LMFDB - Embedded newform 240.2.t.b.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(59,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("240.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			59.4
Character	$\chi$	$=$	240.59
Dual form			240.2.t.b.179.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27807 - 0.605427i) q^{2} +(0.688572 - 1.58930i) q^{3} +(1.26692 + 1.54755i) q^{4} +(1.61678 - 1.54468i) q^{5} +(-1.84225 + 1.61435i) q^{6} -0.970036i q^{7} +(-0.682276 - 2.74490i) q^{8} +(-2.05174 - 2.18869i) q^{9} +O(q^{10})$	\(q+(-1.27807 - 0.605427i) q^{2} +(0.688572 - 1.58930i) q^{3} +(1.26692 + 1.54755i) q^{4} +(1.61678 - 1.54468i) q^{5} +(-1.84225 + 1.61435i) q^{6} -0.970036i q^{7} +(-0.682276 - 2.74490i) q^{8} +(-2.05174 - 2.18869i) q^{9} +(-3.00154 + 0.995364i) q^{10} +(2.22669 + 2.22669i) q^{11} +(3.33189 - 0.947907i) q^{12} +(1.70767 + 1.70767i) q^{13} +(-0.587286 + 1.23977i) q^{14} +(-1.34169 - 3.63316i) q^{15} +(-0.789843 + 3.92124i) q^{16} +2.96185 q^{17} +(1.29717 + 4.03947i) q^{18} +(-5.04637 - 5.04637i) q^{19} +(4.43879 + 0.545070i) q^{20} +(-1.54168 - 0.667940i) q^{21} +(-1.49777 - 4.19397i) q^{22} -5.62738 q^{23} +(-4.83227 - 0.805723i) q^{24} +(0.227937 - 4.99480i) q^{25} +(-1.14865 - 3.21638i) q^{26} +(-4.89125 + 1.75375i) q^{27} +(1.50118 - 1.22896i) q^{28} +(0.650921 + 0.650921i) q^{29} +(-0.484846 + 5.45572i) q^{30} +0.972374i q^{31} +(3.38350 - 4.53342i) q^{32} +(5.07212 - 2.00564i) q^{33} +(-3.78545 - 1.79318i) q^{34} +(-1.49839 - 1.56833i) q^{35} +(0.787736 - 5.94806i) q^{36} +(-5.06457 + 5.06457i) q^{37} +(3.39440 + 9.50481i) q^{38} +(3.88984 - 1.53814i) q^{39} +(-5.34308 - 3.38400i) q^{40} +8.05168 q^{41} +(1.56598 + 1.78704i) q^{42} +(5.72323 + 5.72323i) q^{43} +(-0.624891 + 6.26697i) q^{44} +(-6.69803 - 0.369352i) q^{45} +(7.19217 + 3.40696i) q^{46} -0.635876i q^{47} +(5.68816 + 3.95535i) q^{48} +6.05903 q^{49} +(-3.31531 + 6.24570i) q^{50} +(2.03945 - 4.70726i) q^{51} +(-0.479233 + 4.80618i) q^{52} +(5.63391 + 5.63391i) q^{53} +(7.31312 + 0.719881i) q^{54} +(7.03960 + 0.160542i) q^{55} +(-2.66266 + 0.661833i) q^{56} +(-11.4950 + 4.54540i) q^{57} +(-0.437837 - 1.22601i) q^{58} +(-6.13382 - 6.13382i) q^{59} +(3.92271 - 6.67925i) q^{60} +(-6.62079 + 6.62079i) q^{61} +(0.588701 - 1.24276i) q^{62} +(-2.12311 + 1.99026i) q^{63} +(-7.06900 + 3.74557i) q^{64} +(5.39871 + 0.123121i) q^{65} +(-7.69679 - 0.507449i) q^{66} +(4.07457 - 4.07457i) q^{67} +(3.75242 + 4.58362i) q^{68} +(-3.87485 + 8.94358i) q^{69} +(0.965540 + 2.91160i) q^{70} +11.1600i q^{71} +(-4.60790 + 7.12512i) q^{72} +13.9473 q^{73} +(9.53910 - 3.40664i) q^{74} +(-7.78128 - 3.80154i) q^{75} +(1.41620 - 14.2029i) q^{76} +(2.15997 - 2.15997i) q^{77} +(-5.90272 - 0.389166i) q^{78} +10.6386i q^{79} +(4.78006 + 7.55983i) q^{80} +(-0.580745 + 8.98124i) q^{81} +(-10.2906 - 4.87470i) q^{82} +(-1.90456 - 1.90456i) q^{83} +(-0.919505 - 3.23205i) q^{84} +(4.78865 - 4.57510i) q^{85} +(-3.84968 - 10.7797i) q^{86} +(1.48271 - 0.586302i) q^{87} +(4.59284 - 7.63128i) q^{88} +2.56421 q^{89} +(8.33692 + 4.52722i) q^{90} +(1.65650 - 1.65650i) q^{91} +(-7.12942 - 8.70867i) q^{92} +(1.54539 + 0.669549i) q^{93} +(-0.384976 + 0.812693i) q^{94} +(-15.9539 - 0.363837i) q^{95} +(-4.87518 - 8.49898i) q^{96} +8.52709i q^{97} +(-7.74385 - 3.66830i) q^{98} +(0.304955 - 9.44214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) $ 80 * q - 8 * q^4 - 4 * q^6	$ 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) $ 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.27807	−	0.605427i	−0.903731	−	0.428101i
$2$	−1.27807	−	0.605427i	−0.903731	−	0.428101i
$3$	0.688572	−	1.58930i	0.397547	−	0.917582i
$3$	0.688572	−	1.58930i	0.397547	−	0.917582i
$4$	1.26692	+	1.54755i	0.633458	+	0.773777i
$5$	1.61678	−	1.54468i	0.723045	−	0.690801i
$5$	1.61678	−	1.54468i	0.723045	−	0.690801i
$6$	−1.84225	+	1.61435i	−0.752094	+	0.659056i
$7$		−	0.970036i		−	0.366639i	−0.983053	−	0.183320i	$-0.941316\pi$
$7$		−	0.970036i		−	0.366639i	0.983053	−	0.183320i	$-0.0586843\pi$
$8$	−0.682276	−	2.74490i	−0.241221	−	0.970470i
$9$	−2.05174	−	2.18869i	−0.683913	−	0.729564i
$10$	−3.00154	+	0.995364i	−0.949171	+	0.314762i
$11$	2.22669	+	2.22669i	0.671374	+	0.671374i	0.958033	−	0.286659i	$-0.0925447\pi$
$11$	2.22669	+	2.22669i	0.671374	+	0.671374i	−0.286659	+	0.958033i	$0.592545\pi$
$12$	3.33189	−	0.947907i	0.961833	−	0.273637i
$13$	1.70767	+	1.70767i	0.473622	+	0.473622i	0.903084	−	0.429463i	$-0.141297\pi$
$13$	1.70767	+	1.70767i	0.473622	+	0.473622i	−0.429463	+	0.903084i	$0.641297\pi$
$14$	−0.587286	+	1.23977i	−0.156959	+	0.331343i
$15$	−1.34169	−	3.63316i	−0.346422	−	0.938079i
$16$	−0.789843	+	3.92124i	−0.197461	+	0.980311i
$17$	2.96185			0.718354			0.359177	−	0.933269i	$-0.383057\pi$
$17$	2.96185			0.718354			0.359177	+	0.933269i	$0.383057\pi$
$18$	1.29717	+	4.03947i	0.305746	+	0.952113i
$19$	−5.04637	−	5.04637i	−1.15772	−	1.15772i	−0.984965	−	0.172751i	$-0.944734\pi$
$19$	−5.04637	−	5.04637i	−1.15772	−	1.15772i	−0.172751	−	0.984965i	$-0.555266\pi$
$20$	4.43879	+	0.545070i	0.992545	+	0.121881i
$21$	−1.54168	−	0.667940i	−0.336422	−	0.145756i
$22$	−1.49777	−	4.19397i	−0.319325	−	0.894157i
$23$	−5.62738			−1.17339			−0.586695	−	0.809808i	$-0.699571\pi$
$23$	−5.62738			−1.17339			−0.586695	+	0.809808i	$0.699571\pi$
$24$	−4.83227	−	0.805723i	−0.986382	−	0.164468i
$25$	0.227937	−	4.99480i	0.0455874	−	0.998960i
$26$	−1.14865	−	3.21638i	−0.225268	−	0.630784i
$27$	−4.89125	+	1.75375i	−0.941322	+	0.337510i
$28$	1.50118	−	1.22896i	0.283697	−	0.232251i
$29$	0.650921	+	0.650921i	0.120873	+	0.120873i	0.764956	−	0.644083i	$-0.222761\pi$
$29$	0.650921	+	0.650921i	0.120873	+	0.120873i	−0.644083	+	0.764956i	$0.722761\pi$
$30$	−0.484846	+	5.45572i	−0.0885203	+	0.996074i
$31$			0.972374i			0.174643i	0.996180	+	0.0873217i	$0.0278308\pi$
$31$			0.972374i			0.174643i	−0.996180	+	0.0873217i	$0.972169\pi$
$32$	3.38350	−	4.53342i	0.598124	−	0.801404i
$33$	5.07212	−	2.00564i	0.882943	−	0.349138i
$34$	−3.78545	−	1.79318i	−0.649199	−	0.307528i
$35$	−1.49839	−	1.56833i	−0.253275	−	0.265097i
$36$	0.787736	−	5.94806i	0.131289	−	0.991344i
$37$	−5.06457	+	5.06457i	−0.832611	+	0.832611i	−0.987873	−	0.155262i	$-0.950378\pi$
$37$	−5.06457	+	5.06457i	−0.832611	+	0.832611i	0.155262	+	0.987873i	$0.450378\pi$
$38$	3.39440	+	9.50481i	0.550644	+	1.54188i
$39$	3.88984	−	1.53814i	0.622873	−	0.246300i
$40$	−5.34308	−	3.38400i	−0.844816	−	0.535058i
$41$	8.05168			1.25746			0.628731	−	0.777623i	$-0.283575\pi$
$41$	8.05168			1.25746			0.628731	+	0.777623i	$0.283575\pi$
$42$	1.56598	+	1.78704i	0.241636	+	0.275747i
$43$	5.72323	+	5.72323i	0.872785	+	0.872785i	0.992775	−	0.119990i	$-0.0382863\pi$
$43$	5.72323	+	5.72323i	0.872785	+	0.872785i	−0.119990	+	0.992775i	$0.538286\pi$
$44$	−0.624891	+	6.26697i	−0.0942059	+	0.944781i
$45$	−6.69803	−	0.369352i	−0.998483	−	0.0550598i
$46$	7.19217	+	3.40696i	1.06043	+	0.502329i
$47$		−	0.635876i		−	0.0927520i	−0.998924	−	0.0463760i	$-0.985233\pi$
$47$		−	0.635876i		−	0.0927520i	0.998924	−	0.0463760i	$-0.0147672\pi$
$48$	5.68816	+	3.95535i	0.821015	+	0.570906i
$49$	6.05903			0.865576
$50$	−3.31531	+	6.24570i	−0.468855	+	0.883275i
$51$	2.03945	−	4.70726i	0.285580	−	0.659148i
$52$	−0.479233	+	4.80618i	−0.0664577	+	0.666497i
$53$	5.63391	+	5.63391i	0.773877	+	0.773877i	0.978782	−	0.204905i	$-0.0656884\pi$
$53$	5.63391	+	5.63391i	0.773877	+	0.773877i	−0.204905	+	0.978782i	$0.565688\pi$
$54$	7.31312	+	0.719881i	0.995190	+	0.0979634i
$55$	7.03960	+	0.160542i	0.949219	+	0.0216475i
$56$	−2.66266	+	0.661833i	−0.355812	+	0.0884411i
$57$	−11.4950	+	4.54540i	−1.52255	+	0.602053i
$58$	−0.437837	−	1.22601i	−0.0574908	−	0.160983i
$59$	−6.13382	−	6.13382i	−0.798556	−	0.798556i	0.184312	−	0.982868i	$-0.440994\pi$
$59$	−6.13382	−	6.13382i	−0.798556	−	0.798556i	−0.982868	+	0.184312i	$0.940994\pi$
$60$	3.92271	−	6.67925i	0.506419	−	0.862287i
$61$	−6.62079	+	6.62079i	−0.847705	+	0.847705i	−0.989846	−	0.142142i	$-0.954601\pi$
$61$	−6.62079	+	6.62079i	−0.847705	+	0.847705i	0.142142	+	0.989846i	$0.454601\pi$
$62$	0.588701	−	1.24276i	0.0747651	−	0.157831i
$63$	−2.12311	+	1.99026i	−0.267487	+	0.250749i
$64$	−7.06900	+	3.74557i	−0.883625	+	0.468196i
$65$	5.39871	+	0.123121i	0.669628	+	0.0152712i
$66$	−7.69679	−	0.507449i	−0.947409	−	0.0624627i
$67$	4.07457	−	4.07457i	0.497788	−	0.497788i	−0.412961	−	0.910749i	$-0.635505\pi$
$67$	4.07457	−	4.07457i	0.497788	−	0.497788i	0.910749	+	0.412961i	$0.135505\pi$
$68$	3.75242	+	4.58362i	0.455047	+	0.555846i
$69$	−3.87485	+	8.94358i	−0.466477	+	1.07668i
$70$	0.965540	+	2.91160i	0.115404	+	0.348003i
$71$			11.1600i			1.32444i	0.749308	+	0.662221i	$0.230386\pi$
$71$			11.1600i			1.32444i	−0.749308	+	0.662221i	$0.769614\pi$
$72$	−4.60790	+	7.12512i	−0.543046	+	0.839703i
$73$	13.9473			1.63241			0.816203	−	0.577765i	$-0.196075\pi$
$73$	13.9473			1.63241			0.816203	+	0.577765i	$0.196075\pi$
$74$	9.53910	−	3.40664i	1.10890	−	0.396014i
$75$	−7.78128	−	3.80154i	−0.898505	−	0.438964i
$76$	1.41620	−	14.2029i	0.162449	−	1.62918i
$77$	2.15997	−	2.15997i	0.246152	−	0.246152i
