LMFDB - Embedded newform 273.2.cd.e.242.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (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			242.1
Character	$\chi$	$=$	273.242
Dual form			273.2.cd.e.44.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.69539 - 0.722228i) q^{2} +(1.57685 - 0.716628i) q^{3} +(5.01147 + 2.89338i) q^{4} +(1.51996 + 0.407273i) q^{5} +(-4.76779 + 0.792751i) q^{6} +(-0.780863 - 2.52790i) q^{7} +(-7.47188 - 7.47188i) q^{8} +(1.97289 - 2.26003i) q^{9} +O(q^{10})$	\(q+(-2.69539 - 0.722228i) q^{2} +(1.57685 - 0.716628i) q^{3} +(5.01147 + 2.89338i) q^{4} +(1.51996 + 0.407273i) q^{5} +(-4.76779 + 0.792751i) q^{6} +(-0.780863 - 2.52790i) q^{7} +(-7.47188 - 7.47188i) q^{8} +(1.97289 - 2.26003i) q^{9} +(-3.80275 - 2.19552i) q^{10} +(0.998206 - 0.267468i) q^{11} +(9.97580 + 0.971045i) q^{12} +(-0.226763 + 3.59841i) q^{13} +(0.279015 + 7.37763i) q^{14} +(2.68861 - 0.447041i) q^{15} +(8.95650 + 15.5131i) q^{16} +(2.22855 - 3.85997i) q^{17} +(-6.94996 + 4.66678i) q^{18} +(0.324326 - 1.21040i) q^{19} +(6.43886 + 6.43886i) q^{20} +(-3.04286 - 3.42651i) q^{21} -2.88373 q^{22} +(0.753131 + 1.30446i) q^{23} +(-17.1366 - 6.42745i) q^{24} +(-2.18571 - 1.26192i) q^{25} +(3.21009 - 9.53536i) q^{26} +(1.49134 - 4.97754i) q^{27} +(3.40088 - 14.9278i) q^{28} +5.07947i q^{29} +(-7.56972 - 0.736837i) q^{30} +(3.60020 - 0.964669i) q^{31} +(-7.46748 - 27.8690i) q^{32} +(1.38234 - 1.13710i) q^{33} +(-8.79461 + 8.79461i) q^{34} +(-0.157339 - 4.16033i) q^{35} +(16.4262 - 5.61775i) q^{36} +(0.748788 + 0.200637i) q^{37} +(-1.74837 + 3.02827i) q^{38} +(2.22115 + 5.83665i) q^{39} +(-8.31389 - 14.4001i) q^{40} +(-2.06122 + 2.06122i) q^{41} +(5.72698 + 11.4334i) q^{42} -9.19559i q^{43} +(5.77637 + 1.54777i) q^{44} +(3.91916 - 2.63165i) q^{45} +(-1.08786 - 4.05997i) q^{46} +(-0.858089 + 3.20243i) q^{47} +(25.2402 + 18.0433i) q^{48} +(-5.78051 + 3.94788i) q^{49} +(4.97996 + 4.97996i) q^{50} +(0.747925 - 7.68363i) q^{51} +(-11.5480 + 17.3772i) q^{52} +(-0.565295 - 0.326373i) q^{53} +(-7.61467 + 12.3393i) q^{54} +1.62617 q^{55} +(-13.0536 + 24.7227i) q^{56} +(-0.355996 - 2.14104i) q^{57} +(3.66853 - 13.6912i) q^{58} +(2.19984 - 0.589447i) q^{59} +(14.7674 + 5.53882i) q^{60} +(-0.158868 - 0.275168i) q^{61} -10.4006 q^{62} +(-7.25366 - 3.22248i) q^{63} +44.6851i q^{64} +(-1.81021 + 5.37710i) q^{65} +(-4.54720 + 2.06656i) q^{66} +(-1.66743 + 0.446788i) q^{67} +(22.3367 - 12.8961i) q^{68} +(2.12238 + 1.51722i) q^{69} +(-2.58061 + 11.3274i) q^{70} +(2.88966 - 2.88966i) q^{71} +(-31.6278 + 2.14546i) q^{72} +(0.832602 + 3.10731i) q^{73} +(-1.87337 - 1.08159i) q^{74} +(-4.35086 - 0.423513i) q^{75} +(5.12750 - 5.12750i) q^{76} +(-1.45559 - 2.31450i) q^{77} +(-1.77149 - 17.3362i) q^{78} +(5.46718 + 9.46944i) q^{79} +(7.29547 + 27.2271i) q^{80} +(-1.21543 - 8.91755i) q^{81} +(7.04445 - 4.06712i) q^{82} +(-3.87667 + 3.87667i) q^{83} +(-5.33503 - 25.9760i) q^{84} +(4.95938 - 4.95938i) q^{85} +(-6.64131 + 24.7857i) q^{86} +(3.64009 + 8.00954i) q^{87} +(-9.45697 - 5.45999i) q^{88} +(-4.28583 + 15.9949i) q^{89} +(-12.4643 + 4.26280i) q^{90} +(9.27348 - 2.23663i) q^{91} +8.71636i q^{92} +(4.98564 - 4.10114i) q^{93} +(4.62577 - 8.01208i) q^{94} +(0.985928 - 1.70768i) q^{95} +(-31.7468 - 38.5937i) q^{96} +(6.36370 + 6.36370i) q^{97} +(18.4320 - 6.46624i) q^{98} +(1.36486 - 2.78366i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.69539	−	0.722228i	−1.90593	−	0.510692i	−0.995222	−	0.0976430i	$-0.968870\pi$
$2$	−2.69539	−	0.722228i	−1.90593	−	0.510692i	−0.910709	−	0.413049i	$-0.864464\pi$
$3$	1.57685	−	0.716628i	0.910393	−	0.413746i
$3$	1.57685	−	0.716628i	0.910393	−	0.413746i
$4$	5.01147	+	2.89338i	2.50574	+	1.44669i
$5$	1.51996	+	0.407273i	0.679748	+	0.182138i	0.582142	−	0.813087i	$-0.302215\pi$
$5$	1.51996	+	0.407273i	0.679748	+	0.182138i	0.0976059	+	0.995225i	$0.468882\pi$
$6$	−4.76779	+	0.792751i	−1.94644	+	0.323639i
$7$	−0.780863	−	2.52790i	−0.295138	−	0.955455i
$7$	−0.780863	−	2.52790i	−0.295138	−	0.955455i
$8$	−7.47188	−	7.47188i	−2.64171	−	2.64171i
$9$	1.97289	−	2.26003i	0.657629	−	0.753342i
$10$	−3.80275	−	2.19552i	−1.20254	−	0.694284i
$11$	0.998206	−	0.267468i	0.300970	−	0.0806448i	−0.105174	−	0.994454i	$-0.533540\pi$
$11$	0.998206	−	0.267468i	0.300970	−	0.0806448i	0.406144	+	0.913809i	$0.366873\pi$
$12$	9.97580	+	0.971045i	2.87977	+	0.280317i
$13$	−0.226763	+	3.59841i	−0.0628929	+	0.998020i
$13$	−0.226763	+	3.59841i	−0.0628929	+	0.998020i
$14$	0.279015	+	7.37763i	0.0745698	+	1.97175i
$15$	2.68861	−	0.447041i	0.694196	−	0.115426i
$16$	8.95650	+	15.5131i	2.23913	+	3.87828i
$17$	2.22855	−	3.85997i	0.540504	−	0.936180i	−0.458371	−	0.888761i	$-0.651567\pi$
$17$	2.22855	−	3.85997i	0.540504	−	0.936180i	0.998875	−	0.0474194i	$-0.0150997\pi$
$18$	−6.94996	+	4.66678i	−1.63812	+	1.09997i
$19$	0.324326	−	1.21040i	0.0744056	−	0.277685i	−0.918692	−	0.394974i	$-0.870754\pi$
$19$	0.324326	−	1.21040i	0.0744056	−	0.277685i	0.993098	+	0.117289i	$0.0374203\pi$
$20$	6.43886	+	6.43886i	1.43977	+	1.43977i
$21$	−3.04286	−	3.42651i	−0.664007	−	0.747727i
$22$	−2.88373			−0.614813
$23$	0.753131	+	1.30446i	0.157039	+	0.271999i	0.933799	−	0.357797i	$-0.116472\pi$
$23$	0.753131	+	1.30446i	0.157039	+	0.271999i	−0.776761	+	0.629796i	$0.783139\pi$
$24$	−17.1366	−	6.42745i	−3.49799	−	1.31200i
$25$	−2.18571	−	1.26192i	−0.437143	−	0.252384i
$26$	3.21009	−	9.53536i	0.629551	−	1.87004i
$27$	1.49134	−	4.97754i	0.287009	−	0.957928i
$28$	3.40088	−	14.9278i	0.642705	−	2.82109i
$29$			5.07947i			0.943233i	0.881804	+	0.471617i	$0.156329\pi$
$29$			5.07947i			0.943233i	−0.881804	+	0.471617i	$0.843671\pi$
$30$	−7.56972	−	0.736837i	−1.38204	−	0.134527i
$31$	3.60020	−	0.964669i	0.646614	−	0.173260i	0.0794166	−	0.996842i	$-0.474694\pi$
$31$	3.60020	−	0.964669i	0.646614	−	0.173260i	0.567198	+	0.823582i	$0.308028\pi$
$32$	−7.46748	−	27.8690i	−1.32008	−	4.92659i
$33$	1.38234	−	1.13710i	0.240635	−	0.197944i
$34$	−8.79461	+	8.79461i	−1.50826	+	1.50826i
$35$	−0.157339	−	4.16033i	−0.0265952	−	0.703224i
$36$	16.4262	−	5.61775i	2.73770	−	0.936292i
$37$	0.748788	+	0.200637i	0.123100	+	0.0329845i	0.319843	−	0.947471i	$-0.396370\pi$
$37$	0.748788	+	0.200637i	0.123100	+	0.0329845i	−0.196743	+	0.980455i	$0.563036\pi$
$38$	−1.74837	+	3.02827i	−0.283624	+	0.491251i
$39$	2.22115	+	5.83665i	0.355669	+	0.934612i
$40$	−8.31389	−	14.4001i	−1.31454	−	2.27685i
$41$	−2.06122	+	2.06122i	−0.321908	+	0.321908i	−0.849499	−	0.527591i	$-0.823095\pi$
$41$	−2.06122	+	2.06122i	−0.321908	+	0.321908i	0.527591	+	0.849499i	$0.323095\pi$
$42$	5.72698	+	11.4334i	0.883692	+	1.76422i
$43$		−	9.19559i		−	1.40231i	−0.713007	−	0.701157i	$-0.752667\pi$
$43$		−	9.19559i		−	1.40231i	0.713007	−	0.701157i	$-0.247333\pi$
$44$	5.77637	+	1.54777i	0.870821	+	0.233336i
$45$	3.91916	−	2.63165i	0.584234	−	0.392303i
$46$	−1.08786	−	4.05997i	−0.160397	−	0.598609i
$47$	−0.858089	+	3.20243i	−0.125165	+	0.467123i	−0.999846	−	0.0175774i	$-0.994405\pi$
$47$	−0.858089	+	3.20243i	−0.125165	+	0.467123i	0.874680	+	0.484700i	$0.161071\pi$
$48$	25.2402	+	18.0433i	3.64310	+	2.60433i
$49$	−5.78051	+	3.94788i	−0.825787	+	0.563983i
$50$	4.97996	+	4.97996i	0.704273	+	0.704273i
$51$	0.747925	−	7.68363i	0.104730	−	1.07592i
$52$	−11.5480	+	17.3772i	−1.60142	+	2.40979i
$53$	−0.565295	−	0.326373i	−0.0776492	−	0.0448308i	0.460673	−	0.887570i	$-0.347608\pi$
$53$	−0.565295	−	0.326373i	−0.0776492	−	0.0448308i	−0.538322	+	0.842739i	$0.680942\pi$
$54$	−7.61467	+	12.3393i	−1.03623	+	1.67917i
$55$	1.62617			0.219272
$56$	−13.0536	+	24.7227i	−1.74436	+	3.30370i
$57$	−0.355996	−	2.14104i	−0.0471528	−	0.283588i
$58$	3.66853	−	13.6912i	0.481702	−	1.79774i
$59$	2.19984	−	0.589447i	0.286395	−	0.0767394i	−0.112761	−	0.993622i	$-0.535970\pi$
$59$	2.19984	−	0.589447i	0.286395	−	0.0767394i	0.399157	+	0.916883i	$0.369303\pi$
$60$	14.7674	+	5.53882i	1.90646	+	0.715059i
$61$	−0.158868	−	0.275168i	−0.0203410	−	0.0352316i	0.855676	−	0.517512i	$-0.173142\pi$
$61$	−0.158868	−	0.275168i	−0.0203410	−	0.0352316i	−0.876017	+	0.482281i	$0.839809\pi$
$62$	−10.4006			−1.32088
$63$	−7.25366	−	3.22248i	−0.913875	−	0.405995i
$64$			44.6851i			5.58564i
$65$	−1.81021	+	5.37710i	−0.224529	+	0.666947i
$66$	−4.54720	+	2.06656i	−0.559721	+	0.254376i
$67$	−1.66743	+	0.446788i	−0.203710	+	0.0545838i	−0.359231	−	0.933249i	$-0.616961\pi$
$67$	−1.66743	+	0.446788i	−0.203710	+	0.0545838i	0.155521	+	0.987833i	$0.450294\pi$
$68$	22.3367	−	12.8961i	2.70872	−	1.56388i
$69$	2.12238	+	1.51722i	0.255505	+	0.182652i
$70$	−2.58061	+	11.3274i	−0.308442	+	1.35388i
$71$	2.88966	−	2.88966i	0.342940	−	0.342940i	−0.514532	−	0.857471i	$-0.672034\pi$
$71$	2.88966	−	2.88966i	0.342940	−	0.342940i	0.857471	+	0.514532i	$0.172034\pi$
$72$	−31.6278	+	2.14546i	−3.72738	+	0.252844i
$73$	0.832602	+	3.10731i	0.0974486	+	0.363683i	0.997379	−	0.0723497i	$-0.0230498\pi$
$73$	0.832602	+	3.10731i	0.0974486	+	0.363683i	−0.899931	+	0.436033i	$0.856383\pi$
$74$	−1.87337	−	1.08159i	−0.217775	−	0.125732i
$75$	−4.35086	−	0.423513i	−0.502394	−	0.0489031i
$76$	5.12750	−	5.12750i	0.588165	−	0.588165i
