LMFDB - Embedded newform 546.2.bz.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	546.31
Dual form			546.2.bz.b.229.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.930654 + 3.47325i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.03957 - 1.68528i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.930654 + 3.47325i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.03957 - 1.68528i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.79789 + 3.11403i) q^{10} +(0.653837 - 0.175195i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.65145 + 2.44332i) q^{13} +(-1.53389 - 2.15573i) q^{14} +(2.54259 - 2.54259i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.74997 + 4.76310i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.00922685 - 0.0344351i) q^{19} +(-2.54259 + 2.54259i) q^{20} +(0.923681 + 2.47928i) q^{21} +0.676902 q^{22} +(-5.63078 + 3.25093i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(-6.86720 - 3.96478i) q^{25} +(-3.19348 + 1.67382i) q^{26} -1.00000i q^{27} +(-0.923681 - 2.47928i) q^{28} +5.57843 q^{29} +(3.11403 - 1.79789i) q^{30} +(-2.56852 + 0.688234i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.653837 - 0.175195i) q^{33} +(-3.88905 + 3.88905i) q^{34} +(7.75151 - 5.51552i) q^{35} +1.00000i q^{36} +(-0.558221 + 2.08331i) q^{37} +(0.0178249 - 0.0308736i) q^{38} +(3.51788 - 0.790248i) q^{39} +(-3.11403 + 1.79789i) q^{40} +(3.23112 + 3.23112i) q^{41} +(0.250524 + 2.63386i) q^{42} -6.92586i q^{43} +(0.653837 + 0.175195i) q^{44} +(-3.47325 + 0.930654i) q^{45} +(-6.28032 + 1.68281i) q^{46} +(8.99723 + 2.41080i) q^{47} -1.00000i q^{48} +(1.31969 + 6.87448i) q^{49} +(-5.60705 - 5.60705i) q^{50} +(4.76310 - 2.74997i) q^{51} +(-3.51788 + 0.790248i) q^{52} +(-0.982782 + 1.70223i) q^{53} +(0.258819 - 0.965926i) q^{54} +2.43398i q^{55} +(-0.250524 - 2.63386i) q^{56} +(-0.0252082 + 0.0252082i) q^{57} +(5.38835 + 1.44380i) q^{58} +(-1.52953 - 5.70829i) q^{59} +(3.47325 - 0.930654i) q^{60} +(3.80365 - 2.19604i) q^{61} -2.65913 q^{62} +(0.439707 - 2.60896i) q^{63} +1.00000i q^{64} +(-6.01866 - 11.4830i) q^{65} +(-0.586214 - 0.338451i) q^{66} +(1.39973 + 5.22388i) q^{67} +(-4.76310 + 2.74997i) q^{68} +6.50186 q^{69} +(8.91491 - 3.32135i) q^{70} +(9.32942 - 9.32942i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(0.906511 + 3.38315i) q^{73} +(-1.07840 + 1.86784i) q^{74} +(3.96478 + 6.86720i) q^{75} +(0.0252082 - 0.0252082i) q^{76} +(-1.62880 - 0.744573i) q^{77} +(3.60255 + 0.147174i) q^{78} +(8.22524 + 14.2465i) q^{79} +(-3.47325 + 0.930654i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.28475 + 3.95729i) q^{82} +(1.11723 + 1.11723i) q^{83} +(-0.439707 + 2.60896i) q^{84} +(-13.9841 - 13.9841i) q^{85} +(1.79254 - 6.68987i) q^{86} +(-4.83106 - 2.78922i) q^{87} +(0.586214 + 0.338451i) q^{88} +(5.80124 + 1.55444i) q^{89} -3.59577 q^{90} +(9.52549 - 0.514887i) q^{91} -6.50186 q^{92} +(2.56852 + 0.688234i) q^{93} +(8.06670 + 4.65731i) q^{94} +(0.111014 + 0.0640942i) q^{95} +(0.258819 - 0.965926i) q^{96} +(-11.0677 - 11.0677i) q^{97} +(-0.504522 + 6.98179i) q^{98} +(0.478642 + 0.478642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.930654	+	3.47325i	−0.416201	+	1.55328i	0.366217	+	0.930530i	$0.380653\pi$
$5$	−0.930654	+	3.47325i	−0.416201	+	1.55328i	−0.782418	+	0.622754i	$0.786014\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−2.03957	−	1.68528i	−0.770885	−	0.636974i
$7$	−2.03957	−	1.68528i	−0.770885	−	0.636974i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.79789	+	3.11403i	−0.568541	+	0.984742i
$11$	0.653837	−	0.175195i	0.197139	−	0.0528233i	−0.158898	−	0.987295i	$-0.550794\pi$
$11$	0.653837	−	0.175195i	0.197139	−	0.0528233i	0.356038	+	0.934472i	$0.384128\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−2.65145	+	2.44332i	−0.735381	+	0.677654i
$13$	−2.65145	+	2.44332i	−0.735381	+	0.677654i
$14$	−1.53389	−	2.15573i	−0.409950	−	0.576143i
$15$	2.54259	−	2.54259i	0.656495	−	0.656495i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.74997	+	4.76310i	−0.666967	+	1.15522i	0.311781	+	0.950154i	$0.399074\pi$
$17$	−2.74997	+	4.76310i	−0.666967	+	1.15522i	−0.978748	+	0.205067i	$0.934259\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	0.00922685	−	0.0344351i	0.00211678	−	0.00789994i	−0.964859	−	0.262767i	$-0.915365\pi$
$19$	0.00922685	−	0.0344351i	0.00211678	−	0.00789994i	0.966976	+	0.254867i	$0.0820317\pi$
$20$	−2.54259	+	2.54259i	−0.568541	+	0.568541i
$21$	0.923681	+	2.47928i	0.201564	+	0.541023i
$22$	0.676902			0.144316
$23$	−5.63078	+	3.25093i	−1.17410	+	0.677866i	−0.954642	−	0.297756i	$-0.903762\pi$
$23$	−5.63078	+	3.25093i	−1.17410	+	0.677866i	−0.219456	+	0.975622i	$0.570428\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$	−6.86720	−	3.96478i	−1.37344	−	0.792956i
$26$	−3.19348	+	1.67382i	−0.626294	+	0.328262i
$27$		−	1.00000i		−	0.192450i
$28$	−0.923681	−	2.47928i	−0.174559	−	0.468539i
$29$	5.57843			1.03589			0.517944	−	0.855414i	$-0.326697\pi$
$29$	5.57843			1.03589			0.517944	+	0.855414i	$0.326697\pi$
$30$	3.11403	−	1.79789i	0.568541	−	0.328247i
$31$	−2.56852	+	0.688234i	−0.461321	+	0.123610i	−0.481992	−	0.876176i	$-0.660086\pi$
$31$	−2.56852	+	0.688234i	−0.461321	+	0.123610i	0.0206710	+	0.999786i	$0.493420\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−0.653837	−	0.175195i	−0.113818	−	0.0304976i
$34$	−3.88905	+	3.88905i	−0.666967	+	0.666967i
$35$	7.75151	−	5.51552i	1.31024	−	0.932293i
$36$			1.00000i			0.166667i
$37$	−0.558221	+	2.08331i	−0.0917710	+	0.342494i	−0.996510	−	0.0834721i	$-0.973399\pi$
$37$	−0.558221	+	2.08331i	−0.0917710	+	0.342494i	0.904739	+	0.425966i	$0.140066\pi$
$38$	0.0178249	−	0.0308736i	0.00289158	−	0.00500836i
$39$	3.51788	−	0.790248i	0.563312	−	0.126541i
$40$	−3.11403	+	1.79789i	−0.492371	+	0.284271i
$41$	3.23112	+	3.23112i	0.504616	+	0.504616i	0.912869	−	0.408253i	$-0.133862\pi$
$41$	3.23112	+	3.23112i	0.504616	+	0.504616i	−0.408253	+	0.912869i	$0.633862\pi$
$42$	0.250524	+	2.63386i	0.0386566	+	0.406414i
$43$		−	6.92586i		−	1.05618i	−0.849187	−	0.528092i	$-0.822908\pi$
$43$		−	6.92586i		−	1.05618i	0.849187	−	0.528092i	$-0.177092\pi$
$44$	0.653837	+	0.175195i	0.0985697	+	0.0264117i
$45$	−3.47325	+	0.930654i	−0.517761	+	0.138734i
$46$	−6.28032	+	1.68281i	−0.925982	+	0.248116i
$47$	8.99723	+	2.41080i	1.31238	+	0.351651i	0.846118	−	0.532995i	$-0.178934\pi$
$47$	8.99723	+	2.41080i	1.31238	+	0.351651i	0.466263	+	0.884646i	$0.345600\pi$
$48$		−	1.00000i		−	0.144338i
$49$	1.31969	+	6.87448i	0.188527	+	0.982068i
$50$	−5.60705	−	5.60705i	−0.792956	−	0.792956i
$51$	4.76310	−	2.74997i	0.666967	−	0.385073i
$52$	−3.51788	+	0.790248i	−0.487843	+	0.109588i
$53$	−0.982782	+	1.70223i	−0.134996	+	0.233819i	−0.925596	−	0.378514i	$-0.876435\pi$
$53$	−0.982782	+	1.70223i	−0.134996	+	0.233819i	0.790600	+	0.612333i	$0.209769\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$			2.43398i			0.328198i
$56$	−0.250524	−	2.63386i	−0.0334776	−	0.351965i
$57$	−0.0252082	+	0.0252082i	−0.00333891	+	0.00333891i
$58$	5.38835	+	1.44380i	0.707525	+	0.189581i
$59$	−1.52953	−	5.70829i	−0.199128	−	0.743156i	−0.991160	−	0.132676i	$-0.957643\pi$
$59$	−1.52953	−	5.70829i	−0.199128	−	0.743156i	0.792032	−	0.610480i	$-0.209024\pi$
$60$	3.47325	−	0.930654i	0.448394	−	0.120147i
$61$	3.80365	−	2.19604i	0.487007	−	0.281174i	−0.236325	−	0.971674i	$-0.575943\pi$
$61$	3.80365	−	2.19604i	0.487007	−	0.281174i	0.723332	+	0.690500i	$0.242610\pi$
$62$	−2.65913			−0.337710
$63$	0.439707	−	2.60896i	0.0553978	−	0.328698i
$64$			1.00000i			0.125000i
$65$	−6.01866	−	11.4830i	−0.746523	−	1.42429i
$66$	−0.586214	−	0.338451i	−0.0721580	−	0.0416604i
$67$	1.39973	+	5.22388i	0.171005	+	0.638198i	0.997198	+	0.0748110i	$0.0238354\pi$
$67$	1.39973	+	5.22388i	0.171005	+	0.638198i	−0.826193	+	0.563387i	$0.809498\pi$
$68$	−4.76310	+	2.74997i	−0.577610	+	0.333483i
$69$	6.50186			0.782732
$70$	8.91491	−	3.32135i	1.06554	−	0.396977i
$71$	9.32942	−	9.32942i	1.10720	−	1.10720i	0.113681	−	0.993517i	$-0.463736\pi$
$71$	9.32942	−	9.32942i	1.10720	−	1.10720i	0.993517	−	0.113681i	$-0.0362643\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	0.906511	+	3.38315i	0.106099	+	0.395967i	0.998468	−	0.0553404i	$-0.0176244\pi$
$73$	0.906511	+	3.38315i	0.106099	+	0.395967i	−0.892368	+	0.451308i	$0.850958\pi$
$74$	−1.07840	+	1.86784i	−0.125362	+	0.217133i
$75$	3.96478	+	6.86720i	0.457814	+	0.792956i
$76$	0.0252082	−	0.0252082i	0.00289158	−	0.00289158i
$77$	−1.62880	−	0.744573i	−0.185619	−	0.0848520i
$78$	3.60255	+	0.147174i	0.407908	+	0.0166642i
$79$	8.22524	+	14.2465i	0.925412	+	1.60286i	0.790897	+	0.611950i	$0.209614\pi$
$79$	8.22524	+	14.2465i	0.925412	+	1.60286i	0.134516	+	0.990911i	$0.457052\pi$
$80$	−3.47325	+	0.930654i	−0.388321	+	0.104050i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.28475	+	3.95729i	0.252308	+	0.437010i
$83$	1.11723	+	1.11723i	0.122632	+	0.122632i	0.765759	−	0.643127i	$-0.222363\pi$
