LMFDB - Embedded newform 471.2.e.c.301.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			301.5
Character	$\chi$	$=$	471.301
Dual form			471.2.e.c.169.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.15467 q^{2} +(-0.500000 + 0.866025i) q^{3} -0.666729 q^{4} +(1.08032 - 1.87116i) q^{5} +(0.577337 - 0.999977i) q^{6} -1.15933 q^{7} +3.07920 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.15467 q^{2} +(-0.500000 + 0.866025i) q^{3} -0.666729 q^{4} +(1.08032 - 1.87116i) q^{5} +(0.577337 - 0.999977i) q^{6} -1.15933 q^{7} +3.07920 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.24741 + 2.16058i) q^{10} +(-1.53217 + 2.65380i) q^{11} +(0.333364 - 0.577404i) q^{12} +(-1.04225 - 1.80523i) q^{13} +1.33865 q^{14} +(1.08032 + 1.87116i) q^{15} -2.22201 q^{16} +(-1.80208 + 3.12129i) q^{17} +(0.577337 + 0.999977i) q^{18} +(1.14110 - 1.97644i) q^{19} +(-0.720279 + 1.24756i) q^{20} +(0.579667 - 1.00401i) q^{21} +(1.76916 - 3.06427i) q^{22} -5.21890 q^{23} +(-1.53960 + 2.66667i) q^{24} +(0.165829 + 0.287224i) q^{25} +(1.20346 + 2.08445i) q^{26} +1.00000 q^{27} +0.772962 q^{28} -7.50430 q^{29} +(-1.24741 - 2.16058i) q^{30} +(-0.477495 - 0.827046i) q^{31} -3.59270 q^{32} +(-1.53217 - 2.65380i) q^{33} +(2.08081 - 3.60407i) q^{34} +(-1.25245 + 2.16930i) q^{35} +(0.333364 + 0.577404i) q^{36} +(-5.78530 - 10.0204i) q^{37} +(-1.31759 + 2.28214i) q^{38} +2.08450 q^{39} +(3.32651 - 5.76169i) q^{40} -8.76491 q^{41} +(-0.669326 + 1.15931i) q^{42} +(1.08272 + 1.87533i) q^{43} +(1.02154 - 1.76936i) q^{44} -2.16063 q^{45} +6.02613 q^{46} +(0.0102225 + 0.0177060i) q^{47} +(1.11101 - 1.92432i) q^{48} -5.65594 q^{49} +(-0.191478 - 0.331650i) q^{50} +(-1.80208 - 3.12129i) q^{51} +(0.694898 + 1.20360i) q^{52} +(-1.20159 - 2.08121i) q^{53} -1.15467 q^{54} +(3.31046 + 5.73389i) q^{55} -3.56982 q^{56} +(1.14110 + 1.97644i) q^{57} +8.66501 q^{58} -3.07630 q^{59} +(-0.720279 - 1.24756i) q^{60} +(0.567609 - 0.983128i) q^{61} +(0.551351 + 0.954968i) q^{62} +(0.579667 + 1.00401i) q^{63} +8.59243 q^{64} -4.50384 q^{65} +(1.76916 + 3.06427i) q^{66} -3.29739 q^{67} +(1.20150 - 2.08105i) q^{68} +(2.60945 - 4.51970i) q^{69} +(1.44617 - 2.50484i) q^{70} +(7.52672 + 13.0367i) q^{71} +(-1.53960 - 2.66667i) q^{72} +(0.352114 - 0.609879i) q^{73} +(6.68014 + 11.5703i) q^{74} -0.331658 q^{75} +(-0.760801 + 1.31775i) q^{76} +(1.77630 - 3.07664i) q^{77} -2.40692 q^{78} -7.35838 q^{79} +(-2.40048 + 4.15775i) q^{80} +(-0.500000 + 0.866025i) q^{81} +10.1206 q^{82} +(6.03104 + 10.4461i) q^{83} +(-0.386481 + 0.669404i) q^{84} +(3.89363 + 6.74396i) q^{85} +(-1.25019 - 2.16539i) q^{86} +(3.75215 - 6.49891i) q^{87} +(-4.71787 + 8.17158i) q^{88} +(-1.62478 + 2.81421i) q^{89} +2.49483 q^{90} +(1.20832 + 2.09287i) q^{91} +3.47959 q^{92} +0.954990 q^{93} +(-0.0118037 - 0.0204446i) q^{94} +(-2.46549 - 4.27035i) q^{95} +(1.79635 - 3.11137i) q^{96} +(-2.32461 - 4.02634i) q^{97} +6.53077 q^{98} +3.06434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.15467			−0.816478			−0.408239	−	0.912875i	$-0.633857\pi$
$2$	−1.15467			−0.816478			−0.408239	+	0.912875i	$0.633857\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.666729			−0.333364
$5$	1.08032	−	1.87116i	0.483133	−	0.836810i	−0.516680	−	0.856179i	$-0.672832\pi$
$5$	1.08032	−	1.87116i	0.483133	−	0.836810i	0.999812	+	0.0193685i	$0.00616556\pi$
$6$	0.577337	−	0.999977i	0.235697	−	0.408239i
$7$	−1.15933			−0.438187			−0.219094	−	0.975704i	$-0.570310\pi$
$7$	−1.15933			−0.438187			−0.219094	+	0.975704i	$0.570310\pi$
$8$	3.07920			1.08866
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.24741	+	2.16058i	−0.394467	+	0.683237i
$11$	−1.53217	+	2.65380i	−0.461967	+	0.800151i	−0.999059	−	0.0433732i	$-0.986190\pi$
$11$	−1.53217	+	2.65380i	−0.461967	+	0.800151i	0.537092	+	0.843524i	$0.319523\pi$
$12$	0.333364	−	0.577404i	0.0962340	−	0.166682i
$13$	−1.04225	−	1.80523i	−0.289068	−	0.500681i	0.684519	−	0.728995i	$-0.260012\pi$
$13$	−1.04225	−	1.80523i	−0.289068	−	0.500681i	−0.973588	+	0.228314i	$0.926679\pi$
$14$	1.33865			0.357770
$15$	1.08032	+	1.87116i	0.278937	+	0.483133i
$16$	−2.22201			−0.555504
$17$	−1.80208	+	3.12129i	−0.437068	+	0.757024i	−0.997462	−	0.0712025i	$-0.977316\pi$
$17$	−1.80208	+	3.12129i	−0.437068	+	0.757024i	0.560394	+	0.828226i	$0.310650\pi$
$18$	0.577337	+	0.999977i	0.136080	+	0.235697i
$19$	1.14110	−	1.97644i	0.261785	−	0.453425i	−0.704931	−	0.709276i	$-0.749022\pi$
$19$	1.14110	−	1.97644i	0.261785	−	0.453425i	0.966716	+	0.255850i	$0.0823555\pi$
$20$	−0.720279	+	1.24756i	−0.161059	+	0.278963i
$21$	0.579667	−	1.00401i	0.126494	−	0.219094i
$22$	1.76916	−	3.06427i	0.377186	−	0.653305i
$23$	−5.21890			−1.08822			−0.544108	−	0.839015i	$-0.683132\pi$
$23$	−5.21890			−1.08822			−0.544108	+	0.839015i	$0.683132\pi$
$24$	−1.53960	+	2.66667i	−0.314270	+	0.544331i
$25$	0.165829	+	0.287224i	0.0331658	+	0.0574448i
$26$	1.20346	+	2.08445i	0.236018	+	0.408795i
$27$	1.00000			0.192450
$28$	0.772962			0.146076
$29$	−7.50430			−1.39351			−0.696757	−	0.717308i	$-0.745374\pi$
$29$	−7.50430			−1.39351			−0.696757	+	0.717308i	$0.745374\pi$
$30$	−1.24741	−	2.16058i	−0.227746	−	0.394467i
$31$	−0.477495	−	0.827046i	−0.0857606	−	0.148542i	0.819954	−	0.572429i	$-0.193999\pi$
$31$	−0.477495	−	0.827046i	−0.0857606	−	0.148542i	−0.905715	+	0.423887i	$0.860665\pi$
$32$	−3.59270			−0.635106
$33$	−1.53217	−	2.65380i	−0.266717	−	0.461967i
$34$	2.08081	−	3.60407i	0.356856	−	0.618093i
$35$	−1.25245	+	2.16930i	−0.211702	+	0.366679i
$36$	0.333364	+	0.577404i	0.0555607	+	0.0962340i
$37$	−5.78530	−	10.0204i	−0.951098	−	1.64735i	−0.743055	−	0.669230i	$-0.766624\pi$
$37$	−5.78530	−	10.0204i	−0.951098	−	1.64735i	−0.208043	−	0.978120i	$-0.566709\pi$
$38$	−1.31759	+	2.28214i	−0.213742	+	0.370212i
$39$	2.08450			0.333787
$40$	3.32651	−	5.76169i	0.525968	−	0.911004i
$41$	−8.76491			−1.36885			−0.684424	−	0.729084i	$-0.739946\pi$
$41$	−8.76491			−1.36885			−0.684424	+	0.729084i	$0.739946\pi$
$42$	−0.669326	+	1.15931i	−0.103279	+	0.178885i
$43$	1.08272	+	1.87533i	0.165113	+	0.285985i	0.936696	−	0.350145i	$-0.113868\pi$
$43$	1.08272	+	1.87533i	0.165113	+	0.285985i	−0.771582	+	0.636130i	$0.780534\pi$
$44$	1.02154	−	1.76936i	0.154003	−	0.266742i
$45$	−2.16063			−0.322088
$46$	6.02613			0.888504
$47$	0.0102225	+	0.0177060i	0.00149111	+	0.00258268i	0.866770	−	0.498708i	$-0.166192\pi$
$47$	0.0102225	+	0.0177060i	0.00149111	+	0.00258268i	−0.865279	+	0.501291i	$0.832859\pi$
$48$	1.11101	−	1.92432i	0.160360	−	0.277752i
$49$	−5.65594			−0.807992
$50$	−0.191478	−	0.331650i	−0.0270791	−	0.0469024i
$51$	−1.80208	−	3.12129i	−0.252341	−	0.437068i
$52$	0.694898	+	1.20360i	0.0963651	+	0.166909i
$53$	−1.20159	−	2.08121i	−0.165051	−	0.285877i	0.771622	−	0.636081i	$-0.219446\pi$
$53$	−1.20159	−	2.08121i	−0.165051	−	0.285877i	−0.936673	+	0.350204i	$0.886112\pi$
$54$	−1.15467			−0.157131
$55$	3.31046	+	5.73389i	0.446383	+	0.773158i
$56$	−3.56982			−0.477038
$57$	1.14110	+	1.97644i	0.151142	+	0.261785i
$58$	8.66501			1.13777
$59$	−3.07630			−0.400501			−0.200250	−	0.979745i	$-0.564176\pi$
$59$	−3.07630			−0.400501			−0.200250	+	0.979745i	$0.564176\pi$
$60$	−0.720279	−	1.24756i	−0.0929876	−	0.161059i
$61$	0.567609	−	0.983128i	0.0726749	−	0.125877i	−0.827398	−	0.561616i	$-0.810180\pi$
$61$	0.567609	−	0.983128i	0.0726749	−	0.125877i	0.900073	+	0.435740i	$0.143513\pi$
$62$	0.551351	+	0.954968i	0.0700216	+	0.121281i
$63$	0.579667	+	1.00401i	0.0730312	+	0.126494i
$64$	8.59243			1.07405
$65$	−4.50384			−0.558633
$66$	1.76916	+	3.06427i	0.217768	+	0.377186i
$67$	−3.29739			−0.402840			−0.201420	−	0.979505i	$-0.564556\pi$
$67$	−3.29739			−0.402840			−0.201420	+	0.979505i	$0.564556\pi$
$68$	1.20150	−	2.08105i	0.145703	−	0.252365i
$69$	2.60945	−	4.51970i	0.314141	−	0.544108i
$70$	1.44617	−	2.50484i	0.172850	−	0.299385i
$71$	7.52672	+	13.0367i	0.893257	+	1.54717i	0.835947	+	0.548810i	$0.184919\pi$
$71$	7.52672	+	13.0367i	0.893257	+	1.54717i	0.0573097	+	0.998356i	$0.481748\pi$
$72$	−1.53960	−	2.66667i	−0.181444	−	0.314270i
$73$	0.352114	−	0.609879i	0.0412118	−	0.0713809i	−0.844684	−	0.535266i	$-0.820211\pi$
$73$	0.352114	−	0.609879i	0.0412118	−	0.0713809i	0.885896	+	0.463885i	$0.153545\pi$
$74$	6.68014	+	11.5703i	0.776550	+	1.34502i
$75$	−0.331658			−0.0382965
$76$	−0.760801	+	1.31775i	−0.0872699	+	0.151156i
