LMFDB - Embedded newform 152.2.o.c.107.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(27,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("152.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.7
Character	$\chi$	$=$	152.107
Dual form			152.2.o.c.27.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.285573 + 1.38508i) q^{2} +(0.705625 - 0.407393i) q^{3} +(-1.83690 - 0.791084i) q^{4} +(3.59735 - 2.07693i) q^{5} +(0.362764 + 1.09369i) q^{6} -3.24695i q^{7} +(1.62028 - 2.31834i) q^{8} +(-1.16806 + 2.02314i) q^{9} +O(q^{10})$	\(q+(-0.285573 + 1.38508i) q^{2} +(0.705625 - 0.407393i) q^{3} +(-1.83690 - 0.791084i) q^{4} +(3.59735 - 2.07693i) q^{5} +(0.362764 + 1.09369i) q^{6} -3.24695i q^{7} +(1.62028 - 2.31834i) q^{8} +(-1.16806 + 2.02314i) q^{9} +(1.84941 + 5.57573i) q^{10} -1.21833 q^{11} +(-1.61844 + 0.190130i) q^{12} +(-2.01425 + 3.48878i) q^{13} +(4.49729 + 0.927243i) q^{14} +(1.69225 - 2.93107i) q^{15} +(2.74837 + 2.90628i) q^{16} +(1.50282 + 2.60296i) q^{17} +(-2.46865 - 2.19562i) q^{18} +(-2.16355 + 3.78405i) q^{19} +(-8.25097 + 0.969300i) q^{20} +(-1.32279 - 2.29113i) q^{21} +(0.347922 - 1.68748i) q^{22} +(-3.01328 - 1.73972i) q^{23} +(0.198839 - 2.29597i) q^{24} +(6.12726 - 10.6127i) q^{25} +(-4.25703 - 3.78620i) q^{26} +4.34780i q^{27} +(-2.56861 + 5.96432i) q^{28} +(-2.35755 + 4.08339i) q^{29} +(3.57650 + 3.18094i) q^{30} +5.99801 q^{31} +(-4.81029 + 2.97676i) q^{32} +(-0.859683 + 0.496338i) q^{33} +(-4.03447 + 1.33819i) q^{34} +(-6.74369 - 11.6804i) q^{35} +(3.74608 - 2.79227i) q^{36} +1.34860 q^{37} +(-4.62336 - 4.07731i) q^{38} +3.28236i q^{39} +(1.01370 - 11.7051i) q^{40} +(2.97093 - 1.71527i) q^{41} +(3.55116 - 1.17788i) q^{42} +(-1.01615 - 1.76003i) q^{43} +(2.23794 + 0.963799i) q^{44} +9.70392i q^{45} +(3.27016 - 3.67682i) q^{46} +(-8.37318 - 4.83426i) q^{47} +(3.12332 + 0.931075i) q^{48} -3.54271 q^{49} +(12.9497 + 11.5175i) q^{50} +(2.12085 + 1.22448i) q^{51} +(6.45988 - 4.81509i) q^{52} +(1.22182 - 2.11626i) q^{53} +(-6.02205 - 1.24161i) q^{54} +(-4.38275 + 2.53038i) q^{55} +(-7.52753 - 5.26099i) q^{56} +(0.0149406 + 3.55154i) q^{57} +(-4.98257 - 4.43150i) q^{58} +(-9.35127 + 5.39896i) q^{59} +(-5.42721 + 4.04535i) q^{60} +(-0.300922 - 0.173737i) q^{61} +(-1.71287 + 8.30773i) q^{62} +(6.56905 + 3.79264i) q^{63} +(-2.74937 - 7.51272i) q^{64} +16.7338i q^{65} +(-0.441966 - 1.33247i) q^{66} +(8.31107 + 4.79840i) q^{67} +(-0.701363 - 5.97022i) q^{68} -2.83500 q^{69} +(18.1041 - 6.00494i) q^{70} +(-0.581533 - 1.00725i) q^{71} +(2.79773 + 5.98602i) q^{72} +(1.46675 + 2.54048i) q^{73} +(-0.385123 + 1.86791i) q^{74} -9.98482i q^{75} +(6.96772 - 5.23936i) q^{76} +3.95586i q^{77} +(-4.54634 - 0.937355i) q^{78} +(-2.57780 - 4.46489i) q^{79} +(15.9230 + 4.74671i) q^{80} +(-1.73292 - 3.00151i) q^{81} +(1.52736 + 4.60481i) q^{82} +11.7265 q^{83} +(0.617343 + 5.25501i) q^{84} +(10.8123 + 6.24249i) q^{85} +(2.72797 - 0.904836i) q^{86} +3.84179i q^{87} +(-1.97404 + 2.82449i) q^{88} +(-12.1643 - 7.02306i) q^{89} +(-13.4407 - 2.77118i) q^{90} +(11.3279 + 6.54017i) q^{91} +(4.15882 + 5.57944i) q^{92} +(4.23235 - 2.44355i) q^{93} +(9.08699 - 10.2170i) q^{94} +(0.0761686 + 18.1061i) q^{95} +(-2.18155 + 4.06016i) q^{96} +(12.1187 - 6.99673i) q^{97} +(1.01170 - 4.90694i) q^{98} +(1.42308 - 2.46485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32} + 36 q^{33} - 12 q^{34} - 28 q^{35} - 8 q^{36} + 38 q^{38} - 48 q^{40} + 6 q^{41} + 14 q^{42} + 30 q^{43} + 5 q^{44} - 15 q^{48} - 68 q^{49} - 42 q^{51} + 36 q^{52} + 23 q^{54} - 26 q^{57} + 20 q^{58} - 18 q^{59} - 42 q^{60} + 22 q^{62} + 70 q^{64} - 27 q^{66} + 78 q^{67} + 4 q^{68} + 18 q^{70} - 24 q^{72} + 14 q^{73} + 4 q^{74} + 47 q^{76} - 30 q^{78} - 20 q^{80} + 6 q^{81} + 23 q^{82} - 32 q^{83} + 42 q^{86} - 18 q^{89} - 96 q^{90} - 12 q^{91} + 46 q^{92} + 50 q^{96} + 30 q^{97} + 15 q^{98} - 28 q^{99}+O(q^{100}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.285573	+	1.38508i	−0.201931	+	0.979400i
$2$	−0.285573	+	1.38508i	−0.201931	+	0.979400i
$3$	0.705625	−	0.407393i	0.407393	−	0.235208i	−0.282276	−	0.959333i	$-0.591089\pi$
$3$	0.705625	−	0.407393i	0.407393	−	0.235208i	0.689669	+	0.724125i	$0.257756\pi$
$4$	−1.83690	−	0.791084i	−0.918448	−	0.395542i
$5$	3.59735	−	2.07693i	1.60878	−	0.928831i	0.619139	−	0.785282i	$-0.287482\pi$
$5$	3.59735	−	2.07693i	1.60878	−	0.928831i	0.989643	−	0.143549i	$-0.0458515\pi$
$6$	0.362764	+	1.09369i	0.148098	+	0.446496i
$7$		−	3.24695i		−	1.22723i	−0.789604	−	0.613617i	$-0.789714\pi$
$7$		−	3.24695i		−	1.22723i	0.789604	−	0.613617i	$-0.210286\pi$
$8$	1.62028	−	2.31834i	0.572857	−	0.819656i
$9$	−1.16806	+	2.02314i	−0.389354	+	0.674381i
$10$	1.84941	+	5.57573i	0.584834	+	1.76320i
$11$	−1.21833			−0.367340			−0.183670	−	0.982988i	$-0.558798\pi$
$11$	−1.21833			−0.367340			−0.183670	+	0.982988i	$0.558798\pi$
$12$	−1.61844	+	0.190130i	−0.467204	+	0.0548857i
$13$	−2.01425	+	3.48878i	−0.558652	+	0.967614i	0.438957	+	0.898508i	$0.355348\pi$
$13$	−2.01425	+	3.48878i	−0.558652	+	0.967614i	−0.997609	+	0.0691058i	$0.977985\pi$
$14$	4.49729	+	0.927243i	1.20195	+	0.247816i
$15$	1.69225	−	2.93107i	0.436938	−	0.756798i
$16$	2.74837	+	2.90628i	0.687093	+	0.726569i
$17$	1.50282	+	2.60296i	0.364487	+	0.631310i	0.988694	−	0.149949i	$-0.0479110\pi$
$17$	1.50282	+	2.60296i	0.364487	+	0.631310i	−0.624207	+	0.781259i	$0.714578\pi$
$18$	−2.46865	−	2.19562i	−0.581866	−	0.517511i
$19$	−2.16355	+	3.78405i	−0.496352	+	0.868121i
$19$	−2.16355	+	3.78405i	−0.496352	+	0.868121i
$20$	−8.25097	+	0.969300i	−1.84497	+	0.216742i
$21$	−1.32279	−	2.29113i	−0.288656	−	0.499966i
$22$	0.347922	−	1.68748i	0.0741772	−	0.359772i
$23$	−3.01328	−	1.73972i	−0.628313	−	0.362756i	0.151786	−	0.988413i	$-0.451498\pi$
$23$	−3.01328	−	1.73972i	−0.628313	−	0.362756i	−0.780098	+	0.625657i	$0.784831\pi$
$24$	0.198839	−	2.29597i	0.0405878	−	0.468663i
$25$	6.12726	−	10.6127i	1.22545	−	2.12255i
$26$	−4.25703	−	3.78620i	−0.834872	−	0.742535i
$27$			4.34780i			0.836734i
$28$	−2.56861	+	5.96432i	−0.485422	+	1.12715i
$29$	−2.35755	+	4.08339i	−0.437785	+	0.758266i	−0.997518	−	0.0704067i	$-0.977570\pi$
$29$	−2.35755	+	4.08339i	−0.437785	+	0.758266i	0.559733	+	0.828673i	$0.310904\pi$
$30$	3.57650	+	3.18094i	0.652977	+	0.580757i
$31$	5.99801			1.07728			0.538638	−	0.842538i	$-0.318939\pi$
$31$	5.99801			1.07728			0.538638	+	0.842538i	$0.318939\pi$
$32$	−4.81029	+	2.97676i	−0.850347	+	0.526222i
$33$	−0.859683	+	0.496338i	−0.149652	+	0.0864014i
$34$	−4.03447	+	1.33819i	−0.691906	+	0.229498i
$35$	−6.74369	−	11.6804i	−1.13989	−	1.97435i
$36$	3.74608	−	2.79227i	0.624347	−	0.465378i
$37$	1.34860			0.221708			0.110854	−	0.993837i	$-0.464641\pi$
$37$	1.34860			0.221708			0.110854	+	0.993837i	$0.464641\pi$
$38$	−4.62336	−	4.07731i	−0.750009	−	0.661428i
$39$			3.28236i			0.525599i
$40$	1.01370	−	11.7051i	0.160280	−	1.85073i
$41$	2.97093	−	1.71527i	0.463981	−	0.267880i	−0.249736	−	0.968314i	$-0.580344\pi$
$41$	2.97093	−	1.71527i	0.463981	−	0.267880i	0.713717	+	0.700434i	$0.247010\pi$
$42$	3.55116	−	1.17788i	0.547955	−	0.181751i
$43$	−1.01615	−	1.76003i	−0.154962	−	0.268402i	0.778083	−	0.628161i	$-0.216192\pi$
$43$	−1.01615	−	1.76003i	−0.154962	−	0.268402i	−0.933045	+	0.359759i	$0.882859\pi$
$44$	2.23794	+	0.963799i	0.337382	+	0.145298i
$45$			9.70392i			1.44658i
$46$	3.27016	−	3.67682i	0.482159	−	0.542118i
$47$	−8.37318	−	4.83426i	−1.22135	−	0.705149i	−0.256147	−	0.966638i	$-0.582453\pi$
$47$	−8.37318	−	4.83426i	−1.22135	−	0.705149i	−0.965207	+	0.261489i	$0.915787\pi$
$48$	3.12332	+	0.931075i	0.450812	+	0.134389i
$49$	−3.54271			−0.506102
$50$	12.9497	+	11.5175i	1.83136	+	1.62882i
$51$	2.12085	+	1.22448i	0.296979	+	0.171461i
$52$	6.45988	−	4.81509i	0.895825	−	0.667733i
$53$	1.22182	−	2.11626i	0.167830	−	0.290690i	−0.769827	−	0.638253i	$-0.779657\pi$
$53$	1.22182	−	2.11626i	0.167830	−	0.290690i	0.937657	+	0.347563i	$0.112991\pi$
$54$	−6.02205	−	1.24161i	−0.819497	−	0.168962i
$55$	−4.38275	+	2.53038i	−0.590969	+	0.341196i
$56$	−7.52753	−	5.26099i	−1.00591	−	0.703029i
$57$	0.0149406	+	3.55154i	0.00197893	+	0.470413i
$58$	−4.98257	−	4.43150i	−0.654244	−	0.581884i
$59$	−9.35127	+	5.39896i	−1.21743	+	0.702885i	−0.964368	−	0.264565i	$-0.914772\pi$
$59$	−9.35127	+	5.39896i	−1.21743	+	0.702885i	−0.253064	+	0.967450i	$0.581438\pi$
$60$	−5.42721	+	4.04535i	−0.700650	+	0.522253i
$61$	−0.300922	−	0.173737i	−0.0385291	−	0.0222448i	0.480612	−	0.876934i	$-0.340415\pi$
$61$	−0.300922	−	0.173737i	−0.0385291	−	0.0222448i	−0.519141	+	0.854689i	$0.673748\pi$
$62$	−1.71287	+	8.30773i	−0.217535	+	1.05508i
$63$	6.56905	+	3.79264i	0.827623	+	0.477828i
$64$	−2.74937	−	7.51272i	−0.343671	−	0.939090i
$65$			16.7338i			2.07557i
$66$	−0.441966	−	1.33247i	−0.0544022	−	0.164016i
$67$	8.31107	+	4.79840i	1.01536	+	0.586218i	0.912756	−	0.408505i	$-0.133950\pi$
$67$	8.31107	+	4.79840i	1.01536	+	0.586218i	0.102603	+	0.994722i	$0.467283\pi$
$68$	−0.701363	−	5.97022i	−0.0850528	−	0.723995i
$69$	−2.83500			−0.341294
$70$	18.1041	−	6.00494i	2.16386	−	0.717728i
