
$641$	18.7661	0.741214	0.370607	+	0.928790i	$0.379150\pi$
$642$	−0.0793001	−0.00312973
$643$	−45.8126	−1.80667	−0.903336	−	0.428933i	$-0.858890\pi$
$643$	−45.8126	−1.80667	−0.903336	+	0.428933i	$0.858890\pi$
$644$	−0.0400871	−0.00157965
$645$	1.87865	0.0739718
$646$	43.6566	1.71765
$647$	−38.1842	−1.50118	−0.750588	−	0.660770i	$-0.770230\pi$
$647$	−38.1842	−1.50118	−0.750588	+	0.660770i	$0.770230\pi$
$648$	25.6797	1.00879
$649$	−0.655587	−0.0257340
$650$	8.49419	0.333170
$651$	0.890310	0.0348940
$652$	0.330091	0.0129274
$653$	−9.51917	−0.372514	−0.186257	−	0.982501i	$-0.559636\pi$
$653$	−9.51917	−0.372514	−0.186257	+	0.982501i	$0.559636\pi$
$654$	1.63820	0.0640587
$655$	0.781948	0.0305532
$656$	8.43690	0.329405
$657$	20.8850	0.814802
$658$	5.96396	0.232499
$659$	26.6894	1.03967	0.519836	−	0.854266i	$-0.325993\pi$
$659$	26.6894	1.03967	0.519836	+	0.854266i	$0.325993\pi$
$660$	−0.0121485	−0.000472881 0
$661$	3.65337	0.142100	0.0710499	−	0.997473i	$-0.477365\pi$
$661$	3.65337	0.142100	0.0710499	+	0.997473i	$0.477365\pi$
$662$	−38.9808	−1.51503
$663$	5.02150	0.195019
$664$	−29.1144	−1.12986
$665$	−6.12872	−0.237662
$666$	30.8764	1.19643
$667$	1.28000	0.0495617
$668$	−1.30366	−0.0504403
$669$	1.86011	0.0719160
$670$	−0.568995	−0.0219822
$671$	1.21577	0.0469343
$672$	−0.127150	−0.00490492
$673$	8.23812	0.317556	0.158778	−	0.987314i	$-0.449245\pi$
$673$	8.23812	0.317556	0.158778	+	0.987314i	$0.449245\pi$
$674$	−10.1484	−0.390902
$675$	0.919345	0.0353856
$676$	−3.79593	−0.145997
$677$	−11.7010	−0.449706	−0.224853	−	0.974393i	$-0.572190\pi$
$677$	−11.7010	−0.449706	−0.224853	+	0.974393i	$0.572190\pi$
$678$	3.18103	0.122167
$679$	−6.28472	−0.241185
$680$	−15.2895	−0.586326
$681$	−0.0406124	−0.00155627
$682$	−4.25001	−0.162741
$683$	−18.7867	−0.718854	−0.359427	−	0.933173i	$-0.617028\pi$
$683$	−18.7867	−0.718854	−0.359427	+	0.933173i	$0.617028\pi$
$684$	−2.67083	−0.102122
$685$	12.4279	0.474845
$686$	1.36146	0.0519809
$687$	0.153831	0.00586901
$688$	−45.0117	−1.71606
$689$	−14.4283	−0.549674
$690$	0.0573403	0.00218291
$691$	10.2712	0.390736	0.195368	−	0.980730i	$-0.437410\pi$
$691$	10.2712	0.390736	0.195368	+	0.980730i	$0.437410\pi$
$692$	−0.785936	−0.0298768
$693$	1.60534	0.0609820
$694$	−29.3421	−1.11381
$695$	2.90277	0.110108
$696$	2.10166	0.0796632
$697$	−11.9766	−0.453646
$698$	41.5361	1.57216
$699$	1.54811	0.0585548
$700$	0.146418	0.00553407
$701$	32.3920	1.22343	0.611714	−	0.791079i	$-0.290480\pi$
