LMFDB - Embedded newform 4925.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4925,2,Mod(1,4925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4925, 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("4925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4925 = 5^{2} \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4925.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:	$39.3263229955$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.24217.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} - x^{2} + 3x + 1 $ x^5 - 5x^3 - x^2 + 3x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 197)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.17442$ of defining polynomial
Character	$\chi$	$=$	4925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.17442 q^{2} +3.26823 q^{3} +2.72812 q^{4} +7.10652 q^{6} +0.641841 q^{7} +1.58325 q^{8} +7.68134 q^{9} -0.802676 q^{11} +8.91614 q^{12} +6.11583 q^{13} +1.39564 q^{14} -2.01359 q^{16} -5.40923 q^{17} +16.7025 q^{18} -3.52027 q^{19} +2.09769 q^{21} -1.74536 q^{22} +5.84217 q^{23} +5.17442 q^{24} +13.2984 q^{26} +15.2997 q^{27} +1.75102 q^{28} -0.595055 q^{29} +3.76560 q^{31} -7.54490 q^{32} -2.62333 q^{33} -11.7620 q^{34} +20.9556 q^{36} +8.25810 q^{37} -7.65456 q^{38} +19.9880 q^{39} -10.3739 q^{41} +4.56126 q^{42} -1.82233 q^{43} -2.18980 q^{44} +12.7034 q^{46} -2.71581 q^{47} -6.58088 q^{48} -6.58804 q^{49} -17.6786 q^{51} +16.6847 q^{52} -4.58493 q^{53} +33.2680 q^{54} +1.01619 q^{56} -11.5051 q^{57} -1.29390 q^{58} -10.9514 q^{59} -7.29900 q^{61} +8.18801 q^{62} +4.93020 q^{63} -12.3786 q^{64} -5.70424 q^{66} +3.23179 q^{67} -14.7570 q^{68} +19.0936 q^{69} -6.41588 q^{71} +12.1615 q^{72} -1.90976 q^{73} +17.9566 q^{74} -9.60373 q^{76} -0.515191 q^{77} +43.4623 q^{78} +13.4138 q^{79} +26.9589 q^{81} -22.5573 q^{82} -1.25586 q^{83} +5.72275 q^{84} -3.96252 q^{86} -1.94478 q^{87} -1.27084 q^{88} +7.71576 q^{89} +3.92539 q^{91} +15.9382 q^{92} +12.3069 q^{93} -5.90532 q^{94} -24.6585 q^{96} +13.4118 q^{97} -14.3252 q^{98} -6.16563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 8 q^{3} - 2 q^{6} + 10 q^{7} + 3 q^{8} + 13 q^{9} - 8 q^{11} + 12 q^{12} + 8 q^{13} - 3 q^{14} - 2 q^{16} - 9 q^{17} + q^{18} - 16 q^{19} + 14 q^{21} - 9 q^{22} + q^{23} + 15 q^{24} + 11 q^{26}+ \cdots + 11 q^{99}+O(q^{100}) $ 5 * q + 8 * q^3 - 2 * q^6 + 10 * q^7 + 3 * q^8 + 13 * q^9 - 8 * q^11 + 12 * q^12 + 8 * q^13 - 3 * q^14 - 2 * q^16 - 9 * q^17 + q^18 - 16 * q^19 + 14 * q^21 - 9 * q^22 + q^23 + 15 * q^24 + 11 * q^26 + 29 * q^27 + 2 * q^28 + 2 * q^29 + 2 * q^31 - 4 * q^32 + 2 * q^33 - 20 * q^34 + 40 * q^36 + 17 * q^37 - 5 * q^38 + 23 * q^39 - 5 * q^41 - 29 * q^42 + 26 * q^43 + 16 * q^44 + 13 * q^46 - 16 * q^47 - 14 * q^48 + 11 * q^49 - q^51 + 3 * q^52 - 2 * q^53 + 9 * q^54 - 10 * q^56 - 13 * q^57 + 5 * q^58 - 13 * q^59 - 3 * q^61 + 22 * q^62 + 40 * q^63 - 17 * q^64 - 10 * q^66 + 40 * q^67 - 5 * q^68 + 21 * q^69 - 5 * q^71 + 13 * q^72 + 9 * q^73 + 23 * q^74 - 5 * q^76 - 30 * q^77 + 61 * q^78 + 13 * q^79 + 49 * q^81 - 34 * q^82 + 17 * q^83 + 32 * q^84 - 23 * q^86 - 15 * q^87 + 9 * q^88 + 10 * q^89 - 29 * q^91 + 22 * q^92 - 11 * q^93 + 5 * q^94 - 19 * q^96 + 42 * q^97 - 24 * q^98 + 11 * q^99

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 $

$2$	2.17442	1.53755	0.768775	−	0.639519i	$-0.220866\pi$
$2$	2.17442	1.53755	0.768775	+	0.639519i	$0.220866\pi$
$3$	3.26823	1.88691	0.943457	−	0.331494i	$-0.107553\pi$
$3$	3.26823	1.88691	0.943457	+	0.331494i	$0.107553\pi$
$4$	2.72812	1.36406
$5$	0	0
$5$	0	0
$6$	7.10652	2.90123
$7$	0.641841	0.242593	0.121297	−	0.992616i	$-0.461295\pi$
$7$	0.641841	0.242593	0.121297	+	0.992616i	$0.461295\pi$
$8$	1.58325	0.559763
$9$	7.68134	2.56045
$10$	0	0
$11$	−0.802676	−0.242016	−0.121008	−	0.992652i	$-0.538613\pi$
$11$	−0.802676	−0.242016	−0.121008	+	0.992652i	$0.538613\pi$
$12$	8.91614	2.57387
$13$	6.11583	1.69623	0.848113	−	0.529815i	$-0.177739\pi$
$13$	6.11583	1.69623	0.848113	+	0.529815i	$0.177739\pi$
$14$	1.39564	0.372999
$15$	0	0
$16$	−2.01359	−0.503398
$17$	−5.40923	−1.31193	−0.655965	−	0.754791i	$-0.727738\pi$
$17$	−5.40923	−1.31193	−0.655965	+	0.754791i	$0.727738\pi$
$18$	16.7025	3.93681
$19$	−3.52027	−0.807605	−0.403802	−	0.914846i	$-0.632312\pi$
$19$	−3.52027	−0.807605	−0.403802	+	0.914846i	$0.632312\pi$
$20$	0	0
$21$	2.09769	0.457753
$22$	−1.74536	−0.372112
$23$	5.84217	1.21818	0.609088	−	0.793102i	$-0.291535\pi$
$23$	5.84217	1.21818	0.609088	+	0.793102i	$0.291535\pi$
$24$	5.17442	1.05623
$25$	0	0
$26$	13.2984	2.60803
$27$	15.2997	2.94443
$28$	1.75102	0.330912
$29$	−0.595055	−0.110499	−0.0552495	−	0.998473i	$-0.517595\pi$
$29$	−0.595055	−0.110499	−0.0552495	+	0.998473i	$0.517595\pi$
$30$	0	0
$31$	3.76560	0.676322	0.338161	−	0.941088i	$-0.390195\pi$
$31$	3.76560	0.676322	0.338161	+	0.941088i	$0.390195\pi$
$32$	−7.54490	−1.33376
$33$	−2.62333	−0.456663
$34$	−11.7620	−2.01716
$35$	0	0
$36$	20.9556	3.49261
$37$	8.25810	1.35762	0.678812	−	0.734312i	$-0.262495\pi$
$37$	8.25810	1.35762	0.678812	+	0.734312i	$0.262495\pi$
$38$	−7.65456	−1.24173
$39$	19.9880	3.20063
$40$	0	0
$41$	−10.3739	−1.62014	−0.810068	−	0.586336i	$-0.800570\pi$
$41$	−10.3739	−1.62014	−0.810068	+	0.586336i	$0.800570\pi$
$42$	4.56126	0.703818
$43$	−1.82233	−0.277903	−0.138951	−	0.990299i	$-0.544373\pi$
$43$	−1.82233	−0.277903	−0.138951	+	0.990299i	$0.544373\pi$
$44$	−2.18980	−0.330125
$45$	0	0
$46$	12.7034	1.87301
