LMFDB - Embedded newform 273.2.cd.e.44.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			44.18
Character	$\chi$	$=$	273.44
Dual form			273.2.cd.e.242.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25001 - 0.334940i) q^{2} +(0.248434 - 1.71414i) q^{3} +(-0.281700 + 0.162639i) q^{4} +(3.70264 - 0.992121i) q^{5} +(-0.263589 - 2.22591i) q^{6} +(-1.90960 - 1.83124i) q^{7} +(-2.12780 + 2.12780i) q^{8} +(-2.87656 - 0.851703i) q^{9} +O(q^{10})$	\(q+(1.25001 - 0.334940i) q^{2} +(0.248434 - 1.71414i) q^{3} +(-0.281700 + 0.162639i) q^{4} +(3.70264 - 0.992121i) q^{5} +(-0.263589 - 2.22591i) q^{6} +(-1.90960 - 1.83124i) q^{7} +(-2.12780 + 2.12780i) q^{8} +(-2.87656 - 0.851703i) q^{9} +(4.29606 - 2.48033i) q^{10} +(1.43154 + 0.383581i) q^{11} +(0.208803 + 0.523278i) q^{12} +(2.76474 + 2.31435i) q^{13} +(-3.00038 - 1.64947i) q^{14} +(-0.780772 - 6.59333i) q^{15} +(-1.62182 + 2.80907i) q^{16} +(-0.890309 - 1.54206i) q^{17} +(-3.88101 - 0.101164i) q^{18} +(0.252802 + 0.943471i) q^{19} +(-0.881676 + 0.881676i) q^{20} +(-3.61341 + 2.81838i) q^{21} +1.91793 q^{22} +(-2.91637 + 5.05131i) q^{23} +(3.11874 + 4.17597i) q^{24} +(8.39515 - 4.84694i) q^{25} +(4.23114 + 1.96694i) q^{26} +(-2.17457 + 4.71924i) q^{27} +(0.835765 + 0.205282i) q^{28} -2.31669i q^{29} +(-3.18435 - 7.98025i) q^{30} +(-3.04057 - 0.814718i) q^{31} +(0.471235 - 1.75867i) q^{32} +(1.01316 - 2.35857i) q^{33} +(-1.62940 - 1.62940i) q^{34} +(-8.88738 - 4.88586i) q^{35} +(0.948846 - 0.227918i) q^{36} +(8.74289 - 2.34265i) q^{37} +(0.632013 + 1.09468i) q^{38} +(4.65397 - 4.16420i) q^{39} +(-5.76746 + 9.98953i) q^{40} +(4.21804 + 4.21804i) q^{41} +(-3.57282 + 4.73330i) q^{42} +6.76194i q^{43} +(-0.465650 + 0.124771i) q^{44} +(-11.4959 - 0.299656i) q^{45} +(-1.95362 + 7.29102i) q^{46} +(0.850526 + 3.17421i) q^{47} +(4.41223 + 3.47790i) q^{48} +(0.293149 + 6.99386i) q^{49} +(8.87062 - 8.87062i) q^{50} +(-2.86449 + 1.14302i) q^{51} +(-1.15523 - 0.202295i) q^{52} +(-7.67909 + 4.43352i) q^{53} +(-1.13759 + 6.62747i) q^{54} +5.68105 q^{55} +(7.95976 - 0.166744i) q^{56} +(1.68005 - 0.198949i) q^{57} +(-0.775954 - 2.89590i) q^{58} +(-7.36954 - 1.97466i) q^{59} +(1.29228 + 1.73035i) q^{60} +(-5.58459 + 9.67280i) q^{61} -4.07364 q^{62} +(3.93341 + 6.89407i) q^{63} -8.84347i q^{64} +(12.5330 + 5.82625i) q^{65} +(0.476478 - 3.28759i) q^{66} +(-7.79328 - 2.08820i) q^{67} +(0.501599 + 0.289599i) q^{68} +(7.93413 + 6.25399i) q^{69} +(-12.7458 - 3.13066i) q^{70} +(-3.24997 - 3.24997i) q^{71} +(7.93301 - 4.30850i) q^{72} +(1.49640 - 5.58464i) q^{73} +(10.1441 - 5.85669i) q^{74} +(-6.22270 - 15.5946i) q^{75} +(-0.224660 - 0.224660i) q^{76} +(-2.03125 - 3.35398i) q^{77} +(4.42278 - 6.76411i) q^{78} +(7.93757 - 13.7483i) q^{79} +(-3.21808 + 12.0100i) q^{80} +(7.54921 + 4.89995i) q^{81} +(6.68540 + 3.85982i) q^{82} +(-2.04147 - 2.04147i) q^{83} +(0.559515 - 1.38162i) q^{84} +(-4.82641 - 4.82641i) q^{85} +(2.26485 + 8.45252i) q^{86} +(-3.97114 - 0.575545i) q^{87} +(-3.86222 + 2.22986i) q^{88} +(-0.172387 - 0.643357i) q^{89} +(-14.4704 + 3.47586i) q^{90} +(-1.04144 - 9.48237i) q^{91} -1.89727i q^{92} +(-2.15192 + 5.00956i) q^{93} +(2.12634 + 3.68293i) q^{94} +(1.87207 + 3.24253i) q^{95} +(-2.89754 - 1.24468i) q^{96} +(3.72661 - 3.72661i) q^{97} +(2.70897 + 8.64424i) q^{98} +(-3.79122 - 2.32264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.25001	−	0.334940i	0.883894	−	0.236839i	0.211807	−	0.977311i	$-0.432065\pi$
$2$	1.25001	−	0.334940i	0.883894	−	0.236839i	0.672086	+	0.740473i	$0.265398\pi$
$3$	0.248434	−	1.71414i	0.143434	−	0.989660i
$3$	0.248434	−	1.71414i	0.143434	−	0.989660i
$4$	−0.281700	+	0.162639i	−0.140850	+	0.0813197i
$5$	3.70264	−	0.992121i	1.65587	−	0.443690i	0.694624	−	0.719373i	$-0.255571\pi$
$5$	3.70264	−	0.992121i	1.65587	−	0.443690i	0.961249	+	0.275683i	$0.0889039\pi$
$6$	−0.263589	−	2.22591i	−0.107610	−	0.908725i
$7$	−1.90960	−	1.83124i	−0.721761	−	0.692142i
$7$	−1.90960	−	1.83124i	−0.721761	−	0.692142i
$8$	−2.12780	+	2.12780i	−0.752292	+	0.752292i
$9$	−2.87656	−	0.851703i	−0.958854	−	0.283901i
$10$	4.29606	−	2.48033i	1.35853	−	0.784349i
$11$	1.43154	+	0.383581i	0.431626	+	0.115654i	0.468089	−	0.883681i	$-0.344943\pi$
$11$	1.43154	+	0.383581i	0.431626	+	0.115654i	−0.0364632	+	0.999335i	$0.511609\pi$
$12$	0.208803	+	0.523278i	0.0602762	+	0.151057i
$13$	2.76474	+	2.31435i	0.766802	+	0.641884i
$13$	2.76474	+	2.31435i	0.766802	+	0.641884i
$14$	−3.00038	−	1.64947i	−0.801886	−	0.440839i
$15$	−0.780772	−	6.59333i	−0.201594	−	1.70239i
$16$	−1.62182	+	2.80907i	−0.405455	+	0.702268i
$17$	−0.890309	−	1.54206i	−0.215932	−	0.374005i	0.737629	−	0.675207i	$-0.235946\pi$
$17$	−0.890309	−	1.54206i	−0.215932	−	0.374005i	−0.953560	+	0.301202i	$0.902612\pi$
$18$	−3.88101	−	0.101164i	−0.914763	−	0.0238446i
$19$	0.252802	+	0.943471i	0.0579968	+	0.216447i	0.988842	−	0.148966i	$-0.0475944\pi$
$19$	0.252802	+	0.943471i	0.0579968	+	0.216447i	−0.930846	+	0.365413i	$0.880928\pi$
$20$	−0.881676	+	0.881676i	−0.197149	+	0.197149i
$21$	−3.61341	+	2.81838i	−0.788510	+	0.615022i
$22$	1.91793			0.408903
$23$	−2.91637	+	5.05131i	−0.608106	+	1.05327i	0.383447	+	0.923563i	$0.374737\pi$
$23$	−2.91637	+	5.05131i	−0.608106	+	1.05327i	−0.991552	+	0.129707i	$0.958596\pi$
$24$	3.11874	+	4.17597i	0.636609	+	0.852417i
$25$	8.39515	−	4.84694i	1.67903	−	0.969388i
$26$	4.23114	+	1.96694i	0.829794	+	0.385749i
$27$	−2.17457	+	4.71924i	−0.418497	+	0.908218i
$28$	0.835765	+	0.205282i	0.157945	+	0.0387947i
$29$		−	2.31669i		−	0.430199i	−0.976592	−	0.215099i	$-0.930992\pi$
$29$		−	2.31669i		−	0.430199i	0.976592	−	0.215099i	$-0.0690076\pi$
$30$	−3.18435	−	7.98025i	−0.581380	−	1.45699i
$31$	−3.04057	−	0.814718i	−0.546102	−	0.146328i	−0.0247884	−	0.999693i	$-0.507891\pi$
$31$	−3.04057	−	0.814718i	−0.546102	−	0.146328i	−0.521314	+	0.853365i	$0.674558\pi$
$32$	0.471235	−	1.75867i	0.0833033	−	0.310892i
$33$	1.01316	−	2.35857i	0.176368	−	0.410575i
$34$	−1.62940	−	1.62940i	−0.279439	−	0.279439i
$35$	−8.88738	−	4.88586i	−1.50224	−	0.825861i
$36$	0.948846	−	0.227918i	0.158141	−	0.0379863i
$37$	8.74289	−	2.34265i	1.43732	−	0.385129i	0.545727	−	0.837963i	$-0.316253\pi$
$37$	8.74289	−	2.34265i	1.43732	−	0.385129i	0.891595	+	0.452833i	$0.149587\pi$
$38$	0.632013	+	1.09468i	0.102526	+	0.177580i
$39$	4.65397	−	4.16420i	0.745232	−	0.666805i
$40$	−5.76746	+	9.98953i	−0.911915	+	1.57948i
$41$	4.21804	+	4.21804i	0.658747	+	0.658747i	0.955083	−	0.296337i	$-0.0957651\pi$
$41$	4.21804	+	4.21804i	0.658747	+	0.658747i	−0.296337	+	0.955083i	$0.595765\pi$
$42$	−3.57282	+	4.73330i	−0.551298	+	0.730364i
$43$			6.76194i			1.03119i	0.856834	+	0.515593i	$0.172428\pi$
$43$			6.76194i			1.03119i	−0.856834	+	0.515593i	$0.827572\pi$
$44$	−0.465650	+	0.124771i	−0.0701994	+	0.0188099i
$45$	−11.4959	−	0.299656i	−1.71370	−	0.0446701i
$46$	−1.95362	+	7.29102i	−0.288046	+	1.07500i
$47$	0.850526	+	3.17421i	0.124062	+	0.463005i	0.999804	−	0.0197729i	$-0.00629432\pi$
$47$	0.850526	+	3.17421i	0.124062	+	0.463005i	−0.875743	+	0.482778i	$0.839628\pi$
$48$	4.41223	+	3.47790i	0.636851	+	0.501991i
$49$	0.293149	+	6.99386i	0.0418785	+	0.999123i
$50$	8.87062	−	8.87062i	1.25450	−	1.25450i
$51$	−2.86449	+	1.14302i	−0.401109	+	0.160054i
$52$	−1.15523	−	0.202295i	−0.160202	−	0.0280532i
$53$	−7.67909	+	4.43352i	−1.05480	+	0.608991i	−0.923990	−	0.382416i	$-0.875092\pi$
$53$	−7.67909	+	4.43352i	−1.05480	+	0.608991i	−0.130813	+	0.991407i	$0.541759\pi$
$54$	−1.13759	+	6.62747i	−0.154806	+	0.901885i
$55$	5.68105			0.766033
$56$	7.95976	−	0.166744i	1.06367	−	0.0222822i
$57$	1.68005	−	0.198949i	0.222528	−	0.0263514i
$58$	−0.775954	−	2.89590i	−0.101888	−	0.380250i
$59$	−7.36954	−	1.97466i	−0.959433	−	0.257079i	−0.255073	−	0.966922i	$-0.582099\pi$
$59$	−7.36954	−	1.97466i	−0.959433	−	0.257079i	−0.704360	+	0.709843i	$0.748766\pi$
$60$	1.29228	+	1.73035i	0.166832	+	0.223388i
$61$	−5.58459	+	9.67280i	−0.715034	+	1.23848i	0.247912	+	0.968782i	$0.420255\pi$
$61$	−5.58459	+	9.67280i	−0.715034	+	1.23848i	−0.962946	+	0.269693i	$0.913078\pi$
$62$	−4.07364			−0.517352
$63$	3.93341	+	6.89407i	0.495564	+	0.868572i
$64$		−	8.84347i		−	1.10543i
$65$	12.5330	+	5.82625i	1.55452	+	0.722657i
$66$	0.476478	−	3.28759i	0.0586504	−	0.404675i
$67$	−7.79328	−	2.08820i	−0.952100	−	0.255115i	−0.250847	−	0.968027i	$-0.580709\pi$
$67$	−7.79328	−	2.08820i	−0.952100	−	0.255115i	−0.701253	+	0.712912i	$0.747376\pi$
$68$	0.501599	+	0.289599i	0.0608279	+	0.0351190i
$69$	7.93413	+	6.25399i	0.955156	+	0.752892i
$70$	−12.7458	−	3.13066i	−1.52342	−	0.374185i
$71$	−3.24997	−	3.24997i	−0.385701	−	0.385701i	0.487450	−	0.873151i	$-0.337927\pi$
$71$	−3.24997	−	3.24997i	−0.385701	−	0.385701i	−0.873151	+	0.487450i	$0.837927\pi$
$72$	7.93301	−	4.30850i	0.934914	−	0.507761i
$73$	1.49640	−	5.58464i	0.175140	−	0.653633i	−0.821387	−	0.570371i	$-0.806799\pi$
$73$	1.49640	−	5.58464i	0.175140	−	0.653633i	0.996528	−	0.0832621i	$-0.0265339\pi$
$74$	10.1441	−	5.85669i	1.17923	−	0.680827i
$75$	−6.22270	−	15.5946i	−0.718536	−	1.80071i
$76$	−0.224660	−	0.224660i	−0.0257703	−	0.0257703i
$77$	−2.03125	−	3.35398i	−0.231482	−	0.382221i
$78$	4.42278	−	6.76411i	0.500781	−	0.765885i
