LMFDB - Embedded newform 504.2.cc.b.293.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.17
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12177 + 0.861180i) q^{2} +(-0.0157202 + 1.73198i) q^{3} +(0.516736 - 1.93209i) q^{4} +(-1.10228 - 0.636400i) q^{5} +(-1.47391 - 1.95642i) q^{6} +(-1.73258 + 1.99955i) q^{7} +(1.08422 + 2.61237i) q^{8} +(-2.99951 - 0.0544542i) q^{9} +O(q^{10})$	\(q+(-1.12177 + 0.861180i) q^{2} +(-0.0157202 + 1.73198i) q^{3} +(0.516736 - 1.93209i) q^{4} +(-1.10228 - 0.636400i) q^{5} +(-1.47391 - 1.95642i) q^{6} +(-1.73258 + 1.99955i) q^{7} +(1.08422 + 2.61237i) q^{8} +(-2.99951 - 0.0544542i) q^{9} +(1.78456 - 0.235365i) q^{10} +(3.13927 + 5.43737i) q^{11} +(3.33822 + 0.925350i) q^{12} +(1.74580 - 3.02381i) q^{13} +(0.221582 - 3.73509i) q^{14} +(1.11956 - 1.89912i) q^{15} +(-3.46597 - 1.99677i) q^{16} -4.69263 q^{17} +(3.41165 - 2.52203i) q^{18} -3.31331 q^{19} +(-1.79917 + 1.80085i) q^{20} +(-3.43593 - 3.03222i) q^{21} +(-8.20409 - 3.39600i) q^{22} +(-3.77266 - 2.17814i) q^{23} +(-4.54161 + 1.83678i) q^{24} +(-1.68999 - 2.92715i) q^{25} +(0.645662 + 4.89546i) q^{26} +(0.141466 - 5.19423i) q^{27} +(2.96802 + 4.38074i) q^{28} +(1.85192 + 3.20761i) q^{29} +(0.379594 + 3.09452i) q^{30} +(-1.65681 - 0.956557i) q^{31} +(5.60759 - 0.744911i) q^{32} +(-9.46676 + 5.35167i) q^{33} +(5.26405 - 4.04120i) q^{34} +(3.18229 - 1.10144i) q^{35} +(-1.65516 + 5.76719i) q^{36} -5.75725i q^{37} +(3.71677 - 2.85336i) q^{38} +(5.20973 + 3.07122i) q^{39} +(0.467398 - 3.56955i) q^{40} +(-4.50957 + 7.81080i) q^{41} +(6.46562 + 0.442493i) q^{42} +(-3.03629 + 1.75300i) q^{43} +(12.1277 - 3.25567i) q^{44} +(3.27163 + 1.96891i) q^{45} +(6.10783 - 0.805561i) q^{46} +(-4.04334 - 7.00327i) q^{47} +(3.51284 - 5.97159i) q^{48} +(-0.996363 - 6.92873i) q^{49} +(4.41658 + 1.82820i) q^{50} +(0.0737691 - 8.12753i) q^{51} +(-4.94016 - 4.93555i) q^{52} -5.64307 q^{53} +(4.31447 + 5.94856i) q^{54} -7.99132i q^{55} +(-7.10204 - 2.35818i) q^{56} +(0.0520859 - 5.73858i) q^{57} +(-4.83976 - 2.00337i) q^{58} +(6.06444 + 3.50131i) q^{59} +(-3.09075 - 3.14444i) q^{60} +(0.973767 + 1.68661i) q^{61} +(2.68232 - 0.353771i) q^{62} +(5.30575 - 5.90330i) q^{63} +(-5.64893 + 5.66477i) q^{64} +(-3.84870 + 2.22205i) q^{65} +(6.01078 - 14.1559i) q^{66} +(4.62684 + 2.67131i) q^{67} +(-2.42485 + 9.06659i) q^{68} +(3.83181 - 6.49992i) q^{69} +(-2.62126 + 3.97609i) q^{70} +8.38003i q^{71} +(-3.10987 - 7.89485i) q^{72} +10.4345i q^{73} +(4.95803 + 6.45831i) q^{74} +(5.09633 - 2.88101i) q^{75} +(-1.71211 + 6.40162i) q^{76} +(-16.3113 - 3.14355i) q^{77} +(-8.48899 + 1.04132i) q^{78} +(-2.27516 - 3.94070i) q^{79} +(2.54971 + 4.40673i) q^{80} +(8.99407 + 0.326671i) q^{81} +(-1.66781 - 12.6455i) q^{82} +(-7.47660 + 4.31662i) q^{83} +(-7.63400 + 5.07169i) q^{84} +(5.17258 + 2.98639i) q^{85} +(1.89637 - 4.58126i) q^{86} +(-5.58463 + 3.15706i) q^{87} +(-10.8007 + 14.0962i) q^{88} +8.19765 q^{89} +(-5.36560 + 0.608802i) q^{90} +(3.02152 + 8.72978i) q^{91} +(-6.15785 + 6.16360i) q^{92} +(1.68278 - 2.85452i) q^{93} +(10.5668 + 4.37402i) q^{94} +(3.65218 + 2.10859i) q^{95} +(1.20202 + 9.72395i) q^{96} +(-5.08552 + 2.93613i) q^{97} +(7.08457 + 6.91439i) q^{98} +(-9.12016 - 16.4804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.12177	+	0.861180i	−0.793211	+	0.608947i
$2$	−1.12177	+	0.861180i	−0.793211	+	0.608947i
$3$	−0.0157202	+	1.73198i	−0.00907607	+	0.999959i
$3$	−0.0157202	+	1.73198i	−0.00907607	+	0.999959i
$4$	0.516736	−	1.93209i	0.258368	−	0.966047i
$5$	−1.10228	−	0.636400i	−0.492953	−	0.284607i	0.232846	−	0.972514i	$-0.425196\pi$
$5$	−1.10228	−	0.636400i	−0.492953	−	0.284607i	−0.725799	+	0.687907i	$0.758530\pi$
$6$	−1.47391	−	1.95642i	−0.601722	−	0.798705i
$7$	−1.73258	+	1.99955i	−0.654852	+	0.755757i
$7$	−1.73258	+	1.99955i	−0.654852	+	0.755757i
$8$	1.08422	+	2.61237i	0.383330	+	0.923611i
$9$	−2.99951	−	0.0544542i	−0.999835	−	0.0181514i
$10$	1.78456	−	0.235365i	0.564326	−	0.0744289i
$11$	3.13927	+	5.43737i	0.946524	+	1.63943i	0.752670	+	0.658398i	$0.228766\pi$
$11$	3.13927	+	5.43737i	0.946524	+	1.63943i	0.193854	+	0.981030i	$0.437901\pi$
$12$	3.33822	+	0.925350i	0.963662	+	0.267125i
$13$	1.74580	−	3.02381i	0.484197	−	0.838653i	−0.515638	−	0.856806i	$-0.672445\pi$
$13$	1.74580	−	3.02381i	0.484197	−	0.838653i	0.999835	+	0.0181528i	$0.00577854\pi$
$14$	0.221582	−	3.73509i	0.0592204	−	0.998245i
$15$	1.11956	−	1.89912i	0.289069	−	0.490350i
$16$	−3.46597	−	1.99677i	−0.866492	−	0.499191i
$17$	−4.69263			−1.13813			−0.569065	−	0.822293i	$-0.692695\pi$
$17$	−4.69263			−1.13813			−0.569065	+	0.822293i	$0.692695\pi$
$18$	3.41165	−	2.52203i	0.804134	−	0.594448i
$19$	−3.31331			−0.760125			−0.380062	−	0.924961i	$-0.624097\pi$
$19$	−3.31331			−0.760125			−0.380062	+	0.924961i	$0.624097\pi$
$20$	−1.79917	+	1.80085i	−0.402307	+	0.402682i
$21$	−3.43593	−	3.03222i	−0.749782	−	0.661684i
$22$	−8.20409	−	3.39600i	−1.74912	−	0.724030i
$23$	−3.77266	−	2.17814i	−0.786653	−	0.454175i	0.0521296	−	0.998640i	$-0.483399\pi$
$23$	−3.77266	−	2.17814i	−0.786653	−	0.454175i	−0.838783	+	0.544466i	$0.816732\pi$
$24$	−4.54161	+	1.83678i	−0.927052	+	0.374932i
$25$	−1.68999	−	2.92715i	−0.337998	−	0.585430i
$26$	0.645662	+	4.89546i	0.126625	+	0.960079i
$27$	0.141466	−	5.19423i	0.0272252	−	0.999629i
$28$	2.96802	+	4.38074i	0.560904	+	0.827881i
$29$	1.85192	+	3.20761i	0.343892	+	0.595639i	0.985152	−	0.171685i	$-0.0549212\pi$
$29$	1.85192	+	3.20761i	0.343892	+	0.595639i	−0.641260	+	0.767324i	$0.721588\pi$
$30$	0.379594	+	3.09452i	0.0693040	+	0.564979i
$31$	−1.65681	−	0.956557i	−0.297571	−	0.171803i	0.343780	−	0.939050i	$-0.388293\pi$
$31$	−1.65681	−	0.956557i	−0.297571	−	0.171803i	−0.641351	+	0.767247i	$0.721626\pi$
$32$	5.60759	−	0.744911i	0.991292	−	0.131683i
$33$	−9.46676	+	5.35167i	−1.64795	+	0.931606i
$34$	5.26405	−	4.04120i	0.902777	−	0.693060i
$35$	3.18229	−	1.10144i	0.537905	−	0.186178i
$36$	−1.65516	+	5.76719i	−0.275861	+	0.961198i
$37$		−	5.75725i		−	0.946486i	−0.880932	−	0.473243i	$-0.843083\pi$
$37$		−	5.75725i		−	0.946486i	0.880932	−	0.473243i	$-0.156917\pi$
$38$	3.71677	−	2.85336i	0.602940	−	0.462875i
$39$	5.20973	+	3.07122i	0.834224	+	0.491789i
$40$	0.467398	−	3.56955i	0.0739022	−	0.564396i
$41$	−4.50957	+	7.81080i	−0.704276	+	1.21984i	0.262676	+	0.964884i	$0.415395\pi$
$41$	−4.50957	+	7.81080i	−0.704276	+	1.21984i	−0.966952	+	0.254958i	$0.917938\pi$
$42$	6.46562	+	0.442493i	0.997666	+	0.0682781i
$43$	−3.03629	+	1.75300i	−0.463030	+	0.267331i	−0.713318	−	0.700841i	$-0.752808\pi$
$43$	−3.03629	+	1.75300i	−0.463030	+	0.267331i	0.250287	+	0.968172i	$0.419475\pi$
$44$	12.1277	−	3.25567i	1.82832	−	0.490810i
$45$	3.27163	+	1.96891i	0.487706	+	0.293508i
$46$	6.10783	−	0.805561i	0.900550	−	0.118774i
$47$	−4.04334	−	7.00327i	−0.589782	−	1.02153i	−0.994261	−	0.106985i	$-0.965880\pi$
$47$	−4.04334	−	7.00327i	−0.589782	−	1.02153i	0.404479	−	0.914547i	$-0.367453\pi$
$48$	3.51284	−	5.97159i	0.507035	−	0.861925i
$49$	−0.996363	−	6.92873i	−0.142338	−	0.989818i
$50$	4.41658	+	1.82820i	0.624599	+	0.258547i
$51$	0.0737691	−	8.12753i	0.0103297	−	1.13808i
$52$	−4.94016	−	4.93555i	−0.685077	−	0.684438i
$53$	−5.64307			−0.775136			−0.387568	−	0.921841i	$-0.626685\pi$
$53$	−5.64307			−0.775136			−0.387568	+	0.921841i	$0.626685\pi$
$54$	4.31447	+	5.94856i	0.587125	+	0.809496i
$55$		−	7.99132i		−	1.07755i
$56$	−7.10204	−	2.35818i	−0.949050	−	0.315124i
$57$	0.0520859	−	5.73858i	0.00689895	−	0.760093i
$58$	−4.83976	−	2.00337i	−0.635491	−	0.263055i
$59$	6.06444	+	3.50131i	0.789523	+	0.455831i	0.839795	−	0.542904i	$-0.182675\pi$
$59$	6.06444	+	3.50131i	0.789523	+	0.455831i	−0.0502716	+	0.998736i	$0.516009\pi$
$60$	−3.09075	−	3.14444i	−0.399015	−	0.405945i
$61$	0.973767	+	1.68661i	0.124678	+	0.215949i	0.921607	−	0.388124i	$-0.126877\pi$
$61$	0.973767	+	1.68661i	0.124678	+	0.215949i	−0.796929	+	0.604073i	$0.793544\pi$
$62$	2.68232	−	0.353771i	0.340655	−	0.0449290i
$63$	5.30575	−	5.90330i	0.668462	−	0.743746i
$64$	−5.64893	+	5.66477i	−0.706116	+	0.708096i
$65$	−3.84870	+	2.22205i	−0.477373	+	0.275611i
$66$	6.01078	−	14.1559i	0.739876	−	1.74247i
$67$	4.62684	+	2.67131i	0.565258	+	0.326352i	0.755253	−	0.655433i	$-0.227514\pi$
$67$	4.62684	+	2.67131i	0.565258	+	0.326352i	−0.189995	+	0.981785i	$0.560847\pi$
$68$	−2.42485	+	9.06659i	−0.294056	+	1.09949i
$69$	3.83181	−	6.49992i	0.461296	−	0.782499i
$70$	−2.62126	+	3.97609i	−0.313300	+	0.475234i
$71$			8.38003i			0.994527i	0.867600	+	0.497263i	$0.165662\pi$
$71$			8.38003i			0.994527i	−0.867600	+	0.497263i	$0.834338\pi$
$72$	−3.10987	−	7.89485i	−0.366502	−	0.930417i
$73$			10.4345i			1.22126i	0.791915	+	0.610631i	$0.209084\pi$
$73$			10.4345i			1.22126i	−0.791915	+	0.610631i	$0.790916\pi$
$74$	4.95803	+	6.45831i	0.576359	+	0.750763i
$75$	5.09633	−	2.88101i	0.588473	−	0.332671i
$76$	−1.71211	+	6.40162i	−0.196392	+	0.734316i
$77$	−16.3113	−	3.14355i	−1.85884	−	0.358241i
$78$	−8.48899	+	1.04132i	−0.961189	+	0.117906i
$79$	−2.27516	−	3.94070i	−0.255976	−	0.443363i	0.709184	−	0.705023i	$-0.249063\pi$
