LMFDB - Embedded newform 9025.2.a.cu.1.15

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:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	\(q+0.449373 q^{2} -1.95684 q^{3} -1.79806 q^{4} -0.879352 q^{6} +2.06079 q^{7} -1.70675 q^{8} +0.829224 q^{9} -2.30599 q^{11} +3.51852 q^{12} +4.39611 q^{13} +0.926065 q^{14} +2.82916 q^{16} +5.47185 q^{17} +0.372631 q^{18} -4.03264 q^{21} -1.03625 q^{22} +5.81755 q^{23} +3.33983 q^{24} +1.97549 q^{26} +4.24786 q^{27} -3.70544 q^{28} +5.50466 q^{29} +0.757832 q^{31} +4.68485 q^{32} +4.51245 q^{33} +2.45890 q^{34} -1.49100 q^{36} +6.22555 q^{37} -8.60248 q^{39} -6.53829 q^{41} -1.81216 q^{42} -3.16680 q^{43} +4.14632 q^{44} +2.61425 q^{46} -6.36116 q^{47} -5.53621 q^{48} -2.75314 q^{49} -10.7075 q^{51} -7.90448 q^{52} +3.85028 q^{53} +1.90888 q^{54} -3.51725 q^{56} +2.47365 q^{58} +2.55023 q^{59} +9.94010 q^{61} +0.340550 q^{62} +1.70886 q^{63} -3.55308 q^{64} +2.02778 q^{66} -1.70269 q^{67} -9.83874 q^{68} -11.3840 q^{69} +9.85909 q^{71} -1.41528 q^{72} -10.2167 q^{73} +2.79760 q^{74} -4.75216 q^{77} -3.86572 q^{78} +2.41187 q^{79} -10.8001 q^{81} -2.93813 q^{82} +7.06253 q^{83} +7.25095 q^{84} -1.42307 q^{86} -10.7717 q^{87} +3.93574 q^{88} -2.33452 q^{89} +9.05946 q^{91} -10.4603 q^{92} -1.48296 q^{93} -2.85854 q^{94} -9.16749 q^{96} -6.81539 q^{97} -1.23719 q^{98} -1.91218 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Coefficient data

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

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

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

$2$	0.449373	0.317755	0.158877	−	0.987298i	$-0.449213\pi$
$2$	0.449373	0.317755	0.158877	+	0.987298i	$0.449213\pi$
$3$	−1.95684	−1.12978	−0.564891	−	0.825165i	$-0.691082\pi$
$3$	−1.95684	−1.12978	−0.564891	+	0.825165i	$0.691082\pi$
$4$	−1.79806	−0.899032
$5$	0	0
$5$	0	0
$6$	−0.879352	−0.358994
$7$	2.06079	0.778906	0.389453	−	0.921046i	$-0.372664\pi$
$7$	2.06079	0.778906	0.389453	+	0.921046i	$0.372664\pi$
$8$	−1.70675	−0.603427
$9$	0.829224	0.276408
$10$	0	0
$11$	−2.30599	−0.695282	−0.347641	−	0.937628i	$-0.613017\pi$
$11$	−2.30599	−0.695282	−0.347641	+	0.937628i	$0.613017\pi$
$12$	3.51852	1.01571
$13$	4.39611	1.21926	0.609630	−	0.792686i	$-0.291318\pi$
$13$	4.39611	1.21926	0.609630	+	0.792686i	$0.291318\pi$
$14$	0.926065	0.247501
$15$	0	0
$16$	2.82916	0.707290
$17$	5.47185	1.32712	0.663560	−	0.748123i	$-0.269045\pi$
$17$	5.47185	1.32712	0.663560	+	0.748123i	$0.269045\pi$
$18$	0.372631	0.0878299
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−4.03264	−0.879994
$22$	−1.03625	−0.220929
$23$	5.81755	1.21304	0.606522	−	0.795067i	$-0.292564\pi$
$23$	5.81755	1.21304	0.606522	+	0.795067i	$0.292564\pi$
$24$	3.33983	0.681741
$25$	0	0
$26$	1.97549	0.387426
$27$	4.24786	0.817502
$28$	−3.70544	−0.700262
$29$	5.50466	1.02219	0.511095	−	0.859524i	$-0.329240\pi$
$29$	5.50466	1.02219	0.511095	+	0.859524i	$0.329240\pi$
$30$	0	0
$31$	0.757832	0.136111	0.0680553	−	0.997682i	$-0.478321\pi$
$31$	0.757832	0.136111	0.0680553	+	0.997682i	$0.478321\pi$
$32$	4.68485	0.828171
$33$	4.51245	0.785517
$34$	2.45890	0.421699
$35$	0	0
$36$	−1.49100	−0.248499
$37$	6.22555	1.02347	0.511737	−	0.859142i	$-0.329002\pi$
$37$	6.22555	1.02347	0.511737	+	0.859142i	$0.329002\pi$
$38$	0	0
$39$	−8.60248	−1.37750
$40$	0	0
$41$	−6.53829	−1.02111	−0.510554	−	0.859845i	$-0.670560\pi$
$41$	−6.53829	−1.02111	−0.510554	+	0.859845i	$0.670560\pi$
$42$	−1.81216	−0.279623
$43$	−3.16680	−0.482932	−0.241466	−	0.970409i	$-0.577628\pi$
$43$	−3.16680	−0.482932	−0.241466	+	0.970409i	$0.577628\pi$
$44$	4.14632	0.625081
$45$	0	0
$46$	2.61425	0.385451
$47$	−6.36116	−0.927871	−0.463936	−	0.885869i	$-0.653563\pi$
$47$	−6.36116	−0.927871	−0.463936	+	0.885869i	$0.653563\pi$
$48$	−5.53621	−0.799084
$49$	−2.75314	−0.393305
$50$	0	0
$51$	−10.7075	−1.49936
$52$	−7.90448	−1.09615
$53$	3.85028	0.528876	0.264438	−	0.964403i	$-0.414813\pi$
$53$	3.85028	0.528876	0.264438	+	0.964403i	$0.414813\pi$
$54$	1.90888	0.259765
$55$	0	0
$56$	−3.51725	−0.470013
$57$	0	0
$58$	2.47365	0.324806
$59$	2.55023	0.332012	0.166006	−	0.986125i	$-0.446913\pi$
$59$	2.55023	0.332012	0.166006	+	0.986125i	$0.446913\pi$
$60$	0	0
$61$	9.94010	1.27270	0.636350	−	0.771401i	$-0.280444\pi$
$61$	9.94010	1.27270	0.636350	+	0.771401i	$0.280444\pi$
$62$	0.340550	0.0432498
$63$	1.70886	0.215296
$64$	−3.55308	−0.444135
$65$	0	0
$66$	2.02778	0.249602
$67$	−1.70269	−0.208017	−0.104009	−	0.994576i	$-0.533167\pi$
$67$	−1.70269	−0.208017	−0.104009	+	0.994576i	$0.533167\pi$
$68$	−9.83874	−1.19312
$69$	−11.3840	−1.37048
$70$	0	0
$71$	9.85909	1.17006	0.585029	−	0.811012i	$-0.301083\pi$
$71$	9.85909	1.17006	0.585029	+	0.811012i	$0.301083\pi$
$72$	−1.41528	−0.166792
$73$	−10.2167	−1.19577	−0.597886	−	0.801581i	$-0.703993\pi$
$73$	−10.2167	−1.19577	−0.597886	+	0.801581i	$0.703993\pi$
$74$	2.79760	0.325214
$75$	0	0
$76$	0	0
$77$	−4.75216	−0.541559
$78$	−3.86572	−0.437707
$79$	2.41187	0.271357	0.135679	−	0.990753i	$-0.456679\pi$
$79$	2.41187	0.271357	0.135679	+	0.990753i	$0.456679\pi$
$80$	0	0
$81$	−10.8001	−1.20001
$82$	−2.93813	−0.324462
$83$	7.06253	0.775213	0.387607	−	0.921825i	$-0.373302\pi$