$701$	32.3920	1.22343	0.611714	+	0.791079i	$0.290480\pi$
$702$	7.80909	0.294735
$703$	−46.6991	−1.76129
$704$	4.58290	0.172725
$705$	0.673864	0.0253792
$706$	9.73711	0.366461
$707$	−11.8294	−0.444889
$708$	−0.0273767	−0.00102888
$709$	39.2242	1.47310	0.736548	−	0.676385i	$-0.236454\pi$
$709$	39.2242	1.47310	0.736548	+	0.676385i	$0.236454\pi$
$710$	0.326907	0.0122686
$711$	−21.9414	−0.822867
$712$	−39.2429	−1.47069
$713$	−1.58456	−0.0593422
$714$	−1.09578	−0.0410085
$715$	3.36513	0.125849
$716$	−0.171527	−0.00641027
$717$	2.91163	0.108737
$718$	−38.1725	−1.42458
$719$	33.7109	1.25720	0.628602	−	0.777727i	$-0.283627\pi$
$719$	33.7109	1.25720	0.628602	+	0.777727i	$0.283627\pi$
$720$	−10.9700	−0.408826
$721$	3.21569	0.119759
$722$	−25.2705	−0.940470
$723$	−1.86735	−0.0694476
$724$	1.55085	0.0576369
$725$	−4.67518	−0.173632
$726$	−2.24286	−0.0832402
$727$	−9.10885	−0.337829	−0.168914	−	0.985631i	$-0.554026\pi$
$727$	−9.10885	−0.337829	−0.168914	+	0.985631i	$0.554026\pi$
$728$	18.2321	0.675726
$729$	−25.7305	−0.952983
$730$	−9.55342	−0.353588
$731$	63.8964	2.36329
$732$	0.0507694	0.00187649
$733$	41.0298	1.51547	0.757736	−	0.652562i	$-0.226306\pi$
$733$	41.0298	1.51547	0.757736	+	0.652562i	$0.226306\pi$
$734$	18.6525	0.688476
$735$	0.153831	0.00567414
$736$	0.226300	0.00834151
$737$	−0.225418	−0.00830339
$738$	−9.27572	−0.341444
$739$	10.0128	0.368327	0.184164	−	0.982896i	$-0.441042\pi$
$739$	10.0128	0.368327	0.184164	+	0.982896i	$0.441042\pi$
$740$	1.11566	0.0410125
$741$	−5.88206	−0.216083
$742$	3.14851	0.115585
$743$	−23.4470	−0.860188	−0.430094	−	0.902784i	$-0.641520\pi$
$743$	−23.4470	−0.860188	−0.430094	+	0.902784i	$0.641520\pi$
$744$	−2.60173	−0.0953839
$745$	−8.08313	−0.296143
$746$	−18.8863	−0.691476
$747$	29.6530	1.08495
$748$	−0.413194	−0.0151079
$749$	0.378638	0.0138351
$750$	−0.209435	−0.00764749
$751$	−4.13123	−0.150751	−0.0753753	−	0.997155i	$-0.524015\pi$
$751$	−4.13123	−0.150751	−0.0753753	+	0.997155i	$0.524015\pi$
$752$	−16.1455	−0.588766
$753$	−0.588926	−0.0214617
$754$	−39.7119	−1.44622
$755$	−3.60142	−0.131069
$756$	0.134608	0.00489566
$757$	−41.1485	−1.49557	−0.747783	−	0.663943i	$-0.768882\pi$
$757$	−41.1485	−1.49557	−0.747783	+	0.663943i	$0.768882\pi$
$758$	15.9156	0.578082
$759$	0.0227165	0.000824555 0
$760$	17.9098	0.649656
$761$	−12.9920	−0.470961	−0.235480	−	0.971879i	$-0.575666\pi$
$761$	−12.9920	−0.470961	−0.235480	+	0.971879i	$0.575666\pi$
$762$	−3.05696	−0.110742
$763$	−7.82200	−0.283175
