LMFDB - Embedded newform 1216.2.i.o.961.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, degree $2$, not 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.41342275584.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 13x^{6} + 2x^{5} + 81x^{4} - 8x^{3} + 208x^{2} + 128x + 256 $ x^8 - 2x^7 + 13x^6 + 2x^5 + 81x^4 - 8x^3 + 208x^2 + 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 608)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.4
Root			$0.901794 + 1.56195i$ of defining polynomial
Character	$\chi$	$=$	1216.961
Dual form			1216.2.i.o.577.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 - 0.358719i) q^{3} +(0.401794 - 0.695928i) q^{5} +2.55066 q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(0.207107 - 0.358719i) q^{3} +(0.401794 - 0.695928i) q^{5} +2.55066 q^{7} +(1.41421 + 2.44949i) q^{9} +1.80359 q^{11} +(-0.540678 - 0.936482i) q^{13} +(-0.166429 - 0.288263i) q^{15} +(-1.26291 + 2.18742i) q^{17} +(1.70538 + 4.01144i) q^{19} +(0.528259 - 0.914971i) q^{21} +(0.555803 + 0.962679i) q^{23} +(2.17712 + 3.77089i) q^{25} +2.41421 q^{27} +(-4.36667 - 7.56329i) q^{29} +5.10620 q^{31} +(0.373535 - 0.646982i) q^{33} +(1.02484 - 1.77507i) q^{35} -5.37909 q^{37} -0.447913 q^{39} +(-1.71780 + 2.97532i) q^{41} +(2.30531 - 3.99292i) q^{43} +2.27289 q^{45} +(2.38423 + 4.12961i) q^{47} -0.494141 q^{49} +(0.523114 + 0.906061i) q^{51} +(0.848696 + 1.46998i) q^{53} +(0.724671 - 1.25517i) q^{55} +(1.79218 + 0.219043i) q^{57} +(3.01069 - 5.21468i) q^{59} +(1.23022 + 2.13081i) q^{61} +(3.60718 + 6.24781i) q^{63} -0.868965 q^{65} +(4.22850 + 7.32397i) q^{67} +0.460442 q^{69} +(6.87736 - 11.9119i) q^{71} +(4.85425 - 8.40780i) q^{73} +1.80359 q^{75} +4.60034 q^{77} +(2.63817 - 4.56944i) q^{79} +(-3.74264 + 6.48244i) q^{81} +8.90490 q^{83} +(1.01486 + 1.75779i) q^{85} -3.61746 q^{87} +(-4.09134 - 7.08640i) q^{89} +(-1.37909 - 2.38865i) q^{91} +(1.05753 - 1.83169i) q^{93} +(3.47689 + 0.424951i) q^{95} +(5.34982 - 9.26615i) q^{97} +(2.55066 + 4.41787i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7	$ 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7} + 4 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{17} - 2 q^{19} + 8 q^{21} + 2 q^{23} - 2 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - 6 q^{33} - 4 q^{35} + 8 q^{37} - 12 q^{39} + 8 q^{41} + 18 q^{43} - 16 q^{45} - 6 q^{47} + 32 q^{49} - 18 q^{51} + 10 q^{53} + 20 q^{55} + 10 q^{57} + 8 q^{59} - 18 q^{61} + 8 q^{63} - 36 q^{65} - 4 q^{67} - 52 q^{69} - 6 q^{71} + 4 q^{75} - 16 q^{77} + 14 q^{79} + 4 q^{81} + 4 q^{83} + 22 q^{85} - 60 q^{87} - 2 q^{89} + 40 q^{91} + 16 q^{93} + 50 q^{95} - 12 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7 + 4 * q^11 - 2 * q^13 + 2 * q^15 - 2 * q^17 - 2 * q^19 + 8 * q^21 + 2 * q^23 - 2 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - 6 * q^33 - 4 * q^35 + 8 * q^37 - 12 * q^39 + 8 * q^41 + 18 * q^43 - 16 * q^45 - 6 * q^47 + 32 * q^49 - 18 * q^51 + 10 * q^53 + 20 * q^55 + 10 * q^57 + 8 * q^59 - 18 * q^61 + 8 * q^63 - 36 * q^65 - 4 * q^67 - 52 * q^69 - 6 * q^71 + 4 * q^75 - 16 * q^77 + 14 * q^79 + 4 * q^81 + 4 * q^83 + 22 * q^85 - 60 * q^87 - 2 * q^89 + 40 * q^91 + 16 * q^93 + 50 * q^95 - 12 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	−0.800025	−	0.599966i	$-0.795181\pi$
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	0.919599	+	0.392859i	$0.128514\pi$
$4$		0			0
$5$	0.401794	−	0.695928i	0.179688	−	0.311228i	−0.762086	−	0.647476i	$-0.775825\pi$
$5$	0.401794	−	0.695928i	0.179688	−	0.311228i	0.941774	+	0.336248i	$0.109158\pi$
$6$		0			0
$7$	2.55066			0.964058			0.482029	−	0.876155i	$-0.339900\pi$
$7$	2.55066			0.964058			0.482029	+	0.876155i	$0.339900\pi$
$8$		0			0
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	1.80359			0.543802			0.271901	−	0.962325i	$-0.412348\pi$
$11$	1.80359			0.543802			0.271901	+	0.962325i	$0.412348\pi$
$12$		0			0
$13$	−0.540678	−	0.936482i	−0.149957	−	0.259733i	0.781254	−	0.624213i	$-0.214580\pi$
$13$	−0.540678	−	0.936482i	−0.149957	−	0.259733i	−0.931211	+	0.364480i	$0.881247\pi$
$14$		0			0
$15$	−0.166429	−	0.288263i	−0.0429717	−	0.0744291i
$16$		0			0
$17$	−1.26291	+	2.18742i	−0.306301	+	0.530528i	−0.977550	−	0.210703i	$-0.932425\pi$
$17$	−1.26291	+	2.18742i	−0.306301	+	0.530528i	0.671249	+	0.741232i	$0.265758\pi$
$18$		0			0
$19$	1.70538	+	4.01144i	0.391241	+	0.920288i
$19$	1.70538	+	4.01144i	0.391241	+	0.920288i
$20$		0			0
$21$	0.528259	−	0.914971i	0.115275	−	0.199663i
$22$		0			0
$23$	0.555803	+	0.962679i	0.115893	+	0.200732i	0.918136	−	0.396265i	$-0.129694\pi$
$23$	0.555803	+	0.962679i	0.115893	+	0.200732i	−0.802243	+	0.596997i	$0.796360\pi$
$24$		0			0
$25$	2.17712	+	3.77089i	0.435425	+	0.754178i
$26$		0			0
$27$	2.41421			0.464616
$28$		0			0
$29$	−4.36667	−	7.56329i	−0.810870	−	1.40447i	−0.912256	−	0.409620i	$-0.865661\pi$
$29$	−4.36667	−	7.56329i	−0.810870	−	1.40447i	0.101387	−	0.994847i	$-0.467672\pi$
$30$		0			0
$31$	5.10620			0.917100			0.458550	−	0.888669i	$-0.348369\pi$
$31$	5.10620			0.917100			0.458550	+	0.888669i	$0.348369\pi$
$32$		0			0
$33$	0.373535	−	0.646982i	0.0650241	−	0.112625i
$34$		0			0
$35$	1.02484	−	1.77507i	0.173229	−	0.300042i
$36$		0			0
$37$	−5.37909			−0.884316			−0.442158	−	0.896937i	$-0.645787\pi$
$37$	−5.37909			−0.884316			−0.442158	+	0.896937i	$0.645787\pi$
$38$		0			0
$39$	−0.447913			−0.0717234
$40$		0			0
$41$	−1.71780	+	2.97532i	−0.268276	+	0.464667i	−0.968417	−	0.249338i	$-0.919787\pi$
$41$	−1.71780	+	2.97532i	−0.268276	+	0.464667i	0.700141	+	0.714005i	$0.253120\pi$
$42$		0			0
$43$	2.30531	−	3.99292i	0.351557	−	0.608914i	−0.634966	−	0.772540i	$-0.718986\pi$
$43$	2.30531	−	3.99292i	0.351557	−	0.608914i	0.986522	+	0.163626i	$0.0523190\pi$
$44$		0			0
$45$	2.27289			0.338822
$46$		0			0
$47$	2.38423	+	4.12961i	0.347776	+	0.602365i	0.985854	−	0.167606i	$-0.0536037\pi$
$47$	2.38423	+	4.12961i	0.347776	+	0.602365i	−0.638078	+	0.769971i	$0.720270\pi$
$48$		0			0
$49$	−0.494141			−0.0705916
$50$		0			0
$51$	0.523114	+	0.906061i	0.0732507	+	0.126874i
$52$		0			0
$53$	0.848696	+	1.46998i	0.116577	+	0.201918i	0.918409	−	0.395632i	$-0.129474\pi$
$53$	0.848696	+	1.46998i	0.116577	+	0.201918i	−0.801832	+	0.597550i	$0.796141\pi$
$54$		0			0
$55$	0.724671	−	1.25517i	0.0977146	−	0.169247i
$56$		0			0
$57$	1.79218	+	0.219043i	0.237380	+	0.0290130i
$58$		0			0
$59$	3.01069	−	5.21468i	0.391959	−	0.678893i	−0.600749	−	0.799438i	$-0.705131\pi$
$59$	3.01069	−	5.21468i	0.391959	−	0.678893i	0.992708	+	0.120545i	$0.0384641\pi$
$60$		0			0
$61$	1.23022	+	2.13081i	0.157514	+	0.272822i	0.933971	−	0.357348i	$-0.116319\pi$
