LMFDB - Embedded newform 357.2.p.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(16,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("357.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.p (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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	357.67
Dual form			357.2.p.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34373 - 2.32741i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.61122 + 4.52277i) q^{4} +(2.98396 - 1.72279i) q^{5} +2.68746i q^{6} +(-0.462813 + 2.60496i) q^{7} +8.66019 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.34373 - 2.32741i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.61122 + 4.52277i) q^{4} +(2.98396 - 1.72279i) q^{5} +2.68746i q^{6} +(-0.462813 + 2.60496i) q^{7} +8.66019 q^{8} +(0.500000 + 0.866025i) q^{9} +(-8.01926 - 4.62992i) q^{10} +(0.636072 + 0.367236i) q^{11} +(4.52277 - 2.61122i) q^{12} +6.64148 q^{13} +(6.68470 - 2.42320i) q^{14} -3.44558 q^{15} +(-6.41451 - 11.1103i) q^{16} +(2.64411 - 3.16365i) q^{17} +(1.34373 - 2.32741i) q^{18} +(0.832031 + 1.44112i) q^{19} +17.9943i q^{20} +(1.70329 - 2.02455i) q^{21} -1.97387i q^{22} +(-4.08650 + 2.35934i) q^{23} +(-7.49994 - 4.33009i) q^{24} +(3.43600 - 5.95132i) q^{25} +(-8.92436 - 15.4574i) q^{26} -1.00000i q^{27} +(-10.5731 - 8.89532i) q^{28} +4.36957i q^{29} +(4.62992 + 8.01926i) q^{30} +(-2.56750 - 1.48235i) q^{31} +(-8.57856 + 14.8585i) q^{32} +(-0.367236 - 0.636072i) q^{33} +(-10.9161 - 1.90282i) q^{34} +(3.10678 + 8.57041i) q^{35} -5.22244 q^{36} +(-0.711530 + 0.410802i) q^{37} +(2.23605 - 3.87295i) q^{38} +(-5.75169 - 3.32074i) q^{39} +(25.8416 - 14.9197i) q^{40} -7.21438i q^{41} +(-7.00072 - 1.24379i) q^{42} +3.15651 q^{43} +(-3.32185 + 1.91787i) q^{44} +(2.98396 + 1.72279i) q^{45} +(10.9823 + 6.34064i) q^{46} +(2.84941 + 4.93533i) q^{47} +12.8290i q^{48} +(-6.57161 - 2.41122i) q^{49} -18.4682 q^{50} +(-3.87169 + 1.41775i) q^{51} +(-17.3424 + 30.0379i) q^{52} +(0.253341 - 0.438799i) q^{53} +(-2.32741 + 1.34373i) q^{54} +2.53068 q^{55} +(-4.00805 + 22.5594i) q^{56} -1.66406i q^{57} +(10.1698 - 5.87152i) q^{58} +(5.46350 - 9.46306i) q^{59} +(8.99716 - 15.5835i) q^{60} +(-7.47769 + 4.31725i) q^{61} +7.96749i q^{62} +(-2.48737 + 0.901671i) q^{63} +20.4510 q^{64} +(19.8179 - 11.4419i) q^{65} +(-0.986933 + 1.70942i) q^{66} +(1.05396 - 1.82551i) q^{67} +(7.40413 + 20.2197i) q^{68} +4.71869 q^{69} +(15.7722 - 18.7471i) q^{70} -13.8398i q^{71} +(4.33009 + 7.49994i) q^{72} +(1.85921 + 1.07342i) q^{73} +(1.91221 + 1.10401i) q^{74} +(-5.95132 + 3.43600i) q^{75} -8.69047 q^{76} +(-1.25102 + 1.48698i) q^{77} +17.8487i q^{78} +(10.0684 - 5.81300i) q^{79} +(-38.2813 - 22.1017i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-16.7908 + 9.69418i) q^{82} +3.50718 q^{83} +(4.70893 + 12.9901i) q^{84} +(2.43959 - 13.9954i) q^{85} +(-4.24150 - 7.34649i) q^{86} +(2.18479 - 3.78416i) q^{87} +(5.50850 + 3.18034i) q^{88} +(0.872197 + 1.51069i) q^{89} -9.25985i q^{90} +(-3.07377 + 17.3008i) q^{91} -24.6431i q^{92} +(1.48235 + 2.56750i) q^{93} +(7.65768 - 13.2635i) q^{94} +(4.96549 + 2.86683i) q^{95} +(14.8585 - 8.57856i) q^{96} +12.5471i q^{97} +(3.21858 + 18.5348i) q^{98} +0.734473i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) $ 48 * q - 24 * q^4 + 24 * q^9	$ 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) $ 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34373	−	2.32741i	−0.950161	−	1.64573i	−0.745073	−	0.666983i	$-0.767585\pi$
$2$	−1.34373	−	2.32741i	−0.950161	−	1.64573i	−0.205088	−	0.978744i	$-0.565748\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−2.61122	+	4.52277i	−1.30561	+	2.26138i
$5$	2.98396	−	1.72279i	1.33447	−	0.770454i	0.348485	−	0.937314i	$-0.386696\pi$
$5$	2.98396	−	1.72279i	1.33447	−	0.770454i	0.985981	+	0.166860i	$0.0533628\pi$
$6$			2.68746i			1.09715i
$7$	−0.462813	+	2.60496i	−0.174927	+	0.984581i
$7$	−0.462813	+	2.60496i	−0.174927	+	0.984581i
$8$	8.66019			3.06184
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−8.01926	−	4.62992i	−2.53591	−	1.46411i
$11$	0.636072	+	0.367236i	0.191783	+	0.110726i	0.592817	−	0.805337i	$-0.298016\pi$
$11$	0.636072	+	0.367236i	0.191783	+	0.110726i	−0.401034	+	0.916063i	$0.631349\pi$
$12$	4.52277	−	2.61122i	1.30561	−	0.753795i
$13$	6.64148			1.84202			0.921008	−	0.389543i	$-0.127367\pi$
$13$	6.64148			1.84202			0.921008	+	0.389543i	$0.127367\pi$
$14$	6.68470	−	2.42320i	1.78656	−	0.647629i
$15$	−3.44558			−0.889644
$16$	−6.41451	−	11.1103i	−1.60363	−	2.77757i
$17$	2.64411	−	3.16365i	0.641290	−	0.767299i
$17$	2.64411	−	3.16365i	0.641290	−	0.767299i
$18$	1.34373	−	2.32741i	0.316720	−	0.548576i
$19$	0.832031	+	1.44112i	0.190881	+	0.330616i	0.945542	−	0.325499i	$-0.105532\pi$
$19$	0.832031	+	1.44112i	0.190881	+	0.330616i	−0.754661	+	0.656114i	$0.772199\pi$
$20$			17.9943i			4.02365i
$21$	1.70329	−	2.02455i	0.371688	−	0.441794i
$22$		−	1.97387i		−	0.420830i
$23$	−4.08650	+	2.35934i	−0.852095	+	0.491957i	−0.861357	−	0.508000i	$-0.830385\pi$
$23$	−4.08650	+	2.35934i	−0.852095	+	0.491957i	0.00926217	+	0.999957i	$0.497052\pi$
$24$	−7.49994	−	4.33009i	−1.53092	−	0.883877i
$25$	3.43600	−	5.95132i	0.687199	−	1.19026i
$26$	−8.92436	−	15.4574i	−1.75021	−	3.03146i
$27$		−	1.00000i		−	0.192450i
$28$	−10.5731	−	8.89532i	−1.99813	−	1.68106i
$29$			4.36957i			0.811409i	0.914004	+	0.405704i	$0.132974\pi$
$29$			4.36957i			0.811409i	−0.914004	+	0.405704i	$0.867026\pi$
$30$	4.62992	+	8.01926i	0.845305	+	1.46411i
$31$	−2.56750	−	1.48235i	−0.461136	−	0.266237i	0.251386	−	0.967887i	$-0.419114\pi$
$31$	−2.56750	−	1.48235i	−0.461136	−	0.266237i	−0.712522	+	0.701650i	$0.752447\pi$
$32$	−8.57856	+	14.8585i	−1.51649	+	2.62664i
$33$	−0.367236	−	0.636072i	−0.0639276	−	0.110726i
$34$	−10.9161	−	1.90282i	−1.87209	−	0.326331i
$35$	3.10678	+	8.57041i	0.525141	+	1.44866i
$36$	−5.22244			−0.870407
$37$	−0.711530	+	0.410802i	−0.116975	+	0.0675354i	−0.557346	−	0.830280i	$-0.688180\pi$
$37$	−0.711530	+	0.410802i	−0.116975	+	0.0675354i	0.440371	+	0.897816i	$0.354847\pi$
$38$	2.23605	−	3.87295i	0.362735	−	0.628276i
$39$	−5.75169	−	3.32074i	−0.921008	−	0.531744i
$40$	25.8416	−	14.9197i	4.08592	−	2.35901i
$41$		−	7.21438i		−	1.12670i	−0.826220	−	0.563348i	$-0.809513\pi$
$41$		−	7.21438i		−	1.12670i	0.826220	−	0.563348i	$-0.190487\pi$
$42$	−7.00072	−	1.24379i	−1.08023	−	0.191921i
$43$	3.15651			0.481363			0.240682	−	0.970604i	$-0.422629\pi$
$43$	3.15651			0.481363			0.240682	+	0.970604i	$0.422629\pi$
$44$	−3.32185	+	1.91787i	−0.500788	+	0.289130i
$45$	2.98396	+	1.72279i	0.444822	+	0.256818i
$46$	10.9823	+	6.34064i	1.61925	+	0.934877i
$47$	2.84941	+	4.93533i	0.415629	+	0.719891i	0.995494	−	0.0948214i	$-0.0302280\pi$
$47$	2.84941	+	4.93533i	0.415629	+	0.719891i	−0.579865	+	0.814713i	$0.696895\pi$
$48$			12.8290i			1.85171i
$49$	−6.57161	−	2.41122i	−0.938801	−	0.344460i
$50$	−18.4682			−2.61180
$51$	−3.87169	+	1.41775i	−0.542145	+	0.198525i
$52$	−17.3424	+	30.0379i	−2.40496	+	4.16551i
$53$	0.253341	−	0.438799i	0.0347991	−	0.0602737i	−0.848101	−	0.529834i	$-0.822254\pi$
$53$	0.253341	−	0.438799i	0.0347991	−	0.0602737i	0.882900	+	0.469560i	$0.155588\pi$
$54$	−2.32741	+	1.34373i	−0.316720	+	0.182859i
$55$	2.53068			0.341237
$56$	−4.00805	+	22.5594i	−0.535598	+	3.01463i
$57$		−	1.66406i		−	0.220410i
$58$	10.1698	−	5.87152i	1.33536	−	0.770969i
$59$	5.46350	−	9.46306i	0.711287	−	1.23199i	−0.253087	−	0.967444i	$-0.581446\pi$
$59$	5.46350	−	9.46306i	0.711287	−	1.23199i	0.964374	−	0.264542i	$-0.0852209\pi$
$60$	8.99716	−	15.5835i	1.16153	−	2.01183i
$61$	−7.47769	+	4.31725i	−0.957420	+	0.552767i	−0.895378	−	0.445307i	$-0.853095\pi$
$61$	−7.47769	+	4.31725i	−0.957420	+	0.552767i	−0.0620420	+	0.998074i	$0.519761\pi$
$62$			7.96749i			1.01187i
$63$	−2.48737	+	0.901671i	−0.313379	+	0.113600i
$64$	20.4510			2.55638
$65$	19.8179	−	11.4419i	2.45811	−	1.41919i
$66$	−0.986933	+	1.70942i	−0.121483	+	0.210415i
$67$	1.05396	−	1.82551i	0.128762	−	0.223022i	−0.794435	−	0.607349i	$-0.792233\pi$
$67$	1.05396	−	1.82551i	0.128762	−	0.223022i	0.923197	+	0.384327i	$0.125566\pi$
$68$	7.40413	+	20.2197i	0.897882	+	2.45200i
$69$	4.71869			0.568063
$70$	15.7722	−	18.7471i	1.88514	−	2.24070i
$71$		−	13.8398i		−	1.64248i	−0.570583	−	0.821240i	$-0.693283\pi$
$71$		−	13.8398i		−	1.64248i	0.570583	−	0.821240i	$-0.306717\pi$
$72$	4.33009	+	7.49994i	0.510307	+	0.883877i
$73$	1.85921	+	1.07342i	0.217605	+	0.125634i	0.604841	−	0.796347i	$-0.293237\pi$
$73$	1.85921	+	1.07342i	0.217605	+	0.125634i	−0.387236	+	0.921981i	$0.626570\pi$
$74$	1.91221	+	1.10401i	0.222290	+	0.128339i
$75$	−5.95132	+	3.43600i	−0.687199	+	0.396755i
