LMFDB - Embedded newform 945.2.cs.b.104.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

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

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

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$816$
Relative dimension:	$136$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.17
Character	$\chi$	$=$	945.104
Dual form			945.2.cs.b.209.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.05378 - 0.747516i) q^{2} +(-1.57383 + 0.723218i) q^{3} +(2.12716 + 1.78490i) q^{4} +(1.84479 - 1.26363i) q^{5} +(3.77293 - 0.308866i) q^{6} +(-0.111990 - 2.64338i) q^{7} +(-0.848890 - 1.47032i) q^{8} +(1.95391 - 2.27645i) q^{9} +O(q^{10})$	\(q+(-2.05378 - 0.747516i) q^{2} +(-1.57383 + 0.723218i) q^{3} +(2.12716 + 1.78490i) q^{4} +(1.84479 - 1.26363i) q^{5} +(3.77293 - 0.308866i) q^{6} +(-0.111990 - 2.64338i) q^{7} +(-0.848890 - 1.47032i) q^{8} +(1.95391 - 2.27645i) q^{9} +(-4.73338 + 1.21621i) q^{10} +(5.35903 - 0.944942i) q^{11} +(-4.63866 - 1.27073i) q^{12} +(3.85910 - 1.40460i) q^{13} +(-1.74596 + 5.51264i) q^{14} +(-1.98951 + 3.32293i) q^{15} +(-0.320027 - 1.81496i) q^{16} +(-3.12263 - 1.80285i) q^{17} +(-5.71460 + 3.21476i) q^{18} +(4.74791 - 2.74121i) q^{19} +(6.17960 + 0.604814i) q^{20} +(2.08799 + 4.07925i) q^{21} +(-11.7127 - 2.06526i) q^{22} +(1.98436 + 1.66508i) q^{23} +(2.39938 + 1.70011i) q^{24} +(1.80648 - 4.66226i) q^{25} -8.97571 q^{26} +(-1.42876 + 4.99586i) q^{27} +(4.47994 - 5.82278i) q^{28} +(-2.71758 + 7.46650i) q^{29} +(6.56996 - 5.33738i) q^{30} +(-1.27435 + 1.51871i) q^{31} +(-1.28908 + 7.31074i) q^{32} +(-7.75084 + 5.36293i) q^{33} +(5.06555 + 6.03689i) q^{34} +(-3.54685 - 4.73496i) q^{35} +(8.21951 - 1.35484i) q^{36} +(4.53053 + 2.61570i) q^{37} +(-11.8003 + 2.08071i) q^{38} +(-5.05776 + 5.00157i) q^{39} +(-3.42396 - 1.63975i) q^{40} +(-3.23382 + 1.17702i) q^{41} +(-1.23898 - 9.93870i) q^{42} +(9.33746 - 1.64645i) q^{43} +(13.0861 + 7.55528i) q^{44} +(0.727959 - 6.66859i) q^{45} +(-2.83078 - 4.90305i) q^{46} +(-1.79113 - 2.13459i) q^{47} +(1.81628 + 2.62500i) q^{48} +(-6.97492 + 0.592067i) q^{49} +(-7.19522 + 8.22489i) q^{50} +(6.21837 + 0.579049i) q^{51} +(10.7160 + 3.90030i) q^{52} +3.45521 q^{53} +(6.66886 - 9.19239i) q^{54} +(8.69222 - 8.51505i) q^{55} +(-3.79155 + 2.40860i) q^{56} +(-5.48993 + 7.74798i) q^{57} +(11.1627 - 13.3031i) q^{58} +(-0.890462 + 5.05006i) q^{59} +(-10.1631 + 3.51732i) q^{60} +(0.0122664 + 0.0146185i) q^{61} +(3.75250 - 2.16651i) q^{62} +(-6.23634 - 4.90999i) q^{63} +(6.26942 - 10.8590i) q^{64} +(5.34433 - 7.46766i) q^{65} +(19.9274 - 5.22043i) q^{66} +(1.44818 + 3.97885i) q^{67} +(-3.42443 - 9.40853i) q^{68} +(-4.32727 - 1.18543i) q^{69} +(3.74501 + 12.3759i) q^{70} +(5.88899 + 3.40001i) q^{71} +(-5.00577 - 0.940421i) q^{72} +(-4.21399 - 7.29885i) q^{73} +(-7.34945 - 8.75874i) q^{74} +(0.528730 + 8.64410i) q^{75} +(14.9923 + 2.64355i) q^{76} +(-3.09800 - 14.0601i) q^{77} +(14.1263 - 6.49140i) q^{78} +(-6.10349 - 2.22149i) q^{79} +(-2.88382 - 2.94382i) q^{80} +(-1.36446 - 8.89597i) q^{81} +7.52141 q^{82} +(-1.89050 + 5.19411i) q^{83} +(-2.83955 + 12.4041i) q^{84} +(-8.03873 + 0.619974i) q^{85} +(-20.4079 - 3.59846i) q^{86} +(-1.12288 - 13.7164i) q^{87} +(-5.93860 - 7.07735i) q^{88} +(-5.54827 - 9.60989i) q^{89} +(-6.47995 + 13.1517i) q^{90} +(-4.14507 - 10.0438i) q^{91} +(1.24906 + 7.08376i) q^{92} +(0.907258 - 3.31184i) q^{93} +(2.08296 + 5.72287i) q^{94} +(5.29501 - 11.0565i) q^{95} +(-3.25846 - 12.4382i) q^{96} +(-2.95263 - 16.7452i) q^{97} +(14.7675 + 3.99789i) q^{98} +(8.31997 - 14.0459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) $ 816 * q - 24 * q^4 - 24 * q^9	$ 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) $ 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	−2.05378	−	0.747516i	−1.45224	−	0.528574i	−0.509027	−	0.860751i	$-0.669995\pi$
$2$	−2.05378	−	0.747516i	−1.45224	−	0.528574i	−0.943217	+	0.332177i	$0.892217\pi$
$3$	−1.57383	+	0.723218i	−0.908654	+	0.417550i
$3$	−1.57383	+	0.723218i	−0.908654	+	0.417550i
$4$	2.12716	+	1.78490i	1.06358	+	0.892448i
$5$	1.84479	−	1.26363i	0.825014	−	0.565113i
$5$	1.84479	−	1.26363i	0.825014	−	0.565113i
$6$	3.77293	−	0.308866i	1.54029	−	0.126094i
$7$	−0.111990	−	2.64338i	−0.0423284	−	0.999104i
$7$	−0.111990	−	2.64338i	−0.0423284	−	0.999104i
$8$	−0.848890	−	1.47032i	−0.300128	−	0.519837i
$9$	1.95391	−	2.27645i	0.651304	−	0.758817i
$10$	−4.73338	+	1.21621i	−1.49683	+	0.384601i
$11$	5.35903	−	0.944942i	1.61581	−	0.284911i	0.708607	−	0.705604i	$-0.249324\pi$
$11$	5.35903	−	0.944942i	1.61581	−	0.284911i	0.907203	+	0.420693i	$0.138213\pi$
$12$	−4.63866	−	1.27073i	−1.33907	−	0.366829i
$13$	3.85910	−	1.40460i	1.07032	−	0.389565i	0.254025	−	0.967198i	$-0.418246\pi$
$13$	3.85910	−	1.40460i	1.07032	−	0.389565i	0.816297	+	0.577632i	$0.196023\pi$
$14$	−1.74596	+	5.51264i	−0.466629	+	1.47332i
$15$	−1.98951	+	3.32293i	−0.513689	+	0.857976i
$16$	−0.320027	−	1.81496i	−0.0800066	−	0.453740i
$17$	−3.12263	−	1.80285i	−0.757350	−	0.437256i	0.0709935	−	0.997477i	$-0.477383\pi$
$17$	−3.12263	−	1.80285i	−0.757350	−	0.437256i	−0.828343	+	0.560221i	$0.810716\pi$
$18$	−5.71460	+	3.21476i	−1.34694	+	0.757725i
$19$	4.74791	−	2.74121i	1.08924	−	0.628876i	0.155870	−	0.987778i	$-0.450182\pi$
$19$	4.74791	−	2.74121i	1.08924	−	0.628876i	0.933375	+	0.358902i	$0.116849\pi$
$20$	6.17960	+	0.604814i	1.38180	+	0.135241i
$21$	2.08799	+	4.07925i	0.455638	+	0.890165i
$22$	−11.7127	−	2.06526i	−2.49715	−	0.440314i
$23$	1.98436	+	1.66508i	0.413768	+	0.347192i	0.825786	−	0.563983i	$-0.190732\pi$
$23$	1.98436	+	1.66508i	0.413768	+	0.347192i	−0.412019	+	0.911175i	$0.635176\pi$
$24$	2.39938	+	1.70011i	0.489770	+	0.347033i
$25$	1.80648	−	4.66226i	0.361295	−	0.932451i
$26$	−8.97571			−1.76028
$27$	−1.42876	+	4.99586i	−0.274966	+	0.961454i
$28$	4.47994	−	5.82278i	0.846629	−	1.10040i
$29$	−2.71758	+	7.46650i	−0.504643	+	1.38649i	0.382052	+	0.924141i	$0.375217\pi$
$29$	−2.71758	+	7.46650i	−0.504643	+	1.38649i	−0.886695	+	0.462354i	$0.847005\pi$
$30$	6.56996	−	5.33738i	1.19951	−	0.974468i
$31$	−1.27435	+	1.51871i	−0.228880	+	0.272769i	−0.868246	−	0.496134i	$-0.834753\pi$
$31$	−1.27435	+	1.51871i	−0.228880	+	0.272769i	0.639366	+	0.768903i	$0.279197\pi$
$32$	−1.28908	+	7.31074i	−0.227879	+	1.29237i
$33$	−7.75084	+	5.36293i	−1.34925	+	0.933567i
$34$	5.06555	+	6.03689i	0.868735	+	1.03532i
$35$	−3.54685	−	4.73496i	−0.599528	−	0.800354i
$36$	8.21951	−	1.35484i	1.36992	−	0.225806i
$37$	4.53053	+	2.61570i	0.744815	+	0.430019i	0.823817	−	0.566855i	$-0.191840\pi$
$37$	4.53053	+	2.61570i	0.744815	+	0.430019i	−0.0790023	+	0.996874i	$0.525173\pi$
$38$	−11.8003	+	2.08071i	−1.91426	+	0.337535i
$39$	−5.05776	+	5.00157i	−0.809889	+	0.800893i
$40$	−3.42396	−	1.63975i	−0.541376	−	0.259267i
$41$	−3.23382	+	1.17702i	−0.505038	+	0.183819i	−0.581959	−	0.813218i	$-0.697713\pi$
$41$	−3.23382	+	1.17702i	−0.505038	+	0.183819i	0.0769205	+	0.997037i	$0.475491\pi$
$42$	−1.23898	−	9.93870i	−0.191179	−	1.53358i
$43$	9.33746	−	1.64645i	1.42395	−	0.251081i	0.592002	−	0.805936i	$-0.298338\pi$
$43$	9.33746	−	1.64645i	1.42395	−	0.251081i	0.831947	+	0.554856i	$0.187226\pi$
$44$	13.0861	+	7.55528i	1.97281	+	1.13900i
$45$	0.727959	−	6.66859i	0.108518	−	0.994095i
$46$	−2.83078	−	4.90305i	−0.417375	−	0.722915i
$47$	−1.79113	−	2.13459i	−0.261263	−	0.311361i	0.619427	−	0.785054i	$-0.287365\pi$
$47$	−1.79113	−	2.13459i	−0.261263	−	0.311361i	−0.880690	+	0.473693i	$0.842921\pi$
$48$	1.81628	+	2.62500i	0.262158	+	0.378886i
$49$	−6.97492	+	0.592067i	−0.996417	+	0.0845809i
$50$	−7.19522	+	8.22489i	−1.01756	+	1.16318i
$51$	6.21837	+	0.579049i	0.870745	+	0.0810831i
$52$	10.7160	+	3.90030i	1.48604	+	0.540874i
$53$	3.45521			0.474609			0.237305	−	0.971435i	$-0.423736\pi$
$53$	3.45521			0.474609			0.237305	+	0.971435i	$0.423736\pi$
$54$	6.66886	−	9.19239i	0.907517	−	1.25093i
$55$	8.69222	−	8.51505i	1.17206	−	1.14817i
$56$	−3.79155	+	2.40860i	−0.506667	+	0.321863i
$57$	−5.48993	+	7.74798i	−0.727160	+	1.02624i
$58$	11.1627	−	13.3031i	1.46573	−	1.74679i
$59$	−0.890462	+	5.05006i	−0.115928	+	0.657462i	0.870358	+	0.492419i	$0.163887\pi$
$59$	−0.890462	+	5.05006i	−0.115928	+	0.657462i	−0.986286	+	0.165043i	$0.947224\pi$
$60$	−10.1631	+	3.51732i	−1.31205	+	0.454084i
$61$	0.0122664	+	0.0146185i	0.00157055	+	0.00187170i	0.766829	−	0.641851i	$-0.221833\pi$
$61$	0.0122664	+	0.0146185i	0.00157055	+	0.00187170i	−0.765259	+	0.643723i	$0.777389\pi$
$62$	3.75250	−	2.16651i	0.476568	−	0.275147i
$63$	−6.23634	−	4.90999i	−0.785705	−	0.618601i
$64$	6.26942	−	10.8590i	0.783678	−	1.35737i
$65$	5.34433	−	7.46766i	0.662882	−	0.926249i
$66$	19.9274	−	5.22043i	2.45290	−	0.642590i
$67$	1.44818	+	3.97885i	0.176924	+	0.486094i	0.996179	−	0.0873352i	$-0.0278351\pi$
$67$	1.44818	+	3.97885i	0.176924	+	0.486094i	−0.819255	+	0.573429i	$0.805613\pi$
$68$	−3.42443	−	9.40853i	−0.415273	−	1.14095i
$69$	−4.32727	−	1.18543i	−0.520942	−	0.142709i
$70$	3.74501	+	12.3759i	0.447614	+	1.47920i
$71$	5.88899	+	3.40001i	0.698894	+	0.403507i	0.806935	−	0.590640i	$-0.201125\pi$
$71$	5.88899	+	3.40001i	0.698894	+	0.403507i	−0.108041	+	0.994146i	$0.534458\pi$
$72$	−5.00577	−	0.940421i	−0.589936	−	0.110830i
$73$	−4.21399	−	7.29885i	−0.493210	−	0.854266i	0.506759	−	0.862088i	$-0.330843\pi$
$73$	−4.21399	−	7.29885i	−0.493210	−	0.854266i	−0.999969	+	0.00782221i	$0.997510\pi$
