LMFDB - Embedded newform 315.2.t.c.101.14

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.14
Character	$\chi$	$=$	315.101
Dual form			315.2.t.c.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.32447i q^{2} +(-1.01455 + 1.40381i) q^{3} -3.40314 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.26312 - 2.35828i) q^{6} +(-1.17052 - 2.37274i) q^{7} -3.26155i q^{8} +(-0.941384 - 2.84847i) q^{9} +O(q^{10})$	\(q+2.32447i q^{2} +(-1.01455 + 1.40381i) q^{3} -3.40314 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.26312 - 2.35828i) q^{6} +(-1.17052 - 2.37274i) q^{7} -3.26155i q^{8} +(-0.941384 - 2.84847i) q^{9} +(-2.01305 - 1.16223i) q^{10} +(-3.50939 + 2.02615i) q^{11} +(3.45265 - 4.77737i) q^{12} +(3.52689 - 2.03625i) q^{13} +(5.51534 - 2.72084i) q^{14} +(-0.708464 - 1.58053i) q^{15} +0.775076 q^{16} +(-2.04818 + 3.54756i) q^{17} +(6.62118 - 2.18821i) q^{18} +(-4.39960 + 2.54011i) q^{19} +(1.70157 - 2.94720i) q^{20} +(4.51843 + 0.764056i) q^{21} +(-4.70970 - 8.15745i) q^{22} +(4.66251 + 2.69190i) q^{23} +(4.57860 + 3.30900i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(4.73319 + 8.19813i) q^{26} +(4.95380 + 1.56839i) q^{27} +(3.98346 + 8.07475i) q^{28} +(-6.66716 - 3.84929i) q^{29} +(3.67389 - 1.64680i) q^{30} +4.74104i q^{31} -4.72146i q^{32} +(0.716112 - 6.98215i) q^{33} +(-8.24618 - 4.76093i) q^{34} +(2.64011 + 0.172663i) q^{35} +(3.20366 + 9.69375i) q^{36} +(-3.38696 - 5.86638i) q^{37} +(-5.90439 - 10.2267i) q^{38} +(-0.719684 + 7.01696i) q^{39} +(2.82458 + 1.63077i) q^{40} +(2.50768 + 4.34343i) q^{41} +(-1.77602 + 10.5029i) q^{42} +(-3.96318 + 6.86444i) q^{43} +(11.9429 - 6.89525i) q^{44} +(2.93754 + 0.608974i) q^{45} +(-6.25723 + 10.8378i) q^{46} +2.82897 q^{47} +(-0.786352 + 1.08806i) q^{48} +(-4.25974 + 5.55469i) q^{49} +(2.01305 - 1.16223i) q^{50} +(-2.90213 - 6.47444i) q^{51} +(-12.0025 + 6.92964i) q^{52} +(0.306591 + 0.177011i) q^{53} +(-3.64566 + 11.5149i) q^{54} -4.05229i q^{55} +(-7.73879 + 3.81772i) q^{56} +(0.897766 - 8.75328i) q^{57} +(8.94753 - 15.4976i) q^{58} -5.67326 q^{59} +(2.41100 + 5.37877i) q^{60} -1.52310i q^{61} -11.0204 q^{62} +(-5.65676 + 5.56786i) q^{63} +12.5250 q^{64} +4.07250i q^{65} +(16.2298 + 1.66458i) q^{66} -5.76519 q^{67} +(6.97025 - 12.0728i) q^{68} +(-8.50926 + 3.81423i) q^{69} +(-0.401350 + 6.13685i) q^{70} -8.87212i q^{71} +(-9.29043 + 3.07037i) q^{72} +(5.36715 + 3.09872i) q^{73} +(13.6362 - 7.87286i) q^{74} +(1.72301 + 0.176718i) q^{75} +(14.9724 - 8.64434i) q^{76} +(8.91533 + 5.95519i) q^{77} +(-16.3107 - 1.67288i) q^{78} -9.47533 q^{79} +(-0.387538 + 0.671235i) q^{80} +(-7.22759 + 5.36301i) q^{81} +(-10.0961 + 5.82901i) q^{82} +(-7.28438 + 12.6169i) q^{83} +(-15.3768 - 2.60019i) q^{84} +(-2.04818 - 3.54756i) q^{85} +(-15.9561 - 9.21228i) q^{86} +(12.1678 - 5.45416i) q^{87} +(6.60837 + 11.4460i) q^{88} +(3.57069 + 6.18462i) q^{89} +(-1.41554 + 6.82821i) q^{90} +(-8.95979 - 5.98489i) q^{91} +(-15.8672 - 9.16091i) q^{92} +(-6.65553 - 4.81001i) q^{93} +6.57585i q^{94} -5.08022i q^{95} +(6.62805 + 4.79015i) q^{96} +(8.13886 + 4.69897i) q^{97} +(-12.9117 - 9.90163i) q^{98} +(9.07510 + 8.08901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	$ 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			2.32447i			1.64365i	0.569744	+	0.821823i	$0.307043\pi$
$2$			2.32447i			1.64365i	−0.569744	+	0.821823i	$0.692957\pi$
$3$	−1.01455	+	1.40381i	−0.585750	+	0.810492i
$3$	−1.01455	+	1.40381i	−0.585750	+	0.810492i
$4$	−3.40314			−1.70157
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−3.26312	−	2.35828i	−1.33216	−	0.962765i
$7$	−1.17052	−	2.37274i	−0.442417	−	0.896810i
$7$	−1.17052	−	2.37274i	−0.442417	−	0.896810i
$8$		−	3.26155i		−	1.15313i
$9$	−0.941384	−	2.84847i	−0.313795	−	0.949491i
$10$	−2.01305	−	1.16223i	−0.636581	−	0.367530i
$11$	−3.50939	+	2.02615i	−1.05812	+	0.610906i	−0.924912	−	0.380182i	$-0.875861\pi$
$11$	−3.50939	+	2.02615i	−1.05812	+	0.610906i	−0.133208	+	0.991088i	$0.542528\pi$
$12$	3.45265	−	4.77737i	0.996694	−	1.37911i
$13$	3.52689	−	2.03625i	0.978183	−	0.564754i	0.0764616	−	0.997073i	$-0.475638\pi$
$13$	3.52689	−	2.03625i	0.978183	−	0.564754i	0.901721	+	0.432319i	$0.142304\pi$
$14$	5.51534	−	2.72084i	1.47404	−	0.727176i
$15$	−0.708464	−	1.58053i	−0.182925	−	0.408091i
$16$	0.775076			0.193769
$17$	−2.04818	+	3.54756i	−0.496757	+	0.860409i	−0.999993	−	0.00374009i	$-0.998809\pi$
$17$	−2.04818	+	3.54756i	−0.496757	+	0.860409i	0.503236	+	0.864149i	$0.332143\pi$
$18$	6.62118	−	2.18821i	1.56063	−	0.515767i
$19$	−4.39960	+	2.54011i	−1.00934	+	0.582741i	−0.910997	−	0.412412i	$-0.864686\pi$
$19$	−4.39960	+	2.54011i	−1.00934	+	0.582741i	−0.0983394	+	0.995153i	$0.531353\pi$
$20$	1.70157	−	2.94720i	0.380482	−	0.659015i
$21$	4.51843	+	0.764056i	0.986002	+	0.166731i
$22$	−4.70970	−	8.15745i	−1.00411	−	1.73917i
$23$	4.66251	+	2.69190i	0.972200	+	0.561300i	0.899906	−	0.436083i	$-0.143635\pi$
$23$	4.66251	+	2.69190i	0.972200	+	0.561300i	0.0722938	+	0.997383i	$0.476968\pi$
$24$	4.57860	+	3.30900i	0.934603	+	0.675446i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.73319	+	8.19813i	0.928255	+	1.60779i
$27$	4.95380	+	1.56839i	0.953360	+	0.301836i
$28$	3.98346	+	8.07475i	0.752803	+	1.52598i
$29$	−6.66716	−	3.84929i	−1.23806	−	0.714795i	−0.269363	−	0.963039i	$-0.586813\pi$
$29$	−6.66716	−	3.84929i	−1.23806	−	0.714795i	−0.968698	+	0.248244i	$0.920147\pi$
$30$	3.67389	−	1.64680i	0.670757	−	0.300663i
$31$			4.74104i			0.851516i	0.904837	+	0.425758i	$0.139992\pi$
$31$			4.74104i			0.851516i	−0.904837	+	0.425758i	$0.860008\pi$
$32$		−	4.72146i		−	0.834644i
$33$	0.716112	−	6.98215i	0.124659	−	1.21544i
$34$	−8.24618	−	4.76093i	−1.41421	−	0.816493i
$35$	2.64011	+	0.172663i	0.446260	+	0.0291855i
$36$	3.20366	+	9.69375i	0.533943	+	1.61562i
$37$	−3.38696	−	5.86638i	−0.556812	−	0.964427i	−0.997760	−	0.0668944i	$-0.978691\pi$
$37$	−3.38696	−	5.86638i	−0.556812	−	0.964427i	0.440948	−	0.897533i	$-0.354642\pi$
$38$	−5.90439	−	10.2267i	−0.957819	−	1.65899i
$39$	−0.719684	+	7.01696i	−0.115242	+	1.12361i
$40$	2.82458	+	1.63077i	0.446606	+	0.257848i
$41$	2.50768	+	4.34343i	0.391634	+	0.678329i	0.992665	−	0.120896i	$-0.0385768\pi$
$41$	2.50768	+	4.34343i	0.391634	+	0.678329i	−0.601032	+	0.799225i	$0.705243\pi$
$42$	−1.77602	+	10.5029i	−0.274046	+	1.62064i
$43$	−3.96318	+	6.86444i	−0.604380	+	1.04682i	0.387769	+	0.921757i	$0.373246\pi$
$43$	−3.96318	+	6.86444i	−0.604380	+	1.04682i	−0.992149	+	0.125060i	$0.960088\pi$
$44$	11.9429	−	6.89525i	1.80046	−	1.03950i
$45$	2.93754	+	0.608974i	0.437903	+	0.0907805i
$46$	−6.25723	+	10.8378i	−0.922578	+	1.59795i
$47$	2.82897			0.412648			0.206324	−	0.978484i	$-0.433850\pi$
$47$	2.82897			0.412648			0.206324	+	0.978484i	$0.433850\pi$
$48$	−0.786352	+	1.08806i	−0.113500	+	0.157048i
$49$	−4.25974	+	5.55469i	−0.608535	+	0.793527i
$50$	2.01305	−	1.16223i	0.284688	−	0.164365i
$51$	−2.90213	−	6.47444i	−0.406379	−	0.906602i
$52$	−12.0025	+	6.92964i	−1.66445	+	0.960968i
$53$	0.306591	+	0.177011i	0.0421136	+	0.0243143i	0.520909	−	0.853612i	$-0.325593\pi$
$53$	0.306591	+	0.177011i	0.0421136	+	0.0243143i	−0.478795	+	0.877927i	$0.658926\pi$
$54$	−3.64566	+	11.5149i	−0.496111	+	1.56699i
$55$		−	4.05229i		−	0.546411i
$56$	−7.73879	+	3.81772i	−1.03414	+	0.510164i
$57$	0.897766	−	8.75328i	0.118912	−	1.15940i
$58$	8.94753	−	15.4976i	1.17487	−	2.03493i
$59$	−5.67326			−0.738595			−0.369298	−	0.929311i	$-0.620402\pi$
$59$	−5.67326			−0.738595			−0.369298	+	0.929311i	$0.620402\pi$
$60$	2.41100	+	5.37877i	0.311259	+	0.694396i
$61$		−	1.52310i		−	0.195012i	−0.995235	−	0.0975062i	$-0.968913\pi$
$61$		−	1.52310i		−	0.195012i	0.995235	−	0.0975062i	$-0.0310866\pi$
$62$	−11.0204			−1.39959
$63$	−5.65676	+	5.56786i	−0.712685	+	0.701485i
$64$	12.5250			1.56563
$65$			4.07250i			0.505131i
$66$	16.2298	+	1.66458i	1.99774	+	0.204895i
$67$	−5.76519			−0.704330			−0.352165	−	0.935938i	$-0.614554\pi$
$67$	−5.76519			−0.704330			−0.352165	+	0.935938i	$0.614554\pi$
$68$	6.97025	−	12.0728i	0.845267	−	1.46405i
$69$	−8.50926	+	3.81423i	−1.02439	+	0.459179i
$70$	−0.401350	+	6.13685i	−0.0479705	+	0.733493i
$71$		−	8.87212i		−	1.05293i	−0.850198	−	0.526463i	$-0.823518\pi$
$71$		−	8.87212i		−	1.05293i	0.850198	−	0.526463i	$-0.176482\pi$
$72$	−9.29043	+	3.07037i	−1.09489	+	0.361846i
$73$	5.36715	+	3.09872i	0.628177	+	0.362678i	0.780046	−	0.625723i	$-0.215196\pi$
$73$	5.36715	+	3.09872i	0.628177	+	0.362678i	−0.151869	+	0.988401i	$0.548529\pi$
$74$	13.6362	−	7.87286i	1.58518	−	0.915202i
$75$	1.72301	+	0.176718i	0.198956	+	0.0204056i
$76$	14.9724	−	8.64434i	1.71746	−	0.991574i
$77$	8.91533	+	5.95519i	1.01600	+	0.678657i
$78$	−16.3107	−	1.67288i	−1.84682	−	0.189416i
$79$	−9.47533			−1.06606			−0.533029	−	0.846097i	$-0.678946\pi$
$79$	−9.47533			−1.06606			−0.533029	+	0.846097i	$0.678946\pi$
$80$	−0.387538	+	0.671235i	−0.0433281	+	0.0750464i
$81$	−7.22759	+	5.36301i	−0.803066	+	0.595890i
$82$	−10.0961	+	5.82901i	−1.11493	+	0.643707i
