LMFDB - Embedded newform 182.2.v.a.121.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [182,2,Mod(121,182)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("182.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(182, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.v (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 46 x^{18} + 895 x^{16} + 9634 x^{14} + 62977 x^{12} + 257850 x^{10} + 656102 x^{8} + \cdots + 32041 $ x^20 + 46x^18 + 895x^16 + 9634x^14 + 62977x^12 + 257850x^10 + 656102x^8 + 989866x^6 + 795896x^4 + 273668*x^2 + 32041
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.7
Root			$-2.17431i$ of defining polynomial
Character	$\chi$	$=$	182.121
Dual form			182.2.v.a.179.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} -2.17431 q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.17777 - 1.25733i) q^{5} +(-1.88301 + 1.08715i) q^{6} +(-2.59088 - 0.536046i) q^{7} -1.00000i q^{8} +1.72761 q^{9} -2.51467 q^{10} +0.896829i q^{11} +(-1.08715 + 1.88301i) q^{12} +(-1.69751 - 3.18095i) q^{13} +(-2.51179 + 0.831210i) q^{14} +(4.73514 + 2.73383i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.86911 - 3.23740i) q^{17} +(1.49616 - 0.863806i) q^{18} +1.14077i q^{19} +(-2.17777 + 1.25733i) q^{20} +(5.63337 + 1.16553i) q^{21} +(0.448414 + 0.776676i) q^{22} +(1.19303 + 2.06639i) q^{23} +2.17431i q^{24} +(0.661782 + 1.14624i) q^{25} +(-3.06056 - 1.90603i) q^{26} +2.76656 q^{27} +(-1.75967 + 1.97574i) q^{28} +(3.53950 - 6.13060i) q^{29} +5.46767 q^{30} +(-4.44758 + 2.56781i) q^{31} +(-0.866025 - 0.500000i) q^{32} -1.94998i q^{33} -3.73822i q^{34} +(4.96834 + 4.42499i) q^{35} +(0.863806 - 1.49616i) q^{36} +(-3.96072 + 2.28672i) q^{37} +(0.570383 + 0.987933i) q^{38} +(3.69091 + 6.91637i) q^{39} +(-1.25733 + 2.17777i) q^{40} +(9.36146 + 5.40484i) q^{41} +(5.46140 - 1.80731i) q^{42} +(-4.70395 - 8.14749i) q^{43} +(0.776676 + 0.448414i) q^{44} +(-3.76234 - 2.17219i) q^{45} +(2.06639 + 1.19303i) q^{46} +(-0.437133 - 0.252379i) q^{47} +(1.08715 + 1.88301i) q^{48} +(6.42531 + 2.77766i) q^{49} +(1.14624 + 0.661782i) q^{50} +(-4.06402 + 7.03910i) q^{51} +(-3.60354 - 0.120388i) q^{52} +(-6.11759 - 10.5960i) q^{53} +(2.39591 - 1.38328i) q^{54} +(1.12761 - 1.95308i) q^{55} +(-0.536046 + 2.59088i) q^{56} -2.48038i q^{57} -7.07901i q^{58} +(-7.06660 - 4.07991i) q^{59} +(4.73514 - 2.73383i) q^{60} -10.6298 q^{61} +(-2.56781 + 4.44758i) q^{62} +(-4.47603 - 0.926080i) q^{63} -1.00000 q^{64} +(-0.302737 + 9.06172i) q^{65} +(-0.974991 - 1.68873i) q^{66} -4.32320i q^{67} +(-1.86911 - 3.23740i) q^{68} +(-2.59402 - 4.49297i) q^{69} +(6.51521 + 1.34798i) q^{70} +(2.12122 - 1.22469i) q^{71} -1.72761i q^{72} +(8.45901 - 4.88381i) q^{73} +(-2.28672 + 3.96072i) q^{74} +(-1.43892 - 2.49228i) q^{75} +(0.987933 + 0.570383i) q^{76} +(0.480741 - 2.32357i) q^{77} +(6.65461 + 4.14429i) q^{78} +(-5.85055 + 10.1335i) q^{79} +2.51467i q^{80} -11.1982 q^{81} +10.8097 q^{82} +6.54241i q^{83} +(3.82606 - 4.29587i) q^{84} +(-8.14099 + 4.70020i) q^{85} +(-8.14749 - 4.70395i) q^{86} +(-7.69597 + 13.3298i) q^{87} +0.896829 q^{88} +(11.0376 - 6.37254i) q^{89} -4.34437 q^{90} +(2.69291 + 9.15141i) q^{91} +2.38606 q^{92} +(9.67041 - 5.58321i) q^{93} -0.504758 q^{94} +(1.43433 - 2.48433i) q^{95} +(1.88301 + 1.08715i) q^{96} +(-15.4494 + 8.91974i) q^{97} +(6.95331 - 0.807130i) q^{98} +1.54937i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} + 10 q^{4} - 2 q^{7} + 32 q^{9} + 8 q^{10} - 2 q^{12} + 6 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 10 q^{17} - 24 q^{18} + 14 q^{21} + 2 q^{22} + 18 q^{25} - 6 q^{26} - 28 q^{27} - 4 q^{28}+ \cdots + 12 q^{98}+O(q^{100}) $ 20 * q - 4 * q^3 + 10 * q^4 - 2 * q^7 + 32 * q^9 + 8 * q^10 - 2 * q^12 + 6 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 10 * q^17 - 24 * q^18 + 14 * q^21 + 2 * q^22 + 18 * q^25 - 6 * q^26 - 28 * q^27 - 4 * q^28 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 36 * q^35 + 16 * q^36 - 36 * q^37 - 14 * q^38 - 26 * q^39 + 4 * q^40 + 18 * q^41 - 4 * q^42 + 8 * q^43 - 6 * q^44 - 60 * q^45 + 12 * q^46 - 18 * q^47 + 2 * q^48 - 12 * q^50 - 22 * q^51 - 4 * q^53 - 18 * q^54 + 2 * q^55 - 2 * q^56 - 12 * q^60 + 8 * q^61 - 24 * q^62 + 64 * q^63 - 20 * q^64 - 18 * q^65 + 32 * q^66 + 10 * q^68 - 34 * q^69 + 48 * q^70 - 18 * q^71 + 72 * q^73 + 12 * q^74 - 18 * q^75 + 24 * q^76 + 42 * q^77 + 20 * q^78 + 42 * q^79 + 4 * q^81 + 32 * q^82 + 16 * q^84 - 12 * q^85 - 42 * q^86 - 64 * q^87 + 4 * q^88 - 18 * q^89 + 52 * q^90 + 60 * q^91 + 60 * q^93 - 32 * q^94 - 12 * q^95 + 78 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−2.17431			−1.25534			−0.627668	−	0.778481i	$-0.715991\pi$
$3$	−2.17431			−1.25534			−0.627668	+	0.778481i	$0.715991\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.17777	−	1.25733i	−0.973927	−	0.562297i	−0.0734961	−	0.997296i	$-0.523416\pi$