$47$	−2.71581	−0.396141	−0.198071	−	0.980188i	$-0.563468\pi$
$47$	−2.71581	−0.396141	−0.198071	+	0.980188i	$0.563468\pi$
$48$	−6.58088	−0.949868
$49$	−6.58804	−0.941149
$50$	0	0
$51$	−17.6786	−2.47550
$52$	16.6847	2.31376
$53$	−4.58493	−0.629788	−0.314894	−	0.949127i	$-0.601969\pi$
$53$	−4.58493	−0.629788	−0.314894	+	0.949127i	$0.601969\pi$
$54$	33.2680	4.52721
$55$	0	0
$56$	1.01619	0.135795
$57$	−11.5051	−1.52388
$58$	−1.29390	−0.169898
$59$	−10.9514	−1.42574	−0.712872	−	0.701294i	$-0.752606\pi$
$59$	−10.9514	−1.42574	−0.712872	+	0.701294i	$0.752606\pi$
$60$	0	0
$61$	−7.29900	−0.934542	−0.467271	−	0.884114i	$-0.654763\pi$
$61$	−7.29900	−0.934542	−0.467271	+	0.884114i	$0.654763\pi$
$62$	8.18801	1.03988
$63$	4.93020	0.621147
$64$	−12.3786	−1.54733
$65$	0	0
$66$	−5.70424	−0.702143
$67$	3.23179	0.394827	0.197413	−	0.980320i	$-0.436746\pi$
$67$	3.23179	0.394827	0.197413	+	0.980320i	$0.436746\pi$
$68$	−14.7570	−1.78955
$69$	19.0936	2.29860
$70$	0	0
$71$	−6.41588	−0.761425	−0.380712	−	0.924694i	$-0.624321\pi$
$71$	−6.41588	−0.761425	−0.380712	+	0.924694i	$0.624321\pi$
$72$	12.1615	1.43324
$73$	−1.90976	−0.223521	−0.111760	−	0.993735i	$-0.535649\pi$
$73$	−1.90976	−0.223521	−0.111760	+	0.993735i	$0.535649\pi$
$74$	17.9566	2.08741
$75$	0	0
$76$	−9.60373	−1.10162
$77$	−0.515191	−0.0587114
$78$	43.4623	4.92114
$79$	13.4138	1.50918	0.754588	−	0.656199i	$-0.227837\pi$
$79$	13.4138	1.50918	0.754588	+	0.656199i	$0.227837\pi$
$80$	0	0
$81$	26.9589	2.99544
$82$	−22.5573	−2.49104
$83$	−1.25586	−0.137849	−0.0689245	−	0.997622i	$-0.521957\pi$
$83$	−1.25586	−0.137849	−0.0689245	+	0.997622i	$0.521957\pi$
$84$	5.72275	0.624403
$85$	0	0
$86$	−3.96252	−0.427290
$87$	−1.94478	−0.208502
$88$	−1.27084	−0.135472
$89$	7.71576	0.817868	0.408934	−	0.912564i	$-0.365901\pi$
$89$	7.71576	0.817868	0.408934	+	0.912564i	$0.365901\pi$
$90$	0	0
$91$	3.92539	0.411493
$92$	15.9382	1.66167
$93$	12.3069	1.27616
$94$	−5.90532	−0.609087
$95$	0	0
$96$	−24.6585	−2.51670
$97$	13.4118	1.36177	0.680883	−	0.732393i	$-0.261596\pi$
$97$	13.4118	1.36177	0.680883	+	0.732393i	$0.261596\pi$
$98$	−14.3252	−1.44706
$99$	−6.16563	−0.619669
$100$	0	0
$101$	6.25278	0.622175	0.311087	−	0.950381i	$-0.399307\pi$
$101$	6.25278	0.622175	0.311087	+	0.950381i	$0.399307\pi$
$102$	−38.4408	−3.80621
$103$	18.4509	1.81802	0.909012	−	0.416770i	$-0.136838\pi$
$103$	18.4509	1.81802	0.909012	+	0.416770i	$0.136838\pi$
$104$	9.68289	0.949485
$105$	0	0
$106$	−9.96958	−0.968331
$107$	−6.56392	−0.634558	−0.317279	−	0.948332i	$-0.602769\pi$
$107$	−6.56392	−0.634558	−0.317279	+	0.948332i	$0.602769\pi$
$108$	41.7394	4.01638
$109$	12.4633	1.19377	0.596884	−	0.802328i	$-0.296405\pi$
$109$	12.4633	1.19377	0.596884	+	0.802328i	$0.296405\pi$
$110$	0	0
$111$	26.9894	2.56172
$112$	−1.29241	−0.122121
$113$	−4.47578	−0.421046	−0.210523	−	0.977589i	$-0.567517\pi$
$113$	−4.47578	−0.421046	−0.210523	+	0.977589i	$0.567517\pi$
$114$	−25.0169	−2.34304
$115$	0	0
$116$	−1.62338	−0.150727
$117$	46.9778	4.34310
$118$	−23.8129	−2.19215
$119$	−3.47187	−0.318265
$120$	0	0
$121$	−10.3557	−0.941428
$122$	−15.8711	−1.43691
$123$	−33.9044	−3.05706
$124$	10.2730	0.922545
$125$	0	0
$126$	10.7203	0.955045
$127$	−18.2081	−1.61571	−0.807854	−	0.589383i	$-0.799371\pi$
$127$	−18.2081	−1.61571	−0.807854	+	0.589383i	$0.799371\pi$
$128$	−11.8266	−1.04533
$129$	−5.95580	−0.524379
$130$	0	0
$131$	−2.16344	−0.189021	−0.0945103	−	0.995524i	$-0.530129\pi$
$131$	−2.16344	−0.189021	−0.0945103	+	0.995524i	$0.530129\pi$
$132$	−7.15677	−0.622917
$133$	−2.25945	−0.195919
$134$	7.02729	0.607066
$135$	0	0
$136$	−8.56415	−0.734370
$137$	−4.50345	−0.384756	−0.192378	−	0.981321i	$-0.561620\pi$
$137$	−4.50345	−0.384756	−0.192378	+	0.981321i	$0.561620\pi$
$138$	41.5175	3.53421
$139$	−2.90133	−0.246087	−0.123044	−	0.992401i	$-0.539266\pi$
$139$	−2.90133	−0.246087	−0.123044	+	0.992401i	$0.539266\pi$
$140$	0	0
$141$	−8.87589	−0.747485
$142$	−13.9508	−1.17073
$143$	−4.90903	−0.410514
$144$	−15.4671	−1.28892
$145$	0	0
$146$	−4.15263	−0.343674
$147$	−21.5312	−1.77587
$148$	22.5291	1.85188
$149$	4.46127	0.365482	0.182741	−	0.983161i	$-0.441503\pi$
$149$	4.46127	0.365482	0.182741	+	0.983161i	$0.441503\pi$
$150$	0	0
$151$	4.67943	0.380806	0.190403	−	0.981706i	$-0.439020\pi$
$151$	4.67943	0.380806	0.190403	+	0.981706i	$0.439020\pi$
$152$	−5.57346	−0.452067
$153$	−41.5501	−3.35913
$154$	−1.12024	−0.0902718
$155$	0	0
$156$	54.5296	4.36586
$157$	7.27293	0.580443	0.290222	−	0.956959i	$-0.406271\pi$
$157$	7.27293	0.580443	0.290222	+	0.956959i	$0.406271\pi$
$158$	29.1674	2.32043
$159$	−14.9846	−1.18836
$160$	0	0
$161$	3.74975	0.295522
$162$	58.6202	4.60563
$163$	−9.39619	−0.735967	−0.367983	−	0.929832i	$-0.619952\pi$
$163$	−9.39619	−0.735967	−0.367983	+	0.929832i	$0.619952\pi$
$164$	−28.3014	−2.20997
$165$	0	0
$166$	−2.73078	−0.211950
$167$	−0.485365	−0.0375587	−0.0187793	−	0.999824i	$-0.505978\pi$
$167$	−0.485365	−0.0375587	−0.0187793	+	0.999824i	$0.505978\pi$
$168$	3.32116	0.256233
$169$	24.4034	1.87719
$170$	0	0
$171$	−27.0404	−2.06783
$172$	−4.97154	−0.379077
$173$	−1.73351	−0.131796	−0.0658982	−	0.997826i	$-0.520991\pi$
$173$	−1.73351	−0.131796	−0.0658982	+	0.997826i	$0.520991\pi$
$174$	−4.22877	−0.320582
$175$	0	0
$176$	1.61626	0.121830
$177$	−35.7916	−2.69026
$178$	16.7773	1.25751
$179$	3.34468	0.249993	0.124996	−	0.992157i	$-0.460108\pi$
$179$	3.34468	0.249993	0.124996	+	0.992157i	$0.460108\pi$
$180$	0	0
$181$	−6.89808	−0.512730	−0.256365	−	0.966580i	$-0.582525\pi$