$83$	1.11723	+	1.11723i	0.122632	+	0.122632i	−0.643127	+	0.765759i	$0.722363\pi$
$84$	−0.439707	+	2.60896i	−0.0479759	+	0.284661i
$85$	−13.9841	−	13.9841i	−1.51679	−	1.51679i
$86$	1.79254	−	6.68987i	0.193295	−	0.721387i
$87$	−4.83106	−	2.78922i	−0.517944	−	0.299035i
$88$	0.586214	+	0.338451i	0.0624907	+	0.0360790i
$89$	5.80124	+	1.55444i	0.614930	+	0.164770i	0.552822	−	0.833299i	$-0.313551\pi$
$89$	5.80124	+	1.55444i	0.614930	+	0.164770i	0.0621080	+	0.998069i	$0.480218\pi$
$90$	−3.59577			−0.379027
$91$	9.52549	−	0.514887i	0.998542	−	0.0539748i
$92$	−6.50186			−0.677866
$93$	2.56852	+	0.688234i	0.266344	+	0.0713665i
$94$	8.06670	+	4.65731i	0.832016	+	0.480365i
$95$	0.111014	+	0.0640942i	0.0113898	+	0.00657593i
$96$	0.258819	−	0.965926i	0.0264156	−	0.0985844i
$97$	−11.0677	−	11.0677i	−1.12376	−	1.12376i	−0.991171	−	0.132587i	$-0.957671\pi$
$97$	−11.0677	−	11.0677i	−1.12376	−	1.12376i	−0.132587	−	0.991171i	$-0.542329\pi$
$98$	−0.504522	+	6.98179i	−0.0509644	+	0.705268i
$99$	0.478642	+	0.478642i	0.0481053	+	0.0481053i
$100$	−3.96478	−	6.86720i	−0.396478	−	0.686720i
$101$	1.01834	−	1.76382i	0.101329	−	0.175507i	−0.810904	−	0.585180i	$-0.801024\pi$
$101$	1.01834	−	1.76382i	0.101329	−	0.175507i	0.912232	+	0.409673i	$0.134357\pi$
$102$	5.31254	−	1.42349i	0.526020	−	0.140947i
$103$	1.58882	+	2.75192i	0.156551	+	0.271155i	0.933623	−	0.358257i	$-0.116629\pi$
$103$	1.58882	+	2.75192i	0.156551	+	0.271155i	−0.777071	+	0.629412i	$0.783296\pi$
$104$	−3.60255	−	0.147174i	−0.353259	−	0.0144316i
$105$	−9.47077	+	0.900826i	−0.924252	+	0.0879116i
$106$	−1.38986	+	1.38986i	−0.134996	+	0.134996i
$107$	−7.09118	−	12.2823i	−0.685530	−	1.18737i	−0.973270	−	0.229665i	$-0.926237\pi$
$107$	−7.09118	−	12.2823i	−0.685530	−	1.18737i	0.287739	−	0.957709i	$-0.407096\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−4.78121	−	17.8437i	−0.457957	−	1.70912i	−0.679245	−	0.733911i	$-0.737693\pi$
$109$	−4.78121	−	17.8437i	−0.457957	−	1.70912i	0.221288	−	0.975209i	$-0.428974\pi$
$110$	−0.629961	+	2.35105i	−0.0600645	+	0.224164i
$111$	1.52509	−	1.52509i	0.144755	−	0.144755i
$112$	0.439707	−	2.60896i	0.0415484	−	0.246523i
$113$	11.0369			1.03826			0.519131	−	0.854695i	$-0.326256\pi$
$113$	11.0369			1.03826			0.519131	+	0.854695i	$0.326256\pi$
$114$	−0.0308736	+	0.0178249i	−0.00289158	+	0.00166945i
$115$	−6.05098	−	22.5826i	−0.564257	−	2.10584i
$116$	4.83106	+	2.78922i	0.448553	+	0.258972i
$117$	−3.44170	−	1.07457i	−0.318185	−	0.0993437i
$118$		−	5.90965i		−	0.544028i
$119$	13.6359	−	5.08020i	1.25000	−	0.465701i
$120$	3.59577			0.328247
$121$	−9.12947	+	5.27090i	−0.829952	+	0.479173i
$122$	4.24242	−	1.13675i	0.384091	−	0.102917i
$123$	−1.18267	−	4.41379i	−0.106638	−	0.397978i
$124$	−2.56852	−	0.688234i	−0.230660	−	0.0618052i
$125$	7.44869	−	7.44869i	0.666231	−	0.666231i
$126$	1.09997	−	2.40625i	0.0979933	−	0.214366i
$127$			19.6955i			1.74769i	0.486200	+	0.873847i	$0.338383\pi$
$127$			19.6955i			1.74769i	−0.486200	+	0.873847i	$0.661617\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−3.46293	+	5.99797i	−0.304894	+	0.528092i
$130$	−2.84155	−	12.6495i	−0.249221	−	1.10943i
$131$	−15.4529	+	8.92171i	−1.35012	+	0.779494i	−0.988266	−	0.152740i	$-0.951190\pi$
$131$	−15.4529	+	8.92171i	−1.35012	+	0.779494i	−0.361856	+	0.932234i	$0.617857\pi$
$132$	−0.478642	−	0.478642i	−0.0416604	−	0.0416604i
$133$	−0.0768514	+	0.0546829i	−0.00666386	+	0.00474161i
$134$			5.40816i			0.467193i
$135$	3.47325	+	0.930654i	0.298930	+	0.0800979i
$136$	−5.31254	+	1.42349i	−0.455547	+	0.122063i
$137$	13.3019	−	3.56423i	1.13646	−	0.304513i	0.358932	−	0.933364i	$-0.383141\pi$
$137$	13.3019	−	3.56423i	1.13646	−	0.304513i	0.777526	+	0.628851i	$0.216474\pi$
$138$	6.28032	+	1.68281i	0.534616	+	0.143250i
$139$		−	5.94779i		−	0.504485i	−0.967664	−	0.252243i	$-0.918832\pi$
$139$		−	5.94779i		−	0.504485i	0.967664	−	0.252243i	$-0.0811681\pi$
$140$	9.47077	−	0.900826i	0.800426	−	0.0761337i
$141$	−6.58643	−	6.58643i	−0.554677	−	0.554677i
$142$	11.4262	−	6.59690i	0.958862	−	0.553599i
$143$	−1.30556	+	2.06205i	−0.109176	+	0.172438i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−5.19159	+	19.3753i	−0.431138	+	1.60903i
$146$			3.50249i			0.289868i
$147$	2.29435	−	6.61332i	0.189235	−	0.545457i
$148$	−1.52509	+	1.52509i	−0.125362	+	0.125362i
$149$	5.03935	+	1.35029i	0.412840	+	0.110620i	0.459260	−	0.888302i	$-0.348115\pi$
$149$	5.03935	+	1.35029i	0.412840	+	0.110620i	−0.0464202	+	0.998922i	$0.514781\pi$
$150$	2.05232	+	7.65937i	0.167571	+	0.625385i
$151$	3.31418	−	0.888032i	0.269704	−	0.0722671i	−0.121432	−	0.992600i	$-0.538749\pi$
$151$	3.31418	−	0.888032i	0.269704	−	0.0722671i	0.391137	+	0.920333i	$0.372082\pi$
$152$	0.0308736	−	0.0178249i	0.00250418	−	0.00144579i
$153$	−5.49995			−0.444645
$154$	−1.38059	−	1.14077i	−0.111251	−	0.0919256i
$155$		−	9.56163i		−	0.768008i
$156$	3.44170	+	1.07457i	0.275557	+	0.0860342i
$157$	14.6919	+	8.48238i	1.17254	+	0.676967i	0.954278	−	0.298922i	$-0.0966271\pi$
$157$	14.6919	+	8.48238i	1.17254	+	0.676967i	0.218265	+	0.975890i	$0.429960\pi$
$158$	4.25770	+	15.8900i	0.338724	+	1.26414i
$159$	1.70223	−	0.982782i	0.134996	−	0.0779397i
$160$	−3.59577			−0.284271
$161$	16.9631	+	2.85891i	1.33688	+	0.225314i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−3.16454	+	11.8102i	−0.247866	+	0.925048i	0.724055	+	0.689742i	$0.242276\pi$
$163$	−3.16454	+	11.8102i	−0.247866	+	0.925048i	−0.971921	+	0.235306i	$0.924391\pi$
$164$	1.18267	+	4.41379i	0.0923511	+	0.344659i
$165$	1.21699	−	2.10789i	0.0947427	−	0.164099i
$166$	0.790000	+	1.36832i	0.0613159	+	0.106202i
$167$	−7.46188	+	7.46188i	−0.577418	+	0.577418i	−0.934191	−	0.356773i	$-0.883877\pi$
$167$	−7.46188	+	7.46188i	−0.577418	+	0.577418i	0.356773	+	0.934191i	$0.383877\pi$
$168$	−1.09997	+	2.40625i	−0.0848647	+	0.185647i
$169$	1.06040	−	12.9567i	0.0815694	−	0.996668i
$170$	−9.88828	−	17.1270i	−0.758396	−	1.31358i
$171$	0.0344351	−	0.00922685i	0.00263331	−	0.000705595i
$172$	3.46293	−	5.99797i	0.264046	−	0.457341i
$173$	9.57100	+	16.5775i	0.727670	+	1.26036i	0.957866	+	0.287217i	$0.0927301\pi$
$173$	9.57100	+	16.5775i	0.727670	+	1.26036i	−0.230196	+	0.973144i	$0.573937\pi$
$174$	−3.94455	−	3.94455i	−0.299035	−	0.299035i
$175$	7.32439	+	19.6596i	0.553672	+	1.48612i
$176$	0.478642	+	0.478642i	0.0360790	+	0.0360790i
$177$	−1.52953	+	5.70829i	−0.114967	+	0.429061i
$178$	5.20125	+	3.00294i	0.389850	+	0.225080i
$179$	9.91781	+	5.72605i	0.741292	+	0.427985i	0.822539	−	0.568709i	$-0.192557\pi$
$179$	9.91781	+	5.72605i	0.741292	+	0.427985i	−0.0812471	+	0.996694i	$0.525890\pi$
$180$	−3.47325	−	0.930654i	−0.258881	−	0.0693668i
$181$	−21.6083			−1.60613			−0.803067	−	0.595889i	$-0.796800\pi$
$181$	−21.6083			−1.60613			−0.803067	+	0.595889i	$0.796800\pi$
$182$	9.33418	+	1.96803i	0.691895	+	0.145880i
$183$	−4.39208			−0.324672
$184$	−6.28032	−	1.68281i	−0.462991	−	0.124058i
$185$	−6.71634	−	3.87768i	−0.493795	−	0.285093i
$186$	2.30288	+	1.32957i	0.168855	+	0.0974885i
$187$	−0.963564	+	3.59607i	−0.0704628	+	0.262971i
$188$	6.58643	+	6.58643i	0.480365	+	0.480365i
$189$	−1.68528	+	2.03957i	−0.122586	+	0.148357i
$190$	0.0906429	+	0.0906429i	0.00657593	+	0.00657593i
$191$	6.87007	+	11.8993i	0.497101	+	0.861004i	0.999994	−	0.00334430i	$-0.00106452\pi$
$191$	6.87007	+	11.8993i	0.497101	+	0.861004i	−0.502893	+	0.864348i	$0.667731\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	10.4943	−	2.81194i	0.755398	−	0.202408i	0.139487	−	0.990224i	$-0.455455\pi$
$193$	10.4943	−	2.81194i	0.755398	−	0.202408i	0.615911	+	0.787816i	$0.288788\pi$
$194$	−7.82607	−	13.5552i	−0.561879	−	0.973204i
$195$	−0.529204	+	12.9539i	−0.0378971	+	0.927650i
$196$	−2.29435	+	6.61332i	−0.163882	+	0.472380i
$197$	−17.3271	+	17.3271i	−1.23450	+	1.23450i	−0.272287	+	0.962216i	$0.587780\pi$
$197$	−17.3271	+	17.3271i	−1.23450	+	1.23450i	−0.962216	+	0.272287i	$0.912220\pi$
$198$	0.338451	+	0.586214i	0.0240527	+	0.0416604i
$199$	−0.862176	+	1.49333i	−0.0611180	+	0.105860i	−0.894965	−	0.446136i	$-0.852800\pi$
$199$	−0.862176	+	1.49333i	−0.0611180	+	0.105860i	0.833847	+	0.551995i	$0.186133\pi$
$200$	−2.05232	−	7.65937i	−0.145121	−	0.541599i
$201$	1.39973	−	5.22388i	0.0987296	−	0.368464i
$202$	1.44015	−	1.44015i	0.101329	−	0.101329i
$203$	−11.3776	−	9.40119i	−0.798551	−	0.659834i
$204$	5.49995			0.385073
$205$	−14.2295	+	8.21542i	−0.993833	+	0.573790i
$206$	0.822436	+	3.06937i	0.0573018	+	0.213853i
$207$	−5.63078	−	3.25093i	−0.391366	−	0.225955i
$208$	−3.44170	−	1.07457i	−0.238639	−	0.0745078i
$209$		−	0.0241314i		−	0.00166921i
$210$	−9.38121	−	1.58108i	−0.647365	−	0.109105i
$211$	−9.49353			−0.653561			−0.326781	−	0.945100i	$-0.605964\pi$
$211$	−9.49353			−0.653561			−0.326781	+	0.945100i	$0.605964\pi$
$212$	−1.70223	+	0.982782i	−0.116910	+	0.0674978i
$213$	−12.7442	+	3.41481i	−0.873220	+	0.233979i
$214$	−3.67067	−	13.6991i	−0.250922	−	0.936452i
$215$	24.0552	+	6.44558i	1.64055	+	0.439585i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	6.39855	+	2.92497i	0.434362	+	0.198560i
