LMFDB - Embedded newform 336.2.s.c.155.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.17
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25684 + 0.648355i) q^{2} +(1.61364 - 0.629429i) q^{3} +(1.15927 + 1.62975i) q^{4} +(-3.08691 + 3.08691i) q^{5} +(2.43617 + 0.255120i) q^{6} -1.00000 q^{7} +(0.400356 + 2.79995i) q^{8} +(2.20764 - 2.03134i) q^{9} +O(q^{10})$	\(q+(1.25684 + 0.648355i) q^{2} +(1.61364 - 0.629429i) q^{3} +(1.15927 + 1.62975i) q^{4} +(-3.08691 + 3.08691i) q^{5} +(2.43617 + 0.255120i) q^{6} -1.00000 q^{7} +(0.400356 + 2.79995i) q^{8} +(2.20764 - 2.03134i) q^{9} +(-5.88116 + 1.87833i) q^{10} +(1.97950 + 1.97950i) q^{11} +(2.89645 + 1.90015i) q^{12} +(3.27530 - 3.27530i) q^{13} +(-1.25684 - 0.648355i) q^{14} +(-3.03816 + 6.92415i) q^{15} +(-1.31218 + 3.77865i) q^{16} -2.57205i q^{17} +(4.09167 - 1.12172i) q^{18} +(-1.18763 - 1.18763i) q^{19} +(-8.60948 - 1.45233i) q^{20} +(-1.61364 + 0.629429i) q^{21} +(1.20449 + 3.77132i) q^{22} +1.21005i q^{23} +(2.40840 + 4.26610i) q^{24} -14.0581i q^{25} +(6.24006 - 1.99295i) q^{26} +(2.28374 - 4.66739i) q^{27} +(-1.15927 - 1.62975i) q^{28} +(-1.33641 - 1.33641i) q^{29} +(-8.30778 + 6.73271i) q^{30} -5.84687i q^{31} +(-4.09910 + 3.89838i) q^{32} +(4.44015 + 1.94824i) q^{33} +(1.66760 - 3.23264i) q^{34} +(3.08691 - 3.08691i) q^{35} +(5.86983 + 1.24303i) q^{36} +(5.18528 + 5.18528i) q^{37} +(-0.722652 - 2.26267i) q^{38} +(3.22357 - 7.34670i) q^{39} +(-9.87907 - 7.40734i) q^{40} -0.688196 q^{41} +(-2.43617 - 0.255120i) q^{42} +(0.649101 - 0.649101i) q^{43} +(-0.931315 + 5.52087i) q^{44} +(-0.544230 + 13.0854i) q^{45} +(-0.784542 + 1.52083i) q^{46} -10.5648 q^{47} +(0.261011 + 6.92328i) q^{48} +1.00000 q^{49} +(9.11463 - 17.6687i) q^{50} +(-1.61892 - 4.15035i) q^{51} +(9.13488 + 1.54096i) q^{52} +(3.84828 - 3.84828i) q^{53} +(5.89641 - 4.38546i) q^{54} -12.2211 q^{55} +(-0.400356 - 2.79995i) q^{56} +(-2.66394 - 1.16888i) q^{57} +(-0.813179 - 2.54611i) q^{58} +(-1.99283 - 1.99283i) q^{59} +(-14.8067 + 3.07552i) q^{60} +(-6.62710 + 6.62710i) q^{61} +(3.79085 - 7.34856i) q^{62} +(-2.20764 + 2.03134i) q^{63} +(-7.67943 + 2.24195i) q^{64} +20.2211i q^{65} +(4.31738 + 5.32740i) q^{66} +(4.50400 + 4.50400i) q^{67} +(4.19180 - 2.98170i) q^{68} +(0.761640 + 1.95258i) q^{69} +(5.88116 - 1.87833i) q^{70} +3.91342i q^{71} +(6.57148 + 5.36802i) q^{72} +9.83194i q^{73} +(3.15514 + 9.87895i) q^{74} +(-8.84856 - 22.6846i) q^{75} +(0.558757 - 3.31234i) q^{76} +(-1.97950 - 1.97950i) q^{77} +(8.81476 - 7.14358i) q^{78} -3.86630i q^{79} +(-7.61378 - 15.7150i) q^{80} +(0.747340 - 8.96892i) q^{81} +(-0.864950 - 0.446196i) q^{82} +(-2.99861 + 2.99861i) q^{83} +(-2.89645 - 1.90015i) q^{84} +(7.93969 + 7.93969i) q^{85} +(1.23666 - 0.394965i) q^{86} +(-2.99765 - 1.31530i) q^{87} +(-4.74999 + 6.33500i) q^{88} +10.8761 q^{89} +(-9.16796 + 16.0933i) q^{90} +(-3.27530 + 3.27530i) q^{91} +(-1.97208 + 1.40278i) q^{92} +(-3.68019 - 9.43472i) q^{93} +(-13.2782 - 6.84976i) q^{94} +7.33224 q^{95} +(-4.16070 + 8.87066i) q^{96} -10.1652 q^{97} +(1.25684 + 0.648355i) q^{98} +(8.39105 + 0.348990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.25684	+	0.648355i	0.888717	+	0.458456i
$2$	1.25684	+	0.648355i	0.888717	+	0.458456i
$3$	1.61364	−	0.629429i	0.931633	−	0.363401i
$3$	1.61364	−	0.629429i	0.931633	−	0.363401i
$4$	1.15927	+	1.62975i	0.579636	+	0.814876i
$5$	−3.08691	+	3.08691i	−1.38051	+	1.38051i	−0.536802	+	0.843708i	$0.680368\pi$
$5$	−3.08691	+	3.08691i	−1.38051	+	1.38051i	−0.843708	+	0.536802i	$0.819632\pi$
$6$	2.43617	+	0.255120i	0.994561	+	0.104152i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	0.400356	+	2.79995i	0.141547	+	0.989931i
$9$	2.20764	−	2.03134i	0.735880	−	0.677112i
$10$	−5.88116	+	1.87833i	−1.85979	+	0.593979i
$11$	1.97950	+	1.97950i	0.596842	+	0.596842i	0.939471	−	0.342629i	$-0.111317\pi$
$11$	1.97950	+	1.97950i	0.596842	+	0.596842i	−0.342629	+	0.939471i	$0.611317\pi$
$12$	2.89645	+	1.90015i	0.836134	+	0.548525i
$13$	3.27530	−	3.27530i	0.908404	−	0.908404i	−0.0877398	−	0.996143i	$-0.527964\pi$
$13$	3.27530	−	3.27530i	0.908404	−	0.908404i	0.996143	+	0.0877398i	$0.0279644\pi$
$14$	−1.25684	−	0.648355i	−0.335903	−	0.173280i
$15$	−3.03816	+	6.92415i	−0.784450	+	1.78781i
$16$	−1.31218	+	3.77865i	−0.328045	+	0.944662i
$17$		−	2.57205i		−	0.623813i	−0.950113	−	0.311907i	$-0.899032\pi$
$17$		−	2.57205i		−	0.623813i	0.950113	−	0.311907i	$-0.100968\pi$
$18$	4.09167	−	1.12172i	0.964415	−	0.264393i
$19$	−1.18763	−	1.18763i	−0.272462	−	0.272462i	0.557629	−	0.830090i	$-0.311711\pi$
$19$	−1.18763	−	1.18763i	−0.272462	−	0.272462i	−0.830090	+	0.557629i	$0.811711\pi$
$20$	−8.60948	−	1.45233i	−1.92514	−	0.324751i
$21$	−1.61364	+	0.629429i	−0.352124	+	0.137353i
$22$	1.20449	+	3.77132i	0.256798	+	0.804049i
$23$			1.21005i			0.252313i	0.992010	+	0.126156i	$0.0402641\pi$
$23$			1.21005i			0.252313i	−0.992010	+	0.126156i	$0.959736\pi$
$24$	2.40840	+	4.26610i	0.491612	+	0.870814i
$25$		−	14.0581i		−	2.81162i
$26$	6.24006	−	1.99295i	1.22378	−	0.390850i
$27$	2.28374	−	4.66739i	0.439507	−	0.898239i
$28$	−1.15927	−	1.62975i	−0.219082	−	0.307994i
$29$	−1.33641	−	1.33641i	−0.248165	−	0.248165i	0.572052	−	0.820217i	$-0.306147\pi$
$29$	−1.33641	−	1.33641i	−0.248165	−	0.248165i	−0.820217	+	0.572052i	$0.806147\pi$
$30$	−8.30778	+	6.73271i	−1.51679	+	1.22922i
$31$		−	5.84687i		−	1.05013i	−0.851062	−	0.525065i	$-0.824041\pi$
$31$		−	5.84687i		−	1.05013i	0.851062	−	0.525065i	$-0.175959\pi$
$32$	−4.09910	+	3.89838i	−0.724625	+	0.689143i
$33$	4.44015	+	1.94824i	0.772930	+	0.339145i
$34$	1.66760	−	3.23264i	0.285991	−	0.554393i
$35$	3.08691	−	3.08691i	0.521784	−	0.521784i
$36$	5.86983	+	1.24303i	0.978305	+	0.207172i
$37$	5.18528	+	5.18528i	0.852455	+	0.852455i	0.990435	−	0.137980i	$-0.0440608\pi$
$37$	5.18528	+	5.18528i	0.852455	+	0.852455i	−0.137980	+	0.990435i	$0.544061\pi$
$38$	−0.722652	−	2.26267i	−0.117230	−	0.367053i
$39$	3.22357	−	7.34670i	0.516184	−	1.17641i
$40$	−9.87907	−	7.40734i	−1.56202	−	1.17120i
$41$	−0.688196			−0.107478			−0.0537391	−	0.998555i	$-0.517114\pi$
$41$	−0.688196			−0.107478			−0.0537391	+	0.998555i	$0.517114\pi$
$42$	−2.43617	−	0.255120i	−0.375909	−	0.0393659i
$43$	0.649101	−	0.649101i	0.0989870	−	0.0989870i	−0.655879	−	0.754866i	$-0.727702\pi$
$43$	0.649101	−	0.649101i	0.0989870	−	0.0989870i	0.754866	+	0.655879i	$0.227702\pi$
$44$	−0.931315	+	5.52087i	−0.140401	+	0.832302i
$45$	−0.544230	+	13.0854i	−0.0811290	+	1.95065i
$46$	−0.784542	+	1.52083i	−0.115674	+	0.224235i
$47$	−10.5648			−1.54104			−0.770519	−	0.637417i	$-0.780003\pi$
$47$	−10.5648			−1.54104			−0.770519	+	0.637417i	$0.780003\pi$
$48$	0.261011	+	6.92328i	0.0376737	+	0.999290i
$49$	1.00000			0.142857
$50$	9.11463	−	17.6687i	1.28900	−	2.49873i
$51$	−1.61892	−	4.15035i	−0.226694	−	0.581165i
$52$	9.13488	+	1.54096i	1.26678	+	0.213693i
$53$	3.84828	−	3.84828i	0.528602	−	0.528602i	−0.391554	−	0.920155i	$-0.628062\pi$
$53$	3.84828	−	3.84828i	0.528602	−	0.528602i	0.920155	+	0.391554i	$0.128062\pi$
$54$	5.89641	−	4.38546i	0.802400	−	0.596786i
$55$	−12.2211			−1.64789
$56$	−0.400356	−	2.79995i	−0.0534999	−	0.374159i
$57$	−2.66394	−	1.16888i	−0.352847	−	0.154822i
$58$	−0.813179	−	2.54611i	−0.106776	−	0.334321i
$59$	−1.99283	−	1.99283i	−0.259444	−	0.259444i	0.565384	−	0.824828i	$-0.308728\pi$
$59$	−1.99283	−	1.99283i	−0.259444	−	0.259444i	−0.824828	+	0.565384i	$0.808728\pi$
$60$	−14.8067	+	3.07552i	−1.91154	+	0.397048i
$61$	−6.62710	+	6.62710i	−0.848513	+	0.848513i	−0.989948	−	0.141435i	$-0.954828\pi$
$61$	−6.62710	+	6.62710i	−0.848513	+	0.848513i	0.141435	+	0.989948i	$0.454828\pi$
$62$	3.79085	−	7.34856i	0.481438	−	0.933268i
$63$	−2.20764	+	2.03134i	−0.278136	+	0.255924i
$64$	−7.67943	+	2.24195i	−0.959929	+	0.280244i
$65$			20.2211i			2.50812i
$66$	4.31738	+	5.32740i	0.531433	+	0.655758i
$67$	4.50400	+	4.50400i	0.550251	+	0.550251i	0.926513	−	0.376262i	$-0.122791\pi$
$67$	4.50400	+	4.50400i	0.550251	+	0.550251i	−0.376262	+	0.926513i	$0.622791\pi$
$68$	4.19180	−	2.98170i	0.508330	−	0.361584i
$69$	0.761640	+	1.95258i	0.0916907	+	0.235063i
$70$	5.88116	−	1.87833i	0.702933	−	0.224503i
$71$			3.91342i			0.464438i	0.972664	+	0.232219i	$0.0745986\pi$
$71$			3.91342i			0.464438i	−0.972664	+	0.232219i	$0.925401\pi$
$72$	6.57148	+	5.36802i	0.774457	+	0.632627i
$73$			9.83194i			1.15074i	0.817893	+	0.575371i	$0.195142\pi$
$73$			9.83194i			1.15074i	−0.817893	+	0.575371i	$0.804858\pi$
$74$	3.15514	+	9.87895i	0.366778	+	1.14841i
$75$	−8.84856	−	22.6846i	−1.02174	−	2.61939i
$76$	0.558757	−	3.31234i	0.0640939	−	0.379951i
$77$	−1.97950	−	1.97950i	−0.225585	−	0.225585i
$78$	8.81476	−	7.14358i	0.998076	−	0.808851i
$79$		−	3.86630i		−	0.434992i	−0.976061	−	0.217496i	$-0.930211\pi$
