LMFDB - Embedded newform 627.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(1,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("627.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$627 = 3 \cdot 11 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	627.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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{3} - x^{2} - 4x - 1$ x^3 - x^2 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.65109$ of defining polynomial
Character	$\chi$	$=$	627.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.65109 q^{2} +1.00000 q^{3} +0.726109 q^{4} +2.27389 q^{5} -1.65109 q^{6} +1.37720 q^{7} +2.10331 q^{8} +1.00000 q^{9} -3.75441 q^{10} +1.00000 q^{11} +0.726109 q^{12} +1.89669 q^{13} -2.27389 q^{14} +2.27389 q^{15} -4.92498 q^{16} +0.896688 q^{17} -1.65109 q^{18} +1.00000 q^{19} +1.65109 q^{20} +1.37720 q^{21} -1.65109 q^{22} -3.54778 q^{23} +2.10331 q^{24} +0.170578 q^{25} -3.13161 q^{26} +1.00000 q^{27} +1.00000 q^{28} +7.67939 q^{29} -3.75441 q^{30} -6.37720 q^{31} +3.92498 q^{32} +1.00000 q^{33} -1.48052 q^{34} +3.13161 q^{35} +0.726109 q^{36} -6.30219 q^{37} -1.65109 q^{38} +1.89669 q^{39} +4.78270 q^{40} +10.1599 q^{41} -2.27389 q^{42} -4.72611 q^{43} +0.726109 q^{44} +2.27389 q^{45} +5.85772 q^{46} +8.61212 q^{47} -4.92498 q^{48} -5.10331 q^{49} -0.281641 q^{50} +0.896688 q^{51} +1.37720 q^{52} +4.57608 q^{53} -1.65109 q^{54} +2.27389 q^{55} +2.89669 q^{56} +1.00000 q^{57} -12.6794 q^{58} -1.71836 q^{59} +1.65109 q^{60} -1.02830 q^{61} +10.5294 q^{62} +1.37720 q^{63} +3.36945 q^{64} +4.31286 q^{65} -1.65109 q^{66} +8.70769 q^{67} +0.651093 q^{68} -3.54778 q^{69} -5.17058 q^{70} +0.690063 q^{71} +2.10331 q^{72} -1.44447 q^{73} +10.4055 q^{74} +0.170578 q^{75} +0.726109 q^{76} +1.37720 q^{77} -3.13161 q^{78} +15.7077 q^{79} -11.1989 q^{80} +1.00000 q^{81} -16.7750 q^{82} -3.23492 q^{83} +1.00000 q^{84} +2.03897 q^{85} +7.80325 q^{86} +7.67939 q^{87} +2.10331 q^{88} -7.67939 q^{89} -3.75441 q^{90} +2.61212 q^{91} -2.57608 q^{92} -6.37720 q^{93} -14.2194 q^{94} +2.27389 q^{95} +3.92498 q^{96} +18.4904 q^{97} +8.42605 q^{98} +1.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$3 q + 2 q^{2} + 3 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - q^{7} + 3 q^{8} + 3 q^{9} - q^{10} + 3 q^{11} + 4 q^{12} + 9 q^{13} - 5 q^{14} + 5 q^{15} - 6 q^{16} + 6 q^{17} + 2 q^{18} + 3 q^{19} - 2 q^{20}+ \cdots + 3 q^{99}+O(q^{100})$ 3 * q + 2 * q^2 + 3 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - q^7 + 3 * q^8 + 3 * q^9 - q^10 + 3 * q^11 + 4 * q^12 + 9 * q^13 - 5 * q^14 + 5 * q^15 - 6 * q^16 + 6 * q^17 + 2 * q^18 + 3 * q^19 - 2 * q^20 - q^21 + 2 * q^22 - 7 * q^23 + 3 * q^24 + 2 * q^25 + 6 * q^26 + 3 * q^27 + 3 * q^28 + 4 * q^29 - q^30 - 14 * q^31 + 3 * q^32 + 3 * q^33 + 4 * q^34 - 6 * q^35 + 4 * q^36 - 5 * q^37 + 2 * q^38 + 9 * q^39 - 8 * q^40 + 3 * q^41 - 5 * q^42 - 16 * q^43 + 4 * q^44 + 5 * q^45 + 4 * q^46 + 2 * q^47 - 6 * q^48 - 12 * q^49 - 3 * q^50 + 6 * q^51 - q^52 - 2 * q^53 + 2 * q^54 + 5 * q^55 + 12 * q^56 + 3 * q^57 - 19 * q^58 - 3 * q^59 - 2 * q^60 + 9 * q^61 - 5 * q^62 - q^63 + q^64 + 28 * q^65 + 2 * q^66 - 5 * q^67 - 5 * q^68 - 7 * q^69 - 17 * q^70 + 12 * q^71 + 3 * q^72 - 4 * q^73 + 14 * q^74 + 2 * q^75 + 4 * q^76 - q^77 + 6 * q^78 + 16 * q^79 - 23 * q^80 + 3 * q^81 - 24 * q^82 + 9 * q^83 + 3 * q^84 + 23 * q^85 - 15 * q^86 + 4 * q^87 + 3 * q^88 - 4 * q^89 - q^90 - 16 * q^91 + 8 * q^92 - 14 * q^93 - 16 * q^94 + 5 * q^95 + 3 * q^96 + 2 * q^97 - 8 * q^98 + 3 * 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

)

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

$2$	−1.65109	−1.16750	−0.583750	−	0.811934i	$-0.698415\pi$
$2$	−1.65109	−1.16750	−0.583750	+	0.811934i	$0.698415\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.726109	0.363055
$5$	2.27389	1.01691	0.508457	−	0.861087i	$-0.330216\pi$
$5$	2.27389	1.01691	0.508457	+	0.861087i	$0.330216\pi$
$6$	−1.65109	−0.674056
$7$	1.37720	0.520534	0.260267	−	0.965537i	$-0.416189\pi$
$7$	1.37720	0.520534	0.260267	+	0.965537i	$0.416189\pi$
$8$	2.10331	0.743633
$9$	1.00000	0.333333
$10$	−3.75441	−1.18725
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.726109	0.209610
$13$	1.89669	0.526047	0.263023	−	0.964789i	$-0.415280\pi$
$13$	1.89669	0.526047	0.263023	+	0.964789i	$0.415280\pi$
$14$	−2.27389	−0.607723
$15$	2.27389	0.587116
$16$	−4.92498	−1.23125
$17$	0.896688	0.217479	0.108739	−	0.994070i	$-0.465319\pi$
$17$	0.896688	0.217479	0.108739	+	0.994070i	$0.465319\pi$
$18$	−1.65109	−0.389166
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.65109	0.369196
$21$	1.37720	0.300530
$22$	−1.65109	−0.352014
$23$	−3.54778	−0.739763	−0.369882	−	0.929079i	$-0.620602\pi$
$23$	−3.54778	−0.739763	−0.369882	+	0.929079i	$0.620602\pi$
$24$	2.10331	0.429337
$25$	0.170578	0.0341157
$26$	−3.13161	−0.614159
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	7.67939	1.42603	0.713013	−	0.701150i	$-0.247330\pi$
$29$	7.67939	1.42603	0.713013	+	0.701150i	$0.247330\pi$
$30$	−3.75441	−0.685458
$31$	−6.37720	−1.14538	−0.572690	−	0.819772i	$-0.694100\pi$
$31$	−6.37720	−1.14538	−0.572690	+	0.819772i	$0.694100\pi$
$32$	3.92498	0.693846
$33$	1.00000	0.174078
$34$	−1.48052	−0.253906
$35$	3.13161	0.529338
$36$	0.726109	0.121018
$37$	−6.30219	−1.03607	−0.518037	−	0.855358i	$-0.673337\pi$
$37$	−6.30219	−1.03607	−0.518037	+	0.855358i	$0.673337\pi$
$38$	−1.65109	−0.267843
$39$	1.89669	0.303713
$40$	4.78270	0.756212
$41$	10.1599	1.58671	0.793355	−	0.608759i	$-0.208332\pi$
