LMFDB - Embedded newform 1445.2.d.i.866.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1445,2,Mod(866,1445)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1445.866"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,-6,0,42,0,0,0,-24,-42] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.15
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.i.866.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.704111 q^{2} +3.11994i q^{3} -1.50423 q^{4} -1.00000i q^{5} +2.19679i q^{6} +4.06346i q^{7} -2.46736 q^{8} -6.73405 q^{9} -0.704111i q^{10} +0.231031i q^{11} -4.69311i q^{12} +2.35528 q^{13} +2.86112i q^{14} +3.11994 q^{15} +1.27116 q^{16} -4.74152 q^{18} -7.38657 q^{19} +1.50423i q^{20} -12.6778 q^{21} +0.162671i q^{22} +1.87741i q^{23} -7.69804i q^{24} -1.00000 q^{25} +1.65838 q^{26} -11.6500i q^{27} -6.11237i q^{28} +4.04943i q^{29} +2.19679 q^{30} +0.130455i q^{31} +5.82977 q^{32} -0.720802 q^{33} +4.06346 q^{35} +10.1295 q^{36} -5.82227i q^{37} -5.20096 q^{38} +7.34835i q^{39} +2.46736i q^{40} -8.10305i q^{41} -8.92655 q^{42} +3.69785 q^{43} -0.347523i q^{44} +6.73405i q^{45} +1.32190i q^{46} +1.30633 q^{47} +3.96595i q^{48} -9.51170 q^{49} -0.704111 q^{50} -3.54288 q^{52} -8.26017 q^{53} -8.20291i q^{54} +0.231031 q^{55} -10.0260i q^{56} -23.0457i q^{57} +2.85125i q^{58} -2.29764 q^{59} -4.69311 q^{60} -8.92792i q^{61} +0.0918548i q^{62} -27.3635i q^{63} +1.56248 q^{64} -2.35528i q^{65} -0.507524 q^{66} +14.5995 q^{67} -5.85742 q^{69} +2.86112 q^{70} +11.0065i q^{71} +16.6154 q^{72} +0.471385i q^{73} -4.09952i q^{74} -3.11994i q^{75} +11.1111 q^{76} -0.938783 q^{77} +5.17405i q^{78} +4.31667i q^{79} -1.27116i q^{80} +16.1453 q^{81} -5.70544i q^{82} -15.4238 q^{83} +19.0703 q^{84} +2.60370 q^{86} -12.6340 q^{87} -0.570036i q^{88} +3.68913 q^{89} +4.74152i q^{90} +9.57059i q^{91} -2.82405i q^{92} -0.407012 q^{93} +0.919804 q^{94} +7.38657i q^{95} +18.1885i q^{96} +9.00621i q^{97} -6.69729 q^{98} -1.55577i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 42 q^{4} - 24 q^{8} - 42 q^{9} + 18 q^{13} - 6 q^{15} + 78 q^{16} - 18 q^{18} - 54 q^{19} + 12 q^{21} - 24 q^{25} - 12 q^{26} - 18 q^{30} - 24 q^{32} + 12 q^{35} - 96 q^{36} - 6 q^{38}+ \cdots - 84 q^{98}+O(q^{100}) $ 24 * q - 6 * q^2 + 42 * q^4 - 24 * q^8 - 42 * q^9 + 18 * q^13 - 6 * q^15 + 78 * q^16 - 18 * q^18 - 54 * q^19 + 12 * q^21 - 24 * q^25 - 12 * q^26 - 18 * q^30 - 24 * q^32 + 12 * q^35 - 96 * q^36 - 6 * q^38 - 60 * q^42 - 90 * q^43 + 6 * q^47 - 24 * q^49 + 6 * q^50 + 102 * q^52 + 24 * q^53 - 12 * q^55 - 72 * q^59 - 12 * q^60 + 84 * q^64 + 78 * q^66 + 156 * q^67 - 132 * q^69 + 36 * q^70 - 24 * q^72 - 54 * q^76 + 78 * q^77 + 24 * q^81 - 54 * q^83 + 54 * q^84 + 36 * q^86 - 48 * q^87 + 12 * q^89 + 24 * q^93 - 42 * q^94 - 84 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$-1$	$1$

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 $

$2$	0.704111	0.497881	0.248941	−	0.968519i	$-0.419918\pi$
$2$	0.704111	0.497881	0.248941	+	0.968519i	$0.419918\pi$
$3$	3.11994i	1.80130i	0.434545	+	0.900650i	$0.356909\pi$
$3$	3.11994i	1.80130i	−0.434545	+	0.900650i	$0.643091\pi$
$4$	−1.50423	−0.752114
$5$	− 1.00000i	− 0.447214i
$5$	− 1.00000i	− 0.447214i
$6$	2.19679i	0.896834i
$7$	4.06346i	1.53584i	0.640544	+	0.767922i	$0.278709\pi$
$7$	4.06346i	1.53584i	−0.640544	+	0.767922i	$0.721291\pi$
$8$	−2.46736	−0.872345
$9$	−6.73405	−2.24468
$10$	− 0.704111i	− 0.222659i
$11$	0.231031i	0.0696583i	0.999393	+	0.0348292i	$0.0110887\pi$
$11$	0.231031i	0.0696583i	−0.999393	+	0.0348292i	$0.988911\pi$
$12$	− 4.69311i	− 1.35478i
$13$	2.35528	0.653238	0.326619	−	0.945156i	$-0.394091\pi$
$13$	2.35528	0.653238	0.326619	+	0.945156i	$0.394091\pi$
$14$	2.86112i	0.764668i
$15$	3.11994	0.805566
$16$	1.27116	0.317790
$17$	0	0
$17$	0	0
$18$	−4.74152	−1.11759
$19$	−7.38657	−1.69460	−0.847298	−	0.531118i	$-0.821772\pi$
$19$	−7.38657	−1.69460	−0.847298	+	0.531118i	$0.821772\pi$
$20$	1.50423i	0.336356i
$21$	−12.6778	−2.76651
$22$	0.162671i	0.0346816i
$23$	1.87741i	0.391467i	0.980657	+	0.195734i	$0.0627088\pi$
$23$	1.87741i	0.391467i	−0.980657	+	0.195734i	$0.937291\pi$
$24$	− 7.69804i	− 1.57136i
$25$	−1.00000	−0.200000
$26$	1.65838	0.325235
$27$	− 11.6500i	− 2.24205i
$28$	− 6.11237i	− 1.15513i
$29$	4.04943i	0.751961i	0.926628	+	0.375980i	$0.122694\pi$
$29$	4.04943i	0.751961i	−0.926628	+	0.375980i	$0.877306\pi$
$30$	2.19679	0.401076
$31$	0.130455i	0.0234304i	0.999931	+	0.0117152i	$0.00372915\pi$
$31$	0.130455i	0.0234304i	−0.999931	+	0.0117152i	$0.996271\pi$
$32$	5.82977	1.03057
$33$	−0.720802	−0.125476
$34$	0	0
$35$	4.06346	0.686850
$36$	10.1295	1.68826
$37$	− 5.82227i	− 0.957175i	−0.878040	−	0.478587i	$-0.841149\pi$
$37$	− 5.82227i	− 0.957175i	0.878040	−	0.478587i	$-0.158851\pi$
$38$	−5.20096	−0.843707
$39$	7.34835i	1.17668i
$40$	2.46736i	0.390125i
$41$	− 8.10305i	− 1.26548i	−0.774363	−	0.632742i	$-0.781929\pi$
$41$	− 8.10305i	− 1.26548i	0.774363	−	0.632742i	$-0.218071\pi$
$42$	−8.92655	−1.37740
$43$	3.69785	0.563917	0.281959	−	0.959427i	$-0.409016\pi$
$43$	3.69785	0.563917	0.281959	+	0.959427i	$0.409016\pi$
$44$	− 0.347523i	− 0.0523910i
$45$	6.73405i	1.00385i
$46$	1.32190i	0.194904i
$47$	1.30633	0.190549	0.0952743	−	0.995451i	$-0.469627\pi$
$47$	1.30633	0.190549	0.0952743	+	0.995451i	$0.469627\pi$
$48$	3.96595i	0.572435i
$49$	−9.51170	−1.35881
$50$	−0.704111	−0.0995763
$51$	0	0
$52$	−3.54288	−0.491309
$53$	−8.26017	−1.13462	−0.567311	−	0.823504i	$-0.692016\pi$
$53$	−8.26017	−1.13462	−0.567311	+	0.823504i	$0.692016\pi$
$54$	− 8.20291i	− 1.11627i
$55$	0.231031	0.0311521
$56$	− 10.0260i	− 1.33978i
$57$	− 23.0457i	− 3.05248i
$58$	2.85125i	0.374387i
$59$	−2.29764	−0.299128	−0.149564	−	0.988752i	$-0.547787\pi$
$59$	−2.29764	−0.299128	−0.149564	+	0.988752i	$0.547787\pi$
$60$	−4.69311	−0.605878
$61$	− 8.92792i	− 1.14310i	−0.820566	−	0.571552i	$-0.806342\pi$
