LMFDB - Embedded newform 385.2.i.b.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.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:	$3.07424047782$
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} + 13 x^{10} - 12 x^{9} + 49 x^{8} - 38 x^{7} + 136 x^{6} - 34 x^{5} + 113 x^{4} + \cdots + 4 $ x^12 - 3x^11 + 13x^10 - 12x^9 + 49x^8 - 38x^7 + 136x^6 - 34x^5 + 113x^4 - 72x^3 + 58x^2 - 16*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.1
Root			$1.48136 - 2.56580i$ of defining polynomial
Character	$\chi$	$=$	385.331
Dual form			385.2.i.b.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.981363 + 1.69977i) q^{2} +(-0.263672 - 0.456693i) q^{3} +(-0.926145 - 1.60413i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.03503 q^{6} +(-2.64214 + 0.138161i) q^{7} -0.289915 q^{8} +(1.36095 - 2.35724i) q^{9} +O(q^{10})$	\(q+(-0.981363 + 1.69977i) q^{2} +(-0.263672 - 0.456693i) q^{3} +(-0.926145 - 1.60413i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.03503 q^{6} +(-2.64214 + 0.138161i) q^{7} -0.289915 q^{8} +(1.36095 - 2.35724i) q^{9} +(0.981363 + 1.69977i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.488397 + 0.845928i) q^{12} +0.196809 q^{13} +(2.35806 - 4.62662i) q^{14} -0.527344 q^{15} +(2.13680 - 3.70105i) q^{16} +(-2.50337 - 4.33596i) q^{17} +(2.67118 + 4.62662i) q^{18} +(1.88830 - 3.27063i) q^{19} -1.85229 q^{20} +(0.759755 + 1.17022i) q^{21} -1.96273 q^{22} +(3.54992 - 6.14864i) q^{23} +(0.0764425 + 0.132402i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.193141 + 0.334531i) q^{26} -3.01741 q^{27} +(2.66863 + 4.11038i) q^{28} -0.443503 q^{29} +(0.517515 - 0.896363i) q^{30} +(1.93779 + 3.35635i) q^{31} +(3.90404 + 6.76199i) q^{32} +(0.263672 - 0.456693i) q^{33} +9.82684 q^{34} +(-1.20142 + 2.35724i) q^{35} -5.04176 q^{36} +(5.11078 - 8.85213i) q^{37} +(3.70621 + 6.41934i) q^{38} +(-0.0518931 - 0.0898814i) q^{39} +(-0.144958 + 0.251074i) q^{40} -3.83573 q^{41} +(-2.73470 + 0.143001i) q^{42} +0.847198 q^{43} +(0.926145 - 1.60413i) q^{44} +(-1.36095 - 2.35724i) q^{45} +(6.96751 + 12.0681i) q^{46} +(-6.58641 + 11.4080i) q^{47} -2.25366 q^{48} +(6.96182 - 0.730081i) q^{49} +1.96273 q^{50} +(-1.32013 + 2.28654i) q^{51} +(-0.182274 - 0.315708i) q^{52} +(0.556340 + 0.963609i) q^{53} +(2.96118 - 5.12891i) q^{54} +1.00000 q^{55} +(0.765997 - 0.0400549i) q^{56} -1.99156 q^{57} +(0.435237 - 0.753853i) q^{58} +(-5.74074 - 9.94326i) q^{59} +(0.488397 + 0.845928i) q^{60} +(3.45561 - 5.98529i) q^{61} -7.60670 q^{62} +(-3.27016 + 6.41620i) q^{63} -6.77790 q^{64} +(0.0984047 - 0.170442i) q^{65} +(0.517515 + 0.896363i) q^{66} +(4.44533 + 7.69954i) q^{67} +(-4.63696 + 8.03145i) q^{68} -3.74405 q^{69} +(-2.82774 - 4.35545i) q^{70} -4.95660 q^{71} +(-0.394561 + 0.683400i) q^{72} +(-1.29018 - 2.23465i) q^{73} +(10.0311 + 17.3743i) q^{74} +(-0.263672 + 0.456693i) q^{75} -6.99535 q^{76} +(-1.44072 - 2.21908i) q^{77} +0.203704 q^{78} +(-2.77642 + 4.80890i) q^{79} +(-2.13680 - 3.70105i) q^{80} +(-3.28726 - 5.69369i) q^{81} +(3.76424 - 6.51986i) q^{82} -13.4594 q^{83} +(1.17354 - 2.30254i) q^{84} -5.00673 q^{85} +(-0.831408 + 1.44004i) q^{86} +(0.116939 + 0.202545i) q^{87} +(-0.144958 - 0.251074i) q^{88} +(1.95696 - 3.38955i) q^{89} +5.34236 q^{90} +(-0.519998 + 0.0271913i) q^{91} -13.1510 q^{92} +(1.02188 - 1.76995i) q^{93} +(-12.9273 - 22.3908i) q^{94} +(-1.88830 - 3.27063i) q^{95} +(2.05877 - 3.56589i) q^{96} -7.41996 q^{97} +(-5.59110 + 12.5500i) q^{98} +2.72191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9 - 3 * q^10 + 6 * q^11 - 9 * q^12 + 28 * q^13 - 3 * q^14 - 2 * q^15 - 11 * q^16 - 3 * q^17 + 9 * q^18 + 3 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^22 + 10 * q^23 + 10 * q^24 - 6 * q^25 + 17 * q^26 + 2 * q^27 - 10 * q^28 - 32 * q^29 - 5 * q^30 - 2 * q^31 + 26 * q^32 + q^33 + 60 * q^34 - 3 * q^35 + 16 * q^36 - 5 * q^37 - q^38 - 3 * q^39 - 9 * q^40 - 18 * q^41 - 56 * q^42 - 40 * q^43 + 5 * q^44 - q^45 + 20 * q^46 - q^47 + 82 * q^48 + 15 * q^49 - 6 * q^50 + 5 * q^51 - 23 * q^52 + 24 * q^53 + 7 * q^54 + 12 * q^55 - 66 * q^56 - 60 * q^57 - 31 * q^58 + 7 * q^59 + 9 * q^60 + 14 * q^61 + 48 * q^62 - 13 * q^63 + 30 * q^64 + 14 * q^65 - 5 * q^66 - q^67 + 25 * q^68 - 8 * q^69 - 15 * q^70 - 18 * q^71 + 26 * q^72 - 13 * q^73 + 40 * q^74 - q^75 - 20 * q^76 - 66 * q^78 + 4 * q^79 + 11 * q^80 + 26 * q^81 + 27 * q^82 + 16 * q^83 - 90 * q^84 - 6 * q^85 - 36 * q^86 + 2 * q^87 - 9 * q^88 + 13 * q^89 + 18 * q^90 + 17 * q^91 - 36 * q^92 + 36 * q^93 + q^94 - 3 * q^95 + 89 * q^96 - 6 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.981363	+	1.69977i	−0.693928	+	1.20192i	0.276613	+	0.960982i	$0.410788\pi$
$2$	−0.981363	+	1.69977i	−0.693928	+	1.20192i	−0.970541	+	0.240937i	$0.922545\pi$
$3$	−0.263672	−	0.456693i	−0.152231	−	0.263672i	0.779816	−	0.626008i	$-0.215312\pi$
$3$	−0.263672	−	0.456693i	−0.152231	−	0.263672i	−0.932047	+	0.362337i	$0.881979\pi$
$4$	−0.926145	−	1.60413i	−0.463072	−	0.802065i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.03503			0.422549
$7$	−2.64214	+	0.138161i	−0.998636	+	0.0522199i
$7$	−2.64214	+	0.138161i	−0.998636	+	0.0522199i
$8$	−0.289915			−0.102500
$9$	1.36095	−	2.35724i	0.453651	−	0.785747i
$10$	0.981363	+	1.69977i	0.310334	+	0.537514i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−0.488397	+	0.845928i	−0.140988	+	0.244198i
$13$	0.196809			0.0545851			0.0272925	−	0.999627i	$-0.491311\pi$
$13$	0.196809			0.0545851			0.0272925	+	0.999627i	$0.491311\pi$
$14$	2.35806	−	4.62662i	0.630217	−	1.23652i
$15$	−0.527344			−0.136160
$16$	2.13680	−	3.70105i	0.534200	−	0.925262i
$17$	−2.50337	−	4.33596i	−0.607155	−	1.05162i	−0.991707	−	0.128521i	$-0.958977\pi$
$17$	−2.50337	−	4.33596i	−0.607155	−	1.05162i	0.384551	−	0.923104i	$-0.374356\pi$
$18$	2.67118	+	4.62662i	0.629603	+	1.09050i
$19$	1.88830	−	3.27063i	0.433205	−	0.750334i	−0.563942	−	0.825814i	$-0.690716\pi$
$19$	1.88830	−	3.27063i	0.433205	−	0.750334i	0.997147	+	0.0754809i	$0.0240492\pi$
$20$	−1.85229			−0.414185
$21$	0.759755	+	1.17022i	0.165792	+	0.255363i
$22$	−1.96273			−0.418454
$23$	3.54992	−	6.14864i	0.740209	−	1.28208i	−0.212191	−	0.977228i	$-0.568060\pi$
$23$	3.54992	−	6.14864i	0.740209	−	1.28208i	0.952400	−	0.304852i	$-0.0986069\pi$
$24$	0.0764425	+	0.132402i	0.0156038	+	0.0270265i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.193141	+	0.334531i	−0.0378781	+	0.0656068i
$27$	−3.01741			−0.580701
$28$	2.66863	+	4.11038i	0.504324	+	0.776789i
$29$	−0.443503			−0.0823564			−0.0411782	−	0.999152i	$-0.513111\pi$
$29$	−0.443503			−0.0823564			−0.0411782	+	0.999152i	$0.513111\pi$
$30$	0.517515	−	0.896363i	0.0944849	−	0.163653i
$31$	1.93779	+	3.35635i	0.348037	+	0.602818i	0.985901	−	0.167331i	$-0.0535149\pi$
$31$	1.93779	+	3.35635i	0.348037	+	0.602818i	−0.637863	+	0.770149i	$0.720182\pi$
$32$	3.90404	+	6.76199i	0.690143	+	1.19536i
$33$	0.263672	−	0.456693i	0.0458994	−	0.0795001i
$34$	9.82684			1.68529
$35$	−1.20142	+	2.35724i	−0.203077	+	0.398447i
$36$	−5.04176			−0.840294
$37$	5.11078	−	8.85213i	0.840207	−	1.45528i	−0.0495128	−	0.998773i	$-0.515767\pi$
$37$	5.11078	−	8.85213i	0.840207	−	1.45528i	0.889720	−	0.456507i	$-0.150900\pi$
$38$	3.70621	+	6.41934i	0.601227	+	1.04136i
$39$	−0.0518931	−	0.0898814i	−0.00830954	−	0.0143925i
$40$	−0.144958	+	0.251074i	−0.0229198	+	0.0396983i
$41$	−3.83573			−0.599041			−0.299520	−	0.954090i	$-0.596827\pi$
$41$	−3.83573			−0.599041			−0.299520	+	0.954090i	$0.596827\pi$
$42$	−2.73470	+	0.143001i	−0.421973	+	0.0220655i
$43$	0.847198			0.129196			0.0645982	−	0.997911i	$-0.479423\pi$
$43$	0.847198			0.129196			0.0645982	+	0.997911i	$0.479423\pi$
$44$	0.926145	−	1.60413i	0.139622	−	0.241832i
$45$	−1.36095	−	2.35724i	−0.202879	−	0.351397i
$46$	6.96751	+	12.0681i	1.02730	+	1.77934i
$47$	−6.58641	+	11.4080i	−0.960727	+	1.66403i	−0.240047	+	0.970761i	$0.577163\pi$
$47$	−6.58641	+	11.4080i	−0.960727	+	1.66403i	−0.720681	+	0.693267i	$0.756171\pi$
$48$	−2.25366			−0.325287
$49$	6.96182	−	0.730081i	0.994546	−	0.104297i
$50$	1.96273			0.277571
$51$	−1.32013	+	2.28654i	−0.184856	+	0.320180i
$52$	−0.182274	−	0.315708i	−0.0252768	−	0.0437808i
$53$	0.556340	+	0.963609i	0.0764192	+	0.132362i	0.901703	−	0.432357i	$-0.142318\pi$
$53$	0.556340	+	0.963609i	0.0764192	+	0.132362i	−0.825283	+	0.564719i	$0.808985\pi$
$54$	2.96118	−	5.12891i	0.402965	−	0.697956i
$55$	1.00000			0.134840
$56$	0.765997	−	0.0400549i	0.102361	−	0.00535256i
$57$	−1.99156			−0.263789
$58$	0.435237	−	0.753853i	0.0571494	−	0.0989857i
$59$	−5.74074	−	9.94326i	−0.747381	−	1.29450i	−0.949074	−	0.315054i	$-0.897978\pi$
$59$	−5.74074	−	9.94326i	−0.747381	−	1.29450i	0.201693	−	0.979449i	$-0.435356\pi$
$60$	0.488397	+	0.845928i	0.0630517	+	0.109209i
$61$	3.45561	−	5.98529i	0.442445	−	0.766338i	−0.555425	−	0.831567i	$-0.687444\pi$
