LMFDB - Embedded newform 546.2.bi.e.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (of order $6$, degree $2$, 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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.e.257.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.565041 - 1.63729i) q^{3} +1.00000 q^{4} +(1.26448 - 0.730045i) q^{5} +(0.565041 + 1.63729i) q^{6} +(-1.08820 + 2.41160i) q^{7} -1.00000 q^{8} +(-2.36146 + 1.85028i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.565041 - 1.63729i) q^{3} +1.00000 q^{4} +(1.26448 - 0.730045i) q^{5} +(0.565041 + 1.63729i) q^{6} +(-1.08820 + 2.41160i) q^{7} -1.00000 q^{8} +(-2.36146 + 1.85028i) q^{9} +(-1.26448 + 0.730045i) q^{10} +(1.75974 + 3.04796i) q^{11} +(-0.565041 - 1.63729i) q^{12} +(0.214878 + 3.59914i) q^{13} +(1.08820 - 2.41160i) q^{14} +(-1.90978 - 1.65781i) q^{15} +1.00000 q^{16} -7.58718 q^{17} +(2.36146 - 1.85028i) q^{18} +(-1.72681 + 2.99093i) q^{19} +(1.26448 - 0.730045i) q^{20} +(4.56338 + 0.419048i) q^{21} +(-1.75974 - 3.04796i) q^{22} +3.60696i q^{23} +(0.565041 + 1.63729i) q^{24} +(-1.43407 + 2.48388i) q^{25} +(-0.214878 - 3.59914i) q^{26} +(4.36376 + 2.82092i) q^{27} +(-1.08820 + 2.41160i) q^{28} +(-0.170773 - 0.0985961i) q^{29} +(1.90978 + 1.65781i) q^{30} +(5.34484 - 9.25753i) q^{31} -1.00000 q^{32} +(3.99607 - 4.60343i) q^{33} +7.58718 q^{34} +(0.384576 + 3.84385i) q^{35} +(-2.36146 + 1.85028i) q^{36} -5.56471i q^{37} +(1.72681 - 2.99093i) q^{38} +(5.77144 - 2.38548i) q^{39} +(-1.26448 + 0.730045i) q^{40} +(2.60543 + 1.50425i) q^{41} +(-4.56338 - 0.419048i) q^{42} +(5.61139 + 9.71922i) q^{43} +(1.75974 + 3.04796i) q^{44} +(-1.63522 + 4.06360i) q^{45} -3.60696i q^{46} +(-11.0787 + 6.39629i) q^{47} +(-0.565041 - 1.63729i) q^{48} +(-4.63164 - 5.24861i) q^{49} +(1.43407 - 2.48388i) q^{50} +(4.28707 + 12.4224i) q^{51} +(0.214878 + 3.59914i) q^{52} +(4.21555 + 2.43385i) q^{53} +(-4.36376 - 2.82092i) q^{54} +(4.45029 + 2.56938i) q^{55} +(1.08820 - 2.41160i) q^{56} +(5.87274 + 1.13730i) q^{57} +(0.170773 + 0.0985961i) q^{58} +1.30815i q^{59} +(-1.90978 - 1.65781i) q^{60} +(0.865717 + 0.499822i) q^{61} +(-5.34484 + 9.25753i) q^{62} +(-1.89239 - 7.70836i) q^{63} +1.00000 q^{64} +(2.89925 + 4.39416i) q^{65} +(-3.99607 + 4.60343i) q^{66} +(4.78794 - 2.76432i) q^{67} -7.58718 q^{68} +(5.90566 - 2.03808i) q^{69} +(-0.384576 - 3.84385i) q^{70} +(5.33718 + 9.24427i) q^{71} +(2.36146 - 1.85028i) q^{72} +(-2.94410 + 5.09933i) q^{73} +5.56471i q^{74} +(4.87714 + 0.944496i) q^{75} +(-1.72681 + 2.99093i) q^{76} +(-9.26540 + 0.927001i) q^{77} +(-5.77144 + 2.38548i) q^{78} +(0.174645 + 0.302494i) q^{79} +(1.26448 - 0.730045i) q^{80} +(2.15296 - 8.73869i) q^{81} +(-2.60543 - 1.50425i) q^{82} -3.72979i q^{83} +(4.56338 + 0.419048i) q^{84} +(-9.59380 + 5.53898i) q^{85} +(-5.61139 - 9.71922i) q^{86} +(-0.0649367 + 0.335317i) q^{87} +(-1.75974 - 3.04796i) q^{88} -14.4601i q^{89} +(1.63522 - 4.06360i) q^{90} +(-8.91353 - 3.39839i) q^{91} +3.60696i q^{92} +(-18.1773 - 3.52018i) q^{93} +(11.0787 - 6.39629i) q^{94} +5.04260i q^{95} +(0.565041 + 1.63729i) q^{96} +(-1.72747 - 2.99206i) q^{97} +(4.63164 + 5.24861i) q^{98} +(-9.79510 - 3.94162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.565041	−	1.63729i	−0.326227	−	0.945292i
$3$	−0.565041	−	1.63729i	−0.326227	−	0.945292i
$4$	1.00000			0.500000
$5$	1.26448	−	0.730045i	0.565491	−	0.326486i	−0.189856	−	0.981812i	$-0.560802\pi$
$5$	1.26448	−	0.730045i	0.565491	−	0.326486i	0.755346	+	0.655326i	$0.227469\pi$
$6$	0.565041	+	1.63729i	0.230677	+	0.668422i
$7$	−1.08820	+	2.41160i	−0.411301	+	0.911500i
$7$	−1.08820	+	2.41160i	−0.411301	+	0.911500i
$8$	−1.00000			−0.353553
$9$	−2.36146	+	1.85028i	−0.787152	+	0.616759i
$10$	−1.26448	+	0.730045i	−0.399862	+	0.230861i
$11$	1.75974	+	3.04796i	0.530581	+	0.918993i	0.999363	+	0.0356795i	$0.0113596\pi$
$11$	1.75974	+	3.04796i	0.530581	+	0.918993i	−0.468782	+	0.883314i	$0.655307\pi$
$12$	−0.565041	−	1.63729i	−0.163113	−	0.472646i
$13$	0.214878	+	3.59914i	0.0595966	+	0.998223i
$13$	0.214878	+	3.59914i	0.0595966	+	0.998223i
$14$	1.08820	−	2.41160i	0.290834	−	0.644528i
$15$	−1.90978	−	1.65781i	−0.493103	−	0.428045i
$16$	1.00000			0.250000
$17$	−7.58718			−1.84016			−0.920080	−	0.391729i	$-0.871877\pi$
$17$	−7.58718			−1.84016			−0.920080	+	0.391729i	$0.871877\pi$
$18$	2.36146	−	1.85028i	0.556601	−	0.436114i
$19$	−1.72681	+	2.99093i	−0.396158	+	0.686165i	−0.993248	−	0.116008i	$-0.962990\pi$
$19$	−1.72681	+	2.99093i	−0.396158	+	0.686165i	0.597090	+	0.802174i	$0.296323\pi$
$20$	1.26448	−	0.730045i	0.282745	−	0.163243i
$21$	4.56338	+	0.419048i	0.995810	+	0.0914439i
$22$	−1.75974	−	3.04796i	−0.375177	−	0.649826i
$23$			3.60696i			0.752104i	0.926599	+	0.376052i	$0.122719\pi$
$23$			3.60696i			0.752104i	−0.926599	+	0.376052i	$0.877281\pi$
$24$	0.565041	+	1.63729i	0.115339	+	0.334211i
$25$	−1.43407	+	2.48388i	−0.286814	+	0.496776i
$26$	−0.214878	−	3.59914i	−0.0421411	−	0.705850i
$27$	4.36376	+	2.82092i	0.839807	+	0.542885i
$28$	−1.08820	+	2.41160i	−0.205650	+	0.455750i
$29$	−0.170773	−	0.0985961i	−0.0317118	−	0.0183088i	0.484060	−	0.875035i	$-0.339162\pi$
$29$	−0.170773	−	0.0985961i	−0.0317118	−	0.0183088i	−0.515772	+	0.856726i	$0.672495\pi$
$30$	1.90978	+	1.65781i	0.348676	+	0.302674i
$31$	5.34484	−	9.25753i	0.959961	−	1.66270i	0.237377	−	0.971418i	$-0.423712\pi$
$31$	5.34484	−	9.25753i	0.959961	−	1.66270i	0.722584	−	0.691283i	$-0.242954\pi$
$32$	−1.00000			−0.176777
$33$	3.99607	−	4.60343i	0.695627	−	0.801354i
$34$	7.58718			1.30119
$35$	0.384576	+	3.84385i	0.0650052	+	0.649729i
$36$	−2.36146	+	1.85028i	−0.393576	+	0.308379i
$37$		−	5.56471i		−	0.914833i	−0.889252	−	0.457417i	$-0.848775\pi$
$37$		−	5.56471i		−	0.914833i	0.889252	−	0.457417i	$-0.151225\pi$
$38$	1.72681	−	2.99093i	0.280126	−	0.485192i
$39$	5.77144	−	2.38548i	0.924169	−	0.381983i
$40$	−1.26448	+	0.730045i	−0.199931	+	0.115430i
$41$	2.60543	+	1.50425i	0.406900	+	0.234924i	0.689457	−	0.724327i	$-0.257849\pi$
$41$	2.60543	+	1.50425i	0.406900	+	0.234924i	−0.282557	+	0.959250i	$0.591183\pi$
$42$	−4.56338	−	0.419048i	−0.704144	−	0.0646606i
$43$	5.61139	+	9.71922i	0.855730	+	1.48217i	0.875967	+	0.482372i	$0.160225\pi$
$43$	5.61139	+	9.71922i	0.855730	+	1.48217i	−0.0202369	+	0.999795i	$0.506442\pi$
$44$	1.75974	+	3.04796i	0.265291	+	0.459497i
$45$	−1.63522	+	4.06360i	−0.243764	+	0.605766i
$46$		−	3.60696i		−	0.531818i
$47$	−11.0787	+	6.39629i	−1.61599	+	0.932994i	−0.628051	+	0.778172i	$0.716147\pi$
$47$	−11.0787	+	6.39629i	−1.61599	+	0.932994i	−0.987942	+	0.154822i	$0.950520\pi$
$48$	−0.565041	−	1.63729i	−0.0815567	−	0.236323i
$49$	−4.63164	−	5.24861i	−0.661663	−	0.749801i
$50$	1.43407	−	2.48388i	0.202808	−	0.351273i
$51$	4.28707	+	12.4224i	0.600309	+	1.73949i
$52$	0.214878	+	3.59914i	0.0297983	+	0.499111i
$53$	4.21555	+	2.43385i	0.579051	+	0.334315i	0.760756	−	0.649038i	$-0.224828\pi$
$53$	4.21555	+	2.43385i	0.579051	+	0.334315i	−0.181705	+	0.983353i	$0.558162\pi$
$54$	−4.36376	−	2.82092i	−0.593833	−	0.383878i
$55$	4.45029	+	2.56938i	0.600077	+	0.346455i
$56$	1.08820	−	2.41160i	0.145417	−	0.322264i
$57$	5.87274	+	1.13730i	0.777864	+	0.150639i
$58$	0.170773	+	0.0985961i	0.0224236	+	0.0129463i
$59$			1.30815i			0.170306i	0.996368	+	0.0851532i	$0.0271380\pi$
$59$			1.30815i			0.170306i	−0.996368	+	0.0851532i	$0.972862\pi$
$60$	−1.90978	−	1.65781i	−0.246551	−	0.214023i
$61$	0.865717	+	0.499822i	0.110844	+	0.0639956i	0.554397	−	0.832252i	$-0.312949\pi$
$61$	0.865717	+	0.499822i	0.110844	+	0.0639956i	−0.443553	+	0.896248i	$0.646282\pi$
$62$	−5.34484	+	9.25753i	−0.678795	+	1.17571i
$63$	−1.89239	−	7.70836i	−0.238419	−	0.971162i
$64$	1.00000			0.125000
$65$	2.89925	+	4.39416i	0.359607	+	0.545028i
$66$	−3.99607	+	4.60343i	−0.491883	+	0.566643i
$67$	4.78794	−	2.76432i	0.584940	−	0.337715i	−0.178154	−	0.984003i	$-0.557013\pi$
$67$	4.78794	−	2.76432i	0.584940	−	0.337715i	0.763094	+	0.646287i	$0.223679\pi$
$68$	−7.58718			−0.920080
$69$	5.90566	−	2.03808i	0.710958	−	0.245356i
$70$	−0.384576	−	3.84385i	−0.0459656	−	0.459427i
$71$	5.33718	+	9.24427i	0.633407	+	1.09709i	0.986850	+	0.161637i	$0.0516773\pi$
$71$	5.33718	+	9.24427i	0.633407	+	1.09709i	−0.353443	+	0.935456i	$0.614989\pi$
$72$	2.36146	−	1.85028i	0.278300	−	0.218057i
$73$	−2.94410	+	5.09933i	−0.344581	+	0.596832i	−0.985278	−	0.170963i	$-0.945312\pi$
$73$	−2.94410	+	5.09933i	−0.344581	+	0.596832i	0.640697	+	0.767794i	$0.278646\pi$
$74$			5.56471i			0.646885i
$75$	4.87714	+	0.944496i	0.563164	+	0.109061i
$76$	−1.72681	+	2.99093i	−0.198079	+	0.343083i
$77$	−9.26540	+	0.927001i	−1.05589	+	0.105642i
$78$	−5.77144	+	2.38548i	−0.653486	+	0.270103i
$79$	0.174645	+	0.302494i	0.0196491	+	0.0340332i	0.875683	−	0.482887i	$-0.160412\pi$
$79$	0.174645	+	0.302494i	0.0196491	+	0.0340332i	−0.856034	+	0.516920i	$0.827078\pi$
