LMFDB - Embedded newform 845.2.l.d.654.2

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			654.2
Root			$0.550552 - 0.147520i$ of defining polynomial
Character	$\chi$	$=$	845.654
Dual form			845.2.l.d.699.2

$q$-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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

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

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	−0.191663	+	0.981461i	$0.561388\pi$
$2$	−1.33757	+	2.31673i	−0.945802	+	1.63818i	−0.754138	+	0.656716i	$0.771945\pi$
$3$	0.416726	+	0.240597i	0.240597	+	0.138909i	0.615451	−	0.788175i	$-0.288974\pi$
$3$	0.416726	+	0.240597i	0.240597	+	0.138909i	−0.374854	+	0.927084i	$0.622307\pi$
$4$	−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	$-0.117988\pi$
$7$	0.403032	+	0.698071i	0.152332	+	0.263846i	−0.779753	+	0.626088i	$0.784655\pi$
$8$	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	$-0.520250\pi$
$11$	−3.18276	−	1.83757i	−0.959637	−	0.554047i	−0.896061	+	0.443930i	$0.853584\pi$
$12$		−	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	−0.635057	−	0.772465i	$-0.719024\pi$
$17$	−1.16936	+	0.675131i	−0.283612	+	0.163743i	0.351446	+	0.936208i	$0.385690\pi$
$18$	7.40597			1.74560
$19$	1.45071	−	0.837565i	0.332815	−	0.192151i	−0.324275	−	0.945963i	$-0.605120\pi$
$19$	1.45071	−	0.837565i	0.332815	−	0.192151i	0.657090	+	0.753812i	$0.271787\pi$
$20$	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	0.953766	−	0.300549i	$-0.0971700\pi$
$23$	5.61288	+	3.24060i	1.17037	+	0.675711i	0.216600	+	0.976260i	$0.430503\pi$
$24$	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	−0.731653	−	0.681677i	$-0.761251\pi$
$29$	1.20910	−	2.09421i	0.224523	−	0.388886i	0.956176	+	0.292791i	$0.0945842\pi$
$30$	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	$-0.733083\pi$
$37$	1.88423	−	3.26358i	0.309765	−	0.536528i	0.978311	+	0.207142i	$0.0664163\pi$
$38$			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	$-0.108475\pi$
$41$	7.19897	+	4.15633i	1.12429	+	0.649109i	0.181797	+	0.983336i	$0.441809\pi$
$42$	−0.898598	−	0.518806i	−0.138657	−	0.0800535i
$43$	5.88364	−	3.39692i	0.897247	−	0.518026i	0.0209410	−	0.999781i	$-0.493334\pi$
$43$	5.88364	−	3.39692i	0.897247	−	0.518026i	0.876306	+	0.481755i	$0.160000\pi$
$44$			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	$-0.574835\pi$
$47$	−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
$50$	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	$0.128943\pi$
$53$			5.73813i			0.788193i	−0.919069	+	0.394097i	$0.871057\pi$
$54$	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	$-0.539221\pi$
$59$	5.18557	−	2.99389i	0.675104	−	0.389771i	0.798008	+	0.602647i	$0.205887\pi$
$60$	4.15633	+	3.67513i	0.536579	+	0.474457i
$61$	0.884226	+	1.53152i	0.113214	+	0.196092i	0.917064	−	0.398740i	$-0.130552\pi$
$61$	0.884226	+	1.53152i	0.113214	+	0.196092i	−0.803851	+	0.594831i	$0.797219\pi$
$62$	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	0.387746	+	0.921766i	$0.373254\pi$
$67$	−4.94723	+	8.56885i	−0.604400	+	1.04685i	−0.992146	+	0.125086i	$0.960079\pi$
$68$	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	$-0.497023\pi$
$71$	7.41517	−	4.28115i	0.880018	−	0.508079i	0.870664	+	0.491877i	$0.163689\pi$