$61$	1.23022	+	2.13081i	0.157514	+	0.272822i	−0.776458	+	0.630169i	$0.782985\pi$
$62$		0			0
$63$	3.60718	+	6.24781i	0.454461	+	0.787150i
$64$		0			0
$65$	−0.868965			−0.107782
$66$		0			0
$67$	4.22850	+	7.32397i	0.516593	+	0.894765i	0.999814	+	0.0192672i	$0.00613331\pi$
$67$	4.22850	+	7.32397i	0.516593	+	0.894765i	−0.483221	+	0.875498i	$0.660533\pi$
$68$		0			0
$69$	0.460442			0.0554307
$70$		0			0
$71$	6.87736	−	11.9119i	0.816193	−	1.41369i	−0.0922759	−	0.995733i	$-0.529414\pi$
$71$	6.87736	−	11.9119i	0.816193	−	1.41369i	0.908468	−	0.417954i	$-0.137253\pi$
$72$		0			0
$73$	4.85425	−	8.40780i	0.568147	−	0.984059i	−0.428603	−	0.903493i	$-0.640994\pi$
$73$	4.85425	−	8.40780i	0.568147	−	0.984059i	0.996749	−	0.0805657i	$-0.0256727\pi$
$74$		0			0
$75$	1.80359			0.208260
$76$		0			0
$77$	4.60034			0.524257
$78$		0			0
$79$	2.63817	−	4.56944i	0.296817	−	0.514103i	−0.678589	−	0.734518i	$-0.737408\pi$
$79$	2.63817	−	4.56944i	0.296817	−	0.514103i	0.975406	+	0.220416i	$0.0707414\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		0			0
$83$	8.90490			0.977440			0.488720	−	0.872441i	$-0.337464\pi$
$83$	8.90490			0.977440			0.488720	+	0.872441i	$0.337464\pi$
$84$		0			0
$85$	1.01486	+	1.75779i	0.110077	+	0.190659i
$86$		0			0
$87$	−3.61746			−0.387833
$88$		0			0
$89$	−4.09134	−	7.08640i	−0.433681	−	0.751157i	0.563506	−	0.826112i	$-0.309452\pi$
$89$	−4.09134	−	7.08640i	−0.433681	−	0.751157i	−0.997187	+	0.0749547i	$0.976119\pi$
$90$		0			0
$91$	−1.37909	−	2.38865i	−0.144567	−	0.250398i
$92$		0			0
$93$	1.05753	−	1.83169i	0.109661	−	0.189938i
$94$		0			0
$95$	3.47689	+	0.424951i	0.356721	+	0.0435991i
$96$		0			0
$97$	5.34982	−	9.26615i	0.543192	−	0.940835i	−0.455527	−	0.890222i	$-0.650549\pi$
$97$	5.34982	−	9.26615i	0.543192	−	0.940835i	0.998718	−	0.0506133i	$-0.0161176\pi$
$98$		0			0
$99$	2.55066	+	4.41787i	0.256351	+	0.444013i
$100$		0			0
$101$	1.79117	+	3.10239i	0.178228	+	0.308700i	0.941274	−	0.337645i	$-0.109630\pi$
$101$	1.79117	+	3.10239i	0.178228	+	0.308700i	−0.763046	+	0.646345i	$0.776297\pi$
$102$		0			0
$103$	−2.04968			−0.201961			−0.100980	−	0.994888i	$-0.532198\pi$
$103$	−2.04968			−0.201961			−0.100980	+	0.994888i	$0.532198\pi$
$104$		0			0
$105$	−0.424502	−	0.735260i	−0.0414272	−	0.0717540i
$106$		0			0
$107$	−9.88697			−0.955809			−0.477905	−	0.878412i	$-0.658604\pi$
$107$	−9.88697			−0.955809			−0.477905	+	0.878412i	$0.658604\pi$
$108$		0			0
$109$	−5.72335	+	9.91314i	−0.548198	+	0.949506i	0.450200	+	0.892928i	$0.351353\pi$
$109$	−5.72335	+	9.91314i	−0.548198	+	0.949506i	−0.998398	+	0.0565787i	$0.981981\pi$
$110$		0			0
$111$	−1.11405	+	1.92958i	−0.105740	+	0.183148i
$112$		0			0
$113$	0.970282			0.0912765			0.0456382	−	0.998958i	$-0.485468\pi$
$113$	0.970282			0.0912765			0.0456382	+	0.998958i	$0.485468\pi$
$114$		0			0
$115$	0.893273			0.0832981
$116$		0			0
$117$	1.52927	−	2.64877i	0.141381	−	0.244879i
$118$		0			0
$119$	−3.22125	+	5.57937i	−0.295292	+	0.511460i
$120$		0			0
$121$	−7.74707			−0.704279
$122$		0			0
$123$	0.711537	+	1.23242i	0.0641571	+	0.111123i
$124$		0			0
$125$	7.51696			0.672337
$126$		0			0
$127$	8.65956	+	14.9988i	0.768412	+	1.33093i	0.938424	+	0.345486i	$0.112286\pi$
$127$	8.65956	+	14.9988i	0.768412	+	1.33093i	−0.170012	+	0.985442i	$0.554381\pi$
$128$		0			0
$129$	−0.954892	−	1.65392i	−0.0840735	−	0.145620i
$130$		0			0
$131$	−6.34355	+	10.9874i	−0.554239	+	0.959970i	0.443724	+	0.896164i	$0.353657\pi$
$131$	−6.34355	+	10.9874i	−0.554239	+	0.959970i	−0.997962	+	0.0638059i	$0.979676\pi$
$132$		0			0
$133$	4.34985	+	10.2318i	0.377180	+	0.887211i
$134$		0			0
$135$	0.970016	−	1.68012i	0.0834857	−	0.144602i
$136$		0			0
$137$	−5.29330	−	9.16826i	−0.452237	−	0.783298i	0.546288	−	0.837598i	$-0.316041\pi$
$137$	−5.29330	−	9.16826i	−0.452237	−	0.783298i	−0.998525	+	0.0543001i	$0.982707\pi$
$138$		0			0
$139$	−6.81428	−	11.8027i	−0.577980	−	1.00109i	−0.995711	−	0.0925198i	$-0.970508\pi$
$139$	−6.81428	−	11.8027i	−0.577980	−	1.00109i	0.417731	−	0.908571i	$-0.362825\pi$
$140$		0			0
$141$	1.97516			0.166339
$142$		0			0
$143$	−0.975161	−	1.68903i	−0.0815470	−	0.141244i
$144$		0			0
$145$	−7.01800			−0.582813
$146$		0			0
$147$	−0.102340	+	0.177258i	−0.00844086	+	0.0146200i
$148$		0			0
$149$	1.09378	−	1.89448i	0.0896056	−	0.155202i	−0.817739	−	0.575589i	$-0.804773\pi$
$149$	1.09378	−	1.89448i	0.0896056	−	0.155202i	0.907344	+	0.420388i	$0.138106\pi$
$150$		0			0
$151$	−11.2592			−0.916257			−0.458128	−	0.888886i	$-0.651480\pi$
$151$	−11.2592			−0.916257			−0.458128	+	0.888886i	$0.651480\pi$
$152$		0			0
$153$	−7.14410			−0.577566
$154$		0			0
$155$	2.05164	−	3.55354i	0.164792	−	0.285427i
$156$		0			0
$157$	−10.2843	+	17.8129i	−0.820776	+	1.42163i	0.0843284	+	0.996438i	$0.473126\pi$
$157$	−10.2843	+	17.8129i	−0.820776	+	1.42163i	−0.905105	+	0.425188i	$0.860208\pi$
$158$		0			0
$159$	0.703083			0.0557581
$160$		0			0
$161$	1.41766	+	2.45546i	0.111728	+	0.193518i
$162$		0			0
$163$	16.9546			1.32799			0.663993	−	0.747739i	$-0.268861\pi$
$163$	16.9546			1.32799			0.663993	+	0.747739i	$0.268861\pi$
$164$		0			0
$165$	−0.300168	−	0.519907i	−0.0233681	−	0.0404747i
$166$		0			0
$167$	−10.9836	−	19.0241i	−0.849933	−	1.47213i	−0.881267	−	0.472618i	$-0.843309\pi$
$167$	−10.9836	−	19.0241i	−0.849933	−	1.47213i	0.0313341	−	0.999509i	$-0.490024\pi$
$168$		0			0
$169$	5.91533	−	10.2457i	0.455026	−	0.788128i
$170$		0			0
$171$	−7.41421	+	9.85035i	−0.566979	+	0.753275i
$172$		0			0
$173$	2.84870	−	4.93409i	0.216582	−	0.375132i	−0.737179	−	0.675698i	$-0.763842\pi$
$173$	2.84870	−	4.93409i	0.216582	−	0.375132i	0.953761	+	0.300566i	$0.0971757\pi$
$174$		0			0
$175$	5.55310	+	9.61825i	0.419775	+	0.727071i
$176$		0			0
$177$	−1.24707	−	2.15999i	−0.0937356	−	0.162355i
$178$		0			0
$179$	−8.72447			−0.652098			−0.326049	−	0.945353i	$-0.605717\pi$
$179$	−8.72447			−0.652098			−0.326049	+	0.945353i	$0.605717\pi$
$180$		0			0
$181$	0.0426688	+	0.0739045i	0.00317155	+	0.00549328i	0.867607	−	0.497251i	$-0.165657\pi$
$181$	0.0426688	+	0.0739045i	0.00317155	+	0.00549328i	−0.864435	+	0.502744i	$0.832324\pi$
$182$		0			0
$183$	1.01915			0.0753376
$184$		0			0
$185$	−2.16128	+	3.74345i	−0.158901	+	0.275224i
$186$		0			0
$187$	−2.27777	+	3.94521i	−0.166567	+	0.288502i
$188$		0			0
$189$	6.15783			0.447917
$190$		0			0
$191$	−8.00000			−0.578860			−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000			−0.578860			−0.289430	+	0.957199i	$0.593466\pi$
$192$		0			0
$193$	6.12646	−	10.6113i	0.440993	−	0.763822i	−0.556771	−	0.830666i	$-0.687960\pi$
