LMFDB - Embedded newform 385.2.i.b.331.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 12 x^{9} + 49 x^{8} - 38 x^{7} + 136 x^{6} - 34 x^{5} + 113 x^{4} + \cdots + 4 $ x^12 - 3x^11 + 13x^10 - 12x^9 + 49x^8 - 38x^7 + 136x^6 - 34x^5 + 113x^4 - 72x^3 + 58x^2 - 16*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.6
Root			$-0.863590 + 1.49578i$ of defining polynomial
Character	$\chi$	$=$	385.331
Dual form			385.2.i.b.221.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36359 - 2.36181i) q^{2} +(-1.13978 - 1.97415i) q^{3} +(-2.71876 - 4.70902i) q^{4} +(0.500000 - 0.866025i) q^{5} -6.21675 q^{6} +(2.56678 + 0.641581i) q^{7} -9.37471 q^{8} +(-1.09818 + 1.90211i) q^{9} +O(q^{10})$	\(q+(1.36359 - 2.36181i) q^{2} +(-1.13978 - 1.97415i) q^{3} +(-2.71876 - 4.70902i) q^{4} +(0.500000 - 0.866025i) q^{5} -6.21675 q^{6} +(2.56678 + 0.641581i) q^{7} -9.37471 q^{8} +(-1.09818 + 1.90211i) q^{9} +(-1.36359 - 2.36181i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-6.19755 + 10.7345i) q^{12} +5.46801 q^{13} +(5.01533 - 5.18739i) q^{14} -2.27955 q^{15} +(-7.34575 + 12.7232i) q^{16} +(2.36300 + 4.09284i) q^{17} +(2.99494 + 5.18739i) q^{18} +(1.18137 - 2.04619i) q^{19} -5.43751 q^{20} +(-1.65898 - 5.79848i) q^{21} +2.72718 q^{22} +(0.590344 - 1.02251i) q^{23} +(10.6851 + 18.5071i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(7.45613 - 12.9144i) q^{26} -1.83193 q^{27} +(-3.95723 - 13.8313i) q^{28} -6.61349 q^{29} +(-3.10838 + 5.38387i) q^{30} +(3.47286 + 6.01518i) q^{31} +(10.6585 + 18.4610i) q^{32} +(1.13978 - 1.97415i) q^{33} +12.8887 q^{34} +(1.83902 - 1.90211i) q^{35} +11.9428 q^{36} +(-2.70479 + 4.68483i) q^{37} +(-3.22181 - 5.58034i) q^{38} +(-6.23232 - 10.7947i) q^{39} +(-4.68736 + 8.11874i) q^{40} +1.79671 q^{41} +(-15.9571 - 3.98855i) q^{42} -9.46684 q^{43} +(2.71876 - 4.70902i) q^{44} +(1.09818 + 1.90211i) q^{45} +(-1.60997 - 2.78856i) q^{46} +(-2.80546 + 4.85920i) q^{47} +33.4901 q^{48} +(6.17675 + 3.29360i) q^{49} -2.72718 q^{50} +(5.38660 - 9.32986i) q^{51} +(-14.8662 - 25.7490i) q^{52} +(2.38962 + 4.13895i) q^{53} +(-2.49800 + 4.32666i) q^{54} +1.00000 q^{55} +(-24.0628 - 6.01464i) q^{56} -5.38600 q^{57} +(-9.01809 + 15.6198i) q^{58} +(-0.615772 - 1.06655i) q^{59} +(6.19755 + 10.7345i) q^{60} +(5.57933 - 9.66369i) q^{61} +18.9422 q^{62} +(-4.03915 + 4.17773i) q^{63} +28.7522 q^{64} +(2.73401 - 4.73544i) q^{65} +(-3.10838 - 5.38387i) q^{66} +(-6.03480 - 10.4526i) q^{67} +(12.8489 - 22.2549i) q^{68} -2.69144 q^{69} +(-1.98475 - 6.93710i) q^{70} -0.0153144 q^{71} +(10.2951 - 17.8317i) q^{72} +(0.0687039 + 0.118999i) q^{73} +(7.37645 + 12.7764i) q^{74} +(-1.13978 + 1.97415i) q^{75} -12.8474 q^{76} +(0.727766 + 2.54369i) q^{77} -33.9933 q^{78} +(6.43736 - 11.1498i) q^{79} +(7.34575 + 12.7232i) q^{80} +(5.38254 + 9.32283i) q^{81} +(2.44998 - 4.24349i) q^{82} -10.2471 q^{83} +(-22.7948 + 23.5768i) q^{84} +4.72601 q^{85} +(-12.9089 + 22.3589i) q^{86} +(7.53790 + 13.0560i) q^{87} +(-4.68736 - 8.11874i) q^{88} +(-1.80500 + 3.12635i) q^{89} +5.98988 q^{90} +(14.0352 + 3.50817i) q^{91} -6.42000 q^{92} +(7.91658 - 13.7119i) q^{93} +(7.65099 + 13.2519i) q^{94} +(-1.18137 - 2.04619i) q^{95} +(24.2966 - 42.0829i) q^{96} +5.86881 q^{97} +(16.2014 - 10.0972i) q^{98} -2.19637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9 - 3 * q^10 + 6 * q^11 - 9 * q^12 + 28 * q^13 - 3 * q^14 - 2 * q^15 - 11 * q^16 - 3 * q^17 + 9 * q^18 + 3 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^22 + 10 * q^23 + 10 * q^24 - 6 * q^25 + 17 * q^26 + 2 * q^27 - 10 * q^28 - 32 * q^29 - 5 * q^30 - 2 * q^31 + 26 * q^32 + q^33 + 60 * q^34 - 3 * q^35 + 16 * q^36 - 5 * q^37 - q^38 - 3 * q^39 - 9 * q^40 - 18 * q^41 - 56 * q^42 - 40 * q^43 + 5 * q^44 - q^45 + 20 * q^46 - q^47 + 82 * q^48 + 15 * q^49 - 6 * q^50 + 5 * q^51 - 23 * q^52 + 24 * q^53 + 7 * q^54 + 12 * q^55 - 66 * q^56 - 60 * q^57 - 31 * q^58 + 7 * q^59 + 9 * q^60 + 14 * q^61 + 48 * q^62 - 13 * q^63 + 30 * q^64 + 14 * q^65 - 5 * q^66 - q^67 + 25 * q^68 - 8 * q^69 - 15 * q^70 - 18 * q^71 + 26 * q^72 - 13 * q^73 + 40 * q^74 - q^75 - 20 * q^76 - 66 * q^78 + 4 * q^79 + 11 * q^80 + 26 * q^81 + 27 * q^82 + 16 * q^83 - 90 * q^84 - 6 * q^85 - 36 * q^86 + 2 * q^87 - 9 * q^88 + 13 * q^89 + 18 * q^90 + 17 * q^91 - 36 * q^92 + 36 * q^93 + q^94 - 3 * q^95 + 89 * q^96 - 6 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.36359	−	2.36181i	0.964204	−	1.67005i	0.252464	−	0.967606i	$-0.418759\pi$
$2$	1.36359	−	2.36181i	0.964204	−	1.67005i	0.711739	−	0.702444i	$-0.247908\pi$
$3$	−1.13978	−	1.97415i	−0.658051	−	1.13978i	−0.981120	−	0.193402i	$-0.938048\pi$
$3$	−1.13978	−	1.97415i	−0.658051	−	1.13978i	0.323069	−	0.946375i	$-0.395285\pi$
$4$	−2.71876	−	4.70902i	−1.35938	−	2.35451i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−6.21675			−2.53798
$7$	2.56678	+	0.641581i	0.970153	+	0.242495i
$7$	2.56678	+	0.641581i	0.970153	+	0.242495i
$8$	−9.37471			−3.31446
$9$	−1.09818	+	1.90211i	−0.366061	+	0.634036i
$10$	−1.36359	−	2.36181i	−0.431205	−	0.746869i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−6.19755	+	10.7345i	−1.78908	+	3.09877i
$13$	5.46801			1.51655			0.758277	−	0.651932i	$-0.226041\pi$
$13$	5.46801			1.51655			0.758277	+	0.651932i	$0.226041\pi$
$14$	5.01533	−	5.18739i	1.34040	−	1.38639i
$15$	−2.27955			−0.588578
$16$	−7.34575	+	12.7232i	−1.83644	+	3.18080i
$17$	2.36300	+	4.09284i	0.573113	+	0.992660i	0.996244	+	0.0865919i	$0.0275976\pi$
$17$	2.36300	+	4.09284i	0.573113	+	0.992660i	−0.423131	+	0.906068i	$0.639069\pi$
$18$	2.99494	+	5.18739i	0.705915	+	1.22268i
$19$	1.18137	−	2.04619i	0.271025	−	0.469429i	−0.698100	−	0.716001i	$-0.745971\pi$
$19$	1.18137	−	2.04619i	0.271025	−	0.469429i	0.969125	+	0.246572i	$0.0793040\pi$
$20$	−5.43751			−1.21586
$21$	−1.65898	−	5.79848i	−0.362019	−	1.26533i
$22$	2.72718			0.581437
$23$	0.590344	−	1.02251i	0.123095	−	0.213207i	−0.797892	−	0.602801i	$-0.794051\pi$
$23$	0.590344	−	1.02251i	0.123095	−	0.213207i	0.920987	+	0.389594i	$0.127385\pi$
$24$	10.6851	+	18.5071i	2.18108	+	3.77775i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	7.45613	−	12.9144i	1.46227	−	2.53272i
$27$	−1.83193			−0.352555
$28$	−3.95723	−	13.8313i	−0.747847	−	2.61388i
$29$	−6.61349			−1.22809			−0.614047	−	0.789269i	$-0.710459\pi$
$29$	−6.61349			−1.22809			−0.614047	+	0.789269i	$0.710459\pi$
$30$	−3.10838	+	5.38387i	−0.567509	+	0.982955i
$31$	3.47286	+	6.01518i	0.623745	+	1.08036i	0.988782	+	0.149365i	$0.0477228\pi$
$31$	3.47286	+	6.01518i	0.623745	+	1.08036i	−0.365037	+	0.930993i	$0.618944\pi$
$32$	10.6585	+	18.4610i	1.88417	+	3.26348i
$33$	1.13978	−	1.97415i	0.198410	−	0.343656i
$34$	12.8887			2.21039
$35$	1.83902	−	1.90211i	0.310851	−	0.321515i
$36$	11.9428			1.99046
$37$	−2.70479	+	4.68483i	−0.444665	+	0.770182i	−0.998029	−	0.0627575i	$-0.980011\pi$
$37$	−2.70479	+	4.68483i	−0.444665	+	0.770182i	0.553364	+	0.832940i	$0.313344\pi$
$38$	−3.22181	−	5.58034i	−0.522647	−	0.905251i
$39$	−6.23232	−	10.7947i	−0.997969	−	1.72853i
$40$	−4.68736	+	8.11874i	−0.741136	+	1.28369i
$41$	1.79671			0.280600			0.140300	−	0.990109i	$-0.455193\pi$
$41$	1.79671			0.280600			0.140300	+	0.990109i	$0.455193\pi$
$42$	−15.9571	−	3.98855i	−2.46223	−	0.615447i
$43$	−9.46684			−1.44368			−0.721840	−	0.692060i	$-0.756703\pi$
$43$	−9.46684			−1.44368			−0.721840	+	0.692060i	$0.756703\pi$
$44$	2.71876	−	4.70902i	0.409868	−	0.709912i
$45$	1.09818	+	1.90211i	0.163707	+	0.283550i
$46$	−1.60997	−	2.78856i	−0.237378	−	0.411150i
$47$	−2.80546	+	4.85920i	−0.409218	+	0.708786i	−0.994802	−	0.101825i	$-0.967532\pi$
$47$	−2.80546	+	4.85920i	−0.409218	+	0.708786i	0.585584	+	0.810612i	$0.300865\pi$
$48$	33.4901			4.83388
$49$	6.17675	+	3.29360i	0.882392	+	0.470514i
$50$	−2.72718			−0.385681
$51$	5.38660	−	9.32986i	0.754274	−	1.30644i
$52$	−14.8662	−	25.7490i	−2.06157	−	3.57074i
$53$	2.38962	+	4.13895i	0.328240	+	0.568528i	0.982163	−	0.188033i	$-0.0602113\pi$
$53$	2.38962	+	4.13895i	0.328240	+	0.568528i	−0.653923	+	0.756561i	$0.726878\pi$
$54$	−2.49800	+	4.32666i	−0.339935	+	0.588784i
$55$	1.00000			0.134840
$56$	−24.0628	−	6.01464i	−3.21553	−	0.803740i
$57$	−5.38600			−0.713393
$58$	−9.01809	+	15.6198i	−1.18413	+	2.05098i
$59$	−0.615772	−	1.06655i	−0.0801667	−	0.138853i	0.823155	−	0.567817i	$-0.192212\pi$
$59$	−0.615772	−	1.06655i	−0.0801667	−	0.138853i	−0.903321	+	0.428964i	$0.858879\pi$
$60$	6.19755	+	10.7345i	0.800100	+	1.38581i
$61$	5.57933	−	9.66369i	0.714360	−	1.23731i	−0.248846	−	0.968543i	$-0.580051\pi$
$61$	5.57933	−	9.66369i	0.714360	−	1.23731i	0.963206	−	0.268765i	$-0.0866155\pi$
$62$	18.9422			2.40567
$63$	−4.03915	+	4.17773i	−0.508886	+	0.526344i
