LMFDB - Embedded newform 6025.2.a.q.1.16

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:	$0$
Dimension:	$66$
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.67685 q^{2} +3.17567 q^{3} +0.811815 q^{4} -5.32511 q^{6} +0.164609 q^{7} +1.99240 q^{8} +7.08488 q^{9} +O(q^{10})$	\(q-1.67685 q^{2} +3.17567 q^{3} +0.811815 q^{4} -5.32511 q^{6} +0.164609 q^{7} +1.99240 q^{8} +7.08488 q^{9} -0.583415 q^{11} +2.57806 q^{12} +0.0376548 q^{13} -0.276024 q^{14} -4.96459 q^{16} +1.88357 q^{17} -11.8803 q^{18} +5.31400 q^{19} +0.522743 q^{21} +0.978297 q^{22} +0.253420 q^{23} +6.32722 q^{24} -0.0631414 q^{26} +12.9722 q^{27} +0.133632 q^{28} -0.939996 q^{29} -1.95929 q^{31} +4.34004 q^{32} -1.85273 q^{33} -3.15847 q^{34} +5.75161 q^{36} +10.5054 q^{37} -8.91077 q^{38} +0.119579 q^{39} +6.77657 q^{41} -0.876560 q^{42} +0.523511 q^{43} -0.473625 q^{44} -0.424946 q^{46} -5.15241 q^{47} -15.7659 q^{48} -6.97290 q^{49} +5.98161 q^{51} +0.0305687 q^{52} +5.93416 q^{53} -21.7524 q^{54} +0.327967 q^{56} +16.8755 q^{57} +1.57623 q^{58} +0.860469 q^{59} -10.7210 q^{61} +3.28544 q^{62} +1.16623 q^{63} +2.65159 q^{64} +3.10675 q^{66} -2.97102 q^{67} +1.52911 q^{68} +0.804777 q^{69} -10.1962 q^{71} +14.1159 q^{72} -6.56160 q^{73} -17.6160 q^{74} +4.31399 q^{76} -0.0960352 q^{77} -0.200516 q^{78} +15.0176 q^{79} +19.9408 q^{81} -11.3633 q^{82} +10.4442 q^{83} +0.424371 q^{84} -0.877848 q^{86} -2.98512 q^{87} -1.16240 q^{88} +7.32600 q^{89} +0.00619831 q^{91} +0.205730 q^{92} -6.22207 q^{93} +8.63980 q^{94} +13.7825 q^{96} -6.93110 q^{97} +11.6925 q^{98} -4.13342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9}+O(q^{10}) $ 66 * q + 78 * q^4 + 16 * q^6 + 90 * q^9	$ 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9} + 48 q^{11} + 30 q^{14} + 98 q^{16} + 12 q^{19} + 18 q^{21} + 42 q^{24} + 48 q^{26} + 56 q^{29} + 48 q^{31} + 8 q^{34} + 158 q^{36} + 84 q^{39} + 56 q^{41} + 144 q^{44} + 36 q^{46} + 98 q^{49} + 44 q^{51} + 86 q^{54} + 104 q^{56} + 108 q^{59} + 22 q^{61} + 136 q^{64} + 74 q^{66} + 20 q^{69} + 212 q^{71} + 84 q^{74} + 6 q^{76} + 66 q^{79} + 162 q^{81} - 52 q^{84} + 100 q^{86} + 54 q^{89} + 72 q^{91} - 96 q^{94} + 122 q^{96} + 112 q^{99}+O(q^{100}) $ 66 * q + 78 * q^4 + 16 * q^6 + 90 * q^9 + 48 * q^11 + 30 * q^14 + 98 * q^16 + 12 * q^19 + 18 * q^21 + 42 * q^24 + 48 * q^26 + 56 * q^29 + 48 * q^31 + 8 * q^34 + 158 * q^36 + 84 * q^39 + 56 * q^41 + 144 * q^44 + 36 * q^46 + 98 * q^49 + 44 * q^51 + 86 * q^54 + 104 * q^56 + 108 * q^59 + 22 * q^61 + 136 * q^64 + 74 * q^66 + 20 * q^69 + 212 * q^71 + 84 * q^74 + 6 * q^76 + 66 * q^79 + 162 * q^81 - 52 * q^84 + 100 * q^86 + 54 * q^89 + 72 * q^91 - 96 * q^94 + 122 * q^96 + 112 * 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 $

$2$	−1.67685	−1.18571	−0.592855	−	0.805309i	$-0.701999\pi$
$2$	−1.67685	−1.18571	−0.592855	+	0.805309i	$0.701999\pi$
$3$	3.17567	1.83347	0.916737	−	0.399492i	$-0.130813\pi$
$3$	3.17567	1.83347	0.916737	+	0.399492i	$0.130813\pi$
$4$	0.811815	0.405907
$5$	0	0
$5$	0	0
$6$	−5.32511	−2.17397
$7$	0.164609	0.0622163	0.0311081	−	0.999516i	$-0.490096\pi$
$7$	0.164609	0.0622163	0.0311081	+	0.999516i	$0.490096\pi$
$8$	1.99240	0.704421
$9$	7.08488	2.36163
$10$	0	0
$11$	−0.583415	−0.175906	−0.0879531	−	0.996125i	$-0.528033\pi$
$11$	−0.583415	−0.175906	−0.0879531	+	0.996125i	$0.528033\pi$
$12$	2.57806	0.744221
$13$	0.0376548	0.0104436	0.00522178	−	0.999986i	$-0.498338\pi$
$13$	0.0376548	0.0104436	0.00522178	+	0.999986i	$0.498338\pi$
$14$	−0.276024	−0.0737704
$15$	0	0
$16$	−4.96459	−1.24115
$17$	1.88357	0.456834	0.228417	−	0.973563i	$-0.426645\pi$
$17$	1.88357	0.456834	0.228417	+	0.973563i	$0.426645\pi$
$18$	−11.8803	−2.80020
$19$	5.31400	1.21912	0.609558	−	0.792741i	$-0.291347\pi$
$19$	5.31400	1.21912	0.609558	+	0.792741i	$0.291347\pi$
$20$	0	0
$21$	0.522743	0.114072
$22$	0.978297	0.208574
$23$	0.253420	0.0528416	0.0264208	−	0.999651i	$-0.491589\pi$
$23$	0.253420	0.0528416	0.0264208	+	0.999651i	$0.491589\pi$
$24$	6.32722	1.29154
$25$	0	0
$26$	−0.0631414	−0.0123830
$27$	12.9722	2.49650
$28$	0.133632	0.0252541
$29$	−0.939996	−0.174553	−0.0872764	−	0.996184i	$-0.527816\pi$
$29$	−0.939996	−0.174553	−0.0872764	+	0.996184i	$0.527816\pi$
$30$	0	0
$31$	−1.95929	−0.351900	−0.175950	−	0.984399i	$-0.556300\pi$
$31$	−1.95929	−0.351900	−0.175950	+	0.984399i	$0.556300\pi$
$32$	4.34004	0.767218
$33$	−1.85273	−0.322519
$34$	−3.15847	−0.541672
$35$	0	0
$36$	5.75161	0.958602
$37$	10.5054	1.72708	0.863541	−	0.504279i	$-0.168242\pi$
$37$	10.5054	1.72708	0.863541	+	0.504279i	$0.168242\pi$
$38$	−8.91077	−1.44552
$39$	0.119579	0.0191480
$40$	0	0
$41$	6.77657	1.05832	0.529161	−	0.848521i	$-0.322507\pi$
$41$	6.77657	1.05832	0.529161	+	0.848521i	$0.322507\pi$
$42$	−0.876560	−0.135256
$43$	0.523511	0.0798347	0.0399174	−	0.999203i	$-0.487291\pi$
$43$	0.523511	0.0798347	0.0399174	+	0.999203i	$0.487291\pi$
$44$	−0.473625	−0.0714016
$45$	0	0
$46$	−0.424946	−0.0626548
$47$	−5.15241	−0.751556	−0.375778	−	0.926710i	$-0.622625\pi$
$47$	−5.15241	−0.751556	−0.375778	+	0.926710i	$0.622625\pi$
$48$	−15.7659	−2.27561
$49$	−6.97290	−0.996129
$50$	0	0
$51$	5.98161	0.837593
$52$	0.0305687	0.00423912
$53$	5.93416	0.815119	0.407560	−	0.913179i	$-0.366380\pi$
$53$	5.93416	0.815119	0.407560	+	0.913179i	$0.366380\pi$
$54$	−21.7524	−2.96013
$55$	0	0
$56$	0.327967	0.0438265
$57$	16.8755	2.23522
$58$	1.57623	0.206969
$59$	0.860469	0.112024	0.0560118	−	0.998430i	$-0.482162\pi$
