LMFDB - Embedded newform 231.2.u.a.20.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(20,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6]))

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

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

chi := DirichletCharacter("231.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.20
Character	$\chi$	$=$	231.20
Dual form			231.2.u.a.104.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17237 + 0.380926i) q^{2} +(1.64037 - 0.556045i) q^{3} +(-0.388687 - 0.282397i) q^{4} +(0.966595 + 2.97487i) q^{5} +(2.13493 - 0.0270304i) q^{6} +(0.481870 + 2.60150i) q^{7} +(-1.79724 - 2.47369i) q^{8} +(2.38163 - 1.82424i) q^{9} +O(q^{10})$	\(q+(1.17237 + 0.380926i) q^{2} +(1.64037 - 0.556045i) q^{3} +(-0.388687 - 0.282397i) q^{4} +(0.966595 + 2.97487i) q^{5} +(2.13493 - 0.0270304i) q^{6} +(0.481870 + 2.60150i) q^{7} +(-1.79724 - 2.47369i) q^{8} +(2.38163 - 1.82424i) q^{9} +3.85585i q^{10} +(-2.35123 - 2.33917i) q^{11} +(-0.794615 - 0.247109i) q^{12} +(-1.83070 - 0.594831i) q^{13} +(-0.426050 + 3.23348i) q^{14} +(3.23974 + 4.34242i) q^{15} +(-0.867809 - 2.67084i) q^{16} +(-1.78185 - 5.48398i) q^{17} +(3.48705 - 1.23146i) q^{18} +(3.31616 + 4.56430i) q^{19} +(0.464394 - 1.42926i) q^{20} +(2.23700 + 3.99948i) q^{21} +(-1.86545 - 3.63802i) q^{22} -5.79074i q^{23} +(-4.32362 - 3.05842i) q^{24} +(-3.87048 + 2.81207i) q^{25} +(-1.91967 - 1.39472i) q^{26} +(2.89239 - 4.31672i) q^{27} +(0.547360 - 1.14725i) q^{28} +(-2.41572 + 3.32496i) q^{29} +(2.14403 + 6.32503i) q^{30} +(-3.87003 - 1.25745i) q^{31} +2.65351i q^{32} +(-5.15757 - 2.52972i) q^{33} -7.10801i q^{34} +(-7.27336 + 3.94810i) q^{35} +(-1.44087 + 0.0364915i) q^{36} +(7.22445 + 5.24887i) q^{37} +(2.14910 + 6.61426i) q^{38} +(-3.33378 + 0.0422090i) q^{39} +(5.62171 - 7.73762i) q^{40} +(-2.54229 + 1.84708i) q^{41} +(1.09908 + 5.54100i) q^{42} -6.95014 q^{43} +(0.253313 + 1.57319i) q^{44} +(7.72895 + 5.32174i) q^{45} +(2.20584 - 6.78889i) q^{46} +(-4.70535 + 3.41864i) q^{47} +(-2.90864 - 3.89863i) q^{48} +(-6.53560 + 2.50717i) q^{49} +(-5.60883 + 1.82242i) q^{50} +(-5.97224 - 8.00497i) q^{51} +(0.543591 + 0.748188i) q^{52} +(5.95831 + 1.93597i) q^{53} +(5.03531 - 3.95900i) q^{54} +(4.68606 - 9.25563i) q^{55} +(5.56927 - 5.86752i) q^{56} +(7.97768 + 5.64321i) q^{57} +(-4.09869 + 2.97787i) q^{58} +(-1.83841 - 1.33568i) q^{59} +(-0.0329532 - 2.60273i) q^{60} +(5.18467 - 1.68460i) q^{61} +(-4.05811 - 2.94839i) q^{62} +(5.89339 + 5.31676i) q^{63} +(-2.74641 + 8.45258i) q^{64} -6.02107i q^{65} +(-5.08294 - 4.93043i) q^{66} +3.70934 q^{67} +(-0.856079 + 2.63474i) q^{68} +(-3.21991 - 9.49896i) q^{69} +(-10.0310 + 1.85802i) q^{70} +(12.6990 - 4.12615i) q^{71} +(-8.79296 - 2.61281i) q^{72} +(-4.72522 + 6.50371i) q^{73} +(6.47030 + 8.90560i) q^{74} +(-4.78538 + 6.76499i) q^{75} -2.71056i q^{76} +(4.95238 - 7.24389i) q^{77} +(-3.92451 - 1.22044i) q^{78} +(-2.21664 + 6.82211i) q^{79} +(7.10659 - 5.16324i) q^{80} +(2.34431 - 8.68932i) q^{81} +(-3.68410 + 1.19704i) q^{82} +(-1.93982 - 5.97015i) q^{83} +(0.259953 - 2.18627i) q^{84} +(14.5918 - 10.6016i) q^{85} +(-8.14814 - 2.64749i) q^{86} +(-2.11386 + 6.79741i) q^{87} +(-1.56067 + 10.0203i) q^{88} -2.91353 q^{89} +(7.03400 + 9.18321i) q^{90} +(0.665293 - 5.04920i) q^{91} +(-1.63529 + 2.25078i) q^{92} +(-7.04747 + 0.0892281i) q^{93} +(-6.81866 + 2.21552i) q^{94} +(-10.3728 + 14.2770i) q^{95} +(1.47547 + 4.35274i) q^{96} +(10.0014 + 3.24966i) q^{97} +(-8.61719 + 0.449747i) q^{98} +(-9.86696 - 1.28185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.17237	+	0.380926i	0.828991	+	0.269356i	0.692620	−	0.721302i	$-0.256456\pi$
$2$	1.17237	+	0.380926i	0.828991	+	0.269356i	0.136371	+	0.990658i	$0.456456\pi$
$3$	1.64037	−	0.556045i	0.947068	−	0.321033i
$3$	1.64037	−	0.556045i	0.947068	−	0.321033i
$4$	−0.388687	−	0.282397i	−0.194343	−	0.141199i
$5$	0.966595	+	2.97487i	0.432274	+	1.33040i	0.895854	+	0.444348i	$0.146565\pi$
$5$	0.966595	+	2.97487i	0.432274	+	1.33040i	−0.463580	+	0.886055i	$0.653435\pi$
$6$	2.13493	−	0.0270304i	0.871583	−	0.0110351i
$7$	0.481870	+	2.60150i	0.182130	+	0.983275i
$7$	0.481870	+	2.60150i	0.182130	+	0.983275i
$8$	−1.79724	−	2.47369i	−0.635421	−	0.874582i
$9$	2.38163	−	1.82424i	0.793876	−	0.608079i
$10$			3.85585i			1.21933i
$11$	−2.35123	−	2.33917i	−0.708921	−	0.705288i
$11$	−2.35123	−	2.33917i	−0.708921	−	0.705288i
$12$	−0.794615	−	0.247109i	−0.229386	−	0.0713342i
$13$	−1.83070	−	0.594831i	−0.507745	−	0.164976i	0.0439312	−	0.999035i	$-0.486012\pi$
$13$	−1.83070	−	0.594831i	−0.507745	−	0.164976i	−0.551677	+	0.834058i	$0.686012\pi$
$14$	−0.426050	+	3.23348i	−0.113867	+	0.864183i
$15$	3.23974	+	4.34242i	0.836496	+	1.12121i
$16$	−0.867809	−	2.67084i	−0.216952	−	0.667710i
$17$	−1.78185	−	5.48398i	−0.432163	−	1.33006i	−0.895966	−	0.444122i	$-0.853516\pi$
$17$	−1.78185	−	5.48398i	−0.432163	−	1.33006i	0.463803	−	0.885938i	$-0.346484\pi$
$18$	3.48705	−	1.23146i	0.821906	−	0.290258i
$19$	3.31616	+	4.56430i	0.760779	+	1.04712i	0.997149	+	0.0754593i	$0.0240423\pi$
$19$	3.31616	+	4.56430i	0.760779	+	1.04712i	−0.236370	+	0.971663i	$0.575958\pi$
$20$	0.464394	−	1.42926i	0.103842	−	0.319592i
$21$	2.23700	+	3.99948i	0.488152	+	0.872758i
$22$	−1.86545	−	3.63802i	−0.397716	−	0.775629i
$23$		−	5.79074i		−	1.20745i	−0.797192	−	0.603726i	$-0.793682\pi$
$23$		−	5.79074i		−	1.20745i	0.797192	−	0.603726i	$-0.206318\pi$
$24$	−4.32362	−	3.05842i	−0.882556	−	0.624298i
$25$	−3.87048	+	2.81207i	−0.774096	+	0.562414i
$26$	−1.91967	−	1.39472i	−0.376479	−	0.273528i
$27$	2.89239	−	4.31672i	0.556641	−	0.830753i
$28$	0.547360	−	1.14725i	0.103441	−	0.216809i
$29$	−2.41572	+	3.32496i	−0.448589	+	0.617429i	−0.972094	−	0.234593i	$-0.924624\pi$
$29$	−2.41572	+	3.32496i	−0.448589	+	0.617429i	0.523505	+	0.852023i	$0.324624\pi$
$30$	2.14403	+	6.32503i	0.391444	+	1.15479i
$31$	−3.87003	−	1.25745i	−0.695077	−	0.225844i	−0.0598928	−	0.998205i	$-0.519076\pi$
$31$	−3.87003	−	1.25745i	−0.695077	−	0.225844i	−0.635184	+	0.772361i	$0.719076\pi$
$32$			2.65351i			0.469079i
$33$	−5.15757	−	2.52972i	−0.897817	−	0.440369i
$34$		−	7.10801i		−	1.21901i
$35$	−7.27336	+	3.94810i	−1.22942	+	0.667350i
$36$	−1.44087	+	0.0364915i	−0.240144	+	0.00608192i
$37$	7.22445	+	5.24887i	1.18769	+	0.862909i	0.993018	−	0.117959i	$-0.0376351\pi$
$37$	7.22445	+	5.24887i	1.18769	+	0.862909i	0.194674	+	0.980868i	$0.437635\pi$
$38$	2.14910	+	6.61426i	0.348631	+	1.07298i
$39$	−3.33378	+	0.0422090i	−0.533832	+	0.00675886i
$40$	5.62171	−	7.73762i	0.888871	−	1.22343i
$41$	−2.54229	+	1.84708i	−0.397038	+	0.288465i	−0.768334	−	0.640050i	$-0.778914\pi$
$41$	−2.54229	+	1.84708i	−0.397038	+	0.288465i	0.371295	+	0.928515i	$0.378914\pi$
$42$	1.09908	+	5.54100i	0.169592	+	0.854995i
$43$	−6.95014			−1.05989			−0.529943	−	0.848033i	$-0.677787\pi$
$43$	−6.95014			−1.05989			−0.529943	+	0.848033i	$0.677787\pi$
$44$	0.253313	+	1.57319i	0.0381884	+	0.237167i
$45$	7.72895	+	5.32174i	1.15216	+	0.793319i
$46$	2.20584	−	6.78889i	0.325234	−	1.00097i
$47$	−4.70535	+	3.41864i	−0.686346	+	0.498659i	−0.875457	−	0.483296i	$-0.839439\pi$
$47$	−4.70535	+	3.41864i	−0.686346	+	0.498659i	0.189111	+	0.981956i	$0.439439\pi$
$48$	−2.90864	−	3.89863i	−0.419825	−	0.562718i
$49$	−6.53560	+	2.50717i	−0.933658	+	0.358167i
$50$	−5.60883	+	1.82242i	−0.793208	+	0.257729i
$51$	−5.97224	−	8.00497i	−0.836280	−	1.12092i
$52$	0.543591	+	0.748188i	0.0753824	+	0.103755i
$53$	5.95831	+	1.93597i	0.818436	+	0.265926i	0.688167	−	0.725553i	$-0.258416\pi$
$53$	5.95831	+	1.93597i	0.818436	+	0.265926i	0.130270	+	0.991479i	$0.458416\pi$
$54$	5.03531	−	3.95900i	0.685219	−	0.538752i
$55$	4.68606	−	9.25563i	0.631869	−	1.24803i
$56$	5.56927	−	5.86752i	0.744225	−	0.784080i
$57$	7.97768	+	5.64321i	1.05667	+	0.747461i
$58$	−4.09869	+	2.97787i	−0.538184	+	0.391014i
$59$	−1.83841	−	1.33568i	−0.239341	−	0.173891i	0.461649	−	0.887063i	$-0.347258\pi$
$59$	−1.83841	−	1.33568i	−0.239341	−	0.173891i	−0.700989	+	0.713172i	$0.747258\pi$
$60$	−0.0329532	−	2.60273i	−0.00425424	−	0.336012i
$61$	5.18467	−	1.68460i	0.663829	−	0.215691i	0.0423269	−	0.999104i	$-0.486523\pi$
$61$	5.18467	−	1.68460i	0.663829	−	0.215691i	0.621502	+	0.783413i	$0.286523\pi$
$62$	−4.05811	−	2.94839i	−0.515380	−	0.374446i
$63$	5.89339	+	5.31676i	0.742497	+	0.669849i
$64$	−2.74641	+	8.45258i	−0.343301	+	1.05657i
$65$		−	6.02107i		−	0.746821i
$66$	−5.08294	−	4.93043i	−0.625667	−	0.606894i
$67$	3.70934			0.453168			0.226584	−	0.973992i	$-0.427244\pi$
$67$	3.70934			0.453168			0.226584	+	0.973992i	$0.427244\pi$
$68$	−0.856079	+	2.63474i	−0.103815	+	0.319509i
$69$	−3.21991	−	9.49896i	−0.387632	−	1.14354i
$70$	−10.0310	+	1.85802i	−1.19893	+	0.222076i
$71$	12.6990	−	4.12615i	1.50709	−	0.489684i	0.565015	−	0.825080i	$-0.308870\pi$
$71$	12.6990	−	4.12615i	1.50709	−	0.489684i	0.942077	+	0.335396i	$0.108870\pi$
$72$	−8.79296	−	2.61281i	−1.03626	−	0.307923i
$73$	−4.72522	+	6.50371i	−0.553045	+	0.761201i	−0.990421	−	0.138077i	$-0.955908\pi$
$73$	−4.72522	+	6.50371i	−0.553045	+	0.761201i	0.437376	+	0.899279i	$0.355908\pi$
