LMFDB - Embedded newform 315.2.i.d.211.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(106,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("315.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.4
Root			$-0.978148 + 0.207912i$ of defining polynomial
Character	$\chi$	$=$	315.211
Dual form			315.2.i.d.106.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 + 1.58231i) q^{2} +(0.360114 - 1.69420i) q^{3} +(-0.669131 + 1.15897i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.00973 - 0.977920i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.20906 q^{8} +(-2.74064 - 1.22021i) q^{9} +O(q^{10})$	\(q+(0.913545 + 1.58231i) q^{2} +(0.360114 - 1.69420i) q^{3} +(-0.669131 + 1.15897i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.00973 - 0.977920i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.20906 q^{8} +(-2.74064 - 1.22021i) q^{9} +1.82709 q^{10} +(-0.0864545 - 0.149744i) q^{11} +(1.72256 + 1.55100i) q^{12} +(1.87362 - 3.24520i) q^{13} +(-0.913545 + 1.58231i) q^{14} +(-1.28716 - 1.15897i) q^{15} +(2.44279 + 4.23104i) q^{16} +1.82709 q^{17} +(-0.572949 - 5.45125i) q^{18} -0.138341 q^{19} +(0.669131 + 1.15897i) q^{20} +(1.64728 - 0.535233i) q^{21} +(0.157960 - 0.273595i) q^{22} +(-3.90142 + 6.75746i) q^{23} +(0.435398 - 2.04839i) q^{24} +(-0.500000 - 0.866025i) q^{25} +6.84655 q^{26} +(-3.05422 + 4.20378i) q^{27} -1.33826 q^{28} +(0.489318 + 0.847523i) q^{29} +(0.657960 - 3.09546i) q^{30} +(1.36245 - 2.35983i) q^{31} +(-3.25414 + 5.63634i) q^{32} +(-0.284829 + 0.0925467i) q^{33} +(1.66913 + 2.89102i) q^{34} +1.00000 q^{35} +(3.24803 - 2.35983i) q^{36} -7.88558 q^{37} +(-0.126381 - 0.218898i) q^{38} +(-4.82331 - 4.34293i) q^{39} +(0.604528 - 1.04707i) q^{40} +(-5.02090 + 8.69645i) q^{41} +(2.35177 + 2.11754i) q^{42} +(-3.69693 - 6.40327i) q^{43} +0.231398 q^{44} +(-2.42705 + 1.76336i) q^{45} -14.2565 q^{46} +(2.90063 + 5.02404i) q^{47} +(8.04791 - 2.61492i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.913545 - 1.58231i) q^{50} +(0.657960 - 3.09546i) q^{51} +(2.50739 + 4.34293i) q^{52} -11.7139 q^{53} +(-9.44183 - 0.992377i) q^{54} -0.172909 q^{55} +(0.604528 + 1.04707i) q^{56} +(-0.0498185 + 0.234378i) q^{57} +(-0.894028 + 1.54850i) q^{58} +(0.590068 - 1.02203i) q^{59} +(2.20449 - 0.716282i) q^{60} +(-3.50138 - 6.06457i) q^{61} +4.97864 q^{62} +(-0.313585 - 2.98357i) q^{63} -2.12007 q^{64} +(-1.87362 - 3.24520i) q^{65} +(-0.406642 - 0.366142i) q^{66} +(2.19098 - 3.79489i) q^{67} +(-1.22256 + 2.11754i) q^{68} +(10.0435 + 9.04324i) q^{69} +(0.913545 + 1.58231i) q^{70} +11.2163 q^{71} +(-3.31359 - 1.47530i) q^{72} -1.60792 q^{73} +(-7.20384 - 12.4774i) q^{74} +(-1.64728 + 0.535233i) q^{75} +(0.0925682 - 0.160333i) q^{76} +(0.0864545 - 0.149744i) q^{77} +(2.46553 - 11.5994i) q^{78} +(7.08327 + 12.2686i) q^{79} +4.88558 q^{80} +(6.02218 + 6.68830i) q^{81} -18.3473 q^{82} +(4.63660 + 8.03082i) q^{83} +(-0.481926 + 2.26728i) q^{84} +(0.913545 - 1.58231i) q^{85} +(6.75463 - 11.6994i) q^{86} +(1.61209 - 0.523798i) q^{87} +(-0.104528 - 0.181049i) q^{88} +11.8868 q^{89} +(-5.00739 - 2.22943i) q^{90} +3.74724 q^{91} +(-5.22112 - 9.04324i) q^{92} +(-3.50739 - 3.15807i) q^{93} +(-5.29972 + 9.17938i) q^{94} +(-0.0691705 + 0.119807i) q^{95} +(8.37723 + 7.54289i) q^{96} +(-5.18907 - 8.98774i) q^{97} -1.82709 q^{98} +(0.0542218 + 0.515886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9	$ 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) $ 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9 + 2 * q^10 - 7 * q^11 + 3 * q^12 + 8 * q^13 - q^14 + 3 * q^15 + 9 * q^16 + 2 * q^17 - 18 * q^18 + 6 * q^19 + q^20 - 7 * q^22 + 8 * q^23 + 6 * q^24 - 4 * q^25 - 6 * q^26 - 2 * q^28 - q^29 - 3 * q^30 + 9 * q^34 + 8 * q^35 - 6 * q^36 - 42 * q^37 - 8 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 + 3 * q^42 + 7 * q^43 + 6 * q^44 - 6 * q^45 - 46 * q^46 + 2 * q^47 + 30 * q^48 - 4 * q^49 + q^50 - 3 * q^51 + 7 * q^52 - 16 * q^53 - 36 * q^54 - 14 * q^55 + 3 * q^56 - 24 * q^57 + 19 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 30 * q^62 + 3 * q^63 - 14 * q^64 - 8 * q^65 - 9 * q^66 + 22 * q^67 + q^68 + 51 * q^69 + q^70 + 26 * q^71 - 21 * q^72 - 8 * q^73 - 9 * q^74 + 13 * q^76 + 7 * q^77 - 21 * q^78 + 24 * q^79 + 18 * q^80 + 9 * q^81 + 19 * q^83 - 12 * q^84 + q^85 + 27 * q^86 + 45 * q^87 + q^88 + 30 * q^89 - 27 * q^90 + 16 * q^91 - 3 * q^92 - 15 * q^93 + 7 * q^94 + 3 * q^95 + 30 * q^96 + 12 * q^97 - 2 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.913545	+	1.58231i	0.645974	+	1.11886i	0.984076	+	0.177750i	$0.0568820\pi$
$2$	0.913545	+	1.58231i	0.645974	+	1.11886i	−0.338101	+	0.941110i	$0.609785\pi$
$3$	0.360114	−	1.69420i	0.207912	−	0.978148i
$3$	0.360114	−	1.69420i	0.207912	−	0.978148i
$4$	−0.669131	+	1.15897i	−0.334565	+	0.579484i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	3.00973	−	0.977920i	1.22872	−	0.399234i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.20906			0.427466
$9$	−2.74064	−	1.22021i	−0.913545	−	0.406737i
$10$	1.82709			0.577777
$11$	−0.0864545	−	0.149744i	−0.0260670	−	0.0451494i	0.852698	−	0.522405i	$-0.174965\pi$
$11$	−0.0864545	−	0.149744i	−0.0260670	−	0.0451494i	−0.878765	+	0.477255i	$0.841632\pi$
$12$	1.72256	+	1.55100i	0.497261	+	0.447736i
$13$	1.87362	−	3.24520i	0.519648	−	0.900058i	−0.480091	−	0.877219i	$-0.659396\pi$
$13$	1.87362	−	3.24520i	0.519648	−	0.900058i	0.999739	−	0.0228387i	$-0.00727041\pi$
$14$	−0.913545	+	1.58231i	−0.244155	+	0.422889i
$15$	−1.28716	−	1.15897i	−0.332344	−	0.299244i
$16$	2.44279	+	4.23104i	0.610697	+	1.05776i
$17$	1.82709			0.443135			0.221567	−	0.975145i	$-0.428883\pi$
$17$	1.82709			0.443135			0.221567	+	0.975145i	$0.428883\pi$
$18$	−0.572949	−	5.45125i	−0.135045	−	1.28487i
$19$	−0.138341			−0.0317376			−0.0158688	−	0.999874i	$-0.505051\pi$
$19$	−0.138341			−0.0317376			−0.0158688	+	0.999874i	$0.505051\pi$
$20$	0.669131	+	1.15897i	0.149622	+	0.259153i
$21$	1.64728	−	0.535233i	0.359466	−	0.116797i
$22$	0.157960	−	0.273595i	0.0336773	−	0.0583307i
$23$	−3.90142	+	6.75746i	−0.813502	+	1.40903i	0.0968960	+	0.995295i	$0.469109\pi$
$23$	−3.90142	+	6.75746i	−0.813502	+	1.40903i	−0.910398	+	0.413733i	$0.864225\pi$
$24$	0.435398	−	2.04839i	0.0888752	−	0.418125i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	6.84655			1.34272
$27$	−3.05422	+	4.20378i	−0.587785	+	0.809017i
$28$	−1.33826			−0.252908
$29$	0.489318	+	0.847523i	0.0908641	+	0.157381i	0.907875	−	0.419241i	$-0.137704\pi$
$29$	0.489318	+	0.847523i	0.0908641	+	0.157381i	−0.817011	+	0.576622i	$0.804370\pi$
$30$	0.657960	−	3.09546i	0.120127	−	0.565151i
$31$	1.36245	−	2.35983i	0.244703	−	0.423838i	−0.717345	−	0.696718i	$-0.754643\pi$
$31$	1.36245	−	2.35983i	0.244703	−	0.423838i	0.962048	+	0.272880i	$0.0879762\pi$
$32$	−3.25414	+	5.63634i	−0.575256	+	0.996373i
$33$	−0.284829	+	0.0925467i	−0.0495824	+	0.0161103i
$34$	1.66913	+	2.89102i	0.286254	+	0.495806i
$35$	1.00000			0.169031
$36$	3.24803	−	2.35983i	0.541338	−	0.393305i
$37$	−7.88558			−1.29638			−0.648191	−	0.761478i	$-0.724474\pi$
$37$	−7.88558			−1.29638			−0.648191	+	0.761478i	$0.724474\pi$
$38$	−0.126381	−	0.218898i	−0.0205017	−	0.0355100i
$39$	−4.82331	−	4.34293i	−0.772348	−	0.695425i
$40$	0.604528	−	1.04707i	0.0955843	−	0.165557i
$41$	−5.02090	+	8.69645i	−0.784132	+	1.35816i	0.145384	+	0.989375i	$0.453558\pi$
$41$	−5.02090	+	8.69645i	−0.784132	+	1.35816i	−0.929516	+	0.368782i	$0.879775\pi$
$42$	2.35177	+	2.11754i	0.362885	+	0.326744i
$43$	−3.69693	−	6.40327i	−0.563777	−	0.976490i	−0.997162	−	0.0752814i	$-0.976014\pi$
$43$	−3.69693	−	6.40327i	−0.563777	−	0.976490i	0.433386	−	0.901209i	$-0.357319\pi$
$44$	0.231398			0.0348845
$45$	−2.42705	+	1.76336i	−0.361803	+	0.262866i
$46$	−14.2565			−2.10201
$47$	2.90063	+	5.02404i	0.423100	+	0.732831i	0.996241	−	0.0866257i	$-0.0276084\pi$
$47$	2.90063	+	5.02404i	0.423100	+	0.732831i	−0.573141	+	0.819457i	$0.694275\pi$
$48$	8.04791	−	2.61492i	1.16162	−	0.377432i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.913545	−	1.58231i	0.129195	−	0.223772i
$51$	0.657960	−	3.09546i	0.0921329	−	0.433451i
$52$	2.50739	+	4.34293i	0.347713	+	0.602256i
$53$	−11.7139			−1.60902			−0.804511	−	0.593938i	$-0.797572\pi$
$53$	−11.7139			−1.60902			−0.804511	+	0.593938i	$0.797572\pi$
$54$	−9.44183	−	0.992377i	−1.28487	−	0.135045i
$55$	−0.172909			−0.0233151
$56$	0.604528	+	1.04707i	0.0807835	+	0.139921i
$57$	−0.0498185	+	0.234378i	−0.00659862	+	0.0310441i
$58$	−0.894028	+	1.54850i	−0.117392	+	0.203328i
$59$	0.590068	−	1.02203i	0.0768203	−	0.133057i	−0.825056	−	0.565051i	$-0.808857\pi$
$59$	0.590068	−	1.02203i	0.0768203	−	0.133057i	0.901876	+	0.431994i	$0.142190\pi$
$60$	2.20449	−	0.716282i	0.284598	−	0.0924716i
$61$	−3.50138	−	6.06457i	−0.448306	−	0.776488i	0.549970	−	0.835184i	$-0.314639\pi$
$61$	−3.50138	−	6.06457i	−0.448306	−	0.776488i	−0.998276	+	0.0586959i	$0.981306\pi$
$62$	4.97864			0.632287
$63$	−0.313585	−	2.98357i	−0.0395080	−	0.375894i
$64$	−2.12007			−0.265008
$65$	−1.87362	−	3.24520i	−0.232394	−	0.402518i
$66$	−0.406642	−	0.366142i	−0.0500541	−	0.0450690i