$59$	0.860469	0.112024	0.0560118	+	0.998430i	$0.482162\pi$
$60$	0	0
$61$	−10.7210	−1.37268	−0.686342	−	0.727279i	$-0.740785\pi$
$61$	−10.7210	−1.37268	−0.686342	+	0.727279i	$0.740785\pi$
$62$	3.28544	0.417251
$63$	1.16623	0.146932
$64$	2.65159	0.331448
$65$	0	0
$66$	3.10675	0.382414
$67$	−2.97102	−0.362968	−0.181484	−	0.983394i	$-0.558090\pi$
$67$	−2.97102	−0.362968	−0.181484	+	0.983394i	$0.558090\pi$
$68$	1.52911	0.185432
$69$	0.804777	0.0968837
$70$	0	0
$71$	−10.1962	−1.21006	−0.605032	−	0.796201i	$-0.706840\pi$
$71$	−10.1962	−1.21006	−0.605032	+	0.796201i	$0.706840\pi$
$72$	14.1159	1.66358
$73$	−6.56160	−0.767977	−0.383989	−	0.923338i	$-0.625450\pi$
$73$	−6.56160	−0.767977	−0.383989	+	0.923338i	$0.625450\pi$
$74$	−17.6160	−2.04782
$75$	0	0
$76$	4.31399	0.494848
$77$	−0.0960352	−0.0109442
$78$	−0.200516	−0.0227040
$79$	15.0176	1.68961	0.844805	−	0.535075i	$-0.179717\pi$
$79$	15.0176	1.68961	0.844805	+	0.535075i	$0.179717\pi$
$80$	0	0
$81$	19.9408	2.21565
$82$	−11.3633	−1.25486
$83$	10.4442	1.14639	0.573197	−	0.819417i	$-0.305703\pi$
$83$	10.4442	1.14639	0.573197	+	0.819417i	$0.305703\pi$
$84$	0.424371	0.0463026
$85$	0	0
$86$	−0.877848	−0.0946608
$87$	−2.98512	−0.320038
$88$	−1.16240	−0.123912
$89$	7.32600	0.776555	0.388277	−	0.921543i	$-0.373070\pi$
$89$	7.32600	0.776555	0.388277	+	0.921543i	$0.373070\pi$
$90$	0	0
$91$	0.00619831	0.000649760 0
$92$	0.205730	0.0214488
$93$	−6.22207	−0.645199
$94$	8.63980	0.891128
$95$	0	0
$96$	13.7825	1.40667
$97$	−6.93110	−0.703747	−0.351873	−	0.936048i	$-0.614455\pi$
$97$	−6.93110	−0.703747	−0.351873	+	0.936048i	$0.614455\pi$
$98$	11.6925	1.18112
$99$	−4.13342	−0.415425
$100$	0	0
$101$	11.6176	1.15599	0.577996	−	0.816040i	$-0.303835\pi$
$101$	11.6176	1.15599	0.577996	+	0.816040i	$0.303835\pi$
$102$	−10.0302	−0.993142
$103$	11.0109	1.08493	0.542467	−	0.840077i	$-0.317490\pi$
$103$	11.0109	1.08493	0.542467	+	0.840077i	$0.317490\pi$
$104$	0.0750236	0.00735667
$105$	0	0
$106$	−9.95067	−0.966495
$107$	−1.64201	−0.158739	−0.0793697	−	0.996845i	$-0.525291\pi$
$107$	−1.64201	−0.158739	−0.0793697	+	0.996845i	$0.525291\pi$
$108$	10.5310	1.01335
$109$	17.3517	1.66199	0.830993	−	0.556282i	$-0.187773\pi$
$109$	17.3517	1.66199	0.830993	+	0.556282i	$0.187773\pi$
$110$	0	0
$111$	33.3618	3.16656
$112$	−0.817215	−0.0772195
$113$	−9.38829	−0.883176	−0.441588	−	0.897218i	$-0.645585\pi$
$113$	−9.38829	−0.883176	−0.441588	+	0.897218i	$0.645585\pi$
$114$	−28.2977	−2.65032
$115$	0	0
$116$	−0.763103	−0.0708523
$117$	0.266780	0.0246638
$118$	−1.44288	−0.132827
$119$	0.310053	0.0284225
$120$	0	0
$121$	−10.6596	−0.969057
$122$	17.9775	1.62760
$123$	21.5201	1.94041
$124$	−1.59058	−0.142839
$125$	0	0
$126$	−1.95559	−0.174218
$127$	−11.7090	−1.03901	−0.519503	−	0.854469i	$-0.673883\pi$
$127$	−11.7090	−1.03901	−0.519503	+	0.854469i	$0.673883\pi$
$128$	−13.1264	−1.16022
$129$	1.66250	0.146375
$130$	0	0
$131$	−5.46218	−0.477232	−0.238616	−	0.971114i	$-0.576694\pi$
$131$	−5.46218	−0.477232	−0.238616	+	0.971114i	$0.576694\pi$
$132$	−1.50408	−0.130913
$133$	0.874732	0.0758489
$134$	4.98194	0.430374
$135$	0	0
$136$	3.75284	0.321804
$137$	−1.89755	−0.162118	−0.0810591	−	0.996709i	$-0.525830\pi$
$137$	−1.89755	−0.162118	−0.0810591	+	0.996709i	$0.525830\pi$
$138$	−1.34949	−0.114876
$139$	5.36542	0.455089	0.227545	−	0.973768i	$-0.426930\pi$
$139$	5.36542	0.455089	0.227545	+	0.973768i	$0.426930\pi$
$140$	0	0
$141$	−16.3624	−1.37796
$142$	17.0974	1.43479
$143$	−0.0219684	−0.00183709
$144$	−35.1735	−2.93112
$145$	0	0
$146$	11.0028	0.910598
$147$	−22.1436	−1.82638
$148$	8.52847	0.701036
$149$	−0.998021	−0.0817611	−0.0408806	−	0.999164i	$-0.513016\pi$
$149$	−0.998021	−0.0817611	−0.0408806	+	0.999164i	$0.513016\pi$
$150$	0	0
$151$	6.21150	0.505485	0.252742	−	0.967534i	$-0.418667\pi$
$151$	6.21150	0.505485	0.252742	+	0.967534i	$0.418667\pi$
$152$	10.5876	0.858771
$153$	13.3449	1.07887
$154$	0.161036	0.0129767
$155$	0	0
$156$	0.0970762	0.00777232
$157$	8.91835	0.711762	0.355881	−	0.934531i	$-0.384181\pi$
$157$	8.91835	0.711762	0.355881	+	0.934531i	$0.384181\pi$
$158$	−25.1822	−2.00339
$159$	18.8449	1.49450
$160$	0	0
$161$	0.0417151	0.00328761
$162$	−33.4377	−2.62712
$163$	−19.4775	−1.52560	−0.762798	−	0.646637i	$-0.776175\pi$
$163$	−19.4775	−1.52560	−0.762798	+	0.646637i	$0.776175\pi$
$164$	5.50132	0.429581
$165$	0	0
$166$	−17.5132	−1.35929
$167$	−8.00193	−0.619208	−0.309604	−	0.950866i	$-0.600196\pi$
$167$	−8.00193	−0.619208	−0.309604	+	0.950866i	$0.600196\pi$
$168$	1.04152	0.0803547
$169$	−12.9986	−0.999891
$170$	0	0
$171$	37.6491	2.87910
$172$	0.424994	0.0324055
$173$	24.5819	1.86893	0.934464	−	0.356058i	$-0.115879\pi$
$173$	24.5819	1.86893	0.934464	+	0.356058i	$0.115879\pi$
$174$	5.00558	0.379472
$175$	0	0
$176$	2.89641	0.218325
$177$	2.73257	0.205392
$178$	−12.2846	−0.920768
$179$	−0.874518	−0.0653645	−0.0326823	−	0.999466i	$-0.510405\pi$
$179$	−0.874518	−0.0653645	−0.0326823	+	0.999466i	$0.510405\pi$
$180$	0	0
$181$	1.23360	0.0916926	0.0458463	−	0.998949i	$-0.485402\pi$
$181$	1.23360	0.0916926	0.0458463	+	0.998949i	$0.485402\pi$
$182$	−0.0103936	−0.000770427 0
$183$	−34.0464	−2.51678
$184$	0.504914	0.0372228
$185$	0	0
$186$	10.4335	0.765018
$187$	−1.09891	−0.0803599
$188$	−4.18280	−0.305062
$189$	2.13534	0.155323
$190$	0	0
$191$	10.5151	0.760848	0.380424	−	0.924812i	$-0.375778\pi$
$191$	10.5151	0.760848	0.380424	+	0.924812i	$0.375778\pi$