$41$	10.1599	1.58671	0.793355	+	0.608759i	$0.208332\pi$
$42$	−2.27389	−0.350869
$43$	−4.72611	−0.720725	−0.360362	−	0.932812i	$-0.617347\pi$
$43$	−4.72611	−0.720725	−0.360362	+	0.932812i	$0.617347\pi$
$44$	0.726109	0.109465
$45$	2.27389	0.338972
$46$	5.85772	0.863673
$47$	8.61212	1.25621	0.628104	−	0.778130i	$-0.283831\pi$
$47$	8.61212	1.25621	0.628104	+	0.778130i	$0.283831\pi$
$48$	−4.92498	−0.710860
$49$	−5.10331	−0.729045
$50$	−0.281641	−0.0398300
$51$	0.896688	0.125561
$52$	1.37720	0.190984
$53$	4.57608	0.628573	0.314286	−	0.949328i	$-0.398235\pi$
$53$	4.57608	0.628573	0.314286	+	0.949328i	$0.398235\pi$
$54$	−1.65109	−0.224685
$55$	2.27389	0.306611
$56$	2.89669	0.387086
$57$	1.00000	0.132453
$58$	−12.6794	−1.66489
$59$	−1.71836	−0.223711	−0.111856	−	0.993724i	$-0.535679\pi$
$59$	−1.71836	−0.223711	−0.111856	+	0.993724i	$0.535679\pi$
$60$	1.65109	0.213155
$61$	−1.02830	−0.131660	−0.0658299	−	0.997831i	$-0.520969\pi$
$61$	−1.02830	−0.131660	−0.0658299	+	0.997831i	$0.520969\pi$
$62$	10.5294	1.33723
$63$	1.37720	0.173511
$64$	3.36945	0.421182
$65$	4.31286	0.534944
$66$	−1.65109	−0.203236
$67$	8.70769	1.06381	0.531907	−	0.846803i	$-0.321476\pi$
$67$	8.70769	1.06381	0.531907	+	0.846803i	$0.321476\pi$
$68$	0.651093	0.0789567
$69$	−3.54778	−0.427103
$70$	−5.17058	−0.618002
$71$	0.690063	0.0818954	0.0409477	−	0.999161i	$-0.486962\pi$
$71$	0.690063	0.0818954	0.0409477	+	0.999161i	$0.486962\pi$
$72$	2.10331	0.247878
$73$	−1.44447	−0.169062	−0.0845311	−	0.996421i	$-0.526939\pi$
$73$	−1.44447	−0.169062	−0.0845311	+	0.996421i	$0.526939\pi$
$74$	10.4055	1.20961
$75$	0.170578	0.0196967
$76$	0.726109	0.0832905
$77$	1.37720	0.156947
$78$	−3.13161	−0.354585
$79$	15.7077	1.76725	0.883626	−	0.468193i	$-0.155095\pi$
$79$	15.7077	1.76725	0.883626	+	0.468193i	$0.155095\pi$
$80$	−11.1989	−1.25207
$81$	1.00000	0.111111
$82$	−16.7750	−1.85248
$83$	−3.23492	−0.355079	−0.177539	−	0.984114i	$-0.556814\pi$
$83$	−3.23492	−0.355079	−0.177539	+	0.984114i	$0.556814\pi$
$84$	1.00000	0.109109
$85$	2.03897	0.221157
$86$	7.80325	0.841446
$87$	7.67939	0.823317
$88$	2.10331	0.224214
$89$	−7.67939	−0.814014	−0.407007	−	0.913425i	$-0.633427\pi$
$89$	−7.67939	−0.814014	−0.407007	+	0.913425i	$0.633427\pi$
$90$	−3.75441	−0.395749
$91$	2.61212	0.273825
$92$	−2.57608	−0.268575
$93$	−6.37720	−0.661285
$94$	−14.2194	−1.46662
$95$	2.27389	0.233296
$96$	3.92498	0.400592
$97$	18.4904	1.87741	0.938707	−	0.344715i	$-0.112025\pi$
$97$	18.4904	1.87741	0.938707	+	0.344715i	$0.112025\pi$
$98$	8.42605	0.851159
$99$	1.00000	0.100504
$100$	0.123858	0.0123858
$101$	−4.53711	−0.451459	−0.225730	−	0.974190i	$-0.572477\pi$
$101$	−4.53711	−0.451459	−0.225730	+	0.974190i	$0.572477\pi$
$102$	−1.48052	−0.146593
$103$	−10.5294	−1.03749	−0.518744	−	0.854929i	$-0.673600\pi$
$103$	−10.5294	−1.03749	−0.518744	+	0.854929i	$0.673600\pi$
$104$	3.98933	0.391186
$105$	3.13161	0.305614
$106$	−7.55553	−0.733858
$107$	−8.88601	−0.859043	−0.429522	−	0.903057i	$-0.641318\pi$
$107$	−8.88601	−0.859043	−0.429522	+	0.903057i	$0.641318\pi$
$108$	0.726109	0.0698699
$109$	5.13161	0.491519	0.245759	−	0.969331i	$-0.420963\pi$
$109$	5.13161	0.491519	0.245759	+	0.969331i	$0.420963\pi$
$110$	−3.75441	−0.357969
$111$	−6.30219	−0.598177
$112$	−6.78270	−0.640905
$113$	1.93273	0.181816	0.0909082	−	0.995859i	$-0.471023\pi$
$113$	1.93273	0.181816	0.0909082	+	0.995859i	$0.471023\pi$
$114$	−1.65109	−0.154639
$115$	−8.06727	−0.752276
$116$	5.57608	0.517726
$117$	1.89669	0.175349
$118$	2.83717	0.261183
$119$	1.23492	0.113205
$120$	4.78270	0.436599
$121$	1.00000	0.0909091
$122$	1.69781	0.153713
$123$	10.1599	0.916088
$124$	−4.63055	−0.415835
$125$	−10.9816	−0.982222
$126$	−2.27389	−0.202574
$127$	−15.8315	−1.40482	−0.702411	−	0.711771i	$-0.747893\pi$
$127$	−15.8315	−1.40482	−0.702411	+	0.711771i	$0.747893\pi$
$128$	−13.4132	−1.18557
$129$	−4.72611	−0.416111
$130$	−7.12094	−0.624547
$131$	−3.09556	−0.270461	−0.135230	−	0.990814i	$-0.543177\pi$
$131$	−3.09556	−0.270461	−0.135230	+	0.990814i	$0.543177\pi$
$132$	0.726109	0.0631997
$133$	1.37720	0.119419
$134$	−14.3772	−1.24200
$135$	2.27389	0.195705
$136$	1.88601	0.161724
$137$	3.48052	0.297360	0.148680	−	0.988885i	$-0.452497\pi$
$137$	3.48052	0.297360	0.148680	+	0.988885i	$0.452497\pi$
$138$	5.85772	0.498642
$139$	−12.1989	−1.03470	−0.517348	−	0.855775i	$-0.673081\pi$
$139$	−12.1989	−1.03470	−0.517348	+	0.855775i	$0.673081\pi$
$140$	2.27389	0.192179
$141$	8.61212	0.725272
$142$	−1.13936	−0.0956129
$143$	1.89669	0.158609
$144$	−4.92498	−0.410415
$145$	17.4621	1.45015
$146$	2.38495	0.197380
$147$	−5.10331	−0.420914
$148$	−4.57608	−0.376151
$149$	−12.2944	−1.00720	−0.503600	−	0.863937i	$-0.667991\pi$
$149$	−12.2944	−1.00720	−0.503600	+	0.863937i	$0.667991\pi$
$150$	−0.281641	−0.0229959
$151$	−3.48052	−0.283240	−0.141620	−	0.989921i	$-0.545231\pi$
$151$	−3.48052	−0.283240	−0.141620	+	0.989921i	$0.545231\pi$
$152$	2.10331	0.170601
$153$	0.896688	0.0724929
$154$	−2.27389	−0.183235
$155$	−14.5011	−1.16475
$156$	1.37720	0.110264
$157$	−7.34891	−0.586507	−0.293253	−	0.956035i	$-0.594738\pi$
$157$	−7.34891	−0.586507	−0.293253	+	0.956035i	$0.594738\pi$
$158$	−25.9349	−2.06327
$159$	4.57608	0.362907
$160$	8.92498	0.705582
$161$	−4.88601	−0.385072
$162$	−1.65109	−0.129722
$163$	−4.28164	−0.335364	−0.167682	−	0.985841i	$-0.553628\pi$
$163$	−4.28164	−0.335364	−0.167682	+	0.985841i	$0.553628\pi$
$164$	7.37720	0.576063
$165$	2.27389	0.177022
$166$	5.34116	0.414554
$167$	2.61505	0.202358	0.101179	−	0.994868i	$-0.467738\pi$
