LMFDB - Embedded newform 361.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(1,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("361.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.34730 q^{2} +2.87939 q^{3} -0.184793 q^{4} +0.879385 q^{5} +3.87939 q^{6} +0.347296 q^{7} -2.94356 q^{8} +5.29086 q^{9} +O(q^{10})$	\(q+1.34730 q^{2} +2.87939 q^{3} -0.184793 q^{4} +0.879385 q^{5} +3.87939 q^{6} +0.347296 q^{7} -2.94356 q^{8} +5.29086 q^{9} +1.18479 q^{10} -2.22668 q^{11} -0.532089 q^{12} -2.57398 q^{13} +0.467911 q^{14} +2.53209 q^{15} -3.59627 q^{16} +0.467911 q^{17} +7.12836 q^{18} -0.162504 q^{20} +1.00000 q^{21} -3.00000 q^{22} -2.69459 q^{23} -8.47565 q^{24} -4.22668 q^{25} -3.46791 q^{26} +6.59627 q^{27} -0.0641778 q^{28} +6.87939 q^{29} +3.41147 q^{30} +7.10607 q^{31} +1.04189 q^{32} -6.41147 q^{33} +0.630415 q^{34} +0.305407 q^{35} -0.977711 q^{36} -4.94356 q^{37} -7.41147 q^{39} -2.58853 q^{40} -2.47565 q^{41} +1.34730 q^{42} +3.90167 q^{43} +0.411474 q^{44} +4.65270 q^{45} -3.63041 q^{46} -7.29086 q^{47} -10.3550 q^{48} -6.87939 q^{49} -5.69459 q^{50} +1.34730 q^{51} +0.475652 q^{52} +2.83750 q^{53} +8.88713 q^{54} -1.95811 q^{55} -1.02229 q^{56} +9.26857 q^{58} +6.30541 q^{59} -0.467911 q^{60} +9.12836 q^{61} +9.57398 q^{62} +1.83750 q^{63} +8.59627 q^{64} -2.26352 q^{65} -8.63816 q^{66} -7.67499 q^{67} -0.0864665 q^{68} -7.75877 q^{69} +0.411474 q^{70} +9.30541 q^{71} -15.5740 q^{72} +1.38919 q^{73} -6.66044 q^{74} -12.1702 q^{75} -0.773318 q^{77} -9.98545 q^{78} +11.8452 q^{79} -3.16250 q^{80} +3.12061 q^{81} -3.33544 q^{82} -14.8307 q^{83} -0.184793 q^{84} +0.411474 q^{85} +5.25671 q^{86} +19.8084 q^{87} +6.55438 q^{88} +10.2909 q^{89} +6.26857 q^{90} -0.893933 q^{91} +0.497941 q^{92} +20.4611 q^{93} -9.82295 q^{94} +3.00000 q^{96} -9.45336 q^{97} -9.26857 q^{98} -11.7811 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 6 * q^6 + 6 * q^8	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 3 q^{12} + 6 q^{14} + 3 q^{15} + 3 q^{16} + 6 q^{17} + 3 q^{18} - 3 q^{20} + 3 q^{21} - 9 q^{22} - 6 q^{23} - 6 q^{24} - 6 q^{25} - 15 q^{26} + 6 q^{27} + 9 q^{28} + 15 q^{29} + 9 q^{31} - 9 q^{33} + 9 q^{34} + 3 q^{35} - 9 q^{36} - 12 q^{39} - 18 q^{40} + 12 q^{41} + 3 q^{42} - 9 q^{44} + 15 q^{45} - 18 q^{46} - 6 q^{47} - 6 q^{48} - 15 q^{49} - 15 q^{50} + 3 q^{51} - 18 q^{52} + 6 q^{53} - 3 q^{54} - 9 q^{55} + 3 q^{56} + 18 q^{58} + 21 q^{59} - 6 q^{60} + 9 q^{61} + 21 q^{62} + 3 q^{63} + 12 q^{64} - 12 q^{65} - 9 q^{66} - 18 q^{67} + 15 q^{68} - 12 q^{69} - 9 q^{70} + 30 q^{71} - 39 q^{72} + 3 q^{74} - 15 q^{75} - 9 q^{77} - 12 q^{78} + 9 q^{79} - 12 q^{80} + 15 q^{81} + 18 q^{82} + 3 q^{84} - 9 q^{85} - 21 q^{86} + 21 q^{87} + 9 q^{88} + 15 q^{89} + 9 q^{90} - 15 q^{91} - 24 q^{92} + 24 q^{93} - 9 q^{94} + 9 q^{96} - 15 q^{97} - 18 q^{98} - 18 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 6 * q^6 + 6 * q^8 + 3 * q^12 + 6 * q^14 + 3 * q^15 + 3 * q^16 + 6 * q^17 + 3 * q^18 - 3 * q^20 + 3 * q^21 - 9 * q^22 - 6 * q^23 - 6 * q^24 - 6 * q^25 - 15 * q^26 + 6 * q^27 + 9 * q^28 + 15 * q^29 + 9 * q^31 - 9 * q^33 + 9 * q^34 + 3 * q^35 - 9 * q^36 - 12 * q^39 - 18 * q^40 + 12 * q^41 + 3 * q^42 - 9 * q^44 + 15 * q^45 - 18 * q^46 - 6 * q^47 - 6 * q^48 - 15 * q^49 - 15 * q^50 + 3 * q^51 - 18 * q^52 + 6 * q^53 - 3 * q^54 - 9 * q^55 + 3 * q^56 + 18 * q^58 + 21 * q^59 - 6 * q^60 + 9 * q^61 + 21 * q^62 + 3 * q^63 + 12 * q^64 - 12 * q^65 - 9 * q^66 - 18 * q^67 + 15 * q^68 - 12 * q^69 - 9 * q^70 + 30 * q^71 - 39 * q^72 + 3 * q^74 - 15 * q^75 - 9 * q^77 - 12 * q^78 + 9 * q^79 - 12 * q^80 + 15 * q^81 + 18 * q^82 + 3 * q^84 - 9 * q^85 - 21 * q^86 + 21 * q^87 + 9 * q^88 + 15 * q^89 + 9 * q^90 - 15 * q^91 - 24 * q^92 + 24 * q^93 - 9 * q^94 + 9 * q^96 - 15 * q^97 - 18 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.34730	0.952682	0.476341	−	0.879261i	$-0.341963\pi$
$2$	1.34730	0.952682	0.476341	+	0.879261i	$0.341963\pi$
$3$	2.87939	1.66241	0.831207	−	0.555963i	$-0.187650\pi$
$3$	2.87939	1.66241	0.831207	+	0.555963i	$0.187650\pi$
$4$	−0.184793	−0.0923963
$5$	0.879385	0.393273	0.196637	−	0.980476i	$-0.436998\pi$
$5$	0.879385	0.393273	0.196637	+	0.980476i	$0.436998\pi$
$6$	3.87939	1.58375
$7$	0.347296	0.131266	0.0656328	−	0.997844i	$-0.479093\pi$
$7$	0.347296	0.131266	0.0656328	+	0.997844i	$0.479093\pi$
$8$	−2.94356	−1.04071
$9$	5.29086	1.76362
$10$	1.18479	0.374664
$11$	−2.22668	−0.671370	−0.335685	−	0.941974i	$-0.608968\pi$
$11$	−2.22668	−0.671370	−0.335685	+	0.941974i	$0.608968\pi$
$12$	−0.532089	−0.153601
$13$	−2.57398	−0.713893	−0.356947	−	0.934125i	$-0.616182\pi$
$13$	−2.57398	−0.713893	−0.356947	+	0.934125i	$0.616182\pi$
$14$	0.467911	0.125055
$15$	2.53209	0.653783
$16$	−3.59627	−0.899067
$17$	0.467911	0.113485	0.0567426	−	0.998389i	$-0.481929\pi$
$17$	0.467911	0.113485	0.0567426	+	0.998389i	$0.481929\pi$
$18$	7.12836	1.68017
$19$	0	0
$19$	0	0
$20$	−0.162504	−0.0363370
$21$	1.00000	0.218218
$22$	−3.00000	−0.639602
$23$	−2.69459	−0.561861	−0.280931	−	0.959728i	$-0.590643\pi$
$23$	−2.69459	−0.561861	−0.280931	+	0.959728i	$0.590643\pi$
$24$	−8.47565	−1.73009
$25$	−4.22668	−0.845336
$26$	−3.46791	−0.680113
$27$	6.59627	1.26945
$28$	−0.0641778	−0.0121285
$29$	6.87939	1.27747	0.638735	−	0.769427i	$-0.279458\pi$
$29$	6.87939	1.27747	0.638735	+	0.769427i	$0.279458\pi$
$30$	3.41147	0.622847
$31$	7.10607	1.27629	0.638144	−	0.769917i	$-0.279703\pi$
$31$	7.10607	1.27629	0.638144	+	0.769917i	$0.279703\pi$
$32$	1.04189	0.184182
$33$	−6.41147	−1.11609
$34$	0.630415	0.108115
$35$	0.305407	0.0516233
$36$	−0.977711	−0.162952
$37$	−4.94356	−0.812717	−0.406358	−	0.913714i	$-0.633202\pi$
$37$	−4.94356	−0.812717	−0.406358	+	0.913714i	$0.633202\pi$
$38$	0	0
$39$	−7.41147	−1.18679
$40$	−2.58853	−0.409282
$41$	−2.47565	−0.386632	−0.193316	−	0.981137i	$-0.561924\pi$
$41$	−2.47565	−0.386632	−0.193316	+	0.981137i	$0.561924\pi$
$42$	1.34730	0.207892
$43$	3.90167	0.595000	0.297500	−	0.954722i	$-0.403847\pi$
$43$	3.90167	0.595000	0.297500	+	0.954722i	$0.403847\pi$
$44$	0.411474	0.0620321
$45$	4.65270	0.693584
$46$	−3.63041	−0.535275
$47$	−7.29086	−1.06348	−0.531741	−	0.846907i	$-0.678462\pi$
$47$	−7.29086	−1.06348	−0.531741	+	0.846907i	$0.678462\pi$
$48$	−10.3550	−1.49462
$49$	−6.87939	−0.982769