$5$	−2.17777	−	1.25733i	−0.973927	−	0.562297i	−0.900431	+	0.434998i	$0.856749\pi$
$6$	−1.88301	+	1.08715i	−0.768734	+	0.443829i
$7$	−2.59088	−	0.536046i	−0.979260	−	0.202606i
$7$	−2.59088	−	0.536046i	−0.979260	−	0.202606i
$8$		−	1.00000i		−	0.353553i
$9$	1.72761			0.575871
$10$	−2.51467			−0.795208
$11$			0.896829i			0.270404i	0.990818	+	0.135202i	$0.0431683\pi$
$11$			0.896829i			0.270404i	−0.990818	+	0.135202i	$0.956832\pi$
$12$	−1.08715	+	1.88301i	−0.313834	+	0.543577i
$13$	−1.69751	−	3.18095i	−0.470805	−	0.882237i
$13$	−1.69751	−	3.18095i	−0.470805	−	0.882237i
$14$	−2.51179	+	0.831210i	−0.671304	+	0.222150i
$15$	4.73514	+	2.73383i	1.22261	+	0.705873i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.86911	−	3.23740i	0.453326	−	0.785184i	−0.545264	−	0.838264i	$-0.683571\pi$
$17$	1.86911	−	3.23740i	0.453326	−	0.785184i	0.998590	+	0.0530802i	$0.0169039\pi$
$18$	1.49616	−	0.863806i	0.352647	−	0.203601i
$19$			1.14077i			0.261710i	0.991402	+	0.130855i	$0.0417722\pi$
$19$			1.14077i			0.261710i	−0.991402	+	0.130855i	$0.958228\pi$
$20$	−2.17777	+	1.25733i	−0.486964	+	0.281149i
$21$	5.63337	+	1.16553i	1.22930	+	0.254339i
$22$	0.448414	+	0.776676i	0.0956023	+	0.165588i
$23$	1.19303	+	2.06639i	0.248764	+	0.430873i	0.963183	−	0.268846i	$-0.0866422\pi$
$23$	1.19303	+	2.06639i	0.248764	+	0.430873i	−0.714419	+	0.699718i	$0.753309\pi$
$24$			2.17431i			0.443829i
$25$	0.661782	+	1.14624i	0.132356	+	0.229248i
$26$	−3.06056	−	1.90603i	−0.600226	−	0.373803i
$27$	2.76656			0.532425
$28$	−1.75967	+	1.97574i	−0.332546	+	0.373381i
$29$	3.53950	−	6.13060i	0.657270	−	1.13842i	−0.324050	−	0.946040i	$-0.605045\pi$
$29$	3.53950	−	6.13060i	0.657270	−	1.13842i	0.981320	−	0.192384i	$-0.0616220\pi$
$30$	5.46767			0.998255
$31$	−4.44758	+	2.56781i	−0.798809	+	0.461193i	−0.843055	−	0.537828i	$-0.819245\pi$
$31$	−4.44758	+	2.56781i	−0.798809	+	0.461193i	0.0442454	+	0.999021i	$0.485912\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		−	1.94998i		−	0.339448i
$34$		−	3.73822i		−	0.641100i
$35$	4.96834	+	4.42499i	0.839803	+	0.747959i
$36$	0.863806	−	1.49616i	0.143968	−	0.249359i
$37$	−3.96072	+	2.28672i	−0.651138	+	0.375935i	−0.788892	−	0.614532i	$-0.789345\pi$
$37$	−3.96072	+	2.28672i	−0.651138	+	0.375935i	0.137754	+	0.990467i	$0.456012\pi$
$38$	0.570383	+	0.987933i	0.0925284	+	0.160264i
$39$	3.69091	+	6.91637i	0.591019	+	1.10751i
$40$	−1.25733	+	2.17777i	−0.198802	+	0.344335i
$41$	9.36146	+	5.40484i	1.46201	+	0.844094i	0.999104	−	0.0423110i	$-0.0134720\pi$
$41$	9.36146	+	5.40484i	1.46201	+	0.844094i	0.462910	+	0.886405i	$0.346805\pi$
$42$	5.46140	−	1.80731i	0.842713	−	0.278873i
$43$	−4.70395	−	8.14749i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$43$	−4.70395	−	8.14749i	−0.717346	−	1.24248i	0.244702	−	0.969598i	$-0.421310\pi$
$44$	0.776676	+	0.448414i	0.117088	+	0.0676010i
$45$	−3.76234	−	2.17219i	−0.560856	−	0.323811i
$46$	2.06639	+	1.19303i	0.304673	+	0.175903i
$47$	−0.437133	−	0.252379i	−0.0637624	−	0.0368132i	0.467780	−	0.883845i	$-0.345054\pi$
$47$	−0.437133	−	0.252379i	−0.0637624	−	0.0368132i	−0.531542	+	0.847032i	$0.678387\pi$
$48$	1.08715	+	1.88301i	0.156917	+	0.271788i
$49$	6.42531	+	2.77766i	0.917901	+	0.396809i
$50$	1.14624	+	0.661782i	0.162103	+	0.0935902i
$51$	−4.06402	+	7.03910i	−0.569077	+	0.985671i
$52$	−3.60354	−	0.120388i	−0.499721	−	0.0166949i
$53$	−6.11759	−	10.5960i	−0.840316	−	1.45547i	−0.889628	−	0.456686i	$-0.849036\pi$
$53$	−6.11759	−	10.5960i	−0.840316	−	1.45547i	0.0493122	−	0.998783i	$-0.484297\pi$
$54$	2.39591	−	1.38328i	0.326042	−	0.188241i
$55$	1.12761	−	1.95308i	0.152047	−	0.263354i
$56$	−0.536046	+	2.59088i	−0.0716322	+	0.346221i
$57$		−	2.48038i		−	0.328534i
$58$		−	7.07901i		−	0.929520i
$59$	−7.06660	−	4.07991i	−0.919993	−	0.531158i	−0.0363604	−	0.999339i	$-0.511576\pi$
$59$	−7.06660	−	4.07991i	−0.919993	−	0.531158i	−0.883633	+	0.468180i	$0.844910\pi$
$60$	4.73514	−	2.73383i	0.611304	−	0.352936i
$61$	−10.6298			−1.36101			−0.680506	−	0.732742i	$-0.738240\pi$
$61$	−10.6298			−1.36101			−0.680506	+	0.732742i	$0.738240\pi$
$62$	−2.56781	+	4.44758i	−0.326112	+	0.564843i
$63$	−4.47603	−	0.926080i	−0.563927	−	0.116675i
$64$	−1.00000			−0.125000
$65$	−0.302737	+	9.06172i	−0.0375499	+	1.12397i
$66$	−0.974991	−	1.68873i	−0.120013	−	0.207869i
$67$		−	4.32320i		−	0.528163i	−0.964500	−	0.264082i	$-0.914931\pi$
$67$		−	4.32320i		−	0.528163i	0.964500	−	0.264082i	$-0.0850688\pi$
$68$	−1.86911	−	3.23740i	−0.226663	−	0.392592i
$69$	−2.59402	−	4.49297i	−0.312283	−	0.540890i
$70$	6.51521	+	1.34798i	0.778716	+	0.161114i
$71$	2.12122	−	1.22469i	0.251742	−	0.145343i	−0.368820	−	0.929501i	$-0.620238\pi$
$71$	2.12122	−	1.22469i	0.251742	−	0.145343i	0.620562	+	0.784158i	$0.286905\pi$