$167$	2.61505	0.202358	0.101179	+	0.994868i	$0.467738\pi$
$168$	2.89669	0.223484
$169$	−9.40258	−0.723275
$170$	−3.36653	−0.258201
$171$	1.00000	0.0764719
$172$	−3.43167	−0.261663
$173$	3.42392	0.260316	0.130158	−	0.991493i	$-0.458452\pi$
$173$	3.42392	0.260316	0.130158	+	0.991493i	$0.458452\pi$
$174$	−12.6794	−0.961222
$175$	0.234921	0.0177583
$176$	−4.92498	−0.371235
$177$	−1.71836	−0.129160
$178$	12.6794	0.950360
$179$	−13.0382	−0.974519	−0.487259	−	0.873257i	$-0.662003\pi$
$179$	−13.0382	−0.974519	−0.487259	+	0.873257i	$0.662003\pi$
$180$	1.65109	0.123065
$181$	−5.89669	−0.438297	−0.219149	−	0.975691i	$-0.570328\pi$
$181$	−5.89669	−0.438297	−0.219149	+	0.975691i	$0.570328\pi$
$182$	−4.31286	−0.319690
$183$	−1.02830	−0.0760138
$184$	−7.46209	−0.550113
$185$	−14.3305	−1.05360
$186$	10.5294	0.772050
$187$	0.896688	0.0655723
$188$	6.25334	0.456072
$189$	1.37720	0.100177
$190$	−3.75441	−0.272373
$191$	−23.5860	−1.70662	−0.853310	−	0.521404i	$-0.825408\pi$
$191$	−23.5860	−1.70662	−0.853310	+	0.521404i	$0.825408\pi$
$192$	3.36945	0.243169
$193$	−25.6708	−1.84783	−0.923914	−	0.382601i	$-0.875028\pi$
$193$	−25.6708	−1.84783	−0.923914	+	0.382601i	$0.875028\pi$
$194$	−30.5294	−2.19188
$195$	4.31286	0.308850
$196$	−3.70556	−0.264683
$197$	19.2242	1.36967	0.684835	−	0.728698i	$-0.259874\pi$
$197$	19.2242	1.36967	0.684835	+	0.728698i	$0.259874\pi$
$198$	−1.65109	−0.117338
$199$	−5.48052	−0.388503	−0.194252	−	0.980952i	$-0.562228\pi$
$199$	−5.48052	−0.388503	−0.194252	+	0.980952i	$0.562228\pi$
$200$	0.358779	0.0253695
$201$	8.70769	0.614193
$202$	7.49119	0.527078
$203$	10.5761	0.742295
$204$	0.651093	0.0455857
$205$	23.1025	1.61355
$206$	17.3850	1.21127
$207$	−3.54778	−0.246588
$208$	−9.34116	−0.647693
$209$	1.00000	0.0691714
$210$	−5.17058	−0.356804
$211$	−3.12174	−0.214909	−0.107455	−	0.994210i	$-0.534270\pi$
$211$	−3.12174	−0.214909	−0.107455	+	0.994210i	$0.534270\pi$
$212$	3.32273	0.228206
$213$	0.690063	0.0472823
$214$	14.6716	1.00293
$215$	−10.7467	−0.732916
$216$	2.10331	0.143112
$217$	−8.78270	−0.596209
$218$	−8.47277	−0.573848
$219$	−1.44447	−0.0976082
$220$	1.65109	0.111317
$221$	1.70074	0.114404
$222$	10.4055	0.698371
$223$	16.9066	1.13215	0.566074	−	0.824355i	$-0.308462\pi$
$223$	16.9066	1.13215	0.566074	+	0.824355i	$0.308462\pi$
$224$	5.40550	0.361170
$225$	0.170578	0.0113719
$226$	−3.19112	−0.212270
$227$	10.5838	0.702473	0.351237	−	0.936287i	$-0.385761\pi$
$227$	10.5838	0.702473	0.351237	+	0.936287i	$0.385761\pi$
$228$	0.726109	0.0480878
$229$	−14.4933	−0.957745	−0.478872	−	0.877884i	$-0.658954\pi$
$229$	−14.4933	−0.957745	−0.478872	+	0.877884i	$0.658954\pi$
$230$	13.3198	0.878282
$231$	1.37720	0.0906133
$232$	16.1522	1.06044
$233$	21.5216	1.40993	0.704964	−	0.709243i	$-0.250963\pi$
$233$	21.5216	1.40993	0.704964	+	0.709243i	$0.250963\pi$
$234$	−3.13161	−0.204720
$235$	19.5830	1.27746
$236$	−1.24772	−0.0812195
$237$	15.7077	1.02032
$238$	−2.03897	−0.132167
$239$	15.0360	0.972601	0.486300	−	0.873792i	$-0.338346\pi$
$239$	15.0360	0.972601	0.486300	+	0.873792i	$0.338346\pi$
$240$	−11.1989	−0.722884
$241$	14.3305	0.923108	0.461554	−	0.887112i	$-0.347292\pi$
$241$	14.3305	0.923108	0.461554	+	0.887112i	$0.347292\pi$
$242$	−1.65109	−0.106136
$243$	1.00000	0.0641500
$244$	−0.746656	−0.0477997
$245$	−11.6044	−0.741376
$246$	−16.7750	−1.06953
$247$	1.89669	0.120683
$248$	−13.4132	−0.851742
$249$	−3.23492	−0.205005
$250$	18.1316	1.14674
$251$	−14.5371	−0.917574	−0.458787	−	0.888546i	$-0.651716\pi$
$251$	−14.5371	−0.917574	−0.458787	+	0.888546i	$0.651716\pi$
$252$	1.00000	0.0629941
$253$	−3.54778	−0.223047
$254$	26.1394	1.64013
$255$	2.03897	0.127685
$256$	15.4076	0.962976
$257$	29.8598	1.86261	0.931303	−	0.364246i	$-0.118673\pi$
$257$	29.8598	1.86261	0.931303	+	0.364246i	$0.118673\pi$
$258$	7.80325	0.485809
$259$	−8.67939	−0.539311
$260$	3.13161	0.194214
$261$	7.67939	0.475342
$262$	5.11106	0.315762
$263$	−15.7926	−0.973812	−0.486906	−	0.873454i	$-0.661875\pi$
$263$	−15.7926	−0.973812	−0.486906	+	0.873454i	$0.661875\pi$
$264$	2.10331	0.129450
$265$	10.4055	0.639205
$266$	−2.27389	−0.139421
$267$	−7.67939	−0.469971
$268$	6.32273	0.386222
$269$	−10.3588	−0.631586	−0.315793	−	0.948828i	$-0.602271\pi$
$269$	−10.3588	−0.631586	−0.315793	+	0.948828i	$0.602271\pi$
$270$	−3.75441	−0.228486
$271$	1.04884	0.0637126	0.0318563	−	0.999492i	$-0.489858\pi$
$271$	1.04884	0.0637126	0.0318563	+	0.999492i	$0.489858\pi$
$272$	−4.41617	−0.267770
$273$	2.61212	0.158093
$274$	−5.74666	−0.347168
$275$	0.170578	0.0102863
$276$	−2.57608	−0.155062
$277$	29.7381	1.78679	0.893395	−	0.449272i	$-0.148317\pi$
$277$	29.7381	1.78679	0.893395	+	0.449272i	$0.148317\pi$
$278$	20.1415	1.20801
$279$	−6.37720	−0.381793
$280$	6.58675	0.393634
$281$	−4.97170	−0.296587	−0.148293	−	0.988943i	$-0.547378\pi$
$281$	−4.97170	−0.296587	−0.148293	+	0.988943i	$0.547378\pi$
$282$	−14.2194	−0.846754
$283$	7.46289	0.443623	0.221811	−	0.975090i	$-0.428803\pi$
$283$	7.46289	0.443623	0.221811	+	0.975090i	$0.428803\pi$
$284$	0.501061	0.0297325
$285$	2.27389	0.134694
$286$	−3.13161	−0.185176
$287$	13.9922	0.825936
$288$	3.92498	0.231282
$289$	−16.1960	−0.952703
$290$	−28.8315	−1.69305
$291$	18.4904	1.08393
$292$	−1.04884	−0.0613789
$293$	−33.0510	−1.93086	−0.965429	−	0.260666i	$-0.916058\pi$
$293$	−33.0510	−1.93086	−0.965429	+	0.260666i	$0.916058\pi$
$294$	8.42605	0.491417
$295$	−3.90736	−0.227495
$296$	−13.2555	−0.770458
$297$	1.00000	0.0580259
$298$	20.2993	1.17590
$299$	−6.72903	−0.389150
$300$	0.123858	0.00715097
$301$	−6.50881	−0.375162
$302$	5.74666	0.330683
