LMFDB - Embedded newform 845.2.l.d.699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(654,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("845.654");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.l (of order $6$, degree $2$, not 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			699.1
Root			$-0.147520 + 0.550552i$ of defining polynomial
Character	$\chi$	$=$	845.699
Dual form			845.2.l.d.654.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33757 - 2.31673i) q^{2} +(-0.416726 + 0.240597i) q^{3} +(-2.57816 + 4.46551i) q^{4} +(-1.48119 + 1.67513i) q^{5} +(1.11480 + 0.643629i) q^{6} +(0.403032 - 0.698071i) q^{7} +8.44358 q^{8} +(-1.38423 + 2.39755i) q^{9} +O(q^{10})$	\(q+(-1.33757 - 2.31673i) q^{2} +(-0.416726 + 0.240597i) q^{3} +(-2.57816 + 4.46551i) q^{4} +(-1.48119 + 1.67513i) q^{5} +(1.11480 + 0.643629i) q^{6} +(0.403032 - 0.698071i) q^{7} +8.44358 q^{8} +(-1.38423 + 2.39755i) q^{9} +(5.86202 + 1.19093i) q^{10} +(3.18276 - 1.83757i) q^{11} -2.48119i q^{12} -2.15633 q^{14} +(0.214221 - 1.05444i) q^{15} +(-6.13752 - 10.6305i) q^{16} +(1.16936 + 0.675131i) q^{17} +7.40597 q^{18} +(-1.45071 - 0.837565i) q^{19} +(-3.66155 - 10.9330i) q^{20} +0.387873i q^{21} +(-8.51429 - 4.91573i) q^{22} +(-5.61288 + 3.24060i) q^{23} +(-3.51866 + 2.03150i) q^{24} +(-0.612127 - 4.96239i) q^{25} -2.77575i q^{27} +(2.07816 + 3.59948i) q^{28} +(1.20910 + 2.09421i) q^{29} +(-2.72939 + 0.914093i) q^{30} -5.28726i q^{31} +(-7.97508 + 13.8133i) q^{32} +(-0.884226 + 1.53152i) q^{33} -3.61213i q^{34} +(0.572393 + 1.70911i) q^{35} +(-7.13752 - 12.3625i) q^{36} +(1.88423 + 3.26358i) q^{37} +4.48119i q^{38} +(-12.5066 + 14.1441i) q^{40} +(-7.19897 + 4.15633i) q^{41} +(0.898598 - 0.518806i) q^{42} +(-5.88364 - 3.39692i) q^{43} +18.9502i q^{44} +(-1.96590 - 5.87000i) q^{45} +(15.0152 + 8.66902i) q^{46} -3.19394 q^{47} +(5.11533 + 2.95334i) q^{48} +(3.17513 + 5.49949i) q^{49} +(-10.6778 + 8.05565i) q^{50} -0.649738 q^{51} +5.73813i q^{53} +(-6.43066 + 3.71274i) q^{54} +(-1.63612 + 8.05333i) q^{55} +(3.40303 - 5.89422i) q^{56} +0.806063 q^{57} +(3.23449 - 5.60230i) q^{58} +(-5.18557 - 2.99389i) q^{59} +(4.15633 + 3.67513i) q^{60} +(0.884226 - 1.53152i) q^{61} +(-12.2492 + 7.07205i) q^{62} +(1.11577 + 1.93258i) q^{63} +18.1187 q^{64} +4.73084 q^{66} +(-4.94723 - 8.56885i) q^{67} +(-6.02961 + 3.48119i) q^{68} +(1.55936 - 2.70089i) q^{69} +(3.19394 - 3.61213i) q^{70} +(-7.41517 - 4.28115i) q^{71} +(-11.6878 + 20.2439i) q^{72} -11.7685 q^{73} +(5.04055 - 8.73049i) q^{74} +(1.44903 + 1.92068i) q^{75} +(7.48031 - 4.31876i) q^{76} -2.96239i q^{77} +2.26187 q^{79} +(26.8983 + 5.46468i) q^{80} +(-3.48484 - 6.03592i) q^{81} +(19.2582 + 11.1187i) q^{82} -3.84367 q^{83} +(-1.73205 - 1.00000i) q^{84} +(-2.86298 + 0.958833i) q^{85} +18.1744i q^{86} +(-1.00772 - 0.581810i) q^{87} +(26.8739 - 15.5156i) q^{88} +(2.40387 - 1.38787i) q^{89} +(-10.9697 + 12.4060i) q^{90} -33.4191i q^{92} +(1.27210 + 2.20334i) q^{93} +(4.27210 + 7.39949i) q^{94} +(3.55181 - 1.18953i) q^{95} -7.67513i q^{96} +(0.936996 - 1.62292i) q^{97} +(8.49389 - 14.7119i) q^{98} +10.1744i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 10 q^{4} + 4 q^{5} + 4 q^{7} + 36 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 10 * q^4 + 4 * q^5 + 4 * q^7 + 36 * q^8 + 6 * q^9	$ 12 q - 6 q^{2} - 10 q^{4} + 4 q^{5} + 4 q^{7} + 36 q^{8} + 6 q^{9} + 2 q^{10} + 16 q^{14} - 4 q^{15} - 10 q^{16} - 20 q^{18} + 14 q^{20} - 4 q^{25} + 4 q^{28} + 12 q^{29} + 8 q^{30} - 22 q^{32} + 12 q^{33} - 8 q^{35} - 22 q^{36} - 68 q^{40} + 38 q^{45} - 40 q^{47} + 18 q^{49} - 22 q^{50} - 48 q^{51} + 16 q^{55} + 40 q^{56} + 8 q^{57} - 24 q^{58} + 8 q^{60} - 12 q^{61} + 36 q^{63} + 132 q^{64} - 32 q^{66} - 20 q^{67} - 24 q^{69} + 40 q^{70} - 90 q^{72} - 96 q^{73} - 4 q^{74} + 16 q^{75} + 64 q^{79} + 58 q^{80} - 46 q^{81} - 88 q^{83} - 32 q^{85} - 140 q^{90} - 4 q^{93} + 32 q^{94} + 16 q^{95} + 28 q^{97} + 50 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 10 * q^4 + 4 * q^5 + 4 * q^7 + 36 * q^8 + 6 * q^9 + 2 * q^10 + 16 * q^14 - 4 * q^15 - 10 * q^16 - 20 * q^18 + 14 * q^20 - 4 * q^25 + 4 * q^28 + 12 * q^29 + 8 * q^30 - 22 * q^32 + 12 * q^33 - 8 * q^35 - 22 * q^36 - 68 * q^40 + 38 * q^45 - 40 * q^47 + 18 * q^49 - 22 * q^50 - 48 * q^51 + 16 * q^55 + 40 * q^56 + 8 * q^57 - 24 * q^58 + 8 * q^60 - 12 * q^61 + 36 * q^63 + 132 * q^64 - 32 * q^66 - 20 * q^67 - 24 * q^69 + 40 * q^70 - 90 * q^72 - 96 * q^73 - 4 * q^74 + 16 * q^75 + 64 * q^79 + 58 * q^80 - 46 * q^81 - 88 * q^83 - 32 * q^85 - 140 * q^90 - 4 * q^93 + 32 * q^94 + 16 * q^95 + 28 * q^97 + 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.33757	−	2.31673i	−0.945802	−	1.63818i	−0.754138	−	0.656716i	$-0.771945\pi$
$2$	−1.33757	−	2.31673i	−0.945802	−	1.63818i	−0.191663	−	0.981461i	$-0.561388\pi$
$3$	−0.416726	+	0.240597i	−0.240597	+	0.138909i	−0.615451	−	0.788175i	$-0.711026\pi$
$3$	−0.416726	+	0.240597i	−0.240597	+	0.138909i	0.374854	+	0.927084i	$0.377693\pi$
$4$	−2.57816	+	4.46551i	−1.28908	+	2.23275i
$5$	−1.48119	+	1.67513i	−0.662410	+	0.749141i
$5$	−1.48119	+	1.67513i	−0.662410	+	0.749141i
$6$	1.11480	+	0.643629i	0.455114	+	0.262760i
$7$	0.403032	−	0.698071i	0.152332	−	0.263846i	−0.779753	−	0.626088i	$-0.784655\pi$
$7$	0.403032	−	0.698071i	0.152332	−	0.263846i	0.932084	+	0.362242i	$0.117988\pi$
$8$	8.44358			2.98526
$9$	−1.38423	+	2.39755i	−0.461409	+	0.799183i
$10$	5.86202	+	1.19093i	1.85373	+	0.376606i
$11$	3.18276	−	1.83757i	0.959637	−	0.554047i	0.0635759	−	0.997977i	$-0.479750\pi$
$11$	3.18276	−	1.83757i	0.959637	−	0.554047i	0.896061	+	0.443930i	$0.146416\pi$
$12$		−	2.48119i		−	0.716259i
$13$		0			0
$13$		0			0
$14$	−2.15633			−0.576302
$15$	0.214221	−	1.05444i	0.0553117	−	0.272256i
$16$	−6.13752	−	10.6305i	−1.53438	−	2.65762i
$17$	1.16936	+	0.675131i	0.283612	+	0.163743i	0.635057	−	0.772465i	$-0.280976\pi$
$17$	1.16936	+	0.675131i	0.283612	+	0.163743i	−0.351446	+	0.936208i	$0.614310\pi$
$18$	7.40597			1.74560
$19$	−1.45071	−	0.837565i	−0.332815	−	0.192151i	0.324275	−	0.945963i	$-0.394880\pi$
$19$	−1.45071	−	0.837565i	−0.332815	−	0.192151i	−0.657090	+	0.753812i	$0.728213\pi$
$20$	−3.66155	−	10.9330i	−0.818748	−	2.44470i
$21$			0.387873i			0.0846409i
$22$	−8.51429	−	4.91573i	−1.81525	−	1.04804i
$23$	−5.61288	+	3.24060i	−1.17037	+	0.675711i	−0.953766	−	0.300549i	$-0.902830\pi$
$23$	−5.61288	+	3.24060i	−1.17037	+	0.675711i	−0.216600	+	0.976260i	$0.569497\pi$
$24$	−3.51866	+	2.03150i	−0.718244	+	0.414679i
$25$	−0.612127	−	4.96239i	−0.122425	−	0.992478i
$26$		0			0
$27$		−	2.77575i		−	0.534193i
$28$	2.07816	+	3.59948i	0.392736	+	0.680238i
$29$	1.20910	+	2.09421i	0.224523	+	0.388886i	0.956176	−	0.292791i	$-0.0945842\pi$
$29$	1.20910	+	2.09421i	0.224523	+	0.388886i	−0.731653	+	0.681677i	$0.761251\pi$
$30$	−2.72939	+	0.914093i	−0.498317	+	0.166890i
$31$		−	5.28726i		−	0.949620i	−0.880088	−	0.474810i	$-0.842517\pi$
$31$		−	5.28726i		−	0.949620i	0.880088	−	0.474810i	$-0.157483\pi$
$32$	−7.97508	+	13.8133i	−1.40981	+	2.44186i
$33$	−0.884226	+	1.53152i	−0.153924	+	0.266604i
$34$		−	3.61213i		−	0.619475i
$35$	0.572393	+	1.70911i	0.0967520	+	0.288892i
$36$	−7.13752	−	12.3625i	−1.18959	−	2.06042i
$37$	1.88423	+	3.26358i	0.309765	+	0.536528i	0.978311	−	0.207142i	$-0.0664163\pi$
$37$	1.88423	+	3.26358i	0.309765	+	0.536528i	−0.668546	+	0.743671i	$0.733083\pi$
$38$			4.48119i			0.726946i
$39$		0			0
$40$	−12.5066	+	14.1441i	−1.97747	+	2.23638i
$41$	−7.19897	+	4.15633i	−1.12429	+	0.649109i	−0.942493	−	0.334227i	$-0.891525\pi$
$41$	−7.19897	+	4.15633i	−1.12429	+	0.649109i	−0.181797	+	0.983336i	$0.558191\pi$
$42$	0.898598	−	0.518806i	0.138657	−	0.0800535i
$43$	−5.88364	−	3.39692i	−0.897247	−	0.518026i	−0.0209410	−	0.999781i	$-0.506666\pi$
$43$	−5.88364	−	3.39692i	−0.897247	−	0.518026i	−0.876306	+	0.481755i	$0.840000\pi$
$44$			18.9502i			2.85685i
$45$	−1.96590	−	5.87000i	−0.293059	−	0.875047i
$46$	15.0152	+	8.66902i	2.21387	+	1.27818i
$47$	−3.19394			−0.465884			−0.232942	−	0.972491i	$-0.574835\pi$
$47$	−3.19394			−0.465884			−0.232942	+	0.972491i	$0.574835\pi$
$48$	5.11533	+	2.95334i	0.738335	+	0.426278i
$49$	3.17513	+	5.49949i	0.453590	+	0.785641i
$50$	−10.6778	+	8.05565i	−1.51006	+	1.13924i
$51$	−0.649738			−0.0909816
$52$		0			0
$53$			5.73813i			0.788193i	0.919069	+	0.394097i	$0.128943\pi$
$53$			5.73813i			0.788193i	−0.919069	+	0.394097i	$0.871057\pi$
$54$	−6.43066	+	3.71274i	−0.875102	+	0.505240i
$55$	−1.63612	+	8.05333i	−0.220614	+	1.08591i
$56$	3.40303	−	5.89422i	0.454749	−	0.787649i
$57$	0.806063			0.106766
$58$	3.23449	−	5.60230i	0.424709	−	0.735618i
$59$	−5.18557	−	2.99389i	−0.675104	−	0.389771i	0.122904	−	0.992419i	$-0.460779\pi$
$59$	−5.18557	−	2.99389i	−0.675104	−	0.389771i	−0.798008	+	0.602647i	$0.794113\pi$
$60$	4.15633	+	3.67513i	0.536579	+	0.474457i
