LMFDB - Embedded newform 315.2.t.b.131.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(101,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("315.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.t (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.3
Character	$\chi$	$=$	315.131
Dual form			315.2.t.b.101.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16248i q^{2} +(1.73205 + 0.000611122i) q^{3} -2.67633 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.00132154 - 3.74553i) q^{6} +(-0.841895 - 2.50823i) q^{7} +1.46255i q^{8} +(3.00000 + 0.00211699i) q^{9} +O(q^{10})$	\(q-2.16248i q^{2} +(1.73205 + 0.000611122i) q^{3} -2.67633 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.00132154 - 3.74553i) q^{6} +(-0.841895 - 2.50823i) q^{7} +1.46255i q^{8} +(3.00000 + 0.00211699i) q^{9} +(1.87276 - 1.08124i) q^{10} +(-1.49532 - 0.863325i) q^{11} +(-4.63554 - 0.00163557i) q^{12} +(2.89037 + 1.66875i) q^{13} +(-5.42400 + 1.82058i) q^{14} +(0.865496 + 1.50031i) q^{15} -2.18991 q^{16} +(-2.47597 - 4.28850i) q^{17} +(0.00457795 - 6.48745i) q^{18} +(2.88684 + 1.66672i) q^{19} +(-1.33817 - 2.31777i) q^{20} +(-1.45667 - 4.34489i) q^{21} +(-1.86692 + 3.23361i) q^{22} +(2.31688 - 1.33765i) q^{23} +(-0.000893800 + 2.53322i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.60865 - 6.25037i) q^{26} +(5.19615 + 0.00550010i) q^{27} +(2.25319 + 6.71285i) q^{28} +(-4.72502 + 2.72799i) q^{29} +(3.24438 - 1.87162i) q^{30} +7.78166i q^{31} +7.66076i q^{32} +(-2.58945 - 1.49624i) q^{33} +(-9.27381 + 5.35423i) q^{34} +(1.75124 - 1.98322i) q^{35} +(-8.02899 - 0.00566577i) q^{36} +(-1.70041 + 2.94520i) q^{37} +(3.60425 - 6.24275i) q^{38} +(5.00524 + 2.89213i) q^{39} +(-1.26661 + 0.731277i) q^{40} +(0.394491 - 0.683278i) q^{41} +(-9.39576 + 3.15003i) q^{42} +(5.82305 + 10.0858i) q^{43} +(4.00198 + 2.31054i) q^{44} +(1.49817 + 2.59913i) q^{45} +(-2.89265 - 5.01022i) q^{46} +11.5373 q^{47} +(-3.79304 - 0.00133830i) q^{48} +(-5.58243 + 4.22333i) q^{49} +(1.87276 + 1.08124i) q^{50} +(-4.28588 - 7.42941i) q^{51} +(-7.73558 - 4.46614i) q^{52} +(-5.69516 + 3.28810i) q^{53} +(0.0118939 - 11.2366i) q^{54} -1.72665i q^{55} +(3.66842 - 1.23132i) q^{56} +(4.99914 + 2.88861i) q^{57} +(5.89923 + 10.2178i) q^{58} -10.9119 q^{59} +(-2.31635 - 4.01531i) q^{60} -6.45410i q^{61} +16.8277 q^{62} +(-2.52037 - 7.52647i) q^{63} +12.1864 q^{64} +3.33751i q^{65} +(-3.23558 + 5.59963i) q^{66} -2.12417 q^{67} +(6.62651 + 11.4774i) q^{68} +(4.01378 - 2.31547i) q^{69} +(-4.28867 - 3.78703i) q^{70} -1.34885i q^{71} +(-0.00309621 + 4.38766i) q^{72} +(2.68498 - 1.55018i) q^{73} +(6.36895 + 3.67712i) q^{74} +(-0.866555 + 1.49969i) q^{75} +(-7.72615 - 4.46069i) q^{76} +(-0.906511 + 4.47744i) q^{77} +(6.25419 - 10.8237i) q^{78} +13.6185 q^{79} +(-1.09496 - 1.89652i) q^{80} +(8.99999 + 0.0127019i) q^{81} +(-1.47758 - 0.853079i) q^{82} +(-4.95763 - 8.58686i) q^{83} +(3.89854 + 11.6284i) q^{84} +(2.47597 - 4.28850i) q^{85} +(21.8104 - 12.5922i) q^{86} +(-8.18564 + 4.72213i) q^{87} +(1.26266 - 2.18699i) q^{88} +(5.36098 - 9.28549i) q^{89} +(5.62058 - 3.23976i) q^{90} +(1.75223 - 8.65462i) q^{91} +(-6.20075 + 3.58001i) q^{92} +(-0.00475554 + 13.4782i) q^{93} -24.9492i q^{94} +3.33344i q^{95} +(-0.00468166 + 13.2688i) q^{96} +(-2.88709 + 1.66686i) q^{97} +(9.13288 + 12.0719i) q^{98} +(-4.48414 - 2.59314i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	$ 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	2.16248i		−	1.52911i	−0.644561	−	0.764553i	$-0.722960\pi$
$2$		−	2.16248i		−	1.52911i	0.644561	−	0.764553i	$-0.277040\pi$
$3$	1.73205		0.000611122i	1.00000		0.000352832i
$3$	1.73205		0.000611122i	1.00000		0.000352832i
$4$	−2.67633			−1.33817
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.00132154	−	3.74553i	0.000539517	−	1.52911i
$7$	−0.841895	−	2.50823i	−0.318206	−	0.948021i
$7$	−0.841895	−	2.50823i	−0.318206	−	0.948021i
$8$			1.46255i			0.517091i
$9$	3.00000	+	0.00211699i	1.00000	+	0.000705663i
$10$	1.87276	−	1.08124i	0.592220	−	0.341919i
$11$	−1.49532	−	0.863325i	−0.450857	−	0.260302i	0.257335	−	0.966322i	$-0.417156\pi$
$11$	−1.49532	−	0.863325i	−0.450857	−	0.260302i	−0.708192	+	0.706020i	$0.750489\pi$
$12$	−4.63554	−	0.00163557i	−1.33817	−	0.000472147i
$13$	2.89037	+	1.66875i	0.801643	+	0.462829i	0.844045	−	0.536272i	$-0.180168\pi$
$13$	2.89037	+	1.66875i	0.801643	+	0.462829i	−0.0424021	+	0.999101i	$0.513501\pi$
$14$	−5.42400	+	1.82058i	−1.44963	+	0.486571i
$15$	0.865496	+	1.50031i	0.223470	+	0.387377i
$16$	−2.18991			−0.547478
$17$	−2.47597	−	4.28850i	−0.600510	−	1.04011i	−0.992744	−	0.120248i	$-0.961631\pi$
$17$	−2.47597	−	4.28850i	−0.600510	−	1.04011i	0.392234	−	0.919866i	$-0.371702\pi$
$18$	0.00457795	−	6.48745i	0.00107903	−	1.52911i
$19$	2.88684	+	1.66672i	0.662287	+	0.382372i	0.793148	−	0.609029i	$-0.208441\pi$
$19$	2.88684	+	1.66672i	0.662287	+	0.382372i	−0.130861	+	0.991401i	$0.541774\pi$
$20$	−1.33817	−	2.31777i	−0.299223	−	0.518269i
$21$	−1.45667	−	4.34489i	−0.317872	−	0.948134i
$22$	−1.86692	+	3.23361i	−0.398030	+	0.689408i
$23$	2.31688	−	1.33765i	0.483104	−	0.278920i	−0.238605	−	0.971117i	$-0.576690\pi$
$23$	2.31688	−	1.33765i	0.483104	−	0.278920i	0.721709	+	0.692197i	$0.243357\pi$
$24$	−0.000893800		2.53322i	−0.000182446		0.517091i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.60865	−	6.25037i	0.707715	−	1.22580i
$27$	5.19615	+	0.00550010i	0.999999	+	0.00105849i
$28$	2.25319	+	6.71285i	0.425813	+	1.26861i
$29$	−4.72502	+	2.72799i	−0.877414	+	0.506575i	−0.869805	−	0.493396i	$-0.835755\pi$
$29$	−4.72502	+	2.72799i	−0.877414	+	0.506575i	−0.00760893	+	0.999971i	$0.502422\pi$
$30$	3.24438	−	1.87162i	0.592341	−	0.341710i
$31$			7.78166i			1.39763i	0.715304	+	0.698813i	$0.246288\pi$
$31$			7.78166i			1.39763i	−0.715304	+	0.698813i	$0.753712\pi$
$32$			7.66076i			1.35424i
$33$	−2.58945	−	1.49624i	−0.450765	−	0.260461i
$34$	−9.27381	+	5.35423i	−1.59044	+	0.918244i
$35$	1.75124	−	1.98322i	0.296014	−	0.335225i
$36$	−8.02899	−	0.00566577i	−1.33817	−	0.000944294i
$37$	−1.70041	+	2.94520i	−0.279546	+	0.484189i	−0.971272	−	0.237972i	$-0.923517\pi$
$37$	−1.70041	+	2.94520i	−0.279546	+	0.484189i	0.691726	+	0.722160i	$0.256851\pi$
$38$	3.60425	−	6.24275i	0.584687	−	1.01271i
$39$	5.00524	+	2.89213i	0.801480	+	0.463112i
$40$	−1.26661	+	0.731277i	−0.200269	+	0.115625i
$41$	0.394491	−	0.683278i	0.0616091	−	0.106710i	−0.833576	−	0.552405i	$-0.813710\pi$
$41$	0.394491	−	0.683278i	0.0616091	−	0.106710i	0.895185	+	0.445695i	$0.147043\pi$
$42$	−9.39576	+	3.15003i	−1.44980	+	0.486060i
$43$	5.82305	+	10.0858i	0.888006	+	1.53807i	0.842229	+	0.539120i	$0.181243\pi$
$43$	5.82305	+	10.0858i	0.888006	+	1.53807i	0.0457776	+	0.998952i	$0.485423\pi$
$44$	4.00198	+	2.31054i	0.603321	+	0.348327i
$45$	1.49817	+	2.59913i	0.223333	+	0.387456i
$46$	−2.89265	−	5.01022i	−0.426498	−	0.738717i
$47$	11.5373			1.68289			0.841444	−	0.540345i	$-0.181706\pi$
$47$	11.5373			1.68289			0.841444	+	0.540345i	$0.181706\pi$
$48$	−3.79304	−	0.00133830i	−0.547478	−	0.000193168i
$49$	−5.58243	+	4.22333i	−0.797489	+	0.603333i
$50$	1.87276	+	1.08124i	0.264849	+	0.152911i
$51$	−4.28588	−	7.42941i	−0.600143	−	1.04033i
$52$	−7.73558	−	4.46614i	−1.07273	−	0.619342i
$53$	−5.69516	+	3.28810i	−0.782290	+	0.451656i	−0.837241	−	0.546833i	$-0.815833\pi$
$53$	−5.69516	+	3.28810i	−0.782290	+	0.451656i	0.0549510	+	0.998489i	$0.482500\pi$
$54$	0.0118939	−	11.2366i	0.00161855	−	1.52911i
$55$		−	1.72665i		−	0.232821i
$56$	3.66842	−	1.23132i	0.490214	−	0.164542i
$57$	4.99914	+	2.88861i	0.662152	+	0.382605i
$58$	5.89923	+	10.2178i	0.774607	+	1.34166i
$59$	−10.9119			−1.42061			−0.710306	−	0.703893i	$-0.751443\pi$
$59$	−10.9119			−1.42061			−0.710306	+	0.703893i	$0.751443\pi$
$60$	−2.31635	−	4.01531i	−0.299040	−	0.518375i
$61$		−	6.45410i		−	0.826363i	−0.910649	−	0.413182i	$-0.864418\pi$
$61$		−	6.45410i		−	0.826363i	0.910649	−	0.413182i	$-0.135582\pi$
$62$	16.8277			2.13712
$63$	−2.52037	−	7.52647i	−0.317537	−	0.948246i
$64$	12.1864			1.52330
$65$			3.33751i			0.413967i
$66$	−3.23558	+	5.59963i	−0.398273	+	0.689267i
$67$	−2.12417			−0.259508			−0.129754	−	0.991546i	$-0.541419\pi$
$67$	−2.12417			−0.259508			−0.129754	+	0.991546i	$0.541419\pi$
$68$	6.62651	+	11.4774i	0.803582	+	1.39184i
$69$	4.01378	−	2.31547i	0.483202	−	0.278750i
$70$	−4.28867	−	3.78703i	−0.512594	−	0.452637i
$71$		−	1.34885i		−	0.160079i	−0.996792	−	0.0800395i	$-0.974495\pi$
$71$		−	1.34885i		−	0.160079i	0.996792	−	0.0800395i	$-0.0255047\pi$
$72$	−0.00309621	+	4.38766i	−0.000364892	+	0.517091i
$73$	2.68498	−	1.55018i	0.314254	−	0.181434i	−0.334575	−	0.942369i	$-0.608593\pi$
$73$	2.68498	−	1.55018i	0.314254	−	0.181434i	0.648828	+	0.760935i	$0.275259\pi$
$74$	6.36895	+	3.67712i	0.740376	+	0.427456i
$75$	−0.866555	+	1.49969i	−0.100061	+	0.173170i
$76$	−7.72615	−	4.46069i	−0.886250	−	0.511677i
$77$	−0.906511	+	4.47744i	−0.103307	+	0.510252i
$78$	6.25419	−	10.8237i	0.708147	−	1.22555i
$79$	13.6185			1.53220			0.766098	−	0.642724i	$-0.222196\pi$
$79$	13.6185			1.53220			0.766098	+	0.642724i	$0.222196\pi$