$303$	−4.53711	−0.260650
$304$	−4.92498	−0.282467
$305$	−2.33823	−0.133887
$306$	−1.48052	−0.0846354
$307$	−0.989327	−0.0564638	−0.0282319	−	0.999601i	$-0.508988\pi$
$307$	−0.989327	−0.0564638	−0.0282319	+	0.999601i	$0.508988\pi$
$308$	1.00000	0.0569803
$309$	−10.5294	−0.598994
$310$	23.9426	1.35985
$311$	−28.2731	−1.60322	−0.801610	−	0.597847i	$-0.796023\pi$
$311$	−28.2731	−1.60322	−0.801610	+	0.597847i	$0.796023\pi$
$312$	3.98933	0.225851
$313$	16.4621	0.930492	0.465246	−	0.885181i	$-0.345966\pi$
$313$	16.4621	0.930492	0.465246	+	0.885181i	$0.345966\pi$
$314$	12.1337	0.684746
$315$	3.13161	0.176446
$316$	11.4055	0.641609
$317$	27.2760	1.53197	0.765987	−	0.642856i	$-0.222251\pi$
$317$	27.2760	1.53197	0.765987	+	0.642856i	$0.222251\pi$
$318$	−7.55553	−0.423693
$319$	7.67939	0.429963
$320$	7.66177	0.428306
$321$	−8.88601	−0.495969
$322$	8.06727	0.449571
$323$	0.896688	0.0498930
$324$	0.726109	0.0403394
$325$	0.323534	0.0179464
$326$	7.06939	0.391537
$327$	5.13161	0.283779
$328$	21.3695	1.17993
$329$	11.8606	0.653898
$330$	−3.75441	−0.206673
$331$	6.01280	0.330493	0.165247	−	0.986252i	$-0.447158\pi$
$331$	6.01280	0.330493	0.165247	+	0.986252i	$0.447158\pi$
$332$	−2.34891	−0.128913
$333$	−6.30219	−0.345358
$334$	−4.31769	−0.236253
$335$	19.8003	1.08181
$336$	−6.78270	−0.370027
$337$	2.81875	0.153547	0.0767735	−	0.997049i	$-0.475538\pi$
$337$	2.81875	0.153547	0.0767735	+	0.997049i	$0.475538\pi$
$338$	15.5245	0.844423
$339$	1.93273	0.104972
$340$	1.48052	0.0802922
$341$	−6.37720	−0.345345
$342$	−1.65109	−0.0892809
$343$	−16.6687	−0.900026
$344$	−9.94048	−0.535955
$345$	−8.06727	−0.434327
$346$	−5.65322	−0.303919
$347$	4.41537	0.237030	0.118515	−	0.992952i	$-0.462187\pi$
$347$	4.41537	0.237030	0.118515	+	0.992952i	$0.462187\pi$
$348$	5.57608	0.298909
$349$	0.253344	0.0135612	0.00678061	−	0.999977i	$-0.497842\pi$
$349$	0.253344	0.0135612	0.00678061	+	0.999977i	$0.497842\pi$
$350$	−0.387876	−0.0207329
$351$	1.89669	0.101238
$352$	3.92498	0.209202
$353$	−24.9271	−1.32674	−0.663368	−	0.748293i	$-0.730874\pi$
$353$	−24.9271	−1.32674	−0.663368	+	0.748293i	$0.730874\pi$
$354$	2.83717	0.150794
$355$	1.56913	0.0832807
$356$	−5.57608	−0.295532
$357$	1.23492	0.0653589
$358$	21.5272	1.13775
$359$	25.0956	1.32449	0.662247	−	0.749286i	$-0.269603\pi$
$359$	25.0956	1.32449	0.662247	+	0.749286i	$0.269603\pi$
$360$	4.78270	0.252071
$361$	1.00000	0.0526316
$362$	9.73598	0.511712
$363$	1.00000	0.0524864
$364$	1.89669	0.0994134
$365$	−3.28456	−0.171922
$366$	1.69781	0.0887461
$367$	−29.4621	−1.53791	−0.768954	−	0.639304i	$-0.779223\pi$
$367$	−29.4621	−1.53791	−0.768954	+	0.639304i	$0.779223\pi$
$368$	17.4728	0.910831
$369$	10.1599	0.528904
$370$	23.6610	1.23008
$371$	6.30219	0.327193
$372$	−4.63055	−0.240083
$373$	−18.0870	−0.936510	−0.468255	−	0.883593i	$-0.655117\pi$
$373$	−18.0870	−0.936510	−0.468255	+	0.883593i	$0.655117\pi$
$374$	−1.48052	−0.0765556
$375$	−10.9816	−0.567086
$376$	18.1140	0.934157
$377$	14.5654	0.750156
$378$	−2.27389	−0.116956
$379$	−12.1033	−0.621705	−0.310853	−	0.950458i	$-0.600615\pi$
$379$	−12.1033	−0.621705	−0.310853	+	0.950458i	$0.600615\pi$
$380$	1.65109	0.0846993
$381$	−15.8315	−0.811075
$382$	38.9426	1.99248
$383$	2.43672	0.124511	0.0622553	−	0.998060i	$-0.480171\pi$
$383$	2.43672	0.124511	0.0622553	+	0.998060i	$0.480171\pi$
$384$	−13.4132	−0.684492
$385$	3.13161	0.159602
$386$	42.3850	2.15734
$387$	−4.72611	−0.240242
$388$	13.4260	0.681604
$389$	25.0099	1.26805	0.634025	−	0.773312i	$-0.281401\pi$
$389$	25.0099	1.26805	0.634025	+	0.773312i	$0.281401\pi$
$390$	−7.12094	−0.360583
$391$	−3.18125	−0.160883
$392$	−10.7339	−0.542142
$393$	−3.09556	−0.156150
$394$	−31.7410	−1.59909
$395$	35.7176	1.79715
$396$	0.726109	0.0364884
$397$	12.7592	0.640368	0.320184	−	0.947355i	$-0.396255\pi$
$397$	12.7592	0.640368	0.320184	+	0.947355i	$0.396255\pi$
$398$	9.04884	0.453577
$399$	1.37720	0.0689464
$400$	−0.840095	−0.0420048
$401$	8.18820	0.408899	0.204450	−	0.978877i	$-0.434460\pi$
$401$	8.18820	0.408899	0.204450	+	0.978877i	$0.434460\pi$
$402$	−14.3772	−0.717070
$403$	−12.0956	−0.602523
$404$	−3.29444	−0.163904
$405$	2.27389	0.112991
$406$	−17.4621	−0.866629
$407$	−6.30219	−0.312388
$408$	1.88601	0.0933716
$409$	−36.5109	−1.80535	−0.902675	−	0.430323i	$-0.858399\pi$
$409$	−36.5109	−1.80535	−0.902675	+	0.430323i	$0.858399\pi$
$410$	−38.1444	−1.88382
$411$	3.48052	0.171681
$412$	−7.64547	−0.376665
$413$	−2.36653	−0.116449
$414$	5.85772	0.287891
$415$	−7.35586	−0.361085
$416$	7.44447	0.364995
$417$	−12.1989	−0.597381
$418$	−1.65109	−0.0807576
$419$	−3.47277	−0.169656	−0.0848278	−	0.996396i	$-0.527034\pi$
$419$	−3.47277	−0.169656	−0.0848278	+	0.996396i	$0.527034\pi$
$420$	2.27389	0.110954
$421$	16.0254	0.781029	0.390514	−	0.920597i	$-0.372297\pi$
$421$	16.0254	0.781029	0.390514	+	0.920597i	$0.372297\pi$
$422$	5.15428	0.250906
$423$	8.61212	0.418736
$424$	9.62492	0.467427
$425$	0.152955	0.00741943
$426$	−1.13936	−0.0552021
$427$	−1.41617	−0.0685334
$428$	−6.45222	−0.311880
$429$	1.89669	0.0915729
$430$	17.7437	0.855679
$431$	2.63559	0.126952	0.0634760	−	0.997983i	$-0.479781\pi$
$431$	2.63559	0.126952	0.0634760	+	0.997983i	$0.479781\pi$
$432$	−4.92498	−0.236953
$433$	38.8783	1.86837	0.934185	−	0.356789i	$-0.116128\pi$
$433$	38.8783	1.86837	0.934185	+	0.356789i	$0.116128\pi$
$434$	14.5011	0.696073
$435$	17.4621	0.837243
$436$	3.72611	0.178448
$437$	−3.54778	−0.169713
$438$	2.38495	0.113957
$439$	−22.2944	−1.06406	−0.532028	−	0.846727i	$-0.678570\pi$
$439$	−22.2944	−1.06406	−0.532028	+	0.846727i	$0.678570\pi$