$764$	−1.24116	−0.0449037
$765$	15.5724	0.563021
$766$	35.6011	1.28632
$767$	7.58333	0.273818
$768$	0.537598	0.0193989
$769$	−16.1411	−0.582062	−0.291031	−	0.956714i	$-0.593998\pi$
$769$	−16.1411	−0.582062	−0.291031	+	0.956714i	$0.593998\pi$
$770$	−0.734332	−0.0264635
$771$	−1.85791	−0.0669109
$772$	−2.35195	−0.0846486
$773$	−0.438035	−0.0157550	−0.00787750	−	0.999969i	$-0.502508\pi$
$773$	−0.438035	−0.0157550	−0.00787750	+	0.999969i	$0.502508\pi$
$774$	49.4869	1.77877
$775$	5.78759	0.207896
$776$	18.3656	0.659288
$777$	1.17215	0.0420505
$778$	24.3305	0.872290
$779$	14.0291	0.502645
$780$	0.140525	0.00503160
$781$	0.129510	0.00463425
$782$	1.95025	0.0697408
$783$	−4.29811	−0.153602
$784$	−3.68573	−0.131633
$785$	−10.2462	−0.365703
$786$	−0.163767	−0.00584138
$787$	−9.39113	−0.334758	−0.167379	−	0.985893i	$-0.553530\pi$
$787$	−9.39113	−0.334758	−0.167379	+	0.985893i	$0.553530\pi$
$788$	2.33348	0.0831267
$789$	4.07823	0.145189
$790$	10.0366	0.357088
$791$	−15.1886	−0.540045
$792$	−4.69125	−0.166696
$793$	−14.0631	−0.499395
$794$	25.1575	0.892806
$795$	0.355748	0.0126171
$796$	−0.888295	−0.0314848
$797$	25.1549	0.891033	0.445516	−	0.895274i	$-0.353020\pi$
$797$	25.1549	0.891033	0.445516	+	0.895274i	$0.353020\pi$
$798$	1.28357	0.0454379
$799$	22.9194	0.810829
$800$	−0.826557	−0.0292232
$801$	39.9689	1.41223
$802$	−36.1743	−1.27736
$803$	−3.78477	−0.133562
$804$	−0.00941326	−0.000331980 0
$805$	−0.273786	−0.00964968
$806$	49.1609	1.73162
$807$	−4.56413	−0.160665
$808$	34.5686	1.21612
$809$	6.39882	0.224971	0.112485	−	0.993653i	$-0.464119\pi$
$809$	6.39882	0.224971	0.112485	+	0.993653i	$0.464119\pi$
$810$	11.9640	0.420371
$811$	−9.10330	−0.319660	−0.159830	−	0.987145i	$-0.551095\pi$
$811$	−9.10330	−0.319660	−0.159830	+	0.987145i	$0.551095\pi$
$812$	−0.684530	−0.0240223
$813$	3.31324	0.116200
$814$	−5.59539	−0.196118
$815$	2.25444	0.0789697
$816$	2.96647	0.103847
$817$	−74.8467	−2.61856
$818$	17.3211	0.605617
$819$	−18.5694	−0.648868
$820$	−0.335161	−0.0117043
$821$	43.3239	1.51201	0.756007	−	0.654563i	$-0.227147\pi$
$821$	43.3239	1.51201	0.756007	+	0.654563i	$0.227147\pi$
$822$	−2.60284	−0.0907843
$823$	−41.8271	−1.45800	−0.729001	−	0.684513i	$-0.760015\pi$
$823$	−41.8271	−1.45800	−0.729001	+	0.684513i	$0.760015\pi$
$824$	−9.39711	−0.327364
$825$	−0.0829717	−0.00288870
$826$	−1.65482	−0.0575784
$827$	20.8164	0.723858	0.361929	−	0.932206i	$-0.382118\pi$
$827$	20.8164	0.723858	0.361929	+	0.932206i	$0.382118\pi$