$61$	3.45561	−	5.98529i	0.442445	−	0.766338i	0.997870	+	0.0652287i	$0.0207777\pi$
$62$	−7.60670			−0.966051
$63$	−3.27016	+	6.41620i	−0.412001	+	0.808365i
$64$	−6.77790			−0.847238
$65$	0.0984047	−	0.170442i	0.0122056	−	0.0211407i
$66$	0.517515	+	0.896363i	0.0637017	+	0.110335i
$67$	4.44533	+	7.69954i	0.543084	+	0.940649i	0.998725	+	0.0504851i	$0.0160767\pi$
$67$	4.44533	+	7.69954i	0.543084	+	0.940649i	−0.455641	+	0.890164i	$0.650590\pi$
$68$	−4.63696	+	8.03145i	−0.562314	+	0.973956i
$69$	−3.74405			−0.450731
$70$	−2.82774	−	4.35545i	−0.337980	−	0.520575i
$71$	−4.95660			−0.588240			−0.294120	−	0.955769i	$-0.595026\pi$
$71$	−4.95660			−0.588240			−0.294120	+	0.955769i	$0.595026\pi$
$72$	−0.394561	+	0.683400i	−0.0464995	+	0.0805395i
$73$	−1.29018	−	2.23465i	−0.151004	−	0.261546i	0.780593	−	0.625040i	$-0.214917\pi$
$73$	−1.29018	−	2.23465i	−0.151004	−	0.261546i	−0.931597	+	0.363494i	$0.881584\pi$
$74$	10.0311	+	17.3743i	1.16609	+	2.01972i
$75$	−0.263672	+	0.456693i	−0.0304462	+	0.0527344i
$76$	−6.99535			−0.802422
$77$	−1.44072	−	2.21908i	−0.164185	−	0.252888i
$78$	0.203704			0.0230649
$79$	−2.77642	+	4.80890i	−0.312372	+	0.541043i	−0.978875	−	0.204458i	$-0.934457\pi$
$79$	−2.77642	+	4.80890i	−0.312372	+	0.541043i	0.666504	+	0.745502i	$0.267790\pi$
$80$	−2.13680	−	3.70105i	−0.238902	−	0.413790i
$81$	−3.28726	−	5.69369i	−0.365251	−	0.632633i
$82$	3.76424	−	6.51986i	0.415691	−	0.719998i
$83$	−13.4594			−1.47736			−0.738682	−	0.674054i	$-0.764551\pi$
$83$	−13.4594			−1.47736			−0.738682	+	0.674054i	$0.764551\pi$
$84$	1.17354	−	2.30254i	0.128044	−	0.251227i
$85$	−5.00673			−0.543056
$86$	−0.831408	+	1.44004i	−0.0896530	+	0.155284i
$87$	0.116939	+	0.202545i	0.0125372	+	0.0217151i
$88$	−0.144958	−	0.251074i	−0.0154525	−	0.0267646i
$89$	1.95696	−	3.38955i	0.207437	−	0.359292i	−0.743469	−	0.668770i	$-0.766821\pi$
$89$	1.95696	−	3.38955i	0.207437	−	0.359292i	0.950906	+	0.309478i	$0.100154\pi$
$90$	5.34236			0.563134
$91$	−0.519998	+	0.0271913i	−0.0545106	+	0.00285043i
$92$	−13.1510			−1.37108
$93$	1.02188	−	1.76995i	0.105964	−	0.183535i
$94$	−12.9273	−	22.3908i	−1.33335	−	2.30943i
$95$	−1.88830	−	3.27063i	−0.193735	−	0.335559i
$96$	2.05877	−	3.56589i	0.210122	−	0.363943i
$97$	−7.41996			−0.753383			−0.376692	−	0.926339i	$-0.622938\pi$
$97$	−7.41996			−0.753383			−0.376692	+	0.926339i	$0.622938\pi$
$98$	−5.59110	+	12.5500i	−0.564787	+	1.26774i
$99$	2.72191			0.273562
$100$	−0.926145	+	1.60413i	−0.0926145	+	0.160413i
$101$	−1.09657	−	1.89932i	−0.109113	−	0.188990i	0.806298	−	0.591510i	$-0.201468\pi$
$101$	−1.09657	−	1.89932i	−0.109113	−	0.188990i	−0.915411	+	0.402520i	$0.868134\pi$
$102$	−2.59106	−	4.48785i	−0.256553	−	0.444363i
$103$	6.85471	−	11.8727i	0.675415	−	1.16985i	−0.300933	−	0.953645i	$-0.597298\pi$
$103$	6.85471	−	11.8727i	0.675415	−	1.16985i	0.976347	−	0.216207i	$-0.0693688\pi$
$104$	−0.0570580			−0.00559500
$105$	1.39332	−	0.0728582i	0.135974	−	0.00711023i
$106$	−2.18388			−0.212118
$107$	2.99505	−	5.18758i	0.289543	−	0.501503i	−0.684158	−	0.729334i	$-0.739830\pi$
$107$	2.99505	−	5.18758i	0.289543	−	0.501503i	0.973701	+	0.227831i	$0.0731635\pi$
$108$	2.79456	+	4.84032i	0.268907	+	0.465760i
$109$	−5.37584	−	9.31123i	−0.514912	−	0.891854i	−0.999850	−	0.0173054i	$-0.994491\pi$
$109$	−5.37584	−	9.31123i	−0.514912	−	0.891854i	0.484938	−	0.874548i	$-0.338842\pi$
$110$	−0.981363	+	1.69977i	−0.0935692	+	0.162067i
$111$	−5.39027			−0.511622
$112$	−5.13439	+	10.0739i	−0.485154	+	0.951896i
$113$	−3.95037			−0.371619			−0.185810	−	0.982586i	$-0.559491\pi$
$113$	−3.95037			−0.371619			−0.185810	+	0.982586i	$0.559491\pi$
$114$	1.95445	−	3.38520i	0.183051	−	0.317053i
$115$	−3.54992	−	6.14864i	−0.331032	−	0.573364i
$116$	0.410748	+	0.711436i	0.0381370	+	0.0660552i
$117$	0.267848	−	0.463927i	0.0247626	−	0.0428901i
$118$	22.5350			2.07452
$119$	7.21331	+	11.1103i	0.661243	+	1.01848i
$120$	0.152885			0.0139564
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	6.78241	+	11.7475i	0.614051	+	1.06357i
$123$	1.01137	+	1.75175i	0.0911926	+	0.157950i
$124$	3.58935	−	6.21693i	0.322333	−	0.558297i
$125$	−1.00000			−0.0894427
$126$	−7.69685	−	11.8551i	−0.685690	−	1.05614i
$127$	18.5595			1.64689			0.823443	−	0.567399i	$-0.192050\pi$
$127$	18.5595			1.64689			0.823443	+	0.567399i	$0.192050\pi$
$128$	−1.15650	+	2.00311i	−0.102221	+	0.177052i
$129$	−0.223382	−	0.386909i	−0.0196677	−	0.0340655i
$130$	0.193141	+	0.334531i	0.0169396	+	0.0293403i
$131$	−8.86226	+	15.3499i	−0.774299	+	1.34113i	0.160888	+	0.986973i	$0.448564\pi$
$131$	−8.86226	+	15.3499i	−0.774299	+	1.34113i	−0.935187	+	0.354153i	$0.884769\pi$
$132$	−0.976793			−0.0850189
$133$	−4.53728	+	8.90235i	−0.393432	+	0.771932i
$134$	−17.4499			−1.50744
$135$	−1.50871	+	2.61316i	−0.129849	+	0.224905i
$136$	0.725764	+	1.25706i	0.0622337	+	0.107792i
$137$	8.94845	+	15.4992i	0.764518	+	1.32418i	0.940501	+	0.339790i	$0.110356\pi$
$137$	8.94845	+	15.4992i	0.764518	+	1.32418i	−0.175984	+	0.984393i	$0.556311\pi$
$138$	3.67427	−	6.36403i	0.312775	−	0.541742i
$139$	7.71973			0.654779			0.327390	−	0.944889i	$-0.393831\pi$
$139$	7.71973			0.654779			0.327390	+	0.944889i	$0.393831\pi$
$140$	4.89401	−	0.255914i	0.413619	−	0.0216287i
$141$	6.94661			0.585010
$142$	4.86422	−	8.42507i	0.408196	−	0.707016i
$143$	0.0984047	+	0.170442i	0.00822901	+	0.0142531i
$144$	−5.81618	−	10.0739i	−0.484681	−	0.839493i
$145$	−0.221751	+	0.384085i	−0.0184155	+	0.0318965i
$146$	5.06452			0.419143
$147$	−2.16906	−	2.98691i	−0.178901	−	0.246357i
$148$	−18.9333			−1.55631
$149$	−2.15354	+	3.73004i	−0.176425	+	0.305577i	−0.940653	−	0.339369i	$-0.889787\pi$
$149$	−2.15354	+	3.73004i	−0.176425	+	0.305577i	0.764229	+	0.644946i	$0.223120\pi$
$150$	−0.517515	−	0.896363i	−0.0422549	−	0.0731877i
$151$	9.43274	+	16.3380i	0.767626	+	1.32957i	0.938847	+	0.344334i	$0.111895\pi$
$151$	9.43274	+	16.3380i	0.767626	+	1.32957i	−0.171221	+	0.985233i	$0.554771\pi$
$152$	−0.547446	+	0.948205i	−0.0444038	+	0.0769096i
$153$	−13.6279			−1.10175
$154$	5.18580	−	0.271172i	0.417883	−	0.0218516i
$155$	3.87558			0.311294
$156$	−0.0961210	+	0.166486i	−0.00769584	+	0.0133296i
$157$	−1.92863	−	3.34048i	−0.153921	−	0.266599i	0.778744	−	0.627341i	$-0.215857\pi$
$157$	−1.92863	−	3.34048i	−0.153921	−	0.266599i	−0.932666	+	0.360742i	$0.882524\pi$
$158$	−5.44935	−	9.43855i	−0.433527	−	0.750890i
$159$	0.293382	−	0.508153i	0.0232667	−	0.0402992i
$160$	7.80808			0.617283
$161$	−8.52989	+	16.7360i	−0.672249	+	1.31898i
$162$	12.9040			1.01383
$163$	−6.78294	+	11.7484i	−0.531281	+	0.920206i	0.468052	+	0.883701i	$0.344956\pi$
$163$	−6.78294	+	11.7484i	−0.531281	+	0.920206i	−0.999333	+	0.0365052i	$0.988377\pi$
$164$	3.55244	+	6.15301i	0.277399	+	0.480469i
$165$	−0.263672	−	0.456693i	−0.0205268	−	0.0355535i
$166$	13.2086	−	22.8779i	1.02518	−	1.77567i
$167$	23.0824			1.78617			0.893084	−	0.449891i	$-0.148537\pi$
$167$	23.0824			1.78617			0.893084	+	0.449891i	$0.148537\pi$
$168$	−0.220265	−	0.339264i	−0.0169938	−	0.0261748i
$169$	−12.9613			−0.997020
$170$	4.91342	−	8.51029i	0.376842	−	0.652710i
$171$	−5.13977	−	8.90235i	−0.393048	−	0.680780i
$172$	−0.784628	−	1.35902i	−0.0598273	−	0.103624i
$173$	−1.81418	+	3.14224i	−0.137929	+	0.238900i	−0.926713	−	0.375771i	$-0.877378\pi$
$173$	−1.81418	+	3.14224i	−0.137929	+	0.238900i	0.788783	+	0.614671i	$0.210711\pi$
$174$	−0.459039			−0.0347997
$175$	1.44072	+	2.21908i	0.108908	+	0.167747i
$176$	4.27360			0.322135
$177$	−3.02735	+	5.24352i	−0.227549	+	0.394127i
$178$	3.84097	+	6.65275i	0.287893	+	0.498645i
$179$	4.22905	+	7.32492i	0.316094	+	0.547491i	0.979669	−	0.200619i	$-0.0642952\pi$
$179$	4.22905	+	7.32492i	0.316094	+	0.547491i	−0.663576	+	0.748109i	$0.730962\pi$
$180$	−2.52088	+	4.36629i	−0.187895	+	0.325444i
$181$	11.7923			0.876518			0.438259	−	0.898849i	$-0.355595\pi$
$181$	11.7923			0.876518			0.438259	+	0.898849i	$0.355595\pi$
$182$	0.464088	−	0.910561i	0.0344005	−	0.0674953i
$183$	−3.64459			−0.269416
$184$	−1.02918	+	1.78258i	−0.0758718	+	0.131414i
$185$	−5.11078	−	8.85213i	−0.375752	−	0.650821i
$186$	2.00567	+	3.47392i	0.147063	+	0.254721i
$187$	2.50337	−	4.33596i	0.183064	−	0.317077i
$188$	24.3999			1.77955
$189$	7.97243	−	0.416888i	0.579909	−	0.0303241i
$190$	7.41242			0.537753
$191$	−3.24822	+	5.62608i	−0.235033	+	0.407089i	−0.959282	−	0.282449i	$-0.908853\pi$
$191$	−3.24822	+	5.62608i	−0.235033	+	0.407089i	0.724249	+	0.689538i	$0.242187\pi$
$192$	1.78714	+	3.09542i	0.128976	+	0.223393i
$193$	−2.39923	−	4.15558i	−0.172700	−	0.299125i	0.766663	−	0.642050i	$-0.221916\pi$
$193$	−2.39923	−	4.15558i	−0.172700	−	0.299125i	−0.939363	+	0.342925i	$0.888582\pi$
$194$	7.28167	−	12.6122i	0.522794	−	0.905505i
$195$	−0.103786			−0.00743228
$196$	−7.61880	−	10.4915i	−0.544200	−	0.749393i