$71$	−0.581533	−	1.00725i	−0.0690153	−	0.119538i	0.829453	−	0.558577i	$-0.188652\pi$
$71$	−0.581533	−	1.00725i	−0.0690153	−	0.119538i	−0.898468	+	0.439039i	$0.855319\pi$
$72$	2.79773	+	5.98602i	0.329716	+	0.705460i
$73$	1.46675	+	2.54048i	0.171670	+	0.297341i	0.939004	−	0.343907i	$-0.111750\pi$
$73$	1.46675	+	2.54048i	0.171670	+	0.297341i	−0.767334	+	0.641248i	$0.778417\pi$
$74$	−0.385123	+	1.86791i	−0.0447696	+	0.217141i
$75$		−	9.98482i		−	1.15295i
$76$	6.96772	−	5.23936i	0.799252	−	0.600996i
$77$			3.95586i			0.450812i
$78$	−4.54634	−	0.937355i	−0.514771	−	0.106135i
$79$	−2.57780	−	4.46489i	−0.290026	−	0.502339i	0.683790	−	0.729679i	$-0.260330\pi$
$79$	−2.57780	−	4.46489i	−0.290026	−	0.502339i	−0.973815	+	0.227340i	$0.926997\pi$
$80$	15.9230	+	4.74671i	1.78024	+	0.530698i
$81$	−1.73292	−	3.00151i	−0.192547	−	0.333501i
$82$	1.52736	+	4.60481i	0.168669	+	0.508516i
$83$	11.7265			1.28715			0.643574	−	0.765384i	$-0.277451\pi$
$83$	11.7265			1.28715			0.643574	+	0.765384i	$0.277451\pi$
$84$	0.617343	+	5.25501i	0.0673576	+	0.573368i
$85$	10.8123	+	6.24249i	1.17276	+	0.677093i
$86$	2.72797	−	0.904836i	0.294164	−	0.0975710i
$87$			3.84179i			0.411883i
$88$	−1.97404	+	2.82449i	−0.210433	+	0.301092i
$89$	−12.1643	−	7.02306i	−1.28941	−	0.744443i	−0.310864	−	0.950455i	$-0.600618\pi$
$89$	−12.1643	−	7.02306i	−1.28941	−	0.744443i	−0.978550	+	0.206011i	$0.933952\pi$
$90$	−13.4407	−	2.77118i	−1.41678	−	0.292108i
$91$	11.3279	+	6.54017i	1.18749	+	0.685596i
$92$	4.15882	+	5.57944i	0.433587	+	0.581697i
$93$	4.23235	−	2.44355i	0.438874	−	0.253384i
$94$	9.08699	−	10.2170i	0.937252	−	1.05380i
$95$	0.0761686	+	18.1061i	0.00781474	+	1.85764i
$96$	−2.18155	+	4.06016i	−0.222653	+	0.414388i
$97$	12.1187	−	6.99673i	1.23047	−	0.710410i	0.263339	−	0.964703i	$-0.415176\pi$
$97$	12.1187	−	6.99673i	1.23047	−	0.710410i	0.967127	+	0.254293i	$0.0818428\pi$
$98$	1.01170	−	4.90694i	0.102198	−	0.495676i
$99$	1.42308	−	2.46485i	0.143025	−	0.247727i
$100$	−19.6507	+	14.6473i	−1.96507	+	1.46473i
$101$	−17.3113	−	9.99467i	−1.72254	−	0.994507i	−0.913604	−	0.406604i	$-0.866713\pi$
$101$	−17.3113	−	9.99467i	−1.72254	−	0.994507i	−0.808932	−	0.587903i	$-0.799954\pi$
$102$	−2.30166	+	2.58788i	−0.227898	+	0.256238i
$103$	−1.87110			−0.184365			−0.0921826	−	0.995742i	$-0.529384\pi$
$103$	−1.87110			−0.184365			−0.0921826	+	0.995742i	$0.529384\pi$
$104$	4.82451	+	10.3225i	0.473083	+	1.01221i
$105$	−9.51704	−	5.49467i	−0.928768	−	0.536225i
$106$	2.58227	+	2.29667i	0.250812	+	0.223072i
$107$			4.39763i			0.425135i	0.977146	+	0.212567i	$0.0681825\pi$
$107$			4.39763i			0.425135i	−0.977146	+	0.212567i	$0.931817\pi$
$108$	3.43947	−	7.98645i	0.330963	−	0.768497i
$109$	−1.94786	−	3.37379i	−0.186571	−	0.323150i	0.757534	−	0.652796i	$-0.226404\pi$
$109$	−1.94786	−	3.37379i	−0.186571	−	0.323150i	−0.944105	+	0.329646i	$0.893071\pi$
$110$	−2.25318	−	6.79306i	−0.214833	−	0.647693i
$111$	0.951604	−	0.549409i	0.0903222	−	0.0521476i
$112$	9.43655	−	8.92384i	0.891670	−	0.843224i
$113$		−	0.221322i		−	0.0208202i	−0.999946	−	0.0104101i	$-0.996686\pi$
$113$		−	0.221322i		−	0.0208202i	0.999946	−	0.0104101i	$-0.00331369\pi$
$114$	−4.92343	−	0.993530i	−0.461122	−	0.0930526i
$115$	−14.4531			−1.34776
$116$	7.56087	−	5.63574i	0.702009	−	0.523266i
$117$	−4.70553	−	8.15022i	−0.435027	−	0.753488i
$118$	−4.80752	−	14.4941i	−0.442568	−	1.33429i
$119$	8.45169	−	4.87958i	0.774765	−	0.447311i
$120$	−4.05327	−	8.67237i	−0.370011	−	0.791675i
$121$	−9.51568			−0.865062
$122$	0.326576	−	0.367187i	0.0295668	−	0.0332435i
$123$	1.39758	−	2.42067i	0.126015	−	0.218265i
$124$	−11.0177	−	4.74493i	−0.989421	−	0.426107i
$125$		−	30.1343i		−	2.69529i
$126$	−7.12906	+	8.01559i	−0.635107	+	0.714085i
$127$	−4.30308	+	7.45316i	−0.381837	+	0.661361i	−0.991325	−	0.131435i	$-0.958042\pi$
$127$	−4.30308	+	7.45316i	−0.381837	+	0.661361i	0.609488	+	0.792795i	$0.291375\pi$
$128$	11.1909	−	1.66266i	0.989142	−	0.146960i
$129$	−1.43405	−	0.827947i	−0.126261	−	0.0728967i
$130$	−23.1777	−	4.77873i	−2.03282	−	0.419122i
$131$	0.494676	+	0.856804i	0.0432201	+	0.0748593i	0.886826	−	0.462103i	$-0.152905\pi$
$131$	0.494676	+	0.856804i	0.0432201	+	0.0748593i	−0.843606	+	0.536962i	$0.819572\pi$
$132$	1.97179	−	0.231640i	0.171623	−	0.0201617i
$133$	12.2866	+	7.02495i	1.06539	+	0.609140i
$134$	−9.01959	+	10.1412i	−0.779174	+	0.876067i
$135$	9.03007	+	15.6405i	0.777184	+	1.34612i
$136$	8.46952	+	0.733490i	0.726256	+	0.0628962i
$137$	9.20933	−	15.9510i	0.786806	−	1.36279i	−0.141108	−	0.989994i	$-0.545066\pi$
$137$	9.20933	−	15.9510i	0.786806	−	1.36279i	0.927914	−	0.372794i	$-0.121600\pi$
$138$	0.809599	−	3.92670i	0.0689177	−	0.334263i
$139$	−5.46807	+	9.47098i	−0.463796	+	0.803318i	−0.999146	−	0.0413120i	$-0.986846\pi$
$139$	−5.46807	+	9.47098i	−0.463796	+	0.803318i	0.535350	+	0.844630i	$0.320180\pi$
$140$	3.14727	+	26.7905i	0.265993	+	2.26421i
$141$	−7.87777			−0.663428
$142$	1.56119	−	0.517828i	0.131012	−	0.0434552i
$143$	2.45401	−	4.25048i	0.205215	−	0.355443i
$144$	−9.09008	+	2.16564i	−0.757507	+	0.180470i
$145$			19.5858i			1.62651i
$146$	−3.93764	+	1.30607i	−0.325881	+	0.108091i
$147$	−2.49983	+	1.44328i	−0.206182	+	0.119039i
$148$	−2.47723	−	1.06685i	−0.203627	−	0.0876947i
$149$	−0.679549	+	0.392338i	−0.0556708	+	0.0321416i	−0.527577	−	0.849507i	$-0.676899\pi$
$149$	−0.679549	+	0.392338i	−0.0556708	+	0.0321416i	0.471906	+	0.881649i	$0.343566\pi$
$150$	13.8298	+	2.85140i	1.12920	+	0.232816i
$151$	4.53858			0.369344			0.184672	−	0.982800i	$-0.440878\pi$
$151$	4.53858			0.369344			0.184672	+	0.982800i	$0.440878\pi$
$152$	5.26714	+	11.1471i	0.427222	+	0.904147i
$153$	−7.02154			−0.567658
$154$	−5.47918	−	1.12969i	−0.441525	−	0.0910327i
$155$	21.5769	−	12.4574i	1.73310	−	1.00061i
$156$	2.59662	−	6.02936i	0.207896	−	0.482735i
$157$	7.14123	−	4.12299i	0.569932	−	0.329050i	−0.187190	−	0.982324i	$-0.559938\pi$
$157$	7.14123	−	4.12299i	0.569932	−	0.329050i	0.757122	+	0.653273i	$0.226605\pi$
$158$	6.92038	−	2.29541i	0.550556	−	0.182613i
$159$		−	1.99105i		−	0.157900i
$160$	−11.1217	+	20.6991i	−0.879251	+	1.63641i
$161$	−5.64879	+	9.78399i	−0.445187	+	0.771086i
$162$	4.65221	−	1.54309i	0.365512	−	0.121236i
$163$	3.99098			0.312597			0.156299	−	0.987710i	$-0.450044\pi$
$163$	3.99098			0.312597			0.156299	+	0.987710i	$0.450044\pi$
$164$	−6.81421	+	0.800513i	−0.532100	+	0.0625095i
$165$	−2.06172	+	3.57100i	−0.160505	+	0.278002i
$166$	−3.34877	+	16.2421i	−0.259915	+	1.26063i
$167$	9.24487	−	16.0126i	0.715390	−	1.23909i	−0.247419	−	0.968909i	$-0.579582\pi$
$167$	9.24487	−	16.0126i	0.715390	−	1.23909i	0.962809	−	0.270183i	$-0.0870842\pi$
$168$	−7.45491	−	0.645620i	−0.575159	−	0.0498107i
$169$	−1.61439	−	2.79621i	−0.124184	−	0.215093i
$170$	−11.7341	+	13.1932i	−0.899961	+	1.01188i
$171$	−5.12852	−	8.79718i	−0.392187	−	0.672737i
$172$	0.474237	+	4.03685i	0.0361602	+	0.307807i
$173$	1.81313	+	3.14044i	0.137850	+	0.238763i	0.926683	−	0.375845i	$-0.122647\pi$
$173$	1.81313	+	3.14044i	0.137850	+	0.238763i	−0.788833	+	0.614608i	$0.789314\pi$
$174$	−5.32119	−	1.09711i	−0.403398	−	0.0831719i
$175$	−34.4591	−	19.8949i	−2.60486	−	1.50392i
$176$	−3.34842	−	3.54080i	−0.252397	−	0.266898i
$177$	−4.39900	+	7.61928i	−0.330649	+	0.572700i
$178$	13.2013	−	14.8429i	0.989480	−	1.11253i
$179$		−	15.8678i		−	1.18601i	−0.805197	−	0.593007i	$-0.797940\pi$
$179$		−	15.8678i		−	1.18601i	0.805197	−	0.593007i	$-0.202060\pi$
$180$	7.67662	−	17.8251i	0.572181	−	1.32860i
$181$	2.14373	−	3.71305i	0.159342	−	0.275989i	−0.775289	−	0.631606i	$-0.782396\pi$
$181$	2.14373	−	3.71305i	0.159342	−	0.275989i	0.934632	+	0.355617i	$0.115729\pi$
$182$	−12.2936	+	13.8224i	−0.911263	+	1.02458i
$183$	−0.283118			−0.0209287
$184$	−8.91562	+	4.16696i	−0.657268	+	0.307193i
$185$	4.85137	−	2.80094i	0.356680	−	0.205929i
$186$	2.17587	+	6.55996i	0.159542	+	0.481000i
$187$	−1.83093	−	3.17126i	−0.133891	−	0.231905i
$188$	11.5564	+	15.5039i	0.842834	+	1.13074i
$189$	14.1171			1.02687
$190$	−25.1001	−	5.06511i	−1.82096	−	0.367462i
$191$			1.84103i			0.133212i	0.997779	+	0.0666060i	$0.0212171\pi$
$191$			1.84103i			0.133212i	−0.997779	+	0.0666060i	$0.978783\pi$
$192$	−5.00065	−	4.18109i	−0.360891	−	0.301744i
$193$	−10.8408	+	6.25891i	−0.780335	+	0.450526i	−0.836549	−	0.547892i	$-0.815430\pi$
$193$	−10.8408	+	6.25891i	−0.780335	+	0.450526i	0.0562143	+	0.998419i	$0.482097\pi$
$194$	6.23026	+	18.7834i	0.447307	+	1.34857i
$195$	6.81723	+	11.8078i	0.488192	+	0.845574i
$196$	6.50760	+	2.80258i	0.464828	+	0.200185i
$197$			10.5073i			0.748613i	0.927305	+	0.374307i	$0.122119\pi$
$197$			10.5073i			0.748613i	−0.927305	+	0.374307i	$0.877881\pi$
$198$	3.00762	+	2.67498i	0.213742	+	0.190102i
$199$	5.21989	+	3.01371i	0.370028	+	0.213636i	0.673471	−	0.739214i	$-0.264803\pi$
$199$	5.21989	+	3.01371i	0.370028	+	0.213636i	−0.303443	+	0.952850i	$0.598136\pi$
$200$	−14.6760	−	31.4007i	−1.03775	−	2.22036i
$201$	7.81934			0.551534
$202$	18.7871	−	21.1233i	1.32185	−	1.48623i
$203$	13.2586	+	7.65484i	0.930570	+	0.537265i