$83$	−7.28438	+	12.6169i	−0.799564	+	1.38489i	0.120336	+	0.992733i	$0.461603\pi$
$83$	−7.28438	+	12.6169i	−0.799564	+	1.38489i	−0.919900	+	0.392153i	$0.871731\pi$
$84$	−15.3768	−	2.60019i	−1.67775	−	0.283704i
$85$	−2.04818	−	3.54756i	−0.222157	−	0.384787i
$86$	−15.9561	−	9.21228i	−1.72060	−	0.993386i
$87$	12.1678	−	5.45416i	1.30453	−	0.584747i
$88$	6.60837	+	11.4460i	0.704454	+	1.22015i
$89$	3.57069	+	6.18462i	0.378493	+	0.655568i	0.990843	−	0.135018i	$-0.0431092\pi$
$89$	3.57069	+	6.18462i	0.378493	+	0.655568i	−0.612351	+	0.790586i	$0.709776\pi$
$90$	−1.41554	+	6.82821i	−0.149211	+	0.719757i
$91$	−8.95979	−	5.98489i	−0.939241	−	0.627387i
$92$	−15.8672	−	9.16091i	−1.65427	−	0.955091i
$93$	−6.65553	−	4.81001i	−0.690147	−	0.498775i
$94$			6.57585i			0.678247i
$95$		−	5.08022i		−	0.521219i
$96$	6.62805	+	4.79015i	0.676472	+	0.488892i
$97$	8.13886	+	4.69897i	0.826376	+	0.477109i	0.852610	−	0.522547i	$-0.175018\pi$
$97$	8.13886	+	4.69897i	0.826376	+	0.477109i	−0.0262340	+	0.999656i	$0.508352\pi$
$98$	−12.9117	−	9.90163i	−1.30428	−	1.00022i
$99$	9.07510	+	8.08901i	0.912082	+	0.812976i
$100$	1.70157	+	2.94720i	0.170157	+	0.294720i
$101$	5.23112	+	9.06057i	0.520516	+	0.901561i	0.999715	+	0.0238545i	$0.00759384\pi$
$101$	5.23112	+	9.06057i	0.520516	+	0.901561i	−0.479199	+	0.877706i	$0.659073\pi$
$102$	15.0496	−	6.74590i	1.49013	−	0.667943i
$103$	7.99271	+	4.61459i	0.787545	+	0.454689i	0.839098	−	0.543981i	$-0.183084\pi$
$103$	7.99271	+	4.61459i	0.787545	+	0.454689i	−0.0515526	+	0.998670i	$0.516417\pi$
$104$	−6.64132	−	11.5031i	−0.651235	−	1.12797i
$105$	−2.92091	+	3.53105i	−0.285051	+	0.344595i
$106$	−0.411455	+	0.712661i	−0.0399641	+	0.0692198i
$107$	−14.1104	+	8.14662i	−1.36410	+	0.787564i	−0.990167	−	0.139891i	$-0.955325\pi$
$107$	−14.1104	+	8.14662i	−1.36410	+	0.787564i	−0.373934	+	0.927455i	$0.621991\pi$
$108$	−16.8585	−	5.33744i	−1.62221	−	0.513595i
$109$	4.37462	−	7.57706i	0.419012	−	0.725751i	−0.576828	−	0.816866i	$-0.695710\pi$
$109$	4.37462	−	7.57706i	0.419012	−	0.725751i	0.995840	+	0.0911149i	$0.0290431\pi$
$110$	9.41941			0.898105
$111$	11.6715	+	1.19707i	1.10781	+	0.113621i
$112$	−0.907245	−	1.83905i	−0.0857266	−	0.173774i
$113$	6.78231	−	3.91577i	0.638026	−	0.368365i	−0.145827	−	0.989310i	$-0.546584\pi$
$113$	6.78231	−	3.91577i	0.638026	−	0.368365i	0.783854	+	0.620945i	$0.213251\pi$
$114$	20.3467	+	2.08682i	1.90564	+	0.195449i
$115$	−4.66251	+	2.69190i	−0.434781	+	0.251021i
$116$	22.6893	+	13.0997i	2.10665	+	1.21627i
$117$	−9.12035	−	8.12935i	−0.843177	−	0.751559i
$118$		−	13.1873i		−	1.21399i
$119$	10.8149	+	0.707293i	0.991397	+	0.0648374i
$120$	−5.15498	+	2.31069i	−0.470583	+	0.210936i
$121$	2.71053	−	4.69477i	0.246412	−	0.426798i
$122$	3.54038			0.320531
$123$	−8.64152	−	0.886303i	−0.779180	−	0.0799153i
$124$		−	16.1344i		−	1.44891i
$125$	1.00000			0.0894427
$126$	−12.9423	−	13.1489i	−1.15299	−	1.17140i
$127$	22.1299			1.96371			0.981857	−	0.189625i	$-0.0607271\pi$
$127$	22.1299			1.96371			0.981857	+	0.189625i	$0.0607271\pi$
$128$			19.6710i			1.73869i
$129$	−5.61555	−	12.5279i	−0.494421	−	1.10302i
$130$	−9.46638			−0.830257
$131$	−0.249138	+	0.431519i	−0.0217673	+	0.0377020i	−0.876704	−	0.481031i	$-0.840263\pi$
$131$	−0.249138	+	0.431519i	−0.0217673	+	0.0377020i	0.854937	+	0.518733i	$0.173596\pi$
$132$	−2.43703	+	23.7612i	−0.212116	+	2.06815i
$133$	11.1768	+	7.46582i	0.969155	+	0.647369i
$134$		−	13.4010i		−	1.15767i
$135$	−3.83516	+	3.50593i	−0.330078	+	0.301742i
$136$	11.5705	+	6.68025i	0.992165	+	0.572826i
$137$	−3.49909	+	2.02020i	−0.298947	+	0.172597i	−0.641970	−	0.766730i	$-0.721883\pi$
$137$	−3.49909	+	2.02020i	−0.298947	+	0.172597i	0.343022	+	0.939327i	$0.388549\pi$
$138$	−8.86604	−	19.7795i	−0.754727	−	1.68374i
$139$	5.39219	−	3.11318i	0.457360	−	0.264057i	−0.253574	−	0.967316i	$-0.581606\pi$
$139$	5.39219	−	3.11318i	0.457360	−	0.264057i	0.710933	+	0.703259i	$0.248273\pi$
$140$	−8.98466	−	0.587598i	−0.759343	−	0.0496611i
$141$	−2.87013	+	3.97135i	−0.241709	+	0.334448i
$142$	20.6229			1.73064
$143$	−8.25147	+	14.2920i	−0.690023	+	1.19515i
$144$	−0.729644	−	2.20778i	−0.0608036	−	0.183982i
$145$	6.66716	−	3.84929i	0.553678	−	0.319666i
$146$	−7.20287	+	12.4757i	−0.596114	+	1.03250i
$147$	−3.47603	−	11.6154i	−0.286698	−	0.958021i
$148$	11.5263	+	19.9641i	0.947455	+	1.64104i
$149$	1.23735	+	0.714383i	0.101367	+	0.0585245i	0.549827	−	0.835279i	$-0.314694\pi$
$149$	1.23735	+	0.714383i	0.101367	+	0.0585245i	−0.448459	+	0.893803i	$0.648027\pi$
$150$	−0.410775	+	4.00508i	−0.0335396	+	0.327014i
$151$	6.43583	+	11.1472i	0.523740	+	0.907145i	0.999618	+	0.0276334i	$0.00879709\pi$
$151$	6.43583	+	11.1472i	0.523740	+	0.907145i	−0.475878	+	0.879511i	$0.657870\pi$
$152$	8.28468	+	14.3495i	0.671977	+	1.16390i
$153$	12.0332	+	2.49458i	0.972831	+	0.201675i
$154$	−13.8426	+	20.7234i	−1.11547	+	1.66994i
$155$	−4.10586	−	2.37052i	−0.329791	−	0.190405i
$156$	2.44918	−	23.8797i	0.196092	−	1.91191i
$157$		−	10.8728i		−	0.867743i	−0.900975	−	0.433872i	$-0.857147\pi$
$157$		−	10.8728i		−	0.867743i	0.900975	−	0.433872i	$-0.142853\pi$
$158$		−	22.0251i		−	1.75222i
$159$	−0.559542	+	0.250811i	−0.0443746	+	0.0198906i
$160$	4.08890	+	2.36073i	0.323256	+	0.186632i
$161$	0.929586	−	14.2138i	0.0732616	−	1.12021i
$162$	−12.4661	−	16.8003i	−0.979432	−	1.31996i
$163$	8.44293	+	14.6236i	0.661301	+	1.14541i	0.980274	+	0.197643i	$0.0633287\pi$
$163$	8.44293	+	14.6236i	0.661301	+	1.14541i	−0.318973	+	0.947764i	$0.603338\pi$
$164$	−8.53398	−	14.7813i	−0.666392	−	1.15422i
$165$	5.68866	+	4.11124i	0.442862	+	0.320060i
$166$	−29.3276	−	16.9323i	−2.27626	−	1.31420i
$167$	11.1959	+	19.3919i	0.866364	+	1.50059i	0.865686	+	0.500587i	$0.166883\pi$
$167$	11.1959	+	19.3919i	0.866364	+	1.50059i	0.000678079		1.00000i	$0.499784\pi$
$168$	2.49201	−	14.7371i	0.192262	−	1.13699i
$169$	1.79262	−	3.10491i	0.137894	−	0.238840i
$170$	8.24618	−	4.76093i	0.632453	−	0.365147i
$171$	11.3771	+	10.1409i	0.870032	+	0.775495i
$172$	13.4873	−	23.3606i	1.02839	−	1.78123i
$173$	−8.75418			−0.665568			−0.332784	−	0.943003i	$-0.607988\pi$
$173$	−8.75418			−0.665568			−0.332784	+	0.943003i	$0.607988\pi$
$174$	12.6780	+	28.2837i	0.961117	+	2.14418i
$175$	−1.46959	+	2.20007i	−0.111090	+	0.166310i
$176$	−2.72004	+	1.57042i	−0.205031	+	0.118375i
$177$	5.75579	−	7.96419i	0.432632	−	0.598625i
$178$	−14.3759	+	8.29995i	−1.07752	+	0.622108i
$179$	−0.203742	−	0.117631i	−0.0152284	−	0.00879213i	0.492366	−	0.870388i	$-0.336132\pi$
$179$	−0.203742	−	0.117631i	−0.0152284	−	0.00879213i	−0.507595	+	0.861596i	$0.669465\pi$
$180$	−9.99686	−	2.07242i	−0.745122	−	0.154469i
$181$		−	16.9989i		−	1.26352i	−0.775165	−	0.631758i	$-0.782333\pi$
$181$		−	16.9989i		−	1.26352i	0.775165	−	0.631758i	$-0.217667\pi$
$182$	13.9117	−	20.8267i	1.03120	−	1.54378i
$183$	2.13814	+	1.54525i	0.158056	+	0.114229i
$184$	8.77976	−	15.2070i	0.647252	−	1.12107i
$185$	6.77391			0.498028
$186$	11.1807	−	15.4706i	0.819809	−	1.13436i
$187$		−	16.5997i		−	1.21389i
$188$	−9.62739			−0.702150
$189$	−2.07718	−	13.5899i	−0.151093	−	0.988520i
$190$	11.8088			0.856700
$191$		−	12.2688i		−	0.887742i	−0.896091	−	0.443871i	$-0.853605\pi$
$191$		−	12.2688i		−	0.887742i	0.896091	−	0.443871i	$-0.146395\pi$
$192$	−12.7072	+	17.5828i	−0.917066	+	1.26893i
$193$	2.38941			0.171993			0.0859966	−	0.996295i	$-0.472593\pi$
$193$	2.38941			0.171993			0.0859966	+	0.996295i	$0.472593\pi$
$194$	−10.9226	+	18.9185i	−0.784197	+	1.35827i
$195$	−5.71703	−	4.13175i	−0.409405	−	0.295881i
$196$	14.4965	−	18.9034i	1.03546	−	1.35024i
$197$			1.10713i			0.0788800i	0.999222	+	0.0394400i	$0.0125574\pi$
$197$			1.10713i			0.0788800i	−0.999222	+	0.0394400i	$0.987443\pi$
$198$	−18.8026	+	21.0948i	−1.33624	+	1.49914i
$199$	−8.92259	−	5.15146i	−0.632506	−	0.365177i	0.149216	−	0.988805i	$-0.452325\pi$
$199$	−8.92259	−	5.15146i	−0.632506	−	0.365177i	−0.781722	+	0.623627i	$0.785658\pi$
$200$	−2.82458	+	1.63077i	−0.199728	+	0.115313i
$201$	5.84906	−	8.09325i	0.412561	−	0.570854i
$202$	−21.0610	+	12.1596i	−1.48185	+	0.855544i
$203$	−1.32926	+	20.3251i	−0.0932960	+	1.42654i
$204$	9.87634	+	22.0334i	0.691482	+	1.54265i
$205$	−5.01536			−0.350288
$206$	−10.7265	+	18.5788i	−0.747348	+	1.29444i
$207$	3.27860	−	15.8151i	0.227878	−	1.09923i
$208$	2.73360	−	1.57825i	0.189541	−	0.109432i
$209$	10.2933	−	17.8284i	0.712000	−	1.23322i
$210$	−8.20780	−	6.78955i	−0.566392	−	0.468523i
$211$	−1.33415	−	2.31082i	−0.0918470	−	0.159084i	0.816441	−	0.577428i	$-0.195944\pi$
$211$	−1.33415	−	2.31082i	−0.0918470	−	0.159084i	−0.908288	+	0.418345i	$0.862610\pi$
$212$	−1.04337	−	0.602392i	−0.0716592	−	0.0413724i
$213$	12.4548	+	9.00119i	0.853389	+	0.616751i
$214$	−18.9365	−	32.7991i	−1.29448	−	2.24210i
$215$	−3.96318	−	6.86444i	−0.270287	−	0.468151i
$216$	5.11537	−	16.1571i	0.348057	−	1.09935i
$217$	11.2492	−	5.54950i	0.763648	−	0.376725i
$218$	17.6126	+	10.1686i	1.19288	+	0.688708i
$219$	−9.79526	+	4.39067i	−0.661902	+	0.296694i
$220$			13.7905i			0.929756i
$221$			16.6825i			1.12218i
$222$	−2.78255	+	27.1301i	−0.186753	+	1.82085i
