LMFDB - Embedded newform 183.2.g.c.50.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [183,2,Mod(11,183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(183, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("183.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 183 = 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	183.g (of order $4$, 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:	$1.46126235699$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.4
Character	$\chi$	$=$	183.50
Dual form			183.2.g.c.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06450 - 1.06450i) q^{2} +(0.815973 + 1.52781i) q^{3} +0.266334i q^{4} -4.01835 q^{5} +(0.757748 - 2.49496i) q^{6} +(-0.934712 + 0.934712i) q^{7} +(-1.84549 + 1.84549i) q^{8} +(-1.66838 + 2.49329i) q^{9} +O(q^{10})$	\(q+(-1.06450 - 1.06450i) q^{2} +(0.815973 + 1.52781i) q^{3} +0.266334i q^{4} -4.01835 q^{5} +(0.757748 - 2.49496i) q^{6} +(-0.934712 + 0.934712i) q^{7} +(-1.84549 + 1.84549i) q^{8} +(-1.66838 + 2.49329i) q^{9} +(4.27754 + 4.27754i) q^{10} +(2.21002 - 2.21002i) q^{11} +(-0.406906 + 0.217321i) q^{12} -6.90055 q^{13} +1.99001 q^{14} +(-3.27886 - 6.13925i) q^{15} +4.46173 q^{16} +(-2.41228 + 2.41228i) q^{17} +(4.43011 - 0.878126i) q^{18} -1.09599i q^{19} -1.07022i q^{20} +(-2.19076 - 0.665358i) q^{21} -4.70515 q^{22} +(2.30539 + 2.30539i) q^{23} +(-4.32543 - 1.31368i) q^{24} +11.1471 q^{25} +(7.34566 + 7.34566i) q^{26} +(-5.17062 - 0.514497i) q^{27} +(-0.248945 - 0.248945i) q^{28} +(-1.04965 + 1.04965i) q^{29} +(-3.04489 + 10.0256i) q^{30} +(2.56686 + 2.56686i) q^{31} +(-1.05854 - 1.05854i) q^{32} +(5.17980 + 1.57317i) q^{33} +5.13576 q^{34} +(3.75599 - 3.75599i) q^{35} +(-0.664049 - 0.444346i) q^{36} +(-6.22556 - 6.22556i) q^{37} +(-1.16668 + 1.16668i) q^{38} +(-5.63066 - 10.5427i) q^{39} +(7.41583 - 7.41583i) q^{40} -1.17718 q^{41} +(1.62379 + 3.04034i) q^{42} +(-1.27964 - 1.27964i) q^{43} +(0.588604 + 0.588604i) q^{44} +(6.70412 - 10.0189i) q^{45} -4.90818i q^{46} -7.54269i q^{47} +(3.64065 + 6.81666i) q^{48} +5.25263i q^{49} +(-11.8661 - 11.8661i) q^{50} +(-5.65385 - 1.71714i) q^{51} -1.83785i q^{52} +(1.33749 + 1.33749i) q^{53} +(4.95646 + 6.05182i) q^{54} +(-8.88063 + 8.88063i) q^{55} -3.45001i q^{56} +(1.67445 - 0.894294i) q^{57} +2.23470 q^{58} +(0.619962 - 0.619962i) q^{59} +(1.63509 - 0.873272i) q^{60} +(7.74642 + 0.996455i) q^{61} -5.46487i q^{62} +(-0.771059 - 3.88996i) q^{63} -6.66982i q^{64} +27.7288 q^{65} +(-3.83927 - 7.18855i) q^{66} +(1.30709 + 1.30709i) q^{67} +(-0.642472 - 0.642472i) q^{68} +(-1.64105 + 5.40331i) q^{69} -7.99654 q^{70} +(-3.09149 + 3.09149i) q^{71} +(-1.52238 - 7.68034i) q^{72} -9.94223 q^{73} +13.2543i q^{74} +(9.09573 + 17.0306i) q^{75} +0.291898 q^{76} +4.13147i q^{77} +(-5.22888 + 17.2166i) q^{78} +(-9.78736 + 9.78736i) q^{79} -17.9288 q^{80} +(-3.43303 - 8.31951i) q^{81} +(1.25311 + 1.25311i) q^{82} +10.0039i q^{83} +(0.177207 - 0.583473i) q^{84} +(9.69337 - 9.69337i) q^{85} +2.72437i q^{86} +(-2.46014 - 0.747173i) q^{87} +8.15716i q^{88} +(-6.02484 + 6.02484i) q^{89} +(-17.8017 + 3.52862i) q^{90} +(6.45002 - 6.45002i) q^{91} +(-0.614002 + 0.614002i) q^{92} +(-1.82718 + 6.01616i) q^{93} +(-8.02922 + 8.02922i) q^{94} +4.40405i q^{95} +(0.753506 - 2.48099i) q^{96} +6.80558i q^{97} +(5.59144 - 5.59144i) q^{98} +(1.82308 + 9.19738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9	$ 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{13} - 40 q^{15} + 12 q^{16} - 4 q^{18} - 18 q^{21} - 48 q^{22} + 14 q^{24} + 36 q^{25} - 24 q^{28} - 22 q^{30} + 32 q^{31} + 2 q^{33} + 96 q^{34} + 8 q^{37} + 28 q^{40} + 20 q^{42} - 32 q^{43} - 24 q^{51} - 2 q^{54} - 40 q^{55} - 16 q^{57} - 56 q^{58} + 64 q^{61} + 40 q^{63} - 12 q^{67} - 30 q^{69} - 24 q^{70} + 44 q^{72} - 72 q^{73} + 128 q^{76} - 66 q^{78} + 28 q^{81} - 28 q^{82} + 46 q^{84} - 44 q^{85} - 12 q^{87} - 56 q^{90} - 64 q^{91} + 36 q^{93} - 16 q^{94} + 54 q^{96} + 32 q^{99}+O(q^{100}) $ 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^13 - 40 * q^15 + 12 * q^16 - 4 * q^18 - 18 * q^21 - 48 * q^22 + 14 * q^24 + 36 * q^25 - 24 * q^28 - 22 * q^30 + 32 * q^31 + 2 * q^33 + 96 * q^34 + 8 * q^37 + 28 * q^40 + 20 * q^42 - 32 * q^43 - 24 * q^51 - 2 * q^54 - 40 * q^55 - 16 * q^57 - 56 * q^58 + 64 * q^61 + 40 * q^63 - 12 * q^67 - 30 * q^69 - 24 * q^70 + 44 * q^72 - 72 * q^73 + 128 * q^76 - 66 * q^78 + 28 * q^81 - 28 * q^82 + 46 * q^84 - 44 * q^85 - 12 * q^87 - 56 * q^90 - 64 * q^91 + 36 * q^93 - 16 * q^94 + 54 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/183\mathbb{Z}\right)^\times$.

$n$	$62$	$124$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.06450	−	1.06450i	−0.752717	−	0.752717i	0.222268	−	0.974986i	$-0.428654\pi$
$2$	−1.06450	−	1.06450i	−0.752717	−	0.752717i	−0.974986	+	0.222268i	$0.928654\pi$
$3$	0.815973	+	1.52781i	0.471102	+	0.882079i
$3$	0.815973	+	1.52781i	0.471102	+	0.882079i
$4$			0.266334i			0.133167i
$5$	−4.01835			−1.79706			−0.898529	−	0.438913i	$-0.855364\pi$
$5$	−4.01835			−1.79706			−0.898529	+	0.438913i	$0.855364\pi$
$6$	0.757748	−	2.49496i	0.309349	−	1.01856i
$7$	−0.934712	+	0.934712i	−0.353288	+	0.353288i	−0.861331	−	0.508044i	$-0.830369\pi$
$7$	−0.934712	+	0.934712i	−0.353288	+	0.353288i	0.508044	+	0.861331i	$0.330369\pi$
$8$	−1.84549	+	1.84549i	−0.652480	+	0.652480i
$9$	−1.66838	+	2.49329i	−0.556126	+	0.831098i
$10$	4.27754	+	4.27754i	1.35268	+	1.35268i
$11$	2.21002	−	2.21002i	0.666347	−	0.666347i	−0.290522	−	0.956868i	$-0.593829\pi$
$11$	2.21002	−	2.21002i	0.666347	−	0.666347i	0.956868	+	0.290522i	$0.0938289\pi$
$12$	−0.406906	+	0.217321i	−0.117464	+	0.0627352i
$13$	−6.90055			−1.91387			−0.956934	−	0.290305i	$-0.906243\pi$
$13$	−6.90055			−1.91387			−0.956934	+	0.290305i	$0.906243\pi$
$14$	1.99001			0.531852
$15$	−3.27886	−	6.13925i	−0.846598	−	1.58515i
$16$	4.46173			1.11543
$17$	−2.41228	+	2.41228i	−0.585064	+	0.585064i	−0.936290	−	0.351227i	$-0.885765\pi$
$17$	−2.41228	+	2.41228i	−0.585064	+	0.585064i	0.351227	+	0.936290i	$0.385765\pi$
$18$	4.43011	−	0.878126i	1.04419	−	0.206976i
$19$		−	1.09599i		−	0.251436i	−0.992066	−	0.125718i	$-0.959876\pi$
$19$		−	1.09599i		−	0.251436i	0.992066	−	0.125718i	$-0.0401235\pi$
$20$		−	1.07022i		−	0.239309i
$21$	−2.19076	−	0.665358i	−0.478062	−	0.145193i
$22$	−4.70515			−1.00314
$23$	2.30539	+	2.30539i	0.480706	+	0.480706i	0.905357	−	0.424651i	$-0.139603\pi$
$23$	2.30539	+	2.30539i	0.480706	+	0.480706i	−0.424651	+	0.905357i	$0.639603\pi$
$24$	−4.32543	−	1.31368i	−0.882924	−	0.268154i
$25$	11.1471			2.22942
$26$	7.34566	+	7.34566i	1.44060	+	1.44060i
$27$	−5.17062	−	0.514497i	−0.995086	−	0.0990149i
$28$	−0.248945	−	0.248945i	−0.0470463	−	0.0470463i
$29$	−1.04965	+	1.04965i	−0.194915	+	0.194915i	−0.797816	−	0.602901i	$-0.794011\pi$
$29$	−1.04965	+	1.04965i	−0.194915	+	0.194915i	0.602901	+	0.797816i	$0.294011\pi$
$30$	−3.04489	+	10.0256i	−0.555919	+	1.83042i
$31$	2.56686	+	2.56686i	0.461022	+	0.461022i	0.898990	−	0.437968i	$-0.144302\pi$
$31$	2.56686	+	2.56686i	0.461022	+	0.461022i	−0.437968	+	0.898990i	$0.644302\pi$
$32$	−1.05854	−	1.05854i	−0.187126	−	0.187126i
$33$	5.17980	+	1.57317i	0.901687	+	0.273853i
$34$	5.13576			0.880775
$35$	3.75599	−	3.75599i	0.634879	−	0.634879i
$36$	−0.664049	−	0.444346i	−0.110675	−	0.0740576i
$37$	−6.22556	−	6.22556i	−1.02348	−	1.02348i	−0.999718	−	0.0237584i	$-0.992437\pi$
$37$	−6.22556	−	6.22556i	−1.02348	−	1.02348i	−0.0237584	−	0.999718i	$-0.507563\pi$
$38$	−1.16668	+	1.16668i	−0.189261	+	0.189261i
$39$	−5.63066	−	10.5427i	−0.901627	−	1.68818i
$40$	7.41583	−	7.41583i	1.17255	−	1.17255i
$41$	−1.17718			−0.183845			−0.0919223	−	0.995766i	$-0.529301\pi$
$41$	−1.17718			−0.183845			−0.0919223	+	0.995766i	$0.529301\pi$
$42$	1.62379	+	3.04034i	0.250556	+	0.469135i
$43$	−1.27964	−	1.27964i	−0.195144	−	0.195144i	0.602771	−	0.797914i	$-0.294063\pi$
$43$	−1.27964	−	1.27964i	−0.195144	−	0.195144i	−0.797914	+	0.602771i	$0.794063\pi$
$44$	0.588604	+	0.588604i	0.0887353	+	0.0887353i
$45$	6.70412	−	10.0189i	0.999391	−	1.49353i
$46$		−	4.90818i		−	0.723672i
$47$		−	7.54269i		−	1.10021i	−0.835094	−	0.550107i	$-0.814587\pi$
$47$		−	7.54269i		−	1.10021i	0.835094	−	0.550107i	$-0.185413\pi$
$48$	3.64065	+	6.81666i	0.525483	+	0.983900i
$49$			5.25263i			0.750376i
$50$	−11.8661	−	11.8661i	−1.67812	−	1.67812i
$51$	−5.65385	−	1.71714i	−0.791697	−	0.240448i
$52$		−	1.83785i		−	0.254864i
$53$	1.33749	+	1.33749i	0.183718	+	0.183718i	0.792974	−	0.609256i	$-0.208532\pi$
$53$	1.33749	+	1.33749i	0.183718	+	0.183718i	−0.609256	+	0.792974i	$0.708532\pi$
$54$	4.95646	+	6.05182i	0.674488	+	0.823549i
$55$	−8.88063	+	8.88063i	−1.19746	+	1.19746i