$61$	− 8.92792i	− 1.14310i	0.820566	−	0.571552i	$-0.193658\pi$
$62$	0.0918548i	0.0116656i
$63$	− 27.3635i	− 3.44748i
$64$	1.56248	0.195310
$65$	− 2.35528i	− 0.292137i
$66$	−0.507524	−0.0624719
$67$	14.5995	1.78361	0.891805	−	0.452419i	$-0.149439\pi$
$67$	14.5995	1.78361	0.891805	+	0.452419i	$0.149439\pi$
$68$	0	0
$69$	−5.85742	−0.705150
$70$	2.86112	0.341970
$71$	11.0065i	1.30623i	0.757257	+	0.653117i	$0.226539\pi$
$71$	11.0065i	1.30623i	−0.757257	+	0.653117i	$0.773461\pi$
$72$	16.6154	1.95814
$73$	0.471385i	0.0551714i	0.999619	+	0.0275857i	$0.00878191\pi$
$73$	0.471385i	0.0551714i	−0.999619	+	0.0275857i	$0.991218\pi$
$74$	− 4.09952i	− 0.476560i
$75$	− 3.11994i	− 0.360260i
$76$	11.1111	1.27453
$77$	−0.938783	−0.106984
$78$	5.17405i	0.585846i
$79$	4.31667i	0.485663i	0.970069	+	0.242831i	$0.0780762\pi$
$79$	4.31667i	0.485663i	−0.970069	+	0.242831i	$0.921924\pi$
$80$	− 1.27116i	− 0.142120i
$81$	16.1453	1.79392
$82$	− 5.70544i	− 0.630061i
$83$	−15.4238	−1.69298	−0.846489	−	0.532407i	$-0.821288\pi$
$83$	−15.4238	−1.69298	−0.846489	+	0.532407i	$0.821288\pi$
$84$	19.0703	2.08073
$85$	0	0
$86$	2.60370	0.280764
$87$	−12.6340	−1.35451
$88$	− 0.570036i	− 0.0607661i
$89$	3.68913	0.391047	0.195523	−	0.980699i	$-0.437359\pi$
$89$	3.68913	0.391047	0.195523	+	0.980699i	$0.437359\pi$
$90$	4.74152i	0.499800i
$91$	9.57059i	1.00327i
$92$	− 2.82405i	− 0.294428i
$93$	−0.407012	−0.0422052
$94$	0.919804	0.0948706
$95$	7.38657i	0.757846i
$96$	18.1885i	1.85636i
$97$	9.00621i	0.914442i	0.889353	+	0.457221i	$0.151155\pi$
$97$	9.00621i	0.914442i	−0.889353	+	0.457221i	$0.848845\pi$
$98$	−6.69729	−0.676528
$99$	− 1.55577i	− 0.156361i
$100$	1.50423	0.150423
$101$	−6.94560	−0.691113	−0.345556	−	0.938398i	$-0.612310\pi$
$101$	−6.94560	−0.691113	−0.345556	+	0.938398i	$0.612310\pi$
$102$	0	0
$103$	−1.04422	−0.102891	−0.0514453	−	0.998676i	$-0.516383\pi$
$103$	−1.04422	−0.102891	−0.0514453	+	0.998676i	$0.516383\pi$
$104$	−5.81134	−0.569849
$105$	12.6778i	1.23722i
$106$	−5.81607	−0.564907
$107$	− 10.0027i	− 0.966999i	−0.875345	−	0.483500i	$-0.839365\pi$
$107$	− 10.0027i	− 0.966999i	0.875345	−	0.483500i	$-0.160635\pi$
$108$	17.5243i	1.68628i
$109$	8.14200i	0.779863i	0.920844	+	0.389931i	$0.127501\pi$
$109$	8.14200i	0.779863i	−0.920844	+	0.389931i	$0.872499\pi$
$110$	0.162671	0.0155101
$111$	18.1651	1.72416
$112$	5.16530i	0.488075i
$113$	13.0656i	1.22911i	0.788873	+	0.614556i	$0.210665\pi$
$113$	13.0656i	1.22911i	−0.788873	+	0.614556i	$0.789335\pi$
$114$	− 16.2267i	− 1.51977i
$115$	1.87741	0.175069
$116$	− 6.09127i	− 0.565560i
$117$	−15.8606	−1.46631
$118$	−1.61779	−0.148930
$119$	0	0
$120$	−7.69804	−0.702731
$121$	10.9466	0.995148
$122$	− 6.28624i	− 0.569130i
$123$	25.2811	2.27952
$124$	− 0.196234i	− 0.0176223i
$125$	1.00000i	0.0894427i
$126$	− 19.2670i	− 1.71644i
$127$	−0.745900	−0.0661879	−0.0330939	−	0.999452i	$-0.510536\pi$
$127$	−0.745900	−0.0661879	−0.0330939	+	0.999452i	$0.510536\pi$
$128$	−10.5594	−0.933325
$129$	11.5371i	1.01578i
$130$	− 1.65838i	− 0.145449i
$131$	5.67574i	0.495891i	0.968774	+	0.247946i	$0.0797555\pi$
$131$	5.67574i	0.495891i	−0.968774	+	0.247946i	$0.920245\pi$
$132$	1.08425	0.0943720
$133$	− 30.0150i	− 2.60263i
$134$	10.2797	0.888027
$135$	−11.6500	−1.00267
$136$	0	0
$137$	−19.6850	−1.68180	−0.840900	−	0.541190i	$-0.817974\pi$
$137$	−19.6850	−1.68180	−0.840900	+	0.541190i	$0.817974\pi$
$138$	−4.12427	−0.351081
$139$	− 5.64706i	− 0.478977i	−0.970899	−	0.239489i	$-0.923020\pi$
$139$	− 5.64706i	− 0.478977i	0.970899	−	0.239489i	$-0.0769798\pi$
$140$	−6.11237	−0.516590
$141$	4.07569i	0.343235i
$142$	7.74981i	0.650350i
$143$	0.544142i	0.0455034i
$144$	−8.56005	−0.713338
$145$	4.04943	0.336287
$146$	0.331907i	0.0274688i
$147$	− 29.6760i	− 2.44763i
$148$	8.75802i	0.719905i
$149$	−19.0000	−1.55654	−0.778269	−	0.627931i	$-0.783902\pi$
$149$	−19.0000	−1.55654	−0.778269	+	0.627931i	$0.783902\pi$
$150$	− 2.19679i	− 0.179367i
$151$	−6.95236	−0.565775	−0.282887	−	0.959153i	$-0.591292\pi$
$151$	−6.95236	−0.565775	−0.282887	+	0.959153i	$0.591292\pi$
$152$	18.2254	1.47827
$153$	0	0
$154$	−0.661007	−0.0532655
$155$	0.130455	0.0104784
$156$	− 11.0536i	− 0.884996i
$157$	−7.18338	−0.573296	−0.286648	−	0.958036i	$-0.592541\pi$
$157$	−7.18338	−0.573296	−0.286648	+	0.958036i	$0.592541\pi$
$158$	3.03941i	0.241802i
$159$	− 25.7713i	− 2.04379i
$160$	− 5.82977i	− 0.460883i
$161$	−7.62878	−0.601232
$162$	11.3681	0.893159
$163$	− 12.3259i	− 0.965443i	−0.875774	−	0.482721i	$-0.839648\pi$
$163$	− 12.3259i	− 0.965443i	0.875774	−	0.482721i	$-0.160352\pi$
$164$	12.1888i	0.951788i
$165$	0.720802i	0.0561144i
$166$	−10.8600	−0.842902
$167$	2.10123i	0.162598i	0.996690	+	0.0812990i	$0.0259069\pi$
$167$	2.10123i	0.162598i	−0.996690	+	0.0812990i	$0.974093\pi$
$168$	31.2807	2.41336
$169$	−7.45265	−0.573281
$170$	0	0
$171$	49.7415	3.80383
$172$	−5.56242	−0.424130
$173$	− 2.38845i	− 0.181590i	−0.995870	−	0.0907952i	$-0.971059\pi$
$173$	− 2.38845i	− 0.181590i	0.995870	−	0.0907952i	$-0.0289409\pi$
$174$	−8.89573	−0.674384
$175$	− 4.06346i	− 0.307169i
$176$	0.293677i	0.0221367i
$177$	− 7.16852i	− 0.538819i
$178$	2.59755	0.194695
$179$	2.06564	0.154394	0.0771968	−	0.997016i	$-0.475403\pi$
$179$	2.06564	0.154394	0.0771968	+	0.997016i	$0.475403\pi$
$180$	− 10.1295i	− 0.755012i
$181$	10.0975i	0.750542i	0.926915	+	0.375271i	$0.122450\pi$
$181$	10.0975i	0.750542i	−0.926915	+	0.375271i	$0.877550\pi$
$182$	6.73875i	0.499510i
$183$	27.8546	2.05907
$184$	− 4.63225i	− 0.341494i
$185$	−5.82227	−0.428062
$186$	−0.286582	−0.0210132
$187$	0	0
$188$	−1.96503	−0.143314
$189$	47.3394	3.44343
$190$	5.20096i	0.377317i
$191$	−26.5500	−1.92109	−0.960547	−	0.278119i	$-0.910289\pi$
$191$	−26.5500	−1.92109	−0.960547	+	0.278119i	$0.910289\pi$
$192$	4.87485i	0.351812i
$193$	6.80795i	0.490047i	0.969517	+	0.245023i	$0.0787957\pi$
$193$	6.80795i	0.490047i	−0.969517	+	0.245023i	$0.921204\pi$