$440$	4.78270	0.228006
$441$	−5.10331	−0.243015
$442$	−2.80807	−0.133567
$443$	−26.8753	−1.27689	−0.638443	−	0.769669i	$-0.720421\pi$
$443$	−26.8753	−1.27689	−0.638443	+	0.769669i	$0.720421\pi$
$444$	−4.57608	−0.217171
$445$	−17.4621	−0.827783
$446$	−27.9143	−1.32178
$447$	−12.2944	−0.581507
$448$	4.64042	0.219239
$449$	−13.8676	−0.654452	−0.327226	−	0.944946i	$-0.606114\pi$
$449$	−13.8676	−0.654452	−0.327226	+	0.944946i	$0.606114\pi$
$450$	−0.281641	−0.0132767
$451$	10.1599	0.478411
$452$	1.40338	0.0660093
$453$	−3.48052	−0.163529
$454$	−17.4749	−0.820137
$455$	5.93968	0.278457
$456$	2.10331	0.0984966
$457$	−29.1231	−1.36232	−0.681160	−	0.732135i	$-0.738524\pi$
$457$	−29.1231	−1.36232	−0.681160	+	0.732135i	$0.738524\pi$
$458$	23.9298	1.11817
$459$	0.896688	0.0418538
$460$	−5.85772	−0.273118
$461$	10.0283	0.467064	0.233532	−	0.972349i	$-0.424972\pi$
$461$	10.0283	0.467064	0.233532	+	0.972349i	$0.424972\pi$
$462$	−2.27389	−0.105791
$463$	−14.1239	−0.656391	−0.328196	−	0.944610i	$-0.606441\pi$
$463$	−14.1239	−0.656391	−0.328196	+	0.944610i	$0.606441\pi$
$464$	−37.8209	−1.75579
$465$	−14.5011	−0.672471
$466$	−35.5342	−1.64609
$467$	−16.1111	−0.745531	−0.372766	−	0.927926i	$-0.621590\pi$
$467$	−16.1111	−0.745531	−0.372766	+	0.927926i	$0.621590\pi$
$468$	1.37720	0.0636612
$469$	11.9922	0.553751
$470$	−32.3334	−1.49143
$471$	−7.34891	−0.338620
$472$	−3.61425	−0.166359
$473$	−4.72611	−0.217307
$474$	−25.9349	−1.19123
$475$	0.170578	0.00782667
$476$	0.896688	0.0410996
$477$	4.57608	0.209524
$478$	−24.8259	−1.13551
$479$	−17.9688	−0.821015	−0.410507	−	0.911857i	$-0.634648\pi$
$479$	−17.9688	−0.821015	−0.410507	+	0.911857i	$0.634648\pi$
$480$	8.92498	0.407368
$481$	−11.9533	−0.545023
$482$	−23.6610	−1.07773
$483$	−4.88601	−0.222321
$484$	0.726109	0.0330050
$485$	42.0451	1.90917
$486$	−1.65109	−0.0748951
$487$	8.93486	0.404877	0.202439	−	0.979295i	$-0.435113\pi$
$487$	8.93486	0.404877	0.202439	+	0.979295i	$0.435113\pi$
$488$	−2.16283	−0.0979066
$489$	−4.28164	−0.193622
$490$	19.1599	0.865556
$491$	−30.3043	−1.36761	−0.683807	−	0.729663i	$-0.739677\pi$
$491$	−30.3043	−1.36761	−0.683807	+	0.729663i	$0.739677\pi$
$492$	7.37720	0.332590
$493$	6.88601	0.310130
$494$	−3.13161	−0.140898
$495$	2.27389	0.102204
$496$	31.4076	1.41024
$497$	0.950357	0.0426293
$498$	5.34116	0.239343
$499$	−37.0510	−1.65863	−0.829314	−	0.558782i	$-0.811269\pi$
$499$	−37.0510	−1.65863	−0.829314	+	0.558782i	$0.811269\pi$
$500$	−7.97383	−0.356600
$501$	2.61505	0.116832
$502$	24.0021	1.07127
$503$	15.0926	0.672948	0.336474	−	0.941693i	$-0.390766\pi$
$503$	15.0926	0.672948	0.336474	+	0.941693i	$0.390766\pi$
$504$	2.89669	0.129029
$505$	−10.3169	−0.459095
$506$	5.85772	0.260407
$507$	−9.40258	−0.417583
$508$	−11.4954	−0.510027
$509$	−27.8209	−1.23314	−0.616569	−	0.787301i	$-0.711478\pi$
$509$	−27.8209	−1.23314	−0.616569	+	0.787301i	$0.711478\pi$
$510$	−3.36653	−0.149072
$511$	−1.98933	−0.0880026
$512$	1.38708	0.0613007
$513$	1.00000	0.0441511
$514$	−49.3014	−2.17459
$515$	−23.9426	−1.05504
$516$	−3.43167	−0.151071
$517$	8.61212	0.378761
$518$	14.3305	0.629645
$519$	3.42392	0.150294
$520$	9.07129	0.397802
$521$	4.83717	0.211920	0.105960	−	0.994370i	$-0.466208\pi$
$521$	4.83717	0.211920	0.105960	+	0.994370i	$0.466208\pi$
$522$	−12.6794	−0.554962
$523$	−12.0566	−0.527198	−0.263599	−	0.964632i	$-0.584910\pi$
$523$	−12.0566	−0.527198	−0.263599	+	0.964632i	$0.584910\pi$
$524$	−2.24772	−0.0981920
$525$	0.234921	0.0102528
$526$	26.0750	1.13692
$527$	−5.71836	−0.249096
$528$	−4.92498	−0.214332
$529$	−10.4132	−0.452750
$530$	−17.1805	−0.746271
$531$	−1.71836	−0.0745704
$532$	1.00000	0.0433555
$533$	19.2702	0.834684
$534$	12.6794	0.548691
$535$	−20.2058	−0.873574
$536$	18.3150	0.791087
$537$	−13.0382	−0.562639
$538$	17.1033	0.737376
$539$	−5.10331	−0.219815
$540$	1.65109	0.0710517
$541$	9.95620	0.428051	0.214025	−	0.976828i	$-0.431342\pi$
$541$	9.95620	0.428051	0.214025	+	0.976828i	$0.431342\pi$
$542$	−1.73174	−0.0743845
$543$	−5.89669	−0.253051
$544$	3.51948	0.150897
$545$	11.6687	0.499833
$546$	−4.31286	−0.184573
$547$	7.75653	0.331645	0.165823	−	0.986156i	$-0.446972\pi$
$547$	7.75653	0.331645	0.165823	+	0.986156i	$0.446972\pi$
$548$	2.52723	0.107958
$549$	−1.02830	−0.0438866
$550$	−0.281641	−0.0120092
$551$	7.67939	0.327153
$552$	−7.46209	−0.317608
$553$	21.6327	0.919915
$554$	−49.1004	−2.08608
$555$	−14.3305	−0.608295
$556$	−8.85772	−0.375651
$557$	2.26614	0.0960195	0.0480097	−	0.998847i	$-0.484712\pi$
$557$	2.26614	0.0960195	0.0480097	+	0.998847i	$0.484712\pi$
$558$	10.5294	0.445743
$559$	−8.96395	−0.379135
$560$	−15.4231	−0.651746
$561$	0.896688	0.0378582
$562$	8.20875	0.346265
$563$	4.67434	0.197000	0.0985000	−	0.995137i	$-0.468596\pi$
$563$	4.67434	0.197000	0.0985000	+	0.995137i	$0.468596\pi$
$564$	6.25334	0.263313
$565$	4.39483	0.184892
$566$	−12.3219	−0.517929
$567$	1.37720	0.0578371
$568$	1.45142	0.0609002
$569$	−15.7699	−0.661109	−0.330554	−	0.943787i	$-0.607236\pi$
$569$	−15.7699	−0.661109	−0.330554	+	0.943787i	$0.607236\pi$
$570$	−3.75441	−0.157255
$571$	7.20370	0.301466	0.150733	−	0.988575i	$-0.451837\pi$
$571$	7.20370	0.301466	0.150733	+	0.988575i	$0.451837\pi$
$572$	1.37720	0.0575837
$573$	−23.5860	−0.985317
$574$	−23.1025	−0.964280
$575$	−0.605174	−0.0252375
$576$	3.36945	0.140394
$577$	7.84222	0.326476	0.163238	−	0.986587i	$-0.447806\pi$
$577$	7.84222	0.326476	0.163238	+	0.986587i	$0.447806\pi$
$578$	26.7410	1.11228
$579$	−25.6708	−1.06684
$580$	12.6794	0.526483
$581$	−4.45514	−0.184830
