LMFDB - Embedded newform 585.2.i.e.196.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 $ x^16 - 5x^15 + 20x^14 - 44x^13 + 96x^12 - 107x^11 + 178x^10 - 19x^9 + 231x^8 + 326x^7 + 551x^6 + 859x^5 + 1118x^4 + 1215x^3 + 1103x^2 + 770*x + 268
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.5
Root			$0.252952 + 1.56266i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.e.391.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.247048 + 0.427900i) q^{2} +(0.674928 + 1.59514i) q^{3} +(0.877935 + 1.52063i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.849299 - 0.105275i) q^{6} +(2.14269 - 3.71125i) q^{7} -1.85576 q^{8} +(-2.08895 + 2.15321i) q^{9} +O(q^{10})$	\(q+(-0.247048 + 0.427900i) q^{2} +(0.674928 + 1.59514i) q^{3} +(0.877935 + 1.52063i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.849299 - 0.105275i) q^{6} +(2.14269 - 3.71125i) q^{7} -1.85576 q^{8} +(-2.08895 + 2.15321i) q^{9} -0.494096 q^{10} +(-2.24265 + 3.88439i) q^{11} +(-1.83307 + 2.42674i) q^{12} +(0.500000 + 0.866025i) q^{13} +(1.05870 + 1.83371i) q^{14} +(-1.04397 + 1.38207i) q^{15} +(-1.29741 + 2.24718i) q^{16} +1.57196 q^{17} +(-0.405288 - 1.42580i) q^{18} +1.86934 q^{19} +(-0.877935 + 1.52063i) q^{20} +(7.36613 + 0.913068i) q^{21} +(-1.10808 - 1.91926i) q^{22} +(2.62890 + 4.55339i) q^{23} +(-1.25250 - 2.96020i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.494096 q^{26} +(-4.84456 - 1.87890i) q^{27} +7.52458 q^{28} +(0.375154 - 0.649786i) q^{29} +(-0.333479 - 0.788152i) q^{30} +(-5.10067 - 8.83463i) q^{31} +(-2.49680 - 4.32459i) q^{32} +(-7.70977 - 0.955664i) q^{33} +(-0.388349 + 0.672641i) q^{34} +4.28539 q^{35} +(-5.10819 - 1.28613i) q^{36} +2.78257 q^{37} +(-0.461818 + 0.799892i) q^{38} +(-1.04397 + 1.38207i) q^{39} +(-0.927880 - 1.60713i) q^{40} +(3.18008 + 5.50806i) q^{41} +(-2.21049 + 2.92639i) q^{42} +(-3.79662 + 6.57594i) q^{43} -7.87560 q^{44} +(-2.90921 - 0.732475i) q^{45} -2.59786 q^{46} +(4.13510 - 7.16221i) q^{47} +(-4.46022 - 0.552866i) q^{48} +(-5.68226 - 9.84197i) q^{49} +(-0.247048 - 0.427900i) q^{50} +(1.06096 + 2.50750i) q^{51} +(-0.877935 + 1.52063i) q^{52} +0.0752567 q^{53} +(2.00082 - 1.60881i) q^{54} -4.48530 q^{55} +(-3.97632 + 6.88719i) q^{56} +(1.26167 + 2.98187i) q^{57} +(0.185362 + 0.321057i) q^{58} +(-5.72037 - 9.90797i) q^{59} +(-3.01816 - 0.374115i) q^{60} +(5.98002 - 10.3577i) q^{61} +5.04044 q^{62} +(3.51513 + 12.3663i) q^{63} -2.72231 q^{64} +(-0.500000 + 0.866025i) q^{65} +(2.31361 - 3.06291i) q^{66} +(6.44874 + 11.1696i) q^{67} +(1.38008 + 2.39036i) q^{68} +(-5.48897 + 7.26667i) q^{69} +(-1.05870 + 1.83371i) q^{70} +14.4466 q^{71} +(3.87658 - 3.99584i) q^{72} +9.37293 q^{73} +(-0.687429 + 1.19066i) q^{74} +(-1.71890 - 0.213066i) q^{75} +(1.64116 + 2.84258i) q^{76} +(9.61062 + 16.6461i) q^{77} +(-0.333479 - 0.788152i) q^{78} +(3.04959 - 5.28205i) q^{79} -2.59482 q^{80} +(-0.272617 - 8.99587i) q^{81} -3.14253 q^{82} +(-0.306089 + 0.530162i) q^{83} +(5.07855 + 12.0028i) q^{84} +(0.785980 + 1.36136i) q^{85} +(-1.87589 - 3.24914i) q^{86} +(1.28970 + 0.159865i) q^{87} +(4.16182 - 7.20849i) q^{88} -16.2485 q^{89} +(1.03214 - 1.06389i) q^{90} +4.28539 q^{91} +(-4.61600 + 7.99515i) q^{92} +(10.6499 - 14.0990i) q^{93} +(2.04314 + 3.53882i) q^{94} +(0.934672 + 1.61890i) q^{95} +(5.21317 - 6.90154i) q^{96} +(7.49702 - 12.9852i) q^{97} +5.61517 q^{98} +(-3.67912 - 12.9432i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.247048	+	0.427900i	−0.174689	+	0.302571i	−0.940054	−	0.341026i	$-0.889225\pi$
$2$	−0.247048	+	0.427900i	−0.174689	+	0.302571i	0.765364	+	0.643597i	$0.222559\pi$
$3$	0.674928	+	1.59514i	0.389670	+	0.920955i
$3$	0.674928	+	1.59514i	0.389670	+	0.920955i
$4$	0.877935	+	1.52063i	0.438967	+	0.760314i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.849299	−	0.105275i	−0.346725	−	0.0429783i
$7$	2.14269	−	3.71125i	0.809862	−	1.40272i	−0.103098	−	0.994671i	$-0.532875\pi$
$7$	2.14269	−	3.71125i	0.809862	−	1.40272i	0.912959	−	0.408050i	$-0.133791\pi$
$8$	−1.85576			−0.656110
$9$	−2.08895	+	2.15321i	−0.696315	+	0.717736i
$10$	−0.494096			−0.156247
$11$	−2.24265	+	3.88439i	−0.676185	+	1.17119i	0.299936	+	0.953959i	$0.403035\pi$
$11$	−2.24265	+	3.88439i	−0.676185	+	1.17119i	−0.976121	+	0.217227i	$0.930299\pi$
$12$	−1.83307	+	2.42674i	−0.529162	+	0.700540i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	1.05870	+	1.83371i	0.282948	+	0.490081i
$15$	−1.04397	+	1.38207i	−0.269551	+	0.356850i
$16$	−1.29741	+	2.24718i	−0.324352	+	0.561794i
$17$	1.57196			0.381256			0.190628	−	0.981662i	$-0.438948\pi$
$17$	1.57196			0.381256			0.190628	+	0.981662i	$0.438948\pi$
$18$	−0.405288	−	1.42580i	−0.0955272	−	0.336065i
$19$	1.86934			0.428857			0.214429	−	0.976740i	$-0.431211\pi$
$19$	1.86934			0.428857			0.214429	+	0.976740i	$0.431211\pi$
$20$	−0.877935	+	1.52063i	−0.196312	+	0.340023i
$21$	7.36613	+	0.913068i	1.60742	+	0.199248i
$22$	−1.10808	−	1.91926i	−0.236244	−	0.409187i
$23$	2.62890	+	4.55339i	0.548163	+	0.949447i	0.998400	+	0.0565377i	$0.0180061\pi$
$23$	2.62890	+	4.55339i	0.548163	+	0.949447i	−0.450237	+	0.892909i	$0.648661\pi$
$24$	−1.25250	−	2.96020i	−0.255666	−	0.604248i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.494096			−0.0969002
$27$	−4.84456	−	1.87890i	−0.932335	−	0.361594i
$28$	7.52458			1.42201
$29$	0.375154	−	0.649786i	0.0696644	−	0.120662i	−0.829089	−	0.559116i	$-0.811140\pi$
$29$	0.375154	−	0.649786i	0.0696644	−	0.120662i	0.898754	+	0.438454i	$0.144474\pi$
$30$	−0.333479	−	0.788152i	−0.0608847	−	0.143896i
$31$	−5.10067	−	8.83463i	−0.916108	−	1.58675i	−0.805271	−	0.592907i	$-0.797980\pi$
$31$	−5.10067	−	8.83463i	−0.916108	−	1.58675i	−0.110837	−	0.993839i	$-0.535353\pi$
$32$	−2.49680	−	4.32459i	−0.441377	−	0.764487i
$33$	−7.70977	−	0.955664i	−1.34210	−	0.166360i
$34$	−0.388349	+	0.672641i	−0.0666014	+	0.115357i
$35$	4.28539			0.724362
$36$	−5.10819	−	1.28613i	−0.851364	−	0.214355i
$37$	2.78257			0.457452			0.228726	−	0.973491i	$-0.426544\pi$
$37$	2.78257			0.457452			0.228726	+	0.973491i	$0.426544\pi$
$38$	−0.461818	+	0.799892i	−0.0749167	+	0.129760i
$39$	−1.04397	+	1.38207i	−0.167169	+	0.221309i
$40$	−0.927880	−	1.60713i	−0.146711	−	0.254110i
$41$	3.18008	+	5.50806i	0.496645	+	0.860214i	0.999993	−	0.00386999i	$-0.00123186\pi$
$41$	3.18008	+	5.50806i	0.496645	+	0.860214i	−0.503348	+	0.864084i	$0.667899\pi$
$42$	−2.21049	+	2.92639i	−0.341086	+	0.451552i
$43$	−3.79662	+	6.57594i	−0.578979	+	1.00282i	0.416618	+	0.909082i	$0.363215\pi$
$43$	−3.79662	+	6.57594i	−0.578979	+	1.00282i	−0.995597	+	0.0937394i	$0.970118\pi$
$44$	−7.87560			−1.18729
$45$	−2.90921	−	0.732475i	−0.433679	−	0.109191i
$46$	−2.59786			−0.383033
$47$	4.13510	−	7.16221i	0.603167	−	1.04472i	−0.389171	−	0.921165i	$-0.627239\pi$
$47$	4.13510	−	7.16221i	0.603167	−	1.04472i	0.992338	−	0.123550i	$-0.0394280\pi$
$48$	−4.46022	−	0.552866i	−0.643777	−	0.0797993i
$49$	−5.68226	−	9.84197i	−0.811752	−	1.40600i
$50$	−0.247048	−	0.427900i	−0.0349379	−	0.0605141i
$51$	1.06096	+	2.50750i	0.148564	+	0.351120i
$52$	−0.877935	+	1.52063i	−0.121748	+	0.210873i
$53$	0.0752567			0.0103373			0.00516865	−	0.999987i	$-0.498355\pi$
$53$	0.0752567			0.0103373			0.00516865	+	0.999987i	$0.498355\pi$
$54$	2.00082	−	1.60881i	0.272277	−	0.218931i
$55$	−4.48530			−0.604798
$56$	−3.97632	+	6.88719i	−0.531358	+	0.920340i
$57$	1.26167	+	2.98187i	0.167113	+	0.394958i
$58$	0.185362	+	0.321057i	0.0243392	+	0.0421568i
$59$	−5.72037	−	9.90797i	−0.744728	−	1.28991i	−0.950322	−	0.311270i	$-0.899246\pi$
$59$	−5.72037	−	9.90797i	−0.744728	−	1.28991i	0.205593	−	0.978638i	$-0.434088\pi$
$60$	−3.01816	−	0.374115i	−0.389642	−	0.0482981i
$61$	5.98002	−	10.3577i	0.765663	−	1.32617i	−0.174232	−	0.984705i	$-0.555744\pi$
$61$	5.98002	−	10.3577i	0.765663	−	1.32617i	0.939895	−	0.341463i	$-0.110923\pi$
$62$	5.04044			0.640137
$63$	3.51513	+	12.3663i	0.442865	+	1.55800i
$64$	−2.72231			−0.340289
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	2.31361	−	3.06291i	0.284786	−	0.377018i
$67$	6.44874	+	11.1696i	0.787839	+	1.36458i	0.927288	+	0.374348i	$0.122134\pi$
$67$	6.44874	+	11.1696i	0.787839	+	1.36458i	−0.139449	+	0.990229i	$0.544533\pi$
$68$	1.38008	+	2.39036i	0.167359	+	0.289874i
$69$	−5.48897	+	7.26667i	−0.660795	+	0.874804i
$70$	−1.05870	+	1.83371i	−0.126538	+	0.219171i
$71$	14.4466			1.71450			0.857250	−	0.514900i	$-0.172171\pi$
$71$	14.4466			1.71450			0.857250	+	0.514900i	$0.172171\pi$
$72$	3.87658	−	3.99584i	0.456859	−	0.470914i
$73$	9.37293			1.09702			0.548509	−	0.836144i	$-0.315196\pi$
$73$	9.37293			1.09702			0.548509	+	0.836144i	$0.315196\pi$
$74$	−0.687429	+	1.19066i	−0.0799120	+	0.138412i
$75$	−1.71890	−	0.213066i	−0.198481	−	0.0246027i
$76$	1.64116	+	2.84258i	0.188254	+	0.326066i
$77$	9.61062	+	16.6461i	1.09523	+	1.89700i
$78$	−0.333479	−	0.788152i	−0.0377591	−	0.0892407i
$79$	3.04959	−	5.28205i	0.343106	−	0.594277i	−0.641902	−	0.766787i	$-0.721854\pi$
$79$	3.04959	−	5.28205i	0.343106	−	0.594277i	0.985008	+	0.172510i	$0.0551877\pi$
