LMFDB - Embedded newform 1260.2.n.a.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(71,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 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("1260.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.n (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	1260.71
Dual form			1260.2.n.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26282 + 0.636627i) q^{2} +(1.18941 - 1.60789i) q^{4} +1.00000i q^{5} +1.00000i q^{7} +(-0.478383 + 2.78768i) q^{8} +(-0.636627 - 1.26282i) q^{10} -2.48729 q^{11} +5.41860 q^{13} +(-0.636627 - 1.26282i) q^{14} +(-1.17060 - 3.82488i) q^{16} -7.95206i q^{17} -6.96500i q^{19} +(1.60789 + 1.18941i) q^{20} +(3.14099 - 1.58348i) q^{22} +0.834597 q^{23} -1.00000 q^{25} +(-6.84270 + 3.44963i) q^{26} +(1.60789 + 1.18941i) q^{28} +7.43818i q^{29} +1.06987i q^{31} +(3.91328 + 4.08488i) q^{32} +(5.06250 + 10.0420i) q^{34} -1.00000 q^{35} +0.204600 q^{37} +(4.43411 + 8.79552i) q^{38} +(-2.78768 - 0.478383i) q^{40} +1.84398i q^{41} -4.38652i q^{43} +(-2.95841 + 3.99928i) q^{44} +(-1.05394 + 0.531327i) q^{46} +7.00063 q^{47} -1.00000 q^{49} +(1.26282 - 0.636627i) q^{50} +(6.44495 - 8.71250i) q^{52} -4.95889i q^{53} -2.48729i q^{55} +(-2.78768 - 0.478383i) q^{56} +(-4.73535 - 9.39305i) q^{58} +4.06269 q^{59} +4.54979 q^{61} +(-0.681108 - 1.35105i) q^{62} +(-7.54230 - 2.66716i) q^{64} +5.41860i q^{65} -9.50187i q^{67} +(-12.7860 - 9.45826i) q^{68} +(1.26282 - 0.636627i) q^{70} +9.40833 q^{71} +14.2406 q^{73} +(-0.258372 + 0.130254i) q^{74} +(-11.1989 - 8.28425i) q^{76} -2.48729i q^{77} +17.6352i q^{79} +(3.82488 - 1.17060i) q^{80} +(-1.17393 - 2.32860i) q^{82} -8.48193 q^{83} +7.95206 q^{85} +(2.79258 + 5.53937i) q^{86} +(1.18988 - 6.93376i) q^{88} -13.7181i q^{89} +5.41860i q^{91} +(0.992679 - 1.34194i) q^{92} +(-8.84051 + 4.45679i) q^{94} +6.96500 q^{95} +4.91671 q^{97} +(1.26282 - 0.636627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} - 4 q^{10} - 4 q^{14} + 4 q^{20} - 4 q^{22} - 24 q^{25} - 40 q^{26} + 4 q^{28} + 40 q^{32} + 8 q^{34} - 24 q^{35} + 4 q^{40} + 48 q^{44} + 36 q^{46} + 16 q^{47} - 24 q^{49} + 32 q^{52} + 4 q^{56}+ \cdots + 12 q^{88}+O(q^{100}) $ 24 * q - 4 * q^4 - 4 * q^10 - 4 * q^14 + 4 * q^20 - 4 * q^22 - 24 * q^25 - 40 * q^26 + 4 * q^28 + 40 * q^32 + 8 * q^34 - 24 * q^35 + 4 * q^40 + 48 * q^44 + 36 * q^46 + 16 * q^47 - 24 * q^49 + 32 * q^52 + 4 * q^56 - 28 * q^58 - 16 * q^59 - 32 * q^61 - 56 * q^62 - 4 * q^64 + 64 * q^68 - 32 * q^74 - 72 * q^76 - 40 * q^82 - 80 * q^83 + 32 * q^85 - 80 * q^86 + 12 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	−1.26282	+	0.636627i	−0.892946	+	0.450164i
$2$	−1.26282	+	0.636627i	−0.892946	+	0.450164i
$3$		0			0
$3$		0			0
$4$	1.18941	−	1.60789i	0.594706	−	0.803944i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−0.478383	+	2.78768i	−0.169134	+	0.985593i
$9$		0			0
$10$	−0.636627	−	1.26282i	−0.201319	−	0.399338i
$11$	−2.48729			−0.749945			−0.374973	−	0.927036i	$-0.622348\pi$
$11$	−2.48729			−0.749945			−0.374973	+	0.927036i	$0.622348\pi$
$12$		0			0
$13$	5.41860			1.50285			0.751425	−	0.659819i	$-0.229367\pi$
$13$	5.41860			1.50285			0.751425	+	0.659819i	$0.229367\pi$
$14$	−0.636627	−	1.26282i	−0.170146	−	0.337502i
$15$		0			0
$16$	−1.17060	−	3.82488i	−0.292650	−	0.956219i
$17$		−	7.95206i		−	1.92866i	−0.264709	−	0.964328i	$-0.585276\pi$
$17$		−	7.95206i		−	1.92866i	0.264709	−	0.964328i	$-0.414724\pi$
$18$		0			0
$19$		−	6.96500i		−	1.59788i	−0.601410	−	0.798941i	$-0.705394\pi$
$19$		−	6.96500i		−	1.59788i	0.601410	−	0.798941i	$-0.294606\pi$
$20$	1.60789	+	1.18941i	0.359534	+	0.265960i
$21$		0			0
$22$	3.14099	−	1.58348i	0.669661	−	0.337598i
$23$	0.834597			0.174025			0.0870127	−	0.996207i	$-0.472268\pi$
$23$	0.834597			0.174025			0.0870127	+	0.996207i	$0.472268\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−6.84270	+	3.44963i	−1.34196	+	0.676528i
$27$		0			0
$28$	1.60789	+	1.18941i	0.303862	+	0.224778i
$29$			7.43818i			1.38123i	0.723220	+	0.690617i	$0.242661\pi$
$29$			7.43818i			1.38123i	−0.723220	+	0.690617i	$0.757339\pi$
$30$		0			0
$31$			1.06987i			0.192154i	0.995374	+	0.0960770i	$0.0306295\pi$
$31$			1.06987i			0.192154i	−0.995374	+	0.0960770i	$0.969370\pi$
$32$	3.91328	+	4.08488i	0.691776	+	0.722112i
$33$		0			0
$34$	5.06250	+	10.0420i	0.868211	+	1.72219i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	0.204600			0.0336360			0.0168180	−	0.999859i	$-0.494646\pi$
$37$	0.204600			0.0336360			0.0168180	+	0.999859i	$0.494646\pi$
$38$	4.43411	+	8.79552i	0.719308	+	1.42682i
$39$		0			0
$40$	−2.78768	−	0.478383i	−0.440771	−	0.0756390i
$41$			1.84398i			0.287981i	0.989579	+	0.143990i	$0.0459934\pi$
$41$			1.84398i			0.287981i	−0.989579	+	0.143990i	$0.954007\pi$
$42$		0			0
$43$		−	4.38652i		−	0.668938i	−0.942407	−	0.334469i	$-0.891443\pi$
$43$		−	4.38652i		−	0.668938i	0.942407	−	0.334469i	$-0.108557\pi$
$44$	−2.95841	+	3.99928i	−0.445997	+	0.602914i
$45$		0			0
$46$	−1.05394	+	0.531327i	−0.155395	+	0.0783399i
$47$	7.00063			1.02115			0.510573	−	0.859834i	$-0.329433\pi$
$47$	7.00063			1.02115			0.510573	+	0.859834i	$0.329433\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	1.26282	−	0.636627i	0.178589	−	0.0900327i
$51$		0			0
$52$	6.44495	−	8.71250i	0.893753	−	1.20821i
$53$		−	4.95889i		−	0.681156i	−0.940216	−	0.340578i	$-0.889377\pi$
$53$		−	4.95889i		−	0.681156i	0.940216	−	0.340578i	$-0.110623\pi$
$54$		0			0
$55$		−	2.48729i		−	0.335386i
$56$	−2.78768	−	0.478383i	−0.372519	−	0.0639267i
$57$		0			0
$58$	−4.73535	−	9.39305i	−0.621782	−	1.23337i
$59$	4.06269			0.528917			0.264458	−	0.964397i	$-0.414807\pi$
$59$	4.06269			0.528917			0.264458	+	0.964397i	$0.414807\pi$
$60$		0			0
$61$	4.54979			0.582540			0.291270	−	0.956641i	$-0.405922\pi$
$61$	4.54979			0.582540			0.291270	+	0.956641i	$0.405922\pi$
$62$	−0.681108	−	1.35105i	−0.0865007	−	0.171583i
$63$		0			0
$64$	−7.54230	−	2.66716i	−0.942787	−	0.333395i
$65$			5.41860i			0.672095i
$66$		0			0
$67$		−	9.50187i		−	1.16084i	−0.814318	−	0.580419i	$-0.802889\pi$
$67$		−	9.50187i		−	1.16084i	0.814318	−	0.580419i	$-0.197111\pi$
$68$	−12.7860	−	9.45826i	−1.55053	−	1.14698i
$69$		0			0
$70$	1.26282	−	0.636627i	0.150935	−	0.0760915i
$71$	9.40833			1.11656			0.558282	−	0.829651i	$-0.311461\pi$
$71$	9.40833			1.11656			0.558282	+	0.829651i	$0.311461\pi$
$72$		0			0
$73$	14.2406			1.66674			0.833368	−	0.552718i	$-0.186409\pi$
$73$	14.2406			1.66674			0.833368	+	0.552718i	$0.186409\pi$