$79$		−	3.86630i		−	0.434992i	0.976061	−	0.217496i	$-0.0697890\pi$
$80$	−7.61378	−	15.7150i	−0.851247	−	1.75698i
$81$	0.747340	−	8.96892i	0.0830378	−	0.996546i
$82$	−0.864950	−	0.446196i	−0.0955177	−	0.0492741i
$83$	−2.99861	+	2.99861i	−0.329140	+	0.329140i	−0.852260	−	0.523119i	$-0.824768\pi$
$83$	−2.99861	+	2.99861i	−0.329140	+	0.329140i	0.523119	+	0.852260i	$0.324768\pi$
$84$	−2.89645	−	1.90015i	−0.316029	−	0.207323i
$85$	7.93969	+	7.93969i	0.861180	+	0.861180i
$86$	1.23666	−	0.394965i	0.133353	−	0.0425902i
$87$	−2.99765	−	1.31530i	−0.321382	−	0.141015i
$88$	−4.74999	+	6.33500i	−0.506351	+	0.675314i
$89$	10.8761			1.15286			0.576432	−	0.817145i	$-0.304444\pi$
$89$	10.8761			1.15286			0.576432	+	0.817145i	$0.304444\pi$
$90$	−9.16796	+	16.0933i	−0.966388	+	1.69638i
$91$	−3.27530	+	3.27530i	−0.343344	+	0.343344i
$92$	−1.97208	+	1.40278i	−0.205604	+	0.146250i
$93$	−3.68019	−	9.43472i	−0.381618	−	0.978335i
$94$	−13.2782	−	6.84976i	−1.36955	−	0.706499i
$95$	7.33224			0.752272
$96$	−4.16070	+	8.87066i	−0.424649	+	0.905358i
$97$	−10.1652			−1.03212			−0.516061	−	0.856552i	$-0.672602\pi$
$97$	−10.1652			−1.03212			−0.516061	+	0.856552i	$0.672602\pi$
$98$	1.25684	+	0.648355i	0.126960	+	0.0654937i
$99$	8.39105	+	0.348990i	0.843332	+	0.0350748i
$100$	22.9112	−	16.2971i	2.29112	−	1.62971i
$101$	11.5965	−	11.5965i	1.15389	−	1.15389i	0.168129	−	0.985765i	$-0.446227\pi$
$101$	11.5965	−	11.5965i	1.15389	−	1.15389i	0.985765	−	0.168129i	$-0.0537726\pi$
$102$	0.656182	−	6.26594i	0.0649717	−	0.620420i
$103$	−6.00387			−0.591579			−0.295790	−	0.955253i	$-0.595583\pi$
$103$	−6.00387			−0.591579			−0.295790	+	0.955253i	$0.595583\pi$
$104$	10.4819	+	7.85938i	1.02784	+	0.770675i
$105$	3.03816	−	6.92415i	0.296494	−	0.675728i
$106$	7.33170	−	2.34160i	0.712118	−	0.227437i
$107$	−8.85702	−	8.85702i	−0.856241	−	0.856241i	0.134652	−	0.990893i	$-0.457008\pi$
$107$	−8.85702	−	8.85702i	−0.856241	−	0.856241i	−0.990893	+	0.134652i	$0.957008\pi$
$108$	10.2542	−	1.68884i	0.986707	−	0.162508i
$109$	9.12079	−	9.12079i	0.873613	−	0.873613i	−0.119251	−	0.992864i	$-0.538049\pi$
$109$	9.12079	−	9.12079i	0.873613	−	0.873613i	0.992864	+	0.119251i	$0.0380494\pi$
$110$	−15.3599	−	7.92361i	−1.46451	−	0.755486i
$111$	11.6309	+	5.10339i	1.10396	+	0.484393i
$112$	1.31218	−	3.77865i	0.123989	−	0.357049i
$113$			8.96882i			0.843715i	0.906662	+	0.421858i	$0.138622\pi$
$113$			8.96882i			0.843715i	−0.906662	+	0.421858i	$0.861378\pi$
$114$	−2.59028	−	3.19626i	−0.242602	−	0.299357i
$115$	−3.73532	−	3.73532i	−0.348320	−	0.348320i
$116$	0.628753	−	3.72728i	0.0583783	−	0.346069i
$117$	0.577442	−	13.8839i	0.0533845	−	1.28357i
$118$	−1.21260	−	3.79672i	−0.111629	−	0.349516i
$119$			2.57205i			0.235779i
$120$	−20.6036	−	5.73457i	−1.88084	−	0.523493i
$121$		−	3.16316i		−	0.287560i
$122$	−12.6259	+	4.03246i	−1.14309	+	0.365082i
$123$	−1.11050	+	0.433170i	−0.100130	+	0.0390577i
$124$	9.52895	−	6.77812i	0.855725	−	0.608693i
$125$	27.9615	+	27.9615i	2.50096	+	2.50096i
$126$	−4.09167	+	1.12172i	−0.364515	+	0.0999310i
$127$		−	0.567572i		−	0.0503638i	−0.999683	−	0.0251819i	$-0.991983\pi$
$127$		−	0.567572i		−	0.0503638i	0.999683	−	0.0251819i	$-0.00801650\pi$
$128$	−11.1054	−	2.16123i	−0.981585	−	0.191027i
$129$	0.638850	−	1.45598i	0.0562476	−	0.128191i
$130$	−13.1105	+	25.4146i	−1.14986	+	2.22901i
$131$	3.91258	−	3.91258i	0.341844	−	0.341844i	−0.515216	−	0.857060i	$-0.672288\pi$
$131$	3.91258	−	3.91258i	0.341844	−	0.341844i	0.857060	+	0.515216i	$0.172288\pi$
$132$	1.97219	+	9.49487i	0.171657	+	0.826422i
$133$	1.18763	+	1.18763i	0.102981	+	0.102981i
$134$	2.74059	+	8.58097i	0.236751	+	0.741283i
$135$	7.35811	+	21.4576i	0.633285	+	1.84677i
$136$	7.20160	−	1.02974i	0.617532	−	0.0882991i
$137$	−18.8206			−1.60795			−0.803974	−	0.594664i	$-0.797285\pi$
$137$	−18.8206			−1.60795			−0.803974	+	0.594664i	$0.797285\pi$
$138$	−0.308708	+	2.94788i	−0.0262790	+	0.250941i
$139$	−10.0264	+	10.0264i	−0.850426	+	0.850426i	−0.990186	−	0.139759i	$-0.955367\pi$
$139$	−10.0264	+	10.0264i	−0.850426	+	0.850426i	0.139759	+	0.990186i	$0.455367\pi$
$140$	8.60948	+	1.45233i	0.727633	+	0.122744i
$141$	−17.0478	+	6.64980i	−1.43568	+	0.560015i
$142$	−2.53729	+	4.91853i	−0.212924	+	0.412754i
$143$	12.9669			1.08435
$144$	4.77889	+	11.0074i	0.398241	+	0.917281i
$145$	8.25076			0.685188
$146$	−6.37459	+	12.3571i	−0.527565	+	1.02268i
$147$	1.61364	−	0.629429i	0.133090	−	0.0519144i
$148$	−2.43957	+	14.4619i	−0.200532	+	1.18876i
$149$	−0.117671	+	0.117671i	−0.00963996	+	0.00963996i	−0.711910	−	0.702270i	$-0.752170\pi$
$149$	−0.117671	+	0.117671i	−0.00963996	+	0.00963996i	0.702270	+	0.711910i	$0.252170\pi$
$150$	3.58650	−	34.2479i	0.292837	−	2.79633i
$151$	−24.0766			−1.95933			−0.979663	−	0.200650i	$-0.935694\pi$
$151$	−24.0766			−1.95933			−0.979663	+	0.200650i	$0.935694\pi$
$152$	2.84984	−	3.80079i	0.231152	−	0.308285i
$153$	−5.22470	−	5.67815i	−0.422392	−	0.459051i
$154$	−1.20449	−	3.77132i	−0.0970603	−	0.303902i
$155$	18.0488	+	18.0488i	1.44971	+	1.44971i
$156$	15.7103	−	3.26320i	1.25783	−	0.261265i
$157$	−5.29589	+	5.29589i	−0.422658	+	0.422658i	−0.886118	−	0.463460i	$-0.846608\pi$
$157$	−5.29589	+	5.29589i	−0.422658	+	0.422658i	0.463460	+	0.886118i	$0.346608\pi$
$158$	2.50673	−	4.85930i	0.199425	−	0.386585i
$159$	3.78750	−	8.63194i	0.300368	−	0.684557i
$160$	0.619595	−	24.6875i	0.0489833	−	1.95172i
$161$		−	1.21005i		−	0.0953653i
$162$	6.75433	−	10.7879i	0.530670	−	0.847578i
$163$	15.9523	+	15.9523i	1.24948	+	1.24948i	0.955950	+	0.293529i	$0.0948296\pi$
$163$	15.9523	+	15.9523i	1.24948	+	1.24948i	0.293529	+	0.955950i	$0.405170\pi$
$164$	−0.797806	−	1.12159i	−0.0622982	−	0.0875814i
$165$	−19.7204	+	7.69231i	−1.53523	+	0.598845i
$166$	−5.71292	+	1.82460i	−0.443409	+	0.141616i
$167$		−	16.5911i		−	1.28386i	−0.766765	−	0.641928i	$-0.778135\pi$
$167$		−	16.5911i		−	1.28386i	0.766765	−	0.641928i	$-0.221865\pi$
$168$	−2.40840	−	4.26610i	−0.185812	−	0.329137i
$169$		−	8.45513i		−	0.650394i
$170$	4.83115	+	15.1266i	0.370532	+	1.16016i
$171$	−5.03435	−	0.209382i	−0.384986	−	0.0160119i
$172$	1.81036	+	0.305389i	0.138038	+	0.0232857i
$173$	2.74985	+	2.74985i	0.209067	+	0.209067i	0.803871	−	0.594804i	$-0.202770\pi$
$173$	2.74985	+	2.74985i	0.209067	+	0.209067i	−0.594804	+	0.803871i	$0.702770\pi$
$174$	−2.91477	−	3.59666i	−0.220968	−	0.272662i
$175$			14.0581i			1.06269i
$176$	−10.0773	+	4.88238i	−0.759604	+	0.368023i
$177$	−4.47004	−	1.96135i	−0.335989	−	0.147424i
$178$	13.6695	+	7.05158i	1.02457	+	0.528538i
$179$	−5.58232	+	5.58232i	−0.417242	+	0.417242i	−0.884252	−	0.467010i	$-0.845331\pi$
$179$	−5.58232	+	5.58232i	−0.417242	+	0.417242i	0.467010	+	0.884252i	$0.345331\pi$
$180$	−21.9568	+	14.2825i	−1.63656	+	1.06456i
$181$	6.74062	+	6.74062i	0.501026	+	0.501026i	0.911757	−	0.410731i	$-0.134726\pi$
$181$	6.74062	+	6.74062i	0.501026	+	0.501026i	−0.410731	+	0.911757i	$0.634726\pi$
$182$	−6.24006	+	1.99295i	−0.462544	+	0.147728i
$183$	−6.52243	+	14.8650i	−0.482152	+	1.09885i
$184$	−3.38808	+	0.484451i	−0.249772	+	0.0357142i
$185$	−32.0131			−2.35365
$186$	1.49166	−	14.2440i	0.109374	−	1.04442i
$187$	5.09137	−	5.09137i	0.372318	−	0.372318i
$188$	−12.2475	−	17.2180i	−0.893241	−	1.25575i
$189$	−2.28374	+	4.66739i	−0.166118	+	0.339503i
$190$	9.21543	+	4.75390i	0.668557	+	0.344884i
$191$	−24.3853			−1.76446			−0.882230	−	0.470819i	$-0.843958\pi$
$191$	−24.3853			−1.76446			−0.882230	+	0.470819i	$0.843958\pi$
$192$	−10.9806	+	8.45135i	−0.792460	+	0.609924i
$193$	4.04091			0.290871			0.145435	−	0.989368i	$-0.453542\pi$
$193$	4.04091			0.290871			0.145435	+	0.989368i	$0.453542\pi$
$194$	−12.7760	−	6.59068i	−0.917265	−	0.473183i
$195$	12.7278	+	32.6295i	0.911453	+	2.33665i
$196$	1.15927	+	1.62975i	0.0828051	+	0.116411i
$197$	5.19081	−	5.19081i	0.369830	−	0.369830i	−0.497585	−	0.867415i	$-0.665780\pi$
$197$	5.19081	−	5.19081i	0.369830	−	0.369830i	0.867415	+	0.497585i	$0.165780\pi$
$198$	10.3199	+	5.87900i	0.733404	+	0.417803i
$199$	9.79611			0.694428			0.347214	−	0.937786i	$-0.387128\pi$
$199$	9.79611			0.694428			0.347214	+	0.937786i	$0.387128\pi$
$200$	39.3619	−	5.62824i	2.78331	−	0.397977i
$201$	10.1028	+	4.43286i	0.712593	+	0.312670i
$202$	22.0935	−	7.05624i	1.55450	−	0.496475i
$203$	1.33641	+	1.33641i	0.0937975	+	0.0937975i
$204$	4.88727	−	7.44982i	0.342177	−	0.521592i
$205$	2.12440	−	2.12440i	0.148375	−	0.148375i
$206$	−7.54588	−	3.89264i	−0.525747	−	0.271213i
$207$	2.45802	+	2.67135i	0.170844	+	0.185672i
$208$	8.07842	+	16.6740i	0.560138	+	1.15613i
$209$		−	4.70184i		−	0.325233i
$210$	8.30778	−	6.73271i	0.573291	−	0.464601i
$211$	−5.97473	−	5.97473i	−0.411317	−	0.411317i	0.470880	−	0.882197i	$-0.343936\pi$
$211$	−5.97473	−	5.97473i	−0.411317	−	0.411317i	−0.882197	+	0.470880i	$0.843936\pi$