$61$	0.884226	−	1.53152i	0.113214	−	0.196092i	−0.803851	−	0.594831i	$-0.797219\pi$
$61$	0.884226	−	1.53152i	0.113214	−	0.196092i	0.917064	+	0.398740i	$0.130552\pi$
$62$	−12.2492	+	7.07205i	−1.55564	+	0.898152i
$63$	1.11577	+	1.93258i	0.140574	+	0.243482i
$64$	18.1187			2.26484
$65$		0			0
$66$	4.73084			0.582326
$67$	−4.94723	−	8.56885i	−0.604400	−	1.04685i	−0.992146	−	0.125086i	$-0.960079\pi$
$67$	−4.94723	−	8.56885i	−0.604400	−	1.04685i	0.387746	−	0.921766i	$-0.373254\pi$
$68$	−6.02961	+	3.48119i	−0.731197	+	0.422157i
$69$	1.55936	−	2.70089i	0.187725	−	0.325148i
$70$	3.19394	−	3.61213i	0.381748	−	0.431732i
$71$	−7.41517	−	4.28115i	−0.880018	−	0.508079i	−0.00935389	−	0.999956i	$-0.502977\pi$
$71$	−7.41517	−	4.28115i	−0.880018	−	0.508079i	−0.870664	+	0.491877i	$0.836311\pi$
$72$	−11.6878	+	20.2439i	−1.37742	+	2.38577i
$73$	−11.7685			−1.37739			−0.688697	−	0.725050i	$-0.741817\pi$
$73$	−11.7685			−1.37739			−0.688697	+	0.725050i	$0.741817\pi$
$74$	5.04055	−	8.73049i	0.585952	−	1.01490i
$75$	1.44903	+	1.92068i	0.167319	+	0.221781i
$76$	7.48031	−	4.31876i	0.858051	−	0.495396i
$77$		−	2.96239i		−	0.337596i
$78$		0			0
$79$	2.26187			0.254480			0.127240	−	0.991872i	$-0.459388\pi$
$79$	2.26187			0.254480			0.127240	+	0.991872i	$0.459388\pi$
$80$	26.8983	+	5.46468i	3.00732	+	0.610970i
$81$	−3.48484	−	6.03592i	−0.387205	−	0.670658i
$82$	19.2582	+	11.1187i	2.12671	+	1.22786i
$83$	−3.84367			−0.421898			−0.210949	−	0.977497i	$-0.567655\pi$
$83$	−3.84367			−0.421898			−0.210949	+	0.977497i	$0.567655\pi$
$84$	−1.73205	−	1.00000i	−0.188982	−	0.109109i
$85$	−2.86298	+	0.958833i	−0.310534	+	0.104000i
$86$			18.1744i			1.95980i
$87$	−1.00772	−	0.581810i	−0.108039	−	0.0623765i
$88$	26.8739	−	15.5156i	2.86476	−	1.65397i
$89$	2.40387	−	1.38787i	0.254809	−	0.147114i	−0.367155	−	0.930160i	$-0.619668\pi$
$89$	2.40387	−	1.38787i	0.254809	−	0.147114i	0.621964	+	0.783045i	$0.286335\pi$
$90$	−10.9697	+	12.4060i	−1.15631	+	1.30770i
$91$		0			0
$92$		−	33.4191i		−	3.48419i
$93$	1.27210	+	2.20334i	0.131911	+	0.228476i
$94$	4.27210	+	7.39949i	0.440633	+	0.763199i
$95$	3.55181	−	1.18953i	0.364408	−	0.122043i
$96$		−	7.67513i		−	0.783340i
$97$	0.936996	−	1.62292i	0.0951375	−	0.164783i	−0.814528	−	0.580124i	$-0.803004\pi$
$97$	0.936996	−	1.62292i	0.0951375	−	0.164783i	0.909666	+	0.415341i	$0.136338\pi$
$98$	8.49389	−	14.7119i	0.858013	−	1.48612i
$99$			10.1744i			1.02257i
$100$	23.7378	+	10.0604i	2.37378	+	1.00604i
$101$	5.24965	+	9.09265i	0.522359	+	0.904753i	0.999662	+	0.0260137i	$0.00828136\pi$
$101$	5.24965	+	9.09265i	0.522359	+	0.904753i	−0.477302	+	0.878739i	$0.658385\pi$
$102$	0.869067	+	1.50527i	0.0860505	+	0.149044i
$103$		−	15.3684i		−	1.51429i	−0.653247	−	0.757145i	$-0.726594\pi$
$103$		−	15.3684i		−	1.51429i	0.653247	−	0.757145i	$-0.273406\pi$
$104$		0			0
$105$	−0.649738	−	0.574515i	−0.0634080	−	0.0560670i
$106$	13.2937	−	7.67513i	1.29120	−	0.745475i
$107$	−9.63967	+	5.56547i	−0.931902	+	0.538034i	−0.887413	−	0.460976i	$-0.847499\pi$
$107$	−9.63967	+	5.56547i	−0.931902	+	0.538034i	−0.0444895	+	0.999010i	$0.514166\pi$
$108$	12.3951	+	7.15633i	1.19272	+	0.688618i
$109$		−	9.58769i		−	0.918334i	−0.888350	−	0.459167i	$-0.848148\pi$
$109$		−	9.58769i		−	0.918334i	0.888350	−	0.459167i	$-0.151852\pi$
$110$	20.8458	−	6.98140i	1.98757	−	0.665651i
$111$	−1.57041	−	0.906679i	−0.149057	−	0.0860581i
$112$	−9.89446			−0.934939
$113$	−0.497545	−	0.287258i	−0.0468051	−	0.0270229i	0.476415	−	0.879221i	$-0.341936\pi$
$113$	−0.497545	−	0.287258i	−0.0468051	−	0.0270229i	−0.523220	+	0.852198i	$0.675269\pi$
$114$	−1.07816	−	1.86743i	−0.100979	−	0.174901i
$115$	2.88534	−	14.2023i	0.269059	−	1.32437i
$116$	−12.4690			−1.15772
$117$		0			0
$118$			16.0181i			1.47459i
$119$	0.942579	−	0.544198i	0.0864061	−	0.0498866i
$120$	1.80879	−	8.90327i	0.165120	−	0.812754i
$121$	1.25329	−	2.17077i	0.113936	−	0.197343i
$122$	−4.73084			−0.428310
$123$	2.00000	−	3.46410i	0.180334	−	0.312348i
$124$	23.6103	+	13.6314i	2.12027	+	1.22414i
$125$	9.21933	+	6.32487i	0.824602	+	0.565713i
$126$	2.98484	−	5.16990i	0.265911	−	0.460571i
$127$	−3.71919	+	2.14728i	−0.330025	+	0.190540i	−0.655852	−	0.754889i	$-0.727691\pi$
$127$	−3.71919	+	2.14728i	−0.330025	+	0.190540i	0.325827	+	0.945429i	$0.394357\pi$
$128$	−8.28480	−	14.3497i	−0.732279	−	1.26835i
$129$	3.26916			0.287833
$130$		0			0
$131$	−0.836381			−0.0730749			−0.0365375	−	0.999332i	$-0.511633\pi$
$131$	−0.836381			−0.0730749			−0.0365375	+	0.999332i	$0.511633\pi$
$132$	−4.55936	−	7.89704i	−0.396841	−	0.687349i
$133$	−1.16936	+	0.675131i	−0.101396	+	0.0585413i
$134$	−13.2345	+	22.9228i	−1.14329	+	1.98023i
$135$	4.64974	+	4.11142i	0.400186	+	0.353855i
$136$	9.87360	+	5.70052i	0.846654	+	0.488816i
$137$	−7.46898	+	12.9366i	−0.638118	+	1.10525i	0.347728	+	0.937596i	$0.386953\pi$
$137$	−7.46898	+	12.9366i	−0.638118	+	1.10525i	−0.985845	+	0.167657i	$0.946380\pi$
$138$	−8.34297			−0.710201
$139$	−4.21933	+	7.30809i	−0.357879	+	0.619864i	−0.987606	−	0.156952i	$-0.949833\pi$
$139$	−4.21933	+	7.30809i	−0.357879	+	0.619864i	0.629727	+	0.776816i	$0.283167\pi$
$140$	−9.10777	−	1.85034i	−0.769747	−	0.156382i
$141$	1.33100	−	0.768452i	0.112090	−	0.0647153i
$142$			22.9053i			1.92217i
$143$		0			0
$144$	33.9829			2.83190
$145$	−5.29899	−	1.07655i	−0.440057	−	0.0894022i
$146$	15.7411	+	27.2643i	1.30274	+	2.25641i
$147$	−2.64632	−	1.52785i	−0.218265	−	0.126015i
$148$	−19.4314			−1.59725
$149$	−9.82962	−	5.67513i	−0.805273	−	0.464925i	0.0400384	−	0.999198i	$-0.487252\pi$
$149$	−9.82962	−	5.67513i	−0.805273	−	0.464925i	−0.845312	+	0.534273i	$0.820585\pi$
$150$	2.51154	−	5.92604i	0.205066	−	0.483859i
$151$		−	13.9878i		−	1.13831i	−0.822230	−	0.569155i	$-0.807271\pi$
$151$		−	13.9878i		−	1.13831i	0.822230	−	0.569155i	$-0.192729\pi$
$152$	−12.2492	−	7.07205i	−0.993538	−	0.573619i
$153$	−3.23732	+	1.86907i	−0.261722	+	0.151105i
$154$	−6.86306	+	3.96239i	−0.553041	+	0.319298i
$155$	8.85685	+	7.83146i	0.711399	+	0.629038i
$156$		0			0
$157$		−	2.77575i		−	0.221529i	−0.993847	−	0.110764i	$-0.964670\pi$
$157$		−	2.77575i		−	0.221529i	0.993847	−	0.110764i	$-0.0353299\pi$
$158$	−3.02539	−	5.24013i	−0.240687	−	0.416883i
$159$	−1.38058	−	2.39123i	−0.109487	−	0.189637i
$160$	−11.3264	−	33.8194i	−0.895427	−	2.67366i
$161$			5.22425i			0.411729i
$162$	−9.32241	+	16.1469i	−0.732437	+	1.26862i
$163$	−1.11577	+	1.93258i	−0.0873942	+	0.151371i	−0.906409	−	0.422401i	$-0.861187\pi$
$163$	−1.11577	+	1.93258i	−0.0873942	+	0.151371i	0.819015	+	0.573772i	$0.194521\pi$
$164$		−	42.8627i		−	3.34702i
$165$	−1.25579	−	3.74968i	−0.0977634	−	0.291912i
$166$	5.14117	+	8.90476i	0.399032	+	0.691144i
$167$	−7.84661	−	13.5907i	−0.607189	−	1.05168i	−0.991701	−	0.128563i	$-0.958964\pi$
$167$	−7.84661	−	13.5907i	−0.607189	−	1.05168i	0.384512	−	0.923120i	$-0.374370\pi$
$168$			3.27504i			0.252675i
$169$		0			0
$170$	6.05079	+	5.35026i	0.464074	+	0.410346i
$171$	4.01621	−	2.31876i	0.307127	−	0.177320i
$172$	30.3380	−	17.5156i	2.31325	−	1.33555i
$173$	−22.1596	−	12.7938i	−1.68476	−	0.972698i	−0.958418	−	0.285367i	$-0.907885\pi$
$173$	−22.1596	−	12.7938i	−1.68476	−	0.972698i	−0.726344	−	0.687331i	$-0.758782\pi$
$174$			3.11283i			0.235983i
$175$	−3.71081	−	1.57269i	−0.280511	−	0.118884i
$176$	−39.0685	−	22.5562i	−2.94490	−	1.70024i
$177$	2.88129			0.216571
$178$	−6.43066	−	3.71274i	−0.481998	−	0.278282i
$179$	−6.06300	−	10.5014i	−0.453170	−	0.784914i	0.545411	−	0.838169i	$-0.316374\pi$
$179$	−6.06300	−	10.5014i	−0.453170	−	0.784914i	−0.998581	+	0.0532551i	$0.983040\pi$
$180$	31.2809	+	6.35505i	2.33154	+	0.473678i
$181$	2.73084			0.202982			0.101491	−	0.994836i	$-0.467639\pi$
$181$	2.73084			0.202982			0.101491	+	0.994836i	$0.467639\pi$
$182$		0			0
$183$			0.850969i			0.0629054i
$184$	−47.3928	+	27.3623i	−3.49384	+	2.01717i
$185$	−8.25782	−	1.67766i	−0.607127	−	0.123344i
$186$	3.40303	−	5.89422i	0.249522	−	0.432185i
$187$	4.96239			0.362886
$188$	8.23449	−	14.2626i	0.600562	−	1.04020i
$189$	−1.93767	−	1.11871i	−0.140945	−	0.0813745i
$190$	−7.50659	−	6.63752i	−0.544585	−	0.481536i
$191$	−10.3127	+	17.8620i	−0.746197	+	1.29245i	0.203436	+	0.979088i	$0.434789\pi$
$191$	−10.3127	+	17.8620i	−0.746197	+	1.29245i	−0.949633	+	0.313363i	$0.898544\pi$
$192$	−7.55055	+	4.35931i	−0.544914	+	0.314606i
$193$	10.8945	+	18.8698i	0.784200	+	1.35827i	0.929476	+	0.368884i	$0.120260\pi$
$193$	10.8945	+	18.8698i	0.784200	+	1.35827i	−0.145275	+	0.989391i	$0.546407\pi$
$194$	−5.01317			−0.359925
$195$		0			0
$196$	−32.7440			−2.33886
$197$	−1.00000	−	1.73205i	−0.0712470	−	0.123404i	0.828201	−	0.560431i	$-0.189365\pi$
$197$	−1.00000	−	1.73205i	−0.0712470	−	0.123404i	−0.899448	+	0.437028i	$0.856031\pi$
$198$	23.5714	−	13.6090i	1.67515	−	0.967146i
$199$	8.37565	−	14.5071i	0.593734	−	1.02838i	−0.399990	−	0.916520i	$-0.630986\pi$