$80$	1.26448	−	0.730045i	0.141373	−	0.0816215i
$81$	2.15296	−	8.73869i	0.239218	−	0.970966i
$82$	−2.60543	−	1.50425i	−0.287722	−	0.166116i
$83$		−	3.72979i		−	0.409398i	−0.978825	−	0.204699i	$-0.934379\pi$
$83$		−	3.72979i		−	0.409398i	0.978825	−	0.204699i	$-0.0656215\pi$
$84$	4.56338	+	0.419048i	0.497905	+	0.0457219i
$85$	−9.59380	+	5.53898i	−1.04059	+	0.600787i
$86$	−5.61139	−	9.71922i	−0.605092	−	1.04805i
$87$	−0.0649367	+	0.335317i	−0.00696194	+	0.0359498i
$88$	−1.75974	−	3.04796i	−0.187589	−	0.324913i
$89$		−	14.4601i		−	1.53276i	−0.642385	−	0.766382i	$-0.722055\pi$
$89$		−	14.4601i		−	1.53276i	0.642385	−	0.766382i	$-0.277945\pi$
$90$	1.63522	−	4.06360i	0.172367	−	0.428341i
$91$	−8.91353	−	3.39839i	−0.934392	−	0.356248i
$92$			3.60696i			0.376052i
$93$	−18.1773	−	3.52018i	−1.88490	−	0.365026i
$94$	11.0787	−	6.39629i	1.14268	−	0.659726i
$95$			5.04260i			0.517360i
$96$	0.565041	+	1.63729i	0.0576693	+	0.167106i
$97$	−1.72747	−	2.99206i	−0.175398	−	0.303798i	0.764901	−	0.644148i	$-0.222788\pi$
$97$	−1.72747	−	2.99206i	−0.175398	−	0.303798i	−0.940299	+	0.340350i	$0.889455\pi$
$98$	4.63164	+	5.24861i	0.467866	+	0.530190i
$99$	−9.79510	−	3.94162i	−0.984445	−	0.396147i
$100$	−1.43407	+	2.48388i	−0.143407	+	0.248388i
$101$	−5.80861	−	10.0608i	−0.577979	−	1.00109i	−0.995711	−	0.0925183i	$-0.970508\pi$
$101$	−5.80861	−	10.0608i	−0.577979	−	1.00109i	0.417732	−	0.908570i	$-0.362825\pi$
$102$	−4.28707	−	12.4224i	−0.424483	−	1.23000i
$103$	16.2249	−	9.36744i	1.59869	−	0.923001i	0.606944	−	0.794745i	$-0.292395\pi$
$103$	16.2249	−	9.36744i	1.59869	−	0.923001i	0.991741	−	0.128257i	$-0.0409381\pi$
$104$	−0.214878	−	3.59914i	−0.0210706	−	0.352925i
$105$	6.07620	−	2.80159i	0.592977	−	0.273408i
$106$	−4.21555	−	2.43385i	−0.409451	−	0.236397i
$107$			0.350806i			0.0339137i	0.999856	+	0.0169568i	$0.00539779\pi$
$107$			0.350806i			0.0339137i	−0.999856	+	0.0169568i	$0.994602\pi$
$108$	4.36376	+	2.82092i	0.419903	+	0.271443i
$109$	−8.12542	−	4.69121i	−0.778274	−	0.449337i	0.0575444	−	0.998343i	$-0.481673\pi$
$109$	−8.12542	−	4.69121i	−0.778274	−	0.449337i	−0.835818	+	0.549006i	$0.815006\pi$
$110$	−4.45029	−	2.56938i	−0.424319	−	0.244980i
$111$	−9.11107	+	3.14429i	−0.864784	+	0.298443i
$112$	−1.08820	+	2.41160i	−0.102825	+	0.227875i
$113$	−5.03517	+	2.90706i	−0.473669	+	0.273473i	−0.717774	−	0.696276i	$-0.754839\pi$
$113$	−5.03517	+	2.90706i	−0.473669	+	0.273473i	0.244105	+	0.969749i	$0.421506\pi$
$114$	−5.87274	−	1.13730i	−0.550033	−	0.106518i
$115$	2.63325	+	4.56092i	0.245552	+	0.425308i
$116$	−0.170773	−	0.0985961i	−0.0158559	−	0.00915442i
$117$	−7.16683	−	8.10164i	−0.662574	−	0.748997i
$118$		−	1.30815i		−	0.120425i
$119$	8.25637	−	18.2972i	0.756860	−	1.67731i
$120$	1.90978	+	1.65781i	0.174338	+	0.151337i
$121$	−0.693357	+	1.20093i	−0.0630324	+	0.109175i
$122$	−0.865717	−	0.499822i	−0.0783783	−	0.0452518i
$123$	0.990716	−	5.11581i	0.0893298	−	0.461277i
$124$	5.34484	−	9.25753i	0.479980	−	0.831350i
$125$			11.4882i			1.02754i
$126$	1.89239	+	7.70836i	0.168587	+	0.686716i
$127$	−7.87940	+	13.6475i	−0.699183	+	1.21102i	0.269567	+	0.962982i	$0.413120\pi$
$127$	−7.87940	+	13.6475i	−0.699183	+	1.21102i	−0.968750	+	0.248039i	$0.920214\pi$
$128$	−1.00000			−0.0883883
$129$	12.7425	−	14.6793i	1.12192	−	1.29244i
$130$	−2.89925	−	4.39416i	−0.254281	−	0.385393i
$131$	6.32520	+	10.9556i	0.552635	+	0.957192i	0.998083	+	0.0618843i	$0.0197110\pi$
$131$	6.32520	+	10.9556i	0.552635	+	0.957192i	−0.445448	+	0.895308i	$0.646956\pi$
$132$	3.99607	−	4.60343i	0.347813	−	0.400677i
$133$	−5.33380	−	7.41911i	−0.462499	−	0.643318i
$134$	−4.78794	+	2.76432i	−0.413615	+	0.238801i
$135$	7.57727	+	0.381234i	0.652147	+	0.0328114i
$136$	7.58718			0.650595
$137$	1.25158			0.106930			0.0534648	−	0.998570i	$-0.482974\pi$
$137$	1.25158			0.106930			0.0534648	+	0.998570i	$0.482974\pi$
$138$	−5.90566	+	2.03808i	−0.502723	+	0.173493i
$139$	8.68419	−	5.01382i	0.736583	−	0.425267i	−0.0842424	−	0.996445i	$-0.526847\pi$
$139$	8.68419	−	5.01382i	0.736583	−	0.425267i	0.820826	+	0.571179i	$0.193514\pi$
$140$	0.384576	+	3.84385i	0.0325026	+	0.324864i
$141$	16.7325	+	14.5249i	1.40913	+	1.22322i
$142$	−5.33718	−	9.24427i	−0.447886	−	0.775762i
$143$	−10.5919	+	6.98849i	−0.885739	+	0.584407i
$144$	−2.36146	+	1.85028i	−0.196788	+	0.154190i
$145$	−0.287918			−0.0239103
$146$	2.94410	−	5.09933i	0.243655	−	0.422024i
$147$	−5.97644	+	10.5490i	−0.492929	+	0.870070i
$148$		−	5.56471i		−	0.457417i
$149$	−1.62311	+	2.81131i	−0.132970	+	0.230311i	−0.924820	−	0.380404i	$-0.875785\pi$
$149$	−1.62311	+	2.81131i	−0.132970	+	0.230311i	0.791850	+	0.610716i	$0.209118\pi$
$150$	−4.87714	−	0.944496i	−0.398217	−	0.0771178i
$151$	−8.04225	−	4.64320i	−0.654469	−	0.377858i	0.135697	−	0.990750i	$-0.456673\pi$
$151$	−8.04225	−	4.64320i	−0.654469	−	0.377858i	−0.790166	+	0.612892i	$0.790006\pi$
$152$	1.72681	−	2.99093i	0.140063	−	0.242596i
$153$	17.9168	−	14.0384i	1.44849	−	1.13494i
$154$	9.26540	−	0.927001i	0.746627	−	0.0746999i
$155$		−	15.6079i		−	1.25366i
$156$	5.77144	−	2.38548i	0.462085	−	0.190991i
$157$	−16.2305	−	9.37071i	−1.29534	−	0.747864i	−0.315743	−	0.948845i	$-0.602254\pi$
$157$	−16.2305	−	9.37071i	−1.29534	−	0.747864i	−0.979595	+	0.200981i	$0.935587\pi$
$158$	−0.174645	−	0.302494i	−0.0138940	−	0.0240651i
$159$	1.60297	−	8.27732i	0.127124	−	0.656434i
$160$	−1.26448	+	0.730045i	−0.0999656	+	0.0577151i
$161$	−8.69856	−	3.92510i	−0.685542	−	0.309341i
$162$	−2.15296	+	8.73869i	−0.169153	+	0.686577i
$163$	0.787553	+	0.454694i	0.0616859	+	0.0356144i	0.530526	−	0.847669i	$-0.321995\pi$
$163$	0.787553	+	0.454694i	0.0616859	+	0.0356144i	−0.468840	+	0.883283i	$0.655328\pi$
$164$	2.60543	+	1.50425i	0.203450	+	0.117462i
$165$	1.69223	−	8.73824i	0.131740	−	0.680271i
$166$			3.72979i			0.289488i
$167$	11.6602	+	6.73204i	0.902297	+	0.520941i	0.877945	−	0.478762i	$-0.158914\pi$
$167$	11.6602	+	6.73204i	0.902297	+	0.520941i	0.0243520	+	0.999703i	$0.492248\pi$
$168$	−4.56338	−	0.419048i	−0.352072	−	0.0323303i
$169$	−12.9077	+	1.54676i	−0.992896	+	0.118981i
$170$	9.59380	−	5.53898i	0.735811	−	0.424821i
$171$	−1.45625	−	10.2580i	−0.111362	−	0.784451i
$172$	5.61139	+	9.71922i	0.427865	+	0.741084i
$173$	−5.08435	+	8.80635i	−0.386556	+	0.669534i	−0.991984	−	0.126366i	$-0.959669\pi$
$173$	−5.08435	+	8.80635i	−0.386556	+	0.669534i	0.605428	+	0.795900i	$0.293002\pi$
$174$	0.0649367	−	0.335317i	0.00492284	−	0.0254203i
$175$	−4.42957	−	6.16136i	−0.334844	−	0.465755i
$176$	1.75974	+	3.04796i	0.132645	+	0.229748i
$177$	2.14182	−	0.739157i	0.160989	−	0.0555585i
$178$			14.4601i			1.08383i
$179$	−7.39608	+	4.27013i	−0.552809	+	0.319164i	−0.750254	−	0.661150i	$-0.770069\pi$
$179$	−7.39608	+	4.27013i	−0.552809	+	0.319164i	0.197445	+	0.980314i	$0.436736\pi$
$180$	−1.63522	+	4.06360i	−0.121882	+	0.302883i
$181$			25.4759i			1.89361i	0.321810	+	0.946804i	$0.395709\pi$
$181$			25.4759i			1.89361i	−0.321810	+	0.946804i	$0.604291\pi$
$182$	8.91353	+	3.39839i	0.660715	+	0.251905i
$183$	0.329189	−	1.69985i	0.0243344	−	0.125657i
$184$		−	3.60696i		−	0.265909i
$185$	−4.06249	−	7.03645i	−0.298680	−	0.517330i
$186$	18.1773	+	3.52018i	1.33283	+	0.258112i
$187$	−13.3514	−	23.1254i	−0.976354	−	1.69110i
$188$	−11.0787	+	6.39629i	−0.807997	+	0.466497i
$189$	−11.5516	+	7.45394i	−0.840253	+	0.542194i
$190$		−	5.04260i		−	0.365829i
$191$	17.9487	+	10.3627i	1.29873	+	0.749819i	0.980184	−	0.198089i	$-0.0634737\pi$
$191$	17.9487	+	10.3627i	1.29873	+	0.749819i	0.318541	+	0.947909i	$0.396807\pi$
$192$	−0.565041	−	1.63729i	−0.0407783	−	0.118161i
$193$	−8.21554	+	4.74324i	−0.591367	+	0.341426i	−0.765638	−	0.643272i	$-0.777577\pi$
$193$	−8.21554	+	4.74324i	−0.591367	+	0.341426i	0.174271	+	0.984698i	$0.444243\pi$
$194$	1.72747	+	2.99206i	0.124025	+	0.214818i
$195$	5.55633	−	7.22979i	0.397897	−	0.517736i
$196$	−4.63164	−	5.24861i	−0.330832	−	0.374901i
$197$	3.21420	−	5.56716i	0.229002	−	0.396644i	−0.728510	−	0.685035i	$-0.759787\pi$
$197$	3.21420	−	5.56716i	0.229002	−	0.396644i	0.957513	+	0.288391i	$0.0931203\pi$
$198$	9.79510	+	3.94162i	0.696108	+	0.280118i
$199$			1.26513i			0.0896830i	0.998994	+	0.0448415i	$0.0142783\pi$
$199$			1.26513i			0.0896830i	−0.998994	+	0.0448415i	$0.985722\pi$
$200$	1.43407	−	2.48388i	0.101404	−	0.175637i
$201$	−7.23138	−	6.27731i	−0.510063	−	0.442767i
$202$	5.80861	+	10.0608i	0.408693	+	0.707876i
$203$	0.423610	−	0.304545i	0.0297316	−	0.0213749i
$204$	4.28707	+	12.4224i	0.300155	+	0.869744i
$205$	4.39267			0.306797
$206$	−16.2249	+	9.36744i	−1.13044	+	0.652660i
$207$	−6.67388	−	8.51769i	−0.463867	−	0.592020i
$208$	0.214878	+	3.59914i	0.0148991	+	0.249556i
$209$	−12.1549			−0.840775
$210$	−6.07620	+	2.80159i	−0.419298	+	0.193328i
$211$	−6.24577	+	10.8180i	−0.429977	+	0.744742i	−0.996871	−	0.0790492i	$-0.974812\pi$
$211$	−6.24577	+	10.8180i	−0.429977	+	0.744742i	0.566894	+	0.823791i	$0.308145\pi$