$212$	10.7329	+	1.81054i	0.737141	+	0.124348i
$213$	2.46322	+	6.31484i	0.168777	+	0.432685i
$214$	−5.38933	−	16.8743i	−0.368407	−	1.15350i
$215$			4.00744i			0.273305i
$216$	13.9828	+	4.52575i	0.951406	+	0.307938i
$217$			5.84687i			0.396912i
$218$	17.3768	−	5.54982i	1.17691	−	0.375881i
$219$	6.18851	+	15.8652i	0.418180	+	1.07207i
$220$	−14.1676	−	19.9173i	−0.955177	−	1.34283i
$221$	−8.42422	−	8.42422i	−0.566674	−	0.566674i
$222$	11.3094	+	13.9551i	0.759034	+	0.936605i
$223$		−	10.9984i		−	0.736505i	−0.929726	−	0.368253i	$-0.879956\pi$
$223$		−	10.9984i		−	0.736505i	0.929726	−	0.368253i	$-0.120044\pi$
$224$	4.09910	−	3.89838i	0.273883	−	0.260472i
$225$	−28.5567	−	31.0352i	−1.90378	−	2.06901i
$226$	−5.81498	+	11.2723i	−0.386807	+	0.749824i
$227$	−12.2151	+	12.2151i	−0.810742	+	0.810742i	−0.984745	−	0.174003i	$-0.944330\pi$
$227$	−12.2151	+	12.2151i	−0.810742	+	0.810742i	0.174003	+	0.984745i	$0.444330\pi$
$228$	−1.18325	−	5.69660i	−0.0783626	−	0.377267i
$229$	13.1881	+	13.1881i	0.871496	+	0.871496i	0.992635	−	0.121140i	$-0.0386549\pi$
$229$	13.1881	+	13.1881i	0.871496	+	0.871496i	−0.121140	+	0.992635i	$0.538655\pi$
$230$	−2.27287	−	7.11650i	−0.149869	−	0.469248i
$231$	−4.44015	−	1.94824i	−0.292140	−	0.128185i
$232$	3.20684	−	4.27692i	0.210539	−	0.280793i
$233$	3.56286			0.233411			0.116705	−	0.993167i	$-0.462767\pi$
$233$	3.56286			0.233411			0.116705	+	0.993167i	$0.462767\pi$
$234$	9.72745	−	17.0754i	0.635903	−	1.11625i
$235$	32.6127	−	32.6127i	2.12742	−	2.12742i
$236$	0.937585	−	5.55804i	0.0610316	−	0.361798i
$237$	−2.43356	−	6.23879i	−0.158077	−	0.405253i
$238$	−1.66760	+	3.23264i	−0.108094	+	0.209541i
$239$	1.40979			0.0911918			0.0455959	−	0.998960i	$-0.485481\pi$
$239$	1.40979			0.0911918			0.0455959	+	0.998960i	$0.485481\pi$
$240$	−22.1773	−	20.5659i	−1.43154	−	1.32752i
$241$	8.32598			0.536324			0.268162	−	0.963374i	$-0.413584\pi$
$241$	8.32598			0.536324			0.268162	+	0.963374i	$0.413584\pi$
$242$	2.05085	−	3.97557i	0.131834	−	0.255560i
$243$	−4.43936	−	14.9430i	−0.284785	−	0.958591i
$244$	−18.4831	−	3.11792i	−1.18326	−	0.199604i
$245$	−3.08691	+	3.08691i	−0.197216	+	0.197216i
$246$	−1.67656	−	0.175573i	−0.106894	−	0.0111941i
$247$	−7.77970			−0.495011
$248$	16.3710	−	2.34083i	1.03956	−	0.148643i
$249$	−2.95125	+	6.72608i	−0.187028	+	0.426248i
$250$	17.0140	+	53.2720i	1.07606	+	3.36922i
$251$	7.86006	+	7.86006i	0.496123	+	0.496123i	0.910229	−	0.414106i	$-0.135906\pi$
$251$	7.86006	+	7.86006i	0.496123	+	0.496123i	−0.414106	+	0.910229i	$0.635906\pi$
$252$	−5.86983	−	1.24303i	−0.369764	−	0.0783036i
$253$	−2.39529	+	2.39529i	−0.150591	+	0.150591i
$254$	0.367988	−	0.713344i	0.0230896	−	0.0447592i
$255$	17.8092	+	7.81430i	1.11526	+	0.489350i
$256$	−12.5564	−	9.91653i	−0.784773	−	0.619783i
$257$			13.3701i			0.834004i	0.908906	+	0.417002i	$0.136919\pi$
$257$			13.3701i			0.834004i	−0.908906	+	0.417002i	$0.863081\pi$
$258$	1.74692	−	1.41572i	0.108758	−	0.0881389i
$259$	−5.18528	−	5.18528i	−0.322198	−	0.322198i
$260$	−32.9554	+	23.4418i	−2.04381	+	1.45380i
$261$	−5.66501	−	0.235612i	−0.350655	−	0.0145840i
$262$	7.45422	−	2.38073i	0.460523	−	0.147082i
$263$		−	11.7128i		−	0.722240i	−0.932519	−	0.361120i	$-0.882395\pi$
$263$		−	11.7128i		−	0.722240i	0.932519	−	0.361120i	$-0.117605\pi$
$264$	−3.67732	+	13.2122i	−0.226324	+	0.813153i
$265$			23.7586i			1.45948i
$266$	0.722652	+	2.26267i	0.0443086	+	0.138733i
$267$	17.5501	−	6.84573i	1.07405	−	0.418952i
$268$	−2.11904	+	12.5617i	−0.129441	+	0.767331i
$269$	−17.7527	−	17.7527i	−1.08240	−	1.08240i	−0.996285	−	0.0861135i	$-0.972555\pi$
$269$	−17.7527	−	17.7527i	−1.08240	−	1.08240i	−0.0861135	−	0.996285i	$-0.527445\pi$
$270$	−4.66417	+	31.7393i	−0.283853	+	1.93159i
$271$			8.40389i			0.510500i	0.966875	+	0.255250i	$0.0821577\pi$
$271$			8.40389i			0.510500i	−0.966875	+	0.255250i	$0.917842\pi$
$272$	9.71886	+	3.37499i	0.589293	+	0.204639i
$273$	−3.22357	+	7.34670i	−0.195099	+	0.444642i
$274$	−23.6543	−	12.2024i	−1.42901	−	0.737174i
$275$	27.8280	−	27.8280i	1.67809	−	1.67809i
$276$	−2.29927	+	3.50485i	−0.138400	+	0.210967i
$277$	13.3603	+	13.3603i	0.802743	+	0.802743i	0.983523	−	0.180781i	$-0.0578624\pi$
$277$	13.3603	+	13.3603i	0.802743	+	0.802743i	−0.180781	+	0.983523i	$0.557862\pi$
$278$	−19.1022	+	6.10086i	−1.14567	+	0.365905i
$279$	−11.8770	−	12.9078i	−0.711056	−	0.772769i
$280$	9.87907	+	7.40734i	0.590387	+	0.442673i
$281$	14.3212			0.854330			0.427165	−	0.904174i	$-0.359512\pi$
$281$	14.3212			0.854330			0.427165	+	0.904174i	$0.359512\pi$
$282$	−25.7377	−	2.69530i	−1.53266	−	0.160503i
$283$	−5.80753	+	5.80753i	−0.345222	+	0.345222i	−0.858326	−	0.513104i	$-0.828495\pi$
$283$	−5.80753	+	5.80753i	−0.345222	+	0.345222i	0.513104	+	0.858326i	$0.328495\pi$
$284$	−6.37790	+	4.53672i	−0.378459	+	0.269205i
$285$	11.8316	−	4.61513i	0.700842	−	0.273376i
$286$	16.2973	+	8.40715i	0.963677	+	0.497125i
$287$	0.688196			0.0406229
$288$	−1.13040	+	16.9329i	−0.0666096	+	0.997779i
$289$	10.3846			0.610857
$290$	10.3698	+	5.34942i	0.608939	+	0.314129i
$291$	−16.4030	+	6.39829i	−0.961560	+	0.375074i
$292$	−16.0236	+	11.3979i	−0.937711	+	0.667011i
$293$	−1.00713	+	1.00713i	−0.0588371	+	0.0588371i	−0.735913	−	0.677076i	$-0.763247\pi$
$293$	−1.00713	+	1.00713i	−0.0588371	+	0.0588371i	0.677076	+	0.735913i	$0.263247\pi$
$294$	2.43617	+	0.255120i	0.142080	+	0.0148789i
$295$	12.3034			0.716330
$296$	−12.4426	+	16.5945i	−0.723210	+	0.964535i
$297$	13.7598	−	4.71843i	0.798422	−	0.273791i
$298$	−0.224185	+	0.0716003i	−0.0129867	+	0.00414770i
$299$	3.96327	+	3.96327i	0.229202	+	0.229202i
$300$	26.7124	−	40.7186i	1.54224	−	2.35089i
$301$	−0.649101	+	0.649101i	−0.0374136	+	0.0374136i
$302$	−30.2603	−	15.6102i	−1.74129	−	0.898265i
$303$	11.4133	−	26.0117i	0.655680	−	1.49433i
$304$	6.04604	−	2.92926i	0.346764	−	0.168005i
$305$		−	40.9146i		−	2.34276i
$306$	−2.88512	−	10.5240i	−0.164932	−	0.601615i
$307$	−3.43988	−	3.43988i	−0.196324	−	0.196324i	0.602098	−	0.798422i	$-0.294332\pi$
$307$	−3.43988	−	3.43988i	−0.196324	−	0.196324i	−0.798422	+	0.602098i	$0.794332\pi$
$308$	0.931315	−	5.52087i	0.0530666	−	0.314581i
$309$	−9.68806	+	3.77901i	−0.551135	+	0.214980i
$310$	10.9823	+	34.3864i	0.623755	+	1.95302i
$311$			26.3610i			1.49480i	0.664377	+	0.747398i	$0.268697\pi$
$311$			26.3610i			1.49480i	−0.664377	+	0.747398i	$0.731303\pi$
$312$	21.8610	+	6.08453i	1.23763	+	0.344469i
$313$		−	26.3343i		−	1.48850i	−0.667900	−	0.744251i	$-0.732807\pi$
$313$		−	26.3343i		−	1.48850i	0.667900	−	0.744251i	$-0.267193\pi$
$314$	−10.0897	+	3.22245i	−0.569394	+	0.181853i
$315$	0.544230	−	13.0854i	0.0306639	−	0.737276i
$316$	6.30110	−	4.48209i	0.354465	−	0.252137i
$317$	−6.78539	−	6.78539i	−0.381105	−	0.381105i	0.490395	−	0.871500i	$-0.336853\pi$
$317$	−6.78539	−	6.78539i	−0.381105	−	0.381105i	−0.871500	+	0.490395i	$0.836853\pi$
$318$	10.3568	−	8.39328i	0.580782	−	0.470672i
$319$		−	5.29084i		−	0.296230i
$320$	16.7850	−	30.6265i	0.938311	−	1.71207i
$321$	−19.8669	−	8.71714i	−1.10886	−	0.486543i
$322$	0.784542	−	1.52083i	0.0437208	−	0.0847527i
$323$	−3.05465	+	3.05465i	−0.169965	+	0.169965i
$324$	15.4835	−	9.17943i	0.860193	−	0.509968i
$325$	−46.0444	−	46.0444i	−2.55408	−	2.55408i
$326$	9.70665	+	30.3921i	0.537602	+	1.68326i
$327$	8.97674	−	20.4585i	0.496415	−	1.13136i
$328$	−0.275524	−	1.92691i	−0.0152133	−	0.106396i
$329$	10.5648			0.582458
$330$	−29.7726	−	3.11785i	−1.63893	−	0.171632i
$331$	−16.6074	+	16.6074i	−0.912823	+	0.912823i	−0.996494	−	0.0836701i	$-0.973336\pi$
$331$	−16.6074	+	16.6074i	−0.912823	+	0.912823i	0.0836701	+	0.996494i	$0.473336\pi$
$332$	−8.36319	−	1.41079i	−0.458990	−	0.0774269i
$333$	21.9803	+	0.914177i	1.20451	+	0.0500966i
$334$	10.7569	−	20.8522i	0.588591	−	1.14098i
$335$	−27.8069			−1.51925
$336$	−0.261011	−	6.92328i	−0.0142393	−	0.377696i
$337$	−5.72436			−0.311826			−0.155913	−	0.987771i	$-0.549832\pi$
$337$	−5.72436			−0.311826			−0.155913	+	0.987771i	$0.549832\pi$
$338$	5.48192	−	10.6267i	0.298177	−	0.578017i
$339$	5.64523	+	14.4724i	0.306607	+	0.786033i
$340$	−3.73546	+	22.1440i	−0.202584	+	1.20093i
$341$	11.5739	−	11.5739i	0.626761	−	0.626761i
$342$	−6.19160	−	3.52720i	−0.334803	−	0.190729i
$343$	−1.00000			−0.0539949
$344$	2.07732	+	1.55758i	0.112002	+	0.0839790i
$345$	−8.37856	−	3.67633i	−0.451087	−	0.197927i
$346$	1.67323	+	5.23898i	0.0899533	+	0.281649i
$347$	8.46543	+	8.46543i	0.454448	+	0.454448i	0.896828	−	0.442380i	$-0.145866\pi$
$347$	8.46543	+	8.46543i	0.454448	+	0.454448i	−0.442380	+	0.896828i	$0.645866\pi$
$348$	−1.33147	−	6.41022i	−0.0713746	−	0.343624i
$349$	3.18646	−	3.18646i	0.170567	−	0.170567i	−0.616661	−	0.787229i	$-0.711515\pi$
$349$	3.18646	−	3.18646i	0.170567	−	0.170567i	0.787229	+	0.616661i	$0.211515\pi$
$350$	−9.11463	+	17.6687i	−0.487197	+	0.944432i
