LMFDB - Embedded newform 9295.2.a.bj.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9295,2,Mod(1,9295)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9295, 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("9295.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9295 = 5 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9295.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:	$74.2209486788$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 715)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	9295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.934466 q^{2} -0.693282 q^{3} -1.12677 q^{4} -1.00000 q^{5} -0.647848 q^{6} +0.485111 q^{7} -2.92186 q^{8} -2.51936 q^{9} +O(q^{10})$	\(q+0.934466 q^{2} -0.693282 q^{3} -1.12677 q^{4} -1.00000 q^{5} -0.647848 q^{6} +0.485111 q^{7} -2.92186 q^{8} -2.51936 q^{9} -0.934466 q^{10} -1.00000 q^{11} +0.781172 q^{12} +0.453319 q^{14} +0.693282 q^{15} -0.476832 q^{16} -4.71596 q^{17} -2.35426 q^{18} -6.26788 q^{19} +1.12677 q^{20} -0.336318 q^{21} -0.934466 q^{22} -1.64676 q^{23} +2.02567 q^{24} +1.00000 q^{25} +3.82647 q^{27} -0.546610 q^{28} -10.2556 q^{29} +0.647848 q^{30} -1.89308 q^{31} +5.39814 q^{32} +0.693282 q^{33} -4.40690 q^{34} -0.485111 q^{35} +2.83875 q^{36} +1.72129 q^{37} -5.85712 q^{38} +2.92186 q^{40} -2.81830 q^{41} -0.314278 q^{42} +2.14492 q^{43} +1.12677 q^{44} +2.51936 q^{45} -1.53884 q^{46} -2.90646 q^{47} +0.330579 q^{48} -6.76467 q^{49} +0.934466 q^{50} +3.26949 q^{51} +9.25802 q^{53} +3.57571 q^{54} +1.00000 q^{55} -1.41743 q^{56} +4.34541 q^{57} -9.58348 q^{58} -10.0149 q^{59} -0.781172 q^{60} -14.3001 q^{61} -1.76902 q^{62} -1.22217 q^{63} +5.99804 q^{64} +0.647848 q^{66} -7.15968 q^{67} +5.31382 q^{68} +1.14167 q^{69} -0.453319 q^{70} -4.76178 q^{71} +7.36122 q^{72} +8.36628 q^{73} +1.60849 q^{74} -0.693282 q^{75} +7.06248 q^{76} -0.485111 q^{77} -13.1974 q^{79} +0.476832 q^{80} +4.90526 q^{81} -2.63360 q^{82} -0.355851 q^{83} +0.378955 q^{84} +4.71596 q^{85} +2.00436 q^{86} +7.11001 q^{87} +2.92186 q^{88} +0.571579 q^{89} +2.35426 q^{90} +1.85553 q^{92} +1.31244 q^{93} -2.71599 q^{94} +6.26788 q^{95} -3.74244 q^{96} +6.62212 q^{97} -6.32135 q^{98} +2.51936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 34 q^{4} - 28 q^{5} + 10 q^{6} - 8 q^{7} - 6 q^{8} + 46 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 34 * q^4 - 28 * q^5 + 10 * q^6 - 8 * q^7 - 6 * q^8 + 46 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 34 q^{4} - 28 q^{5} + 10 q^{6} - 8 q^{7} - 6 q^{8} + 46 q^{9} + 2 q^{10} - 28 q^{11} + 22 q^{12} + 16 q^{14} - 6 q^{15} + 54 q^{16} + 26 q^{17} - 36 q^{18} + 8 q^{19} - 34 q^{20} + 10 q^{21} + 2 q^{22} + 30 q^{23} + 26 q^{24} + 28 q^{25} + 4 q^{28} + 36 q^{29} - 10 q^{30} - 20 q^{31} + 16 q^{32} - 6 q^{33} - 8 q^{34} + 8 q^{35} + 58 q^{36} - 50 q^{37} + 18 q^{38} + 6 q^{40} + 6 q^{41} + 74 q^{42} - 34 q^{44} - 46 q^{45} + 24 q^{46} - 10 q^{47} + 50 q^{48} + 46 q^{49} - 2 q^{50} + 12 q^{51} + 52 q^{53} + 38 q^{54} + 28 q^{55} + 10 q^{57} - 42 q^{58} - 12 q^{59} - 22 q^{60} + 4 q^{61} + 14 q^{62} + 48 q^{63} + 56 q^{64} - 10 q^{66} - 52 q^{67} + 92 q^{68} - 16 q^{69} - 16 q^{70} + 20 q^{71} - 50 q^{72} - 40 q^{73} + 32 q^{74} + 6 q^{75} - 16 q^{76} + 8 q^{77} - 6 q^{79} - 54 q^{80} + 116 q^{81} - 36 q^{82} - 22 q^{83} + 86 q^{84} - 26 q^{85} + 32 q^{86} + 16 q^{87} + 6 q^{88} + 8 q^{89} + 36 q^{90} + 18 q^{92} - 40 q^{93} + 66 q^{94} - 8 q^{95} + 4 q^{96} - 48 q^{97} + 70 q^{98} - 46 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 34 * q^4 - 28 * q^5 + 10 * q^6 - 8 * q^7 - 6 * q^8 + 46 * q^9 + 2 * q^10 - 28 * q^11 + 22 * q^12 + 16 * q^14 - 6 * q^15 + 54 * q^16 + 26 * q^17 - 36 * q^18 + 8 * q^19 - 34 * q^20 + 10 * q^21 + 2 * q^22 + 30 * q^23 + 26 * q^24 + 28 * q^25 + 4 * q^28 + 36 * q^29 - 10 * q^30 - 20 * q^31 + 16 * q^32 - 6 * q^33 - 8 * q^34 + 8 * q^35 + 58 * q^36 - 50 * q^37 + 18 * q^38 + 6 * q^40 + 6 * q^41 + 74 * q^42 - 34 * q^44 - 46 * q^45 + 24 * q^46 - 10 * q^47 + 50 * q^48 + 46 * q^49 - 2 * q^50 + 12 * q^51 + 52 * q^53 + 38 * q^54 + 28 * q^55 + 10 * q^57 - 42 * q^58 - 12 * q^59 - 22 * q^60 + 4 * q^61 + 14 * q^62 + 48 * q^63 + 56 * q^64 - 10 * q^66 - 52 * q^67 + 92 * q^68 - 16 * q^69 - 16 * q^70 + 20 * q^71 - 50 * q^72 - 40 * q^73 + 32 * q^74 + 6 * q^75 - 16 * q^76 + 8 * q^77 - 6 * q^79 - 54 * q^80 + 116 * q^81 - 36 * q^82 - 22 * q^83 + 86 * q^84 - 26 * q^85 + 32 * q^86 + 16 * q^87 + 6 * q^88 + 8 * q^89 + 36 * q^90 + 18 * q^92 - 40 * q^93 + 66 * q^94 - 8 * q^95 + 4 * q^96 - 48 * q^97 + 70 * q^98 - 46 * 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 $

$2$	0.934466	0.660767	0.330383	−	0.943847i	$-0.392822\pi$
$2$	0.934466	0.660767	0.330383	+	0.943847i	$0.392822\pi$
$3$	−0.693282	−0.400267	−0.200133	−	0.979769i	$-0.564138\pi$
$3$	−0.693282	−0.400267	−0.200133	+	0.979769i	$0.564138\pi$
$4$	−1.12677	−0.563387
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.647848	−0.264483
$7$	0.485111	0.183355	0.0916773	−	0.995789i	$-0.470777\pi$
$7$	0.485111	0.183355	0.0916773	+	0.995789i	$0.470777\pi$
$8$	−2.92186	−1.03303
$9$	−2.51936	−0.839787
$10$	−0.934466	−0.295504
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.781172	0.225505
$13$	0	0
$13$	0	0
$14$	0.453319	0.121155
$15$	0.693282	0.179005
$16$	−0.476832	−0.119208
$17$	−4.71596	−1.14379	−0.571894	−	0.820328i	$-0.693791\pi$
$17$	−4.71596	−1.14379	−0.571894	+	0.820328i	$0.693791\pi$
$18$	−2.35426	−0.554903
$19$	−6.26788	−1.43795	−0.718975	−	0.695036i	$-0.755388\pi$
$19$	−6.26788	−1.43795	−0.718975	+	0.695036i	$0.755388\pi$
$20$	1.12677	0.251954
$21$	−0.336318	−0.0733907
$22$	−0.934466	−0.199229
$23$	−1.64676	−0.343373	−0.171687	−	0.985152i	$-0.554922\pi$
$23$	−1.64676	−0.343373	−0.171687	+	0.985152i	$0.554922\pi$
$24$	2.02567	0.413489
$25$	1.00000	0.200000
$26$	0	0
$27$	3.82647	0.736405
$28$	−0.546610	−0.103300
$29$	−10.2556	−1.90441	−0.952206	−	0.305455i	$-0.901191\pi$
$29$	−10.2556	−1.90441	−0.952206	+	0.305455i	$0.901191\pi$
$30$	0.647848	0.118280
$31$	−1.89308	−0.340007	−0.170004	−	0.985443i	$-0.554378\pi$