$56$		−	3.45001i		−	0.461027i
$57$	1.67445	−	0.894294i	0.221787	−	0.118452i
$58$	2.23470			0.293431
$59$	0.619962	−	0.619962i	0.0807121	−	0.0807121i	−0.665598	−	0.746310i	$-0.731824\pi$
$59$	0.619962	−	0.619962i	0.0807121	−	0.0807121i	0.746310	+	0.665598i	$0.231824\pi$
$60$	1.63509	−	0.873272i	0.211089	−	0.112739i
$61$	7.74642	+	0.996455i	0.991828	+	0.127583i
$61$	7.74642	+	0.996455i	0.991828	+	0.127583i
$62$		−	5.46487i		−	0.694039i
$63$	−0.771059	−	3.88996i	−0.0971443	−	0.490089i
$64$		−	6.66982i		−	0.833728i
$65$	27.7288			3.43933
$66$	−3.83927	−	7.18855i	−0.472582	−	0.884850i
$67$	1.30709	+	1.30709i	0.159686	+	0.159686i	0.782428	−	0.622742i	$-0.213981\pi$
$67$	1.30709	+	1.30709i	0.159686	+	0.159686i	−0.622742	+	0.782428i	$0.713981\pi$
$68$	−0.642472	−	0.642472i	−0.0779111	−	0.0779111i
$69$	−1.64105	+	5.40331i	−0.197559	+	0.650482i
$70$	−7.99654			−0.955769
$71$	−3.09149	+	3.09149i	−0.366893	+	0.366893i	−0.866343	−	0.499450i	$-0.833535\pi$
$71$	−3.09149	+	3.09149i	−0.366893	+	0.366893i	0.499450	+	0.866343i	$0.333535\pi$
$72$	−1.52238	−	7.68034i	−0.179414	−	0.905136i
$73$	−9.94223			−1.16365			−0.581825	−	0.813314i	$-0.697661\pi$
$73$	−9.94223			−1.16365			−0.581825	+	0.813314i	$0.697661\pi$
$74$			13.2543i			1.54078i
$75$	9.09573	+	17.0306i	1.05028	+	1.96652i
$76$	0.291898			0.0334830
$77$			4.13147i			0.470824i
$78$	−5.22888	+	17.2166i	−0.592054	+	1.94939i
$79$	−9.78736	+	9.78736i	−1.10116	+	1.10116i	−0.106894	+	0.994270i	$0.534090\pi$
$79$	−9.78736	+	9.78736i	−1.10116	+	1.10116i	−0.994270	+	0.106894i	$0.965910\pi$
$80$	−17.9288			−2.00450
$81$	−3.43303	−	8.31951i	−0.381448	−	0.924390i
$82$	1.25311	+	1.25311i	0.138383	+	0.138383i
$83$			10.0039i			1.09807i	0.835800	+	0.549034i	$0.185004\pi$
$83$			10.0039i			1.09807i	−0.835800	+	0.549034i	$0.814996\pi$
$84$	0.177207	−	0.583473i	0.0193349	−	0.0636621i
$85$	9.69337	−	9.69337i	1.05139	−	1.05139i
$86$			2.72437i			0.293776i
$87$	−2.46014	−	0.747173i	−0.263755	−	0.0801054i
$88$			8.15716i			0.869556i
$89$	−6.02484	+	6.02484i	−0.638632	+	0.638632i	−0.950218	−	0.311586i	$-0.899140\pi$
$89$	−6.02484	+	6.02484i	−0.638632	+	0.638632i	0.311586	+	0.950218i	$0.399140\pi$
$90$	−17.8017	+	3.52862i	−1.87647	+	0.371949i
$91$	6.45002	−	6.45002i	0.676146	−	0.676146i
$92$	−0.614002	+	0.614002i	−0.0640142	+	0.0640142i
$93$	−1.82718	+	6.01616i	−0.189469	+	0.623846i
$94$	−8.02922	+	8.02922i	−0.828151	+	0.828151i
$95$			4.40405i			0.451846i
$96$	0.753506	−	2.48099i	0.0769044	−	0.253215i
$97$			6.80558i			0.691002i	0.938418	+	0.345501i	$0.112291\pi$
$97$			6.80558i			0.691002i	−0.938418	+	0.345501i	$0.887709\pi$
$98$	5.59144	−	5.59144i	0.564821	−	0.564821i
$99$	1.82308	+	9.19738i	0.183227	+	0.924372i
$100$			2.96885i			0.296885i
$101$	−11.7172	−	11.7172i	−1.16591	−	1.16591i	−0.983160	−	0.182748i	$-0.941501\pi$
$101$	−11.7172	−	11.7172i	−1.16591	−	1.16591i	−0.182748	−	0.983160i	$-0.558499\pi$
$102$	4.19064	+	7.84644i	0.414935	+	0.776913i
$103$	−3.63875			−0.358536			−0.179268	−	0.983800i	$-0.557373\pi$
$103$	−3.63875			−0.358536			−0.179268	+	0.983800i	$0.557373\pi$
$104$	12.7349	−	12.7349i	1.24876	−	1.24876i
$105$	8.80322	+	2.67364i	0.859106	+	0.260921i
$106$		−	2.84752i		−	0.276576i
$107$	10.0801			0.974483			0.487242	−	0.873267i	$-0.338003\pi$
$107$	10.0801			0.974483			0.487242	+	0.873267i	$0.338003\pi$
$108$	0.137028	−	1.37711i	0.0131855	−	0.132513i
$109$			5.27346i			0.505106i	0.967583	+	0.252553i	$0.0812702\pi$
$109$			5.27346i			0.505106i	−0.967583	+	0.252553i	$0.918730\pi$
$110$	18.9069			1.80270
$111$	4.43156	−	14.5913i	0.420625	−	1.38495i
$112$	−4.17043	+	4.17043i	−0.394069	+	0.394069i
$113$	−2.89011			−0.271878			−0.135939	−	0.990717i	$-0.543405\pi$
$113$	−2.89011			−0.271878			−0.135939	+	0.990717i	$0.543405\pi$
$114$	−2.73444	−	0.830481i	−0.256104	−	0.0777817i
$115$	−9.26384	−	9.26384i	−0.863857	−	0.863857i
$116$	−0.279557	−	0.279557i	−0.0259562	−	0.0259562i
$117$	11.5127	−	17.2051i	1.06435	−	1.59061i
$118$	−1.31990			−0.121507
$119$		−	4.50957i		−	0.413392i
$120$	17.3811	+	5.27883i	1.58667	+	0.481889i
$121$			1.23161i			0.111964i
$122$	−7.18536	−	9.30682i	−0.650532	−	0.842600i
$123$	−0.960546	−	1.79850i	−0.0866095	−	0.162165i
$124$	−0.683642	+	0.683642i	−0.0613929	+	0.0613929i
$125$	−24.7012			−2.20934
$126$	−3.32008	+	4.96167i	−0.295776	+	0.442021i
$127$			20.1573i			1.78867i	0.447397	+	0.894335i	$0.352351\pi$
$127$			20.1573i			1.78867i	−0.447397	+	0.894335i	$0.647649\pi$
$128$	−9.21713	+	9.21713i	−0.814687	+	0.814687i
$129$	0.910891	−	2.99920i	0.0801995	−	0.264065i
$130$	−29.5174	−	29.5174i	−2.58885	−	2.58885i
$131$			15.6373i			1.36624i	0.730307	+	0.683119i	$0.239377\pi$
$131$			15.6373i			1.36624i	−0.730307	+	0.683119i	$0.760623\pi$
$132$	−0.418987	+	1.37956i	−0.0364682	+	0.120075i
$133$	1.02443	+	1.02443i	0.0888294	+	0.0888294i
$134$		−	2.78279i		−	0.240397i
$135$	20.7773	+	2.06743i	1.78823	+	0.177936i
$136$		−	8.90369i		−	0.763485i
$137$		−	15.8862i		−	1.35725i	−0.734486	−	0.678623i	$-0.762577\pi$
$137$		−	15.8862i		−	1.35725i	0.734486	−	0.678623i	$-0.237423\pi$
$138$	7.49874	−	4.00494i	0.638335	−	0.340923i
$139$	−2.23305	−	2.23305i	−0.189405	−	0.189405i	0.606034	−	0.795439i	$-0.292760\pi$
$139$	−2.23305	−	2.23305i	−0.189405	−	0.189405i	−0.795439	+	0.606034i	$0.792760\pi$
$140$	1.00035	+	1.00035i	0.0845449	+	0.0845449i
$141$	11.5238	−	6.15463i	0.970476	−	0.518313i
$142$	6.58181			0.552333
$143$	−15.2504	+	15.2504i	−1.27530	+	1.27530i
$144$	−7.44386	+	11.1244i	−0.620321	+	0.927035i
$145$	4.21784	−	4.21784i	0.350273	−	0.350273i
$146$	10.5835	+	10.5835i	0.875900	+	0.875900i
$147$	−8.02499	+	4.28600i	−0.661890	+	0.353503i
$148$	1.65808	−	1.65808i	0.136293	−	0.136293i
$149$	2.18384			0.178907			0.0894536	−	0.995991i	$-0.471488\pi$
$149$	2.18384			0.178907			0.0894536	+	0.995991i	$0.471488\pi$
$150$	8.44670	−	27.8116i	0.689670	−	2.27080i
$151$	−6.08266	−	6.08266i	−0.495000	−	0.495000i	0.414878	−	0.909877i	$-0.363824\pi$
$151$	−6.08266	−	6.08266i	−0.495000	−	0.495000i	−0.909877	+	0.414878i	$0.863824\pi$
$152$	2.02263	+	2.02263i	0.164057	+	0.164057i
$153$	−1.98993	−	10.0391i	−0.160876	−	0.811614i
$154$	4.39796	−	4.39796i	0.354398	−	0.354398i
$155$	−10.3145	−	10.3145i	−0.828484	−	0.828484i
$156$	2.80788	−	1.49964i	0.224810	−	0.120067i
$157$	3.94845	+	3.94845i	0.315121	+	0.315121i	0.846890	−	0.531769i	$-0.178473\pi$
$157$	3.94845	+	3.94845i	0.315121	+	0.315121i	−0.531769	+	0.846890i	$0.678473\pi$
$158$	20.8374			1.65773
$159$	−0.952069	+	3.13478i	−0.0755040	+	0.248604i
$160$	4.25360	+	4.25360i	0.336276	+	0.336276i
$161$	−4.30974			−0.339655
$162$	−5.20167	+	12.5106i	−0.408682	+	0.982927i
$163$		−	6.28264i		−	0.492094i	−0.969258	−	0.246047i	$-0.920868\pi$
$163$		−	6.28264i		−	0.492094i	0.969258	−	0.246047i	$-0.0791318\pi$
$164$		−	0.313523i		−	0.0244820i
$165$	−20.8142	−	6.32152i	−1.62039	−	0.492130i
$166$	10.6492	−	10.6492i	0.826535	−	0.826535i
$167$	−13.1902			−1.02069			−0.510343	−	0.859971i	$-0.670481\pi$
$167$	−13.1902			−1.02069			−0.510343	+	0.859971i	$0.670481\pi$
$168$	5.27094	−	2.81511i	0.406662	−	0.217191i
$169$	34.6176			2.66289
$170$	−20.6372			−1.58280
$171$	2.73261	+	1.82852i	0.208968	+	0.139830i
$172$	0.340812	−	0.340812i	0.0259867	−	0.0259867i
$173$	3.89452	+	3.89452i	0.296095	+	0.296095i	0.839482	−	0.543387i	$-0.182858\pi$
$173$	3.89452	+	3.89452i	0.296095	+	0.296095i	−0.543387	+	0.839482i	$0.682858\pi$
$174$	1.82346	+	3.41419i	0.138236	+	0.258829i
$175$	−10.4193	+	10.4193i	−0.787627	+	0.787627i
$176$	9.86053	−	9.86053i	0.743265	−	0.743265i
$177$	1.45305	+	0.441309i	0.109218	+	0.0331708i
$178$	12.8269			0.961419
$179$		−	11.3419i		−	0.847733i	−0.905725	−	0.423866i	$-0.860673\pi$
$179$		−	11.3419i		−	0.847733i	0.905725	−	0.423866i	$-0.139327\pi$
$180$	2.66838	+	1.78553i	0.198889	+	0.133086i
$181$	−8.64024	−	8.64024i	−0.642224	−	0.642224i	0.308878	−	0.951102i	$-0.400047\pi$
$181$	−8.64024	−	8.64024i	−0.642224	−	0.642224i	−0.951102	+	0.308878i	$0.900047\pi$
$182$	−13.7321			−1.01789
$183$	4.79848	+	12.6481i	0.354714	+	0.934975i
$184$	−8.50915			−0.627303
$185$	25.0165	+	25.0165i	1.83925	+	1.83925i
$186$	8.34925	−	4.45918i	0.612197	−	0.326963i
$187$			10.6624i			0.779710i
$188$	2.00887			0.146512
$189$	5.31394	−	4.35213i	0.386532	−	0.316571i
$190$	4.68812	−	4.68812i	0.340112	−	0.340112i
$191$	2.19769	−	2.19769i	0.159019	−	0.159019i	−0.623113	−	0.782132i	$-0.714132\pi$
$191$	2.19769	−	2.19769i	0.159019	−	0.159019i	0.782132	+	0.623113i	$0.214132\pi$
$192$	10.1902	−	5.44239i	0.735413	−	0.392771i
$193$	−2.59202	−	2.59202i	−0.186578	−	0.186578i	0.607637	−	0.794215i	$-0.292118\pi$
$193$	−2.59202	−	2.59202i	−0.186578	−	0.186578i	−0.794215	+	0.607637i	$0.792118\pi$
