LMFDB - Embedded newform 9025.2.a.ct.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.96177 q^{2} -0.187708 q^{3} +1.84854 q^{4} +0.368240 q^{6} +0.677067 q^{7} +0.297123 q^{8} -2.96477 q^{9} +O(q^{10})$	\(q-1.96177 q^{2} -0.187708 q^{3} +1.84854 q^{4} +0.368240 q^{6} +0.677067 q^{7} +0.297123 q^{8} -2.96477 q^{9} +2.84069 q^{11} -0.346987 q^{12} -4.76663 q^{13} -1.32825 q^{14} -4.27997 q^{16} +5.18394 q^{17} +5.81619 q^{18} -0.127091 q^{21} -5.57278 q^{22} +1.05091 q^{23} -0.0557724 q^{24} +9.35103 q^{26} +1.11964 q^{27} +1.25159 q^{28} +1.42605 q^{29} -0.271064 q^{31} +7.80208 q^{32} -0.533221 q^{33} -10.1697 q^{34} -5.48050 q^{36} -0.603754 q^{37} +0.894735 q^{39} -6.73563 q^{41} +0.249324 q^{42} -5.62944 q^{43} +5.25114 q^{44} -2.06165 q^{46} +7.89538 q^{47} +0.803386 q^{48} -6.54158 q^{49} -0.973067 q^{51} -8.81132 q^{52} -6.88829 q^{53} -2.19647 q^{54} +0.201172 q^{56} -2.79757 q^{58} +10.1227 q^{59} -7.47195 q^{61} +0.531765 q^{62} -2.00735 q^{63} -6.74594 q^{64} +1.04606 q^{66} -4.11733 q^{67} +9.58273 q^{68} -0.197265 q^{69} +7.60546 q^{71} -0.880900 q^{72} +16.1274 q^{73} +1.18443 q^{74} +1.92334 q^{77} -1.75527 q^{78} -14.8468 q^{79} +8.68413 q^{81} +13.2138 q^{82} +14.1815 q^{83} -0.234933 q^{84} +11.0437 q^{86} -0.267680 q^{87} +0.844034 q^{88} -8.23788 q^{89} -3.22733 q^{91} +1.94266 q^{92} +0.0508809 q^{93} -15.4889 q^{94} -1.46451 q^{96} +5.72847 q^{97} +12.8331 q^{98} -8.42198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

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 $

$2$	−1.96177	−1.38718	−0.693591	−	0.720369i	$-0.743972\pi$
$2$	−1.96177	−1.38718	−0.693591	+	0.720369i	$0.743972\pi$
$3$	−0.187708	−0.108373	−0.0541867	−	0.998531i	$-0.517257\pi$
$3$	−0.187708	−0.108373	−0.0541867	+	0.998531i	$0.517257\pi$
$4$	1.84854	0.924272
$5$	0	0
$5$	0	0
$6$	0.368240	0.150333
$7$	0.677067	0.255907	0.127954	−	0.991780i	$-0.459159\pi$
$7$	0.677067	0.255907	0.127954	+	0.991780i	$0.459159\pi$
$8$	0.297123	0.105049
$9$	−2.96477	−0.988255
$10$	0	0
$11$	2.84069	0.856500	0.428250	−	0.903660i	$-0.359130\pi$
$11$	2.84069	0.856500	0.428250	+	0.903660i	$0.359130\pi$
$12$	−0.346987	−0.100166
$13$	−4.76663	−1.32203	−0.661013	−	0.750375i	$-0.729873\pi$
$13$	−4.76663	−1.32203	−0.661013	+	0.750375i	$0.729873\pi$
$14$	−1.32825	−0.354990
$15$	0	0
$16$	−4.27997	−1.06999
$17$	5.18394	1.25729	0.628645	−	0.777693i	$-0.283610\pi$
$17$	5.18394	1.25729	0.628645	+	0.777693i	$0.283610\pi$
$18$	5.81619	1.37089
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−0.127091	−0.0277336
$22$	−5.57278	−1.18812
$23$	1.05091	0.219131	0.109565	−	0.993980i	$-0.465054\pi$
$23$	1.05091	0.219131	0.109565	+	0.993980i	$0.465054\pi$
$24$	−0.0557724	−0.0113845
$25$	0	0
$26$	9.35103	1.83389
$27$	1.11964	0.215474
$28$	1.25159	0.236528
$29$	1.42605	0.264810	0.132405	−	0.991196i	$-0.457730\pi$
$29$	1.42605	0.264810	0.132405	+	0.991196i	$0.457730\pi$
$30$	0	0
$31$	−0.271064	−0.0486845	−0.0243422	−	0.999704i	$-0.507749\pi$
$31$	−0.271064	−0.0486845	−0.0243422	+	0.999704i	$0.507749\pi$
$32$	7.80208	1.37923
$33$	−0.533221	−0.0928218
$34$	−10.1697	−1.74409
$35$	0	0
$36$	−5.48050	−0.913416
$37$	−0.603754	−0.0992566	−0.0496283	−	0.998768i	$-0.515804\pi$
$37$	−0.603754	−0.0992566	−0.0496283	+	0.998768i	$0.515804\pi$
$38$	0	0
$39$	0.894735	0.143272
$40$	0	0
$41$	−6.73563	−1.05193	−0.525965	−	0.850506i	$-0.676296\pi$
$41$	−6.73563	−1.05193	−0.525965	+	0.850506i	$0.676296\pi$
$42$	0.249324	0.0384715
$43$	−5.62944	−0.858482	−0.429241	−	0.903190i	$-0.641219\pi$
$43$	−5.62944	−0.858482	−0.429241	+	0.903190i	$0.641219\pi$
$44$	5.25114	0.791639
$45$	0	0
$46$	−2.06165	−0.303974
$47$	7.89538	1.15166	0.575829	−	0.817570i	$-0.304679\pi$
$47$	7.89538	1.15166	0.575829	+	0.817570i	$0.304679\pi$
$48$	0.803386	0.115959
$49$	−6.54158	−0.934511
$50$	0	0
$51$	−0.973067	−0.136257
$52$	−8.81132	−1.22191
$53$	−6.88829	−0.946180	−0.473090	−	0.881014i	$-0.656861\pi$
$53$	−6.88829	−0.946180	−0.473090	+	0.881014i	$0.656861\pi$
$54$	−2.19647	−0.298901
$55$	0	0
$56$	0.201172	0.0268828
$57$	0	0
$58$	−2.79757	−0.367339
$59$	10.1227	1.31786	0.658930	−	0.752204i	$-0.271009\pi$
$59$	10.1227	1.31786	0.658930	+	0.752204i	$0.271009\pi$
$60$	0	0
$61$	−7.47195	−0.956686	−0.478343	−	0.878173i	$-0.658762\pi$
$61$	−7.47195	−0.956686	−0.478343	+	0.878173i	$0.658762\pi$
$62$	0.531765	0.0675342
$63$	−2.00735	−0.252902
$64$	−6.74594	−0.843243
$65$	0	0
$66$	1.04606	0.128761
$67$	−4.11733	−0.503012	−0.251506	−	0.967856i	$-0.580926\pi$
$67$	−4.11733	−0.503012	−0.251506	+	0.967856i	$0.580926\pi$
$68$	9.58273	1.16208
$69$	−0.197265	−0.0237480
$70$	0	0
$71$	7.60546	0.902603	0.451301	−	0.892372i	$-0.350960\pi$
$71$	7.60546	0.902603	0.451301	+	0.892372i	$0.350960\pi$
$72$	−0.880900	−0.103815
$73$	16.1274	1.88757	0.943783	−	0.330565i	$-0.107239\pi$
$73$	16.1274	1.88757	0.943783	+	0.330565i	$0.107239\pi$
$74$	1.18443	0.137687
$75$	0	0
$76$	0	0
$77$	1.92334	0.219185
$78$	−1.75527	−0.198745
$79$	−14.8468	−1.67039	−0.835196	−	0.549953i	$-0.814646\pi$
$79$	−14.8468	−1.67039	−0.835196	+	0.549953i	$0.814646\pi$
$80$	0	0
$81$	8.68413	0.964904
$82$	13.2138	1.45922
$83$	14.1815	1.55662	0.778312	−	0.627878i	$-0.216076\pi$
