LMFDB - Embedded newform 273.2.cc.a.50.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (of order $12$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.8
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74208 - 0.466790i) q^{2} +(0.804463 + 1.53390i) q^{3} +(1.08492 + 0.626376i) q^{4} +(0.450139 - 0.450139i) q^{5} +(-0.685436 - 3.04769i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.952961 + 0.952961i) q^{8} +(-1.70568 + 2.46793i) q^{9} +O(q^{10})$	\(q+(-1.74208 - 0.466790i) q^{2} +(0.804463 + 1.53390i) q^{3} +(1.08492 + 0.626376i) q^{4} +(0.450139 - 0.450139i) q^{5} +(-0.685436 - 3.04769i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.952961 + 0.952961i) q^{8} +(-1.70568 + 2.46793i) q^{9} +(-0.994301 + 0.574060i) q^{10} +(0.240742 - 0.898462i) q^{11} +(-0.0880215 + 2.16804i) q^{12} +(3.41809 - 1.14747i) q^{13} -1.80354i q^{14} +(1.05259 + 0.328346i) q^{15} +(-2.46806 - 4.27480i) q^{16} +(-3.80483 + 6.59015i) q^{17} +(4.12344 - 3.50315i) q^{18} +(0.131228 - 0.0351625i) q^{19} +(0.770319 - 0.206406i) q^{20} +(-1.27342 + 1.17405i) q^{21} +(-0.838786 + 1.45282i) q^{22} +(3.38391 + 5.86110i) q^{23} +(-0.695121 + 2.22837i) q^{24} +4.59475i q^{25} +(-6.49022 + 0.403453i) q^{26} +(-5.15770 - 0.630975i) q^{27} +(-0.324236 + 1.21007i) q^{28} +(3.03803 - 1.75401i) q^{29} +(-1.68043 - 1.06334i) q^{30} +(2.26213 + 2.26213i) q^{31} +(1.60651 + 5.99560i) q^{32} +(1.57182 - 0.353506i) q^{33} +(9.70455 - 9.70455i) q^{34} +(0.551305 + 0.318296i) q^{35} +(-3.39637 + 1.60910i) q^{36} +(4.24150 + 1.13651i) q^{37} -0.245024 q^{38} +(4.50982 + 4.31990i) q^{39} +0.857930 q^{40} +(4.55333 + 1.22006i) q^{41} +(2.76644 - 1.45088i) q^{42} +(-7.93975 - 4.58402i) q^{43} +(0.823960 - 0.823960i) q^{44} +(0.343119 + 1.87870i) q^{45} +(-3.15915 - 11.7901i) q^{46} +(2.72828 + 2.72828i) q^{47} +(4.57164 - 7.22467i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(2.14478 - 8.00444i) q^{50} +(-13.1695 - 0.534673i) q^{51} +(4.42708 + 0.896105i) q^{52} -11.6211i q^{53} +(8.69062 + 3.50678i) q^{54} +(-0.296065 - 0.512800i) q^{55} +(-0.673845 + 1.16713i) q^{56} +(0.159504 + 0.173004i) q^{57} +(-6.11126 + 1.63751i) q^{58} +(-9.14017 + 2.44910i) q^{59} +(0.936300 + 1.01554i) q^{60} +(-1.70336 + 2.95031i) q^{61} +(-2.88488 - 4.99676i) q^{62} +(-2.82530 - 1.00881i) q^{63} -1.32251i q^{64} +(1.02210 - 2.05513i) q^{65} +(-2.90325 - 0.117870i) q^{66} +(1.72689 - 6.44486i) q^{67} +(-8.25583 + 4.76651i) q^{68} +(-6.26809 + 9.90560i) q^{69} +(-0.811843 - 0.811843i) q^{70} +(-2.53419 - 9.45773i) q^{71} +(-3.97728 + 0.726395i) q^{72} +(6.92674 - 6.92674i) q^{73} +(-6.85854 - 3.95978i) q^{74} +(-7.04787 + 3.69631i) q^{75} +(0.164396 + 0.0440499i) q^{76} +0.930156 q^{77} +(-5.84000 - 9.63077i) q^{78} -10.9011 q^{79} +(-3.03522 - 0.813286i) q^{80} +(-3.18133 - 8.41897i) q^{81} +(-7.36278 - 4.25090i) q^{82} +(9.22276 - 9.22276i) q^{83} +(-2.11695 + 0.476109i) q^{84} +(1.25378 + 4.67919i) q^{85} +(11.6919 + 11.6919i) q^{86} +(5.13445 + 3.24899i) q^{87} +(1.08562 - 0.626781i) q^{88} +(2.57122 - 9.59592i) q^{89} +(0.279218 - 3.43302i) q^{90} +(1.99303 + 3.00463i) q^{91} +8.47839i q^{92} +(-1.65007 + 5.28967i) q^{93} +(-3.47937 - 6.02644i) q^{94} +(0.0432429 - 0.0748990i) q^{95} +(-7.90424 + 7.28746i) q^{96} +(10.4313 - 2.79505i) q^{97} +(1.74208 - 0.466790i) q^{98} +(1.80671 + 2.12662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

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 $

$2$	−1.74208	−	0.466790i	−1.23184	−	0.330071i	−0.416544	−	0.909115i	$-0.636759\pi$
$2$	−1.74208	−	0.466790i	−1.23184	−	0.330071i	−0.815296	+	0.579045i	$0.803426\pi$
$3$	0.804463	+	1.53390i	0.464457	+	0.885596i
$3$	0.804463	+	1.53390i	0.464457	+	0.885596i
$4$	1.08492	+	0.626376i	0.542458	+	0.313188i
$5$	0.450139	−	0.450139i	0.201308	−	0.201308i	−0.599252	−	0.800560i	$-0.704535\pi$
$5$	0.450139	−	0.450139i	0.201308	−	0.201308i	0.800560	+	0.599252i	$0.204535\pi$
$6$	−0.685436	−	3.04769i	−0.279828	−	1.24422i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	0.952961	+	0.952961i	0.336923	+	0.336923i
$9$	−1.70568	+	2.46793i	−0.568559	+	0.822642i
$10$	−0.994301	+	0.574060i	−0.314426	+	0.181534i
$11$	0.240742	−	0.898462i	0.0725865	−	0.270896i	−0.920089	−	0.391710i	$-0.871884\pi$
$11$	0.240742	−	0.898462i	0.0725865	−	0.270896i	0.992675	+	0.120814i	$0.0385503\pi$
$12$	−0.0880215	+	2.16804i	−0.0254096	+	0.625861i
$13$	3.41809	−	1.14747i	0.948007	−	0.318250i
$13$	3.41809	−	1.14747i	0.948007	−	0.318250i
$14$		−	1.80354i		−	0.482016i
$15$	1.05259	+	0.328346i	0.271777	+	0.0847787i
$16$	−2.46806	−	4.27480i	−0.617015	−	1.06870i
$17$	−3.80483	+	6.59015i	−0.922806	+	1.59835i	−0.127754	+	0.991806i	$0.540777\pi$
$17$	−3.80483	+	6.59015i	−0.922806	+	1.59835i	−0.795052	+	0.606541i	$0.792556\pi$
$18$	4.12344	−	3.50315i	0.971904	−	0.825699i
$19$	0.131228	−	0.0351625i	0.0301058	−	0.00806683i	−0.243735	−	0.969842i	$-0.578373\pi$
$19$	0.131228	−	0.0351625i	0.0301058	−	0.00806683i	0.273841	+	0.961775i	$0.411706\pi$
$20$	0.770319	−	0.206406i	0.172249	−	0.0461539i
$21$	−1.27342	+	1.17405i	−0.277883	+	0.256200i
$22$	−0.838786	+	1.45282i	−0.178830	+	0.309742i
$23$	3.38391	+	5.86110i	0.705593	+	1.22212i	0.966477	+	0.256753i	$0.0826528\pi$
$23$	3.38391	+	5.86110i	0.705593	+	1.22212i	−0.260884	+	0.965370i	$0.584014\pi$
$24$	−0.695121	+	2.22837i	−0.141891	+	0.454863i
$25$			4.59475i			0.918950i
$26$	−6.49022	+	0.403453i	−1.27284	+	0.0791236i
$27$	−5.15770	−	0.630975i	−0.992600	−	0.121431i
$28$	−0.324236	+	1.21007i	−0.0612749	+	0.228681i
$29$	3.03803	−	1.75401i	0.564148	−	0.325711i	−0.190661	−	0.981656i	$-0.561063\pi$
$29$	3.03803	−	1.75401i	0.564148	−	0.325711i	0.754809	+	0.655945i	$0.227730\pi$
$30$	−1.68043	−	1.06334i	−0.306803	−	0.194139i
$31$	2.26213	+	2.26213i	0.406290	+	0.406290i	0.880443	−	0.474153i	$-0.157245\pi$
$31$	2.26213	+	2.26213i	0.406290	+	0.406290i	−0.474153	+	0.880443i	$0.657245\pi$
$32$	1.60651	+	5.99560i	0.283994	+	1.05988i
$33$	1.57182	−	0.353506i	0.273618	−	0.0615375i
$34$	9.70455	−	9.70455i	1.66432	−	1.66432i
$35$	0.551305	+	0.318296i	0.0931876	+	0.0538019i
$36$	−3.39637	+	1.60910i	−0.566061	+	0.268183i
$37$	4.24150	+	1.13651i	0.697298	+	0.186840i	0.590020	−	0.807389i	$-0.299120\pi$
$37$	4.24150	+	1.13651i	0.697298	+	0.186840i	0.107278	+	0.994229i	$0.465786\pi$
$38$	−0.245024			−0.0397482
$39$	4.50982	+	4.31990i	0.722149	+	0.691737i
$40$	0.857930			0.135651
$41$	4.55333	+	1.22006i	0.711111	+	0.190542i	0.596202	−	0.802834i	$-0.296676\pi$
$41$	4.55333	+	1.22006i	0.711111	+	0.190542i	0.114909	+	0.993376i	$0.463342\pi$
$42$	2.76644	−	1.45088i	0.426871	−	0.223876i
$43$	−7.93975	−	4.58402i	−1.21080	−	0.699056i	−0.247867	−	0.968794i	$-0.579730\pi$
$43$	−7.93975	−	4.58402i	−1.21080	−	0.699056i	−0.962934	+	0.269738i	$0.913063\pi$
$44$	0.823960	−	0.823960i	0.124217	−	0.124217i
$45$	0.343119	+	1.87870i	0.0511491	+	0.280060i
$46$	−3.15915	−	11.7901i	−0.465791	−	1.73836i
$47$	2.72828	+	2.72828i	0.397961	+	0.397961i	0.877513	−	0.479552i	$-0.159201\pi$
$47$	2.72828	+	2.72828i	0.397961	+	0.397961i	−0.479552	+	0.877513i	$0.659201\pi$
$48$	4.57164	−	7.22467i	0.659860	−	1.04279i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	2.14478	−	8.00444i	0.303318	−	1.13200i
$51$	−13.1695	−	0.534673i	−1.84409	−	0.0748692i
$52$	4.42708	+	0.896105i	0.613926	+	0.124267i
$53$		−	11.6211i		−	1.59629i	−0.602467	−	0.798143i	$-0.705816\pi$
$53$		−	11.6211i		−	1.59629i	0.602467	−	0.798143i	$-0.294184\pi$
$54$	8.69062	+	3.50678i	1.18264	+	0.477212i
$55$	−0.296065	−	0.512800i	−0.0399214	−	0.0691459i
$56$	−0.673845	+	1.16713i	−0.0900463	+	0.155965i
$57$	0.159504	+	0.173004i	0.0211268	+	0.0229149i
$58$	−6.11126	+	1.63751i	−0.802447	+	0.215015i
$59$	−9.14017	+	2.44910i	−1.18995	+	0.318846i	−0.798866	−	0.601510i	$-0.794566\pi$
$59$	−9.14017	+	2.44910i	−1.18995	+	0.318846i	−0.391083	+	0.920355i	$0.627899\pi$
$60$	0.936300	+	1.01554i	0.120876	+	0.131106i
$61$	−1.70336	+	2.95031i	−0.218093	+	0.377748i	−0.954225	−	0.299090i	$-0.903317\pi$
$61$	−1.70336	+	2.95031i	−0.218093	+	0.377748i	0.736132	+	0.676838i	$0.236650\pi$
$62$	−2.88488	−	4.99676i	−0.366380	−	0.634589i
$63$	−2.82530	−	1.00881i	−0.355954	−	0.127098i
$64$		−	1.32251i		−	0.165313i
$65$	1.02210	−	2.05513i	0.126775	−	0.254908i
$66$	−2.90325	−	0.117870i	−0.357365	−	0.0145088i
$67$	1.72689	−	6.44486i	0.210974	−	0.787365i	−0.776571	−	0.630029i	$-0.783043\pi$
$67$	1.72689	−	6.44486i	0.210974	−	0.787365i	0.987545	−	0.157336i	$-0.0502905\pi$
$68$	−8.25583	+	4.76651i	−1.00117	+	0.578024i
$69$	−6.26809	+	9.90560i	−0.754589	+	1.19249i
$70$	−0.811843	−	0.811843i	−0.0970338	−	0.0970338i
$71$	−2.53419	−	9.45773i	−0.300753	−	1.12243i	−0.936540	−	0.350561i	$-0.885991\pi$
$71$	−2.53419	−	9.45773i	−0.300753	−	1.12243i	0.635787	−	0.771865i	$-0.280676\pi$
$72$	−3.97728	+	0.726395i	−0.468727	+	0.0856064i
$73$	6.92674	−	6.92674i	0.810713	−	0.810713i	−0.174027	−	0.984741i	$-0.555678\pi$
$73$	6.92674	−	6.92674i	0.810713	−	0.810713i	0.984741	+	0.174027i	$0.0556782\pi$
$74$	−6.85854	−	3.95978i	−0.797289	−	0.460315i
$75$	−7.04787	+	3.69631i	−0.813818	+	0.426813i