$64$	28.7522			3.59402
$65$	2.73401	−	4.73544i	0.339112	−	0.587359i
$66$	−3.10838	−	5.38387i	−0.382615	−	0.662708i
$67$	−6.03480	−	10.4526i	−0.737268	−	1.27699i	−0.953721	−	0.300692i	$-0.902782\pi$
$67$	−6.03480	−	10.4526i	−0.737268	−	1.27699i	0.216453	−	0.976293i	$-0.430551\pi$
$68$	12.8489	−	22.2549i	1.55815	−	2.69880i
$69$	−2.69144			−0.324012
$70$	−1.98475	−	6.93710i	−0.237223	−	0.829142i
$71$	−0.0153144			−0.00181748			−0.000908742	−	1.00000i	$-0.500289\pi$
$71$	−0.0153144			−0.00181748			−0.000908742		1.00000i	$0.500289\pi$
$72$	10.2951	−	17.8317i	1.21329	−	2.10149i
$73$	0.0687039	+	0.118999i	0.00804118	+	0.0139277i	0.870018	−	0.493020i	$-0.164107\pi$
$73$	0.0687039	+	0.118999i	0.00804118	+	0.0139277i	−0.861977	+	0.506948i	$0.830774\pi$
$74$	7.37645	+	12.7764i	0.857495	+	1.48522i
$75$	−1.13978	+	1.97415i	−0.131610	+	0.227955i
$76$	−12.8474			−1.47370
$77$	0.727766	+	2.54369i	0.0829366	+	0.289880i
$78$	−33.9933			−3.84898
$79$	6.43736	−	11.1498i	0.724260	−	1.25446i	−0.235018	−	0.971991i	$-0.575515\pi$
$79$	6.43736	−	11.1498i	0.724260	−	1.25446i	0.959278	−	0.282464i	$-0.0911518\pi$
$80$	7.34575	+	12.7232i	0.821280	+	1.42250i
$81$	5.38254	+	9.32283i	0.598060	+	1.03587i
$82$	2.44998	−	4.24349i	0.270555	−	0.468615i
$83$	−10.2471			−1.12476			−0.562380	−	0.826879i	$-0.690114\pi$
$83$	−10.2471			−1.12476			−0.562380	+	0.826879i	$0.690114\pi$
$84$	−22.7948	+	23.5768i	−2.48712	+	2.57244i
$85$	4.72601			0.512608
$86$	−12.9089	+	22.3589i	−1.39200	+	2.41102i
$87$	7.53790	+	13.0560i	0.808148	+	1.39975i
$88$	−4.68736	−	8.11874i	−0.499674	−	0.865460i
$89$	−1.80500	+	3.12635i	−0.191330	+	0.331393i	−0.945691	−	0.325067i	$-0.894613\pi$
$89$	−1.80500	+	3.12635i	−0.191330	+	0.331393i	0.754362	+	0.656459i	$0.227947\pi$
$90$	5.98988			0.631389
$91$	14.0352	+	3.50817i	1.47129	+	0.367757i
$92$	−6.42000			−0.669332
$93$	7.91658	−	13.7119i	0.820911	−	1.42186i
$94$	7.65099	+	13.2519i	0.789139	+	1.36683i
$95$	−1.18137	−	2.04619i	−0.121206	−	0.209935i
$96$	24.2966	−	42.0829i	2.47976	−	4.29507i
$97$	5.86881			0.595888			0.297944	−	0.954583i	$-0.403699\pi$
$97$	5.86881			0.595888			0.297944	+	0.954583i	$0.403699\pi$
$98$	16.2014	−	10.0972i	1.63659	−	1.01997i
$99$	−2.19637			−0.220743
$100$	−2.71876	+	4.70902i	−0.271876	+	0.470902i
$101$	2.39661	+	4.15105i	0.238472	+	0.413045i	0.960276	−	0.279052i	$-0.0900202\pi$
$101$	2.39661	+	4.15105i	0.238472	+	0.413045i	−0.721804	+	0.692097i	$0.756687\pi$
$102$	−14.6902	−	25.4442i	−1.45455	−	2.51935i
$103$	4.02678	−	6.97458i	0.396770	−	0.687226i	−0.596555	−	0.802572i	$-0.703464\pi$
$103$	4.02678	−	6.97458i	0.396770	−	0.687226i	0.993325	+	0.115346i	$0.0367977\pi$
$104$	−51.2610			−5.02656
$105$	−5.85112	−	1.46252i	−0.571011	−	0.142727i
$106$	13.0339			1.26596
$107$	−7.89300	+	13.6711i	−0.763045	+	1.32163i	0.178229	+	0.983989i	$0.442963\pi$
$107$	−7.89300	+	13.6711i	−0.763045	+	1.32163i	−0.941274	+	0.337644i	$0.890370\pi$
$108$	4.98056	+	8.62659i	0.479255	+	0.830094i
$109$	1.99769	+	3.46010i	0.191344	+	0.331417i	0.945696	−	0.325053i	$-0.105382\pi$
$109$	1.99769	+	3.46010i	0.191344	+	0.331417i	−0.754352	+	0.656470i	$0.772049\pi$
$110$	1.36359	−	2.36181i	0.130013	−	0.225189i
$111$	12.3314			1.17045
$112$	−27.0179	+	27.9448i	−2.55295	+	2.64054i
$113$	−7.90376			−0.743523			−0.371761	−	0.928328i	$-0.621246\pi$
$113$	−7.90376			−0.743523			−0.371761	+	0.928328i	$0.621246\pi$
$114$	−7.34429	+	12.7207i	−0.687856	+	1.19140i
$115$	−0.590344	−	1.02251i	−0.0550499	−	0.0953492i
$116$	17.9805	+	31.1431i	1.66944	+	2.89156i
$117$	−6.00488	+	10.4008i	−0.555151	+	0.961550i
$118$	−3.35864			−0.309188
$119$	3.43943	+	12.0215i	0.315292	+	1.10201i
$120$	21.3702			1.95082
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−15.2158	−	26.3546i	−1.37758	−	2.38603i
$123$	−2.04785	−	3.54699i	−0.184649	−	0.319821i
$124$	18.8837	−	32.7076i	1.69581	−	2.93723i
$125$	−1.00000			−0.0894427
$126$	4.35923	+	15.2364i	0.388351	+	1.35737i
$127$	4.54713			0.403493			0.201746	−	0.979438i	$-0.435338\pi$
$127$	4.54713			0.403493			0.201746	+	0.979438i	$0.435338\pi$
$128$	17.8892	−	30.9850i	1.58120	−	2.73871i
$129$	10.7901	+	18.6890i	0.950014	+	1.64547i
$130$	−7.45613	−	12.9144i	−0.653946	−	1.13267i
$131$	1.94211	−	3.36383i	0.169683	−	0.293900i	−0.768625	−	0.639699i	$-0.779059\pi$
$131$	1.94211	−	3.36383i	0.169683	−	0.293900i	0.938308	+	0.345800i	$0.112392\pi$
$132$	−12.3951			−1.07885
$133$	4.34512	−	4.49419i	0.376770	−	0.389696i
$134$	−32.9160			−2.84351
$135$	−0.915964	+	1.58650i	−0.0788336	+	0.136544i
$136$	−22.1525	−	38.3692i	−1.89956	−	3.29013i
$137$	3.22758	+	5.59034i	0.275751	+	0.477615i	0.970324	−	0.241807i	$-0.0777401\pi$
$137$	3.22758	+	5.59034i	0.275751	+	0.477615i	−0.694573	+	0.719422i	$0.744407\pi$
$138$	−3.67002	+	6.35667i	−0.312413	+	0.541115i
$139$	−6.31453			−0.535592			−0.267796	−	0.963476i	$-0.586295\pi$
$139$	−6.31453			−0.535592			−0.267796	+	0.963476i	$0.586295\pi$
$140$	−13.9569	−	3.48860i	−1.17957	−	0.294841i
$141$	12.7904			1.07714
$142$	−0.0208826	+	0.0361697i	−0.00175243	+	0.00303529i
$143$	2.73401	+	4.73544i	0.228629	+	0.395997i
$144$	−16.1340	−	27.9448i	−1.34450	−	2.32874i
$145$	−3.30674	+	5.72745i	−0.274610	+	0.475639i
$146$	0.374736			0.0310134
$147$	−0.538051	−	15.9478i	−0.0443777	−	1.31535i
$148$	29.4147			2.41787
$149$	7.25959	−	12.5740i	0.594729	−	1.03010i	−0.398856	−	0.917014i	$-0.630593\pi$
$149$	7.25959	−	12.5740i	0.594729	−	1.03010i	0.993585	−	0.113087i	$-0.0360740\pi$
$150$	3.10838	+	5.38387i	0.253798	+	0.439591i
$151$	−2.33664	−	4.04717i	−0.190153	−	0.329354i	0.755148	−	0.655554i	$-0.227565\pi$
$151$	−2.33664	−	4.04717i	−0.190153	−	0.329354i	−0.945301	+	0.326200i	$0.894232\pi$
$152$	−11.0750	+	19.1825i	−0.898302	+	1.55590i
$153$	−10.3800			−0.839177
$154$	7.00008	+	1.74971i	0.564082	+	0.140995i
$155$	6.94573			0.557894
$156$	−33.8883	+	58.6962i	−2.71323	+	4.69946i
$157$	7.20807	+	12.4847i	0.575267	+	0.996391i	0.996013	+	0.0892127i	$0.0284351\pi$
$157$	7.20807	+	12.4847i	0.575267	+	0.996391i	−0.420746	+	0.907179i	$0.638232\pi$
$158$	−17.5558	−	30.4076i	−1.39667	−	2.41910i
$159$	5.44727	−	9.43495i	0.431997	−	0.748240i
$160$	21.3169			1.68525
$161$	2.17131	−	2.24580i	0.171123	−	0.176994i
$162$	29.3583			2.30661
$163$	−2.91367	+	5.04663i	−0.228216	+	0.395282i	−0.957280	−	0.289164i	$-0.906623\pi$
$163$	−2.91367	+	5.04663i	−0.228216	+	0.395282i	0.729063	+	0.684446i	$0.239956\pi$
$164$	−4.88483	−	8.46077i	−0.381441	−	0.660675i
$165$	−1.13978	−	1.97415i	−0.0887315	−	0.153687i
$166$	−13.9728	+	24.2016i	−1.08450	+	1.87841i
$167$	18.5452			1.43507			0.717537	−	0.696520i	$-0.245269\pi$
$167$	18.5452			1.43507			0.717537	+	0.696520i	$0.245269\pi$
$168$	15.5525	+	54.3590i	1.19990	+	4.19389i
$169$	16.8992			1.29994
$170$	6.44434	−	11.1619i	0.494258	−	0.856080i
$171$	2.59472	+	4.49419i	0.198423	+	0.343679i
$172$	25.7380	+	44.5796i	1.96251	+	3.39916i
$173$	−9.30477	+	16.1163i	−0.707428	+	1.22530i	0.258380	+	0.966043i	$0.416811\pi$
$173$	−9.30477	+	16.1163i	−0.707428	+	1.22530i	−0.965808	+	0.259258i	$0.916522\pi$
$174$	41.1144			3.11688
$175$	−0.727766	−	2.54369i	−0.0550139	−	0.192285i
$176$	−14.6915			−1.10741
$177$	−1.40368	+	2.43125i	−0.105507	+	0.182744i
$178$	4.92256	+	8.52612i	0.368961	+	0.639060i
$179$	−5.27196	−	9.13131i	−0.394045	−	0.682506i	0.598934	−	0.800799i	$-0.295591\pi$
$179$	−5.27196	−	9.13131i	−0.394045	−	0.682506i	−0.992979	+	0.118292i	$0.962258\pi$
$180$	5.97138	−	10.3427i	0.445080	−	0.770902i
$181$	−11.0967			−0.824813			−0.412406	−	0.911000i	$-0.635312\pi$
$181$	−11.0967			−0.824813			−0.412406	+	0.911000i	$0.635312\pi$
$182$	27.4239	−	28.3647i	2.03279	−	2.10253i
$183$	−25.4368			−1.88034
$184$	−5.53430	+	9.58570i	−0.407994	+	0.706667i
$185$	2.70479	+	4.68483i	0.198860	+	0.344436i
$186$	−21.5899	−	37.3949i	−1.58305	−	2.74192i
$187$	−2.36300	+	4.09284i	−0.172800	+	0.299298i
$188$	30.5094			2.22513
$189$	−4.70216	−	1.17533i	−0.342032	−	0.0854927i
$190$	−6.44362			−0.467470
$191$	7.51105	−	13.0095i	0.543481	−	0.941336i	−0.455220	−	0.890379i	$-0.650439\pi$
$191$	7.51105	−	13.0095i	0.543481	−	0.941336i	0.998701	−	0.0509574i	$-0.0162273\pi$
$192$	−32.7710	−	56.7611i	−2.36505	−	4.09638i
$193$	11.9685	+	20.7301i	0.861515	+	1.49219i	0.870466	+	0.492228i	$0.163817\pi$
$193$	11.9685	+	20.7301i	0.861515	+	1.49219i	−0.00895138	+	0.999960i	$0.502849\pi$
$194$	8.00265	−	13.8610i	0.574557	−	0.995162i
$195$	−12.4646			−0.892611
$196$	−1.28343	−	38.0409i	−0.0916739	−	2.71721i
$197$	15.6349			1.11394			0.556970	−	0.830533i	$-0.311964\pi$
$197$	15.6349			1.11394			0.556970	+	0.830533i	$0.311964\pi$
$198$	−2.99494	+	5.18739i	−0.212841	+	0.368652i