$194$	7.24456	−	7.24456i	0.520129	−	0.520129i
$195$	22.6259	+	42.3642i	1.62028	+	3.03376i
$196$	−1.39895			−0.0999252
$197$	12.2571			0.873280			0.436640	−	0.899636i	$-0.356168\pi$
$197$	12.2571			0.873280			0.436640	+	0.899636i	$0.356168\pi$
$198$	7.84997	−	11.7313i	0.557873	−	0.833709i
$199$	9.98463			0.707792			0.353896	−	0.935285i	$-0.384857\pi$
$199$	9.98463			0.707792			0.353896	+	0.935285i	$0.384857\pi$
$200$	−20.5719	+	20.5719i	−1.45465	+	1.45465i
$201$	−0.930427	+	3.06352i	−0.0656272	+	0.216084i
$202$			24.9461i			1.75520i
$203$		−	1.96223i		−	0.137722i
$204$	0.457332	−	1.50581i	0.0320197	−	0.105428i
$205$	4.73031			0.330380
$206$	3.87346	+	3.87346i	0.269877	+	0.269877i
$207$	−9.59426	+	1.90175i	−0.666847	+	0.132181i
$208$	−30.7884			−2.13479
$209$	−2.42215	−	2.42215i	−0.167544	−	0.167544i
$210$	−6.52495	−	12.2171i	−0.450265	−	0.843063i
$211$	−19.7044	−	19.7044i	−1.35651	−	1.35651i	−0.878181	−	0.478329i	$-0.841243\pi$
$211$	−19.7044	−	19.7044i	−1.35651	−	1.35651i	−0.478329	−	0.878181i	$-0.658757\pi$
$212$	−0.356219	+	0.356219i	−0.0244652	+	0.0244652i
$213$	−7.24577	−	2.20063i	−0.496472	−	0.150784i
$214$	−10.7303	−	10.7303i	−0.733511	−	0.733511i
$215$	5.14205	+	5.14205i	0.350685	+	0.350685i
$216$	10.4918	−	8.59284i	0.713879	−	0.584669i
$217$	−4.79855			−0.325747
$218$	5.61362	−	5.61362i	0.380202	−	0.380202i
$219$	−8.11259	−	15.1898i	−0.548198	−	1.02643i
$220$	−2.36521	−	2.36521i	−0.159463	−	0.159463i
$221$	16.6461	−	16.6461i	1.11973	−	1.11973i
$222$	−20.2499	+	10.8151i	−1.35909	+	0.725863i
$223$	7.91979	−	7.91979i	0.530349	−	0.530349i	−0.390327	−	0.920676i	$-0.627638\pi$
$223$	7.91979	−	7.91979i	0.530349	−	0.530349i	0.920676	+	0.390327i	$0.127638\pi$
$224$	1.97887			0.132219
$225$	−18.5976	+	27.7930i	−1.23984	+	1.85287i
$226$	3.07653	+	3.07653i	0.204647	+	0.204647i
$227$	8.72687	+	8.72687i	0.579223	+	0.579223i	0.934689	−	0.355466i	$-0.115678\pi$
$227$	8.72687	+	8.72687i	0.579223	+	0.579223i	−0.355466	+	0.934689i	$0.615678\pi$
$228$	0.238181	+	0.445963i	0.0157739	+	0.0295347i
$229$		−	8.25947i		−	0.545801i	−0.962042	−	0.272901i	$-0.912017\pi$
$229$		−	8.25947i		−	0.545801i	0.962042	−	0.272901i	$-0.0879830\pi$
$230$			19.7228i			1.30048i
$231$	−6.31207	+	3.37116i	−0.415304	+	0.221806i
$232$		−	3.87423i		−	0.254356i
$233$	1.19909	+	1.19909i	0.0785553	+	0.0785553i	0.745293	−	0.666737i	$-0.232310\pi$
$233$	1.19909	+	1.19909i	0.0785553	+	0.0785553i	−0.666737	+	0.745293i	$0.732310\pi$
$234$	−30.5702	+	6.05955i	−1.99844	+	0.396125i
$235$			30.3091i			1.97715i
$236$	0.165117	+	0.165117i	0.0107482	+	0.0107482i
$237$	−22.9394	−	6.96696i	−1.49007	−	0.452553i
$238$	−4.80045	+	4.80045i	−0.311167	+	0.311167i
$239$		−	3.02435i		−	0.195629i	−0.995205	−	0.0978146i	$-0.968815\pi$
$239$		−	3.02435i		−	0.195629i	0.995205	−	0.0978146i	$-0.0311852\pi$
$240$	−14.6294	−	27.3917i	−0.944324	−	1.76813i
$241$	15.2120			0.979891			0.489945	−	0.871753i	$-0.337017\pi$
$241$	15.2120			0.979891			0.489945	+	0.871753i	$0.337017\pi$
$242$	1.31105	−	1.31105i	0.0842776	−	0.0842776i
$243$	9.90934	−	12.0335i	0.635684	−	0.771949i
$244$	−0.265390	+	2.06314i	−0.0169898	+	0.132079i
$245$		−	21.1069i		−	1.34847i
$246$	−0.892006	+	2.93701i	−0.0568722	+	0.187257i
$247$			7.56290i			0.481216i
$248$	−9.47425			−0.601616
$249$	−15.2840	+	8.16289i	−0.968583	+	0.517302i
$250$	26.2945	+	26.2945i	1.66301	+	1.66301i
$251$	−22.3948	−	22.3948i	−1.41355	−	1.41355i	−0.728470	−	0.685078i	$-0.759768\pi$
$251$	−22.3948	−	22.3948i	−1.41355	−	1.41355i	−0.685078	−	0.728470i	$-0.740232\pi$
$252$	1.03603	−	0.205359i	0.0652637	−	0.0129364i
$253$	10.1899			0.640634
$254$	21.4575	−	21.4575i	1.34636	−	1.34636i
$255$	22.7191	+	6.90006i	1.42273	+	0.432098i
$256$	6.28369			0.392731
$257$			7.12706i			0.444574i	0.974981	+	0.222287i	$0.0713521\pi$
$257$			7.12706i			0.444574i	−0.974981	+	0.222287i	$0.928648\pi$
$258$	−4.16230	+	2.22301i	−0.259134	+	0.138398i
$259$	11.6382			0.723163
$260$			7.38512i			0.458006i
$261$	−0.865871	−	4.36829i	−0.0535961	−	0.270390i
$262$	16.6460	−	16.6460i	1.02839	−	1.02839i
$263$	9.02522			0.556519			0.278259	−	0.960506i	$-0.410243\pi$
$263$	9.02522			0.556519			0.278259	+	0.960506i	$0.410243\pi$
$264$	−12.4625	+	6.65602i	−0.767017	+	0.409650i
$265$	−5.37449	−	5.37449i	−0.330153	−	0.330153i
$266$		−	2.18102i		−	0.133727i
$267$	−14.1209	−	4.28868i	−0.864184	−	0.262463i
$268$	−0.348121	+	0.348121i	−0.0212649	+	0.0212649i
$269$			7.74878i			0.472451i	0.971698	+	0.236226i	$0.0759105\pi$
$269$			7.74878i			0.472451i	−0.971698	+	0.236226i	$0.924090\pi$
$270$	−19.9168	−	24.3183i	−1.21210	−	1.47997i
$271$			3.74342i			0.227396i	0.993515	+	0.113698i	$0.0362697\pi$
$271$			3.74342i			0.227396i	−0.993515	+	0.113698i	$0.963730\pi$
$272$	−10.7629	+	10.7629i	−0.652600	+	0.652600i
$273$	15.1174	+	4.59134i	0.914948	+	0.277880i
$274$	−16.9109	+	16.9109i	−1.02162	+	1.02162i
$275$	24.6353	−	24.6353i	1.48557	−	1.48557i
$276$	−1.43909	−	0.437067i	−0.0866227	−	0.0263083i
$277$	9.01892	−	9.01892i	0.541895	−	0.541895i	−0.382189	−	0.924084i	$-0.624830\pi$
$277$	9.01892	−	9.01892i	0.541895	−	0.541895i	0.924084	+	0.382189i	$0.124830\pi$
$278$			4.75418i			0.285137i
$279$	−10.6824	+	2.11745i	−0.639541	+	0.126768i
$280$			13.8633i			0.828492i
$281$	7.24272	−	7.24272i	0.432064	−	0.432064i	−0.457266	−	0.889330i	$-0.651171\pi$
$281$	7.24272	−	7.24272i	0.432064	−	0.432064i	0.889330	+	0.457266i	$0.151171\pi$
$282$	−18.8187	−	5.71546i	−1.12064	−	0.340351i
$283$			8.36991i			0.497540i	0.968563	+	0.248770i	$0.0800263\pi$
$283$			8.36991i			0.497540i	−0.968563	+	0.248770i	$0.919974\pi$
$284$	−0.823370	−	0.823370i	−0.0488580	−	0.0488580i
$285$	−6.72853	+	3.59358i	−0.398564	+	0.212866i
$286$	32.4681			1.91988
$287$	1.10032	−	1.10032i	0.0649500	−	0.0649500i
$288$	4.40531	−	0.873210i	0.259586	−	0.0514544i
$289$			5.36182i			0.315401i
$290$	−8.97982			−0.527313
$291$	−10.3976	+	5.55317i	−0.609518	+	0.325532i
$292$		−	2.64795i		−	0.154960i
$293$	−14.8584			−0.868040			−0.434020	−	0.900903i	$-0.642905\pi$
$293$	−14.8584			−0.868040			−0.434020	+	0.900903i	$0.642905\pi$
$294$	13.1051	+	3.98017i	0.764304	+	0.232128i
$295$	−2.49122	+	2.49122i	−0.145044	+	0.145044i
$296$	22.9785			1.33560
$297$	−12.5642	+	10.2901i	−0.729050	+	0.597094i
$298$	−2.32470	−	2.32470i	−0.134667	−	0.134667i
$299$	−15.9084	−	15.9084i	−0.920008	−	0.920008i
$300$	−4.53583	+	2.42250i	−0.261876	+	0.139863i
$301$	2.39219			0.137884
$302$			12.9500i			0.745190i
$303$	8.34071	−	27.4626i	0.479161	−	1.57768i
$304$		−	4.89000i		−	0.280461i
$305$	−31.1278	−	4.00410i	−1.78237	−	0.229274i
$306$	−8.56838	+	12.8050i	−0.489822	+	0.732010i
$307$	10.9414	−	10.9414i	0.624461	−	0.624461i	−0.322208	−	0.946669i	$-0.604425\pi$
$307$	10.9414	−	10.9414i	0.624461	−	0.624461i	0.946669	+	0.322208i	$0.104425\pi$
$308$	−1.10035			−0.0626982
$309$	−2.96912	−	5.55930i	−0.168907	−	0.316257i
$310$			21.9597i			1.24723i
$311$	−20.2955	+	20.2955i	−1.15085	+	1.15085i	−0.164473	+	0.986382i	$0.552592\pi$
$311$	−20.2955	+	20.2955i	−1.15085	+	1.15085i	−0.986382	+	0.164473i	$0.947408\pi$
$312$	29.8478	+	9.06513i	1.68980	+	0.513212i
$313$	1.71801	+	1.71801i	0.0971078	+	0.0971078i	0.753992	−	0.656884i	$-0.228126\pi$
$313$	1.71801	+	1.71801i	0.0971078	+	0.0971078i	−0.656884	+	0.753992i	$0.728126\pi$
$314$		−	8.40627i		−	0.474394i
$315$	3.09838	+	15.6312i	0.174574	+	0.880719i
$316$	−2.60671	−	2.60671i	−0.146639	−	0.146639i
$317$		−	3.33855i		−	0.187512i	−0.995595	−	0.0937558i	$-0.970113\pi$
$317$		−	3.33855i		−	0.187512i	0.995595	−	0.0937558i	$-0.0298873\pi$
$318$	4.35046	−	2.32350i	0.243962	−	0.130295i
$319$			4.63948i			0.259761i
$320$			26.8016i			1.49826i
$321$	8.22511	+	15.4005i	0.459081	+	0.859571i
$322$	4.58773	+	4.58773i	0.255664	+	0.255664i
$323$	2.64382	+	2.64382i	0.147106	+	0.147106i
$324$	2.21577	−	0.914333i	0.123098	−	0.0507963i
$325$	−76.9211			−4.26682
$326$	−6.68789	+	6.68789i	−0.370408	+	0.370408i
$327$	−8.05682	+	4.30300i	−0.445543	+	0.237956i
$328$	2.17248	−	2.17248i	0.119955	−	0.119955i
$329$	7.05024	+	7.05024i	0.388692	+	0.388692i
$330$	15.4275	+	28.8861i	0.849257	+	1.59013i
$331$	0.0889297	−	0.0889297i	0.00488802	−	0.00488802i	−0.704659	−	0.709547i	$-0.748900\pi$
$331$	0.0889297	−	0.0889297i	0.00488802	−	0.00488802i	0.709547	+	0.704659i	$0.248900\pi$
$332$	−2.66437			−0.146226
$333$	25.9087	−	5.13557i	1.41979	−	0.281427i
$334$	14.0410	+	14.0410i	0.768288	+	0.768288i
$335$	−5.25232	−	5.25232i	−0.286965	−	0.286965i
$336$	−9.77457	−	2.96865i	−0.533247	−	0.161953i
$337$	11.9730	−	11.9730i	0.652211	−	0.652211i	−0.301314	−	0.953525i	$-0.597425\pi$
$337$	11.9730	−	11.9730i	0.652211	−	0.652211i	0.953525	+	0.301314i	$0.0974252\pi$