$181$	−6.89808	−0.512730	−0.256365	+	0.966580i	$0.582525\pi$
$182$	8.53548	0.632692
$183$	−23.8548	−1.76340
$184$	9.24961	0.681891
$185$	0	0
$186$	26.7603	1.96216
$187$	4.34186	0.317508
$188$	−7.40906	−0.540361
$189$	9.81998	0.714298
$190$	0	0
$191$	−23.4432	−1.69629	−0.848147	−	0.529762i	$-0.822281\pi$
$191$	−23.4432	−1.69629	−0.848147	+	0.529762i	$0.822281\pi$
$192$	−40.4562	−2.91968
$193$	−16.6470	−1.19828	−0.599140	−	0.800644i	$-0.704491\pi$
$193$	−16.6470	−1.19828	−0.599140	+	0.800644i	$0.704491\pi$
$194$	29.1630	2.09378
$195$	0	0
$196$	−17.9730	−1.28378
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−13.4067	−0.952772
$199$	19.6056	1.38980	0.694902	−	0.719104i	$-0.255448\pi$
$199$	19.6056	1.38980	0.694902	+	0.719104i	$0.255448\pi$
$200$	0	0
$201$	10.5623	0.745004
$202$	13.5962	0.956625
$203$	−0.381931	−0.0268063
$204$	−48.2294	−3.37673
$205$	0	0
$206$	40.1202	2.79530
$207$	44.8757	3.11908
$208$	−12.3148	−0.853876
$209$	2.82563	0.195453
$210$	0	0
$211$	−21.2155	−1.46053	−0.730266	−	0.683162i	$-0.760604\pi$
$211$	−21.2155	−1.46053	−0.730266	+	0.683162i	$0.760604\pi$
$212$	−12.5082	−0.859070
$213$	−20.9686	−1.43674
$214$	−14.2727	−0.975665
$215$	0	0
$216$	24.2232	1.64818
$217$	2.41692	0.164071
$218$	27.1005	1.83548
$219$	−6.24154	−0.421764
$220$	0	0
$221$	−33.0819	−2.22533
$222$	58.6864	3.93877
$223$	−4.90678	−0.328582	−0.164291	−	0.986412i	$-0.552534\pi$
$223$	−4.90678	−0.328582	−0.164291	+	0.986412i	$0.552534\pi$
$224$	−4.84263	−0.323562
$225$	0	0
$226$	−9.73224	−0.647379
$227$	8.70887	0.578028	0.289014	−	0.957325i	$-0.406673\pi$
$227$	8.70887	0.578028	0.289014	+	0.957325i	$0.406673\pi$
$228$	−31.3872	−2.07867
$229$	5.35180	0.353657	0.176828	−	0.984242i	$-0.443416\pi$
$229$	5.35180	0.353657	0.176828	+	0.984242i	$0.443416\pi$
$230$	0	0
$231$	−1.68376	−0.110783
$232$	−0.942121	−0.0618532
$233$	26.2053	1.71677	0.858384	−	0.513007i	$-0.171469\pi$
$233$	26.2053	1.71677	0.858384	+	0.513007i	$0.171469\pi$
$234$	102.150	6.67773
$235$	0	0
$236$	−29.8766	−1.94480
$237$	43.8396	2.84769
$238$	−7.54931	−0.489349
$239$	−13.3947	−0.866431	−0.433215	−	0.901290i	$-0.642621\pi$
$239$	−13.3947	−0.866431	−0.433215	+	0.901290i	$0.642621\pi$
$240$	0	0
$241$	−30.3596	−1.95563	−0.977816	−	0.209463i	$-0.932828\pi$
$241$	−30.3596	−1.95563	−0.977816	+	0.209463i	$0.932828\pi$
$242$	−22.5177	−1.44749
$243$	42.2089	2.70770
$244$	−19.9126	−1.27477
$245$	0	0
$246$	−73.7226	−4.70038
$247$	−21.5294	−1.36988
$248$	5.96188	0.378580
$249$	−4.10445	−0.260109
$250$	0	0
$251$	17.8926	1.12937	0.564685	−	0.825306i	$-0.308997\pi$
$251$	17.8926	1.12937	0.564685	+	0.825306i	$0.308997\pi$
$252$	13.4502	0.847283
$253$	−4.68937	−0.294818
$254$	−39.5921	−2.48423
$255$	0	0
$256$	−0.958811	−0.0599257
$257$	−7.04819	−0.439654	−0.219827	−	0.975539i	$-0.570549\pi$
$257$	−7.04819	−0.439654	−0.219827	+	0.975539i	$0.570549\pi$
$258$	−12.9504	−0.806259
$259$	5.30039	0.329350
$260$	0	0
$261$	−4.57082	−0.282927
$262$	−4.70424	−0.290629
$263$	−22.7572	−1.40327	−0.701636	−	0.712536i	$-0.747547\pi$
$263$	−22.7572	−1.40327	−0.701636	+	0.712536i	$0.747547\pi$
$264$	−4.15339	−0.255623
$265$	0	0
$266$	−4.91301	−0.301236
$267$	25.2169	1.54325
$268$	8.81673	0.538568
$269$	−5.98851	−0.365126	−0.182563	−	0.983194i	$-0.558439\pi$
$269$	−5.98851	−0.365126	−0.182563	+	0.983194i	$0.558439\pi$
$270$	0	0
$271$	−1.51925	−0.0922880	−0.0461440	−	0.998935i	$-0.514693\pi$
$271$	−1.51925	−0.0922880	−0.0461440	+	0.998935i	$0.514693\pi$
$272$	10.8920	0.660422
$273$	12.8291	0.776452
$274$	−9.79242	−0.591582
$275$	0	0
$276$	52.0896	3.13543
$277$	23.7824	1.42894	0.714472	−	0.699664i	$-0.246667\pi$
$277$	23.7824	1.42894	0.714472	+	0.699664i	$0.246667\pi$
$278$	−6.30871	−0.378372
$279$	28.9248	1.73169
$280$	0	0
$281$	17.4212	1.03926	0.519631	−	0.854391i	$-0.326070\pi$
$281$	17.4212	1.03926	0.519631	+	0.854391i	$0.326070\pi$
$282$	−19.3000	−1.14930
$283$	−7.48180	−0.444747	−0.222373	−	0.974962i	$-0.571380\pi$
$283$	−7.48180	−0.444747	−0.222373	+	0.974962i	$0.571380\pi$
$284$	−17.5033	−1.03863
$285$	0	0
$286$	−10.6743	−0.631186
$287$	−6.65842	−0.393034
$288$	−57.9549	−3.41503
$289$	12.2597	0.721160
$290$	0	0
$291$	43.8330	2.56953
$292$	−5.21007	−0.304896
$293$	−12.7277	−0.743560	−0.371780	−	0.928321i	$-0.621252\pi$
$293$	−12.7277	−0.743560	−0.371780	+	0.928321i	$0.621252\pi$
$294$	−46.8181	−2.73048
$295$	0	0
$296$	13.0746	0.759948
$297$	−12.2807	−0.712598
$298$	9.70071	0.561947
$299$	35.7297	2.06630
$300$	0	0
$301$	−1.16965	−0.0674174
$302$	10.1751	0.585509
$303$	20.4355	1.17399
$304$	7.08838	0.406546
$305$	0	0
$306$	−90.3475	−5.16483
$307$	26.3035	1.50122	0.750610	−	0.660746i	$-0.229760\pi$
$307$	26.3035	1.50122	0.750610	+	0.660746i	$0.229760\pi$
$308$	−1.40550	−0.0800860
$309$	60.3019	3.43046
$310$	0	0
$311$	8.97930	0.509170	0.254585	−	0.967050i	$-0.418061\pi$
$311$	8.97930	0.509170	0.254585	+	0.967050i	$0.418061\pi$
$312$	31.6459	1.79160
$313$	9.39749	0.531177	0.265589	−	0.964086i	$-0.414434\pi$
$313$	9.39749	0.531177	0.265589	+	0.964086i	$0.414434\pi$
$314$	15.8144	0.892461
$315$	0	0
$316$	36.5946	2.05861
$317$	−22.0900	−1.24070	−0.620350	−	0.784325i	$-0.713009\pi$
$317$	−22.0900	−1.24070	−0.620350	+	0.784325i	$0.713009\pi$
$318$	−32.5829	−1.82716
$319$	0.477637	0.0267425
$320$	0	0
$321$	−21.4524	−1.19736
$322$	8.15354	0.454379
$323$	19.0419	1.05952
$324$	73.5473	4.08596
$325$	0	0
$326$	−20.4313	−1.13159
$327$	40.7329	2.25254