$199$	−5.60569	−	9.70934i	−0.397377	−	0.688277i	0.596024	−	0.802966i	$-0.296746\pi$
$199$	−5.60569	−	9.70934i	−0.397377	−	0.688277i	−0.993401	+	0.114689i	$0.963413\pi$
$200$	4.68736	+	8.11874i	0.331446	+	0.574081i
$201$	−13.7566	+	23.8272i	−0.970319	+	1.68064i
$202$	13.0720			0.919742
$203$	−16.9754	−	4.24309i	−1.19144	−	0.297807i
$204$	−58.5793			−4.10137
$205$	0.898357	−	1.55600i	0.0627440	−	0.108676i
$206$	−10.9817	−	19.0209i	−0.765134	−	1.32525i
$207$	1.29661	+	2.24580i	0.0901207	+	0.156094i
$208$	−40.1667	+	69.5707i	−2.78506	+	4.82386i
$209$	2.36274			0.163434
$210$	−11.4327	+	11.8249i	−0.788932	+	0.815998i
$211$	4.89431			0.336938			0.168469	−	0.985707i	$-0.446118\pi$
$211$	4.89431			0.336938			0.168469	+	0.985707i	$0.446118\pi$
$212$	12.9936	−	22.5056i	0.892404	−	1.54569i
$213$	0.0174550	+	0.0302329i	0.00119600	+	0.00207153i
$214$	21.5256	+	37.2835i	1.47146	+	2.54865i
$215$	−4.73342	+	8.19853i	−0.322817	+	0.559135i
$216$	17.1738			1.16853
$217$	5.05486	+	17.6678i	0.343146	+	1.19937i
$218$	10.8961			0.737977
$219$	0.156614	−	0.271264i	0.0105830	−	0.0183303i
$220$	−2.71876	−	4.70902i	−0.183298	−	0.317482i
$221$	12.9209	+	22.3797i	0.869156	+	1.50542i
$222$	16.8150	−	29.1245i	1.12855	−	1.95471i
$223$	−20.2780			−1.35792			−0.678959	−	0.734177i	$-0.737568\pi$
$223$	−20.2780			−1.35792			−0.678959	+	0.734177i	$0.737568\pi$
$224$	15.5137	+	54.2237i	1.03656	+	3.62297i
$225$	2.19637			0.146424
$226$	−10.7775	+	18.6671i	−0.716908	+	1.24172i
$227$	−9.92346	−	17.1879i	−0.658643	−	1.14080i	−0.980967	−	0.194174i	$-0.937797\pi$
$227$	−9.92346	−	17.1879i	−0.658643	−	1.14080i	0.322324	−	0.946629i	$-0.395536\pi$
$228$	14.6432	+	25.3628i	0.969770	+	1.67969i
$229$	3.94968	−	6.84105i	0.261002	−	0.452069i	−0.705506	−	0.708704i	$-0.749280\pi$
$229$	3.94968	−	6.84105i	0.261002	−	0.452069i	0.966509	+	0.256634i	$0.0826136\pi$
$230$	−3.21995			−0.212317
$231$	4.19214	−	4.33596i	0.275822	−	0.285285i
$232$	61.9995			4.07047
$233$	0.232257	−	0.402280i	0.0152156	−	0.0263543i	−0.858317	−	0.513119i	$-0.828490\pi$
$233$	0.232257	−	0.402280i	0.0152156	−	0.0263543i	0.873533	+	0.486765i	$0.161823\pi$
$234$	16.3764	+	28.3647i	1.07056	+	1.85426i
$235$	2.80546	+	4.85920i	0.183008	+	0.316979i
$236$	−3.34827	+	5.79937i	−0.217954	+	0.377507i
$237$	−29.3486			−1.90640
$238$	33.0824	+	8.26913i	2.14442	+	0.536008i
$239$	−28.2173			−1.82522			−0.912612	−	0.408828i	$-0.865938\pi$
$239$	−28.2173			−1.82522			−0.912612	+	0.408828i	$0.865938\pi$
$240$	16.7450	−	29.0033i	1.08089	−	1.87215i
$241$	−0.00408038	−	0.00706742i	−0.000262840	−	0.000455252i	0.865894	−	0.500228i	$-0.166750\pi$
$241$	−0.00408038	−	0.00706742i	−0.000262840	−	0.000455252i	−0.866157	+	0.499772i	$0.833417\pi$
$242$	1.36359	+	2.36181i	0.0876549	+	0.151823i
$243$	9.52189	−	16.4924i	0.610830	−	1.05799i
$244$	−60.6754			−3.88434
$245$	5.94071	−	3.70242i	0.379538	−	0.236539i
$246$	−11.1697			−0.712156
$247$	6.45975	−	11.1886i	0.411024	−	0.711915i
$248$	−32.5571	−	56.3905i	−2.06738	−	3.58080i
$249$	11.6794	+	20.2292i	0.740149	+	1.28198i
$250$	−1.36359	+	2.36181i	−0.0862410	+	0.149374i
$251$	−3.84910			−0.242953			−0.121476	−	0.992594i	$-0.538763\pi$
$251$	−3.84910			−0.242953			−0.121476	+	0.992594i	$0.538763\pi$
$252$	30.6545	+	7.66225i	1.93105	+	0.482676i
$253$	1.18069			0.0742292
$254$	6.20042	−	10.7394i	0.389049	−	0.673853i
$255$	−5.38660	−	9.32986i	−0.337322	−	0.584258i
$256$	−20.0349	−	34.7015i	−1.25218	−	2.16884i
$257$	−5.03714	+	8.72459i	−0.314208	+	0.544225i	−0.979269	−	0.202565i	$-0.935072\pi$
$257$	−5.03714	+	8.72459i	−0.314208	+	0.544225i	0.665061	+	0.746789i	$0.268406\pi$
$258$	58.8530			3.66403
$259$	−9.94831	+	10.2896i	−0.618158	+	0.639365i
$260$	−29.7324			−1.84392
$261$	7.26282	−	12.5796i	0.449557	−	0.778656i
$262$	−5.29648	−	9.17378i	−0.327218	−	0.566758i
$263$	−5.26103	−	9.11237i	−0.324409	−	0.561893i	0.656984	−	0.753905i	$-0.271832\pi$
$263$	−5.26103	−	9.11237i	−0.324409	−	0.561893i	−0.981393	+	0.192012i	$0.938499\pi$
$264$	−10.6851	+	18.5071i	−0.657621	+	1.13903i
$265$	4.77924			0.293587
$266$	−4.68945	−	16.3906i	−0.287529	−	1.00497i
$267$	8.22919			0.503618
$268$	−32.8143	+	56.8360i	−2.00445	+	3.47181i
$269$	−4.79228	−	8.30048i	−0.292191	−	0.506089i	0.682137	−	0.731225i	$-0.261051\pi$
$269$	−4.79228	−	8.30048i	−0.292191	−	0.506089i	−0.974327	+	0.225135i	$0.927718\pi$
$270$	2.49800	+	4.32666i	0.152023	+	0.263312i
$271$	−3.72409	+	6.45032i	−0.226222	+	0.391829i	−0.956686	−	0.291123i	$-0.905971\pi$
$271$	−3.72409	+	6.45032i	−0.226222	+	0.391829i	0.730463	+	0.682952i	$0.239304\pi$
$272$	−69.4322			−4.20994
$273$	−9.07133	−	31.7062i	−0.549022	−	1.91894i
$274$	17.6044			1.06352
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	7.31737	+	12.6741i	0.440454	+	0.762889i
$277$	−9.83692	−	17.0380i	−0.591043	−	1.02372i	−0.994092	−	0.108539i	$-0.965383\pi$
$277$	−9.83692	−	17.0380i	−0.591043	−	1.02372i	0.403049	−	0.915178i	$-0.367950\pi$
$278$	−8.61043	+	14.9137i	−0.516419	+	0.894465i
$279$	−15.2554			−0.913314
$280$	−17.2403	+	17.8317i	−1.03030	+	1.06565i
$281$	−32.9185			−1.96375			−0.981876	−	0.189525i	$-0.939305\pi$
$281$	−32.9185			−1.96375			−0.981876	+	0.189525i	$0.939305\pi$
$282$	17.4408	−	30.2084i	1.03859	−	1.79889i
$283$	7.58898	+	13.1445i	0.451118	+	0.781359i	0.998456	−	0.0555527i	$-0.0176921\pi$
$283$	7.58898	+	13.1445i	0.451118	+	0.781359i	−0.547338	+	0.836912i	$0.684359\pi$
$284$	0.0416361	+	0.0721158i	0.00247065	+	0.00427929i
$285$	−2.69300	+	4.66441i	−0.159519	+	0.276296i
$286$	14.9123			0.881780
$287$	4.61177	+	1.15274i	0.272224	+	0.0680440i
$288$	−46.8198			−2.75888
$289$	−2.66758	+	4.62038i	−0.156916	+	0.271787i
$290$	9.01809	+	15.6198i	0.529560	+	0.917225i
$291$	−6.68914	−	11.5859i	−0.392124	−	0.679179i
$292$	0.373578	−	0.647056i	0.0218620	−	0.0378661i
$293$	−13.4938			−0.788314			−0.394157	−	0.919043i	$-0.628963\pi$
$293$	−13.4938			−0.788314			−0.394157	+	0.919043i	$0.628963\pi$
$294$	−38.3993	−	20.4755i	−2.23949	−	1.19415i
$295$	−1.23154			−0.0717032
$296$	25.3566	−	43.9190i	1.47382	−	2.55274i
$297$	−0.915964	−	1.58650i	−0.0531496	−	0.0920578i
$298$	−19.7982	−	34.2915i	−1.14688	−	1.98645i
$299$	3.22801	−	5.59108i	0.186681	−	0.323340i
$300$	12.3951			0.715631
$301$	−24.2993	−	6.07375i	−1.40059	−	0.350085i
$302$	−12.7448			−0.733384
$303$	5.46321	−	9.46255i	0.313853	−	0.543609i
$304$	17.3561	+	30.0617i	0.995441	+	1.72416i
$305$	−5.57933	−	9.66369i	−0.319472	−	0.553341i
$306$	−14.1541	+	24.5157i	−0.809137	+	1.40147i
$307$	16.7440			0.955631			0.477816	−	0.878460i	$-0.341429\pi$
$307$	16.7440			0.955631			0.477816	+	0.878460i	$0.341429\pi$
$308$	9.99967	−	10.3427i	0.569784	−	0.589332i
$309$	−18.3585			−1.04438
$310$	9.47112	−	16.4045i	0.537924	−	0.931711i
$311$	−2.53890	−	4.39751i	−0.143968	−	0.249360i	0.785019	−	0.619471i	$-0.212653\pi$
$311$	−2.53890	−	4.39751i	−0.143968	−	0.249360i	−0.928987	+	0.370111i	$0.879320\pi$
$312$	58.4262	+	101.197i	3.30773	+	5.72916i
$313$	−0.969320	+	1.67891i	−0.0547892	+	0.0948977i	−0.892119	−	0.451800i	$-0.850782\pi$
$313$	−0.969320	+	1.67891i	−0.0547892	+	0.0948977i	0.837330	+	0.546698i	$0.184115\pi$
$314$	39.3154			2.21870
$315$	1.59844	+	5.58687i	0.0900619	+	0.314785i
$316$	−70.0065			−3.93817
$317$	6.05282	−	10.4838i	0.339960	−	0.588829i	−0.644464	−	0.764634i	$-0.722920\pi$
$317$	6.05282	−	10.4838i	0.339960	−	0.588829i	0.984425	+	0.175805i	$0.0562530\pi$
$318$	−14.8557	−	25.7308i	−0.833066	−	1.44291i
$319$	−3.30674	−	5.72745i	−0.185142	−	0.320676i
$320$	14.3761	−	24.9001i	0.803647	−	1.39196i
$321$	35.9850			2.00849
$322$	−2.34337	−	8.19055i	−0.130591	−	0.456442i
$323$	11.1663			0.621312
$324$	29.2676	−	50.6930i	1.62598	−	2.81628i
$325$	−2.73401	−	4.73544i	−0.151655	−	0.262675i
$326$	7.94610	+	13.7631i	0.440094	+	0.762265i
$327$	4.55384	−	7.88747i	0.251828	−	0.436178i
$328$	−16.8437			−0.930036
$329$	−10.3186	+	10.6726i	−0.568881	+	0.588398i
$330$	−6.21675			−0.342221
$331$	12.8275	−	22.2178i	0.705062	−	1.22120i	−0.261607	−	0.965174i	$-0.584252\pi$
$331$	12.8275	−	22.2178i	0.705062	−	1.22120i	0.966669	−	0.256029i	$-0.0824142\pi$
$332$	27.8592	+	48.2536i	1.52897	+	2.64826i
$333$	−5.94071	−	10.2896i	−0.325549	−	0.563867i
$334$	25.2881	−	43.8003i	1.38370	−	2.39665i
$335$	−12.0696			−0.659432
$336$	85.9617	+	21.4866i	4.68960	+	1.17219i
$337$	−33.4550			−1.82241			−0.911204	−	0.411954i	$-0.864846\pi$
$337$	−33.4550			−1.82241			−0.911204	+	0.411954i	$0.864846\pi$
$338$	23.0436	−	39.9126i	1.25340	−	2.17096i
$339$	9.00852	+	15.6032i	0.489276	+	0.847450i
$340$	−12.8489	−	22.2549i	−0.696827	−	1.20694i
$341$	−3.47286	+	6.01518i	−0.188066	+	0.325740i