$212$	4.21555	+	2.43385i	0.289525	+	0.167158i
$213$	12.1199	−	13.9619i	0.830438	−	0.956655i
$214$		−	0.350806i		−	0.0239806i
$215$	14.1909	+	8.19314i	0.967814	+	0.558768i
$216$	−4.36376	−	2.82092i	−0.296917	−	0.191939i
$217$	16.5092	+	22.9637i	1.12072	+	1.55887i
$218$	8.12542	+	4.69121i	0.550323	+	0.317729i
$219$	10.0126	+	1.93902i	0.676591	+	0.131027i
$220$	4.45029	+	2.56938i	0.300039	+	0.173227i
$221$	−1.63032	−	27.3073i	−0.109667	−	1.83689i
$222$	9.11107	−	3.14429i	0.611495	−	0.211031i
$223$	−3.78556	+	6.55677i	−0.253500	+	0.439074i	−0.964487	−	0.264131i	$-0.914915\pi$
$223$	−3.78556	+	6.55677i	−0.253500	+	0.439074i	0.710987	+	0.703205i	$0.248248\pi$
$224$	1.08820	−	2.41160i	0.0727084	−	0.161132i
$225$	−1.20937	−	8.51899i	−0.0806247	−	0.567933i
$226$	5.03517	−	2.90706i	0.334935	−	0.193375i
$227$		−	25.4572i		−	1.68965i	−0.535042	−	0.844826i	$-0.679704\pi$
$227$		−	25.4572i		−	1.68965i	0.535042	−	0.844826i	$-0.320296\pi$
$228$	5.87274	+	1.13730i	0.388932	+	0.0753196i
$229$	5.51406	+	9.55063i	0.364379	+	0.631124i	0.988676	−	0.150063i	$-0.0479478\pi$
$229$	5.51406	+	9.55063i	0.364379	+	0.631124i	−0.624297	+	0.781187i	$0.714614\pi$
$230$	−2.63325	−	4.56092i	−0.173631	−	0.300738i
$231$	6.75311	+	14.6464i	0.444322	+	0.963661i
$232$	0.170773	+	0.0985961i	0.0112118	+	0.00647315i
$233$	−6.18721	+	3.57219i	−0.405338	+	0.234022i	−0.688785	−	0.724966i	$-0.741855\pi$
$233$	−6.18721	+	3.57219i	−0.405338	+	0.234022i	0.283447	+	0.958988i	$0.408522\pi$
$234$	7.16683	+	8.10164i	0.468510	+	0.529621i
$235$	−9.33916	+	16.1759i	−0.609219	+	1.05520i
$236$			1.30815i			0.0851532i
$237$	0.396590	−	0.456866i	0.0257613	−	0.0296767i
$238$	−8.25637	+	18.2972i	−0.535181	+	1.18603i
$239$	7.32463			0.473791			0.236896	−	0.971535i	$-0.423870\pi$
$239$	7.32463			0.473791			0.236896	+	0.971535i	$0.423870\pi$
$240$	−1.90978	−	1.65781i	−0.123276	−	0.107011i
$241$	17.4268			1.12256			0.561280	−	0.827626i	$-0.310309\pi$
$241$	17.4268			1.12256			0.561280	+	0.827626i	$0.310309\pi$
$242$	0.693357	−	1.20093i	0.0445707	−	0.0771986i
$243$	−15.5243	+	1.41269i	−0.995885	+	0.0906244i
$244$	0.865717	+	0.499822i	0.0554219	+	0.0319978i
$245$	−9.68832	−	3.25543i	−0.618964	−	0.207982i
$246$	−0.990716	+	5.11581i	−0.0631657	+	0.326172i
$247$	−11.1358	−	5.57236i	−0.708555	−	0.354561i
$248$	−5.34484	+	9.25753i	−0.339397	+	0.587854i
$249$	−6.10676	+	2.10748i	−0.387000	+	0.133556i
$250$		−	11.4882i		−	0.726577i
$251$	−6.39321	−	11.0734i	−0.403536	−	0.698944i	0.590614	−	0.806954i	$-0.298886\pi$
$251$	−6.39321	−	11.0734i	−0.403536	−	0.698944i	−0.994150	+	0.108010i	$0.965552\pi$
$252$	−1.89239	−	7.70836i	−0.119209	−	0.485581i
$253$	−10.9939	+	6.34731i	−0.691178	+	0.399052i
$254$	7.87940	−	13.6475i	0.494397	−	0.856321i
$255$	14.4898	+	12.5781i	0.907388	+	0.787672i
$256$	1.00000			0.0625000
$257$	21.3460			1.33153			0.665764	−	0.746163i	$-0.268106\pi$
$257$	21.3460			1.33153			0.665764	+	0.746163i	$0.268106\pi$
$258$	−12.7425	+	14.6793i	−0.793316	+	0.913891i
$259$	13.4199	+	6.05552i	0.833870	+	0.376272i
$260$	2.89925	+	4.39416i	0.179804	+	0.272514i
$261$	0.585704	−	0.0831475i	0.0362542	−	0.00514670i
$262$	−6.32520	−	10.9556i	−0.390772	−	0.676837i
$263$	−13.7817	+	7.95686i	−0.849816	+	0.490641i	−0.860589	−	0.509301i	$-0.829904\pi$
$263$	−13.7817	+	7.95686i	−0.849816	+	0.490641i	0.0107730	+	0.999942i	$0.496571\pi$
$264$	−3.99607	+	4.60343i	−0.245941	+	0.283321i
$265$	7.10729			0.436597
$266$	5.33380	+	7.41911i	0.327037	+	0.454895i
$267$	−23.6754	+	8.17053i	−1.44891	+	0.500028i
$268$	4.78794	−	2.76432i	0.292470	−	0.168858i
$269$	15.4992			0.945002			0.472501	−	0.881330i	$-0.343351\pi$
$269$	15.4992			0.945002			0.472501	+	0.881330i	$0.343351\pi$
$270$	−7.57727	−	0.381234i	−0.461138	−	0.0232011i
$271$	14.9966			0.910977			0.455489	−	0.890242i	$-0.349465\pi$
$271$	14.9966			0.910977			0.455489	+	0.890242i	$0.349465\pi$
$272$	−7.58718			−0.460040
$273$	−0.527644	+	16.5143i	−0.0319345	+	0.999490i
$274$	−1.25158			−0.0756107
$275$	−10.0943			−0.608711
$276$	5.90566	−	2.03808i	0.355479	−	0.122678i
$277$	−0.719351			−0.0432216			−0.0216108	−	0.999766i	$-0.506879\pi$
$277$	−0.719351			−0.0432216			−0.0216108	+	0.999766i	$0.506879\pi$
$278$	−8.68419	+	5.01382i	−0.520843	+	0.300709i
$279$	4.50738	+	31.7507i	0.269850	+	1.90086i
$280$	−0.384576	−	3.84385i	−0.0229828	−	0.229714i
$281$	7.30448			0.435749			0.217874	−	0.975977i	$-0.430088\pi$
$281$	7.30448			0.435749			0.217874	+	0.975977i	$0.430088\pi$
$282$	−16.7325	−	14.5249i	−0.996406	−	0.864945i
$283$	12.9252	−	7.46234i	0.768320	−	0.443590i	−0.0639547	−	0.997953i	$-0.520371\pi$
$283$	12.9252	−	7.46234i	0.768320	−	0.443590i	0.832275	+	0.554363i	$0.187038\pi$
$284$	5.33718	+	9.24427i	0.316703	+	0.548546i
$285$	8.25622	−	2.84928i	0.489056	−	0.168777i
$286$	10.5919	−	6.98849i	0.626312	−	0.413238i
$287$	−6.46287	+	4.64634i	−0.381491	+	0.274265i
$288$	2.36146	−	1.85028i	0.139150	−	0.109029i
$289$	40.5653			2.38619
$290$	0.287918			0.0169072
$291$	−3.92279	+	4.51901i	−0.229958	+	0.264909i
$292$	−2.94410	+	5.09933i	−0.172290	+	0.298416i
$293$	13.1158	−	7.57239i	0.766231	−	0.442384i	−0.0652973	−	0.997866i	$-0.520800\pi$
$293$	13.1158	−	7.57239i	0.766231	−	0.442384i	0.831529	+	0.555482i	$0.187466\pi$
$294$	5.97644	−	10.5490i	0.348553	−	0.615232i
$295$	0.955007	+	1.65412i	0.0556027	+	0.0963066i
$296$			5.56471i			0.323442i
$297$	−0.918945	+	18.2646i	−0.0533226	+	1.05982i
$298$	1.62311	−	2.81131i	0.0940242	−	0.162855i
$299$	−12.9820	+	0.775059i	−0.750767	+	0.0448228i
$300$	4.87714	+	0.944496i	0.281582	+	0.0545305i
$301$	−29.5452	+	2.95599i	−1.70296	+	0.170380i
$302$	8.04225	+	4.64320i	0.462780	+	0.267186i
$303$	−13.1904	+	15.1952i	−0.757768	+	0.872940i
$304$	−1.72681	+	2.99093i	−0.0990395	+	0.171541i
$305$	1.45957			0.0835748
$306$	−17.9168	+	14.0384i	−1.02424	+	0.802520i
$307$	0.289284			0.0165103			0.00825515	−	0.999966i	$-0.497372\pi$
$307$	0.289284			0.0165103			0.00825515	+	0.999966i	$0.497372\pi$
$308$	−9.26540	+	0.927001i	−0.527945	+	0.0528208i
$309$	−24.5050	−	21.2719i	−1.39404	−	1.21012i
$310$			15.6079i			0.886468i
$311$	−5.96970	+	10.3398i	−0.338511	+	0.586318i	−0.984153	−	0.177322i	$-0.943256\pi$
$311$	−5.96970	+	10.3398i	−0.338511	+	0.586318i	0.645642	+	0.763640i	$0.276590\pi$
$312$	−5.77144	+	2.38548i	−0.326743	+	0.135051i
$313$	−7.95301	+	4.59167i	−0.449530	+	0.259537i	−0.707632	−	0.706581i	$-0.750236\pi$
$313$	−7.95301	+	4.59167i	−0.449530	+	0.259537i	0.258101	+	0.966118i	$0.416903\pi$
$314$	16.2305	+	9.37071i	0.915942	+	0.528820i
$315$	−8.02033	−	8.36551i	−0.451895	−	0.471343i
$316$	0.174645	+	0.302494i	0.00982454	+	0.0170166i
$317$	−11.5121	−	19.9395i	−0.646582	−	1.11991i	−0.983934	−	0.178534i	$-0.942864\pi$
$317$	−11.5121	−	19.9395i	−0.646582	−	1.11991i	0.337352	−	0.941379i	$-0.390469\pi$
$318$	−1.60297	+	8.27732i	−0.0898899	+	0.464169i
$319$		−	0.694013i		−	0.0388573i
$320$	1.26448	−	0.730045i	0.0706863	−	0.0408108i
$321$	0.574372	−	0.198220i	0.0320583	−	0.0110635i
$322$	8.69856	+	3.92510i	0.484752	+	0.218737i
$323$	13.1016	−	22.6927i	0.728994	−	1.26265i
$324$	2.15296	−	8.73869i	0.119609	−	0.485483i
$325$	−9.24798	−	4.62768i	−0.512986	−	0.256698i
$326$	−0.787553	−	0.454694i	−0.0436185	−	0.0251832i
$327$	−3.08969	+	15.9544i	−0.170860	+	0.882281i
$328$	−2.60543	−	1.50425i	−0.143861	−	0.0830581i
$329$	−3.36946	−	33.6778i	−0.185764	−	1.85672i
$330$	−1.69223	+	8.73824i	−0.0931540	+	0.481024i
$331$	−20.4980	−	11.8345i	−1.12667	−	0.650483i	−0.183575	−	0.983006i	$-0.558767\pi$
$331$	−20.4980	−	11.8345i	−1.12667	−	0.650483i	−0.943095	+	0.332522i	$0.892100\pi$
$332$		−	3.72979i		−	0.204699i
$333$	10.2963	+	13.1408i	0.564231	+	0.720113i
$334$	−11.6602	−	6.73204i	−0.638020	−	0.368361i
$335$	4.03616	−	6.99083i	0.220519	−	0.381950i
$336$	4.56338	+	0.419048i	0.248953	+	0.0228610i
$337$	19.1537			1.04337			0.521684	−	0.853139i	$-0.325304\pi$
$337$	19.1537			1.04337			0.521684	+	0.853139i	$0.325304\pi$
$338$	12.9077	−	1.54676i	0.702084	−	0.0841325i
$339$	7.60478	+	6.60144i	0.413035	+	0.358541i
$340$	−9.59380	+	5.53898i	−0.520297	+	0.300394i
$341$	37.6220			2.03735
$342$	1.45625	+	10.2580i	0.0787447	+	0.554690i
$343$	17.6977	−	5.45814i	0.955586	−	0.294712i
$344$	−5.61139	−	9.71922i	−0.302546	−	0.524025i
$345$	5.97967	−	6.88850i	0.321934	−	0.370865i
$346$	5.08435	−	8.80635i	0.273336	−	0.473432i
$347$			31.7120i			1.70239i	0.524852	+	0.851194i	$0.324121\pi$
$347$			31.7120i			1.70239i	−0.524852	+	0.851194i	$0.675879\pi$
$348$	−0.0649367	+	0.335317i	−0.00348097	+	0.0179749i
$349$	−3.87835	+	6.71749i	−0.207603	+	0.359579i	−0.950959	−	0.309317i	$-0.899900\pi$
$349$	−3.87835	+	6.71749i	−0.207603	+	0.359579i	0.743356	+	0.668896i	$0.233233\pi$
$350$	4.42957	+	6.16136i	0.236771	+	0.329338i
$351$	−9.21520	+	16.3120i	−0.491871	+	0.870668i
$352$	−1.75974	−	3.04796i	−0.0937944	−	0.162457i