$67$	2.19098	−	3.79489i	0.267671	−	0.463620i	−0.700589	−	0.713565i	$-0.747079\pi$
$67$	2.19098	−	3.79489i	0.267671	−	0.463620i	0.968260	+	0.249945i	$0.0804126\pi$
$68$	−1.22256	+	2.11754i	−0.148257	+	0.256789i
$69$	10.0435	+	9.04324i	1.20910	+	1.08868i
$70$	0.913545	+	1.58231i	0.109190	+	0.189122i
$71$	11.2163			1.33113			0.665564	−	0.746341i	$-0.268191\pi$
$71$	11.2163			1.33113			0.665564	+	0.746341i	$0.268191\pi$
$72$	−3.31359	−	1.47530i	−0.390510	−	0.173866i
$73$	−1.60792			−0.188193			−0.0940964	−	0.995563i	$-0.529996\pi$
$73$	−1.60792			−0.188193			−0.0940964	+	0.995563i	$0.529996\pi$
$74$	−7.20384	−	12.4774i	−0.837429	−	1.45047i
$75$	−1.64728	+	0.535233i	−0.190211	+	0.0618034i
$76$	0.0925682	−	0.160333i	0.0106183	−	0.0183914i
$77$	0.0864545	−	0.149744i	0.00985241	−	0.0170649i
$78$	2.46553	−	11.5994i	0.279167	−	1.31338i
$79$	7.08327	+	12.2686i	0.796930	+	1.38032i	0.921607	+	0.388125i	$0.126877\pi$
$79$	7.08327	+	12.2686i	0.796930	+	1.38032i	−0.124677	+	0.992197i	$0.539789\pi$
$80$	4.88558			0.546224
$81$	6.02218	+	6.68830i	0.669131	+	0.743145i
$82$	−18.3473			−2.02612
$83$	4.63660	+	8.03082i	0.508933	+	0.881497i	0.999946	+	0.0103453i	$0.00329307\pi$
$83$	4.63660	+	8.03082i	0.508933	+	0.881497i	−0.491014	+	0.871152i	$0.663374\pi$
$84$	−0.481926	+	2.26728i	−0.0525824	+	0.247381i
$85$	0.913545	−	1.58231i	0.0990879	−	0.171625i
$86$	6.75463	−	11.6994i	0.728370	−	1.26157i
$87$	1.61209	−	0.523798i	0.172834	−	0.0561571i
$88$	−0.104528	−	0.181049i	−0.0111428	−	0.0192998i
$89$	11.8868			1.25999			0.629997	−	0.776598i	$-0.283056\pi$
$89$	11.8868			1.25999			0.629997	+	0.776598i	$0.283056\pi$
$90$	−5.00739	−	2.22943i	−0.527825	−	0.235003i
$91$	3.74724			0.392817
$92$	−5.22112	−	9.04324i	−0.544339	−	0.942823i
$93$	−3.50739	−	3.15807i	−0.363700	−	0.327477i
$94$	−5.29972	+	9.17938i	−0.546624	+	0.946780i
$95$	−0.0691705	+	0.119807i	−0.00709675	+	0.0122919i
$96$	8.37723	+	7.54289i	0.854998	+	0.769843i
$97$	−5.18907	−	8.98774i	−0.526871	−	0.912567i	−0.999510	−	0.0313105i	$-0.990032\pi$
$97$	−5.18907	−	8.98774i	−0.526871	−	0.912567i	0.472639	−	0.881256i	$-0.343301\pi$
$98$	−1.82709			−0.184564
$99$	0.0542218	+	0.515886i	0.00544949	+	0.0518485i
$100$	1.33826			0.133826
$101$	−8.85160	−	15.3314i	−0.880767	−	1.52553i	−0.850489	−	0.525992i	$-0.823694\pi$
$101$	−8.85160	−	15.3314i	−0.880767	−	1.52553i	−0.0302779	−	0.999542i	$-0.509639\pi$
$102$	5.49904	−	1.78675i	0.544487	−	0.176914i
$103$	1.07860	−	1.86818i	0.106277	−	0.184078i	−0.807982	−	0.589207i	$-0.799440\pi$
$103$	1.07860	−	1.86818i	0.106277	−	0.184078i	0.914259	+	0.405130i	$0.132774\pi$
$104$	2.26531	−	3.92364i	0.222132	−	0.384744i
$105$	0.360114	−	1.69420i	0.0351435	−	0.165337i
$106$	−10.7011	−	18.5349i	−1.03939	−	1.80027i
$107$	−11.5229			−1.11396			−0.556979	−	0.830527i	$-0.688039\pi$
$107$	−11.5229			−1.11396			−0.556979	+	0.830527i	$0.688039\pi$
$108$	−2.82837	−	6.35262i	−0.272160	−	0.611281i
$109$	6.89492			0.660414			0.330207	−	0.943909i	$-0.392882\pi$
$109$	6.89492			0.660414			0.330207	+	0.943909i	$0.392882\pi$
$110$	−0.157960	−	0.273595i	−0.0150609	−	0.0260863i
$111$	−2.83970	+	13.3598i	−0.269533	+	1.26805i
$112$	−2.44279	+	4.23104i	−0.230822	+	0.399795i
$113$	−3.34848	+	5.79973i	−0.314998	+	0.545593i	−0.979437	−	0.201750i	$-0.935337\pi$
$113$	−3.34848	+	5.79973i	−0.314998	+	0.545593i	0.664439	+	0.747343i	$0.268671\pi$
$114$	−0.416369	+	0.135286i	−0.0389965	+	0.0126707i
$115$	3.90142	+	6.75746i	0.363809	+	0.630136i
$116$	−1.30967			−0.121600
$117$	−9.09474	+	6.60771i	−0.840809	+	0.610883i
$118$	2.15622			0.198496
$119$	0.913545	+	1.58231i	0.0837446	+	0.145050i
$120$	−1.55626	−	1.40126i	−0.142066	−	0.127917i
$121$	5.48505	−	9.50039i	0.498641	−	0.863672i
$122$	6.39734	−	11.0805i	0.579188	−	1.00318i
$123$	12.9254	+	11.6381i	1.16545	+	1.04937i
$124$	1.82331	+	3.15807i	0.163738	+	0.283603i
$125$	−1.00000			−0.0894427
$126$	4.43444	−	3.22181i	0.395052	−	0.287022i
$127$	−16.8604			−1.49611			−0.748057	−	0.663634i	$-0.769013\pi$
$127$	−16.8604			−1.49611			−0.748057	+	0.663634i	$0.769013\pi$
$128$	4.57151	+	7.91808i	0.404068	+	0.699866i
$129$	−12.1797	+	3.95744i	−1.07237	+	0.348433i
$130$	3.42327	−	5.92928i	0.300241	−	0.520032i
$131$	6.33458	−	10.9718i	0.553455	−	0.958613i	−0.444567	−	0.895746i	$-0.646642\pi$
$131$	6.33458	−	10.9718i	0.553455	−	0.958613i	0.998022	−	0.0628668i	$-0.0200243\pi$
$132$	0.0833294	−	0.392034i	0.00725289	−	0.0341222i
$133$	−0.0691705	−	0.119807i	−0.00599785	−	0.0103886i
$134$	8.00625			0.691635
$135$	2.11347	+	4.74692i	0.181898	+	0.408550i
$136$	2.20906			0.189425
$137$	1.69555	+	2.93678i	0.144861	+	0.250906i	0.929321	−	0.369273i	$-0.120393\pi$
$137$	1.69555	+	2.93678i	0.144861	+	0.250906i	−0.784460	+	0.620179i	$0.787060\pi$
$138$	−5.13396	+	24.1534i	−0.437032	+	2.05607i
$139$	−4.06773	+	7.04551i	−0.345020	+	0.597592i	−0.985357	−	0.170501i	$-0.945461\pi$
$139$	−4.06773	+	7.04551i	−0.345020	+	0.597592i	0.640337	+	0.768094i	$0.278795\pi$
$140$	−0.669131	+	1.15897i	−0.0565519	+	0.0979507i
$141$	9.55629	−	3.10503i	0.804785	−	0.261490i
$142$	10.2466	+	17.7476i	0.859874	+	1.48935i
$143$	−0.647932			−0.0541828
$144$	−1.53205	−	14.5764i	−0.127671	−	1.21470i
$145$	0.978636			0.0812713
$146$	−1.46891	−	2.54422i	−0.121568	−	0.210562i
$147$	1.28716	+	1.15897i	0.106164	+	0.0955901i
$148$	5.27648	−	9.13914i	0.433724	−	0.751232i
$149$	2.04131	−	3.53565i	0.167230	−	0.289651i	−0.770215	−	0.637785i	$-0.779851\pi$
$149$	2.04131	−	3.53565i	0.167230	−	0.289651i	0.937445	+	0.348133i	$0.113184\pi$
$150$	−2.35177	−	2.11754i	−0.192021	−	0.172896i
$151$	7.85489	+	13.6051i	0.639222	+	1.10717i	0.985604	+	0.169071i	$0.0540769\pi$
$151$	7.85489	+	13.6051i	0.639222	+	1.10717i	−0.346382	+	0.938094i	$0.612590\pi$
$152$	−0.167262			−0.0135668
$153$	−5.00739	−	2.22943i	−0.404824	−	0.180239i
$154$	0.315921			0.0254576
$155$	−1.36245	−	2.35983i	−0.109435	−	0.189546i
$156$	8.26074	−	2.68408i	0.661389	−	0.214898i
$157$	1.15280	−	1.99671i	0.0920036	−	0.159355i	−0.816351	−	0.577557i	$-0.804006\pi$
$157$	1.15280	−	1.99671i	0.0920036	−	0.159355i	0.908354	+	0.418202i	$0.137340\pi$
$158$	−12.9418	+	22.4158i	−1.02959	+	1.78331i
$159$	−4.21832	+	19.8456i	−0.334534	+	1.57386i
$160$	3.25414	+	5.63634i	0.257263	+	0.445592i
$161$	−7.80284			−0.614950
$162$	−5.08142	+	15.6390i	−0.399234	+	1.22872i
$163$	18.7421			1.46800			0.733998	−	0.679152i	$-0.237652\pi$
$163$	18.7421			1.46800			0.733998	+	0.679152i	$0.237652\pi$
$164$	−6.71927	−	11.6381i	−0.524687	−	0.908785i
$165$	−0.0622669	+	0.292943i	−0.00484747	+	0.0228056i
$166$	−8.47148	+	14.6730i	−0.657515	+	1.13885i
$167$	2.85634	−	4.94732i	0.221030	−	0.382835i	−0.734091	−	0.679051i	$-0.762392\pi$
$167$	2.85634	−	4.94732i	0.221030	−	0.382835i	0.955121	+	0.296216i	$0.0957248\pi$
$168$	1.99165	−	0.647127i	0.153659	−	0.0499270i
$169$	−0.520897	−	0.902221i	−0.0400690	−	0.0694016i
$170$	3.33826			0.256033
$171$	0.379143	+	0.168805i	0.0289938	+	0.0129089i
$172$	9.89492			0.754481
$173$	8.83149	+	15.2966i	0.671446	+	1.16298i	0.977494	+	0.210963i	$0.0676598\pi$
$173$	8.83149	+	15.2966i	0.671446	+	1.16298i	−0.306048	+	0.952016i	$0.599007\pi$
$174$	2.30152	+	2.07230i	0.174478	+	0.157101i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	0.422381	−	0.731585i	0.0318381	−	0.0551453i
$177$	−1.51903	−	1.36774i	−0.114177	−	0.102806i
$178$	10.8591	+	18.8085i	0.813924	+	1.40976i
$179$	3.59700			0.268852			0.134426	−	0.990924i	$-0.457081\pi$
$179$	3.59700			0.268852			0.134426	+	0.990924i	$0.457081\pi$
$180$	−0.419659	−	3.99279i	−0.0312795	−	0.297605i
$181$	−13.8362			−1.02844			−0.514219	−	0.857659i	$-0.671918\pi$
$181$	−13.8362			−1.02844			−0.514219	+	0.857659i	$0.671918\pi$
$182$	3.42327	+	5.92928i	0.253750	+	0.439508i
$183$	−11.5355	+	3.74811i	−0.852728	+	0.277068i
$184$	−4.71704	+	8.17015i	−0.347745	+	0.602312i
$185$	−3.94279	+	6.82911i	−0.289880	+	0.502086i
$186$	1.79287	−	8.43481i	0.131460	−	0.618470i
$187$	−0.157960	−	0.273595i	−0.0115512	−	0.0200073i
$188$	−7.76360			−0.566219
$189$	−5.16769	−	0.543146i	−0.375894	−	0.0395080i
$190$	−0.252762			−0.0183373
$191$	2.99212	+	5.18250i	0.216502	+	0.374993i	0.953736	−	0.300645i	$-0.0972018\pi$
$191$	2.99212	+	5.18250i	0.216502	+	0.374993i	−0.737234	+	0.675637i	$0.763868\pi$
$192$	−0.763465	+	3.59182i	−0.0550984	+	0.259217i
$193$	8.83948	−	15.3104i	0.636279	−	1.10207i	−0.349963	−	0.936763i	$-0.613806\pi$
$193$	8.83948	−	15.3104i	0.636279	−	1.10207i	0.986243	−	0.165305i	$-0.0528608\pi$
$194$	9.48091	−	16.4214i	0.680690	−	1.17899i
$195$	−6.17274	+	2.00565i	−0.442039	+	0.143627i
$196$	−0.669131	−	1.15897i	−0.0477950	−	0.0827834i
$197$	−20.1914			−1.43858			−0.719290	−	0.694710i	$-0.755533\pi$
$197$	−20.1914			−1.43858			−0.719290	+	0.694710i	$0.755533\pi$
$198$	−0.766755	+	0.557080i	−0.0544909	+	0.0395900i
$199$	18.0867			1.28214			0.641068	−	0.767484i	$-0.278492\pi$
$199$	18.0867			1.28214			0.641068	+	0.767484i	$0.278492\pi$
$200$	−0.604528	−	1.04707i	−0.0427466	−	0.0740393i
$201$	−5.64031	−	5.07856i	−0.397837	−	0.358214i
$202$	16.1727	−	28.0119i	1.13791	−	1.97091i