$80$	−1.09496	−	1.89652i	−0.122420	−	0.212037i
$81$	8.99999	+	0.0127019i	0.999999	+	0.00141133i
$82$	−1.47758	−	0.853079i	−0.163171	−	0.0942069i
$83$	−4.95763	−	8.58686i	−0.544170	−	0.942531i	−0.998659	−	0.0517780i	$-0.983511\pi$
$83$	−4.95763	−	8.58686i	−0.544170	−	0.942531i	0.454488	−	0.890753i	$-0.349822\pi$
$84$	3.89854	+	11.6284i	0.425365	+	1.26876i
$85$	2.47597	−	4.28850i	0.268556	−	0.465153i
$86$	21.8104	−	12.5922i	2.35188	−	1.35786i
$87$	−8.18564	+	4.72213i	−0.877592	+	0.506265i
$88$	1.26266	−	2.18699i	0.134600	−	0.233134i
$89$	5.36098	−	9.28549i	0.568263	−	0.984260i	−0.428475	−	0.903554i	$-0.640949\pi$
$89$	5.36098	−	9.28549i	0.568263	−	0.984260i	0.996738	−	0.0807066i	$-0.0257177\pi$
$90$	5.62058	−	3.23976i	0.592461	−	0.341501i
$91$	1.75223	−	8.65462i	0.183684	−	0.907250i
$92$	−6.20075	+	3.58001i	−0.646473	+	0.373241i
$93$	−0.00475554	+	13.4782i	−0.000493127	+	1.39763i
$94$		−	24.9492i		−	2.57331i
$95$			3.33344i			0.342004i
$96$	−0.00468166	+	13.2688i	−0.000477820	+	1.35424i
$97$	−2.88709	+	1.66686i	−0.293139	+	0.169244i	−0.639357	−	0.768910i	$-0.720799\pi$
$97$	−2.88709	+	1.66686i	−0.293139	+	0.169244i	0.346217	+	0.938154i	$0.387466\pi$
$98$	9.13288	+	12.0719i	0.922560	+	1.21945i
$99$	−4.48414	−	2.59314i	−0.450673	−	0.260620i
$100$	1.33817	−	2.31777i	0.133817	−	0.231777i
$101$	−5.42443	+	9.39538i	−0.539751	+	0.934876i	0.459166	+	0.888350i	$0.348148\pi$
$101$	−5.42443	+	9.39538i	−0.539751	+	0.934876i	−0.998917	+	0.0465253i	$0.985185\pi$
$102$	−16.0660	+	9.26814i	−1.59077	+	0.917682i
$103$	−10.0637	+	5.81029i	−0.991608	+	0.572505i	−0.905755	−	0.423803i	$-0.860695\pi$
$103$	−10.0637	+	5.81029i	−0.991608	+	0.572505i	−0.0858535	+	0.996308i	$0.527362\pi$
$104$	−2.44064	+	4.22732i	−0.239325	+	0.414523i
$105$	3.03445	−	3.43396i	0.296132	−	0.335120i
$106$	7.11046	+	12.3157i	0.690629	+	1.19621i
$107$	3.90865	+	2.25666i	0.377863	+	0.218159i	0.676888	−	0.736086i	$-0.263328\pi$
$107$	3.90865	+	2.25666i	0.377863	+	0.218159i	−0.299025	+	0.954245i	$0.596661\pi$
$108$	−13.9066	−	0.0147201i	−1.33816	−	0.00141644i
$109$	−3.20833	−	5.55699i	−0.307302	−	0.532263i	0.670469	−	0.741938i	$-0.266093\pi$
$109$	−3.20833	−	5.55699i	−0.307302	−	0.532263i	−0.977771	+	0.209674i	$0.932760\pi$
$110$	−3.73385			−0.356009
$111$	−2.94700	+	5.10020i	−0.279717	+	0.484090i
$112$	1.84368	+	5.49280i	0.174211	+	0.519021i
$113$	−9.22896	−	5.32834i	−0.868188	−	0.501248i	−0.00144211	−	0.999999i	$-0.500459\pi$
$113$	−9.22896	−	5.32834i	−0.868188	−	0.501248i	−0.866746	+	0.498751i	$0.833792\pi$
$114$	6.24656	−	10.8106i	0.585044	−	1.01250i
$115$	2.31688	+	1.33765i	0.216051	+	0.124737i
$116$	12.6457	−	7.30101i	1.17412	−	0.677881i
$117$	8.66756	+	5.01238i	0.801317	+	0.463395i
$118$			23.5968i			2.17227i
$119$	−8.67203	+	9.82076i	−0.794964	+	0.900267i
$120$	−2.19428	+	1.26584i	−0.200309	+	0.115554i
$121$	−4.00934	−	6.94438i	−0.364486	−	0.631307i
$122$	−13.9569			−1.26360
$123$	0.683695	−	1.18323i	0.0616467	−	0.106688i
$124$		−	20.8263i		−	1.87026i
$125$	−1.00000			−0.0894427
$126$	−16.2759	+	5.45027i	−1.44997	+	0.485548i
$127$	9.18737			0.815247			0.407623	−	0.913150i	$-0.366358\pi$
$127$	9.18737			0.815247			0.407623	+	0.913150i	$0.366358\pi$
$128$		−	11.0314i		−	0.975050i
$129$	10.0796	+	17.4727i	0.887464	+	1.53839i
$130$	7.21730			0.632999
$131$	4.48390	+	7.76635i	0.391760	+	0.678549i	0.992682	−	0.120759i	$-0.0385329\pi$
$131$	4.48390	+	7.76635i	0.391760	+	0.678549i	−0.600921	+	0.799308i	$0.705200\pi$
$132$	6.93022	+	4.00442i	0.603198	+	0.348540i
$133$	1.75009	−	8.64407i	0.151752	−	0.749536i
$134$			4.59347i			0.396816i
$135$	2.59331	+	4.50275i	0.223197	+	0.387535i
$136$	6.27217	−	3.62124i	0.537834	−	0.310518i
$137$	3.93052	+	2.26929i	0.335807	+	0.193878i	0.658416	−	0.752654i	$-0.271227\pi$
$137$	3.93052	+	2.26929i	0.335807	+	0.193878i	−0.322609	+	0.946532i	$0.604560\pi$
$138$	−5.00716	−	8.67973i	−0.426238	−	0.738867i
$139$	−17.8922	−	10.3300i	−1.51759	−	0.876182i	−0.999786	−	0.0206846i	$-0.993415\pi$
$139$	−17.8922	−	10.3300i	−1.51759	−	0.876182i	−0.517806	−	0.855498i	$-0.673251\pi$
$140$	−4.68691	+	5.30775i	−0.396116	+	0.448586i
$141$	19.9832	+	0.00705070i	1.68289	+	0.000593776i
$142$	−2.91687			−0.244778
$143$	−2.88135	−	4.99065i	−0.240951	−	0.417339i
$144$	−6.56974	−	0.00463602i	−0.547478	−	0.000386335i
$145$	−4.72502	−	2.72799i	−0.392391	−	0.226547i
$146$	−3.35223	−	5.80623i	−0.277432	−	0.480527i
$147$	−9.67162	+	7.31161i	−0.797702	+	0.603052i
$148$	4.55087	−	7.88234i	0.374079	−	0.647925i
$149$	−11.7075	+	6.75934i	−0.959117	+	0.553747i	−0.895901	−	0.444253i	$-0.853469\pi$
$149$	−11.7075	+	6.75934i	−0.959117	+	0.553747i	−0.0632161	+	0.998000i	$0.520136\pi$
$150$	3.24306	+	1.87391i	0.264795	+	0.153004i
$151$	9.87326	−	17.1010i	0.803475	−	1.39166i	−0.113841	−	0.993499i	$-0.536316\pi$
$151$	9.87326	−	17.1010i	0.803475	−	1.39166i	0.917316	−	0.398160i	$-0.130351\pi$
$152$	−2.43767	+	4.22217i	−0.197721	+	0.342463i
$153$	−7.41882	−	12.8707i	−0.599776	−	1.04054i
$154$	9.68238	+	1.96032i	0.780229	+	0.157967i
$155$	−6.73911	+	3.89083i	−0.541299	+	0.312519i
$156$	−13.3957	−	7.74031i	−1.07251	−	0.619720i
$157$			5.68853i			0.453994i	0.973895	+	0.226997i	$0.0728908\pi$
$157$			5.68853i			0.453994i	−0.973895	+	0.226997i	$0.927109\pi$
$158$		−	29.4497i		−	2.34289i
$159$	−9.86632	+	5.69168i	−0.782450	+	0.451380i
$160$	−6.63441	+	3.83038i	−0.524496	+	0.302818i
$161$	−5.30572	−	4.68511i	−0.418149	−	0.369239i
$162$	0.0274677	−	19.4623i	0.00215807	−	1.52910i
$163$	−7.27331	+	12.5977i	−0.569689	+	0.986731i	0.426907	+	0.904296i	$0.359603\pi$
$163$	−7.27331	+	12.5977i	−0.569689	+	0.986731i	−0.996596	+	0.0824356i	$0.973730\pi$
$164$	−1.05579	+	1.82868i	−0.0824432	+	0.142796i
$165$	0.00105519	−	2.99064i	8.21467e−5	−	0.232821i
$166$	−18.5689	+	10.7208i	−1.44123	+	0.832094i
$167$	7.00178	−	12.1274i	0.541814	−	0.938450i	−0.456986	−	0.889474i	$-0.651071\pi$
$167$	7.00178	−	12.1274i	0.541814	−	0.938450i	0.998800	−	0.0489756i	$-0.0155956\pi$
$168$	6.35465	−	2.13046i	0.490272	−	0.164369i
$169$	−0.930521	−	1.61171i	−0.0715785	−	0.123978i
$170$	−9.27381	−	5.35423i	−0.711268	−	0.410651i
$171$	8.65700	+	5.00627i	0.662017	+	0.382839i
$172$	−15.5844	−	26.9930i	−1.18830	−	2.05820i
$173$	−0.416489			−0.0316651			−0.0158325	−	0.999875i	$-0.505040\pi$
$173$	−0.416489			−0.0316651			−0.0158325	+	0.999875i	$0.505040\pi$
$174$	10.2115	+	17.7013i	0.774134	+	1.34193i
$175$	2.59314	+	0.525012i	0.196023	+	0.0396872i
$176$	3.27463	+	1.89061i	0.246834	+	0.142510i
$177$	−18.9000	−	0.00666852i	−1.42061	−	0.000501237i
$178$	−20.0797	−	11.5930i	−1.50504	−	0.868934i
$179$	−18.9614	+	10.9474i	−1.41724	+	0.818246i	−0.996056	−	0.0887272i	$-0.971720\pi$
$179$	−18.9614	+	10.9474i	−1.41724	+	0.818246i	−0.421188	+	0.906973i	$0.638387\pi$
$180$	−4.00959	−	6.95614i	−0.298857	−	0.518480i
$181$		−	4.86189i		−	0.361382i	−0.983540	−	0.180691i	$-0.942167\pi$
$181$		−	4.86189i		−	0.361382i	0.983540	−	0.180691i	$-0.0578333\pi$
$182$	−18.7155	−	3.78917i	−1.38728	−	0.280872i
$183$	0.00394425	−	11.1788i	0.000291567	−	0.826363i
$184$	1.95639	+	3.38857i	0.144227	+	0.249809i
$185$	−3.40083			−0.250034
$186$	29.1464	+	0.0102838i	2.13712	+	0.000754043i
$187$			8.55025i			0.625256i
$188$	−30.8776			−2.25198
$189$	−4.36082	−	13.0378i	−0.317203	−	0.948358i
$190$	7.20850			0.522960
$191$			1.07558i			0.0778264i	0.999243	+	0.0389132i	$0.0123896\pi$
$191$			1.07558i			0.0778264i	−0.999243	+	0.0389132i	$0.987610\pi$
$192$	21.1075	+	0.00744740i	1.52330	+	0.000537470i
$193$	8.64191			0.622058			0.311029	−	0.950400i	$-0.399326\pi$
$193$	8.64191			0.622058			0.311029	+	0.950400i	$0.399326\pi$
$194$	3.60456	+	6.24327i	0.258792	+	0.448241i
$195$	−0.00203963	+	5.78073i	−0.000146061	+	0.413967i
$196$	14.9404	−	11.3030i	1.06717	−	0.807360i
$197$			2.66589i			0.189937i	0.995480	+	0.0949685i	$0.0302750\pi$
$197$			2.66589i			0.189937i	−0.995480	+	0.0949685i	$0.969725\pi$
$198$	−5.60762	+	9.69687i	−0.398516	+	0.689127i
$199$	−17.1929	+	9.92633i	−1.21877	+	0.703659i	−0.964655	−	0.263515i	$-0.915118\pi$
$199$	−17.1929	+	9.92633i	−1.21877	+	0.703659i	−0.254117	+	0.967173i	$0.581785\pi$
$200$	−1.26661	−	0.731277i	−0.0895628	−	0.0517091i
$201$	−3.67916	−	0.00129813i	−0.259508	−	9.15627e-5i
$202$	20.3174	+	11.7302i	1.42952	+	0.825336i
$203$	10.8204	+	9.55474i	0.759443	+	0.670612i
$204$	11.4704	+	19.8836i	0.803091	+	1.39213i
$205$	0.788981			0.0551049
$206$	12.5647	+	21.7626i	0.875421	+	1.51627i
$207$	6.95348	−	4.00806i	0.483301	−	0.278579i
$208$	−6.32965	−	3.65443i	−0.438882	−	0.253389i
$209$	−2.87784	−	4.98457i	−0.199064	−	0.344790i
$210$	−7.42588	−	6.56195i	−0.512435	−	0.452818i
$211$	−4.78399	+	8.28611i	−0.329343	+	0.570439i	−0.982382	−	0.186886i	$-0.940161\pi$
$211$	−4.78399	+	8.28611i	−0.329343	+	0.570439i	0.653039	+	0.757325i	$0.273494\pi$
$212$	15.2421	−	8.80005i	1.04683	−	0.604390i
$213$	0.000824313	−	2.33628i	5.64810e−5	−	0.160079i
$214$	4.87999	−	8.45238i	0.333589	−	0.577793i
$215$	−5.82305	+	10.0858i	−0.397129	+	0.687847i
$216$	−0.00804420	+	7.59965i	−0.000547338	+	0.517091i
$217$	19.5182	−	6.55134i	1.32498	−	0.444734i