$199$	8.37565	−	14.5071i	0.593734	−	1.02838i	0.993724	−	0.111859i	$-0.0356803\pi$
$200$	−5.16854	−	41.9003i	−0.365471	−	2.96280i
$201$	4.12328	+	2.38058i	0.290834	+	0.167913i
$202$	14.0435	−	24.3240i	0.988097	−	1.71143i
$203$	1.94921			0.136808
$204$	1.67513	−	2.90141i	0.117283	−	0.203139i
$205$	3.70068	−	18.2155i	0.258467	−	1.27223i
$206$	−35.6044	+	20.5562i	−2.48067	+	1.43222i
$207$		−	17.9429i		−	1.24712i
$208$		0			0
$209$	−6.15633			−0.425842
$210$	−0.461931	+	2.27372i	−0.0318762	+	0.156902i
$211$	2.45088	+	4.24504i	0.168725	+	0.292241i	0.937972	−	0.346711i	$-0.112702\pi$
$211$	2.45088	+	4.24504i	0.168725	+	0.292241i	−0.769247	+	0.638952i	$0.779368\pi$
$212$	−25.6237	−	14.7938i	−1.75984	−	1.01605i
$213$	4.12013			0.282307
$214$	25.7874	+	14.8884i	1.76279	+	1.01775i
$215$	14.4051	−	4.82437i	0.982420	−	0.329019i
$216$		−	23.4372i		−	1.59470i
$217$	−3.69088	−	2.13093i	−0.250553	−	0.144657i
$218$	−22.2121	+	12.8242i	−1.50439	+	0.868562i
$219$	4.90423	−	2.83146i	0.331397	−	0.191332i
$220$	−31.7440	−	28.0689i	−2.14018	−	1.89240i
$221$		0			0
$222$			4.85097i			0.325576i
$223$	12.4538	+	21.5706i	0.833969	+	1.44448i	0.894867	+	0.446333i	$0.147270\pi$
$223$	12.4538	+	21.5706i	0.833969	+	1.44448i	−0.0608976	+	0.998144i	$0.519396\pi$
$224$	6.42842	+	11.1344i	0.429517	+	0.743946i
$225$	12.7449	+	5.40146i	0.849660	+	0.360098i
$226$			1.53690i			0.102233i
$227$	−4.97755	+	8.62136i	−0.330371	+	0.572220i	−0.982585	−	0.185815i	$-0.940507\pi$
$227$	−4.97755	+	8.62136i	−0.330371	+	0.572220i	0.652213	+	0.758036i	$0.273841\pi$
$228$	−2.07816	+	3.59948i	−0.137630	+	0.238382i
$229$			5.35026i			0.353555i	0.984251	+	0.176778i	$0.0565673\pi$
$229$			5.35026i			0.353555i	−0.984251	+	0.176778i	$0.943433\pi$
$230$	−36.7622	+	12.3119i	−2.42402	+	0.811822i
$231$	0.712742	+	1.23451i	0.0468950	+	0.0812245i
$232$	10.2091	+	17.6827i	0.670260	+	1.16092i
$233$			10.7612i			0.704987i	0.935814	+	0.352493i	$0.114666\pi$
$233$			10.7612i			0.704987i	−0.935814	+	0.352493i	$0.885334\pi$
$234$		0			0
$235$	4.73084	−	5.35026i	0.308606	−	0.349013i
$236$	26.7385	−	15.4375i	1.74053	−	1.00489i
$237$	−0.942579	+	0.544198i	−0.0612271	+	0.0353495i
$238$	−2.52152	−	1.45580i	−0.163446	−	0.0943656i
$239$			11.8618i			0.767274i	0.923484	+	0.383637i	$0.125329\pi$
$239$			11.8618i			0.767274i	−0.923484	+	0.383637i	$0.874671\pi$
$240$	−12.5240	+	4.19438i	−0.808423	+	0.270746i
$241$	−24.7902	−	14.3127i	−1.59688	−	0.921959i	−0.992084	−	0.125578i	$-0.959921\pi$
$241$	−24.7902	−	14.3127i	−1.59688	−	0.921959i	−0.604796	−	0.796381i	$-0.706745\pi$
$242$	−6.70545			−0.431043
$243$	10.1161	+	5.84051i	0.648945	+	0.374669i
$244$	4.55936	+	7.89704i	0.291883	+	0.505556i
$245$	−13.9153	−	2.82705i	−0.889019	−	0.180614i
$246$	−10.7005			−0.682240
$247$		0			0
$248$		−	44.6434i		−	2.83486i
$249$	1.60176	−	0.924777i	0.101507	−	0.0586054i
$250$	2.32157	−	29.8186i	0.146829	−	1.88590i
$251$	−9.69323	+	16.7892i	−0.611831	+	1.05972i	0.379100	+	0.925356i	$0.376233\pi$
$251$	−9.69323	+	16.7892i	−0.611831	+	1.05972i	−0.990932	+	0.134367i	$0.957100\pi$
$252$	−11.5066			−0.724847
$253$	−11.9096	+	20.6281i	−0.748751	+	1.29688i
$254$	9.94932	+	5.74424i	0.624276	+	0.360426i
$255$	0.962389	−	1.08840i	0.0602671	−	0.0681580i
$256$	−4.04420	+	7.00476i	−0.252762	+	0.437797i
$257$	19.7997	−	11.4314i	1.23507	−	0.713069i	0.266989	−	0.963700i	$-0.413971\pi$
$257$	19.7997	−	11.4314i	1.23507	−	0.713069i	0.968083	+	0.250631i	$0.0806380\pi$
$258$	−4.37271	−	7.57376i	−0.272233	−	0.471522i
$259$	3.03761			0.188748
$260$		0			0
$261$	−6.69464			−0.414388
$262$	1.11871	+	1.93767i	0.0691144	+	0.119710i
$263$	18.9506	−	10.9411i	1.16854	−	0.674658i	0.215206	−	0.976569i	$-0.430958\pi$
$263$	18.9506	−	10.9411i	1.16854	−	0.674658i	0.953336	+	0.301910i	$0.0976243\pi$
$264$	−7.46604	+	12.9316i	−0.459503	+	0.795882i
$265$	−9.61213	−	8.49929i	−0.590468	−	0.522107i
$266$	3.12819	+	1.80606i	0.191802	+	0.110737i
$267$	−0.667837	+	1.15673i	−0.0408709	+	0.0707905i
$268$	51.0191			3.11648
$269$	11.3757	−	19.7032i	0.693586	−	1.20133i	−0.277069	−	0.960850i	$-0.589363\pi$
$269$	11.3757	−	19.7032i	0.693586	−	1.20133i	0.970655	−	0.240476i	$-0.0773035\pi$
$270$	3.30573	−	16.2715i	0.201180	−	0.990251i
$271$	−0.107074	+	0.0618192i	−0.00650428	+	0.00375525i	−0.503249	−	0.864142i	$-0.667862\pi$
$271$	−0.107074	+	0.0618192i	−0.00650428	+	0.00375525i	0.496744	+	0.867897i	$0.334529\pi$
$272$		−	16.5745i		−	1.00498i
$273$		0			0
$274$	39.9610			2.41413
$275$	−11.0670	−	14.6693i	−0.667363	−	0.884589i
$276$	8.04055	+	13.9266i	0.483984	+	0.838285i
$277$	13.2937	+	7.67513i	0.798742	+	0.461154i	0.843031	−	0.537865i	$-0.180769\pi$
$277$	13.2937	+	7.67513i	0.798742	+	0.461154i	−0.0442891	+	0.999019i	$0.514102\pi$
$278$	22.5745			1.35393
$279$	12.6765	+	7.31876i	0.758920	+	0.438163i
$280$	4.83305	+	14.4310i	0.288830	+	0.862418i
$281$		−	13.9248i		−	0.830683i	−0.909666	−	0.415341i	$-0.863662\pi$
$281$		−	13.9248i		−	0.830683i	0.909666	−	0.415341i	$-0.136338\pi$
$282$	−3.56059	−	2.05571i	−0.212030	−	0.122416i
$283$	−17.6509	+	10.1908i	−1.04924	+	0.605778i	−0.922436	−	0.386150i	$-0.873805\pi$
$283$	−17.6509	+	10.1908i	−1.04924	+	0.605778i	−0.126803	+	0.991928i	$0.540471\pi$
$284$	38.2350	−	22.0750i	2.26883	−	1.30991i
$285$	−1.19394	+	1.35026i	−0.0707227	+	0.0799826i
$286$		0			0
$287$			6.70052i			0.395519i
$288$	−22.0786	−	38.2413i	−1.30100	−	2.25339i
$289$	−7.58840	−	13.1435i	−0.446376	−	0.773146i
$290$	4.59368	+	13.7163i	0.269750	+	0.805448i
$291$			0.901754i			0.0528618i
$292$	30.3410	−	52.5521i	1.77557	−	3.07538i
$293$	−2.69029	+	4.65972i	−0.157168	+	0.272224i	−0.933846	−	0.357674i	$-0.883570\pi$
$293$	−2.69029	+	4.65972i	−0.157168	+	0.272224i	0.776678	+	0.629898i	$0.216903\pi$
$294$			8.17442i			0.476742i
$295$	12.6960	−	4.25198i	0.739189	−	0.247560i
$296$	15.9096	+	27.5563i	0.924728	+	1.60168i
$297$	−5.10062	−	8.83453i	−0.295968	−	0.512631i
$298$			30.3634i			1.75891i
$299$		0			0
$300$	−12.3127	+	1.51881i	−0.710871	+	0.0876883i
$301$	−4.74259	+	2.73813i	−0.273358	+	0.157823i
$302$	−32.4059	+	18.7096i	−1.86475	+	1.07661i
$303$	−4.37533	−	2.52610i	−0.251356	−	0.145121i
$304$			20.5623i			1.17933i
$305$	1.25579	+	3.74968i	0.0719065	+	0.214706i
$306$	8.66025	+	5.00000i	0.495074	+	0.285831i
$307$	19.1695			1.09406			0.547031	−	0.837113i	$-0.315758\pi$
$307$	19.1695			1.09406			0.547031	+	0.837113i	$0.315758\pi$
$308$	13.2286	+	7.63752i	0.753768	+	0.435188i
$309$	3.69758	+	6.40440i	0.210348	+	0.364334i
$310$	6.29676	−	30.9940i	0.357632	−	1.76034i
$311$	25.2506			1.43183			0.715915	−	0.698187i	$-0.246010\pi$
$311$	25.2506			1.43183			0.715915	+	0.698187i	$0.246010\pi$
$312$		0			0
$313$			2.81194i			0.158940i	0.996837	+	0.0794702i	$0.0253229\pi$
$313$			2.81194i			0.158940i	−0.996837	+	0.0794702i	$0.974677\pi$
$314$	−6.43066	+	3.71274i	−0.362903	+	0.209522i
$315$	−4.89000	−	0.993455i	−0.275520	−	0.0559748i
$316$	−5.83146	+	10.1004i	−0.328045	+	0.568191i
$317$	−23.7685			−1.33497			−0.667485	−	0.744624i	$-0.732629\pi$
$317$	−23.7685			−1.33497			−0.667485	+	0.744624i	$0.732629\pi$
$318$	−3.69323	+	6.39686i	−0.207106	+	0.358718i
$319$	7.69651	+	4.44358i	0.430922	+	0.248793i
$320$	−26.8373	+	30.3512i	−1.50025	+	1.69668i
$321$	2.67807	−	4.63855i	0.149475	−	0.258899i
$322$	12.1032	−	6.98778i	0.674485	−	0.389414i
$323$	−1.13093	−	1.95883i	−0.0629268	−	0.108992i
$324$	35.9380			1.99655
$325$		0			0
$326$	5.96968			0.330630
$327$	2.30677	+	3.99544i	0.127565	+	0.220949i
$328$	−60.7851	+	35.0943i	−3.35629	+	1.93776i
$329$	−1.28726	+	2.22960i	−0.0709688	+	0.122922i
$330$	−7.00729	+	7.92478i	−0.385739	+	0.436245i
$331$	10.2201	+	5.90057i	0.561747	+	0.324325i	0.753846	−	0.657051i	$-0.228196\pi$
$331$	10.2201	+	5.90057i	0.561747	+	0.324325i	−0.192100	+	0.981375i	$0.561530\pi$
$332$	9.90962	−	17.1640i	0.543861	−	0.941995i
$333$	−10.4328			−0.571713
$334$	−20.9907	+	36.3570i	−1.14856	+	1.98937i
$335$	21.6818	+	4.40488i	1.18460	+	0.240664i
$336$	4.12328	−	2.38058i	0.224944	−	0.129871i
$337$			16.1114i			0.877645i	0.898574	+	0.438822i	$0.144604\pi$
$337$			16.1114i			0.877645i	−0.898574	+	0.438822i	$0.855396\pi$
$338$		0			0
$339$	0.276454			0.0150149
$340$	3.09956	−	15.2567i	0.168097	−	0.827411i
$341$	−9.71568	−	16.8281i	−0.526134	−	0.911290i
$342$	−10.7439	−	6.20299i	−0.580963	−	0.335419i
$343$	10.7612			0.581048
$344$	−49.6790	−	28.6822i	−2.67851	−	1.54644i
$345$	2.21463	+	6.61266i	0.119231	+	0.356014i
$346$			68.4504i			3.67992i
$347$	23.8108	+	13.7472i	1.27823	+	0.737988i	0.976523	−	0.215413i	$-0.0691096\pi$
$347$	23.8108	+	13.7472i	1.27823	+	0.737988i	0.301709	+	0.953400i	$0.402443\pi$
$348$	5.19615	−	3.00000i	0.278543	−	0.160817i
$349$	−15.2440	+	8.80114i	−0.815994	+	0.471114i	−0.849033	−	0.528340i	$-0.822815\pi$
$349$	−15.2440	+	8.80114i	−0.815994	+	0.471114i	0.0330393	+	0.999454i	$0.489481\pi$
$350$	1.31994	+	10.7005i	0.0705540	+	0.571967i
