LMFDB - Embedded newform 6025.2.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67635 q^{2} -2.41547 q^{3} +5.16285 q^{4} +6.46465 q^{6} -0.976502 q^{7} -8.46490 q^{8} +2.83451 q^{9} +O(q^{10})$	\(q-2.67635 q^{2} -2.41547 q^{3} +5.16285 q^{4} +6.46465 q^{6} -0.976502 q^{7} -8.46490 q^{8} +2.83451 q^{9} +2.37781 q^{11} -12.4707 q^{12} +5.63951 q^{13} +2.61346 q^{14} +12.3293 q^{16} -4.16341 q^{17} -7.58614 q^{18} -1.76589 q^{19} +2.35871 q^{21} -6.36384 q^{22} +3.61254 q^{23} +20.4467 q^{24} -15.0933 q^{26} +0.399741 q^{27} -5.04154 q^{28} +4.75720 q^{29} -4.18013 q^{31} -16.0678 q^{32} -5.74352 q^{33} +11.1428 q^{34} +14.6341 q^{36} -1.75106 q^{37} +4.72613 q^{38} -13.6221 q^{39} +3.06144 q^{41} -6.31275 q^{42} -2.48967 q^{43} +12.2763 q^{44} -9.66843 q^{46} -0.632123 q^{47} -29.7812 q^{48} -6.04644 q^{49} +10.0566 q^{51} +29.1160 q^{52} -4.42986 q^{53} -1.06985 q^{54} +8.26599 q^{56} +4.26545 q^{57} -12.7319 q^{58} -9.05427 q^{59} +8.64652 q^{61} +11.1875 q^{62} -2.76790 q^{63} +18.3445 q^{64} +15.3717 q^{66} +4.20635 q^{67} -21.4951 q^{68} -8.72599 q^{69} -13.2429 q^{71} -23.9938 q^{72} +2.23625 q^{73} +4.68646 q^{74} -9.11702 q^{76} -2.32193 q^{77} +36.4575 q^{78} +13.2139 q^{79} -9.46909 q^{81} -8.19349 q^{82} -4.45242 q^{83} +12.1777 q^{84} +6.66322 q^{86} -11.4909 q^{87} -20.1279 q^{88} -0.784757 q^{89} -5.50700 q^{91} +18.6510 q^{92} +10.0970 q^{93} +1.69178 q^{94} +38.8114 q^{96} +12.4111 q^{97} +16.1824 q^{98} +6.73991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	$ 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.67635	−1.89247	−0.946233	−	0.323486i	$-0.895145\pi$
$2$	−2.67635	−1.89247	−0.946233	+	0.323486i	$0.895145\pi$
$3$	−2.41547	−1.39457	−0.697287	−	0.716792i	$-0.745610\pi$
$3$	−2.41547	−1.39457	−0.697287	+	0.716792i	$0.745610\pi$
$4$	5.16285	2.58143
$5$	0	0
$5$	0	0
$6$	6.46465	2.63918
$7$	−0.976502	−0.369083	−0.184542	−	0.982825i	$-0.559080\pi$
$7$	−0.976502	−0.369083	−0.184542	+	0.982825i	$0.559080\pi$
$8$	−8.46490	−2.99279
$9$	2.83451	0.944836
$10$	0	0
$11$	2.37781	0.716935	0.358468	−	0.933542i	$-0.383299\pi$
$11$	2.37781	0.716935	0.358468	+	0.933542i	$0.383299\pi$
$12$	−12.4707	−3.59999
$13$	5.63951	1.56412	0.782060	−	0.623204i	$-0.214169\pi$
$13$	5.63951	1.56412	0.782060	+	0.623204i	$0.214169\pi$
$14$	2.61346	0.698477
$15$	0	0
$16$	12.3293	3.08233
$17$	−4.16341	−1.00978	−0.504888	−	0.863185i	$-0.668466\pi$
$17$	−4.16341	−1.00978	−0.504888	+	0.863185i	$0.668466\pi$
$18$	−7.58614	−1.78807
$19$	−1.76589	−0.405122	−0.202561	−	0.979270i	$-0.564927\pi$
$19$	−1.76589	−0.405122	−0.202561	+	0.979270i	$0.564927\pi$
$20$	0	0
$21$	2.35871	0.514714
$22$	−6.36384	−1.35678
$23$	3.61254	0.753267	0.376633	−	0.926362i	$-0.377082\pi$
$23$	3.61254	0.753267	0.376633	+	0.926362i	$0.377082\pi$
$24$	20.4467	4.17367
$25$	0	0
$26$	−15.0933	−2.96004
$27$	0.399741	0.0769302
$28$	−5.04154	−0.952761
$29$	4.75720	0.883389	0.441695	−	0.897165i	$-0.354377\pi$
$29$	4.75720	0.883389	0.441695	+	0.897165i	$0.354377\pi$
$30$	0	0
$31$	−4.18013	−0.750773	−0.375386	−	0.926868i	$-0.622490\pi$
$31$	−4.18013	−0.750773	−0.375386	+	0.926868i	$0.622490\pi$
$32$	−16.0678	−2.84042
$33$	−5.74352	−0.999819
$34$	11.1428	1.91097
$35$	0	0
$36$	14.6341	2.43902
$37$	−1.75106	−0.287873	−0.143937	−	0.989587i	$-0.545976\pi$
$37$	−1.75106	−0.287873	−0.143937	+	0.989587i	$0.545976\pi$
$38$	4.72613	0.766680
$39$	−13.6221	−2.18128
$40$	0	0
$41$	3.06144	0.478117	0.239058	−	0.971005i	$-0.423161\pi$
$41$	3.06144	0.478117	0.239058	+	0.971005i	$0.423161\pi$
$42$	−6.31275	−0.974078
$43$	−2.48967	−0.379671	−0.189835	−	0.981816i	$-0.560795\pi$
$43$	−2.48967	−0.379671	−0.189835	+	0.981816i	$0.560795\pi$
$44$	12.2763	1.85072
$45$	0	0
$46$	−9.66843	−1.42553
$47$	−0.632123	−0.0922046	−0.0461023	−	0.998937i	$-0.514680\pi$
$47$	−0.632123	−0.0922046	−0.0461023	+	0.998937i	$0.514680\pi$
$48$	−29.7812	−4.29854
$49$	−6.04644	−0.863778
$50$	0	0
$51$	10.0566	1.40821
$52$	29.1160	4.03766
$53$	−4.42986	−0.608488	−0.304244	−	0.952594i	$-0.598404\pi$
$53$	−4.42986	−0.608488	−0.304244	+	0.952594i	$0.598404\pi$
$54$	−1.06985	−0.145588
$55$	0	0
$56$	8.26599	1.10459
$57$	4.26545	0.564973
$58$	−12.7319	−1.67178
$59$	−9.05427	−1.17877	−0.589383	−	0.807854i	$-0.700629\pi$
$59$	−9.05427	−1.17877	−0.589383	+	0.807854i	$0.700629\pi$
$60$	0	0
$61$	8.64652	1.10707	0.553537	−	0.832825i	$-0.313278\pi$
$61$	8.64652	1.10707	0.553537	+	0.832825i	$0.313278\pi$
$62$	11.1875	1.42081
$63$	−2.76790	−0.348723
$64$	18.3445	2.29306
$65$	0	0
$66$	15.3717	1.89212
$67$	4.20635	0.513888	0.256944	−	0.966426i	$-0.417284\pi$
$67$	4.20635	0.513888	0.256944	+	0.966426i	$0.417284\pi$
$68$	−21.4951	−2.60666
$69$	−8.72599	−1.05049
$70$	0	0
$71$	−13.2429	−1.57164	−0.785822	−	0.618453i	$-0.787760\pi$
$71$	−13.2429	−1.57164	−0.785822	+	0.618453i	$0.787760\pi$
$72$	−23.9938	−2.82770
$73$	2.23625	0.261733	0.130866	−	0.991400i	$-0.458224\pi$
$73$	2.23625	0.261733	0.130866	+	0.991400i	$0.458224\pi$
$74$	4.68646	0.544790
$75$	0	0
$76$	−9.11702	−1.04579
$77$	−2.32193	−0.264609
$78$	36.4575	4.12800
$79$	13.2139	1.48668	0.743340	−	0.668914i	$-0.233241\pi$
$79$	13.2139	1.48668	0.743340	+	0.668914i	$0.233241\pi$
$80$	0	0
$81$	−9.46909	−1.05212
$82$	−8.19349	−0.904819
$83$	−4.45242	−0.488717	−0.244358	−	0.969685i	$-0.578577\pi$