$218$		−	18.4732i		−	1.25116i
$219$	0.906511	−	3.38315i	0.0612563	−	0.228612i
$220$	−1.21699	+	2.10789i	−0.0820496	+	0.142114i
$221$	−4.34633	−	19.3482i	−0.292366	−	1.30150i
$222$	1.86784	−	1.07840i	0.125362	−	0.0723775i
$223$	3.22187	+	3.22187i	0.215753	+	0.215753i	0.806706	−	0.590953i	$-0.201248\pi$
$223$	3.22187	+	3.22187i	0.215753	+	0.215753i	−0.590953	+	0.806706i	$0.701248\pi$
$224$	1.09997	−	2.40625i	0.0734950	−	0.160775i
$225$		−	7.92956i		−	0.528638i
$226$	10.6608	+	2.85655i	0.709146	+	0.190015i
$227$	11.7710	−	3.15403i	0.781268	−	0.209340i	0.153925	−	0.988083i	$-0.450809\pi$
$227$	11.7710	−	3.15403i	0.781268	−	0.209340i	0.627344	+	0.778742i	$0.284142\pi$
$228$	−0.0344351	+	0.00922685i	−0.00228052	+	0.000611063i
$229$	1.52338	+	0.408188i	0.100668	+	0.0269738i	0.308801	−	0.951127i	$-0.400072\pi$
$229$	1.52338	+	0.408188i	0.100668	+	0.0269738i	−0.208134	+	0.978100i	$0.566739\pi$
$230$		−	23.3792i		−	1.54158i
$231$	1.03829	+	1.45922i	0.0683148	+	0.0960095i
$232$	3.94455	+	3.94455i	0.258972	+	0.258972i
$233$	−20.4553	+	11.8099i	−1.34007	+	0.773692i	−0.986818	−	0.161835i	$-0.948259\pi$
$233$	−20.4553	+	11.8099i	−1.34007	+	0.773692i	−0.353256	+	0.935527i	$0.614925\pi$
$234$	−3.04631	−	1.92873i	−0.199143	−	0.126085i
$235$	−16.7466	+	29.0060i	−1.09243	+	1.89214i
$236$	1.52953	−	5.70829i	0.0995640	−	0.371578i
$237$		−	16.4505i		−	1.06857i
$238$	14.4861	−	1.37787i	0.938995	−	0.0893139i
$239$	8.03291	−	8.03291i	0.519606	−	0.519606i	−0.397846	−	0.917452i	$-0.630242\pi$
$239$	8.03291	−	8.03291i	0.519606	−	0.519606i	0.917452	+	0.397846i	$0.130242\pi$
$240$	3.47325	+	0.930654i	0.224197	+	0.0600734i
$241$	−5.43169	−	20.2713i	−0.349886	−	1.30579i	−0.886799	−	0.462155i	$-0.847077\pi$
$241$	−5.43169	−	20.2713i	−0.349886	−	1.30579i	0.536914	−	0.843637i	$-0.319590\pi$
$242$	−10.1826	+	2.72842i	−0.654562	+	0.175389i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	4.39208			0.281174
$245$	−25.1049	−	1.81415i	−1.60390	−	0.115901i
$246$		−	4.56949i		−	0.291340i
$247$	0.0596712	+	0.113847i	0.00379679	+	0.00724391i
$248$	−2.30288	−	1.32957i	−0.146233	−	0.0844275i
$249$	−0.408934	−	1.52616i	−0.0259152	−	0.0967167i
$250$	9.12274	−	5.26702i	0.576973	−	0.333115i
$251$	−8.67739			−0.547712			−0.273856	−	0.961771i	$-0.588299\pi$
$251$	−8.67739			−0.547712			−0.273856	+	0.961771i	$0.588299\pi$
$252$	1.68528	−	2.03957i	0.106162	−	0.128481i
$253$	−3.11206	+	3.11206i	−0.195654	+	0.195654i
$254$	−5.09758	+	19.0244i	−0.319850	+	1.19370i
$255$	5.11855	+	19.1027i	0.320536	+	1.19626i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.67876	−	11.5679i	−0.416609	−	0.721589i	0.578986	−	0.815337i	$-0.303448\pi$
$257$	−6.67876	−	11.5679i	−0.416609	−	0.721589i	−0.995596	+	0.0937484i	$0.970115\pi$
$258$	−4.89732	+	4.89732i	−0.304894	+	0.304894i
$259$	4.64948	−	3.30830i	0.288905	−	0.205568i
$260$	0.529204	−	12.9539i	0.0328198	−	0.803369i
$261$	2.78922	+	4.83106i	0.172648	+	0.299035i
$262$	−17.2354	+	4.61822i	−1.06481	+	0.285315i
$263$	−11.9969	+	20.7793i	−0.739762	+	1.28131i	0.212840	+	0.977087i	$0.431729\pi$
$263$	−11.9969	+	20.7793i	−0.739762	+	1.28131i	−0.952602	+	0.304218i	$0.901605\pi$
$264$	−0.338451	−	0.586214i	−0.0208302	−	0.0360790i
$265$	−4.99763	−	4.99763i	−0.307002	−	0.307002i
$266$	−0.0883857	+	0.0329291i	−0.00541928	+	0.00201901i
$267$	−4.24680	−	4.24680i	−0.259900	−	0.259900i
$268$	−1.39973	+	5.22388i	−0.0855023	+	0.319099i
$269$	22.1924	+	12.8128i	1.35309	+	0.781209i	0.988682	−	0.150029i	$-0.0479368\pi$
$269$	22.1924	+	12.8128i	1.35309	+	0.781209i	0.364412	+	0.931238i	$0.381270\pi$
$270$	3.11403	+	1.79789i	0.189514	+	0.109416i
$271$	−8.61499	−	2.30838i	−0.523323	−	0.140224i	−0.0125200	−	0.999922i	$-0.503985\pi$
$271$	−8.61499	−	2.30838i	−0.523323	−	0.140224i	−0.510803	+	0.859698i	$0.670652\pi$
$272$	−5.49995			−0.333483
$273$	−8.50676	−	4.31684i	−0.514852	−	0.261267i
$274$	13.7711			0.831945
$275$	−5.18464	−	1.38922i	−0.312646	−	0.0837732i
$276$	5.63078	+	3.25093i	0.338933	+	0.195683i
$277$	−4.40484	−	2.54313i	−0.264661	−	0.152802i	0.361798	−	0.932257i	$-0.382163\pi$
$277$	−4.40484	−	2.54313i	−0.264661	−	0.152802i	−0.626459	+	0.779454i	$0.715496\pi$
$278$	1.53940	−	5.74513i	0.0923272	−	0.344570i
$279$	−1.88029	−	1.88029i	−0.112570	−	0.112570i
$280$	9.38121	+	1.58108i	0.560635	+	0.0944879i
$281$	−9.84219	−	9.84219i	−0.587136	−	0.587136i	0.349719	−	0.936855i	$-0.386277\pi$
$281$	−9.84219	−	9.84219i	−0.587136	−	0.587136i	−0.936855	+	0.349719i	$0.886277\pi$
$282$	−4.65731	−	8.06670i	−0.277339	−	0.480365i
$283$	15.2568	−	26.4256i	0.906924	−	1.57084i	0.0886094	−	0.996066i	$-0.471758\pi$
$283$	15.2568	−	26.4256i	0.906924	−	1.57084i	0.818314	−	0.574771i	$-0.194909\pi$
$284$	12.7442	−	3.41481i	0.756231	−	0.202631i
$285$	−0.0640942	−	0.111014i	−0.00379662	−	0.00657593i
$286$	−1.79477	+	1.65389i	−0.106127	+	0.0977964i
$287$	−1.14477	−	12.0354i	−0.0675734	−	0.710428i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	−6.62472	−	11.4744i	−0.389690	−	0.674962i
$290$	−10.0294	+	17.3714i	−0.588945	+	1.02008i
$291$	4.05107	+	15.1188i	0.237478	+	0.886281i
$292$	−0.906511	+	3.38315i	−0.0530495	+	0.197984i
$293$	−13.0884	+	13.0884i	−0.764631	+	0.764631i	−0.977156	−	0.212524i	$-0.931832\pi$
$293$	−13.0884	+	13.0884i	−0.764631	+	0.764631i	0.212524	+	0.977156i	$0.431832\pi$
$294$	3.92783	−	5.79415i	0.229075	−	0.337922i
$295$	21.2498			1.23721
$296$	−1.86784	+	1.07840i	−0.108566	+	0.0626808i
$297$	−0.175195	−	0.653837i	−0.0101659	−	0.0379395i
$298$	4.51816	+	2.60856i	0.261730	+	0.151110i
$299$	6.98669	−	22.3775i	0.404050	−	1.29412i
$300$			7.92956i			0.457814i
$301$	−11.6720	+	14.1258i	−0.672762	+	0.814196i
$302$	3.43109			0.197437
$303$	−1.76382	+	1.01834i	−0.101329	+	0.0585022i
$304$	0.0344351	−	0.00922685i	0.00197499	−	0.000529196i
$305$	4.08750	+	15.2548i	0.234050	+	0.873485i
$306$	−5.31254	−	1.42349i	−0.303698	−	0.0813756i
$307$	12.9461	−	12.9461i	0.738875	−	0.738875i	−0.233485	−	0.972360i	$-0.575013\pi$
$307$	12.9461	−	12.9461i	0.738875	−	0.738875i	0.972360	+	0.233485i	$0.0750131\pi$
$308$	−1.03829	−	1.45922i	−0.0591623	−	0.0831467i
$309$		−	3.17765i		−	0.180770i
$310$	2.47473	−	9.23582i	0.140555	−	0.524559i
$311$	−10.0075	+	17.3335i	−0.567473	+	0.982891i	0.429342	+	0.903142i	$0.358745\pi$
$311$	−10.0075	+	17.3335i	−0.567473	+	0.982891i	−0.996815	+	0.0797496i	$0.974588\pi$
$312$	3.04631	+	1.92873i	0.172463	+	0.109193i
$313$	9.59630	−	5.54042i	0.542415	−	0.313163i	−0.203642	−	0.979045i	$-0.565278\pi$
$313$	9.59630	−	5.54042i	0.542415	−	0.313163i	0.746057	+	0.665882i	$0.231945\pi$
$314$	11.9959	+	11.9959i	0.676967	+	0.676967i
$315$	8.65234	+	3.95525i	0.487504	+	0.222853i
$316$			16.4505i			0.925412i
$317$	17.6873	+	4.73929i	0.993416	+	0.266185i	0.718685	−	0.695336i	$-0.244745\pi$
$317$	17.6873	+	4.73929i	0.993416	+	0.266185i	0.274731	+	0.961521i	$0.411411\pi$
$318$	1.89859	−	0.508725i	0.106468	−	0.0285279i
$319$	3.64739	−	0.977314i	0.204214	−	0.0547191i
$320$	−3.47325	−	0.930654i	−0.194160	−	0.0520251i
$321$			14.1824i			0.791582i
$322$	15.6451	+	7.15187i	0.871869	+	0.398558i
$323$	0.138644	+	0.138644i	0.00771435	+	0.00771435i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	27.8953	−	6.26632i	1.54735	−	0.347593i
$326$	−6.11342	+	10.5888i	−0.338591	+	0.586457i
$327$	−4.78121	+	17.8437i	−0.264402	+	0.986761i
$328$			4.56949i			0.252308i
$329$	−14.2876	−	20.0798i	−0.787702	−	1.10704i
$330$	1.72109	−	1.72109i	0.0947427	−	0.0947427i
$331$	−11.5360	−	3.09105i	−0.634074	−	0.169900i	−0.0725562	−	0.997364i	$-0.523116\pi$
$331$	−11.5360	−	3.09105i	−0.634074	−	0.169900i	−0.561518	+	0.827465i	$0.689782\pi$
$332$	0.408934	+	1.52616i	0.0224432	+	0.0837591i
$333$	−2.08331	+	0.558221i	−0.114165	+	0.0305903i
$334$	−9.13890	+	5.27635i	−0.500059	+	0.288709i
$335$	−19.4465			−1.06247
$336$	−1.68528	+	2.03957i	−0.0919393	+	0.111268i
$337$			10.5949i			0.577141i	0.957459	+	0.288570i	$0.0931799\pi$
$337$			10.5949i			0.577141i	−0.957459	+	0.288570i	$0.906820\pi$
$338$	4.37771	−	12.2407i	0.238116	−	0.665808i
$339$	−9.55821	−	5.51844i	−0.519131	−	0.299720i
$340$	−5.11855	−	19.1027i	−0.277592	−	1.03599i
$341$	−1.55882	+	0.899986i	−0.0844149	+	0.0487370i
$342$	0.0356498			0.00192772
$343$	8.89379	−	16.2450i	0.480219	−	0.877148i
$344$	4.89732	−	4.89732i	0.264046	−	0.264046i
$345$	−6.05098	+	22.5826i	−0.325774	+	1.21581i
$346$	4.95432	+	18.4898i	0.266346	+	0.994016i
$347$	−4.20138	+	7.27700i	−0.225542	+	0.390650i	−0.956482	−	0.291792i	$-0.905749\pi$
$347$	−4.20138	+	7.27700i	−0.225542	+	0.390650i	0.730940	+	0.682442i	$0.239082\pi$
$348$	−2.78922	−	4.83106i	−0.149518	−	0.258972i
$349$	−5.33577	+	5.33577i	−0.285617	+	0.285617i	−0.835344	−	0.549727i	$-0.814732\pi$
$349$	−5.33577	+	5.33577i	−0.285617	+	0.285617i	0.549727	+	0.835344i	$0.314732\pi$
$350$	1.98654	+	20.8854i	0.106185	+	1.11637i
$351$	2.44332	+	2.65145i	0.130415	+	0.141524i
