LMFDB - Embedded newform 731.2.m.c.689.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			689.2
Character	$\chi$	$=$	731.689
Dual form			731.2.m.c.87.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80058 + 1.80058i) q^{2} +(-0.368420 - 0.152604i) q^{3} -4.48416i q^{4} +(0.0622629 - 0.150316i) q^{5} +(0.938144 - 0.388592i) q^{6} +(1.14823 + 2.77206i) q^{7} +(4.47291 + 4.47291i) q^{8} +(-2.00888 - 2.00888i) q^{9} +O(q^{10})$	\(q+(-1.80058 + 1.80058i) q^{2} +(-0.368420 - 0.152604i) q^{3} -4.48416i q^{4} +(0.0622629 - 0.150316i) q^{5} +(0.938144 - 0.388592i) q^{6} +(1.14823 + 2.77206i) q^{7} +(4.47291 + 4.47291i) q^{8} +(-2.00888 - 2.00888i) q^{9} +(0.158546 + 0.382765i) q^{10} +(-1.57389 + 0.651925i) q^{11} +(-0.684302 + 1.65205i) q^{12} -3.00462i q^{13} +(-7.05878 - 2.92384i) q^{14} +(-0.0458778 + 0.0458778i) q^{15} -7.13934 q^{16} +(3.18807 + 2.61461i) q^{17} +7.23427 q^{18} +(0.112162 - 0.112162i) q^{19} +(-0.674040 - 0.279196i) q^{20} -1.19651i q^{21} +(1.66006 - 4.00774i) q^{22} +(2.56809 - 1.06374i) q^{23} +(-0.965323 - 2.33050i) q^{24} +(3.51682 + 3.51682i) q^{25} +(5.41004 + 5.41004i) q^{26} +(0.891359 + 2.15193i) q^{27} +(12.4304 - 5.14882i) q^{28} +(-0.923519 + 2.22957i) q^{29} -0.165213i q^{30} +(-6.86019 - 2.84159i) q^{31} +(3.90910 - 3.90910i) q^{32} +0.679337 q^{33} +(-10.4482 + 1.03256i) q^{34} +0.488177 q^{35} +(-9.00811 + 9.00811i) q^{36} +(7.65833 + 3.17218i) q^{37} +0.403914i q^{38} +(-0.458518 + 1.10696i) q^{39} +(0.950847 - 0.393854i) q^{40} +(3.66091 + 8.83822i) q^{41} +(2.15440 + 2.15440i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(2.92333 + 7.05755i) q^{44} +(-0.427044 + 0.176888i) q^{45} +(-2.70870 + 6.53938i) q^{46} +9.39127i q^{47} +(2.63027 + 1.08949i) q^{48} +(-1.41616 + 1.41616i) q^{49} -12.6646 q^{50} +(-0.775547 - 1.44979i) q^{51} -13.4732 q^{52} +(-8.23127 + 8.23127i) q^{53} +(-5.47968 - 2.26976i) q^{54} +0.277171i q^{55} +(-7.26328 + 17.5351i) q^{56} +(-0.0584394 + 0.0242064i) q^{57} +(-2.35165 - 5.67739i) q^{58} +(0.701014 + 0.701014i) q^{59} +(0.205723 + 0.205723i) q^{60} +(3.38216 + 8.16525i) q^{61} +(17.4688 - 7.23581i) q^{62} +(3.26208 - 7.87537i) q^{63} -0.201396i q^{64} +(-0.451642 - 0.187076i) q^{65} +(-1.22320 + 1.22320i) q^{66} -13.0035 q^{67} +(11.7243 - 14.2958i) q^{68} -1.10846 q^{69} +(-0.879000 + 0.879000i) q^{70} +(-2.99958 - 1.24246i) q^{71} -17.9710i q^{72} +(5.08565 - 12.2778i) q^{73} +(-19.5012 + 8.07765i) q^{74} +(-0.758983 - 1.83235i) q^{75} +(-0.502954 - 0.502954i) q^{76} +(-3.61435 - 3.61435i) q^{77} +(-1.16757 - 2.81876i) q^{78} +(5.26764 - 2.18193i) q^{79} +(-0.444516 + 1.07316i) q^{80} +7.59410i q^{81} +(-22.5056 - 9.32214i) q^{82} +(1.23898 - 1.23898i) q^{83} -5.36532 q^{84} +(0.591516 - 0.316425i) q^{85} +2.54640 q^{86} +(0.680485 - 0.680485i) q^{87} +(-9.95586 - 4.12385i) q^{88} +13.2445i q^{89} +(0.450427 - 1.08743i) q^{90} +(8.32898 - 3.44998i) q^{91} +(-4.76996 - 11.5157i) q^{92} +(2.09379 + 2.09379i) q^{93} +(-16.9097 - 16.9097i) q^{94} +(-0.00987625 - 0.0238434i) q^{95} +(-2.03674 + 0.843644i) q^{96} +(0.993185 - 2.39776i) q^{97} -5.09979i q^{98} +(4.47138 + 1.85210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$

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 $

$2$	−1.80058	+	1.80058i	−1.27320	+	1.27320i	−0.328801	+	0.944399i	$0.606645\pi$
$2$	−1.80058	+	1.80058i	−1.27320	+	1.27320i	−0.944399	+	0.328801i	$0.893355\pi$
$3$	−0.368420	−	0.152604i	−0.212707	−	0.0881062i	0.273786	−	0.961791i	$-0.411724\pi$
$3$	−0.368420	−	0.152604i	−0.212707	−	0.0881062i	−0.486493	+	0.873684i	$0.661724\pi$
$4$		−	4.48416i		−	2.24208i
$5$	0.0622629	−	0.150316i	0.0278448	−	0.0672233i	−0.909346	−	0.416042i	$-0.863417\pi$
$5$	0.0622629	−	0.150316i	0.0278448	−	0.0672233i	0.937190	+	0.348818i	$0.113417\pi$
$6$	0.938144	−	0.388592i	0.382996	−	0.158642i
$7$	1.14823	+	2.77206i	0.433988	+	1.04774i	0.977989	+	0.208656i	$0.0669089\pi$
$7$	1.14823	+	2.77206i	0.433988	+	1.04774i	−0.544001	+	0.839085i	$0.683091\pi$
$8$	4.47291	+	4.47291i	1.58141	+	1.58141i
$9$	−2.00888	−	2.00888i	−0.669625	−	0.669625i
$10$	0.158546	+	0.382765i	0.0501367	+	0.121041i
$11$	−1.57389	+	0.651925i	−0.474544	+	0.196563i	−0.607120	−	0.794610i	$-0.707675\pi$
$11$	−1.57389	+	0.651925i	−0.474544	+	0.196563i	0.132576	+	0.991173i	$0.457675\pi$
$12$	−0.684302	+	1.65205i	−0.197541	+	0.476906i
$13$		−	3.00462i		−	0.833331i	−0.909060	−	0.416665i	$-0.863199\pi$
$13$		−	3.00462i		−	0.833331i	0.909060	−	0.416665i	$-0.136801\pi$
$14$	−7.05878	−	2.92384i	−1.88654	−	0.781430i
$15$	−0.0458778	+	0.0458778i	−0.0118456	+	0.0118456i
$16$	−7.13934			−1.78483
$17$	3.18807	+	2.61461i	0.773221	+	0.634137i
$17$	3.18807	+	2.61461i	0.773221	+	0.634137i
$18$	7.23427			1.70513
$19$	0.112162	−	0.112162i	0.0257318	−	0.0257318i	−0.694124	−	0.719856i	$-0.744208\pi$
$19$	0.112162	−	0.112162i	0.0257318	−	0.0257318i	0.719856	+	0.694124i	$0.244208\pi$
$20$	−0.674040	−	0.279196i	−0.150720	−	0.0624302i
$21$		−	1.19651i		−	0.261099i
$22$	1.66006	−	4.00774i	0.353926	−	0.854454i
$23$	2.56809	−	1.06374i	0.535483	−	0.221804i	−0.0985197	−	0.995135i	$-0.531411\pi$
$23$	2.56809	−	1.06374i	0.535483	−	0.221804i	0.634003	+	0.773331i	$0.281411\pi$
$24$	−0.965323	−	2.33050i	−0.197046	−	0.475710i
$25$	3.51682	+	3.51682i	0.703363	+	0.703363i
$26$	5.41004	+	5.41004i	1.06100	+	1.06100i
$27$	0.891359	+	2.15193i	0.171542	+	0.414139i
$28$	12.4304	−	5.14882i	2.34912	−	0.973036i
$29$	−0.923519	+	2.22957i	−0.171493	+	0.414021i	−0.986135	−	0.165943i	$-0.946933\pi$
$29$	−0.923519	+	2.22957i	−0.171493	+	0.414021i	0.814642	+	0.579964i	$0.196933\pi$
$30$		−	0.165213i		−	0.0301636i
$31$	−6.86019	−	2.84159i	−1.23213	−	0.510364i	−0.330881	−	0.943672i	$-0.607346\pi$
$31$	−6.86019	−	2.84159i	−1.23213	−	0.510364i	−0.901246	+	0.433309i	$0.857346\pi$
$32$	3.90910	−	3.90910i	0.691038	−	0.691038i
$33$	0.679337			0.118257
$34$	−10.4482	+	1.03256i	−1.79185	+	0.177082i
$35$	0.488177			0.0825169
$36$	−9.00811	+	9.00811i	−1.50135	+	1.50135i
$37$	7.65833	+	3.17218i	1.25902	+	0.521504i	0.909609	−	0.415465i	$-0.136381\pi$
$37$	7.65833	+	3.17218i	1.25902	+	0.521504i	0.349412	+	0.936969i	$0.386381\pi$
$38$			0.403914i			0.0655236i
$39$	−0.458518	+	1.10696i	−0.0734216	+	0.177255i
$40$	0.950847	−	0.393854i	0.150342	−	0.0622737i
$41$	3.66091	+	8.83822i	0.571738	+	1.38030i	0.900074	+	0.435737i	$0.143512\pi$
$41$	3.66091	+	8.83822i	0.571738	+	1.38030i	−0.328336	+	0.944561i	$0.606488\pi$
$42$	2.15440	+	2.15440i	0.332431	+	0.332431i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$43$	−0.707107	−	0.707107i	−0.107833	−	0.107833i
$44$	2.92333	+	7.05755i	0.440709	+	1.06397i
$45$	−0.427044	+	0.176888i	−0.0636600	+	0.0263688i
$46$	−2.70870	+	6.53938i	−0.399376	+	0.964179i
$47$			9.39127i			1.36986i	0.728610	+	0.684928i	$0.240167\pi$
$47$			9.39127i			1.36986i	−0.728610	+	0.684928i	$0.759833\pi$
$48$	2.63027	+	1.08949i	0.379647	+	0.157255i
$49$	−1.41616	+	1.41616i	−0.202308	+	0.202308i
$50$	−12.6646			−1.79104
$51$	−0.775547	−	1.44979i	−0.108598	−	0.203011i
$52$	−13.4732			−1.86839
$53$	−8.23127	+	8.23127i	−1.13065	+	1.13065i	−0.140584	+	0.990069i	$0.544898\pi$
$53$	−8.23127	+	8.23127i	−1.13065	+	1.13065i	−0.990069	+	0.140584i	$0.955102\pi$
$54$	−5.47968	−	2.26976i	−0.745690	−	0.308875i
$55$			0.277171i			0.0373737i
$56$	−7.26328	+	17.5351i	−0.970596	+	2.34323i
$57$	−0.0584394	+	0.0242064i	−0.00774048	+	0.00320621i
$58$	−2.35165	−	5.67739i	−0.308787	−	0.745477i
$59$	0.701014	+	0.701014i	0.0912642	+	0.0912642i	0.751265	−	0.660001i	$-0.229444\pi$
$59$	0.701014	+	0.701014i	0.0912642	+	0.0912642i	−0.660001	+	0.751265i	$0.729444\pi$
$60$	0.205723	+	0.205723i	0.0265587	+	0.0265587i
$61$	3.38216	+	8.16525i	0.433041	+	1.04545i	0.978301	+	0.207187i	$0.0664308\pi$
$61$	3.38216	+	8.16525i	0.433041	+	1.04545i	−0.545260	+	0.838267i	$0.683569\pi$
$62$	17.4688	−	7.23581i	2.21854	−	0.918949i
$63$	3.26208	−	7.87537i	0.410984	−	0.992203i
$64$		−	0.201396i		−	0.0251745i
$65$	−0.451642	−	0.187076i	−0.0560193	−	0.0232039i
$66$	−1.22320	+	1.22320i	−0.150565	+	0.150565i
$67$	−13.0035			−1.58863			−0.794315	−	0.607506i	$-0.792170\pi$
$67$	−13.0035			−1.58863			−0.794315	+	0.607506i	$0.792170\pi$
$68$	11.7243	−	14.2958i	1.42178	−	1.73362i
$69$	−1.10846			−0.133443
$70$	−0.879000	+	0.879000i	−0.105061	+	0.105061i
$71$	−2.99958	−	1.24246i	−0.355984	−	0.147453i	0.197522	−	0.980298i	$-0.436711\pi$
$71$	−2.99958	−	1.24246i	−0.355984	−	0.147453i	−0.553506	+	0.832845i	$0.686711\pi$
$72$		−	17.9710i		−	2.11791i
$73$	5.08565	−	12.2778i	0.595230	−	1.43701i	−0.283163	−	0.959072i	$-0.591384\pi$
$73$	5.08565	−	12.2778i	0.595230	−	1.43701i	0.878392	−	0.477940i	$-0.158616\pi$
$74$	−19.5012	+	8.07765i	−2.26696	+	0.939008i
