LMFDB - Embedded newform 361.2.a.h.1.3

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			1.3
Root			$-1.53209$ 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)

$f(q)$	$=$	$q+2.53209 q^{2} +0.652704 q^{3} +4.41147 q^{4} -1.34730 q^{5} +1.65270 q^{6} +1.53209 q^{7} +6.10607 q^{8} -2.57398 q^{9} +O(q^{10})$	\(q+2.53209 q^{2} +0.652704 q^{3} +4.41147 q^{4} -1.34730 q^{5} +1.65270 q^{6} +1.53209 q^{7} +6.10607 q^{8} -2.57398 q^{9} -3.41147 q^{10} -1.18479 q^{11} +2.87939 q^{12} -2.71688 q^{13} +3.87939 q^{14} -0.879385 q^{15} +6.63816 q^{16} +3.87939 q^{17} -6.51754 q^{18} -5.94356 q^{20} +1.00000 q^{21} -3.00000 q^{22} -5.06418 q^{23} +3.98545 q^{24} -3.18479 q^{25} -6.87939 q^{26} -3.63816 q^{27} +6.75877 q^{28} +4.65270 q^{29} -2.22668 q^{30} +3.83750 q^{31} +4.59627 q^{32} -0.773318 q^{33} +9.82295 q^{34} -2.06418 q^{35} -11.3550 q^{36} +4.10607 q^{37} -1.77332 q^{39} -8.22668 q^{40} +9.98545 q^{41} +2.53209 q^{42} -8.70233 q^{43} -5.22668 q^{44} +3.46791 q^{45} -12.8229 q^{46} +0.573978 q^{47} +4.33275 q^{48} -4.65270 q^{49} -8.06418 q^{50} +2.53209 q^{51} -11.9855 q^{52} -2.94356 q^{53} -9.21213 q^{54} +1.59627 q^{55} +9.35504 q^{56} +11.7811 q^{58} +3.93582 q^{59} -3.87939 q^{60} -4.51754 q^{61} +9.71688 q^{62} -3.94356 q^{63} -1.63816 q^{64} +3.66044 q^{65} -1.95811 q^{66} +3.88713 q^{67} +17.1138 q^{68} -3.30541 q^{69} -5.22668 q^{70} +6.93582 q^{71} -15.7169 q^{72} +6.12836 q^{73} +10.3969 q^{74} -2.07873 q^{75} -1.81521 q^{77} -4.49020 q^{78} -9.80840 q^{79} -8.94356 q^{80} +5.34730 q^{81} +25.2841 q^{82} +12.3182 q^{83} +4.41147 q^{84} -5.22668 q^{85} -22.0351 q^{86} +3.03684 q^{87} -7.23442 q^{88} +2.42602 q^{89} +8.78106 q^{90} -4.16250 q^{91} -22.3405 q^{92} +2.50475 q^{93} +1.45336 q^{94} +3.00000 q^{96} -7.36959 q^{97} -11.7811 q^{98} +3.04963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.53209	1.79046	0.895229	−	0.445607i	$-0.147012\pi$
$2$	2.53209	1.79046	0.895229	+	0.445607i	$0.147012\pi$
$3$	0.652704	0.376839	0.188419	−	0.982089i	$-0.439664\pi$
$3$	0.652704	0.376839	0.188419	+	0.982089i	$0.439664\pi$
$4$	4.41147	2.20574
$5$	−1.34730	−0.602529	−0.301265	−	0.953541i	$-0.597409\pi$
$5$	−1.34730	−0.602529	−0.301265	+	0.953541i	$0.597409\pi$
$6$	1.65270	0.674713
$7$	1.53209	0.579075	0.289538	−	0.957167i	$-0.406498\pi$
$7$	1.53209	0.579075	0.289538	+	0.957167i	$0.406498\pi$
$8$	6.10607	2.15882
$9$	−2.57398	−0.857993
$10$	−3.41147	−1.07880
$11$	−1.18479	−0.357228	−0.178614	−	0.983919i	$-0.557161\pi$
$11$	−1.18479	−0.357228	−0.178614	+	0.983919i	$0.557161\pi$
$12$	2.87939	0.831207
$13$	−2.71688	−0.753527	−0.376764	−	0.926309i	$-0.622963\pi$
$13$	−2.71688	−0.753527	−0.376764	+	0.926309i	$0.622963\pi$
$14$	3.87939	1.03681
$15$	−0.879385	−0.227056
$16$	6.63816	1.65954
$17$	3.87939	0.940889	0.470445	−	0.882430i	$-0.344094\pi$
$17$	3.87939	0.940889	0.470445	+	0.882430i	$0.344094\pi$
$18$	−6.51754	−1.53620
$19$	0	0
$19$	0	0
$20$	−5.94356	−1.32902
$21$	1.00000	0.218218
$22$	−3.00000	−0.639602
$23$	−5.06418	−1.05595	−0.527977	−	0.849259i	$-0.677049\pi$
$23$	−5.06418	−1.05595	−0.527977	+	0.849259i	$0.677049\pi$
$24$	3.98545	0.813527
$25$	−3.18479	−0.636959
$26$	−6.87939	−1.34916
$27$	−3.63816	−0.700163
$28$	6.75877	1.27729
$29$	4.65270	0.863985	0.431993	−	0.901877i	$-0.357811\pi$
$29$	4.65270	0.863985	0.431993	+	0.901877i	$0.357811\pi$
$30$	−2.22668	−0.406535
$31$	3.83750	0.689235	0.344617	−	0.938743i	$-0.388009\pi$
$31$	3.83750	0.689235	0.344617	+	0.938743i	$0.388009\pi$
$32$	4.59627	0.812513
$33$	−0.773318	−0.134617
$34$	9.82295	1.68462
$35$	−2.06418	−0.348910
$36$	−11.3550	−1.89251
$37$	4.10607	0.675033	0.337517	−	0.941320i	$-0.390413\pi$
$37$	4.10607	0.675033	0.337517	+	0.941320i	$0.390413\pi$
$38$	0	0
$39$	−1.77332	−0.283958
$40$	−8.22668	−1.30075
$41$	9.98545	1.55947	0.779733	−	0.626112i	$-0.215355\pi$
$41$	9.98545	1.55947	0.779733	+	0.626112i	$0.215355\pi$
$42$	2.53209	0.390710
$43$	−8.70233	−1.32709	−0.663547	−	0.748135i	$-0.730950\pi$
$43$	−8.70233	−1.32709	−0.663547	+	0.748135i	$0.730950\pi$
$44$	−5.22668	−0.787952
$45$	3.46791	0.516966
$46$	−12.8229	−1.89064
$47$	0.573978	0.0837233	0.0418616	−	0.999123i	$-0.486671\pi$
$47$	0.573978	0.0837233	0.0418616	+	0.999123i	$0.486671\pi$
$48$	4.33275	0.625378
$49$	−4.65270	−0.664672
$50$	−8.06418	−1.14045
$51$	2.53209	0.354563
$52$	−11.9855	−1.66208
$53$	−2.94356	−0.404329	−0.202165	−	0.979352i	$-0.564798\pi$
$53$	−2.94356	−0.404329	−0.202165	+	0.979352i	$0.564798\pi$
$54$	−9.21213	−1.25361
$55$	1.59627	0.215241
$56$	9.35504	1.25012
$57$	0	0
$58$	11.7811	1.54693
$59$	3.93582	0.512400	0.256200	−	0.966624i	$-0.417529\pi$
$59$	3.93582	0.512400	0.256200	+	0.966624i	$0.417529\pi$
$60$	−3.87939	−0.500826
$61$	−4.51754	−0.578412	−0.289206	−	0.957267i	$-0.593391\pi$
$61$	−4.51754	−0.578412	−0.289206	+	0.957267i	$0.593391\pi$
$62$	9.71688	1.23405
$63$	−3.94356	−0.496842
$64$	−1.63816	−0.204769
$65$	3.66044	0.454022
$66$	−1.95811	−0.241027
$67$	3.88713	0.474888	0.237444	−	0.971401i	$-0.423690\pi$
$67$	3.88713	0.474888	0.237444	+	0.971401i	$0.423690\pi$
$68$	17.1138	2.07535
$69$	−3.30541	−0.397924
$70$	−5.22668	−0.624708
$71$	6.93582	0.823131	0.411565	−	0.911380i	$-0.364982\pi$
$71$	6.93582	0.823131	0.411565	+	0.911380i	$0.364982\pi$
$72$	−15.7169	−1.85225
$73$	6.12836	0.717270	0.358635	−	0.933478i	$-0.383242\pi$
$73$	6.12836	0.717270	0.358635	+	0.933478i	$0.383242\pi$
$74$	10.3969	1.20862
$75$	−2.07873	−0.240031
$76$	0	0
$77$	−1.81521	−0.206862
$78$	−4.49020	−0.508415
$79$	−9.80840	−1.10353	−0.551766	−	0.833999i	$-0.686046\pi$
$79$	−9.80840	−1.10353	−0.551766	+	0.833999i	$0.686046\pi$
$80$	−8.94356	−0.999921
$81$	5.34730	0.594144
$82$	25.2841	2.79216
$83$	12.3182	1.35210	0.676049	−	0.736857i	$-0.263691\pi$