$76$	−8.69047			−0.996866
$77$	−1.25102	+	1.48698i	−0.142567	+	0.169457i
$78$			17.8487i			2.02097i
$79$	10.0684	−	5.81300i	1.13279	−	0.654014i	0.188151	−	0.982140i	$-0.439750\pi$
$79$	10.0684	−	5.81300i	1.13279	−	0.654014i	0.944634	+	0.328126i	$0.106417\pi$
$80$	−38.2813	−	22.1017i	−4.27997	−	2.47104i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−16.7908	+	9.69418i	−1.85423	+	1.07054i
$83$	3.50718			0.384963			0.192481	−	0.981301i	$-0.438346\pi$
$83$	3.50718			0.384963			0.192481	+	0.981301i	$0.438346\pi$
$84$	4.70893	+	12.9901i	0.513786	+	1.41734i
$85$	2.43959	−	13.9954i	0.264611	−	1.51802i
$86$	−4.24150	−	7.34649i	−0.457373	−	0.792193i
$87$	2.18479	−	3.78416i	0.234234	−	0.405704i
$88$	5.50850	+	3.18034i	0.587209	+	0.339025i
$89$	0.872197	+	1.51069i	0.0924527	+	0.160133i	0.908543	−	0.417792i	$-0.137196\pi$
$89$	0.872197	+	1.51069i	0.0924527	+	0.160133i	−0.816090	+	0.577925i	$0.803863\pi$
$90$		−	9.25985i		−	0.976074i
$91$	−3.07377	+	17.3008i	−0.322218	+	1.81361i
$92$		−	24.6431i		−	2.56922i
$93$	1.48235	+	2.56750i	0.153712	+	0.266237i
$94$	7.65768	−	13.2635i	0.789829	−	1.36802i
$95$	4.96549	+	2.86683i	0.509449	+	0.294130i
$96$	14.8585	−	8.57856i	1.51649	−	0.875546i
$97$			12.5471i			1.27397i	0.770877	+	0.636984i	$0.219818\pi$
$97$			12.5471i			1.27397i	−0.770877	+	0.636984i	$0.780182\pi$
$98$	3.21858	+	18.5348i	0.325126	+	1.87230i
$99$			0.734473i			0.0738173i
$100$	17.9443	+	31.0804i	1.79443	+	3.10804i
$101$	−0.346754	+	0.600595i	−0.0345033	+	0.0597615i	−0.882761	−	0.469822i	$-0.844318\pi$
$101$	−0.346754	+	0.600595i	−0.0345033	+	0.0597615i	0.848258	+	0.529583i	$0.177652\pi$
$102$	8.50219	+	7.10593i	0.841843	+	0.703592i
$103$	−1.53373	−	2.65650i	−0.151123	−	0.261753i	0.780518	−	0.625134i	$-0.214956\pi$
$103$	−1.53373	−	2.65650i	−0.151123	−	0.261753i	−0.931641	+	0.363381i	$0.881622\pi$
$104$	57.5165			5.63996
$105$	1.59466	−	8.97558i	0.155623	−	0.875927i
$106$	−1.36169			−0.132259
$107$	0.0528559	−	0.0305163i	0.00510977	−	0.00295013i	−0.497443	−	0.867497i	$-0.665728\pi$
$107$	0.0528559	−	0.0305163i	0.00510977	−	0.00295013i	0.502553	+	0.864547i	$0.332394\pi$
$108$	4.52277	+	2.61122i	0.435204	+	0.251265i
$109$	−1.11532	−	0.643932i	−0.106829	−	0.0616775i	0.445634	−	0.895215i	$-0.352978\pi$
$109$	−1.11532	−	0.643932i	−0.106829	−	0.0616775i	−0.552462	+	0.833538i	$0.686312\pi$
$110$	−3.40055	−	5.88993i	−0.324230	−	0.561583i
$111$	0.821604			0.0779832
$112$	31.9105	−	11.5676i	3.01526	−	1.09303i
$113$			9.90093i			0.931401i	0.884942	+	0.465701i	$0.154198\pi$
$113$			9.90093i			0.931401i	−0.884942	+	0.465701i	$0.845802\pi$
$114$	−3.87295	+	2.23605i	−0.362735	+	0.209425i
$115$	−8.12930	+	14.0804i	−0.758061	+	1.31300i
$116$	−19.7626	−	11.4099i	−1.83491	−	1.05938i
$117$	3.32074	+	5.75169i	0.307003	+	0.531744i
$118$	−29.3659			−2.70335
$119$	7.01746	+	8.35196i	0.643289	+	0.765623i
$120$	−29.8393			−2.72395
$121$	−5.23027	−	9.05910i	−0.475480	−	0.823555i
$122$	20.0960	+	11.6024i	1.81941	+	1.05043i
$123$	−3.60719	+	6.24783i	−0.325249	+	0.563348i
$124$	13.4086	−	7.74146i	1.20413	−	0.695204i
$125$		−	6.45009i		−	0.576914i
$126$	5.44091	+	4.57752i	0.484714	+	0.407797i
$127$	−11.9764			−1.06273			−0.531365	−	0.847143i	$-0.678321\pi$
$127$	−11.9764			−1.06273			−0.531365	+	0.847143i	$0.678321\pi$
$128$	−10.3236	−	17.8809i	−0.912482	−	1.58047i
$129$	−2.73362	−	1.57826i	−0.240682	−	0.138958i
$130$	−53.2598	−	30.7496i	−4.67119	−	2.69692i
$131$	−14.7194	+	8.49826i	−1.28604	+	0.742497i	−0.977946	−	0.208858i	$-0.933025\pi$
$131$	−14.7194	+	8.49826i	−1.28604	+	0.742497i	−0.308096	+	0.951355i	$0.599692\pi$
$132$	3.83574			0.333859
$133$	−4.13913	+	1.50044i	−0.358908	+	0.130104i
$134$	−5.66495			−0.489377
$135$	−1.72279	−	2.98396i	−0.148274	−	0.256818i
$136$	22.8985	−	27.3978i	1.96353	−	2.34935i
$137$	−3.54214	+	6.13517i	−0.302626	+	0.524163i	−0.976730	−	0.214473i	$-0.931197\pi$
$137$	−3.54214	+	6.13517i	−0.302626	+	0.524163i	0.674104	+	0.738636i	$0.264530\pi$
$138$	−6.34064	−	10.9823i	−0.539751	−	0.934877i
$139$			5.98507i			0.507647i	0.967251	+	0.253823i	$0.0816882\pi$
$139$			5.98507i			0.507647i	−0.967251	+	0.253823i	$0.918312\pi$
$140$	−46.8745	−	8.32801i	−3.96161	−	0.703845i
$141$		−	5.69882i		−	0.479928i
$142$	−32.2108	+	18.5969i	−2.70307	+	1.56062i
$143$	4.22446	+	2.43899i	0.353267	+	0.203959i
$144$	6.41451	−	11.1103i	0.534543	−	0.925855i
$145$	7.52784	+	13.0386i	0.625153	+	1.08280i
$146$		−	5.76953i		−	0.477490i
$147$	4.48557	+	5.37398i	0.369964	+	0.443238i
$148$		−	4.29078i		−	0.352700i
$149$	−6.14891	−	10.6502i	−0.503738	−	0.872500i	−0.999991	−	0.00432206i	$-0.998624\pi$
$149$	−6.14891	−	10.6502i	−0.503738	−	0.872500i	0.496252	−	0.868178i	$-0.334709\pi$
$150$	15.9939	+	9.23410i	1.30590	+	0.753961i
$151$	−8.84711	+	15.3236i	−0.719968	+	1.24702i	0.241044	+	0.970514i	$0.422510\pi$
$151$	−8.84711	+	15.3236i	−0.719968	+	1.24702i	−0.961012	+	0.276507i	$0.910823\pi$
$152$	7.20555	+	12.4804i	0.584447	+	1.01229i
$153$	4.06186	+	0.708036i	0.328382	+	0.0572413i
$154$	5.14184	+	0.913531i	0.414341	+	0.0736144i
$155$	−10.2151			−0.820494
$156$	30.0379	−	17.3424i	2.40496	−	1.38850i
$157$	−7.11934	+	12.3311i	−0.568185	+	0.984126i	0.428560	+	0.903513i	$0.359021\pi$
$157$	−7.11934	+	12.3311i	−0.568185	+	0.984126i	−0.996746	+	0.0806125i	$0.974312\pi$
$158$	−27.0585	−	15.6222i	−2.15266	−	1.24284i
$159$	−0.438799	+	0.253341i	−0.0347991	+	0.0200912i
$160$			59.1162i			4.67354i
$161$	−4.25470	−	11.7371i	−0.335318	−	0.925013i
$162$	2.68746			0.211147
$163$	7.69049	−	4.44011i	0.602366	−	0.347776i	−0.167606	−	0.985854i	$-0.553604\pi$
$163$	7.69049	−	4.44011i	0.602366	−	0.347776i	0.769972	+	0.638078i	$0.220270\pi$
$164$	32.6290	+	18.8383i	2.54789	+	1.47103i
$165$	−2.19163	−	1.26534i	−0.170619	−	0.0985066i
$166$	−4.71270	−	8.16264i	−0.365777	−	0.633544i
$167$		−	15.3605i		−	1.18863i	−0.804231	−	0.594316i	$-0.797423\pi$
$167$		−	15.3605i		−	1.18863i	0.804231	−	0.594316i	$-0.202577\pi$
$168$	14.7508	−	17.5330i	1.13805	−	1.35270i
$169$	31.1093			2.39302
$170$	−35.8513	+	13.1282i	−2.74967	+	1.00688i
$171$	−0.832031	+	1.44112i	−0.0636270	+	0.110205i
$172$	−8.24235	+	14.2762i	−0.628473	+	1.08855i
$173$	−13.5001	+	7.79431i	−1.02640	+	0.592590i	−0.915950	−	0.401292i	$-0.868561\pi$
$173$	−13.5001	+	7.79431i	−1.02640	+	0.592590i	−0.110446	+	0.993882i	$0.535228\pi$
$174$	−11.7430			−0.890238
$175$	13.9127	+	11.7050i	1.05170	+	0.884813i
$176$		−	9.42257i		−	0.710253i
$177$	−9.46306	+	5.46350i	−0.711287	+	0.410662i
$178$	2.34399	−	4.05992i	0.175690	−	0.304304i
$179$	−2.50601	+	4.34053i	−0.187308	+	0.324427i	−0.944352	−	0.328937i	$-0.893310\pi$
$179$	−2.50601	+	4.34053i	−0.187308	+	0.324427i	0.757044	+	0.653364i	$0.226643\pi$
$180$	−15.5835	+	8.99716i	−1.16153	+	0.670609i
$181$			8.58767i			0.638317i	0.947701	+	0.319158i	$0.103400\pi$
$181$			8.58767i			0.638317i	−0.947701	+	0.319158i	$0.896600\pi$
$182$	44.3963	−	16.0937i	3.29087	−	1.19294i
$183$	8.63449			0.638280
$184$	−35.3899	+	20.4324i	−2.60898	+	1.50629i
$185$	−1.41545	+	2.45163i	−0.104066	+	0.180247i
$186$	3.98374	−	6.90005i	0.292102	−	0.505936i
$187$	2.84365	−	1.04130i	0.207948	−	0.0761474i
$188$	−29.7618			−2.17060
$189$	2.60496	+	0.462813i	0.189483	+	0.0336647i
$190$		−	15.4090i		−	1.11788i
$191$	6.42844	+	11.1344i	0.465146	+	0.805656i	0.999208	−	0.0397890i	$-0.0126686\pi$
$191$	6.42844	+	11.1344i	0.465146	+	0.805656i	−0.534062	+	0.845445i	$0.679335\pi$
$192$	−17.7111	−	10.2255i	−1.27819	−	0.737963i
$193$	13.3779	+	7.72374i	0.962963	+	0.555967i	0.897084	−	0.441861i	$-0.145682\pi$
$193$	13.3779	+	7.72374i	0.962963	+	0.555967i	0.0658790	+	0.997828i	$0.479015\pi$
$194$	29.2023	−	16.8600i	2.09660	−	1.21047i
$195$	−22.8837			−1.63874
$196$	28.0653	−	23.4256i	2.00466	−	1.67326i
$197$		−	21.6200i		−	1.54036i	−0.637825	−	0.770182i	$-0.720166\pi$
$197$		−	21.6200i		−	1.54036i	0.637825	−	0.770182i	$-0.279834\pi$
$198$	1.70942	−	0.986933i	0.121483	−	0.0701383i
$199$	1.04803	+	0.605080i	0.0742928	+	0.0428930i	0.536686	−	0.843782i	$-0.319676\pi$
$199$	1.04803	+	0.605080i	0.0742928	+	0.0428930i	−0.462393	+	0.886675i	$0.653009\pi$
$200$	29.7564	−	51.5396i	2.10409	−	3.64440i
$201$	−1.82551	+	1.05396i	−0.128762	+	0.0743405i
$202$	1.86378			0.131135
$203$	−11.3825	−	2.02229i	−0.798898	−	0.141937i
$204$	3.69768	−	21.2128i	0.258889	−	1.48519i
$205$	−12.4288	−	21.5274i	−0.868068	−	1.50354i
$206$	−4.12184	+	7.13924i	−0.287182	+	0.497414i
$207$	−4.08650	−	2.35934i	−0.284032	−	0.163986i
$208$	−42.6019	−	73.7886i	−2.95391	−	5.11632i
$209$			1.22221i			0.0845419i
$210$	−23.0326	+	8.34934i	−1.58940	+	0.576159i
$211$		−	8.26993i		−	0.569325i	−0.958628	−	0.284663i	$-0.908118\pi$
