LMFDB - Embedded newform 630.2.i.g.151.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 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("630.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.i (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 7 x^{10} - 3 x^{9} - 2 x^{8} + 24 x^{7} - 21 x^{6} + 72 x^{5} - 18 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 7x^10 - 3x^9 - 2x^8 + 24x^7 - 21x^6 + 72x^5 - 18x^4 - 81x^3 + 567x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.5
Root			$0.702501 - 1.58319i$ of defining polynomial
Character	$\chi$	$=$	630.151
Dual form			630.2.i.g.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.01983 - 1.39998i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.01983 - 1.39998i) q^{6} +(1.85185 + 1.88962i) q^{7} +1.00000 q^{8} +(-0.919882 - 2.85549i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.01983 - 1.39998i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.01983 - 1.39998i) q^{6} +(1.85185 + 1.88962i) q^{7} +1.00000 q^{8} +(-0.919882 - 2.85549i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(3.22352 + 5.58330i) q^{11} +(1.01983 - 1.39998i) q^{12} +(0.332016 + 0.575068i) q^{13} +(1.85185 + 1.88962i) q^{14} +(0.702501 + 1.58319i) q^{15} +1.00000 q^{16} +(0.411850 - 0.713345i) q^{17} +(-0.919882 - 2.85549i) q^{18} +(-2.77668 - 4.80936i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(4.53400 - 0.665454i) q^{21} +(3.22352 + 5.58330i) q^{22} +(1.74387 - 3.02046i) q^{23} +(1.01983 - 1.39998i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.332016 + 0.575068i) q^{26} +(-4.93575 - 1.62430i) q^{27} +(1.85185 + 1.88962i) q^{28} +(2.03452 - 3.52389i) q^{29} +(0.702501 + 1.58319i) q^{30} -7.63703 q^{31} +1.00000 q^{32} +(11.1039 + 1.18117i) q^{33} +(0.411850 - 0.713345i) q^{34} +(-2.56238 + 0.658939i) q^{35} +(-0.919882 - 2.85549i) q^{36} +(-5.32042 - 9.21523i) q^{37} +(-2.77668 - 4.80936i) q^{38} +(1.14368 + 0.121658i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(0.511800 + 0.886464i) q^{41} +(4.53400 - 0.665454i) q^{42} +(-4.15005 + 7.18810i) q^{43} +(3.22352 + 5.58330i) q^{44} +(2.93287 + 0.631103i) q^{45} +(1.74387 - 3.02046i) q^{46} +2.60076 q^{47} +(1.01983 - 1.39998i) q^{48} +(-0.141315 + 6.99857i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.578650 - 1.30407i) q^{51} +(0.332016 + 0.575068i) q^{52} +(-3.27668 + 5.67538i) q^{53} +(-4.93575 - 1.62430i) q^{54} -6.44704 q^{55} +(1.85185 + 1.88962i) q^{56} +(-9.56475 - 1.01744i) q^{57} +(2.03452 - 3.52389i) q^{58} -2.91633 q^{59} +(0.702501 + 1.58319i) q^{60} -0.767506 q^{61} -7.63703 q^{62} +(3.69230 - 7.02616i) q^{63} +1.00000 q^{64} -0.664031 q^{65} +(11.1039 + 1.18117i) q^{66} +7.28641 q^{67} +(0.411850 - 0.713345i) q^{68} +(-2.45013 - 5.52174i) q^{69} +(-2.56238 + 0.658939i) q^{70} +3.44704 q^{71} +(-0.919882 - 2.85549i) q^{72} +(4.71172 - 8.16093i) q^{73} +(-5.32042 - 9.21523i) q^{74} +(-1.72233 - 0.183212i) q^{75} +(-2.77668 - 4.80936i) q^{76} +(-4.58083 + 16.4306i) q^{77} +(1.14368 + 0.121658i) q^{78} -5.40500 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-7.30763 + 5.25343i) q^{81} +(0.511800 + 0.886464i) q^{82} +(0.897166 - 1.55394i) q^{83} +(4.53400 - 0.665454i) q^{84} +(0.411850 + 0.713345i) q^{85} +(-4.15005 + 7.18810i) q^{86} +(-2.85850 - 6.44206i) q^{87} +(3.22352 + 5.58330i) q^{88} +(-2.06497 - 3.57663i) q^{89} +(2.93287 + 0.631103i) q^{90} +(-0.471816 + 1.69232i) q^{91} +(1.74387 - 3.02046i) q^{92} +(-7.78850 + 10.6917i) q^{93} +2.60076 q^{94} +5.55337 q^{95} +(1.01983 - 1.39998i) q^{96} +(-8.98652 + 15.5651i) q^{97} +(-0.141315 + 6.99857i) q^{98} +(12.9778 - 14.3407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.01983	−	1.39998i	0.588801	−	0.808278i
$3$	1.01983	−	1.39998i	0.588801	−	0.808278i
$4$	1.00000			0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.01983	−	1.39998i	0.416345	−	0.571539i
$7$	1.85185	+	1.88962i	0.699933	+	0.714209i
$7$	1.85185	+	1.88962i	0.699933	+	0.714209i
$8$	1.00000			0.353553
$9$	−0.919882	−	2.85549i	−0.306627	−	0.951830i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	3.22352	+	5.58330i	0.971927	+	1.68343i	0.689723	+	0.724073i	$0.257732\pi$
$11$	3.22352	+	5.58330i	0.971927	+	1.68343i	0.282204	+	0.959354i	$0.408935\pi$
$12$	1.01983	−	1.39998i	0.294400	−	0.404139i
$13$	0.332016	+	0.575068i	0.0920846	+	0.159495i	0.908388	−	0.418128i	$-0.137314\pi$
$13$	0.332016	+	0.575068i	0.0920846	+	0.159495i	−0.816304	+	0.577623i	$0.803980\pi$
$14$	1.85185	+	1.88962i	0.494927	+	0.505022i
$15$	0.702501	+	1.58319i	0.181385	+	0.408778i
$16$	1.00000			0.250000
$17$	0.411850	−	0.713345i	0.0998883	−	0.173012i	−0.811750	−	0.584005i	$-0.801485\pi$
$17$	0.411850	−	0.713345i	0.0998883	−	0.173012i	0.911638	+	0.410994i	$0.134818\pi$
$18$	−0.919882	−	2.85549i	−0.216818	−	0.673045i
$19$	−2.77668	−	4.80936i	−0.637015	−	1.10334i	−0.986084	−	0.166245i	$-0.946836\pi$
$19$	−2.77668	−	4.80936i	−0.637015	−	1.10334i	0.349070	−	0.937097i	$-0.386498\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	4.53400	−	0.665454i	0.989400	−	0.145214i
$22$	3.22352	+	5.58330i	0.687256	+	1.19036i
$23$	1.74387	−	3.02046i	0.363621	−	0.629810i	−0.624933	−	0.780679i	$-0.714874\pi$
$23$	1.74387	−	3.02046i	0.363621	−	0.629810i	0.988554	+	0.150868i	$0.0482069\pi$
$24$	1.01983	−	1.39998i	0.208172	−	0.285770i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.332016	+	0.575068i	0.0651136	+	0.112780i
$27$	−4.93575	−	1.62430i	−0.949886	−	0.312598i
$28$	1.85185	+	1.88962i	0.349966	+	0.357104i
$29$	2.03452	−	3.52389i	0.377800	−	0.654369i	−0.612942	−	0.790128i	$-0.710014\pi$
$29$	2.03452	−	3.52389i	0.377800	−	0.654369i	0.990742	+	0.135759i	$0.0433473\pi$
$30$	0.702501	+	1.58319i	0.128259	+	0.289050i
$31$	−7.63703			−1.37165			−0.685826	−	0.727766i	$-0.740559\pi$
$31$	−7.63703			−1.37165			−0.685826	+	0.727766i	$0.740559\pi$
$32$	1.00000			0.176777
$33$	11.1039	+	1.18117i	1.93295	+	0.205616i
$34$	0.411850	−	0.713345i	0.0706317	−	0.122338i
$35$	−2.56238	+	0.658939i	−0.433122	+	0.111381i
$36$	−0.919882	−	2.85549i	−0.153314	−	0.475915i
$37$	−5.32042	−	9.21523i	−0.874671	−	1.51497i	−0.857113	−	0.515129i	$-0.827744\pi$
$37$	−5.32042	−	9.21523i	−0.874671	−	1.51497i	−0.0175583	−	0.999846i	$-0.505589\pi$
$38$	−2.77668	−	4.80936i	−0.450437	−	0.780181i
$39$	1.14368	+	0.121658i	0.183136	+	0.0194809i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	0.511800	+	0.886464i	0.0799298	+	0.138442i	0.903219	−	0.429179i	$-0.141197\pi$
$41$	0.511800	+	0.886464i	0.0799298	+	0.138442i	−0.823290	+	0.567621i	$0.807864\pi$
$42$	4.53400	−	0.665454i	0.699612	−	0.102682i
$43$	−4.15005	+	7.18810i	−0.632877	+	1.09618i	0.354084	+	0.935214i	$0.384793\pi$
$43$	−4.15005	+	7.18810i	−0.632877	+	1.09618i	−0.986961	+	0.160961i	$0.948541\pi$
$44$	3.22352	+	5.58330i	0.485964	+	0.841714i
$45$	2.93287	+	0.631103i	0.437206	+	0.0940793i
$46$	1.74387	−	3.02046i	0.257119	−	0.445343i
$47$	2.60076			0.379361			0.189680	−	0.981846i	$-0.439255\pi$
$47$	2.60076			0.379361			0.189680	+	0.981846i	$0.439255\pi$
$48$	1.01983	−	1.39998i	0.147200	−	0.202070i
$49$	−0.141315	+	6.99857i	−0.0201879	+	0.999796i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.578650	−	1.30407i	−0.0810272	−	0.182607i
$52$	0.332016	+	0.575068i	0.0460423	+	0.0797476i
$53$	−3.27668	+	5.67538i	−0.450087	+	0.779574i	−0.998391	−	0.0567055i	$-0.981940\pi$
$53$	−3.27668	+	5.67538i	−0.450087	+	0.779574i	0.548304	+	0.836279i	$0.315274\pi$
$54$	−4.93575	−	1.62430i	−0.671671	−	0.221040i
$55$	−6.44704			−0.869318
$56$	1.85185	+	1.88962i	0.247464	+	0.252511i
$57$	−9.56475	−	1.01744i	−1.26688	−	0.134763i
$58$	2.03452	−	3.52389i	0.267145	−	0.462709i
$59$	−2.91633			−0.379674			−0.189837	−	0.981816i	$-0.560796\pi$
$59$	−2.91633			−0.379674			−0.189837	+	0.981816i	$0.560796\pi$
$60$	0.702501	+	1.58319i	0.0906925	+	0.204389i
$61$	−0.767506			−0.0982691			−0.0491346	−	0.998792i	$-0.515646\pi$
$61$	−0.767506			−0.0982691			−0.0491346	+	0.998792i	$0.515646\pi$
$62$	−7.63703			−0.969904
$63$	3.69230	−	7.02616i	0.465186	−	0.885213i
$64$	1.00000			0.125000
$65$	−0.664031			−0.0823629
$66$	11.1039	+	1.18117i	1.36680	+	0.145392i
$67$	7.28641			0.890176			0.445088	−	0.895487i	$-0.353172\pi$
$67$	7.28641			0.890176			0.445088	+	0.895487i	$0.353172\pi$
$68$	0.411850	−	0.713345i	0.0499442	−	0.0865058i
$69$	−2.45013	−	5.52174i	−0.294962	−	0.664740i
$70$	−2.56238	+	0.658939i	−0.306263	+	0.0787582i
$71$	3.44704			0.409088			0.204544	−	0.978857i	$-0.434429\pi$
$71$	3.44704			0.409088			0.204544	+	0.978857i	$0.434429\pi$
$72$	−0.919882	−	2.85549i	−0.108409	−	0.336523i
$73$	4.71172	−	8.16093i	0.551465	−	0.955165i	−0.446704	−	0.894682i	$-0.647402\pi$
$73$	4.71172	−	8.16093i	0.551465	−	0.955165i	0.998169	−	0.0604835i	$-0.0192642\pi$
$74$	−5.32042	−	9.21523i	−0.618486	−	1.07125i
$75$	−1.72233	−	0.183212i	−0.198878	−	0.0211554i
$76$	−2.77668	−	4.80936i	−0.318507	−	0.551671i
$77$	−4.58083	+	16.4306i	−0.522034	+	1.87244i
$78$	1.14368	+	0.121658i	0.129497	+	0.0137751i
$79$	−5.40500			−0.608110			−0.304055	−	0.952654i	$-0.598341\pi$