$77$	1.77630	−	3.07664i	0.202428	−	0.350616i
$78$	−2.40692			−0.272530
$79$	−7.35838			−0.827883			−0.413941	−	0.910304i	$-0.635848\pi$
$79$	−7.35838			−0.827883			−0.413941	+	0.910304i	$0.635848\pi$
$80$	−2.40048	+	4.15775i	−0.268382	+	0.464851i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	10.1206			1.11763
$83$	6.03104	+	10.4461i	0.661993	+	1.14661i	0.980091	+	0.198547i	$0.0636224\pi$
$83$	6.03104	+	10.4461i	0.661993	+	1.14661i	−0.318098	+	0.948058i	$0.603044\pi$
$84$	−0.386481	+	0.669404i	−0.0421685	+	0.0730380i
$85$	3.89363	+	6.74396i	0.422323	+	0.731486i
$86$	−1.25019	−	2.16539i	−0.134811	−	0.233500i
$87$	3.75215	−	6.49891i	0.402273	−	0.696757i
$88$	−4.71787	+	8.17158i	−0.502926	+	0.871094i
$89$	−1.62478	+	2.81421i	−0.172227	+	0.298305i	−0.939198	−	0.343376i	$-0.888429\pi$
$89$	−1.62478	+	2.81421i	−0.172227	+	0.298305i	0.766971	+	0.641681i	$0.221763\pi$
$90$	2.49483			0.262978
$91$	1.20832	+	2.09287i	0.126666	+	0.219392i
$92$	3.47959			0.362773
$93$	0.954990			0.0990279
$94$	−0.0118037	−	0.0204446i	−0.00121746	−	0.00210870i
$95$	−2.46549	−	4.27035i	−0.252954	−	0.438129i
$96$	1.79635	−	3.11137i	0.183339	−	0.317553i
$97$	−2.32461	−	4.02634i	−0.236028	−	0.408813i	0.723543	−	0.690280i	$-0.242512\pi$
$97$	−2.32461	−	4.02634i	−0.236028	−	0.408813i	−0.959571	+	0.281467i	$0.909179\pi$
$98$	6.53077			0.659707
$99$	3.06434			0.307978
$100$	−0.110563	−	0.191500i	−0.0110563	−	0.0191500i
$101$	2.20093			0.219001			0.109500	−	0.993987i	$-0.465075\pi$
$101$	2.20093			0.219001			0.109500	+	0.993987i	$0.465075\pi$
$102$	2.08081	+	3.60407i	0.206031	+	0.356856i
$103$	5.25296			0.517590			0.258795	−	0.965932i	$-0.416675\pi$
$103$	5.25296			0.517590			0.258795	+	0.965932i	$0.416675\pi$
$104$	−3.20930	−	5.55867i	−0.314698	−	0.545072i
$105$	−1.25245	−	2.16930i	−0.122226	−	0.211702i
$106$	1.38744	+	2.40312i	0.134760	+	0.233412i
$107$	−0.327580	−	0.567385i	−0.0316683	−	0.0548512i	0.849757	−	0.527175i	$-0.176749\pi$
$107$	−0.327580	−	0.567385i	−0.0316683	−	0.0548512i	−0.881425	+	0.472324i	$0.843415\pi$
$108$	−0.666729			−0.0641560
$109$	5.65856	−	9.80091i	0.541991	−	0.938757i	−0.456798	−	0.889570i	$-0.651004\pi$
$109$	5.65856	−	9.80091i	0.541991	−	0.938757i	0.998790	−	0.0491863i	$-0.0156628\pi$
$110$	−3.82250	−	6.62077i	−0.364462	−	0.631266i
$111$	11.5706			1.09823
$112$	2.57606			0.243415
$113$	0.195647	−	0.338870i	0.0184049	−	0.0318782i	−0.856676	−	0.515854i	$-0.827475\pi$
$113$	0.195647	−	0.338870i	0.0184049	−	0.0318782i	0.875081	+	0.483976i	$0.160808\pi$
$114$	−1.31759	−	2.28214i	−0.123404	−	0.213742i
$115$	−5.63807	+	9.76542i	−0.525753	+	0.910631i
$116$	5.00333			0.464548
$117$	−1.04225	+	1.80523i	−0.0963561	+	0.166894i
$118$	3.55213			0.327000
$119$	2.08921	−	3.61862i	0.191517	−	0.331718i
$120$	3.32651	+	5.76169i	0.303668	+	0.525968i
$121$	0.804900	+	1.39413i	0.0731727	+	0.126739i
$122$	−0.655404	+	1.13519i	−0.0593374	+	0.102775i
$123$	4.38245	−	7.59063i	0.395153	−	0.684424i
$124$	0.318360	+	0.551415i	0.0285895	+	0.0495186i
$125$	11.5198			1.03036
$126$	−0.669326	−	1.15931i	−0.0596283	−	0.103279i
$127$	−5.36951	−	9.30026i	−0.476467	−	0.825265i	0.523170	−	0.852229i	$-0.324749\pi$
$127$	−5.36951	−	9.30026i	−0.476467	−	0.825265i	−0.999636	+	0.0269640i	$0.991416\pi$
$128$	−2.73604			−0.241834
$129$	−2.16544			−0.190657
$130$	5.20047			0.456111
$131$	6.64384	+	11.5075i	0.580475	+	1.00541i	0.995423	+	0.0955675i	$0.0304666\pi$
$131$	6.64384	+	11.5075i	0.580475	+	1.00541i	−0.414948	+	0.909845i	$0.636200\pi$
$132$	1.02154	+	1.76936i	0.0889139	+	0.154003i
$133$	−1.32291	+	2.29135i	−0.114711	+	0.198685i
$134$	3.80741			0.328910
$135$	1.08032	−	1.87116i	0.0929789	−	0.161044i
$136$	−5.54896	+	9.61108i	−0.475819	+	0.824143i
$137$	6.48509	−	11.2325i	0.554059	−	0.959658i	−0.443917	−	0.896068i	$-0.646412\pi$
$137$	6.48509	−	11.2325i	0.554059	−	0.959658i	0.997976	−	0.0635905i	$-0.0202551\pi$
$138$	−3.01306	+	5.21878i	−0.256489	+	0.444252i
$139$	3.47208	+	6.01382i	0.294498	+	0.510086i	0.974868	−	0.222783i	$-0.0715142\pi$
$139$	3.47208	+	6.01382i	0.294498	+	0.510086i	−0.680370	+	0.732869i	$0.738181\pi$
$140$	0.835044	−	1.44634i	0.0705741	−	0.122238i
$141$	−0.0204451			−0.00172179
$142$	−8.69090	−	15.0531i	−0.729324	−	1.26323i
$143$	6.38763			0.534160
$144$	1.11101	+	1.92432i	0.0925839	+	0.160360i
$145$	−8.10702	+	14.0418i	−0.673252	+	1.16611i
$146$	−0.406576	+	0.704211i	−0.0336485	+	0.0582809i
$147$	2.82797	−	4.89819i	0.233247	−	0.403996i
$148$	3.85723	+	6.68092i	0.317062	+	0.549168i
$149$	−13.4575			−1.10248			−0.551242	−	0.834345i	$-0.685846\pi$
$149$	−13.4575			−1.10248			−0.551242	+	0.834345i	$0.685846\pi$
$150$	0.382956			0.0312682
$151$	2.43564	−	4.21865i	0.198209	−	0.343309i	−0.749738	−	0.661734i	$-0.769821\pi$
$151$	2.43564	−	4.21865i	0.198209	−	0.343309i	0.947948	+	0.318425i	$0.103154\pi$
$152$	3.51366	−	6.08584i	0.284996	−	0.493627i
$153$	3.60415			0.291379
$154$	−2.05105	+	3.55251i	−0.165278	+	0.286270i
$155$	−2.06338			−0.165735
$156$	−1.38980			−0.111273
$157$	−10.7012	−	6.51806i	−0.854046	−	0.520198i
$157$	−10.7012	−	6.51806i	−0.854046	−	0.520198i
$158$	8.49653			0.675947
$159$	2.40318			0.190584
$160$	−3.88126	+	6.72254i	−0.306840	+	0.531463i
$161$	6.05045			0.476842
$162$	0.577337	−	0.999977i	0.0453599	−	0.0785656i
$163$	8.25447	−	14.2972i	0.646540	−	1.11984i	−0.337404	−	0.941360i	$-0.609549\pi$
$163$	8.25447	−	14.2972i	0.646540	−	1.11984i	0.983944	−	0.178480i	$-0.0571179\pi$
$164$	5.84382			0.456326
$165$	−6.62093			−0.515438
$166$	−6.96388	−	12.0618i	−0.540502	−	0.936177i
$167$	2.96248	−	5.13117i	0.229244	−	0.397062i	−0.728340	−	0.685216i	$-0.759708\pi$
$167$	2.96248	−	5.13117i	0.229244	−	0.397062i	0.957584	+	0.288153i	$0.0930413\pi$
$168$	1.78491	−	3.09156i	0.137709	−	0.238519i
$169$	4.32743	−	7.49533i	0.332879	−	0.576564i
$170$	−4.49587	−	7.78708i	−0.344818	−	0.597242i
$171$	−2.28219			−0.174523
$172$	−0.721881	−	1.25034i	−0.0550429	−	0.0953372i
$173$	−20.0369			−1.52338			−0.761689	−	0.647942i	$-0.775630\pi$
$173$	−20.0369			−1.52338			−0.761689	+	0.647942i	$0.775630\pi$
$174$	−4.33251	+	7.50412i	−0.328447	+	0.568886i
$175$	−0.192251	−	0.332988i	−0.0145328	−	0.0251716i
$176$	3.40451	−	5.89678i	0.256624	−	0.444487i
$177$	1.53815	−	2.66416i	0.115615	−	0.200250i
$178$	1.87609	−	3.24949i	0.140619	−	0.243559i
$179$	−9.44938	+	16.3668i	−0.706280	+	1.22331i	0.259948	+	0.965623i	$0.416295\pi$
$179$	−9.44938	+	16.3668i	−0.706280	+	1.22331i	−0.966228	+	0.257690i	$0.917039\pi$
$180$	1.44056			0.107373
$181$	−4.23506	+	7.33535i	−0.314790	+	0.545232i	−0.979393	−	0.201965i	$-0.935267\pi$
$181$	−4.23506	+	7.33535i	−0.314790	+	0.545232i	0.664603	+	0.747197i	$0.268601\pi$
$182$	−1.39521	−	2.41658i	−0.103420	−	0.179129i
$183$	0.567609	+	0.983128i	0.0419589	+	0.0726749i
$184$	−16.0701			−1.18470
$185$	−24.9999			−1.83803
$186$	−1.10270			−0.0808540
$187$	−5.52218	−	9.56470i	−0.403822	−	0.699440i
$188$	−0.00681567	−	0.0118051i	−0.000497083	−	0.000860974i
$189$	−1.15933			−0.0843291
$190$	2.84684	+	4.93087i	0.206531	+	0.357723i
$191$	4.90885	−	8.50239i	0.355192	−	0.615211i	−0.631959	−	0.775002i	$-0.717749\pi$
$191$	4.90885	−	8.50239i	0.355192	−	0.615211i	0.987151	+	0.159791i	$0.0510821\pi$
$192$	−4.29621	+	7.44126i	−0.310052	+	0.537027i
$193$	11.4756	+	19.8763i	0.826030	+	1.43073i	0.901129	+	0.433550i	$0.142739\pi$
$193$	11.4756	+	19.8763i	0.826030	+	1.43073i	−0.0750994	+	0.997176i	$0.523927\pi$
$194$	2.68417	+	4.64911i	0.192712	+	0.333787i
$195$	2.25192	−	3.90044i	0.161263	−	0.279317i
$196$	3.77098			0.269356
$197$	9.17294	−	15.8880i	0.653545	−	1.13197i	−0.328711	−	0.944430i	$-0.606614\pi$
$197$	9.17294	−	15.8880i	0.653545	−	1.13197i	0.982256	−	0.187543i	$-0.0600523\pi$
$198$	−3.53832			−0.251457
$199$	−8.85014	+	15.3289i	−0.627370	+	1.08664i	0.360708	+	0.932679i	$0.382535\pi$
$199$	−8.85014	+	15.3289i	−0.627370	+	1.08664i	−0.988077	+	0.153958i	$0.950798\pi$
$200$	0.510620	+	0.884420i	0.0361063	+	0.0625380i
$201$	1.64869	−	2.85562i	0.116290	−	0.201420i
$202$	−2.54136			−0.178809
$203$	8.69999			0.610619
$204$	1.20150	+	2.08105i	0.0841216	+	0.145703i
$205$	−9.46888	+	16.4006i	−0.661335	+	1.14547i
$206$	−6.06546			−0.422600
$207$	2.60945	+	4.51970i	0.181369	+	0.314141i
$208$	2.31590	+	4.01125i	0.160578	+	0.278130i
$209$	3.49671	+	6.05648i	0.241872	+	0.418935i