$83$	−4.45242	−0.488717	−0.244358	+	0.969685i	$0.578577\pi$
$84$	12.1777	1.32870
$85$	0	0
$86$	6.66322	0.718513
$87$	−11.4909	−1.23195
$88$	−20.1279	−2.14564
$89$	−0.784757	−0.0831841	−0.0415920	−	0.999135i	$-0.513243\pi$
$89$	−0.784757	−0.0831841	−0.0415920	+	0.999135i	$0.513243\pi$
$90$	0	0
$91$	−5.50700	−0.577290
$92$	18.6510	1.94450
$93$	10.0970	1.04701
$94$	1.69178	0.174494
$95$	0	0
$96$	38.8114	3.96117
$97$	12.4111	1.26016	0.630079	−	0.776531i	$-0.283023\pi$
$97$	12.4111	1.26016	0.630079	+	0.776531i	$0.283023\pi$
$98$	16.1824	1.63467
$99$	6.73991	0.677386
$100$	0	0
$101$	−10.4985	−1.04464	−0.522318	−	0.852751i	$-0.674932\pi$
$101$	−10.4985	−1.04464	−0.522318	+	0.852751i	$0.674932\pi$
$102$	−26.9150	−2.66498
$103$	0.828347	0.0816195	0.0408097	−	0.999167i	$-0.487006\pi$
$103$	0.828347	0.0816195	0.0408097	+	0.999167i	$0.487006\pi$
$104$	−47.7379	−4.68109
$105$	0	0
$106$	11.8559	1.15154
$107$	−16.2745	−1.57332	−0.786658	−	0.617389i	$-0.788191\pi$
$107$	−16.2745	−1.57332	−0.786658	+	0.617389i	$0.788191\pi$
$108$	2.06380	0.198590
$109$	3.83725	0.367542	0.183771	−	0.982969i	$-0.441169\pi$
$109$	3.83725	0.367542	0.183771	+	0.982969i	$0.441169\pi$
$110$	0	0
$111$	4.22965	0.401460
$112$	−12.0396	−1.13764
$113$	7.16355	0.673891	0.336945	−	0.941524i	$-0.390606\pi$
$113$	7.16355	0.673891	0.336945	+	0.941524i	$0.390606\pi$
$114$	−11.4158	−1.06919
$115$	0	0
$116$	24.5607	2.28040
$117$	15.9852	1.47784
$118$	24.2324	2.23077
$119$	4.06558	0.372691
$120$	0	0
$121$	−5.34604	−0.486004
$122$	−23.1411	−2.09510
$123$	−7.39482	−0.666769
$124$	−21.5814	−1.93806
$125$	0	0
$126$	7.40788	0.659946
$127$	−18.8636	−1.67387	−0.836935	−	0.547302i	$-0.815655\pi$
$127$	−18.8636	−1.67387	−0.836935	+	0.547302i	$0.815655\pi$
$128$	−16.9606	−1.49912
$129$	6.01372	0.529479
$130$	0	0
$131$	−20.2667	−1.77071	−0.885356	−	0.464914i	$-0.846085\pi$
$131$	−20.2667	−1.77071	−0.885356	+	0.464914i	$0.846085\pi$
$132$	−29.6530	−2.58096
$133$	1.72439	0.149524
$134$	−11.2577	−0.972515
$135$	0	0
$136$	35.2429	3.02205
$137$	−3.66484	−0.313108	−0.156554	−	0.987669i	$-0.550039\pi$
$137$	−3.66484	−0.313108	−0.156554	+	0.987669i	$0.550039\pi$
$138$	23.3538	1.98801
$139$	3.47581	0.294814	0.147407	−	0.989076i	$-0.452907\pi$
$139$	3.47581	0.294814	0.147407	+	0.989076i	$0.452907\pi$
$140$	0	0
$141$	1.52688	0.128586
$142$	35.4427	2.97428
$143$	13.4097	1.12137
$144$	34.9476	2.91230
$145$	0	0
$146$	−5.98498	−0.495321
$147$	14.6050	1.20460
$148$	−9.04048	−0.743123
$149$	−12.6249	−1.03427	−0.517137	−	0.855902i	$-0.673002\pi$
$149$	−12.6249	−1.03427	−0.517137	+	0.855902i	$0.673002\pi$
$150$	0	0
$151$	−2.41024	−0.196143	−0.0980713	−	0.995179i	$-0.531267\pi$
$151$	−2.41024	−0.196143	−0.0980713	+	0.995179i	$0.531267\pi$
$152$	14.9481	1.21245
$153$	−11.8012	−0.954073
$154$	6.21430	0.500763
$155$	0	0
$156$	−70.3288	−5.63081
$157$	−2.85655	−0.227977	−0.113989	−	0.993482i	$-0.536363\pi$
$157$	−2.85655	−0.227977	−0.113989	+	0.993482i	$0.536363\pi$
$158$	−35.3650	−2.81349
$159$	10.7002	0.848582
$160$	0	0
$161$	−3.52765	−0.278018
$162$	25.3426	1.99110
$163$	16.7785	1.31419	0.657096	−	0.753807i	$-0.271785\pi$
$163$	16.7785	1.31419	0.657096	+	0.753807i	$0.271785\pi$
$164$	15.8058	1.23422
$165$	0	0
$166$	11.9162	0.924880
$167$	−8.42613	−0.652033	−0.326017	−	0.945364i	$-0.605707\pi$
$167$	−8.42613	−0.652033	−0.326017	+	0.945364i	$0.605707\pi$
$168$	−19.9663	−1.54043
$169$	18.8041	1.44647
$170$	0	0
$171$	−5.00542	−0.382774
$172$	−12.8538	−0.980091
$173$	12.7992	0.973102	0.486551	−	0.873652i	$-0.338255\pi$
$173$	12.7992	0.973102	0.486551	+	0.873652i	$0.338255\pi$
$174$	30.7536	2.33143
$175$	0	0
$176$	29.3168	2.20983
$177$	21.8703	1.64387
$178$	2.10028	0.157423
$179$	−21.3576	−1.59634	−0.798172	−	0.602429i	$-0.794199\pi$
$179$	−21.3576	−1.59634	−0.798172	+	0.602429i	$0.794199\pi$
$180$	0	0
$181$	−17.0535	−1.26758	−0.633788	−	0.773507i	$-0.718501\pi$
$181$	−17.0535	−1.26758	−0.633788	+	0.773507i	$0.718501\pi$
$182$	14.7387	1.09250
$183$	−20.8854	−1.54390
$184$	−30.5798	−2.25437
$185$	0	0
$186$	−27.0231	−1.98143
$187$	−9.89979	−0.723944
$188$	−3.26356	−0.238019
$189$	−0.390348	−0.0283936
$190$	0	0
$191$	23.9143	1.73038	0.865189	−	0.501446i	$-0.167199\pi$
$191$	23.9143	1.73038	0.865189	+	0.501446i	$0.167199\pi$
$192$	−44.3106	−3.19784
$193$	−5.28249	−0.380242	−0.190121	−	0.981761i	$-0.560888\pi$
$193$	−5.28249	−0.380242	−0.190121	+	0.981761i	$0.560888\pi$
$194$	−33.2165	−2.38480
$195$	0	0
$196$	−31.2169	−2.22978
$197$	15.9937	1.13950	0.569752	−	0.821816i	$-0.307039\pi$
$197$	15.9937	1.13950	0.569752	+	0.821816i	$0.307039\pi$
$198$	−18.0384	−1.28193
$199$	18.6788	1.32411	0.662053	−	0.749457i	$-0.269685\pi$
$199$	18.6788	1.32411	0.662053	+	0.749457i	$0.269685\pi$
$200$	0	0
$201$	−10.1603	−0.716654
$202$	28.0975	1.97694
$203$	−4.64541	−0.326044
$204$	51.9208	3.63518
$205$	0	0
$206$	−2.21695	−0.154462
$207$	10.2398	0.711714
$208$	69.5315	4.82114
$209$	−4.19894	−0.290447
$210$	0	0
$211$	15.8481	1.09103	0.545515	−	0.838101i	$-0.316334\pi$
$211$	15.8481	1.09103	0.545515	+	0.838101i	$0.316334\pi$
$212$	−22.8707	−1.57077
$213$	31.9879	2.19177
$214$	43.5563	2.97745
$215$	0	0
$216$	−3.38377	−0.230236
$217$	4.08190	0.277098
$218$	−10.2698	−0.695561
$219$	−5.40159	−0.365006
$220$	0	0
$221$	−23.4796	−1.57941
$222$	−11.3200	−0.759750