$76$	0.164396	+	0.0440499i	0.0188576	+	0.00505287i
$77$	0.930156			0.106001
$78$	−5.84000	−	9.63077i	−0.661250	−	1.09047i
$79$	−10.9011			−1.22647			−0.613234	−	0.789901i	$-0.710132\pi$
$79$	−10.9011			−1.22647			−0.613234	+	0.789901i	$0.710132\pi$
$80$	−3.03522	−	0.813286i	−0.339348	−	0.0909281i
$81$	−3.18133	−	8.41897i	−0.353481	−	0.935442i
$82$	−7.36278	−	4.25090i	−0.813083	−	0.469434i
$83$	9.22276	−	9.22276i	1.01233	−	1.01233i	0.0124064	−	0.999923i	$-0.496051\pi$
$83$	9.22276	−	9.22276i	1.01233	−	1.01233i	0.999923	−	0.0124064i	$-0.00394917\pi$
$84$	−2.11695	+	0.476109i	−0.230978	+	0.0519477i
$85$	1.25378	+	4.67919i	0.135992	+	0.507529i
$86$	11.6919	+	11.6919i	1.26078	+	1.26078i
$87$	5.13445	+	3.24899i	0.550470	+	0.348328i
$88$	1.08562	−	0.626781i	0.115727	−	0.0668151i
$89$	2.57122	−	9.59592i	0.272549	−	1.01717i	−0.684918	−	0.728620i	$-0.740162\pi$
$89$	2.57122	−	9.59592i	0.272549	−	1.01717i	0.957466	−	0.288545i	$-0.0931715\pi$
$90$	0.279218	−	3.43302i	0.0294322	−	0.361872i
$91$	1.99303	+	3.00463i	0.208927	+	0.314971i
$92$			8.47839i			0.883934i
$93$	−1.65007	+	5.28967i	−0.171104	+	0.548513i
$94$	−3.47937	−	6.02644i	−0.358869	−	0.621580i
$95$	0.0432429	−	0.0748990i	0.00443663	−	0.00768447i
$96$	−7.90424	+	7.28746i	−0.806723	+	0.743774i
$97$	10.4313	−	2.79505i	1.05913	−	0.283794i	0.313113	−	0.949716i	$-0.398628\pi$
$97$	10.4313	−	2.79505i	1.05913	−	0.283794i	0.746022	+	0.665922i	$0.231962\pi$
$98$	1.74208	−	0.466790i	0.175977	−	0.0471529i
$99$	1.80671	+	2.12662i	0.181581	+	0.213733i
$100$	−2.87804	+	4.98491i	−0.287804	+	0.498491i
$101$	−2.62905	−	4.55366i	−0.261601	−	0.453106i	0.705067	−	0.709141i	$-0.250917\pi$
$101$	−2.62905	−	4.55366i	−0.261601	−	0.453106i	−0.966667	+	0.256035i	$0.917584\pi$
$102$	22.6927	+	7.07882i	2.24692	+	0.700908i
$103$			0.616253i			0.0607212i	0.999539	+	0.0303606i	$0.00966557\pi$
$103$			0.616253i			0.0607212i	−0.999539	+	0.0303606i	$0.990334\pi$
$104$	4.35079	+	2.16381i	0.426630	+	0.212179i
$105$	−0.0447286	+	1.10170i	−0.00436506	+	0.107515i
$106$	−5.42464	+	20.2450i	−0.526887	+	1.96637i
$107$	5.08294	−	2.93464i	0.491386	−	0.283702i	−0.233763	−	0.972294i	$-0.575104\pi$
$107$	5.08294	−	2.93464i	0.491386	−	0.283702i	0.725149	+	0.688592i	$0.241771\pi$
$108$	−5.20044	−	3.91521i	−0.500413	−	0.376742i
$109$	−5.98522	−	5.98522i	−0.573281	−	0.573281i	0.359763	−	0.933044i	$-0.382857\pi$
$109$	−5.98522	−	5.98522i	−0.573281	−	0.573281i	−0.933044	+	0.359763i	$0.882857\pi$
$110$	0.276401	+	1.03154i	0.0263538	+	0.0983536i
$111$	1.66885	+	7.42030i	0.158400	+	0.704304i
$112$	3.49036	−	3.49036i	0.329808	−	0.329808i
$113$	11.8048	+	6.81548i	1.11050	+	0.641146i	0.938958	−	0.344031i	$-0.111793\pi$
$113$	11.8048	+	6.81548i	1.11050	+	0.641146i	0.171539	+	0.985177i	$0.445126\pi$
$114$	−0.197113	−	0.375842i	−0.0184613	−	0.0352008i
$115$	4.16154	+	1.11508i	0.388065	+	0.103982i
$116$	4.39467			0.408035
$117$	−2.99829	+	10.3928i	−0.277192	+	0.960814i
$118$	17.0662			1.57107
$119$	−7.35036	−	1.96952i	−0.673807	−	0.180546i
$120$	0.690173	+	1.31598i	0.0630039	+	0.120132i
$121$	8.77700	+	5.06740i	0.797909	+	0.460673i
$122$	4.34457	−	4.34457i	0.393339	−	0.393339i
$123$	1.79154	+	7.96584i	0.161538	+	0.718255i
$124$	1.03727	+	3.87116i	0.0931500	+	0.347640i
$125$	4.31897	+	4.31897i	0.386301	+	0.386301i
$126$	4.45100	+	3.07626i	0.396527	+	0.274055i
$127$	−5.91808	+	3.41680i	−0.525144	+	0.303192i	−0.739037	−	0.673665i	$-0.764719\pi$
$127$	−5.91808	+	3.41680i	−0.525144	+	0.303192i	0.213893	+	0.976857i	$0.431386\pi$
$128$	2.59570	−	9.68727i	0.229429	−	0.856242i
$129$	0.644169	−	15.8664i	0.0567159	−	1.39696i
$130$	−2.73989	+	3.10311i	−0.240305	+	0.272161i
$131$			0.147336i			0.0128728i	0.999979	+	0.00643639i	$0.00204878\pi$
$131$			0.147336i			0.0128728i	−0.999979	+	0.00643639i	$0.997951\pi$
$132$	1.92671	+	0.601023i	0.167699	+	0.0523124i
$133$	0.0679287	+	0.117656i	0.00589017	+	0.0102021i
$134$	−6.01679	+	10.4214i	−0.519772	+	0.900271i
$135$	−2.60571	+	2.03766i	−0.224264	+	0.175373i
$136$	−9.90601	+	2.65431i	−0.849433	+	0.227605i
$137$	−20.1934	+	5.41079i	−1.72523	+	0.462275i	−0.979076	−	0.203493i	$-0.934771\pi$
$137$	−20.1934	+	5.41079i	−1.72523	+	0.462275i	−0.746159	+	0.665768i	$0.768104\pi$
$138$	15.5434	−	14.3305i	1.32314	−	1.21989i
$139$	−4.56906	+	7.91384i	−0.387542	+	0.671243i	−0.992118	−	0.125304i	$-0.960009\pi$
$139$	−4.56906	+	7.91384i	−0.387542	+	0.671243i	0.604576	+	0.796548i	$0.293343\pi$
$140$	0.398746	+	0.690649i	0.0337002	+	0.0583705i
$141$	−1.99010	+	6.37971i	−0.167597	+	0.537269i
$142$			17.6591i			1.48192i
$143$	−0.208076	−	3.34726i	−0.0174002	−	0.279912i
$144$	14.7596	+	1.20044i	1.22997	+	0.100037i
$145$	0.577988	−	2.15708i	0.0479993	−	0.179136i
$146$	−15.3003	+	8.83363i	−1.26626	+	0.731076i
$147$	−1.46363	−	0.926162i	−0.120719	−	0.0763885i
$148$	3.88979	+	3.88979i	0.319739	+	0.319739i
$149$	0.769833	+	2.87306i	0.0630672	+	0.235370i	0.990263	−	0.139206i	$-0.0444550\pi$
$149$	0.769833	+	2.87306i	0.0630672	+	0.235370i	−0.927196	+	0.374576i	$0.877788\pi$
$150$	14.0034	−	3.14940i	1.14337	−	0.257148i
$151$	−4.46400	+	4.46400i	−0.363275	+	0.363275i	−0.865017	−	0.501742i	$-0.832693\pi$
$151$	−4.46400	+	4.46400i	−0.363275	+	0.363275i	0.501742	+	0.865017i	$0.332693\pi$
$152$	0.158564	+	0.0915469i	0.0128612	+	0.00742543i
$153$	−9.77421	−	20.6307i	−0.790198	−	1.66789i
$154$	−1.62041	−	0.434188i	−0.130576	−	0.0349878i
$155$	2.03654			0.163579
$156$	2.18689	+	7.51157i	0.175091	+	0.601407i
$157$	18.7594			1.49716			0.748581	−	0.663043i	$-0.230736\pi$
$157$	18.7594			1.49716			0.748581	+	0.663043i	$0.230736\pi$
$158$	18.9906	+	5.08852i	1.51081	+	0.404821i
$159$	17.8256	−	9.34879i	1.41366	−	0.741407i
$160$	3.42201	+	1.97570i	0.270533	+	0.156193i
$161$	−4.78557	+	4.78557i	−0.377156	+	0.377156i
$162$	1.61225	+	16.1516i	0.126671	+	1.26899i
$163$	0.0202506	+	0.0755764i	0.00158615	+	0.00591960i	0.966714	−	0.255858i	$-0.0823580\pi$
$163$	0.0202506	+	0.0755764i	0.00158615	+	0.00591960i	−0.965128	+	0.261778i	$0.915691\pi$
$164$	4.17576	+	4.17576i	0.326072	+	0.326072i
$165$	0.548409	−	0.866662i	0.0426935	−	0.0674696i
$166$	−20.3719	+	11.7617i	−1.58117	+	0.912888i
$167$	−0.595716	+	2.22324i	−0.0460979	+	0.172040i	−0.985137	−	0.171771i	$-0.945051\pi$
$167$	−0.595716	+	2.22324i	−0.0460979	+	0.172040i	0.939039	+	0.343810i	$0.111718\pi$
$168$	−2.33235	−	0.0946921i	−0.179944	−	0.00730565i
$169$	10.3666	−	7.84428i	0.797434	−	0.603406i
$170$		−	8.73679i		−	0.670082i
$171$	−0.137055	+	0.383838i	−0.0104808	+	0.0293528i
$172$	−5.74264	−	9.94654i	−0.437872	−	0.758417i
$173$	7.84942	−	13.5956i	0.596781	−	1.03365i	−0.396512	−	0.918029i	$-0.629780\pi$
$173$	7.84942	−	13.5956i	0.596781	−	1.03365i	0.993293	−	0.115625i	$-0.0368871\pi$
$174$	−7.42805	−	8.05672i	−0.563119	−	0.610778i
$175$	−4.43819	+	1.18921i	−0.335495	+	0.0898957i
$176$	−4.43491	+	1.18833i	−0.334294	+	0.0895738i
$177$	−11.1096	−	12.0499i	−0.835049	−	0.905723i
$178$	−8.95856	+	15.5167i	−0.671473	+	1.16302i
$179$	0.992395	+	1.71888i	0.0741751	+	0.128475i	0.900727	−	0.434385i	$-0.143034\pi$
$179$	0.992395	+	1.71888i	0.0741751	+	0.128475i	−0.826552	+	0.562860i	$0.809701\pi$
$180$	−0.804520	+	2.25315i	−0.0599654	+	0.167940i
$181$		−	9.35848i		−	0.695610i	−0.937567	−	0.347805i	$-0.886927\pi$
$181$		−	9.35848i		−	0.695610i	0.937567	−	0.347805i	$-0.113073\pi$
$182$	−2.06950	−	6.16465i	−0.153401	−	0.456955i
$183$	−5.89576	−	0.239365i	−0.435827	−	0.0176944i
$184$	−2.36067	+	8.81013i	−0.174031	+	0.649491i
$185$	2.42085	−	1.39768i	0.177984	−	0.102759i
$186$	5.34373	−	8.44481i	0.391821	−	0.619204i
$187$	5.00502	+	5.00502i	0.366003	+	0.366003i
$188$	1.25103	+	4.66889i	0.0912404	+	0.340514i
$189$	−0.725436	−	5.14526i	−0.0527677	−	0.374263i
$190$	−0.110295	+	0.110295i	−0.00800164	+	0.00800164i
$191$	4.25676	+	2.45764i	0.308008	+	0.177828i	0.646035	−	0.763308i	$-0.276426\pi$
$191$	4.25676	+	2.45764i	0.308008	+	0.177828i	−0.338027	+	0.941137i	$0.609759\pi$
$192$	2.02859	−	1.06391i	0.146401	−	0.0767810i
$193$	−6.76081	−	1.81155i	−0.486654	−	0.130398i	0.00714545	−	0.999974i	$-0.497726\pi$
$193$	−6.76081	−	1.81155i	−0.486654	−	0.130398i	−0.493799	+	0.869576i	$0.664392\pi$
$194$	−19.4768			−1.39836
$195$	3.97460	−	0.0854911i	0.284627	−	0.00612214i
$196$	−1.25275			−0.0894823
$197$	−11.8240	−	3.16823i	−0.842425	−	0.225727i	−0.188298	−	0.982112i	$-0.560297\pi$
$197$	−11.8240	−	3.16823i	−0.842425	−	0.225727i	−0.654127	+	0.756385i	$0.726964\pi$
$198$	−2.15476	−	4.54811i	−0.153132	−	0.323220i
$199$	5.41039	+	3.12369i	0.383533	+	0.221433i	0.679354	−	0.733811i	$-0.262260\pi$
$199$	5.41039	+	3.12369i	0.383533	+	0.221433i	−0.295822	+	0.955243i	$0.595593\pi$
$200$	−4.37862	+	4.37862i	−0.309615	+	0.309615i
$201$	11.2750	−	2.53578i	0.795275	−	0.178860i
$202$	2.45443	+	9.16007i	0.172693	+	0.644500i
$203$	2.48054	+	2.48054i	0.174100	+	0.174100i
$204$	−13.9528	−	8.82911i	−0.976894	−	0.618161i
$205$	2.59883	−	1.50044i	0.181510	−	0.104795i
$206$	0.287661	−	1.07356i	0.0200423	−	0.0747988i
$207$	−20.2366	−	1.64591i	−1.40654	−	0.114398i
$208$	−13.3412	−	11.7796i	−0.925048	−	0.816771i
$209$		−	0.126369i		−	0.00874110i