$72$	−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
$75$	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	$-0.567655\pi$
$83$	−3.84367			−0.421898			−0.210949	+	0.977497i	$0.567655\pi$
$84$	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	$-0.380332\pi$
$89$	−2.40387	−	1.38787i	−0.254809	−	0.147114i	−0.621964	+	0.783045i	$0.713665\pi$
$90$	−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	$-0.136338\pi$
$97$	0.936996	+	1.62292i	0.0951375	+	0.164783i	−0.814528	+	0.580124i	$0.803004\pi$
$98$	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	−0.477302	−	0.878739i	$-0.658385\pi$
$101$	5.24965	−	9.09265i	0.522359	−	0.904753i	0.999662	−	0.0260137i	$-0.00828136\pi$
$102$	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	$-0.152501\pi$
$107$	9.63967	+	5.56547i	0.931902	+	0.538034i	0.0444895	+	0.999010i	$0.485834\pi$
$108$	−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	−0.476415	−	0.879221i	$-0.658064\pi$
$113$	0.497545	−	0.287258i	0.0468051	−	0.0270229i	0.523220	+	0.852198i	$0.324731\pi$
$114$	−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	0.655852	−	0.754889i	$-0.272309\pi$
$127$	3.71919	+	2.14728i	0.330025	+	0.190540i	−0.325827	+	0.945429i	$0.605643\pi$
$128$	−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	−0.985845	−	0.167657i	$-0.946380\pi$
$137$	−7.46898	−	12.9366i	−0.638118	−	1.10525i	0.347728	−	0.937596i	$-0.386953\pi$
$138$	−8.34297			−0.710201
$139$	−4.21933	−	7.30809i	−0.357879	−	0.619864i	0.629727	−	0.776816i	$-0.283167\pi$
$139$	−4.21933	−	7.30809i	−0.357879	−	0.619864i	−0.987606	+	0.156952i	$0.949833\pi$
$140$	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	$-0.512748\pi$
$149$	9.82962	−	5.67513i	0.805273	−	0.464925i	0.845312	+	0.534273i	$0.179415\pi$
$150$	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	$-0.964670\pi$
$157$		−	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
$160$	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	$-0.194521\pi$
$163$	−1.11577	−	1.93258i	−0.0873942	−	0.151371i	−0.906409	+	0.422401i	$0.861187\pi$
$164$		−	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	0.384512	+	0.923120i	$0.374370\pi$
$167$	−7.84661	+	13.5907i	−0.607189	+	1.05168i	−0.991701	+	0.128563i	$0.958964\pi$
$168$			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	0.726344	−	0.687331i	$-0.241218\pi$
$173$	22.1596	−	12.7938i	1.68476	−	0.972698i	0.958418	−	0.285367i	$-0.0921153\pi$
$174$			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	−0.998581	−	0.0532551i	$-0.983040\pi$
$179$	−6.06300	+	10.5014i	−0.453170	+	0.784914i	0.545411	+	0.838169i	$0.316374\pi$
$180$	−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	−0.949633	−	0.313363i	$-0.898544\pi$
$191$	−10.3127	−	17.8620i	−0.746197	−	1.29245i	0.203436	−	0.979088i	$-0.434789\pi$
$192$	7.55055	+	4.35931i	0.544914	+	0.314606i
$193$	10.8945	−	18.8698i	0.784200	−	1.35827i	−0.145275	−	0.989391i	$-0.546407\pi$
$193$	10.8945	−	18.8698i	0.784200	−	1.35827i	0.929476	−	0.368884i	$-0.120260\pi$
$194$	−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	$-0.856031\pi$
$197$	−1.00000	+	1.73205i	−0.0712470	+	0.123404i	0.828201	+	0.560431i	$0.189365\pi$
$198$	−23.5714	−	13.6090i	−1.67515	−	0.967146i