$223$	15.5260	1.03970	0.519848	−	0.854259i	$-0.325989\pi$
$223$	15.5260	1.03970	0.519848	+	0.854259i	$0.325989\pi$
$224$	15.6903	1.04835
$225$	0	0
$226$	−19.1722	−1.27531
$227$	−11.6831	−0.775436	−0.387718	−	0.921778i	$-0.626737\pi$
$227$	−11.6831	−0.775436	−0.387718	+	0.921778i	$0.626737\pi$
$228$	22.0219	1.45844
$229$	14.2888	0.944232	0.472116	−	0.881536i	$-0.343490\pi$
$229$	14.2888	0.944232	0.472116	+	0.881536i	$0.343490\pi$
$230$	0	0
$231$	5.60856	0.369016
$232$	−40.2692	−2.64380
$233$	−11.4696	−0.751400	−0.375700	−	0.926741i	$-0.622598\pi$
$233$	−11.4696	−0.751400	−0.375700	+	0.926741i	$0.622598\pi$
$234$	−42.7821	−2.79675
$235$	0	0
$236$	−46.7458	−3.04289
$237$	−31.9178	−2.07328
$238$	−10.8809	−0.705306
$239$	22.7174	1.46947	0.734734	−	0.678355i	$-0.237307\pi$
$239$	22.7174	1.46947	0.734734	+	0.678355i	$0.237307\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	14.3079	0.919745
$243$	21.6731	1.39033
$244$	44.6407	2.85783
$245$	0	0
$246$	19.7911	1.26184
$247$	−9.95875	−0.633660
$248$	35.3844	2.24691
$249$	10.7547	0.681552
$250$	0	0
$251$	8.99666	0.567864	0.283932	−	0.958844i	$-0.408361\pi$
$251$	8.99666	0.567864	0.283932	+	0.958844i	$0.408361\pi$
$252$	−14.2903	−0.900203
$253$	8.58992	0.540044
$254$	50.4855	3.16774
$255$	0	0
$256$	8.70348	0.543968
$257$	19.0561	1.18868	0.594342	−	0.804212i	$-0.297412\pi$
$257$	19.0561	1.18868	0.594342	+	0.804212i	$0.297412\pi$
$258$	−16.0948	−1.00202
$259$	1.70992	0.106249
$260$	0	0
$261$	13.4843	0.834658
$262$	54.2408	3.35101
$263$	17.6624	1.08911	0.544555	−	0.838725i	$-0.316698\pi$
$263$	17.6624	1.08911	0.544555	+	0.838725i	$0.316698\pi$
$264$	48.6184	2.99225
$265$	0	0
$266$	−4.61508	−0.282969
$267$	1.89556	0.116006
$268$	21.7168	1.32656
$269$	19.9483	1.21627	0.608136	−	0.793833i	$-0.291918\pi$
$269$	19.9483	1.21627	0.608136	+	0.793833i	$0.291918\pi$
$270$	0	0
$271$	10.5522	0.641000	0.320500	−	0.947248i	$-0.396149\pi$
$271$	10.5522	0.641000	0.320500	+	0.947248i	$0.396149\pi$
$272$	−51.3322	−3.11247
$273$	13.3020	0.805074
$274$	9.80839	0.592546
$275$	0	0
$276$	−45.0510	−2.71175
$277$	0.840549	0.0505037	0.0252518	−	0.999681i	$-0.491961\pi$
$277$	0.840549	0.0505037	0.0252518	+	0.999681i	$0.491961\pi$
$278$	−9.30249	−0.557926
$279$	−11.8486	−0.709357
$280$	0	0
$281$	1.77458	0.105862	0.0529312	−	0.998598i	$-0.483144\pi$
$281$	1.77458	0.105862	0.0529312	+	0.998598i	$0.483144\pi$
$282$	−4.08645	−0.243345
$283$	11.3853	0.676787	0.338394	−	0.941005i	$-0.390116\pi$
$283$	11.3853	0.676787	0.338394	+	0.941005i	$0.390116\pi$
$284$	−68.3712	−4.05708
$285$	0	0
$286$	−35.8890	−2.12216
$287$	−2.98950	−0.176465
$288$	−45.5444	−2.68373
$289$	0.334023	0.0196484
$290$	0	0
$291$	−29.9787	−1.75738
$292$	11.5454	0.675644
$293$	−30.9503	−1.80814	−0.904069	−	0.427387i	$-0.859434\pi$
$293$	−30.9503	−1.80814	−0.904069	+	0.427387i	$0.859434\pi$
$294$	−39.0882	−2.27967
$295$	0	0
$296$	14.8226	0.861545
$297$	0.950506	0.0551540
$298$	33.7888	1.95733
$299$	20.3730	1.17820
$300$	0	0
$301$	2.43116	0.140130
$302$	6.45065	0.371193
$303$	25.3587	1.45682
$304$	−21.7722	−1.24872
$305$	0	0
$306$	31.5842	1.80555
$307$	−27.9209	−1.59353	−0.796766	−	0.604288i	$-0.793458\pi$
$307$	−27.9209	−1.59353	−0.796766	+	0.604288i	$0.793458\pi$
$308$	−11.9878	−0.683068
$309$	−2.00085	−0.113824
$310$	0	0
$311$	−26.7494	−1.51682	−0.758409	−	0.651779i	$-0.774023\pi$
$311$	−26.7494	−1.51682	−0.758409	+	0.651779i	$0.774023\pi$
$312$	115.310	6.52812
$313$	12.8302	0.725205	0.362602	−	0.931944i	$-0.381888\pi$
$313$	12.8302	0.725205	0.362602	+	0.931944i	$0.381888\pi$
$314$	7.64512	0.431439
$315$	0	0
$316$	68.2214	3.83775
$317$	−10.7876	−0.605892	−0.302946	−	0.953008i	$-0.597970\pi$
$317$	−10.7876	−0.605892	−0.302946	+	0.953008i	$0.597970\pi$
$318$	−28.6375	−1.60591
$319$	11.3117	0.633333
$320$	0	0
$321$	39.3106	2.19411
$322$	9.44124	0.526140
$323$	7.35212	0.409083
$324$	−48.8875	−2.71597
$325$	0	0
$326$	−44.9051	−2.48706
$327$	−9.26878	−0.512565
$328$	−25.9148	−1.43090
$329$	0.617269	0.0340312
$330$	0	0
$331$	−0.553666	−0.0304323	−0.0152161	−	0.999884i	$-0.504844\pi$
$331$	−0.553666	−0.0304323	−0.0152161	+	0.999884i	$0.504844\pi$
$332$	−22.9872	−1.26159
$333$	−4.96340	−0.271993
$334$	22.5513	1.23395
$335$	0	0
$336$	29.0814	1.58652
$337$	23.1367	1.26034	0.630170	−	0.776458i	$-0.282985\pi$
$337$	23.1367	1.26034	0.630170	+	0.776458i	$0.282985\pi$
$338$	−50.3264	−2.73739
$339$	−17.3034	−0.939790
$340$	0	0
$341$	−9.93953	−0.538256
$342$	13.3963	0.724387
$343$	12.7399	0.687889
$344$	21.0748	1.13628
$345$	0	0
$346$	−34.2550	−1.84156
$347$	−11.6086	−0.623181	−0.311591	−	0.950216i	$-0.600862\pi$
$347$	−11.6086	−0.623181	−0.311591	+	0.950216i	$0.600862\pi$
$348$	−59.3257	−3.18019
$349$	20.1708	1.07972	0.539859	−	0.841756i	$-0.318478\pi$
$349$	20.1708	1.07972	0.539859	+	0.841756i	$0.318478\pi$
$350$	0	0
$351$	2.25434	0.120328
$352$	−38.2062	−2.03640
$353$	12.1075	0.644416	0.322208	−	0.946669i	$-0.395575\pi$
$353$	12.1075	0.644416	0.322208	+	0.946669i	$0.395575\pi$
$354$	−58.5327	−3.11098
$355$	0	0
$356$	−4.05158	−0.214734
$357$	−9.82031	−0.519746
$358$	57.1605	3.02103
$359$	−26.3474	−1.39056	−0.695282	−	0.718737i	$-0.744720\pi$
$359$	−26.3474	−1.39056	−0.695282	+	0.718737i	$0.744720\pi$
$360$	0	0
$361$	−15.8816	−0.835876
$362$	45.6411	2.39884
$363$	12.9132	0.677768