$353$	0.491689	−	0.283877i	0.0261700	−	0.0151092i	−0.486858	−	0.873481i	$-0.661857\pi$
$353$	0.491689	−	0.283877i	0.0261700	−	0.0151092i	0.513028	+	0.858372i	$0.328524\pi$
$354$	−2.14182	+	0.739157i	−0.113836	+	0.0392858i
$355$	13.4975	+	7.79277i	0.716371	+	0.413597i
$356$		−	14.4601i		−	0.766382i
$357$	−34.6231	−	3.17939i	−1.83245	−	0.168271i
$358$	7.39608	−	4.27013i	0.390895	−	0.225683i
$359$	3.12906	+	5.41969i	0.165145	+	0.286040i	0.936707	−	0.350115i	$-0.113857\pi$
$359$	3.12906	+	5.41969i	0.165145	+	0.286040i	−0.771562	+	0.636155i	$0.780524\pi$
$360$	1.63522	−	4.06360i	0.0861837	−	0.214170i
$361$	3.53624	+	6.12495i	0.186118	+	0.322366i
$362$		−	25.4759i		−	1.33898i
$363$	2.35805	+	0.456654i	0.123765	+	0.0239681i
$364$	−8.91353	−	3.39839i	−0.467196	−	0.178124i
$365$			8.59731i			0.450004i
$366$	−0.329189	+	1.69985i	−0.0172070	+	0.0888527i
$367$	−18.6936	+	10.7928i	−0.975800	+	0.563378i	−0.900999	−	0.433820i	$-0.857165\pi$
$367$	−18.6936	+	10.7928i	−0.975800	+	0.563378i	−0.0748003	+	0.997199i	$0.523832\pi$
$368$			3.60696i			0.188026i
$369$	−8.93588	+	1.26855i	−0.465183	+	0.0660382i
$370$	4.06249	+	7.03645i	0.211199	+	0.365807i
$371$	−10.4568	+	7.51772i	−0.542892	+	0.390300i
$372$	−18.1773	−	3.52018i	−0.942451	−	0.182513i
$373$	0.378056	−	0.654812i	0.0195750	−	0.0339049i	−0.856072	−	0.516857i	$-0.827102\pi$
$373$	0.378056	−	0.654812i	0.0195750	−	0.0339049i	0.875647	+	0.482952i	$0.160435\pi$
$374$	13.3514	+	23.1254i	0.690387	+	1.19579i
$375$	18.8095	−	6.49130i	0.971320	−	0.335209i
$376$	11.0787	−	6.39629i	0.571340	−	0.329863i
$377$	0.318166	−	0.635824i	0.0163864	−	0.0327466i
$378$	11.5516	−	7.45394i	0.594149	−	0.383389i
$379$	6.26101	+	3.61480i	0.321607	+	0.185680i	0.652108	−	0.758126i	$-0.273885\pi$
$379$	6.26101	+	3.61480i	0.321607	+	0.185680i	−0.330502	+	0.943805i	$0.607218\pi$
$380$			5.04260i			0.258680i
$381$	26.7972	+	5.18947i	1.37286	+	0.265865i
$382$	−17.9487	−	10.3627i	−0.918338	−	0.530202i
$383$	1.16788	+	0.674277i	0.0596760	+	0.0344540i	0.529541	−	0.848284i	$-0.322364\pi$
$383$	1.16788	+	0.674277i	0.0596760	+	0.0344540i	−0.469865	+	0.882738i	$0.655697\pi$
$384$	0.565041	+	1.63729i	0.0288346	+	0.0835528i
$385$	−11.0391	+	7.93633i	−0.562606	+	0.404473i
$386$	8.21554	−	4.74324i	0.418160	−	0.241425i
$387$	−31.2343	−	12.5689i	−1.58773	−	0.638913i
$388$	−1.72747	−	2.99206i	−0.0876989	−	0.151899i
$389$	3.70239	+	2.13758i	0.187719	+	0.108379i	0.590914	−	0.806734i	$-0.298767\pi$
$389$	3.70239	+	2.13758i	0.187719	+	0.108379i	−0.403196	+	0.915114i	$0.632101\pi$
$390$	−5.55633	+	7.22979i	−0.281356	+	0.366095i
$391$		−	27.3667i		−	1.38399i
$392$	4.63164	+	5.24861i	0.233933	+	0.265095i
$393$	14.3635	−	16.5465i	0.724541	−	0.834663i
$394$	−3.21420	+	5.56716i	−0.161929	+	0.280470i
$395$	0.441668	+	0.254997i	0.0222228	+	0.0128303i
$396$	−9.79510	−	3.94162i	−0.492223	−	0.198074i
$397$	−2.86479	+	4.96196i	−0.143780	+	0.249034i	−0.928917	−	0.370288i	$-0.879259\pi$
$397$	−2.86479	+	4.96196i	−0.143780	+	0.249034i	0.785137	+	0.619322i	$0.212592\pi$
$398$		−	1.26513i		−	0.0634155i
$399$	−9.13343	+	12.9251i	−0.457244	+	0.647064i
$400$	−1.43407	+	2.48388i	−0.0717034	+	0.124194i
$401$	21.9761			1.09743			0.548717	−	0.836008i	$-0.315117\pi$
$401$	21.9761			1.09743			0.548717	+	0.836008i	$0.315117\pi$
$402$	7.23138	+	6.27731i	0.360669	+	0.313084i
$403$	34.4676	+	17.2476i	1.71696	+	0.859163i
$404$	−5.80861	−	10.0608i	−0.288989	−	0.500544i
$405$	−3.65728	−	12.6216i	−0.181732	−	0.627173i
$406$	−0.423610	+	0.304545i	−0.0210234	+	0.0151143i
$407$	16.9610	−	9.79244i	0.840726	−	0.485393i
$408$	−4.28707	−	12.4224i	−0.212241	−	0.615002i
$409$	−8.43899			−0.417281			−0.208641	−	0.977992i	$-0.566904\pi$
$409$	−8.43899			−0.417281			−0.208641	+	0.977992i	$0.566904\pi$
$410$	−4.39267			−0.216938
$411$	−0.707194	−	2.04920i	−0.0348833	−	0.101080i
$412$	16.2249	−	9.36744i	0.799343	−	0.461501i
$413$	−3.15473	−	1.42353i	−0.155234	−	0.0700471i
$414$	6.67388	+	8.51769i	0.328003	+	0.418622i
$415$	−2.72292	−	4.71623i	−0.133663	−	0.231511i
$416$	−0.214878	−	3.59914i	−0.0105353	−	0.176462i
$417$	−13.1160	−	11.3856i	−0.642294	−	0.557553i
$418$	12.1549			0.594518
$419$	12.4744	−	21.6063i	0.609413	−	1.05553i	−0.381924	−	0.924194i	$-0.624738\pi$
$419$	12.4744	−	21.6063i	0.609413	−	1.05553i	0.991337	−	0.131341i	$-0.0419282\pi$
$420$	6.07620	−	2.80159i	0.296488	−	0.136704i
$421$		−	23.2628i		−	1.13376i	−0.823800	−	0.566881i	$-0.808150\pi$
$421$		−	23.2628i		−	1.13376i	0.823800	−	0.566881i	$-0.191850\pi$
$422$	6.24577	−	10.8180i	0.304040	−	0.526612i
$423$	14.3270	−	35.6032i	0.696601	−	1.73109i
$424$	−4.21555	−	2.43385i	−0.204725	−	0.118198i
$425$	10.8805	−	18.8456i	0.527783	−	0.914147i
$426$	−12.1199	+	13.9619i	−0.587209	+	0.676457i
$427$	−2.14744	+	1.54386i	−0.103922	+	0.0747125i
$428$			0.350806i			0.0169568i
$429$	17.4271	+	13.3933i	0.841386	+	0.646633i
$430$	−14.1909	−	8.19314i	−0.684348	−	0.395108i
$431$	11.3685	+	19.6908i	0.547602	+	0.948474i	0.998438	+	0.0558673i	$0.0177924\pi$
$431$	11.3685	+	19.6908i	0.547602	+	0.948474i	−0.450837	+	0.892606i	$0.648874\pi$
$432$	4.36376	+	2.82092i	0.209952	+	0.135721i
$433$	11.9025	−	6.87194i	0.572000	−	0.330244i	−0.185948	−	0.982560i	$-0.559536\pi$
$433$	11.9025	−	6.87194i	0.572000	−	0.330244i	0.757948	+	0.652315i	$0.226202\pi$
$434$	−16.5092	−	22.9637i	−0.792468	−	1.10229i
$435$	0.162686	+	0.471407i	0.00780018	+	0.0226022i
$436$	−8.12542	−	4.69121i	−0.389137	−	0.224668i
$437$	−10.7882	−	6.22855i	−0.516068	−	0.297952i
$438$	−10.0126	−	1.93902i	−0.478422	−	0.0926501i
$439$		−	12.1761i		−	0.581134i	−0.956855	−	0.290567i	$-0.906156\pi$
$439$		−	12.1761i		−	0.581134i	0.956855	−	0.290567i	$-0.0938439\pi$
$440$	−4.45029	−	2.56938i	−0.212159	−	0.122490i
$441$	20.6488	+	3.82455i	0.983276	+	0.182121i
$442$	1.63032	+	27.3073i	0.0775465	+	1.29888i
$443$	1.94173	−	1.12106i	0.0922543	−	0.0532630i	−0.453163	−	0.891428i	$-0.649704\pi$
$443$	1.94173	−	1.12106i	0.0922543	−	0.0532630i	0.545417	+	0.838165i	$0.316371\pi$
$444$	−9.11107	+	3.14429i	−0.432392	+	0.149222i
$445$	−10.5565	−	18.2844i	−0.500426	−	0.866763i
$446$	3.78556	−	6.55677i	0.179251	−	0.310472i
$447$	5.52006	+	1.06900i	0.261090	+	0.0505620i
$448$	−1.08820	+	2.41160i	−0.0514126	+	0.113937i
$449$	−3.91929	−	6.78842i	−0.184963	−	0.320365i	0.758601	−	0.651555i	$-0.225883\pi$
$449$	−3.91929	−	6.78842i	−0.184963	−	0.320365i	−0.943564	+	0.331190i	$0.892550\pi$
$450$	1.20937	+	8.51899i	0.0570102	+	0.401589i
$451$			10.5883i			0.498584i
$452$	−5.03517	+	2.90706i	−0.236834	+	0.136736i
$453$	−3.05807	+	15.7911i	−0.143681	+	0.741932i
$454$			25.4572i			1.19476i
$455$	−13.7519	+	2.21010i	−0.644700	+	0.103611i
$456$	−5.87274	−	1.13730i	−0.275016	−	0.0532590i
$457$		−	6.54295i		−	0.306066i	−0.988221	−	0.153033i	$-0.951096\pi$
$457$		−	6.54295i		−	0.306066i	0.988221	−	0.153033i	$-0.0489041\pi$
$458$	−5.51406	−	9.55063i	−0.257655	−	0.446272i
$459$	−33.1087	−	21.4028i	−1.54538	−	0.998997i
$460$	2.63325	+	4.56092i	0.122776	+	0.212654i
$461$	20.3030	−	11.7219i	0.945606	−	0.545946i	0.0538925	−	0.998547i	$-0.482837\pi$
$461$	20.3030	−	11.7219i	0.945606	−	0.545946i	0.891713	+	0.452601i	$0.149504\pi$
$462$	−6.75311	−	14.6464i	−0.314183	−	0.681411i
$463$		−	37.3356i		−	1.73513i	−0.497321	−	0.867567i	$-0.665683\pi$
$463$		−	37.3356i		−	1.73513i	0.497321	−	0.867567i	$-0.334317\pi$
$464$	−0.170773	−	0.0985961i	−0.00792796	−	0.00457721i
$465$	−25.5547	+	8.81910i	−1.18507	+	0.408976i
$466$	6.18721	−	3.57219i	0.286617	−	0.165479i
$467$	−3.36611	−	5.83027i	−0.155765	−	0.269792i	0.777572	−	0.628793i	$-0.216451\pi$
$467$	−3.36611	−	5.83027i	−0.155765	−	0.269792i	−0.933337	+	0.359001i	$0.883118\pi$
$468$	−7.16683	−	8.10164i	−0.331287	−	0.374498i
$469$	1.45620	+	14.5547i	0.0672410	+	0.672075i
$470$	9.33916	−	16.1759i	0.430783	−	0.746138i
$471$	−6.17167	+	31.8690i	−0.284376	+	1.46845i
$472$		−	1.30815i		−	0.0602124i
$473$	−19.7492	+	34.2066i	−0.908068	+	1.57282i
$474$	−0.396590	+	0.456866i	−0.0182160	+	0.0209846i
$475$	−4.95273	−	8.57838i	−0.227247	−	0.393603i
$476$	8.25637	−	18.2972i	0.378430	−	0.838653i
$477$	−14.4581	+	2.05250i	−0.661993	+	0.0939776i
$478$	−7.32463			−0.335021
$479$	−11.2141	+	6.47445i	−0.512384	+	0.295825i	−0.733813	−	0.679351i	$-0.762261\pi$
$479$	−11.2141	+	6.47445i	−0.512384	+	0.295825i	0.221429	+	0.975176i	$0.428928\pi$
$480$	1.90978	+	1.65781i	0.0871691	+	0.0756684i
$481$	20.0282	−	1.19574i	0.913207	−	0.0545209i
$482$	−17.4268			−0.793769
$483$	−1.51149	+	16.4599i	−0.0687753	+	0.748953i
$484$	−0.693357	+	1.20093i	−0.0315162	+	0.0545877i
$485$	−4.36868	−	2.52226i	−0.198372	−	0.114530i
$486$	15.5243	−	1.41269i	0.704197	−	0.0640811i
$487$		−	8.67630i		−	0.393161i	−0.980488	−	0.196580i	$-0.937016\pi$
$487$		−	8.67630i		−	0.393161i	0.980488	−	0.196580i	$-0.0629837\pi$
$488$	−0.865717	−	0.499822i	−0.0391892	−	0.0226259i