$223$	−21.8780	−	12.6313i	−1.46506	−	0.845853i	−0.465822	−	0.884879i	$-0.654241\pi$
$223$	−21.8780	−	12.6313i	−1.46506	−	0.845853i	−0.999238	+	0.0390258i	$0.987575\pi$
$224$	−11.2028	+	5.52658i	−0.748516	+	0.369260i
$225$	−1.99616	+	2.23950i	−0.133077	+	0.149300i
$226$	9.10207	+	15.7653i	0.605461	+	1.04869i
$227$	−8.25664	−	14.3009i	−0.548012	−	0.949185i	−0.998411	−	0.0563573i	$-0.982051\pi$
$227$	−8.25664	−	14.3009i	−0.548012	−	0.949185i	0.450398	−	0.892828i	$-0.351282\pi$
$228$	−3.05522	+	29.7886i	−0.202337	+	1.97280i
$229$	−8.17138	−	4.71775i	−0.539980	−	0.311758i	0.205091	−	0.978743i	$-0.434251\pi$
$229$	−8.17138	−	4.71775i	−0.539980	−	0.311758i	−0.745071	+	0.666985i	$0.767584\pi$
$230$	−6.25723	−	10.8378i	−0.412589	−	0.714626i
$231$	−17.4050	+	6.47363i	−1.14517	+	0.425933i
$232$	−12.5546	+	21.7453i	−0.824252	+	1.42765i
$233$	−2.85233	+	1.64680i	−0.186863	+	0.107885i	−0.590513	−	0.807028i	$-0.701075\pi$
$233$	−2.85233	+	1.64680i	−0.186863	+	0.107885i	0.403650	+	0.914913i	$0.367741\pi$
$234$	18.8964	−	21.1999i	1.23530	−	1.38588i
$235$	−1.41449	+	2.44996i	−0.0922710	+	0.159818i
$236$	19.3069			1.25677
$237$	9.61318	−	13.3016i	0.624443	−	0.864031i
$238$	−1.64408	+	25.1388i	−0.106570	+	1.62950i
$239$	−18.7099	+	10.8022i	−1.21025	+	0.698735i	−0.962813	−	0.270170i	$-0.912920\pi$
$239$	−18.7099	+	10.8022i	−1.21025	+	0.698735i	−0.247432	+	0.968905i	$0.579587\pi$
$240$	−0.549113	−	1.22503i	−0.0354451	−	0.0790754i
$241$	4.03983	−	2.33240i	0.260228	−	0.150243i	−0.364210	−	0.931317i	$-0.618661\pi$
$241$	4.03983	−	2.33240i	0.260228	−	0.150243i	0.624439	+	0.781074i	$0.285328\pi$
$242$	10.9128	+	6.30053i	0.701504	+	0.405013i
$243$	−0.195922	−	15.5872i	−0.0125684	−	0.999921i
$244$			5.18331i			0.331827i
$245$	−2.68063	−	6.46639i	−0.171259	−	0.413123i
$246$	2.06018	−	20.0869i	0.131352	−	1.28069i
$247$	−10.3446	+	17.9174i	−0.658210	+	1.14005i
$248$	15.4631			0.981909
$249$	−10.3214	−	23.0264i	−0.654094	−	1.45924i
$250$			2.32447i			0.147012i
$251$	16.4533			1.03853			0.519263	−	0.854614i	$-0.326206\pi$
$251$	16.4533			1.03853			0.519263	+	0.854614i	$0.326206\pi$
$252$	19.2507	−	18.9482i	1.21268	−	1.19362i
$253$	−21.8167			−1.37161
$254$			51.4402i			3.22765i
$255$	7.05809	+	0.723902i	0.441995	+	0.0453325i
$256$	−20.6746			−1.29216
$257$	−3.55975	+	6.16567i	−0.222051	+	0.384604i	−0.955431	−	0.295215i	$-0.904609\pi$
$257$	−3.55975	+	6.16567i	−0.222051	+	0.384604i	0.733379	+	0.679820i	$0.237942\pi$
$258$	29.1206	−	13.0531i	1.81297	−	0.812653i
$259$	−9.95485	+	14.9031i	−0.618564	+	0.926033i
$260$		−	13.8593i		−	0.859516i
$261$	−4.68823	+	22.6149i	−0.290194	+	1.39983i
$262$	−1.00305	−	0.579112i	−0.0619687	−	0.0357777i
$263$	20.9431	−	12.0915i	1.29141	−	0.745593i	0.312502	−	0.949917i	$-0.398833\pi$
$263$	20.9431	−	12.0915i	1.29141	−	0.745593i	0.978903	+	0.204324i	$0.0654995\pi$
$264$	−22.7726	−	2.33563i	−1.40156	−	0.143748i
$265$	−0.306591	+	0.177011i	−0.0188338	+	0.0108737i
$266$	−17.3540	+	25.9802i	−1.06404	+	1.59295i
$267$	−12.3047	−	1.26201i	−0.753035	−	0.0772338i
$268$	19.6197			1.19847
$269$	−9.90870	+	17.1624i	−0.604144	+	1.04641i	0.388042	+	0.921642i	$0.373152\pi$
$269$	−9.90870	+	17.1624i	−0.604144	+	1.04641i	−0.992186	+	0.124767i	$0.960182\pi$
$270$	−8.14940	−	8.91471i	−0.495957	−	0.542532i
$271$	−8.21211	+	4.74127i	−0.498850	+	0.288011i	−0.728239	−	0.685324i	$-0.759661\pi$
$271$	−8.21211	+	4.74127i	−0.498850	+	0.288011i	0.229388	+	0.973335i	$0.426327\pi$
$272$	−1.58750	+	2.74963i	−0.0962562	+	0.166721i
$273$	17.4918	−	6.50591i	1.05865	−	0.393756i
$274$	−4.69589	−	8.13351i	−0.283689	−	0.491364i
$275$	3.50939	+	2.02615i	0.211624	+	0.122181i
$276$	28.9582	−	12.9803i	1.74308	−	0.781325i
$277$	11.5639	+	20.0292i	0.694805	+	1.20344i	0.970247	+	0.242119i	$0.0778425\pi$
$277$	11.5639	+	20.0292i	0.694805	+	1.20344i	−0.275442	+	0.961318i	$0.588824\pi$
$278$	7.23648	+	12.5340i	0.434016	+	0.751737i
$279$	13.5047	−	4.46314i	0.808507	−	0.267201i
$280$	0.563150	−	8.61085i	0.0336547	−	0.514597i
$281$	−0.666797	−	0.384976i	−0.0397778	−	0.0229657i	0.479979	−	0.877280i	$-0.340644\pi$
$281$	−0.666797	−	0.384976i	−0.0397778	−	0.0229657i	−0.519757	+	0.854314i	$0.673978\pi$
$282$	−9.23127	−	6.67152i	−0.549714	−	0.397283i
$283$		−	11.0305i		−	0.655698i	−0.944730	−	0.327849i	$-0.893676\pi$
$283$		−	11.0305i		−	0.655698i	0.944730	−	0.327849i	$-0.106324\pi$
$284$			30.1930i			1.79163i
$285$	7.13168	+	5.15413i	0.422444	+	0.305304i
$286$	−33.2212	−	19.1803i	−1.96441	−	1.13415i
$287$	7.37050	−	11.0341i	0.435067	−	0.651325i
$288$	−13.4489	+	4.44470i	−0.792487	+	0.261907i
$289$	0.109888	+	0.190331i	0.00646400	+	0.0111960i
$290$	8.94753	+	15.4976i	0.525417	+	0.910049i
$291$	−14.8538	+	6.65811i	−0.870742	+	0.390305i
$292$	−18.2651	−	10.5454i	−1.06889	−	0.617122i
$293$	−9.14260	−	15.8355i	−0.534117	−	0.925117i	−0.999206	−	0.0398531i	$-0.987311\pi$
$293$	−9.14260	−	15.8355i	−0.534117	−	0.925117i	0.465089	−	0.885264i	$-0.346022\pi$
$294$	26.9996	−	8.07991i	1.57465	−	0.471230i
$295$	2.83663	−	4.91318i	0.165155	−	0.286057i
$296$	−19.1335	+	11.0467i	−1.11211	+	0.642078i
$297$	−20.5626	+	4.53305i	−1.19316	+	0.263034i
$298$	−1.66056	+	2.87617i	−0.0961935	+	0.166612i
$299$	21.9255			1.26799
$300$	−5.86365	−	0.601396i	−0.338538	−	0.0347216i
$301$	20.9265	+	1.36859i	1.20618	+	0.0788845i
$302$	−25.9112	+	14.9599i	−1.49102	+	0.860843i
$303$	−18.0266	−	1.84887i	−1.03560	−	0.106215i
$304$	−3.41002	+	1.96878i	−0.195578	+	0.112917i
$305$	1.31904	+	0.761548i	0.0755280	+	0.0436061i
$306$	−5.79857	+	27.9709i	−0.331482	+	1.59899i
$307$			14.3196i			0.817262i	0.912700	+	0.408631i	$0.133994\pi$
$307$			14.3196i			0.817262i	−0.912700	+	0.408631i	$0.866006\pi$
$308$	−30.3401	−	20.2663i	−1.72879	−	1.15478i
$309$	−14.5870	+	6.53854i	−0.829826	+	0.371965i
$310$	5.51019	−	9.54393i	0.312958	−	0.542059i
$311$	−4.52414			−0.256541			−0.128270	−	0.991739i	$-0.540942\pi$
$311$	−4.52414			−0.256541			−0.128270	+	0.991739i	$0.540942\pi$
$312$	22.8862	+	2.34728i	1.29567	+	0.132889i
$313$		−	15.3704i		−	0.868786i	−0.900724	−	0.434393i	$-0.856963\pi$
$313$		−	15.3704i		−	0.868786i	0.900724	−	0.434393i	$-0.143037\pi$
$314$	25.2734			1.42626
$315$	−1.99353	−	7.68283i	−0.112323	−	0.432878i
$316$	32.2458			1.81397
$317$			4.16168i			0.233743i	0.993147	+	0.116872i	$0.0372866\pi$
$317$			4.16168i			0.233743i	−0.993147	+	0.116872i	$0.962713\pi$
$318$	−0.583002	−	1.30064i	−0.0326931	−	0.0729360i
$319$	31.1969			1.74669
$320$	−6.26251	+	10.8470i	−0.350085	+	0.606365i
$321$	2.87931	−	28.0735i	0.160707	−	1.56691i
$322$	33.0396	+	2.16079i	1.84122	+	0.120416i
$323$		−	20.8104i		−	1.15792i
$324$	24.5965	−	18.2511i	1.36647	−	1.01395i
$325$	−3.52689	−	2.03625i	−0.195637	−	0.112951i
$326$	−33.9920	+	19.6253i	−1.88264	+	1.08694i
$327$	6.19852	+	13.8284i	0.342779	+	0.764714i
$328$	14.1663	−	8.17891i	0.782202	−	0.451605i
$329$	−3.31138	−	6.71241i	−0.182563	−	0.370067i
$330$	−9.55644	+	13.2231i	−0.526065	+	0.727907i
$331$	−15.4550			−0.849486			−0.424743	−	0.905314i	$-0.639636\pi$
$331$	−15.4550			−0.849486			−0.424743	+	0.905314i	$0.639636\pi$
$332$	24.7897	−	42.9371i	1.36051	−	2.35648i
$333$	−13.5218	+	15.1702i	−0.740990	+	0.831320i
$334$	−45.0757	+	26.0245i	−2.46643	+	1.42400i
$335$	2.88259	−	4.99280i	0.157493	−	0.272786i
$336$	3.50213	+	0.592202i	0.191057	+	0.0323072i
$337$	−8.02681	−	13.9028i	−0.437248	−	0.757336i	0.560228	−	0.828338i	$-0.310713\pi$
$337$	−8.02681	−	13.9028i	−0.437248	−	0.757336i	−0.997476	+	0.0710025i	$0.977380\pi$
$338$	7.21726	+	4.16689i	0.392567	+	0.226649i
$339$	−1.38397	+	13.4938i	−0.0751672	+	0.732885i
$340$	6.97025	+	12.0728i	0.378015	+	0.654741i
$341$	−9.60603	−	16.6381i	−0.520196	−	0.901006i
$342$	−23.5722	+	26.4458i	−1.27464	+	1.43002i
$343$	18.1659	+	3.60534i	0.980869	+	0.194670i
$344$	22.3887	+	12.9261i	1.20712	+	0.696929i
$345$	0.951414	−	9.27635i	0.0512224	−	0.499422i
$346$		−	20.3488i		−	1.09396i
$347$		−	18.6937i		−	1.00353i	−0.865004	−	0.501764i	$-0.832684\pi$
$347$		−	18.6937i		−	1.00353i	0.865004	−	0.501764i	$-0.167316\pi$
$348$	−41.4088	+	18.5613i	−2.21975	+	0.994988i
$349$	30.3681	+	17.5330i	1.62557	+	0.938522i	0.985394	+	0.170291i	$0.0544707\pi$
$349$	30.3681	+	17.5330i	1.62557	+	0.938522i	0.640173	+	0.768231i	$0.278863\pi$
$350$	−5.11399	−	3.41600i	−0.273354	−	0.182593i
$351$	20.6651	−	4.55566i	1.10302	−	0.243163i
$352$	9.56636	+	16.5694i	0.509889	+	0.883153i
$353$	−3.83734	−	6.64647i	−0.204241	−	0.353756i	0.745650	−	0.666338i	$-0.232139\pi$
$353$	−3.83734	−	6.64647i	−0.204241	−	0.353756i	−0.949891	+	0.312582i	$0.898806\pi$
$354$	18.5125	+	13.3791i	0.983928	+	0.711093i
$355$	7.68348	+	4.43606i	0.407797	+	0.235442i
$356$	−12.1516	−	21.0471i	−0.644031	−	1.11550i
$357$	−11.9651	+	14.4645i	−0.633261	+	0.765541i
$358$	0.273428	−	0.473592i	0.0144511	−	0.0250301i
$359$	−24.4512	+	14.1169i	−1.29049	+	0.745062i	−0.978740	−	0.205104i	$-0.934247\pi$
$359$	−24.4512	+	14.1169i	−1.29049	+	0.745062i	−0.311745	+	0.950166i	$0.600913\pi$