$192$	8.42056	0.607702
$193$	−26.3146	−1.89417	−0.947083	−	0.320988i	$-0.895985\pi$
$193$	−26.3146	−1.89417	−0.947083	+	0.320988i	$0.895985\pi$
$194$	11.6224	0.834439
$195$	0	0
$196$	−5.66071	−0.404336
$197$	0.784383	0.0558850	0.0279425	−	0.999610i	$-0.491104\pi$
$197$	0.784383	0.0558850	0.0279425	+	0.999610i	$0.491104\pi$
$198$	6.93111	0.492573
$199$	26.7063	1.89316	0.946580	−	0.322469i	$-0.104513\pi$
$199$	26.7063	1.89316	0.946580	+	0.322469i	$0.104513\pi$
$200$	0	0
$201$	−9.43497	−0.665491
$202$	−19.4809	−1.37067
$203$	−0.154732	−0.0108600
$204$	4.85596	0.339985
$205$	0	0
$206$	−18.4635	−1.28642
$207$	1.79545	0.124792
$208$	−0.186941	−0.0129620
$209$	−3.10027	−0.214450
$210$	0	0
$211$	6.93352	0.477323	0.238661	−	0.971103i	$-0.423291\pi$
$211$	6.93352	0.477323	0.238661	+	0.971103i	$0.423291\pi$
$212$	4.81744	0.330863
$213$	−32.3797	−2.21862
$214$	2.75340	0.188219
$215$	0	0
$216$	25.8459	1.75859
$217$	−0.322517	−0.0218939
$218$	−29.0961	−1.97063
$219$	−20.8375	−1.40807
$220$	0	0
$221$	0.0709257	0.00477098
$222$	−55.9426	−3.75462
$223$	21.5727	1.44462	0.722308	−	0.691572i	$-0.243081\pi$
$223$	21.5727	1.44462	0.722308	+	0.691572i	$0.243081\pi$
$224$	0.714409	0.0477335
$225$	0	0
$226$	15.7427	1.04719
$227$	−17.0199	−1.12965	−0.564826	−	0.825210i	$-0.691057\pi$
$227$	−17.0199	−1.12965	−0.564826	+	0.825210i	$0.691057\pi$
$228$	13.6998	0.907291
$229$	17.6228	1.16455	0.582273	−	0.812993i	$-0.302163\pi$
$229$	17.6228	1.16455	0.582273	+	0.812993i	$0.302163\pi$
$230$	0	0
$231$	−0.304976	−0.0200660
$232$	−1.87285	−0.122959
$233$	−5.67707	−0.371917	−0.185959	−	0.982558i	$-0.559539\pi$
$233$	−5.67707	−0.371917	−0.185959	+	0.982558i	$0.559539\pi$
$234$	−0.447349	−0.0292441
$235$	0	0
$236$	0.698542	0.0454712
$237$	47.6909	3.09785
$238$	−0.519911	−0.0337008
$239$	5.86832	0.379590	0.189795	−	0.981824i	$-0.439218\pi$
$239$	5.86832	0.379590	0.189795	+	0.981824i	$0.439218\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	17.8746	1.14902
$243$	24.4089	1.56583
$244$	−8.70347	−0.557183
$245$	0	0
$246$	−36.0860	−2.30076
$247$	0.200098	0.0127319
$248$	−3.90370	−0.247886
$249$	33.1672	2.10188
$250$	0	0
$251$	11.1299	0.702513	0.351257	−	0.936279i	$-0.385755\pi$
$251$	11.1299	0.702513	0.351257	+	0.936279i	$0.385755\pi$
$252$	0.946766	0.0596406
$253$	−0.147849	−0.00929517
$254$	19.6342	1.23196
$255$	0	0
$256$	16.7078	1.04424
$257$	−5.56469	−0.347116	−0.173558	−	0.984824i	$-0.555526\pi$
$257$	−5.56469	−0.347116	−0.173558	+	0.984824i	$0.555526\pi$
$258$	−2.78776	−0.173558
$259$	1.72929	0.107453
$260$	0	0
$261$	−6.65975	−0.412228
$262$	9.15923	0.565859
$263$	−3.02034	−0.186242	−0.0931212	−	0.995655i	$-0.529684\pi$
$263$	−3.02034	−0.186242	−0.0931212	+	0.995655i	$0.529684\pi$
$264$	−3.69139	−0.227189
$265$	0	0
$266$	−1.46679	−0.0899347
$267$	23.2650	1.42379
$268$	−2.41192	−0.147331
$269$	18.7002	1.14017	0.570087	−	0.821584i	$-0.306910\pi$
$269$	18.7002	1.14017	0.570087	+	0.821584i	$0.306910\pi$
$270$	0	0
$271$	−19.0286	−1.15591	−0.577954	−	0.816070i	$-0.696149\pi$
$271$	−19.0286	−1.15591	−0.577954	+	0.816070i	$0.696149\pi$
$272$	−9.35117	−0.566998
$273$	0.0196838	0.00119132
$274$	3.18189	0.192225
$275$	0	0
$276$	0.653330	0.0393258
$277$	15.5387	0.933628	0.466814	−	0.884356i	$-0.345402\pi$
$277$	15.5387	0.933628	0.466814	+	0.884356i	$0.345402\pi$
$278$	−8.99699	−0.539604
$279$	−13.8814	−0.831055
$280$	0	0
$281$	26.2127	1.56372	0.781858	−	0.623456i	$-0.214272\pi$
$281$	26.2127	1.56372	0.781858	+	0.623456i	$0.214272\pi$
$282$	27.4372	1.63386
$283$	−11.4229	−0.679024	−0.339512	−	0.940602i	$-0.610262\pi$
$283$	−11.4229	−0.679024	−0.339512	+	0.940602i	$0.610262\pi$
$284$	−8.27741	−0.491174
$285$	0	0
$286$	0.0368376	0.00217825
$287$	1.11548	0.0658449
$288$	30.7487	1.81188
$289$	−13.4521	−0.791303
$290$	0	0
$291$	−22.0109	−1.29030
$292$	−5.32681	−0.311728
$293$	−10.3316	−0.603579	−0.301789	−	0.953375i	$-0.597584\pi$
$293$	−10.3316	−0.603579	−0.301789	+	0.953375i	$0.597584\pi$
$294$	37.1315	2.16555
$295$	0	0
$296$	20.9311	1.21659
$297$	−7.56818	−0.439151
$298$	1.67353	0.0969449
$299$	0.00954247	0.000551855 0
$300$	0	0
$301$	0.0861746	0.00496702
$302$	−10.4157	−0.599358
$303$	36.8936	2.11948
$304$	−26.3818	−1.51310
$305$	0	0
$306$	−22.3773	−1.27923
$307$	8.94677	0.510619	0.255309	−	0.966859i	$-0.417823\pi$
$307$	8.94677	0.510619	0.255309	+	0.966859i	$0.417823\pi$
$308$	−0.0779628	−0.00444234
$309$	34.9669	1.98920
$310$	0	0
$311$	7.01224	0.397628	0.198814	−	0.980037i	$-0.436291\pi$
$311$	7.01224	0.397628	0.198814	+	0.980037i	$0.436291\pi$
$312$	0.238250	0.0134883
$313$	7.07815	0.400080	0.200040	−	0.979788i	$-0.435893\pi$
$313$	7.07815	0.400080	0.200040	+	0.979788i	$0.435893\pi$
$314$	−14.9547	−0.843943
$315$	0	0
$316$	12.1915	0.685825
$317$	−25.6562	−1.44099	−0.720497	−	0.693458i	$-0.756086\pi$
$317$	−25.6562	−1.44099	−0.720497	+	0.693458i	$0.756086\pi$
$318$	−31.6000	−1.77204
$319$	0.548407	0.0307049
$320$	0	0
$321$	−5.21449	−0.291044
$322$	−0.0699498	−0.00389815
$323$	10.0093	0.556934
$324$	16.1883	0.899349
$325$	0	0
$326$	32.6608	1.80891
$327$	55.1031	3.04721
$328$	13.5017	0.745505
$329$	−0.848132	−0.0467590
$330$	0	0
$331$	18.0453	0.991860	0.495930	−	0.868362i	$-0.334827\pi$
$331$	18.0453	0.991860	0.495930	+	0.868362i	$0.334827\pi$
$332$	8.47872	0.465330
$333$	74.4297	4.07872
$334$	13.4180	0.734200
$335$	0	0
$336$	−2.59520	−0.141580
$337$	−21.0372	−1.14597	−0.572986	−	0.819565i	$-0.694215\pi$