$79$	−2.27516	−	3.94070i	−0.255976	−	0.443363i	−0.965160	+	0.261660i	$0.915730\pi$
$80$	2.54971	+	4.40673i	0.285067	+	0.492687i
$81$	8.99407	+	0.326671i	0.999341	+	0.0362968i
$82$	−1.66781	−	12.6455i	−0.184179	−	1.39646i
$83$	−7.47660	+	4.31662i	−0.820663	+	0.473810i	−0.850645	−	0.525740i	$-0.823788\pi$
$83$	−7.47660	+	4.31662i	−0.820663	+	0.473810i	0.0299820	+	0.999550i	$0.490455\pi$
$84$	−7.63400	+	5.07169i	−0.832938	+	0.553367i
$85$	5.17258	+	2.98639i	0.561045	+	0.323919i
$86$	1.89637	−	4.58126i	0.204491	−	0.494010i
$87$	−5.58463	+	3.15706i	−0.598735	+	0.338472i
$88$	−10.8007	+	14.0962i	−1.15136	+	1.50266i
$89$	8.19765			0.868950			0.434475	−	0.900684i	$-0.356934\pi$
$89$	8.19765			0.868950			0.434475	+	0.900684i	$0.356934\pi$
$90$	−5.36560	+	0.608802i	−0.565584	+	0.0641734i
$91$	3.02152	+	8.72978i	0.316741	+	0.915129i
$92$	−6.15785	+	6.16360i	−0.642000	+	0.642600i
$93$	1.68278	−	2.85452i	0.174496	−	0.296000i
$94$	10.5668	+	4.37402i	1.08988	+	0.451145i
$95$	3.65218	+	2.10859i	0.374706	+	0.216337i
$96$	1.20202	+	9.72395i	0.122680	+	0.992446i
$97$	−5.08552	+	2.93613i	−0.516357	+	0.298119i	−0.735443	−	0.677587i	$-0.763026\pi$
$97$	−5.08552	+	2.93613i	−0.516357	+	0.298119i	0.219086	+	0.975706i	$0.429692\pi$
$98$	7.08457	+	6.91439i	0.715650	+	0.698459i
$99$	−9.12016	−	16.4804i	−0.916610	−	1.65634i
$100$	−6.52880	+	1.75265i	−0.652880	+	0.175265i
$101$	4.24754	−	2.45232i	0.422646	−	0.244015i	−0.273563	−	0.961854i	$-0.588202\pi$
$101$	4.24754	−	2.45232i	0.422646	−	0.244015i	0.696209	+	0.717840i	$0.254869\pi$
$102$	6.91652	+	9.18075i	0.684838	+	0.909030i
$103$	13.4323	+	7.75514i	1.32352	+	0.764137i	0.984289	−	0.176565i	$-0.0564986\pi$
$103$	13.4323	+	7.75514i	1.32352	+	0.764137i	0.339235	+	0.940702i	$0.389832\pi$
$104$	9.79213	+	1.28218i	0.960197	+	0.125729i
$105$	1.85765	+	5.52897i	0.181288	+	0.539573i
$106$	6.33023	−	4.85971i	0.614847	−	0.472016i
$107$	0.101350			0.00979788			0.00489894	−	0.999988i	$-0.498441\pi$
$107$	0.101350			0.00979788			0.00489894	+	0.999988i	$0.498441\pi$
$108$	−9.96263	−	2.95737i	−0.958654	−	0.284573i
$109$			0.947778i			0.0907807i	0.998969	+	0.0453904i	$0.0144532\pi$
$109$			0.947778i			0.0907807i	−0.998969	+	0.0453904i	$0.985547\pi$
$110$	6.88196	+	8.96442i	0.656170	+	0.854724i
$111$	9.97143	+	0.0905052i	0.946447	+	0.00859037i
$112$	9.99767	−	3.47081i	0.944691	−	0.327961i
$113$	−14.5062	−	8.37517i	−1.36463	−	0.787870i	−0.374394	−	0.927270i	$-0.622149\pi$
$113$	−14.5062	−	8.37517i	−1.36463	−	0.787870i	−0.990236	+	0.139400i	$0.955483\pi$
$114$	4.88352	+	6.48222i	0.457384	+	0.607116i
$115$	2.77234	+	4.80184i	0.258522	+	0.447774i
$116$	7.15436	−	1.92058i	0.664266	−	0.178322i
$117$	−5.40119	+	8.97486i	−0.499340	+	0.829726i
$118$	−9.81817	+	1.29492i	−0.903835	+	0.119207i
$119$	8.13033	−	9.38312i	0.745306	−	0.860149i
$120$	6.17504	+	0.865639i	0.563702	+	0.0790216i
$121$	−14.2100	+	24.6124i	−1.29182	+	2.23749i
$122$	−2.54482	−	1.05340i	−0.230397	−	0.0953707i
$123$	−13.4573	−	7.93327i	−1.21340	−	0.715319i
$124$	−2.70429	+	2.70681i	−0.242852	+	0.243079i
$125$			10.6660i			0.953999i
$126$	−0.868029	+	11.1914i	−0.0773302	+	0.997006i
$127$	−3.07181			−0.272579			−0.136290	−	0.990669i	$-0.543518\pi$
$127$	−3.07181			−0.272579			−0.136290	+	0.990669i	$0.543518\pi$
$128$	1.45841	−	11.2193i	0.128907	−	0.991657i
$129$	−2.98844	−	5.28636i	−0.263117	−	0.465438i
$130$	2.40377	−	5.80706i	0.210825	−	0.509313i
$131$	−4.00339	−	2.31136i	−0.349778	−	0.201944i	0.314809	−	0.949155i	$-0.398059\pi$
$131$	−4.00339	−	2.31136i	−0.349778	−	0.201944i	−0.664587	+	0.747210i	$0.731393\pi$
$132$	5.44810	+	21.0561i	0.474196	+	1.83270i
$133$	5.74056	−	6.62511i	0.497769	−	0.574470i
$134$	−7.49073	+	0.987951i	−0.647100	+	0.0853460i
$135$	−3.46154	+	5.63545i	−0.297922	+	0.485022i
$136$	−5.08785	−	12.2589i	−0.436279	−	1.05119i
$137$	6.29625	−	3.63514i	0.537925	−	0.310571i	−0.206312	−	0.978486i	$-0.566146\pi$
$137$	6.29625	−	3.63514i	0.537925	−	0.310571i	0.744238	+	0.667915i	$0.232813\pi$
$138$	1.29920	+	10.5913i	0.110595	+	0.901591i
$139$	−5.40059	+	9.35409i	−0.458072	+	0.793403i	−0.998859	−	0.0477559i	$-0.984793\pi$
$139$	−5.40059	+	9.35409i	−0.458072	+	0.793403i	0.540787	+	0.841159i	$0.318126\pi$
$140$	−0.483683	−	6.71763i	−0.0408787	−	0.567744i
$141$	12.1931	−	6.89289i	1.02684	−	0.580486i
$142$	−7.21672	−	9.40047i	−0.605614	−	0.788870i
$143$	21.9221			1.83322
$144$	10.2875	+	6.17805i	0.857288	+	0.514837i
$145$		−	4.71424i		−	0.391496i
$146$	−8.98596	−	11.7051i	−0.743683	−	0.968719i
$147$	12.0161	−	1.61676i	0.991069	−	0.133348i
$148$	−11.1235	−	2.97498i	−0.914349	−	0.244542i
$149$	−11.0512	+	19.1412i	−0.905347	+	1.56811i	−0.0848967	+	0.996390i	$0.527056\pi$
$149$	−11.0512	+	19.1412i	−0.905347	+	1.56811i	−0.820450	+	0.571718i	$0.806277\pi$
$150$	−3.23584	+	7.62069i	−0.264205	+	0.622227i
$151$	4.55315	+	7.88628i	0.370530	+	0.641777i	0.989647	−	0.143522i	$-0.0458428\pi$
$151$	4.55315	+	7.88628i	0.370530	+	0.641777i	−0.619117	+	0.785299i	$0.712509\pi$
$152$	−3.59236	−	8.65558i	−0.291379	−	0.702060i
$153$	14.0756	+	0.255533i	1.13794	+	0.0206586i
$154$	21.0047	−	10.5206i	1.69260	−	0.847776i
$155$	1.21751	+	2.10878i	0.0977924	+	0.169381i
$156$	8.62594	−	8.47867i	0.690628	−	0.678837i
$157$	−11.6887	+	20.2454i	−0.932860	+	1.61576i	−0.154454	+	0.988000i	$0.549362\pi$
$157$	−11.6887	+	20.2454i	−0.932860	+	1.61576i	−0.778406	+	0.627761i	$0.783972\pi$
$158$	5.94586	+	2.46123i	0.473027	+	0.195805i
$159$	0.0887104	−	9.77369i	0.00703519	−	0.775104i
$160$	−6.65518	−	2.74757i	−0.526138	−	0.217215i
$161$	10.8917	−	3.76980i	0.858387	−	0.297102i
$162$	−10.3706	+	7.37907i	−0.814791	+	0.579754i
$163$			13.7674i			1.07835i	0.842194	+	0.539175i	$0.181264\pi$
$163$			13.7674i			1.07835i	−0.842194	+	0.539175i	$0.818736\pi$
$164$	12.7609	+	12.7490i	0.996462	+	0.995532i
$165$	13.8408	+	0.125625i	1.07750	+	0.00977991i
$166$	4.66964	−	11.2809i	0.362434	−	0.875571i
$167$	−0.0915189	+	0.158515i	−0.00708195	+	0.0122663i	−0.869545	−	0.493854i	$-0.835588\pi$
$167$	−0.0915189	+	0.158515i	−0.00708195	+	0.0122663i	0.862463	+	0.506121i	$0.168921\pi$
$168$	4.19596	−	12.2635i	0.323725	−	0.946151i
$169$	0.404390	+	0.700424i	0.0311069	+	0.0538788i
$170$	−8.37426	+	1.10448i	−0.642276	+	0.0847098i
$171$	9.93828	+	0.180423i	0.760000	+	0.0137973i
$172$	1.81800	+	6.77224i	0.138622	+	0.516379i
$173$	9.34311	−	5.39425i	0.710343	−	0.410117i	−0.100845	−	0.994902i	$-0.532155\pi$
$173$	9.34311	−	5.39425i	0.710343	−	0.410117i	0.811188	+	0.584785i	$0.198821\pi$
$174$	3.54588	−	8.35087i	0.268812	−	0.633078i
$175$	8.78100	+	1.69230i	0.663781	+	0.127925i
$176$	−0.0234415	−	25.1141i	−0.00176697	−	1.89305i
$177$	−6.15953	+	10.4484i	−0.462978	+	0.785353i
$178$	−9.19588	+	7.05966i	−0.689261	+	0.529144i
$179$	−2.16504			−0.161822			−0.0809112	−	0.996721i	$-0.525783\pi$
$179$	−2.16504			−0.161822			−0.0809112	+	0.996721i	$0.525783\pi$
$180$	5.49469	−	5.30369i	0.409550	−	0.395314i
$181$	13.5557			1.00759			0.503793	−	0.863824i	$-0.331937\pi$
$181$	13.5557			1.00759			0.503793	+	0.863824i	$0.331937\pi$
$182$	−10.9074	−	7.19073i	−0.808507	−	0.533012i
$183$	−2.93649	+	1.66003i	−0.217072	+	0.122713i
$184$	1.59972	−	12.2172i	0.117933	−	0.900661i
$185$	−3.66391	+	6.34608i	−0.269376	+	0.466573i
$186$	0.570558	+	4.65129i	0.0418353	+	0.341049i
$187$	−14.7314	−	25.5155i	−1.07727	−	1.86588i
$188$	−15.6203	+	4.19327i	−1.13923	+	0.305825i
$189$	10.1410	+	9.28226i	0.737648	+	0.675185i
$190$	−5.91278	+	0.779836i	−0.428958	+	0.0565753i
$191$	−4.82469	+	2.78554i	−0.349103	+	0.201555i	−0.664290	−	0.747475i	$-0.731266\pi$
$191$	−4.82469	+	2.78554i	−0.349103	+	0.201555i	0.315187	+	0.949029i	$0.397933\pi$
$192$	−9.72246	−	9.87288i	−0.701658	−	0.712514i
$193$	10.2386	−	17.7338i	0.736990	−	1.27650i	−0.216854	−	0.976204i	$-0.569580\pi$
$193$	10.2386	−	17.7338i	0.736990	−	1.27650i	0.953845	−	0.300301i	$-0.0970870\pi$
$194$	3.17625	−	7.67321i	0.228042	−	0.550905i
$195$	−3.78804	−	6.70080i	−0.271267	−	0.479855i
$196$	−13.9018	−	1.65526i	−0.992986	−	0.118233i
$197$	−25.8582			−1.84232			−0.921161	−	0.389183i	$-0.872758\pi$
$197$	−25.8582			−1.84232			−0.921161	+	0.389183i	$0.872758\pi$
$198$	24.4233	+	10.6331i	1.73569	+	0.755660i
$199$		−	25.8157i		−	1.83003i	−0.403423	−	0.915013i	$-0.632180\pi$
$199$		−	25.8157i		−	1.83003i	0.403423	−	0.915013i	$-0.367820\pi$
$200$	5.81447	−	7.58855i	0.411145	−	0.536592i
$201$	−4.69938	+	7.97160i	−0.331469	+	0.562273i
$202$	−2.65287	+	6.40883i	−0.186655	+	0.450924i
$203$	−9.62235	−	1.85444i	−0.675357	−	0.130156i
$204$	−15.6650	−	4.34232i	−1.09677	−	0.304023i
$205$	9.94159	−	5.73978i	0.694351	−	0.400883i
$206$	−21.7465	+	2.86815i	−1.51515	+	0.199833i
$207$	11.1975	+	6.73880i	0.778280	+	0.468379i
$208$	−12.0887	+	6.99447i	−0.838201	+	0.484979i
$209$	−10.4014	−	18.0157i	−0.719477	−	1.24617i
$210$	−6.84530	−	4.60247i	−0.472370	−	0.317600i
$211$	17.9224	+	10.3475i	1.23383	+	0.712351i	0.967826	−	0.251621i	$-0.0809636\pi$
$211$	17.9224	+	10.3475i	1.23383	+	0.712351i	0.266003	+	0.963972i	$0.414297\pi$