$197$	26.4315			1.88317			0.941584	−	0.336778i	$-0.109337\pi$
$197$	26.4315			1.88317			0.941584	+	0.336778i	$0.109337\pi$
$198$	−2.67118	+	4.62662i	−0.189832	+	0.328799i
$199$	−1.73285	−	3.00138i	−0.122838	−	0.212762i	0.798048	−	0.602595i	$-0.205866\pi$
$199$	−1.73285	−	3.00138i	−0.122838	−	0.212762i	−0.920886	+	0.389832i	$0.872533\pi$
$200$	0.144958	+	0.251074i	0.0102500	+	0.0177536i
$201$	2.34422	−	4.06030i	0.165348	−	0.286392i
$202$	4.30455			0.302867
$203$	1.17180	−	0.0612747i	0.0822440	−	0.00430064i
$204$	4.89054			0.342406
$205$	−1.91787	+	3.32184i	−0.133950	+	0.232007i
$206$	13.4539	+	23.3029i	0.937379	+	1.62359i
$207$	−9.66256	−	16.7360i	−0.671594	−	1.16323i
$208$	0.420542	−	0.728401i	0.0291594	−	0.0505055i
$209$	3.77660			0.261233
$210$	−1.24351	+	2.43982i	−0.0858101	+	0.168363i
$211$	18.4041			1.26699			0.633495	−	0.773746i	$-0.281620\pi$
$211$	18.4041			1.26699			0.633495	+	0.773746i	$0.281620\pi$
$212$	1.03050	−	1.78488i	0.0707752	−	0.122586i
$213$	1.30691	+	2.26364i	0.0895483	+	0.155102i
$214$	5.87846	+	10.1818i	0.401844	+	0.696013i
$215$	0.423599	−	0.733695i	0.0288892	−	0.0500376i
$216$	0.874794			0.0595222
$217$	−5.58363	−	8.60022i	−0.379041	−	0.583821i
$218$	21.1026			1.42925
$219$	−0.680366	+	1.17843i	−0.0459749	+	0.0796308i
$220$	−0.926145	−	1.60413i	−0.0624407	−	0.108150i
$221$	−0.492686	−	0.853357i	−0.0331416	−	0.0574030i
$222$	5.28981	−	9.16222i	0.355029	−	0.614928i
$223$	−0.289998			−0.0194197			−0.00970985	−	0.999953i	$-0.503091\pi$
$223$	−0.289998			−0.0194197			−0.00970985	+	0.999953i	$0.503091\pi$
$224$	−11.2493	−	17.3268i	−0.751623	−	1.15769i
$225$	−2.72191			−0.181461
$226$	3.87674	−	6.71472i	0.257877	−	0.446656i
$227$	−2.21521	−	3.83685i	−0.147029	−	0.254661i	0.783099	−	0.621897i	$-0.213638\pi$
$227$	−2.21521	−	3.83685i	−0.147029	−	0.254661i	−0.930128	+	0.367236i	$0.880304\pi$
$228$	1.84448	+	3.19473i	0.122153	+	0.211576i
$229$	−2.48412	+	4.30263i	−0.164155	+	0.284326i	−0.936355	−	0.351054i	$-0.885823\pi$
$229$	−2.48412	+	4.30263i	−0.164155	+	0.284326i	0.772200	+	0.635380i	$0.219157\pi$
$230$	13.9350			0.918849
$231$	−0.633561	+	1.24308i	−0.0416853	+	0.0817884i
$232$	0.128578			0.00844157
$233$	14.0696	−	24.3692i	0.921727	−	1.59648i	0.124985	−	0.992159i	$-0.460112\pi$
$233$	14.0696	−	24.3692i	0.921727	−	1.59648i	0.796742	−	0.604319i	$-0.206555\pi$
$234$	0.525713	+	0.910561i	0.0343669	+	0.0595253i
$235$	6.58641	+	11.4080i	0.429650	+	0.744176i
$236$	−10.6335	+	18.4178i	−0.692183	+	1.19890i
$237$	2.92825			0.190211
$238$	−25.9639	+	1.35768i	−1.68299	+	0.0880056i
$239$	−8.57632			−0.554756			−0.277378	−	0.960761i	$-0.589465\pi$
$239$	−8.57632			−0.554756			−0.277378	+	0.960761i	$0.589465\pi$
$240$	−1.12683	+	1.95172i	−0.0727365	+	0.125983i
$241$	5.71706	+	9.90223i	0.368268	+	0.637859i	0.989295	−	0.145930i	$-0.0466176\pi$
$241$	5.71706	+	9.90223i	0.368268	+	0.637859i	−0.621027	+	0.783789i	$0.713284\pi$
$242$	−0.981363	−	1.69977i	−0.0630844	−	0.109265i
$243$	−6.25963	+	10.8420i	−0.401556	+	0.695515i
$244$	−12.8016			−0.819537
$245$	2.84864	−	6.39416i	0.181993	−	0.408508i
$246$	−3.97010			−0.253124
$247$	0.371635	−	0.643690i	0.0236465	−	0.0409570i
$248$	−0.561795	−	0.973057i	−0.0356740	−	0.0617892i
$249$	3.54887	+	6.14683i	0.224901	+	0.389539i
$250$	0.981363	−	1.69977i	0.0620668	−	0.107503i
$251$	−24.2717			−1.53202			−0.766008	−	0.642831i	$-0.777760\pi$
$251$	−24.2717			−1.53202			−0.766008	+	0.642831i	$0.777760\pi$
$252$	13.3211	−	0.696574i	0.839147	−	0.0438800i
$253$	7.09984			0.446363
$254$	−18.2136	+	31.5468i	−1.14282	+	1.97942i
$255$	1.32013	+	2.28654i	0.0826700	+	0.143189i
$256$	−9.04779	−	15.6712i	−0.565487	−	0.979452i
$257$	11.5874	−	20.0699i	0.722800	−	1.25193i	−0.237073	−	0.971492i	$-0.576188\pi$
$257$	11.5874	−	20.0699i	0.722800	−	1.25193i	0.959873	−	0.280435i	$-0.0904788\pi$
$258$	0.876876			0.0545919
$259$	−12.2804	+	24.0947i	−0.763066	+	1.49717i
$260$	−0.364548			−0.0226083
$261$	−0.603587	+	1.04544i	−0.0373611	+	0.0647113i
$262$	−17.3942	−	30.1276i	−1.07462	−	1.86129i
$263$	−12.6459	−	21.9033i	−0.779778	−	1.35062i	−0.932070	−	0.362279i	$-0.881999\pi$
$263$	−12.6459	−	21.9033i	−0.779778	−	1.35062i	0.152292	−	0.988336i	$-0.451335\pi$
$264$	−0.0764425	+	0.132402i	−0.00470471	+	0.00814879i
$265$	1.11268			0.0683514
$266$	−10.6792	−	16.4488i	−0.654786	−	1.00854i
$267$	−2.06398			−0.126313
$268$	8.23404	−	14.2618i	0.502974	−	0.871177i
$269$	1.76408	+	3.05547i	0.107558	+	0.186295i	0.914780	−	0.403952i	$-0.132364\pi$
$269$	1.76408	+	3.05547i	0.107558	+	0.186295i	−0.807223	+	0.590247i	$0.799030\pi$
$270$	−2.96118	−	5.12891i	−0.180211	−	0.312135i
$271$	13.3677	−	23.1536i	0.812033	−	1.40648i	−0.0994060	−	0.995047i	$-0.531694\pi$
$271$	13.3677	−	23.1536i	0.812033	−	1.40648i	0.911439	−	0.411435i	$-0.134972\pi$
$272$	−21.3968			−1.29737
$273$	0.149527	+	0.230310i	0.00904978	+	0.0139390i
$274$	−35.1267			−2.12208
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	3.46754	+	6.00595i	0.208721	+	0.361516i
$277$	7.15911	+	12.3999i	0.430149	+	0.745040i	0.996886	−	0.0788590i	$-0.0251277\pi$
$277$	7.15911	+	12.3999i	0.430149	+	0.745040i	−0.566737	+	0.823899i	$0.691794\pi$
$278$	−7.57586	+	13.1218i	−0.454370	+	0.786991i
$279$	10.5490			0.631550
$280$	0.348310	−	0.683400i	0.0208155	−	0.0408410i
$281$	−1.61340			−0.0962476			−0.0481238	−	0.998841i	$-0.515324\pi$
$281$	−1.61340			−0.0962476			−0.0481238	+	0.998841i	$0.515324\pi$
$282$	−6.81714	+	11.8076i	−0.405955	+	0.703134i
$283$	3.08437	+	5.34228i	0.183347	+	0.317566i	0.943018	−	0.332741i	$-0.107974\pi$
$283$	3.08437	+	5.34228i	0.183347	+	0.317566i	−0.759671	+	0.650307i	$0.774640\pi$
$284$	4.59053	+	7.95102i	0.272398	+	0.471806i
$285$	−0.995782	+	1.72475i	−0.0589850	+	0.102165i
$286$	−0.386283			−0.0228414
$287$	10.1345	−	0.529948i	0.598223	−	0.0312818i
$288$	21.2529			1.25234
$289$	−4.03368	+	6.98654i	−0.237275	+	0.410973i
$290$	−0.435237	−	0.753853i	−0.0255580	−	0.0442678i
$291$	1.95644	+	3.38865i	0.114688	+	0.198646i
$292$	−2.38978	+	4.13922i	−0.139851	+	0.242229i
$293$	−6.55424			−0.382903			−0.191451	−	0.981502i	$-0.561319\pi$
$293$	−6.55424			−0.382903			−0.191451	+	0.981502i	$0.561319\pi$
$294$	7.20570	−	0.755656i	0.420245	−	0.0440707i
$295$	−11.4815			−0.668478
$296$	−1.48169	+	2.56637i	−0.0861216	+	0.149167i
$297$	−1.50871	−	2.61316i	−0.0875440	−	0.151631i
$298$	−4.22681	−	7.32105i	−0.244852	−	0.424097i
$299$	0.698657	−	1.21011i	0.0404044	−	0.0699824i
$300$	0.976793			0.0563952
$301$	−2.23842	+	0.117049i	−0.129020	+	0.00674662i
$302$	−37.0278			−2.13071
$303$	−0.578272	+	1.00160i	−0.0332208	+	0.0575402i
$304$	−8.06984	−	13.9774i	−0.462837	−	0.801657i
$305$	−3.45561	−	5.98529i	−0.197868	−	0.342717i
$306$	13.3739	−	23.1642i	0.764534	−	1.32421i
$307$	6.43081			0.367026			0.183513	−	0.983017i	$-0.441253\pi$
$307$	6.43081			0.367026			0.183513	+	0.983017i	$0.441253\pi$
$308$	−2.22538	+	4.36629i	−0.126803	+	0.248793i
$309$	−7.22958			−0.411276
$310$	−3.80335	+	6.58759i	−0.216016	+	0.374150i
$311$	15.8190	+	27.3992i	0.897011	+	1.55367i	0.831296	+	0.555829i	$0.187599\pi$
$311$	15.8190	+	27.3992i	0.897011	+	1.55367i	0.0657142	+	0.997838i	$0.479067\pi$
$312$	0.0150446	+	0.0260580i	0.000851732	+	0.00147524i
$313$	−7.03560	+	12.1860i	−0.397676	+	0.688794i	−0.993439	−	0.114366i	$-0.963516\pi$
$313$	−7.03560	+	12.1860i	−0.397676	+	0.688794i	0.595763	+	0.803160i	$0.296850\pi$
$314$	7.57073			0.427241
$315$	3.92151	+	6.04014i	0.220952	+	0.340323i
$316$	10.2855			0.578602
$317$	6.13709	−	10.6297i	0.344693	−	0.597026i	−0.640605	−	0.767871i	$-0.721316\pi$
$317$	6.13709	−	10.6297i	0.344693	−	0.597026i	0.985298	+	0.170845i	$0.0546496\pi$
$318$	0.575829	+	0.997365i	0.0322909	+	0.0559294i
$319$	−0.221751	−	0.384085i	−0.0124157	−	0.0215046i
$320$	−3.38895	+	5.86984i	−0.189448	+	0.328134i
$321$	−3.15884			−0.176309
$322$	−20.0765	−	30.9230i	−1.11882	−	1.72327i
$323$	−18.9084			−1.05209
$324$	−6.08895	+	10.5464i	−0.338275	+	0.585910i
$325$	−0.0984047	−	0.170442i	−0.00545851	−	0.00945441i
$326$	−13.3131	−	23.0589i	−0.737342	−	1.27711i
$327$	−2.83491	+	4.91022i	−0.156771	+	0.271536i
$328$	1.11204			0.0614020
$329$	15.8261	−	31.0515i	0.872521	−	1.71193i
$330$	1.03503			0.0569766
$331$	−11.7480	+	20.3481i	−0.645727	+	1.11843i	0.338407	+	0.941000i	$0.390112\pi$
$331$	−11.7480	+	20.3481i	−0.645727	+	1.11843i	−0.984133	+	0.177431i	$0.943221\pi$
$332$	12.4654	+	21.5907i	0.684126	+	1.18494i
$333$	−13.9111	−	24.0947i	−0.762322	−	1.32038i
$334$	−22.6522	+	39.2347i	−1.23947	+	2.14683i
$335$	8.89066			0.485749
$336$	5.95448	−	0.311367i	0.324844	−	0.0169865i
$337$	−2.46187			−0.134107			−0.0670533	−	0.997749i	$-0.521360\pi$
$337$	−2.46187			−0.134107			−0.0670533	+	0.997749i	$0.521360\pi$
$338$	12.7197	−	22.0312i	0.691861	−	1.19834i