$83$	7.06253	0.775213	0.387607	+	0.921825i	$0.373302\pi$
$84$	7.25095	0.791143
$85$	0	0
$86$	−1.42307	−0.153454
$87$	−10.7717	−1.15485
$88$	3.93574	0.419552
$89$	−2.33452	−0.247458	−0.123729	−	0.992316i	$-0.539485\pi$
$89$	−2.33452	−0.247458	−0.123729	+	0.992316i	$0.539485\pi$
$90$	0	0
$91$	9.05946	0.949689
$92$	−10.4603	−1.09056
$93$	−1.48296	−0.153775
$94$	−2.85854	−0.294836
$95$	0	0
$96$	−9.16749	−0.935653
$97$	−6.81539	−0.691998	−0.345999	−	0.938235i	$-0.612460\pi$
$97$	−6.81539	−0.691998	−0.345999	+	0.938235i	$0.612460\pi$
$98$	−1.23719	−0.124975
$99$	−1.91218	−0.192181
$100$	0	0
$101$	12.1976	1.21370	0.606851	−	0.794816i	$-0.292433\pi$
$101$	12.1976	1.21370	0.606851	+	0.794816i	$0.292433\pi$
$102$	−4.81168	−0.476428
$103$	12.9197	1.27302	0.636509	−	0.771269i	$-0.280378\pi$
$103$	12.9197	1.27302	0.636509	+	0.771269i	$0.280378\pi$
$104$	−7.50304	−0.735734
$105$	0	0
$106$	1.73021	0.168053
$107$	−15.1729	−1.46682	−0.733412	−	0.679785i	$-0.762073\pi$
$107$	−15.1729	−1.46682	−0.733412	+	0.679785i	$0.762073\pi$
$108$	−7.63793	−0.734960
$109$	−19.1794	−1.83705	−0.918527	−	0.395359i	$-0.870620\pi$
$109$	−19.1794	−1.83705	−0.918527	+	0.395359i	$0.870620\pi$
$110$	0	0
$111$	−12.1824	−1.15630
$112$	5.83031	0.550913
$113$	−1.91146	−0.179815	−0.0899075	−	0.995950i	$-0.528657\pi$
$113$	−1.91146	−0.179815	−0.0899075	+	0.995950i	$0.528657\pi$
$114$	0	0
$115$	0	0
$116$	−9.89773	−0.918981
$117$	3.64535	0.337013
$118$	1.14601	0.105498
$119$	11.2764	1.03370
$120$	0	0
$121$	−5.68241	−0.516583
$122$	4.46682	0.404406
$123$	12.7944	1.15363
$124$	−1.36263	−0.122368
$125$	0	0
$126$	0.767915	0.0684113
$127$	21.2359	1.88438	0.942191	−	0.335077i	$-0.108762\pi$
$127$	21.2359	1.88438	0.942191	+	0.335077i	$0.108762\pi$
$128$	−10.9663	−0.969297
$129$	6.19692	0.545608
$130$	0	0
$131$	−1.67271	−0.146146	−0.0730728	−	0.997327i	$-0.523281\pi$
$131$	−1.67271	−0.146146	−0.0730728	+	0.997327i	$0.523281\pi$
$132$	−8.11368	−0.706205
$133$	0	0
$134$	−0.765145	−0.0660984
$135$	0	0
$136$	−9.33908	−0.800819
$137$	−17.2880	−1.47701	−0.738506	−	0.674247i	$-0.764468\pi$
$137$	−17.2880	−1.47701	−0.738506	+	0.674247i	$0.764468\pi$
$138$	−5.11567	−0.435475
$139$	12.3265	1.04552	0.522761	−	0.852479i	$-0.324902\pi$
$139$	12.3265	1.04552	0.522761	+	0.852479i	$0.324902\pi$
$140$	0	0
$141$	12.4478	1.04829
$142$	4.43041	0.371792
$143$	−10.1374	−0.847730
$144$	2.34601	0.195501
$145$	0	0
$146$	−4.59111	−0.379963
$147$	5.38745	0.444349
$148$	−11.1939	−0.920136
$149$	4.35901	0.357104	0.178552	−	0.983930i	$-0.442859\pi$
$149$	4.35901	0.357104	0.178552	+	0.983930i	$0.442859\pi$
$150$	0	0
$151$	4.44628	0.361833	0.180917	−	0.983498i	$-0.442094\pi$
$151$	4.44628	0.361833	0.180917	+	0.983498i	$0.442094\pi$
$152$	0	0
$153$	4.53739	0.366826
$154$	−2.13550	−0.172083
$155$	0	0
$156$	15.4678	1.23841
$157$	−19.8432	−1.58366	−0.791831	−	0.610740i	$-0.790872\pi$
$157$	−19.8432	−1.58366	−0.791831	+	0.610740i	$0.790872\pi$
$158$	1.08383	0.0862250
$159$	−7.53438	−0.597515
$160$	0	0
$161$	11.9888	0.944847
$162$	−4.85326	−0.381308
$163$	1.28088	0.100326	0.0501632	−	0.998741i	$-0.484026\pi$
$163$	1.28088	0.100326	0.0501632	+	0.998741i	$0.484026\pi$
$164$	11.7563	0.918009
$165$	0	0
$166$	3.17371	0.246328
$167$	8.03589	0.621836	0.310918	−	0.950437i	$-0.399364\pi$
$167$	8.03589	0.621836	0.310918	+	0.950437i	$0.399364\pi$
$168$	6.88270	0.531012
$169$	6.32574	0.486595
$170$	0	0
$171$	0	0
$172$	5.69410	0.434171
$173$	−2.65910	−0.202167	−0.101084	−	0.994878i	$-0.532231\pi$
$173$	−2.65910	−0.202167	−0.101084	+	0.994878i	$0.532231\pi$
$174$	−4.84053	−0.366960
$175$	0	0
$176$	−6.52401	−0.491766
$177$	−4.99040	−0.375101
$178$	−1.04907	−0.0786311
$179$	8.10201	0.605572	0.302786	−	0.953059i	$-0.402083\pi$
$179$	8.10201	0.605572	0.302786	+	0.953059i	$0.402083\pi$
$180$	0	0
$181$	21.5023	1.59826	0.799128	−	0.601161i	$-0.205295\pi$
$181$	21.5023	1.59826	0.799128	+	0.601161i	$0.205295\pi$
$182$	4.07108	0.301768
$183$	−19.4512	−1.43787
$184$	−9.92910	−0.731983
$185$	0	0
$186$	−0.666401	−0.0488629
$187$	−12.6180	−0.922722
$188$	11.4378	0.834186
$189$	8.75396	0.636757
$190$	0	0
$191$	−19.5939	−1.41777	−0.708884	−	0.705326i	$-0.750801\pi$
$191$	−19.5939	−1.41777	−0.708884	+	0.705326i	$0.750801\pi$
$192$	6.95280	0.501775
$193$	−0.483357	−0.0347928	−0.0173964	−	0.999849i	$-0.505538\pi$
$193$	−0.483357	−0.0347928	−0.0173964	+	0.999849i	$0.505538\pi$
$194$	−3.06265	−0.219886
$195$	0	0
$196$	4.95031	0.353594
$197$	1.26189	0.0899060	0.0449530	−	0.998989i	$-0.485686\pi$
$197$	1.26189	0.0899060	0.0449530	+	0.998989i	$0.485686\pi$
$198$	−0.859283	−0.0610666
$199$	20.6554	1.46423	0.732113	−	0.681183i	$-0.238534\pi$
$199$	20.6554	1.46423	0.732113	+	0.681183i	$0.238534\pi$
$200$	0	0
$201$	3.33190	0.235014
$202$	5.48125	0.385660
$203$	11.3440	0.796190
$204$	19.2528	1.34797
$205$	0	0
$206$	5.80578	0.404508
$207$	4.82405	0.335295
$208$	12.4373	0.862371
$209$	0	0
$210$	0	0
$211$	7.01196	0.482723	0.241361	−	0.970435i	$-0.422406\pi$
$211$	7.01196	0.482723	0.241361	+	0.970435i	$0.422406\pi$
$212$	−6.92305	−0.475477
$213$	−19.2927	−1.32191
$214$	−6.81831	−0.466090
$215$	0	0
$216$	−7.25003	−0.493302
$217$	1.56173	0.106017