$352$	0.338451	+	0.586214i	0.0180395	+	0.0312453i
$353$	−29.0069	+	7.77237i	−1.54388	+	0.413682i	−0.927517	−	0.373780i	$-0.878062\pi$
$353$	−29.0069	+	7.77237i	−1.54388	+	0.413682i	−0.616364	+	0.787462i	$0.711395\pi$
$354$	−2.95483	+	5.11791i	−0.157047	+	0.272014i
$355$	23.7209	+	41.0859i	1.25898	+	2.18061i
$356$	4.24680	+	4.24680i	0.225080	+	0.225080i
$357$	−14.3491	−	2.41836i	−0.759437	−	0.127993i
$358$	8.09786	+	8.09786i	0.427985	+	0.427985i
$359$	1.00826	−	3.76288i	0.0532139	−	0.198597i	−0.934201	−	0.356746i	$-0.883886\pi$
$359$	1.00826	−	3.76288i	0.0532139	−	0.198597i	0.987415	+	0.158149i	$0.0505527\pi$
$360$	−3.11403	−	1.79789i	−0.164124	−	0.0947569i
$361$	16.4534	+	9.49936i	0.865967	+	0.499967i
$362$	−20.8720	−	5.59264i	−1.09701	−	0.293943i
$363$	10.5418			0.553301
$364$	8.50676	+	4.31684i	0.445875	+	0.226264i
$365$	−12.5941			−0.659208
$366$	−4.24242	−	1.13675i	−0.221755	−	0.0594190i
$367$	−26.7917	−	15.4682i	−1.39851	−	0.807432i	−0.404276	−	0.914637i	$-0.632477\pi$
$367$	−26.7917	−	15.4682i	−1.39851	−	0.807432i	−0.994237	+	0.107205i	$0.965810\pi$
$368$	−5.63078	−	3.25093i	−0.293525	−	0.169467i
$369$	−1.18267	+	4.41379i	−0.0615674	+	0.229773i
$370$	−5.48387	−	5.48387i	−0.285093	−	0.285093i
$371$	4.87318	−	1.81556i	0.253003	−	0.0942589i
$372$	1.88029	+	1.88029i	0.0974885	+	0.0974885i
$373$	−6.45102	−	11.1735i	−0.334021	−	0.578542i	0.649275	−	0.760554i	$-0.275072\pi$
$373$	−6.45102	−	11.1735i	−0.334021	−	0.578542i	−0.983296	+	0.182012i	$0.941739\pi$
$374$	−1.86146	+	3.22415i	−0.0962540	+	0.166717i
$375$	−10.1751	+	2.72641i	−0.525440	+	0.140791i
$376$	4.65731	+	8.06670i	0.240182	+	0.416008i
$377$	−14.7909	+	13.6299i	−0.761772	+	0.701974i
$378$	−2.15573	+	1.53389i	−0.110879	+	0.0788949i
$379$	22.4924	−	22.4924i	1.15536	−	1.15536i	0.169893	−	0.985462i	$-0.445658\pi$
$379$	22.4924	−	22.4924i	1.15536	−	1.15536i	0.985462	−	0.169893i	$-0.0543423\pi$
$380$	0.0640942	+	0.111014i	0.00328797	+	0.00569492i
$381$	9.84776	−	17.0568i	0.504516	−	0.873847i
$382$	3.55621	+	13.2720i	0.181952	+	0.679053i
$383$	9.65854	−	36.0462i	0.493528	−	1.84187i	−0.0445920	−	0.999005i	$-0.514199\pi$
$383$	9.65854	−	36.0462i	0.493528	−	1.84187i	0.538120	−	0.842868i	$-0.319135\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	4.10193	−	4.96428i	0.209054	−	0.253003i
$386$	10.8645			0.552990
$387$	5.99797	−	3.46293i	0.304894	−	0.176031i
$388$	−4.05107	−	15.1188i	−0.205662	−	0.767542i
$389$	30.4768	+	17.5958i	1.54524	+	0.892142i	0.998495	+	0.0548393i	$0.0174646\pi$
$389$	30.4768	+	17.5958i	1.54524	+	0.892142i	0.546740	+	0.837303i	$0.315869\pi$
$390$	−3.86390	+	12.3756i	−0.195656	+	0.626661i
$391$		−	35.7599i		−	1.80846i
$392$	−3.92783	+	5.79415i	−0.198385	+	0.292649i
$393$	17.8434			0.900082
$394$	−21.2212	+	12.2521i	−1.06911	+	0.617252i
$395$	−57.1366	+	15.3097i	−2.87486	+	0.770315i
$396$	0.175195	+	0.653837i	0.00880389	+	0.0328566i
$397$	−16.1183	−	4.31889i	−0.808955	−	0.216759i	−0.169443	−	0.985540i	$-0.554197\pi$
$397$	−16.1183	−	4.31889i	−0.808955	−	0.216759i	−0.639512	+	0.768781i	$0.720863\pi$
$398$	−1.21930	+	1.21930i	−0.0611180	+	0.0611180i
$399$	0.0938967	−	0.00893112i	0.00470072	−	0.000447115i
$400$		−	7.92956i		−	0.396478i
$401$	−5.86872	+	21.9024i	−0.293070	+	1.09375i	0.649668	+	0.760218i	$0.274908\pi$
$401$	−5.86872	+	21.9024i	−0.293070	+	1.09375i	−0.942738	+	0.333534i	$0.891759\pi$
$402$	2.70408	−	4.68360i	0.134867	−	0.233597i
$403$	5.12875	−	8.10054i	0.255481	−	0.403517i
$404$	1.76382	−	1.01834i	0.0877533	−	0.0506644i
$405$	−2.54259	−	2.54259i	−0.126342	−	0.126342i
$406$	−8.55671	−	12.0256i	−0.424662	−	0.596820i
$407$			1.45994i			0.0723667i
$408$	5.31254	+	1.42349i	0.263010	+	0.0704733i
$409$	37.8554	−	10.1433i	1.87183	−	0.501555i	0.871898	−	0.489688i	$-0.162889\pi$
$409$	37.8554	−	10.1433i	1.87183	−	0.501555i	0.999930	−	0.0118664i	$-0.00377728\pi$
$410$	−15.8710	+	4.25261i	−0.783811	+	0.210022i
$411$	−13.3019	−	3.56423i	−0.656134	−	0.175811i
$412$			3.17765i			0.156551i
$413$	−6.50045	+	14.2201i	−0.319866	+	0.699727i
$414$	−4.59751	−	4.59751i	−0.225955	−	0.225955i
$415$	−4.92017	+	2.84066i	−0.241522	+	0.139443i
$416$	−3.04631	−	1.92873i	−0.149358	−	0.0945637i
$417$	−2.97390	+	5.15094i	−0.145632	+	0.252243i
$418$	0.00624567	−	0.0233092i	0.000305486	−	0.00114009i
$419$		−	11.6314i		−	0.568233i	−0.958790	−	0.284116i	$-0.908300\pi$
$419$		−	11.6314i		−	0.568233i	0.958790	−	0.284116i	$-0.0917002\pi$
$420$	−8.65234	−	3.95525i	−0.422191	−	0.192996i
$421$	−22.4733	+	22.4733i	−1.09528	+	1.09528i	−0.100327	+	0.994954i	$0.531989\pi$
$421$	−22.4733	+	22.4733i	−1.09528	+	1.09528i	−0.994954	+	0.100327i	$0.968011\pi$
$422$	−9.17004	−	2.45711i	−0.446391	−	0.119610i
$423$	2.41080	+	8.99723i	0.117217	+	0.437460i
$424$	−1.89859	+	0.508725i	−0.0922036	+	0.0247059i
$425$	37.7693	−	21.8061i	1.83208	−	1.05775i
$426$	−13.1938			−0.639241
$427$	−11.4587	−	1.93123i	−0.554527	−	0.0934586i
$428$		−	14.1824i		−	0.685530i
$429$	2.16168	−	1.13301i	0.104367	−	0.0547022i
$430$	21.5673	+	12.4519i	1.04007	+	0.600484i
$431$	7.13356	+	26.6228i	0.343611	+	1.28237i	0.894226	+	0.447615i	$0.147727\pi$
$431$	7.13356	+	26.6228i	0.343611	+	1.28237i	−0.550615	+	0.834759i	$0.685607\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	24.9528			1.19916			0.599578	−	0.800316i	$-0.295335\pi$
$433$	24.9528			1.19916			0.599578	+	0.800316i	$0.295335\pi$
$434$	5.42348	+	4.48137i	0.260336	+	0.215113i
$435$	14.1837	−	14.1837i	0.680055	−	0.680055i
$436$	4.78121	−	17.8437i	0.228979	−	0.854560i
$437$	0.0599917	+	0.223892i	0.00286979	+	0.0107102i
$438$	1.75124	−	3.03325i	0.0836777	−	0.144934i
$439$	3.14335	+	5.44445i	0.150024	+	0.259849i	0.931236	−	0.364416i	$-0.118732\pi$
$439$	3.14335	+	5.44445i	0.150024	+	0.259849i	−0.781212	+	0.624266i	$0.785398\pi$
$440$	−1.72109	+	1.72109i	−0.0820496	+	0.0820496i
$441$	−5.29363	+	4.58012i	−0.252077	+	0.218101i
$442$	0.809450	−	19.8138i	0.0385016	−	0.942447i
$443$	−7.53602	−	13.0528i	−0.358047	−	0.620156i	0.629587	−	0.776930i	$-0.283224\pi$
$443$	−7.53602	−	13.0528i	−0.358047	−	0.620156i	−0.987635	+	0.156774i	$0.949891\pi$
$444$	2.08331	−	0.558221i	0.0988695	−	0.0264920i
$445$	−10.7979	+	18.7025i	−0.511869	+	0.886583i
$446$	2.27821	+	3.94597i	0.107876	+	0.186847i
$447$	−3.68906	−	3.68906i	−0.174487	−	0.174487i
$448$	1.68528	−	2.03957i	0.0796218	−	0.0963606i
$449$	4.51002	+	4.51002i	0.212841	+	0.212841i	0.805473	−	0.592632i	$-0.201911\pi$
$449$	4.51002	+	4.51002i	0.212841	+	0.212841i	−0.592632	+	0.805473i	$0.701911\pi$
$450$	2.05232	−	7.65937i	0.0967474	−	0.361066i
$451$	2.67870	+	1.54655i	0.126135	+	0.0728241i
$452$	9.55821	+	5.51844i	0.449580	+	0.259565i
$453$	−3.31418	−	0.888032i	−0.155714	−	0.0417234i
$454$	12.1862			0.571928
$455$	−7.07660	+	33.5636i	−0.331756	+	1.57348i
$456$	−0.0356498			−0.00166945
$457$	15.1129	+	4.04948i	0.706950	+	0.189427i	0.594342	−	0.804213i	$-0.297413\pi$
$457$	15.1129	+	4.04948i	0.706950	+	0.189427i	0.112609	+	0.993639i	$0.464079\pi$
$458$	1.36582	+	0.788559i	0.0638208	+	0.0368470i
$459$	4.76310	+	2.74997i	0.222322	+	0.128358i
$460$	6.05098	−	22.5826i	0.282129	−	1.05292i
$461$	−0.608309	−	0.608309i	−0.0283318	−	0.0283318i	0.692799	−	0.721131i	$-0.256377\pi$
$461$	−0.608309	−	0.608309i	−0.0283318	−	0.0283318i	−0.721131	+	0.692799i	$0.756377\pi$
$462$	0.625242	+	1.67823i	0.0290889	+	0.0780782i
$463$	21.0215	+	21.0215i	0.976951	+	0.976951i	0.999740	−	0.0227896i	$-0.00725478\pi$
$463$	21.0215	+	21.0215i	0.976951	+	0.976951i	−0.0227896	+	0.999740i	$0.507255\pi$
$464$	2.78922	+	4.83106i	0.129486	+	0.224276i
$465$	−4.78081	+	8.28061i	−0.221705	+	0.384004i
$466$	−22.8150	+	6.11325i	−1.05688	+	0.283191i
$467$	7.41349	+	12.8405i	0.343055	+	0.594190i	0.984999	−	0.172563i	$-0.0552048\pi$
$467$	7.41349	+	12.8405i	0.343055	+	0.594190i	−0.641943	+	0.766752i	$0.721871\pi$
$468$	−2.44332	−	2.65145i	−0.112942	−	0.122563i
$469$	5.94882	−	13.0134i	0.274691	−	0.600903i
$470$	−23.6833	+	23.6833i	−1.09243	+	1.09243i
$471$	−8.48238	−	14.6919i	−0.390847	−	0.676967i
$472$	2.95483	−	5.11791i	0.136007	−	0.235571i
$473$	−1.21338	−	4.52838i	−0.0557911	−	0.208215i
$474$	4.25770	−	15.8900i	0.195563	−	0.729850i
$475$	−0.199890	+	0.199890i	−0.00917159	+	0.00917159i
$476$	14.3491	+	2.41836i	0.657691	+	0.110846i
$477$	−1.96556			−0.0899970
$478$	9.83827	−	5.68013i	0.449992	−	0.259803i
$479$	−9.75804	−	36.4175i	−0.445856	−	1.66396i	−0.713666	−	0.700486i	$-0.752967\pi$
$479$	−9.75804	−	36.4175i	−0.445856	−	1.66396i	0.267810	−	0.963472i	$-0.413700\pi$
$480$	3.11403	+	1.79789i	0.142135	+	0.0820619i
$481$	−3.61009	−	6.88771i	−0.164606	−	0.314053i
$482$		−	20.9864i		−	0.955906i
$483$	−13.2610	−	10.9574i	−0.603397	−	0.498580i
$484$	−10.5418			−0.479173
$485$	48.7412	−	28.1408i	2.21323	−	1.27781i
$486$	0.965926	−	0.258819i	0.0438153	−	0.0117403i
$487$	−4.60908	−	17.2013i	−0.208857	−	0.779466i	−0.988239	−	0.152917i	$-0.951133\pi$
$487$	−4.60908	−	17.2013i	−0.208857	−	0.779466i	0.779382	−	0.626549i	$-0.215533\pi$
