LMFDB - Embedded newform 273.2.cc.a.50.3

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			50.3
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24002 - 0.600211i) q^{2} +(1.07699 - 1.35650i) q^{3} +(2.92537 + 1.68896i) q^{4} +(-2.36227 + 2.36227i) q^{5} +(-3.22666 + 2.39216i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-2.25953 - 2.25953i) q^{8} +(-0.680177 - 2.92188i) q^{9} +O(q^{10})$	\(q+(-2.24002 - 0.600211i) q^{2} +(1.07699 - 1.35650i) q^{3} +(2.92537 + 1.68896i) q^{4} +(-2.36227 + 2.36227i) q^{5} +(-3.22666 + 2.39216i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-2.25953 - 2.25953i) q^{8} +(-0.680177 - 2.92188i) q^{9} +(6.70937 - 3.87366i) q^{10} +(1.27349 - 4.75272i) q^{11} +(5.44168 - 2.14926i) q^{12} +(0.0681230 - 3.60491i) q^{13} -2.31904i q^{14} +(0.660269 + 5.74855i) q^{15} +(0.327270 + 0.566848i) q^{16} +(1.93175 - 3.34589i) q^{17} +(-0.230134 + 6.95330i) q^{18} +(-0.154488 + 0.0413949i) q^{19} +(-10.9003 + 2.92072i) q^{20} +(1.58902 + 0.689207i) q^{21} +(-5.70527 + 9.88182i) q^{22} +(0.481057 + 0.833215i) q^{23} +(-5.49855 + 0.631555i) q^{24} -6.16060i q^{25} +(-2.31630 + 8.03417i) q^{26} +(-4.69607 - 2.22418i) q^{27} +(-0.874272 + 3.26283i) q^{28} +(5.39053 - 3.11222i) q^{29} +(1.97133 - 13.2732i) q^{30} +(-5.97914 - 5.97914i) q^{31} +(1.26123 + 4.70698i) q^{32} +(-5.07553 - 6.84613i) q^{33} +(-6.33540 + 6.33540i) q^{34} +(-2.89317 - 1.67037i) q^{35} +(2.94517 - 9.69637i) q^{36} +(7.59311 + 2.03457i) q^{37} +0.370901 q^{38} +(-4.81668 - 3.97487i) q^{39} +10.6752 q^{40} +(-0.529373 - 0.141845i) q^{41} +(-3.14577 - 2.49758i) q^{42} +(-4.36437 - 2.51977i) q^{43} +(11.7526 - 11.7526i) q^{44} +(8.50900 + 5.29549i) q^{45} +(-0.577471 - 2.15515i) q^{46} +(-1.16778 - 1.16778i) q^{47} +(1.12140 + 0.166550i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-3.69766 + 13.7998i) q^{50} +(-2.45822 - 6.22392i) q^{51} +(6.28784 - 10.4306i) q^{52} +8.49966i q^{53} +(9.18429 + 7.80083i) q^{54} +(8.21888 + 14.2355i) q^{55} +(1.59773 - 2.76735i) q^{56} +(-0.110230 + 0.254144i) q^{57} +(-13.9429 + 3.73598i) q^{58} +(4.12073 - 1.10415i) q^{59} +(-7.77756 + 17.9318i) q^{60} +(-0.889949 + 1.54144i) q^{61} +(9.80463 + 16.9821i) q^{62} +(2.64627 - 1.41324i) q^{63} -12.6098i q^{64} +(8.35482 + 8.67667i) q^{65} +(7.26014 + 18.3818i) q^{66} +(-0.680674 + 2.54031i) q^{67} +(11.3022 - 6.52532i) q^{68} +(1.64835 + 0.244813i) q^{69} +(5.47818 + 5.47818i) q^{70} +(-2.67719 - 9.99142i) q^{71} +(-5.06520 + 8.13896i) q^{72} +(-6.57657 + 6.57657i) q^{73} +(-15.7875 - 9.11493i) q^{74} +(-8.35684 - 6.63491i) q^{75} +(-0.521849 - 0.139829i) q^{76} +4.92038 q^{77} +(8.40370 + 11.7948i) q^{78} +15.6043 q^{79} +(-2.11214 - 0.565947i) q^{80} +(-8.07472 + 3.97478i) q^{81} +(1.10067 + 0.635471i) q^{82} +(-6.31202 + 6.31202i) q^{83} +(3.48444 + 4.69999i) q^{84} +(3.34058 + 12.4672i) q^{85} +(8.26387 + 8.26387i) q^{86} +(1.58383 - 10.6641i) q^{87} +(-13.6164 + 7.86145i) q^{88} +(4.50509 - 16.8132i) q^{89} +(-15.8819 - 16.9692i) q^{90} +(3.49970 - 0.867217i) q^{91} +3.24995i q^{92} +(-14.5502 + 1.67121i) q^{93} +(1.91493 + 3.31675i) q^{94} +(0.267156 - 0.462727i) q^{95} +(7.74335 + 3.35852i) q^{96} +(10.2993 - 2.75970i) q^{97} +(2.24002 - 0.600211i) q^{98} +(-14.7531 - 0.488284i) 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 $

$2$	−2.24002	−	0.600211i	−1.58393	−	0.424413i	−0.643791	−	0.765201i	$-0.722639\pi$
$2$	−2.24002	−	0.600211i	−1.58393	−	0.424413i	−0.940140	+	0.340788i	$0.889306\pi$
$3$	1.07699	−	1.35650i	0.621802	−	0.783175i
$3$	1.07699	−	1.35650i	0.621802	−	0.783175i
$4$	2.92537	+	1.68896i	1.46269	+	0.844482i
$5$	−2.36227	+	2.36227i	−1.05644	+	1.05644i	−0.0581282	+	0.998309i	$0.518513\pi$
$5$	−2.36227	+	2.36227i	−1.05644	+	1.05644i	−0.998309	+	0.0581282i	$0.981487\pi$
$6$	−3.22666	+	2.39216i	−1.31728	+	0.976594i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	−2.25953	−	2.25953i	−0.798866	−	0.798866i
$9$	−0.680177	−	2.92188i	−0.226726	−	0.973959i
$10$	6.70937	−	3.87366i	2.12169	−	1.22496i
$11$	1.27349	−	4.75272i	0.383971	−	1.43300i	−0.455811	−	0.890077i	$-0.650651\pi$
$11$	1.27349	−	4.75272i	0.383971	−	1.43300i	0.839782	−	0.542923i	$-0.182683\pi$
$12$	5.44168	−	2.14926i	1.57088	−	0.620438i
$13$	0.0681230	−	3.60491i	0.0188939	−	0.999821i
$13$	0.0681230	−	3.60491i	0.0188939	−	0.999821i
$14$		−	2.31904i		−	0.619788i
$15$	0.660269	+	5.74855i	0.170481	+	1.48427i
$16$	0.327270	+	0.566848i	0.0818175	+	0.141712i
$17$	1.93175	−	3.34589i	0.468519	−	0.811498i	−0.530834	−	0.847476i	$-0.678121\pi$
$17$	1.93175	−	3.34589i	0.468519	−	0.811498i	0.999353	+	0.0359776i	$0.0114545\pi$
$18$	−0.230134	+	6.95330i	−0.0542432	+	1.63891i
$19$	−0.154488	+	0.0413949i	−0.0354419	+	0.00949664i	−0.276496	−	0.961015i	$-0.589173\pi$
$19$	−0.154488	+	0.0413949i	−0.0354419	+	0.00949664i	0.241055	+	0.970512i	$0.422507\pi$
$20$	−10.9003	+	2.92072i	−2.43738	+	0.653093i
$21$	1.58902	+	0.689207i	0.346753	+	0.150397i
$22$	−5.70527	+	9.88182i	−1.21637	+	2.10681i
$23$	0.481057	+	0.833215i	0.100307	+	0.173737i	0.911811	−	0.410610i	$-0.134684\pi$
$23$	0.481057	+	0.833215i	0.100307	+	0.173737i	−0.811504	+	0.584347i	$0.801351\pi$
$24$	−5.49855	+	0.631555i	−1.12239	+	0.128916i
$25$		−	6.16060i		−	1.23212i
$26$	−2.31630	+	8.03417i	−0.454264	+	1.57563i
$27$	−4.69607	−	2.22418i	−0.903758	−	0.428043i
$28$	−0.874272	+	3.26283i	−0.165222	+	0.616616i
$29$	5.39053	−	3.11222i	1.00100	−	0.577926i	0.0924535	−	0.995717i	$-0.470529\pi$
$29$	5.39053	−	3.11222i	1.00100	−	0.577926i	0.908543	+	0.417791i	$0.137196\pi$
$30$	1.97133	−	13.2732i	0.359914	−	2.42333i
$31$	−5.97914	−	5.97914i	−1.07389	−	1.07389i	−0.997043	−	0.0768420i	$-0.975516\pi$
$31$	−5.97914	−	5.97914i	−1.07389	−	1.07389i	−0.0768420	−	0.997043i	$-0.524484\pi$
$32$	1.26123	+	4.70698i	0.222956	+	0.832085i
$33$	−5.07553	−	6.84613i	−0.883536	−	1.19176i
$34$	−6.33540	+	6.33540i	−1.08651	+	1.08651i
$35$	−2.89317	−	1.67037i	−0.489035	−	0.282345i
$36$	2.94517	−	9.69637i	0.490862	−	1.61606i
$37$	7.59311	+	2.03457i	1.24830	+	0.334481i	0.821679	−	0.569950i	$-0.193038\pi$
$37$	7.59311	+	2.03457i	1.24830	+	0.334481i	0.426620	+	0.904431i	$0.359704\pi$
$38$	0.370901			0.0601681
$39$	−4.81668	−	3.97487i	−0.771287	−	0.636488i
$40$	10.6752			1.68790
$41$	−0.529373	−	0.141845i	−0.0826742	−	0.0221525i	0.217245	−	0.976117i	$-0.430293\pi$
$41$	−0.529373	−	0.141845i	−0.0826742	−	0.0221525i	−0.299919	+	0.953965i	$0.596960\pi$
$42$	−3.14577	−	2.49758i	−0.485403	−	0.385385i
$43$	−4.36437	−	2.51977i	−0.665560	−	0.384261i	0.128832	−	0.991666i	$-0.458877\pi$
$43$	−4.36437	−	2.51977i	−0.665560	−	0.384261i	−0.794392	+	0.607405i	$0.792210\pi$
$44$	11.7526	−	11.7526i	1.77177	−	1.77177i
$45$	8.50900	+	5.29549i	1.26845	+	0.789405i
$46$	−0.577471	−	2.15515i	−0.0851434	−	0.317760i
$47$	−1.16778	−	1.16778i	−0.170338	−	0.170338i	0.616790	−	0.787128i	$-0.288433\pi$
$47$	−1.16778	−	1.16778i	−0.170338	−	0.170338i	−0.787128	+	0.616790i	$0.788433\pi$
$48$	1.12140	+	0.166550i	0.161860	+	0.0240394i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−3.69766	+	13.7998i	−0.522928	+	1.95159i
$51$	−2.45822	−	6.22392i	−0.344219	−	0.871523i
$52$	6.28784	−	10.4306i	0.871967	−	1.44647i
$53$			8.49966i			1.16752i	0.811927	+	0.583759i	$0.198419\pi$
$53$			8.49966i			1.16752i	−0.811927	+	0.583759i	$0.801581\pi$
$54$	9.18429	+	7.80083i	1.24982	+	1.06156i
$55$	8.21888	+	14.2355i	1.10823	+	1.91952i
$56$	1.59773	−	2.76735i	0.213506	−	0.369803i
$57$	−0.110230	+	0.254144i	−0.0146003	+	0.0336623i
$58$	−13.9429	+	3.73598i	−1.83079	+	0.490558i
$59$	4.12073	−	1.10415i	0.536474	−	0.143748i	0.0195976	−	0.999808i	$-0.493761\pi$
$59$	4.12073	−	1.10415i	0.536474	−	0.143748i	0.516876	+	0.856060i	$0.327095\pi$
$60$	−7.77756	+	17.9318i	−1.00408	+	2.31499i
$61$	−0.889949	+	1.54144i	−0.113946	+	0.197361i	−0.917358	−	0.398063i	$-0.869683\pi$
$61$	−0.889949	+	1.54144i	−0.113946	+	0.197361i	0.803412	+	0.595424i	$0.203016\pi$
$62$	9.80463	+	16.9821i	1.24519	+	2.15673i
$63$	2.64627	−	1.41324i	0.333399	−	0.178051i
$64$		−	12.6098i		−	1.57623i
$65$	8.35482	+	8.67667i	1.03629	+	1.07621i
$66$	7.26014	+	18.3818i	0.893662	+	2.26265i
$67$	−0.680674	+	2.54031i	−0.0831575	+	0.310348i	−0.994959	−	0.100283i	$-0.968025\pi$
$67$	−0.680674	+	2.54031i	−0.0831575	+	0.310348i	0.911801	+	0.410632i	$0.134692\pi$
$68$	11.3022	−	6.52532i	1.37059	−	0.791311i
$69$	1.64835	+	0.244813i	0.198438	+	0.0294720i
$70$	5.47818	+	5.47818i	0.654768	+	0.654768i
$71$	−2.67719	−	9.99142i	−0.317724	−	1.18576i	−0.921426	−	0.388554i	$-0.872975\pi$
$71$	−2.67719	−	9.99142i	−0.317724	−	1.18576i	0.603702	−	0.797210i	$-0.293692\pi$
$72$	−5.06520	+	8.13896i	−0.596939	+	0.959186i
$73$	−6.57657	+	6.57657i	−0.769729	+	0.769729i	−0.978059	−	0.208329i	$-0.933197\pi$
$73$	−6.57657	+	6.57657i	−0.769729	+	0.769729i	0.208329	+	0.978059i	$0.433197\pi$
$74$	−15.7875	−	9.11493i	−1.83526	−	1.05959i
$75$	−8.35684	−	6.63491i	−0.964965	−	0.766134i
$76$	−0.521849	−	0.139829i	−0.0598601	−	0.0160395i
$77$	4.92038			0.560729
$78$	8.40370	+	11.7948i	0.951531	+	1.33550i