$328$	−16.4245	−0.906893
$329$	−1.74312	−0.0961012
$330$	0	0
$331$	−7.34328	−0.403623	−0.201811	−	0.979424i	$-0.564683\pi$
$331$	−7.34328	−0.403623	−0.201811	+	0.979424i	$0.564683\pi$
$332$	−3.42615	−0.188034
$333$	63.4333	3.47612
$334$	−1.05539	−0.0577483
$335$	0	0
$336$	−4.22388	−0.230432
$337$	−24.7467	−1.34804	−0.674020	−	0.738713i	$-0.735434\pi$
$337$	−24.7467	−1.34804	−0.674020	+	0.738713i	$0.735434\pi$
$338$	53.0634	2.88627
$339$	−14.6279	−0.794477
$340$	0	0
$341$	−3.02256	−0.163681
$342$	−58.7972	−3.17939
$343$	−8.72137	−0.470910
$344$	−2.88520	−0.155560
$345$	0	0
$346$	−3.76939	−0.202644
$347$	−28.7654	−1.54421	−0.772103	−	0.635498i	$-0.780795\pi$
$347$	−28.7654	−1.54421	−0.772103	+	0.635498i	$0.780795\pi$
$348$	−5.30559	−0.284410
$349$	−3.72460	−0.199374	−0.0996868	−	0.995019i	$-0.531784\pi$
$349$	−3.72460	−0.199374	−0.0996868	+	0.995019i	$0.531784\pi$
$350$	0	0
$351$	93.5704	4.99442
$352$	6.05611	0.322792
$353$	−9.44475	−0.502693	−0.251347	−	0.967897i	$-0.580873\pi$
$353$	−9.44475	−0.502693	−0.251347	+	0.967897i	$0.580873\pi$
$354$	−77.8260	−4.13641
$355$	0	0
$356$	21.0495	1.11562
$357$	−11.3469	−0.600539
$358$	7.27275	0.384377
$359$	2.19917	0.116068	0.0580340	−	0.998315i	$-0.481517\pi$
$359$	2.19917	0.116068	0.0580340	+	0.998315i	$0.481517\pi$
$360$	0	0
$361$	−6.60771	−0.347774
$362$	−14.9994	−0.788349
$363$	−33.8449	−1.77639
$364$	10.7090	0.561302
$365$	0	0
$366$	−51.8705	−2.71132
$367$	−2.37829	−0.124146	−0.0620729	−	0.998072i	$-0.519771\pi$
$367$	−2.37829	−0.124146	−0.0620729	+	0.998072i	$0.519771\pi$
$368$	−11.7637	−0.613227
$369$	−79.6857	−4.14827
$370$	0	0
$371$	−2.94280	−0.152782
$372$	33.5746	1.74076
$373$	1.62799	0.0842943	0.0421471	−	0.999111i	$-0.486580\pi$
$373$	1.62799	0.0842943	0.0421471	+	0.999111i	$0.486580\pi$
$374$	9.44104	0.488185
$375$	0	0
$376$	−4.29980	−0.221745
$377$	−3.63926	−0.187431
$378$	21.3528	1.09827
$379$	5.76391	0.296072	0.148036	−	0.988982i	$-0.452705\pi$
$379$	5.76391	0.296072	0.148036	+	0.988982i	$0.452705\pi$
$380$	0	0
$381$	−59.5083	−3.04870
$382$	−50.9756	−2.60814
$383$	5.45665	0.278822	0.139411	−	0.990235i	$-0.455479\pi$
$383$	5.45665	0.278822	0.139411	+	0.990235i	$0.455479\pi$
$384$	−38.6521	−1.97246
$385$	0	0
$386$	−36.1977	−1.84242
$387$	−13.9979	−0.711555
$388$	36.5891	1.85753
$389$	−4.78289	−0.242502	−0.121251	−	0.992622i	$-0.538691\pi$
$389$	−4.78289	−0.242502	−0.121251	+	0.992622i	$0.538691\pi$
$390$	0	0
$391$	−31.6016	−1.59816
$392$	−10.4305	−0.526820
$393$	−7.07062	−0.356666
$394$	2.17442	0.109546
$395$	0	0
$396$	−16.8206	−0.845266
$397$	−10.8528	−0.544686	−0.272343	−	0.962200i	$-0.587799\pi$
$397$	−10.8528	−0.544686	−0.272343	+	0.962200i	$0.587799\pi$
$398$	42.6309	2.13689
$399$	−7.38442	−0.369683
$400$	0	0
$401$	30.0690	1.50157	0.750787	−	0.660544i	$-0.229674\pi$
$401$	30.0690	1.50157	0.750787	+	0.660544i	$0.229674\pi$
$402$	22.9668	1.14548
$403$	23.0298	1.14720
$404$	17.0584	0.848685
$405$	0	0
$406$	−0.830480	−0.0412160
$407$	−6.62858	−0.328567
$408$	−27.9896	−1.38569
$409$	7.23621	0.357807	0.178904	−	0.983867i	$-0.442745\pi$
$409$	7.23621	0.357807	0.178904	+	0.983867i	$0.442745\pi$
$410$	0	0
$411$	−14.7183	−0.726001
$412$	50.3364	2.47990
$413$	−7.02903	−0.345876
$414$	97.5788	4.79574
$415$	0	0
$416$	−46.1433	−2.26236
$417$	−9.48220	−0.464346
$418$	6.14413	0.300519
$419$	−18.3265	−0.895310	−0.447655	−	0.894206i	$-0.647741\pi$
$419$	−18.3265	−0.895310	−0.447655	+	0.894206i	$0.647741\pi$
$420$	0	0
$421$	11.3063	0.551035	0.275517	−	0.961296i	$-0.411151\pi$
$421$	11.3063	0.551035	0.275517	+	0.961296i	$0.411151\pi$
$422$	−46.1314	−2.24564
$423$	−20.8610	−1.01430
$424$	−7.25908	−0.352532
$425$	0	0
$426$	−45.5946	−2.20906
$427$	−4.68480	−0.226714
$428$	−17.9072	−0.865576
$429$	−16.0439	−0.774605
$430$	0	0
$431$	17.3670	0.836541	0.418271	−	0.908322i	$-0.362636\pi$
$431$	17.3670	0.836541	0.418271	+	0.908322i	$0.362636\pi$
$432$	−30.8073	−1.48222
$433$	11.0939	0.533140	0.266570	−	0.963816i	$-0.414110\pi$
$433$	11.0939	0.533140	0.266570	+	0.963816i	$0.414110\pi$
$434$	5.25541	0.252268
$435$	0	0
$436$	34.0014	1.62837
$437$	−20.5660	−0.983806
$438$	−13.5718	−0.648484
$439$	17.6727	0.843473	0.421737	−	0.906718i	$-0.361421\pi$
$439$	17.6727	0.843473	0.421737	+	0.906718i	$0.361421\pi$
$440$	0	0
$441$	−50.6050	−2.40976
$442$	−71.9341	−3.42156
$443$	−14.9026	−0.708044	−0.354022	−	0.935237i	$-0.615186\pi$
$443$	−14.9026	−0.708044	−0.354022	+	0.935237i	$0.615186\pi$
$444$	73.6304	3.49434
$445$	0	0
$446$	−10.6694	−0.505212
$447$	14.5805	0.689633
$448$	−7.94512	−0.375372
$449$	−26.5481	−1.25288	−0.626442	−	0.779468i	$-0.715489\pi$
$449$	−26.5481	−1.25288	−0.626442	+	0.779468i	$0.715489\pi$
$450$	0	0
$451$	8.32691	0.392099
$452$	−12.2105	−0.574332
$453$	15.2934	0.718549
$454$	18.9368	0.888747
$455$	0	0
$456$	−18.2154	−0.853013
$457$	−1.72034	−0.0804741	−0.0402371	−	0.999190i	$-0.512811\pi$
$457$	−1.72034	−0.0804741	−0.0402371	+	0.999190i	$0.512811\pi$
$458$	11.6371	0.543765
$459$	−82.7595	−3.86288
$460$	0	0
$461$	1.68192	0.0783350	0.0391675	−	0.999233i	$-0.487529\pi$
$461$	1.68192	0.0783350	0.0391675	+	0.999233i	$0.487529\pi$
$462$	−3.66121	−0.170335
$463$	26.6832	1.24007	0.620037	−	0.784573i	$-0.287118\pi$
$463$	26.6832	1.24007	0.620037	+	0.784573i	$0.287118\pi$
$464$	1.19820	0.0556249
$465$	0	0
$466$	56.9815	2.63962
$467$	15.9830	0.739607	0.369804	−	0.929110i	$-0.379425\pi$
$467$	15.9830	0.739607	0.369804	+	0.929110i	$0.379425\pi$
$468$	128.161	5.92425