$83$	14.1815	1.55662	0.778312	+	0.627878i	$0.216076\pi$
$84$	−0.234933	−0.0256333
$85$	0	0
$86$	11.0437	1.19087
$87$	−0.267680	−0.0286983
$88$	0.844034	0.0899743
$89$	−8.23788	−0.873214	−0.436607	−	0.899652i	$-0.643820\pi$
$89$	−8.23788	−0.873214	−0.436607	+	0.899652i	$0.643820\pi$
$90$	0	0
$91$	−3.22733	−0.338316
$92$	1.94266	0.202536
$93$	0.0508809	0.00527610
$94$	−15.4889	−1.59756
$95$	0	0
$96$	−1.46451	−0.149471
$97$	5.72847	0.581638	0.290819	−	0.956778i	$-0.406072\pi$
$97$	5.72847	0.581638	0.290819	+	0.956778i	$0.406072\pi$
$98$	12.8331	1.29634
$99$	−8.42198	−0.846441
$100$	0	0
$101$	−2.02231	−0.201228	−0.100614	−	0.994926i	$-0.532081\pi$
$101$	−2.02231	−0.201228	−0.100614	+	0.994926i	$0.532081\pi$
$102$	1.90893	0.189013
$103$	18.2358	1.79683	0.898415	−	0.439147i	$-0.144719\pi$
$103$	18.2358	1.79683	0.898415	+	0.439147i	$0.144719\pi$
$104$	−1.41627	−0.138877
$105$	0	0
$106$	13.5133	1.31252
$107$	−6.21341	−0.600673	−0.300337	−	0.953833i	$-0.597099\pi$
$107$	−6.21341	−0.600673	−0.300337	+	0.953833i	$0.597099\pi$
$108$	2.06969	0.199156
$109$	−15.9885	−1.53142	−0.765711	−	0.643185i	$-0.777613\pi$
$109$	−15.9885	−1.53142	−0.765711	+	0.643185i	$0.777613\pi$
$110$	0	0
$111$	0.113330	0.0107568
$112$	−2.89783	−0.273819
$113$	7.88392	0.741657	0.370828	−	0.928701i	$-0.379074\pi$
$113$	7.88392	0.741657	0.370828	+	0.928701i	$0.379074\pi$
$114$	0	0
$115$	0	0
$116$	2.63611	0.244756
$117$	14.1319	1.30650
$118$	−19.8584	−1.82811
$119$	3.50988	0.321750
$120$	0	0
$121$	−2.93048	−0.266407
$122$	14.6583	1.32710
$123$	1.26433	0.114001
$124$	−0.501073	−0.0449977
$125$	0	0
$126$	3.93795	0.350821
$127$	−15.7743	−1.39974	−0.699871	−	0.714270i	$-0.746759\pi$
$127$	−15.7743	−1.39974	−0.699871	+	0.714270i	$0.746759\pi$
$128$	−2.37017	−0.209495
$129$	1.05669	0.0930366
$130$	0	0
$131$	−4.06624	−0.355269	−0.177634	−	0.984097i	$-0.556844\pi$
$131$	−4.06624	−0.355269	−0.177634	+	0.984097i	$0.556844\pi$
$132$	−0.985682	−0.0857926
$133$	0	0
$134$	8.07726	0.697769
$135$	0	0
$136$	1.54027	0.132077
$137$	−2.61201	−0.223159	−0.111580	−	0.993756i	$-0.535591\pi$
$137$	−2.61201	−0.223159	−0.111580	+	0.993756i	$0.535591\pi$
$138$	0.386989	0.0329427
$139$	8.97126	0.760932	0.380466	−	0.924795i	$-0.375764\pi$
$139$	8.97126	0.760932	0.380466	+	0.924795i	$0.375764\pi$
$140$	0	0
$141$	−1.48203	−0.124809
$142$	−14.9202	−1.25207
$143$	−13.5405	−1.13232
$144$	12.6891	1.05743
$145$	0	0
$146$	−31.6382	−2.61840
$147$	1.22791	0.101276
$148$	−1.11607	−0.0917401
$149$	−1.72807	−0.141569	−0.0707846	−	0.997492i	$-0.522550\pi$
$149$	−1.72807	−0.141569	−0.0707846	+	0.997492i	$0.522550\pi$
$150$	0	0
$151$	−11.0738	−0.901177	−0.450589	−	0.892732i	$-0.648786\pi$
$151$	−11.0738	−0.901177	−0.450589	+	0.892732i	$0.648786\pi$
$152$	0	0
$153$	−15.3692	−1.24252
$154$	−3.77315	−0.304049
$155$	0	0
$156$	1.65396	0.132423
$157$	−1.96462	−0.156794	−0.0783970	−	0.996922i	$-0.524980\pi$
$157$	−1.96462	−0.156794	−0.0783970	+	0.996922i	$0.524980\pi$
$158$	29.1259	2.31714
$159$	1.29299	0.102541
$160$	0	0
$161$	0.711540	0.0560772
$162$	−17.0363	−1.33850
$163$	20.1311	1.57679	0.788395	−	0.615169i	$-0.210912\pi$
$163$	20.1311	1.57679	0.788395	+	0.615169i	$0.210912\pi$
$164$	−12.4511	−0.972269
$165$	0	0
$166$	−27.8209	−2.15932
$167$	−17.8567	−1.38179	−0.690895	−	0.722956i	$-0.742783\pi$
$167$	−17.8567	−1.38179	−0.690895	+	0.722956i	$0.742783\pi$
$168$	−0.0377617	−0.00291338
$169$	9.72076	0.747751
$170$	0	0
$171$	0	0
$172$	−10.4063	−0.793470
$173$	2.72218	0.206963	0.103482	−	0.994631i	$-0.467002\pi$
$173$	2.72218	0.206963	0.103482	+	0.994631i	$0.467002\pi$
$174$	0.525127	0.0398098
$175$	0	0
$176$	−12.1581	−0.916450
$177$	−1.90011	−0.142821
$178$	16.1608	1.21131
$179$	−7.71634	−0.576746	−0.288373	−	0.957518i	$-0.593114\pi$
$179$	−7.71634	−0.576746	−0.288373	+	0.957518i	$0.593114\pi$
$180$	0	0
$181$	1.07040	0.0795625	0.0397812	−	0.999208i	$-0.487334\pi$
$181$	1.07040	0.0795625	0.0397812	+	0.999208i	$0.487334\pi$
$182$	6.33128	0.469306
$183$	1.40255	0.103679
$184$	0.312251	0.0230194
$185$	0	0
$186$	−0.0998166	−0.00731891
$187$	14.7260	1.07687
$188$	14.5949	1.06445
$189$	0.758069	0.0551414
$190$	0	0
$191$	5.38296	0.389497	0.194749	−	0.980853i	$-0.437611\pi$
$191$	5.38296	0.389497	0.194749	+	0.980853i	$0.437611\pi$
$192$	1.26627	0.0913851
$193$	−15.4699	−1.11355	−0.556774	−	0.830664i	$-0.687961\pi$
$193$	−15.4699	−1.11355	−0.556774	+	0.830664i	$0.687961\pi$
$194$	−11.2379	−0.806837
$195$	0	0
$196$	−12.0924	−0.863742
$197$	−21.2328	−1.51278	−0.756388	−	0.654124i	$-0.773038\pi$
$197$	−21.2328	−1.51278	−0.756388	+	0.654124i	$0.773038\pi$
$198$	16.5220	1.17417
$199$	7.58119	0.537416	0.268708	−	0.963222i	$-0.413403\pi$
$199$	7.58119	0.537416	0.268708	+	0.963222i	$0.413403\pi$
$200$	0	0
$201$	0.772857	0.0545131
$202$	3.96732	0.279139
$203$	0.965529	0.0677668
$204$	−1.79876	−0.125938
$205$	0	0
$206$	−35.7745	−2.49253
$207$	−3.11572	−0.216557
$208$	20.4011	1.41456
$209$	0	0
$210$	0	0
$211$	13.2991	0.915548	0.457774	−	0.889069i	$-0.348647\pi$
$211$	13.2991	0.915548	0.457774	+	0.889069i	$0.348647\pi$
$212$	−12.7333	−0.874527
$213$	−1.42761	−0.0978181
$214$	12.1893	0.833243
$215$	0	0
$216$	0.332669	0.0226353
$217$	−0.183528	−0.0124587
$218$	31.3658	2.12436
