LMFDB - Embedded newform 845.2.l.e.699.6

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			699.6
Root			$-0.147520 + 0.550552i$ of defining polynomial
Character	$\chi$	$=$	845.699
Dual form			845.2.l.e.654.6

$q$-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} +(-1.89963 + 5.67213i) q^{10} +(3.18276 - 1.83757i) q^{11} +2.48119i q^{12} -2.15633 q^{14} +(1.02028 + 0.341700i) q^{15} +(-6.13752 - 10.6305i) q^{16} +(-1.16936 - 0.675131i) q^{17} -7.40597 q^{18} +(-1.45071 - 0.837565i) q^{19} +(-11.2991 + 2.29553i) 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} +(0.573070 + 2.82077i) q^{30} -5.28726i q^{31} +(7.97508 - 13.8133i) q^{32} +(0.884226 - 1.53152i) q^{33} -3.61213i q^{34} +(-1.76633 + 0.358849i) 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} +(-6.06652 + 1.23248i) q^{45} +(15.0152 + 8.66902i) q^{46} +3.19394 q^{47} +(-5.11533 - 2.95334i) q^{48} +(3.17513 + 5.49949i) q^{49} +(-12.3153 + 5.21939i) q^{50} -0.649738 q^{51} -5.73813i q^{53} +(-6.43066 + 3.71274i) q^{54} +(7.79244 + 2.60974i) 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} +(0.938847 + 2.21523i) q^{75} +(7.48031 - 4.31876i) q^{76} +2.96239i q^{77} +2.26187 q^{79} +(8.71661 - 26.0270i) q^{80} +(-3.48484 - 6.03592i) q^{81} +(-19.2582 - 11.1187i) q^{82} +3.84367 q^{83} +(-1.73205 - 1.00000i) q^{84} +(-0.601118 - 2.95883i) 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} +(-0.745746 - 3.67072i) 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	$0.228055\pi$
$2$	1.33757	+	2.31673i	0.945802	+	1.63818i	0.191663	+	0.981461i	$0.438612\pi$
$3$	0.416726	−	0.240597i	0.240597	−	0.138909i	−0.374854	−	0.927084i	$-0.622307\pi$
$3$	0.416726	−	0.240597i	0.240597	−	0.138909i	0.615451	+	0.788175i	$0.288974\pi$
$4$	−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	−0.932084	−	0.362242i	$-0.882012\pi$
$7$	−0.403032	+	0.698071i	−0.152332	+	0.263846i	0.779753	+	0.626088i	$0.215345\pi$
$8$	−8.44358			−2.98526
$9$	−1.38423	+	2.39755i	−0.461409	+	0.799183i
$10$	−1.89963	+	5.67213i	−0.600717	+	1.79368i
$11$	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
$15$	1.02028	+	0.341700i	0.263436	+	0.0882266i
$16$	−6.13752	−	10.6305i	−1.53438	−	2.65762i
$17$	−1.16936	−	0.675131i	−0.283612	−	0.163743i	0.351446	−	0.936208i	$-0.385690\pi$
$17$	−1.16936	−	0.675131i	−0.283612	−	0.163743i	−0.635057	+	0.772465i	$0.719024\pi$
$18$	−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	$0.728213\pi$
$20$	−11.2991	+	2.29553i	−2.52655	+	0.513295i
$21$			0.387873i			0.0846409i
$22$	8.51429	+	4.91573i	1.81525	+	1.04804i
$23$	5.61288	−	3.24060i	1.17037	−	0.675711i	0.216600	−	0.976260i	$-0.430503\pi$
$23$	5.61288	−	3.24060i	1.17037	−	0.675711i	0.953766	+	0.300549i	$0.0971700\pi$
$24$	−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	$0.761251\pi$
$30$	0.573070	+	2.82077i	0.104628	+	0.515000i
$31$		−	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
$35$	−1.76633	+	0.358849i	−0.298564	+	0.0606565i
$36$	−7.13752	−	12.3625i	−1.18959	−	2.06042i
$37$	−1.88423	−	3.26358i	−0.309765	−	0.536528i	0.668546	−	0.743671i	$-0.266917\pi$
$37$	−1.88423	−	3.26358i	−0.309765	−	0.536528i	−0.978311	+	0.207142i	$0.933584\pi$
$38$		−	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	0.876306	−	0.481755i	$-0.160000\pi$
$43$	5.88364	+	3.39692i	0.897247	+	0.518026i	0.0209410	+	0.999781i	$0.493334\pi$
$44$			18.9502i			2.85685i
$45$	−6.06652	+	1.23248i	−0.904343	+	0.183727i
$46$	15.0152	+	8.66902i	2.21387	+	1.27818i
$47$	3.19394			0.465884			0.232942	−	0.972491i	$-0.425165\pi$
$47$	3.19394			0.465884			0.232942	+	0.972491i	$0.425165\pi$
$48$	−5.11533	−	2.95334i	−0.738335	−	0.426278i
$49$	3.17513	+	5.49949i	0.453590	+	0.785641i
$50$	−12.3153	+	5.21939i	−1.74164	+	0.738133i
$51$	−0.649738			−0.0909816
$52$		0			0
$53$		−	5.73813i		−	0.788193i	−0.919069	−	0.394097i	$-0.871057\pi$
$53$		−	5.73813i		−	0.788193i	0.919069	−	0.394097i	$-0.128943\pi$
$54$	−6.43066	+	3.71274i	−0.875102	+	0.505240i
$55$	7.79244	+	2.60974i	1.05073	+	0.351898i
$56$	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	$0.0399206\pi$
$67$	4.94723	+	8.56885i	0.604400	+	1.04685i	−0.387746	+	0.921766i	$0.626746\pi$
$68$	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	$-0.258183\pi$
$73$	11.7685			1.37739			0.688697	+	0.725050i	$0.258183\pi$
$74$	5.04055	−	8.73049i	0.585952	−	1.01490i
$75$	0.938847	+	2.21523i	0.108409	+	0.255793i
$76$	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	$0.459388\pi$