$210$	1.44617	+	2.50484i	0.0997952	+	0.172850i
$211$	17.7784			1.22391			0.611957	−	0.790891i	$-0.290383\pi$
$211$	17.7784			1.22391			0.611957	+	0.790891i	$0.290383\pi$
$212$	0.801134	+	1.38761i	0.0550221	+	0.0953011i
$213$	−15.0534			−1.03144
$214$	0.378248	+	0.655144i	0.0258565	+	0.0447847i
$215$	4.67873			0.319087
$216$	3.07920			0.209513
$217$	0.553576	+	0.958822i	0.0375792	+	0.0650891i
$218$	−6.53379	+	11.3168i	−0.442524	+	0.766474i
$219$	0.352114	+	0.609879i	0.0237936	+	0.0412118i
$220$	−2.20718	−	3.82295i	−0.148808	−	0.257743i
$221$	7.51286			0.505370
$222$	−13.3603			−0.896683
$223$	−10.2434	−	17.7421i	−0.685948	−	1.18810i	−0.973138	−	0.230224i	$-0.926054\pi$
$223$	−10.2434	−	17.7421i	−0.685948	−	1.18810i	0.287189	−	0.957874i	$-0.407279\pi$
$224$	4.16514			0.278295
$225$	0.165829	−	0.287224i	0.0110553	−	0.0191483i
$226$	−0.225908	+	0.391284i	−0.0150272	+	0.0260278i
$227$	−0.586691	+	1.01618i	−0.0389400	+	0.0674461i	−0.884839	−	0.465898i	$-0.845731\pi$
$227$	−0.586691	+	1.01618i	−0.0389400	+	0.0674461i	0.845899	+	0.533344i	$0.179065\pi$
$228$	−0.760801	−	1.31775i	−0.0503853	−	0.0872699i
$229$	5.15228	+	8.92401i	0.340472	+	0.589716i	0.984520	−	0.175270i	$-0.0560797\pi$
$229$	5.15228	+	8.92401i	0.340472	+	0.589716i	−0.644048	+	0.764985i	$0.722746\pi$
$230$	6.51013	−	11.2759i	0.429265	−	0.743509i
$231$	1.77630	+	3.07664i	0.116872	+	0.202428i
$232$	−23.1072			−1.51706
$233$	−8.07810	+	13.9917i	−0.529214	+	0.916626i	0.470205	+	0.882557i	$0.344180\pi$
$233$	−8.07810	+	13.9917i	−0.529214	+	0.916626i	−0.999419	+	0.0340687i	$0.989153\pi$
$234$	1.20346	−	2.08445i	0.0786726	−	0.136265i
$235$	0.0441744			0.00288162
$236$	2.05106			0.133513
$237$	3.67919	−	6.37254i	0.238989	−	0.413941i
$238$	−2.41235	+	4.17832i	−0.156370	+	0.270840i
$239$	−14.7713			−0.955474			−0.477737	−	0.878503i	$-0.658543\pi$
$239$	−14.7713			−0.955474			−0.477737	+	0.878503i	$0.658543\pi$
$240$	−2.40048	−	4.15775i	−0.154950	−	0.268382i
$241$	1.47877	−	2.56130i	0.0952558	−	0.164988i	−0.814460	−	0.580220i	$-0.802966\pi$
$241$	1.47877	−	2.56130i	0.0952558	−	0.164988i	0.909715	+	0.415232i	$0.136300\pi$
$242$	−0.929397	−	1.60976i	−0.0597439	−	0.103479i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.378442	+	0.655480i	−0.0242272	+	0.0419628i
$245$	−6.11022	+	10.5832i	−0.390367	+	0.676136i
$246$	−5.06030	+	8.76470i	−0.322633	+	0.558817i
$247$	−4.75723			−0.302695
$248$	−1.47030	−	2.54664i	−0.0933644	−	0.161712i
$249$	−12.0621			−0.764403
$250$	−13.3016			−0.841265
$251$	−13.2750	−	22.9929i	−0.837909	−	1.45130i	−0.891640	−	0.452746i	$-0.850445\pi$
$251$	−13.2750	−	22.9929i	−0.837909	−	1.45130i	0.0537308	−	0.998555i	$-0.482889\pi$
$252$	−0.386481	−	0.669404i	−0.0243460	−	0.0421685i
$253$	7.99625	−	13.8499i	0.502720	−	0.870737i
$254$	6.20003	+	10.7388i	0.389024	+	0.673810i
$255$	−7.78726			−0.487657
$256$	−14.0256			−0.876601
$257$	−10.2236	−	17.7079i	−0.637733	−	1.10459i	−0.985929	−	0.167164i	$-0.946539\pi$
$257$	−10.2236	−	17.7079i	−0.637733	−	1.10459i	0.348196	−	0.937422i	$-0.386794\pi$
$258$	2.50038			0.155667
$259$	6.70710	+	11.6170i	0.416759	+	0.721847i
$260$	3.00284			0.186228
$261$	3.75215	+	6.49891i	0.232252	+	0.402273i
$262$	−7.67147	−	13.2874i	−0.473945	−	0.820897i
$263$	−13.1264	−	22.7357i	−0.809411	−	1.40194i	−0.913272	−	0.407349i	$-0.866453\pi$
$263$	−13.1264	−	22.7357i	−0.809411	−	1.40194i	0.103861	−	0.994592i	$-0.466880\pi$
$264$	−4.71787	−	8.17158i	−0.290365	−	0.502926i
$265$	−5.19239			−0.318966
$266$	1.52753	−	2.64576i	0.0936589	−	0.162222i
$267$	−1.62478	−	2.81421i	−0.0994351	−	0.172227i
$268$	2.19846			0.134293
$269$	26.8068			1.63444			0.817221	−	0.576325i	$-0.195514\pi$
$269$	26.8068			1.63444			0.817221	+	0.576325i	$0.195514\pi$
$270$	−1.24741	+	2.16058i	−0.0759152	+	0.131489i
$271$	7.69378	+	13.3260i	0.467364	+	0.809498i	0.999305	−	0.0372833i	$-0.0118704\pi$
$271$	7.69378	+	13.3260i	0.467364	+	0.809498i	−0.531941	+	0.846782i	$0.678537\pi$
$272$	4.00424	−	6.93555i	0.242793	−	0.420529i
$273$	−2.41663			−0.146261
$274$	−7.48817	+	12.9699i	−0.452377	+	0.783539i
$275$	−1.01631			−0.0612860
$276$	−1.73980	+	3.01342i	−0.104723	+	0.181386i
$277$	−10.0014	−	17.3229i	−0.600925	−	1.04083i	−0.992681	−	0.120764i	$-0.961466\pi$
$277$	−10.0014	−	17.3229i	−0.600925	−	1.04083i	0.391756	−	0.920069i	$-0.371868\pi$
$278$	−4.00912	−	6.94400i	−0.240451	−	0.416474i
$279$	−0.477495	+	0.827046i	−0.0285869	+	0.0495139i
$280$	−3.85654	+	6.67973i	−0.230472	+	0.399190i
$281$	−0.998161	−	1.72887i	−0.0595453	−	0.103136i	0.834716	−	0.550681i	$-0.185632\pi$
$281$	−0.998161	−	1.72887i	−0.0595453	−	0.103136i	−0.894261	+	0.447545i	$0.852298\pi$
$282$	0.0236074			0.00140580
$283$	−0.746925	−	1.29371i	−0.0444001	−	0.0769032i	0.842971	−	0.537959i	$-0.180804\pi$
$283$	−0.746925	−	1.29371i	−0.0444001	−	0.0769032i	−0.887371	+	0.461055i	$0.847471\pi$
$284$	−5.01828	−	8.69192i	−0.297780	−	0.515770i
$285$	4.93098			0.292086
$286$	−7.37562			−0.436130
$287$	10.1615			0.599812
$288$	1.79635	+	3.11137i	0.105851	+	0.183339i
$289$	2.00504	+	3.47283i	0.117943	+	0.204284i
$290$	9.36097	−	16.2137i	0.549695	−	0.952099i
$291$	4.64922			0.272542
$292$	−0.234764	+	0.406624i	−0.0137385	+	0.0237959i
$293$	−2.97078	+	5.14555i	−0.173555	+	0.300606i	−0.939660	−	0.342109i	$-0.888859\pi$
$293$	−2.97078	+	5.14555i	−0.173555	+	0.300606i	0.766105	+	0.642715i	$0.222192\pi$
$294$	−3.26538	+	5.65581i	−0.190441	+	0.329854i
$295$	−3.32338	+	5.75627i	−0.193495	+	0.335143i
$296$	−17.8141	−	30.8549i	−1.03542	−	1.79341i
$297$	−1.53217	+	2.65380i	−0.0889056	+	0.153989i
$298$	15.5391			0.900153
$299$	5.43940	+	9.42132i	0.314569	+	0.544849i
$300$	0.221126			0.0127667
$301$	−1.25524	−	2.17413i	−0.0723506	−	0.125315i
$302$	−2.81237	+	4.87116i	−0.161834	+	0.280304i
$303$	−1.10046	+	1.90606i	−0.0632200	+	0.109500i
$304$	−2.53553	+	4.39167i	−0.145423	+	0.251879i
$305$	−1.22640	−	2.12418i	−0.0702233	−	0.121630i
$306$	−4.16162			−0.237904
$307$	6.93201			0.395631			0.197815	−	0.980239i	$-0.436615\pi$
$307$	6.93201			0.395631			0.197815	+	0.980239i	$0.436615\pi$
$308$	−1.18431	+	2.05128i	−0.0674823	+	0.116883i
$309$	−2.62648	+	4.54920i	−0.149415	+	0.258795i
$310$	2.38254			0.135319
$311$	−17.4314	+	30.1921i	−0.988444	+	1.71204i	−0.362945	+	0.931811i	$0.618229\pi$
$311$	−17.4314	+	30.1921i	−0.988444	+	1.71204i	−0.625499	+	0.780225i	$0.715105\pi$
$312$	6.41860			0.363382
$313$	3.40634			0.192538			0.0962688	−	0.995355i	$-0.469309\pi$
$313$	3.40634			0.192538			0.0962688	+	0.995355i	$0.469309\pi$
$314$	12.3564	+	7.52623i	0.697309	+	0.424730i
$315$	2.50490			0.141135
$316$	4.90605			0.275987
$317$	11.2447	−	19.4764i	0.631565	−	1.09390i	−0.355667	−	0.934613i	$-0.615746\pi$
$317$	11.2447	−	19.4764i	0.631565	−	1.09390i	0.987232	−	0.159290i	$-0.0509205\pi$
$318$	−2.77489			−0.155608
$319$	11.4979	−	19.9149i	0.643757	−	1.11502i
$320$	9.28255	−	16.0778i	0.518910	−	0.898779i
$321$	0.655159			0.0365674
$322$	−6.98630			−0.389331
$323$	4.11268	+	7.12338i	0.228836	+	0.396355i
$324$	0.333364	−	0.577404i	0.0185202	−	0.0320780i
$325$	0.345670	−	0.598718i	0.0191743	−	0.0332109i
$326$	−9.53122	+	16.5085i	−0.527885	+	0.914324i
$327$	5.65856	+	9.80091i	0.312919	+	0.541991i
$328$	−26.9889			−1.49021
$329$	−0.0118513	−	0.0205271i	−0.000653386	−	0.00113170i
$330$	7.64501			0.420844
$331$	−7.76175	+	13.4437i	−0.426624	+	0.738935i	−0.996571	−	0.0827469i	$-0.973631\pi$
$331$	−7.76175	+	13.4437i	−0.426624	+	0.738935i	0.569946	+	0.821682i	$0.306964\pi$
$332$	−4.02107	−	6.96470i	−0.220685	−	0.382237i
$333$	−5.78530	+	10.0204i	−0.317033	+	0.549117i
$334$	−3.42070	+	5.92483i	−0.187173	+	0.324192i
$335$	−3.56223	+	6.16996i	−0.194625	+	0.337101i
$336$	−1.28803	+	2.23093i	−0.0702677	+	0.121707i
$337$	26.2630			1.43064			0.715318	−	0.698799i	$-0.246282\pi$
$337$	26.2630			1.43064			0.715318	+	0.698799i	$0.246282\pi$
$338$	−4.99677	+	8.65466i	−0.271788	+	0.470751i
$339$	0.195647	+	0.338870i	0.0106261	+	0.0184049i
$340$	−2.59600	−	4.49640i	−0.140788	−	0.243851i
$341$	2.92642			0.158474
$342$	2.63519			0.142494
$343$	14.6725			0.792239
$344$	3.33392	+	5.77451i	0.179753	+	0.311341i
$345$	−5.63807	−	9.76542i	−0.303544	−	0.525753i
$346$	23.1361			1.24380
$347$	11.4769	+	19.8786i	0.616113	+	1.06714i	0.990188	+	0.139741i	$0.0446269\pi$