$219$	−3.02724	−0.204562
$220$	0	0
$221$	−24.7099	−1.66217
$222$	−0.222327	−0.0149216
$223$	−19.8794	−1.33122	−0.665611	−	0.746299i	$-0.731829\pi$
$223$	−19.8794	−1.33122	−0.665611	+	0.746299i	$0.731829\pi$
$224$	5.28253	0.352954
$225$	0	0
$226$	−15.4664	−1.02881
$227$	27.3022	1.81211	0.906054	−	0.423163i	$-0.139080\pi$
$227$	27.3022	1.81211	0.906054	+	0.423163i	$0.139080\pi$
$228$	0	0
$229$	−14.6429	−0.967633	−0.483816	−	0.875170i	$-0.660750\pi$
$229$	−14.6429	−0.967633	−0.483816	+	0.875170i	$0.660750\pi$
$230$	0	0
$231$	−0.361026	−0.0237538
$232$	0.423711	0.0278180
$233$	6.62933	0.434302	0.217151	−	0.976138i	$-0.430324\pi$
$233$	6.62933	0.434302	0.217151	+	0.976138i	$0.430324\pi$
$234$	−27.7236	−1.81235
$235$	0	0
$236$	18.7122	1.21806
$237$	2.78686	0.181026
$238$	−6.88557	−0.446325
$239$	−12.6792	−0.820148	−0.410074	−	0.912052i	$-0.634497\pi$
$239$	−12.6792	−0.820148	−0.410074	+	0.912052i	$0.634497\pi$
$240$	0	0
$241$	−14.1138	−0.909151	−0.454575	−	0.890708i	$-0.650209\pi$
$241$	−14.1138	−0.909151	−0.454575	+	0.890708i	$0.650209\pi$
$242$	5.74893	0.369555
$243$	−4.98899	−0.320044
$244$	−13.8122	−0.884237
$245$	0	0
$246$	−2.48033	−0.158140
$247$	0	0
$248$	−0.0805392	−0.00511425
$249$	−2.66199	−0.168696
$250$	0	0
$251$	6.97395	0.440192	0.220096	−	0.975478i	$-0.429363\pi$
$251$	6.97395	0.440192	0.220096	+	0.975478i	$0.429363\pi$
$252$	−3.71067	−0.233750
$253$	2.98532	0.187686
$254$	30.9455	1.94169
$255$	0	0
$256$	18.1416	1.13385
$257$	15.7808	0.984379	0.492189	−	0.870488i	$-0.336197\pi$
$257$	15.7808	0.984379	0.492189	+	0.870488i	$0.336197\pi$
$258$	−2.07299	−0.129059
$259$	−0.408782	−0.0254005
$260$	0	0
$261$	−4.22789	−0.261700
$262$	7.97703	0.492822
$263$	19.8933	1.22667	0.613336	−	0.789822i	$-0.289827\pi$
$263$	19.8933	1.22667	0.613336	+	0.789822i	$0.289827\pi$
$264$	−0.158432	−0.00975082
$265$	0	0
$266$	0	0
$267$	1.54632	0.0946331
$268$	−7.61107	−0.464920
$269$	11.3590	0.692568	0.346284	−	0.938130i	$-0.387443\pi$
$269$	11.3590	0.692568	0.346284	+	0.938130i	$0.387443\pi$
$270$	0	0
$271$	23.8877	1.45107	0.725536	−	0.688184i	$-0.241592\pi$
$271$	23.8877	1.45107	0.725536	+	0.688184i	$0.241592\pi$
$272$	−22.1871	−1.34529
$273$	0.605796	0.0366645
$274$	5.12416	0.309562
$275$	0	0
$276$	−0.364653	−0.0219496
$277$	4.69303	0.281977	0.140988	−	0.990011i	$-0.454972\pi$
$277$	4.69303	0.281977	0.140988	+	0.990011i	$0.454972\pi$
$278$	−17.5996	−1.05555
$279$	0.803640	0.0481127
$280$	0	0
$281$	−22.4556	−1.33959	−0.669795	−	0.742546i	$-0.733618\pi$
$281$	−22.4556	−1.33959	−0.669795	+	0.742546i	$0.733618\pi$
$282$	2.90740	0.173133
$283$	10.8830	0.646926	0.323463	−	0.946241i	$-0.395153\pi$
$283$	10.8830	0.646926	0.323463	+	0.946241i	$0.395153\pi$
$284$	14.0590	0.834250
$285$	0	0
$286$	26.5634	1.57073
$287$	−4.56048	−0.269197
$288$	−23.1313	−1.36303
$289$	9.87320	0.580777
$290$	0	0
$291$	−1.07528	−0.0630340
$292$	29.8122	1.74462
$293$	12.4712	0.728576	0.364288	−	0.931286i	$-0.381312\pi$
$293$	12.4712	0.728576	0.364288	+	0.931286i	$0.381312\pi$
$294$	−2.40887	−0.140488
$295$	0	0
$296$	−0.179389	−0.0104268
$297$	3.18054	0.184553
$298$	3.39008	0.196382
$299$	−5.00932	−0.289697
$300$	0	0
$301$	−3.81151	−0.219692
$302$	21.7244	1.25010
$303$	0.379605	0.0218077
$304$	0	0
$305$	0	0
$306$	30.1508	1.72360
$307$	4.17858	0.238484	0.119242	−	0.992865i	$-0.461954\pi$
$307$	4.17858	0.238484	0.119242	+	0.992865i	$0.461954\pi$
$308$	3.55538	0.202586
$309$	−3.42302	−0.194729
$310$	0	0
$311$	−12.0909	−0.685611	−0.342806	−	0.939406i	$-0.611377\pi$
$311$	−12.0909	−0.685611	−0.342806	+	0.939406i	$0.611377\pi$
$312$	0.265846	0.0150506
$313$	−9.57859	−0.541414	−0.270707	−	0.962662i	$-0.587257\pi$
$313$	−9.57859	−0.541414	−0.270707	+	0.962662i	$0.587257\pi$
$314$	3.85414	0.217502
$315$	0	0
$316$	−27.4449	−1.54390
$317$	−11.1692	−0.627324	−0.313662	−	0.949535i	$-0.601556\pi$
$317$	−11.1692	−0.627324	−0.313662	+	0.949535i	$0.601556\pi$
$318$	−2.53655	−0.142243
$319$	4.05095	0.226810
$320$	0	0
$321$	1.16631	0.0650970
$322$	−1.39588	−0.0777893
$323$	0	0
$324$	16.0530	0.891833
$325$	0	0
$326$	−39.4926	−2.18729
$327$	3.00118	0.165965
$328$	−2.00131	−0.110504
$329$	5.34570	0.294718
$330$	0	0
$331$	21.6878	1.19207	0.596034	−	0.802959i	$-0.296742\pi$
$331$	21.6878	1.19207	0.596034	+	0.802959i	$0.296742\pi$
$332$	26.2151	1.43874
$333$	1.78999	0.0980909
$334$	35.0307	1.91679
$335$	0	0
$336$	0.543947	0.0296747
$337$	0.0528499	0.00287892	0.00143946	−	0.999999i	$-0.499542\pi$
$337$	0.0528499	0.00287892	0.00143946	+	0.999999i	$0.499542\pi$
$338$	−19.0699	−1.03727
$339$	−1.47988	−0.0803758
$340$	0	0
$341$	−0.770008	−0.0416983
$342$	0	0
$343$	−9.16856	−0.495056
$344$	−1.67264	−0.0901825
$345$	0	0
$346$	−5.34029	−0.287096
$347$	−25.3863	−1.36281	−0.681403	−	0.731908i	$-0.738630\pi$
$347$	−25.3863	−1.36281	−0.681403	+	0.731908i	$0.738630\pi$
$348$	−0.494819	−0.0265251
$349$	−15.6199	−0.836114	−0.418057	−	0.908421i	$-0.637289\pi$
$349$	−15.6199	−0.836114	−0.418057	+	0.908421i	$0.637289\pi$
$350$	0	0
$351$	−5.33689	−0.284862
$352$	22.1633	1.18131
$353$	−12.4713	−0.663779	−0.331890	−	0.943318i	$-0.607686\pi$
$353$	−12.4713	−0.663779	−0.331890	+	0.943318i	$0.607686\pi$
$354$	3.72758	0.198119
$355$	0	0