$80$	8.71661	−	26.0270i	0.974547	−	2.90990i
$81$	−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	$-0.432345\pi$
$83$	3.84367			0.421898			0.210949	+	0.977497i	$0.432345\pi$
$84$	−1.73205	−	1.00000i	−0.188982	−	0.109109i
$85$	−0.601118	−	2.95883i	−0.0652004	−	0.320930i
$86$			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
$95$	−0.745746	−	3.67072i	−0.0765119	−	0.376608i
$96$		−	7.67513i		−	0.783340i
$97$	−0.936996	+	1.62292i	−0.0951375	+	0.164783i	−0.909666	−	0.415341i	$-0.863662\pi$
$97$	−0.936996	+	1.62292i	−0.0951375	+	0.164783i	0.814528	+	0.580124i	$0.196996\pi$
$98$	−8.49389	+	14.7119i	−0.858013	+	1.48612i
$99$			10.1744i			1.02257i
$100$	−20.5814	−	15.5273i	−2.05814	−	1.55273i
$101$	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	$0.273406\pi$
$103$			15.3684i			1.51429i	−0.653247	+	0.757145i	$0.726594\pi$
$104$		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	0.0444895	−	0.999010i	$-0.485834\pi$
$107$	9.63967	−	5.56547i	0.931902	−	0.538034i	0.887413	+	0.460976i	$0.152501\pi$
$108$	−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	$-0.151852\pi$
$110$	4.37683	+	21.5437i	0.417314	+	2.05411i
$111$	−1.57041	−	0.906679i	−0.149057	−	0.0860581i
$112$	9.89446			0.934939
$113$	0.497545	+	0.287258i	0.0468051	+	0.0270229i	0.523220	−	0.852198i	$-0.324731\pi$
$113$	0.497545	+	0.287258i	0.0468051	+	0.0270229i	−0.476415	+	0.879221i	$0.658064\pi$
$114$	−1.07816	−	1.86743i	−0.100979	−	0.174901i
$115$	13.7422	+	4.60235i	1.28147	+	0.429172i
$116$	−12.4690			−1.15772
$117$		0			0
$118$		−	16.0181i		−	1.47459i
$119$	0.942579	−	0.544198i	0.0864061	−	0.0498866i
$120$	−8.61486	−	2.88517i	−0.786425	−	0.263379i
$121$	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	−0.325827	−	0.945429i	$-0.605643\pi$
$127$	3.71919	−	2.14728i	0.330025	−	0.190540i	0.655852	+	0.754889i	$0.272309\pi$
$128$	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	$-0.613047\pi$
$137$	7.46898	−	12.9366i	0.638118	−	1.10525i	0.985845	−	0.167657i	$-0.0536200\pi$
$138$	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	$0.283167\pi$
$140$	2.95144	−	8.81273i	0.249442	−	0.744811i
$141$	1.33100	−	0.768452i	0.112090	−	0.0647153i
$142$		−	22.9053i		−	1.92217i
$143$		0			0
$144$	33.9829			2.83190
$145$	−1.71718	+	5.12733i	−0.142604	+	0.425802i
$146$	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	$0.820585\pi$
$150$	−3.87633	+	5.13808i	−0.316501	+	0.419522i
$151$		−	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	$0.0353299\pi$
$157$			2.77575i			0.221529i	−0.993847	+	0.110764i	$0.964670\pi$
$158$	3.02539	+	5.24013i	0.240687	+	0.416883i
$159$	−1.38058	−	2.39123i	−0.109487	−	0.189637i
$160$	34.9517	−	7.10080i	2.76317	−	0.561368i
$161$			5.22425i			0.411729i
$162$	9.32241	−	16.1469i	0.732437	−	1.26862i
$163$	1.11577	−	1.93258i	0.0873942	−	0.151371i	−0.819015	−	0.573772i	$-0.805479\pi$
$163$	1.11577	−	1.93258i	0.0873942	−	0.151371i	0.906409	+	0.422401i	$0.138813\pi$
$164$		−	42.8627i		−	3.34702i
$165$	3.87521	−	0.787291i	0.301685	−	0.0612905i
$166$	5.14117	+	8.90476i	0.399032	+	0.691144i
$167$	7.84661	+	13.5907i	0.607189	+	1.05168i	0.991701	+	0.128563i	$0.0410364\pi$
$167$	7.84661	+	13.5907i	0.607189	+	1.05168i	−0.384512	+	0.923120i	$0.625630\pi$
$168$		−	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	$0.0921153\pi$
$173$	22.1596	+	12.7938i	1.68476	+	0.972698i	0.726344	+	0.687331i	$0.241218\pi$
$174$			3.11283i			0.235983i
$175$	−3.21740	−	2.42731i	−0.243212	−	0.183487i
$176$	−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	$0.983040\pi$
$180$	10.1368	−	30.2676i	0.755555	−	2.25601i
$181$	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
$185$	2.67601	−	7.99031i	0.196744	−	0.587460i
$186$	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	$-0.879740\pi$
$193$	−10.8945	−	18.8698i	−0.784200	−	1.35827i	0.145275	−	0.989391i	$-0.453593\pi$
$194$	−5.01317			−0.359925
$195$		0			0
$196$	−32.7440			−2.33886
$197$	1.00000	+	1.73205i	0.0712470	+	0.123404i	0.899448	−	0.437028i	$-0.143969\pi$
$197$	1.00000	+	1.73205i	0.0712470	+	0.123404i	−0.828201	+	0.560431i	$0.810635\pi$
$198$	−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
$205$	−17.6255	−	5.90289i	−1.23102	−	0.412275i
$206$	−35.6044	+	20.5562i	−2.48067	+	1.43222i
$207$			17.9429i			1.24712i
$208$		0			0
$209$	−6.15633			−0.425842
$210$	−2.20007	−	0.736817i	−0.151819	−	0.0508452i