$488$	4.24242	+	1.13675i	0.192045	+	0.0514584i
$489$	8.64568	−	8.64568i	0.390971	−	0.390971i
$490$	−23.7800	−	8.24996i	−1.07427	−	0.372695i
$491$			14.2235i			0.641898i	0.947097	+	0.320949i	$0.104002\pi$
$491$			14.2235i			0.641898i	−0.947097	+	0.320949i	$0.895998\pi$
$492$	1.18267	−	4.41379i	0.0533189	−	0.198989i
$493$	−15.3405	+	26.5706i	−0.690903	+	1.19668i
$494$	0.0281722	+	0.125412i	0.00126753	+	0.00564255i
$495$	−2.10789	+	1.21699i	−0.0947427	+	0.0546997i
$496$	−1.88029	−	1.88029i	−0.0844275	−	0.0844275i
$497$	−34.7507	+	3.30536i	−1.55878	+	0.148266i
$498$		−	1.58000i		−	0.0708015i
$499$	7.13111	+	1.91078i	0.319232	+	0.0855380i	0.414877	−	0.909877i	$-0.363825\pi$
$499$	7.13111	+	1.91078i	0.319232	+	0.0855380i	−0.0956447	+	0.995416i	$0.530491\pi$
$500$	10.1751	−	2.72641i	0.455044	−	0.121929i
$501$	10.1931	−	2.73124i	0.455395	−	0.122023i
$502$	−8.38172	−	2.24587i	−0.374094	−	0.100238i
$503$			0.876646i			0.0390877i	0.999809	+	0.0195438i	$0.00622140\pi$
$503$			0.876646i			0.0390877i	−0.999809	+	0.0195438i	$0.993779\pi$
$504$	2.15573	−	1.53389i	0.0960239	−	0.0683250i
$505$	5.17846	+	5.17846i	0.230438	+	0.230438i
$506$	−3.81149	+	2.20056i	−0.169441	+	0.0978269i
$507$	−7.39668	+	10.6906i	−0.328498	+	0.474787i
$508$	−9.84776	+	17.0568i	−0.436924	+	0.756774i
$509$	−0.211436	+	0.789089i	−0.00937172	+	0.0349758i	−0.970453	−	0.241289i	$-0.922430\pi$
$509$	−0.211436	+	0.789089i	−0.00937172	+	0.0349758i	0.961082	+	0.276264i	$0.0890966\pi$
$510$			19.7766i			0.875721i
$511$	3.85264	−	8.42788i	0.170431	−	0.372828i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−0.0344351	−	0.00922685i	−0.00152035	−	0.000407375i
$514$	−3.45718	−	12.9024i	−0.152490	−	0.569099i
$515$	−11.0368	+	2.95729i	−0.486338	+	0.130314i
$516$	−5.99797	+	3.46293i	−0.264046	+	0.152447i
$517$	6.30508			0.277297
$518$	5.34731	−	1.99220i	0.234947	−	0.0875321i
$519$		−	19.1420i		−	0.840241i
$520$	3.86390	−	12.3756i	0.169443	−	0.542704i
$521$	30.6735	+	17.7094i	1.34383	+	0.775861i	0.987367	−	0.158448i	$-0.0506491\pi$
$521$	30.6735	+	17.7094i	1.34383	+	0.775861i	0.356463	+	0.934309i	$0.383982\pi$
$522$	1.44380	+	5.38835i	0.0631936	+	0.235842i
$523$	15.0240	−	8.67408i	0.656952	−	0.379291i	−0.134163	−	0.990959i	$-0.542835\pi$
$523$	15.0240	−	8.67408i	0.656952	−	0.379291i	0.791115	+	0.611668i	$0.209501\pi$
$524$	−17.8434			−0.779494
$525$	3.48668	−	20.6879i	0.152171	−	0.902894i
$526$	−16.9662	+	16.9662i	−0.739762	+	0.739762i
$527$	3.78525	−	14.1268i	0.164888	−	0.615371i
$528$	−0.175195	−	0.653837i	−0.00762439	−	0.0284546i
$529$	9.63711	−	16.6920i	0.419005	−	0.725737i
$530$	−3.53386	−	6.12082i	−0.153501	−	0.265872i
$531$	4.17876	−	4.17876i	0.181343	−	0.181343i
$532$	−0.0938967	+	0.00893112i	−0.00407094	+	0.000387213i
$533$	−16.4618	−	0.672510i	−0.713040	−	0.0291296i
$534$	−3.00294	−	5.20125i	−0.129950	−	0.225080i
$535$	49.2589	−	13.1989i	2.12965	−	0.570637i
$536$	−2.70408	+	4.68360i	−0.116798	+	0.202301i
$537$	−5.72605	−	9.91781i	−0.247097	−	0.427985i
$538$	18.1200	+	18.1200i	0.781209	+	0.781209i
$539$	2.06724	+	4.26358i	0.0890422	+	0.183646i
$540$	2.54259	+	2.54259i	0.109416	+	0.109416i
$541$	4.47115	−	16.6866i	0.192230	−	0.717411i	−0.800737	−	0.599016i	$-0.795558\pi$
$541$	4.47115	−	16.6866i	0.192230	−	0.717411i	0.992967	−	0.118395i	$-0.0377749\pi$
$542$	−7.72399	−	4.45945i	−0.331774	−	0.191550i
$543$	18.7133	+	10.8042i	0.803067	+	0.463651i
$544$	−5.31254	−	1.42349i	−0.227773	−	0.0610317i
$545$	66.4254			2.84535
$546$	−7.09962	−	6.37146i	−0.303836	−	0.272673i
$547$	−27.7864			−1.18806			−0.594031	−	0.804442i	$-0.702464\pi$
$547$	−27.7864			−1.18806			−0.594031	+	0.804442i	$0.702464\pi$
$548$	13.3019	+	3.56423i	0.568229	+	0.152257i
$549$	3.80365	+	2.19604i	0.162336	+	0.0937246i
$550$	−4.64842	−	2.68377i	−0.198209	−	0.114436i
$551$	0.0514713	−	0.192094i	0.00219275	−	0.00818346i
$552$	4.59751	+	4.59751i	0.195683	+	0.195683i
$553$	7.23339	−	42.9186i	0.307595	−	1.82509i
$554$	−3.59653	−	3.59653i	−0.152802	−	0.152802i
$555$	3.87768	+	6.71634i	0.164598	+	0.285093i
$556$	2.97390	−	5.15094i	0.126121	−	0.218449i
$557$	43.5988	−	11.6823i	1.84734	−	0.494993i	0.847955	−	0.530068i	$-0.177834\pi$
$557$	43.5988	−	11.6823i	1.84734	−	0.494993i	0.999385	+	0.0350746i	$0.0111669\pi$
$558$	−1.32957	−	2.30288i	−0.0562850	−	0.0974885i
$559$	16.9221	+	18.3636i	0.715727	+	0.776697i
$560$	8.65234	+	3.95525i	0.365628	+	0.167140i
$561$	2.63251	−	2.63251i	0.111145	−	0.111145i
$562$	−6.95948	−	12.0542i	−0.293568	−	0.508475i
$563$	17.0813	−	29.5857i	0.719892	−	1.24689i	−0.241150	−	0.970488i	$-0.577524\pi$
$563$	17.0813	−	29.5857i	0.719892	−	1.24689i	0.961042	−	0.276402i	$-0.0891422\pi$
$564$	−2.41080	−	8.99723i	−0.101513	−	0.378852i
$565$	−10.2715	+	38.3338i	−0.432125	+	1.61271i
$566$	21.5764	−	21.5764i	0.906924	−	0.906924i
$567$	2.47928	−	0.923681i	0.104120	−	0.0387910i
$568$	13.1938			0.553599
$569$	11.1301	−	6.42594i	0.466596	−	0.269389i	−0.248218	−	0.968704i	$-0.579845\pi$
$569$	11.1301	−	6.42594i	0.466596	−	0.269389i	0.714814	+	0.699315i	$0.246511\pi$
$570$	−0.0331776	−	0.123821i	−0.00138966	−	0.00518627i
$571$	−9.22143	−	5.32399i	−0.385905	−	0.222802i	0.294480	−	0.955658i	$-0.404854\pi$
$571$	−9.22143	−	5.32399i	−0.385905	−	0.222802i	−0.680384	+	0.732856i	$0.738187\pi$
$572$	−2.16168	+	1.13301i	−0.0903842	+	0.0473735i
$573$		−	13.7401i		−	0.574003i
$574$	2.00924	−	11.9216i	0.0838639	−	0.497598i
$575$	51.5569			2.15007
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	17.9622	−	4.81295i	0.747774	−	0.200366i	0.135244	−	0.990812i	$-0.456818\pi$
$577$	17.9622	−	4.81295i	0.747774	−	0.200366i	0.612531	+	0.790447i	$0.290152\pi$
$578$	−3.42921	−	12.7980i	−0.142636	−	0.532326i
$579$	−10.4943	−	2.81194i	−0.436129	−	0.116860i
$580$	−14.1837	+	14.1837i	−0.588945	+	0.588945i
$581$	−0.395828	−	4.16151i	−0.0164217	−	0.172648i
$582$			15.6521i			0.648802i
$583$	−0.344357	+	1.28516i	−0.0142618	+	0.0532258i
$584$	−1.75124	+	3.03325i	−0.0724670	+	0.125517i
$585$	6.93527	−	10.9538i	0.286738	−	0.452885i
$586$	−16.0299	+	9.25488i	−0.662190	+	0.382316i
$587$	−30.0744	−	30.0744i	−1.24131	−	1.24131i	−0.959460	−	0.281845i	$-0.909054\pi$
$587$	−30.0744	−	30.0744i	−1.24131	−	1.24131i	−0.281845	−	0.959460i	$-0.590946\pi$
$588$	5.29363	−	4.58012i	0.218305	−	0.188881i
$589$			0.0947975i			0.00390606i
$590$	20.5257	+	5.49984i	0.845029	+	0.226425i
$591$	23.6692	−	6.34215i	0.973622	−	0.260881i
$592$	−2.08331	+	0.558221i	−0.0856235	+	0.0229428i
$593$	−20.1689	−	5.40425i	−0.828239	−	0.221926i	−0.180294	−	0.983613i	$-0.557705\pi$
$593$	−20.1689	−	5.40425i	−0.828239	−	0.221926i	−0.647945	+	0.761687i	$0.724371\pi$
$594$		−	0.676902i		−	0.0277736i
$595$	4.95450	+	52.0887i	0.203115	+	2.13543i
$596$	3.68906	+	3.68906i	0.151110	+	0.151110i
$597$	1.49333	−	0.862176i	0.0611180	−	0.0352865i
$598$	12.5403	−	19.8067i	0.512812	−	0.809956i
$599$	−1.61466	+	2.79668i	−0.0659733	+	0.114269i	−0.897125	−	0.441776i	$-0.854349\pi$
$599$	−1.61466	+	2.79668i	−0.0659733	+	0.114269i	0.831152	+	0.556045i	$0.187682\pi$
$600$	−2.05232	+	7.65937i	−0.0837857	+	0.312692i
$601$			10.1170i			0.412680i	0.978480	+	0.206340i	$0.0661553\pi$
$601$			10.1170i			0.412680i	−0.978480	+	0.206340i	$0.933845\pi$
$602$	−14.9303	+	10.6235i	−0.608513	+	0.432982i
$603$	−3.82414	+	3.82414i	−0.155731	+	0.155731i
$604$	3.31418	+	0.888032i	0.134852	+	0.0361335i
$605$	−9.81077	−	36.6143i	−0.398865	−	1.48858i
$606$	−1.96728	+	0.527132i	−0.0799155	+	0.0214133i
$607$	26.3708	−	15.2252i	1.07036	−	0.617970i	0.142077	−	0.989856i	$-0.454622\pi$
$607$	26.3708	−	15.2252i	1.07036	−	0.617970i	0.928279	+	0.371885i	$0.121289\pi$
$608$	0.0356498			0.00144579
$609$	5.15269	+	13.8305i	0.208798	+	0.560439i
$610$			15.7929i			0.639436i
$611$	−29.7461	+	15.5910i	−1.20340	+	0.630743i
$612$	−4.76310	−	2.74997i	−0.192537	−	0.111161i
$613$	−11.4027	−	42.5555i	−0.460551	−	1.71880i	−0.671233	−	0.741246i	$-0.734235\pi$
$613$	−11.4027	−	42.5555i	−0.460551	−	1.71880i	0.210682	−	0.977555i	$-0.432432\pi$
$614$	15.8557	−	9.15430i	0.639885	−	0.369438i
$615$	16.4308			0.662555
$616$	−0.625242	−	1.67823i	−0.0251917	−	0.0676177i
$617$	−15.0050	+	15.0050i	−0.604079	+	0.604079i	−0.941393	−	0.337313i	$-0.890482\pi$
$617$	−15.0050	+	15.0050i	−0.604079	+	0.604079i	0.337313	+	0.941393i	$0.390482\pi$
$618$	0.822436	−	3.06937i	0.0330832	−	0.123468i
$619$	1.35338	+	5.05087i	0.0543968	+	0.203012i	0.987776	−	0.155880i	$-0.0498213\pi$
$619$	1.35338	+	5.05087i	0.0543968	+	0.203012i	−0.933379	+	0.358892i	$0.883155\pi$
$620$	4.78081	−	8.28061i	0.192002	−	0.332557i
$621$	3.25093	+	5.63078i	0.130455	+	0.225955i
$622$	−14.1527	+	14.1527i	−0.567473	+	0.567473i
$623$	−9.21237	−	12.9471i	−0.369086	−	0.518713i
$624$	2.44332	+	2.65145i	0.0978110	+	0.106143i
$625$	−0.884922	−	1.53273i	−0.0353969	−	0.0613092i
$626$	10.7033	−	2.86793i	0.427789	−	0.114626i
$627$	−0.0120657	+	0.0208984i	−0.000481858	+	0.000834603i
$628$	8.48238	+	14.6919i	0.338484	+	0.586271i