$72$		−	1.72761i		−	0.203601i
$73$	8.45901	−	4.88381i	0.990052	−	0.571607i	0.0847623	−	0.996401i	$-0.472987\pi$
$73$	8.45901	−	4.88381i	0.990052	−	0.571607i	0.905290	+	0.424794i	$0.139654\pi$
$74$	−2.28672	+	3.96072i	−0.265826	+	0.460424i
$75$	−1.43892	−	2.49228i	−0.166152	−	0.287784i
$76$	0.987933	+	0.570383i	0.113324	+	0.0654275i
$77$	0.480741	−	2.32357i	0.0547856	−	0.264796i
$78$	6.65461	+	4.14429i	0.753486	+	0.469249i
$79$	−5.85055	+	10.1335i	−0.658238	+	1.14010i	0.322833	+	0.946456i	$0.395365\pi$
$79$	−5.85055	+	10.1335i	−0.658238	+	1.14010i	−0.981071	+	0.193646i	$0.937969\pi$
$80$			2.51467i			0.281149i
$81$	−11.1982			−1.24424
$82$	10.8097			1.19373
$83$			6.54241i			0.718123i	0.933314	+	0.359061i	$0.116903\pi$
$83$			6.54241i			0.718123i	−0.933314	+	0.359061i	$0.883097\pi$
$84$	3.82606	−	4.29587i	0.417458	−	0.468718i
$85$	−8.14099	+	4.70020i	−0.883014	+	0.509808i
$86$	−8.14749	−	4.70395i	−0.878566	−	0.507240i
$87$	−7.69597	+	13.3298i	−0.825095	+	1.42911i
$88$	0.896829			0.0956023
$89$	11.0376	−	6.37254i	1.16998	−	0.675488i	0.216304	−	0.976326i	$-0.430600\pi$
$89$	11.0376	−	6.37254i	1.16998	−	0.675488i	0.953675	+	0.300838i	$0.0972664\pi$
$90$	−4.34437			−0.457937
$91$	2.69291	+	9.15141i	0.282294	+	0.959328i
$92$	2.38606			0.248764
$93$	9.67041	−	5.58321i	1.00277	−	0.578952i
$94$	−0.504758			−0.0520618
$95$	1.43433	−	2.48433i	0.147159	−	0.254886i
$96$	1.88301	+	1.08715i	0.192183	+	0.110957i
$97$	−15.4494	+	8.91974i	−1.56865	+	0.905662i	−0.572327	+	0.820026i	$0.693959\pi$
$97$	−15.4494	+	8.91974i	−1.56865	+	0.905662i	−0.996326	+	0.0856369i	$0.972707\pi$
$98$	6.95331	−	0.807130i	0.702391	−	0.0815324i
$99$			1.54937i			0.155718i
$100$	1.32356			0.132356
$101$	4.42362			0.440167			0.220084	−	0.975481i	$-0.429367\pi$
$101$	4.42362			0.440167			0.220084	+	0.975481i	$0.429367\pi$
$102$			8.12805i			0.804797i
$103$	7.46443	−	12.9288i	0.735492	−	1.27391i	−0.219016	−	0.975721i	$-0.570285\pi$
$103$	7.46443	−	12.9288i	0.735492	−	1.27391i	0.954507	−	0.298188i	$-0.0963821\pi$
$104$	−3.18095	+	1.69751i	−0.311918	+	0.166455i
$105$	−10.8027	−	9.62128i	−1.05424	−	0.938941i
$106$	−10.5960	−	6.11759i	−1.02917	−	0.594193i
$107$	7.16680	+	12.4133i	0.692840	+	1.20003i	0.970903	+	0.239472i	$0.0769743\pi$
$107$	7.16680	+	12.4133i	0.692840	+	1.20003i	−0.278063	+	0.960563i	$0.589692\pi$
$108$	1.38328	−	2.39591i	0.133106	−	0.230547i
$109$	−1.12332	+	0.648548i	−0.107594	+	0.0621197i	−0.552832	−	0.833293i	$-0.686453\pi$
$109$	−1.12332	+	0.648548i	−0.107594	+	0.0621197i	0.445237	+	0.895413i	$0.353119\pi$
$110$		−	2.25523i		−	0.215028i
$111$	8.61182	−	4.97204i	0.817398	−	0.471925i
$112$	0.831210	+	2.51179i	0.0785420	+	0.237342i
$113$	−6.62441	−	11.4738i	−0.623172	−	1.07937i	−0.988891	−	0.148640i	$-0.952510\pi$
$113$	−6.62441	−	11.4738i	−0.623172	−	1.07937i	0.365720	−	0.930725i	$-0.380823\pi$
$114$	−1.24019	−	2.14807i	−0.116154	−	0.201185i
$115$		−	6.00016i		−	0.559518i
$116$	−3.53950	−	6.13060i	−0.328635	−	0.569212i
$117$	−2.93264	−	5.49545i	−0.271123	−	0.508055i
$118$	−8.15981			−0.751171
$119$	−6.57804	+	7.38578i	−0.603008	+	0.677053i
$120$	2.73383	−	4.73514i	0.249564	−	0.432257i
$121$	10.1957			0.926882
$122$	−9.20572	+	5.31492i	−0.833446	+	0.481191i
$123$	−20.3547	−	11.7518i	−1.83532	−	1.05962i
$124$			5.13562i			0.461193i
$125$			9.24502i			0.826900i
$126$	−4.33940	+	1.43601i	−0.386584	+	0.127930i
$127$	3.97856	−	6.89106i	0.353040	−	0.611483i	−0.633741	−	0.773546i	$-0.718481\pi$
$127$	3.97856	−	6.89106i	0.353040	−	0.611483i	0.986780	+	0.162063i	$0.0518147\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	10.2278	+	17.7151i	0.900511	+	1.55973i
$130$	4.26868	+	7.99904i	0.374388	+	0.701563i
$131$	5.22033	−	9.04188i	0.456103	−	0.789993i	−0.542648	−	0.839960i	$-0.682578\pi$
$131$	5.22033	−	9.04188i	0.456103	−	0.789993i	0.998751	+	0.0499670i	$0.0159116\pi$
$132$	−1.68873	−	0.974991i	−0.146985	−	0.0848620i
$133$	0.611503	−	2.95559i	0.0530241	−	0.256282i
$134$	−2.16160	−	3.74400i	−0.186734	−	0.323433i
$135$	−6.02493	−	3.47849i	−0.518543	−	0.299381i
$136$	−3.23740	−	1.86911i	−0.277605	−	0.160275i
$137$	11.2799	+	6.51244i	0.963706	+	0.556396i	0.897312	−	0.441398i	$-0.145517\pi$
$137$	11.2799	+	6.51244i	0.963706	+	0.556396i	0.0663941	+	0.997793i	$0.478851\pi$
$138$	−4.49297	−	2.59402i	−0.382467	−	0.220818i
$139$	−5.72292	−	9.91239i	−0.485412	−	0.840758i	0.514448	−	0.857522i	$-0.327997\pi$
$139$	−5.72292	−	9.91239i	−0.485412	−	0.840758i	−0.999859	+	0.0167641i	$0.994664\pi$
$140$	6.31632	−	2.09022i	0.533827	−	0.176656i
$141$	0.950461	+	0.548749i	0.0800433	+	0.0462130i
$142$	1.22469	−	2.12122i	0.102773	−	0.178009i
$143$	2.85277	−	1.52238i	0.238561	−	0.127308i
$144$	−0.863806	−	1.49616i	−0.0719838	−	0.124680i
$145$	−15.4164	+	8.90069i	−1.28027	+	0.739162i