$75$	−0.758983	−	1.83235i	−0.0876398	−	0.211581i
$76$	−0.502954	−	0.502954i	−0.0576928	−	0.0576928i
$77$	−3.61435	−	3.61435i	−0.411894	−	0.411894i
$78$	−1.16757	−	2.81876i	−0.132201	−	0.319162i
$79$	5.26764	−	2.18193i	0.592656	−	0.245486i	−0.0661368	−	0.997811i	$-0.521067\pi$
$79$	5.26764	−	2.18193i	0.592656	−	0.245486i	0.658793	+	0.752324i	$0.271067\pi$
$80$	−0.444516	+	1.07316i	−0.0496984	+	0.119983i
$81$			7.59410i			0.843789i
$82$	−22.5056	−	9.32214i	−2.48533	−	1.02946i
$83$	1.23898	−	1.23898i	0.135996	−	0.135996i	−0.635832	−	0.771828i	$-0.719343\pi$
$83$	1.23898	−	1.23898i	0.135996	−	0.135996i	0.771828	+	0.635832i	$0.219343\pi$
$84$	−5.36532			−0.585404
$85$	0.591516	−	0.316425i	0.0641590	−	0.0343211i
$86$	2.54640			0.274585
$87$	0.680485	−	0.680485i	0.0729557	−	0.0729557i
$88$	−9.95586	−	4.12385i	−1.06130	−	0.439604i
$89$			13.2445i			1.40391i	0.712221	+	0.701956i	$0.247690\pi$
$89$			13.2445i			1.40391i	−0.712221	+	0.701956i	$0.752310\pi$
$90$	0.450427	−	1.08743i	0.0474791	−	0.114625i
$91$	8.32898	−	3.44998i	0.873114	−	0.361656i
$92$	−4.76996	−	11.5157i	−0.497303	−	1.20059i
$93$	2.09379	+	2.09379i	0.217116	+	0.217116i
$94$	−16.9097	−	16.9097i	−1.74410	−	1.74410i
$95$	−0.00987625	−	0.0238434i	−0.00101328	−	0.00244628i
$96$	−2.03674	+	0.843644i	−0.207874	+	0.0861041i
$97$	0.993185	−	2.39776i	0.100843	−	0.243456i	−0.865404	−	0.501075i	$-0.832938\pi$
$97$	0.993185	−	2.39776i	0.100843	−	0.243456i	0.966246	+	0.257619i	$0.0829380\pi$
$98$		−	5.09979i		−	0.515157i
$99$	4.47138	+	1.85210i	0.449390	+	0.186144i
$100$	15.7699	−	15.7699i	1.57699	−	1.57699i
$101$	−2.47613			−0.246384			−0.123192	−	0.992383i	$-0.539313\pi$
$101$	−2.47613			−0.246384			−0.123192	+	0.992383i	$0.539313\pi$
$102$	4.00689	+	1.21402i	0.396741	+	0.120206i
$103$	−8.58040			−0.845452			−0.422726	−	0.906258i	$-0.638927\pi$
$103$	−8.58040			−0.845452			−0.422726	+	0.906258i	$0.638927\pi$
$104$	13.4394	−	13.4394i	1.31784	−	1.31784i
$105$	−0.179854	−	0.0744980i	−0.0175519	−	0.00727026i
$106$		−	29.6421i		−	2.87909i
$107$	−6.44549	+	15.5608i	−0.623109	+	1.50432i	0.224926	+	0.974376i	$0.427786\pi$
$107$	−6.44549	+	15.5608i	−0.623109	+	1.50432i	−0.848034	+	0.529941i	$0.822214\pi$
$108$	9.64960	−	3.99699i	0.928533	−	0.384611i
$109$	3.74542	+	9.04225i	0.358746	+	0.866090i	0.995477	+	0.0950040i	$0.0302864\pi$
$109$	3.74542	+	9.04225i	0.358746	+	0.866090i	−0.636730	+	0.771086i	$0.719714\pi$
$110$	−0.499067	−	0.499067i	−0.0475842	−	0.0475842i
$111$	−2.33739	−	2.33739i	−0.221855	−	0.221855i
$112$	−8.19757	−	19.7907i	−0.774598	−	1.87004i
$113$	4.86196	−	2.01389i	0.457375	−	0.189451i	−0.142087	−	0.989854i	$-0.545381\pi$
$113$	4.86196	−	2.01389i	0.457375	−	0.189451i	0.599462	+	0.800403i	$0.295381\pi$
$114$	0.0616391	−	0.148810i	0.00577303	−	0.0139373i
$115$		−	0.452256i		−	0.0421731i
$116$	9.99775	+	4.14120i	0.928268	+	0.384501i
$117$	−6.03590	+	6.03590i	−0.558019	+	0.558019i
$118$	−2.52446			−0.232395
$119$	−3.58724	+	11.8397i	−0.328842	+	1.08534i
$120$	−0.410414			−0.0374655
$121$	−5.72606	+	5.72606i	−0.520551	+	0.520551i
$122$	−20.7920	−	8.61233i	−1.88242	−	0.779724i
$123$		−	3.81484i		−	0.343973i
$124$	−12.7421	+	30.7622i	−1.14428	+	2.76252i
$125$	1.49918	−	0.620981i	0.134091	−	0.0555422i
$126$	8.30657	+	20.0538i	0.740008	+	1.78654i
$127$	6.33102	+	6.33102i	0.561787	+	0.561787i	0.929815	−	0.368028i	$-0.119967\pi$
$127$	6.33102	+	6.33102i	0.561787	+	0.561787i	−0.368028	+	0.929815i	$0.619967\pi$
$128$	8.18083	+	8.18083i	0.723090	+	0.723090i
$129$	0.152604	+	0.368420i	0.0134361	+	0.0324375i
$130$	1.15006	−	0.476371i	0.100867	−	0.0417805i
$131$	−2.74983	+	6.63867i	−0.240253	+	0.580023i	−0.997308	−	0.0733288i	$-0.976638\pi$
$131$	−2.74983	+	6.63867i	−0.240253	+	0.580023i	0.757054	+	0.653352i	$0.226638\pi$
$132$		−	3.04625i		−	0.265142i
$133$	0.439709	+	0.182133i	0.0381276	+	0.0157930i
$134$	23.4138	−	23.4138i	2.02265	−	2.02265i
$135$	0.378968			0.0326164
$136$	2.56504	+	25.9549i	0.219950	+	2.22561i
$137$	13.4149			1.14611			0.573056	−	0.819516i	$-0.305758\pi$
$137$	13.4149			1.14611			0.573056	+	0.819516i	$0.305758\pi$
$138$	1.99588	−	1.99588i	0.169900	−	0.169900i
$139$	−10.4892	−	4.34475i	−0.889679	−	0.368517i	−0.109436	−	0.993994i	$-0.534904\pi$
$139$	−10.4892	−	4.34475i	−0.889679	−	0.368517i	−0.780243	+	0.625477i	$0.784904\pi$
$140$		−	2.18906i		−	0.185009i
$141$	1.43315	−	3.45993i	0.120693	−	0.291378i
$142$	7.63812	−	3.16381i	0.640977	−	0.265501i
$143$	1.95878	+	4.72892i	0.163802	+	0.395452i
$144$	14.3420	+	14.3420i	1.19517	+	1.19517i
$145$	0.277639	+	0.277639i	0.0230567	+	0.0230567i
$146$	12.9501	+	31.2643i	1.07176	+	2.58745i
$147$	0.737851	−	0.305628i	0.0608569	−	0.0252078i
$148$	14.2246	−	34.3411i	1.16925	−	2.82282i
$149$		−	15.3512i		−	1.25762i	−0.777560	−	0.628808i	$-0.783543\pi$
$149$		−	15.3512i		−	1.25762i	0.777560	−	0.628808i	$-0.216457\pi$
$150$	4.66589	+	1.93267i	0.380968	+	0.157802i
$151$	5.03940	−	5.03940i	0.410101	−	0.410101i	−0.471673	−	0.881774i	$-0.656350\pi$
$151$	5.03940	−	5.03940i	0.410101	−	0.410101i	0.881774	+	0.471673i	$0.156350\pi$
$152$	1.00339			0.0813854
$153$	−1.15201	−	11.6569i	−0.0931344	−	0.942402i
$154$	13.0158			1.04885
$155$	−0.854271	+	0.854271i	−0.0686167	+	0.0686167i
$156$	4.96378	+	2.05606i	0.397420	+	0.164617i
$157$			17.9154i			1.42980i	0.699226	+	0.714901i	$0.253528\pi$
$157$			17.9154i			1.42980i	−0.699226	+	0.714901i	$0.746472\pi$
$158$	−5.55606	+	13.4135i	−0.442017	+	1.06712i
$159$	4.28869	−	1.77643i	0.340115	−	0.140880i
$160$	−0.344208	−	0.830992i	−0.0272121	−	0.0656957i
$161$	5.89749	+	5.89749i	0.464787	+	0.464787i
$162$	−13.6738	−	13.6738i	−1.07431	−	1.07431i
$163$	0.862176	+	2.08148i	0.0675308	+	0.163034i	0.954042	−	0.299674i	$-0.0968779\pi$
$163$	0.862176	+	2.08148i	0.0675308	+	0.163034i	−0.886511	+	0.462708i	$0.846878\pi$
$164$	39.6319	−	16.4161i	3.09473	−	1.28188i
$165$	0.0422975	−	0.102115i	0.00329286	−	0.00794966i
$166$			4.46176i			0.346300i
$167$	10.6600	+	4.41553i	0.824898	+	0.341684i	0.754881	−	0.655862i	$-0.227695\pi$
$167$	10.6600	+	4.41553i	0.824898	+	0.341684i	0.0700172	+	0.997546i	$0.477695\pi$
$168$	5.35187	−	5.35187i	0.412906	−	0.412906i
$169$	3.97228			0.305560
$170$	−0.495324	+	1.63482i	−0.0379896	+	0.125385i
$171$	−0.450641			−0.0344614
$172$	−3.17078	+	3.17078i	−0.241769	+	0.241769i
$173$	−9.51239	−	3.94016i	−0.723213	−	0.299565i	−0.00945355	−	0.999955i	$-0.503009\pi$
$173$	−9.51239	−	3.94016i	−0.723213	−	0.299565i	−0.713760	+	0.700391i	$0.753009\pi$
$174$			2.45053i			0.185774i
$175$	−5.71073	+	13.7869i	−0.431691	+	1.04219i
$176$	11.2365	−	4.65431i	0.846983	−	0.350832i
$177$	−0.151289	−	0.365245i	−0.0113716	−	0.0274535i
$178$	−23.8477	−	23.8477i	−1.78746	−	1.78746i
$179$	1.71183	+	1.71183i	0.127948	+	0.127948i	0.768181	−	0.640233i	$-0.221162\pi$
$179$	1.71183	+	1.71183i	0.127948	+	0.127948i	−0.640233	+	0.768181i	$0.721162\pi$
$180$	0.793191	+	1.91493i	0.0591210	+	0.142731i
$181$	16.2600	−	6.73513i	1.20860	−	0.500618i	0.314831	−	0.949148i	$-0.398052\pi$
$181$	16.2600	−	6.73513i	1.20860	−	0.500618i	0.893768	+	0.448530i	$0.148052\pi$
$182$	−8.78502	+	21.2089i	−0.651189	+	1.57211i
$183$		−	3.52437i		−	0.260529i
$184$	16.2448	+	6.72883i	1.19758	+	0.496056i
$185$	0.953659	−	0.953659i	0.0701144	−	0.0701144i
$186$	−7.54007			−0.552865
$187$	−6.72219	−	2.03672i	−0.491575	−	0.148940i
$188$	42.1119			3.07133
$189$	−4.94181	+	4.94181i	−0.359463	+	0.359463i
$190$	0.0607148	+	0.0251489i	0.00440471	+	0.00182449i
$191$			12.1474i			0.878954i	0.898254	+	0.439477i	$0.144836\pi$
$191$			12.1474i			0.878954i	−0.898254	+	0.439477i	$0.855164\pi$
$192$	−0.0307339	+	0.0741983i	−0.00221803	+	0.00535480i
$193$	10.5663	−	4.37670i	0.760579	−	0.315042i	0.0315290	−	0.999503i	$-0.489962\pi$
$193$	10.5663	−	4.37670i	0.760579	−	0.315042i	0.729050	+	0.684461i	$0.239962\pi$
$194$	2.52905	+	6.10566i	0.181575	+	0.438361i
$195$	0.137845	+	0.137845i	0.00987129	+	0.00987129i
$196$	6.35026	+	6.35026i	0.453590	+	0.453590i
$197$	−9.04424	−	21.8347i	−0.644375	−	1.55566i	−0.820720	−	0.571331i	$-0.806427\pi$
$197$	−9.04424	−	21.8347i	−0.644375	−	1.55566i	0.176344	−	0.984329i	$-0.443573\pi$
$198$	−11.3859	+	4.71620i	−0.809162	+	0.335166i
$199$	−0.0298147	+	0.0719790i	−0.00211351	+	0.00510245i	−0.924933	−	0.380131i	$-0.875879\pi$
$199$	−0.0298147	+	0.0719790i	−0.00211351	+	0.00510245i	0.922819	+	0.385233i	$0.125879\pi$
$200$			31.4608i			2.22462i
$201$	4.79075	+	1.98439i	0.337913	+	0.139968i
$202$	4.45845	−	4.45845i	0.313696	−	0.313696i
$203$	−7.24092			−0.508213
$204$	−6.50108	+	3.47767i	−0.455166	+	0.243486i
$205$	1.55646			0.108708
$206$	15.4497	−	15.4497i	1.07643	−	1.07643i
$207$	−7.29588	−	3.02205i	−0.507099	−	0.210047i
$208$			21.4510i			1.48736i
