LMFDB - Embedded newform 361.2.e.m.62.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			62.4
Character	$\chi$	$=$	361.62
Dual form			361.2.e.m.99.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78740 - 0.650561i) q^{2} +(0.330298 - 1.87322i) q^{3} +(1.23949 - 1.04005i) q^{4} +(-2.47897 - 2.08010i) q^{5} +(-0.628265 - 3.56307i) q^{6} +(-0.118034 - 0.204441i) q^{7} +(-0.363271 + 0.629204i) q^{8} +(-0.580762 - 0.211380i) q^{9} +O(q^{10})$	\(q+(1.78740 - 0.650561i) q^{2} +(0.330298 - 1.87322i) q^{3} +(1.23949 - 1.04005i) q^{4} +(-2.47897 - 2.08010i) q^{5} +(-0.628265 - 3.56307i) q^{6} +(-0.118034 - 0.204441i) q^{7} +(-0.363271 + 0.629204i) q^{8} +(-0.580762 - 0.211380i) q^{9} +(-5.78415 - 2.10526i) q^{10} +(0.690983 - 1.19682i) q^{11} +(-1.53884 - 2.66535i) q^{12} +(-0.126163 - 0.715505i) q^{13} +(-0.343975 - 0.288630i) q^{14} +(-4.71528 + 3.95659i) q^{15} +(-0.801913 + 4.54788i) q^{16} +(6.08182 - 2.21360i) q^{17} -1.17557 q^{18} -5.23607 q^{20} +(-0.421948 + 0.153577i) q^{21} +(0.456461 - 2.58872i) q^{22} +(-0.292603 + 0.245523i) q^{23} +(1.05865 + 0.888311i) q^{24} +(0.950226 + 5.38900i) q^{25} +(-0.690983 - 1.19682i) q^{26} +(2.26538 - 3.92376i) q^{27} +(-0.358931 - 0.130640i) q^{28} +(3.99675 + 1.45470i) q^{29} +(-5.85410 + 10.1396i) q^{30} +(-0.951057 - 1.64728i) q^{31} +(1.27300 + 7.21956i) q^{32} +(-2.01367 - 1.68967i) q^{33} +(9.43057 - 7.91319i) q^{34} +(-0.132655 + 0.752326i) q^{35} +(-0.939693 + 0.342020i) q^{36} -6.60440 q^{37} -1.38197 q^{39} +(2.20935 - 0.804138i) q^{40} +(-0.378488 + 2.14651i) q^{41} +(-0.654280 + 0.549006i) q^{42} +(7.14431 + 5.99479i) q^{43} +(-0.388289 - 2.20210i) q^{44} +(1.00000 + 1.73205i) q^{45} +(-0.363271 + 0.629204i) q^{46} +(10.7803 + 3.92370i) q^{47} +(8.25428 + 3.00431i) q^{48} +(3.47214 - 6.01392i) q^{49} +(5.20431 + 9.01413i) q^{50} +(-2.13774 - 12.1237i) q^{51} +(-0.900539 - 0.755642i) q^{52} +(-3.81475 + 3.20095i) q^{53} +(1.49651 - 8.48711i) q^{54} +(-4.20243 + 1.52956i) q^{55} +0.171513 q^{56} +8.09017 q^{58} +(-8.25428 + 3.00431i) q^{59} +(-1.72947 + 9.80828i) q^{60} +(-7.25608 + 6.08857i) q^{61} +(-2.77157 - 2.32563i) q^{62} +(0.0253349 + 0.143682i) q^{63} +(2.35410 + 4.07742i) q^{64} +(-1.17557 + 2.03615i) q^{65} +(-4.69846 - 1.71010i) q^{66} +(-12.2510 - 4.45901i) q^{67} +(5.23607 - 9.06914i) q^{68} +(0.363271 + 0.629204i) q^{69} +(0.252326 + 1.43101i) q^{70} +(7.76088 + 6.51215i) q^{71} +(0.343975 - 0.288630i) q^{72} +(1.56283 - 8.86327i) q^{73} +(-11.8047 + 4.29656i) q^{74} +10.4086 q^{75} -0.326238 q^{77} +(-2.47013 + 0.899053i) q^{78} +(-0.816543 + 4.63084i) q^{79} +(11.4480 - 9.60599i) q^{80} +(-8.02212 - 6.73136i) q^{81} +(0.719928 + 4.08291i) q^{82} +(1.61803 + 2.80252i) q^{83} +(-0.363271 + 0.629204i) q^{84} +(-19.6812 - 7.16336i) q^{85} +(16.6697 + 6.06729i) q^{86} +(4.04508 - 7.00629i) q^{87} +(0.502029 + 0.869539i) q^{88} +(1.29141 + 7.32395i) q^{89} +(2.91421 + 2.44531i) q^{90} +(-0.131387 + 0.110247i) q^{91} +(-0.107320 + 0.608645i) q^{92} +(-3.39984 + 1.23744i) q^{93} +21.8213 q^{94} +13.9443 q^{96} +(4.15792 - 1.51336i) q^{97} +(2.29368 - 13.0081i) q^{98} +(-0.654280 + 0.549006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7}+O(q^{10}) $ 24 * q + 24 * q^7	$ 24 q + 24 q^{7} + 30 q^{11} - 72 q^{20} - 30 q^{26} - 60 q^{30} - 60 q^{39} + 24 q^{45} - 24 q^{49} + 60 q^{58} - 24 q^{64} + 72 q^{68} + 180 q^{77} + 12 q^{83} + 30 q^{87} + 120 q^{96}+O(q^{100}) $ 24 * q + 24 * q^7 + 30 * q^11 - 72 * q^20 - 30 * q^26 - 60 * q^30 - 60 * q^39 + 24 * q^45 - 24 * q^49 + 60 * q^58 - 24 * q^64 + 72 * q^68 + 180 * q^77 + 12 * q^83 + 30 * q^87 + 120 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	1.78740	−	0.650561i	1.26388	−	0.460016i	0.378813	−	0.925473i	$-0.376332\pi$
$2$	1.78740	−	0.650561i	1.26388	−	0.460016i	0.885070	+	0.465457i	$0.154110\pi$
$3$	0.330298	−	1.87322i	0.190698	−	1.08150i	−0.727715	−	0.685879i	$-0.759418\pi$
$3$	0.330298	−	1.87322i	0.190698	−	1.08150i	0.918413	−	0.395622i	$-0.129471\pi$
$4$	1.23949	−	1.04005i	0.619743	−	0.520026i
$5$	−2.47897	−	2.08010i	−1.10863	−	0.930251i	−0.110655	−	0.993859i	$-0.535295\pi$
$5$	−2.47897	−	2.08010i	−1.10863	−	0.930251i	−0.997975	+	0.0636079i	$0.979739\pi$
$6$	−0.628265	−	3.56307i	−0.256488	−	1.45462i
$7$	−0.118034	−	0.204441i	−0.0446127	−	0.0772714i	0.842857	−	0.538138i	$-0.180872\pi$
$7$	−0.118034	−	0.204441i	−0.0446127	−	0.0772714i	−0.887469	+	0.460866i	$0.847539\pi$
$8$	−0.363271	+	0.629204i	−0.128436	+	0.222457i
$9$	−0.580762	−	0.211380i	−0.193587	−	0.0704600i
$10$	−5.78415	−	2.10526i	−1.82911	−	0.665742i
$11$	0.690983	−	1.19682i	0.208339	−	0.360854i	−0.742852	−	0.669455i	$-0.766528\pi$
$11$	0.690983	−	1.19682i	0.208339	−	0.360854i	0.951191	+	0.308601i	$0.0998609\pi$
$12$	−1.53884	−	2.66535i	−0.444225	−	0.769421i
$13$	−0.126163	−	0.715505i	−0.0349913	−	0.198445i	0.962301	−	0.271987i	$-0.0876808\pi$
$13$	−0.126163	−	0.715505i	−0.0349913	−	0.198445i	−0.997292	+	0.0735419i	$0.976570\pi$
$14$	−0.343975	−	0.288630i	−0.0919313	−	0.0771395i
$15$	−4.71528	+	3.95659i	−1.21748	+	1.02159i
$16$	−0.801913	+	4.54788i	−0.200478	+	1.13697i
$17$	6.08182	−	2.21360i	1.47506	−	0.536877i	0.525589	−	0.850739i	$-0.323845\pi$
$17$	6.08182	−	2.21360i	1.47506	−	0.536877i	0.949469	+	0.313862i	$0.101623\pi$
$18$	−1.17557			−0.277085
$19$		0			0
$19$		0			0
$20$	−5.23607			−1.17082
$21$	−0.421948	+	0.153577i	−0.0920767	+	0.0335132i
$22$	0.456461	−	2.58872i	0.0973179	−	0.551917i
$23$	−0.292603	+	0.245523i	−0.0610119	+	0.0511951i	−0.672784	−	0.739839i	$-0.734902\pi$
$23$	−0.292603	+	0.245523i	−0.0610119	+	0.0511951i	0.611772	+	0.791034i	$0.290457\pi$
$24$	1.05865	+	0.888311i	0.216095	+	0.181326i
$25$	0.950226	+	5.38900i	0.190045	+	1.07780i
$26$	−0.690983	−	1.19682i	−0.135513	−	0.234715i
$27$	2.26538	−	3.92376i	0.435973	−	0.755128i
$28$	−0.358931	−	0.130640i	−0.0678315	−	0.0246887i
$29$	3.99675	+	1.45470i	0.742178	+	0.270131i	0.685311	−	0.728251i	$-0.259666\pi$
$29$	3.99675	+	1.45470i	0.742178	+	0.270131i	0.0568676	+	0.998382i	$0.481889\pi$
$30$	−5.85410	+	10.1396i	−1.06881	+	1.85123i
$31$	−0.951057	−	1.64728i	−0.170815	−	0.295860i	0.767890	−	0.640582i	$-0.221307\pi$
$31$	−0.951057	−	1.64728i	−0.170815	−	0.295860i	−0.938705	+	0.344722i	$0.887973\pi$
$32$	1.27300	+	7.21956i	0.225037	+	1.27625i
$33$	−2.01367	−	1.68967i	−0.350534	−	0.294133i
$34$	9.43057	−	7.91319i	1.61733	−	1.35710i
$35$	−0.132655	+	0.752326i	−0.0224229	+	0.127166i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	−6.60440			−1.08576			−0.542878	−	0.839812i	$-0.682665\pi$
$37$	−6.60440			−1.08576			−0.542878	+	0.839812i	$0.682665\pi$
$38$		0			0
$39$	−1.38197			−0.221292
$40$	2.20935	−	0.804138i	0.349329	−	0.127145i
$41$	−0.378488	+	2.14651i	−0.0591100	+	0.335229i	−0.999994	−	0.00349997i	$-0.998886\pi$
$41$	−0.378488	+	2.14651i	−0.0591100	+	0.335229i	0.940884	+	0.338729i	$0.109997\pi$
$42$	−0.654280	+	0.549006i	−0.100958	+	0.0847135i
$43$	7.14431	+	5.99479i	1.08950	+	0.914197i	0.996675	−	0.0814857i	$-0.0259665\pi$
$43$	7.14431	+	5.99479i	1.08950	+	0.914197i	0.0928230	+	0.995683i	$0.470411\pi$
$44$	−0.388289	−	2.20210i	−0.0585368	−	0.331979i
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	−0.363271	+	0.629204i	−0.0535614	+	0.0927711i
$47$	10.7803	+	3.92370i	1.57247	+	0.572331i	0.973549	−	0.228480i	$-0.0733757\pi$
$47$	10.7803	+	3.92370i	1.57247	+	0.572331i	0.598917	+	0.800811i	$0.295598\pi$
$48$	8.25428	+	3.00431i	1.19140	+	0.433635i
$49$	3.47214	−	6.01392i	0.496019	−	0.859131i
$50$	5.20431	+	9.01413i	0.736001	+	1.27479i
$51$	−2.13774	−	12.1237i	−0.299343	−	1.69766i
$52$	−0.900539	−	0.755642i	−0.124882	−	0.104789i
$53$	−3.81475	+	3.20095i	−0.523996	+	0.439685i	−0.866022	−	0.500006i	$-0.833331\pi$
$53$	−3.81475	+	3.20095i	−0.523996	+	0.439685i	0.342026	+	0.939690i	$0.388887\pi$
$54$	1.49651	−	8.48711i	0.203649	−	1.15495i
$55$	−4.20243	+	1.52956i	−0.566656	+	0.206246i
$56$	0.171513			0.0229194
$57$		0			0
$58$	8.09017			1.06229
$59$	−8.25428	+	3.00431i	−1.07462	+	0.391128i	−0.817901	−	0.575359i	$-0.804862\pi$
$59$	−8.25428	+	3.00431i	−1.07462	+	0.391128i	−0.256715	+	0.966487i	$0.582640\pi$
$60$	−1.72947	+	9.80828i	−0.223273	+	1.26624i
$61$	−7.25608	+	6.08857i	−0.929045	+	0.779562i	−0.975646	−	0.219352i	$-0.929606\pi$
$61$	−7.25608	+	6.08857i	−0.929045	+	0.779562i	0.0466003	+	0.998914i	$0.485161\pi$
$62$	−2.77157	−	2.32563i	−0.351990	−	0.295355i
$63$	0.0253349	+	0.143682i	0.00319190	+	0.0181022i
$64$	2.35410	+	4.07742i	0.294263	+	0.509678i
$65$	−1.17557	+	2.03615i	−0.145812	+	0.252553i
$66$	−4.69846	−	1.71010i	−0.578341	−	0.210499i
$67$	−12.2510	−	4.45901i	−1.49670	−	0.544755i	−0.541498	−	0.840702i	$-0.682142\pi$
$67$	−12.2510	−	4.45901i	−1.49670	−	0.544755i	−0.955204	+	0.295947i	$0.904365\pi$
$68$	5.23607	−	9.06914i	0.634967	−	1.09979i
$69$	0.363271	+	0.629204i	0.0437327	+	0.0757473i
$70$	0.252326	+	1.43101i	0.0301587	+	0.171038i
$71$	7.76088	+	6.51215i	0.921047	+	0.772850i	0.974188	−	0.225737i	$-0.0724790\pi$
$71$	7.76088	+	6.51215i	0.921047	+	0.772850i	−0.0531415	+	0.998587i	$0.516923\pi$