$31$	−1.89308	−0.340007	−0.170004	+	0.985443i	$0.554378\pi$
$32$	5.39814	0.954266
$33$	0.693282	0.120685
$34$	−4.40690	−0.755777
$35$	−0.485111	−0.0819987
$36$	2.83875	0.473125
$37$	1.72129	0.282979	0.141489	−	0.989940i	$-0.454811\pi$
$37$	1.72129	0.282979	0.141489	+	0.989940i	$0.454811\pi$
$38$	−5.85712	−0.950150
$39$	0	0
$40$	2.92186	0.461987
$41$	−2.81830	−0.440144	−0.220072	−	0.975484i	$-0.570629\pi$
$41$	−2.81830	−0.440144	−0.220072	+	0.975484i	$0.570629\pi$
$42$	−0.314278	−0.0484942
$43$	2.14492	0.327098	0.163549	−	0.986535i	$-0.447706\pi$
$43$	2.14492	0.327098	0.163549	+	0.986535i	$0.447706\pi$
$44$	1.12677	0.169868
$45$	2.51936	0.375564
$46$	−1.53884	−0.226890
$47$	−2.90646	−0.423951	−0.211976	−	0.977275i	$-0.567990\pi$
$47$	−2.90646	−0.423951	−0.211976	+	0.977275i	$0.567990\pi$
$48$	0.330579	0.0477150
$49$	−6.76467	−0.966381
$50$	0.934466	0.132153
$51$	3.26949	0.457820
$52$	0	0
$53$	9.25802	1.27169	0.635843	−	0.771818i	$-0.280653\pi$
$53$	9.25802	1.27169	0.635843	+	0.771818i	$0.280653\pi$
$54$	3.57571	0.486592
$55$	1.00000	0.134840
$56$	−1.41743	−0.189412
$57$	4.34541	0.575563
$58$	−9.58348	−1.25837
$59$	−10.0149	−1.30383	−0.651917	−	0.758290i	$-0.726035\pi$
$59$	−10.0149	−1.30383	−0.651917	+	0.758290i	$0.726035\pi$
$60$	−0.781172	−0.100849
$61$	−14.3001	−1.83094	−0.915468	−	0.402390i	$-0.868180\pi$
$61$	−14.3001	−1.83094	−0.915468	+	0.402390i	$0.868180\pi$
$62$	−1.76902	−0.224665
$63$	−1.22217	−0.153979
$64$	5.99804	0.749755
$65$	0	0
$66$	0.647848	0.0797446
$67$	−7.15968	−0.874694	−0.437347	−	0.899293i	$-0.644082\pi$
$67$	−7.15968	−0.874694	−0.437347	+	0.899293i	$0.644082\pi$
$68$	5.31382	0.644395
$69$	1.14167	0.137441
$70$	−0.453319	−0.0541820
$71$	−4.76178	−0.565120	−0.282560	−	0.959250i	$-0.591184\pi$
$71$	−4.76178	−0.565120	−0.282560	+	0.959250i	$0.591184\pi$
$72$	7.36122	0.867529
$73$	8.36628	0.979199	0.489600	−	0.871947i	$-0.337143\pi$
$73$	8.36628	0.979199	0.489600	+	0.871947i	$0.337143\pi$
$74$	1.60849	0.186983
$75$	−0.693282	−0.0800533
$76$	7.06248	0.810122
$77$	−0.485111	−0.0552835
$78$	0	0
$79$	−13.1974	−1.48483	−0.742413	−	0.669942i	$-0.766319\pi$
$79$	−13.1974	−1.48483	−0.742413	+	0.669942i	$0.766319\pi$
$80$	0.476832	0.0533114
$81$	4.90526	0.545028
$82$	−2.63360	−0.290833
$83$	−0.355851	−0.0390598	−0.0195299	−	0.999809i	$-0.506217\pi$
$83$	−0.355851	−0.0390598	−0.0195299	+	0.999809i	$0.506217\pi$
$84$	0.378955	0.0413474
$85$	4.71596	0.511518
$86$	2.00436	0.216135
$87$	7.11001	0.762273
$88$	2.92186	0.311472
$89$	0.571579	0.0605872	0.0302936	−	0.999541i	$-0.490356\pi$
$89$	0.571579	0.0605872	0.0302936	+	0.999541i	$0.490356\pi$
$90$	2.35426	0.248160
$91$	0	0
$92$	1.85553	0.193452
$93$	1.31244	0.136093
$94$	−2.71599	−0.280133
$95$	6.26788	0.643071
$96$	−3.74244	−0.381961
$97$	6.62212	0.672374	0.336187	−	0.941795i	$-0.390863\pi$
$97$	6.62212	0.672374	0.336187	+	0.941795i	$0.390863\pi$
$98$	−6.32135	−0.638553
$99$	2.51936	0.253205
$100$	−1.12677	−0.112677
$101$	−2.48819	−0.247584	−0.123792	−	0.992308i	$-0.539506\pi$
$101$	−2.48819	−0.247584	−0.123792	+	0.992308i	$0.539506\pi$
$102$	3.05523	0.302512
$103$	16.7569	1.65111	0.825553	−	0.564325i	$-0.190864\pi$
$103$	16.7569	1.65111	0.825553	+	0.564325i	$0.190864\pi$
$104$	0	0
$105$	0.336318	0.0328213
$106$	8.65130	0.840288
$107$	−8.03288	−0.776568	−0.388284	−	0.921540i	$-0.626932\pi$
$107$	−8.03288	−0.776568	−0.388284	+	0.921540i	$0.626932\pi$
$108$	−4.31157	−0.414881
$109$	−16.6673	−1.59644	−0.798218	−	0.602369i	$-0.794224\pi$
$109$	−16.6673	−1.59644	−0.798218	+	0.602369i	$0.794224\pi$
$110$	0.934466	0.0890978
$111$	−1.19334	−0.113267
$112$	−0.231316	−0.0218573
$113$	−4.42626	−0.416388	−0.208194	−	0.978088i	$-0.566758\pi$
$113$	−4.42626	−0.416388	−0.208194	+	0.978088i	$0.566758\pi$
$114$	4.06063	0.380313
$115$	1.64676	0.153561
$116$	11.5557	1.07292
$117$	0	0
$118$	−9.35862	−0.861531
$119$	−2.28776	−0.209719
$120$	−2.02567	−0.184918
$121$	1.00000	0.0909091
$122$	−13.3629	−1.20982
$123$	1.95388	0.176175
$124$	2.13307	0.191556
$125$	−1.00000	−0.0894427
$126$	−1.14207	−0.101744
$127$	−1.46185	−0.129719	−0.0648593	−	0.997894i	$-0.520660\pi$
$127$	−1.46185	−0.129719	−0.0648593	+	0.997894i	$0.520660\pi$
$128$	−5.19132	−0.458852
$129$	−1.48704	−0.130926
$130$	0	0
$131$	13.6653	1.19394	0.596970	−	0.802263i	$-0.296371\pi$
$131$	13.6653	1.19394	0.596970	+	0.802263i	$0.296371\pi$
$132$	−0.781172	−0.0679923
$133$	−3.04061	−0.263655
$134$	−6.69048	−0.577969
$135$	−3.82647	−0.329330
$136$	13.7794	1.18157
$137$	12.6688	1.08237	0.541186	−	0.840903i	$-0.317976\pi$
$137$	12.6688	1.08237	0.541186	+	0.840903i	$0.317976\pi$
$138$	1.06685	0.0908163
$139$	1.95925	0.166181	0.0830905	−	0.996542i	$-0.473521\pi$
$139$	1.95925	0.166181	0.0830905	+	0.996542i	$0.473521\pi$
$140$	0.546610	0.0461970
$141$	2.01500	0.169693
$142$	−4.44972	−0.373412
$143$	0	0
$144$	1.20131	0.100109
$145$	10.2556	0.851679
$146$	7.81800	0.647022
$147$	4.68982	0.386810
$148$	−1.93951	−0.159427
$149$	16.6128	1.36097	0.680487	−	0.732760i	$-0.261768\pi$
$149$	16.6128	1.36097	0.680487	+	0.732760i	$0.261768\pi$
$150$	−0.647848	−0.0528966
$151$	9.10563	0.741005	0.370503	−	0.928831i	$-0.379185\pi$
$151$	9.10563	0.741005	0.370503	+	0.928831i	$0.379185\pi$
$152$	18.3139	1.48545
$153$	11.8812	0.960538
$154$	−0.453319	−0.0365295
$155$	1.89308	0.152056
$156$	0	0
$157$	−15.4020	−1.22922	−0.614609	−	0.788832i	$-0.710686\pi$
$157$	−15.4020	−1.22922	−0.614609	+	0.788832i	$0.710686\pi$
$158$	−12.3325	−0.981124
$159$	−6.41842	−0.509013
$160$	−5.39814	−0.426761
$161$	−0.798861	−0.0629590
$162$	4.58379	0.360137
$163$	−2.25027	−0.176255	−0.0881275	−	0.996109i	$-0.528088\pi$
$163$	−2.25027	−0.176255	−0.0881275	+	0.996109i	$0.528088\pi$
$164$	3.17559	0.247972
$165$	−0.693282	−0.0539719
$166$	−0.332531	−0.0258094
$167$	14.6973	1.13731	0.568657	−	0.822575i	$-0.307463\pi$
$167$	14.6973	1.13731	0.568657	+	0.822575i	$0.307463\pi$
$168$	0.982676	0.0758151
$169$	0	0
$170$	4.40690	0.337994
$171$	15.7910	1.20757
$172$	−2.41685	−0.184283
$173$	−5.04990	−0.383937	−0.191968	−	0.981401i	$-0.561487\pi$