$469$	2.07430	0.0957823
$470$	0	0
$471$	23.7696	1.09525
$472$	−17.3387	−0.798079
$473$	1.46274	0.0672569
$474$	95.3258	4.37846
$475$	0	0
$476$	−9.47168	−0.434134
$477$	−35.2184	−1.61254
$478$	−29.1258	−1.33218
$479$	2.44625	0.111772	0.0558860	−	0.998437i	$-0.482202\pi$
$479$	2.44625	0.111772	0.0558860	+	0.998437i	$0.482202\pi$
$480$	0	0
$481$	50.5052	2.30284
$482$	−66.0146	−3.00688
$483$	12.2550	0.557624
$484$	−28.2517	−1.28417
$485$	0	0
$486$	91.7802	4.16323
$487$	15.2624	0.691608	0.345804	−	0.938307i	$-0.387606\pi$
$487$	15.2624	0.691608	0.345804	+	0.938307i	$0.387606\pi$
$488$	−11.5561	−0.523122
$489$	−30.7089	−1.38871
$490$	0	0
$491$	7.46380	0.336837	0.168418	−	0.985716i	$-0.446134\pi$
$491$	7.46380	0.336837	0.168418	+	0.985716i	$0.446134\pi$
$492$	−92.4954	−4.17002
$493$	3.21879	0.144967
$494$	−46.8140	−2.10626
$495$	0	0
$496$	−7.58238	−0.340459
$497$	−4.11798	−0.184716
$498$	−8.92482	−0.399931
$499$	18.1973	0.814623	0.407311	−	0.913289i	$-0.366466\pi$
$499$	18.1973	0.814623	0.407311	+	0.913289i	$0.366466\pi$
$500$	0	0
$501$	−1.58628	−0.0708700
$502$	38.9061	1.73646
$503$	−22.5496	−1.00544	−0.502718	−	0.864451i	$-0.667667\pi$
$503$	−22.5496	−1.00544	−0.502718	+	0.864451i	$0.667667\pi$
$504$	7.80574	0.347695
$505$	0	0
$506$	−10.1967	−0.453298
$507$	79.7560	3.54209
$508$	−49.6739	−2.20392
$509$	11.6759	0.517526	0.258763	−	0.965941i	$-0.416685\pi$
$509$	11.6759	0.517526	0.258763	+	0.965941i	$0.416685\pi$
$510$	0	0
$511$	−1.22576	−0.0542246
$512$	21.5684	0.953196
$513$	−53.8590	−2.37793
$514$	−15.3258	−0.675990
$515$	0	0
$516$	−16.2482	−0.715285
$517$	2.17991	0.0958725
$518$	11.5253	0.506393
$519$	−5.66552	−0.248689
$520$	0	0
$521$	1.29227	0.0566153	0.0283076	−	0.999599i	$-0.490988\pi$
$521$	1.29227	0.0566153	0.0283076	+	0.999599i	$0.490988\pi$
$522$	−9.93890	−0.435014
$523$	12.2632	0.536232	0.268116	−	0.963387i	$-0.413599\pi$
$523$	12.2632	0.536232	0.268116	+	0.963387i	$0.413599\pi$
$524$	−5.90213	−0.257836
$525$	0	0
$526$	−49.4839	−2.15760
$527$	−20.3690	−0.887287
$528$	5.28231	0.229883
$529$	11.1310	0.483955
$530$	0	0
$531$	−84.1210	−3.65054
$532$	−6.16407	−0.267246
$533$	−63.4452	−2.74812
$534$	54.8322	2.37282
$535$	0	0
$536$	5.11674	0.221009
$537$	10.9312	0.471715
$538$	−13.0216	−0.561399
$539$	5.28806	0.227773
$540$	0	0
$541$	−28.2751	−1.21564	−0.607821	−	0.794074i	$-0.707956\pi$
$541$	−28.2751	−1.21564	−0.607821	+	0.794074i	$0.707956\pi$
$542$	−3.30350	−0.141897
$543$	−22.5445	−0.967478
$544$	40.8121	1.74980
$545$	0	0
$546$	27.8959	1.19383
$547$	24.0615	1.02880	0.514398	−	0.857552i	$-0.328015\pi$
$547$	24.0615	1.02880	0.514398	+	0.857552i	$0.328015\pi$
$548$	−12.2860	−0.524831
$549$	−56.0661	−2.39284
$550$	0	0
$551$	2.09475	0.0892395
$552$	30.2299	1.28667
$553$	8.60956	0.366116
$554$	51.7130	2.19707
$555$	0	0
$556$	−7.91517	−0.335678
$557$	21.7650	0.922212	0.461106	−	0.887345i	$-0.347453\pi$
$557$	21.7650	0.922212	0.461106	+	0.887345i	$0.347453\pi$
$558$	62.8949	2.66255
$559$	−11.1451	−0.471386
$560$	0	0
$561$	14.1902	0.599110
$562$	37.8811	1.59792
$563$	−8.19217	−0.345259	−0.172629	−	0.984987i	$-0.555226\pi$
$563$	−8.19217	−0.345259	−0.172629	+	0.984987i	$0.555226\pi$
$564$	−24.2145	−1.01962
$565$	0	0
$566$	−16.2686	−0.683821
$567$	17.3034	0.726673
$568$	−10.1579	−0.426217
$569$	16.8191	0.705092	0.352546	−	0.935795i	$-0.385316\pi$
$569$	16.8191	0.705092	0.352546	+	0.935795i	$0.385316\pi$
$570$	0	0
$571$	23.6048	0.987831	0.493916	−	0.869510i	$-0.335565\pi$
$571$	23.6048	0.987831	0.493916	+	0.869510i	$0.335565\pi$
$572$	−13.3924	−0.559966
$573$	−76.6179	−3.20076
$574$	−14.4782	−0.604310
$575$	0	0
$576$	−95.0845	−3.96185
$577$	12.8776	0.536102	0.268051	−	0.963405i	$-0.413620\pi$
$577$	12.8776	0.536102	0.268051	+	0.963405i	$0.413620\pi$
$578$	26.6579	1.10882
$579$	−54.4064	−2.26105
$580$	0	0
$581$	−0.806065	−0.0334412
$582$	95.3115	3.95079
$583$	3.68021	0.152419
$584$	−3.02363	−0.125119
$585$	0	0
$586$	−27.6754	−1.14326
$587$	40.9492	1.69015	0.845077	−	0.534644i	$-0.179554\pi$
$587$	40.9492	1.69015	0.845077	+	0.534644i	$0.179554\pi$
$588$	−58.7399	−2.42239
$589$	−13.2559	−0.546201
$590$	0	0
$591$	3.26823	0.134437
$592$	−16.6284	−0.683424
$593$	5.07212	0.208287	0.104144	−	0.994562i	$-0.466790\pi$
$593$	5.07212	0.208287	0.104144	+	0.994562i	$0.466790\pi$
$594$	−26.7035	−1.09566
$595$	0	0
$596$	12.1709	0.498540
$597$	64.0756	2.62244
$598$	77.6916	3.17705
$599$	11.4068	0.466071	0.233036	−	0.972468i	$-0.425134\pi$
$599$	11.4068	0.466071	0.233036	+	0.972468i	$0.425134\pi$
$600$	0	0
$601$	−13.6218	−0.555644	−0.277822	−	0.960633i	$-0.589612\pi$
$601$	−13.6218	−0.555644	−0.277822	+	0.960633i	$0.589612\pi$
$602$	−2.54331	−0.103658
$603$	24.8245	1.01093
$604$	12.7661	0.519443
$605$	0	0
$606$	44.4355	1.80507
$607$	14.4219	0.585366	0.292683	−	0.956210i	$-0.405452\pi$
$607$	14.4219	0.585366	0.292683	+	0.956210i	$0.405452\pi$
$608$	26.5601	1.07715
$609$	−1.24824	−0.0505812
$610$	0	0
$611$	−16.6094	−0.671945
$612$	−113.354	−4.58205
$613$	−4.64089	−0.187444	−0.0937219	−	0.995598i	$-0.529876\pi$
$613$	−4.64089	−0.187444	−0.0937219	+	0.995598i	$0.529876\pi$
$614$	57.1949	2.30820
$615$	0	0
$616$	−0.815675	−0.0328645
$617$	48.4293	1.94969	0.974845	−	0.222884i	$-0.0715470\pi$
$617$	48.4293	1.94969	0.974845	+	0.222884i	$0.0715470\pi$
$618$	131.122	5.27450
$619$	−16.5262	−0.664243	−0.332122	−	0.943237i	$-0.607764\pi$
$619$	−16.5262	−0.664243	−0.332122	+	0.943237i	$0.607764\pi$
$620$	0	0
$621$	89.3834	3.58683