$204$	−2.92712	−	3.92701i	−0.204940	−	0.274945i
$205$	7.12497	−	12.3408i	0.497630	−	0.861920i
$206$	0.534337	−	2.59163i	0.0372290	−	0.180567i
$207$	7.03940	−	4.06420i	0.489272	−	0.282481i
$208$	−15.6753	+	3.73451i	−1.08688	+	0.258941i
$209$	2.63591	−	4.61022i	0.182330	−	0.318895i
$210$	10.3284	−	11.6127i	0.712725	−	0.801355i
$211$	12.6720	−	7.31618i	0.872377	−	0.503667i	0.00423928	−	0.999991i	$-0.498651\pi$
$211$	12.6720	−	7.31618i	0.872377	−	0.503667i	0.868137	+	0.496324i	$0.165317\pi$
$212$	−3.91849	+	2.92078i	−0.269123	+	0.200600i
$213$	−0.820689	−	0.473825i	−0.0562327	−	0.0324660i
$214$	−6.09107	−	1.25585i	−0.416377	−	0.0858478i
$215$	−7.31090	−	4.22095i	−0.498599	−	0.287867i
$216$	10.0797	+	7.04466i	0.685834	+	0.479329i
$217$		−	19.4753i		−	1.32207i
$218$	5.22923	−	1.73448i	0.354168	−	0.117474i
$219$	2.06995	+	1.19509i	0.139874	+	0.0807564i
$220$	10.0524	−	1.18092i	0.677732	−	0.0796179i
$221$	−12.1082			−0.814486
$222$	0.489223	+	1.47494i	0.0328345	+	0.0989918i
$223$	13.7578	+	23.8293i	0.921294	+	1.59573i	0.797416	+	0.603430i	$0.206200\pi$
$223$	13.7578	+	23.8293i	0.921294	+	1.59573i	0.123878	+	0.992297i	$0.460467\pi$
$224$	9.66541	+	15.6188i	0.645798	+	1.04357i
$225$	14.3140	+	24.7927i	0.954270	+	1.65284i
$226$	0.306548	+	0.0632035i	0.0203913	+	0.00420423i
$227$			18.4655i			1.22560i	0.790239	+	0.612799i	$0.209956\pi$
$227$			18.4655i			1.22560i	−0.790239	+	0.612799i	$0.790044\pi$
$228$	2.78212	−	6.53563i	0.184250	−	0.432832i
$229$			18.8145i			1.24330i	0.783295	+	0.621650i	$0.213537\pi$
$229$			18.8145i			1.24330i	−0.783295	+	0.621650i	$0.786463\pi$
$230$	4.12741	−	20.0187i	0.272154	−	1.31999i
$231$	1.61159	+	2.79135i	0.106035	+	0.183657i
$232$	5.64678	+	12.0818i	0.370729	+	0.793211i
$233$	−0.339317	−	0.587714i	−0.0222294	−	0.0385024i	0.854697	−	0.519128i	$-0.173743\pi$
$233$	−0.339317	−	0.587714i	−0.0222294	−	0.0385024i	−0.876926	+	0.480625i	$0.840410\pi$
$234$	12.6325	−	4.19006i	0.825812	−	0.273913i
$235$	−40.1616			−2.61986
$236$	21.4483	−	2.51969i	1.39617	−	0.164018i
$237$	−3.63793	−	2.10036i	−0.236309	−	0.136433i
$238$	4.34504	+	13.0997i	0.281647	+	0.849130i
$239$			4.57846i			0.296156i	0.988976	+	0.148078i	$0.0473087\pi$
$239$			4.57846i			0.296156i	−0.988976	+	0.148078i	$0.952691\pi$
$240$	13.1694	−	3.13751i	0.850083	−	0.202525i
$241$	4.98480	+	2.87797i	0.321099	+	0.185387i	0.651882	−	0.758320i	$-0.273980\pi$
$241$	4.98480	+	2.87797i	0.321099	+	0.185387i	−0.330783	+	0.943707i	$0.607313\pi$
$242$	2.71742	−	13.1800i	0.174683	−	0.847241i
$243$	−13.7415	−	7.93366i	−0.881518	−	0.508945i
$244$	0.415322	+	0.557192i	0.0265882	+	0.0356706i
$245$	−12.7444	+	7.35796i	−0.814208	+	0.470083i
$246$	2.95372	+	2.62703i	0.188322	+	0.167494i
$247$	−8.84380	−	15.1702i	−0.562718	−	0.965255i
$248$	9.71848	−	13.9054i	0.617124	−	0.882995i
$249$	8.27450	−	4.77728i	0.524375	−	0.302748i
$250$	41.7384	+	8.60554i	2.63977	+	0.544262i
$251$	−7.52848	+	13.0397i	−0.475194	+	0.823059i	−0.999596	−	0.0284110i	$-0.990955\pi$
$251$	−7.52848	+	13.0397i	−0.475194	+	0.823059i	0.524403	+	0.851470i	$0.324289\pi$
$252$	−9.06637	−	12.1634i	−0.571127	−	0.766220i
$253$	3.67116	+	2.11955i	0.230804	+	0.133255i
$254$	−9.09438	−	8.08854i	−0.570632	−	0.507520i
$255$	10.1726			0.637032
$256$	−0.892892	+	15.9751i	−0.0558057	+	0.998442i
$257$	−10.5279	−	6.07826i	−0.656709	−	0.379151i	0.134313	−	0.990939i	$-0.457117\pi$
$257$	−10.5279	−	6.07826i	−0.656709	−	0.379151i	−0.791022	+	0.611788i	$0.790451\pi$
$258$	1.55630	−	1.74983i	0.0968909	−	0.108940i
$259$		−	4.37883i		−	0.272087i
$260$	13.2378	−	30.7382i	0.820976	−	1.90631i
$261$	−5.50752	−	9.53930i	−0.340907	−	0.590468i
$262$	−1.32801	+	0.440486i	−0.0820447	+	0.0272133i
$263$	8.19758	−	4.73288i	0.505485	−	0.291842i	−0.225491	−	0.974245i	$-0.572399\pi$
$263$	8.19758	−	4.73288i	0.505485	−	0.291842i	0.730976	+	0.682404i	$0.239065\pi$
$264$	−0.242251	+	2.79724i	−0.0149095	+	0.172158i
$265$		−	10.1505i		−	0.623543i
$266$	−13.2389	+	15.0119i	−0.811726	+	0.920436i
$267$	−11.4446			−0.700397
$268$	−11.4706	−	15.3889i	−0.700681	−	0.940028i
$269$	−1.65200	−	2.86135i	−0.100724	−	0.174459i	0.811259	−	0.584687i	$-0.198783\pi$
$269$	−1.65200	−	2.86135i	−0.100724	−	0.174459i	−0.911983	+	0.410227i	$0.865449\pi$
$270$	−24.2421	+	8.04085i	−1.47533	+	0.489351i
$271$	10.3868	−	5.99685i	0.630956	−	0.364282i	−0.150166	−	0.988661i	$-0.547981\pi$
$271$	10.3868	−	5.99685i	0.630956	−	0.364282i	0.781122	+	0.624378i	$0.214648\pi$
$272$	−3.43461	+	11.5215i	−0.208254	+	0.698594i
$273$	10.6577			0.645032
$274$	19.4635	+	17.3108i	1.17583	+	1.04579i
$275$	−7.46502	+	12.9298i	−0.450157	+	0.779695i
$276$	5.20759	+	2.24272i	0.313460	+	0.134996i
$277$			12.2692i			0.737185i	0.929591	+	0.368592i	$0.120160\pi$
$277$			12.2692i			0.737185i	−0.929591	+	0.368592i	$0.879840\pi$
$278$	−11.5565	−	10.2784i	−0.693115	−	0.616456i
$279$	−7.00605	+	12.1348i	−0.419441	+	0.726494i
$280$	−38.0058	−	3.29143i	−2.27128	−	0.196701i
$281$	10.4906	+	6.05677i	0.625819	+	0.361317i	0.779131	−	0.626861i	$-0.215661\pi$
$281$	10.4906	+	6.05677i	0.625819	+	0.361317i	−0.153312	+	0.988178i	$0.548994\pi$
$282$	2.24968	−	10.9113i	0.133967	−	0.649761i
$283$	6.53976	+	11.3272i	0.388748	+	0.673332i	0.992281	−	0.124006i	$-0.0395742\pi$
$283$	6.53976	+	11.3272i	0.388748	+	0.673332i	−0.603533	+	0.797338i	$0.706241\pi$
$284$	0.271401	+	2.31025i	0.0161047	+	0.137088i
$285$	7.43004	+	12.7451i	0.440117	+	0.754953i
$286$	5.18645	+	4.61283i	0.306681	+	0.272762i
$287$	−5.56939	−	9.64647i	−0.328751	−	0.569413i
$288$	−0.403700	−	13.2089i	−0.0237883	−	0.778344i
$289$	3.98307	−	6.89889i	0.234298	−	0.405817i
$290$	−27.1279	−	5.59318i	−1.59301	−	0.328443i
$291$	5.70084	−	9.87414i	0.334189	−	0.578832i
$292$	−0.684529	−	5.82692i	−0.0400590	−	0.340995i
$293$	−11.8661			−0.693224			−0.346612	−	0.938009i	$-0.612668\pi$
$293$	−11.8661			−0.693224			−0.346612	+	0.938009i	$0.612668\pi$
$294$	−1.28517	−	3.87463i	−0.0749527	−	0.225973i
$295$	−22.4265	+	38.8438i	−1.30572	+	2.26158i
$296$	2.18511	−	3.12650i	0.127007	−	0.181724i
$297$		−	5.29704i		−	0.307366i
$298$	−0.349358	−	1.05327i	−0.0202378	−	0.0610144i
$299$	12.1390	−	7.00845i	0.702016	−	0.405309i
$300$	−7.89883	+	18.3411i	−0.456039	+	1.05892i
$301$	−5.71473	+	3.29940i	−0.329392	+	0.190174i
$302$	−1.29610	+	6.28630i	−0.0745820	+	0.361736i
$303$	−16.2870			−0.935666
$304$	−16.9437	+	4.11211i	−0.971791	+	0.235846i
$305$	−1.44336			−0.0826466
$306$	2.00516	−	9.72540i	0.114628	−	0.555964i
$307$	−16.1814	+	9.34236i	−0.923524	+	0.533197i	−0.884758	−	0.466051i	$-0.845676\pi$
$307$	−16.1814	+	9.34236i	−0.923524	+	0.533197i	−0.0387664	+	0.999248i	$0.512343\pi$
$308$	3.12941	−	7.26649i	0.178315	−	0.414047i
$309$	−1.32030	+	0.762274i	−0.0751091	+	0.0433642i
$310$	11.0928	+	33.4433i	0.630027	+	1.89945i
$311$		−	17.9447i		−	1.01755i	−0.860900	−	0.508774i	$-0.830099\pi$
$311$		−	17.9447i		−	1.01755i	0.860900	−	0.508774i	$-0.169901\pi$
$312$	7.60962	+	5.31836i	0.430810	+	0.301093i
$313$	15.8925	−	27.5267i	0.898300	−	1.55590i	0.0686331	−	0.997642i	$-0.478136\pi$
$313$	15.8925	−	27.5267i	0.898300	−	1.55590i	0.829667	−	0.558259i	$-0.188530\pi$
$314$	3.67133	+	11.0686i	0.207185	+	0.624637i
$315$	31.5082			1.77529
$316$	1.20306	+	10.2408i	0.0676773	+	0.576089i
$317$	−4.48565	+	7.76938i	−0.251939	+	0.436372i	−0.964060	−	0.265686i	$-0.914402\pi$
$317$	−4.48565	+	7.76938i	−0.251939	+	0.436372i	0.712120	+	0.702057i	$0.247735\pi$
$318$	2.75776	+	0.568589i	0.154647	+	0.0318849i
$319$	2.87226	−	4.97491i	0.160816	−	0.278541i
$320$	−25.4938	−	21.3156i	−1.42515	−	1.19158i
$321$	1.79156	+	3.10308i	0.0999953	+	0.173197i
$322$	−11.9385	−	10.6181i	−0.665305	−	0.591722i
$323$	−13.1012	+	0.0551139i	−0.728968	+	0.00306662i
$324$	0.808753	+	6.88435i	0.0449307	+	0.382464i
$325$	24.6837	+	42.7534i	1.36920	+	2.37153i
$326$	−1.13972	+	5.52782i	−0.0631230	+	0.306158i
$327$	−2.74892	−	1.58709i	−0.152015	−	0.0877661i
$328$	0.837181	−	9.66683i	0.0462256	−	0.533762i
$329$	−15.6966	+	27.1873i	−0.865382	+	1.49889i
$330$	−4.35735	−	3.87543i	−0.239864	−	0.213335i
$331$		−	29.7989i		−	1.63790i	−0.573868	−	0.818948i	$-0.694558\pi$
$331$		−	29.7989i		−	1.63790i	0.573868	−	0.818948i	$-0.305442\pi$
$332$	−21.5403	−	9.27662i	−1.18218	−	0.509121i
$333$	−1.57524	+	2.72840i	−0.0863228	+	0.149516i
$334$	19.5386	+	17.3777i	1.06911	+	0.950863i
$335$	39.8637			2.17799
$336$	3.02316	−	10.1413i	0.164927	−	0.553252i
$337$	−7.44373	+	4.29764i	−0.405486	+	0.234107i	−0.688848	−	0.724905i	$-0.741883\pi$
$337$	−7.44373	+	4.29764i	−0.405486	+	0.234107i	0.283362	+	0.959013i	$0.408550\pi$
$338$	4.33401	−	1.43754i	0.235739	−	0.0781920i
$339$	−0.0901649	−	0.156170i	−0.00489708	−	0.00848200i
$340$	−14.9228	−	20.0203i	−0.809300	−	1.08575i
$341$	−7.30755			−0.395726
$342$	13.6494	−	4.59117i	0.738073	−	0.248262i
$343$		−	11.2256i		−	0.606128i
$344$	−5.72679	−	0.495960i	−0.308768	−	0.0267404i
$345$	−10.1985	+	5.88809i	−0.549067	+	0.317004i
$346$	−4.86754	+	1.61451i	−0.261681	+	0.0867966i