$337$	−21.0372	−1.14597	−0.572986	+	0.819565i	$0.694215\pi$
$338$	21.7966	1.18558
$339$	−29.8141	−1.61928
$340$	0	0
$341$	1.14308	0.0619013
$342$	−63.1317	−3.41377
$343$	−2.30006	−0.124192
$344$	1.04305	0.0562373
$345$	0	0
$346$	−41.2201	−2.21601
$347$	−21.1868	−1.13737	−0.568684	−	0.822556i	$-0.692547\pi$
$347$	−21.1868	−1.13737	−0.568684	+	0.822556i	$0.692547\pi$
$348$	−2.42336	−0.129906
$349$	−9.78912	−0.524000	−0.262000	−	0.965068i	$-0.584382\pi$
$349$	−9.78912	−0.524000	−0.262000	+	0.965068i	$0.584382\pi$
$350$	0	0
$351$	0.488467	0.0260724
$352$	−2.53204	−0.134958
$353$	30.8270	1.64075	0.820377	−	0.571823i	$-0.193764\pi$
$353$	30.8270	1.64075	0.820377	+	0.571823i	$0.193764\pi$
$354$	−4.58210	−0.243536
$355$	0	0
$356$	5.94736	0.315209
$357$	0.984626	0.0521119
$358$	1.46643	0.0775033
$359$	34.0984	1.79965	0.899823	−	0.436254i	$-0.143695\pi$
$359$	34.0984	1.79965	0.899823	+	0.436254i	$0.143695\pi$
$360$	0	0
$361$	9.23864	0.486244
$362$	−2.06855	−0.108721
$363$	−33.8515	−1.77674
$364$	0.00503188	0.000263742 0
$365$	0	0
$366$	57.0905	2.98417
$367$	−23.8130	−1.24303	−0.621515	−	0.783402i	$-0.713483\pi$
$367$	−23.8130	−1.24303	−0.621515	+	0.783402i	$0.713483\pi$
$368$	−1.25812	−0.0655842
$369$	48.0112	2.49936
$370$	0	0
$371$	0.976815	0.0507137
$372$	−5.05117	−0.261891
$373$	0.329270	0.0170490	0.00852449	−	0.999964i	$-0.497287\pi$
$373$	0.329270	0.0170490	0.00852449	+	0.999964i	$0.497287\pi$
$374$	1.84270	0.0952835
$375$	0	0
$376$	−10.2657	−0.529412
$377$	−0.0353954	−0.00182295
$378$	−3.58064	−0.184168
$379$	10.8125	0.555399	0.277699	−	0.960668i	$-0.410428\pi$
$379$	10.8125	0.555399	0.277699	+	0.960668i	$0.410428\pi$
$380$	0	0
$381$	−37.1839	−1.90499
$382$	−17.6322	−0.902144
$383$	−17.4419	−0.891240	−0.445620	−	0.895222i	$-0.647017\pi$
$383$	−17.4419	−0.891240	−0.445620	+	0.895222i	$0.647017\pi$
$384$	−41.6851	−2.12723
$385$	0	0
$386$	44.1256	2.24593
$387$	3.70901	0.188540
$388$	−5.62677	−0.285656
$389$	27.3777	1.38810	0.694052	−	0.719924i	$-0.255824\pi$
$389$	27.3777	1.38810	0.694052	+	0.719924i	$0.255824\pi$
$390$	0	0
$391$	0.477335	0.0241398
$392$	−13.8928	−0.701695
$393$	−17.3461	−0.874993
$394$	−1.31529	−0.0662634
$395$	0	0
$396$	−3.35557	−0.168624
$397$	19.3059	0.968936	0.484468	−	0.874809i	$-0.339013\pi$
$397$	19.3059	0.968936	0.484468	+	0.874809i	$0.339013\pi$
$398$	−44.7824	−2.24474
$399$	2.77786	0.139067
$400$	0	0
$401$	−8.95402	−0.447142	−0.223571	−	0.974688i	$-0.571772\pi$
$401$	−8.95402	−0.447142	−0.223571	+	0.974688i	$0.571772\pi$
$402$	15.8210	0.789080
$403$	−0.0737768	−0.00367509
$404$	9.43132	0.469226
$405$	0	0
$406$	0.259461	0.0128768
$407$	−6.12902	−0.303804
$408$	11.9178	0.590018
$409$	−33.2344	−1.64334	−0.821669	−	0.569965i	$-0.806957\pi$
$409$	−33.2344	−1.64334	−0.821669	+	0.569965i	$0.806957\pi$
$410$	0	0
$411$	−6.02598	−0.297240
$412$	8.93879	0.440383
$413$	0.141641	0.00696969
$414$	−3.01069	−0.147967
$415$	0	0
$416$	0.163424	0.00801250
$417$	17.0388	0.834394
$418$	5.19867	0.254276
$419$	−4.70397	−0.229804	−0.114902	−	0.993377i	$-0.536655\pi$
$419$	−4.70397	−0.229804	−0.114902	+	0.993377i	$0.536655\pi$
$420$	0	0
$421$	−19.1128	−0.931503	−0.465752	−	0.884916i	$-0.654216\pi$
$421$	−19.1128	−0.931503	−0.465752	+	0.884916i	$0.654216\pi$
$422$	−11.6264	−0.565966
$423$	−36.5042	−1.77490
$424$	11.8232	0.574187
$425$	0	0
$426$	54.2958	2.63064
$427$	−1.76477	−0.0854033
$428$	−1.33301	−0.0644335
$429$	−0.0697643	−0.00336825
$430$	0	0
$431$	35.1161	1.69148	0.845741	−	0.533594i	$-0.179159\pi$
$431$	35.1161	1.69148	0.845741	+	0.533594i	$0.179159\pi$
$432$	−64.4017	−3.09853
$433$	10.2037	0.490356	0.245178	−	0.969478i	$-0.421154\pi$
$433$	10.2037	0.490356	0.245178	+	0.969478i	$0.421154\pi$
$434$	0.540812	0.0259598
$435$	0	0
$436$	14.0863	0.674613
$437$	1.34667	0.0644201
$438$	34.9413	1.66956
$439$	22.9777	1.09667	0.548334	−	0.836259i	$-0.315262\pi$
$439$	22.9777	1.09667	0.548334	+	0.836259i	$0.315262\pi$
$440$	0	0
$441$	−49.4022	−2.35248
$442$	−0.118931	−0.00565699
$443$	4.74832	0.225600	0.112800	−	0.993618i	$-0.464018\pi$
$443$	4.74832	0.225600	0.112800	+	0.993618i	$0.464018\pi$
$444$	27.0836	1.28533
$445$	0	0
$446$	−36.1741	−1.71289
$447$	−3.16939	−0.149907
$448$	0.436475	0.0206215
$449$	−22.5035	−1.06200	−0.531002	−	0.847370i	$-0.678184\pi$
$449$	−22.5035	−1.06200	−0.531002	+	0.847370i	$0.678184\pi$
$450$	0	0
$451$	−3.95355	−0.186165
$452$	−7.62156	−0.358488
$453$	19.7257	0.926793
$454$	28.5398	1.33944
$455$	0	0
$456$	33.6229	1.57453
$457$	−19.7938	−0.925917	−0.462958	−	0.886380i	$-0.653212\pi$
$457$	−19.7938	−0.925917	−0.462958	+	0.886380i	$0.653212\pi$
$458$	−29.5507	−1.38081
$459$	24.4341	1.14049
$460$	0	0
$461$	−3.01426	−0.140388	−0.0701941	−	0.997533i	$-0.522362\pi$
$461$	−3.01426	−0.140388	−0.0701941	+	0.997533i	$0.522362\pi$
$462$	0.511398	0.0237924
$463$	−0.587905	−0.0273222	−0.0136611	−	0.999907i	$-0.504349\pi$
$463$	−0.587905	−0.0273222	−0.0136611	+	0.999907i	$0.504349\pi$
$464$	4.66669	0.216646
$465$	0	0
$466$	9.51958	0.440986
$467$	−0.415703	−0.0192365	−0.00961823	−	0.999954i	$-0.503062\pi$
$467$	−0.415703	−0.0192365	−0.00961823	+	0.999954i	$0.503062\pi$
$468$	0.216576	0.0100112
$469$	−0.489056	−0.0225825
$470$	0	0
$471$	28.3217	1.30500
$472$	1.71440	0.0789118
$473$	−0.305424	−0.0140434
$474$	−79.9703	−3.67316
$475$	0	0
$476$	0.251706	0.0115369
$477$	42.0428	1.92501
$478$	−9.84028	−0.450084
$479$	−36.0356	−1.64651	−0.823255	−	0.567672i	$-0.807844\pi$