$72$	0.343975	−	0.288630i	0.0405379	−	0.0340153i
$73$	1.56283	−	8.86327i	0.182916	−	1.03737i	−0.745688	−	0.666295i	$-0.767879\pi$
$73$	1.56283	−	8.86327i	0.182916	−	1.03737i	0.928604	−	0.371072i	$-0.121010\pi$
$74$	−11.8047	+	4.29656i	−1.37227	+	0.499465i
$75$	10.4086			1.20188
$76$		0			0
$77$	−0.326238			−0.0371783
$78$	−2.47013	+	0.899053i	−0.279687	+	0.101798i
$79$	−0.816543	+	4.63084i	−0.0918682	+	0.521011i	0.903794	+	0.427968i	$0.140770\pi$
$79$	−0.816543	+	4.63084i	−0.0918682	+	0.521011i	−0.995662	+	0.0930426i	$0.970341\pi$
$80$	11.4480	−	9.60599i	1.27992	−	1.07398i
$81$	−8.02212	−	6.73136i	−0.891347	−	0.747929i
$82$	0.719928	+	4.08291i	0.0795027	+	0.450882i
$83$	1.61803	+	2.80252i	0.177602	+	0.307616i	0.941059	−	0.338243i	$-0.109833\pi$
$83$	1.61803	+	2.80252i	0.177602	+	0.307616i	−0.763456	+	0.645859i	$0.776499\pi$
$84$	−0.363271	+	0.629204i	−0.0396361	+	0.0686518i
$85$	−19.6812	−	7.16336i	−2.13472	−	0.776976i
$86$	16.6697	+	6.06729i	1.79754	+	0.654252i
$87$	4.04508	−	7.00629i	0.433679	−	0.751153i
$88$	0.502029	+	0.869539i	0.0535164	+	0.0926932i
$89$	1.29141	+	7.32395i	0.136889	+	0.776338i	0.973525	+	0.228579i	$0.0734078\pi$
$89$	1.29141	+	7.32395i	0.136889	+	0.776338i	−0.836636	+	0.547759i	$0.815481\pi$
$90$	2.91421	+	2.44531i	0.307184	+	0.257758i
$91$	−0.131387	+	0.110247i	−0.0137731	+	0.0115570i
$92$	−0.107320	+	0.608645i	−0.0111889	+	0.0634556i
$93$	−3.39984	+	1.23744i	−0.352547	+	0.128317i
$94$	21.8213			2.25070
$95$		0			0
$96$	13.9443			1.42318
$97$	4.15792	−	1.51336i	0.422173	−	0.153658i	−0.122193	−	0.992506i	$-0.538993\pi$
$97$	4.15792	−	1.51336i	0.422173	−	0.153658i	0.544366	+	0.838848i	$0.316770\pi$
$98$	2.29368	−	13.0081i	0.231697	−	1.31402i
$99$	−0.654280	+	0.549006i	−0.0657576	+	0.0551772i
$100$	6.78264	+	5.69131i	0.678264	+	0.569131i
$101$	0.684916	+	3.88435i	0.0681517	+	0.386507i	0.999736	+	0.0229817i	$0.00731594\pi$
$101$	0.684916	+	3.88435i	0.0681517	+	0.386507i	−0.931584	+	0.363526i	$0.881573\pi$
$102$	−11.7082	−	20.2792i	−1.15928	−	2.00794i
$103$	−5.56758	+	9.64333i	−0.548590	+	0.950186i	0.449781	+	0.893139i	$0.351502\pi$
$103$	−5.56758	+	9.64333i	−0.548590	+	0.950186i	−0.998371	+	0.0570473i	$0.981831\pi$
$104$	0.496030	+	0.180540i	0.0486397	+	0.0177034i
$105$	1.36545	+	0.496984i	0.133255	+	0.0485007i
$106$	−4.73607	+	8.20311i	−0.460008	+	0.796757i
$107$	−2.99193	−	5.18217i	−0.289240	−	0.500979i	0.684388	−	0.729118i	$-0.260069\pi$
$107$	−2.99193	−	5.18217i	−0.289240	−	0.500979i	−0.973629	+	0.228139i	$0.926736\pi$
$108$	−1.27300	−	7.21956i	−0.122495	−	0.694703i
$109$	−2.35764	−	1.97830i	−0.225821	−	0.189486i	0.522856	−	0.852421i	$-0.324866\pi$
$109$	−2.35764	−	1.97830i	−0.225821	−	0.189486i	−0.748678	+	0.662934i	$0.769311\pi$
$110$	−6.51636	+	5.46788i	−0.621311	+	0.521342i
$111$	−2.18142	+	12.3715i	−0.207051	+	1.17425i
$112$	1.02442	−	0.372860i	0.0967990	−	0.0352320i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	1.23607			0.115264
$116$	6.46688	−	2.35375i	0.600435	−	0.218540i
$117$	−0.0779729	+	0.442206i	−0.00720860	+	0.0408820i
$118$	−12.7992	+	10.7398i	−1.17826	+	0.988681i
$119$	−1.17041	−	0.982092i	−0.107291	−	0.0900282i
$120$	−0.776578	−	4.40419i	−0.0708916	−	0.402046i
$121$	4.54508	+	7.87232i	0.413190	+	0.715665i
$122$	−9.00854	+	15.6032i	−0.815595	+	1.41265i
$123$	3.89587	+	1.41798i	0.351279	+	0.127855i
$124$	−2.89208	−	1.05263i	−0.259716	−	0.0945289i
$125$	0.763932	−	1.32317i	0.0683282	−	0.118348i
$126$	0.138757	+	0.240335i	0.0123615	+	0.0214107i
$127$	2.16752	+	12.2926i	0.192336	+	1.09079i	0.916161	+	0.400810i	$0.131271\pi$
$127$	2.16752	+	12.2926i	0.192336	+	1.09079i	−0.723825	+	0.689983i	$0.757618\pi$
$128$	−4.37131	−	3.66796i	−0.386373	−	0.324205i
$129$	13.5893	−	11.4028i	1.19647	−	1.00396i
$130$	−0.776578	+	4.40419i	−0.0681104	+	0.386273i
$131$	−5.72289	+	2.08296i	−0.500011	+	0.181989i	−0.579699	−	0.814831i	$-0.696830\pi$
$131$	−5.72289	+	2.08296i	−0.500011	+	0.181989i	0.0796879	+	0.996820i	$0.474608\pi$
$132$	−4.25325			−0.370198
$133$		0			0
$134$	−24.7984			−2.14225
$135$	−13.7777	+	5.01466i	−1.18579	+	0.431593i
$136$	−0.816543	+	4.63084i	−0.0700180	+	0.397092i
$137$	6.67087	−	5.59753i	0.569931	−	0.478229i	−0.311692	−	0.950183i	$-0.600896\pi$
$137$	6.67087	−	5.59753i	0.569931	−	0.478229i	0.881623	+	0.471954i	$0.156451\pi$
$138$	1.05865	+	0.888311i	0.0901180	+	0.0756180i
$139$	−2.09944	−	11.9065i	−0.178072	−	1.00990i	−0.934538	−	0.355863i	$-0.884187\pi$
$139$	−2.09944	−	11.9065i	−0.178072	−	1.00990i	0.756466	−	0.654033i	$-0.226924\pi$
$140$	0.618034	+	1.07047i	0.0522334	+	0.0904709i
$141$	10.9106	−	18.8978i	0.918842	−	1.59148i
$142$	18.1084	+	6.59090i	1.51962	+	0.553096i
$143$	−0.943505	−	0.343408i	−0.0788999	−	0.0287172i
$144$	1.42705	−	2.47172i	0.118921	−	0.205977i
$145$	−6.88191	−	11.9198i	−0.571511	−	0.989887i
$146$	−2.97269	−	16.8589i	−0.246021	−	1.39526i
$147$	−10.1185	−	8.49045i	−0.834561	−	0.700280i
$148$	−8.18605	+	6.86892i	−0.672890	+	0.564621i
$149$	1.04787	−	5.94277i	0.0858448	−	0.486850i	−0.911326	−	0.411685i	$-0.864940\pi$
$149$	1.04787	−	5.94277i	0.0858448	−	0.486850i	0.997171	−	0.0751654i	$-0.0239485\pi$
$150$	18.6044	−	6.77144i	1.51904	−	0.552886i
$151$	−17.2905			−1.40708			−0.703542	−	0.710654i	$-0.748399\pi$
$151$	−17.2905			−1.40708			−0.703542	+	0.710654i	$0.748399\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	−0.583118	+	0.212238i	−0.0469890	+	0.0171026i
$155$	−1.06887	+	6.06185i	−0.0858536	+	0.486900i
$156$	−1.71293	+	1.43732i	−0.137144	+	0.115077i
$157$	−3.49493	−	2.93259i	−0.278926	−	0.234046i	0.492583	−	0.870266i	$-0.336053\pi$
$157$	−3.49493	−	2.93259i	−0.278926	−	0.234046i	−0.771508	+	0.636219i	$0.780497\pi$
$158$	1.55316	+	8.80839i	0.123562	+	0.700758i
$159$	4.73607	+	8.20311i	0.375595	+	0.650549i
$160$	11.8617	−	20.5451i	0.937750	−	1.62423i
$161$	0.0847320	+	0.0308399i	0.00667782	+	0.00243053i
$162$	−18.7179	−	6.81276i	−1.47062	−	0.535261i
$163$	−7.73607	+	13.3993i	−0.605936	+	1.04951i	0.385967	+	0.922512i	$0.373868\pi$
$163$	−7.73607	+	13.3993i	−0.605936	+	1.04951i	−0.991903	+	0.126999i	$0.959466\pi$
$164$	1.76336	+	3.05422i	0.137695	+	0.238495i
$165$	1.47714	+	8.37728i	0.114995	+	0.652170i
$166$	4.71528	+	3.95659i	0.365977	+	0.307091i
$167$	1.24451	−	1.04427i	0.0963034	−	0.0808082i	−0.593365	−	0.804934i	$-0.702201\pi$
$167$	1.24451	−	1.04427i	0.0963034	−	0.0808082i	0.689668	+	0.724126i	$0.257756\pi$
$168$	0.0566506	−	0.321282i	0.00437069	−	0.0247874i
$169$	11.7200	−	4.26572i	0.901536	−	0.328132i
$170$	−39.8384			−3.05546
$171$		0			0
$172$	15.0902			1.15061
$173$	15.6647	−	5.70147i	1.19096	−	0.433475i	0.330901	−	0.943665i	$-0.392647\pi$
$173$	15.6647	−	5.70147i	1.19096	−	0.433475i	0.860061	+	0.510191i	$0.170425\pi$
$174$	2.67217	−	15.1546i	0.202577	−	1.14887i
$175$	0.989573	−	0.830351i	0.0748047	−	0.0627686i
$176$	4.88887	+	4.10225i	0.368512	+	0.309219i
$177$	2.90135	+	16.4544i	0.218079	+	1.23679i
$178$	7.07295	+	12.2507i	0.530140	+	0.918229i
$179$	4.33901	−	7.51539i	0.324313	−	0.561726i	−0.657060	−	0.753838i	$-0.728200\pi$
$179$	4.33901	−	7.51539i	0.324313	−	0.561726i	0.981373	+	0.192112i	$0.0615336\pi$
$180$	3.04091	+	1.10680i	0.226656	+	0.0824960i
$181$	5.46181	+	1.98794i	0.405973	+	0.147762i	0.536932	−	0.843626i	$-0.319583\pi$
$181$	5.46181	+	1.98794i	0.405973	+	0.147762i	−0.130958	+	0.991388i	$0.541805\pi$
$182$	−0.163119	+	0.282530i	−0.0120912	+	0.0209425i
$183$	9.00854	+	15.6032i	0.665930	+	1.15342i
$184$	−0.0481899	−	0.273298i	−0.00355261	−	0.0201478i
$185$	16.3721	+	13.7378i	1.20370	+	1.01003i
$186$	−5.27185	+	4.42361i	−0.386551	+	0.324355i
$187$	1.55316	−	8.80839i	0.113578	−	0.644133i
$188$	17.4429	−	6.34868i	1.27215	−	0.463025i
$189$	−1.06957			−0.0777997
$190$		0			0
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$	8.41545	−	3.06297i	0.607333	−	0.221051i
$193$	1.47714	−	8.37728i	0.106327	−	0.603009i	−0.884355	−	0.466815i	$-0.845402\pi$
$193$	1.47714	−	8.37728i	0.106327	−	0.603009i	0.990682	−	0.136195i	$-0.0434873\pi$
$194$	6.44734	−	5.40996i	0.462892	−	0.388413i
$195$	3.42585	+	2.87463i	0.245331	+	0.205857i
$196$	−1.95112	−	11.0654i	−0.139366	−	0.790383i
$197$	−5.73607	−	9.93516i	−0.408678	−	0.707851i	0.586064	−	0.810265i	$-0.300677\pi$
$197$	−5.73607	−	9.93516i	−0.408678	−	0.707851i	−0.994742	+	0.102414i	$0.967343\pi$
$198$	−0.812299	+	1.40694i	−0.0577276	+	0.0999871i
$199$	0.992060	+	0.361080i	0.0703253	+	0.0255963i	0.376943	−	0.926236i	$-0.376975\pi$
$199$	0.992060	+	0.361080i	0.0703253	+	0.0255963i	−0.306618	+	0.951833i	$0.599197\pi$
$200$	−3.73597	−	1.35978i	−0.264173	−	0.0961512i
$201$	−12.3992	+	21.4760i	−0.874571	+	1.51480i
$202$	3.75123	+	6.49731i	0.263935	+	0.457149i
$203$	−0.174353	−	0.988803i	−0.0122372	−	0.0694004i
$204$	−15.2590	−	12.8038i	−1.06834	−	0.896446i
$205$	5.40324	−	4.53385i	0.377378	−	0.316658i
$206$	−3.67793	+	20.8586i	−0.256253	+	1.45328i
$207$	0.221831	−	0.0807400i	0.0154183	−	0.00561182i
$208$	3.35520			0.232641
$209$		0			0
$210$	2.76393			0.190729
$211$	−0.583118	+	0.212238i	−0.0401435	+	0.0146110i	−0.362014	−	0.932173i	$-0.617911\pi$