$79$	7.93757	−	13.7483i	0.893047	−	1.54680i	0.0568434	−	0.998383i	$-0.481896\pi$
$79$	7.93757	−	13.7483i	0.893047	−	1.54680i	0.836203	−	0.548419i	$-0.184770\pi$
$80$	−3.21808	+	12.0100i	−0.359792	+	1.34276i
$81$	7.54921	+	4.89995i	0.838801	+	0.544439i
$82$	6.68540	+	3.85982i	0.738279	+	0.426245i
$83$	−2.04147	−	2.04147i	−0.224081	−	0.224081i	0.586134	−	0.810214i	$-0.300649\pi$
$83$	−2.04147	−	2.04147i	−0.224081	−	0.224081i	−0.810214	+	0.586134i	$0.800649\pi$
$84$	0.559515	−	1.38162i	0.0610481	−	0.150747i
$85$	−4.82641	−	4.82641i	−0.523498	−	0.523498i
$86$	2.26485	+	8.45252i	0.244225	+	0.911459i
$87$	−3.97114	−	0.575545i	−0.425751	−	0.0617050i
$88$	−3.86222	+	2.22986i	−0.411714	+	0.237703i
$89$	−0.172387	−	0.643357i	−0.0182730	−	0.0681957i	0.956187	−	0.292756i	$-0.0945722\pi$
$89$	−0.172387	−	0.643357i	−0.0182730	−	0.0681957i	−0.974460	+	0.224560i	$0.927906\pi$
$90$	−14.4704	+	3.47586i	−1.52531	+	0.366388i
$91$	−1.04144	−	9.48237i	−0.109172	−	0.994023i
$92$		−	1.89727i		−	0.197804i
$93$	−2.15192	+	5.00956i	−0.223144	+	0.519467i
$94$	2.12634	+	3.68293i	0.219315	+	0.379865i
$95$	1.87207	+	3.24253i	0.192071	+	0.332676i
$96$	−2.89754	−	1.24468i	−0.295729	−	0.127034i
$97$	3.72661	−	3.72661i	0.378380	−	0.378380i	−0.492138	−	0.870517i	$-0.663784\pi$
$97$	3.72661	−	3.72661i	0.378380	−	0.378380i	0.870517	+	0.492138i	$0.163784\pi$
$98$	2.70897	+	8.64424i	0.273647	+	0.873200i
$99$	−3.79122	−	2.32264i	−0.381032	−	0.233434i
$100$	−1.57661	+	2.73076i	−0.157661	+	0.273076i
$101$	−4.91090	−	8.50593i	−0.488653	−	0.846371i	0.511262	−	0.859425i	$-0.329178\pi$
$101$	−4.91090	−	8.50593i	−0.488653	−	0.846371i	−0.999915	+	0.0130535i	$0.995845\pi$
$102$	−3.19782	+	2.38822i	−0.316631	+	0.236469i
$103$	9.68840	+	5.59360i	0.954627	+	0.551154i	0.894515	−	0.447038i	$-0.147521\pi$
$103$	9.68840	+	5.59360i	0.954627	+	0.551154i	0.0601115	+	0.998192i	$0.480854\pi$
$104$	−10.8073	+	0.958352i	−1.05974	+	0.0939742i
$105$	−10.5830	+	14.0204i	−1.03279	+	1.36825i
$106$	−8.11400	+	8.11400i	−0.788102	+	0.788102i
$107$	−14.9833	−	8.65062i	−1.44849	−	0.836287i	−0.450100	−	0.892978i	$-0.648612\pi$
$107$	−14.9833	−	8.65062i	−1.44849	−	0.836287i	−0.998392	+	0.0566907i	$0.981945\pi$
$108$	−0.154957	−	1.68308i	−0.0149108	−	0.161954i
$109$	8.01976	+	2.14889i	0.768154	+	0.205826i	0.621556	−	0.783370i	$-0.286501\pi$
$109$	8.01976	+	2.14889i	0.768154	+	0.205826i	0.146598	+	0.989196i	$0.453168\pi$
$110$	7.10140	−	1.90281i	0.677092	−	0.181426i
$111$	−1.84360	−	15.5685i	−0.174987	−	1.47770i
$112$	8.24110	−	2.39427i	0.778711	−	0.226238i
$113$		−	8.40669i		−	0.790835i	−0.918501	−	0.395418i	$-0.870600\pi$
$113$		−	8.40669i		−	0.790835i	0.918501	−	0.395418i	$-0.129400\pi$
$114$	2.03345	−	0.811404i	0.190450	−	0.0759950i
$115$	−5.78679	+	21.5966i	−0.539621	+	2.01389i
$116$	0.376785	+	0.652611i	0.0349836	+	0.0605934i
$117$	−5.98181	−	9.01210i	−0.553019	−	0.833169i
$118$	−9.87343			−0.908923
$119$	−1.12374	+	4.57509i	−0.103013	+	0.419398i
$120$	15.6906	+	12.3680i	1.43235	+	1.12904i
$121$	−7.62410	−	4.40178i	−0.693100	−	0.400161i
$122$	−3.74101	+	13.9616i	−0.338695	+	1.26403i
$123$	8.27822	−	6.18241i	0.746422	−	0.557449i
$124$	0.989032	−	0.265010i	0.0888177	−	0.0237986i
$125$	12.7229	−	12.7229i	1.13797	−	1.13797i
$126$	7.22593	+	7.30023i	0.643737	+	0.650356i
$127$		−	12.9225i		−	1.14669i	−0.819314	−	0.573345i	$-0.805645\pi$
$127$		−	12.9225i		−	1.14669i	0.819314	−	0.573345i	$-0.194355\pi$
$128$	−2.01957	−	7.53713i	−0.178506	−	0.666194i
$129$	11.5909	+	1.67990i	1.02052	+	0.147907i
$130$	17.6178	+	3.08509i	1.54519	+	0.270581i
$131$	3.75893	+	2.17022i	0.328419	+	0.189613i	0.655139	−	0.755508i	$-0.272610\pi$
$131$	3.75893	+	2.17022i	0.328419	+	0.189613i	−0.326720	+	0.945121i	$0.605943\pi$
$132$	0.0981910	+	0.829187i	0.00854643	+	0.0721715i
$133$	1.24497	−	2.26459i	0.107952	−	0.196365i
$134$	−10.4411			−0.901977
$135$	−3.36962	+	19.6311i	−0.290011	+	1.68958i
$136$	5.17560	+	1.38680i	0.443804	+	0.118917i
$137$	−18.7248	−	5.01729i	−1.59977	−	0.428656i	−0.654794	−	0.755808i	$-0.727245\pi$
$137$	−18.7248	−	5.01729i	−1.59977	−	0.428656i	−0.944972	+	0.327152i	$0.893911\pi$
$138$	12.0125	+	5.16012i	1.02257	+	0.439259i
$139$	18.2780			1.55032			0.775160	−	0.631765i	$-0.217669\pi$
$139$	18.2780			1.55032			0.775160	+	0.631765i	$0.217669\pi$
$140$	3.29820	−	0.0690922i	0.278749	−	0.00583935i
$141$	5.65234	−	0.669340i	0.476013	−	0.0563686i
$142$	−5.15106	−	2.97397i	−0.432267	−	0.249570i
$143$	3.07011	+	4.37359i	0.256735	+	0.365738i
$144$	7.05775	−	6.69916i	0.588146	−	0.558263i
$145$	−2.29844	−	8.57789i	−0.190875	−	0.712355i
$146$		−	7.48209i		−	0.619222i
$147$	12.0613	+	1.23501i	0.994799	+	0.101862i
$148$	−2.08186	+	2.08186i	−0.171128	+	0.171128i
$149$	6.63217	−	1.77708i	0.543328	−	0.145584i	0.0232922	−	0.999729i	$-0.492585\pi$
$149$	6.63217	−	1.77708i	0.543328	−	0.145584i	0.520036	+	0.854144i	$0.325919\pi$
$150$	−13.0017	−	17.4093i	−1.06159	−	1.42146i
$151$	0.928800	−	3.46633i	0.0755847	−	0.282086i	−0.917781	−	0.397088i	$-0.870021\pi$
$151$	0.928800	−	3.46633i	0.0755847	−	0.282086i	0.993365	+	0.115002i	$0.0366875\pi$
$152$	−2.54543	−	1.46961i	−0.206462	−	0.119201i
$153$	1.24765	+	5.19411i	0.100867	+	0.419919i
$154$	−3.66247	−	3.51217i	−0.295130	−	0.283019i
$155$	−12.0664			−0.969200
$156$	−0.633760	+	1.92997i	−0.0507414	+	0.154521i
$157$	−7.33140	−	12.6984i	−0.585110	−	1.01344i	−0.994862	−	0.101243i	$-0.967718\pi$
$157$	−7.33140	−	12.6984i	−0.585110	−	1.01344i	0.409752	−	0.912197i	$-0.365615\pi$
$158$	5.31723	−	19.8442i	0.423016	−	1.57872i
$159$	5.69194	+	14.2645i	0.451400	+	1.13125i
$160$		−	6.97926i		−	0.551759i
$161$	14.8192	−	4.30541i	1.16792	−	0.339314i
$162$	11.0778	+	3.59647i	0.870355	+	0.282566i
$163$	−17.5190	+	4.69421i	−1.37219	+	0.367679i	−0.868280	−	0.496075i	$-0.834774\pi$
$163$	−17.5190	+	4.69421i	−1.37219	+	0.367679i	−0.503915	+	0.863753i	$0.668108\pi$
$164$	−1.87424	−	0.502200i	−0.146353	−	0.0392153i
$165$	1.41137	−	9.73812i	0.109875	−	0.758112i
$166$	−3.23564	−	1.86810i	−0.251134	−	0.144993i
$167$	−7.84652	+	7.84652i	−0.607182	+	0.607182i	−0.942209	−	0.335027i	$-0.891255\pi$
$167$	−7.84652	+	7.84652i	−0.607182	+	0.607182i	0.335027	+	0.942209i	$0.391255\pi$
$168$	1.69165	−	13.6856i	0.130514	−	1.05587i
$169$	2.28760	+	12.7971i	0.175969	+	0.984396i
$170$	−7.64964	−	4.41652i	−0.586701	−	0.338732i
$171$	0.0763555	−	2.92927i	0.00583905	−	0.224007i
$172$	−1.09976	−	1.90483i	−0.0838557	−	0.145242i
$173$	−9.63489	+	16.6881i	−0.732527	+	1.26877i	0.223272	+	0.974756i	$0.428326\pi$
$173$	−9.63489	+	16.6881i	−0.732527	+	1.26877i	−0.955800	+	0.294019i	$0.905007\pi$
$174$	−5.15675	+	0.610654i	−0.390932	+	0.0462936i
$175$	−24.9073	−	6.11778i	−1.88281	−	0.462460i
$176$	−3.39921	+	3.39921i	−0.256225	+	0.256225i
$177$	−5.21570	+	12.1419i	−0.392036	+	0.912638i
$178$	−0.430972	−	0.746466i	−0.0323027	−	0.0559500i
$179$	−2.58824	−	4.48296i	−0.193454	−	0.335072i	0.752939	−	0.658091i	$-0.228636\pi$
$179$	−2.58824	−	4.48296i	−0.193454	−	0.335072i	−0.946393	+	0.323019i	$0.895302\pi$
$180$	3.28712	−	1.78527i	0.245007	−	0.133066i
$181$		−	2.66916i		−	0.198397i	−0.995068	−	0.0991987i	$-0.968372\pi$
$181$		−	2.66916i		−	0.198397i	0.995068	−	0.0991987i	$-0.0316279\pi$
$182$	−4.47784	−	11.5043i	−0.331920	−	0.852754i
$183$	15.1931	+	11.9758i	1.12311	+	0.885279i
$184$	−4.54272	−	16.9536i	−0.334893	−	1.24984i
$185$	30.0476	−	17.3480i	2.20915	−	1.27545i
$186$	−1.01203	+	6.98279i	−0.0742057	+	0.512003i
$187$	−0.683011	−	2.54903i	−0.0499467	−	0.186404i
$188$	−0.755843	−	0.755843i	−0.0551255	−	0.0551255i
$189$	12.7946	−	5.02970i	0.930671	−	0.365857i
$190$	3.42617	+	3.42617i	0.248561	+	0.248561i
$191$	−3.97121	−	2.29278i	−0.287347	−	0.165900i	0.349398	−	0.936974i	$-0.386386\pi$
$191$	−3.97121	−	2.29278i	−0.287347	−	0.165900i	−0.636745	+	0.771075i	$0.719719\pi$
$192$	−15.1590	−	2.19702i	−1.09400	−	0.158556i
$193$	−1.84201	+	6.87446i	−0.132590	+	0.494834i	−0.999996	−	0.00276724i	$-0.999119\pi$
$193$	−1.84201	+	6.87446i	−0.132590	+	0.494834i	0.867406	+	0.497602i	$0.165786\pi$
$194$	3.41012	−	5.90651i	0.244833	−	0.424063i
$195$	13.1006	−	20.0358i	0.938155	−	1.43480i
$196$	−1.22006	−	1.92249i	−0.0871469	−	0.137321i
$197$	11.0026	+	11.0026i	0.783905	+	0.783905i	0.980487	−	0.196582i	$-0.0629842\pi$
$197$	11.0026	+	11.0026i	0.783905	+	0.783905i	−0.196582	+	0.980487i	$0.562984\pi$
$198$	−5.51703	−	1.63350i	−0.392078	−	0.116088i
$199$	7.74931	−	4.47407i	0.549334	−	0.317158i	−0.199519	−	0.979894i	$-0.563938\pi$
$199$	7.74931	−	4.47407i	0.549334	−	0.317158i	0.748853	+	0.662736i	$0.230605\pi$
$200$	−7.54988	+	28.1765i	−0.533857	+	1.99238i
$201$	−5.51559	+	12.8400i	−0.389040	+	0.905664i
$202$	−8.98767	−	8.98767i	−0.632370	−	0.632370i
$203$	−4.24241	+	4.42396i	−0.297759	+	0.310501i
$204$	0.621027	−	0.787866i	0.0434806	−	0.0551617i
$205$	19.8027	+	11.4331i	1.38308	+	0.798522i
$206$	13.9842	+	3.74705i	0.974323	+	0.261069i
$207$	12.6913	−	12.0465i	0.882109	−	0.837290i
$208$	−10.9851	+	4.01291i	−0.761678	+	0.278245i
$209$			1.44759i			0.100132i
$210$	−8.53289	+	21.0704i	−0.588825	+	1.45399i
$211$	7.52078			0.517752			0.258876	−	0.965911i	$-0.416648\pi$