$351$	−7.80715	−	22.7670i	−0.416715	−	1.21521i
$352$	−15.8310	−	0.397319i	−0.843796	−	0.0211772i
$353$		−	9.14533i		−	0.486757i	−0.969931	−	0.243378i	$-0.921744\pi$
$353$		−	9.14533i		−	0.486757i	0.969931	−	0.243378i	$-0.0782557\pi$
$354$	−4.34645	−	5.36327i	−0.231011	−	0.285055i
$355$	−12.0804	−	12.0804i	−0.641161	−	0.641161i
$356$	12.6084	+	17.7253i	0.668242	+	0.939442i
$357$	1.61892	+	4.15035i	0.0856824	+	0.219660i
$358$	−10.6354	+	3.39673i	−0.562097	+	0.179523i
$359$		−	32.5834i		−	1.71969i	−0.510557	−	0.859844i	$-0.670561\pi$
$359$		−	32.5834i		−	1.71969i	0.510557	−	0.859844i	$-0.329439\pi$
$360$	−36.8562	+	3.71499i	−1.94249	+	0.195797i
$361$		−	16.1791i		−	0.851529i
$362$	4.10153	+	12.8422i	0.215572	+	0.674969i
$363$	−1.99098	−	5.10419i	−0.104500	−	0.267900i
$364$	−9.13488	−	1.54096i	−0.478798	−	0.0807683i
$365$	−30.3504	−	30.3504i	−1.58861	−	1.58861i
$366$	−17.8354	+	14.4540i	−0.932273	+	0.755523i
$367$			34.9220i			1.82292i	0.411394	+	0.911458i	$0.365042\pi$
$367$			34.9220i			1.82292i	−0.411394	+	0.911458i	$0.634958\pi$
$368$	−4.57235	−	1.58780i	−0.238350	−	0.0827699i
$369$	−1.51929	+	1.39796i	−0.0790910	+	0.0727748i
$370$	−40.2352	−	20.7558i	−2.09173	−	1.07904i
$371$	−3.84828	+	3.84828i	−0.199793	+	0.199793i
$372$	11.1099	−	16.9352i	0.576022	−	0.878049i
$373$	−3.26165	−	3.26165i	−0.168882	−	0.168882i	0.617606	−	0.786488i	$-0.288103\pi$
$373$	−3.26165	−	3.26165i	−0.168882	−	0.168882i	−0.786488	+	0.617606i	$0.788103\pi$
$374$	9.70003	−	3.09800i	0.501576	−	0.160194i
$375$	62.7195	+	27.5199i	3.23882	+	1.42112i
$376$	−4.22969	−	29.5810i	−0.218130	−	1.52552i
$377$	−8.75427			−0.450868
$378$	−5.89641	+	4.38546i	−0.303279	+	0.225564i
$379$	5.59162	−	5.59162i	0.287222	−	0.287222i	−0.548759	−	0.835981i	$-0.684899\pi$
$379$	5.59162	−	5.59162i	0.287222	−	0.287222i	0.835981	+	0.548759i	$0.184899\pi$
$380$	8.50006	+	11.9497i	0.436044	+	0.613009i
$381$	−0.357246	−	0.915854i	−0.0183023	−	0.0469206i
$382$	−30.6483	−	15.8103i	−1.56811	−	0.808928i
$383$	12.0233			0.614362			0.307181	−	0.951651i	$-0.400614\pi$
$383$	12.0233			0.614362			0.307181	+	0.951651i	$0.400614\pi$
$384$	−19.2803	+	3.50260i	−0.983896	+	0.178741i
$385$	12.2211			0.622845
$386$	5.07876	+	2.61994i	0.258502	+	0.133352i
$387$	0.114438	−	2.75152i	0.00581721	−	0.139868i
$388$	−11.7843	−	16.5668i	−0.598255	−	0.841052i
$389$	−0.0179418	+	0.0179418i	−0.000909686	+	0.000909686i	−0.707561	−	0.706652i	$-0.750205\pi$
$389$	−0.0179418	+	0.0179418i	−0.000909686	+	0.000909686i	0.706652	+	0.707561i	$0.250205\pi$
$390$	−5.15882	+	49.2620i	−0.261227	+	2.49448i
$391$	3.11231			0.157396
$392$	0.400356	+	2.79995i	0.0202210	+	0.141419i
$393$	3.85079	−	8.77618i	0.194247	−	0.442699i
$394$	9.88948	−	3.15851i	0.498225	−	0.159123i
$395$	11.9349	+	11.9349i	0.600511	+	0.600511i
$396$	9.15874	+	14.0799i	0.460244	+	0.707542i
$397$	−1.15667	+	1.15667i	−0.0580514	+	0.0580514i	−0.735537	−	0.677485i	$-0.763070\pi$
$397$	−1.15667	+	1.15667i	−0.0580514	+	0.0580514i	0.677485	+	0.735537i	$0.263070\pi$
$398$	12.3121	+	6.35136i	0.617150	+	0.318365i
$399$	2.66394	+	1.16888i	0.133364	+	0.0585170i
$400$	53.1206	+	18.4467i	2.65603	+	0.922336i
$401$			7.84082i			0.391552i	0.980649	+	0.195776i	$0.0627225\pi$
$401$			7.84082i			0.391552i	−0.980649	+	0.195776i	$0.937278\pi$
$402$	9.82343	+	12.1216i	0.489948	+	0.604568i
$403$	−19.1502	−	19.1502i	−0.953942	−	0.953942i
$404$	32.3429	+	5.45592i	1.60912	+	0.271442i
$405$	25.3793	+	29.9933i	1.26111	+	1.49038i
$406$	0.813179	+	2.54611i	0.0403574	+	0.126362i
$407$			20.5285i			1.01756i
$408$	10.9726	−	6.19451i	0.543225	−	0.306674i
$409$			16.1657i			0.799344i	0.916658	+	0.399672i	$0.130876\pi$
$409$			16.1657i			0.799344i	−0.916658	+	0.399672i	$0.869124\pi$
$410$	4.04739	−	1.29266i	0.199886	−	0.0638398i
$411$	−30.3695	+	11.8462i	−1.49802	+	0.584330i
$412$	−6.96012	−	9.78482i	−0.342900	−	0.482064i
$413$	1.99283	+	1.99283i	0.0980606	+	0.0980606i
$414$	1.35734	+	4.95112i	0.0667096	+	0.243334i
$415$		−	18.5129i		−	0.908763i
$416$	−0.657406	+	26.1941i	−0.0322320	+	1.28427i
$417$	−9.86803	+	22.4898i	−0.483239	+	1.10133i
$418$	3.04846	−	5.90944i	0.149105	−	0.289040i
$419$	5.12464	−	5.12464i	0.250355	−	0.250355i	−0.570761	−	0.821116i	$-0.693352\pi$
$419$	5.12464	−	5.12464i	0.250355	−	0.250355i	0.821116	+	0.570761i	$0.193352\pi$
$420$	14.8067	−	3.07552i	0.722493	−	0.150070i
$421$	8.36782	+	8.36782i	0.407823	+	0.407823i	0.880979	−	0.473156i	$-0.156885\pi$
$421$	8.36782	+	8.36782i	0.407823	+	0.407823i	−0.473156	+	0.880979i	$0.656885\pi$
$422$	−3.63550	−	11.3830i	−0.176974	−	0.554115i
$423$	−23.3233	+	21.4607i	−1.13402	+	1.04346i
$424$	12.3157	+	9.23430i	0.598102	+	0.448457i
$425$	−36.1581			−1.75392
$426$	−0.998393	+	9.53375i	−0.0483723	+	0.461912i
$427$	6.62710	−	6.62710i	0.320708	−	0.320708i
$428$	4.16705	−	24.7024i	0.201422	−	1.19404i
$429$	20.9238	−	8.16174i	1.01021	−	0.394052i
$430$	−2.59824	+	5.03669i	−0.125298	+	0.242891i
$431$	−27.9027			−1.34403			−0.672014	−	0.740539i	$-0.734570\pi$
$431$	−27.9027			−1.34403			−0.672014	+	0.740539i	$0.734570\pi$
$432$	14.6397	+	14.7539i	0.704355	+	0.709848i
$433$	3.68845			0.177256			0.0886278	−	0.996065i	$-0.471752\pi$
$433$	3.68845			0.177256			0.0886278	+	0.996065i	$0.471752\pi$
$434$	−3.79085	+	7.34856i	−0.181967	+	0.352742i
$435$	13.3137	−	5.19327i	0.638344	−	0.248998i
$436$	25.4381	+	4.29115i	1.21826	+	0.205509i
$437$	1.43710	−	1.43710i	0.0687456	−	0.0687456i
$438$	−2.50833	+	23.9523i	−0.119853	+	1.14448i
$439$	33.8702			1.61654			0.808268	−	0.588814i	$-0.200405\pi$
$439$	33.8702			1.61654			0.808268	+	0.588814i	$0.200405\pi$
$440$	−4.89279	−	34.2184i	−0.233255	−	1.63130i
$441$	2.20764	−	2.03134i	0.105126	−	0.0967303i
$442$	−5.12597	−	16.0497i	−0.243818	−	0.763408i
$443$	−2.28546	−	2.28546i	−0.108586	−	0.108586i	0.650727	−	0.759312i	$-0.274464\pi$
$443$	−2.28546	−	2.28546i	−0.108586	−	0.108586i	−0.759312	+	0.650727i	$0.774464\pi$
$444$	5.16614	+	24.8717i	0.245174	+	1.18036i
$445$	−33.5736	+	33.5736i	−1.59154	+	1.59154i
$446$	7.13085	−	13.8231i	0.337655	−	0.654545i
$447$	−0.115812	+	0.263943i	−0.00547773	+	0.0124841i
$448$	7.67943	−	2.24195i	0.362819	−	0.105922i
$449$		−	0.726262i		−	0.0342744i	−0.999853	−	0.0171372i	$-0.994545\pi$
$449$		−	0.726262i		−	0.0342744i	0.999853	−	0.0171372i	$-0.00545521\pi$
$450$	−15.7693	−	57.5210i	−0.743371	−	2.71157i
$451$	−1.36228	−	1.36228i	−0.0641475	−	0.0641475i
$452$	−14.6169	+	10.3973i	−0.687523	+	0.489048i
$453$	−38.8509	+	15.1545i	−1.82537	+	0.712021i
$454$	−23.2720	+	7.43262i	−1.09221	+	0.348830i
$455$		−	20.2211i		−	0.947981i
$456$	2.20627	−	7.92686i	0.103318	−	0.371209i
$457$		−	5.34320i		−	0.249944i	−0.992160	−	0.124972i	$-0.960116\pi$
$457$		−	5.34320i		−	0.249944i	0.992160	−	0.124972i	$-0.0398842\pi$
$458$	8.02472	+	25.1259i	0.374970	+	1.17406i
$459$	−12.0047	−	5.87390i	−0.560334	−	0.274170i
$460$	1.75739	−	10.4179i	0.0819389	−	0.485737i
$461$	−9.51942	−	9.51942i	−0.443364	−	0.443364i	0.449777	−	0.893141i	$-0.351503\pi$
$461$	−9.51942	−	9.51942i	−0.443364	−	0.443364i	−0.893141	+	0.449777i	$0.851503\pi$
$462$	−4.31738	−	5.32740i	−0.200863	−	0.247853i
$463$		−	10.7468i		−	0.499448i	−0.968317	−	0.249724i	$-0.919660\pi$
$463$		−	10.7468i		−	0.499448i	0.968317	−	0.249724i	$-0.0803399\pi$
$464$	6.80343	−	3.29621i	0.315841	−	0.153023i
$465$	40.4846	+	17.7638i	1.87743	+	0.823774i
$466$	4.47793	+	2.31000i	0.207436	+	0.107009i
$467$	−23.0136	+	23.0136i	−1.06494	+	1.06494i	−0.0672049	+	0.997739i	$0.521408\pi$
$467$	−23.0136	+	23.0136i	−1.06494	+	1.06494i	−0.997739	+	0.0672049i	$0.978592\pi$
$468$	23.2967	−	15.1541i	1.07689	−	0.700500i
$469$	−4.50400	−	4.50400i	−0.207975	−	0.207975i
$470$	62.1334	−	19.8442i	2.86600	−	0.915345i
$471$	−5.21226	+	11.8790i	−0.240168	+	0.547357i
$472$	4.78197	−	6.37765i	0.220108	−	0.293555i
$473$	2.56979			0.118159
$474$	0.986371	−	9.41895i	0.0453055	−	0.432627i
$475$	−16.6958	+	16.6958i	−0.766058	+	0.766058i
$476$	−4.19180	+	2.98170i	−0.192131	+	0.136666i
$477$	0.678460	−	16.3128i	0.0310645	−	0.746910i
$478$	1.77188	+	0.914045i	0.0810437	+	0.0418074i
$479$	36.4521			1.66554			0.832769	−	0.553620i	$-0.186754\pi$
$479$	36.4521			1.66554			0.832769	+	0.553620i	$0.186754\pi$
$480$	−14.5392	−	40.2267i	−0.663623	−	1.83609i
$481$	33.9667			1.54875
$482$	10.4644	+	5.39819i	0.476640	+	0.245881i
$483$	−0.761640	−	1.95258i	−0.0346558	−	0.0888454i
$484$	5.15517	−	3.66696i	0.234326	−	0.166680i
$485$	31.3792	−	31.3792i	1.42486	−	1.42486i
$486$	4.10880	−	21.6591i	0.186379	−	0.982478i
$487$	−24.5053			−1.11044			−0.555221	−	0.831703i	$-0.687366\pi$
$487$	−24.5053			−1.11044			−0.555221	+	0.831703i	$0.687366\pi$
$488$	−21.2087	−	15.9023i	−0.960074	−	0.719865i
$489$	35.7820	+	15.7003i	1.61812	+	0.709994i