$203$	−0.489318	+	0.847523i	−0.0343434	+	0.0594845i
$204$	3.14728	+	2.83382i	0.220354	+	0.198407i
$205$	5.02090	+	8.69645i	0.350675	+	0.607386i
$206$	3.94139			0.274609
$207$	18.9379	−	13.7592i	1.31627	−	0.956329i
$208$	18.3074			1.26939
$209$	0.0119602	+	0.0207157i	0.000827305	+	0.00143293i
$210$	3.00973	−	0.977920i	0.207691	−	0.0674829i
$211$	11.9382	−	20.6775i	0.821857	−	1.42350i	−0.0824414	−	0.996596i	$-0.526272\pi$
$211$	11.9382	−	20.6775i	0.821857	−	1.42350i	0.904298	−	0.426902i	$-0.140395\pi$
$212$	7.83810	−	13.5760i	0.538323	−	0.932402i
$213$	4.03914	−	19.0026i	0.276757	−	1.30204i
$214$	−10.5267	−	18.2327i	−0.719588	−	1.24636i
$215$	−7.39386			−0.504257
$216$	−3.69273	+	5.08260i	−0.251258	+	0.345827i
$217$	2.72490			0.184978
$218$	6.29882	+	10.9099i	0.426610	+	0.738910i
$219$	−0.579034	+	2.72414i	−0.0391275	+	0.184080i
$220$	0.115699	−	0.200396i	0.00780041	−	0.0135107i
$221$	3.42327	−	5.92928i	0.230274	−	0.398847i
$222$	−23.7334	+	7.71146i	−1.59288	+	0.517559i
$223$	−3.81407	−	6.60617i	−0.255409	−	0.442382i	0.709597	−	0.704607i	$-0.248877\pi$
$223$	−3.81407	−	6.60617i	−0.255409	−	0.442382i	−0.965007	+	0.262226i	$0.915544\pi$
$224$	−6.50828			−0.434853
$225$	0.313585	+	2.98357i	0.0209057	+	0.198904i
$226$	−12.2359			−0.813923
$227$	−8.09650	−	14.0236i	−0.537384	−	0.930776i	−0.999044	−	0.0437192i	$-0.986079\pi$
$227$	−8.09650	−	14.0236i	−0.537384	−	0.930776i	0.461660	−	0.887057i	$-0.347254\pi$
$228$	−0.238301	−	0.214567i	−0.0157819	−	0.0142101i
$229$	12.5200	−	21.6854i	0.827348	−	1.43301i	−0.0727638	−	0.997349i	$-0.523182\pi$
$229$	12.5200	−	21.6854i	0.827348	−	1.43301i	0.900112	−	0.435659i	$-0.143485\pi$
$230$	−7.12825	+	12.3465i	−0.470023	+	0.814103i
$231$	−0.222562	−	0.200396i	−0.0146435	−	0.0131851i
$232$	0.591613	+	1.02470i	0.0388413	+	0.0672751i
$233$	−10.2963			−0.674536			−0.337268	−	0.941409i	$-0.609503\pi$
$233$	−10.2963			−0.674536			−0.337268	+	0.941409i	$0.609503\pi$
$234$	−18.7639	−	8.35422i	−1.22663	−	0.546133i
$235$	5.80126			0.378433
$236$	0.789665	+	1.36774i	0.0514028	+	0.0890323i
$237$	23.3362	−	7.58240i	1.51585	−	0.492530i
$238$	−1.66913	+	2.89102i	−0.108194	+	0.187397i
$239$	−9.95235	+	17.2380i	−0.643764	+	1.11503i	0.340821	+	0.940128i	$0.389295\pi$
$239$	−9.95235	+	17.2380i	−0.643764	+	1.11503i	−0.984585	+	0.174904i	$0.944038\pi$
$240$	1.75936	−	8.27716i	0.113566	−	0.534288i
$241$	−5.19868	−	9.00437i	−0.334876	−	0.580023i	0.648585	−	0.761142i	$-0.275361\pi$
$241$	−5.19868	−	9.00437i	−0.334876	−	0.580023i	−0.983461	+	0.181120i	$0.942028\pi$
$242$	20.0434			1.28844
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$	9.37152			0.599950
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	−6.60710	+	31.0840i	−0.421253	+	1.98184i
$247$	−0.259198	+	0.448945i	−0.0164924	+	0.0285657i
$248$	1.64728	−	2.85317i	0.104602	−	0.181176i
$249$	15.2755	−	4.96332i	0.968047	−	0.314538i
$250$	−0.913545	−	1.58231i	−0.0577777	−	0.100074i
$251$	−24.0059			−1.51524			−0.757620	−	0.652696i	$-0.773638\pi$
$251$	−24.0059			−1.51524			−0.757620	+	0.652696i	$0.773638\pi$
$252$	3.66769	+	1.63296i	0.231043	+	0.102867i
$253$	1.34918			0.0848223
$254$	−15.4027	−	26.6783i	−0.966451	−	1.67394i
$255$	−2.35177	−	2.11754i	−0.147273	−	0.132606i
$256$	−10.4726	+	18.1391i	−0.654539	+	1.13369i
$257$	6.03395	−	10.4511i	0.376387	−	0.651922i	−0.614146	−	0.789192i	$-0.710500\pi$
$257$	6.03395	−	10.4511i	0.376387	−	0.651922i	0.990534	+	0.137270i	$0.0438328\pi$
$258$	−17.3886	−	15.6568i	−1.08257	−	0.974750i
$259$	−3.94279	−	6.82911i	−0.244993	−	0.424340i
$260$	5.01478			0.311004
$261$	−0.306886	−	2.91982i	−0.0189958	−	0.180733i
$262$	23.1477			1.43007
$263$	−1.93191	−	3.34616i	−0.119127	−	0.206333i	0.800295	−	0.599606i	$-0.204676\pi$
$263$	−1.93191	−	3.34616i	−0.119127	−	0.206333i	−0.919422	+	0.393273i	$0.871343\pi$
$264$	−0.344375	+	0.111894i	−0.0211948	+	0.00688661i
$265$	−5.85693	+	10.1445i	−0.359788	+	0.623171i
$266$	0.126381	−	0.218898i	0.00774891	−	0.0134215i
$267$	4.28058	−	20.1386i	0.261967	−	1.23246i
$268$	2.93211	+	5.07856i	0.179107	+	0.310222i
$269$	8.48725			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$269$	8.48725			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$270$	−5.58034	+	7.68068i	−0.339609	+	0.467431i
$271$	11.8287			0.718541			0.359270	−	0.933234i	$-0.383026\pi$
$271$	11.8287			0.718541			0.359270	+	0.933234i	$0.383026\pi$
$272$	4.46320	+	7.73049i	0.270621	+	0.468730i
$273$	1.34943	−	6.34858i	0.0816713	−	0.384233i
$274$	−3.09793	+	5.36577i	−0.187153	+	0.324158i
$275$	−0.0864545	+	0.149744i	−0.00521341	+	0.00902988i
$276$	−17.2013	+	5.58903i	−1.03539	+	0.336420i
$277$	13.6581	+	23.6565i	0.820636	+	1.42138i	0.905210	+	0.424965i	$0.139714\pi$
$277$	13.6581	+	23.6565i	0.820636	+	1.42138i	−0.0845742	+	0.996417i	$0.526953\pi$
$278$	−14.8642			−0.891496
$279$	−6.61347	+	4.80496i	−0.395938	+	0.287666i
$280$	1.20906			0.0722550
$281$	−7.94358	−	13.7587i	−0.473874	−	0.820774i	0.525678	−	0.850683i	$-0.323812\pi$
$281$	−7.94358	−	13.7587i	−0.473874	−	0.820774i	−0.999553	+	0.0299091i	$0.990478\pi$
$282$	13.6432	+	12.2844i	0.812441	+	0.731526i
$283$	−8.23065	+	14.2559i	−0.489261	+	0.847425i	−0.999924	−	0.0123561i	$-0.996067\pi$
$283$	−8.23065	+	14.2559i	−0.489261	+	0.847425i	0.510663	+	0.859781i	$0.329400\pi$
$284$	−7.50516	+	12.9993i	−0.445349	+	0.771367i
$285$	0.178068	+	0.160333i	0.0105478	+	0.00949730i
$286$	−0.591915	−	1.02523i	−0.0350007	−	0.0606229i
$287$	−10.0418			−0.592748
$288$	15.7959	−	11.4764i	0.930784	−	0.676255i
$289$	−13.6617			−0.803632
$290$	0.894028	+	1.54850i	0.0524991	+	0.0909312i
$291$	−17.0957	+	5.55473i	−1.00217	+	0.325624i
$292$	1.07591	−	1.86353i	0.0629628	−	0.109055i
$293$	11.9116	−	20.6315i	0.695884	−	1.20531i	−0.273998	−	0.961730i	$-0.588346\pi$
$293$	11.9116	−	20.6315i	0.695884	−	1.20531i	0.969882	−	0.243576i	$-0.0783205\pi$
$294$	−0.657960	+	3.09546i	−0.0383730	+	0.180531i
$295$	−0.590068	−	1.02203i	−0.0343551	−	0.0595047i
$296$	−9.53411			−0.554159
$297$	0.893540	+	0.0939148i	0.0518485	+	0.00544949i
$298$	7.45931			0.432106
$299$	14.6196	+	25.3218i	0.845470	+	1.46440i
$300$	0.481926	−	2.26728i	0.0278240	−	0.130902i
$301$	3.69693	−	6.40327i	0.213088	−	0.369079i
$302$	−14.3516	+	24.8577i	−0.825842	+	1.43040i
$303$	−29.1621	+	9.47534i	−1.67532	+	0.544344i
$304$	−0.337938	−	0.585326i	−0.0193821	−	0.0335708i
$305$	−7.00276			−0.400977
$306$	−1.04683	−	9.95992i	−0.0598433	−	0.569371i
$307$	−23.7097			−1.35318			−0.676591	−	0.736359i	$-0.736543\pi$
$307$	−23.7097			−1.35318			−0.676591	+	0.736359i	$0.736543\pi$
$308$	0.115699	+	0.200396i	0.00659255	+	0.0114186i
$309$	−2.77666	−	2.50012i	−0.157959	−	0.142227i
$310$	2.48932	−	4.31163i	0.141384	−	0.244884i
$311$	7.30983	−	12.6610i	0.414502	−	0.717939i	−0.580874	−	0.813994i	$-0.697289\pi$
$311$	7.30983	−	12.6610i	0.414502	−	0.717939i	0.995376	+	0.0960546i	$0.0306223\pi$
$312$	−5.83166	−	5.25085i	−0.330153	−	0.297271i
$313$	−5.34090	−	9.25071i	−0.301885	−	0.522881i	0.674678	−	0.738113i	$-0.264283\pi$
$313$	−5.34090	−	9.25071i	−0.301885	−	0.522881i	−0.976563	+	0.215232i	$0.930949\pi$
$314$	4.21255			0.237728
$315$	−2.74064	−	1.22021i	−0.154417	−	0.0687510i
$316$	−18.9585			−1.06650
$317$	10.9564	+	18.9771i	0.615375	+	1.06586i	0.990319	+	0.138813i	$0.0443285\pi$
$317$	10.9564	+	18.9771i	0.615375	+	1.06586i	−0.374944	+	0.927047i	$0.622338\pi$
$318$	−35.2555	+	11.4552i	−1.97703	+	0.642376i
$319$	0.0846075	−	0.146545i	0.00473711	−	0.00820492i
$320$	−1.06003	+	1.83603i	−0.0592577	+	0.102637i
$321$	−4.14954	+	19.5221i	−0.231605	+	1.08961i
$322$	−7.12825	−	12.3465i	−0.397242	−	0.688043i
$323$	−0.252762			−0.0140640
$324$	−11.7812	+	2.50416i	−0.654508	+	0.139120i
$325$	−3.74724			−0.207859
$326$	17.1218	+	29.6558i	0.948287	+	1.64248i
$327$	2.48295	−	11.6814i	0.137308	−	0.645982i
$328$	−6.07055	+	10.5145i	−0.335190	+	0.580566i
$329$	−2.90063	+	5.02404i	−0.159917	+	0.276984i
$330$	−0.520409	+	0.169091i	−0.0286476	+	0.00930816i
$331$	11.2591	+	19.5014i	0.618858	+	1.07189i	0.989694	+	0.143195i	$0.0457377\pi$
$331$	11.2591	+	19.5014i	0.618858	+	1.07189i	−0.370836	+	0.928698i	$0.620929\pi$
$332$	−12.4100			−0.681085
$333$	21.6115	+	9.62206i	1.18430	+	0.527286i
$334$	10.4376			0.571118
$335$	−2.19098	−	3.79489i	−0.119706	−	0.207337i
$336$	6.28854	+	5.66223i	0.343068	+	0.308900i
$337$	3.70857	−	6.42343i	0.202019	−	0.349906i	−0.747160	−	0.664644i	$-0.768583\pi$
$337$	3.70857	−	6.42343i	0.202019	−	0.349906i	0.949179	+	0.314738i	$0.101917\pi$
$338$	0.951727	−	1.64844i	0.0517671	−	0.0896633i
$339$	8.62008	+	7.76156i	0.468179	+	0.421550i
$340$	1.22256	+	2.11754i	0.0663028	+	0.114840i
$341$	−0.471160			−0.0255147
$342$	0.0792624	+	0.754131i	0.00428602	+	0.0407787i
$343$	−1.00000			−0.0539949
$344$	−4.46980	−	7.74192i	−0.240996	−	0.417416i
$345$	12.8534	−	4.17634i	0.692006	−	0.224847i
$346$	−16.1359	+	27.9483i	−0.867474	+	1.50251i
$347$	12.0354	−	20.8459i	0.646094	−	1.11907i	−0.337954	−	0.941163i	$-0.609735\pi$
$347$	12.0354	−	20.8459i	0.646094	−	1.11907i	0.984048	−	0.177905i	$-0.0569319\pi$
$348$	−0.471630	+	2.21885i	−0.0252820	+	0.118943i