$193$	6.12646	−	10.6113i	0.440993	−	0.763822i	0.997763	+	0.0668446i	$0.0212932\pi$
$194$		0			0
$195$	−0.179969	+	0.311715i	−0.0128878	+	0.0223224i
$196$		0			0
$197$	−7.72223			−0.550186			−0.275093	−	0.961418i	$-0.588709\pi$
$197$	−7.72223			−0.550186			−0.275093	+	0.961418i	$0.588709\pi$
$198$		0			0
$199$	−6.35154	−	11.0012i	−0.450249	−	0.779854i	0.548152	−	0.836378i	$-0.315331\pi$
$199$	−6.35154	−	11.0012i	−0.450249	−	0.779854i	−0.998401	+	0.0565246i	$0.981998\pi$
$200$		0			0
$201$	3.50300			0.247083
$202$		0			0
$203$	−11.1379	−	19.2914i	−0.781725	−	1.35399i
$204$		0			0
$205$	1.38040	+	2.39093i	0.0964116	+	0.166990i
$206$		0			0
$207$	−1.57205	+	2.72287i	−0.109265	+	0.189252i
$208$		0			0
$209$	3.07581	+	7.23499i	0.212758	+	0.500455i
$210$		0			0
$211$	2.19912	−	3.80898i	0.151393	−	0.262221i	−0.780347	−	0.625347i	$-0.784957\pi$
$211$	2.19912	−	3.80898i	0.151393	−	0.262221i	0.931740	+	0.363126i	$0.118291\pi$
$212$		0			0
$213$	−2.84870	−	4.93409i	−0.195189	−	0.338078i
$214$		0			0
$215$	−1.85252	−	3.20866i	−0.126341	−	0.218829i
$216$		0			0
$217$	13.0242			0.884138
$218$		0			0
$219$	−2.01069	−	3.48263i	−0.135870	−	0.235334i
$220$		0			0
$221$	2.73131			0.183728
$222$		0			0
$223$	−0.580642	+	1.00570i	−0.0388827	+	0.0673468i	−0.884812	−	0.465949i	$-0.845713\pi$
$223$	−0.580642	+	1.00570i	−0.0388827	+	0.0673468i	0.845929	+	0.533295i	$0.179047\pi$
$224$		0			0
$225$	−6.15783	+	10.6657i	−0.410522	+	0.711045i
$226$		0			0
$227$	−11.4507			−0.760009			−0.380004	−	0.924985i	$-0.624078\pi$
$227$	−11.4507			−0.760009			−0.380004	+	0.924985i	$0.624078\pi$
$228$		0			0
$229$	−7.14410			−0.472095			−0.236048	−	0.971742i	$-0.575852\pi$
$229$	−7.14410			−0.472095			−0.236048	+	0.971742i	$0.575852\pi$
$230$		0			0
$231$	0.952761	−	1.65023i	0.0626871	−	0.108577i
$232$		0			0
$233$	−10.0720	+	17.4453i	−0.659842	+	1.14288i	0.320815	+	0.947142i	$0.396043\pi$
$233$	−10.0720	+	17.4453i	−0.659842	+	1.14288i	−0.980656	+	0.195737i	$0.937290\pi$
$234$		0			0
$235$	3.83188			0.249964
$236$		0			0
$237$	−1.09277	−	1.89273i	−0.0709828	−	0.122946i
$238$		0			0
$239$	−26.7085			−1.72763			−0.863814	−	0.503810i	$-0.831931\pi$
$239$	−26.7085			−1.72763			−0.863814	+	0.503810i	$0.831931\pi$
$240$		0			0
$241$	3.66128	+	6.34153i	0.235844	+	0.408494i	0.959518	−	0.281649i	$-0.0908812\pi$
$241$	3.66128	+	6.34153i	0.235844	+	0.408494i	−0.723674	+	0.690142i	$0.757548\pi$
$242$		0			0
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$		0			0
$245$	−0.198543	+	0.343886i	−0.0126844	+	0.0219701i
$246$		0			0
$247$	2.83458	−	3.76596i	0.180360	−	0.239622i
$248$		0			0
$249$	1.84427	−	3.19436i	0.116876	−	0.202435i
$250$		0			0
$251$	−13.8502	−	23.9893i	−0.874218	−	1.51419i	−0.857593	−	0.514329i	$-0.828041\pi$
$251$	−13.8502	−	23.9893i	−0.874218	−	1.51419i	−0.0166252	−	0.999862i	$-0.505292\pi$
$252$		0			0
$253$	1.00244	+	1.73628i	0.0630228	+	0.109159i
$254$		0			0
$255$	0.840737			0.0526490
$256$		0			0
$257$	−5.02582	−	8.70497i	−0.313502	−	0.543001i	0.665616	−	0.746294i	$-0.268169\pi$
$257$	−5.02582	−	8.70497i	−0.313502	−	0.543001i	−0.979118	+	0.203293i	$0.934836\pi$
$258$		0			0
$259$	−13.7202			−0.852532
$260$		0			0
$261$	12.3508	−	21.3922i	0.764495	−	1.32414i
$262$		0			0
$263$	6.48698	−	11.2358i	0.400004	−	0.692827i	−0.593722	−	0.804670i	$-0.702342\pi$
$263$	6.48698	−	11.2358i	0.400004	−	0.692827i	0.993726	+	0.111843i	$0.0356754\pi$
$264$		0			0
$265$	1.36400			0.0837901
$266$		0			0
$267$	−3.38937			−0.207426
$268$		0			0
$269$	1.26779	−	2.19587i	0.0772984	−	0.133885i	−0.824785	−	0.565446i	$-0.808704\pi$
$269$	1.26779	−	2.19587i	0.0772984	−	0.133885i	0.902083	+	0.431562i	$0.142037\pi$
$270$		0			0
$271$	−10.2692	+	17.7867i	−0.623808	+	1.08047i	0.364962	+	0.931022i	$0.381082\pi$
$271$	−10.2692	+	17.7867i	−0.623808	+	1.08047i	−0.988770	+	0.149445i	$0.952251\pi$
$272$		0			0
$273$	−1.14247			−0.0691455
$274$		0			0
$275$	3.92663	+	6.80113i	0.236785	+	0.410123i
$276$		0			0
$277$	2.00202			0.120290			0.0601449	−	0.998190i	$-0.480844\pi$
$277$	2.00202			0.120290			0.0601449	+	0.998190i	$0.480844\pi$
$278$		0			0
$279$	7.22125	+	12.5076i	0.432325	+	0.748809i
$280$		0			0
$281$	14.6738	+	25.4158i	0.875366	+	1.51618i	0.856372	+	0.516359i	$0.172713\pi$
$281$	14.6738	+	25.4158i	0.875366	+	1.51618i	0.0189944	+	0.999820i	$0.493954\pi$
$282$		0			0
$283$	−12.1155	+	20.9846i	−0.720189	+	1.24740i	0.240734	+	0.970591i	$0.422612\pi$
$283$	−12.1155	+	20.9846i	−0.720189	+	1.24740i	−0.960924	+	0.276814i	$0.910722\pi$
$284$		0			0
$285$	0.872525	−	1.15922i	0.0516839	−	0.0686660i
$286$		0			0
$287$	−4.38152	+	7.58902i	−0.258633	+	0.447966i
$288$		0			0
$289$	5.31012	+	9.19739i	0.312360	+	0.541023i
$290$		0			0
$291$	−2.21597	−	3.83817i	−0.129902	−	0.224997i
$292$		0			0
$293$	−10.3274			−0.603336			−0.301668	−	0.953413i	$-0.597543\pi$
$293$	−10.3274			−0.603336			−0.301668	+	0.953413i	$0.597543\pi$
$294$		0			0
$295$	−2.41936	−	4.19045i	−0.140860	−	0.243977i
$296$		0			0
$297$	4.35425			0.252659
$298$		0			0
$299$	0.601021	−	1.04100i	0.0347579	−	0.0602025i
$300$		0			0
$301$	5.88007	−	10.1846i	0.338921	−	0.587029i
$302$		0			0
$303$	1.48385			0.0852451
$304$		0			0
$305$	1.97718			0.113213
$306$		0			0
$307$	−15.2236	+	26.3681i	−0.868858	+	1.50491i	−0.00569274	+	0.999984i	$0.501812\pi$
$307$	−15.2236	+	26.3681i	−0.868858	+	1.50491i	−0.863165	+	0.504922i	$0.831521\pi$
$308$		0			0
$309$	−0.424502	+	0.735260i	−0.0241491	+	0.0418275i
$310$		0			0
$311$	−27.6343			−1.56699			−0.783497	−	0.621395i	$-0.786566\pi$
$311$	−27.6343			−1.56699			−0.783497	+	0.621395i	$0.786566\pi$
$312$		0			0
$313$	−0.939053	−	1.62649i	−0.0530784	−	0.0919345i	0.838265	−	0.545262i	$-0.183570\pi$
$313$	−0.939053	−	1.62649i	−0.0530784	−	0.0919345i	−0.891344	+	0.453328i	$0.850237\pi$
$314$		0			0
$315$	5.79737			0.326645
$316$		0			0
$317$	−9.24917	−	16.0200i	−0.519485	−	0.899775i	−0.999744	−	0.0226477i	$-0.992790\pi$
$317$	−9.24917	−	16.0200i	−0.519485	−	0.899775i	0.480258	−	0.877127i	$-0.340543\pi$
$318$		0			0
$319$	−7.87567	−	13.6411i	−0.440953	−	0.763752i
$320$		0			0
$321$	−2.04766	+	3.54665i	−0.114289	+	0.197955i
$322$		0			0
$323$	−10.9285	−	1.33570i	−0.608076	−	0.0743202i
$324$		0			0
$325$	2.35425	−	4.07767i	0.130590	−	0.226189i
$326$		0			0
$327$	2.37069	+	4.10616i	0.131099	+	0.227071i
$328$		0			0
$329$	6.08136	+	10.5332i	0.335276	+	0.580715i
$330$		0			0
$331$	3.03566			0.166855			0.0834275	−	0.996514i	$-0.473413\pi$
$331$	3.03566			0.166855			0.0834275	+	0.996514i	$0.473413\pi$
$332$		0			0
$333$	−7.60718	−	13.1760i	−0.416871	−	0.722041i
$334$		0			0
$335$	6.79594			0.371302
$336$		0			0