$364$	−28.4318	−1.49023
$365$	0	0
$366$	55.8968	2.92177
$367$	0.674616	0.0352147	0.0176073	−	0.999845i	$-0.494395\pi$
$367$	0.674616	0.0352147	0.0176073	+	0.999845i	$0.494395\pi$
$368$	44.5402	2.32182
$369$	8.67768	0.451742
$370$	0	0
$371$	4.32577	0.224583
$372$	52.1292	2.70277
$373$	−13.7761	−0.713298	−0.356649	−	0.934238i	$-0.616081\pi$
$373$	−13.7761	−0.713298	−0.356649	+	0.934238i	$0.616081\pi$
$374$	26.4953	1.37004
$375$	0	0
$376$	5.35086	0.275949
$377$	26.8283	1.38173
$378$	1.04471	0.0537340
$379$	−15.9579	−0.819700	−0.409850	−	0.912153i	$-0.634419\pi$
$379$	−15.9579	−0.819700	−0.409850	+	0.912153i	$0.634419\pi$
$380$	0	0
$381$	45.5644	2.33434
$382$	−64.0030	−3.27468
$383$	23.8317	1.21774	0.608872	−	0.793268i	$-0.291622\pi$
$383$	23.8317	1.21774	0.608872	+	0.793268i	$0.291622\pi$
$384$	40.9678	2.09063
$385$	0	0
$386$	14.1378	0.719595
$387$	−7.05698	−0.358726
$388$	64.0767	3.25300
$389$	16.8765	0.855672	0.427836	−	0.903856i	$-0.359276\pi$
$389$	16.8765	0.855672	0.427836	+	0.903856i	$0.359276\pi$
$390$	0	0
$391$	−15.0405	−0.760631
$392$	51.1825	2.58511
$393$	48.9537	2.46939
$394$	−42.8048	−2.15647
$395$	0	0
$396$	34.7972	1.74862
$397$	−17.3348	−0.870007	−0.435003	−	0.900429i	$-0.643253\pi$
$397$	−17.3348	−0.870007	−0.435003	+	0.900429i	$0.643253\pi$
$398$	−49.9911	−2.50583
$399$	−4.16522	−0.208522
$400$	0	0
$401$	10.0121	0.499979	0.249990	−	0.968249i	$-0.419573\pi$
$401$	10.0121	0.499979	0.249990	+	0.968249i	$0.419573\pi$
$402$	27.1926	1.35624
$403$	−23.5739	−1.17430
$404$	−54.2020	−2.69665
$405$	0	0
$406$	12.4328	0.617027
$407$	−4.16369	−0.206386
$408$	−85.1282	−4.21448
$409$	1.43025	0.0707214	0.0353607	−	0.999375i	$-0.488742\pi$
$409$	1.43025	0.0707214	0.0353607	+	0.999375i	$0.488742\pi$
$410$	0	0
$411$	8.85231	0.436652
$412$	4.27663	0.210695
$413$	8.84151	0.435062
$414$	−27.4052	−1.34689
$415$	0	0
$416$	−90.6147	−4.44275
$417$	−8.39573	−0.411141
$418$	11.2378	0.549660
$419$	5.14040	0.251125	0.125563	−	0.992086i	$-0.459926\pi$
$419$	5.14040	0.251125	0.125563	+	0.992086i	$0.459926\pi$
$420$	0	0
$421$	20.9012	1.01866	0.509330	−	0.860571i	$-0.329893\pi$
$421$	20.9012	1.01866	0.509330	+	0.860571i	$0.329893\pi$
$422$	−42.4151	−2.06474
$423$	−1.79176	−0.0871182
$424$	37.4983	1.82108
$425$	0	0
$426$	−85.6108	−4.14785
$427$	−8.44335	−0.408602
$428$	−84.0229	−4.06140
$429$	−32.3907	−1.56384
$430$	0	0
$431$	−27.5314	−1.32614	−0.663069	−	0.748558i	$-0.730747\pi$
$431$	−27.5314	−1.32614	−0.663069	+	0.748558i	$0.730747\pi$
$432$	4.92854	0.237125
$433$	8.33924	0.400758	0.200379	−	0.979718i	$-0.435783\pi$
$433$	8.33924	0.400758	0.200379	+	0.979718i	$0.435783\pi$
$434$	−10.9246	−0.524398
$435$	0	0
$436$	19.8112	0.948783
$437$	−6.37934	−0.305165
$438$	14.4566	0.690761
$439$	26.3383	1.25706	0.628530	−	0.777786i	$-0.283657\pi$
$439$	26.3383	1.25706	0.628530	+	0.777786i	$0.283657\pi$
$440$	0	0
$441$	−17.1387	−0.816128
$442$	62.8397	2.98898
$443$	−30.3497	−1.44196	−0.720978	−	0.692958i	$-0.756307\pi$
$443$	−30.3497	−1.44196	−0.720978	+	0.692958i	$0.756307\pi$
$444$	21.8370	1.03634
$445$	0	0
$446$	−41.5529	−1.96759
$447$	30.4952	1.44237
$448$	−17.9134	−0.846329
$449$	31.8401	1.50263	0.751313	−	0.659946i	$-0.229421\pi$
$449$	31.8401	1.50263	0.751313	+	0.659946i	$0.229421\pi$
$450$	0	0
$451$	7.27951	0.342779
$452$	36.9844	1.73960
$453$	5.82187	0.273535
$454$	31.2681	1.46749
$455$	0	0
$456$	−36.1066	−1.69085
$457$	−32.9412	−1.54093	−0.770463	−	0.637485i	$-0.779975\pi$
$457$	−32.9412	−1.54093	−0.770463	+	0.637485i	$0.779975\pi$
$458$	−38.2419	−1.78693
$459$	−1.66429	−0.0776823
$460$	0	0
$461$	−16.0898	−0.749374	−0.374687	−	0.927151i	$-0.622250\pi$
$461$	−16.0898	−0.749374	−0.374687	+	0.927151i	$0.622250\pi$
$462$	−15.0105	−0.698351
$463$	−37.3841	−1.73739	−0.868694	−	0.495349i	$-0.835040\pi$
$463$	−37.3841	−1.73739	−0.868694	+	0.495349i	$0.835040\pi$
$464$	58.6531	2.72290
$465$	0	0
$466$	30.6967	1.42200
$467$	33.3347	1.54254	0.771272	−	0.636506i	$-0.219621\pi$
$467$	33.3347	1.54254	0.771272	+	0.636506i	$0.219621\pi$
$468$	82.5294	3.81493
$469$	−4.10751	−0.189667
$470$	0	0
$471$	6.89991	0.317931
$472$	76.6435	3.52780
$473$	−5.91994	−0.272199
$474$	85.4232	3.92362
$475$	0	0
$476$	20.9900	0.962075
$477$	−12.5565	−0.574922
$478$	−60.7998	−2.78092
$479$	−1.44894	−0.0662039	−0.0331020	−	0.999452i	$-0.510539\pi$
$479$	−1.44894	−0.0662039	−0.0331020	+	0.999452i	$0.510539\pi$
$480$	0	0
$481$	−9.87514	−0.450268
$482$	2.67635	0.121904
$483$	8.52095	0.387717
$484$	−27.6008	−1.25458
$485$	0	0
$486$	−58.0048	−2.63115
$487$	−24.2700	−1.09978	−0.549890	−	0.835237i	$-0.685331\pi$
$487$	−24.2700	−1.09978	−0.549890	+	0.835237i	$0.685331\pi$
$488$	−73.1920	−3.31324
$489$	−40.5280	−1.83274
$490$	0	0
$491$	−29.5543	−1.33377	−0.666883	−	0.745162i	$-0.732372\pi$
$491$	−29.5543	−1.33377	−0.666883	+	0.745162i	$0.732372\pi$
$492$	−38.1784	−1.72121
$493$	−19.8062	−0.892026
$494$	26.6531	1.19918
$495$	0	0
$496$	−51.5382	−2.31413
$497$	12.9317	0.580067
$498$	−28.7834	−1.28981
$499$	21.0939	0.944290	0.472145	−	0.881521i	$-0.343480\pi$
$499$	21.0939	0.944290	0.472145	+	0.881521i	$0.343480\pi$
$500$	0	0
$501$	20.3531	0.909309
$502$	−24.0782	−1.07466
$503$	−26.6208	−1.18696	−0.593480	−	0.804848i	$-0.702247\pi$
$503$	−26.6208	−1.18696	−0.593480	+	0.804848i	$0.702247\pi$
$504$	23.4300	1.04366
