LMFDB - Embedded newform 369.2.e.a.247.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [369,2,Mod(124,369)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(369, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("369.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.e (of order $3$, 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:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.4
Character	$\chi$	$=$	369.247
Dual form			369.2.e.a.124.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.954563 - 1.65335i) q^{2} +(-0.947667 + 1.44980i) q^{3} +(-0.822382 + 1.42441i) q^{4} +(0.112697 - 0.195198i) q^{5} +(3.30164 + 0.182900i) q^{6} +(0.630622 + 1.09227i) q^{7} -0.678190 q^{8} +(-1.20385 - 2.74786i) q^{9} -0.430307 q^{10} +(-0.286098 - 0.495537i) q^{11} +(-1.28577 - 2.54216i) q^{12} +(-1.08799 + 1.88445i) q^{13} +(1.20394 - 2.08528i) q^{14} +(0.176198 + 0.348371i) q^{15} +(2.29214 + 3.97010i) q^{16} -5.85554 q^{17} +(-3.39403 + 4.61340i) q^{18} -3.55710 q^{19} +(0.185361 + 0.321054i) q^{20} +(-2.18119 - 0.120831i) q^{21} +(-0.546198 + 0.946042i) q^{22} +(-2.23419 + 3.86973i) q^{23} +(0.642698 - 0.983241i) q^{24} +(2.47460 + 4.28613i) q^{25} +4.15421 q^{26} +(5.12471 + 0.858708i) q^{27} -2.07445 q^{28} +(0.203998 + 0.353334i) q^{29} +(0.407788 - 0.623860i) q^{30} +(-3.64383 + 6.31130i) q^{31} +(3.69779 - 6.40477i) q^{32} +(0.989556 + 0.0548180i) q^{33} +(5.58948 + 9.68126i) q^{34} +0.284278 q^{35} +(4.90410 + 0.545013i) q^{36} -7.51323 q^{37} +(3.39547 + 5.88113i) q^{38} +(-1.70103 - 3.36320i) q^{39} +(-0.0764302 + 0.132381i) q^{40} +(0.500000 - 0.866025i) q^{41} +(1.88231 + 3.72162i) q^{42} +(3.07700 + 5.32952i) q^{43} +0.941129 q^{44} +(-0.672047 - 0.0746874i) q^{45} +8.53071 q^{46} +(0.511041 + 0.885149i) q^{47} +(-7.92805 - 0.439187i) q^{48} +(2.70463 - 4.68456i) q^{49} +(4.72432 - 8.18277i) q^{50} +(5.54910 - 8.48937i) q^{51} +(-1.78948 - 3.09948i) q^{52} -7.62458 q^{53} +(-3.47211 - 9.29264i) q^{54} -0.128970 q^{55} +(-0.427681 - 0.740765i) q^{56} +(3.37094 - 5.15708i) q^{57} +(0.389457 - 0.674560i) q^{58} +(1.97737 - 3.42490i) q^{59} +(-0.641125 - 0.0355161i) q^{60} +(-0.0158340 - 0.0274253i) q^{61} +13.9131 q^{62} +(2.24223 - 3.04779i) q^{63} -4.95056 q^{64} +(0.245227 + 0.424745i) q^{65} +(-0.853961 - 1.68841i) q^{66} +(0.799832 - 1.38535i) q^{67} +(4.81549 - 8.34067i) q^{68} +(-3.49308 - 6.90635i) q^{69} +(-0.271361 - 0.470011i) q^{70} +1.73394 q^{71} +(0.816441 + 1.86357i) q^{72} -10.0746 q^{73} +(7.17185 + 12.4220i) q^{74} +(-8.55914 - 0.474147i) q^{75} +(2.92529 - 5.06675i) q^{76} +(0.360840 - 0.624993i) q^{77} +(-3.93681 + 6.02279i) q^{78} +(-2.05248 - 3.55499i) q^{79} +1.03327 q^{80} +(-6.10147 + 6.61604i) q^{81} -1.90913 q^{82} +(2.96089 + 5.12841i) q^{83} +(1.96589 - 3.00754i) q^{84} +(-0.659904 + 1.14299i) q^{85} +(5.87438 - 10.1747i) q^{86} +(-0.705587 - 0.0390871i) q^{87} +(0.194029 + 0.336068i) q^{88} -11.4590 q^{89} +(0.518027 + 1.18242i) q^{90} -2.74444 q^{91} +(-3.67472 - 6.36480i) q^{92} +(-5.69700 - 11.2639i) q^{93} +(0.975641 - 1.68986i) q^{94} +(-0.400875 + 0.694337i) q^{95} +(5.78137 + 11.4307i) q^{96} +(-4.41143 - 7.64083i) q^{97} -10.3270 q^{98} +(-1.01725 + 1.38271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{3} - 8 q^{4} + q^{5} + 13 q^{7} + 3 q^{9} - 16 q^{10} - 2 q^{11} - 23 q^{12} + 5 q^{13} + q^{14} + 9 q^{15} + 8 q^{16} + 2 q^{17} + 21 q^{18} - 38 q^{19} + 11 q^{20} - 6 q^{21} + 14 q^{22}+ \cdots + 23 q^{99}+O(q^{100}) $ 32 * q - q^3 - 8 * q^4 + q^5 + 13 * q^7 + 3 * q^9 - 16 * q^10 - 2 * q^11 - 23 * q^12 + 5 * q^13 + q^14 + 9 * q^15 + 8 * q^16 + 2 * q^17 + 21 * q^18 - 38 * q^19 + 11 * q^20 - 6 * q^21 + 14 * q^22 + 2 * q^23 + 15 * q^24 + 3 * q^25 + 30 * q^26 + 11 * q^27 - 48 * q^28 - 10 * q^29 - 59 * q^30 + 39 * q^31 - 10 * q^32 + 6 * q^33 + 18 * q^34 + 4 * q^35 + 14 * q^36 - 52 * q^37 - 14 * q^38 - 20 * q^39 + 18 * q^40 + 16 * q^41 + 11 * q^42 + 20 * q^43 - 46 * q^44 + 31 * q^45 - 52 * q^46 + 5 * q^47 - 72 * q^48 + 7 * q^49 + 9 * q^50 - 31 * q^51 + 14 * q^52 + 14 * q^53 + 36 * q^54 - 74 * q^55 - 2 * q^56 - 6 * q^57 + 24 * q^58 + 6 * q^59 - 17 * q^60 + 21 * q^61 - 10 * q^62 + 56 * q^63 - 68 * q^64 + 2 * q^65 - 23 * q^66 + 32 * q^67 - 8 * q^68 - 29 * q^69 + 22 * q^70 - 40 * q^71 + 87 * q^72 - 34 * q^73 + 28 * q^74 + 24 * q^75 + 40 * q^76 - 22 * q^77 + 30 * q^78 + 69 * q^79 + 78 * q^80 + 63 * q^81 + 10 * q^83 - 70 * q^84 + 42 * q^85 - 8 * q^86 - 58 * q^87 + 42 * q^88 + 22 * q^89 + 49 * q^90 - 102 * q^91 - 10 * q^92 - 5 * q^93 + 13 * q^94 - 22 * q^95 + 21 * q^96 + 25 * q^97 - 96 * q^98 + 23 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.954563	−	1.65335i	−0.674978	−	1.16910i	−0.976475	−	0.215629i	$-0.930820\pi$
$2$	−0.954563	−	1.65335i	−0.674978	−	1.16910i	0.301497	−	0.953467i	$-0.402514\pi$
$3$	−0.947667	+	1.44980i	−0.547136	+	0.837044i
$3$	−0.947667	+	1.44980i	−0.547136	+	0.837044i
$4$	−0.822382	+	1.42441i	−0.411191	+	0.712204i
$5$	0.112697	−	0.195198i	0.0503998	−	0.0872950i	−0.839725	−	0.543012i	$-0.817284\pi$
$5$	0.112697	−	0.195198i	0.0503998	−	0.0872950i	0.890125	+	0.455717i	$0.150617\pi$
$6$	3.30164	+	0.182900i	1.34789	+	0.0746685i
$7$	0.630622	+	1.09227i	0.238353	+	0.412839i	0.960242	−	0.279170i	$-0.0900593\pi$
$7$	0.630622	+	1.09227i	0.238353	+	0.412839i	−0.721889	+	0.692009i	$0.756726\pi$
$8$	−0.678190			−0.239776
$9$	−1.20385	−	2.74786i	−0.401284	−	0.915953i
$10$	−0.430307			−0.136075
$11$	−0.286098	−	0.495537i	−0.0862619	−	0.149410i	0.819666	−	0.572841i	$-0.194159\pi$
$11$	−0.286098	−	0.495537i	−0.0862619	−	0.149410i	−0.905928	+	0.423431i	$0.860826\pi$
$12$	−1.28577	−	2.54216i	−0.371168	−	0.733857i
$13$	−1.08799	+	1.88445i	−0.301754	+	0.522653i	−0.976533	−	0.215367i	$-0.930905\pi$
$13$	−1.08799	+	1.88445i	−0.301754	+	0.522653i	0.674780	+	0.738019i	$0.264239\pi$
$14$	1.20394	−	2.08528i	0.321766	−	0.557315i
$15$	0.176198	+	0.348371i	0.0454942	+	0.0899491i
$16$	2.29214	+	3.97010i	0.573035	+	0.992525i
$17$	−5.85554			−1.42018			−0.710088	−	0.704113i	$-0.751345\pi$
$17$	−5.85554			−1.42018			−0.710088	+	0.704113i	$0.751345\pi$
$18$	−3.39403	+	4.61340i	−0.799980	+	1.08739i
$19$	−3.55710			−0.816054			−0.408027	−	0.912970i	$-0.633783\pi$
$19$	−3.55710			−0.816054			−0.408027	+	0.912970i	$0.633783\pi$
$20$	0.185361	+	0.321054i	0.0414479	+	0.0717899i
$21$	−2.18119	−	0.120831i	−0.475976	−	0.0263674i
$22$	−0.546198	+	0.946042i	−0.116450	+	0.201697i
$23$	−2.23419	+	3.86973i	−0.465861	+	0.806895i	−0.999240	−	0.0389816i	$-0.987589\pi$
$23$	−2.23419	+	3.86973i	−0.465861	+	0.806895i	0.533379	+	0.845876i	$0.320922\pi$
$24$	0.642698	−	0.983241i	0.131190	−	0.200703i
$25$	2.47460	+	4.28613i	0.494920	+	0.857226i
$26$	4.15421			0.814708
$27$	5.12471	+	0.858708i	0.986250	+	0.165258i
$28$	−2.07445			−0.392034
$29$	0.203998	+	0.353334i	0.0378814	+	0.0656125i	0.884345	−	0.466835i	$-0.154606\pi$
$29$	0.203998	+	0.353334i	0.0378814	+	0.0656125i	−0.846463	+	0.532447i	$0.821272\pi$
$30$	0.407788	−	0.623860i	0.0744516	−	0.113901i
$31$	−3.64383	+	6.31130i	−0.654452	+	1.13354i	0.327579	+	0.944824i	$0.393767\pi$
$31$	−3.64383	+	6.31130i	−0.654452	+	1.13354i	−0.982031	+	0.188720i	$0.939566\pi$
$32$	3.69779	−	6.40477i	0.653684	−	1.13221i
$33$	0.989556	+	0.0548180i	0.172260	+	0.00954259i
$34$	5.58948	+	9.68126i	0.958588	+	1.66032i
$35$	0.284278			0.0480517
$36$	4.90410	+	0.545013i	0.817350	+	0.0908356i
$37$	−7.51323			−1.23517			−0.617584	−	0.786505i	$-0.711888\pi$
$37$	−7.51323			−1.23517			−0.617584	+	0.786505i	$0.711888\pi$
$38$	3.39547	+	5.88113i	0.550818	+	0.954045i
$39$	−1.70103	−	3.36320i	−0.272383	−	0.538543i
$40$	−0.0764302	+	0.132381i	−0.0120847	+	0.0209313i
$41$	0.500000	−	0.866025i	0.0780869	−	0.135250i
$41$	0.500000	−	0.866025i	0.0780869	−	0.135250i
$42$	1.88231	+	3.72162i	0.290447	+	0.574259i
$43$	3.07700	+	5.32952i	0.469238	+	0.812744i	0.999382	−	0.0351638i	$-0.0111953\pi$
$43$	3.07700	+	5.32952i	0.469238	+	0.812744i	−0.530143	+	0.847908i	$0.677862\pi$
$44$	0.941129			0.141880
$45$	−0.672047	−	0.0746874i	−0.100183	−	0.0111337i
$46$	8.53071			1.25778
$47$	0.511041	+	0.885149i	0.0745430	+	0.129112i	0.900887	−	0.434053i	$-0.142917\pi$
$47$	0.511041	+	0.885149i	0.0745430	+	0.129112i	−0.826344	+	0.563165i	$0.809584\pi$
$48$	−7.92805	−	0.439187i	−1.14432	−	0.0633911i
$49$	2.70463	−	4.68456i	0.386376	−	0.669223i
$50$	4.72432	−	8.18277i	0.668120	−	1.15722i
$51$	5.54910	−	8.48937i	0.777030	−	1.18875i
$52$	−1.78948	−	3.09948i	−0.248157	−	0.429820i
$53$	−7.62458			−1.04732			−0.523659	−	0.851928i	$-0.675433\pi$
$53$	−7.62458			−1.04732			−0.523659	+	0.851928i	$0.675433\pi$
$54$	−3.47211	−	9.29264i	−0.472494	−	1.26457i
$55$	−0.128970			−0.0173903
$56$	−0.427681	−	0.740765i	−0.0571513	−	0.0989889i
$57$	3.37094	−	5.15708i	0.446492	−	0.683073i
$58$	0.389457	−	0.674560i	0.0511382	−	0.0885740i
$59$	1.97737	−	3.42490i	0.257432	−	0.445884i	−0.708122	−	0.706091i	$-0.750457\pi$
$59$	1.97737	−	3.42490i	0.257432	−	0.445884i	0.965553	+	0.260206i	$0.0837905\pi$
$60$	−0.641125	−	0.0355161i	−0.0827689	−	0.00458511i