$77$	−1.45559	−	2.31450i	−0.165880	−	0.263762i
$78$	−1.77149	−	17.3362i	−0.200581	−	1.96294i
$79$	5.46718	+	9.46944i	0.615106	+	1.06540i	0.990366	+	0.138475i	$0.0442202\pi$
$79$	5.46718	+	9.46944i	0.615106	+	1.06540i	−0.375260	+	0.926920i	$0.622446\pi$
$80$	7.29547	+	27.2271i	0.815659	+	3.04408i
$81$	−1.21543	−	8.91755i	−0.135047	−	0.990839i
$82$	7.04445	−	4.06712i	0.777930	−	0.449138i
$83$	−3.87667	+	3.87667i	−0.425520	+	0.425520i	−0.887099	−	0.461579i	$-0.847283\pi$
$83$	−3.87667	+	3.87667i	−0.425520	+	0.425520i	0.461579	+	0.887099i	$0.347283\pi$
$84$	−5.33503	−	25.9760i	−0.582100	−	2.83422i
$85$	4.95938	−	4.95938i	0.537920	−	0.537920i
$86$	−6.64131	+	24.7857i	−0.716151	+	2.67271i
$87$	3.64009	+	8.00954i	0.390259	+	0.858713i
$88$	−9.45697	−	5.45999i	−1.00812	−	0.582036i
$89$	−4.28583	+	15.9949i	−0.454297	+	1.69546i	0.235851	+	0.971789i	$0.424212\pi$
$89$	−4.28583	+	15.9949i	−0.454297	+	1.69546i	−0.690148	+	0.723669i	$0.742454\pi$
$90$	−12.4643	+	4.26280i	−1.31386	+	0.449338i
$91$	9.27348	−	2.23663i	0.972125	−	0.234463i
$92$			8.71636i			0.908744i
$93$	4.98564	−	4.10114i	0.516987	−	0.425268i
$94$	4.62577	−	8.01208i	0.477112	−	0.826383i
$95$	0.985928	−	1.70768i	0.101154	−	0.175204i
$96$	−31.7468	−	38.5937i	−3.24014	−	3.93896i
$97$	6.36370	+	6.36370i	0.646135	+	0.646135i	0.952057	−	0.305921i	$-0.0989645\pi$
$97$	6.36370	+	6.36370i	0.646135	+	0.646135i	−0.305921	+	0.952057i	$0.598964\pi$
$98$	18.4320	−	6.46624i	1.86191	−	0.653189i
$99$	1.36486	−	2.78366i	0.137174	−	0.279768i
$100$	−7.30243	−	12.6482i	−0.730243	−	1.26482i
$101$	4.27842	−	7.41044i	0.425719	−	0.737367i	−0.570768	−	0.821111i	$-0.693355\pi$
$101$	4.27842	−	7.41044i	0.425719	−	0.737367i	0.996487	+	0.0837443i	$0.0266879\pi$
$102$	−7.56528	+	20.1702i	−0.749074	+	1.99715i
$103$	0.869625	−	0.502078i	0.0856867	−	0.0494713i	−0.456544	−	0.889701i	$-0.650913\pi$
$103$	0.869625	−	0.502078i	0.0856867	−	0.0494713i	0.542231	+	0.840229i	$0.317580\pi$
$104$	28.5813	−	25.1926i	2.80262	−	2.47034i
$105$	−3.22951	−	6.44744i	−0.315168	−	0.629206i
$106$	1.28798	+	1.28798i	0.125099	+	0.125099i
$107$	−9.08095	+	5.24289i	−0.877888	+	0.506849i	−0.869962	−	0.493120i	$-0.835857\pi$
$107$	−9.08095	+	5.24289i	−0.877888	+	0.506849i	−0.00792675	+	0.999969i	$0.502523\pi$
$108$	21.8757	−	20.6298i	2.10499	−	1.98510i
$109$	−6.88195	+	1.84401i	−0.659172	+	0.176625i	−0.572872	−	0.819645i	$-0.694171\pi$
$109$	−6.88195	+	1.84401i	−0.659172	+	0.176625i	−0.0862995	+	0.996269i	$0.527504\pi$
$110$	−4.38316	−	1.17446i	−0.417918	−	0.111981i
$111$	1.32451	−	0.220229i	0.125717	−	0.0209032i
$112$	32.2217	−	34.7547i	3.04467	−	3.28401i
$113$			8.65584i			0.814273i	0.913367	+	0.407137i	$0.133473\pi$
$113$			8.65584i			0.814273i	−0.913367	+	0.407137i	$0.866527\pi$
$114$	−0.586771	+	6.02805i	−0.0549561	+	0.564579i
$115$	0.613459	+	2.28946i	0.0572053	+	0.213493i
$116$	−14.6968	+	25.4556i	−1.36456	+	2.36349i
$117$	7.68513	+	7.61176i	0.710490	+	0.703707i
$118$	−6.35516			−0.585040
$119$	−11.4978	−	2.61945i	−1.05400	−	0.240124i
$120$	−23.4292	−	16.7487i	−2.13879	−	1.52894i
$121$	−8.60140	+	4.96602i	−0.781946	+	0.451457i
$122$	0.229478	+	0.856424i	0.0207760	+	0.0775369i
$123$	−1.77310	+	4.72735i	−0.159875	+	0.426250i
$124$	20.8334	+	5.58230i	1.87090	+	0.501306i
$125$	−8.37170	−	8.37170i	−0.748788	−	0.748788i
$126$	17.2241	+	13.9247i	1.53444	+	1.24051i
$127$			3.56712i			0.316531i	0.987397	+	0.158265i	$0.0505901\pi$
$127$			3.56712i			0.316531i	−0.987397	+	0.158265i	$0.949410\pi$
$128$	17.3379	−	64.7059i	1.53247	−	5.71925i
$129$	−6.58982	−	14.5000i	−0.580201	−	1.27666i
$130$	8.76271	−	13.1860i	0.768540	−	1.15649i
$131$	−3.57752	+	2.06548i	−0.312569	+	0.180462i	−0.648076	−	0.761576i	$-0.724426\pi$
$131$	−3.57752	+	2.06548i	−0.312569	+	0.180462i	0.335506	+	0.942038i	$0.391093\pi$
$132$	10.2176	−	1.69891i	0.889330	−	0.147871i
$133$	−3.31303	+	0.125295i	−0.287276	+	0.0108645i
$134$	4.81707			0.416132
$135$	4.29400	−	6.95829i	0.369569	−	0.598874i
$136$	−45.4928	+	12.1897i	−3.90097	+	1.04526i
$137$	−15.4754	+	4.14663i	−1.32216	+	0.354270i	−0.849785	−	0.527130i	$-0.823268\pi$
$137$	−15.4754	+	4.14663i	−1.32216	+	0.354270i	−0.472370	+	0.881400i	$0.656602\pi$
$138$	−4.62488	−	5.62235i	−0.393696	−	0.478606i
$139$	−13.2575			−1.12448			−0.562242	−	0.826973i	$-0.690061\pi$
$139$	−13.2575			−1.12448			−0.562242	+	0.826973i	$0.690061\pi$
$140$	11.2489	−	21.3046i	0.950705	−	1.80057i
$141$	0.941879	+	5.66467i	0.0793205	+	0.477052i
$142$	−9.87576	+	5.70177i	−0.828756	+	0.478482i
$143$	0.736105	+	3.65261i	0.0615562	+	0.305447i
$144$	52.7302	+	10.3637i	4.39418	+	0.863643i
$145$	−2.06873	+	7.72060i	−0.171798	+	0.641161i
$146$		−	8.97675i		−	0.742921i
$147$	−6.28581	+	10.3677i	−0.518445	+	0.855111i
$148$	3.17201	+	3.17201i	0.260738	+	0.260738i
$149$	17.1820	+	4.60389i	1.40760	+	0.377166i	0.881068	−	0.472989i	$-0.156825\pi$
$149$	17.1820	+	4.60389i	1.40760	+	0.377166i	0.526533	+	0.850155i	$0.323492\pi$
$150$	11.4214	+	4.28385i	0.932554	+	0.349775i
$151$	5.22897	+	19.5148i	0.425527	+	1.58809i	0.762769	+	0.646672i	$0.223840\pi$
$151$	5.22897	+	19.5148i	0.425527	+	1.58809i	−0.337241	+	0.941418i	$0.609494\pi$
$152$	−11.4673	+	6.62066i	−0.930122	+	0.537006i
$153$	−4.32694	−	12.6519i	−0.349812	−	1.02284i
$154$	2.25180	+	7.28977i	0.181455	+	0.587426i
$155$	5.86504			0.471092
$156$	−5.75637	+	35.6769i	−0.460878	+	2.85643i
$157$	−3.30475	+	5.72399i	−0.263748	+	0.456824i	−0.967235	−	0.253884i	$-0.918292\pi$
$157$	−3.30475	+	5.72399i	−0.263748	+	0.456824i	0.703487	+	0.710708i	$0.251625\pi$
$158$	−7.89711	−	29.4724i	−0.628260	−	2.34470i
$159$	−1.12527	−	0.109534i	−0.0892398	−	0.00868661i
$160$		−	45.4011i		−	3.58927i
$161$	2.70945	−	2.92244i	0.213534	−	0.230321i
$162$	−3.16446	+	24.9141i	−0.248623	+	1.95744i
$163$	22.3084	+	5.97753i	1.74733	+	0.468196i	0.984053	−	0.177874i	$-0.0569218\pi$
$163$	22.3084	+	5.97753i	1.74733	+	0.468196i	0.763278	+	0.646070i	$0.223588\pi$
$164$	−16.2936	+	4.36586i	−1.27232	+	0.340916i
$165$	2.56422	−	1.16536i	0.199624	−	0.0907230i
$166$	13.2490	−	7.64930i	1.02832	−	0.593701i
$167$	−8.32656	−	8.32656i	−0.644329	−	0.644329i	0.307288	−	0.951617i	$-0.400579\pi$
$167$	−8.32656	−	8.32656i	−0.644329	−	0.644329i	−0.951617	+	0.307288i	$0.900579\pi$
$168$	−2.86660	+	48.3384i	−0.221163	+	3.72939i
$169$	−12.8972	−	1.63198i	−0.992089	−	0.125537i
$170$	−16.9493	+	9.78567i	−1.29995	+	0.750526i
$171$	−2.09568	−	3.12097i	−0.160261	−	0.238667i
$172$	26.6063	−	46.0835i	2.02871	−	3.51383i
$173$	4.94907	+	8.57204i	0.376271	+	0.651720i	0.990516	−	0.137395i	$-0.0438729\pi$
$173$	4.94907	+	8.57204i	0.376271	+	0.651720i	−0.614246	+	0.789115i	$0.710540\pi$
$174$	−4.02675	−	24.2178i	−0.305267	−	1.83595i
$175$	−1.48326	+	6.51064i	−0.112124	+	0.492158i
$176$	13.0897	+	13.0897i	0.986673	+	0.986673i
$177$	3.04640	−	2.50594i	0.228982	−	0.188358i
$178$	23.1040	−	40.0172i	1.73172	−	2.99942i
$179$	7.57451	−	13.1194i	0.566145	−	0.980592i	−0.430797	−	0.902449i	$-0.641767\pi$
$179$	7.57451	−	13.1194i	0.566145	−	0.980592i	0.996942	−	0.0781434i	$-0.0248992\pi$
$180$	27.2551	−	1.84884i	2.03148	−	0.137804i
$181$		−	3.03128i		−	0.225314i	−0.993634	−	0.112657i	$-0.964064\pi$
$181$		−	3.03128i		−	0.225314i	0.993634	−	0.112657i	$-0.0359361\pi$
$182$	−26.6110	−	0.668967i	−1.97254	−	0.0495871i
$183$	−0.447703	−	0.320048i	−0.0330952	−	0.0236586i
$184$	4.11947	−	15.3741i	0.303692	−	1.13339i
$185$	1.05642	+	0.609922i	0.0776692	+	0.0448423i
$186$	−16.4002	+	7.45340i	−1.20252	+	0.546510i
$187$	1.19214	−	4.44911i	0.0871776	−	0.325351i
$188$	−13.5661	+	13.5661i	−0.989412	+	0.989412i
$189$	−13.7472	+	0.116817i	−0.999964	+	0.00849717i
$190$	−3.89079	+	3.89079i	−0.282268	+	0.282268i
$191$	9.40638	−	5.43078i	0.680622	−	0.392957i	−0.119467	−	0.992838i	$-0.538119\pi$
$191$	9.40638	−	5.43078i	0.680622	−	0.392957i	0.800089	+	0.599881i	$0.204785\pi$
$192$	32.0226	+	70.4615i	2.31103	+	5.08512i
$193$	3.09490	+	11.5503i	0.222776	+	0.831411i	0.983283	+	0.182082i	$0.0582836\pi$
$193$	3.09490	+	11.5503i	0.222776	+	0.831411i	−0.760508	+	0.649329i	$0.775050\pi$
$194$	−12.5566	−	21.7487i	−0.901512	−	1.56147i
$195$	0.998962	+	9.77610i	0.0715371	+	0.700081i
$196$	−40.3916	+	3.05951i	−2.88511	+	0.218537i
$197$	−6.89238	+	6.89238i	−0.491062	+	0.491062i	−0.908641	−	0.417579i	$-0.862879\pi$
$197$	−6.89238	+	6.89238i	−0.491062	+	0.491062i	0.417579	+	0.908641i	$0.362879\pi$
$198$	−5.68928	+	6.51730i	−0.404319	+	0.463164i
$199$	−14.6511	−	8.45883i	−1.03859	−	0.599631i	−0.119157	−	0.992875i	$-0.538019\pi$
$199$	−14.6511	−	8.45883i	−1.03859	−	0.599631i	−0.919434	+	0.393245i	$0.871353\pi$
$200$	6.90246	+	25.7603i	0.488078	+	1.82153i
$201$	−2.30911	+	1.89945i	−0.162872	+	0.133977i
$202$	−16.8841	+	16.8841i	−1.18796	+	1.18796i
$203$	12.8404	−	3.96637i	0.901216	−	0.278384i
$204$	25.9798	−	36.3423i	1.81895	−	2.54447i
$205$	−3.97245	+	2.29349i	−0.277448	+	0.160185i
$206$	−2.70660	+	0.725230i	−0.188578	+	0.0505292i
$207$	4.43396	+	0.871460i	0.308181	+	0.0605707i
$208$	−57.8536	+	28.7114i	−4.01143	+	1.99078i
$209$		−	1.29498i		−	0.0895755i
$210$	4.04827	+	19.7108i	0.279357	+	1.36018i