$79$	−5.40500			−0.608110			−0.304055	+	0.952654i	$0.598341\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−7.30763	+	5.25343i	−0.811959	+	0.583714i
$82$	0.511800	+	0.886464i	0.0565189	+	0.0978936i
$83$	0.897166	−	1.55394i	0.0984768	−	0.170567i	−0.812578	−	0.582853i	$-0.801936\pi$
$83$	0.897166	−	1.55394i	0.0984768	−	0.170567i	0.911054	+	0.412286i	$0.135270\pi$
$84$	4.53400	−	0.665454i	0.494700	−	0.0726070i
$85$	0.411850	+	0.713345i	0.0446714	+	0.0773732i
$86$	−4.15005	+	7.18810i	−0.447512	+	0.775113i
$87$	−2.85850	−	6.44206i	−0.306463	−	0.690661i
$88$	3.22352	+	5.58330i	0.343628	+	0.595181i
$89$	−2.06497	−	3.57663i	−0.218886	−	0.379122i	0.735582	−	0.677436i	$-0.236909\pi$
$89$	−2.06497	−	3.57663i	−0.218886	−	0.379122i	−0.954468	+	0.298314i	$0.903576\pi$
$90$	2.93287	+	0.631103i	0.309151	+	0.0665241i
$91$	−0.471816	+	1.69232i	−0.0494598	+	0.177404i
$92$	1.74387	−	3.02046i	0.181811	−	0.314905i
$93$	−7.78850	+	10.6917i	−0.807629	+	1.10868i
$94$	2.60076			0.268248
$95$	5.55337			0.569763
$96$	1.01983	−	1.39998i	0.104086	−	0.142885i
$97$	−8.98652	+	15.5651i	−0.912443	+	1.58040i	−0.101839	+	0.994801i	$0.532473\pi$
$97$	−8.98652	+	15.5651i	−0.912443	+	1.58040i	−0.810603	+	0.585596i	$0.800861\pi$
$98$	−0.141315	+	6.99857i	−0.0142750	+	0.706963i
$99$	12.9778	−	14.3407i	1.30432	−	1.44129i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−3.30960	−	5.73239i	−0.329317	−	0.570394i	0.653059	−	0.757307i	$-0.273485\pi$
$101$	−3.30960	−	5.73239i	−0.329317	−	0.570394i	−0.982377	+	0.186912i	$0.940152\pi$
$102$	−0.578650	−	1.30407i	−0.0572949	−	0.129123i
$103$	3.05265	−	5.28735i	0.300787	−	0.520978i	−0.675528	−	0.737335i	$-0.736084\pi$
$103$	3.05265	−	5.28735i	0.300787	−	0.520978i	0.976314	+	0.216357i	$0.0694175\pi$
$104$	0.332016	+	0.575068i	0.0325568	+	0.0563901i
$105$	−1.69070	+	4.25929i	−0.164995	+	0.415664i
$106$	−3.27668	+	5.67538i	−0.318260	+	0.551242i
$107$	7.32418	+	12.6859i	0.708056	+	1.22639i	0.965577	+	0.260116i	$0.0837608\pi$
$107$	7.32418	+	12.6859i	0.708056	+	1.22639i	−0.257522	+	0.966272i	$0.582906\pi$
$108$	−4.93575	−	1.62430i	−0.474943	−	0.156299i
$109$	−0.492869	+	0.853674i	−0.0472083	+	0.0817671i	−0.888664	−	0.458559i	$-0.848366\pi$
$109$	−0.492869	+	0.853674i	−0.0472083	+	0.0817671i	0.841456	+	0.540326i	$0.181699\pi$
$110$	−6.44704			−0.614701
$111$	−18.3271	−	1.94952i	−1.73953	−	0.185041i
$112$	1.85185	+	1.88962i	0.174983	+	0.178552i
$113$	4.06408	+	7.03919i	0.382317	+	0.662192i	0.991393	−	0.130920i	$-0.0417931\pi$
$113$	4.06408	+	7.03919i	0.382317	+	0.662192i	−0.609076	+	0.793112i	$0.708460\pi$
$114$	−9.56475	−	1.01744i	−0.895821	−	0.0952921i
$115$	1.74387	+	3.02046i	0.162616	+	0.281660i
$116$	2.03452	−	3.52389i	0.188900	−	0.327185i
$117$	1.33668	−	1.47706i	0.123577	−	0.136554i
$118$	−2.91633			−0.268470
$119$	2.11063	−	0.542768i	0.193482	−	0.0497554i
$120$	0.702501	+	1.58319i	0.0641293	+	0.144525i
$121$	−15.2821	+	26.4694i	−1.38929	+	2.40631i
$122$	−0.767506			−0.0694868
$123$	1.76298	+	0.187536i	0.158963	+	0.0169095i
$124$	−7.63703			−0.685826
$125$	1.00000			0.0894427
$126$	3.69230	−	7.02616i	0.328936	−	0.625940i
$127$	6.95639			0.617280			0.308640	−	0.951179i	$-0.400126\pi$
$127$	6.95639			0.617280			0.308640	+	0.951179i	$0.400126\pi$
$128$	1.00000			0.0883883
$129$	5.83083	+	13.1406i	0.513376	+	1.15697i
$130$	−0.664031			−0.0582394
$131$	4.88725	−	8.46497i	0.427001	−	0.739588i	−0.569604	−	0.821920i	$-0.692903\pi$
$131$	4.88725	−	8.46497i	0.427001	−	0.739588i	0.996605	+	0.0823314i	$0.0262366\pi$
$132$	11.1039	+	1.18117i	0.966475	+	0.102808i
$133$	3.94585	−	14.1531i	0.342149	−	1.22723i
$134$	7.28641			0.629450
$135$	3.87456	−	3.46233i	0.333469	−	0.297990i
$136$	0.411850	−	0.713345i	0.0353159	−	0.0611689i
$137$	6.42809	+	11.1338i	0.549189	+	0.951223i	0.998330	+	0.0577621i	$0.0183965\pi$
$137$	6.42809	+	11.1338i	0.549189	+	0.951223i	−0.449142	+	0.893461i	$0.648270\pi$
$138$	−2.45013	−	5.52174i	−0.208569	−	0.470042i
$139$	−9.29552	−	16.1003i	−0.788436	−	1.36561i	−0.926925	−	0.375247i	$-0.877558\pi$
$139$	−9.29552	−	16.1003i	−0.788436	−	1.36561i	0.138489	−	0.990364i	$-0.455775\pi$
$140$	−2.56238	+	0.658939i	−0.216561	+	0.0556905i
$141$	2.65235	−	3.64102i	0.223368	−	0.306629i
$142$	3.44704			0.289269
$143$	−2.14052	+	3.70748i	−0.178999	+	0.310035i
$144$	−0.919882	−	2.85549i	−0.0766569	−	0.237957i
$145$	2.03452	+	3.52389i	0.168957	+	0.292643i
$146$	4.71172	−	8.16093i	0.389945	−	0.675404i
$147$	9.65374	+	7.33521i	0.796227	+	0.604998i
$148$	−5.32042	−	9.21523i	−0.437336	−	0.757487i
$149$	4.81823	−	8.34542i	0.394725	−	0.683684i	−0.598341	−	0.801242i	$-0.704173\pi$
$149$	4.81823	−	8.34542i	0.394725	−	0.683684i	0.993066	+	0.117558i	$0.0375065\pi$
$150$	−1.72233	−	0.183212i	−0.140628	−	0.0149592i
$151$	−8.83973	−	15.3109i	−0.719367	−	1.24598i	−0.961251	−	0.275675i	$-0.911098\pi$
$151$	−8.83973	−	15.3109i	−0.719367	−	1.24598i	0.241883	−	0.970305i	$-0.422235\pi$
$152$	−2.77668	−	4.80936i	−0.225219	−	0.390090i
$153$	−2.41580	−	0.519840i	−0.195306	−	0.0420265i
$154$	−4.58083	+	16.4306i	−0.369134	+	1.32402i
$155$	3.81852	−	6.61386i	0.306711	−	0.531238i
$156$	1.14368	+	0.121658i	0.0915680	+	0.00974045i
$157$	−13.0284			−1.03978			−0.519888	−	0.854234i	$-0.674026\pi$
$157$	−13.0284			−1.03978			−0.519888	+	0.854234i	$0.674026\pi$
$158$	−5.40500			−0.429999
$159$	4.60375	+	10.3752i	0.365101	+	0.822809i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	8.93690	−	2.29820i	0.704326	−	0.181124i
$162$	−7.30763	+	5.25343i	−0.574142	+	0.412748i
$163$	−4.56357	−	7.90433i	−0.357446	−	0.619115i	0.630087	−	0.776524i	$-0.283019\pi$
$163$	−4.56357	−	7.90433i	−0.357446	−	0.619115i	−0.987533	+	0.157410i	$0.949686\pi$
$164$	0.511800	+	0.886464i	0.0399649	+	0.0692212i
$165$	−6.57490	+	9.02571i	−0.511855	+	0.702651i
$166$	0.897166	−	1.55394i	0.0696336	−	0.120609i
$167$	2.33645	+	4.04686i	0.180800	+	0.313155i	0.942153	−	0.335182i	$-0.108798\pi$
$167$	2.33645	+	4.04686i	0.180800	+	0.313155i	−0.761353	+	0.648337i	$0.775465\pi$
$168$	4.53400	−	0.665454i	0.349806	−	0.0513409i
$169$	6.27953	−	10.8765i	0.483041	−	0.836651i
$170$	0.411850	+	0.713345i	0.0315875	+	0.0547111i
$171$	−11.1788	+	12.3528i	−0.854867	+	0.944645i
$172$	−4.15005	+	7.18810i	−0.316438	+	0.548088i
$173$	−25.6473			−1.94993			−0.974966	−	0.222356i	$-0.928625\pi$
$173$	−25.6473			−1.94993			−0.974966	+	0.222356i	$0.928625\pi$
$174$	−2.85850	−	6.44206i	−0.216702	−	0.488371i
$175$	0.710533	−	2.54856i	0.0537113	−	0.192653i
$176$	3.22352	+	5.58330i	0.242982	+	0.420857i
$177$	−2.97417	+	4.08281i	−0.223553	+	0.306883i
$178$	−2.06497	−	3.57663i	−0.154776	−	0.268079i
$179$	−2.98463	+	5.16954i	−0.223082	+	0.386389i	−0.955742	−	0.294205i	$-0.904945\pi$
$179$	−2.98463	+	5.16954i	−0.223082	+	0.386389i	0.732660	+	0.680594i	$0.238278\pi$
$180$	2.93287	+	0.631103i	0.218603	+	0.0470396i
$181$	−5.42323			−0.403105			−0.201553	−	0.979478i	$-0.564599\pi$
$181$	−5.42323			−0.403105			−0.201553	+	0.979478i	$0.564599\pi$
$182$	−0.471816	+	1.69232i	−0.0349734	+	0.125443i
$183$	−0.782728	+	1.07449i	−0.0578609	+	0.0794288i
$184$	1.74387	−	3.02046i	0.128559	−	0.222672i
$185$	10.6408			0.782330
$186$	−7.78850	+	10.6917i	−0.571080	+	0.783952i
$187$	5.31042			0.388337
$188$	2.60076			0.189680
$189$	−6.07095	−	12.3347i	−0.441596	−	0.897214i
$190$	5.55337			0.402884
$191$	4.97914			0.360278			0.180139	−	0.983641i	$-0.442345\pi$
$191$	4.97914			0.360278			0.180139	+	0.983641i	$0.442345\pi$
$192$	1.01983	−	1.39998i	0.0736001	−	0.101035i
$193$	−23.4191			−1.68575			−0.842873	−	0.538112i	$-0.819138\pi$
$193$	−23.4191			−1.68575			−0.842873	+	0.538112i	$0.819138\pi$
$194$	−8.98652	+	15.5651i	−0.645194	+	1.11751i
$195$	−0.677201	+	0.929630i	−0.0484954	+	0.0665722i
$196$	−0.141315	+	6.99857i	−0.0100939	+	0.499898i
$197$	−11.5441			−0.822480			−0.411240	−	0.911527i	$-0.634904\pi$
$197$	−11.5441			−0.822480			−0.411240	+	0.911527i	$0.634904\pi$
$198$	12.9778	−	14.3407i	0.922291	−	1.01915i
$199$	8.07725	−	13.9902i	0.572581	−	0.991740i	−0.423719	−	0.905794i	$-0.639275\pi$
$199$	8.07725	−	13.9902i	0.572581	−	0.991740i	0.996300	−	0.0859457i	$-0.0273912\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	7.43092	−	10.2008i	0.524136	−	0.719510i
$202$	−3.30960	−	5.73239i	−0.232863	−	0.403330i
$203$	10.4264	−	2.68124i	0.731791	−	0.188186i
$204$	−0.578650	−	1.30407i	−0.0405136	−	0.0913035i
$205$	−1.02360			−0.0714914
$206$	3.05265	−	5.28735i	0.212688	−	0.368387i
$207$	−10.2291	−	2.20112i	−0.710968	−	0.152988i
$208$	0.332016	+	0.575068i	0.0230211	+	0.0398738i
$209$	17.9014	−	31.0061i	1.23826	−	2.14474i
$210$	−1.69070	+	4.25929i	−0.116669	+	0.293919i
$211$	13.0581	+	22.6172i	0.898954	+	1.55703i	0.828833	+	0.559496i	$0.189005\pi$
$211$	13.0581	+	22.6172i	0.898954	+	1.55703i	0.0701210	+	0.997538i	$0.477661\pi$
$212$	−3.27668	+	5.67538i	−0.225044	+	0.389787i
$213$	3.51540	−	4.82578i	0.240871	−	0.330657i
$214$	7.32418	+	12.6859i	0.500671	+	0.867188i
$215$	−4.15005	−	7.18810i	−0.283031	−	0.490224i
$216$	−4.93575	−	1.62430i	−0.335835	−	0.110520i