$61$	−0.0158340	−	0.0274253i	−0.00202734	−	0.00351145i	0.865010	−	0.501755i	$-0.167312\pi$
$61$	−0.0158340	−	0.0274253i	−0.00202734	−	0.00351145i	−0.867037	+	0.498243i	$0.833979\pi$
$62$	13.9131			1.76696
$63$	2.24223	−	3.04779i	0.282494	−	0.383986i
$64$	−4.95056			−0.618820
$65$	0.245227	+	0.424745i	0.0304167	+	0.0526832i
$66$	−0.853961	−	1.68841i	−0.105115	−	0.207829i
$67$	0.799832	−	1.38535i	0.0977150	−	0.169247i	−0.813024	−	0.582231i	$-0.802180\pi$
$67$	0.799832	−	1.38535i	0.0977150	−	0.169247i	0.910738	+	0.412984i	$0.135513\pi$
$68$	4.81549	−	8.34067i	0.583964	−	1.01146i
$69$	−3.49308	−	6.90635i	−0.420517	−	0.831427i
$70$	−0.271361	−	0.470011i	−0.0324339	−	0.0561771i
$71$	1.73394			0.205781			0.102890	−	0.994693i	$-0.467191\pi$
$71$	1.73394			0.205781			0.102890	+	0.994693i	$0.467191\pi$
$72$	0.816441	+	1.86357i	0.0962185	+	0.219624i
$73$	−10.0746			−1.17915			−0.589574	−	0.807714i	$-0.700704\pi$
$73$	−10.0746			−1.17915			−0.589574	+	0.807714i	$0.700704\pi$
$74$	7.17185	+	12.4220i	0.833711	+	1.44403i
$75$	−8.55914	−	0.474147i	−0.988324	−	0.0547498i
$76$	2.92529	−	5.06675i	0.335554	−	0.581197i
$77$	0.360840	−	0.624993i	0.0411215	−	0.0712245i
$78$	−3.93681	+	6.02279i	−0.445756	+	0.681947i
$79$	−2.05248	−	3.55499i	−0.230922	−	0.399968i	0.727158	−	0.686470i	$-0.240841\pi$
$79$	−2.05248	−	3.55499i	−0.230922	−	0.399968i	−0.958080	+	0.286502i	$0.907507\pi$
$80$	1.03327			0.115523
$81$	−6.10147	+	6.61604i	−0.677942	+	0.735116i
$82$	−1.90913			−0.210828
$83$	2.96089	+	5.12841i	0.325000	+	0.562916i	0.981512	−	0.191399i	$-0.0613024\pi$
$83$	2.96089	+	5.12841i	0.325000	+	0.562916i	−0.656513	+	0.754315i	$0.727969\pi$
$84$	1.96589	−	3.00754i	0.214496	−	0.328150i
$85$	−0.659904	+	1.14299i	−0.0715766	+	0.123974i
$86$	5.87438	−	10.1747i	0.633451	−	1.09717i
$87$	−0.705587	−	0.0390871i	−0.0756468	−	0.00419058i
$88$	0.194029	+	0.336068i	0.0206835	+	0.0358249i
$89$	−11.4590			−1.21465			−0.607326	−	0.794452i	$-0.707758\pi$
$89$	−11.4590			−1.21465			−0.607326	+	0.794452i	$0.707758\pi$
$90$	0.518027	+	1.18242i	0.0546048	+	0.124638i
$91$	−2.74444			−0.287695
$92$	−3.67472	−	6.36480i	−0.383116	−	0.663576i
$93$	−5.69700	−	11.2639i	−0.590752	−	1.16801i
$94$	0.975641	−	1.68986i	0.100630	−	0.174296i
$95$	−0.400875	+	0.694337i	−0.0411290	+	0.0712374i
$96$	5.78137	+	11.4307i	0.590058	+	1.16664i
$97$	−4.41143	−	7.64083i	−0.447913	−	0.775809i	0.550337	−	0.834943i	$-0.314499\pi$
$97$	−4.41143	−	7.64083i	−0.447913	−	0.775809i	−0.998250	+	0.0591342i	$0.981166\pi$
$98$	−10.3270			−1.04318
$99$	−1.01725	+	1.38271i	−0.102237	+	0.138968i
$100$	−8.14026			−0.814026
$101$	−3.58420	−	6.20802i	−0.356642	−	0.617721i	0.630756	−	0.775981i	$-0.282745\pi$
$101$	−3.58420	−	6.20802i	−0.356642	−	0.617721i	−0.987397	+	0.158260i	$0.949412\pi$
$102$	−19.3329	−	1.07098i	−1.91424	−	0.106042i
$103$	6.17910	−	10.7025i	0.608844	−	1.05455i	−0.382587	−	0.923920i	$-0.624967\pi$
$103$	6.17910	−	10.7025i	0.608844	−	1.05455i	0.991431	−	0.130630i	$-0.0417000\pi$
$104$	0.737862	−	1.27801i	0.0723533	−	0.125320i
$105$	−0.269401	+	0.412147i	−0.0262908	+	0.0402214i
$106$	7.27815	+	12.6061i	0.706916	+	1.22441i
$107$	16.1626			1.56250			0.781251	−	0.624217i	$-0.214582\pi$
$107$	16.1626			1.56250			0.781251	+	0.624217i	$0.214582\pi$
$108$	−5.43762	+	6.59349i	−0.523235	+	0.634459i
$109$	8.31719			0.796642			0.398321	−	0.917246i	$-0.369593\pi$
$109$	8.31719			0.796642			0.398321	+	0.917246i	$0.369593\pi$
$110$	0.123110	+	0.213233i	0.0117381	+	0.0203310i
$111$	7.12004	−	10.8927i	0.675805	−	1.03389i
$112$	−2.89095	+	5.00727i	−0.273169	+	0.473142i
$113$	−8.95651	+	15.5131i	−0.842558	+	1.45935i	0.0451674	+	0.998979i	$0.485618\pi$
$113$	−8.95651	+	15.5131i	−0.842558	+	1.45935i	−0.887725	+	0.460374i	$0.847715\pi$
$114$	−11.7443	−	0.650592i	−1.09995	−	0.0609335i
$115$	0.503575	+	0.872217i	0.0469586	+	0.0813347i
$116$	−0.671056			−0.0623060
$117$	6.48799	+	0.721037i	0.599814	+	0.0666599i
$118$	−7.55010			−0.695043
$119$	−3.69263	−	6.39582i	−0.338503	−	0.586304i
$120$	−0.119496	−	0.236262i	−0.0109084	−	0.0215677i
$121$	5.33630	−	9.24274i	0.485118	−	0.840249i
$122$	−0.0302291	+	0.0523583i	−0.00273681	+	0.00474030i
$123$	0.781732	+	1.54561i	0.0704864	+	0.139363i
$124$	−5.99325	−	10.3806i	−0.538210	−	0.932206i
$125$	2.24250			0.200575
$126$	−7.17942	−	0.797879i	−0.639594	−	0.0710807i
$127$	10.4508			0.927356			0.463678	−	0.886004i	$-0.346529\pi$
$127$	10.4508			0.927356			0.463678	+	0.886004i	$0.346529\pi$
$128$	−2.66997	−	4.62452i	−0.235994	−	0.408754i
$129$	−10.6427	−	0.589570i	−0.937039	−	0.0519088i
$130$	0.468169	−	0.810893i	0.0410612	−	0.0711200i
$131$	−2.55022	+	4.41712i	−0.222814	+	0.385925i	−0.955661	−	0.294468i	$-0.904858\pi$
$131$	−2.55022	+	4.41712i	−0.222814	+	0.385925i	0.732847	+	0.680393i	$0.238191\pi$
$132$	−0.891877	+	1.36445i	−0.0776279	+	0.118760i
$133$	−2.24318	−	3.88531i	−0.194509	−	0.336899i
$134$	−3.05396			−0.263822
$135$	0.745159	−	0.903557i	0.0641331	−	0.0777658i
$136$	3.97116			0.340524
$137$	8.03418	+	13.9156i	0.686406	+	1.18889i	0.972993	+	0.230836i	$0.0741460\pi$
$137$	8.03418	+	13.9156i	0.686406	+	1.18889i	−0.286587	+	0.958054i	$0.592521\pi$
$138$	−8.08427	+	12.3678i	−0.688179	+	1.05282i
$139$	9.33261	−	16.1646i	0.791581	−	1.37106i	−0.133406	−	0.991061i	$-0.542591\pi$
$139$	9.33261	−	16.1646i	0.791581	−	1.37106i	0.924987	−	0.379998i	$-0.124075\pi$
$140$	−0.233785	+	0.404928i	−0.0197584	+	0.0342226i
$141$	−1.76759	−	0.0979183i	−0.148858	−	0.00824621i
$142$	−1.65515	−	2.86681i	−0.138898	−	0.240578i
$143$	1.24509			0.104119
$144$	8.14989	−	11.0779i	0.679157	−	0.923158i
$145$	0.0919600			0.00763686
$146$	9.61689	+	16.6569i	0.795899	+	1.37854i
$147$	4.22859	+	8.36059i	0.348769	+	0.689570i
$148$	6.17875	−	10.7019i	0.507890	−	0.879691i
$149$	5.05879	−	8.76208i	0.414432	−	0.717817i	−0.580937	−	0.813949i	$-0.697314\pi$
$149$	5.05879	−	8.76208i	0.414432	−	0.717817i	0.995369	+	0.0961314i	$0.0306469\pi$
$150$	7.38631	+	14.6039i	0.603089	+	1.19240i
$151$	−1.71605	−	2.97228i	−0.139650	−	0.241881i	0.787714	−	0.616041i	$-0.211264\pi$
$151$	−1.71605	−	2.97228i	−0.139650	−	0.241881i	−0.927364	+	0.374160i	$0.877931\pi$
$152$	2.41238			0.195670
$153$	7.04921	+	16.0902i	0.569895	+	1.30082i
$154$	−1.37778			−0.111024
$155$	0.821301	+	1.42254i	0.0659685	+	0.114261i
$156$	6.18947	+	0.342875i	0.495554	+	0.0274520i
$157$	−5.14996	+	8.91999i	−0.411011	+	0.711893i	−0.995001	−	0.0998687i	$-0.968158\pi$
$157$	−5.14996	+	8.91999i	−0.411011	+	0.711893i	0.583989	+	0.811761i	$0.301491\pi$
$158$	−3.91844	+	6.78693i	−0.311734	+	0.539939i
$159$	7.22557	−	11.0541i	0.573025	−	0.876650i
$160$	−0.833464	−	1.44360i	−0.0658911	−	0.114127i
$161$	−5.63572			−0.444157
$162$	16.7629	+	3.77245i	1.31702	+	0.296392i
$163$	12.0942			0.947292			0.473646	−	0.880715i	$-0.342938\pi$
$163$	12.0942			0.947292			0.473646	+	0.880715i	$0.342938\pi$
$164$	0.822382	+	1.42441i	0.0642173	+	0.111228i
$165$	0.122221	−	0.186981i	0.00951487	−	0.0145565i
$166$	5.65271	−	9.79078i	0.438736	−	0.759912i
$167$	−5.02593	+	8.70517i	−0.388918	+	0.673626i	−0.992304	−	0.123823i	$-0.960484\pi$
$167$	−5.02593	+	8.70517i	−0.388918	+	0.673626i	0.603386	+	0.797449i	$0.293818\pi$
$168$	1.47926	+	0.0819461i	0.114128	+	0.00632228i
$169$	4.13256	+	7.15781i	0.317890	+	0.550601i
$170$	2.51968			0.193251
$171$	4.28222	+	9.77440i	0.327470	+	0.747467i
$172$	−10.1219			−0.771786
$173$	0.105743	+	0.183152i	0.00803948	+	0.0139248i	0.870017	−	0.493021i	$-0.164108\pi$
$173$	0.105743	+	0.183152i	0.00803948	+	0.0139248i	−0.861978	+	0.506946i	$0.830774\pi$
$174$	0.608902	+	1.20389i	0.0461608	+	0.0912670i
$175$	−3.12107	+	5.40586i	−0.235931	+	0.408644i
$176$	1.31155	−	2.27168i	0.0988621	−	0.171234i
$177$	3.09155	+	6.11246i	0.232375	+	0.459441i
$178$	10.9384	+	18.9458i	0.819864	+	1.42005i
$179$	−6.77185			−0.506152			−0.253076	−	0.967446i	$-0.581442\pi$
$179$	−6.77185			−0.506152			−0.253076	+	0.967446i	$0.581442\pi$
$180$	0.659065	−	0.895848i	0.0491238	−	0.0667725i
$181$	5.24924			0.390173			0.195087	−	0.980786i	$-0.437501\pi$
$181$	5.24924			0.390173			0.195087	+	0.980786i	$0.437501\pi$
$182$	2.61974	+	4.53752i	0.194188	+	0.336343i
$183$	0.0547666	+	0.00303388i	0.00404846	+	0.000224271i
$184$	1.51520	−	2.62441i	0.111702	−	0.193474i
$185$	−0.846722	+	1.46657i	−0.0622522	+	0.107824i
$186$	−13.1850	+	20.1712i	−0.966769	+	1.47903i
$187$	1.67526	+	2.90163i	0.122507	+	0.212188i
$188$	−1.68108			−0.122606
$189$	2.29381	+	6.13908i	0.166850	+	0.446552i
$190$	1.53064			0.111045
$191$	5.33810	+	9.24587i	0.386252	+	0.669007i	0.991942	−	0.126693i	$-0.0404363\pi$
$191$	5.33810	+	9.24587i	0.386252	+	0.669007i	−0.605690	+	0.795700i	$0.707103\pi$
$192$	4.69148	−	7.17733i	0.338579	−	0.517979i
$193$	−0.678307	+	1.17486i	−0.0488256	+	0.0845685i	−0.889405	−	0.457119i	$-0.848881\pi$
$193$	−0.678307	+	1.17486i	−0.0488256	+	0.0845685i	0.840580	+	0.541688i	$0.182215\pi$
$194$	−8.42199	+	14.5873i	−0.604663	+	1.04731i
$195$	−0.848190	−	0.0469868i	−0.0607402	−	0.00336480i