$360$	1.98620	−	9.58093i	0.104682	−	0.504959i
$361$	3.40430	−	5.89643i	0.179174	−	0.310338i
$362$	39.5133			2.07677
$363$	3.84062	+	8.56815i	0.201580	+	0.449711i
$364$	30.4914	+	20.3674i	1.59818	+	1.06754i
$365$	−5.36715	+	3.09872i	−0.280929	+	0.162195i
$366$	−3.59189	+	4.97004i	−0.187751	+	0.259788i
$367$	−9.98457	+	5.76460i	−0.521190	+	0.300909i	−0.737422	−	0.675433i	$-0.763957\pi$
$367$	−9.98457	+	5.76460i	−0.521190	+	0.300909i	0.216231	+	0.976342i	$0.430624\pi$
$368$	3.61380	+	2.08643i	0.188382	+	0.108762i
$369$	10.0114	−	11.2319i	0.521175	−	0.584708i
$370$			15.7457i			0.818581i
$371$	0.0611266	−	0.934656i	0.00317353	−	0.0485249i
$372$	22.6497	+	16.3691i	1.17433	+	0.848701i
$373$	14.1802	−	24.5609i	0.734224	−	1.27171i	−0.220839	−	0.975310i	$-0.570880\pi$
$373$	14.1802	−	24.5609i	0.734224	−	1.27171i	0.955063	−	0.296403i	$-0.0957871\pi$
$374$	38.5854			1.99520
$375$	−1.01455	+	1.40381i	−0.0523910	+	0.0724926i
$376$		−	9.22683i		−	0.475838i
$377$	−31.3524			−1.61473
$378$	31.5892	−	4.82834i	1.62478	−	0.248343i
$379$	29.1171			1.49564			0.747821	−	0.663900i	$-0.231100\pi$
$379$	29.1171			1.49564			0.747821	+	0.663900i	$0.231100\pi$
$380$			17.2887i			0.886891i
$381$	−22.4519	+	31.0663i	−1.15024	+	1.59157i
$382$	28.5185			1.45913
$383$	−10.9778	+	19.0141i	−0.560939	+	0.971575i	0.436476	+	0.899716i	$0.356226\pi$
$383$	−10.9778	+	19.0141i	−0.560939	+	0.971575i	−0.997415	+	0.0718590i	$0.977107\pi$
$384$	−27.6145	−	19.9572i	−1.40920	−	1.01844i
$385$	−9.61501	+	4.74331i	−0.490026	+	0.241741i
$386$			5.55409i			0.282696i
$387$	23.2840	+	4.82696i	1.18359	+	0.245368i
$388$	−27.6977	−	15.9913i	−1.40614	−	0.811833i
$389$	−22.0017	+	12.7027i	−1.11553	+	0.644053i	−0.940257	−	0.340467i	$-0.889415\pi$
$389$	−22.0017	+	12.7027i	−1.11553	+	0.644053i	−0.175275	+	0.984519i	$0.556082\pi$
$390$	9.60410	−	13.2890i	0.486323	−	0.672916i
$391$	−19.0993	+	11.0270i	−0.965895	+	0.557660i
$392$	18.1169	+	13.8934i	0.915041	+	0.701720i
$393$	−0.353010	−	0.787540i	−0.0178070	−	0.0397261i
$394$	−2.57349			−0.129651
$395$	4.73766	−	8.20587i	0.238378	−	0.412882i
$396$	−30.8838	−	27.5280i	−1.55197	−	1.38334i
$397$	14.5041	−	8.37394i	0.727939	−	0.420276i	−0.0897285	−	0.995966i	$-0.528600\pi$
$397$	14.5041	−	8.37394i	0.727939	−	0.420276i	0.817668	+	0.575690i	$0.195267\pi$
$398$	11.9744	−	20.7402i	0.600222	−	1.03961i
$399$	−21.8201	+	8.11577i	−1.09237	+	0.406296i
$400$	−0.387538	−	0.671235i	−0.0193769	−	0.0335618i
$401$	6.99061	+	4.03603i	0.349094	+	0.201550i	0.664286	−	0.747478i	$-0.268736\pi$
$401$	6.99061	+	4.03603i	0.349094	+	0.201550i	−0.315192	+	0.949028i	$0.602069\pi$
$402$	18.8125	+	13.5959i	0.938281	+	0.678104i
$403$	9.65394	+	16.7211i	0.480897	+	0.832938i
$404$	−17.8022	−	30.8344i	−0.885695	−	1.53407i
$405$	−1.03071	−	8.94079i	−0.0512162	−	0.444271i
$406$	−47.2450	−	3.08982i	−2.34473	−	0.153345i
$407$	23.7723	+	13.7249i	1.17835	+	0.680320i
$408$	−21.1167	+	9.46543i	−1.04543	+	0.468608i
$409$		−	9.61321i		−	0.475343i	−0.971346	−	0.237671i	$-0.923616\pi$
$409$		−	9.61321i		−	0.475343i	0.971346	−	0.237671i	$-0.0763841\pi$
$410$		−	11.6580i		−	0.575749i
$411$	0.714012	−	6.96166i	0.0352196	−	0.343393i
$412$	−27.2003	−	15.7041i	−1.34006	−	0.773685i
$413$	6.64069	+	13.4611i	0.326767	+	0.662379i
$414$	36.7617	+	7.62098i	1.80674	+	0.374551i
$415$	−7.28438	−	12.6169i	−0.357576	−	0.619340i
$416$	−9.61407	−	16.6520i	−0.471368	−	0.816434i
$417$	−1.10031	+	10.7281i	−0.0538824	+	0.525357i
$418$	41.4416	+	23.9263i	2.02698	+	1.17027i
$419$	−7.82703	−	13.5568i	−0.382376	−	0.662294i	0.609026	−	0.793151i	$-0.291561\pi$
$419$	−7.82703	−	13.5568i	−0.382376	−	0.662294i	−0.991401	+	0.130856i	$0.958227\pi$
$420$	9.94025	−	12.0166i	0.485035	−	0.586352i
$421$	−6.48065	+	11.2248i	−0.315848	+	0.547064i	−0.979617	−	0.200873i	$-0.935622\pi$
$421$	−6.48065	+	11.2248i	−0.315848	+	0.547064i	0.663770	+	0.747937i	$0.268955\pi$
$422$	5.37143	−	3.10119i	0.261477	−	0.150964i
$423$	−2.66315	−	8.05826i	−0.129487	−	0.391806i
$424$	0.577329	−	0.999963i	0.0280376	−	0.0485625i
$425$	4.09637			0.198703
$426$	−20.9230	+	28.9507i	−1.01372	+	1.40267i
$427$	−3.61390	+	1.78282i	−0.174889	+	0.0862768i
$428$	48.0195	−	27.7241i	2.32111	−	1.34009i
$429$	−11.6917	−	26.0834i	−0.564483	−	1.25932i
$430$	15.9561	−	9.21228i	0.769474	−	0.444256i
$431$	2.61711	+	1.51099i	0.126062	+	0.0727818i	0.561705	−	0.827338i	$-0.310146\pi$
$431$	2.61711	+	1.51099i	0.126062	+	0.0727818i	−0.435643	+	0.900120i	$0.643479\pi$
$432$	3.83957	+	1.21562i	0.184732	+	0.0584865i
$433$			34.4143i			1.65385i	0.562315	+	0.826923i	$0.309911\pi$
$433$			34.4143i			1.65385i	−0.562315	+	0.826923i	$0.690089\pi$
$434$	12.8996	+	26.1484i	0.619202	+	1.25517i
$435$	−1.36048	+	13.2647i	−0.0652298	+	0.635995i
$436$	−14.8874	+	25.7858i	−0.712979	+	1.23492i
$437$	−27.3509			−1.30837
$438$	−10.2060	−	22.7687i	−0.487659	−	1.08793i
$439$		−	10.8177i		−	0.516299i	−0.966105	−	0.258150i	$-0.916887\pi$
$439$		−	10.8177i		−	0.516299i	0.966105	−	0.258150i	$-0.0831127\pi$
$440$	−13.2167			−0.630083
$441$	19.8324	+	6.90467i	0.944402	+	0.328794i
$442$	−38.7778			−1.84447
$443$		−	40.4944i		−	1.92395i	−0.273141	−	0.961974i	$-0.588063\pi$
$443$		−	40.4944i		−	1.92395i	0.273141	−	0.961974i	$-0.411937\pi$
$444$	−39.7199	−	4.07380i	−1.88502	−	0.193334i
$445$	−7.14138			−0.338534
$446$	29.3610	−	50.8547i	1.39028	−	2.40804i
$447$	−2.25821	+	1.01223i	−0.106810	+	0.0478768i
$448$	−14.6608	−	29.7185i	−0.692660	−	1.40407i
$449$		−	26.0853i		−	1.23104i	−0.788121	−	0.615520i	$-0.788946\pi$
$449$		−	26.0853i		−	1.23104i	0.788121	−	0.615520i	$-0.211054\pi$
$450$	−5.20564	−	4.64000i	−0.245396	−	0.218732i
$451$	−17.6008	−	10.1618i	−0.828790	−	0.478502i
$452$	−23.0812	+	13.3259i	−1.08565	+	0.626798i
$453$	−22.1780	−	2.27465i	−1.04201	−	0.106873i
$454$	33.2420	−	19.1923i	1.56012	−	0.900738i
$455$	9.66296	−	4.76696i	0.453007	−	0.223479i
$456$	−28.5492	−	2.92810i	−1.33694	−	0.137121i
$457$	7.19569			0.336600			0.168300	−	0.985736i	$-0.446172\pi$
$457$	7.19569			0.336600			0.168300	+	0.985736i	$0.446172\pi$
$458$	10.9662	−	18.9941i	0.512419	−	0.887535i
$459$	−15.7102	+	14.3616i	−0.733291	+	0.670340i
$460$	15.8672	−	9.16091i	0.739810	−	0.427130i
$461$	3.25682	−	5.64097i	0.151685	−	0.262726i	−0.780162	−	0.625578i	$-0.784863\pi$
$461$	3.25682	−	5.64097i	0.151685	−	0.262726i	0.931847	+	0.362851i	$0.118197\pi$
$462$	−15.0477	−	40.4573i	−0.700083	−	1.88225i
$463$	−0.879129	−	1.52270i	−0.0408566	−	0.0707657i	0.844874	−	0.534965i	$-0.179675\pi$
$463$	−0.879129	−	1.52270i	−0.0408566	−	0.0707657i	−0.885731	+	0.464200i	$0.846342\pi$
$464$	−5.16755	−	2.98349i	−0.239898	−	0.138505i
$465$	7.49336	−	3.35886i	0.347496	−	0.155763i
$466$	−3.82792	−	6.63015i	−0.177325	−	0.307136i
$467$	9.87553	+	17.1049i	0.456985	+	0.791521i	0.998800	−	0.0489767i	$-0.0155960\pi$
$467$	9.87553	+	17.1049i	0.456985	+	0.791521i	−0.541815	+	0.840498i	$0.682263\pi$
$468$	31.0378	+	27.6653i	1.43472	+	1.27883i
$469$	6.74829	+	13.6793i	0.311607	+	0.631650i
$470$	−5.69486	−	3.28793i	−0.262684	−	0.151661i
$471$	15.2634	+	11.0310i	0.703299	+	0.508280i
$472$			18.5036i			0.851697i
$473$		−	32.1199i		−	1.47688i
$474$	30.9191	+	22.3455i	1.42016	+	1.02636i
$475$	4.39960	+	2.54011i	0.201867	+	0.116548i
$476$	−36.8045	−	2.40702i	−1.68693	−	0.110325i
$477$	0.215590	−	1.03995i	0.00987118	−	0.0476161i
$478$	−25.1093	−	43.4906i	−1.14847	−	1.98921i
$479$	−18.4647	−	31.9819i	−0.843676	−	1.46129i	−0.886766	−	0.462218i	$-0.847054\pi$
$479$	−18.4647	−	31.9819i	−0.843676	−	1.46129i	0.0430903	−	0.999071i	$-0.486280\pi$
$480$	−7.46241	+	3.34498i	−0.340611	+	0.152677i
$481$	−23.8908	−	13.7934i	−1.08933	−	0.628924i
$482$	5.42158	+	9.39045i	0.246946	+	0.427723i
$483$	19.0105	+	15.7256i	0.865006	+	0.715539i
$484$	−9.22431	+	15.9770i	−0.419287	+	0.726226i
$485$	−8.13886	+	4.69897i	−0.369567	+	0.213369i
$486$	36.2320	−	0.455414i	1.64352	−	0.0206580i
$487$	20.0328	−	34.6979i	0.907775	−	1.57231i	0.0906260	−	0.995885i	$-0.471113\pi$
$487$	20.0328	−	34.6979i	0.907775	−	1.57231i	0.817149	−	0.576427i	$-0.195553\pi$
$488$	−4.96765			−0.224875
$489$	−29.0945	−	2.98403i	−1.31570	−	0.134943i
$490$	15.0309	−	6.23103i	0.679027	−	0.281489i
$491$	2.56846	−	1.48290i	0.115913	−	0.0669225i	−0.440923	−	0.897545i	$-0.645349\pi$
$491$	2.56846	−	1.48290i	0.115913	−	0.0669225i	0.556836	+	0.830623i	$0.312015\pi$
$492$	29.4083	+	3.01621i	1.32583	+	0.135981i
$493$	27.3111	−	15.7681i	1.23003	−	0.710159i
$494$	−41.6483	−	24.0456i	−1.87384	−	1.08186i
$495$	−11.5428	+	3.81476i	−0.518812	+	0.171461i
$496$			3.67466i			0.164997i
$497$	−21.0512	+	10.3850i	−0.944275	+	0.465832i
$498$	53.5240	−	23.9918i	2.39847	−	1.07510i
$499$	−9.14343	+	15.8369i	−0.409316	+	0.708956i	−0.994813	−	0.101718i	$-0.967566\pi$
$499$	−9.14343	+	15.8369i	−0.409316	+	0.708956i	0.585497	+	0.810674i	$0.300899\pi$
$500$	−3.40314			−0.152193
$501$	−38.5813	−	3.95703i	−1.72369	−	0.176787i
$502$			38.2452i			1.70697i
$503$	26.1335			1.16524			0.582618	−	0.812746i	$-0.302028\pi$