$173$	−5.04990	−0.383937	−0.191968	+	0.981401i	$0.561487\pi$
$174$	6.64406	0.503685
$175$	0.485111	0.0366709
$176$	0.476832	0.0359426
$177$	6.94318	0.521881
$178$	0.534121	0.0400340
$179$	12.5091	0.934975	0.467488	−	0.884000i	$-0.345159\pi$
$179$	12.5091	0.934975	0.467488	+	0.884000i	$0.345159\pi$
$180$	−2.83875	−0.211588
$181$	−12.2525	−0.910721	−0.455361	−	0.890307i	$-0.650490\pi$
$181$	−12.2525	−0.910721	−0.455361	+	0.890307i	$0.650490\pi$
$182$	0	0
$183$	9.91398	0.732863
$184$	4.81161	0.354716
$185$	−1.72129	−0.126552
$186$	1.22643	0.0899261
$187$	4.71596	0.344865
$188$	3.27493	0.238849
$189$	1.85626	0.135023
$190$	5.85712	0.424920
$191$	6.06745	0.439026	0.219513	−	0.975610i	$-0.429553\pi$
$191$	6.06745	0.439026	0.219513	+	0.975610i	$0.429553\pi$
$192$	−4.15833	−0.300102
$193$	−0.0778172	−0.00560140	−0.00280070	−	0.999996i	$-0.500891\pi$
$193$	−0.0778172	−0.00560140	−0.00280070	+	0.999996i	$0.500891\pi$
$194$	6.18814	0.444283
$195$	0	0
$196$	7.62225	0.544447
$197$	−22.0697	−1.57240	−0.786200	−	0.617972i	$-0.787954\pi$
$197$	−22.0697	−1.57240	−0.786200	+	0.617972i	$0.787954\pi$
$198$	2.35426	0.167310
$199$	−20.9771	−1.48703	−0.743513	−	0.668722i	$-0.766842\pi$
$199$	−20.9771	−1.48703	−0.743513	+	0.668722i	$0.766842\pi$
$200$	−2.92186	−0.206607
$201$	4.96368	0.350111
$202$	−2.32513	−0.163596
$203$	−4.97509	−0.349183
$204$	−3.68398	−0.257930
$205$	2.81830	0.196839
$206$	15.6587	1.09100
$207$	4.14878	0.288360
$208$	0	0
$209$	6.26788	0.433558
$210$	0.314278	0.0216872
$211$	21.8969	1.50745	0.753724	−	0.657191i	$-0.228256\pi$
$211$	21.8969	1.50745	0.753724	+	0.657191i	$0.228256\pi$
$212$	−10.4317	−0.716452
$213$	3.30126	0.226199
$214$	−7.50645	−0.513130
$215$	−2.14492	−0.146283
$216$	−11.1804	−0.760732
$217$	−0.918353	−0.0623419
$218$	−15.5750	−1.05487
$219$	−5.80019	−0.391941
$220$	−1.12677	−0.0759671
$221$	0	0
$222$	−1.11514	−0.0748431
$223$	−7.31394	−0.489778	−0.244889	−	0.969551i	$-0.578751\pi$
$223$	−7.31394	−0.489778	−0.244889	+	0.969551i	$0.578751\pi$
$224$	2.61870	0.174969
$225$	−2.51936	−0.167957
$226$	−4.13619	−0.275135
$227$	−18.2367	−1.21041	−0.605207	−	0.796069i	$-0.706909\pi$
$227$	−18.2367	−1.21041	−0.605207	+	0.796069i	$0.706909\pi$
$228$	−4.89629	−0.324265
$229$	2.75048	0.181757	0.0908784	−	0.995862i	$-0.471033\pi$
$229$	2.75048	0.181757	0.0908784	+	0.995862i	$0.471033\pi$
$230$	1.53884	0.101468
$231$	0.336318	0.0221281
$232$	29.9654	1.96732
$233$	14.9838	0.981619	0.490810	−	0.871267i	$-0.336701\pi$
$233$	14.9838	0.981619	0.490810	+	0.871267i	$0.336701\pi$
$234$	0	0
$235$	2.90646	0.189597
$236$	11.2846	0.734563
$237$	9.14954	0.594326
$238$	−2.13783	−0.138575
$239$	−13.9019	−0.899239	−0.449620	−	0.893220i	$-0.648440\pi$
$239$	−13.9019	−0.899239	−0.449620	+	0.893220i	$0.648440\pi$
$240$	−0.330579	−0.0213388
$241$	−17.7304	−1.14212	−0.571059	−	0.820909i	$-0.693467\pi$
$241$	−17.7304	−1.14212	−0.571059	+	0.820909i	$0.693467\pi$
$242$	0.934466	0.0600697
$243$	−14.8801	−0.954562
$244$	16.1130	1.03153
$245$	6.76467	0.432179
$246$	1.82583	0.116411
$247$	0	0
$248$	5.53132	0.351239
$249$	0.246705	0.0156343
$250$	−0.934466	−0.0591008
$251$	−18.0424	−1.13883	−0.569415	−	0.822051i	$-0.692830\pi$
$251$	−18.0424	−1.13883	−0.569415	+	0.822051i	$0.692830\pi$
$252$	1.37711	0.0867496
$253$	1.64676	0.103531
$254$	−1.36605	−0.0857137
$255$	−3.26949	−0.204743
$256$	−16.8472	−1.05295
$257$	21.0361	1.31220	0.656098	−	0.754676i	$-0.272206\pi$
$257$	21.0361	1.31220	0.656098	+	0.754676i	$0.272206\pi$
$258$	−1.38959	−0.0865118
$259$	0.835018	0.0518855
$260$	0	0
$261$	25.8375	1.59930
$262$	12.7697	0.788917
$263$	5.59107	0.344760	0.172380	−	0.985031i	$-0.444854\pi$
$263$	5.59107	0.344760	0.172380	+	0.985031i	$0.444854\pi$
$264$	−2.02567	−0.124672
$265$	−9.25802	−0.568715
$266$	−2.84135	−0.174214
$267$	−0.396265	−0.0242510
$268$	8.06734	0.492792
$269$	−21.8005	−1.32920	−0.664599	−	0.747200i	$-0.731398\pi$
$269$	−21.8005	−1.32920	−0.664599	+	0.747200i	$0.731398\pi$
$270$	−3.57571	−0.217611
$271$	−16.4605	−0.999903	−0.499952	−	0.866053i	$-0.666649\pi$
$271$	−16.4605	−0.999903	−0.499952	+	0.866053i	$0.666649\pi$
$272$	2.24872	0.136349
$273$	0	0
$274$	11.8386	0.715195
$275$	−1.00000	−0.0603023
$276$	−1.28640	−0.0774324
$277$	4.12961	0.248124	0.124062	−	0.992274i	$-0.460408\pi$
$277$	4.12961	0.248124	0.124062	+	0.992274i	$0.460408\pi$
$278$	1.83085	0.109807
$279$	4.76935	0.285533
$280$	1.41743	0.0847074
$281$	25.7497	1.53610	0.768049	−	0.640391i	$-0.221228\pi$
$281$	25.7497	1.53610	0.768049	+	0.640391i	$0.221228\pi$
$282$	1.88295	0.112128
$283$	19.9434	1.18551	0.592755	−	0.805383i	$-0.298040\pi$
$283$	19.9434	1.18551	0.592755	+	0.805383i	$0.298040\pi$
$284$	5.36545	0.318381
$285$	−4.34541	−0.257400
$286$	0	0
$287$	−1.36719	−0.0807025
$288$	−13.5999	−0.801380
$289$	5.24027	0.308251
$290$	9.58348	0.562762
$291$	−4.59100	−0.269129
$292$	−9.42691	−0.551668
$293$	19.4732	1.13764	0.568818	−	0.822463i	$-0.307401\pi$
$293$	19.4732	1.13764	0.568818	+	0.822463i	$0.307401\pi$
$294$	4.38248	0.255591
$295$	10.0149	0.583092
$296$	−5.02938	−0.292327
$297$	−3.82647	−0.222034
$298$	15.5241	0.899287
$299$	0	0
$300$	0.781172	0.0451010
$301$	1.04053	0.0599749
$302$	8.50889	0.489632
$303$	1.72502	0.0990998
$304$	2.98872	0.171415
$305$	14.3001	0.818820
$306$	11.1026	0.634692
$307$	21.7876	1.24348	0.621742	−	0.783222i	$-0.286425\pi$
$307$	21.7876	1.24348	0.621742	+	0.783222i	$0.286425\pi$
$308$	0.546610	0.0311460
$309$	−11.6172	−0.660882
$310$	1.76902	0.100473
$311$	4.99148	0.283041	0.141520	−	0.989935i	$-0.454801\pi$
$311$	4.99148	0.283041	0.141520	+	0.989935i	$0.454801\pi$
$312$	0	0
$313$	−3.04003	−0.171833	−0.0859163	−	0.996302i	$-0.527382\pi$
$313$	−3.04003	−0.171833	−0.0859163	+	0.996302i	$0.527382\pi$
$314$	−14.3927	−0.812226
$315$	1.22217	0.0688614
$316$	14.8705	0.836532
$317$	−11.2479	−0.631743	−0.315871	−	0.948802i	$-0.602297\pi$
$317$	−11.2479	−0.631743	−0.315871	+	0.948802i	$0.602297\pi$
$318$	−5.99779	−0.336339
$319$	10.2556	0.574202
$320$	−5.99804	−0.335301
$321$	5.56905	0.310834
$322$	−0.746508	−0.0416013
$323$	29.5591	1.64471
$324$	−5.52711	−0.307062