$212$	−2.91598	+	10.9029i	−0.200270	+	0.748817i
$213$	−14.5140	−	0.131736i	−0.994486	−	0.00902640i
$214$	−0.113691	+	0.0872807i	−0.00777179	+	0.00596639i
$215$	4.46245			0.304336
$216$	13.7226	−	5.26213i	0.933705	−	0.358042i
$217$	4.78322	−	1.65555i	0.324706	−	0.112386i
$218$	−0.816208	−	1.06319i	−0.0552806	−	0.0720083i
$219$	−18.0723	−	0.164032i	−1.22121	−	0.0110843i
$220$	−15.4400	−	4.12940i	−1.04096	−	0.278404i
$221$	−8.19237	+	14.1896i	−0.551079	+	0.954496i
$222$	−11.2636	+	8.48568i	−0.755963	+	0.569521i
$223$	−13.2687	+	7.66067i	−0.888536	+	0.512996i	−0.873463	−	0.486890i	$-0.838131\pi$
$223$	−13.2687	+	7.66067i	−0.888536	+	0.512996i	−0.0150725	+	0.999886i	$0.504798\pi$
$224$	−8.22610	+	12.5033i	−0.549629	+	0.835409i
$225$	4.90974	+	8.87203i	0.327316	+	0.591468i
$226$	23.4852	−	3.09746i	1.56221	−	0.206040i
$227$	18.4876	−	10.6738i	1.22706	−	0.708446i	0.260650	−	0.965433i	$-0.416063\pi$
$227$	18.4876	−	10.6738i	1.22706	−	0.708446i	0.966415	+	0.256987i	$0.0827299\pi$
$228$	−11.0606	−	3.06597i	−0.732503	−	0.203049i
$229$	4.11091	−	7.12030i	0.271656	−	0.470523i	−0.697630	−	0.716458i	$-0.745762\pi$
$229$	4.11091	−	7.12030i	0.271656	−	0.470523i	0.969286	+	0.245936i	$0.0790953\pi$
$230$	−7.24518	−	2.99907i	−0.477733	−	0.197753i
$231$	5.70098	−	28.2014i	0.375097	−	1.85551i
$232$	−6.37158	+	8.31565i	−0.418314	+	0.545949i
$233$			10.1986i			0.668134i	0.942549	+	0.334067i	$0.108421\pi$
$233$			10.1986i			0.668134i	−0.942549	+	0.334067i	$0.891579\pi$
$234$	−1.67009	−	14.7191i	−0.109177	−	0.962220i
$235$			10.2927i			0.671424i
$236$	9.89857	−	9.90781i	0.644342	−	0.644944i
$237$	6.86097	−	3.87859i	0.445668	−	0.251941i
$238$	−1.03980	+	17.5274i	−0.0674005	+	1.13613i
$239$	−1.81305	−	1.04676i	−0.117276	−	0.0677096i	0.440214	−	0.897893i	$-0.354902\pi$
$239$	−1.81305	−	1.04676i	−0.117276	−	0.0677096i	−0.557491	+	0.830183i	$0.688236\pi$
$240$	−7.67245	+	4.34678i	−0.495254	+	0.280583i
$241$	2.96166	−	1.70991i	0.190777	−	0.110145i	−0.401569	−	0.915829i	$-0.631535\pi$
$241$	2.96166	−	1.70991i	0.190777	−	0.110145i	0.592346	+	0.805683i	$0.298202\pi$
$242$	−5.25539	−	39.8468i	−0.337830	−	2.56145i
$243$	−0.707177	+	15.5724i	−0.0453654	+	0.998970i
$244$	3.76188	−	1.00987i	0.240830	−	0.0646506i
$245$	−3.31117	+	8.27146i	−0.211543	+	0.528444i
$246$	21.9279	−	2.68982i	1.39807	−	0.171497i
$247$	−5.78436	+	10.0188i	−0.368050	+	0.637481i
$248$	0.702535	−	5.36531i	0.0446110	−	0.340697i
$249$	−7.35875	−	13.0172i	−0.466342	−	0.824930i
$250$	−9.18538	−	11.9648i	−0.580935	−	0.756723i
$251$			15.4144i			0.972948i	0.873695	+	0.486474i	$0.161717\pi$
$251$			15.4144i			0.972948i	−0.873695	+	0.486474i	$0.838283\pi$
$252$	−8.66405	−	13.3017i	−0.545784	−	0.837926i
$253$		−	27.3511i		−	1.71955i
$254$	3.44586	−	2.64538i	0.216213	−	0.165986i
$255$	−5.25368	+	8.91185i	−0.328998	+	0.558082i
$256$	8.02585	+	13.8414i	0.501616	+	0.865090i
$257$	0.288031	−	0.498884i	0.0179669	−	0.0311195i	−0.856902	−	0.515479i	$-0.827614\pi$
$257$	0.288031	−	0.498884i	0.0179669	−	0.0311195i	0.874869	+	0.484360i	$0.160947\pi$
$258$	7.90485	+	3.35649i	0.492134	+	0.208966i
$259$	11.5119	+	9.97487i	0.715313	+	0.619808i
$260$	2.30444	+	8.58427i	0.142915	+	0.532374i
$261$	−5.38016	−	9.72210i	−0.333024	−	0.601783i
$262$	6.48138	−	0.854829i	0.400421	−	0.0528115i
$263$	−20.8885	+	12.0600i	−1.28804	+	0.743651i	−0.978305	−	0.207171i	$-0.933574\pi$
$263$	−20.8885	+	12.0600i	−1.28804	+	0.743651i	−0.309737	+	0.950822i	$0.600241\pi$
$264$	−24.2446	−	18.9283i	−1.49215	−	1.16495i
$265$	6.22023	+	3.59125i	0.382106	+	0.220609i
$266$	−0.734170	+	12.3755i	−0.0450149	+	0.758791i
$267$	−0.128869	+	14.1982i	−0.00788665	+	0.868914i
$268$	7.55207	−	7.55912i	0.461316	−	0.461747i
$269$		−	26.4734i		−	1.61411i	−0.590476	−	0.807055i	$-0.701060\pi$
$269$		−	26.4734i		−	1.61411i	0.590476	−	0.807055i	$-0.298940\pi$
$270$	−0.970084	−	9.30269i	−0.0590374	−	0.566144i
$271$		−	10.0266i		−	0.609074i	−0.952500	−	0.304537i	$-0.901498\pi$
$271$		−	10.0266i		−	0.609074i	0.952500	−	0.304537i	$-0.0985018\pi$
$272$	16.2645	+	9.37008i	0.986180	+	0.568144i
$273$	−15.1673	+	5.09597i	−0.917966	+	0.308422i
$274$	−3.93244	+	9.50001i	−0.237567	+	0.573916i
$275$	10.6107	−	18.3782i	0.639847	−	1.10825i
$276$	−10.5784	−	10.7622i	−0.636746	−	0.647806i
$277$	20.3678	−	11.7593i	1.22378	−	0.706550i	0.258059	−	0.966129i	$-0.416917\pi$
$277$	20.3678	−	11.7593i	1.22378	−	0.706550i	0.965722	+	0.259579i	$0.0835839\pi$
$278$	−1.99734	−	15.1440i	−0.119793	−	0.908278i
$279$	4.91751	+	2.95942i	0.294404	+	0.177176i
$280$	6.32768	+	7.11910i	0.378151	+	0.425448i
$281$	11.6875	−	6.74780i	0.697220	−	0.402540i	−0.109091	−	0.994032i	$-0.534794\pi$
$281$	11.6875	−	6.74780i	0.697220	−	0.402540i	0.806311	+	0.591492i	$0.201461\pi$
$282$	−7.74182	+	18.2327i	−0.461018	+	1.08574i
$283$	−7.03951	+	12.1928i	−0.418455	+	0.724786i	−0.995784	−	0.0917258i	$-0.970762\pi$
$283$	−7.03951	+	12.1928i	−0.418455	+	0.724786i	0.577329	+	0.816512i	$0.304095\pi$
$284$	16.1910	+	4.33027i	0.960759	+	0.256954i
$285$	−3.70944	+	6.29236i	−0.219729	+	0.372727i
$286$	−24.5915	+	18.8789i	−1.45413	+	1.11633i
$287$	−7.80488	−	22.5499i	−0.460708	−	1.33108i
$288$	−16.8606	+	1.92901i	−0.993519	+	0.113668i
$289$	5.02075			0.295339
$290$	4.05981	+	5.28829i	0.238400	+	0.310539i
$291$	−5.00537	−	8.85418i	−0.293420	−	0.519041i
$292$	20.1604	+	5.39187i	1.17980	+	0.315535i
$293$	7.36385	+	4.25152i	0.430200	+	0.248376i	0.699432	−	0.714699i	$-0.253436\pi$
$293$	7.36385	+	4.25152i	0.430200	+	0.248376i	−0.269232	+	0.963075i	$0.586770\pi$
$294$	−12.0870	+	12.1616i	−0.704926	+	0.709281i
$295$	−4.45646	−	7.71882i	−0.259465	−	0.449407i
$296$	15.0400	−	6.24213i	0.874185	−	0.362816i
$297$	28.6870	−	15.5369i	1.66459	−	0.901540i
$298$	−4.08714	−	30.9891i	−0.236762	−	1.79515i
$299$	−13.1726	+	7.60520i	−0.761790	+	0.439820i
$300$	−2.93293	−	11.3353i	−0.169333	−	0.654444i
$301$	1.75540	−	9.10842i	0.101179	−	0.525001i
$302$	−11.8991	−	4.92551i	−0.684716	−	0.283432i
$303$	4.18059	+	7.39519i	0.240169	+	0.424843i
$304$	11.4838	+	6.61590i	0.658642	+	0.379448i
$305$		−	2.47882i		−	0.141937i
$306$	−16.0096	+	11.8350i	−0.915208	+	0.676559i
$307$	14.7932			0.844292			0.422146	−	0.906528i	$-0.361277\pi$
$307$	14.7932			0.844292			0.422146	+	0.906528i	$0.361277\pi$
$308$	−14.5023	+	29.8905i	−0.826343	+	1.70317i
$309$	−13.6429	+	23.1426i	−0.776118	+	1.31653i
$310$	−3.18180	−	1.31708i	−0.180714	−	0.0748049i
$311$	−9.69605	+	16.7940i	−0.549812	+	0.952303i	0.448475	+	0.893796i	$0.351967\pi$
$311$	−9.69605	+	16.7940i	−0.549812	+	0.952303i	−0.998287	+	0.0585073i	$0.981366\pi$
$312$	−2.37465	+	16.9396i	−0.134438	+	0.959016i
$313$	10.7235	−	6.19124i	0.606131	−	0.349950i	−0.165319	−	0.986240i	$-0.552865\pi$
$313$	10.7235	−	6.19124i	0.606131	−	0.349950i	0.771450	+	0.636290i	$0.219532\pi$
$314$	−4.32293	−	32.7768i	−0.243957	−	1.84970i
$315$	−9.60527	+	3.13049i	−0.541196	+	0.176383i
$316$	−8.78945	+	2.35952i	−0.494445	+	0.132734i
$317$	−15.2671	−	26.4434i	−0.857485	−	1.48521i	−0.874321	−	0.485349i	$-0.838693\pi$
$317$	−15.2671	−	26.4434i	−0.857485	−	1.48521i	0.0168358	−	0.999858i	$-0.494641\pi$
$318$	8.31740	+	11.0402i	0.466417	+	0.619105i
$319$	−11.6273	+	20.1391i	−0.651005	+	1.12757i
$320$	9.83174	−	2.64917i	0.549611	−	0.148093i
$321$	−0.00159325	+	0.175536i	−8.89263e−5	+	0.00979748i
$322$	−8.97152	+	13.6086i	−0.499963	+	0.758376i
$323$	15.5481			0.865120
$324$	5.27872	−	17.2086i	0.293262	−	0.956032i
$325$	−11.8015			−0.654630
$326$	−11.8562	−	15.4439i	−0.656657	−	0.855359i
$327$	−1.64153	−	0.0148993i	−0.0907770	−	0.000823932i
$328$	−25.2941	−	3.31201i	−1.39663	−	0.182875i
$329$	21.0088	+	4.04886i	1.15825	+	0.223221i
$330$	−15.6344	+	11.7785i	−0.860644	+	0.648385i
$331$	−0.609148	+	0.351692i	−0.0334818	+	0.0193307i	−0.516647	−	0.856198i	$-0.672820\pi$
$331$	−0.609148	+	0.351692i	−0.0334818	+	0.0193307i	0.483166	+	0.875529i	$0.339487\pi$
$332$	4.47667	+	16.6760i	0.245689	+	0.915216i
$333$	−0.313506	+	17.2689i	−0.0171800	+	0.946330i
$334$	−0.0338472	−	0.256632i	−0.00185204	−	0.0140423i
$335$	−3.40004	−	5.88904i	−0.185764	−	0.321753i
$336$	5.85421	+	17.3703i	0.319373	+	0.947629i
$337$	4.19417	−	7.26452i	0.228471	−	0.395724i	−0.728884	−	0.684637i	$-0.759961\pi$
$337$	4.19417	−	7.26452i	0.228471	−	0.395724i	0.957355	+	0.288914i	$0.0932940\pi$
$338$	−1.05682	−	0.437462i	−0.0574836	−	0.0237948i
$339$	14.7337	−	24.9928i	0.800223	−	1.35742i
$340$	8.44284	−	8.45072i	0.457877	−	0.458305i
$341$		−	12.0116i		−	0.650462i
$342$	−11.3038	+	8.35626i	−0.611242	+	0.451855i
$343$	15.5806	+	10.0123i	0.841272	+	0.540612i
$344$	−7.87151	−	6.03127i	−0.424403	−	0.325184i
$345$	−8.36027	+	4.72615i	−0.450102	+	0.254448i
$346$	−5.83540	+	14.0972i	−0.313713	+	0.757870i
$347$	10.0003	−	17.3210i	0.536843	−	0.929839i	−0.462229	−	0.886761i	$-0.652950\pi$
$347$	10.0003	−	17.3210i	0.536843	−	0.929839i	0.999072	−	0.0430784i	$-0.0137165\pi$
$348$	3.21394	+	12.4214i	0.172285	+	0.665857i
$349$	12.6341	+	21.8830i	0.676290	+	1.17137i	0.976090	+	0.217367i	$0.0697467\pi$
$349$	12.6341	+	21.8830i	0.676290	+	1.17137i	−0.299800	+	0.954002i	$0.596920\pi$