$349$	−7.74234	−	13.4101i	−0.414438	−	0.717828i	0.580931	−	0.813953i	$-0.302688\pi$
$349$	−7.74234	−	13.4101i	−0.414438	−	0.717828i	−0.995369	+	0.0961250i	$0.969355\pi$
$350$	1.82709			0.0976621
$351$	7.91966	+	17.7878i	0.422720	+	0.949445i
$352$	1.12534			0.0599809
$353$	−10.7716	−	18.6569i	−0.573312	−	0.993006i	−0.996223	−	0.0868347i	$-0.972325\pi$
$353$	−10.7716	−	18.6569i	−0.573312	−	0.993006i	0.422910	−	0.906172i	$-0.361009\pi$
$354$	0.776482	−	3.65306i	0.0412696	−	0.194158i
$355$	5.60814	−	9.71359i	0.297649	−	0.515544i
$356$	−7.95379	+	13.7764i	−0.421550	+	0.730147i
$357$	3.00973	−	0.977920i	0.159292	−	0.0517570i
$358$	3.28602	+	5.69156i	0.173672	+	0.300808i
$359$	−18.2075			−0.960954			−0.480477	−	0.877007i	$-0.659536\pi$
$359$	−18.2075			−0.960954			−0.480477	+	0.877007i	$0.659536\pi$
$360$	−2.93444	+	2.13200i	−0.154659	+	0.112366i
$361$	−18.9809			−0.998993
$362$	−12.6400	−	21.8932i	−0.664345	−	1.15068i
$363$	−14.1203	−	12.7140i	−0.741125	−	0.667312i
$364$	−2.50739	+	4.34293i	−0.131423	+	0.227631i
$365$	−0.803960	+	1.39250i	−0.0420812	+	0.0728868i
$366$	−16.4689	−	14.8286i	−0.860841	−	0.775105i
$367$	12.5959	+	21.8167i	0.657498	+	1.13882i	0.981261	+	0.192682i	$0.0617186\pi$
$367$	12.5959	+	21.8167i	0.657498	+	1.13882i	−0.323763	+	0.946138i	$0.604948\pi$
$368$	−38.1214			−1.98722
$369$	24.3719	−	17.7073i	1.26875	−	0.921803i
$370$	−14.4077			−0.749019
$371$	−5.85693	−	10.1445i	−0.304076	−	0.526676i
$372$	6.00701	−	1.95179i	0.311449	−	0.101196i
$373$	16.3150	−	28.2583i	0.844757	−	1.46316i	−0.0410753	−	0.999156i	$-0.513078\pi$
$373$	16.3150	−	28.2583i	0.844757	−	1.46316i	0.885832	−	0.464006i	$-0.153588\pi$
$374$	0.288608	−	0.499883i	0.0149236	−	0.0258484i
$375$	−0.360114	+	1.69420i	−0.0185962	+	0.0874882i
$376$	3.50703	+	6.07435i	0.180861	+	0.313261i
$377$	3.66718			0.188869
$378$	−3.86149	−	8.67306i	−0.198614	−	0.446094i
$379$	−2.59358			−0.133223			−0.0666116	−	0.997779i	$-0.521219\pi$
$379$	−2.59358			−0.133223			−0.0666116	+	0.997779i	$0.521219\pi$
$380$	−0.0925682	−	0.160333i	−0.00474865	−	0.00822490i
$381$	−6.07164	+	28.5648i	−0.311060	+	1.46342i
$382$	−5.46688	+	9.46891i	−0.279710	+	0.484471i
$383$	10.8790	−	18.8429i	0.555890	−	0.962829i	−0.441944	−	0.897043i	$-0.645711\pi$
$383$	10.8790	−	18.8429i	0.555890	−	0.962829i	0.997834	−	0.0657867i	$-0.0209557\pi$
$384$	15.0611	−	4.89364i	0.768583	−	0.249728i
$385$	−0.0864545	−	0.149744i	−0.00440613	−	0.00763164i
$386$	32.3011			1.64408
$387$	2.31861	+	22.0601i	0.117861	+	1.12138i
$388$	13.8887			0.705090
$389$	6.03881	+	10.4595i	0.306180	+	0.530319i	0.977523	−	0.210828i	$-0.0676158\pi$
$389$	6.03881	+	10.4595i	0.306180	+	0.530319i	−0.671344	+	0.741146i	$0.734283\pi$
$390$	−8.81263	−	7.93493i	−0.446245	−	0.401801i
$391$	−7.12825	+	12.3465i	−0.360491	+	0.624389i
$392$	−0.604528	+	1.04707i	−0.0305333	+	0.0528852i
$393$	−16.3073	−	14.6832i	−0.822595	−	0.740668i
$394$	−18.4458	−	31.9490i	−0.929285	−	1.60957i
$395$	14.1665			0.712796
$396$	−0.634176	−	0.282354i	−0.0318686	−	0.0141888i
$397$	−33.2451			−1.66852			−0.834262	−	0.551368i	$-0.814106\pi$
$397$	−33.2451			−1.66852			−0.834262	+	0.551368i	$0.814106\pi$
$398$	16.5231	+	28.6188i	0.828227	+	1.43453i
$399$	−0.227886	+	0.0740447i	−0.0114086	+	0.00370687i
$400$	2.44279	−	4.23104i	0.122139	−	0.211552i
$401$	8.81576	−	15.2693i	0.440238	−	0.762514i	−0.557469	−	0.830198i	$-0.688227\pi$
$401$	8.81576	−	15.2693i	0.440238	−	0.762514i	0.997707	+	0.0676835i	$0.0215608\pi$
$402$	2.88316	−	13.5642i	0.143799	−	0.676521i
$403$	−5.10542	−	8.84285i	−0.254319	−	0.440494i
$404$	23.6915			1.17870
$405$	8.80333	−	1.87121i	0.437441	−	0.0929809i
$406$	−1.78806			−0.0887398
$407$	0.681744	+	1.18082i	0.0337928	+	0.0585309i
$408$	0.795511	−	3.74259i	0.0393837	−	0.185286i
$409$	−6.99886	+	12.1224i	−0.346071	+	0.599413i	−0.985548	−	0.169398i	$-0.945818\pi$
$409$	−6.99886	+	12.1224i	−0.346071	+	0.599413i	0.639477	+	0.768811i	$0.279151\pi$
$410$	−9.17364	+	15.8892i	−0.453054	+	0.784712i
$411$	5.58609	−	1.81503i	0.275541	−	0.0895289i
$412$	1.44344	+	2.50012i	0.0711133	+	0.123172i
$413$	1.18014			0.0580707
$414$	39.0719	+	17.3959i	1.92028	+	0.854963i
$415$	9.27319			0.455203
$416$	12.1940	+	21.1207i	0.597862	+	1.03553i
$417$	10.4717	+	9.42873i	0.512800	+	0.461727i
$418$	−0.0218524	+	0.0378495i	−0.00106884	+	0.00185128i
$419$	9.20103	−	15.9367i	0.449500	−	0.778557i	−0.548854	−	0.835919i	$-0.684936\pi$
$419$	9.20103	−	15.9367i	0.449500	−	0.778557i	0.998353	+	0.0573619i	$0.0182689\pi$
$420$	1.72256	+	1.55100i	0.0840524	+	0.0756812i
$421$	−1.38600	−	2.40063i	−0.0675497	−	0.117000i	0.830272	−	0.557358i	$-0.188185\pi$
$421$	−1.38600	−	2.40063i	−0.0675497	−	0.117000i	−0.897822	+	0.440358i	$0.854851\pi$
$422$	43.6242			2.12359
$423$	−1.81919	−	17.3084i	−0.0884521	−	0.841565i
$424$	−14.1627			−0.687802
$425$	−0.913545	−	1.58231i	−0.0443135	−	0.0767532i
$426$	33.7580	−	10.9686i	1.63558	−	0.531432i
$427$	3.50138	−	6.06457i	0.169444	−	0.293485i
$428$	7.71030	−	13.3546i	0.372691	−	0.645521i
$429$	−0.233329	+	1.09773i	−0.0112652	+	0.0529987i
$430$	−6.75463	−	11.6994i	−0.325737	−	0.564193i
$431$	6.55882			0.315927			0.157964	−	0.987445i	$-0.449507\pi$
$431$	6.55882			0.315927			0.157964	+	0.987445i	$0.449507\pi$
$432$	−25.2471	−	2.65358i	−1.21470	−	0.127671i
$433$	3.44922			0.165759			0.0828794	−	0.996560i	$-0.473588\pi$
$433$	3.44922			0.165759			0.0828794	+	0.996560i	$0.473588\pi$
$434$	2.48932	+	4.31163i	0.119491	+	0.206965i
$435$	0.352420	−	1.65801i	0.0168972	−	0.0794953i
$436$	−4.61360	+	7.99099i	−0.220951	+	0.382699i
$437$	0.539727	−	0.934834i	0.0258186	−	0.0447192i
$438$	−4.83940	+	1.57242i	−0.231236	+	0.0751330i
$439$	5.45818	+	9.45384i	0.260505	+	0.451207i	0.966376	−	0.257133i	$-0.0827778\pi$
$439$	5.45818	+	9.45384i	0.260505	+	0.451207i	−0.705872	+	0.708340i	$0.749444\pi$
$440$	−0.209057			−0.00996640
$441$	2.42705	−	1.76336i	0.115574	−	0.0839693i
$442$	12.5093			0.595005
$443$	−6.96293	−	12.0602i	−0.330819	−	0.572995i	0.651854	−	0.758345i	$-0.273992\pi$
$443$	−6.96293	−	12.0602i	−0.330819	−	0.572995i	−0.982673	+	0.185350i	$0.940658\pi$
$444$	−13.5834	−	12.2306i	−0.644640	−	0.580436i
$445$	5.94338	−	10.2942i	0.281743	−	0.487994i
$446$	6.96866	−	12.0701i	0.329976	−	0.571534i
$447$	−5.25499	−	4.73162i	−0.248553	−	0.223798i
$448$	−1.06003	−	1.83603i	−0.0500819	−	0.0867444i
$449$	8.71051			0.411075			0.205537	−	0.978649i	$-0.434106\pi$
$449$	8.71051			0.411075			0.205537	+	0.978649i	$0.434106\pi$
$450$	−4.43444	+	3.22181i	−0.209042	+	0.151878i
$451$	1.73632			0.0817600
$452$	−4.48114	−	7.76156i	−0.210775	−	0.365073i
$453$	25.8784	−	8.40840i	1.21587	−	0.395061i
$454$	14.7931	−	25.6223i	0.694272	−	1.20251i
$455$	1.87362	−	3.24520i	0.0878366	−	0.152137i
$456$	−0.0602334	+	0.283376i	−0.00282069	+	0.0132703i
$457$	0.824467	+	1.42802i	0.0385669	+	0.0667999i	0.884665	−	0.466228i	$-0.154387\pi$
$457$	0.824467	+	1.42802i	0.0385669	+	0.0667999i	−0.846098	+	0.533028i	$0.821054\pi$
$458$	45.7505			2.13778
$459$	−5.58034	+	7.68068i	−0.260468	+	0.358503i
$460$	−10.4422			−0.486872
$461$	−3.17896	−	5.50612i	−0.148059	−	0.256446i	0.782451	−	0.622712i	$-0.213969\pi$
$461$	−3.17896	−	5.50612i	−0.148059	−	0.256446i	−0.930510	+	0.366266i	$0.880636\pi$
$462$	0.113767	−	0.535233i	0.00529293	−	0.0249013i
$463$	−18.5298	+	32.0946i	−0.861153	+	1.49156i	0.00966371	+	0.999953i	$0.496924\pi$
$463$	−18.5298	+	32.0946i	−0.861153	+	1.49156i	−0.870817	+	0.491608i	$0.836409\pi$
$464$	−2.39060	+	4.14064i	−0.110981	+	0.192225i
$465$	−4.48866	+	1.45846i	−0.208157	+	0.0676343i
$466$	−9.40617	−	16.2920i	−0.435733	−	0.754711i
$467$	−11.7091			−0.541834			−0.270917	−	0.962603i	$-0.587327\pi$
$467$	−11.7091			−0.541834			−0.270917	+	0.962603i	$0.587327\pi$
$468$	−1.57256	−	14.9619i	−0.0726917	−	0.691616i
$469$	4.38197			0.202340
$470$	5.29972	+	9.17938i	0.244458	+	0.423413i
$471$	−2.96769	−	2.67212i	−0.136744	−	0.123125i
$472$	0.713426	−	1.23569i	0.0328381	−	0.0568772i
$473$	−0.639233	+	1.10718i	−0.0293920	+	0.0509084i
$474$	33.3164	+	29.9982i	1.53027	+	1.37786i
$475$	0.0691705	+	0.119807i	0.00317376	+	0.00549712i
$476$	−2.44512			−0.112072
$477$	32.1034	+	14.2934i	1.46991	+	0.654448i
$478$	−36.3677			−1.66342
$479$	12.8295	+	22.2214i	0.586197	+	1.01532i	0.994725	+	0.102577i	$0.0327089\pi$
$479$	12.8295	+	22.2214i	0.586197	+	1.01532i	−0.408528	+	0.912746i	$0.633958\pi$
$480$	10.7210	−	3.48345i	0.489342	−	0.158997i
$481$	−14.7746	+	25.5903i	−0.673663	+	1.16682i
$482$	9.49845	−	16.4518i	0.432643	−	0.749359i
$483$	−2.80991	+	13.2196i	−0.127855	+	0.601512i
$484$	7.34043	+	12.7140i	0.333656	+	0.577909i
$485$	−10.3781			−0.471247
$486$	24.6657	+	14.2408i	1.11886	+	0.645974i
$487$	−22.1058			−1.00171			−0.500855	−	0.865531i	$-0.666981\pi$
$487$	−22.1058			−1.00171			−0.500855	+	0.865531i	$0.666981\pi$
$488$	−4.23337	−	7.33241i	−0.191636	−	0.331923i
$489$	6.74929	−	31.7529i	0.305213	−	1.43592i
$490$	−0.913545	+	1.58231i	−0.0412698	+	0.0714814i
$491$	−12.1665	+	21.0731i	−0.549069	+	0.951015i	0.449270	+	0.893396i	$0.351684\pi$