$74$	6.47030	+	8.90560i	0.752157	+	1.03526i
$75$	−4.78538	+	6.76499i	−0.552569	+	0.781154i
$76$		−	2.71056i		−	0.310922i
$77$	4.95238	−	7.24389i	0.564376	−	0.825518i
$78$	−3.92451	−	1.22044i	−0.444363	−	0.138188i
$79$	−2.21664	+	6.82211i	−0.249391	+	0.767548i	0.745492	+	0.666515i	$0.232215\pi$
$79$	−2.21664	+	6.82211i	−0.249391	+	0.767548i	−0.994883	+	0.101033i	$0.967785\pi$
$80$	7.10659	−	5.16324i	0.794541	−	0.577268i
$81$	2.34431	−	8.68932i	0.260479	−	0.965480i
$82$	−3.68410	+	1.19704i	−0.406841	+	0.132191i
$83$	−1.93982	−	5.97015i	−0.212923	−	0.655309i	−0.999295	−	0.0375553i	$-0.988043\pi$
$83$	−1.93982	−	5.97015i	−0.212923	−	0.655309i	0.786372	−	0.617753i	$-0.211957\pi$
$84$	0.259953	−	2.18627i	0.0283632	−	0.238541i
$85$	14.5918	−	10.6016i	1.58270	−	1.14990i
$86$	−8.14814	−	2.64749i	−0.878637	−	0.285486i
$87$	−2.11386	+	6.79741i	−0.226629	+	0.728759i
$88$	−1.56067	+	10.0203i	−0.166368	+	1.06816i
$89$	−2.91353			−0.308833			−0.154417	−	0.988006i	$-0.549350\pi$
$89$	−2.91353			−0.308833			−0.154417	+	0.988006i	$0.549350\pi$
$90$	7.03400	+	9.18321i	0.741449	+	0.967996i
$91$	0.665293	−	5.04920i	0.0697417	−	0.529300i
$92$	−1.63529	+	2.25078i	−0.170491	+	0.234660i
$93$	−7.04747	+	0.0892281i	−0.730789	+	0.00925252i
$94$	−6.81866	+	2.21552i	−0.703291	+	0.228513i
$95$	−10.3728	+	14.2770i	−1.06423	+	1.46479i
$96$	1.47547	+	4.35274i	0.150590	+	0.444250i
$97$	10.0014	+	3.24966i	1.01549	+	0.329953i	0.769039	−	0.639202i	$-0.220735\pi$
$97$	10.0014	+	3.24966i	1.01549	+	0.329953i	0.246453	+	0.969155i	$0.420735\pi$
$98$	−8.61719	+	0.449747i	−0.870468	+	0.0454313i
$99$	−9.86696	−	1.28185i	−0.991667	−	0.128830i
$100$	2.29852			0.229852
$101$	−0.316750	+	0.974858i	−0.0315179	+	0.0970020i	−0.965578	−	0.260114i	$-0.916240\pi$
$101$	−0.316750	+	0.974858i	−0.0315179	+	0.0970020i	0.934060	+	0.357116i	$0.116240\pi$
$102$	−3.95237	−	11.6598i	−0.391343	−	1.15449i
$103$	0.633933	−	0.872534i	0.0624633	−	0.0859734i	−0.776643	−	0.629942i	$-0.783079\pi$
$103$	0.633933	−	0.872534i	0.0624633	−	0.0859734i	0.839106	+	0.543968i	$0.183079\pi$
$104$	1.81879	+	5.59765i	0.178347	+	0.548894i
$105$	−9.73568	+	10.5207i	−0.950105	+	1.02671i
$106$	6.24788	+	4.53935i	0.606848	+	0.440901i
$107$	−1.19592	−	1.64605i	−0.115614	−	0.159129i	0.747288	−	0.664500i	$-0.231356\pi$
$107$	−1.19592	−	1.64605i	−0.115614	−	0.159129i	−0.862902	+	0.505371i	$0.831356\pi$
$108$	−2.34326	+	0.861046i	−0.225481	+	0.0828542i
$109$	9.24914			0.885907			0.442954	−	0.896545i	$-0.353931\pi$
$109$	9.24914			0.885907			0.442954	+	0.896545i	$0.353931\pi$
$110$	9.01952	−	9.06599i	0.859977	−	0.864408i
$111$	14.7694	+	4.59297i	1.40185	+	0.435946i
$112$	6.53002	−	3.54460i	0.617029	−	0.334933i
$113$	2.13147	+	2.93372i	0.200512	+	0.275981i	0.897418	−	0.441182i	$-0.145441\pi$
$113$	2.13147	+	2.93372i	0.200512	+	0.275981i	−0.696906	+	0.717162i	$0.745441\pi$
$114$	7.20315	+	9.65484i	0.674637	+	0.904259i
$115$	17.2267	−	5.59730i	1.60640	−	0.521951i
$116$	1.87792	−	0.610173i	0.174360	−	0.0566531i
$117$	−5.44517	+	1.92297i	−0.503406	+	0.177779i
$118$	−1.64650	−	2.26621i	−0.151573	−	0.208622i
$119$	13.4080	−	7.27805i	1.22910	−	0.667178i
$120$	4.91922	−	15.8185i	0.449062	−	1.44402i
$121$	0.0565275	+	10.9999i	0.00513886	+	0.999987i
$122$	6.72006			0.608406
$123$	−3.14323	+	4.44352i	−0.283416	+	0.400659i
$124$	1.14913	+	1.58164i	0.103195	+	0.142035i
$125$	0.546159	+	0.396808i	0.0488500	+	0.0354916i
$126$	4.88394	+	8.47816i	0.435096	+	0.755295i
$127$	−4.96592	−	15.2835i	−0.440654	−	1.35619i	−0.887180	−	0.461424i	$-0.847339\pi$
$127$	−4.96592	−	15.2835i	−0.440654	−	1.35619i	0.446526	−	0.894771i	$-0.352661\pi$
$128$	−3.32023	+	4.56990i	−0.293470	+	0.403926i
$129$	−11.4008	+	3.86459i	−1.00378	+	0.340258i
$130$	2.29358	−	7.05892i	0.201160	−	0.619108i
$131$	4.69154			0.409902			0.204951	−	0.978772i	$-0.434296\pi$
$131$	4.69154			0.409902			0.204951	+	0.978772i	$0.434296\pi$
$132$	1.29029	+	2.43975i	0.112305	+	0.212353i
$133$	−10.2761	+	10.8264i	−0.891048	+	0.938767i
$134$	4.34872	+	1.41298i	0.375672	+	0.122063i
$135$	15.6375	+	4.43199i	1.34586	+	0.381445i
$136$	−10.3632	+	14.2638i	−0.888641	+	1.22311i
$137$	3.12324	−	1.01480i	0.266836	−	0.0867004i	−0.172543	−	0.985002i	$-0.555198\pi$
$137$	3.12324	−	1.01480i	0.266836	−	0.0867004i	0.439379	+	0.898302i	$0.355198\pi$
$138$	−0.156526	−	12.3628i	−0.0133244	−	1.05240i
$139$	1.74369	−	2.39999i	0.147898	−	0.203564i	−0.728640	−	0.684897i	$-0.759847\pi$
$139$	1.74369	−	2.39999i	0.147898	−	0.203564i	0.876538	+	0.481333i	$0.159847\pi$
$140$	3.94199	+	0.519405i	0.333159	+	0.0438977i
$141$	−5.81760	+	8.22421i	−0.489930	+	0.692604i
$142$	16.4597			1.38127
$143$	2.91298	+	5.68091i	0.243596	+	0.475062i
$144$	−6.93905	−	4.77786i	−0.578254	−	0.398155i
$145$	−12.2264	−	3.97258i	−1.01534	−	0.329905i
$146$	−8.01714	+	5.82479i	−0.663503	+	0.482063i
$147$	−9.32671	+	7.74677i	−0.769254	+	0.638943i
$148$	−1.32578	−	4.08033i	−0.108978	−	0.335401i
$149$	−3.73287	+	1.21288i	−0.305809	+	0.0993633i	−0.457901	−	0.889003i	$-0.651399\pi$
$149$	−3.73287	+	1.21288i	−0.305809	+	0.0993633i	0.152093	+	0.988366i	$0.451399\pi$
$150$	−8.18720	+	6.10820i	−0.668482	+	0.498732i
$151$	−12.1170	+	8.80351i	−0.986067	+	0.716419i	−0.959056	−	0.283216i	$-0.908599\pi$
$151$	−12.1170	+	8.80351i	−0.986067	+	0.716419i	−0.0270105	+	0.999635i	$0.508599\pi$
$152$	5.33073	−	16.4063i	0.432379	−	1.33073i
$153$	−14.2478	−	9.81028i	−1.15187	−	0.793114i
$154$	8.56541	−	6.60603i	0.690220	−	0.532329i
$155$		−	12.7283i		−	1.02236i
$156$	1.30772	+	0.925045i	0.104701	+	0.0740629i
$157$	7.06712	+	9.72705i	0.564017	+	0.776303i	0.991830	−	0.127564i	$-0.0407158\pi$
$157$	7.06712	+	9.72705i	0.564017	+	0.776303i	−0.427813	+	0.903867i	$0.640716\pi$
$158$	−5.19744	+	7.15367i	−0.413486	+	0.569115i
$159$	10.8503	−	0.137376i	0.860486	−	0.0108946i
$160$	−7.89387	+	2.56487i	−0.624065	+	0.202771i
$161$	15.0646	−	2.79038i	1.18726	−	0.219913i
$162$	6.05839	−	9.29409i	0.475992	−	0.730213i
$163$	3.84778	−	11.8422i	0.301381	−	0.927556i	−0.679622	−	0.733563i	$-0.737856\pi$
$163$	3.84778	−	11.8422i	0.301381	−	0.927556i	0.981003	−	0.193993i	$-0.0621440\pi$
$164$	1.50976			0.117893
$165$	2.54033	−	17.7883i	0.197765	−	1.38482i
$166$		−	7.73815i		−	0.600597i
$167$	0.988524	−	3.04236i	0.0764943	−	0.235425i	−0.905497	−	0.424354i	$-0.860501\pi$
$167$	0.988524	−	3.04236i	0.0764943	−	0.235425i	0.981991	+	0.188928i	$0.0605014\pi$
$168$	5.87306	−	12.7217i	0.453116	−	0.981498i
$169$	−7.51957	−	5.46329i	−0.578429	−	0.420253i
$170$	21.1454	−	6.87057i	1.62178	−	0.526948i
$171$	16.2242	+	4.82100i	1.24070	+	0.368671i
$172$	2.70143	+	1.96270i	0.205982	+	0.149655i
$173$	−10.9084	+	7.92540i	−0.829349	+	0.602557i	−0.919375	−	0.393382i	$-0.871305\pi$
$173$	−10.9084	+	7.92540i	−0.829349	+	0.602557i	0.0900261	+	0.995939i	$0.471305\pi$
$174$	−5.06753	+	7.16386i	−0.384169	+	0.543091i
$175$	−9.18066	−	8.71400i	−0.693993	−	0.658717i
$176$	−4.20715	+	8.30971i	−0.317126	+	0.626368i
$177$	−3.75837	−	1.16878i	−0.282497	−	0.0878506i
$178$	−3.41573	−	1.10984i	−0.256020	−	0.0831860i
$179$	−4.81451	−	6.62661i	−0.359854	−	0.495296i	0.590254	−	0.807217i	$-0.299027\pi$
$179$	−4.81451	−	6.62661i	−0.359854	−	0.495296i	−0.950108	+	0.311921i	$0.899027\pi$
$180$	−1.50129	−	4.25112i	−0.111900	−	0.316860i
$181$	3.94617	−	1.28219i	0.293317	−	0.0953043i	−0.158662	−	0.987333i	$-0.550718\pi$
$181$	3.94617	−	1.28219i	0.293317	−	0.0953043i	0.451979	+	0.892029i	$0.350718\pi$
$182$	2.70334	−	5.66611i	0.200385	−	0.420000i
$183$	7.56806	−	5.64628i	0.559447	−	0.417385i
$184$	−14.3245	+	10.4074i	−1.05602	+	0.767241i
$185$	−8.63161	+	26.5654i	−0.634608	+	1.95312i
$186$	−8.29624	−	2.57996i	−0.608310	−	0.189172i
$187$	−8.63844	+	17.0621i	−0.631706	+	1.24771i
$188$	2.79432			0.203797
$189$	12.6237	+	5.44447i	0.918239	+	0.396027i
$190$	−17.5993	+	12.7866i	−1.27679	+	0.927639i
$191$	−4.45001	+	6.12491i	−0.321991	+	0.443183i	−0.939074	−	0.343715i	$-0.888315\pi$
$191$	−4.45001	+	6.12491i	−0.321991	+	0.443183i	0.617082	+	0.786899i	$0.288315\pi$
$192$	0.194884	+	15.3925i	0.0140646	+	1.11086i
$193$	4.62029	+	14.2198i	0.332576	+	1.02356i	0.967904	+	0.251321i	$0.0808651\pi$
$193$	4.62029	+	14.2198i	0.332576	+	1.02356i	−0.635328	+	0.772243i	$0.719135\pi$
$194$	10.4875	+	7.61962i	0.752959	+	0.547057i
$195$	−3.34798	−	9.87678i	−0.239754	−	0.707291i
$196$	3.24832	+	0.871134i	0.232023	+	0.0622239i
$197$			18.2597i			1.30095i	0.759526	+	0.650476i	$0.225431\pi$
$197$			18.2597i			1.30095i	−0.759526	+	0.650476i	$0.774569\pi$
$198$	−11.0794	−	5.26138i	−0.787382	−	0.373910i
$199$		−	25.7556i		−	1.82577i	−0.408220	−	0.912883i	$-0.633851\pi$
$199$		−	25.7556i		−	1.82577i	0.408220	−	0.912883i	$-0.366149\pi$
$200$	13.9124	+	4.52040i	0.983753	+	0.319641i
$201$	6.08469	−	2.06256i	0.429181	−	0.145482i
$202$	−0.742698	+	1.02224i	−0.0522560	+	0.0719243i
$203$	−9.81394	−	4.68231i	−0.688804	−	0.328634i
$204$	0.0607471	+	4.79797i	0.00425315	+	0.335925i
$205$	−7.95219	−	5.77760i	−0.555405	−	0.403525i
$206$	1.07558	−	0.781452i	0.0749389	−	0.0544463i
$207$	−10.5637	−	13.7914i	−0.734227	−	0.958568i
$208$			5.40571i			0.374819i
