LMFDB - Embedded newform 234.2.y.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.25580 - 1.19288i) q^{3} -1.00000i q^{4} +(0.650628 + 0.174335i) q^{5} +(0.0444876 - 1.73148i) q^{6} +(-1.73068 - 0.463733i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.154059 - 2.99604i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.25580 - 1.19288i) q^{3} -1.00000i q^{4} +(0.650628 + 0.174335i) q^{5} +(0.0444876 - 1.73148i) q^{6} +(-1.73068 - 0.463733i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.154059 - 2.99604i) q^{9} +(0.583337 - 0.336790i) q^{10} +(0.696978 + 0.696978i) q^{11} +(-1.19288 - 1.25580i) q^{12} +(0.391864 + 3.58419i) q^{13} +(-1.55168 + 0.895864i) q^{14} +(1.02502 - 0.557194i) q^{15} -1.00000 q^{16} +(-1.20946 + 2.09485i) q^{17} +(-2.00959 - 2.22746i) q^{18} +(6.33213 - 1.69669i) q^{19} +(0.174335 - 0.650628i) q^{20} +(-2.72656 + 1.48214i) q^{21} +0.985676 q^{22} +(-3.16302 + 5.47852i) q^{23} +(-1.73148 - 0.0444876i) q^{24} +(-3.93720 - 2.27315i) q^{25} +(2.81150 + 2.25732i) q^{26} +(-3.38046 - 3.94620i) q^{27} +(-0.463733 + 1.73068i) q^{28} +4.29257i q^{29} +(0.330803 - 1.11879i) q^{30} +(1.49861 - 5.59289i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.70668 + 0.0438503i) q^{33} +(0.626062 + 2.33650i) q^{34} +(-1.04518 - 0.603436i) q^{35} +(-2.99604 - 0.154059i) q^{36} +(6.83094 + 1.83034i) q^{37} +(3.27775 - 5.67724i) q^{38} +(4.76763 + 4.03358i) q^{39} +(-0.336790 - 0.583337i) q^{40} +(1.28786 + 4.80634i) q^{41} +(-0.879938 + 2.97600i) q^{42} +(-0.772736 + 0.446139i) q^{43} +(0.696978 - 0.696978i) q^{44} +(0.622551 - 1.92245i) q^{45} +(1.63730 + 6.11049i) q^{46} +(-3.66378 + 0.981707i) q^{47} +(-1.25580 + 1.19288i) q^{48} +(-3.28199 - 1.89486i) q^{49} +(-4.39138 + 1.17667i) q^{50} +(0.980069 + 4.07345i) q^{51} +(3.58419 - 0.391864i) q^{52} +9.00014i q^{53} +(-5.18073 - 0.400036i) q^{54} +(0.331966 + 0.574981i) q^{55} +(0.895864 + 1.55168i) q^{56} +(5.92793 - 9.68420i) q^{57} +(3.03531 + 3.03531i) q^{58} +(-3.33959 - 3.33959i) q^{59} +(-0.557194 - 1.02502i) q^{60} +(-2.38199 - 4.12572i) q^{61} +(-2.89509 - 5.01445i) q^{62} +(-1.65599 + 5.11374i) q^{63} +1.00000i q^{64} +(-0.369894 + 2.40029i) q^{65} +(1.23781 - 1.17580i) q^{66} +(10.6950 - 2.86571i) q^{67} +(2.09485 + 1.20946i) q^{68} +(2.56311 + 10.6530i) q^{69} +(-1.16575 + 0.312361i) q^{70} +(-1.70900 - 6.37808i) q^{71} +(-2.22746 + 2.00959i) q^{72} +(-8.01788 + 8.01788i) q^{73} +(6.12445 - 3.53595i) q^{74} +(-7.65593 + 1.84201i) q^{75} +(-1.69669 - 6.33213i) q^{76} +(-0.883031 - 1.52946i) q^{77} +(6.22339 - 0.519052i) q^{78} +(-0.807117 + 1.39797i) q^{79} +(-0.650628 - 0.174335i) q^{80} +(-8.95253 - 0.923132i) q^{81} +(4.30925 + 2.48795i) q^{82} +(-1.95885 - 7.31055i) q^{83} +(1.48214 + 2.72656i) q^{84} +(-1.15211 + 1.15211i) q^{85} +(-0.230939 + 0.861875i) q^{86} +(5.12054 + 5.39061i) q^{87} -0.985676i q^{88} +(-0.440877 + 1.64537i) q^{89} +(-0.919169 - 1.79959i) q^{90} +(0.983920 - 6.38480i) q^{91} +(5.47852 + 3.16302i) q^{92} +(-4.78971 - 8.81121i) q^{93} +(-1.89651 + 3.28485i) q^{94} +4.41566 q^{95} +(-0.0444876 + 1.73148i) q^{96} +(-0.497183 + 1.85551i) q^{97} +(-3.66058 + 0.980849i) q^{98} +(2.19555 - 1.98080i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.25580	−	1.19288i	0.725035	−	0.688712i
$3$	1.25580	−	1.19288i	0.725035	−	0.688712i
$4$		−	1.00000i		−	0.500000i
$5$	0.650628	+	0.174335i	0.290970	+	0.0779651i	0.401351	−	0.915924i	$-0.368541\pi$
$5$	0.650628	+	0.174335i	0.290970	+	0.0779651i	−0.110382	+	0.993889i	$0.535207\pi$
$6$	0.0444876	−	1.73148i	0.0181620	−	0.706873i
$7$	−1.73068	−	0.463733i	−0.654134	−	0.175275i	−0.0835368	−	0.996505i	$-0.526622\pi$
$7$	−1.73068	−	0.463733i	−0.654134	−	0.175275i	−0.570597	+	0.821230i	$0.693288\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.154059	−	2.99604i	0.0513529	−	0.998681i
$10$	0.583337	−	0.336790i	0.184467	−	0.106502i
$11$	0.696978	+	0.696978i	0.210147	+	0.210147i	0.804330	−	0.594183i	$-0.202525\pi$
$11$	0.696978	+	0.696978i	0.210147	+	0.210147i	−0.594183	+	0.804330i	$0.702525\pi$
$12$	−1.19288	−	1.25580i	−0.344356	−	0.362518i
$13$	0.391864	+	3.58419i	0.108684	+	0.994076i
$13$	0.391864	+	3.58419i	0.108684	+	0.994076i
$14$	−1.55168	+	0.895864i	−0.414704	+	0.239430i
$15$	1.02502	−	0.557194i	0.264659	−	0.143867i
$16$	−1.00000			−0.250000
$17$	−1.20946	+	2.09485i	−0.293337	+	0.508075i	−0.974597	−	0.223967i	$-0.928099\pi$
$17$	−1.20946	+	2.09485i	−0.293337	+	0.508075i	0.681260	+	0.732042i	$0.261432\pi$
$18$	−2.00959	−	2.22746i	−0.473664	−	0.525017i
$19$	6.33213	−	1.69669i	1.45269	−	0.389247i	0.555732	−	0.831361i	$-0.312438\pi$
$19$	6.33213	−	1.69669i	1.45269	−	0.389247i	0.896959	+	0.442114i	$0.145771\pi$
$20$	0.174335	−	0.650628i	0.0389826	−	0.145485i
$21$	−2.72656	+	1.48214i	−0.594984	+	0.323429i
$22$	0.985676			0.210147
$23$	−3.16302	+	5.47852i	−0.659536	+	1.14235i	0.321200	+	0.947011i	$0.395914\pi$
$23$	−3.16302	+	5.47852i	−0.659536	+	1.14235i	−0.980736	+	0.195338i	$0.937420\pi$
$24$	−1.73148	−	0.0444876i	−0.353437	−	0.00908098i
$25$	−3.93720	−	2.27315i	−0.787441	−	0.454629i
$26$	2.81150	+	2.25732i	0.551380	+	0.442696i
$27$	−3.38046	−	3.94620i	−0.650570	−	0.759446i
$28$	−0.463733	+	1.73068i	−0.0876374	+	0.327067i
$29$			4.29257i			0.797111i	0.917144	+	0.398555i	$0.130488\pi$
$29$			4.29257i			0.797111i	−0.917144	+	0.398555i	$0.869512\pi$
$30$	0.330803	−	1.11879i	0.0603961	−	0.204263i
$31$	1.49861	−	5.59289i	0.269158	−	1.00451i	−0.690498	−	0.723335i	$-0.742608\pi$
$31$	1.49861	−	5.59289i	0.269158	−	1.00451i	0.959656	−	0.281178i	$-0.0907250\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	1.70668	+	0.0438503i	0.297094	+	0.00763336i
$34$	0.626062	+	2.33650i	0.107369	+	0.400706i
$35$	−1.04518	−	0.603436i	−0.176668	−	0.101999i
$36$	−2.99604	−	0.154059i	−0.499340	−	0.0256764i
$37$	6.83094	+	1.83034i	1.12300	+	0.300907i	0.772096	−	0.635505i	$-0.219208\pi$
$37$	6.83094	+	1.83034i	1.12300	+	0.300907i	0.350902	+	0.936412i	$0.385875\pi$
$38$	3.27775	−	5.67724i	0.531722	−	0.920969i
$39$	4.76763	+	4.03358i	0.763431	+	0.645889i
$40$	−0.336790	−	0.583337i	−0.0532512	−	0.0922337i
$41$	1.28786	+	4.80634i	0.201129	+	0.750625i	0.990595	+	0.136830i	$0.0436913\pi$
$41$	1.28786	+	4.80634i	0.201129	+	0.750625i	−0.789465	+	0.613795i	$0.789642\pi$
$42$	−0.879938	+	2.97600i	−0.135777	+	0.459207i
$43$	−0.772736	+	0.446139i	−0.117841	+	0.0680356i	−0.557762	−	0.830001i	$-0.688340\pi$
$43$	−0.772736	+	0.446139i	−0.117841	+	0.0680356i	0.439921	+	0.898037i	$0.355006\pi$
$44$	0.696978	−	0.696978i	0.105073	−	0.105073i
$45$	0.622551	−	1.92245i	0.0928044	−	0.286582i
$46$	1.63730	+	6.11049i	0.241407	+	0.900943i
$47$	−3.66378	+	0.981707i	−0.534417	+	0.143197i	−0.515927	−	0.856632i	$-0.672553\pi$
$47$	−3.66378	+	0.981707i	−0.534417	+	0.143197i	−0.0184899	+	0.999829i	$0.505886\pi$
$48$	−1.25580	+	1.19288i	−0.181259	+	0.172178i
$49$	−3.28199	−	1.89486i	−0.468855	−	0.270694i
$50$	−4.39138	+	1.17667i	−0.621035	+	0.166406i
$51$	0.980069	+	4.07345i	0.137237	+	0.570397i
$52$	3.58419	−	0.391864i	0.497038	−	0.0543418i
$53$			9.00014i			1.23626i	0.786074	+	0.618132i	$0.212110\pi$
$53$			9.00014i			1.23626i	−0.786074	+	0.618132i	$0.787890\pi$