$74$	−7.34945	−	8.75874i	−0.854357	−	1.01818i
$75$	0.528730	+	8.64410i	0.0610525	+	0.998135i
$76$	14.9923	+	2.64355i	1.71974	+	0.303236i
$77$	−3.09800	−	14.0601i	−0.353050	−	1.60230i
$78$	14.1263	−	6.49140i	1.59949	−	0.735006i
$79$	−6.10349	−	2.22149i	−0.686696	−	0.249937i	−0.0249763	−	0.999688i	$-0.507951\pi$
$79$	−6.10349	−	2.22149i	−0.686696	−	0.249937i	−0.661720	+	0.749751i	$0.730173\pi$
$80$	−2.88382	−	2.94382i	−0.322421	−	0.329129i
$81$	−1.36446	−	8.89597i	−0.151606	−	0.988441i
$82$	7.52141			0.830601
$83$	−1.89050	+	5.19411i	−0.207509	+	0.570127i	−0.999166	−	0.0408393i	$-0.986997\pi$
$83$	−1.89050	+	5.19411i	−0.207509	+	0.570127i	0.791656	+	0.610967i	$0.209219\pi$
$84$	−2.83955	+	12.4041i	−0.309820	+	1.35339i
$85$	−8.03873	+	0.619974i	−0.871923	+	0.0672456i
$86$	−20.4079	−	3.59846i	−2.20064	−	0.388032i
$87$	−1.12288	−	13.7164i	−0.120385	−	1.47056i
$88$	−5.93860	−	7.07735i	−0.633057	−	0.754448i
$89$	−5.54827	−	9.60989i	−0.588116	−	1.01865i	−0.994479	−	0.104935i	$-0.966537\pi$
$89$	−5.54827	−	9.60989i	−0.588116	−	1.01865i	0.406363	−	0.913712i	$-0.366797\pi$
$90$	−6.47995	+	13.1517i	−0.683046	+	1.38631i
$91$	−4.14507	−	10.0438i	−0.434521	−	1.05287i
$92$	1.24906	+	7.08376i	0.130223	+	0.738533i
$93$	0.907258	−	3.31184i	0.0940783	−	0.343421i
$94$	2.08296	+	5.72287i	0.214841	+	0.590269i
$95$	5.29501	−	11.0565i	0.543256	−	1.13438i
$96$	−3.25846	−	12.4382i	−0.332565	−	1.26947i
$97$	−2.95263	−	16.7452i	−0.299794	−	1.70021i	−0.647053	−	0.762445i	$-0.723999\pi$
$97$	−2.95263	−	16.7452i	−0.299794	−	1.70021i	0.347259	−	0.937769i	$-0.387112\pi$
$98$	14.7675	+	3.99789i	1.49175	+	0.403847i
$99$	8.31997	−	14.0459i	0.836188	−	1.41167i
$100$	12.1643	−	6.69298i	1.21643	−	0.669298i
$101$	−7.39179	+	6.20245i	−0.735511	+	0.617167i	−0.931628	−	0.363414i	$-0.881611\pi$
$101$	−7.39179	+	6.20245i	−0.735511	+	0.617167i	0.196117	+	0.980580i	$0.437167\pi$
$102$	−12.3383	−	5.83757i	−1.22168	−	0.578005i
$103$	−1.85938	+	10.5451i	−0.183210	+	1.03904i	0.745023	+	0.667039i	$0.232438\pi$
$103$	−1.85938	+	10.5451i	−0.183210	+	1.03904i	−0.928233	+	0.371999i	$0.878673\pi$
$104$	−5.34116	−	4.48177i	−0.523744	−	0.439473i
$105$	9.00657	+	4.88689i	0.878951	+	0.476912i
$106$	−7.09625	−	2.58282i	−0.689249	−	0.250866i
$107$	20.0270			1.93608			0.968039	−	0.250798i	$-0.0806930\pi$
$107$	20.0270			1.93608			0.968039	+	0.250798i	$0.0806930\pi$
$108$	−11.9563	+	8.07678i	−1.15050	+	0.777189i
$109$	0.486236			0.0465730			0.0232865	−	0.999729i	$-0.492587\pi$
$109$	0.486236			0.0465730			0.0232865	+	0.999729i	$0.492587\pi$
$110$	−24.2171	+	10.9905i	−2.30901	+	1.04790i
$111$	−9.02204	−	0.840125i	−0.856334	−	0.0797411i
$112$	−4.76179	+	1.04921i	−0.449947	+	0.0991410i
$113$	0.0414687	−	0.235181i	0.00390105	−	0.0221239i	−0.982795	−	0.184699i	$-0.940869\pi$
$113$	0.0414687	−	0.235181i	0.00390105	−	0.0221239i	0.986696	+	0.162575i	$0.0519800\pi$
$114$	17.0669	−	11.8089i	1.59846	−	1.10600i
$115$	5.76476	+	0.564213i	0.537567	+	0.0526131i
$116$	−19.1077	+	11.0318i	−1.77410	+	1.02428i
$117$	4.34284	−	11.5295i	0.401496	−	1.06590i
$118$	5.60382	−	9.70610i	0.515873	−	0.893519i
$119$	−4.41592	+	8.45621i	−0.404807	+	0.775180i
$120$	6.57465	+	0.104417i	0.600180	+	0.00953194i
$121$	17.4897	−	6.36573i	1.58997	−	0.578703i
$122$	−0.0142649	−	0.0391925i	−0.00129148	−	0.00354832i
$123$	4.23826	−	4.19119i	0.382151	−	0.377906i
$124$	−5.42149	+	0.955955i	−0.486864	+	0.0858473i
$125$	−2.55880	−	10.8836i	−0.228866	−	0.973458i
$126$	9.13780	+	14.7458i	0.814060	+	1.31366i
$127$	−0.504966	+	0.291542i	−0.0448085	+	0.0258702i	−0.522237	−	0.852800i	$-0.674902\pi$
$127$	−0.504966	+	0.291542i	−0.0448085	+	0.0258702i	0.477428	+	0.878671i	$0.341569\pi$
$128$	−9.61980	+	8.07197i	−0.850278	+	0.713468i
$129$	−13.5049	+	9.34425i	−1.18904	+	0.822715i
$130$	−16.5583	+	11.3420i	−1.45226	+	0.994758i
$131$	2.33151	+	1.95637i	0.203705	+	0.170929i	0.738933	−	0.673779i	$-0.235330\pi$
$131$	2.33151	+	1.95637i	0.203705	+	0.170929i	−0.535228	+	0.844708i	$0.679774\pi$
$132$	−26.0595	−	2.42664i	−2.26819	−	0.211212i
$133$	−7.77777	−	12.2435i	−0.674418	−	1.06165i
$134$		−	9.25423i		−	0.799444i
$135$	3.67715	+	11.0217i	0.316479	+	0.948599i
$136$			6.12170i			0.524931i
$137$	−19.0357	−	6.92841i	−1.62633	−	0.591934i	−0.641753	−	0.766911i	$-0.721793\pi$
$137$	−19.0357	−	6.92841i	−1.62633	−	0.591934i	−0.984573	+	0.174977i	$0.944015\pi$
$138$	8.00114	+	5.66932i	0.681103	+	0.482604i
$139$	7.06807	−	8.42340i	0.599506	−	0.714464i	−0.377897	−	0.925848i	$-0.623353\pi$
$139$	7.06807	−	8.42340i	0.599506	−	0.714464i	0.977403	+	0.211384i	$0.0677971\pi$
$140$	0.906697	−	16.4028i	0.0766299	−	1.38629i
$141$	4.36271	+	2.06411i	0.367407	+	0.173829i
$142$	−9.55314	−	11.3850i	−0.801682	−	0.955407i
$143$	19.3538	−	11.1739i	1.61844	−	0.934410i
$144$	−4.75697	−	2.81775i	−0.396414	−	0.234812i
$145$	4.42153	+	17.2081i	0.367188	+	1.42906i
$146$	3.19862	+	18.1403i	0.264720	+	1.50130i
$147$	10.5492	−	5.97620i	0.870081	−	0.492909i
$148$	4.96839	+	13.6505i	0.408399	+	1.12207i
$149$	3.56438	+	9.79306i	0.292006	+	0.802279i	0.995773	+	0.0918483i	$0.0292775\pi$
$149$	3.56438	+	9.79306i	0.292006	+	0.802279i	−0.703767	+	0.710430i	$0.748500\pi$
$150$	5.37570	−	18.1483i	0.438924	−	1.48181i
$151$	−0.513588	−	2.91270i	−0.0417952	−	0.237032i	0.956753	−	0.290902i	$-0.0939555\pi$
$151$	−0.513588	−	2.91270i	−0.0417952	−	0.237032i	−0.998548	+	0.0538700i	$0.982844\pi$
$152$	−8.06091	−	4.65397i	−0.653826	−	0.377487i
$153$	−10.2055	+	3.58590i	−0.825062	+	0.289903i
$154$	−4.14755	+	31.1923i	−0.334219	+	2.51355i
$155$	−0.431815	+	4.41201i	−0.0346842	+	0.354381i
$156$	−19.6859	+	1.61156i	−1.57614	+	0.129028i
$157$	−3.03671	+	17.2221i	−0.242356	+	1.37447i	0.584198	+	0.811611i	$0.301409\pi$
$157$	−3.03671	+	17.2221i	−0.242356	+	1.37447i	−0.826554	+	0.562858i	$0.809702\pi$
$158$	10.8746	+	9.12491i	0.865141	+	0.725939i
$159$	−5.43793	+	2.49887i	−0.431256	+	0.198173i
$160$	6.85999	+	15.1157i	0.542330	+	1.19500i
$161$	4.17920	−	5.43189i	0.329367	−	0.428093i
$162$	−3.84758	+	19.2903i	−0.302295	+	1.51559i
$163$		−	3.36461i		−	0.263536i	−0.991281	−	0.131768i	$-0.957935\pi$
$163$		−	3.36461i		−	0.263536i	0.991281	−	0.131768i	$-0.0420655\pi$
$164$	−8.97970	−	3.26834i	−0.701197	−	0.255215i
$165$	−7.52188	+	19.6877i	−0.585577	+	1.53268i
$166$	7.76536	−	9.25439i	0.602708	−	0.718280i
$167$	−5.70918	−	1.00668i	−0.441789	−	0.0778994i	−0.0516712	−	0.998664i	$-0.516455\pi$
$167$	−5.70918	−	1.00668i	−0.441789	−	0.0778994i	−0.390118	+	0.920765i	$0.627566\pi$
$168$	4.22533	−	6.53286i	0.325991	−	0.504021i
$169$	2.96118	−	2.48473i	0.227783	−	0.191133i
$170$	16.9733	+	4.73579i	1.30179	+	0.363219i
$171$	3.03677	−	16.1645i	0.232228	−	1.23613i
$172$	22.8010	+	13.1641i	1.73856	+	1.00376i
$173$	18.3278	−	3.23168i	1.39343	−	0.245700i	0.573991	−	0.818862i	$-0.305394\pi$
$173$	18.3278	−	3.23168i	1.39343	−	0.245700i	0.819442	+	0.573162i	$0.194283\pi$
$174$	−7.94712	+	29.0100i	−0.602469	+	2.19924i
$175$	−12.5264	−	4.25308i	−0.946909	−	0.321502i
$176$	−3.43007	−	9.42403i	−0.258551	−	0.710363i
$177$	−2.25085	−	8.59196i	−0.169185	−	0.645811i
$178$	4.21140	+	23.8841i	0.315658	+	1.79019i
$179$	8.18808	+	4.72739i	0.612006	+	0.353342i	0.773750	−	0.633491i	$-0.218379\pi$
$179$	8.18808	+	4.72739i	0.612006	+	0.353342i	−0.161744	+	0.986833i	$0.551712\pi$
$180$	13.4512	−	12.8858i	1.00260	−	0.960451i
$181$	−5.24016	+	3.02541i	−0.389498	+	0.224877i	−0.681943	−	0.731406i	$-0.738865\pi$
$181$	−5.24016	+	3.02541i	−0.389498	+	0.224877i	0.292444	+	0.956283i	$0.405531\pi$
$182$	1.00519	+	23.7262i	0.0745099	+	1.75870i
$183$	−0.0298775	−	0.0141358i	−0.00220861	−	0.00104495i
$184$	0.763692	−	4.33111i	0.0563001	−	0.319294i
$185$	11.6632	−	0.899501i	0.857492	−	0.0661326i
$186$	−4.33896	+	6.12360i	−0.318148	+	0.449004i
$187$	−18.4379	−	6.71084i	−1.34831	−	0.490746i
$188$		−	7.73758i		−	0.564321i
$189$	13.3660	+	3.21728i	0.972231	+	0.234023i
$190$	−19.1397	+	18.7496i	−1.38854	+	1.36024i
$191$	−4.33828	+	11.9193i	−0.313907	+	0.862451i	0.677952	+	0.735106i	$0.262868\pi$
$191$	−4.33828	+	11.9193i	−0.313907	+	0.862451i	−0.991858	+	0.127345i	$0.959354\pi$
$192$	−2.01364	+	21.6244i	−0.145322	+	1.56060i
$193$	−15.3283	+	18.2675i	−1.10335	+	1.31493i	−0.158528	+	0.987355i	$0.550675\pi$
$193$	−15.3283	+	18.2675i	−1.10335	+	1.31493i	−0.944826	+	0.327572i	$0.893770\pi$
$194$	−6.45323	+	36.5981i	−0.463315	+	2.62759i
$195$	−3.01034	+	15.6180i	−0.215575	+	1.11843i
$196$	−15.8935	−	11.1901i	−1.13525	−	0.799292i
$197$	−3.75614	−	6.50583i	−0.267614	−	0.463521i	0.700631	−	0.713524i	$-0.252902\pi$
$197$	−3.75614	−	6.50583i	−0.267614	−	0.463521i	−0.968245	+	0.250003i	$0.919569\pi$
$198$	−27.5870	+	22.6280i	−1.96052	+	1.60810i
$199$	14.2119	+	8.20524i	1.00745	+	0.581654i	0.910445	−	0.413629i	$-0.135739\pi$
$199$	14.2119	+	8.20524i	1.00745	+	0.581654i	0.0970091	+	0.995283i	$0.469072\pi$
$200$	−8.38852	+	1.30164i	−0.593158	+	0.0920400i
$201$	−5.15677	−	5.21470i	−0.363731	−	0.367816i
$202$	19.8176	−	7.21300i	1.39436	−	0.507505i
$203$	20.0411	+	6.34743i	1.40661	+	0.445502i
$204$	12.1939	+	12.3309i	0.853744	+	0.863333i
$205$	−4.47840	+	6.25770i	−0.312785	+	0.437057i
$206$	11.7014	−	20.2674i	0.815274	−	1.41210i
$207$	7.66773	−	1.26389i	0.532944	−	0.0878462i
$208$	−3.78430	−	6.55461i	−0.262394	−	0.454480i
$209$	22.8539	−	19.1767i	1.58084	−	1.32648i
$210$	−14.8445	−	16.7692i	−1.02437	−	1.15718i