$79$	15.6043			1.75563			0.877813	−	0.479003i	$-0.159002\pi$
$79$	15.6043			1.75563			0.877813	+	0.479003i	$0.159002\pi$
$80$	−2.11214	−	0.565947i	−0.236145	−	0.0632748i
$81$	−8.07472	+	3.97478i	−0.897191	+	0.441643i
$82$	1.10067	+	0.635471i	0.121548	+	0.0701760i
$83$	−6.31202	+	6.31202i	−0.692834	+	0.692834i	−0.962855	−	0.270020i	$-0.912970\pi$
$83$	−6.31202	+	6.31202i	−0.692834	+	0.692834i	0.270020	+	0.962855i	$0.412970\pi$
$84$	3.48444	+	4.69999i	0.380183	+	0.512811i
$85$	3.34058	+	12.4672i	0.362336	+	1.35226i
$86$	8.26387	+	8.26387i	0.891116	+	0.891116i
$87$	1.58383	−	10.6641i	0.169804	−	1.14331i
$88$	−13.6164	+	7.86145i	−1.45152	+	0.838033i
$89$	4.50509	−	16.8132i	0.477538	−	1.78220i	−0.133998	−	0.990982i	$-0.542782\pi$
$89$	4.50509	−	16.8132i	0.477538	−	1.78220i	0.611536	−	0.791216i	$-0.290552\pi$
$90$	−15.8819	−	16.9692i	−1.67410	−	1.78871i
$91$	3.49970	−	0.867217i	0.366869	−	0.0909090i
$92$			3.24995i			0.338831i
$93$	−14.5502	+	1.67121i	−1.50878	+	0.173296i
$94$	1.91493	+	3.31675i	0.197510	+	0.342097i
$95$	0.267156	−	0.462727i	0.0274096	−	0.0474748i
$96$	7.74335	+	3.35852i	0.790302	+	0.342778i
$97$	10.2993	−	2.75970i	1.04574	−	0.280205i	0.305250	−	0.952272i	$-0.401260\pi$
$97$	10.2993	−	2.75970i	1.04574	−	0.280205i	0.740490	+	0.672067i	$0.234593\pi$
$98$	2.24002	−	0.600211i	0.226276	−	0.0606304i
$99$	−14.7531	−	0.488284i	−1.48274	−	0.0490744i
$100$	10.4050	−	18.0220i	1.04050	−	1.80220i
$101$	0.441165	+	0.764119i	0.0438975	+	0.0760327i	0.887139	−	0.461502i	$-0.152689\pi$
$101$	0.441165	+	0.764119i	0.0438975	+	0.0760327i	−0.843242	+	0.537534i	$0.819356\pi$
$102$	1.77079	+	15.4171i	0.175334	+	1.52652i
$103$			12.2361i			1.20566i	0.797871	+	0.602829i	$0.205960\pi$
$103$			12.2361i			1.20566i	−0.797871	+	0.602829i	$0.794040\pi$
$104$	−8.29934	+	7.99149i	−0.813817	+	0.783630i
$105$	−5.38178	+	2.12561i	−0.525208	+	0.207438i
$106$	5.10158	−	19.0394i	0.495510	−	1.84927i
$107$	−6.60125	+	3.81124i	−0.638167	+	0.368446i	−0.783908	−	0.620877i	$-0.786777\pi$
$107$	−6.60125	+	3.81124i	−0.638167	+	0.368446i	0.145741	+	0.989323i	$0.453443\pi$
$108$	−9.98118	−	14.4380i	−0.960439	−	1.38930i
$109$	−0.152539	−	0.152539i	−0.0146106	−	0.0146106i	0.699764	−	0.714374i	$-0.253289\pi$
$109$	−0.152539	−	0.152539i	−0.0146106	−	0.0146106i	−0.714374	+	0.699764i	$0.753289\pi$
$110$	−9.86612	−	36.8208i	−0.940697	−	3.51073i
$111$	10.9376	−	8.10882i	1.03815	−	0.769656i
$112$	−0.462830	+	0.462830i	−0.0437333	+	0.0437333i
$113$	−6.14627	−	3.54855i	−0.578193	−	0.333820i	0.182222	−	0.983257i	$-0.441671\pi$
$113$	−6.14627	−	3.54855i	−0.578193	−	0.333820i	−0.760415	+	0.649438i	$0.775004\pi$
$114$	0.399457	−	0.503127i	0.0374126	−	0.0471221i
$115$	−3.10466	−	0.831891i	−0.289511	−	0.0775742i
$116$	21.0257			1.95219
$117$	−10.5794	+	2.25293i	−0.978069	+	0.208283i
$118$	−9.89323			−0.910746
$119$	3.73186	+	0.999949i	0.342099	+	0.0916651i
$120$	11.4971	−	14.4809i	1.04954	−	1.32192i
$121$	−11.4403	−	6.60508i	−1.04003	−	0.600461i
$122$	2.91869	−	2.91869i	0.264246	−	0.264246i
$123$	−0.762543	+	0.565328i	−0.0687562	+	0.0509739i
$124$	−7.39265	−	27.5898i	−0.663880	−	2.47763i
$125$	2.74164	+	2.74164i	0.245220	+	0.245220i
$126$	−6.77594	+	1.57735i	−0.603648	+	0.140522i
$127$	7.55602	−	4.36247i	0.670488	−	0.387106i	−0.125774	−	0.992059i	$-0.540141\pi$
$127$	7.55602	−	4.36247i	0.670488	−	0.387106i	0.796262	+	0.604953i	$0.206808\pi$
$128$	−5.04607	+	18.8322i	−0.446014	+	1.66455i
$129$	−8.11846	+	3.20649i	−0.714790	+	0.282316i
$130$	−13.5071	−	24.4505i	−1.18465	−	2.14446i
$131$			9.61324i			0.839913i	0.907544	+	0.419956i	$0.137955\pi$
$131$			9.61324i			0.839913i	−0.907544	+	0.419956i	$0.862045\pi$
$132$	−3.28493	−	28.5999i	−0.285916	−	2.48930i
$133$	−0.0799688	−	0.138510i	−0.00693417	−	0.0120103i
$134$	3.04944	−	5.28179i	0.263432	−	0.456277i
$135$	16.3475	−	5.83925i	1.40696	−	0.502563i
$136$	−11.9250	+	3.19530i	−1.02256	+	0.273995i
$137$	10.9944	−	2.94594i	0.939316	−	0.251689i	0.243493	−	0.969903i	$-0.421707\pi$
$137$	10.9944	−	2.94594i	0.939316	−	0.251689i	0.695823	+	0.718214i	$0.255040\pi$
$138$	−3.54539	−	1.53774i	−0.301804	−	0.130901i
$139$	−5.76644	+	9.98776i	−0.489103	+	0.847151i	−0.999921	−	0.0125376i	$-0.996009\pi$
$139$	−5.76644	+	9.98776i	−0.489103	+	0.847151i	0.510819	+	0.859689i	$0.329342\pi$
$140$	−5.64240	−	9.77293i	−0.476870	−	0.825963i
$141$	−2.84177	+	0.326401i	−0.239320	+	0.0274879i
$142$			23.9878i			2.01301i
$143$	−17.0464	−	4.91458i	−1.42549	−	0.410978i
$144$	1.43366	−	1.34180i	0.119472	−	0.111817i
$145$	−5.38197	+	20.0858i	−0.446948	+	1.66803i
$146$	18.6790	−	10.7843i	1.54588	−	0.892515i
$147$	−0.254453	+	1.71326i	−0.0209869	+	0.141307i
$148$	18.7763	+	18.7763i	1.54341	+	1.54341i
$149$	5.23102	+	19.5224i	0.428542	+	1.59934i	0.756065	+	0.654497i	$0.227120\pi$
$149$	5.23102	+	19.5224i	0.428542	+	1.59934i	−0.327523	+	0.944843i	$0.606214\pi$
$150$	14.7371	+	19.8782i	1.20328	+	1.62305i
$151$	9.10006	−	9.10006i	0.740553	−	0.740553i	−0.232132	−	0.972684i	$-0.574570\pi$
$151$	9.10006	−	9.10006i	0.740553	−	0.740553i	0.972684	+	0.232132i	$0.0745700\pi$
$152$	0.442604	+	0.255537i	0.0358999	+	0.0207268i
$153$	−11.0902	−	3.36854i	−0.896591	−	0.272331i
$154$	−11.0217	−	2.95327i	−0.888157	−	0.237981i
$155$	28.2486			2.26898
$156$	−7.37718	−	19.7632i	−0.590647	−	1.58232i
$157$	6.50873			0.519453			0.259726	−	0.965682i	$-0.416368\pi$
$157$	6.50873			0.519453			0.259726	+	0.965682i	$0.416368\pi$
$158$	−34.9540	−	9.36589i	−2.78079	−	0.745111i
$159$	11.5298	+	9.15406i	0.914370	+	0.725964i
$160$	−14.0985	−	8.13978i	−1.11458	−	0.643506i
$161$	−0.680317	+	0.680317i	−0.0536165	+	0.0536165i
$162$	20.4732	−	4.05705i	1.60853	−	0.318752i
$163$	−3.47770	−	12.9790i	−0.272394	−	1.01659i	−0.957567	−	0.288210i	$-0.906940\pi$
$163$	−3.47770	−	12.9790i	−0.272394	−	1.01659i	0.685173	−	0.728380i	$-0.259727\pi$
$164$	−1.30904	−	1.30904i	−0.102219	−	0.102219i
$165$	28.1621	+	4.18264i	2.19242	+	0.325618i
$166$	17.9276	−	10.3505i	1.39145	−	0.803354i
$167$	−5.34140	+	19.9344i	−0.413330	+	1.54257i	0.374828	+	0.927094i	$0.377702\pi$
$167$	−5.34140	+	19.9344i	−0.413330	+	1.54257i	−0.788158	+	0.615473i	$0.788965\pi$
$168$	−2.03317	−	5.14774i	−0.156862	−	0.397157i
$169$	−12.9907	−	0.491154i	−0.999286	−	0.0377811i
$170$		−	29.9318i		−	2.29566i
$171$	0.226030	+	0.423238i	0.0172849	+	0.0323658i
$172$	−8.51160	−	14.7425i	−0.649003	−	1.12411i
$173$	−10.4222	+	18.0518i	−0.792387	+	1.37245i	0.132098	+	0.991237i	$0.457829\pi$
$173$	−10.4222	+	18.0518i	−0.792387	+	1.37245i	−0.924485	+	0.381218i	$0.875505\pi$
$174$	−9.94851	+	22.9371i	−0.754194	+	1.73886i
$175$	5.95068	−	1.59448i	0.449829	−	0.120531i
$176$	3.11085	−	0.833549i	0.234489	−	0.0628311i
$177$	2.94022	−	6.77892i	0.221001	−	0.509535i
$178$	−20.1829	+	34.9579i	−1.51278	+	2.62020i
$179$	−2.29496	−	3.97498i	−0.171533	−	0.297104i	0.767423	−	0.641141i	$-0.221539\pi$
$179$	−2.29496	−	3.97498i	−0.171533	−	0.297104i	−0.938956	+	0.344037i	$0.888205\pi$
$180$	15.9481	+	29.8627i	1.18870	+	2.22583i
$181$		−	0.470371i		−	0.0349624i	−0.999847	−	0.0174812i	$-0.994435\pi$
$181$		−	0.470371i		−	0.0349624i	0.999847	−	0.0174812i	$-0.00556472\pi$
$182$	−8.35991	−	0.157980i	−0.619678	−	0.0117102i
$183$	1.13249	+	2.86733i	0.0837160	+	0.211959i
$184$	0.795713	−	2.96964i	0.0586607	−	0.218925i
$185$	−22.7431	+	13.1307i	−1.67211	+	0.965392i
$186$	33.5957	+	4.98964i	2.46336	+	0.365858i
$187$	−13.4420	−	13.4420i	−0.982979	−	0.982979i
$188$	−1.44385	−	5.38851i	−0.105303	−	0.392998i
$189$	0.932960	−	5.11171i	0.0678629	−	0.371822i
$190$	−0.876166	+	0.876166i	−0.0635638	+	0.0635638i
$191$	1.96443	+	1.13416i	0.142141	+	0.0820652i	0.569384	−	0.822072i	$-0.307182\pi$
$191$	1.96443	+	1.13416i	0.142141	+	0.0820652i	−0.427243	+	0.904137i	$0.640515\pi$
$192$	−17.1052	−	13.5807i	−1.23446	−	0.980099i
$193$	9.72320	+	2.60532i	0.699891	+	0.187535i	0.591182	−	0.806538i	$-0.298662\pi$
$193$	9.72320	+	2.60532i	0.699891	+	0.187535i	0.108709	+	0.994074i	$0.465328\pi$
$194$	−24.7271			−1.77530
$195$	20.7680	−	1.98860i	1.48723	−	0.142407i
$196$	−3.37793			−0.241281
$197$	−14.3963	−	3.85747i	−1.02569	−	0.274833i	−0.293520	−	0.955953i	$-0.594827\pi$
$197$	−14.3963	−	3.85747i	−1.02569	−	0.274833i	−0.732172	+	0.681120i	$0.761493\pi$
$198$	32.7540	+	9.94871i	2.32773	+	0.707024i
$199$	−3.41451	−	1.97137i	−0.242049	−	0.139747i	0.374069	−	0.927401i	$-0.377962\pi$
$199$	−3.41451	−	1.97137i	−0.242049	−	0.139747i	−0.616118	+	0.787654i	$0.711296\pi$
$200$	−13.9201	+	13.9201i	−0.984298	+	0.984298i
$201$	2.71285	+	3.65923i	0.191349	+	0.258102i
$202$	−0.529583	−	1.97643i	−0.0372614	−	0.139061i
$203$	4.40135	+	4.40135i	0.308914	+	0.308914i
$204$	3.32078	−	22.3591i	0.232501	−	1.56545i
$205$	1.58560	−	0.915444i	0.110743	−	0.0639374i
$206$	7.34423	−	27.4090i	0.511697	−	1.90968i
$207$	2.10735	−	1.97232i	0.146471	−	0.137086i
$208$	2.06573	−	1.14116i	0.143233	−	0.0791254i
$209$			0.786954i			0.0544347i
$210$	13.3311	−	1.53119i	0.919933	−	0.105662i
$211$	−4.23792	−	7.34030i	−0.291751	−	0.505327i	0.682473	−	0.730911i	$-0.260904\pi$