$350$	−11.3076	+	5.66366i	−0.604419	+	0.302735i
$351$	−15.4594	−	9.49583i	−0.825160	−	0.506850i
$352$	21.6541	+	28.1521i	1.15417	+	1.50051i
$353$	−3.69854	−	6.40606i	−0.196854	−	0.340960i	0.750653	−	0.660697i	$-0.229739\pi$
$353$	−3.69854	−	6.40606i	−0.196854	−	0.340960i	−0.947507	+	0.319736i	$0.896406\pi$
$354$	−2.08843	−	17.0252i	−0.110999	−	0.904880i
$355$	5.33305	−	9.23712i	0.283049	−	0.490255i
$356$	4.23603	−	15.8386i	0.224509	−	0.839446i
$357$	16.1236	+	14.2291i	0.853349	+	0.753082i
$358$	2.42867	−	1.86449i	0.128359	−	0.0985413i
$359$		−	0.116139i		−	0.00612960i	−0.999995	−	0.00306480i	$-0.999024\pi$
$359$		−	0.116139i		−	0.00612960i	0.999995	−	0.00306480i	$-0.000975558\pi$
$360$	−1.59634	+	10.6814i	−0.0841346	+	0.562961i
$361$	−8.02200			−0.422210
$362$	−15.2064	+	11.6739i	−0.799229	+	0.613566i
$363$	−42.4048	−	24.9983i	−2.22568	−	1.31207i
$364$	18.4281	−	1.32686i	0.965893	−	0.0695463i
$365$	6.64049	−	11.5017i	0.347579	−	0.602025i
$366$	1.86448	−	4.39102i	0.0974579	−	0.229522i
$367$	−17.2380	+	9.95237i	−0.899817	+	0.519510i	−0.877141	−	0.480233i	$-0.840552\pi$
$367$	−17.2380	+	9.95237i	−0.899817	+	0.519510i	−0.0226761	+	0.999743i	$0.507219\pi$
$368$	8.72666	+	15.0825i	0.454909	+	0.786229i
$369$	13.9518	−	23.1830i	0.726302	−	1.20686i
$370$	−1.35505	−	10.2741i	−0.0704459	−	0.534127i
$371$	9.77705	−	11.2836i	0.507599	−	0.585814i
$372$	−4.64564	−	4.72633i	−0.240865	−	0.245049i
$373$	−14.7253	−	8.50167i	−0.762448	−	0.440200i	0.0677258	−	0.997704i	$-0.478426\pi$
$373$	−14.7253	−	8.50167i	−0.762448	−	0.440200i	−0.830174	+	0.557504i	$0.811759\pi$
$374$	38.4987	+	15.9362i	1.99072	+	0.824040i
$375$	−18.4734	−	0.167672i	−0.953960	−	0.00865857i
$376$	13.9112	−	18.1558i	0.717418	−	0.936313i
$377$	12.9323			0.666046
$378$	−19.3696	−	1.67934i	−0.996263	−	0.0863759i
$379$		−	2.01228i		−	0.103364i	−0.998664	−	0.0516821i	$-0.983542\pi$
$379$		−	2.01228i		−	0.103364i	0.998664	−	0.0516821i	$-0.0164582\pi$
$380$	5.96120	−	5.96677i	0.305803	−	0.306089i
$381$	0.0482895	−	5.32031i	0.00247395	−	0.272568i
$382$	3.01335	−	7.27967i	0.154176	−	0.372460i
$383$	−15.6332	+	27.0775i	−0.798819	+	1.38359i	0.121567	+	0.992583i	$0.461208\pi$
$383$	−15.6332	+	27.0775i	−0.798819	+	1.38359i	−0.920386	+	0.391012i	$0.872125\pi$
$384$	19.4087	+	2.70231i	0.990446	+	0.137902i
$385$	15.9790	+	13.8456i	0.814365	+	0.705635i
$386$	3.78662	+	28.7105i	0.192734	+	1.46133i
$387$	9.20284	−	5.09281i	0.467807	−	0.258882i
$388$	3.04500	+	11.3429i	0.154586	+	0.575849i
$389$	−6.77013	−	11.7262i	−0.343259	−	0.594543i	0.641777	−	0.766892i	$-0.278198\pi$
$389$	−6.77013	−	11.7262i	−0.343259	−	0.594543i	−0.985036	+	0.172349i	$0.944864\pi$
$390$	10.0199	+	4.25458i	0.507378	+	0.215439i
$391$	17.7037	+	10.2212i	0.895313	+	0.516909i
$392$	17.0201	−	10.1151i	0.859645	−	0.510892i
$393$	4.06616	−	6.89746i	0.205111	−	0.347931i
$394$	29.0070	−	22.2686i	1.46135	−	1.12188i
$395$			5.79165i			0.291410i
$396$	−36.5543	+	9.10499i	−1.83692	+	0.457543i
$397$	23.5302			1.18094			0.590472	−	0.807058i	$-0.298941\pi$
$397$	23.5302			1.18094			0.590472	+	0.807058i	$0.298941\pi$
$398$	22.2320	+	28.9593i	1.11439	+	1.45160i
$399$	11.3843	+	10.0467i	0.569928	+	0.502963i
$400$	0.0126195	+	13.5199i	0.000630975	+	0.675996i
$401$	6.25180	+	3.60948i	0.312200	+	0.180249i	0.647911	−	0.761716i	$-0.275643\pi$
$401$	6.25180	+	3.60948i	0.312200	+	0.180249i	−0.335710	+	0.941965i	$0.608976\pi$
$402$	−1.59336	−	12.9893i	−0.0794694	−	0.647848i
$403$	−5.78489	+	3.33991i	−0.288166	+	0.166373i
$404$	−2.54325	−	9.47383i	−0.126531	−	0.471341i
$405$	−9.70606	−	6.08391i	−0.482298	−	0.302312i
$406$	12.3911	−	6.20632i	0.614959	−	0.308015i
$407$	31.3043	−	18.0735i	1.55170	−	0.895872i
$408$	21.3121	−	8.61933i	1.05511	−	0.426721i
$409$	−14.5844	−	8.42031i	−0.721152	−	0.416357i	0.0940245	−	0.995570i	$-0.470027\pi$
$409$	−14.5844	−	8.42031i	−0.721152	−	0.416357i	−0.815177	+	0.579213i	$0.803360\pi$
$410$	−6.20919	+	15.0002i	−0.306650	+	0.740808i
$411$	6.19702	+	10.9621i	0.305676	+	0.540722i
$412$	21.9246	−	21.9451i	1.08015	−	1.08116i
$413$	−17.5081	+	6.05985i	−0.861519	+	0.298186i
$414$	−18.3643	+	2.08369i	−0.902558	+	0.102408i
$415$	10.9884			0.539398
$416$	7.53725	−	18.2567i	0.369544	−	0.895111i
$417$	−16.1162	−	9.50075i	−0.789213	−	0.465254i
$418$	27.1827	+	11.2520i	1.32955	+	0.550353i
$419$	6.87675	+	3.97029i	0.335951	+	0.193961i	0.658480	−	0.752598i	$-0.271200\pi$
$419$	6.87675	+	3.97029i	0.335951	+	0.193961i	−0.322529	+	0.946560i	$0.604533\pi$
$420$	11.6424	−	0.732127i	0.568091	−	0.0357241i
$421$	−2.79460	+	1.61346i	−0.136200	+	0.0786353i	−0.566552	−	0.824026i	$-0.691723\pi$
$421$	−2.79460	+	1.61346i	−0.136200	+	0.0786353i	0.430352	+	0.902661i	$0.358390\pi$
$422$	−29.0159	+	3.82690i	−1.41247	+	0.186291i
$423$	11.7467	+	21.2265i	0.571143	+	1.03207i
$424$	−6.11834	−	14.7418i	−0.297133	−	0.715924i
$425$	7.93049	+	13.7360i	0.384686	+	0.666295i
$426$	16.3949	−	12.3514i	0.794334	−	0.598429i
$427$	−5.05959	−	0.975095i	−0.244851	−	0.0471882i
$428$	0.0523713	−	0.195818i	0.00253146	−	0.00946521i
$429$	−0.344620	+	37.9686i	−0.0166384	+	1.83314i
$430$	−5.00584	+	3.84297i	−0.241403	+	0.185325i
$431$			27.6928i			1.33391i	0.745096	+	0.666957i	$0.232404\pi$
$431$			27.6928i			1.33391i	−0.745096	+	0.666957i	$0.767596\pi$
$432$	−10.8620	+	17.7205i	−0.522597	+	0.852580i
$433$			15.8572i			0.762048i	0.924565	+	0.381024i	$0.124428\pi$
$433$			15.8572i			0.762048i	−0.924565	+	0.381024i	$0.875572\pi$
$434$	−3.93995	+	5.97636i	−0.189124	+	0.286875i
$435$	8.16496	+	0.0741088i	0.391480	+	0.00355325i
$436$	1.83120	+	0.489752i	0.0876984	+	0.0234549i
$437$	12.5000	+	7.21686i	0.597955	+	0.345229i
$438$	20.4142	−	15.3795i	0.975429	−	0.734860i
$439$	−13.3461	+	7.70535i	−0.636972	+	0.367756i	−0.783447	−	0.621458i	$-0.786541\pi$
$439$	−13.3461	+	7.70535i	−0.636972	+	0.367756i	0.146475	+	0.989214i	$0.453207\pi$
$440$	20.8763	−	8.66435i	0.995236	−	0.413057i
$441$	2.61130	+	20.8370i	0.124347	+	0.992239i
$442$	−3.02985	−	22.9726i	−0.144115	−	1.09269i
$443$	14.5960	+	25.2810i	0.693478	+	1.20114i	0.970691	+	0.240330i	$0.0772557\pi$
$443$	14.5960	+	25.2810i	0.693478	+	1.20114i	−0.277214	+	0.960808i	$0.589411\pi$
$444$	5.32747	−	19.2190i	0.252830	−	0.912092i
$445$	−9.03609	−	5.21699i	−0.428352	−	0.247309i
$446$	8.28718	−	20.0202i	0.392409	−	0.947985i
$447$	−32.9784	−	19.4413i	−1.55983	−	0.919542i
$448$	−1.53977	−	21.1099i	−0.0727471	−	0.997350i
$449$		−	9.59739i		−	0.452929i	−0.974019	−	0.226464i	$-0.927283\pi$
$449$		−	9.59739i		−	0.452929i	0.974019	−	0.226464i	$-0.0727167\pi$
$450$	−13.1480	−	5.72420i	−0.619803	−	0.269842i
$451$	−56.6269			−2.66646
$452$	−23.6775	+	23.6996i	−1.11370	+	1.11474i
$453$	−13.7305	+	7.76198i	−0.645113	+	0.364690i
$454$	−11.5467	+	27.8947i	−0.541916	+	1.30916i
$455$	2.22508	−	11.5455i	0.104313	−	0.541263i
$456$	15.0478	−	6.08582i	0.704676	−	0.284995i
$457$	6.21748	+	10.7690i	0.290841	+	0.503752i	0.974009	−	0.226510i	$-0.0727315\pi$
$457$	6.21748	+	10.7690i	0.290841	+	0.503752i	−0.683168	+	0.730262i	$0.739398\pi$
$458$	1.52037	+	11.5276i	0.0710422	+	0.538648i
$459$	−0.663849	+	24.3746i	−0.0309858	+	1.13771i
$460$	10.7102	−	2.87514i	0.499364	−	0.134054i
$461$	−32.3857	+	18.6979i	−1.50835	+	0.870849i	−0.508401	+	0.861120i	$0.669763\pi$
$461$	−32.3857	+	18.6979i	−1.50835	+	0.870849i	−0.999953	+	0.00972827i	$0.996903\pi$
$462$	17.8913	+	36.5450i	0.832378	+	1.70023i
$463$	10.6499	−	18.4461i	0.494941	−	0.857263i	−0.505042	−	0.863095i	$-0.668523\pi$
$463$	10.6499	−	18.4461i	0.494941	−	0.857263i	0.999983	+	0.00583150i	$0.00185623\pi$
$464$	−0.0138286	−	14.8153i	−0.000641978	−	0.687784i
$465$	−3.67151	+	2.07554i	−0.170262	+	0.0962511i
$466$	−8.78285	−	11.4405i	−0.406858	−	0.529971i
$467$			25.5216i			1.18100i	0.807038	+	0.590499i	$0.201069\pi$
$467$			25.5216i			1.18100i	−0.807038	+	0.590499i	$0.798931\pi$
$468$	14.5493	+	15.0732i	0.672541	+	0.696760i
$469$	−13.3578	+	4.62333i	−0.616804	+	0.213486i
$470$	−8.86390	−	11.5461i	−0.408861	−	0.532581i
$471$	−34.8809	−	20.5629i	−1.60723	−	0.947486i
$472$	−2.57150	+	19.6387i	−0.118363	+	0.903946i
$473$	−19.0635	−	11.0063i	−0.876539	−	0.506070i
$474$	−4.35627	+	10.2594i	−0.200090	+	0.471231i
$475$	5.59946	+	9.69854i	0.256921	+	0.445000i
$476$	−13.9278	−	20.5572i	−0.638381	−	0.942236i
$477$	16.9264	+	0.307289i	0.775008	+	0.0140698i
$478$	2.93528	−	0.387133i	0.134256	−	0.0177071i
$479$	3.66280	+	6.34415i	0.167358	+	0.289872i	0.937490	−	0.348012i	$-0.113143\pi$
$479$	3.66280	+	6.34415i	0.167358	+	0.289872i	−0.770132	+	0.637884i	$0.779810\pi$
$480$	4.86336	−	11.4834i	0.221981	−	0.524145i
$481$	−17.4088	−	10.0510i	−0.793773	−	0.458285i
$482$	−1.84975	+	4.46865i	−0.0842540	+	0.203541i
$483$	6.35799	+	18.9235i	0.289299	+	0.861049i
$484$	40.2107	+	40.1731i	1.82776	+	1.82605i
$485$	7.47421			0.339386
$486$	−12.6174	−	18.0777i	−0.572335	−	0.820020i
$487$	−13.3475			−0.604832			−0.302416	−	0.953176i	$-0.597793\pi$
$487$	−13.3475			−0.604832			−0.302416	+	0.953176i	$0.597793\pi$