$146$	4.88381	−	8.45901i	0.404187	−	0.700073i
$147$	−13.9706	−	6.03949i	−1.15228	−	0.498129i
$148$			4.57345i			0.375935i
$149$			1.34482i			0.110172i	0.998482	+	0.0550861i	$0.0175433\pi$
$149$			1.34482i			0.110172i	−0.998482	+	0.0550861i	$0.982457\pi$
$150$	−2.49228	−	1.43892i	−0.203494	−	0.117487i
$151$	0.435354	−	0.251352i	0.0354286	−	0.0204547i	−0.482181	−	0.876072i	$-0.660155\pi$
$151$	0.435354	−	0.251352i	0.0354286	−	0.0204547i	0.517610	+	0.855617i	$0.326822\pi$
$152$	1.14077			0.0925284
$153$	3.22910	−	5.59297i	0.261057	−	0.452165i
$154$	−0.745453	−	2.25265i	−0.0600703	−	0.181523i
$155$	12.9144			1.03731
$156$	7.83521	+	0.261761i	0.627318	+	0.0209577i
$157$	4.72287	+	8.18024i	0.376926	+	0.652855i	0.990613	−	0.136694i	$-0.0436479\pi$
$157$	4.72287	+	8.18024i	0.376926	+	0.652855i	−0.613688	+	0.789549i	$0.710315\pi$
$158$			11.7011i			0.930890i
$159$	13.3015	+	23.0389i	1.05488	+	1.82710i
$160$	1.25733	+	2.17777i	0.0994011	+	0.172168i
$161$	−1.98332	−	5.99329i	−0.156308	−	0.472338i
$162$	−9.69792	+	5.59910i	−0.761940	+	0.439907i
$163$		−	22.0879i		−	1.73006i	−0.501724	−	0.865028i	$-0.667301\pi$
$163$		−	22.0879i		−	1.73006i	0.501724	−	0.865028i	$-0.332699\pi$
$164$	9.36146	−	5.40484i	0.731007	−	0.422047i
$165$	−2.45178	+	4.24661i	−0.190871	+	0.330598i
$166$	3.27120	+	5.66589i	0.253895	+	0.439758i
$167$	6.77796	+	3.91326i	0.524494	+	0.302817i	0.738772	−	0.673956i	$-0.235406\pi$
$167$	6.77796	+	3.91326i	0.524494	+	0.302817i	−0.214277	+	0.976773i	$0.568740\pi$
$168$	1.16553	−	5.63337i	0.0899225	−	0.434624i
$169$	−7.23691	+	10.7994i	−0.556686	+	0.830723i
$170$	−4.70020	+	8.14099i	−0.360489	+	0.624385i
$171$			1.97080i			0.150711i
$172$	−9.40791			−0.717346
$173$	3.32779			0.253007			0.126504	−	0.991966i	$-0.459624\pi$
$173$	3.32779			0.253007			0.126504	+	0.991966i	$0.459624\pi$
$174$			15.3919i			1.16686i
$175$	−1.10016	−	3.32452i	−0.0831643	−	0.251310i
$176$	0.776676	−	0.448414i	0.0585442	−	0.0338005i
$177$	15.3650	+	8.87097i	1.15490	+	0.666783i
$178$	6.37254	−	11.0376i	0.477642	−	0.827300i
$179$	17.2260			1.28754			0.643768	−	0.765221i	$-0.277370\pi$
$179$	17.2260			1.28754			0.643768	+	0.765221i	$0.277370\pi$
$180$	−3.76234	+	2.17219i	−0.280428	+	0.161905i
$181$	23.3206			1.73341			0.866704	−	0.498823i	$-0.166234\pi$
$181$	23.3206			1.73341			0.866704	+	0.498823i	$0.166234\pi$
$182$	6.90783	+	6.57890i	0.512043	+	0.487660i
$183$	23.1126			1.70853
$184$	2.06639	−	1.19303i	0.152336	−	0.0879515i
$185$	11.5007			0.845549
$186$	5.58321	−	9.67041i	0.409381	−	0.709069i
$187$	2.90339	+	1.67627i	0.212317	+	0.122581i
$188$	−0.437133	+	0.252379i	−0.0318812	+	0.0184066i
$189$	−7.16783	−	1.48300i	−0.521383	−	0.107873i
$190$		−	2.86865i		−	0.208114i
$191$	8.49311			0.614540			0.307270	−	0.951622i	$-0.400585\pi$
$191$	8.49311			0.614540			0.307270	+	0.951622i	$0.400585\pi$
$192$	2.17431			0.156917
$193$			14.5131i			1.04467i	0.852739	+	0.522337i	$0.174940\pi$
$193$			14.5131i			1.04467i	−0.852739	+	0.522337i	$0.825060\pi$
$194$	−8.91974	+	15.4494i	−0.640400	+	1.10921i
$195$	0.658243	−	19.7030i	0.0471378	−	1.41096i
$196$	5.61818	−	4.17565i	0.401299	−	0.298261i
$197$	8.75759	+	5.05620i	0.623952	+	0.360239i	0.778406	−	0.627761i	$-0.216028\pi$
$197$	8.75759	+	5.05620i	0.623952	+	0.360239i	−0.154454	+	0.988000i	$0.549362\pi$
$198$	0.774686	+	1.34180i	0.0550546	+	0.0953573i
$199$	5.26652	−	9.12189i	0.373334	−	0.646633i	−0.616742	−	0.787165i	$-0.711548\pi$
$199$	5.26652	−	9.12189i	0.373334	−	0.646633i	0.990076	+	0.140532i	$0.0448812\pi$
$200$	1.14624	−	0.661782i	0.0810514	−	0.0467951i
$201$			9.39997i			0.663023i
$202$	3.83097	−	2.21181i	0.269546	−	0.155623i
$203$	−12.4567	+	13.9863i	−0.874290	+	0.981647i
$204$	4.06402	+	7.03910i	0.284539	+	0.492835i
$205$	−13.5914	−	23.5410i	−0.949264	−	1.64417i
$206$		−	14.9289i		−	1.04014i
$207$	2.06110	+	3.56992i	0.143256	+	0.248127i
$208$	−1.90603	+	3.06056i	−0.132159	+	0.212212i
$209$	−1.02307			−0.0707674
$210$	−14.1661	−	2.93092i	−0.977551	−	0.202253i
$211$	−9.16386	+	15.8723i	−0.630866	+	1.09269i	0.356509	+	0.934292i	$0.383967\pi$
$211$	−9.16386	+	15.8723i	−0.630866	+	1.09269i	−0.987375	+	0.158400i	$0.949366\pi$
$212$	−12.2352			−0.840316
$213$	−4.61218	+	2.66284i	−0.316021	+	0.182455i
$214$	12.4133	+	7.16680i	0.848553	+	0.489912i
$215$			23.6578i			1.61345i
$216$		−	2.76656i		−	0.188241i
$217$	12.8996	−	4.26878i	0.875683	−	0.289784i
$218$	−0.648548	+	1.12332i	−0.0439252	+	0.0760807i
$219$	−18.3925	+	10.6189i	−1.24285	+	0.717559i
$220$	−1.12761	−	1.95308i	−0.0760237	−	0.131677i
$221$	−13.4708	−	0.450039i	−0.906147	−	0.0302729i
$222$	4.97204	−	8.61182i	0.333701	−	0.577988i
$223$	−18.9950	−	10.9668i	−1.27200	−	0.734390i	−0.296637	−	0.954990i	$-0.595865\pi$
$223$	−18.9950	−	10.9668i	−1.27200	−	0.734390i	−0.975364	+	0.220600i	$0.929199\pi$