$351$		0			0
$352$			58.6190i			3.12440i
$353$	7.88423	+	13.6559i	0.419635	+	0.726829i	0.995903	−	0.0904319i	$-0.0288247\pi$
$353$	7.88423	+	13.6559i	0.419635	+	0.726829i	−0.576268	+	0.817261i	$0.695491\pi$
$354$	−3.85391	−	6.67517i	−0.204833	−	0.354781i
$355$	18.1548	−	6.08016i	0.963556	−	0.322701i
$356$			14.3127i			0.758569i
$357$	−0.261865	+	0.453564i	−0.0138594	+	0.0240051i
$358$	−16.2193	+	28.0927i	−0.857218	+	1.48475i
$359$		−	14.8242i		−	0.782389i	−0.920308	−	0.391195i	$-0.872062\pi$
$359$		−	14.8242i		−	0.782389i	0.920308	−	0.391195i	$-0.127938\pi$
$360$	−16.5993	−	49.5638i	−0.874858	−	2.61224i
$361$	−8.09697	−	14.0244i	−0.426156	−	0.738124i
$362$	−3.65268	−	6.32662i	−0.191980	−	0.332520i
$363$			1.20616i			0.0633067i
$364$		0			0
$365$	17.4314	−	19.7137i	0.912399	−	1.03186i
$366$	1.97147	−	1.13823i	0.103050	−	0.0594961i
$367$	23.4098	−	13.5156i	1.22198	−	0.705510i	0.256640	−	0.966507i	$-0.417384\pi$
$367$	23.4098	−	13.5156i	1.22198	−	0.705510i	0.965340	+	0.260997i	$0.0840511\pi$
$368$	68.8983	+	39.7785i	3.59157	+	2.07360i
$369$		−	23.0132i		−	1.19802i
$370$	7.15868	+	21.3751i	0.372162	+	1.11124i
$371$	4.00563	+	2.31265i	0.207962	+	0.120067i
$372$	−13.1187			−0.680174
$373$	−11.2172	−	6.47627i	−0.580806	−	0.335329i	0.180648	−	0.983548i	$-0.442181\pi$
$373$	−11.2172	−	6.47627i	−0.580806	−	0.335329i	−0.761454	+	0.648219i	$0.775514\pi$
$374$	−6.63752	−	11.4965i	−0.343218	−	0.594471i
$375$	−5.36368	−	0.417596i	−0.276979	−	0.0215646i
$376$	−26.9683			−1.39078
$377$		0			0
$378$			5.98541i			0.307856i
$379$	26.2283	−	15.1429i	1.34726	−	0.777840i	0.359397	−	0.933185i	$-0.382982\pi$
$379$	26.2283	−	15.1429i	1.34726	−	0.777840i	0.987860	+	0.155345i	$0.0496489\pi$
$380$	−3.84531	+	18.9274i	−0.197260	+	0.970956i
$381$	1.03326	−	1.78965i	0.0529354	−	0.0916867i
$382$	55.1754			2.82302
$383$	−10.5471	+	18.2682i	−0.538934	+	0.933460i	0.460028	+	0.887904i	$0.347839\pi$
$383$	−10.5471	+	18.2682i	−0.538934	+	0.933460i	−0.998962	+	0.0455560i	$0.985494\pi$
$384$	6.90499	+	3.98660i	0.352369	+	0.203440i
$385$	4.96239	+	4.38787i	0.252907	+	0.223627i
$386$	29.1441	−	50.4791i	1.48340	−	2.56932i
$387$	16.2886	−	9.40422i	0.827995	−	0.478043i
$388$	4.83146	+	8.36833i	0.245280	+	0.424837i
$389$	−6.77575			−0.343544			−0.171772	−	0.985137i	$-0.554949\pi$
$389$	−6.77575			−0.343544			−0.171772	+	0.985137i	$0.554949\pi$
$390$		0			0
$391$	−8.75131			−0.442573
$392$	26.8095	+	46.4354i	1.35408	+	2.34534i
$393$	0.348542	−	0.201231i	0.0175816	−	0.0101508i
$394$	−2.67513	+	4.63346i	−0.134771	+	0.233430i
$395$	−3.35026	+	3.78892i	−0.168570	+	0.190641i
$396$	−45.4340	−	26.2313i	−2.28314	−	1.31817i
$397$	5.23449	−	9.06640i	0.262711	−	0.455030i	−0.704250	−	0.709952i	$-0.748717\pi$
$397$	5.23449	−	9.06640i	0.262711	−	0.455030i	0.966961	+	0.254922i	$0.0820500\pi$
$398$	−44.8119			−2.24622
$399$	0.324869	−	0.562690i	0.0162638	−	0.0281697i
$400$	−48.9957	+	36.9640i	−2.44979	+	1.84820i
$401$	−4.34154	+	2.50659i	−0.216806	+	0.125173i	−0.604470	−	0.796628i	$-0.706615\pi$
$401$	−4.34154	+	2.50659i	−0.216806	+	0.125173i	0.387664	+	0.921801i	$0.373282\pi$
$402$		−	12.7367i		−	0.635250i
$403$		0			0
$404$	−54.1378			−2.69345
$405$	15.2727	+	3.10281i	0.758906	+	0.154180i
$406$	−2.60720	−	4.51581i	−0.129393	−	0.224116i
$407$	11.9941	+	6.92478i	0.594524	+	0.343248i
$408$	−5.48612			−0.271603
$409$	−12.4603	−	7.19394i	−0.616120	−	0.355717i	0.159237	−	0.987240i	$-0.449097\pi$
$409$	−12.4603	−	7.19394i	−0.616120	−	0.355717i	−0.775357	+	0.631523i	$0.782430\pi$
$410$	−47.1504	+	15.7910i	−2.32859	+	0.779861i
$411$		−	7.18806i		−	0.354561i
$412$	68.6275	+	39.6221i	3.38104	+	1.95204i
$413$	−4.17990	+	2.41327i	−0.205679	+	0.118749i
$414$	−41.5688	+	23.9998i	−2.04300	+	1.17952i
$415$	5.69323	−	6.43866i	0.279470	−	0.316061i
$416$		0			0
$417$		−	4.06063i		−	0.198850i
$418$	8.23449	+	14.2626i	0.402762	+	0.697604i
$419$	8.73084	+	15.1223i	0.426529	+	0.738771i	0.996562	−	0.0828515i	$-0.0264027\pi$
$419$	8.73084	+	15.1223i	0.426529	+	0.738771i	−0.570032	+	0.821622i	$0.693069\pi$
$420$	4.24063	−	1.42022i	0.206922	−	0.0692995i
$421$			2.88717i			0.140712i	0.997522	+	0.0703559i	$0.0224135\pi$
$421$			2.88717i			0.140712i	−0.997522	+	0.0703559i	$0.977586\pi$
$422$	6.55642	−	11.3560i	0.319161	−	0.552804i
$423$	4.42113	−	7.65762i	0.214963	−	0.372326i
$424$			48.4504i			2.35296i
$425$	2.63446	−	6.21609i	0.127790	−	0.301525i
$426$	−5.51094	−	9.54523i	−0.267006	−	0.462468i
$427$	−0.712742	−	1.23451i	−0.0344920	−	0.0597419i
$428$		−	57.3947i		−	2.77428i
$429$		0			0
$430$	−30.4445	−	26.9199i	−1.46817	−	1.29819i
$431$	0.770360	−	0.444768i	0.0371070	−	0.0214237i	−0.481332	−	0.876538i	$-0.659847\pi$
$431$	0.770360	−	0.444768i	0.0371070	−	0.0214237i	0.518439	+	0.855115i	$0.326513\pi$
$432$	−29.5076	+	17.0362i	−1.41968	+	0.819654i
$433$	−21.8677	−	12.6253i	−1.05089	−	0.606733i	−0.127994	−	0.991775i	$-0.540854\pi$
$433$	−21.8677	−	12.6253i	−1.05089	−	0.606733i	−0.922899	+	0.385042i	$0.874187\pi$
$434$			11.4010i			0.547268i
$435$	2.46724	−	0.826296i	0.118295	−	0.0396179i
$436$	42.8139	+	24.7186i	2.05041	+	1.18381i
$437$	10.8568			0.519354
$438$	−13.1194	−	7.57452i	−0.626871	−	0.361924i
$439$	−14.4060	−	24.9519i	−0.687560	−	1.19089i	−0.972625	−	0.232380i	$-0.925349\pi$
$439$	−14.4060	−	24.9519i	−0.687560	−	1.19089i	0.285066	−	0.958508i	$-0.407985\pi$
$440$	−13.8147	+	67.9989i	−0.658590	+	3.24172i
$441$	−17.5804			−0.837162
$442$		0			0
$443$			36.9805i			1.75700i	0.477746	+	0.878498i	$0.341454\pi$
$443$			36.9805i			1.75700i	−0.477746	+	0.878498i	$0.658546\pi$
$444$	8.09756	−	4.67513i	0.384293	−	0.221872i
$445$	−1.23572	+	6.08250i	−0.0585790	+	0.288338i
$446$	33.3156	−	57.7043i	1.57754	−	2.73238i
$447$	5.46168			0.258329
$448$	7.30242	−	12.6482i	0.345007	−	0.597569i
$449$	10.9863	+	6.34297i	0.518478	+	0.299343i	0.736312	−	0.676643i	$-0.236566\pi$
$449$	10.9863	+	6.34297i	0.518478	+	0.299343i	−0.217834	+	0.975986i	$0.569899\pi$
$450$	−4.53339	−	36.7513i	−0.213706	−	1.73247i
$451$	−15.2750	+	26.4571i	−0.719273	+	1.24582i
$452$	2.56550	−	1.48119i	0.120671	−	0.0696695i
$453$	3.36542	+	5.82908i	0.158121	+	0.273874i
$454$	26.6312			1.24986
$455$		0			0
$456$	6.80606			0.318723
$457$	12.5247	+	21.6934i	0.585880	+	1.01477i	0.994765	+	0.102188i	$0.0325844\pi$
$457$	12.5247	+	21.6934i	0.585880	+	1.01477i	−0.408885	+	0.912586i	$0.634082\pi$
$458$	12.3951	−	7.15633i	0.579186	−	0.334393i
$459$	1.87399	−	3.24585i	0.0874705	−	0.151503i
$460$	55.9814	+	49.5002i	2.61015	+	2.30796i
$461$	31.9452	+	18.4436i	1.48784	+	0.859003i	0.999904	−	0.0138774i	$-0.00441746\pi$
$461$	31.9452	+	18.4436i	1.48784	+	0.859003i	0.487934	+	0.872881i	$0.337751\pi$
$462$	1.90668	−	3.30246i	0.0887067	−	0.153645i
$463$	−39.0191			−1.81337			−0.906685	−	0.421809i	$-0.861395\pi$
$463$	−39.0191			−1.81337			−0.906685	+	0.421809i	$0.861395\pi$
$464$	14.8417	−	25.7066i	0.689008	−	1.19340i
$465$	−5.57511	−	1.13264i	−0.258540	−	0.0525250i
$466$	24.9307	−	14.3938i	1.15489	−	0.666778i
$467$			32.7694i			1.51639i	0.652029	+	0.758194i	$0.273918\pi$
$467$			32.7694i			1.51639i	−0.652029	+	0.758194i	$0.726082\pi$
$468$		0			0
$469$	−7.97556			−0.368277
$470$	−18.7229	−	3.80376i	−0.863624	−	0.175454i
$471$	0.667837	+	1.15673i	0.0307723	+	0.0532992i
$472$	−43.7848	−	25.2792i	−2.01536	−	1.16357i
$473$	−24.9683			−1.14804
$474$	2.52152	+	1.45580i	0.115817	+	0.0668672i
$475$	−3.26831	+	7.71166i	−0.149960	+	0.353835i
$476$			5.61213i			0.257231i
$477$	−13.7575	−	7.94288i	−0.629911	−	0.363679i
$478$	27.4805	−	15.8659i	1.25693	−	0.725689i
$479$	14.6141	−	8.43747i	0.667737	−	0.385518i	−0.127482	−	0.991841i	$-0.540689\pi$
$479$	14.6141	−	8.43747i	0.667737	−	0.385518i	0.795219	+	0.606323i	$0.207356\pi$
$480$	12.8568	+	11.3684i	0.586832	+	0.518892i
$481$		0			0
$482$			76.5764i			3.48796i
$483$	−1.25694	−	2.17708i	−0.0571928	−	0.0990608i
$484$	6.46239	+	11.1932i	0.293745	+	0.508781i
$485$	1.33074	+	3.97346i	0.0604257	+	0.180425i
$486$		−	31.2482i		−	1.41745i
$487$	4.62236	−	8.00616i	0.209459	−	0.362794i	−0.742085	−	0.670306i	$-0.766163\pi$
$487$	4.62236	−	8.00616i	0.209459	−	0.362794i	0.951544	+	0.307512i	$0.0994963\pi$
$488$	7.46604	−	12.9316i	0.337972	−	0.585384i
$489$		−	1.07381i		−	0.0485593i
$490$	12.0632	+	36.0195i	0.544959	+	1.62719i
$491$	−12.8749	−	22.3001i	−0.581038	−	1.00639i	−0.995357	−	0.0962557i	$-0.969313\pi$
$491$	−12.8749	−	22.3001i	−0.581038	−	1.00639i	0.414318	−	0.910132i	$-0.364020\pi$
$492$	10.3127	+	17.8620i	0.464930	+	0.805283i
$493$			3.26519i			0.147057i
$494$		0			0
$495$	−17.0435	−	15.0703i	−0.766048	−	0.677360i
$496$	−56.2062	+	32.4506i	−2.52373	+	1.45708i
$497$	−5.97709	+	3.45088i	−0.268109	+	0.154793i
$498$	−4.28492	−	2.47390i	−0.192012	−	0.110858i
$499$			27.7015i			1.24009i	0.784567	+	0.620044i	$0.212885\pi$
$499$			27.7015i			1.24009i	−0.784567	+	0.620044i	$0.787115\pi$