$210$	0.592185	−	1.89838i	0.0408647	−	0.131001i
$211$	−3.34169	−	5.78797i	−0.230051	−	0.398461i	0.727772	−	0.685820i	$-0.240556\pi$
$211$	−3.34169	−	5.78797i	−0.230051	−	0.398461i	−0.957823	+	0.287359i	$0.907223\pi$
$212$	7.27921	−	12.6080i	0.499938	−	0.865918i
$213$	12.4685	−	11.4956i	0.854328	−	0.787664i
$214$	−10.2248	+	2.73972i	−0.698951	+	0.187283i
$215$	−5.63744	+	1.51055i	−0.384470	+	0.103018i
$216$	−4.31379	−	5.51638i	−0.293516	−	0.375342i
$217$	−1.59957	+	2.77053i	−0.108586	+	0.188076i
$218$	7.63292	+	13.2206i	0.516967	+	0.895413i
$219$	16.1972	+	5.05259i	1.09451	+	0.341423i
$220$		−	0.741793i		−	0.0500117i
$221$	−5.44326	+	26.8916i	−0.366153	+	1.80893i
$222$	0.556448	−	13.7058i	0.0373464	−	0.919873i
$223$	−3.89176	+	14.5243i	−0.260612	+	0.972617i	0.704270	+	0.709932i	$0.251274\pi$
$223$	−3.89176	+	14.5243i	−0.260612	+	0.972617i	−0.964882	+	0.262684i	$0.915392\pi$
$224$	−5.37550	+	3.10355i	−0.359166	+	0.207365i
$225$	−11.3395	−	7.83716i	−0.755967	−	0.522477i
$226$	−17.3835	−	17.3835i	−1.15633	−	1.15633i
$227$	−6.80091	−	25.3813i	−0.451392	−	1.68462i	−0.698484	−	0.715626i	$-0.746141\pi$
$227$	−6.80091	−	25.3813i	−0.451392	−	1.68462i	0.247092	−	0.968992i	$-0.420525\pi$
$228$	0.0646830	+	0.287604i	0.00428373	+	0.0190470i
$229$	8.56699	−	8.56699i	0.566123	−	0.566123i	−0.364917	−	0.931040i	$-0.618903\pi$
$229$	8.56699	−	8.56699i	0.566123	−	0.566123i	0.931040	+	0.364917i	$0.118903\pi$
$230$	−6.72924	−	3.88513i	−0.443713	−	0.256178i
$231$	0.748276	+	1.42676i	0.0492330	+	0.0938741i
$232$	4.56662	+	1.22362i	0.299813	+	0.0803348i
$233$	11.1310			0.729217			0.364608	−	0.931161i	$-0.381203\pi$
$233$	11.1310			0.729217			0.364608	+	0.931161i	$0.381203\pi$
$234$	10.0745	−	16.7056i	0.658593	−	1.09208i
$235$	2.45621			0.160226
$236$	−11.4504	−	3.06812i	−0.745355	−	0.199717i
$237$	−8.76952	−	16.7211i	−0.569642	−	1.08615i
$238$	11.8856	+	6.86215i	0.770429	+	0.444807i
$239$	−9.14781	+	9.14781i	−0.591723	+	0.591723i	−0.938097	−	0.346374i	$-0.887413\pi$
$239$	−9.14781	+	9.14781i	−0.591723	+	0.591723i	0.346374	+	0.938097i	$0.387413\pi$
$240$	−1.19423	−	5.30998i	−0.0770873	−	0.342758i
$241$	−3.96253	−	14.7884i	−0.255249	−	0.952602i	−0.967952	−	0.251136i	$-0.919196\pi$
$241$	−3.96253	−	14.7884i	−0.255249	−	0.952602i	0.712703	−	0.701466i	$-0.247471\pi$
$242$	−12.9249	−	12.9249i	−0.830842	−	0.830842i
$243$	10.3546	−	11.6526i	0.664246	−	0.747514i
$244$	−3.69600	+	2.13389i	−0.236612	+	0.136608i
$245$	−0.164762	+	0.614901i	−0.0105263	+	0.0392846i
$246$	0.597358	−	14.7134i	0.0380862	−	0.938094i
$247$	0.408202	−	0.270768i	0.0259733	−	0.0172286i
$248$			4.31144i			0.273777i
$249$	21.5661	+	6.72739i	1.36670	+	0.426331i
$250$	−5.50796	−	9.54007i	−0.348354	−	0.603367i
$251$	−13.5100	+	23.4001i	−0.852746	+	1.47700i	0.0259742	+	0.999663i	$0.491731\pi$
$251$	−13.5100	+	23.4001i	−0.852746	+	1.47700i	−0.878720	+	0.477337i	$0.841602\pi$
$252$	−2.43331	−	2.86417i	−0.153284	−	0.180426i
$253$	6.08062	−	1.62930i	0.382285	−	0.102433i
$254$	11.9047	−	3.18986i	0.746969	−	0.200150i
$255$	−6.16876	+	5.68741i	−0.386303	+	0.356159i
$256$	−10.3664	+	17.9550i	−0.647897	+	1.12219i
$257$	13.1644	+	22.8015i	0.821174	+	1.42232i	0.904808	+	0.425819i	$0.140014\pi$
$257$	13.1644	+	22.8015i	0.821174	+	1.42232i	−0.0836338	+	0.996497i	$0.526653\pi$
$258$	−8.52849	+	27.3400i	−0.530961	+	1.70211i
$259$			4.39112i			0.272851i
$260$	2.39617	−	1.58943i	0.148604	−	0.0985722i
$261$	−0.853135	+	10.4894i	−0.0528077	+	0.649278i
$262$	0.0687749	−	0.256671i	0.00424893	−	0.0158572i
$263$	−3.05784	+	1.76545i	−0.188555	+	0.108862i	−0.591306	−	0.806447i	$-0.701387\pi$
$263$	−3.05784	+	1.76545i	−0.188555	+	0.108862i	0.402751	+	0.915310i	$0.368054\pi$
$264$	1.83476	+	1.16100i	0.112921	+	0.0714547i
$265$	−5.23113	−	5.23113i	−0.321346	−	0.321346i
$266$	−0.0634169	−	0.236675i	−0.00388834	−	0.0145115i
$267$	16.7876	−	3.77558i	1.02738	−	0.231062i
$268$	5.91044	−	5.91044i	0.361038	−	0.361038i
$269$	−4.05776	−	2.34275i	−0.247406	−	0.142840i	0.371170	−	0.928565i	$-0.378957\pi$
$269$	−4.05776	−	2.34275i	−0.247406	−	0.142840i	−0.618576	+	0.785725i	$0.712290\pi$
$270$	5.49052	−	2.33345i	0.334143	−	0.142009i
$271$	−17.3574	−	4.65091i	−1.05439	−	0.282522i	−0.310324	−	0.950631i	$-0.600438\pi$
$271$	−17.3574	−	4.65091i	−1.05439	−	0.282522i	−0.744064	+	0.668108i	$0.767104\pi$
$272$	37.5621			2.27754
$273$	−3.00547	+	5.47422i	−0.181900	+	0.331315i
$274$	37.7042			2.27780
$275$	4.12821	+	1.10615i	0.248940	+	0.0667033i
$276$	−13.0050	+	6.82056i	−0.782808	+	0.410549i
$277$	−8.39267	−	4.84551i	−0.504267	−	0.291139i	0.226207	−	0.974079i	$-0.427367\pi$
$277$	−8.39267	−	4.84551i	−0.504267	−	0.291139i	−0.730474	+	0.682941i	$0.760701\pi$
$278$	11.6538	−	11.6538i	0.698948	−	0.698948i
$279$	−9.44123	+	1.72431i	−0.565231	+	0.103232i
$280$	0.222049	+	0.828697i	0.0132699	+	0.0495241i
$281$	−8.59588	−	8.59588i	−0.512787	−	0.512787i	0.402592	−	0.915379i	$-0.368109\pi$
$281$	−8.59588	−	8.59588i	−0.512787	−	0.512787i	−0.915379	+	0.402592i	$0.868109\pi$
$282$	6.44491	−	10.1850i	0.383789	−	0.606510i
$283$	7.23084	−	4.17473i	0.429829	−	0.248162i	−0.269445	−	0.963016i	$-0.586840\pi$
$283$	7.23084	−	4.17473i	0.429829	−	0.248162i	0.699274	+	0.714854i	$0.253507\pi$
$284$	3.17471	−	11.8482i	0.188385	−	0.703061i
$285$	0.149675	+	0.00607671i	0.00886596	+	0.000359954i
$286$	−1.19998	+	5.92835i	−0.0709565	+	0.350550i
$287$			4.71396i			0.278256i
$288$	−17.5369	−	6.26179i	−1.03337	−	0.368979i
$289$	−20.4534	−	35.4264i	−1.20314	−	2.08390i
$290$	−2.01381	+	3.48802i	−0.118255	+	0.204824i
$291$	12.6789	+	13.7520i	0.743249	+	0.806154i
$292$	11.8537	−	3.17618i	0.693683	−	0.185872i
$293$	13.3911	−	3.58812i	0.782314	−	0.209620i	0.154509	−	0.987991i	$-0.450620\pi$
$293$	13.3911	−	3.58812i	0.782314	−	0.209620i	0.627804	+	0.778371i	$0.283954\pi$
$294$	2.11745	+	2.29666i	0.123492	+	0.133944i
$295$	−3.01191	+	5.21678i	−0.175360	+	0.303733i
$296$	2.95894	+	5.12503i	0.171985	+	0.297886i
$297$	−1.80858	+	4.48209i	−0.104945	+	0.260077i
$298$		−	5.36446i		−	0.310755i
$299$	18.2919	+	16.1508i	1.05785	+	0.934027i
$300$	−9.96162	−	0.404437i	−0.575134	−	0.0233502i
$301$	2.37286	−	8.85564i	0.136770	−	0.510431i
$302$	9.86042	−	5.69292i	0.567403	−	0.327591i
$303$	4.86986	−	7.69595i	0.279766	−	0.442121i
$304$	−0.474192	−	0.474192i	−0.0271968	−	0.0271968i
$305$	0.561299	+	2.09480i	0.0321399	+	0.119948i
$306$	7.39730	+	40.5030i	0.422875	+	2.31540i
$307$	4.94256	−	4.94256i	0.282087	−	0.282087i	−0.551854	−	0.833941i	$-0.686079\pi$
$307$	4.94256	−	4.94256i	0.282087	−	0.282087i	0.833941	+	0.551854i	$0.186079\pi$
$308$	1.00914	+	0.582627i	0.0575011	+	0.0331983i
$309$	−0.945268	+	0.495753i	−0.0537744	+	0.0282024i
$310$	−3.54783	−	0.950639i	−0.201503	−	0.0539927i
$311$	25.4370			1.44240			0.721199	−	0.692728i	$-0.243591\pi$
$311$	25.4370			1.44240			0.721199	+	0.692728i	$0.243591\pi$
$312$	0.180988	+	8.41438i	0.0102464	+	0.476370i
$313$	19.6372			1.10996			0.554980	−	0.831864i	$-0.312726\pi$
$313$	19.6372			1.10996			0.554980	+	0.831864i	$0.312726\pi$
$314$	−32.6804	−	8.75670i	−1.84426	−	0.494169i
$315$	−1.72588	+	0.817671i	−0.0972424	+	0.0460705i
$316$	−11.8268	−	6.82818i	−0.665307	−	0.384115i
$317$	−23.9078	+	23.9078i	−1.34279	+	1.34279i	−0.449527	+	0.893267i	$0.648407\pi$
$317$	−23.9078	+	23.9078i	−1.34279	+	1.34279i	−0.893267	+	0.449527i	$0.851593\pi$
$318$	−35.4177	+	7.96555i	−1.98613	+	0.446686i
$319$	−0.844526	−	3.15181i	−0.0472844	−	0.176468i
$320$	−0.595312	−	0.595312i	−0.0332790	−	0.0332790i
$321$	8.59047	+	5.43590i	0.479473	+	0.303402i
$322$	10.5707	−	6.10301i	0.589083	−	0.340107i
$323$	−0.267574	+	0.998602i	−0.0148882	+	0.0555637i
$324$	1.82197	−	11.1266i	0.101221	−	0.618144i
$325$	5.27232	+	15.7053i	0.292456	+	0.871171i
$326$		−	0.141113i		−	0.00781554i
$327$	4.36582	−	13.9956i	0.241430	−	0.773959i
$328$	3.17648	+	5.50182i	0.175392	+	0.303787i
$329$	−1.92919	+	3.34145i	−0.106360	+	0.184220i
$330$	−1.35992	+	1.25381i	−0.0748613	+	0.0690198i
$331$	19.4906	−	5.22249i	1.07130	−	0.287054i	0.320272	−	0.947325i	$-0.396226\pi$
$331$	19.4906	−	5.22249i	1.07130	−	0.287054i	0.751027	+	0.660272i	$0.229559\pi$
$332$	15.7828	−	4.22900i	0.866195	−	0.232096i
$333$	−10.0394	+	8.52920i	−0.550158	+	0.467397i
$334$	2.07557	−	3.59500i	0.113570	−	0.196710i
$335$	−2.12374	−	3.67843i	−0.116032	−	0.200974i
$336$	8.16172	+	2.54599i	0.445258	+	0.138895i
$337$		−	24.8905i		−	1.35587i	−0.735120	−	0.677937i	$-0.762874\pi$
$337$		−	24.8905i		−	1.35587i	0.735120	−	0.677937i	$-0.237126\pi$
$338$	−21.7212	+	8.82635i	−1.18148	+	0.480090i
$339$	−0.957745	+	23.5901i	−0.0520176	+	1.28124i
$340$	−1.57068	+	5.86186i	−0.0851821	+	0.317904i
$341$	2.57702	−	1.48785i	0.139554	−	0.0805714i
$342$	0.417932	−	0.604702i	0.0225992	−	0.0326985i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−3.19788	−	11.9347i	−0.172418	−	0.643474i
$345$	1.63739	+	7.28041i	0.0881539	+	0.391964i
$346$	−20.0207	+	20.0207i	−1.07632	+	1.07632i
$347$	−19.0431	−	10.9946i	−1.02229	−	0.590219i	−0.107523	−	0.994203i	$-0.534292\pi$
$347$	−19.0431	−	10.9946i	−1.02229	−	0.590219i	−0.914766	+	0.403983i	$0.867625\pi$
$348$	3.53535	+	6.74097i	0.189515	+	0.361354i