$83$	12.3182	1.35210	0.676049	+	0.736857i	$0.263691\pi$
$84$	4.41147	0.481331
$85$	−5.22668	−0.566913
$86$	−22.0351	−2.37610
$87$	3.03684	0.325583
$88$	−7.23442	−0.771192
$89$	2.42602	0.257158	0.128579	−	0.991699i	$-0.458958\pi$
$89$	2.42602	0.257158	0.128579	+	0.991699i	$0.458958\pi$
$90$	8.78106	0.925605
$91$	−4.16250	−0.436349
$92$	−22.3405	−2.32916
$93$	2.50475	0.259730
$94$	1.45336	0.149903
$95$	0	0
$96$	3.00000	0.306186
$97$	−7.36959	−0.748268	−0.374134	−	0.927375i	$-0.622060\pi$
$97$	−7.36959	−0.748268	−0.374134	+	0.927375i	$0.622060\pi$
$98$	−11.7811	−1.19007
$99$	3.04963	0.306499
$100$	−14.0496	−1.40496
$101$	2.17024	0.215947	0.107974	−	0.994154i	$-0.465564\pi$
$101$	2.17024	0.215947	0.107974	+	0.994154i	$0.465564\pi$
$102$	6.41147	0.634831
$103$	12.4757	1.22926	0.614631	−	0.788815i	$-0.289305\pi$
$103$	12.4757	1.22926	0.614631	+	0.788815i	$0.289305\pi$
$104$	−16.5895	−1.62673
$105$	−1.34730	−0.131483
$106$	−7.45336	−0.723935
$107$	6.68004	0.645784	0.322892	−	0.946436i	$-0.395345\pi$
$107$	6.68004	0.645784	0.322892	+	0.946436i	$0.395345\pi$
$108$	−16.0496	−1.54438
$109$	−9.45336	−0.905468	−0.452734	−	0.891646i	$-0.649551\pi$
$109$	−9.45336	−0.905468	−0.452734	+	0.891646i	$0.649551\pi$
$110$	4.04189	0.385379
$111$	2.68004	0.254379
$112$	10.1702	0.960998
$113$	−1.31046	−0.123278	−0.0616388	−	0.998099i	$-0.519633\pi$
$113$	−1.31046	−0.123278	−0.0616388	+	0.998099i	$0.519633\pi$
$114$	0	0
$115$	6.82295	0.636243
$116$	20.5253	1.90572
$117$	6.99319	0.646521
$118$	9.96585	0.917431
$119$	5.94356	0.544846
$120$	−5.36959	−0.490174
$121$	−9.59627	−0.872388
$122$	−11.4388	−1.03562
$123$	6.51754	0.587667
$124$	16.9290	1.52027
$125$	11.0273	0.986315
$126$	−9.98545	−0.889575
$127$	14.5030	1.28693	0.643466	−	0.765474i	$-0.277496\pi$
$127$	14.5030	1.28693	0.643466	+	0.765474i	$0.277496\pi$
$128$	−13.3405	−1.17914
$129$	−5.68004	−0.500100
$130$	9.26857	0.812907
$131$	−19.8084	−1.73067	−0.865334	−	0.501196i	$-0.832894\pi$
$131$	−19.8084	−1.73067	−0.865334	+	0.501196i	$0.832894\pi$
$132$	−3.41147	−0.296931
$133$	0	0
$134$	9.84255	0.850267
$135$	4.90167	0.421869
$136$	23.6878	2.03121
$137$	10.2044	0.871820	0.435910	−	0.899990i	$-0.356427\pi$
$137$	10.2044	0.871820	0.435910	+	0.899990i	$0.356427\pi$
$138$	−8.36959	−0.712466
$139$	−1.66044	−0.140837	−0.0704185	−	0.997518i	$-0.522433\pi$
$139$	−1.66044	−0.140837	−0.0704185	+	0.997518i	$0.522433\pi$
$140$	−9.10607	−0.769603
$141$	0.374638	0.0315502
$142$	17.5621	1.47378
$143$	3.21894	0.269181
$144$	−17.0865	−1.42387
$145$	−6.26857	−0.520576
$146$	15.5175	1.28424
$147$	−3.03684	−0.250474
$148$	18.1138	1.48895
$149$	11.2071	0.918120	0.459060	−	0.888405i	$-0.348186\pi$
$149$	11.2071	0.918120	0.459060	+	0.888405i	$0.348186\pi$
$150$	−5.26352	−0.429764
$151$	11.0419	0.898576	0.449288	−	0.893387i	$-0.351678\pi$
$151$	11.0419	0.898576	0.449288	+	0.893387i	$0.351678\pi$
$152$	0	0
$153$	−9.98545	−0.807276
$154$	−4.59627	−0.370378
$155$	−5.17024	−0.415284
$156$	−7.82295	−0.626337
$157$	10.9932	0.877352	0.438676	−	0.898645i	$-0.355448\pi$
$157$	10.9932	0.877352	0.438676	+	0.898645i	$0.355448\pi$
$158$	−24.8357	−1.97583
$159$	−1.92127	−0.152367
$160$	−6.19253	−0.489563
$161$	−7.75877	−0.611477
$162$	13.5398	1.06379
$163$	−6.33275	−0.496019	−0.248010	−	0.968758i	$-0.579776\pi$
$163$	−6.33275	−0.496019	−0.248010	+	0.968758i	$0.579776\pi$
$164$	44.0506	3.43977
$165$	1.04189	0.0811110
$166$	31.1908	2.42087
$167$	13.7784	1.06620	0.533101	−	0.846051i	$-0.321027\pi$
$167$	13.7784	1.06620	0.533101	+	0.846051i	$0.321027\pi$
$168$	6.10607	0.471093
$169$	−5.61856	−0.432197
$170$	−13.2344	−1.01503
$171$	0	0
$172$	−38.3901	−2.92722
$173$	−25.2472	−1.91951	−0.959755	−	0.280838i	$-0.909388\pi$
$173$	−25.2472	−1.91951	−0.959755	+	0.280838i	$0.909388\pi$
$174$	7.68954	0.582943
$175$	−4.87939	−0.368847
$176$	−7.86484	−0.592834
$177$	2.56893	0.193092
$178$	6.14290	0.460430
$179$	−5.83069	−0.435806	−0.217903	−	0.975970i	$-0.569922\pi$
$179$	−5.83069	−0.435806	−0.217903	+	0.975970i	$0.569922\pi$
$180$	15.2986	1.14029
$181$	−13.5621	−1.00806	−0.504032	−	0.863685i	$-0.668151\pi$
$181$	−13.5621	−1.00806	−0.504032	+	0.863685i	$0.668151\pi$
$182$	−10.5398	−0.781264
$183$	−2.94862	−0.217968
$184$	−30.9222	−2.27962
$185$	−5.53209	−0.406727
$186$	6.34224	0.465036
$187$	−4.59627	−0.336112
$188$	2.53209	0.184672
$189$	−5.57398	−0.405447
$190$	0	0
$191$	−10.2841	−0.744128	−0.372064	−	0.928207i	$-0.621350\pi$
$191$	−10.2841	−0.744128	−0.372064	+	0.928207i	$0.621350\pi$
$192$	−1.06923	−0.0771650
$193$	−13.8007	−0.993393	−0.496697	−	0.867924i	$-0.665454\pi$
$193$	−13.8007	−0.993393	−0.496697	+	0.867924i	$0.665454\pi$
$194$	−18.6604	−1.33974
$195$	2.38919	0.171093
$196$	−20.5253	−1.46609
$197$	−7.94087	−0.565764	−0.282882	−	0.959155i	$-0.591290\pi$
$197$	−7.94087	−0.565764	−0.282882	+	0.959155i	$0.591290\pi$
$198$	7.72193	0.548774
$199$	27.0351	1.91647	0.958233	−	0.285988i	$-0.0923219\pi$
$199$	27.0351	1.91647	0.958233	+	0.285988i	$0.0923219\pi$
$200$	−19.4466	−1.37508
$201$	2.53714	0.178956
$202$	5.49525	0.386645
$203$	7.12836	0.500312
$204$	11.1702	0.782074
$205$	−13.4534	−0.939624
$206$	31.5895	2.20094
$207$	13.0351	0.906001
$208$	−18.0351	−1.25051
$209$	0	0
$210$	−3.41147	−0.235414
$211$	8.07192	0.555694	0.277847	−	0.960625i	$-0.410379\pi$
$211$	8.07192	0.555694	0.277847	+	0.960625i	$0.410379\pi$
$212$	−12.9855	−0.891845
$213$	4.52704	0.310187
$214$	16.9145	1.15625
$215$	11.7246	0.799613
$216$	−22.2148	−1.51153
$217$	5.87939	0.399119
$218$	−23.9368	−1.62120
$219$	4.00000	0.270295
$220$	7.04189	0.474764
$221$	−10.5398	−0.708986
$222$	6.78611	0.455454
$223$	15.4757	1.03633	0.518163	−	0.855282i	$-0.326616\pi$
$223$	15.4757	1.03633	0.518163	+	0.855282i	$0.326616\pi$
$224$	7.04189	0.470506
$225$	8.19759	0.546506
$226$	−3.31820	−0.220723