$338$	−36.8505	−	36.8505i	−2.00440	−	2.00440i
$339$	−2.35825	−	4.41552i	−0.128082	−	0.239818i
$340$	2.58167	+	2.58167i	0.140011	+	0.140011i
$341$	11.3456			0.614401
$342$	−0.962414	−	4.85534i	−0.0520414	−	0.262547i
$343$	−11.4527	−	11.4527i	−0.618386	−	0.618386i
$344$	4.72314			0.254655
$345$	6.59430	−	21.7124i	0.355025	−	1.16895i
$346$		−	8.29146i		−	0.445752i
$347$			7.10772i			0.381562i	0.981633	+	0.190781i	$0.0611021\pi$
$347$			7.10772i			0.381562i	−0.981633	+	0.190781i	$0.938898\pi$
$348$	0.198997	−	0.655218i	0.0106674	−	0.0351234i
$349$	−17.7197	+	17.7197i	−0.948515	+	0.948515i	−0.998738	−	0.0502234i	$-0.984007\pi$
$349$	−17.7197	+	17.7197i	−0.948515	+	0.948515i	0.0502234	+	0.998738i	$0.484007\pi$
$350$	22.1828			1.18572
$351$	35.6801	+	3.55031i	1.90446	+	0.189501i
$352$	−4.67881			−0.249381
$353$	−10.7004			−0.569527			−0.284763	−	0.958598i	$-0.591915\pi$
$353$	−10.7004			−0.569527			−0.284763	+	0.958598i	$0.591915\pi$
$354$	−1.07700	−	2.01655i	−0.0572421	−	0.107179i
$355$	12.4227	−	12.4227i	0.659328	−	0.659328i
$356$	−1.60462	−	1.60462i	−0.0850447	−	0.0850447i
$357$	6.88974	−	3.67969i	0.364644	−	0.194750i
$358$	−12.0735	+	12.0735i	−0.638103	+	0.638103i
$359$	−18.8161	+	18.8161i	−0.993075	+	0.993075i	−0.999976	−	0.00690134i	$-0.997803\pi$
$359$	−18.8161	+	18.8161i	−0.993075	+	0.993075i	0.00690134	+	0.999976i	$0.497803\pi$
$360$	6.11744	+	30.8622i	0.322417	+	1.62658i
$361$	17.7988			0.936780
$362$			18.3951i			0.966826i
$363$	−1.88166	+	1.00496i	−0.0987615	+	0.0527467i
$364$	1.71786	+	1.71786i	0.0900403	+	0.0900403i
$365$	39.9513			2.09115
$366$	8.35595	−	18.5719i	0.436773	−	0.970771i
$367$	22.6312			1.18134			0.590671	−	0.806913i	$-0.298863\pi$
$367$	22.6312			1.18134			0.590671	+	0.806913i	$0.298863\pi$
$368$	10.2860	+	10.2860i	0.536196	+	0.536196i
$369$	1.96398	−	2.93506i	0.102241	−	0.152793i
$370$		−	53.2602i		−	2.76887i
$371$	−2.50033			−0.129811
$372$	−1.60231	−	0.486639i	−0.0830757	−	0.0252311i
$373$	−6.62432	+	6.62432i	−0.342994	+	0.342994i	−0.857492	−	0.514498i	$-0.827978\pi$
$373$	−6.62432	+	6.62432i	−0.342994	+	0.342994i	0.514498	+	0.857492i	$0.327978\pi$
$374$	11.3501	−	11.3501i	0.586901	−	0.586901i
$375$	−20.1555	−	37.7386i	−1.04083	−	1.94881i
$376$	13.9200	+	13.9200i	0.717868	+	0.717868i
$377$	7.24314	−	7.24314i	0.373041	−	0.373041i
$378$	−10.2896	−	1.02385i	−0.529238	−	0.0526612i
$379$	23.0486			1.18393			0.591963	−	0.805965i	$-0.298353\pi$
$379$	23.0486			1.18393			0.591963	+	0.805965i	$0.298353\pi$
$380$	−1.17295			−0.0601709
$381$	−30.7964	+	16.4478i	−1.57775	+	0.842646i
$382$	−4.67890			−0.239393
$383$	6.78071	−	6.78071i	0.346478	−	0.346478i	−0.512318	−	0.858796i	$-0.671213\pi$
$383$	6.78071	−	6.78071i	0.346478	−	0.346478i	0.858796	+	0.512318i	$0.171213\pi$
$384$	−21.6029	−	6.56106i	−1.10242	−	0.334818i
$385$		−	16.6017i		−	0.846099i
$386$			5.51843i			0.280881i
$387$	5.32545	−	1.05560i	0.270708	−	0.0536591i
$388$	−1.81256			−0.0920186
$389$	22.1587	+	22.1587i	1.12349	+	1.12349i	0.991213	+	0.132276i	$0.0422285\pi$
$389$	22.1587	+	22.1587i	1.12349	+	1.12349i	0.132276	+	0.991213i	$0.457771\pi$
$390$	21.0114	−	69.1822i	1.06396	−	3.50318i
$391$	−11.1225			−0.562487
$392$	−9.69369	−	9.69369i	−0.489605	−	0.489605i
$393$	−23.8908	+	12.7596i	−1.20513	+	0.643637i
$394$	−13.0477	−	13.0477i	−0.657333	−	0.657333i
$395$	39.3290	−	39.3290i	1.97886	−	1.97886i
$396$	−2.44958	+	0.485549i	−0.123096	+	0.0243998i
$397$	17.8638	+	17.8638i	0.896557	+	0.896557i	0.995130	−	0.0985728i	$-0.0314277\pi$
$397$	17.8638	+	17.8638i	0.896557	+	0.896557i	−0.0985728	+	0.995130i	$0.531428\pi$
$398$	−10.6287	−	10.6287i	−0.532767	−	0.532767i
$399$	−0.729223	+	2.40104i	−0.0365068	+	0.120202i
$400$	49.7354			2.48677
$401$	−21.6305	+	21.6305i	−1.08017	+	1.08017i	−0.0836821	+	0.996492i	$0.526668\pi$
$401$	−21.6305	+	21.6305i	−1.08017	+	1.08017i	−0.996492	+	0.0836821i	$0.973332\pi$
$402$	4.25157	−	2.27068i	0.212049	−	0.113251i
$403$	−17.7128	−	17.7128i	−0.882336	−	0.882336i
$404$	3.12070	−	3.12070i	0.155260	−	0.155260i
$405$	13.7951	+	33.4307i	0.685485	+	1.66118i
$406$	−2.08880	+	2.08880i	−0.103666	+	0.103666i
$407$	−27.5173			−1.36398
$408$	13.6031	−	7.26516i	0.673454	−	0.359679i
$409$	−7.39368	−	7.39368i	−0.365594	−	0.365594i	0.500273	−	0.865868i	$-0.333233\pi$
$409$	−7.39368	−	7.39368i	−0.365594	−	0.365594i	−0.865868	+	0.500273i	$0.833233\pi$
$410$	−5.03543	−	5.03543i	−0.248682	−	0.248682i
$411$	24.2710	−	12.9627i	1.19720	−	0.639402i
$412$		−	0.969122i		−	0.0477452i
$413$			1.15897i			0.0570292i
$414$	12.2375	+	8.18870i	0.601442	+	0.402453i
$415$		−	40.1990i		−	1.97329i
$416$	7.30454	+	7.30454i	0.358134	+	0.358134i
$417$	1.58956	−	5.23378i	0.0778411	−	0.256299i
$418$			5.15678i			0.252226i
$419$	5.98679	+	5.98679i	0.292474	+	0.292474i	0.838057	−	0.545583i	$-0.183692\pi$
$419$	5.98679	+	5.98679i	0.292474	+	0.292474i	−0.545583	+	0.838057i	$0.683692\pi$
$420$	−0.712081	+	2.34459i	−0.0347460	+	0.114405i
$421$	−20.7424	+	20.7424i	−1.01092	+	1.01092i	−0.0109832	+	0.999940i	$0.503496\pi$
$421$	−20.7424	+	20.7424i	−1.01092	+	1.01092i	−0.999940	+	0.0109832i	$0.996504\pi$
$422$			41.9509i			2.04214i
$423$	18.8061	+	12.5841i	0.914386	+	0.611858i
$424$	−4.93665			−0.239745
$425$	−26.8899	+	26.8899i	−1.30435	+	1.30435i
$426$	5.37058	+	10.0557i	0.260205	+	0.487201i
$427$	−8.17207	+	6.30927i	−0.395474	+	0.305327i
$428$			2.68468i			0.129769i
$429$	−35.7435	−	10.8557i	−1.72571	−	0.524119i
$430$		−	10.9474i		−	0.527933i
$431$	24.3963			1.17513			0.587564	−	0.809177i	$-0.300087\pi$
$431$	24.3963			1.17513			0.587564	+	0.809177i	$0.300087\pi$
$432$	−23.0699	−	2.29555i	−1.10995	−	0.110445i
$433$	−6.16887	−	6.16887i	−0.296457	−	0.296457i	0.543167	−	0.839624i	$-0.317225\pi$
$433$	−6.16887	−	6.16887i	−0.296457	−	0.296457i	−0.839624	+	0.543167i	$0.817225\pi$
$434$	5.10807	+	5.10807i	0.245195	+	0.245195i
$435$	9.88569	+	3.00240i	0.473983	+	0.143954i
$436$	−1.40450			−0.0672634
$437$	2.52667	−	2.52667i	0.120867	−	0.120867i
$438$	−7.53371	+	24.8055i	−0.359974	+	1.18525i
$439$	−25.2374			−1.20451			−0.602257	−	0.798303i	$-0.705732\pi$
$439$	−25.2374			−1.20451			−0.602257	+	0.798303i	$0.705732\pi$
$440$		−	32.7783i		−	1.56264i
$441$	−13.0963	−	8.76337i	−0.623636	−	0.417303i
$442$	−35.4395			−1.68569
$443$			9.63218i			0.457639i	0.973469	+	0.228819i	$0.0734865\pi$
$443$			9.63218i			0.457639i	−0.973469	+	0.228819i	$0.926514\pi$
$444$	3.88617	+	1.18027i	0.184429	+	0.0560133i
$445$	24.2099	−	24.2099i	1.14766	−	1.14766i
$446$	−16.8613			−0.798405
$447$	1.78195	+	3.33648i	0.0842835	+	0.157810i
$448$	6.23436	+	6.23436i	0.294546	+	0.294546i
$449$		−	27.2851i		−	1.28766i	−0.765167	−	0.643831i	$-0.777344\pi$
$449$		−	27.2851i		−	1.28766i	0.765167	−	0.643831i	$-0.222656\pi$
$450$	49.3829	−	9.78856i	2.32793	−	0.461437i
$451$	−2.60159	+	2.60159i	−0.122504	+	0.122504i
$452$		−	0.769733i		−	0.0362052i
$453$	4.32983	−	14.2564i	0.203433	−	0.669824i
$454$		−	18.5796i		−	0.871982i
$455$	−25.9184	+	25.9184i	−1.21507	+	1.21507i
$456$	−1.43978	+	4.74060i	−0.0674237	+	0.221999i
$457$	−1.44945	+	1.44945i	−0.0678026	+	0.0678026i	−0.740195	−	0.672392i	$-0.765267\pi$
$457$	−1.44945	+	1.44945i	−0.0678026	+	0.0678026i	0.672392	+	0.740195i	$0.265267\pi$
$458$	−8.79223	+	8.79223i	−0.410834	+	0.410834i
$459$	13.7141	−	11.2319i	0.640119	−	0.524259i
$460$	2.46727	−	2.46727i	0.115037	−	0.115037i
$461$			14.1345i			0.658311i	0.944276	+	0.329156i	$0.106764\pi$
$461$			14.1345i			0.658311i	−0.944276	+	0.329156i	$0.893236\pi$
$462$	10.3078	+	3.13061i	0.479564	+	0.145649i
$463$		−	22.9086i		−	1.06465i	−0.846539	−	0.532327i	$-0.821318\pi$
$463$		−	22.9086i		−	1.06465i	0.846539	−	0.532327i	$-0.178682\pi$
$464$	−4.68325	+	4.68325i	−0.217414	+	0.217414i
$465$	7.34223	−	24.1750i	0.340488	−	1.12109i
$466$		−	2.55288i		−	0.118260i
$467$	13.3863	+	13.3863i	0.619442	+	0.619442i	0.945388	−	0.325946i	$-0.105683\pi$
$467$	13.3863	+	13.3863i	0.619442	+	0.619442i	−0.325946	+	0.945388i	$0.605683\pi$
$468$	4.58230	+	3.06623i	0.211817	+	0.141736i
$469$	−2.44350			−0.112830
$470$	32.2642	−	32.2642i	1.48824	−	1.48824i
$471$	−2.81064	+	9.25429i	−0.129507	+	0.426415i
$472$			2.28827i			0.105326i
$473$	−5.65608			−0.260067
$474$	17.0027	+	31.8354i	0.780960	+	1.46225i
$475$		−	12.2171i		−	0.560557i
$476$	1.20105			0.0550501
$477$	−5.56619	+	1.10332i	−0.254858	+	0.0505174i
$478$	−3.21943	+	3.21943i	−0.147254	+	0.147254i
$479$	5.51477			0.251976			0.125988	−	0.992032i	$-0.459790\pi$
$479$	5.51477			0.251976			0.125988	+	0.992032i	$0.459790\pi$
$480$	−3.02785	+	9.96948i	−0.138202	+	0.455043i
$481$	42.9598	+	42.9598i	1.95880	+	1.95880i