$209$	−0.103409	+	0.249652i	−0.00715298	+	0.0172688i
$210$	0.457980	−	0.189702i	0.0316036	−	0.0130907i
$211$	4.22348	+	10.1964i	0.290756	+	0.701948i	0.999995	−	0.00301995i	$-0.000961281\pi$
$211$	4.22348	+	10.1964i	0.290756	+	0.701948i	−0.709239	+	0.704968i	$0.750961\pi$
$212$	36.9103	+	36.9103i	2.53501	+	2.53501i
$213$	0.915497	+	0.915497i	0.0627288	+	0.0627288i
$214$	−16.4128	−	39.6240i	−1.12196	−	2.70864i
$215$	−0.150316	+	0.0622629i	−0.0102515	+	0.00424629i
$216$	−5.63843	+	13.6124i	−0.383647	+	0.926205i
$217$		−	22.2797i		−	1.51244i
$218$	−23.0252	−	9.53735i	−1.55946	−	0.645951i
$219$	−3.74730	+	3.74730i	−0.253219	+	0.253219i
$220$	1.24288			0.0837948
$221$	7.85591	−	9.57893i	0.528445	−	0.644349i
$222$	8.41730			0.564932
$223$	11.7303	−	11.7303i	0.785520	−	0.785520i	−0.195236	−	0.980756i	$-0.562547\pi$
$223$	11.7303	−	11.7303i	0.785520	−	0.785520i	0.980756	+	0.195236i	$0.0625472\pi$
$224$	15.3248	+	6.34774i	1.02393	+	0.424126i
$225$		−	14.1297i		−	0.941979i
$226$	−5.12817	+	12.3805i	−0.341121	+	0.823538i
$227$	5.42937	−	2.24892i	0.360360	−	0.149266i	−0.195155	−	0.980772i	$-0.562521\pi$
$227$	5.42937	−	2.24892i	0.360360	−	0.149266i	0.555515	+	0.831506i	$0.312521\pi$
$228$	0.108545	+	0.262051i	0.00718858	+	0.0173548i
$229$	6.06871	+	6.06871i	0.401032	+	0.401032i	0.878596	−	0.477565i	$-0.158480\pi$
$229$	6.06871	+	6.06871i	0.401032	+	0.401032i	−0.477565	+	0.878596i	$0.658480\pi$
$230$	0.814321	+	0.814321i	0.0536948	+	0.0536948i
$231$	0.780032	+	1.88316i	0.0513224	+	0.123903i
$232$	−14.1035	+	5.84186i	−0.925941	+	0.383537i
$233$	1.30516	−	3.15095i	0.0855042	−	0.206425i	−0.875344	−	0.483501i	$-0.839365\pi$
$233$	1.30516	−	3.15095i	0.0855042	−	0.206425i	0.960848	+	0.277075i	$0.0893651\pi$
$234$		−	21.7362i		−	1.42094i
$235$	1.41166	+	0.584727i	0.0920863	+	0.0381434i
$236$	3.14345	−	3.14345i	0.204621	−	0.204621i
$237$	−2.27368			−0.147691
$238$	−14.8592	−	27.7774i	−0.963178	−	1.80054i
$239$	24.2461			1.56835			0.784176	−	0.620539i	$-0.213086\pi$
$239$	24.2461			1.56835			0.784176	+	0.620539i	$0.213086\pi$
$240$	0.327537	−	0.327537i	0.0211424	−	0.0211424i
$241$	−10.2243	−	4.23506i	−0.658608	−	0.272804i	0.0282448	−	0.999601i	$-0.491008\pi$
$241$	−10.2243	−	4.23506i	−0.658608	−	0.272804i	−0.686853	+	0.726797i	$0.741008\pi$
$242$		−	20.6204i		−	1.32553i
$243$	3.83297	−	9.25361i	0.245885	−	0.593619i
$244$	36.6143	−	15.1661i	2.34399	−	0.970912i
$245$	0.124697	+	0.301045i	0.00796658	+	0.0192330i
$246$	6.86892	+	6.86892i	0.437946	+	0.437946i
$247$	−0.337005	−	0.337005i	−0.0214431	−	0.0214431i
$248$	−17.9749	−	43.3952i	−1.14141	−	2.75560i
$249$	−0.645539	+	0.267391i	−0.0409094	+	0.0169452i
$250$	−1.58127	+	3.81751i	−0.100008	+	0.241441i
$251$			0.424000i			0.0267626i	0.999910	+	0.0133813i	$0.00425953\pi$
$251$			0.424000i			0.0267626i	−0.999910	+	0.0133813i	$0.995740\pi$
$252$	−35.3144	−	14.6277i	−2.22460	−	0.921458i
$253$	−3.34840	+	3.34840i	−0.210512	+	0.210512i
$254$	−22.7990			−1.43054
$255$	−0.266214	+	0.0263090i	−0.0166710	+	0.00164754i
$256$	−29.0577			−1.81610
$257$	12.9065	−	12.9065i	0.805082	−	0.805082i	−0.178803	−	0.983885i	$-0.557222\pi$
$257$	12.9065	−	12.9065i	0.805082	−	0.805082i	0.983885	+	0.178803i	$0.0572224\pi$
$258$	−0.938144	−	0.388592i	−0.0584063	−	0.0241927i
$259$			24.8717i			1.54545i
$260$	−0.838878	+	2.02523i	−0.0520250	+	0.125600i
$261$	6.33417	−	2.62370i	0.392075	−	0.162403i
$262$	−7.00216	−	16.9047i	−0.432595	−	1.04438i
$263$	−12.4269	−	12.4269i	−0.766275	−	0.766275i	0.211173	−	0.977449i	$-0.432272\pi$
$263$	−12.4269	−	12.4269i	−0.766275	−	0.766275i	−0.977449	+	0.211173i	$0.932272\pi$
$264$	3.03862	+	3.03862i	0.187014	+	0.187014i
$265$	0.724789	+	1.74979i	0.0445234	+	0.107489i
$266$	−1.11968	+	0.463785i	−0.0686517	+	0.0284365i
$267$	2.02117	−	4.87953i	0.123693	−	0.298622i
$268$			58.3097i			3.56183i
$269$	4.57212	+	1.89383i	0.278767	+	0.115469i	0.517687	−	0.855570i	$-0.326793\pi$
$269$	4.57212	+	1.89383i	0.278767	+	0.115469i	−0.238920	+	0.971039i	$0.576793\pi$
$270$	−0.682361	+	0.682361i	−0.0415272	+	0.0415272i
$271$	−13.9202			−0.845590			−0.422795	−	0.906225i	$-0.638951\pi$
$271$	−13.9202			−0.845590			−0.422795	+	0.906225i	$0.638951\pi$
$272$	−22.7607	−	18.6666i	−1.38007	−	1.13183i
$273$	−3.59504			−0.217582
$274$	−24.1545	+	24.1545i	−1.45923	+	1.45923i
$275$	−7.82777	−	3.24237i	−0.472032	−	0.195522i
$276$			4.97053i			0.299191i
$277$	4.02322	−	9.71292i	0.241732	−	0.583593i	−0.755723	−	0.654891i	$-0.772714\pi$
$277$	4.02322	−	9.71292i	0.241732	−	0.583593i	0.997455	+	0.0712987i	$0.0227144\pi$
$278$	26.7096	−	11.0635i	1.60194	−	0.663543i
$279$	8.07288	+	19.4897i	0.483311	+	1.16682i
$280$	2.18357	+	2.18357i	0.130493	+	0.130493i
$281$	0.107633	+	0.107633i	0.00642086	+	0.00642086i	0.710310	−	0.703889i	$-0.248555\pi$
$281$	0.107633	+	0.107633i	0.00642086	+	0.00642086i	−0.703889	+	0.710310i	$0.748555\pi$
$282$	3.64937	+	8.81036i	0.217317	+	0.524649i
$283$	1.66047	−	0.687791i	0.0987050	−	0.0408849i	−0.332785	−	0.943003i	$-0.607988\pi$
$283$	1.66047	−	0.687791i	0.0987050	−	0.0408849i	0.431490	+	0.902118i	$0.357988\pi$
$284$	−5.57141	+	13.4506i	−0.330602	+	0.798144i
$285$			0.0102915i			0.000609617i
$286$	−12.0417	−	4.98785i	−0.712042	−	0.294938i
$287$	−20.2965	+	20.2965i	−1.19807	+	1.19807i
$288$	−15.7058			−0.925473
$289$	3.32761	+	16.6711i	0.195742	+	0.980656i
$290$	−0.999822			−0.0587116
$291$	−0.731818	+	0.731818i	−0.0428999	+	0.0428999i
$292$	−55.0557	−	22.8048i	−3.22189	−	1.33455i
$293$		−	23.4195i		−	1.36818i	−0.729397	−	0.684091i	$-0.760199\pi$
$293$		−	23.4195i		−	1.36818i	0.729397	−	0.684091i	$-0.239801\pi$
$294$	−0.778251	+	1.87886i	−0.0453885	+	0.109578i
$295$	0.149021	−	0.0617264i	0.00867632	−	0.00359385i
$296$	20.0661	+	48.4439i	1.16632	+	2.81575i
$297$	−2.80580	−	2.80580i	−0.162809	−	0.162809i
$298$	27.6410	+	27.6410i	1.60120	+	1.60120i
$299$	−3.19612	−	7.71612i	−0.184836	−	0.446235i
$300$	−8.21652	+	3.40340i	−0.474381	+	0.196495i
$301$	1.14823	−	2.77206i	0.0661826	−	0.159779i
$302$			18.1477i			1.04428i
$303$	0.912253	+	0.377868i	0.0524076	+	0.0217079i
$304$	−0.800766	+	0.800766i	−0.0459271	+	0.0459271i
$305$	1.43795			0.0823368
$306$	23.0634	+	18.9148i	1.31845	+	1.08129i
$307$	7.62887			0.435403			0.217701	−	0.976015i	$-0.430144\pi$
$307$	7.62887			0.435403			0.217701	+	0.976015i	$0.430144\pi$
$308$	−16.2073	+	16.2073i	−0.923497	+	0.923497i
$309$	3.16119	+	1.30941i	0.179834	+	0.0744896i
$310$		−	3.07636i		−	0.174726i
$311$	−0.0647608	+	0.156346i	−0.00367225	+	0.00886559i	−0.925705	−	0.378246i	$-0.876527\pi$
$311$	−0.0647608	+	0.156346i	−0.00367225	+	0.00886559i	0.922033	+	0.387112i	$0.126527\pi$
$312$	−7.00225	+	2.90042i	−0.396424	+	0.164204i
$313$	−3.21174	−	7.75382i	−0.181538	−	0.438272i	0.806746	−	0.590899i	$-0.201227\pi$
$313$	−3.21174	−	7.75382i	−0.181538	−	0.438272i	−0.988284	+	0.152627i	$0.951227\pi$
$314$	−32.2580	−	32.2580i	−1.82042	−	1.82042i
$315$	−0.980686	−	0.980686i	−0.0552554	−	0.0552554i
$316$	−9.78411	−	23.6209i	−0.550399	−	1.32878i
$317$	−1.29237	+	0.535318i	−0.0725869	+	0.0300665i	−0.418681	−	0.908133i	$-0.637508\pi$
$317$	−1.29237	+	0.535318i	−0.0725869	+	0.0300665i	0.346095	+	0.938200i	$0.387508\pi$
$318$	−4.52351	+	10.9207i	−0.253666	+	0.612404i
$319$		−	4.11116i		−	0.230181i
$320$	−0.0302730	−	0.0125395i	−0.00169231	−	0.000700979i
$321$	4.74929	−	4.74929i	0.265079	−	0.265079i
$322$	−21.2378			−1.18353
$323$	0.650843	−	0.0643207i	0.0362139	−	0.00357890i
$324$	34.0531			1.89184
$325$	10.5667	−	10.5667i	0.586134	−	0.586134i
$326$	−5.30027	−	2.19545i	−0.293555	−	0.121594i
$327$		−	3.90291i		−	0.215831i
$328$	−23.1576	+	55.9075i	−1.27867	+	3.08698i
$329$	−26.0332	+	10.7833i	−1.43525	+	0.594502i
$330$	0.107706	+	0.260026i	0.00592904	+	0.0143140i
$331$	−22.6556	−	22.6556i	−1.24526	−	1.24526i	−0.957788	−	0.287476i	$-0.907184\pi$
$331$	−22.6556	−	22.6556i	−1.24526	−	1.24526i	−0.287476	−	0.957788i	$-0.592816\pi$
$332$	−5.55578	−	5.55578i	−0.304913	−	0.304913i
$333$	−9.01210	−	21.7571i	−0.493860	−	1.19228i
$334$	−27.1447	+	11.2437i	−1.48529	+	0.615228i
$335$	−0.809636	+	1.95463i	−0.0442351	+	0.106793i
$336$			8.54226i			0.466019i
$337$	−8.18386	−	3.38986i	−0.445803	−	0.184658i	0.148477	−	0.988916i	$-0.452563\pi$
$337$	−8.18386	−	3.38986i	−0.445803	−	0.184658i	−0.594280	+	0.804258i	$0.702563\pi$
$338$	−7.15240	+	7.15240i	−0.389039	+	0.389039i
$339$	−2.09857			−0.113979
$340$	−1.41890	−	2.65245i	−0.0769505	−	0.143849i
$341$	12.6497			0.685018
$342$	0.811414	−	0.811414i	0.0438762	−	0.0438762i
$343$	13.8527	+	5.73797i	0.747975	+	0.309821i
$344$		−	6.32565i		−	0.341056i
$345$	−0.0690162	+	0.166620i	−0.00371571	+	0.00897052i
$346$	24.2223	−	10.0332i	1.30220	−	0.539389i