$488$	−3.35028	+	4.37250i	−0.151660	+	0.197934i
$489$	−23.8449	−	0.216427i	−1.07830	−	0.00978717i
$490$	−3.40885	−	12.1302i	−0.153996	−	0.547986i
$491$	2.61391	−	4.52742i	0.117964	−	0.204320i	−0.800997	−	0.598669i	$-0.795697\pi$
$491$	2.61391	−	4.52742i	0.117964	−	0.204320i	0.918961	+	0.394349i	$0.129030\pi$
$492$	−22.2817	+	21.9013i	−1.00454	+	0.987385i
$493$	−8.69035	−	15.0521i	−0.391394	−	0.677914i
$494$	−2.13928	−	16.2202i	−0.0962506	−	0.729780i
$495$	−0.435161	+	23.9700i	−0.0195590	+	1.07737i
$496$	3.83241	+	6.62365i	0.172080	+	0.297411i
$497$	−16.7563	−	14.5190i	−0.751621	−	0.651268i
$498$	19.4650	+	8.26506i	0.872246	+	0.370366i
$499$	−1.06064	−	0.612360i	−0.0474807	−	0.0274130i	0.476072	−	0.879406i	$-0.342060\pi$
$499$	−1.06064	−	0.612360i	−0.0474807	−	0.0274130i	−0.523552	+	0.851993i	$0.675394\pi$
$500$	20.6078	+	5.51153i	0.921608	+	0.246483i
$501$	−0.273107	−	0.161001i	−0.0122015	−	0.00719298i
$502$	−13.2746	−	17.2914i	−0.592473	−	0.771753i
$503$	−4.83778			−0.215706			−0.107853	−	0.994167i	$-0.534398\pi$
$503$	−4.83778			−0.215706			−0.107853	+	0.994167i	$0.534398\pi$
$504$	21.1742	+	7.46010i	0.943174	+	0.332299i
$505$	−6.24261			−0.277793
$506$	23.5542	+	30.6817i	1.04711	+	1.36397i
$507$	−1.21948	+	0.689384i	−0.0541589	+	0.0306166i
$508$	−1.58732	+	5.93502i	−0.0704258	+	0.263324i
$509$	−9.42023	−	5.43877i	−0.417544	−	0.241069i	0.276482	−	0.961019i	$-0.410831\pi$
$509$	−9.42023	−	5.43877i	−0.417544	−	0.241069i	−0.694026	+	0.719950i	$0.744165\pi$
$510$	−1.78129	−	14.5214i	−0.0788769	−	0.643019i
$511$	−20.8642	−	18.0785i	−0.922977	−	0.799746i
$512$	−20.9231	−	8.61521i	−0.924681	−	0.380742i
$513$	−0.468722	+	17.2101i	−0.0206946	+	0.759843i
$514$	0.106525	+	0.807680i	0.00469861	+	0.0356252i
$515$	−9.87074	−	17.0966i	−0.434957	−	0.753368i
$516$	−11.7580	+	3.04229i	−0.517616	+	0.133929i
$517$	25.3862	−	43.9703i	1.11649	−	1.93381i
$518$	−21.5038	−	1.27570i	−0.944825	−	0.0560512i
$519$	9.19585	+	16.2669i	0.403653	+	0.714036i
$520$	−9.97766	−	7.64503i	−0.437549	−	0.335257i
$521$	26.7321			1.17116			0.585578	−	0.810616i	$-0.300868\pi$
$521$	26.7321			1.17116			0.585578	+	0.810616i	$0.300868\pi$
$522$	14.4078	+	6.27267i	0.630612	+	0.274547i
$523$	33.0841			1.44667			0.723334	−	0.690499i	$-0.242609\pi$
$523$	33.0841			1.44667			0.723334	+	0.690499i	$0.242609\pi$
$524$	−6.53446	+	6.54056i	−0.285459	+	0.285726i
$525$	−3.06906	+	15.1819i	−0.133945	+	0.662593i
$526$	13.0463	−	31.5173i	0.568845	−	1.37422i
$527$	7.77477	+	4.48877i	0.338674	+	0.195534i
$528$	43.4975	+	0.354199i	1.89299	+	0.0154145i
$529$	−2.01137	−	3.48379i	−0.0874509	−	0.151469i
$530$	−10.0704	+	1.32818i	−0.437430	+	0.0576926i
$531$	−17.9997	−	10.8324i	−0.781119	−	0.470087i
$532$	−9.83397	−	14.5147i	−0.426357	−	0.629293i
$533$	15.7456	+	27.2721i	0.682017	+	1.18129i
$534$	−12.0826	−	16.0381i	−0.522866	−	0.694035i
$535$	−0.111716	−	0.0644992i	−0.00482990	−	0.00278854i
$536$	−1.96192	+	14.9833i	−0.0847420	+	0.647180i
$537$	0.0340349	−	3.74980i	0.00146871	−	0.161816i
$538$	22.7983	+	29.6970i	0.982907	+	1.28033i
$539$	34.5462	−	27.1687i	1.48801	−	1.17024i
$540$	9.09950	+	9.60006i	0.391580	+	0.413121i
$541$			2.90649i			0.124960i	0.998046	+	0.0624798i	$0.0199009\pi$
$541$			2.90649i			0.124960i	−0.998046	+	0.0624798i	$0.980099\pi$
$542$	8.63474	+	11.2476i	0.370894	+	0.483125i
$543$	−0.213098	+	23.4782i	−0.00914492	+	1.00754i
$544$	−26.3143	+	3.49559i	−1.12822	+	0.149872i
$545$	0.603166	−	1.04471i	0.0258368	−	0.0447506i
$546$	12.6257	−	18.7783i	0.540328	−	0.803636i
$547$	−26.5965	+	15.3555i	−1.13719	+	0.656554i	−0.945732	−	0.324948i	$-0.894653\pi$
$547$	−26.5965	+	15.3555i	−1.13719	+	0.656554i	−0.191453	+	0.981502i	$0.561320\pi$
$548$	−3.76993	−	14.0434i	−0.161044	−	0.599903i
$549$	−2.82898	−	5.11204i	−0.120738	−	0.218176i
$550$	3.92423	+	29.7538i	0.167330	+	1.26871i
$551$	−6.13597	−	10.6278i	−0.261401	−	0.452760i
$552$	21.1347	+	2.96274i	0.899553	+	0.126102i
$553$	11.8215	+	2.27827i	0.502701	+	0.0968817i
$554$	−12.7210	+	30.7316i	−0.540465	+	1.30566i
$555$	−10.9337	−	6.44558i	−0.464109	−	0.273600i
$556$	15.2823	+	15.2680i	0.648113	+	0.647509i
$557$	16.5412			0.700871			0.350436	−	0.936587i	$-0.386034\pi$
$557$	16.5412			0.700871			0.350436	+	0.936587i	$0.386034\pi$
$558$	−8.06491	+	0.915076i	−0.341415	+	0.0387382i
$559$			12.2416i			0.517763i
$560$	−13.2290	−	2.53672i	−0.559029	−	0.107196i
$561$	44.4240	−	25.1134i	1.87558	−	1.06029i
$562$	−7.29965	+	17.6346i	−0.307917	+	0.743869i
$563$	−0.986336	−	0.569461i	−0.0415691	−	0.0239999i	0.479071	−	0.877776i	$-0.340973\pi$
$563$	−0.986336	−	0.569461i	−0.0415691	−	0.0239999i	−0.520641	+	0.853776i	$0.674307\pi$
$564$	−7.01709	−	27.1200i	−0.295473	−	1.14196i
$565$	10.6599	+	18.4635i	0.448466	+	0.776766i
$566$	−2.60348	−	19.7398i	−0.109432	−	0.829725i
$567$	−16.2361	+	17.4181i	−0.681852	+	0.731490i
$568$	−21.8917	+	9.08581i	−0.918556	+	0.381232i
$569$	−30.6460	+	17.6935i	−1.28475	+	0.741748i	−0.977712	−	0.209950i	$-0.932670\pi$
$569$	−30.6460	+	17.6935i	−1.28475	+	0.741748i	−0.307034	+	0.951699i	$0.599336\pi$
$570$	−1.25771	−	10.2531i	−0.0526797	−	0.429454i
$571$	−25.6297	−	14.7973i	−1.07257	−	0.619249i	−0.143689	−	0.989623i	$-0.545896\pi$
$571$	−25.6297	−	14.7973i	−1.07257	−	0.619249i	−0.928883	+	0.370373i	$0.879230\pi$
$572$	11.3279	−	42.3555i	0.473645	−	1.77097i
$573$	−4.74865	−	8.40006i	−0.198378	−	0.350918i
$574$	28.1748	+	18.5744i	1.17599	+	0.775280i
$575$			14.7242i			0.614041i
$576$	17.2525	−	16.6839i	0.718853	−	0.695162i
$577$		−	29.8808i		−	1.24395i	−0.783035	−	0.621977i	$-0.786330\pi$
$577$		−	29.8808i		−	1.24395i	0.783035	−	0.621977i	$-0.213670\pi$
$578$	−5.63213	+	4.32378i	−0.234266	+	0.179845i
$579$	30.5536	+	18.0118i	1.26976	+	0.748546i
$580$	−9.10834	−	2.43602i	−0.378203	−	0.101150i
$581$	4.32250	−	22.4287i	0.179328	−	0.930497i
$582$	13.2399	+	5.62183i	0.548812	+	0.233032i
$583$	−17.7151	−	30.6835i	−0.733685	−	1.27078i
$584$	−27.2587	+	11.3133i	−1.12797	+	0.468146i
$585$	11.6652	−	6.45547i	0.482297	−	0.266901i
$586$	−11.9219	+	1.57237i	−0.492488	+	0.0649542i
$587$	10.1592	−	5.86540i	0.419314	−	0.242091i	−0.275470	−	0.961310i	$-0.588833\pi$
$587$	10.1592	−	5.86540i	0.419314	−	0.242091i	0.694784	+	0.719219i	$0.255500\pi$
$588$	3.08542	−	24.0516i	0.127240	−	0.991872i
$589$	5.48951	+	3.16937i	0.226191	+	0.130592i
$590$	11.6464	+	4.82092i	0.479476	+	0.198474i
$591$	0.406497	−	44.7859i	0.0167210	−	1.84225i
$592$	−11.4959	+	19.9544i	−0.472478	+	0.820122i
$593$	−16.6383			−0.683252			−0.341626	−	0.939836i	$-0.610978\pi$
$593$	−16.6383			−0.683252			−0.341626	+	0.939836i	$0.610978\pi$
$594$	−18.8002	+	42.1335i	−0.771382	+	1.72876i
$595$	−14.9333	+	5.16866i	−0.612206	+	0.211894i
$596$	31.2720	+	31.2428i	1.28095	+	1.27976i
$597$	44.7123	+	0.405828i	1.82995	+	0.0166095i
$598$	8.22717	−	19.8753i	0.336434	−	0.812760i
$599$	−13.8777	−	8.01229i	−0.567027	−	0.327373i	0.188934	−	0.981990i	$-0.439497\pi$
$599$	−13.8777	−	8.01229i	−0.567027	−	0.327373i	−0.755961	+	0.654616i	$0.772830\pi$
$600$	13.0518	+	10.1898i	0.532838	+	0.415998i
$601$	24.7145	−	14.2689i	1.00812	−	0.582041i	0.0974826	−	0.995237i	$-0.468921\pi$
$601$	24.7145	−	14.2689i	1.00812	−	0.582041i	0.910642	+	0.413196i	$0.135588\pi$
$602$	5.87484	+	11.7293i	0.239441	+	0.478049i
$603$	−13.7328	−	8.26455i	−0.559242	−	0.336559i
$604$	17.5898	−	4.72197i	0.715719	−	0.192134i
$605$	31.3267	−	18.0865i	1.27361	−	0.735319i
$606$	−11.0583	−	4.69547i	−0.449211	−	0.190740i
$607$	−6.42574	−	3.70991i	−0.260813	−	0.150580i	0.363892	−	0.931441i	$-0.381448\pi$
$607$	−6.42574	−	3.70991i	−0.260813	−	0.150580i	−0.624705	+	0.780861i	$0.714781\pi$
$608$	−18.5797	+	2.46812i	−0.753505	+	0.100095i
$609$	3.36312	−	16.6366i	0.136281	−	0.674148i
$610$	2.13471	+	2.78067i	0.0864320	+	0.112586i
$611$	−28.2354			−1.14228
$612$	7.76707	−	27.0633i	0.313965	−	1.09397i
$613$		−	28.4394i		−	1.14866i	−0.818625	−	0.574328i	$-0.805263\pi$
$613$		−	28.4394i		−	1.14866i	0.818625	−	0.574328i	$-0.194737\pi$
$614$	−16.5946	+	12.7396i	−0.669702	+	0.514129i
$615$	9.78489	+	17.3089i	0.394565	+	0.697960i
$616$	−9.47293	−	46.0194i	−0.381675	−	1.85417i
$617$	1.24160	+	0.716841i	0.0499851	+	0.0288589i	0.524784	−	0.851235i	$-0.324146\pi$
$617$	1.24160	+	0.716841i	0.0499851	+	0.0288589i	−0.474799	+	0.880094i	$0.657479\pi$
$618$	−4.62571	−	37.7096i	−0.186073	−	1.51690i
$619$	−6.94630	−	12.0313i	−0.279195	−	0.483581i	0.691990	−	0.721907i	$-0.256734\pi$
$619$	−6.94630	−	12.0313i	−0.279195	−	0.483581i	−0.971185	+	0.238327i	$0.923401\pi$
$620$	4.70349	−	1.26265i	0.188897	−	0.0507093i
$621$	−11.8475	+	19.2879i	−0.475423	+	0.773997i
$622$	−3.58597	−	27.1891i	−0.143784	−	1.09018i
$623$	−14.2031	+	16.3916i	−0.569033	+	0.656715i
$624$	−11.9242	−	21.0474i	−0.477352	−	0.842568i
$625$	−1.66208	+	2.87882i	−0.0664834	+	0.115153i
$626$	−6.69758	+	16.1801i	−0.267689	+	0.646685i
$627$	31.3663	−	17.7317i	1.25265	−	0.708137i
$628$	33.0761	+	33.0452i	1.31988	+	1.31865i
$629$			27.0166i			1.07722i
$630$	8.07899	−	11.7836i	0.321875	−	0.469468i
$631$	3.67771			0.146407			0.0732037	−	0.997317i	$-0.476678\pi$