$342$	14.1526			0.765282
$343$	13.7413	+	12.4168i	0.741958	+	0.670446i
$344$	88.7489			4.78502
$345$	−1.34572	+	2.33086i	−0.0724512	+	0.125489i
$346$	25.3758	+	43.9521i	1.36421	+	2.36288i
$347$	3.77434	+	6.53735i	0.202617	+	0.350943i	0.949371	−	0.314157i	$-0.101722\pi$
$347$	3.77434	+	6.53735i	0.202617	+	0.350943i	−0.746754	+	0.665101i	$0.768389\pi$
$348$	40.9874	−	70.9923i	2.19716	−	3.80559i
$349$	29.4885			1.57849			0.789243	−	0.614081i	$-0.210473\pi$
$349$	29.4885			1.57849			0.789243	+	0.614081i	$0.210473\pi$
$350$	−7.00008	−	1.74971i	−0.374170	−	0.0935258i
$351$	−10.0170			−0.534668
$352$	−10.6585	+	18.4610i	−0.568099	+	0.983976i
$353$	1.03993	+	1.80121i	0.0553499	+	0.0958688i	0.892373	−	0.451299i	$-0.149039\pi$
$353$	1.03993	+	1.80121i	0.0553499	+	0.0958688i	−0.837023	+	0.547168i	$0.815706\pi$
$354$	3.82810	+	6.63047i	0.203461	+	0.352405i
$355$	−0.00765720	+	0.0132627i	−0.000406402	+	0.000703909i
$356$	19.6294			1.04036
$357$	19.8121	−	20.4918i	1.04857	−	1.08454i
$358$	−28.7552			−1.51976
$359$	−14.0104	+	24.2668i	−0.739442	+	1.28075i	0.213305	+	0.976986i	$0.431577\pi$
$359$	−14.0104	+	24.2668i	−0.739442	+	1.28075i	−0.952747	+	0.303765i	$0.901756\pi$
$360$	−10.2951	−	17.8317i	−0.542602	−	0.939814i
$361$	6.70873	+	11.6199i	0.353091	+	0.611571i
$362$	−15.1314	+	26.2083i	−0.795287	+	1.37748i
$363$	2.27955			0.119646
$364$	−21.6382	−	75.6300i	−1.13415	−	3.96409i
$365$	0.137408			0.00719225
$366$	−34.6853	+	60.0768i	−1.81303	+	3.14026i
$367$	14.3112	+	24.7878i	0.747041	+	1.29391i	0.949235	+	0.314567i	$0.101859\pi$
$367$	14.3112	+	24.7878i	0.747041	+	1.29391i	−0.202195	+	0.979345i	$0.564807\pi$
$368$	8.67304	+	15.0221i	0.452113	+	0.783083i
$369$	−1.97312	+	3.41755i	−0.102717	+	0.177910i
$370$	14.7529			0.766967
$371$	3.47817	+	12.1569i	0.180578	+	0.631155i
$372$	−86.0930			−4.46371
$373$	3.30509	−	5.72459i	0.171131	−	0.296408i	−0.767684	−	0.640828i	$-0.778591\pi$
$373$	3.30509	−	5.72459i	0.171131	−	0.296408i	0.938816	+	0.344420i	$0.111924\pi$
$374$	6.44434	+	11.1619i	0.333229	+	0.577169i
$375$	1.13978	+	1.97415i	0.0588578	+	0.101945i
$376$	26.3004	−	45.5535i	1.35634	−	2.34924i
$377$	−36.1626			−1.86247
$378$	−9.18772	+	9.50293i	−0.472565	+	0.488778i
$379$	17.6377			0.905987			0.452993	−	0.891514i	$-0.350356\pi$
$379$	17.6377			0.905987			0.452993	+	0.891514i	$0.350356\pi$
$380$	−6.42372	+	11.1262i	−0.329530	+	0.570762i
$381$	−5.18271	−	8.97672i	−0.265518	−	0.459891i
$382$	−20.4840	−	35.4793i	−1.04805	−	1.81528i
$383$	−7.41069	+	12.8357i	−0.378669	+	0.655873i	−0.990869	−	0.134830i	$-0.956951\pi$
$383$	−7.41069	+	12.8357i	−0.378669	+	0.655873i	0.612200	+	0.790703i	$0.290285\pi$
$384$	−81.5588			−4.16203
$385$	2.56678	+	0.641581i	0.130815	+	0.0326980i
$386$	65.2808			3.32270
$387$	10.3963	−	18.0070i	0.528475	−	0.915345i
$388$	−15.9559	−	27.6364i	−0.810036	−	1.40302i
$389$	10.0634	+	17.4303i	0.510235	+	0.883754i	0.999930	+	0.0118593i	$0.00377504\pi$
$389$	10.0634	+	17.4303i	0.510235	+	0.883754i	−0.489694	+	0.871894i	$0.662892\pi$
$390$	−16.9966	+	29.4391i	−0.860659	+	1.49070i
$391$	5.57994			0.282190
$392$	−57.9052	−	30.8765i	−2.92466	−	1.55950i
$393$	−8.85429			−0.446640
$394$	21.3196	−	36.9266i	1.07406	−	1.86034i
$395$	−6.43736	−	11.1498i	−0.323899	−	0.561009i
$396$	5.97138	+	10.3427i	0.300073	+	0.519742i
$397$	−5.44830	+	9.43674i	−0.273442	+	0.473616i	−0.969741	−	0.244136i	$-0.921496\pi$
$397$	−5.44830	+	9.43674i	−0.273442	+	0.473616i	0.696299	+	0.717752i	$0.254829\pi$
$398$	−30.5755			−1.53261
$399$	−13.8247	−	3.45555i	−0.692100	−	0.172994i
$400$	14.6915			0.734575
$401$	13.0111	−	22.5359i	0.649743	−	1.12539i	−0.333441	−	0.942771i	$-0.608210\pi$
$401$	13.0111	−	22.5359i	0.649743	−	1.12539i	0.983184	−	0.182618i	$-0.0584570\pi$
$402$	37.5168	+	64.9811i	1.87117	+	3.24096i
$403$	18.9897	+	32.8911i	0.945943	+	1.63842i
$404$	13.0316	−	22.5714i	0.648347	−	1.12297i
$405$	10.7651			0.534921
$406$	−33.1688	+	34.3068i	−1.64614	+	1.70262i
$407$	−5.40958			−0.268143
$408$	−50.4978	+	87.4647i	−2.50001	+	4.33015i
$409$	−14.3438	−	24.8441i	−0.709253	−	1.22846i	−0.965135	−	0.261754i	$-0.915699\pi$
$409$	−14.3438	−	24.8441i	−0.709253	−	1.22846i	0.255882	−	0.966708i	$-0.417634\pi$
$410$	−2.44998	−	4.24349i	−0.120996	−	0.209571i
$411$	7.35745	−	12.7435i	0.362916	−	0.628590i
$412$	−43.7913			−2.15744
$413$	−0.896275	−	3.13266i	−0.0441028	−	0.154148i
$414$	7.07219			0.347579
$415$	−5.12353	+	8.87421i	−0.251504	+	0.435618i
$416$	58.2807	+	100.945i	2.85745	+	4.94924i
$417$	7.19716	+	12.4658i	0.352446	+	0.610455i
$418$	3.22181	−	5.58034i	0.157584	−	0.272943i
$419$	−6.77405			−0.330934			−0.165467	−	0.986215i	$-0.552913\pi$
$419$	−6.77405			−0.330934			−0.165467	+	0.986215i	$0.552913\pi$
$420$	9.02073	+	31.5293i	0.440166	+	1.53847i
$421$	3.06757			0.149504			0.0747520	−	0.997202i	$-0.476183\pi$
$421$	3.06757			0.149504			0.0747520	+	0.997202i	$0.476183\pi$
$422$	6.67383	−	11.5594i	0.324877	−	0.562704i
$423$	−6.16181	−	10.6726i	−0.299597	−	0.518918i
$424$	−22.4020	−	38.8014i	−1.08794	−	1.88436i
$425$	2.36300	−	4.09284i	0.114623	−	0.198532i
$426$	0.0952058			0.00461274
$427$	20.5210	−	21.2250i	0.993079	−	1.02715i
$428$	85.8365			4.14907
$429$	6.23232	−	10.7947i	0.300899	−	0.521172i
$430$	12.9089	+	22.3589i	0.622522	+	1.07824i
$431$	−1.81493	−	3.14355i	−0.0874222	−	0.151420i	0.818999	−	0.573795i	$-0.194530\pi$
$431$	−1.81493	−	3.14355i	−0.0874222	−	0.151420i	−0.906421	+	0.422376i	$0.861196\pi$
$432$	13.4569	−	23.3080i	0.647445	−	1.12141i
$433$	33.6828			1.61869			0.809346	−	0.587332i	$-0.199822\pi$
$433$	33.6828			1.61869			0.809346	+	0.587332i	$0.199822\pi$
$434$	48.6206	+	12.1530i	2.33387	+	0.583362i
$435$	15.0758			0.722829
$436$	10.8624	−	18.8143i	0.520217	−	0.901042i
$437$	−1.39483	−	2.41592i	−0.0667238	−	0.115569i
$438$	−0.427115	−	0.739785i	−0.0204084	−	0.0353483i
$439$	−5.22199	+	9.04475i	−0.249232	+	0.431682i	−0.963313	−	0.268381i	$-0.913511\pi$
$439$	−5.22199	+	9.04475i	−0.249232	+	0.431682i	0.714081	+	0.700063i	$0.246845\pi$
$440$	−9.37471			−0.446922
$441$	−13.0480	+	8.13187i	−0.621332	+	0.387232i
$442$	70.4755			3.35218
$443$	8.89595	−	15.4082i	0.422659	−	0.732067i	−0.573539	−	0.819178i	$-0.694430\pi$
$443$	8.89595	−	15.4082i	0.422659	−	0.732067i	0.996199	+	0.0871106i	$0.0277634\pi$
$444$	−33.5261	−	58.0690i	−1.59108	−	2.75583i
$445$	1.80500	+	3.12635i	0.0855652	+	0.148203i
$446$	−27.6509	+	47.8928i	−1.30931	+	2.26779i
$447$	−33.0973			−1.56545
$448$	73.8005	+	18.4468i	3.48675	+	0.871531i
$449$	−12.1911			−0.575333			−0.287666	−	0.957731i	$-0.592879\pi$
$449$	−12.1911			−0.575333			−0.287666	+	0.957731i	$0.592879\pi$
$450$	2.99494	−	5.18739i	0.141183	−	0.244536i
$451$	0.898357	+	1.55600i	0.0423020	+	0.0732692i
$452$	21.4884	+	37.2190i	1.01073	+	1.75063i
$453$	−5.32649	+	9.22574i	−0.250260	+	0.433463i
$454$	−54.1261			−2.54026
$455$	10.0558	−	10.4008i	0.471422	−	0.487595i
$456$	50.4922			2.36451
$457$	0.111616	−	0.193325i	0.00522120	−	0.00904338i	−0.863403	−	0.504515i	$-0.831671\pi$
$457$	0.111616	−	0.193325i	0.00522120	−	0.00904338i	0.868624	+	0.495471i	$0.165005\pi$
$458$	−10.7715	−	18.6568i	−0.503319	−	0.871774i
$459$	−4.32885	−	7.49779i	−0.202054	−	0.349967i
$460$	−3.21000	+	5.55989i	−0.149667	+	0.259231i
$461$	0.725560			0.0337927			0.0168963	−	0.999857i	$-0.494621\pi$
$461$	0.725560			0.0337927			0.0168963	+	0.999857i	$0.494621\pi$
$462$	−4.52434	−	15.8135i	−0.210491	−	0.735710i
$463$	−37.1959			−1.72864			−0.864320	−	0.502943i	$-0.832251\pi$
$463$	−37.1959			−1.72864			−0.864320	+	0.502943i	$0.832251\pi$
$464$	48.5810	−	84.1448i	2.25532	−	3.90633i
$465$	−7.91658	−	13.7119i	−0.367123	−	0.635875i
$466$	−0.633406	−	1.09709i	−0.0293419	−	0.0508217i
$467$	13.4643	−	23.3209i	0.623055	−	1.07916i	−0.365859	−	0.930670i	$-0.619225\pi$
$467$	13.4643	−	23.3209i	0.623055	−	1.07916i	0.988914	−	0.148492i	$-0.0474421\pi$
$468$	65.3032			3.01864
$469$	−8.78384	−	30.7013i	−0.405600	−	1.41765i
$470$	15.3020			0.705828
$471$	16.4312	−	28.4597i	0.757109	−	1.31135i
$472$	5.77268	+	9.99858i	0.265709	+	0.460222i
$473$	−4.73342	−	8.19853i	−0.217643	−	0.376969i
$474$	−40.0195	+	69.3158i	−1.83816	+	3.18378i
$475$	−2.36274			−0.108410
$476$	47.2585	−	48.8799i	2.16609	−	2.24040i
$477$	−10.4970			−0.480623
$478$	−38.4768	+	66.6437i	−1.75989	+	3.04821i
$479$	10.9525	+	18.9703i	0.500434	+	0.866777i	1.00000		0.000501378i	$0.000159594\pi$
$479$	10.9525	+	18.9703i	0.500434	+	0.866777i	−0.499566	+	0.866276i	$0.666507\pi$
$480$	−24.2966	−	42.0829i	−1.10898	−	1.92081i
$481$	−14.7898	+	25.6167i	−0.674358	+	1.16802i
$482$	−0.0222558			−0.00101373
$483$	−6.90835	−	1.72678i	−0.314341	−	0.0785711i