$828$	−0.119313	−0.00414640
$829$	16.1360	0.560426	0.280213	−	0.959938i	$-0.409595\pi$
$829$	16.1360	0.560426	0.280213	+	0.959938i	$0.409595\pi$
$830$	−13.5642	−0.470819
$831$	−2.24289	−0.0778050
$832$	−53.0115	−1.83784
$833$	5.23207	0.181281
$834$	−0.607941	−0.0210513
$835$	−8.90372	−0.308126
$836$	0.484006	0.0167397
$837$	5.32079	0.183914
$838$	−15.0692	−0.520558
$839$	8.68020	0.299674	0.149837	−	0.988711i	$-0.452125\pi$
$839$	8.68020	0.299674	0.149837	+	0.988711i	$0.452125\pi$
$840$	−0.449535	−0.0155104
$841$	−7.14266	−0.246299
$842$	22.4109	0.772329
$843$	−2.76964	−0.0953914
$844$	0.0522307	0.00179785
$845$	−25.9253	−0.891858
$846$	17.7508	0.610283
$847$	10.7091	0.367968
$848$	−8.52358	−0.292701
$849$	0.414761	0.0142346
$850$	−7.12327	−0.244326
$851$	−2.08617	−0.0715128
$852$	0.00540824	0.000185283 0
$853$	23.1656	0.793177	0.396588	−	0.917997i	$-0.370194\pi$
$853$	23.1656	0.793177	0.396588	+	0.917997i	$0.370194\pi$
$854$	3.06882	0.105013
$855$	−18.2411	−0.623834
$856$	−1.10648	−0.0378188
$857$	−33.9954	−1.16126	−0.580630	−	0.814167i	$-0.697194\pi$
$857$	−33.9954	−1.16126	−0.580630	+	0.814167i	$0.697194\pi$
$858$	−0.704777	−0.0240607
$859$	−22.6096	−0.771428	−0.385714	−	0.922618i	$-0.626045\pi$
$859$	−22.6096	−0.771428	−0.385714	+	0.922618i	$0.626045\pi$
$860$	1.78812	0.0609744
$861$	−0.352130	−0.0120006
$862$	13.6190	0.463865
$863$	−48.5988	−1.65432	−0.827162	−	0.561964i	$-0.810046\pi$
$863$	−48.5988	−1.65432	−0.827162	+	0.561964i	$0.810046\pi$
$864$	−0.759891	−0.0258520
$865$	−5.36776	−0.182509
$866$	16.0329	0.544821
$867$	−1.59593	−0.0542006
$868$	0.847407	0.0287629
$869$	3.97620	0.134883
$870$	0.979147	0.0331962
$871$	2.60747	0.0883506
$872$	22.8580	0.774069
$873$	−18.7054	−0.633083
$874$	−2.28448	−0.0772736
$875$	1.00000	0.0338062
$876$	−0.158048	−0.00533996
$877$	−27.9812	−0.944857	−0.472429	−	0.881369i	$-0.656623\pi$
$877$	−27.9812	−0.944857	−0.472429	+	0.881369i	$0.656623\pi$
$878$	−21.6446	−0.730470
$879$	2.96444	0.0999879
$880$	1.98797	0.0670144
$881$	−39.3307	−1.32509	−0.662543	−	0.749024i	$-0.730523\pi$
$881$	−39.3307	−1.32509	−0.662543	+	0.749024i	$0.730523\pi$
$882$	4.05217	0.136444
$883$	−25.1041	−0.844819	−0.422409	−	0.906405i	$-0.638815\pi$
$883$	−25.1041	−0.844819	−0.422409	+	0.906405i	$0.638815\pi$
$884$	4.77952	0.160753
$885$	−0.186977	−0.00628515
$886$	2.76421	0.0928655
$887$	42.0244	1.41104	0.705521	−	0.708689i	$-0.250713\pi$
$887$	42.0244	1.41104	0.705521	+	0.708689i	$0.250713\pi$