$194$	6.34137i	0.455284i
$195$	7.34835	0.526226
$196$	14.3078	1.02198
$197$	6.05995i	0.431753i	0.976421	+	0.215877i	$0.0692609\pi$
$197$	6.05995i	0.431753i	−0.976421	+	0.215877i	$0.930739\pi$
$198$	− 1.09543i	− 0.0778492i
$199$	11.3467i	0.804343i	0.915564	+	0.402172i	$0.131745\pi$
$199$	11.3467i	0.804343i	−0.915564	+	0.402172i	$0.868255\pi$
$200$	2.46736	0.174469
$201$	45.5496i	3.21282i
$202$	−4.89047	−0.344092
$203$	−16.4547	−1.15489
$204$	0	0
$205$	−8.10305	−0.565942
$206$	−0.735250	−0.0512273
$207$	− 12.6426i	− 0.878720i
$208$	2.99394	0.207592
$209$	− 1.70652i	− 0.118043i
$210$	8.92655i	0.615990i
$211$	13.7348i	0.945543i	0.881185	+	0.472772i	$0.156746\pi$
$211$	13.7348i	0.945543i	−0.881185	+	0.472772i	$0.843254\pi$
$212$	12.4252	0.853365
$213$	−34.3397	−2.35292
$214$	− 7.04302i	− 0.481451i
$215$	− 3.69785i	− 0.252191i
$216$	28.7449i	1.95584i
$217$	−0.530099	−0.0359854
$218$	5.73287i	0.388279i
$219$	−1.47069	−0.0993802
$220$	−0.347523	−0.0234300
$221$	0	0
$222$	12.7903	0.858427
$223$	3.57068	0.239110	0.119555	−	0.992828i	$-0.461853\pi$
$223$	3.57068	0.239110	0.119555	+	0.992828i	$0.461853\pi$
$224$	23.6890i	1.58279i
$225$	6.73405	0.448937
$226$	9.19966i	0.611952i
$227$	23.3475i	1.54963i	0.632187	+	0.774816i	$0.282157\pi$
$227$	23.3475i	1.54963i	−0.632187	+	0.774816i	$0.717843\pi$
$228$	34.6660i	2.29581i
$229$	−25.2530	−1.66877	−0.834384	−	0.551184i	$-0.814176\pi$
$229$	−25.2530	−1.66877	−0.834384	+	0.551184i	$0.814176\pi$
$230$	1.32190	0.0871638
$231$	− 2.92895i	− 0.192711i
$232$	− 9.99142i	− 0.655969i
$233$	− 1.76097i	− 0.115365i	−0.998335	−	0.0576824i	$-0.981629\pi$
$233$	− 1.76097i	− 0.115365i	0.998335	−	0.0576824i	$-0.0183711\pi$
$234$	−11.1676	−0.730049
$235$	− 1.30633i	− 0.0852159i
$236$	3.45618	0.224978
$237$	−13.4678	−0.874825
$238$	0	0
$239$	21.2916	1.37724	0.688621	−	0.725122i	$-0.258216\pi$
$239$	21.2916	1.37724	0.688621	+	0.725122i	$0.258216\pi$
$240$	3.96595	0.256001
$241$	10.1369i	0.652972i	0.945202	+	0.326486i	$0.105865\pi$
$241$	10.1369i	0.652972i	−0.945202	+	0.326486i	$0.894135\pi$
$242$	7.70763	0.495465
$243$	15.4223i	0.989340i
$244$	13.4296i	0.859744i
$245$	9.51170i	0.607680i
$246$	17.8007	1.13493
$247$	−17.3975	−1.10697
$248$	− 0.321880i	− 0.0204394i
$249$	− 48.1213i	− 3.04956i
$250$	0.704111i	0.0445319i
$251$	17.5960	1.11065	0.555326	−	0.831633i	$-0.312593\pi$
$251$	17.5960	1.11065	0.555326	+	0.831633i	$0.312593\pi$
$252$	41.1610i	2.59290i
$253$	−0.433739	−0.0272689
$254$	−0.525196	−0.0329537
$255$	0	0
$256$	−10.5599	−0.659995
$257$	−10.0995	−0.629990	−0.314995	−	0.949093i	$-0.602003\pi$
$257$	−10.0995	−0.629990	−0.314995	+	0.949093i	$0.602003\pi$
$258$	8.12339i	0.505740i
$259$	23.6585	1.47007
$260$	3.54288i	0.219720i
$261$	− 27.2691i	− 1.68791i
$262$	3.99635i	0.246895i
$263$	16.0060	0.986973	0.493487	−	0.869753i	$-0.335722\pi$
$263$	16.0060	0.986973	0.493487	+	0.869753i	$0.335722\pi$
$264$	1.77848	0.109458
$265$	8.26017i	0.507418i
$266$	− 21.1339i	− 1.29580i
$267$	11.5099i	0.704393i
$268$	−21.9610	−1.34148
$269$	13.0629i	0.796457i	0.917286	+	0.398229i	$0.130375\pi$
$269$	13.0629i	0.796457i	−0.917286	+	0.398229i	$0.869625\pi$
$270$	−8.20291	−0.499213
$271$	17.3388	1.05325	0.526627	−	0.850096i	$-0.323456\pi$
$271$	17.3388	1.05325	0.526627	+	0.850096i	$0.323456\pi$
$272$	0	0
$273$	−29.8597	−1.80719
$274$	−13.8604	−0.837337
$275$	− 0.231031i	− 0.0139317i
$276$	8.81089	0.530353
$277$	10.9525i	0.658075i	0.944317	+	0.329037i	$0.106724\pi$
$277$	10.9525i	0.658075i	−0.944317	+	0.329037i	$0.893276\pi$
$278$	− 3.97615i	− 0.238474i
$279$	− 0.878491i	− 0.0525939i
$280$	−10.0260	−0.599170
$281$	3.09350	0.184543	0.0922714	−	0.995734i	$-0.470587\pi$
$281$	3.09350	0.184543	0.0922714	+	0.995734i	$0.470587\pi$
$282$	2.86974i	0.170890i
$283$	− 0.469462i	− 0.0279066i	−0.999903	−	0.0139533i	$-0.995558\pi$
$283$	− 0.469462i	− 0.0279066i	0.999903	−	0.0139533i	$-0.00444162\pi$
$284$	− 16.5563i	− 0.982437i
$285$	−23.0457	−1.36511
$286$	0.383136i	0.0226553i
$287$	32.9264	1.94358
$288$	−39.2579	−2.31330
$289$	0	0
$290$	2.85125	0.167431
$291$	−28.0989	−1.64718
$292$	− 0.709070i	− 0.0414952i
$293$	−20.6954	−1.20904	−0.604520	−	0.796590i	$-0.706635\pi$
$293$	−20.6954	−1.20904	−0.604520	+	0.796590i	$0.706635\pi$
$294$	− 20.8952i	− 1.21863i
$295$	2.29764i	0.133774i
$296$	14.3657i	0.834987i
$297$	2.69151	0.156177
$298$	−13.3781	−0.774971
$299$	4.42183i	0.255721i
$300$	4.69311i	0.270957i
$301$	15.0261i	0.866088i
$302$	−4.89523	−0.281689
$303$	− 21.6699i	− 1.24490i
$304$	−9.38951	−0.538525
$305$	−8.92792	−0.511211
$306$	0	0
$307$	21.9900	1.25504	0.627519	−	0.778601i	$-0.284071\pi$
$307$	21.9900	1.25504	0.627519	+	0.778601i	$0.284071\pi$
$308$	1.41214	0.0804644
$309$	− 3.25792i	− 0.185337i
$310$	0.0918548	0.00521700
$311$	− 24.4834i	− 1.38833i	−0.719817	−	0.694163i	$-0.755774\pi$
$311$	− 24.4834i	− 1.38833i	0.719817	−	0.694163i	$-0.244226\pi$
$312$	− 18.1310i	− 1.02647i
$313$	2.87540i	0.162527i	0.996693	+	0.0812635i	$0.0258955\pi$
$313$	2.87540i	0.162527i	−0.996693	+	0.0812635i	$0.974104\pi$
$314$	−5.05790	−0.285434
$315$	−27.3635	−1.54176
$316$	− 6.49325i	− 0.365274i
$317$	23.5740i	1.32405i	0.749482	+	0.662025i	$0.230303\pi$
$317$	23.5740i	1.32405i	−0.749482	+	0.662025i	$0.769697\pi$
$318$	− 18.1458i	− 1.01757i
$319$	−0.935542	−0.0523803
$320$	− 1.56248i	− 0.0873453i
$321$	31.2079	1.74186
$322$	−5.37150	−0.299342
$323$	0	0
$324$	−24.2862	−1.34923
$325$	−2.35528	−0.130648
$326$	− 8.67883i	− 0.480676i
$327$	−25.4026	−1.40477
$328$	19.9932i	1.10394i
$329$	5.30824i	0.292653i
$330$	0.507524i	0.0279383i
$331$	−25.0816	−1.37861	−0.689306	−	0.724471i	$-0.742084\pi$
$331$	−25.0816	−1.37861	−0.689306	+	0.724471i	$0.742084\pi$
$332$	23.2009	1.27331
$333$	39.2074i	2.14855i
$334$	1.47950i	0.0809545i
$335$	− 14.5995i	− 0.797655i
$336$	−16.1155	−0.879171
$337$	− 16.4774i	− 0.897581i	−0.893637	−	0.448790i	$-0.851855\pi$