$211$	1.44171	−	8.17632i	0.0992511	−	0.562881i	−0.894110	−	0.447847i	$-0.852191\pi$
$211$	1.44171	−	8.17632i	0.0992511	−	0.562881i	0.993362	−	0.115034i	$-0.0366978\pi$
$212$	7.34977	+	6.16719i	0.504784	+	0.423564i
$213$	−11.7272	−	1.09203i	−0.803537	−	0.0748247i
$214$	−41.1310	−	14.9705i	−2.81166	−	1.02336i
$215$	15.1451	−	14.8364i	1.03289	−	1.01184i
$216$	8.55838	−	2.14019i	0.582324	−	0.145622i
$217$	4.15725	+	3.19851i	0.282212	+	0.217129i
$218$	−0.998624	−	0.363470i	−0.0676354	−	0.0246173i
$219$	11.9108	+	8.43955i	0.804856	+	0.570292i
$220$	33.6882	−	2.59815i	2.27126	−	0.175167i
$221$	−14.5828	−	2.57135i	−0.980948	−	0.172968i
$222$	17.9013	+	8.46955i	1.20146	+	0.568439i
$223$	−0.903324	+	0.757979i	−0.0604911	+	0.0507580i	−0.672532	−	0.740068i	$-0.734793\pi$
$223$	−0.903324	+	0.757979i	−0.0604911	+	0.0507580i	0.612041	+	0.790826i	$0.290349\pi$
$224$	19.4694	+	2.58880i	1.30086	+	0.172971i
$225$	−7.08370	−	13.2220i	−0.472247	−	0.881466i
$226$	−0.260969	+	0.452012i	−0.0173594	+	0.0300674i
$227$	10.0540	−	1.77278i	0.667305	−	0.117664i	0.170274	−	0.985397i	$-0.445535\pi$
$227$	10.0540	−	1.77278i	0.667305	−	0.117664i	0.497031	+	0.867733i	$0.334424\pi$
$228$	−25.5073	+	6.68220i	−1.68926	+	0.442539i
$229$	4.41250	+	12.1232i	0.291586	+	0.801127i	0.995835	+	0.0911734i	$0.0290617\pi$
$229$	4.41250	+	12.1232i	0.291586	+	0.801127i	−0.704249	+	0.709953i	$0.748716\pi$
$230$	−11.4178	−	5.46802i	−0.752869	−	0.360551i
$231$	15.0443	+	19.8878i	0.989841	+	1.30852i
$232$	13.2851	−	2.34252i	0.872209	−	0.153794i
$233$	−9.54783	+	16.5373i	−0.625499	+	1.08340i	0.362945	+	0.931811i	$0.381771\pi$
$233$	−9.54783	+	16.5373i	−0.625499	+	1.08340i	−0.988444	+	0.151586i	$0.951562\pi$
$234$	−17.5378	+	20.4328i	−1.14648	+	1.33573i
$235$	−6.00158	−	1.67453i	−0.391500	−	0.109234i
$236$	−10.9080	+	9.15289i	−0.710050	+	0.595803i
$237$	11.2125	−	0.917897i	0.728331	−	0.0596238i
$238$	15.3905	−	14.0663i	0.997618	−	0.911780i
$239$	17.4531	−	20.7998i	1.12895	−	1.34542i	0.198027	−	0.980197i	$-0.436547\pi$
$239$	17.4531	−	20.7998i	1.12895	−	1.34542i	0.930918	−	0.365228i	$-0.119009\pi$
$240$	6.66768	+	2.54746i	0.430397	+	0.164438i
$241$	3.37892	−	9.28351i	0.217655	−	0.598003i	−0.782026	−	0.623246i	$-0.785814\pi$
$241$	3.37892	−	9.28351i	0.217655	−	0.598003i	0.999681	+	0.0252426i	$0.00803581\pi$
$242$	−40.6786			−2.61492
$243$	8.58115	+	13.0140i	0.550481	+	0.834848i
$244$			0.0529899i			0.00339233i
$245$	−12.1191	+	9.90595i	−0.774260	+	0.632868i
$246$	−11.8375	+	5.43962i	−0.754728	+	0.346817i
$247$	14.4724	−	17.2475i	0.920854	−	1.09743i
$248$	3.31478	+	0.584485i	0.210489	+	0.0371148i
$249$	−0.781135	−	9.54191i	−0.0495024	−	0.604694i
$250$	−2.88043	+	24.2653i	−0.182174	+	1.53467i
$251$	−3.73072	−	6.46179i	−0.235481	−	0.407865i	0.723931	−	0.689872i	$-0.242333\pi$
$251$	−3.73072	−	6.46179i	−0.235481	−	0.407865i	−0.959412	+	0.282007i	$0.909000\pi$
$252$	−4.50186	−	21.5756i	−0.283590	−	1.35913i
$253$	12.2077	+	7.04809i	0.767489	+	0.443110i
$254$	1.25502	−	0.221294i	0.0787471	−	0.0138852i
$255$	12.2033	−	6.78949i	0.764198	−	0.425174i
$256$	2.22558	−	0.810047i	0.139099	−	0.0506279i
$257$	−9.82306	−	26.9886i	−0.612746	−	1.68351i	−0.724075	−	0.689722i	$-0.757733\pi$
$257$	−9.82306	−	26.9886i	−0.612746	−	1.68351i	0.111329	−	0.993784i	$-0.464489\pi$
$258$	34.7211	−	9.09595i	2.16164	−	0.566289i
$259$	6.40693	−	12.2689i	0.398107	−	0.762350i
$260$	24.6972	−	6.34581i	1.53166	−	0.393551i
$261$	11.6872	+	20.7753i	0.723420	+	1.28596i
$262$	−3.32600	−	5.76081i	−0.205481	−	0.355904i
$263$	−21.5143	+	18.0526i	−1.32663	+	1.11317i	−0.341776	+	0.939781i	$0.611028\pi$
$263$	−21.5143	+	18.0526i	−1.32663	+	1.11317i	−0.984853	+	0.173393i	$0.944527\pi$
$264$	14.4648	+	6.84368i	0.890249	+	0.421199i
$265$	6.37412	−	4.36611i	0.391559	−	0.268208i
$266$	6.82161	+	30.9596i	0.418260	+	1.89825i
$267$	15.6821	+	11.1118i	0.959730	+	0.680029i
$268$	−4.02132	+	11.0485i	−0.245641	+	0.674894i
$269$	−27.1630			−1.65616			−0.828078	−	0.560613i	$-0.810565\pi$
$269$	−27.1630			−1.65616			−0.828078	+	0.560613i	$0.810565\pi$
$270$	0.686841	−	25.3850i	0.0417998	−	1.54488i
$271$		−	20.8502i		−	1.26656i	−0.773923	−	0.633280i	$-0.781708\pi$
$271$		−	20.8502i		−	1.26656i	0.773923	−	0.633280i	$-0.218292\pi$
$272$	−2.27278	+	6.24442i	−0.137808	+	0.378623i
$273$	13.7875	+	12.8094i	0.834456	+	0.775263i
$274$	33.9160	+	28.4589i	2.04894	+	1.71927i
$275$	5.27541	−	26.6922i	0.318119	−	1.60960i
$276$	−7.08891	−	10.2453i	−0.426702	−	0.616696i
$277$	4.96503	+	5.91709i	0.298320	+	0.355524i	0.894294	−	0.447480i	$-0.147678\pi$
$277$	4.96503	+	5.91709i	0.298320	+	0.355524i	−0.595974	+	0.803004i	$0.703234\pi$
$278$	−20.8129	+	12.0163i	−1.24828	+	0.720692i
$279$	0.967304	+	5.86843i	0.0579110	+	0.351334i
$280$	−3.95102	+	9.23447i	−0.236119	+	0.551865i
$281$	−12.6080	+	2.22314i	−0.752132	+	0.132621i	−0.536555	−	0.843865i	$-0.680275\pi$
$281$	−12.6080	+	2.22314i	−0.752132	+	0.132621i	−0.215578	+	0.976487i	$0.569163\pi$
$282$	−7.41711	−	7.50043i	−0.441683	−	0.446644i
$283$	−26.7923	+	9.75160i	−1.59264	+	0.579672i	−0.977902	−	0.209062i	$-0.932959\pi$
$283$	−26.7923	+	9.75160i	−1.59264	+	0.579672i	−0.614734	+	0.788734i	$0.710737\pi$
$284$	6.45814	+	17.7436i	0.383220	+	1.05289i
$285$	−0.337180	+	21.2306i	−0.0199728	+	1.25759i
$286$	−48.1012	+	8.48153i	−2.84428	+	0.501524i
$287$	3.47346	+	8.41641i	0.205032	+	0.496805i
$288$	14.1238	+	17.2191i	0.832252	+	1.01464i
$289$	−1.99944	−	3.46313i	−0.117614	−	0.203714i
$290$	3.78248	−	38.6469i	0.222115	−	2.26943i
$291$	16.7573	+	24.2187i	0.982333	+	1.41973i
$292$	4.06387	−	23.0473i	0.237820	−	1.34874i
$293$	1.67649	−	1.99796i	0.0979414	−	0.116722i	−0.714847	−	0.699280i	$-0.753504\pi$
$293$	1.67649	−	1.99796i	0.0979414	−	0.116722i	0.812789	+	0.582559i	$0.197948\pi$
$294$	−26.1330	+	4.38814i	−1.52411	+	0.255922i
$295$	4.73870	+	10.4415i	0.275898	+	0.607928i
$296$		−	8.88178i		−	0.516243i
$297$	−2.93600	+	28.1231i	−0.170364	+	1.63187i
$298$		−	22.7773i		−	1.31945i
$299$	9.99661	+	3.63847i	0.578119	+	0.210418i
$300$	−14.3041	+	19.3311i	−0.825849	+	1.11608i
$301$	−5.39789	−	24.4981i	−0.311129	−	1.41205i
$302$	−1.12249	+	6.36597i	−0.0645922	+	0.366321i
$303$	7.14773	−	15.1075i	0.410627	−	0.867903i
$304$	−6.49464	−	7.74001i	−0.372493	−	0.443920i
$305$	0.0411011	+	0.0114678i	0.00235344	+	0.000656646i
$306$	23.6403	+	0.264072i	1.35143	+	0.0150960i
$307$	3.67237	−	6.36074i	0.209593	−	0.363026i	−0.741993	−	0.670407i	$-0.766119\pi$
$307$	3.67237	−	6.36074i	0.209593	−	0.363026i	0.951586	+	0.307381i	$0.0994527\pi$
$308$	18.5060	−	35.4377i	1.05447	−	2.01925i
$309$	−4.70003	−	17.9409i	−0.267375	−	1.02062i
$310$	4.18490	−	8.73852i	0.237687	−	0.496315i
$311$	−10.2969	+	3.74775i	−0.583882	+	0.212516i	−0.617036	−	0.786935i	$-0.711667\pi$
$311$	−10.2969	+	3.74775i	−0.583882	+	0.212516i	0.0331544	+	0.999450i	$0.489445\pi$
$312$	11.6474	+	3.19074i	0.659404	+	0.180640i
$313$	4.88394	+	27.6982i	0.276057	+	1.56560i	0.735585	+	0.677432i	$0.236907\pi$
$313$	4.88394	+	27.6982i	0.276057	+	1.56560i	−0.459529	+	0.888163i	$0.651982\pi$
$314$	19.1105	−	33.1004i	1.07847	−	1.86796i
$315$	−17.7091	−	1.17746i	−0.997797	−	0.0663421i
$316$	−9.01796	−	15.6196i	−0.507300	−	0.878669i
$317$	−9.39916	+	7.88683i	−0.527910	+	0.442969i	−0.867379	−	0.497648i	$-0.834197\pi$
$317$	−9.39916	+	7.88683i	−0.527910	+	0.442969i	0.339469	+	0.940617i	$0.389753\pi$
$318$	13.0363	−	1.06720i	0.731038	−	0.0598454i
$319$	−7.50822	+	42.5812i	−0.420379	+	2.38409i
$320$	−2.15596	−	27.9547i	−0.120522	−	1.56272i
$321$	−31.5191	+	14.4839i	−1.75923	+	0.808410i
$322$	−12.6436	+	8.03191i	−0.704600	+	0.447601i
$323$	−19.7680			−1.09992
$324$	12.9760	−	21.3585i	0.720887	−	1.18659i
$325$	0.422782	−	20.5295i	0.0234517	−	1.13877i
$326$	−2.51510	+	6.91018i	−0.139298	+	0.382719i
$327$	−0.765256	+	0.351655i	−0.0423187	+	0.0194466i
$328$	4.47575	+	3.75560i	0.247132	+	0.207368i
$329$	−5.44193	+	4.97369i	−0.300023	+	0.274208i
$330$	30.1651	−	34.8115i	1.66054	−	1.91631i
$331$	−14.3717	+	12.0593i	−0.789940	+	0.662839i	−0.945731	−	0.324952i	$-0.894652\pi$
$331$	−14.3717	+	12.0593i	−0.789940	+	0.662839i	0.155790	+	0.987790i	$0.450208\pi$
$332$	−13.2923	+	7.67433i	−0.729512	+	0.421184i
$333$	14.8068	−	5.20268i	0.811407	−	0.285105i
$334$	10.9729	+	6.33521i	0.600411	+	0.346647i
$335$	7.69938	+	5.51016i	0.420662	+	0.301052i
$336$	6.73547	−	5.09510i	0.367450	−	0.277960i
$337$	−4.65502	−	12.7896i	−0.253575	−	0.696692i	−0.999529	−	0.0306943i	$-0.990228\pi$
$337$	−4.65502	−	12.7896i	−0.253575	−	0.696692i	0.745954	−	0.665998i	$-0.231994\pi$
$338$	−7.93900	+	2.88956i	−0.431824	+	0.157171i
$339$	0.104822	+	0.400126i	0.00569315	+	0.0217319i
$340$	−18.2062	−	13.0295i	−0.987372	−	0.706625i
$341$	−5.39420	+	9.34302i	−0.292112	+	0.505953i
$342$	−18.3201	+	30.9283i	−0.990636	+	1.67241i
$343$	2.34618	+	18.3710i	0.126682	+	0.991943i
$344$	−10.3473	−	12.3314i	−0.557888	−	0.664865i
$345$	−9.48083	+	3.28120i	−0.510431	+	0.176654i
$346$	−40.0570	−	7.06312i	−2.15348	−	0.379716i
$347$	−10.7847	−	9.04943i	−0.578953	−	0.485799i	0.305650	−	0.952144i	$-0.401126\pi$
$347$	−10.7847	−	9.04943i	−0.578953	−	0.485799i	−0.884603	+	0.466345i	$0.845571\pi$
$348$	22.0939	−	31.1813i	1.18436	−	1.67149i
$349$	5.60797	−	15.4078i	0.300188	−	0.824759i	−0.694279	−	0.719706i	$-0.744276\pi$
$349$	5.60797	−	15.4078i	0.300188	−	0.824759i	0.994467	−	0.105053i	$-0.0335013\pi$
$350$	22.5473	+	18.0986i	1.20520	+	0.967411i