$227$	−9.87258	−0.655266	−0.327633	−	0.944805i	$-0.606251\pi$
$227$	−9.87258	−0.655266	−0.327633	+	0.944805i	$0.606251\pi$
$228$	0	0
$229$	20.1189	1.32949	0.664746	−	0.747070i	$-0.268540\pi$
$229$	20.1189	1.32949	0.664746	+	0.747070i	$0.268540\pi$
$230$	17.2763	1.13917
$231$	−1.18479	−0.0779536
$232$	28.4097	1.86519
$233$	3.53478	0.231571	0.115785	−	0.993274i	$-0.463061\pi$
$233$	3.53478	0.231571	0.115785	+	0.993274i	$0.463061\pi$
$234$	17.7074	1.15757
$235$	−0.773318	−0.0504457
$236$	17.3628	1.13022
$237$	−6.40198	−0.415853
$238$	15.0496	0.975523
$239$	11.9736	0.774507	0.387254	−	0.921973i	$-0.373424\pi$
$239$	11.9736	0.774507	0.387254	+	0.921973i	$0.373424\pi$
$240$	−5.83750	−0.376809
$241$	−12.9017	−0.831070	−0.415535	−	0.909577i	$-0.636406\pi$
$241$	−12.9017	−0.831070	−0.415535	+	0.909577i	$0.636406\pi$
$242$	−24.2986	−1.56197
$243$	14.4047	0.924060
$244$	−19.9290	−1.27582
$245$	6.26857	0.400484
$246$	16.5030	1.05219
$247$	0	0
$248$	23.4320	1.48793
$249$	8.04013	0.509523
$250$	27.9222	1.76596
$251$	14.3628	0.906571	0.453285	−	0.891366i	$-0.350252\pi$
$251$	14.3628	0.906571	0.453285	+	0.891366i	$0.350252\pi$
$252$	−17.3969	−1.09590
$253$	6.00000	0.377217
$254$	36.7229	2.30420
$255$	−3.41147	−0.213635
$256$	−30.5030	−1.90644
$257$	−4.97771	−0.310501	−0.155251	−	0.987875i	$-0.549618\pi$
$257$	−4.97771	−0.310501	−0.155251	+	0.987875i	$0.549618\pi$
$258$	−14.3824	−0.895408
$259$	6.29086	0.390895
$260$	16.1480	1.00145
$261$	−11.9760	−0.741293
$262$	−50.1566	−3.09869
$263$	−24.0428	−1.48254	−0.741272	−	0.671205i	$-0.765777\pi$
$263$	−24.0428	−1.48254	−0.741272	+	0.671205i	$0.765777\pi$
$264$	−4.72193	−0.290615
$265$	3.96585	0.243620
$266$	0	0
$267$	1.58347	0.0969070
$268$	17.1480	1.04748
$269$	13.1111	0.799399	0.399700	−	0.916646i	$-0.369114\pi$
$269$	13.1111	0.799399	0.399700	+	0.916646i	$0.369114\pi$
$270$	12.4115	0.755338
$271$	−26.5699	−1.61400	−0.807002	−	0.590549i	$-0.798911\pi$
$271$	−26.5699	−1.61400	−0.807002	+	0.590549i	$0.798911\pi$
$272$	25.7520	1.56144
$273$	−2.71688	−0.164433
$274$	25.8384	1.56096
$275$	3.77332	0.227540
$276$	−14.5817	−0.877716
$277$	−16.5107	−0.992034	−0.496017	−	0.868313i	$-0.665205\pi$
$277$	−16.5107	−0.992034	−0.496017	+	0.868313i	$0.665205\pi$
$278$	−4.20439	−0.252163
$279$	−9.87763	−0.591358
$280$	−12.6040	−0.753234
$281$	19.3901	1.15672	0.578359	−	0.815783i	$-0.303693\pi$
$281$	19.3901	1.15672	0.578359	+	0.815783i	$0.303693\pi$
$282$	0.948615	0.0564892
$283$	−11.3105	−0.672337	−0.336169	−	0.941802i	$-0.609131\pi$
$283$	−11.3105	−0.672337	−0.336169	+	0.941802i	$0.609131\pi$
$284$	30.5972	1.81561
$285$	0	0
$286$	8.15064	0.481958
$287$	15.2986	0.903048
$288$	−11.8307	−0.697130
$289$	−1.95037	−0.114728
$290$	−15.8726	−0.932070
$291$	−4.81016	−0.281976
$292$	27.0351	1.58211
$293$	−3.89899	−0.227781	−0.113891	−	0.993493i	$-0.536331\pi$
$293$	−3.89899	−0.227781	−0.113891	+	0.993493i	$0.536331\pi$
$294$	−7.68954	−0.448463
$295$	−5.30272	−0.308736
$296$	25.0719	1.45728
$297$	4.31046	0.250118
$298$	28.3773	1.64385
$299$	13.7588	0.795690
$300$	−9.17024	−0.529444
$301$	−13.3327	−0.768487
$302$	27.9590	1.60886
$303$	1.41653	0.0813773
$304$	0	0
$305$	6.08647	0.348510
$306$	−25.2841	−1.44539
$307$	−23.1753	−1.32268	−0.661342	−	0.750084i	$-0.730013\pi$
$307$	−23.1753	−1.32268	−0.661342	+	0.750084i	$0.730013\pi$
$308$	−8.00774	−0.456283
$309$	8.14290	0.463234
$310$	−13.0915	−0.743548
$311$	−3.46110	−0.196261	−0.0981306	−	0.995174i	$-0.531286\pi$
$311$	−3.46110	−0.196261	−0.0981306	+	0.995174i	$0.531286\pi$
$312$	−10.8280	−0.613015
$313$	−22.8898	−1.29381	−0.646904	−	0.762571i	$-0.723937\pi$
$313$	−22.8898	−1.29381	−0.646904	+	0.762571i	$0.723937\pi$
$314$	27.8357	1.57086
$315$	5.31315	0.299362
$316$	−43.2695	−2.43410
$317$	−26.1206	−1.46708	−0.733540	−	0.679646i	$-0.762133\pi$
$317$	−26.1206	−1.46708	−0.733540	+	0.679646i	$0.762133\pi$
$318$	−4.86484	−0.272807
$319$	−5.51249	−0.308640
$320$	2.20708	0.123380
$321$	4.36009	0.243356
$322$	−19.6459	−1.09482
$323$	0	0
$324$	23.5895	1.31053
$325$	8.65270	0.479966
$326$	−16.0351	−0.888101
$327$	−6.17024	−0.341215
$328$	60.9718	3.36661
$329$	0.879385	0.0484821
$330$	2.63816	0.145226
$331$	−19.0446	−1.04678	−0.523392	−	0.852092i	$-0.675334\pi$
$331$	−19.0446	−1.04678	−0.523392	+	0.852092i	$0.675334\pi$
$332$	54.3414	2.98237
$333$	−10.5689	−0.579174
$334$	34.8881	1.90899
$335$	−5.23711	−0.286134
$336$	6.63816	0.362141
$337$	−1.70140	−0.0926812	−0.0463406	−	0.998926i	$-0.514756\pi$
$337$	−1.70140	−0.0926812	−0.0463406	+	0.998926i	$0.514756\pi$
$338$	−14.2267	−0.773829
$339$	−0.855342	−0.0464558
$340$	−23.0574	−1.25046
$341$	−4.54664	−0.246214
$342$	0	0
$343$	−17.8530	−0.963970
$344$	−53.1370	−2.86496
$345$	4.45336	0.239761
$346$	−63.9282	−3.43680
$347$	−4.90167	−0.263136	−0.131568	−	0.991307i	$-0.542001\pi$
$347$	−4.90167	−0.263136	−0.131568	+	0.991307i	$0.542001\pi$
$348$	13.3969	0.718151
$349$	−28.1293	−1.50573	−0.752863	−	0.658177i	$-0.771328\pi$
$349$	−28.1293	−1.50573	−0.752863	+	0.658177i	$0.771328\pi$
$350$	−12.3550	−0.660405
$351$	9.88444	0.527592
$352$	−5.44562	−0.290253
$353$	−8.31996	−0.442827	−0.221413	−	0.975180i	$-0.571067\pi$
$353$	−8.31996	−0.442827	−0.221413	+	0.975180i	$0.571067\pi$
$354$	6.50475	0.345723
$355$	−9.34461	−0.495960
$356$	10.7023	0.567223
$357$	3.87939	0.205319
$358$	−14.7638	−0.780292
$359$	24.9290	1.31570	0.657852	−	0.753148i	$-0.271465\pi$
$359$	24.9290	1.31570	0.657852	+	0.753148i	$0.271465\pi$
$360$	21.1753	1.11604
$361$	0	0
$362$	−34.3405	−1.80490
$363$	−6.26352	−0.328749
$364$	−18.3628	−0.962471
$365$	−8.25671	−0.432176
$366$	−7.46616	−0.390262
$367$	−2.58584	−0.134980	−0.0674898	−	0.997720i	$-0.521499\pi$
$367$	−2.58584	−0.134980	−0.0674898	+	0.997720i	$0.521499\pi$
$368$	−33.6168	−1.75240