$505$	0	0
$506$	−22.9896	−1.02201
$507$	−45.4208	−2.01721
$508$	−97.3898	−4.32097
$509$	9.80234	0.434481	0.217241	−	0.976118i	$-0.430294\pi$
$509$	9.80234	0.434481	0.217241	+	0.976118i	$0.430294\pi$
$510$	0	0
$511$	−2.18370	−0.0966012
$512$	10.6276	0.469676
$513$	−0.705898	−0.0311661
$514$	−51.0007	−2.24955
$515$	0	0
$516$	31.0479	1.36681
$517$	−1.50307	−0.0661047
$518$	−4.57634	−0.201073
$519$	−30.9160	−1.35706
$520$	0	0
$521$	−21.1817	−0.927986	−0.463993	−	0.885839i	$-0.653584\pi$
$521$	−21.1817	−0.927986	−0.463993	+	0.885839i	$0.653584\pi$
$522$	−36.0888	−1.57956
$523$	−15.3847	−0.672724	−0.336362	−	0.941733i	$-0.609197\pi$
$523$	−15.3847	−0.672724	−0.336362	+	0.941733i	$0.609197\pi$
$524$	−104.634	−4.57096
$525$	0	0
$526$	−47.2708	−2.06110
$527$	17.4036	0.758113
$528$	−70.8139	−3.08178
$529$	−9.94955	−0.432589
$530$	0	0
$531$	−25.6644	−1.11374
$532$	8.90279	0.385985
$533$	17.2650	0.747831
$534$	−5.07318	−0.219538
$535$	0	0
$536$	−35.6064	−1.53796
$537$	51.5888	2.22622
$538$	−53.3888	−2.30175
$539$	−14.3773	−0.619273
$540$	0	0
$541$	36.8593	1.58471	0.792353	−	0.610063i	$-0.208856\pi$
$541$	36.8593	1.58471	0.792353	+	0.610063i	$0.208856\pi$
$542$	−28.2414	−1.21307
$543$	41.1922	1.76773
$544$	66.8970	2.86819
$545$	0	0
$546$	−35.6008	−1.52357
$547$	−4.89388	−0.209247	−0.104624	−	0.994512i	$-0.533364\pi$
$547$	−4.89388	−0.209247	−0.104624	+	0.994512i	$0.533364\pi$
$548$	−18.9210	−0.808266
$549$	24.5086	1.04600
$550$	0	0
$551$	−8.40068	−0.357881
$552$	73.8647	3.14389
$553$	−12.9034	−0.548708
$554$	−2.24960	−0.0955765
$555$	0	0
$556$	17.9451	0.761042
$557$	−37.6393	−1.59483	−0.797413	−	0.603434i	$-0.793799\pi$
$557$	−37.6393	−1.59483	−0.797413	+	0.603434i	$0.793799\pi$
$558$	31.7110	1.34243
$559$	−14.0405	−0.593850
$560$	0	0
$561$	23.9127	1.00959
$562$	−4.74939	−0.200341
$563$	42.0537	1.77235	0.886176	−	0.463349i	$-0.153352\pi$
$563$	42.0537	1.77235	0.886176	+	0.463349i	$0.153352\pi$
$564$	7.88303	0.331936
$565$	0	0
$566$	−30.4711	−1.28080
$567$	9.24658	0.388320
$568$	112.100	4.70361
$569$	−1.76353	−0.0739312	−0.0369656	−	0.999317i	$-0.511769\pi$
$569$	−1.76353	−0.0739312	−0.0369656	+	0.999317i	$0.511769\pi$
$570$	0	0
$571$	−33.7468	−1.41226	−0.706131	−	0.708081i	$-0.749561\pi$
$571$	−33.7468	−1.41226	−0.706131	+	0.708081i	$0.749561\pi$
$572$	69.2321	2.89474
$573$	−57.7643	−2.41314
$574$	8.00096	0.333954
$575$	0	0
$576$	51.9975	2.16656
$577$	9.66427	0.402329	0.201164	−	0.979558i	$-0.435527\pi$
$577$	9.66427	0.402329	0.201164	+	0.979558i	$0.435527\pi$
$578$	−0.893963	−0.0371839
$579$	12.7597	0.530276
$580$	0	0
$581$	4.34780	0.180377
$582$	80.2335	3.32579
$583$	−10.5333	−0.436247
$584$	−18.9296	−0.783313
$585$	0	0
$586$	82.8339	3.42184
$587$	−46.3573	−1.91337	−0.956684	−	0.291127i	$-0.905970\pi$
$587$	−46.3573	−1.91337	−0.956684	+	0.291127i	$0.905970\pi$
$588$	75.4036	3.10959
$589$	7.38163	0.304155
$590$	0	0
$591$	−38.6324	−1.58912
$592$	−21.5895	−0.887321
$593$	−14.8184	−0.608517	−0.304259	−	0.952589i	$-0.598409\pi$
$593$	−14.8184	−0.608517	−0.304259	+	0.952589i	$0.598409\pi$
$594$	−2.54389	−0.104377
$595$	0	0
$596$	−65.1807	−2.66990
$597$	−45.1182	−1.84656
$598$	−54.5252	−2.22970
$599$	1.39943	0.0571790	0.0285895	−	0.999591i	$-0.490898\pi$
$599$	1.39943	0.0571790	0.0285895	+	0.999591i	$0.490898\pi$
$600$	0	0
$601$	12.6277	0.515095	0.257548	−	0.966266i	$-0.417086\pi$
$601$	12.6277	0.515095	0.257548	+	0.966266i	$0.417086\pi$
$602$	−6.50665	−0.265191
$603$	11.9229	0.485540
$604$	−12.4437	−0.506328
$605$	0	0
$606$	−67.8689	−2.75698
$607$	−0.785927	−0.0318998	−0.0159499	−	0.999873i	$-0.505077\pi$
$607$	−0.785927	−0.0318998	−0.0159499	+	0.999873i	$0.505077\pi$
$608$	28.3740	1.15072
$609$	11.2209	0.454693
$610$	0	0
$611$	−3.56486	−0.144219
$612$	−60.9280	−2.46287
$613$	−28.2861	−1.14247	−0.571233	−	0.820788i	$-0.693535\pi$
$613$	−28.2861	−1.14247	−0.571233	+	0.820788i	$0.693535\pi$
$614$	74.7262	3.01570
$615$	0	0
$616$	19.6549	0.791920
$617$	−39.3731	−1.58510	−0.792551	−	0.609805i	$-0.791248\pi$
$617$	−39.3731	−1.58510	−0.792551	+	0.609805i	$0.791248\pi$
$618$	5.35497	0.215409
$619$	−36.8672	−1.48182	−0.740910	−	0.671604i	$-0.765605\pi$
$619$	−36.8672	−1.48182	−0.740910	+	0.671604i	$0.765605\pi$
$620$	0	0
$621$	1.44408	0.0579490
$622$	71.5907	2.87053
$623$	0.766317	0.0307018
$624$	−167.951	−6.72343
$625$	0	0
$626$	−34.3381	−1.37242
$627$	10.1424	0.405049
$628$	−14.7479	−0.588507
$629$	7.29040	0.290687
$630$	0	0
$631$	−22.5561	−0.897945	−0.448973	−	0.893545i	$-0.648210\pi$
$631$	−22.5561	−0.897945	−0.448973	+	0.893545i	$0.648210\pi$
$632$	−111.854	−4.44933
$633$	−38.2807	−1.52152
$634$	28.8714	1.14663
$635$	0	0
$636$	55.2436	2.19055
$637$	−34.0990	−1.35105
$638$	−30.2741	−1.19856
$639$	−37.5371	−1.48495
$640$	0	0
$641$	−7.76960	−0.306881	−0.153440	−	0.988158i	$-0.549035\pi$
$641$	−7.76960	−0.306881	−0.153440	+	0.988158i	$0.549035\pi$
$642$	−105.209	−4.15227
$643$	−10.1316	−0.399552	−0.199776	−	0.979842i	$-0.564021\pi$
$643$	−10.1316	−0.399552	−0.199776	+	0.979842i	$0.564021\pi$
$644$	−18.2128	−0.717683
$645$	0	0
$646$	−19.6769	−0.774176
$647$	−24.0280	−0.944640	−0.472320	−	0.881427i	$-0.656583\pi$
$647$	−24.0280	−0.944640	−0.472320	+	0.881427i	$0.656583\pi$
$648$	80.1549	3.14878
$649$	−21.5293	−0.845098
$650$	0	0
$651$	−9.85972	−0.386433