$211$	−4.64950			−0.320085			−0.160042	−	0.987110i	$-0.551163\pi$
$211$	−4.64950			−0.320085			−0.160042	+	0.987110i	$0.551163\pi$
$212$	−1.88864	−	3.27122i	−0.129712	−	0.224668i
$213$	2.48574	−	6.62736i	0.170320	−	0.454099i
$214$	28.2633	−	7.57312i	1.93204	−	0.517688i
$215$	3.74511	−	13.9769i	0.255415	−	0.953220i
$216$	−48.3347	+	26.0485i	−3.28876	+	1.77237i
$217$	−5.24984	−	8.34764i	−0.356382	−	0.566675i
$218$	19.8814			1.34654
$219$	3.53967	+	4.30309i	0.239189	+	0.290776i
$220$	8.14950	+	4.70511i	0.549439	+	0.317219i
$221$	13.3844	+	8.89456i	0.900333	+	0.598313i
$222$	−3.72912	−	0.362993i	−0.250282	−	0.0243625i
$223$	7.54802	+	7.54802i	0.505453	+	0.505453i	0.913127	−	0.407674i	$-0.133660\pi$
$223$	7.54802	+	7.54802i	0.505453	+	0.505453i	−0.407674	+	0.913127i	$0.633660\pi$
$224$	−64.6188	+	40.6389i	−4.31753	+	2.71530i
$225$	−7.16414	+	2.45014i	−0.477610	+	0.163342i
$226$	6.25149	−	23.3309i	0.415843	−	1.55195i
$227$	2.28639	+	8.53292i	0.151753	+	0.566350i	0.999362	+	0.0357279i	$0.0113750\pi$
$227$	2.28639	+	8.53292i	0.151753	+	0.566350i	−0.847609	+	0.530622i	$0.821958\pi$
$228$	4.41077	−	11.7598i	0.292110	−	0.778812i
$229$	−19.8595	−	5.32134i	−1.31235	−	0.351644i	−0.466245	−	0.884656i	$-0.654394\pi$
$229$	−19.8595	−	5.32134i	−1.31235	−	0.351644i	−0.846108	+	0.533012i	$0.821060\pi$
$230$		−	6.61405i		−	0.436118i
$231$	−3.95389	−	2.60650i	−0.260147	−	0.171495i
$232$	37.9532	−	37.9532i	2.49175	−	2.49175i
$233$	10.7918	+	18.6920i	0.706996	+	1.22455i	0.965966	+	0.258667i	$0.0832833\pi$
$233$	10.7918	+	18.6920i	0.706996	+	1.22455i	−0.258971	+	0.965885i	$0.583383\pi$
$234$	−15.2170	−	26.0671i	−0.994767	−	1.70406i
$235$	−2.60853	+	4.51810i	−0.170161	+	0.294728i
$236$	12.7300	+	3.41098i	0.828650	+	0.222036i
$237$	15.4070	+	11.0139i	1.00079	+	0.715430i
$238$	29.0992	+	15.3645i	1.88622	+	0.995930i
$239$	5.53458	−	5.53458i	0.358003	−	0.358003i	−0.505074	−	0.863076i	$-0.668535\pi$
$239$	5.53458	−	5.53458i	0.358003	−	0.358003i	0.863076	+	0.505074i	$0.168535\pi$
$240$	31.0155	+	37.7048i	2.00204	+	2.43383i
$241$	−5.32614	−	19.8774i	−0.343087	−	1.28042i	−0.894831	−	0.446405i	$-0.852704\pi$
$241$	−5.32614	−	19.8774i	−0.343087	−	1.28042i	0.551744	−	0.834014i	$-0.313963\pi$
$242$	26.7708	−	7.17320i	1.72089	−	0.461111i
$243$	−8.30711	−	13.1906i	−0.532901	−	0.846177i
$244$		−	1.83866i		−	0.117708i
$245$	−10.3940	+	3.64638i	−0.664049	+	0.232959i
$246$	8.19341	−	11.4615i	0.522393	−	0.730757i
$247$	4.28198	+	1.44154i	0.272456	+	0.0917227i
$248$	−34.1081	−	19.6923i	−2.16587	−	1.25047i
$249$	−3.33478	+	8.89104i	−0.211333	+	0.563447i
$250$	16.5187	+	28.6113i	1.04474	+	1.80954i
$251$	−1.61907			−0.102195			−0.0510973	−	0.998694i	$-0.516272\pi$
$251$	−1.61907			−0.102195			−0.0510973	+	0.998694i	$0.516272\pi$
$252$	−27.0277	−	37.1370i	−1.70258	−	2.33941i
$253$	1.10068	+	1.10068i	0.0691993	+	0.0691993i
$254$	2.57627	−	9.61479i	0.161650	−	0.603285i
$255$	4.26615	−	11.3742i	0.267156	−	0.712281i
$256$	−48.7797	+	84.4889i	−3.04873	+	5.28056i
$257$	−14.9090	−	25.8231i	−0.929996	−	1.61080i	−0.783323	−	0.621614i	$-0.786477\pi$
$257$	−14.9090	−	25.8231i	−0.929996	−	1.61080i	−0.146672	−	0.989185i	$-0.546856\pi$
$258$	7.28982	+	43.8426i	0.453844	+	2.72952i
$259$	−0.0775111	−	2.04953i	−0.00481630	−	0.127351i
$260$	−24.6298	+	21.7096i	−1.52747	+	1.34637i
$261$	11.4797	+	10.0212i	0.710577	+	0.620298i
$262$	11.1346	−	2.98350i	0.687896	−	0.184321i
$263$	3.55438	+	2.05212i	0.219172	+	0.126539i	0.605567	−	0.795794i	$-0.292946\pi$
$263$	3.55438	+	2.05212i	0.219172	+	0.126539i	−0.386395	+	0.922334i	$0.626280\pi$
$264$	−18.8250	−	1.83242i	−1.15860	−	0.112778i
$265$	−0.726304	−	0.726304i	−0.0446165	−	0.0446165i
$266$	9.02039	+	2.05504i	0.553076	+	0.126003i
$267$	4.70432	+	28.2929i	0.287900	+	1.73150i
$268$	−9.64903	−	2.58545i	−0.589408	−	0.157932i
$269$	19.5170	+	11.2681i	1.18997	+	0.687030i	0.958300	−	0.285765i	$-0.0922475\pi$
$269$	19.5170	+	11.2681i	1.18997	+	0.687030i	0.231671	+	0.972794i	$0.425581\pi$
$270$	−16.5995	+	15.6541i	−1.01021	+	0.952676i
$271$	19.0846	+	5.11370i	1.15931	+	0.310635i	0.786688	−	0.617350i	$-0.211794\pi$
$271$	19.0846	+	5.11370i	1.15931	+	0.310635i	0.372617	+	0.927985i	$0.378461\pi$
$272$	79.8402			4.84102
$273$	13.0200	−	10.1725i	0.788008	−	0.615666i
$274$	44.7072			2.70086
$275$	−2.51932	−	0.675049i	−0.151921	−	0.0407070i
$276$	6.24639	+	13.7444i	0.375989	+	0.827313i
$277$	−16.1557	−	9.32749i	−0.970701	−	0.560435i	−0.0712513	−	0.997458i	$-0.522699\pi$
$277$	−16.1557	−	9.32749i	−0.970701	−	0.560435i	−0.899450	+	0.437024i	$0.856033\pi$
$278$	35.7341	+	9.57492i	2.14319	+	0.574266i
$279$	4.92260	−	10.0397i	0.294709	−	0.601062i
$280$	−29.9099	+	32.2611i	−1.78746	+	1.92797i
$281$	−12.9394	−	12.9394i	−0.771897	−	0.771897i	0.206541	−	0.978438i	$-0.433779\pi$
$281$	−12.9394	−	12.9394i	−0.771897	−	0.771897i	−0.978438	+	0.206541i	$0.933779\pi$
$282$	1.55245	−	15.9488i	0.0924473	−	0.949736i
$283$	−8.84233	−	5.10512i	−0.525622	−	0.303468i	0.213610	−	0.976919i	$-0.431478\pi$
$283$	−8.84233	−	5.10512i	−0.525622	−	0.303468i	−0.739232	+	0.673451i	$0.764811\pi$
$284$	22.8423	−	6.12058i	1.35544	−	0.363190i
$285$	0.330887	−	3.39929i	0.0196000	−	0.201356i
$286$	0.653924	−	10.3769i	0.0386674	−	0.613596i
$287$	6.82006	+	3.60101i	0.402576	+	0.212561i
$288$	−77.7171	−	38.1057i	−4.57953	−	2.24540i
$289$	−1.43291	−	2.48188i	−0.0842891	−	0.145993i
$290$	11.1521	−	19.3159i	0.654872	−	1.13427i
$291$	14.5950	+	5.47417i	0.855573	+	0.320901i
$292$	−4.81806	+	17.9812i	−0.281956	+	1.05227i
$293$	−17.3681	−	17.3681i	−1.01465	−	1.01465i	−0.999891	−	0.0147614i	$-0.995301\pi$
$293$	−17.3681	−	17.3681i	−1.01465	−	1.01465i	−0.0147614	−	0.999891i	$-0.504699\pi$
$294$	24.4305	−	23.4052i	1.42482	−	1.36502i
$295$	3.58375			0.208654
$296$	−4.09572	−	7.09399i	−0.238059	−	0.412330i
$297$	0.157333	−	5.36750i	0.00912936	−	0.311454i
$298$	−42.9871	−	24.8186i	−2.49017	−	1.43770i
$299$	−4.86477	+	2.41427i	−0.281337	+	0.139621i
$300$	−20.5789	−	14.7111i	−1.18812	−	0.849346i
$301$	−23.2455	+	7.18049i	−1.33985	+	0.413877i
$302$		−	56.3765i		−	3.24410i
$303$	1.43588	−	14.7512i	0.0824891	−	0.847433i
$304$	21.6819	−	5.80966i	1.24354	−	0.333207i
$305$	−0.129405	−	0.482947i	−0.00740972	−	0.0276535i
$306$	2.52526	+	37.2268i	0.144359	+	2.12812i
$307$	17.7177	−	17.7177i	1.01120	−	1.01120i	0.0112673	−	0.999937i	$-0.496413\pi$
$307$	17.7177	−	17.7177i	1.01120	−	1.01120i	0.999937	−	0.0112673i	$-0.00358656\pi$
$308$	−0.597943	−	15.8107i	−0.0340710	−	0.900896i
$309$	1.01146	−	1.41490i	0.0575401	−	0.0804908i
$310$	−15.8086	−	4.23590i	−0.897868	−	0.240583i
$311$	10.9972	−	19.0478i	0.623595	−	1.08010i	−0.365215	−	0.930923i	$-0.619005\pi$
$311$	10.9972	−	19.0478i	0.623595	−	1.08010i	0.988811	−	0.149176i	$-0.0476620\pi$
$312$	27.0146	−	60.2070i	1.52940	−	3.40855i
$313$	−13.1951	−	22.8546i	−0.745832	−	1.29182i	−0.949805	−	0.312842i	$-0.898719\pi$
$313$	−13.1951	−	22.8546i	−0.745832	−	1.29182i	0.203973	−	0.978976i	$-0.434614\pi$
$314$	13.0416	−	13.0416i	0.735981	−	0.735981i
$315$	−9.71286	−	7.85227i	−0.547258	−	0.442425i
$316$			63.2745i			3.55947i
$317$	−1.84886	−	0.495400i	−0.103842	−	0.0278244i	0.206524	−	0.978442i	$-0.433785\pi$
$317$	−1.84886	−	0.495400i	−0.103842	−	0.0278244i	−0.310366	+	0.950617i	$0.600452\pi$
$318$	2.95394	+	1.10794i	0.165649	+	0.0621302i
$319$	1.35860	+	5.07035i	0.0760668	+	0.283885i
$320$	−18.1990	+	67.9197i	−1.01736	+	3.79682i
$321$	−10.5621	+	14.7749i	−0.589516	+	0.824654i
$322$	−9.41369	+	5.92028i	−0.524605	+	0.329924i
$323$	−3.94934	−	3.94934i	−0.219747	−	0.219747i
$324$	19.7108	−	48.2068i	1.09504	−	2.67815i
$325$	5.03656	−	7.57894i	0.279378	−	0.420404i
$326$	−55.8129	−	32.2236i	−3.09119	−	1.78470i
$327$	−9.53031	+	7.83953i	−0.527027	+	0.433527i
$328$	30.8023			1.70077
$329$	8.76546	−	0.331501i	0.483256	−	0.0182762i
$330$	−7.75322	+	1.28915i	−0.426801	+	0.0709652i
$331$	7.29685	−	27.2322i	0.401071	−	1.49682i	−0.410117	−	0.912033i	$-0.634512\pi$
$331$	7.29685	−	27.2322i	0.401071	−	1.49682i	0.811188	−	0.584785i	$-0.198821\pi$
$332$	−30.6445	+	8.21117i	−1.68183	+	0.450646i
$333$	1.93072	−	1.29644i	0.105803	−	0.0710447i
$334$	16.4297	+	28.4570i	0.898992	+	1.55710i
$335$	−2.71640			−0.148413
$336$	25.9025	−	77.8938i	1.41310	−	4.24946i
$337$			8.32902i			0.453711i	0.973928	+	0.226855i	$0.0728445\pi$
$337$			8.32902i			0.453711i	−0.973928	+	0.226855i	$0.927156\pi$
$338$	33.5842	+	13.7135i	1.82674	+	0.745916i
$339$	6.20302	+	13.6489i	0.336902	+	0.741308i
$340$	39.2032	−	10.5045i	2.12609	−	0.569684i
$341$	3.33572	−	1.92588i	0.180639	−	0.104292i
$342$	3.39463	+	9.92581i	0.183560	+	0.536726i
$343$	14.4936	+	11.5298i	0.782581	+	0.622549i
$344$	−68.7084	+	68.7084i	−3.70451	+	3.70451i
$345$	2.60802	+	3.17050i	0.140411	+	0.170694i
$346$	−7.14872	−	26.6794i	−0.384317	−	1.43429i
$347$	24.2695	+	14.0120i	1.30286	+	0.752204i	0.980893	−	0.194548i	$-0.0623240\pi$
$347$	24.2695	+	14.0120i	1.30286	+	0.752204i	0.321963	+	0.946752i	$0.395657\pi$
$348$	−4.93239	+	50.6717i	−0.264404	+	2.71629i
$349$	−1.81924	+	1.81924i	−0.0973819	+	0.0973819i	−0.754119	−	0.656737i	$-0.771936\pi$