$211$	−0.583118	+	0.212238i	−0.0401435	+	0.0146110i	0.321870	+	0.946784i	$0.395688\pi$
$212$	−1.39917	+	7.93507i	−0.0960952	+	0.544983i
$213$	14.7621	−	12.3868i	1.01148	−	0.848733i
$214$	−8.71909	−	7.31619i	−0.596025	−	0.500124i
$215$	−5.24076	−	29.7218i	−0.357417	−	2.02701i
$216$	1.64590	+	2.85078i	0.111989	+	0.193971i
$217$	−0.224514	+	0.388870i	−0.0152410	+	0.0263982i
$218$	−5.50106	−	2.00222i	−0.372579	−	0.135608i
$219$	−16.0866	−	5.85505i	−1.08703	−	0.395648i
$220$	−3.61803	+	6.26662i	−0.243928	+	0.422495i
$221$	−2.35114	−	4.07230i	−0.158155	−	0.273932i
$222$	4.14931	+	23.5319i	0.278483	+	1.57936i
$223$	−12.4762	−	10.4687i	−0.835466	−	0.701039i	0.121073	−	0.992644i	$-0.461366\pi$
$223$	−12.4762	−	10.4687i	−0.835466	−	0.701039i	−0.956539	+	0.291605i	$0.905811\pi$
$224$	1.32572	−	1.11241i	0.0885781	−	0.0743259i
$225$	0.587272	−	3.33059i	0.0391515	−	0.222039i
$226$		0			0
$227$	15.7314			1.04413			0.522066	−	0.852905i	$-0.325161\pi$
$227$	15.7314			1.04413			0.522066	+	0.852905i	$0.325161\pi$
$228$		0			0
$229$	−7.09017			−0.468532			−0.234266	−	0.972173i	$-0.575269\pi$
$229$	−7.09017			−0.468532			−0.234266	+	0.972173i	$0.575269\pi$
$230$	2.20935	−	0.804138i	0.145680	−	0.0530233i
$231$	−0.107756	+	0.611114i	−0.00708982	+	0.0402083i
$232$	−2.36721	+	1.98632i	−0.155415	+	0.130408i
$233$	3.46855	+	2.91045i	0.227232	+	0.190670i	0.749294	−	0.662237i	$-0.230393\pi$
$233$	3.46855	+	2.91045i	0.227232	+	0.190670i	−0.522063	+	0.852907i	$0.674837\pi$
$234$	0.148313	+	0.841126i	0.00969554	+	0.0549861i
$235$	−18.5623	−	32.1509i	−1.21087	−	2.09729i
$236$	−7.10642	+	12.3087i	−0.462589	+	0.801227i
$237$	8.40487	+	3.05912i	0.545955	+	0.198711i
$238$	−2.73091	−	0.993969i	−0.177018	−	0.0644294i
$239$	4.57295	−	7.92058i	0.295799	−	0.512340i	−0.679371	−	0.733795i	$-0.737747\pi$
$239$	4.57295	−	7.92058i	0.295799	−	0.512340i	0.975171	+	0.221455i	$0.0710806\pi$
$240$	−14.2128	−	24.6174i	−0.917435	−	1.58904i
$241$	−4.71353	−	26.7317i	−0.303625	−	1.72194i	−0.629907	−	0.776670i	$-0.716907\pi$
$241$	−4.71353	−	26.7317i	−0.303625	−	1.72194i	0.326282	−	0.945272i	$-0.394204\pi$
$242$	13.2453	+	11.1141i	0.851441	+	0.714444i
$243$	−4.84667	+	4.06684i	−0.310914	+	0.260888i
$244$	−2.66137	+	15.0934i	−0.170377	+	0.966256i
$245$	−21.1169	+	7.68592i	−1.34911	+	0.491036i
$246$	7.88597			0.502791
$247$		0			0
$248$	1.38197			0.0877549
$249$	5.78415	−	2.10526i	0.366556	−	0.133415i
$250$	0.504651	−	2.86202i	0.0319169	−	0.181010i
$251$	−12.5757	+	10.5523i	−0.793771	+	0.666053i	−0.946676	−	0.322188i	$-0.895582\pi$
$251$	−12.5757	+	10.5523i	−0.793771	+	0.666053i	0.152905	+	0.988241i	$0.451137\pi$
$252$	0.180839	+	0.151742i	0.0113918	+	0.00955882i
$253$	0.0916626	+	0.519845i	0.00576278	+	0.0326824i
$254$	11.8713	+	20.5617i	0.744873	+	1.29016i
$255$	−19.9192	+	34.5010i	−1.24739	+	2.16054i
$256$	−19.0480	−	6.93292i	−1.19050	−	0.433308i
$257$	10.2029	+	3.71353i	0.636436	+	0.231644i	0.640030	−	0.768350i	$-0.278922\pi$
$257$	10.2029	+	3.71353i	0.636436	+	0.231644i	−0.00359390	+	0.999994i	$0.501144\pi$
$258$	16.8713	−	29.2220i	1.05036	−	1.81928i
$259$	0.779543	+	1.35021i	0.0484385	+	0.0838979i
$260$	0.660597	+	3.74643i	0.0409685	+	0.232344i
$261$	−2.01367	−	1.68967i	−0.124643	−	0.104588i
$262$	−8.87401	+	7.44617i	−0.548238	+	0.460026i
$263$	−4.14820	+	23.5256i	−0.255789	+	1.45065i	0.538250	+	0.842785i	$0.319086\pi$
$263$	−4.14820	+	23.5256i	−0.255789	+	1.45065i	−0.794039	+	0.607867i	$0.792025\pi$
$264$	1.79465	−	0.653200i	0.110453	−	0.0402017i
$265$	16.1150			0.989934
$266$		0			0
$267$	14.1459			0.865715
$268$	−19.8226	+	7.21483i	−1.21086	+	0.440716i
$269$	4.47961	−	25.4051i	0.273127	−	1.54898i	−0.471724	−	0.881746i	$-0.656368\pi$
$269$	4.47961	−	25.4051i	0.273127	−	1.54898i	0.744850	−	0.667231i	$-0.232521\pi$
$270$	−21.3639	+	17.9264i	−1.30016	+	1.09097i
$271$	−14.7621	−	12.3868i	−0.896732	−	0.752447i	0.0728171	−	0.997345i	$-0.476801\pi$
$271$	−14.7621	−	12.3868i	−0.896732	−	0.752447i	−0.969549	+	0.244898i	$0.921246\pi$
$272$	5.19009	+	29.4345i	0.314696	+	1.78473i
$273$	0.163119	+	0.282530i	0.00987241	+	0.0170995i
$274$	8.28199	−	14.3448i	0.500334	−	0.866603i
$275$	7.10624	+	2.58646i	0.428523	+	0.155969i
$276$	1.10467	+	0.402069i	0.0664936	+	0.0242017i
$277$	7.38197	−	12.7859i	0.443539	−	0.768233i	−0.554410	−	0.832244i	$-0.687056\pi$
$277$	7.38197	−	12.7859i	0.443539	−	0.768233i	0.997949	+	0.0640111i	$0.0203893\pi$
$278$	−11.4984	−	19.9159i	−0.689630	−	1.19447i
$279$	0.204136	+	1.15771i	0.0122213	+	0.0693103i
$280$	−0.425177	−	0.356766i	−0.0254092	−	0.0213208i
$281$	−12.0008	+	10.0699i	−0.715908	+	0.600718i	−0.926250	−	0.376910i	$-0.876987\pi$
$281$	−12.0008	+	10.0699i	−0.715908	+	0.600718i	0.210342	+	0.977628i	$0.432542\pi$
$282$	7.20754	−	40.8760i	0.429203	−	2.43413i
$283$	11.3610	−	4.13508i	0.675344	−	0.245805i	0.0184969	−	0.999829i	$-0.494112\pi$
$283$	11.3610	−	4.13508i	0.675344	−	0.245805i	0.656847	+	0.754024i	$0.271890\pi$
$284$	16.3925			0.972714
$285$		0			0
$286$	−1.90983			−0.112931
$287$	0.483510	−	0.175983i	0.0285407	−	0.0103880i
$288$	0.786760	−	4.46194i	0.0463603	−	0.262922i
$289$	19.0657	−	15.9980i	1.12151	−	0.941062i
$290$	−20.0553	−	16.8284i	−1.17769	−	0.988198i
$291$	−1.46149	−	8.28854i	−0.0856743	−	0.485883i
$292$	−7.28115	−	12.6113i	−0.426097	−	0.738022i
$293$	7.64121	−	13.2350i	0.446404	−	0.773195i	−0.551745	−	0.834013i	$-0.686038\pi$
$293$	7.64121	−	13.2350i	0.446404	−	0.773195i	0.998149	+	0.0608184i	$0.0193710\pi$
$294$	−23.6094	−	8.59312i	−1.37693	−	0.501161i
$295$	26.7114	+	9.72216i	1.55520	+	0.566046i
$296$	2.39919	−	4.15551i	0.139450	−	0.241534i
$297$	−3.13068	−	5.42250i	−0.181661	−	0.314646i
$298$	−1.99317	−	11.3038i	−0.115461	−	0.654812i
$299$	0.212588	+	0.178383i	0.0122943	+	0.0103162i
$300$	12.9013	−	10.8255i	0.744859	−	0.625011i
$301$	0.382308	−	2.16818i	0.0220359	−	0.124972i
$302$	−30.9051	+	11.2485i	−1.77839	+	0.647281i
$303$	7.50245			0.431005
$304$		0			0
$305$	30.6525			1.75516
$306$	−7.14961	+	2.60224i	−0.408716	+	0.148760i
$307$	−4.79853	+	27.2138i	−0.273867	+	1.55317i	0.468672	+	0.883372i	$0.344732\pi$
$307$	−4.79853	+	27.2138i	−0.273867	+	1.55317i	−0.742539	+	0.669803i	$0.766379\pi$
$308$	−0.404367	+	0.339304i	−0.0230410	+	0.0193337i
$309$	16.2251	+	13.6145i	0.923013	+	0.774500i
$310$	2.03311	+	11.5303i	0.115473	+	0.654879i
$311$	7.23607	+	12.5332i	0.410320	+	0.710695i	0.994925	−	0.100624i	$-0.0320838\pi$
$311$	7.23607	+	12.5332i	0.410320	+	0.710695i	−0.584605	+	0.811318i	$0.698750\pi$
$312$	0.502029	−	0.869539i	0.0284218	−	0.0492279i
$313$	−5.05739	−	1.84074i	−0.285861	−	0.104045i	0.195110	−	0.980781i	$-0.437494\pi$
$313$	−5.05739	−	1.84074i	−0.285861	−	0.104045i	−0.480971	+	0.876737i	$0.659716\pi$
$314$	−8.15467	−	2.96806i	−0.460195	−	0.167497i
$315$	0.236068	−	0.408882i	0.0133009	−	0.0230379i
$316$	3.80423	+	6.58911i	0.214004	+	0.370667i
$317$	5.44072	+	30.8559i	0.305581	+	1.73304i	0.620756	+	0.784004i	$0.286826\pi$
$317$	5.44072	+	30.8559i	0.305581	+	1.73304i	−0.315174	+	0.949034i	$0.602063\pi$
$318$	13.8019	+	11.5812i	0.773971	+	0.649439i
$319$	4.50270	−	3.77821i	0.252103	−	0.211539i
$320$	2.64572	−	15.0046i	0.147900	−	0.838783i
$321$	−10.6955	+	3.89286i	−0.596967	+	0.217278i
$322$	0.171513			0.00955807
$323$		0			0
$324$	−16.9443			−0.941348
$325$	3.73597	−	1.35978i	0.207234	−	0.0754272i
$326$	−5.11042	+	28.9826i	−0.283040	+	1.60520i
$327$	−4.48450	+	3.76294i	−0.247994	+	0.208091i
$328$	−1.21310	−	1.01791i	−0.0669824	−	0.0562049i
$329$	−0.470275	−	2.66706i	−0.0259271	−	0.147040i
$330$	8.09017	+	14.0126i	0.445349	+	0.771367i
$331$	−10.1311	+	17.5476i	−0.556856	+	0.964503i	0.440901	+	0.897556i	$0.354659\pi$
$331$	−10.1311	+	17.5476i	−0.556856	+	0.964503i	−0.997757	+	0.0669469i	$0.978674\pi$
$332$	4.92029	+	1.79084i	0.270036	+	0.0982852i
$333$	3.83558	+	1.39604i	0.210189	+	0.0765024i
$334$	1.54508	−	2.67617i	0.0845433	−	0.146433i
$335$	21.0948	+	36.5372i	1.15253	+	1.99624i
$336$	−0.360081	−	2.04212i	−0.0196441	−	0.111407i
$337$	−0.425177	−	0.356766i	−0.0231609	−	0.0194343i	0.631134	−	0.775674i	$-0.282590\pi$
$337$	−0.425177	−	0.356766i	−0.0231609	−	0.0194343i	−0.654295	+	0.756240i	$0.727034\pi$
$338$	18.1732	−	15.2491i	0.988491	−	0.829443i
$339$		0			0
$340$	−31.8448	+	11.5906i	−1.72703	+	0.628587i
$341$	−2.62866			−0.142350
$342$		0			0
$343$	−3.29180			−0.177740
$344$	−6.36727	+	2.31750i	−0.343300	+	0.124951i
$345$	0.408271	−	2.31542i	0.0219806	−	0.124658i
$346$	24.2899	−	20.3816i	1.30583	−	1.09572i
$347$	22.0872	+	18.5334i	1.18570	+	0.994924i	0.999924	+	0.0123324i	$0.00392564\pi$
$347$	22.0872	+	18.5334i	1.18570	+	0.994924i	0.185780	+	0.982591i	$0.440519\pi$
$348$	−2.27308	−	12.8913i	−0.121850	−	0.691046i
$349$	−6.80902	−	11.7936i	−0.364478	−	0.631295i	0.624214	−	0.781253i	$-0.285419\pi$
$349$	−6.80902	−	11.7936i	−0.364478	−	0.631295i	−0.988692	+	0.149958i	$0.952086\pi$
$350$	1.22857	−	2.12795i	0.0656699	−	0.113744i
$351$	−3.09328	−	1.12586i	−0.165107	−	0.0600940i
$352$	9.52013	+	3.46504i	0.507424	+	0.184687i
$353$	−12.6910	+	21.9814i	−0.675473	+	1.16995i	0.300858	+	0.953669i	$0.402727\pi$