$211$	−4.23792	−	7.34030i	−0.291751	−	0.505327i	−0.974224	+	0.225584i	$0.927571\pi$
$212$	−14.3556	+	24.8646i	−0.985947	+	1.70771i
$213$	−16.4367	−	7.12907i	−1.12622	−	0.488476i
$214$	17.0745	−	4.57509i	1.16719	−	0.312747i
$215$	16.2622	−	4.35743i	1.10907	−	0.297175i
$216$	5.58531	+	15.6365i	0.380032	+	1.06393i
$217$	4.22789	−	7.32292i	0.287008	−	0.497112i
$218$	0.250135	+	0.433246i	0.0169413	+	0.0293431i
$219$	1.83819	+	16.0040i	0.124214	+	1.08145i
$220$			55.5255i			3.74353i
$221$	−11.9300	−	7.19172i	−0.802501	−	0.483768i
$222$	−29.3674	+	11.5990i	−1.97101	+	0.778476i
$223$	−0.423172	+	1.57930i	−0.0283377	+	0.105758i	−0.978646	−	0.205552i	$-0.934101\pi$
$223$	−0.423172	+	1.57930i	−0.0283377	+	0.105758i	0.950308	+	0.311310i	$0.100768\pi$
$224$	−4.22016	+	2.43651i	−0.281972	+	0.162796i
$225$	−18.0005	+	4.19029i	−1.20003	+	0.279353i
$226$	11.6379	+	11.6379i	0.774140	+	0.774140i
$227$	−3.81054	−	14.2211i	−0.252915	−	0.943890i	−0.969239	−	0.246123i	$-0.920843\pi$
$227$	−3.81054	−	14.2211i	−0.252915	−	0.943890i	0.716324	−	0.697768i	$-0.245823\pi$
$228$	−0.751705	+	0.557292i	−0.0497828	+	0.0369076i
$229$	−6.84751	+	6.84751i	−0.452496	+	0.452496i	−0.896182	−	0.443686i	$-0.853670\pi$
$229$	−6.84751	+	6.84751i	−0.452496	+	0.452496i	0.443686	+	0.896182i	$0.353670\pi$
$230$	6.45518	+	3.72690i	0.425642	+	0.245744i
$231$	5.29921	−	6.67449i	0.348662	−	0.439149i
$232$	−19.2123	−	5.14791i	−1.26135	−	0.337977i
$233$	17.4546			1.14349			0.571744	−	0.820432i	$-0.306267\pi$
$233$	17.4546			1.14349			0.571744	+	0.820432i	$0.306267\pi$
$234$	25.0503	+	1.30329i	1.63759	+	0.0851989i
$235$	5.51720			0.359902
$236$	13.9195	+	3.72973i	0.906084	+	0.242785i
$237$	16.8058	−	21.1673i	1.09165	−	1.37496i
$238$	−7.75925	−	4.47980i	−0.502957	−	0.290383i
$239$	10.0839	−	10.0839i	0.652272	−	0.652272i	−0.301267	−	0.953540i	$-0.597410\pi$
$239$	10.0839	−	10.0839i	0.652272	−	0.652272i	0.953540	+	0.301267i	$0.0974096\pi$
$240$	−3.04247	+	2.25560i	−0.196391	+	0.145598i
$241$	4.69225	+	17.5117i	0.302254	+	1.12803i	0.935283	+	0.353900i	$0.115145\pi$
$241$	4.69225	+	17.5117i	0.302254	+	1.12803i	−0.633029	+	0.774128i	$0.718189\pi$
$242$	21.6621	+	21.6621i	1.39249	+	1.39249i
$243$	−3.30462	+	15.2342i	−0.211992	+	0.977272i
$244$	−5.20686	+	3.00618i	−0.333335	+	0.192451i
$245$	0.864649	−	3.22691i	0.0552404	−	0.206160i
$246$	2.04743	−	0.808657i	0.130539	−	0.0515581i
$247$	0.138701	+	0.559734i	0.00882531	+	0.0356150i
$248$			27.0201i			1.71578i
$249$	1.76425	+	15.3602i	0.111805	+	0.973416i
$250$	−4.49576	−	7.78688i	−0.284337	−	0.492485i
$251$	4.01542	−	6.95492i	0.253451	−	0.438990i	−0.711022	−	0.703169i	$-0.751768\pi$
$251$	4.01542	−	6.95492i	0.253451	−	0.438990i	0.964474	+	0.264179i	$0.0851009\pi$
$252$	10.1282	+	0.335216i	0.638019	+	0.0211166i
$253$	4.57266	−	1.22524i	0.287481	−	0.0770302i
$254$	−19.5440	+	5.23680i	−1.22630	+	0.328586i
$255$	20.5095	+	8.89559i	1.28436	+	0.557063i
$256$	9.99678	−	17.3149i	0.624799	−	1.08218i
$257$	−1.33444	−	2.31131i	−0.0832398	−	0.144176i	0.821400	−	0.570353i	$-0.193193\pi$
$257$	−1.33444	−	2.31131i	−0.0832398	−	0.144176i	−0.904640	+	0.426177i	$0.859860\pi$
$258$	20.1100	−	2.30981i	1.25200	−	0.143802i
$259$			7.86096i			0.488456i
$260$	9.78637	+	39.4935i	0.606925	+	2.44928i
$261$	−12.7600	−	13.6336i	−0.789827	−	0.843899i
$262$	5.76997	−	21.5338i	0.356470	−	1.33036i
$263$	13.6504	−	7.88109i	0.841723	−	0.485969i	−0.0161268	−	0.999870i	$-0.505134\pi$
$263$	13.6504	−	7.88109i	0.841723	−	0.485969i	0.857849	+	0.513901i	$0.171800\pi$
$264$	−4.00074	+	26.9374i	−0.246229	+	1.65788i
$265$	−20.0784	−	20.0784i	−1.23341	−	1.23341i
$266$	0.0959962	+	0.358263i	0.00588591	+	0.0219665i
$267$	−17.9552	−	24.2189i	−1.09884	−	1.48217i
$268$	−6.28171	+	6.28171i	−0.383717	+	0.383717i
$269$	−1.68632	−	0.973597i	−0.102817	−	0.0593612i	0.447710	−	0.894179i	$-0.352240\pi$
$269$	−1.68632	−	0.973597i	−0.102817	−	0.0593612i	−0.550527	+	0.834818i	$0.685573\pi$
$270$	−40.1234	+	3.26811i	−2.44183	+	0.198891i
$271$	−3.25156	−	0.871254i	−0.197518	−	0.0529249i	0.158703	−	0.987326i	$-0.449269\pi$
$271$	−3.25156	−	0.871254i	−0.197518	−	0.0529249i	−0.356222	+	0.934401i	$0.615935\pi$
$272$	2.52882			0.153332
$273$	2.59278	−	5.68133i	0.156922	−	0.343850i
$274$	−26.3959			−1.59463
$275$	−29.2796	−	7.84545i	−1.76563	−	0.473098i
$276$	4.40855	+	3.50017i	0.265364	+	0.210685i
$277$	20.8346	+	12.0288i	1.25183	+	0.722743i	0.971472	−	0.237153i	$-0.0762144\pi$
$277$	20.8346	+	12.0288i	1.25183	+	0.722743i	0.280355	+	0.959896i	$0.409548\pi$
$278$	18.9117	−	18.9117i	1.13425	−	1.13425i
$279$	−13.4034	+	21.5372i	−0.802443	+	1.28940i
$280$	2.76296	+	10.3115i	0.165118	+	0.616229i
$281$	7.81337	+	7.81337i	0.466107	+	0.466107i	0.900651	−	0.434544i	$-0.143090\pi$
$281$	7.81337	+	7.81337i	0.466107	+	0.466107i	−0.434544	+	0.900651i	$0.643090\pi$
$282$	6.56153	+	0.974518i	0.390733	+	0.0580317i
$283$	19.4687	−	11.2402i	1.15729	−	0.668163i	0.206638	−	0.978417i	$-0.433748\pi$
$283$	19.4687	−	11.2402i	1.15729	−	0.668163i	0.950653	+	0.310255i	$0.100414\pi$
$284$	9.04337	−	33.7503i	0.536625	−	2.00271i
$285$	−0.339964	−	0.860749i	−0.0201377	−	0.0509864i
$286$	35.2344	+	21.2402i	2.08345	+	1.25596i
$287$		−	0.548047i		−	0.0323502i
$288$	12.8954	−	6.88674i	0.759866	−	0.405805i
$289$	1.03667	+	1.79556i	0.0609803	+	0.105621i
$290$	24.1114	−	41.7621i	1.41587	−	2.45236i
$291$	7.34878	−	16.9432i	0.430793	−	0.993229i
$292$	−30.3465	+	8.13132i	−1.77589	+	0.475849i
$293$	−14.1486	+	3.79110i	−0.826569	+	0.221479i	−0.647216	−	0.762306i	$-0.724067\pi$
$293$	−14.1486	+	3.79110i	−0.826569	+	0.221479i	−0.179353	+	0.983785i	$0.557400\pi$
$294$	1.59830	−	3.68500i	0.0932145	−	0.214914i
$295$	−7.12597	+	12.3426i	−0.414890	+	0.718611i
$296$	−12.5597	−	21.7541i	−0.730018	−	1.26443i
$297$	−16.5513	+	19.4866i	−0.960403	+	1.13073i
$298$		−	46.8703i		−	2.71512i
$299$	3.03643	−	1.67740i	0.175601	−	0.0970068i
$300$	−13.2407	−	33.5240i	−0.764454	−	1.93551i
$301$	1.30433	−	4.86782i	0.0751803	−	0.280577i
$302$	−25.8463	+	14.9223i	−1.48728	+	0.858684i
$303$	1.51166	+	0.224511i	0.0868425	+	0.0128978i
$304$	−0.0740238	−	0.0740238i	−0.00424556	−	0.00424556i
$305$	−1.53899	−	5.74358i	−0.0881222	−	0.328877i
$306$	22.8204	+	14.2021i	1.30456	+	0.811878i
$307$	14.9266	−	14.9266i	0.851909	−	0.851909i	−0.138459	−	0.990368i	$-0.544215\pi$
$307$	14.9266	−	14.9266i	0.851909	−	0.851909i	0.990368	+	0.138459i	$0.0442150\pi$
$308$	14.3939	+	8.31035i	0.820171	+	0.473526i
$309$	16.5982	+	13.1782i	0.944240	+	0.749680i
$310$	−63.2774	−	16.9551i	−3.59392	−	0.962987i
$311$	6.32952			0.358914			0.179457	−	0.983766i	$-0.442566\pi$
$311$	6.32952			0.358914			0.179457	+	0.983766i	$0.442566\pi$
$312$	1.90212	+	19.8648i	0.107686	+	1.12462i
$313$	−6.46102			−0.365198			−0.182599	−	0.983187i	$-0.558451\pi$
$313$	−6.46102			−0.365198			−0.182599	+	0.983187i	$0.558451\pi$
$314$	−14.5797	−	3.90661i	−0.822778	−	0.220463i
$315$	−2.91276	+	9.58964i	−0.164115	+	0.540315i
$316$	45.6485	+	26.3552i	2.56793	+	1.48259i
$317$	−1.80063	+	1.80063i	−0.101134	+	0.101134i	−0.755863	−	0.654730i	$-0.772783\pi$
$317$	−1.80063	+	1.80063i	−0.101134	+	0.101134i	0.654730	+	0.755863i	$0.272783\pi$
$318$	−20.3325	−	27.4255i	−1.14019	−	1.53795i
$319$	−7.92676	−	29.5831i	−0.443814	−	1.65633i
$320$	29.7877	+	29.7877i	1.66518	+	1.66518i
$321$	−1.93956	+	13.0593i	−0.108256	+	0.728897i
$322$	1.93225	−	1.11559i	0.107680	−	0.0621693i
$323$	−0.159929	+	0.596864i	−0.00889871	+	0.0332104i
$324$	−30.3348	−	2.01019i	−1.68527	−	0.111677i
$325$	−22.2084	−	0.419679i	−1.23190	−	0.0232796i
$326$			31.1604i			1.72582i
$327$	−0.371203	+	0.0426357i	−0.0205276	+	0.00235776i
$328$	0.875633	+	1.51664i	0.0483487	+	0.0837424i
$329$	0.825743	−	1.43023i	0.0455247	−	0.0788510i
$330$	−60.5731	−	26.2724i	−3.33444	−	1.44625i
$331$	−11.6137	+	3.11188i	−0.638347	+	0.171045i	−0.563455	−	0.826147i	$-0.690528\pi$
$331$	−11.6137	+	3.11188i	−0.638347	+	0.171045i	−0.0748926	+	0.997192i	$0.523861\pi$
$332$	−29.1258	+	7.80423i	−1.59848	+	0.428313i
$333$	0.780099	−	23.5700i	0.0427491	−	1.29163i
$334$	23.9296	−	41.4474i	1.30937	−	2.26790i
$335$	−4.39295	−	7.60882i	−0.240013	−	0.415714i
$336$	0.129364	+	1.12629i	0.00705738	+	0.0614442i
$337$			17.7861i			0.968868i	0.874828	+	0.484434i	$0.160975\pi$
$337$			17.7861i			0.968868i	−0.874828	+	0.484434i	$0.839025\pi$
$338$	28.8046	+	8.89736i	1.56677	+	0.483953i
$339$	−11.4331	+	4.51565i	−0.620960	+	0.245256i
$340$	−11.2842	+	42.1133i	−0.611973	+	2.28391i
$341$	−36.0316	+	20.8028i	−1.95122	+	1.12654i
$342$	−0.252278	−	1.08373i	−0.0136416	−	0.0586012i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	4.16794	+	15.5549i	0.224720	+	0.838667i
$345$	−4.47215	+	3.31552i	−0.240772	+	0.178502i
$346$	34.1809	−	34.1809i	1.83757	−	1.83757i
$347$	12.1805	+	7.03241i	0.653883	+	0.377520i	0.789942	−	0.613181i	$-0.210110\pi$
$347$	12.1805	+	7.03241i	0.653883	+	0.377520i	−0.136059	+	0.990701i	$0.543444\pi$
$348$	22.6446	−	28.5214i	1.21388	−	1.52891i