$337$	− 16.4774i	− 0.897581i	0.893637	−	0.448790i	$-0.148145\pi$
$338$	−5.24749	−0.285426
$339$	−40.7641	−2.21400
$340$	0	0
$341$	−0.0301391	−0.00163212
$342$	35.0235	1.89386
$343$	− 10.2062i	− 0.551082i
$344$	−9.12395	−0.491930
$345$	5.85742i	0.315353i
$346$	− 1.68173i	− 0.0904105i
$347$	17.0278i	0.914100i	0.889441	+	0.457050i	$0.151094\pi$
$347$	17.0278i	0.914100i	−0.889441	+	0.457050i	$0.848906\pi$
$348$	19.0044	1.01874
$349$	6.72216	0.359829	0.179915	−	0.983682i	$-0.442418\pi$
$349$	6.72216	0.359829	0.179915	+	0.983682i	$0.442418\pi$
$350$	− 2.86112i	− 0.152934i
$351$	− 27.4391i	− 1.46459i
$352$	1.34685i	0.0717875i
$353$	2.22223	0.118277	0.0591386	−	0.998250i	$-0.481165\pi$
$353$	2.22223	0.118277	0.0591386	+	0.998250i	$0.481165\pi$
$354$	− 5.04743i	− 0.268268i
$355$	11.0065	0.584166
$356$	−5.54929	−0.294112
$357$	0	0
$358$	1.45444	0.0768696
$359$	−16.7305	−0.883000	−0.441500	−	0.897261i	$-0.645553\pi$
$359$	−16.7305	−0.883000	−0.441500	+	0.897261i	$0.645553\pi$
$360$	− 16.6154i	− 0.875706i
$361$	35.5614	1.87165
$362$	7.10977i	0.373681i
$363$	34.1529i	1.79256i
$364$	− 14.3964i	− 0.754574i
$365$	0.471385	0.0246734
$366$	19.6127	1.02517
$367$	17.8974i	0.934237i	0.884195	+	0.467119i	$0.154708\pi$
$367$	17.8974i	0.934237i	−0.884195	+	0.467119i	$0.845292\pi$
$368$	2.38649i	0.124404i
$369$	54.5664i	2.84061i
$370$	−4.09952	−0.213124
$371$	− 33.5648i	− 1.74260i
$372$	0.612240	0.0317431
$373$	16.3386	0.845983	0.422991	−	0.906134i	$-0.360980\pi$
$373$	16.3386	0.845983	0.422991	+	0.906134i	$0.360980\pi$
$374$	0	0
$375$	−3.11994	−0.161113
$376$	−3.22320	−0.166224
$377$	9.53755i	0.491209i
$378$	33.3322	1.71442
$379$	− 14.5126i	− 0.745464i	−0.927939	−	0.372732i	$-0.878421\pi$
$379$	− 14.5126i	− 0.745464i	0.927939	−	0.372732i	$-0.121579\pi$
$380$	− 11.1111i	− 0.569987i
$381$	− 2.32717i	− 0.119224i
$382$	−18.6942	−0.956476
$383$	1.18611	0.0606074	0.0303037	−	0.999541i	$-0.490353\pi$
$383$	1.18611	0.0606074	0.0303037	+	0.999541i	$0.490353\pi$
$384$	− 32.9446i	− 1.68120i
$385$	0.938783i	0.0478448i
$386$	4.79355i	0.243985i
$387$	−24.9015	−1.26582
$388$	− 13.5474i	− 0.687765i
$389$	23.1832	1.17543	0.587717	−	0.809066i	$-0.300027\pi$
$389$	23.1832	1.17543	0.587717	+	0.809066i	$0.300027\pi$
$390$	5.17405	0.261998
$391$	0	0
$392$	23.4688	1.18535
$393$	−17.7080	−0.893249
$394$	4.26687i	0.214962i
$395$	4.31667	0.217195
$396$	2.34023i	0.117601i
$397$	− 35.2709i	− 1.77019i	−0.465406	−	0.885097i	$-0.654092\pi$
$397$	− 35.2709i	− 1.77019i	0.465406	−	0.885097i	$-0.345908\pi$
$398$	7.98930i	0.400468i
$399$	93.6452	4.68812
$400$	−1.27116	−0.0635580
$401$	33.6355i	1.67968i	0.542837	+	0.839838i	$0.317350\pi$
$401$	33.6355i	1.67968i	−0.542837	+	0.839838i	$0.682650\pi$
$402$	32.0719i	1.59960i
$403$	0.307258i	0.0153056i
$404$	10.4478	0.519796
$405$	− 16.1453i	− 0.802265i
$406$	−11.5859	−0.575000
$407$	1.34512	0.0666752
$408$	0	0
$409$	18.0019	0.890135	0.445068	−	0.895497i	$-0.353180\pi$
$409$	18.0019	0.890135	0.445068	+	0.895497i	$0.353180\pi$
$410$	−5.70544	−0.281772
$411$	− 61.4160i	− 3.02943i
$412$	1.57075	0.0773854
$413$	− 9.33638i	− 0.459413i
$414$	− 8.90177i	− 0.437498i
$415$	15.4238i	0.757122i
$416$	13.7307	0.673205
$417$	17.6185	0.862782
$418$	− 1.20158i	− 0.0587712i
$419$	6.34658i	0.310051i	0.987910	+	0.155025i	$0.0495460\pi$
$419$	6.34658i	0.310051i	−0.987910	+	0.155025i	$0.950454\pi$
$420$	− 19.0703i	− 0.930533i
$421$	−22.0829	−1.07625	−0.538127	−	0.842864i	$-0.680868\pi$
$421$	−22.0829	−1.07625	−0.538127	+	0.842864i	$0.680868\pi$
$422$	9.67082i	0.470768i
$423$	−8.79692	−0.427721
$424$	20.3808	0.989781
$425$	0	0
$426$	−24.1790	−1.17148
$427$	36.2782	1.75563
$428$	15.0464i	0.727294i
$429$	−1.69769	−0.0819654
$430$	− 2.60370i	− 0.125561i
$431$	− 32.7753i	− 1.57873i	−0.613924	−	0.789365i	$-0.710410\pi$
$431$	− 32.7753i	− 1.57873i	0.613924	−	0.789365i	$-0.289590\pi$
$432$	− 14.8090i	− 0.712500i
$433$	−2.69414	−0.129472	−0.0647361	−	0.997902i	$-0.520621\pi$
$433$	−2.69414	−0.129472	−0.0647361	+	0.997902i	$0.520621\pi$
$434$	−0.373248	−0.0179165
$435$	12.6340i	0.605754i
$436$	− 12.2474i	− 0.586546i
$437$	− 13.8676i	− 0.663378i
$438$	−1.03553	−0.0494796
$439$	24.3493i	1.16213i	0.813858	+	0.581063i	$0.197363\pi$
$439$	24.3493i	1.16213i	−0.813858	+	0.581063i	$0.802637\pi$
$440$	−0.570036	−0.0271754
$441$	64.0522	3.05011
$442$	0	0
$443$	−31.9645	−1.51868	−0.759341	−	0.650693i	$-0.774478\pi$
$443$	−31.9645	−1.51868	−0.759341	+	0.650693i	$0.774478\pi$
$444$	−27.3245	−1.29676
$445$	− 3.68913i	− 0.174881i
$446$	2.51415	0.119048
$447$	− 59.2788i	− 2.80379i
$448$	6.34907i	0.299965i
$449$	− 35.8993i	− 1.69419i	−0.531438	−	0.847097i	$-0.678348\pi$
$449$	− 35.8993i	− 1.69419i	0.531438	−	0.847097i	$-0.321652\pi$
$450$	4.74152	0.223517
$451$	1.87205	0.0881515
$452$	− 19.6537i	− 0.924433i
$453$	− 21.6910i	− 1.01913i
$454$	16.4393i	0.771532i
$455$	9.57059	0.448676
$456$	56.8621i	2.66281i
$457$	−42.0589	−1.96743	−0.983717	−	0.179724i	$-0.942480\pi$
$457$	−42.0589	−1.96743	−0.983717	+	0.179724i	$0.942480\pi$
$458$	−17.7809	−0.830848
$459$	0	0
$460$	−2.82405	−0.131672
$461$	24.5172	1.14188	0.570940	−	0.820992i	$-0.306579\pi$
$461$	24.5172	1.14188	0.570940	+	0.820992i	$0.306579\pi$
$462$	− 2.06230i	− 0.0959471i
$463$	12.9662	0.602590	0.301295	−	0.953531i	$-0.402581\pi$
$463$	12.9662	0.602590	0.301295	+	0.953531i	$0.402581\pi$
$464$	5.14747i	0.238966i
$465$	0.407012i	0.0188747i
$466$	− 1.23992i	− 0.0574380i
$467$	32.3125	1.49524	0.747622	−	0.664124i	$-0.231195\pi$
$467$	32.3125	1.49524	0.747622	+	0.664124i	$0.231195\pi$
$468$	23.8579	1.10283
$469$	59.3244i	2.73935i
$470$	− 0.919804i	− 0.0424274i
$471$	− 22.4118i	− 1.03268i
$472$	5.66912	0.260942
$473$	0.854317i	0.0392815i
$474$	−9.48279	−0.435559
$475$	7.38657	0.338919
$476$	0	0
$477$	55.6244	2.54687
$478$	14.9917	0.685703
$479$	14.4494i	0.660209i	0.943944	+	0.330104i	$0.107084\pi$