$503$	26.1335			1.16524			0.582618	+	0.812746i	$0.302028\pi$
$504$	18.1598	+	18.4498i	0.808904	+	0.821819i
$505$	−10.4622			−0.465564
$506$		−	50.7122i		−	2.25443i
$507$	2.54002	+	5.66659i	0.112806	+	0.251662i
$508$	−75.3112			−3.34139
$509$	1.57746	−	2.73225i	0.0699199	−	0.121105i	−0.828946	−	0.559329i	$-0.811059\pi$
$509$	1.57746	−	2.73225i	0.0699199	−	0.121105i	0.898866	+	0.438224i	$0.144392\pi$
$510$	−1.68268	+	16.4063i	−0.0745105	+	0.726483i
$511$	1.07007	−	16.3619i	0.0473372	−	0.723810i
$512$		−	8.71538i		−	0.385169i
$513$	−25.7786	+	5.68293i	−1.13815	+	0.250907i
$514$	−14.3319	−	8.27452i	−0.632153	−	0.364973i
$515$	−7.99271	+	4.61459i	−0.352201	+	0.203343i
$516$	19.1105	+	42.6341i	0.841292	+	1.87686i
$517$	−9.92797	+	5.73191i	−0.436631	+	0.252089i
$518$	−34.6417	−	23.1397i	−1.52207	−	1.01670i
$519$	8.88154	−	12.2892i	0.389856	−	0.539438i
$520$	13.2826			0.582483
$521$	0.655216	−	1.13487i	0.0287055	−	0.0497195i	−0.851316	−	0.524654i	$-0.824195\pi$
$521$	0.655216	−	1.13487i	0.0287055	−	0.0497195i	0.880021	+	0.474934i	$0.157528\pi$
$522$	−52.5675	−	10.8976i	−2.30082	−	0.476977i
$523$	10.1765	−	5.87541i	0.444988	−	0.256914i	−0.260723	−	0.965414i	$-0.583961\pi$
$523$	10.1765	−	5.87541i	0.444988	−	0.256914i	0.705711	+	0.708500i	$0.250628\pi$
$524$	0.847850	−	1.46852i	0.0370385	−	0.0641526i
$525$	−1.59752	−	4.29510i	−0.0697216	−	0.187454i
$526$	28.1063	+	48.6815i	1.22549	+	2.12261i
$527$	−16.8191	−	9.71052i	−0.732652	−	0.422997i
$528$	0.555041	−	5.41169i	0.0241551	−	0.235514i
$529$	2.99265	+	5.18342i	0.130115	+	0.225366i
$530$	−0.411455	−	0.712661i	−0.0178725	−	0.0309560i
$531$	5.34071	+	16.1601i	0.231767	+	0.701289i
$532$	−38.0363	−	25.4072i	−1.64908	−	1.10154i
$533$	17.6886	+	10.2125i	0.766178	+	0.442353i
$534$	2.93350	−	28.6018i	0.126945	−	1.23772i
$535$		−	16.2932i		−	0.704419i
$536$			18.8034i			0.812184i
$537$	0.371838	−	0.166674i	0.0160460	−	0.00719252i
$538$	−39.8933	−	23.0324i	−1.71992	−	0.992999i
$539$	3.69448	−	28.1244i	0.159133	−	1.21140i
$540$	13.0516	−	11.9312i	0.561651	−	0.513435i
$541$	15.3510	+	26.5887i	0.659991	+	1.14314i	0.980618	+	0.195932i	$0.0627731\pi$
$541$	15.3510	+	26.5887i	0.659991	+	1.14314i	−0.320627	+	0.947206i	$0.603894\pi$
$542$	−11.0209	−	19.0888i	−0.473389	−	0.819933i
$543$	23.8633	+	17.2462i	1.02407	+	0.740105i
$544$	16.7496	+	9.67041i	0.718135	+	0.414616i
$545$	4.37462	+	7.57706i	0.187388	+	0.324566i
$546$	15.1228	+	40.6591i	0.647195	+	1.74005i
$547$	−3.53653	+	6.12544i	−0.151211	+	0.261905i	−0.931673	−	0.363298i	$-0.881651\pi$
$547$	−3.53653	+	6.12544i	−0.151211	+	0.261905i	0.780462	+	0.625203i	$0.214984\pi$
$548$	11.9079	−	6.87502i	0.508680	−	0.293686i
$549$	−4.33850	+	1.43382i	−0.185163	+	0.0611938i
$550$	−4.70970	+	8.15745i	−0.200822	+	0.347835i
$551$	39.1104			1.66616
$552$	12.4403	+	27.7534i	0.529494	+	1.18126i
$553$	11.0911	+	22.4824i	0.471642	+	0.956051i
$554$	−46.5571	+	26.8798i	−1.97802	+	1.14201i
$555$	−6.87246	+	9.50931i	−0.291720	+	0.403648i
$556$	−18.3504	+	10.5946i	−0.778229	+	0.449311i
$557$	19.5519	+	11.2883i	0.828440	+	0.478300i	0.853318	−	0.521391i	$-0.174587\pi$
$557$	19.5519	+	11.2883i	0.828440	+	0.478300i	−0.0248785	+	0.999690i	$0.507920\pi$
$558$	10.3744	+	31.3913i	0.439184	+	1.32890i
$559$			32.2801i			1.36530i
$560$	2.04629	+	0.133827i	0.0864714	+	0.00565523i
$561$	23.3028	+	16.8412i	0.983847	+	0.711035i
$562$	0.894863	−	1.54995i	0.0377475	−	0.0653806i
$563$	42.2398			1.78020			0.890098	−	0.455769i	$-0.150636\pi$
$563$	42.2398			1.78020			0.890098	+	0.455769i	$0.150636\pi$
$564$	9.76746	−	13.5151i	0.411284	−	0.569087i
$565$			7.83154i			0.329475i
$566$	25.6401			1.07773
$567$	21.1851	+	10.8716i	0.889690	+	0.456566i
$568$	−28.9368			−1.21416
$569$			12.9863i			0.544413i	0.962239	+	0.272206i	$0.0877533\pi$
$569$			12.9863i			0.544413i	−0.962239	+	0.272206i	$0.912247\pi$
$570$	−11.9806	+	16.5773i	−0.501812	+	0.694348i
$571$	−14.1760			−0.593248			−0.296624	−	0.954994i	$-0.595861\pi$
$571$	−14.1760			−0.593248			−0.296624	+	0.954994i	$0.595861\pi$
$572$	28.0809	−	48.6376i	1.17412	−	2.03364i
$573$	17.2232	+	12.4473i	0.719508	+	0.519995i
$574$	25.6485	+	17.1325i	1.07055	+	0.715096i
$575$		−	5.38380i		−	0.224520i
$576$	−11.7908	−	35.6772i	−0.491285	−	1.48655i
$577$	20.0965	+	11.6027i	0.836628	+	0.483028i	0.856117	−	0.516783i	$-0.172870\pi$
$577$	20.0965	+	11.6027i	0.836628	+	0.483028i	−0.0194884	+	0.999810i	$0.506204\pi$
$578$	−0.442419	+	0.255431i	−0.0184022	+	0.0106245i
$579$	−2.42417	+	3.35428i	−0.100745	+	0.139399i
$580$	−22.6893	+	13.0997i	−0.942121	+	0.543934i
$581$	38.4631	+	2.51549i	1.59572	+	0.104360i
$582$	−15.4765	−	34.5270i	−0.641523	−	1.43119i
$583$	−1.43460			−0.0594150
$584$	10.1066	−	17.5052i	0.418215	−	0.724370i
$585$	11.6004	−	3.83378i	0.479618	−	0.158507i
$586$	36.8090	−	21.2517i	1.52056	−	0.877898i
$587$	−22.2189	+	38.4842i	−0.917071	+	1.58841i	−0.113231	+	0.993569i	$0.536120\pi$
$587$	−22.2189	+	38.4842i	−0.917071	+	1.58841i	−0.803840	+	0.594845i	$0.797213\pi$
$588$	11.8294	+	39.5288i	0.487837	+	1.63014i
$589$	−12.0428	−	20.8587i	−0.496213	−	0.859466i
$590$	11.4205	+	6.59364i	0.470176	+	0.271456i
$591$	−1.55421	−	1.12324i	−0.0639316	−	0.0462039i
$592$	−2.62515	−	4.54689i	−0.107893	−	0.186876i
$593$	−6.88728	−	11.9291i	−0.282827	−	0.489871i	0.689253	−	0.724521i	$-0.257939\pi$
$593$	−6.88728	−	11.9291i	−0.282827	−	0.489871i	−0.972080	+	0.234650i	$0.924606\pi$
$594$	−10.5369	−	47.7970i	−0.432335	−	1.96114i
$595$	−6.01997	+	9.01230i	−0.246795	+	0.369468i
$596$	−4.21086	−	2.43114i	−0.172484	−	0.0995835i
$597$	16.2841	−	7.29924i	0.666463	−	0.298738i
$598$			50.9651i			2.08412i
$599$		−	13.9616i		−	0.570456i	−0.958460	−	0.285228i	$-0.907931\pi$
$599$		−	13.9616i		−	0.570456i	0.958460	−	0.285228i	$-0.0920694\pi$
$600$	0.576374	−	5.61969i	0.0235304	−	0.229423i
$601$	15.6037	+	9.00882i	0.636490	+	0.367478i	0.783261	−	0.621693i	$-0.213555\pi$
$601$	15.6037	+	9.00882i	0.636490	+	0.367478i	−0.146771	+	0.989170i	$0.546888\pi$
$602$	−3.18125	+	48.6429i	−0.129658	+	1.98254i
$603$	5.42725	+	16.4220i	0.221015	+	0.668755i
$604$	−21.9020	−	37.9354i	−0.891180	−	1.54357i
$605$	2.71053	+	4.69477i	0.110199	+	0.190870i
$606$	4.29763	−	41.9022i	0.174579	−	1.70216i
$607$	−7.65048	−	4.41701i	−0.310523	−	0.179281i	0.336637	−	0.941634i	$-0.390710\pi$
$607$	−7.65048	−	4.41701i	−0.310523	−	0.179281i	−0.647161	+	0.762354i	$0.724044\pi$
$608$	11.9930	+	20.7725i	0.486381	+	0.842437i
$609$	−27.1840	−	22.4868i	−1.10155	−	0.911212i
$610$	−1.77019	+	3.06606i	−0.0716730	+	0.124141i
$611$	9.97747	−	5.76050i	0.403645	−	0.233045i
$612$	−40.9508	−	8.48941i	−1.65534	−	0.343164i
$613$	5.86841	−	10.1644i	0.237023	−	0.410536i	−0.722836	−	0.691020i	$-0.757162\pi$
$613$	5.86841	−	10.1644i	0.237023	−	0.410536i	0.959859	+	0.280484i	$0.0904951\pi$
$614$	−33.2854			−1.34329
$615$	5.08832	−	7.04062i	0.205181	−	0.283905i
$616$	19.4231	−	29.0778i	0.782581	−	1.17158i
$617$	−22.6566	+	13.0808i	−0.912122	+	0.526614i	−0.881113	−	0.472905i	$-0.843205\pi$
$617$	−22.6566	+	13.0808i	−0.912122	+	0.526614i	−0.0310085	+	0.999519i	$0.509872\pi$
$618$	−15.1986	−	33.9070i	−0.611378	−	1.36394i
$619$	22.4834	−	12.9808i	0.903686	−	0.521743i	0.0252917	−	0.999680i	$-0.491949\pi$
$619$	22.4834	−	12.9808i	0.903686	−	0.521743i	0.878394	+	0.477937i	$0.158615\pi$
$620$	13.9728	+	8.06721i	0.561162	+	0.323987i
$621$	18.8752	+	20.6478i	0.757436	+	0.828566i
$622$		−	10.5162i		−	0.421662i
$623$	10.4949	−	15.7116i	0.420469	−	0.629470i
$624$	−0.557809	+	5.43868i	−0.0223302	+	0.217721i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	35.7279			1.42798
$627$	14.5848	+	32.5376i	0.582461	+	1.29943i
$628$			37.0016i			1.47653i
$629$	27.7484			1.10640
$630$	17.8585	−	4.63389i	0.711498	−	0.184619i
$631$	−48.6049			−1.93493			−0.967465	−	0.253004i	$-0.918581\pi$
$631$	−48.6049			−1.93493			−0.967465	+	0.253004i	$0.918581\pi$
$632$			30.9042i			1.22930i
$633$	4.59753	+	0.471538i	0.182735	+	0.0187420i
$634$	−9.67369			−0.384191
$635$	−11.0650	+	19.1651i	−0.439100	+	0.760543i
$636$	1.90420	−	0.853546i	0.0755064	−	0.0338453i
$637$	−3.71290	+	28.2647i	−0.147111	+	1.11989i
$638$			72.5160i			2.87094i
$639$	−25.2720	+	8.35206i	−0.999744	+	0.330403i
$640$	−17.0356	−	9.83552i	−0.673392	−	0.388783i
$641$	10.9069	−	6.29711i	0.430797	−	0.248721i	−0.268889	−	0.963171i	$-0.586656\pi$
$641$	10.9069	−	6.29711i	0.430797	−	0.248721i	0.699686	+	0.714450i	$0.253323\pi$
$642$	65.2558	+	6.69286i	2.57544	+	0.264146i
$643$	−22.1233	+	12.7729i	−0.872457	+	0.503713i	−0.868164	−	0.496278i	$-0.834700\pi$
$643$	−22.1233	+	12.7729i	−0.872457	+	0.503713i	−0.00429273	+	0.999991i	$0.501366\pi$
$644$	−3.16351	+	48.3716i	−0.124660	+	1.90611i
$645$	13.6572	+	1.40073i	0.537753	+	0.0551538i
$646$	48.3731			1.90322
$647$	−18.7151	+	32.4155i	−0.735766	+	1.27438i	0.218620	+	0.975810i	$0.429844\pi$
$647$	−18.7151	+	32.4155i	−0.735766	+	1.27438i	−0.954386	+	0.298575i	$0.903489\pi$
$648$	17.4917	+	23.5731i	0.687139	+	0.926040i
$649$	19.9097	−	11.4948i	0.781522	−	0.451212i