$349$	−21.7431	−	5.82604i	−1.16388	−	0.311861i	−0.375365	−	0.926877i	$-0.622483\pi$
$349$	−21.7431	−	5.82604i	−1.16388	−	0.311861i	−0.788514	+	0.615016i	$0.789149\pi$
$350$	−14.2866			−0.763653
$351$	−8.33787	+	16.7774i	−0.445042	+	0.895509i
$352$	23.9771			1.27799
$353$	21.4698	+	5.75281i	1.14272	+	0.306191i	0.780045	−	0.625724i	$-0.215196\pi$
$353$	21.4698	+	5.75281i	1.14272	+	0.306191i	0.362677	+	0.931915i	$0.381863\pi$
$354$	−10.6549	+	13.4201i	−0.566303	+	0.713273i
$355$	29.9266	+	17.2782i	1.58834	+	0.917029i
$356$	41.5760	−	41.5760i	2.20352	−	2.20352i
$357$	5.37561	−	3.98532i	0.284508	−	0.210926i
$358$	2.75491	+	10.2815i	0.145602	+	0.543393i
$359$	2.22472	+	2.22472i	0.117416	+	0.117416i	0.763373	−	0.645957i	$-0.223542\pi$
$359$	2.22472	+	2.22472i	0.117416	+	0.117416i	−0.645957	+	0.763373i	$0.723542\pi$
$360$	−7.26105	−	31.1917i	−0.382691	−	1.64395i
$361$	−16.4323	+	9.48721i	−0.864859	+	0.499327i
$362$	−0.282321	+	1.05364i	−0.0148385	+	0.0553780i
$363$	−21.2809	+	8.40517i	−1.11696	+	0.441157i
$364$	11.7026	+	3.37394i	0.613385	+	0.176843i
$365$		−	31.0712i		−	1.62634i
$366$	−0.815793	−	7.10260i	−0.0426422	−	0.371259i
$367$	5.56243	+	9.63441i	0.290357	+	0.502912i	0.973894	−	0.227003i	$-0.0728928\pi$
$367$	5.56243	+	9.63441i	0.290357	+	0.502912i	−0.683537	+	0.729915i	$0.739559\pi$
$368$	−0.314871	+	0.545372i	−0.0164138	+	0.0284295i
$369$	−0.0543866	+	1.64324i	−0.00283125	+	0.0855438i
$370$	58.8262	−	15.7624i	3.05823	−	0.819450i
$371$	−8.21004	+	2.19987i	−0.426244	+	0.114212i
$372$	−45.3873	−	19.6858i	−2.35322	−	1.02066i
$373$	−5.01438	+	8.68517i	−0.259635	+	0.449701i	−0.966144	−	0.258003i	$-0.916936\pi$
$373$	−5.01438	+	8.68517i	−0.259635	+	0.449701i	0.706509	+	0.707704i	$0.250269\pi$
$374$	22.0423	+	38.1785i	1.13978	+	1.97416i
$375$	6.67175	−	0.766306i	0.344528	−	0.0395719i
$376$			5.27726i			0.272154i
$377$	−10.8521	−	19.6444i	−0.558910	−	1.01174i
$378$	−5.15795	+	10.8903i	−0.265296	+	0.560139i
$379$	−1.97780	+	7.38124i	−0.101593	+	0.379149i	−0.997936	−	0.0642110i	$-0.979547\pi$
$379$	−1.97780	+	7.38124i	−0.101593	+	0.379149i	0.896344	+	0.443360i	$0.146214\pi$
$380$	1.56306	−	0.902432i	0.0801832	−	0.0462938i
$381$	2.22009	−	14.9481i	0.113739	−	0.765813i
$382$	−3.71962	−	3.71962i	−0.190312	−	0.190312i
$383$	−1.45691	−	5.43726i	−0.0744445	−	0.277831i	0.918662	−	0.395044i	$-0.129271\pi$
$383$	−1.45691	−	5.43726i	−0.0744445	−	0.277831i	−0.993107	+	0.117213i	$0.962604\pi$
$384$	20.1113	+	27.1271i	1.02630	+	1.38433i
$385$	−11.6232	+	11.6232i	−0.592376	+	0.592376i
$386$	−20.2164	−	11.6719i	−1.02899	−	0.594086i
$387$	−4.39391	+	14.4660i	−0.223355	+	0.735350i
$388$	34.7904	+	9.32207i	1.76622	+	0.473256i
$389$	9.12980			0.462899			0.231450	−	0.972847i	$-0.425653\pi$
$389$	9.12980			0.462899			0.231450	+	0.972847i	$0.425653\pi$
$390$	−47.7142	−	8.01066i	−2.41610	−	0.405636i
$391$	3.71713			0.187983
$392$	3.08658	+	0.827047i	0.155896	+	0.0417722i
$393$	13.0404	+	10.3534i	0.657799	+	0.522259i
$394$	29.9326	+	17.2816i	1.50798	+	0.870634i
$395$	−36.8616	+	36.8616i	−1.85471	+	1.85471i
$396$	−42.3335	−	26.3458i	−2.12734	−	1.32393i
$397$	−4.21270	−	15.7220i	−0.211429	−	0.789066i	−0.987393	−	0.158288i	$-0.949403\pi$
$397$	−4.21270	−	15.7220i	−0.211429	−	0.789066i	0.775964	−	0.630778i	$-0.217264\pi$
$398$	6.46533	+	6.46533i	0.324078	+	0.324078i
$399$	−0.274014	−	0.0406966i	−0.0137179	−	0.00203738i
$400$	3.49212	−	2.01618i	0.174606	−	0.100809i
$401$	2.57548	−	9.61182i	0.128613	−	0.479992i	−0.871329	−	0.490699i	$-0.836742\pi$
$401$	2.57548	−	9.61182i	0.128613	−	0.479992i	0.999943	+	0.0107071i	$0.00340825\pi$
$402$	−3.88051	−	9.82500i	−0.193542	−	0.490027i
$403$	−21.9616	+	21.1469i	−1.09398	+	1.05340i
$404$			2.98044i			0.148283i
$405$	9.68514	−	28.4641i	0.481258	−	1.41439i
$406$	−7.21736	−	12.5008i	−0.358192	−	0.620406i
$407$	19.3395	−	33.4969i	0.958622	−	1.66038i
$408$	−8.50873	+	19.6176i	−0.421245	+	0.971215i
$409$	22.9240	−	6.14248i	1.13352	−	0.303726i	0.357178	−	0.934036i	$-0.383739\pi$
$409$	22.9240	−	6.14248i	1.13352	−	0.303726i	0.776343	+	0.630310i	$0.217072\pi$
$410$	−4.10122	+	1.09892i	−0.202545	+	0.0542717i
$411$	7.84473	−	18.0867i	0.386952	−	0.892149i
$412$	−20.6663	+	35.7951i	−1.01816	+	1.76350i
$413$	2.13305	+	3.69455i	0.104960	+	0.181797i
$414$	−5.90430	+	3.15318i	−0.290180	+	0.154970i
$415$		−	29.8213i		−	1.46387i
$416$	17.0542	−	4.22597i	0.836149	−	0.207195i
$417$	7.33798	+	18.5789i	0.359342	+	0.909813i
$418$	0.472338	−	1.76279i	0.0231028	−	0.0862209i
$419$	21.3110	−	12.3039i	1.04111	−	0.601084i	0.120962	−	0.992657i	$-0.461402\pi$
$419$	21.3110	−	12.3039i	1.04111	−	0.601084i	0.920147	+	0.391573i	$0.128069\pi$
$420$	−19.3338	−	2.87145i	−0.943392	−	0.140113i
$421$	23.1250	+	23.1250i	1.12705	+	1.12705i	0.990655	+	0.136390i	$0.0435502\pi$
$421$	23.1250	+	23.1250i	1.12705	+	1.12705i	0.136390	+	0.990655i	$0.456450\pi$
$422$	5.08729	+	18.9860i	0.247646	+	0.924226i
$423$	−2.61780	+	4.20639i	−0.127282	+	0.204522i
$424$	19.2053	−	19.2053i	0.932690	−	0.932690i
$425$	−20.6127	−	11.9007i	−0.999863	−	0.577271i
$426$	32.5395	+	25.8347i	1.57654	+	1.25170i
$427$	−1.71925	−	0.460672i	−0.0832004	−	0.0222935i
$428$	−25.7482			−1.24458
$429$	−25.0254	+	17.8304i	−1.20824	+	0.860861i
$430$	−39.0429			−1.88282
$431$	26.1423	+	7.00481i	1.25923	+	0.337410i	0.825895	−	0.563823i	$-0.190670\pi$
$431$	26.1423	+	7.00481i	1.25923	+	0.337410i	0.433335	+	0.901233i	$0.357337\pi$
$432$	−0.276109	−	3.38986i	−0.0132843	−	0.163095i
$433$	−2.63668	−	1.52229i	−0.126711	−	0.0731565i	0.435305	−	0.900283i	$-0.356641\pi$
$433$	−2.63668	−	1.52229i	−0.126711	−	0.0731565i	−0.562016	+	0.827127i	$0.689974\pi$
$434$	−13.8658	+	13.8658i	−0.665582	+	0.665582i
$435$	21.4500	+	28.9328i	1.02845	+	1.38722i
$436$	−0.188601	−	0.703867i	−0.00903234	−	0.0337091i
$437$	−0.108808	−	0.108808i	−0.00520500	−	0.00520500i
$438$	5.48820	−	36.9526i	0.262236	−	1.76566i
$439$	−9.89107	+	5.71061i	−0.472075	+	0.272553i	−0.717108	−	0.696962i	$-0.754535\pi$
$439$	−9.89107	+	5.71061i	−0.472075	+	0.272553i	0.245033	+	0.969515i	$0.421201\pi$
$440$	13.5948	−	50.7365i	0.648106	−	2.41877i
$441$	2.04999	+	2.19033i	0.0976185	+	0.104301i
$442$	22.4069	+	23.2701i	1.06579	+	1.10685i
$443$		−	31.8391i		−	1.51272i	−0.654155	−	0.756360i	$-0.726976\pi$
$443$		−	31.8391i		−	1.51272i	0.654155	−	0.756360i	$-0.273024\pi$
$444$	45.6920	−	5.24811i	2.16845	−	0.249064i
$445$	29.0751	+	50.3595i	1.37829	+	2.38727i
$446$	1.89583	−	3.28367i	0.0897700	−	0.155486i
$447$	32.1159	+	13.9296i	1.51903	+	0.658849i
$448$	12.1801	−	3.26366i	0.575457	−	0.154193i
$449$	1.87813	−	0.503244i	0.0886345	−	0.0237495i	−0.214229	−	0.976783i	$-0.568724\pi$
$449$	1.87813	−	0.503244i	0.0886345	−	0.0237495i	0.302864	+	0.953034i	$0.402057\pi$
$450$	42.8365	+	1.41776i	2.01933	+	0.0668341i
$451$	−1.34830	+	2.33533i	−0.0634890	+	0.109966i
$452$	−11.9868	−	20.7617i	−0.563809	−	0.976546i
$453$	−2.54353	−	22.1449i	−0.119505	−	1.04046i
$454$			34.1427i			1.60240i
$455$	−6.21864	+	10.3158i	−0.291534	+	0.483614i
$456$	0.823317	−	0.325180i	0.0385553	−	0.0152279i
$457$	4.76906	−	17.7984i	0.223087	−	0.832572i	−0.760075	−	0.649836i	$-0.774838\pi$
$457$	4.76906	−	17.7984i	0.223087	−	0.832572i	0.983162	−	0.182737i	$-0.0584956\pi$
$458$	19.4485	−	11.2286i	0.908768	−	0.524677i
$459$	−16.5135	+	11.4160i	−0.770784	+	0.532852i
$460$	−7.67724	−	7.67724i	−0.357953	−	0.357953i
$461$	8.38387	+	31.2890i	0.390476	+	1.45728i	0.829351	+	0.558728i	$0.188710\pi$
$461$	8.38387	+	31.2890i	0.390476	+	1.45728i	−0.438875	+	0.898548i	$0.644623\pi$
$462$	−15.8764	+	11.7703i	−0.738638	+	0.547605i
$463$	22.5374	−	22.5374i	1.04740	−	1.04740i	0.0485833	−	0.998819i	$-0.484529\pi$
$463$	22.5374	−	22.5374i	1.04740	−	1.04740i	0.998819	−	0.0485833i	$-0.0154706\pi$
$464$	3.52832	+	2.03707i	0.163798	+	0.0945688i
$465$	30.4236	−	38.3192i	1.41086	−	1.77701i
$466$	−39.0986	−	10.4764i	−1.81121	−	0.485311i
$467$	14.8736			0.688268			0.344134	−	0.938921i	$-0.388173\pi$
$467$	14.8736			0.688268			0.344134	+	0.938921i	$0.388173\pi$
$468$	−34.7539	−	11.2776i	−1.60650	−	0.521308i
$469$	−2.62992			−0.121438
$470$	−12.3586	−	3.31148i	−0.570060	−	0.152747i
$471$	7.00985	−	8.82908i	0.322997	−	0.406822i
$472$	−11.8058	−	6.81608i	−0.543406	−	0.313735i
$473$	−17.5337	+	17.5337i	−0.806202	+	0.806202i
$474$	−50.3500	+	37.3280i	−2.31265	+	1.71453i
$475$	0.255017	+	0.951737i	0.0117010	+	0.0436687i
$476$	9.22820	+	9.22820i	0.422974	+	0.422974i
$477$	24.8349	−	5.78127i	1.13711	−	0.264706i
$478$	−28.6405	+	16.5356i	−1.30999	+	0.756322i
$479$	1.76966	−	6.60445i	0.0808577	−	0.301765i	−0.913640	−	0.406525i	$-0.866741\pi$
$479$	1.76966	−	6.60445i	0.0808577	−	0.301765i	0.994498	+	0.104759i	$0.0334072\pi$
$480$	−26.2256	+	10.3581i	−1.19703	+	0.472782i
$481$	7.85169	−	27.2338i	0.358006	−	1.24176i
$482$		−	42.0429i		−	1.91500i
$483$	0.190153	+	1.65554i	0.00865226	+	0.0753299i
$484$	−22.3115	−	38.6446i	−1.01416	−	1.75657i
$485$	−17.8106	+	30.8489i	−0.808740	+	1.40078i
$486$	16.5461	−	32.1413i	0.750547	−	1.45796i
$487$	−26.2521	+	7.03423i	−1.18960	+	0.318751i	−0.798726	−	0.601695i	$-0.794492\pi$