$500$	−52.0127	+	24.8625i	−2.32608	+	1.11188i
$501$	6.53978	+	3.77575i	0.292176	+	0.168688i
$502$	51.8613			2.31468
$503$	−2.03965	−	1.17759i	−0.0909436	−	0.0525063i	0.453839	−	0.891084i	$-0.350054\pi$
$503$	−2.03965	−	1.17759i	−0.0909436	−	0.0525063i	−0.544782	+	0.838578i	$0.683388\pi$
$504$	9.42113	+	16.3179i	0.419650	+	0.726856i
$505$	−23.0071	−	4.67414i	−1.02380	−	0.207997i
$506$	63.7196			2.83268
$507$		0			0
$508$		−	22.1441i		−	0.982486i
$509$	−18.6303	+	10.7562i	−0.825775	+	0.476762i	−0.852404	−	0.522884i	$-0.824856\pi$
$509$	−18.6303	+	10.7562i	−0.825775	+	0.476762i	0.0266286	+	0.999645i	$0.491523\pi$
$510$	−3.80878	−	0.773794i	−0.168656	−	0.0342642i
$511$	−4.74306	+	8.21522i	−0.209821	+	0.363420i
$512$	−11.5017			−0.508306
$513$	−2.32487	+	4.02679i	−0.102645	+	0.177787i
$514$	−52.9668	−	30.5804i	−2.33627	−	1.34884i
$515$	25.7440	+	22.7635i	1.13442	+	1.00308i
$516$	−8.42842	+	14.5985i	−0.371041	+	0.642661i
$517$	−10.1655	+	5.86907i	−0.447079	+	0.258121i
$518$	−4.06300	−	7.03733i	−0.178518	−	0.309203i
$519$	12.3127			0.540465
$520$		0			0
$521$	37.7440			1.65360			0.826798	−	0.562499i	$-0.190160\pi$
$521$	37.7440			1.65360			0.826798	+	0.562499i	$0.190160\pi$
$522$	8.95452	+	15.5097i	0.391929	+	0.678841i
$523$	20.5609	−	11.8708i	0.899064	−	0.519075i	0.0221676	−	0.999754i	$-0.492943\pi$
$523$	20.5609	−	11.8708i	0.899064	−	0.519075i	0.876896	+	0.480679i	$0.159610\pi$
$524$	2.15633	−	3.73486i	0.0941995	−	0.163158i
$525$	1.92478	−	0.237428i	0.0840042	−	0.0103622i
$526$	−50.6953	−	29.2689i	−2.21042	−	1.27619i
$527$	3.56959	−	6.18271i	0.155494	−	0.269323i
$528$	21.7078			0.944712
$529$	9.50294	−	16.4596i	0.413171	−	0.715634i
$530$	−6.83373	+	33.6371i	−0.296838	+	1.46110i
$531$	14.3560	−	8.28844i	0.622997	−	0.359688i
$532$		−	6.96239i		−	0.301858i
$533$		0			0
$534$	3.57310			0.154623
$535$	4.95534	−	24.3912i	0.214238	−	1.05453i
$536$	−41.7723	−	72.3518i	−1.80429	−	3.12512i
$537$	5.05323	+	2.91748i	0.218063	+	0.125899i
$538$	−60.8627			−2.62398
$539$	20.2113	+	11.6690i	0.870564	+	0.502620i
$540$	−30.3474	+	10.1635i	−1.30594	+	0.437369i
$541$		−	13.0376i		−	0.560531i	−0.959923	−	0.280265i	$-0.909578\pi$
$541$		−	13.0376i		−	0.560531i	0.959923	−	0.280265i	$-0.0904225\pi$
$542$	0.286437	+	0.165374i	0.0123035	+	0.00710344i
$543$	−1.13801	+	0.657032i	−0.0488368	+	0.0281960i
$544$	−18.6515	+	10.7685i	−0.799677	+	0.461694i
$545$	16.0606	+	14.2012i	0.687962	+	0.608314i
$546$		0			0
$547$		−	8.43041i		−	0.360458i	−0.983625	−	0.180229i	$-0.942316\pi$
$547$		−	8.43041i		−	0.360458i	0.983625	−	0.180229i	$-0.0576839\pi$
$548$	−38.5125	−	66.7055i	−1.64517	−	2.84952i
$549$	2.44794	+	4.23995i	0.104475	+	0.180957i
$550$	−19.1819	+	45.2603i	−0.817920	+	1.92990i
$551$		−	4.05079i		−	0.172569i
$552$	13.1666	−	22.8051i	0.560406	−	0.970652i
$553$	0.911603	−	1.57894i	0.0387653	−	0.0671435i
$554$		−	41.0640i		−	1.74464i
$555$	3.84489	−	1.28768i	0.163207	−	0.0546590i
$556$	−21.7562	−	37.6829i	−0.922670	−	1.59811i
$557$	6.84661	+	11.8587i	0.290100	+	0.502469i	0.973833	−	0.227264i	$-0.0729780\pi$
$557$	6.84661	+	11.8587i	0.290100	+	0.502469i	−0.683733	+	0.729732i	$0.739645\pi$
$558$		−	39.1573i		−	1.65766i
$559$		0			0
$560$	14.6556	−	16.5745i	0.619313	−	0.700401i
$561$	−2.06796	+	1.19394i	−0.0873093	+	0.0504080i
$562$	−32.2600	+	18.6253i	−1.36080	+	0.785661i
$563$	−7.68084	−	4.43453i	−0.323709	−	0.186893i	0.329336	−	0.944213i	$-0.393175\pi$
$563$	−7.68084	−	4.43453i	−0.323709	−	0.186893i	−0.653044	+	0.757320i	$0.726509\pi$
$564$			7.92478i			0.333693i
$565$	1.21816	−	0.407968i	0.0512482	−	0.0171634i
$566$	47.2185	+	27.2616i	1.98474	+	1.14589i
$567$	−5.61801			−0.235934
$568$	−62.6106	−	36.1482i	−2.62708	−	1.51675i
$569$	16.3908	+	28.3897i	0.687139	+	1.19016i	0.972760	+	0.231816i	$0.0744668\pi$
$569$	16.3908	+	28.3897i	0.687139	+	1.19016i	−0.285621	+	0.958343i	$0.592200\pi$
$570$	4.72516	+	0.959967i	0.197915	+	0.0402086i
$571$	−40.2882			−1.68601			−0.843005	−	0.537906i	$-0.819215\pi$
$571$	−40.2882			−1.68601			−0.843005	+	0.537906i	$0.819215\pi$
$572$		0			0
$573$		−	9.92478i		−	0.414614i
$574$	15.5233	−	8.96239i	0.647931	−	0.374083i
$575$	19.5169	+	25.8696i	0.813911	+	1.07884i
$576$	−25.0804	+	43.4405i	−1.04502	+	1.81002i
$577$	28.8568			1.20133			0.600663	−	0.799502i	$-0.294903\pi$
$577$	28.8568			1.20133			0.600663	+	0.799502i	$0.294903\pi$
$578$	−20.3000	+	35.1606i	−0.844367	+	1.46249i
$579$	−9.08002	−	5.24235i	−0.377353	−	0.217865i
$580$	18.4690	−	20.8872i	0.766882	−	0.867292i
$581$	−1.54912	+	2.68316i	−0.0642684	+	0.111316i
$582$	2.08912	−	1.20616i	0.0865969	−	0.0499967i
$583$	10.5442	+	18.2631i	0.436696	+	0.756380i
$584$	−99.3679			−4.11187
$585$		0			0
$586$	14.3938			0.594600
$587$	−20.8393	−	36.0948i	−0.860131	−	1.48979i	−0.871802	−	0.489858i	$-0.837048\pi$
$587$	−20.8393	−	36.0948i	−0.860131	−	1.48979i	0.0116712	−	0.999932i	$-0.496285\pi$
$588$	13.6453	−	7.87812i	0.562723	−	0.324888i
$589$	−4.42842	+	7.67026i	−0.182470	+	0.316047i
$590$	−26.8324	−	23.7259i	−1.10467	−	0.976781i
$591$	0.833453	+	0.481194i	0.0342837	+	0.0197937i
$592$	23.1289	−	40.0605i	0.950594	−	1.64648i
$593$	22.4993			0.923935			0.461968	−	0.886897i	$-0.347144\pi$
$593$	22.4993			0.923935			0.461968	+	0.886897i	$0.347144\pi$
$594$	−13.6448	+	23.6335i	−0.559853	+	0.969695i
$595$	−0.484539	+	2.38501i	−0.0198642	+	0.0977757i
$596$	50.6847	−	29.2628i	2.07613	−	1.19865i
$597$			8.06063i			0.329900i
$598$		0			0
$599$	−4.15045			−0.169583			−0.0847913	−	0.996399i	$-0.527022\pi$
$599$	−4.15045			−0.169583			−0.0847913	+	0.996399i	$0.527022\pi$
$600$	12.2350	+	16.2174i	0.499491	+	0.662074i
$601$	−13.9624	−	24.1836i	−0.569538	−	0.986468i	−0.996612	−	0.0822515i	$-0.973789\pi$
$601$	−13.9624	−	24.1836i	−0.569538	−	0.986468i	0.427074	−	0.904217i	$-0.359544\pi$
$602$	12.6870	+	7.32487i	0.517085	+	0.298539i
$603$	27.3923			1.11550
$604$	62.4626	+	36.0628i	2.54157	+	1.46737i
$605$	1.77995	+	5.31476i	0.0723652	+	0.216076i
$606$			13.5153i			0.549021i
$607$	7.09698	+	4.09745i	0.288058	+	0.166310i	0.637066	−	0.770810i	$-0.280148\pi$
$607$	7.09698	+	4.09745i	0.288058	+	0.166310i	−0.349008	+	0.937120i	$0.613481\pi$
$608$	23.1390	−	13.3593i	0.938411	−	0.541792i
$609$	−0.812289	+	0.468976i	−0.0329156	+	0.0190038i
$610$	7.00729	−	7.92478i	0.283717	−	0.320865i
$611$		0			0
$612$		−	19.2750i		−	0.779147i
$613$	16.5696	+	28.6994i	0.669239	+	1.15916i	0.978117	+	0.208055i	$0.0667133\pi$
$613$	16.5696	+	28.6994i	0.669239	+	1.15916i	−0.308878	+	0.951102i	$0.599953\pi$
$614$	−25.6405	−	44.4106i	−1.03476	−	1.79227i
$615$	2.84043	+	8.48127i	0.114537	+	0.341998i
$616$		−	25.0132i		−	1.00781i
$617$	14.5066	−	25.1261i	0.584013	−	1.01154i	−0.410984	−	0.911642i	$-0.634815\pi$
$617$	14.5066	−	25.1261i	0.584013	−	1.01154i	0.994998	−	0.0998982i	$-0.0318517\pi$
$618$	9.89152	−	17.1326i	0.397895	−	0.689175i
$619$			12.2134i			0.490900i	0.969409	+	0.245450i	$0.0789357\pi$
$619$			12.2134i			0.490900i	−0.969409	+	0.245450i	$0.921064\pi$
$620$	−57.8058	+	19.3596i	−2.32154	+	0.777499i
$621$	8.99508	+	15.5799i	0.360960	+	0.625201i
$622$	−33.7743	−	58.4989i	−1.35423	−	2.34559i
$623$		−	2.23743i		−	0.0896406i
$624$		0			0
$625$	−24.2506	+	6.07522i	−0.970024	+	0.243009i
$626$	6.51452	−	3.76116i	0.260372	−	0.150326i
$627$	2.56550	−	1.48119i	0.102456	−	0.0591532i
$628$	12.3951	+	7.15633i	0.494619	+	0.285568i
$629$			5.08840i			0.202888i
$630$	4.23912	+	12.6576i	0.168891	+	0.504292i
$631$	−1.05818	−	0.610942i	−0.0421256	−	0.0243212i	0.478789	−	0.877930i	$-0.341076\pi$
$631$	−1.05818	−	0.610942i	−0.0421256	−	0.0243212i	−0.520915	+	0.853609i	$0.674409\pi$
$632$	19.0982			0.759687
$633$	−2.04269	−	1.17935i	−0.0811897	−	0.0468749i
$634$	31.7919	+	55.0651i	1.26262	+	2.18692i
$635$	1.91188	−	9.41066i	0.0758705	−	0.373451i
$636$	14.2374			0.564551
$637$		0			0
$638$		−	23.7743i		−	0.941235i
$639$	20.5285	−	11.8522i	0.812096	−	0.468864i
$640$	36.3090	+	7.37656i	1.43524	+	0.291584i
$641$	−11.0508	+	19.1405i	−0.436480	+	0.756005i	−0.997415	−	0.0718545i	$-0.977108\pi$
$641$	−11.0508	+	19.1405i	−0.436480	+	0.756005i	0.560935	+	0.827860i	$0.310442\pi$
$642$	−14.3284			−0.565496
$643$	5.83440	−	10.1055i	0.230086	−	0.398521i	−0.727747	−	0.685846i	$-0.759433\pi$
$643$	5.83440	−	10.1055i	0.230086	−	0.398521i	0.957833	+	0.287325i	$0.0927659\pi$
$644$	−23.3289	−	13.4690i	−0.919289	−	0.530752i
$645$	−4.84226	+	5.47627i	−0.190664	+	0.215628i
$646$	−3.02539	+	5.24013i	−0.119032	+	0.206170i
$647$	10.3555	−	5.97873i	0.407115	−	0.235048i	−0.282434	−	0.959287i	$-0.591142\pi$
$647$	10.3555	−	5.97873i	0.407115	−	0.235048i	0.689550	+	0.724238i	$0.257809\pi$
$648$	−29.4245	−	50.9648i	−1.15591	−	2.00209i
$649$	−22.0059			−0.863806
$650$		0			0
$651$	2.05079			0.0803766
$652$	−5.75329	−	9.96500i	−0.225316	−	0.390259i