$582$	−30.5294	−1.26548
$583$	4.57608	0.189522
$584$	−3.03817	−0.125720
$585$	4.31286	0.178315
$586$	54.5702	2.25428
$587$	7.88814	0.325578	0.162789	−	0.986661i	$-0.447951\pi$
$587$	7.88814	0.325578	0.162789	+	0.986661i	$0.447951\pi$
$588$	−3.70556	−0.152815
$589$	−6.37720	−0.262768
$590$	6.45142	0.265601
$591$	19.2242	0.790780
$592$	31.0382	1.27566
$593$	−2.13241	−0.0875676	−0.0437838	−	0.999041i	$-0.513941\pi$
$593$	−2.13241	−0.0875676	−0.0437838	+	0.999041i	$0.513941\pi$
$594$	−1.65109	−0.0677452
$595$	2.80807	0.115120
$596$	−8.92711	−0.365669
$597$	−5.48052	−0.224303
$598$	11.1103	0.454332
$599$	32.1465	1.31347	0.656736	−	0.754121i	$-0.271937\pi$
$599$	32.1465	1.31347	0.656736	+	0.754121i	$0.271937\pi$
$600$	0.358779	0.0146471
$601$	16.8160	0.685941	0.342970	−	0.939346i	$-0.388567\pi$
$601$	16.8160	0.685941	0.342970	+	0.939346i	$0.388567\pi$
$602$	10.7467	0.438001
$603$	8.70769	0.354604
$604$	−2.52723	−0.102832
$605$	2.27389	0.0924468
$606$	7.49119	0.304309
$607$	5.31791	0.215847	0.107924	−	0.994159i	$-0.465580\pi$
$607$	5.31791	0.215847	0.107924	+	0.994159i	$0.465580\pi$
$608$	3.92498	0.159179
$609$	10.5761	0.428564
$610$	3.86064	0.156313
$611$	16.3345	0.660824
$612$	0.651093	0.0263189
$613$	−6.89881	−0.278640	−0.139320	−	0.990247i	$-0.544492\pi$
$613$	−6.89881	−0.278640	−0.139320	+	0.990247i	$0.544492\pi$
$614$	1.63347	0.0659215
$615$	23.1025	0.931583
$616$	2.89669	0.116711
$617$	23.2966	0.937884	0.468942	−	0.883229i	$-0.344635\pi$
$617$	23.2966	0.937884	0.468942	+	0.883229i	$0.344635\pi$
$618$	17.3850	0.699325
$619$	26.4514	1.06317	0.531586	−	0.847004i	$-0.321596\pi$
$619$	26.4514	1.06317	0.531586	+	0.847004i	$0.321596\pi$
$620$	−10.5294	−0.422869
$621$	−3.54778	−0.142368
$622$	46.6815	1.87176
$623$	−10.5761	−0.423722
$624$	−9.34116	−0.373946
$625$	−25.8238	−1.03295
$626$	−27.1805	−1.08635
$627$	1.00000	0.0399362
$628$	−5.33611	−0.212934
$629$	−5.65109	−0.225324
$630$	−5.17058	−0.206001
$631$	7.64547	0.304361	0.152181	−	0.988353i	$-0.451370\pi$
$631$	7.64547	0.304361	0.152181	+	0.988353i	$0.451370\pi$
$632$	33.0382	1.31419
$633$	−3.12174	−0.124078
$634$	−45.0352	−1.78858
$635$	−35.9992	−1.42858
$636$	3.32273	0.131755
$637$	−9.67939	−0.383511
$638$	−12.6794	−0.501982
$639$	0.690063	0.0272985
$640$	−30.5003	−1.20563
$641$	2.66177	0.105133	0.0525667	−	0.998617i	$-0.483260\pi$
$641$	2.66177	0.105133	0.0525667	+	0.998617i	$0.483260\pi$
$642$	14.6716	0.579043
$643$	−17.2504	−0.680290	−0.340145	−	0.940373i	$-0.610476\pi$
$643$	−17.2504	−0.680290	−0.340145	+	0.940373i	$0.610476\pi$
$644$	−3.54778	−0.139802
$645$	−10.7467	−0.423149
$646$	−1.48052	−0.0582501
$647$	3.59238	0.141231	0.0706155	−	0.997504i	$-0.477504\pi$
$647$	3.59238	0.141231	0.0706155	+	0.997504i	$0.477504\pi$
$648$	2.10331	0.0826259
$649$	−1.71836	−0.0674515
$650$	−0.534184	−0.0209524
$651$	−8.78270	−0.344221
$652$	−3.10894	−0.121755
$653$	4.37238	0.171104	0.0855521	−	0.996334i	$-0.472735\pi$
$653$	4.37238	0.171104	0.0855521	+	0.996334i	$0.472735\pi$
$654$	−8.47277	−0.331311
$655$	−7.03897	−0.275035
$656$	−50.0374	−1.95363
$657$	−1.44447	−0.0563541
$658$	−19.5830	−0.763426
$659$	46.1359	1.79720	0.898599	−	0.438771i	$-0.144586\pi$
$659$	46.1359	1.79720	0.898599	+	0.438771i	$0.144586\pi$
$660$	1.65109	0.0642687
$661$	6.80617	0.264729	0.132365	−	0.991201i	$-0.457743\pi$
$661$	6.80617	0.264729	0.132365	+	0.991201i	$0.457743\pi$
$662$	−9.92769	−0.385851
$663$	1.70074	0.0660511
$664$	−6.80405	−0.264048
$665$	3.13161	0.121439
$666$	10.4055	0.403205
$667$	−27.2448	−1.05492
$668$	1.89881	0.0734672
$669$	16.9066	0.653645
$670$	−32.6922	−1.26301
$671$	−1.02830	−0.0396969
$672$	5.40550	0.208522
$673$	33.2624	1.28217	0.641086	−	0.767469i	$-0.278484\pi$
$673$	33.2624	1.28217	0.641086	+	0.767469i	$0.278484\pi$
$674$	−4.65402	−0.179266
$675$	0.170578	0.00656556
$676$	−6.82730	−0.262588
$677$	43.0793	1.65567	0.827835	−	0.560971i	$-0.189572\pi$
$677$	43.0793	1.65567	0.827835	+	0.560971i	$0.189572\pi$
$678$	−3.19112	−0.122554
$679$	25.4650	0.977258
$680$	4.28859	0.164460
$681$	10.5838	0.405573
$682$	10.5294	0.403190
$683$	−31.3714	−1.20039	−0.600196	−	0.799853i	$-0.704911\pi$
$683$	−31.3714	−1.20039	−0.600196	+	0.799853i	$0.704911\pi$
$684$	0.726109	0.0277635
$685$	7.91431	0.302390
$686$	27.5216	1.05078
$687$	−14.4933	−0.552954
$688$	23.2760	0.887390
$689$	8.67939	0.330658
$690$	13.3198	0.507076
$691$	−29.5272	−1.12327	−0.561634	−	0.827385i	$-0.689827\pi$
$691$	−29.5272	−1.12327	−0.561634	+	0.827385i	$0.689827\pi$
$692$	2.48614	0.0945090
$693$	1.37720	0.0523156
$694$	−7.29019	−0.276732
$695$	−27.7389	−1.05220
$696$	16.1522	0.612246
$697$	9.11026	0.345076
$698$	−0.418295	−0.0158327
$699$	21.5216	0.814022
$700$	0.170578	0.00644725
$701$	16.2328	0.613104	0.306552	−	0.951854i	$-0.400825\pi$
$701$	16.2328	0.613104	0.306552	+	0.951854i	$0.400825\pi$
$702$	−3.13161	−0.118195
$703$	−6.30219	−0.237691
$704$	3.36945	0.126991
$705$	19.5830	0.737539
$706$	41.1570	1.54896
$707$	−6.24852	−0.235000
$708$	−1.24772	−0.0468921
$709$	19.6015	0.736148	0.368074	−	0.929797i	$-0.380017\pi$
$709$	19.6015	0.736148	0.368074	+	0.929797i	$0.380017\pi$
$710$	−2.59078	−0.0972301
$711$	15.7077	0.589084
$712$	−16.1522	−0.605328
$713$	22.6249	0.847310
$714$	−2.03897	−0.0763065
$715$	4.31286	0.161292
$716$	−9.46714	−0.353804
$717$	15.0360	0.561531
$718$	−41.4351	−1.54634
$719$	22.4359	0.836719	0.418359	−	0.908282i	$-0.362605\pi$
$719$	22.4359	0.836719	0.418359	+	0.908282i	$0.362605\pi$
$720$	−11.1989	−0.417357
$721$	−14.5011	−0.540048
$722$	−1.65109	−0.0614473