$199$	8.37565	+	14.5071i	0.593734	+	1.02838i	0.993724	+	0.111859i	$0.0356803\pi$
$199$	8.37565	+	14.5071i	0.593734	+	1.02838i	−0.399990	+	0.916520i	$0.630986\pi$
$200$	−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	−0.769247	−	0.638952i	$-0.779368\pi$
$211$	2.45088	−	4.24504i	0.168725	−	0.292241i	0.937972	+	0.346711i	$0.112702\pi$
$212$	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	−0.0608976	−	0.998144i	$-0.519396\pi$
$223$	12.4538	−	21.5706i	0.833969	−	1.44448i	0.894867	−	0.446333i	$-0.147270\pi$
$224$	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	$-0.273841\pi$
$227$	−4.97755	−	8.62136i	−0.330371	−	0.572220i	−0.982585	+	0.185815i	$0.940507\pi$
$228$	−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	$0.114666\pi$
$233$			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	$0.874671\pi$
$240$	2.62957	−	12.9433i	0.169738	−	0.835488i
$241$	24.7902	−	14.3127i	1.59688	−	0.921959i	0.604796	−	0.796381i	$-0.293255\pi$
$241$	24.7902	−	14.3127i	1.59688	−	0.921959i	0.992084	−	0.125578i	$-0.0400786\pi$
$242$	−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	−0.990932	−	0.134367i	$-0.957100\pi$
$251$	−9.69323	−	16.7892i	−0.611831	−	1.05972i	0.379100	−	0.925356i	$-0.376233\pi$
$252$	−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	$-0.586029\pi$
$257$	−19.7997	−	11.4314i	−1.23507	−	0.713069i	−0.968083	+	0.250631i	$0.919362\pi$
$258$	−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	$-0.569042\pi$
$263$	−18.9506	−	10.9411i	−1.16854	−	0.674658i	−0.953336	+	0.301910i	$0.902376\pi$
$264$	−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	0.970655	+	0.240476i	$0.0773035\pi$
$269$	11.3757	+	19.7032i	0.693586	+	1.20133i	−0.277069	+	0.960850i	$0.589363\pi$
$270$	−15.7444	+	5.27290i	−0.958173	+	0.320899i
$271$	0.107074	+	0.0618192i	0.00650428	+	0.00375525i	0.503249	−	0.864142i	$-0.332138\pi$
$271$	0.107074	+	0.0618192i	0.00650428	+	0.00375525i	−0.496744	+	0.867897i	$0.665471\pi$
$272$		−	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	−0.843031	−	0.537865i	$-0.819231\pi$
$277$	−13.2937	+	7.67513i	−0.798742	+	0.461154i	0.0442891	+	0.999019i	$0.485898\pi$
$278$	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	0.922436	−	0.386150i	$-0.126195\pi$
$283$	17.6509	+	10.1908i	1.04924	+	0.605778i	0.126803	+	0.991928i	$0.459529\pi$
$284$	−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	$-0.216903\pi$
$293$	−2.69029	−	4.65972i	−0.157168	−	0.272224i	−0.933846	+	0.357674i	$0.883570\pi$
$294$			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	$-0.315758\pi$
$307$	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
$310$	−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	$0.0253229\pi$
$313$			2.81194i			0.158940i	−0.996837	+	0.0794702i	$0.974677\pi$
$314$	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	$-0.732629\pi$
$317$	−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	$-0.771804\pi$
$331$	−10.2201	+	5.90057i	−0.561747	+	0.324325i	0.192100	+	0.981375i	$0.438470\pi$
$332$	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	$0.144604\pi$
$337$			16.1114i			0.877645i	−0.898574	+	0.438822i	$0.855396\pi$
$338$		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	−0.976523	−	0.215413i	$-0.930890\pi$