$339$	1.04160	+	1.80411i	0.0565720	+	0.0979856i
$340$	4.63696	+	8.03145i	0.251474	+	0.435566i
$341$	−1.93779	+	3.35635i	−0.104937	+	0.181757i
$342$	20.1759			1.09099
$343$	−18.2933	+	2.89083i	−0.987743	+	0.156090i
$344$	−0.245615			−0.0132427
$345$	−1.87203	+	3.24245i	−0.100787	+	0.174567i
$346$	−3.56073	−	6.16736i	−0.191426	−	0.331559i
$347$	16.7287	+	28.9750i	0.898045	+	1.55546i	0.829991	+	0.557777i	$0.188346\pi$
$347$	16.7287	+	28.9750i	0.898045	+	1.55546i	0.0680542	+	0.997682i	$0.478321\pi$
$348$	0.216605	−	0.375171i	0.0116113	−	0.0201113i
$349$	18.4266			0.986351			0.493176	−	0.869930i	$-0.335836\pi$
$349$	18.4266			0.986351			0.493176	+	0.869930i	$0.335836\pi$
$350$	−5.18580	+	0.271172i	−0.277193	+	0.0144947i
$351$	−0.593855			−0.0316976
$352$	−3.90404	+	6.76199i	−0.208086	+	0.360415i
$353$	3.55513	+	6.15766i	0.189220	+	0.327739i	0.944991	−	0.327098i	$-0.106071\pi$
$353$	3.55513	+	6.15766i	0.189220	+	0.327739i	−0.755770	+	0.654837i	$0.772737\pi$
$354$	−5.94185	−	10.2916i	−0.315806	−	0.546991i
$355$	−2.47830	+	4.29254i	−0.131534	+	0.227824i
$356$	−7.24970			−0.384233
$357$	3.17207	−	6.22375i	0.167884	−	0.329396i
$358$	−16.6009			−0.877385
$359$	0.491910	−	0.852013i	0.0259620	−	0.0449675i	−0.852752	−	0.522315i	$-0.825068\pi$
$359$	0.491910	−	0.852013i	0.0259620	−	0.0449675i	0.878715	+	0.477348i	$0.158402\pi$
$360$	0.394561	+	0.683400i	0.0207952	+	0.0360184i
$361$	2.36866	+	4.10264i	0.124666	+	0.215929i
$362$	−11.5726	+	20.0443i	−0.608240	+	1.05350i
$363$	0.527344			0.0276784
$364$	0.525212	+	0.808961i	0.0275286	+	0.0424011i
$365$	−2.58035			−0.135062
$366$	3.57666	−	6.19496i	0.186955	−	0.323816i
$367$	−0.894621	−	1.54953i	−0.0466988	−	0.0808848i	0.841731	−	0.539897i	$-0.181537\pi$
$367$	−0.894621	−	1.54953i	−0.0466988	−	0.0808848i	−0.888430	+	0.459012i	$0.848203\pi$
$368$	−15.1709	−	26.2768i	−0.790840	−	1.36978i
$369$	−5.22026	+	9.04175i	−0.271756	+	0.470695i
$370$	20.0621			1.04298
$371$	−1.60306	−	2.46913i	−0.0832268	−	0.128191i
$372$	−3.78564			−0.196276
$373$	8.03955	−	13.9249i	0.416272	−	0.721005i	−0.579289	−	0.815122i	$-0.696670\pi$
$373$	8.03955	−	13.9249i	0.416272	−	0.721005i	0.995561	+	0.0941176i	$0.0300030\pi$
$374$	4.91342	+	8.51029i	0.254067	+	0.440057i
$375$	0.263672	+	0.456693i	0.0136160	+	0.0235835i
$376$	1.90950	−	3.30735i	0.0984750	−	0.170564i
$377$	−0.0872855			−0.00449543
$378$	−7.11523	+	13.9604i	−0.365968	+	0.718046i
$379$	25.1846			1.29364			0.646822	−	0.762641i	$-0.276098\pi$
$379$	25.1846			1.29364			0.646822	+	0.762641i	$0.276098\pi$
$380$	−3.49767	+	6.05815i	−0.179427	+	0.310777i
$381$	−4.89361	−	8.47598i	−0.250707	−	0.434238i
$382$	−6.37537	−	11.0425i	−0.326192	−	0.564981i
$383$	18.2595	−	31.6263i	0.933016	−	1.61603i	0.154881	−	0.987933i	$-0.450501\pi$
$383$	18.2595	−	31.6263i	0.933016	−	1.61603i	0.778135	−	0.628097i	$-0.216166\pi$
$384$	1.21974			0.0622448
$385$	−2.64214	+	0.138161i	−0.134656	+	0.00704132i
$386$	9.41804			0.479366
$387$	1.15300	−	1.99705i	0.0586102	−	0.101516i
$388$	6.87196	+	11.9026i	0.348871	+	0.604262i
$389$	4.65214	+	8.05774i	0.235873	+	0.408544i	0.959526	−	0.281620i	$-0.0908718\pi$
$389$	4.65214	+	8.05774i	0.235873	+	0.408544i	−0.723653	+	0.690164i	$0.757538\pi$
$390$	0.101852	−	0.176413i	0.00515747	−	0.00893300i
$391$	−35.5470			−1.79769
$392$	−2.01834	+	0.211661i	−0.101941	+	0.0106905i
$393$	9.34692			0.471490
$394$	−25.9389	+	44.9275i	−1.30678	+	2.26342i
$395$	2.77642	+	4.80890i	0.139697	+	0.241962i
$396$	−2.52088	−	4.36629i	−0.126679	−	0.219415i
$397$	−10.1050	+	17.5024i	−0.507157	+	0.878422i	0.492809	+	0.870138i	$0.335970\pi$
$397$	−10.1050	+	17.5024i	−0.507157	+	0.878422i	−0.999966	+	0.00828413i	$0.997363\pi$
$398$	6.80221			0.340964
$399$	5.26199	−	0.275156i	0.263429	−	0.0137750i
$400$	−4.27360			−0.213680
$401$	12.1906	−	21.1148i	0.608770	−	1.05442i	−0.382673	−	0.923884i	$-0.624996\pi$
$401$	12.1906	−	21.1148i	0.608770	−	1.05442i	0.991443	−	0.130537i	$-0.0416703\pi$
$402$	4.60105	+	7.96926i	0.229480	+	0.397471i
$403$	0.381375	+	0.660561i	0.0189976	+	0.0329049i
$404$	−2.03117	+	3.51810i	−0.101055	+	0.175032i
$405$	−6.57451			−0.326690
$406$	−1.04580	+	2.05192i	−0.0519024	+	0.101835i
$407$	10.2216			0.506664
$408$	0.382727	−	0.662902i	0.0189478	−	0.0328186i
$409$	−8.13980	−	14.0985i	−0.402487	−	0.697128i	0.591538	−	0.806277i	$-0.298521\pi$
$409$	−8.13980	−	14.0985i	−0.402487	−	0.697128i	−0.994025	+	0.109149i	$0.965188\pi$
$410$	−3.76424	−	6.51986i	−0.185903	−	0.321993i
$411$	4.71891	−	8.17339i	0.232767	−	0.403164i
$412$	−25.3938			−1.25106
$413$	16.5416	+	25.4784i	0.813960	+	1.25371i
$414$	37.9299			1.86415
$415$	−6.72971	+	11.6562i	−0.330349	+	0.572181i
$416$	0.768351	+	1.33082i	0.0376715	+	0.0652490i
$417$	−2.03548	−	3.52555i	−0.0996777	−	0.172647i
$418$	−3.70621	+	6.41934i	−0.181277	+	0.313980i
$419$	−16.2893			−0.795783			−0.397892	−	0.917432i	$-0.630258\pi$
$419$	−16.2893			−0.795783			−0.397892	+	0.917432i	$0.630258\pi$
$420$	−1.40729	−	2.16758i	−0.0686686	−	0.105767i
$421$	−23.9106			−1.16533			−0.582667	−	0.812711i	$-0.697991\pi$
$421$	−23.9106			−1.16533			−0.582667	+	0.812711i	$0.697991\pi$
$422$	−18.0611	+	31.2827i	−0.879201	+	1.52282i
$423$	17.9276	+	31.0515i	0.871671	+	1.50978i
$424$	−0.161291	−	0.279365i	−0.00783300	−	0.0135672i
$425$	−2.50337	+	4.33596i	−0.121431	+	0.210325i
$426$	−5.13023			−0.248560
$427$	−8.30328	+	16.2914i	−0.401824	+	0.788397i
$428$	−11.0954			−0.536317
$429$	0.0518931	−	0.0898814i	0.00250542	−	0.00433952i
$430$	0.831408	+	1.44004i	0.0400941	+	0.0694449i
$431$	−3.16644	−	5.48444i	−0.152522	−	0.264176i	0.779632	−	0.626238i	$-0.215406\pi$
$431$	−3.16644	−	5.48444i	−0.152522	−	0.264176i	−0.932154	+	0.362062i	$0.882073\pi$
$432$	−6.44761	+	11.1676i	−0.310211	+	0.537301i
$433$	35.4033			1.70137			0.850687	−	0.525673i	$-0.176187\pi$
$433$	35.4033			1.70137			0.850687	+	0.525673i	$0.176187\pi$
$434$	20.0980	−	1.05095i	0.964733	−	0.0504471i
$435$	0.233878			0.0112136
$436$	−9.95761	+	17.2471i	−0.476883	+	0.825986i
$437$	−13.4066	−	23.2209i	−0.641325	−	1.11081i
$438$	−1.33537	−	2.31293i	−0.0638065	−	0.110516i
$439$	6.08633	−	10.5418i	0.290485	−	0.503134i	−0.683440	−	0.730007i	$-0.739517\pi$
$439$	6.08633	−	10.5418i	0.290485	−	0.503134i	0.973924	+	0.226873i	$0.0728501\pi$
$440$	−0.289915			−0.0138212
$441$	7.75375	−	17.4043i	0.369226	−	0.828777i
$442$	1.93401			0.0919916
$443$	15.1776	−	26.2884i	0.721110	−	1.24900i	−0.239445	−	0.970910i	$-0.576965\pi$
$443$	15.1776	−	26.2884i	0.721110	−	1.24900i	0.960555	−	0.278090i	$-0.0897012\pi$
$444$	4.99217	+	8.64670i	0.236918	+	0.410354i
$445$	−1.95696	−	3.38955i	−0.0927687	−	0.160680i
$446$	0.284593	−	0.492930i	0.0134759	−	0.0233409i
$447$	2.27131			0.107429
$448$	17.9082	−	0.936440i	0.846082	−	0.0442426i
$449$	39.0234			1.84163			0.920814	−	0.390002i	$-0.127526\pi$
$449$	39.0234			1.84163			0.920814	+	0.390002i	$0.127526\pi$
$450$	2.67118	−	4.62662i	0.125921	−	0.218101i
$451$	−1.91787	−	3.32184i	−0.0903088	−	0.156419i
$452$	3.65861	+	6.33690i	0.172087	+	0.298063i
$453$	4.97430	−	8.61574i	0.233713	−	0.404803i
$454$	8.69569			0.408109
$455$	−0.236451	+	0.463927i	−0.0110850	+	0.0217492i
$456$	0.577385			0.0270385
$457$	−13.1156	+	22.7169i	−0.613523	+	1.06265i	0.377118	+	0.926165i	$0.376915\pi$
$457$	−13.1156	+	22.7169i	−0.613523	+	1.06265i	−0.990642	+	0.136488i	$0.956418\pi$
$458$	−4.87565	−	8.44487i	−0.227824	−	0.394603i
$459$	7.55369	+	13.0834i	0.352576	+	0.610679i
$460$	−6.57548	+	11.3891i	−0.306583	+	0.531018i
$461$	4.32824			0.201586			0.100793	−	0.994907i	$-0.467862\pi$
$461$	4.32824			0.201586			0.100793	+	0.994907i	$0.467862\pi$
$462$	−1.49119	−	2.29682i	−0.0693765	−	0.106858i
$463$	24.9440			1.15925			0.579624	−	0.814884i	$-0.303200\pi$
$463$	24.9440			1.15925			0.579624	+	0.814884i	$0.303200\pi$
$464$	−0.947677	+	1.64143i	−0.0439948	+	0.0762013i
$465$	−1.02188	−	1.76995i	−0.0473886	−	0.0820795i
$466$	27.6147	+	47.8300i	1.27922	+	2.21568i
$467$	−0.557154	+	0.965018i	−0.0257820	+	0.0446557i	−0.878629	−	0.477506i	$-0.841541\pi$
$467$	−0.557154	+	0.965018i	−0.0257820	+	0.0446557i	0.852847	+	0.522162i	$0.174874\pi$
$468$	−0.992266			−0.0458675
$469$	−12.8090	−	19.7291i	−0.591463	−	0.911005i
$470$	−25.8546			−1.19259
$471$	−1.01705	+	1.76158i	−0.0468632	+	0.0811694i
$472$	1.66433	+	2.88270i	0.0766069	+	0.132687i
$473$	0.423599	+	0.733695i	0.0194771	+	0.0337353i
$474$	−2.87368	+	4.97736i	−0.131992	+	0.228618i
$475$	−3.77660			−0.173282
$476$	11.1419	−	21.8609i	0.510687	−	1.00199i
$477$	3.02861			0.138671
$478$	8.41648	−	14.5778i	0.384961	−	0.666772i
$479$	−10.0110	−	17.3395i	−0.457412	−	0.792262i	0.541411	−	0.840758i	$-0.317890\pi$
$479$	−10.0110	−	17.3395i	−0.457412	−	0.792262i	−0.998823	+	0.0484966i	$0.984557\pi$
$480$	−2.05877	−	3.56589i	−0.0939696	−	0.162760i