$211$		−	8.26993i		−	0.569325i	0.958628	−	0.284663i	$-0.0918816\pi$
$212$	1.32306	+	2.29161i	0.0908681	+	0.157388i
$213$	−6.91989	+	11.9856i	−0.474143	+	0.821240i
$214$	−0.142048	−	0.0820115i	−0.00971020	−	0.00560619i
$215$	9.41889	−	5.43800i	0.642363	−	0.370868i
$216$		−	8.66019i		−	0.589251i
$217$	5.04972	−	6.00217i	0.342797	−	0.407454i
$218$			3.46108i			0.234414i
$219$	−1.07342	−	1.85921i	−0.0725348	−	0.125634i
$220$	−6.60817	+	11.4457i	−0.445523	+	0.771668i
$221$	17.5608	−	21.0114i	1.18127	−	1.41338i
$222$	−1.10401	−	1.91221i	−0.0740965	−	0.128339i
$223$	−7.78894			−0.521586			−0.260793	−	0.965395i	$-0.583984\pi$
$223$	−7.78894			−0.521586			−0.260793	+	0.965395i	$0.583984\pi$
$224$	−34.7355	−	29.2235i	−2.32086	−	1.95258i
$225$	6.87199			0.458133
$226$	23.0435	−	13.3042i	1.53283	−	0.884981i
$227$	19.2546	+	11.1166i	1.27797	+	0.737837i	0.976475	−	0.215631i	$-0.0691808\pi$
$227$	19.2546	+	11.1166i	1.27797	+	0.737837i	0.301496	+	0.953468i	$0.402514\pi$
$228$	7.52617	+	4.34524i	0.498433	+	0.287770i
$229$	9.08552	+	15.7366i	0.600388	+	1.03990i	0.992762	+	0.120097i	$0.0383206\pi$
$229$	9.08552	+	15.7366i	0.600388	+	1.03990i	−0.392374	+	0.919806i	$0.628346\pi$
$230$	43.6943			2.88112
$231$	1.82690	−	0.662253i	0.120201	−	0.0435730i
$232$			37.8413i			2.48440i
$233$	2.24023	−	1.29340i	0.146763	−	0.0847334i	−0.424821	−	0.905278i	$-0.639663\pi$
$233$	2.24023	−	1.29340i	0.146763	−	0.0847334i	0.571583	+	0.820544i	$0.306329\pi$
$234$	8.92436	−	15.4574i	0.583404	−	1.01049i
$235$	17.0050	+	9.81786i	1.10929	+	0.640447i
$236$	28.5328	+	49.4203i	1.85733	+	3.21699i
$237$	−11.6260			−0.755190
$238$	10.0089	−	27.5553i	0.648778	−	1.78614i
$239$	−22.0029			−1.42325			−0.711624	−	0.702560i	$-0.752040\pi$
$239$	−22.0029			−1.42325			−0.711624	+	0.702560i	$0.752040\pi$
$240$	22.1017	+	38.2813i	1.42666	+	2.47104i
$241$	−18.3874	−	10.6160i	−1.18444	−	0.683835i	−0.227400	−	0.973801i	$-0.573022\pi$
$241$	−18.3874	−	10.6160i	−1.18444	−	0.683835i	−0.957037	+	0.289967i	$0.906356\pi$
$242$	−14.0562	+	24.3460i	−0.903564	+	1.56502i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		−	45.0931i		−	2.88679i
$245$	−23.7634	+	4.12652i	−1.51819	+	0.263634i
$246$	19.3884			1.23616
$247$	5.52592	+	9.57118i	0.351606	+	0.608999i
$248$	−22.2350	−	12.8374i	−1.41192	−	0.815175i
$249$	−3.03731	−	1.75359i	−0.192481	−	0.111129i
$250$	−15.0120	+	8.66718i	−0.949442	+	0.548161i
$251$	−8.84862			−0.558520			−0.279260	−	0.960216i	$-0.590089\pi$
$251$	−8.84862			−0.558520			−0.279260	+	0.960216i	$0.590089\pi$
$252$	2.41702	−	13.6042i	0.152258	−	0.856987i
$253$	−3.46575			−0.217890
$254$	16.0930	+	27.8739i	1.00977	+	1.74896i
$255$	−9.11047	+	10.9006i	−0.570520	+	0.682623i
$256$	−7.29311	+	12.6320i	−0.455819	+	0.789502i
$257$	−7.74761	−	13.4193i	−0.483283	−	0.837070i	0.516533	−	0.856267i	$-0.327222\pi$
$257$	−7.74761	−	13.4193i	−0.483283	−	0.837070i	−0.999816	+	0.0191971i	$0.993889\pi$
$258$			8.48300i			0.528128i
$259$	−0.740816	−	2.04363i	−0.0460321	−	0.126985i
$260$			119.509i			7.41163i
$261$	−3.78416	+	2.18479i	−0.234234	+	0.135235i
$262$	39.5579	+	22.8387i	2.44389	+	1.41098i
$263$	−4.05408	+	7.02187i	−0.249985	+	0.432987i	−0.963521	−	0.267631i	$-0.913759\pi$
$263$	−4.05408	+	7.02187i	−0.249985	+	0.432987i	0.713536	+	0.700618i	$0.247092\pi$
$264$	−3.18034	−	5.50850i	−0.195736	−	0.339025i
$265$		−	1.74581i		−	0.107244i
$266$	9.05401	+	7.61727i	0.555137	+	0.467045i
$267$		−	1.74439i		−	0.106755i
$268$	5.50424	+	9.53363i	0.336225	+	0.582359i
$269$	0.439196	+	0.253570i	0.0267783	+	0.0154604i	0.513329	−	0.858192i	$-0.328412\pi$
$269$	0.439196	+	0.253570i	0.0267783	+	0.0154604i	−0.486551	+	0.873652i	$0.661745\pi$
$270$	−4.62992	+	8.01926i	−0.281768	+	0.488037i
$271$	0.0889435	+	0.154055i	0.00540293	+	0.00935815i	0.868714	−	0.495314i	$-0.164947\pi$
$271$	0.0889435	+	0.154055i	0.00540293	+	0.00935815i	−0.863311	+	0.504672i	$0.831614\pi$
$272$	−52.1097	−	9.08341i	−3.15961	−	0.550763i
$273$	11.3124	−	13.4460i	0.684655	−	0.813791i
$274$	19.0387			1.15017
$275$	4.37108	−	2.52365i	0.263586	−	0.152182i
$276$	−12.3215	+	21.3415i	−0.741670	+	1.28461i
$277$	−25.0775	−	14.4785i	−1.50676	−	0.869930i	−0.999969	−	0.00786258i	$-0.997497\pi$
$277$	−25.0775	−	14.4785i	−1.50676	−	0.869930i	−0.506794	−	0.862067i	$-0.669169\pi$
$278$	13.9297	−	8.04232i	0.835448	−	0.482346i
$279$		−	2.96469i		−	0.177491i
$280$	26.9053	+	74.2214i	1.60790	+	4.43557i
$281$	−3.87418			−0.231114			−0.115557	−	0.993301i	$-0.536865\pi$
$281$	−3.87418			−0.231114			−0.115557	+	0.993301i	$0.536865\pi$
$282$	−13.2635	+	7.65768i	−0.789829	+	0.456008i
$283$	−0.795522	−	0.459295i	−0.0472889	−	0.0273022i	0.476169	−	0.879354i	$-0.342025\pi$
$283$	−0.795522	−	0.459295i	−0.0472889	−	0.0273022i	−0.523458	+	0.852051i	$0.675358\pi$
$284$	62.5941	+	36.1387i	3.71428	+	2.14444i
$285$	−2.86683	−	4.96549i	−0.169816	−	0.294130i
$286$		−	13.1094i		−	0.775175i
$287$	18.7931	+	3.33891i	1.10932	+	0.197090i
$288$	−17.1571			−1.01099
$289$	−3.01741	−	16.7301i	−0.177495	−	0.984122i
$290$	20.2308	−	35.0407i	1.18799	−	2.05766i
$291$	6.27357	−	10.8661i	0.367763	−	0.636984i
$292$	−9.70964	+	5.60586i	−0.568214	+	0.328058i
$293$	18.8923			1.10370			0.551849	−	0.833944i	$-0.313922\pi$
$293$	18.8923			1.10370			0.551849	+	0.833944i	$0.313922\pi$
$294$	6.48005	−	17.6609i	0.377924	−	1.03001i
$295$		−	37.6498i		−	2.19206i
$296$	−6.16198	+	3.55762i	−0.358158	+	0.206783i
$297$	0.367236	−	0.636072i	0.0213092	−	0.0369086i
$298$	−16.5250	+	28.6221i	−0.957265	+	1.65803i
$299$	−27.1404	+	15.6695i	−1.56957	+	0.906193i
$300$		−	35.8886i		−	2.07203i
$301$	−1.46087	+	8.22258i	−0.0842034	+	0.473941i
$302$	47.5525			2.73634
$303$	0.600595	−	0.346754i	0.0345033	−	0.0199205i
$304$	10.6742	−	18.4882i	0.612205	−	1.06037i
$305$	−14.8754	+	25.7649i	−0.851763	+	1.47530i
$306$	−3.81015	−	10.4050i	−0.217812	−	0.594815i
$307$	6.79127			0.387598			0.193799	−	0.981041i	$-0.437919\pi$
$307$	6.79127			0.387598			0.193799	+	0.981041i	$0.437919\pi$
$308$	−3.45858	−	9.54090i	−0.197071	−	0.543643i
$309$			3.06746i			0.174502i
$310$	13.7263	+	23.7746i	0.779601	+	1.35031i
$311$	−16.7970	−	9.69776i	−0.952471	−	0.549910i	−0.0586236	−	0.998280i	$-0.518671\pi$
$311$	−16.7970	−	9.69776i	−0.952471	−	0.549910i	−0.893848	+	0.448371i	$0.852005\pi$
$312$	−49.8108	−	28.7583i	−2.81998	−	1.62812i
$313$	−9.84706	+	5.68520i	−0.556589	+	0.321347i	−0.751775	−	0.659420i	$-0.770802\pi$
$313$	−9.84706	+	5.68520i	−0.556589	+	0.321347i	0.195187	+	0.980766i	$0.437469\pi$
$314$	38.2659			2.15947
$315$	−5.86880	+	6.97575i	−0.330670	+	0.393039i
$316$			60.7161i			3.41555i
$317$	−17.2322	+	9.94901i	−0.967856	+	0.558792i	−0.898582	−	0.438805i	$-0.855402\pi$
$317$	−17.2322	+	9.94901i	−0.967856	+	0.558792i	−0.0692744	+	0.997598i	$0.522068\pi$
$318$	1.17926	+	0.680844i	0.0661294	+	0.0381798i
$319$	−1.60467	+	2.77936i	−0.0898440	+	0.155614i
$320$	61.0250	−	35.2328i	3.41140	−	1.96957i
$321$	−0.0610327			−0.00340651
$322$	−21.5999	+	25.6739i	−1.20371	+	1.43075i
$323$	6.75918	+	1.17822i	0.376091	+	0.0655577i
$324$	−2.61122	−	4.52277i	−0.145068	−	0.251265i
$325$	22.8201	−	39.5256i	1.26583	−	2.19249i
$326$	−20.6679	−	11.9326i	−1.14469	−	0.660886i
$327$	0.643932	+	1.11532i	0.0356095	+	0.0616775i
$328$		−	62.4779i		−	3.44976i
$329$	−14.1751	+	5.13846i	−0.781496	+	0.283293i
$330$			6.80111i			0.374389i
$331$	−2.56433	−	4.44156i	−0.140949	−	0.244130i	0.786906	−	0.617073i	$-0.211682\pi$
$331$	−2.56433	−	4.44156i	−0.140949	−	0.244130i	−0.927854	+	0.372943i	$0.878349\pi$
$332$	−9.15802	+	15.8622i	−0.502612	+	0.870549i
$333$	−0.711530	−	0.410802i	−0.0389916	−	0.0225118i
$334$	−35.7502	+	20.6404i	−1.95616	+	1.12939i
$335$		−	7.26299i		−	0.396820i
$336$	−33.4191	−	5.93744i	−1.82316	−	0.323914i
$337$			18.2287i			0.992980i	0.868042	+	0.496490i	$0.165378\pi$
$337$			18.2287i			0.992980i	−0.868042	+	0.496490i	$0.834622\pi$
$338$	−41.8025	−	72.4041i	−2.27376	−	3.93826i
$339$	4.95047	−	8.57446i	0.268872	−	0.465701i
$340$	56.9278	+	47.5789i	3.08734	+	2.58033i
$341$	−1.08874	−	1.88576i	−0.0589587	−	0.102119i
$342$	4.47210			0.241824
$343$	9.32254	−	16.0028i	0.503370	−	0.864071i
$344$	27.3360			1.47386
$345$	14.0804	−	8.12930i	0.758061	−	0.437667i
$346$	36.2811	+	20.9469i	1.95048	+	1.12611i
$347$	−8.51554	−	4.91645i	−0.457138	−	0.263929i	0.253702	−	0.967282i	$-0.418352\pi$
$347$	−8.51554	−	4.91645i	−0.457138	−	0.263929i	−0.710840	+	0.703354i	$0.751685\pi$
$348$	11.4099	+	19.7626i	0.611636	+	1.05938i
$349$	−17.5158			−0.937600			−0.468800	−	0.883304i	$-0.655314\pi$
$349$	−17.5158			−0.937600			−0.468800	+	0.883304i	$0.655314\pi$
$350$	8.54733	−	48.1089i	0.456874	−	2.57153i