$209$	2.87966	−	18.4888i	0.199190	−	1.27890i
$210$	−15.4214	+	8.62553i	−1.06418	+	0.595218i
$211$	1.10921	−	3.41380i	0.0763613	−	0.235016i	−0.905589	−	0.424157i	$-0.860570\pi$
$211$	1.10921	−	3.41380i	0.0763613	−	0.235016i	0.981950	+	0.189141i	$0.0605704\pi$
$212$	−1.76920	−	2.43510i	−0.121509	−	0.167243i
$213$	18.5367	−	13.8296i	1.27011	−	0.947590i
$214$	−0.775043	−	2.38534i	−0.0529808	−	0.163058i
$215$	−6.71797	−	20.6758i	−0.458162	−	1.41008i
$216$	−15.8766	+	0.603298i	−1.08026	+	0.0410492i
$217$	1.40640	−	10.6738i	0.0954728	−	0.724585i
$218$	10.8434	+	3.52324i	0.734409	+	0.238624i
$219$	−4.13476	+	13.2959i	−0.279401	+	0.898455i
$220$	−4.43518	+	2.27421i	−0.299019	+	0.153327i
$221$			11.0994i			0.746629i
$222$	15.5656	+	11.0107i	1.04469	+	0.738990i
$223$	7.35053	+	10.1171i	0.492228	+	0.677493i	0.980797	−	0.195032i	$-0.0624810\pi$
$223$	7.35053	+	10.1171i	0.492228	+	0.677493i	−0.488569	+	0.872525i	$0.662481\pi$
$224$	−6.90311	+	1.27865i	−0.461234	+	0.0854332i
$225$	−4.08816	+	13.7580i	−0.272544	+	0.917199i
$226$	1.38134	+	4.25133i	0.0918855	+	0.282795i
$227$	−18.8958	−	13.7286i	−1.25416	−	0.911202i	−0.255706	−	0.966755i	$-0.582308\pi$
$227$	−18.8958	−	13.7286i	−1.25416	−	0.911202i	−0.998456	+	0.0555530i	$0.982308\pi$
$228$	−1.50719	−	4.44632i	−0.0998161	−	0.294464i
$229$	−22.9123	−	7.44464i	−1.51408	−	0.491956i	−0.569996	−	0.821648i	$-0.693055\pi$
$229$	−22.9123	−	7.44464i	−1.51408	−	0.491956i	−0.944089	+	0.329692i	$0.893055\pi$
$230$	22.3283			1.47228
$231$	4.09580	−	14.6364i	0.269484	−	0.963005i
$232$	12.5666			0.825035
$233$	−3.07237	−	0.998274i	−0.201278	−	0.0653991i	0.206643	−	0.978416i	$-0.433746\pi$
$233$	−3.07237	−	0.998274i	−0.201278	−	0.0653991i	−0.407921	+	0.913017i	$0.633746\pi$
$234$	−7.11626	+	0.180227i	−0.465205	+	0.0117818i
$235$	−14.7182	−	10.6934i	−0.960108	−	0.697559i
$236$	0.337372	+	1.03832i	0.0219610	+	0.0675891i
$237$	0.157292	+	12.4233i	0.0102172	+	0.806983i
$238$	18.4915	−	3.42513i	1.19862	−	0.222018i
$239$	−1.62258	−	2.23329i	−0.104956	−	0.144460i	0.753308	−	0.657668i	$-0.228457\pi$
$239$	−1.62258	−	2.23329i	−0.104956	−	0.144460i	−0.858264	+	0.513208i	$0.828457\pi$
$240$	8.78645	−	12.4212i	0.567163	−	0.801786i
$241$		−	15.9400i		−	1.02678i	−0.858154	−	0.513392i	$-0.828389\pi$
$241$		−	15.9400i		−	1.02678i	0.858154	−	0.513392i	$-0.171611\pi$
$242$	−4.12386	+	12.9174i	−0.265092	+	0.830364i
$243$	−0.986116	−	15.5572i	−0.0632594	−	0.997997i
$244$	−2.49094	−	0.809354i	−0.159466	−	0.0518136i
$245$	−13.7758	−	17.0192i	−0.880103	−	1.08732i
$246$	−5.37768	+	4.01211i	−0.342869	+	0.255803i
$247$	−3.35591	−	10.3284i	−0.213531	−	0.657182i
$248$	3.84483	+	11.8332i	0.244147	+	0.751408i
$249$	−6.50169	−	8.71462i	−0.412028	−	0.552267i
$250$	0.489147	+	0.673252i	0.0309363	+	0.0425802i
$251$	−2.17901	+	6.70629i	−0.137538	+	0.423297i	−0.995976	−	0.0896192i	$-0.971435\pi$
$251$	−2.17901	+	6.70629i	−0.137538	+	0.423297i	0.858438	+	0.512917i	$0.171435\pi$
$252$	−0.789243	−	3.73083i	−0.0497176	−	0.235020i
$253$	−13.5456	+	13.6153i	−0.851601	+	0.855989i
$254$		−	19.8096i		−	1.24297i
$255$	18.0410	−	25.5042i	1.12977	−	1.59714i
$256$	8.74706	−	6.35511i	0.546691	−	0.397194i
$257$	9.08063	+	6.59746i	0.566434	+	0.411538i	0.833808	−	0.552054i	$-0.186156\pi$
$257$	9.08063	+	6.59746i	0.566434	+	0.411538i	−0.267374	+	0.963593i	$0.586156\pi$
$258$	−14.8381	+	0.187865i	−0.923779	+	0.0116960i
$259$	−10.1737	+	21.3237i	−0.632162	+	1.32499i
$260$	−1.70033	+	2.34031i	−0.105450	+	0.145140i
$261$	0.312161	+	12.3257i	0.0193223	+	0.762940i
$262$	5.50023	+	1.78713i	0.339805	+	0.110409i
$263$			8.45856i			0.521577i	0.965396	+	0.260789i	$0.0839825\pi$
$263$			8.45856i			0.521577i	−0.965396	+	0.260789i	$0.916017\pi$
$264$	3.01164	+	17.3048i	0.185353	+	1.06503i
$265$			19.5965i			1.20380i
$266$	−16.1714	+	8.77811i	−0.991533	+	0.538220i
$267$	−4.77927	+	1.62005i	−0.292486	+	0.0991456i
$268$	−1.44177	−	1.04751i	−0.0880701	−	0.0639867i
$269$	−6.36071	−	19.5763i	−0.387819	−	1.19359i	−0.934414	−	0.356188i	$-0.884076\pi$
$269$	−6.36071	−	19.5763i	−0.387819	−	1.19359i	0.546595	−	0.837397i	$-0.315924\pi$
$270$	16.6446	+	11.1526i	1.01296	+	0.678729i
$271$	12.3298	−	16.9706i	0.748984	−	1.03089i	−0.249067	−	0.968486i	$-0.580124\pi$
$271$	12.3298	−	16.9706i	0.748984	−	1.03089i	0.998051	−	0.0624022i	$-0.0198762\pi$
$272$	−13.1005	+	9.51809i	−0.794336	+	0.577119i
$273$	−1.71626	−	8.65249i	−0.103872	−	0.523673i
$274$	4.04816			0.244558
$275$	15.6783	+	2.44192i	0.945436	+	0.147253i
$276$	−1.43094	+	4.60141i	−0.0861327	+	0.276972i
$277$	5.06840	−	15.5989i	0.304531	−	0.937249i	−0.675321	−	0.737524i	$-0.735995\pi$
$277$	5.06840	−	15.5989i	0.304531	−	0.937249i	0.979852	−	0.199725i	$-0.0640049\pi$
$278$	2.95847	−	2.14945i	0.177437	−	0.128916i
$279$	−11.5108	+	4.06508i	−0.689137	+	0.243370i
$280$	22.8384	+	10.8964i	1.36485	+	0.651182i
$281$	−14.2425	+	4.62767i	−0.849636	+	0.276063i	−0.701293	−	0.712873i	$-0.747394\pi$
$281$	−14.2425	+	4.62767i	−0.849636	+	0.276063i	−0.148342	+	0.988936i	$0.547394\pi$
$282$	−9.95320	+	7.42575i	−0.592704	+	0.442197i
$283$	5.76795	+	7.93890i	0.342869	+	0.471918i	0.945277	−	0.326270i	$-0.105792\pi$
$283$	5.76795	+	7.93890i	0.342869	+	0.471918i	−0.602408	+	0.798188i	$0.705792\pi$
$284$	−6.10114	−	1.98238i	−0.362036	−	0.117633i
$285$	−9.07665	+	29.1873i	−0.537654	+	1.72891i
$286$	1.25108	+	7.76977i	0.0739781	+	0.459436i
$287$	−6.03023	−	5.72371i	−0.355953	−	0.337860i
$288$	4.84064	+	6.31968i	0.285238	+	0.372391i
$289$	−13.1457	+	9.55094i	−0.773279	+	0.561820i
$290$	−12.8206	−	9.31468i	−0.752849	−	0.546977i
$291$	18.2130	−	0.230595i	1.06767	−	0.0135177i
$292$	3.67326	−	1.19351i	0.214961	−	0.0698451i
$293$	12.6768	+	9.21022i	0.740585	+	0.538067i	0.892894	−	0.450266i	$-0.148671\pi$
$293$	12.6768	+	9.21022i	0.740585	+	0.538067i	−0.152309	+	0.988333i	$0.548671\pi$
$294$	−13.8853	+	5.52930i	−0.809808	+	0.322475i
$295$	2.19649	−	6.76010i	0.127885	−	0.393588i
$296$		−	27.3045i		−	1.58704i
$297$	−16.8982	+	3.38377i	−0.980535	+	0.196346i
$298$	−4.83833			−0.280277
$299$	−3.44451	+	10.6011i	−0.199201	+	0.613079i
$300$	3.77043	−	1.27808i	0.217686	−	0.0737901i
$301$	−3.34906	−	18.0808i	−0.193037	−	1.04216i
$302$	−17.5591	+	5.70529i	−1.01041	+	0.328303i
$303$	0.0224765	+	1.77525i	0.00129124	+	0.101986i
$304$	9.31273	−	12.8179i	0.534122	−	0.735156i
$305$	10.0229	+	13.7954i	0.573912	+	0.789922i
$306$	−12.9667	−	16.9286i	−0.741257	−	0.967746i
$307$		−	4.77487i		−	0.272516i	−0.990673	−	0.136258i	$-0.956492\pi$
$307$		−	4.77487i		−	0.272516i	0.990673	−	0.136258i	$-0.0435077\pi$
$308$	−3.97058	+	1.41707i	−0.226245	+	0.0807448i
$309$	0.554717	−	1.78377i	0.0315568	−	0.101475i
$310$	4.84854	−	14.9223i	0.275378	−	0.847527i
$311$	7.45330	−	5.41514i	0.422638	−	0.307064i	−0.356060	−	0.934463i	$-0.615880\pi$
$311$	7.45330	−	5.41514i	0.422638	−	0.307064i	0.778698	+	0.627399i	$0.215880\pi$
$312$	6.09602	+	8.17089i	0.345119	+	0.462585i
$313$	−25.7541	+	8.36800i	−1.45571	+	0.472987i	−0.926755	−	0.375666i	$-0.877414\pi$
$313$	−25.7541	+	8.36800i	−1.45571	+	0.472987i	−0.528950	+	0.848653i	$0.677414\pi$
$314$	4.57999	+	14.0958i	0.258464	+	0.795470i
$315$	−10.1202	+	22.6712i	−0.570207	+	1.27738i
$316$	2.78812	−	2.02569i	0.156844	−	0.113954i
$317$	−0.772203	−	0.250904i	−0.0433712	−	0.0140922i	0.287251	−	0.957855i	$-0.407259\pi$
$317$	−0.772203	−	0.250904i	−0.0433712	−	0.0140922i	−0.330622	+	0.943763i	$0.607259\pi$
$318$	12.7729	+	3.97211i	0.716270	+	0.222745i
$319$	13.4576	−	2.16693i	0.753479	−	0.121325i
$320$	−27.8000			−1.55407
$321$	−2.87703	−	2.03514i	−0.160580	−	0.113590i
$322$	18.7242	+	2.46714i	1.04346	+	0.137489i
$323$	19.1216	−	26.3187i	1.06396	−	1.46441i
$324$	−3.36504	+	2.71539i	−0.186947	+	0.150855i
$325$	8.75840	−	2.84578i	0.485829	−	0.157855i
$326$	9.02204	−	12.4178i	0.499685	−	0.687757i
$327$	15.1720	−	5.14294i	0.839014	−	0.284405i
$328$	9.13820	+	2.96918i	0.504573	+	0.163946i
$329$	−11.1609	−	10.5936i	−0.615323	−	0.584046i
$330$	9.75425	−	19.8868i	0.536954	−	1.09473i
$331$	22.3929			1.23083			0.615413	−	0.788205i	$-0.288989\pi$
$331$	22.3929			1.23083			0.615413	+	0.788205i	$0.288989\pi$
$332$	−0.931972	+	2.86832i	−0.0511486	+	0.157419i
$333$	26.7811	−	0.678261i	1.46760	−	0.0371685i
$334$	2.31783	−	3.19022i	0.126826	−	0.174561i
$335$	3.58543	+	11.0348i	0.195893	+	0.602896i
$336$	8.74070	−	9.44544i	0.476844	−	0.515291i
$337$	19.5755	+	14.2224i	1.06634	+	0.774744i	0.975251	−	0.221099i	$-0.0709643\pi$
$337$	19.5755	+	14.2224i	1.06634	+	0.774744i	0.0910919	+	0.995842i	$0.470964\pi$
$338$	−6.73462	−	9.26940i	−0.366315	−	0.504189i
$339$	5.12768	+	3.62719i	0.278497	+	0.197002i
$340$	−8.66550			−0.469953
$341$	6.15792	+	12.0092i	0.333470	+	0.650335i
$342$	17.1844	+	11.8322i	0.929224	+	0.639814i
$343$	−9.67171	−	15.7942i	−0.522223	−	0.852809i
$344$	12.4911	+	17.1925i	0.673474	+	0.926958i
$345$	25.1458	−	18.7605i	1.35381	−	1.01003i
$346$	−15.8077	+	5.13622i	−0.849825	+	0.276125i
$347$	20.4624	−	6.64864i	1.09848	−	0.356918i	0.296962	−	0.954889i	$-0.404026\pi$
$347$	20.4624	−	6.64864i	1.09848	−	0.356918i	0.801517	+	0.597972i	$0.204026\pi$