$349$	−0.734172	−	0.196721i	−0.0392993	−	0.0105302i	0.239116	−	0.970991i	$-0.423142\pi$
$349$	−0.734172	−	0.196721i	−0.0392993	−	0.0105302i	−0.278415	+	0.960461i	$0.589809\pi$
$350$	8.28681			0.442949
$351$	−18.3535	+	3.76156i	−0.979637	+	0.200777i
$352$	5.77357			0.307732
$353$	−15.9289	−	4.26815i	−0.847812	−	0.227171i	−0.191343	−	0.981523i	$-0.561284\pi$
$353$	−15.9289	−	4.26815i	−0.847812	−	0.227171i	−0.656469	+	0.754353i	$0.727951\pi$
$354$	13.7291	+	26.1777i	0.729694	+	1.39133i
$355$	−5.39803	−	3.11655i	−0.286498	−	0.165410i
$356$	8.80021	−	8.80021i	0.466410	−	0.466410i
$357$	−2.89205	−	12.8591i	−0.153064	−	0.680576i
$358$	−0.926481	−	3.45767i	−0.0489660	−	0.182744i
$359$	−15.4150	−	15.4150i	−0.813571	−	0.813571i	0.171596	−	0.985167i	$-0.445108\pi$
$359$	−15.4150	−	15.4150i	−0.813571	−	0.813571i	−0.985167	+	0.171596i	$0.945108\pi$
$360$	−1.46335	+	2.11731i	−0.0771254	+	0.111592i
$361$	−16.4385	+	9.49077i	−0.865184	+	0.499514i
$362$	−4.36845	+	16.3033i	−0.229600	+	0.856880i
$363$	−0.712097	+	17.5396i	−0.0373754	+	0.920588i
$364$	0.280241	+	4.50816i	0.0146886	+	0.236292i
$365$		−	6.23599i		−	0.326407i
$366$	10.1592	+	3.16908i	0.531029	+	0.165650i
$367$	8.92113	+	15.4518i	0.465679	+	0.806580i	0.999232	−	0.0391869i	$-0.0124768\pi$
$367$	8.92113	+	15.4518i	0.465679	+	0.806580i	−0.533553	+	0.845767i	$0.679143\pi$
$368$	16.7034	−	28.9311i	0.870723	−	1.50814i
$369$	−10.7775	+	9.15626i	−0.561056	+	0.476656i
$370$	−4.86975	+	1.30485i	−0.253166	+	0.0678357i
$371$	11.2252	−	3.00777i	0.582781	−	0.156156i
$372$	−5.10351	+	4.70528i	−0.264605	+	0.243957i
$373$	−2.89560	+	5.01533i	−0.149929	+	0.259684i	−0.931201	−	0.364506i	$-0.881238\pi$
$373$	−2.89560	+	5.01533i	−0.149929	+	0.259684i	0.781272	+	0.624190i	$0.214571\pi$
$374$	−6.38287	−	11.0555i	−0.330051	−	0.571664i
$375$	−3.15040	+	10.0993i	−0.162686	+	0.521526i
$376$			5.19990i			0.268164i
$377$	8.37158	−	9.48138i	0.431159	−	0.488316i
$378$	−1.13799	+	9.30211i	−0.0585318	+	0.478449i
$379$	−0.747312	+	2.78901i	−0.0383868	+	0.143262i	−0.982460	−	0.186476i	$-0.940293\pi$
$379$	−0.747312	+	2.78901i	−0.0383868	+	0.143262i	0.944073	+	0.329737i	$0.106960\pi$
$380$	0.0938299	−	0.0541727i	0.00481337	−	0.00277900i
$381$	−10.0019	−	6.32902i	−0.512413	−	0.324246i
$382$	−6.26843	−	6.26843i	−0.320721	−	0.320721i
$383$	−0.921556	−	3.43930i	−0.0470893	−	0.175740i	0.938376	−	0.345616i	$-0.112330\pi$
$383$	−0.921556	−	3.43930i	−0.0470893	−	0.175740i	−0.985465	+	0.169876i	$0.945663\pi$
$384$	16.9474	−	3.81153i	0.864844	−	0.194506i
$385$	0.418699	−	0.418699i	0.0213389	−	0.0213389i
$386$	10.9323	+	6.31176i	0.556439	+	0.321260i
$387$	24.8557	−	11.7759i	1.26349	−	0.598602i
$388$	13.0678	+	3.50150i	0.663416	+	0.177762i
$389$	5.60043			0.283953			0.141977	−	0.989870i	$-0.454654\pi$
$389$	5.60043			0.283953			0.141977	+	0.989870i	$0.454654\pi$
$390$	−6.96400	−	1.70637i	−0.352636	−	0.0864055i
$391$	−51.5007			−2.60450
$392$	−1.30177	−	0.348808i	−0.0657493	−	0.0176175i
$393$	−0.225998	+	0.118526i	−0.0114001	+	0.00597886i
$394$	19.1195	+	11.0387i	0.963227	+	0.556119i
$395$	−4.90700	+	4.90700i	−0.246898	+	0.246898i
$396$	0.628063	+	3.43888i	0.0315614	+	0.172810i
$397$	5.29273	+	19.7527i	0.265635	+	0.991362i	0.961861	+	0.273539i	$0.0881944\pi$
$397$	5.29273	+	19.7527i	0.265635	+	0.991362i	−0.696226	+	0.717822i	$0.745139\pi$
$398$	−7.96725	−	7.96725i	−0.399362	−	0.399362i
$399$	−0.125826	+	0.198846i	−0.00629918	+	0.00995473i
$400$	19.6416	−	11.3401i	0.982082	−	0.567005i
$401$	3.31401	−	12.3680i	0.165494	−	0.617631i	−0.832483	−	0.554050i	$-0.813081\pi$
$401$	3.31401	−	12.3680i	0.165494	−	0.617631i	0.997977	−	0.0635803i	$-0.0202519\pi$
$402$	−20.8256	−	0.845510i	−1.03869	−	0.0421702i
$403$	10.3279	+	5.13644i	0.514468	+	0.255864i
$404$		−	6.58711i		−	0.327721i
$405$	−5.22175	−	2.35767i	−0.259471	−	0.117153i
$406$	−3.16342	−	5.47920i	−0.156998	−	0.271928i
$407$	2.04221	−	3.53722i	0.101229	−	0.175333i
$408$	−12.0405	−	13.0595i	−0.596091	−	0.646542i
$409$	35.0834	−	9.40056i	1.73476	−	0.464828i	0.753490	−	0.657460i	$-0.228369\pi$
$409$	35.0834	−	9.40056i	1.73476	−	0.464828i	0.981271	+	0.192632i	$0.0617024\pi$
$410$	−5.22777	+	1.40078i	−0.258181	+	0.0691794i
$411$	−24.5444	−	26.6217i	−1.21069	−	1.31315i
$412$	−0.386006	+	0.668582i	−0.0190172	+	0.0329387i
$413$	−4.73130	−	8.19485i	−0.232812	−	0.403242i
$414$	34.4856	+	12.3136i	1.69488	+	0.605179i
$415$		−	8.30305i		−	0.407581i
$416$	12.3709	+	18.6500i	0.606536	+	0.914394i
$417$	−15.8147	−	0.642067i	−0.774447	−	0.0314422i
$418$	−0.0589876	+	0.220145i	−0.00288518	+	0.0107676i
$419$	−3.31821	+	1.91577i	−0.162105	+	0.0935914i	−0.578858	−	0.815428i	$-0.696501\pi$
$419$	−3.31821	+	1.91577i	−0.162105	+	0.0935914i	0.416753	+	0.909020i	$0.363168\pi$
$420$	−0.738607	+	1.16724i	−0.0360404	+	0.0569554i
$421$	24.1522	+	24.1522i	1.17711	+	1.17711i	0.980478	+	0.196627i	$0.0629988\pi$
$421$	24.1522	+	24.1522i	1.17711	+	1.17711i	0.196627	+	0.980478i	$0.437001\pi$
$422$	3.11973	+	11.6430i	0.151866	+	0.566773i
$423$	−11.3868	+	2.07964i	−0.553644	+	0.101115i
$424$	11.0745	−	11.0745i	0.537825	−	0.537825i
$425$	−30.2801	−	17.4822i	−1.46880	−	0.848013i
$426$	−27.0872	+	14.2061i	−1.31238	+	0.688288i
$427$	−3.29064	−	0.881724i	−0.159245	−	0.0426696i
$428$	7.35274			0.355408
$429$	4.96697	−	3.01192i	0.239807	−	0.145417i
$430$	10.5260			0.507609
$431$	32.2807	+	8.64960i	1.55491	+	0.416636i	0.931047	−	0.364899i	$-0.118896\pi$
$431$	32.2807	+	8.64960i	1.55491	+	0.416636i	0.623861	+	0.781535i	$0.285563\pi$
$432$	10.0322	+	23.6054i	0.482675	+	1.13572i
$433$	16.4371	+	9.48995i	0.789915	+	0.456058i	0.839933	−	0.542690i	$-0.182594\pi$
$433$	16.4371	+	9.48995i	0.789915	+	0.456058i	−0.0500173	+	0.998748i	$0.515928\pi$
$434$	4.07984	−	4.07984i	0.195838	−	0.195838i
$435$	3.77371	−	0.848719i	0.180936	−	0.0406930i
$436$	−2.74446	−	10.2425i	−0.131436	−	0.490525i
$437$	0.650155	+	0.650155i	0.0311011	+	0.0311011i
$438$	−25.8584	−	16.3627i	−1.23556	−	0.781842i
$439$	−23.2639	+	13.4314i	−1.11033	+	0.641048i	−0.938914	−	0.344151i	$-0.888167\pi$
$439$	−23.2639	+	13.4314i	−1.11033	+	0.641048i	−0.171413	+	0.985199i	$0.554833\pi$
$440$	0.206540	−	0.770817i	0.00984640	−	0.0367473i
$441$	0.243196	−	2.99013i	0.0115808	−	0.142387i
$442$	22.0354	−	44.3066i	1.04812	−	2.10745i
$443$			1.79124i			0.0851043i	0.999094	+	0.0425522i	$0.0135489\pi$
$443$			1.79124i			0.0851043i	−0.999094	+	0.0425522i	$0.986451\pi$
$444$	−2.83734	+	9.09572i	−0.134654	+	0.431664i
$445$	−3.16209	−	5.47690i	−0.149898	−	0.259630i
$446$	13.5596	−	23.4859i	0.642064	−	1.11209i
$447$	−3.78767	+	3.49211i	−0.179151	+	0.165171i
$448$	1.27744	−	0.342290i	0.0603536	−	0.0161717i
$449$	0.247439	−	0.0663010i	0.0116774	−	0.00312894i	−0.252976	−	0.967473i	$-0.581409\pi$
$449$	0.247439	−	0.0663010i	0.0116774	−	0.00312894i	0.264653	+	0.964344i	$0.414743\pi$
$450$	16.0961	+	18.9462i	0.758776	+	0.893131i
$451$	2.19236	−	3.79727i	0.103234	−	0.178807i
$452$	8.53810	+	14.7884i	0.401599	+	0.695589i
$453$	−10.4384	−	3.25619i	−0.490441	−	0.152989i
$454$			47.3910i			2.22417i
$455$	2.24964	+	0.455361i	0.105465	+	0.0213476i
$456$	−0.0128646	+	0.316867i	−0.000602441	+	0.0148386i
$457$	5.70496	−	21.2912i	0.266867	−	0.995961i	−0.694231	−	0.719752i	$-0.744255\pi$
$457$	5.70496	−	21.2912i	0.266867	−	0.995961i	0.961098	−	0.276208i	$-0.0890780\pi$
$458$	−18.9234	+	10.9254i	−0.884233	+	0.510512i
$459$	23.7824	−	31.5893i	1.11007	−	1.47446i
$460$	3.81646	+	3.81646i	0.177943	+	0.177943i
$461$	−9.12249	−	34.0456i	−0.424877	−	1.58566i	−0.764192	−	0.644988i	$-0.776862\pi$
$461$	−9.12249	−	34.0456i	−0.424877	−	1.58566i	0.339316	−	0.940673i	$-0.389804\pi$
$462$	−0.637562	−	2.83483i	−0.0296621	−	0.131888i
$463$	−27.9902	+	27.9902i	−1.30081	+	1.30081i	−0.372969	+	0.927844i	$0.621660\pi$
$463$	−27.9902	+	27.9902i	−1.30081	+	1.30081i	−0.927844	+	0.372969i	$0.878340\pi$
$464$	−14.9961	−	8.65798i	−0.696175	−	0.401937i
$465$	1.63833	+	3.12385i	0.0759755	+	0.144865i
$466$	−19.3912	−	5.19585i	−0.898278	−	0.240693i
$467$	−7.86393			−0.363899			−0.181950	−	0.983308i	$-0.558241\pi$
$467$	−7.86393			−0.363899			−0.181950	+	0.983308i	$0.558241\pi$
$468$	−9.76269	+	9.39725i	−0.451281	+	0.434388i
$469$	6.67221			0.308094
$470$	−4.27893	−	1.14654i	−0.197373	−	0.0528858i
$471$	15.0912	+	28.7750i	0.695368	+	1.32588i
$472$	−11.0441	−	6.37633i	−0.508347	−	0.293494i
$473$	−6.03000	+	6.03000i	−0.277260	+	0.277260i
$474$	7.47199	+	33.2232i	0.343200	+	1.52599i
$475$	0.161563	+	0.602961i	0.00741301	+	0.0276657i
$476$	−6.74086	−	6.74086i	−0.308967	−	0.308967i
$477$	28.6801	+	19.8219i	1.31317	+	0.907583i
$478$	20.2064	−	11.6662i	0.924218	−	0.533597i
$479$	−4.78641	+	17.8631i	−0.218697	+	0.816187i	0.766136	+	0.642679i	$0.222177\pi$
$479$	−4.78641	+	17.8631i	−0.218697	+	0.816187i	−0.984832	+	0.173508i	$0.944490\pi$
$480$	−0.277635	+	6.83838i	−0.0126722	+	0.312128i
$481$	15.8019	−	0.982297i	0.720505	−	0.0447889i
$482$			27.6123i			1.25770i
$483$	−11.1904	−	3.49075i	−0.509180	−	0.158835i
$484$	6.34820	+	10.9954i	0.288555	+	0.499791i
$485$	3.43736	−	5.95368i	0.156082	−	0.270343i
$486$	−23.4779	+	15.4664i	−1.06498	+	0.701569i