$479$	14.4494i	0.660209i	−0.943944	+	0.330104i	$0.892916\pi$
$480$	18.1885	0.830189
$481$	− 13.7131i	− 0.625263i
$482$	7.13747i	0.325103i
$483$	− 23.8014i	− 1.08300i
$484$	−16.4662	−0.748465
$485$	9.00621	0.408951
$486$	10.8590i	0.492574i
$487$	35.3420i	1.60150i	0.598998	+	0.800750i	$0.295566\pi$
$487$	35.3420i	1.60150i	−0.598998	+	0.800750i	$0.704434\pi$
$488$	22.0284i	0.997181i
$489$	38.4563	1.73905
$490$	6.69729i	0.302553i
$491$	−38.2821	−1.72765	−0.863825	−	0.503793i	$-0.831937\pi$
$491$	−38.2821	−1.72765	−0.863825	+	0.503793i	$0.831937\pi$
$492$	−38.0285	−1.71446
$493$	0	0
$494$	−12.2497	−0.551141
$495$	−1.55577	−0.0699267
$496$	0.165829i	0.00744595i
$497$	−44.7246	−2.00617
$498$	− 33.8827i	− 1.51832i
$499$	25.5250i	1.14266i	0.820721	+	0.571329i	$0.193572\pi$
$499$	25.5250i	1.14266i	−0.820721	+	0.571329i	$0.806428\pi$
$500$	− 1.50423i	− 0.0672711i
$501$	−6.55572	−0.292888
$502$	12.3896	0.552973
$503$	− 37.8180i	− 1.68622i	−0.537742	−	0.843110i	$-0.680722\pi$
$503$	− 37.8180i	− 1.68622i	0.537742	−	0.843110i	$-0.319278\pi$
$504$	67.5158i	3.00739i
$505$	6.94560i	0.309075i
$506$	−0.305400	−0.0135767
$507$	− 23.2518i	− 1.03265i
$508$	1.12200	0.0497809
$509$	16.2321	0.719476	0.359738	−	0.933053i	$-0.382866\pi$
$509$	16.2321	0.719476	0.359738	+	0.933053i	$0.382866\pi$
$510$	0	0
$511$	−1.91545	−0.0847346
$512$	13.6834	0.604726
$513$	86.0537i	3.79937i
$514$	−7.11117	−0.313660
$515$	1.04422i	0.0460140i
$516$	− 17.3544i	− 0.763986i
$517$	0.301803i	0.0132733i
$518$	16.6582	0.731921
$519$	7.45183	0.327099
$520$	5.81134i	0.254844i
$521$	− 17.6650i	− 0.773916i	−0.922097	−	0.386958i	$-0.873526\pi$
$521$	− 17.6650i	− 0.773916i	0.922097	−	0.386958i	$-0.126474\pi$
$522$	− 19.2004i	− 0.840381i
$523$	9.51295	0.415972	0.207986	−	0.978132i	$-0.433309\pi$
$523$	9.51295	0.415972	0.207986	+	0.978132i	$0.433309\pi$
$524$	− 8.53760i	− 0.372967i
$525$	12.6778	0.553303
$526$	11.2700	0.491396
$527$	0	0
$528$	−0.916255	−0.0398749
$529$	19.4753	0.846753
$530$	5.81607i	0.252634i
$531$	15.4724	0.671447
$532$	45.1494i	1.95748i
$533$	− 19.0850i	− 0.826662i
$534$	8.10422i	0.350704i
$535$	−10.0027	−0.432455
$536$	−36.0222	−1.55592
$537$	6.44469i	0.278109i
$538$	9.19770i	0.396541i
$539$	− 2.19749i	− 0.0946527i
$540$	17.5243	0.754126
$541$	− 12.2201i	− 0.525382i	−0.964880	−	0.262691i	$-0.915390\pi$
$541$	− 12.2201i	− 0.525382i	0.964880	−	0.262691i	$-0.0846101\pi$
$542$	12.2084	0.524396
$543$	−31.5037	−1.35195
$544$	0	0
$545$	8.14200	0.348765
$546$	−21.0245	−0.899767
$547$	14.8127i	0.633345i	0.948535	+	0.316672i	$0.102566\pi$
$547$	14.8127i	0.633345i	−0.948535	+	0.316672i	$0.897434\pi$
$548$	29.6107	1.26491
$549$	60.1211i	2.56591i
$550$	− 0.162671i	− 0.00693632i
$551$	− 29.9114i	− 1.27427i
$552$	14.4524	0.615134
$553$	−17.5406	−0.745902
$554$	7.71180i	0.327643i
$555$	− 18.1651i	− 0.771068i
$556$	8.49447i	0.360246i
$557$	18.6501	0.790230	0.395115	−	0.918632i	$-0.370705\pi$
$557$	18.6501	0.790230	0.395115	+	0.918632i	$0.370705\pi$
$558$	− 0.618555i	− 0.0261855i
$559$	8.70949	0.368372
$560$	5.16530	0.218274
$561$	0	0
$562$	2.17817	0.0918804
$563$	12.5501	0.528923	0.264461	−	0.964396i	$-0.414806\pi$
$563$	12.5501	0.528923	0.264461	+	0.964396i	$0.414806\pi$
$564$	− 6.13077i	− 0.258152i
$565$	13.0656	0.549676
$566$	− 0.330553i	− 0.0138942i
$567$	65.6057i	2.75518i
$568$	− 27.1571i	− 1.13949i
$569$	−13.8442	−0.580377	−0.290189	−	0.956969i	$-0.593718\pi$
$569$	−13.8442	−0.580377	−0.290189	+	0.956969i	$0.593718\pi$
$570$	−16.2267	−0.679662
$571$	− 45.4021i	− 1.90002i	−0.312224	−	0.950009i	$-0.601074\pi$
$571$	− 45.4021i	− 1.90002i	0.312224	−	0.950009i	$-0.398926\pi$
$572$	− 0.818514i	− 0.0342238i
$573$	− 82.8346i	− 3.46047i
$574$	23.1838	0.967675
$575$	− 1.87741i	− 0.0782934i
$576$	−10.5218	−0.438409
$577$	−18.7645	−0.781177	−0.390588	−	0.920565i	$-0.627728\pi$
$577$	−18.7645	−0.781177	−0.390588	+	0.920565i	$0.627728\pi$
$578$	0	0
$579$	−21.2404	−0.882722
$580$	−6.09127	−0.252926
$581$	− 62.6738i	− 2.60015i
$582$	−19.7847	−0.820103
$583$	− 1.90835i	− 0.0790358i
$584$	− 1.16308i	− 0.0481285i
$585$	15.8606i	0.655755i
$586$	−14.5719	−0.601959
$587$	26.4900	1.09336	0.546679	−	0.837342i	$-0.315892\pi$
$587$	26.4900	1.09336	0.546679	+	0.837342i	$0.315892\pi$
$588$	44.6394i	1.84090i
$589$	− 0.963615i	− 0.0397051i
$590$	1.61779i	0.0666035i
$591$	−18.9067	−0.777717
$592$	− 7.40103i	− 0.304181i
$593$	33.8360	1.38948	0.694740	−	0.719261i	$-0.255520\pi$
$593$	33.8360	1.38948	0.694740	+	0.719261i	$0.255520\pi$
$594$	1.89512	0.0777578
$595$	0	0
$596$	28.5803	1.17069
$597$	−35.4009	−1.44886
$598$	3.11346i	0.127319i
$599$	10.9189	0.446133	0.223067	−	0.974803i	$-0.428393\pi$
$599$	10.9189	0.446133	0.223067	+	0.974803i	$0.428393\pi$
$600$	7.69804i	0.314271i
$601$	− 13.7204i	− 0.559667i	−0.960049	−	0.279833i	$-0.909721\pi$
$601$	− 13.7204i	− 0.559667i	0.960049	−	0.279833i	$-0.0902792\pi$
$602$	10.5800i	0.431209i
$603$	−98.3137	−4.00364
$604$	10.4579	0.425527
$605$	− 10.9466i	− 0.445044i
$606$	− 15.2580i	− 0.619813i
$607$	26.5777i	1.07876i	0.842063	+	0.539379i	$0.181341\pi$
$607$	26.5777i	1.07876i	−0.842063	+	0.539379i	$0.818659\pi$
$608$	−43.0620	−1.74639
$609$	− 51.3377i	− 2.08031i
$610$	−6.28624	−0.254523
$611$	3.07679	0.124473
$612$	0	0
$613$	11.9043	0.480812	0.240406	−	0.970672i	$-0.422719\pi$
$613$	11.9043	0.480812	0.240406	+	0.970672i	$0.422719\pi$
$614$	15.4834	0.624860
$615$	− 25.2811i	− 1.01943i
$616$	2.31632	0.0933272
$617$	7.85884i	0.316385i	0.987408	+	0.158193i	$0.0505667\pi$
$617$	7.85884i	0.316385i	−0.987408	+	0.158193i	$0.949433\pi$
$618$	− 2.29394i	− 0.0922757i
$619$	32.7760i	1.31738i	0.752416	+	0.658689i	$0.228889\pi$
$619$	32.7760i	1.31738i	−0.752416	+	0.658689i	$0.771111\pi$
$620$	−0.196234	−0.00788095
$621$	21.8719	0.877688
$622$	− 17.2390i	− 0.691222i
$623$	14.9906i	0.600587i
$624$	9.34092i	0.373936i
$625$	1.00000	0.0400000
$626$	2.02460i	0.0809192i