$351$	1.50343	+	21.2864i	0.0802470	+	1.13618i
$352$			40.3966i			2.15315i
$353$	3.84226	−	10.5565i	0.204503	−	0.561867i	−0.794464	−	0.607311i	$-0.792248\pi$
$353$	3.84226	−	10.5565i	0.204503	−	0.561867i	0.998967	+	0.0454443i	$0.0144703\pi$
$354$	−1.79986	+	19.3286i	−0.0956616	+	1.02730i
$355$	15.1603	−	1.16921i	0.804624	−	0.0620553i
$356$	5.35061	−	30.3448i	0.283582	−	1.60827i
$357$	0.834250	−	16.5024i	0.0441532	−	0.873397i
$358$	−13.2827	−	15.8298i	−0.702015	−	0.836629i
$359$	15.0146	−	8.66867i	0.792439	−	0.457515i	−0.0483814	−	0.998829i	$-0.515406\pi$
$359$	15.0146	−	8.66867i	0.792439	−	0.457515i	0.840821	+	0.541314i	$0.182073\pi$
$360$	−10.4229	+	4.59057i	−0.549336	+	0.241944i
$361$	5.52842	−	9.57551i	0.290970	−	0.503974i
$362$	13.0237	−	2.29643i	0.684511	−	0.120698i
$363$	−22.9221	+	22.6675i	−1.20310	+	1.18973i
$364$	9.10988	−	28.7632i	0.477487	−	1.50760i
$365$	−16.9970	−	8.13989i	−0.889662	−	0.426061i
$366$	0.0507953	+	0.0513658i	0.00265511	+	0.00268494i
$367$	−0.108720	−	0.616584i	−0.00567516	−	0.0321854i	0.981839	−	0.189718i	$-0.0607573\pi$
$367$	−0.108720	−	0.616584i	−0.00567516	−	0.0321854i	−0.987514	+	0.157532i	$0.949646\pi$
$368$	2.38700	−	4.13441i	0.124431	−	0.215521i
$369$	−3.63919	+	9.66142i	−0.189449	+	0.502953i
$370$	−24.6260	−	6.87101i	−1.28024	−	0.357207i
$371$	−0.386950	−	9.13343i	−0.0200895	−	0.474184i
$372$	7.84117	−	5.42543i	0.406546	−	0.281296i
$373$	5.78285	+	1.01967i	0.299425	+	0.0527966i	0.321342	−	0.946963i	$-0.395866\pi$
$373$	5.78285	+	1.01967i	0.299425	+	0.0527966i	−0.0219175	+	0.999760i	$0.506977\pi$
$374$	32.8510	+	27.5652i	1.69868	+	1.42536i
$375$	11.8983	+	15.2784i	0.614428	+	0.788973i
$376$	−1.61805	+	4.44557i	−0.0834447	+	0.229263i
$377$			32.6311i			1.68059i
$378$	−25.0458	−	16.5989i	−1.28822	−	0.853754i
$379$	−32.5480			−1.67188			−0.835939	−	0.548822i	$-0.815076\pi$
$379$	−32.5480			−1.67188			−0.835939	+	0.548822i	$0.815076\pi$
$380$	30.9981	−	14.0680i	1.59017	−	0.721671i
$381$	0.583884	−	0.824039i	0.0299133	−	0.0422168i
$382$	17.8198	−	21.2368i	0.911738	−	1.08657i
$383$	−33.5617	−	5.91783i	−1.71492	−	0.302387i	−0.772055	−	0.635556i	$-0.780771\pi$
$383$	−33.5617	−	5.91783i	−1.71492	−	0.302387i	−0.942867	+	0.333169i	$0.891882\pi$
$384$	9.30218	−	19.6612i	0.474700	−	1.00333i
$385$	−23.4820	−	22.0232i	−1.19675	−	1.12241i
$386$	45.1363	−	26.0594i	2.29737	−	1.32639i
$387$	14.4965	−	24.4733i	0.736899	−	1.24405i
$388$	23.6077	−	40.8897i	1.19850	−	2.07586i
$389$	23.9278	−	4.21912i	1.21319	−	0.213918i	0.469797	−	0.882774i	$-0.344327\pi$
$389$	23.9278	−	4.21912i	1.21319	−	0.213918i	0.743392	+	0.668856i	$0.233216\pi$
$390$	17.8573	−	29.8257i	0.904238	−	1.51028i
$391$	−3.19454	−	8.77693i	−0.161555	−	0.443869i
$392$	6.79147	+	9.75277i	0.343021	+	0.492589i
$393$	−5.08430	−	1.39281i	−0.256469	−	0.0702582i
$394$	2.85109	+	16.1693i	0.143636	+	0.814599i
$395$	−14.0668	+	3.61438i	−0.707777	+	0.181859i
$396$	42.7684	−	15.0276i	2.14919	−	0.755164i
$397$	1.61055	+	2.78956i	0.0808313	+	0.140004i	0.903607	−	0.428362i	$-0.140909\pi$
$397$	1.61055	+	2.78956i	0.0808313	+	0.140004i	−0.822776	+	0.568366i	$0.807576\pi$
$398$	−23.0546	−	27.4754i	−1.15562	−	1.37722i
$399$	21.0957	+	13.6443i	1.05610	+	0.683069i
$400$	−9.03993	−	1.78664i	−0.451997	−	0.0893320i
$401$	−23.3083	+	27.7777i	−1.16396	+	1.38715i	−0.256749	+	0.966478i	$0.582651\pi$
$401$	−23.3083	+	27.7777i	−1.16396	+	1.38715i	−0.907211	+	0.420676i	$0.861793\pi$
$402$	6.69282	+	14.5646i	0.333808	+	0.726418i
$403$	−2.78467	+	7.65081i	−0.138714	+	0.381114i
$404$	−26.7942			−1.33306
$405$	−13.7583	−	14.6870i	−0.683658	−	0.729803i
$406$	−36.4154	−	28.0173i	−1.80726	−	1.39048i
$407$	26.7510	+	9.73656i	1.32600	+	0.482623i
$408$	−4.42732	−	9.63454i	−0.219185	−	0.476981i
$409$	−4.06639	+	4.84613i	−0.201070	+	0.239626i	−0.857152	−	0.515064i	$-0.827768\pi$
$409$	−4.06639	+	4.84613i	−0.201070	+	0.239626i	0.656082	+	0.754690i	$0.272213\pi$
$410$	13.8754	−	9.50428i	0.685257	−	0.469383i
$411$	34.9697	−	2.86275i	1.72493	−	0.141209i
$412$	−22.7771	+	19.1122i	−1.12215	+	0.941592i
$413$	13.4490	+	1.78827i	0.661780	+	0.0879951i
$414$	−16.6926	−	3.13600i	−0.820398	−	0.154126i
$415$	3.07586	+	11.9709i	0.150988	+	0.587629i
$416$	5.29395	+	30.0235i	0.259557	+	1.47202i
$417$	−5.03203	+	18.3688i	−0.246419	+	0.899524i
$418$	−61.2719	+	22.3011i	−2.99691	+	1.09078i
$419$	25.5614	−	9.30358i	1.24875	−	0.454509i	0.368774	−	0.929519i	$-0.379778\pi$
$419$	25.5614	−	9.30358i	1.24875	−	0.454509i	0.879981	+	0.475010i	$0.157555\pi$
$420$	10.4358	+	26.4710i	0.509214	+	1.29165i
$421$	−5.61680	−	31.8545i	−0.273746	−	1.55249i	−0.742916	−	0.669385i	$-0.766558\pi$
$421$	−5.61680	−	31.8545i	−0.273746	−	1.55249i	0.469170	−	0.883108i	$-0.344553\pi$
$422$	−9.07288	+	15.7147i	−0.441661	+	0.764979i
$423$	−8.35899	−	0.0933732i	−0.406428	−	0.00453996i
$424$	−2.93309	−	5.08027i	−0.142444	−	0.246720i
$425$	−14.0463	+	11.3017i	−0.681347	+	0.548213i
$426$	23.2689	+	11.0091i	1.12738	+	0.533392i
$427$	0.0372685	−	0.0340618i	0.00180355	−	0.00164836i
$428$	42.6005	+	35.7460i	2.05917	+	1.72785i
$429$	−22.3785	+	31.5829i	−1.08044	+	1.52484i
$430$	−42.1953	+	19.1496i	−2.03484	+	0.923476i
$431$		−	5.94633i		−	0.286425i	−0.989692	−	0.143212i	$-0.954257\pi$
$431$		−	5.94633i		−	0.286425i	0.989692	−	0.143212i	$-0.0457432\pi$
$432$	9.52454	+	0.994344i	0.458249	+	0.0478404i
$433$	17.2795			0.830398			0.415199	−	0.909731i	$-0.363712\pi$
$433$	17.2795			0.830398			0.415199	+	0.909731i	$0.363712\pi$
$434$	−6.14715	−	9.67666i	−0.295073	−	0.464495i
$435$	−19.4040	−	23.8850i	−0.930350	−	1.14520i
$436$	1.03430	+	0.867882i	0.0495340	+	0.0415640i
$437$	13.9859	+	2.46609i	0.669035	+	0.117969i
$438$	−18.1535	−	26.2365i	−0.867407	−	1.25363i
$439$	14.1919	+	16.9132i	0.677341	+	0.807224i	0.989763	−	0.142720i	$-0.0455848\pi$
$439$	14.1919	+	16.9132i	0.677341	+	0.807224i	−0.312422	+	0.949943i	$0.601140\pi$
$440$	−19.8986	−	5.55200i	−0.948629	−	0.264681i
$441$	−12.2806	+	17.0349i	−0.584789	+	0.811186i
$442$	28.0279	+	16.1819i	1.33315	+	0.769694i
$443$	−2.09614	−	11.8878i	−0.0995904	−	0.564805i	−0.993244	−	0.116047i	$-0.962978\pi$
$443$	−2.09614	−	11.8878i	−0.0995904	−	0.564805i	0.893653	−	0.448758i	$-0.148134\pi$
$444$	−17.6918	−	17.8905i	−0.839613	−	0.849045i
$445$	−22.3787	−	10.7172i	−1.06085	−	0.508046i
$446$	2.42183	−	0.881476i	0.114677	−	0.0417391i
$447$	−12.6923	−	12.8348i	−0.600324	−	0.607067i
$448$	−29.4065	−	15.3564i	−1.38933	−	0.725520i
$449$	−3.44505	−	1.98900i	−0.162582	−	0.0938666i	0.416502	−	0.909135i	$-0.363256\pi$
$449$	−3.44505	−	1.98900i	−0.162582	−	0.0938666i	−0.579083	+	0.815268i	$0.696589\pi$
$450$	4.66473	+	32.4503i	0.219898	+	1.52972i
$451$	−16.2180	+	9.36344i	−0.763674	+	0.440907i
$452$	0.507983	−	0.426249i	0.0238935	−	0.0200491i
$453$	2.91482	+	4.21268i	0.136950	+	0.197929i
$454$	−21.9738	−	3.87458i	−1.03128	−	0.181843i
$455$	−20.3384	−	13.2908i	−0.953478	−	0.623081i
$456$	16.0524	+	1.49478i	0.751721	+	0.0699996i
$457$	3.16433	−	8.69391i	0.148021	−	0.406684i	−0.843418	−	0.537259i	$-0.819460\pi$
$457$	3.16433	−	8.69391i	0.148021	−	0.406684i	0.991439	+	0.130574i	$0.0416822\pi$
$458$		−	28.1969i		−	1.31756i
$459$	13.4683	−	13.0244i	0.628647	−	0.607927i
$460$	11.2555	+	11.4897i	0.524790	+	0.535709i
$461$	4.45939	+	1.62308i	0.207694	+	0.0755946i	0.443772	−	0.896140i	$-0.353640\pi$
$461$	4.45939	+	1.62308i	0.207694	+	0.0755946i	−0.236078	+	0.971734i	$0.575862\pi$
$462$	−16.0313	−	52.0911i	−0.745841	−	2.42350i
$463$	4.89890	−	5.83828i	0.227671	−	0.271328i	−0.640100	−	0.768291i	$-0.721107\pi$
$463$	4.89890	−	5.83828i	0.227671	−	0.271328i	0.867772	+	0.496963i	$0.165552\pi$
$464$	14.4211	+	2.54283i	0.669483	+	0.118048i
$465$	−2.51124	−	7.25607i	−0.116456	−	0.336492i
$466$	31.9711	−	26.8269i	1.48103	−	1.24273i
$467$	9.69730	−	5.59874i	0.448738	−	0.259079i	−0.258559	−	0.965995i	$-0.583248\pi$
$467$	9.69730	−	5.59874i	0.448738	−	0.259079i	0.707297	+	0.706917i	$0.249914\pi$
$468$	29.8169	−	16.7736i	1.37829	−	0.775358i
$469$	10.3554	−	4.27369i	0.478169	−	0.197341i
$470$	11.0742	+	7.92540i	0.510815	+	0.365571i
$471$	−7.67601	−	29.3009i	−0.353692	−	1.35011i
$472$	8.18112	−	2.97768i	0.376566	−	0.137059i
$473$	48.4840	−	17.6467i	2.22929	−	0.811397i
$474$	−23.7142	−	6.49637i	−1.08923	−	0.298388i
$475$	−4.20322	−	27.0879i	−0.192857	−	1.24288i
$476$	−24.4868	+	10.1057i	−1.12235	+	0.463195i
$477$	6.75117	−	7.86561i	0.309115	−	0.360142i
$478$	−51.3930	+	29.6717i	−2.35066	+	1.35715i
$479$	13.9371	−	11.6946i	0.636801	−	0.534339i	−0.266233	−	0.963909i	$-0.585779\pi$
$479$	13.9371	−	11.6946i	0.636801	−	0.534339i	0.903034	+	0.429569i	$0.141335\pi$
$480$	−21.7284	−	18.8283i	−0.991762	−	0.859390i
$481$	21.1578	+	3.73069i	0.964712	+	0.170105i
$482$	−13.8791	+	16.5405i	−0.632178	+	0.753400i
$483$	−2.64893	+	11.5714i	−0.120530	+	0.526516i
$484$	48.5655	+	17.6764i	2.20752	+	0.803473i
$485$	−26.6067	−	27.1602i	−1.20815	−	1.23328i
$486$	−7.89566	−	33.1425i	−0.358155	−	1.50337i
$487$		−	24.7593i		−	1.12195i	−0.827832	−	0.560976i	$-0.810426\pi$
$487$		−	24.7593i		−	1.12195i	0.827832	−	0.560976i	$-0.189574\pi$
$488$	0.0110811	−	0.0304449i	0.000501616	−	0.00137818i
$489$	2.43334	+	5.29534i	0.110040	+	0.239463i
$490$	32.2948	−	11.2855i	1.45893	−	0.509826i
$491$	−2.93966	−	0.518341i	−0.132665	−	0.0233924i	0.106921	−	0.994267i	$-0.465901\pi$
$491$	−2.93966	−	0.518341i	−0.132665	−	0.0233924i	−0.239586	+	0.970875i	$0.577012\pi$