$74$	−0.258372	+	0.130254i	−0.0300351	+	0.0151417i
$75$		0			0
$76$	−11.1989	−	8.28425i	−1.28461	−	0.950269i
$77$		−	2.48729i		−	0.283453i
$78$		0			0
$79$			17.6352i			1.98411i	0.125801	+	0.992056i	$0.459850\pi$
$79$			17.6352i			1.98411i	−0.125801	+	0.992056i	$0.540150\pi$
$80$	3.82488	−	1.17060i	0.427634	−	0.130877i
$81$		0			0
$82$	−1.17393	−	2.32860i	−0.129638	−	0.257151i
$83$	−8.48193			−0.931013			−0.465506	−	0.885045i	$-0.654128\pi$
$83$	−8.48193			−0.931013			−0.465506	+	0.885045i	$0.654128\pi$
$84$		0			0
$85$	7.95206			0.862522
$86$	2.79258	+	5.53937i	0.301132	+	0.597326i
$87$		0			0
$88$	1.18988	−	6.93376i	0.126841	−	0.739141i
$89$		−	13.7181i		−	1.45412i	−0.686573	−	0.727060i	$-0.740886\pi$
$89$		−	13.7181i		−	1.45412i	0.686573	−	0.727060i	$-0.259114\pi$
$90$		0			0
$91$			5.41860i			0.568024i
$92$	0.992679	−	1.34194i	0.103494	−	0.139907i
$93$		0			0
$94$	−8.84051	+	4.45679i	−0.911829	+	0.459683i
$95$	6.96500			0.714594
$96$		0			0
$97$	4.91671			0.499217			0.249608	−	0.968347i	$-0.419698\pi$
$97$	4.91671			0.499217			0.249608	+	0.968347i	$0.419698\pi$
$98$	1.26282	−	0.636627i	0.127564	−	0.0643091i
$99$		0			0
$100$	−1.18941	+	1.60789i	−0.118941	+	0.160789i
$101$		−	5.73117i		−	0.570273i	−0.958487	−	0.285136i	$-0.907961\pi$
$101$		−	5.73117i		−	0.570273i	0.958487	−	0.285136i	$-0.0920389\pi$
$102$		0			0
$103$			12.8384i			1.26500i	0.774560	+	0.632501i	$0.217972\pi$
$103$			12.8384i			1.26500i	−0.774560	+	0.632501i	$0.782028\pi$
$104$	−2.59217	+	15.1053i	−0.254183	+	1.48120i
$105$		0			0
$106$	3.15696	+	6.26217i	0.306631	+	0.608235i
$107$	14.6535			1.41660			0.708302	−	0.705909i	$-0.249461\pi$
$107$	14.6535			1.41660			0.708302	+	0.705909i	$0.249461\pi$
$108$		0			0
$109$	4.95707			0.474801			0.237401	−	0.971412i	$-0.423705\pi$
$109$	4.95707			0.474801			0.237401	+	0.971412i	$0.423705\pi$
$110$	1.58348	+	3.14099i	0.150978	+	0.299481i
$111$		0			0
$112$	3.82488	−	1.17060i	0.361417	−	0.110611i
$113$		−	13.1965i		−	1.24142i	−0.784039	−	0.620712i	$-0.786844\pi$
$113$		−	13.1965i		−	1.24142i	0.784039	−	0.620712i	$-0.213156\pi$
$114$		0			0
$115$			0.834597i			0.0778265i
$116$	11.9597	+	8.84705i	1.11043	+	0.821428i
$117$		0			0
$118$	−5.13043	+	2.58642i	−0.472294	+	0.238099i
$119$	7.95206			0.728964
$120$		0			0
$121$	−4.81340			−0.437582
$122$	−5.74554	+	2.89652i	−0.520177	+	0.262238i
$123$		0			0
$124$	1.72023	+	1.27251i	0.154481	+	0.114275i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	14.2554i		−	1.26497i	−0.774574	−	0.632483i	$-0.782036\pi$
$127$		−	14.2554i		−	1.26497i	0.774574	−	0.632483i	$-0.217964\pi$
$128$	11.2225	−	1.43350i	0.991940	−	0.126705i
$129$		0			0
$130$	−3.44963	−	6.84270i	−0.302553	−	0.600144i
$131$	−1.49629			−0.130732			−0.0653659	−	0.997861i	$-0.520821\pi$
$131$	−1.49629			−0.130732			−0.0653659	+	0.997861i	$0.520821\pi$
$132$		0			0
$133$	6.96500			0.603942
$134$	6.04915	+	11.9991i	0.522567	+	1.03657i
$135$		0			0
$136$	22.1678	+	3.80413i	1.90087	+	0.326201i
$137$		−	6.20152i		−	0.529832i	−0.964272	−	0.264916i	$-0.914656\pi$
$137$		−	6.20152i		−	0.529832i	0.964272	−	0.264916i	$-0.0853442\pi$
$138$		0			0
$139$			19.8155i			1.68073i	0.542024	+	0.840363i	$0.317658\pi$
$139$			19.8155i			1.68073i	−0.542024	+	0.840363i	$0.682342\pi$
$140$	−1.18941	+	1.60789i	−0.100524	+	0.135891i
$141$		0			0
$142$	−11.8810	+	5.98960i	−0.997031	+	0.502636i
$143$	−13.4776			−1.12706
$144$		0			0
$145$	−7.43818			−0.617707
$146$	−17.9833	+	9.06596i	−1.48831	+	0.750304i
$147$		0			0
$148$	0.243353	−	0.328973i	0.0200035	−	0.0270415i
$149$			2.27455i			0.186338i	0.995650	+	0.0931692i	$0.0296998\pi$
$149$			2.27455i			0.186338i	−0.995650	+	0.0931692i	$0.970300\pi$
$150$		0			0
$151$		−	19.0231i		−	1.54808i	−0.633138	−	0.774039i	$-0.718233\pi$
$151$		−	19.0231i		−	1.54808i	0.633138	−	0.774039i	$-0.281767\pi$
$152$	19.4162	+	3.33194i	1.57486	+	0.270256i
$153$		0			0
$154$	1.58348	+	3.14099i	0.127600	+	0.253108i
$155$	−1.06987			−0.0859339
$156$		0			0
$157$	5.87977			0.469257			0.234628	−	0.972085i	$-0.424613\pi$
$157$	5.87977			0.469257			0.234628	+	0.972085i	$0.424613\pi$
$158$	−11.2270	−	22.2700i	−0.893174	−	1.77170i
$159$		0			0
$160$	−4.08488	+	3.91328i	−0.322938	+	0.309372i
$161$			0.834597i			0.0657754i
$162$		0			0
$163$			5.73523i			0.449218i	0.974449	+	0.224609i	$0.0721105\pi$
$163$			5.73523i			0.449218i	−0.974449	+	0.224609i	$0.927889\pi$
$164$	2.96491	+	2.19325i	0.231520	+	0.171264i
$165$		0			0
$166$	10.7111	−	5.39983i	0.831344	−	0.419108i
$167$	11.6449			0.901112			0.450556	−	0.892748i	$-0.351226\pi$
$167$	11.6449			0.901112			0.450556	+	0.892748i	$0.351226\pi$
$168$		0			0
$169$	16.3612			1.25856
$170$	−10.0420	+	5.06250i	−0.770185	+	0.388276i
$171$		0			0
$172$	−7.05303	−	5.21738i	−0.537788	−	0.397821i
$173$			5.25832i			0.399783i	0.979818	+	0.199891i	$0.0640589\pi$
$173$			5.25832i			0.399783i	−0.979818	+	0.199891i	$0.935941\pi$
$174$		0			0
$175$		−	1.00000i		−	0.0755929i
$176$	2.91162	+	9.51357i	0.219472	+	0.717112i
$177$		0			0
$178$	8.73335	+	17.3235i	0.654592	+	1.29845i
$179$	16.5106			1.23406			0.617028	−	0.786941i	$-0.288336\pi$
$179$	16.5106			1.23406			0.617028	+	0.786941i	$0.288336\pi$
$180$		0			0
$181$	−17.2678			−1.28351			−0.641754	−	0.766911i	$-0.721793\pi$
$181$	−17.2678			−1.28351			−0.641754	+	0.766911i	$0.721793\pi$
$182$	−3.44963	−	6.84270i	−0.255704	−	0.507215i
$183$		0			0
$184$	−0.399257	+	2.32659i	−0.0294336	+	0.171518i
$185$			0.204600i			0.0150425i
$186$		0			0
$187$			19.7790i			1.44639i
$188$	8.32662	−	11.2562i	0.607281	−	0.820944i
$189$		0			0
$190$	−8.79552	+	4.43411i	−0.638094	+	0.321684i
$191$	−8.87665			−0.642292			−0.321146	−	0.947030i	$-0.604068\pi$
$191$	−8.87665			−0.642292			−0.321146	+	0.947030i	$0.604068\pi$
$192$		0			0
$193$	7.86931			0.566445			0.283223	−	0.959054i	$-0.408596\pi$
$193$	7.86931			0.566445			0.283223	+	0.959054i	$0.408596\pi$
$194$	−6.20891	+	3.13011i	−0.445774	+	0.224729i
$195$		0			0
$196$	−1.18941	+	1.60789i	−0.0849579	+	0.114849i
$197$			4.89698i			0.348896i	0.984666	+	0.174448i	$0.0558140\pi$
$197$			4.89698i			0.348896i	−0.984666	+	0.174448i	$0.944186\pi$
$198$		0			0
$199$			9.24144i			0.655108i	0.944832	+	0.327554i	$0.106224\pi$
$199$			9.24144i			0.655108i	−0.944832	+	0.327554i	$0.893776\pi$
$200$	0.478383	−	2.78768i	0.0338268	−	0.197119i
$201$		0			0
$202$	3.64862	+	7.23741i	0.256716	+	0.509223i
$203$	−7.43818			−0.522058
$204$		0			0
$205$	−1.84398			−0.128789