$54$	−5.18073	−	0.400036i	−0.705008	−	0.0544380i
$55$	0.331966	+	0.574981i	0.0447622	+	0.0775305i
$56$	0.895864	+	1.55168i	0.119715	+	0.207352i
$57$	5.92793	−	9.68420i	0.785173	−	1.28270i
$58$	3.03531	+	3.03531i	0.398555	+	0.398555i
$59$	−3.33959	−	3.33959i	−0.434777	−	0.434777i	0.455473	−	0.890250i	$-0.349470\pi$
$59$	−3.33959	−	3.33959i	−0.434777	−	0.434777i	−0.890250	+	0.455473i	$0.849470\pi$
$60$	−0.557194	−	1.02502i	−0.0719334	−	0.132329i
$61$	−2.38199	−	4.12572i	−0.304982	−	0.528245i	0.672275	−	0.740301i	$-0.265317\pi$
$61$	−2.38199	−	4.12572i	−0.304982	−	0.528245i	−0.977257	+	0.212057i	$0.931984\pi$
$62$	−2.89509	−	5.01445i	−0.367677	−	0.636835i
$63$	−1.65599	+	5.11374i	−0.208635	+	0.644270i
$64$			1.00000i			0.125000i
$65$	−0.369894	+	2.40029i	−0.0458797	+	0.297720i
$66$	1.23781	−	1.17580i	0.152364	−	0.144730i
$67$	10.6950	−	2.86571i	1.30660	−	0.350102i	0.462658	−	0.886537i	$-0.346896\pi$
$67$	10.6950	−	2.86571i	1.30660	−	0.350102i	0.843942	+	0.536434i	$0.180229\pi$
$68$	2.09485	+	1.20946i	0.254037	+	0.146669i
$69$	2.56311	+	10.6530i	0.308562	+	1.28247i
$70$	−1.16575	+	0.312361i	−0.139334	+	0.0373343i
$71$	−1.70900	−	6.37808i	−0.202821	−	0.756939i	−0.990103	−	0.140345i	$-0.955179\pi$
$71$	−1.70900	−	6.37808i	−0.202821	−	0.756939i	0.787281	−	0.616594i	$-0.211488\pi$
$72$	−2.22746	+	2.00959i	−0.262508	+	0.236832i
$73$	−8.01788	+	8.01788i	−0.938421	+	0.938421i	−0.998211	−	0.0597896i	$-0.980957\pi$
$73$	−8.01788	+	8.01788i	−0.938421	+	0.938421i	0.0597896	+	0.998211i	$0.480957\pi$
$74$	6.12445	−	3.53595i	0.711953	−	0.411046i
$75$	−7.65593	+	1.84201i	−0.884031	+	0.212697i
$76$	−1.69669	−	6.33213i	−0.194624	−	0.726346i
$77$	−0.883031	−	1.52946i	−0.100631	−	0.174298i
$78$	6.22339	−	0.519052i	0.704660	−	0.0587711i
$79$	−0.807117	+	1.39797i	−0.0908078	+	0.157284i	−0.907851	−	0.419292i	$-0.862278\pi$
$79$	−0.807117	+	1.39797i	−0.0908078	+	0.157284i	0.817043	+	0.576576i	$0.195612\pi$
$80$	−0.650628	−	0.174335i	−0.0727424	−	0.0194913i
$81$	−8.95253	−	0.923132i	−0.994726	−	0.102570i
$82$	4.30925	+	2.48795i	0.475877	+	0.274748i
$83$	−1.95885	−	7.31055i	−0.215012	−	0.802437i	−0.986162	−	0.165783i	$-0.946985\pi$
$83$	−1.95885	−	7.31055i	−0.215012	−	0.802437i	0.771150	−	0.636653i	$-0.219682\pi$
$84$	1.48214	+	2.72656i	0.161715	+	0.297492i
$85$	−1.15211	+	1.15211i	−0.124964	+	0.124964i
$86$	−0.230939	+	0.861875i	−0.0249028	+	0.0929384i
$87$	5.12054	+	5.39061i	0.548979	+	0.577934i
$88$		−	0.985676i		−	0.105073i
$89$	−0.440877	+	1.64537i	−0.0467329	+	0.174409i	−0.985348	−	0.170557i	$-0.945443\pi$
$89$	−0.440877	+	1.64537i	−0.0467329	+	0.174409i	0.938615	+	0.344967i	$0.112110\pi$
$90$	−0.919169	−	1.79959i	−0.0968889	−	0.189693i
$91$	0.983920	−	6.38480i	0.103143	−	0.669309i
$92$	5.47852	+	3.16302i	0.571175	+	0.329768i
$93$	−4.78971	−	8.81121i	−0.496670	−	0.913679i
$94$	−1.89651	+	3.28485i	−0.195610	+	0.338807i
$95$	4.41566			0.453037
$96$	−0.0444876	+	1.73148i	−0.00454049	+	0.176718i
$97$	−0.497183	+	1.85551i	−0.0504812	+	0.188399i	−0.986562	−	0.163386i	$-0.947758\pi$
$97$	−0.497183	+	1.85551i	−0.0504812	+	0.188399i	0.936081	+	0.351785i	$0.114425\pi$
$98$	−3.66058	+	0.980849i	−0.369774	+	0.0990807i
$99$	2.19555	−	1.98080i	0.220661	−	0.199078i
$100$	−2.27315	+	3.93720i	−0.227315	+	0.393720i
$101$	−14.8919			−1.48180			−0.740902	−	0.671613i	$-0.765602\pi$
$101$	−14.8919			−1.48180			−0.740902	+	0.671613i	$0.765602\pi$
$102$	3.57338	+	2.18735i	0.353817	+	0.216580i
$103$	9.08751	−	5.24668i	0.895419	−	0.516971i	0.0197081	−	0.999806i	$-0.493726\pi$
$103$	9.08751	−	5.24668i	0.895419	−	0.516971i	0.875711	+	0.482835i	$0.160393\pi$
$104$	2.25732	−	2.81150i	0.221348	−	0.275690i
$105$	−2.03237	+	0.488986i	−0.198339	+	0.0477202i
$106$	6.36406	+	6.36406i	0.618132	+	0.618132i
$107$	−1.87899	+	1.08484i	−0.181649	+	0.104875i	−0.588067	−	0.808812i	$-0.700111\pi$
$107$	−1.87899	+	1.08484i	−0.181649	+	0.104875i	0.406418	+	0.913687i	$0.366778\pi$
$108$	−3.94620	+	3.38046i	−0.379723	+	0.325285i
$109$	−8.28528	−	8.28528i	−0.793586	−	0.793586i	0.188489	−	0.982075i	$-0.439641\pi$
$109$	−8.28528	−	8.28528i	−0.793586	−	0.793586i	−0.982075	+	0.188489i	$0.939641\pi$
$110$	0.641308	+	0.171838i	0.0611463	+	0.0163841i
$111$	10.7617	−	5.84997i	1.02145	−	0.555254i
$112$	1.73068	+	0.463733i	0.163534	+	0.0438187i
$113$		−	11.0857i		−	1.04285i	−0.853296	−	0.521427i	$-0.825400\pi$
$113$		−	11.0857i		−	1.04285i	0.853296	−	0.521427i	$-0.174600\pi$
$114$	−2.65608	−	11.0394i	−0.248765	−	1.03394i
$115$	−3.01305	+	3.01305i	−0.280968	+	0.280968i
$116$	4.29257			0.398555
$117$	10.7988	−	0.621865i	0.998346	−	0.0574915i
$118$	−4.72289			−0.434777
$119$	3.06463	−	3.06463i	0.280934	−	0.280934i
$120$	−1.11879	−	0.330803i	−0.102131	−	0.0301980i
$121$		−	10.0284i		−	0.911677i
$122$	−4.60165	−	1.23301i	−0.416614	−	0.111631i
$123$	7.35070	+	4.49954i	0.662790	+	0.405710i
$124$	−5.59289	−	1.49861i	−0.502256	−	0.134579i
$125$	−4.54683	−	4.54683i	−0.406681	−	0.406681i
$126$	2.44500	+	4.78692i	0.217818	+	0.426453i
$127$	4.33197	−	2.50106i	0.384400	−	0.221933i	−0.295331	−	0.955395i	$-0.595430\pi$
$127$	4.33197	−	2.50106i	0.384400	−	0.221933i	0.679731	+	0.733462i	$0.262097\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.438208	+	1.48204i	−0.0385821	+	0.130487i
$130$	1.43571	+	1.95882i	0.125920	+	0.171800i
$131$	19.0361	−	10.9905i	1.66319	−	0.960242i	0.692010	−	0.721888i	$-0.256725\pi$
$131$	19.0361	−	10.9905i	1.66319	−	0.960242i	0.971178	−	0.238354i	$-0.0766080\pi$
$132$	0.0438503	−	1.70668i	0.00381668	−	0.148547i
$133$	−11.7457			−1.01848
$134$	5.53613	−	9.58886i	0.478249	−	0.828351i
$135$	−1.51146	−	3.15684i	−0.130086	−	0.271698i
$136$	2.33650	−	0.626062i	0.200353	−	0.0536844i
$137$	3.25829	−	12.1601i	0.278374	−	1.03891i	−0.675172	−	0.737660i	$-0.735931\pi$
$137$	3.25829	−	12.1601i	0.278374	−	1.03891i	0.953546	−	0.301246i	$-0.0974026\pi$
$138$	9.34522	+	5.72044i	0.795518	+	0.486956i
$139$	−19.6965			−1.67063			−0.835316	−	0.549770i	$-0.814715\pi$
$139$	−19.6965			−1.67063			−0.835316	+	0.549770i	$0.814715\pi$
$140$	−0.603436	+	1.04518i	−0.0509996	+	0.0883340i
$141$	−3.42991	+	5.60329i	−0.288850	+	0.471882i
$142$	−5.71843	−	3.30154i	−0.479880	−	0.277059i
$143$	−2.22498	+	2.77122i	−0.186062	+	0.231741i
$144$	−0.154059	+	2.99604i	−0.0128382	+	0.249670i
$145$	−0.748347	+	2.79287i	−0.0621468	+	0.231935i
$146$			11.3390i			0.938421i
$147$	−6.38185	+	1.53547i	−0.526366	+	0.126643i
$148$	1.83034	−	6.83094i	0.150453	−	0.561499i
$149$	−6.83755	+	6.83755i	−0.560154	+	0.560154i	−0.929351	−	0.369197i	$-0.879633\pi$
$149$	−6.83755	+	6.83755i	−0.560154	+	0.560154i	0.369197	+	0.929351i	$0.379633\pi$
$150$	−4.11106	+	6.71606i	−0.335667	+	0.548364i
$151$	−1.28698	−	4.80308i	−0.104733	−	0.390869i	0.893582	−	0.448900i	$-0.148184\pi$
$151$	−1.28698	−	4.80308i	−0.104733	−	0.390869i	−0.998315	+	0.0580316i	$0.981518\pi$
$152$	−5.67724	−	3.27775i	−0.460485	−	0.265861i
$153$	6.08992	+	3.94632i	0.492341	+	0.319041i
$154$	−1.70589	−	0.457091i	−0.137464	−	0.0368334i
$155$	1.95008	−	3.37763i	0.156634	−	0.271298i
$156$	4.03358	−	4.76763i	0.322945	−	0.381716i
$157$	−4.86181	−	8.42090i	−0.388015	−	0.672061i	0.604168	−	0.796857i	$-0.293506\pi$