$482$	−16.1932	−	16.1932i	−0.737581	−	0.737581i
$483$	−3.51663	−	6.58444i	−0.160012	−	0.299603i
$484$	−0.328019			−0.0149100
$485$		−	27.3472i		−	1.24177i
$486$	−23.3582	+	2.26118i	−1.05955	+	0.102569i
$487$			36.2966i			1.64476i	0.568940	+	0.822379i	$0.307353\pi$
$487$			36.2966i			1.64476i	−0.568940	+	0.822379i	$0.692647\pi$
$488$	−16.1349	+	12.4570i	−0.730394	+	0.563903i
$489$	9.59864	−	5.12646i	0.434066	−	0.231826i
$490$	−22.4683	+	22.4683i	−1.01502	+	1.01502i
$491$	−15.1048			−0.681668			−0.340834	−	0.940123i	$-0.610709\pi$
$491$	−15.1048			−0.681668			−0.340834	+	0.940123i	$0.610709\pi$
$492$	0.479002	−	0.255826i	0.0215951	−	0.0115335i
$493$		−	5.06408i		−	0.228075i
$494$	8.05073	−	8.05073i	0.362220	−	0.362220i
$495$	−7.32578	−	36.9583i	−0.329269	−	1.66115i
$496$	11.4527	+	11.4527i	0.514239	+	0.514239i
$497$		−	5.77931i		−	0.259237i
$498$	24.9593	+	7.58042i	1.11845	+	0.339687i
$499$	−20.5734	−	20.5734i	−0.920991	−	0.920991i	0.0761084	−	0.997100i	$-0.475751\pi$
$499$	−20.5734	−	20.5734i	−0.920991	−	0.920991i	−0.997100	+	0.0761084i	$0.975751\pi$
$500$		−	6.57876i		−	0.294211i
$501$	−10.7628	−	20.1520i	−0.480847	−	0.900325i
$502$			47.6787i			2.12800i
$503$		−	30.4987i		−	1.35987i	−0.733273	−	0.679935i	$-0.762008\pi$
$503$		−	30.4987i		−	1.35987i	0.733273	−	0.679935i	$-0.237992\pi$
$504$	8.60188	+	5.75592i	0.383158	+	0.256389i
$505$	47.0839	+	47.0839i	2.09520	+	2.09520i
$506$	−10.8472	−	10.8472i	−0.482216	−	0.482216i
$507$	28.2470	+	52.8889i	1.25449	+	2.34888i
$508$	−5.36857			−0.238192
$509$	−8.71231	+	8.71231i	−0.386167	+	0.386167i	−0.873318	−	0.487151i	$-0.838036\pi$
$509$	−8.71231	+	8.71231i	−0.386167	+	0.386167i	0.487151	+	0.873318i	$0.338036\pi$
$510$	−16.8394	−	31.5297i	−0.745662	−	1.39616i
$511$	9.29312	−	9.29312i	0.411103	−	0.411103i
$512$	11.7453	+	11.7453i	0.519072	+	0.519072i
$513$	−0.563881	+	5.66692i	−0.0248959	+	0.250201i
$514$	7.58678	−	7.58678i	0.334638	−	0.334638i
$515$	14.6217			0.644311
$516$	0.798788	+	0.242601i	0.0351647	+	0.0106799i
$517$	−16.6695	−	16.6695i	−0.733124	−	0.733124i
$518$	−12.3889	−	12.3889i	−0.544337	−	0.544337i
$519$	−2.77225	+	9.12790i	−0.121688	+	0.400670i
$520$	−51.1733	+	51.1733i	−2.24410	+	2.24410i
$521$	1.09620	+	1.09620i	0.0480253	+	0.0480253i	0.730712	−	0.682686i	$-0.239188\pi$
$521$	1.09620	+	1.09620i	0.0480253	+	0.0480253i	−0.682686	+	0.730712i	$0.739188\pi$
$522$	−3.72833	+	5.57178i	−0.163185	+	0.243870i
$523$	−18.8016	−	18.8016i	−0.822138	−	0.822138i	0.164276	−	0.986414i	$-0.447471\pi$
$523$	−18.8016	−	18.8016i	−0.822138	−	0.822138i	−0.986414	+	0.164276i	$0.947471\pi$
$524$	−4.16474			−0.181938
$525$	−24.4206	−	7.41682i	−1.06580	−	0.323696i
$526$	−9.60737	−	9.60737i	−0.418901	−	0.418901i
$527$	−12.3840			−0.539454
$528$	23.1109	+	7.01905i	1.00577	+	0.305465i
$529$		−	12.3704i		−	0.537843i
$530$			11.4423i			0.497023i
$531$	0.511417	+	2.58008i	0.0221936	+	0.111966i
$532$	−0.272841	+	0.272841i	−0.0118291	+	0.0118291i
$533$	8.12319			0.351854
$534$	10.4664	+	19.5970i	0.452926	+	0.848047i
$535$	−40.5055			−1.75120
$536$	−4.82444			−0.208384
$537$	17.3282	−	9.25467i	0.747767	−	0.399369i
$538$	8.24860	−	8.24860i	0.355622	−	0.355622i
$539$	11.6084	+	11.6084i	0.500010	+	0.500010i
$540$	−0.550625	+	5.53371i	−0.0236951	+	0.238133i
$541$	19.3712	−	19.3712i	0.832834	−	0.832834i	−0.155070	−	0.987904i	$-0.549560\pi$
$541$	19.3712	−	19.3712i	0.832834	−	0.832834i	0.987904	+	0.155070i	$0.0495603\pi$
$542$	3.98488	−	3.98488i	0.171165	−	0.171165i
$543$	6.15040	−	20.2508i	0.263939	−	0.869045i
$544$	5.10701			0.218961
$545$		−	21.1906i		−	0.907705i
$546$	−11.2051	−	20.9800i	−0.479532	−	0.897863i
$547$	−26.8211	−	26.8211i	−1.14679	−	1.14679i	−0.987181	−	0.159607i	$-0.948977\pi$
$547$	−26.8211	−	26.8211i	−1.14679	−	1.14679i	−0.159607	−	0.987181i	$-0.551023\pi$
$548$	4.23102			0.180740
$549$	−15.4084	+	17.6516i	−0.657615	+	0.753354i
$550$	−52.4488			−2.23642
$551$	1.15040	+	1.15040i	0.0490086	+	0.0490086i
$552$	−6.94323	−	13.0003i	−0.295523	−	0.553330i
$553$		−	18.2967i		−	0.778056i
$554$	−19.2013			−0.815787
$555$	−17.8075	+	58.6330i	−0.755888	+	2.48883i
$556$	0.594738	−	0.594738i	0.0252225	−	0.0252225i
$557$	−4.57233	+	4.57233i	−0.193736	+	0.193736i	−0.797308	−	0.603572i	$-0.793743\pi$
$557$	−4.57233	+	4.57233i	−0.193736	+	0.193736i	0.603572	+	0.797308i	$0.293743\pi$
$558$	13.6255	+	9.11746i	0.576814	+	0.385973i
$559$	8.83024	+	8.83024i	0.373479	+	0.373479i
$560$	16.7582	−	16.7582i	0.708165	−	0.708165i
$561$	−16.2900	+	8.70021i	−0.687766	+	0.367323i
$562$	−15.4198			−0.650445
$563$	−17.4720			−0.736356			−0.368178	−	0.929755i	$-0.620018\pi$
$563$	−17.4720			−0.736356			−0.368178	+	0.929755i	$0.620018\pi$
$564$	1.63919	+	3.06917i	0.0690222	+	0.129235i
$565$	11.6134			0.488581
$566$	8.90980	−	8.90980i	0.374507	−	0.374507i
$567$	10.9852	+	4.56745i	0.461337	+	0.191815i
$568$		−	11.4107i		−	0.478781i
$569$			40.8532i			1.71266i	0.516432	+	0.856328i	$0.327260\pi$
$569$			40.8532i			1.71266i	−0.516432	+	0.856328i	$0.672740\pi$
$570$	10.9879	+	3.33716i	0.460233	+	0.139778i
$571$	−23.3009			−0.975113			−0.487556	−	0.873091i	$-0.662112\pi$
$571$	−23.3009			−0.975113			−0.487556	+	0.873091i	$0.662112\pi$
$572$	−4.06169	−	4.06169i	−0.169828	−	0.169828i
$573$	5.15090	+	1.56439i	0.215182	+	0.0653533i
$574$	−2.34260			−0.0977780
$575$	25.6984	+	25.6984i	1.07170	+	1.07170i
$576$	16.6298	+	11.1278i	0.692909	+	0.463658i
$577$	−7.83053	−	7.83053i	−0.325989	−	0.325989i	0.525070	−	0.851059i	$-0.324039\pi$
$577$	−7.83053	−	7.83053i	−0.325989	−	0.325989i	−0.851059	+	0.525070i	$0.824039\pi$
$578$	5.70768	−	5.70768i	0.237408	−	0.237408i
$579$	1.84508	−	6.07512i	0.0766791	−	0.252473i
$580$	1.12335	+	1.12335i	0.0466448	+	0.0466448i
$581$	−9.35074	−	9.35074i	−0.387934	−	0.387934i
$582$	16.9796	+	5.15691i	0.703829	+	0.213761i
$583$	5.91176			0.244840
$584$	18.3483	−	18.3483i	0.759259	−	0.759259i
$585$	−46.2621	+	69.1360i	−1.91270	+	2.85842i
$586$	15.8169	+	15.8169i	0.653389	+	0.653389i
$587$	−30.6223	+	30.6223i	−1.26392	+	1.26392i	−0.314737	+	0.949179i	$0.601916\pi$
$587$	−30.6223	+	30.6223i	−1.26392	+	1.26392i	−0.949179	+	0.314737i	$0.898084\pi$
$588$	−1.14151	−	2.13733i	−0.0470750	−	0.0881419i
$589$	2.81324	−	2.81324i	0.115918	−	0.115918i
$590$	5.30382			0.218355
$591$	10.0014	+	18.7264i	0.411404	+	0.770301i
$592$	−27.7768	−	27.7768i	−1.14162	−	1.14162i
$593$	−17.4123	−	17.4123i	−0.715037	−	0.715037i	0.252547	−	0.967585i	$-0.418732\pi$
$593$	−17.4123	−	17.4123i	−0.715037	−	0.715037i	−0.967585	+	0.252547i	$0.918732\pi$
$594$	24.3285	+	2.42078i	0.998212	+	0.0993259i
$595$			18.1210i			0.742889i
$596$			0.581631i			0.0238245i
$597$	8.14719	+	15.2546i	0.333442	+	0.624328i
$598$			33.8691i			1.38501i
$599$	18.8991	+	18.8991i	0.772194	+	0.772194i	0.978490	−	0.206295i	$-0.0661408\pi$
$599$	18.8991	+	18.8991i	0.772194	+	0.772194i	−0.206295	+	0.978490i	$0.566141\pi$
$600$	−48.2160	−	14.6438i	−1.96841	−	0.597829i
$601$			27.0689i			1.10416i	0.833791	+	0.552081i	$0.186166\pi$
$601$			27.0689i			1.10416i	−0.833791	+	0.552081i	$0.813834\pi$
$602$	−2.54650	−	2.54650i	−0.103787	−	0.103787i
$603$	−5.43966	+	1.07824i	−0.221520	+	0.0439092i
$604$	1.62002	−	1.62002i	0.0659176	−	0.0659176i
$605$		−	4.94903i		−	0.201207i
$606$	−38.1127	+	20.3553i	−1.54822	+	0.826877i
$607$	5.19811			0.210985			0.105492	−	0.994420i	$-0.466358\pi$
$607$	5.19811			0.210985			0.105492	+	0.994420i	$0.466358\pi$
$608$	−1.16015	+	1.16015i	−0.0470503	+	0.0470503i
$609$	2.99791	−	1.60113i	0.121482	−	0.0648810i
$610$	28.8733	+	37.3980i	1.16904	+	1.51420i
$611$			52.0487i			2.10567i
$612$	2.67376	−	0.529986i	0.108080	−	0.0214234i
$613$			29.4371i			1.18895i	0.804113	+	0.594477i	$0.202641\pi$
$613$			29.4371i			1.18895i	−0.804113	+	0.594477i	$0.797359\pi$
$614$	−23.2944			−0.940086
$615$	3.85981	+	7.22700i	0.155642	+	0.291421i
$616$	−7.62459	−	7.62459i	−0.307204	−	0.307204i
$617$	17.0925	+	17.0925i	0.688118	+	0.688118i	0.961816	−	0.273698i	$-0.0882468\pi$
$617$	17.0925	+	17.0925i	0.688118	+	0.688118i	−0.273698	+	0.961816i	$0.588247\pi$
$618$	−2.75725	+	9.07852i	−0.110913	+	0.365192i
$619$	4.08524			0.164199			0.0820997	−	0.996624i	$-0.473837\pi$
$619$	4.08524			0.164199			0.0820997	+	0.996624i	$0.473837\pi$
$620$	2.74711	−	2.74711i	0.110327	−	0.110327i
$621$	−10.7342	−	13.1064i	−0.430747	−	0.525941i
$622$	43.2093			1.73254
$623$		−	11.2630i		−	0.451242i
$624$	−25.1225	−	47.0387i	−1.00571	−	1.88306i
$625$	43.5224			1.74090
$626$		−	3.65766i		−	0.146190i
$627$	1.72417	−	5.67699i	0.0688566	−	0.226717i
$628$	−1.05161	+	1.05161i	−0.0419637	+	0.0419637i
$629$	30.0356			1.19760
$630$	13.3412	−	19.9377i	0.531528	−	0.794338i