$490$	−5.88116	+	1.87833i	−0.265684	+	0.0848542i
$491$	4.59091	+	4.59091i	0.207185	+	0.207185i	0.803070	−	0.595885i	$-0.203199\pi$
$491$	4.59091	+	4.59091i	0.207185	+	0.207185i	−0.595885	+	0.803070i	$0.703199\pi$
$492$	−1.99333	−	1.30767i	−0.0898662	−	0.0589545i
$493$	−3.43731	+	3.43731i	−0.154809	+	0.154809i
$494$	−9.77781	−	5.04401i	−0.439924	−	0.226941i
$495$	−26.9798	+	24.8252i	−1.21265	+	1.11581i
$496$	22.0933	+	7.67215i	0.992018	+	0.344490i
$497$		−	3.91342i		−	0.175541i
$498$	−8.07013	+	6.54011i	−0.361631	+	0.293069i
$499$	0.0693040	+	0.0693040i	0.00310247	+	0.00310247i	0.708656	−	0.705554i	$-0.249302\pi$
$499$	0.0693040	+	0.0693040i	0.00310247	+	0.00310247i	−0.705554	+	0.708656i	$0.749302\pi$
$500$	−13.1553	+	77.9853i	−0.588325	+	3.48761i
$501$	−10.4429	−	26.7719i	−0.466554	−	1.19608i
$502$	4.78269	+	14.9749i	0.213462	+	0.668363i
$503$		−	2.99458i		−	0.133522i	−0.997769	−	0.0667609i	$-0.978734\pi$
$503$		−	2.99458i		−	0.133522i	0.997769	−	0.0667609i	$-0.0212665\pi$
$504$	−6.57148	−	5.36802i	−0.292717	−	0.239111i
$505$			71.5948i			3.18593i
$506$	−4.56349	+	1.45749i	−0.202872	+	0.0647933i
$507$	−5.32190	−	13.6435i	−0.236354	−	0.605929i
$508$	0.925001	−	0.657970i	0.0410403	−	0.0291927i
$509$	16.5223	+	16.5223i	0.732339	+	0.732339i	0.971083	−	0.238744i	$-0.0767356\pi$
$509$	16.5223	+	16.5223i	0.732339	+	0.732339i	−0.238744	+	0.971083i	$0.576736\pi$
$510$	17.3168	+	21.3680i	0.766803	+	0.946191i
$511$		−	9.83194i		−	0.434939i
$512$	−9.35187	−	20.6044i	−0.413298	−	0.910596i
$513$	−8.25540	+	2.83090i	−0.364485	+	0.124987i
$514$	−8.66857	+	16.8040i	−0.382354	+	0.741194i
$515$	18.5334	−	18.5334i	0.816681	−	0.816681i
$516$	3.11348	−	0.646705i	0.137063	−	0.0284696i
$517$	−20.9131	−	20.9131i	−0.919756	−	0.919756i
$518$	−3.15514	−	9.87895i	−0.138629	−	0.434056i
$519$	6.16808	+	2.70642i	0.270749	+	0.118798i
$520$	−56.6181	+	8.09565i	−2.48287	+	0.355018i
$521$	10.8943			0.477289			0.238645	−	0.971107i	$-0.423297\pi$
$521$	10.8943			0.477289			0.238645	+	0.971107i	$0.423297\pi$
$522$	−6.96722	−	3.96906i	−0.304947	−	0.173721i
$523$	−0.249542	+	0.249542i	−0.0109117	+	0.0109117i	−0.712542	−	0.701630i	$-0.752456\pi$
$523$	−0.249542	+	0.249542i	−0.0109117	+	0.0109117i	0.701630	+	0.712542i	$0.252456\pi$
$524$	10.9123	+	1.84079i	0.476705	+	0.0804153i
$525$	8.84856	+	22.6846i	0.386183	+	0.990038i
$526$	7.59403	−	14.7210i	0.331115	−	0.641867i
$527$	−15.0384			−0.655085
$528$	−13.1880	+	14.2213i	−0.573933	+	0.618903i
$529$	21.5358			0.936338
$530$	−15.4040	+	29.8607i	−0.669108	+	1.29706i
$531$	−8.44755	−	0.351340i	−0.366592	−	0.0152468i
$532$	−0.558757	+	3.31234i	−0.0242252	+	0.143608i
$533$	−2.25405	+	2.25405i	−0.0976336	+	0.0976336i
$534$	26.4960	+	2.77472i	1.14659	+	0.120074i
$535$	54.6817			2.36410
$536$	−10.8078	+	14.4142i	−0.466824	+	0.622597i
$537$	−5.49416	+	12.5215i	−0.237090	+	0.540343i
$538$	−10.8021	−	33.8222i	−0.465714	−	1.45818i
$539$	1.97950	+	1.97950i	0.0852631	+	0.0852631i
$540$	−26.4404	+	36.8670i	−1.13781	+	1.58650i
$541$	31.1489	−	31.1489i	1.33920	−	1.33920i	0.442356	−	0.896839i	$-0.354143\pi$
$541$	31.1489	−	31.1489i	1.33920	−	1.33920i	0.896839	−	0.442356i	$-0.145857\pi$
$542$	−5.44870	+	10.5623i	−0.234042	+	0.453690i
$543$	15.1196	+	6.63416i	0.648846	+	0.284699i
$544$	10.0268	+	10.5431i	0.429897	+	0.452031i
$545$			56.3102i			2.41206i
$546$	−8.81476	+	7.14358i	−0.377237	+	0.305717i
$547$	0.0905284	+	0.0905284i	0.00387072	+	0.00387072i	0.709039	−	0.705169i	$-0.249129\pi$
$547$	0.0905284	+	0.0905284i	0.00387072	+	0.00387072i	−0.705169	+	0.709039i	$0.749129\pi$
$548$	−21.8181	−	30.6728i	−0.932025	−	1.31028i
$549$	−1.16837	+	28.0921i	−0.0498649	+	1.19894i
$550$	53.0176	−	16.9328i	2.26068	−	0.722016i
$551$			3.17433i			0.135231i
$552$	−5.16220	+	2.91428i	−0.219718	+	0.124040i
$553$			3.86630i			0.164412i
$554$	8.12949	+	25.4539i	0.345389	+	1.08143i
$555$	−51.6574	+	20.1499i	−2.19273	+	0.855317i
$556$	−27.9638	−	4.71721i	−1.18593	−	0.200054i
$557$	3.38154	+	3.38154i	0.143280	+	0.143280i	0.775109	−	0.631828i	$-0.217695\pi$
$557$	3.38154	+	3.38154i	0.143280	+	0.143280i	−0.631828	+	0.775109i	$0.717695\pi$
$558$	−6.55857	−	23.9235i	−0.277647	−	1.01276i
$559$		−	4.25200i		−	0.179840i
$560$	7.61378	+	15.7150i	0.321741	+	0.664078i
$561$	5.01096	−	11.4203i	0.211563	−	0.482164i
$562$	17.9994	+	9.28521i	0.759258	+	0.391673i
$563$	19.9160	−	19.9160i	0.839359	−	0.839359i	−0.149415	−	0.988775i	$-0.547739\pi$
$563$	19.9160	−	19.9160i	0.839359	−	0.839359i	0.988775	+	0.149415i	$0.0477392\pi$
$564$	−30.6005	−	20.0747i	−1.28851	−	0.845298i
$565$	−27.6860	−	27.6860i	−1.16476	−	1.16476i
$566$	−11.0644	+	3.53377i	−0.465073	+	0.148535i
$567$	−0.747340	+	8.96892i	−0.0313854	+	0.376659i
$568$	−10.9574	+	1.56676i	−0.459762	+	0.0657399i
$569$	28.9671			1.21436			0.607182	−	0.794563i	$-0.292300\pi$
$569$	28.9671			1.21436			0.607182	+	0.794563i	$0.292300\pi$
$570$	17.8626	+	1.87060i	0.748181	+	0.0783510i
$571$	2.01378	−	2.01378i	0.0842740	−	0.0842740i	−0.663713	−	0.747987i	$-0.731020\pi$
$571$	2.01378	−	2.01378i	0.0842740	−	0.0842740i	0.747987	+	0.663713i	$0.231020\pi$
$572$	15.0322	+	21.1328i	0.628526	+	0.883607i
$573$	−39.3490	+	15.3488i	−1.64383	+	0.641206i
$574$	0.864950	+	0.446196i	0.0361023	+	0.0186238i
$575$	17.0110			0.709407
$576$	−12.3992	+	20.5489i	−0.516635	+	0.856206i
$577$	1.36897			0.0569909			0.0284954	−	0.999594i	$-0.490928\pi$
$577$	1.36897			0.0569909			0.0284954	+	0.999594i	$0.490928\pi$
$578$	13.0517	+	6.73289i	0.542879	+	0.280051i
$579$	6.52055	−	2.54346i	0.270985	−	0.105703i
$580$	9.56487	+	13.4467i	0.397160	+	0.558343i
$581$	2.99861	−	2.99861i	0.124403	−	0.124403i
$582$	−24.7642	−	2.59336i	−1.02651	−	0.107498i
$583$	15.2353			0.630983
$584$	−27.5289	+	3.93628i	−1.13916	+	0.162884i
$585$	41.0759	+	44.6409i	1.69828	+	1.84568i
$586$	−1.91877	+	0.612818i	−0.0792637	+	0.0253153i
$587$	−17.6935	−	17.6935i	−0.730291	−	0.730291i	0.240386	−	0.970677i	$-0.422726\pi$
$587$	−17.6935	−	17.6935i	−0.730291	−	0.730291i	−0.970677	+	0.240386i	$0.922726\pi$
$588$	2.89645	+	1.90015i	0.119448	+	0.0783607i
$589$	−6.94394	+	6.94394i	−0.286120	+	0.286120i
$590$	15.4633	+	7.97695i	0.636615	+	0.328406i
$591$	5.10883	−	11.6433i	0.210149	−	0.478942i
$592$	−26.3974	+	12.7893i	−1.08493	+	0.525639i
$593$			35.7646i			1.46868i	0.678784	+	0.734338i	$0.262507\pi$
$593$			35.7646i			1.46868i	−0.678784	+	0.734338i	$0.737493\pi$
$594$	20.3530	+	2.99093i	0.835093	+	0.122719i
$595$	−7.93969	−	7.93969i	−0.325496	−	0.325496i
$596$	−0.328186	−	0.0553617i	−0.0134430	−	0.00226770i
$597$	15.8074	−	6.16595i	0.646952	−	0.252356i
$598$	2.41157	+	7.55079i	0.0986166	+	0.308775i
$599$		−	2.49924i		−	0.102116i	−0.998696	−	0.0510580i	$-0.983741\pi$
$599$		−	2.49924i		−	0.102116i	0.998696	−	0.0510580i	$-0.0162593\pi$
$600$	59.9732	−	33.8575i	2.44840	−	1.38222i
$601$		−	38.0455i		−	1.55191i	−0.630788	−	0.775955i	$-0.717268\pi$
$601$		−	38.0455i		−	1.55191i	0.630788	−	0.775955i	$-0.282732\pi$
$602$	−1.23666	+	0.394965i	−0.0504026	+	0.0160976i
$603$	19.0923	+	0.794064i	0.777500	+	0.0323368i
$604$	−27.9113	−	39.2389i	−1.13570	−	1.59661i
$605$	9.76441	+	9.76441i	0.396980	+	0.396980i
$606$	31.2095	−	25.2925i	1.26780	−	1.02744i
$607$			29.7645i			1.20810i	0.796945	+	0.604052i	$0.206448\pi$
$607$			29.7645i			1.20810i	−0.796945	+	0.604052i	$0.793552\pi$
$608$	9.49808	+	0.238378i	0.385198	+	0.00966750i
$609$	2.99765	+	1.31530i	0.121471	+	0.0532988i
$610$	26.5272	−	51.4229i	1.07405	−	2.08205i
$611$	−34.6029	+	34.6029i	−1.39988	+	1.39988i
$612$	3.19714	−	15.0975i	0.129237	−	0.610279i
$613$	1.99144	+	1.99144i	0.0804334	+	0.0804334i	0.746179	−	0.665745i	$-0.231886\pi$
$613$	1.99144	+	1.99144i	0.0804334	+	0.0804334i	−0.665745	+	0.746179i	$0.731886\pi$
$614$	−2.09310	−	6.55363i	−0.0844707	−	0.264483i
$615$	2.09085	−	4.76517i	0.0843113	−	0.192150i
$616$	4.74999	−	6.33500i	0.191383	−	0.255245i
$617$	−21.1861			−0.852919			−0.426459	−	0.904507i	$-0.640239\pi$
$617$	−21.1861			−0.852919			−0.426459	+	0.904507i	$0.640239\pi$
$618$	−14.6264	−	1.53171i	−0.588362	−	0.0616144i
$619$	−11.4071	+	11.4071i	−0.458490	+	0.458490i	−0.898160	−	0.439669i	$-0.855096\pi$
$619$	−11.4071	+	11.4071i	−0.458490	+	0.458490i	0.439669	+	0.898160i	$0.355096\pi$
$620$	−8.49160	+	50.3385i	−0.341031	+	2.02164i
$621$	5.64777	+	2.76344i	0.226637	+	0.110893i
$622$	−17.0913	+	33.1314i	−0.685298	+	1.32845i
$623$	−10.8761			−0.435742
$624$	23.5307	+	21.8209i	0.941982	+	0.873536i
$625$	−102.339			−4.09357
$626$	17.0740	−	33.0979i	0.682413	−	1.32286i
$627$	−2.95947	−	7.58706i	−0.118190	−	0.302998i
$628$	−14.7704	−	2.49161i	−0.589402	−	0.0994261i
$629$	13.3368	−	13.3368i	0.531773	−	0.531773i
$630$	9.16796	−	16.0933i	0.365260	−	0.641172i
$631$	−7.58954			−0.302135			−0.151067	−	0.988523i	$-0.548271\pi$