$217$	−14.1426	−	14.4311i	−0.960064	−	0.979645i
$218$	−0.492869	+	0.853674i	−0.0333813	+	0.0578181i
$219$	−6.61997	−	14.9191i	−0.447336	−	1.00814i
$220$	−6.44704			−0.434659
$221$	0.546963			0.0367927
$222$	−18.3271	−	1.94952i	−1.23003	−	0.130843i
$223$	−0.452684	+	0.784071i	−0.0303139	+	0.0525053i	−0.880784	−	0.473518i	$-0.842984\pi$
$223$	−0.452684	+	0.784071i	−0.0303139	+	0.0525053i	0.850470	+	0.526023i	$0.176317\pi$
$224$	1.85185	+	1.88962i	0.123732	+	0.126255i
$225$	−2.01298	+	2.22439i	−0.134199	+	0.148292i
$226$	4.06408	+	7.03919i	0.270339	+	0.468240i
$227$	10.7112	+	18.5524i	0.710928	+	1.23136i	0.964509	+	0.264050i	$0.0850583\pi$
$227$	10.7112	+	18.5524i	0.710928	+	1.23136i	−0.253581	+	0.967314i	$0.581608\pi$
$228$	−9.56475	−	1.01744i	−0.633441	−	0.0673817i
$229$	7.96073	−	13.7884i	0.526060	−	0.911163i	−0.473479	−	0.880805i	$-0.657002\pi$
$229$	7.96073	−	13.7884i	0.526060	−	0.911163i	0.999539	−	0.0303576i	$-0.00966460\pi$
$230$	1.74387	+	3.02046i	0.114987	+	0.199164i
$231$	18.3309	+	23.1696i	1.20608	+	1.52445i
$232$	2.03452	−	3.52389i	0.133573	−	0.231354i
$233$	−3.45390	−	5.98232i	−0.226272	−	0.391915i	0.730428	−	0.682990i	$-0.239321\pi$
$233$	−3.45390	−	5.98232i	−0.226272	−	0.391915i	−0.956700	+	0.291075i	$0.905987\pi$
$234$	1.33668	−	1.47706i	0.0873818	−	0.0965586i
$235$	−1.30038	+	2.25233i	−0.0848276	+	0.146926i
$236$	−2.91633			−0.189837
$237$	−5.51220	+	7.56689i	−0.358056	+	0.491522i
$238$	2.11063	−	0.542768i	0.136812	−	0.0351824i
$239$	7.95013	+	13.7700i	0.514251	+	0.890709i	0.999863	+	0.0165346i	$0.00526335\pi$
$239$	7.95013	+	13.7700i	0.514251	+	0.890709i	−0.485612	+	0.874174i	$0.661403\pi$
$240$	0.702501	+	1.58319i	0.0453462	+	0.102195i
$241$	−4.67555	−	8.09830i	−0.301179	−	0.521657i	0.675224	−	0.737612i	$-0.264047\pi$
$241$	−4.67555	−	8.09830i	−0.301179	−	0.521657i	−0.976403	+	0.215955i	$0.930713\pi$
$242$	−15.2821	+	26.4694i	−0.982373	+	1.70152i
$243$	−0.0978746	+	15.5882i	−0.00627866	+	0.999980i
$244$	−0.767506			−0.0491346
$245$	−5.99028	−	3.62167i	−0.382705	−	0.231380i
$246$	1.76298	+	0.187536i	0.112404	+	0.0119568i
$247$	1.84380	−	3.19356i	0.117318	−	0.203202i
$248$	−7.63703			−0.484952
$249$	−1.26052	−	2.84077i	−0.0798822	−	0.180026i
$250$	1.00000			0.0632456
$251$	14.3111			0.903310			0.451655	−	0.892193i	$-0.350834\pi$
$251$	14.3111			0.903310			0.451655	+	0.892193i	$0.350834\pi$
$252$	3.69230	−	7.02616i	0.232593	−	0.442606i
$253$	22.4855			1.41365
$254$	6.95639			0.436483
$255$	1.41869	+	0.150911i	0.0888416	+	0.00945044i
$256$	1.00000			0.0625000
$257$	4.08461	−	7.07475i	0.254791	−	0.441311i	−0.710048	−	0.704153i	$-0.751327\pi$
$257$	4.08461	−	7.07475i	0.254791	−	0.441311i	0.964839	+	0.262843i	$0.0846601\pi$
$258$	5.83083	+	13.1406i	0.363012	+	0.818101i
$259$	7.56067	−	27.1188i	0.469797	−	1.68508i
$260$	−0.664031			−0.0411815
$261$	−11.9339	−	2.56798i	−0.738692	−	0.158954i
$262$	4.88725	−	8.46497i	0.301936	−	0.522968i
$263$	−8.24002	−	14.2721i	−0.508101	−	0.880057i	−0.999956	−	0.00937977i	$-0.997014\pi$
$263$	−8.24002	−	14.2721i	−0.508101	−	0.880057i	0.491855	−	0.870677i	$-0.336319\pi$
$264$	11.1039	+	1.18117i	0.683401	+	0.0726961i
$265$	−3.27668	−	5.67538i	−0.201285	−	0.348636i
$266$	3.94585	−	14.1531i	0.241936	−	0.867780i
$267$	−7.11312	−	0.756651i	−0.435316	−	0.0463063i
$268$	7.28641			0.445088
$269$	−12.8752	+	22.3005i	−0.785015	+	1.35969i	0.143976	+	0.989581i	$0.454011\pi$
$269$	−12.8752	+	22.3005i	−0.785015	+	1.35969i	−0.928990	+	0.370104i	$0.879322\pi$
$270$	3.87456	−	3.46233i	0.235798	−	0.210711i
$271$	−10.3794	−	17.9777i	−0.630504	−	1.09207i	−0.987449	−	0.157940i	$-0.949515\pi$
$271$	−10.3794	−	17.9777i	−0.630504	−	1.09207i	0.356944	−	0.934126i	$-0.383819\pi$
$272$	0.411850	−	0.713345i	0.0249721	−	0.0432529i
$273$	1.88804	+	2.38642i	0.114269	+	0.144433i
$274$	6.42809	+	11.1338i	0.388335	+	0.672616i
$275$	3.22352	−	5.58330i	0.194385	−	0.336685i
$276$	−2.45013	−	5.52174i	−0.147481	−	0.332370i
$277$	15.5538	+	26.9400i	0.934540	+	1.61867i	0.775453	+	0.631405i	$0.217522\pi$
$277$	15.5538	+	26.9400i	0.934540	+	1.61867i	0.159087	+	0.987265i	$0.449145\pi$
$278$	−9.29552	−	16.1003i	−0.557508	−	0.965633i
$279$	7.02517	+	21.8075i	0.420586	+	1.30558i
$280$	−2.56238	+	0.658939i	−0.153132	+	0.0393791i
$281$	15.0816	−	26.1221i	0.899692	−	1.55831i	0.0718045	−	0.997419i	$-0.477124\pi$
$281$	15.0816	−	26.1221i	0.899692	−	1.55831i	0.827888	−	0.560894i	$-0.189542\pi$
$282$	2.65235	−	3.64102i	0.157945	−	0.216819i
$283$	22.2721			1.32394			0.661969	−	0.749531i	$-0.269721\pi$
$283$	22.2721			1.32394			0.661969	+	0.749531i	$0.269721\pi$
$284$	3.44704			0.204544
$285$	5.66350	−	7.77460i	0.335477	−	0.460527i
$286$	−2.14052	+	3.70748i	−0.126571	+	0.219228i
$287$	−0.727303	+	2.60871i	−0.0429313	+	0.153987i
$288$	−0.919882	−	2.85549i	−0.0542046	−	0.168261i
$289$	8.16076	+	14.1348i	0.480045	+	0.831462i
$290$	2.03452	+	3.52389i	0.119471	+	0.206930i
$291$	12.6261	+	28.4547i	0.740154	+	1.66805i
$292$	4.71172	−	8.16093i	0.275732	−	0.477583i
$293$	10.9592	+	18.9818i	0.640242	+	1.10893i	0.985379	+	0.170379i	$0.0544991\pi$
$293$	10.9592	+	18.9818i	0.640242	+	1.10893i	−0.345137	+	0.938552i	$0.612168\pi$
$294$	9.65374	+	7.33521i	0.563017	+	0.427798i
$295$	1.45817	−	2.52562i	0.0848978	−	0.147047i
$296$	−5.32042	−	9.21523i	−0.309243	−	0.535624i
$297$	−6.84150	−	32.7937i	−0.396984	−	1.90289i
$298$	4.81823	−	8.34542i	0.279113	−	0.483437i
$299$	2.31596			0.133936
$300$	−1.72233	−	0.183212i	−0.0994390	−	0.0105777i
$301$	−21.2680	+	5.46926i	−1.22587	+	0.315243i
$302$	−8.83973	−	15.3109i	−0.508670	−	0.881041i
$303$	−11.4005	−	1.21271i	−0.654940	−	0.0696686i
$304$	−2.77668	−	4.80936i	−0.159254	−	0.275836i
$305$	0.383753	−	0.664680i	0.0219736	−	0.0380595i
$306$	−2.41580	−	0.519840i	−0.138102	−	0.0297173i
$307$	−8.76843			−0.500441			−0.250220	−	0.968189i	$-0.580503\pi$
$307$	−8.76843			−0.500441			−0.250220	+	0.968189i	$0.580503\pi$
$308$	−4.58083	+	16.4306i	−0.261017	+	0.936222i
$309$	−4.28898	−	9.66585i	−0.243992	−	0.549871i
$310$	3.81852	−	6.61386i	0.216877	−	0.375642i
$311$	28.7971			1.63293			0.816466	−	0.577394i	$-0.195930\pi$
$311$	28.7971			1.63293			0.816466	+	0.577394i	$0.195930\pi$
$312$	1.14368	+	0.121658i	0.0647483	+	0.00688754i
$313$	15.0040			0.848073			0.424037	−	0.905645i	$-0.360613\pi$
$313$	15.0040			0.848073			0.424037	+	0.905645i	$0.360613\pi$
$314$	−13.0284			−0.735233
$315$	4.23868	+	6.71071i	0.238823	+	0.378105i
$316$	−5.40500			−0.304055
$317$	−23.7437			−1.33358			−0.666791	−	0.745245i	$-0.732332\pi$
$317$	−23.7437			−1.33358			−0.666791	+	0.745245i	$0.732332\pi$
$318$	4.60375	+	10.3752i	0.258165	+	0.581814i
$319$	26.2332			1.46878
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	25.2294	+	2.68375i	1.40817	+	0.149792i
$322$	8.93690	−	2.29820i	0.498034	−	0.128074i
$323$	−4.57431			−0.254521
$324$	−7.30763	+	5.25343i	−0.405980	+	0.291857i
$325$	0.332016	−	0.575068i	0.0184169	−	0.0318990i
$326$	−4.56357	−	7.90433i	−0.252753	−	0.437780i
$327$	0.692482	+	1.56061i	0.0382943	+	0.0863019i
$328$	0.511800	+	0.886464i	0.0282595	+	0.0489468i
$329$	4.81622	+	4.91445i	0.265527	+	0.270943i
$330$	−6.57490	+	9.02571i	−0.361936	+	0.496849i
$331$	−3.51509			−0.193207			−0.0966033	−	0.995323i	$-0.530798\pi$
$331$	−3.51509			−0.193207			−0.0966033	+	0.995323i	$0.530798\pi$
$332$	0.897166	−	1.55394i	0.0492384	−	0.0852834i
$333$	−21.4198	+	23.6693i	−1.17380	+	1.29707i
$334$	2.33645	+	4.04686i	0.127845	+	0.221434i
$335$	−3.64320	+	6.31021i	−0.199049	+	0.344764i
$336$	4.53400	−	0.665454i	0.247350	−	0.0363035i
$337$	16.6235	+	28.7927i	0.905538	+	1.56844i	0.820194	+	0.572086i	$0.193866\pi$
$337$	16.6235	+	28.7927i	0.905538	+	1.56844i	0.0853438	+	0.996352i	$0.472801\pi$
$338$	6.27953	−	10.8765i	0.341561	−	0.591602i
$339$	13.9994	+	1.48917i	0.760343	+	0.0808808i
$340$	0.411850	+	0.713345i	0.0223357	+	0.0386866i
$341$	−24.6181	−	42.6398i	−1.33315	−	2.30908i
$342$	−11.1788	+	12.3528i	−0.604482	+	0.667965i
$343$	−13.4863	+	12.6933i	−0.728193	+	0.685372i
$344$	−4.15005	+	7.18810i	−0.223756	+	0.387556i
$345$	6.00704	+	0.638993i	0.323408	+	0.0344022i
$346$	−25.6473			−1.37881
$347$	5.36573			0.288047			0.144024	−	0.989574i	$-0.453996\pi$
$347$	5.36573			0.288047			0.144024	+	0.989574i	$0.453996\pi$
$348$	−2.85850	−	6.44206i	−0.153232	−	0.345330i
$349$	2.39917	−	4.15548i	0.128424	−	0.222438i	−0.794642	−	0.607078i	$-0.792341\pi$
$349$	2.39917	−	4.15548i	0.128424	−	0.222438i	0.923066	+	0.384641i	$0.125675\pi$
$350$	0.710533	−	2.54856i	0.0379796	−	0.136226i
$351$	−0.704661	−	3.37769i	−0.0376120	−	0.180288i
$352$	3.22352	+	5.58330i	0.171814	+	0.297591i
$353$	16.2100	+	28.0765i	0.862770	+	1.49436i	0.869244	+	0.494383i	$0.164606\pi$
$353$	16.2100	+	28.0765i	0.862770	+	1.49436i	−0.00647381	+	0.999979i	$0.502061\pi$
$354$	−2.97417	+	4.08281i	−0.158076	+	0.216999i
$355$	−1.72352	+	2.98522i	−0.0914748	+	0.158439i
$356$	−2.06497	−	3.57663i	−0.109443	−	0.189561i
$357$	1.39263	−	3.50838i	0.0737058	−	0.185683i
$358$	−2.98463	+	5.16954i	−0.157743	+	0.273218i