$348$	2.74120	−	2.04512i	0.146944	−	0.109630i
$349$	1.69693	+	2.33563i	0.0908348	+	0.125023i	0.852016	−	0.523516i	$-0.175380\pi$
$349$	1.69693	+	2.33563i	0.0908348	+	0.125023i	−0.761181	+	0.648540i	$0.775380\pi$
$350$	−7.44374	−	13.7132i	−0.397885	−	0.733001i
$351$	−7.86283	+	6.18214i	−0.419687	+	0.329978i
$352$	6.20703	−	6.23901i	0.330836	−	0.332540i
$353$	33.3905			1.77720			0.888598	−	0.458687i	$-0.151680\pi$
$353$	33.3905			1.77720			0.888598	+	0.458687i	$0.151680\pi$
$354$	−3.96099	−	2.80190i	−0.210524	−	0.148919i
$355$	24.5496	+	33.7896i	1.30295	+	1.79336i
$356$	1.13245	+	0.822773i	0.0600197	+	0.0436069i
$357$	17.9471	−	19.3941i	0.949860	−	1.02645i
$358$	−3.12014	−	9.60282i	−0.164905	−	0.507525i
$359$	3.09333	−	4.25760i	0.163260	−	0.224708i	−0.719548	−	0.694443i	$-0.755651\pi$
$359$	3.09333	−	4.25760i	0.163260	−	0.224708i	0.882807	+	0.469736i	$0.155651\pi$
$360$	−0.726440	−	28.6835i	−0.0382868	−	1.51175i
$361$	−3.96461	+	12.2018i	−0.208664	+	0.642201i
$362$	5.11479			0.268828
$363$	6.20914	+	18.0124i	0.325895	+	0.945406i
$364$	−1.68447	+	1.77468i	−0.0882903	+	0.0930185i
$365$	−23.9151	−	7.77048i	−1.25177	−	0.406725i
$366$	11.0234	−	3.73665i	0.576201	−	0.195318i
$367$	7.14408	−	9.83298i	0.372918	−	0.513277i	−0.580773	−	0.814065i	$-0.697250\pi$
$367$	7.14408	−	9.83298i	0.372918	−	0.513277i	0.953691	+	0.300788i	$0.0972497\pi$
$368$	−15.4661	+	5.02526i	−0.806229	+	0.261960i
$369$	−2.68527	+	9.03679i	−0.139789	+	0.470437i
$370$	−20.2389	+	27.8564i	−1.05217	+	1.44819i
$371$	−2.16530	+	16.4334i	−0.112417	+	0.853181i
$372$	2.76446	+	1.95551i	0.143330	+	0.101388i
$373$	1.61637			0.0836924			0.0418462	−	0.999124i	$-0.486676\pi$
$373$	1.61637			0.0836924			0.0418462	+	0.999124i	$0.486676\pi$
$374$	−16.6269	+	16.7125i	−0.859755	+	0.864185i
$375$	1.11655	+	0.347223i	0.0576582	+	0.0179305i
$376$	16.9133	+	5.49546i	0.872237	+	0.283407i
$377$	6.40026	−	4.65006i	0.329630	−	0.239490i
$378$	12.7257	+	11.1916i	0.654540	+	0.575635i
$379$	2.96126	+	9.11383i	0.152110	+	0.468146i	0.997857	−	0.0654384i	$-0.0208446\pi$
$379$	2.96126	+	9.11383i	0.152110	+	0.468146i	−0.845747	+	0.533585i	$0.820845\pi$
$380$	8.06356	−	2.62001i	0.413652	−	0.134404i
$381$	−16.6443	−	22.3094i	−0.852712	−	1.14294i
$382$	−7.55020	+	5.48554i	−0.386302	+	0.280665i
$383$	−3.63546	+	11.1888i	−0.185763	+	0.571721i	−0.999961	−	0.00886739i	$-0.997177\pi$
$383$	−3.63546	+	11.1888i	−0.185763	+	0.571721i	0.814197	+	0.580588i	$0.197177\pi$
$384$	−2.90533	+	9.34253i	−0.148262	+	0.476759i
$385$	26.3366	+	7.73078i	1.34224	+	0.393997i
$386$			18.4309i			0.938107i
$387$	−16.5527	+	12.6787i	−0.841419	+	0.644495i
$388$	−2.96973	−	4.08748i	−0.150765	−	0.207510i
$389$	−11.4618	+	15.7758i	−0.581134	+	0.799862i	−0.993819	−	0.111011i	$-0.964591\pi$
$389$	−11.4618	+	15.7758i	−0.581134	+	0.799862i	0.412685	+	0.910874i	$0.364591\pi$
$390$	−0.162752	−	12.8546i	−0.00824126	−	0.650917i
$391$	−31.7563	+	10.3182i	−1.60599	+	0.521816i
$392$	17.9480	+	11.6611i	0.906512	+	0.588973i
$393$	7.69587	−	2.60871i	0.388205	−	0.131592i
$394$	−6.95561	+	21.4072i	−0.350419	+	1.07848i
$395$	−22.4375			−1.12895
$396$	3.47316	+	3.28464i	0.174533	+	0.165059i
$397$		−	10.3361i		−	0.518756i	−0.965776	−	0.259378i	$-0.916482\pi$
$397$		−	10.3361i		−	0.518756i	0.965776	−	0.259378i	$-0.0835175\pi$
$398$	9.81099	−	30.1951i	0.491780	−	1.51354i
$399$	−10.8366	+	23.4732i	−0.542509	+	1.17513i
$400$	10.8694	+	7.89710i	0.543471	+	0.394855i
$401$	−33.9387	+	11.0274i	−1.69482	+	0.550680i	−0.987692	−	0.156409i	$-0.950008\pi$
$401$	−33.9387	+	11.0274i	−1.69482	+	0.550680i	−0.707125	+	0.707088i	$0.750008\pi$
$402$	7.91919	−	0.100265i	0.394973	−	0.00500076i
$403$	6.33690	+	4.60402i	0.315663	+	0.229343i
$404$	0.398414	−	0.289465i	0.0198218	−	0.0144014i
$405$	28.1156	−	1.42503i	1.39708	−	0.0708103i
$406$	−9.72196	−	9.22779i	−0.482493	−	0.457967i
$407$	−4.70829	−	29.2405i	−0.233381	−	1.44940i
$408$	−9.06826	+	29.1603i	−0.448946	+	1.44365i
$409$	−10.0010	−	3.24953i	−0.494519	−	0.160679i	0.0511311	−	0.998692i	$-0.483717\pi$
$409$	−10.0010	−	3.24953i	−0.494519	−	0.160679i	−0.545650	+	0.838013i	$0.683717\pi$
$410$	−7.12207	−	9.80268i	−0.351734	−	0.484120i
$411$	4.55899	−	3.40131i	0.224879	−	0.167774i
$412$	−0.492803	+	0.160121i	−0.0242786	+	0.00788861i
$413$	2.58891	−	5.42625i	0.127392	−	0.267008i
$414$	−7.13106	−	20.1926i	−0.350472	−	0.992412i
$415$	15.8854	−	11.5414i	0.779784	−	0.566546i
$416$	1.57839	−	4.85779i	0.0773871	−	0.238173i
$417$	1.52580	−	4.90644i	0.0747188	−	0.240269i
$418$	10.4189	−	20.5788i	0.509604	−	1.00654i
$419$	−33.4067			−1.63203			−0.816013	−	0.578034i	$-0.803820\pi$
$419$	−33.4067			−1.63203			−0.816013	+	0.578034i	$0.803820\pi$
$420$	6.75513	−	1.33991i	0.329617	−	0.0653807i
$421$	9.76280	−	7.09309i	0.475810	−	0.345696i	−0.323891	−	0.946094i	$-0.604991\pi$
$421$	9.76280	−	7.09309i	0.475810	−	0.345696i	0.799701	+	0.600398i	$0.204991\pi$
$422$	2.60081	−	3.57971i	0.126606	−	0.174258i
$423$	−4.96999	+	16.7256i	−0.241649	+	0.813226i
$424$	−5.91952	−	18.2184i	−0.287477	−	0.884764i
$425$	22.3179	+	16.2149i	1.08258	+	0.786540i
$426$	27.0000	−	9.15232i	1.30815	−	0.443431i
$427$	6.88082	+	12.6762i	0.332986	+	0.613442i
$428$			0.977522i			0.0472503i
$429$	7.93721	+	7.69905i	0.383212	+	0.371714i
$430$		−	26.7987i		−	1.29235i
$431$	−25.7987	−	8.38249i	−1.24268	−	0.403771i	−0.387386	−	0.921917i	$-0.626622\pi$
$431$	−25.7987	−	8.38249i	−1.24268	−	0.403771i	−0.855292	+	0.518147i	$0.826622\pi$
$432$	−14.0393	−	3.97904i	−0.675467	−	0.191442i
$433$	−14.1845	+	19.5233i	−0.681664	+	0.938230i	−0.999952	−	0.00976391i	$-0.996892\pi$
$433$	−14.1845	+	19.5233i	−0.681664	+	0.938230i	0.318288	+	0.947994i	$0.396892\pi$
$434$	5.71475	−	11.9779i	0.274317	−	0.574958i
$435$	−22.2647	+	0.281893i	−1.06751	+	0.0135158i
$436$	−3.59502	−	2.61193i	−0.172170	−	0.125089i
$437$	26.4307	−	19.2030i	1.26435	−	0.918605i
$438$	−9.91223	+	14.0127i	−0.473625	+	0.669553i
$439$			26.1523i			1.24818i	0.781353	+	0.624090i	$0.214530\pi$
$439$			26.1523i			1.24818i	−0.781353	+	0.624090i	$0.785470\pi$
$440$	−31.3176	+	5.04274i	−1.49301	+	0.240403i
$441$	−10.9917	+	17.8936i	−0.523415	+	0.852078i
$442$	−4.22807	+	13.0126i	−0.201109	+	0.618949i
$443$	−6.06024	−	8.34121i	−0.287931	−	0.396303i	0.640410	−	0.768033i	$-0.278765\pi$
$443$	−6.06024	−	8.34121i	−0.287931	−	0.396303i	−0.928341	+	0.371731i	$0.878765\pi$
$444$	−4.44362	−	5.95606i	−0.210885	−	0.282662i
$445$	−2.81620	−	8.66738i	−0.133501	−	0.410873i
$446$	4.76366	+	14.6610i	0.225566	+	0.694220i
$447$	−5.44887	+	4.06522i	−0.257723	+	0.192278i
$448$	−23.3128	−	3.07174i	−1.10143	−	0.145126i
$449$	20.3426	+	6.60972i	0.960028	+	0.311932i	0.746784	−	0.665067i	$-0.231597\pi$
$449$	20.3426	+	6.60972i	0.960028	+	0.311932i	0.213244	+	0.976999i	$0.431597\pi$
$450$	−10.0336	+	14.5722i	−0.472989	+	0.686938i
$451$	10.2981	+	1.60395i	0.484920	+	0.0755271i
$452$		−	1.74222i		−	0.0819470i
$453$	−14.9812	+	21.1786i	−0.703878	+	0.995058i
$454$	−16.9233	−	23.2930i	−0.794251	−	1.09319i
$455$	15.6638	−	2.90137i	0.734331	−	0.136018i
$456$	−0.378267	−	29.8765i	−0.0177140	−	1.39910i
$457$	−4.11115	−	12.6528i	−0.192311	−	0.591874i	−0.999997	−	0.00226099i	$-0.999280\pi$
$457$	−4.11115	−	12.6528i	−0.192311	−	0.591874i	0.807686	−	0.589613i	$-0.200720\pi$
$458$	−24.0258	−	17.4558i	−1.12265	−	0.815654i
$459$	−28.8266	−	8.17007i	−1.34551	−	0.381346i
$460$	−8.27646	−	2.68918i	−0.385892	−	0.125384i
$461$	−1.89461			−0.0882406			−0.0441203	−	0.999026i	$-0.514048\pi$
$461$	−1.89461			−0.0882406			−0.0441203	+	0.999026i	$0.514048\pi$
$462$	10.3772	−	15.5991i	0.482791	−	0.725735i
$463$	−5.58207			−0.259421			−0.129710	−	0.991552i	$-0.541405\pi$
$463$	−5.58207			−0.259421			−0.129710	+	0.991552i	$0.541405\pi$
$464$	10.9768	+	3.56659i	0.509586	+	0.165575i
$465$	−7.07749	−	20.8791i	−0.328211	−	0.968245i
$466$	−3.22169	−	2.34069i	−0.149242	−	0.108430i
$467$	−9.05072	−	27.8552i	−0.418817	−	1.28899i	−0.908792	−	0.417250i	$-0.862994\pi$
$467$	−9.05072	−	27.8552i	−0.418817	−	1.28899i	0.489974	−	0.871737i	$-0.337006\pi$
$468$	2.65950	+	0.790267i	0.122936	+	0.0365301i
$469$	1.78742	+	9.64985i	0.0825353	+	0.445588i
$470$	−13.1818	−	18.1431i	−0.608029	−	0.836881i
$471$	17.0014	+	12.0263i	0.783382	+	0.554144i
$472$			6.94820i			0.319817i
$473$	16.3414	+	16.2576i	0.751376	+	0.747525i
$474$	−4.54797	+	14.6247i	−0.208895	+	0.671733i
$475$	−25.6703	−	8.34077i	−1.17783	−	0.382701i
$476$	−7.26679	−	0.957488i	−0.333073	−	0.0438864i
$477$	17.7221	−	6.25861i	0.811441	−	0.286562i
$478$	−1.05155	−	3.23633i	−0.0480967	−	0.148026i
$479$	4.45113	+	13.6992i	0.203377	+	0.625931i	0.999776	+	0.0211595i	$0.00673576\pi$
$479$	4.45113	+	13.6992i	0.203377	+	0.625931i	−0.796399	+	0.604772i	$0.793264\pi$
$480$	−11.5227	+	8.59668i	−0.525936	+	0.392383i
$481$	−10.1036	−	13.9064i	−0.460686	−	0.634079i
$482$	6.07195	−	18.6875i	0.276570	−	0.851194i
$483$	23.1600	−	12.9539i	1.05381	−	0.589421i
$484$	3.08436	−	4.29146i	0.140198	−	0.195066i
$485$			32.8941i			1.49364i
$486$	4.77007	−	18.6145i	0.216375	−	0.844370i
$487$	−21.8845	+	15.9000i	−0.991681	+	0.720498i	−0.960289	−	0.279009i	$-0.909994\pi$