$351$		−	6.64148i		−	0.354496i
$352$	−10.9132	+	6.30072i	−0.581674	+	0.335830i
$353$	−10.3760	+	17.9718i	−0.552261	+	0.956544i	0.445850	+	0.895108i	$0.352901\pi$
$353$	−10.3760	+	17.9718i	−0.552261	+	0.956544i	−0.998111	+	0.0614363i	$0.980432\pi$
$354$	25.4316	+	14.6829i	1.35167	+	0.780390i
$355$	−23.8430	−	41.2973i	−1.26546	−	2.19183i
$356$	−9.11000			−0.482829
$357$	−1.90131	−	10.7417i	−0.100628	−	0.568513i
$358$	13.4696			0.711890
$359$	−0.556750	−	0.964319i	−0.0293841	−	0.0508948i	0.850959	−	0.525232i	$-0.176021\pi$
$359$	−0.556750	−	0.964319i	−0.0293841	−	0.0508948i	−0.880344	+	0.474337i	$0.842688\pi$
$360$	25.8416	+	14.9197i	1.36197	+	0.786336i
$361$	8.11545	−	14.0564i	0.427129	−	0.739809i
$362$	19.9870	−	11.5395i	1.05049	−	0.606504i
$363$			10.4605i			0.549036i
$364$	−70.2212	−	59.0781i	−3.68059	−	3.09653i
$365$	7.39708			0.387181
$366$	−11.6024	−	20.0960i	−0.606469	−	1.05043i
$367$	24.7549	+	14.2922i	1.29219	+	0.746048i	0.979043	−	0.203656i	$-0.0652823\pi$
$367$	24.7549	+	14.2922i	1.29219	+	0.746048i	0.313150	+	0.949704i	$0.398616\pi$
$368$	52.4259	+	30.2681i	2.73289	+	1.57783i
$369$	6.24783	−	3.60719i	0.325249	−	0.187783i
$370$	7.60792			0.395517
$371$	1.02580	+	0.863025i	0.0532571	+	0.0448060i
$372$	−15.4829			−0.802752
$373$	12.7175	+	22.0274i	0.658489	+	1.14054i	0.981007	+	0.193974i	$0.0621376\pi$
$373$	12.7175	+	22.0274i	0.658489	+	1.14054i	−0.322517	+	0.946564i	$0.604529\pi$
$374$	−6.24463	−	5.21911i	−0.322902	−	0.269874i
$375$	−3.22505	+	5.58594i	−0.166541	+	0.288457i
$376$	24.6764	+	42.7409i	1.27259	+	2.20419i
$377$			29.0204i			1.49463i
$378$	−2.42320	−	6.68470i	−0.124636	−	0.343824i
$379$			30.0748i			1.54484i	0.635113	+	0.772419i	$0.280953\pi$
$379$			30.0748i			1.54484i	−0.635113	+	0.772419i	$0.719047\pi$
$380$	−25.9320	+	14.9718i	−1.33028	+	0.768039i
$381$	10.3718	+	5.98818i	0.531365	+	0.306784i
$382$	17.2762	−	29.9232i	0.883927	−	1.53101i
$383$	7.69774	+	13.3329i	0.393336	+	0.681278i	0.992887	−	0.119058i	$-0.0379875\pi$
$383$	7.69774	+	13.3329i	0.393336	+	0.681278i	−0.599551	+	0.800336i	$0.704654\pi$
$384$			20.6471i			1.05364i
$385$	−1.17123	+	6.59232i	−0.0596915	+	0.335976i
$386$		−	41.5145i		−	2.11303i
$387$	1.57826	+	2.73362i	0.0802272	+	0.138958i
$388$	−56.7478	−	32.7634i	−2.88093	−	1.66331i
$389$	13.7754	−	23.8598i	0.698443	−	1.20974i	−0.270563	−	0.962702i	$-0.587210\pi$
$389$	13.7754	−	23.8598i	0.698443	−	1.20974i	0.969006	−	0.247037i	$-0.0794568\pi$
$390$	30.7496	+	53.2598i	1.55706	+	2.69692i
$391$	−3.34100	+	19.1666i	−0.168962	+	0.969299i
$392$	−56.9114	−	20.8816i	−2.87446	−	1.05468i
$393$	16.9965			0.857361
$394$	−50.3186	+	29.0515i	−2.53502	+	1.46359i
$395$	20.0291	−	34.6915i	1.00778	−	1.74552i
$396$	−3.32185	−	1.91787i	−0.166929	−	0.0963767i
$397$	27.4754	−	15.8629i	1.37895	−	0.796138i	0.386918	−	0.922114i	$-0.373539\pi$
$397$	27.4754	−	15.8629i	1.37895	−	0.796138i	0.992033	+	0.125976i	$0.0402062\pi$
$398$		−	3.25225i		−	0.163021i
$399$	4.33481	+	0.770150i	0.217012	+	0.0385557i
$400$	−88.1610			−4.40805
$401$	29.7121	−	17.1543i	1.48375	−	0.856644i	0.483921	−	0.875112i	$-0.339212\pi$
$401$	29.7121	−	17.1543i	1.48375	−	0.856644i	0.999829	+	0.0184679i	$0.00587885\pi$
$402$	4.90599	+	2.83247i	0.244688	+	0.141271i
$403$	−17.0520	−	9.84497i	−0.849420	−	0.490413i
$404$	−1.81090	−	3.13658i	−0.0900958	−	0.156050i
$405$			3.44558i			0.171212i
$406$	10.5884	+	29.2093i	0.525492	+	1.44963i
$407$	−0.603445			−0.0299117
$408$	−33.5296	+	12.2780i	−1.65996	+	0.607851i
$409$	−10.6787	+	18.4960i	−0.528025	+	0.914567i	0.471441	+	0.881898i	$0.343734\pi$
$409$	−10.6787	+	18.4960i	−0.528025	+	0.914567i	−0.999466	+	0.0326691i	$0.989599\pi$
$410$	−33.4020	+	57.8540i	−1.64961	+	2.85721i
$411$	6.13517	−	3.54214i	0.302626	−	0.174721i
$412$	16.0196			0.789231
$413$	22.1223	+	18.6118i	1.08857	+	0.915828i
$414$			12.6813i			0.623251i
$415$	10.4653	−	6.04212i	0.513720	−	0.296596i
$416$	−56.9744	+	98.6825i	−2.79340	+	4.83831i
$417$	2.99253	−	5.18322i	0.146545	−	0.253823i
$418$	2.84458	−	1.64232i	0.139133	−	0.0803284i
$419$		−	13.2879i		−	0.649157i	−0.945859	−	0.324578i	$-0.894778\pi$
$419$		−	13.2879i		−	0.649157i	0.945859	−	0.324578i	$-0.105222\pi$
$420$	36.4305	+	30.6495i	1.77762	+	1.49554i
$421$	−10.8694			−0.529743			−0.264872	−	0.964284i	$-0.585330\pi$
$421$	−10.8694			−0.529743			−0.264872	+	0.964284i	$0.585330\pi$
$422$	−19.2475	+	11.1125i	−0.936954	+	0.540950i
$423$	−2.84941	+	4.93533i	−0.138543	+	0.239964i
$424$	2.19398	−	3.80009i	0.106549	−	0.184549i
$425$	−9.74278	−	26.6062i	−0.472594	−	1.29059i
$426$	37.1939			1.80205
$427$	−7.78547	−	21.4771i	−0.376765	−	1.03935i
$428$			0.318740i			0.0154069i
$429$	−2.43899	−	4.22446i	−0.117756	−	0.203959i
$430$	−25.3129	−	14.6144i	−1.22070	−	0.704769i
$431$	−14.9419	−	8.62668i	−0.719724	−	0.415533i	0.0949273	−	0.995484i	$-0.469738\pi$
$431$	−14.9419	−	8.62668i	−0.719724	−	0.415533i	−0.814651	+	0.579952i	$0.803071\pi$
$432$	−11.1103	+	6.41451i	−0.534543	+	0.308618i
$433$	5.29663			0.254540			0.127270	−	0.991868i	$-0.459379\pi$
$433$	5.29663			0.254540			0.127270	+	0.991868i	$0.459379\pi$
$434$	−20.7550	−	3.68746i	−0.996270	−	0.177004i
$435$		−	15.0557i		−	0.721865i
$436$	5.82471	−	3.36290i	0.278953	−	0.161054i
$437$	−6.80020	−	3.92610i	−0.325298	−	0.187811i
$438$	−2.88477	+	4.99656i	−0.137840	+	0.238745i
$439$	−9.61354	+	5.55038i	−0.458829	+	0.264905i	−0.711552	−	0.702634i	$-0.752007\pi$
$439$	−9.61354	+	5.55038i	−0.458829	+	0.264905i	0.252723	+	0.967539i	$0.418674\pi$
$440$	21.9162			1.04481
$441$	−1.19763	−	6.89679i	−0.0570299	−	0.328418i
$442$	−72.4990	−	12.6375i	−3.44842	−	0.601106i
$443$	5.63408	+	9.75851i	0.267683	+	0.463641i	0.968263	−	0.249933i	$-0.0804086\pi$
$443$	5.63408	+	9.75851i	0.267683	+	0.463641i	−0.700580	+	0.713574i	$0.747075\pi$
$444$	−2.14539	+	3.71592i	−0.101816	+	0.176350i
$445$	5.20519	+	3.00522i	0.246750	+	0.142461i
$446$	10.4662	+	18.1280i	0.495590	+	0.858388i
$447$			12.2978i			0.581667i
$448$	−9.46501	+	53.2741i	−0.447180	+	2.51696i
$449$			21.5839i			1.01861i	0.860587	+	0.509303i	$0.170097\pi$
$449$			21.5839i			1.01861i	−0.860587	+	0.509303i	$0.829903\pi$
$450$	−9.23410	−	15.9939i	−0.435300	−	0.753961i
$451$	2.64938	−	4.58886i	0.124755	−	0.216081i
$452$	−44.7796	−	25.8535i	−2.10626	−	1.21605i
$453$	15.3236	−	8.84711i	0.719968	−	0.415674i
$454$		−	59.7510i		−	2.80425i
$455$	20.6336	+	56.9202i	0.967318	+	2.66846i
$456$		−	14.4111i		−	0.674861i
$457$	−3.68744	−	6.38683i	−0.172491	−	0.298763i	0.766799	−	0.641887i	$-0.221848\pi$
$457$	−3.68744	−	6.38683i	−0.172491	−	0.298763i	−0.939290	+	0.343124i	$0.888515\pi$
$458$	24.4170	−	42.2915i	1.14093	−	1.97615i
$459$	−3.16365	−	2.64411i	−0.147667	−	0.123416i
$460$	−42.4548	−	73.5339i	−1.97947	−	3.42853i
$461$	−17.2157			−0.801816			−0.400908	−	0.916118i	$-0.631305\pi$
$461$	−17.2157			−0.801816			−0.400908	+	0.916118i	$0.631305\pi$
$462$	−3.99620	−	3.36206i	−0.185920	−	0.156417i
$463$	−26.5827			−1.23540			−0.617701	−	0.786413i	$-0.711936\pi$
$463$	−26.5827			−1.23540			−0.617701	+	0.786413i	$0.711936\pi$
$464$	48.5471	−	28.0287i	2.25374	−	1.30120i
$465$	8.84651	+	5.10753i	0.410247	+	0.236856i
$466$	−6.02054	−	3.47596i	−0.278896	−	0.161021i
$467$	−20.8691	−	36.1463i	−0.965706	−	1.67265i	−0.707706	−	0.706507i	$-0.750270\pi$
$467$	−20.8691	−	36.1463i	−0.965706	−	1.67265i	−0.258000	−	0.966145i	$-0.583063\pi$
$468$	−34.6848			−1.60330
$469$	4.26759	+	3.59039i	0.197059	+	0.165789i
$470$		−	52.7702i		−	2.43411i
$471$	12.3311	−	7.11934i	0.568185	−	0.328042i
$472$	47.3150	−	81.9519i	2.17785	−	3.77214i
$473$	2.00777	+	1.15919i	0.0923173	+	0.0532994i
$474$	15.6222	+	27.0585i	0.717552	+	1.24284i
$475$	11.4354			0.524693
$476$	−56.0981	+	9.92951i	−2.57125	+	0.455118i
$477$	0.506682			0.0231994
$478$	29.5659	+	51.2097i	1.35231	+	2.34228i
$479$	−13.1849	−	7.61233i	−0.602436	−	0.347816i	0.167564	−	0.985861i	$-0.446410\pi$
$479$	−13.1849	−	7.61233i	−0.602436	−	0.347816i	−0.769999	+	0.638045i	$0.779743\pi$
$480$	29.5581	−	51.1961i	1.34914	−	2.33677i
$481$	−4.72561	+	2.72833i	−0.215469	+	0.124401i
$482$			57.0600i			2.59901i
$483$	−2.18387	+	12.2920i	−0.0993696	+	0.559305i
$484$	54.6296			2.48316
$485$	21.6161	+	37.4401i	0.981534	+	1.70007i
$486$	−2.32741	−	1.34373i	−0.105573	−	0.0609528i
$487$	5.61774	+	3.24340i	0.254564	+	0.146973i	0.621852	−	0.783135i	$-0.286380\pi$
$487$	5.61774	+	3.24340i	0.254564	+	0.146973i	−0.367288	+	0.930107i	$0.619714\pi$
$488$	−64.7582	+	37.3882i	−2.93147	+	1.69248i
$489$	−8.88021			−0.401577
$490$	41.5357	+	49.7622i	1.87639	+	2.24803i
$491$	−32.0196			−1.44503			−0.722513	−	0.691357i	$-0.757013\pi$