$196$	4.44848	+	7.70500i	0.317749	+	0.550357i
$197$	6.69366			0.476904			0.238452	−	0.971154i	$-0.423360\pi$
$197$	6.69366			0.476904			0.238452	+	0.971154i	$0.423360\pi$
$198$	3.25713	+	0.361979i	0.231474	+	0.0257247i
$199$	−21.5042			−1.52439			−0.762196	−	0.647347i	$-0.775879\pi$
$199$	−21.5042			−1.52439			−0.762196	+	0.647347i	$0.775879\pi$
$200$	−1.67825	−	2.90681i	−0.118670	−	0.205542i
$201$	1.25051	+	2.47245i	0.0882040	+	0.174393i
$202$	−6.84270	+	11.8519i	−0.481451	+	0.833897i
$203$	−0.257291	+	0.445641i	−0.0180583	+	0.0312778i
$204$	7.52884	+	14.8857i	0.527125	+	1.04221i
$205$	−0.112697	−	0.195198i	−0.00787113	−	0.0136332i
$206$	−23.5934			−1.64383
$207$	13.3231	+	1.48065i	0.926021	+	0.102913i
$208$	−9.97528			−0.691661
$209$	1.01768	+	1.76267i	0.0703943	+	0.121927i
$210$	0.938584	+	0.0519943i	0.0647684	+	0.00358795i
$211$	11.3176	−	19.6027i	0.779139	−	1.34951i	−0.153300	−	0.988180i	$-0.548990\pi$
$211$	11.3176	−	19.6027i	0.779139	−	1.34951i	0.932439	−	0.361328i	$-0.117677\pi$
$212$	6.27032	−	10.8605i	0.430648	−	0.745903i
$213$	−1.64320	+	2.51387i	−0.112590	+	0.172247i
$214$	−15.4283	−	26.7225i	−1.05465	−	1.82672i
$215$	1.38708			0.0945980
$216$	−3.47552	−	0.582367i	−0.236479	−	0.0396250i
$217$	−9.19152			−0.623961
$218$	−7.93928	−	13.7512i	−0.537716	−	0.931352i
$219$	9.54741	−	14.6062i	0.645154	−	0.986999i
$220$	0.106063	−	0.183706i	0.00715075	−	0.0123855i
$221$	6.37075	−	11.0345i	0.428543	−	0.742259i
$222$	−24.8060	−	1.37417i	−1.66487	−	0.0922281i
$223$	6.07673	+	10.5252i	0.406928	+	0.704820i	0.994544	−	0.104320i	$-0.0332667\pi$
$223$	6.07673	+	10.5252i	0.406928	+	0.704820i	−0.587616	+	0.809140i	$0.699933\pi$
$224$	9.32764			0.623229
$225$	8.79863	−	11.9597i	0.586576	−	0.797315i
$226$	34.1982			2.27483
$227$	−4.19322	−	7.26287i	−0.278314	−	0.482053i	0.692652	−	0.721272i	$-0.256442\pi$
$227$	−4.19322	−	7.26287i	−0.278314	−	0.482053i	−0.970966	+	0.239218i	$0.923109\pi$
$228$	4.57359	+	9.04269i	0.302893	+	0.598867i
$229$	−9.06684	+	15.7042i	−0.599153	+	1.03776i	0.393793	+	0.919199i	$0.371163\pi$
$229$	−9.06684	+	15.7042i	−0.599153	+	1.03776i	−0.992946	+	0.118565i	$0.962171\pi$
$230$	0.961388	−	1.66517i	0.0633921	−	0.109798i
$231$	0.564160	+	1.11543i	0.0371190	+	0.0733900i
$232$	−0.138349	−	0.239628i	−0.00908306	−	0.0157323i
$233$	−12.9677			−0.849541			−0.424770	−	0.905301i	$-0.639645\pi$
$233$	−12.9677			−0.849541			−0.424770	+	0.905301i	$0.639645\pi$
$234$	−5.00106	−	11.4152i	−0.326930	−	0.746235i
$235$	0.230372			0.0150278
$236$	3.25231	+	5.63316i	0.211707	+	0.366687i
$237$	7.09910	+	0.393266i	0.461136	+	0.0255454i
$238$	−7.04970	+	12.2104i	−0.456964	+	0.791485i
$239$	−12.7379	+	22.0628i	−0.823949	+	1.42712i	0.0787703	+	0.996893i	$0.474901\pi$
$239$	−12.7379	+	22.0628i	−0.823949	+	1.42712i	−0.902720	+	0.430229i	$0.858433\pi$
$240$	−0.979199	+	1.49804i	−0.0632070	+	0.0966981i
$241$	1.99448	+	3.45454i	0.128476	+	0.222526i	0.923086	−	0.384593i	$-0.125658\pi$
$241$	1.99448	+	3.45454i	0.128476	+	0.222526i	−0.794611	+	0.607119i	$0.792325\pi$
$242$	−20.3753			−1.30978
$243$	−3.80979	−	15.1157i	−0.244398	−	0.969675i
$244$	0.0520864			0.00333449
$245$	−0.609610	−	1.05588i	−0.0389466	−	0.0674574i
$246$	1.80922	−	2.76786i	0.115351	−	0.176472i
$247$	3.87008	−	6.70317i	0.246247	−	0.426512i
$248$	2.47121	−	4.28026i	0.156922	−	0.271797i
$249$	−10.2411	−	0.567323i	−0.649005	−	0.0359526i
$250$	−2.14061	−	3.70764i	−0.135384	−	0.234492i
$251$	6.90967			0.436134			0.218067	−	0.975934i	$-0.430025\pi$
$251$	6.90967			0.436134			0.218067	+	0.975934i	$0.430025\pi$
$252$	2.49733	+	5.70030i	0.157317	+	0.359085i
$253$	2.55679			0.160744
$254$	−9.97592	−	17.2788i	−0.625945	−	1.08417i
$255$	−1.03174	−	2.03990i	−0.0646098	−	0.127744i
$256$	−10.0479	+	17.4034i	−0.627992	+	1.08771i
$257$	−10.9995	+	19.0517i	−0.686132	+	1.18842i	0.286948	+	0.957946i	$0.407359\pi$
$257$	−10.9995	+	19.0517i	−0.686132	+	1.18842i	−0.973080	+	0.230469i	$0.925974\pi$
$258$	9.18438	+	18.1590i	0.571795	+	1.13053i
$259$	−4.73801	−	8.20647i	−0.294405	−	0.509925i
$260$	−0.806681			−0.0500282
$261$	0.725330	−	0.985920i	0.0448968	−	0.0610269i
$262$	9.73740			0.601579
$263$	1.54381	+	2.67396i	0.0951956	+	0.164884i	0.909690	−	0.415287i	$-0.136319\pi$
$263$	1.54381	+	2.67396i	0.0951956	+	0.164884i	−0.814495	+	0.580171i	$0.802986\pi$
$264$	−0.671107	−	0.0371770i	−0.0413038	−	0.00228809i
$265$	−0.859271	+	1.48830i	−0.0527846	+	0.0914256i
$266$	−4.28252	+	7.41754i	−0.262578	+	0.454799i
$267$	10.8593	−	16.6133i	0.664580	−	1.01672i
$268$	1.31553	+	2.27857i	0.0803591	+	0.139186i
$269$	18.6282			1.13578			0.567891	−	0.823104i	$-0.307760\pi$
$269$	18.6282			1.13578			0.567891	+	0.823104i	$0.307760\pi$
$270$	−2.20520	−	0.369508i	−0.134204	−	0.0224876i
$271$	−27.2387			−1.65463			−0.827316	−	0.561736i	$-0.810134\pi$
$271$	−27.2387			−1.65463			−0.827316	+	0.561736i	$0.810134\pi$
$272$	−13.4217	−	23.2471i	−0.813811	−	1.40956i
$273$	2.60081	−	3.97889i	0.157408	−	0.240813i
$274$	15.3383	−	26.5666i	0.926618	−	1.60495i
$275$	1.41596	−	2.45251i	0.0853854	−	0.147892i
$276$	12.7101	+	0.704096i	0.765059	+	0.0423816i
$277$	−6.30273	−	10.9166i	−0.378694	−	0.655918i	0.612178	−	0.790720i	$-0.290293\pi$
$277$	−6.30273	−	10.9166i	−0.378694	−	0.655918i	−0.990873	+	0.134802i	$0.956960\pi$
$278$	−35.6343			−2.13720
$279$	21.7292	+	2.41486i	1.30089	+	0.144574i
$280$	−0.192794			−0.0115217
$281$	−5.82954	−	10.0971i	−0.347761	−	0.602340i	0.638090	−	0.769961i	$-0.279725\pi$
$281$	−5.82954	−	10.0971i	−0.347761	−	0.602340i	−0.985851	+	0.167622i	$0.946391\pi$
$282$	1.52538	+	3.01591i	0.0908351	+	0.179595i
$283$	−12.4177	+	21.5080i	−0.738154	+	1.27852i	0.215172	+	0.976576i	$0.430969\pi$
$283$	−12.4177	+	21.5080i	−0.738154	+	1.27852i	−0.953326	+	0.301943i	$0.902365\pi$
$284$	−1.42596	+	2.46984i	−0.0846152	+	0.146558i
$285$	−0.626754	−	1.23919i	−0.0371257	−	0.0734033i
$286$	−1.18851	−	2.05857i	−0.0702783	−	0.121726i
$287$	1.26124			0.0744489
$288$	−22.0510	−	2.45062i	−1.29937	−	0.144404i
$289$	17.2873			1.01690
$290$	−0.0877817	−	0.152042i	−0.00515472	−	0.00892823i
$291$	15.2583	+	0.845255i	0.894455	+	0.0495498i
$292$	8.28521	−	14.3504i	0.484855	−	0.839794i
$293$	−13.8267	+	23.9485i	−0.807763	+	1.39909i	0.106646	+	0.994297i	$0.465989\pi$
$293$	−13.8267	+	23.9485i	−0.807763	+	1.39909i	−0.914410	+	0.404790i	$0.867345\pi$
$294$	9.78653	−	14.9721i	0.570762	−	0.873189i
$295$	−0.445689	−	0.771956i	−0.0259490	−	0.0449450i
$296$	5.09539			0.296164
$297$	−1.04065	−	2.78516i	−0.0603845	−	0.161611i
$298$	−19.3157			−1.11893
$299$	−4.86155	−	8.42044i	−0.281150	−	0.486967i
$300$	7.71426	−	11.8018i	0.445383	−	0.681376i
$301$	−3.88085	+	6.72182i	−0.223688	+	0.387439i
$302$	−3.27615	+	5.67446i	−0.188521	+	0.326529i
$303$	12.3970	+	0.686753i	0.712191	+	0.0394530i
$304$	−8.15336	−	14.1220i	−0.467627	−	0.809954i
$305$	−0.00713780			−0.000408709
$306$	19.8738	−	27.0139i	1.13611	−	1.54428i
$307$	−29.9948			−1.71189			−0.855947	−	0.517064i	$-0.827025\pi$
$307$	−29.9948			−1.71189			−0.855947	+	0.517064i	$0.827025\pi$
$308$	0.593496	+	1.02797i	0.0338176	+	0.0585738i
$309$	9.66079	+	19.1009i	0.549583	+	1.08661i
$310$	1.56797	−	2.71580i	0.0890546	−	0.154247i
$311$	−8.57983	+	14.8607i	−0.486518	+	0.842674i	−0.999880	−	0.0154986i	$-0.995066\pi$
$311$	−8.57983	+	14.8607i	−0.486518	+	0.842674i	0.513362	+	0.858172i	$0.328400\pi$
$312$	1.15362	+	2.28089i	0.0653109	+	0.129130i
$313$	−8.06666	−	13.9719i	−0.455955	−	0.789737i	0.542788	−	0.839870i	$-0.317369\pi$
$313$	−8.06666	−	13.9719i	−0.455955	−	0.789737i	−0.998743	+	0.0501330i	$0.984035\pi$
$314$	19.6638			1.10970
$315$	−0.342229	−	0.781156i	−0.0192824	−	0.0440131i
$316$	6.75168			0.379812
$317$	−13.7205	−	23.7646i	−0.770620	−	1.33475i	−0.937224	−	0.348729i	$-0.886613\pi$
$317$	−13.7205	−	23.7646i	−0.770620	−	1.33475i	0.166604	−	0.986024i	$-0.446720\pi$
$318$	−25.1737	−	1.39453i	−1.41167	−	0.0782016i
$319$	0.116727	−	0.202177i	0.00653544	−	0.0113197i
$320$	−0.557915	+	0.966338i	−0.0311884	+	0.0540199i
$321$	−15.3168	+	23.4326i	−0.854901	+	1.30788i
$322$	5.37965	+	9.31783i	0.299796	+	0.519262i
$323$	20.8287			1.15894
$324$	−4.40620	−	14.1319i	−0.244789	−	0.785106i
$325$	−10.7693			−0.597375
$326$	−11.5447	−	19.9960i	−0.639402	−	1.10748i
$327$	−7.88193	+	12.0583i	−0.435872	+	0.666824i
$328$	−0.339095	+	0.587329i	−0.0187234	+	0.0324298i
$329$	−0.644547	+	1.11639i	−0.0355350	+	0.0615485i
$330$	−0.425813	−	0.0235886i	−0.0234402	−	0.00129851i
$331$	16.2937	+	28.2216i	0.895584	+	1.55120i	0.833080	+	0.553152i	$0.186575\pi$
$331$	16.2937	+	28.2216i	0.895584	+	1.55120i	0.0625041	+	0.998045i	$0.480091\pi$
$332$	−9.73993			−0.534548
$333$	9.04483	+	20.6453i	0.495654	+	1.13136i
$334$	19.1903			1.05005
$335$	−0.180278	−	0.312250i	−0.00984963	−	0.0170601i
$336$	−4.51989	−	8.93652i	−0.246580	−	0.487527i
$337$	−3.04429	+	5.27286i	−0.165833	+	0.287231i	−0.936951	−	0.349462i	$-0.886365\pi$
$337$	−3.04429	+	5.27286i	−0.165833	+	0.287231i	0.771118	+	0.636692i	$0.219698\pi$
$338$	7.88959	−	13.6652i	0.429137	−	0.743287i