$487$	−26.2521	+	7.03423i	−1.18960	+	0.318751i	−0.390870	+	0.920446i	$0.627826\pi$
$488$	5.49380	−	1.47206i	0.248693	−	0.0666370i
$489$	−21.3514	−	9.26073i	−0.965543	−	0.418785i
$490$	−3.87366	+	6.70937i	−0.174994	+	0.303099i
$491$	6.86194	+	11.8852i	0.309675	+	0.536373i	0.978291	−	0.207235i	$-0.0664463\pi$
$491$	6.86194	+	11.8852i	0.309675	+	0.536373i	−0.668616	+	0.743608i	$0.733113\pi$
$492$	−3.18554	+	0.365886i	−0.143615	+	0.0164954i
$493$		−	24.0482i		−	1.08308i
$494$	0.0252669	−	1.33706i	0.00113681	−	0.0601573i
$495$	36.0041	−	33.6972i	1.61826	−	1.51458i
$496$	1.43247	−	5.34606i	0.0643199	−	0.240045i
$497$	8.95807	−	5.17194i	0.401824	−	0.231993i
$498$	5.26743	−	35.4661i	0.236039	−	1.58927i
$499$	−15.8542	−	15.8542i	−0.709729	−	0.709729i	0.256749	−	0.966478i	$-0.417349\pi$
$499$	−15.8542	−	15.8542i	−0.709729	−	0.709729i	−0.966478	+	0.256749i	$0.917349\pi$
$500$	3.38978	+	12.6508i	0.151596	+	0.565763i
$501$	21.2883	+	28.7148i	0.951091	+	1.28288i
$502$	−13.1690	+	13.1690i	−0.587763	+	0.587763i
$503$	−29.7432	−	17.1723i	−1.32618	−	0.765673i	−0.341478	−	0.939890i	$-0.610927\pi$
$503$	−29.7432	−	17.1723i	−1.32618	−	0.765673i	−0.984707	+	0.174217i	$0.944261\pi$
$504$	−9.17260	−	2.78609i	−0.408580	−	0.124102i
$505$	−2.84720	−	0.762905i	−0.126699	−	0.0339488i
$506$	−10.9782			−0.488042
$507$	−14.6571	+	17.0929i	−0.650947	+	0.759123i
$508$	29.4722			1.30762
$509$	−7.19131	−	1.92691i	−0.318749	−	0.0854086i	0.0958970	−	0.995391i	$-0.469428\pi$
$509$	−7.19131	−	1.92691i	−0.318749	−	0.0854086i	−0.414646	+	0.909983i	$0.636095\pi$
$510$	−40.6024	−	32.2363i	−1.79791	−	1.42745i
$511$	−8.05462	−	4.65034i	−0.356315	−	0.205719i
$512$	−5.21329	+	5.21329i	−0.230397	+	0.230397i
$513$	0.817554	+	0.149215i	0.0360959	+	0.00658802i
$514$	1.60189	+	5.97832i	0.0706562	+	0.263692i
$515$	−28.9049	−	28.9049i	−1.27370	−	1.27370i
$516$	−29.1651	−	4.33161i	−1.28392	−	0.190688i
$517$	−7.03727	+	4.06297i	−0.309499	+	0.178689i
$518$	4.71823	−	17.6087i	0.207307	−	0.773681i
$519$	13.2626	+	33.5794i	0.582164	+	1.47397i
$520$	0.727230	−	38.4833i	0.0318911	−	1.68760i
$521$		−	34.6387i		−	1.51755i	−0.651353	−	0.758774i	$-0.725798\pi$
$521$		−	34.6387i		−	1.51755i	0.651353	−	0.758774i	$-0.274202\pi$
$522$	20.3997	+	38.1982i	0.892870	+	1.67189i
$523$	−15.4862	−	26.8228i	−0.677162	−	1.17288i	−0.975832	−	0.218523i	$-0.929876\pi$
$523$	−15.4862	−	26.8228i	−0.677162	−	1.17288i	0.298669	−	0.954357i	$-0.403457\pi$
$524$	−16.2364	+	28.1223i	−0.709291	+	1.22853i
$525$	4.24592	−	9.78933i	0.185307	−	0.427241i
$526$	−35.3075	+	9.46063i	−1.53948	+	0.412503i
$527$	−31.5558	+	8.45535i	−1.37459	+	0.368321i
$528$	2.21965	−	5.11758i	0.0965978	−	0.222714i
$529$	11.0372	−	19.1169i	0.479877	−	0.831171i
$530$	32.9248	+	57.0274i	1.43016	+	2.47711i
$531$	−6.02901	−	11.2893i	−0.261637	−	0.489912i
$532$		−	0.540257i		−	0.0234231i
$533$	−0.547401	+	1.89868i	−0.0237106	+	0.0822409i
$534$	25.6835	+	65.0275i	1.11143	+	2.81402i
$535$	6.59076	−	24.5971i	0.284944	−	1.06342i
$536$	7.27792	−	4.20191i	0.314358	−	0.181495i
$537$	−7.86370	−	1.16792i	−0.339344	−	0.0503994i
$538$	3.19302	+	3.19302i	0.137661	+	0.137661i
$539$	1.27349	+	4.75272i	0.0548530	+	0.204714i
$540$	57.6847	+	10.5283i	2.48235	+	0.453065i
$541$	27.7105	−	27.7105i	1.19137	−	1.19137i	0.214682	−	0.976684i	$-0.431129\pi$
$541$	27.7105	−	27.7105i	1.19137	−	1.19137i	0.976684	−	0.214682i	$-0.0688715\pi$
$542$	6.76062	+	3.90325i	0.290394	+	0.167659i
$543$	−0.638057	−	0.506585i	−0.0273816	−	0.0217397i
$544$	18.1854	+	4.87278i	0.779695	+	0.208919i
$545$	0.720677			0.0308704
$546$	−9.21786	+	11.1701i	−0.394488	+	0.478035i
$547$	−29.1066			−1.24451			−0.622254	−	0.782815i	$-0.713783\pi$
$547$	−29.1066			−1.24451			−0.622254	+	0.782815i	$0.713783\pi$
$548$	37.1383	+	9.95119i	1.58647	+	0.425094i
$549$	5.10921	+	1.55187i	0.218056	+	0.0662323i
$550$	60.8779	+	35.1479i	2.59584	+	1.49871i
$551$	−0.703941	+	0.703941i	−0.0299889	+	0.0299889i
$552$	−3.17134	−	4.27766i	−0.134981	−	0.182069i
$553$	4.03870	+	15.0726i	0.171743	+	0.640954i
$554$	−39.4499	−	39.4499i	−1.67607	−	1.67607i
$555$	−6.68232	+	44.9927i	−0.283649	+	1.90983i
$556$	−33.7379	+	19.4786i	−1.43081	+	0.826077i
$557$	−4.32822	+	16.1532i	−0.183393	+	0.684431i	0.811576	+	0.584247i	$0.198610\pi$
$557$	−4.32822	+	16.1532i	−0.183393	+	0.684431i	−0.994969	+	0.100184i	$0.968057\pi$
$558$	42.9508	−	40.1988i	1.81825	−	1.70175i
$559$	−9.38085	+	15.5615i	−0.396768	+	0.658181i
$560$		−	2.18665i		−	0.0924029i
$561$	−32.7111	+	3.75714i	−1.38106	+	0.158627i
$562$	−12.8124	−	22.1918i	−0.540459	−	0.936103i
$563$	−15.1077	+	26.1672i	−0.636712	+	1.10282i	0.349438	+	0.936960i	$0.386373\pi$
$563$	−15.1077	+	26.1672i	−0.636712	+	1.10282i	−0.986150	+	0.165858i	$0.946961\pi$
$564$	−8.86452	−	3.84481i	−0.373264	−	0.161896i
$565$	22.9017	−	6.13650i	0.963484	−	0.258165i
$566$	−50.3566	+	13.4930i	−2.11665	+	0.567154i
$567$	−5.92924	−	6.77083i	−0.249005	−	0.284348i
$568$	−16.5268	+	28.6252i	−0.693447	+	1.20109i
$569$	−4.58803	−	7.94671i	−0.192340	−	0.333143i	0.753685	−	0.657236i	$-0.228274\pi$
$569$	−4.58803	−	7.94671i	−0.192340	−	0.333143i	−0.946025	+	0.324092i	$0.894941\pi$
$570$	0.244894	+	2.13214i	0.0102575	+	0.0893056i
$571$		−	15.0977i		−	0.631820i	−0.948789	−	0.315910i	$-0.897690\pi$
$571$		−	15.0977i		−	0.631820i	0.948789	−	0.315910i	$-0.102310\pi$
$572$	−41.5664	−	43.1677i	−1.73798	−	1.80493i
$573$	3.65417	−	1.44326i	0.152655	−	0.0602931i
$574$	−0.328944	+	1.22764i	−0.0137299	+	0.0512405i
$575$	5.13310	−	2.96360i	0.214065	−	0.123591i
$576$	−36.8443	+	8.57689i	−1.53518	+	0.357370i
$577$	22.6622	+	22.6622i	0.943442	+	0.943442i	0.998484	−	0.0550424i	$-0.0175294\pi$
$577$	22.6622	+	22.6622i	0.943442	+	0.943442i	−0.0550424	+	0.998484i	$0.517529\pi$
$578$	−1.24444	−	4.64430i	−0.0517617	−	0.193177i
$579$	14.0059	−	10.3836i	0.582066	−	0.431527i
$580$	−49.6684	+	49.6684i	−2.06237	+	2.06237i
$581$	−7.73061	−	4.46327i	−0.320720	−	0.185168i
$582$	−26.6309	+	33.5423i	−1.10389	+	1.39037i
$583$	40.3965	+	10.8242i	1.67305	+	0.448293i
$584$	29.7200			1.22982
$585$	19.6694	−	30.3134i	0.813230	−	1.25331i
$586$	33.9685			1.40323
$587$	33.3701	+	8.94148i	1.37733	+	0.369054i	0.870150	−	0.492786i	$-0.164022\pi$
$587$	33.3701	+	8.94148i	1.37733	+	0.369054i	0.507179	+	0.861841i	$0.330688\pi$
$588$	−3.63800	+	4.58215i	−0.150029	+	0.188965i
$589$	1.17121	+	0.676198i	0.0482589	+	0.0278623i
$590$	23.3704	−	23.3704i	0.962146	−	0.962146i
$591$	−20.7373	+	15.3741i	−0.853019	+	0.632404i
$592$	1.33170	+	4.96999i	0.0547327	+	0.204265i
$593$	18.3209	+	18.3209i	0.752348	+	0.752348i	0.974917	−	0.222569i	$-0.0714442\pi$
$593$	18.3209	+	18.3209i	0.752348	+	0.752348i	−0.222569	+	0.974917i	$0.571444\pi$
$594$	48.7713	−	33.7161i	2.00111	−	1.38339i
$595$	−11.1778	+	6.45350i	−0.458245	+	0.264568i
$596$	−17.6700	+	65.9454i	−0.723792	+	2.70123i
$597$	−6.35157	+	2.50863i	−0.259952	+	0.102672i
$598$	−7.80846	+	1.93491i	−0.319311	+	0.0791245i
$599$		−	19.3701i		−	0.791440i	−0.918371	−	0.395720i	$-0.870495\pi$
$599$		−	19.3701i		−	0.791440i	0.918371	−	0.395720i	$-0.129505\pi$
$600$	3.89075	+	33.8744i	0.158839	+	1.38292i
$601$	18.5692	+	32.1628i	0.757453	+	1.31195i	0.944146	+	0.329528i	$0.106890\pi$
$601$	18.5692	+	32.1628i	0.757453	+	1.31195i	−0.186693	+	0.982418i	$0.559777\pi$
$602$	−5.84344	+	10.1211i	−0.238161	+	0.412506i
$603$	7.88545	+	0.260986i	0.321120	+	0.0106282i
$604$	41.9907	−	11.2514i	1.70858	−	0.457812i
$605$	42.6280	−	11.4221i	1.73308	−	0.464376i
$606$	−3.25138	−	1.41022i	−0.132078	−	0.0572864i
$607$	−13.5471	+	23.4642i	−0.549859	+	0.952384i	0.448424	+	0.893821i	$0.351985\pi$
$607$	−13.5471	+	23.4642i	−0.549859	+	0.952384i	−0.998284	+	0.0585636i	$0.981348\pi$
$608$	−0.389690	−	0.674963i	−0.0158040	−	0.0273734i
$609$	10.7106	−	1.23021i	0.434017	−	0.0498505i
$610$			13.7894i			0.558318i
$611$	−4.28928	+	4.13017i	−0.173526	+	0.167089i
$612$	−26.7537	−	28.5852i	−1.08145	−	1.15549i
$613$	−8.77706	+	32.7565i	−0.354502	+	1.32302i	0.526607	+	0.850109i	$0.323464\pi$
$613$	−8.77706	+	32.7565i	−0.354502	+	1.32302i	−0.881110	+	0.472912i	$0.843203\pi$
$614$	−42.3951	+	24.4768i	−1.71093	+	0.987804i
$615$	0.465875	−	3.13678i	0.0187859	−	0.126487i
$616$	−11.1178	−	11.1178i	−0.447948	−	0.447948i
$617$	4.24456	+	15.8409i	0.170880	+	0.637731i	0.997217	+	0.0745556i	$0.0237538\pi$
$617$	4.24456	+	15.8409i	0.170880	+	0.637731i	−0.826337	+	0.563175i	$0.809580\pi$
$618$	−29.2706	−	39.4817i	−1.17744	−	1.58819i
$619$	−14.8265	+	14.8265i	−0.595929	+	0.595929i	−0.939227	−	0.343298i	$-0.888456\pi$
$619$	−14.8265	+	14.8265i	−0.595929	+	0.595929i	0.343298	+	0.939227i	$0.388456\pi$
$620$	82.6377	+	47.7109i	3.31881	+	1.91612i
$621$	−0.405856	−	4.98279i	−0.0162864	−	0.199952i
$622$	−14.1782	−	3.79904i	−0.568495	−	0.152328i
$623$	17.4063			0.697370
$624$	0.676789	−	4.03118i	0.0270933	−	0.161376i
$625$	17.8500			0.714001
$626$	14.4728	+	3.87797i	0.578449	+	0.154995i
$627$	1.06750	+	0.847543i	0.0426319	+	0.0338476i
$628$	19.0404	+	10.9930i	0.759796	+	0.438669i