$218$	−8.61871	−0.583733
$219$	19.9924	1.35096
$220$	0	0
$221$	24.0548	1.61810
$222$	−5.47445	−0.367421
$223$	19.4374	1.30162	0.650812	−	0.759239i	$-0.274429\pi$
$223$	19.4374	1.30162	0.650812	+	0.759239i	$0.274429\pi$
$224$	9.65449	0.645068
$225$	0	0
$226$	−0.858959	−0.0571371
$227$	6.53998	0.434074	0.217037	−	0.976163i	$-0.430361\pi$
$227$	6.53998	0.434074	0.217037	+	0.976163i	$0.430361\pi$
$228$	0	0
$229$	−20.4005	−1.34810	−0.674052	−	0.738684i	$-0.735448\pi$
$229$	−20.4005	−1.34810	−0.674052	+	0.738684i	$0.735448\pi$
$230$	0	0
$231$	9.29923	0.611844
$232$	−9.39507	−0.616816
$233$	12.0490	0.789357	0.394679	−	0.918819i	$-0.370856\pi$
$233$	12.0490	0.789357	0.394679	+	0.918819i	$0.370856\pi$
$234$	1.63812	0.107088
$235$	0	0
$236$	−4.58548	−0.298489
$237$	−4.71965	−0.306574
$238$	5.06729	0.328464
$239$	−6.12499	−0.396193	−0.198096	−	0.980183i	$-0.563476\pi$
$239$	−6.12499	−0.396193	−0.198096	+	0.980183i	$0.563476\pi$
$240$	0	0
$241$	−7.27309	−0.468501	−0.234250	−	0.972176i	$-0.575264\pi$
$241$	−7.27309	−0.468501	−0.234250	+	0.972176i	$0.575264\pi$
$242$	−2.55352	−0.164147
$243$	8.39040	0.538244
$244$	−17.8729	−1.14420
$245$	0	0
$246$	5.74945	0.366572
$247$	0	0
$248$	−1.29343	−0.0821328
$249$	−13.8202	−0.875822
$250$	0	0
$251$	−24.1866	−1.52664	−0.763321	−	0.646019i	$-0.776433\pi$
$251$	−24.1866	−1.52664	−0.763321	+	0.646019i	$0.776433\pi$
$252$	−3.07263	−0.193558
$253$	−13.4152	−0.843407
$254$	9.54285	0.598771
$255$	0	0
$256$	2.17817	0.136136
$257$	12.2379	0.763382	0.381691	−	0.924290i	$-0.375342\pi$
$257$	12.2379	0.763382	0.381691	+	0.924290i	$0.375342\pi$
$258$	2.78473	0.173370
$259$	12.8296	0.797191
$260$	0	0
$261$	4.56459	0.282541
$262$	−0.751673	−0.0464385
$263$	−12.3859	−0.763746	−0.381873	−	0.924215i	$-0.624721\pi$
$263$	−12.3859	−0.763746	−0.381873	+	0.924215i	$0.624721\pi$
$264$	−7.70162	−0.474002
$265$	0	0
$266$	0	0
$267$	4.56828	0.279574
$268$	3.06155	0.187014
$269$	−4.93880	−0.301124	−0.150562	−	0.988601i	$-0.548108\pi$
$269$	−4.93880	−0.301124	−0.150562	+	0.988601i	$0.548108\pi$
$270$	0	0
$271$	−6.90194	−0.419263	−0.209631	−	0.977780i	$-0.567226\pi$
$271$	−6.90194	−0.419263	−0.209631	+	0.977780i	$0.567226\pi$
$272$	15.4808	0.938658
$273$	−17.7279	−1.07294
$274$	−7.76876	−0.469328
$275$	0	0
$276$	20.4692	1.23210
$277$	−3.96325	−0.238129	−0.119064	−	0.992887i	$-0.537989\pi$
$277$	−3.96325	−0.238129	−0.119064	+	0.992887i	$0.537989\pi$
$278$	5.53921	0.332220
$279$	0.628412	0.0376221
$280$	0	0
$281$	31.1993	1.86119	0.930597	−	0.366045i	$-0.119289\pi$
$281$	31.1993	1.86119	0.930597	+	0.366045i	$0.119289\pi$
$282$	5.59370	0.333100
$283$	10.6270	0.631711	0.315855	−	0.948807i	$-0.397709\pi$
$283$	10.6270	0.631711	0.315855	+	0.948807i	$0.397709\pi$
$284$	−17.7273	−1.05192
$285$	0	0
$286$	−4.55546	−0.269370
$287$	−13.4741	−0.795348
$288$	3.88478	0.228913
$289$	12.9412	0.761246
$290$	0	0
$291$	13.3366	0.781807
$292$	18.3703	1.07504
$293$	−19.6263	−1.14658	−0.573289	−	0.819353i	$-0.694333\pi$
$293$	−19.6263	−1.14658	−0.573289	+	0.819353i	$0.694333\pi$
$294$	2.42097	0.141194
$295$	0	0
$296$	−10.6255	−0.617592
$297$	−9.79553	−0.568394
$298$	1.95882	0.113472
$299$	25.5746	1.47902
$300$	0	0
$301$	−6.52611	−0.376159
$302$	1.99804	0.114974
$303$	−23.8687	−1.37122
$304$	0	0
$305$	0	0
$306$	2.03898	0.116561
$307$	−22.6258	−1.29132	−0.645662	−	0.763623i	$-0.723419\pi$
$307$	−22.6258	−1.29132	−0.645662	+	0.763623i	$0.723419\pi$
$308$	8.54469	0.486879
$309$	−25.2818	−1.43823
$310$	0	0
$311$	24.8577	1.40955	0.704776	−	0.709430i	$-0.251047\pi$
$311$	24.8577	1.40955	0.704776	+	0.709430i	$0.251047\pi$
$312$	14.6823	0.831219
$313$	−22.2026	−1.25497	−0.627484	−	0.778630i	$-0.715915\pi$
$313$	−22.2026	−1.25497	−0.627484	+	0.778630i	$0.715915\pi$
$314$	−8.91701	−0.503216
$315$	0	0
$316$	−4.33670	−0.243959
$317$	−2.03957	−0.114554	−0.0572769	−	0.998358i	$-0.518242\pi$
$317$	−2.03957	−0.114554	−0.0572769	+	0.998358i	$0.518242\pi$
$318$	−3.38575	−0.189863
$319$	−12.6937	−0.710710
$320$	0	0
$321$	29.6910	1.65719
$322$	5.38743	0.300230
$323$	0	0
$324$	19.4192	1.07884
$325$	0	0
$326$	0.575594	0.0318792
$327$	37.5310	2.07547
$328$	11.1592	0.616164
$329$	−13.1090	−0.722725
$330$	0	0
$331$	33.6525	1.84971	0.924855	−	0.380321i	$-0.124186\pi$
$331$	33.6525	1.84971	0.924855	+	0.380321i	$0.124186\pi$
$332$	−12.6989	−0.696941
$333$	5.16237	0.282896
$334$	3.61111	0.197591
$335$	0	0
$336$	−11.4090	−0.622411
$337$	2.58877	0.141019	0.0705096	−	0.997511i	$-0.477537\pi$
$337$	2.58877	0.141019	0.0705096	+	0.997511i	$0.477537\pi$
$338$	2.84262	0.154618
$339$	3.74042	0.203152
$340$	0	0
$341$	−1.74755	−0.0946353
$342$	0	0
$343$	−20.0992	−1.08525
$344$	5.40493	0.291414
$345$	0	0
$346$	−1.19493	−0.0642397
$347$	23.8033	1.27783	0.638913	−	0.769279i	$-0.279384\pi$
$347$	23.8033	1.27783	0.638913	+	0.769279i	$0.279384\pi$
$348$	19.3683	1.03825
$349$	−2.48241	−0.132880	−0.0664402	−	0.997790i	$-0.521164\pi$
$349$	−2.48241	−0.132880	−0.0664402	+	0.997790i	$0.521164\pi$
$350$	0	0
$351$	18.6741	0.996747
$352$	−10.8032	−0.575813
$353$	35.7434	1.90243	0.951216	−	0.308527i	$-0.0998359\pi$
$353$	35.7434	1.90243	0.951216	+	0.308527i	$0.0998359\pi$
$354$	−2.24255	−0.119190
$355$	0	0