$218$	−12.0169	+	6.93796i	−0.813887	+	0.469898i
$219$	4.65147	−	2.68334i	0.314317	−	0.181323i
$220$			4.62109i			0.311554i
$221$		−	16.5271i		−	1.11173i
$222$	11.0291	+	6.37284i	0.740225	+	0.427717i
$223$	11.9147	−	6.87897i	0.797870	−	0.460650i	−0.0448561	−	0.998993i	$-0.514283\pi$
$223$	11.9147	−	6.87897i	0.797870	−	0.460650i	0.842726	+	0.538343i	$0.180950\pi$
$224$	19.2149	−	6.44956i	1.28385	−	0.430929i
$225$	−1.50183	+	2.59702i	−0.100122	+	0.173134i
$226$	−11.5225	+	19.9575i	−0.766462	+	1.32755i
$227$	14.4399	−	25.0106i	0.958409	−	1.66001i	0.232043	−	0.972705i	$-0.425459\pi$
$227$	14.4399	−	25.0106i	0.958409	−	1.66001i	0.726366	−	0.687308i	$-0.241208\pi$
$228$	−13.3794	−	7.73087i	−0.886069	−	0.511989i
$229$	−5.66530	+	3.27086i	−0.374374	+	0.216145i	−0.675368	−	0.737481i	$-0.736015\pi$
$229$	−5.66530	+	3.27086i	−0.374374	+	0.216145i	0.300994	+	0.953626i	$0.402682\pi$
$230$	2.89265	−	5.01022i	0.190736	−	0.330364i
$231$	−1.57286	+	7.75460i	−0.103487	+	0.510215i
$232$	−3.98984	−	6.91060i	−0.261946	−	0.453703i
$233$	−18.1428	−	10.4747i	−1.18857	−	0.686222i	−0.230589	−	0.973051i	$-0.574065\pi$
$233$	−18.1428	−	10.4747i	−1.18857	−	0.686222i	−0.957982	+	0.286829i	$0.907399\pi$
$234$	10.8392	−	18.7435i	0.708580	−	1.22530i
$235$	5.76865	+	9.99159i	0.376305	+	0.651779i
$236$	29.2039			1.90101
$237$	23.5879	+	0.00832254i	1.53220	+	0.000540607i
$238$	21.2372	+	18.7531i	1.37660	+	1.21558i
$239$	25.6748	+	14.8234i	1.66077	+	0.958844i	0.972350	+	0.233528i	$0.0750272\pi$
$239$	25.6748	+	14.8234i	1.66077	+	0.958844i	0.688417	+	0.725316i	$0.258306\pi$
$240$	−1.89536	−	3.28554i	−0.122345	−	0.212081i
$241$	−3.73006	−	2.15355i	−0.240274	−	0.138722i	0.375028	−	0.927013i	$-0.377633\pi$
$241$	−3.73006	−	2.15355i	−0.240274	−	0.138722i	−0.615303	+	0.788291i	$0.710966\pi$
$242$	−15.0171	+	8.67013i	−0.965336	+	0.557337i
$243$	15.5884	+	0.0275005i	0.999998	+	0.00176416i
$244$			17.2733i			1.10581i
$245$	−6.44873	−	2.72286i	−0.411994	−	0.173957i
$246$	−2.55872	−	1.47848i	−0.163138	−	0.0942644i
$247$	5.56269	+	9.63486i	0.353945	+	0.613051i
$248$	−11.3811			−0.722701
$249$	−8.58162	−	14.8759i	−0.543838	−	0.942723i
$250$			2.16248i			0.136767i
$251$	−13.7433			−0.867471			−0.433735	−	0.901040i	$-0.642805\pi$
$251$	−13.7433			−0.867471			−0.433735	+	0.901040i	$0.642805\pi$
$252$	6.74536	+	20.1433i	0.424918	+	1.26891i
$253$	−4.61932			−0.290414
$254$		−	19.8675i		−	1.24660i
$255$	4.29112	−	7.42639i	0.268720	−	0.465058i
$256$	0.517586			0.0323491
$257$	1.41010	+	2.44237i	0.0879597	+	0.152351i	0.906649	−	0.421887i	$-0.138632\pi$
$257$	1.41010	+	2.44237i	0.0879597	+	0.152351i	−0.818689	+	0.574237i	$0.805299\pi$
$258$	37.7844	−	21.7971i	2.35235	−	1.35703i
$259$	8.81882	+	1.78548i	0.547975	+	0.110944i
$260$		−	8.93228i		−	0.553956i
$261$	−14.1808	+	8.17397i	−0.877771	+	0.505956i
$262$	16.7946	−	9.69636i	1.03757	−	0.599043i
$263$	16.0019	+	9.23871i	0.986721	+	0.569683i	0.904292	−	0.426914i	$-0.140399\pi$
$263$	16.0019	+	9.23871i	0.986721	+	0.569683i	0.0824282	+	0.996597i	$0.473732\pi$
$264$	2.18833	−	3.78721i	0.134682	−	0.233086i
$265$	−5.69516	−	3.28810i	−0.349851	−	0.201987i
$266$	−18.6926	−	3.78455i	−1.14612	−	0.232046i
$267$	9.29117	−	16.0797i	0.568610	−	0.984060i
$268$	5.68497			0.347265
$269$	−9.72956	−	16.8521i	−0.593222	−	1.02749i	−0.993795	−	0.111225i	$-0.964522\pi$
$269$	−9.72956	−	16.8521i	−0.593222	−	1.02749i	0.400573	−	0.916265i	$-0.368811\pi$
$270$	9.73711	−	5.60799i	0.592582	−	0.341291i
$271$	16.5777	+	9.57111i	1.00702	+	0.581404i	0.910318	−	0.413910i	$-0.135837\pi$
$271$	16.5777	+	9.57111i	1.00702	+	0.581404i	0.0967028	+	0.995313i	$0.469170\pi$
$272$	5.42215	+	9.39144i	0.328766	+	0.569440i
$273$	3.04024	−	14.9892i	0.184004	−	0.907185i
$274$	4.90730	−	8.49969i	0.296461	−	0.513485i
$275$	1.49532	−	0.863325i	0.0901713	−	0.0520604i
$276$	−10.7422	+	6.19696i	−0.646605	+	0.373013i
$277$	−13.0108	+	22.5354i	−0.781745	+	1.35402i	0.149180	+	0.988810i	$0.452337\pi$
$277$	−13.0108	+	22.5354i	−0.781745	+	1.35402i	−0.930925	+	0.365212i	$0.880997\pi$
$278$	−22.3385	+	38.6915i	−1.33978	+	2.32056i
$279$	−0.0164737	+	23.3450i	−0.000986254	+	1.39763i
$280$	2.90056	+	2.56129i	0.173342	+	0.153066i
$281$	−19.5500	+	11.2872i	−1.16626	+	0.673338i	−0.952795	−	0.303614i	$-0.901807\pi$
$281$	−19.5500	+	11.2872i	−1.16626	+	0.673338i	−0.213460	+	0.976952i	$0.568473\pi$
$282$	0.0152470	−	43.2133i	0.000907946	−	2.57331i
$283$		−	10.6713i		−	0.634342i	−0.948368	−	0.317171i	$-0.897267\pi$
$283$		−	10.6713i		−	0.634342i	0.948368	−	0.317171i	$-0.102733\pi$
$284$			3.60997i			0.214212i
$285$	−0.00203714	+	5.77369i	−0.000120670	+	0.342004i
$286$	−10.7922	+	6.23088i	−0.638156	+	0.368439i
$287$	−2.04594	−	0.414225i	−0.120768	−	0.0244509i
$288$	−0.0162177	+	22.9823i	−0.000955640	+	1.35424i
$289$	−3.76082	+	6.51393i	−0.221225	+	0.383172i
$290$	−5.89923	+	10.2178i	−0.346415	+	0.600008i
$291$	−5.00160	+	2.88532i	−0.293199	+	0.169141i
$292$	−7.18590	+	4.14878i	−0.420523	+	0.242789i
$293$	−0.0874653	+	0.151494i	−0.00510978	+	0.00885040i	−0.868569	−	0.495568i	$-0.834960\pi$
$293$	−0.0874653	+	0.151494i	−0.00510978	+	0.00885040i	0.863459	+	0.504419i	$0.168293\pi$
$294$	15.8112	+	20.9147i	0.922130	+	1.21977i
$295$	−5.45596	−	9.45000i	−0.317658	−	0.550200i
$296$	−4.30752	−	2.48695i	−0.250370	−	0.144551i
$297$	−7.76517	−	4.49419i	−0.450581	−	0.260779i
$298$	14.6170	+	25.3173i	0.846737	+	1.46659i
$299$	8.92886			0.516369
$300$	2.31919	−	4.01368i	0.133898	−	0.231730i
$301$	20.3951	−	23.0967i	1.17556	−	1.33127i
$302$	−36.9806	−	21.3508i	−2.12799	−	1.22860i
$303$	−9.40112	+	16.2700i	−0.540081	+	0.934685i
$304$	−6.32193	−	3.64997i	−0.362588	−	0.209340i
$305$	5.58942	−	3.22705i	0.320049	−	0.184780i
$306$	−27.8327	+	16.0431i	−1.59109	+	0.917121i
$307$		−	29.6519i		−	1.69232i	−0.532928	−	0.846161i	$-0.678908\pi$
$307$		−	29.6519i		−	1.69232i	0.532928	−	0.846161i	$-0.321092\pi$
$308$	2.42612	−	11.9831i	0.138241	−	0.682801i
$309$	−17.4344	+	10.0576i	−0.991810	+	0.572155i
$310$	8.41385	+	14.5732i	0.477874	+	0.827703i
$311$	−2.22083			−0.125932			−0.0629660	−	0.998016i	$-0.520056\pi$
$311$	−2.22083			−0.125932			−0.0629660	+	0.998016i	$0.520056\pi$
$312$	−4.22990	+	7.32044i	−0.239471	+	0.414438i
$313$		−	27.3039i		−	1.54331i	−0.636044	−	0.771653i	$-0.719430\pi$
$313$		−	27.3039i		−	1.54331i	0.636044	−	0.771653i	$-0.280570\pi$
$314$	12.3014			0.694205
$315$	5.25792	−	5.94594i	0.296250	−	0.335016i
$316$	−36.4475			−2.05033
$317$			15.1285i			0.849699i	0.905264	+	0.424849i	$0.139673\pi$
$317$			15.1285i			0.849699i	−0.905264	+	0.424849i	$0.860327\pi$
$318$	12.3082	+	21.3357i	0.690207	+	1.19645i
$319$	9.42056			0.527450
$320$	6.09322	+	10.5538i	0.340621	+	0.589973i
$321$	6.76860	+	3.91104i	0.377786	+	0.218293i
$322$	−10.1315	+	11.4735i	−0.564605	+	0.639394i
$323$		−	16.5070i		−	0.918472i
$324$	−24.0870	−	0.0339946i	−1.33816	−	0.00188859i
$325$	−2.89037	+	1.66875i	−0.160329	+	0.0925658i
$326$	27.2424	+	15.7284i	1.50882	+	0.871116i
$327$	−5.55359	−	9.62695i	−0.307114	−	0.532371i
$328$	0.999332	+	0.576964i	0.0551789	+	0.0318575i
$329$	−9.71319	−	28.9382i	−0.535506	−	1.59541i
$330$	−6.46722	−	0.00228184i	−0.356009	−	0.000125611i
$331$	−22.7606			−1.25104			−0.625518	−	0.780210i	$-0.715112\pi$
$331$	−22.7606			−1.25104			−0.625518	+	0.780210i	$0.715112\pi$
$332$	13.2683	+	22.9813i	0.728190	+	1.26126i
$333$	−5.10748	+	8.83201i	−0.279888	+	0.483991i
$334$	−26.2254	−	15.1412i	−1.43499	−	0.828491i
$335$	−1.06208	−	1.83958i	−0.0580278	−	0.100507i
$336$	3.18999	+	9.51494i	0.174028	+	0.519083i
$337$	9.02581	−	15.6332i	0.491667	−	0.851592i	−0.508287	−	0.861188i	$-0.669721\pi$
$337$	9.02581	−	15.6332i	0.491667	−	0.851592i	0.999954	+	0.00959554i	$0.00305440\pi$
$338$	−3.48529	+	2.01224i	−0.189575	+	0.109451i
$339$	−15.9818	−	9.23460i	−0.868011	−	0.501555i
$340$	−6.62651	+	11.4774i	−0.359373	+	0.622452i
$341$	6.71810	−	11.6361i	0.363805	−	0.630129i
$342$	10.8260	−	18.7206i	0.585401	−	1.01229i
$343$	15.2929	+	10.4464i	0.825739	+	0.564052i
$344$	−14.7511	+	8.51653i	−0.795324	+	0.459180i
$345$	4.01214	+	2.31830i	0.216007	+	0.124813i
$346$			0.900650i			0.0484192i
$347$		−	7.77604i		−	0.417439i	−0.977975	−	0.208720i	$-0.933070\pi$
$347$		−	7.77604i		−	0.417439i	0.977975	−	0.208720i	$-0.0669296\pi$
$348$	21.9075	−	12.6380i	1.17436	−	0.677467i
$349$	23.4206	−	13.5219i	1.25368	−	0.723810i	0.281838	−	0.959462i	$-0.409056\pi$
$349$	23.4206	−	13.5219i	1.25368	−	0.723810i	0.971838	+	0.235652i	$0.0757225\pi$
$350$	1.13533	−	5.60762i	0.0606859	−	0.299740i
$351$	15.0096	+	8.68699i	0.801153	+	0.463677i
$352$	6.61372	−	11.4553i	0.352513	−	0.610570i
$353$	3.00946	−	5.21253i	0.160177	−	0.277435i	−0.774755	−	0.632262i	$-0.782127\pi$
$353$	3.00946	−	5.21253i	0.160177	−	0.277435i	0.934932	+	0.354827i	$0.115460\pi$
$354$	−0.0144206	+	40.8709i	−0.000766444	+	2.17227i
$355$	1.16814	−	0.674425i	0.0619984	−	0.0357948i
$356$	−14.3478	+	24.8511i	−0.760430	+	1.31710i
$357$	−15.0264	+	17.0047i	−0.795282	+	0.899987i
$358$	23.6735	+	41.0038i	1.25119	+	2.16712i
$359$	6.21974	+	3.59097i	0.328265	+	0.189524i	0.655071	−	0.755568i	$-0.272639\pi$