$629$	21.4754	−	21.4754i	0.856282	−	0.856282i
$630$	12.2804	−	19.7327i	0.489264	−	0.786169i
$631$	−6.27854	−	23.4318i	−0.249945	−	0.932807i	−0.970833	−	0.239756i	$-0.922933\pi$
$631$	−6.27854	−	23.4318i	−0.249945	−	0.932807i	0.720888	−	0.693051i	$-0.243734\pi$
$632$	−35.2586	−	35.2586i	−1.40251	−	1.40251i
$633$	−14.5213	−	2.15671i	−0.577171	−	0.0857214i
$634$	5.11421	−	2.95269i	0.203111	−	0.117266i
$635$	−7.54401	+	28.1546i	−0.299375	+	1.11728i
$636$	18.2680	+	46.2524i	0.724373	+	1.83403i
$637$	1.74346	+	3.15600i	0.0690783	+	0.125045i
$638$			71.0243i			2.81188i
$639$	−27.3727	+	14.6184i	−1.08285	+	0.578293i
$640$	−32.5665	−	56.4068i	−1.28730	−	2.22968i
$641$	−3.25542	+	5.63855i	−0.128581	+	0.222709i	−0.923127	−	0.384495i	$-0.874376\pi$
$641$	−3.25542	+	5.63855i	−0.128581	+	0.222709i	0.794546	+	0.607204i	$0.207709\pi$
$642$	12.1830	−	28.0888i	0.480823	−	1.10858i
$643$	32.9121	−	8.81877i	1.29793	−	0.347778i	0.457261	−	0.889333i	$-0.348831\pi$
$643$	32.9121	−	8.81877i	1.29793	−	0.347778i	0.840666	+	0.541554i	$0.182164\pi$
$644$	−3.13921	+	0.841149i	−0.123702	+	0.0331459i
$645$	11.6034	−	26.7525i	0.456882	−	1.05338i
$646$	0.716489	−	1.24099i	0.0281899	−	0.0488263i
$647$	−13.7326	−	23.7856i	−0.539884	−	0.935107i	−0.998910	−	0.0466836i	$-0.985135\pi$
$647$	−13.7326	−	23.7856i	−0.539884	−	0.935107i	0.459026	−	0.888423i	$-0.348199\pi$
$648$	27.2263	+	9.26395i	1.06955	+	0.363922i
$649$		−	20.9908i		−	0.823962i
$650$	49.4953	+	14.2698i	1.94136	+	0.559707i
$651$	−5.38013	−	13.6219i	−0.210864	−	0.533883i
$652$	11.7474	−	43.8420i	0.460064	−	1.71698i
$653$	27.3496	−	15.7903i	1.07027	−	0.617922i	0.142016	−	0.989864i	$-0.454642\pi$
$653$	27.3496	−	15.7903i	1.07027	−	0.617922i	0.928256	+	0.371943i	$0.121308\pi$
$654$	0.857091	+	0.127295i	0.0335149	+	0.00497764i
$655$	−22.7090	−	22.7090i	−0.887315	−	0.887315i
$656$	−0.0928433	−	0.346496i	−0.00362492	−	0.0135284i
$657$	23.6892	+	14.7427i	0.924202	+	0.575167i
$658$	−2.70812	+	2.70812i	−0.105573	+	0.105573i
$659$	−26.1172	−	15.0788i	−1.01738	−	0.587385i	−0.104037	−	0.994573i	$-0.533176\pi$
$659$	−26.1172	−	15.0788i	−1.01738	−	0.587385i	−0.913344	+	0.407188i	$0.866509\pi$
$660$	75.3203	+	59.8006i	2.93184	+	2.32773i
$661$	−17.8214	−	4.77524i	−0.693174	−	0.185735i	−0.105003	−	0.994472i	$-0.533485\pi$
$661$	−17.8214	−	4.77524i	−0.693174	−	0.185735i	−0.588171	+	0.808737i	$0.700152\pi$
$662$	27.8827			1.08369
$663$	−22.6041	+	8.43765i	−0.877871	+	0.327691i
$664$	28.5244			1.10696
$665$	0.516105	+	0.138290i	0.0200137	+	0.00536265i
$666$	−15.8944	+	52.3289i	−0.615895	+	2.02770i
$667$	5.18630	+	2.99431i	0.200814	+	0.115940i
$668$	−49.2940	+	49.2940i	−1.90724	+	1.90724i
$669$	1.68657	+	2.27493i	0.0652064	+	0.0879538i
$670$	5.27339	+	19.6806i	0.203729	+	0.760327i
$671$	6.19269	+	6.19269i	0.239066	+	0.239066i
$672$	−1.23996	+	8.34875i	−0.0478324	+	0.322060i
$673$	−10.0117	+	5.78024i	−0.385921	+	0.222812i	−0.680391	−	0.732849i	$-0.738190\pi$
$673$	−10.0117	+	5.78024i	−0.385921	+	0.222812i	0.294470	+	0.955661i	$0.404857\pi$
$674$	10.6754	−	39.8411i	0.411200	−	1.53462i
$675$	−13.7023	+	28.9306i	−0.527401	+	1.11354i
$676$	−37.1731	−	23.3777i	−1.42974	−	0.899141i
$677$			19.0631i			0.732653i	0.930486	+	0.366326i	$0.119385\pi$
$677$			19.0631i			0.732653i	−0.930486	+	0.366326i	$0.880615\pi$
$678$	28.3207	−	3.25286i	1.08765	−	0.124925i
$679$	5.33133	+	9.23414i	0.204598	+	0.354374i
$680$	20.6219	−	35.7182i	0.790814	−	1.36973i
$681$	−23.3949	−	10.1471i	−0.896494	−	0.388836i
$682$	93.1974	−	24.9722i	3.56871	−	0.956234i
$683$	−29.2703	+	7.84295i	−1.12000	+	0.300102i	−0.770882	−	0.636978i	$-0.780184\pi$
$683$	−29.2703	+	7.84295i	−1.12000	+	0.300102i	−0.349114	+	0.937080i	$0.613518\pi$
$684$	−0.0536136	+	1.61989i	−0.00204997	+	0.0619379i
$685$	−19.0126	+	32.9308i	−0.726435	+	1.25822i
$686$	1.15952	+	2.00834i	0.0442706	+	0.0766789i
$687$	1.91392	+	16.6633i	0.0730207	+	0.635746i
$688$		−	3.29858i		−	0.125757i
$689$	30.6405	+	0.579022i	1.16731	+	0.0220590i
$690$	12.0077	−	4.74260i	0.457125	−	0.180548i
$691$	0.203926	−	0.761063i	0.00775772	−	0.0289522i	−0.961938	−	0.273266i	$-0.911896\pi$
$691$	0.203926	−	0.761063i	0.00775772	−	0.0289522i	0.969696	+	0.244314i	$0.0785627\pi$
$692$	−60.9778	+	35.2055i	−2.31803	+	1.33831i
$693$	−3.34673	−	14.3767i	−0.127132	−	0.546127i
$694$	−23.0636	−	23.0636i	−0.875481	−	0.875481i
$695$	−9.97189	−	37.2156i	−0.378255	−	1.41167i
$696$	−27.6746	+	20.5172i	−1.04900	+	0.777701i
$697$	−1.49722	+	1.49722i	−0.0567111	+	0.0567111i
$698$	45.2080	+	26.1008i	1.71115	+	0.987932i
$699$	18.7984	−	23.6771i	0.711023	−	0.895551i
$700$	20.1010	+	5.38604i	0.759745	+	0.203573i
$701$	−26.6321			−1.00588			−0.502941	−	0.864321i	$-0.667749\pi$
$701$	−26.6321			−1.00588			−0.502941	+	0.864321i	$0.667749\pi$
$702$	28.7469	−	32.5771i	1.08498	−	1.22954i
$703$	−1.25726			−0.0474186
$704$	−59.9309	−	16.0584i	−2.25873	−	0.605225i
$705$	5.94198	−	7.48407i	0.223788	−	0.281866i
$706$	−44.6398	−	25.7728i	−1.68004	−	0.969972i
$707$	−0.623901	+	0.623901i	−0.0234642	+	0.0234642i
$708$	20.0506	−	14.8649i	0.753548	−	0.558659i
$709$	10.2096	+	38.1027i	0.383430	+	1.43098i	0.840628	+	0.541614i	$0.182186\pi$
$709$	10.2096	+	38.1027i	0.383430	+	1.43098i	−0.457198	+	0.889365i	$0.651147\pi$
$710$	−56.6656	−	56.6656i	−2.12662	−	2.12662i
$711$	−10.6137	−	45.5940i	−0.398045	−	1.70991i
$712$	−48.1694	+	27.8106i	−1.80523	+	1.04225i
$713$	2.10560	−	7.85821i	0.0788554	−	0.294292i
$714$	−14.4335	+	5.70069i	−0.540160	+	0.213343i
$715$	51.8776	−	28.6585i	1.94011	−	1.07177i
$716$		−	15.5044i		−	0.579426i
$717$	−2.81851	−	24.5390i	−0.105259	−	0.916427i
$718$	−3.64810	−	6.31870i	−0.136146	−	0.235812i
$719$	−3.28572	+	5.69104i	−0.122537	+	0.212240i	−0.920767	−	0.390112i	$-0.872436\pi$
$719$	−3.28572	+	5.69104i	−0.122537	+	0.212240i	0.798231	+	0.602352i	$0.205770\pi$
$720$	−0.216997	+	6.55637i	−0.00808700	+	0.244341i
$721$	−11.8192	+	3.16693i	−0.440168	+	0.117943i
$722$	42.5030	−	11.3886i	1.58180	−	0.423842i
$723$	28.8081	+	12.4949i	1.07139	+	0.464692i
$724$	0.794439	−	1.37601i	0.0295251	−	0.0511390i
$725$	−19.1732	−	33.2089i	−0.712073	−	1.23335i
$726$	52.7145	−	6.05470i	1.95642	−	0.224711i
$727$		−	24.5557i		−	0.910720i	−0.890307	−	0.455360i	$-0.849511\pi$
$727$		−	24.5557i		−	0.910720i	0.890307	−	0.455360i	$-0.150489\pi$
$728$	−9.86721	−	5.94820i	−0.365703	−	0.220455i
$729$	17.1061	+	20.8898i	0.633558	+	0.773695i
$730$	−18.6493	+	69.6000i	−0.690240	+	2.57601i
$731$	−16.8618	+	9.73514i	−0.623655	+	0.360067i
$732$	−1.52987	+	10.3007i	−0.0565455	+	0.380726i
$733$	−0.136638	−	0.136638i	−0.00504685	−	0.00504685i	0.704579	−	0.709626i	$-0.251136\pi$
$733$	−0.136638	−	0.136638i	−0.00504685	−	0.00504685i	−0.709626	+	0.704579i	$0.751136\pi$
$734$	−6.67726	−	24.9199i	−0.246462	−	0.919809i
$735$	−3.44608	−	4.64826i	−0.127111	−	0.171454i
$736$	−3.31520	+	3.31520i	−0.122200	+	0.122200i
$737$	11.2066	+	6.47011i	0.412799	+	0.238329i
$738$	1.10812	−	3.64825i	0.0407904	−	0.134294i
$739$	4.68566	+	1.25552i	0.172365	+	0.0461850i	0.343969	−	0.938981i	$-0.388228\pi$
$739$	4.68566	+	1.25552i	0.172365	+	0.0461850i	−0.171604	+	0.985166i	$0.554895\pi$
$740$	−88.7094			−3.26102
$741$	0.908658	+	0.414682i	0.0333804	+	0.0152337i
$742$	19.7110			0.723614
$743$	13.1620	+	3.52674i	0.482866	+	0.129384i	0.492037	−	0.870574i	$-0.336252\pi$
$743$	13.1620	+	3.52674i	0.482866	+	0.129384i	−0.00917065	+	0.999958i	$0.502919\pi$
$744$	36.6528	+	29.1005i	1.34376	+	1.06688i
$745$	−58.4742	−	33.7601i	−2.14233	−	1.23688i
$746$	16.4452	−	16.4452i	0.602103	−	0.602103i
$747$	22.7362	+	14.1497i	0.831875	+	0.517709i
$748$	−16.6198	−	62.0261i	−0.607681	−	2.26790i
$749$	−5.38990	−	5.38990i	−0.196943	−	0.196943i
$750$	−15.4048	−	2.28792i	−0.562503	−	0.0835430i
$751$	−35.6637	+	20.5905i	−1.30139	+	0.751356i	−0.980642	−	0.195809i	$-0.937267\pi$
$751$	−35.6637	+	20.5905i	−1.30139	+	0.751356i	−0.320745	+	0.947165i	$0.603933\pi$
$752$	0.279774	−	1.04413i	0.0102023	−	0.0380755i
$753$	−5.10976	−	12.9373i	−0.186210	−	0.471462i
$754$	12.5180	+	50.5173i	0.455880	+	1.83973i
$755$			42.9935i			1.56470i
$756$	11.3627	−	13.3779i	0.413259	−	0.486550i
$757$	−17.3900	−	30.1204i	−0.632052	−	1.09475i	−0.987132	−	0.159910i	$-0.948880\pi$
$757$	−17.3900	−	30.1204i	−0.632052	−	1.09475i	0.355079	−	0.934836i	$-0.384454\pi$
$758$	8.86060	−	15.3470i	0.321831	−	0.557428i
$759$	3.26268	−	7.52238i	0.118428	−	0.273045i
$760$	−1.64919	+	0.441900i	−0.0598226	+	0.0160294i
$761$	−19.3965	+	5.19727i	−0.703122	+	0.188401i	−0.592628	−	0.805476i	$-0.701910\pi$
$761$	−19.3965	+	5.19727i	−0.703122	+	0.188401i	−0.110493	+	0.993877i	$0.535243\pi$
$762$	−13.9450	+	32.1514i	−0.505175	+	1.16472i
$763$	0.107862	−	0.186822i	0.00390485	−	0.00676340i
$764$	3.83112	+	6.63570i	0.138605	+	0.240071i
$765$	34.1554	−	18.2406i	1.23489	−	0.659492i
$766$			13.0540i			0.471660i
$767$	−3.69963	−	14.9301i	−0.133586	−	0.539094i
$768$	−12.7212	−	32.2086i	−0.459038	−	1.16223i
$769$	8.31083	−	31.0165i	0.299696	−	1.11848i	−0.637719	−	0.770269i	$-0.720122\pi$