$211$	7.52078			0.517752			0.258876	+	0.965911i	$0.416648\pi$
$212$	1.44213	−	2.49784i	0.0990459	−	0.171553i
$213$	−6.37832	+	4.76351i	−0.437035	+	0.326390i
$214$	−21.6268	−	5.79489i	−1.47838	−	0.396130i
$215$	6.70866	+	25.0371i	0.457527	+	1.70751i
$216$	−5.41455	−	14.6687i	−0.368413	−	0.998077i
$217$	4.31433	+	7.12378i	0.292876	+	0.483594i
$218$	10.7446			0.727714
$219$	−9.20111	−	3.95246i	−0.621753	−	0.267082i
$220$	−1.60035	+	0.923962i	−0.107896	+	0.0622935i
$221$	1.10739	−	6.32389i	0.0744910	−	0.425391i
$222$	−7.51906	−	18.8434i	−0.504647	−	1.26469i
$223$	−1.48166	+	1.48166i	−0.0992194	+	0.0992194i	−0.754974	−	0.655755i	$-0.772351\pi$
$223$	−1.48166	+	1.48166i	−0.0992194	+	0.0992194i	0.655755	+	0.754974i	$0.272351\pi$
$224$	−4.12041	+	2.49542i	−0.275307	+	0.166732i
$225$	−28.2773	+	6.79235i	−1.88515	+	0.452823i
$226$	−2.81574	−	10.5085i	−0.187300	−	0.699014i
$227$	−1.64074	+	6.12331i	−0.108899	+	0.406418i	−0.998758	−	0.0498176i	$-0.984136\pi$
$227$	−1.64074	+	6.12331i	−0.108899	+	0.406418i	0.889859	+	0.456236i	$0.150803\pi$
$228$	−0.440912	+	0.329286i	−0.0292001	+	0.0218075i
$229$	0.221569	−	0.0593693i	0.0146417	−	0.00392324i	−0.251491	−	0.967860i	$-0.580921\pi$
$229$	0.221569	−	0.0593693i	0.0146417	−	0.00392324i	0.266132	+	0.963936i	$0.414254\pi$
$230$			28.9343i			1.90787i
$231$	−6.25382	+	2.64860i	−0.411471	+	0.174265i
$232$	4.92946	+	4.92946i	0.323635	+	0.323635i
$233$	3.45351	−	5.98165i	0.226247	−	0.391871i	−0.730446	−	0.682970i	$-0.760688\pi$
$233$	3.45351	−	5.98165i	0.226247	−	0.391871i	0.956693	+	0.291100i	$0.0940211\pi$
$234$	−10.4959	−	9.26170i	−0.686136	−	0.605456i
$235$	6.29839	+	10.9091i	0.410862	+	0.711633i
$236$	2.39715	−	0.642316i	0.156041	−	0.0418112i
$237$	−21.5945	−	17.0217i	−1.40272	−	1.10568i
$238$	0.127687	+	6.09531i	0.00827673	+	0.395100i
$239$	11.9412	+	11.9412i	0.772411	+	0.772411i	0.978527	−	0.206116i	$-0.0660825\pi$
$239$	11.9412	+	11.9412i	0.772411	+	0.772411i	−0.206116	+	0.978527i	$0.566083\pi$
$240$	19.7874	+	8.49994i	1.27727	+	0.548669i
$241$	−4.68923	+	17.5004i	−0.302060	+	1.12730i	0.633387	+	0.773835i	$0.281664\pi$
$241$	−4.68923	+	17.5004i	−0.302060	+	1.12730i	−0.935447	+	0.353467i	$0.885003\pi$
$242$	−11.0046	−	2.94867i	−0.707400	−	0.189547i
$243$	10.2747	−	11.7231i	0.659121	−	0.752037i
$244$		−	3.63310i		−	0.232585i
$245$	8.02418	+	25.6049i	0.512646	+	1.63584i
$246$	8.27715	−	10.5008i	0.527732	−	0.669507i
$247$	−1.48459	+	3.19353i	−0.0944620	+	0.203199i
$248$	8.20329	−	4.73617i	0.520909	−	0.300747i
$249$	−4.00654	+	2.99220i	−0.253904	+	0.189623i
$250$	11.6424	−	20.1652i	0.736329	−	1.27536i
$251$	27.0736			1.70887			0.854435	−	0.519558i	$-0.173904\pi$
$251$	27.0736			1.70887			0.854435	+	0.519558i	$0.173904\pi$
$252$	−2.22929	−	1.30233i	−0.140432	−	0.0820391i
$253$	−6.11249	+	6.11249i	−0.384289	+	0.384289i
$254$	−4.32828	−	16.1534i	−0.271581	−	1.01355i
$255$	−9.47219	+	7.07410i	−0.593172	+	0.442998i
$256$	3.79450	+	6.57226i	0.237156	+	0.410766i
$257$	3.59554	−	6.22766i	0.224284	−	0.388471i	−0.731821	−	0.681497i	$-0.761329\pi$
$257$	3.59554	−	6.22766i	0.224284	−	0.388471i	0.956104	+	0.293027i	$0.0946625\pi$
$258$	15.0515	−	1.78237i	0.937064	−	0.110966i
$259$	−20.9854	−	11.5368i	−1.30397	−	0.716860i
$260$	−4.47811	+	0.397103i	−0.277721	+	0.0246273i
$261$	−1.97313	+	6.66411i	−0.122134	+	0.412498i
$262$	5.42561	+	1.45379i	0.335195	+	0.0898153i
$263$	−9.20203	+	5.31279i	−0.567421	+	0.327601i	−0.756119	−	0.654434i	$-0.772907\pi$
$263$	−9.20203	+	5.31279i	−0.567421	+	0.327601i	0.188698	+	0.982035i	$0.439573\pi$
$264$	2.86278	+	7.17437i	0.176192	+	0.441552i
$265$	−24.0343	+	24.0343i	−1.47642	+	1.47642i
$266$	0.797723	−	3.24777i	0.0489115	−	0.199133i
$267$	−1.14563	+	0.135664i	−0.0701115	+	0.00830249i
$268$	2.53499	−	0.679248i	0.154849	−	0.0414917i
$269$	−2.77348	+	1.60127i	−0.169102	+	0.0976313i	−0.582162	−	0.813072i	$-0.697793\pi$
$269$	−2.77348	+	1.60127i	−0.169102	+	0.0976313i	0.413060	+	0.910704i	$0.364460\pi$
$270$	2.36318	+	25.6678i	0.143818	+	1.56209i
$271$	6.41316	−	1.71840i	0.389572	−	0.104385i	−0.0587161	−	0.998275i	$-0.518701\pi$
$271$	6.41316	−	1.71840i	0.389572	−	0.104385i	0.448288	+	0.893889i	$0.352034\pi$
$272$	5.77568			0.350202
$273$	−16.5129	−	0.570573i	−0.999404	−	0.0345327i
$274$	−25.0867			−1.51555
$275$	13.8772	−	3.71838i	0.836827	−	0.224227i
$276$	−3.25218	−	0.471346i	−0.195759	−	0.0283717i
$277$	−20.1422	+	11.6291i	−1.21023	+	0.698724i	−0.962808	−	0.270185i	$-0.912915\pi$
$277$	−20.1422	+	11.6291i	−1.21023	+	0.698724i	−0.247417	+	0.968909i	$0.579582\pi$
$278$	22.8478	−	6.12204i	1.37032	−	0.367176i
$279$	8.05248	+	4.93325i	0.482090	+	0.295346i
$280$	29.3067	−	8.51444i	1.75141	−	0.508835i
$281$	8.31033	−	8.31033i	0.495753	−	0.495753i	−0.414360	−	0.910113i	$-0.635995\pi$
$281$	8.31033	−	8.31033i	0.495753	−	0.495753i	0.910113	+	0.414360i	$0.135995\pi$
$282$	6.84131	−	2.72988i	0.407394	−	0.162562i
$283$	16.9426	−	9.78183i	1.00713	−	0.581469i	0.0967832	−	0.995305i	$-0.469145\pi$
$283$	16.9426	−	9.78183i	1.00713	−	0.581469i	0.910351	+	0.413836i	$0.135811\pi$
$284$	1.44409	+	0.386943i	0.0856909	+	0.0229608i
$285$	6.02324	−	2.40345i	0.356786	−	0.142368i
$286$	5.30257	+	4.43874i	0.313547	+	0.262468i
$287$	−0.330545	−	15.7790i	−0.0195114	−	0.931404i
$288$	−2.85340	+	4.65757i	−0.168138	+	0.274450i
$289$	6.91470	−	11.9766i	0.406747	−	0.704506i
$290$	−5.74616	−	9.95264i	−0.337426	−	0.584439i
$291$	−5.46212	−	7.31375i	−0.320195	−	0.428740i
$292$	0.486747	+	1.81657i	0.0284847	+	0.106306i
$293$	3.10734	−	3.10734i	0.181533	−	0.181533i	−0.610491	−	0.792024i	$-0.709028\pi$
$293$	3.10734	−	3.10734i	0.181533	−	0.181533i	0.792024	+	0.610491i	$0.209028\pi$
$294$	15.4904	−	2.49603i	0.903421	−	0.145571i
$295$	−29.2459			−1.70276
$296$	−13.6184	+	23.5878i	−0.791556	+	1.37102i
$297$	−4.92320	+	5.92167i	−0.285673	+	0.343610i
$298$	7.69509	−	4.44276i	0.445764	−	0.257362i
$299$	−19.7535	+	7.21606i	−1.14237	+	0.417316i
$300$	4.28923	+	3.38094i	0.247639	+	0.195199i
$301$	12.3827	−	12.9126i	0.713727	−	0.744270i
$302$		−	4.64405i		−	0.267235i
$303$	−15.8004	+	6.30481i	−0.907709	+	0.362202i
$304$	−3.06028	−	0.819999i	−0.175519	−	0.0470302i
$305$	−11.0812	+	41.3555i	−0.634507	+	2.36801i
$306$	3.29930	+	6.07483i	0.188608	+	0.347275i
$307$	12.7457	+	12.7457i	0.727435	+	0.727435i	0.970108	−	0.242673i	$-0.0780242\pi$
$307$	12.7457	+	12.7457i	0.727435	+	0.727435i	−0.242673	+	0.970108i	$0.578024\pi$
$308$	1.11769	+	0.614453i	0.0636863	+	0.0350117i
$309$	11.9952	−	15.2176i	0.682380	−	0.865702i
$310$	−15.0832	+	4.04154i	−0.856670	+	0.229544i
$311$	−2.79666	−	4.84396i	−0.158584	−	0.274676i	0.775774	−	0.631011i	$-0.217360\pi$
$311$	−2.79666	−	4.84396i	−0.158584	−	0.274676i	−0.934358	+	0.356335i	$0.884026\pi$
$312$	−1.04215	+	18.7633i	−0.0590001	+	1.06226i
$313$	−7.93436	+	13.7427i	−0.448477	+	0.776785i	−0.998287	−	0.0585049i	$-0.981367\pi$
$313$	−7.93436	+	13.7427i	−0.448477	+	0.776785i	0.549810	+	0.835290i	$0.314700\pi$
$314$	−13.4176	−	13.4176i	−0.757196	−	0.757196i
$315$	21.4038	+	21.6239i	1.20597	+	1.21837i
$316$			5.16385i			0.290489i
$317$	−12.4356	+	3.33212i	−0.698455	+	0.187151i	−0.590539	−	0.807009i	$-0.701085\pi$
$317$	−12.4356	+	3.33212i	−0.698455	+	0.187151i	−0.107917	+	0.994160i	$0.534418\pi$
$318$	11.8928	+	15.9243i	0.666913	+	0.892993i
$319$	0.888638	−	3.31644i	0.0497542	−	0.185685i
$320$	−8.77379	−	32.7442i	−0.490470	−	1.83046i
$321$	−18.5508	+	23.5344i	−1.03540	+	1.31356i
$322$	17.0822	−	10.3454i	0.951954	−	0.576526i
$323$	1.22982	−	1.22982i	0.0684289	−	0.0684289i
$324$	−2.92353	−	0.152516i	−0.162418	−	0.00847309i
$325$	34.4279	+	6.02874i	1.90972	+	0.334414i
$326$	−20.3267	+	11.7356i	−1.12579	+	0.649978i
$327$	5.67588	−	13.2131i	0.313877	−	0.730688i
$328$	−17.9503			−0.991139
$329$	4.18856	−	7.61898i	0.230923	−	0.420048i
$330$	−1.49746	−	12.6455i	−0.0824325	−	0.696113i
$331$	6.27644	+	23.4240i	0.344985	+	1.28750i	0.892630	+	0.450790i	$0.148858\pi$
$331$	6.27644	+	23.4240i	0.344985	+	1.28750i	−0.547646	+	0.836710i	$0.684476\pi$
$332$	0.907105	+	0.243058i	0.0497839	+	0.0133395i
$333$	−27.1447	−	0.707565i	−1.48752	−	0.0387743i
$334$	−7.18015	+	12.4364i	−0.392880	+	0.680488i
$335$	−30.9275			−1.68975
$336$	−2.05675	−	14.7212i	−0.112205	−	0.803109i
$337$			2.85524i			0.155535i	0.996972	+	0.0777674i	$0.0247792\pi$
$337$			2.85524i			0.155535i	−0.996972	+	0.0777674i	$0.975221\pi$
$338$	7.14581	+	15.2304i	0.388681	+	0.828425i
$339$	−14.4103	−	2.08851i	−0.782658	−	0.113432i
$340$	2.14456	+	0.574634i	0.116305	+	0.0311639i
$341$	−4.04019	−	2.33261i	−0.218789	−	0.126318i
$342$	−0.885684	−	3.68720i	−0.0478923	−	0.199381i
$343$	12.2476	−	13.8923i	0.661309	−	0.750114i
$344$	−14.3881	−	14.3881i	−0.775753	−	0.775753i
$345$	35.5820	+	15.2847i	1.91567	+	0.822901i
$346$	−6.45423	+	24.0875i	−0.346982	+	1.29495i
$347$	24.9745	−	14.4190i	1.34070	−	0.774053i	0.353790	−	0.935325i	$-0.384893\pi$
$347$	24.9745	−	14.4190i	1.34070	−	0.774053i	0.986910	+	0.161272i	$0.0515595\pi$
$348$	1.21227	−	0.483732i	0.0649847	−	0.0259308i
$349$	3.66496	+	3.66496i	0.196181	+	0.196181i	0.798361	−	0.602180i	$-0.205701\pi$