$359$	−5.80951	−	10.0624i	−0.306614	−	0.531072i	0.671005	−	0.741453i	$-0.265863\pi$
$359$	−5.80951	−	10.0624i	−0.306614	−	0.531072i	−0.977619	+	0.210381i	$0.932530\pi$
$360$	2.93287	+	0.631103i	0.154576	+	0.0332620i
$361$	−5.91994	+	10.2536i	−0.311576	+	0.539665i
$362$	−5.42323			−0.285039
$363$	21.4714	+	48.3891i	1.12696	+	2.53977i
$364$	−0.471816	+	1.69232i	−0.0247299	+	0.0887018i
$365$	4.71172	+	8.16093i	0.246623	+	0.427163i
$366$	−0.782728	+	1.07449i	−0.0409139	+	0.0561646i
$367$	8.36773	+	14.4933i	0.436792	+	0.756546i	0.997440	−	0.0715082i	$-0.0227812\pi$
$367$	8.36773	+	14.4933i	0.436792	+	0.756546i	−0.560648	+	0.828054i	$0.689448\pi$
$368$	1.74387	−	3.02046i	0.0909053	−	0.157453i
$369$	2.06049	−	2.27688i	0.107265	−	0.118530i
$370$	10.6408			0.553191
$371$	−16.7922	+	4.31827i	−0.871809	+	0.224193i
$372$	−7.78850	+	10.6917i	−0.403815	+	0.554338i
$373$	6.07788	−	10.5272i	0.314701	−	0.545078i	−0.664673	−	0.747134i	$-0.731429\pi$
$373$	6.07788	−	10.5272i	0.314701	−	0.545078i	0.979374	+	0.202057i	$0.0647625\pi$
$374$	5.31042			0.274596
$375$	1.01983	−	1.39998i	0.0526639	−	0.0722946i
$376$	2.60076			0.134124
$377$	2.70197			0.139158
$378$	−6.07095	−	12.3347i	−0.312256	−	0.634426i
$379$	−18.5422			−0.952448			−0.476224	−	0.879324i	$-0.657995\pi$
$379$	−18.5422			−0.952448			−0.476224	+	0.879324i	$0.657995\pi$
$380$	5.55337			0.284882
$381$	7.09436	−	9.73880i	0.363455	−	0.498934i
$382$	4.97914			0.254755
$383$	−4.16276	+	7.21011i	−0.212707	+	0.368420i	−0.952561	−	0.304348i	$-0.901561\pi$
$383$	−4.16276	+	7.21011i	−0.212707	+	0.368420i	0.739854	+	0.672768i	$0.234895\pi$
$384$	1.01983	−	1.39998i	0.0520431	−	0.0714424i
$385$	−11.9389	−	12.1824i	−0.608464	−	0.620875i
$386$	−23.4191			−1.19200
$387$	24.3431	+	5.23822i	1.23743	+	0.266274i
$388$	−8.98652	+	15.5651i	−0.456221	+	0.790198i
$389$	6.54784	+	11.3412i	0.331988	+	0.575021i	0.982902	−	0.184131i	$-0.0589472\pi$
$389$	6.54784	+	11.3412i	0.331988	+	0.575021i	−0.650913	+	0.759152i	$0.725614\pi$
$390$	−0.677201	+	0.929630i	−0.0342914	+	0.0470736i
$391$	−1.43642	−	2.48796i	−0.0726430	−	0.125821i
$392$	−0.141315	+	6.99857i	−0.00713749	+	0.353481i
$393$	−6.86660	−	15.4749i	−0.346374	−	0.780606i
$394$	−11.5441			−0.581581
$395$	2.70250	−	4.68087i	0.135978	−	0.235520i
$396$	12.9778	−	14.3407i	0.652158	−	0.720647i
$397$	13.2600	+	22.9670i	0.665501	+	1.15268i	0.979149	+	0.203143i	$0.0651156\pi$
$397$	13.2600	+	22.9670i	0.665501	+	1.15268i	−0.313648	+	0.949539i	$0.601551\pi$
$398$	8.07725	−	13.9902i	0.404876	−	0.701266i
$399$	−15.7899	−	19.9579i	−0.790483	−	0.999143i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	14.6317	−	25.3429i	0.730672	−	1.26556i	−0.225924	−	0.974145i	$-0.572540\pi$
$401$	14.6317	−	25.3429i	0.730672	−	1.26556i	0.956596	−	0.291417i	$-0.0941266\pi$
$402$	7.43092	−	10.2008i	0.370620	−	0.508771i
$403$	−2.53561	−	4.39181i	−0.126308	−	0.218772i
$404$	−3.30960	−	5.73239i	−0.164659	−	0.285197i
$405$	−0.895785	−	8.95531i	−0.0445119	−	0.444993i
$406$	10.4264	−	2.68124i	0.517454	−	0.133068i
$407$	34.3009	−	59.4109i	1.70023	−	2.94489i
$408$	−0.578650	−	1.30407i	−0.0286475	−	0.0645613i
$409$	14.1459			0.699470			0.349735	−	0.936849i	$-0.386272\pi$
$409$	14.1459			0.699470			0.349735	+	0.936849i	$0.386272\pi$
$410$	−1.02360			−0.0505520
$411$	22.1426	+	2.35540i	1.09222	+	0.116183i
$412$	3.05265	−	5.28735i	0.150393	−	0.260489i
$413$	−5.40061	−	5.51076i	−0.265747	−	0.271167i
$414$	−10.2291	−	2.20112i	−0.502731	−	0.108179i
$415$	0.897166	+	1.55394i	0.0440402	+	0.0762798i
$416$	0.332016	+	0.575068i	0.0162784	+	0.0281950i
$417$	−32.0200	−	3.40609i	−1.56803	−	0.166797i
$418$	17.9014	−	31.0061i	0.875585	−	1.51656i
$419$	−16.6209	−	28.7882i	−0.811982	−	1.40639i	−0.911475	−	0.411356i	$-0.865055\pi$
$419$	−16.6209	−	28.7882i	−0.811982	−	1.40639i	0.0994931	−	0.995038i	$-0.468278\pi$
$420$	−1.69070	+	4.25929i	−0.0824977	+	0.207832i
$421$	9.58351	−	16.5991i	0.467072	−	0.808992i	−0.532220	−	0.846606i	$-0.678642\pi$
$421$	9.58351	−	16.5991i	0.467072	−	0.808992i	0.999292	+	0.0376136i	$0.0119756\pi$
$422$	13.0581	+	22.6172i	0.635657	+	1.10099i
$423$	−2.39240	−	7.42646i	−0.116322	−	0.361087i
$424$	−3.27668	+	5.67538i	−0.159130	+	0.275621i
$425$	−0.823700			−0.0399553
$426$	3.51540	−	4.82578i	0.170322	−	0.233810i
$427$	−1.42131	−	1.45029i	−0.0687818	−	0.0701847i
$428$	7.32418	+	12.6859i	0.354028	+	0.613194i
$429$	3.00743	+	6.77769i	0.145200	+	0.327230i
$430$	−4.15005	−	7.18810i	−0.200133	−	0.346641i
$431$	9.77141	−	16.9246i	0.470672	−	0.815228i	−0.528765	−	0.848768i	$-0.677345\pi$
$431$	9.77141	−	16.9246i	0.470672	−	0.815228i	0.999437	+	0.0335402i	$0.0106782\pi$
$432$	−4.93575	−	1.62430i	−0.237471	−	0.0781494i
$433$	20.6650			0.993097			0.496548	−	0.868009i	$-0.334601\pi$
$433$	20.6650			0.993097			0.496548	+	0.868009i	$0.334601\pi$
$434$	−14.1426	−	14.4311i	−0.678868	−	0.692714i
$435$	7.00823	+	0.745494i	0.336019	+	0.0357437i
$436$	−0.492869	+	0.853674i	−0.0236041	+	0.0408836i
$437$	−19.3687			−0.926528
$438$	−6.61997	−	14.9191i	−0.316315	−	0.712862i
$439$	17.5808			0.839088			0.419544	−	0.907735i	$-0.362190\pi$
$439$	17.5808			0.839088			0.419544	+	0.907735i	$0.362190\pi$
$440$	−6.44704			−0.307350
$441$	20.1143	−	6.03434i	0.957826	−	0.287350i
$442$	0.546963			0.0260164
$443$	16.3960			0.778996			0.389498	−	0.921027i	$-0.372648\pi$
$443$	16.3960			0.778996			0.389498	+	0.921027i	$0.372648\pi$
$444$	−18.3271	−	1.94952i	−0.869764	−	0.0925203i
$445$	4.12993			0.195778
$446$	−0.452684	+	0.784071i	−0.0214352	+	0.0371268i
$447$	−6.76963	−	15.2564i	−0.320192	−	0.721601i
$448$	1.85185	+	1.88962i	0.0874916	+	0.0892761i
$449$	−33.5534			−1.58348			−0.791740	−	0.610858i	$-0.790825\pi$
$449$	−33.5534			−1.58348			−0.791740	+	0.610858i	$0.790825\pi$
$450$	−2.01298	+	2.22439i	−0.0948930	+	0.104859i
$451$	−3.29960	+	5.71507i	−0.155372	+	0.269112i
$452$	4.06408	+	7.03919i	0.191158	+	0.331096i
$453$	−30.4499	−	3.23908i	−1.43066	−	0.152185i
$454$	10.7112	+	18.5524i	0.502702	+	0.870706i
$455$	−1.22969	−	1.25477i	−0.0576485	−	0.0588243i
$456$	−9.56475	−	1.01744i	−0.447910	−	0.0476460i
$457$	19.5171			0.912971			0.456486	−	0.889731i	$-0.349108\pi$
$457$	19.5171			0.912971			0.456486	+	0.889731i	$0.349108\pi$
$458$	7.96073	−	13.7884i	0.371981	−	0.644289i
$459$	−3.19148	+	2.85192i	−0.148966	+	0.133116i
$460$	1.74387	+	3.02046i	0.0813082	+	0.140830i
$461$	−15.2287	+	26.3769i	−0.709272	+	1.22850i	0.255855	+	0.966715i	$0.417643\pi$
$461$	−15.2287	+	26.3769i	−0.709272	+	1.22850i	−0.965127	+	0.261781i	$0.915690\pi$
$462$	18.3309	+	23.1696i	0.852829	+	1.07795i
$463$	−7.56973	−	13.1112i	−0.351795	−	0.609327i	0.634769	−	0.772702i	$-0.281095\pi$
$463$	−7.56973	−	13.1112i	−0.351795	−	0.609327i	−0.986564	+	0.163375i	$0.947762\pi$
$464$	2.03452	−	3.52389i	0.0944501	−	0.163592i
$465$	−5.36502	−	12.0909i	−0.248797	−	0.560701i
$466$	−3.45390	−	5.98232i	−0.159999	−	0.277126i
$467$	0.118683	+	0.205565i	0.00549199	+	0.00951241i	0.868758	−	0.495236i	$-0.164919\pi$
$467$	0.118683	+	0.205565i	0.00549199	+	0.00951241i	−0.863266	+	0.504749i	$0.831585\pi$
$468$	1.33668	−	1.47706i	0.0617883	−	0.0682772i
$469$	13.4933	+	13.7685i	0.623064	+	0.635772i
$470$	−1.30038	+	2.25233i	−0.0599822	+	0.103892i
$471$	−13.2867	+	18.2394i	−0.612221	+	0.840429i
$472$	−2.91633			−0.134235
$473$	−53.5111			−2.46044
$474$	−5.51220	+	7.56689i	−0.253184	+	0.347559i
$475$	−2.77668	+	4.80936i	−0.127403	+	0.220668i
$476$	2.11063	−	0.542768i	0.0967408	−	0.0248777i
$477$	19.2202	+	4.13585i	0.880030	+	0.189367i
$478$	7.95013	+	13.7700i	0.363630	+	0.629826i
$479$	6.76029	+	11.7092i	0.308885	+	0.535005i	0.978119	−	0.208047i	$-0.0667107\pi$
$479$	6.76029	+	11.7092i	0.308885	+	0.535005i	−0.669233	+	0.743052i	$0.733377\pi$
$480$	0.702501	+	1.58319i	0.0320646	+	0.0722624i
$481$	3.53292	−	6.11920i	0.161087	−	0.279012i
$482$	−4.67555	−	8.09830i	−0.212966	−	0.368867i
$483$	5.89671	−	14.8553i	0.268310	−	0.675937i
$484$	−15.2821	+	26.4694i	−0.694643	+	1.20316i
$485$	−8.98652	−	15.5651i	−0.408057	−	0.706775i
$486$	−0.0978746	+	15.5882i	−0.00443968	+	0.707093i
$487$	19.3582	−	33.5294i	0.877203	−	1.51936i	0.0228055	−	0.999740i	$-0.492740\pi$
$487$	19.3582	−	33.5294i	0.877203	−	1.51936i	0.854397	−	0.519620i	$-0.173927\pi$
$488$	−0.767506			−0.0347434
$489$	−15.7200	−	1.67220i	−0.710881	−	0.0756193i
$490$	−5.99028	−	3.62167i	−0.270613	−	0.163610i
$491$	5.10089	+	8.83500i	0.230200	+	0.398718i	0.957867	−	0.287213i	$-0.0927287\pi$
$491$	5.10089	+	8.83500i	0.230200	+	0.398718i	−0.727667	+	0.685931i	$0.759395\pi$
$492$	1.76298	+	0.187536i	0.0794814	+	0.00845475i
$493$	−1.67583	−	2.90263i	−0.0754757	−	0.130728i
$494$	1.84380	−	3.19356i	0.0829567	−	0.143685i
$495$	5.93051	+	18.4094i	0.266557	+	0.827443i
$496$	−7.63703			−0.342913
$497$	6.38339	+	6.51358i	0.286334	+	0.292174i
$498$	−1.26052	−	2.84077i	−0.0564853	−	0.127298i
$499$	5.34312	−	9.25456i	0.239191	−	0.414291i	−0.721291	−	0.692632i	$-0.756451\pi$
$499$	5.34312	−	9.25456i	0.239191	−	0.414291i	0.960482	+	0.278341i	$0.0897845\pi$
$500$	1.00000			0.0447214
$501$	8.04830	+	0.856130i	0.359572	+	0.0382491i