$631$	−8.77848	−	8.77848i	−0.349466	−	0.349466i	0.510445	−	0.859911i	$-0.329481\pi$
$631$	−8.77848	−	8.77848i	−0.349466	−	0.349466i	−0.859911	+	0.510445i	$0.829481\pi$
$632$		−	36.1250i		−	1.43698i
$633$	14.0263	−	46.1828i	0.557494	−	1.83560i
$634$	−3.55390	+	3.55390i	−0.141143	+	0.141143i
$635$		−	80.9990i		−	3.21435i
$636$	−0.834898	−	0.253568i	−0.0331058	−	0.0100546i
$637$		−	36.2460i		−	1.43612i
$638$	4.93875	−	4.93875i	0.195527	−	0.195527i
$639$	−2.55022	−	12.8658i	−0.100885	−	0.508963i
$640$	37.0376	−	37.0376i	1.46404	−	1.46404i
$641$	−3.55230	+	3.55230i	−0.140307	+	0.140307i	−0.773772	−	0.633464i	$-0.781632\pi$
$641$	−3.55230	+	3.55230i	−0.140307	+	0.140307i	0.633464	+	0.773772i	$0.281632\pi$
$642$	7.63820	−	25.1495i	0.301456	−	0.992572i
$643$	−12.4751	+	12.4751i	−0.491970	+	0.491970i	−0.908926	−	0.416957i	$-0.863097\pi$
$643$	−12.4751	+	12.4751i	−0.491970	+	0.491970i	0.416957	+	0.908926i	$0.363097\pi$
$644$		−	1.14783i		−	0.0452308i
$645$	−3.66028	+	12.0518i	−0.144123	+	0.474540i
$646$		−	5.62872i		−	0.221459i
$647$	26.1195	−	26.1195i	1.02686	−	1.02686i	0.0272336	−	0.999629i	$-0.491330\pi$
$647$	26.1195	−	26.1195i	1.02686	−	1.02686i	0.999629	−	0.0272336i	$-0.00866980\pi$
$648$	21.6892	+	9.01797i	0.852034	+	0.354259i
$649$		−	2.74026i		−	0.107564i
$650$	81.8828	+	81.8828i	3.21171	+	3.21171i
$651$	−3.91549	−	7.33125i	−0.153460	−	0.287334i
$652$	1.67328			0.0655307
$653$	−10.3626	+	10.3626i	−0.405518	+	0.405518i	−0.880172	−	0.474654i	$-0.842573\pi$
$653$	−10.3626	+	10.3626i	−0.405518	+	0.405518i	0.474654	+	0.880172i	$0.342573\pi$
$654$	13.1571	+	3.99596i	0.514482	+	0.156254i
$655$		−	62.8361i		−	2.45521i
$656$	−5.25226			−0.205066
$657$	16.5874	−	24.7889i	0.647136	−	0.967107i
$658$		−	15.0100i		−	0.585151i
$659$	−38.1215			−1.48500			−0.742501	−	0.669844i	$-0.766361\pi$
$659$	−38.1215			−1.48500			−0.742501	+	0.669844i	$0.766361\pi$
$660$	1.68364	−	5.54353i	0.0655354	−	0.215782i
$661$	−27.2691	+	27.2691i	−1.06064	+	1.06064i	−0.0626054	+	0.998038i	$0.519941\pi$
$661$	−27.2691	+	27.2691i	−1.06064	+	1.06064i	−0.998038	+	0.0626054i	$0.980059\pi$
$662$	−0.189332			−0.00735860
$663$	39.0146	+	11.8492i	1.51520	+	0.460185i
$664$	−18.4621	−	18.4621i	−0.716468	−	0.716468i
$665$	−4.11652	−	4.11652i	−0.159632	−	0.159632i
$666$	−33.0468	−	22.1131i	−1.28054	−	0.856866i
$667$	−4.83968			−0.187393
$668$		−	3.51299i		−	0.135922i
$669$	18.5622	+	5.63757i	0.717658	+	0.217961i
$670$			11.1822i			0.432007i
$671$	19.3220	−	14.9176i	0.745916	−	0.575887i
$672$	1.61470	+	3.02332i	0.0622884	+	0.116627i
$673$	−2.45798	+	2.45798i	−0.0947483	+	0.0947483i	−0.752892	−	0.658144i	$-0.771342\pi$
$673$	−2.45798	+	2.45798i	−0.0947483	+	0.0947483i	0.658144	+	0.752892i	$0.271342\pi$
$674$	−25.4906			−0.981861
$675$	−57.6374	−	5.73515i	−2.21847	−	0.220746i
$676$			9.21984i			0.354609i
$677$	25.8381	−	25.8381i	0.993040	−	0.993040i	−0.00693626	−	0.999976i	$-0.502208\pi$
$677$	25.8381	−	25.8381i	0.993040	−	0.993040i	0.999976	+	0.00693626i	$0.00220790\pi$
$678$	−2.18997	+	7.21069i	−0.0841054	+	0.276925i
$679$	−6.36125	−	6.36125i	−0.244122	−	0.244122i
$680$			35.7781i			1.37203i
$681$	−6.21207	+	20.4539i	−0.238047	+	0.783793i
$682$	−12.0775	−	12.0775i	−0.462470	−	0.462470i
$683$		−	24.1703i		−	0.924850i	−0.886658	−	0.462425i	$-0.846979\pi$
$683$		−	24.1703i		−	0.924850i	0.886658	−	0.462425i	$-0.153021\pi$
$684$	−0.486996	+	0.727788i	−0.0186208	+	0.0278277i
$685$			63.8361i			2.43905i
$686$			24.3828i			0.930940i
$687$	12.6189	−	6.73950i	0.481440	−	0.257128i
$688$	−5.70942	−	5.70942i	−0.217670	−	0.217670i
$689$	−9.22941	−	9.22941i	−0.351613	−	0.351613i
$690$	−30.1325	+	16.0932i	−1.14713	+	0.612659i
$691$	16.7091			0.635644			0.317822	−	0.948150i	$-0.397049\pi$
$691$	16.7091			0.635644			0.317822	+	0.948150i	$0.397049\pi$
$692$	−1.03724	+	1.03724i	−0.0394301	+	0.0394301i
$693$	−10.3010	−	6.89284i	−0.391301	−	0.261838i
$694$	7.56619	−	7.56619i	0.287209	−	0.287209i
$695$	8.97318	+	8.97318i	0.340372	+	0.340372i
$696$	5.91907	−	3.16127i	0.224362	−	0.119828i
$697$	2.83969	−	2.83969i	0.107561	−	0.107561i
$698$	37.7254			1.42793
$699$	−0.853554	+	2.81041i	−0.0322844	+	0.106299i
$700$	−2.77502	−	2.77502i	−0.104886	−	0.104886i
$701$	−14.1519	−	14.1519i	−0.534509	−	0.534509i	0.387402	−	0.921911i	$-0.373373\pi$
$701$	−14.1519	−	14.1519i	−0.534509	−	0.534509i	−0.921911	+	0.387402i	$0.873373\pi$
$702$	−34.2023	−	41.7609i	−1.29088	−	1.57616i
$703$	−6.82313	+	6.82313i	−0.257339	+	0.257339i
$704$	−14.7404	−	14.7404i	−0.555552	−	0.555552i
$705$	−46.3065	+	24.7314i	−1.74400	+	0.931439i
$706$	11.3906	+	11.3906i	0.428693	+	0.428693i
$707$	21.9045			0.823802
$708$	−0.117536	+	0.386997i	−0.00441726	+	0.0145442i
$709$	16.7152	+	16.7152i	0.627751	+	0.627751i	0.947502	−	0.319750i	$-0.103599\pi$
$709$	16.7152	+	16.7152i	0.627751	+	0.627751i	−0.319750	+	0.947502i	$0.603599\pi$
$710$	−26.4480			−0.992575
$711$	−8.07376	−	40.7318i	−0.302790	−	1.52756i
$712$		−	22.2376i		−	0.833389i
$713$			11.8352i			0.443232i
$714$	−11.2512	−	3.41712i	−0.421065	−	0.127882i
$715$	61.2812	−	61.2812i	2.29179	−	2.29179i
$716$	3.02073			0.112890
$717$	4.62062	−	2.46779i	0.172560	−	0.0921613i
$718$	40.0596			1.49501
$719$	35.1745			1.31179			0.655895	−	0.754853i	$-0.272292\pi$
$719$	35.1745			1.31179			0.655895	+	0.754853i	$0.272292\pi$
$720$	29.9120	−	44.7017i	1.11475	−	1.66594i
$721$	3.40118	−	3.40118i	0.126667	−	0.126667i
$722$	−18.9469	−	18.9469i	−0.705130	−	0.705130i
$723$	12.4126	+	23.2410i	0.461628	+	0.864341i
$724$	2.30119	−	2.30119i	0.0855230	−	0.0855230i
$725$	−11.7005	+	11.7005i	−0.434546	+	0.434546i
$726$	3.07281	+	0.933250i	0.114043	+	0.0346361i
$727$	46.3467			1.71890			0.859452	−	0.511217i	$-0.170805\pi$
$727$	46.3467			1.71890			0.859452	+	0.511217i	$0.170805\pi$
$728$			23.8069i			0.882344i
$729$	26.4706	+	5.32053i	0.980392	+	0.197057i
$730$	−42.5283	−	42.5283i	−1.57404	−	1.57404i
$731$	6.17371			0.228343
$732$	−3.36862	+	1.27800i	−0.124508	+	0.0472362i
$733$	−1.89508			−0.0699962			−0.0349981	−	0.999387i	$-0.511143\pi$
$733$	−1.89508			−0.0699962			−0.0349981	+	0.999387i	$0.511143\pi$
$734$	−24.0910	−	24.0910i	−0.889216	−	0.889216i
$735$	32.2472	−	17.2226i	1.18946	−	0.635266i
$736$		−	4.88070i		−	0.179905i
$737$	5.77738			0.212812
$738$	−5.21504	+	1.03371i	−0.191968	+	0.0380515i
$739$	−20.0209	+	20.0209i	−0.736479	+	0.736479i	−0.971895	−	0.235415i	$-0.924355\pi$
$739$	−20.0209	+	20.0209i	−0.736479	+	0.736479i	0.235415	+	0.971895i	$0.424355\pi$
$740$	−6.66273	+	6.66273i	−0.244927	+	0.244927i
$741$	−11.5546	+	6.17112i	−0.424470	+	0.226702i
$742$	2.66161	+	2.66161i	0.0977109	+	0.0977109i
$743$	−17.5801	+	17.5801i	−0.644951	+	0.644951i	−0.951768	−	0.306817i	$-0.900736\pi$
$743$	−17.5801	+	17.5801i	−0.644951	+	0.644951i	0.306817	+	0.951768i	$0.400736\pi$
$744$	−7.73073	−	14.4748i	−0.283422	−	0.530672i
$745$	−8.77542			−0.321507
$746$	14.1032			0.516355
$747$	−24.9426	−	16.6902i	−0.912602	−	0.610664i
$748$	−2.83975			−0.103832
$749$	−9.42202	+	9.42202i	−0.344273	+	0.344273i
$750$	−18.7173	+	61.6284i	−0.683458	+	2.25035i
$751$		−	11.5349i		−	0.420914i	−0.977603	−	0.210457i	$-0.932505\pi$
$751$		−	11.5349i		−	0.420914i	0.977603	−	0.210457i	$-0.0674953\pi$
$752$		−	33.6535i		−	1.22722i
$753$	15.9414	−	52.4885i	0.580935	−	1.91279i
$754$	−15.4207			−0.561588
$755$	24.4422	+	24.4422i	0.889544	+	0.889544i
$756$	1.15912	+	1.41528i	0.0421568	+	0.0514733i
$757$	−4.44161			−0.161433			−0.0807165	−	0.996737i	$-0.525721\pi$
$757$	−4.44161			−0.161433			−0.0807165	+	0.996737i	$0.525721\pi$
$758$	−24.5353	−	24.5353i	−0.891161	−	0.891161i
$759$	8.31468	+	15.5682i	0.301804	+	0.565089i
$760$	−8.12764	−	8.12764i	−0.294821	−	0.294821i
$761$	−19.7563	+	19.7563i	−0.716165	+	0.716165i	−0.967818	−	0.251653i	$-0.919026\pi$
$761$	−19.7563	+	19.7563i	−0.716165	+	0.716165i	0.251653	+	0.967818i	$0.419026\pi$
$762$	50.2916	+	15.2742i	1.82187	+	0.553324i
$763$	−4.92917	−	4.92917i	−0.178448	−	0.178448i
$764$	0.585320	+	0.585320i	0.0211761	+	0.0211761i
$765$	7.99622	+	40.3406i	0.289104	+	1.45852i
$766$	−14.4362			−0.521600
$767$	−4.27808	+	4.27808i	−0.154472	+	0.154472i
$768$	5.12732	+	9.60026i	0.185016	+	0.346420i
$769$	31.8740	+	31.8740i	1.14940	+	1.14940i	0.986670	+	0.162735i	$0.0520314\pi$
$769$	31.8740	+	31.8740i	1.14940	+	1.14940i	0.162735	+	0.986670i	$0.447969\pi$
$770$	−17.6725	+	17.6725i	−0.636873	+	0.636873i
$771$	−10.8888	+	5.81548i	−0.392149	+	0.209440i
$772$	0.690343	−	0.690343i	0.0248460	−	0.0248460i
$773$	27.3697			0.984418			0.492209	−	0.870477i	$-0.336190\pi$
$773$	27.3697			0.984418			0.492209	+	0.870477i	$0.336190\pi$
$774$	−6.79265	−	4.54527i	−0.244157	−	0.163376i
$775$	28.6131	+	28.6131i	1.02781	+	1.02781i