$50$	−5.69459	−0.805337
$51$	1.34730	0.188659
$52$	0.475652	0.0659611
$53$	2.83750	0.389760	0.194880	−	0.980827i	$-0.437568\pi$
$53$	2.83750	0.389760	0.194880	+	0.980827i	$0.437568\pi$
$54$	8.88713	1.20938
$55$	−1.95811	−0.264032
$56$	−1.02229	−0.136609
$57$	0	0
$58$	9.26857	1.21702
$59$	6.30541	0.820894	0.410447	−	0.911884i	$-0.365373\pi$
$59$	6.30541	0.820894	0.410447	+	0.911884i	$0.365373\pi$
$60$	−0.467911	−0.0604071
$61$	9.12836	1.16877	0.584383	−	0.811478i	$-0.301337\pi$
$61$	9.12836	1.16877	0.584383	+	0.811478i	$0.301337\pi$
$62$	9.57398	1.21590
$63$	1.83750	0.231503
$64$	8.59627	1.07453
$65$	−2.26352	−0.280755
$66$	−8.63816	−1.06328
$67$	−7.67499	−0.937650	−0.468825	−	0.883291i	$-0.655322\pi$
$67$	−7.67499	−0.937650	−0.468825	+	0.883291i	$0.655322\pi$
$68$	−0.0864665	−0.0104856
$69$	−7.75877	−0.934046
$70$	0.411474	0.0491806
$71$	9.30541	1.10435	0.552174	−	0.833729i	$-0.313798\pi$
$71$	9.30541	1.10435	0.552174	+	0.833729i	$0.313798\pi$
$72$	−15.5740	−1.83541
$73$	1.38919	0.162592	0.0812959	−	0.996690i	$-0.474094\pi$
$73$	1.38919	0.162592	0.0812959	+	0.996690i	$0.474094\pi$
$74$	−6.66044	−0.774261
$75$	−12.1702	−1.40530
$76$	0	0
$77$	−0.773318	−0.0881278
$78$	−9.98545	−1.13063
$79$	11.8452	1.33269	0.666347	−	0.745642i	$-0.267857\pi$
$79$	11.8452	1.33269	0.666347	+	0.745642i	$0.267857\pi$
$80$	−3.16250	−0.353579
$81$	3.12061	0.346735
$82$	−3.33544	−0.368337
$83$	−14.8307	−1.62788	−0.813940	−	0.580949i	$-0.802681\pi$
$83$	−14.8307	−1.62788	−0.813940	+	0.580949i	$0.802681\pi$
$84$	−0.184793	−0.0201625
$85$	0.411474	0.0446306
$86$	5.25671	0.566846
$87$	19.8084	2.12368
$88$	6.55438	0.698699
$89$	10.2909	1.09083	0.545414	−	0.838166i	$-0.316372\pi$
$89$	10.2909	1.09083	0.545414	+	0.838166i	$0.316372\pi$
$90$	6.26857	0.660765
$91$	−0.893933	−0.0937097
$92$	0.497941	0.0519139
$93$	20.4611	2.12172
$94$	−9.82295	−1.01316
$95$	0	0
$96$	3.00000	0.306186
$97$	−9.45336	−0.959844	−0.479922	−	0.877311i	$-0.659335\pi$
$97$	−9.45336	−0.959844	−0.479922	+	0.877311i	$0.659335\pi$
$98$	−9.26857	−0.936267
$99$	−11.7811	−1.18404
$100$	0.781059	0.0781059
$101$	−9.24897	−0.920307	−0.460153	−	0.887839i	$-0.652206\pi$
$101$	−9.24897	−0.920307	−0.460153	+	0.887839i	$0.652206\pi$
$102$	1.81521	0.179732
$103$	5.50980	0.542897	0.271448	−	0.962453i	$-0.412497\pi$
$103$	5.50980	0.542897	0.271448	+	0.962453i	$0.412497\pi$
$104$	7.57667	0.742953
$105$	0.879385	0.0858192
$106$	3.82295	0.371318
$107$	−10.2344	−0.989399	−0.494699	−	0.869064i	$-0.664722\pi$
$107$	−10.2344	−0.989399	−0.494699	+	0.869064i	$0.664722\pi$
$108$	−1.21894	−0.117293
$109$	1.82295	0.174607	0.0873034	−	0.996182i	$-0.472175\pi$
$109$	1.82295	0.174607	0.0873034	+	0.996182i	$0.472175\pi$
$110$	−2.63816	−0.251538
$111$	−14.2344	−1.35107
$112$	−1.24897	−0.118017
$113$	17.6878	1.66393	0.831963	−	0.554830i	$-0.187217\pi$
$113$	17.6878	1.66393	0.831963	+	0.554830i	$0.187217\pi$
$114$	0	0
$115$	−2.36959	−0.220965
$116$	−1.27126	−0.118033
$117$	−13.6186	−1.25904
$118$	8.49525	0.782051
$119$	0.162504	0.0148967
$120$	−7.45336	−0.680396
$121$	−6.04189	−0.549263
$122$	12.2986	1.11346
$123$	−7.12836	−0.642742
$124$	−1.31315	−0.117924
$125$	−8.11381	−0.725721
$126$	2.47565	0.220549
$127$	−11.6040	−1.02969	−0.514845	−	0.857284i	$-0.672150\pi$
$127$	−11.6040	−1.02969	−0.514845	+	0.857284i	$0.672150\pi$
$128$	9.49794	0.839507
$129$	11.2344	0.989136
$130$	−3.04963	−0.267470
$131$	1.84524	0.161219	0.0806096	−	0.996746i	$-0.474313\pi$
$131$	1.84524	0.161219	0.0806096	+	0.996746i	$0.474313\pi$
$132$	1.18479	0.103123
$133$	0	0
$134$	−10.3405	−0.893282
$135$	5.80066	0.499241
$136$	−1.37733	−0.118105
$137$	0.255777	0.0218525	0.0109263	−	0.999940i	$-0.496522\pi$
$137$	0.255777	0.0218525	0.0109263	+	0.999940i	$0.496522\pi$
$138$	−10.4534	−0.889849
$139$	4.26352	0.361627	0.180813	−	0.983517i	$-0.442127\pi$
$139$	4.26352	0.361627	0.180813	+	0.983517i	$0.442127\pi$
$140$	−0.0564370	−0.00476980
$141$	−20.9932	−1.76795
$142$	12.5371	1.05209
$143$	5.73143	0.479286
$144$	−19.0273	−1.58561
$145$	6.04963	0.502394
$146$	1.87164	0.154898
$147$	−19.8084	−1.63377
$148$	0.913534	0.0750920
$149$	16.5594	1.35660	0.678301	−	0.734784i	$-0.262717\pi$
$149$	16.5594	1.35660	0.678301	+	0.734784i	$0.262717\pi$
$150$	−16.3969	−1.33880
$151$	4.36184	0.354962	0.177481	−	0.984124i	$-0.443205\pi$
$151$	4.36184	0.354962	0.177481	+	0.984124i	$0.443205\pi$
$152$	0	0
$153$	2.47565	0.200145
$154$	−1.04189	−0.0839578
$155$	6.24897	0.501929
$156$	1.36959	0.109655
$157$	−9.61856	−0.767644	−0.383822	−	0.923407i	$-0.625392\pi$
$157$	−9.61856	−0.767644	−0.383822	+	0.923407i	$0.625392\pi$
$158$	15.9590	1.26963
$159$	8.17024	0.647943
$160$	0.916222	0.0724337
$161$	−0.935822	−0.0737531
$162$	4.20439	0.330328
$163$	8.35504	0.654417	0.327209	−	0.944952i	$-0.393892\pi$
$163$	8.35504	0.654417	0.327209	+	0.944952i	$0.393892\pi$
$164$	0.457482	0.0357233
$165$	−5.63816	−0.438930
$166$	−19.9813	−1.55085
$167$	−4.03508	−0.312244	−0.156122	−	0.987738i	$-0.549899\pi$
$167$	−4.03508	−0.312244	−0.156122	+	0.987738i	$0.549899\pi$
$168$	−2.94356	−0.227101
$169$	−6.37464	−0.490357
$170$	0.554378	0.0425188
$171$	0	0
$172$	−0.721000	−0.0549758
$173$	20.1438	1.53151	0.765754	−	0.643134i	$-0.222366\pi$
$173$	20.1438	1.53151	0.765754	+	0.643134i	$0.222366\pi$
$174$	26.6878	2.02320
$175$	−1.46791	−0.110964
$176$	8.00774	0.603606
$177$	18.1557	1.36467
$178$	13.8648	1.03921
$179$	11.5125	0.860484	0.430242	−	0.902714i	$-0.358428\pi$
$179$	11.5125	0.860484	0.430242	+	0.902714i	$0.358428\pi$
$180$	−0.859785	−0.0640846
$181$	−8.53714	−0.634561	−0.317280	−	0.948332i	$-0.602770\pi$
$181$	−8.53714	−0.634561	−0.317280	+	0.948332i	$0.602770\pi$
$182$	−1.20439	−0.0892755
$183$	26.2841	1.94297
$184$	7.93170	0.584733
$185$	−4.34730	−0.319620
$186$	27.5672	2.02132
$187$	−1.04189	−0.0761905
$188$	1.34730	0.0982617
$189$	2.29086	0.166635
$190$	0	0
$191$	18.3354	1.32671	0.663353	−	0.748307i	$-0.269133\pi$
$191$	18.3354	1.32671	0.663353	+	0.748307i	$0.269133\pi$
$192$	24.7520	1.78632
$193$	−0.297667	−0.0214265	−0.0107133	−	0.999943i	$-0.503410\pi$
$193$	−0.297667	−0.0214265	−0.0107133	+	0.999943i	$0.503410\pi$
$194$	−12.7365	−0.914426
$195$	−6.51754	−0.466731
$196$	1.27126	0.0908042
$197$	13.1411	0.936268	0.468134	−	0.883657i	$-0.344926\pi$