$356$	4.19761	0.222473
$357$	−22.0660	−1.16786
$358$	3.64082	0.192424
$359$	−5.76436	−0.304231	−0.152116	−	0.988363i	$-0.548609\pi$
$359$	−5.76436	−0.304231	−0.152116	+	0.988363i	$0.548609\pi$
$360$	0	0
$361$	0	0
$362$	9.66258	0.507854
$363$	11.1196	0.583626
$364$	−16.2895	−0.853801
$365$	0	0
$366$	−8.74084	−0.456891
$367$	−5.95729	−0.310968	−0.155484	−	0.987838i	$-0.549694\pi$
$367$	−5.95729	−0.310968	−0.155484	+	0.987838i	$0.549694\pi$
$368$	16.4588	0.857974
$369$	−5.42170	−0.282243
$370$	0	0
$371$	7.93462	0.411945
$372$	2.66645	0.138249
$373$	−4.46841	−0.231365	−0.115683	−	0.993286i	$-0.536906\pi$
$373$	−4.46841	−0.231365	−0.115683	+	0.993286i	$0.536906\pi$
$374$	−5.67021	−0.293199
$375$	0	0
$376$	10.8569	0.559902
$377$	24.1991	1.24631
$378$	3.93380	0.202333
$379$	13.3179	0.684095	0.342047	−	0.939683i	$-0.388880\pi$
$379$	13.3179	0.684095	0.342047	+	0.939683i	$0.388880\pi$
$380$	0	0
$381$	−41.5553	−2.12894
$382$	−8.80499	−0.450502
$383$	10.1737	0.519849	0.259925	−	0.965629i	$-0.416302\pi$
$383$	10.1737	0.519849	0.259925	+	0.965629i	$0.416302\pi$
$384$	21.4594	1.09509
$385$	0	0
$386$	−0.217208	−0.0110556
$387$	−2.62598	−0.133486
$388$	12.2545	0.622128
$389$	−11.4104	−0.578530	−0.289265	−	0.957249i	$-0.593411\pi$
$389$	−11.4104	−0.578530	−0.289265	+	0.957249i	$0.593411\pi$
$390$	0	0
$391$	31.8328	1.60985
$392$	4.69891	0.237331
$393$	3.27323	0.165113
$394$	0.567060	0.0285681
$395$	0	0
$396$	3.43822	0.172777
$397$	5.14253	0.258096	0.129048	−	0.991638i	$-0.458808\pi$
$397$	5.14253	0.258096	0.129048	+	0.991638i	$0.458808\pi$
$398$	9.28201	0.465265
$399$	0	0
$400$	0	0
$401$	17.0822	0.853043	0.426522	−	0.904477i	$-0.359739\pi$
$401$	17.0822	0.853043	0.426522	+	0.904477i	$0.359739\pi$
$402$	1.49727	0.0746768
$403$	3.33151	0.165954
$404$	−21.9320	−1.09116
$405$	0	0
$406$	5.09767	0.252993
$407$	−14.3561	−0.711603
$408$	18.2751	0.904751
$409$	−26.0696	−1.28906	−0.644529	−	0.764580i	$-0.722947\pi$
$409$	−26.0696	−1.28906	−0.644529	+	0.764580i	$0.722947\pi$
$410$	0	0
$411$	33.8298	1.66870
$412$	−23.2305	−1.14448
$413$	5.25550	0.258606
$414$	2.16780	0.106542
$415$	0	0
$416$	20.5951	1.00976
$417$	−24.1211	−1.18121
$418$	0	0
$419$	5.77281	0.282020	0.141010	−	0.990008i	$-0.454965\pi$
$419$	5.77281	0.282020	0.141010	+	0.990008i	$0.454965\pi$
$420$	0	0
$421$	25.3007	1.23308	0.616540	−	0.787323i	$-0.288534\pi$
$421$	25.3007	1.23308	0.616540	+	0.787323i	$0.288534\pi$
$422$	3.15099	0.153388
$423$	−5.27483	−0.256471
$424$	−6.57146	−0.319138
$425$	0	0
$426$	−8.66960	−0.420044
$427$	20.4845	0.991314
$428$	27.2819	1.31872
$429$	19.8372	0.957750
$430$	0	0
$431$	−18.7629	−0.903777	−0.451888	−	0.892074i	$-0.649249\pi$
$431$	−18.7629	−0.903777	−0.451888	+	0.892074i	$0.649249\pi$
$432$	12.0179	0.578211
$433$	−8.51298	−0.409108	−0.204554	−	0.978855i	$-0.565574\pi$
$433$	−8.51298	−0.409108	−0.204554	+	0.978855i	$0.565574\pi$
$434$	0.701802	0.0336876
$435$	0	0
$436$	34.4858	1.65157
$437$	0	0
$438$	8.98406	0.429275
$439$	−2.05530	−0.0980941	−0.0490470	−	0.998796i	$-0.515618\pi$
$439$	−2.05530	−0.0980941	−0.0490470	+	0.998796i	$0.515618\pi$
$440$	0	0
$441$	−2.28296	−0.108713
$442$	10.8096	0.514160
$443$	12.0403	0.572054	0.286027	−	0.958222i	$-0.407665\pi$
$443$	12.0403	0.572054	0.286027	+	0.958222i	$0.407665\pi$
$444$	21.9048	1.03955
$445$	0	0
$446$	8.73464	0.413597
$447$	−8.52989	−0.403450
$448$	−7.32215	−0.345939
$449$	7.49400	0.353664	0.176832	−	0.984241i	$-0.443415\pi$
$449$	7.49400	0.353664	0.176832	+	0.984241i	$0.443415\pi$
$450$	0	0
$451$	15.0772	0.709959
$452$	3.43693	0.161659
$453$	−8.70066	−0.408793
$454$	2.93889	0.137929
$455$	0	0
$456$	0	0
$457$	−14.0052	−0.655137	−0.327568	−	0.944827i	$-0.606229\pi$
$457$	−14.0052	−0.655137	−0.327568	+	0.944827i	$0.606229\pi$
$458$	−9.16745	−0.428367
$459$	23.2437	1.08492
$460$	0	0
$461$	−17.6751	−0.823210	−0.411605	−	0.911362i	$-0.635032\pi$
$461$	−17.6751	−0.823210	−0.411605	+	0.911362i	$0.635032\pi$
$462$	4.17882	0.194416
$463$	16.5926	0.771123	0.385562	−	0.922682i	$-0.374008\pi$
$463$	16.5926	0.771123	0.385562	+	0.922682i	$0.374008\pi$
$464$	15.5736	0.722984
$465$	0	0
$466$	5.41451	0.250822
$467$	15.9904	0.739949	0.369975	−	0.929042i	$-0.379366\pi$
$467$	15.9904	0.739949	0.369975	+	0.929042i	$0.379366\pi$
$468$	−6.55458	−0.302985
$469$	−3.50890	−0.162026
$470$	0	0
$471$	38.8300	1.78919
$472$	−4.35261	−0.200345
$473$	7.30260	0.335774
$474$	−2.12089	−0.0974155
$475$	0	0
$476$	−20.2756	−0.929331
$477$	3.19274	0.146186
$478$	−2.75241	−0.125892
$479$	7.39591	0.337928	0.168964	−	0.985622i	$-0.445958\pi$
$479$	7.39591	0.337928	0.168964	+	0.985622i	$0.445958\pi$
$480$	0	0
$481$	27.3682	1.24788
$482$	−3.26833	−0.148868
$483$	−23.4601	−1.06747
$484$	10.2173	0.464425
$485$	0	0
$486$	3.77042	0.171030
$487$	20.1881	0.914811	0.457406	−	0.889258i	$-0.348779\pi$
$487$	20.1881	0.914811	0.457406	+	0.889258i	$0.348779\pi$
$488$	−16.9652	−0.767981
$489$	−2.50648	−0.113347
$490$	0	0
$491$	9.33307	0.421195	0.210598	−	0.977573i	$-0.432459\pi$
$491$	9.33307	0.421195	0.210598	+	0.977573i	$0.432459\pi$
$492$	−23.0051	−1.03715
$493$	30.1207	1.35657
$494$	0	0
$495$	0	0
$496$	2.14403	0.0962697
$497$	20.3175	0.911366
$498$	−6.21044	−0.278297