$347$	−7.95629	−	13.7807i	−0.427116	−	0.739787i	0.569499	−	0.821992i	$-0.307137\pi$
$347$	−7.95629	−	13.7807i	−0.427116	−	0.739787i	−0.996615	+	0.0822050i	$0.973804\pi$
$348$	3.03918	−	7.05697i	0.162917	−	0.378293i
$349$		−	11.3168i		−	0.605776i	−0.953026	−	0.302888i	$-0.902049\pi$
$349$		−	11.3168i		−	0.605776i	0.953026	−	0.302888i	$-0.0979507\pi$
$350$	37.3967	−	42.0471i	1.99894	−	2.24751i
$351$	−15.1685	−	8.75755i	−0.809636	−	0.467443i
$352$	5.86051	−	3.62667i	0.312366	−	0.193302i
$353$	4.52158			0.240660			0.120330	−	0.992734i	$-0.461605\pi$
$353$	4.52158			0.240660			0.120330	+	0.992734i	$0.461605\pi$
$354$	−9.29709	−	8.26883i	−0.494135	−	0.439483i
$355$	−4.18395	−	2.41561i	−0.222061	−	0.128207i
$356$	16.7887	+	22.5236i	0.889801	+	1.19375i
$357$	3.97582	−	6.88632i	0.210422	−	0.364462i
$358$	21.9782	+	4.53142i	1.16158	+	0.239493i
$359$	−29.7521	+	17.1774i	−1.57026	+	0.906589i	−0.574122	+	0.818770i	$0.694656\pi$
$359$	−29.7521	+	17.1774i	−1.57026	+	0.906589i	−0.996136	+	0.0878192i	$0.972010\pi$
$360$	22.4970	+	15.7231i	1.18569	+	0.828680i
$361$	−9.63810	−	16.3740i	−0.507269	−	0.861788i
$362$	4.53068	+	4.02959i	0.238127	+	0.211790i
$363$	−6.71450	+	3.87662i	−0.352420	+	0.203470i
$364$	−15.6344	−	20.9749i	−0.819464	−	1.09939i
$365$	10.5528	+	6.09266i	0.552359	+	0.318904i
$366$	0.0808508	−	0.392141i	0.00422614	−	0.0204975i
$367$	−24.5824	−	14.1927i	−1.28319	−	0.740851i	−0.305760	−	0.952108i	$-0.598911\pi$
$367$	−24.5824	−	14.1927i	−1.28319	−	0.740851i	−0.977430	+	0.211258i	$0.932244\pi$
$368$	−3.22552	−	13.5388i	−0.168142	−	0.705760i
$369$			8.01415i			0.417200i
$370$	2.49410	+	7.51941i	0.129662	+	0.390915i
$371$	−6.87139	−	3.96720i	−0.356745	−	0.205967i
$372$	−9.70744	+	1.14040i	−0.503307	+	0.0591270i
$373$	8.73811			0.452442			0.226221	−	0.974076i	$-0.427363\pi$
$373$	8.73811			0.452442			0.226221	+	0.974076i	$0.427363\pi$
$374$	4.91531	−	1.63035i	0.254165	−	0.0843036i
$375$	−12.2765	−	21.2635i	−0.633955	−	1.09804i
$376$	−24.7744	+	11.5790i	−1.27764	+	0.597140i
$377$	−9.49737	−	16.4499i	−0.489139	−	0.847214i
$378$	−4.03147	+	19.5533i	−0.207356	+	1.00571i
$379$			12.0886i			0.620951i	0.950581	+	0.310475i	$0.100488\pi$
$379$			12.0886i			0.620951i	−0.950581	+	0.310475i	$0.899512\pi$
$380$	14.1835	−	33.3192i	0.727599	−	1.70924i
$381$			7.01218i			0.359245i
$382$	−2.54997	−	0.525748i	−0.130468	−	0.0268996i
$383$	6.03554	+	10.4539i	0.308402	+	0.534167i	0.978013	−	0.208545i	$-0.0668726\pi$
$383$	6.03554	+	10.4539i	0.308402	+	0.534167i	−0.669611	+	0.742712i	$0.733539\pi$
$384$	7.21920	−	5.73230i	0.368403	−	0.292525i
$385$	8.21603	+	14.2306i	0.418728	+	0.725257i
$386$	−5.57327	−	16.8027i	−0.283672	−	0.855235i
$387$	4.74772			0.241340
$388$	−27.7958	+	3.26536i	−1.41112	+	0.165774i
$389$	−5.68110	−	3.27998i	−0.288043	−	0.166302i	0.349016	−	0.937117i	$-0.386516\pi$
$389$	−5.68110	−	3.27998i	−0.288043	−	0.166302i	−0.637059	+	0.770815i	$0.719849\pi$
$390$	−18.3016	+	6.07043i	−0.926736	+	0.307388i
$391$		−	10.4579i		−	0.528880i
$392$	−5.74020	+	8.21320i	−0.289924	+	0.414829i
$393$	0.698112	+	0.403055i	0.0352151	+	0.0203314i
$394$	−14.5534	−	3.00060i	−0.733192	−	0.151168i
$395$	−18.5465	−	10.7078i	−0.933176	−	0.538769i
$396$	−4.56396	+	3.40190i	−0.229347	+	0.170952i
$397$	16.0785	−	9.28295i	0.806959	−	0.465898i	−0.0389397	−	0.999242i	$-0.512398\pi$
$397$	16.0785	−	9.28295i	0.806959	−	0.465898i	0.845899	+	0.533344i	$0.179065\pi$
$398$	−5.66489	+	6.36934i	−0.283955	+	0.319266i
$399$	11.5317	−	0.0485115i	0.577306	−	0.00242861i
$400$	47.6835	−	11.3602i	2.38418	−	0.568011i
$401$	−20.9710	+	12.1076i	−1.04724	+	0.604624i	−0.921875	−	0.387486i	$-0.873343\pi$
$401$	−20.9710	+	12.1076i	−1.04724	+	0.604624i	−0.125365	+	0.992111i	$0.540010\pi$
$402$	−2.23299	+	10.8304i	−0.111372	+	0.540172i
$403$	−12.0815	+	20.9258i	−0.601822	+	1.04239i
$404$	23.8924	+	32.0538i	1.18869	+	1.59474i
$405$	−12.4678	−	7.19831i	−0.619532	−	0.357687i
$406$	−14.3889	+	16.1782i	−0.714108	+	0.802910i
$407$	−1.64303			−0.0814421
$408$	6.27513	−	2.93286i	0.310665	−	0.145198i
$409$	5.79614	+	3.34641i	0.286601	+	0.165469i	0.636408	−	0.771353i	$-0.280420\pi$
$409$	5.79614	+	3.34641i	0.286601	+	0.165469i	−0.349807	+	0.936822i	$0.613753\pi$
$410$	15.0583	+	13.3929i	0.743678	+	0.661427i
$411$		−	15.0073i		−	0.740254i
$412$	3.43702	+	1.48020i	0.169330	+	0.0729241i
$413$	17.5302	+	30.3631i	0.862603	+	1.49407i
$414$	3.61898	+	10.9108i	0.177863	+	0.536235i
$415$	42.1842	−	24.3550i	2.07074	−	1.19554i
$416$	−0.696155	−	22.7780i	−0.0341318	−	1.11678i
$417$			8.91062i			0.436355i
$418$	5.63277	+	4.96751i	0.275508	+	0.242969i
$419$	19.0537			0.930832			0.465416	−	0.885092i	$-0.345905\pi$
$419$	19.0537			0.930832			0.465416	+	0.885092i	$0.345905\pi$
$420$	13.1351	+	17.6219i	0.640926	+	0.859861i
$421$	−17.3507	−	30.0523i	−0.845622	−	1.46466i	−0.885080	−	0.465439i	$-0.845896\pi$
$421$	−17.3507	−	30.0523i	−0.845622	−	1.46466i	0.0394576	−	0.999221i	$-0.487437\pi$
$422$	6.51472	+	19.6410i	0.317132	+	0.956111i
$423$	19.5608	−	11.2934i	0.951078	−	0.549105i
$424$	−2.92650	−	6.26153i	−0.142123	−	0.304087i
$425$	36.8327			1.78665
$426$	0.890653	−	1.00141i	0.0431523	−	0.0485184i
$427$	−0.564118	+	0.977080i	−0.0272996	+	0.0472842i
$428$	3.47889	−	8.07799i	0.168159	−	0.390464i
$429$		−	3.99899i		−	0.193073i
$430$	7.93416	−	8.92080i	0.382619	−	0.430199i
$431$	−13.5200	+	23.4173i	−0.651234	+	1.12797i	0.331590	+	0.943424i	$0.392415\pi$
$431$	−13.5200	+	23.4173i	−0.651234	+	1.12797i	−0.982824	+	0.184547i	$0.940918\pi$
$432$	−12.6359	+	11.9494i	−0.607945	+	0.574914i
$433$	29.7946	+	17.2019i	1.43184	+	0.826670i	0.997261	−	0.0739655i	$-0.0235655\pi$
$433$	29.7946	+	17.2019i	1.43184	+	0.826670i	0.434574	+	0.900636i	$0.356899\pi$
$434$	26.9748	+	5.56162i	1.29483	+	0.266966i
$435$	7.97912	+	13.8202i	0.382570	+	0.662630i
$436$	0.909063	+	7.73822i	0.0435362	+	0.370593i
$437$	13.1026	−	7.63845i	0.626781	−	0.365396i
$438$	−2.24641	+	2.52576i	−0.107338	+	0.120686i
$439$	0.606126	+	1.04984i	0.0289288	+	0.0501062i	0.880127	−	0.474738i	$-0.157457\pi$
$439$	0.606126	+	1.04984i	0.0289288	+	0.0501062i	−0.851199	+	0.524844i	$0.824124\pi$
$440$	−1.23502	+	14.2606i	−0.0588772	+	0.679848i
$441$	4.13811	−	7.16742i	0.197053	−	0.341306i
$442$	3.45778	−	16.7708i	0.164470	−	0.797707i
$443$	12.5887	−	21.8042i	0.598106	−	1.03595i	−0.394994	−	0.918684i	$-0.629253\pi$
$443$	12.5887	−	21.8042i	0.598106	−	1.03595i	0.993100	−	0.117267i	$-0.0374132\pi$
$444$	−2.18262	+	0.256408i	−0.103583	+	0.0121686i
$445$	−58.3456			−2.76585
$446$	−36.9344	+	12.2507i	−1.74889	+	0.580088i
$447$	−0.319671	+	0.553687i	−0.0151199	+	0.0261885i
$448$	−24.3935	+	8.92707i	−1.15248	+	0.421764i
$449$		−	21.4991i		−	1.01460i	−0.861768	−	0.507302i	$-0.830643\pi$
$449$		−	21.4991i		−	1.01460i	0.861768	−	0.507302i	$-0.169357\pi$
$450$	−38.4275	+	12.7460i	−1.81149	+	0.600852i
$451$	−3.61957	+	2.08976i	−0.170439	+	0.0984028i
$452$	−0.175084	+	0.406545i	−0.00823525	+	0.0191223i
$453$	3.20254	−	1.84899i	0.150468	−	0.0868729i
$454$	−25.5762	−	5.27325i	−1.20035	−	0.247486i
$455$	54.3339			2.54721
$456$	8.25787	+	5.71986i	0.386710	+	0.267857i
$457$	26.4299			1.23634			0.618168	−	0.786046i	$-0.287875\pi$
$457$	26.4299			1.23634			0.618168	+	0.786046i	$0.287875\pi$
$458$	−26.0597	−	5.37293i	−1.21769	−	0.251061i
$459$	−11.3171	+	6.53395i	−0.528239	+	0.304979i
$460$	26.5488	+	11.4336i	1.23784	+	0.533094i
$461$	16.0782	−	9.28278i	0.748839	−	0.432342i	−0.0764354	−	0.997075i	$-0.524354\pi$
$461$	16.0782	−	9.28278i	0.748839	−	0.432342i	0.825274	+	0.564732i	$0.191021\pi$
$462$	−4.32647	+	1.43504i	−0.201286	+	0.0667643i
$463$			18.5375i			0.861510i	0.902469	+	0.430755i	$0.141753\pi$
$463$			18.5375i			0.861510i	−0.902469	+	0.430755i	$0.858247\pi$
$464$	−18.3469	+	4.37099i	−0.851732	+	0.202918i
$465$	10.1502	−	17.5806i	0.470702	−	0.815280i
$466$	0.910930	−	0.302146i	0.0421980	−	0.0139966i
$467$	5.96750			0.276143			0.138072	−	0.990422i	$-0.455910\pi$
$467$	5.96750			0.276143			0.138072	+	0.990422i	$0.455910\pi$
$468$	2.19607	+	18.6936i	0.101513	+	0.864111i
$469$	15.5802	−	26.9857i	0.719426	−	1.24608i
$470$	11.4691	−	55.6271i	0.529029	−	2.56589i
$471$	3.35935	−	5.81857i	0.154791	−	0.268106i
$472$	−2.63510	+	30.4272i	−0.121290	+	1.40053i
$473$	1.23801	+	2.14429i	0.0569236	+	0.0985946i
$474$	3.94806	−	4.43902i	0.181340	−	0.203891i
$475$	26.9025	+	46.1471i	1.23437	+	2.11737i
$476$	−19.3850	+	2.27729i	−0.888511	+	0.104380i
$477$	2.85433	+	4.94384i	0.130691	+	0.226363i
$478$	−6.34153	−	1.30749i	−0.290055	−	0.0598030i
$479$	−23.5115	−	13.5744i	−1.07427	−	0.620229i	−0.144924	−	0.989443i	$-0.546294\pi$
$479$	−23.5115	−	13.5744i	−1.07427	−	0.620229i	−0.929344	+	0.369214i	$0.879627\pi$
$480$	0.584868	+	19.1367i	0.0266955	+	0.873467i
$481$	−2.71641	+	4.70496i	−0.123858	+	0.214528i
$482$	−5.40975	+	6.08247i	−0.246407	+	0.277049i
$483$			9.20511i			0.418847i
$484$	17.4793	+	7.52770i	0.794514	+	0.342168i
$485$	29.0634	−	50.3393i	1.31970	−	2.28579i
$486$	14.9130	−	16.7674i	0.676466	−	0.760587i
$487$	−35.4384			−1.60587			−0.802933	−	0.596070i	$-0.796728\pi$