$337$	10.4897	−	18.1687i	0.571411	−	0.989713i	−0.425010	−	0.905188i	$-0.639730\pi$
$337$	10.4897	−	18.1687i	0.571411	−	0.989713i	0.996421	−	0.0845244i	$-0.0269371\pi$
$338$		0			0
$339$	0.200952	−	0.348059i	0.0109142	−	0.0189040i
$340$		0			0
$341$	9.20947			0.498721
$342$		0			0
$343$	−19.1150			−1.03211
$344$		0			0
$345$	0.185003	−	0.320434i	0.00996022	−	0.0172516i
$346$		0			0
$347$	10.7329	−	18.5900i	0.576174	−	0.997962i	−0.419739	−	0.907645i	$-0.637879\pi$
$347$	10.7329	−	18.5900i	0.576174	−	0.997962i	0.995913	−	0.0903174i	$-0.0287881\pi$
$348$		0			0
$349$	−34.1324			−1.82706			−0.913532	−	0.406767i	$-0.866656\pi$
$349$	−34.1324			−1.82706			−0.913532	+	0.406767i	$0.866656\pi$
$350$		0			0
$351$	−1.30531	−	2.26087i	−0.0696724	−	0.120676i
$352$		0			0
$353$	15.1827			0.808092			0.404046	−	0.914739i	$-0.367604\pi$
$353$	15.1827			0.808092			0.404046	+	0.914739i	$0.367604\pi$
$354$		0			0
$355$	−5.52656	−	9.57229i	−0.293320	−	0.508044i
$356$		0			0
$357$	1.33429	+	2.31105i	0.0706179	+	0.122314i
$358$		0			0
$359$	16.0128	−	27.7350i	0.845123	−	1.46380i	−0.0403913	−	0.999184i	$-0.512860\pi$
$359$	16.0128	−	27.7350i	0.845123	−	1.46380i	0.885514	−	0.464612i	$-0.153806\pi$
$360$		0			0
$361$	−13.1833	+	13.6821i	−0.693860	+	0.720110i
$362$		0			0
$363$	−1.60447	+	2.77903i	−0.0842129	+	0.145861i
$364$		0			0
$365$	−3.90081	−	6.75641i	−0.204178	−	0.353647i
$366$		0			0
$367$	14.2375	+	24.6601i	0.743191	+	1.28725i	0.951035	+	0.309083i	$0.100022\pi$
$367$	14.2375	+	24.6601i	0.743191	+	1.28725i	−0.207844	+	0.978162i	$0.566645\pi$
$368$		0			0
$369$	−9.71735			−0.505865
$370$		0			0
$371$	2.16473	+	3.74943i	0.112387	+	0.194661i
$372$		0			0
$373$	−19.8196			−1.02622			−0.513109	−	0.858323i	$-0.671506\pi$
$373$	−19.8196			−1.02622			−0.513109	+	0.858323i	$0.671506\pi$
$374$		0			0
$375$	1.55681	−	2.69648i	0.0803935	−	0.139246i
$376$		0			0
$377$	−4.72192	+	8.17861i	−0.243191	+	0.421220i
$378$		0			0
$379$	4.38307			0.225143			0.112572	−	0.993644i	$-0.464091\pi$
$379$	4.38307			0.225143			0.112572	+	0.993644i	$0.464091\pi$
$380$		0			0
$381$	7.17381			0.367526
$382$		0			0
$383$	9.95628	−	17.2448i	0.508742	−	0.881167i	−0.491207	−	0.871043i	$-0.663444\pi$
$383$	9.95628	−	17.2448i	0.508742	−	0.881167i	0.999949	−	0.0101240i	$-0.00322263\pi$
$384$		0			0
$385$	1.84839	−	3.20150i	0.0942026	−	0.163164i
$386$		0			0
$387$	13.0408			0.662902
$388$		0			0
$389$	8.42419	+	14.5911i	0.427124	+	0.739800i	0.996616	−	0.0821968i	$-0.0261936\pi$
$389$	8.42419	+	14.5911i	0.427124	+	0.739800i	−0.569493	+	0.821997i	$0.692860\pi$
$390$		0			0
$391$	−2.80772			−0.141992
$392$		0			0
$393$	2.62759	+	4.55111i	0.132544	+	0.229573i
$394$		0			0
$395$	−2.12000	−	3.67195i	−0.106669	−	0.184756i
$396$		0			0
$397$	−7.44457	+	12.8944i	−0.373632	+	0.647150i	−0.990121	−	0.140213i	$-0.955221\pi$
$397$	−7.44457	+	12.8944i	−0.373632	+	0.647150i	0.616489	+	0.787364i	$0.288555\pi$
$398$		0			0
$399$	4.57124	+	0.558705i	0.228848	+	0.0279702i
$400$		0			0
$401$	−7.01351	+	12.1478i	−0.350238	+	0.606630i	−0.986291	−	0.165015i	$-0.947233\pi$
$401$	−7.01351	+	12.1478i	−0.350238	+	0.606630i	0.636053	+	0.771645i	$0.280566\pi$
$402$		0			0
$403$	−2.76081	−	4.78186i	−0.137526	−	0.238201i
$404$		0			0
$405$	3.00754	+	5.20921i	0.149446	+	0.258848i
$406$		0			0
$407$	−9.70165			−0.480893
$408$		0			0
$409$	−17.9804	−	31.1430i	−0.889074	−	1.53992i	−0.840972	−	0.541078i	$-0.818016\pi$
$409$	−17.9804	−	31.1430i	−0.889074	−	1.53992i	−0.0481015	−	0.998842i	$-0.515317\pi$
$410$		0			0
$411$	−4.38511			−0.216302
$412$		0			0
$413$	7.67925	−	13.3009i	0.377871	−	0.654492i
$414$		0			0
$415$	3.57794	−	6.19717i	0.175634	−	0.304207i
$416$		0			0
$417$	−5.64514			−0.276444
$418$		0			0
$419$	13.0916			0.639565			0.319782	−	0.947491i	$-0.396390\pi$
$419$	13.0916			0.639565			0.319782	+	0.947491i	$0.396390\pi$
$420$		0			0
$421$	13.1489	−	22.7745i	0.640836	−	1.10996i	−0.344410	−	0.938819i	$-0.611921\pi$
$421$	13.1489	−	22.7745i	0.640836	−	1.10996i	0.985246	−	0.171142i	$-0.0547457\pi$
$422$		0			0
$423$	−6.74362	+	11.6803i	−0.327886	+	0.567915i
$424$		0			0
$425$	−10.9980			−0.533483
$426$		0			0
$427$	3.13787	+	5.43496i	0.151852	+	0.263016i
$428$		0			0
$429$	−0.807850			−0.0390033
$430$		0			0
$431$	13.8311	+	23.9562i	0.666222	+	1.15393i	0.978952	+	0.204089i	$0.0654231\pi$
$431$	13.8311	+	23.9562i	0.666222	+	1.15393i	−0.312730	+	0.949842i	$0.601244\pi$
$432$		0			0
$433$	2.24152	+	3.88243i	0.107721	+	0.186578i	0.914846	−	0.403802i	$-0.132311\pi$
$433$	2.24152	+	3.88243i	0.107721	+	0.186578i	−0.807126	+	0.590379i	$0.798978\pi$
$434$		0			0
$435$	−1.45348	+	2.51749i	−0.0696888	+	0.120705i
$436$		0			0
$437$	−2.91387	+	3.87131i	−0.139390	+	0.185190i
$438$		0			0
$439$	−12.1630	+	21.0669i	−0.580507	+	1.00547i	0.414912	+	0.909862i	$0.363812\pi$
$439$	−12.1630	+	21.0669i	−0.580507	+	1.00547i	−0.995419	+	0.0956066i	$0.969521\pi$
$440$		0			0
$441$	−0.698821	−	1.21039i	−0.0332772	−	0.0576378i
$442$		0			0
$443$	−10.3133	−	17.8632i	−0.490000	−	0.848705i	0.509934	−	0.860214i	$-0.329670\pi$
$443$	−10.3133	−	17.8632i	−0.490000	−	0.848705i	−0.999934	+	0.0115090i	$0.996336\pi$
$444$		0			0
$445$	−6.57550			−0.311708
$446$		0			0
$447$	−0.453057	−	0.784718i	−0.0214289	−	0.0371159i
$448$		0			0
$449$	−17.3729			−0.819876			−0.409938	−	0.912113i	$-0.634450\pi$
$449$	−17.3729			−0.819876			−0.409938	+	0.912113i	$0.634450\pi$
$450$		0			0
$451$	−3.09821	+	5.36625i	−0.145889	+	0.252687i
$452$		0			0
$453$	−2.33185	+	4.03888i	−0.109560	+	0.189763i
$454$		0			0
$455$	−2.21643			−0.103908
$456$		0			0
$457$	28.5791			1.33687			0.668437	−	0.743769i	$-0.266964\pi$
$457$	28.5791			1.33687			0.668437	+	0.743769i	$0.266964\pi$
$458$		0			0
$459$	−3.04893	+	5.28091i	−0.142312	+	0.246492i
$460$		0			0
$461$	2.33053	−	4.03659i	0.108543	−	0.188003i	−0.806637	−	0.591047i	$-0.798715\pi$
$461$	2.33053	−	4.03659i	0.108543	−	0.188003i	0.915180	+	0.403044i	$0.132048\pi$
$462$		0			0
$463$	3.42674			0.159254			0.0796271	−	0.996825i	$-0.474627\pi$
$463$	3.42674			0.159254			0.0796271	+	0.996825i	$0.474627\pi$
$464$		0			0
$465$	−0.849817	−	1.47193i	−0.0394093	−	0.0682589i
$466$		0			0
$467$	30.0559			1.39082			0.695411	−	0.718613i	$-0.255223\pi$
$467$	30.0559			1.39082			0.695411	+	0.718613i	$0.255223\pi$
$468$		0			0
$469$	10.7854	+	18.6809i	0.498026	+	0.862606i
$470$		0			0
$471$	4.25990	+	7.37836i	0.196286	+	0.339977i
$472$		0			0
$473$	4.15783	−	7.20158i	0.191177	−	0.331129i
$474$		0			0
$475$	−11.4139	+	15.1642i	−0.523704	+	0.695782i
$476$		0			0
$477$	−2.40048	+	4.15774i	−0.109910	+	0.190370i