$888$	−3.42532	−0.114946
$889$	14.5962	0.489541
$890$	−18.2830	−0.612846
$891$	4.73975	0.158788
$892$	1.77047	0.0592798
$893$	−26.8472	−0.898407
$894$	1.69289	0.0566187
$895$	−1.17149	−0.0391586
$896$	9.91494	0.331235
$897$	−0.262767	−0.00877352
$898$	43.1779	1.44086
$899$	−27.0581	−0.902437
$900$	0.435789	0.0145263
$901$	12.0996	0.403098
$902$	1.68094	0.0559691
$903$	1.87865	0.0625176
$904$	44.3852	1.47623
$905$	10.5920	0.352088
$906$	0.754264	0.0250588
$907$	14.7922	0.491168	0.245584	−	0.969375i	$-0.421020\pi$
$907$	14.7922	0.491168	0.245584	+	0.969375i	$0.421020\pi$
$908$	−0.0386554	−0.00128282
$909$	−35.2082	−1.16778
$910$	8.49419	0.281580
$911$	−15.0604	−0.498974	−0.249487	−	0.968378i	$-0.580262\pi$
$911$	−15.0604	−0.498974	−0.249487	+	0.968378i	$0.580262\pi$
$912$	−3.47485	−0.115064
$913$	−5.37370	−0.177844
$914$	−7.85968	−0.259975
$915$	0.346743	0.0114630
$916$	0.146418	0.00483778
$917$	0.781948	0.0258222
$918$	−6.54874	−0.216141
$919$	37.2266	1.22799	0.613997	−	0.789309i	$-0.289561\pi$
$919$	37.2266	1.22799	0.613997	+	0.789309i	$0.289561\pi$
$920$	0.800075	0.0263777
$921$	−2.93260	−0.0966325
$922$	9.69730	0.319364
$923$	−1.49808	−0.0493099
$924$	−0.0121485	−0.000399657 0
$925$	7.61970	0.250534
$926$	20.2461	0.665328
$927$	9.57098	0.314352
$928$	3.86431	0.126852
$929$	−6.70418	−0.219957	−0.109978	−	0.993934i	$-0.535078\pi$
$929$	−6.70418	−0.219957	−0.109978	+	0.993934i	$0.535078\pi$
$930$	−1.21212	−0.0397471
$931$	−6.12872	−0.200861
$932$	1.47351	0.0482663
$933$	2.10578	0.0689402
$934$	−17.2709	−0.565122
$935$	−2.82202	−0.0922899
$936$	54.2648	1.77370
$937$	−14.7195	−0.480866	−0.240433	−	0.970666i	$-0.577289\pi$
$937$	−14.7195	−0.480866	−0.240433	+	0.970666i	$0.577289\pi$
$938$	−0.568995	−0.0185783
$939$	0.375186	0.0122437
$940$	0.641391	0.0209199
$941$	14.6861	0.478754	0.239377	−	0.970927i	$-0.423057\pi$
$941$	14.6861	0.478754	0.239377	+	0.970927i	$0.423057\pi$
$942$	2.14592	0.0699177
$943$	0.626715	0.0204087
$944$	4.47989	0.145808
$945$	0.919345	0.0299063
$946$	−8.96799	−0.291574
$947$	−48.8657	−1.58792	−0.793960	−	0.607969i	$-0.791984\pi$
$947$	−48.8657	−1.58792	−0.793960	+	0.607969i	$0.791984\pi$
$948$	0.166043	0.00539282
$949$	43.7793	1.42114
$950$	8.34403	0.270716
$951$	3.12745	0.101415
$952$	−15.2895	−0.495536
$953$	−18.7103	−0.606086	−0.303043	−	0.952977i	$-0.598003\pi$
$953$	−18.7103	−0.606086	−0.303043	+	0.952977i	$0.598003\pi$
$954$	9.37102	0.303398
$955$	−8.47686	−0.274305