$492$	16.4963	−	1.35045i	0.743710	−	0.0608828i
$493$	21.9470	−	18.4157i	0.988445	−	0.829404i
$494$	−42.6159	+	24.6043i	−1.91738	+	1.10700i
$495$	−2.40027	−	36.4251i	−0.107884	−	1.63719i
$496$	3.16423	+	1.82687i	0.142078	+	0.0820288i
$497$	8.32800	−	15.9476i	0.373562	−	0.715348i
$498$	−5.52845	+	20.1809i	−0.247736	+	0.904329i
$499$	−25.6329	+	9.32961i	−1.14749	+	0.417651i	−0.844611	−	0.535380i	$-0.820169\pi$
$499$	−25.6329	+	9.32961i	−1.14749	+	0.417651i	−0.302875	+	0.953030i	$0.597946\pi$
$500$	13.9831	−	27.7183i	0.625344	−	1.23960i
$501$	9.71335	−	2.54463i	0.433961	−	0.113686i
$502$	2.83179	+	16.0599i	0.126389	+	0.716788i
$503$	−12.6414	−	7.29850i	−0.563651	−	0.325424i	0.190959	−	0.981598i	$-0.438840\pi$
$503$	−12.6414	−	7.29850i	−0.563651	−	0.325424i	−0.754609	+	0.656174i	$0.772174\pi$
$504$	−1.92529	+	13.3375i	−0.0857593	+	0.594098i
$505$	−5.79868	+	20.7827i	−0.258038	+	0.924817i
$506$	−19.8033	−	23.6007i	−0.880365	−	1.04918i
$507$	−2.86341	+	6.05213i	−0.127169	+	0.268784i
$508$	−1.59451	−	0.281156i	−0.0707451	−	0.0124743i
$509$	−30.3009	−	25.4254i	−1.34306	−	1.12696i	−0.980828	−	0.194876i	$-0.937570\pi$
$509$	−30.3009	−	25.4254i	−1.34306	−	1.12696i	−0.362234	−	0.932087i	$-0.617986\pi$
$510$	−30.1381	+	4.82201i	−1.33454	+	0.213522i
$511$	−18.8217	+	11.9566i	−0.832623	+	0.528928i
$512$	19.9391			0.881193
$513$	6.91104	+	27.6364i	0.305130	+	1.22018i
$514$			62.7717i			2.76874i
$515$	9.89492	+	21.8030i	0.436022	+	0.960755i
$516$	−45.4055	−	4.22812i	−1.99887	−	0.186133i
$517$	−11.6158	−	9.74680i	−0.510862	−	0.428664i
$518$	−22.3296	+	20.4083i	−0.981106	+	0.896689i
$519$	−26.5077	+	18.3411i	−1.16356	+	0.805084i
$520$	−15.5166	−	1.51865i	−0.680448	−	0.0665973i
$521$	16.8379	+	29.1641i	0.737682	+	1.27770i	0.953536	+	0.301278i	$0.0974132\pi$
$521$	16.8379	+	29.1641i	0.737682	+	1.27770i	−0.215854	+	0.976426i	$0.569253\pi$
$522$	−8.47309	−	51.4044i	−0.370857	−	2.24991i
$523$	−5.01486	+	8.68598i	−0.219284	+	0.379812i	−0.954589	−	0.297925i	$-0.903706\pi$
$523$	−5.01486	+	8.68598i	−0.219284	+	0.379812i	0.735305	+	0.677736i	$0.237039\pi$
$524$	1.46757	+	8.32302i	0.0641112	+	0.363593i
$525$	22.7904	−	2.36569i	0.994656	−	0.103247i
$526$	57.6804	−	20.9939i	2.51498	−	0.915379i
$527$	6.71735	−	2.44491i	0.292612	−	0.106502i
$528$	12.2140	+	12.3512i	0.531545	+	0.537516i
$529$	−2.82870	−	16.0424i	−0.122987	−	0.697494i
$530$	−16.3548	+	4.20228i	−0.710407	+	0.182535i
$531$	9.75633	+	11.8945i	0.423389	+	0.516176i
$532$	5.30891	−	39.9264i	0.230170	−	1.73103i
$533$	−10.8264	+	9.08444i	−0.468944	+	0.393491i
$534$	−23.9014	−	34.5438i	−1.03432	−	1.49486i
$535$	36.9455	−	25.3067i	1.59729	−	1.09410i
$536$	4.62084	−	5.50690i	0.199590	−	0.237862i
$537$	−16.3056	−	1.51837i	−0.703640	−	0.0655224i
$538$	55.7869	+	20.3048i	2.40514	+	0.875400i
$539$	−36.8193	+	9.76380i	−1.58592	+	0.420557i
$540$	−11.8508	+	30.0083i	−0.509976	+	1.29135i
$541$	41.7033			1.79296			0.896481	−	0.443081i	$-0.146115\pi$
$541$	41.7033			1.79296			0.896481	+	0.443081i	$0.146115\pi$
$542$	−15.5859	+	42.8218i	−0.669470	+	1.83935i
$543$	6.05912	−	8.55127i	0.260022	−	0.366970i
$544$	17.2055	−	20.5047i	0.737680	−	0.879133i
$545$	0.897003	−	0.614423i	0.0384234	−	0.0263190i
$546$	−18.7412	−	36.6142i	−0.802051	−	1.56694i
$547$	29.5058	+	35.1637i	1.26158	+	1.50349i	0.778108	+	0.628131i	$0.216180\pi$
$547$	29.5058	+	35.1637i	1.26158	+	1.50349i	0.483471	+	0.875360i	$0.339376\pi$
$548$	−28.1253	−	48.7145i	−1.20145	−	2.08098i
$549$	0.0572456		0.000639456i	0.00244318		2.72913e-5i
$550$	−30.7874	+	50.8766i	−1.31278	+	2.16938i
$551$	7.56438	+	42.8997i	0.322253	+	1.82759i
$552$	1.93041	+	7.36877i	0.0821639	+	0.313636i
$553$	−5.18871	+	16.3826i	−0.220646	+	0.696660i
$554$	−5.77397	−	15.8639i	−0.245313	−	0.673991i
$555$	−17.7053	+	9.85067i	−0.751550	+	0.418137i
$556$	30.0698	−	5.30212i	1.27524	−	0.224860i
$557$	9.08471	−	15.7352i	0.384932	−	0.666721i	−0.606828	−	0.794833i	$-0.707558\pi$
$557$	9.08471	−	15.7352i	0.384932	−	0.666721i	0.991760	+	0.128112i	$0.0408917\pi$
$558$	2.40011	−	12.7756i	0.101605	−	0.540832i
$559$	33.7216	−	19.4692i	1.42627	−	0.823458i
$560$	−7.45868	+	7.95271i	−0.315187	+	0.336063i
$561$	33.8716	−	2.77285i	1.43006	−	0.117070i
$562$	27.5560	+	4.85887i	1.16238	+	0.204959i
$563$	−21.4318	+	25.5414i	−0.903242	+	1.07644i	0.0934866	+	0.995621i	$0.470199\pi$
$563$	−21.4318	+	25.5414i	−0.903242	+	1.07644i	−0.996729	+	0.0808213i	$0.974246\pi$
$564$	5.59596	+	12.1777i	0.235632	+	0.512773i
$565$	−0.220680	−	0.486259i	−0.00928410	−	0.0204571i
$566$	62.3150			2.61930
$567$	−23.3626	+	4.60304i	−0.981138	+	0.193309i
$568$		−	11.5449i		−	0.484415i
$569$	−2.12884	+	5.84894i	−0.0892456	+	0.245200i	−0.976283	−	0.216497i	$-0.930537\pi$
$569$	−2.12884	+	5.84894i	−0.0892456	+	0.245200i	0.887038	+	0.461697i	$0.152759\pi$
$570$	16.5627	−	43.3510i	0.693736	−	1.81577i
$571$	36.0528	+	30.2519i	1.50876	+	1.26600i	0.866117	+	0.499842i	$0.166608\pi$
$571$	36.0528	+	30.2519i	1.50876	+	1.26600i	0.642648	+	0.766162i	$0.277836\pi$
$572$	61.1128	+	10.7758i	2.55526	+	0.450560i
$573$	−1.79253	−	21.8965i	−0.0748841	−	0.914741i
$574$	−0.842326	−	19.8819i	−0.0351580	−	0.829856i
$575$	11.3477	−	6.24368i	0.473232	−	0.260379i
$576$	−12.4700	−	35.4895i	−0.519583	−	1.47873i
$577$	−11.0612	+	19.1585i	−0.460483	+	0.797580i	−0.998985	−	0.0450445i	$-0.985657\pi$
$577$	−11.0612	+	19.1585i	−0.460483	+	0.797580i	0.538502	+	0.842624i	$0.318990\pi$
$578$	1.51767	+	8.60713i	0.0631267	+	0.358009i
$579$	10.9128	−	39.8358i	0.453520	−	1.65552i
$580$	−21.3094	+	44.4964i	−0.884826	+	1.84761i
$581$	13.9417	+	4.41562i	0.578400	+	0.183191i
$582$	−16.3121	−	62.2664i	−0.676157	−	2.58103i
$583$	18.5166	−	3.26497i	0.766878	−	0.135221i
$584$	−7.15443	+	12.3918i	−0.296053	+	0.512778i
$585$	−6.55742	−	26.7572i	−0.271116	−	1.10628i
$586$	−4.93664	+	2.85017i	−0.203931	+	0.117740i
$587$	12.7005	+	15.1358i	0.524204	+	0.624722i	0.961569	−	0.274562i	$-0.0885329\pi$
$587$	12.7005	+	15.1358i	0.524204	+	0.624722i	−0.437366	+	0.899284i	$0.644088\pi$
$588$	33.1066	+	6.11687i	1.36529	+	0.252256i
$589$	−1.88740	+	10.7040i	−0.0777689	+	0.441049i
$590$	−1.92707	−	24.9868i	−0.0793361	−	1.02869i
$591$	10.6167	+	7.52259i	0.436712	+	0.309438i
$592$	3.29751	−	9.05984i	0.135527	−	0.372357i
$593$			28.5050i			1.17056i	0.810831	+	0.585281i	$0.199016\pi$
$593$			28.5050i			1.17056i	−0.810831	+	0.585281i	$0.800984\pi$
$594$	27.0524	−	55.5640i	1.10997	−	2.27982i
$595$	2.53909	+	21.1800i	0.104092	+	0.868295i
$596$	−9.89760	+	27.1934i	−0.405421	+	1.11389i
$597$	−28.3014	−	2.63540i	−1.15830	−	0.107860i
$598$	−17.8111	−	14.9452i	−0.728348	−	0.611157i
$599$	36.4512	+	6.42733i	1.48936	+	0.262614i	0.858310	−	0.513132i	$-0.171515\pi$
$599$	36.4512	+	6.42733i	1.48936	+	0.262614i	0.631046	+	0.775746i	$0.282626\pi$
$600$	12.2608	−	8.11529i	0.500544	−	0.331306i
$601$	−19.6075	−	23.3673i	−0.799807	−	0.953173i	0.199837	−	0.979829i	$-0.435959\pi$
$601$	−19.6075	−	23.3673i	−0.799807	−	0.953173i	−0.999645	+	0.0266557i	$0.991514\pi$
$602$	−7.22660	+	54.3487i	−0.294534	+	2.21509i
$603$	11.8873	+	4.47760i	0.484087	+	0.182342i
$604$	4.10639	−	7.11248i	0.167087	−	0.289403i
$605$	24.2209	−	33.8440i	0.984718	−	1.37595i
$606$	−25.9730	+	25.6845i	−1.05508	+	1.04336i
$607$	3.88643	−	1.41454i	0.157745	−	0.0574146i	−0.261941	−	0.965084i	$-0.584362\pi$
$607$	3.88643	−	1.41454i	0.157745	−	0.0574146i	0.419686	+	0.907669i	$0.362140\pi$
$608$	13.9198	+	38.2443i	0.564522	+	1.55101i
$609$	−36.1320	+	4.50431i	−1.46414	+	0.182524i
$610$	−0.0758405	−	0.0542762i	−0.00307069	−	0.00219758i
$611$	−9.91038	−	5.72176i	−0.400931	−	0.231478i
$612$	−28.1091	−	10.5879i	−1.13624	−	0.427991i
$613$	−11.1543	+	6.43993i	−0.450517	+	0.260106i	−0.708049	−	0.706164i	$-0.750424\pi$
$613$	−11.1543	+	6.43993i	−0.450517	+	0.260106i	0.257531	+	0.966270i	$0.417091\pi$
$614$	−12.2970	+	10.3184i	−0.496267	+	0.416417i
$615$	2.52259	−	13.0874i	0.101720	−	0.527737i
$616$	−18.0431	+	16.4906i	−0.726975	+	0.664424i
$617$	−20.1686	−	16.9234i	−0.811956	−	0.681312i	0.139118	−	0.990276i	$-0.455573\pi$
$617$	−20.1686	−	16.9234i	−0.811956	−	0.681312i	−0.951074	+	0.308964i	$0.900018\pi$
$618$	−3.75831	+	40.3602i	−0.151181	+	1.62352i
$619$	−11.0456	+	30.3476i	−0.443960	+	1.21977i	0.492906	+	0.870083i	$0.335935\pi$
$619$	−11.0456	+	30.3476i	−0.443960	+	1.21977i	−0.936866	+	0.349689i	$0.886287\pi$
$620$	−8.79352	+	8.61429i	−0.353156	+	0.345958i
$621$	−11.1537	+	7.53459i	−0.447582	+	0.302353i
$622$	23.9491			0.960269
$623$	−24.7812	+	15.7424i	−0.992839	+	0.630706i
$624$	10.6963	+	7.57899i	0.428194	+	0.303402i
$625$	−18.4733	−	16.8445i	−0.738931	−	0.673781i
$626$	10.6743	−	60.5369i	0.426631	−	2.41954i
$627$	−22.0994	+	46.7093i	−0.882563	+	1.86539i
$628$	−37.1991	+	31.2138i	−1.48441	+	1.24557i
$629$	−9.43146	−	16.3358i	−0.376057	−	0.651350i
$630$	35.4906	+	15.6561i	1.41398	+	0.623754i
$631$	−14.1012	+	24.4240i	−0.561361	+	0.972305i	0.436017	+	0.899938i	$0.356389\pi$
$631$	−14.1012	+	24.4240i	−0.561361	+	0.972305i	−0.997378	+	0.0723671i	$0.976945\pi$
$632$	1.91489	+	10.8599i	0.0761703	+	0.431983i
$633$	3.64425	+	13.9108i	0.144846	+	0.552906i
$634$	25.1994	−	9.17182i	1.00080	−	0.364260i
$635$	−0.563153	+	1.17592i	−0.0223480	+	0.0466651i
$636$	−16.0275	−	4.39065i	−0.635534	−	0.174101i
$637$	−26.0853	+	12.0818i	−1.03354	+	0.478698i
$638$	47.2504	−	81.8401i	1.87066	−	3.24008i