$622$	19.5248	0.782874
$623$	4.95229	0.198409
$624$	−40.2476	−1.61119
$625$	0	0
$626$	20.4341	0.816712
$627$	9.23483	0.368804
$628$	19.8415	0.791760
$629$	−44.6699	−1.78111
$630$	0	0
$631$	20.0375	0.797679	0.398840	−	0.917021i	$-0.369413\pi$
$631$	20.0375	0.797679	0.398840	+	0.917021i	$0.369413\pi$
$632$	21.2375	0.844781
$633$	−69.3371	−2.75590
$634$	−48.0331	−1.90764
$635$	0	0
$636$	−40.8798	−1.62099
$637$	−40.2913	−1.59640
$638$	1.03858	0.0411180
$639$	−49.2825	−1.94959
$640$	0	0
$641$	16.2197	0.640639	0.320319	−	0.947310i	$-0.396210\pi$
$641$	16.2197	0.640639	0.320319	+	0.947310i	$0.396210\pi$
$642$	−46.6466	−1.84100
$643$	34.7519	1.37048	0.685241	−	0.728316i	$-0.259697\pi$
$643$	34.7519	1.37048	0.685241	+	0.728316i	$0.259697\pi$
$644$	10.2298	0.403110
$645$	0	0
$646$	41.4052	1.62907
$647$	−29.5762	−1.16276	−0.581381	−	0.813631i	$-0.697487\pi$
$647$	−29.5762	−1.16276	−0.581381	+	0.813631i	$0.697487\pi$
$648$	42.6827	1.67673
$649$	8.79039	0.345053
$650$	0	0
$651$	7.89905	0.309588
$652$	−25.6340	−1.00390
$653$	15.3265	0.599774	0.299887	−	0.953975i	$-0.403051\pi$
$653$	15.3265	0.599774	0.299887	+	0.953975i	$0.403051\pi$
$654$	88.5707	3.46339
$655$	0	0
$656$	20.8889	0.815573
$657$	−14.6695	−0.572313
$658$	−3.79028	−0.147760
$659$	9.67569	0.376911	0.188456	−	0.982082i	$-0.439652\pi$
$659$	9.67569	0.376911	0.188456	+	0.982082i	$0.439652\pi$
$660$	0	0
$661$	2.68152	0.104299	0.0521496	−	0.998639i	$-0.483393\pi$
$661$	2.68152	0.104299	0.0521496	+	0.998639i	$0.483393\pi$
$662$	−15.9674	−0.620591
$663$	−108.119	−4.19901
$664$	−1.98834	−0.0771627
$665$	0	0
$666$	137.931	5.34471
$667$	−3.47641	−0.134607
$668$	−1.32414	−0.0512323
$669$	−16.0365	−0.620006
$670$	0	0
$671$	5.85874	0.226174
$672$	−15.8268	−0.610533
$673$	20.1020	0.774876	0.387438	−	0.921896i	$-0.373360\pi$
$673$	20.1020	0.774876	0.387438	+	0.921896i	$0.373360\pi$
$674$	−53.8099	−2.07268
$675$	0	0
$676$	66.5755	2.56060
$677$	−26.3355	−1.01216	−0.506078	−	0.862488i	$-0.668905\pi$
$677$	−26.3355	−1.01216	−0.506078	+	0.862488i	$0.668905\pi$
$678$	−31.8072	−1.22155
$679$	8.60827	0.330355
$680$	0	0
$681$	28.4626	1.09069
$682$	−6.57232	−0.251667
$683$	50.1081	1.91733	0.958667	−	0.284531i	$-0.0918379\pi$
$683$	50.1081	1.91733	0.958667	+	0.284531i	$0.0918379\pi$
$684$	−73.7694	−2.82065
$685$	0	0
$686$	−18.9640	−0.724047
$687$	17.4909	0.667320
$688$	3.66943	0.139896
$689$	−28.0406	−1.06826
$690$	0	0
$691$	−42.3958	−1.61281	−0.806407	−	0.591362i	$-0.798591\pi$
$691$	−42.3958	−1.61281	−0.806407	+	0.591362i	$0.798591\pi$
$692$	−4.72923	−0.179778
$693$	−3.95735	−0.150327
$694$	−62.5481	−2.37429
$695$	0	0
$696$	−3.07907	−0.116712
$697$	56.1150	2.12551
$698$	−8.09887	−0.306547
$699$	85.6451	3.23940
$700$	0	0
$701$	−1.56980	−0.0592906	−0.0296453	−	0.999560i	$-0.509438\pi$
$701$	−1.56980	−0.0592906	−0.0296453	+	0.999560i	$0.509438\pi$
$702$	203.462	7.67917
$703$	−29.0707	−1.09642
$704$	9.93603	0.374478
$705$	0	0
$706$	−20.5369	−0.772917
$707$	4.01329	0.150935
$708$	−97.6438	−3.66968
$709$	−23.0787	−0.866739	−0.433369	−	0.901216i	$-0.642675\pi$
$709$	−23.0787	−0.866739	−0.433369	+	0.901216i	$0.642675\pi$
$710$	0	0
$711$	103.036	3.86416
$712$	12.2160	0.457813
$713$	21.9993	0.823880
$714$	−24.6729	−0.923360
$715$	0	0
$716$	9.12469	0.341006
$717$	−43.7770	−1.63488
$718$	4.78194	0.178460
$719$	−27.8449	−1.03844	−0.519220	−	0.854641i	$-0.673777\pi$
$719$	−27.8449	−1.03844	−0.519220	+	0.854641i	$0.673777\pi$
$720$	0	0
$721$	11.8426	0.441040
$722$	−14.3680	−0.534721
$723$	−99.2222	−3.69011
$724$	−18.8188	−0.699396
$725$	0	0
$726$	−73.5931	−2.73130
$727$	4.15211	0.153993	0.0769966	−	0.997031i	$-0.475467\pi$
$727$	4.15211	0.153993	0.0769966	+	0.997031i	$0.475467\pi$
$728$	6.21488	0.230339
$729$	57.0718	2.11377
$730$	0	0
$731$	9.85740	0.364589
$732$	−65.0789	−2.40539
$733$	29.8478	1.10245	0.551226	−	0.834356i	$-0.314160\pi$
$733$	29.8478	1.10245	0.551226	+	0.834356i	$0.314160\pi$
$734$	−5.17142	−0.190881
$735$	0	0
$736$	−44.0786	−1.62476
$737$	−2.59408	−0.0955543
$738$	−173.271	−6.37818
$739$	−0.294754	−0.0108427	−0.00542135	−	0.999985i	$-0.501726\pi$
$739$	−0.294754	−0.0108427	−0.00542135	+	0.999985i	$0.501726\pi$
$740$	0	0
$741$	−70.3630	−2.58485
$742$	−6.39889	−0.234911
$743$	29.7164	1.09019	0.545095	−	0.838374i	$-0.316493\pi$
$743$	29.7164	1.09019	0.545095	+	0.838374i	$0.316493\pi$
$744$	19.4848	0.714348
$745$	0	0
$746$	3.53995	0.129607
$747$	−9.64671	−0.352955
$748$	11.8451	0.433100
$749$	−4.21299	−0.153939
$750$	0	0
$751$	−0.823196	−0.0300389	−0.0150194	−	0.999887i	$-0.504781\pi$
$751$	−0.823196	−0.0300389	−0.0150194	+	0.999887i	$0.504781\pi$
$752$	5.46852	0.199417
$753$	58.4772	2.13103
$754$	−7.91329	−0.288185
$755$	0	0
$756$	26.7901	0.974347
$757$	−26.5876	−0.966342	−0.483171	−	0.875526i	$-0.660515\pi$
$757$	−26.5876	−0.966342	−0.483171	+	0.875526i	$0.660515\pi$
$758$	12.5332	0.455226
$759$	−15.3260	−0.556297
$760$	0	0
$761$	15.4789	0.561109	0.280555	−	0.959838i	$-0.409482\pi$
$761$	15.4789	0.561109	0.280555	+	0.959838i	$0.409482\pi$
$762$	−129.396	−4.68753
$763$	7.99946	0.289600
$764$	−63.9560	−2.31385
$765$	0	0
$766$	11.8651	0.428702
$767$	−66.9766	−2.41839
$768$	−3.13362	−0.113075
$769$	−14.5671	−0.525302	−0.262651	−	0.964891i	$-0.584597\pi$
$769$	−14.5671	−0.525302	−0.262651	+	0.964891i	$0.584597\pi$
$770$	0	0
$771$	−23.0351	−0.829589
$772$	−45.4152	−1.63453
$773$	46.6724	1.67869	0.839344	−	0.543601i	$-0.182939\pi$
$773$	46.6724	1.67869	0.839344	+	0.543601i	$0.182939\pi$