$78$	−5.90272	−	0.389166i	−0.668351	−	0.0440644i
$79$			10.6386i			1.19694i	0.801145	+	0.598470i	$0.204225\pi$
$79$			10.6386i			1.19694i	−0.801145	+	0.598470i	$0.795775\pi$
$80$	4.78006	+	7.55983i	0.534427	+	0.845215i
$81$	−0.580745	+	8.98124i	−0.0645272	+	0.997916i
$82$	−10.2906	−	4.87470i	−1.13641	−	0.538321i
$83$	−1.90456	−	1.90456i	−0.209052	−	0.209052i	0.594812	−	0.803865i	$-0.297226\pi$
$83$	−1.90456	−	1.90456i	−0.209052	−	0.209052i	−0.803865	+	0.594812i	$0.797226\pi$
$84$	−0.919505	−	3.23205i	−0.100326	−	0.352646i
$85$	4.78865	−	4.57510i	0.519402	−	0.496240i
$86$	−3.84968	−	10.7797i	−0.415122	−	1.16240i
$87$	1.48271	−	0.586302i	0.158964	−	0.0628582i
$88$	4.59284	−	7.63128i	0.489599	−	0.813498i
$89$	2.56421			0.271806			0.135903	−	0.990722i	$-0.456607\pi$
$89$	2.56421			0.271806			0.135903	+	0.990722i	$0.456607\pi$
$90$	8.33692	+	4.52722i	0.878789	+	0.477211i
$91$	1.65650	−	1.65650i	0.173648	−	0.173648i
$92$	−7.12942	−	8.70867i	−0.743293	−	0.907941i
$93$	1.54539	+	0.669549i	0.160250	+	0.0694290i
$94$	−0.384976	+	0.812693i	−0.0397073	+	0.0838228i
$95$	−15.9539	−	0.363837i	−1.63683	−	0.0373289i
$96$	−4.87518	−	8.49898i	−0.497571	−	0.867423i
$97$			8.52709i			0.865795i	0.901443	+	0.432898i	$0.142509\pi$
$97$			8.52709i			0.865795i	−0.901443	+	0.432898i	$0.857491\pi$
$98$	−7.74385	−	3.66830i	−0.782247	−	0.370554i
$99$	0.304955	−	9.44214i	0.0306491	−	0.948971i
$100$	8.01850	−	5.97525i	0.801850	−	0.597525i
$101$	5.38031	−	5.38031i	0.535361	−	0.535361i	−0.386802	−	0.922163i	$-0.626420\pi$
$101$	5.38031	−	5.38031i	0.535361	−	0.535361i	0.922163	+	0.386802i	$0.126420\pi$
$102$	−5.45645	+	4.78147i	−0.540269	+	0.473436i
$103$		−	10.1806i		−	1.00312i	−0.865122	−	0.501561i	$-0.832759\pi$
$103$		−	10.1806i		−	1.00312i	0.865122	−	0.501561i	$-0.167241\pi$
$104$	3.52228	−	5.85248i	0.345388	−	0.573883i
$105$	−3.52430	+	1.30149i	−0.343936	+	0.127012i
$106$	−3.78960	−	10.6114i	−0.368079	−	1.03067i
$107$	1.44455	−	1.44455i	0.139650	−	0.139650i	−0.633826	−	0.773476i	$-0.718516\pi$
$107$	1.44455	−	1.44455i	0.139650	−	0.139650i	0.773476	+	0.633826i	$0.218516\pi$
$108$	−8.91084	−	5.34762i	−0.857446	−	0.514575i
$109$	−8.21793	+	8.21793i	−0.787135	+	0.787135i	−0.981024	−	0.193889i	$-0.937890\pi$
$109$	−8.21793	+	8.21793i	−0.787135	+	0.787135i	0.193889	+	0.981024i	$0.437890\pi$
$110$	−8.89989	−	4.46714i	−0.848571	−	0.425925i
$111$	4.56180	+	11.5364i	0.432986	+	1.09499i
$112$	3.80375	+	0.766176i	0.359420	+	0.0723968i
$113$	−18.2405			−1.71592			−0.857959	−	0.513718i	$-0.828268\pi$
$113$	−18.2405			−1.71592			−0.857959	+	0.513718i	$0.828268\pi$
$114$	17.4433	+	1.15004i	1.63371	+	0.107711i
$115$	−9.09821	+	8.69249i	−0.848413	+	0.810579i
$116$	−0.182672	+	1.83200i	−0.0169607	+	0.170097i
$117$	0.233872	−	7.24124i	0.0216215	−	0.669453i
$118$	4.12586	+	11.5530i	0.379817	+	1.06354i
$119$		−	2.87310i		−	0.263377i
$120$	−9.05728	+	6.16162i	−0.826813	+	0.562477i
$121$		−	1.08366i		−	0.0985148i
$122$	12.4702	−	4.45342i	1.12900	−	0.403193i
$123$	5.54416	−	12.7965i	0.499900	−	1.15382i
$124$	−1.50480	+	1.23192i	−0.135135	+	0.110629i
$125$	−7.34684	−	8.42757i	−0.657121	−	0.753785i
$126$	3.91844	−	1.25830i	0.349082	−	0.112098i
$127$	16.5248			1.46634			0.733170	−	0.680046i	$-0.238040\pi$
$127$	16.5248			1.46634			0.733170	+	0.680046i	$0.238040\pi$
$128$	11.3023	−	0.507329i	0.998994	−	0.0448420i
$129$	13.0368	−	5.15507i	1.14782	−	0.453878i
$130$	−6.82538	−	3.42588i	−0.598626	−	0.300470i
$131$	0.493333	−	0.493333i	0.0431027	−	0.0431027i	−0.685227	−	0.728330i	$-0.740297\pi$
$131$	0.493333	−	0.493333i	0.0431027	−	0.0431027i	0.728330	+	0.685227i	$0.240297\pi$
$132$	9.52979	+	5.30839i	0.829462	+	0.462036i
$133$	−4.89516	+	4.89516i	−0.424464	+	0.424464i
$134$	−7.67444	+	2.74073i	−0.662970	+	0.236763i
$135$	−5.19908	+	10.3908i	−0.447466	+	0.894301i
$136$	−2.02080	−	8.12999i	−0.173282	−	0.697141i
$137$		−	10.9382i		−	0.934511i	−0.884122	−	0.467255i	$-0.845243\pi$
$137$		−	10.9382i		−	0.934511i	0.884122	−	0.467255i	$-0.154757\pi$
$138$	10.3670	−	9.08457i	0.882498	−	0.773330i
$139$	−3.84662	+	3.84662i	−0.326266	+	0.326266i	−0.851165	−	0.524899i	$-0.824103\pi$
$139$	−3.84662	+	3.84662i	−0.326266	+	0.326266i	0.524899	+	0.851165i	$0.324103\pi$
$140$	0.528737	−	4.30579i	0.0446865	−	0.363906i
$141$	−1.01060	−	0.437846i	−0.0851076	−	0.0368733i
$142$	6.75653	−	14.2632i	0.566996	−	1.19694i
$143$			7.60490i			0.635954i
$144$	10.2029	−	6.31664i	0.850245	−	0.526387i
$145$	2.05786	+	0.0469306i	0.170896	+	0.00389738i
$146$	−17.8256	−	8.44406i	−1.47526	−	0.698835i
$147$	4.17208	−	9.62960i	0.344107	−	0.794236i
$148$	−14.2541	−	1.42130i	−1.17168	−	0.116830i
$149$	−2.01293	+	2.01293i	−0.164906	+	0.164906i	−0.784736	−	0.619830i	$-0.787201\pi$
$149$	−2.01293	+	2.01293i	−0.164906	+	0.164906i	0.619830	+	0.784736i	$0.287201\pi$
$150$	7.64345	+	9.56962i	0.624085	+	0.781356i
$151$	9.52610			0.775223			0.387611	−	0.921823i	$-0.373300\pi$
$151$	9.52610			0.775223			0.387611	+	0.921823i	$0.373300\pi$
$152$	−10.4088	+	17.2948i	−0.844264	+	1.40280i
$153$	−6.07694	−	6.48258i	−0.491291	−	0.524085i
$154$	−4.06830	+	1.45289i	−0.327833	+	0.117077i
$155$	1.50200	+	1.57211i	0.120644	+	0.126275i
$156$	7.30846	+	4.07104i	0.585145	+	0.325944i
$157$	−11.0347	−	11.0347i	−0.880661	−	0.880661i	0.112940	−	0.993602i	$-0.463973\pi$
$157$	−11.0347	−	11.0347i	−0.880661	−	0.880661i	−0.993602	+	0.112940i	$0.963973\pi$
$158$	6.44092	−	13.5969i	0.512412	−	1.08171i
$159$	12.8333	−	5.07461i	1.01775	−	0.402443i
$160$	−1.53232	−	12.5560i	−0.121141	−	0.992635i
$161$			5.45876i			0.430211i
$162$	6.17972	−	11.1270i	0.485524	−	0.874223i
$163$	−11.7798	+	11.7798i	−0.922667	+	0.922667i	−0.997217	−	0.0745506i	$-0.976248\pi$
$163$	−11.7798	+	11.7798i	−0.922667	+	0.922667i	0.0745506	+	0.997217i	$0.476248\pi$
$164$	10.2008	+	12.4604i	0.796550	+	0.972994i
$165$	5.10242	−	11.0775i	0.397223	−	0.862380i
$166$	1.28108	+	3.58722i	0.0994314	+	0.278423i
$167$	8.82183			0.682653			0.341327	−	0.939945i	$-0.389124\pi$
$167$	8.82183			0.682653			0.341327	+	0.939945i	$0.389124\pi$
$168$	−0.781581	+	4.68748i	−0.0603003	+	0.361647i
$169$		−	7.16775i		−	0.551365i
$170$	−8.89011	+	2.94812i	−0.681841	+	0.226110i
$171$	−0.691122	+	21.3988i	−0.0528514	+	1.63641i
$172$	−1.60615	+	16.1079i	−0.122468	+	1.22821i
$173$	−3.53536	+	3.53536i	−0.268788	+	0.268788i	−0.828612	−	0.559824i	$-0.810869\pi$
$173$	−3.53536	+	3.53536i	−0.268788	+	0.268788i	0.559824	+	0.828612i	$0.310869\pi$
$174$	−2.24997	−	0.148341i	−0.170570	−	0.0112457i
$175$	−4.84514	−	0.221107i	−0.366258	−	0.0167141i
$176$	−10.4901	+	6.97267i	−0.790725	+	0.525585i
$177$	−13.9721	+	5.52490i	−1.05020	+	0.415277i
$178$	−3.27723	−	1.55244i	−0.245639	−	0.116360i
$179$	−15.7536	+	15.7536i	−1.17748	+	1.17748i	−0.197098	+	0.980384i	$0.563152\pi$
$179$	−15.7536	+	15.7536i	−1.17748	+	1.17748i	−0.980384	+	0.197098i	$0.936848\pi$
$180$	−7.91425	−	10.8335i	−0.589894	−	0.807481i
$181$	5.70832	+	5.70832i	0.424296	+	0.424296i	0.886680	−	0.462384i	$-0.153006\pi$
$181$	5.70832	+	5.70832i	0.424296	+	0.424296i	−0.462384	+	0.886680i	$0.653006\pi$
$182$	−3.12001	+	1.11423i	−0.231270	+	0.0825922i
$183$	5.96352	+	15.0813i	0.440836	+	1.11484i
$184$	3.83943	+	15.4466i	0.283046	+	1.13874i
$185$	−0.365150	+	16.0114i	−0.0268463	+	1.17718i
$186$	−1.56975	−	1.79135i	−0.115100	−	0.131348i
$187$	6.59513	+	6.59513i	0.482284	+	0.482284i
$188$	0.984052	−	0.805602i	0.0717693	−	0.0587545i
$189$	1.70120	+	4.74469i	0.123744	+	0.345126i
$190$	20.1699	+	10.1239i	1.46328	+	0.734466i
$191$	−10.7493			−0.777795			−0.388897	−	0.921281i	$-0.627144\pi$
$191$	−10.7493			−0.777795			−0.388897	+	0.921281i	$0.627144\pi$
$192$	1.08531	+	13.8138i	0.0783254	+	0.996928i
$193$		−	13.9033i		−	1.00078i	−0.865799	−	0.500392i	$-0.833189\pi$
$193$		−	13.9033i		−	1.00078i	0.865799	−	0.500392i	$-0.166811\pi$
$194$	5.16253	−	10.8982i	0.370648	−	0.782446i
$195$	3.91308	−	8.49539i	0.280221	−	0.608367i
$196$	7.67629	+	9.37667i	0.548306	+	0.669762i
$197$	−12.1556	−	12.1556i	−0.866049	−	0.866049i	0.125983	−	0.992032i	$-0.459792\pi$
$197$	−12.1556	−	12.1556i	−0.866049	−	0.866049i	−0.992032	+	0.125983i	$0.959792\pi$
$198$	−6.10628	+	11.8831i	−0.433954	+	0.844493i
$199$	−5.30097			−0.375776			−0.187888	−	0.982190i	$-0.560164\pi$
$199$	−5.30097			−0.375776			−0.187888	+	0.982190i	$0.560164\pi$
$200$	−13.8658	+	2.78217i	−0.980458	+	0.196729i
$201$	−3.67007	−	9.28135i	−0.258867	−	0.654656i
$202$	−10.1338	+	3.61902i	−0.713011	+	0.254633i
$203$	0.631417	−	0.631417i	0.0443168	−	0.0443168i
$204$	9.86855	−	2.80756i	0.690937	−	0.196568i
$205$	13.0178	−	12.4373i	0.909201	−	0.868656i
$206$	−6.16359	+	13.0115i	−0.429438	+	0.906552i
$207$	11.5459	+	12.3166i	0.802496	+	0.856062i
$208$	−8.04496	+	5.34739i	−0.557818	+	0.370775i
$209$		−	22.4735i		−	1.55452i
$210$	5.29225	+	0.470318i	0.365200	+	0.0324550i
$211$	−8.02150	−	8.02150i	−0.552223	−	0.552223i	0.374859	−	0.927082i	$-0.377691\pi$
$211$	−8.02150	−	8.02150i	−0.552223	−	0.552223i	−0.927082	+	0.374859i	$0.877691\pi$
$212$	−1.58108	+	15.8565i	−0.108589	+	1.08903i
$213$	17.7365	+	7.68443i	1.21528	+	0.526528i