$80$	−2.59482			−0.290109
$81$	−0.272617	−	8.99587i	−0.0302907	−	0.999541i
$82$	−3.14253			−0.347034
$83$	−0.306089	+	0.530162i	−0.0335976	+	0.0581928i	−0.882335	−	0.470621i	$-0.844030\pi$
$83$	−0.306089	+	0.530162i	−0.0335976	+	0.0581928i	0.848738	+	0.528814i	$0.177363\pi$
$84$	5.07855	+	12.0028i	0.554115	+	1.30961i
$85$	0.785980	+	1.36136i	0.0852515	+	0.147660i
$86$	−1.87589	−	3.24914i	−0.202283	−	0.350364i
$87$	1.28970	+	0.159865i	0.138271	+	0.0171393i
$88$	4.16182	−	7.20849i	0.443652	−	0.768427i
$89$	−16.2485			−1.72234			−0.861169	−	0.508319i	$-0.830267\pi$
$89$	−16.2485			−1.72234			−0.861169	+	0.508319i	$0.830267\pi$
$90$	1.03214	−	1.06389i	0.108797	−	0.112144i
$91$	4.28539			0.449230
$92$	−4.61600	+	7.99515i	−0.481252	+	0.833552i
$93$	10.6499	−	14.0990i	1.10434	−	1.46200i
$94$	2.04314	+	3.53882i	0.210734	+	0.365001i
$95$	0.934672	+	1.61890i	0.0958954	+	0.166096i
$96$	5.21317	−	6.90154i	0.532067	−	0.704385i
$97$	7.49702	−	12.9852i	0.761207	−	1.31845i	−0.181021	−	0.983479i	$-0.557940\pi$
$97$	7.49702	−	12.9852i	0.761207	−	1.31845i	0.942229	−	0.334971i	$-0.108726\pi$
$98$	5.61517			0.567218
$99$	−3.67912	−	12.9432i	−0.369765	−	1.30084i
$100$	−1.75587			−0.175587
$101$	−5.44487	+	9.43079i	−0.541785	+	0.938399i	0.457017	+	0.889458i	$0.348918\pi$
$101$	−5.44487	+	9.43079i	−0.541785	+	0.938399i	−0.998802	+	0.0489409i	$0.984415\pi$
$102$	−1.33506	−	0.165488i	−0.132191	−	0.0163857i
$103$	0.768667	+	1.33137i	0.0757390	+	0.131184i	0.901407	−	0.432972i	$-0.142535\pi$
$103$	0.768667	+	1.33137i	0.0757390	+	0.131184i	−0.825668	+	0.564156i	$0.809202\pi$
$104$	−0.927880	−	1.60713i	−0.0909861	−	0.157593i
$105$	2.89233	+	6.83579i	0.282262	+	0.667105i
$106$	−0.0185920	+	0.0322023i	−0.00180582	+	0.00312776i
$107$	−5.43803			−0.525715			−0.262857	−	0.964835i	$-0.584665\pi$
$107$	−5.43803			−0.525715			−0.262857	+	0.964835i	$0.584665\pi$
$108$	−1.39610	−	9.01632i	−0.134340	−	0.867596i
$109$	1.44466			0.138374			0.0691868	−	0.997604i	$-0.477960\pi$
$109$	1.44466			0.138374			0.0691868	+	0.997604i	$0.477960\pi$
$110$	1.10808	−	1.91926i	0.105652	−	0.182994i
$111$	1.87804	+	4.43859i	0.178255	+	0.421293i
$112$	5.55989	+	9.63002i	0.525360	+	0.909951i
$113$	−2.23239	−	3.86661i	−0.210006	−	0.363740i	0.741710	−	0.670720i	$-0.234015\pi$
$113$	−2.23239	−	3.86661i	−0.210006	−	0.363740i	−0.951716	+	0.306980i	$0.900682\pi$
$114$	−1.58763	−	0.196795i	−0.148695	−	0.0184315i
$115$	−2.62890	+	4.55339i	−0.245146	+	0.424605i
$116$	1.31744			0.122322
$117$	−2.90921	−	0.732475i	−0.268956	−	0.0677173i
$118$	5.65282			0.520384
$119$	3.36823	−	5.83394i	0.308765	−	0.534796i
$120$	1.93735	−	2.56480i	0.176855	−	0.234133i
$121$	−4.55897	−	7.89637i	−0.414452	−	0.717851i
$122$	2.95470	+	5.11770i	0.267506	+	0.463335i
$123$	−6.63980	+	8.79021i	−0.598691	+	0.792587i
$124$	8.95612	−	15.5124i	0.804283	−	1.39306i
$125$	−1.00000			−0.0894427
$126$	−6.15993	−	1.55094i	−0.548770	−	0.138168i
$127$	−3.92097			−0.347930			−0.173965	−	0.984752i	$-0.555658\pi$
$127$	−3.92097			−0.347930			−0.173965	+	0.984752i	$0.555658\pi$
$128$	5.66615	−	9.81406i	0.500821	−	0.867448i
$129$	−13.0520	−	1.61786i	−1.14916	−	0.142444i
$130$	−0.247048	−	0.427900i	−0.0216675	−	0.0375293i
$131$	−0.387214	−	0.670674i	−0.0338310	−	0.0585971i	0.848614	−	0.529012i	$-0.177437\pi$
$131$	−0.387214	−	0.670674i	−0.0338310	−	0.0585971i	−0.882445	+	0.470415i	$0.844104\pi$
$132$	−5.31546	−	12.5627i	−0.462652	−	1.09344i
$133$	4.00543	−	6.93761i	0.347315	−	0.601567i
$134$	−6.37259			−0.550508
$135$	−0.795103	−	5.13496i	−0.0684316	−	0.441947i
$136$	−2.91718			−0.250146
$137$	−2.35405	+	4.07733i	−0.201120	+	0.348350i	−0.948890	−	0.315608i	$-0.897791\pi$
$137$	−2.35405	+	4.07733i	−0.201120	+	0.348350i	0.747770	+	0.663958i	$0.231125\pi$
$138$	−1.75337	−	4.14395i	−0.149256	−	0.352756i
$139$	3.48346	+	6.03352i	0.295463	+	0.511757i	0.975092	−	0.221799i	$-0.0711928\pi$
$139$	3.48346	+	6.03352i	0.295463	+	0.511757i	−0.679630	+	0.733555i	$0.737859\pi$
$140$	3.76229	+	6.51647i	0.317971	+	0.550743i
$141$	14.2156	+	1.76210i	1.19717	+	0.148395i
$142$	−3.56901	+	6.18171i	−0.299505	+	0.518758i
$143$	−4.48530			−0.375080
$144$	−2.12843	−	7.48782i	−0.177369	−	0.623985i
$145$	0.750308			0.0623097
$146$	−2.31556	+	4.01067i	−0.191637	+	0.331926i
$147$	11.8642	−	15.7066i	0.978543	−	1.29546i
$148$	2.44292	+	4.23126i	0.200807	+	0.347807i
$149$	4.11863	+	7.13367i	0.337411	+	0.584413i	0.983945	−	0.178472i	$-0.0571154\pi$
$149$	4.11863	+	7.13367i	0.337411	+	0.584413i	−0.646534	+	0.762885i	$0.723782\pi$
$150$	0.515820	−	0.682877i	0.0421166	−	0.0557567i
$151$	4.38594	−	7.59667i	0.356923	−	0.618208i	−0.630522	−	0.776171i	$-0.717159\pi$
$151$	4.38594	−	7.59667i	0.356923	−	0.618208i	0.987445	+	0.157963i	$0.0504926\pi$
$152$	−3.46905			−0.281377
$153$	−3.28374	+	3.38476i	−0.265474	+	0.273641i
$154$	−9.49714			−0.765301
$155$	5.10067	−	8.83463i	0.409696	−	0.709614i
$156$	−3.01816	−	0.374115i	−0.241646	−	0.0299532i
$157$	6.69687	+	11.5993i	0.534468	+	0.925726i	0.999189	+	0.0402687i	$0.0128214\pi$
$157$	6.69687	+	11.5993i	0.534468	+	0.925726i	−0.464721	+	0.885457i	$0.653845\pi$
$158$	1.50679	+	2.60984i	0.119874	+	0.207628i
$159$	0.0507928	+	0.120045i	0.00402813	+	0.00952018i
$160$	2.49680	−	4.32459i	0.197390	−	0.341889i
$161$	22.5317			1.77575
$162$	3.91668	+	2.10576i	0.307723	+	0.165444i
$163$	−0.242444			−0.0189897			−0.00949486	−	0.999955i	$-0.503022\pi$
$163$	−0.242444			−0.0189897			−0.00949486	+	0.999955i	$0.503022\pi$
$164$	−5.58380	+	9.67143i	−0.436022	+	0.755212i
$165$	−3.02726	−	7.15469i	−0.235671	−	0.556992i
$166$	−0.151237	−	0.261951i	−0.0117383	−	0.0203313i
$167$	−2.54305	−	4.40470i	−0.196787	−	0.340846i	0.750698	−	0.660646i	$-0.229718\pi$
$167$	−2.54305	−	4.40470i	−0.196787	−	0.340846i	−0.947485	+	0.319800i	$0.896384\pi$
$168$	−13.6698	−	1.69443i	−1.05465	−	0.130728i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−0.776699			−0.0595701
$171$	−3.90496	+	4.02509i	−0.298620	+	0.307806i
$172$	−13.3327			−1.01661
$173$	11.5855	−	20.0667i	0.880831	−	1.52564i	0.0304130	−	0.999537i	$-0.490318\pi$
$173$	11.5855	−	20.0667i	0.880831	−	1.52564i	0.850418	−	0.526107i	$-0.176349\pi$
$174$	−0.387024	+	0.512369i	−0.0293402	+	0.0388426i
$175$	2.14269	+	3.71125i	0.161972	+	0.280544i
$176$	−5.81927	−	10.0793i	−0.438644	−	0.759753i
$177$	11.9438	−	15.8119i	0.897748	−	1.18850i
$178$	4.01416	−	6.95273i	0.300874	−	0.521129i
$179$	13.9237			1.04070			0.520352	−	0.853952i	$-0.325801\pi$
$179$	13.9237			1.04070			0.520352	+	0.853952i	$0.325801\pi$
$180$	−1.44027	−	5.06688i	−0.107351	−	0.377663i
$181$	13.6884			1.01745			0.508725	−	0.860929i	$-0.330117\pi$
$181$	13.6884			1.01745			0.508725	+	0.860929i	$0.330117\pi$
$182$	−1.05870	+	1.83371i	−0.0784757	+	0.135924i
$183$	20.5581	+	2.54827i	1.51970	+	0.188374i
$184$	−4.87860	−	8.44999i	−0.359655	−	0.622942i
$185$	1.39129	+	2.40978i	0.102289	+	0.177170i
$186$	3.40194	+	8.04022i	0.249442	+	0.589537i
$187$	−3.52536	+	6.10610i	−0.257800	+	0.446522i
$188$	14.5214			1.05908
$189$	−17.3535	+	13.9535i	−1.26228	+	1.01497i
$190$	−0.923636			−0.0670076
$191$	3.92168	−	6.79255i	0.283763	−	0.491491i	−0.688546	−	0.725193i	$-0.741751\pi$
$191$	3.92168	−	6.79255i	0.283763	−	0.491491i	0.972308	+	0.233702i	$0.0750839\pi$
$192$	−1.83736	−	4.34247i	−0.132600	−	0.313391i
$193$	10.3259	+	17.8850i	0.743274	+	1.28739i	0.950997	+	0.309200i	$0.100061\pi$
$193$	10.3259	+	17.8850i	0.743274	+	1.28739i	−0.207723	+	0.978188i	$0.566605\pi$
$194$	3.70425	+	6.41595i	0.265950	+	0.460638i
$195$	−1.71890	−	0.213066i	−0.123093	−	0.0152579i
$196$	9.97731	−	17.2812i	0.712665	−	1.23437i
$197$	4.38617			0.312502			0.156251	−	0.987717i	$-0.450059\pi$
$197$	4.38617			0.312502			0.156251	+	0.987717i	$0.450059\pi$
$198$	6.44729	+	1.62329i	0.458189	+	0.115362i
$199$	−13.3916			−0.949304			−0.474652	−	0.880174i	$-0.657426\pi$
$199$	−13.3916			−0.949304			−0.474652	+	0.880174i	$0.657426\pi$
$200$	0.927880	−	1.60713i	0.0656110	−	0.113642i
$201$	−13.4646	+	17.8253i	−0.949717	+	1.25730i
$202$	−2.69029	−	4.65972i	−0.189288	−	0.327856i
$203$	−1.60768	−	2.78458i	−0.112837	−	0.195440i
$204$	−2.88151	+	3.81474i	−0.201746	+	0.267085i
$205$	−3.18008	+	5.50806i	−0.222106	+	0.384699i
$206$	−0.759591			−0.0529232
$207$	−15.2960	−	3.85121i	−1.06315	−	0.267677i
$208$	−2.59482			−0.179918
$209$	−4.19229	+	7.26126i	−0.289987	+	0.502272i
$210$	−3.63958	−	0.451143i	−0.251155	−	0.0311318i
$211$	3.03493	+	5.25665i	0.208933	+	0.361883i	0.951379	−	0.308023i	$-0.0996675\pi$
$211$	3.03493	+	5.25665i	0.208933	+	0.361883i	−0.742446	+	0.669906i	$0.766334\pi$
$212$	0.0660704	+	0.114437i	0.00453774	+	0.00785959i
$213$	9.75044	+	23.0444i	0.668089	+	1.57898i
$214$	1.34345	−	2.32693i	0.0918367	−	0.159066i
$215$	−7.59324			−0.517855
$216$	8.99033	+	3.48679i	0.611715	+	0.237246i
$217$	−43.7167			−2.96768
$218$	−0.356901	+	0.618170i	−0.0241724	+	0.0418678i
$219$	6.32605	+	14.9511i	0.427475	+	1.01030i