$491$	−32.0196			−1.44503			−0.722513	+	0.691357i	$0.757013\pi$
$492$	−18.8383	−	32.6290i	−0.849298	−	1.47103i
$493$	13.8238	+	11.5536i	0.622593	+	0.520348i
$494$	14.8507	−	25.7222i	0.668164	−	1.15729i
$495$	1.26534	+	2.19163i	0.0568728	+	0.0985066i
$496$			38.0341i			1.70778i
$497$	36.0521	+	6.40523i	1.61716	+	0.287314i
$498$			9.42540i			0.422362i
$499$	18.6848	−	10.7877i	0.836447	−	0.482923i	−0.0196078	−	0.999808i	$-0.506242\pi$
$499$	18.6848	−	10.7877i	0.836447	−	0.482923i	0.856055	+	0.516885i	$0.172908\pi$
$500$	29.1723	+	16.8426i	1.30462	+	0.753225i
$501$	−7.68026	+	13.3026i	−0.343129	+	0.594316i
$502$	11.8902	+	20.5944i	0.530684	+	0.919171i
$503$			9.46993i			0.422243i	0.977460	+	0.211122i	$0.0677116\pi$
$503$			9.46993i			0.422243i	−0.977460	+	0.211122i	$0.932288\pi$
$504$	−21.5411	+	7.80864i	−0.959515	+	0.347824i
$505$			2.38953i			0.106333i
$506$	4.65703	+	8.06621i	0.207030	+	0.358587i
$507$	−26.9414	−	15.5547i	−1.19651	−	0.690806i
$508$	31.2730	−	54.1663i	1.38751	−	2.40324i
$509$	−0.920031	−	1.59354i	−0.0407797	−	0.0706325i	0.844915	−	0.534900i	$-0.179651\pi$
$509$	−0.920031	−	1.59354i	−0.0407797	−	0.0706325i	−0.885695	+	0.464268i	$0.846318\pi$
$510$	37.6122	+	6.55631i	1.66550	+	0.290318i
$511$	−3.65668	+	4.34638i	−0.161762	+	0.192273i
$512$	−2.09435			−0.0925583
$513$	1.44112	−	0.832031i	0.0636270	−	0.0367351i
$514$	−20.8214	+	36.0637i	−0.918392	+	1.59070i
$515$	−9.15317	−	5.28459i	−0.403337	−	0.232867i
$516$	14.2762	−	8.24235i	0.628473	−	0.362849i
$517$			4.18563i			0.184084i
$518$	−3.76090	+	4.47027i	−0.165245	+	0.196412i
$519$	15.5886			0.684265
$520$	171.627	−	99.0887i	7.52633	−	4.34533i
$521$	−29.4120	−	16.9810i	−1.28856	−	0.743951i	−0.310164	−	0.950683i	$-0.600384\pi$
$521$	−29.4120	−	16.9810i	−1.28856	−	0.743951i	−0.978398	+	0.206732i	$0.933717\pi$
$522$	10.1698	+	5.87152i	0.445119	+	0.256990i
$523$	13.1172	+	22.7197i	0.573576	+	0.993462i	0.996195	+	0.0871549i	$0.0277775\pi$
$523$	13.1172	+	22.7197i	0.573576	+	0.993462i	−0.422619	+	0.906307i	$0.638889\pi$
$524$		−	88.7634i		−	3.87765i
$525$	−6.19628	−	17.0932i	−0.270428	−	0.746007i
$526$	21.7903			0.950104
$527$	−11.4784	+	4.20319i	−0.500005	+	0.183094i
$528$	−4.71129	+	8.16019i	−0.205032	+	0.355127i
$529$	−0.366990	+	0.635645i	−0.0159561	+	0.0276367i
$530$	−4.06322	+	2.34590i	−0.176495	+	0.101899i
$531$	10.9270			0.474192
$532$	4.02206	−	22.6383i	0.174379	−	0.981495i
$533$		−	47.9142i		−	2.07539i
$534$	−4.05992	+	2.34399i	−0.175690	+	0.101435i
$535$	0.105146	−	0.182119i	0.00454587	−	0.00787368i
$536$	9.12748	−	15.8093i	0.394247	−	0.682856i
$537$	4.34053	−	2.50601i	0.187308	−	0.108142i
$538$		−	1.36292i		−	0.0587596i
$539$	−3.29453	−	3.94704i	−0.141905	−	0.170011i
$540$	17.9943			0.774352
$541$	−32.3222	+	18.6612i	−1.38964	+	0.802308i	−0.993274	−	0.115785i	$-0.963062\pi$
$541$	−32.3222	+	18.6612i	−1.38964	+	0.802308i	−0.396365	+	0.918093i	$0.629728\pi$
$542$	0.239032	−	0.414016i	0.0102673	−	0.0177835i
$543$	4.29384	−	7.43714i	0.184266	−	0.319158i
$544$	24.3245	+	66.4271i	1.04291	+	2.84804i
$545$	−4.43743			−0.190079
$546$	−46.4952	−	8.26062i	−1.98981	−	0.353522i
$547$		−	31.9948i		−	1.36800i	−0.729482	−	0.684000i	$-0.760239\pi$
$547$		−	31.9948i		−	1.36800i	0.729482	−	0.684000i	$-0.239761\pi$
$548$	−18.4986	−	32.0406i	−0.790223	−	1.36871i
$549$	−7.47769	−	4.31725i	−0.319140	−	0.184256i
$550$	−11.7471	−	6.78220i	−0.500898	−	0.289194i
$551$	−6.29708	+	3.63562i	−0.268265	+	0.154883i
$552$	40.8647			1.73932
$553$	10.4828	+	28.9181i	0.445775	+	1.22972i
$554$			77.8209i			3.30629i
$555$	2.45163	−	1.41545i	0.104066	−	0.0600825i
$556$	−27.0691	−	15.6283i	−1.14798	−	0.662789i
$557$	17.5217	−	30.3484i	0.742418	−	1.28591i	−0.208974	−	0.977921i	$-0.567012\pi$
$557$	17.5217	−	30.3484i	0.742418	−	1.28591i	0.951392	−	0.307984i	$-0.0996543\pi$
$558$	−6.90005	+	3.98374i	−0.292102	+	0.168645i
$559$	20.9639			0.886679
$560$	75.2910	−	89.4921i	3.18163	−	3.78173i
$561$	−2.98332	−	0.520033i	−0.125956	−	0.0219558i
$562$	5.20585	+	9.01680i	0.219596	+	0.380351i
$563$	2.52380	−	4.37136i	0.106366	−	0.184231i	−0.807930	−	0.589279i	$-0.799412\pi$
$563$	2.52380	−	4.37136i	0.106366	−	0.184231i	0.914295	+	0.405048i	$0.132745\pi$
$564$	25.7745	+	14.8809i	1.08530	+	0.626599i
$565$	17.0572	+	29.5439i	0.717602	+	1.24292i
$566$			2.46867i			0.103766i
$567$	−2.02455	−	1.70329i	−0.0850232	−	0.0715313i
$568$		−	119.855i		−	5.02901i
$569$	−2.11760	−	3.66780i	−0.0887746	−	0.153762i	0.818219	−	0.574907i	$-0.194962\pi$
$569$	−2.11760	−	3.66780i	−0.0887746	−	0.153762i	−0.906993	+	0.421145i	$0.861628\pi$
$570$	−7.70448	+	13.3446i	−0.322705	+	0.558942i
$571$	14.6099	+	8.43501i	0.611404	+	0.352994i	0.773515	−	0.633778i	$-0.218497\pi$
$571$	14.6099	+	8.43501i	0.611404	+	0.352994i	−0.162111	+	0.986773i	$0.551830\pi$
$572$	−22.0620	+	12.7375i	−0.922459	+	0.532582i
$573$		−	12.8569i		−	0.537104i
$574$	−17.4819	−	48.2259i	−0.729681	−	2.01291i
$575$			32.4268i			1.35229i
$576$	10.2255	+	17.7111i	0.426063	+	0.737963i
$577$	18.1321	−	31.4058i	0.754850	−	1.30744i	−0.190599	−	0.981668i	$-0.561043\pi$
$577$	18.1321	−	31.4058i	0.754850	−	1.30744i	0.945449	−	0.325771i	$-0.105624\pi$
$578$	−34.8831	+	29.5034i	−1.45095	+	1.22718i
$579$	−7.72374	−	13.3779i	−0.320988	−	0.555967i
$580$	−78.6275			−3.26483
$581$	−1.62317	+	9.13605i	−0.0673404	+	0.379027i
$582$	−33.7199			−1.39774
$583$	0.322286	−	0.186072i	0.0133477	−	0.00770632i
$584$	16.1011	+	9.29600i	0.666270	+	0.384671i
$585$	19.8179	+	11.4419i	0.819369	+	0.473063i
$586$	−25.3861	−	43.9701i	−1.04869	−	1.81639i
$587$	−27.2283			−1.12383			−0.561916	−	0.827195i	$-0.689935\pi$
$587$	−27.2283			−1.12383			−0.561916	+	0.827195i	$0.689935\pi$
$588$	−36.0181	+	6.25455i	−1.48536	+	0.257933i
$589$		−	4.93343i		−	0.203278i
$590$	−87.6265	+	50.5912i	−3.60753	+	2.08281i
$591$	−10.8100	+	18.7235i	−0.444665	+	0.770182i
$592$	9.12823	+	5.27019i	0.375168	+	0.216603i
$593$	9.23837	+	16.0013i	0.379374	+	0.657096i	0.990971	−	0.134074i	$-0.0428059\pi$
$593$	9.23837	+	16.0013i	0.379374	+	0.657096i	−0.611597	+	0.791169i	$0.709473\pi$
$594$	−1.97387			−0.0809887
$595$	35.3284	+	12.8323i	1.44833	+	0.526073i
$596$	64.2247			2.63074
$597$	−0.605080	−	1.04803i	−0.0247643	−	0.0428930i
$598$	72.9389	+	42.1113i	2.98269	+	1.72206i
$599$	−13.3034	+	23.0421i	−0.543561	+	0.941475i	0.455135	+	0.890422i	$0.349591\pi$
$599$	−13.3034	+	23.0421i	−0.543561	+	0.941475i	−0.998696	+	0.0510528i	$0.983742\pi$
$600$	−51.5396	+	29.7564i	−2.10409	+	1.21480i
$601$		−	39.2187i		−	1.59976i	−0.600157	−	0.799882i	$-0.704895\pi$
$601$		−	39.2187i		−	1.59976i	0.600157	−	0.799882i	$-0.295105\pi$
$602$	21.1003	−	7.64887i	0.859985	−	0.311745i
$603$	2.10792			0.0858411
$604$	−46.2035	−	80.0269i	−1.88000	−	3.25625i
$605$	−31.2138	−	18.0213i	−1.26902	−	0.732670i
$606$	−1.61408	−	0.931888i	−0.0655674	−	0.0378553i
$607$	1.00085	−	0.577840i	0.0406232	−	0.0234538i	−0.479551	−	0.877514i	$-0.659200\pi$
$607$	1.00085	−	0.577840i	0.0406232	−	0.0234538i	0.520174	+	0.854060i	$0.325867\pi$
$608$	−28.5505			−1.15788
$609$	8.84643	+	7.44263i	0.358475	+	0.301591i
$610$	79.9541			3.23725
$611$	18.9243	+	32.7779i	0.765596	+	1.32605i
$612$	−13.8087	+	16.5220i	−0.558183	+	0.667862i
$613$	3.73593	−	6.47083i	0.150893	−	0.261354i	−0.780663	−	0.624952i	$-0.785118\pi$
$613$	3.73593	−	6.47083i	0.150893	−	0.261354i	0.931556	+	0.363598i	$0.118452\pi$
$614$	−9.12563	−	15.8061i	−0.368280	−	0.637880i
$615$			24.8577i			1.00236i
$616$	−10.8340	+	12.8775i	−0.436516	+	0.518850i
$617$		−	16.1698i		−	0.650971i	−0.945547	−	0.325485i	$-0.894472\pi$
$617$		−	16.1698i		−	0.650971i	0.945547	−	0.325485i	$-0.105528\pi$
$618$	7.13924	−	4.12184i	0.287182	−	0.165805i
$619$	−6.24959	−	3.60821i	−0.251192	−	0.145026i	0.369118	−	0.929383i	$-0.379660\pi$
$619$	−6.24959	−	3.60821i	−0.251192	−	0.145026i	−0.620310	+	0.784357i	$0.712993\pi$
$620$	26.6738	−	46.2004i	1.07125	−	1.85545i
$621$	2.35934	+	4.08650i	0.0946772	+	0.163986i
$622$			52.1247i			2.09001i
$623$	−4.33894	+	1.57287i	−0.173836	+	0.0630157i
$624$			85.2038i			3.41088i
$625$	6.06784	+	10.5098i	0.242714	+	0.420392i
$626$	26.4636	+	15.2788i	1.05770	+	0.610662i
$627$	0.611104	−	1.05846i	0.0244052	−	0.0422710i
$628$	−37.1804	−	64.3983i	−1.48366	−	2.56977i
$629$	−0.581725	+	3.33724i	−0.0231949	+	0.133064i
$630$	24.1215	+	4.28558i	0.961024	+	0.170742i
$631$	−17.5995			−0.700625			−0.350313	−	0.936633i	$-0.613925\pi$
$631$	−17.5995			−0.700625			−0.350313	+	0.936633i	$0.613925\pi$
$632$	87.1944	−	50.3417i	3.46841	−	2.00249i
$633$	−4.13496	+	7.16197i	−0.164350	+	0.284663i
$634$	46.3108	+	26.7376i	1.83924	+	1.06188i
$635$	−35.7370	+	20.6327i	−1.41818	+	0.818785i