$639$	19.2465	−	6.76267i	0.761380	−	0.267527i
$640$	−7.54649	+	27.0469i	−0.298301	+	1.06912i
$641$	5.08162	+	6.05604i	0.200712	+	0.239199i	0.857007	−	0.515305i	$-0.172322\pi$
$641$	5.08162	+	6.05604i	0.200712	+	0.239199i	−0.656294	+	0.754505i	$0.727877\pi$
$642$	75.5604	−	6.18565i	2.98213	−	0.244128i
$643$	4.19477	−	23.7897i	0.165425	−	0.938175i	−0.783199	−	0.621771i	$-0.786413\pi$
$643$	4.19477	−	23.7897i	0.165425	−	0.938175i	0.948625	−	0.316404i	$-0.102475\pi$
$644$	18.5852	−	4.09505i	0.732359	−	0.161367i
$645$	−13.1059	+	34.3033i	−0.516046	+	1.35069i
$646$	40.5991	+	14.7769i	1.59735	+	0.581388i
$647$		−	19.7710i		−	0.777278i	−0.921390	−	0.388639i	$-0.872945\pi$
$647$		−	19.7710i		−	0.777278i	0.921390	−	0.388639i	$-0.127055\pi$
$648$	−11.9217	+	9.55789i	−0.468327	+	0.375469i
$649$			27.9049i			1.09536i
$650$	−16.2144	+	41.8471i	−0.635982	+	1.64138i
$651$	−8.85605	−	2.02733i	−0.347096	−	0.0794575i
$652$	6.00548	−	7.15705i	0.235193	−	0.280292i
$653$	4.65870	−	26.4208i	0.182309	−	1.03392i	−0.747056	−	0.664762i	$-0.768533\pi$
$653$	4.65870	−	26.4208i	0.182309	−	1.03392i	0.929365	−	0.369163i	$-0.120356\pi$
$654$	1.83454	−	0.150182i	0.0717361	−	0.00587258i
$655$	6.77327	+	0.662919i	0.264654	+	0.0259024i
$656$	3.17115	+	5.49258i	0.123812	+	0.214449i
$657$	−24.8492	−	4.66836i	−0.969461	−	0.182130i
$658$	14.8945	−	6.14695i	0.580647	−	0.239633i
$659$	−9.09064	+	1.60293i	−0.354121	+	0.0624411i	−0.347879	−	0.937539i	$-0.613098\pi$
$659$	−9.09064	+	1.60293i	−0.354121	+	0.0624411i	−0.00624204	+	0.999981i	$0.501987\pi$
$660$	−51.1406	+	28.4530i	−1.99065	+	1.10753i
$661$	14.0973	+	38.7321i	0.548323	+	1.50651i	0.835974	+	0.548770i	$0.184904\pi$
$661$	14.0973	+	38.7321i	0.548323	+	1.50651i	−0.287650	+	0.957735i	$0.592874\pi$
$662$	38.5309	−	14.0241i	1.49755	−	0.545062i
$663$	24.8106	−	6.49969i	0.963565	−	0.252427i
$664$	9.24183	−	1.62958i	0.358653	−	0.0632401i
$665$	−29.8196	−	12.7585i	−1.15636	−	0.494753i
$666$	−34.2990	−	0.383134i	−1.32906	−	0.0148461i
$667$	−17.8250	+	10.2912i	−0.690185	+	0.398479i
$668$	−10.3475	−	12.3317i	−0.400357	−	0.477126i
$669$	0.873499	−	1.84623i	0.0337714	−	0.0713795i
$670$	−11.6939	−	17.0721i	−0.451776	−	0.659552i
$671$	0.0795494	+	0.0667499i	0.00307097	+	0.00257685i
$672$	−32.5139	+	10.0063i	−1.25425	+	0.386001i
$673$	6.70207	−	18.4138i	0.258346	−	0.709800i	−0.740924	−	0.671589i	$-0.765612\pi$
$673$	6.70207	−	18.4138i	0.258346	−	0.709800i	0.999270	−	0.0382106i	$-0.0121658\pi$
$674$			29.7467i			1.14580i
$675$	20.7110	+	15.6862i	0.797165	+	0.603761i
$676$	10.7339			0.412841
$677$	−0.436340	+	1.19883i	−0.0167699	+	0.0460749i	−0.947795	−	0.318880i	$-0.896693\pi$
$677$	−0.436340	+	1.19883i	−0.0167699	+	0.0460749i	0.931025	+	0.364955i	$0.118916\pi$
$678$	0.0838193	−	0.900129i	0.00321906	−	0.0345692i
$679$	−43.9332	+	9.68021i	−1.68600	+	0.371492i
$680$	7.73556	+	11.2932i	0.296645	+	0.433076i
$681$	−14.5412	+	10.0613i	−0.557218	+	0.385549i
$682$	18.0626	−	15.1563i	0.691651	−	0.580364i
$683$	−22.0817	−	38.2467i	−0.844934	−	1.46347i	−0.885678	−	0.464299i	$-0.846306\pi$
$683$	−22.0817	−	38.2467i	−0.844934	−	1.46347i	0.0407443	−	0.999170i	$-0.487027\pi$
$684$	35.3116	−	28.9640i	1.35017	−	1.10747i
$685$	−43.8717	+	11.2726i	−1.67625	+	0.430703i
$686$	8.91411	−	39.4840i	0.340342	−	1.50750i
$687$	−15.7123	−	15.8888i	−0.599461	−	0.606195i
$688$	−5.97647	−	16.4202i	−0.227851	−	0.626015i
$689$	13.3340	−	4.85318i	0.507985	−	0.184891i
$690$	21.9243	+	0.348198i	0.834645	+	0.0132557i
$691$	−36.3453	+	6.40866i	−1.38264	+	0.243797i	−0.814991	−	0.579473i	$-0.803258\pi$
$691$	−36.3453	+	6.40866i	−1.38264	+	0.243797i	−0.567650	+	0.823270i	$0.692147\pi$
$692$	44.7542	+	25.8389i	1.70130	+	0.982246i
$693$	−38.0604	−	20.4198i	−1.44580	−	0.775685i
$694$	15.3848	+	26.6473i	0.584000	+	1.01152i
$695$	2.39502	−	24.4708i	0.0908484	−	0.928231i
$696$	−19.2144	+	13.2948i	−0.728319	+	0.503936i
$697$	12.2200	+	2.15472i	0.462867	+	0.0816159i
$698$	−23.0351	+	27.4522i	−0.871892	+	1.03908i
$699$	3.06662	−	32.9322i	0.115990	−	1.24561i
$700$	−19.0544	−	31.4053i	−0.720187	−	1.18701i
$701$		−	24.9732i		−	0.943223i	−0.881806	−	0.471612i	$-0.843672\pi$
$701$		−	24.9732i		−	0.943223i	0.881806	−	0.471612i	$-0.156328\pi$
$702$	12.8242	−	44.8414i	0.484018	−	1.69243i
$703$	28.6807			1.08171
$704$	23.3370	−	64.1178i	0.879545	−	2.41653i
$705$	10.6565	−	1.70502i	0.401349	−	0.0642146i
$706$	−15.7823	+	18.8087i	−0.593976	+	0.707873i
$707$	17.2232	+	18.8447i	0.647746	+	0.708728i
$708$	10.5478	−	22.2940i	0.396412	−	0.837860i
$709$	−5.75776	+	4.83134i	−0.216237	+	0.181445i	−0.744472	−	0.667654i	$-0.767299\pi$
$709$	−5.75776	+	4.83134i	−0.216237	+	0.181445i	0.528234	+	0.849099i	$0.322854\pi$
$710$	−32.0099	−	8.93124i	−1.20131	−	0.335184i
$711$	−16.9828	+	9.55370i	−0.636905	+	0.358292i
$712$	−9.41975	+	16.3155i	−0.353020	+	0.611449i
$713$	−5.05754	+	0.891782i	−0.189407	+	0.0333975i
$714$	−14.0491	+	33.2686i	−0.525776	+	1.24505i
$715$	21.5839	−	45.0695i	0.807193	−	1.68550i
$716$	8.97943	+	24.6708i	0.335577	+	0.921991i
$717$	−12.4255	+	45.3577i	−0.464038	+	1.69392i
$718$	−37.3167	+	6.57993i	−1.39265	+	0.245561i
$719$	8.33550	−	14.4375i	0.310862	−	0.538428i	−0.667688	−	0.744442i	$-0.732716\pi$
$719$	8.33550	−	14.4375i	0.310862	−	0.538428i	0.978549	+	0.206014i	$0.0660491\pi$
$720$	−12.3362	+	0.812908i	−0.459743	+	0.0302953i
$721$	28.0829	+	3.73410i	1.04586	+	0.139065i
$722$	−18.5120	+	15.5334i	−0.688946	+	0.578094i
$723$	1.39614	+	17.0544i	0.0519228	+	0.634260i
$724$	−16.5467	−	2.91763i	−0.614953	−	0.108433i
$725$	29.9015	+	26.1581i	1.11051	+	0.971489i
$726$	64.0213	−	29.4195i	2.37605	−	1.09186i
$727$	2.15649	+	0.784898i	0.0799797	+	0.0291102i	0.381700	−	0.924286i	$-0.375339\pi$
$727$	2.15649	+	0.784898i	0.0799797	+	0.0291102i	−0.301720	+	0.953396i	$0.597561\pi$
$728$	−11.2489	+	14.6206i	−0.416910	+	0.541877i
$729$	−22.9173	−	14.2758i	−0.848787	−	0.528734i
$730$	28.8234	+	29.4231i	1.06680	+	1.08900i
$731$	−32.1258	−	11.6928i	−1.18821	−	0.432475i
$732$	−0.0383233	−	0.0833974i	−0.00141647	−	0.00308246i
$733$	5.16521	+	4.33413i	0.190781	+	0.160085i	0.733175	−	0.680040i	$-0.238037\pi$
$733$	5.16521	+	4.33413i	0.190781	+	0.160085i	−0.542394	+	0.840124i	$0.682482\pi$
$734$	−0.237618	+	1.34760i	−0.00877066	+	0.0497409i
$735$	11.9093	−	24.3551i	0.439280	−	0.898350i
$736$	−14.7309	+	12.3607i	−0.542989	+	0.455622i
$737$	11.5206	+	19.9543i	0.424368	+	0.735027i
$738$	14.6962	−	17.1221i	0.540973	−	0.630274i
$739$	6.65617	−	11.5288i	0.244851	−	0.424094i	−0.717239	−	0.696828i	$-0.754594\pi$
$739$	6.65617	−	11.5288i	0.244851	−	0.424094i	0.962090	+	0.272733i	$0.0879276\pi$
$740$	26.4149	+	18.9041i	0.971030	+	0.694930i
$741$	−10.3034	+	37.6114i	−0.378505	+	1.38169i
$742$	−6.03267	+	19.0473i	−0.221466	+	0.699250i
$743$	−42.7507	+	15.5600i	−1.56837	+	0.570840i	−0.972635	−	0.232340i	$-0.925362\pi$
$743$	−42.7507	+	15.5600i	−1.56837	+	0.570840i	−0.595736	+	0.803180i	$0.703140\pi$
$744$	−5.63962	+	1.47742i	−0.206759	+	0.0541650i
$745$	18.9503	+	13.5620i	0.694286	+	0.496875i
$746$	−11.1145	−	6.41696i	−0.406931	−	0.234942i
$747$	8.13026	+	14.4525i	0.297471	+	0.528788i
$748$	−27.2421	−	47.1848i	−0.996071	−	1.72525i
$749$	−2.24283	−	52.9389i	−0.0819511	−	1.93434i
$750$	−13.0158	−	40.2727i	−0.475268	−	1.47055i
$751$	4.14701	−	23.5188i	0.151326	−	0.858215i	−0.810741	−	0.585404i	$-0.800936\pi$
$751$	4.14701	−	23.5188i	0.151326	−	0.858215i	0.962068	−	0.272810i	$-0.0879531\pi$
$752$	−3.30098	+	3.93395i	−0.120374	+	0.143457i
$753$	10.5448	+	7.47167i	0.384275	+	0.272283i
$754$	24.3923	−	67.0172i	0.888314	−	2.44062i
$755$	−4.62804	−	4.72433i	−0.168432	−	0.171936i
$756$	22.6890	+	30.7005i	0.825191	+	1.11657i
$757$			10.1300i			0.368181i	0.982909	+	0.184090i	$0.0589339\pi$
$757$			10.1300i			0.368181i	−0.982909	+	0.184090i	$0.941066\pi$
$758$	66.8465	+	24.3301i	2.42798	+	0.883711i
$759$	−24.3101	−	2.26374i	−0.882402	−	0.0821686i
$760$	−20.7515	+	1.60043i	−0.752738	+	0.0580536i
$761$	−6.60328	+	37.4491i	−0.239369	+	1.35753i	0.593846	+	0.804579i	$0.297609\pi$
$761$	−6.60328	+	37.4491i	−0.239369	+	1.35753i	−0.833215	+	0.552949i	$0.813502\pi$
$762$	−1.81515	+	1.25594i	−0.0657561	+	0.0454977i
$763$	−0.0544538	−	1.28531i	−0.00197136	−	0.0465313i
$764$	−30.5029	+	17.6109i	−1.10356	+	0.637139i
$765$	−14.2956	+	19.5112i	−0.516860	+	0.705427i
$766$	64.5048	+	37.2418i	2.33065	+	1.34560i
$767$	3.65692	+	20.7394i	0.132044	+	0.748858i
$768$	−2.91686	+	2.88446i	−0.105253	+	0.104084i
$769$	9.03740	+	24.8300i	0.325897	+	0.895394i	0.989138	+	0.146989i	$0.0469581\pi$
$769$	9.03740	+	24.8300i	0.325897	+	0.895394i	−0.663241	+	0.748406i	$0.730820\pi$
$770$	31.7642	+	62.7841i	1.14470	+	2.26258i
$771$	34.9785	+	35.3714i	1.25972	+	1.27387i
$772$	−65.2113	+	11.4985i	−2.34701	+	0.413841i
$773$	13.5089	+	7.79936i	0.485881	+	0.280524i	0.722864	−	0.690990i	$-0.242825\pi$
$773$	13.5089	+	7.79936i	0.485881	+	0.280524i	−0.236983	+	0.971514i	$0.576159\pi$
$774$	−48.0669	+	39.4264i	−1.72773	+	1.41715i
$775$	4.77854	+	8.68487i	0.171650	+	0.311970i
$776$	−22.1143	+	18.5561i	−0.793858	+	0.666126i
$777$	−1.21039	+	23.9428i	−0.0434224	+	0.858942i
$778$	−52.2964	−	9.22127i	−1.87492	−	0.330599i
$779$	−12.1275	+	14.4529i	−0.434511	+	0.517830i
$780$	−34.2799	+	27.8487i	−1.22742	+	0.997145i
$781$	34.7721	+	12.6560i	1.24424	+	0.452867i
$782$			20.4139i			0.729999i
$783$	−33.4188	−	24.2446i	−1.19429	−	0.866430i