$479$	−36.0356	−1.64651	−0.823255	+	0.567672i	$0.807844\pi$
$480$	0	0
$481$	0.395580	0.0180369
$482$	1.67685	0.0763783
$483$	0.132473	0.00602774
$484$	−8.65365	−0.393348
$485$	0	0
$486$	−40.9300	−1.85662
$487$	−22.7662	−1.03164	−0.515818	−	0.856698i	$-0.672512\pi$
$487$	−22.7662	−1.03164	−0.515818	+	0.856698i	$0.672512\pi$
$488$	−21.3606	−0.966948
$489$	−61.8541	−2.79714
$490$	0	0
$491$	0.435669	0.0196615	0.00983074	−	0.999952i	$-0.496871\pi$
$491$	0.435669	0.0196615	0.00983074	+	0.999952i	$0.496871\pi$
$492$	17.4704	0.787625
$493$	−1.77055	−0.0797416
$494$	−0.335533	−0.0150964
$495$	0	0
$496$	9.72708	0.436759
$497$	−1.67838	−0.0752857
$498$	−55.6163	−2.49223
$499$	6.96505	0.311798	0.155899	−	0.987773i	$-0.450172\pi$
$499$	6.96505	0.311798	0.155899	+	0.987773i	$0.450172\pi$
$500$	0	0
$501$	−25.4115	−1.13530
$502$	−18.6631	−0.832977
$503$	−6.52409	−0.290895	−0.145447	−	0.989366i	$-0.546462\pi$
$503$	−6.52409	−0.290895	−0.145447	+	0.989366i	$0.546462\pi$
$504$	2.32361	0.103502
$505$	0	0
$506$	0.247920	0.0110214
$507$	−41.2792	−1.83327
$508$	−9.50554	−0.421740
$509$	34.8922	1.54657	0.773285	−	0.634059i	$-0.218612\pi$
$509$	34.8922	1.54657	0.773285	+	0.634059i	$0.218612\pi$
$510$	0	0
$511$	−1.08010	−0.0477807
$512$	−1.76359	−0.0779404
$513$	68.9344	3.04353
$514$	9.33113	0.411579
$515$	0	0
$516$	1.34964	0.0594147
$517$	3.00599	0.132203
$518$	−2.89975	−0.127408
$519$	78.0640	3.42663
$520$	0	0
$521$	−27.3348	−1.19756	−0.598780	−	0.800914i	$-0.704348\pi$
$521$	−27.3348	−1.19756	−0.598780	+	0.800914i	$0.704348\pi$
$522$	11.1674	0.488783
$523$	23.6792	1.03542	0.517709	−	0.855557i	$-0.326785\pi$
$523$	23.6792	1.03542	0.517709	+	0.855557i	$0.326785\pi$
$524$	−4.43428	−0.193712
$525$	0	0
$526$	5.06465	0.220829
$527$	−3.69048	−0.160760
$528$	9.19805	0.400294
$529$	−22.9358	−0.997208
$530$	0	0
$531$	6.09632	0.264558
$532$	0.710120	0.0307876
$533$	0.255170	0.0110527
$534$	−39.0118	−1.68820
$535$	0	0
$536$	−5.91947	−0.255682
$537$	−2.77718	−0.119844
$538$	−31.3574	−1.35192
$539$	4.06810	0.175225
$540$	0	0
$541$	−37.8148	−1.62578	−0.812892	−	0.582415i	$-0.802108\pi$
$541$	−37.8148	−1.62578	−0.812892	+	0.582415i	$0.802108\pi$
$542$	31.9081	1.37057
$543$	3.91750	0.168116
$544$	8.17479	0.350491
$545$	0	0
$546$	−0.0330067	−0.00141256
$547$	−17.7257	−0.757898	−0.378949	−	0.925417i	$-0.623714\pi$
$547$	−17.7257	−0.757898	−0.378949	+	0.925417i	$0.623714\pi$
$548$	−1.54046	−0.0658050
$549$	−75.9570	−3.24177
$550$	0	0
$551$	−4.99514	−0.212800
$552$	1.60344	0.0682469
$553$	2.47203	0.105121
$554$	−26.0560	−1.10701
$555$	0	0
$556$	4.35573	0.184724
$557$	9.80001	0.415240	0.207620	−	0.978210i	$-0.433428\pi$
$557$	9.80001	0.415240	0.207620	+	0.978210i	$0.433428\pi$
$558$	23.2769	0.985390
$559$	0.0197127	0.000833759 0
$560$	0	0
$561$	−3.48976	−0.147338
$562$	−43.9546	−1.85411
$563$	−6.14480	−0.258973	−0.129486	−	0.991581i	$-0.541333\pi$
$563$	−6.14480	−0.258973	−0.129486	+	0.991581i	$0.541333\pi$
$564$	−13.2832	−0.559324
$565$	0	0
$566$	19.1545	0.805125
$567$	3.28244	0.137850
$568$	−20.3149	−0.852395
$569$	−24.1037	−1.01048	−0.505240	−	0.862979i	$-0.668596\pi$
$569$	−24.1037	−1.01048	−0.505240	+	0.862979i	$0.668596\pi$
$570$	0	0
$571$	−31.0593	−1.29979	−0.649895	−	0.760024i	$-0.725187\pi$
$571$	−31.0593	−1.29979	−0.649895	+	0.760024i	$0.725187\pi$
$572$	−0.0178343	−0.000745688 0
$573$	33.3926	1.39499
$574$	−1.87049	−0.0780729
$575$	0	0
$576$	18.7862	0.782757
$577$	9.39623	0.391170	0.195585	−	0.980687i	$-0.437339\pi$
$577$	9.39623	0.391170	0.195585	+	0.980687i	$0.437339\pi$
$578$	22.5572	0.938255
$579$	−83.5665	−3.47290
$580$	0	0
$581$	1.71920	0.0713244
$582$	36.9089	1.52992
$583$	−3.46208	−0.143384
$584$	−13.0734	−0.540980
$585$	0	0
$586$	17.3245	0.715669
$587$	33.6404	1.38849	0.694245	−	0.719739i	$-0.255738\pi$
$587$	33.6404	1.38849	0.694245	+	0.719739i	$0.255738\pi$
$588$	−17.9765	−0.741340
$589$	−10.4117	−0.429006
$590$	0	0
$591$	2.49094	0.102464
$592$	−52.1551	−2.14356
$593$	41.1938	1.69163	0.845813	−	0.533479i	$-0.179116\pi$
$593$	41.1938	1.69163	0.845813	+	0.533479i	$0.179116\pi$
$594$	12.6907	0.520705
$595$	0	0
$596$	−0.810209	−0.0331874
$597$	84.8104	3.47106
$598$	−0.0160013	−0.000654340 0
$599$	−15.6508	−0.639475	−0.319738	−	0.947506i	$-0.603595\pi$
$599$	−15.6508	−0.639475	−0.319738	+	0.947506i	$0.603595\pi$
$600$	0	0
$601$	−27.4645	−1.12030	−0.560151	−	0.828390i	$-0.689257\pi$
$601$	−27.4645	−1.12030	−0.560151	+	0.828390i	$0.689257\pi$
$602$	−0.144502	−0.00588944
$603$	−21.0493	−0.857193
$604$	5.04259	0.205180
$605$	0	0
$606$	−61.8649	−2.51309
$607$	−45.2064	−1.83487	−0.917436	−	0.397883i	$-0.869745\pi$
$607$	−45.2064	−1.83487	−0.917436	+	0.397883i	$0.869745\pi$
$608$	23.0630	0.935328
$609$	−0.491376	−0.0199116
$610$	0	0
$611$	−0.194013	−0.00784893
$612$	10.8336	0.437922
$613$	−46.6438	−1.88392	−0.941962	−	0.335720i	$-0.891020\pi$
$613$	−46.6438	−1.88392	−0.941962	+	0.335720i	$0.891020\pi$
$614$	−15.0024	−0.605446
$615$	0	0
$616$	−0.191341	−0.00770935
$617$	−28.6236	−1.15234	−0.576172	−	0.817329i	$-0.695454\pi$
$617$	−28.6236	−1.15234	−0.576172	+	0.817329i	$0.695454\pi$
$618$	−58.6341	−2.35861
$619$	33.1305	1.33163	0.665814	−	0.746118i	$-0.268084\pi$
$619$	33.1305	1.33163	0.665814	+	0.746118i	$0.268084\pi$
$620$	0	0
$621$	3.28741	0.131919
$622$	−11.7584	−0.471471
$623$	1.20592	0.0483143
$624$	−0.593662	−0.0237655
$625$	0	0
$626$	−11.8690	−0.474379
$627$	−9.84543	−0.393189
$628$	7.24005	0.288909