$206$	−8.17326	−	16.2125i	−0.569458	−	1.12958i
$207$		0			0
$208$	−6.34302	−	20.7255i	−0.439810	−	1.43705i
$209$			17.3240i			1.19832i
$210$		0			0
$211$			3.49293i			0.240463i	0.992746	+	0.120231i	$0.0383637\pi$
$211$			3.49293i			0.240463i	−0.992746	+	0.120231i	$0.961636\pi$
$212$	−7.97333	−	5.89816i	−0.547611	−	0.405087i
$213$		0			0
$214$	−18.5046	+	9.32880i	−1.26495	+	0.637704i
$215$	4.38652			0.299158
$216$		0			0
$217$	−1.06987			−0.0726274
$218$	−6.25987	+	3.15581i	−0.423972	+	0.213738i
$219$		0			0
$220$	−3.99928	−	2.95841i	−0.269631	−	0.199456i
$221$		−	43.0890i		−	2.89848i
$222$		0			0
$223$			18.5637i			1.24312i	0.783367	+	0.621560i	$0.213501\pi$
$223$			18.5637i			1.24312i	−0.783367	+	0.621560i	$0.786499\pi$
$224$	−4.08488	+	3.91328i	−0.272933	+	0.261467i
$225$		0			0
$226$	8.40126	+	16.6648i	0.558844	+	1.10852i
$227$	−19.3298			−1.28297			−0.641484	−	0.767137i	$-0.721681\pi$
$227$	−19.3298			−1.28297			−0.641484	+	0.767137i	$0.721681\pi$
$228$		0			0
$229$	−13.9289			−0.920449			−0.460224	−	0.887803i	$-0.652231\pi$
$229$	−13.9289			−0.920449			−0.460224	+	0.887803i	$0.652231\pi$
$230$	−0.531327	−	1.05394i	−0.0350347	−	0.0694949i
$231$		0			0
$232$	−20.7352	−	3.55830i	−1.36134	−	0.233614i
$233$			18.7205i			1.22642i	0.789919	+	0.613211i	$0.210122\pi$
$233$			18.7205i			1.22642i	−0.789919	+	0.613211i	$0.789878\pi$
$234$		0			0
$235$			7.00063i			0.456671i
$236$	4.83221	−	6.53234i	0.314550	−	0.425219i
$237$		0			0
$238$	−10.0420	+	5.06250i	−0.650925	+	0.328153i
$239$	−30.6030			−1.97954			−0.989771	−	0.142664i	$-0.954433\pi$
$239$	−30.6030			−1.97954			−0.989771	+	0.142664i	$0.954433\pi$
$240$		0			0
$241$	−3.08754			−0.198886			−0.0994429	−	0.995043i	$-0.531706\pi$
$241$	−3.08754			−0.198886			−0.0994429	+	0.995043i	$0.531706\pi$
$242$	6.07844	−	3.06434i	0.390737	−	0.196983i
$243$		0			0
$244$	5.41157	−	7.31554i	0.346440	−	0.468329i
$245$		−	1.00000i		−	0.0638877i
$246$		0			0
$247$		−	37.7406i		−	2.40138i
$248$	−2.98245	−	0.511807i	−0.189386	−	0.0324998i
$249$		0			0
$250$	0.636627	+	1.26282i	0.0402638	+	0.0798675i
$251$	12.1541			0.767161			0.383581	−	0.923507i	$-0.374691\pi$
$251$	12.1541			0.767161			0.383581	+	0.923507i	$0.374691\pi$
$252$		0			0
$253$	−2.07588			−0.130510
$254$	9.07541	+	18.0020i	0.569442	+	1.12955i
$255$		0			0
$256$	−13.2594	+	8.95482i	−0.828711	+	0.559676i
$257$		−	21.4904i		−	1.34053i	−0.742121	−	0.670266i	$-0.766180\pi$
$257$		−	21.4904i		−	1.34053i	0.742121	−	0.670266i	$-0.233820\pi$
$258$		0			0
$259$			0.204600i			0.0127132i
$260$	8.71250	+	6.44495i	0.540326	+	0.399699i
$261$		0			0
$262$	1.88955	−	0.952582i	0.116736	−	0.0588507i
$263$	29.7602			1.83509			0.917545	−	0.397631i	$-0.130168\pi$
$263$	29.7602			1.83509			0.917545	+	0.397631i	$0.130168\pi$
$264$		0			0
$265$	4.95889			0.304622
$266$	−8.79552	+	4.43411i	−0.539288	+	0.271873i
$267$		0			0
$268$	−15.2779	−	11.3016i	−0.933249	−	0.690357i
$269$		−	1.14752i		−	0.0699653i	−0.999388	−	0.0349827i	$-0.988862\pi$
$269$		−	1.14752i		−	0.0699653i	0.999388	−	0.0349827i	$-0.0111376\pi$
$270$		0			0
$271$		−	22.9369i		−	1.39332i	−0.717404	−	0.696658i	$-0.754670\pi$
$271$		−	22.9369i		−	1.39332i	0.717404	−	0.696658i	$-0.245330\pi$
$272$	−30.4156	+	9.30869i	−1.84422	+	0.564422i
$273$		0			0
$274$	3.94806	+	7.83138i	0.238511	+	0.473111i
$275$	2.48729			0.149989
$276$		0			0
$277$	−13.4681			−0.809218			−0.404609	−	0.914490i	$-0.632592\pi$
$277$	−13.4681			−0.809218			−0.404609	+	0.914490i	$0.632592\pi$
$278$	−12.6151	−	25.0233i	−0.756601	−	1.50080i
$279$		0			0
$280$	0.478383	−	2.78768i	0.0285889	−	0.166596i
$281$		−	30.1002i		−	1.79563i	−0.440377	−	0.897813i	$-0.645155\pi$
$281$		−	30.1002i		−	1.79563i	0.440377	−	0.897813i	$-0.354845\pi$
$282$		0			0
$283$		−	7.88157i		−	0.468511i	−0.972175	−	0.234255i	$-0.924735\pi$
$283$		−	7.88157i		−	0.468511i	0.972175	−	0.234255i	$-0.0752651\pi$
$284$	11.1904	−	15.1275i	0.664026	−	0.897654i
$285$		0			0
$286$	17.0198	−	8.58022i	1.00640	−	0.507359i
$287$	−1.84398			−0.108846
$288$		0			0
$289$	−46.2352			−2.71972
$290$	9.39305	−	4.73535i	0.551579	−	0.278069i
$291$		0			0
$292$	16.9379	−	22.8973i	0.991218	−	1.33996i
$293$		−	6.20476i		−	0.362486i	−0.983438	−	0.181243i	$-0.941988\pi$
$293$		−	6.20476i		−	0.362486i	0.983438	−	0.181243i	$-0.0580121\pi$
$294$		0			0
$295$			4.06269i			0.236539i
$296$	−0.0978772	+	0.570359i	−0.00568899	+	0.0331514i
$297$		0			0
$298$	−1.44804	−	2.87234i	−0.0838827	−	0.166390i
$299$	4.52235			0.261534
$300$		0			0
$301$	4.38652			0.252835
$302$	12.1106	+	24.0227i	0.696888	+	1.38235i
$303$		0			0
$304$	−26.6403	+	8.15324i	−1.52793	+	0.467621i
$305$			4.54979i			0.260520i
$306$		0			0
$307$			16.1323i			0.920720i	0.887732	+	0.460360i	$0.152280\pi$
$307$			16.1323i			0.920720i	−0.887732	+	0.460360i	$0.847720\pi$
$308$	−3.99928	−	2.95841i	−0.227880	−	0.168571i
$309$		0			0
$310$	1.35105	−	0.681108i	0.0767343	−	0.0386843i
$311$	−7.91901			−0.449046			−0.224523	−	0.974469i	$-0.572082\pi$
$311$	−7.91901			−0.449046			−0.224523	+	0.974469i	$0.572082\pi$
$312$		0			0
$313$	22.8934			1.29401			0.647006	−	0.762485i	$-0.276021\pi$
$313$	22.8934			1.29401			0.647006	+	0.762485i	$0.276021\pi$
$314$	−7.42507	+	3.74322i	−0.419021	+	0.211242i
$315$		0			0
$316$	28.3554	+	20.9755i	1.59511	+	1.17996i
$317$		−	5.89061i		−	0.330849i	−0.986222	−	0.165425i	$-0.947101\pi$
$317$		−	5.89061i		−	0.330849i	0.986222	−	0.165425i	$-0.0528995\pi$
$318$		0			0
$319$		−	18.5009i		−	1.03585i
$320$	2.66716	−	7.54230i	0.149099	−	0.421627i
$321$		0			0
$322$	−0.531327	−	1.05394i	−0.0296097	−	0.0587339i
$323$	−55.3861			−3.08176
$324$		0			0
$325$	−5.41860			−0.300570
$326$	−3.65121	−	7.24255i	−0.202222	−	0.401128i
$327$		0			0
$328$	−5.14041	−	0.882127i	−0.283832	−	0.0487073i
$329$			7.00063i			0.385957i
$330$		0			0
$331$			12.1342i			0.666953i	0.942758	+	0.333477i	$0.108222\pi$
$331$			12.1342i			0.666953i	−0.942758	+	0.333477i	$0.891778\pi$
$332$	−10.0885	+	13.6380i	−0.553678	+	0.748482i
$333$		0			0
$334$	−14.7054	+	7.41349i	−0.804645	+	0.405648i
$335$	9.50187			0.519143
$336$		0			0
$337$	−21.8008			−1.18757			−0.593784	−	0.804625i	$-0.702367\pi$
$337$	−21.8008			−1.18757			−0.593784	+	0.804625i	$0.702367\pi$
$338$	−20.6612	+	10.4160i	−1.12382	+	0.566556i
$339$		0			0
$340$	9.45826	−	12.7860i	0.512946	−	0.693419i
$341$		−	2.66107i		−	0.144105i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	12.2282	+	2.09844i	0.659301	+	0.113140i
$345$		0			0
$346$	−3.34759	−	6.64030i	−0.179968	−	0.356984i