$347$	11.4769	+	19.8786i	0.616113	+	1.06714i	−0.374075	+	0.927398i	$0.622040\pi$
$348$	−2.50167	+	4.33301i	−0.134103	+	0.232274i
$349$	0.450642	−	0.780534i	0.0241223	−	0.0417811i	−0.853712	−	0.520745i	$-0.825654\pi$
$349$	0.450642	−	0.780534i	0.0241223	−	0.0417811i	0.877835	+	0.478964i	$0.158988\pi$
$350$	0.221987	+	0.384493i	0.0118657	+	0.0205520i
$351$	−1.04225	−	1.80523i	−0.0556312	−	0.0963561i
$352$	5.50464	−	9.53431i	0.293398	−	0.508180i
$353$	19.3838			1.03170			0.515849	−	0.856679i	$-0.327477\pi$
$353$	19.3838			1.03170			0.515849	+	0.856679i	$0.327477\pi$
$354$	−1.77606	+	3.07623i	−0.0943967	+	0.163500i
$355$	32.5250			1.72625
$356$	1.08329	−	1.87631i	0.0574142	−	0.0994444i
$357$	2.08921	+	3.61862i	0.110573	+	0.191517i
$358$	10.9109	−	18.8983i	0.576662	−	0.998807i
$359$	4.94140			0.260797			0.130399	−	0.991462i	$-0.458374\pi$
$359$	4.94140			0.260797			0.130399	+	0.991462i	$0.458374\pi$
$360$	−6.65303			−0.350645
$361$	6.89580	+	11.9439i	0.362937	+	0.628625i
$362$	4.89012	−	8.46993i	0.257019	−	0.445170i
$363$	−1.60980			−0.0844926
$364$	−0.805619	−	1.39537i	−0.0422259	−	0.0731375i
$365$	−0.760789	−	1.31773i	−0.0398215	−	0.0689729i
$366$	−0.655404	−	1.13519i	−0.0342585	−	0.0593374i
$367$	−12.6925	−	21.9841i	−0.662545	−	1.14756i	−0.979945	−	0.199270i	$-0.936143\pi$
$367$	−12.6925	−	21.9841i	−0.662545	−	1.14756i	0.317400	−	0.948292i	$-0.397190\pi$
$368$	11.5965			0.604508
$369$	4.38245	+	7.59063i	0.228141	+	0.395153i
$370$	28.8667			1.50071
$371$	1.39304	+	2.41282i	0.0723232	+	0.125267i
$372$	−0.636720			−0.0330124
$373$	0.454237			0.0235195			0.0117597	−	0.999931i	$-0.496257\pi$
$373$	0.454237			0.0235195			0.0117597	+	0.999931i	$0.496257\pi$
$374$	6.37632	+	11.0441i	0.329712	+	0.571077i
$375$	−5.75988	+	9.97641i	−0.297439	+	0.515180i
$376$	0.0314773	+	0.0545202i	0.00162332	+	0.00281167i
$377$	7.82136	+	13.5470i	0.402820	+	0.697705i
$378$	1.33865			0.0688528
$379$	5.09765			0.261849			0.130924	−	0.991392i	$-0.458206\pi$
$379$	5.09765			0.261849			0.130924	+	0.991392i	$0.458206\pi$
$380$	1.64381	+	2.84717i	0.0843259	+	0.146057i
$381$	10.7390			0.550176
$382$	−5.66812	+	9.81748i	−0.290006	+	0.502306i
$383$	11.2436	−	19.4745i	0.574521	−	0.995099i	−0.421573	−	0.906795i	$-0.638522\pi$
$383$	11.2436	−	19.4745i	0.574521	−	0.995099i	0.996094	−	0.0883046i	$-0.0281449\pi$
$384$	1.36802	−	2.36948i	0.0698116	−	0.120917i
$385$	−3.83793	−	6.64749i	−0.195599	−	0.338788i
$386$	−13.2505	−	22.9506i	−0.674435	−	1.16816i
$387$	1.08272	−	1.87533i	0.0550378	−	0.0953283i
$388$	1.54988	+	2.68448i	0.0786835	+	0.136284i
$389$	−3.02352			−0.153299			−0.0766493	−	0.997058i	$-0.524422\pi$
$389$	−3.02352			−0.153299			−0.0766493	+	0.997058i	$0.524422\pi$
$390$	−2.60024	+	4.50374i	−0.131668	+	0.228056i
$391$	9.40486	−	16.2897i	0.475624	−	0.823805i
$392$	−17.4158			−0.879630
$393$	−13.2877			−0.670275
$394$	−10.5918	+	18.3455i	−0.533605	+	0.924231i
$395$	−7.94939	+	13.7687i	−0.399977	+	0.692781i
$396$	−2.04309			−0.102669
$397$	3.51003	+	6.07954i	0.176163	+	0.305123i	0.940563	−	0.339619i	$-0.110298\pi$
$397$	3.51003	+	6.07954i	0.176163	+	0.305123i	−0.764400	+	0.644742i	$0.776965\pi$
$398$	10.2190	−	17.6999i	0.512233	−	0.887214i
$399$	−1.32291	−	2.29135i	−0.0662284	−	0.114711i
$400$	−0.368474	−	0.638216i	−0.0184237	−	0.0319108i
$401$	2.94401	−	5.09918i	0.147017	−	0.254641i	−0.783107	−	0.621887i	$-0.786366\pi$
$401$	2.94401	−	5.09918i	0.147017	−	0.254641i	0.930124	+	0.367247i	$0.119699\pi$
$402$	−1.90370	+	3.29731i	−0.0949481	+	0.164455i
$403$	−0.995339	+	1.72398i	−0.0495813	+	0.0858774i
$404$	−1.46742			−0.0730070
$405$	1.08032	+	1.87116i	0.0536814	+	0.0929789i
$406$	−10.0456			−0.498557
$407$	35.4563			1.75750
$408$	−5.54896	−	9.61108i	−0.274714	−	0.475819i
$409$	−10.9443	−	18.9561i	−0.541160	−	0.937316i	−0.998838	−	0.0481983i	$-0.984652\pi$
$409$	−10.9443	−	18.9561i	−0.541160	−	0.937316i	0.457678	−	0.889118i	$-0.348681\pi$
$410$	10.9335	−	18.9373i	0.539966	−	0.935248i
$411$	6.48509	+	11.2325i	0.319886	+	0.554059i
$412$	−3.50230			−0.172546
$413$	3.56646			0.175494
$414$	−3.01306	−	5.21878i	−0.148084	−	0.256489i
$415$	26.0618			1.27932
$416$	3.74449	+	6.48565i	0.183589	+	0.317985i
$417$	−6.94416			−0.340057
$418$	−4.03756	−	6.99325i	−0.197483	−	0.342051i
$419$	5.51691	+	9.55557i	0.269519	+	0.466820i	0.968738	−	0.248088i	$-0.0798021\pi$
$419$	5.51691	+	9.55557i	0.269519	+	0.466820i	−0.699219	+	0.714908i	$0.746469\pi$
$420$	0.835044	+	1.44634i	0.0407460	+	0.0705741i
$421$	7.06517	+	12.2372i	0.344335	+	0.596407i	0.985233	−	0.171220i	$-0.0547709\pi$
$421$	7.06517	+	12.2372i	0.344335	+	0.596407i	−0.640897	+	0.767627i	$0.721438\pi$
$422$	−20.5282			−0.999298
$423$	0.0102225	−	0.0177060i	0.000497037	−	0.000860893i
$424$	−3.69993	−	6.40848i	−0.179685	−	0.311223i
$425$	−1.19534			−0.0579827
$426$	17.3818			0.842151
$427$	−0.658049	+	1.13977i	−0.0318452	+	0.0551575i
$428$	0.218407	+	0.378292i	0.0105571	+	0.0182854i
$429$	−3.19381	+	5.53185i	−0.154199	+	0.267080i
$430$	−5.40240			−0.260527
$431$	−6.31708	+	10.9415i	−0.304283	+	0.527033i	−0.977101	−	0.212774i	$-0.931750\pi$
$431$	−6.31708	+	10.9415i	−0.304283	+	0.527033i	0.672819	+	0.739808i	$0.265083\pi$
$432$	−2.22201			−0.106907
$433$	−10.7632	+	18.6424i	−0.517247	+	0.895898i	0.482552	+	0.875867i	$0.339710\pi$
$433$	−10.7632	+	18.6424i	−0.517247	+	0.895898i	−0.999799	+	0.0200310i	$0.993624\pi$
$434$	−0.639200	−	1.10713i	−0.0306826	−	0.0531438i
$435$	−8.10702	−	14.0418i	−0.388702	−	0.673252i
$436$	−3.77272	+	6.53455i	−0.180681	+	0.312948i
$437$	−5.95526	+	10.3148i	−0.284879	+	0.493425i
$438$	−0.406576	−	0.704211i	−0.0194270	−	0.0336485i
$439$	15.3347			0.731883			0.365942	−	0.930638i	$-0.380747\pi$
$439$	15.3347			0.731883			0.365942	+	0.930638i	$0.380747\pi$
$440$	10.1936	+	17.6558i	0.485960	+	0.841707i
$441$	2.82797	+	4.89819i	0.134665	+	0.233247i
$442$	−8.67490			−0.412623
$443$	−6.41723			−0.304892			−0.152446	−	0.988312i	$-0.548715\pi$
$443$	−6.41723			−0.304892			−0.152446	+	0.988312i	$0.548715\pi$
$444$	−7.71446			−0.366112
$445$	3.51056	+	6.08047i	0.166417	+	0.288242i
$446$	11.8278	+	20.4863i	0.560061	+	0.970055i
$447$	6.72877	−	11.6546i	0.318260	−	0.551242i
$448$	−9.96149			−0.470636
$449$	−3.20000	+	5.54257i	−0.151017	+	0.261570i	−0.931602	−	0.363481i	$-0.881588\pi$
$449$	−3.20000	+	5.54257i	−0.151017	+	0.261570i	0.780584	+	0.625050i	$0.214922\pi$
$450$	−0.191478	+	0.331650i	−0.00902637	+	0.0156341i
$451$	13.4293	−	23.2603i	0.632363	−	1.09529i
$452$	−0.130443	+	0.225934i	−0.00613553	+	0.0106271i
$453$	2.43564	+	4.21865i	0.114436	+	0.198209i
$454$	0.677436	−	1.17335i	0.0317936	−	0.0550682i
$455$	5.22146			0.244786
$456$	3.51366	+	6.08584i	0.164542	+	0.284996i
$457$	−40.4776			−1.89346			−0.946731	−	0.322025i	$-0.895636\pi$
$457$	−40.4776			−1.89346			−0.946731	+	0.322025i	$0.895636\pi$
$458$	−5.94920	−	10.3043i	−0.277988	−	0.481489i
$459$	−1.80208	+	3.12129i	−0.0841137	+	0.145689i
$460$	3.75906	−	6.51089i	0.175267	−	0.303572i
$461$	0.621382	−	1.07627i	0.0289407	−	0.0501267i	−0.851192	−	0.524854i	$-0.824120\pi$
$461$	0.621382	−	1.07627i	0.0289407	−	0.0501267i	0.880133	+	0.474727i	$0.157453\pi$
$462$	−2.05105	−	3.55251i	−0.0954233	−	0.165278i
$463$	−11.8382			−0.550167			−0.275083	−	0.961420i	$-0.588705\pi$
$463$	−11.8382			−0.550167			−0.275083	+	0.961420i	$0.588705\pi$
$464$	16.6747			0.774102
$465$	1.03169	−	1.78694i	0.0478436	−	0.0828675i
$466$	9.32757	−	16.1558i	0.432091	−	0.748404i
$467$	5.50708			0.254837			0.127419	−	0.991849i	$-0.459331\pi$
$467$	5.50708			0.254837			0.127419	+	0.991849i	$0.459331\pi$
$468$	0.694898	−	1.20360i	0.0321217	−	0.0556364i
$469$	3.82278			0.176519
$470$	−0.0510070			−0.00235278
$471$	10.9954	−	6.00845i	0.506641	−	0.276855i
$472$	−9.47256			−0.436010
$473$	−6.63566			−0.305108
$474$	−4.24826	+	7.35821i	−0.195129	+	0.337974i
$475$	0.756906			0.0347292
$476$	−1.39294	+	2.41264i	−0.0638451	+	0.110583i
$477$	−1.20159	+	2.08121i	−0.0550170	+	0.0952922i
$478$	17.0560			0.780123
$479$	16.7113			0.763558			0.381779	−	0.924254i	$-0.375312\pi$
$479$	16.7113			0.763558			0.381779	+	0.924254i	$0.375312\pi$
$480$	−3.88126	−	6.72254i	−0.177154	−	0.306840i
$481$	−12.0595	+	20.8876i	−0.549864	+	0.952393i
$482$	−1.70749	+	2.95747i	−0.0777742	+	0.134709i
$483$	−3.02523	+	5.23984i	−0.137653	+	0.238421i