$325$	0	0
$326$	−2.10280	−0.116464
$327$	11.5551	0.639000
$328$	8.23468	0.454684
$329$	−1.40996	−0.0777334
$330$	−0.647848	−0.0356629
$331$	−9.73984	−0.535350	−0.267675	−	0.963509i	$-0.586255\pi$
$331$	−9.73984	−0.535350	−0.267675	+	0.963509i	$0.586255\pi$
$332$	0.400964	0.0220058
$333$	−4.33656	−0.237642
$334$	13.7342	0.751500
$335$	7.15968	0.391175
$336$	0.160367	0.00874876
$337$	−28.7492	−1.56607	−0.783034	−	0.621978i	$-0.786329\pi$
$337$	−28.7492	−1.56607	−0.783034	+	0.621978i	$0.786329\pi$
$338$	0	0
$339$	3.06865	0.166666
$340$	−5.31382	−0.288182
$341$	1.89308	0.102516
$342$	14.7562	0.797923
$343$	−6.67739	−0.360545
$344$	−6.26718	−0.337903
$345$	−1.14167	−0.0614654
$346$	−4.71895	−0.253693
$347$	23.1260	1.24147	0.620734	−	0.784021i	$-0.286835\pi$
$347$	23.1260	1.24147	0.620734	+	0.784021i	$0.286835\pi$
$348$	−8.01137	−0.429455
$349$	8.81234	0.471714	0.235857	−	0.971788i	$-0.424210\pi$
$349$	8.81234	0.471714	0.235857	+	0.971788i	$0.424210\pi$
$350$	0.453319	0.0242309
$351$	0	0
$352$	−5.39814	−0.287722
$353$	13.4854	0.717753	0.358876	−	0.933385i	$-0.383160\pi$
$353$	13.4854	0.717753	0.358876	+	0.933385i	$0.383160\pi$
$354$	6.48816	0.344842
$355$	4.76178	0.252729
$356$	−0.644040	−0.0341341
$357$	1.58606	0.0839434
$358$	11.6893	0.617801
$359$	33.0899	1.74642	0.873208	−	0.487348i	$-0.162036\pi$
$359$	33.0899	1.74642	0.873208	+	0.487348i	$0.162036\pi$
$360$	−7.36122	−0.387971
$361$	20.2863	1.06770
$362$	−11.4495	−0.601775
$363$	−0.693282	−0.0363879
$364$	0	0
$365$	−8.36628	−0.437911
$366$	9.26428	0.484251
$367$	−34.1822	−1.78430	−0.892148	−	0.451743i	$-0.850802\pi$
$367$	−34.1822	−1.78430	−0.892148	+	0.451743i	$0.850802\pi$
$368$	0.785228	0.0409328
$369$	7.10031	0.369627
$370$	−1.60849	−0.0836214
$371$	4.49116	0.233169
$372$	−1.47882	−0.0766733
$373$	21.9957	1.13890	0.569448	−	0.822027i	$-0.307157\pi$
$373$	21.9957	1.13890	0.569448	+	0.822027i	$0.307157\pi$
$374$	4.40690	0.227875
$375$	0.693282	0.0358009
$376$	8.49228	0.437956
$377$	0	0
$378$	1.73461	0.0892189
$379$	0.373573	0.0191892	0.00959458	−	0.999954i	$-0.496946\pi$
$379$	0.373573	0.0191892	0.00959458	+	0.999954i	$0.496946\pi$
$380$	−7.06248	−0.362298
$381$	1.01348	0.0519220
$382$	5.66983	0.290094
$383$	−17.5084	−0.894636	−0.447318	−	0.894375i	$-0.647621\pi$
$383$	−17.5084	−0.894636	−0.447318	+	0.894375i	$0.647621\pi$
$384$	3.59905	0.183663
$385$	0.485111	0.0247235
$386$	−0.0727175	−0.00370122
$387$	−5.40384	−0.274692
$388$	−7.46163	−0.378807
$389$	18.0925	0.917325	0.458663	−	0.888610i	$-0.348329\pi$
$389$	18.0925	0.917325	0.458663	+	0.888610i	$0.348329\pi$
$390$	0	0
$391$	7.76605	0.392746
$392$	19.7654	0.998305
$393$	−9.47389	−0.477895
$394$	−20.6234	−1.03899
$395$	13.1974	0.664035
$396$	−2.83875	−0.142653
$397$	−14.2472	−0.715049	−0.357524	−	0.933904i	$-0.616379\pi$
$397$	−14.2472	−0.715049	−0.357524	+	0.933904i	$0.616379\pi$
$398$	−19.6024	−0.982577
$399$	2.10800	0.105532
$400$	−0.476832	−0.0238416
$401$	−13.8143	−0.689856	−0.344928	−	0.938629i	$-0.612097\pi$
$401$	−13.8143	−0.689856	−0.344928	+	0.938629i	$0.612097\pi$
$402$	4.63839	0.231342
$403$	0	0
$404$	2.80363	0.139486
$405$	−4.90526	−0.243744
$406$	−4.64905	−0.230728
$407$	−1.72129	−0.0853214
$408$	−9.55300	−0.472944
$409$	−0.709058	−0.0350607	−0.0175303	−	0.999846i	$-0.505580\pi$
$409$	−0.709058	−0.0350607	−0.0175303	+	0.999846i	$0.505580\pi$
$410$	2.63360	0.130064
$411$	−8.78307	−0.433237
$412$	−18.8812	−0.930211
$413$	−4.85835	−0.239064
$414$	3.87689	0.190539
$415$	0.355851	0.0174681
$416$	0	0
$417$	−1.35831	−0.0665167
$418$	5.85712	0.286481
$419$	20.4051	0.996853	0.498426	−	0.866932i	$-0.333911\pi$
$419$	20.4051	0.996853	0.498426	+	0.866932i	$0.333911\pi$
$420$	−0.378955	−0.0184911
$421$	−10.1539	−0.494872	−0.247436	−	0.968904i	$-0.579588\pi$
$421$	−10.1539	−0.494872	−0.247436	+	0.968904i	$0.579588\pi$
$422$	20.4619	0.996072
$423$	7.32242	0.356028
$424$	−27.0507	−1.31370
$425$	−4.71596	−0.228758
$426$	3.08491	0.149465
$427$	−6.93712	−0.335711
$428$	9.05124	0.437508
$429$	0	0
$430$	−2.00436	−0.0966587
$431$	20.9412	1.00870	0.504351	−	0.863499i	$-0.331732\pi$
$431$	20.9412	1.00870	0.504351	+	0.863499i	$0.331732\pi$
$432$	−1.82458	−0.0877853
$433$	25.7361	1.23680	0.618400	−	0.785863i	$-0.287781\pi$
$433$	25.7361	1.23680	0.618400	+	0.785863i	$0.287781\pi$
$434$	−0.858169	−0.0411934
$435$	−7.11001	−0.340899
$436$	18.7803	0.899411
$437$	10.3217	0.493753
$438$	−5.42008	−0.258981
$439$	40.6030	1.93787	0.968937	−	0.247307i	$-0.0795456\pi$
$439$	40.6030	1.93787	0.968937	+	0.247307i	$0.0795456\pi$
$440$	−2.92186	−0.139294
$441$	17.0426	0.811554
$442$	0	0
$443$	−6.46840	−0.307323	−0.153662	−	0.988124i	$-0.549107\pi$
$443$	−6.46840	−0.307323	−0.153662	+	0.988124i	$0.549107\pi$
$444$	1.34463	0.0638132
$445$	−0.571579	−0.0270954
$446$	−6.83463	−0.323629
$447$	−11.5174	−0.544753
$448$	2.90971	0.137471
$449$	−28.8005	−1.35918	−0.679591	−	0.733591i	$-0.737843\pi$
$449$	−28.8005	−1.35918	−0.679591	+	0.733591i	$0.737843\pi$
$450$	−2.35426	−0.110981
$451$	2.81830	0.132709
$452$	4.98740	0.234587
$453$	−6.31277	−0.296600
$454$	−17.0416	−0.799801
$455$	0	0
$456$	−12.6967	−0.594577
$457$	36.1306	1.69012	0.845059	−	0.534674i	$-0.179565\pi$
$457$	36.1306	1.69012	0.845059	+	0.534674i	$0.179565\pi$
$458$	2.57023	0.120099
$459$	−18.0455	−0.842291
$460$	−1.85553	−0.0865144
$461$	−22.3270	−1.03987	−0.519937	−	0.854205i	$-0.674045\pi$
$461$	−22.3270	−1.03987	−0.519937	+	0.854205i	$0.674045\pi$
$462$	0.314278	0.0146215
$463$	8.38209	0.389549	0.194774	−	0.980848i	$-0.437603\pi$
$463$	8.38209	0.389549	0.194774	+	0.980848i	$0.437603\pi$
$464$	4.89019	0.227021
$465$	−1.31244	−0.0608628
$466$	14.0018	0.648622
$467$	36.9610	1.71035	0.855176	−	0.518338i	$-0.173449\pi$
$467$	36.9610	1.71035	0.855176	+	0.518338i	$0.173449\pi$
$468$	0	0
$469$	−3.47324	−0.160379
$470$	2.71599	0.125279
$471$	10.6780	0.492015
$472$	29.2623	1.34691
$473$	−2.14492	−0.0986237
$474$	8.54993	0.392711
$475$	−6.26788	−0.287590
$476$	2.57779	0.118153
$477$	−23.3243	−1.06795
$478$	−12.9908	−0.594188
$479$	13.6225	0.622426	0.311213	−	0.950340i	$-0.399265\pi$