$487$	−7.80656	+	2.09176i	−0.353749	+	0.0947868i	−0.431317	−	0.902200i	$-0.641951\pi$
$487$	−7.80656	+	2.09176i	−0.353749	+	0.0947868i	0.0775683	+	0.996987i	$0.475284\pi$
$488$	−4.43476	+	1.18829i	−0.200752	+	0.0537914i
$489$	−0.0996355	+	0.0918608i	−0.00450567	+	0.00415409i
$490$	0.574060	−	0.994301i	0.0259334	−	0.0449179i
$491$	−8.20416	−	14.2100i	−0.370248	−	0.641289i	0.619355	−	0.785111i	$-0.287394\pi$
$491$	−8.20416	−	14.2100i	−0.370248	−	0.641289i	−0.989604	+	0.143822i	$0.954061\pi$
$492$	−3.04594	+	9.76444i	−0.137322	+	0.440215i
$493$			26.6948i			1.20227i
$494$	−0.837514	+	0.281157i	−0.0376815	+	0.0126498i
$495$	1.77055	+	0.144004i	0.0795801	+	0.00647249i
$496$	4.08709	−	15.2532i	0.183516	−	0.684889i
$497$	8.47957	−	4.89568i	0.380361	−	0.219601i
$498$	−34.4298	−	21.7865i	−1.54283	−	0.976278i
$499$	13.5411	+	13.5411i	0.606182	+	0.606182i	0.941946	−	0.335764i	$-0.108995\pi$
$499$	13.5411	+	13.5411i	0.606182	+	0.606182i	−0.335764	+	0.941946i	$0.608995\pi$
$500$	1.98042	+	7.39102i	0.0885670	+	0.330536i
$501$	−3.88945	+	0.874750i	−0.173768	+	0.0390810i
$502$	34.4586	−	34.4586i	1.53796	−	1.53796i
$503$	26.2220	+	15.1393i	1.16918	+	0.675027i	0.953487	−	0.301433i	$-0.0974651\pi$
$503$	26.2220	+	15.1393i	1.16918	+	0.675027i	0.215695	+	0.976461i	$0.430798\pi$
$504$	−1.73104	−	3.65375i	−0.0771066	−	0.162751i
$505$	−3.23322	−	0.866338i	−0.143876	−	0.0385515i
$506$	−11.3535			−0.504725
$507$	20.3719	+	9.59093i	0.904748	+	0.425948i
$508$	−8.56082			−0.379825
$509$	23.9782	+	6.42494i	1.06281	+	0.284780i	0.747538	−	0.664219i	$-0.231236\pi$
$509$	23.9782	+	6.42494i	1.06281	+	0.284780i	0.315277	+	0.949000i	$0.397903\pi$
$510$	13.4013	−	7.02843i	0.593421	−	0.311224i
$511$	8.48349	+	4.89794i	0.375287	+	0.216672i
$512$	12.2572	−	12.2572i	0.541695	−	0.541695i
$513$	−0.699023	+	0.0985559i	−0.0308626	+	0.00435135i
$514$	−12.2901	−	45.8671i	−0.542091	−	2.02311i
$515$	0.277400	+	0.277400i	0.0122237	+	0.0122237i
$516$	10.6372	−	16.8102i	0.468278	−	0.740030i
$517$	3.10807	−	1.79445i	0.136693	−	0.0789197i
$518$	2.04973	−	7.64971i	0.0900601	−	0.336109i
$519$	27.1688	+	1.10304i	1.19258	+	0.0484181i
$520$	2.93248	−	0.984445i	0.128598	−	0.0431708i
$521$			30.1280i			1.31993i	0.751295	+	0.659967i	$0.229430\pi$
$521$			30.1280i			1.31993i	−0.751295	+	0.659967i	$0.770570\pi$
$522$	6.38258	−	17.8752i	0.279358	−	0.782376i
$523$	−0.924324	−	1.60098i	−0.0404179	−	0.0700058i	0.845109	−	0.534594i	$-0.179536\pi$
$523$	−0.924324	−	1.60098i	−0.0404179	−	0.0700058i	−0.885527	+	0.464589i	$0.846202\pi$
$524$	−0.0922876	+	0.159847i	−0.00403160	+	0.00698294i
$525$	−5.39448	−	5.85105i	−0.235435	−	0.255361i
$526$	6.15112	−	1.64819i	0.268201	−	0.0718643i
$527$	−23.5148	+	6.30076i	−1.02432	+	0.274466i
$528$	−5.39050	−	5.84673i	−0.234591	−	0.254446i
$529$	−11.4017	+	19.7482i	−0.495724	+	0.858619i
$530$	6.67123	+	11.5549i	0.289780	+	0.501913i
$531$	9.54597	−	26.7346i	0.414260	−	1.16018i
$532$			0.170196i			0.00737892i
$533$	16.9637	−	1.05451i	0.734778	−	0.0456761i
$534$	−31.0078	−	1.25890i	−1.34184	−	0.0544780i
$535$	0.967035	−	3.60902i	0.0418086	−	0.156032i
$536$	7.78736	−	4.49604i	0.336363	−	0.194199i
$537$	−1.83824	+	2.90501i	−0.0793258	+	0.125360i
$538$	5.97539	+	5.97539i	0.257617	+	0.257617i
$539$	0.240742	+	0.898462i	0.0103695	+	0.0386995i
$540$	−4.10331	+	0.578530i	−0.176578	+	0.0248960i
$541$	−0.715390	+	0.715390i	−0.0307570	+	0.0307570i	−0.722318	−	0.691561i	$-0.756923\pi$
$541$	−0.715390	+	0.715390i	−0.0307570	+	0.0307570i	0.691561	+	0.722318i	$0.256923\pi$
$542$	28.0671	+	16.2045i	1.20558	+	0.696045i
$543$	14.3549	−	7.52855i	0.616029	−	0.323081i
$544$	−45.6244	−	12.2250i	−1.95613	−	0.524144i
$545$	−5.38837			−0.230812
$546$	7.79110	−	8.13364i	0.333428	−	0.348087i
$547$	−10.4689			−0.447620			−0.223810	−	0.974633i	$-0.571849\pi$
$547$	−10.4689			−0.447620			−0.223810	+	0.974633i	$0.571849\pi$
$548$	−25.2973	−	6.77838i	−1.08065	−	0.289558i
$549$	−4.37576	−	9.23604i	−0.186753	−	0.394185i
$550$	−6.67535	−	3.85401i	−0.284638	−	0.164336i
$551$	0.337000	−	0.337000i	0.0143567	−	0.0143567i
$552$	−15.4129	+	3.46641i	−0.656017	+	0.147540i
$553$	−2.82141	−	10.5296i	−0.119978	−	0.447766i
$554$	12.3589	+	12.3589i	0.525080	+	0.525080i
$555$	4.09138	+	2.58895i	0.173669	+	0.109895i
$556$	−9.91408	+	5.72390i	−0.420451	+	0.242747i
$557$	6.12406	−	22.8553i	0.259485	−	0.968411i	−0.706055	−	0.708157i	$-0.749527\pi$
$557$	6.12406	−	22.8553i	0.259485	−	0.968411i	0.965540	−	0.260254i	$-0.0838063\pi$
$558$	17.2523	+	1.40318i	0.730348	+	0.0594015i
$559$	−32.3988	−	6.55798i	−1.37032	−	0.277373i
$560$		−	3.14230i		−	0.132786i
$561$	−3.65083	+	11.7035i	−0.154138	+	0.494124i
$562$	10.9623	+	18.9872i	0.462416	+	0.800928i
$563$	−16.2577	+	28.1591i	−0.685179	+	1.18677i	0.288201	+	0.957570i	$0.406943\pi$
$563$	−16.2577	+	28.1591i	−0.685179	+	1.18677i	−0.973380	+	0.229196i	$0.926390\pi$
$564$	−6.15519	+	5.67489i	−0.259180	+	0.238956i
$565$	8.38169	−	2.24587i	0.352620	−	0.0944844i
$566$	−14.5455	+	3.89744i	−0.611391	+	0.163822i
$567$	7.30872	−	5.25192i	0.306937	−	0.220560i
$568$	6.59786	−	11.4278i	0.276840	−	0.479501i
$569$	3.52491	+	6.10532i	0.147772	+	0.255948i	0.930404	−	0.366537i	$-0.119457\pi$
$569$	3.52491	+	6.10532i	0.147772	+	0.255948i	−0.782632	+	0.622485i	$0.786123\pi$
$570$	−0.257909	−	0.0804528i	−0.0108026	−	0.00336980i
$571$		−	28.9967i		−	1.21347i	−0.794903	−	0.606737i	$-0.792478\pi$
$571$		−	28.9967i		−	1.21347i	0.794903	−	0.606737i	$-0.207522\pi$
$572$	1.87090	−	3.76183i	0.0782263	−	0.157290i
$573$	−0.345360	+	8.50650i	−0.0144276	+	0.355364i
$574$	2.20043	−	8.21211i	0.0918441	−	0.342767i
$575$	−26.9303	+	15.5482i	−1.12307	+	0.648405i
$576$	3.26385	+	2.25577i	0.135994	+	0.0939904i
$577$	−0.680386	−	0.680386i	−0.0283248	−	0.0283248i	0.692803	−	0.721127i	$-0.256376\pi$
$577$	−0.680386	−	0.680386i	−0.0283248	−	0.0283248i	−0.721127	+	0.692803i	$0.756376\pi$
$578$	19.0949	+	71.2632i	0.794244	+	2.96416i
$579$	−2.66009	−	11.8277i	−0.110549	−	0.491543i
$580$	1.97821	−	1.97821i	0.0821408	−	0.0821408i
$581$	11.2955	+	6.52148i	0.468617	+	0.270556i
$582$	−15.6684	−	29.8755i	−0.649476	−	1.23838i
$583$	−10.4412	−	2.79770i	−0.432428	−	0.115869i
$584$	13.2018			0.546295
$585$	3.32856	+	6.02785i	0.137619	+	0.249221i
$586$	−25.0032			−1.03287
$587$	−13.5401	−	3.62807i	−0.558862	−	0.149747i	−0.0316784	−	0.999498i	$-0.510085\pi$
$587$	−13.5401	−	3.62807i	−0.558862	−	0.149747i	−0.527183	+	0.849752i	$0.676752\pi$
$588$	−1.00779	−	1.92159i	−0.0415607	−	0.0792451i
$589$	0.376397	+	0.217313i	0.0155092	+	0.00895423i
$590$	7.68215	−	7.68215i	0.316269	−	0.316269i
$591$	−4.65224	−	20.6855i	−0.191367	−	0.850888i
$592$	−5.60993	−	20.9365i	−0.230567	−	0.860486i
$593$	21.5424	+	21.5424i	0.884642	+	0.884642i	0.994002	−	0.109361i	$-0.0348803\pi$
$593$	21.5424	+	21.5424i	0.884642	+	0.884642i	−0.109361	+	0.994002i	$0.534880\pi$
$594$	5.24290	−	6.96396i	0.215119	−	0.285735i
$595$	−4.19524	+	2.42213i	−0.171988	+	0.0992975i
$596$	−0.964411	+	3.59923i	−0.0395038	+	0.147430i
$597$	−0.438957	+	10.8119i	−0.0179653	+	0.442501i
$598$	−24.3270	−	36.6746i	−0.994805	−	1.49974i
$599$		−	44.6613i		−	1.82481i	−0.409286	−	0.912406i	$-0.634222\pi$
$599$		−	44.6613i		−	1.82481i	0.409286	−	0.912406i	$-0.365778\pi$
$600$	−10.2388	−	3.19391i	−0.417997	−	0.130391i
$601$	4.23723	+	7.33910i	0.172840	+	0.299368i	0.939412	−	0.342791i	$-0.111372\pi$
$601$	4.23723	+	7.33910i	0.172840	+	0.299368i	−0.766572	+	0.642159i	$0.778039\pi$
$602$	−8.26746	+	14.3197i	−0.336956	+	0.583626i
$603$	12.9599	+	15.2547i	0.527769	+	0.621219i
$604$	−7.63921	+	2.04692i	−0.310835	+	0.0832880i
$605$	6.23191	−	1.66983i	0.253363	−	0.0678884i
$606$	−12.0761	+	11.1338i	−0.490558	+	0.452279i
$607$	14.0522	−	24.3392i	0.570362	−	0.987896i	−0.426167	−	0.904645i	$-0.640136\pi$
$607$	14.0522	−	24.3392i	0.570362	−	0.987896i	0.996529	−	0.0832510i	$-0.0265303\pi$
$608$	0.421640	+	0.730302i	0.0170998	+	0.0296177i
$609$	−1.80939	+	5.80039i	−0.0733201	+	0.235044i
$610$		−	3.91132i		−	0.158365i
$611$	12.4561	+	6.19490i	0.503921	+	0.250619i
$612$	2.31839	−	28.5049i	0.0937154	−	1.15224i
$613$	−9.61633	+	35.8886i	−0.388400	+	1.44953i	0.444337	+	0.895859i	$0.353439\pi$
$613$	−9.61633	+	35.8886i	−0.388400	+	1.44953i	−0.832737	+	0.553668i	$0.813228\pi$
$614$	−10.9175	+	6.30321i	−0.440594	+	0.254377i
$615$	4.39218	+	2.77929i	0.177110	+	0.112072i
$616$	0.886402	+	0.886402i	0.0357142	+	0.0357142i
$617$	−6.00728	−	22.4195i	−0.241844	−	0.902573i	−0.974944	−	0.222452i	$-0.928594\pi$
$617$	−6.00728	−	22.4195i	−0.241844	−	0.902573i	0.733100	−	0.680121i	$-0.238073\pi$
$618$	1.87815	−	0.422402i	0.0755503	−	0.0169915i
$619$	−29.6031	+	29.6031i	−1.18985	+	1.18985i	−0.212740	+	0.977109i	$0.568239\pi$
$619$	−29.6031	+	29.6031i	−1.18985	+	1.18985i	−0.977109	+	0.212740i	$0.931761\pi$
$620$	2.20948	+	1.27564i	0.0887348	+	0.0512310i
$621$	−13.7550	−	32.3650i	−0.551968	−	1.29876i
$622$	−44.3133	−	11.8737i	−1.77680	−	0.476093i
$623$	9.93443			0.398014
$624$	7.33621	−	29.9403i	0.293684	−	1.19857i
$625$	−19.0855			−0.763419
$626$	−34.2096	−	9.16645i	−1.36729	−	0.366365i