$484$	−0.536650	−	0.929505i	−0.0243932	−	0.0422502i
$485$	−10.0453			−0.456132
$486$	0.577337	+	0.999977i	0.0261885	+	0.0453599i
$487$	−42.7287			−1.93622			−0.968112	−	0.250519i	$-0.919399\pi$
$487$	−42.7287			−1.93622			−0.968112	+	0.250519i	$0.919399\pi$
$488$	1.74778	−	3.02725i	0.0791184	−	0.137037i
$489$	8.25447	+	14.2972i	0.373280	+	0.646540i
$490$	7.05530	−	12.2201i	0.318726	−	0.552050i
$491$	−14.1674	+	24.5387i	−0.639366	+	1.10741i	0.346206	+	0.938159i	$0.387470\pi$
$491$	−14.1674	+	24.5387i	−0.639366	+	1.10741i	−0.985572	+	0.169256i	$0.945863\pi$
$492$	−2.92191	+	5.06090i	−0.131730	+	0.228163i
$493$	13.5233	−	23.4231i	0.609060	−	1.05492i
$494$	5.49305			0.247144
$495$	3.31046	−	5.73389i	0.148794	−	0.257719i
$496$	1.06100	+	1.83771i	0.0476403	+	0.0825155i
$497$	−8.72598	−	15.1138i	−0.391414	−	0.677948i
$498$	13.9278			0.624118
$499$	9.15503			0.409835			0.204918	−	0.978779i	$-0.434307\pi$
$499$	9.15503			0.409835			0.204918	+	0.978779i	$0.434307\pi$
$500$	−7.68056			−0.343485
$501$	2.96248	+	5.13117i	0.132354	+	0.229244i
$502$	15.3283	+	26.5493i	0.684134	+	1.18495i
$503$	10.6258			0.473781			0.236891	−	0.971536i	$-0.423872\pi$
$503$	10.6258			0.473781			0.236891	+	0.971536i	$0.423872\pi$
$504$	1.78491	+	3.09156i	0.0795063	+	0.137709i
$505$	2.37770	−	4.11830i	0.105806	−	0.183262i
$506$	−9.23306	+	15.9921i	−0.410460	+	0.710937i
$507$	4.32743	+	7.49533i	0.192188	+	0.332879i
$508$	3.58001	+	6.20075i	0.158837	+	0.275114i
$509$	17.0667	−	29.5604i	0.756469	−	1.31024i	−0.188172	−	0.982136i	$-0.560256\pi$
$509$	17.0667	−	29.5604i	0.756469	−	1.31024i	0.944641	−	0.328106i	$-0.106410\pi$
$510$	8.99174			0.398161
$511$	−0.408217	+	0.707053i	−0.0180585	+	0.0312782i
$512$	21.6671			0.957559
$513$	1.14110	−	1.97644i	0.0503806	−	0.0872617i
$514$	11.8050	+	20.4468i	0.520694	+	0.901869i
$515$	5.67487	−	9.82916i	0.250065	−	0.433124i
$516$	1.44376			0.0635581
$517$	−0.0626508			−0.00275538
$518$	−7.74451	−	13.4139i	−0.340274	−	0.589372i
$519$	10.0185	−	17.3525i	0.439762	−	0.761689i
$520$	−13.8682			−0.608163
$521$	−6.46458	−	11.1970i	−0.283219	−	0.490549i	0.688957	−	0.724802i	$-0.258069\pi$
$521$	−6.46458	−	11.1970i	−0.283219	−	0.490549i	−0.972176	+	0.234253i	$0.924736\pi$
$522$	−4.33251	−	7.50412i	−0.189629	−	0.328447i
$523$	1.15248	+	1.99615i	0.0503943	+	0.0872854i	0.890122	−	0.455722i	$-0.150619\pi$
$523$	1.15248	+	1.99615i	0.0503943	+	0.0872854i	−0.839728	+	0.543007i	$0.817286\pi$
$524$	−4.42964	−	7.67237i	−0.193510	−	0.335169i
$525$	0.384502			0.0167810
$526$	15.1568	+	26.2523i	0.660866	+	1.14465i
$527$	3.44193			0.149933
$528$	3.40451	+	5.89678i	0.148162	+	0.256624i
$529$	4.23694			0.184215
$530$	5.99552			0.260429
$531$	1.53815	+	2.66416i	0.0667501	+	0.115615i
$532$	0.882023	−	1.52771i	0.0382405	−	0.0662346i
$533$	9.13523	+	15.8227i	0.395691	+	0.685356i
$534$	1.87609	+	3.24949i	0.0811865	+	0.140619i
$535$	−1.41556			−0.0612000
$536$	−10.1533			−0.438557
$537$	−9.44938	−	16.3668i	−0.407771	−	0.706280i
$538$	−30.9531			−1.33448
$539$	8.66588	−	15.0097i	0.373266	−	0.646515i
$540$	−0.720279	+	1.24756i	−0.0309959	+	0.0536864i
$541$	−21.1462	+	36.6263i	−0.909145	+	1.57469i	−0.0938914	+	0.995582i	$0.529931\pi$
$541$	−21.1462	+	36.6263i	−0.909145	+	1.57469i	−0.815254	+	0.579104i	$0.803403\pi$
$542$	−8.88381	−	15.3872i	−0.381592	−	0.660937i
$543$	−4.23506	−	7.33535i	−0.181744	−	0.314790i
$544$	6.47432	−	11.2139i	0.277584	−	0.480790i
$545$	−12.2261	−	21.1762i	−0.523707	−	0.907088i
$546$	2.79042			0.119419
$547$	2.36658	−	4.09903i	0.101187	−	0.175262i	−0.810987	−	0.585065i	$-0.801069\pi$
$547$	2.36658	−	4.09903i	0.101187	−	0.175262i	0.912174	+	0.409803i	$0.134402\pi$
$548$	−4.32380	+	7.48904i	−0.184704	+	0.319916i
$549$	−1.13522			−0.0484500
$550$	1.17351			0.0500386
$551$	−8.56312	+	14.8318i	−0.364801	+	0.631854i
$552$	8.03503	−	13.9171i	0.341993	−	0.592350i
$553$	8.53082			0.362767
$554$	11.5483	+	20.0023i	0.490642	+	0.849817i
$555$	12.4999	−	21.6505i	0.530592	−	0.919013i
$556$	−2.31494	−	4.00959i	−0.0981752	−	0.170044i
$557$	2.92470	+	5.06572i	0.123923	+	0.214641i	0.921312	−	0.388825i	$-0.127119\pi$
$557$	2.92470	+	5.06572i	0.123923	+	0.214641i	−0.797388	+	0.603467i	$0.793786\pi$
$558$	0.551351	−	0.954968i	0.0233405	−	0.0404270i
$559$	2.25693	−	3.90912i	0.0954581	−	0.165338i
$560$	2.78296	−	4.82023i	0.117601	−	0.203692i
$561$	11.0444			0.466293
$562$	1.15255	+	1.99628i	0.0486174	+	0.0842078i
$563$	−26.3152			−1.10906			−0.554528	−	0.832165i	$-0.687101\pi$
$563$	−26.3152			−1.10906			−0.554528	+	0.832165i	$0.687101\pi$
$564$	0.0136313			0.000573983
$565$	−0.422721	−	0.732174i	−0.0177840	−	0.0308028i
$566$	0.862455	+	1.49382i	0.0362517	+	0.0627897i
$567$	0.579667	−	1.00401i	0.0243437	−	0.0421646i
$568$	23.1763	+	40.1425i	0.972455	+	1.68434i
$569$	−17.5166			−0.734334			−0.367167	−	0.930155i	$-0.619672\pi$
$569$	−17.5166			−0.734334			−0.367167	+	0.930155i	$0.619672\pi$
$570$	−5.69367			−0.238482
$571$	−4.31470	−	7.47329i	−0.180565	−	0.312747i	0.761508	−	0.648155i	$-0.224459\pi$
$571$	−4.31470	−	7.47329i	−0.180565	−	0.312747i	−0.942073	+	0.335408i	$0.891126\pi$
$572$	−4.25881			−0.178070
$573$	4.90885	+	8.50239i	0.205070	+	0.355192i
$574$	−11.7332			−0.489733
$575$	−0.865444	−	1.49899i	−0.0360915	−	0.0625123i
$576$	−4.29621	−	7.44126i	−0.179009	−	0.310052i
$577$	−20.7164	−	35.8818i	−0.862433	−	1.49378i	−0.869574	−	0.493803i	$-0.835606\pi$
$577$	−20.7164	−	35.8818i	−0.862433	−	1.49378i	0.00714075	−	0.999975i	$-0.497727\pi$
$578$	−2.31517	−	4.00998i	−0.0962982	−	0.166793i
$579$	−22.9512			−0.953817
$580$	5.40519	−	9.36206i	0.224438	−	0.388738i
$581$	−6.99199	−	12.1105i	−0.290077	−	0.502428i
$582$	−5.36833			−0.222524
$583$	7.36416			0.304992
$584$	1.08423	−	1.87794i	0.0448657	−	0.0777097i
$585$	2.25192	+	3.90044i	0.0931055	+	0.161263i
$586$	3.43028	−	5.94143i	0.141704	−	0.245438i
$587$	−21.9961			−0.907878			−0.453939	−	0.891033i	$-0.649982\pi$
$587$	−21.9961			−0.907878			−0.453939	+	0.891033i	$0.649982\pi$
$588$	−1.88549	+	3.26577i	−0.0777563	+	0.134678i
$589$	−2.17947			−0.0898035
$590$	3.83742	−	6.64661i	0.157984	−	0.273637i
$591$	9.17294	+	15.8880i	0.377324	+	0.653545i
$592$	12.8550	+	22.2656i	0.528338	+	0.915109i
$593$	−11.2603	+	19.5034i	−0.462405	+	0.800908i	−0.999080	−	0.0428804i	$-0.986347\pi$
$593$	−11.2603	+	19.5034i	−0.462405	+	0.800908i	0.536676	+	0.843789i	$0.319680\pi$
$594$	1.76916	−	3.06427i	0.0725894	−	0.125729i
$595$	−4.51402	−	7.81851i	−0.185057	−	0.320528i
$596$	8.97253			0.367529
$597$	−8.85014	−	15.3289i	−0.362212	−	0.627370i
$598$	−6.28073	−	10.8785i	−0.256838	−	0.444857i
$599$	−7.15479			−0.292337			−0.146168	−	0.989260i	$-0.546694\pi$
$599$	−7.15479			−0.292337			−0.146168	+	0.989260i	$0.546694\pi$
$600$	−1.02124			−0.0416920
$601$	−32.0406			−1.30696			−0.653482	−	0.756942i	$-0.726692\pi$
$601$	−32.0406			−1.30696			−0.653482	+	0.756942i	$0.726692\pi$
$602$	1.44939	+	2.51041i	0.0590726	+	0.102317i
$603$	1.64869	+	2.85562i	0.0671400	+	0.116290i
$604$	−1.62391	+	2.81270i	−0.0660760	+	0.114447i
$605$	3.47819			0.141409
$606$	1.27068	−	2.20088i	0.0516177	−	0.0894046i
$607$	−16.9875	+	29.4231i	−0.689499	+	1.19425i	0.282501	+	0.959267i	$0.408836\pi$
$607$	−16.9875	+	29.4231i	−0.689499	+	1.19425i	−0.972000	+	0.234981i	$0.924497\pi$
$608$	−4.09961	+	7.10074i	−0.166261	+	0.287973i
$609$	−4.34999	+	7.53441i	−0.176271	+	0.305310i
$610$	1.41609	+	2.45274i	0.0573357	+	0.0993084i
$611$	0.0213089	−	0.0369081i	0.000862066	−	0.00149314i
$612$	−2.40299			−0.0971353
$613$	0.658614	+	1.14075i	0.0266012	+	0.0460745i	0.879020	−	0.476786i	$-0.158198\pi$
$613$	0.658614	+	1.14075i	0.0266012	+	0.0460745i	−0.852418	+	0.522860i	$0.824865\pi$
$614$	−8.00421			−0.323024
$615$	−9.46888	−	16.4006i	−0.381822	−	0.661335i
$616$	5.46958	−	9.47359i	0.220376	−	0.381702i
$617$	−20.4384	+	35.4003i	−0.822818	+	1.42516i	0.0807577	+	0.996734i	$0.474266\pi$
$617$	−20.4384	+	35.4003i	−0.822818	+	1.42516i	−0.903576	+	0.428429i	$0.859067\pi$
$618$	3.03273	−	5.25284i	0.121994	−	0.211300i
$619$	2.15614	+	3.73454i	0.0866625	+	0.150104i	0.906098	−	0.423067i	$-0.139046\pi$
$619$	2.15614	+	3.73454i	0.0866625	+	0.150104i	−0.819436	+	0.573171i	$0.805713\pi$
$620$	1.37572			0.0552502
$621$	−5.21890			−0.209427
$622$	20.1276	−	34.8620i	0.807042	−	1.39784i