$499$	−23.9612	−1.07265	−0.536326	−	0.844011i	$-0.680188\pi$
$499$	−23.9612	−1.07265	−0.536326	+	0.844011i	$0.680188\pi$
$500$	0	0
$501$	−15.7249	−0.702539
$502$	−10.8688	−0.485098
$503$	10.3338	0.460763	0.230382	−	0.973100i	$-0.426003\pi$
$503$	10.3338	0.460763	0.230382	+	0.973100i	$0.426003\pi$
$504$	−2.91659	−0.129915
$505$	0	0
$506$	−6.02844	−0.267997
$507$	−12.3785	−0.549747
$508$	−38.1835	−1.69412
$509$	27.7116	1.22829	0.614147	−	0.789192i	$-0.289500\pi$
$509$	27.7116	1.22829	0.614147	+	0.789192i	$0.289500\pi$
$510$	0	0
$511$	−21.0545	−0.931395
$512$	22.9115	1.01256
$513$	0	0
$514$	5.49940	0.242568
$515$	0	0
$516$	−11.1424	−0.490519
$517$	14.6688	0.645132
$518$	5.76527	0.253311
$519$	5.20343	0.228405
$520$	0	0
$521$	−10.5729	−0.463209	−0.231604	−	0.972810i	$-0.574398\pi$
$521$	−10.5729	−0.463209	−0.231604	+	0.972810i	$0.574398\pi$
$522$	2.05121	0.0897788
$523$	−18.1596	−0.794065	−0.397032	−	0.917805i	$-0.629960\pi$
$523$	−18.1596	−0.794065	−0.397032	+	0.917805i	$0.629960\pi$
$524$	3.00765	0.131390
$525$	0	0
$526$	−5.56588	−0.242684
$527$	4.14675	0.180635
$528$	12.7665	0.555588
$529$	10.8439	0.471475
$530$	0	0
$531$	2.11471	0.0917707
$532$	0	0
$533$	−28.7430	−1.24500
$534$	2.05286	0.0888360
$535$	0	0
$536$	2.90607	0.125523
$537$	−15.8543	−0.684165
$538$	−2.21936	−0.0956835
$539$	6.34870	0.273458
$540$	0	0
$541$	6.10507	0.262478	0.131239	−	0.991351i	$-0.458105\pi$
$541$	6.10507	0.262478	0.131239	+	0.991351i	$0.458105\pi$
$542$	−3.10155	−0.133223
$543$	−42.0766	−1.80568
$544$	25.6348	1.09908
$545$	0	0
$546$	−7.96645	−0.340933
$547$	10.9019	0.466132	0.233066	−	0.972461i	$-0.425124\pi$
$547$	10.9019	0.466132	0.233066	+	0.972461i	$0.425124\pi$
$548$	31.0849	1.32788
$549$	8.24256	0.351784
$550$	0	0
$551$	0	0
$552$	19.4297	0.826981
$553$	4.97037	0.211362
$554$	−1.78098	−0.0756665
$555$	0	0
$556$	−22.1639	−0.939958
$557$	−12.2157	−0.517595	−0.258798	−	0.965932i	$-0.583326\pi$
$557$	−12.2157	−0.517595	−0.258798	+	0.965932i	$0.583326\pi$
$558$	0.282392	0.0119546
$559$	−13.9216	−0.588820
$560$	0	0
$561$	24.6915	1.04247
$562$	14.0201	0.591403
$563$	18.3200	0.772095	0.386048	−	0.922479i	$-0.373840\pi$
$563$	18.3200	0.772095	0.386048	+	0.922479i	$0.373840\pi$
$564$	−22.3819	−0.942448
$565$	0	0
$566$	4.77550	0.200729
$567$	−22.2567	−0.934693
$568$	−16.8270	−0.706044
$569$	32.3240	1.35509	0.677546	−	0.735480i	$-0.263043\pi$
$569$	32.3240	1.35509	0.677546	+	0.735480i	$0.263043\pi$
$570$	0	0
$571$	−13.2641	−0.555083	−0.277542	−	0.960714i	$-0.589520\pi$
$571$	−13.2641	−0.555083	−0.277542	+	0.960714i	$0.589520\pi$
$572$	18.2276	0.762136
$573$	38.3422	1.60177
$574$	−6.05488	−0.252726
$575$	0	0
$576$	−2.94629	−0.122762
$577$	−21.7627	−0.905993	−0.452996	−	0.891512i	$-0.649645\pi$
$577$	−21.7627	−0.905993	−0.452996	+	0.891512i	$0.649645\pi$
$578$	5.81542	0.241890
$579$	0.945853	0.0393083
$580$	0	0
$581$	14.5544	0.603818
$582$	5.99312	0.248423
$583$	−8.87870	−0.367718
$584$	17.4373	0.721561
$585$	0	0
$586$	−8.81952	−0.364331
$587$	−41.5762	−1.71604	−0.858018	−	0.513620i	$-0.828304\pi$
$587$	−41.5762	−1.71604	−0.858018	+	0.513620i	$0.828304\pi$
$588$	−9.68697	−0.399484
$589$	0	0
$590$	0	0
$591$	−2.46932	−0.101574
$592$	17.6131	0.723893
$593$	8.58712	0.352631	0.176315	−	0.984334i	$-0.443582\pi$
$593$	8.58712	0.352631	0.176315	+	0.984334i	$0.443582\pi$
$594$	−4.40185	−0.180610
$595$	0	0
$596$	−7.83778	−0.321048
$597$	−40.4194	−1.65426
$598$	11.4925	0.469964
$599$	41.2980	1.68739	0.843696	−	0.536822i	$-0.180375\pi$
$599$	41.2980	1.68739	0.843696	+	0.536822i	$0.180375\pi$
$600$	0	0
$601$	−1.60121	−0.0653145	−0.0326573	−	0.999467i	$-0.510397\pi$
$601$	−1.60121	−0.0653145	−0.0326573	+	0.999467i	$0.510397\pi$
$602$	−2.93266	−0.119526
$603$	−1.41191	−0.0574975
$604$	−7.99470	−0.325300
$605$	0	0
$606$	−10.7259	−0.435711
$607$	−32.4708	−1.31795	−0.658975	−	0.752165i	$-0.729010\pi$
$607$	−32.4708	−1.31795	−0.658975	+	0.752165i	$0.729010\pi$
$608$	0	0
$609$	−22.1983	−0.899521
$610$	0	0
$611$	−27.9643	−1.13132
$612$	−8.15852	−0.329788
$613$	−13.9352	−0.562839	−0.281420	−	0.959585i	$-0.590805\pi$
$613$	−13.9352	−0.562839	−0.281420	+	0.959585i	$0.590805\pi$
$614$	−10.1674	−0.410325
$615$	0	0
$616$	8.11075	0.326791
$617$	14.4224	0.580625	0.290313	−	0.956932i	$-0.406241\pi$
$617$	14.4224	0.580625	0.290313	+	0.956932i	$0.406241\pi$
$618$	−11.3610	−0.457005
$619$	−4.71305	−0.189434	−0.0947168	−	0.995504i	$-0.530195\pi$
$619$	−4.71305	−0.189434	−0.0947168	+	0.995504i	$0.530195\pi$
$620$	0	0
$621$	24.7122	0.991665
$622$	11.1704	0.447892
$623$	−4.81095	−0.192747
$624$	−24.3378	−0.974291
$625$	0	0
$626$	−9.97728	−0.398772
$627$	0	0
$628$	35.6794	1.42376
$629$	34.0653	1.35827
$630$	0	0
$631$	3.31273	0.131878	0.0659388	−	0.997824i	$-0.478996\pi$
$631$	3.31273	0.131878	0.0659388	+	0.997824i	$0.478996\pi$
$632$	−4.11646	−0.163744
$633$	−13.7213	−0.545372
$634$	−0.916530	−0.0364000
$635$	0	0
$636$	13.5473	0.537185
$637$	−12.1031	−0.479541
$638$	−5.70420	−0.225831
$639$	8.17539	0.323413
$640$	0	0
$641$	−0.0491989	−0.00194324	−0.000971620	−	1.00000i	$-0.500309\pi$
$641$	−0.0491989	−0.00194324	−0.000971620		1.00000i	$0.500309\pi$
$642$	13.3424	0.526581