$349$	−1.81924	+	1.81924i	−0.0973819	+	0.0973819i	0.656737	+	0.754119i	$0.271936\pi$
$350$	8.70015	−	16.4775i	0.465043	−	0.880758i
$351$	17.5731	+	6.49519i	0.937981	+	0.346688i
$352$	−14.9082	−	25.8217i	−0.794607	−	1.37630i
$353$	−6.68403	−	24.9452i	−0.355755	−	1.32770i	−0.879531	−	0.475841i	$-0.842144\pi$
$353$	−6.68403	−	24.9452i	−0.355755	−	1.32770i	0.523776	−	0.851856i	$-0.324523\pi$
$354$	−10.0211	+	4.55429i	−0.532616	+	0.242058i
$355$	5.56905	−	3.21529i	0.295575	−	0.170650i
$356$	−67.7576	+	67.7576i	−3.59115	+	3.59115i
$357$	−20.0074	+	4.10918i	−1.05891	+	0.217481i
$358$	−29.8915	+	29.8915i	−1.57981	+	1.57981i
$359$	0.252966	−	0.944080i	0.0133510	−	0.0498267i	−0.958929	−	0.283646i	$-0.908456\pi$
$359$	0.252966	−	0.944080i	0.0133510	−	0.0498267i	0.972280	+	0.233820i	$0.0751225\pi$
$360$	−48.9469	−	9.62014i	−2.57973	−	0.507026i
$361$	15.0946	+	8.71487i	0.794452	+	0.458677i
$362$	−2.18928	+	8.17050i	−0.115066	+	0.429432i
$363$	−10.0043	+	13.9947i	−0.525090	+	0.734529i
$364$	52.9452	+	15.6228i	2.77508	+	0.818860i
$365$			5.06209i			0.264962i
$366$	0.975589	+	1.18600i	0.0509948	+	0.0619931i
$367$	−6.76464	+	11.7167i	−0.353111	+	0.611607i	−0.986793	−	0.161987i	$-0.948210\pi$
$367$	−6.76464	+	11.7167i	−0.353111	+	0.611607i	0.633682	+	0.773594i	$0.281543\pi$
$368$	−13.4908	+	23.3668i	−0.703258	+	1.21808i
$369$	0.591852	+	8.72495i	0.0308106	+	0.454203i
$370$	−2.40695	−	2.40695i	−0.125131	−	0.125131i
$371$	−0.383619	+	1.68386i	−0.0199165	+	0.0874216i
$372$	36.8516	−	6.12740i	1.91066	−	0.317691i
$373$	−0.132468	−	0.229442i	−0.00685894	−	0.0118800i	0.862576	−	0.505928i	$-0.168850\pi$
$373$	−0.132468	−	0.229442i	−0.00685894	−	0.0118800i	−0.869435	+	0.494048i	$0.835517\pi$
$374$	−6.42655	+	11.1311i	−0.332309	+	0.575576i
$375$	−19.2003	−	7.20149i	−0.991498	−	0.371883i
$376$	30.3398	−	17.5167i	1.56465	−	0.903353i
$377$	−18.2780	−	1.15184i	−0.941366	−	0.0593226i
$378$	37.1385	+	9.61377i	1.91020	+	0.494479i
$379$	−14.8979	−	14.8979i	−0.765254	−	0.765254i	0.212013	−	0.977267i	$-0.431998\pi$
$379$	−14.8979	−	14.8979i	−0.765254	−	0.765254i	−0.977267	+	0.212013i	$0.931998\pi$
$380$	9.88190	−	5.70532i	0.506931	−	0.292677i
$381$	2.55630	+	5.62480i	0.130963	+	0.288167i
$382$	−29.2761	+	7.84452i	−1.49790	+	0.401361i
$383$	24.0935	+	6.45583i	1.23112	+	0.329878i	0.815015	−	0.579439i	$-0.196728\pi$
$383$	24.0935	+	6.45583i	1.23112	+	0.329878i	0.416104	+	0.909317i	$0.363395\pi$
$384$	−19.0309	−	114.456i	−0.971165	−	5.84081i
$385$	−1.26981	−	4.11078i	−0.0647157	−	0.209505i
$386$		−	33.3679i		−	1.69838i
$387$	−20.7823	−	18.1419i	−1.05642	−	0.922203i
$388$	13.4789	+	50.3041i	0.684289	+	2.55380i
$389$	−5.37669	+	9.31271i	−0.272609	+	0.472173i	−0.969529	−	0.244976i	$-0.921220\pi$
$389$	−5.37669	+	9.31271i	−0.272609	+	0.472173i	0.696920	+	0.717149i	$0.254553\pi$
$390$	4.36798	−	27.0719i	0.221181	−	1.37084i
$391$	6.71357			0.339520
$392$	72.6894	+	13.6932i	3.67137	+	0.691610i
$393$	−4.16102	+	5.82070i	−0.209895	+	0.293615i
$394$	23.5555	−	13.5998i	1.18671	−	0.685148i
$395$	4.45327	+	16.6198i	0.224068	+	0.836234i
$396$	14.8941	−	10.0012i	0.748459	−	0.502577i
$397$	−24.1032	−	6.45844i	−1.20971	−	0.324140i	−0.403059	−	0.915174i	$-0.632053\pi$
$397$	−24.1032	−	6.45844i	−1.20971	−	0.324140i	−0.806647	+	0.591034i	$0.798720\pi$
$398$	33.3813	+	33.3813i	1.67325	+	1.67325i
$399$	−5.13434	+	2.57178i	−0.257039	+	0.128750i
$400$		−	45.2096i		−	2.26048i
$401$	−5.60719	+	20.9263i	−0.280010	+	1.04501i	0.672399	+	0.740189i	$0.265264\pi$
$401$	−5.60719	+	20.9263i	−0.280010	+	1.04501i	−0.952409	+	0.304822i	$0.901403\pi$
$402$	7.59578	−	3.45205i	0.378843	−	0.172173i
$403$	2.65489	+	13.1737i	0.132249	+	0.656231i
$404$	42.8824	−	24.7582i	2.13348	−	1.23177i
$405$	1.78447	−	14.0494i	0.0886711	−	0.698118i
$406$	−37.4744	+	1.41725i	−1.85982	+	0.0703367i
$407$	0.801109			0.0397095
$408$	−62.9996	+	51.8228i	−3.11894	+	2.56561i
$409$	9.73562	−	2.60865i	0.481396	−	0.128990i	−0.00995679	−	0.999950i	$-0.503169\pi$
$409$	9.73562	−	2.60865i	0.481396	−	0.128990i	0.491352	+	0.870961i	$0.336503\pi$
$410$	12.3637	−	3.31285i	0.610601	−	0.163610i
$411$	−21.4308	+	17.6287i	−1.05710	+	0.869561i
$412$	5.81081			0.286278
$413$	−3.20784	−	5.10070i	−0.157847	−	0.250989i
$414$	−11.3219	−	5.55126i	−0.556439	−	0.272829i
$415$	−7.47125	+	4.31353i	−0.366749	+	0.211743i
$416$	101.978	−	20.5514i	4.99986	−	1.00762i
$417$	−20.9050	+	9.50068i	−1.02372	+	0.465250i
$418$	−0.935270	+	3.49047i	−0.0457455	+	0.170725i
$419$		−	24.0355i		−	1.17421i	−0.809510	−	0.587106i	$-0.800267\pi$
$419$		−	24.0355i		−	1.17421i	0.809510	−	0.587106i	$-0.199733\pi$
$420$	2.47028	−	41.6554i	0.120537	−	2.03257i
$421$	15.6959	+	15.6959i	0.764971	+	0.764971i	0.977216	−	0.212246i	$-0.0680777\pi$
$421$	15.6959	+	15.6959i	0.764971	+	0.764971i	−0.212246	+	0.977216i	$0.568078\pi$
$422$	12.5322	+	3.35800i	0.610060	+	0.163465i
$423$	5.54466	+	8.25734i	0.269591	+	0.401486i
$424$	1.78520	+	6.66244i	0.0866968	+	0.323557i
$425$	−9.74197	+	5.62453i	−0.472555	+	0.272830i
$426$	−11.4865	+	16.0681i	−0.556523	+	0.778501i
$427$	−0.571541	+	0.616470i	−0.0276588	+	0.0298331i
$428$	−60.6786			−2.93301
$429$	3.77829	+	5.23209i	0.182417	+	0.252608i
$430$	−20.1891	+	34.9685i	−0.973604	+	1.68633i
$431$	−3.14504	−	11.7374i	−0.151491	−	0.565373i	−0.999380	−	0.0351992i	$-0.988793\pi$
$431$	−3.14504	−	11.7374i	−0.151491	−	0.565373i	0.847889	−	0.530174i	$-0.177873\pi$
$432$	90.5744	−	21.4460i	4.35776	−	1.03182i
$433$			10.1150i			0.486097i	0.970014	+	0.243048i	$0.0781474\pi$
$433$			10.1150i			0.486097i	−0.970014	+	0.243048i	$0.921853\pi$
$434$	8.12148	+	26.2917i	0.389844	+	1.26204i
$435$	2.27073	+	13.6567i	0.108873	+	0.654789i
$436$	−39.8242	−	10.6709i	−1.90723	−	0.511041i
$437$	1.82318	−	0.488520i	0.0872147	−	0.0233691i
$438$	−6.43299	−	14.1550i	−0.307380	−	0.676350i
$439$	5.29475	−	3.05693i	0.252705	−	0.145899i	−0.368297	−	0.929708i	$-0.620059\pi$
$439$	5.29475	−	3.05693i	0.252705	−	0.145899i	0.621002	+	0.783809i	$0.286726\pi$
$440$	−12.1505	−	12.1505i	−0.579254	−	0.579254i
$441$	−2.48199	+	20.8528i	−0.118190	+	0.992991i
$442$	−29.6523	−	33.6409i	−1.41042	−	1.60014i
$443$	−27.2631	+	15.7404i	−1.29531	+	0.747848i	−0.979590	−	0.201004i	$-0.935580\pi$
$443$	−27.2631	+	15.7404i	−1.29531	+	0.747848i	−0.315721	+	0.948852i	$0.602246\pi$
$444$	7.27493	+	2.72862i	0.345253	+	0.129495i
$445$	−13.0286	+	22.5662i	−0.617614	+	1.06974i
$446$	−14.8935	−	25.7963i	−0.705227	−	1.22149i
$447$	30.3926	−	5.05345i	1.43752	−	0.239020i
$448$	112.959	−	34.8929i	5.33682	−	1.64854i
$449$	−2.15028	−	2.15028i	−0.101478	−	0.101478i	0.654545	−	0.756023i	$-0.272860\pi$
$449$	−2.15028	−	2.15028i	−0.101478	−	0.101478i	−0.756023	+	0.654545i	$0.772860\pi$
$450$	21.0797	−	1.42993i	0.993708	−	0.0674076i
$451$	−1.50621	+	2.60883i	−0.0709246	+	0.122845i
$452$	−25.0446	+	43.3785i	−1.17800	+	2.04035i
$453$	22.2301	+	27.0246i	1.04446	+	1.26973i
$454$		−	24.6509i		−	1.15692i
$455$	15.0063	+	0.377238i	0.703504	+	0.0176852i
$456$	−13.3376	+	18.6576i	−0.624592	+	0.873721i
$457$	−6.12968	+	22.8763i	−0.286734	+	1.07011i	0.660828	+	0.750537i	$0.270205\pi$
$457$	−6.12968	+	22.8763i	−0.286734	+	1.07011i	−0.947563	+	0.319570i	$0.896461\pi$
$458$	49.6859	+	28.6862i	2.32167	+	1.34042i
$459$	−15.8896	−	16.8493i	−0.741664	−	0.786456i
$460$	−3.54994	+	13.2485i	−0.165517	+	0.617716i
$461$	16.4758	−	16.4758i	0.767354	−	0.767354i	−0.210286	−	0.977640i	$-0.567440\pi$
$461$	16.4758	−	16.4758i	0.767354	−	0.767354i	0.977640	+	0.210286i	$0.0674395\pi$
$462$	8.77479	+	9.88114i	0.408240	+	0.459712i
$463$	8.26830	−	8.26830i	0.384261	−	0.384261i	−0.488374	−	0.872635i	$-0.662410\pi$
$463$	8.26830	−	8.26830i	0.384261	−	0.384261i	0.872635	+	0.488374i	$0.162410\pi$
$464$	−78.7983	+	45.4942i	−3.65812	+	2.11202i
$465$	9.24827	−	4.20306i	0.428878	−	0.194912i
$466$	−15.5883	−	58.1764i	−0.722115	−	2.69497i
$467$	−11.8280	−	20.4867i	−0.547334	−	0.948010i	−0.998456	−	0.0555478i	$-0.982309\pi$
$467$	−11.8280	−	20.4867i	−0.547334	−	0.948010i	0.451122	−	0.892462i	$-0.351024\pi$
$468$	16.4901	+	60.3821i	0.762257	+	2.79116i
$469$	2.43147	+	3.86622i	0.112275	+	0.178525i
$470$	10.2941	−	10.2941i	0.474831	−	0.474831i
$471$	−1.10911	+	11.3941i	−0.0511049	+	0.525014i
$472$	−20.8413	−	12.0327i	−0.959297	−	0.553850i
$473$	−2.45953	−	9.17909i	−0.113089	−	0.422055i
$474$	−33.5733	−	40.8142i	−1.54207	−	1.87466i
$475$	−2.23632	+	2.23632i	−0.102609	+	0.102609i
$476$	−50.0419	−	46.3947i	−2.29367	−	2.12650i
$477$	−1.85288	+	0.633683i	−0.0848373	+	0.0290144i
$478$	−18.9151	+	10.9206i	−0.865157	+	0.499499i
$479$	−36.8563	+	9.87561i	−1.68401	+	0.451228i	−0.968832	−	0.247717i	$-0.920320\pi$
$479$	−36.8563	+	9.87561i	−1.68401	+	0.451228i	−0.715175	+	0.698946i	$0.753653\pi$
$480$	−32.5357	−	71.5906i	−1.48505	−	3.26765i
$481$	−0.891773	+	2.64895i	−0.0406613	+	0.120782i
$482$			57.4242i			2.61560i
$483$	2.17808	−	6.54991i	0.0991060	−	0.298031i
$484$	−57.4743			−2.61247
$485$	7.08082	+	12.2643i	0.321523	+	0.556895i
$486$	12.8643	+	41.5535i	0.583536	+	1.88490i
$487$	13.1386	−	3.52048i	0.595368	−	0.159528i	0.0514625	−	0.998675i	$-0.483612\pi$