$356$	−15.2281	−0.807087
$357$	−0.658832	−0.0348691
$358$	15.1377	0.800051
$359$	−33.6430	−1.77561	−0.887804	−	0.460223i	$-0.847770\pi$
$359$	−33.6430	−1.77561	−0.887804	+	0.460223i	$0.847770\pi$
$360$	0	0
$361$	0	0
$362$	−2.09989	−0.110368
$363$	0.550075	0.0288714
$364$	−5.96586	−0.312696
$365$	0	0
$366$	−2.75147	−0.143822
$367$	25.6100	1.33683	0.668416	−	0.743787i	$-0.266973\pi$
$367$	25.6100	1.33683	0.668416	+	0.743787i	$0.266973\pi$
$368$	−4.49789	−0.234469
$369$	19.9696	1.03957
$370$	0	0
$371$	−4.66384	−0.242134
$372$	0.0940555	0.00487655
$373$	−21.7610	−1.12674	−0.563372	−	0.826204i	$-0.690496\pi$
$373$	−21.7610	−1.12674	−0.563372	+	0.826204i	$0.690496\pi$
$374$	−28.8890	−1.49381
$375$	0	0
$376$	2.34590	0.120980
$377$	−6.79743	−0.350085
$378$	−1.48716	−0.0764911
$379$	6.63029	0.340575	0.170288	−	0.985394i	$-0.445530\pi$
$379$	6.63029	0.340575	0.170288	+	0.985394i	$0.445530\pi$
$380$	0	0
$381$	2.96096	0.151695
$382$	−10.5601	−0.540303
$383$	27.0219	1.38075	0.690377	−	0.723450i	$-0.257445\pi$
$383$	27.0219	1.38075	0.690377	+	0.723450i	$0.257445\pi$
$384$	0.444900	0.0227037
$385$	0	0
$386$	30.3484	1.54469
$387$	16.6900	0.848399
$388$	10.5893	0.537591
$389$	25.9896	1.31773	0.658863	−	0.752263i	$-0.271038\pi$
$389$	25.9896	1.31773	0.658863	+	0.752263i	$0.271038\pi$
$390$	0	0
$391$	5.44788	0.275511
$392$	−1.94365	−0.0981693
$393$	0.763266	0.0385017
$394$	41.6539	2.09849
$395$	0	0
$396$	−15.5684	−0.782341
$397$	−21.3475	−1.07140	−0.535699	−	0.844409i	$-0.679952\pi$
$397$	−21.3475	−1.07140	−0.535699	+	0.844409i	$0.679952\pi$
$398$	−14.8726	−0.745494
$399$	0	0
$400$	0	0
$401$	−26.0611	−1.30143	−0.650716	−	0.759321i	$-0.725531\pi$
$401$	−26.0611	−1.30143	−0.650716	+	0.759321i	$0.725531\pi$
$402$	−1.51617	−0.0756196
$403$	1.29206	0.0643621
$404$	−3.73834	−0.185989
$405$	0	0
$406$	−1.89415	−0.0940049
$407$	−1.71508	−0.0850133
$408$	−0.289121	−0.0143136
$409$	23.3472	1.15444	0.577222	−	0.816587i	$-0.304137\pi$
$409$	23.3472	1.15444	0.577222	+	0.816587i	$0.304137\pi$
$410$	0	0
$411$	0.490296	0.0241845
$412$	33.7097	1.66076
$413$	6.85374	0.337250
$414$	6.11232	0.300404
$415$	0	0
$416$	−37.1896	−1.82337
$417$	−1.68398	−0.0824648
$418$	0	0
$419$	21.9951	1.07453	0.537265	−	0.843413i	$-0.319457\pi$
$419$	21.9951	1.07453	0.537265	+	0.843413i	$0.319457\pi$
$420$	0	0
$421$	−3.73114	−0.181845	−0.0909223	−	0.995858i	$-0.528982\pi$
$421$	−3.73114	−0.181845	−0.0909223	+	0.995858i	$0.528982\pi$
$422$	−26.0898	−1.27003
$423$	−23.4079	−1.13813
$424$	−2.04667	−0.0993951
$425$	0	0
$426$	2.80064	0.135691
$427$	−5.05902	−0.244823
$428$	−11.4858	−0.555185
$429$	2.54167	0.122713
$430$	0	0
$431$	24.9141	1.20007	0.600035	−	0.799974i	$-0.295153\pi$
$431$	24.9141	1.20007	0.600035	+	0.799974i	$0.295153\pi$
$432$	−4.79201	−0.230556
$433$	−10.9722	−0.527292	−0.263646	−	0.964619i	$-0.584925\pi$
$433$	−10.9722	−0.527292	−0.263646	+	0.964619i	$0.584925\pi$
$434$	0.360041	0.0172825
$435$	0	0
$436$	−29.5555	−1.41545
$437$	0	0
$438$	5.93875	0.283765
$439$	8.51973	0.406624	0.203312	−	0.979114i	$-0.434829\pi$
$439$	8.51973	0.406624	0.203312	+	0.979114i	$0.434829\pi$
$440$	0	0
$441$	19.3943	0.923536
$442$	48.4752	2.30573
$443$	9.41714	0.447422	0.223711	−	0.974656i	$-0.428183\pi$
$443$	9.41714	0.447422	0.223711	+	0.974656i	$0.428183\pi$
$444$	0.209495	0.00994218
$445$	0	0
$446$	38.9988	1.84665
$447$	0.324373	0.0153423
$448$	−4.56746	−0.215792
$449$	−9.72743	−0.459066	−0.229533	−	0.973301i	$-0.573720\pi$
$449$	−9.72743	−0.459066	−0.229533	+	0.973301i	$0.573720\pi$
$450$	0	0
$451$	−19.1339	−0.900978
$452$	14.5738	0.685492
$453$	2.07865	0.0976636
$454$	−53.5606	−2.51372
$455$	0	0
$456$	0	0
$457$	10.4686	0.489700	0.244850	−	0.969561i	$-0.421261\pi$
$457$	10.4686	0.489700	0.244850	+	0.969561i	$0.421261\pi$
$458$	28.7261	1.34228
$459$	5.80412	0.270913
$460$	0	0
$461$	−22.6739	−1.05603	−0.528014	−	0.849236i	$-0.677063\pi$
$461$	−22.6739	−1.05603	−0.528014	+	0.849236i	$0.677063\pi$
$462$	0.708251	0.0329508
$463$	−35.6376	−1.65622	−0.828110	−	0.560566i	$-0.810584\pi$
$463$	−35.6376	−1.65622	−0.828110	+	0.560566i	$0.810584\pi$
$464$	−6.10344	−0.283345
$465$	0	0
$466$	−13.0052	−0.602456
$467$	2.90160	0.134270	0.0671350	−	0.997744i	$-0.478614\pi$
$467$	2.90160	0.134270	0.0671350	+	0.997744i	$0.478614\pi$
$468$	26.1235	1.20756
$469$	−2.78771	−0.128725
$470$	0	0
$471$	0.368776	0.0169923
$472$	3.00768	0.138440
$473$	−15.9915	−0.735290
$474$	−5.46718	−0.251116
$475$	0	0
$476$	6.48816	0.297384
$477$	20.4222	0.935067
$478$	24.8736	1.13769
$479$	29.3510	1.34108	0.670540	−	0.741874i	$-0.266063\pi$
$479$	29.3510	1.34108	0.670540	+	0.741874i	$0.266063\pi$
$480$	0	0
$481$	2.87787	0.131220
$482$	27.6881	1.26116
$483$	−0.133562	−0.00607728
$484$	−5.41712	−0.246233
$485$	0	0
$486$	9.78725	0.443959
$487$	3.41683	0.154831	0.0774157	−	0.996999i	$-0.475333\pi$
$487$	3.41683	0.154831	0.0774157	+	0.996999i	$0.475333\pi$
$488$	−2.22009	−0.100499
$489$	−3.77877	−0.170882
$490$	0	0
$491$	−25.1863	−1.13664	−0.568320	−	0.822808i	$-0.692406\pi$
$491$	−25.1863	−1.13664	−0.568320	+	0.822808i	$0.692406\pi$
$492$	2.33718	0.105368
$493$	7.39253	0.332943
$494$	0	0
$495$	0	0
$496$	1.16015	0.0520921
$497$	5.14941	0.230983
$498$	5.22220	0.234013