$347$	6.16474	+	14.8830i	0.330941	+	0.798961i	0.998518	+	0.0544209i	$0.0173313\pi$
$347$	6.16474	+	14.8830i	0.330941	+	0.798961i	−0.667577	+	0.744540i	$0.732669\pi$
$348$	−3.05140	−	3.05140i	−0.163572	−	0.163572i
$349$	−5.14318	−	5.14318i	−0.275308	−	0.275308i	0.555925	−	0.831233i	$-0.312364\pi$
$349$	−5.14318	−	5.14318i	−0.275308	−	0.275308i	−0.831233	+	0.555925i	$0.812364\pi$
$350$	−14.5418	−	35.1070i	−0.777292	−	1.87655i
$351$	6.46573	−	2.67819i	0.345115	−	0.142951i
$352$	−3.60404	+	8.70092i	−0.192096	+	0.463761i
$353$		−	0.838691i		−	0.0446390i	−0.999751	−	0.0223195i	$-0.992895\pi$
$353$		−	0.838691i		−	0.0446390i	0.999751	−	0.0223195i	$-0.00710511\pi$
$354$	0.930060	+	0.385243i	0.0494321	+	0.0204755i
$355$	−0.373525	+	0.373525i	−0.0198246	+	0.0198246i
$356$	59.3903			3.14768
$357$	3.12840	−	3.81455i	0.165572	−	0.201887i
$358$	−6.16455			−0.325807
$359$	19.0296	−	19.0296i	1.00434	−	1.00434i	0.00435358	−	0.999991i	$-0.498614\pi$
$359$	19.0296	−	19.0296i	1.00434	−	1.00434i	0.999991	−	0.00435358i	$-0.00138579\pi$
$360$	−2.70133	−	1.11893i	−0.142373	−	0.0589728i
$361$			18.9748i			0.998676i
$362$	−17.1503	+	41.4046i	−0.901401	+	2.17618i
$363$	2.98342	−	1.23577i	0.156589	−	0.0648612i
$364$	−15.4702	−	37.3484i	−0.810860	−	1.95759i
$365$	−1.52891	−	1.52891i	−0.0800267	−	0.0800267i
$366$	6.34590	+	6.34590i	0.331706	+	0.331706i
$367$	12.2134	+	29.4858i	0.637536	+	1.53915i	0.829952	+	0.557835i	$0.188368\pi$
$367$	12.2134	+	29.4858i	0.637536	+	1.53915i	−0.192416	+	0.981314i	$0.561632\pi$
$368$	−18.3344	+	7.59438i	−0.955749	+	0.395884i
$369$	10.4006	−	25.1092i	0.541432	−	1.30713i
$370$			3.43427i			0.178539i
$371$	−32.2690	−	13.3662i	−1.67532	−	0.693941i
$372$	9.38889	−	9.38889i	0.486791	−	0.486791i
$373$	−8.56426			−0.443441			−0.221720	−	0.975110i	$-0.571167\pi$
$373$	−8.56426			−0.443441			−0.221720	+	0.975110i	$0.571167\pi$
$374$	15.7711	−	8.43656i	0.815504	−	0.436244i
$375$	−0.647092			−0.0334157
$376$	−42.0063	+	42.0063i	−2.16631	+	2.16631i
$377$	6.69901	+	2.77482i	0.345017	+	0.142911i
$378$		−	17.7962i		−	0.915338i
$379$	6.14793	−	14.8424i	0.315798	−	0.762404i	−0.683670	−	0.729791i	$-0.739617\pi$
$379$	6.14793	−	14.8424i	0.315798	−	0.762404i	0.999468	−	0.0326126i	$-0.0103828\pi$
$380$	−0.106917	+	0.0442866i	−0.00548475	+	0.00227186i
$381$	−1.36633	−	3.29861i	−0.0699993	−	0.168993i
$382$	−21.8723	−	21.8723i	−1.11908	−	1.11908i
$383$	6.86923	+	6.86923i	0.351001	+	0.351001i	0.860482	−	0.509481i	$-0.170162\pi$
$383$	6.86923	+	6.86923i	0.351001	+	0.351001i	−0.509481	+	0.860482i	$0.670162\pi$
$384$	−1.76555	−	4.26241i	−0.0900978	−	0.217515i
$385$	−0.768335	+	0.318255i	−0.0391580	+	0.0162198i
$386$	−11.1448	+	26.9060i	−0.567257	+	1.36948i
$387$			2.84098i			0.144415i
$388$	−10.7519	−	4.45360i	−0.545847	−	0.226097i
$389$	5.00466	−	5.00466i	0.253746	−	0.253746i	−0.568758	−	0.822505i	$-0.692576\pi$
$389$	5.00466	−	5.00466i	0.253746	−	0.253746i	0.822505	+	0.568758i	$0.192576\pi$
$390$	−0.496401			−0.0251363
$391$	10.9685	+	3.32328i	0.554701	+	0.168066i
$392$	−12.6687			−0.639865
$393$	2.02618	−	2.02618i	0.102207	−	0.102207i
$394$	55.6000	+	23.0303i	2.80109	+	1.16025i
$395$		−	0.927664i		−	0.0466758i
$396$	8.30513	−	20.0503i	0.417348	−	1.00757i
$397$	6.00058	−	2.48552i	0.301160	−	0.124745i	−0.226986	−	0.973898i	$-0.572887\pi$
$397$	6.00058	−	2.48552i	0.301160	−	0.124745i	0.528147	+	0.849153i	$0.322887\pi$
$398$	−0.0759201	−	0.183287i	−0.00380553	−	0.00918736i
$399$	−0.134203	−	0.134203i	−0.00671856	−	0.00671856i
$400$	−25.1077	−	25.1077i	−1.25539	−	1.25539i
$401$	−6.25536	−	15.1018i	−0.312378	−	0.754147i	−0.999616	−	0.0277147i	$-0.991177\pi$
$401$	−6.25536	−	15.1018i	−0.312378	−	0.754147i	0.687238	−	0.726432i	$-0.258823\pi$
$402$	−12.1992	+	5.05306i	−0.608439	+	0.252024i
$403$	−8.53787	+	20.6122i	−0.425302	+	1.02677i
$404$			11.1033i			0.552411i
$405$	1.14151	+	0.472830i	0.0567223	+	0.0234951i
$406$	13.0378	−	13.0378i	0.647057	−	0.647057i
$407$	−14.1214			−0.699970
$408$	3.01582	−	9.95373i	0.149306	−	0.492783i
$409$	−21.7730			−1.07661			−0.538303	−	0.842751i	$-0.680934\pi$
$409$	−21.7730			−1.07661			−0.538303	+	0.842751i	$0.680934\pi$
$410$	−2.80253	+	2.80253i	−0.138407	+	0.138407i
$411$	−4.94231	−	2.04717i	−0.243786	−	0.100980i
$412$			38.4758i			1.89557i
$413$	−1.13833	+	2.74817i	−0.0560136	+	0.135229i
$414$	18.5782	−	7.69536i	0.913070	−	0.378206i
$415$	−0.109096	−	0.263381i	−0.00535531	−	0.0129289i
$416$	−11.7454	−	11.7454i	−0.575863	−	0.575863i
$417$	3.20138	+	3.20138i	0.156772	+	0.156772i
$418$	−0.263322	−	0.635715i	−0.0128795	−	0.0310938i
$419$	−22.7727	+	9.43276i	−1.11252	+	0.460820i	−0.861804	−	0.507241i	$-0.830666\pi$
$419$	−22.7727	+	9.43276i	−1.11252	+	0.460820i	−0.250715	+	0.968061i	$0.580666\pi$
$420$	−0.334060	+	0.806493i	−0.0163005	+	0.0393528i
$421$			21.7592i			1.06048i	0.847847	+	0.530240i	$0.177898\pi$
$421$			21.7592i			1.06048i	−0.847847	+	0.530240i	$0.822102\pi$
$422$	−25.9641	−	10.7547i	−1.26391	−	0.523529i
$423$	18.8659	−	18.8659i	0.917291	−	0.917291i
$424$	−73.6356			−3.57606
$425$	2.01675	+	20.4070i	0.0978269	+	0.989883i
$426$	−3.29685			−0.159733
$427$	−18.7511	+	18.7511i	−0.907429	+	0.907429i
$428$	69.7770	+	28.9026i	3.37280	+	1.39706i
$429$		−	2.04115i		−	0.0985475i
$430$	0.158546	−	0.382765i	0.00764578	−	0.0184585i
$431$	−32.2380	+	13.3534i	−1.55285	+	0.643211i	−0.983829	−	0.179112i	$-0.942678\pi$
$431$	−32.2380	+	13.3534i	−1.55285	+	0.643211i	−0.569021	+	0.822323i	$0.692678\pi$
$432$	−6.36372	−	15.3634i	−0.306174	−	0.739170i
$433$	21.2287	+	21.2287i	1.02019	+	1.02019i	0.999792	+	0.0203934i	$0.00649188\pi$
$433$	21.2287	+	21.2287i	1.02019	+	1.02019i	0.0203934	+	0.999792i	$0.493508\pi$
$434$	40.1162	+	40.1162i	1.92564	+	1.92564i
$435$	−0.0599188	−	0.144657i	−0.00287289	−	0.00693576i
$436$	40.5469	−	16.7951i	1.94184	−	0.804337i
$437$	0.168732	−	0.407354i	0.00807153	−	0.0194864i
$438$		−	13.4946i		−	0.644798i
$439$	2.04309	+	0.846277i	0.0975116	+	0.0403906i	0.430906	−	0.902397i	$-0.358194\pi$
$439$	2.04309	+	0.846277i	0.0975116	+	0.0403906i	−0.333394	+	0.942787i	$0.608194\pi$
$440$	−1.23976	+	1.23976i	−0.0591033	+	0.0591033i
$441$	5.68976			0.270941
$442$	3.10244	+	31.3928i	0.147568	+	1.49320i
$443$	−11.1197			−0.528313			−0.264156	−	0.964480i	$-0.585094\pi$
$443$	−11.1197			−0.528313			−0.264156	+	0.964480i	$0.585094\pi$
$444$	−10.4812	+	10.4812i	−0.497417	+	0.497417i
$445$	1.99086	+	0.824639i	0.0943756	+	0.0390917i
$446$			42.2427i			2.00025i
$447$	−2.34266	+	5.65567i	−0.110804	+	0.267504i
$448$	0.558282	−	0.231248i	0.0263764	−	0.0109254i
$449$	−10.2861	−	24.8328i	−0.485431	−	1.17193i	−0.956995	−	0.290103i	$-0.906310\pi$
$449$	−10.2861	−	24.8328i	−0.485431	−	1.17193i	0.471564	−	0.881832i	$-0.343690\pi$
$450$	25.4416	+	25.4416i	1.19933	+	1.19933i
$451$	−11.5237	−	11.5237i	−0.542630	−	0.542630i
$452$	−9.03060	−	21.8018i	−0.424763	−	1.02547i
$453$	−2.62565	+	1.08758i	−0.123364	+	0.0510989i
$454$	−5.72664	+	13.8253i	−0.268765	+	0.648855i
$455$		−	1.46678i		−	0.0687639i
$456$	−0.369667	−	0.153121i	−0.0173113	−	0.00717056i
$457$	12.9306	−	12.9306i	0.604868	−	0.604868i	−0.336732	−	0.941600i	$-0.609322\pi$
$457$	12.9306	−	12.9306i	0.604868	−	0.604868i	0.941600	+	0.336732i	$0.109322\pi$
$458$	−21.8544			−1.02119
$459$	−2.78475	+	9.19107i	−0.129981	+	0.429003i
$460$	−2.02798			−0.0945553
$461$	20.6575	−	20.6575i	0.962116	−	0.962116i	−0.0371917	−	0.999308i	$-0.511841\pi$
$461$	20.6575	−	20.6575i	0.962116	−	0.962116i	0.999308	+	0.0371917i	$0.0118412\pi$
$462$	−4.79529	−	1.98627i	−0.223097	−	0.0924099i
$463$			10.9294i			0.507931i	0.967213	+	0.253965i	$0.0817349\pi$
$463$			10.9294i			0.507931i	−0.967213	+	0.253965i	$0.918265\pi$
$464$	6.59332	−	15.9177i	0.306087	−	0.738959i
$465$	0.445096	−	0.184365i	0.0206408	−	0.00854971i
$466$	3.32347	+	8.02357i	0.153957	+	0.371685i
$467$	−27.0662	−	27.0662i	−1.25247	−	1.25247i	−0.954607	−	0.297867i	$-0.903725\pi$
$467$	−27.0662	−	27.0662i	−1.25247	−	1.25247i	−0.297867	−	0.954607i	$-0.596275\pi$
$468$	27.0659	+	27.0659i	1.25112	+	1.25112i
$469$	−14.9310	−	36.0465i	−0.689447	−	1.66447i
$470$	−3.59464	+	1.48895i	−0.165809	+	0.0686801i
$471$	2.73396	−	6.60037i	0.125974	−	0.304129i
$472$			6.27115i			0.288653i
$473$	1.57389	+	0.651925i	0.0723673	+	0.0299755i
$474$	4.09393	−	4.09393i	0.188040	−	0.188040i
$475$	0.788910			0.0361977
$476$	53.0910	+	16.0857i	2.43342	+	0.737289i
$477$	33.0712			1.51423
$478$	−43.6570	+	43.6570i	−1.99683	+	1.99683i
$479$	−22.1856	−	9.18958i	−1.01369	−	0.419883i	−0.186888	−	0.982381i	$-0.559840\pi$
$479$	−22.1856	−	9.18958i	−1.01369	−	0.419883i	−0.826798	+	0.562499i	$0.809840\pi$
$480$			0.358682i			0.0163715i
$481$	9.53119	−	23.0103i	0.434585	−	1.04918i