$487$	13.1386	−	3.52048i	0.595368	−	0.159528i	0.543905	+	0.839147i	$0.316945\pi$
$488$	−0.868976	+	3.24306i	−0.0393367	+	0.146807i
$489$	39.4606	−	6.56121i	1.78447	−	0.296708i
$490$	30.6495	−	2.32158i	1.38460	−	0.104878i
$491$	12.8768			0.581124			0.290562	−	0.956856i	$-0.406158\pi$
$491$	12.8768			0.581124			0.290562	+	0.956856i	$0.406158\pi$
$492$	−22.5638	+	18.5607i	−1.01726	+	0.836783i
$493$	19.6066	+	11.3199i	0.883036	+	0.509821i
$494$	−10.5005	−	6.97807i	−0.472440	−	0.313958i
$495$	3.20825	−	3.67518i	0.144200	−	0.165187i
$496$	47.2102	+	47.2102i	2.11980	+	2.11980i
$497$	−9.56119	−	5.04833i	−0.428878	−	0.226449i
$498$	15.4099	−	21.5564i	0.690534	−	0.965964i
$499$	4.36632	−	16.2953i	0.195463	−	0.729479i	−0.796683	−	0.604397i	$-0.793414\pi$
$499$	4.36632	−	16.2953i	0.195463	−	0.729479i	0.992146	−	0.125082i	$-0.0399193\pi$
$500$	−17.7321	−	66.1771i	−0.793003	−	2.95953i
$501$	−19.0968	−	7.16266i	−0.853180	−	0.320004i
$502$	4.36402	+	1.16934i	0.194776	+	0.0521900i
$503$		−	23.3328i		−	1.04036i	−0.854058	−	0.520178i	$-0.825865\pi$
$503$		−	23.3328i		−	1.04036i	0.854058	−	0.520178i	$-0.174135\pi$
$504$	30.1205	+	78.2765i	1.34167	+	3.48671i
$505$	9.52111	−	9.52111i	0.423684	−	0.423684i
$506$	−2.17183	−	3.76171i	−0.0965494	−	0.167228i
$507$	−21.5064	+	6.66909i	−0.955131	+	0.296185i
$508$	−10.3210	+	17.8765i	−0.457921	+	0.793143i
$509$	4.89245	+	1.31093i	0.216854	+	0.0581059i	0.365610	−	0.930768i	$-0.380860\pi$
$509$	4.89245	+	1.31093i	0.216854	+	0.0581059i	−0.148756	+	0.988874i	$0.547527\pi$
$510$	−19.7137	+	27.5768i	−0.872938	+	1.22112i
$511$	7.20481	−	4.53111i	0.318722	−	0.200445i
$512$	97.7648	−	97.7648i	4.32063	−	4.32063i
$513$	−5.54114	−	3.41947i	−0.244648	−	0.150973i
$514$	21.5353	+	80.3710i	0.949883	+	3.54501i
$515$	1.52628	−	0.408966i	0.0672560	−	0.0180212i
$516$	8.92933	−	91.7334i	0.393092	−	4.03834i
$517$			3.42620i			0.150684i
$518$	−1.27130	+	5.58026i	−0.0558579	+	0.245183i
$519$	13.9469	+	9.97015i	0.612201	+	0.437641i
$520$	53.7027	−	26.6514i	2.35502	−	1.16874i
$521$	−13.1444	−	7.58895i	−0.575869	−	0.332478i	0.183621	−	0.982997i	$-0.441218\pi$
$521$	−13.1444	−	7.58895i	−0.575869	−	0.332478i	−0.759490	+	0.650519i	$0.774551\pi$
$522$	−23.7047	−	35.3021i	−1.03753	−	1.54513i
$523$	−10.2084	−	17.6815i	−0.446384	−	0.773159i	0.551764	−	0.834000i	$-0.313955\pi$
$523$	−10.2084	−	17.6815i	−0.446384	−	0.773159i	−0.998147	+	0.0608411i	$0.980622\pi$
$524$	−23.9049			−1.04429
$525$	2.32683	+	11.3292i	0.101551	+	0.494448i
$526$	−8.09835	−	8.09835i	−0.353105	−	0.353105i
$527$	4.29964	−	16.0465i	0.187295	−	0.698995i
$528$	30.0209	+	11.2600i	1.30649	+	0.490028i
$529$	10.3656	−	17.9537i	0.450678	−	0.780597i
$530$	1.43312	+	2.48223i	0.0622506	+	0.107821i
$531$	3.00788	−	6.13462i	0.130531	−	0.266220i
$532$	−16.9657	−	8.95791i	−0.735555	−	0.388375i
$533$	−6.94970	−	7.88452i	−0.301025	−	0.341516i
$534$	7.75391	−	79.6580i	0.335545	−	3.44714i
$535$	−15.9380	+	4.27057i	−0.689059	+	0.184633i
$536$	15.7972	+	9.12053i	0.682336	+	0.393947i
$537$	2.54208	−	26.1154i	0.109699	−	1.12696i
$538$	−44.4677	−	44.4677i	−1.91714	−	1.91714i
$539$	−4.71420	+	5.48690i	−0.203055	+	0.236337i
$540$	41.6522	−	22.4471i	1.79243	−	0.965970i
$541$	−4.26856	−	1.14376i	−0.183520	−	0.0491740i	0.165889	−	0.986144i	$-0.446951\pi$
$541$	−4.26856	−	1.14376i	−0.183520	−	0.0491740i	−0.349408	+	0.936971i	$0.613617\pi$
$542$	−47.7472	−	27.5668i	−2.05092	−	1.18410i
$543$	−2.17230	−	4.77987i	−0.0932225	−	0.205124i
$544$	−124.215	−	33.2834i	−5.32568	−	1.42701i
$545$	−11.2113			−0.480240
$546$	−42.4409	+	18.0154i	−1.81630	+	0.770986i
$547$	6.98230			0.298542			0.149271	−	0.988796i	$-0.452307\pi$
$547$	6.98230			0.298542			0.149271	+	0.988796i	$0.452307\pi$
$548$	−89.5525	−	23.9955i	−3.82549	−	1.02504i
$549$	−0.935315	−	0.183829i	−0.0399183	−	0.00784563i
$550$	6.30301	+	3.63904i	0.268761	+	0.155169i
$551$	6.14820	+	1.64740i	0.261922	+	0.0701818i
$552$	−4.52173	−	27.1947i	−0.192457	−	1.15748i
$553$	19.6686	−	21.2148i	0.836395	−	0.902145i
$554$	36.8093	+	36.8093i	1.56388	+	1.56388i
$555$	2.10289	+	0.204696i	0.0892628	+	0.00868884i
$556$	−66.4395	−	38.3589i	−2.81766	−	1.62678i
$557$	38.8946	−	10.4218i	1.64802	−	0.441584i	0.688959	−	0.724800i	$-0.258068\pi$
$557$	38.8946	−	10.4218i	1.64802	−	0.441584i	0.959056	+	0.283216i	$0.0914014\pi$
$558$	−20.5193	+	23.5057i	−0.868652	+	0.995077i
$559$	33.0895	+	2.08522i	1.39954	+	0.0881956i
$560$	63.1304	−	39.7028i	2.66775	−	1.67775i
$561$	−1.30854	−	7.86989i	−0.0552468	−	0.332267i
$562$	25.5315	+	44.2218i	1.07698	+	1.86538i
$563$	−14.9695	+	25.9279i	−0.630889	+	1.09273i	0.356482	+	0.934302i	$0.383976\pi$
$563$	−14.9695	+	25.9279i	−0.630889	+	1.09273i	−0.987370	+	0.158429i	$0.949357\pi$
$564$	−11.6698	+	31.1136i	−0.491389	+	1.31012i
$565$	−3.52529	+	13.1565i	−0.148310	+	0.553500i
$566$	20.1465	+	20.1465i	0.846820	+	0.846820i
$567$	−21.5936	+	10.0359i	−0.906844	+	0.421466i
$568$	−43.1824			−1.81189
$569$	9.13425	+	15.8210i	0.382928	+	0.663250i	0.991479	−	0.130264i	$-0.0415826\pi$
$569$	9.13425	+	15.8210i	0.382928	+	0.663250i	−0.608552	+	0.793514i	$0.708249\pi$
$570$	−3.34693	+	8.92344i	−0.140187	+	0.373762i
$571$	36.6005	+	21.1313i	1.53168	+	0.884318i	0.999284	+	0.0378246i	$0.0120428\pi$
$571$	36.6005	+	21.1313i	1.53168	+	0.884318i	0.532399	+	0.846493i	$0.321291\pi$
$572$	−6.87940	+	20.4348i	−0.287642	+	0.854421i
$573$	10.9406	−	15.3044i	0.457049	−	0.639350i
$574$	−15.7820	−	14.6318i	−0.658728	−	0.610719i
$575$		−	3.80157i		−	0.158536i
$576$	100.989	+	88.1587i	4.20789	+	3.67328i
$577$	37.9001	−	10.1553i	1.57780	−	0.422770i	0.639556	−	0.768744i	$-0.279118\pi$
$577$	37.9001	−	10.1553i	1.57780	−	0.422770i	0.938244	+	0.345974i	$0.112451\pi$
$578$	2.06978	+	7.72453i	0.0860916	+	0.321298i
$579$	13.1575	+	15.9952i	0.546806	+	0.664738i
$580$	−32.7060	+	32.7060i	−1.35804	+	1.35804i
$581$	12.8270	+	6.77266i	0.532152	+	0.280977i
$582$	−35.3856	−	25.2959i	−1.46678	−	1.04855i
$583$	−0.651575	−	0.174589i	−0.0269855	−	0.00723074i
$584$	16.9964	−	29.4386i	0.703315	−	1.21818i
$585$	8.58104	+	14.6995i	0.354782	+	0.607750i
$586$	34.2700	+	59.3574i	1.41568	+	2.45203i
$587$	−21.5243	+	21.5243i	−0.888402	+	0.888402i	−0.994370	−	0.105968i	$-0.966206\pi$
$587$	−21.5243	+	21.5243i	−0.888402	+	0.888402i	0.105968	+	0.994370i	$0.466206\pi$
$588$	−61.4987	+	33.7701i	−2.53617	+	1.39266i
$589$		−	4.67055i		−	0.192447i
$590$	−9.65960	−	2.58828i	−0.397679	−	0.106558i
$591$	−5.92895	+	15.8075i	−0.243884	+	0.650234i
$592$	3.59401	+	13.4130i	0.147713	+	0.551273i
$593$	5.55820	−	20.7435i	0.228248	−	0.851833i	−0.752829	−	0.658216i	$-0.771311\pi$
$593$	5.55820	−	20.7435i	0.228248	−	0.851833i	0.981077	−	0.193617i	$-0.0620220\pi$
$594$	−4.30063	+	14.3539i	−0.176457	+	0.588947i
$595$	−16.4094	−	8.66419i	−0.672719	−	0.355197i
$596$	72.7862	+	72.7862i	2.98144	+	2.98144i
$597$	−29.1644	−	2.83887i	−1.19362	−	0.116187i
$598$	14.8561	−	2.99393i	0.607512	−	0.122431i
$599$	−14.4051	−	8.31677i	−0.588575	−	0.339814i	0.175959	−	0.984398i	$-0.443697\pi$
$599$	−14.4051	−	8.31677i	−0.588575	−	0.339814i	−0.764534	+	0.644583i	$0.777031\pi$
$600$	29.3447	+	35.6736i	1.19799	+	1.45637i
$601$	20.5693			0.839041			0.419520	−	0.907746i	$-0.362198\pi$
$601$	20.5693			0.839041			0.419520	+	0.907746i	$0.362198\pi$
$602$	67.8417	−	2.56570i	2.76502	−	0.104570i
$603$	−2.27991	+	4.64991i	−0.0928451	+	0.189359i
$604$	−30.2587	+	112.927i	−1.23121	+	4.59494i
$605$	−15.0963	+	4.04505i	−0.613753	+	0.164455i
$606$	−14.5240	+	38.7232i	−0.589996	+	1.57302i
$607$	8.14247	+	14.1032i	0.330493	+	0.572430i	0.982609	−	0.185689i	$-0.0594517\pi$
$607$	8.14247	+	14.1032i	0.330493	+	0.572430i	−0.652116	+	0.758119i	$0.726118\pi$
$608$	−36.1546			−1.46626
$609$	17.4049	−	15.4561i	0.705280	−	0.626313i
$610$			1.39519i			0.0564896i
$611$	−11.3291	−	3.81395i	−0.458326	−	0.154296i
$612$	14.9223	−	75.9240i	0.603198	−	3.06905i
$613$	−15.4508	+	4.14004i	−0.624053	+	0.167214i	−0.556970	−	0.830533i	$-0.688036\pi$
$613$	−15.4508	+	4.14004i	−0.624053	+	0.167214i	−0.0670834	+	0.997747i	$0.521369\pi$
$614$	−60.5524	+	34.9600i	−2.44370	+	1.41087i
$615$	−4.62036	+	6.46325i	−0.186311	+	0.260624i
$616$	−6.41767	+	28.1697i	−0.258575	+	1.13499i
$617$	0.771778	−	0.771778i	0.0310706	−	0.0310706i	−0.691401	−	0.722471i	$-0.743006\pi$
$617$	0.771778	−	0.771778i	0.0310706	−	0.0310706i	0.722471	+	0.691401i	$0.243006\pi$
$618$	−3.74817	+	3.08320i	−0.150773	+	0.124025i
$619$	−3.76338	−	14.0451i	−0.151263	−	0.564521i	−0.999396	−	0.0347384i	$-0.988940\pi$
$619$	−3.76338	−	14.0451i	−0.151263	−	0.564521i	0.848133	−	0.529783i	$-0.177726\pi$
$620$	29.3925	+	16.9698i	1.18043	+	0.681523i
$621$	7.61618	−	1.80334i	0.305627	−	0.0723655i
$622$	−43.3987	+	43.3987i	−1.74013	+	1.74013i
$623$	43.7801	−	1.65572i	1.75401	−	0.0663350i
$624$	−70.6508	+	86.7330i	−2.82830	+	3.47210i
$625$	−3.00549	−	5.20567i	−0.120220	−	0.208227i
$626$	19.0598	+	71.1320i	0.761781	+	2.84301i
$627$	−0.928018	−	2.04198i	−0.0370615	−	0.0815489i
$628$	−33.1233	+	19.1238i	−1.32176	+	0.763121i
$629$	2.44317	−	2.44317i	0.0974155	−	0.0974155i
$630$	20.5088	+	28.1798i	0.817092	+	1.12271i