$776$	−12.5596	−	12.5596i	−0.450865	−	0.450865i
$777$	9.49646	+	17.7809i	0.340684	+	0.637887i
$778$		−	47.1759i		−	1.69134i
$779$			1.29017i			0.0462252i
$780$	−11.2830	+	6.02605i	−0.403997	+	0.215767i
$781$			13.6645i			0.488956i
$782$	11.8399	+	11.8399i	0.423394	+	0.423394i
$783$	5.96736	−	4.88728i	0.213256	−	0.174657i
$784$			23.4358i			0.836994i
$785$	−15.8662	−	15.8662i	−0.566290	−	0.566290i
$786$	39.0144	+	11.8491i	1.39160	+	0.422645i
$787$	15.9528	−	15.9528i	0.568657	−	0.568657i	−0.363095	−	0.931752i	$-0.618280\pi$
$787$	15.9528	−	15.9528i	0.568657	−	0.568657i	0.931752	+	0.363095i	$0.118280\pi$
$788$			3.26447i			0.116292i
$789$	7.36433	+	13.7888i	0.262177	+	0.490893i
$790$	−83.7317			−2.97904
$791$	2.70141	−	2.70141i	0.0960512	−	0.0960512i
$792$	−20.3382	−	13.6092i	−0.722686	−	0.483583i
$793$	−53.4546	−	6.87609i	−1.89823	−	0.244177i
$794$		−	38.0321i		−	1.34971i
$795$	3.82574	−	12.5966i	0.135685	−	0.446756i
$796$			2.65925i			0.0942545i
$797$	31.7717			1.12541			0.562706	−	0.826657i	$-0.309760\pi$
$797$	31.7717			1.12541			0.562706	+	0.826657i	$0.309760\pi$
$798$	3.33217	−	1.77965i	0.117958	−	0.0629990i
$799$	18.1951	+	18.1951i	0.643695	+	0.643695i
$800$	−11.7997	−	11.7997i	−0.417182	−	0.417182i
$801$	−4.96999	−	25.0734i	−0.175606	−	0.885925i
$802$	46.0514			1.62613
$803$	−21.9725	+	21.9725i	−0.775394	+	0.775394i
$804$	−0.815919	−	0.247804i	−0.0287752	−	0.00873938i
$805$	17.3180			0.610380
$806$			37.7106i			1.32830i
$807$	−11.8386	+	6.32279i	−0.416739	+	0.222573i
$808$	43.2481			1.52146
$809$			0.904973i			0.0318171i	0.999873	+	0.0159086i	$0.00506407\pi$
$809$			0.904973i			0.0318171i	−0.999873	+	0.0159086i	$0.994936\pi$
$810$	20.9021	−	50.2720i	0.734426	−	1.76638i
$811$	−2.79564	+	2.79564i	−0.0981681	+	0.0981681i	−0.754485	−	0.656317i	$-0.772113\pi$
$811$	−2.79564	+	2.79564i	−0.0981681	+	0.0981681i	0.656317	+	0.754485i	$0.272113\pi$
$812$	0.522609			0.0183400
$813$	−5.71921	+	3.05452i	−0.200581	+	0.107127i
$814$	29.2922	+	29.2922i	1.02669	+	1.02669i
$815$			25.2458i			0.884322i
$816$	−25.2260	−	7.66142i	−0.883085	−	0.268203i
$817$	−1.40247	+	1.40247i	−0.0490662	+	0.0490662i
$818$			15.7412i			0.550378i
$819$	5.32073	+	26.8429i	0.185921	+	0.937966i
$820$			1.25984i			0.0439956i
$821$	27.7479	−	27.7479i	0.968409	−	0.968409i	−0.0311074	−	0.999516i	$-0.509903\pi$
$821$	27.7479	−	27.7479i	0.968409	−	0.968409i	0.999516	+	0.0311074i	$0.00990338\pi$
$822$	−39.6353	−	12.0377i	−1.38244	−	0.419863i
$823$	−15.7638	+	15.7638i	−0.549490	+	0.549490i	−0.926293	−	0.376803i	$-0.877023\pi$
$823$	−15.7638	+	15.7638i	−0.549490	+	0.549490i	0.376803	+	0.926293i	$0.377023\pi$
$824$	6.71528	−	6.71528i	0.233938	−	0.233938i
$825$	57.7398	+	17.5362i	2.01024	+	0.610534i
$826$	1.23373	−	1.23373i	0.0429269	−	0.0429269i
$827$			23.5295i			0.818199i	0.912490	+	0.409100i	$0.134157\pi$
$827$			23.5295i			0.818199i	−0.912490	+	0.409100i	$0.865843\pi$
$828$	−0.506501	−	2.55528i	−0.0176021	−	0.0888020i
$829$		−	39.0515i		−	1.35632i	−0.734917	−	0.678158i	$-0.762779\pi$
$829$		−	39.0515i		−	1.35632i	0.734917	−	0.678158i	$-0.237221\pi$
$830$	−42.7920	+	42.7920i	−1.48533	+	1.48533i
$831$	21.1384	+	6.41996i	0.733281	+	0.222706i
$832$			46.0254i			1.59564i
$833$	−12.6708	−	12.6708i	−0.439017	−	0.439017i
$834$	−7.26347	+	3.87928i	−0.251513	+	0.134329i
$835$	53.0026			1.83423
$836$	0.645101	−	0.645101i	0.0223113	−	0.0223113i
$837$	−11.9516	−	14.5929i	−0.413109	−	0.504405i
$838$		−	12.7459i		−	0.440300i
$839$	−37.1760			−1.28346			−0.641729	−	0.766932i	$-0.721782\pi$
$839$	−37.1760			−1.28346			−0.641729	+	0.766932i	$0.721782\pi$
$840$	−21.1805	+	11.3121i	−0.730795	+	0.390304i
$841$			26.7965i			0.924017i
$842$	44.1607			1.52188
$843$	16.9753	+	5.15560i	0.584661	+	0.177568i
$844$	5.24796	−	5.24796i	0.180642	−	0.180642i
$845$	−139.105			−4.78537
$846$	−6.62343	−	33.4150i	−0.227718	−	1.14883i
$847$	−1.15120	−	1.15120i	−0.0395557	−	0.0395557i
$848$	5.96752	+	5.96752i	0.204926	+	0.204926i
$849$	−12.7876	+	6.82962i	−0.438869	+	0.234392i
$850$	57.2488			1.96362
$851$		−	28.7046i		−	0.983982i
$852$	0.586101	−	1.92980i	0.0200795	−	0.0661137i
$853$		−	11.1580i		−	0.382042i	−0.981586	−	0.191021i	$-0.938820\pi$
$853$		−	11.1580i		−	0.382042i	0.981586	−	0.191021i	$-0.0611798\pi$
$854$	15.4154	+	1.98295i	0.527505	+	0.0678553i
$855$	−10.9806	−	7.34762i	−0.375528	−	0.251283i
$856$	−18.6028	+	18.6028i	−0.635831	+	0.635831i
$857$	−18.0949			−0.618108			−0.309054	−	0.951044i	$-0.600012\pi$
$857$	−18.0949			−0.618108			−0.309054	+	0.951044i	$0.600012\pi$
$858$	26.4931	+	49.6050i	0.904459	+	1.69349i
$859$			24.9852i			0.852485i	0.904609	+	0.426242i	$0.140163\pi$
$859$			24.9852i			0.852485i	−0.904609	+	0.426242i	$0.859837\pi$
$860$	−1.36950	+	1.36950i	−0.0466996	+	0.0466996i
$861$	2.57891	+	0.783246i	0.0878891	+	0.0266930i
$862$	−25.9699	−	25.9699i	−0.884540	−	0.884540i
$863$		−	11.7395i		−	0.399617i	−0.979835	−	0.199808i	$-0.935968\pi$
$863$		−	11.7395i		−	0.399617i	0.979835	−	0.199808i	$-0.0640320\pi$
$864$	4.92871	+	6.01794i	0.167678	+	0.204735i
$865$	−15.6495	−	15.6495i	−0.532100	−	0.532100i
$866$			13.1336i			0.446297i
$867$	−8.19182	+	4.37510i	−0.278209	+	0.148586i
$868$		−	1.27802i		−	0.0433787i
$869$			43.2606i			1.46751i
$870$	−7.32728	−	13.7194i	−0.248418	−	0.465132i
$871$	−9.01961	−	9.01961i	−0.305618	−	0.305618i
$872$	−9.73214	−	9.73214i	−0.329572	−	0.329572i
$873$	−16.9683	−	11.3543i	−0.574290	−	0.384284i
$874$	−5.37930			−0.181957
$875$	23.0885	−	23.0885i	0.780533	−	0.780533i
$876$	4.04556	−	2.16066i	0.136687	−	0.0730018i
$877$	−26.1624	+	26.1624i	−0.883443	+	0.883443i	−0.993883	−	0.110440i	$-0.964774\pi$
$877$	−26.1624	+	26.1624i	−0.883443	+	0.883443i	0.110440	+	0.993883i	$0.464774\pi$
$878$	26.8652	+	26.8652i	0.906658	+	0.906658i
$879$	−12.1241	−	22.7008i	−0.408935	−	0.765679i
$880$	−39.6230	+	39.6230i	−1.33569	+	1.33569i
$881$	−9.91485			−0.334040			−0.167020	−	0.985954i	$-0.553414\pi$
$881$	−9.91485			−0.334040			−0.167020	+	0.985954i	$0.553414\pi$
$882$	4.61247	+	23.2697i	0.155310	+	0.783533i
$883$	23.5816	+	23.5816i	0.793584	+	0.793584i	0.982075	−	0.188491i	$-0.0603597\pi$
$883$	23.5816	+	23.5816i	0.793584	+	0.793584i	−0.188491	+	0.982075i	$0.560360\pi$
$884$	4.43341	+	4.43341i	0.149112	+	0.149112i
$885$	−5.83887	−	1.77333i	−0.196271	−	0.0596099i
$886$	10.2535	−	10.2535i	0.344473	−	0.344473i
$887$	34.2561	+	34.2561i	1.15021	+	1.15021i	0.986511	+	0.163697i	$0.0523418\pi$
$887$	34.2561	+	34.2561i	1.15021	+	1.15021i	0.163697	+	0.986511i	$0.447658\pi$
$888$	18.7498	+	35.1066i	0.629202	+	1.17810i
$889$	−18.8413	−	18.8413i	−0.631915	−	0.631915i
$890$	−51.5430			−1.72773
$891$	−25.9734	−	10.7992i	−0.870141	−	0.361788i
$892$	2.10931	+	2.10931i	0.0706249	+	0.0706249i
$893$	−8.26668			−0.276634
$894$	1.65480	−	5.44859i	0.0553448	−	0.182228i
$895$			45.5756i			1.52343i
$896$		−	17.2307i		−	0.575638i
$897$	11.3241	−	37.2858i	0.378102	−	1.24494i
$898$	−29.0451	+	29.0451i	−0.969246	+	0.969246i
$899$	−5.38860			−0.179720
$900$	−7.40222	−	4.95317i	−0.246741	−	0.165106i
$901$	−6.45279			−0.214974
$902$	5.53881			0.184422
$903$	1.95196	+	3.65481i	0.0649573	+	0.121624i
$904$	5.33367	−	5.33367i	0.177395	−	0.177395i
$905$	34.7195	+	34.7195i	1.15411	+	1.15411i
$906$	−19.7851	+	10.5669i	−0.657316	+	0.351060i
$907$	−29.3272	+	29.3272i	−0.973794	+	0.973794i	−0.999665	−	0.0258718i	$-0.991764\pi$
$907$	−29.3272	+	29.3272i	−0.973794	+	0.973794i	0.0258718	+	0.999665i	$0.491764\pi$
$908$	−2.32426	+	2.32426i	−0.0771333	+	0.0771333i
$909$	48.7633	−	9.66574i	1.61738	−	0.320592i
$910$	55.1805			1.82922
$911$		−	47.0833i		−	1.55994i	−0.625818	−	0.779969i	$-0.715235\pi$
$911$		−	47.0833i		−	1.55994i	0.625818	−	0.779969i	$-0.284765\pi$
$912$	7.47096	−	3.99010i	0.247388	−	0.132126i
$913$	22.1088	+	22.1088i	0.731694	+	0.731694i
$914$	3.08590			0.102072
$915$	−19.2819	−	50.8245i	−0.637442	−	1.68021i
$916$	2.19978			0.0726827
$917$	−14.6164	−	14.6164i	−0.482675	−	0.482675i
$918$	−26.5550	−	2.64233i	−0.876447	−	0.0872099i
$919$			31.2913i			1.03220i	0.856527	+	0.516102i	$0.172617\pi$
$919$			31.2913i			1.03220i	−0.856527	+	0.516102i	$0.827383\pi$
$920$	34.1927			1.12730
$921$	25.6443	+	7.78848i	0.845009	+	0.256639i
$922$	15.0463	−	15.0463i	0.495522	−	0.495522i
$923$	21.3330	−	21.3330i	0.702185	−	0.702185i
$924$	−0.897855	−	1.68112i	−0.0295373	−	0.0553048i
$925$	−69.3970	−	69.3970i	−2.28176	−	2.28176i
$926$	−24.3863	+	24.3863i	−0.801383	+	0.801383i
$927$	6.07080	−	9.07247i	0.199391	−	0.297979i
$928$	2.22219			0.0729471
$929$	10.2185			0.335257			0.167628	−	0.985850i	$-0.446389\pi$
$929$	10.2185			0.335257			0.167628	+	0.985850i	$0.446389\pi$