$211$	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
$215$	3.02453	+	14.8874i	0.206271	+	1.01531i
$216$		−	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	$-0.852730\pi$
$223$	−12.4538	−	21.5706i	−0.833969	−	1.44448i	0.0608976	−	0.998144i	$-0.480604\pi$
$224$	6.42842	+	11.1344i	0.429517	+	0.743946i
$225$	−11.0503	−	8.33667i	−0.736683	−	0.555778i
$226$			1.53690i			0.102233i
$227$	4.97755	−	8.62136i	0.330371	−	0.572220i	−0.652213	−	0.758036i	$-0.726159\pi$
$227$	4.97755	−	8.62136i	0.330371	−	0.572220i	0.982585	+	0.185815i	$0.0594927\pi$
$228$	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	$0.943433\pi$
$230$	7.71866	+	37.9929i	0.508953	+	2.50518i
$231$	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	$-0.885334\pi$
$233$		−	10.7612i		−	0.704987i	0.935814	−	0.352493i	$-0.114666\pi$
$234$		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	$0.874671\pi$
$240$	−2.62957	−	12.9433i	−0.169738	−	0.835488i
$241$	−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
$245$	−4.50938	+	13.4646i	−0.288093	+	0.860220i
$246$	−10.7005			−0.682240
$247$		0			0
$248$			44.6434i			2.83486i
$249$	1.60176	−	0.924777i	0.101507	−	0.0586054i
$250$	−26.9845	−	12.8988i	−1.70665	−	0.815791i
$251$	−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	−0.968083	−	0.250631i	$-0.919362\pi$
$257$	−19.7997	+	11.4314i	−1.23507	+	0.713069i	−0.266989	+	0.963700i	$0.586029\pi$
$258$	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	−0.953336	−	0.301910i	$-0.902376\pi$
$263$	−18.9506	+	10.9411i	−1.16854	+	0.674658i	−0.215206	+	0.976569i	$0.569042\pi$
$264$	−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	$-0.0773035\pi$
$270$	−15.7444	−	5.27290i	−0.958173	−	0.320899i
$271$	−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
$275$	7.17046	+	16.9189i	0.432395	+	1.02025i
$276$	8.04055	+	13.9266i	0.483984	+	0.838285i
$277$	−13.2937	−	7.67513i	−0.798742	−	0.461154i	0.0442891	−	0.999019i	$-0.485898\pi$
$277$	−13.2937	−	7.67513i	−0.798742	−	0.461154i	−0.843031	+	0.537865i	$0.819231\pi$
$278$	−22.5745			−1.35393
$279$	12.6765	+	7.31876i	0.758920	+	0.438163i
$280$	14.9141	−	3.02997i	0.891291	−	0.181075i
$281$		−	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	0.126803	−	0.991928i	$-0.459529\pi$
$283$	17.6509	−	10.1908i	1.04924	−	0.605778i	0.922436	+	0.386150i	$0.126195\pi$
$284$	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
$290$	−14.1755	+	2.87990i	−0.832413	+	0.169114i
$291$			0.901754i			0.0528618i
$292$	−30.3410	+	52.5521i	−1.77557	+	3.07538i
$293$	2.69029	−	4.65972i	0.157168	−	0.272224i	−0.776678	−	0.629898i	$-0.783097\pi$
$293$	2.69029	−	4.65972i	0.157168	−	0.272224i	0.933846	+	0.357674i	$0.116430\pi$
$294$			8.17442i			0.476742i
$295$	−2.66568	−	13.1210i	−0.155202	−	0.763937i
$296$	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
$305$	3.87521	−	0.787291i	0.221894	−	0.0450801i
$306$	8.66025	+	5.00000i	0.495074	+	0.285831i
$307$	−19.1695			−1.09406			−0.547031	−	0.837113i	$-0.684242\pi$
$307$	−19.1695			−1.09406			−0.547031	+	0.837113i	$0.684242\pi$
$308$	−13.2286	−	7.63752i	−0.753768	−	0.435188i
$309$	3.69758	+	6.40440i	0.210348	+	0.364334i
$310$	29.9900	+	10.0439i	1.70332	+	0.570453i
$311$	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	$-0.974677\pi$
$313$		−	2.81194i		−	0.158940i	0.996837	−	0.0794702i	$-0.0253229\pi$
$314$	−6.43066	+	3.71274i	−0.362903	+	0.209522i
$315$	1.58464	−	4.73159i	0.0892844	−	0.266595i
$316$	−5.83146	+	10.1004i	−0.328045	+	0.568191i
$317$	23.7685			1.33497			0.667485	−	0.744624i	$-0.267371\pi$
$317$	23.7685			1.33497			0.667485	+	0.744624i	$0.267371\pi$
$318$	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
$335$	−7.02614	+	20.9794i	−0.383879	+	1.14623i
$336$	4.12328	−	2.38058i	0.224944	−	0.129871i
$337$		−	16.1114i		−	0.877645i	−0.898574	−	0.438822i	$-0.855396\pi$
$337$		−	16.1114i		−	0.877645i	0.898574	−	0.438822i	$-0.144604\pi$
$338$		0			0
$339$	0.276454			0.0150149
$340$	14.7625	+	4.94405i	0.800608	+	0.268129i
$341$	−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
$345$	6.83405	−	1.38841i	0.367933	−	0.0747494i
$346$			68.4504i			3.67992i
$347$	−23.8108	−	13.7472i	−1.27823	−	0.737988i	−0.301709	−	0.953400i	$-0.597557\pi$
$347$	−23.8108	−	13.7472i	−1.27823	−	0.737988i	−0.976523	+	0.215413i	$0.930890\pi$
$348$	−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	0.576268	−	0.817261i	$-0.304509\pi$
$353$	−7.88423	−	13.6559i	−0.419635	−	0.726829i	−0.995903	+	0.0904319i	$0.971175\pi$