$224$	1.97574	+	1.75967i	0.132010	+	0.117573i
$225$	1.14330	+	1.98026i	0.0762202	+	0.132017i
$226$	−11.4738	−	6.62441i	−0.763226	−	0.440649i
$227$	−9.45188	−	5.45704i	−0.627343	−	0.362197i	0.152379	−	0.988322i	$-0.451306\pi$
$227$	−9.45188	−	5.45704i	−0.627343	−	0.362197i	−0.779722	+	0.626125i	$0.784640\pi$
$228$	−2.14807	−	1.24019i	−0.142259	−	0.0821335i
$229$	−13.8014	−	7.96824i	−0.912022	−	0.526556i	−0.0309411	−	0.999521i	$-0.509850\pi$
$229$	−13.8014	−	7.96824i	−0.912022	−	0.526556i	−0.881081	+	0.472965i	$0.843184\pi$
$230$	−3.00008	−	5.19629i	−0.197820	−	0.342633i
$231$	−1.04528	+	5.05217i	−0.0687744	+	0.332408i
$232$	−6.13060	−	3.53950i	−0.402494	−	0.232380i
$233$	−2.16332	+	3.74698i	−0.141724	+	0.245473i	−0.928146	−	0.372217i	$-0.878598\pi$
$233$	−2.16332	+	3.74698i	−0.141724	+	0.245473i	0.786422	+	0.617690i	$0.211931\pi$
$234$	−5.28747	−	3.29288i	−0.345653	−	0.215262i
$235$	0.634649	+	1.09924i	0.0414000	+	0.0717068i
$236$	−7.06660	+	4.07991i	−0.459997	+	0.265579i
$237$	12.7209	−	22.0332i	0.826311	−	1.43121i
$238$	−2.00386	+	9.68529i	−0.129891	+	0.627804i
$239$		−	9.21054i		−	0.595780i	−0.954600	−	0.297890i	$-0.903717\pi$
$239$		−	9.21054i		−	0.595780i	0.954600	−	0.297890i	$-0.0962829\pi$
$240$		−	5.46767i		−	0.352936i
$241$	−5.42053	−	3.12954i	−0.349167	−	0.201592i	0.315151	−	0.949041i	$-0.397945\pi$
$241$	−5.42053	−	3.12954i	−0.349167	−	0.201592i	−0.664318	+	0.747450i	$0.731278\pi$
$242$	8.82973	−	5.09785i	0.567597	−	0.327702i
$243$	16.0486			1.02952
$244$	−5.31492	+	9.20572i	−0.340253	+	0.589336i
$245$	−10.5004	−	14.1279i	−0.670845	−	0.902596i
$246$	−23.5036			−1.49853
$247$	3.62872	−	1.93646i	0.230890	−	0.123214i
$248$	2.56781	+	4.44758i	0.163056	+	0.282422i
$249$		−	14.2252i		−	0.901486i
$250$	4.62251	+	8.00642i	0.292353	+	0.506371i
$251$	3.36546	+	5.82916i	0.212426	+	0.367933i	0.952473	−	0.304622i	$-0.0985301\pi$
$251$	3.36546	+	5.82916i	0.212426	+	0.367933i	−0.740047	+	0.672555i	$0.765197\pi$
$252$	−3.04003	+	3.41332i	−0.191504	+	0.215019i
$253$	−1.85320	+	1.06995i	−0.116510	+	0.0672669i
$254$		−	7.95711i		−	0.499274i
$255$	17.7010	−	10.2197i	1.10848	−	0.639981i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−9.92920	−	17.1979i	−0.619366	−	1.07277i	−0.989602	−	0.143836i	$-0.954056\pi$
$257$	−9.92920	−	17.1979i	−0.619366	−	1.07277i	0.370235	−	0.928938i	$-0.379277\pi$
$258$	17.7151	+	10.2278i	1.10290	+	0.636758i
$259$	11.4875	−	3.80150i	0.713801	−	0.236213i
$260$	7.69631	+	4.79304i	0.477305	+	0.297251i
$261$	6.11489	−	10.5913i	0.378502	−	0.655585i
$262$		−	10.4407i		−	0.645027i
$263$	−28.4505			−1.75433			−0.877166	−	0.480188i	$-0.840569\pi$
$263$	−28.4505			−1.75433			−0.877166	+	0.480188i	$0.840569\pi$
$264$	−1.94998			−0.120013
$265$			30.7674i			1.89003i
$266$	−0.948217	−	2.86537i	−0.0581389	−	0.175687i
$267$	−23.9991	+	13.8559i	−1.46872	+	0.847965i
$268$	−3.74400	−	2.16160i	−0.228701	−	0.132041i
$269$	−4.07521	+	7.05848i	−0.248470	+	0.430363i	−0.963102	−	0.269138i	$-0.913261\pi$
$269$	−4.07521	+	7.05848i	−0.248470	+	0.430363i	0.714631	+	0.699501i	$0.246594\pi$
$270$	−6.95699			−0.423389
$271$	0.420048	−	0.242515i	0.0255161	−	0.0147317i	−0.487188	−	0.873297i	$-0.661977\pi$
$271$	0.420048	−	0.242515i	0.0255161	−	0.0147317i	0.512704	+	0.858566i	$0.328644\pi$
$272$	−3.73822			−0.226663
$273$	−5.85521	−	19.8980i	−0.354374	−	1.20428i
$274$	13.0249			0.786862
$275$	−1.02798	+	0.593505i	−0.0619896	+	0.0357897i
$276$	−5.18804			−0.312283
$277$	−1.48613	+	2.57406i	−0.0892931	+	0.154660i	−0.907213	−	0.420673i	$-0.861794\pi$
$277$	−1.48613	+	2.57406i	−0.0892931	+	0.154660i	0.817919	+	0.575333i	$0.195127\pi$
$278$	−9.91239	−	5.72292i	−0.594505	−	0.343238i
$279$	−7.68370	+	4.43618i	−0.460011	+	0.265587i
$280$	4.42499	−	4.96834i	0.264444	−	0.296915i
$281$		−	0.894782i		−	0.0533782i	−0.999644	−	0.0266891i	$-0.991504\pi$
$281$		−	0.894782i		−	0.0533782i	0.999644	−	0.0266891i	$-0.00849641\pi$
$282$	1.09750			0.0653551
$283$	9.83538			0.584653			0.292326	−	0.956319i	$-0.405571\pi$
$283$	9.83538			0.584653			0.292326	+	0.956319i	$0.405571\pi$
$284$		−	2.44937i		−	0.145343i
$285$	−3.11867	+	5.40169i	−0.184734	+	0.319968i
$286$	1.70938	−	2.74480i	0.101078	−	0.162304i
$287$	−21.3572	−	19.0215i	−1.26067	−	1.12280i
$288$	−1.49616	−	0.863806i	−0.0881618	−	0.0509003i
$289$	1.51284	+	2.62031i	0.0889905	+	0.154136i
$290$	−8.90069	+	15.4164i	−0.522666	+	0.905285i
$291$	33.5918	−	19.3943i	1.96919	−	1.13691i
$292$		−	9.76762i		−	0.571607i
$293$	9.45490	−	5.45879i	0.552361	−	0.318906i	−0.197713	−	0.980260i	$-0.563351\pi$
$293$	9.45490	−	5.45879i	0.552361	−	0.318906i	0.750074	+	0.661354i	$0.230018\pi$
$294$	−15.1186	+	1.75495i	−0.881737	+	0.102351i
$295$	10.2596	+	17.7702i	0.597338	+	1.03462i
$296$	2.28672	+	3.96072i	0.132913	+	0.230212i