$643$	12.0003	0.473246	0.236623	−	0.971602i	$-0.423959\pi$
$643$	12.0003	0.473246	0.236623	+	0.971602i	$0.423959\pi$
$644$	−21.5566	−0.849448
$645$	0	0
$646$	0	0
$647$	−36.3971	−1.43092	−0.715458	−	0.698656i	$-0.753782\pi$
$647$	−36.3971	−1.43092	−0.715458	+	0.698656i	$0.753782\pi$
$648$	18.4330	0.724116
$649$	−5.88081	−0.230842
$650$	0	0
$651$	−3.05607	−0.119777
$652$	−2.30311	−0.0901967
$653$	−31.7999	−1.24443	−0.622214	−	0.782847i	$-0.713767\pi$
$653$	−31.7999	−1.24443	−0.622214	+	0.782847i	$0.713767\pi$
$654$	16.8654	0.659491
$655$	0	0
$656$	−18.4979	−0.722220
$657$	−8.47192	−0.330521
$658$	−5.89085	−0.229649
$659$	26.8414	1.04559	0.522796	−	0.852458i	$-0.324889\pi$
$659$	26.8414	1.04559	0.522796	+	0.852458i	$0.324889\pi$
$660$	0	0
$661$	−34.2970	−1.33400	−0.667000	−	0.745057i	$-0.732422\pi$
$661$	−34.2970	−1.33400	−0.667000	+	0.745057i	$0.732422\pi$
$662$	15.1225	0.587754
$663$	−47.0715	−1.82810
$664$	−12.0540	−0.467784
$665$	0	0
$666$	2.31983	0.0898917
$667$	32.0236	1.23996
$668$	−14.4490	−0.559050
$669$	−38.0358	−1.47055
$670$	0	0
$671$	−22.9218	−0.884885
$672$	−18.8923	−0.728786
$673$	21.7196	0.837230	0.418615	−	0.908164i	$-0.362516\pi$
$673$	21.7196	0.837230	0.418615	+	0.908164i	$0.362516\pi$
$674$	1.16332	0.0448096
$675$	0	0
$676$	−11.3741	−0.437465
$677$	8.53064	0.327859	0.163930	−	0.986472i	$-0.447583\pi$
$677$	8.53064	0.327859	0.163930	+	0.986472i	$0.447583\pi$
$678$	1.68085	0.0645525
$679$	−14.0451	−0.539001
$680$	0	0
$681$	−12.7977	−0.490409
$682$	−0.785303	−0.0300708
$683$	−17.3190	−0.662695	−0.331347	−	0.943509i	$-0.607503\pi$
$683$	−17.3190	−0.662695	−0.331347	+	0.943509i	$0.607503\pi$
$684$	0	0
$685$	0	0
$686$	−9.03204	−0.344845
$687$	39.9206	1.52306
$688$	−8.95938	−0.341573
$689$	16.9262	0.644838
$690$	0	0
$691$	17.2709	0.657014	0.328507	−	0.944501i	$-0.393454\pi$
$691$	17.2709	0.657014	0.328507	+	0.944501i	$0.393454\pi$
$692$	4.78122	0.181755
$693$	−3.94061	−0.149691
$694$	10.6966	0.406036
$695$	0	0
$696$	18.3846	0.696868
$697$	−35.7765	−1.35513
$698$	−1.11553	−0.0422234
$699$	−23.5780	−0.891802
$700$	0	0
$701$	21.8816	0.826457	0.413228	−	0.910627i	$-0.364401\pi$
$701$	21.8816	0.826457	0.413228	+	0.910627i	$0.364401\pi$
$702$	8.39162	0.316721
$703$	0	0
$704$	8.19336	0.308799
$705$	0	0
$706$	16.0621	0.604507
$707$	25.1366	0.945360
$708$	8.97305	0.337228
$709$	20.5621	0.772224	0.386112	−	0.922452i	$-0.373818\pi$
$709$	20.5621	0.772224	0.386112	+	0.922452i	$0.373818\pi$
$710$	0	0
$711$	1.99998	0.0750052
$712$	3.98443	0.149323
$713$	4.40873	0.165108
$714$	−9.91588	−0.371092
$715$	0	0
$716$	−14.5679	−0.544429
$717$	11.9856	0.447612
$718$	−2.59035	−0.0966709
$719$	15.6722	0.584473	0.292237	−	0.956346i	$-0.405600\pi$
$719$	15.6722	0.584473	0.292237	+	0.956346i	$0.405600\pi$
$720$	0	0
$721$	26.6249	0.991561
$722$	0	0
$723$	14.2323	0.529304
$724$	−38.6626	−1.43688
$725$	0	0
$726$	4.99684	0.185450
$727$	43.5233	1.61419	0.807095	−	0.590421i	$-0.201038\pi$
$727$	43.5233	1.61419	0.807095	+	0.590421i	$0.201038\pi$
$728$	−15.4622	−0.573068
$729$	15.9815	0.591907
$730$	0	0
$731$	−17.3282	−0.640908
$732$	34.9745	1.29269
$733$	12.6904	0.468729	0.234364	−	0.972149i	$-0.424699\pi$
$733$	12.6904	0.468729	0.234364	+	0.972149i	$0.424699\pi$
$734$	−2.67705	−0.0988116
$735$	0	0
$736$	27.2543	1.00461
$737$	3.92639	0.144630
$738$	−2.43637	−0.0896839
$739$	28.1664	1.03612	0.518059	−	0.855345i	$-0.326655\pi$
$739$	28.1664	1.03612	0.518059	+	0.855345i	$0.326655\pi$
$740$	0	0
$741$	0	0
$742$	3.56561	0.130898
$743$	25.5639	0.937849	0.468924	−	0.883238i	$-0.344642\pi$
$743$	25.5639	0.937849	0.468924	+	0.883238i	$0.344642\pi$
$744$	2.53103	0.0927922
$745$	0	0
$746$	−2.00798	−0.0735175
$747$	5.85641	0.214275
$748$	22.6880	0.829557
$749$	−31.2683	−1.14252
$750$	0	0
$751$	34.6687	1.26508	0.632539	−	0.774529i	$-0.282013\pi$
$751$	34.6687	1.26508	0.632539	+	0.774529i	$0.282013\pi$
$752$	−17.9968	−0.656274
$753$	47.3293	1.72477
$754$	10.8744	0.396023
$755$	0	0
$756$	−15.7402	−0.572465
$757$	45.7467	1.66269	0.831346	−	0.555755i	$-0.187571\pi$
$757$	45.7467	1.66269	0.831346	+	0.555755i	$0.187571\pi$
$758$	5.98471	0.217374
$759$	26.2514	0.952867
$760$	0	0
$761$	2.85442	0.103472	0.0517362	−	0.998661i	$-0.483524\pi$
$761$	2.85442	0.103472	0.0517362	+	0.998661i	$0.483524\pi$
$762$	−18.6738	−0.676481
$763$	−39.5248	−1.43089
$764$	35.2311	1.27462
$765$	0	0
$766$	4.57177	0.165185
$767$	11.2111	0.404809
$768$	−4.26233	−0.153804
$769$	19.5208	0.703937	0.351969	−	0.936012i	$-0.385512\pi$
$769$	19.5208	0.703937	0.351969	+	0.936012i	$0.385512\pi$
$770$	0	0
$771$	−23.9477	−0.862455
$772$	0.869107	0.0312798
$773$	7.24881	0.260722	0.130361	−	0.991467i	$-0.458386\pi$
$773$	7.24881	0.260722	0.130361	+	0.991467i	$0.458386\pi$
$774$	−1.18005	−0.0424159
$775$	0	0
$776$	11.6322	0.417570
$777$	−25.1054	−0.900652
$778$	−5.12753	−0.183831
$779$	0	0
$780$	0	0
$781$	−22.7349	−0.813520
$782$	14.3048	0.511539
$783$	23.3830	0.835641
$784$	−7.78906	−0.278181
$785$	0	0
$786$	1.47090	0.0524654
$787$	4.20711	0.149967	0.0749837	−	0.997185i	$-0.476110\pi$
$787$	4.20711	0.149967	0.0749837	+	0.997185i	$0.476110\pi$
$788$	−2.26896	−0.0808283
$789$	24.2372	0.862867
$790$	0	0
$791$	−3.93912	−0.140059