$157$	−4.86181	−	8.42090i	−0.388015	−	0.672061i	−0.992182	+	0.124796i	$0.960172\pi$
$158$	0.417795	+	1.55923i	0.0332380	+	0.124046i
$159$	10.7361	+	11.3024i	0.851429	+	0.896335i
$160$	−0.583337	+	0.336790i	−0.0461169	+	0.0266256i
$161$	8.01474	−	8.01474i	0.631650	−	0.631650i
$162$	−6.98315	+	5.67764i	−0.548648	+	0.446078i
$163$	1.24717	+	4.65451i	0.0976861	+	0.364570i	0.997413	−	0.0718838i	$-0.0229011\pi$
$163$	1.24717	+	4.65451i	0.0976861	+	0.364570i	−0.899727	+	0.436453i	$0.856234\pi$
$164$	4.80634	−	1.28786i	0.375312	−	0.100565i
$165$	1.10277	+	0.326064i	0.0858503	+	0.0253841i
$166$	−6.55446	−	3.78422i	−0.508724	−	0.293712i
$167$	13.6676	−	3.66224i	1.05763	−	0.283392i	0.312231	−	0.950006i	$-0.398924\pi$
$167$	13.6676	−	3.66224i	1.05763	−	0.283392i	0.745403	+	0.666614i	$0.232257\pi$
$168$	2.97600	+	0.879938i	0.229603	+	0.0678887i
$169$	−12.6929	+	2.80903i	−0.976376	+	0.216079i
$170$			1.62934i			0.124964i
$171$	−4.10784	−	19.2327i	−0.314134	−	1.47076i
$172$	0.446139	+	0.772736i	0.0340178	+	0.0589206i
$173$	11.5989	+	20.0900i	0.881852	+	1.52741i	0.849280	+	0.527942i	$0.177036\pi$
$173$	11.5989	+	20.0900i	0.881852	+	1.52741i	0.0325714	+	0.999469i	$0.489630\pi$
$174$	7.43250	+	0.190966i	0.563456	+	0.0144771i
$175$	5.75989	+	5.75989i	0.435407	+	0.435407i
$176$	−0.696978	−	0.696978i	−0.0525367	−	0.0525367i
$177$	−8.17759	−	0.210110i	−0.614665	−	0.0157928i
$178$	0.851709	+	1.47520i	0.0638383	+	0.110571i
$179$	−2.78545	−	4.82455i	−0.208194	−	0.360603i	0.742951	−	0.669345i	$-0.233425\pi$
$179$	−2.78545	−	4.82455i	−0.208194	−	0.360603i	−0.951146	+	0.308742i	$0.900092\pi$
$180$	−1.92245	−	0.622551i	−0.143291	−	0.0464022i
$181$			20.8410i			1.54910i	0.632514	+	0.774549i	$0.282023\pi$
$181$			20.8410i			1.54910i	−0.632514	+	0.774549i	$0.717977\pi$
$182$	−3.81900	−	5.21047i	−0.283083	−	0.386226i
$183$	−7.91281	−	2.33964i	−0.584931	−	0.172951i
$184$	6.11049	−	1.63730i	0.450471	−	0.120703i
$185$	4.12531	+	2.38175i	0.303298	+	0.175109i
$186$	−9.61730	−	2.84363i	−0.705175	−	0.208505i
$187$	−2.30303	+	0.617094i	−0.168414	+	0.0451264i
$188$	0.981707	+	3.66378i	0.0715983	+	0.267209i
$189$	4.02050	+	8.39722i	0.292448	+	0.610808i
$190$	3.12234	−	3.12234i	0.226518	−	0.226518i
$191$	−15.6514	+	9.03635i	−1.13250	+	0.653847i	−0.944562	−	0.328334i	$-0.893513\pi$
$191$	−15.6514	+	9.03635i	−1.13250	+	0.653847i	−0.187935	+	0.982181i	$0.560179\pi$
$192$	1.19288	+	1.25580i	0.0860889	+	0.0906294i
$193$	1.90556	+	7.11166i	0.137165	+	0.511908i	0.999980	+	0.00638720i	$0.00203312\pi$
$193$	1.90556	+	7.11166i	0.137165	+	0.511908i	−0.862814	+	0.505521i	$0.831300\pi$
$194$	0.960483	+	1.66361i	0.0689587	+	0.119440i
$195$	2.39876	+	3.45552i	0.171779	+	0.247455i
$196$	−1.89486	+	3.28199i	−0.135347	+	0.234428i
$197$	23.6473	+	6.33628i	1.68480	+	0.451441i	0.969040	−	0.246904i	$-0.0794132\pi$
$197$	23.6473	+	6.33628i	1.68480	+	0.451441i	0.715761	+	0.698345i	$0.246080\pi$
$198$	0.151852	−	2.95313i	0.0107916	−	0.209869i
$199$	−6.97794	−	4.02871i	−0.494653	−	0.285588i	0.231850	−	0.972752i	$-0.425522\pi$
$199$	−6.97794	−	4.02871i	−0.494653	−	0.285588i	−0.726503	+	0.687164i	$0.758856\pi$
$200$	1.17667	+	4.39138i	0.0832029	+	0.310517i
$201$	10.0123	−	16.3566i	0.706212	−	1.15371i
$202$	−10.5302	+	10.5302i	−0.740902	+	0.740902i
$203$	1.99061	−	7.42905i	0.139713	−	0.521417i
$204$	4.07345	−	0.980069i	0.285198	−	0.0686186i
$205$			3.35166i			0.234090i
$206$	2.71588	−	10.1358i	0.189224	−	0.706195i
$207$	15.9266	+	10.3206i	1.10697	+	0.717329i
$208$	−0.391864	−	3.58419i	−0.0271709	−	0.248519i
$209$	5.59591	+	3.23080i	0.387077	+	0.223479i
$210$	−1.09133	+	1.78287i	−0.0753092	+	0.123029i
$211$	7.04091	−	12.1952i	0.484716	−	0.839553i	−0.515130	−	0.857112i	$-0.672256\pi$
$211$	7.04091	−	12.1952i	0.484716	−	0.839553i	0.999846	+	0.0175594i	$0.00558961\pi$
$212$	9.00014			0.618132
$213$	−9.75447	−	5.97094i	−0.668365	−	0.409122i
$214$	−0.561553	+	2.09574i	−0.0383870	+	0.143262i
$215$	−0.580542	+	0.155556i	−0.0395926	+	0.0106088i
$216$	−0.400036	+	5.18073i	−0.0272190	+	0.352504i
$217$	−5.18722	+	8.98452i	−0.352131	+	0.609909i
$218$	−11.7172			−0.793586
$219$	−0.504444	+	19.6332i	−0.0340872	+	1.32669i
$220$	0.574981	−	0.331966i	0.0387652	−	0.0223811i
$221$	−7.98227	−	3.51404i	−0.536946	−	0.236380i
$222$	3.47309	−	11.7462i	0.233099	−	0.788353i
$223$	16.7879	+	16.7879i	1.12420	+	1.12420i	0.991103	+	0.133096i	$0.0424918\pi$
$223$	16.7879	+	16.7879i	1.12420	+	1.12420i	0.133096	+	0.991103i	$0.457508\pi$
$224$	1.55168	−	0.895864i	0.103676	−	0.0598574i
$225$	−7.41700	+	11.4458i	−0.494466	+	0.763055i
$226$	−7.83876	−	7.83876i	−0.521427	−	0.521427i
$227$	−23.1257	−	6.19651i	−1.53491	−	0.411277i	−0.610291	−	0.792178i	$-0.708947\pi$
$227$	−23.1257	−	6.19651i	−1.53491	−	0.411277i	−0.924616	+	0.380901i	$0.875614\pi$
$228$	−9.68420	−	5.92793i	−0.641352	−	0.392587i
$229$	−19.8362	−	5.31509i	−1.31081	−	0.351231i	−0.465284	−	0.885161i	$-0.654048\pi$
$229$	−19.8362	−	5.31509i	−1.31081	−	0.351231i	−0.845529	+	0.533930i	$0.820714\pi$
$230$			4.26110i			0.280968i
$231$	−2.93337	−	0.867334i	−0.193002	−	0.0570664i
$232$	3.03531	−	3.03531i	0.199278	−	0.199278i
$233$	2.79071			0.182825			0.0914126	−	0.995813i	$-0.470862\pi$
$233$	2.79071			0.182825			0.0914126	+	0.995813i	$0.470862\pi$
$234$	7.19615	−	8.07560i	0.470427	−	0.527919i
$235$	−2.55490			−0.166664
$236$	−3.33959	+	3.33959i	−0.217389	+	0.217389i
$237$	0.654036	+	2.71836i	0.0424842	+	0.176577i
$238$		−	4.33405i		−	0.280934i
$239$	7.58852	+	2.03334i	0.490861	+	0.131526i	0.495755	−	0.868462i	$-0.334891\pi$
$239$	7.58852	+	2.03334i	0.490861	+	0.131526i	−0.00489453	+	0.999988i	$0.501558\pi$
$240$	−1.02502	+	0.557194i	−0.0661647	+	0.0359667i
$241$	22.4869	+	6.02534i	1.44851	+	0.388126i	0.895504	−	0.445054i	$-0.146815\pi$
$241$	22.4869	+	6.02534i	1.44851	+	0.388126i	0.553002	+	0.833180i	$0.313482\pi$
$242$	−7.09118	−	7.09118i	−0.455838	−	0.455838i
$243$	−12.3438	+	9.52006i	−0.791853	+	0.610712i
$244$	−4.12572	+	2.38199i	−0.264122	+	0.152491i
$245$	−1.80501	−	1.80501i	−0.115318	−	0.115318i
$246$	8.37938	−	2.01607i	0.534250	−	0.128540i
$247$	8.56260	+	22.0307i	0.544825	+	1.40178i
$248$	−5.01445	+	2.89509i	−0.318418	+	0.183839i
$249$	−11.1806	−	6.84388i	−0.708539	−	0.433714i
$250$	−6.43019			−0.406681
$251$	−13.0241	+	22.5583i	−0.822071	+	1.42387i	0.0820668	+	0.996627i	$0.473848\pi$
$251$	−13.0241	+	22.5583i	−0.822071	+	1.42387i	−0.904138	+	0.427241i	$0.859485\pi$
$252$	5.11374	+	1.65599i	0.322135	+	0.104318i
$253$	−6.02296	+	1.61385i	−0.378660	+	0.101462i
$254$	1.29465	−	4.83168i	0.0812333	−	0.303167i
$255$	−0.0724851	+	2.82116i	−0.00453920	+	0.176668i
$256$	1.00000			0.0625000
$257$	−3.60078	+	6.23673i	−0.224610	+	0.389036i	−0.956202	−	0.292706i	$-0.905444\pi$
$257$	−3.60078	+	6.23673i	−0.224610	+	0.389036i	0.731592	+	0.681743i	$0.238778\pi$
$258$	0.738104	+	1.35782i	0.0459523	+	0.0845344i
$259$	−10.9733	−	6.33546i	−0.681851	−	0.393667i
$260$	2.40029	+	0.369894i	0.148860	+	0.0229398i
$261$	12.8607	+	0.661308i	0.796059	+	0.0409339i
$262$	5.68909	−	21.2320i	0.351473	−	1.31172i
$263$			11.4549i			0.706342i	0.935559	+	0.353171i	$0.114897\pi$
$263$			11.4549i			0.706342i	−0.935559	+	0.353171i	$0.885103\pi$
$264$	−1.17580	−	1.23781i	−0.0723652	−	0.0761819i