$723$	14.3305	0.532956
$724$	−4.28164	−0.159126
$725$	1.30994	0.0486498
$726$	−1.65109	−0.0612778
$727$	12.8881	0.477995	0.238997	−	0.971020i	$-0.423181\pi$
$727$	12.8881	0.477995	0.238997	+	0.971020i	$0.423181\pi$
$728$	5.49411	0.203625
$729$	1.00000	0.0370370
$730$	5.42312	0.200719
$731$	−4.23784	−0.156742
$732$	−0.746656	−0.0275972
$733$	14.3489	0.529989	0.264994	−	0.964250i	$-0.414630\pi$
$733$	14.3489	0.529989	0.264994	+	0.964250i	$0.414630\pi$
$734$	48.6447	1.79551
$735$	−11.6044	−0.428034
$736$	−13.9250	−0.513282
$737$	8.70769	0.320752
$738$	−16.7750	−0.617495
$739$	−19.1706	−0.705201	−0.352601	−	0.935774i	$-0.614703\pi$
$739$	−19.1706	−0.705201	−0.352601	+	0.935774i	$0.614703\pi$
$740$	−10.4055	−0.382514
$741$	1.89669	0.0696766
$742$	−10.4055	−0.381998
$743$	32.6404	1.19746	0.598730	−	0.800951i	$-0.295672\pi$
$743$	32.6404	1.19746	0.598730	+	0.800951i	$0.295672\pi$
$744$	−13.4132	−0.491754
$745$	−27.9562	−1.02424
$746$	29.8633	1.09337
$747$	−3.23492	−0.118360
$748$	0.651093	0.0238063
$749$	−12.2378	−0.447161
$750$	18.1316	0.662073
$751$	−51.8513	−1.89208	−0.946040	−	0.324049i	$-0.894956\pi$
$751$	−51.8513	−1.89208	−0.946040	+	0.324049i	$0.894956\pi$
$752$	−42.4146	−1.54670
$753$	−14.5371	−0.529762
$754$	−24.0488	−0.875807
$755$	−7.91431	−0.288031
$756$	1.00000	0.0363696
$757$	35.1367	1.27706	0.638532	−	0.769596i	$-0.279542\pi$
$757$	35.1367	1.27706	0.638532	+	0.769596i	$0.279542\pi$
$758$	19.9837	0.725841
$759$	−3.54778	−0.128776
$760$	4.78270	0.173487
$761$	−53.8230	−1.95108	−0.975541	−	0.219818i	$-0.929454\pi$
$761$	−53.8230	−1.95108	−0.975541	+	0.219818i	$0.929454\pi$
$762$	26.1394	0.946929
$763$	7.06727	0.255852
$764$	−17.1260	−0.619596
$765$	2.03897	0.0737191
$766$	−4.02325	−0.145366
$767$	−3.25919	−0.117683
$768$	15.4076	0.555975
$769$	−14.1084	−0.508760	−0.254380	−	0.967104i	$-0.581871\pi$
$769$	−14.1084	−0.508760	−0.254380	+	0.967104i	$0.581871\pi$
$770$	−5.17058	−0.186335
$771$	29.8598	1.07538
$772$	−18.6398	−0.670862
$773$	−13.4621	−0.484198	−0.242099	−	0.970252i	$-0.577836\pi$
$773$	−13.4621	−0.484198	−0.242099	+	0.970252i	$0.577836\pi$
$774$	7.80325	0.280482
$775$	−1.08781	−0.0390754
$776$	38.8911	1.39611
$777$	−8.67939	−0.311371
$778$	−41.2936	−1.48045
$779$	10.1599	0.364016
$780$	3.13161	0.112130
$781$	0.690063	0.0246924
$782$	5.25254	0.187831
$783$	7.67939	0.274439
$784$	25.1337	0.897633
$785$	−16.7106	−0.596427
$786$	5.11106	0.182306
$787$	−36.9837	−1.31833	−0.659163	−	0.752000i	$-0.729089\pi$
$787$	−36.9837	−1.31833	−0.659163	+	0.752000i	$0.729089\pi$
$788$	13.9589	0.497265
$789$	−15.7926	−0.562231
$790$	−58.9730	−2.09817
$791$	2.66177	0.0946415
$792$	2.10331	0.0747379
$793$	−1.95036	−0.0692592
$794$	−21.0667	−0.747629
$795$	10.4055	0.369045
$796$	−3.97945	−0.141048
$797$	−7.22987	−0.256095	−0.128048	−	0.991768i	$-0.540871\pi$
$797$	−7.22987	−0.256095	−0.128048	+	0.991768i	$0.540871\pi$
$798$	−2.27389	−0.0804949
$799$	7.72239	0.273198
$800$	0.669517	0.0236710
$801$	−7.67939	−0.271338
$802$	−13.5195	−0.477390
$803$	−1.44447	−0.0509742
$804$	6.32273	0.222986
$805$	−11.1103	−0.391585
$806$	19.9709	0.703445
$807$	−10.3588	−0.364646
$808$	−9.54295	−0.335720
$809$	42.5577	1.49625	0.748124	−	0.663559i	$-0.230955\pi$
$809$	42.5577	1.49625	0.748124	+	0.663559i	$0.230955\pi$
$810$	−3.75441	−0.131916
$811$	56.1669	1.97229	0.986143	−	0.165900i	$-0.0530530\pi$
$811$	56.1669	1.97229	0.986143	+	0.165900i	$0.0530530\pi$
$812$	7.67939	0.269494
$813$	1.04884	0.0367845
$814$	10.4055	0.364713
$815$	−9.73598	−0.341037
$816$	−4.41617	−0.154597
$817$	−4.72611	−0.165346
$818$	60.2830	2.10774
$819$	2.61212	0.0912750
$820$	16.7750	0.585807
$821$	−19.2838	−0.673008	−0.336504	−	0.941682i	$-0.609245\pi$
$821$	−19.2838	−0.673008	−0.336504	+	0.941682i	$0.609245\pi$
$822$	−5.74666	−0.200438
$823$	7.35103	0.256241	0.128120	−	0.991759i	$-0.459106\pi$
$823$	7.35103	0.256241	0.128120	+	0.991759i	$0.459106\pi$
$824$	−22.1465	−0.771511
$825$	0.170578	0.00593877
$826$	3.90736	0.135954
$827$	−14.0078	−0.487097	−0.243549	−	0.969889i	$-0.578312\pi$
$827$	−14.0078	−0.487097	−0.243549	+	0.969889i	$0.578312\pi$
$828$	−2.57608	−0.0895249
$829$	28.6901	0.996447	0.498224	−	0.867049i	$-0.333986\pi$
$829$	28.6901	0.996447	0.498224	+	0.867049i	$0.333986\pi$
$830$	12.1452	0.421566
$831$	29.7381	1.03160
$832$	6.39080	0.221561
$833$	−4.57608	−0.158552
$834$	20.1415	0.697442
$835$	5.94633	0.205781
$836$	0.726109	0.0251130
$837$	−6.37720	−0.220428
$838$	5.73386	0.198073
$839$	−47.4124	−1.63686	−0.818430	−	0.574607i	$-0.805155\pi$
$839$	−47.4124	−1.63686	−0.818430	+	0.574607i	$0.805155\pi$
$840$	6.58675	0.227264
$841$	29.9730	1.03355
$842$	−26.4594	−0.911851
$843$	−4.97170	−0.171235
$844$	−2.26672	−0.0780238
$845$	−21.3804	−0.735509
$846$	−14.2194	−0.488874
$847$	1.37720	0.0473213
$848$	−22.5371	−0.773927
$849$	7.46289	0.256126
$850$	−0.252544	−0.00866218
$851$	22.3588	0.766449
$852$	0.501061	0.0171661
$853$	19.7339	0.675674	0.337837	−	0.941205i	$-0.390305\pi$
$853$	19.7339	0.675674	0.337837	+	0.941205i	$0.390305\pi$
$854$	2.33823	0.0800127
$855$	2.27389	0.0777654
$856$	−18.6901	−0.638813
$857$	−53.4712	−1.82654	−0.913270	−	0.407355i	$-0.866451\pi$
$857$	−53.4712	−1.82654	−0.913270	+	0.407355i	$0.866451\pi$
$858$	−3.13161	−0.106911
$859$	−29.7106	−1.01371	−0.506856	−	0.862030i	$-0.669193\pi$
$859$	−29.7106	−1.01371	−0.506856	+	0.862030i	$0.669193\pi$
$860$	−7.80325	−0.266089
$861$	13.9922	0.476855
$862$	−4.35161	−0.148216
$863$	30.0566	1.02314	0.511569	−	0.859242i	$-0.329064\pi$