$623$	1.88367	−	3.26260i	0.0754675	−	0.130713i
$624$	−4.63179			−0.185420
$625$	11.6159	−	20.1193i	0.464634	−	0.804770i
$626$	−3.93321			−0.157203
$627$	−6.99342			−0.279290
$628$	7.13478	+	4.34578i	0.284709	+	0.173415i
$629$	41.7022			1.66278
$630$	−2.89234			−0.115234
$631$	21.5819	−	37.3809i	0.859161	−	1.48811i	−0.0135695	−	0.999908i	$-0.504319\pi$
$631$	21.5819	−	37.3809i	0.859161	−	1.48811i	0.872730	−	0.488202i	$-0.162347\pi$
$632$	−22.6579			−0.901284
$633$	−8.88919	+	15.3965i	−0.353314	+	0.611957i
$634$	−12.9840	+	22.4889i	−0.515659	+	0.893147i
$635$	−23.2031			−0.920786
$636$	−1.60227			−0.0635341
$637$	5.89491	+	10.2103i	0.233565	+	0.404546i
$638$	−13.2763	+	22.9952i	−0.525613	+	0.910389i
$639$	7.52672	−	13.0367i	0.297752	−	0.515722i
$640$	−2.95580	+	5.11959i	−0.116838	+	0.202370i
$641$	−7.82353	−	13.5507i	−0.309011	−	0.535222i	0.669136	−	0.743140i	$-0.266665\pi$
$641$	−7.82353	−	13.5507i	−0.309011	−	0.535222i	−0.978146	+	0.207918i	$0.933331\pi$
$642$	−0.756495			−0.0298565
$643$	18.0707	+	31.2993i	0.712638	+	1.23433i	0.963863	+	0.266397i	$0.0858332\pi$
$643$	18.0707	+	31.2993i	0.712638	+	1.23433i	−0.251225	+	0.967929i	$0.580833\pi$
$644$	−4.03401			−0.158962
$645$	−2.33936	+	4.05190i	−0.0921124	+	0.159543i
$646$	−4.74881	−	8.22517i	−0.186839	−	0.323615i
$647$	6.58022	−	11.3973i	0.258695	−	0.448073i	−0.707198	−	0.707016i	$-0.750041\pi$
$647$	6.58022	−	11.3973i	0.258695	−	0.448073i	0.965893	+	0.258943i	$0.0833742\pi$
$648$	−1.53960	+	2.66667i	−0.0604812	+	0.104757i
$649$	4.71342	−	8.16389i	0.185018	−	0.320461i
$650$	−0.399136	+	0.691324i	−0.0156554	+	0.0271160i
$651$	−1.10715			−0.0433927
$652$	−5.50349	+	9.53233i	−0.215533	+	0.373315i
$653$	11.3672	+	19.6885i	0.444831	+	0.770470i	0.998040	−	0.0625724i	$-0.0199304\pi$
$653$	11.3672	+	19.6885i	0.444831	+	0.770470i	−0.553209	+	0.833042i	$0.686597\pi$
$654$	−6.53379	−	11.3168i	−0.255491	−	0.442524i
$655$	28.7098			1.12179
$656$	19.4758			0.760400
$657$	−0.704227			−0.0274745
$658$	0.0136844	+	0.0237021i	0.000533475	+	0.000924005i
$659$	−24.3779	−	42.2237i	−0.949627	−	1.64480i	−0.746211	−	0.665709i	$-0.768129\pi$
$659$	−24.3779	−	42.2237i	−0.949627	−	1.64480i	−0.203415	−	0.979093i	$-0.565204\pi$
$660$	4.41436			0.171829
$661$	−16.3308	−	28.2858i	−0.635195	−	1.10019i	−0.986474	−	0.163919i	$-0.947587\pi$
$661$	−16.3308	−	28.2858i	−0.635195	−	1.10019i	0.351279	−	0.936271i	$-0.385747\pi$
$662$	8.96229	−	15.5231i	0.348329	−	0.603324i
$663$	−3.75643	+	6.50633i	−0.145888	+	0.252685i
$664$	18.5708	+	32.1656i	0.720686	+	1.24827i
$665$	2.85833	+	4.95077i	0.110841	+	0.191983i
$666$	6.68014	−	11.5703i	0.258850	−	0.448341i
$667$	39.1642			1.51644
$668$	−1.97517	+	3.42110i	−0.0764218	+	0.132366i
$669$	20.4868			0.792065
$670$	4.11321	−	7.12429i	0.158907	−	0.275235i
$671$	1.73935	+	3.01264i	0.0671469	+	0.116302i
$672$	−2.08257	+	3.60712i	−0.0803369	+	0.139148i
$673$	−3.36007			−0.129521			−0.0647606	−	0.997901i	$-0.520628\pi$
$673$	−3.36007			−0.129521			−0.0647606	+	0.997901i	$0.520628\pi$
$674$	−30.3252			−1.16808
$675$	0.165829	+	0.287224i	0.00638275	+	0.0110553i
$676$	−2.88522	+	4.99735i	−0.110970	+	0.192206i
$677$	0.802025			0.0308243			0.0154122	−	0.999881i	$-0.495094\pi$
$677$	0.802025			0.0308243			0.0154122	+	0.999881i	$0.495094\pi$
$678$	−0.225908	−	0.391284i	−0.00867594	−	0.0150272i
$679$	2.69500	+	4.66788i	0.103425	+	0.179137i
$680$	11.9893	+	20.7660i	0.459767	+	0.796341i
$681$	−0.586691	−	1.01618i	−0.0224820	−	0.0389400i
$682$	−3.37906			−0.129391
$683$	−3.84577	−	6.66106i	−0.147154	−	0.254879i	0.783020	−	0.621996i	$-0.213678\pi$
$683$	−3.84577	−	6.66106i	−0.147154	−	0.254879i	−0.930175	+	0.367118i	$0.880345\pi$
$684$	1.52160			0.0581799
$685$	−14.0119	−	24.2694i	−0.535368	−	0.927284i
$686$	−16.9419			−0.646845
$687$	−10.3046			−0.393144
$688$	−2.40582	−	4.16701i	−0.0917211	−	0.158866i
$689$	−2.50471	+	4.33829i	−0.0954220	+	0.165276i
$690$	6.51013	+	11.2759i	0.247836	+	0.429265i
$691$	−16.5450	−	28.6567i	−0.629400	−	1.09015i	−0.987672	−	0.156536i	$-0.949967\pi$
$691$	−16.5450	−	28.6567i	−0.629400	−	1.09015i	0.358272	−	0.933617i	$-0.383366\pi$
$692$	13.3592			0.507840
$693$	−3.55260			−0.134952
$694$	−13.2521	−	22.9533i	−0.503042	−	0.871295i
$695$	15.0038			0.569127
$696$	11.5536	−	20.0115i	0.437939	−	0.758532i
$697$	15.7950	−	27.3578i	0.598280	−	1.03625i
$698$	−0.520344	+	0.901263i	−0.0196953	+	0.0341133i
$699$	−8.07810	−	13.9917i	−0.305542	−	0.529214i
$700$	0.128179	+	0.222013i	0.00484472	+	0.00839130i
$701$	−0.564628	+	0.977964i	−0.0213257	+	0.0369372i	−0.876491	−	0.481418i	$-0.840122\pi$
$701$	−0.564628	+	0.977964i	−0.0213257	+	0.0369372i	0.855166	+	0.518355i	$0.173455\pi$
$702$	1.20346	+	2.08445i	0.0454216	+	0.0786726i
$703$	−26.4063			−0.995934
$704$	−13.1651	+	22.8026i	−0.496177	+	0.859404i
$705$	−0.0220872	+	0.0382561i	−0.000831851	+	0.00144081i
$706$	−22.3820			−0.842358
$707$	−2.55161			−0.0959633
$708$	−1.02553	+	1.77627i	−0.0385418	+	0.0667563i
$709$	−8.61070	+	14.9142i	−0.323382	+	0.560114i	−0.981184	−	0.193077i	$-0.938153\pi$
$709$	−8.61070	+	14.9142i	−0.323382	+	0.560114i	0.657802	+	0.753191i	$0.271486\pi$
$710$	−37.5557			−1.40944
$711$	3.67919	+	6.37254i	0.137980	+	0.238989i
$712$	−5.00303	+	8.66551i	−0.187497	+	0.324754i
$713$	2.49200	+	4.31627i	0.0933261	+	0.161646i
$714$	−2.41235	−	4.17832i	−0.0902801	−	0.156370i
$715$	6.90066	−	11.9523i	0.258070	−	0.446991i
$716$	6.30017	−	10.9122i	0.235449	−	0.407809i
$717$	7.38563	−	12.7923i	0.275822	−	0.477737i
$718$	−5.70570			−0.212935
$719$	22.5231	+	39.0111i	0.839968	+	1.45487i	0.889920	+	0.456116i	$0.150760\pi$
$719$	22.5231	+	39.0111i	0.839968	+	1.45487i	−0.0499523	+	0.998752i	$0.515907\pi$
$720$	4.80096			0.178921
$721$	−6.08994			−0.226801
$722$	−7.96240	−	13.7913i	−0.296330	−	0.513258i
$723$	1.47877	+	2.56130i	0.0549960	+	0.0952558i
$724$	2.82364	−	4.89069i	0.104940	−	0.181761i
$725$	−1.24443	−	2.15541i	−0.0462169	−	0.0800501i
$726$	1.85879			0.0689863
$727$	−53.2629			−1.97541			−0.987705	−	0.156327i	$-0.950035\pi$
$727$	−53.2629			−1.97541			−0.987705	+	0.156327i	$0.950035\pi$
$728$	3.72065	+	6.44435i	0.137896	+	0.238844i
$729$	1.00000			0.0370370
$730$	0.878463	+	1.52154i	0.0325134	+	0.0563148i
$731$	−7.80458			−0.288663
$732$	−0.378442	−	0.655480i	−0.0139876	−	0.0242272i
$733$	8.84842	+	15.3259i	0.326824	+	0.566076i	0.981880	−	0.189505i	$-0.0606883\pi$
$733$	8.84842	+	15.3259i	0.326824	+	0.566076i	−0.655056	+	0.755580i	$0.727355\pi$
$734$	14.6557	+	25.3845i	0.540953	+	0.936958i
$735$	−6.11022	−	10.5832i	−0.225379	−	0.390367i
$736$	18.7500			0.691133
$737$	5.05217	−	8.75061i	0.186099	−	0.322333i
$738$	−5.06030	−	8.76470i	−0.186272	−	0.322633i
$739$	39.1967			1.44187			0.720936	−	0.693001i	$-0.243712\pi$
$739$	39.1967			1.44187			0.720936	+	0.693001i	$0.243712\pi$
$740$	16.6681			0.612733
$741$	2.37861	−	4.11988i	0.0873806	−	0.151348i
$742$	−1.60851	−	2.78602i	−0.0590503	−	0.102278i
$743$	−5.19501	+	8.99802i	−0.190586	+	0.330105i	−0.945445	−	0.325782i	$-0.894372\pi$
$743$	−5.19501	+	8.99802i	−0.190586	+	0.330105i	0.754858	+	0.655888i	$0.227706\pi$
$744$	2.94061			0.107808
$745$	−14.5384	+	25.1813i	−0.532646	+	0.922570i
$746$	−0.524495			−0.0192031
$747$	6.03104	−	10.4461i	0.220664	−	0.382202i
$748$	3.68180	+	6.37706i	0.134620	+	0.233168i
$749$	0.379774	+	0.657788i	0.0138767	+	0.0240351i
$750$	6.65078	−	11.5195i	0.242852	−	0.420632i
$751$	−24.4499	+	42.3484i	−0.892189	+	1.54532i	−0.0549429	+	0.998489i	$0.517498\pi$
$751$	−24.4499	+	42.3484i	−0.892189	+	1.54532i	−0.837246	+	0.546827i	$0.815836\pi$
$752$	−0.0227146	−	0.0393429i	−0.000828318	−	0.00143469i
$753$	26.5500			0.967534
$754$	−9.03111	−	15.6423i	−0.328894	−	0.569661i
$755$	−5.26253	−	9.11496i	−0.191523	−	0.331727i
$756$	0.772962			0.0281123
$757$	46.8558			1.70300			0.851501	−	0.524353i	$-0.175693\pi$
$757$	46.8558			1.70300			0.851501	+	0.524353i	$0.175693\pi$
$758$	−5.88612			−0.213793
$759$	7.99625	+	13.8499i	0.290246	+	0.502720i
$760$	−7.59174	−	13.1493i	−0.275381	−	0.476975i
$761$	1.64214	−	2.84427i	0.0595275	−	0.103105i	−0.834726	−	0.550666i	$-0.814374\pi$
$761$	1.64214	−	2.84427i	0.0595275	−	0.103105i	0.894253	+	0.447561i	$0.147707\pi$
$762$	−12.4001			−0.449207
$763$	−6.56016	+	11.3625i	−0.237494	+	0.411351i
$764$	−3.27288	+	5.66879i	−0.118408	+	0.205090i