$631$	−7.58954			−0.302135			−0.151067	+	0.988523i	$0.548271\pi$
$632$	10.8254	−	1.54790i	0.430613	−	0.0615720i
$633$	−13.4017	−	5.88037i	−0.532669	−	0.233724i
$634$	−4.12878	−	12.9275i	−0.163975	−	0.513415i
$635$	1.75205	+	1.75205i	0.0695278	+	0.0695278i
$636$	18.4587	−	3.83407i	0.731933	−	0.152031i
$637$	3.27530	−	3.27530i	0.129772	−	0.129772i
$638$	3.43034	−	6.64972i	0.135809	−	0.263265i
$639$	7.94948	+	8.63942i	0.314476	+	0.341770i
$640$	40.9528	−	27.6098i	1.61880	−	1.09137i
$641$			8.43526i			0.333173i	0.986027	+	0.166586i	$0.0532745\pi$
$641$			8.43526i			0.333173i	−0.986027	+	0.166586i	$0.946726\pi$
$642$	−19.3176	−	23.8368i	−0.762404	−	0.940763i
$643$	−32.7140	−	32.7140i	−1.29011	−	1.29011i	−0.934714	−	0.355400i	$-0.884345\pi$
$643$	−32.7140	−	32.7140i	−1.29011	−	1.29011i	−0.355400	−	0.934714i	$-0.615655\pi$
$644$	1.97208	−	1.40278i	0.0777108	−	0.0552771i
$645$	2.52240	+	6.46655i	0.0993193	+	0.254620i
$646$	−5.81969	+	1.85869i	−0.228973	+	0.0731294i
$647$		−	27.3057i		−	1.07350i	−0.843742	−	0.536749i	$-0.819652\pi$
$647$		−	27.3057i		−	1.07350i	0.843742	−	0.536749i	$-0.180348\pi$
$648$	25.4117	−	1.49825i	0.998266	−	0.0588567i
$649$		−	7.88960i		−	0.309694i
$650$	−28.0171	−	87.7233i	−1.09892	−	3.44079i
$651$	3.68019	+	9.43472i	0.144238	+	0.369776i
$652$	−7.50523	+	44.4913i	−0.293927	+	1.74241i
$653$	−8.02481	−	8.02481i	−0.314035	−	0.314035i	0.532435	−	0.846471i	$-0.321277\pi$
$653$	−8.02481	−	8.02481i	−0.314035	−	0.314035i	−0.846471	+	0.532435i	$0.821277\pi$
$654$	24.5467	−	19.8929i	0.959850	−	0.777873i
$655$			24.1556i			0.943838i
$656$	0.903037	−	2.60045i	0.0352577	−	0.101531i
$657$	19.9720	+	21.7054i	0.779181	+	0.846807i
$658$	13.2782	+	6.84976i	0.517640	+	0.267031i
$659$	−12.8214	+	12.8214i	−0.499453	+	0.499453i	−0.911268	−	0.411815i	$-0.864895\pi$
$659$	−12.8214	+	12.8214i	−0.499453	+	0.499453i	0.411815	+	0.911268i	$0.364895\pi$
$660$	−35.3978	−	23.2219i	−1.37786	−	0.903910i
$661$	−3.38516	−	3.38516i	−0.131667	−	0.131667i	0.638202	−	0.769869i	$-0.279679\pi$
$661$	−3.38516	−	3.38516i	−0.131667	−	0.131667i	−0.769869	+	0.638202i	$0.779679\pi$
$662$	−31.6402	+	10.1053i	−1.22973	+	0.392752i
$663$	−18.8961	−	8.29117i	−0.733862	−	0.322002i
$664$	−9.59647	−	7.19544i	−0.372415	−	0.279237i
$665$	−7.33224			−0.284332
$666$	27.0329	+	15.4000i	1.04750	+	0.596738i
$667$	1.61712	−	1.61712i	0.0626152	−	0.0626152i
$668$	27.0393	−	19.2335i	1.04618	−	0.744168i
$669$	−6.92269	−	17.7474i	−0.267647	−	0.686153i
$670$	−34.9487	−	18.0287i	−1.35019	−	0.696511i
$671$	−26.2367			−1.01286
$672$	4.16070	−	8.87066i	0.160502	−	0.342193i
$673$	−17.9865			−0.693330			−0.346665	−	0.937989i	$-0.612686\pi$
$673$	−17.9865			−0.693330			−0.346665	+	0.937989i	$0.612686\pi$
$674$	−7.19458	−	3.71142i	−0.277125	−	0.142958i
$675$	−65.6145	−	32.1051i	−2.52550	−	1.23572i
$676$	13.7798	−	9.80179i	0.529991	−	0.376992i
$677$	−20.9528	+	20.9528i	−0.805282	+	0.805282i	−0.983916	−	0.178634i	$-0.942832\pi$
$677$	−20.9528	+	20.9528i	−0.805282	+	0.805282i	0.178634	+	0.983916i	$0.442832\pi$
$678$	−2.28813	+	21.8495i	−0.0878750	+	0.839127i
$679$	10.1652			0.390106
$680$	−19.0520	+	25.4094i	−0.730612	+	0.974407i
$681$	−12.0221	+	27.3991i	−0.460689	+	1.04994i
$682$	22.0505	−	7.04249i	0.844356	−	0.269671i
$683$	−5.56984	−	5.56984i	−0.213124	−	0.213124i	0.592469	−	0.805593i	$-0.298153\pi$
$683$	−5.56984	−	5.56984i	−0.213124	−	0.213124i	−0.805593	+	0.592469i	$0.798153\pi$
$684$	−5.49494	−	8.44747i	−0.210104	−	0.322997i
$685$	58.0975	−	58.0975i	2.21979	−	2.21979i
$686$	−1.25684	−	0.648355i	−0.0479862	−	0.0247543i
$687$	29.5818	+	12.9798i	1.12862	+	0.495212i
$688$	1.60099	+	3.30446i	0.0610371	+	0.125981i
$689$		−	25.2085i		−	0.960367i
$690$	−8.14691	−	10.0528i	−0.310148	−	0.382704i
$691$	29.9017	+	29.9017i	1.13751	+	1.13751i	0.988894	+	0.148621i	$0.0474833\pi$
$691$	29.9017	+	29.9017i	1.13751	+	1.13751i	0.148621	+	0.988894i	$0.452517\pi$
$692$	−1.29375	+	7.66938i	−0.0491809	+	0.291546i
$693$	−8.39105	−	0.348990i	−0.318750	−	0.0132570i
$694$	5.15105	+	16.1283i	0.195531	+	0.612220i
$695$		−	61.9011i		−	2.34804i
$696$	2.48265	−	8.91986i	0.0941047	−	0.338106i
$697$			1.77007i			0.0670463i
$698$	6.07081	−	1.93890i	0.229784	−	0.0733884i
$699$	5.74915	−	2.24256i	0.217453	−	0.0848216i
$700$	−22.9112	+	16.2971i	−0.865961	+	0.615974i
$701$	7.62355	+	7.62355i	0.287938	+	0.287938i	0.836264	−	0.548327i	$-0.184735\pi$
$701$	7.62355	+	7.62355i	0.287938	+	0.287938i	−0.548327	+	0.836264i	$0.684735\pi$
$702$	4.94881	−	33.6762i	0.186781	−	1.27103i
$703$		−	12.3164i		−	0.464523i
$704$	−19.6394	−	10.7635i	−0.740187	−	0.405664i
$705$	32.0977	−	73.1524i	1.20887	−	2.75508i
$706$	5.92942	−	11.4942i	0.223157	−	0.432589i
$707$	−11.5965	+	11.5965i	−0.436131	+	0.436131i
$708$	−1.98547	−	9.55879i	−0.0746185	−	0.359241i
$709$	28.7112	+	28.7112i	1.07827	+	1.07827i	0.996664	+	0.0816082i	$0.0260056\pi$
$709$	28.7112	+	28.7112i	1.07827	+	1.07827i	0.0816082	+	0.996664i	$0.473994\pi$
$710$	−7.35069	−	23.0155i	−0.275866	−	0.863755i
$711$	−7.85375	−	8.53539i	−0.294539	−	0.320102i
$712$	4.35432	+	30.4525i	0.163185	+	1.14126i
$713$	7.07501			0.264961
$714$	−0.656182	+	6.26594i	−0.0245570	+	0.234497i
$715$	−40.0277	+	40.0277i	−1.49695	+	1.49695i
$716$	−15.5692	−	2.62637i	−0.581849	−	0.0981520i
$717$	2.27489	−	0.887363i	0.0849573	−	0.0331392i
$718$	21.1256	−	40.9520i	0.788402	−	1.52832i
$719$	34.9223			1.30238			0.651191	−	0.758913i	$-0.274269\pi$
$719$	34.9223			1.30238			0.651191	+	0.758913i	$0.274269\pi$
$720$	−48.7308	−	19.2268i	−1.81609	−	0.716540i
$721$	6.00387			0.223596
$722$	10.4898	−	20.3344i	0.390389	−	0.756768i
$723$	13.4351	−	5.24061i	0.499657	−	0.194900i
$724$	−3.17132	+	18.7997i	−0.117861	+	0.698687i
$725$	−18.7873	+	18.7873i	−0.697745	+	0.697745i
$726$	0.806987	−	7.70599i	0.0299501	−	0.285996i
$727$	33.6565			1.24825			0.624126	−	0.781324i	$-0.285455\pi$
$727$	33.6565			1.24825			0.624126	+	0.781324i	$0.285455\pi$
$728$	−10.4819	−	7.85938i	−0.388487	−	0.291288i
$729$	−16.5690	−	21.3182i	−0.613668	−	0.789564i
$730$	−18.4676	−	57.8232i	−0.683517	−	2.14013i
$731$	−1.66952	−	1.66952i	−0.0617494	−	0.0617494i
$732$	−31.7875	+	6.60263i	−1.17490	+	0.244040i
$733$	1.66624	−	1.66624i	0.0615441	−	0.0615441i	−0.675665	−	0.737209i	$-0.736143\pi$
$733$	1.66624	−	1.66624i	0.0615441	−	0.0615441i	0.737209	+	0.675665i	$0.236143\pi$
$734$	−22.6419	+	43.8913i	−0.835727	+	1.62006i
$735$	−3.03816	+	6.92415i	−0.112064	+	0.255401i
$736$	−4.71724	−	4.96011i	−0.173880	−	0.182832i
$737$			17.8313i			0.656825i
$738$	−2.81587	+	0.771965i	−0.103654	+	0.0284164i
$739$	16.9821	+	16.9821i	0.624695	+	0.624695i	0.946728	−	0.322033i	$-0.104366\pi$
$739$	16.9821	+	16.9821i	0.624695	+	0.624695i	−0.322033	+	0.946728i	$0.604366\pi$
$740$	−37.1118	−	52.1733i	−1.36426	−	1.91793i
$741$	−12.5536	+	4.89677i	−0.461168	+	0.179887i
$742$	−7.33170	+	2.34160i	−0.269155	+	0.0859629i
$743$		−	28.1960i		−	1.03441i	−0.855861	−	0.517206i	$-0.826972\pi$
$743$		−	28.1960i		−	1.03441i	0.855861	−	0.517206i	$-0.173028\pi$
$744$	24.9434	−	14.0816i	0.914468	−	0.516256i
$745$		−	0.726479i		−	0.0266161i
$746$	−1.98465	−	6.21406i	−0.0726631	−	0.227513i
$747$	−0.528661	+	12.7110i	−0.0193427	+	0.465073i
$748$	14.1999	+	2.39539i	0.519201	+	0.0875840i
$749$	8.85702	+	8.85702i	0.323629	+	0.323629i
$750$	60.9854	+	75.2525i	2.22687	+	2.74783i
$751$		−	45.6010i		−	1.66400i	−0.554773	−	0.832002i	$-0.687195\pi$
$751$		−	45.6010i		−	1.66400i	0.554773	−	0.832002i	$-0.312805\pi$
$752$	13.8629	−	39.9208i	0.505529	−	1.45576i
$753$	17.6306	+	7.73593i	0.642496	+	0.281913i
$754$	−11.0027	−	5.67587i	−0.400694	−	0.206703i
$755$	74.3224	−	74.3224i	2.70487	−	2.70487i
$756$	−10.2542	+	1.68884i	−0.372940	+	0.0614224i
$757$	−10.3540	−	10.3540i	−0.376321	−	0.376321i	0.493452	−	0.869773i	$-0.335735\pi$
$757$	−10.3540	−	10.3540i	−0.376321	−	0.376321i	−0.869773	+	0.493452i	$0.835735\pi$
$758$	10.6531	−	3.40239i	0.386938	−	0.123581i
$759$	−2.35746	+	5.37280i	−0.0855705	+	0.195020i
$760$	2.93551	+	20.5299i	0.106482	+	0.744698i
$761$	43.0264			1.55971			0.779854	−	0.625962i	$-0.215294\pi$
$761$	43.0264			1.55971			0.779854	+	0.625962i	$0.215294\pi$
$762$	0.144799	−	1.38270i	0.00524552	−	0.0500899i
$763$	−9.12079	+	9.12079i	−0.330195	+	0.330195i
$764$	−28.2692	−	39.7420i	−1.02274	−	1.43782i
$765$	33.6562	+	1.39978i	1.21684	+	0.0506093i
$766$	15.1113	+	7.79537i	0.545994	+	0.281658i
$767$	−13.0542			−0.471360
$768$	−26.5032	−	8.09832i	−0.956350	−	0.292223i
$769$	−26.0310			−0.938702			−0.469351	−	0.883012i	$-0.655512\pi$
$769$	−26.0310			−0.938702			−0.469351	+	0.883012i	$0.655512\pi$
$770$	15.3599	+	7.92361i	0.553533	+	0.285547i
$771$	8.41553	+	21.5745i	0.303078	+	0.776986i
$772$	4.68451	+	6.58567i	0.168599	+	0.237024i