$629$	−8.38791	−	8.38791i	−0.334448	−	0.334448i
$630$	7.33382	+	6.05986i	0.292187	+	0.241431i
$631$	−18.4931	−	18.4931i	−0.736199	−	0.736199i	0.235642	−	0.971840i	$-0.424281\pi$
$631$	−18.4931	−	18.4931i	−0.736199	−	0.736199i	−0.971840	+	0.235642i	$0.924281\pi$
$632$	−4.25770	+	15.8900i	−0.169362	+	0.632068i
$633$	8.22164	+	4.74676i	0.326781	+	0.188667i
$634$	15.8580	+	9.15560i	0.629800	+	0.363615i
$635$	−68.4074	−	18.3297i	−2.71467	−	0.727392i
$636$	1.96556			0.0779397
$637$	−20.2956	−	15.0029i	−0.804142	−	0.594437i
$638$	3.77605			0.149495
$639$	12.7442	+	3.41481i	0.504154	+	0.135088i
$640$	−3.11403	−	1.79789i	−0.123093	−	0.0710676i
$641$	−25.0065	−	14.4375i	−0.987696	−	0.570246i	−0.0831109	−	0.996540i	$-0.526486\pi$
$641$	−25.0065	−	14.4375i	−0.987696	−	0.570246i	−0.904585	+	0.426294i	$0.859819\pi$
$642$	−3.67067	+	13.6991i	−0.144870	+	0.540661i
$643$	−26.9605	−	26.9605i	−1.06322	−	1.06322i	−0.997862	−	0.0653555i	$-0.979182\pi$
$643$	−26.9605	−	26.9605i	−1.06322	−	1.06322i	−0.0653555	−	0.997862i	$-0.520818\pi$
$644$	13.2610	+	10.9574i	0.522557	+	0.431783i
$645$	−17.6096	−	17.6096i	−0.693379	−	0.693379i
$646$	0.0980360	+	0.169803i	0.00385718	+	0.00668083i
$647$	−8.33460	+	14.4359i	−0.327667	+	0.567535i	−0.982048	−	0.188629i	$-0.939596\pi$
$647$	−8.33460	+	14.4359i	−0.327667	+	0.567535i	0.654382	+	0.756164i	$0.272929\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−2.00013	−	3.46432i	−0.0785119	−	0.135987i
$650$	28.5666	+	1.16703i	1.12047	+	0.0457745i
$651$	−4.07882	−	5.73237i	−0.159862	−	0.224669i
$652$	−8.64568	+	8.64568i	−0.338591	+	0.338591i
$653$	11.9248	+	20.6544i	0.466654	+	0.808269i	0.999274	−	0.0380853i	$-0.0121259\pi$
$653$	11.9248	+	20.6544i	0.466654	+	0.808269i	−0.532620	+	0.846354i	$0.678793\pi$
$654$	−9.23660	+	15.9983i	−0.361180	+	0.625581i
$655$	−16.6061	−	61.9746i	−0.648852	−	2.42155i
$656$	−1.18267	+	4.41379i	−0.0461755	+	0.172329i
$657$	−2.47663	+	2.47663i	−0.0966227	+	0.0966227i
$658$	−8.60374	−	23.0935i	−0.335409	−	0.900279i
$659$	−21.2843			−0.829119			−0.414559	−	0.910022i	$-0.636064\pi$
$659$	−21.2843			−0.829119			−0.414559	+	0.910022i	$0.636064\pi$
$660$	2.10789	−	1.21699i	0.0820496	−	0.0473714i
$661$	4.69958	+	17.5391i	0.182792	+	0.682191i	0.995092	+	0.0989507i	$0.0315486\pi$
$661$	4.69958	+	17.5391i	0.182792	+	0.682191i	−0.812300	+	0.583240i	$0.801785\pi$
$662$	−10.3429	−	5.97145i	−0.401987	−	0.232087i
$663$	−5.91006	+	18.9292i	−0.229528	+	0.735149i
$664$			1.58000i			0.0613159i
$665$	−0.118405	−	0.317815i	−0.00459156	−	0.0123243i
$666$	−2.15680			−0.0835744
$667$	−31.4109	+	18.1351i	−1.21624	+	0.702194i
$668$	−10.1931	+	2.73124i	−0.394384	+	0.105675i
$669$	−1.17929	−	4.40116i	−0.0455939	−	0.170159i
$670$	−18.7839	−	5.03312i	−0.725684	−	0.194446i
$671$	2.10223	−	2.10223i	0.0811558	−	0.0811558i
$672$	−2.15573	+	1.53389i	−0.0831591	+	0.0591712i
$673$			43.9766i			1.69517i	0.530657	+	0.847587i	$0.321945\pi$
$673$			43.9766i			1.69517i	−0.530657	+	0.847587i	$0.678055\pi$
$674$	−2.74216	+	10.2339i	−0.105624	+	0.394194i
$675$	−3.96478	+	6.86720i	−0.152605	+	0.264319i
$676$	7.39668	−	10.6906i	0.284488	−	0.411177i
$677$	−12.9201	+	7.45943i	−0.496560	+	0.286689i	−0.727292	−	0.686328i	$-0.759221\pi$
$677$	−12.9201	+	7.45943i	−0.496560	+	0.286689i	0.230732	+	0.973017i	$0.425888\pi$
$678$	−7.80425	−	7.80425i	−0.299720	−	0.299720i
$679$	3.92123	+	41.2256i	0.150483	+	1.58209i
$680$		−	19.7766i		−	0.758396i
$681$	−11.7710	−	3.15403i	−0.451066	−	0.120863i
$682$	−1.73864	+	0.465867i	−0.0665759	+	0.0178390i
$683$	5.46019	−	1.46305i	0.208928	−	0.0559821i	−0.152837	−	0.988251i	$-0.548841\pi$
$683$	5.46019	−	1.46305i	0.208928	−	0.0559821i	0.361765	+	0.932269i	$0.382174\pi$
$684$	0.0344351	+	0.00922685i	0.00131666	+	0.000352797i
$685$			49.5179i			1.89198i
$686$	12.7953	−	13.3896i	0.488525	−	0.511217i
$687$	−1.11519	−	1.11519i	−0.0425472	−	0.0425472i
$688$	5.99797	−	3.46293i	0.228670	−	0.132023i
$689$	−1.55328	−	6.91463i	−0.0591754	−	0.263426i
$690$	−11.6896	+	20.2470i	−0.445016	+	0.770790i
$691$	3.94116	−	14.7086i	0.149929	−	0.559542i	−0.849558	−	0.527496i	$-0.823131\pi$
$691$	3.94116	−	14.7086i	0.149929	−	0.559542i	0.999486	−	0.0320460i	$-0.0102023\pi$
$692$			19.1420i			0.727670i
$693$	−0.169580	−	1.78287i	−0.00644181	−	0.0677255i
$694$	−5.94164	+	5.94164i	−0.225542	+	0.225542i
$695$	20.6582	+	5.53534i	0.783609	+	0.209967i
$696$	−1.44380	−	5.38835i	−0.0547272	−	0.204245i
$697$	−24.2756	+	6.50463i	−0.919504	+	0.246380i
$698$	−6.53496	+	3.77296i	−0.247352	+	0.142809i
$699$	23.6198			0.893382
$700$	−3.48668	+	20.6879i	−0.131784	+	0.781929i
$701$		−	32.7508i		−	1.23698i	−0.785792	−	0.618490i	$-0.787745\pi$
$701$		−	32.7508i		−	1.23698i	0.785792	−	0.618490i	$-0.212255\pi$
$702$	1.67382	+	3.19348i	0.0631741	+	0.120530i
$703$	0.0665883	+	0.0384448i	0.00251142	+	0.00144997i
$704$	0.175195	+	0.653837i	0.00660292	+	0.0246424i
$705$	29.0060	−	16.7466i	1.09243	−	0.630714i
$706$	−30.0301			−1.13020
$707$	−5.04950	+	1.88125i	−0.189906	+	0.0707515i
$708$	−4.17876	+	4.17876i	−0.157047	+	0.157047i
$709$	−1.94093	+	7.24363i	−0.0728930	+	0.272040i	−0.992747	−	0.120220i	$-0.961640\pi$
$709$	−1.94093	+	7.24363i	−0.0728930	+	0.272040i	0.919854	+	0.392260i	$0.128307\pi$
$710$	12.2789	+	45.8253i	0.460817	+	1.71979i
$711$	−8.22524	+	14.2465i	−0.308471	+	0.534287i
$712$	3.00294	+	5.20125i	0.112540	+	0.194925i
$713$	12.2254	−	12.2254i	0.457844	−	0.457844i
$714$	−13.2343	−	6.04979i	−0.495280	−	0.226408i
$715$	−5.94700	−	6.45359i	−0.222405	−	0.241351i
$716$	5.72605	+	9.91781i	0.213992	+	0.370646i
$717$	−10.9732	+	2.94025i	−0.409800	+	0.109806i
$718$	1.94781	−	3.37370i	0.0726915	−	0.125905i
$719$	8.09718	+	14.0247i	0.301974	+	0.523034i	0.976583	−	0.215141i	$-0.0690211\pi$
$719$	8.09718	+	14.0247i	0.301974	+	0.523034i	−0.674609	+	0.738175i	$0.735688\pi$
$720$	−2.54259	−	2.54259i	−0.0947569	−	0.0947569i
$721$	1.39723	−	8.29035i	0.0520357	−	0.308749i
$722$	13.4341	+	13.4341i	0.499967	+	0.499967i
$723$	−5.43169	+	20.2713i	−0.202007	+	0.753899i
$724$	−18.7133	−	10.8042i	−0.695476	−	0.401533i
$725$	−38.3082	−	22.1173i	−1.42273	−	0.821414i
$726$	10.1826	+	2.72842i	0.377912	+	0.101261i
$727$	43.7563			1.62283			0.811415	−	0.584470i	$-0.198698\pi$
$727$	43.7563			1.62283			0.811415	+	0.584470i	$0.198698\pi$
$728$	7.09962	+	6.37146i	0.263129	+	0.236142i
$729$	−1.00000			−0.0370370
$730$	−12.1650	−	3.25961i	−0.450247	−	0.120643i
$731$	32.9885	+	19.0459i	1.22012	+	0.704439i
$732$	−3.80365	−	2.19604i	−0.140587	−	0.0811679i
$733$	2.20256	−	8.22007i	0.0813535	−	0.303615i	−0.913245	−	0.407410i	$-0.866432\pi$
$733$	2.20256	−	8.22007i	0.0813535	−	0.303615i	0.994599	+	0.103795i	$0.0330986\pi$
$734$	−21.8753	−	21.8753i	−0.807432	−	0.807432i
$735$	20.8344	+	14.1236i	0.768490	+	0.520955i
$736$	−4.59751	−	4.59751i	−0.169467	−	0.169467i
$737$	1.83040	+	3.17034i	0.0674235	+	0.116781i
$738$	−2.28475	+	3.95729i	−0.0841026	+	0.145670i
$739$	18.5103	−	4.95982i	0.680912	−	0.182450i	0.0982466	−	0.995162i	$-0.468677\pi$
$739$	18.5103	−	4.95982i	0.680912	−	0.182450i	0.582665	+	0.812712i	$0.302010\pi$
$740$	−3.87768	−	6.71634i	−0.142546	−	0.246898i
$741$	0.00524672	−	0.128430i	0.000192743	−	0.00471800i
$742$	5.17703	−	0.492420i	0.190055	−	0.0180773i
$743$	4.27982	−	4.27982i	0.157011	−	0.157011i	−0.624230	−	0.781241i	$-0.714587\pi$
$743$	4.27982	−	4.27982i	0.157011	−	0.157011i	0.781241	+	0.624230i	$0.214587\pi$
$744$	1.32957	+	2.30288i	0.0487442	+	0.0844275i
$745$	−9.37978	+	16.2463i	−0.343649	+	0.595217i
$746$	−3.33930	−	12.4624i	−0.122260	−	0.456282i
$747$	−0.408934	+	1.52616i	−0.0149621	+	0.0558394i
$748$	−2.63251	+	2.63251i	−0.0962540	+	0.0962540i
$749$	−6.23608	+	37.0012i	−0.227861	+	1.35199i
$750$	−10.5340			−0.384649
$751$	−34.1153	+	19.6965i	−1.24489	+	0.718735i	−0.970085	−	0.242766i	$-0.921945\pi$
$751$	−34.1153	+	19.6965i	−1.24489	+	0.718735i	−0.274801	+	0.961501i	$0.588612\pi$
$752$	2.41080	+	8.99723i	0.0879129	+	0.328095i
$753$	7.51484	+	4.33870i	0.273856	+	0.158111i
$754$	−17.8146	+	9.33727i	−0.648770	+	0.340043i
$755$			12.3374i			0.449005i
$756$	−2.47928	+	0.923681i	−0.0901704	+	0.0335940i
$757$	6.46088			0.234825			0.117412	−	0.993083i	$-0.462540\pi$
$757$	6.46088			0.234825			0.117412	+	0.993083i	$0.462540\pi$
$758$	27.5474	−	15.9045i	1.00057	−	0.577678i
$759$	4.25116	−	1.13909i	0.154307	−	0.0413465i
$760$	0.0331776	+	0.123821i	0.00120348	+	0.00449144i
$761$	20.8277	+	5.58076i	0.755003	+	0.202302i	0.615736	−	0.787953i	$-0.288859\pi$
$761$	20.8277	+	5.58076i	0.755003	+	0.202302i	0.139267	+	0.990255i	$0.455525\pi$
$762$	13.9268	−	13.9268i	0.504516	−	0.504516i
$763$	−20.3200	+	44.4512i	−0.735633	+	1.60924i
$764$			13.7401i			0.497101i
$765$	5.11855	−	19.1027i	0.185062	−	0.690659i
$766$	18.6589	−	32.3181i	0.674172	−	1.16770i
$767$	18.0026	+	11.3981i	0.650038	+	0.411562i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	25.2762	+	25.2762i	0.911483	+	0.911483i	0.996389	−	0.0849064i	$-0.0270591\pi$