$197$	13.1411	0.936268	0.468134	+	0.883657i	$0.344926\pi$
$198$	−15.8726	−1.12802
$199$	−0.256711	−0.0181978	−0.00909888	−	0.999959i	$-0.502896\pi$
$199$	−0.256711	−0.0181978	−0.00909888	+	0.999959i	$0.502896\pi$
$200$	12.4415	0.879747
$201$	−22.0993	−1.55876
$202$	−12.4611	−0.876760
$203$	2.38919	0.167688
$204$	−0.248970	−0.0174314
$205$	−2.17705	−0.152052
$206$	7.42333	0.517208
$207$	−14.2567	−0.990910
$208$	9.25671	0.641837
$209$	0	0
$210$	1.18479	0.0817585
$211$	−2.44831	−0.168549	−0.0842743	−	0.996443i	$-0.526857\pi$
$211$	−2.44831	−0.168549	−0.0842743	+	0.996443i	$0.526857\pi$
$212$	−0.524348	−0.0360124
$213$	26.7939	1.83588
$214$	−13.7888	−0.942583
$215$	3.43107	0.233997
$216$	−19.4165	−1.32113
$217$	2.46791	0.167533
$218$	2.45605	0.166345
$219$	4.00000	0.270295
$220$	0.361844	0.0243955
$221$	−1.20439	−0.0810162
$222$	−19.1780	−1.28714
$223$	8.50980	0.569858	0.284929	−	0.958549i	$-0.408030\pi$
$223$	8.50980	0.569858	0.284929	+	0.958549i	$0.408030\pi$
$224$	0.361844	0.0241767
$225$	−22.3628	−1.49085
$226$	23.8307	1.58519
$227$	14.1506	0.939211	0.469606	−	0.882876i	$-0.344396\pi$
$227$	14.1506	0.939211	0.469606	+	0.882876i	$0.344396\pi$
$228$	0	0
$229$	−20.5330	−1.35686	−0.678430	−	0.734665i	$-0.737339\pi$
$229$	−20.5330	−1.35686	−0.678430	+	0.734665i	$0.737339\pi$
$230$	−3.19253	−0.210509
$231$	−2.22668	−0.146505
$232$	−20.2499	−1.32947
$233$	17.6509	1.15635	0.578176	−	0.815912i	$-0.303765\pi$
$233$	17.6509	1.15635	0.578176	+	0.815912i	$0.303765\pi$
$234$	−18.3482	−1.19946
$235$	−6.41147	−0.418238
$236$	−1.16519	−0.0758475
$237$	34.1070	2.21549
$238$	0.218941	0.0141918
$239$	2.35235	0.152161	0.0760804	−	0.997102i	$-0.475759\pi$
$239$	2.35235	0.152161	0.0760804	+	0.997102i	$0.475759\pi$
$240$	−9.10607	−0.587794
$241$	−13.8007	−0.888979	−0.444489	−	0.895784i	$-0.646615\pi$
$241$	−13.8007	−0.888979	−0.444489	+	0.895784i	$0.646615\pi$
$242$	−8.14022	−0.523273
$243$	−10.8033	−0.693035
$244$	−1.68685	−0.107990
$245$	−6.04963	−0.386497
$246$	−9.60401	−0.612329
$247$	0	0
$248$	−20.9172	−1.32824
$249$	−42.7033	−2.70621
$250$	−10.9317	−0.691382
$251$	−4.16519	−0.262905	−0.131452	−	0.991322i	$-0.541964\pi$
$251$	−4.16519	−0.262905	−0.131452	+	0.991322i	$0.541964\pi$
$252$	−0.339556	−0.0213900
$253$	6.00000	0.377217
$254$	−15.6340	−0.980967
$255$	1.18479	0.0741946
$256$	−4.39599	−0.274750
$257$	−0.667252	−0.0416220	−0.0208110	−	0.999783i	$-0.506625\pi$
$257$	−0.667252	−0.0416220	−0.0208110	+	0.999783i	$0.506625\pi$
$258$	15.1361	0.942332
$259$	−1.71688	−0.106682
$260$	0.418281	0.0259407
$261$	36.3979	2.25297
$262$	2.48608	0.153591
$263$	11.3996	0.702930	0.351465	−	0.936201i	$-0.385684\pi$
$263$	11.3996	0.702930	0.351465	+	0.936201i	$0.385684\pi$
$264$	18.8726	1.16153
$265$	2.49525	0.153282
$266$	0	0
$267$	29.6313	1.81341
$268$	1.41828	0.0866353
$269$	−19.3901	−1.18224	−0.591118	−	0.806585i	$-0.701313\pi$
$269$	−19.3901	−1.18224	−0.591118	+	0.806585i	$0.701313\pi$
$270$	7.81521	0.475618
$271$	−13.3942	−0.813642	−0.406821	−	0.913508i	$-0.633363\pi$
$271$	−13.3942	−0.813642	−0.406821	+	0.913508i	$0.633363\pi$
$272$	−1.68273	−0.102031
$273$	−2.57398	−0.155784
$274$	0.344608	0.0208185
$275$	9.41147	0.567533
$276$	1.43376	0.0863024
$277$	17.7469	1.06631	0.533154	−	0.846018i	$-0.321007\pi$
$277$	17.7469	1.06631	0.533154	+	0.846018i	$0.321007\pi$
$278$	5.74422	0.344516
$279$	37.5972	2.25089
$280$	−0.898986	−0.0537247
$281$	−18.2790	−1.09043	−0.545217	−	0.838295i	$-0.683553\pi$
$281$	−18.2790	−1.09043	−0.545217	+	0.838295i	$0.683553\pi$
$282$	−28.2841	−1.68429
$283$	7.68779	0.456991	0.228496	−	0.973545i	$-0.426619\pi$
$283$	7.68779	0.456991	0.228496	+	0.973545i	$0.426619\pi$
$284$	−1.71957	−0.102038
$285$	0	0
$286$	7.72193	0.456608
$287$	−0.859785	−0.0507515
$288$	5.51249	0.324827
$289$	−16.7811	−0.987121
$290$	8.15064	0.478622
$291$	−27.2199	−1.59566
$292$	−0.256711	−0.0150229
$293$	10.5030	0.613591	0.306796	−	0.951775i	$-0.400743\pi$
$293$	10.5030	0.613591	0.306796	+	0.951775i	$0.400743\pi$
$294$	−26.6878	−1.55646
$295$	5.54488	0.322836
$296$	14.5517	0.845800
$297$	−14.6878	−0.852272
$298$	22.3105	1.29241
$299$	6.93582	0.401109
$300$	2.24897	0.129844
$301$	1.35504	0.0781030
$302$	5.87670	0.338166
$303$	−26.6313	−1.52993
$304$	0	0
$305$	8.02734	0.459644
$306$	3.33544	0.190674
$307$	11.6955	0.667499	0.333749	−	0.942662i	$-0.391686\pi$
$307$	11.6955	0.667499	0.333749	+	0.942662i	$0.391686\pi$
$308$	0.142903	0.00814268
$309$	15.8648	0.902519
$310$	8.41921	0.478179
$311$	15.9659	0.905340	0.452670	−	0.891678i	$-0.350471\pi$
$311$	15.9659	0.905340	0.452670	+	0.891678i	$0.350471\pi$
$312$	21.8161	1.23510
$313$	−26.6287	−1.50514	−0.752570	−	0.658512i	$-0.771186\pi$
$313$	−26.6287	−1.50514	−0.752570	+	0.658512i	$0.771186\pi$
$314$	−12.9590	−0.731321
$315$	1.61587	0.0910438
$316$	−2.18891	−0.123136
$317$	−29.5321	−1.65869	−0.829344	−	0.558739i	$-0.811285\pi$
$317$	−29.5321	−1.65869	−0.829344	+	0.558739i	$0.811285\pi$
$318$	11.0077	0.617283
$319$	−15.3182	−0.857655
$320$	7.55943	0.422585
$321$	−29.4688	−1.64479
$322$	−1.26083	−0.0702633
$323$	0	0
$324$	−0.576666	−0.0320370
$325$	10.8794	0.603480
$326$	11.2567	0.623452
$327$	5.24897	0.290269
$328$	7.28724	0.402370
$329$	−2.53209	−0.139599
$330$	−7.59627	−0.418161
$331$	−27.6655	−1.52063	−0.760317	−	0.649553i	$-0.774956\pi$
$331$	−27.6655	−1.52063	−0.760317	+	0.649553i	$0.774956\pi$
$332$	2.74060	0.150410
$333$	−26.1557	−1.43332
$334$	−5.43645	−0.297469
$335$	−6.74928	−0.368752
$336$	−3.59627	−0.196192
$337$	−17.8598	−0.972884	−0.486442	−	0.873713i	$-0.661706\pi$
$337$	−17.8598	−0.972884	−0.486442	+	0.873713i	$0.661706\pi$
$338$	−8.58853	−0.467154
$339$	50.9299	2.76614
$340$	−0.0760373	−0.00412370
$341$	−15.8229	−0.856861
$342$	0	0
$343$	−4.82026	−0.260270
$344$	−11.4848	−0.619220
$345$	−6.82295	−0.367335
$346$	27.1397	1.45904
$347$	−5.80066	−0.311396	−0.155698	−	0.987805i	$-0.549763\pi$
$347$	−5.80066	−0.311396	−0.155698	+	0.987805i	$0.549763\pi$
$348$	−3.66044	−0.196220
$349$	5.37227	0.287571	0.143786	−	0.989609i	$-0.454072\pi$
$349$	5.37227	0.287571	0.143786	+	0.989609i	$0.454072\pi$
$350$	−1.97771	−0.105713
$351$	−16.9786	−0.906253
$352$	−2.31996	−0.123654
$353$	−25.2344	−1.34309	−0.671546	−	0.740963i	$-0.734370\pi$
$353$	−25.2344	−1.34309	−0.671546	+	0.740963i	$0.734370\pi$