$930$	−33.5502	+	17.9185i	−1.10015	+	0.587572i
$931$	5.75681			0.188672
$932$	−0.319359	+	0.319359i	−0.0104610	+	0.0104610i
$933$	−47.5682	−	14.4470i	−1.55731	−	0.472974i
$934$		−	28.4994i		−	0.932530i
$935$		−	42.8451i		−	1.40119i
$936$	10.5052	+	52.9985i	0.343375	+	1.73231i
$937$	11.3137			0.369601			0.184801	−	0.982776i	$-0.440836\pi$
$937$	11.3137			0.369601			0.184801	+	0.982776i	$0.440836\pi$
$938$	2.60111	+	2.60111i	0.0849293	+	0.0849293i
$939$	−1.22294	+	4.02664i	−0.0399091	+	0.131404i
$940$	−8.07235			−0.263291
$941$	−23.5355	−	23.5355i	−0.767236	−	0.767236i	0.210383	−	0.977619i	$-0.432529\pi$
$941$	−23.5355	−	23.5355i	−0.767236	−	0.767236i	−0.977619	+	0.210383i	$0.932529\pi$
$942$	12.8432	−	6.85929i	0.418452	−	0.223488i
$943$	−2.71385	−	2.71385i	−0.0883752	−	0.0883752i
$944$	2.76610	−	2.76610i	0.0900290	−	0.0900290i
$945$	−21.3533	+	17.4884i	−0.694622	+	0.568897i
$946$	6.02091	+	6.02091i	0.195757	+	0.195757i
$947$	−23.6912	−	23.6912i	−0.769861	−	0.769861i	0.208221	−	0.978082i	$-0.433233\pi$
$947$	−23.6912	−	23.6912i	−0.769861	−	0.769861i	−0.978082	+	0.208221i	$0.933233\pi$
$948$	1.85554	−	6.10954i	0.0602651	−	0.198429i
$949$	68.6069			2.22707
$950$	−13.0051	+	13.0051i	−0.421941	+	0.421941i
$951$	5.10065	−	2.72417i	0.165400	−	0.0883371i
$952$	8.32238	+	8.32238i	0.269730	+	0.269730i
$953$	14.0577	−	14.0577i	0.455375	−	0.455375i	−0.441759	−	0.897134i	$-0.645645\pi$
$953$	14.0577	−	14.0577i	0.455375	−	0.455375i	0.897134	+	0.441759i	$0.145645\pi$
$954$	7.09971	+	4.75074i	0.229862	+	0.153811i
$955$	−8.83109	+	8.83109i	−0.285767	+	0.285767i
$956$	0.805488			0.0260513
$957$	−7.08823	+	3.78569i	−0.229130	+	0.122374i
$958$	−5.87049	−	5.87049i	−0.189667	−	0.189667i
$959$	14.8490	+	14.8490i	0.479499	+	0.479499i
$960$	−40.9477	+	21.8694i	−1.32158	+	0.705832i
$961$		−	17.8224i		−	0.574917i
$962$		−	91.4617i		−	2.94884i
$963$	−16.8175	+	25.1327i	−0.541935	+	0.809891i
$964$			4.05147i			0.130489i
$965$	10.4156	+	10.4156i	0.335291	+	0.335291i
$966$	−3.26570	+	10.7526i	−0.105072	+	0.345960i
$967$		−	48.4137i		−	1.55688i	−0.627719	−	0.778440i	$-0.716011\pi$
$967$		−	48.4137i		−	1.55688i	0.627719	−	0.778440i	$-0.283989\pi$
$968$	−2.27293	−	2.27293i	−0.0730546	−	0.0730546i
$969$	−1.88196	+	6.19653i	−0.0604573	+	0.199061i
$970$	−29.1111	+	29.1111i	−0.934703	+	0.934703i
$971$			46.9676i			1.50726i	0.657298	+	0.753631i	$0.271699\pi$
$971$			46.9676i			1.50726i	−0.657298	+	0.753631i	$0.728301\pi$
$972$	3.20493	+	2.63919i	0.102798	+	0.0846521i
$973$	4.17452			0.133829
$974$	38.6379	−	38.6379i	1.23804	−	1.23804i
$975$	−62.7655	−	117.521i	−2.01011	−	3.76367i
$976$	34.5625	+	4.44592i	1.10632	+	0.142310i
$977$			0.361984i			0.0115809i	0.999983	+	0.00579044i	$0.00184317\pi$
$977$			0.361984i			0.0115809i	−0.999983	+	0.00579044i	$0.998157\pi$
$978$	−15.6749	−	4.76066i	−0.501229	−	0.152229i
$979$			26.6301i			0.851100i
$980$	5.62148			0.179572
$981$	−13.1483	−	8.79813i	−0.419793	−	0.280903i
$982$	16.0791	+	16.0791i	0.513104	+	0.513104i
$983$	26.0416	+	26.0416i	0.830599	+	0.830599i	0.987599	−	0.157000i	$-0.0501822\pi$
$983$	26.0416	+	26.0416i	0.830599	+	0.830599i	−0.157000	+	0.987599i	$0.550182\pi$
$984$	5.09180	+	1.54644i	0.162321	+	0.0492987i
$985$	−49.2531			−1.56934
$986$	−5.39073	+	5.39073i	−0.171676	+	0.171676i
$987$	−5.01859	+	16.5242i	−0.159744	+	0.525971i
$988$	−2.01426			−0.0640821
$989$		−	5.90014i		−	0.187614i
$990$	−31.5439	+	47.1405i	−1.00253	+	1.49822i
$991$	−3.47091			−0.110257			−0.0551285	−	0.998479i	$-0.517557\pi$
$991$	−3.47091			−0.110257			−0.0551285	+	0.998479i	$0.517557\pi$
$992$		−	5.43427i		−	0.172538i
$993$	0.208432	+	0.0633031i	0.00661437	+	0.00200886i
$994$	−6.15209	+	6.15209i	−0.195133	+	0.195133i
$995$	−40.1217			−1.27194
$996$	−2.17405	−	4.07064i	−0.0688876	−	0.128983i
$997$	−10.9701	−	10.9701i	−0.347427	−	0.347427i	0.511723	−	0.859150i	$-0.329007\pi$
$997$	−10.9701	−	10.9701i	−0.347427	−	0.347427i	−0.859150	+	0.511723i	$0.829007\pi$
$998$			43.8009i			1.38649i
$999$	28.9870	+	35.3930i	0.917107	+	1.11979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	183.2.g.c.50.4	yes	28
3.2	odd	2	inner	183.2.g.c.50.11	yes	28
61.11	odd	4	inner	183.2.g.c.11.11	yes	28
183.11	even	4	inner	183.2.g.c.11.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.g.c.11.4	✓	28	183.11	even	4	inner
183.2.g.c.11.11	yes	28	61.11	odd	4	inner
183.2.g.c.50.4	yes	28	1.1	even	1	trivial
183.2.g.c.50.11	yes	28	3.2	odd	2	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:	\( N \)	\(=\)	\( 183 = 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	183.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.06450 - 1.06450i) q^{2} +(0.815973 + 1.52781i) q^{3} +0.266334i q^{4} -4.01835 q^{5} +(0.757748 - 2.49496i) q^{6} +(-0.934712 + 0.934712i) q^{7} +(-1.84549 + 1.84549i) q^{8} +(-1.66838 + 2.49329i) q^{9} +O(q^{10})\)	\(q+(-1.06450 - 1.06450i) q^{2} +(0.815973 + 1.52781i) q^{3} +0.266334i q^{4} -4.01835 q^{5} +(0.757748 - 2.49496i) q^{6} +(-0.934712 + 0.934712i) q^{7} +(-1.84549 + 1.84549i) q^{8} +(-1.66838 + 2.49329i) q^{9} +(4.27754 + 4.27754i) q^{10} +(2.21002 - 2.21002i) q^{11} +(-0.406906 + 0.217321i) q^{12} -6.90055 q^{13} +1.99001 q^{14} +(-3.27886 - 6.13925i) q^{15} +4.46173 q^{16} +(-2.41228 + 2.41228i) q^{17} +(4.43011 - 0.878126i) q^{18} -1.09599i q^{19} -1.07022i q^{20} +(-2.19076 - 0.665358i) q^{21} -4.70515 q^{22} +(2.30539 + 2.30539i) q^{23} +(-4.32543 - 1.31368i) q^{24} +11.1471 q^{25} +(7.34566 + 7.34566i) q^{26} +(-5.17062 - 0.514497i) q^{27} +(-0.248945 - 0.248945i) q^{28} +(-1.04965 + 1.04965i) q^{29} +(-3.04489 + 10.0256i) q^{30} +(2.56686 + 2.56686i) q^{31} +(-1.05854 - 1.05854i) q^{32} +(5.17980 + 1.57317i) q^{33} +5.13576 q^{34} +(3.75599 - 3.75599i) q^{35} +(-0.664049 - 0.444346i) q^{36} +(-6.22556 - 6.22556i) q^{37} +(-1.16668 + 1.16668i) q^{38} +(-5.63066 - 10.5427i) q^{39} +(7.41583 - 7.41583i) q^{40} -1.17718 q^{41} +(1.62379 + 3.04034i) q^{42} +(-1.27964 - 1.27964i) q^{43} +(0.588604 + 0.588604i) q^{44} +(6.70412 - 10.0189i) q^{45} -4.90818i q^{46} -7.54269i q^{47} +(3.64065 + 6.81666i) q^{48} +5.25263i q^{49} +(-11.8661 - 11.8661i) q^{50} +(-5.65385 - 1.71714i) q^{51} -1.83785i q^{52} +(1.33749 + 1.33749i) q^{53} +(4.95646 + 6.05182i) q^{54} +(-8.88063 + 8.88063i) q^{55} -3.45001i q^{56} +(1.67445 - 0.894294i) q^{57} +2.23470 q^{58} +(0.619962 - 0.619962i) q^{59} +(1.63509 - 0.873272i) q^{60} +(7.74642 + 0.996455i) q^{61} -5.46487i q^{62} +(-0.771059 - 3.88996i) q^{63} -6.66982i q^{64} +27.7288 q^{65} +(-3.83927 - 7.18855i) q^{66} +(1.30709 + 1.30709i) q^{67} +(-0.642472 - 0.642472i) q^{68} +(-1.64105 + 5.40331i) q^{69} -7.99654 q^{70} +(-3.09149 + 3.09149i) q^{71} +(-1.52238 - 7.68034i) q^{72} -9.94223 q^{73} +13.2543i q^{74} +(9.09573 + 17.0306i) q^{75} +0.291898 q^{76} +4.13147i q^{77} +(-5.22888 + 17.2166i) q^{78} +(-9.78736 + 9.78736i) q^{79} -17.9288 q^{80} +(-3.43303 - 8.31951i) q^{81} +(1.25311 + 1.25311i) q^{82} +10.0039i q^{83} +(0.177207 - 0.583473i) q^{84} +(9.69337 - 9.69337i) q^{85} +2.72437i q^{86} +(-2.46014 - 0.747173i) q^{87} +8.15716i q^{88} +(-6.02484 + 6.02484i) q^{89} +(-17.8017 + 3.52862i) q^{90} +(6.45002 - 6.45002i) q^{91} +(-0.614002 + 0.614002i) q^{92} +(-1.82718 + 6.01616i) q^{93} +(-8.02922 + 8.02922i) q^{94} +4.40405i q^{95} +(0.753506 - 2.48099i) q^{96} +6.80558i q^{97} +(5.59144 - 5.59144i) q^{98} +(1.82308 + 9.19738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9	\( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{13} - 40 q^{15} + 12 q^{16} - 4 q^{18} - 18 q^{21} - 48 q^{22} + 14 q^{24} + 36 q^{25} - 24 q^{28} - 22 q^{30} + 32 q^{31} + 2 q^{33} + 96 q^{34} + 8 q^{37} + 28 q^{40} + 20 q^{42} - 32 q^{43} - 24 q^{51} - 2 q^{54} - 40 q^{55} - 16 q^{57} - 56 q^{58} + 64 q^{61} + 40 q^{63} - 12 q^{67} - 30 q^{69} - 24 q^{70} + 44 q^{72} - 72 q^{73} + 128 q^{76} - 66 q^{78} + 28 q^{81} - 28 q^{82} + 46 q^{84} - 44 q^{85} - 12 q^{87} - 56 q^{90} - 64 q^{91} + 36 q^{93} - 16 q^{94} + 54 q^{96} + 32 q^{99}+O(q^{100}) \) 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^13 - 40 * q^15 + 12 * q^16 - 4 * q^18 - 18 * q^21 - 48 * q^22 + 14 * q^24 + 36 * q^25 - 24 * q^28 - 22 * q^30 + 32 * q^31 + 2 * q^33 + 96 * q^34 + 8 * q^37 + 28 * q^40 + 20 * q^42 - 32 * q^43 - 24 * q^51 - 2 * q^54 - 40 * q^55 - 16 * q^57 - 56 * q^58 + 64 * q^61 + 40 * q^63 - 12 * q^67 - 30 * q^69 - 24 * q^70 + 44 * q^72 - 72 * q^73 + 128 * q^76 - 66 * q^78 + 28 * q^81 - 28 * q^82 + 46 * q^84 - 44 * q^85 - 12 * q^87 - 56 * q^90 - 64 * q^91 + 36 * q^93 - 16 * q^94 + 54 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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