$499$	−34.7335	−1.55488	−0.777442	−	0.628955i	$-0.783483\pi$
$499$	−34.7335	−1.55488	−0.777442	+	0.628955i	$0.783483\pi$
$500$	0	0
$501$	3.35184	0.149749
$502$	−13.6813	−0.610626
$503$	−22.4582	−1.00136	−0.500682	−	0.865631i	$-0.666917\pi$
$503$	−22.4582	−1.00136	−0.500682	+	0.865631i	$0.666917\pi$
$504$	−0.596429	−0.0265670
$505$	0	0
$506$	−5.85652	−0.260354
$507$	−1.82467	−0.0810363
$508$	−29.1594	−1.29374
$509$	−2.34801	−0.104074	−0.0520369	−	0.998645i	$-0.516571\pi$
$509$	−2.34801	−0.104074	−0.0520369	+	0.998645i	$0.516571\pi$
$510$	0	0
$511$	10.9193	0.483042
$512$	−30.8493	−1.36336
$513$	0	0
$514$	−30.9583	−1.36551
$515$	0	0
$516$	1.95334	0.0859911
$517$	22.4283	0.986396
$518$	0.801937	0.0352351
$519$	−0.510975	−0.0224293
$520$	0	0
$521$	−1.52393	−0.0667645	−0.0333822	−	0.999443i	$-0.510628\pi$
$521$	−1.52393	−0.0667645	−0.0333822	+	0.999443i	$0.510628\pi$
$522$	8.29415	0.363025
$523$	13.4269	0.587117	0.293559	−	0.955941i	$-0.405160\pi$
$523$	13.4269	0.587117	0.293559	+	0.955941i	$0.405160\pi$
$524$	−7.51662	−0.328365
$525$	0	0
$526$	−39.0261	−1.70162
$527$	−1.40518	−0.0612105
$528$	2.28217	0.0993187
$529$	−21.8956	−0.951982
$530$	0	0
$531$	−30.0114	−1.30238
$532$	0	0
$533$	32.1063	1.39068
$534$	−3.03352	−0.131273
$535$	0	0
$536$	−1.22335	−0.0528408
$537$	1.44842	0.0625039
$538$	−22.2837	−0.960718
$539$	−18.5826	−0.800409
$540$	0	0
$541$	16.2283	0.697709	0.348854	−	0.937177i	$-0.386571\pi$
$541$	16.2283	0.697709	0.348854	+	0.937177i	$0.386571\pi$
$542$	−46.8621	−2.01290
$543$	−0.200924	−0.00862245
$544$	40.4455	1.73409
$545$	0	0
$546$	−1.18843	−0.0508602
$547$	9.91482	0.423927	0.211964	−	0.977278i	$-0.432014\pi$
$547$	9.91482	0.423927	0.211964	+	0.977278i	$0.432014\pi$
$548$	−4.82841	−0.206260
$549$	22.1526	0.945449
$550$	0	0
$551$	0	0
$552$	−0.0586120	−0.00249469
$553$	−10.0523	−0.427466
$554$	−9.20665	−0.391153
$555$	0	0
$556$	16.5838	0.703308
$557$	−22.8831	−0.969589	−0.484795	−	0.874628i	$-0.661106\pi$
$557$	−22.8831	−0.969589	−0.484795	+	0.874628i	$0.661106\pi$
$558$	−1.57656	−0.0667410
$559$	26.8335	1.13493
$560$	0	0
$561$	−2.76418	−0.116704
$562$	44.0528	1.85826
$563$	12.4801	0.525972	0.262986	−	0.964800i	$-0.415293\pi$
$563$	12.4801	0.525972	0.262986	+	0.964800i	$0.415293\pi$
$564$	−2.73959	−0.115358
$565$	0	0
$566$	−21.3499	−0.897403
$567$	5.87974	0.246926
$568$	2.25976	0.0948173
$569$	−1.90233	−0.0797500	−0.0398750	−	0.999205i	$-0.512696\pi$
$569$	−1.90233	−0.0797500	−0.0398750	+	0.999205i	$0.512696\pi$
$570$	0	0
$571$	−12.2153	−0.511193	−0.255596	−	0.966784i	$-0.582272\pi$
$571$	−12.2153	−0.511193	−0.255596	+	0.966784i	$0.582272\pi$
$572$	−25.0302	−1.04657
$573$	−1.01042	−0.0422111
$574$	8.94661	0.373424
$575$	0	0
$576$	20.0001	0.833339
$577$	−25.2903	−1.05285	−0.526425	−	0.850221i	$-0.676468\pi$
$577$	−25.2903	−1.05285	−0.526425	+	0.850221i	$0.676468\pi$
$578$	−19.3690	−0.805643
$579$	2.90383	0.120679
$580$	0	0
$581$	9.60184	0.398351
$582$	2.10945	0.0874396
$583$	−19.5675	−0.810403
$584$	4.79181	0.198287
$585$	0	0
$586$	−24.4657	−1.01067
$587$	−6.32179	−0.260928	−0.130464	−	0.991453i	$-0.541647\pi$
$587$	−6.32179	−0.260928	−0.130464	+	0.991453i	$0.541647\pi$
$588$	2.26984	0.0936067
$589$	0	0
$590$	0	0
$591$	3.98557	0.163945
$592$	2.58405	0.106204
$593$	0.583715	0.0239703	0.0119851	−	0.999928i	$-0.496185\pi$
$593$	0.583715	0.0239703	0.0119851	+	0.999928i	$0.496185\pi$
$594$	−6.23948	−0.256009
$595$	0	0
$596$	−3.19442	−0.130848
$597$	−1.42305	−0.0582416
$598$	9.82714	0.401862
$599$	−42.5221	−1.73740	−0.868702	−	0.495335i	$-0.835045\pi$
$599$	−42.5221	−1.73740	−0.868702	+	0.495335i	$0.835045\pi$
$600$	0	0
$601$	−16.2762	−0.663920	−0.331960	−	0.943294i	$-0.607710\pi$
$601$	−16.2762	−0.663920	−0.331960	+	0.943294i	$0.607710\pi$
$602$	7.47731	0.304752
$603$	12.2069	0.497105
$604$	−20.4705	−0.832932
$605$	0	0
$606$	−0.744698	−0.0302513
$607$	6.86749	0.278743	0.139371	−	0.990240i	$-0.455492\pi$
$607$	6.86749	0.278743	0.139371	+	0.990240i	$0.455492\pi$
$608$	0	0
$609$	−0.181238	−0.00734412
$610$	0	0
$611$	−37.6343	−1.52252
$612$	−28.4106	−1.14843
$613$	5.84296	0.235995	0.117997	−	0.993014i	$-0.462353\pi$
$613$	5.84296	0.235995	0.117997	+	0.993014i	$0.462353\pi$
$614$	−8.19741	−0.330821
$615$	0	0
$616$	0.571468	0.0230251
$617$	−38.5625	−1.55247	−0.776234	−	0.630444i	$-0.782873\pi$
$617$	−38.5625	−1.55247	−0.776234	+	0.630444i	$0.782873\pi$
$618$	6.71517	0.270124
$619$	10.9201	0.438917	0.219459	−	0.975622i	$-0.429571\pi$
$619$	10.9201	0.438917	0.219459	+	0.975622i	$0.429571\pi$
$620$	0	0
$621$	1.17664	0.0472170
$622$	23.7195	0.951067
$623$	−5.57760	−0.223462
$624$	−3.82944	−0.153300
$625$	0	0
$626$	18.7910	0.751039
$627$	0	0
$628$	−3.63169	−0.144920
$629$	−3.12982	−0.124794
$630$	0	0
$631$	8.11401	0.323014	0.161507	−	0.986872i	$-0.448365\pi$
$631$	8.11401	0.323014	0.161507	+	0.986872i	$0.448365\pi$
$632$	−4.41131	−0.175473
$633$	−2.49635	−0.0992210
$634$	21.9114	0.870212
$635$	0	0
$636$	2.39015	0.0947755
$637$	31.1813	1.23545
$638$	−7.94704	−0.314626
$639$	−22.5484	−0.892002
$640$	0	0
$641$	−13.9078	−0.549323	−0.274662	−	0.961541i	$-0.588566\pi$
$641$	−13.9078	−0.549323	−0.274662	+	0.961541i	$0.588566\pi$
$642$	−2.28803	−0.0903013