$214$	−2.72080	+	0.971662i	−0.185990	+	0.0664214i
$215$	18.0937	+	0.412638i	1.23398	+	0.0281417i
$216$	8.15107	+	12.2295i	0.554610	+	0.832111i
$217$	0.943238			0.0640311
$218$	15.4784	−	5.52772i	1.04833	−	0.374384i
$219$	9.60371	−	22.1664i	0.648958	−	1.49787i
$220$	8.67014	+	11.0975i	0.584540	+	0.748196i
$221$	5.05785	+	5.05785i	0.340228	+	0.340228i
$222$	1.15418	−	17.5062i	0.0774637	−	1.17494i
$223$	−24.0209			−1.60856			−0.804280	−	0.594251i	$-0.797449\pi$
$223$	−24.0209			−1.60856			−0.804280	+	0.594251i	$0.797449\pi$
$224$	−4.39759	−	3.28212i	−0.293826	−	0.219296i
$225$	−11.3997	+	9.74914i	−0.759983	+	0.649943i
$226$	23.3126	+	11.0433i	1.55073	+	0.734587i
$227$	18.7426	+	18.7426i	1.24399	+	1.24399i	0.958330	+	0.285662i	$0.0922135\pi$
$227$	18.7426	+	18.7426i	1.24399	+	1.24399i	0.285662	+	0.958330i	$0.407787\pi$
$228$	−21.5974	−	12.0304i	−1.43032	−	0.796736i
$229$	−8.06032	−	8.06032i	−0.532641	−	0.532641i	0.388717	−	0.921357i	$-0.372919\pi$
$229$	−8.06032	−	8.06032i	−0.532641	−	0.532641i	−0.921357	+	0.388717i	$0.872919\pi$
$230$	16.8908	−	5.60129i	1.11375	−	0.369338i
$231$	−1.94555	−	4.92014i	−0.128008	−	0.323722i
$232$	1.34261	−	2.23082i	0.0881465	−	0.146461i
$233$		−	2.58876i		−	0.169595i	−0.996398	−	0.0847977i	$-0.972976\pi$
$233$		−	2.58876i		−	0.169595i	0.996398	−	0.0847977i	$-0.0270244\pi$
$234$	−4.68294	+	9.11321i	−0.306134	+	0.595749i
$235$	−0.982224	−	1.02807i	−0.0640732	−	0.0670639i
$236$	1.72137	−	17.2635i	0.112052	−	1.12376i
$237$	16.9080	+	7.32547i	1.09829	+	0.475840i
$238$	−1.73945	+	3.67202i	−0.112752	+	0.238022i
$239$	17.9563			1.16150			0.580749	−	0.814082i	$-0.302760\pi$
$239$	17.9563			1.16150			0.580749	+	0.814082i	$0.302760\pi$
$240$	15.3062	−	2.39146i	0.988013	−	0.154368i
$241$	−6.24097			−0.402016			−0.201008	−	0.979590i	$-0.564422\pi$
$241$	−6.24097			−0.402016			−0.201008	+	0.979590i	$0.564422\pi$
$242$	−0.656079	+	1.38500i	−0.0421743	+	0.0890309i
$243$	13.8740	+	7.10721i	0.890017	+	0.455928i
$244$	−18.6340	−	1.85803i	−1.19292	−	0.118948i
$245$	9.79610	−	9.35925i	0.625850	−	0.597941i
$246$	−14.8332	+	12.9982i	−0.945729	+	0.828738i
$247$		−	17.2350i		−	1.09664i
$248$	2.66907	−	0.663427i	0.169486	−	0.0421277i
$249$	−4.33833	+	1.71548i	−0.274931	+	0.108714i
$250$	4.28748	+	15.2190i	0.271164	+	0.962533i
$251$	3.08533	+	3.08533i	0.194744	+	0.194744i	0.797743	−	0.602998i	$-0.206027\pi$
$251$	3.08533	+	3.08533i	0.194744	+	0.194744i	−0.602998	+	0.797743i	$0.706027\pi$
$252$	−5.76984	−	0.764133i	−0.363466	−	0.0481358i
$253$	−12.5304	−	12.5304i	−0.787783	−	0.787783i
$254$	−21.1198	−	10.0046i	−1.32518	−	0.627742i
$255$	−3.97388	−	10.7609i	−0.248854	−	0.673873i
$256$	−14.7523	−	6.19433i	−0.922019	−	0.387146i
$257$	6.43874			0.401638			0.200819	−	0.979628i	$-0.435640\pi$
$257$	6.43874			0.401638			0.200819	+	0.979628i	$0.435640\pi$
$258$	−19.7829	−	1.30429i	−1.23163	−	0.0812014i
$259$	4.91282	+	4.91282i	0.305268	+	0.305268i
$260$	6.64918	+	8.51078i	0.412365	+	0.527816i
$261$	0.0891464	−	2.76019i	0.00551802	−	0.170851i
$262$	−0.929190	+	0.331836i	−0.0574056	+	0.0205009i
$263$	−6.56057			−0.404542			−0.202271	−	0.979330i	$-0.564832\pi$
$263$	−6.56057			−0.404542			−0.202271	+	0.979330i	$0.564832\pi$
$264$	−8.96588	−	12.5541i	−0.551812	−	0.772650i
$265$	17.8114	+	0.406198i	1.09414	+	0.0249526i
$266$	9.22002	−	3.29269i	0.565315	−	0.201888i
$267$	1.76564	−	4.07529i	0.108056	−	0.249404i
$268$	11.4678	+	1.14347i	0.700505	+	0.0698487i
$269$	11.7438	+	11.7438i	0.716029	+	0.716029i	0.967790	−	0.251760i	$-0.0810095\pi$
$269$	11.7438	+	11.7438i	0.716029	+	0.716029i	−0.251760	+	0.967790i	$0.581009\pi$
$270$	12.9357	−	10.1325i	0.787240	−	0.616647i
$271$		−	25.1578i		−	1.52823i	−0.645081	−	0.764114i	$-0.723177\pi$
$271$		−	25.1578i		−	1.52823i	0.645081	−	0.764114i	$-0.276823\pi$
$272$	−2.33939	+	11.6141i	−0.141847	+	0.704210i
$273$	−1.49205	−	3.77329i	−0.0903031	−	0.228370i
$274$	−6.62226	+	13.9797i	−0.400065	+	0.844546i
$275$	11.6294	−	10.6144i	0.701282	−	0.640069i
$276$	−18.7498	+	5.33423i	−1.12860	+	0.321083i
$277$	−18.1064	+	18.1064i	−1.08791	+	1.08791i	−0.0921635	+	0.995744i	$0.529378\pi$
$277$	−18.1064	+	18.1064i	−1.08791	+	1.08791i	−0.995744	+	0.0921635i	$0.970622\pi$
$278$	7.24509	−	2.58740i	0.434532	−	0.155182i
$279$	2.12823	−	1.99506i	0.127414	−	0.119441i
$280$	−3.28260	+	5.18298i	−0.196173	+	0.309743i
$281$	3.55148			0.211863			0.105932	−	0.994373i	$-0.466218\pi$
$281$	3.55148			0.211863			0.105932	+	0.994373i	$0.466218\pi$
$282$	1.02653	+	1.17144i	0.0611288	+	0.0697582i
$283$	3.49887	+	3.49887i	0.207986	+	0.207986i	0.803411	−	0.595425i	$-0.203016\pi$
$283$	3.49887	+	3.49887i	0.207986	+	0.207986i	−0.595425	+	0.803411i	$0.703016\pi$
$284$	−17.2706	+	14.1387i	−1.02482	+	0.838980i
$285$	−11.5636	+	25.1049i	−0.684971	+	1.48709i
$286$	4.60421	−	9.71959i	0.272253	−	0.574731i
$287$		−	7.81042i		−	0.461035i
$288$	−16.8643	+	1.89596i	−0.993740	+	0.111721i
$289$	−8.22745			−0.483968
$290$	−2.60167	−	1.30586i	−0.152775	−	0.0766829i
$291$	13.5521	+	5.87152i	0.794438	+	0.344194i
$292$	17.6701	+	21.5842i	1.03406	+	1.26312i
$293$	−18.0974	−	18.0974i	−1.05726	−	1.05726i	−0.998258	−	0.0590061i	$-0.981207\pi$
$293$	−18.0974	−	18.0974i	−1.05726	−	1.05726i	−0.0590061	−	0.998258i	$-0.518793\pi$
$294$	−11.1622	+	9.78141i	−0.650994	+	0.570463i
$295$	−19.3918	−	0.442241i	−1.12903	−	0.0257483i
$296$	17.3572	+	10.4463i	1.00887	+	0.607181i
$297$	−14.7964	−	6.98626i	−0.858574	−	0.405384i
$298$	3.79134	−	1.35398i	0.219627	−	0.0784339i
$299$	−9.60968	−	9.60968i	−0.555742	−	0.555742i
$300$	−3.97515	−	16.8582i	−0.229505	−	0.973307i
$301$	5.55174	−	5.55174i	0.319997	−	0.319997i
$302$	−12.1750	−	5.76735i	−0.700593	−	0.331874i
$303$	−4.84619	−	12.2556i	−0.278406	−	0.704068i
$304$	23.7739	−	15.8022i	1.36353	−	0.906319i
$305$	−0.477351	+	20.9313i	−0.0273330	+	1.19852i
$306$	3.84202	+	11.9643i	0.219633	+	0.683954i
$307$	4.01425	−	4.01425i	0.229105	−	0.229105i	−0.583214	−	0.812319i	$-0.698205\pi$
$307$	4.01425	−	4.01425i	0.229105	−	0.229105i	0.812319	+	0.583214i	$0.198205\pi$
$308$	6.07918	+	0.606167i	0.346394	+	0.0345396i
$309$	−16.1800	−	7.01006i	−0.920446	−	0.398788i
$310$	−0.967866	−	2.91862i	−0.0549711	−	0.165766i
$311$		−	19.0362i		−	1.07944i	−0.841844	−	0.539722i	$-0.818529\pi$
$311$		−	19.0362i		−	1.07944i	0.841844	−	0.539722i	$-0.181471\pi$
$312$	−6.87600	−	9.62781i	−0.389277	−	0.545067i
$313$	1.57634			0.0891001			0.0445500	−	0.999007i	$-0.485815\pi$
$313$	1.57634			0.0891001			0.0445500	+	0.999007i	$0.485815\pi$
$314$	7.42237	+	20.7837i	0.418868	+	1.17289i
$315$	−0.358285	+	6.49733i	−0.0201871	+	0.366083i
$316$	−16.4639	+	13.4783i	−0.926165	+	0.758212i
$317$	−17.8028	+	17.8028i	−0.999904	+	0.999904i	−1.00000		9.57940e-5i	$-0.999970\pi$
$317$	−17.8028	+	17.8028i	−0.999904	+	0.999904i	9.57940e−5		1.00000i	$0.499970\pi$
$318$	−19.4742	−	1.28393i	−1.09206	−	0.0719993i
$319$			2.89880i			0.162302i
$320$	−5.64330	+	16.9751i	−0.315470	+	0.948936i
$321$	−1.30114	−	3.29049i	−0.0726226	−	0.183657i
$322$	3.30488	−	6.97667i	0.184174	−	0.388795i
$323$	−14.9466	−	14.9466i	−0.831651	−	0.831651i
$324$	−14.6347	+	10.4798i	−0.813039	+	0.582209i
$325$	8.91870	−	8.14022i	0.494720	−	0.451538i
$326$	22.1872	−	7.92360i	1.22884	−	0.438847i
$327$	7.40211	+	18.7194i	0.409337	+	1.03518i
$328$	−5.49347	−	22.1011i	−0.303326	−	1.22033i
$329$	−0.616823			−0.0340065
$330$	−13.2278	+	11.0686i	−0.728168	+	0.609308i
$331$	8.54434	−	8.54434i	0.469639	−	0.469639i	−0.432159	−	0.901798i	$-0.642248\pi$
$331$	8.54434	−	8.54434i	0.469639	−	0.469639i	0.901798	+	0.432159i	$0.142248\pi$
$332$	0.534488	−	5.36032i	0.0293338	−	0.294186i
$333$	21.4760	+	0.693615i	1.17688	+	0.0380098i
$334$	−11.2749	−	5.34097i	−0.616935	−	0.292245i
$335$	0.293772	−	12.8816i	0.0160505	−	0.703796i
$336$	3.83684	−	5.51772i	0.209317	−	0.301016i
$337$		−	12.3337i		−	0.671858i	−0.941887	−	0.335929i	$-0.890950\pi$
$337$		−	12.3337i		−	0.671858i	0.941887	−	0.335929i	$-0.109050\pi$
$338$	−4.33955	+	9.16087i	−0.236040	+	0.498286i
$339$	−12.5599	+	28.9895i	−0.682158	+	1.57450i
$340$	13.1470	+	1.61441i	0.712998	+	0.0875539i
$341$	−2.16518	+	2.16518i	−0.117251	+	0.117251i
$342$	13.8387	−	26.9307i	0.748311	−	1.45624i
$343$		−	12.6677i		−	0.683993i
$344$	11.8049	−	19.6146i	0.636478	−	1.05755i
$345$	7.55018	+	20.4452i	0.406488	+	1.10073i
$346$	6.65883	−	2.37803i	0.357981	−	0.127844i
$347$	−7.85907	+	7.85907i	−0.421897	+	0.421897i	−0.885856	−	0.463960i	$-0.846428\pi$
$347$	−7.85907	+	7.85907i	−0.421897	+	0.421897i	0.463960	+	0.885856i	$0.346428\pi$
$348$	2.78581	+	1.55178i	0.149335	+	0.0831843i
$349$	7.76258	−	7.76258i	0.415521	−	0.415521i	−0.468136	−	0.883657i	$-0.655074\pi$
$349$	7.76258	−	7.76258i	0.415521	−	0.415521i	0.883657	+	0.468136i	$0.155074\pi$
$350$	6.05855	+	3.21597i	0.323843	+	0.171901i
$351$	−11.3475	−	5.35781i	−0.605682	−	0.285979i
$352$	17.6286	−	2.56053i	0.939606	−	0.136477i
$353$	16.7037			0.889051			0.444525	−	0.895766i	$-0.353372\pi$
$353$	16.7037			0.889051			0.444525	+	0.895766i	$0.353372\pi$
$354$	21.2022	+	1.39786i	1.12688	+	0.0742953i