$220$	−3.93780	−	6.82047i	−0.265487	−	0.459836i
$221$	0.785980	+	1.36136i	0.0528707	+	0.0915748i
$222$	−2.36324	−	0.292935i	−0.158610	−	0.0196605i
$223$	11.4941	−	19.9083i	0.769700	−	1.33316i	−0.168026	−	0.985783i	$-0.553739\pi$
$223$	11.4941	−	19.9083i	0.769700	−	1.33316i	0.937726	−	0.347377i	$-0.112928\pi$
$224$	−21.3995			−1.42982
$225$	−0.820261	−	2.88568i	−0.0546841	−	0.192379i
$226$	2.20603			0.146743
$227$	9.41732	−	16.3113i	0.625050	−	1.08262i	−0.363482	−	0.931601i	$-0.618412\pi$
$227$	9.41732	−	16.3113i	0.625050	−	1.08262i	0.988531	−	0.151016i	$-0.0482546\pi$
$228$	−3.42664	+	4.53642i	−0.226935	+	0.300432i
$229$	2.70463	+	4.68455i	0.178727	+	0.309564i	0.941445	−	0.337167i	$-0.109469\pi$
$229$	2.70463	+	4.68455i	0.178727	+	0.309564i	−0.762718	+	0.646731i	$0.776135\pi$
$230$	−1.29893	−	2.24981i	−0.0856488	−	0.148348i
$231$	−20.0664	+	26.5652i	−1.32027	+	1.74786i
$232$	−0.696196	+	1.20585i	−0.0457075	+	0.0791677i
$233$	−7.45934			−0.488677			−0.244339	−	0.969690i	$-0.578571\pi$
$233$	−7.45934			−0.488677			−0.244339	+	0.969690i	$0.578571\pi$
$234$	1.03214	−	1.06389i	0.0674731	−	0.0695488i
$235$	8.27021			0.539489
$236$	10.0442	−	17.3971i	0.653823	−	1.13245i
$237$	10.4839	+	1.29953i	0.681000	+	0.0844133i
$238$	1.66423	+	2.88253i	0.107876	+	0.186846i
$239$	−3.84036	−	6.65171i	−0.248412	−	0.430263i	0.714673	−	0.699459i	$-0.246576\pi$
$239$	−3.84036	−	6.65171i	−0.248412	−	0.430263i	−0.963086	+	0.269196i	$0.913242\pi$
$240$	−1.75131	−	4.13909i	−0.113047	−	0.267177i
$241$	−14.6400	+	25.3573i	−0.943048	+	1.63341i	−0.183434	+	0.983032i	$0.558721\pi$
$241$	−14.6400	+	25.3573i	−0.943048	+	1.63341i	−0.759614	+	0.650375i	$0.774612\pi$
$242$	4.50514			0.289601
$243$	14.1657	−	6.50642i	0.908729	−	0.417387i
$244$	21.0003			1.34440
$245$	5.68226	−	9.84197i	0.363027	−	0.628780i
$246$	−2.12098	−	5.01277i	−0.135229	−	0.319603i
$247$	0.934672	+	1.61890i	0.0594718	+	0.103008i
$248$	9.46562	+	16.3949i	0.601068	+	1.04108i
$249$	−1.05227	−	0.130434i	−0.0666849	−	0.00826593i
$250$	0.247048	−	0.427900i	0.0156247	−	0.0270627i
$251$	−26.6402			−1.68152			−0.840758	−	0.541412i	$-0.817890\pi$
$251$	−26.6402			−1.68152			−0.840758	+	0.541412i	$0.817890\pi$
$252$	−15.7184	+	16.2020i	−0.990168	+	1.02063i
$253$	−23.5828			−1.48264
$254$	0.968667	−	1.67778i	0.0607796	−	0.105273i
$255$	−1.64108	+	2.17257i	−0.102768	+	0.136051i
$256$	0.0773104	+	0.133905i	0.00483190	+	0.00836909i
$257$	0.356142	+	0.616855i	0.0222155	+	0.0384784i	0.876919	−	0.480637i	$-0.159595\pi$
$257$	0.356142	+	0.616855i	0.0222155	+	0.0384784i	−0.854704	+	0.519116i	$0.826261\pi$
$258$	3.91675	−	5.18525i	0.243846	−	0.322820i
$259$	5.96220	−	10.3268i	0.370473	−	0.641678i
$260$	−1.75587			−0.108894
$261$	0.615449	+	2.16515i	0.0380953	+	0.134020i
$262$	0.382641			0.0236397
$263$	6.60152	−	11.4342i	0.407067	−	0.705061i	−0.587493	−	0.809230i	$-0.699885\pi$
$263$	6.60152	−	11.4342i	0.407067	−	0.705061i	0.994560	+	0.104169i	$0.0332182\pi$
$264$	14.3075	+	1.77348i	0.880564	+	0.109150i
$265$	0.0376283	+	0.0651742i	0.00231149	+	0.00400362i
$266$	1.97907	+	3.42784i	0.121344	+	0.210175i
$267$	−10.9666	−	25.9186i	−0.671143	−	1.58619i
$268$	−11.3231	+	19.6123i	−0.691671	+	1.19801i
$269$	−18.3263			−1.11737			−0.558687	−	0.829379i	$-0.688695\pi$
$269$	−18.3263			−1.11737			−0.558687	+	0.829379i	$0.688695\pi$
$270$	2.39368	+	0.928357i	0.145674	+	0.0564980i
$271$	−28.9102			−1.75617			−0.878084	−	0.478507i	$-0.841178\pi$
$271$	−28.9102			−1.75617			−0.878084	+	0.478507i	$0.841178\pi$
$272$	−2.03947	+	3.53247i	−0.123661	+	0.214187i
$273$	2.89233	+	6.83579i	0.175052	+	0.413721i
$274$	−1.16313	−	2.01459i	−0.0702670	−	0.121706i
$275$	−2.24265	−	3.88439i	−0.135237	−	0.234237i
$276$	−15.8689	−	1.96702i	−0.955193	−	0.118401i
$277$	−13.0652	+	22.6297i	−0.785014	+	1.35968i	0.143977	+	0.989581i	$0.454011\pi$
$277$	−13.0652	+	22.6297i	−0.785014	+	1.35968i	−0.928991	+	0.370103i	$0.879322\pi$
$278$	−3.44232			−0.206457
$279$	29.6778	+	7.47223i	1.77676	+	0.447351i
$280$	−7.95265			−0.475261
$281$	−13.8389	+	23.9697i	−0.825559	+	1.42991i	0.0759316	+	0.997113i	$0.475807\pi$
$281$	−13.8389	+	23.9697i	−0.825559	+	1.42991i	−0.901491	+	0.432798i	$0.857526\pi$
$282$	−4.26594	+	5.64754i	−0.254033	+	0.336306i
$283$	−13.0720	−	22.6414i	−0.777053	−	1.34589i	−0.933634	−	0.358229i	$-0.883381\pi$
$283$	−13.0720	−	22.6414i	−0.777053	−	1.34589i	0.156581	−	0.987665i	$-0.449953\pi$
$284$	12.6832	+	21.9680i	0.752610	+	1.30356i
$285$	−1.95154	+	2.58357i	−0.115599	+	0.153038i
$286$	1.10808	−	1.91926i	0.0655224	−	0.113488i
$287$	27.2557			1.60885
$288$	14.5274	+	3.65769i	0.856037	+	0.215532i
$289$	−14.5289			−0.854644
$290$	−0.185362	+	0.321057i	−0.0108848	+	0.0188531i
$291$	25.7732	+	3.19471i	1.51085	+	0.187278i
$292$	8.22882	+	14.2527i	0.481555	+	0.834078i
$293$	−2.00825	−	3.47840i	−0.117323	−	0.203210i	0.801383	−	0.598152i	$-0.204098\pi$
$293$	−2.00825	−	3.47840i	−0.117323	−	0.203210i	−0.918706	+	0.394942i	$0.870765\pi$
$294$	3.78983	+	8.95698i	0.221027	+	0.522382i
$295$	5.72037	−	9.90797i	0.333053	−	0.576864i
$296$	−5.16379			−0.300139
$297$	18.1630	−	14.6044i	1.05393	−	0.847434i
$298$	−4.06999			−0.235768
$299$	−2.62890	+	4.55339i	−0.152033	+	0.263329i
$300$	−1.18508	−	2.80086i	−0.0684209	−	0.161708i
$301$	16.2700	+	28.1804i	0.937786	+	1.62429i
$302$	2.16708	+	3.75348i	0.124701	+	0.215989i
$303$	−18.7183	−	2.32023i	−1.07534	−	0.133294i
$304$	−2.42530	+	4.20075i	−0.139101	+	0.240929i
$305$	11.9600			0.684830
$306$	−0.637096	−	2.24131i	−0.0364203	−	0.128127i
$307$	−7.51331			−0.428807			−0.214404	−	0.976745i	$-0.568781\pi$
$307$	−7.51331			−0.428807			−0.214404	+	0.976745i	$0.568781\pi$
$308$	−16.8750	+	29.2284i	−0.961542	+	1.66544i
$309$	−1.60493	+	2.12471i	−0.0913012	+	0.120871i
$310$	2.52022	+	4.36515i	0.143139	+	0.247924i
$311$	−10.5200	−	18.2213i	−0.596537	−	1.03323i	−0.993328	−	0.115323i	$-0.963210\pi$
$311$	−10.5200	−	18.2213i	−0.596537	−	1.03323i	0.396791	−	0.917909i	$-0.370124\pi$
$312$	1.93735	−	2.56480i	0.109681	−	0.145203i
$313$	3.25007	−	5.62929i	0.183705	−	0.318186i	−0.759435	−	0.650584i	$-0.774524\pi$
$313$	3.25007	−	5.62929i	0.183705	−	0.318186i	0.943139	+	0.332398i	$0.107858\pi$
$314$	−6.61779			−0.373463
$315$	−8.95193	+	9.22733i	−0.504384	+	0.519901i
$316$	10.7094			0.602449
$317$	5.72790	−	9.92101i	0.321711	−	0.557220i	−0.659130	−	0.752029i	$-0.729075\pi$
$317$	5.72790	−	9.92101i	0.321711	−	0.557220i	0.980841	+	0.194809i	$0.0624088\pi$
$318$	−0.0639154	−	0.00792263i	−0.00358420	−	0.000444279i
$319$	1.68268	+	2.91449i	0.0942120	+	0.163180i
$320$	−1.36116	−	2.35759i	−0.0760909	−	0.131793i
$321$	−3.67028	−	8.67443i	−0.204855	−	0.484159i
$322$	−5.56641	+	9.64130i	−0.310204	+	0.537289i
$323$	2.93853			0.163504
$324$	13.4400	−	8.31233i	0.746668	−	0.461796i
$325$	−1.00000			−0.0554700
$326$	0.0598954	−	0.103742i	0.00331730	−	0.00574573i
$327$	0.975043	+	2.30444i	0.0539200	+	0.127436i
$328$	−5.90146	−	10.2216i	−0.325854	−	0.564395i
$329$	−17.7205	−	30.6928i	−0.976964	−	1.69215i
$330$	3.80936	+	0.472189i	0.209699	+	0.0259932i
$331$	12.1797	−	21.0958i	0.669456	−	1.15953i	−0.308601	−	0.951192i	$-0.599861\pi$
$331$	12.1797	−	21.0958i	0.669456	−	1.15953i	0.978057	−	0.208340i	$-0.0668060\pi$
$332$	−1.07490			−0.0589931
$333$	−5.81264	+	5.99146i	−0.318531	+	0.328330i
$334$	2.51302			0.137507
$335$	−6.44874	+	11.1696i	−0.352332	+	0.610258i
$336$	−11.6087	+	15.3684i	−0.633307	+	0.838413i
$337$	−5.80009	−	10.0460i	−0.315951	−	0.547243i	0.663688	−	0.748009i	$-0.268990\pi$
$337$	−5.80009	−	10.0460i	−0.315951	−	0.547243i	−0.979639	+	0.200766i	$0.935657\pi$
$338$	−0.247048	−	0.427900i	−0.0134376	−	0.0232747i
$339$	4.66109	−	6.17066i	0.253155	−	0.335144i
$340$	−1.38008	+	2.39036i	−0.0748452	+	0.129636i
$341$	45.7561			2.47783
$342$	−0.757622	−	2.66532i	−0.0409675	−	0.144124i
$343$	−18.7037			−1.00990
$344$	7.04561	−	12.2034i	0.379874	−	0.657961i
$345$	−9.03761	−	1.12026i	−0.486568	−	0.0603125i
$346$	5.72436	+	9.91488i	0.307744	+	0.533028i
$347$	6.09100	+	10.5499i	0.326982	+	0.566349i	0.981911	−	0.189341i	$-0.0606351\pi$
$347$	6.09100	+	10.5499i	0.326982	+	0.566349i	−0.654930	+	0.755690i	$0.727302\pi$
$348$	0.889179	+	2.10151i	0.0476650	+	0.112653i
$349$	−3.95551	+	6.85114i	−0.211734	+	0.366733i	−0.952257	−	0.305297i	$-0.901244\pi$
$349$	−3.95551	+	6.85114i	−0.211734	+	0.366733i	0.740524	+	0.672030i	$0.234578\pi$
$350$	−2.11739			−0.113179
$351$	−0.795103	−	5.13496i	−0.0424395	−	0.274084i
$352$	22.3978			1.19381
$353$	−10.6294	+	18.4107i	−0.565747	+	0.979903i	0.431233	+	0.902241i	$0.358079\pi$
$353$	−10.6294	+	18.4107i	−0.565747	+	0.979903i	−0.996980	+	0.0776620i	$0.975254\pi$
$354$	3.81524	+	9.01704i	0.202778	+	0.479250i
$355$	7.22332	+	12.5112i	0.383374	+	0.664023i
$356$	−14.2651	−	24.7079i	−0.756050	−	1.30952i
$357$	11.5793	+	1.43531i	0.612839	+	0.0759645i
$358$	−3.43981	+	5.95793i	−0.181800	+	0.314886i
$359$	−7.59638			−0.400922			−0.200461	−	0.979702i	$-0.564244\pi$