$487$	−35.4384			−1.60587			−0.802933	+	0.596070i	$0.796728\pi$
$488$	−0.890361	+	0.416135i	−0.0403047	+	0.0188375i
$489$	2.81613	−	1.62590i	0.127350	−	0.0735255i
$490$	−6.55192	−	19.7532i	−0.295986	−	0.892359i
$491$	5.05769	+	8.76018i	0.228250	+	0.395341i	0.957290	−	0.289131i	$-0.0933662\pi$
$491$	5.05769	+	8.76018i	0.228250	+	0.395341i	−0.729039	+	0.684472i	$0.760033\pi$
$492$	−4.48216	+	3.34092i	−0.202071	+	0.150620i
$493$	−14.1719			−0.638268
$494$	23.5375	−	7.91718i	1.05900	−	0.356211i
$495$		−	11.8226i		−	0.531385i
$496$	16.4848	+	17.4319i	0.740189	+	0.782715i
$497$	−3.27048	+	1.88821i	−0.146701	+	0.0846979i
$498$	4.25395	+	12.8251i	0.190624	+	0.574707i
$499$	5.83840	+	10.1124i	0.261363	+	0.452693i	0.966604	−	0.256274i	$-0.0824948\pi$
$499$	5.83840	+	10.1124i	0.261363	+	0.452693i	−0.705242	+	0.708967i	$0.749161\pi$
$500$	−23.8387	+	55.3535i	−1.06610	+	2.47548i
$501$		−	15.0652i		−	0.673063i
$502$	−15.9111	−	14.1513i	−0.710148	−	0.631605i
$503$	26.1068	+	15.0728i	1.16405	+	0.672062i	0.952270	−	0.305256i	$-0.0987421\pi$
$503$	26.1068	+	15.0728i	1.16405	+	0.672062i	0.211776	+	0.977318i	$0.432075\pi$
$504$	19.4363	−	9.08412i	0.865764	−	0.404639i
$505$	−83.0329			−3.69491
$506$	−3.98413	+	4.47957i	−0.177116	+	0.199141i
$507$	−2.27831	−	1.31539i	−0.101184	−	0.0584183i
$508$	13.8004	−	10.2866i	0.612293	−	0.456393i
$509$	−3.66628	+	6.35018i	−0.162505	+	0.281467i	−0.935766	−	0.352620i	$-0.885291\pi$
$509$	−3.66628	+	6.35018i	−0.162505	+	0.281467i	0.773261	+	0.634087i	$0.218624\pi$
$510$	−2.90502	+	14.0899i	−0.128636	+	0.623909i
$511$	8.24883	−	4.76246i	0.364907	−	0.210679i
$512$	−21.8718	−	5.79878i	−0.966605	−	0.256272i
$513$	−16.4523	−	9.40668i	−0.726387	−	0.415315i
$514$	11.4253	−	12.8461i	0.503951	−	0.566619i
$515$	−6.73100	+	3.88615i	−0.296603	+	0.171244i
$516$	1.97922	+	2.65530i	0.0871302	+	0.116893i
$517$	10.2013	+	5.88971i	0.448652	+	0.259029i
$518$	6.06503	+	1.25048i	0.266482	+	0.0549428i
$519$	2.55879	+	1.47732i	0.112318	+	0.0648469i
$520$	38.7946	+	27.1135i	1.70125	+	1.18901i
$521$			33.7736i			1.47965i	0.672800	+	0.739825i	$0.265092\pi$
$521$			33.7736i			1.47965i	−0.672800	+	0.739825i	$0.734908\pi$
$522$	14.7855	−	4.90419i	0.647144	−	0.214650i
$523$	−10.2580	−	5.92247i	−0.448552	−	0.258972i	0.258666	−	0.965967i	$-0.416717\pi$
$523$	−10.2580	−	5.92247i	−0.448552	−	0.258972i	−0.707219	+	0.706995i	$0.750050\pi$
$524$	−0.230865	−	1.96519i	−0.0100854	−	0.0858497i
$525$	−32.4202			−1.41494
$526$	4.21441	+	12.7059i	0.183757	+	0.554003i
$527$	9.01393	+	15.6126i	0.392653	+	0.680095i
$528$	−3.80523	−	1.13435i	−0.165601	−	0.0493664i
$529$	−5.44676	−	9.43406i	−0.236815	−	0.410176i
$530$	14.0593	+	2.89872i	0.610698	+	0.125912i
$531$		−	25.2253i		−	1.09468i
$532$	−17.0120	−	22.6239i	−0.737562	−	0.980869i
$533$			13.8199i			0.598606i
$534$	3.26827	−	15.8517i	0.141432	−	0.685969i
$535$	9.13356	+	15.8198i	0.394878	+	0.683949i
$536$	24.5906	−	11.4931i	1.06215	−	0.496426i
$537$	−6.46443	−	11.1967i	−0.278961	−	0.483174i
$538$	4.43496	−	1.47103i	0.191205	−	0.0634205i
$539$	4.31619			0.185911
$540$	−4.21432	−	35.8736i	−0.181355	−	1.54375i
$541$	2.24678	+	1.29718i	0.0965967	+	0.0557701i	0.547520	−	0.836792i	$-0.315572\pi$
$541$	2.24678	+	1.29718i	0.0965967	+	0.0557701i	−0.450923	+	0.892563i	$0.648905\pi$
$542$	5.33991	+	16.0991i	0.229369	+	0.691518i
$543$		−	3.49336i		−	0.149915i
$544$	−14.9774	−	8.04745i	−0.642150	−	0.345031i
$545$	−14.0142	−	8.09112i	−0.600304	−	0.346586i
$546$	−3.04355	+	14.7617i	−0.130252	+	0.631745i
$547$	7.78965	+	4.49735i	0.333061	+	0.192293i	0.657199	−	0.753717i	$-0.271741\pi$
$547$	7.78965	+	4.49735i	0.333061	+	0.192293i	−0.324138	+	0.946010i	$0.605074\pi$
$548$	−29.5352	+	22.0150i	−1.26168	+	0.940435i
$549$	0.702991	−	0.405872i	0.0300029	−	0.0173222i
$550$	−15.7770	−	14.0320i	−0.672733	−	0.598329i
$551$	−10.3511	−	17.7557i	−0.440971	−	0.756418i
$552$	−4.59350	+	6.57248i	−0.195512	+	0.279743i
$553$	−14.4973	+	8.37001i	−0.616487	+	0.355929i
$554$	−16.9938	−	3.50376i	−0.721999	−	0.148860i
$555$	2.28216	−	3.95283i	0.0968725	−	0.167788i
$556$	17.5366	−	13.0715i	0.743718	−	0.554355i
$557$	27.7574	+	16.0257i	1.17612	+	0.679032i	0.955113	−	0.296241i	$-0.0957331\pi$
$557$	27.7574	+	16.0257i	1.17612	+	0.679032i	0.221004	+	0.975273i	$0.429066\pi$
$558$	−14.8070	−	13.1693i	−0.626830	−	0.557502i
$559$	8.18713			0.346279
$560$	15.4123	−	51.7012i	0.651291	−	2.18477i
$561$	−2.58389	−	1.49181i	−0.109092	−	0.0629844i
$562$	−11.3850	+	12.8007i	−0.480246	+	0.539966i
$563$		−	30.9719i		−	1.30531i	−0.757655	−	0.652656i	$-0.773655\pi$
$563$		−	30.9719i		−	1.30531i	0.757655	−	0.652656i	$-0.226345\pi$
$564$	14.4706	+	6.23198i	0.609324	+	0.262414i
$565$	−0.459669	−	0.796170i	−0.0193384	−	0.0334951i
$566$	−17.5567	+	5.82335i	−0.737961	+	0.244774i
$567$	−9.74577	+	5.62672i	−0.409284	+	0.236300i
$568$	−3.27738	−	0.283832i	−0.137516	−	0.0119093i
$569$			9.72745i			0.407796i	0.978992	+	0.203898i	$0.0653611\pi$
$569$			9.72745i			0.407796i	−0.978992	+	0.203898i	$0.934639\pi$
$570$	−19.7748	+	6.65155i	−0.828274	+	0.278603i
$571$	41.7629			1.74772			0.873862	−	0.486174i	$-0.161608\pi$
$571$	41.7629			1.74772			0.873862	+	0.486174i	$0.161608\pi$
$572$	−7.87025	+	5.86636i	−0.329072	+	0.245285i
$573$	0.750022	+	1.29908i	0.0313326	+	0.0542697i
$574$	14.9516	−	4.95928i	0.624068	−	0.206997i
$575$	−36.9263	+	21.3194i	−1.53993	+	0.889082i
$576$	18.4107	+	3.21296i	0.767114	+	0.133873i
$577$	37.1247			1.54552			0.772761	−	0.634698i	$-0.218875\pi$
$577$	37.1247			1.54552			0.772761	+	0.634698i	$0.218875\pi$
$578$	8.41805	+	7.48701i	0.350145	+	0.311419i
$579$	−5.09967	+	8.83290i	−0.211935	+	0.367083i
$580$	15.4940	−	35.9771i	0.643354	−	1.49387i
$581$		−	38.0753i		−	1.57963i
$582$	12.0485	+	10.7159i	0.499425	+	0.444189i
$583$	−1.48858	+	2.57829i	−0.0616506	+	0.106782i
$584$	8.26624	+	0.715884i	0.342059	+	0.0296235i
$585$	−33.8549	−	19.5461i	−1.39973	−	0.808132i
$586$	3.38863	−	16.4355i	0.139983	−	0.678943i
$587$	−20.9655	−	36.3133i	−0.865338	−	1.49881i	−0.866711	−	0.498810i	$-0.833770\pi$
$587$	−20.9655	−	36.3133i	−0.865338	−	1.49881i	0.00137323	−	0.999999i	$-0.499563\pi$
$588$	5.73368	−	0.673575i	0.236453	−	0.0277778i
$589$	−12.9770	+	22.6968i	−0.534708	+	0.935205i
$590$	−47.3974	−	42.1553i	−1.95132	−	1.73550i
$591$	4.28059	+	7.41421i	0.176080	+	0.304980i
$592$	3.70645	+	3.91939i	0.152334	+	0.161086i
$593$	2.27252	−	3.93612i	0.0933212	−	0.161637i	−0.815586	−	0.578637i	$-0.803585\pi$
$593$	2.27252	−	3.93612i	0.0933212	−	0.161637i	0.908907	+	0.417000i	$0.136918\pi$
$594$	7.33683	+	1.51269i	0.301034	+	0.0620666i
$595$	20.2691	−	35.1071i	0.830952	−	1.43925i
$596$	1.55863	−	0.183103i	0.0638441	−	0.00750021i
$597$	4.91105			0.200996
$598$	6.24070	+	18.8149i	0.255201	+	0.769399i
$599$	−17.1887	+	29.7716i	−0.702309	+	1.21644i	0.265344	+	0.964154i	$0.414514\pi$
$599$	−17.1887	+	29.7716i	−0.702309	+	1.21644i	−0.967654	+	0.252282i	$0.918819\pi$
$600$	−23.1482	−	16.1782i	−0.945020	−	0.660473i
$601$			43.0249i			1.75502i	0.479554	+	0.877512i	$0.340798\pi$
$601$			43.0249i			1.75502i	−0.479554	+	0.877512i	$0.659202\pi$
$602$	−2.93796	−	8.85758i	−0.119742	−	0.361008i
$603$	−19.4157	+	11.2097i	−0.790668	+	0.456492i
$604$	−8.33690	−	3.59040i	−0.339224	−	0.146091i
$605$	−34.2312	+	19.7634i	−1.39170	+	0.803496i
$606$	4.65114	−	22.5589i	0.188940	−	0.916391i
$607$	−38.5179			−1.56339			−0.781696	−	0.623660i	$-0.785645\pi$
$607$	−38.5179			−1.56339			−0.781696	+	0.623660i	$0.785645\pi$
$608$	−0.856925	−	24.6428i	−0.0347529	−	0.999396i
$609$	12.4741			0.505477
$610$	0.412185	−	1.99917i	0.0166889	−	0.0809441i
$611$	33.7313	−	19.4748i	1.36462	−	0.787866i
$612$	12.8978	+	5.55463i	0.521364	+	0.224532i
$613$	8.20483	−	4.73706i	0.331390	−	0.191328i	−0.325068	−	0.945691i	$-0.605387\pi$
$613$	8.20483	−	4.73706i	0.331390	−	0.191328i	0.656458	+	0.754362i	$0.272054\pi$
$614$	−8.31894	−	25.0805i	−0.335725	−	1.01217i
$615$		−	11.6107i		−	0.468187i
$616$	9.17100	+	6.40960i	0.369510	+	0.258250i
$617$	−10.5392	+	18.2545i	−0.424294	+	0.734899i	−0.996354	−	0.0853127i	$-0.972811\pi$
$617$	−10.5392	+	18.2545i	−0.424294	+	0.734899i	0.572060	+	0.820212i	$0.306144\pi$
$618$	−0.678769	−	2.04640i	−0.0273041	−	0.0823184i
$619$	2.62181			0.105380			0.0526898	−	0.998611i	$-0.483221\pi$
$619$	2.62181			0.105380			0.0526898	+	0.998611i	$0.483221\pi$
$620$	−49.4895	+	5.81387i	−1.98754	+	0.233491i
$621$	7.56395	−	13.1011i	0.303531	−	0.525731i
$622$	24.8548	+	5.12451i	0.996586	+	0.205474i
$623$	−22.8036	+	39.4969i	−0.913606	+	1.58241i
$624$	−9.53946	+	9.02116i	−0.381884	+	0.361135i
$625$	−31.9504	−	55.3397i	−1.27802	−	2.21359i
$626$	33.5882	+	29.8733i	1.34245	+	1.19398i
$627$	−0.0182026	−	4.32694i	−0.000726940	−	0.172801i
$628$	−16.3793	+	1.92419i	−0.653606	+	0.0767837i
$629$	2.02669	+	3.51034i	0.0808096	+	0.139966i
$630$	−8.99790	+	43.6414i	−0.358485	+	1.73871i
$631$	37.2197	+	21.4888i	1.48169	+	0.855455i	0.999784	−	0.0207671i	$-0.00661086\pi$