$489$	0.299467	−	1.54638i	0.0135424	−	0.0699295i
$490$	9.68832	+	3.25543i	0.437674	+	0.147065i
$491$	14.7725	+	8.52893i	0.666676	+	0.384905i	0.794816	−	0.606851i	$-0.207567\pi$
$491$	14.7725	+	8.52893i	0.666676	+	0.384905i	−0.128140	+	0.991756i	$0.540901\pi$
$492$	0.990716	−	5.11581i	0.0446649	−	0.230639i
$493$	1.29569	+	0.748066i	0.0583549	+	0.0336912i
$494$	11.1358	+	5.57236i	0.501024	+	0.250712i
$495$	−15.2632	+	2.16679i	−0.686031	+	0.0973901i
$496$	5.34484	−	9.25753i	0.239990	−	0.415675i
$497$	−28.1014	+	2.81154i	−1.26052	+	0.126115i
$498$	6.10676	−	2.10748i	0.273650	−	0.0944386i
$499$	20.1546	−	11.6362i	0.902243	−	0.520910i	0.0243156	−	0.999704i	$-0.492259\pi$
$499$	20.1546	−	11.6362i	0.902243	−	0.520910i	0.877927	+	0.478794i	$0.158926\pi$
$500$			11.4882i			0.513768i
$501$	4.43381	−	22.8951i	0.198088	−	1.02288i
$502$	6.39321	+	11.0734i	0.285343	+	0.494228i
$503$	−4.33129	−	7.50201i	−0.193122	−	0.334498i	0.753161	−	0.657836i	$-0.228528\pi$
$503$	−4.33129	−	7.50201i	−0.193122	−	0.334498i	−0.946283	+	0.323338i	$0.895195\pi$
$504$	1.89239	+	7.70836i	0.0842937	+	0.343358i
$505$	−14.6897	−	8.48110i	−0.653683	−	0.377404i
$506$	10.9939	−	6.34731i	0.488737	−	0.282172i
$507$	9.82585	+	20.2596i	0.436381	+	0.899762i
$508$	−7.87940	+	13.6475i	−0.349592	+	0.605511i
$509$			5.78402i			0.256372i	0.991750	+	0.128186i	$0.0409155\pi$
$509$			5.78402i			0.256372i	−0.991750	+	0.128186i	$0.959085\pi$
$510$	−14.4898	−	12.5781i	−0.641621	−	0.556968i
$511$	−9.09378	−	12.6491i	−0.402285	−	0.559563i
$512$	−1.00000			−0.0441942
$513$	−15.9725	+	8.18050i	−0.705205	+	0.361178i
$514$	−21.3460			−0.941532
$515$	13.6773	−	23.6898i	0.602694	−	1.04390i
$516$	12.7425	−	14.6793i	0.560959	−	0.646218i
$517$	−38.9912	−	22.5116i	−1.71483	−	0.990058i
$518$	−13.4199	−	6.05552i	−0.589635	−	0.266064i
$519$	17.2914	+	3.34862i	0.759010	+	0.146988i
$520$	−2.89925	−	4.39416i	−0.127140	−	0.192697i
$521$	−5.46547	+	9.46647i	−0.239447	+	0.414734i	−0.960556	−	0.278088i	$-0.910299\pi$
$521$	−5.46547	+	9.46647i	−0.239447	+	0.414734i	0.721109	+	0.692822i	$0.243633\pi$
$522$	−0.585704	+	0.0831475i	−0.0256356	+	0.00363927i
$523$		−	13.6134i		−	0.595270i	−0.954680	−	0.297635i	$-0.903802\pi$
$523$		−	13.6134i		−	0.595270i	0.954680	−	0.297635i	$-0.0961979\pi$
$524$	6.32520	+	10.9556i	0.276318	+	0.478596i
$525$	−7.58506	+	10.7339i	−0.331039	+	0.468467i
$526$	13.7817	−	7.95686i	0.600910	−	0.346936i
$527$	−40.5522	+	70.2385i	−1.76648	+	3.05964i
$528$	3.99607	−	4.60343i	0.173907	−	0.200338i
$529$	9.98981			0.434340
$530$	−7.10729			−0.308721
$531$	−2.42043	−	3.08913i	−0.105038	−	0.134057i
$532$	−5.33380	−	7.41911i	−0.231250	−	0.321659i
$533$	−4.85414	+	9.70054i	−0.210256	+	0.420177i
$534$	23.6754	−	8.17053i	1.02453	−	0.353573i
$535$	0.256104	+	0.443585i	0.0110723	+	0.0191779i
$536$	−4.78794	+	2.76432i	−0.206808	+	0.119400i
$537$	11.1705	+	9.69675i	0.482044	+	0.418446i
$538$	−15.4992			−0.668218
$539$	7.84705	−	23.3532i	0.337996	−	1.00589i
$540$	7.57727	+	0.381234i	0.326074	+	0.0164057i
$541$	−3.38852	+	1.95636i	−0.145684	+	0.0841105i	−0.571070	−	0.820901i	$-0.693472\pi$
$541$	−3.38852	+	1.95636i	−0.145684	+	0.0841105i	0.425386	+	0.905012i	$0.360138\pi$
$542$	−14.9966			−0.644158
$543$	41.7115	−	14.3949i	1.79001	−	0.617746i
$544$	7.58718			0.325298
$545$	−13.6992			−0.586809
$546$	0.527644	−	16.5143i	0.0225811	−	0.706746i
$547$	−10.8125			−0.462308			−0.231154	−	0.972917i	$-0.574250\pi$
$547$	−10.8125			−0.462308			−0.231154	+	0.972917i	$0.574250\pi$
$548$	1.25158			0.0534648
$549$	−2.96916	+	0.421507i	−0.126721	+	0.0179895i
$550$	10.0943			0.430424
$551$	0.589787	−	0.340514i	0.0251258	−	0.0145064i
$552$	−5.90566	+	2.03808i	−0.251361	+	0.0867466i
$553$	−0.919543	+	0.0920001i	−0.0391030	+	0.00391224i
$554$	0.719351			0.0305623
$555$	−9.22525	+	10.6274i	−0.391590	+	0.451107i
$556$	8.68419	−	5.01382i	0.368292	−	0.212633i
$557$	11.6199	+	20.1263i	0.492351	+	0.852778i	0.999961	−	0.00880939i	$-0.00280415\pi$
$557$	11.6199	+	20.1263i	0.492351	+	0.852778i	−0.507610	+	0.861587i	$0.669471\pi$
$558$	−4.50738	−	31.7507i	−0.190812	−	1.34411i
$559$	−33.7751	+	22.2847i	−1.42853	+	0.942541i
$560$	0.384576	+	3.84385i	0.0162513	+	0.162432i
$561$	−30.3189	+	34.9270i	−1.28007	+	1.47462i
$562$	−7.30448			−0.308121
$563$	−11.8776			−0.500580			−0.250290	−	0.968171i	$-0.580526\pi$
$563$	−11.8776			−0.500580			−0.250290	+	0.968171i	$0.580526\pi$
$564$	16.7325	+	14.5249i	0.704566	+	0.611609i
$565$	−4.24457	+	7.35181i	−0.178570	+	0.309293i
$566$	−12.9252	+	7.46234i	−0.543285	+	0.313666i
$567$	18.7314	+	14.7015i	0.786645	+	0.617406i
$568$	−5.33718	−	9.24427i	−0.223943	−	0.387881i
$569$		−	1.93128i		−	0.0809635i	−0.999180	−	0.0404817i	$-0.987111\pi$
$569$		−	1.93128i		−	0.0809635i	0.999180	−	0.0404817i	$-0.0128893\pi$
$570$	−8.25622	+	2.84928i	−0.345815	+	0.119343i
$571$	6.46083	−	11.1905i	0.270377	−	0.468307i	−0.698581	−	0.715531i	$-0.746185\pi$
$571$	6.46083	−	11.1905i	0.270377	−	0.468307i	0.968958	+	0.247224i	$0.0795182\pi$
$572$	−10.5919	+	6.98849i	−0.442869	+	0.292203i
$573$	6.82502	−	35.2427i	0.285119	−	1.47229i
$574$	6.46287	−	4.64634i	0.269755	−	0.193934i
$575$	−8.95926	−	5.17263i	−0.373627	−	0.215714i
$576$	−2.36146	+	1.85028i	−0.0983940	+	0.0770948i
$577$	18.9813	−	32.8766i	0.790203	−	1.36867i	−0.135638	−	0.990758i	$-0.543308\pi$
$577$	18.9813	−	32.8766i	0.790203	−	1.36867i	0.925841	−	0.377913i	$-0.123358\pi$
$578$	−40.5653			−1.68729
$579$	12.4082	+	10.7711i	0.515667	+	0.447632i
$580$	−0.287918			−0.0119552
$581$	8.99477	+	4.05876i	0.373166	+	0.168386i
$582$	3.92279	−	4.51901i	0.162605	−	0.187319i
$583$			17.1318i			0.709525i
$584$	2.94410	−	5.09933i	0.121828	−	0.211012i
$585$	−14.9768	−	5.01221i	−0.619216	−	0.207229i
$586$	−13.1158	+	7.57239i	−0.541807	+	0.312813i
$587$	3.62595	+	2.09345i	0.149659	+	0.0864058i	0.572960	−	0.819584i	$-0.305795\pi$
$587$	3.62595	+	2.09345i	0.149659	+	0.0864058i	−0.423300	+	0.905989i	$0.639129\pi$
$588$	−5.97644	+	10.5490i	−0.246464	+	0.435035i
$589$	18.4591	+	31.9720i	0.760592	+	1.31738i
$590$	−0.955007	−	1.65412i	−0.0393170	−	0.0680991i
$591$	−10.9312	−	2.11692i	−0.449651	−	0.0870783i
$592$		−	5.56471i		−	0.228708i
$593$	25.7814	−	14.8849i	1.05872	−	0.611250i	0.133639	−	0.991030i	$-0.457334\pi$
$593$	25.7814	−	14.8849i	1.05872	−	0.611250i	0.925077	+	0.379780i	$0.124000\pi$
$594$	0.918945	−	18.2646i	0.0377048	−	0.749407i
$595$	−2.91785	−	29.1639i	−0.119620	−	1.19561i
$596$	−1.62311	+	2.81131i	−0.0664852	+	0.115156i
$597$	2.07140	−	0.714853i	0.0847766	−	0.0292570i
$598$	12.9820	−	0.775059i	0.530873	−	0.0316945i
$599$	−14.8413	−	8.56865i	−0.606401	−	0.350106i	0.165155	−	0.986268i	$-0.447188\pi$
$599$	−14.8413	−	8.56865i	−0.606401	−	0.350106i	−0.771556	+	0.636162i	$0.780521\pi$
$600$	−4.87714	−	0.944496i	−0.199109	−	0.0385589i
$601$	−17.6704	−	10.2020i	−0.720790	−	0.416149i	0.0942531	−	0.995548i	$-0.469954\pi$
$601$	−17.6704	−	10.2020i	−0.720790	−	0.416149i	−0.815044	+	0.579400i	$0.803287\pi$
$602$	29.5452	−	2.95599i	1.20417	−	0.120477i
$603$	−6.19177	+	15.3868i	−0.252148	+	0.626600i
$604$	−8.04225	−	4.64320i	−0.327235	−	0.188929i
$605$			2.02473i			0.0823169i
$606$	13.1904	−	15.1952i	0.535823	−	0.617262i
$607$	−9.18240	−	5.30146i	−0.372702	−	0.215180i	0.301936	−	0.953328i	$-0.402367\pi$
$607$	−9.18240	−	5.30146i	−0.372702	−	0.215180i	−0.674638	+	0.738149i	$0.735700\pi$
$608$	1.72681	−	2.99093i	0.0700315	−	0.121298i
$609$	−0.737987	−	0.521493i	−0.0299047	−	0.0211320i
$610$	−1.45957			−0.0590963
$611$	−25.4017	−	38.4994i	−1.02764	−	1.55752i
$612$	17.9168	−	14.0384i	0.724244	−	0.567468i
$613$	19.7900	−	11.4258i	0.799310	−	0.461482i	−0.0439195	−	0.999035i	$-0.513985\pi$
$613$	19.7900	−	11.4258i	0.799310	−	0.461482i	0.843230	+	0.537553i	$0.180651\pi$
$614$	−0.289284			−0.0116745
$615$	−2.48204	−	7.19209i	−0.100085	−	0.290013i
$616$	9.26540	−	0.927001i	0.373314	−	0.0373500i
$617$	2.03229	+	3.52003i	0.0818170	+	0.141711i	0.904030	−	0.427468i	$-0.140594\pi$
$617$	2.03229	+	3.52003i	0.0818170	+	0.141711i	−0.822213	+	0.569179i	$0.807261\pi$
$618$	24.5050	+	21.2719i	0.985734	+	0.855681i
$619$	5.71042	−	9.89074i	0.229521	−	0.397542i	−0.728145	−	0.685423i	$-0.759617\pi$
$619$	5.71042	−	9.89074i	0.229521	−	0.397542i	0.957666	+	0.287881i	$0.0929506\pi$
$620$		−	15.6079i		−	0.626828i
$621$	−10.1749	+	15.7399i	−0.408306	+	0.631622i
$622$	5.96970	−	10.3398i	0.239363	−	0.414589i
$623$	34.8719	+	15.7354i	1.39711	+	0.630427i
$624$	5.77144	−	2.38548i	0.231042	−	0.0954957i
$625$	1.21656	+	2.10715i	0.0486624	+	0.0842858i
$626$	7.95301	−	4.59167i	0.317866	−	0.183520i
$627$	6.86804	+	19.9012i	0.274283	+	0.794778i
$628$	−16.2305	−	9.37071i	−0.647669	−	0.373932i
$629$			42.2205i			1.68344i
$630$	8.02033	+	8.36551i	0.319538	+	0.333290i
$631$	−2.43600	+	1.40642i	−0.0969755	+	0.0559888i	−0.547703	−	0.836673i	$-0.684498\pi$