$481$	1.00585	−	1.74218i	0.0458628	−	0.0794366i
$482$	−22.4420			−1.02221
$483$	9.89232	−	0.517281i	0.450116	−	0.0235371i
$484$	1.85229			0.0841950
$485$	−3.70998	+	6.42588i	−0.168462	+	0.291784i
$486$	−12.2859	−	21.2799i	−0.557301	−	0.965274i
$487$	1.44114	+	2.49613i	0.0653044	+	0.113111i	0.896829	−	0.442377i	$-0.145865\pi$
$487$	1.44114	+	2.49613i	0.0653044	+	0.113111i	−0.831525	+	0.555488i	$0.812531\pi$
$488$	−1.00183	+	1.73523i	−0.0453509	+	0.0785500i
$489$	7.15389			0.323510
$490$	8.07304	+	11.1170i	0.364703	+	0.502216i
$491$	−11.3920			−0.514113			−0.257057	−	0.966396i	$-0.582753\pi$
$491$	−11.3920			−0.514113			−0.257057	+	0.966396i	$0.582753\pi$
$492$	1.87336	−	3.24475i	0.0844575	−	0.146285i
$493$	1.11025	+	1.92301i	0.0500031	+	0.0866080i
$494$	0.729417	+	1.26339i	0.0328180	+	0.0568424i
$495$	1.36095	−	2.35724i	0.0611703	−	0.105950i
$496$	16.5627			0.743686
$497$	13.0960	−	0.684807i	0.587437	−	0.0307178i
$498$	−13.9309			−0.624259
$499$	2.42804	−	4.20549i	0.108694	−	0.188263i	−0.806547	−	0.591169i	$-0.798666\pi$
$499$	2.42804	−	4.20549i	0.108694	−	0.188263i	0.915241	+	0.402906i	$0.132000\pi$
$500$	0.926145	+	1.60413i	0.0414185	+	0.0717389i
$501$	−6.08617	−	10.5416i	−0.271910	−	0.470962i
$502$	23.8193	−	41.2563i	1.06311	−	1.84136i
$503$	−16.9049			−0.753753			−0.376876	−	0.926264i	$-0.623002\pi$
$503$	−16.9049			−0.753753			−0.376876	+	0.926264i	$0.623002\pi$
$504$	0.948068	−	1.86015i	0.0422303	−	0.0828578i
$505$	−2.19315			−0.0975939
$506$	−6.96751	+	12.0681i	−0.309744	+	0.536492i
$507$	3.41752	+	5.91932i	0.151777	+	0.262886i
$508$	−17.1888	−	29.7718i	−0.762628	−	1.32091i
$509$	−15.5695	+	26.9671i	−0.690104	+	1.19529i	0.281700	+	0.959503i	$0.409102\pi$
$509$	−15.5695	+	26.9671i	−0.690104	+	1.19529i	−0.971803	+	0.235792i	$0.924232\pi$
$510$	−5.18212			−0.229468
$511$	3.71757	+	5.72601i	0.164455	+	0.253304i
$512$	30.8907			1.36519
$513$	−5.69777	+	9.86883i	−0.251563	+	0.435720i
$514$	22.7428	+	39.3917i	1.00314	+	1.73749i
$515$	−6.85471	−	11.8727i	−0.302055	−	0.523174i
$516$	−0.413768	+	0.716668i	−0.0182151	+	0.0315496i
$517$	−13.1728			−0.579340
$518$	−28.9039	−	44.5194i	−1.26996	−	1.95607i
$519$	1.91339			0.0839884
$520$	−0.0285290	+	0.0494137i	−0.00125108	+	0.00216693i
$521$	3.84572	+	6.66098i	0.168484	+	0.291823i	0.937887	−	0.346941i	$-0.112780\pi$
$521$	3.84572	+	6.66098i	0.168484	+	0.291823i	−0.769403	+	0.638764i	$0.779446\pi$
$522$	−1.18468	−	2.05192i	−0.0518518	−	0.0898100i
$523$	−12.4489	+	21.5621i	−0.544352	+	0.942846i	0.454295	+	0.890851i	$0.349891\pi$
$523$	−12.4489	+	21.5621i	−0.544352	+	0.942846i	−0.998647	+	0.0519944i	$0.983442\pi$
$524$	32.8309			1.43423
$525$	0.633561	−	1.24308i	0.0276509	−	0.0542523i
$526$	49.6407			2.16444
$527$	9.70199	−	16.8043i	0.422625	−	0.732009i
$528$	−1.12683	−	1.95172i	−0.0490389	−	0.0849379i
$529$	−13.7038	−	23.7358i	−0.595820	−	1.03199i
$530$	−1.09194	+	1.89130i	−0.0474309	+	0.0821528i
$531$	−31.2516			−1.35620
$532$	18.4827	−	0.966483i	0.801327	−	0.0419023i
$533$	−0.754908			−0.0326987
$534$	2.02551	−	3.50829i	0.0876524	−	0.151818i
$535$	−2.99505	−	5.18758i	−0.129487	−	0.224279i
$536$	−1.28877	−	2.23221i	−0.0556663	−	0.0964169i
$537$	2.23016	−	3.86275i	0.0962386	−	0.166690i
$538$	−6.92479			−0.298549
$539$	4.11318	+	5.66408i	0.177167	+	0.243969i
$540$	5.58912			0.240517
$541$	5.20344	−	9.01262i	0.223713	−	0.387483i	−0.732219	−	0.681069i	$-0.761515\pi$
$541$	5.20344	−	9.01262i	0.223713	−	0.387483i	0.955933	+	0.293586i	$0.0948488\pi$
$542$	26.2372	+	45.4442i	1.12698	+	1.95200i
$543$	−3.10931	−	5.38548i	−0.133433	−	0.231113i
$544$	19.5465	−	33.8555i	0.838048	−	1.45154i
$545$	−10.7517			−0.460551
$546$	−0.538214	+	0.0281439i	−0.0230334	+	0.00120445i
$547$	−42.7482			−1.82778			−0.913891	−	0.405960i	$-0.866937\pi$
$547$	−42.7482			−1.82778			−0.913891	+	0.405960i	$0.866937\pi$
$548$	16.5751	−	28.7089i	0.708054	−	1.22639i
$549$	−9.40585	−	16.2914i	−0.401432	−	0.695301i
$550$	0.981363	+	1.69977i	0.0418454	+	0.0724784i
$551$	−0.837466	+	1.45053i	−0.0356772	+	0.0617948i
$552$	1.08546			0.0462002
$553$	6.67129	−	13.0894i	0.283692	−	0.556617i
$554$	−28.1027			−1.19397
$555$	−2.69514	+	4.66811i	−0.114402	+	0.198150i
$556$	−7.14959	−	12.3835i	−0.303210	−	0.525175i
$557$	−5.36270	−	9.28846i	−0.227225	−	0.393565i	0.729760	−	0.683704i	$-0.239632\pi$
$557$	−5.36270	−	9.28846i	−0.227225	−	0.393565i	−0.956985	+	0.290139i	$0.906299\pi$
$558$	−10.3524	+	17.9308i	−0.438251	+	0.759072i
$559$	0.166736			0.00705220
$560$	6.15707	+	9.48347i	0.260184	+	0.400750i
$561$	−2.64027			−0.111472
$562$	1.58333	−	2.74241i	0.0667889	−	0.115682i
$563$	−2.60619	−	4.51405i	−0.109838	−	0.190244i	0.805867	−	0.592097i	$-0.201700\pi$
$563$	−2.60619	−	4.51405i	−0.109838	−	0.190244i	−0.915704	+	0.401853i	$0.868366\pi$
$564$	−6.43356	−	11.1433i	−0.270902	−	0.469216i
$565$	−1.97518	+	3.42112i	−0.0830966	+	0.143928i
$566$	−12.1075			−0.508918
$567$	9.47204	+	14.5894i	0.397788	+	0.612696i
$568$	1.43699			0.0602949
$569$	5.27258	−	9.13237i	0.221038	−	0.382849i	−0.734085	−	0.679057i	$-0.762389\pi$
$569$	5.27258	−	9.13237i	0.221038	−	0.382849i	0.955123	+	0.296208i	$0.0957222\pi$
$570$	−1.95445	−	3.38520i	−0.0818627	−	0.141790i
$571$	−12.7892	−	22.1515i	−0.535210	−	0.927011i	−0.999153	−	0.0411462i	$-0.986899\pi$
$571$	−12.7892	−	22.1515i	−0.535210	−	0.927011i	0.463943	−	0.885865i	$-0.346434\pi$
$572$	0.182274	−	0.315708i	0.00762125	−	0.0132004i
$573$	3.42586			0.143117
$574$	−9.04488	+	17.7465i	−0.377526	+	0.740723i
$575$	−7.09984			−0.296084
$576$	−9.22441	+	15.9772i	−0.384351	+	0.665715i
$577$	−7.92141	−	13.7203i	−0.329773	−	0.571183i	0.652694	−	0.757622i	$-0.273639\pi$
$577$	−7.92141	−	13.7203i	−0.329773	−	0.571183i	−0.982467	+	0.186439i	$0.940305\pi$
$578$	−7.91701	−	13.7127i	−0.329304	−	0.570372i
$579$	−1.26522	+	2.19142i	−0.0525806	+	0.0910723i
$580$	0.821496			0.0341107
$581$	35.5617	−	1.85956i	1.47535	−	0.0771477i
$582$	−7.67989			−0.318342
$583$	−0.556340	+	0.963609i	−0.0230412	+	0.0399086i
$584$	0.374041	+	0.647859i	0.0154779	+	0.0268086i
$585$	−0.267848	−	0.463927i	−0.0110742	−	0.0191810i
$586$	6.43208	−	11.1407i	0.265707	−	0.460218i
$587$	−23.1639			−0.956078			−0.478039	−	0.878339i	$-0.658652\pi$
$587$	−23.1639			−0.956078			−0.478039	+	0.878339i	$0.658652\pi$
$588$	−2.78254	+	6.24577i	−0.114750	+	0.257571i
$589$	14.6365			0.603086
$590$	11.2675	−	19.5159i	0.463876	−	0.803456i
$591$	−6.96925	−	12.0711i	−0.286677	−	0.496538i
$592$	−21.8414	−	37.8305i	−0.897677	−	1.55482i
$593$	5.00682	−	8.67207i	0.205606	−	0.356119i	−0.744720	−	0.667377i	$-0.767417\pi$
$593$	5.00682	−	8.67207i	0.205606	−	0.356119i	0.950326	+	0.311258i	$0.100750\pi$
$594$	5.92235			0.242997
$595$	13.2285	−	0.691734i	0.542315	−	0.0283583i
$596$	7.97796			0.326790
$597$	−0.913807	+	1.58276i	−0.0373996	+	0.0647781i
$598$	1.37127	+	2.37511i	0.0560755	+	0.0971256i
$599$	15.8553	+	27.4622i	0.647831	+	1.12208i	0.983640	+	0.180146i	$0.0576571\pi$
$599$	15.8553	+	27.4622i	0.647831	+	1.12208i	−0.335809	+	0.941930i	$0.609010\pi$
$600$	0.0764425	−	0.132402i	0.00312075	−	0.00540530i
$601$	−19.5236			−0.796382			−0.398191	−	0.917302i	$-0.630362\pi$
$601$	−19.5236			−0.796382			−0.398191	+	0.917302i	$0.630362\pi$
$602$	1.99774	−	3.91966i	0.0814218	−	0.159753i
$603$	24.1996			0.985483
$604$	17.4722	−	30.2627i	0.710933	−	1.23137i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−1.13499	−	1.96586i	−0.0461058	−	0.0798575i
$607$	2.25543	−	3.90651i	0.0915450	−	0.158561i	−0.816616	−	0.577181i	$-0.804153\pi$
$607$	2.25543	−	3.90651i	0.0915450	−	0.158561i	0.908161	+	0.418620i	$0.137486\pi$
$608$	29.4880			1.19589
$609$	−0.336954	−	0.518995i	−0.0136541	−	0.0210307i
$610$	13.5648			0.549224
$611$	−1.29627	+	2.24520i	−0.0524414	+	0.0908311i
$612$	12.6214	+	21.8609i	0.510189	+	0.883673i
$613$	20.6515	+	35.7694i	0.834105	+	1.44471i	0.894757	+	0.446553i	$0.147349\pi$
$613$	20.6515	+	35.7694i	0.834105	+	1.44471i	−0.0606523	+	0.998159i	$0.519318\pi$
$614$	−6.31096	+	10.9309i	−0.254690	+	0.441135i
$615$	2.02275			0.0815651
$616$	0.417687	+	0.643345i	0.0168291	+	0.0259211i
$617$	22.8105			0.918314			0.459157	−	0.888355i	$-0.348151\pi$
$617$	22.8105			0.918314			0.459157	+	0.888355i	$0.348151\pi$
$618$	7.09484	−	12.2886i	0.285396	−	0.494321i
$619$	3.82098	+	6.61813i	0.153578	+	0.266005i	0.932540	−	0.361066i	$-0.117587\pi$
$619$	3.82098	+	6.61813i	0.153578	+	0.266005i	−0.778962	+	0.627071i	$0.784254\pi$
$620$	−3.58935	−	6.21693i	−0.144152	−	0.249678i
$621$	−10.7116	+	18.5530i	−0.429840	+	0.744506i
$622$	−62.0965			−2.48984
$623$	−4.70226	+	9.22604i	−0.188392	+	0.369634i
$624$	−0.443541			−0.0177558
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.8089	−	23.9178i	−0.551917	−	0.955948i
$627$	−0.995782	−	1.72475i	−0.0397677	−	0.0688797i