$369$	−25.7023	−1.33801
$370$	−14.0077	−0.728228
$371$	−4.50980	−0.234137
$372$	11.0496	0.572897
$373$	23.3833	1.21074	0.605371	−	0.795943i	$-0.293025\pi$
$373$	23.3833	1.21074	0.605371	+	0.795943i	$0.293025\pi$
$374$	−11.6382	−0.601795
$375$	7.19759	0.371682
$376$	3.50475	0.180744
$377$	−12.6408	−0.651037
$378$	−14.1138	−0.725936
$379$	−25.4388	−1.30670	−0.653352	−	0.757054i	$-0.726638\pi$
$379$	−25.4388	−1.30670	−0.653352	+	0.757054i	$0.726638\pi$
$380$	0	0
$381$	9.46616	0.484966
$382$	−26.0401	−1.33233
$383$	27.4807	1.40420	0.702099	−	0.712079i	$-0.252246\pi$
$383$	27.4807	1.40420	0.702099	+	0.712079i	$0.252246\pi$
$384$	−8.70739	−0.444347
$385$	2.44562	0.124640
$386$	−34.9445	−1.77863
$387$	22.3996	1.13864
$388$	−32.5107	−1.65048
$389$	−3.34224	−0.169458	−0.0847292	−	0.996404i	$-0.527003\pi$
$389$	−3.34224	−0.169458	−0.0847292	+	0.996404i	$0.527003\pi$
$390$	6.04963	0.306335
$391$	−19.6459	−0.993536
$392$	−28.4097	−1.43491
$393$	−12.9290	−0.652183
$394$	−20.1070	−1.01298
$395$	13.2148	0.664910
$396$	13.4534	0.676057
$397$	−13.1233	−0.658640	−0.329320	−	0.944218i	$-0.606819\pi$
$397$	−13.1233	−0.658640	−0.329320	+	0.944218i	$0.606819\pi$
$398$	68.4552	3.43135
$399$	0	0
$400$	−21.1411	−1.05706
$401$	−17.1138	−0.854623	−0.427311	−	0.904105i	$-0.640539\pi$
$401$	−17.1138	−0.854623	−0.427311	+	0.904105i	$0.640539\pi$
$402$	6.42427	0.320413
$403$	−10.4260	−0.519357
$404$	9.57398	0.476323
$405$	−7.20439	−0.357989
$406$	18.0496	0.895788
$407$	−4.86484	−0.241141
$408$	15.4611	0.765439
$409$	8.79797	0.435032	0.217516	−	0.976057i	$-0.430205\pi$
$409$	8.79797	0.435032	0.217516	+	0.976057i	$0.430205\pi$
$410$	−34.0651	−1.68236
$411$	6.66044	0.328535
$412$	55.0360	2.71143
$413$	6.03003	0.296718
$414$	33.0060	1.62216
$415$	−16.5963	−0.814679
$416$	−12.4875	−0.612251
$417$	−1.08378	−0.0530728
$418$	0	0
$419$	6.84018	0.334165	0.167082	−	0.985943i	$-0.446565\pi$
$419$	6.84018	0.334165	0.167082	+	0.985943i	$0.446565\pi$
$420$	−5.94356	−0.290016
$421$	4.82295	0.235056	0.117528	−	0.993070i	$-0.462503\pi$
$421$	4.82295	0.235056	0.117528	+	0.993070i	$0.462503\pi$
$422$	20.4388	0.994946
$423$	−1.47741	−0.0718340
$424$	−17.9736	−0.872875
$425$	−12.3550	−0.599307
$426$	11.4629	0.555377
$427$	−6.92127	−0.334944
$428$	29.4688	1.42443
$429$	2.10101	0.101438
$430$	29.6878	1.43167
$431$	−1.30365	−0.0627947	−0.0313974	−	0.999507i	$-0.509996\pi$
$431$	−1.30365	−0.0627947	−0.0313974	+	0.999507i	$0.509996\pi$
$432$	−24.1506	−1.16195
$433$	−19.8239	−0.952675	−0.476337	−	0.879263i	$-0.658036\pi$
$433$	−19.8239	−0.952675	−0.476337	+	0.879263i	$0.658036\pi$
$434$	14.8871	0.714605
$435$	−4.09152	−0.196173
$436$	−41.7033	−1.99722
$437$	0	0
$438$	10.1284	0.483952
$439$	34.5672	1.64980	0.824901	−	0.565278i	$-0.191231\pi$
$439$	34.5672	1.64980	0.824901	+	0.565278i	$0.191231\pi$
$440$	9.74691	0.464666
$441$	11.9760	0.570284
$442$	−26.6878	−1.26941
$443$	17.0101	0.808174	0.404087	−	0.914720i	$-0.367589\pi$
$443$	17.0101	0.808174	0.404087	+	0.914720i	$0.367589\pi$
$444$	11.8229	0.561092
$445$	−3.26857	−0.154945
$446$	39.1857	1.85550
$447$	7.31490	0.345983
$448$	−2.50980	−0.118577
$449$	−37.4097	−1.76547	−0.882737	−	0.469868i	$-0.844302\pi$
$449$	−37.4097	−1.76547	−0.882737	+	0.469868i	$0.844302\pi$
$450$	20.7570	0.978495
$451$	−11.8307	−0.557085
$452$	−5.78106	−0.271918
$453$	7.20708	0.338618
$454$	−24.9982	−1.17323
$455$	5.60813	0.262913
$456$	0	0
$457$	9.11112	0.426200	0.213100	−	0.977030i	$-0.431644\pi$
$457$	9.11112	0.426200	0.213100	+	0.977030i	$0.431644\pi$
$458$	50.9427	2.38040
$459$	−14.1138	−0.658776
$460$	30.0993	1.40339
$461$	−24.4483	−1.13867	−0.569336	−	0.822105i	$-0.692800\pi$
$461$	−24.4483	−1.13867	−0.569336	+	0.822105i	$0.692800\pi$
$462$	−3.00000	−0.139573
$463$	−0.250725	−0.0116522	−0.00582609	−	0.999983i	$-0.501855\pi$
$463$	−0.250725	−0.0116522	−0.00582609	+	0.999983i	$0.501855\pi$
$464$	30.8854	1.43382
$465$	−3.37464	−0.156495
$466$	8.95037	0.414618
$467$	15.3618	0.710861	0.355431	−	0.934703i	$-0.384334\pi$
$467$	15.3618	0.710861	0.355431	+	0.934703i	$0.384334\pi$
$468$	30.8503	1.42606
$469$	5.95542	0.274996
$470$	−1.95811	−0.0903209
$471$	7.17530	0.330620
$472$	24.0324	1.10618
$473$	10.3105	0.474075
$474$	−16.2104	−0.744567
$475$	0	0
$476$	26.2199	1.20179
$477$	7.57667	0.346912
$478$	30.3182	1.38672
$479$	−0.719246	−0.0328632	−0.0164316	−	0.999865i	$-0.505231\pi$
$479$	−0.719246	−0.0328632	−0.0164316	+	0.999865i	$0.505231\pi$
$480$	−4.04189	−0.184486
$481$	−11.1557	−0.508656
$482$	−32.6682	−1.48800
$483$	−5.06418	−0.230428
$484$	−42.3337	−1.92426
$485$	9.92902	0.450853
$486$	36.4739	1.65449
$487$	−11.7469	−0.532303	−0.266152	−	0.963931i	$-0.585752\pi$
$487$	−11.7469	−0.532303	−0.266152	+	0.963931i	$0.585752\pi$
$488$	−27.5844	−1.24869
$489$	−4.13341	−0.186919
$490$	15.8726	0.717050
$491$	0.0888306	0.00400887	0.00200443	−	0.999998i	$-0.499362\pi$
$491$	0.0888306	0.00400887	0.00200443	+	0.999998i	$0.499362\pi$
$492$	28.7520	1.29624
$493$	18.0496	0.812914
$494$	0	0
$495$	−4.10876	−0.184675
$496$	25.4739	1.14381
$497$	10.6263	0.476655
$498$	20.3583	0.912279
$499$	14.6905	0.657636	0.328818	−	0.944393i	$-0.393350\pi$
$499$	14.6905	0.657636	0.328818	+	0.944393i	$0.393350\pi$
$500$	48.6468	2.17555
$501$	8.99319	0.401786
$502$	36.3678	1.62318
$503$	−4.90404	−0.218660	−0.109330	−	0.994005i	$-0.534871\pi$
$503$	−4.90404	−0.218660	−0.109330	+	0.994005i	$0.534871\pi$
$504$	−24.0797	−1.07259
$505$	−2.92396	−0.130115
$506$	15.1925	0.675390
$507$	−3.66725	−0.162868
$508$	63.9796	2.83863
$509$	−6.41384	−0.284288	−0.142144	−	0.989846i	$-0.545400\pi$
$509$	−6.41384	−0.284288	−0.142144	+	0.989846i	$0.545400\pi$
$510$	−8.63816	−0.382504
$511$	9.38919	0.415353
$512$	−50.5553	−2.23425
$513$	0	0
$514$	−12.6040	−0.555939