$347$	−23.8108	+	13.7472i	−1.27823	+	0.737988i	−0.301709	+	0.953400i	$0.597557\pi$
$348$	−5.19615	−	3.00000i	−0.278543	−	0.160817i
$349$	15.2440	+	8.80114i	0.815994	+	0.471114i	0.849033	−	0.528340i	$-0.177185\pi$
$349$	15.2440	+	8.80114i	0.815994	+	0.471114i	−0.0330393	+	0.999454i	$0.510519\pi$
$350$	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	$-0.695491\pi$
$353$	7.88423	−	13.6559i	0.419635	−	0.726829i	0.995903	+	0.0904319i	$0.0288247\pi$
$354$	−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	−0.256640	−	0.966507i	$-0.582616\pi$
$367$	−23.4098	−	13.5156i	−1.22198	−	0.705510i	−0.965340	+	0.260997i	$0.915949\pi$
$368$	−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	−0.180648	−	0.983548i	$-0.557819\pi$
$373$	11.2172	−	6.47627i	0.580806	−	0.335329i	0.761454	+	0.648219i	$0.224486\pi$
$374$	−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	$-0.617018\pi$
$379$	−26.2283	−	15.1429i	−1.34726	−	0.777840i	−0.987860	+	0.155345i	$0.950351\pi$
$380$	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	−0.998962	−	0.0455560i	$-0.985494\pi$
$383$	−10.5471	−	18.2682i	−0.538934	−	0.933460i	0.460028	−	0.887904i	$-0.347839\pi$
$384$	−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	$-0.0820500\pi$
$397$	5.23449	+	9.06640i	0.262711	+	0.455030i	−0.704250	+	0.709952i	$0.748717\pi$
$398$	−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	$-0.293385\pi$
$401$	4.34154	+	2.50659i	0.216806	+	0.125173i	−0.387664	+	0.921801i	$0.626718\pi$
$402$		−	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	$-0.550903\pi$
$409$	12.4603	−	7.19394i	0.616120	−	0.355717i	0.775357	+	0.631523i	$0.217570\pi$
$410$	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	−0.570032	−	0.821622i	$-0.693069\pi$
$419$	8.73084	−	15.1223i	0.426529	−	0.738771i	0.996562	+	0.0828515i	$0.0264027\pi$
$420$	−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	$-0.340153\pi$
$431$	−0.770360	−	0.444768i	−0.0371070	−	0.0214237i	−0.518439	+	0.855115i	$0.673487\pi$
$432$	29.5076	+	17.0362i	1.41968	+	0.819654i
$433$	21.8677	−	12.6253i	1.05089	−	0.606733i	0.127994	−	0.991775i	$-0.459146\pi$
$433$	21.8677	−	12.6253i	1.05089	−	0.606733i	0.922899	+	0.385042i	$0.125813\pi$
$434$			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	0.285066	+	0.958508i	$0.407985\pi$
$439$	−14.4060	+	24.9519i	−0.687560	+	1.19089i	−0.972625	+	0.232380i	$0.925349\pi$
$440$	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	$0.341454\pi$
$443$			36.9805i			1.75700i	−0.477746	+	0.878498i	$0.658546\pi$
$444$	−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	$-0.763434\pi$
$449$	−10.9863	+	6.34297i	−0.518478	+	0.299343i	0.217834	+	0.975986i	$0.430101\pi$
$450$	−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	−0.408885	−	0.912586i	$-0.634082\pi$
$457$	12.5247	−	21.6934i	0.585880	−	1.01477i	0.994765	−	0.102188i	$-0.0325844\pi$
$458$	−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	$-0.995583\pi$
$461$	−31.9452	+	18.4436i	−1.48784	+	0.859003i	−0.487934	+	0.872881i	$0.662249\pi$
$462$	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
$465$	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	$0.273918\pi$
$467$			32.7694i			1.51639i	−0.652029	+	0.758194i	$0.726082\pi$