$631$	12.9442	−	12.9442i	0.515300	−	0.515300i	−0.400846	−	0.916146i	$-0.631284\pi$
$631$	12.9442	−	12.9442i	0.515300	−	0.515300i	0.916146	+	0.400846i	$0.131284\pi$
$632$	29.9044	−	111.605i	1.18953	−	4.43940i
$633$	−7.33155	+	3.33197i	−0.291403	+	0.132434i
$634$	4.62561	+	2.67060i	0.183706	+	0.106063i
$635$	−1.45279	+	5.42189i	−0.0576522	+	0.215161i
$636$	−5.32235	−	3.80476i	−0.211045	−	0.150869i
$637$	−12.8953	−	21.6959i	−0.510930	−	0.859622i
$638$		−	14.6478i		−	0.579912i
$639$	−0.829729	−	12.2317i	−0.0328236	−	0.483878i
$640$	52.7059	−	91.2892i	2.08338	−	3.60852i
$641$	21.7902	−	37.7418i	0.860663	−	1.49071i	−0.0106275	−	0.999944i	$-0.503383\pi$
$641$	21.7902	−	37.7418i	0.860663	−	1.49071i	0.871290	−	0.490768i	$-0.163284\pi$
$642$	39.1397	−	32.1959i	1.54472	−	1.27067i
$643$	−35.0831	−	35.0831i	−1.38354	−	1.38354i	−0.838239	−	0.545303i	$-0.816415\pi$
$643$	−35.0831	−	35.0831i	−1.38354	−	1.38354i	−0.545303	−	0.838239i	$-0.683585\pi$
$644$	22.0340	−	6.80628i	0.868263	−	0.268205i
$645$	−4.11081	−	24.7234i	−0.161863	−	0.973481i
$646$	7.79269	+	13.4973i	0.306599	+	0.531046i
$647$	−21.7667	+	37.7011i	−0.855739	+	1.48218i	0.0202185	+	0.999796i	$0.493564\pi$
$647$	−21.7667	+	37.7011i	−0.855739	+	1.48218i	−0.875958	+	0.482388i	$0.839770\pi$
$648$	−57.5494	+	75.7124i	−2.26075	+	2.97427i
$649$	2.03824	−	1.17678i	0.0800079	−	0.0461926i
$650$	−19.0492	+	16.7907i	−0.747172	+	0.658585i
$651$	−14.2603	−	9.40076i	−0.558907	−	0.368445i
$652$	94.5029	+	94.5029i	3.70102	+	3.70102i
$653$	24.3200	−	14.0411i	0.951714	−	0.549472i	0.0581008	−	0.998311i	$-0.481496\pi$
$653$	24.3200	−	14.0411i	0.951714	−	0.549472i	0.893613	+	0.448839i	$0.148162\pi$
$654$	31.3499	−	14.2475i	1.22588	−	0.557123i
$655$	−6.27891	+	1.68243i	−0.245337	+	0.0657379i
$656$	−50.4372	−	13.5146i	−1.96924	−	0.527656i
$657$	8.66523	+	4.24868i	0.338063	+	0.165757i
$658$	−23.8658	−	5.43714i	−0.930385	−	0.211962i
$659$		−	22.2850i		−	0.868100i	−0.900889	−	0.434050i	$-0.857084\pi$
$659$		−	22.2850i		−	0.868100i	0.900889	−	0.434050i	$-0.142916\pi$
$660$	16.2223	+	1.57908i	0.631453	+	0.0614657i
$661$	4.74855	+	17.7218i	0.184697	+	0.689300i	0.994695	+	0.102867i	$0.0328016\pi$
$661$	4.74855	+	17.7218i	0.184697	+	0.689300i	−0.809998	+	0.586433i	$0.800532\pi$
$662$	−39.3357	+	68.1315i	−1.52883	+	2.64801i
$663$	27.4793	+	4.43371i	1.06721	+	0.172191i
$664$	57.9320			2.24820
$665$	−5.08670	−	1.15886i	−0.197254	−	0.0449387i
$666$	−6.14038	+	2.10001i	−0.237935	+	0.0813736i
$667$	−6.62596	+	3.82550i	−0.256558	+	0.148124i
$668$	−17.6365	−	65.8202i	−0.682376	−	2.54666i
$669$	17.3112	+	6.49295i	0.669290	+	0.251032i
$670$	7.32177	+	1.96186i	0.282865	+	0.0757933i
$671$	−0.232182	−	0.232182i	−0.00896327	−	0.00896327i
$672$	−72.7710	+	110.389i	−2.80720	+	4.25834i
$673$			30.0715i			1.15917i	0.814912	+	0.579585i	$0.196785\pi$
$673$			30.0715i			1.15917i	−0.814912	+	0.579585i	$0.803215\pi$
$674$	6.01545	−	22.4500i	0.231707	−	0.864741i
$675$	−9.54092	+	8.99752i	−0.367230	+	0.346315i
$676$	−59.9119	−	45.4949i	−2.30430	−	1.74981i
$677$	−37.8020	+	21.8250i	−1.45285	+	0.838802i	−0.998642	−	0.0520941i	$-0.983410\pi$
$677$	−37.8020	+	21.8250i	−1.45285	+	0.838802i	−0.454206	+	0.890897i	$0.650077\pi$
$678$	−6.86193	−	41.2692i	−0.263531	−	1.58493i
$679$	11.1176	−	21.0559i	0.426654	−	0.808052i
$680$	−74.1118			−2.84206
$681$	9.72022	+	11.8166i	0.372480	+	0.452814i
$682$	−10.3820	+	2.78185i	−0.397547	+	0.106522i
$683$	2.92598	−	0.784014i	0.111960	−	0.0299995i	−0.202404	−	0.979302i	$-0.564875\pi$
$683$	2.92598	−	0.784014i	0.111960	−	0.0299995i	0.314364	+	0.949303i	$0.398209\pi$
$684$	−1.47230	−	21.7043i	−0.0562947	−	0.829884i
$685$	−25.2109			−0.963258
$686$	−30.7388	−	41.5449i	−1.17361	−	1.58619i
$687$	−35.1288	+	5.84095i	−1.34025	+	0.222846i
$688$	142.652	−	82.3603i	5.43857	−	3.13996i
$689$	1.30261	−	1.96016i	0.0496256	−	0.0746760i
$690$	−4.73981	−	10.4293i	−0.180442	−	0.397038i
$691$	4.52773	−	16.8977i	0.172243	−	0.642819i	−0.824762	−	0.565480i	$-0.808691\pi$
$691$	4.52773	−	16.8977i	0.172243	−	0.642819i	0.997005	−	0.0773390i	$-0.0246424\pi$
$692$			57.2781i			2.17739i
$693$	−8.10256	−	1.27658i	−0.307791	−	0.0484931i
$694$	−55.2960	−	55.2960i	−2.09901	−	2.09901i
$695$	−20.1509	−	5.39941i	−0.764366	−	0.204811i
$696$	32.6480	−	87.0447i	1.23752	−	3.29942i
$697$	3.36270	+	12.5498i	0.127371	+	0.475356i
$698$	6.21749	−	3.58967i	0.235335	−	0.135871i
$699$	30.4122	+	21.7407i	1.15030	+	0.822307i
$700$	−26.2711	+	28.3363i	−0.992954	+	1.07101i
$701$	24.1061			0.910474			0.455237	−	0.890370i	$-0.349554\pi$
$701$	24.1061			0.910474			0.455237	+	0.890370i	$0.349554\pi$
$702$	−42.6753	−	30.1989i	−1.61067	−	1.13978i
$703$	0.485703	−	0.841263i	0.0183187	−	0.0317288i
$704$	11.9519	+	44.6049i	0.450452	+	1.68111i
$705$	−0.875447	+	8.99369i	−0.0329712	+	0.338722i
$706$			72.0644i			2.71218i
$707$	−22.0737	−	5.02886i	−0.830166	−	0.189130i
$708$	22.5176	−	3.74405i	0.846263	−	0.140710i
$709$	−19.6208	−	5.25737i	−0.736873	−	0.197445i	−0.129185	−	0.991620i	$-0.541236\pi$
$709$	−19.6208	−	5.25737i	−0.736873	−	0.197445i	−0.607688	+	0.794176i	$0.707903\pi$
$710$	−17.3330	+	4.64435i	−0.650494	+	0.174299i
$711$	32.1873	+	6.32617i	1.20712	+	0.237250i
$712$	151.535	−	87.4890i	5.67903	−	3.27879i
$713$	3.96979	+	3.96979i	0.148670	+	0.148670i
$714$	56.8956	+	3.37407i	2.12927	+	0.126271i
$715$	−0.368755	+	5.85162i	−0.0137907	+	0.218838i
$716$	75.9189	−	43.8318i	2.83722	−	1.63807i
$717$	4.76095	−	12.6934i	0.177801	−	0.474045i
$718$	−1.36368	+	2.36197i	−0.0508922	+	0.0881479i
$719$	18.3989	+	31.8678i	0.686162	+	1.18847i	0.973070	+	0.230509i	$0.0740391\pi$
$719$	18.3989	+	31.8678i	0.686162	+	1.18847i	−0.286908	+	0.957958i	$0.592628\pi$
$720$	75.9270	+	37.2280i	2.82963	+	1.38741i
$721$	−1.94826	−	1.80627i	−0.0725570	−	0.0672689i
$722$	−34.3917	−	34.3917i	−1.27993	−	1.27993i
$723$	−22.6432	−	27.5268i	−0.842111	−	1.02373i
$724$	8.77065	−	15.1912i	0.325959	−	0.564577i
$725$	6.40989	−	11.1023i	0.238057	−	0.412328i
$726$	37.0728	−	30.4957i	1.37590	−	1.13180i
$727$			18.1195i			0.672014i	0.941860	+	0.336007i	$0.109077\pi$
$727$			18.1195i			0.672014i	−0.941860	+	0.336007i	$0.890923\pi$
$728$	−86.0023	−	52.5785i	−3.18746	−	1.94869i
$729$	−22.5518	−	14.8464i	−0.835252	−	0.549868i
$730$	3.65598	−	13.6443i	0.135314	−	0.504999i
$731$	−35.4947	−	20.4929i	−1.31282	−	0.757957i
$732$	−1.31764	−	2.89928i	−0.0487012	−	0.107161i
$733$	4.20772	−	15.7034i	0.155416	−	0.580019i	−0.843654	−	0.536888i	$-0.819600\pi$
$733$	4.20772	−	15.7034i	0.155416	−	0.580019i	0.999069	−	0.0431317i	$-0.0137335\pi$
$734$	26.6955	−	26.6955i	0.985348	−	0.985348i
$735$	−13.7767	+	13.1984i	−0.508160	+	0.486831i
$736$	30.7300	−	30.7300i	1.13272	−	1.13272i
$737$	−1.54494	+	0.891972i	−0.0569087	+	0.0328562i
$738$	4.70613	−	23.9446i	0.173235	−	0.881413i
$739$	−5.00198	−	18.6677i	−0.184001	−	0.686701i	−0.994842	−	0.101435i	$-0.967657\pi$
$739$	−5.00198	−	18.6677i	−0.184001	−	0.686701i	0.810841	−	0.585266i	$-0.199010\pi$
$740$	3.52947	+	6.11321i	0.129746	+	0.224726i
$741$	7.78507	−	0.795511i	0.285992	−	0.0292238i
$742$	2.25014	−	4.26160i	0.0826051	−	0.156448i
$743$	−23.1956	+	23.1956i	−0.850965	+	0.850965i	−0.990252	−	0.139287i	$-0.955519\pi$
$743$	−23.1956	+	23.1956i	−0.850965	+	0.850965i	0.139287	+	0.990252i	$0.455519\pi$
$744$	−67.8954	−	6.60894i	−2.48917	−	0.242296i
$745$	24.2409	+	13.9955i	0.888118	+	0.512755i
$746$	0.191345	+	0.714108i	0.00700562	+	0.0261453i
$747$	1.11314	+	16.4096i	0.0407275	+	0.600396i
$748$	18.8473	−	18.8473i	0.689126	−	0.689126i
$749$	20.3444	+	18.8617i	0.743370	+	0.689192i
$750$	46.5512	+	33.2778i	1.69981	+	1.21513i
$751$	−24.0745	+	13.8994i	−0.878491	+	0.507197i	−0.870161	−	0.492768i	$-0.835985\pi$
$751$	−24.0745	+	13.8994i	−0.878491	+	0.507197i	−0.00833061	+	0.999965i	$0.502652\pi$
$752$	−57.3652	+	15.3710i	−2.09189	+	0.560521i
$753$	−2.55302	+	1.16027i	−0.0930372	+	0.0422825i
$754$	48.4345	+	16.3056i	1.76388	+	0.593813i
$755$			31.7913i			1.15700i
$756$	−69.2319	−	39.1905i	−2.51794	−	1.42534i
$757$	−7.74434			−0.281473			−0.140736	−	0.990047i	$-0.544947\pi$
$757$	−7.74434			−0.281473			−0.140736	+	0.990047i	$0.544947\pi$
$758$	29.3960	+	50.9154i	1.06771	+	1.84933i
$759$	2.52438	+	0.946826i	0.0916294	+	0.0343676i
$760$	−20.1263	+	5.39283i	−0.730058	+	0.195618i
$761$	11.3485	−	42.3532i	0.411383	−	1.53530i	−0.380588	−	0.924745i	$-0.624278\pi$
$761$	11.3485	−	42.3532i	0.411383	−	1.53530i	0.791971	−	0.610558i	$-0.209055\pi$
$762$	−2.82784	−	17.0073i	−0.102442	−	0.616108i
$763$	10.0353	+	15.9569i	0.363304	+	0.577680i
$764$	62.8531			2.27395
$765$	−1.42402	−	20.9926i	−0.0514856	−	0.758990i
$766$	−60.2788	−	34.8020i	−2.17796	−	1.25745i
$767$	1.62223	+	8.04961i	0.0585753	+	0.290655i
$768$	−16.3709	+	168.183i	−0.590735	+	6.06878i
$769$	−27.2658	−	27.2658i	−0.983229	−	0.983229i	0.0166329	−	0.999862i	$-0.494705\pi$
$769$	−27.2658	−	27.2658i	−0.983229	−	0.983229i	−0.999862	+	0.0166329i	$0.994705\pi$
$770$	0.453724	+	11.9973i	0.0163511	+	0.432351i
$771$	−42.0147	−	30.0348i	−1.51312	−	1.08168i
$772$	−17.9094	+	66.8389i	−0.644574	+	2.40558i