$631$	37.2197	+	21.4888i	1.48169	+	0.855455i	0.481907	+	0.876222i	$0.339944\pi$
$632$	−14.5279	−	1.25816i	−0.577888	−	0.0500471i
$633$	5.96112	−	10.3250i	0.236933	−	0.410381i
$634$	−9.48023	−	8.43172i	−0.376508	−	0.334866i
$635$			35.7488i			1.41865i
$636$	−1.57508	+	3.65734i	−0.0624561	+	0.145023i
$637$	7.13591	−	12.3598i	0.282735	−	0.489711i
$638$	6.07040	+	5.39902i	0.240330	+	0.213749i
$639$	2.71707			0.107486
$640$	36.8042	−	29.2238i	1.45481	−	1.15517i
$641$	−24.4261	+	14.1024i	−0.964773	+	0.557012i	−0.897639	−	0.440732i	$-0.854719\pi$
$641$	−24.4261	+	14.1024i	−0.964773	+	0.557012i	−0.0671340	+	0.997744i	$0.521386\pi$
$642$	−4.80964	+	1.59530i	−0.189821	+	0.0629616i
$643$	3.71938	+	6.44216i	0.146678	+	0.254054i	0.929998	−	0.367565i	$-0.119809\pi$
$643$	3.71938	+	6.44216i	0.146678	+	0.254054i	−0.783320	+	0.621619i	$0.786475\pi$
$644$	18.1162	−	13.5035i	0.713878	−	0.532113i
$645$	−6.87835			−0.270835
$646$	3.66500	−	18.1619i	0.144198	−	0.714570i
$647$			18.5510i			0.729316i	0.931141	+	0.364658i	$0.118814\pi$
$647$			18.5510i			0.729316i	−0.931141	+	0.364658i	$0.881186\pi$
$648$	−9.76634	−	0.845798i	−0.383658	−	0.0332261i
$649$	11.3929	−	6.57770i	0.447211	−	0.258197i
$650$	−66.2658	+	21.9796i	−2.59916	+	0.862113i
$651$	−7.93409	−	13.7423i	−0.310962	−	0.538601i
$652$	−7.33101	−	3.15720i	−0.287104	−	0.123645i
$653$			23.6341i			0.924874i	0.886652	+	0.462437i	$0.153025\pi$
$653$			23.6341i			0.924874i	−0.886652	+	0.462437i	$0.846975\pi$
$654$	2.98326	−	3.35424i	0.116655	−	0.131161i
$655$	3.55904	+	2.05481i	0.139063	+	0.0802882i
$656$	13.1503	+	3.92015i	0.513432	+	0.153056i
$657$	−6.85301			−0.267361
$658$	−33.1741	−	29.5051i	−1.29326	−	1.15023i
$659$	−24.6089	−	14.2079i	−0.958625	−	0.553463i	−0.0628757	−	0.998021i	$-0.520027\pi$
$659$	−24.6089	−	14.2079i	−0.958625	−	0.553463i	−0.895750	+	0.444559i	$0.853360\pi$
$660$	6.61212	−	4.92856i	0.257376	−	0.191844i
$661$	−18.8702	+	32.6841i	−0.733964	+	1.27126i	0.221212	+	0.975226i	$0.428999\pi$
$661$	−18.8702	+	32.6841i	−0.733964	+	1.27126i	−0.955176	+	0.296038i	$0.904335\pi$
$662$	41.2739	+	8.50977i	1.60415	+	0.330742i
$663$	−8.54385	+	4.93280i	−0.331816	+	0.191574i
$664$	19.0002	−	27.1859i	0.737351	−	1.05502i
$665$	58.7896	−	0.247316i	2.27976	−	0.00959051i
$666$	−3.32921	−	2.96100i	−0.129004	−	0.114736i
$667$	14.2079	−	8.20293i	0.550132	−	0.317619i
$668$	−29.6492	+	22.1000i	−1.14716	+	0.855074i
$669$	19.4158	+	11.2097i	0.750657	+	0.433392i
$670$	−11.3840	+	55.2145i	−0.439803	+	2.13312i
$671$	0.366622	+	0.211669i	0.0141533	+	0.00817140i
$672$	13.1831	+	7.08339i	0.508551	+	0.273248i
$673$		−	7.92449i		−	0.305467i	−0.988267	−	0.152733i	$-0.951192\pi$
$673$		−	7.92449i		−	0.305467i	0.988267	−	0.152733i	$-0.0488075\pi$
$674$	−3.82685	−	11.5375i	−0.147405	−	0.444406i
$675$	46.1420	+	26.6401i	1.77601	+	1.02538i
$676$	0.753436	+	6.41347i	0.0289783	+	0.246672i
$677$	−13.1739			−0.506315			−0.253158	−	0.967425i	$-0.581469\pi$
$677$	−13.1739			−0.506315			−0.253158	+	0.967425i	$0.581469\pi$
$678$	0.242057	−	0.0802876i	0.00929614	−	0.00308343i
$679$	−22.7181	−	39.3488i	−0.871839	−	1.51007i
$680$	31.9912	−	14.9520i	1.22681	−	0.573382i
$681$	7.52271	+	13.0297i	0.288271	+	0.499300i
$682$	2.08684	−	10.1215i	0.0799092	−	0.387574i
$683$			25.6624i			0.981945i	0.871175	+	0.490972i	$0.163358\pi$
$683$			25.6624i			0.981945i	−0.871175	+	0.490972i	$0.836642\pi$
$684$	2.46125	+	20.2166i	0.0941081	+	0.773000i
$685$		−	76.5085i		−	2.92324i
$686$	15.5484	+	3.20574i	0.593642	+	0.122396i
$687$	7.66491	+	13.2760i	0.292435	+	0.506512i
$688$	2.32236	−	7.79043i	0.0885392	−	0.297007i
$689$	4.92210	+	8.52533i	0.187517	+	0.324789i
$690$	−5.24307	−	15.8072i	−0.199600	−	0.601769i
$691$	−42.3757			−1.61205			−0.806024	−	0.591883i	$-0.798385\pi$
$691$	−42.3757			−1.61205			−0.806024	+	0.591883i	$0.798385\pi$
$692$	−0.846187	−	7.20300i	−0.0321672	−	0.273817i
$693$	−8.00326	−	4.62068i	−0.304019	−	0.175525i
$694$	21.3595	−	7.08470i	0.810795	−	0.268932i
$695$			45.4272i			1.72315i
$696$	8.90656	+	6.22479i	0.337602	+	0.235950i
$697$	8.92954	+	5.15547i	0.338230	+	0.195277i
$698$	15.6747	+	3.23178i	0.593296	+	0.122325i
$699$	−0.478861	−	0.276470i	−0.0181122	−	0.0104571i
$700$	47.5591	+	63.8050i	1.79757	+	2.41160i
$701$	−10.6725	+	6.16178i	−0.403096	+	0.232727i	−0.687819	−	0.725882i	$-0.741432\pi$
$701$	−10.6725	+	6.16178i	−0.403096	+	0.232727i	0.284723	+	0.958610i	$0.408098\pi$
$702$	16.4616	−	18.5087i	0.621304	−	0.698566i
$703$	−2.91776	+	5.10316i	−0.110045	+	0.192469i
$704$	3.34963	+	9.15296i	0.126244	+	0.344965i
$705$	−28.3391	+	16.3616i	−1.06731	+	0.616212i
$706$	−1.29124	+	6.26276i	−0.0485966	+	0.235702i
$707$	−32.4522	+	56.2089i	−1.22049	+	2.11395i
$708$	14.1080	−	10.5159i	0.530211	−	0.395210i
$709$	−8.81856	−	5.09140i	−0.331188	−	0.191212i	0.325180	−	0.945652i	$-0.394575\pi$
$709$	−8.81856	−	5.09140i	−0.331188	−	0.191212i	−0.656368	+	0.754440i	$0.727908\pi$
$710$	4.54063	−	5.10528i	0.170407	−	0.191598i
$711$	12.0441			0.451690
$712$	−35.9914	+	16.8216i	−1.34884	+	0.630416i
$713$	−18.0737	−	10.4349i	−0.676866	−	0.390789i
$714$	8.40271	+	7.47337i	0.314464	+	0.279684i
$715$		−	20.3873i		−	0.762440i
$716$	−12.5528	+	29.1475i	−0.469119	+	1.08929i
$717$	1.86523	+	3.23068i	0.0696584	+	0.120652i
$718$	−15.2957	−	46.1145i	−0.570830	−	1.72098i
$719$	43.2292	−	24.9584i	1.61218	−	0.930791i	0.623312	−	0.781973i	$-0.285787\pi$
$719$	43.2292	−	24.9584i	1.61218	−	0.930791i	0.988865	−	0.148817i	$-0.0475466\pi$
$720$	−28.2023	+	26.6700i	−1.05104	+	0.993932i
$721$			6.07538i			0.226259i
$722$	25.4317	−	8.67358i	0.946468	−	0.322797i
$723$	4.68987			0.174418
$724$	−6.87515	+	5.12462i	−0.255513	+	0.190455i
$725$	28.8906	+	50.0400i	1.07297	+	1.85844i
$726$	−3.45195	−	10.4072i	−0.128114	−	0.386247i
$727$	4.69030	−	2.70795i	0.173954	−	0.100432i	−0.410495	−	0.911863i	$-0.634644\pi$
$727$	4.69030	−	2.70795i	0.173954	−	0.100432i	0.584449	+	0.811431i	$0.301311\pi$
$728$	33.5167	−	15.6650i	1.24221	−	0.580583i
$729$	−2.53093			−0.0937382
$730$	−11.4524	+	12.8766i	−0.423873	+	0.476583i
$731$	3.05419	−	5.29000i	0.112963	−	0.195658i
$732$	0.520058	+	0.223970i	0.0192219	+	0.00827816i
$733$		−	13.6183i		−	0.503003i	−0.967857	−	0.251502i	$-0.919076\pi$
$733$		−	13.6183i		−	0.503003i	0.967857	−	0.251502i	$-0.0809244\pi$
$734$	26.6780	−	29.9956i	0.984705	−	1.10716i
$735$	−5.99517	+	10.3839i	−0.221135	+	0.383017i
$736$	19.6735	−	0.601274i	0.725174	−	0.0221632i
$737$	−10.1256	−	5.84602i	−0.372982	−	0.215341i
$738$	−11.1002	−	2.28863i	−0.408606	−	0.0842455i
$739$	9.19703	+	15.9297i	0.338318	+	0.585984i	0.984117	−	0.177524i	$-0.0568086\pi$
$739$	9.19703	+	15.9297i	0.338318	+	0.585984i	−0.645798	+	0.763508i	$0.723475\pi$
$740$	−11.1272	+	1.30719i	−0.409045	+	0.0480534i
$741$	−12.4206	−	7.10156i	−0.456283	−	0.260882i
$742$	7.45717	−	8.38450i	0.273761	−	0.307805i
$743$	1.99704	+	3.45898i	0.0732643	+	0.126898i	0.900330	−	0.435207i	$-0.143325\pi$
$743$	1.99704	+	3.45898i	0.0732643	+	0.126898i	−0.827066	+	0.562105i	$0.809992\pi$
$744$	1.19264	−	13.7713i	0.0437242	−	0.504879i
$745$	−1.62971	+	2.82275i	−0.0597081	+	0.103418i
$746$	−2.49537	+	12.1030i	−0.0913620	+	0.443122i
$747$	−13.6972	+	23.7243i	−0.501156	+	0.868028i
$748$	0.854490	+	7.27368i	0.0312433	+	0.265952i
$749$	14.2789			0.521740
$750$	32.9575	−	10.9316i	1.20344	−	0.399167i
$751$	−0.00116611	+	0.00201977i	−4.25521e−5	+	7.37023e-5i	−0.866047	−	0.499963i	$-0.833347\pi$
$751$	−0.00116611	+	0.00201977i	−4.25521e−5	+	7.37023e-5i	0.866004	+	0.500037i	$0.166680\pi$
$752$	−8.96293	−	37.6211i	−0.326844	−	1.37190i
$753$			12.2682i			0.447078i
$754$	25.4967	−	8.45696i	0.928533	−	0.307984i
$755$	16.3268	−	9.42630i	0.594194	−	0.343058i
$756$	−25.9317	−	11.1678i	−0.943125	−	0.406169i
$757$	−9.96007	+	5.75045i	−0.362005	+	0.209004i	−0.669960	−	0.742397i	$-0.733689\pi$
$757$	−9.96007	+	5.75045i	−0.362005	+	0.209004i	0.307955	+	0.951401i	$0.400355\pi$
$758$	−16.7437	−	3.45219i	−0.608159	−	0.125389i
$759$	3.45396			0.125371
$760$	42.0994	+	29.1604i	1.52711	+	1.05776i
$761$	13.5383			0.490765			0.245382	−	0.969426i	$-0.421086\pi$
$761$	13.5383			0.490765			0.245382	+	0.969426i	$0.421086\pi$
$762$	−9.71244	−	2.00249i	−0.351844	−	0.0725426i
$763$	−10.9545	+	6.32461i	−0.396581	+	0.228966i
$764$	1.45641	−	3.38178i	0.0526909	−	0.122348i
$765$	−25.2589	+	14.5832i	−0.913238	+	0.527258i
$766$	−16.2030	+	5.37436i	−0.585439	+	0.194184i
$767$		−	43.4994i		−	1.57067i
$768$	5.87808	+	11.6362i	0.212107	+	0.419884i
$769$	4.16442	−	7.21299i	0.150173	−	0.260107i	−0.781118	−	0.624383i	$-0.785350\pi$
$769$	4.16442	−	7.21299i	0.150173	−	0.260107i	0.931291	+	0.364276i	$0.118684\pi$
$770$	−22.0568	+	7.31599i	−0.794871	+	0.263650i
$771$	−9.90496			−0.356718
$772$	24.8647	−	2.92103i	0.894899	−	0.105130i
$773$	0.0685585	−	0.118747i	0.00246588	−	0.00427103i	−0.864790	−	0.502134i	$-0.832548\pi$
$773$	0.0685585	−	0.118747i	0.00246588	−	0.00427103i	0.867256	+	0.497863i	$0.165882\pi$
$774$	−1.35582	+	6.57597i	−0.0487340	+	0.236368i
$775$	36.7514	−	63.6553i	1.32015	−	2.28657i