$297$			2.48113i			0.143970i
$298$	0.672411	+	1.16465i	0.0389517	+	0.0674664i
$299$	4.54791	−	7.30270i	0.263012	−	0.422326i
$300$	−2.87784			−0.166152
$301$	7.81995	+	23.6307i	0.450734	+	1.36205i
$302$	0.251352	−	0.435354i	0.0144637	−	0.0250518i
$303$	−9.61832			−0.552558
$304$	0.987933	−	0.570383i	0.0566618	−	0.0327137i
$305$	23.1493	+	13.3653i	1.32553	+	0.765294i
$306$		−	6.45820i		−	0.369191i
$307$			6.11376i			0.348931i	0.984663	+	0.174465i	$0.0558197\pi$
$307$			6.11376i			0.348931i	−0.984663	+	0.174465i	$0.944180\pi$
$308$	−1.77190	−	1.57812i	−0.100964	−	0.0899218i
$309$	−16.2300	+	28.1111i	−0.923290	+	1.59918i
$310$	11.1842	−	6.45720i	0.635220	−	0.366744i
$311$	−15.6959	−	27.1860i	−0.890031	−	1.54158i	−0.839837	−	0.542839i	$-0.817350\pi$
$311$	−15.6959	−	27.1860i	−0.890031	−	1.54158i	−0.0501936	−	0.998740i	$-0.515984\pi$
$312$	6.91637	−	3.69091i	0.391562	−	0.208957i
$313$	−1.05484	+	1.82704i	−0.0596232	+	0.103270i	−0.894296	−	0.447475i	$-0.852323\pi$
$313$	−1.05484	+	1.82704i	−0.0596232	+	0.103270i	0.834673	+	0.550746i	$0.185657\pi$
$314$	8.18024	+	4.72287i	0.461638	+	0.266527i
$315$	8.58337	+	7.64466i	0.483618	+	0.430728i
$316$	5.85055	+	10.1335i	0.329119	+	0.570051i
$317$	−27.4190	−	15.8303i	−1.54000	−	0.889120i	−0.998838	−	0.0482035i	$-0.984650\pi$
$317$	−27.4190	−	15.8303i	−1.54000	−	0.889120i	−0.541164	−	0.840917i	$-0.682016\pi$
$318$	23.0389	+	13.3015i	1.29196	+	0.745912i
$319$	5.49810	+	3.17433i	0.307835	+	0.177728i
$320$	2.17777	+	1.25733i	0.121741	+	0.0702872i
$321$	−15.5828	−	26.9902i	−0.869748	−	1.50645i
$322$	−4.71425	−	4.19868i	−0.262715	−	0.233983i
$323$	3.69311	+	2.13222i	0.205490	+	0.118640i
$324$	−5.59910	+	9.69792i	−0.311061	+	0.538773i
$325$	2.52275	−	4.05085i	0.139937	−	0.224701i
$326$	−11.0439	−	19.1287i	−0.611667	−	1.05944i
$327$	2.44244	−	1.41014i	0.135067	−	0.0779811i
$328$	5.40484	−	9.36146i	0.298432	−	0.516900i
$329$	0.997272	+	0.888206i	0.0549814	+	0.0489684i
$330$			4.90356i			0.269932i
$331$		−	1.59312i		−	0.0875659i	−0.999041	−	0.0437830i	$-0.986059\pi$
$331$		−	1.59312i		−	0.0875659i	0.999041	−	0.0437830i	$-0.0139410\pi$
$332$	5.66589	+	3.27120i	0.310956	+	0.179531i
$333$	−6.84259	+	3.95057i	−0.374972	+	0.216490i
$334$	7.82651			0.428248
$335$	−5.43571	+	9.41493i	−0.296985	+	0.514393i
$336$	−1.80731	−	5.46140i	−0.0985966	−	0.297944i
$337$	−6.70668			−0.365336			−0.182668	−	0.983175i	$-0.558473\pi$
$337$	−6.70668			−0.365336			−0.182668	+	0.983175i	$0.558473\pi$
$338$	−0.867649	+	12.9710i	−0.0471939	+	0.705530i
$339$	14.4035	+	24.9476i	0.782290	+	1.35497i
$340$			9.40040i			0.509808i
$341$	−2.30289	−	3.98872i	−0.124708	−	0.216001i
$342$	0.985401	+	1.70677i	0.0532844	+	0.0922913i
$343$	−15.1582	−	10.6408i	−0.818468	−	0.574552i
$344$	−8.14749	+	4.70395i	−0.439283	+	0.253620i
$345$			13.0462i			0.702384i
$346$	2.88195	−	1.66390i	0.154935	−	0.0894516i
$347$	−2.53090	+	4.38365i	−0.135866	+	0.235326i	−0.925928	−	0.377700i	$-0.876715\pi$
$347$	−2.53090	+	4.38365i	−0.135866	+	0.235326i	0.790062	+	0.613027i	$0.210048\pi$
$348$	7.69597	+	13.3298i	0.412547	+	0.714553i
$349$	−5.81459	−	3.35706i	−0.311248	−	0.179699i	0.336237	−	0.941777i	$-0.390846\pi$
$349$	−5.81459	−	3.35706i	−0.311248	−	0.179699i	−0.647485	+	0.762078i	$0.724179\pi$
$350$	−2.61503	−	2.32904i	−0.139779	−	0.124492i
$351$	−4.69627	−	8.80030i	−0.250668	−	0.469725i
$352$	0.448414	−	0.776676i	0.0239006	−	0.0413970i
$353$			23.0072i			1.22455i	0.790646	+	0.612274i	$0.209745\pi$
$353$			23.0072i			1.22455i	−0.790646	+	0.612274i	$0.790255\pi$
$354$	17.7419			0.942973
$355$	−6.15936			−0.326905
$356$		−	12.7451i		−	0.675488i
$357$	14.3027	−	16.0589i	0.756978	−	0.849929i
$358$	14.9182	−	8.61302i	0.788451	−	0.455212i
$359$	−11.0494	−	6.37935i	−0.583163	−	0.336689i	0.179227	−	0.983808i	$-0.442640\pi$
$359$	−11.0494	−	6.37935i	−0.583163	−	0.336689i	−0.762389	+	0.647119i	$0.775974\pi$
$360$	−2.17219	+	3.76234i	−0.114484	+	0.198293i
$361$	17.6987			0.931508
$362$	20.1962	−	11.6603i	1.06149	−	0.612852i
$363$	−22.1686			−1.16355
$364$	9.27181	+	2.24358i	0.485975	+	0.117595i
$365$	−24.5623			−1.28565
$366$	20.0161	−	11.5563i	1.04626	−	0.604056i
$367$	7.18498			0.375053			0.187526	−	0.982260i	$-0.439953\pi$
$367$	7.18498			0.375053			0.187526	+	0.982260i	$0.439953\pi$
$368$	1.19303	−	2.06639i	0.0621911	−	0.107718i
$369$	16.1730	+	9.33747i	0.841931	+	0.486089i
$370$	9.95991	−	5.75035i	0.517791	−	0.298947i
$371$	10.1700	+	30.7322i	0.528000	+	1.59554i
$372$		−	11.1664i		−	0.578952i
$373$	20.3645			1.05443			0.527217	−	0.849731i	$-0.323236\pi$
$373$	20.3645			1.05443			0.527217	+	0.849731i	$0.323236\pi$
$374$	3.35255			0.173356
$375$		−	20.1015i		−	1.03804i
$376$	−0.252379	+	0.437133i	−0.0130154	+	0.0225434i
$377$	−25.5095	−	0.852230i	−1.31381	−	0.0438921i