$265$	−1.56904	+	5.85574i	−0.0963855	+	0.359715i
$266$	−8.30546	+	8.30546i	−0.509240	+	0.509240i
$267$	1.40909	+	2.59217i	0.0862348	+	0.158638i
$268$	−2.86571	−	10.6950i	−0.175051	−	0.653300i
$269$	21.7795	+	12.5744i	1.32792	+	0.766674i	0.984977	−	0.172683i	$-0.0552437\pi$
$269$	21.7795	+	12.5744i	1.32792	+	0.766674i	0.342941	+	0.939357i	$0.388577\pi$
$270$	−3.30099	−	1.16346i	−0.200892	−	0.0708058i
$271$	6.17248	+	1.65391i	0.374952	+	0.100468i	0.441373	−	0.897324i	$-0.354492\pi$
$271$	6.17248	+	1.65391i	0.374952	+	0.100468i	−0.0664215	+	0.997792i	$0.521158\pi$
$272$	1.20946	−	2.09485i	0.0733343	−	0.127019i
$273$	−6.38072	−	9.19172i	−0.386178	−	0.556308i
$274$	−6.29452	−	10.9024i	−0.380266	−	0.658640i
$275$	−1.15981	−	4.32848i	−0.0699393	−	0.261017i
$276$	10.6530	−	2.56311i	0.641237	−	0.154281i
$277$	16.8380	−	9.72143i	1.01170	−	0.584104i	0.100010	−	0.994986i	$-0.468113\pi$
$277$	16.8380	−	9.72143i	1.01170	−	0.584104i	0.911688	+	0.410882i	$0.134779\pi$
$278$	−13.9275	+	13.9275i	−0.835316	+	0.835316i
$279$	−16.5257	−	5.35153i	−0.989365	−	0.320388i
$280$	0.312361	+	1.16575i	0.0186672	+	0.0696668i
$281$	28.7919	−	7.71478i	1.71758	−	0.460225i	0.740320	−	0.672255i	$-0.234674\pi$
$281$	28.7919	−	7.71478i	1.71758	−	0.460225i	0.977263	+	0.212030i	$0.0680074\pi$
$282$	1.53681	+	6.38743i	0.0915158	+	0.380366i
$283$	19.1183	+	11.0380i	1.13647	+	0.656139i	0.945553	−	0.325467i	$-0.105522\pi$
$283$	19.1183	+	11.0380i	1.13647	+	0.656139i	0.190914	+	0.981607i	$0.438855\pi$
$284$	−6.37808	+	1.70900i	−0.378470	+	0.101411i
$285$	5.54518	−	5.26736i	0.328468	−	0.312012i
$286$	0.386251	+	3.53285i	0.0228395	+	0.208902i
$287$		−	8.91545i		−	0.526262i
$288$	2.00959	+	2.22746i	0.118416	+	0.131254i
$289$	5.57442	+	9.65517i	0.327907	+	0.567951i
$290$	1.44570	+	2.50402i	0.0848941	+	0.147041i
$291$	1.58905	+	2.92323i	0.0931516	+	0.171363i
$292$	8.01788	+	8.01788i	0.469211	+	0.469211i
$293$	−6.70889	−	6.70889i	−0.391938	−	0.391938i	0.483440	−	0.875378i	$-0.339387\pi$
$293$	−6.70889	−	6.70889i	−0.391938	−	0.391938i	−0.875378	+	0.483440i	$0.839387\pi$
$294$	−3.42691	+	5.59839i	−0.199861	+	0.326505i
$295$	−1.59062	−	2.75504i	−0.0926096	−	0.160404i
$296$	−3.53595	−	6.12445i	−0.205523	−	0.355976i
$297$	0.394306	−	5.10652i	0.0228799	−	0.296310i
$298$			9.66976i			0.560154i
$299$	−20.8755	−	9.19005i	−1.20726	−	0.531475i
$300$	1.84201	+	7.65593i	0.106349	+	0.442015i
$301$	1.54425	−	0.413779i	0.0890088	−	0.0238498i
$302$	−4.30632	−	2.48626i	−0.247801	−	0.143068i
$303$	−18.7013	+	17.7643i	−1.07436	+	1.02054i
$304$	−6.33213	+	1.69669i	−0.363173	+	0.0973119i
$305$	−0.830529	−	3.09958i	−0.0475560	−	0.177481i
$306$	7.09669	−	1.51575i	0.405691	−	0.0866498i
$307$	3.35703	−	3.35703i	0.191596	−	0.191596i	−0.604790	−	0.796385i	$-0.706743\pi$
$307$	3.35703	−	3.35703i	0.191596	−	0.191596i	0.796385	+	0.604790i	$0.206743\pi$
$308$	−1.52946	+	0.883031i	−0.0871488	+	0.0503154i
$309$	5.15341	−	17.4291i	0.293167	−	0.991508i
$310$	−1.00943	−	3.76726i	−0.0573320	−	0.213966i
$311$	−10.5634	−	18.2964i	−0.598996	−	1.03749i	−0.992970	−	0.118370i	$-0.962233\pi$
$311$	−10.5634	−	18.2964i	−0.598996	−	1.03749i	0.393973	−	0.919122i	$-0.371100\pi$
$312$	−0.519052	−	6.22339i	−0.0293856	−	0.352330i
$313$	−5.16590	+	8.94760i	−0.291994	+	0.505748i	−0.974281	−	0.225336i	$-0.927652\pi$
$313$	−5.16590	+	8.94760i	−0.291994	+	0.505748i	0.682287	+	0.731084i	$0.260985\pi$
$314$	−9.39229	−	2.51666i	−0.530038	−	0.142023i
$315$	−1.96894	+	3.03844i	−0.110937	+	0.171197i
$316$	1.39797	+	0.807117i	0.0786419	+	0.0454039i
$317$	−4.33708	−	16.1862i	−0.243595	−	0.909108i	−0.974084	−	0.226185i	$-0.927375\pi$
$317$	−4.33708	−	16.1862i	−0.243595	−	0.909108i	0.730490	−	0.682924i	$-0.239292\pi$
$318$	15.5836	+	0.400394i	0.873882	+	0.0224530i
$319$	−2.99183	+	2.99183i	−0.167510	+	0.167510i
$320$	−0.174335	+	0.650628i	−0.00974564	+	0.0363712i
$321$	−1.06555	+	3.60376i	−0.0594733	+	0.201142i
$322$		−	11.3346i		−	0.631650i
$323$	−4.10416	+	15.3169i	−0.228361	+	0.852256i
$324$	−0.923132	+	8.95253i	−0.0512851	+	0.497363i
$325$	6.60454	−	15.0025i	0.366354	−	0.832187i
$326$	4.17312	+	2.40935i	0.231128	+	0.133442i
$327$	−20.2880	−	0.521267i	−1.12193	−	0.0288262i
$328$	2.48795	−	4.30925i	0.137374	−	0.237939i
$329$	6.79607			0.374679
$330$	1.01034	−	0.549212i	0.0556172	−	0.0302331i
$331$	3.81878	−	14.2519i	0.209899	−	0.783354i	−0.778001	−	0.628263i	$-0.783766\pi$
$331$	3.81878	−	14.2519i	0.209899	−	0.783354i	0.987900	−	0.155091i	$-0.0495671\pi$
$332$	−7.31055	+	1.95885i	−0.401218	+	0.107506i
$333$	6.53615	−	20.1838i	0.358179	−	1.10606i
$334$	7.07490	−	12.2541i	0.387121	−	0.670513i
$335$	7.45805			0.407477
$336$	2.72656	−	1.48214i	0.148746	−	0.0808573i
$337$	3.36489	−	1.94272i	0.183297	−	0.105827i	−0.405544	−	0.914076i	$-0.632918\pi$
$337$	3.36489	−	1.94272i	0.183297	−	0.105827i	0.588841	+	0.808249i	$0.299584\pi$
$338$	−6.98894	+	10.9615i	−0.380148	+	0.596228i
$339$	−13.2239	−	13.9214i	−0.718225	−	0.756106i
$340$	1.15211	+	1.15211i	0.0624822	+	0.0624822i
$341$	4.94262	−	2.85362i	0.267658	−	0.154532i
$342$	−16.5043	−	10.6949i	−0.892449	−	0.578315i
$343$	13.6699	+	13.6699i	0.738108	+	0.738108i
$344$	0.861875	+	0.230939i	0.0464692	+	0.0124514i
$345$	−0.189566	+	7.37800i	−0.0102059	+	0.397218i
$346$	22.4074	+	6.00406i	1.20463	+	0.322780i
$347$		−	32.3179i		−	1.73492i	−0.497510	−	0.867459i	$-0.665752\pi$
$347$		−	32.3179i		−	1.73492i	0.497510	−	0.867459i	$-0.334248\pi$
$348$	5.39061	−	5.12054i	0.288967	−	0.274490i
$349$	13.4101	−	13.4101i	0.717828	−	0.717828i	−0.250332	−	0.968160i	$-0.580540\pi$
$349$	13.4101	−	13.4101i	0.717828	−	0.717828i	0.968160	+	0.250332i	$0.0805399\pi$
$350$	8.14572			0.435407
$351$	12.8193	−	13.6626i	0.684241	−	0.729256i
$352$	−0.985676			−0.0525367
$353$	−13.8574	+	13.8574i	−0.737554	+	0.737554i	−0.972104	−	0.234550i	$-0.924638\pi$
$353$	−13.8574	+	13.8574i	−0.737554	+	0.737554i	0.234550	+	0.972104i	$0.424638\pi$
$354$	−5.93100	+	5.63386i	−0.315229	+	0.299436i
$355$		−	4.44770i		−	0.236059i
$356$	1.64537	+	0.440877i	0.0872047	+	0.0233664i
$357$	0.192811	−	7.50431i	0.0102046	−	0.397170i
$358$	−5.38108	−	1.44186i	−0.284399	−	0.0762045i
$359$	19.2085	+	19.2085i	1.01379	+	1.01379i	0.999904	+	0.0138835i	$0.00441940\pi$
$359$	19.2085	+	19.2085i	1.01379	+	1.01379i	0.0138835	+	0.999904i	$0.495581\pi$
$360$	−1.79959	+	0.919169i	−0.0948466	+	0.0484444i
$361$	20.7627	−	11.9873i	1.09277	−	0.630913i
$362$	14.7368	+	14.7368i	0.774549	+	0.774549i
$363$	−11.9628	−	12.5937i	−0.627882	−	0.660998i
$364$	−6.38480	−	0.983920i	−0.334654	−	0.0515714i
$365$	−6.61445	+	3.81886i	−0.346216	+	0.199888i
$366$	−7.24958	+	3.94082i	−0.378941	+	0.205990i
$367$	7.69429			0.401639			0.200819	−	0.979628i	$-0.435640\pi$
$367$	7.69429			0.401639			0.200819	+	0.979628i	$0.435640\pi$
$368$	3.16302	−	5.47852i	0.164884	−	0.285587i
$369$	14.5984	−	3.11801i	0.759963	−	0.162317i
$370$	4.60118	−	1.23288i	0.239204	−	0.0640945i
$371$	4.17366	−	15.5763i	0.216686	−	0.808683i
$372$	−8.81121	+	4.78971i	−0.456840	+	0.248335i
$373$	−16.0980			−0.833521			−0.416760	−	0.909016i	$-0.636835\pi$
$373$	−16.0980			−0.833521			−0.416760	+	0.909016i	$0.636835\pi$
$374$	−1.19213	+	2.06484i	−0.0616438	+	0.106770i