$353$	−12.6910	+	21.9814i	−0.675473	+	1.16995i	−0.976330	+	0.216284i	$0.930606\pi$
$354$	15.8904	+	27.5231i	0.844568	+	1.46283i
$355$	−5.69305	−	32.2869i	−0.302156	−	1.71361i
$356$	9.21798	+	7.73480i	0.488552	+	0.409944i
$357$	−2.22626	+	1.86805i	−0.117826	+	0.0988677i
$358$	2.86634	−	16.2558i	0.151491	−	0.859146i
$359$	33.2482	−	12.1013i	1.75477	−	0.638685i	0.754918	−	0.655819i	$-0.227677\pi$
$359$	33.2482	−	12.1013i	1.75477	−	0.638685i	0.999853	+	0.0171344i	$0.00545430\pi$
$360$	−1.45309			−0.0765843
$361$		0			0
$362$	11.0557			0.581076
$363$	16.2478	−	5.91371i	0.852788	−	0.310389i
$364$	−0.0481899	+	0.273298i	−0.00252584	+	0.0143247i
$365$	−22.3107	+	18.7209i	−1.16780	+	0.979899i
$366$	26.2527	+	22.0287i	1.37225	+	1.15146i
$367$	2.17544	+	12.3375i	0.113557	+	0.644014i	0.987454	+	0.157904i	$0.0504736\pi$
$367$	2.17544	+	12.3375i	0.113557	+	0.644014i	−0.873897	+	0.486110i	$0.838415\pi$
$368$	−0.881966	−	1.52761i	−0.0459757	−	0.0796322i
$369$	0.673542	−	1.16661i	0.0350632	−	0.0607312i
$370$	38.2008	+	13.9040i	1.98597	+	0.722833i
$371$	1.10467	+	0.402069i	0.0573519	+	0.0208744i
$372$	−2.92705	+	5.06980i	−0.151761	+	0.262857i
$373$	18.3803	+	31.8357i	0.951698	+	1.64839i	0.741749	+	0.670677i	$0.233996\pi$
$373$	18.3803	+	31.8357i	0.951698	+	1.64839i	0.209949	+	0.977712i	$0.432670\pi$
$374$	−2.95428	−	16.7546i	−0.152762	−	0.866357i
$375$	−2.22626	−	1.86805i	−0.114963	−	0.0964657i
$376$	−6.38498	+	5.35763i	−0.329280	+	0.276299i
$377$	0.536602	−	3.04322i	0.0276364	−	0.156734i
$378$	−1.91175	+	0.695820i	−0.0983298	+	0.0357891i
$379$	−21.3723			−1.09782			−0.548910	−	0.835882i	$-0.684957\pi$
$379$	−21.3723			−1.09782			−0.548910	+	0.835882i	$0.684957\pi$
$380$		0			0
$381$	23.7426			1.21637
$382$	−30.3858	+	11.0595i	−1.55467	+	0.565855i
$383$	−1.96338	+	11.1349i	−0.100324	+	0.568967i	0.892661	+	0.450729i	$0.148836\pi$
$383$	−1.96338	+	11.1349i	−0.100324	+	0.568967i	−0.992985	+	0.118238i	$0.962275\pi$
$384$	−8.31472	+	6.97688i	−0.424309	+	0.356038i
$385$	0.808735	+	0.678609i	0.0412169	+	0.0345851i
$386$	−2.80969	−	15.9345i	−0.143009	−	0.811046i
$387$	−2.88197	−	4.99171i	−0.146499	−	0.253743i
$388$	3.57971	−	6.20024i	0.181732	−	0.314770i
$389$	−1.79465	−	0.653200i	−0.0909925	−	0.0331186i	0.296123	−	0.955150i	$-0.404306\pi$
$389$	−1.79465	−	0.653200i	−0.0909925	−	0.0331186i	−0.387115	+	0.922031i	$0.626528\pi$
$390$	7.99350	+	2.90940i	0.404767	+	0.147323i
$391$	−1.23607	+	2.14093i	−0.0625106	+	0.108272i
$392$	2.52265	+	4.36937i	0.127413	+	0.220686i
$393$	2.01157	+	11.4082i	0.101470	+	0.575468i
$394$	−16.7161	−	14.0265i	−0.842144	−	0.706643i
$395$	11.6568	−	9.78124i	0.586519	−	0.492147i
$396$	−0.239976	+	1.36097i	−0.0120592	+	0.0683914i
$397$	−1.21389	+	0.441820i	−0.0609235	+	0.0221743i	−0.372302	−	0.928112i	$-0.621431\pi$
$397$	−1.21389	+	0.441820i	−0.0609235	+	0.0221743i	0.311379	+	0.950286i	$0.399209\pi$
$398$	2.00811			0.100658
$399$		0			0
$400$	−25.2705			−1.26353
$401$	−4.41870	+	1.60828i	−0.220659	+	0.0803134i	−0.449984	−	0.893037i	$-0.648570\pi$
$401$	−4.41870	+	1.60828i	−0.220659	+	0.0803134i	0.229325	+	0.973350i	$0.426348\pi$
$402$	−8.19086	+	46.4527i	−0.408523	+	2.31685i
$403$	−1.05865	+	0.888311i	−0.0527350	+	0.0442499i
$404$	4.88887	+	4.10225i	0.243230	+	0.204094i
$405$	5.88468	+	33.3737i	0.292412	+	1.65835i
$406$	−0.954915	−	1.65396i	−0.0473916	−	0.0820847i
$407$	−4.56352	+	7.90426i	−0.226206	+	0.391799i
$408$	8.40487	+	3.05912i	0.416103	+	0.151449i
$409$	22.6151	+	8.23121i	1.11824	+	0.407007i	0.834011	−	0.551749i	$-0.186039\pi$
$409$	22.6151	+	8.23121i	1.11824	+	0.407007i	0.284232	+	0.958756i	$0.408261\pi$
$410$	6.70820	−	11.6190i	0.331295	−	0.573819i
$411$	−8.28199	−	14.3448i	−0.408521	−	0.707579i
$412$	3.12863	+	17.7434i	0.154137	+	0.874152i
$413$	1.58849	+	1.33290i	0.0781645	+	0.0655878i
$414$	0.343975	−	0.288630i	0.0169055	−	0.0141854i
$415$	1.81847	−	10.3130i	0.0892651	−	0.506247i
$416$	5.00503	−	1.82168i	0.245392	−	0.0893152i
$417$	−22.9969			−1.12616
$418$		0			0
$419$	−6.58359			−0.321630			−0.160815	−	0.986985i	$-0.551412\pi$
$419$	−6.58359			−0.321630			−0.160815	+	0.986985i	$0.551412\pi$
$420$	2.20935	−	0.804138i	0.107805	−	0.0392379i
$421$	5.62645	−	31.9092i	0.274216	−	1.55516i	−0.467224	−	0.884139i	$-0.654746\pi$
$421$	5.62645	−	31.9092i	0.274216	−	1.55516i	0.741440	−	0.671019i	$-0.234143\pi$
$422$	−0.904193	+	0.758708i	−0.0440154	+	0.0369333i
$423$	−5.43139	−	4.55747i	−0.264083	−	0.221592i
$424$	−0.628265	−	3.56307i	−0.0305112	−	0.173038i
$425$	17.7082	+	30.6715i	0.858974	+	1.48779i
$426$	18.3273	−	31.7439i	0.887963	−	1.53800i
$427$	2.10122	+	0.764780i	0.101685	+	0.0370103i
$428$	−9.09818	−	3.31147i	−0.439777	−	0.160066i
$429$	−0.954915	+	1.65396i	−0.0461037	+	0.0798540i
$430$	−28.7032	−	49.7154i	−1.38419	−	2.39749i
$431$	2.16752	+	12.2926i	0.104406	+	0.592114i	0.991456	+	0.130442i	$0.0416395\pi$
$431$	2.16752	+	12.2926i	0.104406	+	0.592114i	−0.887050	+	0.461673i	$0.847249\pi$
$432$	16.0281	+	13.4492i	0.771154	+	0.647075i
$433$	14.4898	−	12.1584i	0.696337	−	0.584296i	−0.224392	−	0.974499i	$-0.572040\pi$
$433$	14.4898	−	12.1584i	0.696337	−	0.584296i	0.920729	+	0.390203i	$0.127595\pi$
$434$	−0.148313	+	0.841126i	−0.00711926	+	0.0403754i
$435$	−24.6015	+	8.95420i	−1.17955	+	0.429321i
$436$	−4.97980			−0.238489
$437$		0			0
$438$	−32.5623			−1.55589
$439$	5.62298	−	2.04660i	0.268370	−	0.0976788i	−0.204330	−	0.978902i	$-0.565502\pi$
$439$	5.62298	−	2.04660i	0.268370	−	0.0976788i	0.472700	+	0.881223i	$0.343279\pi$
$440$	0.564217	−	3.19983i	0.0268980	−	0.152546i
$441$	−3.28771	+	2.75871i	−0.156557	+	0.131367i
$442$	−6.85171	−	5.74927i	−0.325903	−	0.273465i
$443$	2.63604	+	14.9497i	0.125242	+	0.710282i	0.981164	+	0.193177i	$0.0618793\pi$
$443$	2.63604	+	14.9497i	0.125242	+	0.710282i	−0.855922	+	0.517105i	$0.827010\pi$
$444$	10.1631	+	17.6030i	0.482320	+	0.835403i
$445$	12.0332	−	20.8421i	0.570429	−	0.988013i
$446$	−29.1105	−	10.5953i	−1.37842	−	0.501704i
$447$	−10.7860	−	3.92577i	−0.510159	−	0.185683i
$448$	0.555728	−	0.962549i	0.0262557	−	0.0454762i
$449$	−12.1190	−	20.9907i	−0.571930	−	0.990612i	−0.996368	−	0.0851545i	$-0.972862\pi$
$449$	−12.1190	−	20.9907i	−0.571930	−	0.990612i	0.424438	−	0.905457i	$-0.360472\pi$
$450$	−1.11706	−	6.33515i	−0.0526586	−	0.298642i
$451$	2.30746	+	1.93619i	0.108654	+	0.0911715i
$452$		0			0
$453$	−5.71104	+	32.3889i	−0.268328	+	1.52176i
$454$	28.1184	−	10.2343i	1.31966	−	0.480318i
$455$	0.555029			0.0260202
$456$		0			0
$457$	6.29180			0.294318			0.147159	−	0.989113i	$-0.452987\pi$
$457$	6.29180			0.294318			0.147159	+	0.989113i	$0.452987\pi$
$458$	−12.6730	+	4.61259i	−0.592170	+	0.215532i
$459$	5.09202	−	28.8783i	0.237675	−	1.34792i
$460$	1.53209	−	1.28558i	0.0714340	−	0.0599403i
$461$	−9.05438	−	7.59753i	−0.421705	−	0.353852i	0.407106	−	0.913381i	$-0.366538\pi$
$461$	−9.05438	−	7.59753i	−0.421705	−	0.353852i	−0.828811	+	0.559528i	$0.810982\pi$
$462$	0.204964	+	1.16241i	0.00953578	+	0.0540801i
$463$	−5.07295	−	8.78661i	−0.235760	−	0.408348i	0.723733	−	0.690080i	$-0.242425\pi$
$463$	−5.07295	−	8.78661i	−0.235760	−	0.408348i	−0.959493	+	0.281732i	$0.909091\pi$
$464$	−9.82084	+	17.0102i	−0.455921	+	0.789678i
$465$	11.0021	+	4.00444i	0.510211	+	0.185702i
$466$	8.09311	+	2.94565i	0.374906	+	0.136455i
$467$	−2.11803	+	3.66854i	−0.0980109	+	0.169760i	−0.910861	−	0.412713i	$-0.864581\pi$
$467$	−2.11803	+	3.66854i	−0.0980109	+	0.169760i	0.812850	+	0.582473i	$0.197915\pi$
$468$	0.363271	+	0.629204i	0.0167922	+	0.0290850i
$469$	0.534434	+	3.03093i	0.0246779	+	0.139955i
$470$	−54.0944	−	45.3906i	−2.49519	−	2.09371i
$471$	−6.64775	+	5.57812i	−0.306312	+	0.257026i
$472$	1.10822	−	6.28501i	0.0510098	−	0.289291i
$473$	12.1113	−	4.40814i	0.556877	−	0.202687i
$474$	17.0130			0.781434
$475$		0			0
$476$	−2.47214			−0.113310
$477$	2.89208	−	1.05263i	0.132419	−	0.0481966i
$478$	3.02088	−	17.1322i	0.138172	−	0.783610i
$479$	−12.1876	+	10.2266i	−0.556867	+	0.467267i	−0.877259	−	0.480018i	$-0.840630\pi$
$479$	−12.1876	+	10.2266i	−0.556867	+	0.467267i	0.320391	+	0.947285i	$0.396186\pi$
$480$	−34.5675	−	29.0055i	−1.57778	−	1.32392i
$481$	0.833229	+	4.72548i	0.0379920	+	0.215463i
$482$	−25.8156	−	44.7139i	−1.17587	−	2.03666i
$483$	0.0857567	−	0.148535i	0.00390207	−	0.00675858i
$484$	13.8212	+	5.03050i	0.628236	+	0.228659i
$485$	−13.4553	−	4.89733i	−0.610974	−	0.222377i
$486$	−6.01722	+	10.4221i	−0.272947	+	0.472758i
$487$	−8.33499	−	14.4366i	−0.377695	−	0.654186i	0.613032	−	0.790058i	$-0.289950\pi$
$487$	−8.33499	−	14.4366i	−0.377695	−	0.654186i	−0.990726	+	0.135872i	$0.956616\pi$
$488$	−1.19503	−	6.77736i	−0.0540965	−	0.306797i
$489$	22.5445	+	18.9171i	1.01950	+	0.855460i
$490$	−32.7442	+	27.4757i	−1.47923	+	1.24122i
$491$	2.99899	−	17.0081i	0.135343	−	0.767566i	−0.839278	−	0.543703i	$-0.817022\pi$
$491$	2.99899	−	17.0081i	0.135343	−	0.767566i	0.974621	−	0.223864i	$-0.0718670\pi$
$492$	6.30365	−	2.29434i	0.284190	−	0.103437i
$493$	27.5276			1.23978
$494$		0			0
$495$	2.76393			0.124230
$496$	8.25428	−	3.00431i	0.370628	−	0.134898i