$627$	0.193836	−	0.101659i	0.00774108	−	0.00405987i
$628$	20.3523	+	11.7504i	0.812147	+	0.468893i
$629$	−23.6279	+	23.6279i	−0.942107	+	0.942107i
$630$	3.38831	−	0.618828i	0.134994	−	0.0246547i
$631$	−8.46555	−	31.5938i	−0.337008	−	1.25773i	−0.901676	−	0.432413i	$-0.857662\pi$
$631$	−8.46555	−	31.5938i	−0.337008	−	1.25773i	0.564668	−	0.825318i	$-0.309004\pi$
$632$	−10.3883	−	10.3883i	−0.413225	−	0.413225i
$633$	6.18989	−	9.78202i	0.246026	−	0.388800i
$634$	52.8093	−	30.4894i	2.09732	−	1.21089i
$635$	−1.12592	+	4.20199i	−0.0446808	+	0.166751i
$636$	25.1952	+	1.02291i	0.999053	+	0.0405610i
$637$	−2.38642	+	2.70278i	−0.0945533	+	0.107088i
$638$			5.88495i			0.232987i
$639$	27.6635	+	9.87763i	1.09435	+	0.390753i
$640$	−3.19219	−	5.52904i	−0.126183	−	0.218555i
$641$	16.0871	−	27.8636i	0.635401	−	1.10055i	−0.351029	−	0.936365i	$-0.614168\pi$
$641$	16.0871	−	27.8636i	0.635401	−	1.10055i	0.986430	−	0.164182i	$-0.0524985\pi$
$642$	−12.4279	−	13.4797i	−0.490490	−	0.532003i
$643$	44.5195	−	11.9290i	1.75568	−	0.470432i	0.769855	−	0.638219i	$-0.220329\pi$
$643$	44.5195	−	11.9290i	1.75568	−	0.470432i	0.985823	+	0.167787i	$0.0536620\pi$
$644$	−8.18950	+	2.19437i	−0.322712	+	0.0864703i
$645$	−6.85214	−	7.43207i	−0.269803	−	0.292637i
$646$	0.932275	−	1.61475i	0.0366799	−	0.0635314i
$647$	−7.79666	−	13.5042i	−0.306518	−	0.530906i	0.671080	−	0.741385i	$-0.265831\pi$
$647$	−7.79666	−	13.5042i	−0.306518	−	0.530906i	−0.977598	+	0.210480i	$0.932497\pi$
$648$	4.99127	−	11.0546i	0.196076	−	0.434267i
$649$			8.80169i			0.345497i
$650$	−1.85376	−	29.8210i	−0.0727106	−	1.16967i
$651$	−5.53650	−	0.224779i	−0.216992	−	0.00880978i
$652$	−0.0253690	+	0.0946785i	−0.000993528	+	0.00370790i
$653$	−18.2824	+	10.5554i	−0.715446	+	0.413063i	−0.813074	−	0.582160i	$-0.802208\pi$
$653$	−18.2824	+	10.5554i	−0.715446	+	0.413063i	0.0976281	+	0.995223i	$0.468874\pi$
$654$	−14.1386	+	22.3436i	−0.552865	+	0.873704i
$655$	0.0663216	+	0.0663216i	0.00259140	+	0.00259140i
$656$	−6.02237	−	22.4758i	−0.235134	−	0.877532i
$657$	5.27991	+	28.9095i	0.205989	+	1.12787i
$658$	4.92057	−	4.92057i	0.191824	−	0.191824i
$659$	−30.9075	−	17.8444i	−1.20398	−	0.695121i	−0.242546	−	0.970140i	$-0.577982\pi$
$659$	−30.9075	−	17.8444i	−1.20398	−	0.695121i	−0.961439	+	0.275019i	$0.911316\pi$
$660$	1.13783	−	0.596745i	0.0442901	−	0.0232283i
$661$	3.68868	+	0.988379i	0.143473	+	0.0384435i	0.329841	−	0.944037i	$-0.393005\pi$
$661$	3.68868	+	0.988379i	0.143473	+	0.0384435i	−0.186368	+	0.982480i	$0.559672\pi$
$662$	−36.3920			−1.41442
$663$	−45.6279	+	13.2839i	−1.77204	+	0.515906i
$664$	17.5779			0.682153
$665$	0.0835389	+	0.0223842i	0.00323950	+	0.000868022i
$666$	21.4709	−	10.1723i	0.831981	−	0.394168i
$667$	20.5608	+	11.8708i	0.796118	+	0.459639i
$668$	−2.03889	+	2.03889i	−0.0788869	+	0.0788869i
$669$	−25.4095	+	5.71467i	−0.982388	+	0.220942i
$670$	1.98268	+	7.39947i	0.0765977	+	0.285866i
$671$	2.24067	+	2.24067i	0.0865000	+	0.0865000i
$672$	−9.08492	−	5.74877i	−0.350458	−	0.221764i
$673$	−33.2751	+	19.2114i	−1.28266	+	0.740544i	−0.977334	−	0.211704i	$-0.932099\pi$
$673$	−33.2751	+	19.2114i	−1.28266	+	0.740544i	−0.305326	+	0.952248i	$0.598765\pi$
$674$	−11.6187	+	43.3614i	−0.447534	+	1.67022i
$675$	2.89917	−	23.6983i	0.111589	−	0.912150i
$676$	16.1604	−	2.01696i	0.621554	−	0.0775752i
$677$			25.0417i			0.962431i	0.876602	+	0.481215i	$0.159805\pi$
$677$			25.0417i			0.962431i	−0.876602	+	0.481215i	$0.840195\pi$
$678$	12.6801	−	40.6488i	0.486976	−	1.56111i
$679$	5.39962	+	9.35241i	0.207218	+	0.358913i
$680$	−3.26427	+	5.65389i	−0.125179	+	0.216817i
$681$	33.4613	−	30.8502i	1.28224	−	1.18218i
$682$	−5.18391	+	1.38902i	−0.198502	+	0.0531885i
$683$	11.3743	−	3.04775i	0.435227	−	0.116619i	−0.0345516	−	0.999403i	$-0.511000\pi$
$683$	11.3743	−	3.04775i	0.435227	−	0.116619i	0.469779	+	0.882784i	$0.344334\pi$
$684$	−0.389119	+	0.330584i	−0.0148783	+	0.0126402i
$685$	−6.65421	+	11.5254i	−0.254244	+	0.440364i
$686$	0.901769	+	1.56191i	0.0344297	+	0.0596340i
$687$	20.0327	+	6.24905i	0.764295	+	0.238416i
$688$			45.2545i			1.72531i
$689$	−13.3349	−	39.7221i	−0.508018	−	1.51329i
$690$	0.545958	−	13.4474i	0.0207843	−	0.511934i
$691$	8.96377	−	33.4532i	0.340998	−	1.27262i	−0.556221	−	0.831034i	$-0.687749\pi$
$691$	8.96377	−	33.4532i	0.340998	−	1.27262i	0.897219	−	0.441586i	$-0.145584\pi$
$692$	17.0319	−	9.83338i	0.647456	−	0.373809i
$693$	−1.58655	+	2.29556i	−0.0602679	+	0.0872010i
$694$	28.0426	+	28.0426i	1.06448	+	1.06448i
$695$	1.50562	+	5.61904i	0.0571113	+	0.213142i
$696$	1.79677	+	7.98909i	0.0681064	+	0.302825i
$697$	−25.3650	+	25.3650i	−0.960769	+	0.960769i
$698$	1.18716	+	0.685409i	0.0449348	+	0.0259431i
$699$	8.95449	+	17.0738i	0.338690	+	0.645791i
$700$	−5.55995	−	1.48978i	−0.210146	−	0.0563085i
$701$	−35.6659			−1.34708			−0.673541	−	0.739150i	$-0.735227\pi$
$701$	−35.6659			−1.34708			−0.673541	+	0.739150i	$0.735227\pi$
$702$	33.7292	+	2.01428i	1.27303	+	0.0760242i
$703$	0.596567			0.0224999
$704$	−1.18822	−	0.318383i	−0.0447828	−	0.0119995i
$705$	1.97593	+	3.76758i	0.0744180	+	0.141895i
$706$	25.7572	+	14.8709i	0.969386	+	0.559676i
$707$	3.71804	−	3.71804i	0.139831	−	0.139831i
$708$	−4.50523	−	20.0319i	−0.169317	−	0.752844i
$709$	−4.51893	−	16.8649i	−0.169712	−	0.633374i	−0.997392	−	0.0721738i	$-0.977006\pi$
$709$	−4.51893	−	16.8649i	−0.169712	−	0.633374i	0.827680	−	0.561200i	$-0.189660\pi$
$710$	7.94905	+	7.94905i	0.298322	+	0.298322i
$711$	18.5937	−	26.9031i	0.697319	−	1.00894i
$712$	11.5948	−	6.69427i	0.434534	−	0.250878i
$713$	−5.60372	+	20.9134i	−0.209861	+	0.783212i
$714$	−0.964304	+	23.7516i	−0.0360882	+	0.888882i
$715$	−1.60040	−	1.41307i	−0.0598515	−	0.0528459i
$716$			2.48645i			0.0929230i
$717$	−21.3909	−	6.67272i	−0.798857	−	0.249197i
$718$	19.6586	+	34.0498i	0.733654	+	1.27073i
$719$	5.97820	−	10.3545i	0.222949	−	0.386159i	−0.732753	−	0.680495i	$-0.761765\pi$
$719$	5.97820	−	10.3545i	0.222949	−	0.386159i	0.955702	+	0.294335i	$0.0950983\pi$
$720$	7.18424	−	6.10351i	0.267741	−	0.227464i
$721$	−0.595255	+	0.159498i	−0.0221684	+	0.00594002i
$722$	33.0675	−	8.86040i	1.23064	−	0.329750i
$723$	19.4961	−	17.9748i	0.725068	−	0.668490i
$724$	5.86193	−	10.1532i	0.217857	−	0.377339i
$725$	8.05922	+	13.9590i	0.299312	+	0.518423i
$726$	9.42783	−	30.2230i	0.349899	−	1.12168i
$727$		−	21.8697i		−	0.811102i	−0.914072	−	0.405551i	$-0.867080\pi$
$727$		−	21.8697i		−	0.811102i	0.914072	−	0.405551i	$-0.132920\pi$
$728$	−0.964015	+	4.76258i	−0.0357288	+	0.176513i
$729$	26.2037	+	6.50876i	0.970509	+	0.241065i
$730$	−2.91090	+	10.8636i	−0.107737	+	0.402081i
$731$	60.4188	−	34.8828i	2.23467	−	1.29019i
$732$	−6.24647	−	3.95265i	−0.230876	−	0.146094i
$733$	8.29483	+	8.29483i	0.306377	+	0.306377i	0.843502	−	0.537126i	$-0.180490\pi$
$733$	8.29483	+	8.29483i	0.306377	+	0.306377i	−0.537126	+	0.843502i	$0.680490\pi$
$734$	−8.32859	−	31.0827i	−0.307414	−	1.14728i
$735$	−1.07574	+	0.241937i	−0.0396793	+	0.00892399i
$736$	−29.7045	+	29.7045i	−1.09492	+	1.09492i
$737$	−5.37472	−	3.10310i	−0.197980	−	0.114304i
$738$	23.0494	−	10.9201i	0.848462	−	0.401976i
$739$	−0.386764	−	0.103633i	−0.0142273	−	0.00381220i	0.251698	−	0.967806i	$-0.419011\pi$
$739$	−0.386764	−	0.103633i	−0.0142273	−	0.00381220i	−0.265926	+	0.963994i	$0.585678\pi$
$740$	3.50189			0.128732
$741$	0.743714	+	0.408316i	0.0273210	+	0.0149999i
$742$	−20.9592			−0.769436
$743$	5.86368	+	1.57117i	0.215118	+	0.0576406i	0.364768	−	0.931098i	$-0.381148\pi$
$743$	5.86368	+	1.57117i	0.215118	+	0.0576406i	−0.149651	+	0.988739i	$0.547815\pi$
$744$	−6.61330	+	3.46839i	−0.242455	+	0.127158i
$745$	1.63981	+	0.946743i	0.0600779	+	0.0346860i
$746$	7.38550	−	7.38550i	0.270402	−	0.270402i
$747$	7.03005	+	38.4922i	0.257216	+	1.40835i
$748$	2.29500	+	8.56505i	0.0839134	+	0.313169i
$749$	4.15020	+	4.15020i	0.151645	+	0.151645i
$750$	10.2025	−	16.1233i	0.372543	−	0.588739i
$751$	−28.5391	+	16.4770i	−1.04141	+	0.601256i	−0.920231	−	0.391375i	$-0.871999\pi$
$751$	−28.5391	+	16.4770i	−1.04141	+	0.601256i	−0.121175	+	0.992631i	$0.538666\pi$
$752$	4.92931	−	18.3964i	0.179754	−	0.670849i
$753$	−46.7616	−	1.89850i	−1.70409	−	0.0691851i
$754$	−19.0098	+	12.6096i	−0.692297	+	0.459214i
$755$			4.01884i			0.146261i
$756$	2.43583	−	6.03657i	0.0885904	−	0.219548i
$757$	13.0902	+	22.6728i	0.475770	+	0.824058i	0.999615	−	0.0277559i	$-0.00883611\pi$
$757$	13.0902	+	22.6728i	0.475770	+	0.824058i	−0.523845	+	0.851814i	$0.675503\pi$
$758$	2.60376	−	4.50985i	0.0945728	−	0.163805i
$759$	7.39081	+	8.01633i	0.268269	+	0.290974i
$760$	0.112585	−	0.0301670i	0.00408387	−	0.00109427i
$761$	−23.9567	+	6.41918i	−0.868430	+	0.232695i	−0.665409	−	0.746479i	$-0.731743\pi$
$761$	−23.9567	+	6.41918i	−0.868430	+	0.232695i	−0.203021	+	0.979174i	$0.565076\pi$
$762$	14.4698	+	15.6945i	0.524187	+	0.568551i
$763$	4.23219	−	7.33037i	0.153216	−	0.265377i
$764$	3.07881	+	5.33266i	0.111388	+	0.192929i
$765$	−13.6864	−	4.88693i	−0.494834	−	0.176687i
$766$			6.42172i			0.232026i
$767$	−28.4316	+	18.8593i	−1.02661	+	0.680969i
$768$	−35.8805	−	1.45673i	−1.29473	−	0.0525653i
$769$	−6.75412	+	25.2067i	−0.243560	+	0.908977i	0.730542	+	0.682868i	$0.239267\pi$