$776$	3.41494	−	39.4319i	0.122589	−	1.41552i
$777$	−1.78390	−	3.08981i	−0.0639972	−	0.110846i
$778$	6.16541	−	6.93210i	0.221041	−	0.248528i
$779$	0.0629052	+	14.9532i	0.00225381	+	0.535755i
$780$	−3.18159	−	27.0827i	−0.113919	−	0.969716i
$781$	0.708498	+	1.22715i	0.0253521	+	0.0439111i
$782$	14.4851	+	2.98650i	0.517985	+	0.106797i
$783$	−17.7538	−	10.2501i	−0.634467	−	0.366310i
$784$	−9.73670	−	10.2961i	−0.347739	−	0.367718i
$785$	17.1263	−	29.6636i	0.611264	−	1.05874i
$786$	−0.757626	+	0.851840i	−0.0270236	+	0.0303841i
$787$		−	27.2431i		−	0.971113i	−0.874205	−	0.485556i	$-0.838617\pi$
$787$		−	27.2431i		−	0.971113i	0.874205	−	0.485556i	$-0.161383\pi$
$788$	8.31214	−	19.3008i	0.296108	−	0.687562i
$789$	3.85628	−	6.67928i	0.137287	−	0.237789i
$790$	20.1276	−	22.6305i	0.716107	−	0.805158i
$791$	−0.718621			−0.0255512
$792$	−3.40856	−	7.29294i	−0.121118	−	0.259143i
$793$	1.21226	−	0.699901i	0.0430488	−	0.0248542i
$794$	8.26603	+	24.9210i	0.293351	+	0.884415i
$795$	−4.13526	−	7.16248i	−0.146663	−	0.254027i
$796$	−7.20430	−	9.66523i	−0.255350	−	0.342575i
$797$	39.2885			1.39167			0.695835	−	0.718202i	$-0.255035\pi$
$797$	39.2885			1.39167			0.695835	+	0.718202i	$0.255035\pi$
$798$	−3.22595	+	15.9862i	−0.114197	+	0.565904i
$799$		−	29.0600i		−	1.02807i
$800$	2.11768	+	69.2897i	0.0748712	+	2.44976i
$801$	28.4173	−	16.4067i	1.00408	−	0.579704i
$802$	−10.7812	−	32.5041i	−0.380699	−	1.14776i
$803$	−1.78698	−	3.09514i	−0.0630611	−	0.109225i
$804$	−14.3633	−	6.18575i	−0.506555	−	0.218155i
$805$			46.9285i			1.65401i
$806$	−25.5337	−	22.7097i	−0.899387	−	0.799914i
$807$	−2.33139	−	1.34603i	−0.0820687	−	0.0473824i
$808$	−51.2202	+	23.9392i	−1.80192	+	0.842177i
$809$	41.6938			1.46588			0.732938	−	0.680295i	$-0.238148\pi$
$809$	41.6938			1.46588			0.732938	+	0.680295i	$0.238148\pi$
$810$	13.5307	−	15.2133i	0.475421	−	0.534542i
$811$	8.50428	+	4.90995i	0.298626	+	0.172412i	0.641825	−	0.766851i	$-0.278177\pi$
$811$	8.50428	+	4.90995i	0.298626	+	0.172412i	−0.343200	+	0.939262i	$0.611511\pi$
$812$	−18.2990	−	24.5498i	−0.642169	−	0.861529i
$813$	4.88615	−	8.46305i	0.171365	−	0.296812i
$814$	0.469206	−	2.27573i	0.0164457	−	0.0797644i
$815$	14.3569	−	8.28897i	0.502901	−	0.290350i
$816$	2.27023	+	9.52910i	0.0794740	+	0.333585i
$817$	8.85853	−	0.0372661i	0.309921	−	0.00130377i
$818$	−6.29026	+	7.07248i	−0.219934	+	0.247284i
$819$	−26.4634	+	15.2787i	−0.924706	+	0.533879i
$820$	−22.8505	+	17.0323i	−0.797973	+	0.594795i
$821$	−22.9743	−	13.2642i	−0.801809	−	0.462925i	0.0422942	−	0.999105i	$-0.486533\pi$
$821$	−22.9743	−	13.2642i	−0.801809	−	0.462925i	−0.844103	+	0.536180i	$0.819867\pi$
$822$	20.7863	+	4.28567i	0.725004	+	0.149480i
$823$	33.1763	+	19.1543i	1.15645	+	0.667678i	0.950451	−	0.310874i	$-0.100622\pi$
$823$	33.1763	+	19.1543i	1.15645	+	0.667678i	0.206001	+	0.978552i	$0.433955\pi$
$824$	−3.03171	+	4.33784i	−0.105615	+	0.151116i
$825$			12.1648i			0.423523i
$826$	−47.0616	+	15.6098i	−1.63748	+	0.543134i
$827$	39.0052	+	22.5196i	1.35634	+	0.783085i	0.989129	−	0.147052i	$-0.0469785\pi$
$827$	39.0052	+	22.5196i	1.35634	+	0.783085i	0.367214	+	0.930137i	$0.380312\pi$
$828$	−16.1458	+	1.89676i	−0.561104	+	0.0659168i
$829$	24.9335			0.865977			0.432989	−	0.901399i	$-0.357459\pi$
$829$	24.9335			0.865977			0.432989	+	0.901399i	$0.357459\pi$
$830$	21.6870	+	65.3836i	0.752768	+	2.26950i
$831$	4.99839	+	8.65746i	0.173392	+	0.300324i
$832$	31.7481	+	5.54055i	1.10067	+	0.192084i
$833$	−5.32406	−	9.22154i	−0.184468	−	0.319507i
$834$	−12.3419	−	2.54463i	−0.427366	−	0.0881135i
$835$		−	76.8038i		−	2.65790i
$836$	−8.48896	+	6.38326i	−0.293597	+	0.220770i
$837$			26.0782i			0.901393i
$838$	−5.44122	+	26.3909i	−0.187964	+	0.911657i
$839$	−9.87363	−	17.1016i	−0.340876	−	0.590414i	0.643720	−	0.765261i	$-0.277390\pi$
$839$	−9.87363	−	17.1016i	−0.340876	−	0.590414i	−0.984596	+	0.174847i	$0.944057\pi$
$840$	−28.1588	+	13.1608i	−0.971570	+	0.454090i
$841$	3.38396	+	5.86119i	0.116688	+	0.202110i
$842$	46.5798	−	15.4500i	1.60525	−	0.532442i
$843$	9.86995			0.339939
$844$	−29.0649	+	3.41445i	−1.00045	+	0.117530i
$845$	−11.6151	−	6.70596i	−0.399570	−	0.230692i
$846$	10.0563	+	30.3184i	0.345742	+	1.04237i
$847$			30.8970i			1.06163i
$848$	9.50845	−	2.26531i	0.326521	−	0.0777911i
$849$	9.22924	+	5.32850i	0.316747	+	0.182874i
$850$	−10.5184	+	51.0162i	−0.360779	+	1.74984i
$851$	−4.06370	−	2.34618i	−0.139302	−	0.0804260i
$852$	1.13269	+	1.51960i	0.0388052	+	0.0520607i
$853$	−6.13275	+	3.54074i	−0.209981	+	0.121233i	−0.601303	−	0.799021i	$-0.705351\pi$
$853$	−6.13275	+	3.54074i	−0.209981	+	0.121233i	0.391321	+	0.920254i	$0.372018\pi$
$854$	−1.19224	−	1.06038i	−0.0407976	−	0.0362853i
$855$	−36.7202	−	20.9949i	−1.25580	−	0.718011i
$856$	10.1952	+	7.12540i	0.348464	+	0.243541i
$857$	10.7446	−	6.20337i	0.367027	−	0.211903i	−0.305132	−	0.952310i	$-0.598701\pi$
$857$	10.7446	−	6.20337i	0.367027	−	0.211903i	0.672159	+	0.740407i	$0.265367\pi$
$858$	5.53893	+	1.14201i	0.189096	+	0.0389874i
$859$	21.2782	−	36.8549i	0.726003	−	1.25747i	−0.232557	−	0.972583i	$-0.574709\pi$
$859$	21.2782	−	36.8549i	0.726003	−	1.25747i	0.958560	−	0.284891i	$-0.0919576\pi$
$860$	10.0902	+	13.5370i	0.344074	+	0.461607i
$861$	−7.85981	−	4.53786i	−0.267862	−	0.154650i
$862$	−28.5739	−	25.4136i	−0.973230	−	0.865591i
$863$	−2.40464			−0.0818549			−0.0409275	−	0.999162i	$-0.513031\pi$
$863$	−2.40464			−0.0818549			−0.0409275	+	0.999162i	$0.513031\pi$
$864$	−12.9424	−	20.9142i	−0.440308	−	0.711515i
$865$	13.0449	+	7.53149i	0.443541	+	0.256078i
$866$	−32.3345	+	36.3555i	−1.09877	+	1.23541i
$867$		−	6.49071i		−	0.220436i
$868$	−15.4066	+	35.7741i	−0.522933	+	1.21425i
$869$	3.14061	+	5.43969i	0.106538	+	0.184529i
$870$	−21.4208	+	7.10504i	−0.726232	+	0.240883i
$871$	−33.4811	+	19.3303i	−1.13446	+	0.654984i
$872$	−10.9777	−	0.950703i	−0.371750	−	0.0321949i
$873$			32.6904i			1.10640i
$874$	6.83812	+	20.3295i	0.231303	+	0.687654i
$875$	−97.8446			−3.30775
$876$	−2.85687	−	3.83275i	−0.0965246	−	0.129497i
$877$	−19.4607	−	33.7069i	−0.657141	−	1.13820i	−0.981353	−	0.192217i	$-0.938432\pi$
$877$	−19.4607	−	33.7069i	−0.657141	−	1.13820i	0.324212	−	0.945985i	$-0.394901\pi$
$878$	−1.62721	+	0.539727i	−0.0549156	+	0.0182149i
$879$	−8.37300	+	4.83416i	−0.282414	+	0.163052i
$880$	−19.3994	−	5.78305i	−0.653954	−	0.194946i
$881$	−44.6764			−1.50519			−0.752593	−	0.658486i	$-0.771197\pi$
$881$	−44.6764			−1.50519			−0.752593	+	0.658486i	$0.771197\pi$
$882$	8.74572	+	7.77844i	0.294484	+	0.261914i
$883$	−4.20011	+	7.27481i	−0.141345	+	0.244817i	−0.928003	−	0.372572i	$-0.878476\pi$
$883$	−4.20011	+	7.27481i	−0.141345	+	0.244817i	0.786658	+	0.617389i	$0.211809\pi$
$884$	22.2415	+	9.57860i	0.748063	+	0.322163i
$885$			36.5456i			1.22847i
$886$	26.6056	+	23.6630i	0.893833	+	0.794975i
$887$	21.0193	−	36.4065i	0.705759	−	1.22241i	−0.260658	−	0.965431i	$-0.583940\pi$
$887$	21.0193	−	36.4065i	0.705759	−	1.22241i	0.966417	−	0.256979i	$-0.0827271\pi$
$888$	0.268153	−	3.09633i	0.00899863	−	0.103906i
$889$	24.2001	+	13.9719i	0.811644	+	0.468603i
$890$	16.6619	−	80.8133i	0.558509	−	2.70887i
$891$	2.11127	+	3.65682i	0.0707301	+	0.122508i
$892$	−6.42077	−	54.6555i	−0.214983	−	1.83000i
$893$	36.4089	−	21.2254i	1.21838	−	0.710281i
$894$	−0.675611	−	0.600889i	−0.0225958	−	0.0200967i
$895$	−32.9563	−	57.0820i	−1.10161	−	1.90804i
$896$	−5.39859	−	36.3362i	−0.180354	−	1.21391i
$897$	5.71039	−	9.89068i	0.190664	−	0.330240i
$898$	29.7779	+	6.13956i	0.993703	+	0.204880i
$899$	−14.1406	+	24.4922i	−0.471615	+	0.816862i
$900$	−6.68035	−	56.8651i	−0.222678	−	1.89550i
$901$	7.34470			0.244688
$902$	−1.86083	−	5.61017i	−0.0619589	−	0.186798i
$903$	−2.68831	+	4.65628i	−0.0894612	+	0.154951i
$904$	−0.513098	−	0.358604i	−0.0170654	−	0.0119270i
$905$		−	17.8095i		−	0.592008i
$906$	1.64643	+	4.96379i	0.0546991	+	0.164911i
$907$	−17.4703	+	10.0865i	−0.580092	+	0.334916i	−0.761170	−	0.648552i	$-0.775375\pi$
$907$	−17.4703	+	10.0865i	−0.580092	+	0.334916i	0.181078	+	0.983469i	$0.442041\pi$
$908$	14.6077	−	33.9192i	0.484775	−	1.12565i
$909$	40.4413	−	23.3488i	1.34135	−	0.774430i
$910$	−15.5163	+	75.2568i	−0.514360	+	2.49474i
$911$	42.5350			1.40925			0.704623	−	0.709582i	$-0.251116\pi$
$911$	42.5350			1.40925			0.704623	+	0.709582i	$0.251116\pi$
$912$	−10.2807	+	9.80437i	−0.340428	+	0.324655i
$913$	−14.2867			−0.472820
$914$	−7.54766	+	36.6075i	−0.249654	+	1.21087i
$915$	−1.01847	+	0.588015i	−0.0336697	+	0.0194392i
$916$	14.8839	−	34.5604i	0.491777	−	1.14191i
$917$	2.78200	−	1.60619i	0.0918699	−	0.0530411i
$918$	−5.81818	−	17.5411i	−0.192029	−	0.578941i
$919$		−	8.32732i		−	0.274693i	−0.990523	−	0.137346i	$-0.956143\pi$
$919$		−	8.32732i		−	0.274693i	0.990523	−	0.137346i	$-0.0438574\pi$
$920$	−23.4181	+	33.5071i	−0.772072	+	1.10470i
$921$	−7.61203	+	13.1844i	−0.250825	+	0.434441i
$922$	8.26588	+	24.9206i	0.272222	+	0.820716i
$923$	4.68541			0.154222
$924$	−0.752126	−	6.40232i	−0.0247431	−	0.210621i
$925$	8.26320	−	14.3123i	0.271692	−	0.470585i
$926$	−25.6759	−	5.29381i	−0.843762	−	0.173965i