$863$	30.0566	1.02314	0.511569	+	0.859242i	$0.329064\pi$
$864$	3.92498	0.133531
$865$	7.78563	0.264719
$866$	−64.1916	−2.18132
$867$	−16.1960	−0.550043
$868$	−6.37720	−0.216456
$869$	15.7077	0.532847
$870$	−28.8315	−0.977481
$871$	16.5158	0.559615
$872$	10.7934	0.365510
$873$	18.4904	0.625805
$874$	5.85772	0.198140
$875$	−15.1239	−0.511280
$876$	−1.04884	−0.0354371
$877$	31.2816	1.05631	0.528153	−	0.849149i	$-0.322885\pi$
$877$	31.2816	1.05631	0.528153	+	0.849149i	$0.322885\pi$
$878$	36.8102	1.24228
$879$	−33.0510	−1.11478
$880$	−11.1989	−0.377514
$881$	7.70769	0.259679	0.129839	−	0.991535i	$-0.458554\pi$
$881$	7.70769	0.259679	0.129839	+	0.991535i	$0.458554\pi$
$882$	8.42605	0.283720
$883$	−18.7750	−0.631827	−0.315914	−	0.948788i	$-0.602311\pi$
$883$	−18.7750	−0.631827	−0.315914	+	0.948788i	$0.602311\pi$
$884$	1.23492	0.0415349
$885$	−3.90736	−0.131345
$886$	44.3737	1.49076
$887$	34.8959	1.17169	0.585845	−	0.810423i	$-0.300763\pi$
$887$	34.8959	1.17169	0.585845	+	0.810423i	$0.300763\pi$
$888$	−13.2555	−0.444824
$889$	−21.8032	−0.731257
$890$	28.8315	0.966436
$891$	1.00000	0.0335013
$892$	12.2760	0.411031
$893$	8.61212	0.288194
$894$	20.2993	0.678909
$895$	−29.6474	−0.991002
$896$	−18.4728	−0.617132
$897$	−6.72903	−0.224676
$898$	22.8967	0.764072
$899$	−48.9730	−1.63334
$900$	0.123858	0.00412862
$901$	4.10331	0.136701
$902$	−16.7750	−0.558545
$903$	−6.50881	−0.216600
$904$	4.06514	0.135205
$905$	−13.4084	−0.445711
$906$	5.74666	0.190920
$907$	−4.46209	−0.148161	−0.0740807	−	0.997252i	$-0.523602\pi$
$907$	−4.46209	−0.148161	−0.0740807	+	0.997252i	$0.523602\pi$
$908$	7.68502	0.255036
$909$	−4.53711	−0.150486
$910$	−9.80697	−0.325098
$911$	39.3764	1.30460	0.652299	−	0.757962i	$-0.273805\pi$
$911$	39.3764	1.30460	0.652299	+	0.757962i	$0.273805\pi$
$912$	−4.92498	−0.163083
$913$	−3.23492	−0.107060
$914$	48.0849	1.59051
$915$	−2.33823	−0.0772996
$916$	−10.5237	−0.347714
$917$	−4.26322	−0.140784
$918$	−1.48052	−0.0488643
$919$	11.7905	0.388931	0.194466	−	0.980909i	$-0.437703\pi$
$919$	11.7905	0.388931	0.194466	+	0.980909i	$0.437703\pi$
$920$	−16.9680	−0.559418
$921$	−0.989327	−0.0325994
$922$	−16.5577	−0.545297
$923$	1.30883	0.0430808
$924$	1.00000	0.0328976
$925$	−1.07502	−0.0353463
$926$	23.3198	0.766336
$927$	−10.5294	−0.345829
$928$	30.1415	0.989443
$929$	−34.4239	−1.12941	−0.564706	−	0.825292i	$-0.691010\pi$
$929$	−34.4239	−1.12941	−0.564706	+	0.825292i	$0.691010\pi$
$930$	23.9426	0.785109
$931$	−5.10331	−0.167254
$932$	15.6270	0.511881
$933$	−28.2731	−0.925619
$934$	26.6009	0.870407
$935$	2.03897	0.0666814
$936$	3.98933	0.130395
$937$	1.84785	0.0603665	0.0301832	−	0.999544i	$-0.490391\pi$
$937$	1.84785	0.0603665	0.0301832	+	0.999544i	$0.490391\pi$
$938$	−19.8003	−0.646504
$939$	16.4621	0.537220
$940$	14.2194	0.463786
$941$	−4.80032	−0.156486	−0.0782431	−	0.996934i	$-0.524931\pi$
$941$	−4.80032	−0.156486	−0.0782431	+	0.996934i	$0.524931\pi$
$942$	12.1337	0.395338
$943$	−36.0451	−1.17379
$944$	8.46289	0.275444
$945$	3.13161	0.101871
$946$	7.80325	0.253705
$947$	29.9292	0.972569	0.486285	−	0.873800i	$-0.338352\pi$
$947$	29.9292	0.972569	0.486285	+	0.873800i	$0.338352\pi$
$948$	11.4055	0.370433
$949$	−2.73971	−0.0889346
$950$	−0.281641	−0.00913763
$951$	27.2760	0.884485
$952$	2.59742	0.0841830
$953$	40.8860	1.32443	0.662214	−	0.749315i	$-0.269617\pi$
$953$	40.8860	1.32443	0.662214	+	0.749315i	$0.269617\pi$
$954$	−7.55553	−0.244619
$955$	−53.6319	−1.73549
$956$	10.9178	0.353107
$957$	7.67939	0.248239
$958$	29.6681	0.958534
$959$	4.79338	0.154786
$960$	7.66177	0.247282
$961$	9.66872	0.311894
$962$	19.7360	0.636314
$963$	−8.88601	−0.286348
$964$	10.4055	0.335139
$965$	−58.3727	−1.87908
$966$	8.06727	0.259560
$967$	61.7557	1.98593	0.992965	−	0.118407i	$-0.0377787\pi$
$967$	61.7557	1.98593	0.992965	+	0.118407i	$0.0377787\pi$
$968$	2.10331	0.0676030
$969$	0.896688	0.0288058
$970$	−69.4204	−2.22896
$971$	−52.7042	−1.69136	−0.845679	−	0.533692i	$-0.820804\pi$
$971$	−52.7042	−1.69136	−0.845679	+	0.533692i	$0.820804\pi$
$972$	0.726109	0.0232900
$973$	−16.8003	−0.538594
$974$	−14.7523	−0.472694
$975$	0.323534	0.0103614
$976$	5.06434	0.162106
$977$	26.9434	0.861996	0.430998	−	0.902353i	$-0.358162\pi$
$977$	26.9434	0.861996	0.430998	+	0.902353i	$0.358162\pi$
$978$	7.06939	0.226054
$979$	−7.67939	−0.245434
$980$	−8.42605	−0.269160
$981$	5.13161	0.163840
$982$	50.0352	1.59669
$983$	54.9349	1.75215	0.876075	−	0.482175i	$-0.160153\pi$
$983$	54.9349	1.75215	0.876075	+	0.482175i	$0.160153\pi$
$984$	21.3695	0.681233
$985$	43.7138	1.39284
$986$	−11.3695	−0.362077
$987$	11.8606	0.377528
$988$	1.37720	0.0438147
$989$	16.7672	0.533166
$990$	−3.75441	−0.119323
$991$	−54.3892	−1.72773	−0.863865	−	0.503724i	$-0.831963\pi$
$991$	−54.3892	−1.72773	−0.863865	+	0.503724i	$0.831963\pi$
$992$	−25.0304	−0.794717
$993$	6.01280	0.190810
$994$	−1.56913	−0.0497697
$995$	−12.4621	−0.395075
$996$	−2.34891	−0.0744280
$997$	32.8422	1.04012	0.520062	−	0.854129i	$-0.325909\pi$
$997$	32.8422	1.04012	0.520062	+	0.854129i	$0.325909\pi$
$998$	61.1746	1.93645
$999$	−6.30219	−0.199392

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.a.g.1.1	✓	3
3.2	odd	2		1881.2.a.f.1.3		3
11.10	odd	2		6897.2.a.m.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.a.g.1.1	✓	3	1.1	even	1	trivial
1881.2.a.f.1.3		3	3.2	odd	2
6897.2.a.m.1.3		3	11.10	odd	2

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	627.2.a.g.1.1

Level	$627$
Weight	$2$
Character	627.1
Self dual	yes
Analytic conductor	$5.007$
Analytic rank	$0$
Dimension	$3$
CM	no
Inner twists	$1$