$487$	−21.8845	+	15.9000i	−0.991681	+	0.720498i	−0.0313924	+	0.999507i	$0.509994\pi$
$488$	−13.4853	−	9.79763i	−0.610450	−	0.443518i
$489$	−0.273037	−	21.5652i	−0.0123472	−	0.975212i
$490$	−9.66727	−	25.2003i	−0.436723	−	1.13844i
$491$	−12.5047	+	17.2112i	−0.564328	+	0.776731i	−0.991869	−	0.127265i	$-0.959380\pi$
$491$	−12.5047	+	17.2112i	−0.564328	+	0.776731i	0.427541	+	0.903996i	$0.359380\pi$
$492$	2.47657	−	0.839495i	0.111652	−	0.0378474i
$493$	22.5385	+	7.32319i	1.01508	+	0.329820i
$494$		−	13.3871i		−	0.602314i
$495$	−5.72402	−	30.5920i	−0.257276	−	1.37501i
$496$			11.4274i			0.513108i
$497$	16.8534	+	31.0481i	0.755980	+	1.39270i
$498$	−4.30276	−	12.6934i	−0.192811	−	0.568806i
$499$	−30.9021	−	22.4517i	−1.38337	−	1.00508i	−0.996556	−	0.0829165i	$-0.973577\pi$
$499$	−30.9021	−	22.4517i	−1.38337	−	1.00508i	−0.386811	−	0.922159i	$-0.626423\pi$
$500$	−0.100227	−	0.308468i	−0.00448230	−	0.0137951i
$501$	−0.0701454	−	5.54027i	−0.00313386	−	0.247521i
$502$	−5.10920	+	7.03222i	−0.228035	+	0.313863i
$503$	6.59860	−	4.79417i	0.294217	−	0.213761i	−0.430878	−	0.902410i	$-0.641796\pi$
$503$	6.59860	−	4.79417i	0.294217	−	0.213761i	0.725095	+	0.688649i	$0.241796\pi$
$504$	2.56018	−	24.1339i	0.114039	−	1.07501i
$505$	−3.20625			−0.142676
$506$	−21.0668	+	10.8024i	−0.936535	+	0.480224i
$507$	−15.3727	−	4.78060i	−0.682726	−	0.212314i
$508$	−2.38584	+	7.34287i	−0.105855	+	0.325787i
$509$	−10.4037	+	7.55873i	−0.461136	+	0.335035i	−0.793977	−	0.607948i	$-0.791993\pi$
$509$	−10.4037	+	7.55873i	−0.461136	+	0.335035i	0.332841	+	0.942983i	$0.391993\pi$
$510$	30.8660	−	23.0281i	1.36677	−	1.01970i
$511$	−19.1963	−	9.15872i	−0.849196	−	0.405158i
$512$	23.4201	−	7.60965i	1.03503	−	0.336302i
$513$	29.2944	−	1.11317i	1.29338	−	0.0491475i
$514$	8.13271	+	11.1937i	0.358719	+	0.493734i
$515$	3.20844	+	1.04248i	0.141381	+	0.0459373i
$516$	5.52269	+	1.71744i	0.243123	+	0.0756062i
$517$	19.0601	+	2.96864i	0.838263	+	0.130561i
$518$	−20.0501	+	21.1238i	−0.880950	+	0.928128i
$519$	−13.4869	+	19.0661i	−0.592009	+	0.836911i
$520$	−14.8943	+	10.8213i	−0.653156	+	0.474546i
$521$	7.99606	+	5.80948i	0.350314	+	0.254518i	0.749001	−	0.662569i	$-0.230534\pi$
$521$	7.99606	+	5.80948i	0.350314	+	0.254518i	−0.398687	+	0.917087i	$0.630534\pi$
$522$	−4.32920	+	14.5692i	−0.189484	+	0.637675i
$523$	26.6518	−	8.65971i	1.16540	−	0.378663i	0.338478	−	0.940974i	$-0.390088\pi$
$523$	26.6518	−	8.65971i	1.16540	−	0.378663i	0.826926	+	0.562311i	$0.190088\pi$
$524$	−1.82354	−	1.32488i	−0.0796617	−	0.0578776i
$525$	−19.9051	−	9.18933i	−0.868728	−	0.401055i
$526$	−3.22209	+	9.91656i	−0.140490	+	0.432383i
$527$			23.4637i			1.02210i
$528$	−2.28071	+	15.9704i	−0.0992552	+	0.695021i
$529$	−10.5327			−0.457942
$530$	−7.46482	+	22.9744i	−0.324251	+	0.997942i
$531$	−6.81502	+	0.172598i	−0.295746	+	0.00749010i
$532$	7.05151	−	1.30614i	0.305722	−	0.0566281i
$533$	5.75287	−	1.86922i	0.249184	−	0.0809649i
$534$	−6.22019	+	0.0787539i	−0.269174	+	0.00340801i
$535$	3.74081	−	5.14878i	0.161729	−	0.222601i
$536$	−6.66658	−	9.17576i	−0.287952	−	0.396332i
$537$	−11.5823	−	8.19301i	−0.499812	−	0.353554i
$538$		−	25.3736i		−	1.09393i
$539$	21.2314	+	9.39300i	0.914500	+	0.404585i
$540$	−4.82649	−	6.13863i	−0.207699	−	0.264165i
$541$	1.43316	−	4.41081i	0.0616163	−	0.189635i	−0.915510	−	0.402295i	$-0.868213\pi$
$541$	1.43316	−	4.41081i	0.0616163	−	0.189635i	0.977126	+	0.212660i	$0.0682126\pi$
$542$	20.9197	−	15.1990i	0.898577	−	0.652854i
$543$	5.76023	−	4.29751i	0.247195	−	0.184424i
$544$	14.5518	−	4.72817i	0.623904	−	0.202719i
$545$	8.94017	+	27.5150i	0.382955	+	1.17861i
$546$	1.28387	−	10.7977i	0.0549448	−	0.462099i
$547$	−15.3131	+	11.1256i	−0.654739	+	0.475696i	−0.864882	−	0.501975i	$-0.832607\pi$
$547$	−15.3131	+	11.1256i	−0.654739	+	0.475696i	0.210143	+	0.977671i	$0.432607\pi$
$548$	−1.50054	−	0.487555i	−0.0640998	−	0.0208273i
$549$	9.27484	−	13.4702i	0.395840	−	0.574892i
$550$	17.4506	+	8.83511i	0.744095	+	0.376730i
$551$	−23.1870			−0.987801
$552$	−17.7105	+	25.0370i	−0.753810	+	1.06564i
$553$	−18.8159	−	2.47922i	−0.800132	−	0.105427i
$554$	11.8841	−	16.3570i	0.504906	−	0.694944i
$555$	0.612496	+	48.3766i	0.0259990	+	2.05347i
$556$	−1.35550	+	0.440428i	−0.0574860	+	0.0186783i
$557$	19.7648	−	27.2039i	0.837460	−	1.15266i	−0.149028	−	0.988833i	$-0.547615\pi$
$557$	19.7648	−	27.2039i	0.837460	−	1.15266i	0.986488	−	0.163832i	$-0.0523854\pi$
$558$	−15.0435	+	0.380992i	−0.636841	+	0.0161287i
$559$	12.7236	+	4.13416i	0.538153	+	0.174856i
$560$	16.8566	+	15.9998i	0.712323	+	0.676115i
$561$	−4.68293	+	32.7916i	−0.197714	+	1.38446i
$562$	−18.4603			−0.778700
$563$	14.2357	−	43.8130i	0.599964	−	1.84650i	0.0716850	−	0.997427i	$-0.477162\pi$
$563$	14.2357	−	43.8130i	0.599964	−	1.84650i	0.528279	−	0.849071i	$-0.322838\pi$
$564$	4.58372	−	1.55377i	0.193009	−	0.0654254i
$565$	−6.66717	+	9.17657i	−0.280490	+	0.386061i
$566$	3.73803	+	11.5045i	0.157121	+	0.483570i
$567$	23.7349	+	1.91160i	0.996772	+	0.0802796i
$568$	−33.0300	−	23.9977i	−1.38591	−	1.00692i
$569$	−7.84790	−	10.8017i	−0.329001	−	0.452831i	0.612188	−	0.790712i	$-0.290290\pi$
$569$	−7.84790	−	10.8017i	−0.329001	−	0.452831i	−0.941189	+	0.337882i	$0.890290\pi$
$570$	−21.7594	+	30.7608i	−0.911401	+	1.28843i
$571$	26.4899			1.10857			0.554284	−	0.832328i	$-0.312992\pi$
$571$	26.4899			1.10857			0.554284	+	0.832328i	$0.312992\pi$
$572$	0.472038	−	3.03071i	0.0197369	−	0.126720i
$573$	−3.89394	+	12.5215i	−0.162672	+	0.523095i
$574$	−4.88935	−	9.00737i	−0.204077	−	0.375960i
$575$	16.2840	+	22.4129i	0.679088	+	0.934684i
$576$	8.87860	+	25.1410i	0.369942	+	1.04754i
$577$	−8.97599	+	2.91648i	−0.373675	+	0.121414i	−0.489833	−	0.871816i	$-0.662942\pi$
$577$	−8.97599	+	2.91648i	−0.373675	+	0.121414i	0.116158	+	0.993231i	$0.462942\pi$
$578$	−19.0499	+	6.18968i	−0.792371	+	0.257457i
$579$	15.4858	+	20.7567i	0.643570	+	0.862617i
$580$	3.63037	+	4.99678i	0.150743	+	0.207480i
$581$	14.5966	−	7.92327i	0.605569	−	0.328713i
$582$	21.4402	+	6.66747i	0.888726	+	0.276376i
$583$	−9.48075	−	18.4894i	−0.392653	−	0.765754i
$584$	24.5805			1.01715
$585$	−10.9839	−	14.3399i	−0.454127	−	0.592884i
$586$	11.3535	+	15.6267i	0.469007	+	0.645533i
$587$	34.5165	+	25.0777i	1.42465	+	1.03507i	0.990982	+	0.133995i	$0.0427807\pi$
$587$	34.5165	+	25.0777i	1.42465	+	1.03507i	0.433667	+	0.901073i	$0.357219\pi$
$588$	5.81283	−	0.377228i	0.239717	−	0.0155566i
$589$	−7.09425	−	21.8339i	−0.292314	−	0.899649i
$590$	5.15020	−	7.08864i	0.212030	−	0.291835i
$591$	10.1532	+	29.9527i	0.417648	+	1.23209i
$592$	7.74946	−	23.8504i	0.318501	−	0.980244i
$593$	20.9004			0.858275			0.429137	−	0.903239i	$-0.358818\pi$
$593$	20.9004			0.858275			0.429137	+	0.903239i	$0.358818\pi$
$594$	−21.0999	−	2.46995i	−0.865741	−	0.101343i
$595$	34.6113	+	32.8520i	1.41893	+	1.34680i
$596$	1.79343	+	0.582721i	0.0734618	+	0.0238692i
$597$	−14.3213	−	42.2487i	−0.586131	−	1.72913i
$598$	−8.07649	+	11.1163i	−0.330272	+	0.454581i
$599$	−19.9847	+	6.49343i	−0.816554	+	0.265315i	−0.687371	−	0.726306i	$-0.741235\pi$
$599$	−19.9847	+	6.49343i	−0.816554	+	0.265315i	−0.129183	+	0.991621i	$0.541235\pi$
$600$	25.3350	−	0.320767i	1.03430	−	0.0130952i
$601$	25.0526	−	34.4819i	1.02191	−	1.40655i	0.111062	−	0.993813i	$-0.464575\pi$
$601$	25.0526	−	34.4819i	1.02191	−	1.40655i	0.910853	−	0.412732i	$-0.135425\pi$
$602$	2.96111	−	22.4731i	0.120686	−	0.915936i
$603$	8.83427	−	6.76672i	0.359759	−	0.275562i
$604$	7.19580			0.292793
$605$	−32.6685	+	10.8006i	−1.32816	+	0.439105i
$606$	−0.649890	+	2.08982i	−0.0264000	+	0.0848931i
$607$	2.68800	+	0.873384i	0.109102	+	0.0354495i	0.363059	−	0.931766i	$-0.381732\pi$
$607$	2.68800	+	0.873384i	0.109102	+	0.0354495i	−0.253957	+	0.967216i	$0.581732\pi$
$608$	−12.1114	+	8.79947i	−0.491184	+	0.356866i
$609$	−18.7021	−	2.22373i	−0.757846	−	0.0901100i
$610$	6.49557	+	19.9913i	0.262998	+	0.809425i
$611$	10.6476	−	3.45962i	0.430756	−	0.139961i
$612$	2.76753	+	7.83666i	0.111871	+	0.316778i
$613$	12.6556	−	9.19486i	0.511156	−	0.371377i	−0.302106	−	0.953274i	$-0.597690\pi$
$613$	12.6556	−	9.19486i	0.511156	−	0.371377i	0.813262	+	0.581898i	$0.197690\pi$
$614$	1.81887	−	5.59792i	0.0734038	−	0.225914i
$615$	−16.2571	−	5.05563i	−0.655551	−	0.203863i
$616$	−26.8198	+	0.768373i	−1.08060	+	0.0309586i
$617$			12.1157i			0.487761i	0.969805	+	0.243880i	$0.0784205\pi$
$617$			12.1157i			0.487761i	−0.969805	+	0.243880i	$0.921580\pi$
$618$	1.32982	−	1.87994i	0.0534932	−	0.0756222i
$619$	−20.0531	−	27.6008i	−0.806004	−	1.10937i	−0.991928	−	0.126805i	$-0.959528\pi$
$619$	−20.0531	−	27.6008i	−0.806004	−	1.10937i	0.185924	−	0.982564i	$-0.440472\pi$
$620$	−3.59443	+	4.94731i	−0.144356	+	0.198689i
$621$	−24.9970	−	16.7491i	−1.00309	−	0.672118i
$622$	10.8008	−	3.50939i	0.433073	−	0.140714i
$623$	−1.40394	−	7.57954i	−0.0562477	−	0.303668i
$624$	3.00582	+	8.86737i	0.120329	+	0.354979i
$625$	−8.04450	+	24.7584i	−0.321780	+	0.990337i
$626$	−33.3809			−1.33417
$627$	−5.55688	−	31.9297i	−0.221921	−	1.27515i
$628$		−	5.77651i		−	0.230508i
$629$	15.9118	−	48.9715i	0.634445	−	1.95262i