$339$	−14.0032	−	27.6865i	−0.760549	−	1.50372i
$340$	−1.08539	−	1.87994i	−0.0588633	−	0.101954i
$341$	4.16998			0.225817
$342$	12.0729	−	16.4103i	0.652826	−	0.887368i
$343$	15.6511			0.845080
$344$	−2.08679	−	3.61442i	−0.112512	−	0.194877i
$345$	−1.74176	−	0.0964878i	−0.0937734	−	0.00519473i
$346$	0.201876	−	0.349660i	0.0108529	−	0.0187979i
$347$	6.74382	−	11.6806i	0.362027	−	0.627050i	−0.626267	−	0.779609i	$-0.715418\pi$
$347$	6.74382	−	11.6806i	0.362027	−	0.627050i	0.988294	+	0.152559i	$0.0487514\pi$
$348$	0.635938	−	0.972899i	0.0340899	−	0.0521528i
$349$	−0.664107	−	1.15027i	−0.0355489	−	0.0615724i	0.847704	−	0.530470i	$-0.177985\pi$
$349$	−0.664107	−	1.15027i	−0.0355489	−	0.0615724i	−0.883252	+	0.468898i	$0.844651\pi$
$350$	11.9170			0.636993
$351$	−7.19381	+	8.72299i	−0.383977	+	0.465599i
$352$	−4.23173			−0.225552
$353$	−4.03798	−	6.99399i	−0.214920	−	0.372253i	0.738328	−	0.674442i	$-0.235616\pi$
$353$	−4.03798	−	6.99399i	−0.214920	−	0.372253i	−0.953248	+	0.302189i	$0.902282\pi$
$354$	7.15498	−	10.9461i	0.380283	−	0.581781i
$355$	0.195410	−	0.338461i	0.0103713	−	0.0179636i
$356$	9.42369	−	16.3223i	0.499454	−	0.865080i
$357$	12.7721	+	0.707528i	0.675969	+	0.0374464i
$358$	6.46416	+	11.1963i	0.341642	+	0.591741i
$359$	4.50619			0.237827			0.118914	−	0.992905i	$-0.462059\pi$
$359$	4.50619			0.237827			0.118914	+	0.992905i	$0.462059\pi$
$360$	0.455775	+	0.0506522i	0.0240215	+	0.00266961i
$361$	−6.34707			−0.334057
$362$	−5.01073	−	8.67885i	−0.263358	−	0.456150i
$363$	8.34311	+	16.4956i	0.437899	+	0.865795i
$364$	2.25698	−	3.90920i	0.118298	−	0.204898i
$365$	−1.13539	+	1.96655i	−0.0594289	+	0.102934i
$366$	−0.0472621	−	0.0934445i	−0.00247043	−	0.00488442i
$367$	9.76963	+	16.9215i	0.509970	+	0.883294i	0.999933	+	0.0115512i	$0.00367695\pi$
$367$	9.76963	+	16.9215i	0.509970	+	0.883294i	−0.489963	+	0.871743i	$0.662990\pi$
$368$	−20.4843			−1.06782
$369$	−2.98164	−	0.331363i	−0.155218	−	0.0172500i
$370$	3.23300			0.168076
$371$	−4.80823	−	8.32810i	−0.249631	−	0.432373i
$372$	20.7294	+	1.14834i	1.07477	+	0.0595386i
$373$	14.9523	−	25.8982i	0.774202	−	1.34096i	−0.161041	−	0.986948i	$-0.551485\pi$
$373$	14.9523	−	25.8982i	0.774202	−	1.34096i	0.935242	−	0.354009i	$-0.115182\pi$
$374$	3.19828	−	5.53959i	0.165379	−	0.286445i
$375$	−2.12514	+	3.25118i	−0.109742	+	0.167890i
$376$	−0.346582	−	0.600298i	−0.0178736	−	0.0309580i
$377$	−0.887788			−0.0457234
$378$	7.96047	−	9.65262i	0.409442	−	0.496477i
$379$	−16.3888			−0.841837			−0.420919	−	0.907098i	$-0.638292\pi$
$379$	−16.3888			−0.841837			−0.420919	+	0.907098i	$0.638292\pi$
$380$	−0.659346	−	1.14202i	−0.0338237	−	0.0585844i
$381$	−9.90385	+	15.1515i	−0.507390	+	0.776237i
$382$	10.1911	−	17.6515i	0.521423	−	0.903131i
$383$	−0.309153	+	0.535469i	−0.0157970	+	0.0273612i	−0.873816	−	0.486257i	$-0.838362\pi$
$383$	−0.309153	+	0.535469i	−0.0157970	+	0.0273612i	0.858019	+	0.513618i	$0.171695\pi$
$384$	9.23488	+	0.511581i	0.471265	+	0.0261065i
$385$	−0.0813314	−	0.140870i	−0.00414503	−	0.00717940i
$386$	2.58995			0.131825
$387$	10.9405	−	14.8711i	0.556138	−	0.755942i
$388$	14.5115			0.736712
$389$	14.3497	+	24.8544i	0.727557	+	1.26017i	0.957913	+	0.287060i	$0.0926778\pi$
$389$	14.3497	+	24.8544i	0.727557	+	1.26017i	−0.230355	+	0.973107i	$0.573989\pi$
$390$	0.731966	+	1.44721i	0.0370645	+	0.0732823i
$391$	13.0824	−	22.6594i	0.661605	−	1.14593i
$392$	−1.83425	+	3.17702i	−0.0926438	+	0.160464i
$393$	−3.98718	−	7.88328i	−0.201127	−	0.397659i
$394$	−6.38952	−	11.0670i	−0.321900	−	0.557546i
$395$	−0.925235			−0.0465536
$396$	−1.13298	−	2.58609i	−0.0569344	−	0.129956i
$397$	14.8778			0.746694			0.373347	−	0.927692i	$-0.378210\pi$
$397$	14.8778			0.746694			0.373347	+	0.927692i	$0.378210\pi$
$398$	20.5271	+	35.5540i	1.02893	+	1.78216i
$399$	7.75871	+	0.429806i	0.388422	+	0.0215172i
$400$	−11.3442	+	19.6488i	−0.567212	+	0.982441i
$401$	−4.63874	+	8.03453i	−0.231648	+	0.401225i	−0.958293	−	0.285787i	$-0.907745\pi$
$401$	−4.63874	+	8.03453i	−0.231648	+	0.401225i	0.726646	+	0.687013i	$0.241078\pi$
$402$	2.89414	−	4.42764i	0.144346	−	0.220830i
$403$	−7.92890	−	13.7332i	−0.394966	−	0.684102i
$404$	11.7903			0.586591
$405$	0.603816	+	1.93660i	0.0300038	+	0.0962306i
$406$	0.982401			0.0487558
$407$	2.14952	+	3.72308i	0.106548	+	0.184546i
$408$	−3.76334	+	5.75740i	−0.186313	+	0.285034i
$409$	9.93887	−	17.2146i	0.491446	−	0.851209i	−0.508506	−	0.861059i	$-0.669802\pi$
$409$	9.93887	−	17.2146i	0.491446	−	0.851209i	0.999951	+	0.00984972i	$0.00313531\pi$
$410$	−0.215154	+	0.372657i	−0.0106257	+	0.0184042i
$411$	−27.7886	−	1.53939i	−1.37071	−	0.0759327i
$412$	10.1632	+	17.6031i	0.500703	+	0.867243i
$413$	4.98789			0.245438
$414$	−10.2697	−	23.4412i	−0.504729	−	1.15207i
$415$	1.33474			0.0655197
$416$	8.04631	+	13.9366i	0.394503	+	0.683299i
$417$	14.5912	+	28.8491i	0.714534	+	1.41274i
$418$	1.94288	−	3.36516i	0.0950292	−	0.164595i
$419$	5.45511	−	9.44852i	0.266499	−	0.461591i	−0.701456	−	0.712713i	$-0.747466\pi$
$419$	5.45511	−	9.44852i	0.266499	−	0.461591i	0.967955	+	0.251122i	$0.0807996\pi$
$420$	−0.365514	−	0.722679i	−0.0178353	−	0.0352631i
$421$	−4.44066	−	7.69146i	−0.216425	−	0.374859i	0.737288	−	0.675579i	$-0.236106\pi$
$421$	−4.44066	−	7.69146i	−0.216425	−	0.374859i	−0.953712	+	0.300720i	$0.902773\pi$
$422$	−43.2136			−2.10361
$423$	1.81705	−	2.46986i	0.0883478	−	0.120089i
$424$	5.17091			0.251122
$425$	−14.4901	−	25.0976i	−0.702873	−	1.21741i
$426$	5.72485	+	0.317137i	0.277370	+	0.0153653i
$427$	0.0199705	−	0.0345900i	0.000966442	−	0.00167393i
$428$	−13.2919	+	23.0222i	−0.642487	+	1.11282i
$429$	−1.17993	+	1.80513i	−0.0569674	+	0.0871524i
$430$	−1.32406	−	2.29333i	−0.0638516	−	0.110594i
$431$	40.3474			1.94347			0.971733	−	0.236081i	$-0.0758630\pi$
$431$	40.3474			1.94347			0.971733	+	0.236081i	$0.0758630\pi$
$432$	8.33738	+	22.3139i	0.401133	+	1.07358i
$433$	23.9799			1.15240			0.576200	−	0.817309i	$-0.304535\pi$
$433$	23.9799			1.15240			0.576200	+	0.817309i	$0.304535\pi$
$434$	8.77389	+	15.1968i	0.421160	+	0.729471i
$435$	−0.0871475	+	0.133324i	−0.00417840	+	0.00639239i
$436$	−6.83991	+	11.8471i	−0.327572	+	0.567372i
$437$	7.94723	−	13.7650i	0.380167	−	0.658469i
$438$	−33.2629	−	1.84265i	−1.58936	−	0.0880452i
$439$	4.21991	+	7.30911i	0.201406	+	0.348845i	0.948982	−	0.315332i	$-0.102116\pi$
$439$	4.21991	+	7.30911i	0.201406	+	0.348845i	−0.747576	+	0.664176i	$0.768782\pi$
$440$	0.0874662			0.00416979
$441$	−16.1285	−	1.79243i	−0.768024	−	0.0853537i
$442$	−24.3252			−1.15703
$443$	12.4779	+	21.6124i	0.592844	+	1.02684i	0.993847	+	0.110760i	$0.0353284\pi$
$443$	12.4779	+	21.6124i	0.592844	+	1.02684i	−0.401003	+	0.916077i	$0.631338\pi$
$444$	9.66025	+	19.0998i	0.458455	+	0.906437i
$445$	−1.29140	+	2.23677i	−0.0612183	+	0.106033i
$446$	11.6012	−	20.0939i	0.549335	−	0.951476i
$447$	7.90923	+	15.6378i	0.374094	+	0.739641i
$448$	−3.12193	−	5.40734i	−0.147497	−	0.255473i
$449$	−14.0468			−0.662912			−0.331456	−	0.943471i	$-0.607540\pi$
$449$	−14.0468			−0.662912			−0.331456	+	0.943471i	$0.607540\pi$
$450$	−28.1725	−	3.13093i	−1.32806	−	0.147593i
$451$	−0.572197			−0.0269437
$452$	−14.7314	−	25.5155i	−0.692905	−	1.20015i
$453$	5.93546	+	0.328804i	0.278872	+	0.0154486i
$454$	−8.00539	+	13.8657i	−0.375711	+	0.650751i
$455$	−0.309291	+	0.535707i	−0.0144998	+	0.0251144i
$456$	−2.28614	+	3.49748i	−0.107058	+	0.163785i
$457$	8.41329	+	14.5722i	0.393557	+	0.681661i	0.992916	−	0.118820i	$-0.0379110\pi$
$457$	8.41329	+	14.5722i	0.393557	+	0.681661i	−0.599359	+	0.800481i	$0.704578\pi$
$458$	34.6195			1.61766
$459$	−30.0079	−	5.02820i	−1.40065	−	0.234696i
$460$	−1.65652			−0.0772359
$461$	−17.8734	−	30.9576i	−0.832446	−	1.44184i	−0.896093	−	0.443867i	$-0.853606\pi$
$461$	−17.8734	−	30.9576i	−0.832446	−	1.44184i	0.0636465	−	0.997973i	$-0.479727\pi$
$462$	1.30567	−	1.99750i	0.0607455	−	0.0929323i
$463$	−10.5384	+	18.2531i	−0.489761	+	0.848292i	−0.999931	−	0.0117825i	$-0.996249\pi$
$463$	−10.5384	+	18.2531i	−0.489761	+	0.848292i	0.510169	+	0.860074i	$0.329583\pi$
$464$	−0.935182	+	1.61978i	−0.0434147	+	0.0751965i
$465$	−2.84072	−	0.157366i	−0.131735	−	0.00729767i
$466$	12.3785	+	21.4401i	0.573422	+	0.993195i
$467$	12.3221			0.570198			0.285099	−	0.958498i	$-0.407974\pi$
$467$	12.3221			0.570198			0.285099	+	0.958498i	$0.407974\pi$
$468$	−6.36265	+	8.64857i	−0.294114	+	0.399780i
$469$	2.01756			0.0931625
$470$	−0.219905	−	0.380886i	−0.0101434	−	0.0175690i
$471$	−8.05178	−	15.9196i	−0.371006	−	0.733537i
$472$	−1.34103	+	2.32273i	−0.0617260	+	0.106912i
$473$	1.76065	−	3.04953i	0.0809547	−	0.140218i
$474$	−6.12634	−	12.1127i	−0.281392	−	0.556355i
$475$	−8.80238	−	15.2462i	−0.403881	−	0.699542i
$476$	12.1470			0.556757
$477$	9.17888	+	20.9513i	0.420272	+	0.959294i
$478$	48.6367			2.22459
$479$	15.3524	+	26.5912i	0.701470	+	1.21498i	0.967951	+	0.251141i	$0.0808057\pi$
$479$	15.3524	+	26.5912i	0.701470	+	1.21498i	−0.266481	+	0.963840i	$0.585861\pi$
$480$	2.88278	+	0.159696i	0.131580	+	0.00728911i
$481$	8.17431	−	14.1583i	0.372716	−	0.645564i