$650$	4.73319	−	8.19813i	0.185651	−	0.321557i
$651$	−3.62242	+	21.4221i	−0.141974	+	0.839597i
$652$	−28.7324	−	49.7661i	−1.12525	−	1.94899i
$653$	14.7891	+	8.53851i	0.578744	+	0.334138i	0.760634	−	0.649181i	$-0.224888\pi$
$653$	14.7891	+	8.53851i	0.578744	+	0.334138i	−0.181890	+	0.983319i	$0.558222\pi$
$654$	−32.1437	+	14.4082i	−1.25692	+	0.563407i
$655$	−0.249138	−	0.431519i	−0.00973462	−	0.0168608i
$656$	1.94364	+	3.36648i	0.0758864	+	0.131439i
$657$	3.77409	−	18.2053i	0.147241	−	0.710255i
$658$	15.6028	−	7.69720i	0.608259	−	0.300068i
$659$	0.282893	+	0.163328i	0.0110199	+	0.00636237i	0.505500	−	0.862827i	$-0.331308\pi$
$659$	0.282893	+	0.163328i	0.0110199	+	0.00636237i	−0.494480	+	0.869189i	$0.664641\pi$
$660$	−19.3593	−	13.9911i	−0.753560	−	0.544604i
$661$			14.8322i			0.576908i	0.957494	+	0.288454i	$0.0931412\pi$
$661$			14.8322i			0.576908i	−0.957494	+	0.288454i	$0.906859\pi$
$662$		−	35.9247i		−	1.39625i
$663$	−23.4190	−	16.9252i	−0.909520	−	0.657318i
$664$	41.1506	+	23.7583i	1.59695	+	0.922002i
$665$	−12.0540	+	5.94652i	−0.467434	+	0.230596i
$666$	−35.2625	−	31.4310i	−1.36640	−	1.21792i
$667$	−20.7238	−	35.8947i	−0.802428	−	1.38985i
$668$	−38.1012	−	65.9932i	−1.47418	−	2.55335i
$669$	39.9283	−	17.8976i	1.54372	−	0.691961i
$670$	11.6056	+	6.70049i	0.448363	+	0.258862i
$671$	3.08601	+	5.34513i	0.119134	+	0.206347i
$672$	3.60746	−	21.3336i	0.139161	−	0.822961i
$673$	−15.4472	+	26.7553i	−0.595446	+	1.03134i	0.398038	+	0.917369i	$0.369691\pi$
$673$	−15.4472	+	26.7553i	−0.595446	+	1.03134i	−0.993484	+	0.113973i	$0.963642\pi$
$674$	32.3167	−	18.6580i	1.24479	−	0.718681i
$675$	−1.11864	−	5.07431i	−0.0430564	−	0.195310i
$676$	−6.10054	+	10.5665i	−0.234636	+	0.406402i
$677$	−10.9122			−0.419389			−0.209694	−	0.977767i	$-0.567247\pi$
$677$	−10.9122			−0.419389			−0.209694	+	0.977767i	$0.567247\pi$
$678$	−31.3660	−	3.21700i	−1.20460	−	0.123548i
$679$	1.62268	−	24.8116i	0.0622728	−	0.952183i
$680$	−11.5705	+	6.68025i	−0.443709	+	0.256176i
$681$	28.4526	+	2.91819i	1.09030	+	0.111825i
$682$	38.6748	−	22.3289i	1.48093	−	0.855018i
$683$	−9.58443	−	5.53357i	−0.366738	−	0.211736i	0.305294	−	0.952258i	$-0.401245\pi$
$683$	−9.58443	−	5.53357i	−0.366738	−	0.211736i	−0.672032	+	0.740522i	$0.734578\pi$
$684$	−38.7180	−	34.5109i	−1.48042	−	1.31956i
$685$		−	4.04040i		−	0.154376i
$686$	−8.38049	+	42.2261i	−0.319969	+	1.61220i
$687$	14.9131	−	6.68471i	0.568970	−	0.255037i
$688$	−3.07177	+	5.32046i	−0.117110	+	0.202841i
$689$	1.44175			0.0549264
$690$	21.5626	+	2.21153i	0.820873	+	0.0841915i
$691$		−	11.7812i		−	0.448177i	−0.974569	−	0.224088i	$-0.928060\pi$
$691$		−	11.7812i		−	0.448177i	0.974569	−	0.224088i	$-0.0719404\pi$
$692$	29.7917			1.13251
$693$	8.57046	−	31.0012i	0.325565	−	1.17764i
$694$	43.4528			1.64944
$695$			6.22637i			0.236179i
$696$	−17.7890	−	39.6860i	−0.674291	−	1.50429i
$697$	−20.5447			−0.778188
$698$	−40.7549	+	70.5896i	−1.54260	+	2.67186i
$699$	0.582037	−	5.67490i	0.0220147	−	0.214644i
$700$	5.00121	−	7.48715i	0.189028	−	0.282988i
$701$			17.3680i			0.655981i	0.944681	+	0.327991i	$0.106371\pi$
$701$			17.3680i			0.655981i	−0.944681	+	0.327991i	$0.893629\pi$
$702$	10.5895	+	48.0354i	0.399674	+	1.81298i
$703$	29.8025	+	17.2065i	1.12402	+	0.648955i
$704$	−43.9551	+	25.3775i	−1.65662	+	0.956451i
$705$	−2.00423	−	4.47128i	−0.0754835	−	0.168398i
$706$	15.4495	−	8.91976i	0.581449	−	0.335700i
$707$	15.3752	−	23.0177i	0.578243	−	0.865670i
$708$	−19.5878	+	27.1033i	−0.736153	+	1.01860i
$709$	41.5086			1.55889			0.779444	−	0.626471i	$-0.215501\pi$
$709$	41.5086			1.55889			0.779444	+	0.626471i	$0.215501\pi$
$710$	−10.3115	+	17.8600i	−0.386982	+	0.670273i
$711$	8.91992	+	26.9902i	0.334523	+	1.01221i
$712$	20.1714	−	11.6460i	0.755956	−	0.436452i
$713$	−12.7624	+	22.1051i	−0.477956	+	0.827844i
$714$	−33.6222	−	27.8125i	−1.25828	−	1.04086i
$715$	−8.25147	−	14.2920i	−0.308588	−	0.534489i
$716$	0.693363	+	0.400314i	0.0259122	+	0.0149604i
$717$	3.81788	−	37.2246i	0.142581	−	1.39018i
$718$	−32.8143	−	56.8360i	−1.22462	−	2.12110i
$719$	7.17651	+	12.4301i	0.267639	+	0.463564i	0.968252	−	0.249978i	$-0.0804233\pi$
$719$	7.17651	+	12.4301i	0.267639	+	0.463564i	−0.700613	+	0.713542i	$0.747090\pi$
$720$	2.27682	+	0.472001i	0.0848520	+	0.0175904i
$721$	1.59354	−	24.3661i	0.0593467	−	0.907440i
$722$	13.7060	+	7.91318i	0.510086	+	0.294498i
$723$	−0.824353	+	8.03750i	−0.0306580	+	0.298918i
$724$			57.8496i			2.14996i
$725$			7.69857i			0.285918i
$726$	−19.9164	+	8.92740i	−0.739166	+	0.331327i
$727$	3.74617	+	2.16285i	0.138938	+	0.0802157i	0.567858	−	0.823127i	$-0.307772\pi$
$727$	3.74617	+	2.16285i	0.138938	+	0.0802157i	−0.428920	+	0.903343i	$0.641106\pi$
$728$	−19.5200	+	29.2228i	−0.723459	+	1.08307i
$729$	22.0803	+	15.5390i	0.817790	+	0.575517i
$730$	−7.20287	−	12.4757i	−0.266590	−	0.461748i
$731$	−16.2347	−	28.1193i	−0.600461	−	1.04003i
$732$	−7.27640	−	5.25872i	−0.268943	−	0.194368i
$733$	−33.7127	−	19.4640i	−1.24521	−	0.718921i	−0.275058	−	0.961428i	$-0.588697\pi$
$733$	−33.7127	−	19.4640i	−1.24521	−	0.718921i	−0.970150	+	0.242507i	$0.922030\pi$
$734$	−13.3996	−	23.2088i	−0.494588	−	0.856652i
$735$	11.7972	+	2.79736i	0.435148	+	0.103182i
$736$	12.7097	−	22.0138i	0.468485	−	0.811441i
$737$	20.2323	−	11.6811i	0.745265	−	0.430279i
$738$	26.1081	+	23.2713i	0.961053	+	0.856627i
$739$	−21.2648	+	36.8317i	−0.782238	+	1.35488i	0.148398	+	0.988928i	$0.452588\pi$
$739$	−21.2648	+	36.8317i	−0.782238	+	1.35488i	−0.930635	+	0.365948i	$0.880745\pi$
$740$	−23.0526			−0.847429
$741$	−14.6575	−	32.6999i	−0.538458	−	1.20126i
$742$	2.17257	+	0.142087i	0.0797577	+	0.00521616i
$743$	0.237044	−	0.136858i	0.00869631	−	0.00502082i	−0.495646	−	0.868525i	$-0.665068\pi$
$743$	0.237044	−	0.136858i	0.00869631	−	0.00502082i	0.504342	+	0.863504i	$0.331735\pi$
$744$	−15.6881	+	21.7073i	−0.575153	+	0.795830i
$745$	−1.23735	+	0.714383i	−0.0453329	+	0.0261730i
$746$	57.0909	+	32.9614i	2.09024	+	1.20680i
$747$	42.7963	+	8.87200i	1.56584	+	0.324609i
$748$			56.4910i			2.06551i
$749$	35.8463	+	23.9443i	1.30980	+	0.874907i
$750$	−3.26312	−	2.35828i	−0.119152	−	0.0861123i
$751$	−3.78520	+	6.55616i	−0.138124	+	0.239238i	−0.926786	−	0.375589i	$-0.877441\pi$
$751$	−3.78520	+	6.55616i	−0.138124	+	0.239238i	0.788663	+	0.614826i	$0.210774\pi$
$752$	2.19267			0.0799584
$753$	−16.6927	+	23.0974i	−0.608316	+	0.841717i
$754$		−	72.8776i		−	2.65405i
$755$	−12.8717			−0.468448
$756$	7.06894	+	46.2483i	0.257095	+	1.68203i
$757$	−36.9202			−1.34189			−0.670944	−	0.741508i	$-0.734111\pi$
$757$	−36.9202			−1.34189			−0.670944	+	0.741508i	$0.734111\pi$
$758$			67.6816i			2.45831i
$759$	22.1341	−	30.6266i	0.803418	−	1.11168i
$760$	−16.5694			−0.601034
$761$	−1.64155	+	2.84324i	−0.0595060	+	0.103067i	−0.894244	−	0.447580i	$-0.852286\pi$
$761$	−1.64155	+	2.84324i	−0.0595060	+	0.103067i	0.834738	+	0.550648i	$0.185619\pi$
$762$	−72.2125	−	52.1886i	−2.61598	−	1.89059i
$763$	−23.0990	−	1.51067i	−0.836238	−	0.0546901i
$764$			41.7526i			1.51055i
$765$	−8.17700	+	9.17381i	−0.295640	+	0.331680i
$766$	−44.1976	−	25.5175i	−1.59692	−	0.921985i
$767$	−20.0089	+	11.5522i	−0.722481	+	0.417125i
$768$	20.9754	−	29.0233i	0.756885	−	1.04729i
$769$	−38.5608	+	22.2631i	−1.39054	+	0.802828i	−0.993375	−	0.114920i	$-0.963339\pi$
$769$	−38.5608	+	22.2631i	−1.39054	+	0.802828i	−0.397163	+	0.917748i	$0.630005\pi$
$770$	−11.0256	−	22.3498i	−0.397337	−	0.805429i
$771$	−5.04391	−	11.2526i	−0.181652	−	0.405253i
$772$	−8.13148			−0.292658
$773$	−19.7695	+	34.2417i	−0.711058	+	1.23159i	0.253402	+	0.967361i	$0.418450\pi$
$773$	−19.7695	+	34.2417i	−0.711058	+	1.23159i	−0.964460	+	0.264228i	$0.914883\pi$
$774$	−11.2201	+	54.1229i	−0.403298	+	1.94541i
$775$	4.10586	−	2.37052i	0.147487	−	0.0851516i
$776$	15.3259	−	26.5453i	0.550169	−	0.952920i
$777$	−10.8215	−	29.0947i	−0.388219	−	1.04377i
$778$	−29.5270	−	51.1423i	−1.05859	−	1.83354i
$779$	−22.0655	−	12.7395i	−0.790580	−	0.456442i
$780$	19.4558	+	14.0609i	0.696631	+	0.503461i
$781$	17.9762	+	31.1357i	0.643239	+	1.11412i
$782$	−25.6319	−	44.3958i	−0.916595	−	1.58759i
$783$	−26.9906	−	29.5253i	−0.964567	−	1.05515i
$784$	−3.30162	+	4.30531i	−0.117915	+	0.153761i
$785$	9.41611	+	5.43640i	0.336076	+	0.194033i
$786$	1.83061	−	0.820560i	0.0652957	−	0.0292684i
$787$			29.8599i			1.06439i	0.846621	+	0.532196i	$0.178633\pi$
$787$			29.8599i			1.06439i	−0.846621	+	0.532196i	$0.821367\pi$
$788$		−	3.76773i		−	0.134220i
$789$	−4.27357	+	41.6676i	−0.152143	+	1.48340i
$790$	19.0743	+	11.0125i	0.678632	+	0.391808i
$791$	−17.2300	−	11.5091i	−0.612627	−	0.409218i
$792$	26.3827	−	29.5989i	0.937468	−	1.05175i
$793$	−3.10140	−	5.37179i	−0.110134	−	0.190758i
$794$	19.4649	+	33.7142i	0.690785	+	1.19647i
$795$	0.0625619	−	0.609983i	0.00221884	−	0.0216339i
$796$	30.3648	+	17.5311i	1.07625	+	0.621374i
$797$	10.3298	+	17.8918i	0.365901	+	0.633759i	0.988920	−	0.148447i	$-0.0474275\pi$
$797$	10.3298	+	17.8918i	0.365901	+	0.633759i	−0.623019	+	0.782207i	$0.714094\pi$
$798$	−18.8648	−	50.7200i	−0.667807	−	1.79547i