$653$	−9.52505	+	5.49929i	−0.372744	+	0.215204i	−0.674657	−	0.738132i	$-0.735708\pi$
$653$	−9.52505	+	5.49929i	−0.372744	+	0.215204i	0.301912	+	0.953336i	$0.402375\pi$
$654$	6.17091	−	10.6883i	0.241302	−	0.417947i
$655$	1.23884	−	1.40105i	0.0484056	−	0.0547434i
$656$	88.3676	+	51.0191i	3.45017	+	1.99196i
$657$	16.2902	−	28.2154i	0.635541	−	1.10079i
$658$	6.88717			0.268490
$659$	−1.31994	+	2.28621i	−0.0514177	+	0.0890581i	−0.890589	−	0.454810i	$-0.849707\pi$
$659$	−1.31994	+	2.28621i	−0.0514177	+	0.0890581i	0.839171	+	0.543868i	$0.183041\pi$
$660$	19.9819	+	4.05953i	0.777793	+	0.158017i
$661$	−15.8507	+	9.15140i	−0.616520	+	0.355948i	−0.775513	−	0.631332i	$-0.782509\pi$
$661$	−15.8507	+	9.15140i	−0.616520	+	0.355948i	0.158993	+	0.987280i	$0.449175\pi$
$662$		−	31.5696i		−	1.22699i
$663$		0			0
$664$	−32.4544			−1.25947
$665$	0.601118	−	2.95883i	0.0233104	−	0.114739i
$666$	13.9545	+	24.1699i	0.540727	+	0.936566i
$667$	−13.5730	−	7.83638i	−0.525549	−	0.303426i
$668$	80.9194			3.13087
$669$	−10.3797	−	5.99271i	−0.401301	−	0.231691i
$670$	−18.7959	−	56.1226i	−0.726147	−	2.16821i
$671$		−	6.49929i		−	0.250902i
$672$	−5.35779	−	3.09332i	−0.206681	−	0.119327i
$673$	−5.81135	+	3.35519i	−0.224011	+	0.129333i	−0.607806	−	0.794085i	$-0.707950\pi$
$673$	−5.81135	+	3.35519i	−0.224011	+	0.129333i	0.383795	+	0.923418i	$0.374617\pi$
$674$	37.3258	−	21.5501i	1.43774	−	0.830078i
$675$	−13.7743	+	1.69911i	−0.530174	+	0.0653987i
$676$		0			0
$677$			1.57593i			0.0605679i	0.999541	+	0.0302840i	$0.00964116\pi$
$677$			1.57593i			0.0605679i	−0.999541	+	0.0302840i	$0.990359\pi$
$678$	−0.369775	−	0.640469i	−0.0142011	−	0.0245971i
$679$	−0.755278	−	1.30818i	−0.0289849	−	0.0502033i
$680$	−24.1738	+	8.09598i	−0.927024	+	0.310467i
$681$		−	4.79033i		−	0.183566i
$682$	−25.9907	+	45.0172i	−0.995236	+	1.72380i
$683$	−7.59697	+	13.1583i	−0.290690	+	0.503490i	−0.973973	−	0.226664i	$-0.927218\pi$
$683$	−7.59697	+	13.1583i	−0.290690	+	0.503490i	0.683283	+	0.730154i	$0.260551\pi$
$684$			23.9126i			0.914320i
$685$	−10.6076	−	31.6732i	−0.405294	−	1.21017i
$686$	−14.3938	−	24.9307i	−0.549556	−	0.951859i
$687$	−1.28726	−	2.22960i	−0.0491119	−	0.0850644i
$688$			83.3947i			3.17939i
$689$		0			0
$690$	12.3576	−	13.9756i	0.470444	−	0.532041i
$691$	−16.2057	+	9.35637i	−0.616494	+	0.355933i	−0.775503	−	0.631344i	$-0.782504\pi$
$691$	−16.2057	+	9.35637i	−0.616494	+	0.355933i	0.159009	+	0.987277i	$0.449170\pi$
$692$	114.262	−	65.9692i	4.34359	−	2.50777i
$693$	7.10247	+	4.10062i	0.269801	+	0.155769i
$694$		−	73.5510i		−	2.79196i
$695$	−5.99237	−	17.8926i	−0.227303	−	0.678706i
$696$	−8.50880	−	4.91256i	−0.322525	−	0.186210i
$697$	−11.2243			−0.425149
$698$	40.7797	+	23.5442i	1.54354	+	0.891161i
$699$	−2.58910	−	4.48446i	−0.0979289	−	0.169618i
$700$	16.5899	−	12.5160i	0.627041	−	0.473060i
$701$	−24.3028			−0.917904			−0.458952	−	0.888461i	$-0.651775\pi$
$701$	−24.3028			−0.917904			−0.458952	+	0.888461i	$0.651775\pi$
$702$		0			0
$703$		−	6.31265i		−	0.238086i
$704$	57.6675	−	33.2943i	2.17342	−	1.25483i
$705$	−0.684209	+	3.36782i	−0.0257688	+	0.126840i
$706$	21.0913	−	36.5313i	0.793783	−	1.37487i
$707$	8.46310			0.318287
$708$	−7.42842	+	12.8664i	−0.279177	+	0.483549i
$709$	8.36833	+	4.83146i	0.314279	+	0.181449i	0.648840	−	0.760925i	$-0.275255\pi$
$709$	8.36833	+	4.83146i	0.314279	+	0.181449i	−0.334561	+	0.942374i	$0.608588\pi$
$710$	−38.3693	−	33.9271i	−1.43997	−	1.27326i
$711$	−3.13093	+	5.42293i	−0.117419	+	0.203376i
$712$	20.2972	−	11.7186i	0.760672	−	0.439174i
$713$	17.1339	+	29.6767i	0.641669	+	1.11140i
$714$	1.40105			0.0524329
$715$		0			0
$716$	62.5256			2.33669
$717$	−2.85391	−	4.94312i	−0.106581	−	0.184604i
$718$	−34.3436	+	19.8283i	−1.28169	+	0.739985i
$719$	−14.2071	+	24.6074i	−0.529836	+	0.917703i	0.469558	+	0.882901i	$0.344413\pi$
$719$	−14.2071	+	24.6074i	−0.529836	+	0.917703i	−0.999394	+	0.0348012i	$0.988920\pi$
$720$	−50.3352	+	56.9257i	−1.87588	+	2.12150i
$721$	−10.7282	−	6.19394i	−0.399540	−	0.230674i
$722$	−21.6604	+	37.5170i	−0.806118	+	1.39624i
$723$	13.7743			0.512273
$724$	−7.04055	+	12.1946i	−0.261660	+	0.453208i
$725$	9.65219	−	7.28192i	0.358473	−	0.270444i
$726$	2.79434	−	1.61331i	0.103708	−	0.0598756i
$727$		−	34.8545i		−	1.29268i	−0.763049	−	0.646341i	$-0.776299\pi$
$727$		−	34.8545i		−	1.29268i	0.763049	−	0.646341i	$-0.223701\pi$
$728$		0			0
$729$	15.2882			0.566230
$730$	−68.9869	−	14.0154i	−2.55332	−	0.518734i
$731$	−4.58673	−	7.94446i	−0.169646	−	0.293836i
$732$	−3.80001	−	2.19394i	−0.140452	−	0.0810902i
$733$	−6.25202			−0.230923			−0.115462	−	0.993312i	$-0.536835\pi$
$733$	−6.25202			−0.230923			−0.115462	+	0.993312i	$0.536835\pi$
$734$	−62.6242	−	36.1561i	−2.31150	−	1.33455i
$735$	6.47907	−	2.16989i	0.238984	−	0.0800375i
$736$		−	103.376i		−	3.81050i
$737$	−31.4917	−	18.1817i	−1.16001	−	0.669732i
$738$	−53.3153	+	30.7816i	−1.96256	+	1.13309i
$739$	−27.7861	+	16.0423i	−1.02213	+	0.590126i	−0.914720	−	0.404089i	$-0.867589\pi$
$739$	−27.7861	+	16.0423i	−1.02213	+	0.590126i	−0.107408	+	0.994215i	$0.534255\pi$
$740$	28.7816	−	32.5501i	1.05803	−	1.19656i
$741$		0			0
$742$		−	12.3733i		−	0.454238i
$743$	−15.2721	−	26.4521i	−0.560279	−	0.970432i	−0.997472	−	0.0710638i	$-0.977361\pi$
$743$	−15.2721	−	26.4521i	−0.560279	−	0.970432i	0.437193	−	0.899368i	$-0.355973\pi$
$744$	10.7411	+	18.6041i	0.393787	+	0.682059i
$745$	24.0662	−	8.05992i	0.881716	−	0.295293i
$746$			34.6497i			1.26862i
$747$	5.32051	−	9.21540i	0.194667	−	0.337174i
$748$	−12.7938	+	22.1596i	−0.467789	+	0.810235i
$749$			8.97224i			0.327838i
$750$	6.20682	+	12.9848i	0.226641	+	0.474137i
$751$	14.0811	+	24.3892i	0.513827	+	0.889974i	0.999871	+	0.0160400i	$0.00510591\pi$
$751$	14.0811	+	24.3892i	0.513827	+	0.889974i	−0.486045	+	0.873934i	$0.661561\pi$
$752$	19.6028	+	33.9531i	0.714842	+	1.23814i
$753$		−	9.32865i		−	0.339955i
$754$		0			0
$755$	23.4314	+	20.7186i	0.852755	+	0.754028i
$756$	9.99125	−	5.76845i	0.363378	−	0.209797i
$757$	−30.6667	+	17.7054i	−1.11460	+	0.643515i	−0.940017	−	0.341127i	$-0.889191\pi$
$757$	−30.6667	+	17.7054i	−1.11460	+	0.643515i	−0.174584	+	0.984642i	$0.555858\pi$
$758$	−70.1642	−	40.5093i	−2.54848	−	1.47136i
$759$		−	11.4617i		−	0.416033i
$760$	29.9900	−	10.0439i	1.08785	−	0.364329i
$761$	−16.6613	−	9.61942i	−0.603973	−	0.348704i	0.166630	−	0.986019i	$-0.446711\pi$
$761$	−16.6613	−	9.61942i	−0.603973	−	0.348704i	−0.770603	+	0.637316i	$0.780045\pi$
$762$	−5.52820			−0.200265
$763$	−6.69289	−	3.86414i	−0.242299	−	0.139891i
$764$	−53.1754	−	92.1025i	−1.92382	−	3.33215i
$765$	1.66417	−	8.19139i	0.0601681	−	0.296160i
$766$	56.4299			2.03890
$767$		0			0
$768$		−	3.89209i		−	0.140444i
$769$	−42.4043	+	24.4821i	−1.52914	+	0.882849i	−0.529741	+	0.848159i	$0.677711\pi$
$769$	−42.4043	+	24.4821i	−1.52914	+	0.882849i	−0.999398	+	0.0346894i	$0.988956\pi$
$770$	3.52800	−	17.3656i	0.127140	−	0.625812i
$771$	−5.50071	+	9.52750i	−0.198103	+	0.343125i
$772$	−112.351			−4.04359
$773$	23.0840	−	39.9827i	0.830275	−	1.43808i	−0.0675447	−	0.997716i	$-0.521517\pi$
$773$	23.0840	−	39.9827i	0.830275	−	1.43808i	0.897820	−	0.440363i	$-0.145150\pi$
$774$	−43.5741	−	25.1575i	−1.56624	−	0.904268i
$775$	−26.2374	+	3.23647i	−0.942476	+	0.116258i
$776$	7.91160	−	13.7033i	0.284010	−	0.491920i
$777$	−1.26585	+	0.730841i	−0.0454122	+	0.0262188i
$778$	9.06300	+	15.6976i	0.324924	+	0.562786i
$779$	13.9248			0.498907
$780$		0			0
$781$	−31.4676			−1.12600
$782$	11.7054	+	20.2744i	0.418586	+	0.725012i
$783$	5.81301	−	3.35614i	0.207740	−	0.119939i
$784$	38.9749	−	67.5064i	1.39196	−	2.41094i
$785$	4.64974	+	4.11142i	0.165956	+	0.146743i
$786$	−0.932395	−	0.538319i	−0.0332574	−	0.0192012i
$787$	−11.3229	+	19.6118i	−0.403617	+	0.699086i	−0.994159	−	0.107921i	$-0.965581\pi$
$787$	−11.3229	+	19.6118i	−0.403617	+	0.699086i	0.590542	+	0.807007i	$0.298914\pi$
$788$	10.3127			0.367373
$789$	−5.26480	+	9.11891i	−0.187432	+	0.324642i
$790$	13.2591	+	2.69373i	0.471738	+	0.0958385i
$791$	−0.401053	+	0.231548i	−0.0142598	+	0.00823290i
$792$			85.9086i			3.05263i
$793$		0			0
$794$	−28.0059			−0.993891
$795$	6.05053	+	1.22923i	0.214590	+	0.0435963i
$796$	43.1876	+	74.8031i	1.53074	+	2.65133i
$797$	−7.13382	−	4.11871i	−0.252693	−	0.145892i	0.368304	−	0.929706i	$-0.379939\pi$
$797$	−7.13382	−	4.11871i	−0.252693	−	0.145892i	−0.620997	+	0.783813i	$0.713272\pi$
$798$	−1.73813			−0.0615293
$799$	−3.73486	−	2.15633i	−0.132130	−	0.0762853i
$800$	73.4285	+	31.1200i	2.59609	+	1.10026i
$801$			7.68452i			0.271519i
$802$	11.6142	+	6.70545i	0.410111	+	0.236778i
$803$	−37.4561	+	21.6253i	−1.32180	+	0.763140i
$804$	−21.2610	+	12.2750i	−0.749817	+	0.432907i
$805$	−8.75131	−	7.73813i	−0.308443	−	0.272733i
$806$		0			0
$807$			10.9478i			0.385381i
$808$	44.3258	+	76.7746i	1.55938	+	2.70092i
$809$	22.0659	+	38.2193i	0.775797	+	1.34372i	0.934345	+	0.356369i	$0.115985\pi$