$482$	3.80771	−	6.59515i	0.173436	−	0.300401i
$483$	5.34079	−	8.17068i	0.243014	−	0.371779i
$484$	8.77695	+	15.2021i	0.398952	+	0.691006i
$485$	−1.98863			−0.0902990
$486$	−21.3550	+	20.7278i	−0.968680	+	0.940234i
$487$	−42.3595			−1.91949			−0.959745	−	0.280873i	$-0.909376\pi$
$487$	−42.3595			−1.91949			−0.959745	+	0.280873i	$0.909376\pi$
$488$	0.0107385	+	0.0185995i	0.000486107	+	0.000841962i
$489$	−11.4613	+	17.5342i	−0.518298	+	0.792925i
$490$	−1.16382	+	2.01580i	−0.0525762	+	0.0910646i
$491$	−2.86475	+	4.96189i	−0.129284	+	0.223927i	−0.923399	−	0.383840i	$-0.874601\pi$
$491$	−2.86475	+	4.96189i	−0.129284	+	0.223927i	0.794115	+	0.607767i	$0.207935\pi$
$492$	−2.84445	−	0.157573i	−0.128238	−	0.00710394i
$493$	−1.19452	−	2.06896i	−0.0537983	−	0.0931814i
$494$	−14.7769			−0.664846
$495$	0.155261	+	0.354392i	0.00697847	+	0.0159287i
$496$	−33.4087			−1.50009
$497$	1.09346	+	1.89393i	0.0490484	+	0.0849543i
$498$	8.83781	+	17.4737i	0.396032	+	0.783016i
$499$	−3.20896	+	5.55809i	−0.143653	+	0.248814i	−0.928870	−	0.370407i	$-0.879218\pi$
$499$	−3.20896	+	5.55809i	−0.143653	+	0.248814i	0.785217	+	0.619221i	$0.212552\pi$
$500$	−1.84419	+	3.19423i	−0.0824747	+	0.142850i
$501$	−7.85786	−	15.5362i	−0.351063	−	0.694107i
$502$	−6.59571	−	11.4241i	−0.294381	−	0.509883i
$503$	28.1661			1.25586			0.627931	−	0.778269i	$-0.283902\pi$
$503$	28.1661			1.25586			0.627931	+	0.778269i	$0.283902\pi$
$504$	−1.52065	+	2.06698i	−0.0677353	+	0.0920707i
$505$	−1.61572			−0.0718987
$506$	−2.44062	−	4.22728i	−0.108499	−	0.187925i
$507$	−14.2937	−	0.791822i	−0.634806	−	0.0351661i
$508$	−8.59453	+	14.8862i	−0.381320	+	0.660466i
$509$	−14.8928	+	25.7951i	−0.660113	+	1.14335i	0.320473	+	0.947258i	$0.396158\pi$
$509$	−14.8928	+	25.7951i	−0.660113	+	1.14335i	−0.980586	+	0.196091i	$0.937175\pi$
$510$	−2.38782	+	3.65304i	−0.105734	+	0.161759i
$511$	−6.35329	−	11.0042i	−0.281053	−	0.486798i
$512$	27.6854			1.22353
$513$	−18.2291	−	3.05451i	−0.804833	−	0.134860i
$514$	41.9990			1.85250
$515$	−1.39274	−	2.41229i	−0.0613713	−	0.106298i
$516$	9.59217	−	14.6747i	0.422272	−	0.646019i
$517$	0.292416	−	0.506479i	0.0128604	−	0.0222749i
$518$	−9.04546	+	15.6672i	−0.397435	+	0.688377i
$519$	−0.365743	−	0.0202609i	−0.0160543	−	0.000889356i
$520$	−0.166310	−	0.288058i	−0.00729319	−	0.0126322i
$521$	38.5304			1.68805			0.844023	−	0.536307i	$-0.180181\pi$
$521$	38.5304			1.68805			0.844023	+	0.536307i	$0.180181\pi$
$522$	−2.32245	−	0.258103i	−0.101651	−	0.0112969i
$523$	−39.9146			−1.74534			−0.872672	−	0.488308i	$-0.837614\pi$
$523$	−39.9146			−1.74534			−0.872672	+	0.488308i	$0.837614\pi$
$524$	−4.19452	−	7.26512i	−0.183238	−	0.317378i
$525$	−4.87968	−	9.64789i	−0.212967	−	0.421068i
$526$	2.94734	−	5.10493i	0.128510	−	0.222586i
$527$	21.3366	−	36.9561i	0.929437	−	1.60983i
$528$	2.05057	+	4.05429i	0.0892395	+	0.176440i
$529$	1.51679	+	2.62715i	0.0659472	+	0.114224i
$530$	3.28091			0.142514
$531$	−11.7916	−	1.31045i	−0.511713	−	0.0568688i
$532$	7.37901			0.319921
$533$	1.08799	+	1.88445i	0.0471260	+	0.0816246i
$534$	−37.8336	−	2.09585i	−1.63722	−	0.0906963i
$535$	1.82149	−	3.15491i	0.0787498	−	0.136399i
$536$	−0.542437	+	0.939529i	−0.0234297	+	0.0405815i
$537$	6.41746	−	9.81785i	0.276934	−	0.423671i
$538$	−17.7818	−	30.7990i	−0.766628	−	1.32784i
$539$	−3.09516			−0.133318
$540$	0.674228	+	1.80448i	0.0290141	+	0.0776524i
$541$	−4.19484			−0.180350			−0.0901751	−	0.995926i	$-0.528743\pi$
$541$	−4.19484			−0.180350			−0.0901751	+	0.995926i	$0.528743\pi$
$542$	26.0011	+	45.0351i	1.11684	+	1.93443i
$543$	−4.97453	+	7.61036i	−0.213478	+	0.326592i
$544$	−21.6526	+	37.5034i	−0.928346	+	1.60794i
$545$	0.937326	−	1.62350i	0.0401506	−	0.0695429i
$546$	−9.06115	−	0.501956i	−0.387781	−	0.0214818i
$547$	−7.81809	−	13.5413i	−0.334277	−	0.578985i	0.649069	−	0.760730i	$-0.275159\pi$
$547$	−7.81809	−	13.5413i	−0.334277	−	0.578985i	−0.983346	+	0.181745i	$0.941826\pi$
$548$	−26.4287			−1.12898
$549$	−0.0562991	+	0.0765256i	−0.00240278	+	0.00326603i
$550$	−5.40648			−0.230533
$551$	−0.725639	−	1.25684i	−0.0309133	−	0.0535433i
$552$	2.36897	+	4.68382i	0.100830	+	0.199356i
$553$	2.58867	−	4.48371i	0.110082	−	0.190667i
$554$	−12.0327	+	20.8413i	−0.511221	+	0.885460i
$555$	−1.32382	−	2.61739i	−0.0561930	−	0.111102i
$556$	15.3499	+	26.5869i	0.650983	+	1.12753i
$557$	−23.9951			−1.01670			−0.508352	−	0.861150i	$-0.669745\pi$
$557$	−23.9951			−1.01670			−0.508352	+	0.861150i	$0.669745\pi$
$558$	−16.7493	−	38.2312i	−0.709055	−	1.61846i
$559$	−13.3910			−0.566377
$560$	0.651604	+	1.12861i	0.0275353	+	0.0476926i
$561$	−5.79438	−	0.320989i	−0.244639	−	0.0135522i
$562$	−11.1293	+	19.2766i	−0.469462	+	0.813132i
$563$	15.3973	−	26.6689i	0.648919	−	1.12396i	−0.334463	−	0.942409i	$-0.608555\pi$
$563$	15.3973	−	26.6689i	0.648919	−	1.12396i	0.983382	−	0.181551i	$-0.0581117\pi$
$564$	1.59311	−	2.43724i	0.0670819	−	0.102626i
$565$	2.01875	+	3.49658i	0.0849295	+	0.147102i
$566$	47.4138			1.99295
$567$	−11.0742	−	2.49223i	−0.465074	−	0.104664i
$568$	−1.17594			−0.0493413
$569$	20.9120	+	36.2207i	0.876679	+	1.51845i	0.854964	+	0.518688i	$0.173579\pi$
$569$	20.9120	+	36.2207i	0.876679	+	1.51845i	0.0217149	+	0.999764i	$0.493087\pi$
$570$	−1.45054	+	2.21913i	−0.0607565	+	0.0929492i
$571$	12.3073	−	21.3170i	0.515046	−	0.892087i	−0.484801	−	0.874624i	$-0.661108\pi$
$571$	12.3073	−	21.3170i	0.515046	−	0.892087i	0.999848	−	0.0174622i	$-0.00555867\pi$
$572$	−1.02394	+	1.77351i	−0.0428129	+	0.0741542i
$573$	−18.4634	−	1.02281i	−0.771321	−	0.0427285i
$574$	−1.20394	−	2.08528i	−0.0502514	−	0.0870379i
$575$	−22.1149			−0.922255
$576$	5.95975	+	13.6034i	0.248323	+	0.566810i
$577$	−24.1285			−1.00448			−0.502242	−	0.864727i	$-0.667491\pi$
$577$	−24.1285			−1.00448			−0.502242	+	0.864727i	$0.667491\pi$
$578$	−16.5018	−	28.5820i	−0.686386	−	1.18886i
$579$	−1.06051	−	2.09679i	−0.0440732	−	0.0871396i
$580$	−0.0756263	+	0.130989i	−0.00314021	+	0.00543900i
$581$	−3.73440	+	6.46818i	−0.154929	+	0.268345i
$582$	−13.1675	−	26.0341i	−0.545809	−	1.07915i
$583$	2.18138	+	3.77826i	0.0903435	+	0.156480i
$584$	6.83252			0.282732
$585$	0.871924	−	1.18518i	0.0360496	−	0.0490012i
$586$	52.7938			2.18089
$587$	−2.77389	−	4.80452i	−0.114491	−	0.198304i	0.803085	−	0.595864i	$-0.203190\pi$
$587$	−2.77389	−	4.80452i	−0.114491	−	0.198304i	−0.917576	+	0.397560i	$0.869857\pi$
$588$	−15.3864	−	0.852354i	−0.634525	−	0.0351505i
$589$	12.9615	−	22.4499i	0.534068	−	0.925033i
$590$	−0.850876	+	1.47376i	−0.0350300	+	0.0606738i
$591$	−6.34336	+	9.70448i	−0.260931	+	0.399189i
$592$	−17.2214	−	29.8283i	−0.707794	−	1.22594i
$593$	−30.9119			−1.26940			−0.634699	−	0.772759i	$-0.718876\pi$
$593$	−30.9119			−1.26940			−0.634699	+	0.772759i	$0.718876\pi$
$594$	−3.61148	+	4.37917i	−0.148181	+	0.179679i
$595$	−1.66460			−0.0682419
$596$	8.32051	+	14.4116i	0.340822	+	0.590320i
$597$	20.3788	−	31.1768i	0.834049	−	1.27598i
$598$	−9.28131	+	16.0757i	−0.379541	+	0.657384i
$599$	−8.33536	+	14.4373i	−0.340574	+	0.589891i	−0.984539	−	0.175163i	$-0.943955\pi$
$599$	−8.33536	+	14.4373i	−0.340574	+	0.589891i	0.643966	+	0.765054i	$0.277288\pi$
$600$	5.80472	+	0.321561i	0.236977	+	0.0131277i
$601$	0.493032	+	0.853957i	0.0201112	+	0.0348336i	0.875906	−	0.482482i	$-0.160265\pi$
$601$	0.493032	+	0.853957i	0.0201112	+	0.0348336i	−0.855795	+	0.517316i	$0.826931\pi$
$602$	14.8181			0.603939
$603$	−4.76963	−	0.530068i	−0.194234	−	0.0215861i
$604$	5.64499			0.229691
$605$	−1.20277	−	2.08326i	−0.0488997	−	0.0846968i
$606$	−10.6983	−	21.1522i	−0.434589	−	0.859250i
$607$	−23.2370	+	40.2477i	−0.943161	+	1.63360i	−0.183769	+	0.982970i	$0.558830\pi$
$607$	−23.2370	+	40.2477i	−0.943161	+	1.63360i	−0.759392	+	0.650633i	$0.774504\pi$
$608$	−13.1534	+	22.7824i	−0.533441	+	0.923947i
$609$	−0.402265	−	0.795340i	−0.0163006	−	0.0322288i
$610$	0.00681348	+	0.0118013i	0.000275870	+	0.000477821i
$611$	−2.22402			−0.0899744
$612$	−28.7161	−	3.19135i	−1.16078	−	0.129003i
$613$	25.0158			1.01038			0.505189	−	0.863009i	$-0.331423\pi$
$613$	25.0158			1.01038			0.505189	+	0.863009i	$0.331423\pi$
$614$	28.6319	+	49.5920i	1.15549	+	2.00137i
$615$	0.389798	+	0.0215935i	0.0157182	+	0.000870732i
$616$	−0.244718	+	0.423863i	−0.00985996	+	0.0170779i
$617$	9.75785	−	16.9011i	0.392836	−	0.680412i	−0.599986	−	0.800010i	$-0.704827\pi$
$617$	9.75785	−	16.9011i	0.392836	−	0.680412i	0.992822	+	0.119598i	$0.0381606\pi$
$618$	22.3586	−	34.2057i	0.899397	−	1.37596i
$619$	13.1489	+	22.7745i	0.528499	+	0.915386i	0.999448	+	0.0332261i	$0.0105781\pi$
$619$	13.1489	+	22.7745i	0.528499	+	0.915386i	−0.470949	+	0.882160i	$0.656089\pi$
$620$	−2.70169			−0.108503
$621$	−14.7725	+	17.9127i	−0.592802	+	0.718813i
$622$	32.7600			1.31356
$623$	−7.22630	−	12.5163i	−0.289516	−	0.501456i
$624$	9.45325	−	14.4622i	0.378433	−	0.578951i
$625$	−12.1203	+	20.9929i	−0.484811	+	0.839717i
$626$	−15.4003	+	26.6741i	−0.615519	+	1.06611i
$627$	−3.51995	−	0.194993i	−0.140573	−	0.00778727i
$628$	−8.47047	−	14.6713i	−0.338009	−	0.585448i
$629$	43.9940			1.75416