$773$	−3.70219	−	13.8168i	−0.133159	−	0.496955i	0.866840	−	0.498586i	$-0.166147\pi$
$773$	−3.70219	−	13.8168i	−0.133159	−	0.496955i	−0.999999	+	0.00163167i	$0.999481\pi$
$774$	42.9138	+	63.9090i	1.54250	+	2.29716i
$775$	−9.08633	−	2.43468i	−0.326391	−	0.0874561i
$776$		−	95.0976i		−	3.41380i
$777$	−1.59097	−	3.17624i	−0.0570758	−	0.113947i
$778$	21.2182	−	21.2182i	0.760709	−	0.760709i
$779$	1.82639	+	3.16341i	0.0654374	+	0.113341i
$780$	−23.2797	+	51.8831i	−0.833546	+	1.85771i
$781$	2.11158	−	3.65737i	0.0755584	−	0.130871i
$782$	−18.0957	−	4.84873i	−0.647101	−	0.173390i
$783$	25.2832	+	7.57523i	0.903549	+	0.270717i
$784$	−113.017	−	54.3145i	−4.03632	−	1.93980i
$785$	−7.35431	+	7.35431i	−0.262487	+	0.262487i
$786$	15.4194	−	12.6839i	0.549993	−	0.452418i
$787$	−2.00314	−	7.47581i	−0.0714042	−	0.266484i	0.920990	−	0.389587i	$-0.127382\pi$
$787$	−2.00314	−	7.47581i	−0.0714042	−	0.266484i	−0.992394	+	0.123103i	$0.960716\pi$
$788$	−54.4832	+	14.5987i	−1.94089	+	0.520059i
$789$	7.07532	+	0.688712i	0.251888	+	0.0245188i
$790$		−	48.0132i		−	1.70823i
$791$	21.8811	−	6.75902i	0.778001	−	0.240323i
$792$	−30.9973	+	10.6011i	−1.10144	+	0.376692i
$793$	1.02619	−	0.509275i	0.0364412	−	0.0180849i
$794$	60.3032	+	34.8161i	2.14008	+	1.23558i
$795$	−1.66576	−	0.624780i	−0.0590784	−	0.0221587i
$796$	−48.9492	−	84.7825i	−1.73496	−	3.00503i
$797$	−10.4603			−0.370523			−0.185261	−	0.982689i	$-0.559313\pi$
$797$	−10.4603			−0.370523			−0.185261	+	0.982689i	$0.559313\pi$
$798$	15.6965	−	3.22379i	0.555649	−	0.114121i
$799$	10.4490	+	10.4490i	0.369659	+	0.369659i
$800$	−18.8467	+	70.3370i	−0.666333	+	2.48679i
$801$	27.6935	+	41.2423i	0.978500	+	1.45722i
$802$	30.2272	−	52.3550i	1.06736	−	1.84872i
$803$	1.66222	+	2.87904i	0.0586583	+	0.101599i
$804$	−17.0678	+	2.83791i	−0.601937	+	0.100085i
$805$	5.30849	−	3.33851i	0.187100	−	0.117667i
$806$	2.35849	−	37.4258i	0.0830742	−	1.31827i
$807$	38.8503	+	3.78169i	1.36760	+	0.133122i
$808$	−87.3379	+	23.4021i	−3.07254	+	0.823283i
$809$	25.4842	+	14.7133i	0.895978	+	0.517293i	0.875893	−	0.482505i	$-0.160273\pi$
$809$	25.4842	+	14.7133i	0.895978	+	0.517293i	0.0200848	+	0.999798i	$0.493606\pi$
$810$	−14.9567	+	36.5797i	−0.525524	+	1.28528i
$811$	−7.62739	−	7.62739i	−0.267834	−	0.267834i	0.560393	−	0.828227i	$-0.310650\pi$
$811$	−7.62739	−	7.62739i	−0.267834	−	0.267834i	−0.828227	+	0.560393i	$0.810650\pi$
$812$	75.8253	+	17.2746i	2.66095	+	0.606221i
$813$	33.7581	−	5.61303i	1.18395	−	0.196858i
$814$	−2.15930	−	0.578583i	−0.0756835	−	0.0202793i
$815$	31.4735	+	18.1712i	1.10247	+	0.636510i
$816$	125.896	−	57.2158i	4.40723	−	2.00295i
$817$	−11.1304	−	2.98237i	−0.389402	−	0.104340i
$818$	−28.1254			−0.983380
$819$	13.2407	−	25.3709i	0.462667	−	0.886532i
$820$	−26.5438			−0.926948
$821$	12.1138	+	3.24588i	0.422775	+	0.113282i	0.463933	−	0.885871i	$-0.346438\pi$
$821$	12.1138	+	3.24588i	0.422775	+	0.113282i	−0.0411579	+	0.999153i	$0.513105\pi$
$822$	70.4963	−	32.0384i	2.45884	−	1.11747i
$823$	−30.3860	−	17.5434i	−1.05919	−	0.611524i	−0.133982	−	0.990984i	$-0.542776\pi$
$823$	−30.3860	−	17.5434i	−1.05919	−	0.611524i	−0.925208	+	0.379460i	$0.876110\pi$
$824$	−10.2492	−	2.74627i	−0.357048	−	0.0956708i
$825$	−4.45633	+	0.740965i	−0.155150	+	0.0257971i
$826$	4.96251	+	16.0652i	0.172668	+	0.558979i
$827$	−3.81401	−	3.81401i	−0.132626	−	0.132626i	0.637677	−	0.770304i	$-0.279895\pi$
$827$	−3.81401	−	3.81401i	−0.132626	−	0.132626i	−0.770304	+	0.637677i	$0.779895\pi$
$828$	19.6992	+	17.1964i	0.684594	+	0.597616i
$829$	42.6888	+	24.6464i	1.48264	+	0.856004i	0.999806	−	0.0197061i	$-0.00627304\pi$
$829$	42.6888	+	24.6464i	1.48264	+	0.856004i	0.482837	+	0.875710i	$0.339606\pi$
$830$	23.2533	−	6.23070i	0.807134	−	0.216271i
$831$	−32.1594	−	3.13040i	−1.11560	−	0.108592i
$832$	−160.795	−	10.1329i	−5.57458	−	0.351297i
$833$	2.35652	+	31.1106i	0.0816485	+	1.07792i
$834$	63.2088	−	10.5099i	2.18874	−	0.363928i
$835$	−9.26488	−	16.0472i	−0.320624	−	0.555337i
$836$	3.74686	−	6.48975i	0.129588	−	0.224453i
$837$	0.567446	−	19.3588i	0.0196138	−	0.669137i
$838$	−17.3591	+	64.7851i	−0.599661	+	2.23796i
$839$	−5.61230	−	5.61230i	−0.193758	−	0.193758i	0.603560	−	0.797318i	$-0.293749\pi$
$839$	−5.61230	−	5.61230i	−0.193758	−	0.193758i	−0.797318	+	0.603560i	$0.793749\pi$
$840$	−24.0440	+	72.3051i	−0.829598	+	2.49476i
$841$	3.19902			0.110311
$842$	−30.9706	−	53.6426i	−1.06732	−	1.84865i
$843$	−29.6761	−	11.1307i	−1.02210	−	0.383360i
$844$	−23.3009	−	13.4528i	−0.802049	−	0.463063i
$845$	−18.9385	−	7.73320i	−0.651505	−	0.266030i
$846$	−8.98136	−	26.2613i	−0.308785	−	0.902882i
$847$	19.2701	+	17.8657i	0.662129	+	0.613871i
$848$		−	11.6926i		−	0.401527i
$849$	−17.6015	−	1.71333i	−0.604081	−	0.0588013i
$850$	30.3206	−	8.12438i	1.03999	−	0.278664i
$851$	0.302212	+	1.12787i	0.0103597	+	0.0386629i
$852$	31.6327	−	26.0207i	1.08372	−	0.891454i
$853$	9.25853	−	9.25853i	0.317006	−	0.317006i	−0.530610	−	0.847616i	$-0.678037\pi$
$853$	9.25853	−	9.25853i	0.317006	−	0.317006i	0.847616	+	0.530610i	$0.178037\pi$
$854$	1.98576	−	1.24885i	0.0679512	−	0.0427346i
$855$	−1.91427	−	5.59728i	−0.0654666	−	0.191423i
$856$	107.026	+	28.6775i	3.65807	+	0.980178i
$857$	−12.6175	+	21.8541i	−0.431005	+	0.746522i	−0.996960	−	0.0779138i	$-0.975174\pi$
$857$	−12.6175	+	21.8541i	−0.431005	+	0.746522i	0.565955	+	0.824436i	$0.308507\pi$
$858$	−6.40521	−	16.8313i	−0.218670	−	0.574612i
$859$	−20.8538	−	36.1198i	−0.711523	−	1.23239i	−0.964286	−	0.264865i	$-0.914673\pi$
$859$	−20.8538	−	36.1198i	−0.711523	−	1.23239i	0.252763	−	0.967528i	$-0.418661\pi$
$860$	59.2091	−	59.2091i	2.01901	−	2.01901i
$861$	13.3348	+	0.790789i	0.454448	+	0.0269500i
$862$			33.9085i			1.15493i
$863$	−18.0959	−	4.84877i	−0.615990	−	0.165054i	−0.0626859	−	0.998033i	$-0.519967\pi$
$863$	−18.0959	−	4.84877i	−0.615990	−	0.165054i	−0.553304	+	0.832979i	$0.686633\pi$
$864$	−149.856	−	4.39258i	−5.09819	−	0.149439i
$865$	4.03124	+	15.0448i	0.137066	+	0.511538i
$866$	7.30535	−	27.2639i	0.248246	−	0.926466i
$867$	−4.03807	−	2.88668i	−0.137140	−	0.0980367i
$868$	−2.15658	−	57.0238i	−0.0731991	−	1.93551i
$869$	7.99015	+	7.99015i	0.271047	+	0.271047i
$870$	3.74274	−	38.4501i	0.126891	−	1.30358i
$871$	−1.22961	−	6.10143i	−0.0416639	−	0.206739i
$872$	65.1994	+	37.6429i	2.20793	+	1.27475i
$873$	26.9370	−	1.82725i	0.911678	−	0.0618432i
$874$	−5.26702			−0.178159
$875$	−14.6256	+	27.6999i	−0.494437	+	0.936429i
$876$	5.28853	+	31.8064i	0.178683	+	1.07464i
$877$	3.02134	−	11.2758i	0.102023	−	0.380756i	−0.895967	−	0.444120i	$-0.853516\pi$
$877$	3.02134	−	11.2758i	0.102023	−	0.380756i	0.997990	+	0.0633642i	$0.0201830\pi$
$878$	−16.4792	+	4.41560i	−0.556147	+	0.149019i
$879$	−39.8332	−	14.9403i	−1.34354	−	0.503924i
$880$	14.5648	+	25.2269i	0.490978	+	0.850399i
$881$	49.8798			1.68049			0.840246	−	0.542206i	$-0.182411\pi$
$881$	49.8798			1.68049			0.840246	+	0.542206i	$0.182411\pi$
$882$	21.7504	−	54.4139i	0.732375	−	1.83221i
$883$		−	27.0254i		−	0.909477i	−0.890625	−	0.454739i	$-0.849733\pi$
$883$		−	27.0254i		−	0.909477i	0.890625	−	0.454739i	$-0.150267\pi$
$884$	41.3403	+	83.3010i	1.39043	+	2.80172i
$885$	5.65102	−	2.56821i	0.189957	−	0.0863295i
$886$	84.8530	−	22.7363i	2.85069	−	0.763841i
$887$	23.2493	−	13.4230i	0.780636	−	0.450701i	−0.0560194	−	0.998430i	$-0.517841\pi$
$887$	23.2493	−	13.4230i	0.780636	−	0.450701i	0.836656	+	0.547729i	$0.184508\pi$
$888$	−11.5421	−	8.25103i	−0.387327	−	0.276886i
$889$	9.01730	−	2.78543i	0.302431	−	0.0934204i
$890$	51.4151	−	51.4151i	1.72344	−	1.72344i
$891$	−3.59841	−	8.57646i	−0.120551	−	0.287322i
$892$	15.9875	+	59.6660i	0.535300	+	1.99777i
$893$	3.59793	+	2.07727i	0.120400	+	0.0695131i
$894$	−85.5697	−	8.32936i	−2.86188	−	0.278576i
$895$	16.8561	−	16.8561i	0.563439	−	0.563439i
$896$	−177.108	+	6.69805i	−5.91677	+	0.223766i
$897$	−5.94086	+	7.29317i	−0.198360	+	0.243512i
$898$	4.24286	+	7.34884i	0.141586	+	0.245234i
$899$	4.90001	+	18.2871i	0.163424	+	0.609908i
$900$	−42.9921	−	8.44977i	−1.43307	−	0.281659i
$901$	−2.51958	+	1.45468i	−0.0839394	+	0.0484625i
$902$	5.94399	−	5.94399i	0.197913	−	0.197913i
$903$	−31.5088	+	27.9809i	−1.04855	+	0.931146i
$904$	64.6754	−	64.6754i	2.15107	−	2.15107i
$905$	1.23456	−	4.60744i	0.0410381	−	0.153156i
$906$	−40.4010	−	88.8970i	−1.34223	−	2.95341i
$907$	−8.43118	−	4.86775i	−0.279953	−	0.161631i	0.353449	−	0.935454i	$-0.385009\pi$
$907$	−8.43118	−	4.86775i	−0.279953	−	0.161631i	−0.633402	+	0.773823i	$0.718342\pi$
$908$	−13.2308	+	49.3779i	−0.439079	+	1.63866i
$909$	−8.30694	−	24.2893i	−0.275524	−	0.805626i
$910$	−40.1753	−	11.8547i	−1.33180	−	0.392981i
$911$			34.9168i			1.15685i	0.815737	+	0.578423i	$0.196331\pi$
$911$			34.9168i			1.15685i	−0.815737	+	0.578423i	$0.803669\pi$
$912$	30.0257	−	24.6988i	0.994251	−	0.817860i
$913$	−2.83283	+	4.90660i	−0.0937529	+	0.162385i
$914$	33.0438	−	57.2335i	1.09299	−	1.89312i
$915$	−0.550145	−	0.668797i	−0.0181872	−	0.0221098i
$916$	−84.1288	−	84.1288i	−2.77969	−	2.77969i
$917$	8.01487	+	7.43074i	0.264674	+	0.245385i
$918$	30.6597	+	56.8913i	1.01192	+	1.87769i
$919$	−2.38927	−	4.13833i	−0.0788147	−	0.136511i	0.823924	−	0.566700i	$-0.191780\pi$