$809$	22.0659	+	38.2193i	0.775797	+	1.34372i	−0.158548	+	0.987351i	$0.550681\pi$
$810$	−13.2398	−	39.5329i	−0.465201	−	1.38905i
$811$			22.6883i			0.796694i	0.917235	+	0.398347i	$0.130416\pi$
$811$			22.6883i			0.796694i	−0.917235	+	0.398347i	$0.869584\pi$
$812$	−5.02539	+	8.70424i	−0.176357	+	0.305459i
$813$	0.0297470	−	0.0515234i	0.00104327	−	0.00180700i
$814$		−	37.0494i		−	1.29858i
$815$	−1.58464	−	4.73159i	−0.0555076	−	0.165740i
$816$	3.98778	+	6.90704i	0.139600	+	0.241795i
$817$	5.69029	+	9.85587i	0.199078	+	0.344813i
$818$			38.4894i			1.34575i
$819$		0			0
$820$	71.8007	+	63.4880i	2.50739	+	2.21710i
$821$	−43.5382	+	25.1368i	−1.51949	+	0.877281i	−0.519759	+	0.854313i	$0.673978\pi$
$821$	−43.5382	+	25.1368i	−1.51949	+	0.877281i	−0.999736	+	0.0229677i	$0.992689\pi$
$822$	−16.6528	+	9.61450i	−0.580833	+	0.335344i
$823$	4.44352	+	2.56547i	0.154891	+	0.0894265i	0.575442	−	0.817842i	$-0.304830\pi$
$823$	4.44352	+	2.56547i	0.154891	+	0.0894265i	−0.420551	+	0.907269i	$0.638163\pi$
$824$		−	129.764i		−	4.52054i
$825$	8.14128	+	3.45039i	0.283443	+	0.120127i
$826$	11.1818	+	6.45580i	0.389064	+	0.224626i
$827$	−18.6946			−0.650076			−0.325038	−	0.945701i	$-0.605377\pi$
$827$	−18.6946			−0.650076			−0.325038	+	0.945701i	$0.605377\pi$
$828$	80.1241	+	46.2597i	2.78450	+	1.60763i
$829$	1.72061	+	2.98018i	0.0597591	+	0.103506i	0.894357	−	0.447353i	$-0.147633\pi$
$829$	1.72061	+	2.98018i	0.0597591	+	0.103506i	−0.834598	+	0.550859i	$0.814300\pi$
$830$	−22.5317	−	4.57756i	−0.782087	−	0.158889i
$831$	−7.38646			−0.256233
$832$		0			0
$833$			8.57452i			0.297089i
$834$	−9.40740	+	5.43136i	−0.325752	+	0.188073i
$835$	34.3886	+	6.98641i	1.19007	+	0.241775i
$836$	15.8720	−	27.4911i	0.548945	−	0.950800i
$837$	−14.6761			−0.507280
$838$	23.3561	−	40.4540i	0.806825	−	1.39746i
$839$	45.5744	+	26.3124i	1.57340	+	0.908406i	0.995747	+	0.0921263i	$0.0293664\pi$
$839$	45.5744	+	26.3124i	1.57340	+	0.908406i	0.577657	+	0.816279i	$0.303967\pi$
$840$	−5.48612	−	4.85097i	−0.189289	−	0.167374i
$841$	11.5762	−	20.0505i	0.399179	−	0.691398i
$842$	6.68879	−	3.86177i	0.230511	−	0.133085i
$843$	3.35026	+	5.80282i	0.115389	+	0.199860i
$844$	−25.2750			−0.870003
$845$		0			0
$846$	−23.6542			−0.813248
$847$	−1.01023	−	1.74978i	−0.0347121	−	0.0601230i
$848$	60.9992	−	35.2179i	2.09472	−	1.20939i
$849$	4.90374	−	8.49353i	0.168296	−	0.291497i
$850$	−17.9248	+	2.21108i	−0.614815	+	0.0758394i
$851$	−21.1519	−	12.2120i	−0.725077	−	0.418623i
$852$	−10.6224	+	18.3985i	−0.363916	+	0.630321i
$853$	−6.31853			−0.216342			−0.108171	−	0.994132i	$-0.534499\pi$
$853$	−6.31853			−0.216342			−0.108171	+	0.994132i	$0.534499\pi$
$854$	−1.90668	+	3.30246i	−0.0652452	+	0.113008i
$855$	−2.06456	+	10.1622i	−0.0706065	+	0.347540i
$856$	−81.3934	+	46.9925i	−2.78197	+	1.60617i
$857$		−	0.775746i		−	0.0264990i	−0.999912	−	0.0132495i	$-0.995782\pi$
$857$		−	0.775746i		−	0.0264990i	0.999912	−	0.0132495i	$-0.00421757\pi$
$858$		0			0
$859$	−3.24869			−0.110844			−0.0554220	−	0.998463i	$-0.517650\pi$
$859$	−3.24869			−0.110844			−0.0554220	+	0.998463i	$0.517650\pi$
$860$	−15.5954	+	76.7641i	−0.531800	+	2.61764i
$861$	−1.61213	−	2.79229i	−0.0549411	−	0.0951608i
$862$	−2.06081	−	1.18981i	−0.0701916	−	0.0405252i
$863$	19.9208			0.678112			0.339056	−	0.940766i	$-0.389892\pi$
$863$	19.9208			0.678112			0.339056	+	0.940766i	$0.389892\pi$
$864$	38.3421	+	22.1368i	1.30442	+	0.753110i
$865$	54.2540	−	18.1700i	1.84469	−	0.617800i
$866$			67.5487i			2.29540i
$867$	6.32457	+	3.65149i	0.214794	+	0.124011i
$868$	19.0314	−	10.9878i	0.645968	−	0.372950i
$869$	7.19897	−	4.15633i	0.244208	−	0.140994i
$870$	−5.21440	−	4.61071i	−0.176785	−	0.156318i
$871$		0			0
$872$		−	80.9544i		−	2.74146i
$873$	2.59403	+	4.49299i	0.0877946	+	0.152065i
$874$	−14.5217	−	25.1524i	−0.491205	−	0.850793i
$875$	8.13089	−	3.88663i	0.274874	−	0.131392i
$876$			29.1998i			0.986570i
$877$	−11.0689	+	19.1719i	−0.373770	+	0.647388i	−0.990142	−	0.140067i	$-0.955268\pi$
$877$	−11.0689	+	19.1719i	−0.373770	+	0.647388i	0.616372	+	0.787455i	$0.288602\pi$
$878$	−38.5379	+	66.7495i	−1.30059	+	2.25269i
$879$		−	2.58910i		−	0.0873283i
$880$	95.6525	−	32.0347i	3.22445	−	1.07989i
$881$	1.11577	+	1.93258i	0.0375914	+	0.0651102i	0.884209	−	0.467092i	$-0.154698\pi$
$881$	1.11577	+	1.93258i	0.0375914	+	0.0651102i	−0.846618	+	0.532202i	$0.821365\pi$
$882$	23.5149	+	40.7291i	0.791789	+	1.37142i
$883$			4.30440i			0.144855i	0.997374	+	0.0724273i	$0.0230745\pi$
$883$			4.30440i			0.144855i	−0.997374	+	0.0724273i	$0.976925\pi$
$884$		0			0
$885$	−4.26774	+	4.82653i	−0.143459	+	0.162242i
$886$	85.6739	−	49.4638i	2.87827	−	1.66177i
$887$	−13.7984	+	7.96651i	−0.463305	+	0.267489i	−0.713433	−	0.700723i	$-0.752861\pi$
$887$	−13.7984	+	7.96651i	−0.463305	+	0.267489i	0.250128	+	0.968213i	$0.419527\pi$
$888$	−13.2599	−	7.65562i	−0.444974	−	0.256906i
$889$			3.46168i			0.116101i
$890$	15.7444	−	5.27290i	0.527753	−	0.176748i
$891$	−22.1828	−	12.8072i	−0.743152	−	0.429059i
$892$	−128.432			−4.30022
$893$	4.63346	+	2.67513i	0.155053	+	0.0895198i
$894$	−7.30536	−	12.6532i	−0.244328	−	0.423188i
$895$	26.5718	+	5.39833i	0.888196	+	0.180446i
$896$	−13.3561			−0.446197
$897$		0			0
$898$		−	33.9365i		−	1.13248i
$899$	11.0727	−	6.39280i	0.369294	−	0.213212i
$900$	−56.9787	+	42.9866i	−1.89929	+	1.43289i
$901$	−3.87399	+	6.70995i	−0.129061	+	0.223541i
$902$	81.7255			2.72116
$903$	1.31757	−	2.28211i	0.0438461	−	0.0759438i
$904$	−4.20106	−	2.42548i	−0.139725	−	0.0806704i
$905$	−4.04491	+	4.57452i	−0.134457	+	0.152062i
$906$	9.00294	−	15.5935i	0.299103	−	0.518061i
$907$	−44.9542	+	25.9543i	−1.49268	+	0.861798i	−0.999965	−	0.00839339i	$-0.997328\pi$
$907$	−44.9542	+	25.9543i	−1.49268	+	0.861798i	−0.492713	+	0.870192i	$0.663995\pi$
$908$	−25.6659	−	44.4546i	−0.851751	−	1.47528i
$909$	−29.0668			−0.964085
$910$		0			0
$911$	−9.67750			−0.320630			−0.160315	−	0.987066i	$-0.551251\pi$
$911$	−9.67750			−0.320630			−0.160315	+	0.987066i	$0.551251\pi$
$912$	−4.94723	−	8.56885i	−0.163819	−	0.283743i
$913$	−12.2335	+	7.06300i	−0.404869	+	0.233751i
$914$	33.5052	−	58.0327i	1.10825	−	1.91955i
$915$	−1.42548	−	1.26045i	−0.0471251	−	0.0416692i
$916$	−23.8916	−	13.7938i	−0.789402	−	0.455761i
$917$	−0.337088	+	0.583853i	−0.0111316	+	0.0192805i
$918$	−10.0263			−0.330919
$919$	6.77575	−	11.7359i	0.223511	−	0.387133i	−0.732361	−	0.680917i	$-0.761581\pi$
$919$	6.77575	−	11.7359i	0.223511	−	0.387133i	0.955872	+	0.293784i	$0.0949147\pi$
$920$	24.3626	−	119.918i	0.803211	−	3.95358i
$921$	−7.98844	+	4.61213i	−0.263228	+	0.151975i
$922$		−	98.6780i		−	3.24979i
$923$		0			0
$924$	−7.35026			−0.241806
$925$	15.0417	−	11.3480i	0.494569	−	0.373119i
$926$	52.1905	+	90.3967i	1.71509	+	2.97062i
$927$	36.8464	+	21.2733i	1.21019	+	0.698706i
$928$	−38.5705			−1.26614
$929$	−8.18387	−	4.72496i	−0.268504	−	0.155021i	0.359704	−	0.933067i	$-0.382878\pi$
$929$	−8.18387	−	4.72496i	−0.268504	−	0.155021i	−0.628208	+	0.778046i	$0.716211\pi$
$930$	4.83305	+	14.4310i	0.158482	+	0.473212i
$931$		−	10.6375i		−	0.348631i
$932$	−48.0540	−	27.7440i	−1.57406	−	0.908785i
$933$	−10.5226	+	6.07522i	−0.344494	+	0.198894i
$934$	75.9179	−	43.8312i	2.48411	−	1.43420i
$935$	−7.35026	+	8.31265i	−0.240379	+	0.271853i
$936$		0			0
$937$		−	16.0409i		−	0.524035i	−0.965063	−	0.262017i	$-0.915612\pi$
$937$		−	16.0409i		−	0.524035i	0.965063	−	0.262017i	$-0.0843877\pi$
$938$	10.6678	+	18.4772i	0.348317	+	0.603303i
$939$	−0.676545	−	1.17181i	−0.0220782	−	0.0382406i
$940$	11.6948	+	34.9195i	0.381441	+	1.13895i
$941$		−	21.6747i		−	0.706574i	−0.935515	−	0.353287i	$-0.885064\pi$
$941$		−	21.6747i		−	0.706574i	0.935515	−	0.353287i	$-0.114936\pi$
$942$	1.78655	−	3.09440i	0.0582090	−	0.100821i
$943$	26.9380	−	46.6579i	0.877220	−	1.51939i
$944$			73.5002i			2.39223i
$945$	4.74406	−	1.58882i	0.154324	−	0.0516842i
$946$	33.3967	+	57.8448i	1.08582	+	1.88070i
$947$	−2.31559	−	4.01072i	−0.0752466	−	0.130331i	0.825947	−	0.563748i	$-0.190641\pi$
$947$	−2.31559	−	4.01072i	−0.0752466	−	0.130331i	−0.901193	+	0.433417i	$0.857308\pi$
$948$		−	5.61213i		−	0.182273i
$949$		0			0
$950$	22.2374	−	2.74306i	0.721477	−	0.0889966i
$951$	9.90494	−	5.71862i	0.321190	−	0.185439i
$952$	7.95874	−	4.59498i	0.257944	−	0.148924i
$953$	22.7748	+	13.1490i	0.737748	+	0.425939i	0.821250	−	0.570569i	$-0.193277\pi$
$953$	22.7748	+	13.1490i	0.737748	+	0.425939i	−0.0835021	+	0.996508i	$0.526611\pi$
$954$			42.4965i			1.37587i
$955$	−14.6462	−	43.7322i	−0.473940	−	1.41514i
$956$	−52.9689	−	30.5816i	−1.71314	−	0.989079i
$957$	−4.27645			−0.138238
$958$	−39.0947	−	22.5713i	−1.26309	−	0.729247i
$959$	6.02047	+	10.4278i	0.194411	+	0.336730i
$960$	3.88141	−	19.1051i	0.125272	−	0.616616i
$961$	3.04491			0.0982228
$962$		0			0
$963$		−	30.8155i		−	0.993014i
$964$	127.827	−	73.8007i	4.11702	−	2.37696i
$965$	−47.7461	−	9.70013i	−1.53700	−	0.312258i