$643$	−38.1086	−1.50286	−0.751428	−	0.659815i	$-0.770635\pi$
$643$	−38.1086	−1.50286	−0.751428	+	0.659815i	$0.770635\pi$
$644$	1.31531	0.0518306
$645$	0	0
$646$	0	0
$647$	−28.6072	−1.12466	−0.562332	−	0.826912i	$-0.690096\pi$
$647$	−28.6072	−1.12466	−0.562332	+	0.826912i	$0.690096\pi$
$648$	2.58025	0.101362
$649$	28.7554	1.12875
$650$	0	0
$651$	0.0344498	0.00135019
$652$	37.2132	1.45738
$653$	−11.8861	−0.465139	−0.232569	−	0.972580i	$-0.574713\pi$
$653$	−11.8861	−0.465139	−0.232569	+	0.972580i	$0.574713\pi$
$654$	−5.88762	−0.230224
$655$	0	0
$656$	28.8283	1.12556
$657$	−47.8139	−1.86540
$658$	−10.4870	−0.408827
$659$	36.9129	1.43792	0.718961	−	0.695051i	$-0.244618\pi$
$659$	36.9129	1.43792	0.718961	+	0.695051i	$0.244618\pi$
$660$	0	0
$661$	9.04095	0.351652	0.175826	−	0.984421i	$-0.443740\pi$
$661$	9.04095	0.351652	0.175826	+	0.984421i	$0.443740\pi$
$662$	−42.5465	−1.65361
$663$	4.63825	0.180135
$664$	4.21365	0.163521
$665$	0	0
$666$	−3.51155	−0.136070
$667$	1.49865	0.0580280
$668$	−33.0088	−1.27715
$669$	3.73152	0.144269
$670$	0	0
$671$	−21.2255	−0.819401
$672$	−0.991575	−0.0382508
$673$	−39.8365	−1.53558	−0.767791	−	0.640700i	$-0.778644\pi$
$673$	−39.8365	−1.53558	−0.767791	+	0.640700i	$0.778644\pi$
$674$	−0.103679	−0.00399358
$675$	0	0
$676$	17.9692	0.691125
$677$	18.0388	0.693288	0.346644	−	0.937997i	$-0.387321\pi$
$677$	18.0388	0.693288	0.346644	+	0.937997i	$0.387321\pi$
$678$	2.90318	0.111496
$679$	3.87856	0.148845
$680$	0	0
$681$	−5.12484	−0.196384
$682$	1.51058	0.0578430
$683$	−15.4271	−0.590301	−0.295151	−	0.955451i	$-0.595370\pi$
$683$	−15.4271	−0.590301	−0.295151	+	0.955451i	$0.595370\pi$
$684$	0	0
$685$	0	0
$686$	17.9866	0.686732
$687$	2.74860	0.104866
$688$	24.0939	0.918570
$689$	32.8339	1.25087
$690$	0	0
$691$	3.03824	0.115580	0.0577901	−	0.998329i	$-0.481595\pi$
$691$	3.03824	0.115580	0.0577901	+	0.998329i	$0.481595\pi$
$692$	5.03206	0.191290
$693$	−5.70225	−0.216611
$694$	49.8020	1.89046
$695$	0	0
$696$	−0.0795340	−0.00301473
$697$	−34.9171	−1.32258
$698$	30.6427	1.15984
$699$	−1.24438	−0.0470668
$700$	0	0
$701$	−45.7925	−1.72956	−0.864780	−	0.502151i	$-0.832542\pi$
$701$	−45.7925	−1.72956	−0.864780	+	0.502151i	$0.832542\pi$
$702$	10.4697	0.395155
$703$	0	0
$704$	−19.1631	−0.722238
$705$	0	0
$706$	24.4658	0.920782
$707$	−1.36924	−0.0514957
$708$	−3.51244	−0.132005
$709$	22.0549	0.828289	0.414144	−	0.910211i	$-0.364081\pi$
$709$	22.0549	0.828289	0.414144	+	0.910211i	$0.364081\pi$
$710$	0	0
$711$	44.0172	1.65077
$712$	−2.44766	−0.0917301
$713$	−0.284865	−0.0106683
$714$	1.29248	0.0483698
$715$	0	0
$716$	−14.2640	−0.533070
$717$	2.37999	0.0888822
$718$	65.9998	2.46309
$719$	−7.09458	−0.264583	−0.132292	−	0.991211i	$-0.542234\pi$
$719$	−7.09458	−0.264583	−0.132292	+	0.991211i	$0.542234\pi$
$720$	0	0
$721$	12.3469	0.459822
$722$	0	0
$723$	2.64928	0.0985277
$724$	1.97869	0.0735374
$725$	0	0
$726$	−1.07912	−0.0400499
$727$	−28.2127	−1.04635	−0.523176	−	0.852225i	$-0.675253\pi$
$727$	−28.2127	−1.04635	−0.523176	+	0.852225i	$0.675253\pi$
$728$	−0.958914	−0.0355397
$729$	−25.1159	−0.930219
$730$	0	0
$731$	−29.1827	−1.07936
$732$	2.59267	0.0958278
$733$	−1.03586	−0.0382604	−0.0191302	−	0.999817i	$-0.506090\pi$
$733$	−1.03586	−0.0382604	−0.0191302	+	0.999817i	$0.506090\pi$
$734$	−50.2410	−1.85443
$735$	0	0
$736$	8.19932	0.302231
$737$	−11.6961	−0.430830
$738$	−39.1757	−1.44208
$739$	19.4150	0.714191	0.357095	−	0.934068i	$-0.383767\pi$
$739$	19.4150	0.714191	0.357095	+	0.934068i	$0.383767\pi$
$740$	0	0
$741$	0	0
$742$	9.14938	0.335884
$743$	−12.7028	−0.466021	−0.233011	−	0.972474i	$-0.574858\pi$
$743$	−12.7028	−0.466021	−0.233011	+	0.972474i	$0.574858\pi$
$744$	0.0151179	0.000554248 0
$745$	0	0
$746$	42.6901	1.56300
$747$	−42.0449	−1.53834
$748$	27.2216	0.995319
$749$	−4.20690	−0.153717
$750$	0	0
$751$	4.61794	0.168511	0.0842555	−	0.996444i	$-0.473149\pi$
$751$	4.61794	0.168511	0.0842555	+	0.996444i	$0.473149\pi$
$752$	−33.7920	−1.23227
$753$	−1.30907	−0.0477051
$754$	13.3350	0.485632
$755$	0	0
$756$	1.40132	0.0509656
$757$	6.81005	0.247515	0.123758	−	0.992312i	$-0.460505\pi$
$757$	6.81005	0.247515	0.123758	+	0.992312i	$0.460505\pi$
$758$	−13.0071	−0.472439
$759$	−0.560370	−0.0203401
$760$	0	0
$761$	24.4864	0.887632	0.443816	−	0.896118i	$-0.353624\pi$
$761$	24.4864	0.887632	0.443816	+	0.896118i	$0.353624\pi$
$762$	−5.80873	−0.210428
$763$	−10.8253	−0.391902
$764$	9.95063	0.360001
$765$	0	0
$766$	−53.0107	−1.91536
$767$	−48.2511	−1.74225
$768$	−3.40533	−0.122879
$769$	2.99156	0.107878	0.0539391	−	0.998544i	$-0.482822\pi$
$769$	2.99156	0.107878	0.0539391	+	0.998544i	$0.482822\pi$
$770$	0	0
$771$	−2.96218	−0.106680
$772$	−28.5968	−1.02922
$773$	19.7642	0.710869	0.355434	−	0.934701i	$-0.384333\pi$
$773$	19.7642	0.710869	0.355434	+	0.934701i	$0.384333\pi$
$774$	−32.7419	−1.17688
$775$	0	0
$776$	1.70206	0.0611003
$777$	0.0767318	0.00275274
$778$	−50.9857	−1.82792
$779$	0	0
$780$	0	0
$781$	21.6048	0.773079
$782$	−10.6875	−0.382184
$783$	1.59665	0.0570596
$784$	27.9978	0.999921
$785$	0	0
$786$	−1.49735	−0.0534088
$787$	23.5466	0.839346	0.419673	−	0.907675i	$-0.362145\pi$
$787$	23.5466	0.839346	0.419673	+	0.907675i	$0.362145\pi$
$788$	−39.2498	−1.39822