$482$	26.0353	−	10.7842i	1.18587	−	0.491205i
$483$	−1.27277	−	3.07273i	−0.0579129	−	0.139814i
$484$	25.6766	+	25.6766i	1.16712	+	1.16712i
$485$	−0.298583	−	0.298583i	−0.0135580	−	0.0135580i
$486$	9.76028	+	23.5634i	0.442735	+	1.06886i
$487$	−8.56842	+	3.54915i	−0.388272	+	0.160828i	−0.568275	−	0.822838i	$-0.692389\pi$
$487$	−8.56842	+	3.54915i	−0.388272	+	0.160828i	0.180003	+	0.983666i	$0.442389\pi$
$488$	−21.3944	+	51.6506i	−0.968477	+	2.33811i
$489$		−	0.898429i		−	0.0406284i
$490$	−0.766580	−	0.317528i	−0.0346306	−	0.0143444i
$491$	−24.1775	+	24.1775i	−1.09112	+	1.09112i	−0.0957066	+	0.995410i	$0.530511\pi$
$491$	−24.1775	+	24.1775i	−1.09112	+	1.09112i	−0.995410	+	0.0957066i	$0.969489\pi$
$492$	−17.1064			−0.771214
$493$	−8.77371	+	4.69339i	−0.395148	+	0.211380i
$494$	1.21361			0.0546028
$495$	0.556802	−	0.556802i	0.0250264	−	0.0250264i
$496$	48.9772	+	20.2870i	2.19914	+	0.910915i
$497$		−	9.74164i		−	0.436972i
$498$	0.680884	−	1.64380i	0.0305112	−	0.0736605i
$499$	33.0118	−	13.6739i	1.47781	−	0.612129i	0.509186	−	0.860657i	$-0.329947\pi$
$499$	33.0118	−	13.6739i	1.47781	−	0.612129i	0.968625	+	0.248528i	$0.0799467\pi$
$500$	−2.78457	−	6.72256i	−0.124530	−	0.300642i
$501$	−3.25354	−	3.25354i	−0.145357	−	0.145357i
$502$	−0.763444	−	0.763444i	−0.0340742	−	0.0340742i
$503$	−11.3444	−	27.3877i	−0.505820	−	1.22116i	−0.946269	−	0.323379i	$-0.895181\pi$
$503$	−11.3444	−	27.3877i	−0.505820	−	1.22116i	0.440450	−	0.897777i	$-0.354819\pi$
$504$	49.8169	−	20.6348i	2.21902	−	0.919148i
$505$	−0.154171	+	0.372201i	−0.00686051	+	0.0165627i
$506$		−	12.0581i		−	0.536048i
$507$	−1.46347	−	0.606188i	−0.0649949	−	0.0269218i
$508$	28.3893	−	28.3893i	1.25957	−	1.25957i
$509$	−18.0632			−0.800638			−0.400319	−	0.916376i	$-0.631101\pi$
$509$	−18.0632			−0.800638			−0.400319	+	0.916376i	$0.631101\pi$
$510$	0.431968	−	0.526711i	0.0191278	−	0.0233231i
$511$	39.8744			1.76394
$512$	35.9589	−	35.9589i	1.58917	−	1.58917i
$513$	0.341343	+	0.141389i	0.0150707	+	0.00624247i
$514$			46.4781i			2.05006i
$515$	−0.534241	+	1.28977i	−0.0235415	+	0.0568341i
$516$	1.65205	−	0.684302i	0.0727275	−	0.0301247i
$517$	−6.12240	−	14.7808i	−0.269263	−	0.650058i
$518$	−44.7835	−	44.7835i	−1.96767	−	1.96767i
$519$	2.90327	+	2.90327i	0.127439	+	0.127439i
$520$	−1.18338	−	2.85693i	−0.0518946	−	0.125285i
$521$	−37.3721	+	15.4800i	−1.63730	+	0.678193i	−0.996022	−	0.0891123i	$-0.971597\pi$
$521$	−37.3721	+	15.4800i	−1.63730	+	0.678193i	−0.641282	+	0.767306i	$0.721597\pi$
$522$	−6.68099	+	16.1293i	−0.292419	+	0.705962i
$523$			25.9565i			1.13500i	0.823374	+	0.567498i	$0.192089\pi$
$523$			25.9565i			1.13500i	−0.823374	+	0.567498i	$0.807911\pi$
$524$	29.7688	+	12.3306i	1.30046	+	0.538667i
$525$	4.20789	−	4.20789i	0.183647	−	0.183647i
$526$	44.7512			1.95124
$527$	−14.4411	−	26.9959i	−0.629066	−	1.17596i
$528$	−4.85002			−0.211070
$529$	−10.7999	+	10.7999i	−0.469562	+	0.469562i
$530$	−4.45568	−	1.84560i	−0.193542	−	0.0801678i
$531$		−	2.81650i		−	0.122226i
$532$	0.816715	−	1.97172i	0.0354091	−	0.0854851i
$533$	26.5554	−	10.9996i	1.15024	−	0.476447i
$534$	5.14670	+	12.4252i	0.222719	+	0.537692i
$535$	1.93772	+	1.93772i	0.0837749	+	0.0837749i
$536$	−58.1635	−	58.1635i	−2.51228	−	2.51228i
$537$	−0.369438	−	0.891903i	−0.0159424	−	0.0384885i
$538$	−11.6424	+	4.82246i	−0.501941	+	0.207911i
$539$	1.30564	−	3.15209i	0.0562379	−	0.135770i
$540$		−	1.69935i		−	0.0731285i
$541$	35.0983	+	14.5382i	1.50900	+	0.625046i	0.975350	−	0.220662i	$-0.0708219\pi$
$541$	35.0983	+	14.5382i	1.50900	+	0.625046i	0.533645	+	0.845709i	$0.320822\pi$
$542$	25.0643	−	25.0643i	1.07660	−	1.07660i
$543$	−7.01833			−0.301185
$544$	22.6833	−	2.24171i	0.972538	−	0.0961127i
$545$	1.59240			0.0682107
$546$	6.47315	−	6.47315i	0.277025	−	0.277025i
$547$	−29.3635	−	12.1628i	−1.25549	−	0.520043i	−0.346971	−	0.937876i	$-0.612790\pi$
$547$	−29.3635	−	12.1628i	−1.25549	−	0.520043i	−0.908524	+	0.417833i	$0.862790\pi$
$548$		−	60.1545i		−	2.56967i
$549$	9.60864	−	23.1973i	0.410087	−	0.990037i
$550$	19.9326	−	8.25636i	0.849930	−	0.352053i
$551$	0.146490	+	0.353659i	0.00624069	+	0.0150664i
$552$	−4.95807	−	4.95807i	−0.211029	−	0.211029i
$553$	12.0969	+	12.0969i	0.514412	+	0.514412i
$554$	10.2447	+	24.7330i	0.435257	+	1.05080i
$555$	−0.496880	+	0.205814i	−0.0210914	+	0.00873633i
$556$	−19.4825	+	47.0350i	−0.826244	+	1.99473i
$557$			0.745532i			0.0315892i	0.999875	+	0.0157946i	$0.00502778\pi$
$557$			0.745532i			0.0315892i	−0.999875	+	0.0157946i	$0.994972\pi$
$558$	−49.6285	−	20.5568i	−2.10094	−	0.870238i
$559$	−2.12458	+	2.12458i	−0.0898603	+	0.0898603i
$560$	−3.48526			−0.147279
$561$	2.16578	+	1.77620i	0.0914391	+	0.0749914i
$562$	−0.387604			−0.0163501
$563$	−13.0471	+	13.0471i	−0.549870	+	0.549870i	−0.926403	−	0.376533i	$-0.877116\pi$
$563$	−13.0471	+	13.0471i	−0.549870	+	0.549870i	0.376533	+	0.926403i	$0.377116\pi$
$564$	−15.5149	−	6.42646i	−0.653293	−	0.270603i
$565$		−	0.856221i		−	0.0360215i
$566$	−1.75139	+	4.22823i	−0.0736165	+	0.177726i
$567$	−21.0513	+	8.71974i	−0.884072	+	0.366194i
$568$	−7.85940	−	18.9743i	−0.329773	−	0.796143i
$569$	−4.07468	−	4.07468i	−0.170819	−	0.170819i	0.616520	−	0.787339i	$-0.288542\pi$
$569$	−4.07468	−	4.07468i	−0.170819	−	0.170819i	−0.787339	+	0.616520i	$0.788542\pi$
$570$	−0.0185307	−	0.0185307i	−0.000776165	−	0.000776165i
$571$	1.34284	+	3.24191i	0.0561962	+	0.135670i	0.949484	−	0.313816i	$-0.101607\pi$
$571$	1.34284	+	3.24191i	0.0561962	+	0.135670i	−0.893288	+	0.449485i	$0.851607\pi$
$572$	21.2052	−	8.78349i	0.886635	−	0.367256i
$573$	1.85374	−	4.47533i	0.0774413	−	0.186960i
$574$		−	73.0909i		−	3.05076i
$575$	12.7725	+	5.29052i	0.532648	+	0.220630i
$576$	−0.404580	+	0.404580i	−0.0168575	+	0.0168575i
$577$	37.8915			1.57744			0.788721	−	0.614751i	$-0.210743\pi$
$577$	37.8915			1.57744			0.788721	+	0.614751i	$0.210743\pi$
$578$	−36.0093	−	24.0261i	−1.49779	−	0.999353i
$579$	−4.56074			−0.189538
$580$	1.24498	−	1.24498i	0.0516949	−	0.0516949i
$581$	4.85716	+	2.01190i	0.201509	+	0.0834677i
$582$		−	2.63539i		−	0.109240i
$583$	7.58891	−	18.3213i	0.314301	−	0.758789i
$584$	77.6653	−	32.1700i	3.21381	−	1.33121i
$585$	0.531479	+	1.28310i	0.0219740	+	0.0530498i
$586$	42.1686	+	42.1686i	1.74197	+	1.74197i
$587$	3.69726	+	3.69726i	0.152602	+	0.152602i	0.779279	−	0.626677i	$-0.215585\pi$
$587$	3.69726	+	3.69726i	0.152602	+	0.152602i	−0.626677	+	0.779279i	$0.715585\pi$
$588$	−1.37048	−	3.30864i	−0.0565178	−	0.136446i
$589$	−1.08818	+	0.450737i	−0.0448375	+	0.0185723i
$590$	−0.157180	+	0.379466i	−0.00647100	+	0.0156224i
$591$			9.42453i			0.387674i
$592$	−54.6754	−	22.6473i	−2.24714	−	0.930798i
$593$	0.436422	−	0.436422i	0.0179217	−	0.0179217i	−0.698089	−	0.716011i	$-0.745966\pi$
$593$	0.436422	−	0.436422i	0.0179217	−	0.0179217i	0.716011	+	0.698089i	$0.245966\pi$
$594$	10.1041			0.414576
$595$	1.55634	+	1.27639i	0.0638038	+	0.0523270i
$596$	−68.8370			−2.81967
$597$	0.0219686	−	0.0219686i	0.000899116	−	0.000899116i
$598$	19.6483	+	8.13860i	0.803480	+	0.332812i
$599$			37.8178i			1.54519i	0.634898	+	0.772596i	$0.281042\pi$
$599$			37.8178i			1.54519i	−0.634898	+	0.772596i	$0.718958\pi$
$600$	4.80106	−	11.5908i	0.196003	−	0.473192i
$601$	−24.4020	+	10.1076i	−0.995377	+	0.412299i	−0.820100	−	0.572221i	$-0.806082\pi$
$601$	−24.4020	+	10.1076i	−0.995377	+	0.412299i	−0.175277	+	0.984519i	$0.556082\pi$
$602$	2.92384	+	7.05878i	0.119167	+	0.287694i
$603$	26.1224	+	26.1224i	1.06379	+	1.06379i
$604$	−22.5975	−	22.5975i	−0.919477	−	0.919477i
$605$	0.504197	+	1.21724i	0.0204985	+	0.0494878i
$606$	−2.32296	+	0.962203i	−0.0943639	+	0.0390868i
$607$	16.3866	−	39.5607i	0.665111	−	1.60572i	−0.124576	−	0.992210i	$-0.539757\pi$
$607$	16.3866	−	39.5607i	0.665111	−	1.60572i	0.789687	−	0.613510i	$-0.210243\pi$
$608$		−	0.876909i		−	0.0355634i
$609$	2.66770	+	1.10500i	0.108101	+	0.0447767i
$610$	−2.58914	+	2.58914i	−0.104831	+	0.104831i
$611$	28.2171			1.14154
$612$	−52.2712	+	5.16579i	−2.11294	+	0.208815i
$613$	−22.0812			−0.891851			−0.445926	−	0.895070i	$-0.647125\pi$
$613$	−22.0812			−0.891851			−0.445926	+	0.895070i	$0.647125\pi$
$614$	−13.7364	+	13.7364i	−0.554355	+	0.554355i
$615$	−0.573432	−	0.237523i	−0.0231230	−	0.00957786i
$616$		−	32.3334i		−	1.30275i
$617$	5.81495	−	14.0385i	0.234101	−	0.565170i	−0.762551	−	0.646928i	$-0.776053\pi$
$617$	5.81495	−	14.0385i	0.234101	−	0.565170i	0.996652	+	0.0817578i	$0.0260534\pi$
$618$	−8.04965	+	3.33428i	−0.323804	+	0.134124i
$619$	−14.0465	−	33.9113i	−0.564577	−	1.36301i	−0.906071	−	0.423126i	$-0.860933\pi$
$619$	−14.0465	−	33.9113i	−0.564577	−	1.36301i	0.341493	−	0.939884i	$-0.389067\pi$
$620$	3.83068	+	3.83068i	0.153844	+	0.153844i
$621$	4.57818	+	4.57818i	0.183716	+	0.183716i