$784$	3.30674	+	12.4697i	0.118098	+	0.445347i
$785$	16.1602	+	35.6083i	0.576783	+	1.27091i
$786$	9.40090	+	6.66113i	0.335319	+	0.237595i
$787$	8.85984	+	7.43429i	0.315819	+	0.265004i	0.786892	−	0.617090i	$-0.211689\pi$
$787$	8.85984	+	7.43429i	0.315819	+	0.265004i	−0.471073	+	0.882094i	$0.656133\pi$
$788$	3.62233	−	20.5432i	0.129040	−	0.731823i
$789$	20.8040	−	43.9714i	0.740641	−	1.56542i
$790$	31.5919	+	3.09199i	1.12399	+	0.110008i
$791$	−0.626316	−	0.0832795i	−0.0222692	−	0.00296108i
$792$	−27.7147	−	0.309585i	−0.984800	−	0.0110006i
$793$	0.0678701	+	0.0391848i	0.00241014	+	0.00139149i
$794$	−1.22249	−	6.93306i	−0.0433844	−	0.246045i
$795$	−6.87417	+	11.4814i	−0.243802	+	0.407204i
$796$	15.5854	+	42.8206i	0.552411	+	1.51774i
$797$	−1.36927	−	3.76205i	−0.0485022	−	0.133259i	0.913076	−	0.407789i	$-0.133700\pi$
$797$	−1.36927	−	3.76205i	−0.0485022	−	0.133259i	−0.961579	+	0.274530i	$0.911478\pi$
$798$	−33.1266	−	43.7918i	−1.17267	−	1.55021i
$799$	1.74470	+	9.89467i	0.0617230	+	0.350048i
$800$	31.7558	+	19.2167i	1.12274	+	0.679413i
$801$	−32.7173	−	6.14651i	−1.15601	−	0.217176i
$802$	68.6345	−	39.6261i	2.42357	−	1.39925i
$803$	−29.4799	−	35.1328i	−1.04032	−	1.23981i
$804$	−1.66157	−	20.2968i	−0.0585990	−	0.715813i
$805$	0.845831	−	15.3016i	0.0298116	−	0.539312i
$806$	11.4382	−	13.6315i	0.402894	−	0.480150i
$807$	42.7500	−	19.6447i	1.50487	−	0.691528i
$808$	15.3944	+	5.60311i	0.541573	+	0.197117i
$809$			7.14232i			0.251111i	0.992087	+	0.125555i	$0.0400713\pi$
$809$			7.14232i			0.251111i	−0.992087	+	0.125555i	$0.959929\pi$
$810$	17.2779	+	40.4485i	0.607083	+	1.42122i
$811$			9.40889i			0.330391i	0.986261	+	0.165195i	$0.0528255\pi$
$811$			9.40889i			0.330391i	−0.986261	+	0.165195i	$0.947175\pi$
$812$	31.3012	+	49.2734i	1.09846	+	1.72916i
$813$	15.0792	+	32.8148i	0.528852	+	1.15086i
$814$	−47.6625	−	39.9936i	−1.67057	−	1.40177i
$815$	−4.25162	−	6.20698i	−0.148928	−	0.217421i
$816$	−0.939091	−	11.4714i	−0.0328747	−	0.401579i
$817$	39.8201	−	33.4131i	1.39313	−	1.16898i
$818$	11.9740	−	6.91322i	0.418663	−	0.241715i
$819$	−30.9632	−	10.1886i	−1.08194	−	0.356018i
$820$	−20.6956	+	5.31762i	−0.722722	+	0.185699i
$821$	−28.1224	+	4.95875i	−0.981480	+	0.173061i	−0.641293	−	0.767296i	$-0.721602\pi$
$821$	−28.1224	+	4.95875i	−0.981480	+	0.173061i	−0.340187	+	0.940358i	$0.610491\pi$
$822$	−73.9602	−	20.2610i	−2.57966	−	0.706682i
$823$	15.4287	+	42.3899i	0.537809	+	1.47762i	0.849579	+	0.527461i	$0.176856\pi$
$823$	15.4287	+	42.3899i	0.537809	+	1.47762i	−0.311770	+	0.950158i	$0.600922\pi$
$824$	17.0831	−	6.21773i	0.595117	−	0.216605i
$825$	11.0017	+	45.8244i	0.383029	+	1.59540i
$826$	−26.2845	−	13.7260i	−0.914554	−	0.477590i
$827$	−16.1570	+	27.9848i	−0.561835	+	0.973127i	0.435501	+	0.900188i	$0.356571\pi$
$827$	−16.1570	+	27.9848i	−0.561835	+	0.973127i	−0.997336	+	0.0729389i	$0.976762\pi$
$828$	18.5664	+	10.9976i	0.645226	+	0.382194i
$829$	−12.8352	+	7.41040i	−0.445785	+	0.257374i	−0.706048	−	0.708164i	$-0.749524\pi$
$829$	−12.8352	+	7.41040i	−0.445785	+	0.257374i	0.260264	+	0.965538i	$0.416191\pi$
$830$	2.63130	−	26.8849i	0.0913337	−	0.933189i
$831$	−12.0935	−	5.72173i	−0.419518	−	0.198484i
$832$	8.94186	−	50.7118i	0.310003	−	1.75812i
$833$	22.8475	+	10.7259i	0.791620	+	0.371632i
$834$	24.0657	−	33.9640i	0.833326	−	1.17608i
$835$	−11.8043	+	5.35718i	−0.408504	+	0.185393i
$836$	82.8423			2.86516
$837$	−5.76653	−	8.53636i	−0.199320	−	0.295060i
$838$	−59.4521			−2.05374
$839$	1.88911	+	0.687579i	0.0652193	+	0.0237379i	0.374424	−	0.927258i	$-0.377841\pi$
$839$	1.88911	+	0.687579i	0.0652193	+	0.0237379i	−0.309205	+	0.950996i	$0.600063\pi$
$840$	−0.460283	−	17.3910i	−0.0158813	−	0.600046i
$841$	−26.1481	−	21.9409i	−0.901659	−	0.756582i
$842$	−12.2760	+	69.6209i	−0.423060	+	2.39929i
$843$	18.2352	−	12.6172i	0.628052	−	0.434560i
$844$	17.6606	−	14.8190i	0.607903	−	0.510092i
$845$	2.32297	−	8.32563i	0.0799127	−	0.286410i
$846$	17.0978	+	6.44025i	0.587833	+	0.221420i
$847$	−18.7857	−	45.5191i	−0.645486	−	1.56405i
$848$	−1.10576	−	6.27107i	−0.0379719	−	0.215349i
$849$	35.1141	−	34.7241i	1.20511	−	1.19173i
$850$	37.2963	−	12.7114i	1.27925	−	0.435997i
$851$	4.63486	+	12.7342i	0.158881	+	0.436522i
$852$	−22.9965	−	23.2548i	−0.787848	−	0.796697i
$853$	8.24789	+	46.7761i	0.282403	+	1.60158i	0.714419	+	0.699718i	$0.246691\pi$
$853$	8.24789	+	46.7761i	0.282403	+	1.60158i	−0.432016	+	0.901866i	$0.642198\pi$
$854$	−0.102003	+	0.0420967i	−0.00349047	+	0.00144052i
$855$	−14.8237	−	33.6573i	−0.506960	−	1.15106i
$856$	−17.0007	−	29.4461i	−0.581072	−	1.00645i
$857$	2.16363	+	2.57852i	0.0739082	+	0.0880804i	0.801732	−	0.597684i	$-0.203912\pi$
$857$	2.16363	+	2.57852i	0.0739082	+	0.0880804i	−0.727823	+	0.685765i	$0.759468\pi$
$858$	69.5693	−	48.1361i	2.37506	−	1.64334i
$859$	−16.7213	−	2.94842i	−0.570524	−	0.100599i	−0.119058	−	0.992887i	$-0.537987\pi$
$859$	−16.7213	−	2.94842i	−0.570524	−	0.100599i	−0.451465	+	0.892289i	$0.649099\pi$
$860$	58.6976	−	4.52695i	2.00157	−	0.154368i
$861$	−11.5535	−	10.7340i	−0.393744	−	0.365813i
$862$	−4.44498	+	12.2125i	−0.151397	+	0.415959i
$863$	56.2160			1.91362			0.956808	−	0.290720i	$-0.0938949\pi$
$863$	56.2160			1.91362			0.956808	+	0.290720i	$0.0938949\pi$
$864$	−34.6816	−	16.8854i	−1.17989	−	0.574453i
$865$	29.7272	−	29.1213i	1.01075	−	0.990153i
$866$	−35.4883	−	12.9167i	−1.20594	−	0.438926i
$867$	5.65138	+	4.00436i	0.191931	+	0.135995i
$868$	3.13411	+	14.2240i	0.106379	+	0.482794i
$869$	−34.8080	−	6.13759i	−1.18078	−	0.208203i
$870$	21.9972	+	63.5595i	0.745773	+	2.15487i
$871$	11.1774	+	13.3207i	0.378730	+	0.451353i
$872$	−0.412761	−	0.714924i	−0.0139779	−	0.0242104i
$873$	−43.8887	−	25.9971i	−1.48541	−	0.879868i
$874$	−26.8805	−	15.5195i	−0.909247	−	0.524954i
$875$	−28.4829	+	7.98275i	−0.962898	+	0.269866i
$876$	10.2724	+	39.2118i	0.347072	+	1.32484i
$877$	9.34900	+	25.6862i	0.315693	+	0.867360i	0.991480	+	0.130263i	$0.0415820\pi$
$877$	9.34900	+	25.6862i	0.315693	+	0.867360i	−0.675786	+	0.737098i	$0.736196\pi$
$878$	−16.5041	−	45.3447i	−0.556987	−	1.53031i
$879$	−1.19355	+	4.35692i	−0.0402575	+	0.146955i
$880$	−18.2362	−	13.0510i	−0.614743	−	0.439949i
$881$	−4.09845	+	7.09873i	−0.138080	+	0.239162i	−0.926770	−	0.375629i	$-0.877427\pi$
$881$	−4.09845	+	7.09873i	−0.138080	+	0.239162i	0.788690	+	0.614792i	$0.210760\pi$
$882$	37.9555	−	25.8061i	1.27803	−	0.868936i
$883$	−30.0105	+	17.3266i	−1.00994	+	0.583086i	−0.911173	−	0.412025i	$-0.864822\pi$
$883$	−30.0105	+	17.3266i	−1.00994	+	0.583086i	−0.0987624	+	0.995111i	$0.531488\pi$
$884$	−26.4304	−	31.4985i	−0.888950	−	1.05941i
$885$	−15.0094	−	13.0061i	−0.504536	−	0.437195i
$886$	−4.58129	+	25.9818i	−0.153912	+	0.872876i
$887$	−10.0935	+	12.0290i	−0.338906	+	0.403893i	−0.908400	−	0.418103i	$-0.862695\pi$
$887$	−10.0935	+	12.0290i	−0.338906	+	0.403893i	0.569493	+	0.821996i	$0.307139\pi$
$888$	6.42347	+	13.9785i	0.215557	+	0.469086i
$889$	0.827208	+	1.30217i	0.0277437	+	0.0436733i
$890$	37.9498	+	38.7393i	1.27208	+	1.29855i
$891$	−15.7183	−	46.3845i	−0.526584	−	1.55394i
$892$	−3.27443			−0.109636
$893$	−14.3555	−	5.22496i	−0.480387	−	0.174847i
$894$	16.4729	+	35.8476i	0.550937	+	1.19892i
$895$	21.0789	−	1.62568i	0.704591	−	0.0543404i
$896$	22.4146	+	24.5248i	0.748820	+	0.819316i
$897$	−18.3644	+	1.50338i	−0.613170	+	0.0501963i
$898$	5.58857	+	6.66020i	0.186493	+	0.222254i
$899$	−7.87631	−	13.6422i	−0.262690	−	0.454992i
$900$	8.53175	−	40.7689i	0.284392	−	1.35896i
$901$	−10.7894	−	6.22924i	−0.359445	−	0.207526i
$902$	40.3075	−	7.10730i	1.34209	−	0.236647i
$903$	26.2128	+	34.6521i	0.872308	+	1.15315i
$904$	−0.380993	+	0.138670i	−0.0126717	+	0.00461210i
$905$	−5.84398	+	12.2029i	−0.194261	+	0.405637i
$906$	−2.83737	−	10.8308i	−0.0942652	−	0.359829i
$907$	19.5972	−	3.45552i	0.650715	−	0.114739i	0.161460	−	0.986879i	$-0.448380\pi$
$907$	19.5972	−	3.45552i	0.650715	−	0.114739i	0.489255	+	0.872141i	$0.337269\pi$
$908$	24.5506	+	14.1743i	0.814740	+	0.470390i
$909$	−0.323339	+	28.9461i	−0.0107245	+	0.960081i
$910$	31.8355	+	42.4996i	1.05534	+	1.40885i
$911$	21.5030	+	25.6263i	0.712426	+	0.849037i	0.993872	−	0.110541i	$-0.0352582\pi$
$911$	21.5030	+	25.6263i	0.712426	+	0.849037i	−0.281445	+	0.959577i	$0.590814\pi$
$912$	15.8192	+	7.48446i	0.523826	+	0.247835i
$913$	−5.22312	+	29.6218i	−0.172860	+	0.980339i
$914$	−12.9977	+	15.4900i	−0.429925	+	0.512365i
$915$	−0.0729801	+	0.0116766i	−0.00241265	+	0.000386017i
$916$	−12.2527	+	33.6639i	−0.404839	+	1.11229i
$917$	4.91033	−	6.38217i	0.162153	−	0.210758i
$918$	−37.3969	+	16.6815i	−1.23428	+	0.550571i
$919$	6.85829			0.226234			0.113117	−	0.993582i	$-0.463916\pi$
$919$	6.85829			0.226234			0.113117	+	0.993582i	$0.463916\pi$
$920$	−4.06408	−	8.95501i	−0.133989	−	0.295238i
$921$	−1.17951	+	12.6667i	−0.0388662	+	0.417381i
$922$	−7.94533	−	6.66693i	−0.261666	−	0.219564i
$923$	27.5018	+	4.84931i	0.905234	+	0.159617i
$924$	−3.49612	+	69.1570i	−0.115014	+	2.27510i
$925$	20.3794	−	16.3973i	0.670070	−	0.539140i
$926$	−14.4255	+	8.32856i	−0.474051	+	0.273693i
$927$	20.3723	+	24.8369i	0.669114	+	0.815752i
$928$	−51.0824	−	29.4925i	−1.67686	−	0.968138i
$929$	−2.15215	−	12.2055i	−0.0706099	−	0.400449i	−0.999544	−	0.0302030i	$-0.990385\pi$
$929$	−2.15215	−	12.2055i	−0.0706099	−	0.400449i	0.928934	−	0.370246i	$-0.120726\pi$
$930$	−0.266490	+	16.7796i	−0.00873855	+	0.550224i
$931$	−31.4933	+	21.9308i	−1.03215	+	0.718752i