$349$	3.66496	+	3.66496i	0.196181	+	0.196181i	−0.602180	+	0.798361i	$0.705701\pi$
$350$	−33.1835	+	0.695143i	−1.77373	+	0.0371569i
$351$	−16.9341	+	8.01476i	−0.903875	+	0.427796i
$352$	1.34918	−	2.33686i	0.0719118	−	0.124555i
$353$	−6.76121	+	25.2332i	−0.359863	+	1.34303i	0.514390	+	0.857557i	$0.328019\pi$
$353$	−6.76121	+	25.2332i	−0.359863	+	1.34303i	−0.874253	+	0.485471i	$0.838648\pi$
$354$	−2.45290	+	16.9245i	−0.130370	+	0.899525i
$355$	−15.2579	−	8.80913i	−0.809803	−	0.467540i
$356$	0.153196	+	0.153196i	0.00811939	+	0.00811939i
$357$	7.56317	+	3.06286i	0.400285	+	0.162104i
$358$	−4.73686	−	4.73686i	−0.250351	−	0.250351i
$359$	−5.98702	−	22.3439i	−0.315983	−	1.17926i	−0.923071	−	0.384630i	$-0.874329\pi$
$359$	−5.98702	−	22.3439i	−0.315983	−	1.17926i	0.607088	−	0.794635i	$-0.292338\pi$
$360$	25.0986	−	23.8233i	1.32281	−	1.25560i
$361$	15.6283	−	9.02298i	0.822540	−	0.474893i
$362$	−0.894011	−	3.33649i	−0.0469882	−	0.175362i
$363$	−9.43935	+	11.9752i	−0.495438	+	0.628537i
$364$	1.83558	+	2.50180i	0.0962105	+	0.131130i
$365$		−	22.1626i		−	1.16004i
$366$	23.0028	+	9.88117i	1.20238	+	0.516497i
$367$	−7.46154	−	12.9238i	−0.389489	−	0.674616i	0.602891	−	0.797823i	$-0.294015\pi$
$367$	−7.46154	−	12.9238i	−0.389489	−	0.674616i	−0.992381	+	0.123208i	$0.960682\pi$
$368$	−9.45965	−	16.3846i	−0.493119	−	0.854106i
$369$	−8.54093	−	15.7260i	−0.444623	−	0.818660i
$370$	31.7494	−	31.7494i	1.65057	−	1.65057i
$371$	22.7828	+	5.59596i	1.18282	+	0.290528i
$372$	−0.208556	−	1.76118i	−0.0108131	−	0.0913128i
$373$	15.1061	−	26.1645i	0.782164	−	1.35475i	−0.148515	−	0.988910i	$-0.547449\pi$
$373$	15.1061	−	26.1645i	0.782164	−	1.35475i	0.930679	−	0.365837i	$-0.119217\pi$
$374$	−1.70755	−	2.95756i	−0.0882951	−	0.152932i
$375$	−18.6480	−	24.9696i	−0.962979	−	1.28943i
$376$	−8.56383	−	4.94433i	−0.441646	−	0.254984i
$377$	5.36163	−	6.40506i	0.276138	−	0.329877i
$378$	14.3088	−	10.5726i	0.735965	−	0.543798i
$379$	−15.3869	+	15.3869i	−0.790374	+	0.790374i	−0.981555	−	0.191181i	$-0.938768\pi$
$379$	−15.3869	+	15.3869i	−0.790374	+	0.790374i	0.191181	+	0.981555i	$0.438768\pi$
$380$	−1.05473	−	0.608946i	−0.0541063	−	0.0312383i
$381$	−22.1511	−	3.21040i	−1.13483	−	0.164474i
$382$	−5.73202	−	1.53589i	−0.293276	−	0.0785829i
$383$	−17.6074	+	4.71790i	−0.899698	+	0.241073i	−0.678886	−	0.734243i	$-0.737537\pi$
$383$	−17.6074	+	4.71790i	−0.899698	+	0.241073i	−0.220811	+	0.975317i	$0.570870\pi$
$384$	−13.4214	+	1.58934i	−0.684910	+	0.0811059i
$385$	−10.8485	−	10.4033i	−0.552893	−	0.530204i
$386$			9.21013i			0.468784i
$387$	5.75916	−	19.4511i	0.292754	−	0.988756i
$388$	−0.443691	+	1.65588i	−0.0225250	+	0.0840644i
$389$	−4.78065	−	8.28033i	−0.242389	−	0.419829i	0.719006	−	0.695004i	$-0.244598\pi$
$389$	−4.78065	−	8.28033i	−0.242389	−	0.419829i	−0.961394	+	0.275175i	$0.911264\pi$
$390$	9.66516	−	29.4330i	0.489414	−	1.49040i
$391$	10.3859			0.525237
$392$	−15.5053	−	14.2578i	−0.783137	−	0.720127i
$393$	4.65391	−	5.90418i	0.234759	−	0.297826i
$394$	17.4387	+	10.0682i	0.878548	+	0.507230i
$395$	15.7501	−	58.7800i	0.792472	−	2.95754i
$396$	1.44574	+	0.0376852i	0.0726511	+	0.00189375i
$397$	4.95510	−	1.32771i	0.248689	−	0.0666360i	−0.132321	−	0.991207i	$-0.542243\pi$
$397$	4.95510	−	1.32771i	0.248689	−	0.0666360i	0.381010	+	0.924571i	$0.375576\pi$
$398$	8.18821	−	8.18821i	0.410438	−	0.410438i
$399$	−3.57254	−	2.69665i	−0.178851	−	0.135001i
$400$			31.4434i			1.57217i
$401$	6.47542	+	24.1666i	0.323367	+	1.20682i	0.915943	+	0.401308i	$0.131444\pi$
$401$	6.47542	+	24.1666i	0.323367	+	1.20682i	−0.592576	+	0.805515i	$0.701889\pi$
$402$	−2.59393	+	17.8976i	−0.129374	+	0.892650i
$403$	−6.52085	−	9.28941i	−0.324827	−	0.462739i
$404$	2.76680	+	1.59741i	0.137653	+	0.0794741i
$405$	32.8134	+	10.6530i	1.63051	+	0.529354i
$406$	−3.82131	+	6.95096i	−0.189649	+	0.344971i
$407$	13.4144			0.664928
$408$	3.66297	−	8.52719i	0.181344	−	0.422159i
$409$	38.4401	+	10.3000i	1.90074	+	0.509301i	0.996633	+	0.0819915i	$0.0261280\pi$
$409$	38.4401	+	10.3000i	1.90074	+	0.509301i	0.904105	+	0.427310i	$0.140539\pi$
$410$	28.5831	+	7.65881i	1.41162	+	0.378242i
$411$	−13.2522	+	30.8504i	−0.653684	+	1.52174i
$412$	−3.63896			−0.179279
$413$	10.4568	+	17.2662i	0.514546	+	0.849614i
$414$	11.8295	−	19.3091i	0.581388	−	0.948993i
$415$	−9.58423	−	5.53346i	−0.470471	−	0.271627i
$416$	5.37302	−	3.77167i	0.263434	−	0.184921i
$417$	4.54088	−	31.3311i	0.222368	−	1.53429i
$418$	0.484856	+	1.80951i	0.0237151	+	0.0885059i
$419$			35.0848i			1.71401i	0.515312	+	0.857003i	$0.327676\pi$
$419$			35.0848i			1.71401i	−0.515312	+	0.857003i	$0.672324\pi$
$420$	0.700953	−	5.67075i	0.0342030	−	0.276704i
$421$	7.19039	−	7.19039i	0.350438	−	0.350438i	−0.509834	−	0.860273i	$-0.670293\pi$
$421$	7.19039	−	7.19039i	0.350438	−	0.350438i	0.860273	+	0.509834i	$0.170293\pi$
$422$	9.40108	−	2.51901i	0.457637	−	0.122624i
$423$	0.256890	−	9.85519i	0.0124904	−	0.479176i
$424$	6.90592	−	25.7732i	0.335381	−	1.25166i
$425$	−14.9486	−	8.63055i	−0.725111	−	0.418643i
$426$	−6.37750	+	8.09081i	−0.308991	+	0.392001i
$427$	28.3775	−	8.24448i	1.37328	−	0.398978i
$428$	5.62773			0.272026
$429$	8.25967	−	4.17605i	0.398780	−	0.201622i
$430$	16.7718	+	29.0497i	0.808810	+	1.40090i
$431$	6.53304	−	24.3816i	0.314685	−	1.17442i	−0.609597	−	0.792712i	$-0.708669\pi$
$431$	6.53304	−	24.3816i	0.314685	−	1.17442i	0.924282	−	0.381710i	$-0.124665\pi$
$432$	−9.72992	−	13.7623i	−0.468131	−	0.662138i
$433$		−	15.7187i		−	0.755394i	−0.925929	−	0.377697i	$-0.876716\pi$
$433$		−	15.7187i		−	0.755394i	0.925929	−	0.377697i	$-0.123284\pi$
$434$	7.77902	+	7.45979i	0.373405	+	0.358081i
$435$	−15.2747	+	1.80881i	−0.732367	+	0.0867257i
$436$	−2.60866	+	0.698987i	−0.124932	+	0.0334754i
$437$	−5.50303	−	1.47453i	−0.263246	−	0.0705364i
$438$	−12.8254	−	1.85881i	−0.612819	−	0.0888172i
$439$	9.47409	+	5.46987i	0.452174	+	0.261063i	0.708748	−	0.705462i	$-0.249260\pi$
$439$	9.47409	+	5.46987i	0.452174	+	0.261063i	−0.256574	+	0.966525i	$0.582594\pi$
$440$	−12.0882	+	12.0882i	−0.576280	+	0.576280i
$441$	5.11343	−	20.3679i	0.243496	−	0.969902i
$442$	−0.733873	−	8.27586i	−0.0349068	−	0.393642i
$443$	11.9352	+	6.89078i	0.567058	+	0.327391i	0.755973	−	0.654602i	$-0.227164\pi$
$443$	11.9352	+	6.89078i	0.567058	+	0.327391i	−0.188916	+	0.981993i	$0.560497\pi$
$444$	3.05140	+	4.08581i	0.144813	+	0.193904i
$445$	−1.27658	−	2.21109i	−0.0605155	−	0.104816i
$446$	−1.35583	+	2.34837i	−0.0642004	+	0.111198i
$447$	−1.39852	−	11.8100i	−0.0661475	−	0.558592i
$448$	−16.1945	+	16.8875i	−0.765118	+	0.797859i
$449$	−17.2469	+	17.2469i	−0.813931	+	0.813931i	−0.985221	−	0.171289i	$-0.945207\pi$
$449$	−17.2469	+	17.2469i	−0.813931	+	0.813931i	0.171289	+	0.985221i	$0.445207\pi$
$450$	−33.0720	+	17.9618i	−1.55903	+	0.846725i
$451$	4.42034	+	7.65626i	0.208146	+	0.360519i
$452$	1.36726	+	2.36816i	0.0643104	+	0.111389i
$453$	−5.71103	−	2.45325i	−0.268328	−	0.115264i
$454$			8.20377i			0.385022i
$455$	−13.2637	−	34.0766i	−0.621813	−	1.59754i
$456$	−3.15149	+	3.99813i	−0.147582	+	0.187230i
$457$	−1.05340	−	3.93136i	−0.0492761	−	0.183901i	0.936901	−	0.349594i	$-0.113681\pi$
$457$	−1.05340	−	3.93136i	−0.0492761	−	0.183901i	−0.986177	+	0.165693i	$0.947014\pi$
$458$	0.257080	−	0.148425i	0.0120125	−	0.00693545i
$459$	9.21340	−	0.848257i	0.430045	−	0.0395932i
$460$	−1.88232	−	7.02491i	−0.0877635	−	0.327538i
$461$	−6.28561	−	6.28561i	−0.292750	−	0.292750i	0.545416	−	0.838166i	$-0.316372\pi$
$461$	−6.28561	−	6.28561i	−0.292750	−	0.292750i	−0.838166	+	0.545416i	$0.816372\pi$
$462$	−6.93025	+	5.40545i	−0.322424	+	0.251484i
$463$	−20.3623	−	20.3623i	−0.946318	−	0.946318i	0.0523129	−	0.998631i	$-0.483341\pi$
$463$	−20.3623	−	20.3623i	−0.946318	−	0.946318i	−0.998631	+	0.0523129i	$0.983341\pi$
$464$	6.50775	+	3.75725i	0.302115	+	0.174426i
$465$	−2.99772	+	20.6836i	−0.139016	+	0.959178i
$466$	2.31344	−	8.63387i	0.107168	−	0.399956i
$467$	7.33823	−	12.7102i	0.339573	−	0.588158i	−0.644779	−	0.764369i	$-0.723051\pi$
$467$	7.33823	−	12.7102i	0.339573	−	0.588158i	0.984352	+	0.176211i	$0.0563841\pi$
$468$	3.15080	+	1.56583i	0.145646	+	0.0723803i
$469$	11.0581	+	18.2590i	0.510614	+	0.843121i
$470$	11.5270	+	11.5270i	0.531700	+	0.531700i
$471$	−23.5882	+	9.41235i	−1.08688	+	0.433698i
$472$	19.8826	−	11.4792i	0.915172	−	0.528375i
$473$	−2.59375	+	9.68000i	−0.119261	+	0.445087i
$474$	−32.6947	−	14.0444i	−1.50172	−	0.645083i
$475$	6.69526	+	6.69526i	0.307200	+	0.307200i
$476$	−0.427531	−	1.47156i	−0.0195959	−	0.0674491i
$477$	25.8654	−	6.21300i	1.18430	−	0.284474i
$478$	18.9262	+	10.9271i	0.865666	+	0.499793i
$479$	−20.6864	−	5.54291i	−0.945187	−	0.253262i	−0.246868	−	0.969049i	$-0.579402\pi$
$479$	−20.6864	−	5.54291i	−0.945187	−	0.253262i	−0.698319	+	0.715787i	$0.746068\pi$
$480$	−11.9634	−	1.73389i	−0.546053	−	0.0791407i
$481$	29.5935	+	13.7573i	1.34935	+	0.627277i
$482$			23.4464i			1.06796i
$483$	−3.69848	−	26.4719i	−0.168286	−	1.20451i
$484$	2.86361			0.130164
$485$	10.1011	−	17.4956i	0.458666	−	0.794432i
$486$	8.91697	−	18.0954i	0.404482	−	0.820826i
$487$	−2.67104	−	0.715703i	−0.121036	−	0.0324316i	0.197792	−	0.980244i	$-0.436623\pi$
$487$	−2.67104	−	0.715703i	−0.121036	−	0.0324316i	−0.318829	+	0.947812i	$0.603289\pi$