$484$	5.43751			0.247160
$485$	2.93441	−	5.08254i	0.133245	−	0.230786i
$486$	−25.9679	−	44.9777i	−1.17793	−	2.04023i
$487$	−9.96769	−	17.2645i	−0.451679	−	0.782331i	0.546811	−	0.837256i	$-0.315841\pi$
$487$	−9.96769	−	17.2645i	−0.451679	−	0.782331i	−0.998490	+	0.0549247i	$0.982508\pi$
$488$	−52.3046	+	90.5943i	−2.36772	+	4.10101i
$489$	13.2837			0.600711
$490$	−0.643705	−	19.0794i	−0.0290796	−	0.861920i
$491$	12.3067			0.555395			0.277698	−	0.960669i	$-0.410429\pi$
$491$	12.3067			0.555395			0.277698	+	0.960669i	$0.410429\pi$
$492$	−11.1352	+	19.2868i	−0.502015	+	0.869515i
$493$	−15.6277	−	27.0680i	−0.703836	−	1.21908i
$494$	−17.6169	−	30.5134i	−0.792622	−	1.37286i
$495$	−1.09818	+	1.90211i	−0.0493596	+	0.0854934i
$496$	−102.043			−4.58187
$497$	−0.0393087	−	0.00982543i	−0.00176324	−	0.000440731i
$498$	63.7034			2.85462
$499$	2.07361	−	3.59159i	0.0928273	−	0.160782i	−0.815872	−	0.578232i	$-0.803743\pi$
$499$	2.07361	−	3.59159i	0.0928273	−	0.160782i	0.908700	+	0.417450i	$0.137076\pi$
$500$	2.71876	+	4.70902i	0.121586	+	0.210594i
$501$	−21.1374	−	36.6111i	−0.944351	−	1.63566i
$502$	−5.24859	+	9.09082i	−0.234256	+	0.405743i
$503$	36.7497			1.63859			0.819294	−	0.573374i	$-0.194366\pi$
$503$	36.7497			1.63859			0.819294	+	0.573374i	$0.194366\pi$
$504$	37.8659	−	39.1650i	1.68668	−	1.74455i
$505$	4.79322			0.213296
$506$	1.60997	−	2.78856i	0.0715721	−	0.123966i
$507$	−19.2613	−	33.3615i	−0.855424	−	1.48164i
$508$	−12.3625	−	21.4125i	−0.548499	−	0.950028i
$509$	2.57918	−	4.46727i	0.114320	−	0.198008i	−0.803188	−	0.595726i	$-0.796864\pi$
$509$	2.57918	−	4.46727i	0.114320	−	0.198008i	0.917508	+	0.397718i	$0.130198\pi$
$510$	−29.3804			−1.30099
$511$	0.100001	+	0.349523i	0.00442377	+	0.0154620i
$512$	−37.7208			−1.66704
$513$	−2.16419	+	3.74848i	−0.0955512	+	0.165499i
$514$	13.7372	+	23.7935i	0.605922	+	1.04949i
$515$	−4.02678	−	6.97458i	−0.177441	−	0.307337i
$516$	58.6712	−	101.622i	2.58286	−	4.47364i
$517$	−5.61092			−0.246768
$518$	10.7367	+	37.5268i	0.471742	+	1.64883i
$519$	42.4214			1.86209
$520$	−25.6305	+	44.3934i	−1.12397	+	1.94678i
$521$	−7.78776	−	13.4888i	−0.341188	−	0.590955i	0.643466	−	0.765475i	$-0.277496\pi$
$521$	−7.78776	−	13.4888i	−0.341188	−	0.590955i	−0.984654	+	0.174520i	$0.944163\pi$
$522$	−19.8070	−	34.3068i	−0.866930	−	1.50157i
$523$	−8.12305	+	14.0695i	−0.355196	+	0.615218i	−0.987152	−	0.159787i	$-0.948919\pi$
$523$	−8.12305	+	14.0695i	−0.355196	+	0.615218i	0.631955	+	0.775005i	$0.282253\pi$
$524$	−21.1205			−0.922653
$525$	−4.19214	+	4.33596i	−0.182960	+	0.189237i
$526$	−28.6955			−1.25118
$527$	−16.4128	+	28.4278i	−0.714952	+	1.23833i
$528$	16.7450	+	29.0033i	0.728734	+	1.26220i
$529$	10.8030	+	18.7113i	0.469695	+	0.813536i
$530$	6.51693	−	11.2877i	0.283077	−	0.490304i
$531$	2.70492			0.117384
$532$	−32.9766	−	8.24267i	−1.42972	−	0.357365i
$533$	9.82446			0.425545
$534$	11.2212	−	19.4358i	0.485590	−	0.841067i
$535$	7.89300	+	13.6711i	0.341244	+	0.591052i
$536$	56.5745	+	97.9899i	2.44365	+	4.23252i
$537$	−12.0177	+	20.8153i	−0.518603	+	0.898247i
$538$	−26.1388			−1.12693
$539$	0.236033	+	6.99602i	0.0101667	+	0.301340i
$540$	9.96113			0.428659
$541$	6.55818	−	11.3591i	0.281958	−	0.488366i	−0.689909	−	0.723896i	$-0.742349\pi$
$541$	6.55818	−	11.3591i	0.281958	−	0.488366i	0.971867	+	0.235530i	$0.0756827\pi$
$542$	10.1563	+	17.5912i	0.436249	+	0.755606i
$543$	12.6478	+	21.9066i	0.542768	+	0.940102i
$544$	−50.3720	+	87.2469i	−2.15968	+	3.74068i
$545$	3.99537			0.171143
$546$	−87.2534	−	21.8095i	−3.73410	−	0.933359i
$547$	−18.5433			−0.792856			−0.396428	−	0.918066i	$-0.629750\pi$
$547$	−18.5433			−0.792856			−0.396428	+	0.918066i	$0.629750\pi$
$548$	17.5500	−	30.3975i	0.749700	−	1.29852i
$549$	12.2543	+	21.2250i	0.522999	+	0.905860i
$550$	−1.36359	−	2.36181i	−0.0581437	−	0.100708i
$551$	−7.81298	+	13.5325i	−0.332844	+	0.576503i
$552$	25.2315			1.07392
$553$	23.6768	−	24.4891i	1.00684	−	1.04138i
$554$	−53.6541			−2.27954
$555$	6.16572	−	10.6793i	0.261720	−	0.453312i
$556$	17.1677	+	29.7353i	0.728071	+	1.26106i
$557$	−16.1744	−	28.0149i	−0.685332	−	1.18703i	−0.973332	−	0.229400i	$-0.926324\pi$
$557$	−16.1744	−	28.0149i	−0.685332	−	1.18703i	0.288000	−	0.957630i	$-0.407010\pi$
$558$	−20.8021	+	36.0302i	−0.880621	+	1.52528i
$559$	−51.7648			−2.18942
$560$	10.6920	+	37.3706i	0.451818	+	1.57920i
$561$	10.7732			0.454844
$562$	−44.8873	+	77.7471i	−1.89346	+	3.27956i
$563$	3.87345	+	6.70901i	0.163246	+	0.282751i	0.936031	−	0.351917i	$-0.114470\pi$
$563$	3.87345	+	6.70901i	0.163246	+	0.282751i	−0.772785	+	0.634668i	$0.781137\pi$
$564$	−34.7739	−	60.2302i	−1.46425	−	2.53615i
$565$	−3.95188	+	6.84485i	−0.166257	+	0.287965i
$566$	41.3930			1.73988
$567$	7.83445	+	27.3830i	0.329016	+	1.14998i
$568$	0.143568			0.00602398
$569$	−3.36364	+	5.82600i	−0.141011	+	0.244239i	−0.927878	−	0.372885i	$-0.878369\pi$
$569$	−3.36364	+	5.82600i	−0.141011	+	0.244239i	0.786866	+	0.617123i	$0.211702\pi$
$570$	7.34429	+	12.7207i	0.307619	+	0.532811i
$571$	10.1712	+	17.6170i	0.425652	+	0.737250i	0.996481	−	0.0838184i	$-0.0267116\pi$
$571$	10.1712	+	17.6170i	0.425652	+	0.737250i	−0.570829	+	0.821069i	$0.693378\pi$
$572$	14.8662	−	25.7490i	0.621587	−	1.07662i
$573$	−34.2437			−1.43055
$574$	9.01111	−	9.32026i	0.376117	−	0.389020i
$575$	−1.18069			−0.0492381
$576$	−31.5751	+	54.6897i	−1.31563	+	2.27874i
$577$	−8.03874	−	13.9235i	−0.334657	−	0.579643i	0.648762	−	0.760992i	$-0.275287\pi$
$577$	−8.03874	−	13.9235i	−0.334657	−	0.579643i	−0.983419	+	0.181348i	$0.941954\pi$
$578$	7.27496	+	12.6006i	0.302599	+	0.524116i
$579$	27.2830	−	47.2555i	1.13384	−	1.96387i
$580$	35.9609			1.49320
$581$	−26.3020	−	6.57431i	−1.09119	−	0.272749i
$582$	−36.4850			−1.51235
$583$	−2.38962	+	4.13895i	−0.0989680	+	0.171418i
$584$	−0.644079	−	1.11558i	−0.0266522	−	0.0461629i
$585$	6.00488	+	10.4008i	0.248271	+	0.430018i
$586$	−18.4000	+	31.8697i	−0.760095	+	1.31652i
$587$	−17.5446			−0.724142			−0.362071	−	0.932151i	$-0.617930\pi$
$587$	−17.5446			−0.724142			−0.362071	+	0.932151i	$0.617930\pi$
$588$	−73.6357	+	45.8919i	−3.03669	+	1.89255i
$589$	16.4110			0.676202
$590$	−1.67932	+	2.90867i	−0.0691365	+	0.119748i
$591$	−17.8203	−	30.8656i	−0.733029	−	1.26964i
$592$	−39.7374	−	68.8272i	−1.63320	−	2.82878i
$593$	−3.84732	+	6.66376i	−0.157991	+	0.273648i	−0.934144	−	0.356896i	$-0.883835\pi$
$593$	−3.84732	+	6.66376i	−0.157991	+	0.273648i	0.776153	+	0.630544i	$0.217168\pi$
$594$	−4.99600			−0.204988
$595$	12.1306	+	3.03212i	0.497308	+	0.124305i
$596$	−78.9482			−3.23384
$597$	−12.7785	+	22.1330i	−0.522988	+	0.905842i
$598$	−8.80336	−	15.2479i	−0.359996	−	0.623532i
$599$	−7.97120	−	13.8065i	−0.325694	−	0.564119i	0.655958	−	0.754797i	$-0.272265\pi$
$599$	−7.97120	−	13.8065i	−0.325694	−	0.564119i	−0.981653	+	0.190678i	$0.938931\pi$
$600$	10.6851	−	18.5071i	0.436217	−	0.755549i
$601$	31.7950			1.29694			0.648472	−	0.761238i	$-0.275408\pi$
$601$	31.7950			1.29694			0.648472	+	0.761238i	$0.275408\pi$
$602$	−47.4793	+	49.1082i	−1.93511	+	2.00150i
$603$	26.5092			1.07954
$604$	−12.7055	+	22.0065i	−0.516979	+	0.895433i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−14.8991	−	25.8061i	−0.605237	−	1.04830i
$607$	−22.8434	+	39.5659i	−0.927183	+	1.60593i	−0.139171	+	0.990268i	$0.544444\pi$
$607$	−22.8434	+	39.5659i	−0.927183	+	1.60593i	−0.788012	+	0.615660i	$0.788889\pi$
$608$	50.3664			2.04263
$609$	10.9717	+	38.3482i	0.444594	+	1.55395i
$610$	−30.4317			−1.23214
$611$	−15.3403	+	26.5701i	−0.620601	+	1.07491i
$612$	28.2208	+	48.8799i	1.14076	+	1.97585i
$613$	−6.53260	−	11.3148i	−0.263849	−	0.457001i	0.703412	−	0.710782i	$-0.251659\pi$
$613$	−6.53260	−	11.3148i	−0.263849	−	0.457001i	−0.967262	+	0.253782i	$0.918326\pi$
$614$	22.8320	−	39.5461i	0.921423	−	1.59595i
$615$	−4.09571			−0.165155
$616$	−6.82259	−	23.8464i	−0.274890	−	0.960797i
$617$	−10.0586			−0.404944			−0.202472	−	0.979288i	$-0.564897\pi$
$617$	−10.0586			−0.404944			−0.202472	+	0.979288i	$0.564897\pi$
$618$	−25.0335	+	43.3593i	−1.00699	+	1.74416i
$619$	−7.13123	−	12.3517i	−0.286628	−	0.496455i	0.686374	−	0.727248i	$-0.259201\pi$
$619$	−7.13123	−	12.3517i	−0.286628	−	0.496455i	−0.973003	+	0.230793i	$0.925868\pi$
$620$	−18.8837	−	32.7076i	−0.758389	−	1.31357i
$621$	−1.08147	+	1.87316i	−0.0433978	+	0.0751672i
$622$	−13.8481			−0.555258
$623$	−6.63885	+	6.86661i	−0.265980	+	0.275105i
$624$	183.124			7.33083
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.64351	+	4.57869i	0.105656	+	0.183001i
$627$	−2.69300	−	4.66441i	−0.107548	−	0.186279i
$628$	39.1940	−	67.8859i	1.56401	−	2.70894i
$629$	−25.5657			−1.01937
$630$	15.3747	+	3.84300i	0.612544	+	0.153109i