$502$	14.3111			0.638736
$503$	−5.82335			−0.259651			−0.129825	−	0.991537i	$-0.541442\pi$
$503$	−5.82335			−0.259651			−0.129825	+	0.991537i	$0.541442\pi$
$504$	3.69230	−	7.02616i	0.164468	−	0.312970i
$505$	6.61920			0.294550
$506$	22.4855			0.999604
$507$	−8.82275	−	19.8834i	−0.391832	−	0.883052i
$508$	6.95639			0.308640
$509$	−14.7801	+	25.5999i	−0.655118	+	1.13470i	0.326746	+	0.945112i	$0.394048\pi$
$509$	−14.7801	+	25.5999i	−0.655118	+	1.13470i	−0.981864	+	0.189585i	$0.939286\pi$
$510$	1.41869	+	0.150911i	0.0628205	+	0.00668247i
$511$	24.1464	−	6.20946i	1.06818	−	0.274691i
$512$	1.00000			0.0441942
$513$	5.89315	+	28.2480i	0.260189	+	1.24718i
$514$	4.08461	−	7.07475i	0.180164	−	0.312054i
$515$	3.05265	+	5.28735i	0.134516	+	0.232988i
$516$	5.83083	+	13.1406i	0.256688	+	0.578485i
$517$	8.38361	+	14.5208i	0.368711	+	0.638626i
$518$	7.56067	−	27.1188i	0.332197	−	1.19153i
$519$	−26.1560	+	35.9057i	−1.14812	+	1.57609i
$520$	−0.664031			−0.0291197
$521$	−19.4542	+	33.6957i	−0.852306	+	1.47624i	0.0268165	+	0.999640i	$0.491463\pi$
$521$	−19.4542	+	33.6957i	−0.852306	+	1.47624i	−0.879122	+	0.476596i	$0.841870\pi$
$522$	−11.9339	−	2.56798i	−0.522334	−	0.112397i
$523$	9.81571	+	17.0013i	0.429211	+	0.743415i	0.996803	−	0.0798944i	$-0.0254583\pi$
$523$	9.81571	+	17.0013i	0.429211	+	0.743415i	−0.567592	+	0.823310i	$0.692125\pi$
$524$	4.88725	−	8.46497i	0.213501	−	0.369794i
$525$	−2.84330	−	3.59383i	−0.124092	−	0.156848i
$526$	−8.24002	−	14.2721i	−0.359282	−	0.622294i
$527$	−3.14531	+	5.44784i	−0.137012	+	0.237312i
$528$	11.1039	+	1.18117i	0.483237	+	0.0514039i
$529$	5.41786	+	9.38402i	0.235559	+	0.408001i
$530$	−3.27668	−	5.67538i	−0.142330	−	0.246523i
$531$	2.68268	+	8.32756i	0.116419	+	0.361385i
$532$	3.94585	−	14.1531i	0.171074	−	0.613613i
$533$	−0.339852	+	0.588640i	−0.0147206	+	0.0254968i
$534$	−7.11312	−	0.756651i	−0.307815	−	0.0327435i
$535$	−14.6484			−0.633304
$536$	7.28641			0.314725
$537$	4.19341	+	9.45048i	0.180959	+	0.407818i
$538$	−12.8752	+	22.3005i	−0.555089	+	0.961443i
$539$	−39.5306	+	21.7710i	−1.70271	+	0.937744i
$540$	3.87456	−	3.46233i	0.166735	−	0.148995i
$541$	−0.957774	−	1.65891i	−0.0411779	−	0.0713222i	0.844702	−	0.535237i	$-0.179778\pi$
$541$	−0.957774	−	1.65891i	−0.0411779	−	0.0713222i	−0.885880	+	0.463915i	$0.846444\pi$
$542$	−10.3794	−	17.9777i	−0.445834	−	0.772207i
$543$	−5.53079	+	7.59241i	−0.237349	+	0.325821i
$544$	0.411850	−	0.713345i	0.0176579	−	0.0305844i
$545$	−0.492869	−	0.853674i	−0.0211122	−	0.0365674i
$546$	1.88804	+	2.38642i	0.0808007	+	0.102129i
$547$	0.366029	−	0.633981i	0.0156503	−	0.0271071i	−0.858094	−	0.513492i	$-0.828351\pi$
$547$	0.366029	−	0.633981i	0.0156503	−	0.0271071i	0.873744	+	0.486385i	$0.161685\pi$
$548$	6.42809	+	11.1338i	0.274594	+	0.475611i
$549$	0.706016	+	2.19161i	0.0301320	+	0.0935355i
$550$	3.22352	−	5.58330i	0.137451	−	0.238073i
$551$	−22.5968			−0.962657
$552$	−2.45013	−	5.52174i	−0.104285	−	0.235021i
$553$	−10.0092	−	10.2134i	−0.425636	−	0.434318i
$554$	15.5538	+	26.9400i	0.660819	+	1.14457i
$555$	10.8519	−	14.8969i	0.460636	−	0.632340i
$556$	−9.29552	−	16.1003i	−0.394218	−	0.682805i
$557$	−2.32694	+	4.03038i	−0.0985957	+	0.170773i	−0.911104	−	0.412177i	$-0.864768\pi$
$557$	−2.32694	+	4.03038i	−0.0985957	+	0.170773i	0.812508	+	0.582950i	$0.198102\pi$
$558$	7.02517	+	21.8075i	0.297399	+	0.923183i
$559$	−5.51153			−0.233113
$560$	−2.56238	+	0.658939i	−0.108280	+	0.0278452i
$561$	5.41574	−	7.43448i	0.228653	−	0.313884i
$562$	15.0816	−	26.1221i	0.636178	−	1.10189i
$563$	−30.9455			−1.30420			−0.652100	−	0.758133i	$-0.726112\pi$
$563$	−30.9455			−1.30420			−0.652100	+	0.758133i	$0.726112\pi$
$564$	2.65235	−	3.64102i	0.111684	−	0.153314i
$565$	−8.12816			−0.341954
$566$	22.2721			0.936166
$567$	−23.4596	−	4.08009i	−0.985211	−	0.171347i
$568$	3.44704			0.144634
$569$	−21.2645			−0.891453			−0.445727	−	0.895169i	$-0.647055\pi$
$569$	−21.2645			−0.891453			−0.445727	+	0.895169i	$0.647055\pi$
$570$	5.66350	−	7.77460i	0.237218	−	0.325642i
$571$	−3.81210			−0.159531			−0.0797656	−	0.996814i	$-0.525417\pi$
$571$	−3.81210			−0.159531			−0.0797656	+	0.996814i	$0.525417\pi$
$572$	−2.14052	+	3.70748i	−0.0894995	+	0.155018i
$573$	5.07789	−	6.97069i	0.212132	−	0.291205i
$574$	−0.727303	+	2.60871i	−0.0303570	+	0.108885i
$575$	−3.48773			−0.145448
$576$	−0.919882	−	2.85549i	−0.0383284	−	0.118979i
$577$	−6.39547	+	11.0773i	−0.266247	+	0.461153i	−0.967890	−	0.251376i	$-0.919117\pi$
$577$	−6.39547	+	11.0773i	−0.266247	+	0.461153i	0.701643	+	0.712529i	$0.252450\pi$
$578$	8.16076	+	14.1348i	0.339443	+	0.587932i
$579$	−23.8836	+	32.7863i	−0.992568	+	1.36255i
$580$	2.03452	+	3.52389i	0.0844787	+	0.146321i
$581$	4.59776	−	1.18235i	0.190747	−	0.0490523i
$582$	12.6261	+	28.4547i	0.523368	+	1.17949i
$583$	−42.2498			−1.74981
$584$	4.71172	−	8.16093i	0.194972	−	0.337702i
$585$	0.610831	+	1.89613i	0.0252547	+	0.0783955i
$586$	10.9592	+	18.9818i	0.452719	+	0.784133i
$587$	−0.214025	+	0.370702i	−0.00883376	+	0.0153005i	−0.870408	−	0.492330i	$-0.836145\pi$
$587$	−0.214025	+	0.370702i	−0.00883376	+	0.0153005i	0.861575	+	0.507631i	$0.169479\pi$
$588$	9.65374	+	7.33521i	0.398113	+	0.302499i
$589$	21.2056	+	36.7292i	0.873762	+	1.51340i
$590$	1.45817	−	2.52562i	0.0600318	−	0.103978i
$591$	−11.7730	+	16.1614i	−0.484277	+	0.664792i
$592$	−5.32042	−	9.21523i	−0.218668	−	0.378744i
$593$	−1.28439	−	2.22463i	−0.0527437	−	0.0913548i	0.838448	−	0.544981i	$-0.183463\pi$
$593$	−1.28439	−	2.22463i	−0.0527437	−	0.0913548i	−0.891192	+	0.453627i	$0.850130\pi$
$594$	−6.84150	−	32.7937i	−0.280710	−	1.34554i
$595$	−0.585266	+	2.09925i	−0.0239936	+	0.0860607i
$596$	4.81823	−	8.34542i	0.197363	−	0.341842i
$597$	−11.3486	−	25.5757i	−0.464465	−	1.04674i
$598$	2.31596			0.0947068
$599$	22.4250			0.916263			0.458131	−	0.888885i	$-0.348519\pi$
$599$	22.4250			0.916263			0.458131	+	0.888885i	$0.348519\pi$
$600$	−1.72233	−	0.183212i	−0.0703140	−	0.00747958i
$601$	10.5605	−	18.2913i	0.430772	−	0.746119i	−0.566168	−	0.824290i	$-0.691575\pi$
$601$	10.5605	−	18.2913i	0.430772	−	0.746119i	0.996940	+	0.0781708i	$0.0249080\pi$
$602$	−21.2680	+	5.46926i	−0.866820	+	0.222910i
$603$	−6.70264	−	20.8063i	−0.272953	−	0.847296i
$604$	−8.83973	−	15.3109i	−0.359684	−	0.622990i
$605$	−15.2821	−	26.4694i	−0.621307	−	1.07614i
$606$	−11.4005	−	1.21271i	−0.463112	−	0.0492631i
$607$	8.80365	−	15.2484i	0.357329	−	0.618912i	−0.630185	−	0.776445i	$-0.717021\pi$
$607$	8.80365	−	15.2484i	0.357329	−	0.618912i	0.987514	+	0.157533i	$0.0503541\pi$
$608$	−2.77668	−	4.80936i	−0.112609	−	0.195045i
$609$	6.87952	−	17.3312i	0.278772	−	0.702295i
$610$	0.383753	−	0.664680i	0.0155377	−	0.0269121i
$611$	0.863495	+	1.49562i	0.0349333	+	0.0605062i
$612$	−2.41580	−	0.519840i	−0.0976531	−	0.0210133i
$613$	−5.45250	+	9.44400i	−0.220224	+	0.381440i	−0.954876	−	0.297005i	$-0.904012\pi$
$613$	−5.45250	+	9.44400i	−0.220224	+	0.381440i	0.734652	+	0.678444i	$0.237346\pi$
$614$	−8.76843			−0.353865
$615$	−1.04390	+	1.43302i	−0.0420942	+	0.0577849i
$616$	−4.58083	+	16.4306i	−0.184567	+	0.662009i
$617$	−3.11423	−	5.39400i	−0.125374	−	0.217154i	0.796505	−	0.604632i	$-0.206680\pi$
$617$	−3.11423	−	5.39400i	−0.125374	−	0.217154i	−0.921879	+	0.387478i	$0.873346\pi$
$618$	−4.28898	−	9.66585i	−0.172528	−	0.388818i
$619$	15.1300	+	26.2060i	0.608128	+	1.05331i	0.991549	+	0.129734i	$0.0414124\pi$
$619$	15.1300	+	26.2060i	0.608128	+	1.05331i	−0.383421	+	0.923574i	$0.625254\pi$
$620$	3.81852	−	6.61386i	0.153355	−	0.265619i
$621$	−13.5134	+	12.0757i	−0.542276	+	0.484581i
$622$	28.7971			1.15466
$623$	2.93445	−	10.5254i	0.117566	−	0.421690i
$624$	1.14368	+	0.121658i	0.0457840	+	0.00487023i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	15.0040			0.599678
$627$	−25.1515	−	56.6826i	−1.00445	−	2.26368i
$628$	−13.0284			−0.519888
$629$	−8.76486			−0.349478
$630$	4.23868	+	6.71071i	0.168873	+	0.267361i
$631$	−18.3294			−0.729681			−0.364841	−	0.931070i	$-0.618876\pi$
$631$	−18.3294			−0.729681			−0.364841	+	0.931070i	$0.618876\pi$
$632$	−5.40500			−0.214999
$633$	44.9807	+	4.78478i	1.78782	+	0.190178i
$634$	−23.7437			−0.942984
$635$	−3.47820	+	6.02441i	−0.138028	+	0.239072i
$636$	4.60375	+	10.3752i	0.182550	+	0.411405i
$637$	−4.07157	+	2.24237i	−0.161322	+	0.0888459i
$638$	26.2332			1.03858
$639$	−3.17087	−	9.84297i	−0.125438	−	0.389382i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−16.0332	−	27.7703i	−0.633273	−	1.09686i	−0.986878	−	0.161467i	$-0.948378\pi$
$641$	−16.0332	−	27.7703i	−0.633273	−	1.09686i	0.353605	−	0.935395i	$-0.384956\pi$
$642$	25.2294	+	2.68375i	0.995724	+	0.105919i
$643$	10.2036	+	17.6732i	0.402391	+	0.696962i	0.994014	−	0.109253i	$-0.0348458\pi$
$643$	10.2036	+	17.6732i	0.402391	+	0.696962i	−0.591623	+	0.806215i	$0.701512\pi$
$644$	8.93690	−	2.29820i	0.352163	−	0.0905618i
$645$	−14.2955	−	1.52067i	−0.562887	−	0.0598765i
$646$	−4.57431			−0.179974
$647$	8.83588	−	15.3042i	0.347374	−	0.601670i	−0.638408	−	0.769698i	$-0.720407\pi$
$647$	8.83588	−	15.3042i	0.347374	−	0.601670i	0.985782	+	0.168028i	$0.0537400\pi$