$799$	−5.79426	+	10.0360i	−0.204986	+	0.355046i
$800$	−4.08890	+	2.36073i	−0.144565	+	0.0834644i
$801$	14.2553	−	15.9931i	0.503687	−	0.565089i
$802$	−9.38161	+	16.2494i	−0.331276	+	0.573787i
$803$	−25.1139			−0.886249
$804$	−19.9052	+	27.5424i	−0.702001	+	0.971347i
$805$	11.8447	+	7.91196i	0.417472	+	0.278860i
$806$	−38.8676	+	22.4402i	−1.36905	+	0.790424i
$807$	−14.0399	−	31.3220i	−0.494228	−	1.10259i
$808$	29.5515	−	17.0616i	1.03962	−	0.600224i
$809$	−4.36299	−	2.51897i	−0.153395	−	0.0885624i	0.421338	−	0.906904i	$-0.361561\pi$
$809$	−4.36299	−	2.51897i	−0.153395	−	0.0885624i	−0.574733	+	0.818341i	$0.694894\pi$
$810$	20.7825	−	2.39584i	0.730224	−	0.0841813i
$811$		−	6.52827i		−	0.229239i	−0.993409	−	0.114619i	$-0.963435\pi$
$811$		−	6.52827i		−	0.229239i	0.993409	−	0.114619i	$-0.0365648\pi$
$812$	4.52367	−	69.1691i	0.158750	−	2.42736i
$813$	1.67573	−	16.3385i	0.0587706	−	0.573017i
$814$	−31.9031	+	55.2578i	−1.11820	+	1.93679i
$815$	−16.8859			−0.591486
$816$	−2.24937	−	5.01818i	−0.0787437	−	0.175671i
$817$		−	40.2677i		−	1.40879i
$818$	22.3456			0.781295
$819$	−8.61320	+	31.1558i	−0.300969	+	1.08867i
$820$	17.0680			0.596039
$821$		−	11.2530i		−	0.392732i	−0.980531	−	0.196366i	$-0.937086\pi$
$821$		−	11.2530i		−	0.392732i	0.980531	−	0.196366i	$-0.0629141\pi$
$822$	16.1821	+	1.65970i	0.564417	+	0.0578885i
$823$	−6.40893			−0.223401			−0.111701	−	0.993742i	$-0.535630\pi$
$823$	−6.40893			−0.223401			−0.111701	+	0.993742i	$0.535630\pi$
$824$	15.0507	−	26.0686i	0.524316	−	0.908143i
$825$	−6.40477	+	2.87090i	−0.222986	+	0.0999519i
$826$	−31.2899	+	15.4360i	−1.08872	+	0.537089i
$827$		−	1.30994i		−	0.0455510i	−0.999741	−	0.0227755i	$-0.992750\pi$
$827$		−	1.30994i		−	0.0455510i	0.999741	−	0.0227755i	$-0.00725030\pi$
$828$	−11.1575	+	53.8211i	−0.387751	+	1.87041i
$829$	−0.807959	−	0.466476i	−0.0280616	−	0.0162014i	0.485904	−	0.874012i	$-0.338491\pi$
$829$	−0.807959	−	0.466476i	−0.0280616	−	0.0162014i	−0.513965	+	0.857811i	$0.671824\pi$
$830$	29.3276	−	16.9323i	1.01797	−	0.587728i
$831$	−39.8493	−	4.08708i	−1.38236	−	0.141779i
$832$	44.1743	−	25.5041i	1.53147	−	0.884194i
$833$	−10.9808	−	26.4887i	−0.380464	−	0.917780i
$834$	−24.9371	−	2.55763i	−0.863501	−	0.0885636i
$835$	−22.3918			−0.774900
$836$	−35.0294	+	60.6727i	−1.21152	+	2.09841i
$837$	−7.43578	+	23.4862i	−0.257018	+	0.811801i
$838$	31.5124	−	18.1937i	1.08858	−	0.628490i
$839$	−3.69094	+	6.39290i	−0.127426	+	0.220707i	−0.922678	−	0.385570i	$-0.874005\pi$
$839$	−3.69094	+	6.39290i	−0.127426	+	0.220707i	0.795253	+	0.606278i	$0.207338\pi$
$840$	11.5167	+	9.52668i	0.397363	+	0.328702i
$841$	15.1340	+	26.2129i	0.521863	+	0.903893i
$842$	−26.0917	−	15.0640i	−0.899179	−	0.519141i
$843$	1.21693	−	0.545483i	0.0419134	−	0.0187874i
$844$	4.54031	+	7.86405i	0.156284	+	0.270692i
$845$	1.79262	+	3.10491i	0.0616681	+	0.106812i
$846$	18.7311	−	6.19040i	0.643990	−	0.212830i
$847$	−14.3122	−	0.936019i	−0.491773	−	0.0321620i
$848$	0.237632	+	0.137197i	0.00816030	+	0.00471135i
$849$	15.4848	+	11.1910i	0.531438	+	0.384075i
$850$			9.52186i			0.326597i
$851$		−	36.4694i		−	1.25015i
$852$	−42.3854	−	30.6323i	−1.45210	−	1.04945i
$853$	−38.1814	−	22.0441i	−1.30731	−	0.754774i	−0.325662	−	0.945486i	$-0.605587\pi$
$853$	−38.1814	−	22.0441i	−1.30731	−	0.754774i	−0.981646	+	0.190712i	$0.938920\pi$
$854$	−4.14411	−	8.40039i	−0.141808	−	0.287456i
$855$	−14.4709	+	4.78243i	−0.494893	+	0.163556i
$856$	26.5706	+	46.0216i	0.908164	+	1.57299i
$857$	23.2288	+	40.2335i	0.793482	+	1.37435i	0.923799	+	0.382879i	$0.125067\pi$
$857$	23.2288	+	40.2335i	0.793482	+	1.37435i	−0.130317	+	0.991472i	$0.541599\pi$
$858$	60.6300	−	27.1770i	2.06987	−	0.927809i
$859$	44.5146	+	25.7005i	1.51882	+	0.876891i	0.999755	+	0.0221557i	$0.00705295\pi$
$859$	44.5146	+	25.7005i	1.51882	+	0.876891i	0.519065	+	0.854735i	$0.326280\pi$
$860$	13.4873	+	23.3606i	0.459912	+	0.796591i
$861$	8.01215	+	21.5415i	0.273053	+	0.734132i
$862$	−3.51224	+	6.08338i	−0.119627	+	0.207201i
$863$	35.5899	−	20.5478i	1.21149	−	0.699457i	0.248410	−	0.968655i	$-0.420092\pi$
$863$	35.5899	−	20.5478i	1.21149	−	0.699457i	0.963085	+	0.269198i	$0.0867587\pi$
$864$	7.40507	−	23.3892i	0.251926	−	0.795716i
$865$	4.37709	−	7.58134i	0.148826	−	0.257773i
$866$	−79.9949			−2.71834
$867$	−0.378676	−	0.0388383i	−0.0128605	−	0.00131902i
$868$	−38.2827	+	18.8857i	−1.29940	+	0.641023i
$869$	33.2526	−	19.1984i	1.12802	−	0.651261i
$870$	−30.8334	−	3.16238i	−1.04535	−	0.107215i
$871$	−20.3332	+	11.7394i	−0.688963	+	0.397773i
$872$	−24.7129	−	14.2680i	−0.836886	−	0.483176i
$873$	5.72311	−	27.6069i	0.193698	−	0.934351i
$874$		−	63.5762i		−	2.15050i
$875$	−1.17052	−	2.37274i	−0.0395710	−	0.0802131i
$876$	33.3346	−	14.9420i	1.12627	−	0.504845i
$877$	−28.0613	+	48.6036i	−0.947562	+	1.64123i	−0.197023	+	0.980399i	$0.563127\pi$
$877$	−28.0613	+	48.6036i	−0.947562	+	1.64123i	−0.750539	+	0.660827i	$0.770206\pi$
$878$	25.1453			0.848612
$879$	31.5056	+	3.23132i	1.06266	+	0.108990i
$880$		−	3.14083i		−	0.105877i
$881$	−2.61895			−0.0882345			−0.0441173	−	0.999026i	$-0.514048\pi$
$881$	−2.61895			−0.0882345			−0.0441173	+	0.999026i	$0.514048\pi$
$882$	−16.0497	+	46.0998i	−0.540420	+	1.55226i
$883$	−2.72438			−0.0916826			−0.0458413	−	0.998949i	$-0.514597\pi$
$883$	−2.72438			−0.0916826			−0.0458413	+	0.998949i	$0.514597\pi$
$884$		−	56.7727i		−	1.90947i
$885$	4.01930	+	8.96676i	0.135107	+	0.301414i
$886$	94.1279			3.16229
$887$	−3.59294	+	6.22316i	−0.120639	+	0.208953i	−0.920020	−	0.391872i	$-0.871828\pi$
$887$	−3.59294	+	6.22316i	−0.120639	+	0.208953i	0.799381	+	0.600825i	$0.205161\pi$
$888$	3.90431	−	38.0673i	0.131020	−	1.27745i
$889$	−25.9036	−	52.5084i	−0.868780	−	1.76108i
$890$		−	16.5999i		−	0.556430i
$891$	14.4982	−	33.4650i	0.485707	−	1.12112i
$892$	74.4539	+	42.9860i	2.49290	+	1.43928i
$893$	−12.4463	+	7.18590i	−0.416501	+	0.240467i
$894$	−2.35289	−	5.24913i	−0.0786924	−	0.175557i
$895$	0.203742	−	0.117631i	0.00681035	−	0.00393196i
$896$	46.6742	−	23.0254i	1.55928	−	0.769226i
$897$	−22.2445	+	30.7793i	−0.742722	+	1.02769i
$898$	60.6344			2.02339
$899$	18.2496	−	31.6093i	0.608659	−	1.05423i
$900$	6.79320	−	7.62132i	0.226440	−	0.254044i
$901$	−1.25591	+	0.725101i	−0.0418405	+	0.0241566i
$902$	23.6208	−	40.9125i	0.786488	−	1.36224i
$903$	−23.1522	+	27.9884i	−0.770457	+	0.931395i
$904$	−12.7715	−	22.1208i	−0.424773	−	0.735728i
$905$	14.7215	+	8.49944i	0.489358	+	0.282531i
$906$	5.28735	−	51.5520i	0.175660	−	1.71270i
$907$	−27.1985	−	47.1092i	−0.903112	−	1.56424i	−0.823432	−	0.567415i	$-0.807944\pi$
$907$	−27.1985	−	47.1092i	−0.903112	−	1.56424i	−0.0796797	−	0.996821i	$-0.525390\pi$
$908$	28.0985	+	48.6680i	0.932481	+	1.61510i
$909$	20.8843	−	23.4302i	0.692689	−	0.777130i
$910$	11.0806	+	22.4612i	0.367319	+	0.744582i
$911$	−47.7761	−	27.5835i	−1.58289	−	0.913883i	−0.994435	−	0.105354i	$-0.966402\pi$
$911$	−47.7761	−	27.5835i	−1.58289	−	0.913883i	−0.588457	−	0.808529i	$-0.700264\pi$
$912$	0.695836	−	6.78445i	0.0230414	−	0.224656i
$913$		−	59.0368i		−	1.95383i
$914$			16.7261i			0.553251i
$915$	−2.40730	+	1.07906i	−0.0795829	+	0.0356726i
$916$	27.8083	+	16.0551i	0.918813	+	0.530477i
$917$	1.31550	+	0.0860340i	0.0434417	+	0.00284109i
$918$	−33.3829	−	36.5179i	−1.10180	−	1.20527i
$919$	3.27108	+	5.66568i	0.107903	+	0.186893i	0.914921	−	0.403634i	$-0.132253\pi$
$919$	3.27108	+	5.66568i	0.107903	+	0.186893i	−0.807018	+	0.590527i	$0.798920\pi$
$920$	8.77976	+	15.2070i	0.289460	+	0.501360i
$921$	−20.1020	−	14.5279i	−0.662384	−	0.478711i
$922$	13.1122	+	7.57036i	0.431829	+	0.249317i
$923$	−18.0658	−	31.2910i	−0.594644	−	1.02995i
$924$	59.2317	−	22.0307i	1.94858	−	0.724755i
$925$	−3.38696	+	5.86638i	−0.111362	+	0.192885i
$926$	3.53945	−	2.04350i	0.116314	−	0.0671537i
$927$	5.62034	−	27.1111i	0.184596	−	0.890446i
$928$	−18.1742	+	31.4787i	−0.596599	+	1.03334i
$929$	−15.0597			−0.494091			−0.247046	−	0.969004i	$-0.579460\pi$
$929$	−15.0597			−0.494091			−0.247046	+	0.969004i	$0.579460\pi$
$930$	7.80754	+	17.4181i	0.256019	+	0.571161i
$931$	4.63164	−	35.2586i	0.151796	−	1.15555i
$932$	9.70689	−	5.60428i	0.317960	−	0.183574i
$933$	4.58996	−	6.35105i	0.150269	−	0.207924i
$934$	−39.7598	+	22.9553i	−1.30098	+	0.751121i
$935$	14.3757	+	8.29983i	0.470137	+	0.271434i
$936$	−26.5143	+	29.7465i	−0.866646	+	0.972294i
$937$			5.51783i			0.180259i	0.995930	+	0.0901297i	$0.0287282\pi$
$937$			5.51783i			0.180259i	−0.995930	+	0.0901297i	$0.971272\pi$
$938$	−31.7970	+	15.6862i	−1.03821	+	0.512172i
$939$	21.5772	+	15.5940i	0.704144	+	0.508891i
$940$	4.81370	−	8.33757i	0.157005	−	0.271941i
$941$	−27.0250			−0.880989			−0.440495	−	0.897755i	$-0.645197\pi$
$941$	−27.0250			−0.880989			−0.440495	+	0.897755i	$0.645197\pi$
$942$	−25.6411	+	35.4792i	−0.835433	+	1.15597i
$943$			27.0017i			0.879295i
$944$	−4.39720			−0.143117
$945$	12.8078	+	4.99606i	0.416637	+	0.162522i
$946$	74.6617			2.42746
$947$		−	20.6755i		−	0.671864i	−0.941886	−	0.335932i	$-0.890949\pi$