$355$	17.2385	+	18.0432i	0.914927	+	0.957632i
$356$	3.24864	+	3.96825i	0.172178	+	0.210317i
$357$	−4.56621	−	1.97834i	−0.241670	−	0.104705i
$358$	29.6719	−	10.5965i	1.56821	−	0.560045i
$359$			18.2543i			0.963424i	0.876329	+	0.481712i	$0.159985\pi$
$359$			18.2543i			0.963424i	−0.876329	+	0.481712i	$0.840015\pi$
$360$	3.55607	+	18.6374i	0.187421	+	0.982280i
$361$			31.9317i			1.68062i
$362$	−3.83965	−	10.7516i	−0.201808	−	0.565091i
$363$	−1.72226	−	0.746180i	−0.0903954	−	0.0391643i
$364$	4.66217	+	0.464874i	0.244364	+	0.0243660i
$365$	22.5497	−	21.5441i	1.18030	−	1.12767i
$366$	1.50883	−	22.8854i	0.0788680	−	1.19624i
$367$	−6.14456			−0.320744			−0.160372	−	0.987057i	$-0.551269\pi$
$367$	−6.14456			−0.320744			−0.160372	+	0.987057i	$0.551269\pi$
$368$	4.44474	−	22.0663i	0.231698	−	1.15029i
$369$	−16.5199	−	17.6226i	−0.859994	−	0.917398i
$370$	10.1604	−	20.2426i	0.528216	−	1.05236i
$371$	5.46510	−	5.46510i	0.283734	−	0.283734i
$372$	0.921720	+	3.23984i	0.0477890	+	0.167978i
$373$	−8.50757	+	8.50757i	−0.440505	+	0.440505i	−0.892182	−	0.451677i	$-0.850826\pi$
$373$	−8.50757	+	8.50757i	−0.440505	+	0.440505i	0.451677	+	0.892182i	$0.350826\pi$
$374$	−4.43616	−	12.4219i	−0.229388	−	0.642321i
$375$	−18.4528	+	5.87333i	−0.952896	+	0.303297i
$376$	−1.74542	+	0.433843i	−0.0900131	+	0.0223737i
$377$			2.22311i			0.114496i
$378$	0.698311	−	7.09400i	0.0359172	−	0.364876i
$379$	3.78073	−	3.78073i	0.194203	−	0.194203i	−0.603306	−	0.797509i	$-0.706150\pi$
$379$	3.78073	−	3.78073i	0.194203	−	0.194203i	0.797509	+	0.603306i	$0.206150\pi$
$380$	−19.6492	−	25.1504i	−1.00798	−	1.29019i
$381$	11.3785	−	26.2629i	0.582939	−	1.34549i
$382$	13.7384	+	6.50794i	0.702917	+	0.332975i
$383$		−	0.150196i		−	0.00767464i	−0.999993	−	0.00383732i	$-0.998779\pi$
$383$		−	0.150196i		−	0.00767464i	0.999993	−	0.00383732i	$-0.00122146\pi$
$384$	6.97617	−	18.3121i	0.356001	−	0.934486i
$385$	0.155732	−	6.82866i	0.00793682	−	0.348021i
$386$	−8.41745	+	17.7694i	−0.428437	+	0.904439i
$387$	0.783821	−	24.2690i	0.0398438	−	1.23366i
$388$	−13.1961	+	10.8031i	−0.669932	+	0.548445i
$389$	−14.1800	+	14.1800i	−0.718952	+	0.718952i	−0.968391	−	0.249438i	$-0.919754\pi$
$389$	−14.1800	+	14.1800i	−0.718952	+	0.718952i	0.249438	+	0.968391i	$0.419754\pi$
$390$	−10.1445	+	8.48860i	−0.513687	+	0.429837i
$391$	−16.6674			−0.842909
$392$	−4.13393	−	16.6315i	−0.208795	−	0.840015i
$393$	−0.444358	−	1.12375i	−0.0224149	−	0.0566856i
$394$	8.17635	+	22.8950i	0.411919	+	1.15343i
$395$	16.4333	+	17.2003i	0.826848	+	0.865442i
$396$	14.9986	−	11.4905i	0.753707	−	0.577418i
$397$	−3.06320	−	3.06320i	−0.153737	−	0.153737i	0.626047	−	0.779785i	$-0.284672\pi$
$397$	−3.06320	−	3.06320i	−0.153737	−	0.153737i	−0.779785	+	0.626047i	$0.784672\pi$
$398$	6.77500	+	3.20935i	0.339600	+	0.160870i
$399$	4.40920	+	11.1505i	0.220736	+	0.558226i
$400$	19.4058	+	4.83890i	0.970290	+	0.241945i
$401$			7.76081i			0.387557i	0.981045	+	0.193778i	$0.0620742\pi$
$401$			7.76081i			0.387557i	−0.981045	+	0.193778i	$0.937926\pi$
$402$	−0.928568	+	14.0842i	−0.0463128	+	0.702454i
$403$	−1.66049	+	1.66049i	−0.0827149	+	0.0827149i
$404$	15.1427	+	1.50991i	0.753378	+	0.0751208i
$405$	12.9342	+	15.4177i	0.642705	+	0.766113i
$406$	−1.18927	+	0.424717i	−0.0590225	+	0.0210784i
$407$	−22.5545			−1.11799
$408$	−14.3124	−	2.38643i	−0.708572	−	0.118146i
$409$			16.1245i			0.797304i	0.917102	+	0.398652i	$0.130522\pi$
$409$			16.1245i			0.797304i	−0.917102	+	0.398652i	$0.869478\pi$
$410$	−24.1675	+	8.01436i	−1.19355	+	0.395801i
$411$	−17.3840	−	7.53171i	−0.857490	−	0.371512i
$412$	15.7550	−	12.8979i	0.776192	−	0.635436i
$413$	−5.95003	+	5.95003i	−0.292782	+	0.292782i
$414$	−7.29966	−	22.7316i	−0.358758	−	1.11720i
$415$	−6.02117	−	0.137316i	−0.295568	−	0.00674059i
$416$	13.5195	−	1.96369i	0.662846	−	0.0962779i
$417$	3.46475	+	8.76210i	0.169670	+	0.429082i
$418$	−13.6060	+	28.7226i	−0.665493	+	1.40487i
$419$	−9.18464	+	9.18464i	−0.448699	+	0.448699i	−0.894922	−	0.446223i	$-0.852769\pi$
$419$	−9.18464	+	9.18464i	−0.448699	+	0.448699i	0.446223	+	0.894922i	$0.352769\pi$
$420$	−6.47911	−	3.80517i	−0.316148	−	0.185673i
$421$	8.52495	+	8.52495i	0.415481	+	0.415481i	0.883643	−	0.468162i	$-0.155084\pi$
$421$	8.52495	+	8.52495i	0.415481	+	0.415481i	−0.468162	+	0.883643i	$0.655084\pi$
$422$	5.39560	+	15.1085i	0.262654	+	0.735468i
$423$	−1.39174	+	1.30465i	−0.0676685	+	0.0634343i
$424$	11.6207	−	19.3084i	0.564349	−	0.937701i
$425$	0.675116	−	14.7938i	0.0327479	−	0.717607i
$426$	−18.0161	−	20.5594i	−0.872883	−	0.996105i
$427$	6.42240	+	6.42240i	0.310802	+	0.310802i
$428$	4.06563	+	0.405392i	0.196520	+	0.0195954i
$429$	12.0865	+	5.23652i	0.583540	+	0.252822i
$430$	−22.8752	−	11.4818i	−1.10314	−	0.553702i
$431$	5.57870			0.268716			0.134358	−	0.990933i	$-0.457103\pi$
$431$	5.57870			0.268716			0.134358	+	0.990933i	$0.457103\pi$
$432$	−3.01357	−	20.5650i	−0.144990	−	0.989433i
$433$			9.29054i			0.446475i	0.974764	+	0.223237i	$0.0716625\pi$
$433$			9.29054i			0.446475i	−0.974764	+	0.223237i	$0.928337\pi$
$434$	−1.20552	−	0.571061i	−0.0578669	−	0.0274118i
$435$	1.49157	−	3.23824i	0.0715153	−	0.155261i
$436$	−23.1291	−	2.30625i	−1.10768	−	0.110449i
$437$	28.3978	+	28.3978i	1.35845	+	1.35845i
$438$	−25.6943	+	22.5158i	−1.22772	+	1.07585i
$439$	−2.97426			−0.141954			−0.0709769	−	0.997478i	$-0.522612\pi$
$439$	−2.97426			−0.141954			−0.0709769	+	0.997478i	$0.522612\pi$
$440$	−4.36228	−	19.4326i	−0.207963	−	0.926410i
$441$	−12.4315	−	13.2613i	−0.591978	−	0.631493i
$442$	−3.40212	−	9.52644i	−0.161822	−	0.453126i
$443$	−6.01388	+	6.01388i	−0.285728	+	0.285728i	−0.835388	−	0.549660i	$-0.814757\pi$
$443$	−6.01388	+	6.01388i	−0.285728	+	0.285728i	0.549660	+	0.835388i	$0.314757\pi$
$444$	−12.0738	+	21.6753i	−0.572999	+	1.02867i
$445$	4.14575	−	3.96088i	0.196528	−	0.187764i
$446$	30.7004	+	14.5429i	1.45370	+	0.688626i
$447$	1.81310	+	4.58519i	0.0857566	+	0.216872i
$448$	3.63334	+	6.85719i	0.171659	+	0.323972i
$449$		−	39.8136i		−	1.87892i	−0.342661	−	0.939459i	$-0.611328\pi$
$449$		−	39.8136i		−	1.87892i	0.342661	−	0.939459i	$-0.388672\pi$
$450$	20.4720	−	5.55835i	0.965062	−	0.262023i
$451$	17.9286	+	17.9286i	0.844226	+	0.844226i
$452$	−23.1092	−	28.2281i	−1.08696	−	1.32774i
$453$	6.55940	−	15.1398i	0.308188	−	0.711330i
$454$	−12.6071	−	35.3017i	−0.591679	−	1.65679i
$455$	0.119432	−	5.23695i	0.00559904	−	0.245512i
$456$	20.3194	+	28.4514i	0.951545	+	1.33236i
$457$	−11.9012			−0.556715			−0.278357	−	0.960478i	$-0.589790\pi$
$457$	−11.9012			−0.556715			−0.278357	+	0.960478i	$0.589790\pi$
$458$	5.42170	+	15.1816i	0.253340	+	0.709388i
$459$	−14.4872	+	5.19435i	−0.676202	+	0.242451i
$460$	−24.9788	−	3.06731i	−1.16464	−	0.143014i
$461$	−22.0413	−	22.0413i	−1.02657	−	1.02657i	−0.999637	−	0.0269292i	$-0.991427\pi$
$461$	−22.0413	−	22.0413i	−1.02657	−	1.02657i	−0.0269292	−	0.999637i	$-0.508573\pi$
$462$	−0.492244	+	7.46616i	−0.0229013	+	0.347357i
$463$	20.4647			0.951073			0.475537	−	0.879696i	$-0.342254\pi$
$463$	20.4647			0.951073			0.475537	+	0.879696i	$0.342254\pi$
$464$	−3.06655	+	2.03829i	−0.142361	+	0.0946255i
$465$	3.53279	−	1.30462i	0.163829	−	0.0605004i
$466$	−1.56731	+	3.30861i	−0.0726040	+	0.153269i
$467$	9.05437	+	9.05437i	0.418986	+	0.418986i	0.884854	−	0.465868i	$-0.154258\pi$
$467$	9.05437	+	9.05437i	0.418986	+	0.418986i	−0.465868	+	0.884854i	$0.654258\pi$
$468$	11.5025	−	8.81212i	0.531703	−	0.407340i
$469$	−3.95248	−	3.95248i	−0.182509	−	0.182509i
$470$	0.632928	+	1.90861i	0.0291948	+	0.0880375i
$471$	−25.1355	+	9.93921i	−1.15818	+	0.457974i
$472$	−12.6518	+	21.0217i	−0.582346	+	0.967603i
$473$			25.4878i			1.17193i
$474$	−17.1745	−	19.5990i	−0.788851	−	0.900211i
$475$	−26.3559	+	24.0554i	−1.20929	+	1.10374i
$476$	4.44628	−	3.63998i	0.203795	−	0.166838i
$477$	0.771588	−	23.8902i	0.0353286	−	1.09386i
$478$	−22.9494	−	10.8712i	−1.04968	−	0.497239i
$479$	35.2798			1.61198			0.805988	−	0.591932i	$-0.201635\pi$
$479$	35.2798			1.61198			0.805988	+	0.591932i	$0.201635\pi$
$480$	−21.0103	−	6.21036i	−0.958983	−	0.283463i
$481$	−17.2972			−0.788685
$482$	7.97638	+	3.77845i	0.363314	+	0.172104i
$483$	8.67560	+	3.75875i	0.394753	+	0.171029i
$484$	1.67703	−	1.37291i	0.0762285	−	0.0624051i
$485$	13.1716	+	13.7864i	0.598092	+	0.626009i
$486$	−13.4290	−	17.4832i	−0.609152	−	0.793053i
$487$		−	25.4699i		−	1.15415i	−0.816691	−	0.577076i	$-0.804194\pi$
$487$		−	25.4699i		−	1.15415i	0.816691	−	0.577076i	$-0.195806\pi$
$488$	22.6906	+	13.6562i	1.02716	+	0.618188i
$489$	10.6104	+	26.8329i	0.479819	+	1.21343i
$490$	−18.1864	+	6.03094i	−0.821579	+	0.272450i
$491$	−13.4144	−	13.4144i	−0.605385	−	0.605385i	0.336351	−	0.941737i	$-0.390807\pi$
$491$	−13.4144	−	13.4144i	−0.605385	−	0.605385i	−0.941737	+	0.336351i	$0.890807\pi$
$492$	26.8273	−	7.63225i	1.20947	−	0.344088i
$493$	1.92793	+	1.92793i	0.0868296	+	0.0868296i
$494$	−10.4346	+	22.0276i	−0.469473	+	0.991067i
$495$	−14.0920	−	15.7369i	−0.633390	−	0.707321i
$496$	−3.81291	−	0.768022i	−0.171205	−	0.0344852i
$497$	10.8256			0.485593
$498$	6.58329	+	0.434036i	0.295004	+	0.0194496i