$789$	−3.73413	−0.132939
$790$	0	0
$791$	5.33795	0.189795
$792$	−2.50236	−0.0889176
$793$	35.6160	1.26476
$794$	41.8788	1.48622
$795$	0	0
$796$	14.0142	0.496719
$797$	5.96976	0.211460	0.105730	−	0.994395i	$-0.466282\pi$
$797$	5.96976	0.211460	0.105730	+	0.994395i	$0.466282\pi$
$798$	0	0
$799$	40.9291	1.44797
$800$	0	0
$801$	24.4234	0.862958
$802$	51.1260	1.80532
$803$	45.8129	1.61670
$804$	1.42866	0.0503849
$805$	0	0
$806$	−2.53473	−0.0892819
$807$	−2.13217	−0.0750559
$808$	−0.600876	−0.0211387
$809$	−25.9066	−0.910829	−0.455414	−	0.890280i	$-0.650509\pi$
$809$	−25.9066	−0.910829	−0.455414	+	0.890280i	$0.650509\pi$
$810$	0	0
$811$	−27.6473	−0.970828	−0.485414	−	0.874284i	$-0.661331\pi$
$811$	−27.6473	−0.970828	−0.485414	+	0.874284i	$0.661331\pi$
$812$	1.78482	0.0626350
$813$	−4.48391	−0.157258
$814$	3.36459	0.117929
$815$	0	0
$816$	4.16470	0.145794
$817$	0	0
$818$	−45.8018	−1.60142
$819$	9.56828	0.334343
$820$	0	0
$821$	−10.3541	−0.361362	−0.180681	−	0.983542i	$-0.557830\pi$
$821$	−10.3541	−0.361362	−0.180681	+	0.983542i	$0.557830\pi$
$822$	−0.961847	−0.0335483
$823$	−42.3497	−1.47622	−0.738108	−	0.674683i	$-0.764281\pi$
$823$	−42.3497	−1.47622	−0.738108	+	0.674683i	$0.764281\pi$
$824$	5.41829	0.188755
$825$	0	0
$826$	−13.4455	−0.467827
$827$	−22.5822	−0.785260	−0.392630	−	0.919696i	$-0.628435\pi$
$827$	−22.5822	−0.785260	−0.392630	+	0.919696i	$0.628435\pi$
$828$	−5.75954	−0.200158
$829$	12.6489	0.439315	0.219657	−	0.975577i	$-0.429506\pi$
$829$	12.6489	0.439315	0.219657	+	0.975577i	$0.429506\pi$
$830$	0	0
$831$	−0.880920	−0.0305588
$832$	32.1554	1.11479
$833$	−33.9111	−1.17495
$834$	3.30358	0.114394
$835$	0	0
$836$	0	0
$837$	−0.303492	−0.0104902
$838$	−43.1493	−1.49057
$839$	−46.1433	−1.59304	−0.796522	−	0.604610i	$-0.793329\pi$
$839$	−46.1433	−1.59304	−0.796522	+	0.604610i	$0.793329\pi$
$840$	0	0
$841$	−26.9664	−0.929876
$842$	7.31964	0.252252
$843$	4.21511	0.145176
$844$	24.5840	0.846215
$845$	0	0
$846$	45.9210	1.57880
$847$	−1.98413	−0.0681756
$848$	29.4817	1.01241
$849$	−2.04282	−0.0701095
$850$	0	0
$851$	−0.634494	−0.0217502
$852$	−2.63900	−0.0904105
$853$	−37.4633	−1.28272	−0.641359	−	0.767241i	$-0.721629\pi$
$853$	−37.4633	−1.28272	−0.641359	+	0.767241i	$0.721629\pi$
$854$	9.92463	0.339614
$855$	0	0
$856$	−1.84615	−0.0631000
$857$	33.8342	1.15575	0.577876	−	0.816124i	$-0.303882\pi$
$857$	33.8342	1.15575	0.577876	+	0.816124i	$0.303882\pi$
$858$	−4.98617	−0.170225
$859$	−21.2143	−0.723822	−0.361911	−	0.932213i	$-0.617876\pi$
$859$	−21.2143	−0.723822	−0.361911	+	0.932213i	$0.617876\pi$
$860$	0	0
$861$	0.856039	0.0291737
$862$	−48.8758	−1.66472
$863$	−29.1392	−0.991909	−0.495955	−	0.868348i	$-0.665182\pi$
$863$	−29.1392	−0.991909	−0.495955	+	0.868348i	$0.665182\pi$
$864$	8.73548	0.297187
$865$	0	0
$866$	21.5250	0.731450
$867$	−1.85328	−0.0629407
$868$	−0.339260	−0.0115152
$869$	−42.1751	−1.43069
$870$	0	0
$871$	19.6258	0.664995
$872$	−4.75055	−0.160874
$873$	−16.9836	−0.574806
$874$	0	0
$875$	0	0
$876$	−5.59599	−0.189071
$877$	6.43824	0.217404	0.108702	−	0.994074i	$-0.465331\pi$
$877$	6.43824	0.217404	0.108702	+	0.994074i	$0.465331\pi$
$878$	−16.7137	−0.564062
$879$	−2.34095	−0.0789582
$880$	0	0
$881$	14.3999	0.485145	0.242573	−	0.970133i	$-0.422009\pi$
$881$	14.3999	0.485145	0.242573	+	0.970133i	$0.422009\pi$
$882$	−38.0471	−1.28111
$883$	25.8016	0.868292	0.434146	−	0.900843i	$-0.357050\pi$
$883$	25.8016	0.868292	0.434146	+	0.900843i	$0.357050\pi$
$884$	−45.6773	−1.53630
$885$	0	0
$886$	−18.4743	−0.620655
$887$	−25.9435	−0.871099	−0.435549	−	0.900165i	$-0.643446\pi$
$887$	−25.9435	−0.871099	−0.435549	+	0.900165i	$0.643446\pi$
$888$	0.0336728	0.00112999
$889$	−10.6803	−0.358204
$890$	0	0
$891$	24.6689	0.826440
$892$	−36.7479	−1.23041
$893$	0	0
$894$	−0.636346	−0.0212826
$895$	0	0
$896$	−1.60476	−0.0536114
$897$	0.940291	0.0313954
$898$	19.0830	0.636808
$899$	−0.386549	−0.0128921
$900$	0	0
$901$	−35.7085	−1.18962
$902$	37.5362	1.24982
$903$	0.715452	0.0238087
$904$	2.34249	0.0779102
$905$	0	0
$906$	−4.07784	−0.135477
$907$	−29.9257	−0.993665	−0.496832	−	0.867846i	$-0.665504\pi$
$907$	−29.9257	−0.993665	−0.496832	+	0.867846i	$0.665504\pi$
$908$	50.4692	1.67488
$909$	5.99569	0.198864
$910$	0	0
$911$	−3.36120	−0.111362	−0.0556808	−	0.998449i	$-0.517733\pi$
$911$	−3.36120	−0.111362	−0.0556808	+	0.998449i	$0.517733\pi$
$912$	0	0
$913$	40.2853	1.33325
$914$	−20.5370	−0.679302
$915$	0	0
$916$	−27.0681	−0.894355
$917$	−2.75312	−0.0909160
$918$	−11.3863	−0.375806
$919$	6.92467	0.228424	0.114212	−	0.993456i	$-0.463566\pi$
$919$	6.92467	0.228424	0.114212	+	0.993456i	$0.463566\pi$
$920$	0	0
$921$	−0.784353	−0.0258453
$922$	44.4809	1.46490
$923$	−36.2524	−1.19326
$924$	−0.667373	−0.0219550
$925$	0	0
$926$	69.9128	2.29748
$927$	−54.0650	−1.77573
$928$	11.1261	0.365233
$929$	27.3408	0.897024	0.448512	−	0.893777i	$-0.351954\pi$
$929$	27.3408	0.897024	0.448512	+	0.893777i	$0.351954\pi$
$930$	0	0
$931$	0	0
$932$	12.2546	0.401413
$933$	2.26956	0.0743020
$934$	−5.69227	−0.186257
$935$	0	0
$936$	4.19892	0.137246
$937$	−37.1376	−1.21323	−0.606617	−	0.794995i	$-0.707474\pi$
$937$	−37.1376	−1.21323	−0.606617	+	0.794995i	$0.707474\pi$
$938$	5.46885	0.178564