$630$	−20.5007	+	22.7241i	−0.816766	+	0.905348i
$631$	35.9036	+	26.0855i	1.42930	+	1.03845i	0.990146	+	0.140036i	$0.0447217\pi$
$631$	35.9036	+	26.0855i	1.42930	+	1.03845i	0.439154	+	0.898412i	$0.355278\pi$
$632$	20.8596	−	6.77771i	0.829752	−	0.269603i
$633$	−0.0787093	−	6.21667i	−0.00312841	−	0.247091i
$634$	−0.809732	−	0.588304i	−0.0321586	−	0.0233646i
$635$	40.6666	−	29.5460i	1.61380	−	1.17250i
$636$	−4.25617	−	3.01070i	−0.168768	−	0.119382i
$637$	13.4561	−	0.702297i	0.533149	−	0.0278260i
$638$	16.6027	+	2.58590i	0.657307	+	0.102377i
$639$	22.7172	−	32.9929i	0.898678	−	1.30518i
$640$	−16.8042	−	5.46001i	−0.664244	−	0.215826i
$641$	14.6480	+	20.1612i	0.578561	+	0.796321i	0.993537	−	0.113512i	$-0.0362100\pi$
$641$	14.6480	+	20.1612i	0.578561	+	0.796321i	−0.414976	+	0.909832i	$0.636210\pi$
$642$	−2.59771	−	3.48188i	−0.102523	−	0.137419i
$643$	−11.9536	+	3.88397i	−0.471405	+	0.153169i	−0.535079	−	0.844802i	$-0.679718\pi$
$643$	−11.9536	+	3.88397i	−0.471405	+	0.153169i	0.0636739	+	0.997971i	$0.479718\pi$
$644$	−6.64341	−	3.16962i	−0.261787	−	0.124901i
$645$	−22.5166	−	30.1805i	−0.886591	−	1.18835i
$646$	32.4431	−	23.5713i	1.27646	−	0.927400i
$647$	−6.82359	+	21.0009i	−0.268263	+	0.825629i	0.722661	+	0.691203i	$0.242919\pi$
$647$	−6.82359	+	21.0009i	−0.268263	+	0.825629i	−0.990924	+	0.134426i	$0.957081\pi$
$648$	−25.7080	+	9.81771i	−1.00990	+	0.385676i
$649$	1.19812	+	7.44086i	0.0470304	+	0.292079i
$650$	11.3521			0.445267
$651$	−3.62809	−	18.2910i	−0.142196	−	0.716881i
$652$	−4.83980	+	3.51632i	−0.189541	+	0.137710i
$653$	2.68737	−	3.69885i	0.105165	−	0.144747i	−0.753191	−	0.657802i	$-0.771486\pi$
$653$	2.68737	−	3.69885i	0.105165	−	0.144747i	0.858356	+	0.513055i	$0.171486\pi$
$654$	19.7463	−	0.250008i	0.772141	−	0.00977609i
$655$	4.53482	+	13.9567i	0.177190	+	0.545335i
$656$	7.13947	+	5.18713i	0.278750	+	0.202523i
$657$	0.610595	+	24.1093i	0.0238216	+	0.940595i
$658$	−9.04937	−	16.6712i	−0.352781	−	0.649909i
$659$		−	3.09680i		−	0.120634i	−0.998179	−	0.0603171i	$-0.980789\pi$
$659$		−	3.09680i		−	0.120634i	0.998179	−	0.0603171i	$-0.0192112\pi$
$660$	−6.01077	+	6.19670i	−0.233969	+	0.241206i
$661$			23.9352i			0.930970i	0.885056	+	0.465485i	$0.154120\pi$
$661$			23.9352i			0.930970i	−0.885056	+	0.465485i	$0.845880\pi$
$662$	26.2528	+	8.53004i	1.02034	+	0.331530i
$663$	6.17178	+	18.2072i	0.239692	+	0.707108i
$664$	−11.2820	+	15.5283i	−0.437826	+	0.602615i
$665$	−42.1399	−	20.1053i	−1.63412	−	0.779649i
$666$	31.6558	+	9.40647i	1.22664	+	0.364493i
$667$	19.2540	+	13.9888i	0.745517	+	0.541650i
$668$	−1.24338	+	0.903370i	−0.0481079	+	0.0349524i
$669$	17.6832	+	12.5086i	0.683671	+	0.483611i
$670$			14.3027i			0.552560i
$671$	−16.1309	−	8.16696i	−0.622726	−	0.315282i
$672$	−10.6127	+	5.93590i	−0.409393	+	0.228982i
$673$	1.90522	−	5.86365i	0.0734407	−	0.226027i	−0.907598	−	0.419841i	$-0.862086\pi$
$673$	1.90522	−	5.86365i	0.0734407	−	0.226027i	0.981038	+	0.193814i	$0.0620858\pi$
$674$	17.5320	+	24.1307i	0.675308	+	0.929481i
$675$	0.943954	+	24.8414i	0.0363328	+	0.956145i
$676$	1.37994	+	4.24702i	0.0530746	+	0.163347i
$677$	−15.3544	−	47.2560i	−0.590118	−	1.81620i	−0.577665	−	0.816274i	$-0.696036\pi$
$677$	−15.3544	−	47.2560i	−0.590118	−	1.81620i	−0.0124536	−	0.999922i	$-0.503964\pi$
$678$	4.62985	+	6.20567i	0.177808	+	0.238328i
$679$	−3.63461	+	27.5846i	−0.139484	+	1.05860i
$680$	−52.4500	−	17.0420i	−2.01137	−	0.653533i
$681$	−38.6299	−	12.0131i	−1.48030	−	0.460343i
$682$	2.64474	+	16.4250i	0.101272	+	0.628944i
$683$			12.4987i			0.478250i	0.970989	+	0.239125i	$0.0768606\pi$
$683$			12.4987i			0.478250i	−0.970989	+	0.239125i	$0.923139\pi$
$684$	−4.94470	−	6.45554i	−0.189065	−	0.246834i
$685$	6.03782	+	8.31034i	0.230693	+	0.317522i
$686$	−5.32238	−	22.2009i	−0.203209	−	0.847635i
$687$	−41.7241	+	0.528270i	−1.59188	+	0.0201547i
$688$	6.03139	+	18.5627i	0.229945	+	0.707697i
$689$	−9.75631	−	7.08837i	−0.371686	−	0.270045i
$690$	36.6266	−	12.4155i	1.39435	−	0.472650i
$691$	−33.6956	−	10.9484i	−1.28184	−	0.416496i	−0.412613	−	0.910906i	$-0.635384\pi$
$691$	−33.6956	−	10.9484i	−1.28184	−	0.416496i	−0.869228	+	0.494411i	$0.835384\pi$
$692$	6.47805			0.246259
$693$	−1.41986	−	26.2866i	−0.0539362	−	0.998544i
$694$	26.5222			1.00677
$695$	8.82510	+	2.86745i	0.334755	+	0.108768i
$696$	20.6138	−	6.98757i	0.781364	−	0.264863i
$697$	14.6593	+	10.6506i	0.555261	+	0.403421i
$698$	1.09973	+	3.38463i	0.0416255	+	0.128110i
$699$	−5.59491	+	0.0708372i	−0.211619	+	0.00267931i
$700$	1.10759	+	5.97961i	0.0418629	+	0.226008i
$701$	−10.1240	−	13.9345i	−0.382379	−	0.526300i	0.573834	−	0.818972i	$-0.305456\pi$
$701$	−10.1240	−	13.9345i	−0.382379	−	0.526300i	−0.956213	+	0.292672i	$0.905456\pi$
$702$	−11.5731	+	4.25260i	−0.436798	+	0.160504i
$703$			50.3807i			1.90014i
$704$	26.2295	−	13.4496i	0.988561	−	0.506901i
$705$	−30.0893	−	9.35714i	−1.13323	−	0.352410i
$706$	39.1460	+	12.7193i	1.47328	+	0.478697i
$707$	−2.68872	−	0.354272i	−0.101120	−	0.0133238i
$708$	1.13077	+	1.51564i	0.0424969	+	0.0569613i
$709$	−6.38878	−	19.6626i	−0.239936	−	0.738446i	−0.996428	−	0.0844436i	$-0.973089\pi$
$709$	−6.38878	−	19.6626i	−0.239936	−	0.738446i	0.756493	−	0.654002i	$-0.226911\pi$
$710$	15.9098	+	48.9654i	0.597086	+	1.83764i
$711$	7.16595	+	20.2914i	0.268744	+	0.760988i
$712$	5.23631	+	7.20717i	0.196239	+	0.270100i
$713$	−7.28155	+	22.4103i	−0.272696	+	0.839273i
$714$	28.4284	−	15.9006i	1.06390	−	0.595064i
$715$	−14.0843	+	14.1569i	−0.526724	+	0.529438i
$716$			3.93528i			0.147068i
$717$	−3.90345	−	2.76120i	−0.145777	−	0.103119i
$718$	5.24836	−	3.81316i	0.195867	−	0.142306i
$719$	29.6020	+	21.5071i	1.10397	+	0.802081i	0.981703	−	0.190417i	$-0.0609839\pi$
$719$	29.6020	+	21.5071i	1.10397	+	0.802081i	0.122266	+	0.992497i	$0.460984\pi$
$720$	7.50628	−	25.2610i	0.279743	−	0.941424i
$721$	2.57537	+	1.22873i	0.0959118	+	0.0457603i
$722$	−9.29599	+	12.7948i	−0.345961	+	0.476174i
$723$	−8.86333	−	26.1474i	−0.329631	−	0.972434i
$724$	−1.89591	−	0.616019i	−0.0704609	−	0.0228941i
$725$		−	19.6624i		−	0.730242i
$726$	0.418013	+	23.4824i	0.0155139	+	0.871515i
$727$		−	32.5843i		−	1.20848i	−0.796801	−	0.604242i	$-0.793476\pi$
$727$		−	32.5843i		−	1.20848i	0.796801	−	0.604242i	$-0.206524\pi$
$728$	−13.6859	+	7.42891i	−0.507232	+	0.275334i
$729$	−10.2681	−	24.9713i	−0.380301	−	0.924863i
$730$	−25.0773	−	18.2198i	−0.928154	−	0.674344i
$731$	12.3841	+	38.1144i	0.458044	+	1.40971i
$732$	−4.53610	+	0.0574315i	−0.167659	+	0.00212273i
$733$	16.7614	−	23.0701i	0.619098	−	0.852115i	−0.378189	−	0.925728i	$-0.623453\pi$
$733$	16.7614	−	23.0701i	0.619098	−	0.852115i	0.997287	+	0.0736133i	$0.0234530\pi$
$734$	12.1211	−	8.80653i	0.447400	−	0.325055i
$735$	−32.0608	−	20.2578i	−1.18258	−	0.747220i
$736$	15.3658			0.566391
$737$	−8.72149	−	8.67679i	−0.321260	−	0.319614i
$738$	−6.59048	+	9.57158i	−0.242599	+	0.352335i
$739$	−5.41889	+	16.6776i	−0.199337	+	0.613496i	0.800561	+	0.599251i	$0.204535\pi$
$739$	−5.41889	+	16.6776i	−0.199337	+	0.613496i	−0.999899	+	0.0142458i	$0.995465\pi$
$740$	10.8570	−	7.88805i	0.399110	−	0.289971i
$741$	−11.2480	−	15.0764i	−0.413206	−	0.553846i
$742$	−8.79845	+	18.4412i	−0.323001	+	0.676999i
$743$	6.36882	−	2.06935i	0.233649	−	0.0759172i	−0.189852	−	0.981813i	$-0.560801\pi$
$743$	6.36882	−	2.06935i	0.233649	−	0.0759172i	0.423501	+	0.905895i	$0.360801\pi$
$744$	12.8867	+	17.2729i	0.472451	+	0.633255i
$745$	−7.21635	−	9.93245i	−0.264387	−	0.363897i
$746$	1.89498	+	0.615717i	0.0693802	+	0.0225430i
$747$	−15.5109	−	10.6800i	−0.567514	−	0.390760i
$748$	8.17595	−	4.19235i	0.298942	−	0.153288i
$749$	3.70591	−	3.90438i	0.135411	−	0.142663i
$750$	1.17674	+	0.832396i	0.0429685	+	0.0303948i
$751$	−6.35762	+	4.61908i	−0.231993	+	0.168553i	−0.697709	−	0.716382i	$-0.745797\pi$
$751$	−6.35762	+	4.61908i	−0.231993	+	0.168553i	0.465716	+	0.884934i	$0.345797\pi$
$752$	13.2140	+	9.60052i	0.481864	+	0.350095i
$753$	0.154622	+	12.2124i	0.00563472	+	0.445045i
$754$	9.27480	−	3.01357i	0.337768	−	0.109748i
$755$	−37.9015	−	27.5371i	−1.37938	−	1.00218i
$756$	−3.36916	−	5.68109i	−0.122535	−	0.206619i
$757$	13.7778	−	42.4038i	0.500764	−	1.54119i	−0.307014	−	0.951705i	$-0.599330\pi$
$757$	13.7778	−	42.4038i	0.500764	−	1.54119i	0.807777	−	0.589488i	$-0.200670\pi$
$758$			11.8128i			0.429061i
$759$	−14.6490	+	29.8661i	−0.531724	+	1.08407i
$760$	53.9593			1.95731
$761$	1.62328	−	4.99596i	0.0588440	−	0.181103i	−0.917314	−	0.398165i	$-0.869647\pi$
$761$	1.62328	−	4.99596i	0.0588440	−	0.181103i	0.976158	+	0.217062i	$0.0696472\pi$
$762$	−11.0150	−	32.4951i	−0.399033	−	1.17717i
$763$	4.45688	+	24.0616i	0.161350	+	0.871090i
$764$	3.45932	−	1.12400i	0.125154	−	0.0406649i
$765$	15.4125	−	51.8680i	0.557239	−	1.87529i
$766$	−8.52421	+	11.7326i	−0.307992	+	0.423915i
$767$	2.57108	+	3.53878i	0.0928362	+	0.127778i
$768$	10.8147	−	15.2885i	0.390241	−	0.551676i
$769$		−	20.4914i		−	0.738937i	−0.929243	−	0.369468i	$-0.879540\pi$
$769$		−	20.4914i		−	0.738937i	0.929243	−	0.369468i	$-0.120460\pi$
$770$	27.9314	+	19.0956i	1.00658	+	0.688159i
$771$	18.5641	+	5.77304i	0.668569	+	0.207911i