$499$	9.77782	+	9.77782i	0.437715	+	0.437715i	0.891242	−	0.453527i	$-0.149834\pi$
$499$	9.77782	+	9.77782i	0.437715	+	0.437715i	−0.453527	+	0.891242i	$0.649834\pi$
$500$	3.73428	−	22.0467i	0.167002	−	0.985957i
$501$	6.07446	−	14.0205i	0.271387	−	0.626390i
$502$	−2.07532	−	5.81121i	−0.0926262	−	0.259367i
$503$	−3.56941			−0.159152			−0.0795761	−	0.996829i	$-0.525357\pi$
$503$	−3.56941			−0.159152			−0.0795761	+	0.996829i	$0.525357\pi$
$504$	6.91162	+	4.46983i	0.307868	+	0.199102i
$505$	0.387914	−	17.0096i	0.0172619	−	0.756918i
$506$	8.42850	+	23.6010i	0.374693	+	1.04919i
$507$	−11.3917	−	4.93551i	−0.505923	−	0.219194i
$508$	20.9356	+	25.5730i	0.928865	+	1.13462i
$509$	26.0392	+	26.0392i	1.15417	+	1.15417i	0.985709	+	0.168457i	$0.0538785\pi$
$509$	26.0392	+	26.0392i	1.15417	+	1.15417i	0.168457	+	0.985709i	$0.446121\pi$
$510$	−1.43604	+	16.1590i	−0.0635889	+	0.715534i
$511$		−	13.5294i		−	0.598504i
$512$	15.1042	+	16.8482i	0.667519	+	0.744593i
$513$	33.5332	+	15.8330i	1.48053	+	0.699044i
$514$	−8.22915	−	3.89819i	−0.362972	−	0.171942i
$515$	−15.7257	−	16.4597i	−0.692958	−	0.725302i
$516$	24.4943	+	13.6441i	1.07830	+	0.600647i
$517$	1.41590	−	1.41590i	0.0622713	−	0.0622713i
$518$	−3.30457	−	9.25327i	−0.145194	−	0.406565i
$519$	3.18439	+	8.05309i	0.139779	+	0.353491i
$520$	−3.34546	−	14.9030i	−0.146708	−	0.653538i
$521$	−41.0863			−1.80002			−0.900011	−	0.435867i	$-0.856442\pi$
$521$	−41.0863			−1.80002			−0.900011	+	0.435867i	$0.856442\pi$
$522$	−1.78502	+	3.47373i	−0.0781284	+	0.152041i
$523$	−10.3308	−	10.3308i	−0.451736	−	0.451736i	0.444195	−	0.895930i	$-0.353490\pi$
$523$	−10.3308	−	10.3308i	−0.451736	−	0.451736i	−0.895930	+	0.444195i	$0.853490\pi$
$524$	1.38847	+	0.138447i	0.0606557	+	0.00604809i
$525$	−3.68763	+	7.54812i	−0.160941	+	0.329427i
$526$	8.38486	+	3.97195i	0.365597	+	0.173185i
$527$			2.88002i			0.125456i
$528$	3.85844	+	21.4732i	0.167917	+	0.934499i
$529$	8.66737			0.376842
$530$	−22.5182	−	11.3026i	−0.978129	−	0.490955i
$531$	−0.840053	+	26.0100i	−0.0364552	+	1.12874i
$532$	−13.7773	−	1.37376i	−0.597321	−	0.0595601i
$533$	13.7496	+	13.7496i	0.595561	+	0.595561i
$534$	−4.72390	+	4.13954i	−0.204423	+	0.179135i
$535$	0.104150	−	4.56687i	0.00450280	−	0.197443i
$536$	−13.9643	−	8.40433i	−0.603166	−	0.363012i
$537$	14.1897	+	35.8847i	0.612331	+	1.54854i
$538$	−7.89934	−	22.1193i	−0.340565	−	0.953631i
$539$	13.4916	+	13.4916i	0.581125	+	0.581125i
$540$	−22.6672	+	5.11847i	−0.975440	+	0.220264i
$541$	3.58236	−	3.58236i	0.154018	−	0.154018i	−0.625892	−	0.779910i	$-0.715265\pi$
$541$	3.58236	−	3.58236i	0.154018	−	0.154018i	0.779910	+	0.625892i	$0.215265\pi$
$542$	−15.2312	+	32.1534i	−0.654236	+	1.38111i
$543$	13.0028	−	5.14163i	0.558004	−	0.220649i
$544$	10.0214	−	13.4273i	0.429664	−	0.575692i
$545$	−0.592503	+	25.9806i	−0.0253800	+	1.11289i
$546$	−0.377505	+	5.72585i	−0.0161557	+	0.245044i
$547$	−15.7705	+	15.7705i	−0.674298	+	0.674298i	−0.958704	−	0.284406i	$-0.908204\pi$
$547$	−15.7705	+	15.7705i	−0.674298	+	0.674298i	0.284406	+	0.958704i	$0.408204\pi$
$548$	16.9274	−	13.8577i	0.723102	−	0.591974i
$549$	28.0750	+	0.906744i	1.19821	+	0.0386989i
$550$	−21.2894	+	6.52509i	−0.907785	+	0.278231i
$551$		−	6.56958i		−	0.279873i
$552$	27.1930	+	4.53411i	1.15741	+	0.192984i
$553$	10.3199			0.438845
$554$	34.1033	−	12.1791i	1.44891	−	0.517441i
$555$	25.1955	+	11.6053i	1.06949	+	0.492620i
$556$	−10.8262	−	1.07950i	−0.459133	−	0.0457811i
$557$	10.2240	−	10.2240i	0.433205	−	0.433205i	−0.456512	−	0.889717i	$-0.650902\pi$
$557$	10.2240	−	10.2240i	0.433205	−	0.433205i	0.889717	+	0.456512i	$0.150902\pi$
$558$	−3.92788	+	1.26133i	−0.166280	+	0.0533964i
$559$			19.5467i			0.826739i
$560$	7.33331	−	4.63683i	0.309889	−	0.195942i
$561$	15.0229	−	5.94041i	0.634266	−	0.250804i
$562$	−4.53903	−	2.15016i	−0.191468	−	0.0906990i
$563$	−13.6516	−	13.6516i	−0.575345	−	0.575345i	0.358272	−	0.933617i	$-0.383366\pi$
$563$	−13.6516	−	13.6516i	−0.575345	−	0.575345i	−0.933617	+	0.358272i	$0.883366\pi$
$564$	−0.602751	−	2.11867i	−0.0253804	−	0.0892119i
$565$	−29.4908	+	28.1756i	−1.24069	+	1.18536i
$566$	−2.35349	−	6.59011i	−0.0989245	−	0.277003i
$567$	8.71213	+	0.563343i	0.365875	+	0.0236582i
$568$	30.6330	−	7.61417i	1.28533	−	0.319484i
$569$	−18.5447			−0.777432			−0.388716	−	0.921358i	$-0.627081\pi$
$569$	−18.5447			−0.777432			−0.388716	+	0.921358i	$0.627081\pi$
$570$	29.9783	−	25.0849i	1.25565	−	1.05069i
$571$	14.8825	−	14.8825i	0.622815	−	0.622815i	−0.323435	−	0.946250i	$-0.604838\pi$
$571$	14.8825	−	14.8825i	0.622815	−	0.622815i	0.946250	+	0.323435i	$0.104838\pi$
$572$	−11.7690	+	9.63478i	−0.492086	+	0.402850i
$573$	−7.40169	+	17.0839i	−0.309210	+	0.713690i
$574$	−4.72864	+	9.98225i	−0.197370	+	0.416651i
$575$	−1.28269	+	28.1076i	−0.0534918	+	1.17217i
$576$	22.7016	+	7.78694i	0.945901	+	0.324456i
$577$			34.3979i			1.43200i	0.698098	+	0.716002i	$0.254030\pi$
$577$			34.3979i			1.43200i	−0.698098	+	0.716002i	$0.745970\pi$
$578$	10.5152	+	4.98112i	0.437376	+	0.207187i
$579$	−22.0965	−	9.57344i	−0.918301	−	0.397859i
$580$	2.53451	+	3.24410i	0.105240	+	0.134704i
$581$	−1.84749	+	1.84749i	−0.0766468	+	0.0766468i
$582$	−13.7657	−	15.7090i	−0.570608	−	0.651159i
$583$			25.0900i			1.03912i
$584$	−9.51590	−	38.2840i	−0.393771	−	1.58420i
$585$	−10.8073	−	12.0687i	−0.446826	−	0.498981i
$586$	12.1731	+	34.0864i	0.502866	+	1.40810i
$587$	9.72401	−	9.72401i	0.401353	−	0.401353i	−0.477357	−	0.878710i	$-0.658405\pi$
$587$	9.72401	−	9.72401i	0.401353	−	0.401353i	0.878710	+	0.477357i	$0.158405\pi$
$588$	20.1880	−	5.74340i	0.832539	−	0.236854i
$589$	4.90696	−	4.90696i	0.202188	−	0.202188i
$590$	24.5163	+	12.3055i	1.00932	+	0.506611i
$591$	−27.6888	+	10.9489i	−1.13897	+	0.450376i
$592$	−15.8592	−	23.8596i	−0.651810	−	0.980625i
$593$	−36.0122			−1.47884			−0.739422	−	0.673242i	$-0.764901\pi$
$593$	−36.0122			−1.47884			−0.739422	+	0.673242i	$0.764901\pi$
$594$	14.6811	+	17.8870i	0.602374	+	0.733914i
$595$	−4.43802	−	4.64516i	−0.181941	−	0.190433i
$596$	−5.66533	−	0.564901i	−0.232061	−	0.0231392i
$597$	−3.65010	+	8.42482i	−0.149389	+	0.344805i
$598$	6.46387	+	18.0998i	0.264327	+	0.740156i
$599$		−	45.5674i		−	1.86184i	−0.365229	−	0.930918i	$-0.619009\pi$
$599$		−	45.5674i		−	1.86184i	0.365229	−	0.930918i	$-0.380991\pi$
$600$	−5.12588	+	23.9526i	−0.209263	+	0.977859i
$601$			20.4142i			0.832714i	0.909201	+	0.416357i	$0.136693\pi$
$601$			20.4142i			0.832714i	−0.909201	+	0.416357i	$0.863307\pi$
$602$	−10.4567	+	3.73433i	−0.426183	+	0.152200i
$603$	−17.2779	−	0.558030i	−0.703612	−	0.0227247i
$604$	12.0688	+	14.7421i	0.491071	+	0.599849i
$605$	−1.67391	−	1.75204i	−0.0680542	−	0.0712306i
$606$	−1.22614	+	18.5976i	−0.0498084	+	0.755474i
$607$	−10.6194			−0.431028			−0.215514	−	0.976501i	$-0.569143\pi$
$607$	−10.6194			−0.431028			−0.215514	+	0.976501i	$0.569143\pi$
$608$	−39.9517	+	5.80296i	−1.62026	+	0.235341i
$609$	−0.568734	−	1.43829i	−0.0230463	−	0.0582823i
$610$	13.2825	−	26.4627i	0.537791	−	1.07144i
$611$	1.08586	−	1.08586i	0.0439293	−	0.0439293i
$612$	2.33316	−	17.6173i	0.0943122	−	0.712136i
$613$	25.6453	−	25.6453i	1.03580	−	1.03580i	0.0364672	−	0.999335i	$-0.488390\pi$
$613$	25.6453	−	25.6453i	1.03580	−	1.03580i	0.999335	−	0.0364672i	$-0.0116105\pi$
$614$	−7.56082	+	2.70015i	−0.305130	+	0.108969i
$615$	−10.8028	−	29.2531i	−0.435613	−	1.17960i
$616$	−7.40262	−	4.45522i	−0.298260	−	0.179506i
$617$		−	40.9105i		−	1.64700i	−0.567320	−	0.823498i	$-0.692020\pi$
$617$		−	40.9105i		−	1.64700i	0.567320	−	0.823498i	$-0.307980\pi$
$618$	16.4350	+	18.7551i	0.661114	+	0.754441i
$619$	8.51504	−	8.51504i	0.342248	−	0.342248i	−0.514964	−	0.857212i	$-0.672195\pi$
$619$	8.51504	−	8.51504i	0.342248	−	0.342248i	0.857212	+	0.514964i	$0.172195\pi$
$620$	−0.530011	+	4.31617i	−0.0212858	+	0.173341i
$621$	27.5249	−	9.86902i	1.10454	−	0.396030i
$622$	−11.5250	+	24.3295i	−0.462111	+	0.975526i
$623$		−	2.48738i		−	0.0996546i
$624$	2.95906	+	16.4679i	0.118457	+	0.659244i
$625$	−24.8961	−	2.27700i	−0.995844	−	0.0910801i
$626$	−2.01467	−	0.954359i	−0.0805225	−	0.0381439i
$627$	−35.7170	−	15.4746i	−1.42640	−	0.617995i
$628$	3.09673	−	31.0567i	0.123573	−	1.23930i
$629$	−15.0005	+	15.0005i	−0.598109	+	0.598109i
$630$	4.39157	−	8.08712i	0.174964	−	0.322198i
$631$	11.9680			0.476437			0.238218	−	0.971212i	$-0.423437\pi$
$631$	11.9680			0.476437			0.238218	+	0.971212i	$0.423437\pi$
$632$	29.2021	−	7.25849i	1.16160	−	0.288727i
$633$	−18.2719	+	7.22518i	−0.726245	+	0.287175i
$634$	33.5315	−	11.9749i	1.33170	−	0.475584i
$635$	26.7169	−	25.5255i	1.06023	−	1.01295i
$636$	24.1120	+	13.4311i	0.956103	+	0.532579i
$637$	10.3468	+	10.3468i	0.409955	+	0.409955i
$638$	1.75501	−	3.70487i	0.0694817	−	0.146677i
$639$	24.4257	−	22.8973i	0.966266	−	0.905803i
$640$	17.4897	−	18.2787i	0.691341	−	0.722529i
$641$			2.38187i			0.0940784i	0.998893	+	0.0470392i	$0.0149786\pi$
$641$			2.38187i			0.0940784i	−0.998893	+	0.0470392i	$0.985021\pi$
$642$	−0.329203	+	4.99321i	−0.0129926	+	0.197066i
$643$	18.3347	−	18.3347i	0.723049	−	0.723049i	−0.246176	−	0.969225i	$-0.579174\pi$
$643$	18.3347	−	18.3347i	0.723049	−	0.723049i	0.969225	+	0.246176i	$0.0791743\pi$