$927$	2.18556	−	3.78551i	0.0717833	−	0.124332i
$928$	−0.814804	−	26.6601i	−0.0267473	−	0.875162i
$929$	−6.55867	−	11.3599i	−0.215183	−	0.372708i	0.738146	−	0.674641i	$-0.235701\pi$
$929$	−6.55867	−	11.3599i	−0.215183	−	0.372708i	−0.953329	+	0.301933i	$0.902368\pi$
$930$	21.4519	+	19.0793i	0.703436	+	0.625636i
$931$	7.66484	−	13.4058i	0.251205	−	0.439358i
$932$	0.158359	+	1.34800i	0.00518721	+	0.0441551i
$933$	−7.31053	−	12.6622i	−0.239336	−	0.414542i
$934$	−1.70416	+	8.26547i	−0.0557618	+	0.270454i
$935$	−13.1729	−	7.60540i	−0.430801	−	0.248723i
$936$	−26.5193	−	2.29666i	−0.866809	−	0.0750686i
$937$	−15.9089	+	27.5550i	−0.519721	+	0.900183i	0.480016	+	0.877260i	$0.340631\pi$
$937$	−15.9089	+	27.5550i	−0.519721	+	0.900183i	−0.999737	+	0.0229235i	$0.992703\pi$
$938$	32.9280	+	29.2862i	1.07514	+	0.956228i
$939$		−	25.8980i		−	0.845151i
$940$	73.7727	+	31.7712i	2.40620	+	1.03626i
$941$	−20.6578	+	35.7804i	−0.673426	+	1.16641i	0.303500	+	0.952831i	$0.401845\pi$
$941$	−20.6578	+	35.7804i	−0.673426	+	1.16641i	−0.976926	+	0.213577i	$0.931489\pi$
$942$	7.09985	+	6.31460i	0.231326	+	0.205741i
$943$	−11.9363			−0.388700
$944$	−41.3916	−	12.3390i	−1.34718	−	0.401601i
$945$	50.7841	−	29.3202i	1.65201	−	0.953787i
$946$	−3.32356	+	1.10239i	−0.108058	+	0.0358417i
$947$	10.0389	+	17.3878i	0.326220	+	0.565029i	0.981758	−	0.190133i	$-0.0608918\pi$
$947$	10.0389	+	17.3878i	0.326220	+	0.565029i	−0.655539	+	0.755161i	$0.727558\pi$
$948$	5.02093	+	6.73604i	0.163072	+	0.218777i
$949$	−11.8176			−0.383615
$950$	−71.6000	+	24.0838i	−2.32301	+	0.781380i
$951$			7.30970i			0.237033i
$952$	2.38161	−	27.5002i	0.0771883	−	0.891285i
$953$	−46.5493	+	26.8753i	−1.50788	+	0.870575i	−0.507923	+	0.861403i	$0.669586\pi$
$953$	−46.5493	+	26.8753i	−1.50788	+	0.870575i	−0.999958	+	0.00917274i	$0.997080\pi$
$954$	−7.66273	+	2.54164i	−0.248090	+	0.0822887i
$955$	3.82368	+	6.62281i	0.123731	+	0.214309i
$956$	3.62194	−	8.41015i	0.117142	−	0.272004i
$957$		−	4.68056i		−	0.151301i
$958$	25.5159	−	28.6888i	0.824380	−	0.926895i
$959$	−51.7923	−	29.9023i	−1.67246	−	0.965595i
$960$	−26.6729	−	4.65484i	−0.860864	−	0.150234i
$961$	4.97618			0.160522
$962$	−5.74101	−	5.10605i	−0.185098	−	0.164626i
$963$	−8.89703	−	5.13670i	−0.286703	−	0.165528i
$964$	−6.87984	−	9.22993i	−0.221585	−	0.297276i
$965$	−25.9986	+	45.0309i	−0.836925	+	1.44960i
$966$	−12.7498	−	2.62873i	−0.410219	−	0.0845781i
$967$	−37.3255	+	21.5499i	−1.20031	+	0.692999i	−0.960624	−	0.277852i	$-0.910377\pi$
$967$	−37.3255	+	21.5499i	−1.20031	+	0.692999i	−0.239685	+	0.970851i	$0.577044\pi$
$968$	−15.4181	+	22.0605i	−0.495556	+	0.709053i
$969$	−9.22205	+	5.37621i	−0.296255	+	0.172709i
$970$	61.4243	+	54.6307i	1.97221	+	1.75409i
$971$	−15.8067	+	9.12598i	−0.507260	+	0.292866i	−0.731706	−	0.681620i	$-0.761276\pi$
$971$	−15.8067	+	9.12598i	−0.507260	+	0.292866i	0.224447	+	0.974486i	$0.427942\pi$
$972$	18.9655	+	25.4440i	0.608319	+	0.816116i
$973$	30.7518	+	17.7546i	0.985859	+	0.569186i
$974$	10.1202	−	49.0850i	0.324274	−	1.57278i
$975$	34.8348	+	20.1119i	1.11561	+	0.644096i
$976$	−0.322117	−	1.35206i	−0.0103107	−	0.0432783i
$977$		−	1.36452i		−	0.0436550i	−0.999762	−	0.0218275i	$-0.993052\pi$
$977$		−	1.36452i		−	0.0436550i	0.999762	−	0.0218275i	$-0.00694846\pi$
$978$	1.44778	+	4.36488i	0.0462950	+	0.139574i
$979$	14.8201	+	8.55639i	0.473653	+	0.273463i
$980$	29.2308	−	3.43395i	0.933745	−	0.109694i
$981$	9.10088			0.290569
$982$	−13.5779	+	4.50364i	−0.433288	+	0.143717i
$983$	−25.1141	−	43.4988i	−0.801014	−	1.38740i	−0.918949	−	0.394376i	$-0.870961\pi$
$983$	−25.1141	−	43.4988i	−0.801014	−	1.38740i	0.117935	−	0.993021i	$-0.462373\pi$
$984$	−3.34746	−	7.16222i	−0.106713	−	0.228323i
$985$	21.8229	+	37.7983i	0.695335	+	1.20436i
$986$	4.04710	−	19.6292i	0.128886	−	0.625120i
$987$			25.5788i			0.814181i
$988$	4.24426	+	34.8622i	0.135028	+	1.10911i
$989$			7.07128i			0.224854i
$990$	16.3752	+	3.37621i	0.520438	+	0.107303i
$991$	16.9365	+	29.3349i	0.538007	+	0.931855i	0.999011	+	0.0444574i	$0.0141559\pi$
$991$	16.9365	+	29.3349i	0.538007	+	0.931855i	−0.461004	+	0.887398i	$0.652511\pi$
$992$	−28.8522	+	17.8547i	−0.916058	+	0.566886i
$993$	−12.1399	−	21.0269i	−0.385247	−	0.667267i
$994$	−1.68136	−	5.06910i	−0.0533296	−	0.160782i
$995$	25.0370			0.793726
$996$	−18.9786	+	2.22955i	−0.601361	+	0.0706460i
$997$	9.16830	+	5.29332i	0.290363	+	0.167641i	0.638106	−	0.769949i	$-0.279718\pi$
$997$	9.16830	+	5.29332i	0.290363	+	0.167641i	−0.347743	+	0.937590i	$0.613052\pi$
$998$	−15.6738	+	5.19882i	−0.496145	+	0.164566i
$999$			5.86342i			0.185511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.107.7	yes	28
4.3	odd	2		608.2.s.c.335.6		28
8.3	odd	2	inner	152.2.o.c.107.3	yes	28
8.5	even	2		608.2.s.c.335.5		28
19.8	odd	6	inner	152.2.o.c.27.3	✓	28
76.27	even	6		608.2.s.c.559.5		28
152.27	even	6	inner	152.2.o.c.27.7	yes	28
152.141	odd	6		608.2.s.c.559.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.3	✓	28	19.8	odd	6	inner
152.2.o.c.27.7	yes	28	152.27	even	6	inner
152.2.o.c.107.3	yes	28	8.3	odd	2	inner
152.2.o.c.107.7	yes	28	1.1	even	1	trivial
608.2.s.c.335.5		28	8.5	even	2
608.2.s.c.335.6		28	4.3	odd	2
608.2.s.c.559.5		28	76.27	even	6
608.2.s.c.559.6		28	152.141	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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.285573 + 1.38508i) q^{2} +(0.705625 - 0.407393i) q^{3} +(-1.83690 - 0.791084i) q^{4} +(3.59735 - 2.07693i) q^{5} +(0.362764 + 1.09369i) q^{6} -3.24695i q^{7} +(1.62028 - 2.31834i) q^{8} +(-1.16806 + 2.02314i) q^{9} +O(q^{10})\)	\(q+(-0.285573 + 1.38508i) q^{2} +(0.705625 - 0.407393i) q^{3} +(-1.83690 - 0.791084i) q^{4} +(3.59735 - 2.07693i) q^{5} +(0.362764 + 1.09369i) q^{6} -3.24695i q^{7} +(1.62028 - 2.31834i) q^{8} +(-1.16806 + 2.02314i) q^{9} +(1.84941 + 5.57573i) q^{10} -1.21833 q^{11} +(-1.61844 + 0.190130i) q^{12} +(-2.01425 + 3.48878i) q^{13} +(4.49729 + 0.927243i) q^{14} +(1.69225 - 2.93107i) q^{15} +(2.74837 + 2.90628i) q^{16} +(1.50282 + 2.60296i) q^{17} +(-2.46865 - 2.19562i) q^{18} +(-2.16355 + 3.78405i) q^{19} +(-8.25097 + 0.969300i) q^{20} +(-1.32279 - 2.29113i) q^{21} +(0.347922 - 1.68748i) q^{22} +(-3.01328 - 1.73972i) q^{23} +(0.198839 - 2.29597i) q^{24} +(6.12726 - 10.6127i) q^{25} +(-4.25703 - 3.78620i) q^{26} +4.34780i q^{27} +(-2.56861 + 5.96432i) q^{28} +(-2.35755 + 4.08339i) q^{29} +(3.57650 + 3.18094i) q^{30} +5.99801 q^{31} +(-4.81029 + 2.97676i) q^{32} +(-0.859683 + 0.496338i) q^{33} +(-4.03447 + 1.33819i) q^{34} +(-6.74369 - 11.6804i) q^{35} +(3.74608 - 2.79227i) q^{36} +1.34860 q^{37} +(-4.62336 - 4.07731i) q^{38} +3.28236i q^{39} +(1.01370 - 11.7051i) q^{40} +(2.97093 - 1.71527i) q^{41} +(3.55116 - 1.17788i) q^{42} +(-1.01615 - 1.76003i) q^{43} +(2.23794 + 0.963799i) q^{44} +9.70392i q^{45} +(3.27016 - 3.67682i) q^{46} +(-8.37318 - 4.83426i) q^{47} +(3.12332 + 0.931075i) q^{48} -3.54271 q^{49} +(12.9497 + 11.5175i) q^{50} +(2.12085 + 1.22448i) q^{51} +(6.45988 - 4.81509i) q^{52} +(1.22182 - 2.11626i) q^{53} +(-6.02205 - 1.24161i) q^{54} +(-4.38275 + 2.53038i) q^{55} +(-7.52753 - 5.26099i) q^{56} +(0.0149406 + 3.55154i) q^{57} +(-4.98257 - 4.43150i) q^{58} +(-9.35127 + 5.39896i) q^{59} +(-5.42721 + 4.04535i) q^{60} +(-0.300922 - 0.173737i) q^{61} +(-1.71287 + 8.30773i) q^{62} +(6.56905 + 3.79264i) q^{63} +(-2.74937 - 7.51272i) q^{64} +16.7338i q^{65} +(-0.441966 - 1.33247i) q^{66} +(8.31107 + 4.79840i) q^{67} +(-0.701363 - 5.97022i) q^{68} -2.83500 q^{69} +(18.1041 - 6.00494i) q^{70} +(-0.581533 - 1.00725i) q^{71} +(2.79773 + 5.98602i) q^{72} +(1.46675 + 2.54048i) q^{73} +(-0.385123 + 1.86791i) q^{74} -9.98482i q^{75} +(6.96772 - 5.23936i) q^{76} +3.95586i q^{77} +(-4.54634 - 0.937355i) q^{78} +(-2.57780 - 4.46489i) q^{79} +(15.9230 + 4.74671i) q^{80} +(-1.73292 - 3.00151i) q^{81} +(1.52736 + 4.60481i) q^{82} +11.7265 q^{83} +(0.617343 + 5.25501i) q^{84} +(10.8123 + 6.24249i) q^{85} +(2.72797 - 0.904836i) q^{86} +3.84179i q^{87} +(-1.97404 + 2.82449i) q^{88} +(-12.1643 - 7.02306i) q^{89} +(-13.4407 - 2.77118i) q^{90} +(11.3279 + 6.54017i) q^{91} +(4.15882 + 5.57944i) q^{92} +(4.23235 - 2.44355i) q^{93} +(9.08699 - 10.2170i) q^{94} +(0.0761686 + 18.1061i) q^{95} +(-2.18155 + 4.06016i) q^{96} +(12.1187 - 6.99673i) q^{97} +(1.01170 - 4.90694i) q^{98} +(1.42308 - 2.46485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32} + 36 q^{33} - 12 q^{34} - 28 q^{35} - 8 q^{36} + 38 q^{38} - 48 q^{40} + 6 q^{41} + 14 q^{42} + 30 q^{43} + 5 q^{44} - 15 q^{48} - 68 q^{49} - 42 q^{51} + 36 q^{52} + 23 q^{54} - 26 q^{57} + 20 q^{58} - 18 q^{59} - 42 q^{60} + 22 q^{62} + 70 q^{64} - 27 q^{66} + 78 q^{67} + 4 q^{68} + 18 q^{70} - 24 q^{72} + 14 q^{73} + 4 q^{74} + 47 q^{76} - 30 q^{78} - 20 q^{80} + 6 q^{81} + 23 q^{82} - 32 q^{83} + 42 q^{86} - 18 q^{89} - 96 q^{90} - 12 q^{91} + 46 q^{92} + 50 q^{96} + 30 q^{97} + 15 q^{98} - 28 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

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