$354$	−3.85391	−	6.67517i	−0.204833	−	0.354781i
$355$	−3.81182	−	18.7626i	−0.202310	−	0.995815i
$356$			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	$-0.127938\pi$
$360$	51.2231	−	10.4065i	2.69970	−	0.548472i
$361$	−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	−0.965340	−	0.260997i	$-0.915949\pi$
$367$	−23.4098	+	13.5156i	−1.22198	+	0.705510i	−0.256640	+	0.966507i	$0.582616\pi$
$368$	−68.8983	−	39.7785i	−3.59157	−	2.07360i
$369$		−	23.0132i		−	1.19802i
$370$	22.0908	−	4.48797i	1.14844	−	0.233318i
$371$	4.00563	+	2.31265i	0.207962	+	0.120067i
$372$	13.1187			0.680174
$373$	11.2172	+	6.47627i	0.580806	+	0.335329i	0.761454	−	0.648219i	$-0.224486\pi$
$373$	11.2172	+	6.47627i	0.580806	+	0.335329i	−0.180648	+	0.983548i	$0.557819\pi$
$374$	−6.63752	−	11.4965i	−0.343218	−	0.594471i
$375$	−2.32019	+	4.85388i	−0.119814	+	0.250654i
$376$	−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	$0.0496489\pi$
$380$	18.3143	+	6.13358i	0.939503	+	0.314646i
$381$	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	$-0.652161\pi$
$383$	10.5471	−	18.2682i	0.538934	−	0.933460i	0.998962	−	0.0455560i	$-0.0145060\pi$
$384$	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	−0.966961	−	0.254922i	$-0.917950\pi$
$397$	−5.23449	+	9.06640i	−0.262711	+	0.455030i	0.704250	+	0.709952i	$0.251283\pi$
$398$	44.8119			2.24622
$399$	0.324869	−	0.562690i	0.0162638	−	0.0281697i
$400$	56.5096	−	23.9495i	2.82548	−	1.19748i
$401$	−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
$405$	4.94923	−	14.7779i	0.245929	−	0.734322i
$406$	−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	$0.782430\pi$
$410$	−9.89980	−	48.7289i	−0.488916	−	2.40655i
$411$		−	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	$0.693069\pi$
$420$	−0.890373	−	4.38261i	−0.0434457	−	0.213849i
$421$			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
$425$	4.06606	−	5.38956i	0.197233	−	0.261432i
$426$	−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	0.922899	−	0.385042i	$-0.125813\pi$
$433$	21.8677	+	12.6253i	1.05089	+	0.606733i	0.127994	+	0.991775i	$0.459146\pi$
$434$			11.4010i			0.547268i
$435$	0.518028	+	2.54984i	0.0248375	+	0.122256i
$436$	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	$-0.407985\pi$
$440$	−65.7961	−	22.0356i	−3.13671	−	1.05050i
$441$	−17.5804			−0.837162
$442$		0			0
$443$		−	36.9805i		−	1.75700i	−0.477746	−	0.878498i	$-0.658546\pi$
$443$		−	36.9805i		−	1.75700i	0.477746	−	0.878498i	$-0.341454\pi$
$444$	8.09756	−	4.67513i	0.384293	−	0.221872i
$445$	5.88546	+	1.97108i	0.278998	+	0.0934382i
$446$	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	$-0.967416\pi$
$457$	−12.5247	−	21.6934i	−0.585880	−	1.01477i	0.408885	−	0.912586i	$-0.365918\pi$
$458$	−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	$-0.138605\pi$
$463$	39.0191			1.81337			0.906685	+	0.421809i	$0.138605\pi$
$464$	14.8417	−	25.7066i	0.689008	−	1.19340i
$465$	1.80666	−	5.39451i	0.0837817	−	0.250164i
$466$	24.9307	−	14.3938i	1.15489	−	0.666778i
$467$		−	32.7694i		−	1.51639i	−0.652029	−	0.758194i	$-0.726082\pi$
$467$		−	32.7694i		−	1.51639i	0.652029	−	0.758194i	$-0.273918\pi$
$468$		0			0
$469$	−7.97556			−0.368277
$470$	−6.06731	+	18.1164i	−0.279864	+	0.835648i
$471$	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
$475$	5.04434	−	6.68627i	0.231450	−	0.306787i
$476$			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
$485$	−4.10648	+	0.834276i	−0.186466	+	0.0378825i
$486$		−	31.2482i		−	1.41745i
$487$	−4.62236	+	8.00616i	−0.209459	+	0.362794i	−0.951544	−	0.307512i	$-0.900504\pi$
$487$	−4.62236	+	8.00616i	−0.209459	+	0.362794i	0.742085	+	0.670306i	$0.233837\pi$
$488$	−7.46604	+	12.9316i	−0.337972	+	0.585384i
$489$		−	1.07381i		−	0.0485593i
$490$	−37.2254	+	7.56273i	−1.68167	+	0.341649i
$491$	−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	$0.787115\pi$
$500$	−4.47483	−	57.4755i	−0.200120	−	2.57038i
$501$	6.53978	+	3.77575i	0.292176	+	0.168688i
$502$	−51.8613			−2.31468
$503$	2.03965	+	1.17759i	0.0909436	+	0.0525063i	0.544782	−	0.838578i	$-0.316612\pi$
$503$	2.03965	+	1.17759i	0.0909436	+	0.0525063i	−0.453839	+	0.891084i	$0.649946\pi$
$504$	9.42113	+	16.3179i	0.419650	+	0.726856i
$505$	−7.45564	+	22.2618i	−0.331772	+	0.990639i
$506$	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	$0.491523\pi$
$510$	1.23426	−	3.68540i	0.0546542	−	0.163192i