$515$	−16.8084	−0.740667
$516$	−25.0574	−1.10309
$517$	−0.680045	−0.0299083
$518$	15.9290	0.699881
$519$	−16.4789	−0.723346
$520$	22.3509	0.980153
$521$	35.8135	1.56902	0.784508	−	0.620119i	$-0.212916\pi$
$521$	35.8135	1.56902	0.784508	+	0.620119i	$0.212916\pi$
$522$	−30.3242	−1.32725
$523$	−38.7725	−1.69540	−0.847701	−	0.530474i	$-0.822014\pi$
$523$	−38.7725	−1.69540	−0.847701	+	0.530474i	$0.822014\pi$
$524$	−87.3842	−3.81740
$525$	−3.18479	−0.138996
$526$	−60.8786	−2.65443
$527$	14.8871	0.648493
$528$	−5.13341	−0.223403
$529$	2.64590	0.115039
$530$	10.0419	0.436192
$531$	−10.1307	−0.439636
$532$	0	0
$533$	−27.1293	−1.17510
$534$	4.00950	0.173508
$535$	−9.00000	−0.389104
$536$	23.7351	1.02520
$537$	−3.80571	−0.164229
$538$	33.1985	1.43129
$539$	5.51249	0.237440
$540$	21.6236	0.930532
$541$	9.49020	0.408016	0.204008	−	0.978969i	$-0.434603\pi$
$541$	9.49020	0.408016	0.204008	+	0.978969i	$0.434603\pi$
$542$	−67.2772	−2.88981
$543$	−8.85204	−0.379878
$544$	17.8307	0.764484
$545$	12.7365	0.545571
$546$	−6.87939	−0.294411
$547$	−14.2121	−0.607667	−0.303833	−	0.952725i	$-0.598267\pi$
$547$	−14.2121	−0.607667	−0.303833	+	0.952725i	$0.598267\pi$
$548$	45.0164	1.92301
$549$	11.6281	0.496273
$550$	9.55438	0.407400
$551$	0	0
$552$	−20.1830	−0.859047
$553$	−15.0273	−0.639028
$554$	−41.8066	−1.77619
$555$	−3.61081	−0.153271
$556$	−7.32501	−0.310650
$557$	22.5398	0.955043	0.477522	−	0.878620i	$-0.341535\pi$
$557$	22.5398	0.955043	0.477522	+	0.878620i	$0.341535\pi$
$558$	−25.0110	−1.05880
$559$	23.6432	1.00000
$560$	−13.7023	−0.579029
$561$	−3.00000	−0.126660
$562$	49.0975	2.07105
$563$	42.9718	1.81105	0.905524	−	0.424296i	$-0.139478\pi$
$563$	42.9718	1.81105	0.905524	+	0.424296i	$0.139478\pi$
$564$	1.65270	0.0695914
$565$	1.76558	0.0742784
$566$	−28.6391	−1.20379
$567$	8.19253	0.344054
$568$	42.3506	1.77699
$569$	−7.42696	−0.311354	−0.155677	−	0.987808i	$-0.549756\pi$
$569$	−7.42696	−0.311354	−0.155677	+	0.987808i	$0.549756\pi$
$570$	0	0
$571$	4.04458	0.169260	0.0846301	−	0.996412i	$-0.473029\pi$
$571$	4.04458	0.169260	0.0846301	+	0.996412i	$0.473029\pi$
$572$	14.2003	0.593743
$573$	−6.71244	−0.280416
$574$	38.7374	1.61687
$575$	16.1284	0.672599
$576$	4.21658	0.175691
$577$	3.23442	0.134651	0.0673254	−	0.997731i	$-0.478553\pi$
$577$	3.23442	0.134651	0.0673254	+	0.997731i	$0.478553\pi$
$578$	−4.93851	−0.205415
$579$	−9.00774	−0.374349
$580$	−27.6536	−1.14825
$581$	18.8726	0.782966
$582$	−12.1797	−0.504866
$583$	3.48751	0.144438
$584$	37.4201	1.54846
$585$	−9.42190	−0.389548
$586$	−9.87258	−0.407832
$587$	−40.8084	−1.68434	−0.842171	−	0.539210i	$-0.818723\pi$
$587$	−40.8084	−1.68434	−0.842171	+	0.539210i	$0.818723\pi$
$588$	−13.3969	−0.552480
$589$	0	0
$590$	−13.4270	−0.552779
$591$	−5.18304	−0.213202
$592$	27.2567	1.12024
$593$	−11.0642	−0.454351	−0.227176	−	0.973854i	$-0.572949\pi$
$593$	−11.0642	−0.454351	−0.227176	+	0.973854i	$0.572949\pi$
$594$	10.9145	0.447826
$595$	−8.00774	−0.328285
$596$	49.4397	2.02513
$597$	17.6459	0.722198
$598$	34.8384	1.42465
$599$	44.5577	1.82058	0.910289	−	0.413974i	$-0.135860\pi$
$599$	44.5577	1.82058	0.910289	+	0.413974i	$0.135860\pi$
$600$	−12.6928	−0.518183
$601$	4.99907	0.203916	0.101958	−	0.994789i	$-0.467489\pi$
$601$	4.99907	0.203916	0.101958	+	0.994789i	$0.467489\pi$
$602$	−33.7597	−1.37594
$603$	−10.0054	−0.407450
$604$	48.7110	1.98202
$605$	12.9290	0.525639
$606$	3.58677	0.145703
$607$	31.1881	1.26589	0.632943	−	0.774199i	$-0.281847\pi$
$607$	31.1881	1.26589	0.632943	+	0.774199i	$0.281847\pi$
$608$	0	0
$609$	4.65270	0.188537
$610$	15.4115	0.623992
$611$	−1.55943	−0.0630878
$612$	−44.0506	−1.78064
$613$	16.3696	0.661161	0.330581	−	0.943778i	$-0.392755\pi$
$613$	16.3696	0.661161	0.330581	+	0.943778i	$0.392755\pi$
$614$	−58.6819	−2.36821
$615$	−8.78106	−0.354086
$616$	−11.0838	−0.446578
$617$	16.0583	0.646483	0.323241	−	0.946317i	$-0.395227\pi$
$617$	16.0583	0.646483	0.323241	+	0.946317i	$0.395227\pi$
$618$	20.6186	0.829400
$619$	23.8425	0.958313	0.479156	−	0.877730i	$-0.340943\pi$
$619$	23.8425	0.958313	0.479156	+	0.877730i	$0.340943\pi$
$620$	−22.8084	−0.916007
$621$	18.4243	0.739340
$622$	−8.76382	−0.351397
$623$	3.71688	0.148914
$624$	−11.7716	−0.471240
$625$	1.06687	0.0426746
$626$	−57.9590	−2.31651
$627$	0	0
$628$	48.4962	1.93521
$629$	15.9290	0.635131
$630$	13.4534	0.535995
$631$	21.4730	0.854825	0.427413	−	0.904057i	$-0.359425\pi$
$631$	21.4730	0.854825	0.427413	+	0.904057i	$0.359425\pi$
$632$	−59.8907	−2.38233
$633$	5.26857	0.209407
$634$	−66.1397	−2.62674
$635$	−19.5398	−0.775414
$636$	−8.47565	−0.336081
$637$	12.6408	0.500848
$638$	−13.9581	−0.552607
$639$	−17.8527	−0.706240
$640$	17.9736	0.710469
$641$	−12.7537	−0.503742	−0.251871	−	0.967761i	$-0.581046\pi$
$641$	−12.7537	−0.503742	−0.251871	+	0.967761i	$0.581046\pi$
$642$	11.0401	0.435719
$643$	28.6081	1.12819	0.564097	−	0.825708i	$-0.309224\pi$
$643$	28.6081	1.12819	0.564097	+	0.825708i	$0.309224\pi$
$644$	−34.2276	−1.34876
$645$	7.65270	0.301325
$646$	0	0
$647$	16.7128	0.657046	0.328523	−	0.944496i	$-0.393449\pi$
$647$	16.7128	0.657046	0.328523	+	0.944496i	$0.393449\pi$
$648$	32.6509	1.28265
$649$	−4.66313	−0.183044
$650$	21.9094	0.859358
$651$	3.83750	0.150403
$652$	−27.9368	−1.09409
$653$	27.0000	1.05659	0.528296	−	0.849060i	$-0.322831\pi$
$653$	27.0000	1.05659	0.528296	+	0.849060i	$0.322831\pi$
$654$	−15.6236	−0.610931
$655$	26.6878	1.04278
$656$	66.2850	2.58799
$657$	−15.7743	−0.615412
$658$	2.22668	0.0868051
$659$	43.9009	1.71013	0.855067	−	0.518517i	$-0.173516\pi$
$659$	43.9009	1.71013	0.855067	+	0.518517i	$0.173516\pi$
$660$	4.59627	0.178909
$661$	10.7561	0.418363	0.209182	−	0.977877i	$-0.432920\pi$
$661$	10.7561	0.418363	0.209182	+	0.977877i	$0.432920\pi$
$662$	−48.2226	−1.87422
$663$	−6.87939	−0.267173