$497$	0.415302	−	2.35530i	0.0186288	−	0.105649i
$498$	8.96900	−	7.52589i	0.401911	−	0.337243i
$499$	23.3430	+	19.5871i	1.04498	+	0.876840i	0.992556	−	0.121786i	$-0.0388620\pi$
$499$	23.3430	+	19.5871i	1.04498	+	0.876840i	0.0524202	+	0.998625i	$0.483306\pi$
$500$	−0.429282	−	2.43458i	−0.0191981	−	0.108878i
$501$	−1.54508	−	2.67617i	−0.0690293	−	0.119562i
$502$	−15.6129	+	27.0424i	−0.696839	+	1.20696i
$503$	−19.3546	−	7.04450i	−0.862979	−	0.314099i	−0.127659	−	0.991818i	$-0.540746\pi$
$503$	−19.3546	−	7.04450i	−0.862979	−	0.314099i	−0.735321	+	0.677719i	$0.762968\pi$
$504$	−0.0996085	−	0.0362545i	−0.00443691	−	0.00161490i
$505$	6.38197	−	11.0539i	0.283994	−	0.491892i
$506$	0.502029	+	0.869539i	0.0223179	+	0.0386557i
$507$	−4.11953	−	23.3630i	−0.182955	−	1.03759i
$508$	15.4716	+	12.9822i	0.686440	+	0.575991i
$509$	−13.9333	+	11.6914i	−0.617581	+	0.518212i	−0.897042	−	0.441945i	$-0.854289\pi$
$509$	−13.9333	+	11.6914i	−0.617581	+	0.518212i	0.279461	+	0.960157i	$0.409844\pi$
$510$	−13.1586	+	74.6259i	−0.582671	+	3.30449i
$511$	−1.99648	+	0.726660i	−0.0883192	+	0.0321455i
$512$	−27.1441			−1.19961
$513$		0			0
$514$	20.6525			0.910942
$515$	33.8610	−	12.3244i	1.49209	−	0.543078i
$516$	4.98426	−	28.2671i	0.219420	−	1.24439i
$517$	12.1449	−	10.1908i	0.534134	−	0.448192i
$518$	2.27175	+	1.90622i	0.0998149	+	0.0837547i
$519$	−5.50607	−	31.2265i	−0.241690	−	1.37069i
$520$	−0.854102	−	1.47935i	−0.0374548	−	0.0648737i
$521$	−10.9106	+	18.8978i	−0.478004	+	0.827928i	−0.999682	−	0.0252149i	$-0.991973\pi$
$521$	−10.9106	+	18.8978i	−0.478004	+	0.827928i	0.521678	+	0.853143i	$0.325306\pi$
$522$	−4.69846	−	1.71010i	−0.205646	−	0.0748491i
$523$	−32.3344	−	11.7688i	−1.41388	−	0.514612i	−0.481617	−	0.876382i	$-0.659950\pi$
$523$	−32.3344	−	11.7688i	−1.41388	−	0.514612i	−0.932267	+	0.361770i	$0.882173\pi$
$524$	−4.92705	+	8.53390i	−0.215239	+	0.372805i
$525$	−1.22857	−	2.12795i	−0.0536192	−	0.0928712i
$526$	7.89035	+	44.7484i	0.344036	+	1.95112i
$527$	−9.43057	−	7.91319i	−0.410802	−	0.344704i
$528$	9.29918	−	7.80294i	0.404695	−	0.339579i
$529$	−3.96857	+	22.5069i	−0.172547	+	0.978561i
$530$	28.8039	−	10.4838i	1.25116	−	0.455386i
$531$	5.42882			0.235591
$532$		0			0
$533$	1.58359			0.0685930
$534$	25.2844	−	9.20277i	1.09416	−	0.398243i
$535$	−3.36255	+	19.0700i	−0.145376	+	0.824467i
$536$	7.25608	−	6.08857i	0.313415	−	0.262986i
$537$	−12.6448	−	10.6102i	−0.545662	−	0.457865i
$538$	−8.52072	−	48.3234i	−0.367354	−	2.08337i
$539$	−4.79837	−	8.31103i	−0.206681	−	0.357981i
$540$	−11.8617	+	20.5451i	−0.510447	+	0.884119i
$541$	−6.30365	−	2.29434i	−0.271015	−	0.0986414i	0.202938	−	0.979192i	$-0.434951\pi$
$541$	−6.30365	−	2.29434i	−0.271015	−	0.0986414i	−0.473953	+	0.880550i	$0.657173\pi$
$542$	−34.4441	−	12.5366i	−1.47950	−	0.538495i
$543$	5.52786	−	9.57454i	0.237223	−	0.410883i
$544$	23.7234	+	41.0902i	1.01713	+	1.76173i
$545$	1.72947	+	9.80828i	0.0740821	+	0.420141i
$546$	0.475362	+	0.398876i	0.0203436	+	0.0170703i
$547$	−15.8657	+	13.3129i	−0.678370	+	0.569220i	−0.915529	−	0.402251i	$-0.868228\pi$
$547$	−15.8657	+	13.3129i	−0.678370	+	0.569220i	0.237160	+	0.971471i	$0.423784\pi$
$548$	2.44673	−	13.8761i	0.104519	−	0.592758i
$549$	5.50106	−	2.00222i	0.234779	−	0.0854527i
$550$	14.3844			0.613351
$551$		0			0
$552$	−0.527864			−0.0224674
$553$	1.04311	−	0.379662i	0.0443577	−	0.0161449i
$554$	4.87650	−	27.6560i	0.207183	−	1.17499i
$555$	31.1416	−	26.1309i	1.32189	−	1.10920i
$556$	−14.9856	−	12.5744i	−0.635531	−	0.533274i
$557$	−6.83491	−	38.7627i	−0.289604	−	1.64243i	−0.688359	−	0.725371i	$-0.741668\pi$
$557$	−6.83491	−	38.7627i	−0.289604	−	1.64243i	0.398754	−	0.917058i	$-0.369443\pi$
$558$	1.11803	+	1.93649i	0.0473302	+	0.0819782i
$559$	3.38795	−	5.86811i	0.143295	−	0.248195i
$560$	−3.31511	−	1.20660i	−0.140089	−	0.0509882i
$561$	−15.9870	−	5.81879i	−0.674972	−	0.245670i
$562$	−14.8992	+	25.8061i	−0.628484	+	1.08857i
$563$	−10.8576	−	18.8060i	−0.457595	−	0.792578i	0.541238	−	0.840869i	$-0.317956\pi$
$563$	−10.8576	−	18.8060i	−0.457595	−	0.792578i	−0.998833	+	0.0482911i	$0.984622\pi$
$564$	−6.13110	−	34.7712i	−0.258166	−	1.46413i
$565$		0			0
$566$	17.6166	−	14.7821i	0.740482	−	0.621338i
$567$	−0.429282	+	2.43458i	−0.0180281	+	0.102243i
$568$	−6.91678	+	2.51750i	−0.290221	+	0.105632i
$569$	25.4540			1.06709			0.533544	−	0.845772i	$-0.320860\pi$
$569$	25.4540			1.06709			0.533544	+	0.845772i	$0.320860\pi$
$570$		0			0
$571$	−46.1033			−1.92936			−0.964682	−	0.263417i	$-0.915150\pi$
$571$	−46.1033			−1.92936			−0.964682	+	0.263417i	$0.915150\pi$
$572$	−1.52662	+	0.555645i	−0.0638313	+	0.0232327i
$573$	−5.61507	+	31.8447i	−0.234573	+	1.33033i
$574$	0.749738	−	0.629105i	0.0312935	−	0.0262583i
$575$	−1.60116	−	1.34354i	−0.0667731	−	0.0560293i
$576$	−0.505287	−	2.86562i	−0.0210536	−	0.119401i
$577$	7.64590	+	13.2431i	0.318303	+	0.551317i	0.980134	−	0.198336i	$-0.0635538\pi$
$577$	7.64590	+	13.2431i	0.318303	+	0.551317i	−0.661831	+	0.749653i	$0.730220\pi$
$578$	23.6704	−	40.9984i	0.984559	−	1.70531i
$579$	−15.2045	−	5.53400i	−0.631879	−	0.229985i
$580$	−20.9273	−	7.61690i	−0.868957	−	0.316275i
$581$	0.381966	−	0.661585i	0.0158466	−	0.0274472i
$582$	−8.00448	−	13.8642i	−0.331796	−	0.574688i
$583$	1.19503	+	6.77736i	0.0494931	+	0.280689i
$584$	5.00907	+	4.20311i	0.207277	+	0.173926i
$585$	1.11313	−	0.934025i	0.0460222	−	0.0386172i
$586$	5.04776	−	28.6273i	0.208521	−	1.18258i
$587$	−15.8053	+	5.75266i	−0.652355	+	0.237438i	−0.646932	−	0.762548i	$-0.723948\pi$
$587$	−15.8053	+	5.75266i	−0.652355	+	0.237438i	−0.00542275	+	0.999985i	$0.501726\pi$
$588$	−21.3723			−0.881378
$589$		0			0
$590$	54.0689			2.22598
$591$	−20.5053	+	7.46332i	−0.843476	+	0.307000i
$592$	5.29615	−	30.0360i	0.217670	−	1.23447i
$593$	13.2463	−	11.1150i	0.543960	−	0.456436i	−0.328930	−	0.944354i	$-0.606688\pi$
$593$	13.2463	−	11.1150i	0.543960	−	0.456436i	0.872889	+	0.487918i	$0.162243\pi$
$594$	−9.12346	−	7.65549i	−0.374340	−	0.314109i
$595$	0.858564	+	4.86916i	0.0351977	+	0.199616i
$596$	−4.88197	−	8.45581i	−0.199973	−	0.346364i
$597$	1.00406	−	1.73908i	0.0410933	−	0.0711757i
$598$	0.496030	+	0.180540i	0.0202842	+	0.00738284i
$599$	−4.57987	−	1.66694i	−0.187128	−	0.0681092i	0.246756	−	0.969078i	$-0.420635\pi$
$599$	−4.57987	−	1.66694i	−0.187128	−	0.0681092i	−0.433885	+	0.900968i	$0.642857\pi$
$600$	−3.78115	+	6.54915i	−0.154365	+	0.267368i
$601$	4.87380	+	8.44166i	0.198806	+	0.344343i	0.948142	−	0.317848i	$-0.102960\pi$
$601$	4.87380	+	8.44166i	0.198806	+	0.344343i	−0.749335	+	0.662191i	$0.769627\pi$
$602$	−0.727194	−	4.12412i	−0.0296382	−	0.168087i
$603$	6.17239	+	5.17925i	0.251359	+	0.210915i
$604$	−21.4314	+	17.9831i	−0.872030	+	0.731720i
$605$	5.10811	−	28.9695i	0.207674	−	1.17778i
$606$	13.4099	−	4.88080i	0.544740	−	0.198269i
$607$	−27.9767			−1.13554			−0.567769	−	0.823188i	$-0.692193\pi$
$607$	−27.9767			−1.13554			−0.567769	+	0.823188i	$0.692193\pi$
$608$		0			0
$609$	−1.90983			−0.0773902
$610$	54.7883	−	19.9413i	2.21831	−	0.807400i
$611$	1.44736	−	8.20837i	0.0585538	−	0.332075i
$612$	−4.95794	+	4.16021i	−0.200413	+	0.168166i
$613$	−25.6411	−	21.5155i	−1.03564	−	0.869002i	−0.0441252	−	0.999026i	$-0.514050\pi$
$613$	−25.6411	−	21.5155i	−1.03564	−	0.869002i	−0.991511	+	0.130024i	$0.958494\pi$
$614$	9.12735	+	51.7638i	0.368350	+	2.08902i
$615$	−6.70820	−	11.6190i	−0.270501	−	0.468521i
$616$	0.118513	−	0.205270i	0.00477502	−	0.00827058i
$617$	15.2893	+	5.56484i	0.615523	+	0.224032i	0.630918	−	0.775849i	$-0.282678\pi$
$617$	15.2893	+	5.56484i	0.615523	+	0.224032i	−0.0153950	+	0.999881i	$0.504901\pi$
$618$	37.8578	+	13.7791i	1.52286	+	0.554277i
$619$	17.3885	−	30.1178i	0.698905	−	1.21054i	−0.269942	−	0.962877i	$-0.587005\pi$
$619$	17.3885	−	30.1178i	0.698905	−	1.21054i	0.968847	−	0.247662i	$-0.0796621\pi$
$620$	4.97980	+	8.62526i	0.199993	+	0.346399i
$621$	0.300515	+	1.70431i	0.0120593	+	0.0683915i
$622$	21.0874	+	17.6944i	0.845527	+	0.709482i
$623$	1.34489	−	1.12849i	0.0538817	−	0.0452121i
$624$	1.10822	−	6.28501i	0.0443642	−	0.251602i
$625$	21.0645	−	7.66686i	0.842581	−	0.306675i
$626$	−10.2371			−0.409157
$627$		0			0
$628$	−7.38197			−0.294573
$629$	−40.1667	+	14.6195i	−1.60155	+	0.582917i
$630$	0.155946	−	0.884412i	0.00621303	−	0.0352358i
$631$	−19.1511	+	16.0697i	−0.762394	+	0.639724i	−0.938749	−	0.344602i	$-0.888014\pi$
$631$	−19.1511	+	16.0697i	−0.762394	+	0.639724i	0.176355	+	0.984327i	$0.443569\pi$
$632$	−2.61712	−	2.19602i	−0.104103	−	0.0873532i
$633$	0.204964	+	1.16241i	0.00814658	+	0.0462016i
$634$	29.7984	+	51.6123i	1.18344	+	2.04979i
$635$	20.1967	−	34.9817i	0.801482	−	1.38821i
$636$	14.4020	+	5.24188i	0.571075	+	0.207854i
$637$	−4.74104	−	1.72560i	−0.187847	−	0.0683707i
$638$	5.59017	−	9.68246i	0.221317	−	0.383332i
$639$	−3.13068	−	5.42250i	−0.123848	−	0.214511i
$640$	3.20660	+	18.1856i	0.126752	+	0.718847i
$641$	−35.8400	−	30.0733i	−1.41559	−	1.18783i	−0.953651	−	0.300916i	$-0.902708\pi$
$641$	−35.8400	−	30.0733i	−1.41559	−	1.18783i	−0.461944	−	0.886909i	$-0.652848\pi$
$642$	−16.5847	+	13.9162i	−0.654546	+	0.549229i