$359$	6.21974	+	3.59097i	0.328265	+	0.189524i	−0.326805	+	0.945092i	$0.605972\pi$
$360$	−3.80138	+	2.19115i	−0.200350	+	0.115484i
$361$	−3.94409	−	6.83137i	−0.207584	−	0.359546i
$362$	−10.5138			−0.552591
$363$	−6.94014	−	12.0305i	−0.364263	−	0.631436i
$364$	−4.68955	+	23.1626i	−0.245799	+	1.21405i
$365$	2.68498	+	1.55018i	0.140538	+	0.0811399i
$366$	−24.1740	−	0.00852936i	−1.26360	−	0.000445837i
$367$	−19.0195	−	10.9809i	−0.992809	−	0.573199i	−0.0866964	−	0.996235i	$-0.527631\pi$
$367$	−19.0195	−	10.9809i	−0.992809	−	0.573199i	−0.906113	+	0.423036i	$0.860964\pi$
$368$	−5.07378	+	2.92935i	−0.264489	+	0.152703i
$369$	1.18492	−	2.04900i	0.0616844	−	0.106667i
$370$			7.35423i			0.382328i
$371$	13.0420	+	11.5165i	0.677109	+	0.597908i
$372$	0.0127274	−	36.0722i	0.000659886	−	1.87026i
$373$	−18.4404	−	31.9397i	−0.954806	−	1.65377i	−0.734811	−	0.678272i	$-0.762729\pi$
$373$	−18.4404	−	31.9397i	−0.954806	−	1.65377i	−0.219995	−	0.975501i	$-0.570604\pi$
$374$	18.4898			0.956083
$375$	−1.73205		0.000611122i	−0.0894427		3.15582e-5i
$376$			16.8739i			0.870206i
$377$	−18.2094			−0.937831
$378$	−28.1939	+	9.43019i	−1.45014	+	0.485037i
$379$	7.89653			0.405618			0.202809	−	0.979218i	$-0.434993\pi$
$379$	7.89653			0.405618			0.202809	+	0.979218i	$0.434993\pi$
$380$		−	8.92139i		−	0.457657i
$381$	15.9130	+	0.00561460i	0.815247	+	0.000287645i
$382$	2.32593			0.119005
$383$	11.0758	+	19.1838i	0.565946	+	0.980247i	0.996961	+	0.0779021i	$0.0248221\pi$
$383$	11.0758	+	19.1838i	0.565946	+	0.980247i	−0.431015	+	0.902345i	$0.641845\pi$
$384$	0.00674155	−	19.1070i	0.000344028	−	0.975050i
$385$	−4.33083	+	1.45366i	−0.220720	+	0.0740853i
$386$		−	18.6880i		−	0.951193i
$387$	17.4478	+	30.2698i	0.886921	+	1.53870i
$388$	7.72680	−	4.46107i	0.392269	−	0.226477i
$389$	11.6628	+	6.73351i	0.591326	+	0.341402i	0.765622	−	0.643291i	$-0.222431\pi$
$389$	11.6628	+	6.73351i	0.591326	+	0.341402i	−0.174296	+	0.984693i	$0.555765\pi$
$390$	12.5007	+	0.00441066i	0.632999	+	0.000223342i
$391$	−11.4731	−	6.62397i	−0.580217	−	0.334989i
$392$	−6.17685	−	8.16460i	−0.311978	−	0.412375i
$393$	7.76160	+	13.4544i	0.391521	+	0.678687i
$394$	5.76495			0.290434
$395$	6.80923	+	11.7939i	0.342609	+	0.593417i
$396$	12.0010	+	6.94010i	0.603075	+	0.348753i
$397$	2.97013	+	1.71481i	0.149067	+	0.0860637i	0.572678	−	0.819780i	$-0.305904\pi$
$397$	2.97013	+	1.71481i	0.149067	+	0.0860637i	−0.423611	+	0.905844i	$0.639238\pi$
$398$	21.4655	+	37.1794i	1.07597	+	1.86363i
$399$	3.03654	−	14.9709i	0.152017	−	0.749482i
$400$	1.09496	−	1.89652i	0.0547478	−	0.0948260i
$401$	9.21467	−	5.32009i	0.460159	−	0.265673i	−0.251952	−	0.967740i	$-0.581073\pi$
$401$	9.21467	−	5.32009i	0.460159	−	0.265673i	0.712111	+	0.702067i	$0.247739\pi$
$402$	−0.00280717	+	7.95613i	−0.000140009	+	0.396816i
$403$	−12.9857	+	22.4918i	−0.646862	+	1.12040i
$404$	14.5176	−	25.1452i	0.722276	−	1.25102i
$405$	4.48900	+	7.80057i	0.223060	+	0.387614i
$406$	20.6620	−	23.3989i	1.02544	−	1.16127i
$407$	5.08533	−	2.93602i	0.252071	−	0.145533i
$408$	10.8659	−	6.26833i	0.537943	−	0.310329i
$409$			8.67681i			0.429041i	0.976720	+	0.214520i	$0.0688188\pi$
$409$			8.67681i			0.429041i	−0.976720	+	0.214520i	$0.931181\pi$
$410$		−	1.70616i		−	0.0842612i
$411$	6.80648	+	3.93293i	0.335739	+	0.193997i
$412$	26.9339	−	15.5503i	1.32694	−	0.766107i
$413$	9.18670	+	27.3696i	0.452048	+	1.34677i
$414$	−8.66735	−	15.0368i	−0.425977	−	0.739018i
$415$	4.95763	−	8.58686i	0.243360	−	0.421513i
$416$	−12.7839	+	22.1424i	−0.626783	+	1.08562i
$417$	−30.9838	−	17.9031i	−1.51728	−	0.876718i
$418$	−10.7790	+	6.22328i	−0.527220	+	0.304391i
$419$	9.02520	−	15.6321i	0.440910	−	0.763678i	−0.556848	−	0.830615i	$-0.687989\pi$
$419$	9.02520	−	15.6321i	0.440910	−	0.763678i	0.997757	+	0.0669367i	$0.0213226\pi$
$420$	−8.12120	+	9.19042i	−0.396274	+	0.448447i
$421$	−14.6491	−	25.3730i	−0.713953	−	1.23660i	−0.963362	−	0.268204i	$-0.913570\pi$
$421$	−14.6491	−	25.3730i	−0.713953	−	1.23660i	0.249409	−	0.968398i	$-0.419764\pi$
$422$	17.9186	+	10.3453i	0.872262	+	0.503601i
$423$	34.6119	+	0.0244243i	1.68289	+	0.00118755i
$424$	−4.80903	−	8.32948i	−0.233547	−	0.404515i
$425$	4.95193			0.240204
$426$	−5.05216	−	0.00178256i	−0.244778	−	8.63654e-5i
$427$	−16.1884	+	5.43368i	−0.783410	+	0.262954i
$428$	−10.4608	−	6.03957i	−0.505644	−	0.291934i
$429$	−4.98760	−	8.64582i	−0.240804	−	0.417424i
$430$	21.8104	+	12.5922i	1.05179	+	0.607252i
$431$	−28.5071	+	16.4586i	−1.37314	+	0.792783i	−0.991322	−	0.131455i	$-0.958035\pi$
$431$	−28.5071	+	16.4586i	−1.37314	+	0.792783i	−0.381818	+	0.924238i	$0.624702\pi$
$432$	−11.3791	−	0.0120447i	−0.547478	−	0.000579503i
$433$		−	7.13725i		−	0.342994i	−0.985185	−	0.171497i	$-0.945140\pi$
$433$		−	7.13725i		−	0.342994i	0.985185	−	0.171497i	$-0.0548604\pi$
$434$	−14.1672	−	42.2077i	−0.680045	−	2.02604i
$435$	−8.18230	−	4.72790i	−0.392311	−	0.226686i
$436$	8.58655	+	14.8723i	0.411221	+	0.712256i
$437$	8.91798			0.426605
$438$	−5.80268	−	10.0587i	−0.277263	−	0.480625i
$439$			22.6941i			1.08313i	0.840658	+	0.541566i	$0.182168\pi$
$439$			22.6941i			1.08313i	−0.840658	+	0.541566i	$0.817832\pi$
$440$	2.52532			0.120390
$441$	−16.7562	+	12.6582i	−0.797915	+	0.602770i
$442$	−35.7396			−1.69996
$443$		−	2.36318i		−	0.112278i	−0.998423	−	0.0561390i	$-0.982121\pi$
$443$		−	2.36318i		−	0.112278i	0.998423	−	0.0561390i	$-0.0178790\pi$
$444$	7.88716	−	13.6498i	0.374308	−	0.647793i
$445$	10.7220			0.508270
$446$	−14.8757	−	25.7654i	−0.704383	−	1.22003i
$447$	−20.2821	+	11.7004i	−0.959313	+	0.553408i
$448$	−10.2597	−	30.5664i	−0.484725	−	1.44412i
$449$			2.75417i			0.129978i	0.997886	+	0.0649888i	$0.0207012\pi$
$449$			2.75417i			0.129978i	−0.997886	+	0.0649888i	$0.979299\pi$
$450$	5.61600	+	3.24769i	0.264741	+	0.153097i
$451$	−1.17978	+	0.681147i	−0.0555537	+	0.0320740i
$452$	24.6998	+	14.2604i	1.16178	+	0.670753i
$453$	17.1114	−	29.6137i	0.803966	−	1.39138i
$454$	−54.0850	−	31.2260i	−2.53834	−	1.46551i
$455$	8.37123	−	2.80983i	0.392449	−	0.131727i
$456$	−4.22475	+	7.31152i	−0.197842	+	0.342393i
$457$	8.91969			0.417245			0.208623	−	0.977996i	$-0.433102\pi$
$457$	8.91969			0.417245			0.208623	+	0.977996i	$0.433102\pi$
$458$	7.07319	+	12.2511i	0.330508	+	0.572457i
$459$	−12.8419	−	22.2973i	−0.599409	−	1.04075i
$460$	−6.20075	−	3.58001i	−0.289111	−	0.166919i
$461$	4.13030	+	7.15390i	0.192367	+	0.333190i	0.946034	−	0.324066i	$-0.105050\pi$
$461$	4.13030	+	7.15390i	0.192367	+	0.333190i	−0.753667	+	0.657257i	$0.771717\pi$
$462$	16.7692	+	3.40128i	0.780173	+	0.158242i
$463$	1.50983	−	2.61509i	0.0701675	−	0.121534i	−0.828807	−	0.559534i	$-0.810980\pi$
$463$	1.50983	−	2.61509i	0.0701675	−	0.121534i	0.898975	+	0.438001i	$0.144313\pi$
$464$	10.3474	−	5.97406i	0.480365	−	0.277339i
$465$	−11.6749	+	6.73499i	−0.541409	+	0.312328i
$466$	−22.6514	+	39.2334i	−1.04931	+	1.81745i
$467$	14.6749	−	25.4177i	0.679074	−	1.17619i	−0.296186	−	0.955130i	$-0.595715\pi$
$467$	14.6749	−	25.4177i	0.679074	−	1.17619i	0.975260	−	0.221061i	$-0.0709518\pi$
$468$	−23.1973	−	13.4148i	−1.07229	−	0.620099i
$469$	1.78833	+	5.32790i	0.0825772	+	0.246019i
$470$	21.6066	−	12.4746i	0.996640	−	0.575410i
$471$	−0.00347639	+	9.85283i	−0.000160184	+	0.453994i
$472$		−	15.9593i		−	0.734586i
$473$		−	20.1087i		−	0.924600i
$474$	0.0179974	−	51.0083i	0.000826646	−	2.34289i
$475$	−2.88684	+	1.66672i	−0.132457	+	0.0764743i
$476$	23.2092	−	26.2836i	1.06379	−	1.20471i
$477$	−17.0924	+	9.85225i	−0.782609	+	0.451103i
$478$	32.0553	−	55.5214i	1.46617	−	2.53949i
$479$	0.398107	−	0.689542i	0.0181900	−	0.0315060i	−0.856787	−	0.515670i	$-0.827543\pi$
$479$	0.398107	−	0.689542i	0.0181900	−	0.0315060i	0.874977	+	0.484164i	$0.160876\pi$
$480$	−11.4935	+	6.63036i	−0.524603	+	0.302633i
$481$	−9.82964	+	5.67515i	−0.448193	+	0.258764i
$482$	−4.65702	+	8.06619i	−0.212121	+	0.367405i
$483$	−9.18691	−	8.11809i	−0.418019	−	0.369386i
$484$	10.7303	+	18.5855i	0.487742	+	0.844794i
$485$	−2.88709	−	1.66686i	−0.131096	−	0.0756882i
$486$	0.0594693	−	33.7097i	0.00269758	−	1.52910i
$487$	−4.82550	−	8.35802i	−0.218664	−	0.378738i	0.735736	−	0.677269i	$-0.236837\pi$
$487$	−4.82550	−	8.35802i	−0.218664	−	0.378738i	−0.954400	+	0.298531i	$0.903503\pi$
$488$	9.43948			0.427305
$489$	−12.6054	+	21.8155i	−0.570038	+	0.986530i
$490$	−5.88813	+	13.9453i	−0.265999	+	0.629982i
$491$	11.0595	+	6.38522i	0.499110	+	0.288161i	0.728346	−	0.685210i	$-0.240289\pi$
$491$	11.0595	+	6.38522i	0.499110	+	0.288161i	−0.229236	+	0.973371i	$0.573623\pi$
$492$	−1.82980	+	3.16672i	−0.0824936	+	0.142767i
$493$	23.3980	+	13.5088i	1.05379	+	0.608407i
$494$	20.8352	−	12.0292i	0.937421	−	0.541220i
$495$	0.00365530	−	5.17995i	0.000164293	−	0.232821i
$496$		−	17.0412i		−	0.765170i
$497$	−3.38323	+	1.13559i	−0.151758	+	0.0509382i
$498$	−32.1689	+	18.5576i	−1.44152	+	0.831586i
$499$	16.8393	+	29.1665i	0.753831	+	1.30567i	0.945953	+	0.324303i	$0.105130\pi$
$499$	16.8393	+	29.1665i	0.753831	+	1.30567i	−0.192123	+	0.981371i	$0.561537\pi$
$500$	2.67633			0.119689
$501$	12.1349	−	21.0011i	0.542145	−	0.938258i
$502$			29.7197i			1.32645i