$644$	−8.44772	+	6.91580i	−0.332887	+	0.272521i
$645$	13.1146	−	28.4722i	0.516389	−	1.12109i
$646$	10.0537	+	28.1518i	0.395557	+	1.10762i
$647$	−26.9671			−1.06019			−0.530093	−	0.847939i	$-0.677843\pi$
$647$	−26.9671			−1.06019			−0.530093	+	0.847939i	$0.677843\pi$
$648$	25.0489	−	4.53360i	0.984013	−	0.178097i
$649$		−	27.3163i		−	1.07226i
$650$	−16.3270	+	5.00413i	−0.640398	+	0.196278i
$651$	0.649487	−	1.49909i	0.0254554	−	0.0587538i
$652$	−33.1540	−	3.30585i	−1.29841	−	0.129467i
$653$	18.0392	−	18.0392i	0.705928	−	0.705928i	−0.259748	−	0.965676i	$-0.583640\pi$
$653$	18.0392	−	18.0392i	0.705928	−	0.705928i	0.965676	+	0.259748i	$0.0836397\pi$
$654$	1.87281	−	28.4061i	0.0732328	−	1.11077i
$655$	0.0355687	−	1.55965i	0.00138979	−	0.0609406i
$656$	−6.35956	+	31.5726i	−0.248299	+	1.23270i
$657$	−28.6162	−	30.5263i	−1.11642	−	1.19094i
$658$	0.788341	+	0.373441i	0.0307327	+	0.0145582i
$659$	9.57045	−	9.57045i	0.372812	−	0.372812i	−0.495688	−	0.868500i	$-0.665084\pi$
$659$	9.57045	−	9.57045i	0.372812	−	0.372812i	0.868500	+	0.495688i	$0.165084\pi$
$660$	23.6073	−	6.13798i	0.918914	−	0.238920i
$661$	−7.15010	−	7.15010i	−0.278107	−	0.278107i	0.554246	−	0.832353i	$-0.313007\pi$
$661$	−7.15010	−	7.15010i	−0.278107	−	0.278107i	−0.832353	+	0.554246i	$0.813007\pi$
$662$	−16.0932	+	5.74728i	−0.625480	+	0.223374i
$663$	11.5211	−	4.55574i	0.447444	−	0.176930i
$664$	−3.92839	+	6.52726i	−0.152451	+	0.253307i
$665$	−0.352935	+	15.4758i	−0.0136863	+	0.600127i
$666$	−27.0278	−	13.8886i	−1.04731	−	0.538173i
$667$	−3.66298	−	3.66298i	−0.141831	−	0.141831i
$668$	11.1765	+	13.6522i	0.432433	+	0.528221i
$669$	−16.5401	+	38.1764i	−0.639478	+	1.47598i
$670$	−8.17431	+	16.2857i	−0.315801	+	0.629171i
$671$	−29.4849			−1.13825
$672$	−8.24432	+	4.72910i	−0.318031	+	0.182429i
$673$			25.1331i			0.968809i	0.874844	+	0.484404i	$0.160964\pi$
$673$			25.1331i			0.968809i	−0.874844	+	0.484404i	$0.839036\pi$
$674$	−7.46713	+	15.7633i	−0.287623	+	0.607178i
$675$	7.64474	+	24.8306i	0.294246	+	0.955730i
$676$	11.0925	−	9.08094i	0.426634	−	0.349267i
$677$	−13.8480	−	13.8480i	−0.532220	−	0.532220i	0.389012	−	0.921233i	$-0.372816\pi$
$677$	−13.8480	−	13.8480i	−0.532220	−	0.532220i	−0.921233	+	0.389012i	$0.872816\pi$
$678$	33.6034	−	29.4465i	1.29053	−	1.13089i
$679$	8.27159			0.317435
$680$	−15.8254	−	10.0229i	−0.606877	−	0.384361i
$681$	42.6933	−	16.8820i	1.63601	−	0.646919i
$682$	4.07810	−	1.45639i	0.156159	−	0.0557680i
$683$	−18.0386	+	18.0386i	−0.690229	+	0.690229i	−0.962282	−	0.272053i	$-0.912297\pi$
$683$	−18.0386	+	18.0386i	−0.690229	+	0.690229i	0.272053	+	0.962282i	$0.412297\pi$
$684$	−33.9913	+	26.0409i	−1.29969	+	0.995700i
$685$	−16.8959	−	17.6846i	−0.645561	−	0.675693i
$686$	−7.66938	+	16.1902i	−0.292818	+	0.618146i
$687$	−18.3604	+	7.26014i	−0.700491	+	0.276992i
$688$	−26.9626	+	17.9217i	−1.02794	+	0.683260i
$689$			19.2417i			0.733050i
$690$	2.72841	−	30.7014i	0.103869	−	1.16878i
$691$	−13.0585	−	13.0585i	−0.496768	−	0.496768i	0.413662	−	0.910430i	$-0.364249\pi$
$691$	−13.0585	−	13.0585i	−0.496768	−	0.496768i	−0.910430	+	0.413662i	$0.864249\pi$
$692$	−9.95016	−	0.992150i	−0.378248	−	0.0377159i
$693$	−9.15922	−	0.295818i	−0.347930	−	0.0112372i
$694$	14.8025	−	5.28633i	0.561896	−	0.200666i
$695$	−0.277337	+	12.1609i	−0.0105200	+	0.461290i
$696$	−2.62096	−	3.66989i	−0.0993473	−	0.139107i
$697$	23.8479			0.903302
$698$	−14.6208	+	5.22143i	−0.553404	+	0.197634i
$699$	−4.11431	−	1.78255i	−0.155618	−	0.0674222i
$700$	−5.79621	−	7.77824i	−0.219076	−	0.293990i
$701$	−17.3103	−	17.3103i	−0.653802	−	0.653802i	0.300104	−	0.953906i	$-0.402979\pi$
$701$	−17.3103	−	17.3103i	−0.653802	−	0.653802i	−0.953906	+	0.300104i	$0.902979\pi$
$702$	11.2591	+	13.7177i	0.424946	+	0.517741i
$703$	51.1154			1.92786
$704$	−24.0807	−	7.40027i	−0.907577	−	0.278908i
$705$	−2.31024	+	0.853147i	−0.0870087	+	0.0321314i
$706$	−21.3485	−	10.1129i	−0.803462	−	0.380604i
$707$	−5.21909	−	5.21909i	−0.196284	−	0.196284i
$708$	−26.2515	−	14.6229i	−0.986592	−	0.549563i
$709$	−12.1684	−	12.1684i	−0.456993	−	0.456993i	0.440674	−	0.897667i	$-0.354739\pi$
$709$	−12.1684	−	12.1684i	−0.456993	−	0.456993i	−0.897667	+	0.440674i	$0.854739\pi$
$710$	−11.1082	−	33.4971i	−0.416884	−	1.25712i
$711$	23.2847	−	21.8277i	0.873245	−	0.818603i
$712$	−1.74950	−	7.03851i	−0.0655652	−	0.263779i
$713$		−	5.47191i		−	0.204925i
$714$	4.63820	+	5.29296i	0.173580	+	0.198084i
$715$	11.7471	+	12.2954i	0.439318	+	0.459823i
$716$	−44.3381	−	4.42104i	−1.65699	−	0.165222i
$717$	12.3642	−	28.5380i	0.461751	−	1.06577i
$718$	11.0516	−	23.3302i	0.412443	−	0.870676i
$719$	22.1693			0.826775			0.413388	−	0.910555i	$-0.364345\pi$
$719$	22.1693			0.826775			0.413388	+	0.910555i	$0.364345\pi$
$720$	6.73871	−	25.9729i	0.251137	−	0.967952i
$721$	−9.87553			−0.367784
$722$	19.3323	−	40.8109i	0.719474	−	1.51883i
$723$	−4.29736	+	9.91876i	−0.159820	+	0.368883i
$724$	−1.60196	+	16.0659i	−0.0595364	+	0.597084i
$725$	3.39959	−	3.10285i	0.126258	−	0.115237i
$726$	1.74941	+	1.99637i	0.0649268	+	0.0740924i
$727$			33.0556i			1.22596i	0.790097	+	0.612982i	$0.210030\pi$
$727$			33.0556i			1.22596i	−0.790097	+	0.612982i	$0.789970\pi$
$728$	−5.67712	−	3.41674i	−0.210408	−	0.126633i
$729$	20.8487	−	17.1561i	0.772174	−	0.635411i
$730$	−41.8633	+	13.8826i	−1.54943	+	0.513819i
$731$	16.9514	+	16.9514i	0.626968	+	0.626968i
$732$	−15.7838	+	28.3356i	−0.583387	+	1.04731i
$733$	10.7397	+	10.7397i	0.396680	+	0.396680i	0.877060	−	0.480381i	$-0.159501\pi$
$733$	10.7397	+	10.7397i	0.396680	+	0.396680i	−0.480381	+	0.877060i	$0.659501\pi$
$734$	7.85317	+	3.72008i	0.289866	+	0.137311i
$735$	−8.12932	−	22.0134i	−0.299855	−	0.811978i
$736$	−19.0402	+	25.5113i	−0.701832	+	0.940359i
$737$	18.1457			0.668404
$738$	10.4444	+	32.5246i	0.384463	+	1.19725i
$739$	−22.5896	−	22.5896i	−0.830971	−	0.830971i	0.156679	−	0.987650i	$-0.449921\pi$
$739$	−22.5896	−	22.5896i	−0.830971	−	0.830971i	−0.987650	+	0.156679i	$0.949921\pi$
$740$	−25.2412	+	19.7201i	−0.927883	+	0.724924i
$741$	−27.3916	−	11.8676i	−1.00626	−	0.435966i
$742$	−10.2935	+	3.67605i	−0.377886	+	0.134952i
$743$	19.2008			0.704410			0.352205	−	0.935923i	$-0.385432\pi$
$743$	19.2008			0.704410			0.352205	+	0.935923i	$0.385432\pi$
$744$	0.783464	−	4.69877i	0.0287232	−	0.172265i
$745$	−0.145130	+	6.36379i	−0.00531714	+	0.233151i
$746$	16.0240	−	5.72254i	0.586679	−	0.209517i
$747$	−0.260837	+	8.07614i	−0.00954353	+	0.295490i
$748$	−1.85083	+	18.5618i	−0.0676732	+	0.678687i
$749$	−1.40126	−	1.40126i	−0.0512010	−	0.0512010i
$750$	27.1397	+	3.66527i	0.991003	+	0.133837i
$751$		−	41.0729i		−	1.49877i	−0.662133	−	0.749386i	$-0.730349\pi$
$751$		−	41.0729i		−	1.49877i	0.662133	−	0.749386i	$-0.269651\pi$
$752$	2.49342	+	0.502242i	0.0909258	+	0.0183149i
$753$	7.02798	−	2.77904i	0.256114	−	0.101274i
$754$	1.34593	−	2.84129i	0.0490159	−	0.103474i
$755$	15.4016	−	14.7148i	0.560521	−	0.535525i
$756$	−5.18738	+	8.64383i	−0.188663	+	0.314373i
$757$	38.6574	−	38.6574i	1.40503	−	1.40503i	0.622051	−	0.782976i	$-0.286300\pi$
$757$	38.6574	−	38.6574i	1.40503	−	1.40503i	0.782976	−	0.622051i	$-0.213700\pi$
$758$	−7.12098	+	2.54308i	−0.258646	+	0.0923687i
$759$	−28.5427	+	11.2865i	−1.03604	+	0.409674i
$760$	9.88625	+	44.0401i	0.358612	+	1.59750i
$761$	7.48155			0.271206			0.135603	−	0.990763i	$-0.456703\pi$
$761$	7.48155			0.271206			0.135603	+	0.990763i	$0.456703\pi$
$762$	−30.4428	+	26.6769i	−1.10282	+	0.966401i
$763$	7.97169	+	7.97169i	0.288595	+	0.288595i
$764$	−13.6185	−	16.6352i	−0.492701	−	0.601839i
$765$	−19.8385	−	1.09397i	−0.717264	−	0.0395524i
$766$	−0.0909324	+	0.191960i	−0.00328552	+	0.00693581i
$767$		−	20.9490i		−	0.756426i
$768$	−20.0027	+	19.1806i	−0.721784	+	0.692119i
$769$	44.4806			1.60401			0.802005	−	0.597317i	$-0.203767\pi$
$769$	44.4806			1.60401			0.802005	+	0.597317i	$0.203767\pi$
$770$	−4.33329	+	8.63321i	−0.156161	+	0.311119i
$771$	4.43354	−	10.2331i	0.159670	−	0.368535i
$772$	21.5161	−	17.6144i	0.774383	−	0.633955i
$773$	−13.3538	−	13.3538i	−0.480302	−	0.480302i	0.424926	−	0.905228i	$-0.360300\pi$
$773$	−13.3538	−	13.3538i	−0.480302	−	0.480302i	−0.905228	+	0.424926i	$0.860300\pi$
$774$	−15.6949	+	30.5428i	−0.564140	+	1.09784i
$775$	4.85681	+	0.221640i	0.174462	+	0.00796155i
$776$	23.4061	−	5.81783i	0.840228	−	0.208848i
$777$	11.1908	−	4.42511i	0.401467	−	0.158750i
$778$	26.7079	−	9.53803i	0.957524	−	0.341955i
$779$	−40.6318	−	40.6318i	−1.45578	−	1.45578i
$780$	18.1046	−	4.70725i	0.648249	−	0.168547i
$781$	−24.8498	+	24.8498i	−0.889196	+	0.889196i
$782$	21.3021	+	10.0909i	0.761763	+	0.360850i
$783$	−4.32537	−	2.04227i	−0.154576	−	0.0729846i
$784$	−4.78568	+	23.7589i	−0.170917	+	0.848533i
$785$	−34.8856	−	0.795586i	−1.24512	−	0.0283957i
$786$	−0.112427	+	1.70525i	−0.00401015	+	0.0608244i
$787$	2.52501	−	2.52501i	0.0900067	−	0.0900067i	−0.660670	−	0.750677i	$-0.729728\pi$
$787$	2.52501	−	2.52501i	0.0900067	−	0.0900067i	0.750677	+	0.660670i	$0.229728\pi$
$788$	3.41130	−	34.2115i	0.121522	−	1.21874i
$789$	−4.51742	+	10.4267i	−0.160825	+	0.371201i