$354$	24.4611	1.30009
$355$	8.18304	0.434311
$356$	−1.90167	−0.100789
$357$	0.467911	0.0247645
$358$	15.5107	0.819768
$359$	6.68685	0.352919	0.176459	−	0.984308i	$-0.443536\pi$
$359$	6.68685	0.352919	0.176459	+	0.984308i	$0.443536\pi$
$360$	−13.6955	−0.721818
$361$	0	0
$362$	−11.5021	−0.604535
$363$	−17.3969	−0.913102
$364$	0.165192	0.00865842
$365$	1.22163	0.0639430
$366$	35.4124	1.85104
$367$	8.11886	0.423801	0.211901	−	0.977291i	$-0.432035\pi$
$367$	8.11886	0.423801	0.211901	+	0.977291i	$0.432035\pi$
$368$	9.69047	0.505151
$369$	−13.0983	−0.681872
$370$	−5.85710	−0.304496
$371$	0.985452	0.0511621
$372$	−3.78106	−0.196039
$373$	−34.8976	−1.80693	−0.903463	−	0.428665i	$-0.858984\pi$
$373$	−34.8976	−1.80693	−0.903463	+	0.428665i	$0.858984\pi$
$374$	−1.40373	−0.0725853
$375$	−23.3628	−1.20645
$376$	21.4611	1.10677
$377$	−17.7074	−0.911977
$378$	3.08647	0.158751
$379$	−1.70140	−0.0873950	−0.0436975	−	0.999045i	$-0.513914\pi$
$379$	−1.70140	−0.0873950	−0.0436975	+	0.999045i	$0.513914\pi$
$380$	0	0
$381$	−33.4124	−1.71177
$382$	24.7033	1.26393
$383$	−2.93676	−0.150061	−0.0750306	−	0.997181i	$-0.523905\pi$
$383$	−2.93676	−0.150061	−0.0750306	+	0.997181i	$0.523905\pi$
$384$	27.3482	1.39561
$385$	−0.680045	−0.0346583
$386$	−0.401045	−0.0204127
$387$	20.6432	1.04935
$388$	1.74691	0.0886860
$389$	−24.5672	−1.24561	−0.622803	−	0.782379i	$-0.714006\pi$
$389$	−24.5672	−1.24561	−0.622803	+	0.782379i	$0.714006\pi$
$390$	−8.78106	−0.444646
$391$	−1.26083	−0.0637629
$392$	20.2499	1.02277
$393$	5.31315	0.268013
$394$	17.7050	0.891966
$395$	10.4165	0.524112
$396$	2.17705	0.109401
$397$	−31.8357	−1.59779	−0.798895	−	0.601470i	$-0.794582\pi$
$397$	−31.8357	−1.59779	−0.798895	+	0.601470i	$0.794582\pi$
$398$	−0.345866	−0.0173367
$399$	0	0
$400$	15.2003	0.760014
$401$	0.0864665	0.00431793	0.00215896	−	0.999998i	$-0.499313\pi$
$401$	0.0864665	0.00431793	0.00215896	+	0.999998i	$0.499313\pi$
$402$	−29.7743	−1.48500
$403$	−18.2909	−0.911133
$404$	1.70914	0.0850329
$405$	2.74422	0.136362
$406$	3.21894	0.159753
$407$	11.0077	0.545633
$408$	−3.96585	−0.196339
$409$	−20.0060	−0.989232	−0.494616	−	0.869112i	$-0.664691\pi$
$409$	−20.0060	−0.989232	−0.494616	+	0.869112i	$0.664691\pi$
$410$	−2.93313	−0.144857
$411$	0.736482	0.0363280
$412$	−1.01817	−0.0501616
$413$	2.18984	0.107755
$414$	−19.2080	−0.944022
$415$	−13.0419	−0.640201
$416$	−2.68180	−0.131486
$417$	12.2763	0.601174
$418$	0	0
$419$	25.4097	1.24135	0.620673	−	0.784070i	$-0.286859\pi$
$419$	25.4097	1.24135	0.620673	+	0.784070i	$0.286859\pi$
$420$	−0.162504	−0.00792937
$421$	−4.36959	−0.212961	−0.106480	−	0.994315i	$-0.533958\pi$
$421$	−4.36959	−0.212961	−0.106480	+	0.994315i	$0.533958\pi$
$422$	−3.29860	−0.160573
$423$	−38.5749	−1.87558
$424$	−8.35235	−0.405626
$425$	−1.97771	−0.0959331
$426$	36.0993	1.74901
$427$	3.17024	0.153419
$428$	1.89124	0.0914168
$429$	16.5030	0.796772
$430$	4.62267	0.222925
$431$	38.3063	1.84515	0.922576	−	0.385816i	$-0.126080\pi$
$431$	38.3063	1.84515	0.922576	+	0.385816i	$0.126080\pi$
$432$	−23.7219	−1.14132
$433$	18.1310	0.871322	0.435661	−	0.900111i	$-0.356515\pi$
$433$	18.1310	0.871322	0.435661	+	0.900111i	$0.356515\pi$
$434$	3.32501	0.159605
$435$	17.4192	0.835187
$436$	−0.336867	−0.0161330
$437$	0	0
$438$	5.38919	0.257505
$439$	6.09059	0.290688	0.145344	−	0.989381i	$-0.453571\pi$
$439$	6.09059	0.290688	0.145344	+	0.989381i	$0.453571\pi$
$440$	5.76382	0.274779
$441$	−36.3979	−1.73323
$442$	−1.62267	−0.0771827
$443$	−29.8931	−1.42026	−0.710132	−	0.704068i	$-0.751365\pi$
$443$	−29.8931	−1.42026	−0.710132	+	0.704068i	$0.751365\pi$
$444$	2.63041	0.124834
$445$	9.04963	0.428994
$446$	11.4652	0.542894
$447$	47.6810	2.25523
$448$	2.98545	0.141049
$449$	11.2499	0.530916	0.265458	−	0.964122i	$-0.414477\pi$
$449$	11.2499	0.530916	0.265458	+	0.964122i	$0.414477\pi$
$450$	−30.1293	−1.42031
$451$	5.51249	0.259573
$452$	−3.26857	−0.153741
$453$	12.5594	0.590093
$454$	19.0651	0.894770
$455$	−0.786112	−0.0368535
$456$	0	0
$457$	−23.3901	−1.09414	−0.547072	−	0.837086i	$-0.684258\pi$
$457$	−23.3901	−1.09414	−0.547072	+	0.837086i	$0.684258\pi$
$458$	−27.6641	−1.29266
$459$	3.08647	0.144064
$460$	0.437882	0.0204163
$461$	−36.6236	−1.70573	−0.852866	−	0.522130i	$-0.825137\pi$
$461$	−36.6236	−1.70573	−0.852866	+	0.522130i	$0.825137\pi$
$462$	−3.00000	−0.139573
$463$	−42.9864	−1.99775	−0.998873	−	0.0474549i	$-0.984889\pi$
$463$	−42.9864	−1.99775	−0.998873	+	0.0474549i	$0.984889\pi$
$464$	−24.7401	−1.14853
$465$	17.9932	0.834414
$466$	23.7811	1.10164
$467$	25.5963	1.18445	0.592227	−	0.805771i	$-0.298249\pi$
$467$	25.5963	1.18445	0.592227	+	0.805771i	$0.298249\pi$
$468$	2.51661	0.116330
$469$	−2.66550	−0.123081
$470$	−8.63816	−0.398448
$471$	−27.6955	−1.27614
$472$	−18.5604	−0.854310
$473$	−8.68779	−0.399465
$474$	45.9522	2.11066
$475$	0	0
$476$	−0.0300295	−0.00137640
$477$	15.0128	0.687389
$478$	3.16931	0.144961
$479$	38.1762	1.74432	0.872158	−	0.489224i	$-0.162720\pi$
$479$	38.1762	1.74432	0.872158	+	0.489224i	$0.162720\pi$
$480$	2.63816	0.120415
$481$	12.7246	0.580193
$482$	−18.5936	−0.846914
$483$	−2.69459	−0.122608
$484$	1.11650	0.0507498
$485$	−8.31315	−0.377481
$486$	−14.5553	−0.660242
$487$	−7.76382	−0.351812	−0.175906	−	0.984407i	$-0.556286\pi$
$487$	−7.76382	−0.351812	−0.175906	+	0.984407i	$0.556286\pi$
$488$	−26.8699	−1.21634
$489$	24.0574	1.08791
$490$	−8.15064	−0.368209
$491$	−36.7229	−1.65728	−0.828640	−	0.559782i	$-0.810885\pi$
$491$	−36.7229	−1.65728	−0.828640	+	0.559782i	$0.810885\pi$
$492$	1.31727	0.0593870
$493$	3.21894	0.144974
$494$	0	0
$495$	−10.3601	−0.465651
$496$	−25.5553	−1.14747
$497$	3.23173	0.144963
$498$	−57.5340	−2.57816
$499$	4.92633	0.220533	0.110266	−	0.993902i	$-0.464830\pi$
$499$	4.92633	0.220533	0.110266	+	0.993902i	$0.464830\pi$
$500$	1.49937	0.0670539
$501$	−11.6186	−0.519079
$502$	−5.61175	−0.250465
$503$	32.9495	1.46915	0.734574	−	0.678529i	$-0.237382\pi$
$503$	32.9495	1.46915	0.734574	+	0.678529i	$0.237382\pi$
$504$	−5.40879	−0.240926
$505$	−8.13341	−0.361932
$506$	8.08378	0.359368
$507$	−18.3550	−0.815176
$508$	2.14433	0.0951394
$509$	36.9350	1.63712	0.818558	−	0.574424i	$-0.194774\pi$
$509$	36.9350	1.63712	0.818558	+	0.574424i	$0.194774\pi$
$510$	1.59627	0.0706839
$511$	0.482459	0.0213427