$375$	−11.1337	−	0.286063i	−0.574944	−	0.0147722i
$376$	3.28485	+	1.89651i	0.169403	+	0.0978051i
$377$	−15.3854	+	1.68210i	−0.792389	+	0.0866328i
$378$	8.78066	+	3.09481i	0.451628	+	0.159180i
$379$	6.71919	−	25.0764i	0.345142	−	1.28809i	−0.547305	−	0.836933i	$-0.684346\pi$
$379$	6.71919	−	25.0764i	0.345142	−	1.28809i	0.892446	−	0.451153i	$-0.148987\pi$
$380$		−	4.41566i		−	0.226518i
$381$	2.45660	−	8.30836i	0.125856	−	0.425650i
$382$	−4.67756	+	17.4569i	−0.239325	+	0.893172i
$383$	−22.2443	+	22.2443i	−1.13663	+	1.13663i	−0.147581	+	0.989050i	$0.547149\pi$
$383$	−22.2443	+	22.2443i	−1.13663	+	1.13663i	−0.989050	+	0.147581i	$0.952851\pi$
$384$	1.73148	+	0.0444876i	0.0883592	+	0.00227025i
$385$	−0.307887	−	1.14905i	−0.0156914	−	0.0585610i
$386$	6.37614	+	3.68127i	0.324537	+	0.187372i
$387$	1.21761	+	2.38388i	0.0618944	+	0.121179i
$388$	1.85551	+	0.497183i	0.0941993	+	0.0252406i
$389$	12.6984	−	21.9943i	0.643836	−	1.11516i	−0.340733	−	0.940160i	$-0.610675\pi$
$389$	12.6984	−	21.9943i	0.643836	−	1.11516i	0.984569	−	0.174997i	$-0.0559915\pi$
$390$	4.13960	+	0.747246i	0.209617	+	0.0378383i
$391$	−7.65110	−	13.2521i	−0.386933	−	0.670187i
$392$	0.980849	+	3.66058i	0.0495404	+	0.184887i
$393$	10.7951	−	36.5096i	0.544541	−	1.84167i
$394$	21.2016	−	12.2407i	1.06812	−	0.616680i
$395$	−0.768848	+	0.768848i	−0.0386850	+	0.0386850i
$396$	−1.98080	−	2.19555i	−0.0995389	−	0.110331i
$397$	0.337126	+	1.25817i	0.0169199	+	0.0631458i	0.973870	−	0.227108i	$-0.0729270\pi$
$397$	0.337126	+	1.25817i	0.0169199	+	0.0631458i	−0.956950	+	0.290254i	$0.906260\pi$
$398$	−7.78288	+	2.08542i	−0.390120	+	0.104532i
$399$	−14.7502	+	14.0112i	−0.738434	+	0.701439i
$400$	3.93720	+	2.27315i	0.196860	+	0.113657i
$401$	1.38859	−	0.372073i	0.0693431	−	0.0185804i	−0.223981	−	0.974594i	$-0.571905\pi$
$401$	1.38859	−	0.372073i	0.0693431	−	0.0185804i	0.293324	+	0.956013i	$0.405239\pi$
$402$	−4.48613	−	18.6456i	−0.223748	−	0.929960i
$403$	20.6332	+	3.17966i	1.02782	+	0.158390i
$404$			14.8919i			0.740902i
$405$	−5.66383	−	2.16136i	−0.281438	−	0.107399i
$406$	−3.84556	−	6.66071i	−0.190852	−	0.330565i
$407$	3.48530	+	6.03672i	0.172760	+	0.299229i
$408$	2.18735	−	3.57338i	0.108290	−	0.176908i
$409$	16.2435	+	16.2435i	0.803189	+	0.803189i	0.983593	−	0.180404i	$-0.0577405\pi$
$409$	16.2435	+	16.2435i	0.803189	+	0.803189i	−0.180404	+	0.983593i	$0.557741\pi$
$410$	2.36998	+	2.36998i	0.117045	+	0.117045i
$411$	−10.4138	−	19.1574i	−0.513676	−	0.944963i
$412$	−5.24668	−	9.08751i	−0.258485	−	0.447710i
$413$	4.23107	+	7.32842i	0.208197	+	0.360608i
$414$	18.5595	−	3.96405i	0.912151	−	0.194822i
$415$		−	5.09794i		−	0.250248i
$416$	−2.81150	−	2.25732i	−0.137845	−	0.110674i
$417$	−24.7348	+	23.4956i	−1.21127	+	1.15058i
$418$	6.24143	−	1.67239i	0.305278	−	0.0817991i
$419$	−5.72052	−	3.30274i	−0.279466	−	0.161350i	0.353716	−	0.935353i	$-0.384918\pi$
$419$	−5.72052	−	3.30274i	−0.279466	−	0.161350i	−0.633182	+	0.774003i	$0.718251\pi$
$420$	0.488986	+	2.03237i	0.0238601	+	0.0991693i
$421$	9.08681	−	2.43480i	0.442864	−	0.118665i	−0.0304944	−	0.999535i	$-0.509708\pi$
$421$	9.08681	−	2.43480i	0.442864	−	0.118665i	0.473359	+	0.880870i	$0.343042\pi$
$422$	−3.64464	−	13.6020i	−0.177418	−	0.662134i
$423$	2.37680	+	11.1281i	0.115564	+	0.541066i
$424$	6.36406	−	6.36406i	0.309066	−	0.309066i
$425$	9.52378	−	5.49855i	0.461971	−	0.266719i
$426$	−11.1195	+	2.67536i	−0.538744	+	0.129621i
$427$	2.20921	+	8.24490i	0.106911	+	0.398999i
$428$	1.08484	+	1.87899i	0.0524376	+	0.0908246i
$429$	0.511617	+	6.13424i	0.0247011	+	0.296164i
$430$	−0.300510	+	0.520499i	−0.0144919	+	0.0251007i
$431$	−1.92865	−	0.516780i	−0.0928998	−	0.0248924i	0.212070	−	0.977255i	$-0.431980\pi$
$431$	−1.92865	−	0.516780i	−0.0928998	−	0.0248924i	−0.304970	+	0.952362i	$0.598646\pi$
$432$	3.38046	+	3.94620i	0.162643	+	0.189862i
$433$	−27.7623	−	16.0286i	−1.33417	−	0.770285i	−0.348236	−	0.937407i	$-0.613219\pi$
$433$	−27.7623	−	16.0286i	−1.33417	−	0.770285i	−0.985936	+	0.167122i	$0.946553\pi$
$434$	2.68510	+	10.0209i	0.128889	+	0.481020i
$435$	2.39179	+	4.39997i	0.114678	+	0.210962i
$436$	−8.28528	+	8.28528i	−0.396793	+	0.396793i
$437$	−10.7333	+	40.0574i	−0.513445	+	1.91620i
$438$	13.5261	+	14.2395i	0.646302	+	0.680389i
$439$			26.1293i			1.24708i	0.781790	+	0.623542i	$0.214307\pi$
$439$			26.1293i			1.24708i	−0.781790	+	0.623542i	$0.785693\pi$
$440$	0.171838	−	0.641308i	0.00819206	−	0.0305732i
$441$	−6.18268	+	9.54105i	−0.294414	+	0.454336i
$442$	−8.12912	+	3.15952i	−0.386663	+	0.150283i
$443$	9.85727	+	5.69110i	0.468333	+	0.270392i	0.715542	−	0.698570i	$-0.246180\pi$
$443$	9.85727	+	5.69110i	0.468333	+	0.270392i	−0.247209	+	0.968962i	$0.579513\pi$
$444$	−5.84997	−	10.7617i	−0.277627	−	0.510726i
$445$	−0.573694	+	0.993667i	−0.0271957	+	0.0471043i
$446$	23.7416			1.12420
$447$	−0.430184	+	16.7430i	−0.0203470	+	0.791916i
$448$	0.463733	−	1.73068i	0.0219093	−	0.0817668i
$449$	13.3760	−	3.58409i	0.631253	−	0.169144i	0.0710148	−	0.997475i	$-0.477376\pi$
$449$	13.3760	−	3.58409i	0.631253	−	0.169144i	0.560238	+	0.828331i	$0.310710\pi$
$450$	2.84881	+	13.3380i	0.134294	+	0.628761i
$451$	−2.45231	+	4.24752i	−0.115475	+	0.200008i
$452$	−11.0857			−0.521427
$453$	−7.34570	−	4.49648i	−0.345131	−	0.211263i
$454$	−20.7339	+	11.9707i	−0.973092	+	0.561815i
$455$	1.75326	−	3.98260i	0.0821942	−	0.186707i
$456$	−11.0394	+	2.65608i	−0.516969	+	0.124382i
$457$	23.8139	+	23.8139i	1.11397	+	1.11397i	0.992609	+	0.121357i	$0.0387244\pi$
$457$	23.8139	+	23.8139i	1.11397	+	1.11397i	0.121357	+	0.992609i	$0.461276\pi$
$458$	−17.7846	+	10.2680i	−0.831022	+	0.479791i
$459$	12.3552	−	2.30878i	0.576692	−	0.107765i
$460$	3.01305	+	3.01305i	0.140484	+	0.140484i
$461$	8.68738	+	2.32778i	0.404612	+	0.108415i	0.455385	−	0.890295i	$-0.349502\pi$
$461$	8.68738	+	2.32778i	0.404612	+	0.108415i	−0.0507728	+	0.998710i	$0.516168\pi$
$462$	−2.68750	+	1.46091i	−0.125034	+	0.0679676i
$463$	−18.3164	−	4.90786i	−0.851234	−	0.228087i	−0.193278	−	0.981144i	$-0.561912\pi$
$463$	−18.3164	−	4.90786i	−0.851234	−	0.228087i	−0.657956	+	0.753057i	$0.728579\pi$
$464$		−	4.29257i		−	0.199278i
$465$	−1.58022	−	6.56783i	−0.0732808	−	0.304576i
$466$	1.97333	−	1.97333i	0.0914126	−	0.0914126i
$467$	−33.1417			−1.53362			−0.766808	−	0.641877i	$-0.778156\pi$
$467$	−33.1417			−1.53362			−0.766808	+	0.641877i	$0.778156\pi$
$468$	−0.621865	−	10.7988i	−0.0287457	−	0.499173i
$469$	−19.8385			−0.916056
$470$	−1.80659	+	1.80659i	−0.0833318	+	0.0833318i
$471$	−16.1506	−	4.77538i	−0.744180	−	0.220038i
$472$			4.72289i			0.217389i
$473$	−0.849529	−	0.227631i	−0.0390614	−	0.0104665i
$474$	2.38465	+	1.45970i	0.109530	+	0.0670462i
$475$	−28.7877	−	7.71365i	−1.32087	−	0.353926i
$476$	−3.06463	−	3.06463i	−0.140467	−	0.140467i
$477$	26.9648	+	1.38655i	1.23463	+	0.0634857i
$478$	6.80368	−	3.92811i	0.311193	−	0.179667i
$479$	−21.8028	−	21.8028i	−0.996195	−	0.996195i	0.00379781	−	0.999993i	$-0.498791\pi$
$479$	−21.8028	−	21.8028i	−0.996195	−	0.996195i	−0.999993	+	0.00379781i	$0.998791\pi$
$480$	−0.330803	+	1.11879i	−0.0150990	+	0.0510657i
$481$	−3.88351	+	25.2006i	−0.177073	+	1.14905i
$482$	20.1612	−	11.6401i	0.918316	−	0.530190i
$483$	0.504247	−	19.6255i	0.0229440	−	0.892993i