$769$	8.31083	−	31.0165i	0.299696	−	1.11848i	0.937415	−	0.348213i	$-0.113211\pi$
$770$	33.0127	−	19.0599i	1.18969	−	0.686870i
$771$	−4.57247	−	0.679103i	−0.164673	−	0.0244573i
$772$	24.0437	+	24.0437i	0.865350	+	0.865350i
$773$	7.03808	+	26.2665i	0.253142	+	0.944739i	0.969115	+	0.246611i	$0.0793169\pi$
$773$	7.03808	+	26.2665i	0.253142	+	0.944739i	−0.715973	+	0.698128i	$0.754016\pi$
$774$	18.5251	−	29.7669i	0.665871	−	1.06995i
$775$	−36.8351	+	36.8351i	−1.32315	+	1.32315i
$776$	−29.5074	−	17.0361i	−1.05925	−	0.611560i
$777$	10.6634	+	8.46619i	0.382547	+	0.303723i
$778$	−20.4509	−	5.47980i	−0.733201	−	0.196461i
$779$	0.0876533			0.00314051
$780$	64.1127	+	29.2590i	2.29560	+	1.04764i
$781$	−50.8958			−1.82120
$782$	−8.32643	−	2.23106i	−0.297753	−	0.0797826i
$783$	−32.2364	+	2.62571i	−1.15204	+	0.0938351i
$784$	−0.566848	−	0.327270i	−0.0202446	−	0.0116882i
$785$	−15.3753	+	15.3753i	−0.548769	+	0.548769i
$786$	−22.9964	−	31.0187i	−0.820254	−	1.10640i
$787$	2.41027	+	8.99524i	0.0859167	+	0.320646i	0.995486	−	0.0949063i	$-0.0302551\pi$
$787$	2.41027	+	8.99524i	0.0859167	+	0.320646i	−0.909569	+	0.415552i	$0.863588\pi$
$788$	−35.5993	−	35.5993i	−1.26817	−	1.26817i
$789$	4.01074	−	27.0047i	0.142786	−	0.961392i
$790$	104.695	−	60.4459i	3.72489	−	2.15057i
$791$	1.83687	−	6.85528i	0.0653114	−	0.243746i
$792$	32.2318	+	34.4383i	1.14531	+	1.22371i
$793$	5.49611	+	3.31319i	0.195173	+	0.117655i
$794$			37.7461i			1.33956i
$795$	−48.8607	+	5.61206i	−1.73291	+	0.199039i
$796$	−6.65915	−	11.5340i	−0.236027	−	0.408811i
$797$	−4.13751	+	7.16638i	−0.146558	+	0.253846i	−0.929953	−	0.367678i	$-0.880153\pi$
$797$	−4.13751	+	7.16638i	−0.146558	+	0.253846i	0.783395	+	0.621524i	$0.213486\pi$
$798$	0.589370	+	0.255627i	0.0208635	+	0.00904911i
$799$	−6.16311	+	1.65140i	−0.218035	+	0.0584223i
$800$	28.9978	−	7.76994i	1.02523	−	0.274709i
$801$	−52.1904	−	1.72735i	−1.84406	−	0.0610330i
$802$	−11.5382	+	19.9848i	−0.407429	+	0.705688i
$803$	22.8814	+	39.6318i	0.807468	+	1.39858i
$804$	1.75578	+	15.2865i	0.0619216	+	0.539113i
$805$		−	3.21418i		−	0.113285i
$806$	61.8869	−	34.1879i	2.17987	−	1.20422i
$807$	−3.13683	+	1.23893i	−0.110422	+	0.0436125i
$808$	0.729728	−	2.72338i	0.0256717	−	0.0958082i
$809$	20.4871	−	11.8282i	0.720287	−	0.415858i	−0.0945713	−	0.995518i	$-0.530148\pi$
$809$	20.4871	−	11.8282i	0.720287	−	0.415858i	0.814858	+	0.579660i	$0.196815\pi$
$810$	−38.7793	+	57.9470i	−1.36257	+	2.03605i
$811$	16.9787	+	16.9787i	0.596202	+	0.596202i	0.939300	−	0.343097i	$-0.111476\pi$
$811$	16.9787	+	16.9787i	0.596202	+	0.596202i	−0.343097	+	0.939300i	$0.611476\pi$
$812$	5.44186	+	20.3093i	0.190972	+	0.712717i
$813$	−4.68376	+	3.47241i	−0.164267	+	0.121783i
$814$	−63.4259	+	63.4259i	−2.22308	+	2.22308i
$815$	38.8750	+	22.4445i	1.36173	+	0.786196i
$816$	2.72352	−	3.43034i	0.0953421	−	0.120086i
$817$	0.778547	+	0.208611i	0.0272379	+	0.00729838i
$818$	−55.0370			−1.92432
$819$	−4.91432	−	9.63584i	−0.171720	−	0.336704i
$820$	6.18461			0.215976
$821$	5.26510	+	1.41078i	0.183753	+	0.0492365i	0.349522	−	0.936928i	$-0.386344\pi$
$821$	5.26510	+	1.41078i	0.183753	+	0.0492365i	−0.165769	+	0.986165i	$0.553011\pi$
$822$	−28.4281	+	35.8059i	−0.991545	+	1.24888i
$823$	−13.6925	−	7.90538i	−0.477291	−	0.275564i	0.241996	−	0.970277i	$-0.422198\pi$
$823$	−13.6925	−	7.90538i	−0.477291	−	0.275564i	−0.719287	+	0.694713i	$0.755531\pi$
$824$	27.6479	−	27.6479i	0.963158	−	0.963158i
$825$	−42.1763	+	31.2683i	−1.46839	+	1.08862i
$826$	−2.56056	−	9.55612i	−0.0890931	−	0.332500i
$827$	23.7448	+	23.7448i	0.825687	+	0.825687i	0.986917	−	0.161230i	$-0.0515460\pi$
$827$	23.7448	+	23.7448i	0.825687	+	0.825687i	−0.161230	+	0.986917i	$0.551546\pi$
$828$	9.49595	−	2.21054i	0.330007	−	0.0768216i
$829$	−42.6752	+	24.6385i	−1.48217	+	0.855732i	−0.999795	−	0.0202321i	$-0.993559\pi$
$829$	−42.6752	+	24.6385i	−1.48217	+	0.855732i	−0.482376	+	0.875964i	$0.660226\pi$
$830$	−17.8991	+	66.8003i	−0.621286	+	2.31867i
$831$	38.7558	−	15.3071i	1.34442	−	0.530997i
$832$	−45.4572	−	0.859018i	−1.57594	−	0.0297811i
$833$			3.86350i			0.133863i
$834$	−5.28594	−	46.0214i	−0.183037	−	1.59359i
$835$	−34.4725	−	59.7081i	−1.19297	−	2.06628i
$836$	−1.32914	+	2.30213i	−0.0459691	+	0.0796209i
$837$	14.7798	+	41.3771i	0.510863	+	1.43020i
$838$	−55.1218	+	14.7699i	−1.90415	+	0.510216i
$839$	48.3449	−	12.9540i	1.66905	−	0.447221i	0.704198	−	0.710004i	$-0.251307\pi$
$839$	48.3449	−	12.9540i	1.66905	−	0.447221i	0.964855	+	0.262783i	$0.0846403\pi$
$840$	16.9632	+	7.35745i	0.585286	+	0.253856i
$841$	4.87188	−	8.43835i	0.167996	−	0.290978i
$842$	−37.9206	−	65.6804i	−1.30683	−	2.26350i
$843$	19.0138	−	2.18389i	0.654869	−	0.0752171i
$844$		−	28.6308i		−	0.985513i
$845$	31.8478	−	29.5273i	1.09560	−	1.01577i
$846$	8.38864	−	7.85115i	0.288408	−	0.269928i
$847$	3.41904	−	12.7600i	0.117480	−	0.438440i
$848$	−4.81801	+	2.78168i	−0.165451	+	0.0955233i
$849$	5.72023	−	38.5148i	0.196318	−	1.32183i
$850$	39.0298	+	39.0298i	1.33871	+	1.33871i
$851$	1.95748	+	7.30543i	0.0671017	+	0.250427i
$852$	−36.0426	−	48.6161i	−1.23480	−	1.66556i
$853$	33.8064	−	33.8064i	1.15751	−	1.15751i	0.172501	−	0.985009i	$-0.444815\pi$
$853$	33.8064	−	33.8064i	1.15751	−	1.15751i	0.985009	−	0.172501i	$-0.0551848\pi$
$854$	3.57465	+	2.06382i	0.122322	+	0.0706226i
$855$	−1.53374	−	0.465859i	−0.0524529	−	0.0159321i
$856$	23.5274	+	6.30414i	0.804149	+	0.215471i
$857$	8.42222			0.287698			0.143849	−	0.989600i	$-0.454052\pi$
$857$	8.42222			0.287698			0.143849	+	0.989600i	$0.454052\pi$
$858$	66.7594	−	24.9199i	2.27913	−	0.850752i
$859$	5.00245			0.170682			0.0853408	−	0.996352i	$-0.472802\pi$
$859$	5.00245			0.170682			0.0853408	+	0.996352i	$0.472802\pi$
$860$	54.9324	+	14.7191i	1.87318	+	0.501917i
$861$	−0.743425	−	0.590243i	−0.0253359	−	0.0201154i
$862$	−54.3548	−	31.3818i	−1.85133	−	1.06887i
$863$	−18.9871	+	18.9871i	−0.646330	+	0.646330i	−0.952104	−	0.305774i	$-0.901085\pi$
$863$	−18.9871	+	18.9871i	−0.646330	+	0.646330i	0.305774	+	0.952104i	$0.401085\pi$
$864$	4.54634	−	24.9095i	0.154670	−	0.847438i
$865$	−18.0231	−	67.2633i	−0.612805	−	2.28702i
$866$	4.99251	+	4.99251i	0.169652	+	0.169652i
$867$	3.55215	+	0.527566i	0.120637	+	0.0179171i
$868$	24.7363	−	14.2815i	0.839605	−	0.484746i
$869$	19.8720	−	74.1631i	0.674110	−	2.51581i
$870$	−30.6825	−	77.6845i	−1.04023	−	2.63375i
$871$	9.11121	+	2.62682i	0.308722	+	0.0890064i
$872$			0.689335i			0.0233438i
$873$	−15.0689	−	28.2163i	−0.510004	−	0.954978i
$874$	0.178424	+	0.309040i	0.00603529	+	0.0104534i
$875$	−1.93863	+	3.35781i	−0.0655377	+	0.113515i
$876$	−21.6528	+	49.9223i	−0.731581	+	1.68672i
$877$	−33.0079	+	8.84444i	−1.11460	+	0.298656i	−0.768696	−	0.639615i	$-0.779094\pi$
$877$	−33.0079	+	8.84444i	−1.11460	+	0.298656i	−0.345903	+	0.938270i	$0.612427\pi$
$878$	25.5837	−	6.85514i	0.863409	−	0.231350i
$879$	−10.0953	+	23.2755i	−0.340506	+	0.785064i
$880$	−5.37958	+	9.31771i	−0.181346	+	0.314100i
$881$	−3.94100	−	6.82602i	−0.132776	−	0.229974i	0.791970	−	0.610560i	$-0.209056\pi$
$881$	−3.94100	−	6.82602i	−0.132776	−	0.229974i	−0.924746	+	0.380586i	$0.875722\pi$
$882$	−3.27735	−	6.13680i	−0.110354	−	0.206637i
$883$			10.1586i			0.341865i	0.985283	+	0.170933i	$0.0546781\pi$
$883$			10.1586i			0.341865i	−0.985283	+	0.170933i	$0.945322\pi$
$884$	−22.7532	−	41.1879i	−0.765274	−	1.38530i
$885$	9.06803	+	22.9592i	0.304819	+	0.771765i
$886$	−19.1102	+	71.3201i	−0.642018	+	2.39604i
$887$	45.3886	−	26.2051i	1.52400	−	0.879882i	0.524404	−	0.851469i	$-0.324288\pi$
$887$	45.3886	−	26.2051i	1.52400	−	0.879882i	0.999596	−	0.0284126i	$-0.00904523\pi$
$888$	−43.0360	−	6.39171i	−1.44420	−	0.214492i
$889$	6.16946	+	6.16946i	0.206917	+	0.206917i
$890$	−34.9023	−	130.257i	−1.16993	−	4.36624i
$891$	8.60798	+	43.4387i	0.288378	+	1.45525i
$892$	−3.90532	+	3.90532i	−0.130760	+	0.130760i
$893$	0.228747	+	0.132067i	0.00765473	+	0.00441946i
$894$	−63.5795	−	50.4789i	−2.12642	−	1.68827i
$895$	14.8113	+	3.96866i	0.495086	+	0.132658i
$896$	−19.4965			−0.651333
$897$	0.994818	−	5.92547i	0.0332160	−	0.197846i
$898$	−4.50910			−0.150471
$899$	−50.8392	−	13.6223i	−1.69558	−	0.454330i
$900$	−59.7354	−	18.1440i	−1.99118	−	0.604801i
$901$	28.4389	+	16.4192i	0.947439	+	0.547004i
$902$	4.42190	−	4.42190i	0.147233	−	0.147233i
$903$	−5.19844	−	7.01193i	−0.172993	−	0.233342i
$904$	5.86964	+	21.9058i	0.195221	+	0.728576i
$905$	1.11114	+	1.11114i	0.0369355	+	0.0369355i
$906$	−7.59407	+	51.1316i	−0.252296	+	1.69874i
$907$	48.2082	−	27.8330i	1.60073	−	0.924180i	0.609384	−	0.792875i	$-0.291417\pi$
$907$	48.2082	−	27.8330i	1.60073	−	0.924180i	0.991342	−	0.131304i	$-0.0419165\pi$
$908$	12.8717	−	48.0380i	0.427164	−	1.59420i
$909$	1.93259	−	1.80876i	0.0641000	−	0.0599929i
$910$	20.1215	−	19.3751i	0.667022	−	0.642280i
$911$			20.7333i			0.686923i	0.939167	+	0.343462i	$0.111600\pi$
$911$			20.7333i			0.686923i	−0.939167	+	0.343462i	$0.888400\pi$
$912$	−0.180136	+	0.0206901i	−0.00596491	+	0.000685119i
$913$	21.9610	+	38.0376i	0.726803	+	1.25886i
$914$	−21.3655	+	37.0062i	−0.706709	+	1.22406i