$511$	−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	−0.876896	−	0.480679i	$-0.840390\pi$
$523$	−20.5609	+	11.8708i	−0.899064	+	0.519075i	−0.0221676	+	0.999754i	$0.507057\pi$
$524$	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
$530$	32.5474	+	10.9004i	1.41377	+	0.473481i
$531$	14.3560	−	8.28844i	0.622997	−	0.359688i
$532$			6.96239i			0.301858i
$533$		0			0
$534$	3.57310			0.154623
$535$	23.6011	+	7.90417i	1.02036	+	0.341727i
$536$	−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
$540$	−6.37180	−	31.3634i	−0.274199	−	1.34966i
$541$		−	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	$0.0576839\pi$
$547$			8.43041i			0.360458i	−0.983625	+	0.180229i	$0.942316\pi$
$548$	38.5125	+	66.7055i	1.64517	+	2.84952i
$549$	2.44794	+	4.23995i	0.104475	+	0.180957i
$550$	−29.6056	+	39.2422i	−1.26239	+	1.67329i
$551$		−	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
$555$	−0.807282	−	3.97362i	−0.0342672	−	0.168671i
$556$	−21.7562	−	37.6829i	−0.922670	−	1.59811i
$557$	−6.84661	−	11.8587i	−0.290100	−	0.502469i	0.683733	−	0.729732i	$-0.260355\pi$
$557$	−6.84661	−	11.8587i	−0.290100	−	0.502469i	−0.973833	+	0.227264i	$0.927022\pi$
$558$			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	0.653044	−	0.757320i	$-0.273491\pi$
$563$	7.68084	+	4.43453i	0.323709	+	0.186893i	−0.329336	+	0.944213i	$0.606825\pi$
$564$			7.92478i			0.333693i
$565$	0.255767	+	1.25894i	0.0107602	+	0.0529639i
$566$	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	$0.592200\pi$
$570$	1.53123	−	4.57209i	0.0641360	−	0.191504i
$571$	−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
$575$	12.6453	+	29.8369i	0.527346	+	1.24429i
$576$	−25.0804	+	43.4405i	−1.04502	+	1.81002i
$577$	−28.8568			−1.20133			−0.600663	−	0.799502i	$-0.705097\pi$
$577$	−28.8568			−1.20133			−0.600663	+	0.799502i	$0.705097\pi$
$578$	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	$0.162952\pi$
$587$	20.8393	+	36.0948i	0.860131	+	1.48979i	−0.0116712	+	0.999932i	$0.503715\pi$
$588$	−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	$-0.652856\pi$
$593$	−22.4993			−0.923935			−0.461968	+	0.886897i	$0.652856\pi$
$594$	−13.6448	+	23.6335i	−0.559853	+	0.969695i
$595$	2.30775	+	0.772880i	0.0946084	+	0.0316850i
$596$	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	$0.527022\pi$
$600$	−7.92723	−	18.7045i	−0.323628	−	0.763609i
$601$	−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
$605$	5.49269	−	1.11590i	0.223310	−	0.0453677i
$606$			13.5153i			0.549021i
$607$	−7.09698	−	4.09745i	−0.288058	−	0.166310i	0.349008	−	0.937120i	$-0.386519\pi$
$607$	−7.09698	−	4.09745i	−0.288058	−	0.166310i	−0.637066	+	0.770810i	$0.719852\pi$
$608$	−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	$-0.933287\pi$
$613$	−16.5696	−	28.6994i	−0.669239	−	1.15916i	0.308878	−	0.951102i	$-0.400047\pi$
$614$	−25.6405	−	44.4106i	−1.03476	−	1.79227i
$615$	−8.76521	+	1.78075i	−0.353447	+	0.0718066i
$616$		−	25.0132i		−	1.00781i
$617$	−14.5066	+	25.1261i	−0.584013	+	1.01154i	0.410984	+	0.911642i	$0.365185\pi$
$617$	−14.5066	+	25.1261i	−0.584013	+	1.01154i	−0.994998	+	0.0998982i	$0.968148\pi$
$618$	−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	$0.921064\pi$
$620$	12.1370	+	59.7411i	0.487435	+	2.39926i
$621$	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
$630$	13.0814	−	2.65762i	0.521175	−	0.105882i
$631$	−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
$635$	9.10581	+	3.04960i	0.361353	+	0.121020i
$636$	14.2374			0.564551
$637$		0			0
$638$			23.7743i			0.941235i
$639$	20.5285	−	11.8522i	0.812096	−	0.468864i
$640$	−11.7662	+	35.1328i	−0.465100	+	1.38875i
$641$	−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	−0.957833	−	0.287325i	$-0.907234\pi$
$643$	−5.83440	+	10.1055i	−0.230086	+	0.398521i	0.727747	+	0.685846i	$0.240567\pi$
$644$	−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	−0.689550	−	0.724238i	$-0.742191\pi$
$647$	−10.3555	+	5.97873i	−0.407115	+	0.235048i	0.282434	+	0.959287i	$0.408858\pi$
$648$	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	−0.301912	−	0.953336i	$-0.597625\pi$
$653$	9.52505	−	5.49929i	0.372744	−	0.215204i	0.674657	+	0.738132i	$0.264292\pi$
$654$	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	$0.183041\pi$
$660$	−6.47528	+	19.3346i	−0.252050	+	0.752597i
$661$	−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
$665$	2.86298	+	0.958833i	0.111022	+	0.0371819i
$666$	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