$773$	−14.6325	+	14.6325i	−0.526293	+	0.526293i	−0.919465	−	0.393172i	$-0.871378\pi$
$773$	−14.6325	+	14.6325i	−0.526293	+	0.526293i	0.393172	+	0.919465i	$0.371378\pi$
$774$	1.92779	−	3.38402i	0.0692931	−	0.121636i
$775$	−82.1959			−2.95256
$776$	−4.06971	−	28.4621i	−0.146094	−	1.02173i
$777$	−11.6309	−	5.10339i	−0.417257	−	0.183083i
$778$	−0.0341826	+	0.0109172i	−0.00122550	+	0.000391402i
$779$	0.817325	+	0.817325i	0.0292837	+	0.0292837i
$780$	−38.4231	+	58.5695i	−1.37577	+	2.09713i
$781$	−7.74662	+	7.74662i	−0.277196	+	0.277196i
$782$	3.91166	+	2.01788i	0.139881	+	0.0721592i
$783$	−9.28955	+	3.18553i	−0.331982	+	0.113841i
$784$	−1.31218	+	3.77865i	−0.0468635	+	0.134952i
$785$		−	32.6960i		−	1.16697i
$786$	10.5299	−	8.53353i	0.375589	−	0.304381i
$787$	8.57358	+	8.57358i	0.305615	+	0.305615i	0.843206	−	0.537591i	$-0.180665\pi$
$787$	8.57358	+	8.57358i	0.305615	+	0.305615i	−0.537591	+	0.843206i	$0.680665\pi$
$788$	14.4773	+	2.44217i	0.515732	+	0.0869987i
$789$	−7.37235	−	18.9001i	−0.262463	−	0.672862i
$790$	7.26217	+	22.7383i	0.258377	+	0.808993i
$791$		−	8.96882i		−	0.318894i
$792$	2.38226	+	23.6342i	0.0846498	+	0.839806i
$793$			43.4114i			1.54158i
$794$	−2.20367	+	0.703809i	−0.0782053	+	0.0249772i
$795$	14.9544	+	38.3377i	0.530376	+	1.35970i
$796$	11.3564	+	15.9652i	0.402515	+	0.565872i
$797$	−11.4463	−	11.4463i	−0.405448	−	0.405448i	0.474700	−	0.880148i	$-0.342557\pi$
$797$	−11.4463	−	11.4463i	−0.405448	−	0.405448i	−0.880148	+	0.474700i	$0.842557\pi$
$798$	2.59028	+	3.19626i	0.0916951	+	0.113146i
$799$			27.1732i			0.961320i
$800$	54.8038	+	57.6255i	1.93761	+	2.03737i
$801$	24.0105	−	22.0930i	0.848370	−	0.780619i
$802$	−5.08363	+	9.85462i	−0.179509	+	0.347979i
$803$	−19.4623	+	19.4623i	−0.686811	+	0.686811i
$804$	4.48737	+	21.6039i	0.158257	+	0.761910i
$805$	3.73532	+	3.73532i	0.131653	+	0.131653i
$806$	−11.6526	−	36.4849i	−0.410444	−	1.28512i
$807$	−39.8204	−	17.4723i	−1.40174	−	0.615054i
$808$	37.1123	+	27.8269i	1.30561	+	0.978945i
$809$	38.0993			1.33950			0.669749	−	0.742587i	$-0.266402\pi$
$809$	38.0993			1.33950			0.669749	+	0.742587i	$0.266402\pi$
$810$	12.4513	+	54.1514i	0.437495	+	1.90269i
$811$	−16.3455	+	16.3455i	−0.573968	+	0.573968i	−0.933235	−	0.359267i	$-0.883027\pi$
$811$	−16.3455	+	16.3455i	−0.573968	+	0.573968i	0.359267	+	0.933235i	$0.383027\pi$
$812$	−0.628753	+	3.72728i	−0.0220649	+	0.130802i
$813$	5.28965	+	13.5608i	0.185516	+	0.475598i
$814$	−13.3098	+	25.8010i	−0.466508	+	0.904324i
$815$	−98.4866			−3.44984
$816$	17.8070	−	0.671333i	0.623370	−	0.0235014i
$817$	−1.54179			−0.0539403
$818$	−10.4811	+	20.3177i	−0.366464	+	0.710390i
$819$	−0.577442	+	13.8839i	−0.0201774	+	0.485143i
$820$	5.92501	+	0.999489i	0.206910	+	0.0349037i
$821$	−21.2492	+	21.2492i	−0.741602	+	0.741602i	−0.972886	−	0.231285i	$-0.925707\pi$
$821$	−21.2492	+	21.2492i	−0.741602	+	0.741602i	0.231285	+	0.972886i	$0.425707\pi$
$822$	−45.8500	−	4.80151i	−1.59920	−	0.167472i
$823$	−8.76959			−0.305689			−0.152844	−	0.988250i	$-0.548843\pi$
$823$	−8.76959			−0.305689			−0.152844	+	0.988250i	$0.548843\pi$
$824$	−2.40369	−	16.8105i	−0.0837365	−	0.585623i
$825$	27.3885	−	62.4199i	0.953545	−	2.17318i
$826$	1.21260	+	3.79672i	0.0421916	+	0.132105i
$827$	29.9690	+	29.9690i	1.04212	+	1.04212i	0.999073	+	0.0430513i	$0.0137079\pi$
$827$	29.9690	+	29.9690i	1.04212	+	1.04212i	0.0430513	+	0.999073i	$0.486292\pi$
$828$	−1.50413	+	7.10278i	−0.0522721	+	0.246839i
$829$	−33.5844	+	33.5844i	−1.16644	+	1.16644i	−0.183397	+	0.983039i	$0.558709\pi$
$829$	−33.5844	+	33.5844i	−1.16644	+	1.16644i	−0.983039	+	0.183397i	$0.941291\pi$
$830$	12.0029	−	23.2677i	0.416628	−	0.807633i
$831$	29.9680	+	13.1493i	1.03958	+	0.456144i
$832$	−17.8093	+	32.4955i	−0.617428	+	1.12658i
$833$		−	2.57205i		−	0.0891162i
$834$	−26.9839	+	21.8680i	−0.934375	+	0.757227i
$835$	51.2152	+	51.2152i	1.77237	+	1.77237i
$836$	7.66283	−	5.45071i	0.265024	−	0.188517i
$837$	−27.2896	−	13.3528i	−0.943268	−	0.461539i
$838$	9.76341	−	3.11824i	0.337271	−	0.107718i
$839$			30.1442i			1.04069i	0.853955	+	0.520346i	$0.174197\pi$
$839$			30.1442i			1.04069i	−0.853955	+	0.520346i	$0.825803\pi$
$840$	20.6036	+	5.73457i	0.710892	+	0.197862i
$841$		−	25.4280i		−	0.876828i
$842$	5.09166	+	15.9423i	0.175470	+	0.549408i
$843$	23.1092	−	9.01416i	0.795922	−	0.310464i
$844$	2.81099	−	16.6636i	0.0967582	−	0.573586i
$845$	26.1003	+	26.1003i	0.897876	+	0.897876i
$846$	−43.2277	+	11.8508i	−1.48620	+	0.407439i
$847$			3.16316i			0.108688i
$848$	9.49166	+	19.5909i	0.325945	+	0.672755i
$849$	−5.71581	+	13.0267i	−0.196166	+	0.447074i
$850$	−45.4447	−	23.4433i	−1.55874	−	0.804097i
$851$	−6.27445	+	6.27445i	−0.215085	+	0.215085i
$852$	−7.43607	+	11.3350i	−0.254756	+	0.388332i
$853$	10.2839	+	10.2839i	0.352114	+	0.352114i	0.860896	−	0.508782i	$-0.169904\pi$
$853$	10.2839	+	10.2839i	0.352114	+	0.352114i	−0.508782	+	0.860896i	$0.669904\pi$
$854$	12.6259	−	4.03246i	0.432049	−	0.137988i
$855$	16.1870	−	14.8943i	0.553582	−	0.509373i
$856$	21.2532	−	28.3452i	0.726421	−	0.968818i
$857$	26.6729			0.911130			0.455565	−	0.890203i	$-0.349437\pi$
$857$	26.6729			0.911130			0.455565	+	0.890203i	$0.349437\pi$
$858$	31.5895	+	3.30812i	1.07845	+	0.112937i
$859$	28.1639	−	28.1639i	0.960940	−	0.960940i	−0.0383253	−	0.999265i	$-0.512202\pi$
$859$	28.1639	−	28.1639i	0.960940	−	0.960940i	0.999265	+	0.0383253i	$0.0122023\pi$
$860$	−6.53113	+	4.64571i	−0.222710	+	0.158417i
$861$	1.11050	−	0.433170i	0.0378457	−	0.0147624i
$862$	−35.0691	−	18.0909i	−1.19446	−	0.616178i
$863$	26.6348			0.906660			0.453330	−	0.891343i	$-0.350236\pi$
$863$	26.6348			0.906660			0.453330	+	0.891343i	$0.350236\pi$
$864$	8.83398	+	28.0350i	0.300538	+	0.953770i
$865$	−16.9771			−0.577238
$866$	4.63578	+	2.39143i	0.157530	+	0.0812639i
$867$	16.7569	−	6.53635i	0.569095	−	0.221986i
$868$	−9.52895	+	6.77812i	−0.323434	+	0.230064i
$869$	7.65333	−	7.65333i	0.259622	−	0.259622i
$870$	20.1002	+	2.10494i	0.681462	+	0.0713640i
$871$	29.5038			0.999699
$872$	29.1893	+	21.8862i	0.988474	+	0.741159i
$873$	−22.4412	+	20.6490i	−0.759518	+	0.698863i
$874$	2.73794	−	0.874445i	0.0926122	−	0.0295785i
$875$	−27.9615	−	27.9615i	−0.945272	−	0.945272i
$876$	−18.6821	+	28.4778i	−0.631210	+	0.962175i
$877$	−4.02186	+	4.02186i	−0.135809	+	0.135809i	−0.771743	−	0.635934i	$-0.780615\pi$
$877$	−4.02186	+	4.02186i	−0.135809	+	0.135809i	0.635934	+	0.771743i	$0.280615\pi$
$878$	42.5693	+	21.9599i	1.43664	+	0.741111i
$879$	−0.991223	+	2.25905i	−0.0334331	+	0.0761960i
$880$	16.0363	−	46.1792i	0.540582	−	1.55670i
$881$		−	29.0328i		−	0.978139i	−0.872245	−	0.489070i	$-0.837336\pi$
$881$		−	29.0328i		−	0.978139i	0.872245	−	0.489070i	$-0.162664\pi$
$882$	4.09167	−	1.12172i	0.137774	−	0.0377704i
$883$	15.0006	+	15.0006i	0.504809	+	0.504809i	0.912929	−	0.408119i	$-0.133815\pi$
$883$	15.0006	+	15.0006i	0.504809	+	0.504809i	−0.408119	+	0.912929i	$0.633815\pi$
$884$	3.96342	−	23.4953i	0.133304	−	0.790234i
$885$	19.8532	−	7.74410i	0.667357	−	0.260315i
$886$	−1.39066	−	4.35425i	−0.0467202	−	0.146284i
$887$		−	18.7872i		−	0.630811i	−0.948957	−	0.315405i	$-0.897859\pi$
$887$		−	18.7872i		−	0.630811i	0.948957	−	0.315405i	$-0.102141\pi$
$888$	−9.63272	+	34.6092i	−0.323253	+	1.16141i
$889$			0.567572i			0.0190357i
$890$	−63.9641	+	20.4289i	−2.14408	+	0.684778i
$891$	19.2333	−	16.2746i	0.644341	−	0.545220i
$892$	17.9246	−	12.7501i	0.600160	−	0.426905i
$893$	12.5471	+	12.5471i	0.419874	+	0.419874i
$894$	−0.316686	+	0.256645i	−0.0105916	+	0.00858351i
$895$		−	34.4643i		−	1.15201i
$896$	11.1054	+	2.16123i	0.371004	+	0.0722016i
$897$	8.88987	+	3.90068i	0.296824	+	0.130240i
$898$	0.470876	−	0.912792i	0.0157133	−	0.0304603i
$899$	−7.81382	+	7.81382i	−0.260605	+	0.260605i
$900$	17.4746	−	82.5185i	0.582488	−	2.75062i
$901$	−9.89796	−	9.89796i	−0.329749	−	0.329749i
$902$	−0.828924	−	2.59541i	−0.0276001	−	0.0864177i
$903$	−0.638850	+	1.45598i	−0.0212596	+	0.0484518i
$904$	−25.1122	+	3.59072i	−0.835220	+	0.119426i
$905$	−41.6154			−1.38334
$906$	−58.6546	−	6.14243i	−1.94867	−	0.204069i
$907$	−26.4990	+	26.4990i	−0.879884	+	0.879884i	−0.993522	−	0.113638i	$-0.963750\pi$
$907$	−26.4990	+	26.4990i	−0.879884	+	0.879884i	0.113638	+	0.993522i	$0.463750\pi$
$908$	−34.0681	−	5.74694i	−1.13059	−	0.190719i
$909$	2.04449	−	49.1573i	0.0678113	−	1.63044i
$910$	13.1105	−	25.4146i	0.434608	−	0.842486i
$911$	−5.12785			−0.169893			−0.0849466	−	0.996386i	$-0.527072\pi$
$911$	−5.12785			−0.169893			−0.0849466	+	0.996386i	$0.527072\pi$
$912$	7.91234	−	8.53231i	0.262004	−	0.282533i
$913$	−11.8715			−0.392889
$914$	3.46429	−	6.71553i	0.114589	−	0.222130i
$915$	−25.7528	−	66.0212i	−0.851361	−	2.18259i
$916$	−6.20475	+	36.7820i	−0.205011	+	1.21531i
$917$	−3.91258	+	3.91258i	−0.129205	+	0.129205i