$378$	−6.94902	+	2.29959i	−0.357419	+	0.118278i
$379$	−5.46427	−	3.15480i	−0.280680	−	0.162051i	0.353051	−	0.935604i	$-0.385144\pi$
$379$	−5.46427	−	3.15480i	−0.280680	−	0.162051i	−0.633731	+	0.773553i	$0.718478\pi$
$380$	−1.43433	−	2.48433i	−0.0735794	−	0.127443i
$381$	−8.65060	+	14.9833i	−0.443184	+	0.767617i
$382$	7.35525	−	4.24656i	0.376327	−	0.217273i
$383$			0.0244098i			0.00124728i	1.00000		0.000623640i	$0.000198511\pi$
$383$			0.0244098i			0.00124728i	−1.00000		0.000623640i	$0.999801\pi$
$384$	1.88301	−	1.08715i	0.0960917	−	0.0554786i
$385$	−3.96846	+	4.45575i	−0.202251	+	0.227086i
$386$	7.25654	+	12.5687i	0.369348	+	0.639730i
$387$	−8.12661	−	14.0757i	−0.413099	−	0.715508i
$388$			17.8395i			0.905662i
$389$	−3.25714	−	5.64153i	−0.165144	−	0.286037i	0.771563	−	0.636153i	$-0.219475\pi$
$389$	−3.25714	−	5.64153i	−0.165144	−	0.286037i	−0.936706	+	0.350116i	$0.886142\pi$
$390$	−9.28142	−	17.3924i	−0.469983	−	0.880697i
$391$	8.91964			0.451086
$392$	2.77766	−	6.42531i	0.140293	−	0.324527i
$393$	−11.3506	+	19.6598i	−0.572563	+	0.991708i
$394$	10.1124			0.509455
$395$	25.4823	−	14.7122i	1.28215	−	0.740251i
$396$	1.34180	+	0.774686i	0.0674278	+	0.0389294i
$397$			18.2054i			0.913704i	0.889543	+	0.456852i	$0.151023\pi$
$397$			18.2054i			0.913704i	−0.889543	+	0.456852i	$0.848977\pi$
$398$		−	10.5330i		−	0.527974i
$399$	−1.32960	+	6.42636i	−0.0665631	+	0.321720i
$400$	0.661782	−	1.14624i	0.0330891	−	0.0573120i
$401$	−16.7963	+	9.69737i	−0.838769	+	0.484264i	−0.856846	−	0.515573i	$-0.827579\pi$
$401$	−16.7963	+	9.69737i	−0.838769	+	0.484264i	0.0180765	+	0.999837i	$0.494246\pi$
$402$	4.69999	+	8.14061i	0.234414	+	0.406017i
$403$	15.7179	+	9.78865i	0.782965	+	0.487608i
$404$	2.21181	−	3.83097i	0.110042	−	0.190598i
$405$	24.3871	+	14.0799i	1.21180	+	0.699635i
$406$	−3.79467	+	18.3409i	−0.188327	+	0.910242i
$407$	−2.05080	−	3.55209i	−0.101654	−	0.176070i
$408$	7.03910	+	4.06402i	0.348487	+	0.201199i
$409$	0.955871	+	0.551872i	0.0472648	+	0.0272883i	0.523446	−	0.852059i	$-0.324646\pi$
$409$	0.955871	+	0.551872i	0.0472648	+	0.0272883i	−0.476181	+	0.879347i	$0.657979\pi$
$410$	−23.5410	−	13.5914i	−1.16261	−	0.671231i
$411$	−24.5259	−	14.1601i	−1.20978	−	0.698464i
$412$	−7.46443	−	12.9288i	−0.367746	−	0.636954i
$413$	16.1217	+	14.3586i	0.793297	+	0.706539i
$414$	3.56992	+	2.06110i	0.175452	+	0.101297i
$415$	8.22600	−	14.2478i	0.403798	−	0.699399i
$416$	−0.120388	+	3.60354i	−0.00590252	+	0.176678i
$417$	12.4434	+	21.5526i	0.609355	+	1.05543i
$418$	−0.886007	+	0.511536i	−0.0433360	+	0.0250201i
$419$	9.14982	−	15.8480i	0.446998	−	0.774223i	−0.551191	−	0.834379i	$-0.685826\pi$
$419$	9.14982	−	15.8480i	0.446998	−	0.774223i	0.998189	+	0.0601558i	$0.0191598\pi$
$420$	−13.7336	+	4.54478i	−0.670132	+	0.221762i
$421$		−	8.92354i		−	0.434907i	−0.976071	−	0.217453i	$-0.930225\pi$
$421$		−	8.92354i		−	0.434907i	0.976071	−	0.217453i	$-0.0697750\pi$
$422$			18.3277i			0.892180i
$423$	−0.755196	−	0.436013i	−0.0367189	−	0.0211997i
$424$	−10.5960	+	6.11759i	−0.514586	+	0.297096i
$425$	4.94778			0.240003
$426$	−2.66284	+	4.61218i	−0.129015	+	0.223461i
$427$	27.5406	+	5.69809i	1.33279	+	0.275750i
$428$	14.3336			0.692840
$429$	−6.20280	+	3.31011i	−0.299474	+	0.159814i
$430$	11.8289	+	20.4882i	0.570440	+	0.988031i
$431$		−	30.4142i		−	1.46500i	−0.680767	−	0.732500i	$-0.738353\pi$
$431$		−	30.4142i		−	1.46500i	0.680767	−	0.732500i	$-0.261647\pi$
$432$	−1.38328	−	2.39591i	−0.0665531	−	0.115273i
$433$	4.87813	+	8.44916i	0.234428	+	0.406041i	0.959106	−	0.283046i	$-0.0913450\pi$
$433$	4.87813	+	8.44916i	0.234428	+	0.406041i	−0.724678	+	0.689087i	$0.758012\pi$
$434$	9.03700	−	10.1467i	0.433790	−	0.487056i
$435$	33.5201	−	19.3528i	1.60716	−	0.927897i
$436$			1.29710i			0.0621197i
$437$	−2.35727	+	1.36097i	−0.112764	+	0.0651041i
$438$	−10.6189	+	18.3925i	−0.507391	+	0.878827i
$439$	−0.522067	−	0.904247i	−0.0249169	−	0.0431574i	0.853298	−	0.521423i	$-0.174599\pi$
$439$	−0.522067	−	0.904247i	−0.0249169	−	0.0431574i	−0.878215	+	0.478266i	$0.841265\pi$
$440$	−1.95308	−	1.12761i	−0.0931097	−	0.0537569i
$441$	11.1004	+	4.79872i	0.528593	+	0.228511i
$442$	−11.8911	+	6.34568i	−0.565603	+	0.301833i
$443$	−10.1104	+	17.5117i	−0.480358	+	0.832004i	−0.999746	−	0.0225344i	$-0.992826\pi$
$443$	−10.1104	+	17.5117i	−0.480358	+	0.832004i	0.519388	+	0.854538i	$0.326160\pi$
$444$		−	9.94408i		−	0.471925i
$445$	−32.0497			−1.51930
$446$	−21.9336			−1.03858
$447$		−	2.92406i		−	0.138303i
$448$	2.59088	+	0.536046i	0.122408	+	0.0253258i
$449$	0.897966	−	0.518441i	0.0423776	−	0.0244667i	−0.478662	−	0.878000i	$-0.658878\pi$
$449$	0.897966	−	0.518441i	0.0423776	−	0.0244667i	0.521039	+	0.853533i	$0.325545\pi$
$450$	1.98026	+	1.14330i	0.0933503	+	0.0538958i
$451$	−4.84722	+	8.39563i	−0.228247	+	0.395335i