$484$	−10.0284			−0.455838
$485$	−0.646962	+	1.12057i	−0.0293770	+	0.0508825i
$486$	−1.99666	+	15.4601i	−0.0905703	+	0.701282i
$487$	−19.5417	+	5.23619i	−0.885520	+	0.237274i	−0.672787	−	0.739836i	$-0.734903\pi$
$487$	−19.5417	+	5.23619i	−0.885520	+	0.237274i	−0.212733	+	0.977110i	$0.568236\pi$
$488$	−1.23301	+	4.60165i	−0.0558156	+	0.208307i
$489$	7.11849	+	4.35740i	0.321909	+	0.197048i
$490$	−2.55267			−0.115318
$491$	−7.55120	+	13.0791i	−0.340781	+	0.590250i	−0.984578	−	0.174946i	$-0.944025\pi$
$491$	−7.55120	+	13.0791i	−0.340781	+	0.590250i	0.643797	+	0.765196i	$0.277358\pi$
$492$	4.49954	−	7.35070i	0.202855	−	0.331395i
$493$	−8.99228	−	5.19169i	−0.404992	−	0.233822i
$494$	21.6327	+	9.52340i	0.973303	+	0.428478i
$495$	1.77381	−	0.906002i	0.0797268	−	0.0407218i
$496$	−1.49861	+	5.59289i	−0.0672896	+	0.251128i
$497$			11.8309i			0.530689i
$498$	−12.7452	+	3.06649i	−0.571126	+	0.137413i
$499$	−10.8485	+	40.4871i	−0.485645	+	1.81245i	0.0914956	+	0.995805i	$0.470835\pi$
$499$	−10.8485	+	40.4871i	−0.485645	+	1.81245i	−0.577140	+	0.816645i	$0.695831\pi$
$500$	−4.54683	+	4.54683i	−0.203340	+	0.203340i
$501$	12.7952	−	20.9029i	0.571647	−	0.933875i
$502$	6.74174	+	25.1605i	0.300899	+	1.12297i
$503$	−10.9025	−	6.29458i	−0.486120	−	0.280661i	0.236843	−	0.971548i	$-0.423887\pi$
$503$	−10.9025	−	6.29458i	−0.486120	−	0.280661i	−0.722963	+	0.690886i	$0.757220\pi$
$504$	4.78692	−	2.44500i	0.213226	−	0.108909i
$505$	−9.68912	−	2.59619i	−0.431160	−	0.115529i
$506$	−3.11771	+	5.40004i	−0.138599	+	0.240061i
$507$	−12.5889	+	18.6687i	−0.559091	+	0.829107i
$508$	−2.50106	−	4.33197i	−0.110967	−	0.192200i
$509$	8.59675	+	32.0835i	0.381044	+	1.42208i	0.844309	+	0.535857i	$0.180011\pi$
$509$	8.59675	+	32.0835i	0.381044	+	1.42208i	−0.463264	+	0.886220i	$0.653322\pi$
$510$	1.94361	+	2.04612i	0.0860644	+	0.0906035i
$511$	17.5945	−	10.1582i	0.778335	−	0.449372i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−28.1010	−	19.2523i	−1.24069	−	0.850008i
$514$	1.86390	+	6.95616i	0.0822130	+	0.306823i
$515$	6.82727	−	1.82936i	0.300846	−	0.0806113i
$516$	1.48204	+	0.438208i	0.0652434	+	0.0192910i
$517$	−3.23780	−	1.86935i	−0.142398	−	0.0822137i
$518$	−12.2392	+	3.27948i	−0.537759	+	0.144092i
$519$	38.5309	+	11.3928i	1.69132	+	0.500086i
$520$	1.95882	−	1.43571i	0.0858998	−	0.0629600i
$521$		−	17.5549i		−	0.769094i	−0.923105	−	0.384547i	$-0.874358\pi$
$521$		−	17.5549i		−	0.769094i	0.923105	−	0.384547i	$-0.125642\pi$
$522$	9.56152	−	8.62629i	0.418496	−	0.377563i
$523$	−4.19432	−	7.26477i	−0.183405	−	0.317666i	0.759633	−	0.650352i	$-0.225379\pi$
$523$	−4.19432	−	7.26477i	−0.183405	−	0.317666i	−0.943038	+	0.332686i	$0.892045\pi$
$524$	−10.9905	−	19.0361i	−0.480121	−	0.831594i
$525$	14.1041	+	0.362383i	0.615555	+	0.0158157i
$526$	8.09986	+	8.09986i	0.353171	+	0.353171i
$527$	9.90373	+	9.90373i	0.431413	+	0.431413i
$528$	−1.70668	−	0.0438503i	−0.0742736	−	0.00190834i
$529$	−8.50943	−	14.7388i	−0.369975	−	0.640816i
$530$	3.03116	+	5.25012i	0.131665	+	0.228050i
$531$	−10.5200	+	9.49105i	−0.456531	+	0.411876i
$532$			11.7457i			0.509240i
$533$	−16.7222	+	6.49936i	−0.724319	+	0.281518i
$534$	2.82932	+	0.836568i	0.122437	+	0.0362018i
$535$	−1.41165	+	0.378251i	−0.0610310	+	0.0163532i
$536$	−9.58886	−	5.53613i	−0.414176	−	0.239124i
$537$	−9.25309	−	2.73594i	−0.399300	−	0.118064i
$538$	24.2918	−	6.50898i	1.04730	−	0.280622i
$539$	−0.966799	−	3.60814i	−0.0416430	−	0.155414i
$540$	−3.15684	+	1.51146i	−0.135849	+	0.0650430i
$541$	1.43745	−	1.43745i	0.0618007	−	0.0618007i	−0.675531	−	0.737332i	$-0.736086\pi$
$541$	1.43745	−	1.43745i	0.0618007	−	0.0618007i	0.737332	+	0.675531i	$0.236086\pi$
$542$	5.53410	−	3.19511i	0.237710	−	0.137242i
$543$	24.8608	+	26.1721i	1.06688	+	1.12315i
$544$	−0.626062	−	2.33650i	−0.0268422	−	0.100176i
$545$	−3.94622	−	6.83505i	−0.169037	−	0.292781i
$546$	−11.0114	−	1.98768i	−0.471243	−	0.0850649i
$547$	5.93332	−	10.2768i	0.253691	−	0.439405i	−0.710848	−	0.703345i	$-0.751689\pi$
$547$	5.93332	−	10.2768i	0.253691	−	0.439405i	0.964539	+	0.263940i	$0.0850222\pi$
$548$	−12.1601	−	3.25829i	−0.519453	−	0.139187i
$549$	−12.7278	+	6.50093i	−0.543210	+	0.277453i
$550$	−3.88080	−	2.24058i	−0.165478	−	0.0955388i
$551$	7.28317	+	27.1811i	0.310273	+	1.15796i
$552$	5.72044	−	9.34522i	0.243478	−	0.397759i
$553$	2.04514	−	2.04514i	0.0869683	−	0.0869683i
$554$	5.03218	−	18.7804i	0.213797	−	0.797901i
$555$	8.02170	−	1.93002i	0.340502	−	0.0819246i
$556$			19.6965i			0.835316i
$557$	9.18337	−	34.2728i	0.389112	−	1.45219i	−0.442470	−	0.896783i	$-0.645898\pi$
$557$	9.18337	−	34.2728i	0.389112	−	1.45219i	0.831582	−	0.555402i	$-0.187436\pi$
$558$	−15.4695	+	7.90130i	−0.654876	+	0.334489i
$559$	−1.90186	−	2.59481i	−0.0804400	−	0.109749i
$560$	1.04518	+	0.603436i	0.0441670	+	0.0254998i
$561$	−2.15602	+	3.52219i	−0.0910271	+	0.148707i
$562$	14.9038	−	25.8141i	0.628679	−	1.08890i
$563$	36.9752			1.55832			0.779159	−	0.626826i	$-0.215647\pi$
$563$	36.9752			1.55832			0.779159	+	0.626826i	$0.215647\pi$
$564$	5.60329	+	3.42991i	0.235941	+	0.144425i
$565$	1.93263	−	7.21266i	0.0813062	−	0.303439i
$566$	21.3237	−	5.71368i	0.896303	−	0.240164i
$567$	15.0658	+	5.74923i	0.632706	+	0.241445i
$568$	−3.30154	+	5.71843i	−0.138529	+	0.239940i
$569$	24.5310			1.02840			0.514198	−	0.857672i	$-0.328090\pi$
$569$	24.5310			1.02840			0.514198	+	0.857672i	$0.328090\pi$
$570$	0.196442	−	7.64562i	0.00822804	−	0.320240i
$571$	−7.42838	+	4.28878i	−0.310868	+	0.179480i	−0.647315	−	0.762223i	$-0.724108\pi$
$571$	−7.42838	+	4.28878i	−0.310868	+	0.179480i	0.336447	+	0.941702i	$0.390775\pi$
$572$	2.77122	+	2.22498i	0.115871	+	0.0930312i
$573$	−8.87571	+	30.0181i	−0.370788	+	1.25403i
$574$	−6.30417	−	6.30417i	−0.263131	−	0.263131i
$575$	24.9069	−	14.3800i	1.03869	−	0.599688i
$576$	2.99604	+	0.154059i	0.124835	+	0.00641911i
$577$	−0.991168	−	0.991168i	−0.0412629	−	0.0412629i	0.686174	−	0.727437i	$-0.259289\pi$
$577$	−0.991168	−	0.991168i	−0.0412629	−	0.0412629i	−0.727437	+	0.686174i	$0.759289\pi$
$578$	10.7689	+	2.88553i	0.447929	+	0.120022i
$579$	10.8764	+	6.65770i	0.452007	+	0.276684i
$580$	2.79287	+	0.748347i	0.115968	+	0.0310734i
$581$			13.5606i			0.562587i
$582$	3.19066	+	0.943408i	0.132257	+	0.0391055i
$583$	−6.27290	+	6.27290i	−0.259797	+	0.259797i
$584$	11.3390			0.469211
$585$	7.13439	+	1.47800i	0.294971	+	0.0611079i
$586$	−9.48781			−0.391938
$587$	−26.9762	+	26.9762i	−1.11343	+	1.11343i	−0.120743	+	0.992684i	$0.538528\pi$
$587$	−26.9762	+	26.9762i	−1.11343	+	1.11343i	−0.992684	+	0.120743i	$0.961472\pi$
$588$	1.53547	+	6.38185i	0.0633217	+	0.263183i
$589$		−	37.9576i		−	1.56402i
$590$	−3.07284	−	0.823366i	−0.126507	−	0.0338975i
$591$	37.2547	−	20.2514i	1.53245	−	0.833031i
$592$	−6.83094	−	1.83034i	−0.280750	−	0.0752267i
$593$	−22.4411	−	22.4411i	−0.921547	−	0.921547i	0.0755923	−	0.997139i	$-0.475915\pi$
$593$	−22.4411	−	22.4411i	−0.921547	−	0.921547i	−0.997139	+	0.0755923i	$0.975915\pi$
$594$	−3.33204	−	3.88967i	−0.136715	−	0.159595i
$595$	2.52821	−	1.45966i	0.103647	−	0.0598403i
$596$	6.83755	+	6.83755i	0.280077	+	0.280077i
$597$	−13.5687	+	3.26461i	−0.555329	+	0.133612i
$598$	−21.2596	+	8.26289i	−0.869369	+	0.337895i