$622$	−0.164907	−	0.398120i	−0.00661216	−	0.0159632i
$623$	−36.7145	+	15.2076i	−1.47094	+	0.609281i
$624$	3.27351	−	7.90296i	0.131045	−	0.316372i
$625$			24.6036i			0.984145i
$626$	19.7443	+	8.17837i	0.789142	+	0.326873i
$627$	0.0761961	−	0.0761961i	0.00304298	−	0.00304298i
$628$	80.3352			3.20572
$629$	16.1213	+	30.1367i	0.642797	+	1.20163i
$630$	3.53160			0.140702
$631$	8.59921	−	8.59921i	0.342329	−	0.342329i	−0.514913	−	0.857242i	$-0.672176\pi$
$631$	8.59921	−	8.59921i	0.342329	−	0.342329i	0.857242	+	0.514913i	$0.172176\pi$
$632$	33.3213	+	13.8021i	1.32545	+	0.549019i
$633$		−	4.40107i		−	0.174927i
$634$	1.36313	−	3.29090i	0.0541370	−	0.130698i
$635$	1.34584	−	0.557466i	0.0534081	−	0.0221223i
$636$	−7.96581	−	19.2312i	−0.315865	−	0.762565i
$637$	4.25500	+	4.25500i	0.168589	+	0.168589i
$638$	7.40246	+	7.40246i	0.293066	+	0.293066i
$639$	3.52982	+	8.52173i	0.139637	+	0.337114i
$640$	1.73907	−	0.720347i	0.0687429	−	0.0284742i
$641$	4.82099	−	11.6389i	0.190418	−	0.459709i	−0.799621	−	0.600505i	$-0.794966\pi$
$641$	4.82099	−	11.6389i	0.190418	−	0.459709i	0.990039	+	0.140796i	$0.0449662\pi$
$642$			17.1029i			0.674998i
$643$	40.7743	+	16.8893i	1.60798	+	0.666048i	0.992516	−	0.122116i	$-0.0389680\pi$
$643$	40.7743	+	16.8893i	1.60798	+	0.666048i	0.615466	+	0.788164i	$0.288968\pi$
$644$	26.4452	−	26.4452i	1.04209	−	1.04209i
$645$	0.0648809			0.00255468
$646$	−1.05608	+	1.28771i	−0.0415509	+	0.0506642i
$647$	20.3328			0.799364			0.399682	−	0.916654i	$-0.369121\pi$
$647$	20.3328			0.799364			0.399682	+	0.916654i	$0.369121\pi$
$648$	−33.9677	+	33.9677i	−1.33438	+	1.33438i
$649$	−1.56032	−	0.646307i	−0.0612481	−	0.0253698i
$650$			38.0522i			1.49253i
$651$	−3.39997	+	8.20827i	−0.133256	+	0.321707i
$652$	9.33367	−	3.86613i	0.365535	−	0.151409i
$653$	5.47254	+	13.2119i	0.214157	+	0.517021i	0.994054	−	0.108887i	$-0.0347286\pi$
$653$	5.47254	+	13.2119i	0.214157	+	0.517021i	−0.779897	+	0.625908i	$0.784729\pi$
$654$	7.02749	+	7.02749i	0.274797	+	0.274797i
$655$	0.826685	+	0.826685i	0.0323013	+	0.0323013i
$656$	−26.1365	−	63.0990i	−1.02046	−	2.46360i
$657$	−34.8811	+	14.4482i	−1.36084	+	0.563678i
$658$	27.4586	−	66.2909i	1.07045	−	2.58429i
$659$		−	4.34674i		−	0.169325i	−0.996410	−	0.0846625i	$-0.973019\pi$
$659$		−	4.34674i		−	0.169325i	0.996410	−	0.0846625i	$-0.0269812\pi$
$660$	−0.457900	−	0.189669i	−0.0178238	−	0.00738284i
$661$	−11.7887	+	11.7887i	−0.458528	+	0.458528i	−0.898172	−	0.439644i	$-0.855104\pi$
$661$	−11.7887	+	11.7887i	−0.458528	+	0.458528i	0.439644	+	0.898172i	$0.355104\pi$
$662$	81.5863			3.17094
$663$	−4.35606	+	2.33022i	−0.169175	+	0.0904983i
$664$	11.0837			0.430131
$665$	0.0547551	−	0.0547551i	0.00212331	−	0.00212331i
$666$	55.4024	+	22.9484i	2.14680	+	0.889234i
$667$			6.70812i			0.259739i
$668$	19.7999	−	47.8012i	0.766082	−	1.84949i
$669$	−6.11178	+	2.53158i	−0.236295	+	0.0978766i
$670$	−2.06166	−	4.97728i	−0.0796488	−	0.192289i
$671$	−10.6463	−	10.6463i	−0.410994	−	0.410994i
$672$	−4.67727	−	4.67727i	−0.180429	−	0.180429i
$673$	12.6526	+	30.5462i	0.487723	+	1.17747i	0.955863	+	0.293813i	$0.0949244\pi$
$673$	12.6526	+	30.5462i	0.487723	+	1.17747i	−0.468140	+	0.883654i	$0.655076\pi$
$674$	20.8394	−	8.63195i	0.802703	−	0.332490i
$675$	−4.43320	+	10.7027i	−0.170634	+	0.411947i
$676$		−	17.8123i		−	0.685090i
$677$	−10.4822	−	4.34188i	−0.402865	−	0.166872i	0.172044	−	0.985089i	$-0.444963\pi$
$677$	−10.4822	−	4.34188i	−0.402865	−	0.166872i	−0.574909	+	0.818217i	$0.694963\pi$
$678$	3.77864	−	3.77864i	0.145118	−	0.145118i
$679$	7.78714			0.298843
$680$	4.06114	+	1.23046i	0.155738	+	0.0471860i
$681$	−2.34348			−0.0898023
$682$	−22.7767	+	22.7767i	−0.872165	+	0.872165i
$683$	1.72666	+	0.715205i	0.0660687	+	0.0273665i	0.415473	−	0.909605i	$-0.363616\pi$
$683$	1.72666	+	0.715205i	0.0660687	+	0.0273665i	−0.349404	+	0.936972i	$0.613616\pi$
$684$			2.02074i			0.0772651i
$685$	0.835250	−	2.01647i	0.0319133	−	0.0770454i
$686$	−35.2745	+	14.6112i	−1.34679	+	0.557857i
$687$	−1.30972	−	3.16194i	−0.0499689	−	0.120636i
$688$	5.04827	+	5.04827i	0.192464	+	0.192464i
$689$	24.7318	+	24.7318i	0.942207	+	0.942207i
$690$	−0.175743	−	0.424281i	−0.00669042	−	0.0161521i
$691$	10.4367	−	4.32302i	0.397030	−	0.164455i	−0.175230	−	0.984528i	$-0.556067\pi$
$691$	10.4367	−	4.32302i	0.397030	−	0.164455i	0.572260	+	0.820072i	$0.306067\pi$
$692$	−17.6683	+	42.6550i	−0.671648	+	1.62150i
$693$			14.5216i			0.551629i
$694$	−37.8981	−	15.6979i	−1.43859	−	0.595884i
$695$	−1.30617	+	1.30617i	−0.0495459	+	0.0495459i
$696$	6.08750			0.230746
$697$	−11.4373	+	37.7487i	−0.433217	+	1.42983i
$698$	18.5214			0.701045
$699$	−0.961697	+	0.961697i	−0.0363747	+	0.0363747i
$700$	61.8227	+	25.6078i	2.33668	+	0.967884i
$701$		−	15.7253i		−	0.593938i	−0.954887	−	0.296969i	$-0.904024\pi$
$701$		−	15.7253i		−	0.593938i	0.954887	−	0.296969i	$-0.0959758\pi$
$702$	−6.81975	+	16.4643i	−0.257395	+	0.621406i
$703$	1.21478	−	0.503177i	0.0458162	−	0.0189777i
$704$	0.131295	+	0.316974i	0.00494837	+	0.0119464i
$705$	−0.430850	−	0.430850i	−0.0162268	−	0.0162268i
$706$	1.51013	+	1.51013i	0.0568344	+	0.0568344i
$707$	−2.84315	−	6.86397i	−0.106928	−	0.258146i
$708$	−1.63782	+	0.678405i	−0.0615529	+	0.0254960i
$709$	−4.60534	+	11.1183i	−0.172957	+	0.417556i	−0.986459	−	0.164006i	$-0.947558\pi$
$709$	−4.60534	+	11.1183i	−0.172957	+	0.417556i	0.813502	+	0.581562i	$0.197558\pi$
$710$		−	1.34512i		−	0.0504814i
$711$	−14.9653	−	6.19881i	−0.561241	−	0.232474i
$712$	−59.2414	+	59.2414i	−2.22016	+	2.22016i
$713$	−20.6403			−0.772984
$714$	1.23546	+	12.5013i	0.0462360	+	0.467850i
$715$	0.832792			0.0311447
$716$	7.67610	−	7.67610i	0.286869	−	0.286869i
$717$	−8.93275	−	3.70007i	−0.333600	−	0.138182i
$718$			68.5285i			2.55746i
$719$	−4.23836	+	10.2323i	−0.158064	+	0.381601i	−0.982995	−	0.183633i	$-0.941214\pi$
$719$	−4.23836	+	10.2323i	−0.158064	+	0.381601i	0.824931	+	0.565234i	$0.191214\pi$
$720$	3.04881	−	1.26286i	0.113623	−	0.0470640i
$721$	−9.85223	−	23.7854i	−0.366916	−	0.885814i
$722$	−34.1657	−	34.1657i	−1.27151	−	1.27151i
$723$	3.12056	+	3.12056i	0.116055	+	0.116055i
$724$	−30.2014	−	72.9125i	−1.12242	−	2.70977i
$725$	−11.0888	+	4.59315i	−0.411829	+	0.170585i
$726$	−3.14677	+	7.59698i	−0.116788	+	0.281950i
$727$		−	41.0360i		−	1.52194i	−0.648786	−	0.760971i	$-0.724723\pi$
$727$		−	41.0360i		−	1.52194i	0.648786	−	0.760971i	$-0.275277\pi$
$728$	52.6862	+	21.8234i	1.95268	+	0.808827i
$729$	13.2852	−	13.2852i	0.492045	−	0.492045i
$730$	5.50583			0.203780
$731$	−0.405497	−	4.10312i	−0.0149979	−	0.151759i
$732$	−15.8038			−0.584126
$733$	−30.9445	+	30.9445i	−1.14296	+	1.14296i	−0.155055	+	0.987906i	$0.549555\pi$
$733$	−30.9445	+	30.9445i	−1.14296	+	1.14296i	−0.987906	+	0.155055i	$0.950445\pi$
$734$	−75.0828	−	31.1003i	−2.77136	−	1.14793i
$735$		−	0.129940i		−	0.00479291i
$736$	5.88066	−	14.1972i	0.216764	−	0.523315i
$737$	20.4660	−	8.47731i	0.753876	−	0.312266i
$738$	26.4840	+	63.9380i	0.974890	+	2.35359i
$739$	12.6882	+	12.6882i	0.466744	+	0.466744i	0.900858	−	0.434114i	$-0.142938\pi$
$739$	12.6882	+	12.6882i	0.466744	+	0.466744i	−0.434114	+	0.900858i	$0.642938\pi$
$740$	−4.27636	−	4.27636i	−0.157202	−	0.157202i
$741$	0.0727309	+	0.175588i	0.00267184	+	0.00645038i
$742$	82.1697	−	34.0358i	3.01654	−	1.24949i
$743$	12.3987	−	29.9330i	0.454863	−	1.09814i	−0.515588	−	0.856836i	$-0.672427\pi$
$743$	12.3987	−	29.9330i	0.454863	−	1.09814i	0.970451	−	0.241299i	$-0.0775734\pi$
$744$			18.7307i			0.686701i
$745$	−2.30752	−	0.955808i	−0.0845412	−	0.0350181i
$746$	15.4206	−	15.4206i	0.564589	−	0.564589i
$747$	−4.97792			−0.182132
$748$	−9.13296	+	30.1434i	−0.333934	+	1.10215i
$749$	−50.5363			−1.84656
$750$	1.16514	−	1.16514i	0.0425449	−	0.0425449i
$751$	−47.5885	−	19.7118i	−1.73653	−	0.719293i	−0.999034	−	0.0439394i	$-0.986009\pi$
$751$	−47.5885	−	19.7118i	−1.73653	−	0.719293i	−0.737494	−	0.675354i	$-0.763991\pi$
$752$		−	67.0474i		−	2.44497i
$753$	0.0647042	−	0.156210i	0.00235795	−	0.00569260i
$754$	−17.0584	+	7.06581i	−0.621229	+	0.257321i
$755$	−0.443734	−	1.07127i	−0.0161492	−	0.0389875i
$756$	22.1598	+	22.1598i	0.805945	+	0.805945i
$757$	3.80989	+	3.80989i	0.138473	+	0.138473i	0.772945	−	0.634473i	$-0.218783\pi$
$757$	3.80989	+	3.80989i	0.138473	+	0.138473i	−0.634473	+	0.772945i	$0.718783\pi$
$758$	15.6551	+	37.7947i	0.568619	+	1.37277i
$759$	1.74460	−	0.722636i	0.0633249	−	0.0262300i
$760$	0.0624737	−	0.150825i	0.00226616	−	0.00547099i
$761$			14.7009i			0.532907i	0.963848	+	0.266454i	$0.0858519\pi$
$761$			14.7009i			0.532907i	−0.963848	+	0.266454i	$0.914148\pi$
$762$	8.39959	+	3.47923i	0.304285	+	0.126039i
$763$	−20.7651	+	20.7651i	−0.751746	+	0.751746i
$764$	54.4707			1.97068
$765$	−1.82394	−	0.552625i	−0.0659447	−	0.0199802i