$479$	13.6225	0.622426	0.311213	+	0.950340i	$0.399265\pi$
$480$	3.74244	0.170818
$481$	0	0
$482$	−16.5685	−0.754674
$483$	0.553836	0.0252004
$484$	−1.12677	−0.0512170
$485$	−6.62212	−0.300695
$486$	−13.9050	−0.630743
$487$	−9.64662	−0.437130	−0.218565	−	0.975822i	$-0.570138\pi$
$487$	−9.64662	−0.437130	−0.218565	+	0.975822i	$0.570138\pi$
$488$	41.7828	1.89142
$489$	1.56007	0.0705490
$490$	6.32135	0.285569
$491$	24.2474	1.09427	0.547135	−	0.837044i	$-0.315718\pi$
$491$	24.2474	1.09427	0.547135	+	0.837044i	$0.315718\pi$
$492$	−2.20158	−0.0992548
$493$	48.3649	2.17824
$494$	0	0
$495$	−2.51936	−0.113237
$496$	0.902681	0.0405316
$497$	−2.30999	−0.103617
$498$	0.230538	0.0103306
$499$	−36.9871	−1.65577	−0.827885	−	0.560898i	$-0.810456\pi$
$499$	−36.9871	−1.65577	−0.827885	+	0.560898i	$0.810456\pi$
$500$	1.12677	0.0503909
$501$	−10.1894	−0.455229
$502$	−16.8600	−0.752501
$503$	32.6693	1.45665	0.728326	−	0.685230i	$-0.240298\pi$
$503$	32.6693	1.45665	0.728326	+	0.685230i	$0.240298\pi$
$504$	3.57101	0.159065
$505$	2.48819	0.110723
$506$	1.53884	0.0684098
$507$	0	0
$508$	1.64718	0.0730817
$509$	−1.60620	−0.0711935	−0.0355967	−	0.999366i	$-0.511333\pi$
$509$	−1.60620	−0.0711935	−0.0355967	+	0.999366i	$0.511333\pi$
$510$	−3.05523	−0.135288
$511$	4.05857	0.179541
$512$	−5.36048	−0.236902
$513$	−23.9839	−1.05891
$514$	19.6575	0.867056
$515$	−16.7569	−0.738397
$516$	1.67556	0.0737622
$517$	2.90646	0.127826
$518$	0.780295	0.0342842
$519$	3.50100	0.153677
$520$	0	0
$521$	−9.12602	−0.399818	−0.199909	−	0.979814i	$-0.564065\pi$
$521$	−9.12602	−0.399818	−0.199909	+	0.979814i	$0.564065\pi$
$522$	24.1442	1.05676
$523$	−22.1835	−0.970016	−0.485008	−	0.874510i	$-0.661183\pi$
$523$	−22.1835	−0.970016	−0.485008	+	0.874510i	$0.661183\pi$
$524$	−15.3977	−0.672651
$525$	−0.336318	−0.0146781
$526$	5.22466	0.227806
$527$	8.92768	0.388896
$528$	−0.330579	−0.0143866
$529$	−20.2882	−0.882095
$530$	−8.65130	−0.375788
$531$	25.2312	1.09494
$532$	3.42609	0.148540
$533$	0	0
$534$	−0.370296	−0.0160243
$535$	8.03288	0.347292
$536$	20.9196	0.903589
$537$	−8.67234	−0.374239
$538$	−20.3718	−0.878291
$539$	6.76467	0.291375
$540$	4.31157	0.185540
$541$	2.71087	0.116549	0.0582746	−	0.998301i	$-0.481440\pi$
$541$	2.71087	0.116549	0.0582746	+	0.998301i	$0.481440\pi$
$542$	−15.3818	−0.660703
$543$	8.49444	0.364531
$544$	−25.4574	−1.09148
$545$	16.6673	0.713948
$546$	0	0
$547$	−1.46672	−0.0627125	−0.0313563	−	0.999508i	$-0.509983\pi$
$547$	−1.46672	−0.0627125	−0.0313563	+	0.999508i	$0.509983\pi$
$548$	−14.2749	−0.609794
$549$	36.0270	1.53760
$550$	−0.934466	−0.0398457
$551$	64.2807	2.73845
$552$	−3.33580	−0.141981
$553$	−6.40221	−0.272250
$554$	3.85898	0.163952
$555$	1.19334	0.0506545
$556$	−2.20763	−0.0936242
$557$	22.6950	0.961620	0.480810	−	0.876825i	$-0.340343\pi$
$557$	22.6950	0.961620	0.480810	+	0.876825i	$0.340343\pi$
$558$	4.45679	0.188671
$559$	0	0
$560$	0.231316	0.00977489
$561$	−3.26949	−0.138038
$562$	24.0622	1.01500
$563$	18.3791	0.774587	0.387293	−	0.921957i	$-0.373410\pi$
$563$	18.3791	0.774587	0.387293	+	0.921957i	$0.373410\pi$
$564$	−2.27045	−0.0956031
$565$	4.42626	0.186214
$566$	18.6364	0.783345
$567$	2.37959	0.0999334
$568$	13.9133	0.583788
$569$	−16.8857	−0.707885	−0.353943	−	0.935267i	$-0.615159\pi$
$569$	−16.8857	−0.707885	−0.353943	+	0.935267i	$0.615159\pi$
$570$	−4.06063	−0.170081
$571$	−19.9745	−0.835906	−0.417953	−	0.908469i	$-0.637252\pi$
$571$	−19.9745	−0.835906	−0.417953	+	0.908469i	$0.637252\pi$
$572$	0	0
$573$	−4.20646	−0.175727
$574$	−1.27759	−0.0533255
$575$	−1.64676	−0.0686746
$576$	−15.1112	−0.629634
$577$	−34.4390	−1.43371	−0.716857	−	0.697221i	$-0.754420\pi$
$577$	−34.4390	−1.43371	−0.716857	+	0.697221i	$0.754420\pi$
$578$	4.89685	0.203682
$579$	0.0539493	0.00224205
$580$	−11.5557	−0.479825
$581$	−0.172627	−0.00716179
$582$	−4.29013	−0.177832
$583$	−9.25802	−0.383428
$584$	−24.4451	−1.01155
$585$	0	0
$586$	18.1970	0.751713
$587$	−18.9271	−0.781205	−0.390603	−	0.920559i	$-0.627733\pi$
$587$	−18.9271	−0.781205	−0.390603	+	0.920559i	$0.627733\pi$
$588$	−5.28437	−0.217924
$589$	11.8656	0.488913
$590$	9.35862	0.385288
$591$	15.3005	0.629379
$592$	−0.820768	−0.0337333
$593$	−20.2898	−0.833202	−0.416601	−	0.909089i	$-0.636779\pi$
$593$	−20.2898	−0.833202	−0.416601	+	0.909089i	$0.636779\pi$
$594$	−3.57571	−0.146713
$595$	2.28776	0.0937891
$596$	−18.7189	−0.766756
$597$	14.5430	0.595206
$598$	0	0
$599$	−2.20289	−0.0900075	−0.0450038	−	0.998987i	$-0.514330\pi$
$599$	−2.20289	−0.0900075	−0.0450038	+	0.998987i	$0.514330\pi$
$600$	2.02567	0.0826978
$601$	0.920862	0.0375627	0.0187814	−	0.999824i	$-0.494021\pi$
$601$	0.920862	0.0375627	0.0187814	+	0.999824i	$0.494021\pi$
$602$	0.972335	0.0396294
$603$	18.0378	0.734557
$604$	−10.2600	−0.417473
$605$	−1.00000	−0.0406558
$606$	1.61197	0.0654818
$607$	40.6628	1.65045	0.825226	−	0.564803i	$-0.191048\pi$
$607$	40.6628	1.65045	0.825226	+	0.564803i	$0.191048\pi$
$608$	−33.8349	−1.37219
$609$	3.44914	0.139766
$610$	13.3629	0.541049
$611$	0	0
$612$	−13.3874	−0.541155
$613$	−20.7711	−0.838938	−0.419469	−	0.907770i	$-0.637784\pi$
$613$	−20.7711	−0.838938	−0.419469	+	0.907770i	$0.637784\pi$
$614$	20.3598	0.821654
$615$	−1.95388	−0.0787879
$616$	1.41743	0.0571097
$617$	−25.0550	−1.00868	−0.504339	−	0.863506i	$-0.668264\pi$
$617$	−25.0550	−1.00868	−0.504339	+	0.863506i	$0.668264\pi$
$618$	−10.8559	−0.436689
$619$	−33.8540	−1.36071	−0.680354	−	0.732883i	$-0.738174\pi$
$619$	−33.8540	−1.36071	−0.680354	+	0.732883i	$0.738174\pi$
$620$	−2.13307	−0.0856663
$621$	−6.30128	−0.252862
$622$	4.66436	0.187024
$623$	0.277279	0.0111089
$624$	0	0
$625$	1.00000	0.0400000
$626$	−2.84080	−0.113541
$627$	−4.34541	−0.173539
$628$	17.3546	0.692525
$629$	−8.11755	−0.323668
$630$	1.14207	0.0455013
$631$	10.9682	0.436635	0.218318	−	0.975878i	$-0.429943\pi$
$631$	10.9682	0.436635	0.218318	+	0.975878i	$0.429943\pi$
$632$	38.5611	1.53388
$633$	−15.1808	−0.603381
$634$	−10.5107	−0.417435
$635$	1.46185	0.0580119
$636$	7.23210	0.286772
$637$	0	0
$638$	9.58348	0.379414
$639$	11.9966	0.474580