$599$	12.9383	−	7.46992i	0.528644	−	0.305213i	−0.211820	−	0.977309i	$-0.567939\pi$
$599$	12.9383	−	7.46992i	0.528644	−	0.305213i	0.740464	+	0.672096i	$0.234606\pi$
$600$	6.71606	+	4.11106i	0.274182	+	0.167833i
$601$	−9.43517			−0.384869			−0.192434	−	0.981310i	$-0.561638\pi$
$601$	−9.43517			−0.384869			−0.192434	+	0.981310i	$0.561638\pi$
$602$	0.799360	−	1.38453i	0.0325795	−	0.0564293i
$603$	−6.93814	−	32.4841i	−0.282543	−	1.32285i
$604$	−4.80308	+	1.28698i	−0.195434	+	0.0523665i
$605$	1.74831	−	6.52479i	0.0710790	−	0.265270i
$606$	−0.662506	+	25.7851i	−0.0269125	+	1.04745i
$607$	8.22930			0.334017			0.167008	−	0.985955i	$-0.446589\pi$
$607$	8.22930			0.334017			0.167008	+	0.985955i	$0.446589\pi$
$608$	−3.27775	+	5.67724i	−0.132930	+	0.230242i
$609$	−6.36219	−	11.7040i	−0.257809	−	0.474268i
$610$	−2.77901	−	1.60446i	−0.112519	−	0.0649627i
$611$	−4.95433	−	12.7470i	−0.200431	−	0.515688i
$612$	3.94632	−	6.08992i	0.159521	−	0.246170i
$613$	−5.26589	+	19.6526i	−0.212687	+	0.793760i	0.774280	+	0.632843i	$0.218112\pi$
$613$	−5.26589	+	19.6526i	−0.212687	+	0.793760i	−0.986968	+	0.160918i	$0.948555\pi$
$614$		−	4.74755i		−	0.191596i
$615$	3.99814	+	4.20901i	0.161221	+	0.169724i
$616$	−0.457091	+	1.70589i	−0.0184167	+	0.0687321i
$617$	23.1593	−	23.1593i	0.932360	−	0.932360i	−0.0654935	−	0.997853i	$-0.520862\pi$
$617$	23.1593	−	23.1593i	0.932360	−	0.932360i	0.997853	+	0.0654935i	$0.0208622\pi$
$618$	−8.68023	−	15.9683i	−0.349170	−	0.642337i
$619$	2.50985	+	9.36687i	0.100879	+	0.376486i	0.997845	−	0.0656133i	$-0.0209004\pi$
$619$	2.50985	+	9.36687i	0.100879	+	0.376486i	−0.896966	+	0.442100i	$0.854234\pi$
$620$	−3.37763	−	1.95008i	−0.135649	−	0.0783169i
$621$	32.3118	−	6.03800i	1.29663	−	0.242297i
$622$	−20.4069	−	5.46802i	−0.818244	−	0.219248i
$623$	1.52603	−	2.64316i	0.0611391	−	0.105896i
$624$	−4.76763	−	4.03358i	−0.190858	−	0.161472i
$625$	9.20010	+	15.9350i	0.368004	+	0.637402i
$626$	2.67407	+	9.97975i	0.106877	+	0.398871i
$627$	10.8813	−	2.61804i	0.434558	−	0.104554i
$628$	−8.42090	+	4.86181i	−0.336030	+	0.194007i
$629$	−12.0960	+	12.0960i	−0.482300	+	0.482300i
$630$	0.756254	+	3.54075i	0.0301299	+	0.141067i
$631$	−5.85572	−	21.8539i	−0.233113	−	0.869988i	−0.978991	−	0.203906i	$-0.934636\pi$
$631$	−5.85572	−	21.8539i	−0.233113	−	0.869988i	0.745878	−	0.666083i	$-0.232030\pi$
$632$	1.55923	−	0.417795i	0.0620229	−	0.0166190i
$633$	−5.70550	−	23.7137i	−0.226773	−	0.942535i
$634$	−14.5122	−	8.37860i	−0.576352	−	0.332757i
$635$	3.25452	−	0.872047i	0.129152	−	0.0346061i
$636$	11.3024	−	10.7361i	0.448168	−	0.425715i
$637$	5.50544	−	12.5058i	0.218133	−	0.495498i
$638$			4.23108i			0.167510i
$639$	−19.3723	+	4.13764i	−0.766356	+	0.163683i
$640$	0.336790	+	0.583337i	0.0133128	+	0.0230584i
$641$	5.39399	+	9.34267i	0.213050	+	0.369013i	0.952668	−	0.304014i	$-0.0983270\pi$
$641$	5.39399	+	9.34267i	0.213050	+	0.369013i	−0.739618	+	0.673027i	$0.764994\pi$
$642$	1.79478	+	3.30170i	0.0708344	+	0.130308i
$643$	7.58253	+	7.58253i	0.299026	+	0.299026i	0.840632	−	0.541606i	$-0.182184\pi$
$643$	7.58253	+	7.58253i	0.299026	+	0.299026i	−0.541606	+	0.840632i	$0.682184\pi$
$644$	−8.01474	−	8.01474i	−0.315825	−	0.315825i
$645$	−0.543483	+	0.887865i	−0.0213996	+	0.0349596i
$646$	7.92862	+	13.7328i	0.311947	+	0.540309i
$647$	2.44136	+	4.22856i	0.0959799	+	0.166242i	0.910017	−	0.414571i	$-0.136068\pi$
$647$	2.44136	+	4.22856i	0.0959799	+	0.166242i	−0.814037	+	0.580813i	$0.802735\pi$
$648$	5.67764	+	6.98315i	0.223039	+	0.274324i
$649$		−	4.65524i		−	0.182734i
$650$	−5.93822	−	15.2785i	−0.232916	−	0.599270i
$651$	4.20339	+	17.4705i	0.164744	+	0.684723i
$652$	4.65451	−	1.24717i	0.182285	−	0.0488431i
$653$	−19.0037	−	10.9718i	−0.743673	−	0.429360i	0.0797303	−	0.996816i	$-0.474594\pi$
$653$	−19.0037	−	10.9718i	−0.743673	−	0.429360i	−0.823403	+	0.567457i	$0.807927\pi$
$654$	−14.7144	+	13.9772i	−0.575378	+	0.546552i
$655$	14.3014	−	3.83206i	0.558803	−	0.149731i
$656$	−1.28786	−	4.80634i	−0.0502823	−	0.187656i
$657$	22.7867	+	25.2571i	0.888993	+	0.985374i
$658$	4.80554	−	4.80554i	0.187340	−	0.187340i
$659$	36.6396	−	21.1539i	1.42728	−	0.824038i	0.430371	−	0.902652i	$-0.358383\pi$
$659$	36.6396	−	21.1539i	1.42728	−	0.824038i	0.996905	+	0.0786138i	$0.0250494\pi$
$660$	0.326064	−	1.10277i	0.0126920	−	0.0429252i
$661$	−8.10585	−	30.2514i	−0.315281	−	1.17664i	−0.923728	−	0.383050i	$-0.874874\pi$
$661$	−8.10585	−	30.2514i	−0.315281	−	1.17664i	0.608447	−	0.793595i	$-0.291793\pi$
$662$	−7.37732	−	12.7779i	−0.286728	−	0.496627i
$663$	−14.2160	+	5.10899i	−0.552103	+	0.198417i
$664$	−3.78422	+	6.55446i	−0.146856	+	0.254362i
$665$	−7.64207	−	2.04769i	−0.296347	−	0.0794059i
$666$	−9.65034	−	18.8938i	−0.373943	−	0.732122i
$667$	−23.5169	−	13.5775i	−0.910579	−	0.525723i
$668$	−3.66224	−	13.6676i	−0.141696	−	0.528817i
$669$	41.1082	+	1.05621i	1.58933	+	0.0408353i
$670$	5.27364	−	5.27364i	0.203738	−	0.203738i
$671$	1.21535	−	4.53573i	0.0469179	−	0.175100i
$672$	0.879938	−	2.97600i	0.0339444	−	0.114802i
$673$			38.0352i			1.46615i	0.680148	+	0.733075i	$0.261915\pi$
$673$			38.0352i			1.46615i	−0.680148	+	0.733075i	$0.738085\pi$
$674$	1.00563	−	3.75304i	0.0387352	−	0.144562i
$675$	4.33928	+	23.2213i	0.167019	+	0.893787i
$676$	2.80903	+	12.6929i	0.108040	+	0.488188i
$677$	−4.73877	−	2.73593i	−0.182126	−	0.105150i	0.406165	−	0.913800i	$-0.366866\pi$
$677$	−4.73877	−	2.73593i	−0.182126	−	0.105150i	−0.588291	+	0.808649i	$0.700199\pi$
$678$	−19.1946	−	0.493175i	−0.737166	−	0.0189403i
$679$	1.72092	−	2.98073i	0.0660430	−	0.114390i
$680$	1.62934			0.0624822
$681$	−36.4329	+	19.8047i	−1.39611	+	0.758917i
$682$	1.47714	−	5.51277i	0.0565627	−	0.211095i
$683$	−24.9699	+	6.69067i	−0.955447	+	0.256011i	−0.702672	−	0.711514i	$-0.748010\pi$
$683$	−24.9699	+	6.69067i	−0.955447	+	0.256011i	−0.252775	+	0.967525i	$0.581343\pi$
$684$	−19.2327	+	4.10784i	−0.735382	+	0.157067i
$685$	4.23986	−	7.34366i	0.161997	−	0.280587i
$686$	19.3322			0.738108
$687$	−31.2505	+	16.9876i	−1.19228	+	0.648117i
$688$	0.772736	−	0.446139i	0.0294603	−	0.0170089i
$689$	−32.2582	+	3.52683i	−1.22894	+	0.134362i
$690$	5.08299	+	5.35108i	0.193506	+	0.203712i
$691$	−23.9424	−	23.9424i	−0.910811	−	0.910811i	0.0855252	−	0.996336i	$-0.472743\pi$
$691$	−23.9424	−	23.9424i	−0.910811	−	0.910811i	−0.996336	+	0.0855252i	$0.972743\pi$
$692$	20.0900	−	11.5989i	0.763706	−	0.440926i
$693$	−4.71835	+	2.40997i	−0.179235	+	0.0915473i
$694$	−22.8522	−	22.8522i	−0.867459	−	0.867459i
$695$	−12.8151	−	3.43379i	−0.486103	−	0.130251i
$696$	0.190966	−	7.43250i	0.00723855	−	0.281728i
$697$	−11.6262	−	3.11522i	−0.440372	−	0.117997i
$698$		−	18.9648i		−	0.717828i
$699$	3.50456	−	3.32899i	0.132555	−	0.125914i
$700$	5.75989	−	5.75989i	0.217703	−	0.217703i
$701$	−29.4689			−1.11303			−0.556513	−	0.830839i	$-0.687861\pi$
$701$	−29.4689			−1.11303			−0.556513	+	0.830839i	$0.687861\pi$
$702$	−0.596336	−	18.7255i	−0.0225073	−	0.706748i
$703$	46.3599			1.74850
$704$	−0.696978	+	0.696978i	−0.0262683	+	0.0262683i
$705$	−3.20844	+	3.04770i	−0.120837	+	0.114783i
$706$			19.5973i			0.737554i
$707$	25.7731	+	6.90589i	0.969298	+	0.259723i
$708$	−0.210110	+	8.17759i	−0.00789641	+	0.307332i