$628$	−3.57238	+	6.18754i	−0.142553	+	0.246910i
$629$	−51.1766			−2.04054
$630$	−14.1153	+	0.738104i	−0.562366	+	0.0294068i
$631$	13.1421			0.523179			0.261590	−	0.965179i	$-0.415753\pi$
$631$	13.1421			0.523179			0.261590	+	0.965179i	$0.415753\pi$
$632$	0.804926	−	1.39417i	0.0320182	−	0.0554572i
$633$	−4.85264	−	8.40503i	−0.192875	−	0.334070i
$634$	12.0454	+	20.8633i	0.478385	+	0.828586i
$635$	9.27973	−	16.0730i	0.368255	−	0.637836i
$636$	−1.08686			−0.0430967
$637$	1.37015	−	0.143687i	0.0542874	−	0.00569307i
$638$	0.870474			0.0344624
$639$	−6.74570	+	11.6839i	−0.266856	+	0.462208i
$640$	1.15650	+	2.00311i	0.0457146	+	0.0791800i
$641$	16.1170	+	27.9154i	0.636582	+	1.10259i	0.986178	+	0.165692i	$0.0529857\pi$
$641$	16.1170	+	27.9154i	0.636582	+	1.10259i	−0.349595	+	0.936901i	$0.613681\pi$
$642$	3.09997	−	5.36931i	0.122346	−	0.211910i
$643$	−18.2564			−0.719961			−0.359981	−	0.932960i	$-0.617217\pi$
$643$	−18.2564			−0.719961			−0.359981	+	0.932960i	$0.617217\pi$
$644$	34.7467	−	1.81695i	1.36921	−	0.0715977i
$645$	−0.446764			−0.0175913
$646$	18.5560	−	32.1399i	0.730076	−	1.26453i
$647$	−14.3749	−	24.8981i	−0.565136	−	0.978844i	−0.997037	−	0.0769231i	$-0.975490\pi$
$647$	−14.3749	−	24.8981i	−0.565136	−	0.978844i	0.431901	−	0.901921i	$-0.357843\pi$
$648$	0.953025	+	1.65069i	0.0374384	+	0.0648452i
$649$	5.74074	−	9.94326i	0.225344	−	0.390307i
$650$	0.386283			0.0151512
$651$	−2.45542	+	4.81764i	−0.0962354	+	0.188818i
$652$	25.1280			0.984086
$653$	7.44641	−	12.8976i	0.291401	−	0.504721i	−0.682741	−	0.730661i	$-0.739212\pi$
$653$	7.44641	−	12.8976i	0.291401	−	0.504721i	0.974141	+	0.225940i	$0.0725454\pi$
$654$	−5.56416	−	9.63740i	−0.217576	−	0.376852i
$655$	8.86226	+	15.3499i	0.346277	+	0.599770i
$656$	−8.19620	+	14.1962i	−0.320008	+	0.554270i
$657$	−7.02348			−0.274012
$658$	37.2493	+	57.3736i	1.45213	+	2.23665i
$659$	11.8423			0.461310			0.230655	−	0.973036i	$-0.425913\pi$
$659$	11.8423			0.461310			0.230655	+	0.973036i	$0.425913\pi$
$660$	−0.488397	+	0.845928i	−0.0190108	+	0.0329277i
$661$	16.1811	+	28.0264i	0.629371	+	1.09010i	0.987678	+	0.156498i	$0.0500206\pi$
$661$	16.1811	+	28.0264i	0.629371	+	1.09010i	−0.358307	+	0.933604i	$0.616646\pi$
$662$	−23.0580	−	39.9377i	−0.896176	−	1.55222i
$663$	−0.259815	+	0.450012i	−0.0100904	+	0.0174770i
$664$	3.90209			0.151431
$665$	5.44102	+	8.38057i	0.210994	+	0.324985i
$666$	54.6072			2.11599
$667$	−1.57440	+	2.72694i	−0.0609610	+	0.105588i
$668$	−21.3776	−	37.0271i	−0.827125	−	1.43262i
$669$	0.0764643	+	0.132440i	0.00295628	+	0.00512043i
$670$	−8.72496	+	15.1121i	−0.337075	+	0.583831i
$671$	6.91122			0.266805
$672$	−4.94689	+	9.70604i	−0.190831	+	0.374419i
$673$	−14.3303			−0.552391			−0.276196	−	0.961101i	$-0.589074\pi$
$673$	−14.3303			−0.552391			−0.276196	+	0.961101i	$0.589074\pi$
$674$	2.41599	−	4.18461i	0.0930603	−	0.161185i
$675$	1.50871	+	2.61316i	0.0580701	+	0.100580i
$676$	12.0040	+	20.7916i	0.461693	+	0.799675i
$677$	1.28227	−	2.22096i	0.0492817	−	0.0853585i	−0.840332	−	0.542072i	$-0.817640\pi$
$677$	1.28227	−	2.22096i	0.0492817	−	0.0853585i	0.889614	+	0.456713i	$0.150973\pi$
$678$	−4.08875			−0.157028
$679$	19.6046	−	1.02515i	0.752355	−	0.0393416i
$680$	1.45153			0.0556635
$681$	−1.16818	+	2.02334i	−0.0447646	+	0.0775346i
$682$	−3.80335	−	6.58759i	−0.145638	−	0.252252i
$683$	−12.2013	−	21.1333i	−0.466871	−	0.808644i	0.532413	−	0.846485i	$-0.321285\pi$
$683$	−12.2013	−	21.1333i	−0.466871	−	0.808644i	−0.999284	+	0.0378404i	$0.987952\pi$
$684$	−9.52035	+	16.4897i	−0.364020	+	0.630501i
$685$	17.8969			0.683805
$686$	13.0386	−	33.9313i	0.497815	−	1.29550i
$687$	2.61997			0.0999582
$688$	1.81029	−	3.13552i	0.0690168	−	0.119541i
$689$	0.109493	+	0.189647i	0.00417135	+	0.00722498i
$690$	−3.67427	−	6.36403i	−0.139877	−	0.242275i
$691$	2.61043	−	4.52140i	0.0993055	−	0.172002i	−0.812092	−	0.583530i	$-0.801671\pi$
$691$	2.61043	−	4.52140i	0.0993055	−	0.172002i	0.911397	+	0.411527i	$0.135005\pi$
$692$	6.72076			0.255485
$693$	−7.19167	+	0.376061i	−0.273189	+	0.0142854i
$694$	−65.6678			−2.49271
$695$	3.85987	−	6.68549i	0.146413	−	0.253595i
$696$	−0.0339024	−	0.0587208i	−0.00128507	−	0.00222580i
$697$	9.60224	+	16.6316i	0.363711	+	0.629966i
$698$	−18.0831	+	31.3209i	−0.684457	+	1.18551i
$699$	−14.8390			−0.561262
$700$	2.22538	−	4.36629i	0.0841114	−	0.165030i
$701$	−26.0062			−0.982241			−0.491120	−	0.871092i	$-0.663412\pi$
$701$	−26.0062			−0.982241			−0.491120	+	0.871092i	$0.663412\pi$
$702$	0.582787	−	1.00942i	0.0219959	−	0.0380980i
$703$	−19.3013	−	33.4309i	−0.727964	−	1.26087i
$704$	−3.38895	−	5.86984i	−0.127726	−	0.221228i
$705$	3.47330	−	6.01594i	0.130812	−	0.226573i
$706$	−13.9555			−0.525221
$707$	3.15972	+	4.86678i	0.118833	+	0.183034i
$708$	11.2150			0.421487
$709$	21.1256	−	36.5905i	0.793387	−	1.37419i	−0.130471	−	0.991452i	$-0.541649\pi$
$709$	21.1256	−	36.5905i	0.793387	−	1.37419i	0.923858	−	0.382734i	$-0.125018\pi$
$710$	−4.86422	−	8.42507i	−0.182551	−	0.316187i
$711$	7.55716	+	13.0894i	0.283416	+	0.490890i
$712$	−0.567352	+	0.982682i	−0.0212624	+	0.0368276i
$713$	27.5160			1.03048
$714$	7.46599	+	11.4995i	0.279408	+	0.430360i
$715$	0.196809			0.00736025
$716$	7.83342	−	13.5679i	0.292749	−	0.507055i
$717$	2.26133	+	3.91675i	0.0844511	+	0.146274i
$718$	0.965484	+	1.67227i	0.0360316	+	0.0624085i
$719$	−18.8008	+	32.5639i	−0.701150	+	1.21443i	0.266913	+	0.963721i	$0.413996\pi$
$719$	−18.8008	+	32.5639i	−0.701150	+	1.21443i	−0.968063	+	0.250707i	$0.919337\pi$
$720$	−11.6324			−0.433512
$721$	−16.4708	+	32.3164i	−0.613404	+	1.20353i
$722$	−9.29806			−0.346038
$723$	3.01485	−	5.22188i	0.112124	−	0.194204i
$724$	−10.9214	−	18.9164i	−0.405891	−	0.703024i
$725$	0.221751	+	0.384085i	0.00823564	+	0.0142645i
$726$	−0.517515	+	0.896363i	−0.0192068	+	0.0332671i
$727$	1.68321			0.0624267			0.0312134	−	0.999513i	$-0.490063\pi$
$727$	1.68321			0.0624267			0.0312134	+	0.999513i	$0.490063\pi$
$728$	0.150755	−	0.00788318i	0.00558736	−	0.000292170i
$729$	−13.1216			−0.485985
$730$	2.53226	−	4.38600i	0.0937231	−	0.162333i
$731$	−2.12085	−	3.67341i	−0.0784423	−	0.135866i
$732$	3.37542	+	5.84639i	0.124759	+	0.216089i
$733$	−22.6708	+	39.2669i	−0.837364	+	1.45036i	0.0547264	+	0.998501i	$0.482571\pi$
$733$	−22.6708	+	39.2669i	−0.837364	+	1.45036i	−0.892091	+	0.451856i	$0.850762\pi$
$734$	3.51179			0.129623
$735$	−3.67127	+	0.385003i	−0.135417	+	0.0142011i
$736$	55.4361			2.04340
$737$	−4.44533	+	7.69954i	−0.163746	+	0.283616i
$738$	−10.2459	−	17.7465i	−0.377158	−	0.653256i
$739$	16.4648	+	28.5179i	0.605668	+	1.04905i	0.991946	+	0.126665i	$0.0404273\pi$
$739$	16.4648	+	28.5179i	0.605668	+	1.04905i	−0.386278	+	0.922383i	$0.626239\pi$
$740$	−9.46664	+	16.3967i	−0.348001	+	0.602755i
$741$	−0.391958			−0.0143989
$742$	5.77013	−	0.301727i	0.211828	−	0.0110768i
$743$	13.6169			0.499557			0.249779	−	0.968303i	$-0.419642\pi$
$743$	13.6169			0.499557			0.249779	+	0.968303i	$0.419642\pi$
$744$	−0.296259	+	0.513135i	−0.0108614	+	0.0188125i
$745$	2.15354	+	3.73004i	0.0788996	+	0.136658i
$746$	15.7794	+	27.3308i	0.577726	+	1.00065i
$747$	−18.3177	+	31.7271i	−0.670208	+	1.16083i
$748$	−9.27392			−0.339088
$749$	−7.19663	+	14.1201i	−0.262959	+	0.515938i
$750$	−1.03503			−0.0377940
$751$	1.80669	−	3.12927i	0.0659269	−	0.114189i	−0.831178	−	0.556007i	$-0.812333\pi$
$751$	1.80669	−	3.12927i	0.0659269	−	0.114189i	0.897105	+	0.441818i	$0.145666\pi$
$752$	28.1477	+	48.7533i	1.02644	+	1.77785i
$753$	6.39976	+	11.0847i	0.233220	+	0.403949i
$754$	0.0856587	−	0.148365i	0.00311951	−	0.00540314i
$755$	18.8655			0.686585
$756$	−8.05237	−	12.4027i	−0.292862	−	0.451082i
$757$	−5.98671			−0.217591			−0.108795	−	0.994064i	$-0.534699\pi$
$757$	−5.98671			−0.217591			−0.108795	+	0.994064i	$0.534699\pi$
$758$	−24.7152	+	42.8080i	−0.897696	+	1.55486i
$759$	−1.87203	−	3.24245i	−0.0679503	−	0.117693i
$760$	0.547446	+	0.948205i	0.0198580	+	0.0343950i
$761$	8.39535	−	14.5412i	0.304331	−	0.527117i	−0.672781	−	0.739842i	$-0.734900\pi$
$761$	8.39535	−	14.5412i	0.304331	−	0.527117i	0.977112	+	0.212725i	$0.0682337\pi$
$762$	19.2096			0.695891
$763$	15.4902	+	23.8588i	0.560782	+	0.863748i
$764$	12.0333			0.435349
$765$	−6.81393	+	11.8021i	−0.246358	+	0.426705i
$766$	35.8383	+	62.0738i	1.29489	+	2.24282i
$767$	−1.12983	−	1.95693i	−0.0407959	−	0.0706605i
$768$	−4.77129	+	8.26412i	−0.172169	+	0.298206i
$769$	−52.6831			−1.89980			−0.949900	−	0.312554i	$-0.898815\pi$
$769$	−52.6831			−1.89980			−0.949900	+	0.312554i	$0.898815\pi$
$770$	2.35806	−	4.62662i	0.0849785	−	0.166732i
$771$	−12.2211			−0.440131
$772$	−4.44406	+	7.69734i	−0.159945	+	0.277033i
$773$	20.9022	+	36.2036i	0.751799	+	1.30215i	0.946950	+	0.321380i	$0.104147\pi$
$773$	20.9022	+	36.2036i	0.751799	+	1.30215i	−0.195152	+	0.980773i	$0.562520\pi$