$664$	75.2158	2.91894
$665$	0	0
$666$	−26.7615	−1.03699
$667$	−23.5621	−0.912329
$668$	60.7829	2.35176
$669$	10.1010	0.390528
$670$	−13.2608	−0.512311
$671$	5.35235	0.206625
$672$	4.59627	0.177305
$673$	−4.65776	−0.179543	−0.0897717	−	0.995962i	$-0.528614\pi$
$673$	−4.65776	−0.179543	−0.0897717	+	0.995962i	$0.528614\pi$
$674$	−4.30810	−0.165942
$675$	11.5868	0.445975
$676$	−24.7861	−0.953312
$677$	−3.26857	−0.125621	−0.0628107	−	0.998025i	$-0.520006\pi$
$677$	−3.26857	−0.125621	−0.0628107	+	0.998025i	$0.520006\pi$
$678$	−2.16580	−0.0831771
$679$	−11.2909	−0.433303
$680$	−31.9145	−1.22386
$681$	−6.44387	−0.246930
$682$	−11.5125	−0.440836
$683$	−6.21894	−0.237961	−0.118981	−	0.992897i	$-0.537963\pi$
$683$	−6.21894	−0.237961	−0.118981	+	0.992897i	$0.537963\pi$
$684$	0	0
$685$	−13.7483	−0.525297
$686$	−45.2053	−1.72595
$687$	13.1317	0.501004
$688$	−57.7674	−2.20236
$689$	7.99731	0.304673
$690$	11.2763	0.429282
$691$	22.2175	0.845194	0.422597	−	0.906318i	$-0.361119\pi$
$691$	22.2175	0.845194	0.422597	+	0.906318i	$0.361119\pi$
$692$	−111.377	−4.23393
$693$	4.67230	0.177486
$694$	−12.4115	−0.471133
$695$	2.23711	0.0848584
$696$	18.5431	0.702875
$697$	38.7374	1.46728
$698$	−71.2259	−2.69594
$699$	2.30716	0.0872649
$700$	−21.5253	−0.813579
$701$	−27.7725	−1.04895	−0.524476	−	0.851425i	$-0.675739\pi$
$701$	−27.7725	−1.04895	−0.524476	+	0.851425i	$0.675739\pi$
$702$	25.0283	0.944631
$703$	0	0
$704$	1.94087	0.0731495
$705$	−0.504748	−0.0190099
$706$	−21.0669	−0.792862
$707$	3.32501	0.125050
$708$	11.3327	0.425911
$709$	−6.10782	−0.229384	−0.114692	−	0.993401i	$-0.536588\pi$
$709$	−6.10782	−0.229384	−0.114692	+	0.993401i	$0.536588\pi$
$710$	−23.6614	−0.887996
$711$	25.2466	0.946822
$712$	14.8135	0.555158
$713$	−19.4338	−0.727800
$714$	9.82295	0.367615
$715$	−4.33687	−0.162190
$716$	−25.7219	−0.961274
$717$	7.81521	0.291864
$718$	63.1225	2.35571
$719$	38.7238	1.44415	0.722077	−	0.691813i	$-0.243188\pi$
$719$	38.7238	1.44415	0.722077	+	0.691813i	$0.243188\pi$
$720$	23.0205	0.857925
$721$	19.1138	0.711835
$722$	0	0
$723$	−8.42097	−0.313179
$724$	−59.8289	−2.22352
$725$	−14.8179	−0.550323
$726$	−15.8598	−0.588612
$727$	−11.0779	−0.410857	−0.205428	−	0.978672i	$-0.565859\pi$
$727$	−11.0779	−0.410857	−0.205428	+	0.978672i	$0.565859\pi$
$728$	−25.4165	−0.941999
$729$	−6.63991	−0.245923
$730$	−20.9067	−0.773793
$731$	−33.7597	−1.24865
$732$	−13.0077	−0.480780
$733$	−15.8075	−0.583862	−0.291931	−	0.956439i	$-0.594298\pi$
$733$	−15.8075	−0.583862	−0.291931	+	0.956439i	$0.594298\pi$
$734$	−6.54757	−0.241675
$735$	4.09152	0.150918
$736$	−23.2763	−0.857976
$737$	−4.60544	−0.169643
$738$	−65.0806	−2.39565
$739$	1.54933	0.0569928	0.0284964	−	0.999594i	$-0.490928\pi$
$739$	1.54933	0.0569928	0.0284964	+	0.999594i	$0.490928\pi$
$740$	−24.4047	−0.897133
$741$	0	0
$742$	−11.4192	−0.419213
$743$	−38.1634	−1.40008	−0.700040	−	0.714103i	$-0.746835\pi$
$743$	−38.1634	−1.40008	−0.700040	+	0.714103i	$0.746835\pi$
$744$	15.2942	0.560711
$745$	−15.0993	−0.553194
$746$	59.2086	2.16778
$747$	−31.7068	−1.16009
$748$	−20.2763	−0.741375
$749$	10.2344	0.373958
$750$	18.2249	0.665480
$751$	25.3482	0.924970	0.462485	−	0.886627i	$-0.346958\pi$
$751$	25.3482	0.924970	0.462485	+	0.886627i	$0.346958\pi$
$752$	3.81016	0.138942
$753$	9.37464	0.341631
$754$	−32.0077	−1.16565
$755$	−14.8767	−0.541418
$756$	−24.5895	−0.894310
$757$	42.3705	1.53998	0.769991	−	0.638054i	$-0.220260\pi$
$757$	42.3705	1.53998	0.769991	+	0.638054i	$0.220260\pi$
$758$	−64.4133	−2.33960
$759$	3.91622	0.142150
$760$	0	0
$761$	−2.85710	−0.103570	−0.0517848	−	0.998658i	$-0.516491\pi$
$761$	−2.85710	−0.103570	−0.0517848	+	0.998658i	$0.516491\pi$
$762$	23.9691	0.868311
$763$	−14.4834	−0.524334
$764$	−45.3678	−1.64135
$765$	13.4534	0.486407
$766$	69.5836	2.51416
$767$	−10.6932	−0.386108
$768$	−19.9094	−0.718419
$769$	19.1206	0.689507	0.344754	−	0.938693i	$-0.387963\pi$
$769$	19.1206	0.689507	0.344754	+	0.938693i	$0.387963\pi$
$770$	6.19253	0.223163
$771$	−3.24897	−0.117009
$772$	−60.8813	−2.19116
$773$	−2.51485	−0.0904530	−0.0452265	−	0.998977i	$-0.514401\pi$
$773$	−2.51485	−0.0904530	−0.0452265	+	0.998977i	$0.514401\pi$
$774$	56.7178	2.03868
$775$	−12.2216	−0.439014
$776$	−44.9992	−1.61538
$777$	4.10607	0.147304
$778$	−8.46286	−0.303408
$779$	0	0
$780$	10.5398	0.377386
$781$	−8.21751	−0.294046
$782$	−49.7452	−1.77888
$783$	−16.9273	−0.604931
$784$	−30.8854	−1.10305
$785$	−14.8111	−0.528630
$786$	−32.7374	−1.16770
$787$	−2.72605	−0.0971733	−0.0485866	−	0.998819i	$-0.515472\pi$
$787$	−2.72605	−0.0971733	−0.0485866	+	0.998819i	$0.515472\pi$
$788$	−35.0310	−1.24793
$789$	−15.6928	−0.558680
$790$	33.4611	1.19049
$791$	−2.00774	−0.0713870
$792$	18.6212	0.661677
$793$	12.2736	0.435849
$794$	−33.2294	−1.17927
$795$	2.58853	0.0918056
$796$	119.265	4.22722
$797$	−22.0327	−0.780439	−0.390219	−	0.920722i	$-0.627601\pi$
$797$	−22.0327	−0.780439	−0.390219	+	0.920722i	$0.627601\pi$
$798$	0	0
$799$	2.22668	0.0787743
$800$	−14.6382	−0.517537
$801$	−6.24453	−0.220640
$802$	−43.3337	−1.53017
$803$	−7.26083	−0.256229
$804$	11.1925	0.394730
$805$	10.4534	0.368433
$806$	−26.3996	−0.929887
$807$	8.55768	0.301244
$808$	13.2517	0.466192
$809$	54.7205	1.92387	0.961935	−	0.273278i	$-0.0881077\pi$
$809$	54.7205	1.92387	0.961935	+	0.273278i	$0.0881077\pi$
$810$	−18.2422	−0.640964
$811$	2.31046	0.0811312	0.0405656	−	0.999177i	$-0.487084\pi$
$811$	2.31046	0.0811312	0.0405656	+	0.999177i	$0.487084\pi$
$812$	31.4466	1.10356
$813$	−17.3422	−0.608219
$814$	−12.3182	−0.431753
$815$	8.53209	0.298866
$816$	16.8084	0.588412
$817$	0	0
$818$	22.2772	0.778906
$819$	10.7142	0.374384
$820$	−59.3492	−2.07256
$821$	1.11112	0.0387783	0.0193892	−	0.999812i	$-0.493828\pi$
$821$	1.11112	0.0387783	0.0193892	+	0.999812i	$0.493828\pi$