$709$	−12.5359	−	3.35900i	−0.470797	−	0.126150i	0.0156169	−	0.999878i	$-0.495029\pi$
$709$	−12.5359	−	3.35900i	−0.470797	−	0.126150i	−0.486414	+	0.873728i	$0.661695\pi$
$710$	−3.14500	−	3.14500i	−0.118030	−	0.118030i
$711$	4.06403	+	2.63353i	0.152413	+	0.0987649i
$712$	1.47520	−	0.851709i	0.0552856	−	0.0319191i
$713$	25.9006	+	25.9006i	0.969985	+	0.969985i
$714$	−5.17001	−	5.44269i	−0.193483	−	0.203687i
$715$	−1.93076	+	1.41514i	−0.0722063	+	0.0529234i
$716$	−4.82455	+	2.78545i	−0.180302	+	0.104097i
$717$	11.9552	−	6.49876i	0.446475	−	0.242701i
$718$	27.1650			1.01379
$719$	1.46802	−	2.54269i	0.0547480	−	0.0948263i	−0.837353	−	0.546663i	$-0.815898\pi$
$719$	1.46802	−	2.54269i	0.0547480	−	0.0948263i	0.892101	+	0.451837i	$0.149231\pi$
$720$	−0.622551	+	1.92245i	−0.0232011	+	0.0716455i
$721$	−18.1606	+	4.86612i	−0.676336	+	0.181224i
$722$	6.20510	−	23.1578i	0.230930	−	0.861843i
$723$	35.4265	−	19.2576i	1.31753	−	0.716198i
$724$	20.8410			0.774549
$725$	9.75764	−	16.9007i	0.362390	−	0.627677i
$726$	−17.3640	−	0.446141i	−0.644440	−	0.0165578i
$727$	−34.7895	−	20.0857i	−1.29027	−	0.744938i	−0.311569	−	0.950224i	$-0.600854\pi$
$727$	−34.7895	−	20.0857i	−1.29027	−	0.744938i	−0.978702	+	0.205285i	$0.934188\pi$
$728$	−5.21047	+	3.81900i	−0.193113	+	0.141541i
$729$	−4.14496	+	26.6799i	−0.153517	+	0.988146i
$730$	−1.97679	+	7.37746i	−0.0731641	+	0.273052i
$731$		−	2.15835i		−	0.0798294i
$732$	−2.33964	+	7.91281i	−0.0864757	+	0.292466i
$733$	−3.39197	+	12.6590i	−0.125285	+	0.467571i	−0.999850	−	0.0173384i	$-0.994481\pi$
$733$	−3.39197	+	12.6590i	−0.125285	+	0.467571i	0.874564	+	0.484909i	$0.161147\pi$
$734$	5.44068	−	5.44068i	0.200819	−	0.200819i
$735$	−4.41990	−	0.113562i	−0.163030	−	0.00418880i
$736$	−1.63730	−	6.11049i	−0.0603517	−	0.225236i
$737$	9.45150	+	5.45683i	0.348151	+	0.201005i
$738$	8.11787	−	12.5274i	0.298823	−	0.461140i
$739$	−20.2177	−	5.41732i	−0.743721	−	0.199279i	−0.132990	−	0.991117i	$-0.542458\pi$
$739$	−20.2177	−	5.41732i	−0.743721	−	0.199279i	−0.610731	+	0.791838i	$0.709124\pi$
$740$	2.38175	−	4.12531i	0.0875547	−	0.151649i
$741$	37.0330	+	17.4520i	1.36044	+	0.641114i
$742$	−8.06290	−	13.9654i	−0.295998	−	0.512684i
$743$	−4.33508	−	16.1787i	−0.159039	−	0.593540i	−0.998726	−	0.0504696i	$-0.983928\pi$
$743$	−4.33508	−	16.1787i	−0.159039	−	0.593540i	0.839687	−	0.543071i	$-0.182738\pi$
$744$	−2.84363	+	9.61730i	−0.104252	+	0.352587i
$745$	−5.64073	+	3.25668i	−0.206660	+	0.119315i
$746$	−11.3830	+	11.3830i	−0.416760	+	0.416760i
$747$	−22.2045	+	4.74256i	−0.812419	+	0.173521i
$748$	0.617094	+	2.30303i	0.0225632	+	0.0842070i
$749$	3.75500	−	1.00615i	0.137205	−	0.0367639i
$750$	−8.07502	+	7.67046i	−0.294858	+	0.280086i
$751$	−8.11367	−	4.68443i	−0.296072	−	0.170937i	0.344605	−	0.938748i	$-0.388013\pi$
$751$	−8.11367	−	4.68443i	−0.296072	−	0.170937i	−0.640677	+	0.767810i	$0.721346\pi$
$752$	3.66378	−	0.981707i	0.133604	−	0.0357992i
$753$	10.5539	+	43.8649i	0.384604	+	1.59852i
$754$	−9.68970	+	12.0686i	−0.352878	+	0.439511i
$755$		−	3.34938i		−	0.121897i
$756$	8.39722	−	4.02050i	0.305404	−	0.146224i
$757$	1.46922	+	2.54477i	0.0533999	+	0.0924913i	0.891490	−	0.453041i	$-0.149661\pi$
$757$	1.46922	+	2.54477i	0.0533999	+	0.0924913i	−0.838090	+	0.545532i	$0.816328\pi$
$758$	−12.9805	−	22.4829i	−0.471472	−	0.816614i
$759$	−5.63849	+	9.21136i	−0.204664	+	0.334351i
$760$	−3.12234	−	3.12234i	−0.113259	−	0.113259i
$761$	−7.31204	−	7.31204i	−0.265061	−	0.265061i	0.562045	−	0.827106i	$-0.310015\pi$
$761$	−7.31204	−	7.31204i	−0.265061	−	0.265061i	−0.827106	+	0.562045i	$0.810015\pi$
$762$	−4.13782	−	7.61198i	−0.149897	−	0.275753i
$763$	10.4970	+	18.1813i	0.380016	+	0.658207i
$764$	9.03635	+	15.6514i	0.326924	+	0.566248i
$765$	3.27429	+	3.62927i	0.118382	+	0.131217i
$766$			31.4582i			1.13663i
$767$	10.6611	−	13.2784i	0.384949	−	0.479455i
$768$	1.25580	−	1.19288i	0.0453147	−	0.0430445i
$769$	−0.0675077	+	0.0180886i	−0.00243439	+	0.000652292i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.25580 - 1.19288i) q^{3} -1.00000i q^{4} +(0.650628 + 0.174335i) q^{5} +(0.0444876 - 1.73148i) q^{6} +(-1.73068 - 0.463733i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.154059 - 2.99604i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.25580 - 1.19288i) q^{3} -1.00000i q^{4} +(0.650628 + 0.174335i) q^{5} +(0.0444876 - 1.73148i) q^{6} +(-1.73068 - 0.463733i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.154059 - 2.99604i) q^{9} +(0.583337 - 0.336790i) q^{10} +(0.696978 + 0.696978i) q^{11} +(-1.19288 - 1.25580i) q^{12} +(0.391864 + 3.58419i) q^{13} +(-1.55168 + 0.895864i) q^{14} +(1.02502 - 0.557194i) q^{15} -1.00000 q^{16} +(-1.20946 + 2.09485i) q^{17} +(-2.00959 - 2.22746i) q^{18} +(6.33213 - 1.69669i) q^{19} +(0.174335 - 0.650628i) q^{20} +(-2.72656 + 1.48214i) q^{21} +0.985676 q^{22} +(-3.16302 + 5.47852i) q^{23} +(-1.73148 - 0.0444876i) q^{24} +(-3.93720 - 2.27315i) q^{25} +(2.81150 + 2.25732i) q^{26} +(-3.38046 - 3.94620i) q^{27} +(-0.463733 + 1.73068i) q^{28} +4.29257i q^{29} +(0.330803 - 1.11879i) q^{30} +(1.49861 - 5.59289i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(1.70668 + 0.0438503i) q^{33} +(0.626062 + 2.33650i) q^{34} +(-1.04518 - 0.603436i) q^{35} +(-2.99604 - 0.154059i) q^{36} +(6.83094 + 1.83034i) q^{37} +(3.27775 - 5.67724i) q^{38} +(4.76763 + 4.03358i) q^{39} +(-0.336790 - 0.583337i) q^{40} +(1.28786 + 4.80634i) q^{41} +(-0.879938 + 2.97600i) q^{42} +(-0.772736 + 0.446139i) q^{43} +(0.696978 - 0.696978i) q^{44} +(0.622551 - 1.92245i) q^{45} +(1.63730 + 6.11049i) q^{46} +(-3.66378 + 0.981707i) q^{47} +(-1.25580 + 1.19288i) q^{48} +(-3.28199 - 1.89486i) q^{49} +(-4.39138 + 1.17667i) q^{50} +(0.980069 + 4.07345i) q^{51} +(3.58419 - 0.391864i) q^{52} +9.00014i q^{53} +(-5.18073 - 0.400036i) q^{54} +(0.331966 + 0.574981i) q^{55} +(0.895864 + 1.55168i) q^{56} +(5.92793 - 9.68420i) q^{57} +(3.03531 + 3.03531i) q^{58} +(-3.33959 - 3.33959i) q^{59} +(-0.557194 - 1.02502i) q^{60} +(-2.38199 - 4.12572i) q^{61} +(-2.89509 - 5.01445i) q^{62} +(-1.65599 + 5.11374i) q^{63} +1.00000i q^{64} +(-0.369894 + 2.40029i) q^{65} +(1.23781 - 1.17580i) q^{66} +(10.6950 - 2.86571i) q^{67} +(2.09485 + 1.20946i) q^{68} +(2.56311 + 10.6530i) q^{69} +(-1.16575 + 0.312361i) q^{70} +(-1.70900 - 6.37808i) q^{71} +(-2.22746 + 2.00959i) q^{72} +(-8.01788 + 8.01788i) q^{73} +(6.12445 - 3.53595i) q^{74} +(-7.65593 + 1.84201i) q^{75} +(-1.69669 - 6.33213i) q^{76} +(-0.883031 - 1.52946i) q^{77} +(6.22339 - 0.519052i) q^{78} +(-0.807117 + 1.39797i) q^{79} +(-0.650628 - 0.174335i) q^{80} +(-8.95253 - 0.923132i) q^{81} +(4.30925 + 2.48795i) q^{82} +(-1.95885 - 7.31055i) q^{83} +(1.48214 + 2.72656i) q^{84} +(-1.15211 + 1.15211i) q^{85} +(-0.230939 + 0.861875i) q^{86} +(5.12054 + 5.39061i) q^{87} -0.985676i q^{88} +(-0.440877 + 1.64537i) q^{89} +(-0.919169 - 1.79959i) q^{90} +(0.983920 - 6.38480i) q^{91} +(5.47852 + 3.16302i) q^{92} +(-4.78971 - 8.81121i) q^{93} +(-1.89651 + 3.28485i) q^{94} +4.41566 q^{95} +(-0.0444876 + 1.73148i) q^{96} +(-0.497183 + 1.85551i) q^{97} +(-3.66058 + 0.980849i) q^{98} +(2.19555 - 1.98080i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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