$488$	−8.69890	−	32.4647i	−0.393780	−	1.46961i
$489$	3.69421	+	31.1963i	0.167058	+	1.41074i
$490$	18.6065	+	29.3189i	0.840555	+	1.32449i
$491$	3.45508			0.155925			0.0779627	−	0.996956i	$-0.475158\pi$
$491$	3.45508			0.155925			0.0779627	+	0.996956i	$0.475158\pi$
$492$	−1.32647	+	3.08794i	−0.0598018	+	0.139215i
$493$	−3.57248	+	2.06257i	−0.160896	+	0.0928936i
$494$	−0.786113	+	4.48920i	−0.0353689	+	0.201979i
$495$	−16.3419	−	4.83857i	−0.734513	−	0.217477i
$496$	7.21985	−	7.21985i	0.324181	−	0.324181i
$497$	0.254683	+	12.1576i	0.0114241	+	0.545344i
$498$	−4.00603	+	5.08225i	−0.179514	+	0.227741i
$499$	5.87182	+	21.9139i	0.262859	+	0.981003i	0.963548	+	0.267536i	$0.0862094\pi$
$499$	5.87182	+	21.9139i	0.262859	+	0.981003i	−0.700689	+	0.713467i	$0.747124\pi$
$500$	−1.51479	+	5.65327i	−0.0677434	+	0.252822i
$501$	11.5007	+	15.3994i	0.513813	+	0.687994i
$502$	33.8424	−	9.06804i	1.51046	−	0.404726i
$503$		−	21.8711i		−	0.975184i	−0.873072	−	0.487592i	$-0.837875\pi$
$503$		−	21.8711i		−	0.975184i	0.873072	−	0.487592i	$-0.162125\pi$
$504$	−23.0388	−	6.29970i	−1.02623	−	0.280611i
$505$	−26.6222	−	26.6222i	−1.18467	−	1.18467i
$506$	−5.59339	+	9.68803i	−0.248656	+	0.430685i
$507$	22.5044	−	0.742019i	0.999457	−	0.0329542i
$508$	2.10171	+	3.64028i	0.0932485	+	0.161511i
$509$	−34.7228	+	9.30395i	−1.53906	+	0.412390i	−0.925963	−	0.377615i	$-0.876744\pi$
$509$	−34.7228	+	9.30395i	−1.53906	+	0.412390i	−0.613099	+	0.790006i	$0.710078\pi$
$510$	−9.47098	+	12.0154i	−0.419382	+	0.532049i
$511$	−13.0843	+	7.92418i	−0.578817	+	0.350545i
$512$	17.9796	+	17.9796i	0.794594	+	0.794594i
$513$	−5.00221	−	0.858614i	−0.220853	−	0.0379087i
$514$	2.40858	−	8.98895i	0.106238	−	0.396486i
$515$	41.4222	+	11.0991i	1.82528	+	0.489083i
$516$	−3.53837	+	1.41191i	−0.155768	+	0.0621560i
$517$			4.87025i			0.214194i
$518$	−30.0962	−	7.39228i	−1.32235	−	0.324798i
$519$	26.2122	+	20.6615i	1.15059	+	0.906938i
$520$	−39.0648	+	14.2706i	−1.71310	+	0.625806i
$521$	−15.3735	+	8.87590i	−0.673525	+	0.388860i	−0.797411	−	0.603436i	$-0.793798\pi$
$521$	−15.3735	+	8.87590i	−0.673525	+	0.388860i	0.123886	+	0.992296i	$0.460464\pi$
$522$	−0.234366	+	8.99111i	−0.0102579	+	0.393530i
$523$	−1.56142	+	2.70445i	−0.0682759	+	0.118257i	−0.898142	−	0.439705i	$-0.855083\pi$
$523$	−1.56142	+	2.70445i	−0.0682759	+	0.118257i	0.829867	+	0.557962i	$0.188416\pi$
$524$	−1.41185			−0.0616770
$525$	−16.6745	+	41.1747i	−0.727737	+	1.79701i
$526$	−9.72320	+	9.72320i	−0.423952	+	0.423952i
$527$	1.45070	+	5.41409i	0.0631936	+	0.235842i
$528$	4.98224	+	6.67120i	0.216824	+	0.290327i
$529$	−5.51046	−	9.54440i	−0.239585	−	0.414974i
$530$	−21.9932	+	38.0933i	−0.955324	+	1.65467i
$531$	19.5171	+	11.9569i	0.846971	+	0.518885i
$532$	0.0176054	+	0.840416i	0.000763290	+	0.0364366i
$533$	1.89978	+	21.4238i	0.0822888	+	0.927967i
$534$	−1.38662	+	0.553300i	−0.0600048	+	0.0239436i
$535$	−64.0604	−	17.1649i	−2.76957	−	0.742104i
$536$	21.0258	−	12.1393i	0.908178	−	0.524337i
$537$	−8.32743	+	3.32289i	−0.359355	+	0.143393i
$538$	−2.93056	+	2.93056i	−0.126346	+	0.126346i
$539$	−2.26305	+	10.1245i	−0.0974766	+	0.436091i
$540$	−2.24357	−	6.07811i	−0.0965479	−	0.261560i
$541$	−5.65703	+	1.51580i	−0.243215	+	0.0651691i	−0.378367	−	0.925656i	$-0.623514\pi$
$541$	−5.65703	+	1.51580i	−0.243215	+	0.0651691i	0.135152	+	0.990825i	$0.456848\pi$
$542$	7.44098	−	4.29605i	0.319617	−	0.184531i
$543$	−4.57532	−	0.663111i	−0.196346	−	0.0284568i
$544$	−3.13152	+	0.839089i	−0.134263	+	0.0359756i
$545$	31.8263			1.36329
$546$	−20.8324	+	4.81760i	−0.891545	+	0.206174i
$547$	1.31098			0.0560535			0.0280268	−	0.999607i	$-0.491078\pi$
$547$	1.31098			0.0560535			0.0280268	+	0.999607i	$0.491078\pi$
$548$	6.09077	−	1.63202i	0.260185	−	0.0697163i
$549$	24.3028	−	23.0680i	1.03722	−	0.984518i
$550$	16.1013	−	9.29607i	0.686560	−	0.396386i
$551$	2.18573	−	0.585665i	0.0931153	−	0.0249502i
$552$	−30.1895	+	3.57499i	−1.28495	+	0.152162i
$553$	−40.3339	+	11.7182i	−1.71517	+	0.498307i
$554$	−21.2829	+	21.2829i	−0.904226	+	0.904226i
$555$	−22.2721	−	55.8157i	−0.945397	−	2.36925i
$556$	−5.14891	+	2.97272i	−0.218362	+	0.126072i
$557$	4.16840	+	1.11692i	0.176621	+	0.0473254i	0.346045	−	0.938218i	$-0.387524\pi$
$557$	4.16840	+	1.11692i	0.176621	+	0.0473254i	−0.169425	+	0.985543i	$0.554191\pi$
$558$	11.7181	+	3.46953i	0.496065	+	0.146877i
$559$	−15.6495	+	18.6950i	−0.661902	+	0.790715i
$560$	28.1385	−	17.0413i	1.18907	−	0.720127i
$561$	−4.53908	+	0.537511i	−0.191640	+	0.0226937i
$562$	7.60457	−	13.1715i	0.320779	−	0.555606i
$563$	17.4211	+	30.1742i	0.734211	+	1.27169i	0.955069	+	0.296384i	$0.0957808\pi$
$563$	17.4211	+	30.1742i	0.734211	+	1.27169i	−0.220858	+	0.975306i	$0.570886\pi$
$564$	−1.48340	+	1.10785i	−0.0624624	+	0.0466487i
$565$	−8.34045	−	31.1270i	−0.350886	−	1.30952i
$566$	17.9022	−	17.9022i	0.752486	−	0.752486i
$567$	−5.44301	−	23.1813i	−0.228585	−	0.973524i
$568$	13.8306			0.580319
$569$	23.0336	−	39.8954i	0.965620	−	1.67250i	0.257678	−	0.966231i	$-0.417043\pi$
$569$	23.0336	−	39.8954i	0.965620	−	1.67250i	0.707941	−	0.706271i	$-0.249624\pi$
$570$	6.72413	−	5.02177i	0.281643	−	0.210339i
$571$	−12.9813	+	7.49477i	−0.543252	+	0.313647i	−0.746396	−	0.665502i	$-0.768217\pi$
$571$	−12.9813	+	7.49477i	−0.543252	+	0.313647i	0.203144	+	0.979149i	$0.434884\pi$
$572$	−1.57616	−	0.732717i	−0.0659028	−	0.0306365i
$573$	−4.91673	+	6.23761i	−0.205400	+	0.260580i
$574$	−5.69821	−	19.6132i	−0.237839	−	0.818641i
$575$			56.5419i			2.35796i
$576$	−7.53201	+	25.4388i	−0.313834	+	1.05995i
$577$	18.6297	+	4.99180i	0.775563	+	0.207812i	0.624828	−	0.780763i	$-0.285169\pi$
$577$	18.6297	+	4.99180i	0.775563	+	0.207812i	0.150735	+	0.988574i	$0.451836\pi$
$578$	4.63202	−	17.2869i	0.192667	−	0.719042i
$579$	11.3262	+	4.86531i	0.470700	+	0.202195i
$580$	2.04257	+	2.04257i	0.0848131	+	0.0848131i
$581$	0.159979	+	7.63681i	0.00663705	+	0.316828i
$582$	−9.27740	−	7.31281i	−0.384560	−	0.303126i
$583$	−12.6936	+	3.40123i	−0.525713	+	0.140864i
$584$	8.69897	+	15.0671i	0.359966	+	0.623480i
$585$	−31.0896	−	27.4339i	−1.28540	−	1.13425i
$586$	2.84345	−	4.92500i	0.117462	−	0.203450i
$587$	−27.9851	−	27.9851i	−1.15507	−	1.15507i	−0.985522	−	0.169548i	$-0.945769\pi$
$587$	−27.9851	−	27.9851i	−1.15507	−	1.15507i	−0.169548	−	0.985522i	$-0.554231\pi$
$588$	−3.59852	+	1.61374i	−0.148401	+	0.0665494i
$589$		−	3.07465i		−	0.126689i
$590$	−36.5578	+	9.79563i	−1.50506	+	0.403280i
$591$	21.5935	−	16.1266i	0.888238	−	0.663362i
$592$	−7.59871	+	28.3588i	−0.312305	+	1.16554i
$593$	−1.21118	−	4.52020i	−0.0497374	−	0.185622i	0.936588	−	0.350433i	$-0.113965\pi$
$593$	−1.21118	−	4.52020i	−0.0497374	−	0.185622i	−0.986325	+	0.164810i	$0.947299\pi$
$594$	−4.17067	+	9.05115i	−0.171125	+	0.371373i
$595$	0.378220	+	18.0548i	0.0155055	+	0.740175i
$596$	−1.57925	+	1.57925i	−0.0646888	+	0.0646888i
$597$	−5.74399	−	14.3949i	−0.235086	−	0.589145i
$598$	−22.2752	+	15.6364i	−0.910901	+	0.639421i
$599$	1.70959	−	0.987035i	0.0698521	−	0.0403291i	−0.464667	−	0.885485i	$-0.653826\pi$
$599$	1.70959	−	0.987035i	0.0698521	−	0.0403291i	0.534519	+	0.845156i	$0.320493\pi$
$600$	46.4229	+	19.9416i	1.89521	+	0.814112i
$601$	22.1442			0.903281			0.451641	−	0.892200i	$-0.350839\pi$
$601$	22.1442			0.903281			0.451641	+	0.892200i	$0.350839\pi$
$602$	11.1536	−	20.2884i	0.454587	−	0.826894i
$603$	20.6393	+	12.6444i	0.840498	+	0.514920i
$604$	0.302119	+	1.12752i	0.0122930	+	0.0458783i
$605$	−32.5964	−	8.73419i	−1.32523	−	0.355095i
$606$	−17.6390	+	13.1733i	−0.716535	+	0.535129i
$607$	3.46982	−	6.00991i	0.140836	−	0.243935i	−0.786976	−	0.616984i	$-0.788354\pi$
$607$	3.46982	−	6.00991i	0.140836	−	0.243935i	0.927812	+	0.373049i	$0.121688\pi$
$608$	1.77839			0.0721230
$609$	6.52933	+	8.37115i	0.264582	+	0.339216i
$610$			55.4066i			2.24335i
$611$	−4.99473	+	10.7443i	−0.202065	+	0.434667i
$612$	−1.19623	−	1.26026i	−0.0483547	−	0.0509431i
$613$	14.1349	+	3.78743i	0.570903	+	0.152973i	0.532711	−	0.846298i	$-0.321173\pi$
$613$	14.1349	+	3.78743i	0.570903	+	0.152973i	0.0381921	+	0.999270i	$0.487840\pi$
$614$	20.2013	+	11.6633i	0.815260	+	0.470691i
$615$	24.5176	−	31.1042i	0.988645	−	1.25424i
$616$	11.4587	+	2.81451i	0.461684	+	0.113400i
$617$	−24.6732	−	24.6732i	−0.993306	−	0.993306i	0.00667207	−	0.999978i	$-0.497876\pi$
$617$	−24.6732	−	24.6732i	−0.993306	−	0.993306i	−0.999978	+	0.00667207i	$0.997876\pi$
$618$	9.89711	−	23.0399i	0.398120	−	0.926802i
$619$	3.26864	−	12.1987i	0.131378	−	0.490309i	−0.868609	−	0.495499i	$-0.834985\pi$
$619$	3.26864	−	12.1987i	0.131378	−	0.490309i	0.999987	+	0.00519004i	$0.00165205\pi$
$620$	3.39911	−	1.96248i	0.136512	−	0.0788150i
$621$	−17.4965	−	24.7475i	−0.702109	−	0.993083i
$622$	−5.11831	−	5.11831i	−0.205225	−	0.205225i
$623$	−0.848948	+	1.54424i	−0.0340124	+	0.0618685i
$624$	4.14963	+	19.8269i	0.166118	+	0.793712i
$625$	10.2510	−	17.7552i	0.410039	−	0.710208i
$626$	−5.31508	+	19.8361i	−0.212433	+	0.792812i
$627$	2.48137	+	0.359631i	0.0990965	+	0.0143623i
$628$	4.13051	+	2.38475i	0.164825	+	0.0951618i
$629$	−11.3964	−	11.3964i	−0.454404	−	0.454404i
$630$	33.9978	+	19.8612i	1.35450	+	0.791288i