$790$	−10.5893	−	31.9323i	−0.376751	−	1.13610i
$791$			17.6939i			0.629123i
$792$	−26.1258	+	5.60508i	−0.928341	+	0.199168i
$793$	−22.6122			−0.802982
$794$	2.06043	+	5.76952i	0.0731221	+	0.204753i
$795$	12.9100	−	28.0279i	0.457870	−	0.994046i
$796$	−6.71589	−	8.20353i	−0.238038	−	0.290766i
$797$	−37.1771	+	37.1771i	−1.31688	+	1.31688i	−0.400649	+	0.916232i	$0.631215\pi$
$797$	−37.1771	+	37.1771i	−1.31688	+	1.31688i	−0.916232	+	0.400649i	$0.868785\pi$
$798$	1.11558	−	16.9206i	0.0394910	−	0.598983i
$799$		−	1.88337i		−	0.0666288i
$800$	−21.8723	−	17.9332i	−0.773304	−	0.634036i
$801$	−5.26108	−	5.61226i	−0.185891	−	0.198300i
$802$	4.69860	−	9.91885i	0.165913	−	0.350247i
$803$	31.0563	+	31.0563i	1.09595	+	1.09595i
$804$	9.71370	−	17.4383i	0.342576	−	0.615002i
$805$	8.43203	+	8.82560i	0.297190	+	0.311061i
$806$	3.12752	−	1.11691i	0.110162	−	0.0393416i
$807$	26.7507	−	10.5779i	0.941671	−	0.372360i
$808$	−18.4393	−	11.0976i	−0.648692	−	0.390411i
$809$	4.78411			0.168200			0.0841002	−	0.996457i	$-0.473198\pi$
$809$	4.78411			0.168200			0.0841002	+	0.996457i	$0.473198\pi$
$810$	−7.19648	−	27.5356i	−0.252859	−	0.967503i
$811$	1.57941	−	1.57941i	0.0554604	−	0.0554604i	−0.678833	−	0.734293i	$-0.737514\pi$
$811$	1.57941	−	1.57941i	0.0554604	−	0.0554604i	0.734293	+	0.678833i	$0.237514\pi$
$812$	1.77710	+	0.177199i	0.0623642	+	0.00621845i
$813$	−39.9833	−	17.3230i	−1.40227	−	0.607543i
$814$	28.8262	+	13.6551i	1.01036	+	0.478611i
$815$	−0.849311	+	37.2414i	−0.0297501	+	1.30451i
$816$	16.8475	+	11.7152i	0.589780	+	0.410113i
$817$		−	57.7631i		−	2.02088i
$818$	9.76219	−	20.6082i	0.341327	−	0.720548i
$819$	−7.02427	−	0.226864i	−0.245448	−	0.00792728i
$820$	35.7398	+	4.38873i	1.24809	+	0.153261i
$821$	−2.67698	+	2.67698i	−0.0934271	+	0.0934271i	−0.752276	−	0.658849i	$-0.771044\pi$
$821$	−2.67698	+	2.67698i	−0.0934271	+	0.0934271i	0.658849	+	0.752276i	$0.271044\pi$
$822$	17.6580	+	20.1508i	0.615895	+	0.702839i
$823$			14.7860i			0.515408i	0.966224	+	0.257704i	$0.0829660\pi$
$823$			14.7860i			0.515408i	−0.966224	+	0.257704i	$0.917034\pi$
$824$	−27.9447	+	6.94596i	−0.973500	+	0.241974i
$825$	−8.86166	−	25.7914i	−0.308523	−	0.897941i
$826$	11.2069	−	4.00224i	0.389936	−	0.139256i
$827$	29.8610	−	29.8610i	1.03837	−	1.03837i	0.0391342	−	0.999234i	$-0.487540\pi$
$827$	29.8610	−	29.8610i	1.03837	−	1.03837i	0.999234	−	0.0391342i	$-0.0124600\pi$
$828$	−4.43289	+	33.4720i	−0.154053	+	1.16323i
$829$	8.42220	−	8.42220i	0.292515	−	0.292515i	−0.545558	−	0.838073i	$-0.683682\pi$
$829$	8.42220	−	8.42220i	0.292515	−	0.292515i	0.838073	+	0.545558i	$0.183682\pi$
$830$	7.61233	+	3.82088i	0.264228	+	0.132625i
$831$	16.3089	+	41.2440i	0.565750	+	1.43074i
$832$	−18.4677	−	5.67531i	−0.640251	−	0.196756i
$833$	17.9459			0.621790
$834$	0.876620	−	13.2962i	0.0303549	−	0.460411i
$835$	14.2629	−	13.6269i	0.493589	−	0.471578i
$836$	34.7789	−	28.4720i	1.20285	−	0.984725i
$837$	−1.70530	−	4.75612i	−0.0589438	−	0.164396i
$838$	17.2992	−	6.17797i	0.597592	−	0.213414i
$839$			29.6714i			1.02437i	0.858875	+	0.512185i	$0.171164\pi$
$839$			29.6714i			1.02437i	−0.858875	+	0.512185i	$0.828836\pi$
$840$	5.97700	+	8.78589i	0.206226	+	0.303142i
$841$		−	28.1526i		−	0.970779i
$842$	−5.73424	−	16.0567i	−0.197615	−	0.553350i
$843$	2.44545	−	5.64436i	0.0842257	−	0.194402i
$844$	2.25113	−	22.5763i	0.0774869	−	0.777108i
$845$	−11.0719	−	11.5887i	−0.380884	−	0.398662i
$846$	2.56860	−	0.824838i	0.0883104	−	0.0283585i
$847$	−1.05119			−0.0361194
$848$	−26.5418	+	17.6420i	−0.911451	+	0.605830i
$849$	7.96998	−	3.15153i	0.273529	−	0.108160i
$850$	−9.81944	+	18.4988i	−0.336804	+	0.634504i
$851$	28.5003	−	28.5003i	0.976977	−	0.976977i
$852$	10.5786	+	37.1837i	0.362417	+	1.27389i
$853$	−9.45541	+	9.45541i	−0.323747	+	0.323747i	−0.850203	−	0.526456i	$-0.823521\pi$
$853$	−9.45541	+	9.45541i	−0.323747	+	0.323747i	0.526456	+	0.850203i	$0.323521\pi$
$854$	−4.31998	−	12.0966i	−0.147827	−	0.413936i
$855$	31.9368	+	35.6646i	1.09222	+	1.21970i
$856$	−4.95072	−	2.97956i	−0.169212	−	0.101839i
$857$			18.3503i			0.626835i	0.949615	+	0.313417i	$0.101474\pi$
$857$			18.3503i			0.626835i	−0.949615	+	0.313417i	$0.898526\pi$
$858$	−12.2770	−	14.0101i	−0.419130	−	0.478297i
$859$	−2.33254	+	2.33254i	−0.0795853	+	0.0795853i	−0.745779	−	0.666194i	$-0.767922\pi$
$859$	−2.33254	+	2.33254i	−0.0795853	+	0.0795853i	0.666194	+	0.745779i	$0.267922\pi$
$860$	22.2847	+	28.5238i	0.759902	+	0.972654i
$861$	−12.4131	−	5.37804i	−0.423037	−	0.183283i
$862$	−7.12996	−	3.37749i	−0.242847	−	0.115038i
$863$		−	0.0825874i		−	0.00281131i	−0.999999	−	0.00140565i	$-0.999553\pi$
$863$		−	0.0825874i		−	0.00281131i	0.999999	−	0.00140565i	$-0.000447433\pi$
$864$	−8.59904	+	28.1079i	−0.292545	+	0.956252i
$865$	−0.254895	+	11.1769i	−0.00866670	+	0.380025i
$866$	5.62474	−	11.8739i	0.191137	−	0.403493i
$867$	−5.66519	+	13.0759i	−0.192400	+	0.444080i
$868$	1.19500	+	1.45971i	0.0405611	+	0.0495458i
$869$	−23.6890	+	23.6890i	−0.803594	+	0.803594i
$870$	−3.86684	+	3.23565i	−0.131098	+	0.109699i
$871$	13.9160			0.471526
$872$	28.1643	+	16.9505i	0.953764	+	0.574017i
$873$	18.6632	−	17.4954i	0.631653	−	0.592128i
$874$	−19.1016	−	53.4872i	−0.646120	−	1.80923i
$875$	−8.17505	+	7.12670i	−0.276367	+	0.240926i
$876$	46.4708	−	13.2207i	1.57010	−	0.446687i
$877$	37.7836	+	37.7836i	1.27586	+	1.27586i	0.942962	+	0.332900i	$0.108027\pi$
$877$	37.7836	+	37.7836i	1.27586	+	1.27586i	0.332900	+	0.942962i	$0.391973\pi$
$878$	3.80131	+	1.80070i	0.128288	+	0.0607706i
$879$	−41.2236	+	16.3008i	−1.39044	+	0.549814i
$880$	−6.18970	+	27.4772i	−0.208655	+	0.926255i
$881$		−	11.0776i		−	0.373213i	−0.982435	−	0.186607i	$-0.940251\pi$
$881$		−	11.0776i		−	0.373213i	0.982435	−	0.186607i	$-0.0597490\pi$
$882$	7.85958	+	24.4753i	0.264646	+	0.824126i
$883$	−8.34797	+	8.34797i	−0.280931	+	0.280931i	−0.833480	−	0.552549i	$-0.813655\pi$
$883$	−8.34797	+	8.34797i	−0.280931	+	0.280931i	0.552549	+	0.833480i	$0.313655\pi$
$884$	−1.41942	+	14.2352i	−0.0477402	+	0.478781i
$885$	−14.0555	+	30.5149i	−0.472471	+	1.02575i
$886$	11.3271	−	4.04518i	0.380542	−	0.135901i
$887$	17.9204			0.601710			0.300855	−	0.953670i	$-0.402728\pi$
$887$	17.9204			0.601710			0.300855	+	0.953670i	$0.402728\pi$
$888$	28.5540	−	20.3927i	0.958210	−	0.684335i
$889$		−	16.0297i		−	0.537618i
$890$	−7.69658	+	2.55232i	−0.257990	+	0.0855540i
$891$	−21.2916	+	18.7053i	−0.713296	+	0.626653i
$892$	−30.4325	−	37.1736i	−1.01896	−	1.24467i
$893$	−3.20886	+	3.20886i	−0.107381	+	0.107381i
$894$	0.458733	−	6.95788i	0.0153423	−	0.232706i
$895$	−1.13582	+	49.8044i	−0.0379662	+	1.66478i
$896$	−0.492127	−	10.9637i	−0.0164408	−	0.366270i
$897$	−21.8896	+	8.65570i	−0.730873	+	0.289005i
$898$	−24.1042	+	50.8844i	−0.804367	+	1.69804i
$899$	−0.632938	+	0.632938i	−0.0211097	+	0.0211097i
$900$	−29.5298	−	5.29037i	−0.984328	−	0.176346i
$901$	16.6868	+	16.6868i	0.555918	+	0.555918i
$902$	−12.0595	−	33.7685i	−0.401539	−	1.12437i
$903$	−5.00060	−	12.6462i	−0.166410	−	0.420838i
$904$	12.4450	+	50.0683i	0.413916	+	1.66525i
$905$	18.0466	+	0.411563i	0.599889	+	0.0136808i
$906$	−17.5494	+	15.3785i	−0.583040	+	0.510915i
$907$	1.21556	+	1.21556i	0.0403621	+	0.0403621i	0.727000	−	0.686638i	$-0.240914\pi$
$907$	1.21556	+	1.21556i	0.0403621	+	0.0403621i	−0.686638	+	0.727000i	$0.740914\pi$
$908$	−5.25987	+	52.7506i	−0.174555	+	1.75059i
$909$	−22.8148	−	0.736856i	−0.756720	−	0.0244400i
$910$	−3.32323	+	6.62087i	−0.110164	+	0.219480i
$911$	24.7058			0.818540			0.409270	−	0.912413i	$-0.365783\pi$
$911$	24.7058			0.818540			0.409270	+	0.912413i	$0.365783\pi$
$912$	−8.74439	−	48.6648i	−0.289556	−	1.61145i
$913$		−	8.48173i		−	0.280704i
$914$	15.2105	+	7.20530i	0.503120	+	0.238330i
$915$	32.9374	+	15.1714i	1.08888	+	0.501550i
$916$	2.26202	−	22.6855i	0.0747392	−	0.749551i
$917$	−0.478551	−	0.478551i	−0.0158031	−	0.0158031i
$918$	21.6604	+	2.13218i	0.714899	+	0.0703724i
$919$	−17.3632			−0.572759			−0.286379	−	0.958116i	$-0.592452\pi$
$919$	−17.3632			−0.572759			−0.286379	+	0.958116i	$0.592452\pi$
$920$	30.0675	+	19.0431i	0.991298	+	0.627831i
$921$	−3.61574	−	9.14394i	−0.119143	−	0.301303i
$922$	14.8259	+	41.5147i	0.488265	+	1.36721i
$923$	−19.0575	+	19.0575i	−0.627285	+	0.627285i
$924$	5.14934	−	9.24425i	0.169401	−	0.304113i
$925$	24.1421	+	26.4509i	0.793789	+	0.869702i
$926$	−26.1552	−	12.3899i	−0.859514	−	0.407156i
$927$	−22.2821	+	20.8879i	−0.731841	+	0.686048i
$928$	5.15329	−	0.748511i	0.169165	−	0.0245711i
$929$			21.7500i			0.713594i	0.934182	+	0.356797i	$0.116131\pi$
$929$			21.7500i			0.713594i	−0.934182	+	0.356797i	$0.883869\pi$
$930$	−5.30500	−	0.471451i	−0.173958	−	0.0154595i
$931$	−30.5761	−	30.5761i	−1.00209	−	1.00209i
$932$	4.00625	−	3.27975i	0.131229	−	0.107432i
$933$	−30.2542	−	13.1078i	−0.990477	−	0.429130i
$934$	−6.09035	−	17.0539i	−0.199282	−	0.558020i
$935$	20.8502	+	0.475501i	0.681875	+	0.0155506i
$936$	−20.0361	+	4.29857i	−0.654900	+	0.140503i
$937$	7.60852			0.248560			0.124280	−	0.992247i	$-0.460338\pi$
$937$	7.60852			0.248560			0.124280	+	0.992247i	$0.460338\pi$
$938$	2.65860	+	7.44448i	0.0868065	+	0.243071i