$774$	2.26302	+	3.91966i	0.0813425	+	0.140889i
$775$	1.93779	−	3.35635i	0.0696075	−	0.120564i
$776$	2.15116			0.0772221
$777$	14.2419	−	0.744724i	0.510924	−	0.0267168i
$778$	−18.2617			−0.654715
$779$	−7.24301	+	12.5453i	−0.259508	+	0.449480i
$780$	0.0961210	+	0.166486i	0.00344168	+	0.00596117i
$781$	−2.47830	−	4.29254i	−0.0886805	−	0.153599i
$782$	34.8845	−	60.4217i	1.24747	−	2.16068i
$783$	1.33823			0.0478245
$784$	12.1740	−	27.3261i	0.434785	−	0.975932i
$785$	−3.85725			−0.137671
$786$	−9.17271	+	15.8876i	−0.327180	+	0.566692i
$787$	−12.5230	−	21.6905i	−0.446398	−	0.773184i	0.551751	−	0.834009i	$-0.313960\pi$
$787$	−12.5230	−	21.6905i	−0.446398	−	0.773184i	−0.998148	+	0.0608254i	$0.980627\pi$
$788$	−24.4794	−	42.3996i	−0.872043	−	1.51042i
$789$	−6.66872	+	11.5506i	−0.237413	+	0.411211i
$790$	−10.8987			−0.387758
$791$	10.4374	−	0.545786i	0.371112	−	0.0194059i
$792$	−0.789123			−0.0280402
$793$	0.680096	−	1.17796i	0.0241509	−	0.0418306i
$794$	−19.8334	−	34.3525i	−0.703861	−	1.21912i
$795$	−0.293382	−	0.508153i	−0.0104052	−	0.0180223i
$796$	−3.20974	+	5.55943i	−0.113766	+	0.197049i
$797$	−30.2429			−1.07126			−0.535630	−	0.844453i	$-0.679926\pi$
$797$	−30.2429			−1.07126			−0.535630	+	0.844453i	$0.679926\pi$
$798$	−4.69622	+	9.21421i	−0.166244	+	0.326179i
$799$	65.9528			2.33324
$800$	3.90404	−	6.76199i	0.138029	−	0.239073i
$801$	−5.32666	−	9.22604i	−0.188208	−	0.325986i
$802$	23.9268	+	41.4425i	0.844886	+	1.46339i
$803$	1.29018	−	2.23465i	0.0455293	−	0.0788591i
$804$	−8.68434			−0.306273
$805$	10.2289	+	15.7551i	0.360521	+	0.555295i
$806$	−1.49707			−0.0527320
$807$	0.930274	−	1.61128i	0.0327472	−	0.0567198i
$808$	0.317914	+	0.550643i	0.0111842	+	0.0193715i
$809$	−10.2270	−	17.7136i	−0.359561	−	0.622777i	0.628327	−	0.777949i	$-0.283740\pi$
$809$	−10.2270	−	17.7136i	−0.359561	−	0.622777i	−0.987887	+	0.155172i	$0.950407\pi$
$810$	6.45198	−	11.1752i	0.226699	−	0.392655i
$811$	−15.5933			−0.547554			−0.273777	−	0.961793i	$-0.588273\pi$
$811$	−15.5933			−0.547554			−0.273777	+	0.961793i	$0.588273\pi$
$812$	−1.18355	−	1.82297i	−0.0415343	−	0.0639735i
$813$	−14.0988			−0.494466
$814$	−10.0311	+	17.3743i	−0.351588	+	0.608969i
$815$	6.78294	+	11.7484i	0.237596	+	0.411529i
$816$	5.64173	+	9.77176i	0.197500	+	0.342080i
$817$	1.59976	−	2.77087i	0.0559686	−	0.0969404i
$818$	31.9524			1.11719
$819$	−0.643597	+	1.26277i	−0.0224891	+	0.0441247i
$820$	7.10489			0.248113
$821$	−1.85510	+	3.21313i	−0.0647434	+	0.112139i	−0.896580	−	0.442882i	$-0.853956\pi$
$821$	−1.85510	+	3.21313i	−0.0647434	+	0.112139i	0.831837	+	0.555020i	$0.187290\pi$
$822$	9.26192	+	16.0421i	0.323047	+	0.559533i
$823$	−10.4614	−	18.1197i	−0.364663	−	0.631615i	0.624059	−	0.781377i	$-0.285482\pi$
$823$	−10.4614	−	18.1197i	−0.364663	−	0.631615i	−0.988722	+	0.149762i	$0.952149\pi$
$824$	−1.98728	+	3.44208i	−0.0692304	+	0.119910i
$825$	−0.527344			−0.0183598
$826$	−59.5407	+	3.11345i	−2.07169	+	0.108331i
$827$	−3.95828			−0.137643			−0.0688215	−	0.997629i	$-0.521924\pi$
$827$	−3.95828			−0.137643			−0.0688215	+	0.997629i	$0.521924\pi$
$828$	−17.8978	+	31.0000i	−0.621993	+	1.07732i
$829$	−19.9882	−	34.6207i	−0.694220	−	1.20242i	−0.970443	−	0.241331i	$-0.922416\pi$
$829$	−19.9882	−	34.6207i	−0.694220	−	1.20242i	0.276222	−	0.961094i	$-0.410917\pi$
$830$	−13.2086	−	22.8779i	−0.458476	−	0.794104i
$831$	3.77531	−	6.53903i	0.130964	−	0.226836i
$832$	−1.33395			−0.0462465
$833$	−20.5936	−	28.3585i	−0.713526	−	0.982564i
$834$	7.99016			0.276677
$835$	11.5412	−	19.9899i	0.399399	−	0.691780i
$836$	−3.49767	−	6.05815i	−0.120970	−	0.209525i
$837$	−5.84711	−	10.1275i	−0.202106	−	0.350057i
$838$	15.9857	−	27.6880i	0.552216	−	0.956467i
$839$	9.67953			0.334174			0.167087	−	0.985942i	$-0.446564\pi$
$839$	9.67953			0.334174			0.167087	+	0.985942i	$0.446564\pi$
$840$	−0.403944	+	0.0211227i	−0.0139374	+	0.000728802i
$841$	−28.8033			−0.993217
$842$	23.4650	−	40.6426i	0.808658	−	1.40064i
$843$	0.425409	+	0.736830i	0.0146519	+	0.0253778i
$844$	−17.0449	−	29.5226i	−0.586708	−	1.01621i
$845$	−6.48063	+	11.2248i	−0.222941	+	0.386144i
$846$	−70.3740			−2.41951
$847$	1.20142	−	2.35724i	0.0412813	−	0.0809958i
$848$	4.75515			0.163293
$849$	1.62652	−	2.81722i	0.0558221	−	0.0966867i
$850$	−4.91342	−	8.51029i	−0.168529	−	0.291901i
$851$	−36.2857	−	62.8487i	−1.24386	−	2.15442i
$852$	2.42078	−	4.19292i	0.0829347	−	0.143647i
$853$	30.1771			1.03325			0.516623	−	0.856213i	$-0.327189\pi$
$853$	30.1771			1.03325			0.516623	+	0.856213i	$0.327189\pi$
$854$	−19.5431	−	30.1014i	−0.668752	−	1.03005i
$855$	−10.2795			−0.351553
$856$	−0.868311	+	1.50396i	−0.0296783	+	0.0514043i
$857$	22.3634	+	38.7345i	0.763919	+	1.32315i	0.940816	+	0.338917i	$0.110060\pi$
$857$	22.3634	+	38.7345i	0.763919	+	1.32315i	−0.176898	+	0.984229i	$0.556606\pi$
$858$	0.101852	+	0.176413i	0.00347716	+	0.00602263i
$859$	10.8447	−	18.7836i	0.370017	−	0.640889i	−0.619551	−	0.784957i	$-0.712685\pi$
$859$	10.8447	−	18.7836i	0.370017	−	0.640889i	0.989568	+	0.144068i	$0.0460184\pi$
$860$	−1.56926			−0.0535112
$861$	−2.91422	−	4.48864i	−0.0993163	−	0.152973i
$862$	12.4297			0.423358
$863$	10.0970	−	17.4886i	0.343707	−	0.595317i	−0.641411	−	0.767197i	$-0.721651\pi$
$863$	10.0970	−	17.4886i	0.343707	−	0.595317i	0.985118	+	0.171880i	$0.0549841\pi$
$864$	−11.7801	−	20.4037i	−0.400767	−	0.694149i
$865$	1.81418	+	3.14224i	0.0616838	+	0.106840i
$866$	−34.7435	+	60.1774i	−1.18063	+	2.04491i
$867$	4.25427			0.144483
$868$	−8.62463	+	16.9219i	−0.292739	+	0.574367i
$869$	−5.55284			−0.188367
$870$	−0.229520	+	0.397539i	−0.00778144	+	0.0134778i
$871$	0.874883	+	1.51534i	0.0296443	+	0.0513454i
$872$	1.55854	+	2.69947i	0.0527787	+	0.0914154i
$873$	−10.0982	+	17.4907i	−0.341773	+	0.591969i
$874$	52.6270			1.78013
$875$	2.64214	−	0.138161i	0.0893207	−	0.00467069i
$876$	2.52047			0.0851587
$877$	19.0808	−	33.0489i	0.644313	−	1.11598i	−0.340147	−	0.940372i	$-0.610477\pi$
$877$	19.0808	−	33.0489i	0.644313	−	1.11598i	0.984460	−	0.175610i	$-0.0561899\pi$
$878$	11.9458	+	20.6907i	0.403151	+	0.698278i
$879$	1.72817	+	2.99327i	0.0582896	+	0.100961i
$880$	2.13680	−	3.70105i	0.0720316	−	0.124762i
$881$	−0.0571827			−0.00192653			−0.000963266	−	1.00000i	$-0.500307\pi$
$881$	−0.0571827			−0.00192653			−0.000963266		1.00000i	$0.500307\pi$
$882$	21.9741	+	30.2595i	0.739906	+	1.01889i
$883$	−47.5184			−1.59912			−0.799560	−	0.600586i	$-0.794934\pi$
$883$	−47.5184			−1.59912			−0.799560	+	0.600586i	$0.794934\pi$
$884$	−0.912597	+	1.58066i	−0.0306939	+	0.0531635i
$885$	3.02735	+	5.24352i	0.101763	+	0.176259i
$886$	29.7895	+	51.5969i	1.00080	+	1.73343i
$887$	2.51653	−	4.35876i	0.0844968	−	0.146353i	−0.820680	−	0.571388i	$-0.806405\pi$
$887$	2.51653	−	4.35876i	0.0844968	−	0.146353i	0.905177	+	0.425036i	$0.139738\pi$
$888$	1.56272			0.0524415
$889$	−49.0367	+	2.56419i	−1.64464	+	0.0860002i
$890$	7.68194			0.257499
$891$	3.28726	−	5.69369i	0.110127	−	0.190746i
$892$	0.268580	+	0.465194i	0.00899272	+	0.0155759i
$893$	24.8742	+	43.0834i	0.832384	+	1.44173i
$894$	−2.22898	+	3.86071i	−0.0745483	+	0.129121i
$895$	8.45809			0.282723
$896$	2.77888	−	5.45229i	0.0928358	−	0.182148i
$897$	−0.736865			−0.0246032
$898$	−38.2961	+	66.3308i	−1.27796	+	2.21349i
$899$	−0.859415	−	1.48855i	−0.0286631	−	0.0496459i
$900$	2.52088	+	4.36629i	0.0840294	+	0.145543i
$901$	2.78545	−	4.82453i	0.0927966	−	0.160728i
$902$	7.52849			0.250671
$903$	0.643663	+	0.991406i	0.0214198	+	0.0329919i
$904$	1.14527			0.0380912
$905$	5.89617	−	10.2125i	0.195995	−	0.339474i
$906$	9.76318	+	16.9103i	0.324360	+	0.561808i
$907$	−13.2901	−	23.0192i	−0.441291	−	0.764339i	0.556494	−	0.830852i	$-0.312146\pi$
$907$	−13.2901	−	23.0192i	−0.441291	−	0.764339i	−0.997786	+	0.0665123i	$0.978813\pi$
$908$	−4.10321	+	7.10696i	−0.136170	+	0.235853i
$909$	−5.96955			−0.197998
$910$	−0.556526	−	0.857192i	−0.0184486	−	0.0284157i
$911$	−24.8730			−0.824078			−0.412039	−	0.911166i	$-0.635183\pi$
$911$	−24.8730			−0.824078			−0.412039	+	0.911166i	$0.635183\pi$
$912$	−4.25558	+	7.37088i	−0.140916	+	0.244074i
$913$	−6.72971	−	11.6562i	−0.222721	−	0.385764i
$914$	−25.7424	−	44.5871i	−0.851482	−	1.47481i
$915$	−1.82229	+	3.15631i	−0.0602432	+	0.104344i
$916$	9.20263			0.304063
$917$	21.2946	−	41.7810i	0.703210	−	1.37973i
$918$	−29.6516			−0.978649
$919$	17.7754	−	30.7879i	0.586357	−	1.01560i	−0.408348	−	0.912826i	$-0.633895\pi$
$919$	17.7754	−	30.7879i	0.586357	−	1.01560i	0.994705	−	0.102773i	$-0.0327716\pi$
$920$	1.02918	+	1.78258i	0.0339309	+	0.0587701i
$921$	−1.69562	−	2.93691i	−0.0558727	−	0.0967744i
$922$	−4.24757	+	7.35701i	−0.139886	+	0.242290i
$923$	−0.975504			−0.0321091
$924$	2.58083	−	0.134954i	0.0849029	−	0.00443968i
$925$	−10.2216			−0.336083
$926$	−24.4791	+	42.3991i	−0.804434	+	1.39332i
$927$	−18.6579	−	32.3164i	−0.612806	−	1.06141i