$468$		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	$-0.459311\pi$
$479$	−14.6141	−	8.43747i	−0.667737	−	0.385518i	−0.795219	+	0.606323i	$0.792644\pi$
$480$	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	$-0.0994963\pi$
$487$	4.62236	+	8.00616i	0.209459	+	0.362794i	−0.742085	+	0.670306i	$0.766163\pi$
$488$	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	0.414318	+	0.910132i	$0.364020\pi$
$491$	−12.8749	+	22.3001i	−0.581038	+	1.00639i	−0.995357	+	0.0962557i	$0.969313\pi$
$492$	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	−0.453839	−	0.891084i	$-0.649946\pi$
$503$	2.03965	−	1.17759i	0.0909436	−	0.0525063i	0.544782	+	0.838578i	$0.316612\pi$
$504$	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	$-0.175144\pi$
$509$	18.6303	+	10.7562i	0.825775	+	0.476762i	−0.0266286	+	0.999645i	$0.508477\pi$
$510$	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	−0.0221676	−	0.999754i	$-0.507057\pi$
$523$	−20.5609	−	11.8708i	−0.899064	−	0.519075i	−0.876896	+	0.480679i	$0.840390\pi$
$524$	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	$-0.942316\pi$
$547$		−	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
$550$	−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	$-0.739645\pi$
$557$	6.84661	−	11.8587i	0.290100	−	0.502469i	0.973833	+	0.227264i	$0.0729780\pi$
$558$		−	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	$-0.606825\pi$
$563$	7.68084	−	4.43453i	0.323709	−	0.186893i	0.653044	+	0.757320i	$0.273491\pi$
$564$			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	−0.285621	−	0.958343i	$-0.592200\pi$
$569$	16.3908	−	28.3897i	0.687139	−	1.19016i	0.972760	−	0.231816i	$-0.0744668\pi$
$570$	−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	$-0.294903\pi$
$577$	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	0.0116712	+	0.999932i	$0.496285\pi$
$587$	−20.8393	+	36.0948i	−0.860131	+	1.48979i	−0.871802	+	0.489858i	$0.837048\pi$
$588$	−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
$595$	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	0.427074	+	0.904217i	$0.359544\pi$
$601$	−13.9624	+	24.1836i	−0.569538	+	0.986468i	−0.996612	+	0.0822515i	$0.973789\pi$
$602$	−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	−0.637066	−	0.770810i	$-0.719852\pi$
$607$	−7.09698	+	4.09745i	−0.288058	+	0.166310i	0.349008	+	0.937120i	$0.386519\pi$
$608$	−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	−0.308878	−	0.951102i	$-0.599953\pi$
$613$	16.5696	−	28.6994i	0.669239	−	1.15916i	0.978117	−	0.208055i	$-0.0667133\pi$
$614$	−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	0.994998	+	0.0998982i	$0.0318517\pi$
$617$	14.5066	+	25.1261i	0.584013	+	1.01154i	−0.410984	+	0.911642i	$0.634815\pi$
$618$	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	$-0.658924\pi$
$631$	1.05818	−	0.610942i	0.0421256	−	0.0243212i	0.520915	+	0.853609i	$0.325591\pi$
$632$	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	0.560935	−	0.827860i	$-0.310442\pi$
$641$	−11.0508	−	19.1405i	−0.436480	−	0.756005i	−0.997415	+	0.0718545i	$0.977108\pi$
$642$	−14.3284			−0.565496
$643$	5.83440	+	10.1055i	0.230086	+	0.398521i	0.957833	−	0.287325i	$-0.0927659\pi$
$643$	5.83440	+	10.1055i	0.230086	+	0.398521i	−0.727747	+	0.685846i	$0.759433\pi$