$630$	−0.964846	+	1.31149i	−0.0384404	+	0.0522509i
$631$	13.9821			0.556620			0.278310	−	0.960491i	$-0.410226\pi$
$631$	13.9821			0.556620			0.278310	+	0.960491i	$0.410226\pi$
$632$	1.39197	+	2.41096i	0.0553695	+	0.0959028i
$633$	17.6947	+	34.9852i	0.703302	+	1.39054i
$634$	−26.1942	+	45.3696i	−1.04030	+	1.80186i
$635$	1.17777	−	2.03997i	0.0467386	−	0.0809536i
$636$	9.80342	+	19.3829i	0.388731	+	0.768581i
$637$	5.88521	+	10.1935i	0.233181	+	0.403881i
$638$	−0.445692			−0.0176451
$639$	−2.08741	−	4.76462i	−0.0825766	−	0.188486i
$640$	−1.20359			−0.0475762
$641$	−23.1501	−	40.0972i	−0.914374	−	1.58374i	−0.807815	−	0.589436i	$-0.799350\pi$
$641$	−23.1501	−	40.0972i	−0.914374	−	1.58374i	−0.106559	−	0.994306i	$-0.533983\pi$
$642$	53.3633	+	2.95614i	2.10608	+	0.116670i
$643$	13.0415	−	22.5886i	0.514307	−	0.890807i	−0.485555	−	0.874206i	$-0.661382\pi$
$643$	13.0415	−	22.5886i	0.514307	−	0.890807i	0.999862	−	0.0166003i	$-0.00528428\pi$
$644$	4.63471	−	8.02756i	0.182633	−	0.316330i
$645$	−1.31449	+	2.01099i	−0.0517580	+	0.0791827i
$646$	−19.8823	−	34.4372i	−0.782259	−	1.35491i
$647$	38.0322			1.49520			0.747600	−	0.664149i	$-0.231206\pi$
$647$	38.0322			1.49520			0.747600	+	0.664149i	$0.231206\pi$
$648$	4.13796	−	4.48693i	0.162554	−	0.176263i
$649$	−2.26289			−0.0888261
$650$	10.2800	+	17.8055i	0.403215	+	0.698389i
$651$	8.71051	−	13.3259i	0.341392	−	0.522283i
$652$	−9.94607	+	17.2271i	−0.389518	+	0.674665i
$653$	9.10940	−	15.7779i	0.356478	−	0.617439i	−0.630891	−	0.775871i	$-0.717311\pi$
$653$	9.10940	−	15.7779i	0.356478	−	0.617439i	0.987370	+	0.158433i	$0.0506440\pi$
$654$	27.4604	+	1.52121i	1.07379	+	0.0594841i
$655$	0.574807	+	0.995595i	0.0224596	+	0.0389011i
$656$	4.58428			0.178986
$657$	12.1284	+	27.6837i	0.473174	+	1.08004i
$658$	2.46104			0.0959415
$659$	18.7384	+	32.4558i	0.729943	+	1.26430i	0.956907	+	0.290395i	$0.0937866\pi$
$659$	18.7384	+	32.4558i	0.729943	+	1.26430i	−0.226964	+	0.973903i	$0.572880\pi$
$660$	0.165825	+	0.327862i	0.00645474	+	0.0127620i
$661$	1.73073	−	2.99771i	0.0673176	−	0.116597i	−0.830402	−	0.557165i	$-0.811889\pi$
$661$	1.73073	−	2.99771i	0.0673176	−	0.116597i	0.897720	+	0.440567i	$0.145223\pi$
$662$	31.1068	−	53.8785i	1.20900	−	2.09405i
$663$	9.96044	+	19.6933i	0.386832	+	0.764826i
$664$	−2.00804	−	3.47803i	−0.0779272	−	0.134974i
$665$	−1.01120			−0.0392128
$666$	25.5001	−	34.6615i	0.988109	−	1.34311i
$667$	−1.82308			−0.0705899
$668$	−8.26647	−	14.3180i	−0.319839	−	0.553978i
$669$	−21.0182	−	1.16434i	−0.812610	−	0.0450158i
$670$	−0.344173	+	0.596126i	−0.0132966	+	0.0230303i
$671$	−0.00906016	+	0.0156927i	−0.000349764	+	0.000605808i
$672$	−8.83950	+	13.5232i	−0.340991	+	0.521670i
$673$	−6.72374	−	11.6459i	−0.259181	−	0.448915i	0.706842	−	0.707372i	$-0.250119\pi$
$673$	−6.72374	−	11.6459i	−0.259181	−	0.448915i	−0.966023	+	0.258457i	$0.916786\pi$
$674$	11.6239			0.447734
$675$	9.00106	+	24.0901i	0.346451	+	0.927229i
$676$	−13.5942			−0.522853
$677$	15.4744	+	26.8024i	0.594729	+	1.03010i	0.993585	+	0.113087i	$0.0360740\pi$
$677$	15.4744	+	26.8024i	0.594729	+	1.03010i	−0.398856	+	0.917014i	$0.630593\pi$
$678$	−32.4085	+	49.5807i	−1.24464	+	1.90413i
$679$	5.56389	−	9.63695i	0.213523	−	0.369832i
$680$	0.447540	−	0.775162i	0.0171624	−	0.0297261i
$681$	14.5035	+	0.803444i	0.555775	+	0.0307880i
$682$	−3.98051	−	6.89444i	−0.152422	−	0.264002i
$683$	−23.0423			−0.881690			−0.440845	−	0.897583i	$-0.645321\pi$
$683$	−23.0423			−0.881690			−0.440845	+	0.897583i	$0.645321\pi$
$684$	−17.4444	−	1.93866i	−0.667002	−	0.0741267i
$685$	3.62172			0.138379
$686$	−14.9400	−	25.8768i	−0.570411	−	0.987980i
$687$	−14.1757	−	28.0275i	−0.540836	−	1.06932i
$688$	−14.1058	+	24.4320i	−0.537780	+	0.931461i
$689$	8.29546	−	14.3682i	0.316032	−	0.547383i
$690$	1.50310	+	2.97185i	0.0572219	+	0.113137i
$691$	−6.22546	−	10.7828i	−0.236828	−	0.410197i	0.722975	−	0.690875i	$-0.242774\pi$
$691$	−6.22546	−	10.7828i	−0.236828	−	0.410197i	−0.959802	+	0.280677i	$0.909441\pi$
$692$	−0.347844			−0.0132231
$693$	−2.15179	−	0.239137i	−0.0817398	−	0.00908408i
$694$	−25.7496			−0.977442
$695$	−2.10352	−	3.64341i	−0.0797911	−	0.138202i
$696$	0.478521	+	0.0265085i	0.0181383	+	0.00100480i
$697$	−2.92777	+	5.07104i	−0.110897	+	0.192079i
$698$	−1.26787	+	2.19601i	−0.0479894	+	0.0831201i
$699$	12.2890	−	18.8006i	0.464814	−	0.711103i
$700$	−5.13343	−	8.89136i	−0.194025	−	0.336062i
$701$	−8.66234			−0.327172			−0.163586	−	0.986529i	$-0.552306\pi$
$701$	−8.66234			−0.327172			−0.163586	+	0.986529i	$0.552306\pi$
$702$	21.2891	+	3.56726i	0.803506	+	0.134637i
$703$	26.7253			1.00796
$704$	1.41635	+	2.45318i	0.0533806	+	0.0924579i
$705$	−0.218316	+	0.333994i	−0.00822225	+	0.0125789i
$706$	−7.70902	+	13.3524i	−0.290133	+	0.502525i
$707$	4.52055	−	7.82983i	0.170013	−	0.294471i
$708$	−11.2491	−	0.623160i	−0.422766	−	0.0234198i
$709$	20.7191	+	35.8865i	0.778120	+	1.34774i	0.933024	+	0.359814i	$0.117160\pi$
$709$	20.7191	+	35.8865i	0.778120	+	1.34774i	−0.154904	+	0.987930i	$0.549507\pi$
$710$	−0.746127			−0.0280016
$711$	−7.29775	+	9.91961i	−0.273687	+	0.372014i
$712$	7.77138			0.291245
$713$	−16.2820	−	28.2013i	−0.609767	−	1.05615i
$714$	−11.0219	−	21.7921i	−0.412486	−	0.815549i
$715$	0.140318	−	0.243038i	0.00524759	−	0.00908910i
$716$	5.56905	−	9.64588i	0.208125	−	0.360483i
$717$	−19.9153	−	39.3757i	−0.743751	−	1.47051i
$718$	−4.30144	−	7.45031i	−0.160528	−	0.278043i
$719$	−3.31000			−0.123442			−0.0617211	−	0.998093i	$-0.519659\pi$
$719$	−3.31000			−0.123442			−0.0617211	+	0.998093i	$0.519659\pi$
$720$	−1.24391	−	2.83929i	−0.0463577	−	0.105814i
$721$	15.5867			0.580479
$722$	6.05868	+	10.4939i	0.225481	+	0.390544i
$723$	−6.89849	−	0.382153i	−0.256558	−	0.0142124i
$724$	−4.31688	+	7.47706i	−0.160436	+	0.277883i
$725$	−1.00962	+	1.74872i	−0.0374965	+	0.0649459i
$726$	19.3090	−	29.5402i	0.716625	−	1.09634i
$727$	7.69655	+	13.3308i	0.285449	+	0.494412i	0.972718	−	0.231991i	$-0.0745239\pi$
$727$	7.69655	+	13.3308i	0.285449	+	0.494412i	−0.687269	+	0.726403i	$0.741191\pi$
$728$	1.86125			0.0689824
$729$	25.5252	+	8.80125i	0.945379	+	0.325972i
$730$	4.33519			0.160453
$731$	−18.0175	−	31.2072i	−0.666401	−	1.15424i
$732$	−0.0493606	+	0.0755150i	−0.00182442	+	0.00279111i
$733$	−14.3136	+	24.7920i	−0.528687	+	0.915712i	0.470754	+	0.882265i	$0.343982\pi$
$733$	−14.3136	+	24.7920i	−0.528687	+	0.915712i	−0.999440	+	0.0334474i	$0.989351\pi$
$734$	18.6515	−	32.3053i	0.688438	−	1.19241i
$735$	2.10852	+	0.116805i	0.0777739	+	0.00430841i
$736$	16.5232	+	28.6189i	0.609052	+	1.05491i
$737$	−0.915322			−0.0337163
$738$	2.29831	+	5.24601i	0.0846019	+	0.193108i
$739$	26.7073			0.982443			0.491221	−	0.871035i	$-0.336551\pi$
$739$	26.7073			0.982443			0.491221	+	0.871035i	$0.336551\pi$
$740$	−1.39266	−	2.41215i	−0.0511951	−	0.0886725i
$741$	6.05073	+	11.9632i	0.222279	+	0.439480i
$742$	−9.17952	+	15.8994i	−0.336991	+	0.583685i
$743$	13.0323	−	22.5726i	0.478109	−	0.828108i	−0.521576	−	0.853205i	$-0.674656\pi$
$743$	13.0323	−	22.5726i	0.478109	−	0.828108i	0.999685	+	0.0250962i	$0.00798922\pi$
$744$	3.86365	+	7.63903i	0.141648	+	0.280060i
$745$	−1.14022	−	1.97493i	−0.0417746	−	0.0723557i
$746$	−57.0917			−2.09028
$747$	10.5277	−	14.3100i	0.385188	−	0.523574i
$748$	−5.51081			−0.201495
$749$	10.1925	+	17.6540i	0.372426	+	0.645061i
$750$	7.40392	+	0.410152i	0.270353	+	0.0149766i
$751$	−3.22948	+	5.59362i	−0.117845	+	0.204114i	−0.918914	−	0.394459i	$-0.870932\pi$
$751$	−3.22948	+	5.59362i	−0.117845	+	0.204114i	0.801068	+	0.598573i	$0.204265\pi$
$752$	−2.34275	+	4.05777i	−0.0854314	+	0.147972i
$753$	−6.54807	+	10.0177i	−0.238625	+	0.365063i
$754$	0.847450	+	1.46783i	0.0308623	+	0.0534551i
$755$	−0.773577			−0.0281533
$756$	−10.6309	−	1.78135i	−0.386644	−	0.0647869i
$757$	31.1435			1.13193			0.565965	−	0.824429i	$-0.308504\pi$
$757$	31.1435			1.13193			0.565965	+	0.824429i	$0.308504\pi$
$758$	15.6442	+	27.0965i	0.568222	+	0.984189i
$759$	−2.42299	+	3.70684i	−0.0879489	+	0.134550i
$760$	0.271870	−	0.470892i	0.00986174	−	0.0170810i
$761$	−4.91659	+	8.51579i	−0.178226	+	0.308697i	−0.941273	−	0.337646i	$-0.890369\pi$
$761$	−4.91659	+	8.51579i	−0.178226	+	0.308697i	0.763047	+	0.646343i	$0.223703\pi$
$762$	34.5047	+	1.91144i	1.24997	+	0.0692442i
$763$	5.24500	+	9.08461i	0.189882	+	0.328885i
$764$	−17.5598			−0.635293
$765$	3.93520	+	0.437335i	0.142277	+	0.0158119i
$766$	1.18043			0.0426505
$767$	4.30271	+	7.45251i	0.155362	+	0.269094i
$768$	−15.7095	−	31.0601i	−0.566867	−	1.12078i
$769$	−9.23495	+	15.9954i	−0.333021	+	0.576809i	−0.983103	−	0.183055i	$-0.941401\pi$
$769$	−9.23495	+	15.9954i	−0.333021	+	0.576809i	0.650082	+	0.759864i	$0.274735\pi$
$770$	−0.155272	+	0.268939i	−0.00559561	+	0.00969188i
$771$	−17.1974	−	34.0019i	−0.619348	−	1.22455i
$772$	−1.11566	−	1.93237i	−0.0401533	−	0.0695476i
$773$	2.33137			0.0838535			0.0419267	−	0.999121i	$-0.486650\pi$
$773$	2.33137			0.0838535			0.0419267	+	0.999121i	$0.486650\pi$
$774$	−35.0306	−	3.89310i	−1.25915	−	0.139935i
$775$	−36.0681			−1.29560