$636$		−	2.64612i		−	0.104925i
$637$	−43.6452	−	16.0141i	−1.72929	−	0.634500i
$638$	8.62495			0.341465
$639$	11.9856	−	6.91989i	0.474143	−	0.273747i
$640$	−61.6101	−	35.5706i	−2.43535	−	1.40605i
$641$	27.2757	+	15.7476i	1.07733	+	0.621995i	0.930174	−	0.367119i	$-0.119656\pi$
$641$	27.2757	+	15.7476i	1.07733	+	0.621995i	0.147153	+	0.989114i	$0.452989\pi$
$642$	0.0820115	+	0.142048i	0.00323673	+	0.00560619i
$643$		−	32.3288i		−	1.27492i	−0.770483	−	0.637461i	$-0.779985\pi$
$643$		−	32.3288i		−	1.27492i	0.770483	−	0.637461i	$-0.220015\pi$
$644$	64.1942	+	11.4051i	2.52961	+	0.449426i
$645$	−10.8760			−0.428242
$646$	−6.34033	−	17.3146i	−0.249457	−	0.681234i
$647$	−8.68766	+	15.0475i	−0.341547	+	0.591577i	−0.984720	−	0.174144i	$-0.944284\pi$
$647$	−8.68766	+	15.0475i	−0.341547	+	0.591577i	0.643173	+	0.765721i	$0.277618\pi$
$648$	−4.33009	+	7.49994i	−0.170102	+	0.294626i
$649$	6.95036	−	4.01279i	0.272826	−	0.157516i
$650$	−122.656			−4.81098
$651$	−7.37427	+	2.67318i	−0.289020	+	0.104770i
$652$			46.3764i			1.81624i
$653$	31.6791	−	18.2899i	1.23970	−	0.715740i	0.270666	−	0.962673i	$-0.412756\pi$
$653$	31.6791	−	18.2899i	1.23970	−	0.715740i	0.969033	+	0.246933i	$0.0794227\pi$
$654$	1.73054	−	2.99739i	0.0676696	−	0.117207i
$655$	−29.2814	+	50.7169i	−1.14412	+	1.98167i
$656$	−80.1536	+	46.2767i	−3.12947	+	1.80680i
$657$			2.14684i			0.0837560i
$658$	31.0068	+	26.0865i	1.20877	+	1.01696i
$659$	−44.2263			−1.72281			−0.861407	−	0.507915i	$-0.830416\pi$
$659$	−44.2263			−1.72281			−0.861407	+	0.507915i	$0.830416\pi$
$660$	11.4457	−	6.60817i	0.445523	−	0.257223i
$661$	−17.3426	+	30.0383i	−0.674550	+	1.16836i	0.302050	+	0.953292i	$0.402329\pi$
$661$	−17.3426	+	30.0383i	−0.674550	+	1.16836i	−0.976600	+	0.215063i	$0.931004\pi$
$662$	−6.89155	+	11.9365i	−0.267848	+	0.463926i
$663$	−25.7138	+	9.41597i	−0.998640	+	0.365686i
$664$	30.3728			1.17869
$665$	−9.76606	+	11.6081i	−0.378711	+	0.450142i
$666$			2.20803i			0.0855593i
$667$	−10.3093	−	17.8563i	−0.399178	−	0.691397i
$668$	69.4721	+	40.1097i	2.68795	+	1.55189i
$669$	6.74542	+	3.89447i	0.260793	+	0.150569i
$670$	−16.9040	+	9.75950i	−0.653057	+	0.377042i
$671$	−6.34180			−0.244822
$672$	15.4701	+	42.6761i	0.596771	+	1.64626i
$673$			22.6579i			0.873396i	0.899608	+	0.436698i	$0.143852\pi$
$673$			22.6579i			0.873396i	−0.899608	+	0.436698i	$0.856148\pi$
$674$	42.4256	−	24.4944i	1.63417	−	0.943491i
$675$	−5.95132	−	3.43600i	−0.229066	−	0.132252i
$676$	−81.2333	+	140.700i	−3.12436	+	5.41155i
$677$	10.9284	−	6.30950i	0.420012	−	0.242494i	−0.275071	−	0.961424i	$-0.588701\pi$
$677$	10.9284	−	6.30950i	0.420012	−	0.242494i	0.695082	+	0.718930i	$0.255368\pi$
$678$	−26.6084			−1.02189
$679$	−32.6848	−	5.80698i	−1.25433	−	0.222851i
$680$	21.1273	−	121.203i	0.810196	−	4.64793i
$681$	−11.1166	−	19.2546i	−0.425990	−	0.737837i
$682$	−2.92595	+	5.06790i	−0.112040	+	0.194060i
$683$	13.0266	+	7.52091i	0.498449	+	0.287780i	0.728073	−	0.685500i	$-0.240416\pi$
$683$	13.0266	+	7.52091i	0.498449	+	0.287780i	−0.229624	+	0.973279i	$0.573750\pi$
$684$	−4.34524	−	7.52617i	−0.166144	−	0.287770i
$685$			24.4095i			0.932637i
$686$	−49.7721	−	0.193905i	−1.90031	−	0.00740331i
$687$		−	18.1710i		−	0.693269i
$688$	−20.2475	−	35.0697i	−0.771928	−	1.33702i
$689$	1.68256	−	2.91428i	0.0641004	−	0.111025i
$690$	−37.8404	−	21.8472i	−1.44056	−	0.831708i
$691$	24.7520	−	14.2906i	0.941610	−	0.543639i	0.0511453	−	0.998691i	$-0.483713\pi$
$691$	24.7520	−	14.2906i	0.941610	−	0.543639i	0.890465	+	0.455053i	$0.150380\pi$
$692$		−	81.4107i		−	3.09477i
$693$	−1.91327	−	0.339924i	−0.0726791	−	0.0129126i
$694$			26.4255i			1.00310i
$695$	10.3110	+	17.8592i	0.391119	+	0.677437i
$696$	18.9207	−	32.7715i	0.717185	−	1.24220i
$697$	−22.8238	−	19.0756i	−0.864513	−	0.722539i
$698$	23.5365	+	40.7665i	0.890871	+	1.54303i
$699$	−2.58680			−0.0978417
$700$	−89.2681	+	32.3597i	−3.37402	+	1.22308i
$701$	−5.30427			−0.200339			−0.100170	−	0.994970i	$-0.531939\pi$
$701$	−5.30427			−0.200339			−0.100170	+	0.994970i	$0.531939\pi$
$702$	−15.4574	+	8.92436i	−0.583404	+	0.336828i
$703$	−1.18403	−	0.683600i	−0.0446565	−	0.0257825i
$704$	13.0083	+	7.51037i	0.490270	+	0.283058i
$705$	−9.81786	−	17.0050i	−0.369762	−	0.640447i
$706$	55.7704			2.09895
$707$	−1.40404	−	1.18124i	−0.0528045	−	0.0444252i
$708$		−	57.0657i		−	2.14466i
$709$	−16.9648	+	9.79460i	−0.637125	+	0.367844i	−0.783506	−	0.621384i	$-0.786571\pi$
$709$	−16.9648	+	9.79460i	−0.637125	+	0.367844i	0.146381	+	0.989228i	$0.453237\pi$
$710$	−64.0772	+	110.985i	−2.40477	+	4.16519i
$711$	10.0684	+	5.81300i	0.377595	+	0.218005i
$712$	7.55339	+	13.0829i	0.283075	+	0.490301i
$713$	13.9895			0.523909
$714$	−22.4456	+	18.8591i	−0.840004	+	0.705785i
$715$	16.8075			0.628564
$716$	−13.0875	−	22.6682i	−0.489102	−	0.847150i
$717$	19.0551	+	11.0014i	0.711624	+	0.410856i
$718$	−1.49624	+	2.59157i	−0.0558393	+	0.0967165i
$719$	−12.9412	+	7.47159i	−0.482624	+	0.278643i	−0.721510	−	0.692405i	$-0.756551\pi$
$719$	−12.9412	+	7.47159i	−0.482624	+	0.278643i	0.238885	+	0.971048i	$0.423218\pi$
$720$		−	44.2034i		−	1.64736i
$721$	7.62990	−	2.76584i	0.284152	−	0.103005i
$722$	−43.6199			−1.62336
$723$	10.6160	+	18.3874i	0.394812	+	0.683835i
$724$	−38.8401	−	22.4243i	−1.44348	−	0.833393i
$725$	26.0047	+	15.0138i	0.965791	+	0.557600i
$726$	24.3460	−	14.0562i	0.903564	−	0.521673i
$727$	50.3145			1.86606			0.933030	−	0.359799i	$-0.117155\pi$
$727$	50.3145			1.86606			0.933030	+	0.359799i	$0.117155\pi$
$728$	−26.6194	+	149.828i	−0.986580	+	5.55300i
$729$	−1.00000			−0.0370370
$730$	−9.93968	−	17.2160i	−0.367884	−	0.637194i
$731$	8.34615	−	9.98611i	0.308693	−	0.369349i
$732$	−22.5466	+	39.0518i	−0.833345	+	1.44340i
$733$	15.7899	+	27.3489i	0.583213	+	1.01015i	0.995096	+	0.0989173i	$0.0315379\pi$
$733$	15.7899	+	27.3489i	0.583213	+	1.01015i	−0.411883	+	0.911237i	$0.635129\pi$
$734$		−	76.8196i		−	2.83546i
$735$	22.6430	+	8.30803i	0.835199	+	0.306446i
$736$		−	80.9591i		−	2.98419i
$737$	1.34079	−	0.774104i	0.0493886	−	0.0285145i
$738$	−16.7908	−	9.69418i	−0.618078	−	0.356848i
$739$	6.67523	−	11.5618i	0.245552	−	0.425309i	−0.716734	−	0.697346i	$-0.754364\pi$
$739$	6.67523	−	11.5618i	0.245552	−	0.425309i	0.962287	+	0.272037i	$0.0876974\pi$
$740$	−7.39210	−	12.8035i	−0.271739	−	0.470666i
$741$		−	11.0518i		−	0.406000i
$742$	0.630207	−	3.54714i	0.0231356	−	0.130220i
$743$		−	14.5369i		−	0.533308i	−0.963792	−	0.266654i	$-0.914082\pi$
$743$		−	14.5369i		−	0.533308i	0.963792	−	0.266654i	$-0.0859180\pi$
$744$	12.8374	+	22.2350i	0.470642	+	0.815175i
$745$	−36.6962	−	21.1865i	−1.34444	−	0.776215i
$746$	34.1779	−	59.1978i	1.25134	−	2.16739i
$747$	1.75359	+	3.03731i	0.0641605	+	0.111129i
$748$	−2.71584	+	15.5802i	−0.0993011	+	0.569670i
$749$	0.0550314	+	0.151811i	0.00201080	+	0.00554704i
$750$	17.3344			0.632962
$751$	32.5004	−	18.7641i	1.18596	−	0.684713i	0.228573	−	0.973527i	$-0.426594\pi$
$751$	32.5004	−	18.7641i	1.18596	−	0.684713i	0.957385	+	0.288814i	$0.0932608\pi$
$752$	36.5552	−	63.3154i	1.33303	−	2.30888i
$753$	7.66313	+	4.42431i	0.279260	+	0.161231i
$754$	67.5424	−	38.9956i	2.45975	−	1.42014i
$755$			60.9668i			2.21881i
$756$	−8.89532	+	10.5731i	−0.323520	+	0.384540i
$757$	−5.81812			−0.211463			−0.105732	−	0.994395i	$-0.533718\pi$
$757$	−5.81812			−0.211463			−0.105732	+	0.994395i	$0.533718\pi$
$758$	69.9963	−	40.4124i	2.54238	−	1.46784i
$759$	3.00143	+	1.73287i	0.108945	+	0.0628993i
$760$	43.0021	+	24.8273i	1.55985	+	0.900579i
$761$	−2.67536	−	4.63385i	−0.0969816	−	0.167977i	0.813452	−	0.581632i	$-0.197585\pi$
$761$	−2.67536	−	4.63385i	−0.0969816	−	0.167977i	−0.910434	+	0.413655i	$0.864252\pi$
$762$		−	32.1860i		−	1.16598i
$763$	2.19360	−	2.60735i	0.0794137	−	0.0943924i
$764$	−67.1444			−2.42920
$765$	13.3402	−	4.88497i	0.482316	−	0.176616i
$766$	20.6874	−	35.8316i	0.747465	−	1.29465i
$767$	36.2858	−	62.8488i	1.31020	−	2.26934i
$768$	12.6320	−	7.29311i	0.455819	−	0.263167i
$769$	4.98467			0.179752			0.0898759	−	0.995953i	$-0.471353\pi$
$769$	4.98467			0.179752			0.0898759	+	0.995953i	$0.471353\pi$
$770$	16.9168	−	6.13236i	0.609641	−	0.220995i
$771$			15.4952i			0.558047i
$772$	−69.8653	+	40.3368i	−2.51451	+	1.45175i
$773$	3.38408	−	5.86140i	0.121717	−	0.210820i	−0.798728	−	0.601692i	$-0.794493\pi$
$773$	3.38408	−	5.86140i	0.121717	−	0.210820i	0.920445	+	0.390872i	$0.127827\pi$
$774$	4.24150	−	7.34649i	0.152458	−	0.264064i
$775$	−17.6438	+	10.1867i	−0.633785	+	0.365916i
$776$			108.661i			3.90069i
$777$	−0.380249	+	2.14024i	−0.0136414	+	0.0767808i
$778$	−74.0419			−2.65453
$779$	10.3968	−	6.00259i	0.372504	−	0.215065i
$780$	59.7545	−	103.498i	2.13955	−	3.70582i