$512$	−24.9186	−1.10126
$513$	0	0
$514$	−0.898986	−0.0396526
$515$	4.84524	0.213507
$516$	−2.07604	−0.0913924
$517$	16.2344	0.713989
$518$	−2.31315	−0.101634
$519$	58.0019	2.54600
$520$	6.66281	0.292183
$521$	−9.29179	−0.407081	−0.203540	−	0.979067i	$-0.565245\pi$
$521$	−9.29179	−0.407081	−0.203540	+	0.979067i	$0.565245\pi$
$522$	49.0387	2.14637
$523$	28.4151	1.24251	0.621253	−	0.783610i	$-0.286624\pi$
$523$	28.4151	1.24251	0.621253	+	0.783610i	$0.286624\pi$
$524$	−0.340986	−0.0148960
$525$	−4.22668	−0.184468
$526$	15.3587	0.669669
$527$	3.32501	0.144840
$528$	23.0574	1.00344
$529$	−15.7392	−0.684312
$530$	3.36184	0.146029
$531$	33.3610	1.44775
$532$	0	0
$533$	6.37227	0.276014
$534$	39.9222	1.72760
$535$	−9.00000	−0.389104
$536$	22.5918	0.975818
$537$	33.1489	1.43048
$538$	−26.1242	−1.12630
$539$	15.3182	0.659802
$540$	−1.07192	−0.0461280
$541$	14.9855	0.644275	0.322137	−	0.946693i	$-0.395599\pi$
$541$	14.9855	0.644275	0.322137	+	0.946693i	$0.395599\pi$
$542$	−18.0460	−0.775142
$543$	−24.5817	−1.05490
$544$	0.487511	0.0209019
$545$	1.60307	0.0686681
$546$	−3.46791	−0.148413
$547$	3.88713	0.166202	0.0831008	−	0.996541i	$-0.473518\pi$
$547$	3.88713	0.166202	0.0831008	+	0.996541i	$0.473518\pi$
$548$	−0.0472658	−0.00201909
$549$	48.2968	2.06126
$550$	12.6800	0.540679
$551$	0	0
$552$	22.8384	0.972068
$553$	4.11381	0.174937
$554$	23.9103	1.01585
$555$	−12.5175	−0.531340
$556$	−0.787866	−0.0334130
$557$	13.2044	0.559488	0.279744	−	0.960075i	$-0.409750\pi$
$557$	13.2044	0.559488	0.279744	+	0.960075i	$0.409750\pi$
$558$	50.6546	2.14438
$559$	−10.0428	−0.424766
$560$	−1.09833	−0.0464127
$561$	−3.00000	−0.126660
$562$	−24.6272	−1.03884
$563$	−10.7128	−0.451489	−0.225745	−	0.974187i	$-0.572481\pi$
$563$	−10.7128	−0.451489	−0.225745	+	0.974187i	$0.572481\pi$
$564$	3.87939	0.163352
$565$	15.5544	0.654378
$566$	10.3577	0.435368
$567$	1.08378	0.0455144
$568$	−27.3911	−1.14930
$569$	13.4706	0.564717	0.282358	−	0.959309i	$-0.408883\pi$
$569$	13.4706	0.564717	0.282358	+	0.959309i	$0.408883\pi$
$570$	0	0
$571$	12.6655	0.530035	0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655	0.530035	0.265017	+	0.964244i	$0.414622\pi$
$572$	−1.05913	−0.0442843
$573$	52.7948	2.20553
$574$	−1.15839	−0.0483501
$575$	11.3892	0.474962
$576$	45.4816	1.89507
$577$	−10.5544	−0.439384	−0.219692	−	0.975569i	$-0.570505\pi$
$577$	−10.5544	−0.439384	−0.219692	+	0.975569i	$0.570505\pi$
$578$	−22.6091	−0.940413
$579$	−0.857097	−0.0356197
$580$	−1.11793	−0.0464194
$581$	−5.15064	−0.213685
$582$	−36.6732	−1.52015
$583$	−6.31820	−0.261673
$584$	−4.08915	−0.169210
$585$	−11.9760	−0.495145
$586$	14.1506	0.584558
$587$	−19.1548	−0.790602	−0.395301	−	0.918552i	$-0.629360\pi$
$587$	−19.1548	−0.790602	−0.395301	+	0.918552i	$0.629360\pi$
$588$	3.66044	0.150954
$589$	0	0
$590$	7.47060	0.307560
$591$	37.8384	1.55647
$592$	17.7784	0.730687
$593$	−8.69459	−0.357044	−0.178522	−	0.983936i	$-0.557132\pi$
$593$	−8.69459	−0.357044	−0.178522	+	0.983936i	$0.557132\pi$
$594$	−19.7888	−0.811944
$595$	0.142903	0.00585847
$596$	−3.06006	−0.125345
$597$	−0.739170	−0.0302522
$598$	9.34461	0.382129
$599$	−19.8316	−0.810298	−0.405149	−	0.914251i	$-0.632780\pi$
$599$	−19.8316	−0.810298	−0.405149	+	0.914251i	$0.632780\pi$
$600$	35.8239	1.46250
$601$	33.7615	1.37716	0.688579	−	0.725161i	$-0.258235\pi$
$601$	33.7615	1.37716	0.688579	+	0.725161i	$0.258235\pi$
$602$	1.82564	0.0744074
$603$	−40.6073	−1.65366
$604$	−0.806036	−0.0327971
$605$	−5.31315	−0.216010
$606$	−35.8803	−1.45754
$607$	−35.2850	−1.43217	−0.716087	−	0.698011i	$-0.754068\pi$
$607$	−35.2850	−1.43217	−0.716087	+	0.698011i	$0.754068\pi$
$608$	0	0
$609$	6.87939	0.278767
$610$	10.8152	0.437895
$611$	18.7665	0.759212
$612$	−0.457482	−0.0184926
$613$	18.4534	0.745324	0.372662	−	0.927967i	$-0.378445\pi$
$613$	18.4534	0.745324	0.372662	+	0.927967i	$0.378445\pi$
$614$	15.7573	0.635914
$615$	−6.26857	−0.252773
$616$	2.27631	0.0917152
$617$	−35.6854	−1.43664	−0.718320	−	0.695712i	$-0.755089\pi$
$617$	−35.6854	−1.43664	−0.718320	+	0.695712i	$0.755089\pi$
$618$	21.3746	0.859814
$619$	3.65951	0.147088	0.0735441	−	0.997292i	$-0.476569\pi$
$619$	3.65951	0.147088	0.0735441	+	0.997292i	$0.476569\pi$
$620$	−1.15476	−0.0463764
$621$	−17.7743	−0.713256
$622$	21.5107	0.862502
$623$	3.57398	0.143188
$624$	26.6536	1.06700
$625$	13.9982	0.559930
$626$	−35.8767	−1.43392
$627$	0	0
$628$	1.77744	0.0709275
$629$	−2.31315	−0.0922313
$630$	2.17705	0.0867358
$631$	−0.793852	−0.0316028	−0.0158014	−	0.999875i	$-0.505030\pi$
$631$	−0.793852	−0.0316028	−0.0158014	+	0.999875i	$0.505030\pi$
$632$	−34.8672	−1.38694
$633$	−7.04963	−0.280198
$634$	−39.7885	−1.58020
$635$	−10.2044	−0.404949
$636$	−1.50980	−0.0598675
$637$	17.7074	0.701592
$638$	−20.6382	−0.817072
$639$	49.2336	1.94765
$640$	8.35235	0.330156
$641$	−29.3824	−1.16053	−0.580267	−	0.814426i	$-0.697052\pi$
$641$	−29.3824	−1.16053	−0.580267	+	0.814426i	$0.697052\pi$
$642$	−39.7033	−1.56696
$643$	22.2139	0.876030	0.438015	−	0.898968i	$-0.355682\pi$
$643$	22.2139	0.876030	0.438015	+	0.898968i	$0.355682\pi$
$644$	0.172933	0.00681451
$645$	9.87939	0.389000
$646$	0	0
$647$	11.2591	0.442640	0.221320	−	0.975201i	$-0.428963\pi$
$647$	11.2591	0.442640	0.221320	+	0.975201i	$0.428963\pi$
$648$	−9.18573	−0.360849
$649$	−14.0401	−0.551123
$650$	14.6578	0.574924
$651$	7.10607	0.278509
$652$	−1.54395	−0.0604657
$653$	27.0000	1.05659	0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000	1.05659	0.528296	+	0.849060i	$0.322831\pi$
$654$	7.07192	0.276534
$655$	1.62267	0.0634031
$656$	8.90310	0.347608
$657$	7.34998	0.286750
$658$	−3.41147	−0.132993
$659$	−28.0259	−1.09173	−0.545867	−	0.837872i	$-0.683800\pi$
$659$	−28.0259	−1.09173	−0.545867	+	0.837872i	$0.683800\pi$
$660$	1.04189	0.0405555
$661$	−11.3678	−0.442157	−0.221079	−	0.975256i	$-0.570958\pi$
$661$	−11.3678	−0.442157	−0.221079	+	0.975256i	$0.570958\pi$
$662$	−37.2736	−1.44868
$663$	−3.46791	−0.134683
$664$	43.6551	1.69415
$665$	0	0
$666$	−35.2395	−1.36550
$667$	−18.5371	−0.717761
$668$	0.745653	0.0288502
$669$	24.5030	0.947340
$670$	−9.09327	−0.351304
$671$	−20.3259	−0.784674
$672$	1.04189	0.0401917
$673$	16.5672	0.638618	0.319309	−	0.947651i	$-0.396549\pi$
$673$	16.5672	0.638618	0.319309	+	0.947651i	$0.396549\pi$
$674$	−24.0624	−0.926850