$643$	−0.991219	+	5.62148i	−0.0390899	+	0.221690i	−0.998095	−	0.0616999i	$-0.980348\pi$
$643$	−0.991219	+	5.62148i	−0.0390899	+	0.221690i	0.959005	+	0.283390i	$0.0914589\pi$
$644$	0.137099	−	0.0499001i	0.00540247	−	0.00196634i
$645$	−57.4064			−2.26038
$646$		0			0
$647$	8.12461			0.319411			0.159706	−	0.987165i	$-0.448945\pi$
$647$	8.12461			0.319411			0.159706	+	0.987165i	$0.448945\pi$
$648$	7.14961	−	2.60224i	0.280863	−	0.102226i
$649$	−2.10795	+	11.9548i	−0.0827444	+	0.469267i
$650$	5.79306	−	4.86096i	0.227223	−	0.190662i
$651$	0.654280	+	0.549006i	0.0256433	+	0.0215172i
$652$	4.34719	+	24.6541i	0.170249	+	0.965530i
$653$	11.3713	+	19.6957i	0.444994	+	0.770753i	0.998052	−	0.0623904i	$-0.0198724\pi$
$653$	11.3713	+	19.6957i	0.444994	+	0.770753i	−0.553058	+	0.833143i	$0.686539\pi$
$654$	−5.56758	+	9.64333i	−0.217710	+	0.377084i
$655$	18.5197	+	6.74060i	0.723623	+	0.263377i
$656$	−9.45856	−	3.44264i	−0.369295	−	0.134412i
$657$	−2.78115	+	4.81710i	−0.108503	+	0.187933i
$658$	−2.57565	−	4.46117i	−0.100409	−	0.173914i
$659$	−6.56916	−	37.2555i	−0.255898	−	1.45127i	−0.793757	−	0.608235i	$-0.791878\pi$
$659$	−6.56916	−	37.2555i	−0.255898	−	1.45127i	0.537859	−	0.843035i	$-0.319233\pi$
$660$	10.5437	+	8.84721i	0.410413	+	0.344377i
$661$	25.8027	−	21.6510i	1.00361	−	0.842127i	0.0161277	−	0.999870i	$-0.494866\pi$
$661$	25.8027	−	21.6510i	1.00361	−	0.842127i	0.987480	+	0.157743i	$0.0504217\pi$
$662$	−6.69258	+	37.9555i	−0.260114	+	1.47518i
$663$	−8.40487	+	3.05912i	−0.326418	+	0.118806i
$664$	−2.35114			−0.0912420
$665$		0			0
$666$	7.76393			0.300846
$667$	−1.52662	+	0.555645i	−0.0591111	+	0.0215147i
$668$	0.456461	−	2.58872i	0.0176610	−	0.100161i
$669$	−23.7311	+	19.9127i	−0.917496	+	0.769871i
$670$	61.4745	+	51.5832i	2.37497	+	1.99283i
$671$	2.27308	+	12.8913i	0.0877514	+	0.497663i
$672$	−1.64590	−	2.85078i	−0.0634919	−	0.109971i
$673$	−4.78804	+	8.29313i	−0.184565	+	0.319677i	−0.943430	−	0.331572i	$-0.892421\pi$
$673$	−4.78804	+	8.29313i	−0.184565	+	0.319677i	0.758865	+	0.651248i	$0.225754\pi$
$674$	−0.992060	−	0.361080i	−0.0382127	−	0.0139083i
$675$	23.2978	+	8.47970i	0.896732	+	0.326384i
$676$	10.0902	−	17.4767i	0.388083	−	0.672180i
$677$	−7.55545	−	13.0864i	−0.290380	−	0.502952i	0.683520	−	0.729932i	$-0.260448\pi$
$677$	−7.55545	−	13.0864i	−0.290380	−	0.502952i	−0.973899	+	0.226980i	$0.927115\pi$
$678$		0			0
$679$	−0.800169	−	0.671421i	−0.0307077	−	0.0257668i
$680$	11.6568	−	9.78124i	0.447019	−	0.375093i
$681$	5.19607	−	29.4684i	0.199114	−	1.12923i
$682$	−4.69846	+	1.71010i	−0.179913	+	0.0654831i
$683$	40.2219			1.53905			0.769524	−	0.638618i	$-0.220494\pi$
$683$	40.2219			1.53905			0.769524	+	0.638618i	$0.220494\pi$
$684$		0			0
$685$	−28.1803			−1.07672
$686$	−5.88376	+	2.14151i	−0.224643	+	0.0817634i
$687$	−2.34187	+	13.2814i	−0.0893480	+	0.506718i
$688$	−32.9927	+	27.6841i	−1.25783	+	1.05545i
$689$	2.77157	+	2.32563i	0.105589	+	0.0885993i
$690$	−0.776578	−	4.40419i	−0.0295638	−	0.167665i
$691$	8.15248	+	14.1205i	0.310135	+	0.537169i	0.978391	−	0.206762i	$-0.0662925\pi$
$691$	8.15248	+	14.1205i	0.310135	+	0.537169i	−0.668257	+	0.743931i	$0.732959\pi$
$692$	13.4863	−	23.3590i	0.512672	−	0.887975i
$693$	0.189467	+	0.0689602i	0.00719724	+	0.00261958i
$694$	51.5358	+	18.7575i	1.95627	+	0.712025i
$695$	−19.5623	+	33.8829i	−0.742041	+	1.28525i
$696$	2.93893	+	5.09037i	0.111400	+	0.192950i
$697$	2.44963	+	13.8925i	0.0927863	+	0.526217i
$698$	−19.8429	−	16.6502i	−0.751064	−	0.630218i
$699$	6.59756	−	5.53601i	0.249543	−	0.209391i
$700$	0.362954	−	2.05842i	0.0137184	−	0.0778008i
$701$	−8.21540	+	2.99016i	−0.310291	+	0.112937i	−0.492472	−	0.870328i	$-0.663907\pi$
$701$	−8.21540	+	2.99016i	−0.310291	+	0.112937i	0.182181	+	0.983265i	$0.441684\pi$
$702$	−6.26137			−0.236320
$703$		0			0
$704$	6.50658			0.245226
$705$	−66.3566	+	24.1518i	−2.49913	+	0.909610i
$706$	−8.38362	+	47.5459i	−0.315522	+	1.78941i
$707$	0.713276	−	0.598510i	0.0268255	−	0.0225093i
$708$	20.7096	+	17.3774i	0.778314	+	0.653083i
$709$	−2.32973	−	13.2126i	−0.0874950	−	0.496209i	−0.996790	−	0.0800573i	$-0.974490\pi$
$709$	−2.32973	−	13.2126i	−0.0874950	−	0.496209i	0.909295	−	0.416152i	$-0.136621\pi$
$710$	−31.1803	−	54.0059i	−1.17018	−	2.02681i
$711$	1.45309	−	2.51682i	0.0544949	−	0.0943880i
$712$	−5.07740	−	1.84802i	−0.190283	−	0.0692575i
$713$	0.682727	+	0.248492i	0.0255683	+	0.00930611i
$714$	−2.76393	+	4.78727i	−0.103438	+	0.179159i
$715$	1.62460	+	2.81389i	0.0607565	+	0.105233i
$716$	−2.43825	−	13.8280i	−0.0911218	−	0.516777i
$717$	−13.3265	−	11.1823i	−0.497688	−	0.417610i
$718$	51.5552	−	43.2599i	1.92402	−	1.61445i
$719$	2.53839	−	14.3960i	0.0946662	−	0.536878i	−0.900183	−	0.435512i	$-0.856567\pi$
$719$	2.53839	−	14.3960i	0.0946662	−	0.536878i	0.994849	−	0.101367i	$-0.0323215\pi$
$720$	−8.67906	+	3.15892i	−0.323450	+	0.117726i
$721$	2.62866			0.0978962
$722$		0			0
$723$	−51.6312			−1.92018
$724$	8.83740	−	3.21655i	0.328439	−	0.119542i
$725$	−4.04155	+	22.9208i	−0.150100	+	0.851257i
$726$	25.1941	−	21.1403i	0.935040	−	0.784592i
$727$	−28.3010	−	23.7473i	−1.04962	−	0.880739i	−0.0565703	−	0.998399i	$-0.518016\pi$
$727$	−28.3010	−	23.7473i	−1.04962	−	0.880739i	−0.993054	+	0.117659i	$0.962461\pi$
$728$	−0.0216386	−	0.122719i	−0.000801980	−	0.00454826i
$729$	−9.69098	−	16.7853i	−0.358925	−	0.621677i
$730$	−27.6992	+	47.9763i	−1.02519	+	1.77568i
$731$	56.7205	+	20.6446i	2.09788	+	0.763567i
$732$	27.3941	+	9.97065i	1.01252	+	0.368526i
$733$	−6.40983	+	11.1022i	−0.236752	+	0.410067i	−0.959781	−	0.280751i	$-0.909416\pi$
$733$	−6.40983	+	11.1022i	−0.236752	+	0.410067i	0.723028	+	0.690819i	$0.242750\pi$
$734$	11.9147	+	20.6369i	0.439780	+	0.761721i
$735$	7.42251	+	42.0952i	0.273783	+	1.55270i
$736$	−2.14505	−	1.79991i	−0.0790677	−	0.0663457i
$737$	−13.8019	+	11.5812i	−0.508399	+	0.426597i
$738$	0.444940	−	2.52338i	0.0163785	−	0.0928869i
$739$	−18.2978	+	6.65986i	−0.673096	+	0.244987i	−0.655880	−	0.754865i	$-0.727702\pi$
$739$	−18.2978	+	6.65986i	−0.673096	+	0.244987i	−0.0172158	+	0.999852i	$0.505480\pi$
$740$	34.5811			1.27123
$741$		0			0
$742$	2.23607			0.0820886
$743$	−34.5437	+	12.5729i	−1.26729	+	0.461255i	−0.886208	−	0.463288i	$-0.846670\pi$
$743$	−34.5437	+	12.5729i	−1.26729	+	0.461255i	−0.381079	+	0.924542i	$0.624447\pi$
$744$	0.456461	−	2.58872i	0.0167347	−	0.0949071i
$745$	−14.9592	+	12.5523i	−0.548063	+	0.459880i
$746$	53.5641	+	44.9456i	1.96112	+	1.64558i
$747$	−0.347296	−	1.96962i	−0.0127069	−	0.0720645i
$748$	−7.23607	−	12.5332i	−0.264577	−	0.458261i
$749$	−0.706298	+	1.22334i	−0.0258076	+	0.0447000i
$750$	−5.19449	−	1.89064i	−0.189676	−	0.0690364i
$751$	−11.3456	−	4.12945i	−0.414006	−	0.150686i	0.126615	−	0.991952i	$-0.459589\pi$
$751$	−11.3456	−	4.12945i	−0.414006	−	0.150686i	−0.540621	+	0.841266i	$0.681811\pi$
$752$	−26.4894	+	45.8809i	−0.965967	+	1.67310i
$753$	15.6129	+	27.0424i	0.568967	+	0.985480i
$754$	−1.02068	−	5.78855i	−0.0371709	−	0.210807i
$755$	42.8627	+	35.9661i	1.55993	+	1.30894i
$756$	−1.32572	+	1.11241i	−0.0482158	+	0.0404579i
$757$	−6.47196	+	36.7043i	−0.235227	+	1.33404i	0.606907	+	0.794773i	$0.292410\pi$
$757$	−6.47196	+	36.7043i	−0.235227	+	1.33404i	−0.842135	+	0.539267i	$0.818701\pi$
$758$	−38.2008	+	13.9040i	−1.38752	+	0.505015i
$759$	1.00406			0.0364450
$760$		0			0
$761$	−23.9443			−0.867979			−0.433990	−	0.900918i	$-0.642895\pi$
$761$	−23.9443			−0.867979			−0.433990	+	0.900918i	$0.642895\pi$
$762$	42.4376	−	15.4460i	1.53735	−	0.559551i
$763$	−0.126163	+	0.715505i	−0.00456740	+	0.0259030i
$764$	−21.0713	+	17.6809i	−0.762331	+	0.639672i
$765$	9.91589	+	8.32042i	0.358510	+	0.300825i
$766$	3.73458	+	21.1798i	0.134936	+	0.765259i
$767$	3.19098	+	5.52694i	0.115220	+	0.199566i
$768$	−19.2784	+	33.3912i	−0.695649	+	1.20490i
$769$	−31.1593	−	11.3411i	−1.12363	−	0.408969i	−0.287657	−	0.957734i	$-0.592876\pi$
$769$	−31.1593	−	11.3411i	−1.12363	−	0.408969i	−0.835977	+	0.548764i	$0.815098\pi$
$770$	1.88701	+	0.686815i	0.0680031	+	0.0247511i
$771$	10.3262	−	17.8856i	0.371890	−	0.644133i
$772$	−6.88191	−	11.9198i	−0.247685	−	0.429004i
$773$	−2.14911	−	12.1882i	−0.0772982	−	0.438380i	−0.998754	−	0.0498975i	$-0.984111\pi$
$773$	−2.14911	−	12.1882i	−0.0772982	−	0.438380i	0.921456	−	0.388482i	$-0.127001\pi$
$774$	−8.39864	−	7.04730i	−0.301883	−	0.253310i
$775$	7.97347	−	6.69053i	0.286415	−	0.240331i
$776$	−0.558241	+	3.16594i	−0.0200397	+	0.113651i
$777$	2.78671	−	1.01428i	0.0999728	−	0.0363871i
$778$	−3.63271			−0.130239
$779$		0			0
$780$	7.23607			0.259093
$781$	13.1565	−	4.78857i	0.470776	−	0.171349i
$782$	−0.816543	+	4.63084i	−0.0291995	+	0.165599i
$783$	14.7621	−	12.3868i	0.527553	−	0.442670i
$784$	24.5662	+	20.6135i	0.877364	+	0.736196i
$785$	2.56373	+	14.5396i	0.0915034	+	0.518942i
$786$	11.0172	+	19.0824i	0.392971	+	0.680646i
$787$	9.68208	−	16.7699i	0.345129	−	0.597781i	−0.640248	−	0.768168i	$-0.721169\pi$
$787$	9.68208	−	16.7699i	0.345129	−	0.597781i	0.985377	+	0.170387i	$0.0545019\pi$
$788$	−17.4429	−	6.34868i	−0.621376	−	0.226162i
$789$	42.6984	+	15.5410i	1.52010	+	0.553273i