$631$	4.81881	+	4.81881i	0.191834	+	0.191834i	0.796488	−	0.604654i	$-0.206689\pi$
$631$	4.81881	+	4.81881i	0.191834	+	0.191834i	−0.604654	+	0.796488i	$0.706689\pi$
$632$	12.3640	+	46.1432i	0.491815	+	1.83548i
$633$	1.86842	−	12.8917i	0.0742629	−	0.512398i
$634$	−14.4287	+	8.33040i	−0.573036	+	0.330842i
$635$	−12.8207	−	47.8476i	−0.508775	−	1.89877i
$636$	−3.92338	−	3.09256i	−0.155572	−	0.122628i
$637$	−15.3757	+	20.0147i	−0.609209	+	0.793010i
$638$		−	4.44324i		−	0.175910i
$639$	6.58074	+	12.1168i	0.260330	+	0.479331i
$640$	−14.9555	−	25.9037i	−0.591167	−	1.02393i
$641$	4.86631	+	8.42869i	0.192208	+	0.332913i	0.945982	−	0.324220i	$-0.105102\pi$
$641$	4.86631	+	8.42869i	0.192208	+	0.332913i	−0.753774	+	0.657134i	$0.771769\pi$
$642$	−15.3061	+	35.6318i	−0.604083	+	1.40627i
$643$	9.13194	−	9.13194i	0.360129	−	0.360129i	−0.503732	−	0.863860i	$-0.668040\pi$
$643$	9.13194	−	9.13194i	0.360129	−	0.360129i	0.863860	+	0.503732i	$0.168040\pi$
$644$	−3.47434	+	3.62302i	−0.136908	+	0.142767i
$645$	44.5837	−	5.27953i	1.75548	−	0.207881i
$646$	1.12537	−	1.94921i	0.0442773	−	0.0766905i
$647$	12.3473	+	21.3862i	0.485423	+	0.840777i	0.999860	−	0.0167510i	$-0.00533226\pi$
$647$	12.3473	+	21.3862i	0.485423	+	0.840777i	−0.514437	+	0.857528i	$0.671999\pi$
$648$	−26.4893	+	5.63710i	−1.04060	+	0.221446i
$649$	−9.79237	−	5.65363i	−0.384384	−	0.221924i
$650$	45.0547	−	3.99529i	1.76719	−	0.156708i
$651$	13.2830	−	5.62558i	0.520602	−	0.220484i
$652$	4.17164	−	4.17164i	0.163374	−	0.163374i
$653$	−21.5537	−	12.4440i	−0.843460	−	0.486972i	0.0149789	−	0.999888i	$-0.495232\pi$
$653$	−21.5537	−	12.4440i	−0.843460	−	0.486972i	−0.858439	+	0.512916i	$0.828565\pi$
$654$	2.66932	−	18.4177i	0.104379	−	0.720189i
$655$	16.0711	+	4.30624i	0.627950	+	0.168259i
$656$	−18.6897	+	5.00788i	−0.729709	+	0.195525i
$657$	−9.06094	+	14.7901i	−0.353501	+	0.577016i
$658$	2.68385	−	10.9268i	0.104627	−	0.425969i
$659$			24.4285i			0.951600i	0.879554	+	0.475800i	$0.157841\pi$
$659$			24.4285i			0.951600i	−0.879554	+	0.475800i	$0.842159\pi$
$660$	1.18622	+	2.97277i	0.0461736	+	0.115715i
$661$	3.26929	−	12.2012i	0.127161	−	0.474570i	−0.872747	−	0.488173i	$-0.837663\pi$
$661$	3.26929	−	12.2012i	0.127161	−	0.474570i	0.999907	+	0.0136029i	$0.00433007\pi$
$662$	15.6913	+	27.1781i	0.609859	+	1.05631i
$663$	−10.5649	−	3.46929i	−0.410307	−	0.134736i
$664$	8.68770			0.337148
$665$	2.36292	−	9.62015i	0.0916301	−	0.373053i
$666$	−34.1683	+	8.20739i	−1.32399	+	0.318030i
$667$	11.7023	+	6.75634i	0.453116	+	0.261606i
$668$	0.934209	−	3.48651i	0.0361456	−	0.134897i
$669$	2.17168	+	2.90787i	0.0839621	+	0.112425i
$670$	−38.6598	+	10.3589i	−1.49356	+	0.400198i
$671$	−11.7049	+	11.7049i	−0.451862	+	0.451862i
$672$	3.25385	+	7.68292i	0.125520	+	0.296375i
$673$		−	32.5521i		−	1.25479i	−0.778700	−	0.627396i	$-0.784121\pi$
$673$		−	32.5521i		−	1.25479i	0.778700	−	0.627396i	$-0.215879\pi$
$674$	0.956335	+	3.56909i	0.0368367	+	0.137476i
$675$	4.61800	+	50.1588i	0.177747	+	1.93061i
$676$	−2.72573	−	3.23290i	−0.104836	−	0.124342i
$677$	27.7679	+	16.0318i	1.06721	+	0.616152i	0.927417	−	0.374030i	$-0.122024\pi$
$677$	27.7679	+	16.0318i	1.06721	+	0.616152i	0.139789	+	0.990181i	$0.455358\pi$
$678$	−18.7126	+	2.21591i	−0.718652	+	0.0851015i
$679$	−13.9406	+	0.292034i	−0.534993	+	0.0112072i
$680$	20.5393			0.787646
$681$	10.0886	+	4.33369i	0.386596	+	0.166067i
$682$	−5.83158	−	1.56257i	−0.223303	−	0.0598338i
$683$	25.3970	+	6.80511i	0.971790	+	0.260390i	0.709583	−	0.704621i	$-0.248883\pi$
$683$	25.3970	+	6.80511i	0.971790	+	0.260390i	0.262207	+	0.965012i	$0.415550\pi$
$684$	0.454904	+	0.837591i	0.0173937	+	0.0320261i
$685$	−74.3089			−2.83920
$686$	10.6566	−	21.4678i	0.406871	−	0.819644i
$687$	−0.0467220	−	0.394551i	−0.00178256	−	0.0150530i
$688$	−18.9948	−	10.9666i	−0.724169	−	0.418099i
$689$	−31.4914	−	5.51452i	−1.19973	−	0.210087i
$690$	49.5974	+	7.18826i	1.88814	+	0.273652i
$691$	1.39650	+	5.21180i	0.0531252	+	0.198266i	0.987388	−	0.158319i	$-0.0506075\pi$
$691$	1.39650	+	5.21180i	0.0531252	+	0.198266i	−0.934263	+	0.356585i	$0.883941\pi$
$692$		−	6.26805i		−	0.238276i
$693$	2.98642	+	11.3779i	0.113445	+	0.432212i
$694$	26.3889	−	26.3889i	1.00171	−	1.00171i
$695$	67.6770	−	18.1340i	2.56713	−	0.687862i
$696$	9.67444	−	7.22515i	0.366709	−	0.273869i
$697$	2.74911	−	10.2598i	0.104130	−	0.388619i
$698$	5.80880	+	3.35371i	0.219866	+	0.126940i
$699$	−9.39542	−	7.40584i	−0.355367	−	0.280115i
$700$	8.01136	−	2.32753i	0.302801	−	0.0879723i
$701$	−34.6806			−1.30987			−0.654935	−	0.755685i	$-0.727304\pi$
$701$	−34.6806			−1.30987			−0.654935	+	0.755685i	$0.727304\pi$
$702$	−18.4834	+	15.6905i	−0.697611	+	0.592199i
$703$	4.42045	+	7.65644i	0.166720	+	0.288768i
$704$	3.39218	−	12.6598i	0.127848	−	0.477134i
$705$	20.2645	−	8.08613i	0.763206	−	0.304541i
$706$			33.8065i			1.27232i
$707$	−6.19850	+	25.2359i	−0.233119	+	0.949095i
$708$	−0.505485	−	4.26864i	−0.0189973	−	0.160425i
$709$	14.4578	−	3.87395i	0.542974	−	0.145489i	0.0231010	−	0.999733i	$-0.492646\pi$
$709$	14.4578	−	3.87395i	0.542974	−	0.145489i	0.519873	+	0.854244i	$0.325979\pi$
$710$	−22.0231	−	5.90107i	−0.826512	−	0.221463i
$711$	−34.5424	+	32.7873i	−1.29544	+	1.22962i
$712$	1.73574	+	1.00213i	0.0650497	+	0.0375564i
$713$	12.9828	−	12.9828i	0.486210	−	0.486210i
$714$	10.4799	+	1.29541i	0.392202	+	0.0484795i
$715$	15.7066	+	13.1479i	0.587395	+	0.491704i
$716$	1.45821	+	0.841899i	0.0544959	+	0.0314632i
$717$	23.4355	−	17.5023i	0.875214	−	0.653635i
$718$	−14.9677	−	25.9249i	−0.558591	−	0.967507i
$719$	13.5897	−	23.5381i	0.506812	−	0.877824i	−0.493157	−	0.869940i	$-0.664157\pi$
$719$	13.5897	−	23.5381i	0.506812	−	0.877824i	0.999969	−	0.00788373i	$-0.00250950\pi$
$720$	19.4860	−	31.8067i	0.726199	−	1.18537i
$721$	−8.25777	−	28.4233i	−0.307536	−	1.05854i
$722$	16.5134	−	16.5134i	0.614565	−	0.614565i
$723$	28.8333	+	12.3857i	1.07232	+	0.460630i
$724$	0.434111	+	0.751902i	0.0161336	+	0.0279442i
$725$	−11.2289	−	19.4490i	−0.417030	−	0.722317i
$726$	−7.78834	+	18.1308i	−0.289052	+	0.672898i
$727$			19.6171i			0.727559i	0.931485	+	0.363780i	$0.118514\pi$
$727$			19.6171i			0.727559i	−0.931485	+	0.363780i	$0.881486\pi$
$728$	22.3926	+	17.9606i	0.829925	+	0.665666i
$729$	−17.5425	−	20.5247i	−0.649720	−	0.760173i
$730$	−7.42314	−	27.7035i	−0.274743	−	1.02535i
$731$	10.4273	−	6.02022i	0.385668	−	0.222666i
$732$	−6.22764	−	0.902586i	−0.230180	−	0.0333605i
$733$	−9.35544	−	34.9150i	−0.345551	−	1.28961i	−0.891967	−	0.452100i	$-0.850675\pi$
$733$	−9.35544	−	34.9150i	−0.345551	−	1.28961i	0.546416	−	0.837514i	$-0.315992\pi$
$734$	−13.6557	−	13.6557i	−0.504042	−	0.504042i
$735$	45.8840	−	7.39344i	1.69246	−	0.272711i
$736$	7.50929	+	7.50929i	0.276796	+	0.276796i
$737$	−10.3554	−	5.97870i	−0.381447	−	0.220228i
$738$	−15.9435	−	16.7970i	−0.586890	−	0.618305i
$739$	−1.84955	+	6.90263i	−0.0680369	+	0.253917i	−0.991564	−	0.129615i	$-0.958626\pi$
$739$	−1.84955	+	6.90263i	−0.0680369	+	0.253917i	0.923527	+	0.383532i	$0.125293\pi$
$740$	−5.64294	+	9.77385i	−0.207438	+	0.359294i
$741$	5.10534	+	3.33817i	0.187549	+	0.122631i
$742$	30.3532	−	0.635851i	1.11430	−	0.0233428i
$743$	4.27421	+	4.27421i	0.156806	+	0.156806i	0.781150	−	0.624344i	$-0.214634\pi$
$743$	4.27421	+	4.27421i	0.156806	+	0.156806i	−0.624344	+	0.781150i	$0.714634\pi$
$744$	−6.08049	−	15.2382i	−0.222922	−	0.558660i
$745$	22.7935	−	13.1598i	0.835088	−	0.482138i
$746$	10.1193	−	37.7657i	0.370493	−	1.38270i
$747$	4.13369	+	7.61115i	0.151244	+	0.278477i
$748$	0.606976	+	0.606976i	0.0221933	+	0.0221933i
$749$	12.7708	+	43.9572i	0.466636	+	1.60616i
$750$	−31.6736	−	24.9664i	−1.15656	−	0.911644i
$751$	16.4809	+	9.51527i	0.601398	+	0.347217i	0.769591	−	0.638537i	$-0.220460\pi$
$751$	16.4809	+	9.51527i	0.601398	+	0.347217i	−0.168193	+	0.985754i	$0.553793\pi$
$752$	−10.2960	−	2.75880i	−0.375455	−	0.100603i
$753$	6.72600	−	46.4080i	0.245109	−	1.69120i
$754$	4.55680	−	9.80224i	0.165949	−	0.356977i
$755$		−	13.7561i		−	0.500635i
$756$	−2.78621	+	3.49777i	−0.101333	+	0.127213i
$757$	−0.926509			−0.0336745			−0.0168373	−	0.999858i	$-0.505360\pi$
$757$	−0.926509			−0.0336745			−0.0168373	+	0.999858i	$0.505360\pi$
$758$	−14.0802	+	24.3876i	−0.511416	+	0.885798i
$759$	8.95913	+	11.9962i	0.325196	+	0.435436i
$760$	−10.8829	−	2.91606i	−0.394763	−	0.105776i
$761$	0.157093	+	0.586277i	0.00569460	+	0.0212525i	0.968715	−	0.248177i	$-0.0798315\pi$
$761$	0.157093	+	0.586277i	0.00569460	+	0.0212525i	−0.963020	+	0.269430i	$0.913165\pi$
$762$	−28.7645	+	3.40624i	−1.04203	+	0.123395i
$763$	−11.3794	−	18.7896i	−0.411962	−	0.680229i
$764$	1.49158			0.0539636
$765$	9.77280	+	17.9941i	0.353336	+	0.650579i
$766$	−20.4293	+	11.7949i	−0.738142	+	0.426166i
$767$	−15.8048	−	22.5151i	−0.570679	−	0.812974i
$768$	12.2085	−	4.87153i	0.440535	−	0.175786i
$769$	−10.9430	+	10.9430i	−0.394614	+	0.394614i	−0.876328	−	0.481714i	$-0.840014\pi$
$769$	−10.9430	+	10.9430i	−0.394614	+	0.394614i	0.481714	+	0.876328i	$0.340014\pi$
$770$	−17.0453	−	9.37072i	−0.614271	−	0.337697i
$771$	−9.78183	−	7.71043i	−0.352284	−	0.277684i
$772$	−0.599165	−	2.23611i	−0.0215644	−	0.0804795i