$675$	−27.8803	−1.07311
$676$	1.17799	0.0453071
$677$	9.04963	0.347806	0.173903	−	0.984763i	$-0.444362\pi$
$677$	9.04963	0.347806	0.173903	+	0.984763i	$0.444362\pi$
$678$	68.6177	2.63525
$679$	−3.28312	−0.125995
$680$	−1.21120	−0.0464474
$681$	40.7452	1.56136
$682$	−21.3182	−0.816316
$683$	−8.73143	−0.334099	−0.167049	−	0.985949i	$-0.553424\pi$
$683$	−8.73143	−0.334099	−0.167049	+	0.985949i	$0.553424\pi$
$684$	0	0
$685$	0.224927	0.00859402
$686$	−6.49432	−0.247954
$687$	−59.1225	−2.25566
$688$	−14.0315	−0.534944
$689$	−7.30365	−0.278247
$690$	−9.19253	−0.349954
$691$	34.7202	1.32082	0.660409	−	0.750906i	$-0.270383\pi$
$691$	34.7202	1.32082	0.660409	+	0.750906i	$0.270383\pi$
$692$	−3.72243	−0.141506
$693$	−4.09152	−0.155424
$694$	−7.81521	−0.296661
$695$	3.74928	0.142218
$696$	−58.3073	−2.21013
$697$	−1.15839	−0.0438770
$698$	7.23804	0.273964
$699$	50.8239	1.92234
$700$	0.271259	0.0102526
$701$	39.4151	1.48869	0.744344	−	0.667797i	$-0.232762\pi$
$701$	39.4151	1.48869	0.744344	+	0.667797i	$0.232762\pi$
$702$	−22.8753	−0.863371
$703$	0	0
$704$	−19.1411	−0.721409
$705$	−18.4611	−0.695285
$706$	−33.9982	−1.27954
$707$	−3.21213	−0.120805
$708$	−3.35504	−0.126090
$709$	−41.1215	−1.54435	−0.772176	−	0.635409i	$-0.780832\pi$
$709$	−41.1215	−1.54435	−0.772176	+	0.635409i	$0.780832\pi$
$710$	11.0250	0.413760
$711$	62.6715	2.35036
$712$	−30.2918	−1.13523
$713$	−19.1480	−0.717097
$714$	0.630415	0.0235927
$715$	5.04013	0.188490
$716$	−2.12742	−0.0795055
$717$	6.77332	0.252954
$718$	9.00917	0.336219
$719$	−42.3955	−1.58109	−0.790543	−	0.612407i	$-0.790201\pi$
$719$	−42.3955	−1.58109	−0.790543	+	0.612407i	$0.790201\pi$
$720$	−16.7324	−0.623578
$721$	1.91353	0.0712637
$722$	0	0
$723$	−39.7374	−1.47785
$724$	1.57760	0.0586310
$725$	−29.0770	−1.07989
$726$	−23.4388	−0.869896
$727$	51.6563	1.91583	0.957914	−	0.287057i	$-0.0926769\pi$
$727$	51.6563	1.91583	0.957914	+	0.287057i	$0.0926769\pi$
$728$	2.63135	0.0975243
$729$	−40.4688	−1.49885
$730$	1.64590	0.0609174
$731$	1.82564	0.0675236
$732$	−4.85710	−0.179523
$733$	−22.9162	−0.846430	−0.423215	−	0.906029i	$-0.639098\pi$
$733$	−22.9162	−0.846430	−0.423215	+	0.906029i	$0.639098\pi$
$734$	10.9385	0.403748
$735$	−17.4192	−0.642517
$736$	−2.80747	−0.103485
$737$	17.0898	0.629510
$738$	−17.6473	−0.649607
$739$	28.1266	1.03465	0.517327	−	0.855788i	$-0.326927\pi$
$739$	28.1266	1.03465	0.517327	+	0.855788i	$0.326927\pi$
$740$	0.803348	0.0295317
$741$	0	0
$742$	1.32770	0.0487413
$743$	−6.13247	−0.224979	−0.112489	−	0.993653i	$-0.535882\pi$
$743$	−6.13247	−0.224979	−0.112489	+	0.993653i	$0.535882\pi$
$744$	−60.2285	−2.20809
$745$	14.5621	0.533515
$746$	−47.0173	−1.72143
$747$	−78.4671	−2.87096
$748$	0.192533	0.00703972
$749$	−3.55438	−0.129874
$750$	−31.4766	−1.14936
$751$	−5.64084	−0.205837	−0.102919	−	0.994690i	$-0.532818\pi$
$751$	−5.64084	−0.205837	−0.102919	+	0.994690i	$0.532818\pi$
$752$	26.2199	0.956140
$753$	−11.9932	−0.437056
$754$	−23.8571	−0.868824
$755$	3.83574	0.139597
$756$	−0.423334	−0.0153965
$757$	15.6919	0.570332	0.285166	−	0.958478i	$-0.407951\pi$
$757$	15.6919	0.570332	0.285166	+	0.958478i	$0.407951\pi$
$758$	−2.29229	−0.0832597
$759$	17.2763	0.627090
$760$	0	0
$761$	4.86484	0.176350	0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484	0.176350	0.0881751	+	0.996105i	$0.471896\pi$
$762$	−45.0164	−1.63077
$763$	0.633103	0.0229199
$764$	−3.38825	−0.122583
$765$	2.17705	0.0787115
$766$	−3.95668	−0.142961
$767$	−16.2300	−0.586031
$768$	−12.6578	−0.456747
$769$	22.5321	0.812528	0.406264	−	0.913756i	$-0.366831\pi$
$769$	22.5321	0.812528	0.406264	+	0.913756i	$0.366831\pi$
$770$	−0.916222	−0.0330183
$771$	−1.92127	−0.0691930
$772$	0.0550065	0.00197973
$773$	26.4320	0.950693	0.475347	−	0.879799i	$-0.342323\pi$
$773$	26.4320	0.950693	0.475347	+	0.879799i	$0.342323\pi$
$774$	27.8125	0.999700
$775$	−30.0351	−1.07889
$776$	27.8266	0.998916
$777$	−4.94356	−0.177349
$778$	−33.0993	−1.18667
$779$	0	0
$780$	1.20439	0.0431242
$781$	−20.7202	−0.741426
$782$	−1.69871	−0.0607458
$783$	45.3783	1.62169
$784$	24.7401	0.883575
$785$	−8.45842	−0.301894
$786$	7.15839	0.255331
$787$	15.5577	0.554571	0.277286	−	0.960788i	$-0.410565\pi$
$787$	15.5577	0.554571	0.277286	+	0.960788i	$0.410565\pi$
$788$	−2.42839	−0.0865077
$789$	32.8239	1.16856
$790$	14.0341	0.499313
$791$	6.14290	0.218417
$792$	34.6783	1.23224
$793$	−23.4962	−0.834374
$794$	−42.8922	−1.52219
$795$	7.18479	0.254818
$796$	0.0474383	0.00168141
$797$	−33.4935	−1.18640	−0.593200	−	0.805055i	$-0.702136\pi$
$797$	−33.4935	−1.18640	−0.593200	+	0.805055i	$0.702136\pi$
$798$	0	0
$799$	−3.41147	−0.120689
$800$	−4.40373	−0.155695
$801$	54.4475	1.92381
$802$	0.116496	0.00411362
$803$	−3.09327	−0.109159
$804$	4.08378	0.144024
$805$	−0.822948	−0.0290051
$806$	−24.6432	−0.868020
$807$	−55.8316	−1.96537
$808$	27.2249	0.957770
$809$	41.1162	1.44557	0.722784	−	0.691074i	$-0.242862\pi$
$809$	41.1162	1.44557	0.722784	+	0.691074i	$0.242862\pi$
$810$	3.69728	0.129909
$811$	−16.6878	−0.585987	−0.292994	−	0.956114i	$-0.594651\pi$
$811$	−16.6878	−0.585987	−0.292994	+	0.956114i	$0.594651\pi$
$812$	−0.441504	−0.0154937
$813$	−38.5672	−1.35261
$814$	14.8307	0.519815
$815$	7.34730	0.257365
$816$	−4.84524	−0.169617
$817$	0	0
$818$	−26.9540	−0.942424
$819$	−4.72967	−0.165268
$820$	0.402303	0.0140490
$821$	−31.3901	−1.09552	−0.547761	−	0.836635i	$-0.684520\pi$
$821$	−31.3901	−1.09552	−0.547761	+	0.836635i	$0.684520\pi$
$822$	0.992259	0.0346090
$823$	46.3259	1.61482	0.807410	−	0.589990i	$-0.200868\pi$
$823$	46.3259	1.61482	0.807410	+	0.589990i	$0.200868\pi$
$824$	−16.2184	−0.564996
$825$	27.0993	0.943475
$826$	2.95037	0.102657
$827$	−40.7588	−1.41732	−0.708661	−	0.705549i	$-0.750700\pi$
$827$	−40.7588	−1.41732	−0.708661	+	0.705549i	$0.750700\pi$
$828$	2.63453	0.0915564
$829$	35.4834	1.23239	0.616195	−	0.787594i	$-0.288673\pi$
$829$	35.4834	1.23239	0.616195	+	0.787594i	$0.288673\pi$
$830$	−17.5713	−0.609908
$831$	51.1002	1.77265
$832$	−22.1266	−0.767102
$833$	−3.21894	−0.111530
$834$	16.5398	0.572727
$835$	−3.54839	−0.122797
$836$	0	0
$837$	46.8735	1.62019
$838$	34.2344	1.18261
$839$	38.2026	1.31890	0.659451	−	0.751748i	$-0.270789\pi$
$839$	38.2026	1.31890	0.659451	+	0.751748i	$0.270789\pi$
$840$	−2.58853	−0.0893126