$359$	−7.59638			−0.400922			−0.200461	+	0.979702i	$0.564244\pi$
$360$	5.39879	+	1.35930i	0.284541	+	0.0716413i
$361$	−15.5056			−0.816082
$362$	−3.38169	+	5.85725i	−0.177738	+	0.307850i
$363$	9.51884	−	12.6017i	0.499609	−	0.661416i
$364$	3.76229	+	6.51647i	0.197197	+	0.341556i
$365$	4.68647	+	8.11720i	0.245301	+	0.424873i
$366$	−6.16924	+	8.16725i	−0.322471	+	0.426909i
$367$	−10.8071	+	18.7184i	−0.564124	+	0.977092i	0.433006	+	0.901391i	$0.357453\pi$
$367$	−10.8071	+	18.7184i	−0.564124	+	0.977092i	−0.997131	+	0.0757010i	$0.975881\pi$
$368$	−13.6430			−0.711191
$369$	−18.5030	−	4.65866i	−0.963228	−	0.242520i
$370$	−1.37486			−0.0714754
$371$	0.161252	−	0.279297i	0.00837178	−	0.0145004i
$372$	30.7893	+	3.81648i	1.59635	+	0.197875i
$373$	6.00668	+	10.4039i	0.311014	+	0.538692i	0.978582	−	0.205857i	$-0.0659981\pi$
$373$	6.00668	+	10.4039i	0.311014	+	0.538692i	−0.667568	+	0.744549i	$0.732665\pi$
$374$	−1.74186	−	3.01700i	−0.0900697	−	0.156005i
$375$	−0.674928	−	1.59514i	−0.0348531	−	0.0823727i
$376$	−7.67376	+	13.2913i	−0.395744	+	0.685448i
$377$	0.750308			0.0386429
$378$	−1.68354	−	10.8727i	−0.0865922	−	0.559232i
$379$	−3.44005			−0.176704			−0.0883518	−	0.996089i	$-0.528160\pi$
$379$	−3.44005			−0.176704			−0.0883518	+	0.996089i	$0.528160\pi$
$380$	−1.64116	+	2.84258i	−0.0841899	+	0.145821i
$381$	−2.64637	−	6.25449i	−0.135578	−	0.320427i
$382$	1.93768	+	3.35617i	0.0991406	+	0.171717i
$383$	−13.4494	−	23.2950i	−0.687232	−	1.19032i	−0.972730	−	0.231941i	$-0.925492\pi$
$383$	−13.4494	−	23.2950i	−0.687232	−	1.19032i	0.285498	−	0.958379i	$-0.407841\pi$
$384$	19.4790	+	2.41452i	0.994035	+	0.123216i
$385$	−9.61062	+	16.6461i	−0.489803	+	0.848363i
$386$	−10.2040			−0.519368
$387$	−6.22844	−	21.9117i	−0.316609	−	1.11383i
$388$	26.3276			1.33658
$389$	−1.66758	+	2.88833i	−0.0845494	+	0.146444i	−0.905199	−	0.424988i	$-0.860278\pi$
$389$	−1.66758	+	2.88833i	−0.0845494	+	0.146444i	0.820650	+	0.571432i	$0.193612\pi$
$390$	0.515820	−	0.682877i	0.0261196	−	0.0345788i
$391$	4.13252	+	7.15774i	0.208991	+	0.361982i
$392$	10.5449	+	18.2643i	0.532599	+	0.922488i
$393$	0.808478	−	1.07032i	0.0407823	−	0.0539903i
$394$	−1.08359	+	1.87684i	−0.0545907	+	0.0945538i
$395$	6.09918			0.306883
$396$	16.4517	−	16.9578i	0.826729	−	0.852163i
$397$	0.768687			0.0385793			0.0192897	−	0.999814i	$-0.493860\pi$
$397$	0.768687			0.0385793			0.0192897	+	0.999814i	$0.493860\pi$
$398$	3.30836	−	5.73025i	0.165833	−	0.287232i
$399$	13.7698	+	1.70684i	0.689354	+	0.0854488i
$400$	−1.29741	−	2.24718i	−0.0648704	−	0.112359i
$401$	−14.8015	−	25.6370i	−0.739153	−	1.28025i	−0.952877	−	0.303357i	$-0.901892\pi$
$401$	−14.8015	−	25.6370i	−0.739153	−	1.28025i	0.213723	−	0.976894i	$-0.431441\pi$
$402$	−4.30104	−	10.1652i	−0.214516	−	0.506993i
$403$	5.10067	−	8.83463i	0.254083	−	0.440084i
$404$	−19.1210			−0.951303
$405$	7.65434	−	4.73403i	0.380347	−	0.235236i
$406$	1.58870			0.0788457
$407$	−6.24034	+	10.8086i	−0.309322	+	0.535762i
$408$	−1.96888	−	4.65331i	−0.0974743	−	0.230373i
$409$	8.10055	+	14.0306i	0.400546	+	0.693766i	0.993792	−	0.111255i	$-0.0354871\pi$
$409$	8.10055	+	14.0306i	0.400546	+	0.693766i	−0.593246	+	0.805021i	$0.702154\pi$
$410$	−1.57126	−	2.72151i	−0.0775992	−	0.134406i
$411$	−8.09273	−	1.00313i	−0.399185	−	0.0494809i
$412$	−1.34968	+	2.33771i	−0.0664939	+	0.115171i
$413$	−49.0279			−2.41251
$414$	5.42678	−	5.59373i	0.266712	−	0.274917i
$415$	−0.612178			−0.0300506
$416$	2.49680	−	4.32459i	0.122416	−	0.212030i
$417$	−7.27323	+	9.62879i	−0.356172	+	0.471524i
$418$	−2.07139	−	3.58776i	−0.101315	−	0.175483i
$419$	−5.70634	−	9.88368i	−0.278773	−	0.482849i	0.692307	−	0.721603i	$-0.256594\pi$
$419$	−5.70634	−	9.88368i	−0.278773	−	0.482849i	−0.971080	+	0.238754i	$0.923261\pi$
$420$	−7.85542	+	10.3995i	−0.383305	+	0.507445i
$421$	−5.19917	+	9.00522i	−0.253392	+	0.438888i	−0.964458	−	0.264238i	$-0.914880\pi$
$421$	−5.19917	+	9.00522i	−0.253392	+	0.438888i	0.711066	+	0.703126i	$0.248213\pi$
$422$	−2.99909			−0.145994
$423$	6.78373	+	23.8652i	0.329836	+	1.16037i
$424$	−0.139658			−0.00678241
$425$	−0.785980	+	1.36136i	−0.0381256	+	0.0660355i
$426$	−12.2695	−	1.52087i	−0.594460	−	0.0736863i
$427$	−25.6267	−	44.3868i	−1.24016	−	2.14803i
$428$	−4.77424	−	8.26922i	−0.230771	−	0.399708i
$429$	−3.02726	−	7.15469i	−0.146157	−	0.345432i
$430$	1.87589	−	3.24914i	0.0904637	−	0.156688i
$431$	−0.879972			−0.0423868			−0.0211934	−	0.999775i	$-0.506747\pi$
$431$	−0.879972			−0.0423868			−0.0211934	+	0.999775i	$0.506747\pi$
$432$	10.5076	−	8.44887i	0.505546	−	0.406497i
$433$	31.4562			1.51169			0.755845	−	0.654750i	$-0.227226\pi$
$433$	31.4562			1.51169			0.755845	+	0.654750i	$0.227226\pi$
$434$	10.8001	−	18.7064i	0.518422	−	0.897934i
$435$	0.506404	+	1.19685i	0.0242802	+	0.0573844i
$436$	1.26832	+	2.19679i	0.0607415	+	0.105207i
$437$	4.91432	+	8.51185i	0.235084	+	0.407177i
$438$	−7.96042	−	0.986734i	−0.380364	−	0.0471480i
$439$	2.88207	−	4.99189i	0.137554	−	0.238250i	−0.789016	−	0.614372i	$-0.789409\pi$
$439$	2.88207	−	4.99189i	0.137554	−	0.238250i	0.926570	+	0.376122i	$0.122743\pi$
$440$	8.32364			0.396814
$441$	33.0618	+	8.32423i	1.57437	+	0.396392i
$442$	−0.776699			−0.0369438
$443$	−2.06423	+	3.57535i	−0.0980746	+	0.169870i	−0.910888	−	0.412654i	$-0.864602\pi$
$443$	−2.06423	+	3.57535i	−0.0980746	+	0.169870i	0.812813	+	0.582525i	$0.197935\pi$
$444$	−5.10065	+	6.75259i	−0.242066	+	0.320464i
$445$	−8.12425	−	14.0716i	−0.385126	−	0.667058i
$446$	5.67917	+	9.83662i	0.268917	+	0.465777i
$447$	−8.59943	+	11.3845i	−0.406739	+	0.538468i
$448$	−5.83307	+	10.1032i	−0.275587	+	0.477330i
$449$	−30.3402			−1.43184			−0.715921	−	0.698181i	$-0.753993\pi$
$449$	−30.3402			−1.43184			−0.715921	+	0.698181i	$0.753993\pi$
$450$	1.43743	+	0.361913i	0.0677609	+	0.0170607i
$451$	−28.5272			−1.34329
$452$	3.91978	−	6.78927i	0.184371	−	0.319340i
$453$	15.0779	+	1.86899i	0.708424	+	0.0878126i
$454$	4.65306	+	8.05934i	0.218379	+	0.378243i
$455$	2.14269	+	3.71125i	0.100451	+	0.173986i
$456$	−2.34136	−	5.53363i	−0.109644	−	0.259136i
$457$	4.23141	−	7.32902i	0.197937	−	0.342837i	−0.749922	−	0.661526i	$-0.769909\pi$
$457$	4.23141	−	7.32902i	0.197937	−	0.342837i	0.947859	+	0.318689i	$0.103242\pi$
$458$	−2.67269			−0.124887
$459$	−7.61545	−	2.95355i	−0.355459	−	0.137860i
$460$	−9.23201			−0.430444
$461$	−8.81541	+	15.2687i	−0.410575	+	0.711136i	−0.994953	−	0.100345i	$-0.968005\pi$
$461$	−8.81541	+	15.2687i	−0.410575	+	0.711136i	0.584378	+	0.811482i	$0.301339\pi$
$462$	−6.40988	−	15.1493i	−0.298215	−	0.704808i
$463$	0.627193	+	1.08633i	0.0291481	+	0.0504860i	0.880231	−	0.474545i	$-0.157387\pi$
$463$	0.627193	+	1.08633i	0.0291481	+	0.0504860i	−0.851083	+	0.525031i	$0.824054\pi$
$464$	0.973456	+	1.68608i	0.0451916	+	0.0782741i
$465$	17.5351	+	2.17356i	0.813169	+	0.100796i
$466$	1.84281	−	3.19185i	0.0853667	−	0.147859i
$467$	11.3158			0.523634			0.261817	−	0.965117i	$-0.415678\pi$
$467$	11.3158			0.523634			0.261817	+	0.965117i	$0.415678\pi$
$468$	−1.44027	−	5.06688i	−0.0665766	−	0.234217i
$469$	55.2707			2.55216
$470$	−2.04314	+	3.53882i	−0.0942429	+	0.163234i
$471$	−13.9826	+	18.5111i	−0.644286	+	0.852948i
$472$	10.6156	+	18.3868i	0.488624	+	0.846321i
$473$	−17.0290	−	29.4951i	−0.782994	−	1.35618i
$474$	−3.14608	+	4.16500i	−0.144504	+	0.191305i
$475$	−0.934672	+	1.61890i	−0.0428857	+	0.0742802i
$476$	11.8283			0.542151
$477$	−0.157207	+	0.162043i	−0.00719802	+	0.00741945i
$478$	3.79502			0.173580
$479$	16.6918	−	28.9110i	0.762667	−	1.32098i	−0.178804	−	0.983885i	$-0.557223\pi$
$479$	16.6918	−	28.9110i	0.762667	−	1.32098i	0.941471	−	0.337094i	$-0.109444\pi$
$480$	8.58349	+	1.06397i	0.391781	+	0.0485632i
$481$	1.39129	+	2.40978i	0.0634372	+	0.109876i
$482$	−7.23358	−	12.5289i	−0.329481	−	0.570677i
$483$	15.2073	+	35.9412i	0.691954	+	1.63538i
$484$	8.00495	−	13.8650i	0.363862	−	0.630227i
$485$	14.9940			0.680844
$486$	−0.715506	+	7.66889i	−0.0324560	+	0.347868i
$487$	−42.2806			−1.91592			−0.957959	−	0.286904i	$-0.907374\pi$
$487$	−42.2806			−1.91592			−0.957959	+	0.286904i	$0.907374\pi$
$488$	−11.0975	+	19.2214i	−0.502360	+	0.870112i
$489$	−0.163632	−	0.386733i	−0.00739972	−	0.0174887i
$490$	2.80758	+	4.86288i	0.126834	+	0.219682i
$491$	−5.73286	−	9.92961i	−0.258720	−	0.448117i	0.707179	−	0.707035i	$-0.249967\pi$
$491$	−5.73286	−	9.92961i	−0.258720	−	0.448117i	−0.965899	+	0.258918i	$0.916634\pi$
$492$	−19.1959	−	2.37943i	−0.865420	−	0.107273i
$493$	0.589727	−	1.02144i	0.0265600	−	0.0460032i
$494$	−0.923636			−0.0415563
$495$	9.36955	−	9.65779i	0.421130	−	0.434086i
$496$	26.4706			1.18857
$497$	30.9547	−	53.6151i	1.38851	−	2.40497i
$498$	0.315774	−	0.418043i	0.0141502	−	0.0187329i
$499$	−3.35426	−	5.80976i	−0.150157	−	0.260080i	0.781128	−	0.624371i	$-0.214645\pi$
$499$	−3.35426	−	5.80976i	−0.150157	−	0.260080i	−0.931285	+	0.364291i	$0.881311\pi$
$500$	−0.877935	−	1.52063i	−0.0392624	−	0.0680045i
$501$	5.30973	−	7.02938i	0.237221	−	0.314049i
$502$	6.58141	−	11.3993i	0.293743	−	0.508777i