$792$	3.26361	0.115967
$793$	43.6977	1.55175
$794$	2.31091	0.0820113
$795$	0	0
$796$	−37.1398	−1.31639
$797$	25.6411	0.908253	0.454127	−	0.890937i	$-0.349951\pi$
$797$	25.6411	0.908253	0.454127	+	0.890937i	$0.349951\pi$
$798$	0	0
$799$	−34.8074	−1.23140
$800$	0	0
$801$	−1.93584	−0.0683994
$802$	7.67627	0.271059
$803$	23.5596	0.831399
$804$	−5.99096	−0.211285
$805$	0	0
$806$	1.49709	0.0527328
$807$	9.66444	0.340204
$808$	−20.8181	−0.732380
$809$	−0.516056	−0.0181436	−0.00907179	−	0.999959i	$-0.502888\pi$
$809$	−0.516056	−0.0181436	−0.00907179	+	0.999959i	$0.502888\pi$
$810$	0	0
$811$	−24.0377	−0.844078	−0.422039	−	0.906578i	$-0.638685\pi$
$811$	−24.0377	−0.844078	−0.422039	+	0.906578i	$0.638685\pi$
$812$	−20.3972	−0.715800
$813$	13.5060	0.473676
$814$	−6.45123	−0.226115
$815$	0	0
$816$	−30.2934	−1.06048
$817$	0	0
$818$	−11.7150	−0.409605
$819$	7.51232	0.262502
$820$	0	0
$821$	38.7573	1.35264	0.676320	−	0.736608i	$-0.263574\pi$
$821$	38.7573	1.35264	0.676320	+	0.736608i	$0.263574\pi$
$822$	15.2022	0.530238
$823$	−3.48827	−0.121593	−0.0607967	−	0.998150i	$-0.519364\pi$
$823$	−3.48827	−0.121593	−0.0607967	+	0.998150i	$0.519364\pi$
$824$	−22.0507	−0.768173
$825$	0	0
$826$	2.36168	0.0821734
$827$	27.4821	0.955645	0.477823	−	0.878456i	$-0.341426\pi$
$827$	27.4821	0.955645	0.477823	+	0.878456i	$0.341426\pi$
$828$	−8.67395	−0.301441
$829$	−8.60945	−0.299019	−0.149509	−	0.988760i	$-0.547769\pi$
$829$	−8.60945	−0.299019	−0.149509	+	0.988760i	$0.547769\pi$
$830$	0	0
$831$	7.75545	0.269034
$832$	−15.6197	−0.541516
$833$	−15.0648	−0.521963
$834$	−10.8394	−0.375336
$835$	0	0
$836$	0	0
$837$	3.21917	0.111271
$838$	2.59415	0.0896133
$839$	11.9397	0.412206	0.206103	−	0.978530i	$-0.433922\pi$
$839$	11.9397	0.412206	0.206103	+	0.978530i	$0.433922\pi$
$840$	0	0
$841$	1.30126	0.0448710
$842$	11.3695	0.391817
$843$	−61.0520	−2.10274
$844$	−12.6079	−0.433983
$845$	0	0
$846$	−2.37037	−0.0814949
$847$	−11.7103	−0.402370
$848$	10.8931	0.374069
$849$	−20.7954	−0.713695
$850$	0	0
$851$	36.2175	1.24152
$852$	34.6894	1.18844
$853$	−28.9175	−0.990117	−0.495059	−	0.868860i	$-0.664853\pi$
$853$	−28.9175	−0.990117	−0.495059	+	0.868860i	$0.664853\pi$
$854$	9.20518	0.314995
$855$	0	0
$856$	25.8964	0.885121
$857$	55.2147	1.88610	0.943050	−	0.332651i	$-0.107943\pi$
$857$	55.2147	1.88610	0.943050	+	0.332651i	$0.107943\pi$
$858$	8.91431	0.304330
$859$	−26.6572	−0.909532	−0.454766	−	0.890611i	$-0.650277\pi$
$859$	−26.6572	−0.909532	−0.454766	+	0.890611i	$0.650277\pi$
$860$	0	0
$861$	26.3666	0.898570
$862$	−8.43154	−0.287180
$863$	1.21123	0.0412307	0.0206154	−	0.999787i	$-0.493437\pi$
$863$	1.21123	0.0412307	0.0206154	+	0.999787i	$0.493437\pi$
$864$	19.9006	0.677031
$865$	0	0
$866$	−3.82551	−0.129996
$867$	−25.3238	−0.860042
$868$	−2.80810	−0.0953131
$869$	−5.56176	−0.188670
$870$	0	0
$871$	−7.48522	−0.253627
$872$	32.7344	1.10853
$873$	−5.65148	−0.191274
$874$	0	0
$875$	0	0
$876$	−35.9476	−1.21456
$877$	−49.5420	−1.67291	−0.836457	−	0.548032i	$-0.815377\pi$
$877$	−49.5420	−1.67291	−0.836457	+	0.548032i	$0.815377\pi$
$878$	−0.923597	−0.0311699
$879$	38.4055	1.29538
$880$	0	0
$881$	−30.5639	−1.02972	−0.514861	−	0.857273i	$-0.672157\pi$
$881$	−30.5639	−1.02972	−0.514861	+	0.857273i	$0.672157\pi$
$882$	−1.02590	−0.0345440
$883$	−5.57841	−0.187729	−0.0938643	−	0.995585i	$-0.529922\pi$
$883$	−5.57841	−0.187729	−0.0938643	+	0.995585i	$0.529922\pi$
$884$	−43.2521	−1.45473
$885$	0	0
$886$	5.41061	0.181773
$887$	0.666360	0.0223742	0.0111871	−	0.999937i	$-0.496439\pi$
$887$	0.666360	0.0223742	0.0111871	+	0.999937i	$0.496439\pi$
$888$	20.7923	0.697744
$889$	43.7628	1.46776
$890$	0	0
$891$	24.9048	0.834343
$892$	−34.9497	−1.17020
$893$	0	0
$894$	−3.83310	−0.128198
$895$	0	0
$896$	−22.5994	−0.754992
$897$	−50.0454	−1.67097
$898$	3.36760	0.112378
$899$	4.17161	0.139131
$900$	0	0
$901$	21.0682	0.701882
$902$	6.77530	0.225593
$903$	12.7706	0.424978
$904$	3.26238	0.108505
$905$	0	0
$906$	−3.90984	−0.129896
$907$	−52.7812	−1.75257	−0.876286	−	0.481792i	$-0.839986\pi$
$907$	−52.7812	−1.75257	−0.876286	+	0.481792i	$0.839986\pi$
$908$	−11.7593	−0.390246
$909$	10.1145	0.335477
$910$	0	0
$911$	−13.0586	−0.432650	−0.216325	−	0.976321i	$-0.569407\pi$
$911$	−13.0586	−0.432650	−0.216325	+	0.976321i	$0.569407\pi$
$912$	0	0
$913$	−16.2861	−0.538992
$914$	−6.29357	−0.208173
$915$	0	0
$916$	36.6814	1.21199
$917$	−3.44712	−0.113834
$918$	10.4451	0.344739
$919$	−46.0539	−1.51918	−0.759589	−	0.650403i	$-0.774600\pi$
$919$	−46.0539	−1.51918	−0.759589	+	0.650403i	$0.774600\pi$
$920$	0	0
$921$	44.2751	1.45892
$922$	−7.94271	−0.261579
$923$	43.3416	1.42661
$924$	−16.7206	−0.550067
$925$	0	0
$926$	7.45627	0.245028
$927$	10.7133	0.351872
$928$	25.7885	0.846548
$929$	30.9736	1.01621	0.508105	−	0.861295i	$-0.330346\pi$
$929$	30.9736	1.01621	0.508105	+	0.861295i	$0.330346\pi$
$930$	0	0
$931$	0	0
$932$	−21.6649	−0.709657
$933$	−48.6426	−1.59249
$934$	7.18568	0.235123
$935$	0	0
$936$	−6.22170	−0.203363
$937$	34.8133	1.13730	0.568650	−	0.822580i	$-0.307466\pi$
$937$	34.8133	1.13730	0.568650	+	0.822580i	$0.307466\pi$
$938$	−1.57680	−0.0514845
$939$	43.4470	1.41784
$940$	0	0
$941$	−16.2153	−0.528604	−0.264302	−	0.964440i	$-0.585142\pi$