$790$	14.4721	−	25.0665i	0.514895	−	0.891825i
$791$		0			0
$792$	−0.107756	−	0.611114i	−0.00382894	−	0.0217150i
$793$	5.27185	+	4.42361i	0.187209	+	0.157087i
$794$	−1.88228	+	1.57942i	−0.0667996	+	0.0560515i
$795$	5.32275	−	30.1868i	0.188778	−	1.07062i
$796$	1.60519	−	0.584240i	0.0568943	−	0.0207078i
$797$	13.2088			0.467879			0.233940	−	0.972251i	$-0.424838\pi$
$797$	13.2088			0.467879			0.233940	+	0.972251i	$0.424838\pi$
$798$		0			0
$799$	74.2492			2.62675
$800$	−37.6966	+	13.7204i	−1.33278	+	0.485091i
$801$	0.798136	−	4.52645i	0.0282007	−	0.159934i
$802$	−6.85171	+	5.74927i	−0.241942	+	0.203014i
$803$	−9.52783	−	7.99480i	−0.336230	−	0.282130i
$804$	6.96757	+	39.5150i	0.245727	+	1.39359i
$805$	−0.145898	−	0.252703i	−0.00514223	−	0.00890660i
$806$	−1.31433	+	2.27648i	−0.0462952	+	0.0801857i
$807$	−46.1097	−	16.7825i	−1.62314	−	0.590774i
$808$	−2.69286	−	0.980121i	−0.0947345	−	0.0344805i
$809$	17.1353	−	29.6791i	0.602443	−	1.04346i	−0.390006	−	0.920812i	$-0.627527\pi$
$809$	17.1353	−	29.6791i	0.602443	−	1.04346i	0.992450	−	0.122651i	$-0.0391394\pi$
$810$	32.2299	+	55.8239i	1.13244	+	1.96145i
$811$	3.85583	+	21.8675i	0.135396	+	0.767871i	0.974583	+	0.224027i	$0.0719204\pi$
$811$	3.85583	+	21.8675i	0.135396	+	0.767871i	−0.839187	+	0.543844i	$0.816968\pi$
$812$	−1.24451	−	1.04427i	−0.0436739	−	0.0366468i
$813$	−28.0791	+	23.5612i	−0.984778	+	0.826327i
$814$	−3.01465	+	17.0969i	−0.105663	+	0.599247i
$815$	47.0494	−	17.1246i	1.64807	−	0.599847i
$816$	56.8514			1.99020
$817$		0			0
$818$	45.7771			1.60056
$819$	0.0996085	−	0.0362545i	0.00348060	−	0.00126684i
$820$	1.98179	−	11.2393i	0.0692071	−	0.392493i
$821$	7.68683	−	6.45001i	0.268272	−	0.225107i	−0.498721	−	0.866763i	$-0.666197\pi$
$821$	7.68683	−	6.45001i	0.268272	−	0.225107i	0.766993	+	0.641656i	$0.221752\pi$
$822$	−24.1354	−	20.2520i	−0.841820	−	0.706371i
$823$	8.80767	+	49.9508i	0.307016	+	1.74118i	0.613860	+	0.789415i	$0.289616\pi$
$823$	8.80767	+	49.9508i	0.307016	+	1.74118i	−0.306844	+	0.951760i	$0.599273\pi$
$824$	−4.04508	−	7.00629i	−0.140917	−	0.244076i
$825$	7.19218	−	12.4572i	0.250400	−	0.433705i
$826$	3.70640	+	1.34902i	0.128962	+	0.0469384i
$827$	27.9157	+	10.1605i	0.970724	+	0.353315i	0.778227	−	0.627983i	$-0.216119\pi$
$827$	27.9157	+	10.1605i	0.970724	+	0.353315i	0.192497	+	0.981298i	$0.438341\pi$
$828$	0.190983	−	0.330792i	0.00663712	−	0.0114958i
$829$	−7.55545	−	13.0864i	−0.262412	−	0.454510i	0.704471	−	0.709733i	$-0.251185\pi$
$829$	−7.55545	−	13.0864i	−0.262412	−	0.454510i	−0.966882	+	0.255223i	$0.917851\pi$
$830$	−3.45893	−	19.6166i	−0.120061	−	0.680901i
$831$	−21.5126	−	18.0512i	−0.746263	−	0.626189i
$832$	2.62042	−	2.19879i	0.0908466	−	0.0762293i
$833$	7.80449	−	44.2615i	0.270410	−	1.53357i
$834$	−41.1046	+	14.9609i	−1.42334	+	0.518052i
$835$	−5.25731			−0.181937
$836$		0			0
$837$	−8.61803			−0.297883
$838$	−11.7675	+	4.28303i	−0.406502	+	0.147955i
$839$	−2.94290	+	16.6900i	−0.101600	+	0.576204i	0.890924	+	0.454153i	$0.150058\pi$
$839$	−2.94290	+	16.6900i	−0.101600	+	0.576204i	−0.992524	+	0.122051i	$0.961053\pi$
$840$	−0.808735	+	0.678609i	−0.0279040	+	0.0234142i
$841$	−8.35741	−	7.01270i	−0.288187	−	0.241817i
$842$	−10.7021	−	60.6949i	−0.368820	−	2.09168i
$843$	14.8992	+	25.8061i	0.513155	+	0.888811i
$844$	−0.502029	+	0.869539i	−0.0172805	+	0.0299308i
$845$	−37.9266	−	13.8042i	−1.30472	−	0.474878i
$846$	−12.6730	−	4.61259i	−0.435706	−	0.158584i
$847$	1.07295	−	1.85840i	0.0368670	−	0.0638555i
$848$	−11.4984	−	19.9159i	−0.394858	−	0.683914i
$849$	−3.99336	−	22.6475i	−0.137052	−	0.777260i
$850$	51.6054	+	43.3020i	1.77005	+	1.48525i
$851$	1.93247	−	1.62153i	0.0662441	−	0.0555854i
$852$	5.41441	−	30.7066i	0.185495	−	1.05199i
$853$	−37.8743	+	13.7851i	−1.29679	+	0.471993i	−0.895950	−	0.444155i	$-0.853504\pi$
$853$	−37.8743	+	13.7851i	−1.29679	+	0.471993i	−0.400840	+	0.916148i	$0.631282\pi$
$854$	4.25325			0.145543
$855$		0			0
$856$	4.34752			0.148595
$857$	51.9958	−	18.9249i	1.77614	−	0.646463i	0.776272	−	0.630398i	$-0.217108\pi$
$857$	51.9958	−	18.9249i	1.77614	−	0.646463i	0.999871	−	0.0160655i	$-0.00511403\pi$
$858$	−0.630814	+	3.57752i	−0.0215356	+	0.122135i
$859$	29.8330	−	25.0329i	1.01789	−	0.854111i	0.0285293	−	0.999593i	$-0.490918\pi$
$859$	29.8330	−	25.0329i	1.01789	−	0.854111i	0.989361	+	0.145482i	$0.0464732\pi$
$860$	−37.4081	−	31.3891i	−1.27561	−	1.07036i
$861$	−0.169952	−	0.963845i	−0.00579194	−	0.0328477i
$862$	11.8713	+	20.5617i	0.404339	+	0.700335i
$863$	16.2865	−	28.2090i	0.554398	−	0.960246i	−0.443552	−	0.896249i	$-0.646282\pi$
$863$	16.2865	−	28.2090i	0.554398	−	0.960246i	0.997950	−	0.0639969i	$-0.0203848\pi$
$864$	31.2117	+	11.3601i	1.06184	+	0.386479i
$865$	−50.6919	−	18.4504i	−1.72358	−	0.627331i
$866$	17.9894	−	31.1585i	0.611303	−	1.05881i
$867$	−23.6704	−	40.9984i	−0.803889	−	1.39238i
$868$	0.126163	+	0.715505i	0.00428224	+	0.0242858i
$869$	4.97806	+	4.17709i	0.168869	+	0.141698i
$870$	−38.1475	+	32.0095i	−1.29332	+	1.08522i
$871$	−1.64482	+	9.32823i	−0.0557326	+	0.316075i
$872$	2.10122	−	0.764780i	0.0711562	−	0.0258987i
$873$	−2.73466			−0.0925541
$874$		0			0
$875$	−0.360680			−0.0121932
$876$	−26.0287	+	9.47367i	−0.879428	+	0.320086i
$877$	−1.69265	+	9.59950i	−0.0571568	+	0.324152i	−0.999958	−	0.00920428i	$-0.997070\pi$
$877$	−1.69265	+	9.59950i	−0.0571568	+	0.324152i	0.942801	+	0.333356i	$0.108181\pi$
$878$	8.71909	−	7.31619i	0.294255	−	0.246909i
$879$	−22.2681	−	18.6851i	−0.751083	−	0.630233i
$880$	−3.58626	−	20.3387i	−0.120893	−	0.685618i
$881$	−20.2877	−	35.1394i	−0.683511	−	1.18388i	−0.973902	−	0.226968i	$-0.927119\pi$
$881$	−20.2877	−	35.1394i	−0.683511	−	1.18388i	0.290391	−	0.956908i	$-0.406215\pi$
$882$	−4.08174	+	7.06978i	−0.137439	+	0.238052i
$883$	−13.1233	−	4.77650i	−0.441635	−	0.160742i	0.111625	−	0.993750i	$-0.464394\pi$
$883$	−13.1233	−	4.77650i	−0.441635	−	0.160742i	−0.553261	+	0.833008i	$0.686617\pi$
$884$	−7.14961	−	2.60224i	−0.240467	−	0.0875229i
$885$	27.0344	−	46.8250i	0.908753	−	1.57401i
$886$	14.4374	+	25.0062i	0.485033	+	0.840101i
$887$	−2.85790	−	16.2080i	−0.0959589	−	0.544210i	−0.994449	−	0.105217i	$-0.966446\pi$
$887$	−2.85790	−	16.2080i	−0.0959589	−	0.544210i	0.898490	−	0.438993i	$-0.144665\pi$
$888$	−6.99173	−	5.86675i	−0.234627	−	0.196875i
$889$	2.25727	−	1.89408i	0.0757065	−	0.0635253i
$890$	7.94911	−	45.0816i	0.266455	−	1.51114i
$891$	−13.5994	+	4.94976i	−0.455596	+	0.165823i
$892$	−26.3521			−0.882332
$893$		0			0
$894$	−21.8328			−0.730199
$895$	−26.3891	+	9.60484i	−0.882090	+	0.321054i
$896$	−0.233919	+	1.32662i	−0.00781467	+	0.0443192i
$897$	0.404367	−	0.339304i	0.0135014	−	0.0113290i
$898$	−35.3172	−	29.6346i	−1.17855	−	0.988921i
$899$	−1.40484	−	7.96726i	−0.0468541	−	0.265723i
$900$	−2.73607	−	4.73901i	−0.0912023	−	0.157967i
$901$	−16.1150	+	27.9119i	−0.536867	+	0.929881i
$902$	5.38396	+	1.95960i	0.179266	+	0.0652476i
$903$	−3.93519	−	1.43229i	−0.130955	−	0.0476637i
$904$		0			0
$905$	−9.40456	−	16.2892i	−0.312618	−	0.541471i
$906$	10.8630	+	61.6073i	0.360900	+	2.04677i
$907$	22.2005	+	18.6284i	0.737156	+	0.618548i	0.932072	−	0.362272i	$-0.117999\pi$
$907$	22.2005	+	18.6284i	0.737156	+	0.618548i	−0.194916	+	0.980820i	$0.562443\pi$
$908$	19.4989	−	16.3615i	0.647094	−	0.542976i
$909$	0.423301	−	2.40066i	0.0140400	−	0.0796249i
$910$	0.992060	−	0.361080i	0.0328865	−	0.0119697i
$911$	25.4540			0.843329			0.421665	−	0.906752i	$-0.361446\pi$
$911$	25.4540			0.843329			0.421665	+	0.906752i	$0.361446\pi$
$912$		0			0
$913$	4.47214			0.148006
$914$	11.2460	−	4.09320i	0.371984	−	0.135391i
$915$	10.1245	−	57.4187i	0.334705	−	1.89820i
$916$	−8.78817	+	7.37415i	−0.290369	+	0.243649i
$917$	1.10134	+	0.924132i	0.0363694	+	0.0305175i
$918$	−9.68559	−	54.9297i	−0.319672	−	1.81295i
$919$	23.6803	+	41.0156i	0.781142	+	1.35298i	0.931277	+	0.364313i	$0.118696\pi$
$919$	23.6803	+	41.0156i	0.781142	+	1.35298i	−0.150134	+	0.988666i	$0.547971\pi$
$920$	−0.449028	+	0.777739i	−0.0148040	+	0.0256413i
$921$	49.3924	+	17.9774i	1.62754	+	0.592374i
$922$	−21.1265	−	7.68941i	−0.695764	−	0.253237i
$923$	3.68034	−	6.37454i	0.121140	−	0.209820i
$924$	0.502029	+	0.869539i	0.0165155	+	0.0286057i
$925$	−6.27567	−	35.5911i	−0.206343	−	1.17023i
$926$	−14.7836	−	12.4049i	−0.485820	−	0.407651i
$927$	5.27185	−	4.42361i	0.173150	−	0.145290i
$928$	−5.41441	+	30.7066i	−0.177737	+	1.00799i
$929$	−15.5111	+	5.64558i	−0.508903	+	0.185226i	−0.583694	−	0.811974i	$-0.698393\pi$
$929$	−15.5111	+	5.64558i	−0.508903	+	0.185226i	0.0747910	+	0.997199i	$0.476171\pi$
$930$	22.2703			0.730273
$931$		0			0
$932$	7.32624			0.239979
$933$	25.8675	−	9.41501i	0.846865	−	0.308233i
$934$	−1.39917	+	7.93507i	−0.0457821	+	0.259643i
$935$	−22.1726	+	18.6050i	−0.725122	+	0.608449i
$936$	−0.249913	−	0.209702i	−0.00816865	−	0.00685431i
$937$	−2.98703	−	16.9403i	−0.0975821	−	0.553415i	−0.993926	−	0.110055i	$-0.964897\pi$
$937$	−2.98703	−	16.9403i	−0.0975821	−	0.553415i	0.896343	−	0.443360i	$-0.146214\pi$
$938$	2.92705	+	5.06980i	0.0955716	+	0.165535i
$939$	−5.11855	+	8.86560i	−0.167038	+	0.289318i