$503$	13.1409			0.585925			0.292963	−	0.956124i	$-0.405359\pi$
$503$	13.1409			0.585925			0.292963	+	0.956124i	$0.405359\pi$
$504$	−6.52324	−	22.9488i	−0.290568	−	1.02222i
$505$	−10.8897			−0.484587
$506$	5.82609	−	10.0911i	0.259001	−	0.448603i
$507$	−1.71890	−	0.213066i	−0.0763388	−	0.00946257i
$508$	−3.44235	−	5.96233i	−0.152730	−	0.264536i
$509$	15.5601	+	26.9508i	0.689687	+	1.19457i	0.971939	+	0.235233i	$0.0755854\pi$
$509$	15.5601	+	26.9508i	0.689687	+	1.19457i	−0.282252	+	0.959340i	$0.591081\pi$
$510$	−0.524215	−	1.23894i	−0.0232127	−	0.0548613i
$511$	20.0833	−	34.7853i	0.888433	−	1.53881i
$512$	22.5882			0.998267
$513$	−9.05615	−	3.51231i	−0.399839	−	0.155072i
$514$	−0.351936			−0.0155232
$515$	−0.768667	+	1.33137i	−0.0338715	+	0.0586672i
$516$	−8.99863	−	21.2676i	−0.396143	−	0.936253i
$517$	18.5472	+	32.1247i	0.815705	+	1.41284i
$518$	2.94590	+	5.10244i	0.129435	+	0.224189i
$519$	39.8286	+	4.93695i	1.74828	+	0.216708i
$520$	0.927880	−	1.60713i	0.0406902	−	0.0704775i
$521$	10.6889			0.468287			0.234144	−	0.972202i	$-0.424771\pi$
$521$	10.6889			0.468287			0.234144	+	0.972202i	$0.424771\pi$
$522$	−1.07851	−	0.271546i	−0.0472053	−	0.0118853i
$523$	−22.8750			−1.00025			−0.500127	−	0.865952i	$-0.666713\pi$
$523$	−22.8750			−1.00025			−0.500127	+	0.865952i	$0.666713\pi$
$524$	0.679897	−	1.17762i	0.0297014	−	0.0514444i
$525$	−4.47381	+	5.92272i	−0.195253	+	0.258489i
$526$	3.26178	+	5.64958i	0.142221	+	0.246333i
$527$	−8.01805	−	13.8877i	−0.349272	−	0.604957i
$528$	12.1503	−	16.0853i	0.528772	−	0.700024i
$529$	−2.32222	+	4.02220i	−0.100966	+	0.174878i
$530$	−0.0371840			−0.00161517
$531$	33.2834	+	8.38005i	1.44438	+	0.363663i
$532$	14.0660			0.609840
$533$	−3.18008	+	5.50806i	−0.137744	+	0.238580i
$534$	13.7998	+	1.71056i	0.597178	+	0.0740231i
$535$	−2.71902	−	4.70948i	−0.117553	−	0.203608i
$536$	−11.9673	−	20.7280i	−0.516909	−	0.895313i
$537$	9.39746	+	22.2102i	0.405530	+	0.958440i
$538$	4.52747	−	7.84181i	0.195193	−	0.338085i
$539$	50.9733			2.19558
$540$	7.11031	−	5.71721i	0.305979	−	0.246030i
$541$	−13.5880			−0.584192			−0.292096	−	0.956389i	$-0.594353\pi$
$541$	−13.5880			−0.584192			−0.292096	+	0.956389i	$0.594353\pi$
$542$	7.14220	−	12.3707i	0.306784	−	0.531365i
$543$	9.23867	+	21.8349i	0.396469	+	0.937025i
$544$	−3.92487	−	6.79808i	−0.168278	−	0.291465i
$545$	0.722331	+	1.25111i	0.0309413	+	0.0535919i
$546$	−3.63958	−	0.451143i	−0.155759	−	0.0193071i
$547$	−11.9818	+	20.7531i	−0.512305	+	0.887338i	0.487593	+	0.873071i	$0.337875\pi$
$547$	−11.9818	+	20.7531i	−0.512305	+	0.887338i	−0.999898	+	0.0142675i	$0.995458\pi$
$548$	−8.26680			−0.353140
$549$	9.81036	+	34.5129i	0.418696	+	1.47298i
$550$	2.21617			0.0944978
$551$	0.701293	−	1.21467i	0.0298761	−	0.0517469i
$552$	10.1862	−	13.4852i	0.433554	−	0.573968i
$553$	−13.0687	−	22.6356i	−0.555737	−	0.962564i
$554$	−6.45548	−	11.1812i	−0.274267	−	0.475045i
$555$	−2.90492	+	3.84572i	−0.123307	+	0.163242i
$556$	−6.11649	+	10.5941i	−0.259397	+	0.449289i
$557$	0.501996			0.0212702			0.0106351	−	0.999943i	$-0.496615\pi$
$557$	0.501996			0.0212702			0.0106351	+	0.999943i	$0.496615\pi$
$558$	−10.5292	+	10.8531i	−0.445737	+	0.459450i
$559$	−7.59324			−0.321160
$560$	−5.55989	+	9.63002i	−0.234948	+	0.406942i
$561$	−12.1194	−	1.50226i	−0.511683	−	0.0634257i
$562$	−6.83774	−	11.8433i	−0.288433	−	0.499580i
$563$	−8.45763	−	14.6490i	−0.356447	−	0.617384i	0.630918	−	0.775850i	$-0.282679\pi$
$563$	−8.45763	−	14.6490i	−0.356447	−	0.617384i	−0.987364	+	0.158466i	$0.949345\pi$
$564$	9.80090	+	23.1637i	0.412692	+	0.975367i
$565$	2.23239	−	3.86661i	0.0939173	−	0.162670i
$566$	12.9177			0.542971
$567$	−33.9701	−	18.2636i	−1.42661	−	0.767001i
$568$	−26.8095			−1.12490
$569$	12.0627	−	20.8931i	0.505693	−	0.875885i	−0.494286	−	0.869300i	$-0.664570\pi$
$569$	12.0627	−	20.8931i	0.505693	−	0.875885i	0.999978	−	0.00658582i	$-0.00209635\pi$
$570$	−0.623387	−	1.47333i	−0.0261108	−	0.0617109i
$571$	7.32786	+	12.6922i	0.306661	+	0.531153i	0.977630	−	0.210333i	$-0.0674548\pi$
$571$	7.32786	+	12.6922i	0.306661	+	0.531153i	−0.670968	+	0.741486i	$0.734121\pi$
$572$	−3.93780	−	6.82047i	−0.164648	−	0.285178i
$573$	13.4819	+	1.67115i	0.563215	+	0.0698133i
$574$	−6.73347	+	11.6627i	−0.281050	+	0.486792i
$575$	−5.25780			−0.219265
$576$	5.68676	−	5.86170i	0.236948	−	0.244238i
$577$	4.42835			0.184355			0.0921774	−	0.995743i	$-0.470617\pi$
$577$	4.42835			0.184355			0.0921774	+	0.995743i	$0.470617\pi$
$578$	3.58935	−	6.21693i	0.149297	−	0.258590i
$579$	−21.5598	+	28.5423i	−0.895995	+	1.18618i
$580$	0.658722	+	1.14094i	0.0273519	+	0.0473749i
$581$	1.31171	+	2.27195i	0.0544189	+	0.0942563i
$582$	−7.73423	+	10.2391i	−0.320594	+	0.424424i
$583$	−0.168774	+	0.292326i	−0.00698992	+	0.0121069i
$584$	−17.3939			−0.719765
$585$	−0.820261	−	2.88568i	−0.0339136	−	0.119308i
$586$	1.98454			0.0819806
$587$	3.40578	−	5.89899i	0.140572	−	0.243477i	−0.787140	−	0.616774i	$-0.788439\pi$
$587$	3.40578	−	5.89899i	0.140572	−	0.243477i	0.927712	+	0.373297i	$0.121773\pi$
$588$	34.2999	+	4.25164i	1.41451	+	0.175335i
$589$	−9.53492	−	16.5150i	−0.392879	−	0.680487i
$590$	2.82641	+	4.89548i	0.116361	+	0.201544i
$591$	2.96035	+	6.99655i	0.121772	+	0.287800i
$592$	−3.61013	+	6.25293i	−0.148375	+	0.256994i
$593$	9.71004			0.398744			0.199372	−	0.979924i	$-0.436110\pi$
$593$	9.71004			0.398744			0.199372	+	0.979924i	$0.436110\pi$
$594$	1.76208	+	11.3799i	0.0722992	+	0.466925i
$595$	6.73645			0.276168
$596$	−7.23177	+	12.5258i	−0.296225	+	0.513077i
$597$	−9.03835	−	21.3614i	−0.369915	−	0.874266i
$598$	−1.29893	−	2.24981i	−0.0531171	−	0.0920016i
$599$	−11.1367	−	19.2893i	−0.455032	−	0.788138i	0.543658	−	0.839307i	$-0.317039\pi$
$599$	−11.1367	−	19.2893i	−0.455032	−	0.788138i	−0.998690	+	0.0511684i	$0.983705\pi$
$600$	3.18986	+	0.395398i	0.130225	+	0.0161421i
$601$	−6.77115	+	11.7280i	−0.276201	+	0.478394i	−0.970437	−	0.241353i	$-0.922409\pi$
$601$	−6.77115	+	11.7280i	−0.276201	+	0.478394i	0.694236	+	0.719747i	$0.255742\pi$
$602$	−16.0779			−0.655285
$603$	−37.5214	−	9.44709i	−1.52799	−	0.384715i
$604$	15.4023			0.626710
$605$	4.55897	−	7.89637i	0.185348	−	0.321033i
$606$	5.61715	−	7.43636i	0.228181	−	0.302081i
$607$	2.38199	+	4.12572i	0.0966818	+	0.167458i	0.910309	−	0.413929i	$-0.135844\pi$
$607$	2.38199	+	4.12572i	0.0966818	+	0.167458i	−0.813627	+	0.581387i	$0.802510\pi$
$608$	−4.66739	−	8.08415i	−0.189288	−	0.327856i
$609$	3.35673	−	4.44387i	0.136022	−	0.180075i
$610$	−2.95470	+	5.11770i	−0.119633	+	0.207210i
$611$	8.27021			0.334577
$612$	−8.02986	−	2.02174i	−0.324588	−	0.0817242i
$613$	−7.58211			−0.306238			−0.153119	−	0.988208i	$-0.548932\pi$
$613$	−7.58211			−0.306238			−0.153119	+	0.988208i	$0.548932\pi$
$614$	1.85615	−	3.21494i	0.0749080	−	0.129745i
$615$	−10.9324	−	1.35513i	−0.440839	−	0.0546441i
$616$	−17.8350	−	30.8911i	−0.718593	−	1.24464i
$617$	−7.28208	−	12.6129i	−0.293166	−	0.507778i	0.681391	−	0.731920i	$-0.261375\pi$
$617$	−7.28208	−	12.6129i	−0.293166	−	0.507778i	−0.974556	+	0.224142i	$0.928042\pi$
$618$	−0.512669	−	1.21165i	−0.0206226	−	0.0487399i
$619$	21.3509	−	36.9808i	0.858165	−	1.48639i	−0.0155124	−	0.999880i	$-0.504938\pi$
$619$	21.3509	−	36.9808i	0.858165	−	1.48639i	0.873677	−	0.486506i	$-0.161729\pi$
$620$	17.9122			0.719373
$621$	−4.18049	−	26.9986i	−0.167757	−	1.08342i
$622$	10.3958			0.416835
$623$	−34.8155	+	60.3023i	−1.39486	+	2.41596i
$624$	−1.75131	−	4.13909i	−0.0701086	−	0.165696i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.60585	+	2.78141i	0.0641825	+	0.111167i
$627$	−14.4122	−	1.78646i	−0.575568	−	0.0713445i
$628$	−11.7588	+	20.3669i	−0.469228	+	0.812727i
$629$	4.37409			0.174406
$630$	−1.73681	−	6.11012i	−0.0691963	−	0.243433i
$631$	−35.7936			−1.42492			−0.712461	−	0.701712i	$-0.752419\pi$
$631$	−35.7936			−1.42492			−0.712461	+	0.701712i	$0.752419\pi$
$632$	−5.65931	+	9.80221i	−0.225115	+	0.389911i
$633$	−6.33674	+	8.38900i	−0.251863	+	0.333433i
$634$	2.83013	+	4.90193i	0.112399	+	0.194681i
$635$	−1.96048	−	3.39566i	−0.0777994	−	0.134753i
$636$	−0.137951	+	0.182629i	−0.00547011	+	0.00724169i
$637$	5.68226	−	9.84197i	0.225140	−	0.389953i
$638$	−1.66281			−0.0658313
$639$	−30.1782	+	31.1066i	−1.19383	+	1.23056i
$640$	11.3323			0.447948
$641$	−5.73418	+	9.93189i	−0.226486	+	0.392286i	−0.956764	−	0.290864i	$-0.906057\pi$
$641$	−5.73418	+	9.93189i	−0.226486	+	0.392286i	0.730278	+	0.683150i	$0.239391\pi$
$642$	4.61852	+	0.572488i	0.182278	+	0.0225943i
$643$	14.4978	+	25.1109i	0.571738	+	0.990279i	0.996388	+	0.0849212i	$0.0270639\pi$
$643$	14.4978	+	25.1109i	0.571738	+	0.990279i	−0.424650	+	0.905358i	$0.639603\pi$
$644$	19.7814	+	34.2623i	0.779494	+	1.35012i
$645$	−5.12489	−	12.1123i	−0.201792	−	0.476921i
$646$	−0.725959	+	1.25740i	−0.0285625	+	0.0494716i
$647$	−11.2588			−0.442630			−0.221315	−	0.975202i	$-0.571035\pi$
$647$	−11.2588			−0.442630			−0.221315	+	0.975202i	$0.571035\pi$
$648$	0.505911	+	16.6942i	0.0198741	+	0.655809i
$649$	51.3151			2.01430