$503$	9.90713			0.441737			0.220869	−	0.975304i	$-0.429111\pi$
$503$	9.90713			0.441737			0.220869	+	0.975304i	$0.429111\pi$
$504$	11.0079	−	3.68619i	0.490330	−	0.164196i
$505$	−10.8489			−0.482768
$506$			9.98920i			0.444074i
$507$	−1.61072	−	2.79213i	−0.0715348	−	0.124003i
$508$	−24.5884			−1.09094
$509$	17.8389	+	30.8979i	0.790695	+	1.36952i	0.925537	+	0.378657i	$0.123614\pi$
$509$	17.8389	+	30.8979i	0.790695	+	1.36952i	−0.134842	+	0.990867i	$0.543053\pi$
$510$	−16.0594	−	9.27947i	−0.711123	−	0.410902i
$511$	−6.14867	−	5.42947i	−0.272001	−	0.240185i
$512$		−	23.1821i		−	1.02452i
$513$	14.9913	+	8.67640i	0.661882	+	0.383072i
$514$	5.28158	−	3.04932i	0.232960	−	0.134500i
$515$	−10.0637	−	5.81029i	−0.443461	−	0.256032i
$516$	−26.9765	−	46.7627i	−1.18757	−	2.05861i
$517$	−17.2520	−	9.96043i	−0.758741	−	0.438059i
$518$	3.86106	−	19.0705i	0.169645	−	0.837911i
$519$	−0.721380		0.000254526i	−0.0316650		1.11724e-5i
$520$	−4.88129			−0.214059
$521$	9.14291	+	15.8360i	0.400558	+	0.693787i	0.993793	−	0.111242i	$-0.0354829\pi$
$521$	9.14291	+	15.8360i	0.400558	+	0.693787i	−0.593235	+	0.805029i	$0.702150\pi$
$522$	17.6761	+	30.6658i	0.773660	+	1.34221i
$523$	−17.6652	−	10.1990i	−0.772446	−	0.445972i	0.0613005	−	0.998119i	$-0.480475\pi$
$523$	−17.6652	−	10.1990i	−0.772446	−	0.445972i	−0.833746	+	0.552147i	$0.813809\pi$
$524$	−12.0004	−	20.7853i	−0.524240	−	0.908011i
$525$	4.49112	+	0.910932i	0.196009	+	0.0397563i
$526$	19.9786	−	34.6039i	0.871106	−	1.50880i
$527$	33.3716	−	19.2671i	1.45369	−	0.839289i
$528$	5.67066	+	3.27663i	0.246784	+	0.142597i
$529$	−7.92136	+	13.7202i	−0.344407	+	0.596531i
$530$	−7.11046	+	12.3157i	−0.308859	+	0.534959i
$531$	−32.7358	−	0.0231004i	−1.42061	−	0.00100247i
$532$	−4.68383	+	23.1344i	−0.203070	+	1.00300i
$533$	2.28045	−	1.31662i	0.0987771	−	0.0570290i
$534$	−34.7720	−	20.0920i	−1.50473	−	0.869465i
$535$			4.51332i			0.195128i
$536$		−	3.10671i		−	0.134189i
$537$	−32.8489	+	18.9498i	−1.41753	+	0.817746i
$538$	−36.4424	+	21.0400i	−1.57114	+	0.907099i
$539$	11.9936	−	1.49580i	0.516602	−	0.0644285i
$540$	−6.94056	−	12.0508i	−0.298674	−	0.518586i
$541$	−3.98849	+	6.90827i	−0.171479	+	0.297010i	−0.938937	−	0.344089i	$-0.888188\pi$
$541$	−3.98849	+	6.90827i	−0.171479	+	0.297010i	0.767458	+	0.641099i	$0.221521\pi$
$542$	20.6974	−	35.8489i	0.889028	−	1.53984i
$543$	0.00297121	−	8.42104i	0.000127507	−	0.361382i
$544$	32.8532	−	18.9678i	1.40857	−	0.813237i
$545$	3.20833	−	5.55699i	0.137430	−	0.238035i
$546$	−32.4138	−	6.57447i	−1.38718	−	0.281361i
$547$	−8.04726	−	13.9383i	−0.344076	−	0.595957i	0.641109	−	0.767449i	$-0.278474\pi$
$547$	−8.04726	−	13.9383i	−0.344076	−	0.595957i	−0.985185	+	0.171492i	$0.945141\pi$
$548$	−10.5194	−	6.07337i	−0.449366	−	0.259442i
$549$	0.0136633	−	19.3623i	0.000583134	−	0.826363i
$550$	−1.86692	−	3.23361i	−0.0796059	−	0.137882i
$551$	−18.1872			−0.774800
$552$	3.38650	+	5.87037i	0.144139	+	0.249860i
$553$	−11.4653	−	34.1582i	−0.487555	−	1.45255i
$554$	48.7324	+	28.1357i	2.07044	+	1.19537i
$555$	−5.89041	−	0.00207832i	−0.250034	−	8.82199e-5i
$556$	47.8853	+	27.6466i	2.03079	+	1.17248i
$557$	−4.36517	+	2.52023i	−0.184958	+	0.106786i	−0.589620	−	0.807681i	$-0.700723\pi$
$557$	−4.36517	+	2.52023i	−0.184958	+	0.106786i	0.404662	+	0.914466i	$0.367389\pi$
$558$	50.4831	+	0.0356241i	2.13712	+	0.00150809i
$559$			38.8689i			1.64398i
$560$	−3.83507	+	4.34307i	−0.162061	+	0.183528i
$561$	−0.00522525	+	14.8095i	−0.000220610	+	0.625256i
$562$	24.4084	+	42.2766i	1.02961	+	1.78333i
$563$	−25.4581			−1.07293			−0.536465	−	0.843923i	$-0.680241\pi$
$563$	−25.4581			−1.07293			−0.536465	+	0.843923i	$0.680241\pi$
$564$	−53.4816	−	0.0188700i	−2.25198	−	0.000794570i
$565$		−	10.6567i		−	0.448330i
$566$	−23.0765			−0.969976
$567$	−7.54519	−	22.5847i	−0.316868	−	0.948470i
$568$	1.97277			0.0827755
$569$			15.6019i			0.654065i	0.945013	+	0.327032i	$0.106049\pi$
$569$			15.6019i			0.654065i	−0.945013	+	0.327032i	$0.893951\pi$
$570$	12.4855	+	0.00440528i	0.522960	+	0.000184517i
$571$	−12.0340			−0.503609			−0.251804	−	0.967778i	$-0.581024\pi$
$571$	−12.0340			−0.503609			−0.251804	+	0.967778i	$0.581024\pi$
$572$	7.71145	+	13.3566i	0.322432	+	0.558469i
$573$	−0.000657313		1.86296i	−2.74596e−5		0.0778264i
$574$	−0.895754	+	4.42430i	−0.0373880	+	0.184667i
$575$			2.67531i			0.111568i
$576$	36.5593	+	0.0257986i	1.52330	+	0.00107494i
$577$	−2.90129	+	1.67506i	−0.120782	+	0.0697337i	−0.559174	−	0.829050i	$-0.688882\pi$
$577$	−2.90129	+	1.67506i	−0.120782	+	0.0697337i	0.438392	+	0.898784i	$0.355548\pi$
$578$	14.0863	+	8.13270i	0.585911	+	0.338276i
$579$	14.9682	+	0.00528126i	0.622058	+	0.000219482i
$580$	12.6457	+	7.30101i	0.525085	+	0.303158i
$581$	−17.3640	+	19.6641i	−0.720381	+	0.815805i
$582$	6.23946	+	10.8159i	0.258634	+	0.448332i
$583$	11.3548			0.470268
$584$	2.26722	+	3.92694i	0.0938181	+	0.162498i
$585$	−0.00706547	+	10.0125i	−0.000292121	+	0.413967i
$586$	0.327604	+	0.189142i	0.0135332	+	0.00781340i
$587$	21.0363	+	36.4359i	0.868260	+	1.50387i	0.863773	+	0.503881i	$0.168095\pi$
$587$	21.0363	+	36.4359i	0.868260	+	1.50387i	0.00448747	+	0.999990i	$0.498572\pi$
$588$	25.8845	−	19.5683i	1.06746	−	0.806983i
$589$	−12.9698	+	22.4644i	−0.534413	+	0.925630i
$590$	−20.4355	+	11.7984i	−0.841315	+	0.485733i
$591$	−0.00162919	+	4.61746i	−6.70158e−5	+	0.189937i
$592$	3.72376	−	6.44974i	0.153046	−	0.265083i
$593$	13.5045	−	23.3905i	0.554564	−	0.960534i	−0.443373	−	0.896337i	$-0.646218\pi$
$593$	13.5045	−	23.3905i	0.554564	−	0.960534i	0.997937	−	0.0641964i	$-0.0204484\pi$
$594$	−9.71860	+	16.7920i	−0.398759	+	0.688986i
$595$	−12.8410	−	2.59982i	−0.526431	−	0.106582i
$596$	31.3332	−	18.0902i	1.28346	−	0.741005i
$597$	−29.7851	+	17.1824i	−1.21902	+	0.703229i
$598$		−	19.3085i		−	0.789584i
$599$			22.3737i			0.914165i	0.889424	+	0.457082i	$0.151106\pi$
$599$			22.3737i			0.914165i	−0.889424	+	0.457082i	$0.848894\pi$
$600$	−2.19339	−	1.26738i	−0.0895446	−	0.0517407i
$601$	33.0130	−	19.0601i	1.34663	−	0.777476i	0.358858	−	0.933392i	$-0.383166\pi$
$601$	33.0130	−	19.0601i	1.34663	−	0.777476i	0.987770	+	0.155916i	$0.0498330\pi$
$602$	−49.9463	−	44.1041i	−2.03566	−	1.79755i
$603$	−6.37250	−	0.00449684i	−0.259508	−	0.000183125i
$604$	−26.4241	+	45.7679i	−1.07518	+	1.86227i
$605$	4.00934	−	6.94438i	0.163003	−	0.282329i
$606$	35.1835	+	20.3298i	1.42923	+	0.825840i
$607$	−2.64350	+	1.52623i	−0.107296	+	0.0619476i	−0.552688	−	0.833388i	$-0.686398\pi$
$607$	−2.64350	+	1.52623i	−0.107296	+	0.0619476i	0.445391	+	0.895336i	$0.353065\pi$
$608$	−12.7683	+	22.1154i	−0.517824	+	0.896898i
$609$	18.7356	+	16.5559i	0.759206	+	0.670879i
$610$	−6.97844	−	12.0870i	−0.282549	−	0.489389i
$611$	33.3470	+	19.2529i	1.34908	+	0.778889i
$612$	19.8552	+	34.4464i	0.802600	+	1.39241i
$613$	19.9401	+	34.5372i	0.805372	+	1.39495i	0.916040	+	0.401088i	$0.131368\pi$
$613$	19.9401	+	34.5372i	0.805372	+	1.39495i	−0.110668	+	0.993857i	$0.535299\pi$
$614$	−64.1216			−2.58774
$615$	1.36656		0.000482164i	0.0551049		1.94427e-5i
$616$	−6.54850	−	1.32582i	−0.263847	−	0.0534189i
$617$	9.69826	+	5.59929i	0.390437	+	0.225419i	0.682350	−	0.731026i	$-0.260958\pi$
$617$	9.69826	+	5.59929i	0.390437	+	0.225419i	−0.291912	+	0.956445i	$0.594292\pi$
$618$	21.7493	+	37.7017i	0.874886	+	1.51658i
$619$	34.2583	+	19.7790i	1.37696	+	0.794986i	0.991792	−	0.127862i	$-0.0408115\pi$
$619$	34.2583	+	19.7790i	1.37696	+	0.794986i	0.385164	+	0.922848i	$0.374145\pi$
$620$	18.0361	−	10.4131i	0.724347	−	0.418202i
$621$	12.0462	−	6.93791i	0.483399	−	0.278409i
$622$			4.80252i			0.192563i
$623$	−27.8035	−	5.62916i	−1.11392	−	0.225527i
$624$	−10.9610	−	6.33352i	−0.438793	−	0.253544i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−59.0442			−2.35988
$627$	−4.98152	−	8.63528i	−0.198943	−	0.344860i
$628$		−	15.2244i		−	0.607520i
$629$	16.8407			0.671482
$630$	−12.8580	−	11.3702i	−0.512275	−	0.452998i
$631$	−31.1354			−1.23948			−0.619740	−	0.784807i	$-0.712762\pi$
$631$	−31.1354			−1.23948			−0.619740	+	0.784807i	$0.712762\pi$
$632$			19.9177i			0.792285i
$633$	−8.29117	+	14.3490i	−0.329544	+	0.570323i
$634$	32.7150			1.29928
$635$	4.59368	+	7.95649i	0.182295	+	0.315744i
$636$	26.4055	−	15.2328i	1.04705	−	0.604021i
$637$	−23.1830	+	2.89128i	−0.918542	+	0.114557i
$638$		−	20.3718i		−	0.806528i
$639$	0.00285550	−	4.04655i	0.000112962	−	0.160079i
$640$	9.55350	−	5.51572i	0.377635	−	0.218028i
$641$	−37.1877	−	21.4703i	−1.46882	−	0.848026i	−0.469435	−	0.882967i	$-0.655542\pi$
$641$	−37.1877	−	21.4703i	−1.46882	−	0.848026i	−0.999389	+	0.0349413i	$0.988876\pi$
$642$	8.45755	−	14.6370i	0.333793	−	0.577675i
$643$	25.1028	+	14.4931i	0.989959	+	0.571553i	0.905262	−	0.424854i	$-0.139674\pi$
$643$	25.1028	+	14.4931i	0.989959	+	0.571553i	0.0846970	+	0.996407i	$0.473008\pi$
$644$	14.1999	+	12.5389i	0.559553	+	0.494102i
$645$	−10.0920	+	17.4656i	−0.397371	+	0.687707i
$646$	−35.6960			−1.40444
$647$	14.4462	+	25.0215i	0.567937	+	0.983696i	0.996770	+	0.0803122i	$0.0255917\pi$
$647$	14.4462	+	25.0215i	0.567937	+	0.983696i	−0.428833	+	0.903384i	$0.641075\pi$
$648$	−0.0185773	+	13.1630i	−0.000729784	+	0.517091i