$631$	−2.43600	+	1.40642i	−0.0969755	+	0.0559888i	0.450728	+	0.892661i	$0.351164\pi$
$632$	−0.174645	−	0.302494i	−0.00694700	−	0.0120326i
$633$	21.2414	+	4.11355i	0.844268	+	0.163499i
$634$	11.5121	+	19.9395i	0.457203	+	0.791898i
$635$			23.0093i			0.913095i
$636$	1.60297	−	8.27732i	0.0635618	−	0.328217i
$637$	17.8953	−	17.7978i	0.709036	−	0.705173i
$638$			0.694013i			0.0274762i
$639$	−29.7080	−	11.9547i	−1.17523	−	0.472920i
$640$	−1.26448	+	0.730045i	−0.0499828	+	0.0288576i
$641$			22.9946i			0.908232i	0.890943	+	0.454116i	$0.150045\pi$
$641$			22.9946i			0.908232i	−0.890943	+	0.454116i	$0.849955\pi$
$642$	−0.574372	+	0.198220i	−0.0226686	+	0.00782310i
$643$	−5.08228	−	8.80277i	−0.200426	−	0.347147i	0.748240	−	0.663428i	$-0.230899\pi$
$643$	−5.08228	−	8.80277i	−0.200426	−	0.347147i	−0.948666	+	0.316281i	$0.897566\pi$
$644$	−8.69856	−	3.92510i	−0.342771	−	0.154671i
$645$	5.39611	−	27.8642i	0.212472	−	1.09715i
$646$	−13.1016	+	22.6927i	−0.515477	+	0.892832i
$647$	21.2471	+	36.8010i	0.835309	+	1.44680i	0.893778	+	0.448509i	$0.148045\pi$
$647$	21.2471	+	36.8010i	0.835309	+	1.44680i	−0.0584688	+	0.998289i	$0.518622\pi$
$648$	−2.15296	+	8.73869i	−0.0845763	+	0.343288i
$649$	−3.98718	+	2.30200i	−0.156510	+	0.0903613i
$650$	9.24798	+	4.62768i	0.362736	+	0.181513i
$651$	28.2698	−	40.0058i	1.10798	−	1.56795i
$652$	0.787553	+	0.454694i	0.0308430	+	0.0178072i
$653$			21.6406i			0.846862i	0.905928	+	0.423431i	$0.139174\pi$
$653$			21.6406i			0.846862i	−0.905928	+	0.423431i	$0.860826\pi$
$654$	3.08969	−	15.9544i	0.120817	−	0.623867i
$655$	15.9961	+	9.23536i	0.625020	+	0.360855i
$656$	2.60543	+	1.50425i	0.101725	+	0.0587309i
$657$	−2.48280	−	17.4893i	−0.0968633	−	0.682321i
$658$	3.36946	+	33.6778i	0.131355	+	1.31290i
$659$	4.44211	−	2.56466i	0.173040	−	0.0999048i	−0.410978	−	0.911645i	$-0.634813\pi$
$659$	4.44211	−	2.56466i	0.173040	−	0.0999048i	0.584019	+	0.811740i	$0.301480\pi$
$660$	1.69223	−	8.73824i	0.0658698	−	0.340135i
$661$	11.9740	+	20.7396i	0.465736	+	0.806678i	0.999234	−	0.0391228i	$-0.0124563\pi$
$661$	11.9740	+	20.7396i	0.465736	+	0.806678i	−0.533499	+	0.845801i	$0.679123\pi$
$662$	20.4980	+	11.8345i	0.796676	+	0.459961i
$663$	−43.7889	+	18.0991i	−1.70062	+	0.702910i
$664$			3.72979i			0.144744i
$665$	−12.1607	−	5.48736i	−0.471574	−	0.212791i
$666$	−10.2963	−	13.1408i	−0.398972	−	0.509197i
$667$	0.355633	−	0.615974i	0.0137701	−	0.0238506i
$668$	11.6602	+	6.73204i	0.451148	+	0.260471i
$669$	12.8744	+	2.49322i	0.497751	+	0.0963933i
$670$	−4.03616	+	6.99083i	−0.155930	+	0.270079i
$671$			3.51822i			0.135819i
$672$	−4.56338	−	0.419048i	−0.176036	−	0.0161651i
$673$	−8.33251	+	14.4323i	−0.321195	+	0.556326i	−0.980735	−	0.195344i	$-0.937418\pi$
$673$	−8.33251	+	14.4323i	−0.321195	+	0.556326i	0.659540	+	0.751669i	$0.270751\pi$
$674$	−19.1537			−0.737772
$675$	−13.2647	+	6.79367i	−0.510560	+	0.261489i
$676$	−12.9077	+	1.54676i	−0.496448	+	0.0594906i
$677$	−18.1468	−	31.4312i	−0.697439	−	1.20800i	−0.969352	−	0.245678i	$-0.920989\pi$
$677$	−18.1468	−	31.4312i	−0.697439	−	1.20800i	0.271913	−	0.962322i	$-0.412344\pi$
$678$	−7.60478	−	6.60144i	−0.292060	−	0.253527i
$679$	9.09550	−	0.910002i	0.349053	−	0.0349227i
$680$	9.59380	−	5.53898i	0.367905	−	0.212410i
$681$	−41.6808	+	14.3843i	−1.59721	+	0.551209i
$682$	−37.6220			−1.44062
$683$	36.5747			1.39949			0.699747	−	0.714391i	$-0.253296\pi$
$683$	36.5747			1.39949			0.699747	+	0.714391i	$0.253296\pi$
$684$	−1.45625	−	10.2580i	−0.0556809	−	0.392225i
$685$	1.58259	−	0.913710i	0.0604677	−	0.0349110i
$686$	−17.6977	+	5.45814i	−0.675701	+	0.208393i
$687$	12.5215	−	14.4246i	0.477726	−	0.550334i
$688$	5.61139	+	9.71922i	0.213932	+	0.370542i
$689$	−7.85394	+	15.6954i	−0.299211	+	0.597946i
$690$	−5.97967	+	6.88850i	−0.227642	+	0.262241i
$691$	17.4627			0.664312			0.332156	−	0.943225i	$-0.392224\pi$
$691$	17.4627			0.664312			0.332156	+	0.943225i	$0.392224\pi$
$692$	−5.08435	+	8.80635i	−0.193278	+	0.334767i
$693$	20.1646	−	19.3326i	0.765991	−	0.734386i
$694$		−	31.7120i		−	1.20377i
$695$	7.32063	−	12.6797i	0.277687	−	0.480969i
$696$	0.0649367	−	0.335317i	0.00246142	−	0.0127102i
$697$	−19.7679	−	11.4130i	−0.748761	−	0.432297i
$698$	3.87835	−	6.71749i	0.146798	−	0.254261i
$699$	9.34475	+	8.11185i	0.353451	+	0.306818i
$700$	−4.42957	−	6.16136i	−0.167422	−	0.232877i
$701$			42.7684i			1.61534i	0.589635	+	0.807670i	$0.299272\pi$
$701$			42.7684i			1.61534i	−0.589635	+	0.807670i	$0.700728\pi$
$702$	9.21520	−	16.3120i	0.347805	−	0.615655i
$703$	16.6436	+	9.60922i	0.627727	+	0.362418i
$704$	1.75974	+	3.04796i	0.0663226	+	0.114874i
$705$	31.7617	+	6.15089i	1.19621	+	0.231656i
$706$	−0.491689	+	0.283877i	−0.0185050	+	0.0106838i
$707$	30.5836	−	3.05988i	1.15021	−	0.115079i
$708$	2.14182	−	0.739157i	0.0804946	−	0.0277792i
$709$	31.6856	+	18.2937i	1.18998	+	0.687033i	0.958301	−	0.285760i	$-0.0922459\pi$
$709$	31.6856	+	18.2937i	1.18998	+	0.687033i	0.231675	+	0.972793i	$0.425579\pi$
$710$	−13.4975	−	7.79277i	−0.506551	−	0.292457i
$711$	−0.972114	−	0.391185i	−0.0364571	−	0.0146706i
$712$			14.4601i			0.541914i
$713$	33.3916	+	19.2786i	1.25052	+	0.721990i
$714$	34.6231	+	3.17939i	1.29574	+	0.118986i
$715$	−8.29128	+	16.5693i	−0.310076	+	0.619658i
$716$	−7.39608	+	4.27013i	−0.276404	+	0.159582i
$717$	−4.13872	−	11.9926i	−0.154563	−	0.447871i
$718$	−3.12906	−	5.41969i	−0.116775	−	0.202261i
$719$	−9.53832	+	16.5209i	−0.355719	+	0.616124i	−0.987241	−	0.159234i	$-0.949097\pi$
$719$	−9.53832	+	16.5209i	−0.355719	+	0.616124i	0.631521	+	0.775358i	$0.282431\pi$
$720$	−1.63522	+	4.06360i	−0.0609410	+	0.151441i
$721$	4.93461	+	49.3216i	0.183775	+	1.83683i
$722$	−3.53624	−	6.12495i	−0.131605	−	0.227947i
$723$	−9.84686	−	28.5328i	−0.366209	−	1.06115i
$724$			25.4759i			0.946804i
$725$	0.489801	−	0.282787i	0.0181908	−	0.0105024i
$726$	−2.35805	−	0.456654i	−0.0875154	−	0.0169480i
$727$			9.70964i			0.360111i	0.983656	+	0.180055i	$0.0576277\pi$
$727$			9.70964i			0.360111i	−0.983656	+	0.180055i	$0.942372\pi$
$728$	8.91353	+	3.39839i	0.330357	+	0.125953i
$729$	11.0849	+	24.6196i	0.410551	+	0.911838i
$730$		−	8.59731i		−	0.318201i
$731$	−42.5746	−	73.7414i	−1.57468	−	2.72743i
$732$	0.329189	−	1.69985i	0.0121672	−	0.0628284i
$733$	16.1353	+	27.9472i	0.595972	+	1.03225i	0.993409	+	0.114624i	$0.0365664\pi$
$733$	16.1353	+	27.9472i	0.595972	+	1.03225i	−0.397437	+	0.917629i	$0.630100\pi$
$734$	18.6936	−	10.7928i	0.689995	−	0.398369i
$735$	0.144207	+	17.7021i	0.00531916	+	0.652951i
$736$		−	3.60696i		−	0.132954i
$737$	16.8510	+	9.72896i	0.620716	+	0.358371i
$738$	8.93588	−	1.26855i	0.328934	−	0.0466960i
$739$	19.4708	−	11.2415i	0.716246	−	0.413525i	−0.0971231	−	0.995272i	$-0.530964\pi$
$739$	19.4708	−	11.2415i	0.716246	−	0.413525i	0.813370	+	0.581747i	$0.197631\pi$
$740$	−4.06249	−	7.03645i	−0.149340	−	0.258665i
$741$	−2.83138	+	21.3812i	−0.104013	+	0.785459i
$742$	10.4568	−	7.51772i	0.383883	−	0.275984i
$743$	19.9808	−	34.6077i	0.733023	−	1.26963i	−0.222562	−	0.974919i	$-0.571442\pi$
$743$	19.9808	−	34.6077i	0.733023	−	1.26963i	0.955585	−	0.294715i	$-0.0952248\pi$
$744$	18.1773	+	3.52018i	0.666413	+	0.129056i
$745$			4.73977i			0.173652i
$746$	−0.378056	+	0.654812i	−0.0138416	+	0.0239744i
$747$	6.90114	+	8.80774i	0.252499	+	0.322258i
$748$	−13.3514	−	23.1254i	−0.488177	−	0.845548i
$749$	−0.846003	−	0.381747i	−0.0309123	−	0.0139487i
$750$	−18.8095	+	6.49130i	−0.686827	+	0.237029i
$751$	31.2080			1.13880			0.569399	−	0.822061i	$-0.307176\pi$
$751$	31.2080			1.13880			0.569399	+	0.822061i	$0.307176\pi$
$752$	−11.0787	+	6.39629i	−0.403998	+	0.233249i
$753$	−14.5179	+	16.7245i	−0.529062	+	0.609473i
$754$	−0.318166	+	0.635824i	−0.0115869	+	0.0231553i
$755$	−13.5590			−0.493462
$756$	−11.5516	+	7.45394i	−0.420127	+	0.271097i
$757$	−0.452106	+	0.783071i	−0.0164321	+	0.0284612i	−0.874125	−	0.485702i	$-0.838564\pi$
$757$	−0.452106	+	0.783071i	−0.0164321	+	0.0284612i	0.857692	+	0.514163i	$0.171897\pi$
$758$	−6.26101	−	3.61480i	−0.227410	−	0.131295i
$759$	16.6044	+	14.4137i	0.602701	+	0.523184i
$760$		−	5.04260i		−	0.182914i
$761$	−36.2071	−	20.9042i	−1.31251	−	0.757776i	−0.329996	−	0.943982i	$-0.607047\pi$
$761$	−36.2071	−	20.9042i	−1.31251	−	0.757776i	−0.982511	+	0.186206i	$0.940381\pi$
$762$	−26.7972	−	5.18947i	−0.970759	−	0.187995i
$763$	20.1554	−	14.4903i	0.729675	−	0.524584i
$764$	17.9487	+	10.3627i	0.649363	+	0.374910i
$765$	12.4067	−	30.8312i	0.448565	−	1.11471i
$766$	−1.16788	−	0.674277i	−0.0421973	−	0.0243626i
$767$	−4.70821	+	0.281093i	−0.170004	+	0.0101497i
$768$	−0.565041	−	1.63729i	−0.0203892	−	0.0590807i
$769$	−10.4819	+	18.1551i	−0.377986	+	0.654691i	−0.990769	−	0.135560i	$-0.956717\pi$
$769$	−10.4819	+	18.1551i	−0.377986	+	0.654691i	0.612783	+	0.790251i	$0.290050\pi$
$770$	11.0391	−	7.93633i	0.397822	−	0.286006i
$771$	−12.0614	−	34.9497i	−0.434380	−	1.25868i