$347$	−33.4581			−1.79612			−0.898062	−	0.439868i	$-0.855025\pi$
$347$	−33.4581			−1.79612			−0.898062	+	0.439868i	$0.855025\pi$
$348$		0			0
$349$	−18.6864			−1.00026			−0.500130	−	0.865950i	$-0.666714\pi$
$349$	−18.6864			−1.00026			−0.500130	+	0.865950i	$0.666714\pi$
$350$	0.636627	+	1.26282i	0.0340292	+	0.0675004i
$351$		0			0
$352$	−9.73344	−	10.1603i	−0.518794	−	0.541544i
$353$		−	3.89401i		−	0.207257i	−0.994616	−	0.103629i	$-0.966955\pi$
$353$		−	3.89401i		−	0.207257i	0.994616	−	0.103629i	$-0.0330454\pi$
$354$		0			0
$355$			9.40833i			0.499342i
$356$	−22.0572	−	16.3165i	−1.16903	−	0.864774i
$357$		0			0
$358$	−20.8498	+	10.5111i	−1.10195	+	0.555527i
$359$	23.4636			1.23836			0.619180	−	0.785249i	$-0.287465\pi$
$359$	23.4636			1.23836			0.619180	+	0.785249i	$0.287465\pi$
$360$		0			0
$361$	−29.5113			−1.55322
$362$	21.8061	−	10.9932i	1.14610	−	0.577788i
$363$		0			0
$364$	8.71250	+	6.44495i	0.456659	+	0.337807i
$365$			14.2406i			0.745387i
$366$		0			0
$367$			13.4974i			0.704557i	0.935895	+	0.352278i	$0.114593\pi$
$367$			13.4974i			0.704557i	−0.935895	+	0.352278i	$0.885407\pi$
$368$	−0.976980	−	3.19223i	−0.0509286	−	0.166407i
$369$		0			0
$370$	−0.130254	−	0.258372i	−0.00677158	−	0.0134321i
$371$	4.95889			0.257453
$372$		0			0
$373$	12.8282			0.664222			0.332111	−	0.943240i	$-0.392239\pi$
$373$	12.8282			0.664222			0.332111	+	0.943240i	$0.392239\pi$
$374$	−12.5919	−	24.9773i	−0.651111	−	1.29155i
$375$		0			0
$376$	−3.34898	+	19.5155i	−0.172711	+	1.00643i
$377$			40.3045i			2.07579i
$378$		0			0
$379$			7.52696i			0.386634i	0.981136	+	0.193317i	$0.0619245\pi$
$379$			7.52696i			0.386634i	−0.981136	+	0.193317i	$0.938075\pi$
$380$	8.28425	−	11.1989i	0.424973	−	0.574493i
$381$		0			0
$382$	11.2096	−	5.65112i	0.573532	−	0.289136i
$383$	5.83122			0.297961			0.148981	−	0.988840i	$-0.452401\pi$
$383$	5.83122			0.297961			0.148981	+	0.988840i	$0.452401\pi$
$384$		0			0
$385$	2.48729			0.126764
$386$	−9.93749	+	5.00982i	−0.505805	+	0.254993i
$387$		0			0
$388$	5.84800	−	7.90552i	0.296887	−	0.401342i
$389$			30.7081i			1.55696i	0.627667	+	0.778482i	$0.284010\pi$
$389$			30.7081i			1.55696i	−0.627667	+	0.778482i	$0.715990\pi$
$390$		0			0
$391$		−	6.63676i		−	0.335635i
$392$	0.478383	−	2.78768i	0.0241620	−	0.140799i
$393$		0			0
$394$	−3.11755	−	6.18399i	−0.157060	−	0.311545i
$395$	−17.6352			−0.887321
$396$		0			0
$397$	−29.4317			−1.47713			−0.738567	−	0.674180i	$-0.764497\pi$
$397$	−29.4317			−1.47713			−0.738567	+	0.674180i	$0.764497\pi$
$398$	−5.88335	−	11.6702i	−0.294906	−	0.584976i
$399$		0			0
$400$	1.17060	+	3.82488i	0.0585301	+	0.191244i
$401$		−	2.74458i		−	0.137058i	−0.997649	−	0.0685289i	$-0.978169\pi$
$401$		−	2.74458i		−	0.137058i	0.997649	−	0.0685289i	$-0.0218305\pi$
$402$		0			0
$403$			5.79719i			0.288779i
$404$	−9.21507	−	6.81672i	−0.458467	−	0.339144i
$405$		0			0
$406$	9.39305	−	4.73535i	0.466169	−	0.235011i
$407$	−0.508899			−0.0252252
$408$		0			0
$409$	−4.41741			−0.218427			−0.109213	−	0.994018i	$-0.534833\pi$
$409$	−4.41741			−0.218427			−0.109213	+	0.994018i	$0.534833\pi$
$410$	2.32860	−	1.17393i	0.115002	−	0.0579761i
$411$		0			0
$412$	20.6426	+	15.2701i	1.01699	+	0.752304i
$413$			4.06269i			0.199912i
$414$		0			0
$415$		−	8.48193i		−	0.416362i
$416$	21.2045	+	22.1343i	1.03964	+	1.08523i
$417$		0			0
$418$	−11.0289	−	21.8770i	−0.539442	−	1.07004i
$419$	−2.73140			−0.133438			−0.0667188	−	0.997772i	$-0.521253\pi$
$419$	−2.73140			−0.133438			−0.0667188	+	0.997772i	$0.521253\pi$
$420$		0			0
$421$	14.9534			0.728785			0.364392	−	0.931245i	$-0.381277\pi$
$421$	14.9534			0.728785			0.364392	+	0.931245i	$0.381277\pi$
$422$	−2.22369	−	4.41093i	−0.108248	−	0.214720i
$423$		0			0
$424$	13.8238	+	2.37225i	0.671342	+	0.115207i
$425$			7.95206i			0.385731i
$426$		0			0
$427$			4.54979i			0.220180i
$428$	17.4290	−	23.5611i	0.842463	−	1.13887i
$429$		0			0
$430$	−5.53937	+	2.79258i	−0.267132	+	0.134670i
$431$	−14.5881			−0.702682			−0.351341	−	0.936248i	$-0.614274\pi$
$431$	−14.5881			−0.702682			−0.351341	+	0.936248i	$0.614274\pi$
$432$		0			0
$433$	30.6750			1.47415			0.737074	−	0.675812i	$-0.236207\pi$
$433$	30.6750			1.47415			0.737074	+	0.675812i	$0.236207\pi$
$434$	1.35105	−	0.681108i	0.0648524	−	0.0326942i
$435$		0			0
$436$	5.89600	−	7.97041i	0.282367	−	0.381714i
$437$		−	5.81297i		−	0.278072i
$438$		0			0
$439$		−	5.75530i		−	0.274686i	−0.990524	−	0.137343i	$-0.956144\pi$
$439$		−	5.75530i		−	0.274686i	0.990524	−	0.137343i	$-0.0438562\pi$
$440$	6.93376	+	1.18988i	0.330554	+	0.0567251i
$441$		0			0
$442$	27.4316	+	54.4135i	1.30479	+	2.58819i
$443$	−13.8296			−0.657064			−0.328532	−	0.944493i	$-0.606554\pi$
$443$	−13.8296			−0.657064			−0.328532	+	0.944493i	$0.606554\pi$
$444$		0			0
$445$	13.7181			0.650303
$446$	−11.8182	−	23.4426i	−0.559607	−	1.11004i
$447$		0			0
$448$	2.66716	−	7.54230i	0.126011	−	0.356340i
$449$			12.2246i			0.576914i	0.957493	+	0.288457i	$0.0931422\pi$
$449$			12.2246i			0.576914i	−0.957493	+	0.288457i	$0.906858\pi$
$450$		0			0
$451$		−	4.58650i		−	0.215970i
$452$	−21.2185	−	15.6961i	−0.998035	−	0.738282i
$453$		0			0
$454$	24.4101	−	12.3059i	1.14562	−	0.577545i
$455$	−5.41860			−0.254028
$456$		0			0
$457$	2.93542			0.137313			0.0686565	−	0.997640i	$-0.478129\pi$
$457$	2.93542			0.137313			0.0686565	+	0.997640i	$0.478129\pi$
$458$	17.5897	−	8.86753i	0.821911	−	0.414352i
$459$		0			0
$460$	1.34194	+	0.992679i	0.0625682	+	0.0462839i
$461$			12.9345i			0.602421i	0.953558	+	0.301210i	$0.0973906\pi$
$461$			12.9345i			0.602421i	−0.953558	+	0.301210i	$0.902609\pi$
$462$		0			0
$463$		−	24.0549i		−	1.11793i	−0.829193	−	0.558963i	$-0.811199\pi$
$463$		−	24.0549i		−	1.11793i	0.829193	−	0.558963i	$-0.188801\pi$
$464$	28.4501	−	8.70714i	1.32076	−	0.404219i
$465$		0			0
$466$	−11.9180	−	23.6406i	−0.552090	−	1.09513i
$467$	28.8997			1.33732			0.668659	−	0.743569i	$-0.266869\pi$
$467$	28.8997			1.33732			0.668659	+	0.743569i	$0.266869\pi$
$468$		0			0
$469$	9.50187			0.438756
$470$	−4.45679	−	8.84051i	−0.205576	−	0.407782i
$471$		0			0
$472$	−1.94352	+	11.3255i	−0.0894579	+	0.521297i
$473$			10.9105i			0.501667i
$474$		0			0
$475$			6.96500i			0.319576i
$476$	9.45826	−	12.7860i	0.433519	−	0.586046i
$477$		0			0
$478$	38.6460	−	19.4827i	1.76762	−	0.891118i
$479$	−6.95060			−0.317581			−0.158790	−	0.987312i	$-0.550759\pi$
$479$	−6.95060			−0.317581			−0.158790	+	0.987312i	$0.550759\pi$
$480$		0			0
$481$	1.10865			0.0505499