$670$	−58.0015	+	11.7836i	−2.24080	+	0.455241i
$671$		−	6.49929i		−	0.250902i
$672$	5.35779	+	3.09332i	0.206681	+	0.119327i
$673$	5.81135	−	3.35519i	0.224011	−	0.129333i	−0.383795	−	0.923418i	$-0.625383\pi$
$673$	5.81135	−	3.35519i	0.224011	−	0.129333i	0.607806	+	0.794085i	$0.292050\pi$
$674$	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	$-0.990359\pi$
$677$		−	1.57593i		−	0.0605679i	0.999541	−	0.0302840i	$-0.00964116\pi$
$678$	0.369775	+	0.640469i	0.0142011	+	0.0245971i
$679$	−0.755278	−	1.30818i	−0.0289849	−	0.0502033i
$680$	5.07559	+	24.9831i	0.194640	+	0.958060i
$681$		−	4.79033i		−	0.183566i
$682$	25.9907	−	45.0172i	0.995236	−	1.72380i
$683$	7.59697	−	13.1583i	0.290690	−	0.503490i	−0.683283	−	0.730154i	$-0.739449\pi$
$683$	7.59697	−	13.1583i	0.290690	−	0.503490i	0.973973	+	0.226664i	$0.0727819\pi$
$684$			23.9126i			0.914320i
$685$	32.7336	−	6.65017i	1.25069	−	0.254090i
$686$	−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
$695$	−18.4917	+	3.75678i	−0.701429	+	0.142503i
$696$	−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
$700$	19.1341	−	8.10931i	0.723202	−	0.306503i
$701$	−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
$705$	3.25872	+	1.09137i	0.122731	+	0.0411033i
$706$	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
$725$	−11.1324	+	4.71808i	−0.413448	+	0.175225i
$726$	2.79434	−	1.61331i	0.103708	−	0.0598756i
$727$			34.8545i			1.29268i	0.763049	+	0.646341i	$0.223701\pi$
$727$			34.8545i			1.29268i	−0.763049	+	0.646341i	$0.776299\pi$
$728$		0			0
$729$	15.2882			0.566230
$730$	−22.3557	+	66.7521i	−0.827423	+	2.47061i
$731$	−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	$-0.463165\pi$
$733$	6.25202			0.230923			0.115462	+	0.993312i	$0.463165\pi$
$734$	−62.6242	−	36.1561i	−2.31150	−	1.33455i
$735$	1.36036	+	6.69599i	0.0501777	+	0.246985i
$736$		−	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	$0.0226394\pi$
$743$	15.2721	+	26.4521i	0.560279	+	0.970432i	−0.437193	+	0.899368i	$0.644027\pi$
$744$	10.7411	+	18.6041i	0.393787	+	0.682059i
$745$	−5.05298	−	24.8719i	−0.185127	−	0.911235i
$746$			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
$750$	−14.3486	+	1.11712i	−0.523935	+	0.0407916i
$751$	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	0.174584	−	0.984642i	$-0.444142\pi$
$757$	30.6667	−	17.7054i	1.11460	−	0.643515i	0.940017	+	0.341127i	$0.110809\pi$
$758$	70.1642	+	40.5093i	2.54848	+	1.47136i
$759$		−	11.4617i		−	0.416033i
$760$	6.29676	+	30.9940i	0.228408	+	1.12427i
$761$	−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
$765$	7.92603	+	2.65448i	0.286566	+	0.0959730i
$766$	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	$0.988956\pi$
$770$	−16.8030	−	5.62745i	−0.605540	−	0.202799i
$771$	−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	$0.478483\pi$
$773$	−23.0840	+	39.9827i	−0.830275	+	1.43808i	−0.897820	+	0.440363i	$0.854850\pi$
$774$	−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	−0.590542	−	0.807007i	$-0.701086\pi$
$787$	11.3229	−	19.6118i	0.403617	−	0.699086i	0.994159	+	0.107921i	$0.0344194\pi$
$788$	−10.3127			−0.367373
$789$	−5.26480	+	9.11891i	−0.187432	+	0.324642i
$790$	−4.29672	+	12.8296i	−0.152870	+	0.456456i
$791$	−0.401053	+	0.231548i	−0.0142598	+	0.00823290i
$792$		−	85.9086i		−	3.05263i
$793$		0			0
$794$	−28.0059			−0.993891
$795$	1.96072	−	5.85453i	0.0695397	−	0.207639i
$796$	43.1876	+	74.8031i	1.53074	+	2.65133i
$797$	7.13382	+	4.11871i	0.252693	+	0.145892i	0.620997	−	0.783813i	$-0.286728\pi$
$797$	7.13382	+	4.11871i	0.252693	+	0.145892i	−0.368304	+	0.929706i	$0.620061\pi$
$798$	1.73813			0.0615293
$799$	−3.73486	−	2.15633i	−0.132130	−	0.0762853i
$800$	63.6650	+	48.0309i	2.25090	+	1.69815i
$801$			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	$0.550681\pi$
$810$	40.8564	−	8.30042i	1.43555	−	0.291647i
$811$			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
$815$	4.89000	−	0.993455i	0.171289	−	0.0347992i
$816$	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	0.420551	−	0.907269i	$-0.361837\pi$
$823$	−4.44352	−	2.56547i	−0.154891	−	0.0894265i	−0.575442	+	0.817842i	$0.695170\pi$
$824$		−	129.764i		−	4.52054i
$825$	7.05876	+	5.32536i	0.245755	+	0.185405i
$826$	11.1818	+	6.45580i	0.389064	+	0.224626i
$827$	18.6946			0.650076			0.325038	−	0.945701i	$-0.394623\pi$
$827$	18.6946			0.650076			0.325038	+	0.945701i	$0.394623\pi$
$828$	−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	$0.814300\pi$