$491$	−12.1665	+	21.0731i	−0.549069	+	0.951015i	−0.998339	+	0.0576186i	$0.981649\pi$
$492$	−22.1370	+	7.19275i	−0.998014	+	0.324274i
$493$	0.894028	+	1.54850i	0.0402650	+	0.0697410i
$494$	−0.947158			−0.0426147
$495$	0.473881	+	0.210985i	0.0212994	+	0.00948309i
$496$	13.3127			0.597758
$497$	5.60814	+	9.71359i	0.251560	+	0.435714i
$498$	21.8084	+	19.6364i	0.977257	+	0.879926i
$499$	−11.5859	+	20.0674i	−0.518656	+	0.898339i	0.481109	+	0.876661i	$0.340234\pi$
$499$	−11.5859	+	20.0674i	−0.518656	+	0.898339i	−0.999765	+	0.0216781i	$0.993099\pi$
$500$	0.669131	−	1.15897i	0.0299244	−	0.0518306i
$501$	−7.35315	−	6.62080i	−0.328514	−	0.295796i
$502$	−21.9305	−	37.9847i	−0.978806	−	1.69534i
$503$	34.4400			1.53561			0.767803	−	0.640686i	$-0.221350\pi$
$503$	34.4400			1.53561			0.767803	+	0.640686i	$0.221350\pi$
$504$	−0.379143	−	3.60730i	−0.0168884	−	0.160682i
$505$	−17.7032			−0.787782
$506$	1.23254	+	2.13482i	0.0547930	+	0.0949043i
$507$	−1.71613	+	0.557603i	−0.0762158	+	0.0247640i
$508$	11.2818	−	19.5406i	0.500548	−	0.866974i
$509$	−20.0258	+	34.6858i	−0.887629	+	1.53742i	−0.0449590	+	0.998989i	$0.514316\pi$
$509$	−20.0258	+	34.6858i	−0.887629	+	1.53742i	−0.842670	+	0.538430i	$0.819018\pi$
$510$	1.20215	−	5.65569i	0.0532322	−	0.250438i
$511$	−0.803960	−	1.39250i	−0.0355651	−	0.0616006i
$512$	−19.9828			−0.883126
$513$	0.422524	−	0.581555i	0.0186549	−	0.0256763i
$514$	22.0491			0.972546
$515$	−1.07860	−	1.86818i	−0.0475286	−	0.0823220i
$516$	3.56330	−	16.7640i	0.156865	−	0.737993i
$517$	0.501545	−	0.868702i	0.0220579	−	0.0382055i
$518$	7.20384	−	12.4774i	0.316518	−	0.548226i
$519$	29.0959	−	9.45382i	1.27717	−	0.414976i
$520$	−2.26531	−	3.92364i	−0.0993405	−	0.172063i
$521$	−17.2174			−0.754309			−0.377154	−	0.926150i	$-0.623097\pi$
$521$	−17.2174			−0.754309			−0.377154	+	0.926150i	$0.623097\pi$
$522$	4.33970	−	3.15298i	0.189944	−	0.138002i
$523$	27.1363			1.18659			0.593293	−	0.804987i	$-0.297828\pi$
$523$	27.1363			1.18659			0.593293	+	0.804987i	$0.297828\pi$
$524$	8.47733	+	14.6832i	0.370334	+	0.641437i
$525$	−1.28716	−	1.15897i	−0.0561765	−	0.0505815i
$526$	3.52977	−	6.11374i	0.153905	−	0.266572i
$527$	2.48932	−	4.31163i	0.108436	−	0.187817i
$528$	−1.08735	−	0.979051i	−0.0473207	−	0.0426077i
$529$	−18.9422	−	32.8088i	−0.823572	−	1.42647i
$530$	−21.4023			−0.929655
$531$	−2.86425	+	2.08100i	−0.124298	+	0.0903077i
$532$	0.185136			0.00802669
$533$	18.8145	+	32.5877i	0.814946	+	1.41153i
$534$	35.7759	−	11.6243i	1.54817	−	0.503032i
$535$	−5.76143	+	9.97909i	−0.249088	+	0.431434i
$536$	2.64902	−	4.58824i	0.114420	−	0.198182i
$537$	1.29533	−	6.09404i	0.0558976	−	0.262977i
$538$	7.75349	+	13.4294i	0.334277	+	0.578984i
$539$	0.172909			0.00744772
$540$	−6.91572	−	0.726871i	−0.297605	−	0.0312795i
$541$	16.6450			0.715624			0.357812	−	0.933794i	$-0.383523\pi$
$541$	16.6450			0.715624			0.357812	+	0.933794i	$0.383523\pi$
$542$	10.8060	+	18.7166i	0.464159	+	0.803946i
$543$	−4.98261	+	23.4414i	−0.213824	+	1.00596i
$544$	−5.94561	+	10.2981i	−0.254916	+	0.441528i
$545$	3.44746	−	5.97118i	0.147673	−	0.255777i
$546$	11.2782	−	3.66450i	0.482661	−	0.156826i
$547$	11.8219	+	20.4761i	0.505468	+	0.875495i	0.999980	+	0.00632492i	$0.00201330\pi$
$547$	11.8219	+	20.4761i	0.505468	+	0.875495i	−0.494512	+	0.869171i	$0.664653\pi$
$548$	−4.53818			−0.193861
$549$	2.19596	+	20.8932i	0.0937214	+	0.891700i
$550$	−0.315921			−0.0134709
$551$	−0.0676928	−	0.117247i	−0.00288381	−	0.00499490i
$552$	12.1432	+	10.9338i	0.516849	+	0.465373i
$553$	−7.08327	+	12.2686i	−0.301211	+	0.521713i
$554$	−24.9546	+	43.2226i	−1.06022	+	1.83635i
$555$	10.1500	+	9.13914i	0.430845	+	0.387935i
$556$	−5.44368	−	9.42873i	−0.230864	−	0.399867i
$557$	37.1981			1.57613			0.788067	−	0.615590i	$-0.211082\pi$
$557$	37.1981			1.57613			0.788067	+	0.615590i	$0.211082\pi$
$558$	−13.6446	−	6.07498i	−0.577623	−	0.257174i
$559$	−27.7066			−1.17186
$560$	2.44279	+	4.23104i	0.103227	+	0.178794i
$561$	−0.520409	+	0.169091i	−0.0219717	+	0.00713904i
$562$	14.5136	−	25.1384i	0.612221	−	1.06040i
$563$	12.8803	−	22.3093i	0.542840	−	0.940226i	−0.455900	−	0.890031i	$-0.650682\pi$
$563$	12.8803	−	22.3093i	0.542840	−	0.940226i	0.998739	−	0.0501948i	$-0.0159842\pi$
$564$	−2.79578	+	13.1531i	−0.117724	+	0.553846i
$565$	3.34848	+	5.79973i	0.140871	+	0.243997i
$566$	−30.0763			−1.26420
$567$	−2.78115	+	8.55951i	−0.116797	+	0.359466i
$568$	13.5611			0.569012
$569$	−2.32571	−	4.02825i	−0.0974989	−	0.168873i	0.813150	−	0.582054i	$-0.197751\pi$
$569$	−2.32571	−	4.02825i	−0.0974989	−	0.168873i	−0.910649	+	0.413181i	$0.864418\pi$
$570$	−0.0910229	+	0.428229i	−0.00381253	+	0.0179365i
$571$	−13.9779	+	24.2105i	−0.584958	+	1.01318i	0.409923	+	0.912120i	$0.365556\pi$
$571$	−13.9779	+	24.2105i	−0.584958	+	1.01318i	−0.994881	+	0.101056i	$0.967778\pi$
$572$	0.433551	−	0.750932i	0.0181277	−	0.0313980i
$573$	9.85771	−	3.20296i	0.411812	−	0.133806i
$574$	−9.17364	−	15.8892i	−0.382900	−	0.663203i
$575$	7.80284			0.325401
$576$	5.81033	+	2.58693i	0.242097	+	0.107789i
$577$	−5.63651			−0.234651			−0.117326	−	0.993094i	$-0.537432\pi$
$577$	−5.63651			−0.234651			−0.117326	+	0.993094i	$0.537432\pi$
$578$	−12.4806	−	21.6171i	−0.519125	−	0.899151i
$579$	−22.7557	−	20.4893i	−0.945696	−	0.851508i
$580$	−0.654835	+	1.13421i	−0.0271906	+	0.0470954i
$581$	−4.63660	+	8.03082i	−0.192358	+	0.333175i
$582$	−24.4070	−	21.9761i	−1.01170	−	0.910940i
$583$	1.01272	+	1.75407i	0.0419424	+	0.0726464i
$584$	−1.94407			−0.0804461
$585$	1.17508	+	11.1801i	0.0485835	+	0.462242i
$586$	43.5272			1.79809
$587$	−14.8898	−	25.7899i	−0.614569	−	1.06446i	−0.990460	−	0.137800i	$-0.955997\pi$
$587$	−14.8898	−	25.7899i	−0.614569	−	1.06446i	0.375892	−	0.926664i	$-0.377337\pi$
$588$	−2.20449	+	0.716282i	−0.0909116	+	0.0295390i
$589$	−0.188483	+	0.326462i	−0.00776629	+	0.0134516i
$590$	1.07811	−	1.86734i	0.0443850	−	0.0768771i
$591$	−7.27121	+	34.2083i	−0.299098	+	1.40714i
$592$	−19.2628	−	33.3642i	−0.791697	−	1.37126i
$593$	−46.0749			−1.89207			−0.946035	−	0.324064i	$-0.894951\pi$
$593$	−46.0749			−1.89207			−0.946035	+	0.324064i	$0.894951\pi$
$594$	0.667687	+	1.49965i	0.0273955	+	0.0615314i
$595$	1.82709			0.0749034
$596$	2.73180	+	4.73162i	0.111899	+	0.193815i
$597$	6.51328	−	30.6426i	0.266571	−	1.25412i
$598$	−26.7112	+	46.2652i	−1.09230	+	1.89193i
$599$	−6.41929	+	11.1185i	−0.262285	+	0.454291i	−0.966849	−	0.255349i	$-0.917809\pi$
$599$	−6.41929	+	11.1185i	−0.262285	+	0.454291i	0.704564	+	0.709641i	$0.251143\pi$
$600$	−1.99165	+	0.647127i	−0.0813089	+	0.0264189i
$601$	0.326789	+	0.566015i	0.0133300	+	0.0230883i	0.872613	−	0.488411i	$-0.162423\pi$
$601$	0.326789	+	0.566015i	0.0133300	+	0.0230883i	−0.859283	+	0.511500i	$0.829090\pi$
$602$	13.5093			0.550596
$603$	−10.6353	+	7.72696i	−0.433101	+	0.314666i
$604$	−21.0238			−0.855446
$605$	−5.48505	−	9.50039i	−0.222999	−	0.386246i
$606$	−41.6338	−	37.4872i	−1.69126	−	1.52282i
$607$	−16.0765	+	27.8453i	−0.652524	+	1.13021i	0.329984	+	0.943987i	$0.392957\pi$
$607$	−16.0765	+	27.8453i	−0.652524	+	1.13021i	−0.982508	+	0.186219i	$0.940377\pi$
$608$	0.450181	−	0.779737i	0.0182573	−	0.0316225i
$609$	1.25967	+	1.13421i	0.0510442	+	0.0459604i
$610$	−6.39734	−	11.0805i	−0.259021	−	0.448637i
$611$	21.7387			0.879454
$612$	5.93444	−	4.31163i	0.239886	−	0.174287i
$613$	7.74782			0.312931			0.156466	−	0.987683i	$-0.449990\pi$
$613$	7.74782			0.312931			0.156466	+	0.987683i	$0.449990\pi$
$614$	−21.6599	−	37.5160i	−0.874120	−	1.51402i
$615$	16.5416	−	5.37470i	0.667023	−	0.216729i
$616$	0.104528	−	0.181049i	0.00421157	−	0.00729466i
$617$	−15.3193	+	26.5338i	−0.616732	+	1.06821i	0.373346	+	0.927692i	$0.378210\pi$
$617$	−15.3193	+	26.5338i	−0.616732	+	1.06821i	−0.990078	+	0.140519i	$0.955123\pi$
$618$	1.41935	−	6.67750i	0.0570945	−	0.268608i
$619$	−15.9913	−	27.6977i	−0.642745	−	1.11327i	−0.984817	−	0.173593i	$-0.944462\pi$
$619$	−15.9913	−	27.6977i	−0.642745	−	1.11327i	0.342073	−	0.939673i	$-0.388871\pi$
$620$	3.64662			0.146452
$621$	−16.4910	−	37.0395i	−0.661762	−	1.48634i
$622$	26.7114			1.07103
$623$	5.94338	+	10.2942i	0.238116	+	0.412430i
$624$	6.59275	−	31.0165i	0.263921	−	1.24165i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	9.75831	−	16.9019i	0.390020	−	0.675535i
$627$	0.0394036	−	0.0128030i	0.00157363	−	0.000511303i
$628$	1.54275	+	2.67212i	0.0615624	+	0.106629i
$629$	−14.4077			−0.574471
$630$	−0.572949	−	5.45125i	−0.0228268	−	0.217183i
$631$	8.65557			0.344573			0.172286	−	0.985047i	$-0.444885\pi$
$631$	8.65557			0.344573			0.172286	+	0.985047i	$0.444885\pi$
$632$	8.56407	+	14.8334i	0.340661	+	0.590041i
$633$	−30.7327	−	27.6719i	−1.22152	−	1.09986i
$634$	−20.0184	+	34.6729i	−0.795032	+	1.37704i
$635$	−8.43018	+	14.6015i	−0.334541	+	0.579443i
$636$	−20.1778	−	18.1682i	−0.800103	−	0.720416i
$637$	1.87362	+	3.24520i	0.0742355	+	0.128580i
$638$	0.309171			0.0122402
$639$	−30.7398	−	13.6862i	−1.21605	−	0.541419i
$640$	9.14301			0.361409
$641$	2.06538	+	3.57734i	0.0815776	+	0.141296i	0.903928	−	0.427685i	$-0.140671\pi$
$641$	2.06538	+	3.57734i	0.0815776	+	0.141296i	−0.822350	+	0.568982i	$0.807338\pi$