$482$	3.89899	−	1.96561i	0.177594	−	0.0895311i
$483$		0			0
$484$	−5.72511	+	7.73941i	−0.260232	+	0.351791i
$485$			4.91671i			0.223256i
$486$		0			0
$487$		−	38.8925i		−	1.76239i	−0.472756	−	0.881193i	$-0.656741\pi$
$487$		−	38.8925i		−	1.76239i	0.472756	−	0.881193i	$-0.343259\pi$
$488$	−2.17654	+	12.6833i	−0.0985274	+	0.574148i
$489$		0			0
$490$	0.636627	+	1.26282i	0.0287599	+	0.0570482i
$491$	−24.8414			−1.12108			−0.560539	−	0.828128i	$-0.689406\pi$
$491$	−24.8414			−1.12108			−0.560539	+	0.828128i	$0.689406\pi$
$492$		0			0
$493$	59.1488			2.66393
$494$	24.0267	+	47.6594i	1.08101	+	2.14430i
$495$		0			0
$496$	4.09212	−	1.25239i	0.183741	−	0.0562340i
$497$			9.40833i			0.422021i
$498$		0			0
$499$			3.88746i			0.174027i	0.996207	+	0.0870133i	$0.0277323\pi$
$499$			3.88746i			0.174027i	−0.996207	+	0.0870133i	$0.972268\pi$
$500$	−1.60789	−	1.18941i	−0.0719069	−	0.0531921i
$501$		0			0
$502$	−15.3484	+	7.73765i	−0.685034	+	0.345348i
$503$	9.05859			0.403903			0.201951	−	0.979396i	$-0.435272\pi$
$503$	9.05859			0.403903			0.201951	+	0.979396i	$0.435272\pi$
$504$		0			0
$505$	5.73117			0.255034
$506$	2.62146	−	1.32156i	0.116538	−	0.0587506i
$507$		0			0
$508$	−22.9211	−	16.9556i	−1.01696	−	0.752283i
$509$			26.1427i			1.15876i	0.815059	+	0.579378i	$0.196704\pi$
$509$			26.1427i			1.15876i	−0.815059	+	0.579378i	$0.803296\pi$
$510$		0			0
$511$			14.2406i			0.629967i
$512$	11.0433	−	19.7496i	0.488049	−	0.872816i
$513$		0			0
$514$	13.6814	+	27.1384i	0.603459	+	1.19702i
$515$	−12.8384			−0.565726
$516$		0			0
$517$	−17.4126			−0.765804
$518$	−0.130254	−	0.258372i	−0.00572303	−	0.0113522i
$519$		0			0
$520$	−15.1053	−	2.59217i	−0.662412	−	0.113674i
$521$			27.1627i			1.19002i	0.803718	+	0.595011i	$0.202852\pi$
$521$			27.1627i			1.19002i	−0.803718	+	0.595011i	$0.797148\pi$
$522$		0			0
$523$		−	37.3095i		−	1.63143i	−0.578453	−	0.815716i	$-0.696343\pi$
$523$		−	37.3095i		−	1.63143i	0.578453	−	0.815716i	$-0.303657\pi$
$524$	−1.77971	+	2.40587i	−0.0777470	+	0.105101i
$525$		0			0
$526$	−37.5816	+	18.9461i	−1.63864	+	0.826091i
$527$	8.50765			0.370599
$528$		0			0
$529$	−22.3034			−0.969715
$530$	−6.26217	+	3.15696i	−0.272011	+	0.137130i
$531$		0			0
$532$	8.28425	−	11.1989i	0.359168	−	0.485536i
$533$			9.99177i			0.432792i
$534$		0			0
$535$			14.6535i			0.633525i
$536$	26.4882	+	4.54554i	1.14411	+	0.196337i
$537$		0			0
$538$	0.730541	+	1.44910i	0.0314958	+	0.0624753i
$539$	2.48729			0.107135
$540$		0			0
$541$	−20.6030			−0.885792			−0.442896	−	0.896573i	$-0.646049\pi$
$541$	−20.6030			−0.885792			−0.442896	+	0.896573i	$0.646049\pi$
$542$	14.6022	+	28.9651i	0.627220	+	1.24416i
$543$		0			0
$544$	32.4832	−	31.1186i	1.39271	−	1.33420i
$545$			4.95707i			0.212338i
$546$		0			0
$547$			23.5518i			1.00700i	0.863995	+	0.503501i	$0.167955\pi$
$547$			23.5518i			1.00700i	−0.863995	+	0.503501i	$0.832045\pi$
$548$	−9.97135	−	7.37616i	−0.425955	−	0.315094i
$549$		0			0
$550$	−3.14099	+	1.58348i	−0.133932	+	0.0675196i
$551$	51.8069			2.20705
$552$		0			0
$553$	−17.6352			−0.749923
$554$	17.0077	−	8.57415i	0.722588	−	0.364281i
$555$		0			0
$556$	31.8610	+	23.5687i	1.35121	+	0.999537i
$557$		−	22.7028i		−	0.961950i	−0.876734	−	0.480975i	$-0.840283\pi$
$557$		−	22.7028i		−	0.961950i	0.876734	−	0.480975i	$-0.159717\pi$
$558$		0			0
$559$		−	23.7688i		−	1.00531i
$560$	1.17060	+	3.82488i	0.0494670	+	0.161631i
$561$		0			0
$562$	19.1626	+	38.0110i	0.808325	+	1.60340i
$563$	−5.57405			−0.234918			−0.117459	−	0.993078i	$-0.537475\pi$
$563$	−5.57405			−0.234918			−0.117459	+	0.993078i	$0.537475\pi$
$564$		0			0
$565$	13.1965			0.555182
$566$	5.01762	+	9.95297i	0.210906	+	0.418355i
$567$		0			0
$568$	−4.50079	+	26.2274i	−0.188849	+	1.10048i
$569$		−	19.6588i		−	0.824142i	−0.911152	−	0.412071i	$-0.864806\pi$
$569$		−	19.6588i		−	0.824142i	0.911152	−	0.412071i	$-0.135194\pi$
$570$		0			0
$571$		−	13.8200i		−	0.578351i	−0.957276	−	0.289175i	$-0.906619\pi$
$571$		−	13.8200i		−	0.578351i	0.957276	−	0.289175i	$-0.0933811\pi$
$572$	−16.0304	+	21.6705i	−0.670266	+	0.906089i
$573$		0			0
$574$	2.32860	−	1.17393i	0.0971940	−	0.0489987i
$575$	−0.834597			−0.0348051
$576$		0			0
$577$	7.85582			0.327042			0.163521	−	0.986540i	$-0.447715\pi$
$577$	7.85582			0.327042			0.163521	+	0.986540i	$0.447715\pi$
$578$	58.3866	−	29.4346i	2.42856	−	1.22432i
$579$		0			0
$580$	−8.84705	+	11.9597i	−0.367354	+	0.496602i
$581$		−	8.48193i		−	0.351890i
$582$		0			0
$583$			12.3342i			0.510829i
$584$	−6.81247	+	39.6982i	−0.281902	+	1.64272i
$585$		0			0
$586$	3.95012	+	7.83548i	0.163178	+	0.323681i
$587$	−12.4434			−0.513595			−0.256798	−	0.966465i	$-0.582667\pi$
$587$	−12.4434			−0.513595			−0.256798	+	0.966465i	$0.582667\pi$
$588$		0			0
$589$	7.45164			0.307039
$590$	−2.58642	−	5.13043i	−0.106481	−	0.211216i
$591$		0			0
$592$	−0.239505	−	0.782570i	−0.00984359	−	0.0321634i
$593$			26.8790i			1.10379i	0.833915	+	0.551893i	$0.186094\pi$
$593$			26.8790i			1.10379i	−0.833915	+	0.551893i	$0.813906\pi$
$594$		0			0
$595$			7.95206i			0.326002i
$596$	3.65722	+	2.70538i	0.149806	+	0.110816i
$597$		0			0
$598$	−5.71089	+	2.87905i	−0.233536	+	0.117733i
$599$	3.61279			0.147615			0.0738074	−	0.997273i	$-0.476485\pi$
$599$	3.61279			0.147615			0.0738074	+	0.997273i	$0.476485\pi$
$600$		0			0
$601$	−2.08012			−0.0848497			−0.0424248	−	0.999100i	$-0.513508\pi$
$601$	−2.08012			−0.0848497			−0.0424248	+	0.999100i	$0.513508\pi$
$602$	−5.53937	+	2.79258i	−0.225768	+	0.113817i
$603$		0			0
$604$	−30.5870	−	22.6263i	−1.24457	−	0.920651i
$605$		−	4.81340i		−	0.195693i
$606$		0			0
$607$			17.2015i			0.698186i	0.937088	+	0.349093i	$0.113510\pi$
$607$			17.2015i			0.698186i	−0.937088	+	0.349093i	$0.886490\pi$
$608$	28.4512	−	27.2560i	1.15385	−	1.10538i
$609$		0			0
$610$	−2.89652	−	5.74554i	−0.117277	−	0.232630i
$611$	37.9336			1.53463
$612$		0			0
$613$	−34.6310			−1.39873			−0.699367	−	0.714763i	$-0.746534\pi$
$613$	−34.6310			−1.39873			−0.699367	+	0.714763i	$0.746534\pi$
$614$	−10.2703	−	20.3722i	−0.414475	−	0.822154i
$615$		0			0
$616$	6.93376	+	1.18988i	0.279369	+	0.0479415i
$617$		−	30.9408i		−	1.24563i	−0.782369	−	0.622815i	$-0.785989\pi$
$617$		−	30.9408i		−	1.24563i	0.782369	−	0.622815i	$-0.214011\pi$
$618$		0			0
$619$		−	5.93399i		−	0.238507i	−0.992864	−	0.119254i	$-0.961950\pi$
$619$		−	5.93399i		−	0.238507i	0.992864	−	0.119254i	$-0.0380501\pi$
$620$	−1.27251	+	1.72023i	−0.0511054	+	0.0690860i
$621$		0			0
$622$	10.0003	−	5.04146i	0.400974	−	0.202144i