$773$	6.73753	−	25.1448i	0.242332	−	0.904395i	−0.732374	−	0.680903i	$-0.761588\pi$
$773$	6.73753	−	25.1448i	0.242332	−	0.904395i	0.974706	−	0.223492i	$-0.0717458\pi$
$774$	0.684065	−	26.2432i	0.0245882	−	0.943291i
$775$	−29.4749	+	7.89778i	−1.05877	+	0.283697i
$776$			15.8590i			0.569304i
$777$	−24.9891	+	33.1058i	−0.896480	+	1.18766i
$778$	−8.74930	−	8.74930i	−0.313678	−	0.313678i
$779$	−2.91327	+	5.04593i	−0.104379	+	0.180789i
$780$	−0.431825	+	7.77476i	−0.0154618	+	0.278381i
$781$	−3.40585	−	5.89910i	−0.121871	−	0.211086i
$782$	12.9825	−	3.47866i	0.464254	−	0.124396i
$783$	10.9330	+	5.03782i	0.390714	+	0.180037i
$784$	−20.1217	−	10.5193i	−0.718632	−	0.375689i
$785$	−39.7439	−	39.7439i	−1.41852	−	1.41852i
$786$	3.83990	−	8.93909i	0.136965	−	0.318847i
$787$	−4.04618	+	15.1006i	−0.144231	+	0.538277i	0.855558	+	0.517708i	$0.173215\pi$
$787$	−4.04618	+	15.1006i	−0.144231	+	0.538277i	−0.999788	+	0.0205692i	$0.993452\pi$
$788$	−4.88890	−	1.30998i	−0.174160	−	0.0466660i
$789$	6.82078	+	17.0935i	0.242826	+	0.608543i
$790$		−	78.7512i		−	2.80184i
$791$	−15.3946	+	16.0534i	−0.547370	+	0.570794i
$792$	13.0091	−	3.12485i	0.462258	−	0.111037i
$793$	−37.8262	+	13.8181i	−1.34325	+	0.490696i
$794$	5.74924	−	3.31932i	0.204033	−	0.117798i
$795$	35.2273	+	47.1692i	1.24938	+	1.67292i
$796$	−1.45532	+	2.52069i	−0.0515824	+	0.0893433i
$797$	−34.0241			−1.20519			−0.602597	−	0.798045i	$-0.705867\pi$
$797$	−34.0241			−1.20519			−0.602597	+	0.798045i	$0.705867\pi$
$798$	−5.36895	−	2.17427i	−0.190059	−	0.0769682i
$799$	4.13759	−	4.13759i	0.146377	−	0.146377i
$800$	−4.56809	−	17.0484i	−0.161506	−	0.602750i
$801$	−0.0520671	+	1.99748i	−0.00183970	+	0.0705774i
$802$	16.1887	+	28.0397i	0.571645	+	0.990117i
$803$	4.28432	−	7.42066i	0.151190	−	0.261870i
$804$	−0.534549	−	4.51407i	−0.0188521	−	0.159199i
$805$	50.5989	−	30.6439i	1.78338	−	1.08005i
$806$	−11.2626	−	9.42781i	−0.396707	−	0.332080i
$807$	2.05578	+	5.15195i	0.0723668	+	0.181357i
$808$	28.5484	+	7.64951i	1.00433	+	0.269109i
$809$	−6.04265	+	3.48873i	−0.212448	+	0.122657i	−0.602449	−	0.798158i	$-0.705808\pi$
$809$	−6.04265	+	3.48873i	−0.212448	+	0.122657i	0.390000	+	0.920815i	$0.372475\pi$
$810$	44.5853	+	2.32594i	1.56657	+	0.0817252i
$811$	13.5578	−	13.5578i	0.476080	−	0.476080i	−0.427796	−	0.903875i	$-0.640710\pi$
$811$	13.5578	−	13.5578i	0.476080	−	0.476080i	0.903875	+	0.427796i	$0.140710\pi$
$812$	0.475576	−	1.93621i	0.0166894	−	0.0679476i
$813$	−1.35233	−	11.4200i	−0.0474284	−	0.400516i
$814$	16.7682	−	4.49303i	0.587726	−	0.157481i
$815$	−60.2095	+	34.7619i	−2.10905	+	1.21766i
$816$	1.43488	−	9.90033i	0.0502307	−	0.346581i
$817$	−6.37969	+	1.70943i	−0.223197	+	0.0598055i
$818$	51.5005			1.80067
$819$	−5.08040	+	28.1636i	−0.177524	+	0.984117i
$820$	−7.43788			−0.259742
$821$	−30.6778	+	8.22009i	−1.07066	+	0.286883i	−0.750765	−	0.660569i	$-0.770315\pi$
$821$	−30.6778	+	8.22009i	−1.07066	+	0.286883i	−0.319897	+	0.947452i	$0.603648\pi$
$822$	−6.23240	+	43.0022i	−0.217380	+	1.49987i
$823$	12.0020	−	6.92934i	0.418362	−	0.241541i	−0.276014	−	0.961154i	$-0.589014\pi$
$823$	12.0020	−	6.92934i	0.418362	−	0.241541i	0.694376	+	0.719612i	$0.255680\pi$
$824$	−32.5171	+	8.71293i	−1.13279	+	0.303529i
$825$	−2.92627	−	24.7113i	−0.101880	−	0.860336i
$826$	18.8543	+	18.0806i	0.656025	+	0.629104i
$827$	8.15226	−	8.15226i	0.283482	−	0.283482i	−0.551014	−	0.834496i	$-0.685759\pi$
$827$	8.15226	−	8.15226i	0.283482	−	0.283482i	0.834496	+	0.551014i	$0.185759\pi$
$828$	−1.61591	+	5.45761i	−0.0561567	+	0.189665i
$829$	−17.9082	+	10.3393i	−0.621978	+	0.359099i	−0.777639	−	0.628711i	$-0.783583\pi$
$829$	−17.9082	+	10.3393i	−0.621978	+	0.359099i	0.155661	+	0.987811i	$0.450249\pi$
$830$	−13.8338	−	3.70676i	−0.480178	−	0.128663i
$831$	14.9299	+	37.4156i	0.517912	+	1.29793i
$832$	20.4669	−	24.4499i	0.709561	−	0.847649i
$833$	10.5240	−	6.67875i	0.364634	−	0.231405i
$834$	−4.81788	−	40.6852i	−0.166830	−	1.40881i
$835$	−21.2682	+	36.8376i	−0.736016	+	1.27482i
$836$	−0.235435	−	0.407785i	−0.00814269	−	0.0141035i
$837$	10.4568	−	12.5775i	0.361440	−	0.434742i
$838$	11.7513	+	43.8565i	0.405943	+	1.51500i
$839$	−23.7018	+	23.7018i	−0.818279	+	0.818279i	−0.985859	−	0.167580i	$-0.946405\pi$
$839$	−23.7018	+	23.7018i	−0.818279	+	0.818279i	0.167580	+	0.985859i	$0.446405\pi$
$840$	−7.31416	−	52.3512i	−0.252362	−	1.80629i
$841$	23.6329			0.814929
$842$	6.57974	−	11.3964i	0.226753	−	0.392747i
$843$	−12.1805	−	16.3097i	−0.419519	−	0.561734i
$844$	−2.11860	+	1.22317i	−0.0729252	+	0.0421034i
$845$	21.1665	+	45.1137i	0.728149	+	1.55196i
$846$	−2.97979	−	12.4052i	−0.102447	−	0.426499i
$847$	6.49830	+	22.3672i	0.223284	+	0.768545i
$848$		−	28.7615i		−	0.987673i
$849$	−12.5583	−	31.4722i	−0.431000	−	1.08012i
$850$	−21.5766	−	5.78144i	−0.740072	−	0.198302i
$851$	−13.6641	+	50.9951i	−0.468399	+	1.74809i
$852$	1.02204	−	2.37924i	0.0350144	−	0.0815115i
$853$	32.3425	+	32.3425i	1.10739	+	1.10739i	0.993493	+	0.113892i	$0.0363319\pi$
$853$	32.3425	+	32.3425i	1.10739	+	1.10739i	0.113892	+	0.993493i	$0.463668\pi$
$854$	32.7109	−	19.8105i	1.11934	−	0.677901i
$855$	−2.62347	−	10.9218i	−0.0897207	−	0.373517i
$856$	50.2884	−	13.4747i	1.71882	−	0.460557i
$857$	23.1753	+	40.1408i	0.791654	+	1.37118i	0.924942	+	0.380107i	$0.124113\pi$
$857$	23.1753	+	40.1408i	0.791654	+	1.37118i	−0.133289	+	0.991077i	$0.542554\pi$
$858$	8.92597	−	7.98662i	0.304728	−	0.272659i
$859$	−5.68192	+	9.84137i	−0.193865	+	0.335783i	−0.946528	−	0.322623i	$-0.895436\pi$
$859$	−5.68192	+	9.84137i	−0.193865	+	0.335783i	0.752663	+	0.658406i	$0.228769\pi$
$860$	−5.96183	−	5.96183i	−0.203297	−	0.203297i
$861$	−27.1295	−	3.35344i	−0.924572	−	0.114285i
$862$		−	32.6656i		−	1.11259i
$863$	3.23552	−	0.866956i	0.110139	−	0.0295115i	−0.203329	−	0.979111i	$-0.565176\pi$
$863$	3.23552	−	0.866956i	0.110139	−	0.0295115i	0.313467	+	0.949599i	$0.398509\pi$
$864$	7.27486	+	6.04823i	0.247496	+	0.205765i
$865$	−19.1180	+	71.3492i	−0.650030	+	2.42594i
$866$	−5.26484	−	19.6487i	−0.178907	−	0.667688i
$867$	−18.8118	−	14.8282i	−0.638881	−	0.503591i
$868$	−2.37395	−	1.30509i	−0.0805772	−	0.0442975i
$869$	16.6365	−	16.6365i	0.564356	−	0.564356i
$870$	−18.4878	+	7.37716i	−0.626795	+	0.250109i
$871$	−16.7136	−	23.8097i	−0.566318	−	0.806760i
$872$	−21.6369	+	12.4921i	−0.732717	+	0.423034i
$873$	−13.8938	+	7.54586i	−0.470233	+	0.255389i
$874$	−7.37275			−0.249387
$875$	−47.5942	+	0.997023i	−1.60898	+	0.0337055i
$876$	3.23477	−	0.383057i	0.109293	−	0.0129423i
$877$	−7.76004	−	28.9609i	−0.262038	−	0.977939i	−0.964038	−	0.265763i	$-0.914376\pi$
$877$	−7.76004	−	28.9609i	−0.262038	−	0.977939i	0.702000	−	0.712177i	$-0.252290\pi$
$878$	13.6748	+	3.66416i	0.461503	+	0.123659i
$879$	−4.55446	−	6.09840i	−0.153618	−	0.205694i
$880$	−9.21363	+	15.9585i	−0.310591	+	0.537960i
$881$	10.4997			0.353745			0.176872	−	0.984234i	$-0.443402\pi$
$881$	10.4997			0.353745			0.176872	+	0.984234i	$0.443402\pi$
$882$	−0.430188	−	27.1729i	−0.0144852	−	0.914959i
$883$			5.98699i			0.201478i	0.994913	+	0.100739i	$0.0321208\pi$
$883$			5.98699i			0.201478i	−0.994913	+	0.100739i	$0.967879\pi$
$884$	0.716562	+	1.96154i	0.0241006	+	0.0659737i
$885$	−7.26568	+	50.1316i	−0.244233	+	1.68516i
$886$	17.2272	+	4.61600i	0.578758	+	0.155078i
$887$	−11.3970	−	6.58006i	−0.382674	−	0.220937i	0.296307	−	0.955093i	$-0.404245\pi$
$887$	−11.3970	−	6.58006i	−0.382674	−	0.220937i	−0.678981	+	0.734156i	$0.737578\pi$
$888$	37.0496	+	29.2040i	1.24330	+	0.980021i
$889$	−23.6642	+	24.6769i	−0.793673	+	0.827637i
$890$	−2.33632	−	2.33632i	−0.0783137	−	0.0783137i
$891$	8.92748	+	9.91021i	0.299082	+	0.332005i
$892$	0.176407	−	0.658360i	0.00590654	−	0.0220435i
$893$	−2.77976	+	1.60489i	−0.0930210	+	0.0537057i
$894$	−5.70380	−	14.2942i	−0.190764	−	0.478070i
$895$	−14.0310	−	14.0310i	−0.469003	−	0.469003i
$896$	−9.94569	+	18.0912i	−0.332262	+	0.604385i
$897$	7.46191	+	35.6530i	0.249146	+	1.19042i
$898$	−15.7822	+	27.3356i	−0.526658	+	0.912199i
$899$	−1.88745	+	7.04406i	−0.0629500	+	0.234933i
$900$	6.86100	−	6.51240i	0.228700	−	0.217080i
$901$	13.6735	+	7.89441i	0.455531	+	0.263001i
$902$	8.08988	+	8.08988i	0.269364	+	0.269364i
$903$	−19.0577	−	24.4336i	−0.634202	−	0.813100i
$904$	17.8878	+	17.8878i	0.594939	+	0.594939i
$905$	−2.64813	−	9.88296i	−0.0880269	−	0.328521i
$906$	−7.96057	−	1.15374i	−0.264472	−	0.0383305i
$907$	−50.0583	+	28.9012i	−1.66216	+	0.959648i	−0.690478	+	0.723354i	$0.742600\pi$
$907$	−50.0583	+	28.9012i	−1.66216	+	0.959648i	−0.971682	+	0.236294i	$0.924067\pi$
$908$	−0.533696	−	1.99178i	−0.0177113	−	0.0660996i
$909$	6.88198	+	28.6504i	0.228261	+	0.950275i
$910$	−27.9935	−	38.1537i	−0.927975	−	1.26478i
$911$		−	21.8759i		−	0.724780i	−0.932027	−	0.362390i	$-0.881961\pi$
$911$		−	21.8759i		−	0.724780i	0.932027	−	0.362390i	$-0.118039\pi$
$912$	−2.16587	+	5.04203i	−0.0717192	+	0.166958i
$913$	−2.13938	−	3.70552i	−0.0708033	−	0.122635i
$914$	−2.63354	−	4.56143i	−0.0871098	−	0.150879i
$915$	68.1363	+	29.2688i	2.25252	+	0.967598i
$916$	−0.0527602	+	0.0527602i	−0.00174325	+	0.00174325i
$917$	−3.20387	−	11.0277i	−0.105801	−	0.364168i
$918$	11.2328	−	4.14627i	0.370737	−	0.136847i