$640$	5.19132	0.205205
$641$	−26.2503	−1.03682	−0.518412	−	0.855131i	$-0.673477\pi$
$641$	−26.2503	−1.03682	−0.518412	+	0.855131i	$0.673477\pi$
$642$	5.20409	0.205389
$643$	−30.8400	−1.21621	−0.608105	−	0.793856i	$-0.708070\pi$
$643$	−30.8400	−1.21621	−0.608105	+	0.793856i	$0.708070\pi$
$644$	0.900136	0.0354703
$645$	1.48704	0.0585520
$646$	27.6219	1.08677
$647$	−33.8945	−1.33253	−0.666264	−	0.745716i	$-0.732108\pi$
$647$	−33.8945	−1.33253	−0.666264	+	0.745716i	$0.732108\pi$
$648$	−14.3325	−0.563033
$649$	10.0149	0.393121
$650$	0	0
$651$	0.636678	0.0249534
$652$	2.53555	0.0992998
$653$	34.7455	1.35970	0.679848	−	0.733353i	$-0.262046\pi$
$653$	34.7455	1.35970	0.679848	+	0.733353i	$0.262046\pi$
$654$	10.7979	0.422230
$655$	−13.6653	−0.533947
$656$	1.34385	0.0524687
$657$	−21.0777	−0.822318
$658$	−1.31755	−0.0513636
$659$	−0.319346	−0.0124399	−0.00621997	−	0.999981i	$-0.501980\pi$
$659$	−0.319346	−0.0124399	−0.00621997	+	0.999981i	$0.501980\pi$
$660$	0.781172	0.0304071
$661$	32.4708	1.26297	0.631484	−	0.775389i	$-0.282446\pi$
$661$	32.4708	1.26297	0.631484	+	0.775389i	$0.282446\pi$
$662$	−9.10154	−0.353742
$663$	0	0
$664$	1.03975	0.0403501
$665$	3.04061	0.117910
$666$	−4.05236	−0.157026
$667$	16.8885	0.653924
$668$	−16.5606	−0.640748
$669$	5.07062	0.196042
$670$	6.69048	0.258476
$671$	14.3001	0.552048
$672$	−1.81549	−0.0700342
$673$	14.0168	0.540310	0.270155	−	0.962817i	$-0.412925\pi$
$673$	14.0168	0.540310	0.270155	+	0.962817i	$0.412925\pi$
$674$	−26.8651	−1.03481
$675$	3.82647	0.147281
$676$	0	0
$677$	21.7671	0.836578	0.418289	−	0.908314i	$-0.362630\pi$
$677$	21.7671	0.836578	0.418289	+	0.908314i	$0.362630\pi$
$678$	2.86755	0.110127
$679$	3.21246	0.123283
$680$	−13.7794	−0.528415
$681$	12.6432	0.484488
$682$	1.76902	0.0677392
$683$	−14.3964	−0.550865	−0.275432	−	0.961320i	$-0.588821\pi$
$683$	−14.3964	−0.550865	−0.275432	+	0.961320i	$0.588821\pi$
$684$	−17.7929	−0.680330
$685$	−12.6688	−0.484051
$686$	−6.23979	−0.238236
$687$	−1.90686	−0.0727511
$688$	−1.02277	−0.0389927
$689$	0	0
$690$	−1.06685	−0.0406143
$691$	−5.60911	−0.213380	−0.106690	−	0.994292i	$-0.534025\pi$
$691$	−5.60911	−0.213380	−0.106690	+	0.994292i	$0.534025\pi$
$692$	5.69009	0.216305
$693$	1.22217	0.0464263
$694$	21.6104	0.820321
$695$	−1.95925	−0.0743184
$696$	−20.7745	−0.787454
$697$	13.2910	0.503432
$698$	8.23483	0.311693
$699$	−10.3880	−0.392909
$700$	−0.546610	−0.0206599
$701$	6.30685	0.238206	0.119103	−	0.992882i	$-0.461998\pi$
$701$	6.30685	0.238206	0.119103	+	0.992882i	$0.461998\pi$
$702$	0	0
$703$	−10.7889	−0.406910
$704$	−5.99804	−0.226060
$705$	−2.01500	−0.0758892
$706$	12.6016	0.474267
$707$	−1.20705	−0.0453957
$708$	−7.82339	−0.294021
$709$	−10.0121	−0.376013	−0.188007	−	0.982168i	$-0.560203\pi$
$709$	−10.0121	−0.376013	−0.188007	+	0.982168i	$0.560203\pi$
$710$	4.44972	0.166995
$711$	33.2491	1.24694
$712$	−1.67007	−0.0625887
$713$	3.11745	0.116749
$714$	1.48212	0.0554670
$715$	0	0
$716$	−14.0949	−0.526753
$717$	9.63794	0.359935
$718$	30.9213	1.15397
$719$	−4.08309	−0.152274	−0.0761368	−	0.997097i	$-0.524259\pi$
$719$	−4.08309	−0.152274	−0.0761368	+	0.997097i	$0.524259\pi$
$720$	−1.20131	−0.0447702
$721$	8.12894	0.302738
$722$	18.9568	0.705501
$723$	12.2922	0.457152
$724$	13.8058	0.513089
$725$	−10.2556	−0.380883
$726$	−0.647848	−0.0240439
$727$	32.4256	1.20260	0.601299	−	0.799024i	$-0.294650\pi$
$727$	32.4256	1.20260	0.601299	+	0.799024i	$0.294650\pi$
$728$	0	0
$729$	−4.39963	−0.162949
$730$	−7.81800	−0.289357
$731$	−10.1154	−0.374131
$732$	−11.1708	−0.412885
$733$	−50.7325	−1.87385	−0.936924	−	0.349533i	$-0.886340\pi$
$733$	−50.7325	−1.87385	−0.936924	+	0.349533i	$0.886340\pi$
$734$	−31.9421	−1.17900
$735$	−4.68982	−0.172987
$736$	−8.88945	−0.327669
$737$	7.15968	0.263730
$738$	6.63500	0.244238
$739$	−8.64532	−0.318023	−0.159012	−	0.987277i	$-0.550831\pi$
$739$	−8.64532	−0.318023	−0.159012	+	0.987277i	$0.550831\pi$
$740$	1.93951	0.0712978
$741$	0	0
$742$	4.19684	0.154071
$743$	−46.0364	−1.68891	−0.844456	−	0.535625i	$-0.820076\pi$
$743$	−46.0364	−1.68891	−0.844456	+	0.535625i	$0.820076\pi$
$744$	−3.83476	−0.140589
$745$	−16.6128	−0.608646
$746$	20.5543	0.752545
$747$	0.896518	0.0328019
$748$	−5.31382	−0.194293
$749$	−3.89683	−0.142387
$750$	0.647848	0.0236561
$751$	−49.4164	−1.80323	−0.901614	−	0.432541i	$-0.857617\pi$
$751$	−49.4164	−1.80323	−0.901614	+	0.432541i	$0.857617\pi$
$752$	1.38589	0.0505383
$753$	12.5085	0.455835
$754$	0	0
$755$	−9.10563	−0.331388
$756$	−2.09159	−0.0760703
$757$	37.6198	1.36732	0.683658	−	0.729803i	$-0.260388\pi$
$757$	37.6198	1.36732	0.683658	+	0.729803i	$0.260388\pi$
$758$	0.349091	0.0126796
$759$	−1.14167	−0.0414400
$760$	−18.3139	−0.664314
$761$	−20.6522	−0.748641	−0.374321	−	0.927299i	$-0.622124\pi$
$761$	−20.6522	−0.748641	−0.374321	+	0.927299i	$0.622124\pi$
$762$	0.947059	0.0343083
$763$	−8.08547	−0.292714
$764$	−6.83665	−0.247341
$765$	−11.8812	−0.429566
$766$	−16.3610	−0.591146
$767$	0	0
$768$	11.6799	0.421461
$769$	−29.6252	−1.06831	−0.534157	−	0.845385i	$-0.679371\pi$
$769$	−29.6252	−1.06831	−0.534157	+	0.845385i	$0.679371\pi$
$770$	0.453319	0.0163365
$771$	−14.5840	−0.525228
$772$	0.0876824	0.00315576
$773$	−37.5956	−1.35222	−0.676109	−	0.736801i	$-0.736335\pi$
$773$	−37.5956	−1.35222	−0.676109	+	0.736801i	$0.736335\pi$
$774$	−5.04970	−0.181508
$775$	−1.89308	−0.0680014
$776$	−19.3489	−0.694586
$777$	−0.578903	−0.0207680
$778$	16.9068	0.606138
$779$	17.6648	0.632906
$780$	0	0
$781$	4.76178	0.170390
$782$	7.25711	0.259514
$783$	−39.2427	−1.40242
$784$	3.22561	0.115200
$785$	15.4020	0.549723
$786$	−8.85302	−0.315777
$787$	−41.2179	−1.46926	−0.734629	−	0.678469i	$-0.762644\pi$
$787$	−41.2179	−1.46926	−0.734629	+	0.678469i	$0.762644\pi$
$788$	24.8676	0.885870
$789$	−3.87619	−0.137996
$790$	12.3325	0.438772
$791$	−2.14723	−0.0763466
$792$	−7.36122	−0.261570
$793$	0	0
$794$	−13.3136	−0.472481
$795$	6.41842	0.227638
$796$	23.6364	0.837771
$797$	−11.2220	−0.397502	−0.198751	−	0.980050i	$-0.563689\pi$
$797$	−11.2220	−0.397502	−0.198751	+	0.980050i	$0.563689\pi$
$798$	1.96986	0.0697322