$642$	−34.6807	+	11.2684i	−1.36874	+	0.444730i
$643$	−7.21704	+	12.5003i	−0.284612	+	0.492963i	−0.972515	−	0.232840i	$-0.925198\pi$
$643$	−7.21704	+	12.5003i	−0.284612	+	0.492963i	0.687903	+	0.725803i	$0.258532\pi$
$644$	5.22112	−	9.04324i	0.205741	−	0.356354i
$645$	−2.66263	+	12.5267i	−0.104841	+	0.493238i
$646$	−0.230909	−	0.399947i	−0.00908501	−	0.0157357i
$647$	28.1790			1.10783			0.553916	−	0.832573i	$-0.313133\pi$
$647$	28.1790			1.10783			0.553916	+	0.832573i	$0.313133\pi$
$648$	7.28115	+	8.08654i	0.286031	+	0.317669i
$649$	−0.204056			−0.00800991
$650$	−3.42327	−	5.92928i	−0.134272	−	0.232566i
$651$	0.981273	−	4.61653i	0.0384591	−	0.180936i
$652$	−12.5409	+	21.7215i	−0.491140	+	0.850680i
$653$	2.96698	−	5.13896i	0.116107	−	0.201103i	−0.802115	−	0.597170i	$-0.796292\pi$
$653$	2.96698	−	5.13896i	0.116107	−	0.201103i	0.918222	+	0.396067i	$0.129625\pi$
$654$	20.7518	−	6.74268i	0.811461	−	0.263660i
$655$	−6.33458	−	10.9718i	−0.247513	−	0.428705i
$656$	−49.0600			−1.91547
$657$	4.40673	+	1.96200i	0.171923	+	0.0765449i
$658$	−10.5994			−0.413209
$659$	−19.7763	−	34.2536i	−0.770376	−	1.33433i	−0.937357	−	0.348370i	$-0.886735\pi$
$659$	−19.7763	−	34.2536i	−0.770376	−	1.33433i	0.166981	−	0.985960i	$-0.446598\pi$
$660$	−0.297847	−	0.268182i	−0.0115937	−	0.0104390i
$661$	20.8000	−	36.0266i	0.809025	−	1.40127i	−0.104514	−	0.994523i	$-0.533329\pi$
$661$	20.8000	−	36.0266i	0.809025	−	1.40127i	0.913540	−	0.406749i	$-0.133338\pi$
$662$	−20.5715	+	35.6308i	−0.799533	+	1.38483i
$663$	−8.81263	−	7.93493i	−0.342254	−	0.308167i
$664$	5.60591	+	9.70972i	0.217551	+	0.376810i
$665$	−0.138341			−0.00536464
$666$	4.51803	+	42.9862i	0.175070	+	1.66568i
$667$	−7.63614			−0.295672
$668$	3.82252	+	6.62080i	0.147898	+	0.256167i
$669$	−12.5657	+	4.08284i	−0.485817	+	0.157852i
$670$	4.00313	−	6.93362i	0.154654	−	0.267869i
$671$	−0.605420	+	1.04862i	−0.0233720	+	0.0404815i
$672$	−2.34372	+	11.0263i	−0.0904110	+	0.425350i
$673$	16.6716	+	28.8760i	0.642643	+	1.11309i	0.984841	+	0.173462i	$0.0554953\pi$
$673$	16.6716	+	28.8760i	0.642643	+	1.11309i	−0.342198	+	0.939628i	$0.611171\pi$
$674$	13.5518			0.521995
$675$	5.16769	+	0.543146i	0.198904	+	0.0209057i
$676$	1.39419			0.0536228
$677$	9.09786	+	15.7580i	0.349659	+	0.605628i	0.986189	−	0.165625i	$-0.0529640\pi$
$677$	9.09786	+	15.7580i	0.349659	+	0.605628i	−0.636530	+	0.771252i	$0.719631\pi$
$678$	−4.40633	+	20.7301i	−0.169224	+	0.796137i
$679$	5.18907	−	8.98774i	0.199138	−	0.344918i
$680$	1.10453	−	1.91310i	0.0423567	−	0.0733640i
$681$	−26.6744	+	8.66704i	−1.02216	+	0.332122i
$682$	−0.430426	−	0.745519i	−0.0164819	−	0.0285474i
$683$	−14.0903			−0.539150			−0.269575	−	0.962979i	$-0.586883\pi$
$683$	−14.0903			−0.539150			−0.269575	+	0.962979i	$0.586883\pi$
$684$	−0.449336	+	0.326462i	−0.0171808	+	0.0124826i
$685$	3.39110			0.129567
$686$	−0.913545	−	1.58231i	−0.0348793	−	0.0604128i
$687$	−32.2307	−	29.0207i	−1.22968	−	1.10721i
$688$	18.0617	−	31.2837i	0.688594	−	1.19268i
$689$	−21.9473	+	38.0138i	−0.836125	+	1.44821i
$690$	18.3505	+	16.5228i	0.698590	+	0.629013i
$691$	16.1752	+	28.0162i	0.615333	+	1.06579i	0.990326	+	0.138760i	$0.0443116\pi$
$691$	16.1752	+	28.0162i	0.615333	+	1.06579i	−0.374993	+	0.927027i	$0.622355\pi$
$692$	−23.6377			−0.898570
$693$	−0.419659	+	0.304900i	−0.0159415	+	0.0115822i
$694$	43.9795			1.66944
$695$	4.06773	+	7.04551i	0.154298	+	0.267251i
$696$	1.94910	−	0.633302i	0.0738806	−	0.0240052i
$697$	−9.17364	+	15.8892i	−0.347476	+	0.601846i
$698$	14.1460	−	24.5015i	0.535432	−	0.927396i
$699$	−3.70785	+	17.4441i	−0.140244	+	0.659795i
$700$	0.669131	+	1.15897i	0.0252908	+	0.0438049i
$701$	26.0054			0.982210			0.491105	−	0.871100i	$-0.336593\pi$
$701$	26.0054			0.982210			0.491105	+	0.871100i	$0.336593\pi$
$702$	−20.9109	+	28.7813i	−0.789230	+	1.08628i
$703$	1.09090			0.0411441
$704$	0.183289	+	0.317467i	0.00690798	+	0.0119650i
$705$	2.08911	−	9.82850i	0.0786805	−	0.370163i
$706$	19.6806	−	34.0878i	0.740690	−	1.28291i
$707$	8.85160	−	15.3314i	0.332899	−	0.576598i
$708$	2.60160	−	0.845310i	0.0977740	−	0.0317687i
$709$	8.55973	+	14.8259i	0.321467	+	0.556798i	0.980791	−	0.195061i	$-0.0624906\pi$
$709$	8.55973	+	14.8259i	0.321467	+	0.556798i	−0.659324	+	0.751859i	$0.729157\pi$
$710$	20.4932			0.769095
$711$	−4.44242	−	42.2668i	−0.166604	−	1.58513i
$712$	14.3718			0.538605
$713$	10.6310	+	18.4134i	0.398133	+	0.689587i
$714$	4.29689	+	3.86894i	0.160807	+	0.144791i
$715$	−0.323966	+	0.561125i	−0.0121156	+	0.0209849i
$716$	−2.40686	+	4.16881i	−0.0899487	+	0.155796i
$717$	25.6206	+	23.0689i	0.956820	+	0.861525i
$718$	−16.6334	−	28.8098i	−0.620751	−	1.07517i
$719$	21.1007			0.786923			0.393461	−	0.919341i	$-0.371278\pi$
$719$	21.1007			0.786923			0.393461	+	0.919341i	$0.371278\pi$
$720$	−13.3896	−	5.96143i	−0.499001	−	0.222169i
$721$	2.15719			0.0803380
$722$	−17.3399	−	30.0336i	−0.645324	−	1.11773i
$723$	−17.1273	+	5.56501i	−0.636972	+	0.206965i
$724$	9.25824	−	16.0357i	0.344080	−	0.595964i
$725$	0.489318	−	0.847523i	0.0181728	−	0.0314762i
$726$	7.21789	−	33.9575i	0.267881	−	1.26028i
$727$	−7.34228	−	12.7172i	−0.272310	−	0.471655i	0.697143	−	0.716932i	$-0.254454\pi$
$727$	−7.34228	−	12.7172i	−0.272310	−	0.471655i	−0.969453	+	0.245277i	$0.921121\pi$
$728$	4.53062			0.167916
$729$	−8.34346	−	25.6785i	−0.309017	−	0.951057i
$730$	−2.93782			−0.108734
$731$	−6.75463	−	11.6994i	−0.249829	−	0.432717i
$732$	3.37481	−	15.8772i	0.124737	−	0.586840i
$733$	−21.2290	+	36.7698i	−0.784112	+	1.35812i	0.145416	+	0.989371i	$0.453548\pi$
$733$	−21.2290	+	36.7698i	−0.784112	+	1.35812i	−0.929528	+	0.368752i	$0.879785\pi$
$734$	−23.0138	+	39.8610i	−0.849454	+	1.47130i
$735$	1.64728	−	0.535233i	0.0607608	−	0.0197424i
$736$	−25.3915	−	43.9795i	−0.935945	−	1.62110i
$737$	−0.757682			−0.0279096
$738$	50.2832	+	22.3875i	1.85095	+	0.824096i
$739$	28.5354			1.04969			0.524846	−	0.851197i	$-0.324123\pi$
$739$	28.5354			1.04969			0.524846	+	0.851197i	$0.324123\pi$
$740$	−5.27648	−	9.13914i	−0.193967	−	0.335961i
$741$	0.667262	+	0.600806i	0.0245125	+	0.0220711i
$742$	10.7011	−	18.5349i	0.392851	−	0.680438i
$743$	−16.1206	+	27.9217i	−0.591408	+	1.02435i	0.402635	+	0.915360i	$0.368094\pi$
$743$	−16.1206	+	27.9217i	−0.591408	+	1.02435i	−0.994043	+	0.108988i	$0.965239\pi$
$744$	−4.24064	−	3.81829i	−0.155469	−	0.139985i
$745$	−2.04131	−	3.53565i	−0.0747877	−	0.129536i
$746$	59.6179			2.18276
$747$	−2.90794	−	27.6672i	−0.106396	−	1.01229i
$748$	0.422784			0.0154585
$749$	−5.76143	−	9.97909i	−0.210518	−	0.364628i
$750$	−3.00973	+	0.977920i	−0.109900	+	0.0357086i
$751$	13.1046	−	22.6978i	0.478192	−	0.828253i	−0.521495	−	0.853254i	$-0.674626\pi$
$751$	13.1046	−	22.6978i	0.478192	−	0.828253i	0.999687	+	0.0250009i	$0.00795886\pi$
$752$	−14.1713	+	24.5453i	−0.516773	+	0.895076i
$753$	−8.64486	+	40.6709i	−0.315036	+	1.48213i
$754$	3.35014	+	5.80261i	0.122005	+	0.211319i
$755$	15.7098			0.571738
$756$	4.08735	−	5.62575i	0.148655	−	0.204607i
$757$	15.1032			0.548937			0.274468	−	0.961596i	$-0.411498\pi$
$757$	15.1032			0.548937			0.274468	+	0.961596i	$0.411498\pi$
$758$	−2.36935	−	4.10384i	−0.0860588	−	0.149058i
$759$	0.485859	−	2.28579i	0.0176356	−	0.0829688i
$760$	−0.0836311	+	0.144853i	−0.00303362	+	0.00525438i
$761$	−4.76604	+	8.25502i	−0.172769	+	0.299244i	−0.939387	−	0.342859i	$-0.888605\pi$
$761$	−4.76604	+	8.25502i	−0.172769	+	0.299244i	0.766618	+	0.642103i	$0.221938\pi$
$762$	−50.7451	+	16.4881i	−1.83830	+	0.597300i
$763$	3.44746	+	5.97118i	0.124806	+	0.216171i
$764$	−8.00848			−0.289737
$765$	−4.43444	+	3.22181i	−0.160328	+	0.116485i
$766$	39.7538			1.43636
$767$	−2.21112	−	3.82978i	−0.0798391	−	0.138285i
$768$	26.9600	+	24.2749i	0.972835	+	0.875944i
$769$	14.5886	−	25.2682i	0.526079	−	0.911196i	−0.473459	−	0.880816i	$-0.656995\pi$
$769$	14.5886	−	25.2682i	0.526079	−	0.911196i	0.999538	−	0.0303802i	$-0.00967182\pi$
$770$	0.157960	−	0.273595i	0.00569249	−	0.00985969i
$771$	−15.5334	−	13.9863i	−0.559421	−	0.503705i
$772$	11.8295	+	20.4893i	0.425754	+	0.737428i
$773$	−2.52384			−0.0907762			−0.0453881	−	0.998969i	$-0.514452\pi$
$773$	−2.52384			−0.0907762			−0.0453881	+	0.998969i	$0.514452\pi$
$774$	−32.7877	+	23.8216i	−1.17853	+	0.856251i
$775$	−2.72490			−0.0978812
$776$	−6.27388	−	10.8667i	−0.225219	−	0.390091i
$777$	−12.9897	+	4.22062i	−0.466004	+	0.151414i
$778$	−11.0334	+	19.1105i	−0.395568	+	0.685144i
$779$	0.694596	−	1.20308i	0.0248865	−	0.0431047i
$780$	1.80589	−	8.49605i	0.0646613	−	0.304208i
$781$	−0.969699	−	1.67957i	−0.0346985	−	0.0600996i
$782$	−26.0479			−0.931472
$783$	−5.05728	−	0.531542i	−0.180733	−	0.0189958i
$784$	−4.88558			−0.174485
$785$	−1.15280	−	1.99671i	−0.0411453	−	0.0712657i
$786$	8.33581	−	39.2169i	0.297329	−	1.39882i
$787$	−4.55935	+	7.89702i	−0.162523	+	0.281498i	−0.935773	−	0.352603i	$-0.885297\pi$
$787$	−4.55935	+	7.89702i	−0.162523	+	0.281498i	0.773250	+	0.634102i	$0.218630\pi$
$788$	13.5107	−	23.4012i	0.481299	−	0.833634i
$789$	−6.36478	+	2.06804i	−0.226592	+	0.0736243i
$790$	12.9418	+	22.4158i	0.460448	+	0.797519i
$791$	−6.69695			−0.238116