$772$	−8.21554	+	4.74324i	−0.295684	+	0.170713i
$773$		−	23.1443i		−	0.832442i	−0.909263	−	0.416221i	$-0.863354\pi$
$773$		−	23.1443i		−	0.832442i	0.909263	−	0.416221i	$-0.136646\pi$
$774$	31.2343	+	12.5689i	1.12269	+	0.451780i
$775$	15.3297	+	26.5518i	0.550660	+	0.953770i
$776$	1.72747	+	2.99206i	0.0620125	+	0.107409i
$777$	2.33188	−	25.3939i	0.0836559	−	0.911000i
$778$	−3.70239	−	2.13758i	−0.132737	−	0.0766358i
$779$	−8.99817	+	5.19510i	−0.322393	+	0.186134i
$780$	5.55633	−	7.22979i	0.198949	−	0.258868i
$781$	−18.7841	+	32.5350i	−0.672147	+	1.16419i
$782$			27.3667i			0.978630i
$783$	−0.467084	−	0.911987i	−0.0166922	−	0.0325918i
$784$	−4.63164	−	5.24861i	−0.165416	−	0.187450i
$785$	−27.3642			−0.976669
$786$	−14.3635	+	16.5465i	−0.512328	+	0.590196i
$787$	−32.3033			−1.15149			−0.575743	−	0.817630i	$-0.695287\pi$
$787$	−32.3033			−1.15149			−0.575743	+	0.817630i	$0.695287\pi$
$788$	3.21420	−	5.56716i	0.114501	−	0.198322i
$789$	20.8149	+	18.0687i	0.741032	+	0.643263i
$790$	−0.441668	−	0.254997i	−0.0157139	−	0.00907240i
$791$	−1.53139	−	15.3063i	−0.0544500	−	0.544229i
$792$	9.79510	+	3.94162i	0.348054	+	0.140059i
$793$	−1.61291	+	3.22324i	−0.0572760	+	0.114461i
$794$	2.86479	−	4.96196i	0.101668	−	0.176094i
$795$	−4.01591	−	11.6367i	−0.142430	−	0.412712i
$796$			1.26513i			0.0448415i
$797$	6.10975	+	10.5824i	0.216418	+	0.374848i	0.953710	−	0.300727i	$-0.0972291\pi$
$797$	6.10975	+	10.5824i	0.216418	+	0.374848i	−0.737292	+	0.675574i	$0.763896\pi$
$798$	9.13343	−	12.9251i	0.323320	−	0.457544i
$799$	84.0560	−	48.5298i	2.97369	−	1.71686i
$800$	1.43407	−	2.48388i	0.0507020	−	0.0878184i
$801$	26.7551	+	34.1468i	0.945345	+	1.20652i
$802$	−21.9761			−0.776003
$803$	−20.7234			−0.731312
$804$	−7.23138	−	6.27731i	−0.255031	−	0.221384i
$805$	−13.8646	+	1.38715i	−0.488663	+	0.0488907i
$806$	−34.4676	−	17.2476i	−1.21407	−	0.607520i
$807$	−8.75768	−	25.3767i	−0.308285	−	0.893303i
$808$	5.80861	+	10.0608i	0.204346	+	0.353938i
$809$	−25.5113	+	14.7289i	−0.896929	+	0.517842i	−0.876202	−	0.481943i	$-0.839931\pi$
$809$	−25.5113	+	14.7289i	−0.896929	+	0.517842i	−0.0207261	+	0.999785i	$0.506598\pi$
$810$	3.65728	+	12.6216i	0.128504	+	0.443479i
$811$	−36.5632			−1.28391			−0.641954	−	0.766743i	$-0.721876\pi$
$811$	−36.5632			−1.28391			−0.641954	+	0.766743i	$0.721876\pi$
$812$	0.423610	−	0.304545i	0.0148658	−	0.0106874i
$813$	−8.47368	−	24.5538i	−0.297185	−	0.861139i
$814$	−16.9610	+	9.79244i	−0.594483	+	0.343225i
$815$	1.32779			0.0465104
$816$	4.28707	+	12.4224i	0.150077	+	0.434872i
$817$	−38.7593			−1.35602
$818$	8.43899			0.295062
$819$	27.3369	−	8.46734i	0.955227	−	0.295873i
$820$	4.39267			0.153399
$821$	23.6479			0.825317			0.412658	−	0.910886i	$-0.364600\pi$
$821$	23.6479			0.825317			0.412658	+	0.910886i	$0.364600\pi$
$822$	0.707194	+	2.04920i	0.0246662	+	0.0714741i
$823$	14.2248			0.495845			0.247923	−	0.968780i	$-0.420252\pi$
$823$	14.2248			0.495845			0.247923	+	0.968780i	$0.420252\pi$
$824$	−16.2249	+	9.36744i	−0.565221	+	0.326330i
$825$	5.70371	+	16.5274i	0.198578	+	0.575410i
$826$	3.15473	+	1.42353i	0.109767	+	0.0495308i
$827$	−38.3054			−1.33201			−0.666004	−	0.745948i	$-0.731997\pi$
$827$	−38.3054			−1.33201			−0.666004	+	0.745948i	$0.731997\pi$
$828$	−6.67388	−	8.51769i	−0.231933	−	0.296010i
$829$	−18.9848	+	10.9609i	−0.659368	+	0.380687i	−0.792036	−	0.610474i	$-0.790979\pi$
$829$	−18.9848	+	10.9609i	−0.659368	+	0.380687i	0.132668	+	0.991161i	$0.457646\pi$
$830$	2.72292	+	4.71623i	0.0945138	+	0.163703i
$831$	0.406463	+	1.17779i	0.0141000	+	0.0408570i
$832$	0.214878	+	3.59914i	0.00744957	+	0.124778i
$833$	35.1411	+	39.8221i	1.21757	+	1.37975i
$834$	13.1160	+	11.3856i	0.454170	+	0.394249i
$835$	19.6588			0.680320
$836$	−12.1549			−0.420388
$837$	49.4383	−	25.3203i	1.70884	−	0.875199i
$838$	−12.4744	+	21.6063i	−0.430920	+	0.746376i
$839$	−28.0544	+	16.1972i	−0.968547	+	0.559191i	−0.898793	−	0.438373i	$-0.855555\pi$
$839$	−28.0544	+	16.1972i	−0.968547	+	0.559191i	−0.0697541	+	0.997564i	$0.522221\pi$
$840$	−6.07620	+	2.80159i	−0.209649	+	0.0966642i
$841$	−14.4806	−	25.0811i	−0.499330	−	0.864864i
$842$			23.2628i			0.801690i
$843$	−4.12733	−	11.9596i	−0.142153	−	0.411910i
$844$	−6.24577	+	10.8180i	−0.214988	+	0.372371i
$845$	−15.1922	+	11.3790i	−0.522628	+	0.391450i
$846$	−14.3270	+	35.6032i	−0.492571	+	1.22406i
$847$	−2.14165	−	2.97895i	−0.0735880	−	0.102358i
$848$	4.21555	+	2.43385i	0.144763	+	0.0835788i
$849$	−19.5213	−	16.9457i	−0.669968	−	0.581576i
$850$	−10.8805	+	18.8456i	−0.373199	+	0.646400i
$851$	20.0717			0.688050
$852$	12.1199	−	13.9619i	0.415219	−	0.478328i
$853$	14.9608			0.512249			0.256125	−	0.966644i	$-0.417554\pi$
$853$	14.9608			0.512249			0.256125	+	0.966644i	$0.417554\pi$
$854$	2.14744	−	1.54386i	0.0734840	−	0.0528297i
$855$	−9.33021	−	11.9079i	−0.319086	−	0.407241i
$856$		−	0.350806i		−	0.0119903i
$857$	−1.02659	+	1.77810i	−0.0350675	+	0.0607387i	−0.883027	−	0.469323i	$-0.844498\pi$
$857$	−1.02659	+	1.77810i	−0.0350675	+	0.0607387i	0.847959	+	0.530062i	$0.177831\pi$
$858$	−17.4271	−	13.3933i	−0.594950	−	0.457238i
$859$	−45.8673	+	26.4815i	−1.56497	+	0.903536i	−0.568230	+	0.822870i	$0.692372\pi$
$859$	−45.8673	+	26.4815i	−1.56497	+	0.903536i	−0.996741	+	0.0806667i	$0.974295\pi$
$860$	14.1909	+	8.19314i	0.483907	+	0.279384i
$861$	11.2592	+	7.95624i	0.383713	+	0.271148i
$862$	−11.3685	−	19.6908i	−0.387213	−	0.670672i
$863$	−10.0096	−	17.3372i	−0.340732	−	0.590165i	0.643837	−	0.765163i	$-0.277342\pi$
$863$	−10.0096	−	17.3372i	−0.340732	−	0.590165i	−0.984569	+	0.174998i	$0.944008\pi$
$864$	−4.36376	−	2.82092i	−0.148458	−	0.0959695i
$865$			14.8472i			0.504820i
$866$	−11.9025	+	6.87194i	−0.404465	+	0.233518i
$867$	−22.9210	−	66.4172i	−0.778439	−	2.25565i
$868$	16.5092	+	22.9637i	0.560359	+	0.779437i
$869$	−0.614659	+	1.06462i	−0.0208509	+	0.0361148i
$870$	−0.162686	−	0.471407i	−0.00551556	−	0.0159822i
$871$	10.9780	+	16.6385i	0.371976	+	0.563774i
$872$	8.12542	+	4.69121i	0.275161	+	0.158864i
$873$	9.61549	+	3.86934i	0.325435	+	0.130957i
$874$	10.7882	+	6.22855i	0.364915	+	0.210684i
$875$	−27.7049	−	12.5014i	−0.936598	−	0.422626i
$876$	10.0126	+	1.93902i	0.338296	+	0.0655135i
$877$	−0.209887	−	0.121178i	−0.00708737	−	0.00409190i	0.496452	−	0.868064i	$-0.334636\pi$
$877$	−0.209887	−	0.121178i	−0.00708737	−	0.00409190i	−0.503540	+	0.863972i	$0.667969\pi$
$878$			12.1761i			0.410924i
$879$	−19.8092	−	17.1956i	−0.668147	−	0.579995i
$880$	4.45029	+	2.56938i	0.150019	+	0.0866137i
$881$	13.7225	−	23.7681i	0.462323	−	0.800768i	−0.536753	−	0.843740i	$-0.680349\pi$
$881$	13.7225	−	23.7681i	0.462323	−	0.800768i	0.999076	+	0.0429719i	$0.0136826\pi$
$882$	−20.6488	−	3.82455i	−0.695281	−	0.128779i
$883$	13.7372			0.462293			0.231146	−	0.972919i	$-0.425752\pi$
$883$	13.7372			0.462293			0.231146	+	0.972919i	$0.425752\pi$
$884$	−1.63032	−	27.3073i	−0.0548336	−	0.918445i
$885$	2.16866	−	2.49827i	0.0728988	−	0.0839785i
$886$	−1.94173	+	1.12106i	−0.0652336	+	0.0376626i
$887$	50.7830			1.70513			0.852563	−	0.522625i	$-0.175047\pi$
$887$	50.7830			1.70513			0.852563	+	0.522625i	$0.175047\pi$
$888$	9.11107	−	3.14429i	0.305747	−	0.105516i
$889$	−24.3380	−	33.8532i	−0.816271	−	1.13540i
$890$	10.5565	+	18.2844i	0.353855	+	0.612894i
$891$	30.4238	−	8.81569i	1.01924	−	0.295337i
$892$	−3.78556	+	6.55677i	−0.126750	+	0.219537i
$893$		−	44.1807i		−	1.47845i
$894$	−5.52006	−	1.06900i	−0.184618	−	0.0357528i
$895$	−6.23477	+	10.7989i	−0.208405	+	0.360969i
$896$	1.08820	−	2.41160i	0.0363542	−	0.0805659i
$897$	8.60435	+	20.8174i	0.287291	+	0.695071i
$898$	3.91929	+	6.78842i	0.130789	+	0.226532i
$899$	−1.82551	+	1.05396i	−0.0608842	+	0.0351515i
$900$	−1.20937	−	8.51899i	−0.0403123	−	0.283966i
$901$	−31.9842	−	18.4661i	−1.06555	−	0.615194i
$902$		−	10.5883i		−	0.352552i
$903$	21.5341	+	46.7039i	0.716609	+	1.55421i
$904$	5.03517	−	2.90706i	0.167467	−	0.0966873i
$905$	18.5986	+	32.2137i	0.618237	+	1.07082i
$906$	3.05807	−	15.7911i	0.101598	−	0.524625i
$907$	−8.93711	−	15.4795i	−0.296752	−	0.513990i	0.678639	−	0.734472i	$-0.262570\pi$
$907$	−8.93711	−	15.4795i	−0.296752	−	0.513990i	−0.975391	+	0.220483i	$0.929237\pi$
$908$		−	25.4572i		−	0.844826i
$909$	32.3321	+	13.0106i	1.07239	+	0.431536i
$910$	13.7519	−	2.21010i	0.455871	−	0.0732642i
$911$		−	43.8367i		−	1.45238i	−0.687496	−	0.726188i	$-0.741290\pi$
$911$		−	43.8367i		−	1.45238i	0.687496	−	0.726188i	$-0.258710\pi$
$912$	5.87274	+	1.13730i	0.194466	+	0.0376598i
$913$	11.3682	−	6.56345i	0.376234	−	0.217219i
$914$			6.54295i			0.216421i
$915$	−0.824717	−	2.38975i	−0.0272643	−	0.0790025i
$916$	5.51406	+	9.55063i	0.182190	+	0.315562i
$917$	−33.3035	+	3.33201i	−1.09978	+	0.110033i
$918$	33.1087	+	21.4028i	1.09275	+	0.706397i
$919$	−26.8620	+	46.5264i	−0.886096	+	1.53476i	−0.0416430	+	0.999133i	$0.513259\pi$