$841$	18.3259	0.631929
$842$	−5.88713	−0.202884
$843$	−52.6323	−1.81275
$844$	0.452430	0.0155733
$845$	−5.60576	−0.192844
$846$	−51.9718	−1.78683
$847$	−2.09833	−0.0720993
$848$	−10.2044	−0.350420
$849$	22.1361	0.759709
$850$	−2.66456	−0.0913938
$851$	13.3209	0.456634
$852$	−4.95130	−0.169629
$853$	−25.6016	−0.876584	−0.438292	−	0.898833i	$-0.644416\pi$
$853$	−25.6016	−0.876584	−0.438292	+	0.898833i	$0.644416\pi$
$854$	4.27126	0.146159
$855$	0	0
$856$	30.1257	1.02967
$857$	21.0865	0.720300	0.360150	−	0.932894i	$-0.382726\pi$
$857$	21.0865	0.720300	0.360150	+	0.932894i	$0.382726\pi$
$858$	22.2344	0.759071
$859$	−19.5672	−0.667623	−0.333812	−	0.942640i	$-0.608335\pi$
$859$	−19.5672	−0.667623	−0.333812	+	0.942640i	$0.608335\pi$
$860$	−0.634037	−0.0216205
$861$	−2.47565	−0.0843700
$862$	51.6100	1.75784
$863$	−4.94894	−0.168464	−0.0842319	−	0.996446i	$-0.526844\pi$
$863$	−4.94894	−0.168464	−0.0842319	+	0.996446i	$0.526844\pi$
$864$	6.87258	0.233810
$865$	17.7142	0.602301
$866$	24.4279	0.830093
$867$	−48.3191	−1.64100
$868$	−0.456052	−0.0154794
$869$	−26.3756	−0.894730
$870$	23.4688	0.795668
$871$	19.7553	0.669381
$872$	−5.36596	−0.181714
$873$	−50.0164	−1.69280
$874$	0	0
$875$	−2.81790	−0.0952623
$876$	−0.739170	−0.0249742
$877$	−1.21987	−0.0411922	−0.0205961	−	0.999788i	$-0.506556\pi$
$877$	−1.21987	−0.0411922	−0.0205961	+	0.999788i	$0.506556\pi$
$878$	8.20582	0.276933
$879$	30.2422	1.02004
$880$	7.04189	0.237382
$881$	46.5030	1.56673	0.783363	−	0.621565i	$-0.213503\pi$
$881$	46.5030	1.56673	0.783363	+	0.621565i	$0.213503\pi$
$882$	−49.0387	−1.65122
$883$	12.9249	0.434957	0.217479	−	0.976065i	$-0.430217\pi$
$883$	12.9249	0.434957	0.217479	+	0.976065i	$0.430217\pi$
$884$	0.222563	0.00748560
$885$	15.9659	0.536686
$886$	−40.2749	−1.35306
$887$	23.2243	0.779796	0.389898	−	0.920858i	$-0.372510\pi$
$887$	23.2243	0.779796	0.389898	+	0.920858i	$0.372510\pi$
$888$	41.8999	1.40607
$889$	−4.03003	−0.135163
$890$	12.1925	0.408695
$891$	−6.94862	−0.232787
$892$	−1.57255	−0.0526528
$893$	0	0
$894$	64.2404	2.14852
$895$	10.1239	0.338405
$896$	3.29860	0.110198
$897$	19.9709	0.666809
$898$	15.1570	0.505794
$899$	48.8854	1.63042
$900$	4.13247	0.137749
$901$	1.32770	0.0442320
$902$	7.42696	0.247291
$903$	3.90167	0.129840
$904$	−52.0651	−1.73166
$905$	−7.50744	−0.249556
$906$	16.9213	0.562172
$907$	39.9968	1.32807	0.664036	−	0.747700i	$-0.268842\pi$
$907$	39.9968	1.32807	0.664036	+	0.747700i	$0.268842\pi$
$908$	−2.61493	−0.0867796
$909$	−48.9350	−1.62307
$910$	−1.05913	−0.0351097
$911$	18.7997	0.622863	0.311431	−	0.950269i	$-0.399192\pi$
$911$	18.7997	0.622863	0.311431	+	0.950269i	$0.399192\pi$
$912$	0	0
$913$	33.0232	1.09291
$914$	−31.5134	−1.04237
$915$	23.1138	0.764119
$916$	3.79435	0.125369
$917$	0.640844	0.0211625
$918$	4.15839	0.137247
$919$	39.8316	1.31392	0.656962	−	0.753924i	$-0.271841\pi$
$919$	39.8316	1.31392	0.656962	+	0.753924i	$0.271841\pi$
$920$	6.97502	0.229960
$921$	33.6759	1.10966
$922$	−49.3429	−1.62502
$923$	−23.9519	−0.788387
$924$	0.411474	0.0135365
$925$	20.8949	0.687019
$926$	−57.9154	−1.90322
$927$	29.1516	0.957463
$928$	7.16756	0.235287
$929$	26.9540	0.884332	0.442166	−	0.896933i	$-0.354210\pi$
$929$	26.9540	0.884332	0.442166	+	0.896933i	$0.354210\pi$
$930$	24.2422	0.794932
$931$	0	0
$932$	−3.26176	−0.106843
$933$	45.9718	1.50505
$934$	34.4858	1.12841
$935$	−0.916222	−0.0299637
$936$	40.0871	1.31029
$937$	2.62361	0.0857095	0.0428548	−	0.999081i	$-0.486355\pi$
$937$	2.62361	0.0857095	0.0428548	+	0.999081i	$0.486355\pi$
$938$	−3.59121	−0.117257
$939$	−76.6742	−2.50217
$940$	1.18479	0.0386437
$941$	18.6696	0.608612	0.304306	−	0.952574i	$-0.401575\pi$
$941$	18.6696	0.608612	0.304306	+	0.952574i	$0.401575\pi$
$942$	−37.3141	−1.21576
$943$	6.67087	0.217234
$944$	−22.6759	−0.738039
$945$	2.01455	0.0655332
$946$	−11.7050	−0.380563
$947$	8.39961	0.272951	0.136475	−	0.990643i	$-0.456423\pi$
$947$	8.39961	0.272951	0.136475	+	0.990643i	$0.456423\pi$
$948$	−6.30272	−0.204703
$949$	−3.57573	−0.116073
$950$	0	0
$951$	−85.0343	−2.75742
$952$	−0.478340	−0.0155031
$953$	−33.6928	−1.09142	−0.545709	−	0.837975i	$-0.683740\pi$
$953$	−33.6928	−1.09142	−0.545709	+	0.837975i	$0.683740\pi$
$954$	20.2267	0.654863
$955$	16.1239	0.521758
$956$	−0.434696	−0.0140591
$957$	−44.1070	−1.42578
$958$	51.4347	1.66178
$959$	0.0888306	0.00286849
$960$	21.7665	0.702511
$961$	19.4962	0.628909
$962$	17.1438	0.552739
$963$	−54.1489	−1.74492
$964$	2.55026	0.0821383
$965$	−0.261764	−0.00842647
$966$	−3.63041	−0.116807
$967$	11.7433	0.377639	0.188819	−	0.982012i	$-0.439534\pi$
$967$	11.7433	0.377639	0.188819	+	0.982012i	$0.439534\pi$
$968$	17.7847	0.571621
$969$	0	0
$970$	−11.2003	−0.359619
$971$	−12.8093	−0.411071	−0.205536	−	0.978650i	$-0.565894\pi$
$971$	−12.8093	−0.411071	−0.205536	+	0.978650i	$0.565894\pi$
$972$	1.99638	0.0640339
$973$	1.48070	0.0474692
$974$	−10.4602	−0.335165
$975$	31.3259	1.00323
$976$	−32.8280	−1.05080
$977$	−14.5276	−0.464781	−0.232390	−	0.972623i	$-0.574655\pi$
$977$	−14.5276	−0.464781	−0.232390	+	0.972623i	$0.574655\pi$
$978$	32.4124	1.03643
$979$	−22.9145	−0.732350
$980$	1.11793	0.0357108
$981$	9.64496	0.307940
$982$	−49.4766	−1.57886
$983$	37.0502	1.18172	0.590860	−	0.806774i	$-0.298789\pi$
$983$	37.0502	1.18172	0.590860	+	0.806774i	$0.298789\pi$
$984$	20.9828	0.668906
$985$	11.5561	0.368209
$986$	4.33687	0.138114
$987$	−7.29086	−0.232071
$988$	0	0
$989$	−10.5134	−0.334307
$990$	−13.9581	−0.443618
$991$	−3.43140	−0.109002	−0.0545010	−	0.998514i	$-0.517357\pi$
$991$	−3.43140	−0.109002	−0.0545010	+	0.998514i	$0.517357\pi$
$992$	7.40373	0.235069
$993$	−79.6596	−2.52792
$994$	4.35410	0.138104
$995$	−0.225748	−0.00715669
$996$	7.89124	0.250044
$997$	12.7760	0.404620	0.202310	−	0.979322i	$-0.435155\pi$
$997$	12.7760	0.404620	0.202310	+	0.979322i	$0.435155\pi$
$998$	6.63722	0.210098
$999$	−32.6091	−1.03170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.a.h.1.2		3
3.2	odd	2		3249.2.a.s.1.2		3
4.3	odd	2		5776.2.a.bi.1.1		3
5.4	even	2		9025.2.a.x.1.2		3
19.2	odd	18		361.2.e.f.99.1		6
19.3	odd	18		19.2.e.a.9.1	✓	6
19.4	even	9		361.2.e.a.54.1		6
19.5	even	9		361.2.e.a.234.1		6
19.6	even	9		361.2.e.h.245.1		6
19.7	even	3		361.2.c.h.68.2		6
19.8	odd	6		361.2.c.i.292.2		6
19.9	even	9		361.2.e.b.62.1		6