$915$	−9.44864	−	4.09816i	−0.312362	−	0.135481i
$916$	−31.5967	+	8.46631i	−1.04398	+	0.279735i
$917$	−9.28568	+	2.48809i	−0.306640	+	0.0821640i
$918$	43.8425	−	15.6604i	1.44702	−	0.516870i
$919$	4.48174	−	7.76260i	0.147839	−	0.256065i	−0.782590	−	0.622538i	$-0.786102\pi$
$919$	4.48174	−	7.76260i	0.147839	−	0.256065i	0.930429	+	0.366473i	$0.119435\pi$
$920$	5.13539	+	8.89476i	0.169309	+	0.293252i
$921$	−4.17210	−	36.3239i	−0.137475	−	1.19691i
$922$		−	75.1201i		−	2.47395i
$923$	−36.2005	+	8.97039i	−1.19156	+	0.295264i
$924$	26.7751	−	10.5752i	0.880837	−	0.347898i
$925$	12.5341	−	46.7781i	0.412120	−	1.53805i
$926$	−64.0114	+	36.9570i	−2.10354	+	1.21448i
$927$	35.7523	−	8.32270i	1.17426	−	0.273353i
$928$	21.4479	+	21.4479i	0.704062	+	0.704062i
$929$	−2.22137	−	8.29027i	−0.0728809	−	0.271995i	0.919864	−	0.392238i	$-0.128299\pi$
$929$	−2.22137	−	8.29027i	−0.0728809	−	0.271995i	−0.992744	+	0.120243i	$0.961633\pi$
$930$	−91.1489	+	67.5752i	−2.98889	+	2.21588i
$931$	0.113093	−	0.113093i	0.00370647	−	0.00370647i
$932$	51.0611	+	29.4802i	1.67256	+	0.965655i
$933$	6.81684	−	8.58598i	0.223173	−	0.281092i
$934$	−33.3171	−	8.92729i	−1.09017	−	0.292110i
$935$	63.5073			2.07691
$936$	28.9951	+	18.8140i	0.947736	+	0.614955i
$937$	20.9116			0.683152			0.341576	−	0.939854i	$-0.389039\pi$
$937$	20.9116			0.683152			0.341576	+	0.939854i	$0.389039\pi$
$938$	5.89107	+	1.57851i	0.192350	+	0.0515401i
$939$	−6.95846	+	8.76436i	−0.227081	+	0.286014i
$940$	16.1398	+	9.31834i	0.526424	+	0.303931i
$941$	5.39386	−	5.39386i	0.175835	−	0.175835i	−0.613703	−	0.789537i	$-0.710321\pi$
$941$	5.39386	−	5.39386i	0.175835	−	0.175835i	0.789537	+	0.613703i	$0.210321\pi$
$942$	−21.0015	+	15.5699i	−0.684265	+	0.507295i
$943$	−0.136471	−	0.509317i	−0.00444411	−	0.0165856i
$944$	1.97447	+	1.97447i	0.0642637	+	0.0642637i
$945$	9.87132	+	14.2791i	0.321114	+	0.464500i
$946$	49.7998	−	28.7519i	1.61913	−	0.934806i
$947$	−10.8109	+	40.3467i	−0.351306	+	1.31109i	0.533764	+	0.845633i	$0.320777\pi$
$947$	−10.8109	+	40.3467i	−0.351306	+	1.31109i	−0.885070	+	0.465458i	$0.845890\pi$
$948$	84.9138	−	33.5378i	2.75787	−	1.08926i
$949$	23.2599	+	24.1559i	0.755049	+	0.784135i
$950$		−	2.28497i		−	0.0741343i
$951$	0.503289	+	4.38182i	0.0163203	+	0.142090i
$952$	−6.17284	−	10.6917i	−0.200063	−	0.346519i
$953$	−0.994219	+	1.72204i	−0.0322059	+	0.0557823i	−0.881679	−	0.471849i	$-0.843587\pi$
$953$	−0.994219	+	1.72204i	−0.0322059	+	0.0557823i	0.849473	+	0.527632i	$0.176920\pi$
$954$	−59.1007	−	1.95606i	−1.91345	−	0.0633299i
$955$	−7.31970	+	1.96131i	−0.236860	+	0.0634664i
$956$	46.5304	−	12.4678i	1.50490	−	0.403237i
$957$	−48.6665	−	21.1081i	−1.57316	−	0.682328i
$958$	−7.92813	+	13.7319i	−0.256146	+	0.443658i
$959$	5.69113	+	9.85732i	0.183776	+	0.318310i
$960$	72.4881	−	8.32586i	2.33954	−	0.268716i
$961$			40.5002i			1.30646i
$962$	−33.9340	+	56.2916i	−1.09407	+	1.81491i
$963$	15.6260	+	16.6957i	0.503540	+	0.538013i
$964$	−15.8501	+	59.1533i	−0.510497	+	1.90520i
$965$	−29.1232	+	16.8143i	−0.937510	+	0.541272i
$966$	0.567730	−	3.82258i	0.0182664	−	0.122989i
$967$	−3.48539	−	3.48539i	−0.112082	−	0.112082i	0.648841	−	0.760924i	$-0.275254\pi$
$967$	−3.48539	−	3.48539i	−0.112082	−	0.112082i	−0.760924	+	0.648841i	$0.775254\pi$
$968$	10.9254	+	40.7742i	0.351156	+	1.31053i
$969$	0.637403	+	0.859762i	0.0204763	+	0.0276195i
$970$	58.4120	−	58.4120i	1.87550	−	1.87550i
$971$	13.9546	+	8.05668i	0.447824	+	0.258551i	0.706911	−	0.707303i	$-0.250088\pi$
$971$	13.9546	+	8.05668i	0.447824	+	0.258551i	−0.259087	+	0.965854i	$0.583422\pi$
$972$	−35.3972	+	38.9842i	−1.13537	+	1.25042i
$973$	−11.1399	−	2.98493i	−0.357129	−	0.0956924i
$974$	63.0271			2.01952
$975$	−24.4875	+	29.6737i	−0.784229	+	0.950317i
$976$	−1.16501			−0.0372912
$977$	55.9100	+	14.9810i	1.78872	+	0.479286i	0.992128	−	0.125231i	$-0.0399671\pi$
$977$	55.9100	+	14.9810i	1.78872	+	0.479286i	0.796592	+	0.604517i	$0.206634\pi$
$978$	42.2691	+	33.5595i	1.35162	+	1.07312i
$979$	−74.1714	−	42.8229i	−2.37053	−	1.36863i
$980$	7.97956	−	7.97956i	0.254898	−	0.254898i
$981$	−0.341947	+	0.549455i	−0.0109175	+	0.0175427i
$982$	−8.23722	−	30.7417i	−0.262860	−	0.981008i
$983$	−15.9509	−	15.9509i	−0.508754	−	0.508754i	0.405390	−	0.914144i	$-0.367136\pi$
$983$	−15.9509	−	15.9509i	−0.508754	−	0.508754i	−0.914144	+	0.405390i	$0.867136\pi$
$984$	3.00037	+	0.445615i	0.0956483	+	0.0142057i
$985$	43.1202	−	24.8955i	1.37392	−	0.793235i
$986$	−14.4340	+	53.8683i	−0.459672	+	1.71552i
$987$	−1.05078	−	2.66046i	−0.0334468	−	0.0846835i
$988$	−0.539620	+	1.87169i	−0.0171676	+	0.0595464i
$989$		−	4.84861i		−	0.154177i
$990$	−100.875	+	53.8722i	−3.20603	+	1.71217i
$991$	7.60068	+	13.1648i	0.241444	+	0.418193i	0.961126	−	0.276111i	$-0.0890458\pi$
$991$	7.60068	+	13.1648i	0.241444	+	0.418193i	−0.719682	+	0.694304i	$0.755712\pi$
$992$	20.6026	−	35.6848i	0.654134	−	1.13299i
$993$	−8.28661	+	19.1055i	−0.262968	+	0.606293i
$994$	−23.1705	+	6.20851i	−0.734923	+	0.196922i
$995$	12.7229	−	3.40909i	0.403343	−	0.108075i
$996$	−20.7818	+	47.9142i	−0.658497	+	1.51822i
$997$	−0.371475	+	0.643413i	−0.0117647	+	0.0203771i	−0.871848	−	0.489777i	$-0.837078\pi$
$997$	−0.371475	+	0.643413i	−0.0117647	+	0.0203771i	0.860083	+	0.510154i	$0.170412\pi$
$998$	25.9977	+	45.0294i	0.822944	+	1.42538i
$999$	−31.1325	−	26.4429i	−0.984988	−	0.836616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.3	✓	112
3.2	odd	2	inner	273.2.cc.a.50.26	yes	112
13.6	odd	12	inner	273.2.cc.a.71.26	yes	112
39.32	even	12	inner	273.2.cc.a.71.3	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.3	✓	112	1.1	even	1	trivial
273.2.cc.a.50.26	yes	112	3.2	odd	2	inner
273.2.cc.a.71.3	yes	112	39.32	even	12	inner
273.2.cc.a.71.26	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)

\(f(q)\)	\(=\)	\(q+(-2.24002 - 0.600211i) q^{2} +(1.07699 - 1.35650i) q^{3} +(2.92537 + 1.68896i) q^{4} +(-2.36227 + 2.36227i) q^{5} +(-3.22666 + 2.39216i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-2.25953 - 2.25953i) q^{8} +(-0.680177 - 2.92188i) q^{9} +O(q^{10})\)	\(q+(-2.24002 - 0.600211i) q^{2} +(1.07699 - 1.35650i) q^{3} +(2.92537 + 1.68896i) q^{4} +(-2.36227 + 2.36227i) q^{5} +(-3.22666 + 2.39216i) q^{6} +(0.258819 + 0.965926i) q^{7} +(-2.25953 - 2.25953i) q^{8} +(-0.680177 - 2.92188i) q^{9} +(6.70937 - 3.87366i) q^{10} +(1.27349 - 4.75272i) q^{11} +(5.44168 - 2.14926i) q^{12} +(0.0681230 - 3.60491i) q^{13} -2.31904i q^{14} +(0.660269 + 5.74855i) q^{15} +(0.327270 + 0.566848i) q^{16} +(1.93175 - 3.34589i) q^{17} +(-0.230134 + 6.95330i) q^{18} +(-0.154488 + 0.0413949i) q^{19} +(-10.9003 + 2.92072i) q^{20} +(1.58902 + 0.689207i) q^{21} +(-5.70527 + 9.88182i) q^{22} +(0.481057 + 0.833215i) q^{23} +(-5.49855 + 0.631555i) q^{24} -6.16060i q^{25} +(-2.31630 + 8.03417i) q^{26} +(-4.69607 - 2.22418i) q^{27} +(-0.874272 + 3.26283i) q^{28} +(5.39053 - 3.11222i) q^{29} +(1.97133 - 13.2732i) q^{30} +(-5.97914 - 5.97914i) q^{31} +(1.26123 + 4.70698i) q^{32} +(-5.07553 - 6.84613i) q^{33} +(-6.33540 + 6.33540i) q^{34} +(-2.89317 - 1.67037i) q^{35} +(2.94517 - 9.69637i) q^{36} +(7.59311 + 2.03457i) q^{37} +0.370901 q^{38} +(-4.81668 - 3.97487i) q^{39} +10.6752 q^{40} +(-0.529373 - 0.141845i) q^{41} +(-3.14577 - 2.49758i) q^{42} +(-4.36437 - 2.51977i) q^{43} +(11.7526 - 11.7526i) q^{44} +(8.50900 + 5.29549i) q^{45} +(-0.577471 - 2.15515i) q^{46} +(-1.16778 - 1.16778i) q^{47} +(1.12140 + 0.166550i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-3.69766 + 13.7998i) q^{50} +(-2.45822 - 6.22392i) q^{51} +(6.28784 - 10.4306i) q^{52} +8.49966i q^{53} +(9.18429 + 7.80083i) q^{54} +(8.21888 + 14.2355i) q^{55} +(1.59773 - 2.76735i) q^{56} +(-0.110230 + 0.254144i) q^{57} +(-13.9429 + 3.73598i) q^{58} +(4.12073 - 1.10415i) q^{59} +(-7.77756 + 17.9318i) q^{60} +(-0.889949 + 1.54144i) q^{61} +(9.80463 + 16.9821i) q^{62} +(2.64627 - 1.41324i) q^{63} -12.6098i q^{64} +(8.35482 + 8.67667i) q^{65} +(7.26014 + 18.3818i) q^{66} +(-0.680674 + 2.54031i) q^{67} +(11.3022 - 6.52532i) q^{68} +(1.64835 + 0.244813i) q^{69} +(5.47818 + 5.47818i) q^{70} +(-2.67719 - 9.99142i) q^{71} +(-5.06520 + 8.13896i) q^{72} +(-6.57657 + 6.57657i) q^{73} +(-15.7875 - 9.11493i) q^{74} +(-8.35684 - 6.63491i) q^{75} +(-0.521849 - 0.139829i) q^{76} +4.92038 q^{77} +(8.40370 + 11.7948i) q^{78} +15.6043 q^{79} +(-2.11214 - 0.565947i) q^{80} +(-8.07472 + 3.97478i) q^{81} +(1.10067 + 0.635471i) q^{82} +(-6.31202 + 6.31202i) q^{83} +(3.48444 + 4.69999i) q^{84} +(3.34058 + 12.4672i) q^{85} +(8.26387 + 8.26387i) q^{86} +(1.58383 - 10.6641i) q^{87} +(-13.6164 + 7.86145i) q^{88} +(4.50509 - 16.8132i) q^{89} +(-15.8819 - 16.9692i) q^{90} +(3.49970 - 0.867217i) q^{91} +3.24995i q^{92} +(-14.5502 + 1.67121i) q^{93} +(1.91493 + 3.31675i) q^{94} +(0.267156 - 0.462727i) q^{95} +(7.74335 + 3.35852i) q^{96} +(10.2993 - 2.75970i) q^{97} +(2.24002 - 0.600211i) q^{98} +(-14.7531 - 0.488284i) 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

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