$781$	5.08247	−	8.80310i	0.181865	−	0.315000i
$782$	49.0980	−	17.9789i	1.75574	−	0.642925i
$783$	4.36957			0.156156
$784$	15.3644	+	88.4791i	0.548729	+	3.15997i
$785$			49.0605i			1.75104i
$786$	−22.8387	−	39.5579i	−0.814631	−	1.41098i
$787$	−15.4922	−	8.94444i	−0.552238	−	0.318835i	0.197786	−	0.980245i	$-0.436625\pi$
$787$	−15.4922	−	8.94444i	−0.552238	−	0.318835i	−0.750024	+	0.661410i	$0.769958\pi$
$788$	97.7824	+	56.4547i	3.48335	+	2.01111i
$789$	7.02187	−	4.05408i	0.249985	−	0.144329i
$790$	−107.655			−3.83019
$791$	−25.7915	−	4.58228i	−0.917040	−	0.162927i
$792$			6.36067i			0.226017i
$793$	−49.6630	+	28.6729i	−1.76358	+	1.01821i
$794$	−73.8391	−	42.6310i	−2.62045	−	1.51292i
$795$	−0.872906	+	1.51192i	−0.0309588	+	0.0536222i
$796$	−5.47327	+	3.15999i	−0.193995	+	0.112003i
$797$	39.7704			1.40874			0.704369	−	0.709834i	$-0.251230\pi$
$797$	39.7704			1.40874			0.704369	+	0.709834i	$0.251230\pi$
$798$	−4.03236	−	11.1238i	−0.142744	−	0.393777i
$799$	23.1478	+	4.03497i	0.818911	+	0.142747i
$800$	58.9518	+	102.108i	2.08426	+	3.61005i
$801$	−0.872197	+	1.51069i	−0.0308176	+	0.0533776i
$802$	−79.8500	−	46.1014i	−2.81960	−	1.62790i
$803$	0.788396	+	1.36554i	0.0278219	+	0.0481889i
$804$		−	11.0085i		−	0.388239i
$805$	−32.9164	−	27.6931i	−1.16015	−	0.976052i
$806$			52.9159i			1.86388i
$807$	−0.253570	−	0.439196i	−0.00892609	−	0.0154604i
$808$	−3.00295	+	5.20127i	−0.105644	+	0.182980i
$809$	−18.1506	−	10.4793i	−0.638142	−	0.368431i	0.145757	−	0.989320i	$-0.453438\pi$
$809$	−18.1506	−	10.4793i	−0.638142	−	0.368431i	−0.783898	+	0.620889i	$0.786772\pi$
$810$	8.01926	−	4.62992i	0.281768	−	0.162679i
$811$			5.99034i			0.210349i	0.994454	+	0.105175i	$0.0335401\pi$
$811$			5.99034i			0.210349i	−0.994454	+	0.105175i	$0.966460\pi$
$812$	38.8687	−	46.2000i	1.36402	−	1.62130i
$813$		−	0.177887i		−	0.00623877i
$814$	0.810868	+	1.40446i	0.0284209	+	0.0492265i
$815$	15.2987	−	26.4982i	0.535891	−	0.928190i
$816$	40.5866	+	33.9213i	1.42082	+	1.18748i
$817$	2.62632	+	4.54891i	0.0918832	+	0.159146i
$818$	57.3969			2.00684
$819$	−16.5198	+	5.98843i	−0.577249	+	0.209253i
$820$	129.818			4.53344
$821$	−0.182498	+	0.105365i	−0.00636923	+	0.00367728i	−0.503181	−	0.864181i	$-0.667837\pi$
$821$	−0.182498	+	0.105365i	−0.00636923	+	0.00367728i	0.496812	+	0.867858i	$0.334504\pi$
$822$	−16.4880	−	9.51937i	−0.575086	−	0.332026i
$823$	−15.5360	−	8.96969i	−0.541550	−	0.312664i	0.204157	−	0.978938i	$-0.434555\pi$
$823$	−15.5360	−	8.96969i	−0.541550	−	0.312664i	−0.745707	+	0.666274i	$0.767888\pi$
$824$	−13.2824	−	23.0058i	−0.462714	−	0.801445i
$825$	−5.04729			−0.175724
$826$	13.5909	−	76.4969i	0.472889	−	2.66167i
$827$		−	19.3366i		−	0.672399i	−0.941791	−	0.336199i	$-0.890858\pi$
$827$		−	19.3366i		−	0.672399i	0.941791	−	0.336199i	$-0.109142\pi$
$828$	21.3415	−	12.3215i	0.741670	−	0.428203i
$829$	−21.4942	+	37.2290i	−0.746524	+	1.29302i	0.202955	+	0.979188i	$0.434945\pi$
$829$	−21.4942	+	37.2290i	−0.746524	+	1.29302i	−0.949479	+	0.313829i	$0.898388\pi$
$830$	−28.1250	−	16.2380i	−0.976233	−	0.563628i
$831$	14.4785	+	25.0775i	0.502254	+	0.869930i
$832$	135.825			4.70889
$833$	−25.0043	+	14.4148i	−0.866347	+	0.499443i
$834$	−16.0846			−0.556965
$835$	−26.4629	−	45.8351i	−0.915787	−	1.58619i
$836$	−5.52777	−	3.19146i	−0.191182	−	0.110379i
$837$	−1.48235	+	2.56750i	−0.0512373	+	0.0887457i
$838$	−30.9264	+	17.8554i	−1.06833	+	0.616803i
$839$			54.7774i			1.89113i	0.325438	+	0.945563i	$0.394488\pi$
$839$			54.7774i			1.89113i	−0.325438	+	0.945563i	$0.605512\pi$
$840$	13.8100	−	77.7302i	0.476492	−	2.68195i
$841$	9.90686			0.341616
$842$	14.6056	+	25.2976i	0.503341	+	0.871813i
$843$	3.35514	+	1.93709i	0.115557	+	0.0667169i
$844$	37.4030	+	21.5946i	1.28746	+	0.743317i
$845$	92.8288	−	53.5947i	3.19341	−	1.84371i
$846$	15.3154			0.526553
$847$	26.0192	−	9.43197i	0.894031	−	0.324086i
$848$	−6.50024			−0.223219
$849$	0.459295	+	0.795522i	0.0157630	+	0.0273022i
$850$	−48.8319	+	58.4270i	−1.67492	+	2.00403i
$851$	1.93845	−	3.35749i	0.0664491	−	0.115093i
$852$	−36.1387	−	62.5941i	−1.23809	−	2.14444i
$853$			1.08867i			0.0372754i	0.999826	+	0.0186377i	$0.00593291\pi$
$853$			1.08867i			0.0372754i	−0.999826	+	0.0186377i	$0.994067\pi$
$854$	−39.5245	+	46.9795i	−1.35250	+	1.60760i
$855$			5.73365i			0.196087i
$856$	0.457742	−	0.264277i	0.0156453	−	0.00903281i
$857$	0.762520	+	0.440241i	0.0260472	+	0.0150384i	0.512967	−	0.858408i	$-0.328546\pi$
$857$	0.762520	+	0.440241i	0.0260472	+	0.0150384i	−0.486920	+	0.873447i	$0.661880\pi$
$858$	−6.55470	+	11.3531i	−0.223774	+	0.387588i
$859$	17.6373	+	30.5487i	0.601777	+	1.04231i	0.992552	+	0.121821i	$0.0388735\pi$
$859$	17.6373	+	30.5487i	0.601777	+	1.04231i	−0.390776	+	0.920486i	$0.627793\pi$
$860$			56.7993i			1.93684i
$861$	−14.6059	−	12.2882i	−0.497767	−	0.418779i
$862$			46.3677i			1.57929i
$863$	−8.21302	−	14.2254i	−0.279574	−	0.484237i	0.691705	−	0.722181i	$-0.256860\pi$
$863$	−8.21302	−	14.2254i	−0.279574	−	0.484237i	−0.971279	+	0.237943i	$0.923527\pi$
$864$	14.8585	+	8.57856i	0.505497	+	0.291849i
$865$	−26.8559	+	46.5158i	−0.913128	+	1.58158i
$866$	−7.11724	−	12.3274i	−0.241854	−	0.418903i
$867$	−5.75188	+	15.9974i	−0.195344	+	0.543299i
$868$	13.9605	+	38.5117i	0.473850	+	1.30717i
$869$	8.53898			0.289665
$870$	−35.0407	+	20.2308i	−1.18799	+	0.685888i
$871$	6.99985	−	12.1241i	0.237181	−	0.410809i
$872$	−9.65891	−	5.57657i	−0.327092	−	0.188847i
$873$	−10.8661	+	6.27357i	−0.367763	+	0.212328i
$874$			21.1025i			0.713801i
$875$	16.8022	+	2.98519i	0.568019	+	0.100918i
$876$	11.2117			0.378809
$877$	−37.6791	+	21.7540i	−1.27233	+	0.734582i	−0.975427	−	0.220325i	$-0.929288\pi$
$877$	−37.6791	+	21.7540i	−1.27233	+	0.734582i	−0.296907	+	0.954907i	$0.595955\pi$
$878$	25.8360	+	14.9164i	0.871923	+	0.503405i
$879$	−16.3612	−	9.44614i	−0.551849	−	0.318610i
$880$	−16.2331	−	28.1165i	−0.547217	−	0.947808i
$881$			36.7445i			1.23795i	0.785410	+	0.618976i	$0.212452\pi$
$881$			36.7445i			1.23795i	−0.785410	+	0.618976i	$0.787548\pi$
$882$	−14.4424	+	12.0548i	−0.486299	+	0.405906i
$883$	41.9518			1.41179			0.705895	−	0.708317i	$-0.250545\pi$
$883$	41.9518			1.41179			0.705895	+	0.708317i	$0.250545\pi$
$884$	49.1744	+	134.289i	1.65391	+	4.51662i
$885$	−18.8249	+	32.6057i	−0.632793	+	1.09603i
$886$	15.1414	−	26.2256i	0.508684	−	0.881067i
$887$	37.6524	−	21.7386i	1.26424	−	0.729911i	0.290351	−	0.956920i	$-0.406228\pi$
$887$	37.6524	−	21.7386i	1.26424	−	0.729911i	0.973893	+	0.227009i	$0.0728946\pi$
$888$	7.11524			0.238772
$889$	5.54282	−	31.1979i	0.185900	−	1.04634i
$890$		−	16.1528i		−	0.541444i
$891$	−0.636072	+	0.367236i	−0.0213092	+	0.0123029i
$892$	20.3386	−	35.2276i	0.680988	−	1.17951i
$893$	−4.74160	+	8.21269i	−0.158672	+	0.274827i
$894$	28.6221	−	16.5250i	0.957265	−	0.552677i
$895$			17.2693i			0.577248i
$896$	51.3569	−	18.6169i	1.71571	−	0.621947i
$897$	31.3391			1.04638
$898$	50.2345	−	29.0029i	1.67635	−	0.967840i
$899$	6.47721	−	11.2189i	0.216027	−	0.374170i
$900$	−17.9443	+	31.0804i	−0.598143	+	1.03601i
$901$	−0.718349	−	1.96172i	−0.0239317	−	0.0653542i
$902$	−14.2402			−0.474147
$903$	5.37644	−	6.39052i	0.178917	−	0.212663i
$904$			85.7439i			2.85180i
$905$	14.7947	+	25.6252i	0.491794	+	0.851812i
$906$	−41.1817	−	23.7763i	−1.36817	−	0.789913i
$907$	−10.5810	−	6.10893i	−0.351336	−	0.202844i	0.313938	−	0.949444i	$-0.398352\pi$
$907$	−10.5810	−	6.10893i	−0.351336	−	0.202844i	−0.665273	+	0.746600i	$0.731685\pi$
$908$	−100.556	+	58.0560i	−3.33706	+	1.92666i
$909$	−0.693508			−0.0230022
$910$	104.751	−	124.508i	3.47245	−	4.12741i
$911$			41.7422i			1.38298i	0.722386	+	0.691490i	$0.243045\pi$
$911$			41.7422i			1.38298i	−0.722386	+	0.691490i	$0.756955\pi$
$912$	−18.4882	+	10.6742i	−0.612205	+	0.353457i
$913$	2.23082	+	1.28796i	0.0738293	+	0.0426254i
$914$	−9.90985	+	17.1644i	−0.327789	+	0.567747i
$915$	25.7649	−	14.8754i	0.851763	−	0.491766i
$916$	−94.8973			−3.13549
$917$	−15.3253	−	42.2766i	−0.506085	−	1.39610i
$918$	−1.90282	+	10.9161i	−0.0628024	+	0.360284i
$919$	−12.4550	−	21.5726i	−0.410852	−	0.711616i	0.584132	−	0.811659i	$-0.301435\pi$
$919$	−12.4550	−	21.5726i	−0.410852	−	0.711616i	−0.994983	+	0.100043i	$0.968102\pi$
$920$	−70.4013	+	121.939i	−2.32106	+	4.02020i
$921$	−5.88141	−	3.39563i	−0.193799	−	0.111890i
$922$	23.1333	+	40.0680i	0.761854	+	1.31957i
$923$		−	91.9167i		−	3.02548i
$924$	−1.77523	+	9.99195i	−0.0584008	+	0.328711i
$925$			5.64605i			0.185641i
$926$	35.7200	+	61.8688i	1.17383	+	2.03313i
$927$	1.53373	−	2.65650i	0.0503743	−	0.0872509i
$928$	−64.9253	−	37.4846i	−2.13128	−	1.23049i
$929$	10.4166	−	6.01403i	0.341758	−	0.197314i	−0.319291	−	0.947657i	$-0.603445\pi$