$478$		0			0
$479$	−10.4280	−	18.0619i	−0.476468	−	0.825267i	0.523168	−	0.852230i	$-0.324750\pi$
$479$	−10.4280	−	18.0619i	−0.476468	−	0.825267i	−0.999636	+	0.0269621i	$0.991417\pi$
$480$		0			0
$481$	2.90835	+	5.03742i	0.132610	+	0.229686i
$482$		0			0
$483$	1.17443			0.0534385
$484$		0			0
$485$	−4.29905	−	7.44617i	−0.195210	−	0.338113i
$486$		0			0
$487$	36.5551			1.65647			0.828236	−	0.560380i	$-0.189345\pi$
$487$	36.5551			1.65647			0.828236	+	0.560380i	$0.189345\pi$
$488$		0			0
$489$	3.51141	−	6.08194i	0.158791	−	0.275035i
$490$		0			0
$491$	3.94221	−	6.82810i	0.177909	−	0.308148i	−0.763255	−	0.646097i	$-0.776400\pi$
$491$	3.94221	−	6.82810i	0.177909	−	0.308148i	0.941164	+	0.337949i	$0.109733\pi$
$492$		0			0
$493$	22.0588			0.993479
$494$		0			0
$495$	4.09936			0.184252
$496$		0			0
$497$	17.5418	−	30.3833i	0.786857	−	1.36288i
$498$		0			0
$499$	10.5414	−	18.2582i	0.471898	−	0.817351i	−0.527585	−	0.849502i	$-0.676903\pi$
$499$	10.5414	−	18.2582i	0.471898	−	0.817351i	0.999483	+	0.0321514i	$0.0102359\pi$
$500$		0			0
$501$	−9.09908			−0.406517
$502$		0			0
$503$	−5.20921	−	9.02261i	−0.232267	−	0.402298i	0.726208	−	0.687475i	$-0.241281\pi$
$503$	−5.20921	−	9.02261i	−0.232267	−	0.402298i	−0.958475	+	0.285177i	$0.907948\pi$
$504$		0			0
$505$	2.87872			0.128101
$506$		0			0
$507$	−2.45021	−	4.24389i	−0.108818	−	0.188478i
$508$		0			0
$509$	18.0260	+	31.2219i	0.798987	+	1.38389i	0.920277	+	0.391268i	$0.127964\pi$
$509$	18.0260	+	31.2219i	0.798987	+	1.38389i	−0.121290	+	0.992617i	$0.538703\pi$
$510$		0			0
$511$	12.3815	−	21.4454i	0.547726	−	0.948690i
$512$		0			0
$513$	4.11716	+	9.68448i	0.181777	+	0.427580i
$514$		0			0
$515$	−0.823548	+	1.42643i	−0.0362899	+	0.0628559i
$516$		0			0
$517$	4.30017	+	7.44811i	0.189121	+	0.327568i
$518$		0			0
$519$	−1.17997	−	2.04377i	−0.0517949	−	0.0897113i
$520$		0			0
$521$	−32.5888			−1.42774			−0.713871	−	0.700277i	$-0.753060\pi$
$521$	−32.5888			−1.42774			−0.713871	+	0.700277i	$0.753060\pi$
$522$		0			0
$523$	−0.275595	−	0.477344i	−0.0120509	−	0.0208728i	0.859937	−	0.510400i	$-0.170503\pi$
$523$	−0.275595	−	0.477344i	−0.0120509	−	0.0208728i	−0.871988	+	0.489527i	$0.837169\pi$
$524$		0			0
$525$	4.60034			0.200775
$526$		0			0
$527$	−6.44866	+	11.1694i	−0.280908	+	0.486547i
$528$		0			0
$529$	10.8822	−	18.8485i	0.473138	−	0.819498i
$530$		0			0
$531$	17.0311			0.739085
$532$		0			0
$533$	3.71511			0.160919
$534$		0			0
$535$	−3.97252	+	6.88061i	−0.171747	+	0.297475i
$536$		0			0
$537$	−1.80690	+	3.12964i	−0.0779734	+	0.135054i
$538$		0			0
$539$	−0.891227			−0.0383879
$540$		0			0
$541$	−7.33743	−	12.7088i	−0.315461	−	0.546394i	0.664075	−	0.747666i	$-0.268826\pi$
$541$	−7.33743	−	12.7088i	−0.315461	−	0.546394i	−0.979535	+	0.201272i	$0.935492\pi$
$542$		0			0
$543$	0.0353480			0.00151693
$544$		0			0
$545$	4.59922	+	7.96608i	0.197009	+	0.341229i
$546$		0			0
$547$	21.5045	+	37.2469i	0.919466	+	1.59256i	0.800228	+	0.599696i	$0.204712\pi$
$547$	21.5045	+	37.2469i	0.919466	+	1.59256i	0.119238	+	0.992866i	$0.461955\pi$
$548$		0			0
$549$	−3.47959	+	6.02683i	−0.148505	+	0.257219i
$550$		0			0
$551$	22.8929	−	30.4149i	0.975269	−	1.29572i
$552$		0			0
$553$	6.72907	−	11.6551i	0.286149	−	0.495625i
$554$		0			0
$555$	0.895233	+	1.55059i	0.0380005	+	0.0658189i
$556$		0			0
$557$	21.6882	+	37.5651i	0.918960	+	1.59168i	0.800998	+	0.598666i	$0.204302\pi$
$557$	21.6882	+	37.5651i	0.918960	+	1.59168i	0.117961	+	0.993018i	$0.462364\pi$
$558$		0			0
$559$	−4.98573			−0.210874
$560$		0			0
$561$	0.943483	+	1.63416i	0.0398339	+	0.0689943i
$562$		0			0
$563$	−37.9925			−1.60119			−0.800597	−	0.599203i	$-0.795484\pi$
$563$	−37.9925			−1.60119			−0.800597	+	0.599203i	$0.795484\pi$
$564$		0			0
$565$	0.389853	−	0.675246i	0.0164013	−	0.0284078i
$566$		0			0
$567$	−9.54620	+	16.5345i	−0.400903	+	0.694384i
$568$		0			0
$569$	28.3448			1.18827			0.594137	−	0.804364i	$-0.297494\pi$
$569$	28.3448			1.18827			0.594137	+	0.804364i	$0.297494\pi$
$570$		0			0
$571$	42.9591			1.79778			0.898890	−	0.438173i	$-0.144374\pi$
$571$	42.9591			1.79778			0.898890	+	0.438173i	$0.144374\pi$
$572$		0			0
$573$	−1.65685	+	2.86976i	−0.0692161	+	0.119886i
$574$		0			0
$575$	−2.42010	+	4.19174i	−0.100925	+	0.174808i
$576$		0			0
$577$	−33.8775			−1.41034			−0.705169	−	0.709039i	$-0.749129\pi$
$577$	−33.8775			−1.41034			−0.705169	+	0.709039i	$0.749129\pi$
$578$		0			0
$579$	−2.53766	−	4.39536i	−0.105462	−	0.182665i
$580$		0			0
$581$	22.7134			0.942309
$582$		0			0
$583$	1.53070	+	2.65125i	0.0633950	+	0.109803i
$584$		0			0
$585$	−1.22890	−	2.12852i	−0.0508089	−	0.0880035i
$586$		0			0
$587$	0.325273	−	0.563390i	0.0134255	−	0.0232536i	−0.859235	−	0.511582i	$-0.829060\pi$
$587$	0.325273	−	0.563390i	0.0134255	−	0.0232536i	0.872660	+	0.488328i	$0.162393\pi$
$588$		0			0
$589$	8.70801	+	20.4832i	0.358807	+	0.843996i
$590$		0			0
$591$	−1.59933	+	2.77011i	−0.0657875	+	0.113947i
$592$		0			0
$593$	−12.4152	−	21.5037i	−0.509831	−	0.883053i	−0.999935	−	0.0113892i	$-0.996375\pi$
$593$	−12.4152	−	21.5037i	−0.509831	−	0.883053i	0.490104	−	0.871664i	$-0.336959\pi$
$594$		0			0
$595$	2.58856	+	4.48352i	0.106121	+	0.183806i
$596$		0			0
$597$	−5.26179			−0.215351
$598$		0			0
$599$	1.54206	+	2.67093i	0.0630070	+	0.109131i	0.895808	−	0.444441i	$-0.146598\pi$
$599$	1.54206	+	2.67093i	0.0630070	+	0.109131i	−0.832801	+	0.553572i	$0.813264\pi$
$600$		0			0
$601$	−15.9545			−0.650799			−0.325399	−	0.945577i	$-0.605499\pi$
$601$	−15.9545			−0.650799			−0.325399	+	0.945577i	$0.605499\pi$
$602$		0			0
$603$	−11.9600	+	20.7153i	−0.487049	+	0.843593i
$604$		0			0
$605$	−3.11273	+	5.39140i	−0.126550	+	0.219192i
$606$		0			0
$607$	30.7258			1.24712			0.623561	−	0.781775i	$-0.285685\pi$
$607$	30.7258			1.24712			0.623561	+	0.781775i	$0.285685\pi$
$608$		0			0
$609$	−9.22692			−0.373894
$610$		0			0
$611$	2.57820	−	4.46558i	0.104303	−	0.180658i
$612$		0			0
$613$	−10.0776	+	17.4549i	−0.407030	+	0.704997i	−0.994555	−	0.104209i	$-0.966769\pi$
$613$	−10.0776	+	17.4549i	−0.407030	+	0.704997i	0.587525	+	0.809206i	$0.300102\pi$
$614$		0			0
$615$	1.14356			0.0461130
$616$		0			0
$617$	−13.9253	−	24.1194i	−0.560612	−	0.971009i	−0.997443	−	0.0714650i	$-0.977233\pi$
$617$	−13.9253	−	24.1194i	−0.560612	−	0.971009i	0.436831	−	0.899544i	$-0.356101\pi$
$618$		0			0
$619$	20.5555			0.826197			0.413098	−	0.910686i	$-0.364447\pi$
$619$	20.5555			0.826197			0.413098	+	0.910686i	$0.364447\pi$
$620$		0			0
$621$	1.34183	+	2.32411i	0.0538457	+	0.0932634i
$622$		0			0
$623$	−10.4356	−	18.0750i	−0.418094	−	0.724159i
$624$		0			0