$623$	13.7181			0.549606
$624$		0			0
$625$	1.00000			0.0400000
$626$	−28.9102	+	14.5746i	−1.15548	+	0.582517i
$627$		0			0
$628$	6.99347	−	9.45401i	0.279070	−	0.377256i
$629$		−	1.62699i		−	0.0648723i
$630$		0			0
$631$		−	33.4702i		−	1.33243i	−0.745761	−	0.666214i	$-0.767914\pi$
$631$		−	33.4702i		−	1.33243i	0.745761	−	0.666214i	$-0.232086\pi$
$632$	−49.1612	−	8.43637i	−1.95553	−	0.335581i
$633$		0			0
$634$	3.75012	+	7.43876i	0.148936	+	0.295431i
$635$	14.2554			0.565710
$636$		0			0
$637$	−5.41860			−0.214693
$638$	11.7782	+	23.3632i	0.466302	+	0.924959i
$639$		0			0
$640$	1.43350	+	11.2225i	0.0566642	+	0.443609i
$641$			21.5133i			0.849725i	0.905258	+	0.424862i	$0.139677\pi$
$641$			21.5133i			0.849725i	−0.905258	+	0.424862i	$0.860323\pi$
$642$		0			0
$643$			37.2929i			1.47069i	0.677693	+	0.735345i	$0.262980\pi$
$643$			37.2929i			1.47069i	−0.677693	+	0.735345i	$0.737020\pi$
$644$	1.34194	+	0.992679i	0.0528797	+	0.0391170i
$645$		0			0
$646$	69.9425	−	35.2603i	2.75185	−	1.38730i
$647$	2.94206			0.115664			0.0578321	−	0.998326i	$-0.481581\pi$
$647$	2.94206			0.115664			0.0578321	+	0.998326i	$0.481581\pi$
$648$		0			0
$649$	−10.1051			−0.396659
$650$	6.84270	−	3.44963i	0.268393	−	0.135306i
$651$		0			0
$652$	9.22161	+	6.82155i	0.361146	+	0.267153i
$653$			30.8516i			1.20731i	0.797244	+	0.603657i	$0.206290\pi$
$653$			30.8516i			1.20731i	−0.797244	+	0.603657i	$0.793710\pi$
$654$		0			0
$655$		−	1.49629i		−	0.0584651i
$656$	7.05298	−	2.15856i	0.275373	−	0.0842777i
$657$		0			0
$658$	−4.45679	−	8.84051i	−0.173744	−	0.344639i
$659$	11.9174			0.464237			0.232119	−	0.972687i	$-0.425434\pi$
$659$	11.9174			0.464237			0.232119	+	0.972687i	$0.425434\pi$
$660$		0			0
$661$	−21.8793			−0.851007			−0.425503	−	0.904957i	$-0.639903\pi$
$661$	−21.8793			−0.851007			−0.425503	+	0.904957i	$0.639903\pi$
$662$	−7.72493	−	15.3232i	−0.300238	−	0.595553i
$663$		0			0
$664$	4.05761	−	23.6449i	0.157466	−	0.917600i
$665$			6.96500i			0.270091i
$666$		0			0
$667$			6.20788i			0.240370i
$668$	13.8506	−	18.7237i	0.535897	−	0.724443i
$669$		0			0
$670$	−11.9991	+	6.04915i	−0.463566	+	0.233699i
$671$	−11.3166			−0.436873
$672$		0			0
$673$	3.93612			0.151726			0.0758632	−	0.997118i	$-0.475829\pi$
$673$	3.93612			0.151726			0.0758632	+	0.997118i	$0.475829\pi$
$674$	27.5305	−	13.8790i	1.06043	−	0.534600i
$675$		0			0
$676$	19.4602	−	26.3070i	0.748471	−	1.01181i
$677$			37.4472i			1.43921i	0.694382	+	0.719606i	$0.255678\pi$
$677$			37.4472i			1.43921i	−0.694382	+	0.719606i	$0.744322\pi$
$678$		0			0
$679$			4.91671i			0.188686i
$680$	−3.80413	+	22.1678i	−0.145882	+	0.850095i
$681$		0			0
$682$	1.69411	+	3.36044i	0.0648708	+	0.128678i
$683$	−10.9267			−0.418098			−0.209049	−	0.977905i	$-0.567037\pi$
$683$	−10.9267			−0.418098			−0.209049	+	0.977905i	$0.567037\pi$
$684$		0			0
$685$	6.20152			0.236948
$686$	0.636627	+	1.26282i	0.0243065	+	0.0482146i
$687$		0			0
$688$	−16.7779	+	5.13487i	−0.639652	+	0.195765i
$689$		−	26.8702i		−	1.02367i
$690$		0			0
$691$		−	15.0065i		−	0.570873i	−0.958398	−	0.285437i	$-0.907861\pi$
$691$		−	15.0065i		−	0.570873i	0.958398	−	0.285437i	$-0.0921386\pi$
$692$	8.45479	+	6.25431i	0.321403	+	0.237753i
$693$		0			0
$694$	42.2514	−	21.3003i	1.60384	−	0.808550i
$695$	−19.8155			−0.751643
$696$		0			0
$697$	14.6634			0.555416
$698$	23.5975	−	11.8963i	0.893179	−	0.450281i
$699$		0			0
$700$	−1.60789	−	1.18941i	−0.0607724	−	0.0449555i
$701$		−	5.70228i		−	0.215372i	−0.994185	−	0.107686i	$-0.965656\pi$
$701$		−	5.70228i		−	0.215372i	0.994185	−	0.107686i	$-0.0343441\pi$
$702$		0			0
$703$		−	1.42504i		−	0.0537463i
$704$	18.7599	+	6.63399i	0.707039	+	0.250028i
$705$		0			0
$706$	2.47904	+	4.91743i	0.0932998	+	0.185070i
$707$	5.73117			0.215543
$708$		0			0
$709$	10.1141			0.379843			0.189922	−	0.981799i	$-0.439177\pi$
$709$	10.1141			0.379843			0.189922	+	0.981799i	$0.439177\pi$
$710$	−5.98960	−	11.8810i	−0.224786	−	0.445886i
$711$		0			0
$712$	38.2418	+	6.56253i	1.43317	+	0.245941i
$713$			0.892909i			0.0334397i
$714$		0			0
$715$		−	13.4776i		−	0.504034i
$716$	19.6378	−	26.5471i	0.733901	−	0.992112i
$717$		0			0
$718$	−29.6302	+	14.9375i	−1.10579	+	0.557464i
$719$	24.4097			0.910328			0.455164	−	0.890408i	$-0.349581\pi$
$719$	24.4097			0.910328			0.455164	+	0.890408i	$0.349581\pi$
$720$		0			0
$721$	−12.8384			−0.478126
$722$	37.2673	−	18.7877i	1.38695	−	0.699205i
$723$		0			0
$724$	−20.5386	+	27.7647i	−0.763309	+	1.03187i
$725$		−	7.43818i		−	0.276247i
$726$		0			0
$727$		−	8.07951i		−	0.299653i	−0.988712	−	0.149826i	$-0.952129\pi$
$727$		−	8.07951i		−	0.299653i	0.988712	−	0.149826i	$-0.0478714\pi$
$728$	−15.1053	−	2.59217i	−0.559840	−	0.0960721i
$729$		0			0
$730$	−9.06596	−	17.9833i	−0.335546	−	0.665591i
$731$	−34.8819			−1.29015
$732$		0			0
$733$	−16.7898			−0.620145			−0.310072	−	0.950713i	$-0.600353\pi$
$733$	−16.7898			−0.620145			−0.310072	+	0.950713i	$0.600353\pi$
$734$	−8.59279	−	17.0447i	−0.317166	−	0.629131i
$735$		0			0
$736$	3.26601	+	3.40923i	0.120387	+	0.125666i
$737$			23.6339i			0.870565i
$738$		0			0
$739$		−	5.36772i		−	0.197455i	−0.995115	−	0.0987273i	$-0.968523\pi$
$739$		−	5.36772i		−	0.197455i	0.995115	−	0.0987273i	$-0.0314772\pi$
$740$	0.328973	+	0.243353i	0.0120933	+	0.00894585i
$741$		0			0
$742$	−6.26217	+	3.15696i	−0.229891	+	0.115896i
$743$	−33.4658			−1.22774			−0.613870	−	0.789407i	$-0.710388\pi$
$743$	−33.4658			−1.22774			−0.613870	+	0.789407i	$0.710388\pi$
$744$		0			0
$745$	−2.27455			−0.0833331
$746$	−16.1997	+	8.16681i	−0.593114	+	0.299008i
$747$		0			0
$748$	31.8025	+	23.5254i	1.16281	+	0.860175i
$749$			14.6535i			0.535426i
$750$		0			0
$751$			13.1817i			0.481008i	0.970648	+	0.240504i	$0.0773128\pi$
$751$			13.1817i			0.481008i	−0.970648	+	0.240504i	$0.922687\pi$
$752$	−8.19495	−	26.7765i	−0.298839	−	0.976440i
$753$		0			0
$754$	−25.6590	−	50.8972i	−0.934444	−	1.85357i
$755$	19.0231			0.692322
$756$		0			0
$757$	51.4957			1.87164			0.935821	−	0.352475i	$-0.114660\pi$
$757$	51.4957			1.87164			0.935821	+	0.352475i	$0.114660\pi$
$758$	−4.79187	−	9.50516i	−0.174048	−	0.345243i
$759$		0			0
$760$	−3.33194	+	19.4162i	−0.120862	+	0.704299i
$761$			5.75865i			0.208751i	0.994538	+	0.104375i	$0.0332843\pi$
$761$			5.75865i			0.208751i	−0.994538	+	0.104375i	$0.966716\pi$
$762$		0			0
$763$			4.95707i			0.179458i
$764$	−10.5580	+	14.2727i	−0.381975	+	0.516367i
$765$		0			0
$766$	−7.36375	+	3.71231i	−0.266063	+	0.134131i
$767$	22.0141			0.794883
$768$		0			0