$956$	2.77132	0.0896309
$957$	0.387908	0.0125393
$958$	16.8132	0.543210
$959$	12.4279	0.401318
$960$	1.30707	0.0421854
$961$	2.49623	0.0805237
$962$	64.7232	2.08676
$963$	1.12695	0.0363156
$964$	−1.77737	−0.0572451
$965$	−16.0633	−0.517096
$966$	0.0573403	0.00184489
$967$	−11.3486	−0.364946	−0.182473	−	0.983211i	$-0.558410\pi$
$967$	−11.3486	−0.364946	−0.182473	+	0.983211i	$0.558410\pi$
$968$	−31.2948	−1.00585
$969$	4.93273	0.158462
$970$	8.55641	0.274730
$971$	−11.8305	−0.379658	−0.189829	−	0.981817i	$-0.560793\pi$
$971$	−11.8305	−0.379658	−0.189829	+	0.981817i	$0.560793\pi$
$972$	0.601753	0.0193012
$973$	2.90277	0.0930585
$974$	15.7332	0.504124
$975$	0.959753	0.0307367
$976$	−8.30783	−0.265927
$977$	36.7674	1.17629	0.588146	−	0.808755i	$-0.299858\pi$
$977$	36.7674	1.17629	0.588146	+	0.808755i	$0.299858\pi$
$978$	−0.472159	−0.0150980
$979$	−7.24314	−0.231492
$980$	0.146418	0.00467715
$981$	−23.2809	−0.743302
$982$	−10.6693	−0.340473
$983$	−19.8285	−0.632430	−0.316215	−	0.948688i	$-0.602412\pi$
$983$	−19.8285	−0.632430	−0.316215	+	0.948688i	$0.602412\pi$
$984$	1.02902	0.0328039
$985$	15.9371	0.507798
$986$	33.3026	1.06057
$987$	0.673864	0.0214493
$988$	−5.59861	−0.178116
$989$	−3.34359	−0.106320
$990$	−2.18562	−0.0694635
$991$	−43.7413	−1.38949	−0.694745	−	0.719257i	$-0.744483\pi$
$991$	−43.7413	−1.38949	−0.694745	+	0.719257i	$0.744483\pi$
$992$	−4.78378	−0.151885
$993$	−4.40442	−0.139770
$994$	0.326907	0.0103689
$995$	−6.06685	−0.192332
$996$	−0.224401	−0.00711042
$997$	44.1340	1.39774	0.698869	−	0.715250i	$-0.253687\pi$
$997$	44.1340	1.39774	0.698869	+	0.715250i	$0.253687\pi$
$998$	50.2781	1.59153
$999$	7.00513	0.221633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.k.1.15	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.k.1.15	✓	49	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)

\(f(q)\)	\(=\)	\(q-1.36146 q^{2} -0.153831 q^{3} -0.146418 q^{4} -1.00000 q^{5} +0.209435 q^{6} -1.00000 q^{7} +2.92227 q^{8} -2.97634 q^{9} +O(q^{10})\)	\(q-1.36146 q^{2} -0.153831 q^{3} -0.146418 q^{4} -1.00000 q^{5} +0.209435 q^{6} -1.00000 q^{7} +2.92227 q^{8} -2.97634 q^{9} +1.36146 q^{10} +0.539369 q^{11} +0.0225236 q^{12} -6.23902 q^{13} +1.36146 q^{14} +0.153831 q^{15} -3.68573 q^{16} +5.23207 q^{17} +4.05217 q^{18} -6.12872 q^{19} +0.146418 q^{20} +0.153831 q^{21} -0.734332 q^{22} -0.273786 q^{23} -0.449535 q^{24} +1.00000 q^{25} +8.49419 q^{26} +0.919345 q^{27} +0.146418 q^{28} -4.67518 q^{29} -0.209435 