$627$	5.32426	0.212630
$628$	10.8054	0.431184
$629$	0	0
$630$	−19.2670	−0.767614
$631$	12.5294	0.498789	0.249395	−	0.968402i	$-0.419768\pi$
$631$	12.5294	0.498789	0.249395	+	0.968402i	$0.419768\pi$
$632$	− 10.6508i	− 0.423666i
$633$	−42.8518	−1.70321
$634$	16.5987i	0.659220i
$635$	0.745900i	0.0296001i
$636$	38.7659i	1.53717i
$637$	−22.4027	−0.887628
$638$	−0.658725	−0.0260792
$639$	− 74.1185i	− 2.93208i
$640$	10.5594i	0.417396i
$641$	− 19.4356i	− 0.767660i	−0.923404	−	0.383830i	$-0.874605\pi$
$641$	− 19.4356i	− 0.767660i	0.923404	−	0.383830i	$-0.125395\pi$
$642$	21.9738	0.867238
$643$	16.0075i	0.631276i	0.948880	+	0.315638i	$0.102218\pi$
$643$	16.0075i	0.631276i	−0.948880	+	0.315638i	$0.897782\pi$
$644$	11.4754	0.452195
$645$	11.5371	0.454273
$646$	0	0
$647$	−41.3567	−1.62590	−0.812949	−	0.582335i	$-0.802139\pi$
$647$	−41.3567	−1.62590	−0.812949	+	0.582335i	$0.802139\pi$
$648$	−39.8363	−1.56492
$649$	− 0.530826i	− 0.0208367i
$650$	−1.65838	−0.0650470
$651$	− 1.65388i	− 0.0648206i
$652$	18.5410i	0.726123i
$653$	− 5.21693i	− 0.204154i	−0.994776	−	0.102077i	$-0.967451\pi$
$653$	− 5.21693i	− 0.204154i	0.994776	−	0.102077i	$-0.0325488\pi$
$654$	−17.8862	−0.699407
$655$	5.67574	0.221769
$656$	− 10.3003i	− 0.402158i
$657$	− 3.17433i	− 0.123842i
$658$	3.73759i	0.145706i
$659$	−10.7781	−0.419854	−0.209927	−	0.977717i	$-0.567323\pi$
$659$	−10.7781	−0.419854	−0.209927	+	0.977717i	$0.567323\pi$
$660$	− 1.08425i	− 0.0422044i
$661$	10.3851	0.403935	0.201968	−	0.979392i	$-0.435266\pi$
$661$	10.3851	0.403935	0.201968	+	0.979392i	$0.435266\pi$
$662$	−17.6602	−0.686385
$663$	0	0
$664$	38.0560	1.47686
$665$	−30.0150	−1.16393
$666$	27.6064i	1.06973i
$667$	−7.60245	−0.294368
$668$	− 3.16073i	− 0.122292i
$669$	11.1403i	0.430709i
$670$	− 10.2797i	− 0.397138i
$671$	2.06262	0.0796267
$672$	−73.9084	−2.85108
$673$	− 13.1346i	− 0.506302i	−0.967427	−	0.253151i	$-0.918533\pi$
$673$	− 13.1346i	− 0.506302i	0.967427	−	0.253151i	$-0.0814669\pi$
$674$	− 11.6019i	− 0.446889i
$675$	11.6500i	0.448410i
$676$	11.2105	0.431172
$677$	18.9820i	0.729539i	0.931098	+	0.364769i	$0.118852\pi$
$677$	18.9820i	0.729539i	−0.931098	+	0.364769i	$0.881148\pi$
$678$	−28.7024	−1.10231
$679$	−36.5964	−1.40444
$680$	0	0
$681$	−72.8430	−2.79135
$682$	−0.0212213	−0.000812604 0
$683$	− 14.9579i	− 0.572347i	−0.958178	−	0.286173i	$-0.907617\pi$
$683$	− 14.9579i	− 0.572347i	0.958178	−	0.286173i	$-0.0923834\pi$
$684$	−74.8226	−2.86091
$685$	19.6850i	0.752124i
$686$	− 7.18628i	− 0.274373i
$687$	− 78.7880i	− 3.00595i
$688$	4.70056	0.179207
$689$	−19.4550	−0.741177
$690$	4.12427i	0.157008i
$691$	− 11.3095i	− 0.430233i	−0.976588	−	0.215116i	$-0.930987\pi$
$691$	− 11.3095i	− 0.430233i	0.976588	−	0.215116i	$-0.0690131\pi$
$692$	3.59277i	0.136577i
$693$	6.32181	0.240146
$694$	11.9895i	0.455113i
$695$	−5.64706	−0.214205
$696$	31.1727	1.18160
$697$	0	0
$698$	4.73315	0.179152
$699$	5.49412	0.207807
$700$	6.11237i	0.231026i
$701$	−13.0707	−0.493674	−0.246837	−	0.969057i	$-0.579391\pi$
$701$	−13.0707	−0.493674	−0.246837	+	0.969057i	$0.579391\pi$
$702$	− 19.3202i	− 0.729192i
$703$	43.0066i	1.62202i
$704$	0.360980i	0.0136050i
$705$	4.07569	0.153499
$706$	1.56469	0.0588880
$707$	− 28.2232i	− 1.06144i
$708$	10.7831i	0.405253i
$709$	− 48.6798i	− 1.82821i	−0.405479	−	0.914105i	$-0.632895\pi$
$709$	− 48.6798i	− 1.82821i	0.405479	−	0.914105i	$-0.367105\pi$
$710$	7.74981	0.290845
$711$	− 29.0686i	− 1.09016i
$712$	−9.10242	−0.341128
$713$	−0.244918	−0.00917224
$714$	0	0
$715$	0.544142	0.0203498
$716$	−3.10720	−0.116122
$717$	66.4287i	2.48083i
$718$	−11.7801	−0.439629
$719$	− 31.8171i	− 1.18658i	−0.804990	−	0.593289i	$-0.797829\pi$
$719$	− 31.8171i	− 1.18658i	0.804990	−	0.593289i	$-0.202171\pi$
$720$	8.56005i	0.319014i
$721$	− 4.24316i	− 0.158024i
$722$	25.0392	0.931861
$723$	−31.6264	−1.17620
$724$	− 15.1890i	− 0.564493i
$725$	− 4.04943i	− 0.150392i
$726$	24.0474i	0.892482i
$727$	6.69618	0.248348	0.124174	−	0.992260i	$-0.460372\pi$
$727$	6.69618	0.248348	0.124174	+	0.992260i	$0.460372\pi$
$728$	− 23.6141i	− 0.875198i
$729$	0.319170	0.0118211
$730$	0.331907	0.0122844
$731$	0	0
$732$	−41.8997	−1.54866
$733$	38.7110	1.42982	0.714912	−	0.699215i	$-0.246467\pi$
$733$	38.7110	1.42982	0.714912	+	0.699215i	$0.246467\pi$
$734$	12.6018i	0.465139i
$735$	−29.6760	−1.09461
$736$	10.9449i	0.403433i
$737$	3.37293i	0.124243i
$738$	38.4207i	1.41429i
$739$	−19.1997	−0.706271	−0.353136	−	0.935572i	$-0.614885\pi$
$739$	−19.1997	−0.706271	−0.353136	+	0.935572i	$0.614885\pi$
$740$	8.75802	0.321951
$741$	− 54.2791i	− 1.99399i
$742$	− 23.6334i	− 0.867608i
$743$	− 2.12614i	− 0.0780004i	−0.999239	−	0.0390002i	$-0.987583\pi$
$743$	− 2.12614i	− 0.0780004i	0.999239	−	0.0390002i	$-0.0124173\pi$
$744$	1.00425	0.0368175
$745$	19.0000i	0.696105i
$746$	11.5042	0.421199
$747$	103.864	3.80020
$748$	0	0
$749$	40.6456	1.48516
$750$	−2.19679	−0.0802153
$751$	9.76463i	0.356316i	0.984002	+	0.178158i	$0.0570139\pi$
$751$	9.76463i	0.356316i	−0.984002	+	0.178158i	$0.942986\pi$
$752$	1.66056	0.0605544
$753$	54.8987i	2.00062i
$754$	6.71549i	0.244564i
$755$	6.95236i	0.253022i
$756$	−71.2093	−2.58986
$757$	29.2324	1.06247	0.531236	−	0.847224i	$-0.321728\pi$
$757$	29.2324	1.06247	0.531236	+	0.847224i	$0.321728\pi$
$758$	− 10.2185i	− 0.371153i
$759$	− 1.35324i	− 0.0491196i
$760$	− 18.2254i	− 0.661103i
$761$	−11.3975	−0.413161	−0.206580	−	0.978430i	$-0.566234\pi$
$761$	−11.3975	−0.413161	−0.206580	+	0.978430i	$0.566234\pi$
$762$	− 1.63858i	− 0.0593595i
$763$	−33.0847	−1.19775
$764$	39.9373	1.44488
$765$	0	0
$766$	0.835153	0.0301753
$767$	−5.41160	−0.195401
$768$	− 32.9464i	− 1.18885i
$769$	14.6414	0.527984	0.263992	−	0.964525i	$-0.414961\pi$
$769$	14.6414	0.527984	0.263992	+	0.964525i	$0.414961\pi$
$770$	0.661007i	0.0238210i
$771$	− 31.5099i	− 1.13480i
$772$	− 10.2407i	− 0.368571i
$773$	−16.8387	−0.605646	−0.302823	−	0.953047i	$-0.597929\pi$