$772$	2.21979	−	6.83181i	0.0798919	−	0.245882i
$773$	−14.4866	+	10.5251i	−0.521046	+	0.378562i	−0.816998	−	0.576641i	$-0.804363\pi$
$773$	−14.4866	+	10.5251i	−0.521046	+	0.378562i	0.295952	+	0.955203i	$0.404363\pi$
$774$	−24.2355	+	8.55881i	−0.871127	+	0.307640i
$775$	18.5149	−	6.01585i	0.665074	−	0.216096i
$776$	−9.93633	−	30.5809i	−0.356694	−	1.09779i
$777$	−4.83170	+	40.6358i	−0.173336	+	1.45780i
$778$	−19.4468	+	14.1289i	−0.697202	+	0.506547i
$779$	−16.8612	−	5.47855i	−0.604117	−	0.196289i
$780$	−1.48786	+	4.78443i	−0.0532739	+	0.171310i
$781$	−39.5100	−	20.0036i	−1.41378	−	0.715786i
$782$	−41.1606			−1.47190
$783$	7.36569	+	20.0451i	0.263228	+	0.716353i
$784$	12.3679	+	15.2798i	0.441711	+	0.545708i
$785$	−22.1057	+	30.4259i	−0.788987	+	1.08595i
$786$	10.0161	−	0.126814i	0.357264	−	0.00452332i
$787$	27.7323	−	9.01078i	0.988551	−	0.321200i	0.230270	−	0.973127i	$-0.426039\pi$
$787$	27.7323	−	9.01078i	0.988551	−	0.321200i	0.758282	+	0.651927i	$0.226039\pi$
$788$	5.15650	−	7.09732i	0.183693	−	0.252831i
$789$	4.70334	+	13.8752i	0.167443	+	0.493969i
$790$	−26.3051	−	8.54704i	−0.935893	−	0.304090i
$791$	−6.60497	+	6.95869i	−0.234846	+	0.247422i
$792$	14.5624	+	26.7116i	0.517453	+	0.949155i
$793$	−10.4936			−0.372640
$794$	3.93731	−	12.1178i	0.139730	−	0.430044i
$795$	10.8965	+	32.1455i	0.386460	+	1.14008i
$796$	−7.27331	+	10.0109i	−0.257796	+	0.354825i
$797$	6.06662	+	18.6711i	0.214891	+	0.661366i	0.999161	+	0.0409467i	$0.0130374\pi$
$797$	6.06662	+	18.6711i	0.214891	+	0.661366i	−0.784271	+	0.620419i	$0.786963\pi$
$798$	−21.6461	+	23.3914i	−0.766263	+	0.828046i
$799$	27.1320	+	19.7125i	0.959860	+	0.697379i
$800$	−7.46186	−	10.2704i	−0.263817	−	0.363112i
$801$	−6.93894	+	5.31497i	−0.245175	+	0.187795i
$802$	−43.9893			−1.55332
$803$	26.3234	−	4.23857i	0.928931	−	0.149576i
$804$	−2.94750	−	0.916611i	−0.103950	−	0.0323264i
$805$	22.8624	+	42.1181i	0.805794	+	1.48447i
$806$	5.67540	+	7.81151i	0.199907	+	0.275149i
$807$	−21.3192	−	28.5755i	−0.750471	−	1.00590i
$808$	2.98077	−	0.968512i	0.104863	−	0.0340721i
$809$	−15.1424	+	4.92008i	−0.532380	+	0.172981i	−0.562856	−	0.826555i	$-0.690298\pi$
$809$	−15.1424	+	4.92008i	−0.532380	+	0.172981i	0.0304764	+	0.999535i	$0.490298\pi$
$810$	33.5047	+	9.03931i	1.17724	+	0.317609i
$811$	−23.1351	−	31.8428i	−0.812384	−	1.11815i	−0.990951	−	0.134223i	$-0.957146\pi$
$811$	−23.1351	−	31.8428i	−0.812384	−	1.11815i	0.178567	−	0.983928i	$-0.442854\pi$
$812$	2.49228	+	4.59138i	0.0874618	+	0.161126i
$813$	10.7891	−	34.6940i	0.378390	−	1.21677i
$814$	5.61862	−	36.0742i	0.196933	−	1.26440i
$815$	38.9484			1.36430
$816$	−16.1972	+	22.8977i	−0.567017	+	0.801579i
$817$	−23.0478	−	31.7225i	−0.806340	−	1.10983i
$818$	−10.4871	−	7.61931i	−0.366672	−	0.266403i
$819$	−7.62647	−	13.2390i	−0.266490	−	0.462607i
$820$	1.45933	+	4.49135i	0.0509620	+	0.156845i
$821$	−14.6595	+	20.1770i	−0.511619	+	0.704183i	−0.984191	−	0.177109i	$-0.943326\pi$
$821$	−14.6595	+	20.1770i	−0.511619	+	0.704183i	0.472572	+	0.881292i	$0.343326\pi$
$822$	6.64048	−	2.25096i	0.231613	−	0.0785112i
$823$	−1.62188	+	4.99164i	−0.0565352	+	0.173998i	−0.975337	−	0.220723i	$-0.929158\pi$
$823$	−1.62188	+	4.99164i	−0.0565352	+	0.173998i	0.918801	+	0.394720i	$0.129158\pi$
$824$	−3.29771			−0.114881
$825$	27.0760	−	4.71218i	0.942666	−	0.164057i
$826$	5.10216	−	5.37539i	0.177527	−	0.187034i
$827$	21.3099	+	6.92399i	0.741016	+	0.240771i	0.655111	−	0.755533i	$-0.272622\pi$
$827$	21.3099	+	6.92399i	0.741016	+	0.240771i	0.0859052	+	0.996303i	$0.472622\pi$
$828$	0.211313	+	8.34369i	0.00734363	+	0.289963i
$829$	7.27790	−	10.0172i	0.252772	−	0.347911i	−0.663708	−	0.747992i	$-0.731018\pi$
$829$	7.27790	−	10.0172i	0.252772	−	0.347911i	0.916480	+	0.400081i	$0.131018\pi$
$830$	23.0200	−	7.47966i	0.799036	−	0.259623i
$831$	−0.359652	−	28.4063i	−0.0124762	−	0.985403i
$832$	10.0557	−	13.8405i	0.348619	−	0.479833i
$833$	25.3947	+	31.3737i	0.879876	+	1.08703i
$834$	3.65779	−	5.17094i	0.126659	−	0.179055i
$835$	10.0062			0.346277
$836$	−6.34046	+	6.37313i	−0.219290	+	0.220419i
$837$	−16.6217	+	13.0688i	−0.574530	+	0.451723i
$838$	−39.1651	−	12.7255i	−1.35293	−	0.439595i
$839$	1.79187	−	1.30187i	0.0618624	−	0.0449457i	−0.556424	−	0.830898i	$-0.687827\pi$
$839$	1.79187	−	1.30187i	0.0618624	−	0.0449457i	0.618287	+	0.785953i	$0.287827\pi$
$840$	43.5222	+	5.17491i	1.50166	+	0.178551i
$841$	3.74186	+	11.5163i	0.129030	+	0.397113i
$842$	14.1476	−	4.59682i	0.487557	−	0.158417i
$843$	−20.7898	+	15.5105i	−0.716038	+	0.534212i
$844$	−1.39518	+	1.01366i	−0.0480242	+	0.0348916i
$845$	8.98421	−	27.6506i	0.309066	−	0.951209i
$846$	−12.1979	+	17.7154i	−0.419372	+	0.609068i
$847$	−28.5889	+	5.44755i	−0.982326	+	0.187180i
$848$		−	17.5937i		−	0.604172i
$849$	13.8759	+	9.81549i	0.476221	+	0.336867i
$850$	19.9882	+	27.5114i	0.685590	+	0.943633i
$851$	30.3948	−	41.8349i	1.04192	−	1.43408i
$852$	−11.1104	+	0.140669i	−0.380637	+	0.00481924i
$853$	49.8461	−	16.1960i	1.70670	−	0.554540i	0.716921	−	0.697154i	$-0.245551\pi$
$853$	49.8461	−	16.1960i	1.70670	−	0.554540i	0.989778	+	0.142614i	$0.0455508\pi$
$854$	3.23819	+	17.4822i	0.110809	+	0.598230i
$855$	1.34038	+	52.9250i	0.0458401	+	1.81000i
$856$	−1.92245	+	5.91669i	−0.0657080	+	0.202228i
$857$	2.43184			0.0830702			0.0415351	−	0.999137i	$-0.486775\pi$
$857$	2.43184			0.0830702			0.0415351	+	0.999137i	$0.486775\pi$
$858$	6.37258	+	12.0496i	0.217556	+	0.411368i
$859$		−	7.77125i		−	0.265152i	−0.991173	−	0.132576i	$-0.957675\pi$
$859$		−	7.77125i		−	0.265152i	0.991173	−	0.132576i	$-0.0423248\pi$
$860$	−3.22760	+	9.93354i	−0.110060	+	0.338731i
$861$	−13.0744	−	6.03592i	−0.445576	−	0.205704i
$862$	−27.0525	−	19.6548i	−0.921411	−	0.669444i
$863$	34.3219	−	11.1519i	1.16833	−	0.379614i	0.340312	−	0.940313i	$-0.389467\pi$
$863$	34.3219	−	11.1519i	1.16833	−	0.379614i	0.828020	+	0.560699i	$0.189467\pi$
$864$	11.4545	+	7.67501i	0.389689	+	0.261109i
$865$	−34.1211	−	24.7904i	−1.16015	−	0.842899i
$866$	−24.0664	+	17.4853i	−0.817811	+	0.594174i
$867$	−16.2531	+	22.9767i	−0.551985	+	0.780330i
$868$	−3.56090	+	3.75160i	−0.120865	+	0.127338i
$869$	21.1699	−	10.8552i	0.718141	−	0.368238i
$870$	−26.2098	−	8.15072i	−0.888597	−	0.276335i
$871$	−6.79069	−	2.20643i	−0.230094	−	0.0747620i
$872$	−16.6229	−	22.8795i	−0.562924	−	0.774798i
$873$	29.7479	−	10.5055i	1.00681	−	0.355558i
$874$	38.3015	−	12.4449i	1.29557	−	0.420955i
$875$	−0.769118	+	1.61204i	−0.0260009	+	0.0544970i
$876$	5.36186	−	4.00030i	0.181160	−	0.135158i
$877$	1.66592	−	1.21036i	0.0562540	−	0.0408709i	−0.559303	−	0.828963i	$-0.688931\pi$
$877$	1.66592	−	1.21036i	0.0562540	−	0.0408709i	0.615557	+	0.788092i	$0.288931\pi$
$878$	−9.96208	+	30.6601i	−0.336204	+	1.03473i
$879$	25.9159	+	8.05931i	0.874122	+	0.271834i
$880$	−28.7869	−	4.48361i	−0.970407	−	0.151143i
$881$	22.2425			0.749368			0.374684	−	0.927153i	$-0.377751\pi$
$881$	22.2425			0.749368			0.374684	+	0.927153i	$0.377751\pi$
$882$	−19.7025	+	16.7909i	−0.663418	+	0.565381i
$883$	16.1682	−	11.7469i	0.544104	−	0.395315i	−0.281503	−	0.959560i	$-0.590833\pi$
$883$	16.1682	−	11.7469i	0.544104	−	0.395315i	0.825607	+	0.564246i	$0.190833\pi$
$884$	3.13445	−	4.31420i	0.105423	−	0.145102i
$885$	−0.155862	−	12.3104i	−0.00523925	−	0.413810i
$886$	−3.92746	−	12.0875i	−0.131946	−	0.406087i
$887$	−17.7763	−	12.9152i	−0.596869	−	0.433651i	0.247897	−	0.968786i	$-0.420261\pi$
$887$	−17.7763	−	12.9152i	−0.596869	−	0.433651i	−0.844766	+	0.535135i	$0.820261\pi$
$888$	−15.1825	−	44.7896i	−0.509493	−	1.50304i
$889$	37.3672	−	20.2835i	1.25326	−	0.680287i
$890$		−	11.2341i		−	0.376569i
$891$	−25.8378	+	14.9468i	−0.865600	+	0.500737i
$892$		−	6.00816i		−	0.201168i
$893$	−31.2074	−	10.1399i	−1.04431	−	0.339318i
$894$	−7.93665	+	2.69033i	−0.265441	+	0.0899780i
$895$	15.0596	−	20.7278i	0.503388	−	0.692855i
$896$	−13.4885	−	6.43548i	−0.450620	−	0.214994i
$897$	0.244422	+	19.3051i	0.00816100	+	0.644577i
$898$	21.3313	+	15.4981i	0.711834	+	0.517178i
$899$	13.5299	−	9.83003i	0.451247	−	0.327850i
$900$	5.47423	−	4.19306i	0.182474	−	0.139769i
$901$		−	36.1248i		−	1.20349i
$902$	11.4622	+	5.80325i	0.381651	+	0.193227i
$903$	−15.5474	−	27.7970i	−0.517386	−	0.925025i
$904$	3.42634	−	10.5452i	0.113958	−	0.350728i
$905$	7.62870	+	10.5000i	0.253586	+	0.349032i
$906$	−25.6310	+	19.1224i	−0.851533	+	0.635300i
$907$	−3.44050	−	10.5888i	−0.114240	−	0.351594i	0.877548	−	0.479489i	$-0.159178\pi$
$907$	−3.44050	−	10.5888i	−0.114240	−	0.351594i	−0.991788	+	0.127895i	$0.959178\pi$
$908$	3.46763	+	10.6723i	0.115077	+	0.354172i
$909$	1.02399	+	2.89958i	0.0339636	+	0.0961729i
$910$	19.4690	+	2.56527i	0.645391	+	0.0850380i
$911$	−56.4618	−	18.3456i	−1.87066	−	0.607816i	−0.991292	−	0.131681i	$-0.957963\pi$
$911$	−56.4618	−	18.3456i	−1.87066	−	0.607816i	−0.879372	−	0.476135i	$-0.842037\pi$
$912$	8.14901	−	26.2044i	0.269841	−	0.867713i
$913$	−9.40426	+	18.5747i	−0.311236	+	0.614734i
$914$		−	16.3998i		−	0.542458i
$915$	24.1122	+	17.0564i	0.797125	+	0.563866i
$916$	6.80334	+	9.36399i	0.224789	+	0.309395i
$917$	2.26071	+	12.2050i	0.0746553	+	0.403046i
$918$	−30.6833	−	20.5592i	−1.01270	−	0.678553i