$769$	−6.75412	+	25.2067i	−0.243560	+	0.908977i	−0.974102	+	0.226110i	$0.927399\pi$
$770$	−0.924855	+	0.533965i	−0.0333295	+	0.0192428i
$771$	−24.3848	+	38.5358i	−0.878196	+	1.38783i
$772$	−6.20019	−	6.20019i	−0.223150	−	0.223150i
$773$	8.69395	+	32.4463i	0.312700	+	1.16701i	0.926112	+	0.377249i	$0.123130\pi$
$773$	8.69395	+	32.4463i	0.312700	+	1.16701i	−0.613412	+	0.789763i	$0.710204\pi$
$774$	−48.7976	+	8.91219i	−1.75399	+	0.320342i
$775$	−10.3939	+	10.3939i	−0.373360	+	0.373360i
$776$	12.6042	+	7.27701i	0.452463	+	0.261230i
$777$	−6.73553	+	3.53250i	−0.241636	+	0.126728i
$778$	−9.75642	−	2.61423i	−0.349785	−	0.0937245i
$779$	0.640426			0.0229457
$780$	4.36565	+	2.39684i	0.156316	+	0.0858208i
$781$	−9.10749			−0.325892
$782$	89.7186	+	24.0400i	3.20833	+	0.859670i
$783$	−16.7760	+	7.12972i	−0.599524	+	0.254795i
$784$	4.27480	+	2.46806i	0.152672	+	0.0881449i
$785$	8.44433	−	8.44433i	0.301391	−	0.301391i
$786$	0.449034	−	0.100989i	0.0160165	−	0.00360216i
$787$	1.99147	+	7.43228i	0.0709883	+	0.264932i	0.992294	−	0.123908i	$-0.0395426\pi$
$787$	1.99147	+	7.43228i	0.0709883	+	0.264932i	−0.921305	+	0.388840i	$0.872876\pi$
$788$	−10.8435	−	10.8435i	−0.386285	−	0.386285i
$789$	−5.16794	−	3.27018i	−0.183983	−	0.116421i
$790$	10.8390	−	6.25787i	0.385633	−	0.222645i
$791$	−3.52795	+	13.1665i	−0.125439	+	0.468146i
$792$	−0.304861	+	3.74831i	−0.0108328	+	0.133190i
$793$	−2.43686	+	12.0390i	−0.0865354	+	0.427516i
$794$		−	36.8815i		−	1.30888i
$795$	3.81576	−	12.2323i	0.135331	−	0.433834i
$796$	3.91321	+	6.77788i	0.138700	+	0.240236i
$797$	−6.31270	+	10.9339i	−0.223607	+	0.387299i	−0.955901	−	0.293690i	$-0.905117\pi$
$797$	−6.31270	+	10.9339i	−0.223607	+	0.387299i	0.732293	+	0.680989i	$0.238450\pi$
$798$	0.312019	−	0.287672i	0.0110453	−	0.0101835i
$799$	−28.3605	+	7.59916i	−1.00332	+	0.268839i
$800$	−27.5483	+	7.38153i	−0.973978	+	0.260977i
$801$	19.2964	+	22.7131i	0.681803	+	0.802529i
$802$	−11.5466	+	19.9992i	−0.407723	+	0.706198i
$803$	−4.55585	−	7.89097i	−0.160772	−	0.278466i
$804$	13.8207	+	4.31127i	0.487420	+	0.152047i
$805$			4.30834i			0.151849i
$806$	−15.5944	−	13.7691i	−0.549288	−	0.484994i
$807$	0.329215	−	8.10883i	0.0115889	−	0.285444i
$808$	1.83407	−	6.84484i	0.0645223	−	0.240801i
$809$	33.0594	−	19.0868i	1.16230	−	0.671057i	0.210450	−	0.977605i	$-0.432507\pi$
$809$	33.0594	−	19.0868i	1.16230	−	0.671057i	0.951855	+	0.306548i	$0.0991739\pi$
$810$	7.99619	+	6.54472i	0.280958	+	0.229958i
$811$	−20.5992	−	20.5992i	−0.723335	−	0.723335i	0.245948	−	0.969283i	$-0.420901\pi$
$811$	−20.5992	−	20.5992i	−0.723335	−	0.723335i	−0.969283	+	0.245948i	$0.920901\pi$
$812$	1.13742	+	4.24493i	0.0399158	+	0.148968i
$813$	−6.82940	−	30.3660i	−0.239517	−	1.06498i
$814$	−5.20885	+	5.20885i	−0.182570	+	0.182570i
$815$	0.0431355	+	0.0249043i	0.00151097	+	0.000872359i
$816$	30.2174	+	57.6164i	1.05782	+	2.01698i
$817$	−1.20311	−	0.322371i	−0.0420913	−	0.0112783i
$818$	−65.5063			−2.29037
$819$	−10.8147	−	0.206274i	−0.377896	−	0.00720779i
$820$	3.75935			0.131282
$821$	30.7712	+	8.24513i	1.07392	+	0.287757i	0.752104	−	0.659044i	$-0.229039\pi$
$821$	30.7712	+	8.24513i	1.07392	+	0.287757i	0.321819	+	0.946801i	$0.395706\pi$
$822$	30.3317	+	57.8344i	1.05794	+	2.01721i
$823$	38.1344	+	22.0169i	1.32928	+	0.767461i	0.985189	−	0.171475i	$-0.0548532\pi$
$823$	38.1344	+	22.0169i	1.32928	+	0.767461i	0.344093	+	0.938936i	$0.388187\pi$
$824$	−0.587265	+	0.587265i	−0.0204583	+	0.0204583i
$825$	1.62427	+	7.22210i	0.0565499	+	0.251441i
$826$	4.41705	+	16.4846i	0.153689	+	0.573574i
$827$	31.9426	+	31.9426i	1.11075	+	1.11075i	0.993049	+	0.117705i	$0.0375536\pi$
$827$	31.9426	+	31.9426i	1.11075	+	1.11075i	0.117705	+	0.993049i	$0.462446\pi$
$828$	−20.9241	−	14.4614i	−0.727161	−	0.502569i
$829$	−17.2402	+	9.95363i	−0.598777	+	0.345704i	−0.768560	−	0.639778i	$-0.779026\pi$
$829$	−17.2402	+	9.95363i	−0.598777	+	0.345704i	0.169784	+	0.985481i	$0.445693\pi$
$830$	−3.87578	+	14.4646i	−0.134530	+	0.502074i
$831$	0.680916	−	16.7715i	0.0236207	−	0.581798i
$832$	−1.51753	−	4.52045i	−0.0526109	−	0.156718i
$833$		−	7.60965i		−	0.263659i
$834$	27.2508	+	8.50066i	0.943616	+	0.294354i
$835$	0.732613	+	1.26892i	0.0253531	+	0.0439129i
$836$	0.0791543	−	0.137099i	0.00273761	−	0.00474168i
$837$	−10.2400	−	13.0947i	−0.353947	−	0.452620i
$838$	6.67486	−	1.78852i	0.230579	−	0.0617835i
$839$	28.6187	−	7.66836i	0.988028	−	0.264741i	0.271606	−	0.962409i	$-0.412445\pi$
$839$	28.6187	−	7.66836i	0.988028	−	0.264741i	0.716422	+	0.697667i	$0.245779\pi$
$840$	−1.09250	+	1.00726i	−0.0376950	+	0.0347536i
$841$	−8.34692	+	14.4573i	−0.287825	+	0.498527i
$842$	−30.8011	−	53.3492i	−1.06148	−	1.83853i
$843$	6.27012	−	20.1003i	0.215954	−	0.692290i
$844$		−	8.37261i		−	0.288197i
$845$	1.13542	−	8.19745i	0.0390595	−	0.282001i
$846$	20.8075	+	1.69234i	0.715376	+	0.0581837i
$847$	−2.62308	+	9.78947i	−0.0901302	+	0.336370i
$848$	−49.6781	+	28.6817i	−1.70595	+	0.984932i
$849$	12.2205	+	7.73294i	0.419408	+	0.265394i
$850$	44.5900	+	44.5900i	1.52942	+	1.52942i
$851$	7.69166	+	28.7057i	0.263667	+	0.984018i
$852$	20.7278	−	4.66175i	0.710124	−	0.159709i
$853$	26.1256	−	26.1256i	0.894523	−	0.894523i	−0.100422	−	0.994945i	$-0.532019\pi$
$853$	26.1256	−	26.1256i	0.894523	−	0.894523i	0.994945	+	0.100422i	$0.0320192\pi$
$854$	5.32099	+	3.07208i	0.182081	+	0.105124i
$855$	0.111087	+	0.234474i	0.00379909	+	0.00801884i
$856$	7.64044	+	2.04725i	0.261145	+	0.0699735i
$857$	20.6228			0.704461			0.352231	−	0.935913i	$-0.385423\pi$
$857$	20.6228			0.704461			0.352231	+	0.935913i	$0.385423\pi$
$858$	−10.0588	+	2.92849i	−0.343402	+	0.0999769i
$859$	−35.2413			−1.20242			−0.601209	−	0.799092i	$-0.705314\pi$
$859$	−35.2413			−1.20242			−0.601209	+	0.799092i	$0.705314\pi$
$860$	−7.06231	−	1.89234i	−0.240823	−	0.0645283i
$861$	−7.23072	+	3.79221i	−0.246422	+	0.129238i
$862$	−52.1982	−	30.1367i	−1.77788	−	1.02646i
$863$	27.9491	−	27.9491i	0.951399	−	0.951399i	−0.0474736	−	0.998872i	$-0.515117\pi$
$863$	27.9491	−	27.9491i	0.951399	−	0.951399i	0.998872	+	0.0474736i	$0.0151170\pi$
$864$	−4.50285	−	31.9372i	−0.153190	−	1.08652i
$865$	−2.58658	−	9.65324i	−0.0879463	−	0.328220i
$866$	−24.2050	−	24.2050i	−0.822518	−	0.822518i
$867$	37.8863	−	59.8726i	1.28669	−	2.03338i
$868$	−3.47079	+	2.00386i	−0.117806	+	0.0680154i
$869$	−2.62435	+	9.79420i	−0.0890249	+	0.332246i
$870$	−6.97030	−	0.282991i	−0.236315	−	0.00959428i
$871$	−1.49258	−	24.0106i	−0.0505740	−	0.813570i
$872$		−	11.4074i		−	0.386302i
$873$	−10.8944	+	30.5110i	−0.368719	+	1.03264i
$874$	−0.829139	−	1.43611i	−0.0280461	−	0.0485772i
$875$	−3.05397	+	5.28964i	−0.103243	+	0.178822i
$876$	14.4078	+	15.6272i	0.486794	+	0.527993i
$877$	−35.7843	+	9.58839i	−1.20835	+	0.323777i	−0.806115	−	0.591759i	$-0.798434\pi$
$877$	−35.7843	+	9.58839i	−1.20835	+	0.323777i	−0.402237	+	0.915536i	$0.631767\pi$
$878$	46.7974	−	12.5393i	1.57934	−	0.423182i
$879$	16.2764	+	17.6540i	0.548990	+	0.595454i
$880$	−1.46141	+	2.53124i	−0.0492642	+	0.0853281i
$881$	14.8980	+	25.8042i	0.501928	+	0.869364i	0.999998	+	0.00222717i	$0.000708930\pi$
$881$	14.8980	+	25.8042i	0.501928	+	0.869364i	−0.498070	+	0.867137i	$0.665958\pi$
$882$	−1.81943	+	5.09553i	−0.0612634	+	0.171575i
$883$		−	34.1142i		−	1.14804i	−0.818843	−	0.574018i	$-0.805384\pi$
$883$		−	34.1142i		−	1.14804i	0.818843	−	0.574018i	$-0.194616\pi$
$884$	−22.7497	+	25.7656i	−0.765157	+	0.866591i
$885$	−10.4250	−	0.423249i	−0.350432	−	0.0142274i
$886$	0.836133	−	3.12049i	0.0280904	−	0.104835i
$887$	6.88242	−	3.97357i	0.231089	−	0.133419i	−0.379985	−	0.924993i	$-0.624071\pi$
$887$	6.88242	−	3.97357i	0.231089	−	0.133419i	0.611074	+	0.791573i	$0.290738\pi$
$888$	−5.48091	+	8.66160i	−0.183927	+	0.290664i
$889$	−4.83209	−	4.83209i	−0.162063	−	0.162063i
$890$	2.95207	+	11.0173i	0.0989535	+	0.369300i
$891$	−8.33001	+	0.831502i	−0.279066	+	0.0278564i
$892$	−13.3199	+	13.3199i	−0.445983	+	0.445983i
$893$	0.453961	+	0.262095i	0.0151912	+	0.00877066i
$894$	8.22853	−	4.31551i	0.275203	−	0.144332i
$895$	1.22045	+	0.327019i	0.0407952	+	0.0109310i
$896$	10.0290			0.335045
$897$	−10.0585	+	41.0506i	−0.335845	+	1.37064i
$898$	−0.462008			−0.0154174
$899$	10.8402	+	2.90462i	0.361541	+	0.0968745i
$900$	−7.39340	−	15.6055i	−0.246447	−	0.520182i
$901$	76.5851	+	44.2164i	2.55142	+	1.47306i
$902$	−5.59180	+	5.59180i	−0.186187	+	0.186187i
$903$	15.4925	−	3.48432i	0.515559	−	0.115951i
$904$	4.75458	+	17.7444i	0.158135	+	0.590168i
$905$	−4.21262	−	4.21262i	−0.140032	−	0.140032i
$906$	16.6647	+	10.5451i	0.553647	+	0.350338i
$907$	32.5389	−	18.7863i	1.08044	−	0.623790i	0.149423	−	0.988773i	$-0.452259\pi$
$907$	32.5389	−	18.7863i	1.08044	−	0.623790i	0.931014	+	0.364983i	$0.118925\pi$
$908$	8.51985	−	31.7965i	0.282741	−	1.05520i
$909$	15.7224	+	1.27875i	0.521479	+	0.0424135i
$910$	−3.70651	−	1.84339i	−0.122870	−	0.0611077i
$911$			0.0496669i			0.00164554i	1.00000		0.000822769i	$0.000261895\pi$
$911$			0.0496669i			0.00164554i	−1.00000		0.000822769i	$0.999738\pi$
$912$	0.345891	−	1.10883i	0.0114536	−	0.0367171i
$913$	−6.06599	−	10.5066i	−0.200755	−	0.347718i