$774$	−30.4375	−1.09405
$775$	0	0
$776$	21.2343	0.762266
$777$	17.3229	0.621456
$778$	−10.4000	−0.372859
$779$	36.5190	1.30843
$780$	0	0
$781$	5.14987	0.184277
$782$	−68.7154	−2.45726
$783$	−9.10416	−0.325356
$784$	13.2656	0.473772
$785$	0	0
$786$	−15.3745	−0.548391
$787$	−20.3538	−0.725535	−0.362768	−	0.931880i	$-0.618168\pi$
$787$	−20.3538	−0.725535	−0.362768	+	0.931880i	$0.618168\pi$
$788$	2.72812	0.0971854
$789$	−74.3759	−2.64785
$790$	0	0
$791$	−2.87274	−0.102143
$792$	−9.76172	−0.346868
$793$	−44.6395	−1.58519
$794$	−23.5986	−0.837482
$795$	0	0
$796$	53.4865	1.89578
$797$	15.9131	0.563669	0.281835	−	0.959463i	$-0.409057\pi$
$797$	15.9131	0.563669	0.281835	+	0.959463i	$0.409057\pi$
$798$	−16.0569	−0.568407
$799$	14.6904	0.519710
$800$	0	0
$801$	59.2673	2.09411
$802$	65.3828	2.30875
$803$	1.53292	0.0540956
$804$	28.8151	1.01623
$805$	0	0
$806$	50.0765	1.76387
$807$	−19.5718	−0.688961
$808$	9.89971	0.348271
$809$	4.20699	0.147910	0.0739550	−	0.997262i	$-0.476438\pi$
$809$	4.20699	0.147910	0.0739550	+	0.997262i	$0.476438\pi$
$810$	0	0
$811$	−24.1310	−0.847355	−0.423678	−	0.905813i	$-0.639261\pi$
$811$	−24.1310	−0.847355	−0.423678	+	0.905813i	$0.639261\pi$
$812$	−1.04195	−0.0365654
$813$	−4.96527	−0.174139
$814$	−14.4133	−0.505188
$815$	0	0
$816$	35.5975	1.24616
$817$	6.41510	0.224436
$818$	15.7346	0.550147
$819$	30.1523	1.05361
$820$	0	0
$821$	24.0770	0.840294	0.420147	−	0.907456i	$-0.361978\pi$
$821$	24.0770	0.840294	0.420147	+	0.907456i	$0.361978\pi$
$822$	−32.0039	−1.11626
$823$	32.1941	1.12222	0.561108	−	0.827743i	$-0.310375\pi$
$823$	32.1941	1.12222	0.561108	+	0.827743i	$0.310375\pi$
$824$	29.2124	1.01766
$825$	0	0
$826$	−15.2841	−0.531802
$827$	−41.6832	−1.44947	−0.724733	−	0.689030i	$-0.758037\pi$
$827$	−41.6832	−1.44947	−0.724733	+	0.689030i	$0.758037\pi$
$828$	122.426	4.25461
$829$	6.67442	0.231812	0.115906	−	0.993260i	$-0.463023\pi$
$829$	6.67442	0.231812	0.115906	+	0.993260i	$0.463023\pi$
$830$	0	0
$831$	77.7263	2.69630
$832$	−75.7057	−2.62462
$833$	35.6362	1.23472
$834$	−20.6183	−0.713955
$835$	0	0
$836$	7.70868	0.266610
$837$	57.6125	1.99138
$838$	−39.8497	−1.37658
$839$	−38.9406	−1.34438	−0.672189	−	0.740380i	$-0.734646\pi$
$839$	−38.9406	−1.34438	−0.672189	+	0.740380i	$0.734646\pi$
$840$	0	0
$841$	−28.6459	−0.987790
$842$	24.5847	0.847244
$843$	56.9365	1.96100
$844$	−57.8784	−1.99226
$845$	0	0
$846$	−45.3608	−1.55953
$847$	−6.64672	−0.228384
$848$	9.23216	0.317034
$849$	−24.4523	−0.839199
$850$	0	0
$851$	48.2452	1.65383
$852$	−57.2049	−1.95981
$853$	36.9545	1.26530	0.632649	−	0.774438i	$-0.281967\pi$
$853$	36.9545	1.26530	0.632649	+	0.774438i	$0.281967\pi$
$854$	−10.1868	−0.348583
$855$	0	0
$856$	−10.3923	−0.355202
$857$	−24.2311	−0.827719	−0.413859	−	0.910341i	$-0.635820\pi$
$857$	−24.2311	−0.827719	−0.413859	+	0.910341i	$0.635820\pi$
$858$	−34.8862	−1.19099
$859$	56.9012	1.94144	0.970721	−	0.240209i	$-0.0772159\pi$
$859$	56.9012	1.94144	0.970721	+	0.240209i	$0.0772159\pi$
$860$	0	0
$861$	−21.7613	−0.741622
$862$	37.7633	1.28622
$863$	−23.7648	−0.808964	−0.404482	−	0.914546i	$-0.632548\pi$
$863$	−23.7648	−0.808964	−0.404482	+	0.914546i	$0.632548\pi$
$864$	−115.435	−3.92717
$865$	0	0
$866$	24.1229	0.819730
$867$	40.0676	1.36077
$868$	6.59365	0.223803
$869$	−10.7670	−0.365245
$870$	0	0
$871$	19.7651	0.669715
$872$	19.7325	0.668227
$873$	103.021	3.48673
$874$	−44.7192	−1.51265
$875$	0	0
$876$	−17.0277	−0.575313
$877$	−57.8679	−1.95406	−0.977030	−	0.213101i	$-0.931644\pi$
$877$	−57.8679	−1.95406	−0.977030	+	0.213101i	$0.931644\pi$
$878$	38.4280	1.29688
$879$	−41.5971	−1.40303
$880$	0	0
$881$	−0.710312	−0.0239310	−0.0119655	−	0.999928i	$-0.503809\pi$
$881$	−0.710312	−0.0239310	−0.0119655	+	0.999928i	$0.503809\pi$
$882$	−110.037	−3.70513
$883$	−51.0213	−1.71700	−0.858501	−	0.512811i	$-0.828604\pi$
$883$	−51.0213	−1.71700	−0.858501	+	0.512811i	$0.828604\pi$
$884$	−90.2516	−3.03549
$885$	0	0
$886$	−32.4046	−1.08865
$887$	45.0994	1.51429	0.757145	−	0.653247i	$-0.226594\pi$
$887$	45.0994	1.51429	0.757145	+	0.653247i	$0.226594\pi$
$888$	42.7309	1.43396
$889$	−11.6867	−0.391960
$890$	0	0
$891$	−21.6393	−0.724943
$892$	−13.3863	−0.448206
$893$	9.56037	0.319926
$894$	31.7042	1.06035
$895$	0	0
$896$	−7.59081	−0.253591
$897$	116.773	3.89894
$898$	−57.7269	−1.92637
$899$	−2.24074	−0.0747329
$900$	0	0
$901$	24.8009	0.826238
$902$	18.1062	0.602872
$903$	−3.82268	−0.127211
$904$	−7.08627	−0.235686
$905$	0	0
$906$	33.2545	1.10481
$907$	24.6849	0.819647	0.409824	−	0.912165i	$-0.365590\pi$
$907$	24.6849	0.819647	0.409824	+	0.912165i	$0.365590\pi$
$908$	23.7589	0.788466
$909$	48.0297	1.59304
$910$	0	0
$911$	−38.9583	−1.29075	−0.645374	−	0.763867i	$-0.723298\pi$
$911$	−38.9583	−1.29075	−0.645374	+	0.763867i	$0.723298\pi$
$912$	23.1665	0.767118
$913$	1.00805	0.0333616
$914$	−3.74075	−0.123733
$915$	0	0
$916$	14.6004	0.482410
$917$	−1.38858	−0.0458551
$918$	−179.954	−5.93938
$919$	20.7203	0.683499	0.341749	−	0.939791i	$-0.388981\pi$
$919$	20.7203	0.683499	0.341749	+	0.939791i	$0.388981\pi$
$920$	0	0
$921$	85.9659	2.83267
$922$	3.65722	0.120444
$923$	−39.2384	−1.29155
$924$	−4.59351	−0.151115
$925$	0	0
$926$	58.0206	1.90668
$927$	141.728	4.65495
$928$	4.48963	0.147379
$929$	−28.9907	−0.951154	−0.475577	−	0.879674i	$-0.657761\pi$
$929$	−28.9907	−0.951154	−0.475577	+	0.879674i	$0.657761\pi$
$930$	0	0
$931$	23.1917	0.760076
$932$	71.4914	2.34178
$933$	29.3464	0.960759