$769$	51.9385			1.87295			0.936476	−	0.350733i	$-0.114067\pi$
$769$	51.9385			1.87295			0.936476	+	0.350733i	$0.114067\pi$
$770$	−3.14099	+	1.58348i	−0.113193	+	0.0570645i
$771$		0			0
$772$	9.35984	−	12.6530i	0.336868	−	0.455390i
$773$			54.9369i			1.97594i	0.154640	+	0.987971i	$0.450578\pi$
$773$			54.9369i			1.97594i	−0.154640	+	0.987971i	$0.549422\pi$
$774$		0			0
$775$		−	1.06987i		−	0.0384308i
$776$	−2.35207	+	13.7062i	−0.0844345	+	0.492025i
$777$		0			0
$778$	−19.5496	−	38.7787i	−0.700888	−	1.39029i
$779$	12.8433			0.460159
$780$		0			0
$781$	−23.4012			−0.837361
$782$	4.22514	+	8.38101i	0.151091	+	0.299704i
$783$		0			0
$784$	1.17060	+	3.82488i	0.0418072	+	0.136603i
$785$			5.87977i			0.209858i
$786$		0			0
$787$		−	27.4559i		−	0.978696i	−0.872089	−	0.489348i	$-0.837235\pi$
$787$		−	27.4559i		−	0.978696i	0.872089	−	0.489348i	$-0.162765\pi$
$788$	7.87380	+	5.82453i	0.280492	+	0.207490i
$789$		0			0
$790$	22.2700	−	11.2270i	0.792330	−	0.399440i
$791$	13.1965			0.469214
$792$		0			0
$793$	24.6535			0.875470
$794$	37.1668	−	18.7370i	1.31900	−	0.664952i
$795$		0			0
$796$	14.8592	+	10.9919i	0.526670	+	0.389596i
$797$		−	20.4682i		−	0.725022i	−0.931979	−	0.362511i	$-0.881920\pi$
$797$		−	20.4682i		−	0.725022i	0.931979	−	0.362511i	$-0.118080\pi$
$798$		0			0
$799$		−	55.6694i		−	1.96944i
$800$	−3.91328	−	4.08488i	−0.138355	−	0.144422i
$801$		0			0
$802$	1.74727	+	3.46590i	0.0616984	+	0.122385i
$803$	−35.4205			−1.24996
$804$		0			0
$805$	−0.834597			−0.0294157
$806$	−3.69065	−	7.32079i	−0.129998	−	0.257864i
$807$		0			0
$808$	15.9767	+	2.74170i	0.562057	+	0.0964525i
$809$		−	26.2422i		−	0.922625i	−0.887238	−	0.461313i	$-0.847379\pi$
$809$		−	26.2422i		−	0.922625i	0.887238	−	0.461313i	$-0.152621\pi$
$810$		0			0
$811$		−	12.9694i		−	0.455417i	−0.973729	−	0.227709i	$-0.926877\pi$
$811$		−	12.9694i		−	0.455417i	0.973729	−	0.227709i	$-0.0731234\pi$
$812$	−8.84705	+	11.9597i	−0.310471	+	0.419705i
$813$		0			0
$814$	0.642646	−	0.323979i	0.0225247	−	0.0113555i
$815$	−5.73523			−0.200896
$816$		0			0
$817$	−30.5521			−1.06888
$818$	5.57838	−	2.81224i	0.195043	−	0.0983278i
$819$		0			0
$820$	−2.19325	+	2.96491i	−0.0765915	+	0.103539i
$821$			1.78987i			0.0624670i	0.999512	+	0.0312335i	$0.00994355\pi$
$821$			1.78987i			0.0624670i	−0.999512	+	0.0312335i	$0.990056\pi$
$822$		0			0
$823$		−	3.90306i		−	0.136052i	−0.997684	−	0.0680261i	$-0.978330\pi$
$823$		−	3.90306i		−	0.136052i	0.997684	−	0.0680261i	$-0.0216701\pi$
$824$	−35.7892	−	6.14166i	−1.24678	−	0.213955i
$825$		0			0
$826$	−2.58642	−	5.13043i	−0.0899930	−	0.178510i
$827$	−53.0808			−1.84580			−0.922900	−	0.385039i	$-0.874188\pi$
$827$	−53.0808			−1.84580			−0.922900	+	0.385039i	$0.874188\pi$
$828$		0			0
$829$	−50.5236			−1.75476			−0.877379	−	0.479798i	$-0.840710\pi$
$829$	−50.5236			−1.75476			−0.877379	+	0.479798i	$0.840710\pi$
$830$	5.39983	+	10.7111i	0.187431	+	0.371788i
$831$		0			0
$832$	−40.8687	−	14.4523i	−1.41687	−	0.501042i
$833$			7.95206i			0.275522i
$834$		0			0
$835$			11.6449i			0.402990i
$836$	27.8550	+	20.6053i	0.963384	+	0.712650i
$837$		0			0
$838$	3.44925	−	1.73888i	0.119153	−	0.0600687i
$839$	2.21893			0.0766059			0.0383030	−	0.999266i	$-0.487805\pi$
$839$	2.21893			0.0766059			0.0383030	+	0.999266i	$0.487805\pi$
$840$		0			0
$841$	−26.3265			−0.907810
$842$	−18.8834	+	9.51975i	−0.650766	+	0.328072i
$843$		0			0
$844$	5.61623	+	4.15453i	0.193319	+	0.143005i
$845$			16.3612i			0.562844i
$846$		0			0
$847$		−	4.81340i		−	0.165390i
$848$	−18.9671	+	5.80488i	−0.651334	+	0.199341i
$849$		0			0
$850$	−5.06250	−	10.0420i	−0.173642	−	0.344437i
$851$	0.170758			0.00585352
$852$		0			0
$853$	0.751556			0.0257328			0.0128664	−	0.999917i	$-0.495904\pi$
$853$	0.751556			0.0257328			0.0128664	+	0.999917i	$0.495904\pi$
$854$	−2.89652	−	5.74554i	−0.0991168	−	0.196608i
$855$		0			0
$856$	−7.00998	+	40.8492i	−0.239596	+	1.39620i
$857$			5.58659i			0.190834i	0.995437	+	0.0954172i	$0.0304185\pi$
$857$			5.58659i			0.190834i	−0.995437	+	0.0954172i	$0.969581\pi$
$858$		0			0
$859$			34.8451i			1.18890i	0.804132	+	0.594451i	$0.202630\pi$
$859$			34.8451i			1.18890i	−0.804132	+	0.594451i	$0.797370\pi$
$860$	5.21738	−	7.05303i	0.177911	−	0.240506i
$861$		0			0
$862$	18.4220	−	9.28715i	0.627457	−	0.316322i
$863$	2.59624			0.0883771			0.0441885	−	0.999023i	$-0.485930\pi$
$863$	2.59624			0.0883771			0.0441885	+	0.999023i	$0.485930\pi$
$864$		0			0
$865$	−5.25832			−0.178788
$866$	−38.7369	+	19.5286i	−1.31633	+	0.663608i
$867$		0			0
$868$	−1.27251	+	1.72023i	−0.0431919	+	0.0583883i
$869$		−	43.8637i		−	1.48797i
$870$		0			0
$871$		−	51.4869i		−	1.74457i
$872$	−2.37138	+	13.8187i	−0.0803051	+	0.467961i
$873$		0			0
$874$	3.70069	+	7.34071i	0.125178	+	0.248303i
$875$	1.00000			0.0338062
$876$		0			0
$877$	36.7477			1.24088			0.620440	−	0.784254i	$-0.286954\pi$
$877$	36.7477			1.24088			0.620440	+	0.784254i	$0.286954\pi$
$878$	3.66398	+	7.26789i	0.123653	+	0.245279i
$879$		0			0
$880$	−9.51357	+	2.91162i	−0.320702	+	0.0981508i
$881$		−	27.7667i		−	0.935482i	−0.883866	−	0.467741i	$-0.845068\pi$
$881$		−	27.7667i		−	0.935482i	0.883866	−	0.467741i	$-0.154932\pi$
$882$		0			0
$883$			35.2319i			1.18565i	0.805333	+	0.592823i	$0.201987\pi$
$883$			35.2319i			1.18565i	−0.805333	+	0.592823i	$0.798013\pi$
$884$	−69.2823	−	51.2506i	−2.33022	−	1.72374i
$885$		0			0
$886$	17.4642	−	8.80430i	0.586723	−	0.295786i
$887$	−17.2658			−0.579730			−0.289865	−	0.957068i	$-0.593610\pi$
$887$	−17.2658			−0.579730			−0.289865	+	0.957068i	$0.593610\pi$
$888$		0			0
$889$	14.2554			0.478112
$890$	−17.3235	+	8.73335i	−0.580685	+	0.292743i
$891$		0			0
$892$	29.8484	+	22.0799i	0.999398	+	0.739290i
$893$		−	48.7594i		−	1.63167i
$894$		0			0
$895$			16.5106i			0.551887i
$896$	1.43350	+	11.2225i	0.0478900	+	0.374918i
$897$		0			0
$898$	−7.78250	−	15.4374i	−0.259705	−	0.515153i
$899$	−7.95787			−0.265410
$900$		0			0
$901$	−39.4334			−1.31372
$902$	2.91989	+	5.79191i	0.0972217	+	0.192849i
$903$		0			0
$904$	36.7876	+	6.31299i	1.22354	+	0.209967i
$905$		−	17.2678i		−	0.574002i
$906$		0			0
$907$		−	16.3067i		−	0.541455i	−0.962656	−	0.270727i	$-0.912736\pi$
$907$		−	16.3067i		−	0.541455i	0.962656	−	0.270727i	$-0.0872642\pi$
$908$	−22.9911	+	31.0802i	−0.762988	+	1.03143i
$909$		0			0
$910$	6.84270	−	3.44963i	0.226833	−	0.114354i
$911$	−20.3584			−0.674502			−0.337251	−	0.941415i	$-0.609497\pi$
$911$	−20.3584			−0.674502			−0.337251	+	0.941415i	$0.609497\pi$
$912$		0			0
$913$	21.0970			0.698209