q^{30} +5.78759 q^{31} -0.826557 q^{32} -0.0829717 q^{33} -7.12327 q^{34} +1.00000 q^{35} +0.435789 q^{36} +7.61970 q^{37} +8.34403 q^{38} +0.959753 q^{39} -2.92227 q^{40} -2.28907 q^{41} -0.209435 q^{42} +12.2124 q^{43} -0.0789733 q^{44} +2.97634 q^{45} +0.372749 q^{46} +4.38055 q^{47} +0.566978 q^{48} +1.00000 q^{49} -1.36146 q^{50} -0.804854 q^{51} +0.913503 q^{52} +2.31259 q^{53} -1.25165 q^{54} -0.539369 q^{55} -2.92227 q^{56} +0.942787 q^{57} +6.36509 q^{58} -1.21547 q^{59} -0.0225236 q^{60} +2.25406 q^{61} -7.87960 q^{62} +2.97634 q^{63} +8.49678 q^{64} +6.23902 q^{65} +0.112963 q^{66} -0.417929 q^{67} -0.766069 q^{68} +0.0421167 q^{69} -1.36146 q^{70} +0.240115 q^{71} -8.69765 q^{72} -7.01702 q^{73} -10.3739 q^{74} -0.153831 q^{75} +0.897355 q^{76} -0.539369 q^{77} -1.30667 q^{78} +7.37195 q^{79} +3.68573 q^{80} +8.78758 q^{81} +3.11649 q^{82} -9.96293 q^{83} -0.0225236 q^{84} -5.23207 q^{85} -16.6268 q^{86} +0.719187 q^{87} +1.57618 q^{88} -13.4289 q^{89} -4.05217 q^{90} +6.23902 q^{91} +0.0400871 q^{92} -0.890310 q^{93} -5.96396 q^{94} +6.12872 q^{95} +0.127150 q^{96} +6.28472 q^{97} -1.36146 q^{98} -1.60534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9	\( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 49 * q - 3 * q^2 - 10 * q^3 + 49 * q^4 - 49 * q^5 + 10 * q^6 - 49 * q^7 - 6 * q^8 + 39 * q^9 + 3 * q^10 + 16 * q^11 - 26 * q^12 - 31 * q^13 + 3 * q^14 + 10 * q^15 + 49 * q^16 - 18 * q^17 + 4 * q^18 - 16 * q^19 - 49 * q^20 + 10 * q^21 + 10 * q^22 + 10 * q^23 + 2 * q^24 + 49 * q^25 - 22 * q^26 - 58 * q^27 - 49 * q^28 + 31 * q^29 - 10 * q^30 - 35 * q^31 - 5 * q^32 - 82 * q^33 - 41 * q^34 + 49 * q^35 + 49 * q^36 - 24 * q^37 - 20 * q^38 + 41 * q^39 + 6 * q^40 + 30 * q^41 - 10 * q^42 - 19 * q^43 + 27 * q^44 - 39 * q^45 + 15 * q^46 - 39 * q^47 - 51 * q^48 + 49 * q^49 - 3 * q^50 + 46 * q^51 - 94 * q^52 - 17 * q^53 + 9 * q^54 - 16 * q^55 + 6 * q^56 - 23 * q^57 - 46 * q^58 + 11 * q^59 + 26 * q^60 - 9 * q^61 - 49 * q^62 - 39 * q^63 + 10 * q^64 + 31 * q^65 - 10 * q^66 - 2 * q^67 - 73 * q^68 - 47 * q^69 - 3 * q^70 + 26 * q^71 - 39 * q^72 - 100 * q^73 + 8 * q^74 - 10 * q^75 - 71 * q^76 - 16 * q^77 - 51 * q^78 + 50 * q^79 - 49 * q^80 + 61 * q^81 - 36 * q^82 - 67 * q^83 + 26 * q^84 + 18 * q^85 + 33 * q^86 - 45 * q^87 - q^88 - 19 * q^89 - 4 * q^90 + 31 * q^91 + 7 * q^92 + 9 * q^93 - 33 * q^94 + 16 * q^95 - 8 * q^96 - 85 * q^97 - 3 * q^98 + 27 * q^99

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