$822$	16.8648	0.588229
$823$	20.6477	0.719732	0.359866	−	0.933004i	$-0.382822\pi$
$823$	20.6477	0.719732	0.359866	+	0.933004i	$0.382822\pi$
$824$	76.1772	2.65376
$825$	2.46286	0.0857457
$826$	15.2686	0.531262
$827$	−36.3054	−1.26246	−0.631231	−	0.775595i	$-0.717450\pi$
$827$	−36.3054	−1.26246	−0.631231	+	0.775595i	$0.717450\pi$
$828$	57.5039	1.99840
$829$	7.14971	0.248320	0.124160	−	0.992262i	$-0.460376\pi$
$829$	7.14971	0.248320	0.124160	+	0.992262i	$0.460376\pi$
$830$	−42.0232	−1.45865
$831$	−10.7766	−0.373837
$832$	4.45067	0.154299
$833$	−18.0496	−0.625383
$834$	−2.74422	−0.0950247
$835$	−18.5635	−0.642418
$836$	0	0
$837$	−13.9614	−0.482577
$838$	17.3200	0.598308
$839$	34.6067	1.19476	0.597378	−	0.801960i	$-0.296209\pi$
$839$	34.6067	1.19476	0.597378	+	0.801960i	$0.296209\pi$
$840$	−8.22668	−0.283847
$841$	−7.35235	−0.253529
$842$	12.2121	0.420858
$843$	12.6560	0.435896
$844$	35.6091	1.22571
$845$	7.56986	0.260411
$846$	−3.74092	−0.128616
$847$	−14.7023	−0.505178
$848$	−19.5398	−0.671001
$849$	−7.38238	−0.253363
$850$	−31.2841	−1.07303
$851$	−20.7939	−0.712804
$852$	19.9709	0.684192
$853$	33.2508	1.13849	0.569243	−	0.822169i	$-0.307236\pi$
$853$	33.2508	1.13849	0.569243	+	0.822169i	$0.307236\pi$
$854$	−17.5253	−0.599703
$855$	0	0
$856$	40.7888	1.39413
$857$	3.88619	0.132750	0.0663749	−	0.997795i	$-0.478857\pi$
$857$	3.88619	0.132750	0.0663749	+	0.997795i	$0.478857\pi$
$858$	5.31996	0.181620
$859$	1.65776	0.0565619	0.0282810	−	0.999600i	$-0.490997\pi$
$859$	1.65776	0.0565619	0.0282810	+	0.999600i	$0.490997\pi$
$860$	51.7229	1.76374
$861$	9.98545	0.340303
$862$	−3.30096	−0.112431
$863$	52.7187	1.79457	0.897284	−	0.441455i	$-0.145537\pi$
$863$	52.7187	1.79457	0.897284	+	0.441455i	$0.145537\pi$
$864$	−16.7219	−0.568892
$865$	34.0155	1.15656
$866$	−50.1958	−1.70572
$867$	−1.27301	−0.0432338
$868$	25.9368	0.880351
$869$	11.6209	0.394213
$870$	−10.3601	−0.351240
$871$	−10.5609	−0.357841
$872$	−57.7229	−1.95474
$873$	18.9691	0.642008
$874$	0	0
$875$	16.8949	0.571151
$876$	17.6459	0.596200
$877$	21.1898	0.715530	0.357765	−	0.933812i	$-0.383539\pi$
$877$	21.1898	0.715530	0.357765	+	0.933812i	$0.383539\pi$
$878$	87.5271	2.95390
$879$	−2.54488	−0.0858367
$880$	10.5963	0.357200
$881$	32.1010	1.08151	0.540755	−	0.841180i	$-0.318138\pi$
$881$	32.1010	1.08151	0.540755	+	0.841180i	$0.318138\pi$
$882$	30.3242	1.02107
$883$	−47.2968	−1.59167	−0.795833	−	0.605516i	$-0.792967\pi$
$883$	−47.2968	−1.59167	−0.795833	+	0.605516i	$0.792967\pi$
$884$	−46.4962	−1.56384
$885$	−3.46110	−0.116344
$886$	43.0711	1.44700
$887$	−10.5631	−0.354673	−0.177336	−	0.984150i	$-0.556748\pi$
$887$	−10.5631	−0.354673	−0.177336	+	0.984150i	$0.556748\pi$
$888$	16.3645	0.549158
$889$	22.2199	0.745231
$890$	−8.27631	−0.277423
$891$	−6.33544	−0.212245
$892$	68.2704	2.28586
$893$	0	0
$894$	18.5220	0.619468
$895$	7.85567	0.262586
$896$	−20.4388	−0.682813
$897$	8.98040	0.299847
$898$	−94.7247	−3.16101
$899$	17.8547	0.595489
$900$	36.1634	1.20545
$901$	−11.4192	−0.380429
$902$	−29.9564	−0.997438
$903$	−8.70233	−0.289596
$904$	−8.00175	−0.266134
$905$	18.2722	0.607388
$906$	18.2490	0.606281
$907$	−42.9205	−1.42515	−0.712575	−	0.701596i	$-0.752471\pi$
$907$	−42.9205	−1.42515	−0.712575	+	0.701596i	$0.752471\pi$
$908$	−43.5526	−1.44534
$909$	−5.58616	−0.185281
$910$	14.2003	0.470735
$911$	55.1411	1.82691	0.913454	−	0.406942i	$-0.133405\pi$
$911$	55.1411	1.82691	0.913454	+	0.406942i	$0.133405\pi$
$912$	0	0
$913$	−14.5945	−0.483008
$914$	23.0702	0.763093
$915$	3.97266	0.131332
$916$	88.7538	2.93251
$917$	−30.3482	−1.00219
$918$	−35.7374	−1.17951
$919$	−24.5577	−0.810083	−0.405041	−	0.914298i	$-0.632743\pi$
$919$	−24.5577	−0.810083	−0.405041	+	0.914298i	$0.632743\pi$
$920$	41.6614	1.37353
$921$	−15.1266	−0.498438
$922$	−61.9053	−2.03874
$923$	−18.8438	−0.620251
$924$	−5.22668	−0.171945
$925$	−13.0770	−0.429968
$926$	−0.634858	−0.0208627
$927$	−32.1121	−1.05470
$928$	21.3851	0.701999
$929$	−22.2772	−0.730893	−0.365446	−	0.930832i	$-0.619084\pi$
$929$	−22.2772	−0.730893	−0.365446	+	0.930832i	$0.619084\pi$
$930$	−8.54488	−0.280198
$931$	0	0
$932$	15.5936	0.510785
$933$	−2.25908	−0.0739588
$934$	38.8976	1.27277
$935$	6.19253	0.202517
$936$	42.7009	1.39572
$937$	−9.55169	−0.312040	−0.156020	−	0.987754i	$-0.549866\pi$
$937$	−9.55169	−0.312040	−0.156020	+	0.987754i	$0.549866\pi$
$938$	15.0797	0.492368
$939$	−14.9403	−0.487557
$940$	−3.41147	−0.111270
$941$	55.7256	1.81660	0.908301	−	0.418318i	$-0.137380\pi$
$941$	55.7256	1.81660	0.908301	+	0.418318i	$0.137380\pi$
$942$	18.1685	0.591961
$943$	−50.5681	−1.64672
$944$	26.1266	0.850348
$945$	7.50980	0.244294
$946$	26.1070	0.848812
$947$	−27.0428	−0.878774	−0.439387	−	0.898298i	$-0.644804\pi$
$947$	−27.0428	−0.878774	−0.439387	+	0.898298i	$0.644804\pi$
$948$	−28.2422	−0.917263
$949$	−16.6500	−0.540482
$950$	0	0
$951$	−17.0490	−0.552852
$952$	36.2918	1.17622
$953$	−23.1310	−0.749288	−0.374644	−	0.927169i	$-0.622235\pi$
$953$	−23.1310	−0.749288	−0.374644	+	0.927169i	$0.622235\pi$
$954$	19.1848	0.621131
$955$	13.8557	0.448359
$956$	52.8212	1.70836
$957$	−3.59802	−0.116308
$958$	−1.82119	−0.0588401
$959$	15.6340	0.504849
$960$	1.44057	0.0464942
$961$	−16.2736	−0.524956
$962$	−28.2472	−0.910727
$963$	−17.1943	−0.554078
$964$	−56.9154	−1.83312
$965$	18.5936	0.598548
$966$	−12.8229	−0.412572
$967$	39.0351	1.25528	0.627642	−	0.778502i	$-0.284020\pi$
$967$	39.0351	1.25528	0.627642	+	0.778502i	$0.284020\pi$
$968$	−58.5954	−1.88333
$969$	0	0
$970$	25.1411	0.807234
$971$	41.2026	1.32226	0.661128	−	0.750273i	$-0.270078\pi$
$971$	41.2026	1.32226	0.661128	+	0.750273i	$0.270078\pi$
$972$	63.5458	2.03823
$973$	−2.54395	−0.0815552
$974$	−29.7442	−0.953066
$975$	5.64765	0.180870
$976$	−29.9881	−0.959897