$769$	25.2762	+	25.2762i	0.911483	+	0.911483i	−0.0849064	+	0.996389i	$0.527059\pi$
$770$	5.24702	−	3.73347i	0.189089	−	0.134545i
$771$			13.3575i			0.481059i
$772$	10.4943	+	2.81194i	0.377699	+	0.101204i
$773$	22.9179	−	6.14084i	0.824301	−	0.220871i	0.178075	−	0.984017i	$-0.443013\pi$
$773$	22.9179	−	6.14084i	0.824301	−	0.220871i	0.646226	+	0.763146i	$0.276346\pi$
$774$	6.68987	−	1.79254i	0.240462	−	0.0644317i
$775$	20.3673	+	5.45739i	0.731614	+	0.196035i
$776$		−	15.6521i		−	0.561879i
$777$	−5.68072	+	0.540330i	−0.203795	+	0.0193842i
$778$	24.8842	+	24.8842i	0.892142	+	0.892142i
$779$	0.141077	−	0.0814507i	0.00505460	−	0.00291827i
$780$	−6.93527	+	10.9538i	−0.248322	+	0.392210i
$781$	4.46545	−	7.73439i	0.159786	−	0.276758i
$782$	9.25535	−	34.5414i	0.330971	−	1.23520i
$783$		−	5.57843i		−	0.199357i
$784$	−5.29363	+	4.58012i	−0.189058	+	0.163576i
$785$	−43.1345	+	43.1345i	−1.53954	+	1.53954i
$786$	17.2354	+	4.61822i	0.614767	+	0.164726i
$787$	0.370015	+	1.38091i	0.0131896	+	0.0492243i	0.972207	−	0.234123i	$-0.0752218\pi$
$787$	0.370015	+	1.38091i	0.0131896	+	0.0492243i	−0.959017	+	0.283347i	$0.908555\pi$
$788$	−23.6692	+	6.34215i	−0.843181	+	0.225930i
$789$	20.7793	−	11.9969i	0.739762	−	0.427102i
$790$	−59.1522			−2.10454
$791$	−22.5105	−	18.6002i	−0.800380	−	0.661346i
$792$			0.676902i			0.0240527i
$793$	−4.71958	+	15.1162i	−0.167597	+	0.536792i
$794$	−14.4513	−	8.34345i	−0.512857	−	0.296098i
$795$	1.82926	+	6.82689i	0.0648772	+	0.242125i
$796$	−1.49333	+	0.862176i	−0.0529298	+	0.0305590i
$797$	23.3642			0.827603			0.413802	−	0.910367i	$-0.364201\pi$
$797$	23.3642			0.827603			0.413802	+	0.910367i	$0.364201\pi$
$798$	0.0930088	+	0.0156755i	0.00329248	+	0.000554905i
$799$	−36.2250	+	36.2250i	−1.28155	+	1.28155i
$800$	2.05232	−	7.65937i	0.0725605	−	0.270800i
$801$	1.55444	+	5.80124i	0.0549233	+	0.204977i
$802$	−11.3375	+	19.6371i	−0.400341	+	0.693411i
$803$	1.18542	+	2.05321i	0.0418326	+	0.0724562i
$804$	3.82414	−	3.82414i	0.134867	−	0.134867i
$805$	−25.7165	+	56.2563i	−0.906386	+	1.98277i
$806$	7.05056	−	6.49710i	0.248345	−	0.228851i
$807$	−12.8128	−	22.1924i	−0.451031	−	0.781209i
$808$	1.96728	−	0.527132i	0.0692088	−	0.0185444i
$809$	15.0354	−	26.0421i	0.528616	−	0.915590i	−0.470827	−	0.882225i	$-0.656044\pi$
$809$	15.0354	−	26.0421i	0.528616	−	0.915590i	0.999443	−	0.0333644i	$-0.0106222\pi$
$810$	−1.79789	−	3.11403i	−0.0631712	−	0.109416i
$811$	−4.67851	−	4.67851i	−0.164285	−	0.164285i	0.620177	−	0.784462i	$-0.287061\pi$
$811$	−4.67851	−	4.67851i	−0.164285	−	0.164285i	−0.784462	+	0.620177i	$0.787061\pi$
$812$	−5.15269	−	13.8305i	−0.180824	−	0.485354i
$813$	6.30661	+	6.30661i	0.221183	+	0.221183i
$814$	−0.377861	+	1.41020i	−0.0132440	+	0.0494274i
$815$	−38.0747	−	21.9825i	−1.33370	−	0.770012i
$816$	4.76310	+	2.74997i	0.166742	+	0.0962684i
$817$	−0.238492	−	0.0639038i	−0.00834379	−	0.00223571i
$818$	39.1908			1.37027
$819$	5.20865	+	7.99187i	0.182005	+	0.279259i
$820$	−16.4308			−0.573790
$821$	−2.10235	−	0.563323i	−0.0733725	−	0.0196601i	0.221946	−	0.975059i	$-0.428759\pi$
$821$	−2.10235	−	0.563323i	−0.0733725	−	0.0196601i	−0.295319	+	0.955399i	$0.595426\pi$
$822$	−11.9262	−	6.88557i	−0.415973	−	0.240162i
$823$	−7.40111	−	4.27303i	−0.257987	−	0.148949i	0.365429	−	0.930839i	$-0.380922\pi$
$823$	−7.40111	−	4.27303i	−0.257987	−	0.148949i	−0.623416	+	0.781891i	$0.714256\pi$
$824$	−0.822436	+	3.06937i	−0.0286509	+	0.106927i
$825$	3.79542	+	3.79542i	0.132140	+	0.132140i
$826$	−9.95940	+	12.0532i	−0.346532	+	0.419383i
$827$	11.5515	+	11.5515i	0.401687	+	0.401687i	0.878827	−	0.477140i	$-0.158327\pi$
$827$	11.5515	+	11.5515i	0.401687	+	0.401687i	−0.477140	+	0.878827i	$0.658327\pi$
$828$	−3.25093	−	5.63078i	−0.112978	−	0.195683i
$829$	14.0849	−	24.3957i	0.489188	−	0.847298i	−0.510735	−	0.859738i	$-0.670627\pi$
$829$	14.0849	−	24.3957i	0.489188	−	0.847298i	0.999923	+	0.0124401i	$0.00395990\pi$
$830$	−5.48773	+	1.47043i	−0.190482	+	0.0510395i
$831$	2.54313	+	4.40484i	0.0882203	+	0.152802i
$832$	−2.44332	−	2.65145i	−0.0847068	−	0.0919226i
$833$	−36.3729	−	12.6188i	−1.26025	−	0.437216i
$834$	−4.20573	+	4.20573i	−0.145632	+	0.145632i
$835$	−18.9725	−	32.8614i	−0.656572	−	1.13722i
$836$	0.0120657	−	0.0208984i	0.000417301	−	0.000722787i
$837$	0.688234	+	2.56852i	0.0237888	+	0.0887812i
$838$	3.01044	−	11.2351i	0.103994	−	0.388110i
$839$	−10.4833	+	10.4833i	−0.361923	+	0.361923i	−0.864520	−	0.502598i	$-0.832378\pi$
$839$	−10.4833	+	10.4833i	−0.361923	+	0.361923i	0.502598	+	0.864520i	$0.332378\pi$
$840$	−7.33382	−	6.05986i	−0.253041	−	0.209085i
$841$	2.11888			0.0730650
$842$	−27.5241	+	15.8910i	−0.948542	+	0.547641i
$843$	3.60249	+	13.4447i	0.124076	+	0.463059i
$844$	−8.22164	−	4.74676i	−0.283000	−	0.163390i
$845$	44.0149	+	15.7412i	1.51416	+	0.541515i
$846$			9.31462i			0.320243i
$847$	27.5031	+	4.63530i	0.945018	+	0.159271i
$848$	−1.96556			−0.0674978
$849$	−26.4256	+	15.2568i	−0.906924	+	0.523613i
$850$	42.1261	−	11.2877i	1.44491	−	0.387164i
$851$	−3.62948	−	13.5454i	−0.124417	−	0.464330i
$852$	−12.7442	−	3.41481i	−0.436610	−	0.116989i
$853$	−19.0558	+	19.0558i	−0.652457	+	0.652457i	−0.953584	−	0.301127i	$-0.902637\pi$
$853$	−19.0558	+	19.0558i	−0.652457	+	0.652457i	0.301127	+	0.953584i	$0.402637\pi$
$854$	−10.5685	−	4.83116i	−0.361645	−	0.165319i
$855$			0.128188i			0.00438395i
$856$	3.67067	−	13.6991i	0.125461	−	0.468226i
$857$	−0.612591	+	1.06104i	−0.0209257	+	0.0362444i	−0.876299	−	0.481768i	$-0.839995\pi$
$857$	−0.612591	+	1.06104i	−0.0209257	+	0.0362444i	0.855373	+	0.518013i	$0.173328\pi$
$858$	2.38126	−	0.534921i	0.0812950	−	0.0182619i
$859$	20.4758	−	11.8217i	0.698626	−	0.403352i	−0.108209	−	0.994128i	$-0.534512\pi$
$859$	20.4758	−	11.8217i	0.698626	−	0.403352i	0.806836	+	0.590776i	$0.201178\pi$
$860$	17.6096	+	17.6096i	0.600484	+	0.600484i
$861$	−5.02631	+	10.9954i	−0.171296	+	0.374721i
$862$			27.5619i			0.938763i
$863$	−14.4966	−	3.88435i	−0.493470	−	0.132225i	0.00349778	−	0.999994i	$-0.498887\pi$
$863$	−14.4966	−	3.88435i	−0.493470	−	0.132225i	−0.496968	+	0.867769i	$0.665553\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−66.4849	+	17.8146i	−2.26056	+	0.605714i
$866$	24.1026	+	6.45826i	0.819039	+	0.219461i
$867$			13.2494i			0.449975i
$868$	4.07882	+	5.73237i	0.138444	+	0.194569i
$869$	7.87390	+	7.87390i	0.267104	+	0.267104i
$870$	17.3714	−	10.0294i	0.588945	−	0.340028i
$871$	−16.4749	−	10.4309i	−0.558231	−	0.353437i
$872$	9.23660	−	15.9983i	0.312791	−	0.541769i
$873$	4.05107	−	15.1188i	0.137108	−	0.511694i
$874$			0.231790i			0.00784042i
$875$	−27.7452	+	2.63903i	−0.937959	+	0.0892154i
$876$	2.47663	−	2.47663i	0.0836777	−	0.0836777i
$877$	4.94627	+	1.32535i	0.167024	+	0.0447539i	0.341362	−	0.939932i	$-0.389112\pi$
$877$	4.94627	+	1.32535i	0.167024	+	0.0447539i	−0.174338	+	0.984686i	$0.555779\pi$
$878$	1.62712	+	6.07249i	0.0549126	+	0.204937i
$879$	17.8791	−	4.79068i	0.603046	−	0.161586i
$880$	−2.10789	+	1.21699i	−0.0710570	+	0.0410248i
$881$	20.1823			0.679958			0.339979	−	0.940433i	$-0.389580\pi$
$881$	20.1823			0.679958			0.339979	+	0.940433i	$0.389580\pi$
$882$	−6.29867	+	3.05397i	−0.212087	+	0.102832i
$883$		−	18.2999i		−	0.615840i	−0.951412	−	0.307920i	$-0.900367\pi$
$883$		−	18.2999i		−	0.615840i	0.951412	−	0.307920i	$-0.0996329\pi$
$884$	5.91006	−	18.9292i	0.198777	−	0.636657i
$885$	−18.4028	−	10.6249i	−0.618604	−	0.357151i
$886$	−3.90093	−	14.5585i	−0.131054	−	0.489102i
$887$	−34.5328	+	19.9375i	−1.15950	+	0.669437i	−0.951184	−	0.308625i	$-0.900131\pi$
$887$	−34.5328	+	19.9375i	−1.15950	+	0.669437i	−0.208315	+	0.978062i	$0.566798\pi$
$888$	2.15680			0.0723775
$889$	33.1924	−	40.1704i	1.11324	−	1.34727i
$890$	−15.2705	+	15.2705i	−0.511869	+	0.511869i
$891$	−0.175195	+	0.653837i	−0.00586926	+	0.0219044i
$892$	1.17929	+	4.40116i	0.0394855	+	0.147362i
$893$	0.166032	−	0.287576i	0.00555605	−	0.00962337i
$894$	−2.60856	−	4.51816i	−0.0872433	−	0.151110i
$895$	−29.1180	+	29.1180i	−0.973308	+	0.973308i
$896$	2.15573	−	1.53389i	0.0720179	−	0.0512437i
$897$	−17.2394	+	15.8861i	−0.575606	+	0.530422i
$898$	3.18906	+	5.52362i	0.106420	+	0.184326i
$899$	−14.3283	+	3.83927i	−0.477877	+	0.128047i
$900$	3.96478	−	6.86720i	0.132159	−	0.228907i
$901$	−5.40525	−	9.36217i	−0.180075	−	0.311899i
$902$	2.18715	+	2.18715i	0.0728241	+	0.0728241i
$903$	17.1711	−	6.39729i	0.571419	−	0.212888i
$904$	7.80425	+	7.80425i	0.259565	+	0.259565i
$905$	20.1099	−	75.0510i	0.668474	−	2.49478i
$906$	−2.97141	−	1.71555i	−0.0987186	−	0.0569952i
$907$	−24.6276	−	14.2188i	−0.817747	−	0.472127i	0.0318916	−	0.999491i	$-0.489847\pi$
$907$	−24.6276	−	14.2188i	−0.817747	−	0.472127i	−0.849639	+	0.527365i	$0.823180\pi$
$908$	11.7710	+	3.15403i	0.390634	+	0.104670i
$909$	2.03668			0.0675525
$910$	−15.5224	+	30.5883i	−0.514561	+	1.01399i
$911$	47.3725			1.56952			0.784761	−	0.619798i	$-0.212786\pi$
$911$	47.3725			1.56952			0.784761	+	0.619798i	$0.212786\pi$
$912$	−0.0344351	−	0.00922685i	−0.00114026	−	0.000305531i