$773$	−16.8387	−0.605646	−0.302823	+	0.953047i	$0.597929\pi$
$774$	−17.5334	−0.630226
$775$	− 0.130455i	− 0.00468608i
$776$	− 22.2216i	− 0.797709i
$777$	73.8133i	2.64804i
$778$	16.3235	0.585227
$779$	59.8538i	2.14448i
$780$	−11.0536	−0.395782
$781$	−2.54284	−0.0909901
$782$	0	0
$783$	47.1760	1.68593
$784$	−12.0909	−0.431817
$785$	7.18338i	0.256386i
$786$	−12.4684	−0.444732
$787$	17.4487i	0.621979i	0.950413	+	0.310990i	$0.100660\pi$
$787$	17.4487i	0.621979i	−0.950413	+	0.310990i	$0.899340\pi$
$788$	− 9.11554i	− 0.324728i
$789$	49.9379i	1.77784i
$790$	3.03941	0.108137
$791$	−53.0917	−1.88772
$792$	3.83865i	0.136401i
$793$	− 21.0278i	− 0.746718i
$794$	− 24.8346i	− 0.881347i
$795$	−25.7713	−0.914012
$796$	− 17.0680i	− 0.604958i
$797$	−25.0208	−0.886282	−0.443141	−	0.896452i	$-0.646136\pi$
$797$	−25.0208	−0.886282	−0.443141	+	0.896452i	$0.646136\pi$
$798$	65.9366	2.33413
$799$	0	0
$800$	−5.82977	−0.206113
$801$	−24.8428	−0.877776
$802$	23.6831i	0.836279i
$803$	−0.108904	−0.00384315
$804$	− 68.5170i	− 2.41641i
$805$	7.62878i	0.268879i
$806$	0.216344i	0.00762039i
$807$	−40.7554	−1.43466
$808$	17.1373	0.602889
$809$	19.6531i	0.690966i	0.938425	+	0.345483i	$0.112285\pi$
$809$	19.6531i	0.690966i	−0.938425	+	0.345483i	$0.887715\pi$
$810$	− 11.3681i	− 0.399433i
$811$	30.7782i	1.08077i	0.841418	+	0.540385i	$0.181721\pi$
$811$	30.7782i	1.08077i	−0.841418	+	0.540385i	$0.818279\pi$
$812$	24.7516	0.868612
$813$	54.0960i	1.89723i
$814$	0.947114	0.0331963
$815$	−12.3259	−0.431759
$816$	0	0
$817$	−27.3144	−0.955612
$818$	12.6753	0.443182
$819$	− 64.4488i	− 2.25202i
$820$	12.1888	0.425653
$821$	35.0315i	1.22261i	0.791397	+	0.611303i	$0.209354\pi$
$821$	35.0315i	1.22261i	−0.791397	+	0.611303i	$0.790646\pi$
$822$	− 43.2437i	− 1.50830i
$823$	30.1072i	1.04947i	0.851265	+	0.524736i	$0.175836\pi$
$823$	30.1072i	1.04947i	−0.851265	+	0.524736i	$0.824164\pi$
$824$	2.57648	0.0897560
$825$	0.720802	0.0250951
$826$	− 6.57384i	− 0.228733i
$827$	− 20.7366i	− 0.721082i	−0.932743	−	0.360541i	$-0.882592\pi$
$827$	− 20.7366i	− 0.721082i	0.932743	−	0.360541i	$-0.117408\pi$
$828$	19.0173i	0.660898i
$829$	54.3221	1.88669	0.943343	−	0.331820i	$-0.107663\pi$
$829$	54.3221	1.88669	0.943343	+	0.331820i	$0.107663\pi$
$830$	10.8600i	0.376957i
$831$	−34.1713	−1.18539
$832$	3.68008	0.127584
$833$	0	0
$834$	12.4054	0.429563
$835$	2.10123	0.0727160
$836$	2.56700i	0.0887816i
$837$	1.51980	0.0525321
$838$	4.46870i	0.154369i
$839$	− 10.7461i	− 0.370997i	−0.982645	−	0.185498i	$-0.940610\pi$
$839$	− 10.7461i	− 0.370997i	0.982645	−	0.185498i	$-0.0593900\pi$
$840$	− 31.2807i	− 1.07929i
$841$	12.6021	0.434555
$842$	−15.5488	−0.535847
$843$	9.65155i	0.332417i
$844$	− 20.6603i	− 0.711156i
$845$	7.45265i	0.256379i
$846$	−6.19401	−0.212954
$847$	44.4812i	1.52839i
$848$	−10.5000	−0.360571
$849$	1.46469	0.0502682
$850$	0	0
$851$	10.9308	0.374703
$852$	51.6548	1.76966
$853$	− 43.7616i	− 1.49837i	−0.662362	−	0.749184i	$-0.730446\pi$
$853$	− 43.7616i	− 1.49837i	0.662362	−	0.749184i	$-0.269554\pi$
$854$	25.5439	0.874094
$855$	− 49.7415i	− 1.70112i
$856$	24.6803i	0.843557i
$857$	− 0.857197i	− 0.0292813i	−0.999893	−	0.0146406i	$-0.995340\pi$
$857$	− 0.857197i	− 0.0292813i	0.999893	−	0.0146406i	$-0.00466043\pi$
$858$	−1.19536	−0.0408090
$859$	38.5994	1.31700	0.658498	−	0.752583i	$-0.271192\pi$
$859$	38.5994	1.31700	0.658498	+	0.752583i	$0.271192\pi$
$860$	5.56242i	0.189677i
$861$	102.729i	3.50098i
$862$	− 23.0774i	− 0.786021i
$863$	18.0234	0.613522	0.306761	−	0.951787i	$-0.400755\pi$
$863$	18.0234	0.613522	0.306761	+	0.951787i	$0.400755\pi$
$864$	− 67.9169i	− 2.31058i
$865$	−2.38845	−0.0812097
$866$	−1.89697	−0.0644618
$867$	0	0
$868$	0.797389	0.0270652
$869$	−0.997281	−0.0338305
$870$	8.89573i	0.301594i
$871$	34.3859	1.16512
$872$	− 20.0893i	− 0.680309i
$873$	− 60.6483i	− 2.05263i
$874$	− 9.76434i	− 0.330284i
$875$	−4.06346	−0.137370
$876$	2.21226	0.0747453
$877$	26.7943i	0.904780i	0.891820	+	0.452390i	$0.149428\pi$
$877$	26.7943i	0.904780i	−0.891820	+	0.452390i	$0.850572\pi$
$878$	17.1446i	0.578601i
$879$	− 64.5686i	− 2.17785i
$880$	0.293677	0.00989984
$881$	21.6063i	0.727933i	0.931412	+	0.363967i	$0.118578\pi$
$881$	21.6063i	0.727933i	−0.931412	+	0.363967i	$0.881422\pi$
$882$	45.0999	1.51859
$883$	20.8987	0.703297	0.351649	−	0.936132i	$-0.385621\pi$
$883$	20.8987	0.703297	0.351649	+	0.936132i	$0.385621\pi$
$884$	0	0
$885$	−7.16852	−0.240967
$886$	−22.5066	−0.756123
$887$	− 33.8887i	− 1.13787i	−0.822382	−	0.568936i	$-0.807355\pi$
$887$	− 33.8887i	− 1.13787i	0.822382	−	0.568936i	$-0.192645\pi$
$888$	−44.8200	−1.50406
$889$	− 3.03093i	− 0.101654i
$890$	− 2.59755i	− 0.0870702i
$891$	3.73005i	0.124961i
$892$	−5.37111	−0.179838
$893$	−9.64933	−0.322903
$894$	− 41.7388i	− 1.39596i
$895$	− 2.06564i	− 0.0690469i
$896$	− 42.9076i	− 1.43344i
$897$	−13.7959	−0.460631
$898$	− 25.2771i	− 0.843508i
$899$	−0.528269	−0.0176187
$900$	−10.1295	−0.337652
$901$	0	0
$902$	1.31813	0.0438890
$903$	−46.8805	−1.56009
$904$	− 32.2377i	− 1.07221i
$905$	10.0975	0.335653
$906$	− 15.2728i	− 0.507406i
$907$	17.3527i	0.576187i	0.957602	+	0.288093i	$0.0930214\pi$
$907$	17.3527i	0.576187i	−0.957602	+	0.288093i	$0.906979\pi$
$908$	− 35.1200i	− 1.16550i
$909$	46.7720	1.55133
$910$	6.73875	0.223388
$911$	44.2282i	1.46535i	0.680581	+	0.732673i	$0.261727\pi$
$911$	44.2282i	1.46535i	−0.680581	+	0.732673i	$0.738273\pi$
$912$	− 29.2947i	− 0.970046i
$913$	− 3.56336i	− 0.117930i
$914$	−29.6141	−0.979549
$915$	− 27.8546i	− 0.920845i
$916$	37.9863	1.25510
$917$	−23.0631	−0.761611
$918$	0	0
$919$	4.31977	0.142496	0.0712480	−	0.997459i	$-0.477302\pi$
$919$	4.31977	0.142496	0.0712480	+	0.997459i	$0.477302\pi$
$920$	−4.63225	−0.152721
$921$	68.6077i	2.26070i
$922$	17.2628	0.568521
$923$	25.9235i	0.853282i
$924$	4.40581i	0.144941i
$925$	5.82227i	0.191435i
$926$	9.12963	0.300018
$927$	7.03186	0.230957