$934$	34.7539	1.13718
$935$	0	0
$936$	74.3775	2.43111
$937$	−48.8231	−1.59498	−0.797490	−	0.603332i	$-0.793840\pi$
$937$	−48.8231	−1.59498	−0.797490	+	0.603332i	$0.793840\pi$
$938$	4.51041	0.147270
$939$	30.7132	1.00229
$940$	0	0
$941$	16.5106	0.538230	0.269115	−	0.963108i	$-0.413269\pi$
$941$	16.5106	0.538230	0.269115	+	0.963108i	$0.413269\pi$
$942$	51.6853	1.68400
$943$	−60.6063	−1.97361
$944$	22.0515	0.717716
$945$	0	0
$946$	3.18062	0.103411
$947$	4.92047	0.159894	0.0799469	−	0.996799i	$-0.474525\pi$
$947$	4.92047	0.159894	0.0799469	+	0.996799i	$0.474525\pi$
$948$	119.600	3.88442
$949$	−11.6798	−0.379142
$950$	0	0
$951$	−72.1953	−2.34109
$952$	−5.49683	−0.178153
$953$	31.0718	1.00651	0.503257	−	0.864137i	$-0.332135\pi$
$953$	31.0718	1.00651	0.503257	+	0.864137i	$0.332135\pi$
$954$	−76.5797	−2.47936
$955$	0	0
$956$	−36.5424	−1.18187
$957$	1.56103	0.0504608
$958$	5.31918	0.171855
$959$	−2.89050	−0.0933392
$960$	0	0
$961$	−16.8203	−0.542589
$962$	109.820	3.54073
$963$	−50.4197	−1.62475
$964$	−82.8247	−2.66760
$965$	0	0
$966$	26.6477	0.857375
$967$	19.1582	0.616085	0.308042	−	0.951373i	$-0.400326\pi$
$967$	19.1582	0.616085	0.308042	+	0.951373i	$0.400326\pi$
$968$	−16.3957	−0.526977
$969$	62.2334	1.99923
$970$	0	0
$971$	32.5259	1.04380	0.521902	−	0.853005i	$-0.325223\pi$
$971$	32.5259	1.04380	0.521902	+	0.853005i	$0.325223\pi$
$972$	115.151	3.69348
$973$	−1.86219	−0.0596991
$974$	33.1870	1.06338
$975$	0	0
$976$	14.6972	0.470446
$977$	−32.4844	−1.03927	−0.519633	−	0.854389i	$-0.673931\pi$
$977$	−32.4844	−1.03927	−0.519633	+	0.854389i	$0.673931\pi$
$978$	−66.7743	−2.13521
$979$	−6.19325	−0.197937
$980$	0	0
$981$	95.7348	3.05658
$982$	16.2295	0.517903
$983$	23.8026	0.759184	0.379592	−	0.925154i	$-0.376064\pi$
$983$	23.8026	0.759184	0.379592	+	0.925154i	$0.376064\pi$
$984$	−53.6791	−1.71123
$985$	0	0
$986$	6.99901	0.222894
$987$	−5.69691	−0.181335
$988$	−58.7348	−1.86860
$989$	−10.6464	−0.338535
$990$	0	0
$991$	33.2089	1.05492	0.527458	−	0.849581i	$-0.323145\pi$
$991$	33.2089	1.05492	0.527458	+	0.849581i	$0.323145\pi$
$992$	−28.4111	−0.902052
$993$	−23.9995	−0.761602
$994$	−8.95423	−0.284011
$995$	0	0
$996$	−11.1975	−0.354805
$997$	−41.3000	−1.30799	−0.653993	−	0.756501i	$-0.726907\pi$
$997$	−41.3000	−1.30799	−0.653993	+	0.756501i	$0.726907\pi$
$998$	39.5686	1.25252
$999$	126.346	3.99742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4925.2.a.h.1.5		5
5.4	even	2		197.2.a.b.1.1	✓	5
15.14	odd	2		1773.2.a.e.1.5		5
20.19	odd	2		3152.2.a.j.1.4		5
35.34	odd	2		9653.2.a.h.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.a.b.1.1	✓	5	5.4	even	2
1773.2.a.e.1.5		5	15.14	odd	2
3152.2.a.j.1.4		5	20.19	odd	2
4925.2.a.h.1.5		5	1.1	even	1	trivial
9653.2.a.h.1.1		5	35.34	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:	\( N \)	\(=\)	\( 4925 = 5^{2} \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4925.a (trivial)

\(f(q)\)	\(=\)	\(q+2.17442 q^{2} +3.26823 q^{3} +2.72812 q^{4} +7.10652 q^{6} +0.641841 q^{7} +1.58325 q^{8} +7.68134 q^{9} -0.802676 q^{11} +8.91614 q^{12} +6.11583 q^{13} +1.39564 q^{14} -2.01359 q^{16} -5.40923 q^{17} +16.7025 q^{18} -3.52027 q^{19} +2.09769 q^{21} -1.74536 q^{22} +5.84217 q^{23} +5.17442 q^{24} +13.2984 q^{26} +15.2997 q^{27} +1.75102 q^{28} -0.595055 q^{29} +3.76560 q^{31} -7.54490 q^{32} -2.62333 q^{33} -11.7620 q^{34} +20.9556 q^{36} +8.25810 q^{37} -7.65456 q^{38} +19.9880 q^{39} -10.3739 q^{41} +4.56126 q^{42} -1.82233 q^{43} -2.18980 q^{44} +12.7034 q^{46} -2.71581 q^{47} -6.58088 q^{48} -6.58804 q^{49} -17.6786 q^{51} +16.6847 q^{52} -4.58493 q^{53} +33.2680 q^{54} +1.01619 q^{56} -11.5051 q^{57} -1.29390 q^{58} -10.9514 q^{59} -7.29900 q^{61} +8.18801 q^{62} +4.93020 q^{63} -12.3786 q^{64} -5.70424 q^{66} +3.23179 q^{67} -14.7570 q^{68} +19.0936 q^{69} -6.41588 q^{71} +12.1615 q^{72} -1.90976 q^{73} +17.9566 q^{74} -9.60373 q^{76} -0.515191 q^{77} +43.4623 q^{78} +13.4138 q^{79} +26.9589 q^{81} -22.5573 q^{82} -1.25586 q^{83} +5.72275 q^{84} -3.96252 q^{86} -1.94478 q^{87} -1.27084 q^{88} +7.71576 q^{89} +3.92539 q^{91} +15.9382 q^{92} +12.3069 q^{93} -5.90532 q^{94} -24.6585 q^{96} +13.4118 q^{97} -14.3252 q^{98} -6.16563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 8 q^{3} - 2 q^{6} + 10 q^{7} + 3 q^{8} + 13 q^{9} - 8 q^{11} + 12 q^{12} + 8 q^{13} - 3 q^{14} - 2 q^{16} - 9 q^{17} + q^{18} - 16 q^{19} + 14 q^{21} - 9 q^{22} + q^{23} + 15 q^{24} + 11 q^{26}+ \cdots + 11 q^{99}+O(q^{100}) \) 5 * q + 8 * q^3 - 2 * q^6 + 10 * q^7 + 3 * q^8 + 13 * q^9 - 8 * q^11 + 12 * q^12 + 8 * q^13 - 3 * q^14 - 2 * q^16 - 9 * q^17 + q^18 - 16 * q^19 + 14 * q^21 - 9 * q^22 + q^23 + 15 * q^24 + 11 * q^26 + 29 * q^27 + 2 * q^28 + 2 * q^29 + 2 * q^31 - 4 * q^32 + 2 * q^33 - 20 * q^34 + 40 * q^36 + 17 * q^37 - 5 * q^38 + 23 * q^39 - 5 * q^41 - 29 * q^42 + 26 * q^43 + 16 * q^44 + 13 * q^46 - 16 * q^47 - 14 * q^48 + 11 * q^49 - q^51 + 3 * q^52 - 2 * q^53 + 9 * q^54 - 10 * q^56 - 13 * q^57 + 5 * q^58 - 13 * q^59 - 3 * q^61 + 22 * q^62 + 40 * q^63 - 17 * q^64 - 10 * q^66 + 40 * q^67 - 5 * q^68 + 21 * q^69 - 5 * q^71 + 13 * q^72 + 9 * q^73 + 23 * q^74 - 5 * q^76 - 30 * q^77 + 61 * q^78 + 13 * q^79 + 49 * q^81 - 34 * q^82 + 17 * q^83 + 32 * q^84 - 23 * q^86 - 15 * q^87 + 9 * q^88 + 10 * q^89 - 29 * q^91 + 22 * q^92 - 11 * q^93 + 5 * q^94 - 19 * q^96 + 42 * q^97 - 24 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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