$947$		−	20.6755i		−	0.671864i	0.941886	−	0.335932i	$-0.109051\pi$
$948$	−32.7150	+	45.2672i	−1.06253	+	1.47021i
$949$	25.2391			0.819296
$950$	−5.90439	+	10.2267i	−0.191564	+	0.331798i
$951$	−5.84223	−	4.22223i	−0.189447	−	0.136915i
$952$	2.30687	−	35.2732i	0.0747661	−	1.14321i
$953$			33.3683i			1.08091i	0.841374	+	0.540453i	$0.181747\pi$
$953$			33.3683i			1.08091i	−0.841374	+	0.540453i	$0.818253\pi$
$954$	2.41733	+	0.501131i	0.0782641	+	0.0162247i
$955$	10.6251	+	6.13442i	0.343821	+	0.198505i
$956$	63.6725	−	36.7613i	2.05932	−	1.18895i
$957$	−31.6507	+	43.7946i	−1.02312	+	1.41568i
$958$	74.3408	−	42.9207i	2.40184	−	1.38670i
$959$	8.88917	+	5.93772i	0.287046	+	0.191739i
$960$	−8.87352	−	19.7962i	−0.286392	−	0.638919i
$961$	8.52254			0.274921
$962$	32.0622	−	55.5334i	1.03373	−	1.79047i
$963$	36.4887	+	32.5239i	1.17583	+	1.04807i
$964$	−13.7481	+	7.93747i	−0.442797	+	0.255649i
$965$	−1.19470	+	2.06929i	−0.0384589	+	0.0666127i
$966$	−36.5536	+	44.1891i	−1.17609	+	1.42176i
$967$	12.6162	+	21.8519i	0.405710	+	0.702711i	0.994404	−	0.105645i	$-0.0336908\pi$
$967$	12.6162	+	21.8519i	0.405710	+	0.702711i	−0.588693	+	0.808356i	$0.700357\pi$
$968$	−15.3122	−	8.84052i	−0.492154	−	0.284145i
$969$	29.2140	+	21.1132i	0.938488	+	0.678253i
$970$	−10.9226	−	18.9185i	−0.350704	−	0.607437i
$971$	−3.65494	−	6.33055i	−0.117293	−	0.203157i	0.801401	−	0.598127i	$-0.204088\pi$
$971$	−3.65494	−	6.33055i	−0.117293	−	0.203157i	−0.918694	+	0.394970i	$0.870755\pi$
$972$	0.666750	+	53.0455i	0.0213860	+	1.70143i
$973$	−13.6984	−	9.15018i	−0.439152	−	0.293341i
$974$	80.6541	+	46.5656i	2.58432	+	1.49206i
$975$	6.43671	−	2.88522i	0.206140	−	0.0924009i
$976$		−	1.18051i		−	0.0377874i
$977$		−	22.1355i		−	0.708176i	−0.935212	−	0.354088i	$-0.884791\pi$
$977$		−	22.1355i		−	0.708176i	0.935212	−	0.354088i	$-0.115209\pi$
$978$	6.93628	−	67.6292i	0.221798	−	2.16254i
$979$	−25.0619	−	14.4695i	−0.800981	−	0.462447i
$980$	9.12256	+	22.0060i	0.291409	+	0.702957i
$981$	−25.7012	−	5.32806i	−0.820578	−	0.170112i
$982$	3.44696	+	5.97030i	0.109997	+	0.190520i
$983$	−3.49436	−	6.05241i	−0.111453	−	0.193042i	0.804903	−	0.593406i	$-0.202217\pi$
$983$	−3.49436	−	6.05241i	−0.111453	−	0.193042i	−0.916356	+	0.400364i	$0.868884\pi$
$984$	−2.89072	+	28.1847i	−0.0921528	+	0.898496i
$985$	−0.958806	−	0.553567i	−0.0305501	−	0.0176381i
$986$	36.6524	+	63.4838i	1.16725	+	2.02174i
$987$	12.7825	+	2.16150i	0.406872	+	0.0688012i
$988$	35.2041	−	60.9752i	1.11999	−	1.93988i
$989$	−36.9568	+	21.3370i	−1.17516	+	0.678477i
$990$	−8.86728	−	26.8309i	−0.281821	−	0.852743i
$991$	14.9005	−	25.8084i	0.473329	−	0.819829i	−0.526205	−	0.850358i	$-0.676386\pi$
$991$	14.9005	−	25.8084i	0.473329	−	0.819829i	0.999534	+	0.0305283i	$0.00971896\pi$
$992$	22.3846			0.710712
$993$	15.6799	−	21.6960i	0.497586	−	0.688502i
$994$	−24.1396	−	48.9327i	−0.765663	−	1.55205i
$995$	8.92259	−	5.15146i	0.282865	−	0.163312i
$996$	35.1253	+	78.3619i	1.11299	+	2.48299i
$997$	−10.6048	+	6.12270i	−0.335858	+	0.193908i	−0.658439	−	0.752634i	$-0.728783\pi$
$997$	−10.6048	+	6.12270i	−0.335858	+	0.193908i	0.322581	+	0.946542i	$0.395450\pi$
$998$	−36.8123	−	21.2536i	−1.16527	−	0.672770i
$999$	−7.57756	−	34.3730i	−0.239743	−	1.08751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.t.c.101.14	✓	32
3.2	odd	2		945.2.t.c.521.3		32
7.5	odd	6		315.2.be.c.236.14	yes	32
9.4	even	3		945.2.be.c.206.3		32
9.5	odd	6		315.2.be.c.311.14	yes	32
21.5	even	6		945.2.be.c.656.3		32
63.5	even	6	inner	315.2.t.c.131.3	yes	32
63.40	odd	6		945.2.t.c.341.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.14	✓	32	1.1	even	1	trivial
315.2.t.c.131.3	yes	32	63.5	even	6	inner
315.2.be.c.236.14	yes	32	7.5	odd	6
315.2.be.c.311.14	yes	32	9.5	odd	6
945.2.t.c.341.14		32	63.40	odd	6
945.2.t.c.521.3		32	3.2	odd	2
945.2.be.c.206.3		32	9.4	even	3
945.2.be.c.656.3		32	21.5	even	6

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)

\(f(q)\)	\(=\)	\(q+2.32447i q^{2} +(-1.01455 + 1.40381i) q^{3} -3.40314 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.26312 - 2.35828i) q^{6} +(-1.17052 - 2.37274i) q^{7} -3.26155i q^{8} +(-0.941384 - 2.84847i) q^{9} +O(q^{10})\)	\(q+2.32447i q^{2} +(-1.01455 + 1.40381i) q^{3} -3.40314 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.26312 - 2.35828i) q^{6} +(-1.17052 - 2.37274i) q^{7} -3.26155i q^{8} +(-0.941384 - 2.84847i) q^{9} +(-2.01305 - 1.16223i) q^{10} +(-3.50939 + 2.02615i) q^{11} +(3.45265 - 4.77737i) q^{12} +(3.52689 - 2.03625i) q^{13} +(5.51534 - 2.72084i) q^{14} +(-0.708464 - 1.58053i) q^{15} +0.775076 q^{16} +(-2.04818 + 3.54756i) q^{17} +(6.62118 - 2.18821i) q^{18} +(-4.39960 + 2.54011i) q^{19} +(1.70157 - 2.94720i) q^{20} +(4.51843 + 0.764056i) q^{21} +(-4.70970 - 8.15745i) q^{22} +(4.66251 + 2.69190i) q^{23} +(4.57860 + 3.30900i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(4.73319 + 8.19813i) q^{26} +(4.95380 + 1.56839i) q^{27} +(3.98346 + 8.07475i) q^{28} +(-6.66716 - 3.84929i) q^{29} +(3.67389 - 1.64680i) q^{30} +4.74104i q^{31} -4.72146i q^{32} +(0.716112 - 6.98215i) q^{33} +(-8.24618 - 4.76093i) q^{34} +(2.64011 + 0.172663i) q^{35} +(3.20366 + 9.69375i) q^{36} +(-3.38696 - 5.86638i) q^{37} +(-5.90439 - 10.2267i) q^{38} +(-0.719684 + 7.01696i) q^{39} +(2.82458 + 1.63077i) q^{40} +(2.50768 + 4.34343i) q^{41} +(-1.77602 + 10.5029i) q^{42} +(-3.96318 + 6.86444i) q^{43} +(11.9429 - 6.89525i) q^{44} +(2.93754 + 0.608974i) q^{45} +(-6.25723 + 10.8378i) q^{46} +2.82897 q^{47} +(-0.786352 + 1.08806i) q^{48} +(-4.25974 + 5.55469i) q^{49} +(2.01305 - 1.16223i) q^{50} +(-2.90213 - 6.47444i) q^{51} +(-12.0025 + 6.92964i) q^{52} +(0.306591 + 0.177011i) q^{53} +(-3.64566 + 11.5149i) q^{54} -4.05229i q^{55} +(-7.73879 + 3.81772i) q^{56} +(0.897766 - 8.75328i) q^{57} +(8.94753 - 15.4976i) q^{58} -5.67326 q^{59} +(2.41100 + 5.37877i) q^{60} -1.52310i q^{61} -11.0204 q^{62} +(-5.65676 + 5.56786i) q^{63} +12.5250 q^{64} +4.07250i q^{65} +(16.2298 + 1.66458i) q^{66} -5.76519 q^{67} +(6.97025 - 12.0728i) q^{68} +(-8.50926 + 3.81423i) q^{69} +(-0.401350 + 6.13685i) q^{70} -8.87212i q^{71} +(-9.29043 + 3.07037i) q^{72} +(5.36715 + 3.09872i) q^{73} +(13.6362 - 7.87286i) q^{74} +(1.72301 + 0.176718i) q^{75} +(14.9724 - 8.64434i) q^{76} +(8.91533 + 5.95519i) q^{77} +(-16.3107 - 1.67288i) q^{78} -9.47533 q^{79} +(-0.387538 + 0.671235i) q^{80} +(-7.22759 + 5.36301i) q^{81} +(-10.0961 + 5.82901i) q^{82} +(-7.28438 + 12.6169i) q^{83} +(-15.3768 - 2.60019i) q^{84} +(-2.04818 - 3.54756i) q^{85} +(-15.9561 - 9.21228i) q^{86} +(12.1678 - 5.45416i) q^{87} +(6.60837 + 11.4460i) q^{88} +(3.57069 + 6.18462i) q^{89} +(-1.41554 + 6.82821i) q^{90} +(-8.95979 - 5.98489i) q^{91} +(-15.8672 - 9.16091i) q^{92} +(-6.65553 - 4.81001i) q^{93} +6.57585i q^{94} -5.08022i q^{95} +(6.62805 + 4.79015i) q^{96} +(8.13886 + 4.69897i) q^{97} +(-12.9117 - 9.90163i) q^{98} +(9.07510 + 8.08901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9}+O(q^{10}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9	\( 32 q - q^{3} - 32 q^{4} - 16 q^{5} - 2 q^{6} + q^{7} + q^{9} + 3 q^{11} + 12 q^{12} + 6 q^{13} - 15 q^{14} - q^{15} + 32 q^{16} - 3 q^{17} - 13 q^{18} + 16 q^{20} - q^{21} - 21 q^{22} - 9 q^{23} - 4 q^{24} - 16 q^{25} + 12 q^{26} + 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 19 q^{33} - 30 q^{34} + q^{35} + 18 q^{36} - q^{37} - 30 q^{38} + 21 q^{39} + 6 q^{41} + 19 q^{42} - 19 q^{43} + 21 q^{44} - 8 q^{45} + 6 q^{46} - 30 q^{47} - 35 q^{48} + 5 q^{49} + 36 q^{51} + 21 q^{52} - 24 q^{53} - 59 q^{54} + 30 q^{56} + 27 q^{57} + 30 q^{59} + 3 q^{60} - 32 q^{63} + 76 q^{64} + 26 q^{66} - 50 q^{67} - 3 q^{68} - 50 q^{69} + 9 q^{70} - 14 q^{72} + 12 q^{73} + 60 q^{74} + 2 q^{75} + 54 q^{76} - 27 q^{77} - 42 q^{78} + 4 q^{79} - 16 q^{80} - 23 q^{81} - 24 q^{82} - 42 q^{83} - 72 q^{84} - 3 q^{85} + 51 q^{86} + 34 q^{87} + 42 q^{88} + 30 q^{89} + 41 q^{90} - 57 q^{91} + 6 q^{92} - 33 q^{93} + 15 q^{96} - 42 q^{97} + 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q - q^3 - 32 * q^4 - 16 * q^5 - 2 * q^6 + q^7 + q^9 + 3 * q^11 + 12 * q^12 + 6 * q^13 - 15 * q^14 - q^15 + 32 * q^16 - 3 * q^17 - 13 * q^18 + 16 * q^20 - q^21 - 21 * q^22 - 9 * q^23 - 4 * q^24 - 16 * q^25 + 12 * q^26 + 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 19 * q^33 - 30 * q^34 + q^35 + 18 * q^36 - q^37 - 30 * q^38 + 21 * q^39 + 6 * q^41 + 19 * q^42 - 19 * q^43 + 21 * q^44 - 8 * q^45 + 6 * q^46 - 30 * q^47 - 35 * q^48 + 5 * q^49 + 36 * q^51 + 21 * q^52 - 24 * q^53 - 59 * q^54 + 30 * q^56 + 27 * q^57 + 30 * q^59 + 3 * q^60 - 32 * q^63 + 76 * q^64 + 26 * q^66 - 50 * q^67 - 3 * q^68 - 50 * q^69 + 9 * q^70 - 14 * q^72 + 12 * q^73 + 60 * q^74 + 2 * q^75 + 54 * q^76 - 27 * q^77 - 42 * q^78 + 4 * q^79 - 16 * q^80 - 23 * q^81 - 24 * q^82 - 42 * q^83 - 72 * q^84 - 3 * q^85 + 51 * q^86 + 34 * q^87 + 42 * q^88 + 30 * q^89 + 41 * q^90 - 57 * q^91 + 6 * q^92 - 33 * q^93 + 15 * q^96 - 42 * q^97 + 6 * q^98 - q^99

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