$650$	0.247048	−	0.427900i	0.00969002	−	0.0167836i
$651$	−29.5056	−	69.7343i	−1.15642	−	2.73310i
$652$	−0.212850	−	0.368668i	−0.00833586	−	0.0144381i
$653$	17.2419	+	29.8639i	0.674729	+	1.16866i	0.976548	+	0.215299i	$0.0690726\pi$
$653$	17.2419	+	29.8639i	0.674729	+	1.16866i	−0.301820	+	0.953365i	$0.597594\pi$
$654$	−1.22695	−	0.152087i	−0.0479776	−	0.00594706i
$655$	0.387214	−	0.670674i	0.0151297	−	0.0262054i
$656$	−16.5034			−0.644351
$657$	−19.5795	+	20.1819i	−0.763871	+	0.787370i
$658$	17.5113			0.682660
$659$	−15.2334	+	26.3850i	−0.593408	+	1.02781i	0.400362	+	0.916357i	$0.368885\pi$
$659$	−15.2334	+	26.3850i	−0.593408	+	1.02781i	−0.993769	+	0.111455i	$0.964449\pi$
$660$	8.22188	−	10.8847i	0.320036	−	0.423685i
$661$	−10.7408	−	18.6036i	−0.417769	−	0.723597i	0.577946	−	0.816075i	$-0.303855\pi$
$661$	−10.7408	−	18.6036i	−0.417769	−	0.723597i	−0.995715	+	0.0924779i	$0.970521\pi$
$662$	6.01793	+	10.4234i	0.233893	+	0.405115i
$663$	−1.64108	+	2.17257i	−0.0637341	+	0.0843754i
$664$	0.568028	−	0.983853i	0.0220438	−	0.0381809i
$665$	8.01086			0.310648
$666$	−1.12774	−	3.96740i	−0.0436991	−	0.153734i
$667$	3.94497			0.152750
$668$	4.46527	−	7.73407i	0.172766	−	0.299240i
$669$	39.5142	+	4.89798i	1.52771	+	0.189367i
$670$	−3.18630	−	5.51883i	−0.123097	−	0.213211i
$671$	26.8222	+	46.4574i	1.03546	+	1.79347i
$672$	−14.4431	−	34.1353i	−0.557156	−	1.31680i
$673$	−4.55275	+	7.88559i	−0.175496	+	0.303967i	−0.940333	−	0.340256i	$-0.889486\pi$
$673$	−4.55275	+	7.88559i	−0.175496	+	0.303967i	0.764837	+	0.644224i	$0.222819\pi$
$674$	5.73160			0.220773
$675$	4.04945	−	3.25606i	0.155864	−	0.125326i
$676$	−1.75587			−0.0675334
$677$	−1.72288	+	2.98411i	−0.0662155	+	0.114689i	−0.897233	−	0.441558i	$-0.854426\pi$
$677$	−1.72288	+	2.98411i	−0.0662155	+	0.114689i	0.831017	+	0.556247i	$0.187759\pi$
$678$	1.48891	+	3.51893i	0.0571812	+	0.135144i
$679$	−32.1276	−	55.6467i	−1.23295	−	2.13552i
$680$	−1.45859	−	2.52635i	−0.0559343	−	0.0968811i
$681$	32.3748	+	4.01301i	1.24060	+	0.153779i
$682$	−11.3040	+	19.5790i	−0.432851	+	0.749720i
$683$	36.2676			1.38774			0.693870	−	0.720100i	$-0.255904\pi$
$683$	36.2676			1.38774			0.693870	+	0.720100i	$0.255904\pi$
$684$	−9.54896	−	2.40422i	−0.365114	−	0.0919277i
$685$	−4.70810			−0.179887
$686$	4.62071	−	8.00330i	0.176419	−	0.305567i
$687$	−5.64709	+	7.47600i	−0.215450	+	0.285227i
$688$	−9.85153	−	17.0633i	−0.375586	−	0.650534i
$689$	0.0376283	+	0.0651742i	0.00143353	+	0.00248294i
$690$	2.71208	−	3.59043i	0.103247	−	0.136685i
$691$	19.1163	−	33.1104i	0.727218	−	1.25958i	−0.230837	−	0.972993i	$-0.574146\pi$
$691$	19.1163	−	33.1104i	0.727218	−	1.25958i	0.958055	−	0.286586i	$-0.0925204\pi$
$692$	40.6853			1.54662
$693$	−55.9186	−	14.0791i	−2.12417	−	0.534820i
$694$	−6.01907			−0.228481
$695$	−3.48346	+	6.03352i	−0.132135	+	0.228865i
$696$	−2.39338	−	0.296671i	−0.0907207	−	0.0112453i
$697$	4.99895	+	8.65844i	0.189349	+	0.327962i
$698$	−1.95440	−	3.38512i	−0.0739752	−	0.128129i
$699$	−5.03451	−	11.8987i	−0.190423	−	0.450050i
$700$	−3.76229	+	6.51647i	−0.142201	+	0.246300i
$701$	−2.09523			−0.0791359			−0.0395679	−	0.999217i	$-0.512598\pi$
$701$	−2.09523			−0.0791359			−0.0395679	+	0.999217i	$0.512598\pi$
$702$	2.39368	+	0.928357i	0.0903435	+	0.0350386i
$703$	5.20159			0.196182
$704$	6.10519	−	10.5745i	0.230098	−	0.398542i
$705$	5.58179	+	13.1921i	0.210222	+	0.496845i
$706$	−5.25195	−	9.09665i	−0.197660	−	0.342357i
$707$	23.3334	+	40.4146i	0.877542	+	1.51995i
$708$	34.5299	+	4.28015i	1.29771	+	0.160858i
$709$	9.93869	−	17.2143i	0.373255	−	0.646497i	−0.616809	−	0.787113i	$-0.711575\pi$
$709$	9.93869	−	17.2143i	0.373255	−	0.646497i	0.990064	+	0.140616i	$0.0449082\pi$
$710$	−7.13803			−0.267885
$711$	5.00292	+	17.6003i	0.187624	+	0.660064i
$712$	30.1533			1.13004
$713$	26.8183	−	46.4507i	1.00435	−	1.73959i
$714$	−3.47480	+	4.60017i	−0.130041	+	0.172157i
$715$	−2.24265	−	3.88439i	−0.0838704	−	0.145268i
$716$	12.2241	+	21.1727i	0.456835	+	0.791261i
$717$	8.01844	−	10.6153i	0.299454	−	0.396437i
$718$	1.87667	−	3.25049i	0.0700367	−	0.121307i
$719$	−15.9997			−0.596687			−0.298344	−	0.954459i	$-0.596434\pi$
$719$	−15.9997			−0.596687			−0.298344	+	0.954459i	$0.596434\pi$
$720$	5.42043	−	5.58718i	0.202007	−	0.208222i
$721$	6.58807			0.245353
$722$	3.83061	−	6.63482i	0.142561	−	0.246922i
$723$	−50.3294	−	6.23858i	−1.87177	−	0.232015i
$724$	12.0175	+	20.8149i	0.446627	+	0.773581i
$725$	0.375154	+	0.649786i	0.0139329	+	0.0241325i
$726$	3.04064	+	7.18632i	0.112849	+	0.266709i
$727$	15.2862	−	26.4765i	0.566934	−	0.981959i	−0.429933	−	0.902861i	$-0.641463\pi$
$727$	15.2862	−	26.4765i	0.566934	−	0.981959i	0.996867	−	0.0790977i	$-0.0252039\pi$
$728$	−7.95265			−0.294745
$729$	19.9395	+	18.2049i	0.738499	+	0.674255i
$730$	−4.63113			−0.171406
$731$	−5.96813	+	10.3371i	−0.220739	+	0.382332i
$732$	14.1737	+	33.4984i	0.523874	+	1.23814i
$733$	−13.8308	−	23.9556i	−0.510852	−	0.884821i	−0.999921	−	0.0125762i	$-0.995997\pi$
$733$	−13.8308	−	23.9556i	−0.510852	−	0.884821i	0.489069	−	0.872245i	$-0.337337\pi$
$734$	−5.33973	−	9.24868i	−0.197093	−	0.341375i
$735$	19.5344	+	2.42139i	0.720539	+	0.0893143i
$736$	13.1277	−	22.7378i	0.483893	−	0.838127i
$737$	−57.8491			−2.13090
$738$	6.56457	−	6.76652i	0.241645	−	0.249079i
$739$	−2.03805			−0.0749710			−0.0374855	−	0.999297i	$-0.511935\pi$
$739$	−2.03805			−0.0749710			−0.0374855	+	0.999297i	$0.511935\pi$
$740$	−2.44292	+	4.23126i	−0.0898034	+	0.155544i
$741$	−1.95154	+	2.58357i	−0.0716915	+	0.0949100i
$742$	0.0796739	+	0.137999i	0.00292492	+	0.00506611i
$743$	−4.23249	−	7.33089i	−0.155275	−	0.268944i	0.777884	−	0.628408i	$-0.216293\pi$
$743$	−4.23249	−	7.33089i	−0.155275	−	0.268944i	−0.933159	+	0.359463i	$0.882960\pi$
$744$	−19.7636	+	26.1644i	−0.724570	+	0.959233i
$745$	−4.11863	+	7.13367i	−0.150895	+	0.261358i
$746$	−5.93575			−0.217323
$747$	−0.502146	−	1.76655i	−0.0183726	−	0.0646348i
$748$	−12.3801			−0.452662
$749$	−11.6520	+	20.1819i	−0.425756	+	0.737431i
$750$	0.849299	+	0.105275i	0.0310120	+	0.00384409i
$751$	9.34897	+	16.1929i	0.341149	+	0.590887i	0.984646	−	0.174561i	$-0.0558506\pi$
$751$	9.34897	+	16.1929i	0.341149	+	0.590887i	−0.643497	+	0.765448i	$0.722517\pi$
$752$	10.7298	+	18.5846i	0.391277	+	0.677711i
$753$	−17.9802	−	42.4949i	−0.655236	−	1.54860i
$754$	−0.185362	+	0.321057i	−0.00675049	+	0.0116922i
$755$	8.77188			0.319241
$756$	−36.4532	−	14.1379i	−1.32579	−	0.514191i
$757$	−4.02963			−0.146459			−0.0732296	−	0.997315i	$-0.523331\pi$
$757$	−4.02963			−0.146459			−0.0732296	+	0.997315i	$0.523331\pi$
$758$	0.849858	−	1.47200i	0.0308682	−	0.0534653i
$759$	−15.9167	−	37.6179i	−0.577739	−	1.36544i
$760$	−1.73453	−	3.00429i	−0.0629179	−	0.108977i
$761$	−8.21661	−	14.2316i	−0.297852	−	0.515895i	0.677792	−	0.735253i	$-0.262937\pi$
$761$	−8.21661	−	14.2316i	−0.297852	−	0.515895i	−0.975644	+	0.219359i	$0.929604\pi$
$762$	3.33008	+	0.412779i	0.120636	+	0.0149534i
$763$	3.09547	−	5.36151i	0.112063	−	0.194100i
$764$	13.7719			0.498250
$765$	−4.57315	−	1.15142i	−0.165343	−	0.0416297i
$766$	13.2906			0.480208
$767$	5.72037	−	9.90797i	0.206550	−	0.357756i
$768$	−0.161419	+	0.213697i	−0.00582471	+	0.00771114i
$769$	13.5335	+	23.4407i	0.488031	+	0.845295i	0.999905	−	0.0137657i	$-0.00438191\pi$
$769$	13.5335	+	23.4407i	0.488031	+	0.845295i	−0.511874	+	0.859060i	$0.671049\pi$
$770$	−4.74857	−	8.22477i	−0.171127	−	0.296400i
$771$	−0.743601	+	0.984428i	−0.0267801	+	0.0354533i
$772$	−18.1309	+	31.4037i	−0.652546	+	1.13024i
$773$	−50.3630			−1.81143			−0.905716	−	0.423886i	$-0.860666\pi$
$773$	−50.3630			−1.81143			−0.905716	+	0.423886i	$0.860666\pi$
$774$	10.9147	+	2.74809i	0.392322	+	0.0987781i
$775$	10.2013			0.366443
$776$	−13.9127	+	24.0975i	−0.499436	+	0.865048i
$777$	20.4968	+	2.54068i	0.735318	+	0.0911463i
$778$	−0.823942	−	1.42711i	−0.0295398	−	0.0511644i
$779$	5.94466	+	10.2965i	0.212990	+	0.368909i
$780$	−1.18508	−	2.80086i	−0.0424328	−	0.100287i
$781$	−32.3988	+	56.1163i	−1.15932	+	2.00800i
$782$	−4.08372			−0.146034
$783$	−3.03834	+	2.44305i	−0.108581	+	0.0873075i
$784$	29.4889			1.05317
$785$	−6.69687	+	11.5993i	−0.239021	+	0.413997i
$786$	0.258255	+	0.610367i	0.00921166	+	0.0217711i
$787$	17.9756	+	31.1346i	0.640760	+	1.10983i	0.985263	+	0.171044i	$0.0547141\pi$
$787$	17.9756	+	31.1346i	0.640760	+	1.10983i	−0.344503	+	0.938785i	$0.611953\pi$
$788$	3.85077	+	6.66973i	0.137178	+	0.237599i
$789$	22.6946	+	2.81311i	0.807951	+	0.100149i
$790$	−1.50679	+	2.60984i	−0.0536092	+	0.0928539i
$791$	−19.1333			−0.680302
$792$	6.82756	+	24.0194i	0.242607	+	0.853492i
$793$	11.9600			0.424714
$794$	−0.189903	+	0.328921i	−0.00673939	+	0.0116730i
$795$	−0.0785656	+	0.104010i	−0.00278643	+	0.00368887i
$796$	−11.7569	−	20.3636i	−0.416713	−	0.721769i
$797$	16.1395	+	27.9544i	0.571690	+	0.990196i	0.996393	+	0.0848631i	$0.0270453\pi$
$797$	16.1395	+	27.9544i	0.571690	+	0.990196i	−0.424703	+	0.905333i	$0.639621\pi$
$798$	−4.13217	+	5.47044i	−0.146277	+	0.193651i