$644$	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	$-0.408858\pi$
$647$	−10.3555	−	5.97873i	−0.407115	−	0.235048i	−0.689550	+	0.724238i	$0.742191\pi$
$648$	−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	$-0.264292\pi$
$653$	9.52505	+	5.49929i	0.372744	+	0.215204i	−0.301912	+	0.953336i	$0.597625\pi$
$654$	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	0.839171	−	0.543868i	$-0.183041\pi$
$659$	−1.31994	−	2.28621i	−0.0514177	−	0.0890581i	−0.890589	+	0.454810i	$0.849707\pi$
$660$	−6.47528	−	19.3346i	−0.252050	−	0.752597i
$661$	15.8507	+	9.15140i	0.616520	+	0.355948i	0.775513	−	0.631332i	$-0.217491\pi$
$661$	15.8507	+	9.15140i	0.616520	+	0.355948i	−0.158993	+	0.987280i	$0.550825\pi$
$662$		−	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	0.607806	−	0.794085i	$-0.292050\pi$
$673$	5.81135	+	3.35519i	0.224011	+	0.129333i	−0.383795	+	0.923418i	$0.625383\pi$
$674$	−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
$680$	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	$-0.260551\pi$
$683$	−7.59697	−	13.1583i	−0.290690	−	0.503490i	−0.973973	+	0.226664i	$0.927218\pi$
$684$			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	$-0.217496\pi$
$691$	16.2057	+	9.35637i	0.616494	+	0.355933i	−0.159009	+	0.987277i	$0.550830\pi$
$692$	−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	$-0.724745\pi$
$709$	−8.36833	+	4.83146i	−0.314279	+	0.181449i	0.334561	+	0.942374i	$0.391412\pi$
$710$	−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	−0.999394	−	0.0348012i	$-0.988920\pi$
$719$	−14.2071	−	24.6074i	−0.529836	−	0.917703i	0.469558	−	0.882901i	$-0.344413\pi$
$720$	−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	$-0.776299\pi$
$727$		−	34.8545i		−	1.29268i	0.763049	−	0.646341i	$-0.223701\pi$
$728$		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	$-0.536835\pi$
$733$	−6.25202			−0.230923			−0.115462	+	0.993312i	$0.536835\pi$
$734$	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	$-0.132411\pi$
$739$	27.7861	+	16.0423i	1.02213	+	0.590126i	0.107408	+	0.994215i	$0.465745\pi$
$740$	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	0.437193	+	0.899368i	$0.355973\pi$
$743$	−15.2721	+	26.4521i	−0.560279	+	0.970432i	−0.997472	+	0.0710638i	$0.977361\pi$
$744$	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	−0.486045	−	0.873934i	$-0.661561\pi$
$751$	14.0811	−	24.3892i	0.513827	−	0.889974i	0.999871	−	0.0160400i	$-0.00510591\pi$
$752$	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	$-0.110809\pi$
$757$	30.6667	+	17.7054i	1.11460	+	0.643515i	0.174584	+	0.984642i	$0.444142\pi$
$758$	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	$-0.553289\pi$
$761$	16.6613	−	9.61942i	0.603973	−	0.348704i	0.770603	+	0.637316i	$0.219955\pi$
$762$	−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	0.999398	+	0.0346894i	$0.0110442\pi$
$769$	42.4043	+	24.4821i	1.52914	+	0.882849i	0.529741	+	0.848159i	$0.322289\pi$
$770$	−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	0.897820	+	0.440363i	$0.145150\pi$
$773$	23.0840	+	39.9827i	0.830275	+	1.43808i	−0.0675447	+	0.997716i	$0.521517\pi$
$774$	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	$-0.298914\pi$
$787$	−11.3229	−	19.6118i	−0.403617	−	0.699086i	−0.994159	+	0.107921i	$0.965581\pi$