$629$	19.7878	0.788990
$630$	0	0
$631$	31.6457	1.25979	0.629897	−	0.776678i	$-0.283097\pi$
$631$	31.6457	1.25979	0.629897	+	0.776678i	$0.283097\pi$
$632$	29.9211	1.19020
$633$	22.0186	0.875159
$634$	43.0215	1.70860
$635$	0	0
$636$	15.2986	0.606629
$637$	−0.262563	−0.0104031
$638$	−0.919595	−0.0364071
$639$	−72.2387	−2.85772
$640$	0	0
$641$	17.6901	0.698716	0.349358	−	0.936989i	$-0.386400\pi$
$641$	17.6901	0.698716	0.349358	+	0.936989i	$0.386400\pi$
$642$	8.74390	0.345094
$643$	−9.68538	−0.381954	−0.190977	−	0.981595i	$-0.561166\pi$
$643$	−9.68538	−0.381954	−0.190977	+	0.981595i	$0.561166\pi$
$644$	0.0338649	0.00133447
$645$	0	0
$646$	−16.7841	−0.660362
$647$	8.49280	0.333886	0.166943	−	0.985967i	$-0.446610\pi$
$647$	8.49280	0.333886	0.166943	+	0.985967i	$0.446610\pi$
$648$	39.7302	1.56075
$649$	−0.502011	−0.0197056
$650$	0	0
$651$	−1.02421	−0.0401419
$652$	−15.8121	−0.619251
$653$	−11.7106	−0.458271	−0.229136	−	0.973395i	$-0.573590\pi$
$653$	−11.7106	−0.458271	−0.229136	+	0.973395i	$0.573590\pi$
$654$	−92.3995	−3.61311
$655$	0	0
$656$	−33.6429	−1.31353
$657$	−46.4881	−1.81368
$658$	1.42219	0.0554427
$659$	9.74746	0.379707	0.189854	−	0.981812i	$-0.439199\pi$
$659$	9.74746	0.379707	0.189854	+	0.981812i	$0.439199\pi$
$660$	0	0
$661$	16.0354	0.623704	0.311852	−	0.950131i	$-0.399051\pi$
$661$	16.0354	0.623704	0.311852	+	0.950131i	$0.399051\pi$
$662$	−30.2592	−1.17606
$663$	0.225236	0.00874746
$664$	20.8090	0.807545
$665$	0	0
$666$	−124.807	−4.83618
$667$	−0.238213	−0.00922365
$668$	−6.49608	−0.251341
$669$	68.5078	2.64866
$670$	0	0
$671$	6.25479	0.241464
$672$	2.26873	0.0875181
$673$	16.4182	0.632876	0.316438	−	0.948613i	$-0.397513\pi$
$673$	16.4182	0.632876	0.316438	+	0.948613i	$0.397513\pi$
$674$	35.2762	1.35879
$675$	0	0
$676$	−10.5524	−0.405863
$677$	34.0479	1.30857	0.654284	−	0.756249i	$-0.272970\pi$
$677$	34.0479	1.30857	0.654284	+	0.756249i	$0.272970\pi$
$678$	49.9937	1.92000
$679$	−1.14092	−0.0437845
$680$	0	0
$681$	−54.0497	−2.07119
$682$	−1.91677	−0.0733970
$683$	48.0392	1.83817	0.919085	−	0.394060i	$-0.128930\pi$
$683$	48.0392	1.83817	0.919085	+	0.394060i	$0.128930\pi$
$684$	30.5641	1.16865
$685$	0	0
$686$	3.85685	0.147255
$687$	55.9642	2.13517
$688$	−2.59902	−0.0990866
$689$	0.223450	0.00851275
$690$	0	0
$691$	26.1215	0.993707	0.496854	−	0.867834i	$-0.334489\pi$
$691$	26.1215	0.993707	0.496854	+	0.867834i	$0.334489\pi$
$692$	19.9560	0.758612
$693$	−0.680398	−0.0258462
$694$	35.5270	1.34859
$695$	0	0
$696$	−5.94756	−0.225442
$697$	12.7642	0.483477
$698$	16.4149	0.621311
$699$	−18.0285	−0.681900
$700$	0	0
$701$	38.2555	1.44489	0.722445	−	0.691428i	$-0.243018\pi$
$701$	38.2555	1.44489	0.722445	+	0.691428i	$0.243018\pi$
$702$	−0.819084	−0.0309143
$703$	55.8259	2.10551
$704$	−1.54698	−0.0583038
$705$	0	0
$706$	−51.6921	−1.94546
$707$	1.91236	0.0719215
$708$	2.21834	0.0833703
$709$	−45.4471	−1.70680	−0.853401	−	0.521256i	$-0.825464\pi$
$709$	−45.4471	−1.70680	−0.853401	+	0.521256i	$0.825464\pi$
$710$	0	0
$711$	106.398	3.99023
$712$	14.5964	0.547022
$713$	−0.496523	−0.0185949
$714$	−1.65107	−0.0617896
$715$	0	0
$716$	−0.709947	−0.0265319
$717$	18.6359	0.695969
$718$	−57.1779	−2.13386
$719$	−26.3489	−0.982648	−0.491324	−	0.870977i	$-0.663487\pi$
$719$	−26.3489	−0.982648	−0.491324	+	0.870977i	$0.663487\pi$
$720$	0	0
$721$	1.81249	0.0675005
$722$	−15.4918	−0.576544
$723$	−3.17567	−0.118104
$724$	1.00145	0.0372187
$725$	0	0
$726$	56.7637	2.10670
$727$	8.30504	0.308017	0.154008	−	0.988070i	$-0.450782\pi$
$727$	8.30504	0.308017	0.154008	+	0.988070i	$0.450782\pi$
$728$	0.0123495	0.000457705 0
$729$	17.6920	0.655260
$730$	0	0
$731$	0.986073	0.0364712
$732$	−27.6393	−1.02158
$733$	44.0122	1.62563	0.812814	−	0.582523i	$-0.197934\pi$
$733$	44.0122	1.62563	0.812814	+	0.582523i	$0.197934\pi$
$734$	39.9308	1.47387
$735$	0	0
$736$	1.09985	0.0405411
$737$	1.73334	0.0638482
$738$	−80.5073	−2.96352
$739$	−15.6261	−0.574814	−0.287407	−	0.957808i	$-0.592793\pi$
$739$	−15.6261	−0.574814	−0.287407	+	0.957808i	$0.592793\pi$
$740$	0	0
$741$	0.635445	0.0233436
$742$	−1.63797	−0.0601317
$743$	2.45008	0.0898846	0.0449423	−	0.998990i	$-0.485690\pi$
$743$	2.45008	0.0898846	0.0449423	+	0.998990i	$0.485690\pi$
$744$	−12.3969	−0.454492
$745$	0	0
$746$	−0.552136	−0.0202151
$747$	73.9955	2.70736
$748$	−0.892108	−0.0326187
$749$	−0.270290	−0.00987617
$750$	0	0
$751$	32.5444	1.18756	0.593781	−	0.804626i	$-0.297634\pi$
$751$	32.5444	1.18756	0.593781	+	0.804626i	$0.297634\pi$
$752$	25.5796	0.932792
$753$	35.3449	1.28804
$754$	0.0593526	0.00216149
$755$	0	0
$756$	1.73350	0.0630469
$757$	−5.61641	−0.204132	−0.102066	−	0.994778i	$-0.532545\pi$
$757$	−5.61641	−0.204132	−0.102066	+	0.994778i	$0.532545\pi$
$758$	−18.1308	−0.658542
$759$	−0.469519	−0.0170424
$760$	0	0
$761$	1.98260	0.0718692	0.0359346	−	0.999354i	$-0.488559\pi$
$761$	1.98260	0.0718692	0.0359346	+	0.999354i	$0.488559\pi$
$762$	62.3517	2.25877
$763$	2.85623	0.103403
$764$	8.53633	0.308834
$765$	0	0
$766$	29.2474	1.05675
$767$	0.0324008	0.00116993
$768$	53.0584	1.91458
$769$	−13.2422	−0.477527	−0.238763	−	0.971078i	$-0.576742\pi$
$769$	−13.2422	−0.477527	−0.238763	+	0.971078i	$0.576742\pi$
$770$	0	0
$771$	−17.6716	−0.636428
$772$	−21.3626	−0.768856
$773$	43.7232	1.57262	0.786308	−	0.617835i	$-0.211990\pi$
$773$	43.7232	1.57262	0.786308	+	0.617835i	$0.211990\pi$
$774$	−6.21945	−0.223553
$775$	0	0
$776$	−13.8096	−0.495734
$777$	5.49164	0.197012