$919$	−2.38927	−	4.13833i	−0.0788147	−	0.136511i	−0.902739	+	0.430189i	$0.858447\pi$
$920$	12.5229	−	21.6903i	0.412867	−	0.715107i
$921$	15.2411	−	40.6351i	0.502211	−	1.33897i
$922$	−56.3080	+	32.5094i	−1.85440	+	1.07064i
$923$	9.74292	+	11.0535i	0.320692	+	0.363829i
$924$	−12.2732	−	24.5025i	−0.403760	−	0.806072i
$925$	−1.38345	−	1.38345i	−0.0454875	−	0.0454875i
$926$	−28.2579	+	16.3147i	−0.928613	+	0.536135i
$927$	0.580964	−	2.95592i	0.0190813	−	0.0970851i
$928$	141.560	−	37.9308i	4.64692	−	1.24514i
$929$	15.7266	+	4.21392i	0.515972	+	0.138254i	0.507403	−	0.861709i	$-0.330606\pi$
$929$	15.7266	+	4.21392i	0.515972	+	0.138254i	0.00856905	+	0.999963i	$0.497272\pi$
$930$	−27.9633	+	4.64952i	−0.916952	+	0.152464i
$931$	2.90375	+	8.27714i	0.0951666	+	0.271272i
$932$			124.899i			4.09121i
$933$	3.69077	−	37.9163i	0.120831	−	1.24132i
$934$	17.0850	+	63.7621i	0.559039	+	2.08636i
$935$	3.62400	−	6.27696i	0.118518	−	0.205278i
$936$	−0.548200	−	114.297i	−0.0179185	−	3.73590i
$937$	2.36909			0.0773949			0.0386974	−	0.999251i	$-0.487679\pi$
$937$	2.36909			0.0773949			0.0386974	+	0.999251i	$0.487679\pi$
$938$	−3.76147	−	12.1771i	−0.122816	−	0.397595i
$939$	−37.1849	−	26.5822i	−1.21348	−	0.867477i
$940$	−26.1451	+	15.0949i	−0.852760	+	0.492341i
$941$	−4.57302	−	17.0667i	−0.149076	−	0.556359i	−0.999540	−	0.0303262i	$-0.990345\pi$
$941$	−4.57302	−	17.0667i	−0.149076	−	0.556359i	0.850464	−	0.526033i	$-0.176321\pi$
$942$	11.2186	−	29.9106i	0.365523	−	0.974541i
$943$	−4.24114	−	1.13641i	−0.138111	−	0.0370066i
$944$	28.8471	+	28.8471i	0.938892	+	0.938892i
$945$	−20.9428	−	5.42131i	−0.681271	−	0.176355i
$946$			26.5176i			0.862161i
$947$	−2.67590	+	9.98660i	−0.0869551	+	0.324521i	−0.995677	−	0.0928807i	$-0.970392\pi$
$947$	−2.67590	+	9.98660i	−0.0869551	+	0.324521i	0.908722	+	0.417402i	$0.137059\pi$
$948$	45.3443	+	99.7741i	1.47271	+	3.24051i
$949$	−11.3702	+	2.29142i	−0.369092	+	0.0743826i
$950$	7.64289	−	4.41262i	0.247968	−	0.143164i
$951$	−3.27038	+	0.543774i	−0.106049	+	0.0176331i
$952$	66.3380	+	105.482i	2.15003	+	3.41870i
$953$	−9.93929			−0.321965			−0.160983	−	0.986957i	$-0.551466\pi$
$953$	−9.93929			−0.321965			−0.160983	+	0.986957i	$0.551466\pi$
$954$	5.45189	−	0.369826i	0.176511	−	0.0119735i
$955$	16.5091	−	4.42361i	0.534223	−	0.143145i
$956$	43.7501	−	11.7228i	1.41498	−	0.379142i
$957$	5.77586	+	7.02156i	0.186707	+	0.226975i
$958$	106.475			3.44004
$959$	22.5664	+	35.8823i	0.728708	+	1.15870i
$960$	19.9761	+	120.141i	0.644726	+	3.87753i
$961$	−14.8160	+	8.55400i	−0.477934	+	0.275936i
$962$	4.31683	−	6.49590i	0.139180	−	0.209436i
$963$	−6.06663	+	30.8668i	−0.195495	+	0.994669i
$964$	30.8211	−	115.026i	0.992680	−	3.70473i
$965$			18.8165i			0.605726i
$966$	−10.6013	+	16.0815i	−0.341091	+	0.517414i
$967$	−9.76636	−	9.76636i	−0.314065	−	0.314065i	0.532417	−	0.846482i	$-0.321284\pi$
$967$	−9.76636	−	9.76636i	−0.314065	−	0.314065i	−0.846482	+	0.532417i	$0.821284\pi$
$968$	101.374	+	27.1631i	3.25829	+	0.873057i
$969$	−9.05771	−	3.39729i	−0.290976	−	0.109137i
$970$	−10.2279	−	38.1712i	−0.328399	−	1.22560i
$971$	−44.8600	+	25.8999i	−1.43963	+	0.831169i	−0.997823	−	0.0659435i	$-0.978994\pi$
$971$	−44.8600	+	25.8999i	−1.43963	+	0.831169i	−0.441803	+	0.897112i	$0.645661\pi$
$972$	−3.46551	−	90.1400i	−0.111156	−	2.89124i
$973$	10.3523	+	33.5135i	0.331879	+	1.07439i
$974$	−37.9563			−1.21620
$975$	2.51059	−	15.5602i	0.0804033	−	0.498324i
$976$	2.84580	−	4.92908i	0.0910920	−	0.157776i
$977$	9.86518	+	36.8173i	0.315615	+	1.17789i	0.923416	+	0.383802i	$0.125385\pi$
$977$	9.86518	+	36.8173i	0.315615	+	1.17789i	−0.607801	+	0.794090i	$0.707948\pi$
$978$	−111.101	−	10.8145i	−3.55261	−	0.345811i
$979$			17.1125i			0.546919i
$980$	−62.6397	−	11.8000i	−2.00095	−	0.376938i
$981$	−9.40981	+	19.1914i	−0.300432	+	0.612735i
$982$	−34.7081	−	9.30002i	−1.10758	−	0.296775i
$983$	−23.4298	+	6.27800i	−0.747295	+	0.200237i	−0.612318	−	0.790611i	$-0.709763\pi$
$983$	−23.4298	+	6.27800i	−0.747295	+	0.200237i	−0.134977	+	0.990849i	$0.543096\pi$
$984$	48.5705	−	22.0738i	1.54837	−	0.703688i
$985$	−13.2832	+	7.66908i	−0.423239	+	0.244357i
$986$	−44.6719	−	44.6719i	−1.42264	−	1.42264i
$987$	13.5842	−	6.80431i	0.432391	−	0.216583i
$988$	17.2881	+	19.6136i	0.550009	+	0.623992i
$989$	11.9953	−	6.92548i	0.381428	−	0.220217i
$990$	−11.3018	+	7.58896i	−0.359195	+	0.241193i
$991$	22.7939	−	39.4802i	0.724073	−	1.25413i	−0.235281	−	0.971927i	$-0.575601\pi$
$991$	22.7939	−	39.4802i	0.724073	−	1.25413i	0.959354	−	0.282204i	$-0.0910655\pi$
$992$	−53.7687	−	93.1302i	−1.70716	−	2.95689i
$993$	−8.00936	−	48.1701i	−0.254169	−	1.52863i
$994$	22.1251	+	20.5126i	0.701766	+	0.650620i
$995$	−18.8241	−	18.8241i	−0.596764	−	0.596764i
$996$	−42.4373	+	34.9085i	−1.34468	+	1.10612i
$997$	−17.5851	+	30.4583i	−0.556925	+	0.964622i	0.440826	+	0.897593i	$0.354686\pi$
$997$	−17.5851	+	30.4583i	−0.556925	+	0.964622i	−0.997751	+	0.0670299i	$0.978648\pi$
$998$	−23.5379	+	40.7688i	−0.745079	+	1.29051i
$999$	2.11538	−	3.42790i	0.0669276	−	0.108454i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.242.1	yes	112
3.2	odd	2	inner	273.2.cd.e.242.28	yes	112
7.2	even	3	inner	273.2.cd.e.86.28	yes	112
13.5	odd	4	inner	273.2.cd.e.200.1	yes	112
21.2	odd	6	inner	273.2.cd.e.86.1	yes	112
39.5	even	4	inner	273.2.cd.e.200.28	yes	112
91.44	odd	12	inner	273.2.cd.e.44.28	yes	112
273.44	even	12	inner	273.2.cd.e.44.1	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.1	✓	112	273.44	even	12	inner
273.2.cd.e.44.28	yes	112	91.44	odd	12	inner
273.2.cd.e.86.1	yes	112	21.2	odd	6	inner
273.2.cd.e.86.28	yes	112	7.2	even	3	inner
273.2.cd.e.200.1	yes	112	13.5	odd	4	inner
273.2.cd.e.200.28	yes	112	39.5	even	4	inner
273.2.cd.e.242.1	yes	112	1.1	even	1	trivial
273.2.cd.e.242.28	yes	112	3.2	odd	2	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.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.69539 - 0.722228i) q^{2} +(1.57685 - 0.716628i) q^{3} +(5.01147 + 2.89338i) q^{4} +(1.51996 + 0.407273i) q^{5} +(-4.76779 + 0.792751i) q^{6} +(-0.780863 - 2.52790i) q^{7} +(-7.47188 - 7.47188i) q^{8} +(1.97289 - 2.26003i) q^{9} +O(q^{10})\)	\(q+(-2.69539 - 0.722228i) q^{2} +(1.57685 - 0.716628i) q^{3} +(5.01147 + 2.89338i) q^{4} +(1.51996 + 0.407273i) q^{5} +(-4.76779 + 0.792751i) q^{6} +(-0.780863 - 2.52790i) q^{7} +(-7.47188 - 7.47188i) q^{8} +(1.97289 - 2.26003i) q^{9} +(-3.80275 - 2.19552i) q^{10} +(0.998206 - 0.267468i) q^{11} +(9.97580 + 0.971045i) q^{12} +(-0.226763 + 3.59841i) q^{13} +(0.279015 + 7.37763i) q^{14} +(2.68861 - 0.447041i) q^{15} +(8.95650 + 15.5131i) q^{16} +(2.22855 - 3.85997i) q^{17} +(-6.94996 + 4.66678i) q^{18} +(0.324326 - 1.21040i) q^{19} +(6.43886 + 6.43886i) q^{20} +(-3.04286 - 3.42651i) q^{21} -2.88373 q^{22} +(0.753131 + 1.30446i) q^{23} +(-17.1366 - 6.42745i) q^{24} +(-2.18571 - 1.26192i) q^{25} +(3.21009 - 9.53536i) q^{26} +(1.49134 - 4.97754i) q^{27} +(3.40088 - 14.9278i) q^{28} +5.07947i q^{29} +(-7.56972 - 0.736837i) q^{30} +(3.60020 - 0.964669i) q^{31} +(-7.46748 - 27.8690i) q^{32} +(1.38234 - 1.13710i) q^{33} +(-8.79461 + 8.79461i) q^{34} +(-0.157339 - 4.16033i) q^{35} +(16.4262 - 5.61775i) q^{36} +(0.748788 + 0.200637i) q^{37} +(-1.74837 + 3.02827i) q^{38} +(2.22115 + 5.83665i) q^{39} +(-8.31389 - 14.4001i) q^{40} +(-2.06122 + 2.06122i) q^{41} +(5.72698 + 11.4334i) q^{42} -9.19559i q^{43} +(5.77637 + 1.54777i) q^{44} +(3.91916 - 2.63165i) q^{45} +(-1.08786 - 4.05997i) q^{46} +(-0.858089 + 3.20243i) q^{47} +(25.2402 + 18.0433i) q^{48} +(-5.78051 + 3.94788i) q^{49} +(4.97996 + 4.97996i) q^{50} +(0.747925 - 7.68363i) q^{51} +(-11.5480 + 17.3772i) q^{52} +(-0.565295 - 0.326373i) q^{53} +(-7.61467 + 12.3393i) q^{54} +1.62617 q^{55} +(-13.0536 + 24.7227i) q^{56} +(-0.355996 - 2.14104i) q^{57} +(3.66853 - 13.6912i) q^{58} +(2.19984 - 0.589447i) q^{59} +(14.7674 + 5.53882i) q^{60} +(-0.158868 - 0.275168i) q^{61} -10.4006 q^{62} +(-7.25366 - 3.22248i) q^{63} +44.6851i q^{64} +(-1.81021 + 5.37710i) q^{65} +(-4.54720 + 2.06656i) q^{66} +(-1.66743 + 0.446788i) q^{67} +(22.3367 - 12.8961i) q^{68} +(2.12238 + 1.51722i) q^{69} +(-2.58061 + 11.3274i) q^{70} +(2.88966 - 2.88966i) q^{71} +(-31.6278 + 2.14546i) q^{72} +(0.832602 + 3.10731i) q^{73} +(-1.87337 - 1.08159i) q^{74} +(-4.35086 - 0.423513i) q^{75} +(5.12750 - 5.12750i) q^{76} +(-1.45559 - 2.31450i) q^{77} +(-1.77149 - 17.3362i) q^{78} +(5.46718 + 9.46944i) q^{79} +(7.29547 + 27.2271i) q^{80} +(-1.21543 - 8.91755i) q^{81} +(7.04445 - 4.06712i) q^{82} +(-3.87667 + 3.87667i) q^{83} +(-5.33503 - 25.9760i) q^{84} +(4.95938 - 4.95938i) q^{85} +(-6.64131 + 24.7857i) q^{86} +(3.64009 + 8.00954i) q^{87} +(-9.45697 - 5.45999i) q^{88} +(-4.28583 + 15.9949i) q^{89} +(-12.4643 + 4.26280i) q^{90} +(9.27348 - 2.23663i) q^{91} +8.71636i q^{92} +(4.98564 - 4.10114i) q^{93} +(4.62577 - 8.01208i) q^{94} +(0.985928 - 1.70768i) q^{95} +(-31.7468 - 38.5937i) q^{96} +(6.36370 + 6.36370i) q^{97} +(18.4320 - 6.46624i) q^{98} +(1.36486 - 2.78366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

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