$631$	3.67771			0.146407			0.0732037	+	0.997317i	$0.476678\pi$
$632$	7.82777	−	10.2161i	0.311372	−	0.406377i
$633$	−18.2034	+	30.8786i	−0.723520	+	1.22731i
$634$	39.8987	+	16.5157i	1.58458	+	0.655921i
$635$	3.38599	+	1.95490i	0.134369	+	0.0775778i
$636$	−18.8378	−	5.22182i	−0.746969	−	0.207059i
$637$	−22.6906	−	9.08334i	−0.899034	−	0.359895i
$638$	−4.30022	−	32.6047i	−0.170248	−	1.29083i
$639$	0.456328	−	25.1360i	0.0180520	−	0.994363i
$640$	−8.74754	+	11.4387i	−0.345777	+	0.452153i
$641$	29.1479	−	16.8285i	1.15127	−	0.664687i	0.202075	−	0.979370i	$-0.435231\pi$
$641$	29.1479	−	16.8285i	1.15127	−	0.664687i	0.949197	+	0.314683i	$0.101898\pi$
$642$	−0.149381	−	0.198283i	−0.00589560	−	0.00782562i
$643$	14.1784	−	24.5578i	0.559143	−	0.968464i	−0.438425	−	0.898768i	$-0.644464\pi$
$643$	14.1784	−	24.5578i	0.559143	−	0.968464i	0.997568	−	0.0696966i	$-0.0222031\pi$
$644$	−1.65546	−	22.9918i	−0.0652341	−	0.906004i
$645$	−0.0701507	+	7.72887i	−0.00276218	+	0.304324i
$646$	−17.4414	+	13.3897i	−0.686223	+	0.526812i
$647$	−49.2414			−1.93588			−0.967939	−	0.251185i	$-0.919180\pi$
$647$	−49.2414			−1.93588			−0.967939	+	0.251185i	$0.919180\pi$
$648$	8.89818	+	23.8500i	0.349553	+	0.936916i
$649$			43.9661i			1.72582i
$650$	13.2386	−	10.1632i	0.519260	−	0.398635i
$651$	2.79219	+	8.31047i	0.109434	+	0.325713i
$652$	26.6000	+	7.11414i	1.04174	+	0.278611i
$653$	2.44370	−	4.23260i	0.0956292	−	0.165635i	−0.814242	−	0.580526i	$-0.802847\pi$
$653$	2.44370	−	4.23260i	0.0956292	−	0.165635i	0.909871	+	0.414891i	$0.136180\pi$
$654$	1.85425	−	1.39694i	0.0725070	−	0.0546248i
$655$	2.94190	+	5.09552i	0.114949	+	0.199098i
$656$	31.2264	−	18.0674i	1.21918	−	0.705415i
$657$	0.568200	−	31.2982i	0.0221676	−	1.22106i
$658$	−27.0538	+	13.5504i	−1.05467	+	0.528251i
$659$	−12.2863	−	21.2805i	−0.478605	−	0.828969i	0.521094	−	0.853499i	$-0.325524\pi$
$659$	−12.2863	−	21.2805i	−0.478605	−	0.828969i	−0.999699	+	0.0245308i	$0.992191\pi$
$660$	7.39476	−	26.6768i	0.287841	−	1.03839i
$661$	−18.3991	+	31.8681i	−0.715640	+	1.23953i	0.247072	+	0.968997i	$0.420532\pi$
$661$	−18.3991	+	31.8681i	−0.715640	+	1.23953i	−0.962712	+	0.270528i	$0.912802\pi$
$662$	0.380454	−	0.919104i	0.0147868	−	0.0357220i
$663$	−24.4473	−	14.4121i	−0.949455	−	0.559719i
$664$	−19.3829	−	14.8515i	−0.752201	−	0.576348i
$665$	−10.5439	+	3.64941i	−0.408875	+	0.141518i
$666$	−14.5200	−	19.6417i	−0.562637	−	0.761101i
$667$		−	16.1350i		−	0.624748i
$668$	0.258975	+	0.258734i	0.0100201	+	0.0100107i
$669$	−13.0595	−	23.1015i	−0.504911	−	0.893155i
$670$	8.88559	+	3.67810i	0.343280	+	0.142098i
$671$	−6.11383	+	10.5895i	−0.236022	+	0.408802i
$672$	−21.5261	−	14.4440i	−0.830386	−	0.557189i
$673$	4.12350	+	7.14211i	0.158949	+	0.275308i	0.934490	−	0.355989i	$-0.115856\pi$
$673$	4.12350	+	7.14211i	0.158949	+	0.275308i	−0.775541	+	0.631297i	$0.782523\pi$
$674$	1.55116	+	11.7611i	0.0597486	+	0.453019i
$675$	−15.4434	+	8.36410i	−0.594415	+	0.321934i
$676$	1.56225	−	0.419384i	0.0600864	−	0.0161302i
$677$	16.8817	−	9.74663i	0.648815	−	0.374593i	−0.139187	−	0.990266i	$-0.544449\pi$
$677$	16.8817	−	9.74663i	0.648815	−	0.374593i	0.788002	+	0.615673i	$0.211116\pi$
$678$	4.99554	+	40.7245i	0.191853	+	1.56402i
$679$	2.94013	−	15.2558i	0.112832	−	0.585464i
$680$	−2.19333	+	16.7506i	−0.0841102	+	0.642355i
$681$	18.1962	+	32.1879i	0.697280	+	1.23344i
$682$	10.3441	+	13.4742i	0.396097	+	0.515954i
$683$	19.5324			0.747385			0.373692	−	0.927553i	$-0.378092\pi$
$683$	19.5324			0.747385			0.373692	+	0.927553i	$0.378092\pi$
$684$	5.48407	−	19.1085i	0.209689	−	0.730630i
$685$	−9.25362			−0.353563
$686$	−26.1002	+	2.18622i	−0.996510	+	0.0834703i
$687$	12.2676	+	7.23194i	0.468038	+	0.275916i
$688$	14.0240	−	0.0130900i	0.534661	−	0.000499053i
$689$	−9.85166	+	17.0636i	−0.375318	+	0.650070i
$690$	5.30823	−	12.5014i	0.202081	−	0.475919i
$691$	−15.0696	−	26.1013i	−0.573275	−	0.992942i	−0.996227	−	0.0867893i	$-0.972339\pi$
$691$	−15.0696	−	26.1013i	−0.573275	−	0.992942i	0.422952	−	0.906152i	$-0.360994\pi$
$692$	−5.59426	−	20.8392i	−0.212662	−	0.792186i
$693$	48.7546	+	10.3173i	1.85203	+	0.391922i
$694$	3.69848	+	28.0422i	0.140393	+	1.06447i
$695$	11.9059	−	6.87386i	0.451616	−	0.260741i
$696$	−14.3024	−	11.1662i	−0.542130	−	0.423252i
$697$	21.1617	−	36.6532i	0.801557	−	1.38834i
$698$	−33.0178	−	13.6674i	−1.24974	−	0.517318i
$699$	−17.6638	−	0.160324i	−0.668106	−	0.00606403i
$700$	7.80714	−	16.0912i	0.295082	−	0.608192i
$701$	14.1730			0.535308			0.267654	−	0.963515i	$-0.413752\pi$
$701$	14.1730			0.535308			0.267654	+	0.963515i	$0.413752\pi$
$702$	25.5195	−	2.66117i	0.963171	−	0.100439i
$703$			19.0755i			0.719447i
$704$	−48.5349	−	12.9321i	−1.82923	−	0.487396i
$705$	−17.8268	−	0.161804i	−0.671396	−	0.00609389i
$706$	9.66569	+	4.00102i	0.363773	+	0.150580i
$707$	−2.45566	+	12.7420i	−0.0923546	+	0.479211i
$708$	17.0045	+	17.2999i	0.639069	+	0.650169i
$709$	−23.1267	+	13.3522i	−0.868541	+	0.501452i	−0.866863	−	0.498546i	$-0.833867\pi$
$709$	−23.1267	+	13.3522i	−0.868541	+	0.501452i	−0.00167799	+	0.999999i	$0.500534\pi$
$710$	1.97237	+	14.9546i	0.0740216	+	0.561238i
$711$	6.60978	+	11.9440i	0.247886	+	0.447936i
$712$	8.88807	+	21.4153i	0.333095	+	0.802572i
$713$	4.16704	+	7.21753i	0.156057	+	0.270298i
$714$	−30.3407	−	2.07645i	−1.13547	−	0.0777093i
$715$	−24.1642	−	13.9512i	−0.903690	−	0.521746i
$716$	−1.11875	+	4.18305i	−0.0418098	+	0.156328i
$717$	1.84148	−	3.12371i	0.0687712	−	0.116657i
$718$	0.100017	+	0.130282i	0.00373260	+	0.00486207i
$719$	19.7874			0.737945			0.368973	−	0.929440i	$-0.379710\pi$
$719$	19.7874			0.737945			0.368973	+	0.929440i	$0.379710\pi$
$720$	−7.40792	−	13.3569i	−0.276077	−	0.497781i
$721$	−38.7792	+	13.4221i	−1.44421	+	0.499866i
$722$	8.99884	−	6.90839i	0.334902	−	0.257104i
$723$	2.91498	+	5.15641i	0.108409	+	0.191769i
$724$	7.00472	−	26.1908i	0.260328	−	0.973375i
$725$	6.25944	−	10.8417i	0.232470	−	0.402649i
$726$	69.0965	−	8.47583i	2.56441	−	0.314568i
$727$	−10.2124	+	5.89615i	−0.378758	+	0.218676i	−0.677278	−	0.735727i	$-0.736840\pi$
$727$	−10.2124	+	5.89615i	−0.378758	+	0.218676i	0.298520	+	0.954403i	$0.403507\pi$
$728$	−19.5294	+	17.3583i	−0.723807	+	0.643342i
$729$	−26.9600	−	1.46962i	−0.998518	−	0.0544303i
$730$	2.45591	+	18.6209i	0.0908972	+	0.689190i
$731$	14.2482	−	8.22620i	0.526988	−	0.304257i
$732$	1.68994	+	6.53137i	0.0624621	+	0.241406i
$733$	−5.16168	+	8.94030i	−0.190651	+	0.330217i	−0.945466	−	0.325720i	$-0.894393\pi$
$733$	−5.16168	+	8.94030i	−0.190651	+	0.330217i	0.754815	+	0.655938i	$0.227727\pi$
$734$	10.7663	−	26.0093i	0.397391	−	0.960021i
$735$	−14.2740	−	5.86491i	−0.526503	−	0.216331i
$736$	−22.7781	−	9.40386i	−0.839610	−	0.346631i
$737$			33.5438i			1.23560i
$738$	4.31401	+	38.0210i	0.158801	+	1.39957i
$739$			16.8945i			0.621473i	0.950496	+	0.310737i	$0.100576\pi$
$739$			16.8945i			0.621473i	−0.950496	+	0.310737i	$0.899424\pi$
$740$	10.3679	+	10.3583i	0.381133	+	0.380778i
$741$	−17.2614	−	10.1759i	−0.634115	−	0.373821i
$742$	−1.25041	+	21.0774i	−0.0459038	+	0.773776i
$743$	−4.99429	−	2.88345i	−0.183223	−	0.105784i	0.405583	−	0.914058i	$-0.367068\pi$
$743$	−4.99429	−	2.88345i	−0.183223	−	0.105784i	−0.588806	+	0.808274i	$0.700402\pi$
$744$	9.28155	+	1.30112i	0.340278	+	0.0477014i
$745$	24.3629	−	14.0659i	0.892588	−	0.515336i
$746$	23.8399	−	3.14424i	0.872841	−	0.115119i
$747$	22.6612	−	12.5406i	0.829128	−	0.458836i
$748$	−56.9107	+	15.2776i	−2.08086	+	0.558606i
$749$	−0.175597	+	0.202654i	−0.00641616	+	0.00740482i
$750$	20.8673	−	15.7208i	0.761965	−	0.574043i
$751$	−1.28939	+	2.23329i	−0.0470505	+	0.0814938i	−0.888592	−	0.458699i	$-0.848315\pi$
$751$	−1.28939	+	2.23329i	−0.0470505	+	0.0814938i	0.841541	+	0.540193i	$0.181649\pi$
$752$	0.0301924	+	32.3467i	0.00110100	+	1.17956i
$753$	−26.6974	−	0.242318i	−0.972908	−	0.00883054i
$754$	−14.5070	+	11.1370i	−0.528315	+	0.405586i
$755$		−	11.5905i		−	0.421821i
$756$	23.1744	−	14.7969i	0.842845	−	0.538156i
$757$			34.1200i			1.24011i	0.784558	+	0.620056i	$0.212890\pi$
$757$			34.1200i			1.24011i	−0.784558	+	0.620056i	$0.787110\pi$
$758$	1.73294	+	2.25732i	0.0629432	+	0.0819896i
$759$	47.3716	+	0.429965i	1.71948	+	0.0156068i
$760$	−1.54863	+	11.8270i	−0.0561749	+	0.429011i
$761$	6.52600	−	11.3034i	0.236567	−	0.409747i	−0.723160	−	0.690681i	$-0.757311\pi$
$761$	6.52600	−	11.3034i	0.236567	−	0.409747i	0.959727	+	0.280934i	$0.0906442\pi$
$762$	4.52758	+	6.00975i	0.164017	+	0.217710i
$763$	−1.89513	−	1.64210i	−0.0686082	−	0.0594479i
$764$	2.88882	+	10.7611i	0.104514	+	0.389325i
$765$	−15.3525	−	9.23936i	−0.555073	−	0.334050i
$766$	−5.78175	−	43.8377i	−0.208903	−	1.58392i
$767$	21.1746	−	12.2251i	0.764569	−	0.441424i
$768$	−24.0993	+	13.6830i	−0.869608	+	0.493744i
$769$	−29.2410	−	16.8823i	−1.05446	−	0.608791i	−0.130563	−	0.991440i	$-0.541679\pi$
$769$	−29.2410	−	16.8823i	−1.05446	−	0.608791i	−0.923894	+	0.382649i	$0.875012\pi$
$770$	−29.8483	−	1.77073i	−1.07566	−	0.0638128i
$771$	0.859529	+	0.506706i	0.0309552	+	0.0182486i
$772$	−28.9726	−	28.9456i	−1.04275	−	1.04178i