$919$	10.1870	+	31.3523i	0.336037	+	1.03422i	0.966209	+	0.257760i	$0.0829844\pi$
$919$	10.1870	+	31.3523i	0.336037	+	1.03422i	−0.630172	+	0.776456i	$0.717016\pi$
$920$	−44.8066	−	32.5539i	−1.47723	−	1.07327i
$921$	−2.65504	−	7.83256i	−0.0874866	−	0.258092i
$922$	−2.22118	−	0.721705i	−0.0731507	−	0.0237681i
$923$	−25.7024			−0.846006
$924$	−5.72527	+	4.53233i	−0.188347	+	0.149103i
$925$	−42.7223			−1.40470
$926$	−6.54426	−	2.12636i	−0.215058	−	0.0698764i
$927$	−0.0819171	−	3.23450i	−0.00269051	−	0.106235i
$928$	−8.82282	−	6.41016i	−0.289623	−	0.210424i
$929$	2.81397	+	8.66050i	0.0923233	+	0.284142i	0.986547	−	0.163479i	$-0.0522715\pi$
$929$	2.81397	+	8.66050i	0.0923233	+	0.284142i	−0.894224	+	0.447621i	$0.852272\pi$
$930$	−0.344051	−	27.1740i	−0.0112819	−	0.891072i
$931$	−33.1166	−	21.5163i	−1.08535	−	0.705168i
$932$	0.912279	+	1.25564i	0.0298827	+	0.0411300i
$933$	9.21511	−	13.0272i	0.301689	−	0.426491i
$934$		−	36.1043i		−	1.18137i
$935$	−59.1076	−	9.20610i	−1.93302	−	0.301072i
$936$	14.5431	+	10.0136i	0.475356	+	0.327305i
$937$	−13.9446	−	4.53088i	−0.455551	−	0.148018i	0.0722481	−	0.997387i	$-0.476983\pi$
$937$	−13.9446	−	4.53088i	−0.455551	−	0.148018i	−0.527799	+	0.849369i	$0.676983\pi$
$938$	−1.58036	+	11.9941i	−0.0516007	+	0.391620i
$939$	−37.5932	+	28.0470i	−1.22681	+	0.915280i
$940$	2.70097	+	8.31275i	0.0880961	+	0.271132i
$941$	10.2176	+	31.4465i	0.333084	+	1.02513i	0.967658	+	0.252265i	$0.0811753\pi$
$941$	10.2176	+	31.4465i	0.333084	+	1.02513i	−0.634575	+	0.772862i	$0.718825\pi$
$942$	15.3508	+	20.5756i	0.500155	+	0.670389i
$943$	10.6960	+	14.7217i	0.348308	+	0.479405i
$944$	−1.97201	+	6.06922i	−0.0641834	+	0.197536i
$945$	−3.99459	+	42.8165i	−0.129944	+	1.39282i
$946$	12.9652	+	25.2848i	0.421534	+	0.822079i
$947$			59.6811i			1.93938i	0.244347	+	0.969688i	$0.421426\pi$
$947$			59.6811i			1.93938i	−0.244347	+	0.969688i	$0.578574\pi$
$948$	3.44718	−	4.87320i	0.111959	−	0.158274i
$949$	12.5191	−	9.09564i	0.406386	−	0.295257i
$950$	−26.9178	−	19.5569i	−0.873329	−	0.634511i
$951$	−1.40621	+	0.0178041i	−0.0455995	+	0.000577336i
$952$	−42.1010	−	20.0867i	−1.36450	−	0.651014i
$953$	18.2905	−	25.1747i	0.592486	−	0.815487i	−0.402508	−	0.915416i	$-0.631862\pi$
$953$	18.2905	−	25.1747i	0.592486	−	0.815487i	0.994995	+	0.0999290i	$0.0318616\pi$
$954$	23.1610	−	0.586577i	0.749865	−	0.0189911i
$955$	−22.5222	−	7.31791i	−0.728801	−	0.236802i
$956$			1.32626i			0.0428944i
$957$	20.8705	−	11.0376i	0.674647	−	0.356794i
$958$			17.7561i			0.573672i
$959$	4.14500	+	7.63611i	0.133849	+	0.246583i
$960$	−45.6023	+	15.4581i	−1.47181	+	0.498907i
$961$	−11.6836	−	8.48863i	−0.376890	−	0.273827i
$962$	−6.54786	−	20.1522i	−0.211111	−	0.649734i
$963$	−5.85103	−	1.73862i	−0.188547	−	0.0560264i
$964$	−4.50140	+	6.19565i	−0.144980	+	0.199548i
$965$	−37.8362	+	27.4896i	−1.21799	+	0.884921i
$966$	32.0865	−	6.36448i	1.03237	−	0.204774i
$967$	−35.2253			−1.13277			−0.566385	−	0.824141i	$-0.691658\pi$
$967$	−35.2253			−1.13277			−0.566385	+	0.824141i	$0.691658\pi$
$968$	27.1086	−	19.9092i	0.871305	−	0.639907i
$969$	16.7322	−	53.8048i	0.537515	−	1.72846i
$970$	−12.5302	+	38.5641i	−0.402321	+	1.23822i
$971$	−45.5422	+	33.0883i	−1.46152	+	1.06185i	−0.478553	+	0.878059i	$0.658839\pi$
$971$	−45.5422	+	33.0883i	−1.46152	+	1.06185i	−0.982964	+	0.183796i	$0.941161\pi$
$972$	−4.01003	+	6.32536i	−0.128622	+	0.202886i
$973$	7.08380	+	3.37973i	0.227096	+	0.108349i
$974$	−31.7135	+	10.3043i	−1.01616	+	0.330172i
$975$	12.7846	−	9.53819i	0.409436	−	0.305467i
$976$	−8.99860	−	12.3855i	−0.288038	−	0.396451i
$977$	5.42072	+	1.76130i	0.173424	+	0.0563490i	0.394442	−	0.918921i	$-0.370938\pi$
$977$	5.42072	+	1.76130i	0.173424	+	0.0563490i	−0.221018	+	0.975270i	$0.570938\pi$
$978$	7.89465	−	25.3864i	0.252443	−	0.811768i
$979$	6.85036	+	6.81525i	0.218939	+	0.217816i
$980$	0.548294	+	10.5054i	0.0175146	+	0.335582i
$981$	22.0280	−	16.8726i	0.703300	−	0.538702i
$982$	−21.2163	+	15.4146i	−0.677040	+	0.491898i
$983$	−28.4046	−	20.6371i	−0.905965	−	0.658222i	0.0340265	−	0.999421i	$-0.489167\pi$
$983$	−28.4046	−	20.6371i	−0.905965	−	0.658222i	−0.939991	+	0.341199i	$0.889167\pi$
$984$	16.6410	−	0.210692i	0.530497	−	0.00671662i
$985$	−54.3204	+	17.6498i	−1.73079	+	0.562369i
$986$	23.6338	+	17.1710i	0.752655	+	0.546836i
$987$	−24.1986	−	11.1715i	−0.770250	−	0.355592i
$988$	−1.61232	+	4.96222i	−0.0512948	+	0.157869i
$989$			40.2465i			1.27976i
$990$	4.94262	−	38.0456i	0.157087	−	1.20917i
$991$	−52.8169			−1.67778			−0.838892	−	0.544298i	$-0.816796\pi$
$991$	−52.8169			−1.67778			−0.838892	+	0.544298i	$0.816796\pi$
$992$	3.33665	−	10.2692i	0.105939	−	0.326046i
$993$	36.7326	−	12.4515i	1.16568	−	0.395135i
$994$	7.93142	+	42.8198i	0.251569	+	1.35816i
$995$	76.6197	−	24.8952i	2.42901	−	0.789232i
$996$	0.0661325	+	5.22332i	0.00209549	+	0.165507i
$997$	−35.3849	+	48.7031i	−1.12065	+	1.54244i	−0.315936	+	0.948781i	$0.602318\pi$
$997$	−35.3849	+	48.7031i	−1.12065	+	1.54244i	−0.804715	+	0.593662i	$0.797682\pi$
$998$	−27.6763	−	38.0931i	−0.876077	−	1.20582i
$999$	43.5539	−	16.0041i	1.37798	−	0.506348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.u.a.20.20	yes	112
3.2	odd	2	inner	231.2.u.a.20.9	✓	112
7.6	odd	2	inner	231.2.u.a.20.19	yes	112
11.5	even	5	inner	231.2.u.a.104.10	yes	112
21.20	even	2	inner	231.2.u.a.20.10	yes	112
33.5	odd	10	inner	231.2.u.a.104.19	yes	112
77.27	odd	10	inner	231.2.u.a.104.9	yes	112
231.104	even	10	inner	231.2.u.a.104.20	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.u.a.20.9	✓	112	3.2	odd	2	inner
231.2.u.a.20.10	yes	112	21.20	even	2	inner
231.2.u.a.20.19	yes	112	7.6	odd	2	inner
231.2.u.a.20.20	yes	112	1.1	even	1	trivial
231.2.u.a.104.9	yes	112	77.27	odd	10	inner
231.2.u.a.104.10	yes	112	11.5	even	5	inner
231.2.u.a.104.19	yes	112	33.5	odd	10	inner
231.2.u.a.104.20	yes	112	231.104	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17237 + 0.380926i) q^{2} +(1.64037 - 0.556045i) q^{3} +(-0.388687 - 0.282397i) q^{4} +(0.966595 + 2.97487i) q^{5} +(2.13493 - 0.0270304i) q^{6} +(0.481870 + 2.60150i) q^{7} +(-1.79724 - 2.47369i) q^{8} +(2.38163 - 1.82424i) q^{9} +O(q^{10})\)	\(q+(1.17237 + 0.380926i) q^{2} +(1.64037 - 0.556045i) q^{3} +(-0.388687 - 0.282397i) q^{4} +(0.966595 + 2.97487i) q^{5} +(2.13493 - 0.0270304i) q^{6} +(0.481870 + 2.60150i) q^{7} +(-1.79724 - 2.47369i) q^{8} +(2.38163 - 1.82424i) q^{9} +3.85585i q^{10} +(-2.35123 - 2.33917i) q^{11} +(-0.794615 - 0.247109i) q^{12} +(-1.83070 - 0.594831i) q^{13} +(-0.426050 + 3.23348i) q^{14} +(3.23974 + 4.34242i) q^{15} +(-0.867809 - 2.67084i) q^{16} +(-1.78185 - 5.48398i) q^{17} +(3.48705 - 1.23146i) q^{18} +(3.31616 + 4.56430i) q^{19} +(0.464394 - 1.42926i) q^{20} +(2.23700 + 3.99948i) q^{21} +(-1.86545 - 3.63802i) q^{22} -5.79074i q^{23} +(-4.32362 - 3.05842i) q^{24} +(-3.87048 + 2.81207i) q^{25} +(-1.91967 - 1.39472i) q^{26} +(2.89239 - 4.31672i) q^{27} +(0.547360 - 1.14725i) q^{28} +(-2.41572 + 3.32496i) q^{29} +(2.14403 + 6.32503i) q^{30} +(-3.87003 - 1.25745i) q^{31} +2.65351i q^{32} +(-5.15757 - 2.52972i) q^{33} -7.10801i q^{34} +(-7.27336 + 3.94810i) q^{35} +(-1.44087 + 0.0364915i) q^{36} +(7.22445 + 5.24887i) q^{37} +(2.14910 + 6.61426i) q^{38} +(-3.33378 + 0.0422090i) q^{39} +(5.62171 - 7.73762i) q^{40} +(-2.54229 + 1.84708i) q^{41} +(1.09908 + 5.54100i) q^{42} -6.95014 q^{43} +(0.253313 + 1.57319i) q^{44} +(7.72895 + 5.32174i) q^{45} +(2.20584 - 6.78889i) q^{46} +(-4.70535 + 3.41864i) q^{47} +(-2.90864 - 3.89863i) q^{48} +(-6.53560 + 2.50717i) q^{49} +(-5.60883 + 1.82242i) q^{50} +(-5.97224 - 8.00497i) q^{51} +(0.543591 + 0.748188i) q^{52} +(5.95831 + 1.93597i) q^{53} +(5.03531 - 3.95900i) q^{54} +(4.68606 - 9.25563i) q^{55} +(5.56927 - 5.86752i) q^{56} +(7.97768 + 5.64321i) q^{57} +(-4.09869 + 2.97787i) q^{58} +(-1.83841 - 1.33568i) q^{59} +(-0.0329532 - 2.60273i) q^{60} +(5.18467 - 1.68460i) q^{61} +(-4.05811 - 2.94839i) q^{62} +(5.89339 + 5.31676i) q^{63} +(-2.74641 + 8.45258i) q^{64} -6.02107i q^{65} +(-5.08294 - 4.93043i) q^{66} +3.70934 q^{67} +(-0.856079 + 2.63474i) q^{68} +(-3.21991 - 9.49896i) q^{69} +(-10.0310 + 1.85802i) q^{70} +(12.6990 - 4.12615i) q^{71} +(-8.79296 - 2.61281i) q^{72} +(-4.72522 + 6.50371i) q^{73} +(6.47030 + 8.90560i) q^{74} +(-4.78538 + 6.76499i) q^{75} -2.71056i q^{76} +(4.95238 - 7.24389i) q^{77} +(-3.92451 - 1.22044i) q^{78} +(-2.21664 + 6.82211i) q^{79} +(7.10659 - 5.16324i) q^{80} +(2.34431 - 8.68932i) q^{81} +(-3.68410 + 1.19704i) q^{82} +(-1.93982 - 5.97015i) q^{83} +(0.259953 - 2.18627i) q^{84} +(14.5918 - 10.6016i) q^{85} +(-8.14814 - 2.64749i) q^{86} +(-2.11386 + 6.79741i) q^{87} +(-1.56067 + 10.0203i) q^{88} -2.91353 q^{89} +(7.03400 + 9.18321i) q^{90} +(0.665293 - 5.04920i) q^{91} +(-1.63529 + 2.25078i) q^{92} +(-7.04747 + 0.0892281i) q^{93} +(-6.81866 + 2.21552i) q^{94} +(-10.3728 + 14.2770i) q^{95} +(1.47547 + 4.35274i) q^{96} +(10.0014 + 3.24966i) q^{97} +(-8.61719 + 0.449747i) q^{98} +(-9.86696 - 1.28185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

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