$928$	23.6072i	0.774945i
$929$	9.99294i	0.327858i	0.986472	+	0.163929i	$0.0524167\pi$
$929$	9.99294i	0.327858i	−0.986472	+	0.163929i	$0.947583\pi$
$930$	0.286582i	0.00939738i
$931$	70.2588	2.30264
$932$	2.64890i	0.0867676i
$933$	76.3869	2.50079
$934$	22.7516	0.744454
$935$	0	0
$936$	39.1338	1.27913
$937$	−41.6190	−1.35964	−0.679818	−	0.733381i	$-0.737941\pi$
$937$	−41.6190	−1.35964	−0.679818	+	0.733381i	$0.737941\pi$
$938$	41.7709i	1.36387i
$939$	−8.97108	−0.292760
$940$	1.96503i	0.0640921i
$941$	22.4168i	0.730767i	0.930857	+	0.365384i	$0.119062\pi$
$941$	22.4168i	0.730767i	−0.930857	+	0.365384i	$0.880938\pi$
$942$	− 15.7804i	− 0.514152i
$943$	15.2128	0.495395
$944$	−2.92067	−0.0950597
$945$	− 47.3394i	− 1.53995i
$946$	0.601533i	0.0195575i
$947$	− 44.0389i	− 1.43107i	−0.698577	−	0.715535i	$-0.746183\pi$
$947$	− 44.0389i	− 1.43107i	0.698577	−	0.715535i	$-0.253817\pi$
$948$	20.2586	0.657968
$949$	1.11024i	0.0360400i
$950$	5.20096	0.168741
$951$	−73.5497	−2.38501
$952$	0	0
$953$	−43.8375	−1.42004	−0.710019	−	0.704183i	$-0.751314\pi$
$953$	−43.8375	−1.42004	−0.710019	+	0.704183i	$0.751314\pi$
$954$	39.1657	1.26804
$955$	26.5500i	0.859139i
$956$	−32.0275	−1.03584
$957$	− 2.91884i	− 0.0943527i
$958$	10.1740i	0.328706i
$959$	− 79.9891i	− 2.58298i
$960$	4.87485	0.157335
$961$	30.9830	0.999451
$962$	− 9.65553i	− 0.311307i
$963$	67.3588i	2.17061i
$964$	− 15.2481i	− 0.491110i
$965$	6.80795	0.219156
$966$	− 16.7588i	− 0.539205i
$967$	9.41429	0.302743	0.151372	−	0.988477i	$-0.451631\pi$
$967$	9.41429	0.302743	0.151372	+	0.988477i	$0.451631\pi$
$968$	−27.0093	−0.868112
$969$	0	0
$970$	6.34137	0.203609
$971$	14.2960	0.458780	0.229390	−	0.973335i	$-0.426327\pi$
$971$	14.2960	0.458780	0.229390	+	0.973335i	$0.426327\pi$
$972$	− 23.1986i	− 0.744097i
$973$	22.9466	0.735634
$974$	24.8847i	0.797357i
$975$	− 7.34835i	− 0.235335i
$976$	− 11.3488i	− 0.363267i
$977$	2.92222	0.0934900	0.0467450	−	0.998907i	$-0.485115\pi$
$977$	2.92222	0.0934900	0.0467450	+	0.998907i	$0.485115\pi$
$978$	27.0775	0.865842
$979$	0.852301i	0.0272397i
$980$	− 14.3078i	− 0.457045i
$981$	− 54.8287i	− 1.75054i
$982$	−26.9549	−0.860164
$983$	− 1.35448i	− 0.0432013i	−0.999767	−	0.0216007i	$-0.993124\pi$
$983$	− 1.35448i	− 0.0432013i	0.999767	−	0.0216007i	$-0.00687624\pi$
$984$	−62.3776	−1.98853
$985$	6.05995	0.193086
$986$	0	0
$987$	−16.5614	−0.527155
$988$	26.1697	0.832571
$989$	6.94239i	0.220755i
$990$	−1.09543	−0.0348152
$991$	49.6083i	1.57586i	0.615765	+	0.787930i	$0.288847\pi$
$991$	49.6083i	1.57586i	−0.615765	+	0.787930i	$0.711153\pi$
$992$	0.760522i	0.0241466i
$993$	− 78.2533i	− 2.48329i
$994$	−31.4910	−0.998835
$995$	11.3467	0.359713
$996$	72.3854i	2.29362i
$997$	12.3189i	0.390143i	0.980789	+	0.195072i	$0.0624939\pi$
$997$	12.3189i	0.390143i	−0.980789	+	0.195072i	$0.937506\pi$
$998$	17.9724i	0.568908i
$999$	−67.8296	−2.14603

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.i.866.15		24
17.4	even	4		1445.2.a.r.1.5	✓	12
17.13	even	4		1445.2.a.s.1.5	yes	12
17.16	even	2	inner	1445.2.d.i.866.16		24
85.4	even	4		7225.2.a.bo.1.8		12
85.64	even	4		7225.2.a.bn.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1445.2.a.r.1.5	✓	12	17.4	even	4
1445.2.a.s.1.5	yes	12	17.13	even	4
1445.2.d.i.866.15		24	1.1	even	1	trivial
1445.2.d.i.866.16		24	17.16	even	2	inner
7225.2.a.bn.1.8		12	85.64	even	4
7225.2.a.bo.1.8		12	85.4	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.704111 q^{2} +3.11994i q^{3} -1.50423 q^{4} -1.00000i q^{5} +2.19679i q^{6} +4.06346i q^{7} -2.46736 q^{8} -6.73405 q^{9} -0.704111i q^{10} +0.231031i q^{11} -4.69311i q^{12} +2.35528 q^{13} +2.86112i q^{14} +3.11994 q^{15} +1.27116 q^{16} -4.74152 q^{18} -7.38657 q^{19} +1.50423i q^{20} -12.6778 q^{21} +0.162671i q^{22} +1.87741i q^{23} -7.69804i q^{24} -1.00000 q^{25} +1.65838 q^{26} -11.6500i q^{27} -6.11237i q^{28} +4.04943i q^{29} +2.19679 q^{30} +0.130455i q^{31} +5.82977 q^{32} -0.720802 q^{33} +4.06346 q^{35} +10.1295 q^{36} -5.82227i q^{37} -5.20096 q^{38} +7.34835i q^{39} +2.46736i q^{40} -8.10305i q^{41} -8.92655 q^{42} +3.69785 q^{43} -0.347523i q^{44} +6.73405i q^{45} +1.32190i q^{46} +1.30633 q^{47} +3.96595i q^{48} -9.51170 q^{49} -0.704111 q^{50} -3.54288 q^{52} -8.26017 q^{53} -8.20291i q^{54} +0.231031 q^{55} -10.0260i q^{56} -23.0457i q^{57} +2.85125i q^{58} -2.29764 q^{59} -4.69311 q^{60} -8.92792i q^{61} +0.0918548i q^{62} -27.3635i q^{63} +1.56248 q^{64} -2.35528i q^{65} -0.507524 q^{66} +14.5995 q^{67} -5.85742 q^{69} +2.86112 q^{70} +11.0065i q^{71} +16.6154 q^{72} +0.471385i q^{73} -4.09952i q^{74} -3.11994i q^{75} +11.1111 q^{76} -0.938783 q^{77} +5.17405i q^{78} +4.31667i q^{79} -1.27116i q^{80} +16.1453 q^{81} -5.70544i q^{82} -15.4238 q^{83} +19.0703 q^{84} +2.60370 q^{86} -12.6340 q^{87} -0.570036i q^{88} +3.68913 q^{89} +4.74152i q^{90} +9.57059i q^{91} -2.82405i q^{92} -0.407012 q^{93} +0.919804 q^{94} +7.38657i q^{95} +18.1885i q^{96} +9.00621i q^{97} -6.69729 q^{98} -1.55577i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 42 q^{4} - 24 q^{8} - 42 q^{9} + 18 q^{13} - 6 q^{15} + 78 q^{16} - 18 q^{18} - 54 q^{19} + 12 q^{21} - 24 q^{25} - 12 q^{26} - 18 q^{30} - 24 q^{32} + 12 q^{35} - 96 q^{36} - 6 q^{38}+ \cdots - 84 q^{98}+O(q^{100}) \) 24 * q - 6 * q^2 + 42 * q^4 - 24 * q^8 - 42 * q^9 + 18 * q^13 - 6 * q^15 + 78 * q^16 - 18 * q^18 - 54 * q^19 + 12 * q^21 - 24 * q^25 - 12 * q^26 - 18 * q^30 - 24 * q^32 + 12 * q^35 - 96 * q^36 - 6 * q^38 - 60 * q^42 - 90 * q^43 + 6 * q^47 - 24 * q^49 + 6 * q^50 + 102 * q^52 + 24 * q^53 - 12 * q^55 - 72 * q^59 - 12 * q^60 + 84 * q^64 + 78 * q^66 + 156 * q^67 - 132 * q^69 + 36 * q^70 - 24 * q^72 - 54 * q^76 + 78 * q^77 + 24 * q^81 - 54 * q^83 + 54 * q^84 + 36 * q^86 - 48 * q^87 + 12 * q^89 + 24 * q^93 - 42 * q^94 - 84 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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