$830$	−7.30157	+	21.8018i	−0.253441	+	0.756752i
$831$	−7.38646			−0.256233
$832$		0			0
$833$		−	8.57452i		−	0.297089i
$834$	−9.40740	+	5.43136i	−0.325752	+	0.188073i
$835$	−11.1439	+	33.2746i	−0.385651	+	1.15152i
$836$	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	$-0.465501\pi$
$853$	6.31853			0.216342			0.108171	+	0.994132i	$0.465501\pi$
$854$	−1.90668	+	3.30246i	−0.0652452	+	0.113008i
$855$	9.83301	+	3.29314i	0.336282	+	0.112623i
$856$	−81.3934	+	46.9925i	−2.78197	+	1.60617i
$857$			0.775746i			0.0264990i	0.999912	+	0.0132495i	$0.00421757\pi$
$857$			0.775746i			0.0264990i	−0.999912	+	0.0132495i	$0.995782\pi$
$858$		0			0
$859$	−3.24869			−0.110844			−0.0554220	−	0.998463i	$-0.517650\pi$
$859$	−3.24869			−0.110844			−0.0554220	+	0.998463i	$0.517650\pi$
$860$	−74.2774	−	24.8760i	−2.53284	−	0.848265i
$861$	−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	$-0.610108\pi$
$863$	−19.9208			−0.678112			−0.339056	+	0.940766i	$0.610108\pi$
$864$	38.3421	+	22.1368i	1.30442	+	0.753110i
$865$	11.3913	+	56.0704i	0.387316	+	1.90645i
$866$			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
$875$	−0.699528	−	8.98487i	−0.0236484	−	0.303744i
$876$			29.1998i			0.986570i
$877$	11.0689	−	19.1719i	0.373770	−	0.647388i	−0.616372	−	0.787455i	$-0.711398\pi$
$877$	11.0689	−	19.1719i	0.373770	−	0.647388i	0.990142	+	0.140067i	$0.0447317\pi$
$878$	38.5379	−	66.7495i	1.30059	−	2.25269i
$879$		−	2.58910i		−	0.0873283i
$880$	−20.0834	−	98.8549i	−0.677012	−	3.33240i
$881$	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	$-0.976925\pi$
$883$		−	4.30440i		−	0.144855i	0.997374	−	0.0724273i	$-0.0230745\pi$
$884$		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	−0.250128	−	0.968213i	$-0.580473\pi$
$887$	13.7984	−	7.96651i	0.463305	−	0.267489i	0.713433	+	0.700723i	$0.247139\pi$
$888$	13.2599	+	7.65562i	0.444974	+	0.256906i
$889$			3.46168i			0.116101i
$890$	3.30573	+	16.2715i	0.110808	+	0.545421i
$891$	−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
$895$	8.61078	−	25.7110i	0.287827	−	0.859423i
$896$	−13.3561			−0.446197
$897$		0			0
$898$			33.9365i			1.13248i
$899$	11.0727	−	6.39280i	0.369294	−	0.213212i
$900$	65.7168	−	27.8517i	2.19056	−	0.928390i
$901$	−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	0.492713	−	0.870192i	$-0.336005\pi$
$907$	44.9542	−	25.9543i	1.49268	−	0.861798i	0.999965	+	0.00839339i	$0.00267173\pi$
$908$	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	$0.0949147\pi$
$920$	−116.033	−	38.8603i	−3.82550	−	1.28119i
$921$	−7.98844	+	4.61213i	−0.263228	+	0.151975i
$922$			98.6780i			3.24979i
$923$		0			0
$924$	−7.35026			−0.241806
$925$	17.3485	−	7.35254i	0.570416	−	0.241750i
$926$	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	$0.716211\pi$
$930$	14.9141	−	3.02997i	0.489054	−	0.0993565i
$931$		−	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	$0.0843877\pi$
$937$			16.0409i			0.524035i	−0.965063	+	0.262017i	$0.915612\pi$
$938$	−10.6678	−	18.4772i	−0.348317	−	0.603303i
$939$	−0.676545	−	1.17181i	−0.0220782	−	0.0382406i
$940$	−36.0885	+	7.33176i	−1.17708	+	0.239136i
$941$		−	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
$945$	−0.996072	−	4.90288i	−0.0324022	−	0.159491i
$946$	33.3967	+	57.8448i	1.08582	+	1.88070i
$947$	2.31559	+	4.01072i	0.0752466	+	0.130331i	0.901193	−	0.433417i	$-0.142692\pi$
$947$	2.31559	+	4.01072i	0.0752466	+	0.130331i	−0.825947	+	0.563748i	$0.809359\pi$
$948$			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	0.0835021	−	0.996508i	$-0.473389\pi$
$953$	−22.7748	−	13.1490i	−0.737748	−	0.425939i	−0.821250	+	0.570569i	$0.806723\pi$
$954$			42.4965i			1.37587i
$955$	−45.1963	+	9.18210i	−1.46252	+	0.297126i
$956$	−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
$960$	18.4862	+	6.19117i	0.596641	+	0.199819i
$961$	3.04491			0.0982228
$962$		0			0
$963$			30.8155i			0.993014i
$964$	127.827	−	73.8007i	4.11702	−	2.37696i
$965$	15.4725	−	46.1994i	0.498077	−	1.48721i
$966$	−3.36248	+	5.82399i	−0.108186	+	0.187384i
$967$	11.9405			0.383981			0.191990	−	0.981397i	$-0.438506\pi$
$967$	11.9405			0.383981			0.191990	+	0.981397i	$0.438506\pi$
$968$	−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	0.996944	−	0.0781216i	$-0.0248922\pi$
$977$	13.4660	+	23.3239i	0.430817	+	0.746196i	−0.566127	+	0.824318i	$0.691559\pi$
$978$	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	$-0.393503\pi$