$919$	10.3917	−	17.9989i	0.342789	−	0.593728i	−0.642161	−	0.766570i	$-0.721962\pi$
$919$	10.3917	−	17.9989i	0.342789	−	0.593728i	0.984950	+	0.172842i	$0.0552951\pi$
$920$	−33.6401	−	58.2664i	−1.10908	−	1.92099i
$921$	25.0144	−	18.6815i	0.824252	−	0.615575i
$922$	−9.96241	−	5.75180i	−0.328094	−	0.189425i
$923$	−1.46377	−	16.5069i	−0.0481807	−	0.543331i
$924$	1.33093	−	1.76323i	0.0437845	−	0.0580059i
$925$	62.0432	−	62.0432i	2.03997	−	2.03997i
$926$	−32.2734	−	18.6330i	−1.06057	−	0.612320i
$927$	−23.1052	−	24.3420i	−0.758874	−	0.799495i
$928$	−4.07430	−	1.09171i	−0.133745	−	0.0358370i
$929$	51.7619	−	13.8696i	1.69825	−	0.455045i	0.725754	−	0.687954i	$-0.241491\pi$
$929$	51.7619	−	13.8696i	1.69825	−	0.455045i	0.972499	+	0.232909i	$0.0748243\pi$
$930$	3.18058	+	26.8588i	0.104295	+	0.880736i
$931$	−6.52440	+	2.04464i	−0.213828	+	0.0670104i
$932$			2.24670i			0.0735932i
$933$	−8.99802	+	3.59047i	−0.294582	+	0.117547i
$934$	4.91574	−	18.3458i	0.160848	−	0.600293i
$935$	−5.05789	−	8.76053i	−0.165411	−	0.286500i
$936$	31.9041	+	6.44784i	1.04282	+	0.210754i
$937$	19.4261			0.634624			0.317312	−	0.948321i	$-0.397220\pi$
$937$	19.4261			0.634624			0.317312	+	0.948321i	$0.397220\pi$
$938$	19.9384	+	19.1202i	0.651012	+	0.624296i
$939$	21.5858	+	17.0148i	0.704426	+	0.555257i
$940$	−3.54851	−	2.04873i	−0.115740	−	0.0668223i
$941$	9.75204	−	36.3951i	0.317907	−	1.18645i	−0.603345	−	0.797480i	$-0.706166\pi$
$941$	9.75204	−	36.3951i	0.317907	−	1.18645i	0.921252	−	0.388966i	$-0.127168\pi$
$942$	−26.3330	+	19.6662i	−0.857974	+	0.640759i
$943$	−33.6080	+	9.00523i	−1.09443	+	0.293251i
$944$	17.4990	−	17.4990i	0.569545	−	0.569545i
$945$	42.3838	−	31.3170i	1.37875	−	1.01874i
$946$			12.9689i			0.421655i
$947$	2.99008	+	11.1591i	0.0971644	+	0.362623i	0.997339	−	0.0729072i	$-0.0232277\pi$
$947$	2.99008	+	11.1591i	0.0971644	+	0.362623i	−0.900174	+	0.435530i	$0.856561\pi$
$948$	8.85156	+	1.28288i	0.287485	+	0.0416659i
$949$	17.0620	−	11.9769i	0.553855	−	0.388787i
$950$	10.6117	+	6.12666i	0.344289	+	0.198775i
$951$	2.62229	+	22.1443i	0.0850335	+	0.718077i
$952$	−7.34378	−	12.1260i	−0.238013	−	0.393005i
$953$	−31.4054			−1.01732			−0.508660	−	0.860968i	$-0.669859\pi$
$953$	−31.4054			−1.01732			−0.508660	+	0.860968i	$0.669859\pi$
$954$	30.2511	−	16.4297i	0.979417	−	0.531932i
$955$	−16.9787	−	4.54943i	−0.549418	−	0.147216i
$956$	−5.30593	−	1.42172i	−0.171606	−	0.0459817i
$957$	−5.46408	−	2.34717i	−0.176629	−	0.0758732i
$958$	−27.7149			−0.895427
$959$	26.5690	+	43.8705i	0.857958	+	1.41665i
$960$	−58.3080	+	6.90473i	−1.88188	+	0.222849i
$961$	−18.2655	−	10.5456i	−0.589210	−	0.340180i
$962$	41.6002	+	7.28470i	1.34125	+	0.234868i
$963$	35.7327	+	37.6454i	1.15147	+	1.21311i
$964$	−1.52531	−	5.69252i	−0.0491268	−	0.183344i
$965$			27.2812i			0.878212i
$966$	−13.4897	−	31.8515i	−0.434022	−	1.02480i
$967$	−13.4501	+	13.4501i	−0.432526	+	0.432526i	−0.889487	−	0.456961i	$-0.848938\pi$
$967$	−13.4501	+	13.4501i	−0.432526	+	0.432526i	0.456961	+	0.889487i	$0.348938\pi$
$968$	25.5887	−	6.85647i	0.822452	−	0.220375i
$969$	−1.80255	−	2.41361i	−0.0579063	−	0.0775363i
$970$	6.76651	−	25.2530i	0.217259	−	0.810823i
$971$	34.3678	+	19.8423i	1.10292	+	0.636769i	0.936985	−	0.349368i	$-0.113604\pi$
$971$	34.3678	+	19.8423i	1.10292	+	0.636769i	0.165931	+	0.986137i	$0.446937\pi$
$972$	−0.987739	+	4.97346i	−0.0316817	+	0.159524i
$973$	−34.9037	−	33.4714i	−1.11896	−	1.07304i
$974$	−3.57856			−0.114664
$975$	18.8872	−	57.5166i	0.604874	−	1.84200i
$976$	−18.1144	−	31.3750i	−0.579828	−	1.00429i
$977$	−0.539931	+	2.01505i	−0.0172739	+	0.0644672i	−0.974025	−	0.226441i	$-0.927291\pi$
$977$	−0.539931	+	2.01505i	−0.0172739	+	0.0644672i	0.956751	+	0.290908i	$0.0939575\pi$
$978$	15.0667	+	37.7584i	0.481780	+	1.20738i
$979$		−	0.987117i		−	0.0315484i
$980$	−6.42478	−	5.90785i	−0.205232	−	0.188719i
$981$	−21.2391	−	13.0119i	−0.678113	−	0.415437i
$982$	4.31889	−	1.15724i	0.137821	−	0.0369292i
$983$	11.0216	+	2.95323i	0.351534	+	0.0941933i	0.430265	−	0.902703i	$-0.358420\pi$
$983$	11.0216	+	2.95323i	0.351534	+	0.0941933i	−0.0787308	+	0.996896i	$0.525087\pi$
$984$	−4.45947	+	30.7693i	−0.142163	+	0.980891i
$985$	51.6548	+	29.8229i	1.64586	+	0.950237i
$986$	−3.77481	+	3.77481i	−0.120215	+	0.120215i
$987$	−12.0194	−	9.07259i	−0.382583	−	0.288784i
$988$	−0.101186	−	1.14107i	−0.00321915	−	0.0363022i
$989$	−34.1566	−	19.7203i	−1.08612	−	0.627070i
$990$	−22.0482	−	0.574718i	−0.700739	−	0.0182657i
$991$	−20.4842	−	35.4796i	−0.650701	−	1.12705i	−0.982953	−	0.183856i	$-0.941142\pi$
$991$	−20.4842	−	35.4796i	−0.650701	−	1.12705i	0.332253	−	0.943190i	$-0.392191\pi$
$992$	−2.86564	+	4.96344i	−0.0909842	+	0.157589i
$993$	41.7113	−	4.93939i	1.32367	−	0.156747i
$994$	4.39043	+	15.1119i	0.139256	+	0.479320i
$995$	24.2541	−	24.2541i	0.768908	−	0.768908i
$996$	0.641992	−	1.49452i	0.0203423	−	0.0473558i
$997$	−7.33796	−	12.7097i	−0.232396	−	0.402521i	0.726117	−	0.687571i	$-0.241323\pi$
$997$	−7.33796	−	12.7097i	−0.232396	−	0.402521i	−0.958513	+	0.285050i	$0.907990\pi$
$998$	14.6797	+	25.4260i	0.464679	+	0.804847i
$999$	−7.95654	+	46.3541i	−0.251734	+	1.46658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.44.18	yes	112
3.2	odd	2	inner	273.2.cd.e.44.11	✓	112
7.4	even	3	inner	273.2.cd.e.200.11	yes	112
13.8	odd	4	inner	273.2.cd.e.86.18	yes	112
21.11	odd	6	inner	273.2.cd.e.200.18	yes	112
39.8	even	4	inner	273.2.cd.e.86.11	yes	112
91.60	odd	12	inner	273.2.cd.e.242.11	yes	112
273.242	even	12	inner	273.2.cd.e.242.18	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.11	✓	112	3.2	odd	2	inner
273.2.cd.e.44.18	yes	112	1.1	even	1	trivial
273.2.cd.e.86.11	yes	112	39.8	even	4	inner
273.2.cd.e.86.18	yes	112	13.8	odd	4	inner
273.2.cd.e.200.11	yes	112	7.4	even	3	inner
273.2.cd.e.200.18	yes	112	21.11	odd	6	inner
273.2.cd.e.242.11	yes	112	91.60	odd	12	inner
273.2.cd.e.242.18	yes	112	273.242	even	12	inner

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25001 - 0.334940i) q^{2} +(0.248434 - 1.71414i) q^{3} +(-0.281700 + 0.162639i) q^{4} +(3.70264 - 0.992121i) q^{5} +(-0.263589 - 2.22591i) q^{6} +(-1.90960 - 1.83124i) q^{7} +(-2.12780 + 2.12780i) q^{8} +(-2.87656 - 0.851703i) q^{9} +O(q^{10})\)	\(q+(1.25001 - 0.334940i) q^{2} +(0.248434 - 1.71414i) q^{3} +(-0.281700 + 0.162639i) q^{4} +(3.70264 - 0.992121i) q^{5} +(-0.263589 - 2.22591i) q^{6} +(-1.90960 - 1.83124i) q^{7} +(-2.12780 + 2.12780i) q^{8} +(-2.87656 - 0.851703i) q^{9} +(4.29606 - 2.48033i) q^{10} +(1.43154 + 0.383581i) q^{11} +(0.208803 + 0.523278i) q^{12} +(2.76474 + 2.31435i) q^{13} +(-3.00038 - 1.64947i) q^{14} +(-0.780772 - 6.59333i) q^{15} +(-1.62182 + 2.80907i) q^{16} +(-0.890309 - 1.54206i) q^{17} +(-3.88101 - 0.101164i) q^{18} +(0.252802 + 0.943471i) q^{19} +(-0.881676 + 0.881676i) q^{20} +(-3.61341 + 2.81838i) q^{21} +1.91793 q^{22} +(-2.91637 + 5.05131i) q^{23} +(3.11874 + 4.17597i) q^{24} +(8.39515 - 4.84694i) q^{25} +(4.23114 + 1.96694i) q^{26} +(-2.17457 + 4.71924i) q^{27} +(0.835765 + 0.205282i) q^{28} -2.31669i q^{29} +(-3.18435 - 7.98025i) q^{30} +(-3.04057 - 0.814718i) q^{31} +(0.471235 - 1.75867i) q^{32} +(1.01316 - 2.35857i) q^{33} +(-1.62940 - 1.62940i) q^{34} +(-8.88738 - 4.88586i) q^{35} +(0.948846 - 0.227918i) q^{36} +(8.74289 - 2.34265i) q^{37} +(0.632013 + 1.09468i) q^{38} +(4.65397 - 4.16420i) q^{39} +(-5.76746 + 9.98953i) q^{40} +(4.21804 + 4.21804i) q^{41} +(-3.57282 + 4.73330i) q^{42} +6.76194i q^{43} +(-0.465650 + 0.124771i) q^{44} +(-11.4959 - 0.299656i) q^{45} +(-1.95362 + 7.29102i) q^{46} +(0.850526 + 3.17421i) q^{47} +(4.41223 + 3.47790i) q^{48} +(0.293149 + 6.99386i) q^{49} +(8.87062 - 8.87062i) q^{50} +(-2.86449 + 1.14302i) q^{51} +(-1.15523 - 0.202295i) q^{52} +(-7.67909 + 4.43352i) q^{53} +(-1.13759 + 6.62747i) q^{54} +5.68105 q^{55} +(7.95976 - 0.166744i) q^{56} +(1.68005 - 0.198949i) q^{57} +(-0.775954 - 2.89590i) q^{58} +(-7.36954 - 1.97466i) q^{59} +(1.29228 + 1.73035i) q^{60} +(-5.58459 + 9.67280i) q^{61} -4.07364 q^{62} +(3.93341 + 6.89407i) q^{63} -8.84347i q^{64} +(12.5330 + 5.82625i) q^{65} +(0.476478 - 3.28759i) q^{66} +(-7.79328 - 2.08820i) q^{67} +(0.501599 + 0.289599i) q^{68} +(7.93413 + 6.25399i) q^{69} +(-12.7458 - 3.13066i) q^{70} +(-3.24997 - 3.24997i) q^{71} +(7.93301 - 4.30850i) q^{72} +(1.49640 - 5.58464i) q^{73} +(10.1441 - 5.85669i) q^{74} +(-6.22270 - 15.5946i) q^{75} +(-0.224660 - 0.224660i) q^{76} +(-2.03125 - 3.35398i) q^{77} +(4.42278 - 6.76411i) q^{78} +(7.93757 - 13.7483i) q^{79} +(-3.21808 + 12.0100i) q^{80} +(7.54921 + 4.89995i) q^{81} +(6.68540 + 3.85982i) q^{82} +(-2.04147 - 2.04147i) q^{83} +(0.559515 - 1.38162i) q^{84} +(-4.82641 - 4.82641i) q^{85} +(2.26485 + 8.45252i) q^{86} +(-3.97114 - 0.575545i) q^{87} +(-3.86222 + 2.22986i) q^{88} +(-0.172387 - 0.643357i) q^{89} +(-14.4704 + 3.47586i) q^{90} +(-1.04144 - 9.48237i) q^{91} -1.89727i q^{92} +(-2.15192 + 5.00956i) q^{93} +(2.12634 + 3.68293i) q^{94} +(1.87207 + 3.24253i) q^{95} +(-2.89754 - 1.24468i) q^{96} +(3.72661 - 3.72661i) q^{97} +(2.70897 + 8.64424i) q^{98} +(-3.79122 - 2.32264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

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