$914$	−3.70689	+	1.86877i	−0.122613	+	0.0618133i
$915$		0			0
$916$	−16.5672	+	22.3961i	−0.547396	+	0.739989i
$917$		−	1.49629i		−	0.0494120i
$918$		0			0
$919$		−	49.8797i		−	1.64538i	−0.568490	−	0.822690i	$-0.692472\pi$
$919$		−	49.8797i		−	1.64538i	0.568490	−	0.822690i	$-0.307528\pi$
$920$	−2.32659	−	0.399257i	−0.0767053	−	0.0131631i
$921$		0			0
$922$	−8.23447	−	16.3339i	−0.271188	−	0.537929i
$923$	50.9800			1.67803
$924$		0			0
$925$	−0.204600			−0.00672720
$926$	15.3140	+	30.3769i	0.503250	+	0.998248i
$927$		0			0
$928$	−30.3841	+	29.1077i	−0.997406	+	0.955505i
$929$		−	8.44716i		−	0.277142i	−0.990352	−	0.138571i	$-0.955749\pi$
$929$		−	8.44716i		−	0.277142i	0.990352	−	0.138571i	$-0.0442510\pi$
$930$		0			0
$931$			6.96500i			0.228269i
$932$	30.1005	+	22.2664i	0.985974	+	0.729360i
$933$		0			0
$934$	−36.4950	+	18.3983i	−1.19415	+	0.602011i
$935$	−19.7790			−0.646844
$936$		0			0
$937$	−36.2899			−1.18554			−0.592769	−	0.805372i	$-0.701965\pi$
$937$	−36.2899			−1.18554			−0.592769	+	0.805372i	$0.701965\pi$
$938$	−11.9991	+	6.04915i	−0.391785	+	0.197512i
$939$		0			0
$940$	11.2562	+	8.32662i	0.367137	+	0.271585i
$941$			14.0802i			0.459000i	0.973309	+	0.229500i	$0.0737092\pi$
$941$			14.0802i			0.459000i	−0.973309	+	0.229500i	$0.926291\pi$
$942$		0			0
$943$			1.53898i			0.0501160i
$944$	−4.75579	−	15.5393i	−0.154788	−	0.505761i
$945$		0			0
$946$	−6.94595	−	13.7780i	−0.225832	−	0.447962i
$947$	10.6173			0.345015			0.172508	−	0.985008i	$-0.444813\pi$
$947$	10.6173			0.345015			0.172508	+	0.985008i	$0.444813\pi$
$948$		0			0
$949$	77.1642			2.50485
$950$	−4.43411	−	8.79552i	−0.143862	−	0.285364i
$951$		0			0
$952$	−3.80413	+	22.1678i	−0.123293	+	0.718462i
$953$			17.9791i			0.582401i	0.956662	+	0.291201i	$0.0940547\pi$
$953$			17.9791i			0.582401i	−0.956662	+	0.291201i	$0.905945\pi$
$954$		0			0
$955$		−	8.87665i		−	0.287242i
$956$	−36.3995	+	49.2061i	−1.17724	+	1.59144i
$957$		0			0
$958$	8.77733	−	4.42494i	0.283583	−	0.142963i
$959$	6.20152			0.200258
$960$		0			0
$961$	29.8554			0.963077
$962$	−1.40002	+	0.705794i	−0.0451383	+	0.0227557i
$963$		0			0
$964$	−3.67235	+	4.96441i	−0.118278	+	0.159893i
$965$			7.86931i			0.253322i
$966$		0			0
$967$			43.6700i			1.40433i	0.712013	+	0.702167i	$0.247784\pi$
$967$			43.6700i			1.40433i	−0.712013	+	0.702167i	$0.752216\pi$
$968$	2.30265	−	13.4182i	0.0740100	−	0.431278i
$969$		0			0
$970$	−3.13011	−	6.20891i	−0.100502	−	0.199356i
$971$	46.5960			1.49534			0.747668	−	0.664072i	$-0.231173\pi$
$971$	46.5960			1.49534			0.747668	+	0.664072i	$0.231173\pi$
$972$		0			0
$973$	−19.8155			−0.635255
$974$	24.7600	+	49.1141i	0.793362	+	1.57372i
$975$		0			0
$976$	−5.32599	−	17.4024i	−0.170481	−	0.557036i
$977$			36.9817i			1.18315i	0.806251	+	0.591574i	$0.201493\pi$
$977$			36.9817i			1.18315i	−0.806251	+	0.591574i	$0.798507\pi$
$978$		0			0
$979$			34.1210i			1.09051i
$980$	−1.60789	−	1.18941i	−0.0513621	−	0.0379943i
$981$		0			0
$982$	31.3701	−	15.8147i	1.00106	−	0.504668i
$983$	47.8010			1.52461			0.762307	−	0.647215i	$-0.224067\pi$
$983$	47.8010			1.52461			0.762307	+	0.647215i	$0.224067\pi$
$984$		0			0
$985$	−4.89698			−0.156031
$986$	−74.6941	+	37.6557i	−2.37874	+	1.19920i
$987$		0			0
$988$	−60.6826	−	44.8891i	−1.93057	−	1.42811i
$989$		−	3.66098i		−	0.116412i
$990$		0			0
$991$			43.3244i			1.37625i	0.725594	+	0.688123i	$0.241565\pi$
$991$			43.3244i			1.37625i	−0.725594	+	0.688123i	$0.758435\pi$
$992$	−4.37029	+	4.18669i	−0.138757	+	0.132928i
$993$		0			0
$994$	−5.98960	−	11.8810i	−0.189979	−	0.376842i
$995$	−9.24144			−0.292973
$996$		0			0
$997$	2.18200			0.0691047			0.0345523	−	0.999403i	$-0.488999\pi$
$997$	2.18200			0.0691047			0.0345523	+	0.999403i	$0.488999\pi$
$998$	−2.47486	−	4.90915i	−0.0783404	−	0.155396i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.n.a.71.4	yes	24
3.2	odd	2		1260.2.n.b.71.21	yes	24
4.3	odd	2		1260.2.n.b.71.22	yes	24
12.11	even	2	inner	1260.2.n.a.71.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.n.a.71.3	✓	24	12.11	even	2	inner
1260.2.n.a.71.4	yes	24	1.1	even	1	trivial
1260.2.n.b.71.21	yes	24	3.2	odd	2
1260.2.n.b.71.22	yes	24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26282 + 0.636627i) q^{2} +(1.18941 - 1.60789i) q^{4} +1.00000i q^{5} +1.00000i q^{7} +(-0.478383 + 2.78768i) q^{8} +(-0.636627 - 1.26282i) q^{10} -2.48729 q^{11} +5.41860 q^{13} +(-0.636627 - 1.26282i) q^{14} +(-1.17060 - 3.82488i) q^{16} -7.95206i q^{17} -6.96500i q^{19} +(1.60789 + 1.18941i) q^{20} +(3.14099 - 1.58348i) q^{22} +0.834597 q^{23} -1.00000 q^{25} +(-6.84270 + 3.44963i) q^{26} +(1.60789 + 1.18941i) q^{28} +7.43818i q^{29} +1.06987i q^{31} +(3.91328 + 4.08488i) q^{32} +(5.06250 + 10.0420i) q^{34} -1.00000 q^{35} +0.204600 q^{37} +(4.43411 + 8.79552i) q^{38} +(-2.78768 - 0.478383i) q^{40} +1.84398i q^{41} -4.38652i q^{43} +(-2.95841 + 3.99928i) q^{44} +(-1.05394 + 0.531327i) q^{46} +7.00063 q^{47} -1.00000 q^{49} +(1.26282 - 0.636627i) q^{50} +(6.44495 - 8.71250i) q^{52} -4.95889i q^{53} -2.48729i q^{55} +(-2.78768 - 0.478383i) q^{56} +(-4.73535 - 9.39305i) q^{58} +4.06269 q^{59} +4.54979 q^{61} +(-0.681108 - 1.35105i) q^{62} +(-7.54230 - 2.66716i) q^{64} +5.41860i q^{65} -9.50187i q^{67} +(-12.7860 - 9.45826i) q^{68} +(1.26282 - 0.636627i) q^{70} +9.40833 q^{71} +14.2406 q^{73} +(-0.258372 + 0.130254i) q^{74} +(-11.1989 - 8.28425i) q^{76} -2.48729i q^{77} +17.6352i q^{79} +(3.82488 - 1.17060i) q^{80} +(-1.17393 - 2.32860i) q^{82} -8.48193 q^{83} +7.95206 q^{85} +(2.79258 + 5.53937i) q^{86} +(1.18988 - 6.93376i) q^{88} -13.7181i q^{89} +5.41860i q^{91} +(0.992679 - 1.34194i) q^{92} +(-8.84051 + 4.45679i) q^{94} +6.96500 q^{95} +4.91671 q^{97} +(1.26282 - 0.636627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} - 4 q^{10} - 4 q^{14} + 4 q^{20} - 4 q^{22} - 24 q^{25} - 40 q^{26} + 4 q^{28} + 40 q^{32} + 8 q^{34} - 24 q^{35} + 4 q^{40} + 48 q^{44} + 36 q^{46} + 16 q^{47} - 24 q^{49} + 32 q^{52} + 4 q^{56}+ \cdots + 12 q^{88}+O(q^{100}) \) 24 * q - 4 * q^4 - 4 * q^10 - 4 * q^14 + 4 * q^20 - 4 * q^22 - 24 * q^25 - 40 * q^26 + 4 * q^28 + 40 * q^32 + 8 * q^34 - 24 * q^35 + 4 * q^40 + 48 * q^44 + 36 * q^46 + 16 * q^47 - 24 * q^49 + 32 * q^52 + 4 * q^56 - 28 * q^58 - 16 * q^59 - 32 * q^61 - 56 * q^62 - 4 * q^64 + 64 * q^68 - 32 * q^74 - 72 * q^76 - 40 * q^82 - 80 * q^83 + 32 * q^85 - 80 * q^86 + 12 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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