$625$	−7.86535	+	13.6232i	−0.314614	+	0.544927i
$626$		0			0
$627$	3.23235	+	0.395064i	0.129088	+	0.0157773i
$628$		0			0
$629$	6.79330	−	11.7663i	0.270867	−	0.469155i
$630$		0			0
$631$	17.2127	+	29.8132i	0.685225	+	1.18684i	0.973366	+	0.229257i	$0.0736295\pi$
$631$	17.2127	+	29.8132i	0.685225	+	1.18684i	−0.288141	+	0.957588i	$0.593037\pi$
$632$		0			0
$633$	−0.910904	−	1.57773i	−0.0362052	−	0.0627092i
$634$		0			0
$635$	13.9174			0.552297
$636$		0			0
$637$	0.267171	+	0.462754i	0.0105857	+	0.0183350i
$638$		0			0
$639$	38.9042			1.53903
$640$		0			0
$641$	2.22711	−	3.85747i	0.0879656	−	0.152361i	−0.818685	−	0.574242i	$-0.805297\pi$
$641$	2.22711	−	3.85747i	0.0879656	−	0.152361i	0.906651	+	0.421881i	$0.138630\pi$
$642$		0			0
$643$	11.9267	−	20.6577i	0.470343	−	0.814658i	−0.529082	−	0.848571i	$-0.677463\pi$
$643$	11.9267	−	20.6577i	0.470343	−	0.814658i	0.999425	+	0.0339127i	$0.0107968\pi$
$644$		0			0
$645$	−1.53468			−0.0604279
$646$		0			0
$647$	28.8836			1.13553			0.567767	−	0.823189i	$-0.307808\pi$
$647$	28.8836			1.13553			0.567767	+	0.823189i	$0.307808\pi$
$648$		0			0
$649$	5.43005	−	9.40513i	0.213148	−	0.369184i
$650$		0			0
$651$	2.69739	−	4.67202i	0.105719	−	0.183111i
$652$		0			0
$653$	−19.7094			−0.771288			−0.385644	−	0.922648i	$-0.626021\pi$
$653$	−19.7094			−0.771288			−0.385644	+	0.922648i	$0.626021\pi$
$654$		0			0
$655$	5.09760	+	8.82930i	0.199180	+	0.344989i
$656$		0			0
$657$	27.4598			1.07131
$658$		0			0
$659$	−22.1400	−	38.3475i	−0.862450	−	1.49381i	−0.869557	−	0.493833i	$-0.835595\pi$
$659$	−22.1400	−	38.3475i	−0.862450	−	1.49381i	0.00710614	−	0.999975i	$-0.497738\pi$
$660$		0			0
$661$	10.2921	+	17.8265i	0.400318	+	0.693371i	0.993764	−	0.111502i	$-0.0355663\pi$
$661$	10.2921	+	17.8265i	0.400318	+	0.693371i	−0.593446	+	0.804874i	$0.702233\pi$
$662$		0			0
$663$	0.565673	−	0.979775i	0.0219689	−	0.0380513i
$664$		0			0
$665$	8.86835	+	1.08391i	0.343900	+	0.0420320i
$666$		0			0
$667$	4.85401	−	8.40739i	0.187948	−	0.325536i
$668$		0			0
$669$	0.240510	+	0.416575i	0.00929865	+	0.0161057i
$670$		0			0
$671$	2.21881	+	3.84309i	0.0856563	+	0.148361i
$672$		0			0
$673$	−19.4695			−0.750495			−0.375247	−	0.926925i	$-0.622442\pi$
$673$	−19.4695			−0.750495			−0.375247	+	0.926925i	$0.622442\pi$
$674$		0			0
$675$	5.25604	+	9.10373i	0.202305	+	0.350403i
$676$		0			0
$677$	−44.7238			−1.71888			−0.859438	−	0.511241i	$-0.829186\pi$
$677$	−44.7238			−1.71888			−0.859438	+	0.511241i	$0.829186\pi$
$678$		0			0
$679$	13.6456	−	23.6348i	0.523668	−	0.907020i
$680$		0			0
$681$	−2.37151	+	4.10758i	−0.0908766	+	0.157403i
$682$		0			0
$683$	31.5797			1.20836			0.604182	−	0.796847i	$-0.293500\pi$
$683$	31.5797			1.20836			0.604182	+	0.796847i	$0.293500\pi$
$684$		0			0
$685$	−8.50726			−0.325046
$686$		0			0
$687$	−1.47959	+	2.56273i	−0.0564499	+	0.0977741i
$688$		0			0
$689$	0.917743	−	1.58958i	0.0349632	−	0.0605581i
$690$		0			0
$691$	1.65685			0.0630297			0.0315149	−	0.999503i	$-0.489967\pi$
$691$	1.65685			0.0630297			0.0315149	+	0.999503i	$0.489967\pi$
$692$		0			0
$693$	6.50586	+	11.2685i	0.247137	+	0.428054i
$694$		0			0
$695$	−10.9518			−0.415424
$696$		0			0
$697$	−4.33886	−	7.51512i	−0.164346	−	0.284655i
$698$		0			0
$699$	4.17198	+	7.22608i	0.157799	+	0.273315i
$700$		0			0
$701$	12.5990	−	21.8221i	0.475858	−	0.824211i	−0.523759	−	0.851866i	$-0.675471\pi$
$701$	12.5990	−	21.8221i	0.475858	−	0.824211i	0.999618	+	0.0276556i	$0.00880416\pi$
$702$		0			0
$703$	−9.17340	−	21.5779i	−0.345981	−	0.813826i
$704$		0			0
$705$	0.793608	−	1.37457i	0.0298890	−	0.0517693i
$706$		0			0
$707$	4.56866	+	7.91315i	0.171822	+	0.297605i
$708$		0			0
$709$	−19.6472	−	34.0300i	−0.737866	−	1.27802i	−0.953454	−	0.301538i	$-0.902500\pi$
$709$	−19.6472	−	34.0300i	−0.737866	−	1.27802i	0.215588	−	0.976484i	$-0.430833\pi$
$710$		0			0
$711$	14.9237			0.559684
$712$		0			0
$713$	2.83804	+	4.91563i	0.106285	+	0.184092i
$714$		0			0
$715$	−1.56725			−0.0586120
$716$		0			0
$717$	−5.53151	+	9.58086i	−0.206578	+	0.357804i
$718$		0			0
$719$	−2.36385	+	4.09431i	−0.0881568	+	0.152692i	−0.906732	−	0.421707i	$-0.861431\pi$
$719$	−2.36385	+	4.09431i	−0.0881568	+	0.152692i	0.818575	+	0.574399i	$0.194764\pi$
$720$		0			0
$721$	−5.22803			−0.194702
$722$		0			0
$723$	3.03311			0.112802
$724$		0			0
$725$	19.0135	−	32.9324i	0.706145	−	1.22308i
$726$		0			0
$727$	−24.2530	+	42.0074i	−0.899494	+	1.55797i	−0.0713515	+	0.997451i	$0.522731\pi$
$727$	−24.2530	+	42.0074i	−0.899494	+	1.55797i	−0.828142	+	0.560518i	$0.810602\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$		0			0
$731$	5.82280	+	10.0854i	0.215364	+	0.373022i
$732$		0			0
$733$	30.3496			1.12099			0.560495	−	0.828158i	$-0.310611\pi$
$733$	30.3496			1.12099			0.560495	+	0.828158i	$0.310611\pi$
$734$		0			0
$735$	0.0822392	+	0.142442i	0.00303344	+	0.00525407i
$736$		0			0
$737$	7.62646	+	13.2094i	0.280924	+	0.486575i
$738$		0			0
$739$	2.82538	−	4.89371i	0.103933	−	0.180018i	−0.809369	−	0.587301i	$-0.800190\pi$
$739$	2.82538	−	4.89371i	0.103933	−	0.180018i	0.913302	+	0.407283i	$0.133524\pi$
$740$		0			0
$741$	−0.763862	−	1.79678i	−0.0280612	−	0.0660062i
$742$		0			0
$743$	6.29544	−	10.9040i	0.230957	−	0.400030i	−0.727133	−	0.686497i	$-0.759148\pi$
$743$	6.29544	−	10.9040i	0.230957	−	0.400030i	0.958090	+	0.286467i	$0.0924809\pi$
$744$		0			0
$745$	−0.878945	−	1.52238i	−0.0322021	−	0.0557756i
$746$		0			0
$747$	12.5934	+	21.8125i	0.460770	+	0.798077i
$748$		0			0
$749$	−25.2183			−0.921456
$750$		0			0
$751$	−6.09861	−	10.5631i	−0.222542	−	0.385453i	0.733038	−	0.680188i	$-0.238102\pi$
$751$	−6.09861	−	10.5631i	−0.222542	−	0.385453i	−0.955579	+	0.294735i	$0.904769\pi$
$752$		0			0
$753$	−11.4739			−0.418132
$754$		0			0
$755$	−4.52386	+	7.83555i	−0.164640	+	0.285165i
$756$		0			0
$757$	−8.30230	+	14.3800i	−0.301752	+	0.522650i	−0.976533	−	0.215368i	$-0.930905\pi$
$757$	−8.30230	+	14.3800i	−0.301752	+	0.522650i	0.674781	+	0.738018i	$0.264238\pi$
$758$		0			0
$759$	0.830448			0.0301434
$760$		0			0
$761$	−17.9722			−0.651493			−0.325747	−	0.945457i	$-0.605616\pi$
$761$	−17.9722			−0.651493			−0.325747	+	0.945457i	$0.605616\pi$
$762$		0			0
$763$	−14.5983	+	25.2850i	−0.528495	+	0.915379i
$764$		0			0
$765$	−2.87045	+	4.97177i	−0.103782	+	0.179755i
$766$		0			0
$767$	−6.51127			−0.235108
$768$		0			0
$769$	27.4284	+	47.5074i	0.989093	+	1.71316i	0.622104	+	0.782934i	$0.286278\pi$
$769$	27.4284	+	47.5074i	0.989093	+	1.71316i	0.366989	+	0.930225i	$0.380389\pi$
$770$		0			0
$771$	−4.16353			−0.149946
$772$		0			0
$773$	18.9250	+	32.7790i	0.680684	+	1.17898i	0.974772	+	0.223201i	$0.0716507\pi$