$652$	86.6248	3.39249
$653$	21.6720	0.848091	0.424045	−	0.905641i	$-0.360610\pi$
$653$	21.6720	0.848091	0.424045	+	0.905641i	$0.360610\pi$
$654$	24.8065	0.970011
$655$	0	0
$656$	37.7455	1.47372
$657$	6.33866	0.247295
$658$	−1.65203	−0.0644028
$659$	−41.9456	−1.63397	−0.816983	−	0.576661i	$-0.804355\pi$
$659$	−41.9456	−1.63397	−0.816983	+	0.576661i	$0.804355\pi$
$660$	0	0
$661$	5.29152	0.205816	0.102908	−	0.994691i	$-0.467185\pi$
$661$	5.29152	0.205816	0.102908	+	0.994691i	$0.467185\pi$
$662$	1.48181	0.0575920
$663$	56.7144	2.20260
$664$	37.6893	1.46263
$665$	0	0
$666$	13.2838	0.514737
$667$	17.1856	0.665428
$668$	−43.5028	−1.68318
$669$	−37.5026	−1.44993
$670$	0	0
$671$	20.5597	0.793700
$672$	−37.8994	−1.46200
$673$	−27.0900	−1.04424	−0.522121	−	0.852872i	$-0.674859\pi$
$673$	−27.0900	−1.04424	−0.522121	+	0.852872i	$0.674859\pi$
$674$	−61.9221	−2.38515
$675$	0	0
$676$	97.0828	3.73395
$677$	18.2935	0.703077	0.351538	−	0.936173i	$-0.385659\pi$
$677$	18.2935	0.703077	0.351538	+	0.936173i	$0.385659\pi$
$678$	46.3099	1.77852
$679$	−12.1195	−0.465103
$680$	0	0
$681$	28.2203	1.08140
$682$	26.6017	1.01863
$683$	29.2520	1.11930	0.559649	−	0.828730i	$-0.310936\pi$
$683$	29.2520	1.11930	0.559649	+	0.828730i	$0.310936\pi$
$684$	−25.8423	−0.988104
$685$	0	0
$686$	−34.0964	−1.30181
$687$	−34.5143	−1.31680
$688$	−30.6959	−1.17027
$689$	−24.9823	−0.951748
$690$	0	0
$691$	−9.16111	−0.348505	−0.174253	−	0.984701i	$-0.555751\pi$
$691$	−9.16111	−0.348505	−0.174253	+	0.984701i	$0.555751\pi$
$692$	66.0802	2.51199
$693$	−6.58154	−0.250012
$694$	31.0686	1.17935
$695$	0	0
$696$	97.2692	3.68698
$697$	−12.7460	−0.482791
$698$	−53.9841	−2.04333
$699$	27.7046	1.04788
$700$	0	0
$701$	22.1470	0.836480	0.418240	−	0.908337i	$-0.362647\pi$
$701$	22.1470	0.836480	0.418240	+	0.908337i	$0.362647\pi$
$702$	−6.03342	−0.227717
$703$	3.09218	0.116624
$704$	43.6196	1.64397
$705$	0	0
$706$	−32.4039	−1.21954
$707$	10.2518	0.385557
$708$	112.913	4.24354
$709$	−29.7529	−1.11739	−0.558696	−	0.829372i	$-0.688698\pi$
$709$	−29.7529	−1.11739	−0.558696	+	0.829372i	$0.688698\pi$
$710$	0	0
$711$	37.4549	1.40467
$712$	6.64289	0.248953
$713$	−15.1009	−0.565532
$714$	26.2826	0.983601
$715$	0	0
$716$	−110.266	−4.12084
$717$	−54.8733	−2.04928
$718$	70.5149	2.63159
$719$	−49.9575	−1.86310	−0.931550	−	0.363612i	$-0.881543\pi$
$719$	−49.9575	−1.86310	−0.931550	+	0.363612i	$0.881543\pi$
$720$	0	0
$721$	−0.808883	−0.0301244
$722$	42.5048	1.58187
$723$	2.41547	0.0898324
$724$	−88.0447	−3.27215
$725$	0	0
$726$	−34.5603	−1.28265
$727$	−25.7174	−0.953807	−0.476903	−	0.878956i	$-0.658241\pi$
$727$	−25.7174	−0.953807	−0.476903	+	0.878956i	$0.658241\pi$
$728$	46.6162	1.72771
$729$	−23.9435	−0.886797
$730$	0	0
$731$	10.3655	0.383382
$732$	−107.828	−3.98545
$733$	4.43153	0.163682	0.0818411	−	0.996645i	$-0.473920\pi$
$733$	4.43153	0.163682	0.0818411	+	0.996645i	$0.473920\pi$
$734$	−1.80551	−0.0666426
$735$	0	0
$736$	−58.0457	−2.13959
$737$	10.0019	0.368424
$738$	−23.2245	−0.854906
$739$	−27.5684	−1.01412	−0.507061	−	0.861910i	$-0.669268\pi$
$739$	−27.5684	−1.01412	−0.507061	+	0.861910i	$0.669268\pi$
$740$	0	0
$741$	24.0551	0.883685
$742$	−11.5773	−0.425015
$743$	−8.69776	−0.319090	−0.159545	−	0.987191i	$-0.551003\pi$
$743$	−8.69776	−0.319090	−0.159545	+	0.987191i	$0.551003\pi$
$744$	−85.4699	−3.13348
$745$	0	0
$746$	36.8696	1.34989
$747$	−12.6204	−0.461757
$748$	−51.1112	−1.86881
$749$	15.8921	0.580685
$750$	0	0
$751$	−1.65059	−0.0602308	−0.0301154	−	0.999546i	$-0.509587\pi$
$751$	−1.65059	−0.0602308	−0.0301154	+	0.999546i	$0.509587\pi$
$752$	−7.79366	−0.284205
$753$	−21.7312	−0.791928
$754$	−71.8019	−2.61487
$755$	0	0
$756$	−2.01531	−0.0732961
$757$	38.2737	1.39108	0.695541	−	0.718486i	$-0.255165\pi$
$757$	38.2737	1.39108	0.695541	+	0.718486i	$0.255165\pi$
$758$	42.7088	1.55125
$759$	−20.7487	−0.753131
$760$	0	0
$761$	8.38299	0.303883	0.151942	−	0.988389i	$-0.451447\pi$
$761$	8.38299	0.303883	0.151942	+	0.988389i	$0.451447\pi$
$762$	−121.946	−4.41765
$763$	−3.74709	−0.135654
$764$	123.466	4.46684
$765$	0	0
$766$	−63.7821	−2.30454
$767$	−51.0616	−1.84373
$768$	−21.0230	−0.758603
$769$	−49.6622	−1.79087	−0.895433	−	0.445196i	$-0.853134\pi$
$769$	−49.6622	−1.79087	−0.895433	+	0.445196i	$0.853134\pi$
$770$	0	0
$771$	−46.0294	−1.65771
$772$	−27.2727	−0.981567
$773$	−15.7214	−0.565460	−0.282730	−	0.959200i	$-0.591240\pi$
$773$	−15.7214	−0.565460	−0.282730	+	0.959200i	$0.591240\pi$
$774$	18.8869	0.678877
$775$	0	0
$776$	−105.059	−3.77139
$777$	−4.13026	−0.148172
$778$	−45.1674	−1.61933
$779$	−5.40616	−0.193696
$780$	0	0
$781$	−31.4891	−1.12677
$782$	40.2537	1.43947
$783$	1.90165	0.0679593
$784$	−74.5486	−2.66245
$785$	0	0
$786$	−131.017	−4.67323
$787$	−31.0037	−1.10516	−0.552582	−	0.833459i	$-0.686357\pi$
$787$	−31.0037	−1.10516	−0.552582	+	0.833459i	$0.686357\pi$
$788$	82.5732	2.94155
$789$	−42.6631	−1.51885
$790$	0	0
$791$	−6.99523	−0.248722
$792$	−57.0527	−2.02728
$793$	48.7622	1.73160
$794$	46.3939	1.64646
$795$	0	0
$796$	96.4360	3.41808
$797$	18.2180	0.645314	0.322657	−	0.946516i	$-0.395424\pi$
$797$	18.2180	0.645314	0.322657	+	0.946516i	$0.395424\pi$
$798$	11.1476	0.394621
$799$	2.63179	0.0931060
$800$	0	0
$801$	−2.22440	−0.0785953
$802$	−26.7958	−0.946194
$803$	5.31736	0.187646
$804$	−52.4563	−1.84999
$805$	0	0