$631$	48.8052			1.94291			0.971453	−	0.237231i	$-0.0762400\pi$
$631$	48.8052			1.94291			0.971453	+	0.237231i	$0.0762400\pi$
$632$	−60.3484	+	104.527i	−2.40053	+	4.15784i
$633$	−5.57842	−	9.66211i	−0.221722	−	0.384034i
$634$	−16.5071	−	28.5912i	−0.655582	−	1.13550i
$635$	2.27356	−	3.93793i	0.0902237	−	0.156272i
$636$	−59.2392			−2.34899
$637$	33.7745	+	18.0094i	1.33820	+	0.713560i
$638$	−18.0362			−0.714059
$639$	0.0168180	−	0.0291296i	0.000665310	−	0.00115235i
$640$	−17.8892	−	30.9850i	−0.707133	−	1.22479i
$641$	18.7362	+	32.4521i	0.740037	+	1.28178i	0.952478	+	0.304608i	$0.0985255\pi$
$641$	18.7362	+	32.4521i	0.740037	+	1.28178i	−0.212441	+	0.977174i	$0.568141\pi$
$642$	49.0688	−	84.9897i	1.93659	−	3.35428i
$643$	24.1431			0.952109			0.476055	−	0.879416i	$-0.342066\pi$
$643$	24.1431			0.952109			0.476055	+	0.879416i	$0.342066\pi$
$644$	−16.4788	−	4.11895i	−0.649354	−	0.162310i
$645$	21.5802			0.849719
$646$	15.2263	−	26.3727i	0.599071	−	1.03762i
$647$	4.07895	+	7.06494i	0.160360	+	0.277752i	0.934998	−	0.354654i	$-0.115401\pi$
$647$	4.07895	+	7.06494i	0.160360	+	0.277752i	−0.774638	+	0.632405i	$0.782068\pi$
$648$	−50.4597	−	87.3988i	−1.98225	−	3.43335i
$649$	0.615772	−	1.06655i	0.0241712	−	0.0418657i
$650$	−14.9123			−0.584907
$651$	29.1174	−	30.1164i	1.14120	−	1.18035i
$652$	31.6862			1.24093
$653$	−11.7211	+	20.3015i	−0.458682	+	0.794460i	−0.998892	−	0.0470703i	$-0.985012\pi$
$653$	−11.7211	+	20.3015i	−0.458682	+	0.794460i	0.540210	+	0.841530i	$0.318345\pi$
$654$	−12.4191	−	21.5106i	−0.485626	−	0.841130i
$655$	−1.94211	−	3.36383i	−0.0758845	−	0.131436i
$656$	−13.1982	+	22.8600i	−0.515304	+	0.892532i
$657$	−0.301798			−0.0117743
$658$	11.1363	+	38.9235i	0.434136	+	1.51740i
$659$	−18.6914			−0.728113			−0.364056	−	0.931377i	$-0.618608\pi$
$659$	−18.6914			−0.728113			−0.364056	+	0.931377i	$0.618608\pi$
$660$	−6.19755	+	10.7345i	−0.241239	+	0.417839i
$661$	13.6071	+	23.5682i	0.529255	+	0.916697i	0.999418	+	0.0341168i	$0.0108618\pi$
$661$	13.6071	+	23.5682i	0.529255	+	0.916697i	−0.470163	+	0.882580i	$0.655805\pi$
$662$	−34.9828	−	60.5921i	−1.35965	−	2.35498i
$663$	29.4540	−	51.0158i	1.14390	−	1.98129i
$664$	96.0631			3.72797
$665$	−1.71952	−	6.01008i	−0.0666802	−	0.233061i
$666$	−32.4028			−1.25558
$667$	−3.90423	+	6.76233i	−0.151173	+	0.261838i
$668$	−50.4200	−	87.3300i	−1.95081	−	3.37890i
$669$	23.1124	+	40.0319i	0.893578	+	1.54772i
$670$	−16.4580	+	28.5061i	−0.635827	+	1.10128i
$671$	11.1587			0.430775
$672$	89.3636	−	92.4294i	3.44728	−	3.56554i
$673$	−6.11464			−0.235702			−0.117851	−	0.993031i	$-0.537601\pi$
$673$	−6.11464			−0.235702			−0.117851	+	0.993031i	$0.537601\pi$
$674$	−45.6189	+	79.0142i	−1.75717	+	3.04351i
$675$	0.915964	+	1.58650i	0.0352555	+	0.0610643i
$676$	−45.9447	−	79.5786i	−1.76711	−	3.06072i
$677$	19.6548	−	34.0432i	0.755397	−	1.30839i	−0.189780	−	0.981827i	$-0.560777\pi$
$677$	19.6548	−	34.0432i	0.755397	−	1.30839i	0.945177	−	0.326559i	$-0.105889\pi$
$678$	49.1357			1.88705
$679$	15.0640	+	3.76532i	0.578102	+	0.144500i
$680$	−44.3050			−1.69902
$681$	−22.6211	+	39.1808i	−0.866841	+	1.50141i
$682$	9.47112	+	16.4045i	0.362668	+	0.628160i
$683$	21.1454	+	36.6249i	0.809105	+	1.40141i	0.913485	+	0.406873i	$0.133381\pi$
$683$	21.1454	+	36.6249i	0.809105	+	1.40141i	−0.104380	+	0.994538i	$0.533286\pi$
$684$	14.1088	−	24.4372i	0.539465	−	0.934380i
$685$	6.45517			0.246639
$686$	48.0636	−	15.5227i	1.83508	−	0.592660i
$687$	−18.0070			−0.687011
$688$	69.5411	−	120.449i	2.65123	−	4.59206i
$689$	13.0665	+	22.6318i	0.497793	+	0.862203i
$690$	3.67002	+	6.35667i	0.139715	+	0.241994i
$691$	12.6916	−	21.9826i	0.482812	−	0.836256i	−0.516993	−	0.855990i	$-0.672949\pi$
$691$	12.6916	−	21.9826i	0.482812	−	0.836256i	0.999805	+	0.0197340i	$0.00628195\pi$
$692$	101.190			3.84665
$693$	−5.63759	−	1.40915i	−0.214154	−	0.0535291i
$694$	20.5866			0.781457
$695$	−3.15727	+	5.46855i	−0.119762	+	0.207434i
$696$	−70.6656	−	122.396i	−2.67857	−	4.63943i
$697$	4.24564	+	7.35367i	0.160815	+	0.278540i
$698$	40.2103	−	69.6463i	1.52198	−	2.63615i
$699$	−1.05888			−0.0400506
$700$	−9.99967	+	10.3427i	−0.377952	+	0.390919i
$701$	−38.8573			−1.46762			−0.733809	−	0.679355i	$-0.762259\pi$
$701$	−38.8573			−1.46762			−0.733809	+	0.679355i	$0.762259\pi$
$702$	−13.6591	+	23.6582i	−0.515529	+	0.892923i
$703$	6.39072	+	11.0691i	0.241031	+	0.417477i
$704$	14.3761	+	24.9001i	0.541819	+	0.938458i
$705$	6.39519	−	11.0768i	0.240857	−	0.417176i
$706$	5.67215			0.213474
$707$	3.48834	+	12.1925i	0.131193	+	0.458545i
$708$	15.2651			0.573698
$709$	−6.77507	+	11.7348i	−0.254443	+	0.440708i	−0.964744	−	0.263190i	$-0.915225\pi$
$709$	−6.77507	+	11.7348i	−0.254443	+	0.440708i	0.710301	+	0.703898i	$0.248559\pi$
$710$	0.0208826	+	0.0361697i	0.000783708	+	0.00135742i
$711$	14.1388	+	24.4891i	0.530247	+	0.918414i
$712$	16.9213	−	29.3086i	0.634154	−	1.09839i
$713$	8.20074			0.307120
$714$	−21.3821	−	74.7347i	−0.800204	−	2.79688i
$715$	5.46801			0.204492
$716$	−28.6664	+	49.6516i	−1.07131	+	1.85557i
$717$	32.1614	+	55.7052i	1.20109	+	2.08035i
$718$	38.2090	+	66.1798i	1.42595	+	2.46981i
$719$	−8.64269	+	14.9696i	−0.322318	+	0.558271i	−0.980966	−	0.194180i	$-0.937795\pi$
$719$	−8.64269	+	14.9696i	−0.322318	+	0.558271i	0.658648	+	0.752451i	$0.271129\pi$
$720$	−32.2679			−1.20255
$721$	14.8106	−	15.3187i	0.551576	−	0.570499i
$722$	36.5918			1.36181
$723$	−0.00930144	+	0.0161106i	−0.000345924	+	0.000599158i
$724$	30.1693	+	52.2547i	1.12123	+	1.94203i
$725$	3.30674	+	5.72745i	0.122809	+	0.212712i
$726$	3.10838	−	5.38387i	0.115363	−	0.199814i
$727$	8.84654			0.328100			0.164050	−	0.986452i	$-0.447544\pi$
$727$	8.84654			0.328100			0.164050	+	0.986452i	$0.447544\pi$
$728$	−131.576	−	32.8881i	−4.87653	−	1.21891i
$729$	−11.1161			−0.411708
$730$	0.187368	−	0.324531i	0.00693480	−	0.0120114i
$731$	−22.3702	−	38.7463i	−0.827391	−	1.43308i
$732$	69.1564	+	119.782i	2.55609	+	4.42728i
$733$	−0.999337	+	1.73090i	−0.0369113	+	0.0639323i	−0.883891	−	0.467693i	$-0.845085\pi$
$733$	−0.999337	+	1.73090i	−0.0369113	+	0.0639323i	0.846980	+	0.531625i	$0.178419\pi$
$734$	78.0587			2.88120
$735$	−14.0802	−	7.50794i	−0.519357	−	0.276934i
$736$	25.1687			0.927729
$737$	6.03480	−	10.4526i	0.222295	−	0.385026i
$738$	5.38105	+	9.32026i	0.198079	+	0.343084i
$739$	11.9330	+	20.6686i	0.438963	+	0.760307i	0.997610	−	0.0690992i	$-0.0220125\pi$
$739$	11.9330	+	20.6686i	0.438963	+	0.760307i	−0.558647	+	0.829406i	$0.688679\pi$
$740$	14.7073	−	25.4738i	0.540652	−	0.936437i
$741$	−29.4507			−1.08190
$742$	33.4551	+	8.36228i	1.22817	+	0.306989i
$743$	−4.51085			−0.165487			−0.0827435	−	0.996571i	$-0.526368\pi$
$743$	−4.51085			−0.165487			−0.0827435	+	0.996571i	$0.526368\pi$
$744$	−74.2156	+	128.545i	−2.72088	+	4.71270i
$745$	−7.25959	−	12.5740i	−0.265971	−	0.460675i
$746$	−9.01358	−	15.6120i	−0.330011	−	0.571595i
$747$	11.2531	−	19.4910i	0.411731	−	0.713138i
$748$	25.6977			0.939602
$749$	−29.0307	+	30.0267i	−1.06076	+	1.09715i
$750$	6.21675			0.227004
$751$	9.07067	−	15.7109i	0.330993	−	0.573297i	−0.651714	−	0.758465i	$-0.725950\pi$
$751$	9.07067	−	15.7109i	0.330993	−	0.573297i	0.982707	+	0.185168i	$0.0592829\pi$
$752$	−41.2164	−	71.3889i	−1.50301	−	2.60328i
$753$	4.38711	+	7.59870i	0.159875	+	0.276912i
$754$	−49.3110	+	85.4092i	−1.79580	+	3.11042i
$755$	−4.67327			−0.170078
$756$	7.24937	+	25.3380i	0.263657	+	0.921535i
$757$	−33.7552			−1.22685			−0.613426	−	0.789752i	$-0.710209\pi$
$757$	−33.7552			−1.22685			−0.613426	+	0.789752i	$0.710209\pi$
$758$	24.0506	−	41.6568i	0.873556	−	1.51304i
$759$	−1.34572	−	2.33086i	−0.0488466	−	0.0846048i
$760$	11.0750	+	19.1825i	0.401733	+	0.695822i
$761$	−3.81565	+	6.60890i	−0.138317	+	0.239572i	−0.926860	−	0.375408i	$-0.877503\pi$
$761$	−3.81565	+	6.60890i	−0.138317	+	0.239572i	0.788543	+	0.614980i	$0.210836\pi$
$762$	−28.2684			−1.02406
$763$	2.90770	+	10.1630i	0.105266	+	0.367925i
$764$	−81.6829			−2.95518
$765$	−5.19002	+	8.98938i	−0.187646	+	0.325012i
$766$	20.2103	+	35.0052i	0.730227	+	1.26479i
$767$	−3.36705	−	5.83190i	−0.121577	−	0.210578i
$768$	−45.6707	+	79.1039i	−1.64800	+	2.85442i
$769$	3.79188			0.136739			0.0683694	−	0.997660i	$-0.478220\pi$
$769$	3.79188			0.136739			0.0683694	+	0.997660i	$0.478220\pi$
$770$	5.01533	−	5.18739i	0.180740	−	0.186941i
$771$	22.9649			0.827060
$772$	65.0791	−	112.720i	2.34225	−	4.05689i
$773$	13.2375	+	22.9281i	0.476121	+	0.824665i	0.999626	−	0.0273574i	$-0.00870920\pi$
$773$	13.2375	+	22.9281i	0.476121	+	0.824665i	−0.523505	+	0.852023i	$0.675376\pi$
$774$	−28.3526	−	49.1082i	−1.01911	−	1.76516i
$775$	3.47286	−	6.01518i	0.124749	−	0.216072i