$918$	−11.2796	−	15.1659i	−0.372283	−	0.500548i
$919$	24.4708			0.807217			0.403609	−	0.914932i	$-0.367756\pi$
$919$	24.4708			0.807217			0.403609	+	0.914932i	$0.367756\pi$
$920$	8.96325	−	11.9542i	0.295510	−	0.394117i
$921$	−7.71588	−	3.38556i	−0.254247	−	0.111558i
$922$	−5.79238	−	18.1363i	−0.190762	−	0.597288i
$923$	12.8176	+	12.8176i	0.421897	+	0.421897i
$924$	−1.97219	−	9.49487i	−0.0648803	−	0.312358i
$925$	72.8952	−	72.8952i	2.39678	−	2.39678i
$926$	6.96776	−	13.5070i	0.228975	−	0.443868i
$927$	−13.2544	+	12.1959i	−0.435331	+	0.400566i
$928$	10.6879	+	0.268240i	0.350848	+	0.00880539i
$929$			2.48396i			0.0814959i	0.999169	+	0.0407480i	$0.0129741\pi$
$929$			2.48396i			0.0814959i	−0.999169	+	0.0407480i	$0.987026\pi$
$930$	39.3653	+	48.5745i	1.29084	+	1.59282i
$931$	−1.18763	−	1.18763i	−0.0389231	−	0.0389231i
$932$	4.13032	+	5.80657i	0.135293	+	0.190201i
$933$	16.5924	+	42.5371i	0.543210	+	1.39260i
$934$	−43.8454	+	14.0034i	−1.43466	+	0.458204i
$935$			31.4332i			1.02798i
$936$	39.1054	−	3.94170i	1.27820	−	0.128838i
$937$			38.5530i			1.25947i	0.776809	+	0.629737i	$0.216837\pi$
$937$			38.5530i			1.25947i	−0.776809	+	0.629737i	$0.783163\pi$
$938$	−2.74059	−	8.58097i	−0.0894836	−	0.280179i
$939$	−16.5756	−	42.4939i	−0.540923	−	1.38674i
$940$	90.9576	+	15.3436i	2.96671	+	0.500454i
$941$	26.7665	+	26.7665i	0.872561	+	0.872561i	0.992751	−	0.120190i	$-0.0383503\pi$
$941$	26.7665	+	26.7665i	0.872561	+	0.872561i	−0.120190	+	0.992751i	$0.538350\pi$
$942$	−14.2528	+	11.5506i	−0.464381	+	0.376339i
$943$		−	0.832752i		−	0.0271181i
$944$	10.1451	−	4.91525i	0.330196	−	0.159978i
$945$	−7.35811	−	21.4576i	−0.239359	−	0.698014i
$946$	3.22980	+	1.66614i	0.105010	+	0.0541708i
$947$	−23.3797	+	23.3797i	−0.759740	+	0.759740i	−0.976275	−	0.216535i	$-0.930524\pi$
$947$	−23.3797	+	23.3797i	−0.759740	+	0.759740i	0.216535	+	0.976275i	$0.430524\pi$
$948$	7.34653	−	11.1986i	0.238604	−	0.363712i
$949$	32.2025	+	32.2025i	1.04534	+	1.04534i
$950$	−31.8088	+	10.1591i	−1.03201	+	0.329605i
$951$	−15.2201	−	6.67822i	−0.493544	−	0.216556i
$952$	−7.20160	+	1.02974i	−0.233405	+	0.0333739i
$953$	−35.9288			−1.16385			−0.581924	−	0.813243i	$-0.697700\pi$
$953$	−35.9288			−1.16385			−0.581924	+	0.813243i	$0.697700\pi$
$954$	11.4292	−	20.0626i	0.370033	−	0.649550i
$955$	75.2754	−	75.2754i	2.43585	−	2.43585i
$956$	1.63433	+	2.29761i	0.0528580	+	0.0743100i
$957$	−3.33021	−	8.53749i	−0.107650	−	0.275978i
$958$	45.8143	+	23.6339i	1.48019	+	0.763576i
$959$	18.8206			0.607748
$960$	7.80773	−	59.9849i	0.251993	−	1.93601i
$961$	−3.18594			−0.102772
$962$	42.6905	+	22.0225i	1.37640	+	0.710033i
$963$	−37.5447	−	1.56151i	−1.20986	−	0.0503190i
$964$	9.65208	+	13.5693i	0.310872	+	0.437037i
$965$	−12.4739	+	12.4739i	−0.401550	+	0.401550i
$966$	0.308708	−	2.94788i	0.00993252	−	0.0948466i
$967$	−2.08883			−0.0671722			−0.0335861	−	0.999436i	$-0.510693\pi$
$967$	−2.08883			−0.0671722			−0.0335861	+	0.999436i	$0.510693\pi$
$968$	8.85669	−	1.26639i	0.284665	−	0.0407034i
$969$	−3.00641	+	6.85177i	−0.0965797	+	0.220111i
$970$	59.7834	−	19.0936i	1.91953	−	0.613060i
$971$	1.66314	+	1.66314i	0.0533728	+	0.0533728i	0.733289	−	0.679917i	$-0.237984\pi$
$971$	1.66314	+	1.66314i	0.0533728	+	0.0533728i	−0.679917	+	0.733289i	$0.737984\pi$
$972$	19.2069	−	24.5580i	0.616061	−	0.787698i
$973$	10.0264	−	10.0264i	0.321431	−	0.321431i
$974$	−30.7991	−	15.8881i	−0.986868	−	0.509089i
$975$	−103.281	−	45.3172i	−3.30762	−	1.45131i
$976$	−16.3455	−	33.7374i	−0.523208	−	1.07991i
$977$			41.6292i			1.33184i	0.746025	+	0.665918i	$0.231960\pi$
$977$			41.6292i			1.33184i	−0.746025	+	0.665918i	$0.768040\pi$
$978$	34.7927	+	42.9322i	1.11255	+	1.37282i
$979$	21.5292	+	21.5292i	0.688078	+	0.688078i
$980$	−8.60948	−	1.45233i	−0.275020	−	0.0463930i
$981$	1.60801	−	38.6628i	0.0513399	−	1.23441i
$982$	2.79348	+	8.74655i	0.0891434	+	0.279114i
$983$		−	4.18786i		−	0.133572i	−0.997767	−	0.0667861i	$-0.978726\pi$
$983$		−	4.18786i		−	0.133572i	0.997767	−	0.0667861i	$-0.0212745\pi$
$984$	−1.65745	−	2.93592i	−0.0528376	−	0.0935936i
$985$			32.0472i			1.02111i
$986$	−6.54873	+	2.09153i	−0.208554	+	0.0666080i
$987$	17.0478	−	6.64980i	0.542637	−	0.211666i
$988$	−9.01879	−	12.6790i	−0.286926	−	0.403372i
$989$	0.785445	+	0.785445i	0.0249757	+	0.0249757i
$990$	−50.0046	+	13.7087i	−1.58925	+	0.435690i
$991$			6.94973i			0.220766i	0.993889	+	0.110383i	$0.0352077\pi$
$991$			6.94973i			0.220766i	−0.993889	+	0.110383i	$0.964792\pi$
$992$	22.7934	+	23.9669i	0.723690	+	0.760950i
$993$	−16.3451	+	37.2514i	−0.518696	+	1.18214i
$994$	2.53729	−	4.91853i	0.0804778	−	0.156006i
$995$	−30.2398	+	30.2398i	−0.958665	+	0.958665i
$996$	−14.3831	+	2.98754i	−0.455747	+	0.0946638i
$997$	−7.18530	−	7.18530i	−0.227561	−	0.227561i	0.584112	−	0.811673i	$-0.301443\pi$
$997$	−7.18530	−	7.18530i	−0.227561	−	0.227561i	−0.811673	+	0.584112i	$0.801443\pi$
$998$	0.0421702	+	0.132037i	0.00133487	+	0.00417957i
$999$	36.0436	−	12.3599i	1.14037	−	0.391049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.17	yes	40
3.2	odd	2	inner	336.2.s.c.155.4	✓	40
4.3	odd	2		1344.2.s.c.911.3		40
12.11	even	2		1344.2.s.c.911.14		40
16.3	odd	4	inner	336.2.s.c.323.4	yes	40
16.13	even	4		1344.2.s.c.239.14		40
48.29	odd	4		1344.2.s.c.239.3		40
48.35	even	4	inner	336.2.s.c.323.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.4	✓	40	3.2	odd	2	inner
336.2.s.c.155.17	yes	40	1.1	even	1	trivial
336.2.s.c.323.4	yes	40	16.3	odd	4	inner
336.2.s.c.323.17	yes	40	48.35	even	4	inner
1344.2.s.c.239.3		40	48.29	odd	4
1344.2.s.c.239.14		40	16.13	even	4
1344.2.s.c.911.3		40	4.3	odd	2
1344.2.s.c.911.14		40	12.11	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25684 + 0.648355i) q^{2} +(1.61364 - 0.629429i) q^{3} +(1.15927 + 1.62975i) q^{4} +(-3.08691 + 3.08691i) q^{5} +(2.43617 + 0.255120i) q^{6} -1.00000 q^{7} +(0.400356 + 2.79995i) q^{8} +(2.20764 - 2.03134i) q^{9} +O(q^{10})\)	\(q+(1.25684 + 0.648355i) q^{2} +(1.61364 - 0.629429i) q^{3} +(1.15927 + 1.62975i) q^{4} +(-3.08691 + 3.08691i) q^{5} +(2.43617 + 0.255120i) q^{6} -1.00000 q^{7} +(0.400356 + 2.79995i) q^{8} +(2.20764 - 2.03134i) q^{9} +(-5.88116 + 1.87833i) q^{10} +(1.97950 + 1.97950i) q^{11} +(2.89645 + 1.90015i) q^{12} +(3.27530 - 3.27530i) q^{13} +(-1.25684 - 0.648355i) q^{14} +(-3.03816 + 6.92415i) q^{15} +(-1.31218 + 3.77865i) q^{16} -2.57205i q^{17} +(4.09167 - 1.12172i) q^{18} +(-1.18763 - 1.18763i) q^{19} +(-8.60948 - 1.45233i) q^{20} +(-1.61364 + 0.629429i) q^{21} +(1.20449 + 3.77132i) q^{22} +1.21005i q^{23} +(2.40840 + 4.26610i) q^{24} -14.0581i q^{25} +(6.24006 - 1.99295i) q^{26} +(2.28374 - 4.66739i) q^{27} +(-1.15927 - 1.62975i) q^{28} +(-1.33641 - 1.33641i) q^{29} +(-8.30778 + 6.73271i) q^{30} -5.84687i q^{31} +(-4.09910 + 3.89838i) q^{32} +(4.44015 + 1.94824i) q^{33} +(1.66760 - 3.23264i) q^{34} +(3.08691 - 3.08691i) q^{35} +(5.86983 + 1.24303i) q^{36} +(5.18528 + 5.18528i) q^{37} +(-0.722652 - 2.26267i) q^{38} +(3.22357 - 7.34670i) q^{39} +(-9.87907 - 7.40734i) q^{40} -0.688196 q^{41} +(-2.43617 - 0.255120i) q^{42} +(0.649101 - 0.649101i) q^{43} +(-0.931315 + 5.52087i) q^{44} +(-0.544230 + 13.0854i) q^{45} +(-0.784542 + 1.52083i) q^{46} -10.5648 q^{47} +(0.261011 + 6.92328i) q^{48} +1.00000 q^{49} +(9.11463 - 17.6687i) q^{50} +(-1.61892 - 4.15035i) q^{51} +(9.13488 + 1.54096i) q^{52} +(3.84828 - 3.84828i) q^{53} +(5.89641 - 4.38546i) q^{54} -12.2211 q^{55} +(-0.400356 - 2.79995i) q^{56} +(-2.66394 - 1.16888i) q^{57} +(-0.813179 - 2.54611i) q^{58} +(-1.99283 - 1.99283i) q^{59} +(-14.8067 + 3.07552i) q^{60} +(-6.62710 + 6.62710i) q^{61} +(3.79085 - 7.34856i) q^{62} +(-2.20764 + 2.03134i) q^{63} +(-7.67943 + 2.24195i) q^{64} +20.2211i q^{65} +(4.31738 + 5.32740i) q^{66} +(4.50400 + 4.50400i) q^{67} +(4.19180 - 2.98170i) q^{68} +(0.761640 + 1.95258i) q^{69} +(5.88116 - 1.87833i) q^{70} +3.91342i q^{71} +(6.57148 + 5.36802i) q^{72} +9.83194i q^{73} +(3.15514 + 9.87895i) q^{74} +(-8.84856 - 22.6846i) q^{75} +(0.558757 - 3.31234i) q^{76} +(-1.97950 - 1.97950i) q^{77} +(8.81476 - 7.14358i) q^{78} -3.86630i q^{79} +(-7.61378 - 15.7150i) q^{80} +(0.747340 - 8.96892i) q^{81} +(-0.864950 - 0.446196i) q^{82} +(-2.99861 + 2.99861i) q^{83} +(-2.89645 - 1.90015i) q^{84} +(7.93969 + 7.93969i) q^{85} +(1.23666 - 0.394965i) q^{86} +(-2.99765 - 1.31530i) q^{87} +(-4.74999 + 6.33500i) q^{88} +10.8761 q^{89} +(-9.16796 + 16.0933i) q^{90} +(-3.27530 + 3.27530i) q^{91} +(-1.97208 + 1.40278i) q^{92} +(-3.68019 - 9.43472i) q^{93} +(-13.2782 - 6.84976i) q^{94} +7.33224 q^{95} +(-4.16070 + 8.87066i) q^{96} -10.1652 q^{97} +(1.25684 + 0.648355i) q^{98} +(8.39105 + 0.348990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

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