$939$	1.08542	−	2.50528i	0.0354215	−	0.0817566i
$940$	0.346597	−	2.82252i	0.0113047	−	0.0920605i
$941$	16.2609	+	16.2609i	0.530091	+	0.530091i	0.920599	−	0.390508i	$-0.127701\pi$
$941$	16.2609	+	16.2609i	0.530091	+	0.530091i	−0.390508	+	0.920599i	$0.627701\pi$
$942$	38.1424	+	2.51473i	1.24275	+	0.0819342i
$943$	−45.3098			−1.47549
$944$	28.8970	−	19.2075i	0.940516	−	0.625149i
$945$	10.0795	+	5.04330i	0.327886	+	0.164059i
$946$	15.4310	−	32.5751i	0.501705	−	1.05911i
$947$	24.8716	+	24.8716i	0.808219	+	0.808219i	0.984364	−	0.176146i	$-0.0563629\pi$
$947$	24.8716	+	24.8716i	0.808219	+	0.808219i	−0.176146	+	0.984364i	$0.556363\pi$
$948$	10.0844	+	35.4468i	0.327528	+	1.15126i
$949$	23.8173	+	23.8173i	0.773143	+	0.773143i
$950$	48.2484	−	14.7878i	1.56538	−	0.479781i
$951$	16.0354	+	40.5524i	0.519985	+	1.31500i
$952$	−7.88639	+	1.96025i	−0.255599	+	0.0635320i
$953$			16.9947i			0.550514i	0.961371	+	0.275257i	$0.0887629\pi$
$953$			16.9947i			0.550514i	−0.961371	+	0.275257i	$0.911237\pi$
$954$	−15.4499	+	30.0662i	−0.500209	+	0.973428i
$955$	−17.3793	+	16.6043i	−0.562380	+	0.537301i
$956$	22.7492	+	27.7884i	0.735761	+	0.898741i
$957$	4.60707	+	1.99604i	0.148925	+	0.0645227i
$958$	−45.0900	−	21.3593i	−1.45679	−	0.690089i
$959$	−10.6104			−0.342628
$960$	23.0926	+	20.6574i	0.745312	+	0.666716i
$961$	30.0545			0.969500
$962$	22.1070	+	10.4722i	0.712759	+	0.337637i
$963$	−6.12550	−	0.197837i	−0.197391	−	0.00637520i
$964$	−7.90679	−	9.65823i	−0.254661	−	0.311071i
$965$	−21.4762	−	22.4786i	−0.691343	−	0.723611i
$966$	−8.81236	−	10.0564i	−0.283533	−	0.323559i
$967$			33.0817i			1.06384i	0.846796	+	0.531918i	$0.178528\pi$
$967$			33.0817i			1.06384i	−0.846796	+	0.531918i	$0.821472\pi$
$968$	−2.97455	+	0.739358i	−0.0956057	+	0.0237639i
$969$	−34.0464	+	13.4628i	−1.09373	+	0.432487i
$970$	−8.48756	−	25.5944i	−0.272519	−	0.821787i
$971$	14.4289	+	14.4289i	0.463045	+	0.463045i	0.899652	−	0.436607i	$-0.143820\pi$
$971$	14.4289	+	14.4289i	0.463045	+	0.463045i	−0.436607	+	0.899652i	$0.643820\pi$
$972$	6.57841	+	30.4750i	0.211003	+	0.977485i
$973$	3.73136	+	3.73136i	0.119622	+	0.119622i
$974$	−15.4202	+	32.5523i	−0.494094	+	1.04304i
$975$	−6.79607	−	19.7796i	−0.217648	−	0.633454i
$976$	−20.7323	−	31.1911i	−0.663626	−	0.998403i
$977$	8.64246			0.276497			0.138248	−	0.990398i	$-0.455853\pi$
$977$	8.64246			0.276497			0.138248	+	0.990398i	$0.455853\pi$
$978$	2.68454	−	40.7181i	0.0858423	−	1.30202i
$979$	5.70971	+	5.70971i	0.182483	+	0.182483i
$980$	26.8948	+	3.30259i	0.859123	+	0.105497i
$981$	34.8475	+	1.12548i	1.11260	+	0.0359338i
$982$	9.02311	+	25.2660i	0.287939	+	0.806271i
$983$	36.3557			1.15957			0.579784	−	0.814770i	$-0.303137\pi$
$983$	36.3557			1.15957			0.579784	+	0.814770i	$0.303137\pi$
$984$	−38.9079	−	6.48743i	−1.24034	−	0.206812i
$985$	−38.4293	−	0.876403i	−1.22446	−	0.0279245i
$986$	−1.29681	−	3.63125i	−0.0412987	−	0.115642i
$987$	−0.424727	+	0.980315i	−0.0135192	+	0.0312038i
$988$	26.6721	−	21.8354i	0.848554	−	0.694675i
$989$	−32.2068	−	32.2068i	−1.02412	−	1.02412i
$990$	8.48304	+	28.6445i	0.269609	+	0.910383i
$991$			47.3323i			1.50356i	0.659414	+	0.751780i	$0.270804\pi$
$991$			47.3323i			1.50356i	−0.659414	+	0.751780i	$0.729196\pi$
$992$	4.40818	+	3.29002i	0.139960	+	0.104458i
$993$	−7.69611	−	19.4629i	−0.244229	−	0.617636i
$994$	−13.8358	−	6.55408i	−0.438845	−	0.207883i
$995$	−8.57049	+	8.18829i	−0.271703	+	0.259586i
$996$	−8.15111	−	4.54043i	−0.258278	−	0.143869i
$997$	−4.38113	+	4.38113i	−0.138752	+	0.138752i	−0.773071	−	0.634319i	$-0.781280\pi$
$997$	−4.38113	+	4.38113i	−0.138752	+	0.138752i	0.634319	+	0.773071i	$0.281280\pi$
$998$	−6.57697	−	18.4165i	−0.208190	−	0.582963i
$999$	15.8901	−	33.6541i	0.502741	−	1.06477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.t.b.59.4	yes	80
3.2	odd	2	inner	240.2.t.b.59.38	yes	80
4.3	odd	2		960.2.t.b.719.14		80
5.4	even	2	inner	240.2.t.b.59.37	yes	80
12.11	even	2		960.2.t.b.719.7		80
15.14	odd	2	inner	240.2.t.b.59.3	✓	80
16.3	odd	4	inner	240.2.t.b.179.3	yes	80
16.13	even	4		960.2.t.b.239.34		80
20.19	odd	2		960.2.t.b.719.27		80
48.29	odd	4		960.2.t.b.239.27		80
48.35	even	4	inner	240.2.t.b.179.37	yes	80
60.59	even	2		960.2.t.b.719.34		80
80.19	odd	4	inner	240.2.t.b.179.38	yes	80
80.29	even	4		960.2.t.b.239.7		80
240.29	odd	4		960.2.t.b.239.14		80
240.179	even	4	inner	240.2.t.b.179.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.t.b.59.3	✓	80	15.14	odd	2	inner
240.2.t.b.59.4	yes	80	1.1	even	1	trivial
240.2.t.b.59.37	yes	80	5.4	even	2	inner
240.2.t.b.59.38	yes	80	3.2	odd	2	inner
240.2.t.b.179.3	yes	80	16.3	odd	4	inner
240.2.t.b.179.4	yes	80	240.179	even	4	inner
240.2.t.b.179.37	yes	80	48.35	even	4	inner
240.2.t.b.179.38	yes	80	80.19	odd	4	inner
960.2.t.b.239.7		80	80.29	even	4
960.2.t.b.239.14		80	240.29	odd	4
960.2.t.b.239.27		80	48.29	odd	4
960.2.t.b.239.34		80	16.13	even	4
960.2.t.b.719.7		80	12.11	even	2
960.2.t.b.719.14		80	4.3	odd	2
960.2.t.b.719.27		80	20.19	odd	2
960.2.t.b.719.34		80	60.59	even	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27807 - 0.605427i) q^{2} +(0.688572 - 1.58930i) q^{3} +(1.26692 + 1.54755i) q^{4} +(1.61678 - 1.54468i) q^{5} +(-1.84225 + 1.61435i) q^{6} -0.970036i q^{7} +(-0.682276 - 2.74490i) q^{8} +(-2.05174 - 2.18869i) q^{9} +O(q^{10})\)	\(q+(-1.27807 - 0.605427i) q^{2} +(0.688572 - 1.58930i) q^{3} +(1.26692 + 1.54755i) q^{4} +(1.61678 - 1.54468i) q^{5} +(-1.84225 + 1.61435i) q^{6} -0.970036i q^{7} +(-0.682276 - 2.74490i) q^{8} +(-2.05174 - 2.18869i) q^{9} +(-3.00154 + 0.995364i) q^{10} +(2.22669 + 2.22669i) q^{11} +(3.33189 - 0.947907i) q^{12} +(1.70767 + 1.70767i) q^{13} +(-0.587286 + 1.23977i) q^{14} +(-1.34169 - 3.63316i) q^{15} +(-0.789843 + 3.92124i) q^{16} +2.96185 q^{17} +(1.29717 + 4.03947i) q^{18} +(-5.04637 - 5.04637i) q^{19} +(4.43879 + 0.545070i) q^{20} +(-1.54168 - 0.667940i) q^{21} +(-1.49777 - 4.19397i) q^{22} -5.62738 q^{23} +(-4.83227 - 0.805723i) q^{24} +(0.227937 - 4.99480i) q^{25} +(-1.14865 - 3.21638i) q^{26} +(-4.89125 + 1.75375i) q^{27} +(1.50118 - 1.22896i) q^{28} +(0.650921 + 0.650921i) q^{29} +(-0.484846 + 5.45572i) q^{30} +0.972374i q^{31} +(3.38350 - 4.53342i) q^{32} +(5.07212 - 2.00564i) q^{33} +(-3.78545 - 1.79318i) q^{34} +(-1.49839 - 1.56833i) q^{35} +(0.787736 - 5.94806i) q^{36} +(-5.06457 + 5.06457i) q^{37} +(3.39440 + 9.50481i) q^{38} +(3.88984 - 1.53814i) q^{39} +(-5.34308 - 3.38400i) q^{40} +8.05168 q^{41} +(1.56598 + 1.78704i) q^{42} +(5.72323 + 5.72323i) q^{43} +(-0.624891 + 6.26697i) q^{44} +(-6.69803 - 0.369352i) q^{45} +(7.19217 + 3.40696i) q^{46} -0.635876i q^{47} +(5.68816 + 3.95535i) q^{48} +6.05903 q^{49} +(-3.31531 + 6.24570i) q^{50} +(2.03945 - 4.70726i) q^{51} +(-0.479233 + 4.80618i) q^{52} +(5.63391 + 5.63391i) q^{53} +(7.31312 + 0.719881i) q^{54} +(7.03960 + 0.160542i) q^{55} +(-2.66266 + 0.661833i) q^{56} +(-11.4950 + 4.54540i) q^{57} +(-0.437837 - 1.22601i) q^{58} +(-6.13382 - 6.13382i) q^{59} +(3.92271 - 6.67925i) q^{60} +(-6.62079 + 6.62079i) q^{61} +(0.588701 - 1.24276i) q^{62} +(-2.12311 + 1.99026i) q^{63} +(-7.06900 + 3.74557i) q^{64} +(5.39871 + 0.123121i) q^{65} +(-7.69679 - 0.507449i) q^{66} +(4.07457 - 4.07457i) q^{67} +(3.75242 + 4.58362i) q^{68} +(-3.87485 + 8.94358i) q^{69} +(0.965540 + 2.91160i) q^{70} +11.1600i q^{71} +(-4.60790 + 7.12512i) q^{72} +13.9473 q^{73} +(9.53910 - 3.40664i) q^{74} +(-7.78128 - 3.80154i) q^{75} +(1.41620 - 14.2029i) q^{76} +(2.15997 - 2.15997i) q^{77} +(-5.90272 - 0.389166i) q^{78} +10.6386i q^{79} +(4.78006 + 7.55983i) q^{80} +(-0.580745 + 8.98124i) q^{81} +(-10.2906 - 4.87470i) q^{82} +(-1.90456 - 1.90456i) q^{83} +(-0.919505 - 3.23205i) q^{84} +(4.78865 - 4.57510i) q^{85} +(-3.84968 - 10.7797i) q^{86} +(1.48271 - 0.586302i) q^{87} +(4.59284 - 7.63128i) q^{88} +2.56421 q^{89} +(8.33692 + 4.52722i) q^{90} +(1.65650 - 1.65650i) q^{91} +(-7.12942 - 8.70867i) q^{92} +(1.54539 + 0.669549i) q^{93} +(-0.384976 + 0.812693i) q^{94} +(-15.9539 - 0.363837i) q^{95} +(-4.87518 - 8.49898i) q^{96} +8.52709i q^{97} +(-7.74385 - 3.66830i) q^{98} +(0.304955 - 9.44214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 8 q^{4} - 4 q^{6}+O(q^{10}) \) 80 * q - 8 * q^4 - 4 * q^6	\( 80 q - 8 q^{4} - 4 q^{6} + 16 q^{10} - 32 q^{16} + 16 q^{19} + 8 q^{21} - 56 q^{24} + 8 q^{30} - 16 q^{34} - 40 q^{36} - 8 q^{39} - 8 q^{40} - 12 q^{45} - 24 q^{46} - 112 q^{49} + 32 q^{51} + 60 q^{54} - 40 q^{55} + 40 q^{60} + 16 q^{61} - 32 q^{64} - 56 q^{66} - 40 q^{69} + 48 q^{70} - 36 q^{75} - 128 q^{76} + 64 q^{81} + 128 q^{84} - 64 q^{85} + 72 q^{90} + 48 q^{91} + 56 q^{94} - 24 q^{96} - 8 q^{99}+O(q^{100}) \) 80 * q - 8 * q^4 - 4 * q^6 + 16 * q^10 - 32 * q^16 + 16 * q^19 + 8 * q^21 - 56 * q^24 + 8 * q^30 - 16 * q^34 - 40 * q^36 - 8 * q^39 - 8 * q^40 - 12 * q^45 - 24 * q^46 - 112 * q^49 + 32 * q^51 + 60 * q^54 - 40 * q^55 + 40 * q^60 + 16 * q^61 - 32 * q^64 - 56 * q^66 - 40 * q^69 + 48 * q^70 - 36 * q^75 - 128 * q^76 + 64 * q^81 + 128 * q^84 - 64 * q^85 + 72 * q^90 + 48 * q^91 + 56 * q^94 - 24 * q^96 - 8 * q^99

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