$765$	3.89363	−	6.74396i	0.140774	−	0.243829i
$766$	−12.9827	+	22.4867i	−0.469083	+	0.812476i
$767$	3.20628	+	5.55344i	0.115772	+	0.200523i
$768$	7.01281	−	12.1465i	0.253053	−	0.438300i
$769$	−3.87745			−0.139824			−0.0699122	−	0.997553i	$-0.522272\pi$
$769$	−3.87745			−0.139824			−0.0699122	+	0.997553i	$0.522272\pi$
$770$	4.43156	+	7.67569i	0.159702	+	0.276613i
$771$	20.4473			0.736390
$772$	−7.65110	−	13.2521i	−0.275369	−	0.476953i
$773$	−5.71460	+	9.89798i	−0.205540	+	0.356006i	−0.950305	−	0.311322i	$-0.899228\pi$
$773$	−5.71460	+	9.89798i	−0.205540	+	0.356006i	0.744765	+	0.667327i	$0.232562\pi$
$774$	−1.25019	+	2.16539i	−0.0449371	+	0.0778334i
$775$	0.158365	−	0.274296i	0.00568863	−	0.00985300i
$776$	−7.15794	−	12.3979i	−0.256955	−	0.445059i
$777$	−13.4142			−0.481232
$778$	3.49118			0.125165
$779$	−10.0016	+	17.3233i	−0.358344	+	0.620671i
$780$	−1.50142	+	2.60054i	−0.0537595	+	0.0931142i
$781$	−46.1289			−1.65062
$782$	−10.8595	+	18.8093i	−0.388337	+	0.672619i
$783$	−7.50430			−0.268182
$784$	12.5676			0.448843
$785$	−23.7570	+	12.9821i	−0.847924	+	0.463350i
$786$	15.3429			0.547265
$787$	−0.633986			−0.0225992			−0.0112996	−	0.999936i	$-0.503597\pi$
$787$	−0.633986			−0.0225992			−0.0112996	+	0.999936i	$0.503597\pi$
$788$	−6.11587	+	10.5930i	−0.217869	+	0.377360i
$789$	26.2529			0.934627
$790$	9.17895	−	15.8984i	0.326572	−	0.565640i
$791$	−0.226820	+	0.392863i	−0.00806478	+	0.0139686i
$792$	9.43573			0.335284
$793$	−2.36636			−0.0840321
$794$	−4.05293	−	7.01989i	−0.143833	−	0.249126i
$795$	2.59620	−	4.49674i	0.0920776	−	0.159483i
$796$	5.90065	−	10.2202i	0.209143	−	0.362246i
$797$	6.54996	−	11.3449i	0.232012	−	0.401856i	−0.726388	−	0.687284i	$-0.758803\pi$
$797$	6.54996	−	11.3449i	0.232012	−	0.401856i	0.958400	+	0.285429i	$0.0921359\pi$
$798$	1.52753	+	2.64576i	0.0540740	+	0.0936589i
$799$	−0.0736872			−0.00260687
$800$	−0.595773	−	1.03191i	−0.0210638	−	0.0364835i
$801$	3.24956			0.114818
$802$	−3.39937	+	5.88789i	−0.120036	+	0.207909i
$803$	1.07900	+	1.86888i	0.0380770	+	0.0659513i
$804$	−1.09923	+	1.90393i	−0.0387669	+	0.0671463i
$805$	6.53641	−	11.3214i	0.230378	−	0.399027i
$806$	1.14929	−	1.99063i	0.0404821	−	0.0701170i
$807$	−13.4034	+	23.2154i	−0.471823	+	0.817221i
$808$	6.77711			0.238418
$809$	7.99552	−	13.8486i	0.281108	−	0.486893i	−0.690550	−	0.723284i	$-0.742632\pi$
$809$	7.99552	−	13.8486i	0.281108	−	0.486893i	0.971658	+	0.236392i	$0.0759649\pi$
$810$	−1.24741	−	2.16058i	−0.0438297	−	0.0759152i
$811$	3.77699	+	6.54194i	0.132628	+	0.229718i	0.924689	−	0.380724i	$-0.124325\pi$
$811$	3.77699	+	6.54194i	0.132628	+	0.229718i	−0.792061	+	0.610442i	$0.790992\pi$
$812$	−5.80053			−0.203559
$813$	−15.3876			−0.539666
$814$	−40.9405			−1.43496
$815$	−17.8349	−	30.8909i	−0.624729	−	1.08206i
$816$	4.00424	+	6.93555i	0.140176	+	0.242793i
$817$	4.94195			0.172897
$818$	12.6371	+	21.8881i	0.441845	+	0.765298i
$819$	1.20832	−	2.09287i	0.0422220	−	0.0731306i
$820$	6.31318	−	10.9347i	0.220466	−	0.381858i
$821$	15.0019	+	25.9840i	0.523569	+	0.906849i	0.999624	+	0.0274328i	$0.00873322\pi$
$821$	15.0019	+	25.9840i	0.523569	+	0.906849i	−0.476054	+	0.879416i	$0.657933\pi$
$822$	−7.48817	−	12.9699i	−0.261180	−	0.452377i
$823$	10.0280	−	17.3689i	0.349553	−	0.605443i	−0.636617	−	0.771180i	$-0.719667\pi$
$823$	10.0280	−	17.3689i	0.349553	−	0.605443i	0.986170	+	0.165737i	$0.0530002\pi$
$824$	16.1749			0.563480
$825$	0.508156	−	0.880153i	0.0176917	−	0.0306430i
$826$	−4.11810			−0.143287
$827$	−18.7087	+	32.4044i	−0.650564	+	1.12681i	0.332422	+	0.943131i	$0.392134\pi$
$827$	−18.7087	+	32.4044i	−0.650564	+	1.12681i	−0.982986	+	0.183679i	$0.941199\pi$
$828$	−1.73980	−	3.01342i	−0.0604621	−	0.104723i
$829$	−22.5713	+	39.0946i	−0.783934	+	1.35781i	0.145701	+	0.989329i	$0.453456\pi$
$829$	−22.5713	+	39.0946i	−0.783934	+	1.35781i	−0.929634	+	0.368484i	$0.879877\pi$
$830$	−30.0928			−1.04454
$831$	20.0028			0.693889
$832$	−8.95546	−	15.5113i	−0.310475	−	0.537758i
$833$	10.1924	−	17.6538i	0.353147	−	0.611669i
$834$	8.01824			0.277649
$835$	−6.40085	−	11.0866i	−0.221510	−	0.383667i
$836$	−2.33136	−	4.03803i	−0.0806316	−	0.139658i
$837$	−0.477495	−	0.827046i	−0.0165046	−	0.0285869i
$838$	−6.37023	−	11.0336i	−0.220056	−	0.381148i
$839$	−31.7473			−1.09604			−0.548019	−	0.836466i	$-0.684618\pi$
$839$	−31.7473			−1.09604			−0.548019	+	0.836466i	$0.684618\pi$
$840$	−3.85654	−	6.67973i	−0.133063	−	0.230472i
$841$	27.3145			0.941879
$842$	−8.15797	−	14.1300i	−0.281142	−	0.486953i
$843$	1.99632			0.0687570
$844$	−11.8534			−0.408009
$845$	−9.34999	−	16.1947i	−0.321650	−	0.557113i
$846$	−0.0118037	+	0.0204446i	−0.000405820	+	0.000702900i
$847$	−0.933148	−	1.61626i	−0.0320633	−	0.0555353i
$848$	2.66995	+	4.62449i	0.0916864	+	0.158806i
$849$	1.49385			0.0512688
$850$	1.38023			0.0473416
$851$	30.1929	+	52.2957i	1.03500	+	1.79267i
$852$	10.0366			0.343847
$853$	−8.29293	+	14.3638i	−0.283945	+	0.491806i	−0.972353	−	0.233517i	$-0.924976\pi$
$853$	−8.29293	+	14.3638i	−0.283945	+	0.491806i	0.688408	+	0.725324i	$0.258310\pi$
$854$	0.759832	−	1.31607i	0.0260009	−	0.0450349i
$855$	−2.46549	+	4.27035i	−0.0843180	+	0.146043i
$856$	−1.00868	−	1.74709i	−0.0344761	−	0.0597144i
$857$	−1.35427	−	2.34567i	−0.0462610	−	0.0801265i	0.841968	−	0.539528i	$-0.181397\pi$
$857$	−1.35427	−	2.34567i	−0.0462610	−	0.0801265i	−0.888229	+	0.459401i	$0.848064\pi$
$858$	3.68781	−	6.38748i	0.125900	−	0.218065i
$859$	−15.4136	−	26.6972i	−0.525906	−	0.910895i	−0.999545	−	0.0301762i	$-0.990393\pi$
$859$	−15.4136	−	26.6972i	−0.525906	−	0.910895i	0.473639	−	0.880719i	$-0.342940\pi$
$860$	−3.11944			−0.106372
$861$	−5.08073	+	8.80008i	−0.173151	+	0.299906i
$862$	7.29416	−	12.6339i	0.248440	−	0.430311i
$863$	−24.3069			−0.827418			−0.413709	−	0.910409i	$-0.635767\pi$
$863$	−24.3069			−0.827418			−0.413709	+	0.910409i	$0.635767\pi$
$864$	−3.59270			−0.122226
$865$	−21.6462	+	37.4924i	−0.735994	+	1.27478i
$866$	12.4280	−	21.5259i	0.422321	−	0.731481i
$867$	−4.01008			−0.136189
$868$	−0.369085	−	0.639274i	−0.0125276	−	0.0216984i
$869$	11.2743	−	19.5277i	0.382455	−	0.662431i
$870$	9.36097	+	16.2137i	0.317366	+	0.549695i
$871$	3.43671	+	5.95255i	0.116448	+	0.201694i
$872$	17.4238	−	30.1790i	0.590045	−	1.02199i
$873$	−2.32461	+	4.02634i	−0.0786761	+	0.136271i
$874$	6.87639	−	11.9103i	0.232597	−	0.402870i
$875$	−13.3553			−0.451490
$876$	−0.234764	−	0.406624i	−0.00793195	−	0.0137385i
$877$	27.8957			0.941970			0.470985	−	0.882141i	$-0.343899\pi$
$877$	27.8957			0.941970			0.470985	+	0.882141i	$0.343899\pi$
$878$	−17.7065			−0.597566
$879$	−2.97078	−	5.14555i	−0.100202	−	0.173555i
$880$	−7.35590	−	12.7408i	−0.247967	−	0.429492i
$881$	−20.0576	+	34.7408i	−0.675757	+	1.17045i	0.300490	+	0.953785i	$0.402850\pi$
$881$	−20.0576	+	34.7408i	−0.675757	+	1.17045i	−0.976247	+	0.216661i	$0.930483\pi$
$882$	−3.26538	−	5.65581i	−0.109951	−	0.190441i
$883$	38.0237			1.27960			0.639800	−	0.768542i	$-0.279017\pi$
$883$	38.0237			1.27960			0.639800	+	0.768542i	$0.279017\pi$
$884$	−5.00904			−0.168472
$885$	−3.32338	−	5.75627i	−0.111714	−	0.193495i
$886$	7.40980			0.248937
$887$	18.1011	+	31.3520i	0.607775	+	1.05270i	0.991606	+	0.129293i	$0.0412709\pi$
$887$	18.1011	+	31.3520i	0.607775	+	1.05270i	−0.383832	+	0.923403i	$0.625396\pi$
$888$	35.6282			1.19561
$889$	6.22505	+	10.7821i	0.208782	+	0.361620i
$890$	−4.05355	−	7.02096i	−0.135875	−	0.235343i
$891$	−1.53217	−	2.65380i	−0.0513297	−	0.0889056i
$892$	6.82957	+	11.8292i	0.228671	+	0.396069i
$893$	0.0466596			0.00156140
$894$	−7.76953	+	13.4572i	−0.259852	+	0.450077i
$895$	20.4167	+	35.3627i	0.682454	+	1.18204i
$896$	3.17199			0.105969
$897$	−10.8788			−0.363233
$898$	3.69496	−	6.39985i	0.123302	−	0.213566i
$899$	3.58326	+	6.20640i	0.119509	+	0.206995i
$900$	−0.110563	+	0.191500i	−0.00368543	+	0.00638335i
$901$	8.66142			0.288554
$902$	−15.5065	+	26.8581i	−0.516310	+	0.894276i
$903$	2.51047			0.0835432
$904$	0.602435	−	1.04345i	0.0200367	−	0.0347046i
$905$	9.15043	+	15.8490i	0.304170	+	0.526839i
$906$	−2.81237	−	4.87116i	−0.0934347	−	0.161834i
$907$	0.414034	−	0.717128i	0.0137478	−	0.0238118i	−0.859070	−	0.511859i	$-0.828957\pi$
$907$	0.414034	−	0.717128i	0.0137478	−	0.0238118i	0.872817	+	0.488047i	$0.162290\pi$
$908$	0.391164	−	0.677515i	0.0129812	−	0.0224841i