$773$	18.9250	+	32.7790i	0.680684	+	1.17898i	−0.294088	+	0.955778i	$0.595016\pi$
$774$		0			0
$775$	11.1168	+	19.2549i	0.399328	+	0.691656i
$776$		0			0
$777$	−2.84155	+	4.92171i	−0.101940	+	0.176565i
$778$		0			0
$779$	−14.8648	−	1.81681i	−0.532588	−	0.0650938i
$780$		0			0
$781$	12.4039	−	21.4842i	0.443847	−	0.768766i
$782$		0			0
$783$	−10.5421	−	18.2594i	−0.376743	−	0.652537i
$784$		0			0
$785$	8.26434	+	14.3143i	0.294967	+	0.510898i
$786$		0			0
$787$	10.5892			0.377466			0.188733	−	0.982028i	$-0.439562\pi$
$787$	10.5892			0.377466			0.188733	+	0.982028i	$0.439562\pi$
$788$		0			0
$789$	−2.68699	−	4.65401i	−0.0956595	−	0.165687i
$790$		0			0
$791$	2.47486			0.0879958
$792$		0			0
$793$	1.33031	−	2.30416i	0.0472406	−	0.0818231i
$794$		0			0
$795$	0.282494	−	0.489295i	0.0100190	−	0.0173535i
$796$		0			0
$797$	−19.2209			−0.680838			−0.340419	−	0.940274i	$-0.610569\pi$
$797$	−19.2209			−0.680838			−0.340419	+	0.940274i	$0.610569\pi$
$798$		0			0
$799$	−12.0443			−0.426096
$800$		0			0
$801$	11.5720	−	20.0434i	0.408878	−	0.708198i
$802$		0			0
$803$	8.75506	−	15.1642i	0.308959	−	0.535133i
$804$		0			0
$805$	2.27843			0.0803043
$806$		0			0
$807$	−0.525135	−	0.909561i	−0.0184856	−	0.0320181i
$808$		0			0
$809$	14.4108			0.506658			0.253329	−	0.967380i	$-0.418475\pi$
$809$	14.4108			0.506658			0.253329	+	0.967380i	$0.418475\pi$
$810$		0			0
$811$	1.60447	+	2.77903i	0.0563406	+	0.0975848i	0.892820	−	0.450413i	$-0.148723\pi$
$811$	1.60447	+	2.77903i	0.0563406	+	0.0975848i	−0.836480	+	0.547998i	$0.815390\pi$
$812$		0			0
$813$	4.25363	+	7.36751i	0.149181	+	0.258390i
$814$		0			0
$815$	6.81225	−	11.7992i	0.238623	−	0.413307i
$816$		0			0
$817$	19.9488	+	2.43818i	0.697920	+	0.0853011i
$818$		0			0
$819$	3.90064	−	6.75611i	0.136300	−	0.236078i
$820$		0			0
$821$	−21.0191	−	36.4061i	−0.733570	−	1.27058i	−0.955348	−	0.295484i	$-0.904519\pi$
$821$	−21.0191	−	36.4061i	−0.733570	−	1.27058i	0.221778	−	0.975097i	$-0.428814\pi$
$822$		0			0
$823$	18.8422	+	32.6357i	0.656799	+	1.13761i	0.981440	+	0.191772i	$0.0614233\pi$
$823$	18.8422	+	32.6357i	0.656799	+	1.13761i	−0.324641	+	0.945837i	$0.605243\pi$
$824$		0			0
$825$	3.25293			0.113252
$826$		0			0
$827$	9.33867	+	16.1751i	0.324737	+	0.562462i	0.981459	−	0.191671i	$-0.0613907\pi$
$827$	9.33867	+	16.1751i	0.324737	+	0.562462i	−0.656722	+	0.754133i	$0.728057\pi$
$828$		0			0
$829$	6.28371			0.218242			0.109121	−	0.994028i	$-0.465196\pi$
$829$	6.28371			0.218242			0.109121	+	0.994028i	$0.465196\pi$
$830$		0			0
$831$	0.414632	−	0.718164i	0.0143834	−	0.0249128i
$832$		0			0
$833$	0.624056	−	1.08090i	0.0216222	−	0.0374508i
$834$		0			0
$835$	−17.6525			−0.610890
$836$		0			0
$837$	12.3274			0.426099
$838$		0			0
$839$	8.27458	−	14.3320i	0.285670	−	0.494796i	−0.687101	−	0.726562i	$-0.741117\pi$
$839$	8.27458	−	14.3320i	0.285670	−	0.494796i	0.972772	+	0.231766i	$0.0744504\pi$
$840$		0			0
$841$	−23.6355	+	40.9380i	−0.815019	+	1.41165i
$842$		0			0
$843$	12.1562			0.418681
$844$		0			0
$845$	−4.75349	−	8.23329i	−0.163525	−	0.283234i
$846$		0			0
$847$	−19.7601			−0.678966
$848$		0			0
$849$	5.01839	+	8.69210i	0.172231	+	0.298312i
$850$		0			0
$851$	−2.98971	−	5.17833i	−0.102486	−	0.177511i
$852$		0			0
$853$	21.2071	−	36.7319i	0.726119	−	1.25767i	−0.232393	−	0.972622i	$-0.574656\pi$
$853$	21.2071	−	36.7319i	0.726119	−	1.25767i	0.958512	−	0.285053i	$-0.0920111\pi$
$854$		0			0
$855$	3.87615	+	9.11757i	0.132561	+	0.311814i
$856$		0			0
$857$	22.3484	−	38.7085i	0.763406	−	1.32226i	−0.177679	−	0.984089i	$-0.556859\pi$
$857$	22.3484	−	38.7085i	0.763406	−	1.32226i	0.941085	−	0.338170i	$-0.109808\pi$
$858$		0			0
$859$	−6.45320	−	11.1773i	−0.220180	−	0.381363i	0.734682	−	0.678411i	$-0.237331\pi$
$859$	−6.45320	−	11.1773i	−0.220180	−	0.381363i	−0.954863	+	0.297048i	$0.903998\pi$
$860$		0			0
$861$	1.81489	+	3.14348i	0.0618512	+	0.107129i
$862$		0			0
$863$	−14.3069			−0.487012			−0.243506	−	0.969899i	$-0.578297\pi$
$863$	−14.3069			−0.487012			−0.243506	+	0.969899i	$0.578297\pi$
$864$		0			0
$865$	−2.28918	−	3.96497i	−0.0778344	−	0.134813i
$866$		0			0
$867$	4.39905			0.149399
$868$		0			0
$869$	4.75817	−	8.24139i	0.161410	−	0.279570i
$870$		0			0
$871$	4.57251	−	7.91982i	0.154934	−	0.268353i
$872$		0			0
$873$	30.2631			1.02425
$874$		0			0
$875$	19.1732			0.648172
$876$		0			0
$877$	25.5307	−	44.2205i	0.862111	−	1.49322i	−0.00777597	−	0.999970i	$-0.502475\pi$
$877$	25.5307	−	44.2205i	0.862111	−	1.49322i	0.869887	−	0.493251i	$-0.164191\pi$
$878$		0			0
$879$	−2.13888	+	3.70466i	−0.0721428	+	0.124955i
$880$		0			0
$881$	−31.1375			−1.04905			−0.524524	−	0.851396i	$-0.675757\pi$
$881$	−31.1375			−1.04905			−0.524524	+	0.851396i	$0.675757\pi$
$882$		0			0
$883$	−19.7460	−	34.2011i	−0.664505	−	1.15096i	−0.979419	−	0.201837i	$-0.935309\pi$
$883$	−19.7460	−	34.2011i	−0.664505	−	1.15096i	0.314914	−	0.949120i	$-0.398024\pi$
$884$		0			0
$885$	−2.00426			−0.0673725
$886$		0			0
$887$	16.5853	+	28.7266i	0.556881	+	0.964546i	0.997755	+	0.0669765i	$0.0213353\pi$
$887$	16.5853	+	28.7266i	0.556881	+	0.964546i	−0.440874	+	0.897569i	$0.645331\pi$
$888$		0			0
$889$	22.0876	+	38.2568i	0.740794	+	1.28309i
$890$		0			0
$891$	−6.75018	+	11.6917i	−0.226140	+	0.391685i
$892$		0			0
$893$	−12.4997	+	16.6068i	−0.418285	+	0.555724i
$894$		0			0
$895$	−3.50544	+	6.07160i	−0.117174	+	0.202951i
$896$		0			0
$897$	−0.248951	−	0.431196i	−0.00831223	−	0.0143972i
$898$		0			0
$899$	−22.2971	−	38.6196i	−0.743648	−	1.28804i
$900$		0			0
$901$	−4.28731			−0.142831
$902$		0			0
$903$	−2.43560	−	4.21859i	−0.0810518	−	0.140386i
$904$		0			0
$905$	0.0685763			0.00227955
$906$		0			0
$907$	−12.3726	+	21.4300i	−0.410825	+	0.711570i	−0.994980	−	0.100072i	$-0.968093\pi$
$907$	−12.3726	+	21.4300i	−0.410825	+	0.711570i	0.584155	+	0.811642i	$0.301426\pi$
$908$		0			0
$909$	−5.06619	+	8.77490i	−0.168035	+	0.291045i
$910$		0			0
$911$	−23.4852			−0.778100			−0.389050	−	0.921217i	$-0.627197\pi$
$911$	−23.4852			−0.778100			−0.389050	+	0.921217i	$0.627197\pi$
$912$		0			0
$913$	16.0608			0.531534
$914$		0			0
$915$	0.409488	−	0.709254i	0.0135372	−	0.0234472i
$916$		0			0
$917$	−16.1802	+	28.0250i	−0.534318	+	0.925467i
$918$		0			0
$919$	−11.6516			−0.384350			−0.192175	−	0.981361i	$-0.561554\pi$
$919$	−11.6516			−0.384350			−0.192175	+	0.981361i	$0.561554\pi$
$920$		0			0
$921$	6.30583	+	10.9220i	0.207784	+	0.359893i
$922$		0			0
$923$	−14.8738			−0.489576
$924$		0			0
$925$	−11.7109	−	20.2839i	−0.385053	−	0.666931i
$926$		0			0
$927$	−2.89868	−	5.02067i	−0.0952052	−	0.164900i
$928$		0			0