$773$			9.10747i			0.327573i	0.986496	+	0.163786i	$0.0523708\pi$
$773$			9.10747i			0.327573i	−0.986496	+	0.163786i	$0.947629\pi$
$774$	−5.93764	+	13.6383i	−0.213424	+	0.490217i
$775$			6.46629i			0.232276i
$776$	−13.1841	−	10.1018i	−0.473281	−	0.362635i
$777$	−17.4572	+	19.7815i	−0.626275	+	0.709658i
$778$	17.6929	+	7.32381i	0.634322	+	0.262571i
$779$	14.9416	−	25.8796i	0.535338	−	0.927232i
$780$	−14.9040	+	3.85630i	−0.533649	+	0.138078i
$781$	−45.5653	+	26.3071i	−1.63046	+	0.941344i
$782$	−28.6618	+	3.78020i	−1.02494	+	0.135180i
$783$	16.9231	−	9.16550i	0.604780	−	0.327548i
$784$	−10.3817	+	26.0042i	−0.370774	+	0.928723i
$785$	25.7684	−	14.8774i	0.919713	−	0.530996i
$786$	1.37866	+	11.2391i	0.0491751	+	0.400884i
$787$	−9.98641	+	17.2970i	−0.355977	+	0.616570i	−0.987285	−	0.158962i	$-0.949185\pi$
$787$	−9.98641	+	17.2970i	−0.355977	+	0.616570i	0.631308	+	0.775532i	$0.282519\pi$
$788$	−13.3619	+	49.9605i	−0.475997	+	1.77977i
$789$	−20.5593	−	36.3681i	−0.731930	−	1.29474i
$790$	−4.98766	−	6.49690i	−0.177453	−	0.231149i
$791$	41.8797	−	14.4952i	1.48907	−	0.515391i
$792$	33.1645	−	41.6936i	1.17845	−	1.48152i
$793$	6.80000			0.241475
$794$	−26.3954	+	20.2637i	−0.936739	+	0.719132i
$795$	−6.31776	+	10.7169i	−0.224068	+	0.380088i
$796$	−49.8783	−	13.3399i	−1.76789	−	0.472821i
$797$	10.3053	+	5.94979i	0.365034	+	0.210753i	0.671287	−	0.741198i	$-0.265742\pi$
$797$	10.3053	+	5.94979i	0.365034	+	0.210753i	−0.306253	+	0.951950i	$0.599075\pi$
$798$	−21.4226	−	1.46611i	−0.758351	−	0.0518999i
$799$	18.9739	+	32.8638i	0.671248	+	1.16264i
$800$	−11.6572	−	15.1554i	−0.412146	−	0.535823i
$801$	−24.5889	−	0.446397i	−0.868806	−	0.0157726i
$802$	−10.1215	+	1.33492i	−0.357403	+	0.0471378i
$803$	−56.7360	+	32.7566i	−2.00217	+	1.15595i
$804$	12.9735	+	13.1989i	0.457541	+	0.465488i
$805$	−14.4048	−	2.77612i	−0.507702	−	0.0978455i
$806$	3.61305	−	8.72844i	0.127264	−	0.307446i
$807$	45.8513	+	0.416167i	1.61404	+	0.0146498i
$808$	11.0116	+	8.43727i	0.387387	+	0.296822i
$809$		−	13.9299i		−	0.489749i	−0.969555	−	0.244874i	$-0.921253\pi$
$809$		−	13.9299i		−	0.489749i	0.969555	−	0.244874i	$-0.0787468\pi$
$810$	16.1273	−	1.53393i	0.566656	−	0.0538967i
$811$	50.8542			1.78573			0.892867	−	0.450321i	$-0.148691\pi$
$811$	50.8542			1.78573			0.892867	+	0.450321i	$0.148691\pi$
$812$	−8.55517	+	17.6330i	−0.300228	+	0.618798i
$813$	17.3659	+	0.157621i	0.609049	+	0.00552800i
$814$	−19.5516	+	47.2330i	−0.685284	+	1.65552i
$815$	8.76160	−	15.1755i	0.306905	−	0.531576i
$816$	−16.4845	+	28.0225i	−0.577072	+	0.980983i
$817$	10.0602	−	5.80824i	0.351961	−	0.203205i
$818$	23.6117	−	3.11415i	0.825565	−	0.108884i
$819$	−8.58768	−	26.3495i	−0.300078	−	0.920728i
$820$	−5.95260	−	22.1740i	−0.207874	−	0.774350i
$821$	4.59857	+	7.96496i	0.160491	+	0.277979i	0.935045	−	0.354529i	$-0.115359\pi$
$821$	4.59857	+	7.96496i	0.160491	+	0.277979i	−0.774554	+	0.632508i	$0.782025\pi$
$822$	−16.3920	−	6.96024i	−0.571737	−	0.242766i
$823$	−28.1429	+	48.7450i	−0.981001	+	1.69914i	−0.322488	+	0.946574i	$0.604519\pi$
$823$	−28.1429	+	48.7450i	−0.981001	+	1.69914i	−0.658513	+	0.752569i	$0.728814\pi$
$824$	−5.69570	+	43.4984i	−0.198419	+	1.51534i
$825$	31.6639	+	18.6664i	1.10239	+	0.649879i
$826$	14.4215	−	21.8754i	0.501787	−	0.761143i
$827$	19.2776			0.670347			0.335174	−	0.942156i	$-0.391205\pi$
$827$	19.2776			0.670347			0.335174	+	0.942156i	$0.391205\pi$
$828$	18.8061	−	18.1524i	0.653558	−	0.630841i
$829$	−24.4426			−0.848928			−0.424464	−	0.905445i	$-0.639537\pi$
$829$	−24.4426			−0.848928			−0.424464	+	0.905445i	$0.639537\pi$
$830$	−12.3264	+	9.46297i	−0.427857	+	0.328465i
$831$	20.0467	+	35.4614i	0.695414	+	1.23014i
$832$	7.26729	+	26.9708i	0.251948	+	0.935045i
$833$	4.67556	+	32.5139i	0.161999	+	1.12654i
$834$	26.2605	−	3.22129i	0.909327	−	0.111544i
$835$	0.201758	−	0.116485i	0.00698214	−	0.00403114i
$836$	−40.1827	+	10.7870i	−1.38975	+	0.373077i
$837$	−5.20296	+	8.47050i	−0.179841	+	0.292783i
$838$	−11.1333	+	1.46837i	−0.384592	+	0.0507238i
$839$	−3.60473	−	6.24357i	−0.124449	−	0.215552i	0.797068	−	0.603889i	$-0.206383\pi$
$839$	−3.60473	−	6.24357i	−0.124449	−	0.215552i	−0.921517	+	0.388337i	$0.873050\pi$
$840$	−12.4296	+	10.8475i	−0.428862	+	0.374274i
$841$	7.64081	−	13.2343i	0.263476	−	0.456354i
$842$	1.74542	−	4.21659i	0.0601510	−	0.145313i
$843$	11.5033	+	20.3486i	0.396195	+	0.700845i
$844$	29.2535	−	29.2808i	1.00695	−	1.00789i
$845$		−	1.02941i		−	0.0354129i
$846$	−31.4569	−	13.6953i	−1.08151	−	0.470854i
$847$	−24.5938	−	71.0564i	−0.845052	−	2.44153i
$848$	19.5587	+	11.2679i	0.671649	+	0.386941i
$849$	−21.0070	−	12.3840i	−0.720958	−	0.425016i
$850$	−20.7254	−	8.57907i	−0.710875	−	0.294260i
$851$	−12.5401	+	21.7201i	−0.429870	+	0.744556i
$852$	−7.75446	+	27.9744i	−0.265663	+	0.958387i
$853$	−25.2367	−	43.7112i	−0.864087	−	1.49664i	−0.867951	−	0.496649i	$-0.834563\pi$
$853$	−25.2367	−	43.7112i	−0.864087	−	1.49664i	0.00386463	−	0.999993i	$-0.498770\pi$
$854$	6.51543	−	3.26339i	0.222953	−	0.111671i
$855$	−10.8399	−	6.52360i	−0.370717	−	0.223102i
$856$	0.109886	+	0.264764i	0.00375582	+	0.00904944i
$857$	17.1805	+	29.7575i	0.586874	+	1.01650i	0.994639	+	0.103408i	$0.0329748\pi$
$857$	17.1805	+	29.7575i	0.586874	+	1.01650i	−0.407765	+	0.913087i	$0.633692\pi$
$858$	−32.3112	−	42.8888i	−1.10309	−	1.46420i
$859$	17.9017	−	31.0066i	0.610798	−	1.05793i	−0.380309	−	0.924860i	$-0.624182\pi$
$859$	17.9017	−	31.0066i	0.610798	−	1.05793i	0.991106	−	0.133073i	$-0.0424844\pi$
$860$	2.30591	−	8.62187i	0.0786309	−	0.294003i
$861$	39.1786	−	13.1634i	1.33520	−	0.448608i
$862$	−23.8485	−	31.0649i	−0.812283	−	1.05808i
$863$		−	31.3395i		−	1.06681i	−0.845861	−	0.533404i	$-0.820913\pi$
$863$		−	31.3395i		−	1.06681i	0.845861	−	0.533404i	$-0.179087\pi$
$864$	−3.07595	−	29.2325i	−0.104646	−	0.994510i
$865$	−13.7316			−0.466888
$866$	−13.6559	−	17.7881i	−0.464046	−	0.604465i
$867$	−0.0789274	+	8.69584i	−0.00268051	+	0.295326i
$868$	−0.727013	−	10.0971i	−0.0246764	−	0.342718i
$869$	14.2847	−	24.7418i	0.484575	−	0.839308i
$870$	−9.22303	+	6.94837i	−0.312690	+	0.235572i
$871$	16.1550	−	9.32712i	0.547393	−	0.316037i
$872$	−2.47595	+	1.02760i	−0.0838461	+	0.0347990i
$873$	15.4139	−	8.53000i	0.521683	−	0.288697i
$874$	−20.2371	+	2.66907i	−0.684531	+	0.0902827i
$875$	−21.3272	−	18.4797i	−0.720992	−	0.624729i
$876$	−9.65553	+	34.8326i	−0.326230	+	1.17688i
$877$	−7.35227	−	4.24484i	−0.248269	−	0.143338i	0.370703	−	0.928752i	$-0.379117\pi$
$877$	−7.35227	−	4.24484i	−0.248269	−	0.143338i	−0.618971	+	0.785414i	$0.712450\pi$
$878$	8.33551	−	20.1370i	0.281310	−	0.679591i
$879$	−7.47930	+	12.6872i	−0.252271	+	0.427928i
$880$	−15.9568	+	27.6976i	−0.537903	+	0.933687i
$881$	−21.8272			−0.735377			−0.367689	−	0.929949i	$-0.619851\pi$
$881$	−21.8272			−0.735377			−0.367689	+	0.929949i	$0.619851\pi$
$882$	−20.8737	−	21.1255i	−0.702854	−	0.711334i
$883$			4.68838i			0.157776i	0.996883	+	0.0788882i	$0.0251370\pi$
$883$			4.68838i			0.157776i	−0.996883	+	0.0788882i	$0.974863\pi$
$884$	23.1823	+	23.1607i	0.779706	+	0.778979i
$885$	13.4389	−	7.59716i	0.451744	−	0.255376i
$886$	−38.1449	−	15.7897i	−1.28150	−	0.530466i
$887$	26.4358	−	45.7881i	0.887626	−	1.53741i	0.0449523	−	0.998989i	$-0.485686\pi$
$887$	26.4358	−	45.7881i	0.887626	−	1.53741i	0.842674	−	0.538424i	$-0.180980\pi$
$888$	10.5748	+	26.1472i	0.354867	+	0.877442i
$889$	5.32214	−	6.14222i	0.178499	−	0.206004i
$890$	14.6292	−	1.92944i	0.490371	−	0.0646750i
$891$	26.4585	+	49.9296i	0.886395	+	1.67270i
$892$	7.94472	+	29.5948i	0.266009	+	0.990909i
$893$	13.3968	+	23.2040i	0.448308	+	0.776492i
$894$	53.7367	−	6.59170i	1.79722	−	0.220459i
$895$	2.38647	+	1.37783i	0.0797709	+	0.0460558i
$896$	19.9067	+	22.3545i	0.665037	+	0.746811i
$897$	−12.9650	−	22.9342i	−0.432888	−	0.765751i
$898$	8.26508	+	10.7661i	0.275809	+	0.359268i
$899$		−	7.08586i		−	0.236326i
$900$	19.6786	−	4.90157i	0.655954	−	0.163386i
$901$	26.4808			0.882205
$902$	63.5224	−	48.7660i	2.11506	−	1.62373i
$903$	15.7480	+	3.18350i	0.524061	+	0.105940i
$904$	6.15107	−	46.9761i	0.204582	−	1.56240i
$905$	−14.9421	−	8.62684i	−0.496693	−	0.286766i
$906$	8.71795	−	20.5316i	0.289634	−	0.682115i
$907$	−7.97257	+	4.60297i	−0.264725	+	0.152839i	−0.626488	−	0.779431i	$-0.715508\pi$
$907$	−7.97257	+	4.60297i	−0.264725	+	0.152839i	0.361763	+	0.932270i	$0.382175\pi$
$908$	−11.0696	−	41.2353i	−0.367357	−	1.36844i
$909$	−12.8740	+	7.12444i	−0.427005	+	0.236303i
$910$	7.44675	+	14.8676i	0.246857	+	0.492857i
$911$	−21.6571	+	12.5037i	−0.717531	+	0.414267i	−0.813843	−	0.581085i	$-0.802629\pi$
$911$	−21.6571	+	12.5037i	−0.717531	+	0.414267i	0.0963123	+	0.995351i	$0.469295\pi$
$912$	−11.6391	+	19.7857i	−0.385410	+	0.655171i
$913$	−46.9421	−	27.1020i	−1.55356	−	0.896946i
$914$	−16.2486	−	6.72596i	−0.537457	−	0.222475i
$915$	4.29327	+	0.0389676i	0.141931	+	0.00128823i
$916$	−11.6328	−	11.6220i	−0.384359	−	0.384001i
$917$	11.5578	−	4.00036i	0.381674	−	0.132103i
$918$	−20.2462	−	27.9144i	−0.668225	−	0.921311i
$919$	21.7406			0.717155			0.358578	−	0.933500i	$-0.383262\pi$