$649$	16.3168	+	9.42053i	0.640492	+	0.369788i
$650$	3.60865	+	6.25037i	0.141543	+	0.245160i
$651$	33.8105	−	11.3353i	1.32514	−	0.444266i
$652$	19.4658	−	33.7157i	0.762339	−	1.32041i
$653$	−38.2426	+	22.0794i	−1.49655	+	0.864033i	−0.999992	−	0.00397126i	$-0.998736\pi$
$653$	−38.2426	+	22.0794i	−1.49655	+	0.864033i	−0.496557	+	0.868004i	$0.665403\pi$
$654$	−20.8181	+	12.0095i	−0.814052	+	0.469611i
$655$	−4.48390	+	7.76635i	−0.175201	+	0.303456i
$656$	−0.863900	+	1.49632i	−0.0337296	+	0.0584215i
$657$	8.05823	−	4.64484i	0.314381	−	0.181213i
$658$	−62.5783	+	21.0046i	−2.43956	+	0.818845i
$659$	−11.1900	+	6.46056i	−0.435901	+	0.251668i	−0.701858	−	0.712317i	$-0.747646\pi$
$659$	−11.1900	+	6.46056i	−0.435901	+	0.251668i	0.265956	+	0.963985i	$0.414312\pi$
$660$	−0.00282405	+	8.00395i	−0.000109926	+	0.311554i
$661$		−	19.3188i		−	0.751413i	−0.926739	−	0.375706i	$-0.877400\pi$
$661$		−	19.3188i		−	0.751413i	0.926739	−	0.375706i	$-0.122600\pi$
$662$			49.2194i			1.91297i
$663$	0.0101001	−	28.6258i	0.000392255	−	1.11173i
$664$	12.5588	−	7.25080i	0.487374	−	0.281386i
$665$	8.36103	−	2.80641i	0.324227	−	0.108828i
$666$	19.0991	+	11.0448i	0.740074	+	0.427978i
$667$	−7.29821	+	12.6409i	−0.282588	+	0.489457i
$668$	−18.7391	+	32.4570i	−0.725037	+	1.25580i
$669$	20.6411	−	11.9075i	0.798032	−	0.460369i
$670$	−3.97806	+	2.29674i	−0.153686	+	0.0887307i
$671$	−5.57199	+	9.65096i	−0.215104	+	0.372571i
$672$	33.2852	−	11.1592i	1.28400	−	0.430476i
$673$	13.1315	+	22.7444i	0.506180	+	0.876730i	0.999974	+	0.00715136i	$0.00227637\pi$
$673$	13.1315	+	22.7444i	0.506180	+	0.876730i	−0.493794	+	0.869579i	$0.664390\pi$
$674$	−33.8064	−	19.5181i	−1.30217	−	0.751811i
$675$	−2.60284	+	4.49725i	−0.100183	+	0.173099i
$676$	2.49038	+	4.31347i	0.0957839	+	0.165903i
$677$	−6.52747			−0.250871			−0.125436	−	0.992102i	$-0.540033\pi$
$677$	−6.52747			−0.250871			−0.125436	+	0.992102i	$0.540033\pi$
$678$	−19.9697	+	34.5603i	−0.766930	+	1.32728i
$679$	6.61149	+	5.83815i	0.253726	+	0.224048i
$680$	6.27217	+	3.62124i	0.240527	+	0.138868i
$681$	25.0259	−	43.3108i	0.958995	−	1.65968i
$682$	−25.1628	−	14.5278i	−0.963535	−	0.556297i
$683$	4.15228	−	2.39732i	0.158883	−	0.0917309i	−0.418451	−	0.908240i	$-0.637427\pi$
$683$	4.15228	−	2.39732i	0.158883	−	0.0917309i	0.577333	+	0.816509i	$0.304093\pi$
$684$	−23.1690	−	13.3984i	−0.885889	−	0.512302i
$685$			4.53858i			0.173410i
$686$	22.5902	−	33.0706i	0.862496	−	1.26264i
$687$	−9.81459	+	5.66184i	−0.374450	+	0.216013i
$688$	−12.7520	−	22.0871i	−0.486164	−	0.842061i
$689$	−21.9481			−0.836157
$690$	5.01328	−	8.67619i	0.190852	−	0.330297i
$691$			11.2767i			0.428987i	0.976725	+	0.214493i	$0.0688100\pi$
$691$			11.2767i			0.428987i	−0.976725	+	0.214493i	$0.931190\pi$
$692$	1.11466			0.0423731
$693$	−2.72901	+	13.4304i	−0.103667	+	0.510179i
$694$	−16.8155			−0.638309
$695$		−	20.6601i		−	0.783681i
$696$	−6.90637	−	11.9719i	−0.261785	−	0.453795i
$697$	−3.90698			−0.147988
$698$	−29.2408	−	50.6466i	−1.10678	−	1.91700i
$699$	−31.4178	−	18.1538i	−1.18833	−	0.686641i
$700$	−6.94010	−	1.40511i	−0.262311	−	0.0531080i
$701$			25.1208i			0.948799i	0.880310	+	0.474399i	$0.157335\pi$
$701$			25.1208i			0.948799i	−0.880310	+	0.474399i	$0.842665\pi$
$702$	18.7855	−	32.4580i	0.709012	−	1.22505i
$703$	−9.81766	+	5.66823i	−0.370280	+	0.213781i
$704$	−18.2226	−	10.5208i	−0.686792	−	0.396519i
$705$	9.98548	+	17.3095i	0.376075	+	0.651912i
$706$	−11.2720	−	6.50790i	−0.424228	−	0.244928i
$707$	28.1326	+	5.69578i	1.05803	+	0.214212i
$708$	50.5827	+	0.0178472i	1.90101	+	0.000670738i
$709$	21.0971			0.792318			0.396159	−	0.918182i	$-0.370343\pi$
$709$	21.0971			0.792318			0.396159	+	0.918182i	$0.370343\pi$
$710$	−1.45843	−	2.52608i	−0.0547340	−	0.0948021i
$711$	40.8554	+	0.0288301i	1.53220	+	0.00108121i
$712$	13.5805	+	7.84073i	0.508952	+	0.293844i
$713$	10.4092	+	18.0292i	0.389826	+	0.675199i
$714$	36.7725	+	32.4943i	1.37618	+	1.21607i
$715$	2.88135	−	4.99065i	0.107756	−	0.186640i
$716$	50.7471	−	29.2988i	1.89651	−	1.09495i
$717$	44.4610	+	25.6905i	1.66043	+	0.959430i
$718$	7.76541	−	13.4501i	0.289802	−	0.501952i
$719$	18.8427	−	32.6366i	0.702716	−	1.21714i	−0.264794	−	0.964305i	$-0.585304\pi$
$719$	18.8427	−	32.6366i	0.702716	−	1.21714i	0.967510	−	0.252835i	$-0.0813629\pi$
$720$	−3.28085	−	5.69188i	−0.122270	−	0.212124i
$721$	23.0461	+	20.3505i	0.858283	+	0.757891i
$722$	−14.7727	+	8.52903i	−0.549784	+	0.317418i
$723$	−6.45934	−	3.73234i	−0.240225	−	0.138807i
$724$			13.0120i			0.483588i
$725$		−	5.45598i		−	0.202630i
$726$	−26.0157	+	15.0079i	−0.965533	+	0.556996i
$727$	13.1307	−	7.58102i	0.486991	−	0.281165i	−0.236334	−	0.971672i	$-0.575946\pi$
$727$	13.1307	−	7.58102i	0.486991	−	0.281165i	0.723325	+	0.690507i	$0.242613\pi$
$728$	12.6579	+	2.56273i	0.469131	+	0.0949813i
$729$	26.9999	+	0.0571587i	0.999998	+	0.00211699i
$730$	3.35223	−	5.80623i	0.124072	−	0.214898i
$731$	28.8353	−	49.9443i	1.06651	−	1.84726i
$732$	−0.0105561	+	29.9183i	−0.000390165	+	1.10581i
$733$	8.42408	−	4.86364i	0.311150	−	0.179643i	−0.336291	−	0.941758i	$-0.609172\pi$
$733$	8.42408	−	4.86364i	0.311150	−	0.179643i	0.647441	+	0.762115i	$0.275839\pi$
$734$	−23.7460	+	41.1293i	−0.876482	+	1.51811i
$735$	−11.1679	−	4.72007i	−0.411933	−	0.174102i
$736$	10.2474	+	17.7491i	0.377726	+	0.654240i
$737$	3.17631	+	1.83385i	0.117001	+	0.0675506i
$738$	−4.43092	−	2.56237i	−0.163105	−	0.0943220i
$739$	1.17078	+	2.02785i	0.0430678	+	0.0745956i	0.886756	−	0.462238i	$-0.152954\pi$
$739$	1.17078	+	2.02785i	0.0430678	+	0.0745956i	−0.843688	+	0.536834i	$0.819620\pi$
$740$	9.10175			0.334587
$741$	9.62897	+	16.6915i	0.353729	+	0.613176i
$742$	24.9043	−	28.2032i	0.914265	−	1.03537i
$743$	−22.8122	−	13.1707i	−0.836900	−	0.483185i	0.0193092	−	0.999814i	$-0.493853\pi$
$743$	−22.8122	−	13.1707i	−0.836900	−	0.483185i	−0.856209	+	0.516629i	$0.827187\pi$
$744$	−19.7126	−	0.00695524i	−0.722701	−	0.000254992i
$745$	−11.7075	−	6.75934i	−0.428930	−	0.247643i
$746$	−69.0690	+	39.8770i	−2.52879	+	1.46000i
$747$	−14.8547	−	25.7711i	−0.543505	−	0.942914i
$748$		−	22.8833i		−	0.836697i
$749$	2.36955	−	11.7037i	0.0865813	−	0.427642i
$750$	−0.00132154	+	3.74553i	−4.82559e−5	+	0.136767i
$751$	23.3253	+	40.4005i	0.851151	+	1.47424i	0.880170	+	0.474658i	$0.157428\pi$
$751$	23.3253	+	40.4005i	0.851151	+	1.47424i	−0.0290193	+	0.999579i	$0.509238\pi$
$752$	−25.2657			−0.921344
$753$	−23.8041	−	0.00839885i	−0.867471	−	0.000306071i
$754$			39.3775i			1.43404i
$755$	19.7465			0.718650
$756$	11.6710	+	34.8934i	0.424470	+	1.26906i
$757$	4.42659			0.160887			0.0804435	−	0.996759i	$-0.474366\pi$
$757$	4.42659			0.160887			0.0804435	+	0.996759i	$0.474366\pi$
$758$		−	17.0761i		−	0.620232i
$759$	−8.00089	−	0.00282297i	−0.290414	−	0.000102467i
$760$	−4.87534			−0.176847
$761$	−22.6869	−	39.2948i	−0.822398	−	1.42443i	−0.903892	−	0.427761i	$-0.859302\pi$
$761$	−22.6869	−	39.2948i	−0.822398	−	1.42443i	0.0814940	−	0.996674i	$-0.474031\pi$
$762$	0.0121415	−	34.4116i	0.000439840	−	1.24660i
$763$	−11.2371	+	12.7256i	−0.406811	+	0.460699i
$764$		−	2.87862i		−	0.104145i
$765$	7.43698	−	12.8603i	0.268884	−	0.464963i
$766$	41.4846	−	23.9512i	1.49890	−	0.865391i
$767$	−31.5395	−	18.2093i	−1.13882	−	0.657500i
$768$	0.896485		0.000316308i	0.0323491		1.14138e-5i
$769$	9.23372	+	5.33109i	0.332976	+	0.192244i	0.657162	−	0.753750i	$-0.271757\pi$
$769$	9.23372	+	5.33109i	0.332976	+	0.192244i	−0.324185	+	0.945994i	$0.605090\pi$
$770$	3.14351	+	9.36535i	0.113284	+	0.337504i
$771$	2.44087	+	4.23117i	0.0879060	+	0.152382i
$772$	−23.1286			−0.832417
$773$	−7.19154	−	12.4561i	−0.258662	−	0.448015i	0.707222	−	0.706992i	$-0.249948\pi$
$773$	−7.19154	−	12.4561i	−0.258662	−	0.448015i	−0.965884	+	0.258976i	$0.916615\pi$
$774$	65.4578	−	37.7305i	2.35283	−	1.35620i
$775$	−6.73911	−	3.89083i	−0.242076	−	0.139763i
$776$	−2.43787	−	4.22252i	−0.0875146	−	0.151580i
$777$	15.2735	+	3.09792i	0.547935	+	0.111137i
$778$	14.5611	−	25.2205i	0.522040	−	0.904200i
$779$	2.27767	−	1.31501i	0.0816058	−	0.0471151i
$780$	0.00545871	−	15.4712i	0.000195453	−	0.553956i
$781$	−1.16450	+	2.01697i	−0.0416689	+	0.0721727i
$782$	−14.3242	+	24.8103i	−0.512233	+	0.887214i
$783$	−24.5669	+	14.1491i	−0.877949	+	0.505646i
$784$	12.2250	−	9.24873i	0.436608	−	0.330312i
$785$	−4.92641	+	2.84427i	−0.175831	+	0.101516i
$786$	29.0950	−	16.7843i	1.03778	−	0.598677i
$787$			21.4108i			0.763212i	0.924325	+	0.381606i	$0.124629\pi$
$787$			21.4108i			0.763212i	−0.924325	+	0.381606i	$0.875371\pi$
$788$		−	7.13481i		−	0.254167i
$789$	27.7105	+	16.0117i	0.986520	+	0.570032i
$790$	25.5042	−	14.7248i	0.907398	−	0.523886i
$791$	−5.59489	+	27.6343i	−0.198931	+	0.982561i
$792$	3.79261	−	6.55830i	0.134764	−	0.233039i
$793$	10.7703	−	18.6547i	0.382465	−	0.662448i
$794$	3.70824	−	6.42286i	0.131601	−	0.227939i
$795$	−9.86230	−	5.69864i	−0.349780	−	0.202110i
$796$	46.0139	−	26.5661i	1.63092	−	0.941612i
$797$	8.94216	−	15.4883i	0.316748	−	0.548623i	−0.663060	−	0.748566i	$-0.730743\pi$
$797$	8.94216	−	15.4883i	0.316748	−	0.548623i	0.979807	+	0.199944i	$0.0640759\pi$