$792$	0.0655572	+	0.623735i	0.00232947	+	0.0221635i
$793$	−26.2410			−0.931846
$794$	−30.3709	−	52.6040i	−1.07782	−	1.86685i
$795$	15.0777	+	13.5760i	0.534749	+	0.481490i
$796$	−12.1024	+	20.9620i	−0.428958	+	0.742977i
$797$	−21.3529	+	36.9843i	−0.756358	+	1.31005i	0.188339	+	0.982104i	$0.439690\pi$
$797$	−21.3529	+	36.9843i	−0.756358	+	1.31005i	−0.944696	+	0.327946i	$0.893644\pi$
$798$	−0.325346	−	0.292943i	−0.0115171	−	0.0103701i
$799$	5.29972	+	9.17938i	0.187490	+	0.324743i
$800$	6.50828			0.230103
$801$	−32.5773	−	14.5043i	−1.15106	−	0.512486i
$802$	32.2144			1.13753
$803$	0.139012	+	0.240776i	0.00490563	+	0.00849680i
$804$	9.65999	−	3.13872i	0.340682	−	0.110694i
$805$	−3.90142	+	6.75746i	−0.137507	+	0.238169i
$806$	9.32807	−	16.1567i	0.328567	−	0.569095i
$807$	3.05637	−	14.3791i	0.107589	−	0.506169i
$808$	−10.7021	−	18.5366i	−0.376498	−	0.652114i
$809$	−4.68059			−0.164561			−0.0822804	−	0.996609i	$-0.526220\pi$
$809$	−4.68059			−0.164561			−0.0822804	+	0.996609i	$0.526220\pi$
$810$	11.0031	+	12.2201i	0.386608	+	0.429372i
$811$	33.6854			1.18285			0.591427	−	0.806359i	$-0.298565\pi$
$811$	33.6854			1.18285			0.591427	+	0.806359i	$0.298565\pi$
$812$	−0.654835	−	1.13421i	−0.0229802	−	0.0398029i
$813$	4.25967	−	20.0401i	0.149393	−	0.702839i
$814$	−1.24561	+	2.15746i	−0.0436586	+	0.0756188i
$815$	9.37106	−	16.2311i	0.328254	−	0.568552i
$816$	14.7043	−	4.77770i	0.514752	−	0.167253i
$817$	0.511437	+	0.885836i	0.0178929	+	0.0309915i
$818$	−25.5751			−0.894212
$819$	−10.2698	−	4.57242i	−0.358856	−	0.159773i
$820$	−13.4385			−0.469294
$821$	3.95458	+	6.84954i	0.138016	+	0.239051i	0.926746	−	0.375690i	$-0.122594\pi$
$821$	3.95458	+	6.84954i	0.138016	+	0.239051i	−0.788730	+	0.614740i	$0.789261\pi$
$822$	7.97508	+	7.18080i	0.278163	+	0.250459i
$823$	21.8538	−	37.8519i	0.761775	−	1.31943i	−0.180160	−	0.983637i	$-0.557662\pi$
$823$	21.8538	−	37.8519i	0.761775	−	1.31943i	0.941935	−	0.335795i	$-0.109005\pi$
$824$	1.30408	−	2.25874i	0.0454299	−	0.0786869i
$825$	0.222562	+	0.200396i	0.00774863	+	0.00697690i
$826$	1.07811	+	1.86734i	0.0375122	+	0.0649730i
$827$	−23.5601			−0.819265			−0.409633	−	0.912251i	$-0.634343\pi$
$827$	−23.5601			−0.819265			−0.409633	+	0.912251i	$0.634343\pi$
$828$	3.27453	+	31.1551i	0.113798	+	1.08271i
$829$	−27.9043			−0.969156			−0.484578	−	0.874748i	$-0.661027\pi$
$829$	−27.9043			−0.969156			−0.484578	+	0.874748i	$0.661027\pi$
$830$	8.47148	+	14.6730i	0.294049	+	0.509309i
$831$	44.9974	−	14.6205i	1.56094	−	0.507181i
$832$	−3.97220	+	6.88005i	−0.137711	+	0.238523i
$833$	−0.913545	+	1.58231i	−0.0316525	+	0.0548237i
$834$	−5.35281	+	25.1830i	−0.185353	+	0.872015i
$835$	−2.85634	−	4.94732i	−0.0988476	−	0.171209i
$836$	−0.0320118			−0.00110715
$837$	5.75898	+	12.9349i	0.199059	+	0.447095i
$838$	33.6222			1.16146
$839$	−2.51039	−	4.34813i	−0.0866684	−	0.150114i	0.819433	−	0.573176i	$-0.194289\pi$
$839$	−2.51039	−	4.34813i	−0.0866684	−	0.150114i	−0.906101	+	0.423062i	$0.860955\pi$
$840$	0.435398	−	2.04839i	0.0150227	−	0.0706760i
$841$	14.0211	−	24.2853i	0.483487	−	0.837425i
$842$	2.53236	−	4.38617i	0.0872708	−	0.151157i
$843$	−26.1706	+	8.50333i	−0.901362	+	0.292870i
$844$	15.9764	+	27.6719i	0.549929	+	0.952506i
$845$	−1.04179			−0.0358388
$846$	25.7254	−	18.6906i	0.884456	−	0.642595i
$847$	10.9701			0.376937
$848$	−28.6145	−	49.5617i	−0.982625	−	1.70196i
$849$	21.1884	+	19.0781i	0.727184	+	0.654759i
$850$	1.66913	−	2.89102i	0.0572507	−	0.0991611i
$851$	30.7650	−	53.2865i	1.05461	−	1.82664i
$852$	19.3207	+	17.3965i	0.661918	+	0.595994i
$853$	8.91069	+	15.4338i	0.305096	+	0.528442i	0.977283	−	0.211940i	$-0.0679780\pi$
$853$	8.91069	+	15.4338i	0.305096	+	0.528442i	−0.672186	+	0.740382i	$0.734645\pi$
$854$	12.7947			0.437825
$855$	0.335761	−	0.243945i	0.0114828	−	0.00834273i
$856$	−13.9318			−0.476179
$857$	−12.9518	−	22.4332i	−0.442425	−	0.766303i	0.555444	−	0.831554i	$-0.312548\pi$
$857$	−12.9518	−	22.4332i	−0.442425	−	0.766303i	−0.997869	+	0.0652514i	$0.979215\pi$
$858$	−1.95010	+	0.633625i	−0.0665752	+	0.0216316i
$859$	−9.01087	+	15.6073i	−0.307447	+	0.532514i	−0.977803	−	0.209526i	$-0.932808\pi$
$859$	−9.01087	+	15.6073i	−0.307447	+	0.532514i	0.670356	+	0.742039i	$0.266141\pi$
$860$	4.94746	−	8.56925i	0.168707	−	0.292209i
$861$	−3.61619	+	17.0128i	−0.123239	+	0.579795i
$862$	5.99178	+	10.3781i	0.204081	+	0.353478i
$863$	24.3762			0.829774			0.414887	−	0.909873i	$-0.363821\pi$
$863$	24.3762			0.829774			0.414887	+	0.909873i	$0.363821\pi$
$864$	−13.7550	−	30.8943i	−0.467956	−	1.05105i
$865$	17.6630			0.600560
$866$	3.15102	+	5.45772i	0.107076	+	0.185461i
$867$	−4.91978	+	23.1457i	−0.167084	+	0.786070i
$868$	−1.82331	+	3.15807i	−0.0618873	+	0.107192i
$869$	1.22476	−	2.12135i	0.0415472	−	0.0719618i
$870$	2.94543	−	0.957027i	0.0998593	−	0.0324463i
$871$	−8.21014	−	14.2204i	−0.278190	−	0.481839i
$872$	8.33635			0.282304
$873$	3.25443	+	30.9639i	0.110146	+	1.04797i
$874$	1.97226			0.0667127
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	−2.76974	−	2.49389i	−0.0935810	−	0.0842607i
$877$	16.4715	−	28.5294i	0.556202	−	0.963370i	−0.441607	−	0.897209i	$-0.645591\pi$
$877$	16.4715	−	28.5294i	0.556202	−	0.963370i	0.997809	−	0.0661615i	$-0.0210753\pi$
$878$	−9.97259	+	17.2730i	−0.336558	+	0.582936i
$879$	−30.6644	−	27.6104i	−1.03429	−	0.931274i
$880$	−0.422381	−	0.731585i	−0.0142384	−	0.0246617i
$881$	−22.2765			−0.750513			−0.375257	−	0.926921i	$-0.622445\pi$
$881$	−22.2765			−0.750513			−0.375257	+	0.926921i	$0.622445\pi$
$882$	5.00739	+	2.22943i	0.168608	+	0.0750690i
$883$	−5.07478			−0.170780			−0.0853900	−	0.996348i	$-0.527214\pi$
$883$	−5.07478			−0.170780			−0.0853900	+	0.996348i	$0.527214\pi$
$884$	4.58123	+	7.93493i	0.154084	+	0.266881i
$885$	−1.94401	+	0.631648i	−0.0653472	+	0.0212326i
$886$	12.7219	−	22.0350i	0.427401	−	0.740280i
$887$	4.30954	−	7.46434i	0.144700	−	0.250628i	−0.784561	−	0.620052i	$-0.787112\pi$
$887$	4.30954	−	7.46434i	0.144700	−	0.250628i	0.929261	+	0.369424i	$0.120445\pi$
$888$	−3.43336	+	16.1527i	−0.115216	+	0.542049i
$889$	−8.43018	−	14.6015i	−0.282739	−	0.489718i
$890$	21.7182			0.727995
$891$	0.480887	−	1.48002i	0.0161103	−	0.0495824i
$892$	10.2085			0.341804
$893$	−0.401276	−	0.695031i	−0.0134282	−	0.0232583i
$894$	2.68620	−	12.6376i	0.0898399	−	0.422663i
$895$	1.79850	−	3.11509i	0.0601172	−	0.104126i
$896$	−4.57151	+	7.91808i	−0.152723	+	0.264524i
$897$	48.1649	−	15.6497i	1.60818	−	0.522529i
$898$	7.95745	+	13.7827i	0.265544	+	0.459935i
$899$	2.66668			0.0889388
$900$	−3.66769	−	1.63296i	−0.122256	−	0.0544320i
$901$	−21.4023			−0.713013
$902$	1.58620	+	2.74739i	0.0528148	+	0.0914780i
$903$	−9.51712	−	8.56925i	−0.316710	−	0.285167i
$904$	−4.04850	+	7.01221i	−0.134651	+	0.233222i
$905$	−6.91811	+	11.9825i	−0.229966	+	0.398313i
$906$	36.9457	+	33.2661i	1.22744	+	1.10519i
$907$	24.1539	+	41.8358i	0.802017	+	1.38914i	0.918286	+	0.395917i	$0.129573\pi$
$907$	24.1539	+	41.8358i	0.802017	+	1.38914i	−0.116269	+	0.993218i	$0.537093\pi$
$908$	21.6705			0.719160
$909$	5.55147	+	52.8187i	0.184131	+	1.75188i
$910$	6.84655			0.226961
$911$	8.60304	+	14.9009i	0.285032	+	0.493689i	0.972617	−	0.232415i	$-0.0746626\pi$
$911$	8.60304	+	14.9009i	0.285032	+	0.493689i	−0.687585	+	0.726104i	$0.741329\pi$
$912$	−1.11336	+	0.361751i	−0.0368669	+	0.0119788i
$913$	0.801710	−	1.38860i	0.0265327	−	0.0459560i
$914$	−1.50638	+	2.60912i	−0.0498265	+	0.0863020i
$915$	−2.52179	+	11.8641i	−0.0833678	+	0.392215i
$916$	16.7551	+	29.0207i	0.553604	+	0.958870i
$917$	12.6692			0.418373
$918$	−17.2511	−	1.81316i	−0.569371	−	0.0598433i
$919$	32.7547			1.08048			0.540240	−	0.841511i	$-0.318334\pi$
$919$	32.7547			1.08048			0.540240	+	0.841511i	$0.318334\pi$
$920$	4.71704	+	8.17015i	0.155516	+	0.269362i
$921$	−8.53817	+	40.1689i	−0.281342	+	1.32361i
$922$	5.80825	−	10.0602i	0.191284	−	0.331314i
$923$	21.0150	−	36.3991i	0.691719	−	1.19809i
$924$	0.381176	−	0.123852i	0.0125398	−	0.00407442i
$925$	3.94279	+	6.82911i	0.129638	+	0.224540i
$926$	−67.7113			−2.22513
$927$	−5.23561	+	3.80390i	−0.171960	+	0.124936i
$928$	−6.36924			−0.209081
$929$	19.9714	+	34.5916i	0.655242	+	1.13491i	0.981833	+	0.189746i	$0.0607666\pi$
$929$	19.9714	+	34.5916i	0.655242	+	1.13491i	−0.326591	+	0.945166i	$0.605900\pi$
$930$	−6.40832	−	5.77008i	−0.210137	−	0.189208i
$931$	0.0691705	−	0.119807i	0.00226697	−	0.00392651i
$932$	6.88960	−	11.9331i	0.225676	−	0.390883i
$933$	−18.8179	−	16.9437i	−0.616071	−	0.554712i
$934$	−10.6968	−	18.5275i	−0.350011	−	0.606237i
$935$	−0.315921			−0.0103317
$936$	−10.9961	+	7.98910i	−0.359417	+	0.261132i
$937$	−44.0780			−1.43997			−0.719983	−	0.693992i	$-0.755850\pi$
$937$	−44.0780			−1.43997			−0.719983	+	0.693992i	$0.755850\pi$
$938$	4.00313	+	6.93362i	0.130707	+	0.226391i
$939$	−17.5959	+	5.71725i	−0.574220	+	0.186575i
$940$	−3.88180	+	6.72348i	−0.126610	+	0.219296i
$941$	−11.8989	+	20.6094i	−0.387892	+	0.671848i	−0.992166	−	0.124928i	$-0.960130\pi$
$941$	−11.8989	+	20.6094i	−0.387892	+	0.671848i	0.604274	+	0.796777i	$0.293463\pi$
$942$	1.51700	−	7.13690i	0.0494264	−	0.232533i