$648$	−7.30763	+	5.25343i	−0.287071	+	0.206374i
$649$	−9.40086	−	16.2828i	−0.369016	−	0.639154i
$650$	0.332016	−	0.575068i	0.0130227	−	0.0225560i
$651$	−34.6263	+	5.08209i	−1.35711	+	0.199183i
$652$	−4.56357	−	7.90433i	−0.178723	−	0.309557i
$653$	8.41493	−	14.5751i	0.329302	−	0.570367i	−0.653072	−	0.757296i	$-0.726520\pi$
$653$	8.41493	−	14.5751i	0.329302	−	0.570367i	0.982373	+	0.186929i	$0.0598534\pi$
$654$	0.692482	+	1.56061i	0.0270782	+	0.0610247i
$655$	4.88725	+	8.46497i	0.190961	+	0.330754i
$656$	0.511800	+	0.886464i	0.0199824	+	0.0346106i
$657$	−27.6377	−	5.94716i	−1.07825	−	0.232021i
$658$	4.81622	+	4.91445i	0.187756	+	0.191585i
$659$	−10.8307	+	18.7593i	−0.421904	+	0.730760i	−0.996126	−	0.0879404i	$-0.971972\pi$
$659$	−10.8307	+	18.7593i	−0.421904	+	0.730760i	0.574221	+	0.818700i	$0.305305\pi$
$660$	−6.57490	+	9.02571i	−0.255928	+	0.351325i
$661$	−26.9171			−1.04696			−0.523478	−	0.852039i	$-0.675366\pi$
$661$	−26.9171			−1.04696			−0.523478	+	0.852039i	$0.675366\pi$
$662$	−3.51509			−0.136618
$663$	0.557810	−	0.765736i	0.0216636	−	0.0297387i
$664$	0.897166	−	1.55394i	0.0348168	−	0.0603045i
$665$	10.2840	+	10.4937i	0.398796	+	0.406930i
$666$	−21.4198	+	23.6693i	−0.830002	+	0.917167i
$667$	−7.09585	−	12.2904i	−0.274752	−	0.475885i
$668$	2.33645	+	4.04686i	0.0904001	+	0.156578i
$669$	0.636021	+	1.43337i	0.0245900	+	0.0554172i
$670$	−3.64320	+	6.31021i	−0.140749	+	0.243785i
$671$	−2.47407	−	4.28522i	−0.0955104	−	0.165429i
$672$	4.53400	−	0.665454i	0.174903	−	0.0256705i
$673$	−6.59897	+	11.4298i	−0.254372	+	0.440585i	−0.964725	−	0.263261i	$-0.915202\pi$
$673$	−6.59897	+	11.4298i	−0.254372	+	0.440585i	0.710353	+	0.703846i	$0.248535\pi$
$674$	16.6235	+	28.7927i	0.640312	+	1.10905i
$675$	1.06119	+	5.08664i	0.0408451	+	0.195785i
$676$	6.27953	−	10.8765i	0.241520	−	0.418326i
$677$	−38.1698			−1.46698			−0.733492	−	0.679698i	$-0.762111\pi$
$677$	−38.1698			−1.46698			−0.733492	+	0.679698i	$0.762111\pi$
$678$	13.9994	+	1.48917i	0.537644	+	0.0571914i
$679$	−46.0538	+	11.8431i	−1.76738	+	0.454497i
$680$	0.411850	+	0.713345i	0.0157937	+	0.0273555i
$681$	36.8966	+	3.92484i	1.41388	+	0.150400i
$682$	−24.6181	−	42.6398i	−0.942676	−	1.63276i
$683$	10.2925	−	17.8271i	0.393830	−	0.682134i	−0.599121	−	0.800659i	$-0.704483\pi$
$683$	10.2925	−	17.8271i	0.393830	−	0.682134i	0.992951	+	0.118525i	$0.0378165\pi$
$684$	−11.1788	+	12.3528i	−0.427434	+	0.472322i
$685$	−12.8562			−0.491209
$686$	−13.4863	+	12.6933i	−0.514910	+	0.484631i
$687$	−11.1848	−	25.2067i	−0.426728	−	0.961696i
$688$	−4.15005	+	7.18810i	−0.158219	+	0.274044i
$689$	−4.35164			−0.165784
$690$	6.00704	+	0.638993i	0.228684	+	0.0243260i
$691$	−21.6237			−0.822605			−0.411303	−	0.911499i	$-0.634926\pi$
$691$	−21.6237			−0.822605			−0.411303	+	0.911499i	$0.634926\pi$
$692$	−25.6473			−0.974966
$693$	51.1313	−	2.03374i	1.94232	−	0.0772552i
$694$	5.36573			0.203680
$695$	18.5910			0.705198
$696$	−2.85850	−	6.44206i	−0.108351	−	0.244185i
$697$	0.843140			0.0319362
$698$	2.39917	−	4.15548i	0.0908097	−	0.157287i
$699$	−11.8975	−	1.26559i	−0.450006	−	0.0478689i
$700$	0.710533	−	2.54856i	0.0268556	−	0.0963264i
$701$	27.0870			1.02306			0.511530	−	0.859265i	$-0.329079\pi$
$701$	27.0870			1.02306			0.511530	+	0.859265i	$0.329079\pi$
$702$	−0.704661	−	3.37769i	−0.0265957	−	0.127483i
$703$	−29.5462	+	51.1756i	−1.11436	+	1.93012i
$704$	3.22352	+	5.58330i	0.121491	+	0.210428i
$705$	1.82704	+	4.11751i	0.0688103	+	0.155074i
$706$	16.2100	+	28.0765i	0.610071	+	1.05667i
$707$	4.70316	−	16.8694i	0.176881	−	0.634439i
$708$	−2.97417	+	4.08281i	−0.111776	+	0.153441i
$709$	−11.6415			−0.437208			−0.218604	−	0.975814i	$-0.570150\pi$
$709$	−11.6415			−0.437208			−0.218604	+	0.975814i	$0.570150\pi$
$710$	−1.72352	+	2.98522i	−0.0646825	+	0.112033i
$711$	4.97197	+	15.4339i	0.186463	+	0.578817i
$712$	−2.06497	−	3.57663i	−0.0773879	−	0.134040i
$713$	−13.3180	+	23.0674i	−0.498761	+	0.863880i
$714$	1.39263	−	3.50838i	0.0521179	−	0.131298i
$715$	−2.14052	−	3.70748i	−0.0800508	−	0.138652i
$716$	−2.98463	+	5.16954i	−0.111541	+	0.193195i
$717$	27.3855	+	2.91311i	1.02273	+	0.108792i
$718$	−5.80951	−	10.0624i	−0.216809	−	0.375524i
$719$	10.0296	+	17.3718i	0.374040	+	0.647857i	0.990183	−	0.139778i	$-0.0446388\pi$
$719$	10.0296	+	17.3718i	0.374040	+	0.647857i	−0.616142	+	0.787635i	$0.711305\pi$
$720$	2.93287	+	0.631103i	0.109302	+	0.0235198i
$721$	15.6441	−	4.02302i	0.582617	−	0.149825i
$722$	−5.91994	+	10.2536i	−0.220317	+	0.381601i
$723$	−16.1057	−	1.71323i	−0.598978	−	0.0637157i
$724$	−5.42323			−0.201553
$725$	−4.06903			−0.151120
$726$	21.4714	+	48.3891i	0.796880	+	1.79589i
$727$	22.3086	−	38.6397i	0.827381	−	1.43307i	−0.0727056	−	0.997353i	$-0.523163\pi$
$727$	22.3086	−	38.6397i	0.827381	−	1.43307i	0.900086	−	0.435712i	$-0.143503\pi$
$728$	−0.471816	+	1.69232i	−0.0174867	+	0.0627216i
$729$	21.7233	+	16.0343i	0.804565	+	0.593864i
$730$	4.71172	+	8.16093i	0.174388	+	0.302050i
$731$	3.41840	+	5.92084i	0.126434	+	0.218990i
$732$	−0.782728	+	1.07449i	−0.0289305	+	0.0397144i
$733$	14.3012	−	24.7703i	0.528225	−	0.914913i	−0.471233	−	0.882009i	$-0.656191\pi$
$733$	14.3012	−	24.7703i	0.528225	−	0.914913i	0.999458	−	0.0329046i	$-0.0104757\pi$
$734$	8.36773	+	14.4933i	0.308859	+	0.534959i
$735$	−11.1793	+	4.69278i	−0.412357	+	0.173096i
$736$	1.74387	−	3.02046i	0.0642797	−	0.111336i
$737$	23.4879	+	40.6822i	0.865187	+	1.49855i
$738$	2.06049	−	2.27688i	0.0758478	−	0.0838132i
$739$	15.3554	−	26.5963i	0.564858	−	0.978362i	−0.432205	−	0.901775i	$-0.642264\pi$
$739$	15.3554	−	26.5963i	0.564858	−	0.978362i	0.997063	−	0.0765870i	$-0.0244023\pi$
$740$	10.6408			0.391165
$741$	−2.59055	−	5.83819i	−0.0951662	−	0.214471i
$742$	−16.7922	+	4.31827i	−0.616462	+	0.158529i
$743$	−14.6908	−	25.4452i	−0.538953	−	0.933493i	−0.998961	−	0.0455786i	$-0.985487\pi$
$743$	−14.6908	−	25.4452i	−0.538953	−	0.933493i	0.460008	−	0.887915i	$-0.347846\pi$
$744$	−7.78850	+	10.6917i	−0.285540	+	0.391976i
$745$	4.81823	+	8.34542i	0.176526	+	0.305753i
$746$	6.07788	−	10.5272i	0.222527	−	0.385428i
$747$	−5.26254	−	1.13241i	−0.192546	−	0.0414327i
$748$	5.31042			0.194168
$749$	−10.4082	+	37.3322i	−0.380306	+	1.36409i
$750$	1.01983	−	1.39998i	0.0372390	−	0.0511200i
$751$	−24.0333	+	41.6269i	−0.876987	+	1.51899i	−0.0223556	+	0.999750i	$0.507117\pi$
$751$	−24.0333	+	41.6269i	−0.876987	+	1.51899i	−0.854631	+	0.519236i	$0.826217\pi$
$752$	2.60076			0.0948401
$753$	14.5949	−	20.0353i	0.531869	−	0.730126i
$754$	2.70197			0.0983998
$755$	17.6795			0.643422
$756$	−6.07095	−	12.3347i	−0.220798	−	0.448607i
$757$	−34.8053			−1.26502			−0.632510	−	0.774553i	$-0.717975\pi$
$757$	−34.8053			−1.26502			−0.632510	+	0.774553i	$0.717975\pi$
$758$	−18.5422			−0.673483
$759$	22.9315	−	31.4793i	0.832360	−	1.14263i
$760$	5.55337			0.201442
$761$	−4.22209	+	7.31287i	−0.153050	+	0.265091i	−0.932347	−	0.361564i	$-0.882243\pi$
$761$	−4.22209	+	7.31287i	−0.153050	+	0.265091i	0.779297	+	0.626655i	$0.215576\pi$
$762$	7.09436	−	9.73880i	0.257001	−	0.352800i
$763$	−2.52584	+	0.649540i	−0.0914414	+	0.0235149i
$764$	4.97914			0.180139
$765$	1.65810	−	1.83223i	0.0599486	−	0.0662443i
$766$	−4.16276	+	7.21011i	−0.150407	+	0.260512i
$767$	−0.968269	−	1.67709i	−0.0349622	−	0.0605562i
$768$	1.01983	−	1.39998i	0.0368000	−	0.0505174i
$769$	−17.1205	−	29.6535i	−0.617380	−	1.06933i	−0.989962	−	0.141334i	$-0.954861\pi$
$769$	−17.1205	−	29.6535i	−0.617380	−	1.06933i	0.372582	−	0.927999i	$-0.378473\pi$
$770$	−11.9389	−	12.1824i	−0.430249	−	0.439025i
$771$	−5.73888	−	12.9334i	−0.206681	−	0.465786i
$772$	−23.4191			−0.842873
$773$	−5.43968	+	9.42179i	−0.195652	+	0.338878i	−0.947114	−	0.320898i	$-0.896015\pi$
$773$	−5.43968	+	9.42179i	−0.195652	+	0.338878i	0.751462	+	0.659776i	$0.229349\pi$
$774$	24.3431	+	5.23822i	0.874995	+	0.188284i
$775$	3.81852	+	6.61386i	0.137165	+	0.237577i
$776$	−8.98652	+	15.5651i	−0.322597	+	0.558755i
$777$	−30.2551	−	38.2414i	−1.08540	−	1.37190i
$778$	6.54784	+	11.3412i	0.234751	+	0.406601i
$779$	2.84222	−	4.92286i	0.101833	−	0.176380i
$780$	−0.677201	+	0.929630i	−0.0242477	+	0.0332861i
$781$	11.1116	+	19.2458i	0.397604	+	0.688670i
$782$	−1.43642	−	2.48796i	−0.0513664	−	0.0889692i
$783$	−15.7657	+	14.0883i	−0.563421	+	0.503476i
$784$	−0.141315	+	6.99857i	−0.00504697	+	0.249949i
$785$	6.51418	−	11.2829i	0.232501	−	0.402704i
$786$	−6.86660	−	15.4749i	−0.244924	−	0.551972i
$787$	39.1930			1.39708			0.698540	−	0.715571i	$-0.253834\pi$
$787$	39.1930			1.39708			0.698540	+	0.715571i	$0.253834\pi$
$788$	−11.5441			−0.411240
$789$	−28.3841	−	3.01933i	−1.01050	−	0.107491i
$790$	2.70250	−	4.68087i	0.0961507	−	0.166538i
$791$	−5.77533	+	20.7151i	−0.205347	+	0.736544i
$792$	12.9778	−	14.3407i	0.461145	−	0.509574i
$793$	−0.254824	−	0.441368i	−0.00904907	−	0.0156734i
$794$	13.2600	+	22.9670i	0.470581	+	0.815069i
$795$	−11.2871	−	1.20065i	−0.400312	−	0.0425828i
$796$	8.07725	−	13.9902i	0.286291	−	0.495870i
$797$	4.92224	+	8.52558i	0.174355	+	0.301991i	0.939938	−	0.341346i	$-0.110883\pi$