$806$	63.0919	2.22232
$807$	−48.1847	−1.69618
$808$	88.8684	3.12638
$809$	50.7213	1.78327	0.891633	−	0.452759i	$-0.149560\pi$
$809$	50.7213	1.78327	0.891633	+	0.452759i	$0.149560\pi$
$810$	0	0
$811$	21.7304	0.763058	0.381529	−	0.924357i	$-0.375398\pi$
$811$	21.7304	0.763058	0.381529	+	0.924357i	$0.375398\pi$
$812$	−23.9836	−0.841659
$813$	−25.4885	−0.893922
$814$	11.1435	0.390579
$815$	0	0
$816$	123.991	4.34057
$817$	4.39647	0.153813
$818$	−3.82785	−0.133838
$819$	−15.6096	−0.545444
$820$	0	0
$821$	23.0153	0.803241	0.401621	−	0.915806i	$-0.368447\pi$
$821$	23.0153	0.803241	0.401621	+	0.915806i	$0.368447\pi$
$822$	−23.6919	−0.826350
$823$	−10.8439	−0.377996	−0.188998	−	0.981977i	$-0.560524\pi$
$823$	−10.8439	−0.377996	−0.188998	+	0.981977i	$0.560524\pi$
$824$	−7.01188	−0.244270
$825$	0	0
$826$	−23.6630	−0.823340
$827$	2.12590	0.0739249	0.0369624	−	0.999317i	$-0.488232\pi$
$827$	2.12590	0.0739249	0.0369624	+	0.999317i	$0.488232\pi$
$828$	52.8665	1.83724
$829$	11.2110	0.389376	0.194688	−	0.980865i	$-0.437631\pi$
$829$	11.2110	0.389376	0.194688	+	0.980865i	$0.437631\pi$
$830$	0	0
$831$	−2.03032	−0.0704311
$832$	103.454	3.58662
$833$	25.1739	0.872222
$834$	22.4699	0.778069
$835$	0	0
$836$	−21.6785	−0.749766
$837$	−1.67097	−0.0577571
$838$	−13.7575	−0.475246
$839$	−5.45368	−0.188282	−0.0941410	−	0.995559i	$-0.530010\pi$
$839$	−5.45368	−0.188282	−0.0941410	+	0.995559i	$0.530010\pi$
$840$	0	0
$841$	−6.36907	−0.219623
$842$	−55.9388	−1.92778
$843$	−4.28645	−0.147633
$844$	81.8215	2.81641
$845$	0	0
$846$	4.79537	0.164868
$847$	5.22042	0.179376
$848$	−54.6173	−1.87556
$849$	−27.5009	−0.943830
$850$	0	0
$851$	−6.32579	−0.216845
$852$	165.149	5.65790
$853$	47.1274	1.61361	0.806805	−	0.590817i	$-0.201195\pi$
$853$	47.1274	1.61361	0.806805	+	0.590817i	$0.201195\pi$
$854$	22.5974	0.773266
$855$	0	0
$856$	137.762	4.70861
$857$	3.81105	0.130183	0.0650915	−	0.997879i	$-0.479266\pi$
$857$	3.81105	0.130183	0.0650915	+	0.997879i	$0.479266\pi$
$858$	86.6888	2.95951
$859$	−35.8788	−1.22417	−0.612084	−	0.790793i	$-0.709668\pi$
$859$	−35.8788	−1.22417	−0.612084	+	0.790793i	$0.709668\pi$
$860$	0	0
$861$	7.22106	0.246093
$862$	73.6836	2.50967
$863$	33.8545	1.15242	0.576210	−	0.817302i	$-0.304531\pi$
$863$	33.8545	1.15242	0.576210	+	0.817302i	$0.304531\pi$
$864$	−6.42297	−0.218514
$865$	0	0
$866$	−22.3187	−0.758421
$867$	−0.806823	−0.0274012
$868$	21.0743	0.715307
$869$	31.4201	1.06585
$870$	0	0
$871$	23.7218	0.803782
$872$	−32.4820	−1.09998
$873$	35.1794	1.19064
$874$	17.0734	0.577515
$875$	0	0
$876$	−27.8876	−0.942236
$877$	−31.8555	−1.07568	−0.537842	−	0.843046i	$-0.680760\pi$
$877$	−31.8555	−1.07568	−0.537842	+	0.843046i	$0.680760\pi$
$878$	−70.4906	−2.37894
$879$	74.7597	2.52158
$880$	0	0
$881$	−30.4305	−1.02523	−0.512615	−	0.858618i	$-0.671323\pi$
$881$	−30.4305	−1.02523	−0.512615	+	0.858618i	$0.671323\pi$
$882$	45.8692	1.54449
$883$	−25.5625	−0.860246	−0.430123	−	0.902770i	$-0.641530\pi$
$883$	−25.5625	−0.860246	−0.430123	+	0.902770i	$0.641530\pi$
$884$	−121.222	−4.07713
$885$	0	0
$886$	81.2264	2.72885
$887$	37.6929	1.26560	0.632801	−	0.774314i	$-0.281905\pi$
$887$	37.6929	1.26560	0.632801	+	0.774314i	$0.281905\pi$
$888$	−35.8035	−1.20149
$889$	18.4203	0.617797
$890$	0	0
$891$	−22.5157	−0.754303
$892$	80.1583	2.68390
$893$	1.11626	0.0373542
$894$	−81.6158	−2.72964
$895$	0	0
$896$	16.5620	0.553299
$897$	−49.2103	−1.64309
$898$	−85.2152	−2.84367
$899$	−19.8857	−0.663225
$900$	0	0
$901$	18.4433	0.614437
$902$	−19.4825	−0.648697
$903$	−5.87241	−0.195422
$904$	−60.6388	−2.01682
$905$	0	0
$906$	−15.5814	−0.517656
$907$	16.8086	0.558121	0.279061	−	0.960273i	$-0.409977\pi$
$907$	16.8086	0.558121	0.279061	+	0.960273i	$0.409977\pi$
$908$	−60.3182	−2.00173
$909$	−29.7580	−0.987009
$910$	0	0
$911$	21.1652	0.701234	0.350617	−	0.936519i	$-0.385972\pi$
$911$	21.1652	0.701234	0.350617	+	0.936519i	$0.385972\pi$
$912$	52.5902	1.74144
$913$	−10.5870	−0.350378
$914$	88.1623	2.91615
$915$	0	0
$916$	73.7711	2.43747
$917$	19.7905	0.653540
$918$	4.45422	0.147011
$919$	46.9802	1.54973	0.774867	−	0.632124i	$-0.217817\pi$
$919$	46.9802	1.54973	0.774867	+	0.632124i	$0.217817\pi$
$920$	0	0
$921$	67.4422	2.22230
$922$	43.0618	1.41817
$923$	−74.6835	−2.45824
$924$	28.9562	0.952589
$925$	0	0
$926$	100.053	3.28795
$927$	2.34796	0.0771170
$928$	−76.4378	−2.50920
$929$	41.4529	1.36003	0.680014	−	0.733200i	$-0.261974\pi$
$929$	41.4529	1.36003	0.680014	+	0.733200i	$0.261974\pi$
$930$	0	0
$931$	10.6773	0.349936
$932$	−59.2160	−1.93968
$933$	64.6124	2.11531
$934$	−89.2152	−2.91921
$935$	0	0
$936$	−135.314	−4.42286
$937$	14.4020	0.470494	0.235247	−	0.971936i	$-0.424410\pi$
$937$	14.4020	0.470494	0.235247	+	0.971936i	$0.424410\pi$
$938$	10.9931	0.358939
$939$	−30.9909	−1.01135
$940$	0	0
$941$	28.1131	0.916462	0.458231	−	0.888833i	$-0.348483\pi$
$941$	28.1131	0.916462	0.458231	+	0.888833i	$0.348483\pi$
$942$	−18.4666	−0.601674
$943$	11.0596	0.360149
$944$	−111.633	−3.63335
$945$	0	0
$946$	15.8438	0.515128
$947$	9.93853	0.322959	0.161479	−	0.986876i	$-0.448373\pi$
$947$	9.93853	0.322959	0.161479	+	0.986876i	$0.448373\pi$
$948$	−164.787	−5.35203
$949$	12.6113	0.409382
$950$	0	0
$951$	26.0571	0.844961
$952$	−34.4148	−1.11539
$953$	50.2333	1.62722	0.813608	−	0.581414i	$-0.197500\pi$