$983$	20.5902			0.656727			0.328363	+	0.944551i	$0.393503\pi$
$984$	16.8872	−	29.2494i	0.538343	−	0.932438i
$985$	−1.42022	+	4.24063i	−0.0452519	+	0.135118i
$986$	7.56457	−	4.36741i	0.240905	−	0.139087i
$987$			1.23884i			0.0394328i
$988$		0			0
$989$	44.0322			1.40014
$990$	−57.7106	−	19.3277i	−1.83416	−	0.614274i
$991$	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
$995$	36.7072	−	7.45746i	1.16370	−	0.236417i
$996$			9.53690i			0.302188i
$997$	−28.9473	−	16.7127i	−0.916771	−	0.529298i	−0.0341674	−	0.999416i	$-0.510878\pi$
$997$	−28.9473	−	16.7127i	−0.916771	−	0.529298i	−0.882603	+	0.470118i	$0.844211\pi$
$998$	−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.e.699.6		12
5.4	even	2		845.2.l.d.699.1		12
13.2	odd	12		65.2.b.a.14.6	yes	6
13.3	even	3		845.2.d.a.844.2		6
13.4	even	6		845.2.l.d.654.1		12
13.5	odd	4		845.2.n.f.484.6		12
13.6	odd	12		845.2.n.f.529.1		12
13.7	odd	12		845.2.n.g.529.6		12
13.8	odd	4		845.2.n.g.484.1		12
13.9	even	3	inner	845.2.l.e.654.5		12
13.10	even	6		845.2.d.b.844.6		6
13.11	odd	12		845.2.b.c.339.1		6
13.12	even	2		845.2.l.d.699.2		12
39.2	even	12		585.2.c.b.469.1		6
52.15	even	12		1040.2.d.c.209.3		6
65.2	even	12		325.2.a.j.1.1		3
65.4	even	6	inner	845.2.l.e.654.6		12
65.9	even	6		845.2.l.d.654.2		12
65.19	odd	12		845.2.n.f.529.6		12
65.24	odd	12		845.2.b.c.339.6		6
65.28	even	12		325.2.a.k.1.3		3
65.29	even	6		845.2.d.b.844.5		6
65.34	odd	4		845.2.n.g.484.6		12
65.37	even	12		4225.2.a.bh.1.3		3
65.44	odd	4		845.2.n.f.484.1		12
65.49	even	6		845.2.d.a.844.1		6
65.54	odd	12		65.2.b.a.14.1	✓	6
65.59	odd	12		845.2.n.g.529.1		12
65.63	even	12		4225.2.a.ba.1.1		3
65.64	even	2	inner	845.2.l.e.699.5		12
195.2	odd	12		2925.2.a.bj.1.3		3
195.119	even	12		585.2.c.b.469.6		6
195.158	odd	12		2925.2.a.bf.1.1		3
260.67	odd	12		5200.2.a.cj.1.1		3
260.119	even	12		1040.2.d.c.209.4		6
260.223	odd	12		5200.2.a.cb.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.1	✓	6	65.54	odd	12
65.2.b.a.14.6	yes	6	13.2	odd	12
325.2.a.j.1.1		3	65.2	even	12
325.2.a.k.1.3		3	65.28	even	12
585.2.c.b.469.1		6	39.2	even	12
585.2.c.b.469.6		6	195.119	even	12
845.2.b.c.339.1		6	13.11	odd	12
845.2.b.c.339.6		6	65.24	odd	12
845.2.d.a.844.1		6	65.49	even	6
845.2.d.a.844.2		6	13.3	even	3
845.2.d.b.844.5		6	65.29	even	6
845.2.d.b.844.6		6	13.10	even	6
845.2.l.d.654.1		12	13.4	even	6
845.2.l.d.654.2		12	65.9	even	6
845.2.l.d.699.1		12	5.4	even	2
845.2.l.d.699.2		12	13.12	even	2
845.2.l.e.654.5		12	13.9	even	3	inner
845.2.l.e.654.6		12	65.4	even	6	inner
845.2.l.e.699.5		12	65.64	even	2	inner
845.2.l.e.699.6		12	1.1	even	1	trivial
845.2.n.f.484.1		12	65.44	odd	4
845.2.n.f.484.6		12	13.5	odd	4
845.2.n.f.529.1		12	13.6	odd	12
845.2.n.f.529.6		12	65.19	odd	12
845.2.n.g.484.1		12	13.8	odd	4
845.2.n.g.484.6		12	65.34	odd	4
845.2.n.g.529.1		12	65.59	odd	12
845.2.n.g.529.6		12	13.7	odd	12
1040.2.d.c.209.3		6	52.15	even	12
1040.2.d.c.209.4		6	260.119	even	12
2925.2.a.bf.1.1		3	195.158	odd	12
2925.2.a.bj.1.3		3	195.2	odd	12
4225.2.a.ba.1.1		3	65.63	even	12
4225.2.a.bh.1.3		3	65.37	even	12
5200.2.a.cb.1.3		3	260.223	odd	12
5200.2.a.cj.1.1		3	260.67	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} +(-1.89963 + 5.67213i) q^{10} +(3.18276 - 1.83757i) q^{11} +2.48119i q^{12} -2.15633 q^{14} +(1.02028 + 0.341700i) q^{15} +(-6.13752 - 10.6305i) q^{16} +(-1.16936 - 0.675131i) q^{17} -7.40597 q^{18} +(-1.45071 - 0.837565i) q^{19} +(-11.2991 + 2.29553i) 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} +(0.573070 + 2.82077i) q^{30} -5.28726i q^{31} +(7.97508 - 13.8133i) q^{32} +(0.884226 - 1.53152i) q^{33} -3.61213i q^{34} +(-1.76633 + 0.358849i) 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} +(-6.06652 + 1.23248i) q^{45} +(15.0152 + 8.66902i) q^{46} +3.19394 q^{47} +(-5.11533 - 2.95334i) q^{48} +(3.17513 + 5.49949i) q^{49} +(-12.3153 + 5.21939i) q^{50} -0.649738 q^{51} -5.73813i q^{53} +(-6.43066 + 3.71274i) q^{54} +(7.79244 + 2.60974i) 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} +(0.938847 + 2.21523i) q^{75} +(7.48031 - 4.31876i) q^{76} +2.96239i q^{77} +2.26187 q^{79} +(8.71661 - 26.0270i) q^{80} +(-3.48484 - 6.03592i) q^{81} +(-19.2582 - 11.1187i) q^{82} +3.84367 q^{83} +(-1.73205 - 1.00000i) q^{84} +(-0.601118 - 2.95883i) 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} +(-0.745746 - 3.67072i) 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

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