$913$	0.926219	+	0.534753i	0.0306534	+	0.0176977i
$914$	13.5498	+	7.82300i	0.448188	+	0.258762i
$915$	4.08750	−	15.2548i	0.135129	−	0.504307i
$916$	1.11519	+	1.11519i	0.0368470	+	0.0368470i
$917$	46.5527	+	7.84588i	1.53731	+	0.259094i
$918$	3.88905	+	3.88905i	0.128358	+	0.128358i
$919$	25.0995	+	43.4736i	0.827956	+	1.43406i	0.899639	+	0.436634i	$0.143829\pi$
$919$	25.0995	+	43.4736i	0.827956	+	1.43406i	−0.0716836	+	0.997427i	$0.522837\pi$
$920$	11.6896	−	20.2470i	0.385395	−	0.667523i
$921$	−17.6848	+	4.73861i	−0.582732	+	0.156143i
$922$	−0.430139	−	0.745023i	−0.0141659	−	0.0245360i
$923$	−1.94178	+	47.5313i	−0.0639146	+	1.56451i
$924$	0.169580	+	1.78287i	0.00557877	+	0.0586520i
$925$	12.0933	−	12.0933i	0.397625	−	0.397625i
$926$	14.8644	+	25.7459i	0.488475	+	0.846064i
$927$	−1.58882	+	2.75192i	−0.0521838	+	0.0903850i
$928$	1.44380	+	5.38835i	0.0473952	+	0.176881i
$929$	−4.27608	+	15.9586i	−0.140294	+	0.523583i	0.859626	+	0.510924i	$0.170696\pi$
$929$	−4.27608	+	15.9586i	−0.140294	+	0.523583i	−0.999920	+	0.0126597i	$0.995970\pi$
$930$	−6.76109	+	6.76109i	−0.221705	+	0.221705i
$931$	0.248900	+	0.0179861i	0.00815735	+	0.000589471i
$932$	−23.6198			−0.773692
$933$	17.3335	−	10.0075i	0.567473	−	0.327630i
$934$	3.83751	+	14.3218i	0.125567	+	0.468622i
$935$	−11.5933	−	6.69339i	−0.379141	−	0.218897i
$936$	−1.67382	−	3.19348i	−0.0547104	−	0.104382i
$937$		−	10.1910i		−	0.332924i	−0.986048	−	0.166462i	$-0.946766\pi$
$937$		−	10.1910i		−	0.332924i	0.986048	−	0.166462i	$-0.0532343\pi$
$938$	9.11423	−	11.0303i	0.297590	−	0.360152i
$939$	−11.0808			−0.361610
$940$	−29.0060	+	16.7466i	−0.946071	+	0.546214i
$941$	10.2229	−	2.73921i	0.333256	−	0.0892956i	−0.0883110	−	0.996093i	$-0.528147\pi$
$941$	10.2229	−	2.73921i	0.333256	−	0.0892956i	0.421567	+	0.906797i	$0.361480\pi$
$942$	−4.39080	−	16.3867i	−0.143060	−	0.533907i
$943$	−28.6978	−	7.68956i	−0.934530	−	0.250407i
$944$	4.17876	−	4.17876i	0.136007	−	0.136007i
$945$	−5.51552	−	7.75151i	−0.179420	−	0.252157i
$946$		−	4.68813i		−	0.152424i
$947$	4.66662	−	17.4161i	0.151645	−	0.565946i	−0.847725	−	0.530437i	$-0.822028\pi$
$947$	4.66662	−	17.4161i	0.151645	−	0.565946i	0.999369	−	0.0355092i	$-0.0113053\pi$
$948$	8.22524	−	14.2465i	0.267144	−	0.462706i
$949$	−10.6697	−	6.75536i	−0.346352	−	0.219288i
$950$	−0.244814	+	0.141344i	−0.00794283	+	0.00458579i
$951$	−12.9480	−	12.9480i	−0.419867	−	0.419867i
$952$	13.2343	+	6.04979i	0.428925	+	0.196075i
$953$		−	1.65771i		−	0.0536985i	−0.999639	−	0.0268492i	$-0.991453\pi$
$953$		−	1.65771i		−	0.0536985i	0.999639	−	0.0268492i	$-0.00854740\pi$
$954$	−1.89859	−	0.508725i	−0.0614691	−	0.0164706i
$955$	−47.7229	+	12.7873i	−1.54428	+	0.413788i
$956$	10.9732	−	2.94025i	0.354897	−	0.0950945i
$957$	−3.64739	−	0.977314i	−0.117903	−	0.0315921i
$958$		−	37.7022i		−	1.21810i
$959$	−33.1369	−	15.1479i	−1.07005	−	0.489150i
$960$	2.54259	+	2.54259i	0.0820619	+	0.0820619i
$961$	−20.7231	+	11.9645i	−0.668488	+	0.385952i
$962$	−1.70441	−	7.58738i	−0.0549523	−	0.244627i
$963$	7.09118	−	12.2823i	0.228510	−	0.395791i
$964$	5.43169	−	20.2713i	0.174943	−	0.652896i
$965$			39.0663i			1.25759i
$966$	−9.97315	−	14.0163i	−0.320881	−	0.450966i
$967$	−5.13419	+	5.13419i	−0.165104	+	0.165104i	−0.784824	−	0.619719i	$-0.787246\pi$
$967$	−5.13419	+	5.13419i	−0.165104	+	0.165104i	0.619719	+	0.784824i	$0.287246\pi$
$968$	−10.1826	−	2.72842i	−0.327281	−	0.0876947i
$969$	−0.0507472	−	0.189391i	−0.00163023	−	0.00608412i
$970$	54.3638	−	14.5667i	1.74552	−	0.467710i
$971$	−20.0687	+	11.5867i	−0.644037	+	0.371835i	−0.786168	−	0.618013i	$-0.787938\pi$
$971$	−20.0687	+	11.5867i	−0.644037	+	0.371835i	0.142131	+	0.989848i	$0.454605\pi$
$972$	1.00000			0.0320750
$973$	−10.0237	+	12.1309i	−0.321344	+	0.388900i
$974$		−	17.8081i		−	0.570609i
$975$	−27.2912	−	8.52084i	−0.874017	−	0.272885i
$976$	3.80365	+	2.19604i	0.121752	+	0.0702935i
$977$	14.5454	+	54.2842i	0.465349	+	1.73671i	0.655730	+	0.754996i	$0.272361\pi$
$977$	14.5454	+	54.2842i	0.465349	+	1.73671i	−0.190381	+	0.981710i	$0.560972\pi$
$978$	10.5888	−	6.11342i	0.338591	−	0.195486i
$979$	4.06539			0.129931
$980$	−20.8344	−	14.1236i	−0.665532	−	0.451161i
$981$	13.0625	−	13.0625i	0.417054	−	0.417054i
$982$	−3.68131	+	13.7388i	−0.117475	+	0.438424i
$983$	12.7710	+	47.6621i	0.407332	+	1.52018i	0.799714	+	0.600381i	$0.204984\pi$
$983$	12.7710	+	47.6621i	0.407332	+	1.52018i	−0.392382	+	0.919802i	$0.628349\pi$
$984$	2.28475	−	3.95729i	0.0728350	−	0.126154i
$985$	−44.0557	−	76.3067i	−1.40373	−	2.43133i
$986$	−21.6948	+	21.6948i	−0.690903	+	0.690903i
$987$	2.33353	+	24.5334i	0.0742772	+	0.780908i
$988$	−0.00524672	+	0.128430i	−0.000166921	+	0.00408590i
$989$	22.5155	+	38.9980i	0.715951	+	1.24006i
$990$	−2.35105	+	0.629961i	−0.0747212	+	0.0200215i
$991$	−0.0208370	+	0.0360907i	−0.000661908	+	0.00114646i	−0.866356	−	0.499427i	$-0.833544\pi$
$991$	−0.0208370	+	0.0360907i	−0.000661908	+	0.00114646i	0.865694	+	0.500573i	$0.166877\pi$
$992$	−1.32957	−	2.30288i	−0.0422138	−	0.0731164i
$993$	8.44491	+	8.44491i	0.267991	+	0.267991i
$994$	−34.4220	−	5.80140i	−1.09180	−	0.184009i
$995$	−4.38433	−	4.38433i	−0.138992	−	0.138992i
$996$	0.408934	−	1.52616i	0.0129576	−	0.0483583i
$997$	−30.9815	−	17.8872i	−0.981193	−	0.566492i	−0.0785628	−	0.996909i	$-0.525033\pi$
$997$	−30.9815	−	17.8872i	−0.981193	−	0.566492i	−0.902630	+	0.430417i	$0.858366\pi$
$998$	6.39358	+	3.69133i	0.202385	+	0.116847i
$999$	2.08331	+	0.558221i	0.0659130	+	0.0176613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.b.31.6	yes	40
7.5	odd	6		546.2.bz.a.187.1	yes	40
13.8	odd	4		546.2.bz.a.73.1	✓	40
91.47	even	12	inner	546.2.bz.b.229.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.1	✓	40	13.8	odd	4
546.2.bz.a.187.1	yes	40	7.5	odd	6
546.2.bz.b.31.6	yes	40	1.1	even	1	trivial
546.2.bz.b.229.6	yes	40	91.47	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.930654 + 3.47325i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.03957 - 1.68528i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.930654 + 3.47325i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-2.03957 - 1.68528i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.79789 + 3.11403i) q^{10} +(0.653837 - 0.175195i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.65145 + 2.44332i) q^{13} +(-1.53389 - 2.15573i) q^{14} +(2.54259 - 2.54259i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.74997 + 4.76310i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.00922685 - 0.0344351i) q^{19} +(-2.54259 + 2.54259i) q^{20} +(0.923681 + 2.47928i) q^{21} +0.676902 q^{22} +(-5.63078 + 3.25093i) q^{23} +(-0.258819 - 0.965926i) q^{24} +(-6.86720 - 3.96478i) q^{25} +(-3.19348 + 1.67382i) q^{26} -1.00000i q^{27} +(-0.923681 - 2.47928i) q^{28} +5.57843 q^{29} +(3.11403 - 1.79789i) q^{30} +(-2.56852 + 0.688234i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.653837 - 0.175195i) q^{33} +(-3.88905 + 3.88905i) q^{34} +(7.75151 - 5.51552i) q^{35} +1.00000i q^{36} +(-0.558221 + 2.08331i) q^{37} +(0.0178249 - 0.0308736i) q^{38} +(3.51788 - 0.790248i) q^{39} +(-3.11403 + 1.79789i) q^{40} +(3.23112 + 3.23112i) q^{41} +(0.250524 + 2.63386i) q^{42} -6.92586i q^{43} +(0.653837 + 0.175195i) q^{44} +(-3.47325 + 0.930654i) q^{45} +(-6.28032 + 1.68281i) q^{46} +(8.99723 + 2.41080i) q^{47} -1.00000i q^{48} +(1.31969 + 6.87448i) q^{49} +(-5.60705 - 5.60705i) q^{50} +(4.76310 - 2.74997i) q^{51} +(-3.51788 + 0.790248i) q^{52} +(-0.982782 + 1.70223i) q^{53} +(0.258819 - 0.965926i) q^{54} +2.43398i q^{55} +(-0.250524 - 2.63386i) q^{56} +(-0.0252082 + 0.0252082i) q^{57} +(5.38835 + 1.44380i) q^{58} +(-1.52953 - 5.70829i) q^{59} +(3.47325 - 0.930654i) q^{60} +(3.80365 - 2.19604i) q^{61} -2.65913 q^{62} +(0.439707 - 2.60896i) q^{63} +1.00000i q^{64} +(-6.01866 - 11.4830i) q^{65} +(-0.586214 - 0.338451i) q^{66} +(1.39973 + 5.22388i) q^{67} +(-4.76310 + 2.74997i) q^{68} +6.50186 q^{69} +(8.91491 - 3.32135i) q^{70} +(9.32942 - 9.32942i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(0.906511 + 3.38315i) q^{73} +(-1.07840 + 1.86784i) q^{74} +(3.96478 + 6.86720i) q^{75} +(0.0252082 - 0.0252082i) q^{76} +(-1.62880 - 0.744573i) q^{77} +(3.60255 + 0.147174i) q^{78} +(8.22524 + 14.2465i) q^{79} +(-3.47325 + 0.930654i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.28475 + 3.95729i) q^{82} +(1.11723 + 1.11723i) q^{83} +(-0.439707 + 2.60896i) q^{84} +(-13.9841 - 13.9841i) q^{85} +(1.79254 - 6.68987i) q^{86} +(-4.83106 - 2.78922i) q^{87} +(0.586214 + 0.338451i) q^{88} +(5.80124 + 1.55444i) q^{89} -3.59577 q^{90} +(9.52549 - 0.514887i) q^{91} -6.50186 q^{92} +(2.56852 + 0.688234i) q^{93} +(8.06670 + 4.65731i) q^{94} +(0.111014 + 0.0640942i) q^{95} +(0.258819 - 0.965926i) q^{96} +(-11.0677 - 11.0677i) q^{97} +(-0.504522 + 6.98179i) q^{98} +(0.478642 + 0.478642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

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