$929$	10.4166	−	6.01403i	0.341758	−	0.197314i	0.661049	+	0.750343i	$0.270112\pi$
$930$		−	27.4526i		−	0.900206i
$931$	−1.99293	−	11.4767i	−0.0653156	−	0.376133i
$932$			13.5094i			0.442515i
$933$	9.69776	+	16.7970i	0.317490	+	0.549910i
$934$	−56.0848	+	97.1418i	−1.83515	+	3.17858i
$935$	6.69139	−	8.00620i	0.218832	−	0.261831i
$936$	28.7583	+	49.8108i	0.939993	+	1.62812i
$937$	−42.1980			−1.37855			−0.689274	−	0.724501i	$-0.742070\pi$
$937$	−42.1980			−1.37855			−0.689274	+	0.724501i	$0.742070\pi$
$938$	2.62181	−	14.7569i	0.0856052	−	0.481831i
$939$	11.3704			0.371059
$940$	−88.8079	+	51.2732i	−2.89659	+	1.67235i
$941$	8.83666	+	5.10185i	0.288067	+	0.166315i	0.637070	−	0.770806i	$-0.280146\pi$
$941$	8.83666	+	5.10185i	0.288067	+	0.166315i	−0.349003	+	0.937122i	$0.613480\pi$
$942$	−33.1392	−	19.1329i	−1.07973	−	0.623385i
$943$	17.0212	+	29.4816i	0.554287	+	0.960052i
$944$	−140.183			−4.56256
$945$	8.57041	−	3.10678i	0.278795	−	0.101063i
$946$		−	6.23053i		−	0.202572i
$947$	11.0487	−	6.37898i	0.359035	−	0.207289i	−0.309622	−	0.950860i	$-0.600203\pi$
$947$	11.0487	−	6.37898i	0.359035	−	0.207289i	0.668657	+	0.743571i	$0.266869\pi$
$948$	30.3581	−	52.5817i	0.985984	−	1.70778i
$949$	12.3479	+	7.12909i	0.400831	+	0.231420i
$950$	−15.3661	−	26.6149i	−0.498543	−	0.863502i
$951$	19.8980			0.645238
$952$	60.7725	+	72.3296i	1.96965	+	2.34422i
$953$	−40.4442			−1.31012			−0.655058	−	0.755579i	$-0.727356\pi$
$953$	−40.4442			−1.31012			−0.655058	+	0.755579i	$0.727356\pi$
$954$	−0.680844	−	1.17926i	−0.0220431	−	0.0381798i
$955$	38.3644	+	22.1497i	1.24144	+	0.716747i
$956$	57.4544	−	99.5140i	1.85821	−	3.21851i
$957$	2.77936	−	1.60467i	0.0898440	−	0.0518715i
$958$			40.9157i			1.32193i
$959$	−14.3425	−	12.0666i	−0.463144	−	0.389650i
$960$	−70.4656			−2.27427
$961$	−11.1053	−	19.2350i	−0.358236	−	0.620482i
$962$	12.6999	+	7.33229i	0.409461	+	0.236402i
$963$	0.0528559	+	0.0305163i	0.00170326	+	0.000983375i
$964$	96.0272	−	55.4413i	3.09283	−	1.78564i
$965$	53.2254			1.71339
$966$	31.5430	−	11.4343i	1.01488	−	0.367894i
$967$	48.1460			1.54827			0.774135	−	0.633020i	$-0.218185\pi$
$967$	48.1460			1.54827			0.774135	+	0.633020i	$0.218185\pi$
$968$	−45.2952	−	78.4535i	−1.45584	−	2.52159i
$969$	−5.26452	−	4.39996i	−0.169121	−	0.141347i
$970$	58.0923	−	100.619i	1.86523	−	3.23067i
$971$	−11.9858	−	20.7600i	−0.384642	−	0.666220i	0.607077	−	0.794643i	$-0.292342\pi$
$971$	−11.9858	−	20.7600i	−0.384642	−	0.666220i	−0.991719	+	0.128423i	$0.959008\pi$
$972$			5.22244i			0.167510i
$973$	−15.5908	−	2.76997i	−0.499820	−	0.0888011i
$974$		−	17.4330i		−	0.558590i
$975$	−39.5256	+	22.8201i	−1.26583	+	0.730828i
$976$	95.9315	+	55.3861i	3.07069	+	1.77287i
$977$	−9.23058	+	15.9878i	−0.295312	+	0.511496i	−0.975058	−	0.221952i	$-0.928757\pi$
$977$	−9.23058	+	15.9878i	−0.295312	+	0.511496i	0.679745	+	0.733448i	$0.262090\pi$
$978$	11.9326	+	20.6679i	0.381563	+	0.660886i
$979$			1.28121i			0.0409476i
$980$	43.3882	−	118.252i	1.38599	−	3.77741i
$981$		−	1.28786i		−	0.0411183i
$982$	43.0258	+	74.5228i	1.37301	+	2.37812i
$983$	−9.54106	−	5.50854i	−0.304313	−	0.175695i	0.340066	−	0.940402i	$-0.389551\pi$
$983$	−9.54106	−	5.50854i	−0.304313	−	0.175695i	−0.644379	+	0.764707i	$0.722884\pi$
$984$	−31.2389	+	54.1074i	−0.995861	+	1.72488i
$985$	−37.2467	−	64.5132i	−1.18678	−	2.05556i
$986$	8.31450	−	47.6986i	0.264788	−	1.51903i
$987$	14.8452	+	2.63749i	0.472528	+	0.0839522i
$988$	−57.7176			−1.83624
$989$	−12.8991	+	7.44730i	−0.410167	+	0.236810i
$990$	3.40055	−	5.88993i	0.108077	−	0.187194i
$991$	46.0523	+	26.5883i	1.46290	+	0.844606i	0.999144	−	0.0413565i	$-0.0131679\pi$
$991$	46.0523	+	26.5883i	1.46290	+	0.844606i	0.463756	+	0.885963i	$0.346501\pi$
$992$	44.0509	−	25.4328i	1.39862	−	0.807492i
$993$			5.12867i			0.162753i
$994$	−33.5366	−	92.5148i	−1.06372	−	2.93439i
$995$	4.16969			0.132188
$996$	15.8622	−	9.15802i	0.502612	−	0.290183i
$997$	−25.6469	−	14.8073i	−0.812246	−	0.468950i	0.0354892	−	0.999370i	$-0.488701\pi$
$997$	−25.6469	−	14.8073i	−0.812246	−	0.468950i	−0.847735	+	0.530420i	$0.822034\pi$
$998$	−50.2147	−	28.9915i	−1.58952	−	0.917709i
$999$	0.410802	+	0.711530i	0.0129972	+	0.0225118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.p.a.67.1	yes	48
7.2	even	3	inner	357.2.p.a.16.2	yes	48
17.16	even	2	inner	357.2.p.a.67.2	yes	48
119.16	even	6	inner	357.2.p.a.16.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.p.a.16.1	✓	48	119.16	even	6	inner
357.2.p.a.16.2	yes	48	7.2	even	3	inner
357.2.p.a.67.1	yes	48	1.1	even	1	trivial
357.2.p.a.67.2	yes	48	17.16	even	2	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34373 - 2.32741i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.61122 + 4.52277i) q^{4} +(2.98396 - 1.72279i) q^{5} +2.68746i q^{6} +(-0.462813 + 2.60496i) q^{7} +8.66019 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.34373 - 2.32741i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-2.61122 + 4.52277i) q^{4} +(2.98396 - 1.72279i) q^{5} +2.68746i q^{6} +(-0.462813 + 2.60496i) q^{7} +8.66019 q^{8} +(0.500000 + 0.866025i) q^{9} +(-8.01926 - 4.62992i) q^{10} +(0.636072 + 0.367236i) q^{11} +(4.52277 - 2.61122i) q^{12} +6.64148 q^{13} +(6.68470 - 2.42320i) q^{14} -3.44558 q^{15} +(-6.41451 - 11.1103i) q^{16} +(2.64411 - 3.16365i) q^{17} +(1.34373 - 2.32741i) q^{18} +(0.832031 + 1.44112i) q^{19} +17.9943i q^{20} +(1.70329 - 2.02455i) q^{21} -1.97387i q^{22} +(-4.08650 + 2.35934i) q^{23} +(-7.49994 - 4.33009i) q^{24} +(3.43600 - 5.95132i) q^{25} +(-8.92436 - 15.4574i) q^{26} -1.00000i q^{27} +(-10.5731 - 8.89532i) q^{28} +4.36957i q^{29} +(4.62992 + 8.01926i) q^{30} +(-2.56750 - 1.48235i) q^{31} +(-8.57856 + 14.8585i) q^{32} +(-0.367236 - 0.636072i) q^{33} +(-10.9161 - 1.90282i) q^{34} +(3.10678 + 8.57041i) q^{35} -5.22244 q^{36} +(-0.711530 + 0.410802i) q^{37} +(2.23605 - 3.87295i) q^{38} +(-5.75169 - 3.32074i) q^{39} +(25.8416 - 14.9197i) q^{40} -7.21438i q^{41} +(-7.00072 - 1.24379i) q^{42} +3.15651 q^{43} +(-3.32185 + 1.91787i) q^{44} +(2.98396 + 1.72279i) q^{45} +(10.9823 + 6.34064i) q^{46} +(2.84941 + 4.93533i) q^{47} +12.8290i q^{48} +(-6.57161 - 2.41122i) q^{49} -18.4682 q^{50} +(-3.87169 + 1.41775i) q^{51} +(-17.3424 + 30.0379i) q^{52} +(0.253341 - 0.438799i) q^{53} +(-2.32741 + 1.34373i) q^{54} +2.53068 q^{55} +(-4.00805 + 22.5594i) q^{56} -1.66406i q^{57} +(10.1698 - 5.87152i) q^{58} +(5.46350 - 9.46306i) q^{59} +(8.99716 - 15.5835i) q^{60} +(-7.47769 + 4.31725i) q^{61} +7.96749i q^{62} +(-2.48737 + 0.901671i) q^{63} +20.4510 q^{64} +(19.8179 - 11.4419i) q^{65} +(-0.986933 + 1.70942i) q^{66} +(1.05396 - 1.82551i) q^{67} +(7.40413 + 20.2197i) q^{68} +4.71869 q^{69} +(15.7722 - 18.7471i) q^{70} -13.8398i q^{71} +(4.33009 + 7.49994i) q^{72} +(1.85921 + 1.07342i) q^{73} +(1.91221 + 1.10401i) q^{74} +(-5.95132 + 3.43600i) q^{75} -8.69047 q^{76} +(-1.25102 + 1.48698i) q^{77} +17.8487i q^{78} +(10.0684 - 5.81300i) q^{79} +(-38.2813 - 22.1017i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-16.7908 + 9.69418i) q^{82} +3.50718 q^{83} +(4.70893 + 12.9901i) q^{84} +(2.43959 - 13.9954i) q^{85} +(-4.24150 - 7.34649i) q^{86} +(2.18479 - 3.78416i) q^{87} +(5.50850 + 3.18034i) q^{88} +(0.872197 + 1.51069i) q^{89} -9.25985i q^{90} +(-3.07377 + 17.3008i) q^{91} -24.6431i q^{92} +(1.48235 + 2.56750i) q^{93} +(7.65768 - 13.2635i) q^{94} +(4.96549 + 2.86683i) q^{95} +(14.8585 - 8.57856i) q^{96} +12.5471i q^{97} +(3.21858 + 18.5348i) q^{98} +0.734473i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{4} + 24 q^{9}+O(q^{10}) \) 48 * q - 24 * q^4 + 24 * q^9	\( 48 q - 24 q^{4} + 24 q^{9} + 16 q^{13} - 40 q^{16} + 8 q^{17} + 16 q^{19} + 36 q^{25} - 52 q^{26} + 24 q^{30} + 20 q^{32} - 8 q^{33} - 32 q^{34} - 36 q^{35} - 48 q^{36} + 40 q^{38} + 4 q^{42} + 40 q^{43} - 80 q^{50} - 12 q^{52} - 60 q^{53} - 24 q^{59} + 112 q^{64} + 4 q^{66} - 4 q^{67} + 88 q^{68} + 64 q^{69} - 24 q^{70} - 184 q^{76} - 72 q^{77} - 24 q^{81} - 88 q^{83} - 20 q^{84} + 16 q^{85} + 60 q^{86} + 36 q^{87} + 12 q^{89} - 24 q^{93} - 32 q^{94} + 48 q^{98}+O(q^{100}) \) 48 * q - 24 * q^4 + 24 * q^9 + 16 * q^13 - 40 * q^16 + 8 * q^17 + 16 * q^19 + 36 * q^25 - 52 * q^26 + 24 * q^30 + 20 * q^32 - 8 * q^33 - 32 * q^34 - 36 * q^35 - 48 * q^36 + 40 * q^38 + 4 * q^42 + 40 * q^43 - 80 * q^50 - 12 * q^52 - 60 * q^53 - 24 * q^59 + 112 * q^64 + 4 * q^66 - 4 * q^67 + 88 * q^68 + 64 * q^69 - 24 * q^70 - 184 * q^76 - 72 * q^77 - 24 * q^81 - 88 * q^83 - 20 * q^84 + 16 * q^85 + 60 * q^86 + 36 * q^87 + 12 * q^89 - 24 * q^93 - 32 * q^94 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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