$928$	−1.73145	−	2.99896i	−0.0568377	−	0.0984458i
$929$	−15.9366	+	27.6030i	−0.522862	+	0.905624i	0.476784	+	0.879020i	$0.341802\pi$
$929$	−15.9366	+	27.6030i	−0.522862	+	0.905624i	−0.999646	+	0.0266031i	$0.991531\pi$
$930$	4.01134			0.131537
$931$	10.7582	−	24.1481i	0.352585	−	0.791423i
$932$	−52.1218			−1.70731
$933$	8.34203	−	14.4488i	0.273106	−	0.473033i
$934$	−1.09354	−	1.89407i	−0.0357817	−	0.0619757i
$935$	−2.50337	−	4.33596i	−0.0818688	−	0.141801i
$936$	−0.0776533	+	0.134500i	−0.00253818	+	0.00439625i
$937$	61.0225			1.99352			0.996759	−	0.0804484i	$-0.0256352\pi$
$937$	61.0225			1.99352			0.996759	+	0.0804484i	$0.0256352\pi$
$938$	46.1052	−	2.41090i	1.50539	−	0.0787185i
$939$	7.42036			0.242154
$940$	12.1999	−	21.1309i	0.397918	−	0.689215i
$941$	−11.7300	−	20.3169i	−0.382387	−	0.662314i	0.609016	−	0.793158i	$-0.291565\pi$
$941$	−11.7300	−	20.3169i	−0.382387	−	0.662314i	−0.991403	+	0.130844i	$0.958231\pi$
$942$	−1.99619	−	3.45750i	−0.0650393	−	0.112651i
$943$	−13.6165	+	23.5845i	−0.443415	+	0.768018i
$944$	−49.0673			−1.59701
$945$	3.62518	−	7.11277i	0.117927	−	0.231378i
$946$	−1.66282			−0.0540628
$947$	−11.9801	+	20.7501i	−0.389301	+	0.674289i	−0.992356	−	0.123411i	$-0.960617\pi$
$947$	−11.9801	+	20.7501i	−0.389301	+	0.674289i	0.603055	+	0.797700i	$0.293950\pi$
$948$	−2.71199	−	4.69730i	−0.0880812	−	0.152561i
$949$	−0.253919	−	0.439800i	−0.00824254	−	0.0142765i
$950$	3.70621	−	6.41934i	0.120245	−	0.208271i
$951$	−6.47271			−0.209892
$952$	−2.09125	−	3.22106i	−0.0677777	−	0.104395i
$953$	−40.1238			−1.29974			−0.649869	−	0.760046i	$-0.725176\pi$
$953$	−40.1238			−1.29974			−0.649869	+	0.760046i	$0.725176\pi$
$954$	−2.97217	+	5.14794i	−0.0962275	+	0.166671i
$955$	3.24822	+	5.62608i	0.105110	+	0.182056i
$956$	7.94292	+	13.7575i	0.256892	+	0.444950i
$957$	−0.116939	+	0.202545i	−0.00378011	+	0.00654734i
$958$	39.2975			1.26965
$959$	−25.7844	−	39.7147i	−0.832623	−	1.28245i
$960$	3.57428			0.115360
$961$	7.98994	−	13.8390i	0.257740	−	0.446419i
$962$	1.97420	+	3.41942i	0.0636509	+	0.110247i
$963$	−8.15226	−	14.1201i	−0.262703	−	0.455015i
$964$	10.5896	−	18.3418i	0.341069	−	0.590750i
$965$	−4.79845			−0.154468
$966$	−8.82869	+	17.3223i	−0.284059	+	0.557336i
$967$	−4.33561			−0.139424			−0.0697119	−	0.997567i	$-0.522208\pi$
$967$	−4.33561			−0.139424			−0.0697119	+	0.997567i	$0.522208\pi$
$968$	0.144958	−	0.251074i	0.00465911	−	0.00806982i
$969$	4.98561	+	8.63534i	0.160161	+	0.277407i
$970$	−7.28167	−	12.6122i	−0.233800	−	0.404954i
$971$	−2.86563	+	4.96342i	−0.0919625	+	0.159284i	−0.908337	−	0.418239i	$-0.862647\pi$
$971$	−2.86563	+	4.96342i	−0.0919625	+	0.159284i	0.816374	+	0.577523i	$0.195981\pi$
$972$	23.1893			0.743797
$973$	−20.3966	+	1.06656i	−0.653886	+	0.0341925i
$974$	−5.65713			−0.181266
$975$	−0.0518931	+	0.0898814i	−0.00166191	+	0.00287851i
$976$	−14.7679	−	25.5788i	−0.472709	−	0.818756i
$977$	21.6457	+	37.4914i	0.692506	+	1.19946i	0.971014	+	0.239022i	$0.0768267\pi$
$977$	21.6457	+	37.4914i	0.692506	+	1.19946i	−0.278508	+	0.960434i	$0.589840\pi$
$978$	−7.02055	+	12.1600i	−0.224493	+	0.388833i
$979$	3.91391			0.125089
$980$	−12.8953	+	1.35232i	−0.411926	+	0.0431983i
$981$	−29.2651			−0.934362
$982$	11.1797	−	19.3638i	0.356758	−	0.617923i
$983$	9.64464	+	16.7050i	0.307616	+	0.532807i	0.977840	−	0.209352i	$-0.0671354\pi$
$983$	9.64464	+	16.7050i	0.307616	+	0.532807i	−0.670224	+	0.742159i	$0.733802\pi$
$984$	−0.293213	−	0.507859i	−0.00934728	−	0.0161900i
$985$	13.2158	−	22.8904i	0.421089	−	0.729348i
$986$	−4.35823			−0.138794
$987$	−18.3539	+	0.959749i	−0.584212	+	0.0305491i
$988$	−1.37675			−0.0438002
$989$	3.00748	−	5.20911i	0.0956324	−	0.165640i
$990$	2.67118	+	4.62662i	0.0848956	+	0.147044i
$991$	−3.75156	−	6.49790i	−0.119172	−	0.206413i	0.800268	−	0.599643i	$-0.204691\pi$
$991$	−3.75156	−	6.49790i	−0.119172	−	0.206413i	−0.919440	+	0.393230i	$0.871357\pi$
$992$	−15.1304	+	26.2066i	−0.480391	+	0.832062i
$993$	12.3904			0.393198
$994$	−11.6879	+	22.9323i	−0.370719	+	0.727368i
$995$	−3.46570			−0.109870
$996$	6.57354	−	11.3857i	0.208291	−	0.360770i
$997$	6.42181	+	11.1229i	0.203381	+	0.352266i	0.949616	−	0.313417i	$-0.101474\pi$
$997$	6.42181	+	11.1229i	0.203381	+	0.352266i	−0.746235	+	0.665683i	$0.768140\pi$
$998$	4.76557	+	8.25421i	0.150852	+	0.261283i
$999$	−15.4213	+	26.7105i	−0.487909	+	0.845083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.b.331.1	yes	12
7.2	even	3		2695.2.a.r.1.6		6
7.4	even	3	inner	385.2.i.b.221.1	✓	12
7.5	odd	6		2695.2.a.q.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.b.221.1	✓	12	7.4	even	3	inner
385.2.i.b.331.1	yes	12	1.1	even	1	trivial
2695.2.a.q.1.6		6	7.5	odd	6
2695.2.a.r.1.6		6	7.2	even	3

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.981363 + 1.69977i) q^{2} +(-0.263672 - 0.456693i) q^{3} +(-0.926145 - 1.60413i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.03503 q^{6} +(-2.64214 + 0.138161i) q^{7} -0.289915 q^{8} +(1.36095 - 2.35724i) q^{9} +O(q^{10})\)	\(q+(-0.981363 + 1.69977i) q^{2} +(-0.263672 - 0.456693i) q^{3} +(-0.926145 - 1.60413i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.03503 q^{6} +(-2.64214 + 0.138161i) q^{7} -0.289915 q^{8} +(1.36095 - 2.35724i) q^{9} +(0.981363 + 1.69977i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.488397 + 0.845928i) q^{12} +0.196809 q^{13} +(2.35806 - 4.62662i) q^{14} -0.527344 q^{15} +(2.13680 - 3.70105i) q^{16} +(-2.50337 - 4.33596i) q^{17} +(2.67118 + 4.62662i) q^{18} +(1.88830 - 3.27063i) q^{19} -1.85229 q^{20} +(0.759755 + 1.17022i) q^{21} -1.96273 q^{22} +(3.54992 - 6.14864i) q^{23} +(0.0764425 + 0.132402i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.193141 + 0.334531i) q^{26} -3.01741 q^{27} +(2.66863 + 4.11038i) q^{28} -0.443503 q^{29} +(0.517515 - 0.896363i) q^{30} +(1.93779 + 3.35635i) q^{31} +(3.90404 + 6.76199i) q^{32} +(0.263672 - 0.456693i) q^{33} +9.82684 q^{34} +(-1.20142 + 2.35724i) q^{35} -5.04176 q^{36} +(5.11078 - 8.85213i) q^{37} +(3.70621 + 6.41934i) q^{38} +(-0.0518931 - 0.0898814i) q^{39} +(-0.144958 + 0.251074i) q^{40} -3.83573 q^{41} +(-2.73470 + 0.143001i) q^{42} +0.847198 q^{43} +(0.926145 - 1.60413i) q^{44} +(-1.36095 - 2.35724i) q^{45} +(6.96751 + 12.0681i) q^{46} +(-6.58641 + 11.4080i) q^{47} -2.25366 q^{48} +(6.96182 - 0.730081i) q^{49} +1.96273 q^{50} +(-1.32013 + 2.28654i) q^{51} +(-0.182274 - 0.315708i) q^{52} +(0.556340 + 0.963609i) q^{53} +(2.96118 - 5.12891i) q^{54} +1.00000 q^{55} +(0.765997 - 0.0400549i) q^{56} -1.99156 q^{57} +(0.435237 - 0.753853i) q^{58} +(-5.74074 - 9.94326i) q^{59} +(0.488397 + 0.845928i) q^{60} +(3.45561 - 5.98529i) q^{61} -7.60670 q^{62} +(-3.27016 + 6.41620i) q^{63} -6.77790 q^{64} +(0.0984047 - 0.170442i) q^{65} +(0.517515 + 0.896363i) q^{66} +(4.44533 + 7.69954i) q^{67} +(-4.63696 + 8.03145i) q^{68} -3.74405 q^{69} +(-2.82774 - 4.35545i) q^{70} -4.95660 q^{71} +(-0.394561 + 0.683400i) q^{72} +(-1.29018 - 2.23465i) q^{73} +(10.0311 + 17.3743i) q^{74} +(-0.263672 + 0.456693i) q^{75} -6.99535 q^{76} +(-1.44072 - 2.21908i) q^{77} +0.203704 q^{78} +(-2.77642 + 4.80890i) q^{79} +(-2.13680 - 3.70105i) q^{80} +(-3.28726 - 5.69369i) q^{81} +(3.76424 - 6.51986i) q^{82} -13.4594 q^{83} +(1.17354 - 2.30254i) q^{84} -5.00673 q^{85} +(-0.831408 + 1.44004i) q^{86} +(0.116939 + 0.202545i) q^{87} +(-0.144958 - 0.251074i) q^{88} +(1.95696 - 3.38955i) q^{89} +5.34236 q^{90} +(-0.519998 + 0.0271913i) q^{91} -13.1510 q^{92} +(1.02188 - 1.76995i) q^{93} +(-12.9273 - 22.3908i) q^{94} +(-1.88830 - 3.27063i) q^{95} +(2.05877 - 3.56589i) q^{96} -7.41996 q^{97} +(-5.59110 + 12.5500i) q^{98} +2.72191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9 - 3 * q^10 + 6 * q^11 - 9 * q^12 + 28 * q^13 - 3 * q^14 - 2 * q^15 - 11 * q^16 - 3 * q^17 + 9 * q^18 + 3 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^22 + 10 * q^23 + 10 * q^24 - 6 * q^25 + 17 * q^26 + 2 * q^27 - 10 * q^28 - 32 * q^29 - 5 * q^30 - 2 * q^31 + 26 * q^32 + q^33 + 60 * q^34 - 3 * q^35 + 16 * q^36 - 5 * q^37 - q^38 - 3 * q^39 - 9 * q^40 - 18 * q^41 - 56 * q^42 - 40 * q^43 + 5 * q^44 - q^45 + 20 * q^46 - q^47 + 82 * q^48 + 15 * q^49 - 6 * q^50 + 5 * q^51 - 23 * q^52 + 24 * q^53 + 7 * q^54 + 12 * q^55 - 66 * q^56 - 60 * q^57 - 31 * q^58 + 7 * q^59 + 9 * q^60 + 14 * q^61 + 48 * q^62 - 13 * q^63 + 30 * q^64 + 14 * q^65 - 5 * q^66 - q^67 + 25 * q^68 - 8 * q^69 - 15 * q^70 - 18 * q^71 + 26 * q^72 - 13 * q^73 + 40 * q^74 - q^75 - 20 * q^76 - 66 * q^78 + 4 * q^79 + 11 * q^80 + 26 * q^81 + 27 * q^82 + 16 * q^83 - 90 * q^84 - 6 * q^85 - 36 * q^86 + 2 * q^87 - 9 * q^88 + 13 * q^89 + 18 * q^90 + 17 * q^91 - 36 * q^92 + 36 * q^93 + q^94 - 3 * q^95 + 89 * q^96 - 6 * q^97 + 18 * q^98 + 2 * q^99

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