$932$	−49.8272	+	18.1356i	−1.63214	+	0.594051i
$933$	13.4951	−	13.3452i	0.441811	−	0.436903i
$934$	−24.1013	+	4.24971i	−0.788619	+	0.139055i
$935$	−42.4940	+	10.9186i	−1.38970	+	0.357076i
$936$	−20.6387	+	3.40191i	−0.674596	+	0.111195i
$937$	19.6773	+	34.0821i	0.642829	+	1.11341i	0.984798	+	0.173701i	$0.0555728\pi$
$937$	19.6773	+	34.0821i	0.642829	+	1.11341i	−0.341969	+	0.939711i	$0.611094\pi$
$938$	−24.4624	+	1.03639i	−0.798727	+	0.0338392i
$939$	−27.7184	−	40.0602i	−0.904554	−	1.30732i
$940$	−9.77744	−	14.2742i	−0.318905	−	0.465573i
$941$	−29.8522	−	25.0489i	−0.973152	−	0.816572i	0.00988987	−	0.999951i	$-0.496852\pi$
$941$	−29.8522	−	25.0489i	−0.973152	−	0.816572i	−0.983042	+	0.183379i	$0.941296\pi$
$942$	−6.13801	+	65.9156i	−0.199987	+	2.14765i
$943$	−8.37689	−	3.04894i	−0.272789	−	0.0992871i
$944$	9.45064			0.307592
$945$	28.7228	−	10.9544i	0.934353	−	0.356348i
$946$	−112.767			−3.66636
$947$	23.9935	+	8.73294i	0.779686	+	0.283782i	0.701042	−	0.713120i	$-0.252719\pi$
$947$	23.9935	+	8.73294i	0.779686	+	0.283782i	0.0786440	+	0.996903i	$0.474941\pi$
$948$	25.4891	+	18.0607i	0.827848	+	0.586583i
$949$	−26.5142	−	22.2480i	−0.860686	−	0.722201i
$950$	−11.6161	+	58.7746i	−0.376877	+	1.90690i
$951$	9.08883	−	19.2102i	0.294725	−	0.622934i
$952$	16.1820	−	0.685572i	0.524461	−	0.0222195i
$953$	−5.33623	−	9.24263i	−0.172858	−	0.299398i	0.766560	−	0.642172i	$-0.221967\pi$
$953$	−5.33623	−	9.24263i	−0.172858	−	0.299398i	−0.939418	+	0.342774i	$0.888633\pi$
$954$	−19.7451	+	11.1077i	−0.639272	+	0.359624i
$955$	7.05841	+	27.4706i	0.228405	+	0.888927i
$956$	74.2508	−	13.0924i	2.40144	−	0.423439i
$957$	−18.9788	−	72.4459i	−0.613497	−	2.34184i
$958$	−37.3656	+	13.6000i	−1.20723	+	0.439395i
$959$	−16.1826	+	51.0944i	−0.522564	+	1.64992i
$960$	23.6105	+	42.4369i	0.762024	+	1.36964i
$961$	4.70058	+	26.6583i	0.151632	+	0.859945i
$962$	−40.6648	−	23.4778i	−1.31108	−	0.756955i
$963$	39.1309	−	45.5904i	1.26098	−	1.46913i
$964$	23.7576	−	13.7165i	0.765181	−	0.441777i
$965$	−5.19401	+	53.0690i	−0.167201	+	1.70835i
$966$	14.0901	−	21.7850i	0.453342	−	0.700920i
$967$	−2.03634	−	0.359061i	−0.0654842	−	0.0115466i	0.140810	−	0.990037i	$-0.455029\pi$
$967$	−2.03634	−	0.359061i	−0.0654842	−	0.0115466i	−0.206294	+	0.978490i	$0.566140\pi$
$968$	−24.2065	−	20.3117i	−0.778027	−	0.652842i
$969$	31.1115	−	14.2965i	0.999446	−	0.459271i
$970$	34.3416	+	75.6702i	1.10264	+	2.42962i
$971$	−47.4757			−1.52357			−0.761783	−	0.647832i	$-0.775676\pi$
$971$	−47.4757			−1.52357			−0.761783	+	0.647832i	$0.775676\pi$
$972$	−4.97517	+	42.9993i	−0.159578	+	1.37920i
$973$	−23.0578	−	17.7403i	−0.739199	−	0.568727i
$974$	−18.5080	+	50.8503i	−0.593034	+	1.62935i
$975$	14.1819	+	32.6158i	0.454184	+	1.04454i
$976$	0.0226064	−	0.0269412i	0.000723613	−	0.000862368i
$977$	3.75193	−	21.2783i	0.120035	−	0.680752i	−0.864098	−	0.503323i	$-0.832111\pi$
$977$	3.75193	−	21.2783i	0.120035	−	0.680752i	0.984133	−	0.177430i	$-0.0567782\pi$
$978$	−1.03921	−	12.6944i	−0.0332304	−	0.405923i
$979$	−38.8142	−	46.2569i	−1.24051	−	1.47838i
$980$	−43.4603	−	0.559793i	−1.38829	−	0.0178819i
$981$	0.950063	−	1.10689i	0.0303332	−	0.0353404i
$982$	5.64996	+	3.26200i	0.180297	+	0.104095i
$983$	−33.8736	+	5.97282i	−1.08040	+	0.190503i	−0.685392	−	0.728175i	$-0.740369\pi$
$983$	−33.8736	+	5.97282i	−1.08040	+	0.190503i	−0.395007	+	0.918678i	$0.629258\pi$
$984$	−9.76021	−	2.67375i	−0.311144	−	0.0852361i
$985$	−15.1502	−	7.25549i	−0.482727	−	0.231179i
$986$	−58.8405	+	21.4162i	−1.87386	+	0.682031i
$987$	4.96764	−	11.7635i	0.158122	−	0.374435i
$988$	61.5700	−	10.8564i	1.95880	−	0.345390i
$989$	21.2703	+	12.2804i	0.676358	+	0.390495i
$990$	−22.2987	+	76.6035i	−0.708699	+	2.43462i
$991$	4.25666	+	7.37275i	0.135217	+	0.234203i	0.925680	−	0.378306i	$-0.123493\pi$
$991$	4.25666	+	7.37275i	0.135217	+	0.234203i	−0.790463	+	0.612510i	$0.790160\pi$
$992$	−9.46017	−	11.2742i	−0.300361	−	0.357956i
$993$	13.8972	−	29.3732i	0.441014	−	0.932131i
$994$	−29.0250	+	26.5276i	−0.920617	+	0.841404i
$995$	36.5863	−	2.82166i	1.15986	−	0.0894526i
$996$	15.3697	−	21.6914i	0.487008	−	0.687318i
$997$	45.6634	+	16.6201i	1.44617	+	0.526365i	0.941520	−	0.336957i	$-0.109398\pi$
$997$	45.6634	+	16.6201i	1.44617	+	0.526365i	0.504655	+	0.863321i	$0.331620\pi$
$998$	59.6184			1.88719
$999$	−19.5408	+	18.8967i	−0.618242	+	0.597865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.b.104.17	✓	816
5.4	even	2	inner	945.2.cs.b.104.120	yes	816
7.6	odd	2	inner	945.2.cs.b.104.18	yes	816
27.20	odd	18	inner	945.2.cs.b.209.119	yes	816
35.34	odd	2	inner	945.2.cs.b.104.119	yes	816
135.74	odd	18	inner	945.2.cs.b.209.18	yes	816
189.20	even	18	inner	945.2.cs.b.209.120	yes	816
945.209	even	18	inner	945.2.cs.b.209.17	yes	816

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.b.104.17	✓	816	1.1	even	1	trivial
945.2.cs.b.104.18	yes	816	7.6	odd	2	inner
945.2.cs.b.104.119	yes	816	35.34	odd	2	inner
945.2.cs.b.104.120	yes	816	5.4	even	2	inner
945.2.cs.b.209.17	yes	816	945.209	even	18	inner
945.2.cs.b.209.18	yes	816	135.74	odd	18	inner
945.2.cs.b.209.119	yes	816	27.20	odd	18	inner
945.2.cs.b.209.120	yes	816	189.20	even	18	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.05378 - 0.747516i) q^{2} +(-1.57383 + 0.723218i) q^{3} +(2.12716 + 1.78490i) q^{4} +(1.84479 - 1.26363i) q^{5} +(3.77293 - 0.308866i) q^{6} +(-0.111990 - 2.64338i) q^{7} +(-0.848890 - 1.47032i) q^{8} +(1.95391 - 2.27645i) q^{9} +O(q^{10})\)	\(q+(-2.05378 - 0.747516i) q^{2} +(-1.57383 + 0.723218i) q^{3} +(2.12716 + 1.78490i) q^{4} +(1.84479 - 1.26363i) q^{5} +(3.77293 - 0.308866i) q^{6} +(-0.111990 - 2.64338i) q^{7} +(-0.848890 - 1.47032i) q^{8} +(1.95391 - 2.27645i) q^{9} +(-4.73338 + 1.21621i) q^{10} +(5.35903 - 0.944942i) q^{11} +(-4.63866 - 1.27073i) q^{12} +(3.85910 - 1.40460i) q^{13} +(-1.74596 + 5.51264i) q^{14} +(-1.98951 + 3.32293i) q^{15} +(-0.320027 - 1.81496i) q^{16} +(-3.12263 - 1.80285i) q^{17} +(-5.71460 + 3.21476i) q^{18} +(4.74791 - 2.74121i) q^{19} +(6.17960 + 0.604814i) q^{20} +(2.08799 + 4.07925i) q^{21} +(-11.7127 - 2.06526i) q^{22} +(1.98436 + 1.66508i) q^{23} +(2.39938 + 1.70011i) q^{24} +(1.80648 - 4.66226i) q^{25} -8.97571 q^{26} +(-1.42876 + 4.99586i) q^{27} +(4.47994 - 5.82278i) q^{28} +(-2.71758 + 7.46650i) q^{29} +(6.56996 - 5.33738i) q^{30} +(-1.27435 + 1.51871i) q^{31} +(-1.28908 + 7.31074i) q^{32} +(-7.75084 + 5.36293i) q^{33} +(5.06555 + 6.03689i) q^{34} +(-3.54685 - 4.73496i) q^{35} +(8.21951 - 1.35484i) q^{36} +(4.53053 + 2.61570i) q^{37} +(-11.8003 + 2.08071i) q^{38} +(-5.05776 + 5.00157i) q^{39} +(-3.42396 - 1.63975i) q^{40} +(-3.23382 + 1.17702i) q^{41} +(-1.23898 - 9.93870i) q^{42} +(9.33746 - 1.64645i) q^{43} +(13.0861 + 7.55528i) q^{44} +(0.727959 - 6.66859i) q^{45} +(-2.83078 - 4.90305i) q^{46} +(-1.79113 - 2.13459i) q^{47} +(1.81628 + 2.62500i) q^{48} +(-6.97492 + 0.592067i) q^{49} +(-7.19522 + 8.22489i) q^{50} +(6.21837 + 0.579049i) q^{51} +(10.7160 + 3.90030i) q^{52} +3.45521 q^{53} +(6.66886 - 9.19239i) q^{54} +(8.69222 - 8.51505i) q^{55} +(-3.79155 + 2.40860i) q^{56} +(-5.48993 + 7.74798i) q^{57} +(11.1627 - 13.3031i) q^{58} +(-0.890462 + 5.05006i) q^{59} +(-10.1631 + 3.51732i) q^{60} +(0.0122664 + 0.0146185i) q^{61} +(3.75250 - 2.16651i) q^{62} +(-6.23634 - 4.90999i) q^{63} +(6.26942 - 10.8590i) q^{64} +(5.34433 - 7.46766i) q^{65} +(19.9274 - 5.22043i) q^{66} +(1.44818 + 3.97885i) q^{67} +(-3.42443 - 9.40853i) q^{68} +(-4.32727 - 1.18543i) q^{69} +(3.74501 + 12.3759i) q^{70} +(5.88899 + 3.40001i) q^{71} +(-5.00577 - 0.940421i) q^{72} +(-4.21399 - 7.29885i) q^{73} +(-7.34945 - 8.75874i) q^{74} +(0.528730 + 8.64410i) q^{75} +(14.9923 + 2.64355i) q^{76} +(-3.09800 - 14.0601i) q^{77} +(14.1263 - 6.49140i) q^{78} +(-6.10349 - 2.22149i) q^{79} +(-2.88382 - 2.94382i) q^{80} +(-1.36446 - 8.89597i) q^{81} +7.52141 q^{82} +(-1.89050 + 5.19411i) q^{83} +(-2.83955 + 12.4041i) q^{84} +(-8.03873 + 0.619974i) q^{85} +(-20.4079 - 3.59846i) q^{86} +(-1.12288 - 13.7164i) q^{87} +(-5.93860 - 7.07735i) q^{88} +(-5.54827 - 9.60989i) q^{89} +(-6.47995 + 13.1517i) q^{90} +(-4.14507 - 10.0438i) q^{91} +(1.24906 + 7.08376i) q^{92} +(0.907258 - 3.31184i) q^{93} +(2.08296 + 5.72287i) q^{94} +(5.29501 - 11.0565i) q^{95} +(-3.25846 - 12.4382i) q^{96} +(-2.95263 - 16.7452i) q^{97} +(14.7675 + 3.99789i) q^{98} +(8.31997 - 14.0459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 816 q - 24 q^{4} - 24 q^{9}+O(q^{10}) \) 816 * q - 24 * q^4 - 24 * q^9	\( 816 q - 24 q^{4} - 24 q^{9} - 12 q^{11} - 6 q^{14} + 24 q^{21} - 12 q^{25} + 12 q^{29} + 78 q^{30} - 36 q^{35} + 12 q^{36} - 84 q^{39} - 36 q^{44} - 12 q^{46} + 6 q^{49} + 24 q^{50} - 60 q^{51} + 120 q^{56} - 150 q^{60} - 444 q^{64} + 162 q^{65} + 21 q^{70} - 36 q^{71} - 48 q^{74} - 48 q^{79} - 48 q^{81} + 66 q^{84} - 102 q^{85} - 192 q^{86} - 6 q^{91} - 210 q^{95} - 216 q^{99}+O(q^{100}) \) 816 * q - 24 * q^4 - 24 * q^9 - 12 * q^11 - 6 * q^14 + 24 * q^21 - 12 * q^25 + 12 * q^29 + 78 * q^30 - 36 * q^35 + 12 * q^36 - 84 * q^39 - 36 * q^44 - 12 * q^46 + 6 * q^49 + 24 * q^50 - 60 * q^51 + 120 * q^56 - 150 * q^60 - 444 * q^64 + 162 * q^65 + 21 * q^70 - 36 * q^71 - 48 * q^74 - 48 * q^79 - 48 * q^81 + 66 * q^84 - 102 * q^85 - 192 * q^86 - 6 * q^91 - 210 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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