$766$	−24.7372			−0.893790
$767$	2.10628	−	2.10628i	0.0760532	−	0.0760532i
$768$	10.7054	+	4.43433i	0.386298	+	0.160010i
$769$		−	21.5252i		−	0.776220i	−0.921613	−	0.388110i	$-0.873128\pi$
$769$		−	21.5252i		−	0.776220i	0.921613	−	0.388110i	$-0.126872\pi$
$770$	0.810404	−	1.95649i	0.0292049	−	0.0705069i
$771$	−6.72457	+	2.78541i	−0.242180	+	0.100314i
$772$	−19.6258	−	47.3809i	−0.706349	−	1.70528i
$773$	7.25214	+	7.25214i	0.260841	+	0.260841i	0.825396	−	0.564554i	$-0.190952\pi$
$773$	7.25214	+	7.25214i	0.260841	+	0.260841i	−0.564554	+	0.825396i	$0.690952\pi$
$774$	−5.11540	−	5.11540i	−0.183869	−	0.183869i
$775$	−14.1327	−	34.1194i	−0.507662	−	1.22560i
$776$	15.1674	−	6.28255i	0.544478	−	0.225530i
$777$	3.79554	−	9.16324i	0.136164	−	0.328729i
$778$			18.0226i			0.646140i
$779$	1.40193	+	0.580700i	0.0502295	+	0.0208057i
$780$	0.618119	−	0.618119i	0.0221322	−	0.0221322i
$781$	5.53098			0.197914
$782$	−25.7335	+	13.7658i	−0.920227	+	0.492264i
$783$	−5.62108			−0.200881
$784$	10.1104	−	10.1104i	0.361086	−	0.361086i
$785$	2.69296	+	1.11546i	0.0961160	+	0.0398125i
$786$			7.29659i			0.260261i
$787$	13.7280	−	33.1422i	0.489349	−	1.18139i	−0.465700	−	0.884943i	$-0.654197\pi$
$787$	13.7280	−	33.1422i	0.489349	−	1.18139i	0.955049	−	0.296450i	$-0.0958026\pi$
$788$	−97.9103	+	40.5558i	−3.48791	+	1.44474i
$789$	2.68191	+	6.47471i	0.0954787	+	0.230506i
$790$	1.67033	+	1.67033i	0.0594277	+	0.0594277i
$791$	11.1653	+	11.1653i	0.396991	+	0.396991i
$792$	11.7158	+	28.2844i	0.416302	+	1.00504i
$793$	24.5334	−	10.1621i	0.871208	−	0.360866i
$794$	−6.32913	+	15.2799i	−0.224613	+	0.542263i
$795$		−	0.755265i		−	0.0267865i
$796$	0.322765	+	0.133694i	0.0114401	+	0.00473864i
$797$	−12.4351	+	12.4351i	−0.440473	+	0.440473i	−0.892171	−	0.451698i	$-0.850818\pi$
$797$	−12.4351	+	12.4351i	−0.440473	+	0.440473i	0.451698	+	0.892171i	$0.350818\pi$
$798$	0.483286			0.0171081
$799$	−24.5545	+	29.9400i	−0.868676	+	1.05920i
$800$	27.4952			0.972102
$801$	26.6065	−	26.6065i	0.940094	−	0.940094i
$802$	38.4552	+	15.9287i	1.35790	+	0.562461i
$803$			22.6394i			0.798926i
$804$	8.89832	−	21.4825i	0.313820	−	0.757628i
$805$	1.25368	−	0.519292i	0.0441864	−	0.0183026i
$806$	−21.7408	−	52.4870i	−0.765789	−	1.84878i
$807$	−1.39545	−	1.39545i	−0.0491222	−	0.0491222i
$808$	−11.0755	−	11.0755i	−0.389635	−	0.389635i
$809$	17.0585	+	41.1828i	0.599743	+	1.44791i	0.873843	+	0.486207i	$0.161620\pi$
$809$	17.0585	+	41.1828i	0.599743	+	1.44791i	−0.274100	+	0.961701i	$0.588380\pi$
$810$	−2.90675	+	1.20402i	−0.102133	+	0.0423048i
$811$	7.49177	−	18.0867i	0.263072	−	0.635111i	−0.736054	−	0.676923i	$-0.763313\pi$
$811$	7.49177	−	18.0867i	0.263072	−	0.635111i	0.999125	+	0.0418120i	$0.0133131\pi$
$812$			32.4694i			1.13945i
$813$	5.12846	+	2.12428i	0.179863	+	0.0745017i
$814$	25.4266	−	25.4266i	0.891202	−	0.891202i
$815$	0.366561			0.0128401
$816$	5.53689	+	10.3505i	0.193830	+	0.362341i
$817$	−0.158622			−0.00554947
$818$	39.2040	−	39.2040i	1.37073	−	1.37073i
$819$	−23.6625	−	9.80131i	−0.826833	−	0.342485i
$820$		−	6.97942i		−	0.243732i
$821$	19.5759	−	47.2604i	0.683204	−	1.64940i	−0.0748381	−	0.997196i	$-0.523844\pi$
$821$	19.5759	−	47.2604i	0.683204	−	1.64940i	0.758042	−	0.652205i	$-0.226156\pi$
$822$	12.5851	−	5.21292i	0.438956	−	0.181821i
$823$	−21.4191	−	51.7104i	−0.746624	−	1.80251i	−0.576519	−	0.817084i	$-0.695589\pi$
$823$	−21.4191	−	51.7104i	−0.746624	−	1.80251i	−0.170105	−	0.985426i	$-0.554411\pi$
$824$	−38.3794	−	38.3794i	−1.33701	−	1.33701i
$825$	2.38910	+	2.38910i	0.0831779	+	0.0831779i
$826$	−2.89865	−	6.99795i	−0.100857	−	0.243490i
$827$	−16.8227	+	6.96819i	−0.584982	+	0.242308i	−0.655490	−	0.755204i	$-0.727538\pi$
$827$	−16.8227	+	6.96819i	−0.584982	+	0.242308i	0.0705079	+	0.997511i	$0.477538\pi$
$828$	−13.5514	+	32.7159i	−0.470942	+	1.13695i
$829$		−	25.4223i		−	0.882954i	−0.897273	−	0.441477i	$-0.854455\pi$
$829$		−	25.4223i		−	0.882954i	0.897273	−	0.441477i	$-0.145545\pi$
$830$	0.670674	+	0.277802i	0.0232794	+	0.00964265i
$831$	−2.96447	+	2.96447i	−0.102836	+	0.102836i
$832$	−0.605118			−0.0209787
$833$	−8.21750	+	0.812108i	−0.284720	+	0.0281379i
$834$	−11.5287			−0.399205
$835$	1.32745	−	1.32745i	0.0459383	−	0.0459383i
$836$	1.11948	+	0.463704i	0.0387180	+	0.0160375i
$837$		−	17.2955i		−	0.597821i
$838$	24.0196	−	57.9884i	0.829743	−	2.00318i
$839$	−26.4056	+	10.9376i	−0.911623	+	0.377607i	−0.788678	−	0.614807i	$-0.789234\pi$
$839$	−26.4056	+	10.9376i	−0.911623	+	0.377607i	−0.122945	+	0.992413i	$0.539234\pi$
$840$	−0.471248	−	1.13769i	−0.0162596	−	0.0392542i
$841$	16.3880	+	16.3880i	0.565103	+	0.565103i
$842$	−39.1792	−	39.1792i	−1.35020	−	1.35020i
$843$	−0.0232289	−	0.0560795i	−0.000800045	−	0.00193148i
$844$	45.7222	−	18.9387i	1.57382	−	0.651899i
$845$	0.247326	−	0.597097i	0.00850827	−	0.0205408i
$846$			67.9389i			2.33579i
$847$	−22.4478	−	9.29819i	−0.771316	−	0.319490i
$848$	58.7659	−	58.7659i	2.01803	−	2.01803i
$849$	−0.716712			−0.0245975
$850$	−40.3756	−	33.1130i	−1.38487	−	1.13577i
$851$	23.0416			0.789857
$852$	4.10523	−	4.10523i	0.140643	−	0.140643i
$853$	−14.1722	−	5.87033i	−0.485248	−	0.200996i	0.126627	−	0.991950i	$-0.459585\pi$
$853$	−14.1722	−	5.87033i	−0.485248	−	0.200996i	−0.611876	+	0.790954i	$0.709585\pi$
$854$		−	67.5256i		−	2.31068i
$855$	−0.0280582	+	0.0677385i	−0.000959570	+	0.00231661i
$856$	−98.4321	+	40.7719i	−3.36434	+	1.39356i
$857$	16.2360	+	39.1971i	0.554610	+	1.33895i	0.913983	+	0.405753i	$0.132991\pi$
$857$	16.2360	+	39.1971i	0.554610	+	1.33895i	−0.359373	+	0.933194i	$0.617009\pi$
$858$	3.67524	+	3.67524i	0.125471	+	0.125471i
$859$	22.6971	+	22.6971i	0.774415	+	0.774415i	0.978875	−	0.204460i	$-0.0655437\pi$
$859$	22.6971	+	22.6971i	0.774415	+	0.774415i	−0.204460	+	0.978875i	$0.565544\pi$
$860$	0.279196	+	0.674040i	0.00952052	+	0.0229846i
$861$	10.5750	−	4.38030i	0.360394	−	0.149280i
$862$	34.0031	−	82.0908i	1.15815	−	2.79602i
$863$			22.1675i			0.754590i	0.926093	+	0.377295i	$0.123146\pi$
$863$			22.1675i			0.754590i	−0.926093	+	0.377295i	$0.876854\pi$
$864$	11.8965	+	4.92771i	0.404728	+	0.167644i
$865$	−1.18454	+	1.18454i	−0.0402755	+	0.0402755i
$866$	−76.4478			−2.59780
$867$	1.31813	−	6.64979i	0.0447662	−	0.225839i
$868$	−99.9054			−3.39101
$869$	−6.86821	+	6.86821i	−0.232988	+	0.232988i
$870$	0.368354	+	0.152577i	0.0124884	+	0.00517285i
$871$			39.0705i			1.32385i
$872$	−23.6922	+	57.1981i	−0.802321	+	1.93697i
$873$	−6.81199	+	2.82162i	−0.230551	+	0.0954973i
$874$	0.429658	+	1.03729i	0.0145334	+	0.0350868i
$875$	3.44279	+	3.44279i	0.116388	+	0.116388i
$876$	16.8035	+	16.8035i	0.567737	+	0.567737i
$877$	−6.86729	−	16.5791i	−0.231892	−	0.559837i	0.764508	−	0.644614i	$-0.222982\pi$
$877$	−6.86729	−	16.5791i	−0.231892	−	0.559837i	−0.996400	+	0.0847775i	$0.972982\pi$
$878$	−5.20254	+	2.15496i	−0.175577	+	0.0727264i
$879$	−3.57392	+	8.62821i	−0.120545	+	0.291022i
$880$		−	1.97882i		−	0.0667059i
$881$	−37.3539	−	15.4725i	−1.25849	−	0.521282i	−0.349042	−	0.937107i	$-0.613493\pi$
$881$	−37.3539	−	15.4725i	−1.25849	−	0.521282i	−0.909445	+	0.415825i	$0.863493\pi$
$882$	−10.2448	+	10.2448i	−0.344962	+	0.344962i
$883$	−34.6000			−1.16438			−0.582192	−	0.813052i	$-0.697805\pi$
$883$	−34.6000			−1.16438			−0.582192	+	0.813052i	$0.697805\pi$
$884$	−42.9534	−	35.2271i	−1.44468	−	1.18482i
$885$	−0.0643219			−0.00216216
$886$	20.0219	−	20.0219i	0.672648	−	0.672648i
$887$	17.9351	+	7.42897i	0.602202	+	0.249440i	0.662891	−	0.748716i	$-0.269329\pi$
$887$	17.9351	+	7.42897i	0.602202	+	0.249440i	−0.0606880	+	0.998157i	$0.519329\pi$
$888$		−	20.9099i		−	0.701690i
$889$	−10.2805	+	24.8194i	−0.344798	+	0.832417i
$890$	−5.06952	+	2.09986i	−0.169931	+	0.0703875i
$891$	−4.95078	−	11.9522i	−0.165857	−	0.400415i
$892$	−52.6006	−	52.6006i	−1.76120	−	1.76120i
$893$	1.05335	+	1.05335i	0.0352489	+	0.0352489i
$894$	−5.96534	−	14.4016i	−0.199511	−	0.481662i
$895$	0.363898	−	0.150732i	0.0121638	−	0.00503840i
$896$	−13.2843	+	32.0712i	−0.443798	+	1.07142i
$897$			3.33051i			0.111203i
$898$	63.2344	+	26.1925i	2.11016	+	0.874056i
$899$	12.6710	−	12.6710i	0.422603	−	0.422603i
$900$	−63.3597			−2.11199
$901$	−47.7635	+	4.72031i	−1.59123	+	0.157256i
$902$	41.4986			1.38175
$903$	−0.846058	+	0.846058i	−0.0281550	+	0.0281550i
$904$	30.7551	+	12.7392i	1.02290	+	0.423699i
$905$		−	2.86349i		−	0.0951857i
$906$	2.76941	−	6.68596i	0.0920076	−	0.222126i
$907$	−36.7515	+	15.2230i	−1.22031	+	0.505471i	−0.897510	−	0.440995i	$-0.854626\pi$
$907$	−36.7515	+	15.2230i	−1.22031	+	0.505471i	−0.322805	+	0.946466i	$0.604626\pi$
$908$	−10.0845	−	24.3461i	−0.334666	−	0.807954i
$909$	4.97423	+	4.97423i	0.164985	+	0.164985i
$910$	2.64106	+	2.64106i	0.0875502	+	0.0875502i