$776$	2.99179	+	5.18193i	0.107399	+	0.186020i
$777$	16.3878	+	0.907829i	0.587910	+	0.0325682i
$778$	27.3953	−	47.4501i	0.982171	−	1.70117i
$779$	−1.77855	+	3.08053i	−0.0637231	+	0.110372i
$780$	0.764465	−	1.16953i	0.0273722	−	0.0418758i
$781$	−0.496077	−	0.859231i	−0.0177510	−	0.0307457i
$782$	−49.9519			−1.78627
$783$	0.742017	+	1.98591i	0.0265175	+	0.0709706i
$784$	24.7976			0.885628
$785$	1.16077	+	2.01052i	0.0414298	+	0.0717585i
$786$	−9.22781	+	14.1173i	−0.329145	+	0.503548i
$787$	14.6463	−	25.3682i	0.522086	−	0.904279i	−0.477584	−	0.878586i	$-0.658487\pi$
$787$	14.6463	−	25.3682i	0.522086	−	0.904279i	0.999670	−	0.0256932i	$-0.00817930\pi$
$788$	−5.50475	+	9.53450i	−0.196099	+	0.339653i
$789$	−5.33974	−	0.295803i	−0.190100	−	0.0105309i
$790$	0.883196	+	1.52974i	0.0314227	+	0.0544257i
$791$	−22.5927			−0.803304
$792$	0.689885	−	0.937741i	0.0245140	−	0.0333212i
$793$	0.0689088			0.00244702
$794$	−14.2018	−	24.5982i	−0.504002	−	0.872958i
$795$	−1.34344	−	2.65619i	−0.0476469	−	0.0942052i
$796$	17.6847	−	30.6307i	0.626816	−	1.08568i
$797$	26.2344	−	45.4393i	0.929271	−	1.60954i	0.144726	−	0.989472i	$-0.453770\pi$
$797$	26.2344	−	45.4393i	0.929271	−	1.60954i	0.784545	−	0.620072i	$-0.212897\pi$
$798$	−6.69556	−	13.2382i	−0.237020	−	0.468626i
$799$	−2.99242	−	5.18302i	−0.105864	−	0.183362i
$800$	36.6022			1.29408
$801$	13.7950	+	31.4878i	0.487421	+	1.11257i
$802$	17.7119			0.625428
$803$	2.88234	+	4.99236i	0.101716	+	0.176176i
$804$	−4.55017	−	0.252064i	−0.160472	−	0.00888960i
$805$	−0.635131	+	1.10008i	−0.0223854	+	0.0387727i
$806$	−15.1373	+	26.2185i	−0.533187	+	0.923508i
$807$	−17.6533	+	27.0072i	−0.621427	+	0.950699i
$808$	2.43077	+	4.21022i	0.0855142	+	0.148115i
$809$	−40.4478			−1.42207			−0.711035	−	0.703157i	$-0.751773\pi$
$809$	−40.4478			−1.42207			−0.711035	+	0.703157i	$0.751773\pi$
$810$	2.62551	−	2.84693i	0.0922510	−	0.100031i
$811$	3.43456			0.120604			0.0603019	−	0.998180i	$-0.480794\pi$
$811$	3.43456			0.120604			0.0603019	+	0.998180i	$0.480794\pi$
$812$	−0.423183	−	0.732974i	−0.0148508	−	0.0257223i
$813$	25.8132	−	39.4907i	0.905309	−	1.38500i
$814$	4.10371	−	7.10783i	0.143835	−	0.249129i
$815$	1.36299	−	2.36076i	0.0477434	−	0.0826939i
$816$	46.4230	+	2.57167i	1.62513	+	0.0900266i
$817$	−10.9452	−	18.9576i	−0.382923	−	0.663243i
$818$	−37.9491			−1.32686
$819$	3.30390	+	7.54133i	0.115448	+	0.263515i
$820$	0.370721			0.0129462
$821$	−22.2964	−	38.6185i	−0.778150	−	1.34780i	−0.933007	−	0.359859i	$-0.882825\pi$
$821$	−22.2964	−	38.6185i	−0.778150	−	1.34780i	0.154857	−	0.987937i	$-0.450508\pi$
$822$	23.9808	+	47.4138i	0.836427	+	1.65375i
$823$	−8.28020	+	14.3417i	−0.288630	+	0.499921i	−0.973483	−	0.228760i	$-0.926533\pi$
$823$	−8.28020	+	14.3417i	−0.288630	+	0.499921i	0.684853	+	0.728681i	$0.259866\pi$
$824$	−4.19060	+	7.25833i	−0.145986	+	0.252856i
$825$	2.21380	+	4.37702i	0.0770745	+	0.152388i
$826$	−4.76126	−	8.24674i	−0.165665	−	0.286941i
$827$	−8.40405			−0.292238			−0.146119	−	0.989267i	$-0.546678\pi$
$827$	−8.40405			−0.292238			−0.146119	+	0.989267i	$0.546678\pi$
$828$	−13.0658	+	17.7599i	−0.454066	+	0.617199i
$829$	−29.8881			−1.03806			−0.519028	−	0.854757i	$-0.673706\pi$
$829$	−29.8881			−1.03806			−0.519028	+	0.854757i	$0.673706\pi$
$830$	−1.27409	−	2.20679i	−0.0442244	−	0.0765989i
$831$	21.7999	+	1.20764i	0.756229	+	0.0418925i
$832$	5.38615	−	9.32909i	0.186731	−	0.323428i
$833$	−15.8371	+	27.4306i	−0.548722	+	0.950415i
$834$	33.7694	−	51.6626i	1.16934	−	1.78893i
$835$	1.13282	+	1.96210i	0.0392028	+	0.0679013i
$836$	−3.34768			−0.115782
$837$	−24.0931	+	29.2146i	−0.832781	+	1.00980i
$838$	−20.8290			−0.719525
$839$	18.2191	+	31.5564i	0.628993	+	1.08945i	0.987754	+	0.156019i	$0.0498660\pi$
$839$	18.2191	+	31.5564i	0.628993	+	1.08945i	−0.358761	+	0.933430i	$0.616801\pi$
$840$	0.182705	−	0.279514i	0.00630391	−	0.00964413i
$841$	14.4168	−	24.9706i	0.497130	−	0.861054i
$842$	−8.47779	+	14.6840i	−0.292164	+	0.506043i
$843$	20.1632	+	1.11697i	0.694457	+	0.0384705i
$844$	18.6149	+	32.2419i	0.640750	+	1.10981i
$845$	1.86292			0.0640863
$846$	−5.81803	−	0.646582i	−0.200028	−	0.0222300i
$847$	13.4607			0.462516
$848$	−17.4766	−	30.2704i	−0.600149	−	1.03949i
$849$	−19.4146	−	38.3856i	−0.666306	−	1.31739i
$850$	−27.6634	+	47.9145i	−0.948848	+	1.64345i
$851$	16.7860	−	29.0742i	0.575416	−	0.996650i
$852$	−2.22944	−	4.40795i	−0.0763793	−	0.151014i
$853$	−8.67652	−	15.0282i	−0.297079	−	0.514555i	0.678388	−	0.734704i	$-0.262679\pi$
$853$	−8.67652	−	15.0282i	−0.297079	−	0.514555i	−0.975466	+	0.220149i	$0.929346\pi$
$854$	−0.0762525			−0.00260931
$855$	2.39054	+	0.265670i	0.0817546	+	0.00908573i
$856$	−10.9613			−0.374651
$857$	−17.3924	−	30.1245i	−0.594112	−	1.02903i	−0.993672	−	0.112325i	$-0.964170\pi$
$857$	−17.3924	−	30.1245i	−0.594112	−	1.02903i	0.399559	−	0.916707i	$-0.369163\pi$
$858$	4.11083	+	0.227726i	0.140341	+	0.00777443i
$859$	−26.9963	+	46.7590i	−0.921103	+	1.59540i	−0.123391	+	0.992358i	$0.539377\pi$
$859$	−26.9963	+	46.7590i	−0.921103	+	1.59540i	−0.797712	+	0.603039i	$0.793957\pi$
$860$	−1.14071	+	1.97577i	−0.0388979	+	0.0673731i
$861$	−1.19524	+	1.82855i	−0.0407337	+	0.0623170i
$862$	−38.5142	−	66.7085i	−1.31180	−	2.27210i
$863$	−38.8795			−1.32347			−0.661737	−	0.749736i	$-0.730180\pi$
$863$	−38.8795			−1.32347			−0.661737	+	0.749736i	$0.730180\pi$
$864$	24.4499	−	29.6472i	0.831804	−	1.00862i
$865$	0.0476678			0.00162075
$866$	−22.8903	−	39.6472i	−0.777844	−	1.34727i
$867$	−16.3826	+	25.0632i	−0.556383	+	0.851190i
$868$	7.55895	−	13.0925i	0.256567	−	0.444388i
$869$	−1.17442	+	2.03416i	−0.0398395	+	0.0690040i
$870$	0.303619	+	0.0168195i	0.0102937	+	0.000570233i
$871$	1.74041	+	3.01449i	0.0589717	+	0.102142i
$872$	−5.64063			−0.191016
$873$	−15.6852	+	21.3204i	−0.530864	+	0.721588i
$874$	−30.3445			−1.02642
$875$	1.41417	+	2.44941i	0.0478076	+	0.0828052i
$876$	12.9536	+	25.6113i	0.437663	+	0.865327i
$877$	−4.82596	+	8.35881i	−0.162961	+	0.282257i	−0.935929	−	0.352188i	$-0.885438\pi$
$877$	−4.82596	+	8.35881i	−0.162961	+	0.282257i	0.772968	+	0.634445i	$0.218771\pi$
$878$	8.05635	−	13.9540i	0.271889	−	0.470925i
$879$	−21.6175	−	42.7412i	−0.729141	−	1.44162i
$880$	−0.295618	−	0.512025i	−0.00996526	−	0.0172603i
$881$	−24.3532			−0.820480			−0.410240	−	0.911978i	$-0.634555\pi$
$881$	−24.3532			−0.820480			−0.410240	+	0.911978i	$0.634555\pi$
$882$	12.4322	+	28.3771i	0.418613	+	0.955506i
$883$	33.1825			1.11668			0.558339	−	0.829613i	$-0.311439\pi$
$883$	33.1825			1.11668			0.558339	+	0.829613i	$0.311439\pi$
$884$	10.4784	+	18.1491i	0.352426	+	0.610420i
$885$	1.54155	+	0.0853965i	0.0518186	+	0.00287057i
$886$	23.8219	−	41.2608i	0.800314	−	1.38618i
$887$	0.529930	−	0.917866i	0.0177933	−	0.0308189i	−0.856992	−	0.515330i	$-0.827669\pi$
$887$	0.529930	−	0.917866i	0.0177933	−	0.0308189i	0.874785	+	0.484511i	$0.161003\pi$
$888$	−4.82874	+	7.38731i	−0.162042	+	0.247902i
$889$	6.59048	+	11.4151i	0.221038	+	0.382849i
$890$	4.93090			0.165284
$891$	5.02411	+	1.13067i	0.168314	+	0.0378787i
$892$	−19.9896			−0.669301
$893$	−1.81782	−	3.14856i	−0.0608310	−	0.105362i
$894$	18.3049	−	28.0040i	0.612207	−	0.936594i
$895$	−0.763170	+	1.32185i	−0.0255100	+	0.0441846i
$896$	3.36748	−	5.83264i	0.112500	−	0.194855i
$897$	16.8151	+	0.931499i	0.561440	+	0.0311019i
$898$	13.4086	+	23.2244i	0.447451	+	0.775008i
$899$	−2.97333			−0.0991662
$900$	9.79968	+	22.3683i	0.326656	+	0.745610i
$901$	44.6460			1.48738
$902$	0.546198	+	0.946042i	0.0181864	+	0.0314998i
$903$	−6.06756	−	11.9965i	−0.201916	−	0.399219i
$904$	6.07421	−	10.5208i	0.202025	−	0.349918i
$905$	0.591576	−	1.02464i	0.0196647	−	0.0340602i
$906$	−5.12215	−	10.1273i	−0.170172	−	0.336456i
$907$	−13.2093	−	22.8792i	−0.438608	−	0.759692i	0.558974	−	0.829185i	$-0.311195\pi$
$907$	−13.2093	−	22.8792i	−0.438608	−	0.759692i	−0.997582	+	0.0694931i	$0.977862\pi$
$908$	13.7937			0.457761
$909$	−12.7439	+	17.3224i	−0.422689	+	0.574549i
$910$	1.18095			0.0391481
$911$	13.7819	+	23.8710i	0.456615	+	0.790881i	0.998779	−	0.0493918i	$-0.0157283\pi$
$911$	13.7819	+	23.8710i	0.456615	+	0.790881i	−0.542164	+	0.840272i	$0.682395\pi$
$912$	28.2008	+	1.56223i	0.933823	+	0.0517306i
$913$	1.69421	−	2.93446i	0.0560702	−	0.0971164i
$914$	16.0620	−	27.8203i	0.531285	−	0.920213i
$915$	0.00676426	−	0.0103484i	0.000223620	−	0.000342108i
$916$	−14.9128	−	25.8297i	−0.492733	−	0.853439i
$917$	−6.43291			−0.212433
$918$	20.3311	+	54.4134i	0.671025	+	1.79591i
$919$	25.5145			0.841644			0.420822	−	0.907143i	$-0.361742\pi$
$919$	25.5145			0.841644			0.420822	+	0.907143i	$0.361742\pi$
$920$	−0.341519	−	0.591529i	−0.0112596	−	0.0195021i
$921$	28.4251	−	43.4865i	0.936639	−	1.43293i
$922$	−34.1225	+	59.1020i	−1.12377	+	1.94642i
$923$	−1.88651	+	3.26752i	−0.0620951	+	0.107552i
$924$	−2.05278	−	0.113717i	−0.0675316	−	0.00374102i
$925$	−18.5922	−	32.2027i	−0.611309	−	1.05882i
$926$	40.2383			1.32231
$927$	−36.8477	−	4.09504i	−1.21024	−	0.134499i
$928$	3.01737			0.0990499
$929$	−9.79772	−	16.9701i	−0.321453	−	0.556772i	0.659335	−	0.751849i	$-0.270838\pi$