$929$	2.97418	−	5.15143i	0.0975797	−	0.169013i	−0.813103	−	0.582120i	$-0.802223\pi$
$929$	2.97418	−	5.15143i	0.0975797	−	0.169013i	0.910682	+	0.413107i	$0.135557\pi$
$930$		0			0
$931$	−0.842699	−	1.98222i	−0.0276184	−	0.0649646i
$932$		0			0
$933$	−5.72324	+	9.91295i	−0.187371	+	0.324535i
$934$		0			0
$935$	1.83039	+	3.17032i	0.0598601	+	0.103681i
$936$		0			0
$937$	16.5608	+	28.6841i	0.541017	+	0.937069i	0.998846	+	0.0480287i	$0.0152939\pi$
$937$	16.5608	+	28.6841i	0.541017	+	0.937069i	−0.457829	+	0.889040i	$0.651373\pi$
$938$		0			0
$939$	−0.777937			−0.0253870
$940$		0			0
$941$	−24.2526	−	42.0068i	−0.790613	−	1.36938i	−0.925588	−	0.378533i	$-0.876429\pi$
$941$	−24.2526	−	42.0068i	−0.790613	−	1.36938i	0.134975	−	0.990849i	$-0.456905\pi$
$942$		0			0
$943$	−3.81904			−0.124365
$944$		0			0
$945$	2.47418	−	4.28541i	0.0804851	−	0.139404i
$946$		0			0
$947$	−14.7734	+	25.5883i	−0.480071	+	0.831508i	−0.999739	−	0.0228609i	$-0.992723\pi$
$947$	−14.7734	+	25.5883i	−0.480071	+	0.831508i	0.519667	+	0.854369i	$0.326056\pi$
$948$		0			0
$949$	−10.4983			−0.340791
$950$		0			0
$951$	−7.66226			−0.248466
$952$		0			0
$953$	8.88592	−	15.3909i	0.287843	−	0.498559i	−0.685451	−	0.728118i	$-0.740395\pi$
$953$	8.88592	−	15.3909i	0.287843	−	0.498559i	0.973295	+	0.229559i	$0.0737284\pi$
$954$		0			0
$955$	−3.21435	+	5.56742i	−0.104014	+	0.180157i
$956$		0			0
$957$	−6.52442			−0.210904
$958$		0			0
$959$	−13.5014	−	23.3851i	−0.435983	−	0.755145i
$960$		0			0
$961$	−4.92677			−0.158928
$962$		0			0
$963$	−13.9823	−	24.2180i	−0.450573	−	0.780415i
$964$		0			0
$965$	−4.92315	−	8.52715i	−0.158482	−	0.274499i
$966$		0			0
$967$	8.83458	−	15.3019i	0.284101	−	0.492077i	−0.688290	−	0.725436i	$-0.741638\pi$
$967$	8.83458	−	15.3019i	0.284101	−	0.492077i	0.972391	+	0.233358i	$0.0749716\pi$
$968$		0			0
$969$	−2.74250	+	3.64362i	−0.0881018	+	0.117050i
$970$		0			0
$971$	−8.67986	+	15.0340i	−0.278550	+	0.482463i	−0.971025	−	0.238980i	$-0.923187\pi$
$971$	−8.67986	+	15.0340i	−0.278550	+	0.482463i	0.692475	+	0.721442i	$0.256520\pi$
$972$		0			0
$973$	−17.3809	−	30.1046i	−0.557206	−	0.965110i
$974$		0			0
$975$	−0.975161	−	1.68903i	−0.0312301	−	0.0540922i
$976$		0			0
$977$	−9.07940			−0.290476			−0.145238	−	0.989397i	$-0.546395\pi$
$977$	−9.07940			−0.290476			−0.145238	+	0.989397i	$0.546395\pi$
$978$		0			0
$979$	−7.37909	−	12.7810i	−0.235837	−	0.408481i
$980$		0			0
$981$	−32.3762			−1.03369
$982$		0			0
$983$	−10.1697	+	17.6144i	−0.324362	+	0.561812i	−0.981383	−	0.192060i	$-0.938483\pi$
$983$	−10.1697	+	17.6144i	−0.324362	+	0.561812i	0.657021	+	0.753873i	$0.271816\pi$
$984$		0			0
$985$	−3.10275	+	5.37411i	−0.0988617	+	0.171233i
$986$		0			0
$987$	5.03796			0.160360
$988$		0			0
$989$	5.12520			0.162972
$990$		0			0
$991$	18.7306	−	32.4424i	0.594998	−	1.03057i	−0.398549	−	0.917147i	$-0.630486\pi$
$991$	18.7306	−	32.4424i	0.594998	−	1.03057i	0.993547	−	0.113420i	$-0.0361805\pi$
$992$		0			0
$993$	0.628706	−	1.08895i	0.0199514	−	0.0345568i
$994$		0			0
$995$	−10.2080			−0.323617
$996$		0			0
$997$	16.1668	+	28.0017i	0.512008	+	0.886824i	0.999903	+	0.0139214i	$0.00443146\pi$
$997$	16.1668	+	28.0017i	0.512008	+	0.886824i	−0.487895	+	0.872902i	$0.662235\pi$
$998$		0			0
$999$	−12.9863			−0.410867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.o.961.4		8
4.3	odd	2		1216.2.i.q.961.2		8
8.3	odd	2		608.2.i.c.353.3	✓	8
8.5	even	2		608.2.i.e.353.1	yes	8
19.7	even	3	inner	1216.2.i.o.577.4		8
76.7	odd	6		1216.2.i.q.577.2		8
152.45	even	6		608.2.i.e.577.1	yes	8
152.83	odd	6		608.2.i.c.577.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
608.2.i.c.353.3	✓	8	8.3	odd	2
608.2.i.c.577.3	yes	8	152.83	odd	6
608.2.i.e.353.1	yes	8	8.5	even	2
608.2.i.e.577.1	yes	8	152.45	even	6
1216.2.i.o.577.4		8	19.7	even	3	inner
1216.2.i.o.961.4		8	1.1	even	1	trivial
1216.2.i.q.577.2		8	76.7	odd	6
1216.2.i.q.961.2		8	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:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{3} +(0.401794 - 0.695928i) q^{5} +2.55066 q^{7} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(0.207107 - 0.358719i) q^{3} +(0.401794 - 0.695928i) q^{5} +2.55066 q^{7} +(1.41421 + 2.44949i) q^{9} +1.80359 q^{11} +(-0.540678 - 0.936482i) q^{13} +(-0.166429 - 0.288263i) q^{15} +(-1.26291 + 2.18742i) q^{17} +(1.70538 + 4.01144i) q^{19} +(0.528259 - 0.914971i) q^{21} +(0.555803 + 0.962679i) q^{23} +(2.17712 + 3.77089i) q^{25} +2.41421 q^{27} +(-4.36667 - 7.56329i) q^{29} +5.10620 q^{31} +(0.373535 - 0.646982i) q^{33} +(1.02484 - 1.77507i) q^{35} -5.37909 q^{37} -0.447913 q^{39} +(-1.71780 + 2.97532i) q^{41} +(2.30531 - 3.99292i) q^{43} +2.27289 q^{45} +(2.38423 + 4.12961i) q^{47} -0.494141 q^{49} +(0.523114 + 0.906061i) q^{51} +(0.848696 + 1.46998i) q^{53} +(0.724671 - 1.25517i) q^{55} +(1.79218 + 0.219043i) q^{57} +(3.01069 - 5.21468i) q^{59} +(1.23022 + 2.13081i) q^{61} +(3.60718 + 6.24781i) q^{63} -0.868965 q^{65} +(4.22850 + 7.32397i) q^{67} +0.460442 q^{69} +(6.87736 - 11.9119i) q^{71} +(4.85425 - 8.40780i) q^{73} +1.80359 q^{75} +4.60034 q^{77} +(2.63817 - 4.56944i) q^{79} +(-3.74264 + 6.48244i) q^{81} +8.90490 q^{83} +(1.01486 + 1.75779i) q^{85} -3.61746 q^{87} +(-4.09134 - 7.08640i) q^{89} +(-1.37909 - 2.38865i) q^{91} +(1.05753 - 1.83169i) q^{93} +(3.47689 + 0.424951i) q^{95} +(5.34982 - 9.26615i) q^{97} +(2.55066 + 4.41787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7	\( 8 q - 4 q^{3} - 2 q^{5} - 8 q^{7} + 4 q^{11} - 2 q^{13} + 2 q^{15} - 2 q^{17} - 2 q^{19} + 8 q^{21} + 2 q^{23} - 2 q^{25} + 8 q^{27} + 10 q^{29} + 24 q^{31} - 6 q^{33} - 4 q^{35} + 8 q^{37} - 12 q^{39} + 8 q^{41} + 18 q^{43} - 16 q^{45} - 6 q^{47} + 32 q^{49} - 18 q^{51} + 10 q^{53} + 20 q^{55} + 10 q^{57} + 8 q^{59} - 18 q^{61} + 8 q^{63} - 36 q^{65} - 4 q^{67} - 52 q^{69} - 6 q^{71} + 4 q^{75} - 16 q^{77} + 14 q^{79} + 4 q^{81} + 4 q^{83} + 22 q^{85} - 60 q^{87} - 2 q^{89} + 40 q^{91} + 16 q^{93} + 50 q^{95} - 12 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 - 2 * q^5 - 8 * q^7 + 4 * q^11 - 2 * q^13 + 2 * q^15 - 2 * q^17 - 2 * q^19 + 8 * q^21 + 2 * q^23 - 2 * q^25 + 8 * q^27 + 10 * q^29 + 24 * q^31 - 6 * q^33 - 4 * q^35 + 8 * q^37 - 12 * q^39 + 8 * q^41 + 18 * q^43 - 16 * q^45 - 6 * q^47 + 32 * q^49 - 18 * q^51 + 10 * q^53 + 20 * q^55 + 10 * q^57 + 8 * q^59 - 18 * q^61 + 8 * q^63 - 36 * q^65 - 4 * q^67 - 52 * q^69 - 6 * q^71 + 4 * q^75 - 16 * q^77 + 14 * q^79 + 4 * q^81 + 4 * q^83 + 22 * q^85 - 60 * q^87 - 2 * q^89 + 40 * q^91 + 16 * q^93 + 50 * q^95 - 12 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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