$799$	13.7068	0.484910
$800$	5.39814	0.190853
$801$	−1.44001	−0.0508803
$802$	−12.9090	−0.455834
$803$	−8.36628	−0.295240
$804$	−5.59294	−0.197248
$805$	0.798861	0.0281561
$806$	0	0
$807$	15.1139	0.532034
$808$	7.27016	0.255763
$809$	−35.2295	−1.23860	−0.619302	−	0.785153i	$-0.712585\pi$
$809$	−35.2295	−1.23860	−0.619302	+	0.785153i	$0.712585\pi$
$810$	−4.58379	−0.161058
$811$	6.48294	0.227647	0.113823	−	0.993501i	$-0.463690\pi$
$811$	6.48294	0.227647	0.113823	+	0.993501i	$0.463690\pi$
$812$	5.60580	0.196725
$813$	11.4118	0.400228
$814$	−1.60849	−0.0563775
$815$	2.25027	0.0788237
$816$	−1.55900	−0.0545758
$817$	−13.4441	−0.470350
$818$	−0.662591	−0.0231669
$819$	0	0
$820$	−3.17559	−0.110896
$821$	−18.9667	−0.661944	−0.330972	−	0.943641i	$-0.607377\pi$
$821$	−18.9667	−0.661944	−0.330972	+	0.943641i	$0.607377\pi$
$822$	−8.20748	−0.286269
$823$	29.6229	1.03259	0.516295	−	0.856411i	$-0.327311\pi$
$823$	29.6229	1.03259	0.516295	+	0.856411i	$0.327311\pi$
$824$	−48.9613	−1.70565
$825$	0.693282	0.0241370
$826$	−4.53997	−0.157966
$827$	−6.65258	−0.231333	−0.115666	−	0.993288i	$-0.536900\pi$
$827$	−6.65258	−0.231333	−0.115666	+	0.993288i	$0.536900\pi$
$828$	−4.67474	−0.162458
$829$	14.6924	0.510288	0.255144	−	0.966903i	$-0.417877\pi$
$829$	14.6924	0.510288	0.255144	+	0.966903i	$0.417877\pi$
$830$	0.332531	0.0115423
$831$	−2.86298	−0.0993158
$832$	0	0
$833$	31.9019	1.10534
$834$	−1.26929	−0.0439520
$835$	−14.6973	−0.508623
$836$	−7.06248	−0.244261
$837$	−7.24382	−0.250383
$838$	19.0678	0.658687
$839$	−47.0525	−1.62443	−0.812216	−	0.583357i	$-0.801739\pi$
$839$	−47.0525	−1.62443	−0.812216	+	0.583357i	$0.801739\pi$
$840$	−0.982676	−0.0339056
$841$	76.1769	2.62679
$842$	−9.48850	−0.326995
$843$	−17.8518	−0.614849
$844$	−24.6729	−0.849277
$845$	0	0
$846$	6.84255	0.235252
$847$	0.485111	0.0166686
$848$	−4.41452	−0.151595
$849$	−13.8264	−0.474520
$850$	−4.40690	−0.151155
$851$	−2.83456	−0.0971674
$852$	−3.71977	−0.127437
$853$	−12.4589	−0.426584	−0.213292	−	0.976989i	$-0.568419\pi$
$853$	−12.4589	−0.426584	−0.213292	+	0.976989i	$0.568419\pi$
$854$	−6.48250	−0.221826
$855$	−15.7910	−0.540042
$856$	23.4710	0.802221
$857$	−42.2785	−1.44421	−0.722103	−	0.691786i	$-0.756824\pi$
$857$	−42.2785	−1.44421	−0.722103	+	0.691786i	$0.756824\pi$
$858$	0	0
$859$	−1.55124	−0.0529276	−0.0264638	−	0.999650i	$-0.508425\pi$
$859$	−1.55124	−0.0529276	−0.0264638	+	0.999650i	$0.508425\pi$
$860$	2.41685	0.0824137
$861$	0.947846	0.0323025
$862$	19.5688	0.666517
$863$	34.1869	1.16373	0.581867	−	0.813284i	$-0.302322\pi$
$863$	34.1869	1.16373	0.581867	+	0.813284i	$0.302322\pi$
$864$	20.6558	0.702726
$865$	5.04990	0.171702
$866$	24.0495	0.817237
$867$	−3.63298	−0.123383
$868$	1.03478	0.0351226
$869$	13.1974	0.447692
$870$	−6.64406	−0.225255
$871$	0	0
$872$	48.6995	1.64917
$873$	−16.6835	−0.564651
$874$	9.64526	0.326256
$875$	−0.485111	−0.0163997
$876$	6.53551	0.220814
$877$	29.4072	0.993010	0.496505	−	0.868034i	$-0.334616\pi$
$877$	29.4072	0.993010	0.496505	+	0.868034i	$0.334616\pi$
$878$	37.9421	1.28048
$879$	−13.5004	−0.455358
$880$	−0.476832	−0.0160740
$881$	47.4494	1.59861	0.799306	−	0.600924i	$-0.205201\pi$
$881$	47.4494	1.59861	0.799306	+	0.600924i	$0.205201\pi$
$882$	15.9258	0.536248
$883$	16.2877	0.548124	0.274062	−	0.961712i	$-0.411633\pi$
$883$	16.2877	0.548124	0.274062	+	0.961712i	$0.411633\pi$
$884$	0	0
$885$	−6.94318	−0.233392
$886$	−6.04450	−0.203069
$887$	−12.7320	−0.427500	−0.213750	−	0.976888i	$-0.568568\pi$
$887$	−12.7320	−0.427500	−0.213750	+	0.976888i	$0.568568\pi$
$888$	3.48678	0.117009
$889$	−0.709161	−0.0237845
$890$	−0.534121	−0.0179038
$891$	−4.90526	−0.164332
$892$	8.24116	0.275934
$893$	18.2173	0.609620
$894$	−10.7626	−0.359955
$895$	−12.5091	−0.418134
$896$	−2.51837	−0.0841327
$897$	0	0
$898$	−26.9131	−0.898102
$899$	19.4146	0.647514
$900$	2.83875	0.0946250
$901$	−43.6604	−1.45454
$902$	2.63360	0.0876894
$903$	−0.721378	−0.0240059
$904$	12.9329	0.430143
$905$	12.2525	0.407287
$906$	−5.89906	−0.195983
$907$	21.9610	0.729202	0.364601	−	0.931164i	$-0.381205\pi$
$907$	21.9610	0.729202	0.364601	+	0.931164i	$0.381205\pi$
$908$	20.5487	0.681931
$909$	6.26865	0.207918
$910$	0	0
$911$	10.6485	0.352800	0.176400	−	0.984319i	$-0.443555\pi$
$911$	10.6485	0.352800	0.176400	+	0.984319i	$0.443555\pi$
$912$	−2.07203	−0.0686117
$913$	0.355851	0.0117770
$914$	33.7628	1.11677
$915$	−9.91398	−0.327746
$916$	−3.09917	−0.102399
$917$	6.62917	0.218915
$918$	−16.8629	−0.556558
$919$	−35.3383	−1.16570	−0.582851	−	0.812579i	$-0.698063\pi$
$919$	−35.3383	−1.16570	−0.582851	+	0.812579i	$0.698063\pi$
$920$	−4.81161	−0.158634
$921$	−15.1050	−0.497725
$922$	−20.8639	−0.687114
$923$	0	0
$924$	−0.378955	−0.0124667
$925$	1.72129	0.0565958
$926$	7.83277	0.257401
$927$	−42.2166	−1.38658
$928$	−55.3611	−1.81732
$929$	20.7233	0.679908	0.339954	−	0.940442i	$-0.389588\pi$
$929$	20.7233	0.679908	0.339954	+	0.940442i	$0.389588\pi$
$930$	−1.22643	−0.0402162
$931$	42.4001	1.38961
$932$	−16.8833	−0.553032
$933$	−3.46050	−0.113292
$934$	34.5388	1.13014
$935$	−4.71596	−0.154228
$936$	0	0
$937$	21.4701	0.701399	0.350700	−	0.936488i	$-0.385944\pi$
$937$	21.4701	0.701399	0.350700	+	0.936488i	$0.385944\pi$
$938$	−3.24562	−0.105973
$939$	2.10760	0.0687788
$940$	−3.27493	−0.106816
$941$	−24.4222	−0.796141	−0.398070	−	0.917355i	$-0.630320\pi$
$941$	−24.4222	−0.796141	−0.398070	+	0.917355i	$0.630320\pi$
$942$	9.97819	0.325107
$943$	4.64106	0.151134
$944$	4.77544	0.155427
$945$	−1.85626	−0.0603842
$946$	−2.00436	−0.0651673
$947$	−29.6465	−0.963382	−0.481691	−	0.876341i	$-0.659977\pi$
$947$	−29.6465	−0.963382	−0.481691	+	0.876341i	$0.659977\pi$
$948$	−10.3095	−0.334836
$949$	0	0
$950$	−5.85712	−0.190030
$951$	7.79794	0.252866
$952$	6.68453	0.216647
$953$	43.3290	1.40356	0.701782	−	0.712392i	$-0.252388\pi$
$953$	43.3290	1.40356	0.701782	+	0.712392i	$0.252388\pi$
$954$	−21.7957	−0.705663
$955$	−6.06745	−0.196338
$956$	15.6643	0.506620
$957$	−7.11001	−0.229834
$958$	12.7297	0.411278
$959$	6.14578	0.198458
$960$	4.15833	0.134210
$961$	−27.4163	−0.884395
$962$	0	0