$788$	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	−0.368304	−	0.929706i	$-0.620061\pi$
$797$	7.13382	−	4.11871i	0.252693	−	0.145892i	0.620997	+	0.783813i	$0.286728\pi$
$798$	−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	−0.158548	−	0.987351i	$-0.550681\pi$
$809$	22.0659	−	38.2193i	0.775797	−	1.34372i	0.934345	−	0.356369i	$-0.115985\pi$
$810$	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	0.999736	+	0.0229677i	$0.00731148\pi$
$821$	43.5382	+	25.1368i	1.51949	+	0.877281i	0.519759	+	0.854313i	$0.326022\pi$
$822$	16.6528	+	9.61450i	0.580833	+	0.335344i
$823$	−4.44352	+	2.56547i	−0.154891	+	0.0894265i	−0.575442	−	0.817842i	$-0.695170\pi$
$823$	−4.44352	+	2.56547i	−0.154891	+	0.0894265i	0.420551	+	0.907269i	$0.361837\pi$
$824$		−	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	$-0.605377\pi$
$827$	−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	−0.834598	−	0.550859i	$-0.814300\pi$
$829$	1.72061	−	2.98018i	0.0597591	−	0.103506i	0.894357	+	0.447353i	$0.147633\pi$
$830$	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	−0.577657	+	0.816279i	$0.696033\pi$
$839$	−45.5744	+	26.3124i	−1.57340	+	0.908406i	−0.995747	+	0.0921263i	$0.970634\pi$
$840$	−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
$855$	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	$-0.995782\pi$
$857$		−	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	$0.517650\pi$
$860$	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	$-0.389892\pi$
$863$	19.9208			0.678112			0.339056	+	0.940766i	$0.389892\pi$
$864$	−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	$-0.288602\pi$
$877$	−11.0689	−	19.1719i	−0.373770	−	0.647388i	−0.990142	+	0.140067i	$0.955268\pi$
$878$	−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	−0.846618	−	0.532202i	$-0.821365\pi$
$881$	1.11577	−	1.93258i	0.0375914	−	0.0651102i	0.884209	+	0.467092i	$0.154698\pi$
$882$	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	$-0.247139\pi$
$887$	13.7984	+	7.96651i	0.463305	+	0.267489i	−0.250128	+	0.968213i	$0.580473\pi$
$888$	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	0.999965	−	0.00839339i	$-0.00267173\pi$
$907$	44.9542	+	25.9543i	1.49268	+	0.861798i	0.492713	+	0.870192i	$0.336005\pi$
$908$	−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	0.955872	−	0.293784i	$-0.0949147\pi$
$919$	6.77575	+	11.7359i	0.223511	+	0.387133i	−0.732361	+	0.680917i	$0.761581\pi$
$920$	−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	$-0.617122\pi$
$929$	8.18387	−	4.72496i	0.268504	−	0.155021i	0.628208	+	0.778046i	$0.283789\pi$
$930$	−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	$-0.915612\pi$
$937$		−	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
$940$	−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	$-0.857308\pi$
$947$	−2.31559	+	4.01072i	−0.0752466	+	0.130331i	0.825947	+	0.563748i	$0.190641\pi$
$948$		−	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	$-0.806723\pi$
$953$	−22.7748	+	13.1490i	−0.737748	+	0.425939i	0.0835021	+	0.996508i	$0.473389\pi$
$954$			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	$-0.561494\pi$
$967$	−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	0.516010	−	0.856583i	$-0.327417\pi$