$798$	−32.3743	−	6.56646i	−1.14604	−	0.232450i
$799$	−28.5659	−	49.4777i	−1.01059	−	1.75039i
$800$	−6.63441	−	3.83038i	−0.234562	−	0.135424i
$801$	16.1026	−	27.8451i	0.568957	−	0.983859i
$802$	−11.5046	−	19.9266i	−0.406242	−	0.703632i
$803$	−5.35322			−0.188911
$804$	9.84666	+	0.00347421i	0.347265	+	0.000122526i
$805$	1.40457	−	6.93744i	0.0495045	−	0.244513i
$806$	48.6382	+	28.0813i	1.71321	+	0.989121i
$807$	−16.8418	−	29.1946i	−0.592859	−	1.02770i
$808$	−13.7413	−	7.93352i	−0.483416	−	0.279100i
$809$	−28.6232	+	16.5256i	−1.00634	+	0.581010i	−0.910118	−	0.414349i	$-0.864009\pi$
$809$	−28.6232	+	16.5256i	−1.00634	+	0.581010i	−0.0962218	+	0.995360i	$0.530676\pi$
$810$	16.8686	−	9.70737i	0.592702	−	0.341082i
$811$			35.2859i			1.23905i	0.784975	+	0.619527i	$0.212676\pi$
$811$			35.2859i			1.23905i	−0.784975	+	0.619527i	$0.787324\pi$
$812$	−28.9590	−	25.5717i	−1.01626	−	0.897389i
$813$	28.7075	+	16.5878i	1.00682	+	0.581759i
$814$	−6.34909	−	10.9969i	−0.222536	−	0.385443i
$815$	−14.5466			−0.509546
$816$	9.38570	+	16.2698i	0.328565	+	0.569556i
$817$			38.8215i			1.35819i
$818$	18.7635			0.656049
$819$	5.27501	−	25.9601i	0.184324	−	0.907121i
$820$	−2.11158			−0.0737394
$821$		−	5.02905i		−	0.175515i	−0.996142	−	0.0877576i	$-0.972030\pi$
$821$		−	5.02905i		−	0.175515i	0.996142	−	0.0877576i	$-0.0279701\pi$
$822$	8.50489	−	14.7189i	0.296642	−	0.513380i
$823$	−2.69021			−0.0937750			−0.0468875	−	0.998900i	$-0.514930\pi$
$823$	−2.69021			−0.0937750			−0.0468875	+	0.998900i	$0.514930\pi$
$824$	−8.49787	−	14.7187i	−0.296037	−	0.512752i
$825$	2.59050	−	1.49441i	0.0901897	−	0.0520286i
$826$	59.1863	−	19.8661i	2.05935	−	0.691229i
$827$		−	18.8965i		−	0.657097i	−0.944487	−	0.328548i	$-0.893441\pi$
$827$		−	18.8965i		−	0.657097i	0.944487	−	0.328548i	$-0.106559\pi$
$828$	−18.6098	+	10.7269i	−0.646736	+	0.372785i
$829$	−15.3012	+	8.83413i	−0.531432	+	0.306822i	−0.741599	−	0.670843i	$-0.765932\pi$
$829$	−15.3012	+	8.83413i	−0.531432	+	0.306822i	0.210168	+	0.977665i	$0.432599\pi$
$830$	−18.5689	−	10.7208i	−0.644537	−	0.372124i
$831$	−22.5492	+	39.0245i	−0.782222	+	1.35375i
$832$	35.2233	+	20.3362i	1.22115	+	0.705029i
$833$	31.9337	+	13.4834i	1.10644	+	0.467172i
$834$	−38.7151	+	67.0019i	−1.34059	+	2.32009i
$835$	14.0036			0.484613
$836$	7.70205	+	13.3403i	0.266381	+	0.461386i
$837$	−0.0427999	+	40.4347i	−0.00147938	+	1.39763i
$838$	−33.8041	−	19.5168i	−1.16774	−	0.674198i
$839$	−6.02682	−	10.4388i	−0.208069	−	0.360386i	0.743037	−	0.669250i	$-0.233384\pi$
$839$	−6.02682	−	10.4388i	−0.208069	−	0.360386i	−0.951106	+	0.308864i	$0.900051\pi$
$840$	5.02236	+	4.43805i	0.173288	+	0.153127i
$841$	0.383861	−	0.664866i	0.0132366	−	0.0229264i
$842$	−54.8686	+	31.6784i	−1.89090	+	1.09171i
$843$	−33.8685	+	19.5381i	−1.16649	+	0.672926i
$844$	12.8035	−	22.1764i	0.440716	−	0.763342i
$845$	0.930521	−	1.61171i	0.0320109	−	0.0554445i
$846$	0.0528172	−	74.8476i	0.00181589	−	2.57331i
$847$	−14.0427	+	15.9028i	−0.482511	+	0.546426i
$848$	12.4719	−	7.20066i	0.428287	−	0.247272i
$849$	0.00652146	−	18.4832i	0.000223816	−	0.634342i
$850$		−	10.7085i		−	0.367297i
$851$			9.09826i			0.311884i
$852$	−0.00220613	+	6.25265i	−7.55809e−5	+	0.214212i
$853$	10.5988	−	6.11923i	0.362896	−	0.209518i	−0.307454	−	0.951563i	$-0.599477\pi$
$853$	10.5988	−	6.11923i	0.362896	−	0.209518i	0.670351	+	0.742045i	$0.266144\pi$
$854$	11.7502	+	35.0071i	0.402085	+	1.19792i
$855$	−0.00705686	+	10.0003i	−0.000241339	+	0.342004i
$856$	−3.30049	+	5.71661i	−0.112808	+	0.195390i
$857$	0.295520	−	0.511856i	0.0100948	−	0.0174847i	−0.860934	−	0.508717i	$-0.830120\pi$
$857$	0.295520	−	0.511856i	0.0100948	−	0.0174847i	0.871029	+	0.491232i	$0.163453\pi$
$858$	−18.6964	+	10.7856i	−0.638286	+	0.368214i
$859$	−10.6664	+	6.15827i	−0.363934	+	0.210117i	−0.670805	−	0.741634i	$-0.734051\pi$
$859$	−10.6664	+	6.15827i	−0.363934	+	0.210117i	0.306871	+	0.951751i	$0.400718\pi$
$860$	15.5844	−	26.9930i	0.531424	−	0.920453i
$861$	−3.54341	−	0.718708i	−0.120759	−	0.0244935i
$862$	35.5914	+	61.6462i	1.21225	+	2.09968i
$863$	−7.47167	−	4.31377i	−0.254339	−	0.146843i	0.367411	−	0.930059i	$-0.380244\pi$
$863$	−7.47167	−	4.31377i	−0.254339	−	0.146843i	−0.621749	+	0.783216i	$0.713578\pi$
$864$	−0.0421349	+	39.8064i	−0.00143346	+	1.35424i
$865$	−0.208244	−	0.360690i	−0.00708052	−	0.0122638i
$866$	−15.4342			−0.524474
$867$	−6.51791	+	11.2802i	−0.221360	+	0.383094i
$868$	−52.2371	+	17.5336i	−1.77304	+	0.595128i
$869$	−20.3640	−	11.7571i	−0.690801	−	0.398834i
$870$	−10.2240	+	17.6941i	−0.346626	+	0.599886i
$871$	−6.13962	−	3.54471i	−0.208033	−	0.120108i
$872$	8.12740	−	4.69236i	0.275229	−	0.158903i
$873$	−8.66479	+	4.99447i	−0.293259	+	0.169037i
$874$		−	19.2850i		−	0.652324i
$875$	0.841895	+	2.50823i	0.0284613	+	0.0847936i
$876$	−12.4489	+	7.18151i	−0.420609	+	0.242641i
$877$	−9.73598	−	16.8632i	−0.328761	−	0.569430i	0.653506	−	0.756922i	$-0.273298\pi$
$877$	−9.73598	−	16.8632i	−0.328761	−	0.569430i	−0.982266	+	0.187492i	$0.939964\pi$
$878$	49.0757			1.65622
$879$	−0.151587	+	0.262343i	−0.00511290	+	0.00884859i
$880$			3.78121i			0.127465i
$881$	35.4636			1.19480			0.597400	−	0.801944i	$-0.296201\pi$
$881$	35.4636			1.19480			0.597400	+	0.801944i	$0.296201\pi$
$882$	27.3731	+	36.2350i	0.921700	+	1.22010i
$883$	−45.6972			−1.53783			−0.768916	−	0.639350i	$-0.779204\pi$
$883$	−45.6972			−1.53783			−0.768916	+	0.639350i	$0.779204\pi$
$884$			44.2320i			1.48768i
$885$	−9.44423	−	16.3712i	−0.317464	−	0.550313i
$886$	−5.11033			−0.171685
$887$	−2.71700	−	4.70598i	−0.0912280	−	0.158011i	0.816800	−	0.576921i	$-0.195746\pi$
$887$	−2.71700	−	4.70598i	−0.0912280	−	0.158011i	−0.908028	+	0.418909i	$0.862413\pi$
$888$	−7.45933	−	4.31016i	−0.250319	−	0.144639i
$889$	−7.73480	−	23.0440i	−0.259417	−	0.772872i
$890$		−	23.1861i		−	0.777198i
$891$	−13.4469	−	7.78891i	−0.450489	−	0.260938i
$892$	−31.8878	+	18.4104i	−1.06768	+	0.616426i
$893$	33.3064	+	19.2294i	1.11455	+	0.643488i
$894$	25.3018	+	43.8598i	0.846220	+	1.46689i
$895$	−18.9614	−	10.9474i	−0.633811	−	0.365931i
$896$	−27.6694	+	9.28731i	−0.924368	+	0.310267i
$897$	15.4652	+	0.00545663i	0.516369	+	0.000182191i
$898$	5.95586			0.198749
$899$	−21.2283	−	36.7685i	−0.708003	−	1.22630i
$900$	4.01940	−	6.95048i	0.133980	−	0.231683i
$901$	28.2020	+	16.2825i	0.939546	+	0.542447i
$902$	1.47297	+	2.55126i	0.0490445	+	0.0849476i
$903$	35.3395	−	39.9922i	1.17603	−	1.33086i
$904$	7.79299	−	13.4979i	0.259191	−	0.448932i
$905$	4.21052	−	2.43095i	0.139962	−	0.0808074i
$906$	−64.0392	−	37.0032i	−2.12756	−	1.22935i
$907$	27.0409	−	46.8363i	0.897880	−	1.55517i	0.0676800	−	0.997707i	$-0.478440\pi$
$907$	27.0409	−	46.8363i	0.897880	−	1.55517i	0.830200	−	0.557466i	$-0.188226\pi$
$908$	−38.6459	+	66.9367i	−1.28251	+	2.22137i
$909$	−16.2932	+	28.1747i	−0.540410	+	0.934494i
$910$	−6.07621	−	18.1026i	−0.201424	−	0.600097i
$911$	25.6198	−	14.7916i	0.848822	−	0.490068i	−0.0114310	−	0.999935i	$-0.503639\pi$
$911$	25.6198	−	14.7916i	0.848822	−	0.490068i	0.860253	+	0.509867i	$0.170305\pi$
$912$	−10.9477	−	6.32580i	−0.362514	−	0.209468i
$913$			17.1202i			0.566595i
$914$		−	19.2887i		−	0.638012i
$915$	9.68312	−	5.58600i	0.320114	−	0.184667i
$916$	15.1622	−	8.75391i	0.500974	−	0.289237i
$917$	15.7048	−	17.7851i	0.518618	−	0.587316i
$918$	−48.2175	+	27.7704i	−1.59142	+	0.916560i
$919$	26.3746	−	45.6822i	0.870019	−	1.50692i	0.00804249	−	0.999968i	$-0.497440\pi$
$919$	26.3746	−	45.6822i	0.870019	−	1.50692i	0.861976	−	0.506949i	$-0.169227\pi$
$920$	−1.95639	+	3.38857i	−0.0645003	+	0.111718i
$921$	0.0181209	−	51.3585i	0.000597105	−	1.69232i
$922$	15.4702	−	8.93171i	0.509483	−	0.294150i
$923$	2.25090	−	3.89867i	0.0740892	−	0.128326i
$924$	4.20949	−	20.7539i	0.138482	−	0.682752i
$925$	−1.70041	−	2.94520i	−0.0559093	−	0.0968377i
$926$	−5.65510	−	3.26497i	−0.185838	−	0.107294i
$927$	−30.2035	+	17.4096i	−0.992012	+	0.571805i
$928$	−20.8985	−	36.1972i	−0.686026	−	1.18823i
$929$	−10.0087			−0.328374			−0.164187	−	0.986429i	$-0.552500\pi$
$929$	−10.0087			−0.328374			−0.164187	+	0.986429i	$0.552500\pi$
$930$	14.5643	+	25.2467i	0.477582	+	0.827871i
$931$	−23.1547	+	2.88776i	−0.758864	+	0.0946424i
$932$	48.5560	+	28.0338i	1.59051	+	0.918279i
$933$	−3.84660	−	0.00135720i	−0.125932	−	4.44328e-5i
$934$	−54.9653	−	31.7342i	−1.79852	−	1.03838i
$935$	−7.40473	+	4.27513i	−0.242161	+	0.139812i
$936$	−7.33088	+	12.6768i	−0.239617	+	0.414354i
$937$		−	11.9255i		−	0.389590i	−0.980844	−	0.194795i	$-0.937596\pi$
$937$		−	11.9255i		−	0.389590i	0.980844	−	0.194795i	$-0.0624042\pi$
$938$	11.5215	−	3.86722i	0.376190	−	0.126269i
$939$	0.0166860	−	47.2917i	0.000544527	−	1.54331i
$940$	−15.4388	−	26.7408i	−0.503558	−	0.872189i
$941$	−25.0522			−0.816679			−0.408339	−	0.912830i	$-0.633892\pi$
$941$	−25.0522			−0.816679			−0.408339	+	0.912830i	$0.633892\pi$
$942$	21.3066	+	0.00751763i	0.694205	+	0.000244938i
$943$		−	2.11077i		−	0.0687361i
$944$	23.8962			0.777754
$945$	9.11063	−	10.2955i	0.296369	−	0.334911i
$946$	−43.4848			−1.41381
$947$		−	9.67413i		−	0.314367i	−0.987569	−	0.157184i	$-0.949759\pi$
$947$		−	9.67413i		−	0.314367i	0.987569	−	0.157184i	$-0.0502414\pi$