$799$	6.50022	−	11.2587i	0.229961	−	0.398304i
$800$	4.99361			0.176551
$801$	33.9422	−	34.9864i	1.19929	−	1.23618i
$802$	14.6268			0.516489
$803$	−21.0202	+	36.4081i	−0.741787	+	1.28481i
$804$	−38.9266	−	4.82515i	−1.37284	−	0.170170i
$805$	11.2658	+	19.5130i	0.397069	+	0.687743i
$806$	2.52022	+	4.36515i	0.0887710	+	0.153756i
$807$	−12.3689	−	29.2330i	−0.435407	−	1.02905i
$808$	10.1044	−	17.5013i	0.355471	−	0.615693i
$809$	42.4707			1.49319			0.746594	−	0.665279i	$-0.231688\pi$
$809$	42.4707			1.49319			0.746594	+	0.665279i	$0.231688\pi$
$810$	0.134699	+	4.44482i	0.00473283	+	0.156175i
$811$	−14.1284			−0.496116			−0.248058	−	0.968745i	$-0.579792\pi$
$811$	−14.1284			−0.496116			−0.248058	+	0.968745i	$0.579792\pi$
$812$	2.82288	−	4.88937i	0.0990636	−	0.171583i
$813$	−19.5123	−	46.1158i	−0.684325	−	1.61735i
$814$	−3.08333	−	5.34048i	−0.108071	−	0.187184i
$815$	−0.121222	−	0.209963i	−0.00424623	−	0.00735468i
$816$	−7.01128	−	0.869083i	−0.245444	−	0.0304240i
$817$	−7.09719	+	12.2927i	−0.248299	+	0.430067i
$818$	−8.00489			−0.279885
$819$	−8.95193	+	9.22733i	−0.312806	+	0.322429i
$820$	−11.1676			−0.389990
$821$	22.0898	−	38.2606i	0.770939	−	1.33531i	−0.166110	−	0.986107i	$-0.553121\pi$
$821$	22.0898	−	38.2606i	0.770939	−	1.33531i	0.937049	−	0.349198i	$-0.113546\pi$
$822$	2.42853	−	3.21505i	0.0847048	−	0.112138i
$823$	13.1598	+	22.7934i	0.458721	+	0.794529i	0.998894	−	0.0470259i	$-0.0149743\pi$
$823$	13.1598	+	22.7934i	0.458721	+	0.794529i	−0.540172	+	0.841554i	$0.681641\pi$
$824$	−1.42646	−	2.47070i	−0.0496932	−	0.0860711i
$825$	4.68251	−	6.19902i	0.163024	−	0.215822i
$826$	12.1123	−	20.9790i	0.421439	−	0.729954i
$827$	−52.3359			−1.81990			−0.909949	−	0.414720i	$-0.863879\pi$
$827$	−52.3359			−1.81990			−0.909949	+	0.414720i	$0.863879\pi$
$828$	−7.57265	−	26.6407i	−0.263168	−	0.925827i
$829$	−44.0239			−1.52901			−0.764506	−	0.644617i	$-0.777017\pi$
$829$	−44.0239			−1.52901			−0.764506	+	0.644617i	$0.777017\pi$
$830$	0.151237	−	0.261951i	0.00524953	−	0.00909245i
$831$	−44.9156	−	5.56751i	−1.55810	−	0.193135i
$832$	−1.36116	−	2.35759i	−0.0471896	−	0.0817347i
$833$	−8.93229	−	15.4712i	−0.309485	−	0.536045i
$834$	−2.32332	−	5.49099i	−0.0804500	−	0.190137i
$835$	2.54305	−	4.40470i	0.0880059	−	0.152431i
$836$	−14.7222			−0.509179
$837$	8.11113	+	52.3835i	0.280362	+	1.81064i
$838$	5.63896			0.194795
$839$	−3.99553	+	6.92046i	−0.137941	+	0.238921i	−0.926717	−	0.375760i	$-0.877382\pi$
$839$	−3.99553	+	6.92046i	−0.137941	+	0.238921i	0.788776	+	0.614681i	$0.210715\pi$
$840$	−5.36746	−	12.6856i	−0.185195	−	0.437694i
$841$	14.2185	+	24.6272i	0.490294	+	0.849214i
$842$	−2.56889	−	4.44944i	−0.0885297	−	0.153338i
$843$	−47.5752	−	5.89719i	−1.63858	−	0.203110i
$844$	−5.32894	+	9.23000i	−0.183430	+	0.317710i
$845$	−1.00000			−0.0344010
$846$	−11.8878	−	2.99310i	−0.408712	−	0.102905i
$847$	−39.0739			−1.34259
$848$	−0.0976386	+	0.169115i	−0.00335292	+	0.00580743i
$849$	27.2936	−	36.1331i	0.936714	−	1.24008i
$850$	−0.388349	−	0.672641i	−0.0133203	−	0.0230714i
$851$	7.31510	+	12.6701i	0.250758	+	0.434326i
$852$	−26.4817	+	35.0583i	−0.907249	+	1.20108i
$853$	8.36352	−	14.4860i	0.286361	−	0.495992i	−0.686577	−	0.727057i	$-0.740888\pi$
$853$	8.36352	−	14.4860i	0.286361	−	0.495992i	0.972938	+	0.231065i	$0.0742209\pi$
$854$	25.3241			0.866573
$855$	−5.43831	−	1.36925i	−0.185986	−	0.0468273i
$856$	10.0917			0.344927
$857$	−11.7587	+	20.3667i	−0.401669	+	0.695712i	−0.993928	−	0.110037i	$-0.964903\pi$
$857$	−11.7587	+	20.3667i	−0.401669	+	0.695712i	0.592258	+	0.805748i	$0.298237\pi$
$858$	3.80936	+	0.472189i	0.130050	+	0.0161203i
$859$	9.92549	+	17.1914i	0.338653	+	0.586565i	0.984180	−	0.177173i	$-0.0566953\pi$
$859$	9.92549	+	17.1914i	0.338653	+	0.586565i	−0.645526	+	0.763738i	$0.723362\pi$
$860$	−6.66637	−	11.5465i	−0.227321	−	0.393732i
$861$	18.3956	+	43.4767i	0.626922	+	1.48168i
$862$	0.217395	−	0.376540i	0.00740451	−	0.0128250i
$863$	11.3010			0.384690			0.192345	−	0.981327i	$-0.438391\pi$
$863$	11.3010			0.384690			0.192345	+	0.981327i	$0.438391\pi$
$864$	3.97043	+	25.6420i	0.135077	+	0.872358i
$865$	23.1711			0.787839
$866$	−7.77120	+	13.4601i	−0.264076	+	0.457393i
$867$	−9.80599	−	23.1757i	−0.333029	−	0.787088i
$868$	−38.3804	−	66.4768i	−1.30272	−	2.25637i
$869$	13.6783	+	23.6916i	0.464006	+	0.803682i
$870$	−0.637237	−	0.0789886i	−0.0216043	−	0.00267796i
$871$	−6.44874	+	11.1696i	−0.218507	+	0.378466i
$872$	−2.68095			−0.0907883
$873$	12.2990	+	43.2681i	0.416259	+	1.46440i
$874$	−4.85629			−0.164266
$875$	−2.14269	+	3.71125i	−0.0724362	+	0.125463i
$876$	−17.1813	+	22.7457i	−0.580501	+	0.768506i
$877$	−23.6189	−	40.9091i	−0.797552	−	1.38140i	−0.921206	−	0.389076i	$-0.872794\pi$
$877$	−23.6189	−	40.9091i	−0.797552	−	1.38140i	0.123653	−	0.992325i	$-0.460539\pi$
$878$	1.42402	+	2.46647i	0.0480583	+	0.0832395i
$879$	4.19310	−	5.55111i	0.141430	−	0.187234i
$880$	5.81927	−	10.0793i	0.196167	−	0.339772i
$881$	5.64812			0.190290			0.0951450	−	0.995463i	$-0.469669\pi$
$881$	5.64812			0.190290			0.0951450	+	0.995463i	$0.469669\pi$
$882$	−11.7298	+	12.0906i	−0.394962	+	0.407113i
$883$	16.3032			0.548645			0.274323	−	0.961638i	$-0.411546\pi$
$883$	16.3032			0.548645			0.274323	+	0.961638i	$0.411546\pi$
$884$	−1.38008	+	2.39036i	−0.0464170	+	0.0803967i
$885$	19.6654	+	2.43763i	0.661046	+	0.0819399i
$886$	−1.01993	−	1.76657i	−0.0342652	−	0.0593490i
$887$	18.8459	+	32.6420i	0.632783	+	1.09601i	0.986980	+	0.160842i	$0.0514208\pi$
$887$	18.8459	+	32.6420i	0.632783	+	1.09601i	−0.354197	+	0.935171i	$0.615246\pi$
$888$	−3.48518	−	8.23696i	−0.116955	−	0.276414i
$889$	−8.40143	+	14.5517i	−0.281775	+	0.488048i
$890$	8.02832			0.269110
$891$	35.5548	+	19.1157i	1.19113	+	0.640398i
$892$	40.3642			1.35149
$893$	7.72993	−	13.3886i	0.258672	−	0.448034i
$894$	−2.74695	−	6.49221i	−0.0918718	−	0.217132i
$895$	6.96183	+	12.0582i	0.232708	+	0.403063i
$896$	−24.2816	−	42.0570i	−0.811192	−	1.40503i
$897$	−9.03761	−	1.12026i	−0.301757	−	0.0374043i
$898$	7.49548	−	12.9826i	0.250127	−	0.433233i
$899$	−7.65416			−0.255280
$900$	3.66791	−	3.78075i	0.122264	−	0.126025i
$901$	0.118300			0.00394116
$902$	7.04759	−	12.2068i	0.234659	−	0.406442i
$903$	−33.9707	+	44.9727i	−1.13047	+	1.49660i
$904$	4.14278	+	7.17550i	0.137787	+	0.238654i
$905$	6.84419	+	11.8545i	0.227509	+	0.394057i
$906$	−4.52471	+	5.99012i	−0.150324	+	0.199008i
$907$	−11.9264	+	20.6571i	−0.396009	+	0.685908i	−0.993229	−	0.116169i	$-0.962939\pi$
$907$	−11.9264	+	20.6571i	−0.396009	+	0.685908i	0.597220	+	0.802077i	$0.296272\pi$
$908$	33.0712			1.09751
$909$	−8.93243	−	31.4244i	−0.296270	−	1.04228i
$910$	−2.11739			−0.0701908
$911$	−23.3805	+	40.4962i	−0.774630	+	1.34170i	0.160372	+	0.987057i	$0.448731\pi$
$911$	−23.3805	+	40.4962i	−0.774630	+	1.34170i	−0.935002	+	0.354642i	$0.884603\pi$
$912$	−8.33768	−	1.03350i	−0.276088	−	0.0342225i
$913$	−1.37290	−	2.37794i	−0.0454364	−	0.0786982i
$914$	2.09072	+	3.62124i	0.0691550	+	0.119780i
$915$	8.07217	+	19.0780i	0.266858	+	0.630698i
$916$	−4.74897	+	8.22546i	−0.156910	+	0.271777i
$917$	−3.31872			−0.109594
$918$	3.14521	−	2.52898i	0.103807	−	0.0834687i
$919$	−12.3909			−0.408738			−0.204369	−	0.978894i	$-0.565514\pi$
$919$	−12.3909			−0.408738			−0.204369	+	0.978894i	$0.565514\pi$
$920$	4.87860	−	8.44999i	0.160843	−	0.278588i
$921$	−5.07094	−	11.9848i	−0.167093	−	0.394912i
$922$	−4.35566	−	7.54422i	−0.143446	−	0.248456i
$923$	7.22332	+	12.5112i	0.237758	+	0.411810i
$924$	−58.0127	−	7.19096i	−1.90848	−	0.236565i
$925$	−1.39129	+	2.40978i	−0.0457452	+	0.0792330i
$926$	−0.619787			−0.0203675
$927$	−4.47242	−	1.12606i	−0.146894	−	0.0369846i
$928$	−3.74675			−0.122993
$929$	−5.11063	+	8.85188i	−0.167674	+	0.290421i	−0.937602	−	0.347711i	$-0.886959\pi$
$929$	−5.11063	+	8.85188i	−0.167674	+	0.290421i	0.769927	+	0.638132i	$0.220292\pi$
$930$	−5.26206	+	6.96627i	−0.172550	+	0.228433i
$931$	−10.6221	−	18.3980i	−0.348126	−	0.602971i
$932$	−6.54881	−	11.3429i	−0.214513	−	0.371548i
$933$	21.9652	−	29.0790i	0.719108	−	0.952003i
$934$	−2.79555	+	4.84204i	−0.0914733	+	0.158436i
$935$	−7.05071			−0.230583
$936$	5.39879	+	1.35930i	0.176465	+	0.0444300i
$937$	23.8520			0.779212			0.389606	−	0.920982i	$-0.372611\pi$
$937$	23.8520			0.779212			0.389606	+	0.920982i	$0.372611\pi$
$938$	−13.6545	+	23.6503i	−0.445836	+	0.772210i
$939$	11.1731	+	1.38496i	0.364619	+	0.0451963i
$940$	7.26070	+	12.5759i	0.236818	+	0.410181i
$941$	12.6596	+	21.9271i	0.412692	+	0.714804i	0.995183	−	0.0980332i	$-0.0312551\pi$
$941$	12.6596	+	21.9271i	0.412692	+	0.714804i	−0.582491	+	0.812837i	$0.697922\pi$
$942$	−4.46653	−	10.5563i	−0.145527	−	0.343943i
$943$	−16.7202	+	28.9602i	−0.544485	+	0.943075i
$944$	29.6866			0.966216
$945$	−20.7608	−	8.05181i	−0.675349	−	0.261925i
$946$	16.8279			0.547122
$947$	11.5509	−	20.0068i	0.375355	−	0.650134i	−0.615025	−	0.788508i	$-0.710854\pi$
$947$	11.5509	−	20.0068i	0.375355	−	0.650134i	0.990380	+	0.138374i	$0.0441875\pi$