$939$	1.79798	0.0586748
$940$	0	0
$941$	−50.6874	−1.65236	−0.826180	−	0.563406i	$-0.809491\pi$
$941$	−50.6874	−1.65236	−0.826180	+	0.563406i	$0.809491\pi$
$942$	−0.723453	−0.0235714
$943$	−7.07858	−0.230510
$944$	−43.3248	−1.41010
$945$	0	0
$946$	31.3717	1.01998
$947$	4.06669	0.132150	0.0660749	−	0.997815i	$-0.478952\pi$
$947$	4.06669	0.132150	0.0660749	+	0.997815i	$0.478952\pi$
$948$	5.15163	0.167317
$949$	−76.8732	−2.49541
$950$	0	0
$951$	2.09655	0.0679852
$952$	1.04286	0.0337994
$953$	14.8332	0.480495	0.240247	−	0.970712i	$-0.422771\pi$
$953$	14.8332	0.480495	0.240247	+	0.970712i	$0.422771\pi$
$954$	−40.0636	−1.29711
$955$	0	0
$956$	−23.4380	−0.758040
$957$	−0.760397	−0.0245801
$958$	−57.5798	−1.86032
$959$	−1.76851	−0.0571081
$960$	0	0
$961$	−30.9265	−0.997630
$962$	−5.64573	−0.182026
$963$	18.4213	0.593619
$964$	−26.0900	−0.840302
$965$	0	0
$966$	0.262018	0.00843028
$967$	−56.7201	−1.82400	−0.911998	−	0.410194i	$-0.865461\pi$
$967$	−56.7201	−1.82400	−0.911998	+	0.410194i	$0.865461\pi$
$968$	−0.870712	−0.0279858
$969$	0	0
$970$	0	0
$971$	12.5938	0.404154	0.202077	−	0.979370i	$-0.435231\pi$
$971$	12.5938	0.404154	0.202077	+	0.979370i	$0.435231\pi$
$972$	−9.22236	−0.295807
$973$	6.07415	0.194728
$974$	−6.70304	−0.214779
$975$	0	0
$976$	31.9798	1.02365
$977$	−36.8973	−1.18045	−0.590224	−	0.807239i	$-0.700961\pi$
$977$	−36.8973	−1.18045	−0.590224	+	0.807239i	$0.700961\pi$
$978$	7.41309	0.237044
$979$	−23.4013	−0.747908
$980$	0	0
$981$	47.4022	1.51344
$982$	49.4097	1.57673
$983$	9.56063	0.304937	0.152468	−	0.988308i	$-0.451278\pi$
$983$	9.56063	0.304937	0.152468	+	0.988308i	$0.451278\pi$
$984$	0.375662	0.0119757
$985$	0	0
$986$	−14.5024	−0.461852
$987$	−1.00343	−0.0319396
$988$	0	0
$989$	−5.91606	−0.188120
$990$	0	0
$991$	16.2633	0.516621	0.258310	−	0.966062i	$-0.416834\pi$
$991$	16.2633	0.516621	0.258310	+	0.966062i	$0.416834\pi$
$992$	−2.11486	−0.0671469
$993$	−4.07097	−0.129188
$994$	−10.1020	−0.320415
$995$	0	0
$996$	−4.92080	−0.155921
$997$	−36.6404	−1.16041	−0.580207	−	0.814469i	$-0.697028\pi$
$997$	−36.6404	−1.16041	−0.580207	+	0.814469i	$0.697028\pi$
$998$	68.1391	2.15690
$999$	−0.675985	−0.0213872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.ct.1.4		24
5.2	odd	4		1805.2.b.l.1084.4		24
5.3	odd	4		1805.2.b.l.1084.21		24
5.4	even	2	inner	9025.2.a.ct.1.21		24
19.3	odd	18		475.2.l.f.351.8		48
19.13	odd	18		475.2.l.f.226.8		48
19.18	odd	2		9025.2.a.cu.1.21		24
95.3	even	36		95.2.p.a.9.8	yes	48
95.13	even	36		95.2.p.a.74.1	yes	48
95.18	even	4		1805.2.b.k.1084.4		24
95.22	even	36		95.2.p.a.9.1	✓	48
95.32	even	36		95.2.p.a.74.8	yes	48
95.37	even	4		1805.2.b.k.1084.21		24
95.79	odd	18		475.2.l.f.351.1		48
95.89	odd	18		475.2.l.f.226.1		48
95.94	odd	2		9025.2.a.cu.1.4		24
285.32	odd	36		855.2.da.b.739.1		48
285.98	odd	36		855.2.da.b.199.1		48
285.203	odd	36		855.2.da.b.739.8		48
285.212	odd	36		855.2.da.b.199.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.9.1	✓	48	95.22	even	36
95.2.p.a.9.8	yes	48	95.3	even	36
95.2.p.a.74.1	yes	48	95.13	even	36
95.2.p.a.74.8	yes	48	95.32	even	36
475.2.l.f.226.1		48	95.89	odd	18
475.2.l.f.226.8		48	19.13	odd	18
475.2.l.f.351.1		48	95.79	odd	18
475.2.l.f.351.8		48	19.3	odd	18
855.2.da.b.199.1		48	285.98	odd	36
855.2.da.b.199.8		48	285.212	odd	36
855.2.da.b.739.1		48	285.32	odd	36
855.2.da.b.739.8		48	285.203	odd	36
1805.2.b.k.1084.4		24	95.18	even	4
1805.2.b.k.1084.21		24	95.37	even	4
1805.2.b.l.1084.4		24	5.2	odd	4
1805.2.b.l.1084.21		24	5.3	odd	4
9025.2.a.ct.1.4		24	1.1	even	1	trivial
9025.2.a.ct.1.21		24	5.4	even	2	inner
9025.2.a.cu.1.4		24	95.94	odd	2
9025.2.a.cu.1.21		24	19.18	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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q-1.96177 q^{2} -0.187708 q^{3} +1.84854 q^{4} +0.368240 q^{6} +0.677067 q^{7} +0.297123 q^{8} -2.96477 q^{9} +O(q^{10})\)	\(q-1.96177 q^{2} -0.187708 q^{3} +1.84854 q^{4} +0.368240 q^{6} +0.677067 q^{7} +0.297123 q^{8} -2.96477 q^{9} +2.84069 q^{11} -0.346987 q^{12} -4.76663 q^{13} -1.32825 q^{14} -4.27997 q^{16} +5.18394 q^{17} +5.81619 q^{18} -0.127091 q^{21} -5.57278 q^{22} +1.05091 q^{23} -0.0557724 q^{24} +9.35103 q^{26} +1.11964 q^{27} +1.25159 q^{28} +1.42605 q^{29} -0.271064 q^{31} +7.80208 q^{32} -0.533221 q^{33} -10.1697 q^{34} -5.48050 q^{36} -0.603754 q^{37} +0.894735 q^{39} -6.73563 q^{41} +0.249324 q^{42} -5.62944 q^{43} +5.25114 q^{44} -2.06165 q^{46} +7.89538 q^{47} +0.803386 q^{48} -6.54158 q^{49} -0.973067 q^{51} -8.81132 q^{52} -6.88829 q^{53} -2.19647 q^{54} +0.201172 q^{56} -2.79757 q^{58} +10.1227 q^{59} -7.47195 q^{61} +0.531765 q^{62} -2.00735 q^{63} -6.74594 q^{64} +1.04606 q^{66} -4.11733 q^{67} +9.58273 q^{68} -0.197265 q^{69} +7.60546 q^{71} -0.880900 q^{72} +16.1274 q^{73} +1.18443 q^{74} +1.92334 q^{77} -1.75527 q^{78} -14.8468 q^{79} +8.68413 q^{81} +13.2138 q^{82} +14.1815 q^{83} -0.234933 q^{84} +11.0437 q^{86} -0.267680 q^{87} +0.844034 q^{88} -8.23788 q^{89} -3.22733 q^{91} +1.94266 q^{92} +0.0508809 q^{93} -15.4889 q^{94} -1.46451 q^{96} +5.72847 q^{97} +12.8331 q^{98} -8.42198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

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