$948$	−63.1289	−	0.0222739i	−2.05033	−	0.000723422i
$949$	10.3474			0.335892
$950$	3.60425	+	6.24275i	0.116937	+	0.202541i
$951$	−0.00924534	+	26.2032i	−0.000299801	+	0.849698i
$952$	−14.3634	−	12.6833i	−0.465520	−	0.411069i
$953$			26.6999i			0.864895i	0.901659	+	0.432447i	$0.142350\pi$
$953$			26.6999i			0.864895i	−0.901659	+	0.432447i	$0.857650\pi$
$954$	21.3053	+	36.9621i	0.689785	+	1.19669i
$955$	−0.931482	+	0.537791i	−0.0301421	+	0.0174025i
$956$	−68.7143	−	39.6722i	−2.22238	−	1.28309i
$957$	16.3169	+	0.00575712i	0.527450	+	0.000186101i
$958$	−1.49112	−	0.860900i	−0.0481760	−	0.0278144i
$959$	2.38281	−	11.7692i	0.0769449	−	0.380046i
$960$	10.5473	+	18.2834i	0.340413	+	0.590093i
$961$	−29.5542			−0.953361
$962$	12.2724	+	21.2564i	0.395678	+	0.685335i
$963$	11.7212	+	6.77825i	0.377709	+	0.218426i
$964$	9.98288	+	5.76362i	0.321527	+	0.185634i
$965$	4.32095	+	7.48411i	0.139096	+	0.240922i
$966$	−17.5552	+	19.8665i	−0.564831	+	0.639195i
$967$	−1.97863	+	3.42710i	−0.0636286	+	0.110208i	−0.896085	−	0.443883i	$-0.853601\pi$
$967$	−1.97863	+	3.42710i	−0.0636286	+	0.110208i	0.832456	+	0.554091i	$0.186934\pi$
$968$	10.1565	−	5.86388i	0.326444	−	0.188472i
$969$	0.0100878	−	28.5909i	0.000324066	−	0.918472i
$970$	−3.60456	+	6.24327i	−0.115735	+	0.200459i
$971$	15.7464	−	27.2736i	0.505327	−	0.875251i	−0.494654	−	0.869090i	$-0.664705\pi$
$971$	15.7464	−	27.2736i	0.505327	−	0.875251i	0.999981	−	0.00616165i	$-0.00196133\pi$
$972$	−41.7198	−	0.0736004i	−1.33816	−	0.00236073i
$973$	−10.8468	+	53.5744i	−0.347732	+	1.71752i
$974$	−18.0741	+	10.4351i	−0.579130	+	0.334361i
$975$	−5.00728	+	2.88860i	−0.160361	+	0.0925092i
$976$			14.1339i			0.452416i
$977$			13.9913i			0.447620i	0.974633	+	0.223810i	$0.0718495\pi$
$977$			13.9913i			0.447620i	−0.974633	+	0.223810i	$0.928151\pi$
$978$	47.1756	+	27.2590i	1.50851	+	0.871648i
$979$	−16.0328	+	9.25654i	−0.512410	+	0.295840i
$980$	17.2589	+	7.28727i	0.551316	+	0.232783i
$981$	−9.61322	−	16.6778i	−0.306927	−	0.532480i
$982$	13.8079	−	23.9161i	0.440629	−	0.763192i
$983$	−1.01212	+	1.75305i	−0.0322818	+	0.0559136i	−0.881715	−	0.471783i	$-0.843611\pi$
$983$	−1.01212	+	1.75305i	−0.0322818	+	0.0559136i	0.849433	+	0.527696i	$0.176944\pi$
$984$	1.73054	+	0.999942i	0.0551676	+	0.0318770i
$985$	−2.30873	+	1.33295i	−0.0735623	+	0.0424712i
$986$	29.2126	−	50.5977i	0.930319	−	1.61136i
$987$	−16.8061	−	50.1283i	−0.534943	−	1.59560i
$988$	−14.8876	−	25.7861i	−0.473638	−	0.820364i
$989$	26.9827	+	15.5784i	0.857999	+	0.495366i
$990$	−11.2015	−	0.00790452i	−0.356008	−	0.000251222i
$991$	−12.3884	−	21.4573i	−0.393529	−	0.681612i	0.599383	−	0.800462i	$-0.295413\pi$
$991$	−12.3884	−	21.4573i	−0.393529	−	0.681612i	−0.992912	+	0.118850i	$0.962079\pi$
$992$	−59.6134			−1.89273
$993$	−39.4225	−	0.0139095i	−1.25104	−	0.000441405i
$994$	2.45569	+	7.31617i	0.0778899	+	0.232055i
$995$	−17.1929	−	9.92633i	−0.545052	−	0.314686i
$996$	22.9672	+	39.8129i	0.727745	+	1.26152i
$997$	10.6204	+	6.13172i	0.336353	+	0.194193i	0.658658	−	0.752442i	$-0.271124\pi$
$997$	10.6204	+	6.13172i	0.336353	+	0.194193i	−0.322305	+	0.946636i	$0.604458\pi$
$998$	63.0721	−	36.4147i	1.99651	−	1.15269i
$999$	−8.85181	+	15.2944i	−0.280059	+	0.483892i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.b.131.3	yes	30
3.2	odd	2		945.2.t.b.341.13		30
7.3	odd	6		315.2.be.b.311.13	yes	30
9.2	odd	6		315.2.be.b.236.13	yes	30
9.7	even	3		945.2.be.b.656.3		30
21.17	even	6		945.2.be.b.206.3		30
63.38	even	6	inner	315.2.t.b.101.13	✓	30
63.52	odd	6		945.2.t.b.521.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.13	✓	30	63.38	even	6	inner
315.2.t.b.131.3	yes	30	1.1	even	1	trivial
315.2.be.b.236.13	yes	30	9.2	odd	6
315.2.be.b.311.13	yes	30	7.3	odd	6
945.2.t.b.341.13		30	3.2	odd	2
945.2.t.b.521.3		30	63.52	odd	6
945.2.be.b.206.3		30	21.17	even	6
945.2.be.b.656.3		30	9.7	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.16248i q^{2} +(1.73205 + 0.000611122i) q^{3} -2.67633 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.00132154 - 3.74553i) q^{6} +(-0.841895 - 2.50823i) q^{7} +1.46255i q^{8} +(3.00000 + 0.00211699i) q^{9} +O(q^{10})\)	\(q-2.16248i q^{2} +(1.73205 + 0.000611122i) q^{3} -2.67633 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.00132154 - 3.74553i) q^{6} +(-0.841895 - 2.50823i) q^{7} +1.46255i q^{8} +(3.00000 + 0.00211699i) q^{9} +(1.87276 - 1.08124i) q^{10} +(-1.49532 - 0.863325i) q^{11} +(-4.63554 - 0.00163557i) q^{12} +(2.89037 + 1.66875i) q^{13} +(-5.42400 + 1.82058i) q^{14} +(0.865496 + 1.50031i) q^{15} -2.18991 q^{16} +(-2.47597 - 4.28850i) q^{17} +(0.00457795 - 6.48745i) q^{18} +(2.88684 + 1.66672i) q^{19} +(-1.33817 - 2.31777i) q^{20} +(-1.45667 - 4.34489i) q^{21} +(-1.86692 + 3.23361i) q^{22} +(2.31688 - 1.33765i) q^{23} +(-0.000893800 + 2.53322i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.60865 - 6.25037i) q^{26} +(5.19615 + 0.00550010i) q^{27} +(2.25319 + 6.71285i) q^{28} +(-4.72502 + 2.72799i) q^{29} +(3.24438 - 1.87162i) q^{30} +7.78166i q^{31} +7.66076i q^{32} +(-2.58945 - 1.49624i) q^{33} +(-9.27381 + 5.35423i) q^{34} +(1.75124 - 1.98322i) q^{35} +(-8.02899 - 0.00566577i) q^{36} +(-1.70041 + 2.94520i) q^{37} +(3.60425 - 6.24275i) q^{38} +(5.00524 + 2.89213i) q^{39} +(-1.26661 + 0.731277i) q^{40} +(0.394491 - 0.683278i) q^{41} +(-9.39576 + 3.15003i) q^{42} +(5.82305 + 10.0858i) q^{43} +(4.00198 + 2.31054i) q^{44} +(1.49817 + 2.59913i) q^{45} +(-2.89265 - 5.01022i) q^{46} +11.5373 q^{47} +(-3.79304 - 0.00133830i) q^{48} +(-5.58243 + 4.22333i) q^{49} +(1.87276 + 1.08124i) q^{50} +(-4.28588 - 7.42941i) q^{51} +(-7.73558 - 4.46614i) q^{52} +(-5.69516 + 3.28810i) q^{53} +(0.0118939 - 11.2366i) q^{54} -1.72665i q^{55} +(3.66842 - 1.23132i) q^{56} +(4.99914 + 2.88861i) q^{57} +(5.89923 + 10.2178i) q^{58} -10.9119 q^{59} +(-2.31635 - 4.01531i) q^{60} -6.45410i q^{61} +16.8277 q^{62} +(-2.52037 - 7.52647i) q^{63} +12.1864 q^{64} +3.33751i q^{65} +(-3.23558 + 5.59963i) q^{66} -2.12417 q^{67} +(6.62651 + 11.4774i) q^{68} +(4.01378 - 2.31547i) q^{69} +(-4.28867 - 3.78703i) q^{70} -1.34885i q^{71} +(-0.00309621 + 4.38766i) q^{72} +(2.68498 - 1.55018i) q^{73} +(6.36895 + 3.67712i) q^{74} +(-0.866555 + 1.49969i) q^{75} +(-7.72615 - 4.46069i) q^{76} +(-0.906511 + 4.47744i) q^{77} +(6.25419 - 10.8237i) q^{78} +13.6185 q^{79} +(-1.09496 - 1.89652i) q^{80} +(8.99999 + 0.0127019i) q^{81} +(-1.47758 - 0.853079i) q^{82} +(-4.95763 - 8.58686i) q^{83} +(3.89854 + 11.6284i) q^{84} +(2.47597 - 4.28850i) q^{85} +(21.8104 - 12.5922i) q^{86} +(-8.18564 + 4.72213i) q^{87} +(1.26266 - 2.18699i) q^{88} +(5.36098 - 9.28549i) q^{89} +(5.62058 - 3.23976i) q^{90} +(1.75223 - 8.65462i) q^{91} +(-6.20075 + 3.58001i) q^{92} +(-0.00475554 + 13.4782i) q^{93} -24.9492i q^{94} +3.33344i q^{95} +(-0.00468166 + 13.2688i) q^{96} +(-2.88709 + 1.66686i) q^{97} +(9.13288 + 12.0719i) q^{98} +(-4.48414 - 2.59314i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9}+O(q^{10}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9	\( 30 q + 4 q^{3} - 30 q^{4} + 15 q^{5} - q^{6} - 3 q^{7} - 2 q^{9} + 3 q^{10} + 9 q^{11} + 15 q^{12} - 12 q^{13} - 27 q^{14} - q^{15} + 42 q^{16} - 3 q^{17} - 4 q^{18} - 15 q^{20} + 4 q^{21} + 15 q^{22} + q^{24} - 15 q^{25} + 24 q^{26} - 5 q^{27} + 27 q^{28} - 2 q^{30} - 25 q^{33} + 48 q^{34} - 6 q^{35} + 21 q^{36} - 3 q^{37} - 30 q^{38} - 3 q^{39} + 3 q^{40} - 18 q^{41} - 16 q^{42} + 12 q^{43} + 15 q^{44} - 7 q^{45} + 9 q^{46} - 60 q^{47} - 40 q^{48} - 15 q^{49} + 3 q^{50} - 48 q^{51} - 33 q^{52} - 30 q^{53} + 35 q^{54} + 42 q^{56} - 21 q^{57} + 30 q^{59} + 33 q^{60} + 12 q^{62} - 47 q^{63} - 138 q^{64} + 100 q^{66} + 12 q^{67} - 21 q^{68} + 32 q^{69} - 18 q^{70} + 85 q^{72} + 6 q^{73} + 54 q^{74} - 5 q^{75} - 54 q^{76} - 9 q^{77} - 18 q^{78} + 24 q^{79} + 21 q^{80} - 14 q^{81} + 6 q^{82} - 6 q^{83} - 9 q^{84} + 3 q^{85} - 60 q^{86} - 16 q^{87} - 48 q^{88} - 3 q^{89} + 22 q^{90} + 15 q^{91} - 3 q^{92} + 69 q^{93} - 48 q^{96} + 36 q^{97} + 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 4 * q^3 - 30 * q^4 + 15 * q^5 - q^6 - 3 * q^7 - 2 * q^9 + 3 * q^10 + 9 * q^11 + 15 * q^12 - 12 * q^13 - 27 * q^14 - q^15 + 42 * q^16 - 3 * q^17 - 4 * q^18 - 15 * q^20 + 4 * q^21 + 15 * q^22 + q^24 - 15 * q^25 + 24 * q^26 - 5 * q^27 + 27 * q^28 - 2 * q^30 - 25 * q^33 + 48 * q^34 - 6 * q^35 + 21 * q^36 - 3 * q^37 - 30 * q^38 - 3 * q^39 + 3 * q^40 - 18 * q^41 - 16 * q^42 + 12 * q^43 + 15 * q^44 - 7 * q^45 + 9 * q^46 - 60 * q^47 - 40 * q^48 - 15 * q^49 + 3 * q^50 - 48 * q^51 - 33 * q^52 - 30 * q^53 + 35 * q^54 + 42 * q^56 - 21 * q^57 + 30 * q^59 + 33 * q^60 + 12 * q^62 - 47 * q^63 - 138 * q^64 + 100 * q^66 + 12 * q^67 - 21 * q^68 + 32 * q^69 - 18 * q^70 + 85 * q^72 + 6 * q^73 + 54 * q^74 - 5 * q^75 - 54 * q^76 - 9 * q^77 - 18 * q^78 + 24 * q^79 + 21 * q^80 - 14 * q^81 + 6 * q^82 - 6 * q^83 - 9 * q^84 + 3 * q^85 - 60 * q^86 - 16 * q^87 - 48 * q^88 - 3 * q^89 + 22 * q^90 + 15 * q^91 - 3 * q^92 + 69 * q^93 - 48 * q^96 + 36 * q^97 + 24 * q^98 - q^99

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