$776$	−55.0184			−1.97505
$777$	31.6521	+	7.91161i	1.13551	+	0.283828i
$778$	54.8895			1.96788
$779$	2.12259	−	3.67643i	0.0760495	−	0.131722i
$780$	33.8883	+	58.6962i	1.21340	+	2.10166i
$781$	−0.00765720	−	0.0132627i	−0.000273996	−	0.000474575i
$782$	7.60875	−	13.1787i	0.272088	−	0.471271i
$783$	12.1154			0.432970
$784$	−87.2780	+	54.3941i	−3.11707	+	1.94265i
$785$	14.4161			0.514534
$786$	−12.0736	+	20.9121i	−0.430652	+	0.745911i
$787$	0.0162484	+	0.0281430i	0.000579192	+	0.00100319i	0.866315	−	0.499498i	$-0.166482\pi$
$787$	0.0162484	+	0.0281430i	0.000579192	+	0.00100319i	−0.865736	+	0.500502i	$0.833149\pi$
$788$	−42.5074	−	73.6251i	−1.51426	−	2.62278i
$789$	−11.9928	+	20.7721i	−0.426955	+	0.739507i
$790$	−35.1117			−1.24922
$791$	−20.2872	−	5.07090i	−0.721331	−	0.180300i
$792$	20.5903			0.731644
$793$	30.5079	−	52.8412i	1.08337	−	1.87645i
$794$	14.8585	+	25.7357i	0.527309	+	0.913325i
$795$	−5.44727	−	9.43495i	−0.193195	−	0.334623i
$796$	−30.4810	+	52.7947i	−1.08037	+	1.87126i
$797$	43.9580			1.55707			0.778536	−	0.627600i	$-0.215963\pi$
$797$	43.9580			1.55707			0.778536	+	0.627600i	$0.215963\pi$
$798$	−27.0126	+	27.9393i	−0.956234	+	0.989040i
$799$	−26.5172			−0.938112
$800$	10.6585	−	18.4610i	0.376834	−	0.652696i
$801$	−3.96444	−	6.86661i	−0.140077	−	0.242620i
$802$	−35.4836	−	61.4594i	−1.25297	−	2.17021i
$803$	−0.0687039	+	0.118999i	−0.00242451	+	0.00419937i
$804$	149.604			5.27612
$805$	−0.859264	−	3.00330i	−0.0302851	−	0.105853i
$806$	103.576			3.64833
$807$	−10.9243	+	18.9214i	−0.384553	+	0.666065i
$808$	−22.4675	−	38.9149i	−0.790406	−	1.36902i
$809$	−9.02272	−	15.6278i	−0.317222	−	0.549445i	0.662685	−	0.748898i	$-0.269417\pi$
$809$	−9.02272	−	15.6278i	−0.317222	−	0.549445i	−0.979907	+	0.199453i	$0.936083\pi$
$810$	14.6791	−	25.4250i	0.515773	−	0.893345i
$811$	−41.4420			−1.45523			−0.727613	−	0.685988i	$-0.759370\pi$
$811$	−41.4420			−1.45523			−0.727613	+	0.685988i	$0.759370\pi$
$812$	26.1711	+	91.4734i	0.918426	+	3.21009i
$813$	16.9785			0.595463
$814$	−7.37645	+	12.7764i	−0.258544	+	0.447812i
$815$	2.91367	+	5.04663i	0.102061	+	0.176776i
$816$	79.1372	+	137.070i	2.77036	+	4.79840i
$817$	−11.1839	+	19.3710i	−0.391273	+	0.677706i
$818$	−78.2360			−2.73546
$819$	−22.0861	+	22.8439i	−0.771753	+	0.798229i
$820$	−9.76965			−0.341171
$821$	−11.1529	+	19.3173i	−0.389238	+	0.674180i	−0.992347	−	0.123479i	$-0.960595\pi$
$821$	−11.1529	+	19.3173i	−0.389238	+	0.674180i	0.603109	+	0.797659i	$0.293928\pi$
$822$	−20.0651	−	34.7538i	−0.699851	−	1.21218i
$823$	6.43124	+	11.1392i	0.224179	+	0.388290i	0.956073	−	0.293129i	$-0.0946966\pi$
$823$	6.43124	+	11.1392i	0.224179	+	0.388290i	−0.731894	+	0.681419i	$0.761363\pi$
$824$	−37.7499	+	65.3847i	−1.31508	+	2.27778i
$825$	−2.27955			−0.0793639
$826$	−8.62090	−	2.15484i	−0.299960	−	0.0749765i
$827$	−42.2135			−1.46791			−0.733954	−	0.679199i	$-0.762327\pi$
$827$	−42.2135			−1.46791			−0.733954	+	0.679199i	$0.762327\pi$
$828$	7.05034	−	12.2115i	0.245016	−	0.424380i
$829$	−12.4329	−	21.5344i	−0.431812	−	0.747920i	0.565218	−	0.824942i	$-0.308792\pi$
$829$	−12.4329	−	21.5344i	−0.431812	−	0.747920i	−0.997029	+	0.0770218i	$0.975459\pi$
$830$	13.9728	+	24.2016i	0.485002	+	0.840048i
$831$	−22.4238	+	38.8391i	−0.777873	+	1.34732i
$832$	157.217			5.45052
$833$	1.11550	+	33.0632i	0.0386496	+	1.14557i
$834$	39.2559			1.35932
$835$	9.27262	−	16.0607i	0.320892	−	0.555802i
$836$	−6.42372	−	11.1262i	−0.222169	−	0.384808i
$837$	−6.36203	−	11.0194i	−0.219904	−	0.380885i
$838$	−9.23702	+	15.9990i	−0.319088	+	0.552676i
$839$	36.3882			1.25626			0.628130	−	0.778108i	$-0.283820\pi$
$839$	36.3882			1.25626			0.628130	+	0.778108i	$0.283820\pi$
$840$	54.8526	+	13.7107i	1.89259	+	0.473064i
$841$	14.7382			0.508215
$842$	4.18290	−	7.24500i	0.144152	−	0.249679i
$843$	37.5197	+	64.9861i	1.29225	+	2.23824i
$844$	−13.3064	−	23.0474i	−0.458026	−	0.793325i
$845$	8.44959	−	14.6351i	0.290675	−	0.503463i
$846$	−33.6087			−1.15549
$847$	−1.83902	+	1.90211i	−0.0631894	+	0.0653572i
$848$	−70.2143			−2.41117
$849$	17.2995	−	29.9636i	0.593717	−	1.02835i
$850$	−6.44434	−	11.1619i	−0.221039	−	0.382851i
$851$	3.19351	+	5.53133i	0.109472	+	0.189611i
$852$	0.0949117	−	0.164392i	0.00325162	−	0.00563198i
$853$	40.3899			1.38292			0.691462	−	0.722413i	$-0.256967\pi$
$853$	40.3899			1.38292			0.691462	+	0.722413i	$0.256967\pi$
$854$	−22.1471	−	77.4088i	−0.757859	−	2.64887i
$855$	5.18945			0.177475
$856$	73.9946	−	128.162i	2.52908	−	4.38050i
$857$	−15.4455	−	26.7524i	−0.527608	−	0.913843i	−0.999482	−	0.0321775i	$-0.989756\pi$
$857$	−15.4455	−	26.7524i	−0.527608	−	0.913843i	0.471875	−	0.881666i	$-0.343578\pi$
$858$	−16.9966	−	29.4391i	−0.580256	−	1.00503i
$859$	5.61335	−	9.72261i	0.191525	−	0.331731i	−0.754231	−	0.656609i	$-0.771990\pi$
$859$	5.61335	−	9.72261i	0.191525	−	0.331731i	0.945756	+	0.324878i	$0.105323\pi$
$860$	51.4761			1.75532
$861$	−2.98072	−	10.4182i	−0.101582	−	0.355052i
$862$	−9.89929			−0.337171
$863$	−22.1378	+	38.3438i	−0.753580	+	1.30524i	0.192497	+	0.981298i	$0.438341\pi$
$863$	−22.1378	+	38.3438i	−0.753580	+	1.30524i	−0.946077	+	0.323941i	$0.894992\pi$
$864$	−19.5256	−	33.8193i	−0.664273	−	1.15055i
$865$	9.30477	+	16.1163i	0.316372	+	0.547972i
$866$	45.9295	−	79.5523i	1.56075	−	2.70330i
$867$	12.1618			0.413035
$868$	69.4550	−	71.8378i	2.35746	−	2.43833i
$869$	12.8747			0.436745
$870$	20.5572	−	35.6061i	0.696955	−	1.20716i
$871$	−32.9984	−	57.1548i	−1.11811	−	1.93662i
$872$	−18.7277	−	32.4374i	−0.634201	−	1.09847i
$873$	−6.44503	+	11.1631i	−0.218131	+	0.377814i
$874$	−7.60791			−0.257341
$875$	−2.56678	−	0.641581i	−0.0867731	−	0.0216894i
$876$	−1.70318			−0.0575452
$877$	2.32101	−	4.02011i	0.0783750	−	0.135750i	−0.824174	−	0.566337i	$-0.808360\pi$
$877$	2.32101	−	4.02011i	0.0783750	−	0.135750i	0.902549	+	0.430587i	$0.141694\pi$
$878$	14.2413	+	24.6667i	0.480621	+	0.832459i
$879$	15.3799	+	26.6387i	0.518750	+	0.898502i
$880$	−7.34575	+	12.7232i	−0.247625	+	0.428899i
$881$	30.4736			1.02668			0.513340	−	0.858185i	$-0.328408\pi$
$881$	30.4736			1.02668			0.513340	+	0.858185i	$0.328408\pi$
$882$	1.41381	+	41.9053i	0.0476055	+	1.41103i
$883$	−3.75846			−0.126482			−0.0632411	−	0.997998i	$-0.520144\pi$
$883$	−3.75846			−0.126482			−0.0632411	+	0.997998i	$0.520144\pi$
$884$	70.2578	−	121.690i	2.36302	−	4.09288i
$885$	1.40368	+	2.43125i	0.0471844	+	0.0817257i
$886$	−24.2609	−	42.0210i	−0.815059	−	1.41172i
$887$	18.0470	−	31.2583i	0.605959	−	1.04955i	−0.385940	−	0.922524i	$-0.626123\pi$
$887$	18.0470	−	31.2583i	0.605959	−	1.04955i	0.991899	−	0.127028i	$-0.0405439\pi$
$888$	−115.604			−3.87940
$889$	11.6715	+	2.91735i	0.391449	+	0.0978449i
$890$	9.84512			0.330009
$891$	−5.38254	+	9.32283i	−0.180322	+	0.312326i
$892$	55.1310	+	95.4897i	1.84592	+	3.19723i
$893$	6.62857	+	11.4810i	0.221817	+	0.384198i
$894$	−45.1311	+	78.1693i	−1.50941	+	2.61437i
$895$	−10.5439			−0.352445
$896$	65.7971	−	68.0544i	2.19813	−	2.27354i
$897$	−14.7168			−0.491381
$898$	−16.6236	+	28.7930i	−0.554738	+	0.960834i
$899$	−22.9677	−	39.7813i	−0.766017	−	1.32678i
$900$	−5.97138	−	10.3427i	−0.199046	−	0.344758i
$901$	−11.2934	+	19.5607i	−0.376237	+	0.651661i
$902$	4.89996			0.163151
$903$	15.7053	+	54.8933i	0.522640	+	1.82673i
$904$	74.0954			2.46438
$905$	−5.54836	+	9.61004i	−0.184434	+	0.319449i
$906$	14.5263	+	25.1603i	0.482604	+	0.835894i
$907$	17.3460	+	30.0441i	0.575964	+	0.997598i	0.995936	+	0.0900616i	$0.0287064\pi$
$907$	17.3460	+	30.0441i	0.575964	+	0.997598i	−0.419972	+	0.907537i	$0.637960\pi$
$908$	−53.9589	+	93.4596i	−1.79069	+	3.10157i
$909$	−10.5277			−0.349181
$910$	−10.8526	−	37.9322i	−0.359761	−	1.25744i
$911$	31.6528			1.04870			0.524351	−	0.851502i	$-0.324308\pi$
$911$	31.6528			1.04870			0.524351	+	0.851502i	$0.324308\pi$
$912$	39.5642	−	68.5272i	1.31010	−	2.26916i
$913$	−5.12353	−	8.87421i	−0.169564	−	0.293693i
$914$	−0.304398	−	0.527233i	−0.0100686	−	0.0174393i
$915$	−12.7184	+	22.0289i	−0.420457	+	0.728253i
$916$	−42.9529			−1.41920
$917$	7.14315	−	7.38821i	0.235888	−	0.243980i
$918$	−23.6111			−0.779283
$919$	−18.5898	+	32.1984i	−0.613220	+	1.06213i	0.377474	+	0.926020i	$0.376793\pi$
$919$	−18.5898	+	32.1984i	−0.613220	+	1.06213i	−0.990694	+	0.136108i	$0.956541\pi$
$920$	5.53430	+	9.58570i	0.182461	+	0.316031i
$921$	−19.0844	−	33.0552i	−0.628854	−	1.08921i
$922$	0.989366	−	1.71363i	0.0325830	−	0.0564355i
$923$	−0.0837393			−0.00275631
$924$	−31.8155	−	7.95246i	−1.04665	−	0.261617i
$925$	5.40958			0.177866
$926$	−50.7199	+	87.8495i	−1.66676	+	2.88691i
$927$	8.84427	+	15.3187i	0.290484	+	0.503133i
$928$	−70.4897	−	122.092i	−2.31394	−	4.00786i