$940$	−56.4463	−	20.5448i	−1.84107	−	0.670096i
$941$	−26.1283	−	9.50992i	−0.851758	−	0.310015i	−0.121001	−	0.992652i	$-0.538610\pi$
$941$	−26.1283	−	9.50992i	−0.851758	−	0.310015i	−0.730757	+	0.682638i	$0.760833\pi$
$942$	−8.25329	+	14.2951i	−0.268907	+	0.465760i
$943$	−0.416272	−	0.721004i	−0.0135557	−	0.0234791i
$944$	−7.04402	−	39.9486i	−0.229263	−	1.30022i
$945$	2.65143	+	2.22482i	0.0862511	+	0.0723733i
$946$	18.7799	−	15.7582i	0.610588	−	0.512345i
$947$	−4.89346	+	27.7522i	−0.159016	+	0.901826i	0.796005	+	0.605290i	$0.206943\pi$
$947$	−4.89346	+	27.7522i	−0.159016	+	0.901826i	−0.955022	+	0.296536i	$0.904168\pi$
$948$	13.5994	−	4.94976i	0.441687	−	0.160761i
$949$	−6.53888			−0.212261
$950$		0			0
$951$	59.5967			1.93256
$952$	1.04311	−	0.379662i	0.0338075	−	0.0123049i
$953$	−3.54828	+	20.1233i	−0.114940	+	0.651857i	0.871840	+	0.489791i	$0.162927\pi$
$953$	−3.54828	+	20.1233i	−0.114940	+	0.651857i	−0.986780	+	0.162066i	$0.948184\pi$
$954$	4.48450	−	3.76294i	0.145191	−	0.121830i
$955$	42.1425	+	35.3618i	1.36370	+	1.14428i
$956$	−2.56971	−	14.5736i	−0.0831104	−	0.471342i
$957$	−5.59017	−	9.68246i	−0.180705	−	0.312989i
$958$	−15.1311	+	26.2079i	−0.488865	+	0.846739i
$959$	−1.93175	−	0.703100i	−0.0623795	−	0.0227043i
$960$	−27.2330	−	9.91199i	−0.878940	−	0.319908i
$961$	13.6910	−	23.7135i	0.441645	−	0.764951i
$962$	4.56352	+	7.90426i	0.147134	+	0.254843i
$963$	0.642190	+	3.64204i	0.0206943	+	0.117363i
$964$	−33.6448	−	28.2313i	−1.08362	−	0.909269i
$965$	−21.0874	+	17.6944i	−0.678827	+	0.569604i
$966$	0.0566506	−	0.321282i	0.00182270	−	0.0103371i
$967$	−19.0681	+	6.94020i	−0.613187	+	0.223182i	−0.629897	−	0.776678i	$-0.716903\pi$
$967$	−19.0681	+	6.94020i	−0.613187	+	0.223182i	0.0167100	+	0.999860i	$0.494681\pi$
$968$	−6.60440			−0.212273
$969$		0			0
$970$	−27.2361			−0.874497
$971$	41.9541	−	15.2701i	1.34637	−	0.490039i	0.434559	−	0.900644i	$-0.356904\pi$
$971$	41.9541	−	15.2701i	1.34637	−	0.490039i	0.911814	+	0.410604i	$0.134682\pi$
$972$	−1.77766	+	10.0816i	−0.0570183	+	0.323367i
$973$	−2.18637	+	1.83458i	−0.0700918	+	0.0588140i
$974$	−24.2899	−	20.3816i	−0.778298	−	0.653070i
$975$	−1.31318	−	7.44742i	−0.0420554	−	0.238508i
$976$	−21.8713	−	37.8822i	−0.700084	−	1.21258i
$977$	−4.78804	+	8.29313i	−0.153183	+	0.265321i	−0.932396	−	0.361439i	$-0.882286\pi$
$977$	−4.78804	+	8.29313i	−0.153183	+	0.265321i	0.779213	+	0.626759i	$0.215619\pi$
$978$	52.6028	+	19.1458i	1.68205	+	0.612217i
$979$	9.65778	+	3.51515i	0.308664	+	0.112345i
$980$	−18.1803	+	31.4893i	−0.580750	+	1.00589i
$981$	0.951057	+	1.64728i	0.0303649	+	0.0525935i
$982$	−5.70442	−	32.3514i	−0.182035	−	1.03237i
$983$	−30.0426	−	25.2087i	−0.958210	−	0.804034i	0.0224508	−	0.999748i	$-0.492853\pi$
$983$	−30.0426	−	25.2087i	−0.958210	−	0.804034i	−0.980661	+	0.195714i	$0.937298\pi$
$984$	−2.30746	+	1.93619i	−0.0735590	+	0.0617234i
$985$	−6.44662	+	36.5606i	−0.205406	+	1.16492i
$986$	49.2029	−	17.9084i	1.56694	−	0.570320i
$987$	−5.15131			−0.163968
$988$		0			0
$989$	−3.56231			−0.113275
$990$	4.94026	−	1.79811i	0.157012	−	0.0571476i
$991$	9.60844	−	54.4922i	0.305222	−	1.73100i	−0.317235	−	0.948347i	$-0.602754\pi$
$991$	9.60844	−	54.4922i	0.305222	−	1.73100i	0.622457	−	0.782654i	$-0.286134\pi$
$992$	10.6819	−	8.96321i	0.339152	−	0.284582i
$993$	29.5241	+	24.7737i	0.936920	+	0.786169i
$994$	−0.789952	−	4.48004i	−0.0250557	−	0.142098i
$995$	−1.70820	−	2.95870i	−0.0541537	−	0.0937970i
$996$	4.97980	−	8.62526i	0.157791	−	0.273302i
$997$	31.1270	+	11.3293i	0.985801	+	0.358802i	0.784093	−	0.620644i	$-0.213129\pi$
$997$	31.1270	+	11.3293i	0.985801	+	0.358802i	0.201708	+	0.979446i	$0.435351\pi$
$998$	54.4659	+	19.8240i	1.72409	+	0.627517i
$999$	−14.9615	+	25.9141i	−0.473361	+	0.819885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.m.62.4		24
19.2	odd	18		361.2.a.i.1.4	yes	4
19.3	odd	18		361.2.c.j.292.1		8
19.4	even	9	inner	361.2.e.m.99.4		24
19.5	even	9		361.2.c.j.68.4		8
19.6	even	9	inner	361.2.e.m.28.1		24
19.7	even	3	inner	361.2.e.m.245.1		24
19.8	odd	6	inner	361.2.e.m.54.4		24
19.9	even	9	inner	361.2.e.m.234.1		24
19.10	odd	18	inner	361.2.e.m.234.4		24
19.11	even	3	inner	361.2.e.m.54.1		24
19.12	odd	6	inner	361.2.e.m.245.4		24
19.13	odd	18	inner	361.2.e.m.28.4		24
19.14	odd	18		361.2.c.j.68.1		8
19.15	odd	18	inner	361.2.e.m.99.1		24
19.16	even	9		361.2.c.j.292.4		8
19.17	even	9		361.2.a.i.1.1	✓	4
19.18	odd	2	inner	361.2.e.m.62.1		24
57.2	even	18		3249.2.a.bc.1.1		4
57.17	odd	18		3249.2.a.bc.1.4		4
76.55	odd	18		5776.2.a.bu.1.1		4
76.59	even	18		5776.2.a.bu.1.4		4
95.59	odd	18		9025.2.a.bj.1.1		4
95.74	even	18		9025.2.a.bj.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.i.1.1	✓	4	19.17	even	9
361.2.a.i.1.4	yes	4	19.2	odd	18
361.2.c.j.68.1		8	19.14	odd	18
361.2.c.j.68.4		8	19.5	even	9
361.2.c.j.292.1		8	19.3	odd	18
361.2.c.j.292.4		8	19.16	even	9
361.2.e.m.28.1		24	19.6	even	9	inner
361.2.e.m.28.4		24	19.13	odd	18	inner
361.2.e.m.54.1		24	19.11	even	3	inner
361.2.e.m.54.4		24	19.8	odd	6	inner
361.2.e.m.62.1		24	19.18	odd	2	inner
361.2.e.m.62.4		24	1.1	even	1	trivial
361.2.e.m.99.1		24	19.15	odd	18	inner
361.2.e.m.99.4		24	19.4	even	9	inner
361.2.e.m.234.1		24	19.9	even	9	inner
361.2.e.m.234.4		24	19.10	odd	18	inner
361.2.e.m.245.1		24	19.7	even	3	inner
361.2.e.m.245.4		24	19.12	odd	6	inner
3249.2.a.bc.1.1		4	57.2	even	18
3249.2.a.bc.1.4		4	57.17	odd	18
5776.2.a.bu.1.1		4	76.55	odd	18
5776.2.a.bu.1.4		4	76.59	even	18
9025.2.a.bj.1.1		4	95.59	odd	18
9025.2.a.bj.1.4		4	95.74	even	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.78740 - 0.650561i) q^{2} +(0.330298 - 1.87322i) q^{3} +(1.23949 - 1.04005i) q^{4} +(-2.47897 - 2.08010i) q^{5} +(-0.628265 - 3.56307i) q^{6} +(-0.118034 - 0.204441i) q^{7} +(-0.363271 + 0.629204i) q^{8} +(-0.580762 - 0.211380i) q^{9} +O(q^{10})\)	\(q+(1.78740 - 0.650561i) q^{2} +(0.330298 - 1.87322i) q^{3} +(1.23949 - 1.04005i) q^{4} +(-2.47897 - 2.08010i) q^{5} +(-0.628265 - 3.56307i) q^{6} +(-0.118034 - 0.204441i) q^{7} +(-0.363271 + 0.629204i) q^{8} +(-0.580762 - 0.211380i) q^{9} +(-5.78415 - 2.10526i) q^{10} +(0.690983 - 1.19682i) q^{11} +(-1.53884 - 2.66535i) q^{12} +(-0.126163 - 0.715505i) q^{13} +(-0.343975 - 0.288630i) q^{14} +(-4.71528 + 3.95659i) q^{15} +(-0.801913 + 4.54788i) q^{16} +(6.08182 - 2.21360i) q^{17} -1.17557 q^{18} -5.23607 q^{20} +(-0.421948 + 0.153577i) q^{21} +(0.456461 - 2.58872i) q^{22} +(-0.292603 + 0.245523i) q^{23} +(1.05865 + 0.888311i) q^{24} +(0.950226 + 5.38900i) q^{25} +(-0.690983 - 1.19682i) q^{26} +(2.26538 - 3.92376i) q^{27} +(-0.358931 - 0.130640i) q^{28} +(3.99675 + 1.45470i) q^{29} +(-5.85410 + 10.1396i) q^{30} +(-0.951057 - 1.64728i) q^{31} +(1.27300 + 7.21956i) q^{32} +(-2.01367 - 1.68967i) q^{33} +(9.43057 - 7.91319i) q^{34} +(-0.132655 + 0.752326i) q^{35} +(-0.939693 + 0.342020i) q^{36} -6.60440 q^{37} -1.38197 q^{39} +(2.20935 - 0.804138i) q^{40} +(-0.378488 + 2.14651i) q^{41} +(-0.654280 + 0.549006i) q^{42} +(7.14431 + 5.99479i) q^{43} +(-0.388289 - 2.20210i) q^{44} +(1.00000 + 1.73205i) q^{45} +(-0.363271 + 0.629204i) q^{46} +(10.7803 + 3.92370i) q^{47} +(8.25428 + 3.00431i) q^{48} +(3.47214 - 6.01392i) q^{49} +(5.20431 + 9.01413i) q^{50} +(-2.13774 - 12.1237i) q^{51} +(-0.900539 - 0.755642i) q^{52} +(-3.81475 + 3.20095i) q^{53} +(1.49651 - 8.48711i) q^{54} +(-4.20243 + 1.52956i) q^{55} +0.171513 q^{56} +8.09017 q^{58} +(-8.25428 + 3.00431i) q^{59} +(-1.72947 + 9.80828i) q^{60} +(-7.25608 + 6.08857i) q^{61} +(-2.77157 - 2.32563i) q^{62} +(0.0253349 + 0.143682i) q^{63} +(2.35410 + 4.07742i) q^{64} +(-1.17557 + 2.03615i) q^{65} +(-4.69846 - 1.71010i) q^{66} +(-12.2510 - 4.45901i) q^{67} +(5.23607 - 9.06914i) q^{68} +(0.363271 + 0.629204i) q^{69} +(0.252326 + 1.43101i) q^{70} +(7.76088 + 6.51215i) q^{71} +(0.343975 - 0.288630i) q^{72} +(1.56283 - 8.86327i) q^{73} +(-11.8047 + 4.29656i) q^{74} +10.4086 q^{75} -0.326238 q^{77} +(-2.47013 + 0.899053i) q^{78} +(-0.816543 + 4.63084i) q^{79} +(11.4480 - 9.60599i) q^{80} +(-8.02212 - 6.73136i) q^{81} +(0.719928 + 4.08291i) q^{82} +(1.61803 + 2.80252i) q^{83} +(-0.363271 + 0.629204i) q^{84} +(-19.6812 - 7.16336i) q^{85} +(16.6697 + 6.06729i) q^{86} +(4.04508 - 7.00629i) q^{87} +(0.502029 + 0.869539i) q^{88} +(1.29141 + 7.32395i) q^{89} +(2.91421 + 2.44531i) q^{90} +(-0.131387 + 0.110247i) q^{91} +(-0.107320 + 0.608645i) q^{92} +(-3.39984 + 1.23744i) q^{93} +21.8213 q^{94} +13.9443 q^{96} +(4.15792 - 1.51336i) q^{97} +(2.29368 - 13.0081i) q^{98} +(-0.654280 + 0.549006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7}+O(q^{10}) \) 24 * q + 24 * q^7	\( 24 q + 24 q^{7} + 30 q^{11} - 72 q^{20} - 30 q^{26} - 60 q^{30} - 60 q^{39} + 24 q^{45} - 24 q^{49} + 60 q^{58} - 24 q^{64} + 72 q^{68} + 180 q^{77} + 12 q^{83} + 30 q^{87} + 120 q^{96}+O(q^{100}) \) 24 * q + 24 * q^7 + 30 * q^11 - 72 * q^20 - 30 * q^26 - 60 * q^30 - 60 * q^39 + 24 * q^45 - 24 * q^49 + 60 * q^58 - 24 * q^64 + 72 * q^68 + 180 * q^77 + 12 * q^83 + 30 * q^87 + 120 * q^96

Introduction

L-functions

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