$909$	−1.10046	−	1.90606i	−0.0365001	−	0.0632200i
$910$	−6.02908			−0.199862
$911$	−12.5750	−	21.7806i	−0.416630	−	0.721624i	0.578968	−	0.815350i	$-0.303456\pi$
$911$	−12.5750	−	21.7806i	−0.416630	−	0.721624i	−0.995598	+	0.0937262i	$0.970122\pi$
$912$	−2.53553	−	4.39167i	−0.0839598	−	0.145423i
$913$	−36.9624			−1.22328
$914$	46.7384			1.54597
$915$	2.45279			0.0810868
$916$	−3.43518	−	5.94990i	−0.113501	−	0.196590i
$917$	−7.70243	−	13.3410i	−0.254357	−	0.440559i
$918$	2.08081	−	3.60407i	0.0686770	−	0.118952i
$919$	−17.5843			−0.580053			−0.290027	−	0.957019i	$-0.593664\pi$
$919$	−17.5843			−0.580053			−0.290027	+	0.957019i	$0.593664\pi$
$920$	−17.3608	+	30.0697i	−0.572367	+	0.991369i
$921$	−3.46601	+	6.00330i	−0.114209	+	0.197815i
$922$	−0.717494	+	1.24274i	−0.0236294	+	0.0409273i
$923$	15.6894	−	27.1749i	0.516424	−	0.894473i
$924$	−1.18431	−	2.05128i	−0.0389609	−	0.0674823i
$925$	1.91874	−	3.32335i	0.0630878	−	0.109271i
$926$	13.6692			0.449199
$927$	−2.62648	−	4.54920i	−0.0862650	−	0.149415i
$928$	26.9607			0.885028
$929$	−12.5215	−	21.6878i	−0.410816	−	0.711554i	0.584163	−	0.811636i	$-0.301423\pi$
$929$	−12.5215	−	21.6878i	−0.410816	−	0.711554i	−0.994979	+	0.100082i	$0.968089\pi$
$930$	−1.19127	+	2.06334i	−0.0390632	+	0.0676595i
$931$	−6.45397	+	11.1786i	−0.211520	+	0.366364i
$932$	5.38591	−	9.32866i	0.176421	−	0.305570i
$933$	−17.4314	−	30.1921i	−0.570678	−	0.988444i
$934$	−6.35888			−0.208069
$935$	−23.8628			−0.780398
$936$	−3.20930	+	5.55867i	−0.104899	+	0.181691i
$937$	18.6145	−	32.2412i	0.608108	−	1.05327i	−0.383444	−	0.923564i	$-0.625262\pi$
$937$	18.6145	−	32.2412i	0.608108	−	1.05327i	0.991552	−	0.129710i	$-0.0414047\pi$
$938$	−4.41406			−0.144124
$939$	−1.70317	+	2.94998i	−0.0555808	+	0.0962688i
$940$	−0.0294523			−0.000960629
$941$	25.5500			0.832905			0.416453	−	0.909157i	$-0.363273\pi$
$941$	25.5500			0.832905			0.416453	+	0.909157i	$0.363273\pi$
$942$	−12.6961	+	6.93780i	−0.413661	+	0.226046i
$943$	45.7432			1.48960
$944$	6.83559			0.222480
$945$	−1.25245	+	2.16930i	−0.0407422	+	0.0705675i
$946$	7.66202			0.249114
$947$	−2.89374	+	5.01211i	−0.0940340	+	0.162872i	−0.909205	−	0.416349i	$-0.863310\pi$
$947$	−2.89374	+	5.01211i	−0.0940340	+	0.162872i	0.815171	+	0.579220i	$0.196643\pi$
$948$	−2.45302	+	4.24876i	−0.0796705	+	0.137993i
$949$	−1.46796			−0.0476521
$950$	−0.873979			−0.0283556
$951$	11.2447	+	19.4764i	0.364634	+	0.631565i
$952$	6.43309	−	11.1424i	0.208498	−	0.361129i
$953$	17.3555	−	30.0605i	0.562198	−	0.973756i	−0.435106	−	0.900379i	$-0.643289\pi$
$953$	17.3555	−	30.0605i	0.562198	−	0.973756i	0.997304	−	0.0733768i	$-0.0233776\pi$
$954$	1.38744	−	2.40312i	0.0449201	−	0.0778039i
$955$	−10.6062	−	18.3705i	−0.343210	−	0.594457i
$956$	9.84843			0.318521
$957$	11.4979	+	19.9149i	0.371673	+	0.643757i
$958$	−19.2961			−0.623428
$959$	−7.51839	+	13.0222i	−0.242781	+	0.420510i
$960$	9.28255	+	16.0778i	0.299593	+	0.518910i
$961$	15.0440	−	26.0570i	0.485290	−	0.840547i
$962$	13.9247	−	24.1184i	0.448952	−	0.777608i
$963$	−0.327580	+	0.567385i	−0.0105561	+	0.0182837i
$964$	−0.985937	+	1.70769i	−0.0317549	+	0.0550011i
$965$	49.5891			1.59633
$966$	3.49315	−	6.05031i	0.112390	−	0.194666i
$967$	9.76226	+	16.9087i	0.313933	+	0.543748i	0.979210	−	0.202849i	$-0.0650199\pi$
$967$	9.76226	+	16.9087i	0.313933	+	0.543748i	−0.665277	+	0.746597i	$0.731687\pi$
$968$	2.47845	+	4.29280i	0.0796604	+	0.137976i
$969$	−8.22536			−0.264237
$970$	11.5990			0.372422
$971$	−25.1329			−0.806554			−0.403277	−	0.915078i	$-0.632129\pi$
$971$	−25.1329			−0.806554			−0.403277	+	0.915078i	$0.632129\pi$
$972$	0.333364	+	0.577404i	0.0106927	+	0.0185202i
$973$	−4.02530	−	6.97203i	−0.129045	−	0.223513i
$974$	49.3377			1.58088
$975$	0.345670	+	0.598718i	0.0110703	+	0.0191743i
$976$	−1.26124	+	2.18453i	−0.0403712	+	0.0699250i
$977$	21.4417	−	37.1381i	0.685980	−	1.18815i	−0.287148	−	0.957886i	$-0.592707\pi$
$977$	21.4417	−	37.1381i	0.685980	−	1.18815i	0.973128	−	0.230266i	$-0.0739596\pi$
$978$	−9.53122	−	16.5085i	−0.304775	−	0.527885i
$979$	−4.97889	−	8.62369i	−0.159126	−	0.275614i
$980$	4.07386	−	7.05613i	0.130135	−	0.225400i
$981$	−11.3171			−0.361328
$982$	16.3587	−	28.3342i	0.522028	−	0.904179i
$983$	−30.6483			−0.977529			−0.488764	−	0.872416i	$-0.662552\pi$
$983$	−30.6483			−0.977529			−0.488764	+	0.872416i	$0.662552\pi$
$984$	13.4945	−	23.3731i	0.430188	−	0.745107i
$985$	−19.8194	−	34.3282i	−0.631498	−	1.09379i
$986$	−15.6150	+	27.0460i	−0.497284	+	0.861320i
$987$	0.0237027			0.000754465
$988$	3.17178			0.100908
$989$	−5.65061	−	9.78715i	−0.179679	−	0.311213i
$990$	−3.82250	+	6.62077i	−0.121487	+	0.210422i
$991$	4.17274			0.132551			0.0662757	−	0.997801i	$-0.478888\pi$
$991$	4.17274			0.132551			0.0662757	+	0.997801i	$0.478888\pi$
$992$	1.71550	+	2.97133i	0.0544671	+	0.0943398i
$993$	−7.76175	−	13.4437i	−0.246312	−	0.426624i
$994$	10.0757	+	17.4515i	0.319580	+	0.553530i
$995$	19.1219	+	33.1201i	0.606206	+	1.04998i
$996$	8.04214			0.254825
$997$	18.0979	+	31.3464i	0.573165	+	0.992751i	0.996238	+	0.0866557i	$0.0276180\pi$
$997$	18.0979	+	31.3464i	0.573165	+	0.992751i	−0.423073	+	0.906096i	$0.639049\pi$
$998$	−10.5711			−0.334621
$999$	−5.78530	−	10.0204i	−0.183039	−	0.317033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.301.5	yes	28
157.12	even	3	inner	471.2.e.c.169.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.5	✓	28	157.12	even	3	inner
471.2.e.c.301.5	yes	28	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.15467 q^{2} +(-0.500000 + 0.866025i) q^{3} -0.666729 q^{4} +(1.08032 - 1.87116i) q^{5} +(0.577337 - 0.999977i) q^{6} -1.15933 q^{7} +3.07920 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.15467 q^{2} +(-0.500000 + 0.866025i) q^{3} -0.666729 q^{4} +(1.08032 - 1.87116i) q^{5} +(0.577337 - 0.999977i) q^{6} -1.15933 q^{7} +3.07920 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.24741 + 2.16058i) q^{10} +(-1.53217 + 2.65380i) q^{11} +(0.333364 - 0.577404i) q^{12} +(-1.04225 - 1.80523i) q^{13} +1.33865 q^{14} +(1.08032 + 1.87116i) q^{15} -2.22201 q^{16} +(-1.80208 + 3.12129i) q^{17} +(0.577337 + 0.999977i) q^{18} +(1.14110 - 1.97644i) q^{19} +(-0.720279 + 1.24756i) q^{20} +(0.579667 - 1.00401i) q^{21} +(1.76916 - 3.06427i) q^{22} -5.21890 q^{23} +(-1.53960 + 2.66667i) q^{24} +(0.165829 + 0.287224i) q^{25} +(1.20346 + 2.08445i) q^{26} +1.00000 q^{27} +0.772962 q^{28} -7.50430 q^{29} +(-1.24741 - 2.16058i) q^{30} +(-0.477495 - 0.827046i) q^{31} -3.59270 q^{32} +(-1.53217 - 2.65380i) q^{33} +(2.08081 - 3.60407i) q^{34} +(-1.25245 + 2.16930i) q^{35} +(0.333364 + 0.577404i) q^{36} +(-5.78530 - 10.0204i) q^{37} +(-1.31759 + 2.28214i) q^{38} +2.08450 q^{39} +(3.32651 - 5.76169i) q^{40} -8.76491 q^{41} +(-0.669326 + 1.15931i) q^{42} +(1.08272 + 1.87533i) q^{43} +(1.02154 - 1.76936i) q^{44} -2.16063 q^{45} +6.02613 q^{46} +(0.0102225 + 0.0177060i) q^{47} +(1.11101 - 1.92432i) q^{48} -5.65594 q^{49} +(-0.191478 - 0.331650i) q^{50} +(-1.80208 - 3.12129i) q^{51} +(0.694898 + 1.20360i) q^{52} +(-1.20159 - 2.08121i) q^{53} -1.15467 q^{54} +(3.31046 + 5.73389i) q^{55} -3.56982 q^{56} +(1.14110 + 1.97644i) q^{57} +8.66501 q^{58} -3.07630 q^{59} +(-0.720279 - 1.24756i) q^{60} +(0.567609 - 0.983128i) q^{61} +(0.551351 + 0.954968i) q^{62} +(0.579667 + 1.00401i) q^{63} +8.59243 q^{64} -4.50384 q^{65} +(1.76916 + 3.06427i) q^{66} -3.29739 q^{67} +(1.20150 - 2.08105i) q^{68} +(2.60945 - 4.51970i) q^{69} +(1.44617 - 2.50484i) q^{70} +(7.52672 + 13.0367i) q^{71} +(-1.53960 - 2.66667i) q^{72} +(0.352114 - 0.609879i) q^{73} +(6.68014 + 11.5703i) q^{74} -0.331658 q^{75} +(-0.760801 + 1.31775i) q^{76} +(1.77630 - 3.07664i) q^{77} -2.40692 q^{78} -7.35838 q^{79} +(-2.40048 + 4.15775i) q^{80} +(-0.500000 + 0.866025i) q^{81} +10.1206 q^{82} +(6.03104 + 10.4461i) q^{83} +(-0.386481 + 0.669404i) q^{84} +(3.89363 + 6.74396i) q^{85} +(-1.25019 - 2.16539i) q^{86} +(3.75215 - 6.49891i) q^{87} +(-4.71787 + 8.17158i) q^{88} +(-1.62478 + 2.81421i) q^{89} +2.49483 q^{90} +(1.20832 + 2.09287i) q^{91} +3.47959 q^{92} +0.954990 q^{93} +(-0.0118037 - 0.0204446i) q^{94} +(-2.46549 - 4.27035i) q^{95} +(1.79635 - 3.11137i) q^{96} +(-2.32461 - 4.02634i) q^{97} +6.53077 q^{98} +3.06434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

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