$953$	50.2333	1.62722	0.813608	+	0.581414i	$0.197500\pi$
$954$	33.6055	1.08802
$955$	0	0
$956$	117.287	3.79332
$957$	−27.3231	−0.883230
$958$	3.87788	0.125289
$959$	3.57872	0.115563
$960$	0	0
$961$	−13.5265	−0.436340
$962$	26.4293	0.852116
$963$	−46.1302	−1.48653
$964$	−5.16285	−0.166284
$965$	0	0
$966$	−22.8051	−0.733741
$967$	−52.1499	−1.67703	−0.838514	−	0.544881i	$-0.816575\pi$
$967$	−52.1499	−1.67703	−0.838514	+	0.544881i	$0.816575\pi$
$968$	45.2537	1.45451
$969$	−17.7589	−0.570497
$970$	0	0
$971$	29.2981	0.940221	0.470110	−	0.882608i	$-0.344214\pi$
$971$	29.2981	0.940221	0.470110	+	0.882608i	$0.344214\pi$
$972$	111.895	3.58903
$973$	−3.39414	−0.108811
$974$	64.9552	2.08130
$975$	0	0
$976$	106.606	3.41237
$977$	−29.7967	−0.953281	−0.476641	−	0.879098i	$-0.658146\pi$
$977$	−29.7967	−0.953281	−0.476641	+	0.879098i	$0.658146\pi$
$978$	108.467	3.46839
$979$	−1.86600	−0.0596376
$980$	0	0
$981$	10.8767	0.347267
$982$	79.0976	2.52411
$983$	2.14822	0.0685174	0.0342587	−	0.999413i	$-0.489093\pi$
$983$	2.14822	0.0685174	0.0342587	+	0.999413i	$0.489093\pi$
$984$	62.5965	1.99550
$985$	0	0
$986$	53.0083	1.68813
$987$	−1.49100	−0.0474590
$988$	−51.4155	−1.63575
$989$	−8.99402	−0.285993
$990$	0	0
$991$	−49.6327	−1.57663	−0.788317	−	0.615269i	$-0.789048\pi$
$991$	−49.6327	−1.57663	−0.788317	+	0.615269i	$0.789048\pi$
$992$	67.1656	2.13251
$993$	1.33737	0.0424400
$994$	−34.6098	−1.09776
$995$	0	0
$996$	55.5249	1.75938
$997$	42.7356	1.35345	0.676725	−	0.736236i	$-0.263399\pi$
$997$	42.7356	1.35345	0.676725	+	0.736236i	$0.263399\pi$
$998$	−56.4545	−1.78704
$999$	−0.699972	−0.0221461

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.l.1.3	✓	40
5.4	even	2		6025.2.a.o.1.38	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.3	✓	40	1.1	even	1	trivial
6025.2.a.o.1.38	yes	40	5.4	even	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67635 q^{2} -2.41547 q^{3} +5.16285 q^{4} +6.46465 q^{6} -0.976502 q^{7} -8.46490 q^{8} +2.83451 q^{9} +O(q^{10})\)	\(q-2.67635 q^{2} -2.41547 q^{3} +5.16285 q^{4} +6.46465 q^{6} -0.976502 q^{7} -8.46490 q^{8} +2.83451 q^{9} +2.37781 q^{11} -12.4707 q^{12} +5.63951 q^{13} +2.61346 q^{14} +12.3293 q^{16} -4.16341 q^{17} -7.58614 q^{18} -1.76589 q^{19} +2.35871 q^{21} -6.36384 q^{22} +3.61254 q^{23} +20.4467 q^{24} -15.0933 q^{26} +0.399741 q^{27} -5.04154 q^{28} +4.75720 q^{29} -4.18013 q^{31} -16.0678 q^{32} -5.74352 q^{33} +11.1428 q^{34} +14.6341 q^{36} -1.75106 q^{37} +4.72613 q^{38} -13.6221 q^{39} +3.06144 q^{41} -6.31275 q^{42} -2.48967 q^{43} +12.2763 q^{44} -9.66843 q^{46} -0.632123 q^{47} -29.7812 q^{48} -6.04644 q^{49} +10.0566 q^{51} +29.1160 q^{52} -4.42986 q^{53} -1.06985 q^{54} +8.26599 q^{56} +4.26545 q^{57} -12.7319 q^{58} -9.05427 q^{59} +8.64652 q^{61} +11.1875 q^{62} -2.76790 q^{63} +18.3445 q^{64} +15.3717 q^{66} +4.20635 q^{67} -21.4951 q^{68} -8.72599 q^{69} -13.2429 q^{71} -23.9938 q^{72} +2.23625 q^{73} +4.68646 q^{74} -9.11702 q^{76} -2.32193 q^{77} +36.4575 q^{78} +13.2139 q^{79} -9.46909 q^{81} -8.19349 q^{82} -4.45242 q^{83} +12.1777 q^{84} +6.66322 q^{86} -11.4909 q^{87} -20.1279 q^{88} -0.784757 q^{89} -5.50700 q^{91} +18.6510 q^{92} +10.0970 q^{93} +1.69178 q^{94} +38.8114 q^{96} +12.4111 q^{97} +16.1824 q^{98} +6.73991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9	\( 40 q - 11 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 16 q^{7} - 33 q^{8} + 38 q^{9} + q^{11} - 14 q^{12} - 9 q^{13} - q^{14} + 43 q^{16} - 12 q^{17} - 42 q^{18} + 2 q^{21} - 5 q^{22} - 77 q^{23} - 2 q^{24} + 2 q^{26} - 38 q^{27} - 42 q^{28} + 2 q^{29} + q^{31} - 72 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 28 q^{37} - 23 q^{38} - 2 q^{39} - 2 q^{41} - 37 q^{42} - 31 q^{43} + 3 q^{44} + 14 q^{46} - 96 q^{47} - 13 q^{48} + 40 q^{49} - 10 q^{51} - 42 q^{52} - 54 q^{53} + 4 q^{54} - 15 q^{56} - 37 q^{57} - 27 q^{58} + q^{59} + 5 q^{61} - 39 q^{62} - 70 q^{63} + 65 q^{64} - 52 q^{66} - 34 q^{67} - 52 q^{68} + 21 q^{69} - 9 q^{71} - 70 q^{72} - 25 q^{73} + 22 q^{74} - 47 q^{76} - 54 q^{77} - 58 q^{78} + 13 q^{79} + 12 q^{81} + 5 q^{82} - 63 q^{83} + 95 q^{84} - 18 q^{86} - 47 q^{87} - 13 q^{88} + 19 q^{89} - 31 q^{91} - 137 q^{92} - 52 q^{93} + 120 q^{94} - 49 q^{96} - 36 q^{97} - 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q - 11 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 16 * q^7 - 33 * q^8 + 38 * q^9 + q^11 - 14 * q^12 - 9 * q^13 - q^14 + 43 * q^16 - 12 * q^17 - 42 * q^18 + 2 * q^21 - 5 * q^22 - 77 * q^23 - 2 * q^24 + 2 * q^26 - 38 * q^27 - 42 * q^28 + 2 * q^29 + q^31 - 72 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 28 * q^37 - 23 * q^38 - 2 * q^39 - 2 * q^41 - 37 * q^42 - 31 * q^43 + 3 * q^44 + 14 * q^46 - 96 * q^47 - 13 * q^48 + 40 * q^49 - 10 * q^51 - 42 * q^52 - 54 * q^53 + 4 * q^54 - 15 * q^56 - 37 * q^57 - 27 * q^58 + q^59 + 5 * q^61 - 39 * q^62 - 70 * q^63 + 65 * q^64 - 52 * q^66 - 34 * q^67 - 52 * q^68 + 21 * q^69 - 9 * q^71 - 70 * q^72 - 25 * q^73 + 22 * q^74 - 47 * q^76 - 54 * q^77 - 58 * q^78 + 13 * q^79 + 12 * q^81 + 5 * q^82 - 63 * q^83 + 95 * q^84 - 18 * q^86 - 47 * q^87 - 13 * q^88 + 19 * q^89 - 31 * q^91 - 137 * q^92 - 52 * q^93 + 120 * q^94 - 49 * q^96 - 36 * q^97 - 64 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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