$797$	4.92224	+	8.52558i	0.174355	+	0.301991i	−0.765583	+	0.643337i	$0.777549\pi$
$798$	−15.7899	−	19.9579i	−0.558956	−	0.706501i
$799$	1.07113	−	1.85524i	0.0378937	−	0.0656338i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−8.31349	+	9.18656i	−0.293743	+	0.324591i
$802$	14.6317	−	25.3429i	0.516663	−	0.894887i
$803$	60.7532			2.14393
$804$	7.43092	−	10.2008i	0.262068	−	0.359755i
$805$	−2.47815	+	8.88868i	−0.0873433	+	0.313285i
$806$	−2.53561	−	4.39181i	−0.0893132	−	0.154695i
$807$	18.0897	+	40.7678i	0.636787	+	1.43509i
$808$	−3.30960	−	5.73239i	−0.116431	−	0.201665i
$809$	23.6574	−	40.9759i	0.831751	−	1.44064i	−0.0648970	−	0.997892i	$-0.520672\pi$
$809$	23.6574	−	40.9759i	0.831751	−	1.44064i	0.896648	−	0.442744i	$-0.145995\pi$
$810$	−0.895785	−	8.95531i	−0.0314747	−	0.314658i
$811$	−46.7680			−1.64225			−0.821124	−	0.570750i	$-0.806652\pi$
$811$	−46.7680			−1.64225			−0.821124	+	0.570750i	$0.806652\pi$
$812$	10.4264	−	2.68124i	0.365895	−	0.0940932i
$813$	−35.7536	−	3.80326i	−1.25393	−	0.133386i
$814$	34.3009	−	59.4109i	1.20225	−	2.08235i
$815$	9.12713			0.319709
$816$	−0.578650	−	1.30407i	−0.0202568	−	0.0456517i
$817$	46.0935			1.61261
$818$	14.1459			0.494600
$819$	5.26642	−	0.209470i	0.184024	−	0.00731949i
$820$	−1.02360			−0.0357457
$821$	−26.4273			−0.922319			−0.461159	−	0.887317i	$-0.652566\pi$
$821$	−26.4273			−0.922319			−0.461159	+	0.887317i	$0.652566\pi$
$822$	22.1426	+	2.35540i	0.772313	+	0.0821540i
$823$	2.27855			0.0794252			0.0397126	−	0.999211i	$-0.487356\pi$
$823$	2.27855			0.0794252			0.0397126	+	0.999211i	$0.487356\pi$
$824$	3.05265	−	5.28735i	0.106344	−	0.184193i
$825$	−4.52905	−	10.2069i	−0.157681	−	0.355358i
$826$	−5.40061	−	5.51076i	−0.187911	−	0.191744i
$827$	49.2996			1.71431			0.857157	−	0.515055i	$-0.172229\pi$
$827$	49.2996			1.71431			0.857157	+	0.515055i	$0.172229\pi$
$828$	−10.2291	−	2.20112i	−0.355484	−	0.0764941i
$829$	−3.70244	+	6.41282i	−0.128591	+	0.222726i	−0.923131	−	0.384486i	$-0.874379\pi$
$829$	−3.70244	+	6.41282i	−0.128591	+	0.222726i	0.794540	+	0.607212i	$0.207712\pi$
$830$	0.897166	+	1.55394i	0.0311411	+	0.0539380i
$831$	53.5778	+	5.69929i	1.85859	+	0.197706i
$832$	0.332016	+	0.575068i	0.0115106	+	0.0199369i
$833$	4.93420	+	2.98317i	0.170960	+	0.103361i
$834$	−32.0200	−	3.40609i	−1.10876	−	0.117943i
$835$	−4.67291			−0.161713
$836$	17.9014	−	31.0061i	0.619132	−	1.07237i
$837$	37.6945	+	12.4049i	1.30291	+	0.428775i
$838$	−16.6209	−	28.7882i	−0.574158	−	0.994471i
$839$	20.2441	−	35.0638i	0.698904	−	1.21054i	−0.269943	−	0.962876i	$-0.587005\pi$
$839$	20.2441	−	35.0638i	0.698904	−	1.21054i	0.968847	−	0.247660i	$-0.0796617\pi$
$840$	−1.69070	+	4.25929i	−0.0583347	+	0.146959i
$841$	6.22148	+	10.7759i	0.214534	+	0.371584i
$842$	9.58351	−	16.5991i	0.330270	−	0.572044i
$843$	−21.1897	−	47.7541i	−0.729811	−	1.64474i
$844$	13.0581	+	22.6172i	0.449477	+	0.778517i
$845$	6.27953	+	10.8765i	0.216022	+	0.374162i
$846$	−2.39240	−	7.42646i	−0.0822523	−	0.255327i
$847$	−78.3173	+	20.1400i	−2.69102	+	0.692018i
$848$	−3.27668	+	5.67538i	−0.112522	+	0.194893i
$849$	22.7138	−	31.1805i	0.779536	−	1.07011i
$850$	−0.823700			−0.0282527
$851$	−37.1124			−1.27220
$852$	3.51540	−	4.82578i	0.120436	−	0.165328i
$853$	−27.6859	+	47.9534i	−0.947947	+	1.64189i	−0.198206	+	0.980160i	$0.563512\pi$
$853$	−27.6859	+	47.9534i	−0.947947	+	1.64189i	−0.749741	+	0.661732i	$0.769822\pi$
$854$	−1.42131	−	1.45029i	−0.0486361	−	0.0496280i
$855$	−5.10844	−	15.8576i	−0.174705	−	0.542318i
$856$	7.32418	+	12.6859i	0.250335	+	0.433594i
$857$	15.4437	+	26.7493i	0.527547	+	0.913739i	0.999484	+	0.0321065i	$0.0102216\pi$
$857$	15.4437	+	26.7493i	0.527547	+	0.913739i	−0.471937	+	0.881632i	$0.656445\pi$
$858$	3.00743	+	6.77769i	0.102672	+	0.231387i
$859$	−10.2344	+	17.7266i	−0.349195	+	0.604823i	−0.986107	−	0.166114i	$-0.946878\pi$
$859$	−10.2344	+	17.7266i	−0.349195	+	0.604823i	0.636912	+	0.770936i	$0.280211\pi$
$860$	−4.15005	−	7.18810i	−0.141516	−	0.245112i
$861$	2.91041	+	3.67865i	0.0991864	+	0.125368i
$862$	9.77141	−	16.9246i	0.332815	−	0.576453i
$863$	5.65435	+	9.79362i	0.192476	+	0.333379i	0.946070	−	0.323961i	$-0.105015\pi$
$863$	5.65435	+	9.79362i	0.192476	+	0.333379i	−0.753594	+	0.657340i	$0.771681\pi$
$864$	−4.93575	−	1.62430i	−0.167918	−	0.0552600i
$865$	12.8237	−	22.2112i	0.436018	−	0.755205i
$866$	20.6650			0.702225
$867$	28.1111	+	2.99029i	0.954703	+	0.101556i
$868$	−14.1426	−	14.4311i	−0.480032	−	0.489823i
$869$	−17.4231	−	30.1777i	−0.591039	−	1.02371i
$870$	7.00823	+	0.745494i	0.237601	+	0.0252746i
$871$	2.41920	+	4.19018i	0.0819715	+	0.141979i
$872$	−0.492869	+	0.853674i	−0.0166906	+	0.0289090i
$873$	52.7125	+	11.3428i	1.78405	+	0.383897i
$874$	−19.3687			−0.655154
$875$	1.85185	+	1.88962i	0.0626039	+	0.0638808i
$876$	−6.61997	−	14.9191i	−0.223668	−	0.504069i
$877$	−12.0717	+	20.9088i	−0.407633	+	0.706040i	−0.994624	−	0.103553i	$-0.966979\pi$
$877$	−12.0717	+	20.9088i	−0.407633	+	0.706040i	0.586991	+	0.809593i	$0.300312\pi$
$878$	17.5808			0.593325
$879$	37.7507	+	4.01569i	1.27330	+	0.135446i
$880$	−6.44704			−0.217330
$881$	22.1574			0.746502			0.373251	−	0.927730i	$-0.378243\pi$
$881$	22.1574			0.746502			0.373251	+	0.927730i	$0.378243\pi$
$882$	20.1143	−	6.03434i	0.677285	−	0.203187i
$883$	15.5148			0.522115			0.261057	−	0.965323i	$-0.415929\pi$
$883$	15.5148			0.522115			0.261057	+	0.965323i	$0.415929\pi$
$884$	0.546963			0.0183963
$885$	−2.04873	−	4.61711i	−0.0688672	−	0.155203i
$886$	16.3960			0.550833
$887$	−24.8136	+	42.9784i	−0.833159	+	1.44307i	0.0623617	+	0.998054i	$0.480137\pi$
$887$	−24.8136	+	42.9784i	−0.833159	+	1.44307i	−0.895521	+	0.445020i	$0.853197\pi$
$888$	−18.3271	−	1.94952i	−0.615016	−	0.0654217i
$889$	12.8822	+	13.1449i	0.432055	+	0.440867i
$890$	4.12993			0.138436
$891$	−52.8877	−	23.8662i	−1.77181	−	0.799547i
$892$	−0.452684	+	0.784071i	−0.0151570	+	0.0262526i
$893$	−7.22150	−	12.5080i	−0.241658	−	0.418564i
$894$	−6.76963	−	15.2564i	−0.226410	−	0.510249i
$895$	−2.98463	−	5.16954i	−0.0997653	−	0.172799i
$896$	1.85185	+	1.88962i	0.0618659	+	0.0631277i
$897$	2.36189	−	3.24230i	0.0788614	−	0.108257i
$898$	−33.5534			−1.11969
$899$	−15.5377	+	26.9120i	−0.518210	+	0.897567i
$900$	−2.01298	+	2.22439i	−0.0670995	+	0.0741462i
$901$	2.69900	+	4.67481i	0.0899169	+	0.155741i
$902$	−3.29960	+	5.71507i	−0.109865	+	0.190291i
$903$	−14.0330	+	35.3525i	−0.466989	+	1.17646i
$904$	4.06408	+	7.03919i	0.135169	+	0.234120i
$905$	2.71161	−	4.69665i	0.0901371	−	0.156122i
$906$	−30.4499	−	3.23908i	−1.01163	−	0.107611i
$907$	−5.91561	−	10.2461i	−0.196424	−	0.340217i	0.750942	−	0.660368i	$-0.229600\pi$
$907$	−5.91561	−	10.2461i	−0.196424	−	0.340217i	−0.947367	+	0.320151i	$0.896266\pi$
$908$	10.7112	+	18.5524i	0.355464	+	0.615682i
$909$	−13.3243	+	14.7237i	−0.441941	+	0.488353i
$910$	−1.22969	−	1.25477i	−0.0407637	−	0.0415951i
$911$	6.74673	−	11.6857i	0.223529	−	0.387164i	−0.732348	−	0.680931i	$-0.761576\pi$
$911$	6.74673	−	11.6857i	0.223529	−	0.387164i	0.955877	+	0.293767i	$0.0949088\pi$
$912$	−9.56475	−	1.01744i	−0.316721	−	0.0336908i
$913$	11.5681			0.382849
$914$	19.5171			0.645568
$915$	−0.539174	−	1.21511i	−0.0178245	−	0.0401703i
$916$	7.96073	−	13.7884i	0.263030	−	0.455581i
$917$	25.0460	−	6.44080i	0.827093	−	0.212694i
$918$	−3.19148	+	2.85192i	−0.105335	+	0.0941275i
$919$	−5.38406	−	9.32547i	−0.177604	−	0.307619i	0.763455	−	0.645861i	$-0.223501\pi$
$919$	−5.38406	−	9.32547i	−0.177604	−	0.307619i	−0.941059	+	0.338242i	$0.890168\pi$
$920$	1.74387	+	3.02046i	0.0574936	+	0.0995818i
$921$	−8.94233	+	12.2756i	−0.294660	+	0.404495i
$922$	−15.2287	+	26.3769i	−0.501531	+	0.868678i
$923$	1.14447	+	1.98228i	0.0376707	+	0.0652475i
$924$	18.3309	+	23.1696i	0.603041	+	0.762223i
$925$	−5.32042	+	9.21523i	−0.174934	+	0.302995i
$926$	−7.56973	−	13.1112i	−0.248757	−	0.430859i
$927$	−17.9060	−	3.85307i	−0.588111	−	0.126552i
$928$	2.03452	−	3.52389i	0.0667863	−	0.115677i
$929$	−18.3053			−0.600576			−0.300288	−	0.953849i	$-0.597083\pi$
$929$	−18.3053			−0.600576			−0.300288	+	0.953849i	$0.597083\pi$
$930$	−5.36502	−	12.0909i	−0.175926	−	0.396475i
$931$	34.0510	−	18.7532i	1.11598	−	0.614611i
$932$	−3.45390	−	5.98232i	−0.113136	−	0.195957i
$933$	29.3682	−	40.3153i	0.961471	−	1.31986i
$934$	0.118683	+	0.205565i	0.00388343	+	0.00672629i
$935$	−2.65521	+	4.59896i	−0.0868347	+	0.150402i
$936$	1.33668	−	1.47706i	0.0436909	−	0.0482793i
$937$	24.6739			0.806061			0.403030	−	0.915187i	$-0.367957\pi$
$937$	24.6739			0.806061			0.403030	+	0.915187i	$0.367957\pi$
$938$	13.4933	+	13.7685i	0.440573	+	0.449558i
$939$	15.3015	−	21.0052i	0.499346	−	0.685479i
$940$	−1.30038	+	2.25233i	−0.0424138	+	0.0734629i
$941$	35.5744			1.15969			0.579846	−	0.814726i	$-0.303113\pi$
$941$	35.5744			1.15969			0.579846	+	0.814726i	$0.303113\pi$
$942$	−13.2867	+	18.2394i	−0.432906	+	0.594273i
$943$	3.57005			0.116257
$944$	−2.91633			−0.0949186
$945$	13.7176	+	0.909733i	0.446233	+	0.0295936i
$946$	−53.5111			−1.73979
$947$	−10.4955			−0.341059			−0.170530	−	0.985353i	$-0.554548\pi$