$966$	−3.36248	+	5.82399i	−0.108186	+	0.187384i
$967$	−11.9405			−0.383981			−0.191990	−	0.981397i	$-0.561494\pi$
$967$	−11.9405			−0.383981			−0.191990	+	0.981397i	$0.561494\pi$
$968$	10.5823	−	18.3291i	0.340128	−	0.589118i
$969$	0.942579	+	0.544198i	0.0302800	+	0.0174822i
$970$	7.42548	−	8.39772i	0.238418	−	0.269635i
$971$	−15.0762	+	26.1127i	−0.483818	+	0.837997i	−0.999827	−	0.0185861i	$-0.994084\pi$
$971$	−15.0762	+	26.1127i	−0.483818	+	0.837997i	0.516010	+	0.856583i	$0.327417\pi$
$972$	−52.1617	+	30.1155i	−1.67309	+	0.965957i
$973$	3.40105	+	5.89079i	0.109033	+	0.188850i
$974$	−24.7308			−0.792427
$975$		0			0
$976$	−21.7078			−0.694850
$977$	−13.4660	−	23.3239i	−0.430817	−	0.746196i	0.566127	−	0.824318i	$-0.308441\pi$
$977$	−13.4660	−	23.3239i	−0.430817	−	0.746196i	−0.996944	+	0.0781216i	$0.975108\pi$
$978$	−2.48772	+	1.43629i	−0.0795487	+	0.0459274i
$979$	5.10062	−	8.83453i	0.163016	−	0.282353i
$980$	48.5002	−	54.8505i	1.54928	−	1.75214i
$981$	22.9870	+	13.2715i	0.733917	+	0.423727i
$982$	−34.4422	+	59.6556i	−1.09909	+	1.90369i
$983$	−20.5902			−0.656727			−0.328363	−	0.944551i	$-0.606497\pi$
$983$	−20.5902			−0.656727			−0.328363	+	0.944551i	$0.606497\pi$
$984$	16.8872	−	29.2494i	0.538343	−	0.932438i
$985$	4.38261	+	0.890373i	0.139641	+	0.0283696i
$986$	7.56457	−	4.36741i	0.240905	−	0.139087i
$987$		−	1.23884i		−	0.0394328i
$988$		0			0
$989$	44.0322			1.40014
$990$	−12.1170	+	59.6427i	−0.385105	+	1.89557i
$991$	24.0689	+	41.6885i	0.764573	+	1.32428i	0.940472	+	0.339871i	$0.110384\pi$
$991$	24.0689	+	41.6885i	0.764573	+	1.32428i	−0.175899	+	0.984408i	$0.556283\pi$
$992$	73.0342	+	42.1663i	2.31884	+	1.33878i
$993$	−5.67864			−0.180206
$994$	15.9895	+	9.23155i	0.507156	+	0.292807i
$995$	11.8953	+	35.5181i	0.377105	+	1.12600i
$996$			9.53690i			0.302188i
$997$	28.9473	+	16.7127i	0.916771	+	0.529298i	0.882603	−	0.470118i	$-0.155789\pi$
$997$	28.9473	+	16.7127i	0.916771	+	0.529298i	0.0341674	+	0.999416i	$0.489122\pi$
$998$	64.1769	−	37.0525i	2.03148	−	1.17288i
$999$	9.05886	−	5.23013i	0.286610	−	0.165474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.l.d.699.1		12
5.4	even	2		845.2.l.e.699.6		12
13.2	odd	12		65.2.b.a.14.1	✓	6
13.3	even	3		845.2.d.b.844.5		6
13.4	even	6		845.2.l.e.654.6		12
13.5	odd	4		845.2.n.f.484.1		12
13.6	odd	12		845.2.n.f.529.6		12
13.7	odd	12		845.2.n.g.529.1		12
13.8	odd	4		845.2.n.g.484.6		12
13.9	even	3	inner	845.2.l.d.654.2		12
13.10	even	6		845.2.d.a.844.1		6
13.11	odd	12		845.2.b.c.339.6		6
13.12	even	2		845.2.l.e.699.5		12
39.2	even	12		585.2.c.b.469.6		6
52.15	even	12		1040.2.d.c.209.4		6
65.2	even	12		325.2.a.k.1.3		3
65.4	even	6	inner	845.2.l.d.654.1		12
65.9	even	6		845.2.l.e.654.5		12
65.19	odd	12		845.2.n.f.529.1		12
65.24	odd	12		845.2.b.c.339.1		6
65.28	even	12		325.2.a.j.1.1		3
65.29	even	6		845.2.d.a.844.2		6
65.34	odd	4		845.2.n.g.484.1		12
65.37	even	12		4225.2.a.ba.1.1		3
65.44	odd	4		845.2.n.f.484.6		12
65.49	even	6		845.2.d.b.844.6		6
65.54	odd	12		65.2.b.a.14.6	yes	6
65.59	odd	12		845.2.n.g.529.6		12
65.63	even	12		4225.2.a.bh.1.3		3
65.64	even	2	inner	845.2.l.d.699.2		12
195.2	odd	12		2925.2.a.bf.1.1		3
195.119	even	12		585.2.c.b.469.1		6
195.158	odd	12		2925.2.a.bj.1.3		3
260.67	odd	12		5200.2.a.cb.1.3		3
260.119	even	12		1040.2.d.c.209.3		6
260.223	odd	12		5200.2.a.cj.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.1	✓	6	13.2	odd	12
65.2.b.a.14.6	yes	6	65.54	odd	12
325.2.a.j.1.1		3	65.28	even	12
325.2.a.k.1.3		3	65.2	even	12
585.2.c.b.469.1		6	195.119	even	12
585.2.c.b.469.6		6	39.2	even	12
845.2.b.c.339.1		6	65.24	odd	12
845.2.b.c.339.6		6	13.11	odd	12
845.2.d.a.844.1		6	13.10	even	6
845.2.d.a.844.2		6	65.29	even	6
845.2.d.b.844.5		6	13.3	even	3
845.2.d.b.844.6		6	65.49	even	6
845.2.l.d.654.1		12	65.4	even	6	inner
845.2.l.d.654.2		12	13.9	even	3	inner
845.2.l.d.699.1		12	1.1	even	1	trivial
845.2.l.d.699.2		12	65.64	even	2	inner
845.2.l.e.654.5		12	65.9	even	6
845.2.l.e.654.6		12	13.4	even	6
845.2.l.e.699.5		12	13.12	even	2
845.2.l.e.699.6		12	5.4	even	2
845.2.n.f.484.1		12	13.5	odd	4
845.2.n.f.484.6		12	65.44	odd	4
845.2.n.f.529.1		12	65.19	odd	12
845.2.n.f.529.6		12	13.6	odd	12
845.2.n.g.484.1		12	65.34	odd	4
845.2.n.g.484.6		12	13.8	odd	4
845.2.n.g.529.1		12	13.7	odd	12
845.2.n.g.529.6		12	65.59	odd	12
1040.2.d.c.209.3		6	260.119	even	12
1040.2.d.c.209.4		6	52.15	even	12
2925.2.a.bf.1.1		3	195.2	odd	12
2925.2.a.bj.1.3		3	195.158	odd	12
4225.2.a.ba.1.1		3	65.37	even	12
4225.2.a.bh.1.3		3	65.63	even	12
5200.2.a.cb.1.3		3	260.67	odd	12
5200.2.a.cj.1.1		3	260.223	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.33757 - 2.31673i) q^{2} +(-0.416726 + 0.240597i) q^{3} +(-2.57816 + 4.46551i) q^{4} +(-1.48119 + 1.67513i) q^{5} +(1.11480 + 0.643629i) q^{6} +(0.403032 - 0.698071i) q^{7} +8.44358 q^{8} +(-1.38423 + 2.39755i) q^{9} +O(q^{10})\)	\(q+(-1.33757 - 2.31673i) q^{2} +(-0.416726 + 0.240597i) q^{3} +(-2.57816 + 4.46551i) q^{4} +(-1.48119 + 1.67513i) q^{5} +(1.11480 + 0.643629i) q^{6} +(0.403032 - 0.698071i) q^{7} +8.44358 q^{8} +(-1.38423 + 2.39755i) q^{9} +(5.86202 + 1.19093i) q^{10} +(3.18276 - 1.83757i) q^{11} -2.48119i q^{12} -2.15633 q^{14} +(0.214221 - 1.05444i) q^{15} +(-6.13752 - 10.6305i) q^{16} +(1.16936 + 0.675131i) q^{17} +7.40597 q^{18} +(-1.45071 - 0.837565i) q^{19} +(-3.66155 - 10.9330i) q^{20} +0.387873i q^{21} +(-8.51429 - 4.91573i) q^{22} +(-5.61288 + 3.24060i) q^{23} +(-3.51866 + 2.03150i) q^{24} +(-0.612127 - 4.96239i) q^{25} -2.77575i q^{27} +(2.07816 + 3.59948i) q^{28} +(1.20910 + 2.09421i) q^{29} +(-2.72939 + 0.914093i) q^{30} -5.28726i q^{31} +(-7.97508 + 13.8133i) q^{32} +(-0.884226 + 1.53152i) q^{33} -3.61213i q^{34} +(0.572393 + 1.70911i) q^{35} +(-7.13752 - 12.3625i) q^{36} +(1.88423 + 3.26358i) q^{37} +4.48119i q^{38} +(-12.5066 + 14.1441i) q^{40} +(-7.19897 + 4.15633i) q^{41} +(0.898598 - 0.518806i) q^{42} +(-5.88364 - 3.39692i) q^{43} +18.9502i q^{44} +(-1.96590 - 5.87000i) q^{45} +(15.0152 + 8.66902i) q^{46} -3.19394 q^{47} +(5.11533 + 2.95334i) q^{48} +(3.17513 + 5.49949i) q^{49} +(-10.6778 + 8.05565i) q^{50} -0.649738 q^{51} +5.73813i q^{53} +(-6.43066 + 3.71274i) q^{54} +(-1.63612 + 8.05333i) q^{55} +(3.40303 - 5.89422i) q^{56} +0.806063 q^{57} +(3.23449 - 5.60230i) q^{58} +(-5.18557 - 2.99389i) q^{59} +(4.15633 + 3.67513i) q^{60} +(0.884226 - 1.53152i) q^{61} +(-12.2492 + 7.07205i) q^{62} +(1.11577 + 1.93258i) q^{63} +18.1187 q^{64} +4.73084 q^{66} +(-4.94723 - 8.56885i) q^{67} +(-6.02961 + 3.48119i) q^{68} +(1.55936 - 2.70089i) q^{69} +(3.19394 - 3.61213i) q^{70} +(-7.41517 - 4.28115i) q^{71} +(-11.6878 + 20.2439i) q^{72} -11.7685 q^{73} +(5.04055 - 8.73049i) q^{74} +(1.44903 + 1.92068i) q^{75} +(7.48031 - 4.31876i) q^{76} -2.96239i q^{77} +2.26187 q^{79} +(26.8983 + 5.46468i) q^{80} +(-3.48484 - 6.03592i) q^{81} +(19.2582 + 11.1187i) q^{82} -3.84367 q^{83} +(-1.73205 - 1.00000i) q^{84} +(-2.86298 + 0.958833i) q^{85} +18.1744i q^{86} +(-1.00772 - 0.581810i) q^{87} +(26.8739 - 15.5156i) q^{88} +(2.40387 - 1.38787i) q^{89} +(-10.9697 + 12.4060i) q^{90} -33.4191i q^{92} +(1.27210 + 2.20334i) q^{93} +(4.27210 + 7.39949i) q^{94} +(3.55181 - 1.18953i) q^{95} -7.67513i q^{96} +(0.936996 - 1.62292i) q^{97} +(8.49389 - 14.7119i) q^{98} +10.1744i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 10 q^{4} + 4 q^{5} + 4 q^{7} + 36 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 10 * q^4 + 4 * q^5 + 4 * q^7 + 36 * q^8 + 6 * q^9	\( 12 q - 6 q^{2} - 10 q^{4} + 4 q^{5} + 4 q^{7} + 36 q^{8} + 6 q^{9} + 2 q^{10} + 16 q^{14} - 4 q^{15} - 10 q^{16} - 20 q^{18} + 14 q^{20} - 4 q^{25} + 4 q^{28} + 12 q^{29} + 8 q^{30} - 22 q^{32} + 12 q^{33} - 8 q^{35} - 22 q^{36} - 68 q^{40} + 38 q^{45} - 40 q^{47} + 18 q^{49} - 22 q^{50} - 48 q^{51} + 16 q^{55} + 40 q^{56} + 8 q^{57} - 24 q^{58} + 8 q^{60} - 12 q^{61} + 36 q^{63} + 132 q^{64} - 32 q^{66} - 20 q^{67} - 24 q^{69} + 40 q^{70} - 90 q^{72} - 96 q^{73} - 4 q^{74} + 16 q^{75} + 64 q^{79} + 58 q^{80} - 46 q^{81} - 88 q^{83} - 32 q^{85} - 140 q^{90} - 4 q^{93} + 32 q^{94} + 16 q^{95} + 28 q^{97} + 50 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 10 * q^4 + 4 * q^5 + 4 * q^7 + 36 * q^8 + 6 * q^9 + 2 * q^10 + 16 * q^14 - 4 * q^15 - 10 * q^16 - 20 * q^18 + 14 * q^20 - 4 * q^25 + 4 * q^28 + 12 * q^29 + 8 * q^30 - 22 * q^32 + 12 * q^33 - 8 * q^35 - 22 * q^36 - 68 * q^40 + 38 * q^45 - 40 * q^47 + 18 * q^49 - 22 * q^50 - 48 * q^51 + 16 * q^55 + 40 * q^56 + 8 * q^57 - 24 * q^58 + 8 * q^60 - 12 * q^61 + 36 * q^63 + 132 * q^64 - 32 * q^66 - 20 * q^67 - 24 * q^69 + 40 * q^70 - 90 * q^72 - 96 * q^73 - 4 * q^74 + 16 * q^75 + 64 * q^79 + 58 * q^80 - 46 * q^81 - 88 * q^83 - 32 * q^85 - 140 * q^90 - 4 * q^93 + 32 * q^94 + 16 * q^95 + 28 * q^97 + 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more