$929$	−9.79772	−	16.9701i	−0.321453	−	0.556772i	−0.980788	+	0.195077i	$0.937504\pi$
$930$	2.45146	+	4.84692i	0.0803866	+	0.158937i
$931$	−9.62063	+	16.6634i	−0.315304	+	0.546122i
$932$	10.6644	−	18.4713i	0.349324	−	0.605046i
$933$	−13.4143	−	26.5221i	−0.439163	−	0.868294i
$934$	−11.7622	−	20.3727i	−0.384871	−	0.666616i
$935$	0.755189			0.0246973
$936$	−4.40008	−	0.489000i	−0.143821	−	0.0159835i
$937$	26.1451			0.854122			0.427061	−	0.904223i	$-0.359549\pi$
$937$	26.1451			0.854122			0.427061	+	0.904223i	$0.359549\pi$
$938$	−1.92589	−	3.33575i	−0.0628827	−	0.108916i
$939$	27.9010	+	1.54562i	0.910514	+	0.0504393i
$940$	−0.189454	+	0.328144i	−0.00617930	+	0.0107029i
$941$	10.1008	−	17.4951i	0.329276	−	0.570323i	−0.653092	−	0.757278i	$-0.726529\pi$
$941$	10.1008	−	17.4951i	0.329276	−	0.570323i	0.982368	+	0.186955i	$0.0598619\pi$
$942$	−18.6348	+	28.5087i	−0.607154	+	0.928863i
$943$	2.23419	+	3.86973i	0.0727553	+	0.126016i
$944$	18.1296			0.590069
$945$	1.45684	+	0.244112i	0.0473910	+	0.00794095i
$946$	−6.72260			−0.218571
$947$	−0.169981	−	0.294415i	−0.00552363	−	0.00956721i	0.863250	−	0.504776i	$-0.168425\pi$
$947$	−0.169981	−	0.294415i	−0.00552363	−	0.00956721i	−0.868774	+	0.495209i	$0.835092\pi$
$948$	−6.39835	+	9.78860i	−0.207809	+	0.317919i
$949$	10.9611	−	18.9852i	0.355812	−	0.616285i
$950$	−16.8049	+	29.1069i	−0.545222	+	0.944352i
$951$	47.4564	+	2.62892i	1.53888	+	0.0852487i
$952$	2.50430	+	4.33758i	0.0811649	+	0.140582i
$953$	−55.3331			−1.79242			−0.896208	−	0.443635i	$-0.853689\pi$
$953$	−55.3331			−1.79242			−0.896208	+	0.443635i	$0.853689\pi$
$954$	25.8780	−	35.1753i	0.837833	−	1.13884i
$955$	2.40636			0.0778680
$956$	−20.9509	−	36.2881i	−0.677601	−	1.17364i
$957$	0.182498	+	0.360827i	0.00589932	+	0.0116639i
$958$	29.3097	−	50.7659i	0.946953	−	1.64017i
$959$	−10.1331	+	17.5510i	−0.327213	+	0.566750i
$960$	−0.872280	−	1.72463i	−0.0281527	−	0.0556623i
$961$	−11.0550	−	19.1479i	−0.356614	−	0.617674i
$962$	−31.2116			−1.00630
$963$	−19.4575	−	44.4127i	−0.627008	−	1.43118i
$964$	−6.56089			−0.211312
$965$	0.152887	+	0.264808i	0.00492161	+	0.00852447i
$966$	−18.6071	−	1.03077i	−0.598674	−	0.0331645i
$967$	−1.07250	+	1.85763i	−0.0344894	+	0.0597374i	−0.882755	−	0.469834i	$-0.844314\pi$
$967$	−1.07250	+	1.85763i	−0.0344894	+	0.0597374i	0.848265	+	0.529571i	$0.177647\pi$
$968$	−3.61902	+	6.26833i	−0.116320	+	0.201472i
$969$	−19.7387	+	30.1975i	−0.634098	+	0.970083i
$970$	1.89827	+	3.28790i	0.0609498	+	0.105568i
$971$	−55.6321			−1.78532			−0.892659	−	0.450733i	$-0.851163\pi$
$971$	−55.6321			−1.78532			−0.892659	+	0.450733i	$0.851163\pi$
$972$	24.6641	+	7.00423i	0.791101	+	0.224661i
$973$	23.5414			0.754702
$974$	40.4348	+	70.0351i	1.29561	+	2.24407i
$975$	10.2057	−	15.6134i	0.326845	−	0.500029i
$976$	0.0725875	−	0.125725i	0.00232347	−	0.00402436i
$977$	29.1397	−	50.4715i	0.932263	−	1.61473i	0.152820	−	0.988254i	$-0.451164\pi$
$977$	29.1397	−	50.4715i	0.932263	−	1.61473i	0.779443	−	0.626473i	$-0.215502\pi$
$978$	39.9308	+	2.21203i	1.27685	+	0.0707329i
$979$	3.27840	+	5.67836i	0.104778	+	0.181481i
$980$	2.00533			0.0640579
$981$	−10.0127	−	22.8545i	−0.319680	−	0.729687i
$982$	10.9383			0.349056
$983$	−15.5812	−	26.9875i	−0.496964	−	0.860767i	0.503030	−	0.864269i	$-0.332219\pi$
$983$	−15.5812	−	26.9875i	−0.496964	−	0.860767i	−0.999994	+	0.00350230i	$0.998885\pi$
$984$	−0.530162	−	1.04821i	−0.0169010	−	0.0334158i
$985$	0.754358	−	1.30659i	0.0240359	−	0.0416313i
$986$	−2.28048	+	3.94991i	−0.0726253	+	0.125791i
$987$	−1.00773	−	1.99243i	−0.0320763	−	0.0634197i
$988$	6.36537	+	11.0251i	0.202509	+	0.350756i
$989$	−27.4984			−0.874399
$990$	0.437728	−	0.594991i	0.0139119	−	0.0189101i
$991$	−27.4529			−0.872072			−0.436036	−	0.899929i	$-0.643618\pi$
$991$	−27.4529			−0.872072			−0.436036	+	0.899929i	$0.643618\pi$
$992$	26.9483	+	46.6758i	0.855609	+	1.48196i
$993$	−56.3567	−	3.12197i	−1.78843	−	0.0990727i
$994$	2.08755	−	3.61575i	0.0662132	−	0.114685i
$995$	−2.42347	+	4.19757i	−0.0768290	+	0.133072i
$996$	9.23021	−	14.1210i	0.292471	−	0.447440i
$997$	6.67927	+	11.5688i	0.211535	+	0.366389i	0.952195	−	0.305491i	$-0.0988206\pi$
$997$	6.67927	+	11.5688i	0.211535	+	0.366389i	−0.740660	+	0.671880i	$0.765487\pi$
$998$	12.2526			0.387850
$999$	−38.5031	−	6.45167i	−1.21818	−	0.204122i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.e.a.247.4	yes	32
3.2	odd	2		1107.2.e.a.739.13		32
9.2	odd	6		1107.2.e.a.370.13		32
9.4	even	3		3321.2.a.i.1.13		16
9.5	odd	6		3321.2.a.j.1.4		16
9.7	even	3	inner	369.2.e.a.124.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
369.2.e.a.124.4	✓	32	9.7	even	3	inner
369.2.e.a.247.4	yes	32	1.1	even	1	trivial
1107.2.e.a.370.13		32	9.2	odd	6
1107.2.e.a.739.13		32	3.2	odd	2
3321.2.a.i.1.13		16	9.4	even	3
3321.2.a.j.1.4		16	9.5	odd	6

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.954563 - 1.65335i) q^{2} +(-0.947667 + 1.44980i) q^{3} +(-0.822382 + 1.42441i) q^{4} +(0.112697 - 0.195198i) q^{5} +(3.30164 + 0.182900i) q^{6} +(0.630622 + 1.09227i) q^{7} -0.678190 q^{8} +(-1.20385 - 2.74786i) q^{9} -0.430307 q^{10} +(-0.286098 - 0.495537i) q^{11} +(-1.28577 - 2.54216i) q^{12} +(-1.08799 + 1.88445i) q^{13} +(1.20394 - 2.08528i) q^{14} +(0.176198 + 0.348371i) q^{15} +(2.29214 + 3.97010i) q^{16} -5.85554 q^{17} +(-3.39403 + 4.61340i) q^{18} -3.55710 q^{19} +(0.185361 + 0.321054i) q^{20} +(-2.18119 - 0.120831i) q^{21} +(-0.546198 + 0.946042i) q^{22} +(-2.23419 + 3.86973i) q^{23} +(0.642698 - 0.983241i) q^{24} +(2.47460 + 4.28613i) q^{25} +4.15421 q^{26} +(5.12471 + 0.858708i) q^{27} -2.07445 q^{28} +(0.203998 + 0.353334i) q^{29} +(0.407788 - 0.623860i) q^{30} +(-3.64383 + 6.31130i) q^{31} +(3.69779 - 6.40477i) q^{32} +(0.989556 + 0.0548180i) q^{33} +(5.58948 + 9.68126i) q^{34} +0.284278 q^{35} +(4.90410 + 0.545013i) q^{36} -7.51323 q^{37} +(3.39547 + 5.88113i) q^{38} +(-1.70103 - 3.36320i) q^{39} +(-0.0764302 + 0.132381i) q^{40} +(0.500000 - 0.866025i) q^{41} +(1.88231 + 3.72162i) q^{42} +(3.07700 + 5.32952i) q^{43} +0.941129 q^{44} +(-0.672047 - 0.0746874i) q^{45} +8.53071 q^{46} +(0.511041 + 0.885149i) q^{47} +(-7.92805 - 0.439187i) q^{48} +(2.70463 - 4.68456i) q^{49} +(4.72432 - 8.18277i) q^{50} +(5.54910 - 8.48937i) q^{51} +(-1.78948 - 3.09948i) q^{52} -7.62458 q^{53} +(-3.47211 - 9.29264i) q^{54} -0.128970 q^{55} +(-0.427681 - 0.740765i) q^{56} +(3.37094 - 5.15708i) q^{57} +(0.389457 - 0.674560i) q^{58} +(1.97737 - 3.42490i) q^{59} +(-0.641125 - 0.0355161i) q^{60} +(-0.0158340 - 0.0274253i) q^{61} +13.9131 q^{62} +(2.24223 - 3.04779i) q^{63} -4.95056 q^{64} +(0.245227 + 0.424745i) q^{65} +(-0.853961 - 1.68841i) q^{66} +(0.799832 - 1.38535i) q^{67} +(4.81549 - 8.34067i) q^{68} +(-3.49308 - 6.90635i) q^{69} +(-0.271361 - 0.470011i) q^{70} +1.73394 q^{71} +(0.816441 + 1.86357i) q^{72} -10.0746 q^{73} +(7.17185 + 12.4220i) q^{74} +(-8.55914 - 0.474147i) q^{75} +(2.92529 - 5.06675i) q^{76} +(0.360840 - 0.624993i) q^{77} +(-3.93681 + 6.02279i) q^{78} +(-2.05248 - 3.55499i) q^{79} +1.03327 q^{80} +(-6.10147 + 6.61604i) q^{81} -1.90913 q^{82} +(2.96089 + 5.12841i) q^{83} +(1.96589 - 3.00754i) q^{84} +(-0.659904 + 1.14299i) q^{85} +(5.87438 - 10.1747i) q^{86} +(-0.705587 - 0.0390871i) q^{87} +(0.194029 + 0.336068i) q^{88} -11.4590 q^{89} +(0.518027 + 1.18242i) q^{90} -2.74444 q^{91} +(-3.67472 - 6.36480i) q^{92} +(-5.69700 - 11.2639i) q^{93} +(0.975641 - 1.68986i) q^{94} +(-0.400875 + 0.694337i) q^{95} +(5.78137 + 11.4307i) q^{96} +(-4.41143 - 7.64083i) q^{97} -10.3270 q^{98} +(-1.01725 + 1.38271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{3} - 8 q^{4} + q^{5} + 13 q^{7} + 3 q^{9} - 16 q^{10} - 2 q^{11} - 23 q^{12} + 5 q^{13} + q^{14} + 9 q^{15} + 8 q^{16} + 2 q^{17} + 21 q^{18} - 38 q^{19} + 11 q^{20} - 6 q^{21} + 14 q^{22}+ \cdots + 23 q^{99}+O(q^{100}) \) 32 * q - q^3 - 8 * q^4 + q^5 + 13 * q^7 + 3 * q^9 - 16 * q^10 - 2 * q^11 - 23 * q^12 + 5 * q^13 + q^14 + 9 * q^15 + 8 * q^16 + 2 * q^17 + 21 * q^18 - 38 * q^19 + 11 * q^20 - 6 * q^21 + 14 * q^22 + 2 * q^23 + 15 * q^24 + 3 * q^25 + 30 * q^26 + 11 * q^27 - 48 * q^28 - 10 * q^29 - 59 * q^30 + 39 * q^31 - 10 * q^32 + 6 * q^33 + 18 * q^34 + 4 * q^35 + 14 * q^36 - 52 * q^37 - 14 * q^38 - 20 * q^39 + 18 * q^40 + 16 * q^41 + 11 * q^42 + 20 * q^43 - 46 * q^44 + 31 * q^45 - 52 * q^46 + 5 * q^47 - 72 * q^48 + 7 * q^49 + 9 * q^50 - 31 * q^51 + 14 * q^52 + 14 * q^53 + 36 * q^54 - 74 * q^55 - 2 * q^56 - 6 * q^57 + 24 * q^58 + 6 * q^59 - 17 * q^60 + 21 * q^61 - 10 * q^62 + 56 * q^63 - 68 * q^64 + 2 * q^65 - 23 * q^66 + 32 * q^67 - 8 * q^68 - 29 * q^69 + 22 * q^70 - 40 * q^71 + 87 * q^72 - 34 * q^73 + 28 * q^74 + 24 * q^75 + 40 * q^76 - 22 * q^77 + 30 * q^78 + 69 * q^79 + 78 * q^80 + 63 * q^81 + 10 * q^83 - 70 * q^84 + 42 * q^85 - 8 * q^86 - 58 * q^87 + 42 * q^88 + 22 * q^89 + 49 * q^90 - 102 * q^91 - 10 * q^92 - 5 * q^93 + 13 * q^94 - 22 * q^95 + 21 * q^96 + 25 * q^97 - 96 * q^98 + 23 * q^99

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