$971$	−15.0762	−	26.1127i	−0.483818	−	0.837997i	−0.999827	+	0.0185861i	$0.994084\pi$
$972$	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	$-0.975108\pi$
$977$	−13.4660	+	23.3239i	−0.430817	+	0.746196i	0.566127	+	0.824318i	$0.308441\pi$
$978$	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
$985$	−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	−0.175899	−	0.984408i	$-0.556283\pi$
$991$	24.0689	−	41.6885i	0.764573	−	1.32428i	0.940472	−	0.339871i	$-0.110384\pi$
$992$	−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	−0.882603	−	0.470118i	$-0.844211\pi$
$997$	−28.9473	+	16.7127i	−0.916771	+	0.529298i	−0.0341674	+	0.999416i	$0.510878\pi$
$998$	−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.654.2		12
5.4	even	2		845.2.l.e.654.5		12
13.2	odd	12		845.2.n.f.484.1		12
13.3	even	3	inner	845.2.l.d.699.1		12
13.4	even	6		845.2.d.a.844.1		6
13.5	odd	4		845.2.n.f.529.6		12
13.6	odd	12		65.2.b.a.14.1	✓	6
13.7	odd	12		845.2.b.c.339.6		6
13.8	odd	4		845.2.n.g.529.1		12
13.9	even	3		845.2.d.b.844.5		6
13.10	even	6		845.2.l.e.699.5		12
13.11	odd	12		845.2.n.g.484.6		12
13.12	even	2		845.2.l.e.654.6		12
39.32	even	12		585.2.c.b.469.6		6
52.19	even	12		1040.2.d.c.209.4		6
65.4	even	6		845.2.d.b.844.6		6
65.7	even	12		4225.2.a.ba.1.1		3
65.9	even	6		845.2.d.a.844.2		6
65.19	odd	12		65.2.b.a.14.6	yes	6
65.24	odd	12		845.2.n.g.484.1		12
65.29	even	6		845.2.l.e.699.6		12
65.32	even	12		325.2.a.k.1.3		3
65.33	even	12		4225.2.a.bh.1.3		3
65.34	odd	4		845.2.n.g.529.6		12
65.44	odd	4		845.2.n.f.529.1		12
65.49	even	6	inner	845.2.l.d.699.2		12
65.54	odd	12		845.2.n.f.484.6		12
65.58	even	12		325.2.a.j.1.1		3
65.59	odd	12		845.2.b.c.339.1		6
65.64	even	2	inner	845.2.l.d.654.1		12
195.32	odd	12		2925.2.a.bf.1.1		3
195.149	even	12		585.2.c.b.469.1		6
195.188	odd	12		2925.2.a.bj.1.3		3
260.19	even	12		1040.2.d.c.209.3		6
260.123	odd	12		5200.2.a.cj.1.1		3
260.227	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	13.6	odd	12
65.2.b.a.14.6	yes	6	65.19	odd	12
325.2.a.j.1.1		3	65.58	even	12
325.2.a.k.1.3		3	65.32	even	12
585.2.c.b.469.1		6	195.149	even	12
585.2.c.b.469.6		6	39.32	even	12
845.2.b.c.339.1		6	65.59	odd	12
845.2.b.c.339.6		6	13.7	odd	12
845.2.d.a.844.1		6	13.4	even	6
845.2.d.a.844.2		6	65.9	even	6
845.2.d.b.844.5		6	13.9	even	3
845.2.d.b.844.6		6	65.4	even	6
845.2.l.d.654.1		12	65.64	even	2	inner
845.2.l.d.654.2		12	1.1	even	1	trivial
845.2.l.d.699.1		12	13.3	even	3	inner
845.2.l.d.699.2		12	65.49	even	6	inner
845.2.l.e.654.5		12	5.4	even	2
845.2.l.e.654.6		12	13.12	even	2
845.2.l.e.699.5		12	13.10	even	6
845.2.l.e.699.6		12	65.29	even	6
845.2.n.f.484.1		12	13.2	odd	12
845.2.n.f.484.6		12	65.54	odd	12
845.2.n.f.529.1		12	65.44	odd	4
845.2.n.f.529.6		12	13.5	odd	4
845.2.n.g.484.1		12	65.24	odd	12
845.2.n.g.484.6		12	13.11	odd	12
845.2.n.g.529.1		12	13.8	odd	4
845.2.n.g.529.6		12	65.34	odd	4
1040.2.d.c.209.3		6	260.19	even	12
1040.2.d.c.209.4		6	52.19	even	12
2925.2.a.bf.1.1		3	195.32	odd	12
2925.2.a.bj.1.3		3	195.188	odd	12
4225.2.a.ba.1.1		3	65.7	even	12
4225.2.a.bh.1.3		3	65.33	even	12
5200.2.a.cb.1.3		3	260.227	odd	12
5200.2.a.cj.1.1		3	260.123	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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