$911$	3.87078	+	9.34489i	0.128245	+	0.309610i	0.974940	−	0.222468i	$-0.0714113\pi$
$911$	3.87078	+	9.34489i	0.128245	+	0.309610i	−0.846695	+	0.532078i	$0.821411\pi$
$912$	0.417218	−	0.172818i	0.0138155	−	0.00572256i
$913$	−1.14229	+	2.75774i	−0.0378043	+	0.0912678i
$914$			46.5651i			1.54024i
$915$	−0.529769	−	0.219438i	−0.0175136	−	0.00725438i
$916$	27.2130	−	27.2130i	0.899144	−	0.899144i
$917$	−21.5602			−0.711981
$918$	−11.5351	−	21.5634i	−0.380714	−	0.711698i
$919$	−53.6406			−1.76944			−0.884721	−	0.466121i	$-0.845651\pi$
$919$	−53.6406			−1.76944			−0.884721	+	0.466121i	$0.845651\pi$
$920$	2.02290	−	2.02290i	0.0666931	−	0.0666931i
$921$	−2.81063	−	1.16420i	−0.0926133	−	0.0383617i
$922$			74.3909i			2.44993i
$923$	−3.73313	+	9.01257i	−0.122877	+	0.296652i
$924$	8.44440	−	3.49779i	0.277800	−	0.115069i
$925$	15.7769	+	38.0889i	0.518743	+	1.25236i
$926$	−19.6792	−	19.6792i	−0.646697	−	0.646697i
$927$	17.2370	+	17.2370i	0.566136	+	0.566136i
$928$	5.10550	+	12.3258i	0.167596	+	0.404613i
$929$	−13.4925	+	5.58879i	−0.442676	+	0.183362i	−0.592877	−	0.805293i	$-0.702008\pi$
$929$	−13.4925	+	5.58879i	−0.442676	+	0.183362i	0.150201	+	0.988655i	$0.452008\pi$
$930$	−0.469466	+	1.13339i	−0.0153944	+	0.0371654i
$931$			0.317679i			0.0104115i
$932$	−14.1293	−	5.85256i	−0.462822	−	0.191707i
$933$	0.0477183	−	0.0477183i	0.00156223	−	0.00156223i
$934$	97.4696			3.18930
$935$	−0.724694	+	0.883641i	−0.0237000	+	0.0288981i
$936$	−53.9961			−1.76492
$937$	41.5825	−	41.5825i	1.35844	−	1.35844i	0.482601	−	0.875840i	$-0.339692\pi$
$937$	41.5825	−	41.5825i	1.35844	−	1.35844i	0.875840	−	0.482601i	$-0.160308\pi$
$938$	91.7889	+	38.0202i	2.99701	+	1.24140i
$939$			3.34679i			0.109218i
$940$	2.62201	−	6.33009i	0.0855205	−	0.206465i
$941$	35.8086	−	14.8324i	1.16733	−	0.483522i	0.287018	−	0.957925i	$-0.407336\pi$
$941$	35.8086	−	14.8324i	1.16733	−	0.483522i	0.880308	+	0.474403i	$0.157336\pi$
$942$	6.96176	+	16.8072i	0.226827	+	0.547608i
$943$	18.8031	+	18.8031i	0.612312	+	0.612312i
$944$	−5.00477	−	5.00477i	−0.162891	−	0.162891i
$945$	0.435141	+	1.05052i	0.0141551	+	0.0341735i
$946$	−4.00774	+	1.66006i	−0.130303	+	0.0539733i
$947$	15.6701	−	37.8309i	0.509209	−	1.22934i	−0.435131	−	0.900367i	$-0.643298\pi$
$947$	15.6701	−	37.8309i	0.509209	−	1.22934i	0.944340	−	0.328971i	$-0.106702\pi$
$948$			10.1955i			0.331135i
$949$	−36.8902	−	15.2804i	−1.19751	−	0.496023i
$950$	−1.42049	+	1.42049i	−0.0460869	+	0.0460869i
$951$	0.557827			0.0180888
$952$	−69.0033	+	36.9125i	−2.23641	+	1.19634i
$953$	24.2658			0.786045			0.393022	−	0.919529i	$-0.371429\pi$
$953$	24.2658			0.786045			0.393022	+	0.919529i	$0.371429\pi$
$954$	−59.5473	+	59.5473i	−1.92791	+	1.92791i
$955$	1.82594	+	0.756331i	0.0590862	+	0.0244743i
$956$		−	108.723i		−	3.51637i
$957$	−0.627381	+	1.51463i	−0.0202803	+	0.0489611i
$958$	56.4934	−	23.4004i	1.82522	−	0.756031i
$959$	15.4033	+	37.1869i	0.497399	+	1.20083i
$960$	0.00923960	+	0.00923960i	0.000298207	+	0.000298207i
$961$	17.0673	+	17.0673i	0.550559	+	0.550559i
$962$	24.2702	+	58.5935i	0.782504	+	1.88913i
$963$	44.2078	−	18.3115i	1.42458	−	0.590079i
$964$	−18.9907	+	45.8475i	−0.611648	+	1.47665i
$965$		−	1.86079i		−	0.0599009i
$966$	7.82441	+	3.24098i	0.251746	+	0.104277i
$967$	2.07750	−	2.07750i	0.0668078	−	0.0668078i	−0.672913	−	0.739721i	$-0.734957\pi$
$967$	2.07750	−	2.07750i	0.0668078	−	0.0668078i	0.739721	+	0.672913i	$0.234957\pi$
$968$	−51.2244			−1.64641
$969$	−0.249599	−	0.0756246i	−0.00801828	−	0.00242941i
$970$	1.07524			0.0345240
$971$	−16.7943	+	16.7943i	−0.538956	+	0.538956i	−0.923222	−	0.384266i	$-0.874454\pi$
$971$	−16.7943	+	16.7943i	−0.538956	+	0.538956i	0.384266	+	0.923222i	$0.374454\pi$
$972$	−41.4946	−	17.1876i	−1.33094	−	0.551294i
$973$		−	34.0653i		−	1.09208i
$974$	9.03757	−	21.8186i	0.289582	−	0.699114i
$975$	−5.50550	+	2.28045i	−0.176317	+	0.0730329i
$976$	−24.1464	−	58.2945i	−0.772907	−	1.86596i
$977$	−13.8043	−	13.8043i	−0.441640	−	0.441640i	0.450923	−	0.892563i	$-0.351095\pi$
$977$	−13.8043	−	13.8043i	−0.441640	−	0.441640i	−0.892563	+	0.450923i	$0.851095\pi$
$978$	1.61769	+	1.61769i	0.0517280	+	0.0517280i
$979$	−8.63440	−	20.8453i	−0.275957	−	0.666218i
$980$	1.34993	−	0.559160i	0.0431220	−	0.0178617i
$981$	10.6407	−	25.6888i	0.339730	−	0.820182i
$982$		−	87.0670i		−	2.77842i
$983$	22.5989	+	9.36077i	0.720793	+	0.298562i	0.712762	−	0.701406i	$-0.247444\pi$
$983$	22.5989	+	9.36077i	0.720793	+	0.298562i	0.00803047	+	0.999968i	$0.497444\pi$
$984$	17.0635	−	17.0635i	0.543963	−	0.543963i
$985$	−3.84523			−0.122519
$986$	7.34693	−	24.2486i	0.233974	−	0.772232i
$987$	11.2367			0.357668
$988$	−1.51118	+	1.51118i	−0.0480772	+	0.0480772i
$989$	−2.56809	−	1.06374i	−0.0816604	−	0.0338249i
$990$			2.00513i			0.0637272i
$991$	−12.2726	+	29.6287i	−0.389852	+	0.941186i	0.600118	+	0.799911i	$0.295120\pi$
$991$	−12.2726	+	29.6287i	−0.389852	+	0.941186i	−0.989970	+	0.141275i	$0.954880\pi$
$992$	−37.9252	+	15.7092i	−1.20413	+	0.498766i
$993$	4.88942	+	11.8041i	0.155161	+	0.374592i
$994$	17.5406	+	17.5406i	0.556353	+	0.556353i
$995$	0.00896324	+	0.00896324i	0.000284154	+	0.000284154i
$996$	1.19902	+	2.89470i	0.0379925	+	0.0917220i
$997$	−16.3269	+	6.76281i	−0.517077	+	0.214180i	−0.625932	−	0.779877i	$-0.715281\pi$
$997$	−16.3269	+	6.76281i	−0.517077	+	0.214180i	0.108855	+	0.994058i	$0.465281\pi$
$998$	−34.8193	+	84.0612i	−1.10219	+	2.66091i
$999$			19.3078i			0.610870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.689.2	yes	128
17.2	even	8	inner	731.2.m.c.87.2	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.2	✓	128	17.2	even	8	inner
731.2.m.c.689.2	yes	128	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80058 + 1.80058i) q^{2} +(-0.368420 - 0.152604i) q^{3} -4.48416i q^{4} +(0.0622629 - 0.150316i) q^{5} +(0.938144 - 0.388592i) q^{6} +(1.14823 + 2.77206i) q^{7} +(4.47291 + 4.47291i) q^{8} +(-2.00888 - 2.00888i) q^{9} +O(q^{10})\)	\(q+(-1.80058 + 1.80058i) q^{2} +(-0.368420 - 0.152604i) q^{3} -4.48416i q^{4} +(0.0622629 - 0.150316i) q^{5} +(0.938144 - 0.388592i) q^{6} +(1.14823 + 2.77206i) q^{7} +(4.47291 + 4.47291i) q^{8} +(-2.00888 - 2.00888i) q^{9} +(0.158546 + 0.382765i) q^{10} +(-1.57389 + 0.651925i) q^{11} +(-0.684302 + 1.65205i) q^{12} -3.00462i q^{13} +(-7.05878 - 2.92384i) q^{14} +(-0.0458778 + 0.0458778i) q^{15} -7.13934 q^{16} +(3.18807 + 2.61461i) q^{17} +7.23427 q^{18} +(0.112162 - 0.112162i) q^{19} +(-0.674040 - 0.279196i) q^{20} -1.19651i q^{21} +(1.66006 - 4.00774i) q^{22} +(2.56809 - 1.06374i) q^{23} +(-0.965323 - 2.33050i) q^{24} +(3.51682 + 3.51682i) q^{25} +(5.41004 + 5.41004i) q^{26} +(0.891359 + 2.15193i) q^{27} +(12.4304 - 5.14882i) q^{28} +(-0.923519 + 2.22957i) q^{29} -0.165213i q^{30} +(-6.86019 - 2.84159i) q^{31} +(3.90910 - 3.90910i) q^{32} +0.679337 q^{33} +(-10.4482 + 1.03256i) q^{34} +0.488177 q^{35} +(-9.00811 + 9.00811i) q^{36} +(7.65833 + 3.17218i) q^{37} +0.403914i q^{38} +(-0.458518 + 1.10696i) q^{39} +(0.950847 - 0.393854i) q^{40} +(3.66091 + 8.83822i) q^{41} +(2.15440 + 2.15440i) q^{42} +(-0.707107 - 0.707107i) q^{43} +(2.92333 + 7.05755i) q^{44} +(-0.427044 + 0.176888i) q^{45} +(-2.70870 + 6.53938i) q^{46} +9.39127i q^{47} +(2.63027 + 1.08949i) q^{48} +(-1.41616 + 1.41616i) q^{49} -12.6646 q^{50} +(-0.775547 - 1.44979i) q^{51} -13.4732 q^{52} +(-8.23127 + 8.23127i) q^{53} +(-5.47968 - 2.26976i) q^{54} +0.277171i q^{55} +(-7.26328 + 17.5351i) q^{56} +(-0.0584394 + 0.0242064i) q^{57} +(-2.35165 - 5.67739i) q^{58} +(0.701014 + 0.701014i) q^{59} +(0.205723 + 0.205723i) q^{60} +(3.38216 + 8.16525i) q^{61} +(17.4688 - 7.23581i) q^{62} +(3.26208 - 7.87537i) q^{63} -0.201396i q^{64} +(-0.451642 - 0.187076i) q^{65} +(-1.22320 + 1.22320i) q^{66} -13.0035 q^{67} +(11.7243 - 14.2958i) q^{68} -1.10846 q^{69} +(-0.879000 + 0.879000i) q^{70} +(-2.99958 - 1.24246i) q^{71} -17.9710i q^{72} +(5.08565 - 12.2778i) q^{73} +(-19.5012 + 8.07765i) q^{74} +(-0.758983 - 1.83235i) q^{75} +(-0.502954 - 0.502954i) q^{76} +(-3.61435 - 3.61435i) q^{77} +(-1.16757 - 2.81876i) q^{78} +(5.26764 - 2.18193i) q^{79} +(-0.444516 + 1.07316i) q^{80} +7.59410i q^{81} +(-22.5056 - 9.32214i) q^{82} +(1.23898 - 1.23898i) q^{83} -5.36532 q^{84} +(0.591516 - 0.316425i) q^{85} +2.54640 q^{86} +(0.680485 - 0.680485i) q^{87} +(-9.95586 - 4.12385i) q^{88} +13.2445i q^{89} +(0.450427 - 1.08743i) q^{90} +(8.32898 - 3.44998i) q^{91} +(-4.76996 - 11.5157i) q^{92} +(2.09379 + 2.09379i) q^{93} +(-16.9097 - 16.9097i) q^{94} +(-0.00987625 - 0.0238434i) q^{95} +(-2.03674 + 0.843644i) q^{96} +(0.993185 - 2.39776i) q^{97} -5.09979i q^{98} +(4.47138 + 1.85210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

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