$963$	20.2377	0.652151
$964$	19.9782	0.643454
$965$	0.0778172	0.00250502
$966$	0.517540	0.0166516
$967$	−6.77238	−0.217785	−0.108893	−	0.994054i	$-0.534730\pi$
$967$	−6.77238	−0.217785	−0.108893	+	0.994054i	$0.534730\pi$
$968$	−2.92186	−0.0939122
$969$	−20.4928	−0.658322
$970$	−6.18814	−0.198689
$971$	23.0491	0.739682	0.369841	−	0.929095i	$-0.379412\pi$
$971$	23.0491	0.739682	0.369841	+	0.929095i	$0.379412\pi$
$972$	16.7666	0.537788
$973$	0.950451	0.0304701
$974$	−9.01443	−0.288841
$975$	0	0
$976$	6.81873	0.218262
$977$	49.1770	1.57331	0.786656	−	0.617391i	$-0.211810\pi$
$977$	49.1770	1.57331	0.786656	+	0.617391i	$0.211810\pi$
$978$	1.45784	0.0466165
$979$	−0.571579	−0.0182677
$980$	−7.62225	−0.243484
$981$	41.9909	1.34067
$982$	22.6584	0.723058
$983$	−35.9873	−1.14782	−0.573908	−	0.818920i	$-0.694573\pi$
$983$	−35.9873	−1.14782	−0.573908	+	0.818920i	$0.694573\pi$
$984$	−5.70896	−0.181995
$985$	22.0697	0.703199
$986$	45.1953	1.43931
$987$	0.977497	0.0311141
$988$	0	0
$989$	−3.53218	−0.112317
$990$	−2.35426	−0.0748231
$991$	−46.4157	−1.47444	−0.737222	−	0.675651i	$-0.763863\pi$
$991$	−46.4157	−1.47444	−0.737222	+	0.675651i	$0.763863\pi$
$992$	−10.2191	−0.324457
$993$	6.75246	0.214283
$994$	−2.15861	−0.0684669
$995$	20.9771	0.665018
$996$	−0.277981	−0.00880817
$997$	38.4415	1.21745	0.608727	−	0.793380i	$-0.291680\pi$
$997$	38.4415	1.21745	0.608727	+	0.793380i	$0.291680\pi$
$998$	−34.5632	−1.09408
$999$	6.58648	0.208387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9295.2.a.bj.1.20		28
13.2	odd	12		715.2.z.c.56.19	✓	56
13.7	odd	12		715.2.z.c.166.19	yes	56
13.12	even	2		9295.2.a.bk.1.9		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
715.2.z.c.56.19	✓	56	13.2	odd	12
715.2.z.c.166.19	yes	56	13.7	odd	12
9295.2.a.bj.1.20		28	1.1	even	1	trivial
9295.2.a.bk.1.9		28	13.12	even	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:	\( N \)	\(=\)	\( 9295 = 5 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9295.a (trivial)

\(f(q)\)	\(=\)	\(q+0.934466 q^{2} -0.693282 q^{3} -1.12677 q^{4} -1.00000 q^{5} -0.647848 q^{6} +0.485111 q^{7} -2.92186 q^{8} -2.51936 q^{9} +O(q^{10})\)	\(q+0.934466 q^{2} -0.693282 q^{3} -1.12677 q^{4} -1.00000 q^{5} -0.647848 q^{6} +0.485111 q^{7} -2.92186 q^{8} -2.51936 q^{9} -0.934466 q^{10} -1.00000 q^{11} +0.781172 q^{12} +0.453319 q^{14} +0.693282 q^{15} -0.476832 q^{16} -4.71596 q^{17} -2.35426 q^{18} -6.26788 q^{19} +1.12677 q^{20} -0.336318 q^{21} -0.934466 q^{22} -1.64676 q^{23} +2.02567 q^{24} +1.00000 q^{25} +3.82647 q^{27} -0.546610 q^{28} -10.2556 q^{29} +0.647848 q^{30} -1.89308 q^{31} +5.39814 q^{32} +0.693282 q^{33} -4.40690 q^{34} -0.485111 q^{35} +2.83875 q^{36} +1.72129 q^{37} -5.85712 q^{38} +2.92186 q^{40} -2.81830 q^{41} -0.314278 q^{42} +2.14492 q^{43} +1.12677 q^{44} +2.51936 q^{45} -1.53884 q^{46} -2.90646 q^{47} +0.330579 q^{48} -6.76467 q^{49} +0.934466 q^{50} +3.26949 q^{51} +9.25802 q^{53} +3.57571 q^{54} +1.00000 q^{55} -1.41743 q^{56} +4.34541 q^{57} -9.58348 q^{58} -10.0149 q^{59} -0.781172 q^{60} -14.3001 q^{61} -1.76902 q^{62} -1.22217 q^{63} +5.99804 q^{64} +0.647848 q^{66} -7.15968 q^{67} +5.31382 q^{68} +1.14167 q^{69} -0.453319 q^{70} -4.76178 q^{71} +7.36122 q^{72} +8.36628 q^{73} +1.60849 q^{74} -0.693282 q^{75} +7.06248 q^{76} -0.485111 q^{77} -13.1974 q^{79} +0.476832 q^{80} +4.90526 q^{81} -2.63360 q^{82} -0.355851 q^{83} +0.378955 q^{84} +4.71596 q^{85} +2.00436 q^{86} +7.11001 q^{87} +2.92186 q^{88} +0.571579 q^{89} +2.35426 q^{90} +1.85553 q^{92} +1.31244 q^{93} -2.71599 q^{94} +6.26788 q^{95} -3.74244 q^{96} +6.62212 q^{97} -6.32135 q^{98} +2.51936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 34 q^{4} - 28 q^{5} + 10 q^{6} - 8 q^{7} - 6 q^{8} + 46 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 34 * q^4 - 28 * q^5 + 10 * q^6 - 8 * q^7 - 6 * q^8 + 46 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 34 q^{4} - 28 q^{5} + 10 q^{6} - 8 q^{7} - 6 q^{8} + 46 q^{9} + 2 q^{10} - 28 q^{11} + 22 q^{12} + 16 q^{14} - 6 q^{15} + 54 q^{16} + 26 q^{17} - 36 q^{18} + 8 q^{19} - 34 q^{20} + 10 q^{21} + 2 q^{22} + 30 q^{23} + 26 q^{24} + 28 q^{25} + 4 q^{28} + 36 q^{29} - 10 q^{30} - 20 q^{31} + 16 q^{32} - 6 q^{33} - 8 q^{34} + 8 q^{35} + 58 q^{36} - 50 q^{37} + 18 q^{38} + 6 q^{40} + 6 q^{41} + 74 q^{42} - 34 q^{44} - 46 q^{45} + 24 q^{46} - 10 q^{47} + 50 q^{48} + 46 q^{49} - 2 q^{50} + 12 q^{51} + 52 q^{53} + 38 q^{54} + 28 q^{55} + 10 q^{57} - 42 q^{58} - 12 q^{59} - 22 q^{60} + 4 q^{61} + 14 q^{62} + 48 q^{63} + 56 q^{64} - 10 q^{66} - 52 q^{67} + 92 q^{68} - 16 q^{69} - 16 q^{70} + 20 q^{71} - 50 q^{72} - 40 q^{73} + 32 q^{74} + 6 q^{75} - 16 q^{76} + 8 q^{77} - 6 q^{79} - 54 q^{80} + 116 q^{81} - 36 q^{82} - 22 q^{83} + 86 q^{84} - 26 q^{85} + 32 q^{86} + 16 q^{87} + 6 q^{88} + 8 q^{89} + 36 q^{90} + 18 q^{92} - 40 q^{93} + 66 q^{94} - 8 q^{95} + 4 q^{96} - 48 q^{97} + 70 q^{98} - 46 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 34 * q^4 - 28 * q^5 + 10 * q^6 - 8 * q^7 - 6 * q^8 + 46 * q^9 + 2 * q^10 - 28 * q^11 + 22 * q^12 + 16 * q^14 - 6 * q^15 + 54 * q^16 + 26 * q^17 - 36 * q^18 + 8 * q^19 - 34 * q^20 + 10 * q^21 + 2 * q^22 + 30 * q^23 + 26 * q^24 + 28 * q^25 + 4 * q^28 + 36 * q^29 - 10 * q^30 - 20 * q^31 + 16 * q^32 - 6 * q^33 - 8 * q^34 + 8 * q^35 + 58 * q^36 - 50 * q^37 + 18 * q^38 + 6 * q^40 + 6 * q^41 + 74 * q^42 - 34 * q^44 - 46 * q^45 + 24 * q^46 - 10 * q^47 + 50 * q^48 + 46 * q^49 - 2 * q^50 + 12 * q^51 + 52 * q^53 + 38 * q^54 + 28 * q^55 + 10 * q^57 - 42 * q^58 - 12 * q^59 - 22 * q^60 + 4 * q^61 + 14 * q^62 + 48 * q^63 + 56 * q^64 - 10 * q^66 - 52 * q^67 + 92 * q^68 - 16 * q^69 - 16 * q^70 + 20 * q^71 - 50 * q^72 - 40 * q^73 + 32 * q^74 + 6 * q^75 - 16 * q^76 + 8 * q^77 - 6 * q^79 - 54 * q^80 + 116 * q^81 - 36 * q^82 - 22 * q^83 + 86 * q^84 - 26 * q^85 + 32 * q^86 + 16 * q^87 + 6 * q^88 + 8 * q^89 + 36 * q^90 + 18 * q^92 - 40 * q^93 + 66 * q^94 - 8 * q^95 + 4 * q^96 - 48 * q^97 + 70 * q^98 - 46 * q^99

Introduction

L-functions

Modular forms

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