$919$	21.7406			0.717155			0.358578	+	0.933500i	$0.383262\pi$
$920$	−9.53833	+	12.4486i	−0.314470	+	0.410419i
$921$	−0.232552	+	25.6215i	−0.00766285	+	0.844257i
$922$	20.2271	−	48.8647i	0.666143	−	1.60927i
$923$	25.3396	+	14.6298i	0.834063	+	0.481547i
$924$	−51.5418	−	25.5875i	−1.69560	−	0.841767i
$925$	−16.8523	+	9.72969i	−0.554101	+	0.319910i
$926$	3.93873	+	29.8638i	0.129435	+	0.981384i
$927$	−39.8680	−	23.9930i	−1.30944	−	0.788035i
$928$	12.7742	+	16.6075i	0.419333	+	0.545167i
$929$	−26.2799	−	45.5181i	−0.862216	−	1.49340i	−0.869785	−	0.493430i	$-0.835743\pi$
$929$	−26.2799	−	45.5181i	−0.862216	−	1.49340i	0.00756952	−	0.999971i	$-0.497591\pi$
$930$	2.33117	−	5.49011i	0.0764420	−	0.180028i
$931$	3.30126	+	22.9570i	0.108194	+	0.752385i
$932$	19.7047	+	5.27000i	0.645448	+	0.172625i
$933$	−28.9345	−	17.0574i	−0.947274	−	0.558433i
$934$	−21.9787	−	28.6294i	−0.719165	−	0.936782i
$935$			37.5003i			1.22639i
$936$	−29.3017	−	4.37914i	−0.957757	−	0.143137i
$937$			31.9676i			1.04433i	0.852843	+	0.522167i	$0.174876\pi$
$937$			31.9676i			1.04433i	−0.852843	+	0.522167i	$0.825124\pi$
$938$	11.0028	−	16.6898i	0.359254	−	0.544940i
$939$	10.5545	+	18.6703i	0.344434	+	0.609282i
$940$	19.8865	+	5.31863i	0.648626	+	0.173475i
$941$	14.8170	+	8.55458i	0.483019	+	0.278871i	0.721674	−	0.692233i	$-0.243373\pi$
$941$	14.8170	+	8.55458i	0.483019	+	0.278871i	−0.238655	+	0.971105i	$0.576706\pi$
$942$	56.8367	−	6.97196i	1.85184	−	0.227159i
$943$	34.0261	−	19.6450i	1.10804	−	0.639729i
$944$	−14.0279	−	24.2447i	−0.456568	−	0.789097i
$945$	−5.27095	−	16.6853i	−0.171464	−	0.542774i
$946$	30.8632	−	4.07055i	1.00345	−	0.132345i
$947$	2.26136	+	3.91679i	0.0734842	+	0.127278i	0.900426	−	0.435009i	$-0.143255\pi$
$947$	2.26136	+	3.91679i	0.0734842	+	0.127278i	−0.826942	+	0.562287i	$0.809921\pi$
$948$	−3.94848	−	15.2602i	−0.128241	−	0.495630i
$949$	31.5518	+	18.2165i	1.02422	+	0.591331i
$950$	−14.6335	−	6.05739i	−0.474773	−	0.196528i
$951$	46.0394	−	26.0266i	1.49293	−	0.843970i
$952$	33.3272	+	11.0660i	1.08014	+	0.358652i
$953$			23.7679i			0.769919i	0.922934	+	0.384959i	$0.125785\pi$
$953$			23.7679i			0.769919i	−0.922934	+	0.384959i	$0.874215\pi$
$954$	−19.2522	+	14.2320i	−0.623313	+	0.460778i
$955$	7.09087			0.229455
$956$	−2.95931	+	2.96208i	−0.0957111	+	0.0958004i
$957$	−34.6977	−	20.4549i	−1.12162	−	0.661212i
$958$	−9.57228	−	3.96235i	−0.309266	−	0.128018i
$959$	−3.64010	+	18.8878i	−0.117545	+	0.609919i
$960$	4.43375	+	17.0700i	0.143099	+	0.550933i
$961$	−13.6700	−	23.6771i	−0.440968	−	0.763778i
$962$	28.1844	−	3.71724i	0.908701	−	0.119849i
$963$	−0.304000	−	0.00551894i	−0.00979627	−	0.000177845i
$964$	−1.77332	−	6.60577i	−0.0571147	−	0.212758i
$965$	−22.5715	+	13.0317i	−0.726604	+	0.419505i
$966$	−23.4287	−	15.7524i	−0.753808	−	0.506826i
$967$	17.9107	−	31.0222i	0.575968	−	0.997607i	−0.419967	−	0.907539i	$-0.637958\pi$
$967$	17.9107	−	31.0222i	0.575968	−	0.997607i	0.995936	−	0.0900673i	$-0.0287082\pi$
$968$	−79.7034	−	10.4364i	−2.56177	−	0.335439i
$969$	−0.244420	+	26.9290i	−0.00785189	+	0.865085i
$970$	−8.38434	+	6.43664i	−0.269205	+	0.206668i
$971$			40.8117i			1.30971i	0.755754	+	0.654856i	$0.227271\pi$
$971$			40.8117i			1.30971i	−0.755754	+	0.654856i	$0.772729\pi$
$972$	29.7219	+	9.41316i	0.953331	+	0.301927i
$973$	−9.34700	−	27.0054i	−0.299651	−	0.865753i
$974$	14.9728	−	11.4946i	0.479760	−	0.368311i
$975$	0.185522	−	20.4400i	0.00594147	−	0.654603i
$976$	−0.00727131	−	7.79014i	−0.000232749	−	0.249356i
$977$	5.98473	+	3.45529i	0.191469	+	0.110544i	0.592670	−	0.805445i	$-0.298074\pi$
$977$	5.98473	+	3.45529i	0.191469	+	0.110544i	−0.401201	+	0.915990i	$0.631407\pi$
$978$	26.9349	−	20.2920i	0.861283	−	0.648867i
$979$	25.7346	+	44.5737i	0.822482	+	1.42458i
$980$	14.2702	+	10.6717i	0.455846	+	0.340894i
$981$	0.0516105	−	2.84287i	0.00164780	−	0.0907658i
$982$	0.966723	+	7.32977i	0.0308494	+	0.233902i
$983$	−8.95933	−	15.5180i	−0.285758	−	0.494948i	0.687034	−	0.726625i	$-0.258912\pi$
$983$	−8.95933	−	15.5180i	−0.285758	−	0.494948i	−0.972793	+	0.231677i	$0.925579\pi$
$984$	6.13397	−	43.7567i	0.195544	−	1.39491i
$985$	28.5029	+	16.4562i	0.908178	+	0.524337i
$986$	22.7112	+	9.40107i	0.723271	+	0.299391i
$987$	−7.34280	+	36.3231i	−0.233724	+	1.15618i
$988$	16.3683	+	16.3530i	0.520744	+	0.520258i
$989$	15.2732			0.485659
$990$	−20.1543	−	27.2636i	−0.640547	−	0.866493i
$991$	50.5900			1.60704			0.803522	−	0.595276i	$-0.202957\pi$
$991$	50.5900			1.60704			0.803522	+	0.595276i	$0.202957\pi$
$992$	−10.0032	−	4.12981i	−0.317603	−	0.131122i
$993$	−0.599547	−	1.06056i	−0.0190260	−	0.0336559i
$994$	31.3002	+	1.85687i	0.992781	+	0.0588963i
$995$	−16.4291	+	28.4561i	−0.520838	+	0.902118i
$996$	−28.9529	+	7.49135i	−0.917408	+	0.237373i
$997$	27.8729	+	48.2773i	0.882744	+	1.52896i	0.848278	+	0.529552i	$0.177640\pi$
$997$	27.8729	+	48.2773i	0.882744	+	1.52896i	0.0344663	+	0.999406i	$0.489027\pi$
$998$	1.71715	−	0.226474i	0.0543553	−	0.00716891i
$999$	−29.9044	−	0.814457i	−0.946135	−	0.0257683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.17	yes	168
7.6	odd	2	inner	504.2.cc.b.293.18	yes	168
8.5	even	2	inner	504.2.cc.b.293.12	yes	168
9.2	odd	6	inner	504.2.cc.b.461.11	yes	168
56.13	odd	2	inner	504.2.cc.b.293.11	✓	168
63.20	even	6	inner	504.2.cc.b.461.12	yes	168
72.29	odd	6	inner	504.2.cc.b.461.18	yes	168
504.461	even	6	inner	504.2.cc.b.461.17	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.11	✓	168	56.13	odd	2	inner
504.2.cc.b.293.12	yes	168	8.5	even	2	inner
504.2.cc.b.293.17	yes	168	1.1	even	1	trivial
504.2.cc.b.293.18	yes	168	7.6	odd	2	inner
504.2.cc.b.461.11	yes	168	9.2	odd	6	inner
504.2.cc.b.461.12	yes	168	63.20	even	6	inner
504.2.cc.b.461.17	yes	168	504.461	even	6	inner
504.2.cc.b.461.18	yes	168	72.29	odd	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12177 + 0.861180i) q^{2} +(-0.0157202 + 1.73198i) q^{3} +(0.516736 - 1.93209i) q^{4} +(-1.10228 - 0.636400i) q^{5} +(-1.47391 - 1.95642i) q^{6} +(-1.73258 + 1.99955i) q^{7} +(1.08422 + 2.61237i) q^{8} +(-2.99951 - 0.0544542i) q^{9} +O(q^{10})\)	\(q+(-1.12177 + 0.861180i) q^{2} +(-0.0157202 + 1.73198i) q^{3} +(0.516736 - 1.93209i) q^{4} +(-1.10228 - 0.636400i) q^{5} +(-1.47391 - 1.95642i) q^{6} +(-1.73258 + 1.99955i) q^{7} +(1.08422 + 2.61237i) q^{8} +(-2.99951 - 0.0544542i) q^{9} +(1.78456 - 0.235365i) q^{10} +(3.13927 + 5.43737i) q^{11} +(3.33822 + 0.925350i) q^{12} +(1.74580 - 3.02381i) q^{13} +(0.221582 - 3.73509i) q^{14} +(1.11956 - 1.89912i) q^{15} +(-3.46597 - 1.99677i) q^{16} -4.69263 q^{17} +(3.41165 - 2.52203i) q^{18} -3.31331 q^{19} +(-1.79917 + 1.80085i) q^{20} +(-3.43593 - 3.03222i) q^{21} +(-8.20409 - 3.39600i) q^{22} +(-3.77266 - 2.17814i) q^{23} +(-4.54161 + 1.83678i) q^{24} +(-1.68999 - 2.92715i) q^{25} +(0.645662 + 4.89546i) q^{26} +(0.141466 - 5.19423i) q^{27} +(2.96802 + 4.38074i) q^{28} +(1.85192 + 3.20761i) q^{29} +(0.379594 + 3.09452i) q^{30} +(-1.65681 - 0.956557i) q^{31} +(5.60759 - 0.744911i) q^{32} +(-9.46676 + 5.35167i) q^{33} +(5.26405 - 4.04120i) q^{34} +(3.18229 - 1.10144i) q^{35} +(-1.65516 + 5.76719i) q^{36} -5.75725i q^{37} +(3.71677 - 2.85336i) q^{38} +(5.20973 + 3.07122i) q^{39} +(0.467398 - 3.56955i) q^{40} +(-4.50957 + 7.81080i) q^{41} +(6.46562 + 0.442493i) q^{42} +(-3.03629 + 1.75300i) q^{43} +(12.1277 - 3.25567i) q^{44} +(3.27163 + 1.96891i) q^{45} +(6.10783 - 0.805561i) q^{46} +(-4.04334 - 7.00327i) q^{47} +(3.51284 - 5.97159i) q^{48} +(-0.996363 - 6.92873i) q^{49} +(4.41658 + 1.82820i) q^{50} +(0.0737691 - 8.12753i) q^{51} +(-4.94016 - 4.93555i) q^{52} -5.64307 q^{53} +(4.31447 + 5.94856i) q^{54} -7.99132i q^{55} +(-7.10204 - 2.35818i) q^{56} +(0.0520859 - 5.73858i) q^{57} +(-4.83976 - 2.00337i) q^{58} +(6.06444 + 3.50131i) q^{59} +(-3.09075 - 3.14444i) q^{60} +(0.973767 + 1.68661i) q^{61} +(2.68232 - 0.353771i) q^{62} +(5.30575 - 5.90330i) q^{63} +(-5.64893 + 5.66477i) q^{64} +(-3.84870 + 2.22205i) q^{65} +(6.01078 - 14.1559i) q^{66} +(4.62684 + 2.67131i) q^{67} +(-2.42485 + 9.06659i) q^{68} +(3.83181 - 6.49992i) q^{69} +(-2.62126 + 3.97609i) q^{70} +8.38003i q^{71} +(-3.10987 - 7.89485i) q^{72} +10.4345i q^{73} +(4.95803 + 6.45831i) q^{74} +(5.09633 - 2.88101i) q^{75} +(-1.71211 + 6.40162i) q^{76} +(-16.3113 - 3.14355i) q^{77} +(-8.48899 + 1.04132i) q^{78} +(-2.27516 - 3.94070i) q^{79} +(2.54971 + 4.40673i) q^{80} +(8.99407 + 0.326671i) q^{81} +(-1.66781 - 12.6455i) q^{82} +(-7.47660 + 4.31662i) q^{83} +(-7.63400 + 5.07169i) q^{84} +(5.17258 + 2.98639i) q^{85} +(1.89637 - 4.58126i) q^{86} +(-5.58463 + 3.15706i) q^{87} +(-10.8007 + 14.0962i) q^{88} +8.19765 q^{89} +(-5.36560 + 0.608802i) q^{90} +(3.02152 + 8.72978i) q^{91} +(-6.15785 + 6.16360i) q^{92} +(1.68278 - 2.85452i) q^{93} +(10.5668 + 4.37402i) q^{94} +(3.65218 + 2.10859i) q^{95} +(1.20202 + 9.72395i) q^{96} +(-5.08552 + 2.93613i) q^{97} +(7.08457 + 6.91439i) q^{98} +(-9.12016 - 16.4804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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