$943$	−39.1773	−	67.8570i	−1.27579	−	2.20973i
$944$	5.76565			0.187656
$945$	−3.05422	+	4.20378i	−0.0993538	+	0.136749i
$946$	−2.33587			−0.0759458
$947$	1.69901	+	2.94277i	0.0552103	+	0.0956271i	0.892310	−	0.451424i	$-0.149084\pi$
$947$	1.69901	+	2.94277i	0.0552103	+	0.0956271i	−0.837099	+	0.547051i	$0.815750\pi$
$948$	−6.82722	+	32.1196i	−0.221738	+	1.04319i
$949$	−3.01263	+	5.21803i	−0.0977941	+	0.169384i
$950$	−0.126381	+	0.218898i	−0.00410034	+	0.00710199i
$951$	36.0966	−	11.7285i	1.17051	−	0.380322i
$952$	1.10453	+	1.91310i	0.0357980	+	0.0620039i
$953$	43.2045			1.39953			0.699765	−	0.714373i	$-0.253288\pi$
$953$	43.2045			1.39953			0.699765	+	0.714373i	$0.253288\pi$
$954$	6.71144	+	63.8551i	0.217291	+	2.06738i
$955$	5.98424			0.193645
$956$	−13.3188	−	23.0689i	−0.430762	−	0.746102i
$957$	−0.217808	−	0.196115i	−0.00704072	−	0.00633949i
$958$	−23.4408	+	40.6006i	−0.757336	+	1.31175i
$959$	−1.69555	+	2.93678i	−0.0547522	+	0.0948336i
$960$	2.72888	+	2.45709i	0.0880741	+	0.0793023i
$961$	11.7875	+	20.4165i	0.380241	+	0.658596i
$962$	−53.9890			−1.74067
$963$	31.5800	+	14.0603i	1.01765	+	0.453087i
$964$	13.9144			0.448152
$965$	−8.83948	−	15.3104i	−0.284553	−	0.492860i
$966$	−23.4844	+	7.63055i	−0.755599	+	0.245509i
$967$	−3.85325	+	6.67402i	−0.123912	+	0.214622i	−0.921307	−	0.388836i	$-0.872877\pi$
$967$	−3.85325	+	6.67402i	−0.123912	+	0.214622i	0.797395	+	0.603458i	$0.206211\pi$
$968$	6.63174	−	11.4865i	0.213152	−	0.369190i
$969$	−0.0910229	+	0.428229i	−0.00292408	+	0.0137567i
$970$	−9.48091	−	16.4214i	−0.304414	−	0.527260i
$971$	−3.89455			−0.124982			−0.0624911	−	0.998046i	$-0.519905\pi$
$971$	−3.89455			−0.124982			−0.0624911	+	0.998046i	$0.519905\pi$
$972$			20.8614i			0.669131i
$973$	−8.13545			−0.260811
$974$	−20.1947	−	34.9782i	−0.647079	−	1.12077i
$975$	−1.34943	+	6.34858i	−0.0432164	+	0.203317i
$976$	17.1063	−	29.6289i	0.547558	−	0.948399i
$977$	−3.89947	+	6.75408i	−0.124755	+	0.216082i	−0.921637	−	0.388053i	$-0.873148\pi$
$977$	−3.89947	+	6.75408i	−0.124755	+	0.216082i	0.796882	+	0.604135i	$0.206481\pi$
$978$	56.4086	−	18.3283i	1.80375	−	0.586074i
$979$	−1.02766	−	1.77997i	−0.0328443	−	0.0568880i
$980$	−1.33826			−0.0427492
$981$	−18.8965	−	8.41325i	−0.603318	−	0.268614i
$982$	−44.4588			−1.41874
$983$	−2.19529	−	3.80236i	−0.0700189	−	0.121276i	0.828890	−	0.559411i	$-0.188973\pi$
$983$	−2.19529	−	3.80236i	−0.0700189	−	0.121276i	−0.898909	+	0.438135i	$0.855639\pi$
$984$	15.6276	+	14.0712i	0.498190	+	0.448572i
$985$	−10.0957	+	17.4863i	−0.321676	+	0.557160i
$986$	−1.63347	+	2.82925i	−0.0520203	+	0.0901018i
$987$	7.46718	+	6.72348i	0.237683	+	0.214011i
$988$	−0.346875	−	0.600806i	−0.0110356	−	0.0191142i
$989$	57.6931			1.83453
$990$	0.0990681	+	0.942570i	0.00314859	+	0.0299568i
$991$	4.07623			0.129486			0.0647428	−	0.997902i	$-0.479377\pi$
$991$	4.07623			0.129486			0.0647428	+	0.997902i	$0.479377\pi$
$992$	8.86720	+	15.3584i	0.281534	+	0.487631i
$993$	37.0939	−	12.0525i	1.17714	−	0.382475i
$994$	−10.2466	+	17.7476i	−0.325002	+	0.562920i
$995$	9.04337	−	15.6636i	0.286694	−	0.496569i
$996$	−4.46899	+	21.0250i	−0.141605	+	0.666201i
$997$	11.8064	+	20.4492i	0.373911	+	0.647633i	0.990163	−	0.139916i	$-0.0446832\pi$
$997$	11.8064	+	20.4492i	0.373911	+	0.647633i	−0.616252	+	0.787549i	$0.711350\pi$
$998$	−42.3370			−1.34015
$999$	24.0843	−	33.1492i	0.761994	−	1.04879i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.i.d.211.4	yes	8
3.2	odd	2		945.2.i.c.631.1		8
9.2	odd	6		945.2.i.c.316.1		8
9.4	even	3		2835.2.a.l.1.1		4
9.5	odd	6		2835.2.a.q.1.4		4
9.7	even	3	inner	315.2.i.d.106.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.i.d.106.4	✓	8	9.7	even	3	inner
315.2.i.d.211.4	yes	8	1.1	even	1	trivial
945.2.i.c.316.1		8	9.2	odd	6
945.2.i.c.631.1		8	3.2	odd	2
2835.2.a.l.1.1		4	9.4	even	3
2835.2.a.q.1.4		4	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 + 1.58231i) q^{2} +(0.360114 - 1.69420i) q^{3} +(-0.669131 + 1.15897i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.00973 - 0.977920i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.20906 q^{8} +(-2.74064 - 1.22021i) q^{9} +O(q^{10})\)	\(q+(0.913545 + 1.58231i) q^{2} +(0.360114 - 1.69420i) q^{3} +(-0.669131 + 1.15897i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.00973 - 0.977920i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.20906 q^{8} +(-2.74064 - 1.22021i) q^{9} +1.82709 q^{10} +(-0.0864545 - 0.149744i) q^{11} +(1.72256 + 1.55100i) q^{12} +(1.87362 - 3.24520i) q^{13} +(-0.913545 + 1.58231i) q^{14} +(-1.28716 - 1.15897i) q^{15} +(2.44279 + 4.23104i) q^{16} +1.82709 q^{17} +(-0.572949 - 5.45125i) q^{18} -0.138341 q^{19} +(0.669131 + 1.15897i) q^{20} +(1.64728 - 0.535233i) q^{21} +(0.157960 - 0.273595i) q^{22} +(-3.90142 + 6.75746i) q^{23} +(0.435398 - 2.04839i) q^{24} +(-0.500000 - 0.866025i) q^{25} +6.84655 q^{26} +(-3.05422 + 4.20378i) q^{27} -1.33826 q^{28} +(0.489318 + 0.847523i) q^{29} +(0.657960 - 3.09546i) q^{30} +(1.36245 - 2.35983i) q^{31} +(-3.25414 + 5.63634i) q^{32} +(-0.284829 + 0.0925467i) q^{33} +(1.66913 + 2.89102i) q^{34} +1.00000 q^{35} +(3.24803 - 2.35983i) q^{36} -7.88558 q^{37} +(-0.126381 - 0.218898i) q^{38} +(-4.82331 - 4.34293i) q^{39} +(0.604528 - 1.04707i) q^{40} +(-5.02090 + 8.69645i) q^{41} +(2.35177 + 2.11754i) q^{42} +(-3.69693 - 6.40327i) q^{43} +0.231398 q^{44} +(-2.42705 + 1.76336i) q^{45} -14.2565 q^{46} +(2.90063 + 5.02404i) q^{47} +(8.04791 - 2.61492i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.913545 - 1.58231i) q^{50} +(0.657960 - 3.09546i) q^{51} +(2.50739 + 4.34293i) q^{52} -11.7139 q^{53} +(-9.44183 - 0.992377i) q^{54} -0.172909 q^{55} +(0.604528 + 1.04707i) q^{56} +(-0.0498185 + 0.234378i) q^{57} +(-0.894028 + 1.54850i) q^{58} +(0.590068 - 1.02203i) q^{59} +(2.20449 - 0.716282i) q^{60} +(-3.50138 - 6.06457i) q^{61} +4.97864 q^{62} +(-0.313585 - 2.98357i) q^{63} -2.12007 q^{64} +(-1.87362 - 3.24520i) q^{65} +(-0.406642 - 0.366142i) q^{66} +(2.19098 - 3.79489i) q^{67} +(-1.22256 + 2.11754i) q^{68} +(10.0435 + 9.04324i) q^{69} +(0.913545 + 1.58231i) q^{70} +11.2163 q^{71} +(-3.31359 - 1.47530i) q^{72} -1.60792 q^{73} +(-7.20384 - 12.4774i) q^{74} +(-1.64728 + 0.535233i) q^{75} +(0.0925682 - 0.160333i) q^{76} +(0.0864545 - 0.149744i) q^{77} +(2.46553 - 11.5994i) q^{78} +(7.08327 + 12.2686i) q^{79} +4.88558 q^{80} +(6.02218 + 6.68830i) q^{81} -18.3473 q^{82} +(4.63660 + 8.03082i) q^{83} +(-0.481926 + 2.26728i) q^{84} +(0.913545 - 1.58231i) q^{85} +(6.75463 - 11.6994i) q^{86} +(1.61209 - 0.523798i) q^{87} +(-0.104528 - 0.181049i) q^{88} +11.8868 q^{89} +(-5.00739 - 2.22943i) q^{90} +3.74724 q^{91} +(-5.22112 - 9.04324i) q^{92} +(-3.50739 - 3.15807i) q^{93} +(-5.29972 + 9.17938i) q^{94} +(-0.0691705 + 0.119807i) q^{95} +(8.37723 + 7.54289i) q^{96} +(-5.18907 - 8.98774i) q^{97} -1.82709 q^{98} +(0.0542218 + 0.515886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9	\( 8 q + q^{2} + 3 q^{3} - q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 3 q^{9} + 2 q^{10} - 7 q^{11} + 3 q^{12} + 8 q^{13} - q^{14} + 3 q^{15} + 9 q^{16} + 2 q^{17} - 18 q^{18} + 6 q^{19} + q^{20} - 7 q^{22} + 8 q^{23} + 6 q^{24} - 4 q^{25} - 6 q^{26} - 2 q^{28} - q^{29} - 3 q^{30} + 9 q^{34} + 8 q^{35} - 6 q^{36} - 42 q^{37} - 8 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} + 3 q^{42} + 7 q^{43} + 6 q^{44} - 6 q^{45} - 46 q^{46} + 2 q^{47} + 30 q^{48} - 4 q^{49} + q^{50} - 3 q^{51} + 7 q^{52} - 16 q^{53} - 36 q^{54} - 14 q^{55} + 3 q^{56} - 24 q^{57} + 19 q^{58} - 19 q^{59} + 15 q^{60} + 12 q^{61} + 30 q^{62} + 3 q^{63} - 14 q^{64} - 8 q^{65} - 9 q^{66} + 22 q^{67} + q^{68} + 51 q^{69} + q^{70} + 26 q^{71} - 21 q^{72} - 8 q^{73} - 9 q^{74} + 13 q^{76} + 7 q^{77} - 21 q^{78} + 24 q^{79} + 18 q^{80} + 9 q^{81} + 19 q^{83} - 12 q^{84} + q^{85} + 27 q^{86} + 45 q^{87} + q^{88} + 30 q^{89} - 27 q^{90} + 16 q^{91} - 3 q^{92} - 15 q^{93} + 7 q^{94} + 3 q^{95} + 30 q^{96} + 12 q^{97} - 2 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q + q^2 + 3 * q^3 - q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 3 * q^9 + 2 * q^10 - 7 * q^11 + 3 * q^12 + 8 * q^13 - q^14 + 3 * q^15 + 9 * q^16 + 2 * q^17 - 18 * q^18 + 6 * q^19 + q^20 - 7 * q^22 + 8 * q^23 + 6 * q^24 - 4 * q^25 - 6 * q^26 - 2 * q^28 - q^29 - 3 * q^30 + 9 * q^34 + 8 * q^35 - 6 * q^36 - 42 * q^37 - 8 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 + 3 * q^42 + 7 * q^43 + 6 * q^44 - 6 * q^45 - 46 * q^46 + 2 * q^47 + 30 * q^48 - 4 * q^49 + q^50 - 3 * q^51 + 7 * q^52 - 16 * q^53 - 36 * q^54 - 14 * q^55 + 3 * q^56 - 24 * q^57 + 19 * q^58 - 19 * q^59 + 15 * q^60 + 12 * q^61 + 30 * q^62 + 3 * q^63 - 14 * q^64 - 8 * q^65 - 9 * q^66 + 22 * q^67 + q^68 + 51 * q^69 + q^70 + 26 * q^71 - 21 * q^72 - 8 * q^73 - 9 * q^74 + 13 * q^76 + 7 * q^77 - 21 * q^78 + 24 * q^79 + 18 * q^80 + 9 * q^81 + 19 * q^83 - 12 * q^84 + q^85 + 27 * q^86 + 45 * q^87 + q^88 + 30 * q^89 - 27 * q^90 + 16 * q^91 - 3 * q^92 - 15 * q^93 + 7 * q^94 + 3 * q^95 + 30 * q^96 + 12 * q^97 - 2 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more