$929$	18.3712	−	31.8199i	0.602741	−	1.04398i	−0.389664	−	0.920957i	$-0.627409\pi$
$929$	18.3712	−	31.8199i	0.602741	−	1.04398i	0.992404	−	0.123020i	$-0.0392579\pi$
$930$	−43.1799			−1.41592
$931$	14.0364	−	8.74786i	0.460024	−	0.286700i
$932$	−2.52580			−0.0827352
$933$	−5.78757	+	10.0244i	−0.189476	+	0.328183i
$934$	−36.7197	−	63.6003i	−1.20150	−	2.08107i
$935$	2.36300	+	4.09284i	0.0772785	+	0.133850i
$936$	56.2940	−	97.5041i	1.84003	−	3.18702i
$937$	−9.75916			−0.318818			−0.159409	−	0.987213i	$-0.550959\pi$
$937$	−9.75916			−0.318818			−0.159409	+	0.987213i	$0.550959\pi$
$938$	−84.4881	−	21.1183i	−2.75863	−	0.689535i
$939$	4.41923			0.144216
$940$	15.2547	−	26.4219i	0.497554	−	0.861788i
$941$	−18.4754	−	32.0003i	−0.602280	−	1.04318i	−0.992475	−	0.122448i	$-0.960926\pi$
$941$	−18.4754	−	32.0003i	−0.602280	−	1.04318i	0.390195	−	0.920732i	$-0.372408\pi$
$942$	−44.8108	−	77.6146i	−1.46002	−	2.52882i
$943$	1.06068	−	1.83715i	0.0345405	−	0.0598259i
$944$	18.0932			0.588884
$945$	−3.36895	+	3.48453i	−0.109592	+	0.113352i
$946$	−25.8178			−0.839409
$947$	0.858037	−	1.48616i	0.0278825	−	0.0482938i	−0.851747	−	0.523953i	$-0.824457\pi$
$947$	0.858037	−	1.48616i	0.0278825	−	0.0482938i	0.879630	+	0.475659i	$0.157790\pi$
$948$	79.7918	+	138.203i	2.59152	+	4.48864i
$949$	0.375674	+	0.650686i	0.0121949	+	0.0211222i
$950$	−3.22181	+	5.58034i	−0.104529	+	0.181050i
$951$	−27.5955			−0.894845
$952$	−32.2436	−	112.698i	−1.04502	−	3.65257i
$953$	3.57532			0.115816			0.0579079	−	0.998322i	$-0.481557\pi$
$953$	3.57532			0.115816			0.0579079	+	0.998322i	$0.481557\pi$
$954$	−14.3136	+	24.7918i	−0.463419	+	0.802664i
$955$	−7.51105	−	13.0095i	−0.243052	−	0.420978i
$956$	76.7158	+	132.876i	2.48117	+	4.29751i
$957$	−7.53790	+	13.0560i	−0.243666	+	0.422041i
$958$	59.7391			1.93008
$959$	4.69785	+	16.4199i	0.151702	+	0.530228i
$960$	−65.5421			−2.11536
$961$	−8.62156	+	14.9330i	−0.278115	+	0.481709i
$962$	40.3345	+	69.8615i	1.30044	+	2.25242i
$963$	−17.3359	−	30.0267i	−0.558642	−	0.967596i
$964$	−0.0221871	+	0.0384292i	−0.000714598	+	0.00123772i
$965$	23.9371			0.770562
$966$	−13.4985	+	13.9616i	−0.434306	+	0.449206i
$967$	−31.1812			−1.00272			−0.501360	−	0.865239i	$-0.667167\pi$
$967$	−31.1812			−1.00272			−0.501360	+	0.865239i	$0.667167\pi$
$968$	4.68736	−	8.11874i	0.150657	−	0.260946i
$969$	−12.7271	−	22.0440i	−0.408854	−	0.708157i
$970$	−8.00265	−	13.8610i	−0.256950	−	0.445050i
$971$	−19.1804	+	33.2214i	−0.615528	+	1.06613i	0.374764	+	0.927120i	$0.377724\pi$
$971$	−19.1804	+	33.2214i	−0.615528	+	1.06613i	−0.990292	+	0.139005i	$0.955609\pi$
$972$	−103.551			−3.32139
$973$	−16.2080	−	4.05128i	−0.519606	−	0.129878i
$974$	−54.3674			−1.74204
$975$	−6.23232	+	10.7947i	−0.199594	+	0.345707i
$976$	81.9688	+	141.974i	2.62376	+	4.54448i
$977$	−26.6264	−	46.1184i	−0.851855	−	1.47546i	−0.879532	−	0.475840i	$-0.842144\pi$
$977$	−26.6264	−	46.1184i	−0.851855	−	1.47546i	0.0276765	−	0.999617i	$-0.491189\pi$
$978$	18.1136	−	31.3736i	0.579208	−	1.00322i
$979$	−3.61000			−0.115376
$980$	−33.5861	−	17.9090i	−1.07287	−	0.572081i
$981$	−8.77530			−0.280174
$982$	16.7813	−	29.0661i	0.535514	−	0.927538i
$983$	10.0549	+	17.4155i	0.320700	+	0.555469i	0.980633	−	0.195856i	$-0.0627485\pi$
$983$	10.0549	+	17.4155i	0.320700	+	0.555469i	−0.659933	+	0.751325i	$0.729415\pi$
$984$	19.1980	+	33.2520i	0.612011	+	1.06003i
$985$	7.81745	−	13.5402i	0.249085	−	0.431427i
$986$	−85.2391			−2.71457
$987$	32.8301	+	8.20607i	1.04499	+	0.261202i
$988$	−70.2500			−2.23495
$989$	−5.58869	+	9.67990i	−0.177710	+	0.307803i
$990$	2.99494	+	5.18739i	0.0951855	+	0.164866i
$991$	−29.4163	−	50.9505i	−0.934439	−	1.61850i	−0.775631	−	0.631187i	$-0.782568\pi$
$991$	−29.4163	−	50.9505i	−0.934439	−	1.61850i	−0.158809	−	0.987309i	$-0.550765\pi$
$992$	−74.0309	+	128.225i	−2.35048	+	4.07115i
$993$	−58.4819			−1.85587
$994$	−0.0768068	+	0.0794418i	−0.00243616	+	0.00251974i
$995$	−11.2114			−0.355425
$996$	63.5066	−	109.997i	2.01228	−	3.48538i
$997$	−17.7687	−	30.7763i	−0.562741	−	0.974695i	−0.997256	−	0.0740309i	$-0.976414\pi$
$997$	−17.7687	−	30.7763i	−0.562741	−	0.974695i	0.434515	−	0.900664i	$-0.356920\pi$
$998$	−5.65509	−	9.79491i	−0.179009	−	0.310052i
$999$	4.95498	−	8.58228i	0.156769	−	0.271531i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.b.331.6	yes	12
7.2	even	3		2695.2.a.r.1.1		6
7.4	even	3	inner	385.2.i.b.221.6	✓	12
7.5	odd	6		2695.2.a.q.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.b.221.6	✓	12	7.4	even	3	inner
385.2.i.b.331.6	yes	12	1.1	even	1	trivial
2695.2.a.q.1.1		6	7.5	odd	6
2695.2.a.r.1.1		6	7.2	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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36359 - 2.36181i) q^{2} +(-1.13978 - 1.97415i) q^{3} +(-2.71876 - 4.70902i) q^{4} +(0.500000 - 0.866025i) q^{5} -6.21675 q^{6} +(2.56678 + 0.641581i) q^{7} -9.37471 q^{8} +(-1.09818 + 1.90211i) q^{9} +O(q^{10})\)	\(q+(1.36359 - 2.36181i) q^{2} +(-1.13978 - 1.97415i) q^{3} +(-2.71876 - 4.70902i) q^{4} +(0.500000 - 0.866025i) q^{5} -6.21675 q^{6} +(2.56678 + 0.641581i) q^{7} -9.37471 q^{8} +(-1.09818 + 1.90211i) q^{9} +(-1.36359 - 2.36181i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-6.19755 + 10.7345i) q^{12} +5.46801 q^{13} +(5.01533 - 5.18739i) q^{14} -2.27955 q^{15} +(-7.34575 + 12.7232i) q^{16} +(2.36300 + 4.09284i) q^{17} +(2.99494 + 5.18739i) q^{18} +(1.18137 - 2.04619i) q^{19} -5.43751 q^{20} +(-1.65898 - 5.79848i) q^{21} +2.72718 q^{22} +(0.590344 - 1.02251i) q^{23} +(10.6851 + 18.5071i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(7.45613 - 12.9144i) q^{26} -1.83193 q^{27} +(-3.95723 - 13.8313i) q^{28} -6.61349 q^{29} +(-3.10838 + 5.38387i) q^{30} +(3.47286 + 6.01518i) q^{31} +(10.6585 + 18.4610i) q^{32} +(1.13978 - 1.97415i) q^{33} +12.8887 q^{34} +(1.83902 - 1.90211i) q^{35} +11.9428 q^{36} +(-2.70479 + 4.68483i) q^{37} +(-3.22181 - 5.58034i) q^{38} +(-6.23232 - 10.7947i) q^{39} +(-4.68736 + 8.11874i) q^{40} +1.79671 q^{41} +(-15.9571 - 3.98855i) q^{42} -9.46684 q^{43} +(2.71876 - 4.70902i) q^{44} +(1.09818 + 1.90211i) q^{45} +(-1.60997 - 2.78856i) q^{46} +(-2.80546 + 4.85920i) q^{47} +33.4901 q^{48} +(6.17675 + 3.29360i) q^{49} -2.72718 q^{50} +(5.38660 - 9.32986i) q^{51} +(-14.8662 - 25.7490i) q^{52} +(2.38962 + 4.13895i) q^{53} +(-2.49800 + 4.32666i) q^{54} +1.00000 q^{55} +(-24.0628 - 6.01464i) q^{56} -5.38600 q^{57} +(-9.01809 + 15.6198i) q^{58} +(-0.615772 - 1.06655i) q^{59} +(6.19755 + 10.7345i) q^{60} +(5.57933 - 9.66369i) q^{61} +18.9422 q^{62} +(-4.03915 + 4.17773i) q^{63} +28.7522 q^{64} +(2.73401 - 4.73544i) q^{65} +(-3.10838 - 5.38387i) q^{66} +(-6.03480 - 10.4526i) q^{67} +(12.8489 - 22.2549i) q^{68} -2.69144 q^{69} +(-1.98475 - 6.93710i) q^{70} -0.0153144 q^{71} +(10.2951 - 17.8317i) q^{72} +(0.0687039 + 0.118999i) q^{73} +(7.37645 + 12.7764i) q^{74} +(-1.13978 + 1.97415i) q^{75} -12.8474 q^{76} +(0.727766 + 2.54369i) q^{77} -33.9933 q^{78} +(6.43736 - 11.1498i) q^{79} +(7.34575 + 12.7232i) q^{80} +(5.38254 + 9.32283i) q^{81} +(2.44998 - 4.24349i) q^{82} -10.2471 q^{83} +(-22.7948 + 23.5768i) q^{84} +4.72601 q^{85} +(-12.9089 + 22.3589i) q^{86} +(7.53790 + 13.0560i) q^{87} +(-4.68736 - 8.11874i) q^{88} +(-1.80500 + 3.12635i) q^{89} +5.98988 q^{90} +(14.0352 + 3.50817i) q^{91} -6.42000 q^{92} +(7.91658 - 13.7119i) q^{93} +(7.65099 + 13.2519i) q^{94} +(-1.18137 - 2.04619i) q^{95} +(24.2966 - 42.0829i) q^{96} +5.86881 q^{97} +(16.2014 - 10.0972i) q^{98} -2.19637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9 - 3 * q^10 + 6 * q^11 - 9 * q^12 + 28 * q^13 - 3 * q^14 - 2 * q^15 - 11 * q^16 - 3 * q^17 + 9 * q^18 + 3 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^22 + 10 * q^23 + 10 * q^24 - 6 * q^25 + 17 * q^26 + 2 * q^27 - 10 * q^28 - 32 * q^29 - 5 * q^30 - 2 * q^31 + 26 * q^32 + q^33 + 60 * q^34 - 3 * q^35 + 16 * q^36 - 5 * q^37 - q^38 - 3 * q^39 - 9 * q^40 - 18 * q^41 - 56 * q^42 - 40 * q^43 + 5 * q^44 - q^45 + 20 * q^46 - q^47 + 82 * q^48 + 15 * q^49 - 6 * q^50 + 5 * q^51 - 23 * q^52 + 24 * q^53 + 7 * q^54 + 12 * q^55 - 66 * q^56 - 60 * q^57 - 31 * q^58 + 7 * q^59 + 9 * q^60 + 14 * q^61 + 48 * q^62 - 13 * q^63 + 30 * q^64 + 14 * q^65 - 5 * q^66 - q^67 + 25 * q^68 - 8 * q^69 - 15 * q^70 - 18 * q^71 + 26 * q^72 - 13 * q^73 + 40 * q^74 - q^75 - 20 * q^76 - 66 * q^78 + 4 * q^79 + 11 * q^80 + 26 * q^81 + 27 * q^82 + 16 * q^83 - 90 * q^84 - 6 * q^85 - 36 * q^86 + 2 * q^87 - 9 * q^88 + 13 * q^89 + 18 * q^90 + 17 * q^91 - 36 * q^92 + 36 * q^93 + q^94 - 3 * q^95 + 89 * q^96 - 6 * q^97 + 18 * q^98 + 2 * q^99

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