$977$	−22.4938	−0.719641	−0.359821	−	0.933022i	$-0.617162\pi$
$977$	−22.4938	−0.719641	−0.359821	+	0.933022i	$0.617162\pi$
$978$	−10.4662	−0.334671
$979$	−2.87433	−0.0918641
$980$	27.6536	0.883363
$981$	24.3327	0.776885
$982$	0.224927	0.00717771
$983$	44.5461	1.42080	0.710401	−	0.703798i	$-0.248514\pi$
$983$	44.5461	1.42080	0.710401	+	0.703798i	$0.248514\pi$
$984$	39.7965	1.26867
$985$	10.6987	0.340889
$986$	45.7033	1.45549
$987$	0.573978	0.0182699
$988$	0	0
$989$	44.0702	1.40135
$990$	−10.4037	−0.330652
$991$	45.3296	1.43994	0.719971	−	0.694005i	$-0.244155\pi$
$991$	45.3296	1.43994	0.719971	+	0.694005i	$0.244155\pi$
$992$	17.6382	0.560012
$993$	−12.4305	−0.394469
$994$	26.9067	0.853430
$995$	−36.4243	−1.15473
$996$	35.4688	1.12387
$997$	−10.4911	−0.332258	−0.166129	−	0.986104i	$-0.553127\pi$
$997$	−10.4911	−0.332258	−0.166129	+	0.986104i	$0.553127\pi$
$998$	37.1976	1.17747
$999$	−14.9385	−0.472634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.a.h.1.3		3
3.2	odd	2		3249.2.a.s.1.1		3
4.3	odd	2		5776.2.a.bi.1.2		3
5.4	even	2		9025.2.a.x.1.1		3
19.2	odd	18		361.2.e.g.99.1		6
19.3	odd	18		361.2.e.f.28.1		6
19.4	even	9		361.2.e.h.54.1		6
19.5	even	9		361.2.e.h.234.1		6
19.6	even	9		361.2.e.b.245.1		6
19.7	even	3		361.2.c.h.68.1		6
19.8	odd	6		361.2.c.i.292.3		6
19.9	even	9		361.2.e.a.62.1		6
19.10	odd	18		361.2.e.g.62.1		6
19.11	even	3		361.2.c.h.292.1		6
19.12	odd	6		361.2.c.i.68.3		6
19.13	odd	18		361.2.e.f.245.1		6
19.14	odd	18		19.2.e.a.6.1	✓	6
19.15	odd	18		19.2.e.a.16.1	yes	6
19.16	even	9		361.2.e.b.28.1		6
19.17	even	9		361.2.e.a.99.1		6
19.18	odd	2		361.2.a.g.1.1		3
57.14	even	18		171.2.u.c.82.1		6
57.53	even	18		171.2.u.c.73.1		6
57.56	even	2		3249.2.a.z.1.3		3
76.15	even	18		304.2.u.b.225.1		6
76.71	even	18		304.2.u.b.177.1		6
76.75	even	2		5776.2.a.br.1.2		3
95.14	odd	18		475.2.l.a.101.1		6
95.33	even	36		475.2.u.a.424.2		12
95.34	odd	18		475.2.l.a.301.1		6
95.52	even	36		475.2.u.a.424.1		12
95.53	even	36		475.2.u.a.149.1		12
95.72	even	36		475.2.u.a.149.2		12
95.94	odd	2		9025.2.a.bd.1.3		3
133.33	even	18		931.2.x.b.557.1		6
133.34	even	18		931.2.w.a.491.1		6
133.52	even	18		931.2.v.a.177.1		6
133.53	odd	18		931.2.x.a.814.1		6
133.72	odd	18		931.2.v.b.263.1		6
133.90	even	18		931.2.w.a.785.1		6
133.109	odd	18		931.2.v.b.177.1		6
133.110	even	18		931.2.v.a.263.1		6
133.128	odd	18		931.2.x.a.557.1		6
133.129	even	18		931.2.x.b.814.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.6.1	✓	6	19.14	odd	18
19.2.e.a.16.1	yes	6	19.15	odd	18
171.2.u.c.73.1		6	57.53	even	18
171.2.u.c.82.1		6	57.14	even	18
304.2.u.b.177.1		6	76.71	even	18
304.2.u.b.225.1		6	76.15	even	18
361.2.a.g.1.1		3	19.18	odd	2
361.2.a.h.1.3		3	1.1	even	1	trivial
361.2.c.h.68.1		6	19.7	even	3
361.2.c.h.292.1		6	19.11	even	3
361.2.c.i.68.3		6	19.12	odd	6
361.2.c.i.292.3		6	19.8	odd	6
361.2.e.a.62.1		6	19.9	even	9
361.2.e.a.99.1		6	19.17	even	9
361.2.e.b.28.1		6	19.16	even	9
361.2.e.b.245.1		6	19.6	even	9
361.2.e.f.28.1		6	19.3	odd	18
361.2.e.f.245.1		6	19.13	odd	18
361.2.e.g.62.1		6	19.10	odd	18
361.2.e.g.99.1		6	19.2	odd	18
361.2.e.h.54.1		6	19.4	even	9
361.2.e.h.234.1		6	19.5	even	9
475.2.l.a.101.1		6	95.14	odd	18
475.2.l.a.301.1		6	95.34	odd	18
475.2.u.a.149.1		12	95.53	even	36
475.2.u.a.149.2		12	95.72	even	36
475.2.u.a.424.1		12	95.52	even	36
475.2.u.a.424.2		12	95.33	even	36
931.2.v.a.177.1		6	133.52	even	18
931.2.v.a.263.1		6	133.110	even	18
931.2.v.b.177.1		6	133.109	odd	18
931.2.v.b.263.1		6	133.72	odd	18
931.2.w.a.491.1		6	133.34	even	18
931.2.w.a.785.1		6	133.90	even	18
931.2.x.a.557.1		6	133.128	odd	18
931.2.x.a.814.1		6	133.53	odd	18
931.2.x.b.557.1		6	133.33	even	18
931.2.x.b.814.1		6	133.129	even	18
3249.2.a.s.1.1		3	3.2	odd	2
3249.2.a.z.1.3		3	57.56	even	2
5776.2.a.bi.1.2		3	4.3	odd	2
5776.2.a.br.1.2		3	76.75	even	2
9025.2.a.x.1.1		3	5.4	even	2
9025.2.a.bd.1.3		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)

\(f(q)\)	\(=\)	\(q+2.53209 q^{2} +0.652704 q^{3} +4.41147 q^{4} -1.34730 q^{5} +1.65270 q^{6} +1.53209 q^{7} +6.10607 q^{8} -2.57398 q^{9} +O(q^{10})\)	\(q+2.53209 q^{2} +0.652704 q^{3} +4.41147 q^{4} -1.34730 q^{5} +1.65270 q^{6} +1.53209 q^{7} +6.10607 q^{8} -2.57398 q^{9} -3.41147 q^{10} -1.18479 q^{11} +2.87939 q^{12} -2.71688 q^{13} +3.87939 q^{14} -0.879385 q^{15} +6.63816 q^{16} +3.87939 q^{17} -6.51754 q^{18} -5.94356 q^{20} +1.00000 q^{21} -3.00000 q^{22} -5.06418 q^{23} +3.98545 q^{24} -3.18479 q^{25} -6.87939 q^{26} -3.63816 q^{27} +6.75877 q^{28} +4.65270 q^{29} -2.22668 q^{30} +3.83750 q^{31} +4.59627 q^{32} -0.773318 q^{33} +9.82295 q^{34} -2.06418 q^{35} -11.3550 q^{36} +4.10607 q^{37} -1.77332 q^{39} -8.22668 q^{40} +9.98545 q^{41} +2.53209 q^{42} -8.70233 q^{43} -5.22668 q^{44} +3.46791 q^{45} -12.8229 q^{46} +0.573978 q^{47} +4.33275 q^{48} -4.65270 q^{49} -8.06418 q^{50} +2.53209 q^{51} -11.9855 q^{52} -2.94356 q^{53} -9.21213 q^{54} +1.59627 q^{55} +9.35504 q^{56} +11.7811 q^{58} +3.93582 q^{59} -3.87939 q^{60} -4.51754 q^{61} +9.71688 q^{62} -3.94356 q^{63} -1.63816 q^{64} +3.66044 q^{65} -1.95811 q^{66} +3.88713 q^{67} +17.1138 q^{68} -3.30541 q^{69} -5.22668 q^{70} +6.93582 q^{71} -15.7169 q^{72} +6.12836 q^{73} +10.3969 q^{74} -2.07873 q^{75} -1.81521 q^{77} -4.49020 q^{78} -9.80840 q^{79} -8.94356 q^{80} +5.34730 q^{81} +25.2841 q^{82} +12.3182 q^{83} +4.41147 q^{84} -5.22668 q^{85} -22.0351 q^{86} +3.03684 q^{87} -7.23442 q^{88} +2.42602 q^{89} +8.78106 q^{90} -4.16250 q^{91} -22.3405 q^{92} +2.50475 q^{93} +1.45336 q^{94} +3.00000 q^{96} -7.36959 q^{97} -11.7811 q^{98} +3.04963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 6 q^{6} + 6 q^{8}+O(q^{10}) \) 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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