$941$	−16.2153	−0.528604	−0.264302	+	0.964440i	$0.585142\pi$
$942$	17.4492	0.568525
$943$	−38.0368	−1.23865
$944$	7.21502	0.234829
$945$	0	0
$946$	3.28159	0.106694
$947$	−14.6403	−0.475746	−0.237873	−	0.971296i	$-0.576450\pi$
$947$	−14.6403	−0.475746	−0.237873	+	0.971296i	$0.576450\pi$
$948$	8.48624	0.275620
$949$	−44.9136	−1.45796
$950$	0	0
$951$	3.99112	0.129421
$952$	−19.2459	−0.623763
$953$	−40.8271	−1.32252	−0.661260	−	0.750156i	$-0.729978\pi$
$953$	−40.8271	−1.32252	−0.661260	+	0.750156i	$0.729978\pi$
$954$	1.43473	0.0464512
$955$	0	0
$956$	11.0131	0.356190
$957$	24.8395	0.802947
$958$	3.32352	0.107378
$959$	−35.6269	−1.15045
$960$	0	0
$961$	−30.4257	−0.981474
$962$	12.2985	0.396520
$963$	−12.5818	−0.405442
$964$	13.0775	0.421197
$965$	0	0
$966$	−10.5423	−0.339194
$967$	24.1608	0.776958	0.388479	−	0.921458i	$-0.373001\pi$
$967$	24.1608	0.776958	0.388479	+	0.921458i	$0.373001\pi$
$968$	9.69845	0.311720
$969$	0	0
$970$	0	0
$971$	27.7592	0.890836	0.445418	−	0.895323i	$-0.353055\pi$
$971$	27.7592	0.890836	0.445418	+	0.895323i	$0.353055\pi$
$972$	−15.0865	−0.483899
$973$	25.4024	0.814364
$974$	9.07201	0.290686
$975$	0	0
$976$	28.1221	0.900168
$977$	3.56499	0.114054	0.0570270	−	0.998373i	$-0.481838\pi$
$977$	3.56499	0.114054	0.0570270	+	0.998373i	$0.481838\pi$
$978$	−1.12635	−0.0360166
$979$	5.38337	0.172053
$980$	0	0
$981$	−15.9040	−0.507776
$982$	4.19403	0.133837
$983$	−1.63550	−0.0521643	−0.0260822	−	0.999660i	$-0.508303\pi$
$983$	−1.63550	−0.0521643	−0.0260822	+	0.999660i	$0.508303\pi$
$984$	−21.8368	−0.696131
$985$	0	0
$986$	13.5354	0.431056
$987$	25.6523	0.816521
$988$	0	0
$989$	−18.4230	−0.585818
$990$	0	0
$991$	1.50405	0.0477778	0.0238889	−	0.999715i	$-0.492395\pi$
$991$	1.50405	0.0477778	0.0238889	+	0.999715i	$0.492395\pi$
$992$	3.55033	0.112723
$993$	−65.8526	−2.08977
$994$	9.13015	0.289591
$995$	0	0
$996$	24.8497	0.787392
$997$	−51.4138	−1.62829	−0.814146	−	0.580660i	$-0.802795\pi$
$997$	−51.4138	−1.62829	−0.814146	+	0.580660i	$0.802795\pi$
$998$	−10.7675	−0.340841
$999$	26.4453	0.836692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cu.1.15		24
5.2	odd	4		1805.2.b.k.1084.15		24
5.3	odd	4		1805.2.b.k.1084.10		24
5.4	even	2	inner	9025.2.a.cu.1.10		24
19.4	even	9		475.2.l.f.301.5		48
19.5	even	9		475.2.l.f.101.5		48
19.18	odd	2		9025.2.a.ct.1.10		24
95.4	even	18		475.2.l.f.301.4		48
95.18	even	4		1805.2.b.l.1084.15		24
95.23	odd	36		95.2.p.a.54.5	yes	48
95.24	even	18		475.2.l.f.101.4		48
95.37	even	4		1805.2.b.l.1084.10		24
95.42	odd	36		95.2.p.a.54.4	yes	48
95.43	odd	36		95.2.p.a.44.4	✓	48
95.62	odd	36		95.2.p.a.44.5	yes	48
95.94	odd	2		9025.2.a.ct.1.15		24
285.23	even	36		855.2.da.b.244.4		48
285.62	even	36		855.2.da.b.424.4		48
285.137	even	36		855.2.da.b.244.5		48
285.233	even	36		855.2.da.b.424.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.44.4	✓	48	95.43	odd	36
95.2.p.a.44.5	yes	48	95.62	odd	36
95.2.p.a.54.4	yes	48	95.42	odd	36
95.2.p.a.54.5	yes	48	95.23	odd	36
475.2.l.f.101.4		48	95.24	even	18
475.2.l.f.101.5		48	19.5	even	9
475.2.l.f.301.4		48	95.4	even	18
475.2.l.f.301.5		48	19.4	even	9
855.2.da.b.244.4		48	285.23	even	36
855.2.da.b.244.5		48	285.137	even	36
855.2.da.b.424.4		48	285.62	even	36
855.2.da.b.424.5		48	285.233	even	36
1805.2.b.k.1084.10		24	5.3	odd	4
1805.2.b.k.1084.15		24	5.2	odd	4
1805.2.b.l.1084.10		24	95.37	even	4
1805.2.b.l.1084.15		24	95.18	even	4
9025.2.a.ct.1.10		24	19.18	odd	2
9025.2.a.ct.1.15		24	95.94	odd	2
9025.2.a.cu.1.10		24	5.4	even	2	inner
9025.2.a.cu.1.15		24	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+0.449373 q^{2} -1.95684 q^{3} -1.79806 q^{4} -0.879352 q^{6} +2.06079 q^{7} -1.70675 q^{8} +0.829224 q^{9} -2.30599 q^{11} +3.51852 q^{12} +4.39611 q^{13} +0.926065 q^{14} +2.82916 q^{16} +5.47185 q^{17} +0.372631 q^{18} -4.03264 q^{21} -1.03625 q^{22} +5.81755 q^{23} +3.33983 q^{24} +1.97549 q^{26} +4.24786 q^{27} -3.70544 q^{28} +5.50466 q^{29} +0.757832 q^{31} +4.68485 q^{32} +4.51245 q^{33} +2.45890 q^{34} -1.49100 q^{36} +6.22555 q^{37} -8.60248 q^{39} -6.53829 q^{41} -1.81216 q^{42} -3.16680 q^{43} +4.14632 q^{44} +2.61425 q^{46} -6.36116 q^{47} -5.53621 q^{48} -2.75314 q^{49} -10.7075 q^{51} -7.90448 q^{52} +3.85028 q^{53} +1.90888 q^{54} -3.51725 q^{56} +2.47365 q^{58} +2.55023 q^{59} +9.94010 q^{61} +0.340550 q^{62} +1.70886 q^{63} -3.55308 q^{64} +2.02778 q^{66} -1.70269 q^{67} -9.83874 q^{68} -11.3840 q^{69} +9.85909 q^{71} -1.41528 q^{72} -10.2167 q^{73} +2.79760 q^{74} -4.75216 q^{77} -3.86572 q^{78} +2.41187 q^{79} -10.8001 q^{81} -2.93813 q^{82} +7.06253 q^{83} +7.25095 q^{84} -1.42307 q^{86} -10.7717 q^{87} +3.93574 q^{88} -2.33452 q^{89} +9.05946 q^{91} -10.4603 q^{92} -1.48296 q^{93} -2.85854 q^{94} -9.16749 q^{96} -6.81539 q^{97} -1.23719 q^{98} -1.91218 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} + 24 q^{14} + 6 q^{16} + 6 q^{21} - 42 q^{24} - 12 q^{26} + 36 q^{29} + 42 q^{31} + 6 q^{34} - 6 q^{36} + 24 q^{39} + 60 q^{41} - 30 q^{44} + 6 q^{46} + 12 q^{49}+ \cdots - 120 q^{96}+O(q^{100}) \) 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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