$947$	−10.4955			−0.341059			−0.170530	+	0.985353i	$0.554548\pi$
$948$	−5.51220	+	7.56689i	−0.179028	+	0.245761i
$949$	6.25746			0.203126
$950$	−2.77668	+	4.80936i	−0.0900875	+	0.156036i
$951$	−24.2146	+	33.2407i	−0.785214	+	1.07790i
$952$	2.11063	−	0.542768i	0.0684060	−	0.0175912i
$953$	−5.72697			−0.185515			−0.0927574	−	0.995689i	$-0.529568\pi$
$953$	−5.72697			−0.185515			−0.0927574	+	0.995689i	$0.529568\pi$
$954$	19.2202	+	4.13585i	0.622275	+	0.133903i
$955$	−2.48957	+	4.31206i	−0.0805605	+	0.139535i
$956$	7.95013	+	13.7700i	0.257125	+	0.445354i
$957$	26.7535	−	36.7259i	0.864817	−	1.18718i
$958$	6.76029	+	11.7092i	0.218415	+	0.378306i
$959$	−9.13474	+	32.7647i	−0.294976	+	1.05803i
$960$	0.702501	+	1.58319i	0.0226731	+	0.0510973i
$961$	27.3243			0.881428
$962$	3.53292	−	6.11920i	0.113906	−	0.197291i
$963$	29.4869	−	32.5836i	0.950203	−	1.04999i
$964$	−4.67555	−	8.09830i	−0.150589	−	0.260829i
$965$	11.7096	−	20.2816i	0.376944	−	0.652887i
$966$	5.89671	−	14.8553i	0.189724	−	0.477960i
$967$	−25.0249	−	43.3445i	−0.804748	−	1.39386i	−0.916461	−	0.400124i	$-0.868967\pi$
$967$	−25.0249	−	43.3445i	−0.804748	−	1.39386i	0.111713	−	0.993740i	$-0.464366\pi$
$968$	−15.2821	+	26.4694i	−0.491186	+	0.850760i
$969$	−4.66503	+	6.40394i	−0.149862	+	0.205724i
$970$	−8.98652	−	15.5651i	−0.288540	−	0.499765i
$971$	−0.713412	−	1.23567i	−0.0228945	−	0.0396544i	0.854351	−	0.519696i	$-0.173955\pi$
$971$	−0.713412	−	1.23567i	−0.0228945	−	0.0396544i	−0.877246	+	0.480042i	$0.840622\pi$
$972$	−0.0978746	+	15.5882i	−0.00313933	+	0.499990i
$973$	13.2096	−	47.3803i	0.423479	−	1.51894i
$974$	19.3582	−	33.5294i	0.620276	−	1.07435i
$975$	−0.466483	−	1.05129i	−0.0149394	−	0.0336682i
$976$	−0.767506			−0.0245673
$977$	56.7098			1.81431			0.907154	−	0.420799i	$-0.138250\pi$
$977$	56.7098			1.81431			0.907154	+	0.420799i	$0.138250\pi$
$978$	−15.7200	−	1.67220i	−0.502669	−	0.0534709i
$979$	13.3129	−	23.0586i	0.425482	−	0.736957i
$980$	−5.99028	−	3.62167i	−0.191353	−	0.115690i
$981$	2.89104	+	0.622102i	0.0923037	+	0.0198622i
$982$	5.10089	+	8.83500i	0.162776	+	0.281936i
$983$	14.4756	+	25.0724i	0.461699	+	0.799686i	0.999046	−	0.0436753i	$-0.0139067\pi$
$983$	14.4756	+	25.0724i	0.461699	+	0.799686i	−0.537347	+	0.843361i	$0.680573\pi$
$984$	1.76298	+	0.187536i	0.0562018	+	0.00597841i
$985$	5.77203	−	9.99744i	0.183912	−	0.318545i
$986$	−1.67583	−	2.90263i	−0.0533694	−	0.0924384i
$987$	11.7919	−	1.73069i	0.375339	−	0.0550885i
$988$	1.84380	−	3.19356i	0.0586592	−	0.101601i
$989$	14.4743	+	25.0702i	0.460255	+	0.797185i
$990$	5.93051	+	18.4094i	0.188484	+	0.585090i
$991$	12.3215	−	21.3414i	0.391404	−	0.677931i	−0.601231	−	0.799075i	$-0.705323\pi$
$991$	12.3215	−	21.3414i	0.391404	−	0.677931i	0.992635	+	0.121144i	$0.0386562\pi$
$992$	−7.63703			−0.242476
$993$	−3.58480	+	4.92105i	−0.113760	+	0.156165i
$994$	6.38339	+	6.51358i	0.202469	+	0.206598i
$995$	8.07725	+	13.9902i	0.256066	+	0.443519i
$996$	−1.26052	−	2.84077i	−0.0399411	−	0.0900132i
$997$	−12.7388	−	22.0642i	−0.403441	−	0.698780i	0.590698	−	0.806893i	$-0.298853\pi$
$997$	−12.7388	−	22.0642i	−0.403441	−	0.698780i	−0.994139	+	0.108113i	$0.965519\pi$
$998$	5.34312	−	9.25456i	0.169134	−	0.292948i
$999$	11.2919	+	54.1261i	0.357260	+	1.71247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.g.151.5	yes	12
3.2	odd	2		1890.2.i.g.991.5		12
7.2	even	3		630.2.l.g.331.4	yes	12
9.4	even	3		630.2.l.g.571.4	yes	12
9.5	odd	6		1890.2.l.g.361.2		12
21.2	odd	6		1890.2.l.g.1801.2		12
63.23	odd	6		1890.2.i.g.1171.5		12
63.58	even	3	inner	630.2.i.g.121.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.g.121.5	✓	12	63.58	even	3	inner
630.2.i.g.151.5	yes	12	1.1	even	1	trivial
630.2.l.g.331.4	yes	12	7.2	even	3
630.2.l.g.571.4	yes	12	9.4	even	3
1890.2.i.g.991.5		12	3.2	odd	2
1890.2.i.g.1171.5		12	63.23	odd	6
1890.2.l.g.361.2		12	9.5	odd	6
1890.2.l.g.1801.2		12	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.01983 - 1.39998i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.01983 - 1.39998i) q^{6} +(1.85185 + 1.88962i) q^{7} +1.00000 q^{8} +(-0.919882 - 2.85549i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.01983 - 1.39998i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.01983 - 1.39998i) q^{6} +(1.85185 + 1.88962i) q^{7} +1.00000 q^{8} +(-0.919882 - 2.85549i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(3.22352 + 5.58330i) q^{11} +(1.01983 - 1.39998i) q^{12} +(0.332016 + 0.575068i) q^{13} +(1.85185 + 1.88962i) q^{14} +(0.702501 + 1.58319i) q^{15} +1.00000 q^{16} +(0.411850 - 0.713345i) q^{17} +(-0.919882 - 2.85549i) q^{18} +(-2.77668 - 4.80936i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(4.53400 - 0.665454i) q^{21} +(3.22352 + 5.58330i) q^{22} +(1.74387 - 3.02046i) q^{23} +(1.01983 - 1.39998i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.332016 + 0.575068i) q^{26} +(-4.93575 - 1.62430i) q^{27} +(1.85185 + 1.88962i) q^{28} +(2.03452 - 3.52389i) q^{29} +(0.702501 + 1.58319i) q^{30} -7.63703 q^{31} +1.00000 q^{32} +(11.1039 + 1.18117i) q^{33} +(0.411850 - 0.713345i) q^{34} +(-2.56238 + 0.658939i) q^{35} +(-0.919882 - 2.85549i) q^{36} +(-5.32042 - 9.21523i) q^{37} +(-2.77668 - 4.80936i) q^{38} +(1.14368 + 0.121658i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(0.511800 + 0.886464i) q^{41} +(4.53400 - 0.665454i) q^{42} +(-4.15005 + 7.18810i) q^{43} +(3.22352 + 5.58330i) q^{44} +(2.93287 + 0.631103i) q^{45} +(1.74387 - 3.02046i) q^{46} +2.60076 q^{47} +(1.01983 - 1.39998i) q^{48} +(-0.141315 + 6.99857i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.578650 - 1.30407i) q^{51} +(0.332016 + 0.575068i) q^{52} +(-3.27668 + 5.67538i) q^{53} +(-4.93575 - 1.62430i) q^{54} -6.44704 q^{55} +(1.85185 + 1.88962i) q^{56} +(-9.56475 - 1.01744i) q^{57} +(2.03452 - 3.52389i) q^{58} -2.91633 q^{59} +(0.702501 + 1.58319i) q^{60} -0.767506 q^{61} -7.63703 q^{62} +(3.69230 - 7.02616i) q^{63} +1.00000 q^{64} -0.664031 q^{65} +(11.1039 + 1.18117i) q^{66} +7.28641 q^{67} +(0.411850 - 0.713345i) q^{68} +(-2.45013 - 5.52174i) q^{69} +(-2.56238 + 0.658939i) q^{70} +3.44704 q^{71} +(-0.919882 - 2.85549i) q^{72} +(4.71172 - 8.16093i) q^{73} +(-5.32042 - 9.21523i) q^{74} +(-1.72233 - 0.183212i) q^{75} +(-2.77668 - 4.80936i) q^{76} +(-4.58083 + 16.4306i) q^{77} +(1.14368 + 0.121658i) q^{78} -5.40500 q^{79} +(-0.500000 + 0.866025i) q^{80} +(-7.30763 + 5.25343i) q^{81} +(0.511800 + 0.886464i) q^{82} +(0.897166 - 1.55394i) q^{83} +(4.53400 - 0.665454i) q^{84} +(0.411850 + 0.713345i) q^{85} +(-4.15005 + 7.18810i) q^{86} +(-2.85850 - 6.44206i) q^{87} +(3.22352 + 5.58330i) q^{88} +(-2.06497 - 3.57663i) q^{89} +(2.93287 + 0.631103i) q^{90} +(-0.471816 + 1.69232i) q^{91} +(1.74387 - 3.02046i) q^{92} +(-7.78850 + 10.6917i) q^{93} +2.60076 q^{94} +5.55337 q^{95} +(1.01983 - 1.39998i) q^{96} +(-8.98652 + 15.5651i) q^{97} +(-0.141315 + 6.99857i) q^{98} +(12.9778 - 14.3407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9	\( 12 q + 12 q^{2} + 12 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} + 4 q^{9} - 6 q^{10} + 3 q^{11} - 2 q^{13} + 4 q^{14} + 3 q^{15} + 12 q^{16} + q^{17} + 4 q^{18} + 8 q^{19} - 6 q^{20} + 5 q^{21} + 3 q^{22} + 11 q^{23} - 6 q^{25} - 2 q^{26} - 27 q^{27} + 4 q^{28} + 13 q^{29} + 3 q^{30} - 42 q^{31} + 12 q^{32} + 17 q^{33} + q^{34} + 4 q^{35} + 4 q^{36} + 18 q^{37} + 8 q^{38} - 24 q^{39} - 6 q^{40} + 5 q^{41} + 5 q^{42} - 11 q^{43} + 3 q^{44} + q^{45} + 11 q^{46} + 46 q^{47} - 6 q^{50} - 27 q^{51} - 2 q^{52} + 2 q^{53} - 27 q^{54} - 6 q^{55} + 4 q^{56} - 44 q^{57} + 13 q^{58} - 2 q^{59} + 3 q^{60} + 2 q^{61} - 42 q^{62} + 9 q^{63} + 12 q^{64} + 4 q^{65} + 17 q^{66} - 4 q^{67} + q^{68} - 24 q^{69} + 4 q^{70} - 30 q^{71} + 4 q^{72} + 22 q^{73} + 18 q^{74} - 3 q^{75} + 8 q^{76} - 31 q^{77} - 24 q^{78} - 54 q^{79} - 6 q^{80} + 52 q^{81} + 5 q^{82} + 6 q^{83} + 5 q^{84} + q^{85} - 11 q^{86} - 28 q^{87} + 3 q^{88} - 18 q^{89} + q^{90} + 14 q^{91} + 11 q^{92} - 38 q^{93} + 46 q^{94} - 16 q^{95} - 4 q^{97} + 63 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 + 4 * q^9 - 6 * q^10 + 3 * q^11 - 2 * q^13 + 4 * q^14 + 3 * q^15 + 12 * q^16 + q^17 + 4 * q^18 + 8 * q^19 - 6 * q^20 + 5 * q^21 + 3 * q^22 + 11 * q^23 - 6 * q^25 - 2 * q^26 - 27 * q^27 + 4 * q^28 + 13 * q^29 + 3 * q^30 - 42 * q^31 + 12 * q^32 + 17 * q^33 + q^34 + 4 * q^35 + 4 * q^36 + 18 * q^37 + 8 * q^38 - 24 * q^39 - 6 * q^40 + 5 * q^41 + 5 * q^42 - 11 * q^43 + 3 * q^44 + q^45 + 11 * q^46 + 46 * q^47 - 6 * q^50 - 27 * q^51 - 2 * q^52 + 2 * q^53 - 27 * q^54 - 6 * q^55 + 4 * q^56 - 44 * q^57 + 13 * q^58 - 2 * q^59 + 3 * q^60 + 2 * q^61 - 42 * q^62 + 9 * q^63 + 12 * q^64 + 4 * q^65 + 17 * q^66 - 4 * q^67 + q^68 - 24 * q^69 + 4 * q^70 - 30 * q^71 + 4 * q^72 + 22 * q^73 + 18 * q^74 - 3 * q^75 + 8 * q^76 - 31 * q^77 - 24 * q^78 - 54 * q^79 - 6 * q^80 + 52 * q^81 + 5 * q^82 + 6 * q^83 + 5 * q^84 + q^85 - 11 * q^86 - 28 * q^87 + 3 * q^88 - 18 * q^89 + q^90 + 14 * q^91 + 11 * q^92 - 38 * q^93 + 46 * q^94 - 16 * q^95 - 4 * q^97 + 63 * q^99

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