$919$	−26.8620	+	46.5264i	−0.886096	+	1.53476i	−0.844453	+	0.535630i	$0.820074\pi$
$920$	−2.63325	−	4.56092i	−0.0868156	−	0.150369i
$921$	−0.163457	−	0.473642i	−0.00538610	−	0.0156070i
$922$	−20.3030	+	11.7219i	−0.668644	+	0.386042i
$923$	−32.1246	+	21.1957i	−1.05739	+	0.697664i
$924$	6.75311	+	14.6464i	0.222161	+	0.481831i
$925$	13.8221	+	7.98018i	0.454467	+	0.262387i
$926$			37.3356i			1.22692i
$927$	−20.9820	+	52.1413i	−0.689140	+	1.71255i
$928$	0.170773	+	0.0985961i	0.00560591	+	0.00323657i
$929$	−6.58944	−	3.80441i	−0.216193	−	0.124819i	0.387994	−	0.921662i	$-0.373168\pi$
$929$	−6.58944	−	3.80441i	−0.216193	−	0.124819i	−0.604186	+	0.796843i	$0.706502\pi$
$930$	25.5547	−	8.81910i	0.837971	−	0.289190i
$931$	23.6962	−	4.78954i	0.776611	−	0.156971i
$932$	−6.18721	+	3.57219i	−0.202669	+	0.117011i
$933$	20.3024	+	3.93172i	0.664672	+	0.128719i
$934$	3.36611	+	5.83027i	0.110142	+	0.190772i
$935$	−33.7652	−	19.4943i	−1.10424	−	0.637532i
$936$	7.16683	+	8.10164i	0.234255	+	0.264810i
$937$		−	25.7440i		−	0.841020i	−0.907288	−	0.420510i	$-0.861851\pi$
$937$		−	25.7440i		−	0.841020i	0.907288	−	0.420510i	$-0.138149\pi$
$938$	−1.45620	−	14.5547i	−0.0475466	−	0.475229i
$939$	12.0117	+	10.4269i	0.391987	+	0.340270i
$940$	−9.33916	+	16.1759i	−0.304610	+	0.527599i
$941$	−17.8743	−	10.3197i	−0.582684	−	0.336413i	0.179515	−	0.983755i	$-0.442547\pi$
$941$	−17.8743	−	10.3197i	−0.582684	−	0.336413i	−0.762199	+	0.647342i	$0.775880\pi$
$942$	6.17167	−	31.8690i	0.201084	−	1.03835i
$943$	−5.42576	+	9.39769i	−0.176687	+	0.306031i
$944$			1.30815i			0.0425766i
$945$	−9.16497	+	17.8585i	−0.298136	+	0.580937i
$946$	19.7492	−	34.2066i	0.642101	−	1.11215i
$947$	60.7640			1.97456			0.987282	−	0.158978i	$-0.0508200\pi$
$947$	60.7640			1.97456			0.987282	+	0.158978i	$0.0508200\pi$
$948$	0.396590	−	0.456866i	0.0128806	−	0.0148383i
$949$	−18.9858	−	9.50050i	−0.616307	−	0.308399i
$950$	4.95273	+	8.57838i	0.160688	+	0.278319i
$951$	−26.1420	+	30.1153i	−0.847712	+	0.976554i
$952$	−8.25637	+	18.2972i	−0.267590	+	0.593017i
$953$	3.76601	−	2.17431i	0.121993	−	0.0704328i	−0.437762	−	0.899091i	$-0.644229\pi$
$953$	3.76601	−	2.17431i	0.121993	−	0.0704328i	0.559755	+	0.828658i	$0.310895\pi$
$954$	14.4581	−	2.05250i	0.468100	−	0.0664522i
$955$	30.2610			0.979223
$956$	7.32463			0.236896
$957$	−1.13630	+	0.392146i	−0.0367315	+	0.0126763i
$958$	11.2141	−	6.47445i	0.362310	−	0.209180i
$959$	−1.36197	+	3.01831i	−0.0439803	+	0.0974663i
$960$	−1.90978	−	1.65781i	−0.0616378	−	0.0535056i
$961$	−41.6345	−	72.1131i	−1.34305	−	2.32623i
$962$	−20.0282	+	1.19574i	−0.645735	+	0.0385521i
$963$	−0.649087	−	0.828412i	−0.0209165	−	0.0266952i
$964$	17.4268			0.561280
$965$	−6.92556	+	11.9954i	−0.222942	+	0.386146i
$966$	1.51149	−	16.4599i	0.0486315	−	0.529590i
$967$			34.3376i			1.10422i	0.833771	+	0.552111i	$0.186177\pi$
$967$			34.3376i			1.10422i	−0.833771	+	0.552111i	$0.813823\pi$
$968$	0.693357	−	1.20093i	0.0222853	−	0.0385993i
$969$	−44.5575	−	8.62891i	−1.43139	−	0.277200i
$970$	4.36868	+	2.52226i	0.140270	+	0.0809849i
$971$	0.620174	−	1.07417i	0.0199023	−	0.0344718i	−0.855903	−	0.517137i	$-0.826998\pi$
$971$	0.620174	−	1.07417i	0.0199023	−	0.0344718i	0.875805	+	0.482665i	$0.160331\pi$
$972$	−15.5243	+	1.41269i	−0.497943	+	0.0453122i
$973$	2.64120	+	26.3988i	0.0846729	+	0.846308i
$974$			8.67630i			0.278007i
$975$	−2.35138	+	17.7565i	−0.0753045	+	0.568663i
$976$	0.865717	+	0.499822i	0.0277109	+	0.0159989i
$977$	−0.286041	−	0.495437i	−0.00915126	−	0.0158504i	0.861414	−	0.507904i	$-0.169580\pi$
$977$	−0.286041	−	0.495437i	−0.00915126	−	0.0158504i	−0.870565	+	0.492054i	$0.836246\pi$
$978$	−0.299467	+	1.54638i	−0.00957591	+	0.0494476i
$979$	44.0736	−	25.4459i	1.40860	−	0.813255i
$980$	−9.68832	−	3.25543i	−0.309482	−	0.103991i
$981$	27.8679	−	3.95617i	0.889752	−	0.126311i
$982$	−14.7725	−	8.52893i	−0.471411	−	0.272169i
$983$	6.05482	+	3.49575i	0.193119	+	0.111497i	0.593442	−	0.804877i	$-0.297769\pi$
$983$	6.05482	+	3.49575i	0.193119	+	0.111497i	−0.400323	+	0.916374i	$0.631102\pi$
$984$	−0.990716	+	5.11581i	−0.0315829	+	0.163086i
$985$		−	9.38605i		−	0.299064i
$986$	−1.29569	−	0.748066i	−0.0412631	−	0.0238233i
$987$	−53.2366	+	24.5461i	−1.69454	+	0.781312i
$988$	−11.1358	−	5.57236i	−0.354278	−	0.177280i
$989$	−35.0569	+	20.2401i	−1.11474	+	0.643598i
$990$	15.2632	−	2.16679i	0.485097	−	0.0688652i
$991$	21.3759	+	37.0241i	0.679028	+	1.17611i	0.975274	+	0.220999i	$0.0709317\pi$
$991$	21.3759	+	37.0241i	0.679028	+	1.17611i	−0.296247	+	0.955112i	$0.595735\pi$
$992$	−5.34484	+	9.25753i	−0.169699	+	0.293927i
$993$	−7.79436	+	40.2482i	−0.247347	+	1.27724i
$994$	28.1014	−	2.81154i	0.891323	−	0.0891766i
$995$	0.923605	+	1.59973i	0.0292803	+	0.0507149i
$996$	−6.10676	+	2.10748i	−0.193500	+	0.0667782i
$997$			8.93718i			0.283043i	0.989935	+	0.141522i	$0.0451995\pi$
$997$			8.93718i			0.283043i	−0.989935	+	0.141522i	$0.954800\pi$
$998$	−20.1546	+	11.6362i	−0.637982	+	0.368339i
$999$	15.6976	−	24.2831i	0.496650	−	0.768283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.e.17.7	✓	34
3.2	odd	2		546.2.bi.f.17.13	yes	34
7.5	odd	6		546.2.bn.f.173.2	yes	34
13.10	even	6		546.2.bn.e.101.16	yes	34
21.5	even	6		546.2.bn.e.173.16	yes	34
39.23	odd	6		546.2.bn.f.101.2	yes	34
91.75	odd	6		546.2.bi.f.257.13	yes	34
273.257	even	6	inner	546.2.bi.e.257.7	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.7	✓	34	1.1	even	1	trivial
546.2.bi.e.257.7	yes	34	273.257	even	6	inner
546.2.bi.f.17.13	yes	34	3.2	odd	2
546.2.bi.f.257.13	yes	34	91.75	odd	6
546.2.bn.e.101.16	yes	34	13.10	even	6
546.2.bn.e.173.16	yes	34	21.5	even	6
546.2.bn.f.101.2	yes	34	39.23	odd	6
546.2.bn.f.173.2	yes	34	7.5	odd	6

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.565041 - 1.63729i) q^{3} +1.00000 q^{4} +(1.26448 - 0.730045i) q^{5} +(0.565041 + 1.63729i) q^{6} +(-1.08820 + 2.41160i) q^{7} -1.00000 q^{8} +(-2.36146 + 1.85028i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.565041 - 1.63729i) q^{3} +1.00000 q^{4} +(1.26448 - 0.730045i) q^{5} +(0.565041 + 1.63729i) q^{6} +(-1.08820 + 2.41160i) q^{7} -1.00000 q^{8} +(-2.36146 + 1.85028i) q^{9} +(-1.26448 + 0.730045i) q^{10} +(1.75974 + 3.04796i) q^{11} +(-0.565041 - 1.63729i) q^{12} +(0.214878 + 3.59914i) q^{13} +(1.08820 - 2.41160i) q^{14} +(-1.90978 - 1.65781i) q^{15} +1.00000 q^{16} -7.58718 q^{17} +(2.36146 - 1.85028i) q^{18} +(-1.72681 + 2.99093i) q^{19} +(1.26448 - 0.730045i) q^{20} +(4.56338 + 0.419048i) q^{21} +(-1.75974 - 3.04796i) q^{22} +3.60696i q^{23} +(0.565041 + 1.63729i) q^{24} +(-1.43407 + 2.48388i) q^{25} +(-0.214878 - 3.59914i) q^{26} +(4.36376 + 2.82092i) q^{27} +(-1.08820 + 2.41160i) q^{28} +(-0.170773 - 0.0985961i) q^{29} +(1.90978 + 1.65781i) q^{30} +(5.34484 - 9.25753i) q^{31} -1.00000 q^{32} +(3.99607 - 4.60343i) q^{33} +7.58718 q^{34} +(0.384576 + 3.84385i) q^{35} +(-2.36146 + 1.85028i) q^{36} -5.56471i q^{37} +(1.72681 - 2.99093i) q^{38} +(5.77144 - 2.38548i) q^{39} +(-1.26448 + 0.730045i) q^{40} +(2.60543 + 1.50425i) q^{41} +(-4.56338 - 0.419048i) q^{42} +(5.61139 + 9.71922i) q^{43} +(1.75974 + 3.04796i) q^{44} +(-1.63522 + 4.06360i) q^{45} -3.60696i q^{46} +(-11.0787 + 6.39629i) q^{47} +(-0.565041 - 1.63729i) q^{48} +(-4.63164 - 5.24861i) q^{49} +(1.43407 - 2.48388i) q^{50} +(4.28707 + 12.4224i) q^{51} +(0.214878 + 3.59914i) q^{52} +(4.21555 + 2.43385i) q^{53} +(-4.36376 - 2.82092i) q^{54} +(4.45029 + 2.56938i) q^{55} +(1.08820 - 2.41160i) q^{56} +(5.87274 + 1.13730i) q^{57} +(0.170773 + 0.0985961i) q^{58} +1.30815i q^{59} +(-1.90978 - 1.65781i) q^{60} +(0.865717 + 0.499822i) q^{61} +(-5.34484 + 9.25753i) q^{62} +(-1.89239 - 7.70836i) q^{63} +1.00000 q^{64} +(2.89925 + 4.39416i) q^{65} +(-3.99607 + 4.60343i) q^{66} +(4.78794 - 2.76432i) q^{67} -7.58718 q^{68} +(5.90566 - 2.03808i) q^{69} +(-0.384576 - 3.84385i) q^{70} +(5.33718 + 9.24427i) q^{71} +(2.36146 - 1.85028i) q^{72} +(-2.94410 + 5.09933i) q^{73} +5.56471i q^{74} +(4.87714 + 0.944496i) q^{75} +(-1.72681 + 2.99093i) q^{76} +(-9.26540 + 0.927001i) q^{77} +(-5.77144 + 2.38548i) q^{78} +(0.174645 + 0.302494i) q^{79} +(1.26448 - 0.730045i) q^{80} +(2.15296 - 8.73869i) q^{81} +(-2.60543 - 1.50425i) q^{82} -3.72979i q^{83} +(4.56338 + 0.419048i) q^{84} +(-9.59380 + 5.53898i) q^{85} +(-5.61139 - 9.71922i) q^{86} +(-0.0649367 + 0.335317i) q^{87} +(-1.75974 - 3.04796i) q^{88} -14.4601i q^{89} +(1.63522 - 4.06360i) q^{90} +(-8.91353 - 3.39839i) q^{91} +3.60696i q^{92} +(-18.1773 - 3.52018i) q^{93} +(11.0787 - 6.39629i) q^{94} +5.04260i q^{95} +(0.565041 + 1.63729i) q^{96} +(-1.72747 - 2.99206i) q^{97} +(4.63164 + 5.24861i) q^{98} +(-9.79510 - 3.94162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * q^84 - 42 * q^85 + 3 * q^86 + 81 * q^87 + 9 * q^88 - 9 * q^90 - 72 * q^91 + 17 * q^93 - 27 * q^94 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more