$948$	7.22805	+	17.0829i	0.234756	+	0.554828i
$949$	4.68647	+	8.11720i	0.152129	+	0.263495i
$950$	−0.461818	−	0.799892i	−0.0149833	−	0.0259519i
$951$	19.6913	+	2.44084i	0.638535	+	0.0791496i
$952$	−6.25062	+	10.8264i	−0.202584	+	0.350885i
$953$	46.4511			1.50470			0.752350	−	0.658764i	$-0.228920\pi$
$953$	46.4511			1.50470			0.752350	+	0.658764i	$0.228920\pi$
$954$	−0.0305006	−	0.107301i	−0.000987493	−	0.00347401i
$955$	7.84336			0.253805
$956$	6.74318	−	11.6795i	0.218090	−	0.377743i
$957$	−3.51333	+	4.65118i	−0.113570	+	0.150351i
$958$	8.24734	+	14.2848i	0.266460	+	0.461521i
$959$	10.0880	+	17.4729i	0.325759	+	0.564231i
$960$	2.84200	−	3.76244i	0.0917253	−	0.121432i
$961$	−36.5337	+	63.2783i	−1.17851	+	2.04124i
$962$	−1.37486			−0.0443272
$963$	11.3598	−	11.7092i	0.366063	−	0.377324i
$964$	−51.4120			−1.65587
$965$	−10.3259	+	17.8850i	−0.332402	+	0.575737i
$966$	−19.1362	−	2.37202i	−0.615696	−	0.0763185i
$967$	3.87128	+	6.70525i	0.124492	+	0.215626i	0.921534	−	0.388297i	$-0.126937\pi$
$967$	3.87128	+	6.70525i	0.124492	+	0.215626i	−0.797042	+	0.603923i	$0.793603\pi$
$968$	8.46035	+	14.6538i	0.271926	+	0.470990i
$969$	1.98330	+	4.68737i	0.0637127	+	0.150580i
$970$	−3.70425	+	6.41595i	−0.118936	+	0.206004i
$971$	−2.78737			−0.0894511			−0.0447256	−	0.998999i	$-0.514241\pi$
$971$	−2.78737			−0.0894511			−0.0447256	+	0.998999i	$0.514241\pi$
$972$	22.3304	+	15.8285i	0.716247	+	0.507699i
$973$	29.8559			0.957136
$974$	10.4453	−	18.0919i	0.334690	−	0.579701i
$975$	−0.674928	−	1.59514i	−0.0216150	−	0.0510854i
$976$	15.5171	+	26.8763i	0.496689	+	0.860290i
$977$	5.73927	+	9.94071i	0.183616	+	0.318031i	0.943109	−	0.332483i	$-0.107887\pi$
$977$	5.73927	+	9.94071i	0.183616	+	0.318031i	−0.759494	+	0.650515i	$0.774553\pi$
$978$	0.205908	+	0.0255233i	0.00658421	+	0.000816145i
$979$	36.4397	−	63.1154i	1.16462	−	2.01718i
$980$	19.9546			0.637427
$981$	−3.01782	+	3.11066i	−0.0963516	+	0.0993157i
$982$	5.66517			0.180783
$983$	14.4750	−	25.0714i	0.461679	−	0.799652i	−0.537366	−	0.843349i	$-0.680580\pi$
$983$	14.4750	−	25.0714i	0.461679	−	0.799652i	0.999045	+	0.0436975i	$0.0139138\pi$
$984$	12.3219	−	16.3125i	0.392807	−	0.520024i
$985$	2.19308	+	3.79853i	0.0698775	+	0.121031i
$986$	0.291382	+	0.504688i	0.00927949	+	0.0160725i
$987$	36.9993	−	48.9821i	1.17770	−	1.55912i
$988$	−1.64116	+	2.84258i	−0.0522123	+	0.0904344i
$989$	−39.9237			−1.26950
$990$	1.81784	+	6.39516i	0.0577747	+	0.203252i
$991$	−5.40688			−0.171755			−0.0858776	−	0.996306i	$-0.527369\pi$
$991$	−5.40688			−0.171755			−0.0858776	+	0.996306i	$0.527369\pi$
$992$	−25.4708	+	44.1167i	−0.808697	+	1.40071i
$993$	41.8712	+	5.19014i	1.32874	+	0.164704i
$994$	15.2946	+	26.4910i	0.485115	+	0.840244i
$995$	−6.69579	−	11.5974i	−0.212271	−	0.367664i
$996$	−0.725483	−	1.71462i	−0.0229878	−	0.0543299i
$997$	18.4622	−	31.9774i	0.584703	−	1.01273i	−0.410210	−	0.911991i	$-0.634545\pi$
$997$	18.4622	−	31.9774i	0.584703	−	1.01273i	0.994912	−	0.100743i	$-0.0321221\pi$
$998$	3.31466			0.104924
$999$	−13.4803	−	5.22818i	−0.426499	−	0.165412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.e.196.5	✓	16
3.2	odd	2		1755.2.i.f.586.4		16
9.2	odd	6		5265.2.a.ba.1.5		8
9.4	even	3	inner	585.2.i.e.391.5	yes	16
9.5	odd	6		1755.2.i.f.1171.4		16
9.7	even	3		5265.2.a.bf.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.e.196.5	✓	16	1.1	even	1	trivial
585.2.i.e.391.5	yes	16	9.4	even	3	inner
1755.2.i.f.586.4		16	3.2	odd	2
1755.2.i.f.1171.4		16	9.5	odd	6
5265.2.a.ba.1.5		8	9.2	odd	6
5265.2.a.bf.1.4		8	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.247048 + 0.427900i) q^{2} +(0.674928 + 1.59514i) q^{3} +(0.877935 + 1.52063i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.849299 - 0.105275i) q^{6} +(2.14269 - 3.71125i) q^{7} -1.85576 q^{8} +(-2.08895 + 2.15321i) q^{9} +O(q^{10})\)	\(q+(-0.247048 + 0.427900i) q^{2} +(0.674928 + 1.59514i) q^{3} +(0.877935 + 1.52063i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.849299 - 0.105275i) q^{6} +(2.14269 - 3.71125i) q^{7} -1.85576 q^{8} +(-2.08895 + 2.15321i) q^{9} -0.494096 q^{10} +(-2.24265 + 3.88439i) q^{11} +(-1.83307 + 2.42674i) q^{12} +(0.500000 + 0.866025i) q^{13} +(1.05870 + 1.83371i) q^{14} +(-1.04397 + 1.38207i) q^{15} +(-1.29741 + 2.24718i) q^{16} +1.57196 q^{17} +(-0.405288 - 1.42580i) q^{18} +1.86934 q^{19} +(-0.877935 + 1.52063i) q^{20} +(7.36613 + 0.913068i) q^{21} +(-1.10808 - 1.91926i) q^{22} +(2.62890 + 4.55339i) q^{23} +(-1.25250 - 2.96020i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.494096 q^{26} +(-4.84456 - 1.87890i) q^{27} +7.52458 q^{28} +(0.375154 - 0.649786i) q^{29} +(-0.333479 - 0.788152i) q^{30} +(-5.10067 - 8.83463i) q^{31} +(-2.49680 - 4.32459i) q^{32} +(-7.70977 - 0.955664i) q^{33} +(-0.388349 + 0.672641i) q^{34} +4.28539 q^{35} +(-5.10819 - 1.28613i) q^{36} +2.78257 q^{37} +(-0.461818 + 0.799892i) q^{38} +(-1.04397 + 1.38207i) q^{39} +(-0.927880 - 1.60713i) q^{40} +(3.18008 + 5.50806i) q^{41} +(-2.21049 + 2.92639i) q^{42} +(-3.79662 + 6.57594i) q^{43} -7.87560 q^{44} +(-2.90921 - 0.732475i) q^{45} -2.59786 q^{46} +(4.13510 - 7.16221i) q^{47} +(-4.46022 - 0.552866i) q^{48} +(-5.68226 - 9.84197i) q^{49} +(-0.247048 - 0.427900i) q^{50} +(1.06096 + 2.50750i) q^{51} +(-0.877935 + 1.52063i) q^{52} +0.0752567 q^{53} +(2.00082 - 1.60881i) q^{54} -4.48530 q^{55} +(-3.97632 + 6.88719i) q^{56} +(1.26167 + 2.98187i) q^{57} +(0.185362 + 0.321057i) q^{58} +(-5.72037 - 9.90797i) q^{59} +(-3.01816 - 0.374115i) q^{60} +(5.98002 - 10.3577i) q^{61} +5.04044 q^{62} +(3.51513 + 12.3663i) q^{63} -2.72231 q^{64} +(-0.500000 + 0.866025i) q^{65} +(2.31361 - 3.06291i) q^{66} +(6.44874 + 11.1696i) q^{67} +(1.38008 + 2.39036i) q^{68} +(-5.48897 + 7.26667i) q^{69} +(-1.05870 + 1.83371i) q^{70} +14.4466 q^{71} +(3.87658 - 3.99584i) q^{72} +9.37293 q^{73} +(-0.687429 + 1.19066i) q^{74} +(-1.71890 - 0.213066i) q^{75} +(1.64116 + 2.84258i) q^{76} +(9.61062 + 16.6461i) q^{77} +(-0.333479 - 0.788152i) q^{78} +(3.04959 - 5.28205i) q^{79} -2.59482 q^{80} +(-0.272617 - 8.99587i) q^{81} -3.14253 q^{82} +(-0.306089 + 0.530162i) q^{83} +(5.07855 + 12.0028i) q^{84} +(0.785980 + 1.36136i) q^{85} +(-1.87589 - 3.24914i) q^{86} +(1.28970 + 0.159865i) q^{87} +(4.16182 - 7.20849i) q^{88} -16.2485 q^{89} +(1.03214 - 1.06389i) q^{90} +4.28539 q^{91} +(-4.61600 + 7.99515i) q^{92} +(10.6499 - 14.0990i) q^{93} +(2.04314 + 3.53882i) q^{94} +(0.934672 + 1.61890i) q^{95} +(5.21317 - 6.90154i) q^{96} +(7.49702 - 12.9852i) q^{97} +5.61517 q^{98} +(-3.67912 - 12.9432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9	\( 16 q - 3 q^{2} + q^{3} - 9 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 12 q^{8} + q^{9} - 6 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 10 q^{14} + 5 q^{15} - 11 q^{16} - 4 q^{17} + 5 q^{18} - 20 q^{19} + 9 q^{20} + 11 q^{21} - 3 q^{22} - 6 q^{23} - 57 q^{24} - 8 q^{25} - 6 q^{26} - 14 q^{27} - 68 q^{28} - 14 q^{29} + 7 q^{30} + 31 q^{31} - q^{32} - 31 q^{33} + 7 q^{34} + 22 q^{35} + 2 q^{36} + 2 q^{37} - 9 q^{38} + 5 q^{39} - 6 q^{40} + 12 q^{41} - 26 q^{42} - 15 q^{43} + 32 q^{44} - 16 q^{45} - 64 q^{46} + 18 q^{47} - 4 q^{48} - 17 q^{49} - 3 q^{50} + 32 q^{51} + 9 q^{52} + 4 q^{53} + 2 q^{54} - 12 q^{55} - 16 q^{56} + 45 q^{57} + 42 q^{58} - 24 q^{59} - 8 q^{60} + 9 q^{61} - 40 q^{62} + 47 q^{63} - 60 q^{64} - 8 q^{65} + 55 q^{66} + 18 q^{67} + 14 q^{68} - 12 q^{69} + 10 q^{70} + 20 q^{71} - 9 q^{72} + 12 q^{73} + 37 q^{74} + 4 q^{75} + 53 q^{76} + 34 q^{77} + 7 q^{78} + 3 q^{79} - 22 q^{80} + 13 q^{81} - 68 q^{82} + 10 q^{83} + 22 q^{84} - 2 q^{85} - 60 q^{86} + 11 q^{87} + 14 q^{88} - 26 q^{89} + 19 q^{90} + 22 q^{91} - 5 q^{92} + 74 q^{93} - 17 q^{94} - 10 q^{95} + 13 q^{96} + 34 q^{97} - 60 q^{98} - 43 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 + q^3 - 9 * q^4 + 8 * q^5 + 8 * q^6 + 11 * q^7 - 12 * q^8 + q^9 - 6 * q^10 - 6 * q^11 + 2 * q^12 + 8 * q^13 - 10 * q^14 + 5 * q^15 - 11 * q^16 - 4 * q^17 + 5 * q^18 - 20 * q^19 + 9 * q^20 + 11 * q^21 - 3 * q^22 - 6 * q^23 - 57 * q^24 - 8 * q^25 - 6 * q^26 - 14 * q^27 - 68 * q^28 - 14 * q^29 + 7 * q^30 + 31 * q^31 - q^32 - 31 * q^33 + 7 * q^34 + 22 * q^35 + 2 * q^36 + 2 * q^37 - 9 * q^38 + 5 * q^39 - 6 * q^40 + 12 * q^41 - 26 * q^42 - 15 * q^43 + 32 * q^44 - 16 * q^45 - 64 * q^46 + 18 * q^47 - 4 * q^48 - 17 * q^49 - 3 * q^50 + 32 * q^51 + 9 * q^52 + 4 * q^53 + 2 * q^54 - 12 * q^55 - 16 * q^56 + 45 * q^57 + 42 * q^58 - 24 * q^59 - 8 * q^60 + 9 * q^61 - 40 * q^62 + 47 * q^63 - 60 * q^64 - 8 * q^65 + 55 * q^66 + 18 * q^67 + 14 * q^68 - 12 * q^69 + 10 * q^70 + 20 * q^71 - 9 * q^72 + 12 * q^73 + 37 * q^74 + 4 * q^75 + 53 * q^76 + 34 * q^77 + 7 * q^78 + 3 * q^79 - 22 * q^80 + 13 * q^81 - 68 * q^82 + 10 * q^83 + 22 * q^84 - 2 * q^85 - 60 * q^86 + 11 * q^87 + 14 * q^88 - 26 * q^89 + 19 * q^90 + 22 * q^91 - 5 * q^92 + 74 * q^93 - 17 * q^94 - 10 * q^95 + 13 * q^96 + 34 * q^97 - 60 * q^98 - 43 * q^99

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