$778$	−45.9082	−1.64589
$779$	36.0107	1.29022
$780$	0	0
$781$	5.94860	0.212858
$782$	−0.800417	−0.0286228
$783$	−12.1938	−0.435772
$784$	34.6176	1.23634
$785$	0	0
$786$	29.0867	1.03749
$787$	27.6390	0.985225	0.492613	−	0.870249i	$-0.336042\pi$
$787$	27.6390	0.985225	0.492613	+	0.870249i	$0.336042\pi$
$788$	0.636774	0.0226841
$789$	−9.59161	−0.341470
$790$	0	0
$791$	−1.54540	−0.0549479
$792$	−8.23545	−0.292634
$793$	−0.403697	−0.0143357
$794$	−32.3730	−1.14888
$795$	0	0
$796$	21.6806	0.768448
$797$	−27.8554	−0.986689	−0.493344	−	0.869834i	$-0.664226\pi$
$797$	−27.8554	−0.986689	−0.493344	+	0.869834i	$0.664226\pi$
$798$	−4.65804	−0.164893
$799$	−9.70495	−0.343337
$800$	0	0
$801$	51.9038	1.83393
$802$	15.0145	0.530181
$803$	3.82814	0.135092
$804$	−7.65945	−0.270128
$805$	0	0
$806$	0.123712	0.00435759
$807$	59.3858	2.09048
$808$	23.1469	0.814305
$809$	−18.5727	−0.652981	−0.326490	−	0.945201i	$-0.605866\pi$
$809$	−18.5727	−0.652981	−0.326490	+	0.945201i	$0.605866\pi$
$810$	0	0
$811$	−12.4272	−0.436378	−0.218189	−	0.975907i	$-0.570015\pi$
$811$	−12.4272	−0.436378	−0.218189	+	0.975907i	$0.570015\pi$
$812$	−0.125613	−0.00440817
$813$	−60.4287	−2.11933
$814$	10.2774	0.360224
$815$	0	0
$816$	−29.6962	−1.03958
$817$	2.78194	0.0973278
$818$	55.7291	1.94852
$819$	0.0439143	0.00153449
$820$	0	0
$821$	43.0099	1.50105	0.750527	−	0.660839i	$-0.229799\pi$
$821$	43.0099	1.50105	0.750527	+	0.660839i	$0.229799\pi$
$822$	10.1046	0.352440
$823$	26.5806	0.926540	0.463270	−	0.886217i	$-0.346676\pi$
$823$	26.5806	0.926540	0.463270	+	0.886217i	$0.346676\pi$
$824$	21.9381	0.764250
$825$	0	0
$826$	−0.237510	−0.00826403
$827$	40.0958	1.39427	0.697134	−	0.716941i	$-0.254458\pi$
$827$	40.0958	1.39427	0.697134	+	0.716941i	$0.254458\pi$
$828$	1.45757	0.0506541
$829$	−18.7559	−0.651419	−0.325709	−	0.945470i	$-0.605603\pi$
$829$	−18.7559	−0.651419	−0.325709	+	0.945470i	$0.605603\pi$
$830$	0	0
$831$	49.3457	1.71178
$832$	0.0998450	0.00346150
$833$	−13.1340	−0.455066
$834$	−28.5715	−0.989349
$835$	0	0
$836$	−2.51684	−0.0870469
$837$	−25.4164	−0.878519
$838$	7.88784	0.272481
$839$	49.4414	1.70691	0.853453	−	0.521169i	$-0.174504\pi$
$839$	49.4414	1.70691	0.853453	+	0.521169i	$0.174504\pi$
$840$	0	0
$841$	−28.1164	−0.969531
$842$	32.0493	1.10449
$843$	83.2428	2.86703
$844$	5.62873	0.193749
$845$	0	0
$846$	61.2120	2.10451
$847$	−1.75467	−0.0602911
$848$	−29.4606	−1.01168
$849$	−36.2755	−1.24497
$850$	0	0
$851$	2.66228	0.0912618
$852$	−26.2863	−0.900555
$853$	−26.3021	−0.900568	−0.450284	−	0.892885i	$-0.648677\pi$
$853$	−26.3021	−0.900568	−0.450284	+	0.892885i	$0.648677\pi$
$854$	2.95925	0.101264
$855$	0	0
$856$	−3.27155	−0.111819
$857$	−2.10923	−0.0720500	−0.0360250	−	0.999351i	$-0.511470\pi$
$857$	−2.10923	−0.0720500	−0.0360250	+	0.999351i	$0.511470\pi$
$858$	0.116984	0.00399377
$859$	−26.8812	−0.917173	−0.458587	−	0.888650i	$-0.651644\pi$
$859$	−26.8812	−0.917173	−0.458587	+	0.888650i	$0.651644\pi$
$860$	0	0
$861$	3.54240	0.120725
$862$	−58.8843	−2.00561
$863$	−12.6346	−0.430087	−0.215044	−	0.976604i	$-0.568989\pi$
$863$	−12.6346	−0.430087	−0.215044	+	0.976604i	$0.568989\pi$
$864$	56.3000	1.91536
$865$	0	0
$866$	−17.1100	−0.581420
$867$	−42.7196	−1.45083
$868$	−0.261824	−0.00888689
$869$	−8.76148	−0.297213
$870$	0	0
$871$	−0.111873	−0.00379068
$872$	34.5715	1.17074
$873$	−49.1060	−1.66199
$874$	−2.25816	−0.0763835
$875$	0	0
$876$	−16.9162	−0.571545
$877$	26.4167	0.892030	0.446015	−	0.895025i	$-0.352843\pi$
$877$	26.4167	0.892030	0.446015	+	0.895025i	$0.352843\pi$
$878$	−38.5302	−1.30033
$879$	−32.8098	−1.10665
$880$	0	0
$881$	42.5380	1.43314	0.716570	−	0.697515i	$-0.245711\pi$
$881$	42.5380	1.43314	0.716570	+	0.697515i	$0.245711\pi$
$882$	82.8399	2.78936
$883$	−32.3070	−1.08722	−0.543609	−	0.839338i	$-0.682943\pi$
$883$	−32.3070	−1.08722	−0.543609	+	0.839338i	$0.682943\pi$
$884$	0.0575785	0.00193657
$885$	0	0
$886$	−7.96221	−0.267496
$887$	−52.9425	−1.77764	−0.888818	−	0.458261i	$-0.848473\pi$
$887$	−52.9425	−1.77764	−0.888818	+	0.458261i	$0.848473\pi$
$888$	66.4701	2.23059
$889$	−1.92741	−0.0646431
$890$	0	0
$891$	−11.6338	−0.389747
$892$	17.5131	0.586380
$893$	−27.3799	−0.916235
$894$	5.31458	0.177746
$895$	0	0
$896$	−2.16072	−0.0721846
$897$	0.0303037	0.00101181
$898$	37.7349	1.25923
$899$	1.84173	0.0614251
$900$	0	0
$901$	11.1774	0.372374
$902$	6.62950	0.220738
$903$	0.273662	0.00910690
$904$	−18.7053	−0.622128
$905$	0	0
$906$	−33.0769	−1.09891
$907$	−36.7613	−1.22064	−0.610320	−	0.792155i	$-0.708959\pi$
$907$	−36.7613	−1.22064	−0.610320	+	0.792155i	$0.708959\pi$
$908$	−13.8170	−0.458534
$909$	82.3091	2.73002
$910$	0	0
$911$	−10.5338	−0.349000	−0.174500	−	0.984657i	$-0.555831\pi$
$911$	−10.5338	−0.349000	−0.174500	+	0.984657i	$0.555831\pi$
$912$	−83.7800	−2.77423
$913$	−6.09327	−0.201658
$914$	33.1912	1.09787
$915$	0	0
$916$	14.3064	0.472698
$917$	−0.899122	−0.0296916
$918$	−40.9723	−1.35229
$919$	−24.6293	−0.812446	−0.406223	−	0.913774i	$-0.633154\pi$
$919$	−24.6293	−0.812446	−0.406223	+	0.913774i	$0.633154\pi$
$920$	0	0
$921$	28.4120	0.936206
$922$	5.05446	0.166460
$923$	−0.383935	−0.0126374
$924$	−0.247584	−0.00814492
$925$	0	0
$926$	0.985826	0.0323962
$927$	78.0107	2.56221
$928$	−4.07962	−0.133920
$929$	34.0286	1.11644	0.558222	−	0.829692i	$-0.311484\pi$
$929$	34.0286	1.11644	0.558222	+	0.829692i	$0.311484\pi$
$930$	0	0
$931$	−37.0540	−1.21440
$932$	−4.60873	−0.150964
$933$	22.2686	0.729040