19.10	odd	18		361.2.e.f.62.1		6
19.11	even	3		361.2.c.h.292.2		6
19.12	odd	6		361.2.c.i.68.2		6
19.13	odd	18		19.2.e.a.17.1	yes	6
19.14	odd	18		361.2.e.g.234.1		6
19.15	odd	18		361.2.e.g.54.1		6
19.16	even	9		361.2.e.h.28.1		6
19.17	even	9		361.2.e.b.99.1		6
19.18	odd	2		361.2.a.g.1.2		3
57.32	even	18		171.2.u.c.55.1		6
57.41	even	18		171.2.u.c.28.1		6
57.56	even	2		3249.2.a.z.1.2		3
76.3	even	18		304.2.u.b.161.1		6
76.51	even	18		304.2.u.b.17.1		6
76.75	even	2		5776.2.a.br.1.3		3
95.3	even	36		475.2.u.a.199.1		12
95.13	even	36		475.2.u.a.74.2		12
95.22	even	36		475.2.u.a.199.2		12
95.32	even	36		475.2.u.a.74.1		12
95.79	odd	18		475.2.l.a.351.1		6
95.89	odd	18		475.2.l.a.226.1		6
95.94	odd	2		9025.2.a.bd.1.2		3
133.3	even	18		931.2.v.a.275.1		6
133.13	even	18		931.2.w.a.834.1		6
133.32	odd	18		931.2.x.a.226.1		6
133.41	even	18		931.2.w.a.883.1		6
133.51	odd	18		931.2.v.b.606.1		6
133.60	odd	18		931.2.v.b.275.1		6
133.79	odd	18		931.2.x.a.655.1		6
133.89	even	18		931.2.v.a.606.1		6
133.108	even	18		931.2.x.b.226.1		6
133.117	even	18		931.2.x.b.655.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	19.3	odd	18
19.2.e.a.17.1	yes	6	19.13	odd	18
171.2.u.c.28.1		6	57.41	even	18
171.2.u.c.55.1		6	57.32	even	18
304.2.u.b.17.1		6	76.51	even	18
304.2.u.b.161.1		6	76.3	even	18
361.2.a.g.1.2		3	19.18	odd	2
361.2.a.h.1.2		3	1.1	even	1	trivial
361.2.c.h.68.2		6	19.7	even	3
361.2.c.h.292.2		6	19.11	even	3
361.2.c.i.68.2		6	19.12	odd	6
361.2.c.i.292.2		6	19.8	odd	6
361.2.e.a.54.1		6	19.4	even	9
361.2.e.a.234.1		6	19.5	even	9
361.2.e.b.62.1		6	19.9	even	9
361.2.e.b.99.1		6	19.17	even	9
361.2.e.f.62.1		6	19.10	odd	18
361.2.e.f.99.1		6	19.2	odd	18
361.2.e.g.54.1		6	19.15	odd	18
361.2.e.g.234.1		6	19.14	odd	18
361.2.e.h.28.1		6	19.16	even	9
361.2.e.h.245.1		6	19.6	even	9
475.2.l.a.226.1		6	95.89	odd	18
475.2.l.a.351.1		6	95.79	odd	18
475.2.u.a.74.1		12	95.32	even	36
475.2.u.a.74.2		12	95.13	even	36
475.2.u.a.199.1		12	95.3	even	36
475.2.u.a.199.2		12	95.22	even	36
931.2.v.a.275.1		6	133.3	even	18
931.2.v.a.606.1		6	133.89	even	18
931.2.v.b.275.1		6	133.60	odd	18
931.2.v.b.606.1		6	133.51	odd	18
931.2.w.a.834.1		6	133.13	even	18
931.2.w.a.883.1		6	133.41	even	18
931.2.x.a.226.1		6	133.32	odd	18
931.2.x.a.655.1		6	133.79	odd	18
931.2.x.b.226.1		6	133.108	even	18
931.2.x.b.655.1		6	133.117	even	18
3249.2.a.s.1.2		3	3.2	odd	2
3249.2.a.z.1.2		3	57.56	even	2
5776.2.a.bi.1.1		3	4.3	odd	2
5776.2.a.br.1.3		3	76.75	even	2
9025.2.a.x.1.2		3	5.4	even	2
9025.2.a.bd.1.2		3	95.94	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.a (trivial)

\(f(q)\)	\(=\)	\(q+1.34730 q^{2} +2.87939 q^{3} -0.184793 q^{4} +0.879385 q^{5} +3.87939 q^{6} +0.347296 q^{7} -2.94356 q^{8} +5.29086 q^{9} +O(q^{10})\)	\(q+1.34730 q^{2} +2.87939 q^{3} -0.184793 q^{4} +0.879385 q^{5} +3.87939 q^{6} +0.347296 q^{7} -2.94356 q^{8} +5.29086 q^{9} +1.18479 q^{10} -2.22668 q^{11} -0.532089 q^{12} -2.57398 q^{13} +0.467911 q^{14} +2.53209 q^{15} -3.59627 q^{16} +0.467911 q^{17} +7.12836 q^{18} -0.162504 q^{20} +1.00000 q^{21} -3.00000 q^{22} -2.69459 q^{23} -8.47565 q^{24} -4.22668 q^{25} -3.46791 q^{26} +6.59627 q^{27} -0.0641778 q^{28} +6.87939 q^{29} +3.41147 q^{30} +7.10607 q^{31} +1.04189 q^{32} -6.41147 q^{33} +0.630415 q^{34} +0.305407 q^{35} -0.977711 q^{36} -4.94356 q^{37} -7.41147 q^{39} -2.58853 q^{40} -2.47565 q^{41} +1.34730 q^{42} +3.90167 q^{43} +0.411474 q^{44} +4.65270 q^{45} -3.63041 q^{46} -7.29086 q^{47} -10.3550 q^{48} -6.87939 q^{49} -5.69459 q^{50} +1.34730 q^{51} +0.475652 q^{52} +2.83750 q^{53} +8.88713 q^{54} -1.95811 q^{55} -1.02229 q^{56} +9.26857 q^{58} +6.30541 q^{59} -0.467911 q^{60} +9.12836 q^{61} +9.57398 q^{62} +1.83750 q^{63} +8.59627 q^{64} -2.26352 q^{65} -8.63816 q^{66} -7.67499 q^{67} -0.0864665 q^{68} -7.75877 q^{69} +0.411474 q^{70} +9.30541 q^{71} -15.5740 q^{72} +1.38919 q^{73} -6.66044 q^{74} -12.1702 q^{75} -0.773318 q^{77} -9.98545 q^{78} +11.8452 q^{79} -3.16250 q^{80} +3.12061 q^{81} -3.33544 q^{82} -14.8307 q^{83} -0.184793 q^{84} +0.411474 q^{85} +5.25671 q^{86} +19.8084 q^{87} +6.55438 q^{88} +10.2909 q^{89} +6.26857 q^{90} -0.893933 q^{91} +0.497941 q^{92} +20.4611 q^{93} -9.82295 q^{94} +3.00000 q^{96} -9.45336 q^{97} -9.26857 q^{98} -11.7811 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 6 * q^6 + 6 * q^8	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8} + 3 q^{12} + 6 q^{14} + 3 q^{15} + 3 q^{16} + 6 q^{17} + 3 q^{18} - 3 q^{20} + 3 q^{21} - 9 q^{22} - 6 q^{23} - 6 q^{24} - 6 q^{25} - 15 q^{26} + 6 q^{27} + 9 q^{28} + 15 q^{29} + 9 q^{31} - 9 q^{33} + 9 q^{34} + 3 q^{35} - 9 q^{36} - 12 q^{39} - 18 q^{40} + 12 q^{41} + 3 q^{42} - 9 q^{44} + 15 q^{45} - 18 q^{46} - 6 q^{47} - 6 q^{48} - 15 q^{49} - 15 q^{50} + 3 q^{51} - 18 q^{52} + 6 q^{53} - 3 q^{54} - 9 q^{55} + 3 q^{56} + 18 q^{58} + 21 q^{59} - 6 q^{60} + 9 q^{61} + 21 q^{62} + 3 q^{63} + 12 q^{64} - 12 q^{65} - 9 q^{66} - 18 q^{67} + 15 q^{68} - 12 q^{69} - 9 q^{70} + 30 q^{71} - 39 q^{72} + 3 q^{74} - 15 q^{75} - 9 q^{77} - 12 q^{78} + 9 q^{79} - 12 q^{80} + 15 q^{81} + 18 q^{82} + 3 q^{84} - 9 q^{85} - 21 q^{86} + 21 q^{87} + 9 q^{88} + 15 q^{89} + 9 q^{90} - 15 q^{91} - 24 q^{92} + 24 q^{93} - 9 q^{94} + 9 q^{96} - 15 q^{97} - 18 q^{98} - 18 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 6 * q^6 + 6 * q^8 + 3 * q^12 + 6 * q^14 + 3 * q^15 + 3 * q^16 + 6 * q^17 + 3 * q^18 - 3 * q^20 + 3 * q^21 - 9 * q^22 - 6 * q^23 - 6 * q^24 - 6 * q^25 - 15 * q^26 + 6 * q^27 + 9 * q^28 + 15 * q^29 + 9 * q^31 - 9 * q^33 + 9 * q^34 + 3 * q^35 - 9 * q^36 - 12 * q^39 - 18 * q^40 + 12 * q^41 + 3 * q^42 - 9 * q^44 + 15 * q^45 - 18 * q^46 - 6 * q^47 - 6 * q^48 - 15 * q^49 - 15 * q^50 + 3 * q^51 - 18 * q^52 + 6 * q^53 - 3 * q^54 - 9 * q^55 + 3 * q^56 + 18 * q^58 + 21 * q^59 - 6 * q^60 + 9 * q^61 + 21 * q^62 + 3 * q^63 + 12 * q^64 - 12 * q^65 - 9 * q^66 - 18 * q^67 + 15 * q^68 - 12 * q^69 - 9 * q^70 + 30 * q^71 - 39 * q^72 + 3 * q^74 - 15 * q^75 - 9 * q^77 - 12 * q^78 + 9 * q^79 - 12 * q^80 + 15 * q^81 + 18 * q^82 + 3 * q^84 - 9 * q^85 - 21 * q^86 + 21 * q^87 + 9 * q^88 + 15 * q^89 + 9 * q^90 - 15 * q^91 - 24 * q^92 + 24 * q^93 - 9 * q^94 + 9 * q^96 - 15 * q^97 - 18 * q^98 - 18 * q^99

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