$914$	−19.8771	+	34.4281i	−0.657474	+	1.13878i
$915$	−2.76166	+	2.54616i	−0.0912976	+	0.0841736i
$916$	14.6606	−	3.92830i	0.484400	−	0.129795i
$917$	−0.142315	+	0.0381333i	−0.00469967	+	0.00125927i
$918$	−56.1765	+	43.9298i	−1.85410	+	1.44990i
$919$	11.3403	−	19.6420i	0.374082	−	0.647928i	−0.616108	−	0.787662i	$-0.711291\pi$
$919$	11.3403	−	19.6420i	0.374082	−	0.647928i	0.990189	+	0.139734i	$0.0446247\pi$
$920$	2.90315	+	5.02841i	0.0957142	+	0.165782i
$921$	11.5575	+	3.60526i	0.380832	+	0.118797i
$922$			63.5686i			2.09352i
$923$	−19.5145	−	29.4194i	−0.642328	−	0.968353i
$924$	−0.0818737	+	2.01662i	−0.00269345	+	0.0663419i
$925$	−5.22196	+	19.4886i	−0.171697	+	0.640782i
$926$	61.8268	−	35.6957i	2.03175	−	1.17303i
$927$	−1.52087	−	1.05113i	−0.0499518	−	0.0345236i
$928$	15.3969	+	15.3969i	0.505430	+	0.505430i
$929$	−5.59372	−	20.8761i	−0.183524	−	0.684921i	−0.994942	−	0.100454i	$-0.967970\pi$
$929$	−5.59372	−	20.8761i	−0.183524	−	0.684921i	0.811418	−	0.584467i	$-0.198696\pi$
$930$	−1.39592	−	6.20676i	−0.0457740	−	0.203528i
$931$	−0.0960657	+	0.0960657i	−0.00314843	+	0.00314843i
$932$	12.0762	+	6.97220i	0.395569	+	0.228382i
$933$	20.4631	+	39.0177i	0.669932	+	1.27738i
$934$	13.6996	+	3.67081i	0.448266	+	0.120112i
$935$	4.50591			0.147359
$936$	−12.7612	+	7.04668i	−0.417112	+	0.230328i
$937$	−6.60800			−0.215874			−0.107937	−	0.994158i	$-0.534424\pi$
$937$	−6.60800			−0.215874			−0.107937	+	0.994158i	$0.534424\pi$
$938$	−11.6236	−	3.11452i	−0.379523	−	0.101693i
$939$	15.7974	+	30.1214i	0.515529	+	0.982975i
$940$	2.66478	+	1.53851i	0.0869157	+	0.0501808i
$941$	31.1107	−	31.1107i	1.01418	−	1.01418i	0.0142804	−	0.999898i	$-0.495454\pi$
$941$	31.1107	−	31.1107i	1.01418	−	1.01418i	0.999898	−	0.0142804i	$-0.00454576\pi$
$942$	−12.8584	−	57.1729i	−0.418948	−	1.86279i
$943$	8.25715	+	30.8161i	0.268890	+	1.00351i
$944$	33.0279	+	33.0279i	1.07497	+	1.07497i
$945$	−2.64263	−	1.98954i	−0.0859648	−	0.0647196i
$946$	13.3195	−	7.69002i	0.433055	−	0.250024i
$947$	11.3161	−	42.2322i	0.367723	−	1.37236i	−0.495968	−	0.868341i	$-0.665187\pi$
$947$	11.3161	−	42.2322i	0.367723	−	1.37236i	0.863691	−	0.504021i	$-0.168147\pi$
$948$	0.959530	−	23.6340i	0.0311641	−	0.767598i
$949$	15.7280	−	31.6244i	0.510553	−	1.02657i
$950$		−	1.12583i		−	0.0365266i
$951$	−55.9050	−	17.4391i	−1.81284	−	0.565502i
$952$	−5.12773	−	8.88149i	−0.166191	−	0.287851i
$953$	−21.9357	+	37.9938i	−0.710568	+	1.23074i	0.254076	+	0.967184i	$0.418229\pi$
$953$	−21.9357	+	37.9938i	−0.710568	+	1.23074i	−0.964644	+	0.263556i	$0.915105\pi$
$954$	−40.7106	−	47.9191i	−1.31805	−	1.55144i
$955$	3.02241	−	0.809853i	0.0978029	−	0.0262062i
$956$	−15.6546	+	4.19463i	−0.506305	+	0.135664i
$957$	4.15517	−	3.83094i	0.134317	−	0.123837i
$958$	16.6767	−	28.8848i	0.538799	−	0.933227i
$959$	−10.4529	−	18.1049i	−0.337540	−	0.584637i
$960$	0.434240	−	1.39205i	0.0140150	−	0.0449284i
$961$		−	20.7656i		−	0.669857i
$962$	−27.9868	−	5.66494i	−0.902331	−	0.182645i
$963$	−1.42738	+	17.5499i	−0.0459968	+	0.565537i
$964$	4.96407	−	18.5262i	0.159882	−	0.596687i
$965$	−3.85875	+	2.22785i	−0.124218	+	0.0717171i
$966$	17.8651	+	11.3047i	0.574801	+	0.363724i
$967$	−26.3544	−	26.3544i	−0.847501	−	0.847501i	0.142320	−	0.989821i	$-0.454544\pi$
$967$	−26.3544	−	26.3544i	−0.847501	−	0.847501i	−0.989821	+	0.142320i	$0.954544\pi$
$968$	3.53510	+	13.1932i	0.113622	+	0.424045i
$969$	−1.74701	+	0.392907i	−0.0561219	+	0.0126220i
$970$	−8.76729	+	8.76729i	−0.281501	+	0.281501i
$971$	−21.5428	−	12.4377i	−0.691341	−	0.399146i	0.112773	−	0.993621i	$-0.464027\pi$
$971$	−21.5428	−	12.4377i	−0.691341	−	0.399146i	−0.804114	+	0.594475i	$0.797360\pi$
$972$	18.5327	−	6.15622i	0.594438	−	0.197461i
$973$	−8.82674	−	2.36512i	−0.282972	−	0.0758222i
$974$	14.5761			0.467049
$975$	−19.8489	+	20.7215i	−0.635672	+	0.663619i
$976$	16.8160			0.538266
$977$	12.8168	+	3.43425i	0.410046	+	0.109871i	0.457945	−	0.888981i	$-0.348586\pi$
$977$	12.8168	+	3.43425i	0.410046	+	0.109871i	−0.0478987	+	0.998852i	$0.515252\pi$
$978$	0.216453	−	0.113520i	0.00692141	−	0.00362998i
$979$	−8.00257	−	4.62028i	−0.255763	−	0.147665i
$980$	−0.563913	+	0.563913i	−0.0180135	+	0.0180135i
$981$	24.9800	−	4.56224i	0.797549	−	0.145661i
$982$	7.65924	+	28.5847i	0.244416	+	0.912174i
$983$	−19.0728	−	19.0728i	−0.608327	−	0.608327i	0.334182	−	0.942509i	$-0.391540\pi$
$983$	−19.0728	−	19.0728i	−0.608327	−	0.608327i	−0.942509	+	0.334182i	$0.891540\pi$
$984$	−5.88386	+	9.29840i	−0.187571	+	0.296422i
$985$	−6.74859	+	3.89630i	−0.215028	+	0.124146i
$986$	12.4609	−	46.5045i	0.396834	−	1.48101i
$987$	−6.67740	−	0.271099i	−0.212544	−	0.00862918i
$988$	0.612467	−	0.0380729i	0.0194852	−	0.00121126i
$989$		−	62.0476i		−	1.97300i
$990$	−3.01722	−	1.07734i	−0.0958935	−	0.0342401i
$991$	10.3369	+	17.9040i	0.328362	+	0.568740i	0.982187	−	0.187906i	$-0.0601701\pi$
$991$	10.3369	+	17.9040i	0.328362	+	0.568740i	−0.653825	+	0.756646i	$0.726837\pi$
$992$	−9.92866	+	17.1969i	−0.315235	+	0.546003i
$993$	23.6902	+	25.6952i	0.751786	+	0.815414i
$994$	−17.0574	+	4.57051i	−0.541027	+	0.144968i
$995$	3.84152	−	1.02933i	0.121785	−	0.0326321i
$996$	19.1836	+	20.8072i	0.607854	+	0.659300i
$997$	−14.7253	+	25.5050i	−0.466355	+	0.807750i	−0.999262	−	0.0384240i	$-0.987766\pi$
$997$	−14.7253	+	25.5050i	−0.466355	+	0.807750i	0.532907	+	0.846174i	$0.321100\pi$
$998$	−17.2689	−	29.9105i	−0.546636	−	0.946802i
$999$	−21.1593	−	8.53804i	−0.669450	−	0.270132i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.8	✓	112
3.2	odd	2	inner	273.2.cc.a.50.21	yes	112
13.6	odd	12	inner	273.2.cc.a.71.21	yes	112
39.32	even	12	inner	273.2.cc.a.71.8	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.8	✓	112	1.1	even	1	trivial
273.2.cc.a.50.21	yes	112	3.2	odd	2	inner
273.2.cc.a.71.8	yes	112	39.32	even	12	inner
273.2.cc.a.71.21	yes	112	13.6	odd	12	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.74208 - 0.466790i) q^{2} +(0.804463 + 1.53390i) q^{3} +(1.08492 + 0.626376i) q^{4} +(0.450139 - 0.450139i) q^{5} +(-0.685436 - 3.04769i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.952961 + 0.952961i) q^{8} +(-1.70568 + 2.46793i) q^{9} +O(q^{10})\)	\(q+(-1.74208 - 0.466790i) q^{2} +(0.804463 + 1.53390i) q^{3} +(1.08492 + 0.626376i) q^{4} +(0.450139 - 0.450139i) q^{5} +(-0.685436 - 3.04769i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.952961 + 0.952961i) q^{8} +(-1.70568 + 2.46793i) q^{9} +(-0.994301 + 0.574060i) q^{10} +(0.240742 - 0.898462i) q^{11} +(-0.0880215 + 2.16804i) q^{12} +(3.41809 - 1.14747i) q^{13} -1.80354i q^{14} +(1.05259 + 0.328346i) q^{15} +(-2.46806 - 4.27480i) q^{16} +(-3.80483 + 6.59015i) q^{17} +(4.12344 - 3.50315i) q^{18} +(0.131228 - 0.0351625i) q^{19} +(0.770319 - 0.206406i) q^{20} +(-1.27342 + 1.17405i) q^{21} +(-0.838786 + 1.45282i) q^{22} +(3.38391 + 5.86110i) q^{23} +(-0.695121 + 2.22837i) q^{24} +4.59475i q^{25} +(-6.49022 + 0.403453i) q^{26} +(-5.15770 - 0.630975i) q^{27} +(-0.324236 + 1.21007i) q^{28} +(3.03803 - 1.75401i) q^{29} +(-1.68043 - 1.06334i) q^{30} +(2.26213 + 2.26213i) q^{31} +(1.60651 + 5.99560i) q^{32} +(1.57182 - 0.353506i) q^{33} +(9.70455 - 9.70455i) q^{34} +(0.551305 + 0.318296i) q^{35} +(-3.39637 + 1.60910i) q^{36} +(4.24150 + 1.13651i) q^{37} -0.245024 q^{38} +(4.50982 + 4.31990i) q^{39} +0.857930 q^{40} +(4.55333 + 1.22006i) q^{41} +(2.76644 - 1.45088i) q^{42} +(-7.93975 - 4.58402i) q^{43} +(0.823960 - 0.823960i) q^{44} +(0.343119 + 1.87870i) q^{45} +(-3.15915 - 11.7901i) q^{46} +(2.72828 + 2.72828i) q^{47} +(4.57164 - 7.22467i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(2.14478 - 8.00444i) q^{50} +(-13.1695 - 0.534673i) q^{51} +(4.42708 + 0.896105i) q^{52} -11.6211i q^{53} +(8.69062 + 3.50678i) q^{54} +(-0.296065 - 0.512800i) q^{55} +(-0.673845 + 1.16713i) q^{56} +(0.159504 + 0.173004i) q^{57} +(-6.11126 + 1.63751i) q^{58} +(-9.14017 + 2.44910i) q^{59} +(0.936300 + 1.01554i) q^{60} +(-1.70336 + 2.95031i) q^{61} +(-2.88488 - 4.99676i) q^{62} +(-2.82530 - 1.00881i) q^{63} -1.32251i q^{64} +(1.02210 - 2.05513i) q^{65} +(-2.90325 - 0.117870i) q^{66} +(1.72689 - 6.44486i) q^{67} +(-8.25583 + 4.76651i) q^{68} +(-6.26809 + 9.90560i) q^{69} +(-0.811843 - 0.811843i) q^{70} +(-2.53419 - 9.45773i) q^{71} +(-3.97728 + 0.726395i) q^{72} +(6.92674 - 6.92674i) q^{73} +(-6.85854 - 3.95978i) q^{74} +(-7.04787 + 3.69631i) q^{75} +(0.164396 + 0.0440499i) q^{76} +0.930156 q^{77} +(-5.84000 - 9.63077i) q^{78} -10.9011 q^{79} +(-3.03522 - 0.813286i) q^{80} +(-3.18133 - 8.41897i) q^{81} +(-7.36278 - 4.25090i) q^{82} +(9.22276 - 9.22276i) q^{83} +(-2.11695 + 0.476109i) q^{84} +(1.25378 + 4.67919i) q^{85} +(11.6919 + 11.6919i) q^{86} +(5.13445 + 3.24899i) q^{87} +(1.08562 - 0.626781i) q^{88} +(2.57122 - 9.59592i) q^{89} +(0.279218 - 3.43302i) q^{90} +(1.99303 + 3.00463i) q^{91} +8.47839i q^{92} +(-1.65007 + 5.28967i) q^{93} +(-3.47937 - 6.02644i) q^{94} +(0.0432429 - 0.0748990i) q^{95} +(-7.90424 + 7.28746i) q^{96} +(10.4313 - 2.79505i) q^{97} +(1.74208 - 0.466790i) q^{98} +(1.80671 + 2.12662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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