$934$	0.697071	0.0228089
$935$	0	0
$936$	0.531533	0.0173737
$937$	−45.0263	−1.47095	−0.735473	−	0.677554i	$-0.763040\pi$
$937$	−45.0263	−1.47095	−0.735473	+	0.677554i	$0.763040\pi$
$938$	0.820071	0.0267763
$939$	22.4779	0.733537
$940$	0	0
$941$	−54.0249	−1.76116	−0.880581	−	0.473895i	$-0.842848\pi$
$941$	−54.0249	−1.76116	−0.880581	+	0.473895i	$0.842848\pi$
$942$	−47.4912	−1.54735
$943$	1.71731	0.0559235
$944$	−4.27187	−0.139038
$945$	0	0
$946$	0.512150	0.0166514
$947$	4.51844	0.146830	0.0734148	−	0.997301i	$-0.476610\pi$
$947$	4.51844	0.146830	0.0734148	+	0.997301i	$0.476610\pi$
$948$	38.7162	1.25744
$949$	−0.247076	−0.00802042
$950$	0	0
$951$	−81.4755	−2.64202
$952$	0.617751	0.0200214
$953$	−23.0457	−0.746523	−0.373262	−	0.927726i	$-0.621761\pi$
$953$	−23.0457	−0.746523	−0.373262	+	0.927726i	$0.621761\pi$
$954$	−70.4993	−2.28250
$955$	0	0
$956$	4.76399	0.154079
$957$	1.74156	0.0562967
$958$	60.4262	1.95228
$959$	−0.312353	−0.0100864
$960$	0	0
$961$	−27.1612	−0.876167
$962$	−0.663327	−0.0213865
$963$	−11.6335	−0.374883
$964$	−0.811815	−0.0261468
$965$	0	0
$966$	−0.222137	−0.00714716
$967$	−44.9913	−1.44682	−0.723411	−	0.690418i	$-0.757427\pi$
$967$	−44.9913	−1.44682	−0.723411	+	0.690418i	$0.757427\pi$
$968$	−21.2383	−0.682624
$969$	31.7863	1.02112
$970$	0	0
$971$	12.2170	0.392061	0.196031	−	0.980598i	$-0.437195\pi$
$971$	12.2170	0.392061	0.196031	+	0.980598i	$0.437195\pi$
$972$	19.8155	0.635583
$973$	0.883196	0.0283140
$974$	38.1755	1.22322
$975$	0	0
$976$	53.2254	1.70370
$977$	11.7505	0.375931	0.187966	−	0.982176i	$-0.439811\pi$
$977$	11.7505	0.375931	0.187966	+	0.982176i	$0.439811\pi$
$978$	103.720	3.31660
$979$	−4.27410	−0.136601
$980$	0	0
$981$	122.934	3.92499
$982$	−0.730550	−0.0233128
$983$	−34.5877	−1.10317	−0.551587	−	0.834117i	$-0.685978\pi$
$983$	−34.5877	−1.10317	−0.551587	+	0.834117i	$0.685978\pi$
$984$	42.8768	1.36686
$985$	0	0
$986$	2.96894	0.0945504
$987$	−2.69339	−0.0857315
$988$	0.162442	0.00516798
$989$	0.132668	0.00421860
$990$	0	0
$991$	12.4235	0.394646	0.197323	−	0.980339i	$-0.436775\pi$
$991$	12.4235	0.394646	0.197323	+	0.980339i	$0.436775\pi$
$992$	−8.50342	−0.269984
$993$	57.3060	1.81855
$994$	2.81439	0.0892670
$995$	0	0
$996$	26.9256	0.853171
$997$	−40.9484	−1.29685	−0.648425	−	0.761279i	$-0.724572\pi$
$997$	−40.9484	−1.29685	−0.648425	+	0.761279i	$0.724572\pi$
$998$	−11.6793	−0.369702
$999$	136.279	4.31167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.q.1.16		66
5.2	odd	4		1205.2.b.d.724.16	✓	66
5.3	odd	4		1205.2.b.d.724.51	yes	66
5.4	even	2	inner	6025.2.a.q.1.51		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.d.724.16	✓	66	5.2	odd	4
1205.2.b.d.724.51	yes	66	5.3	odd	4
6025.2.a.q.1.16		66	1.1	even	1	trivial
6025.2.a.q.1.51		66	5.4	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-1.67685 q^{2} +3.17567 q^{3} +0.811815 q^{4} -5.32511 q^{6} +0.164609 q^{7} +1.99240 q^{8} +7.08488 q^{9} +O(q^{10})\)	\(q-1.67685 q^{2} +3.17567 q^{3} +0.811815 q^{4} -5.32511 q^{6} +0.164609 q^{7} +1.99240 q^{8} +7.08488 q^{9} -0.583415 q^{11} +2.57806 q^{12} +0.0376548 q^{13} -0.276024 q^{14} -4.96459 q^{16} +1.88357 q^{17} -11.8803 q^{18} +5.31400 q^{19} +0.522743 q^{21} +0.978297 q^{22} +0.253420 q^{23} +6.32722 q^{24} -0.0631414 q^{26} +12.9722 q^{27} +0.133632 q^{28} -0.939996 q^{29} -1.95929 q^{31} +4.34004 q^{32} -1.85273 q^{33} -3.15847 q^{34} +5.75161 q^{36} +10.5054 q^{37} -8.91077 q^{38} +0.119579 q^{39} +6.77657 q^{41} -0.876560 q^{42} +0.523511 q^{43} -0.473625 q^{44} -0.424946 q^{46} -5.15241 q^{47} -15.7659 q^{48} -6.97290 q^{49} +5.98161 q^{51} +0.0305687 q^{52} +5.93416 q^{53} -21.7524 q^{54} +0.327967 q^{56} +16.8755 q^{57} +1.57623 q^{58} +0.860469 q^{59} -10.7210 q^{61} +3.28544 q^{62} +1.16623 q^{63} +2.65159 q^{64} +3.10675 q^{66} -2.97102 q^{67} +1.52911 q^{68} +0.804777 q^{69} -10.1962 q^{71} +14.1159 q^{72} -6.56160 q^{73} -17.6160 q^{74} +4.31399 q^{76} -0.0960352 q^{77} -0.200516 q^{78} +15.0176 q^{79} +19.9408 q^{81} -11.3633 q^{82} +10.4442 q^{83} +0.424371 q^{84} -0.877848 q^{86} -2.98512 q^{87} -1.16240 q^{88} +7.32600 q^{89} +0.00619831 q^{91} +0.205730 q^{92} -6.22207 q^{93} +8.63980 q^{94} +13.7825 q^{96} -6.93110 q^{97} +11.6925 q^{98} -4.13342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9}+O(q^{10}) \) 66 * q + 78 * q^4 + 16 * q^6 + 90 * q^9	\( 66 q + 78 q^{4} + 16 q^{6} + 90 q^{9} + 48 q^{11} + 30 q^{14} + 98 q^{16} + 12 q^{19} + 18 q^{21} + 42 q^{24} + 48 q^{26} + 56 q^{29} + 48 q^{31} + 8 q^{34} + 158 q^{36} + 84 q^{39} + 56 q^{41} + 144 q^{44} + 36 q^{46} + 98 q^{49} + 44 q^{51} + 86 q^{54} + 104 q^{56} + 108 q^{59} + 22 q^{61} + 136 q^{64} + 74 q^{66} + 20 q^{69} + 212 q^{71} + 84 q^{74} + 6 q^{76} + 66 q^{79} + 162 q^{81} - 52 q^{84} + 100 q^{86} + 54 q^{89} + 72 q^{91} - 96 q^{94} + 122 q^{96} + 112 q^{99}+O(q^{100}) \) 66 * q + 78 * q^4 + 16 * q^6 + 90 * q^9 + 48 * q^11 + 30 * q^14 + 98 * q^16 + 12 * q^19 + 18 * q^21 + 42 * q^24 + 48 * q^26 + 56 * q^29 + 48 * q^31 + 8 * q^34 + 158 * q^36 + 84 * q^39 + 56 * q^41 + 144 * q^44 + 36 * q^46 + 98 * q^49 + 44 * q^51 + 86 * q^54 + 104 * q^56 + 108 * q^59 + 22 * q^61 + 136 * q^64 + 74 * q^66 + 20 * q^69 + 212 * q^71 + 84 * q^74 + 6 * q^76 + 66 * q^79 + 162 * q^81 - 52 * q^84 + 100 * q^86 + 54 * q^89 + 72 * q^91 - 96 * q^94 + 122 * q^96 + 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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