$452$	−13.2488			−0.623172
$453$	−0.946593	+	0.546516i	−0.0444748	+	0.0256776i
$454$	−10.9141			−0.512223
$455$	5.64185	−	23.3155i	0.264494	−	1.09305i
$456$	−2.48038			−0.116154
$457$	21.2980	−	12.2964i	0.996280	−	0.575203i	0.0891347	−	0.996020i	$-0.471590\pi$
$457$	21.2980	−	12.2964i	0.996280	−	0.575203i	0.907146	+	0.420817i	$0.138256\pi$
$458$	−15.9365			−0.744663
$459$	5.17101	−	8.95646i	0.241362	−	0.418052i
$460$	−5.19629	−	3.00008i	−0.242278	−	0.139880i
$461$	22.4541	−	12.9639i	1.04579	−	0.603787i	0.124322	−	0.992242i	$-0.460324\pi$
$461$	22.4541	−	12.9639i	1.04579	−	0.603787i	0.921468	+	0.388454i	$0.126991\pi$
$462$	1.62084	+	4.89794i	0.0754085	+	0.227873i
$463$			1.71146i			0.0795384i	0.999209	+	0.0397692i	$0.0126623\pi$
$463$			1.71146i			0.0795384i	−0.999209	+	0.0397692i	$0.987338\pi$
$464$	−7.07901			−0.328635
$465$	−28.0799			−1.30217
$466$			4.32664i			0.200428i
$467$	14.6456	−	25.3670i	0.677719	−	1.17384i	−0.297947	−	0.954582i	$-0.596302\pi$
$467$	14.6456	−	25.3670i	0.677719	−	1.17384i	0.975666	−	0.219261i	$-0.0703648\pi$
$468$	−6.22552	−	0.207984i	−0.287775	−	0.00961408i
$469$	−2.31744	+	11.2009i	−0.107009	+	0.517209i
$470$	1.09924	+	0.634649i	0.0507044	+	0.0292742i
$471$	−10.2690	−	17.7864i	−0.473169	−	0.819552i
$472$	−4.07991	+	7.06660i	−0.187793	+	0.325267i
$473$	7.30690	−	4.21864i	0.335972	−	0.193973i
$474$		−	25.4418i		−	1.16858i
$475$	−1.30759	+	0.754939i	−0.0599965	+	0.0346390i
$476$	3.10725	+	9.38964i	0.142421	+	0.430373i
$477$	−10.5688	−	18.3057i	−0.483913	−	0.838162i
$478$	−4.60527	−	7.97656i	−0.210640	−	0.364839i
$479$		−	24.3592i		−	1.11300i	−0.830847	−	0.556501i	$-0.812144\pi$
$479$		−	24.3592i		−	1.11300i	0.830847	−	0.556501i	$-0.187856\pi$
$480$	−2.73383	−	4.73514i	−0.124782	−	0.216128i
$481$	13.9973	+	8.71713i	0.638223	+	0.397467i
$482$	−6.25909			−0.285094
$483$	4.31235	+	13.0313i	0.196219	+	0.592943i
$484$	5.09785	−	8.82973i	0.231720	−	0.401352i
$485$	44.8604			2.03701
$486$	13.8985	−	8.02431i	0.630450	−	0.363990i
$487$	25.7024	+	14.8393i	1.16469	+	0.672433i	0.952423	−	0.304779i	$-0.0985827\pi$
$487$	25.7024	+	14.8393i	1.16469	+	0.672433i	0.212265	+	0.977212i	$0.431916\pi$
$488$			10.6298i			0.481191i
$489$			48.0258i			2.17180i
$490$	−16.1575	−	6.98490i	−0.729923	−	0.315546i
$491$	−14.2889	+	24.7491i	−0.644848	+	1.11691i	0.339488	+	0.940610i	$0.389746\pi$
$491$	−14.2889	+	24.7491i	−0.644848	+	1.11691i	−0.984337	+	0.176300i	$0.943587\pi$
$492$	−20.3547	+	11.7518i	−0.917660	+	0.529811i
$493$	−13.2315	−	22.9176i	−0.595915	−	1.03216i
$494$	2.17434	−	3.49139i	0.0978280	−	0.157085i
$495$	1.94808	−	3.37417i	0.0875597	−	0.151658i
$496$	4.44758	+	2.56781i	0.199702	+	0.115298i
$497$	−6.15231	+	2.03594i	−0.275969	+	0.0913245i
$498$	−7.11260	−	12.3194i	−0.318723	−	0.552045i
$499$	5.27630	+	3.04628i	0.236200	+	0.136370i	0.613429	−	0.789750i	$-0.289790\pi$
$499$	5.27630	+	3.04628i	0.236200	+	0.136370i	−0.377229	+	0.926120i	$0.623123\pi$
$500$	8.00642	+	4.62251i	0.358058	+	0.206725i
$501$	−14.7374	−	8.50862i	−0.658417	−	0.380137i
$502$	5.82916	+	3.36546i	0.260168	+	0.150208i
$503$	0.788353	+	1.36547i	0.0351509	+	0.0608832i	0.883066	−	0.469249i	$-0.155475\pi$
$503$	0.788353	+	1.36547i	0.0351509	+	0.0608832i	−0.847915	+	0.530133i	$0.822142\pi$
$504$	−0.926080	+	4.47603i	−0.0412509	+	0.199378i
$505$	−9.63363	−	5.56198i	−0.428691	−	0.247505i
$506$	−1.06995	+	1.85320i	−0.0475649	+	0.0823848i
$507$	15.7353	−	23.4812i	0.698828	−	1.04284i
$508$	−3.97856	−	6.89106i	−0.176520	−	0.305741i
$509$	−2.64527	+	1.52725i	−0.117250	+	0.0676941i	−0.557478	−	0.830192i	$-0.688231\pi$
$509$	−2.64527	+	1.52725i	−0.117250	+	0.0676941i	0.440228	+	0.897886i	$0.354898\pi$
$510$	10.2197	−	17.7010i	0.452535	−	0.783814i
$511$	−24.5342	+	8.11895i	−1.08533	+	0.359161i
$512$			1.00000i			0.0441942i
$513$			3.15600i			0.139341i
$514$	−17.1979	−	9.92920i	−0.758566	−	0.437958i
$515$	−32.5116	+	18.7706i	−1.43263	+	0.827130i
$516$	20.4557			0.900511
$517$	0.226341	−	0.392033i	0.00995445	−	0.0172416i
$518$	8.04775	−	9.03596i	0.353598	−	0.397017i
$519$	−7.23564			−0.317609
$520$	9.06172	+	0.302737i	0.397383	+	0.0132759i
$521$	4.20500	+	7.28327i	0.184224	+	0.319086i	0.943315	−	0.331899i	$-0.107689\pi$
$521$	4.20500	+	7.28327i	0.184224	+	0.319086i	−0.759091	+	0.650985i	$0.774356\pi$
$522$		−	12.2298i		−	0.535283i
$523$	1.36342	+	2.36151i	0.0596181	+	0.103262i	0.894294	−	0.447480i	$-0.147678\pi$
$523$	1.36342	+	2.36151i	0.0596181	+	0.103262i	−0.834676	+	0.550741i	$0.814345\pi$
$524$	−5.22033	−	9.04188i	−0.228051	−	0.394997i
$525$	2.39209	+	7.22852i	0.104399	+	0.315479i
$526$	−24.6388	+	14.2252i	−1.07430	+	0.620250i
$527$			19.1981i			0.836283i
$528$	−1.68873	+	0.974991i	−0.0734927	+	0.0424310i
$529$	8.65335	−	14.9880i	0.376233	−	0.651654i
$530$	15.3837	+	26.6454i	0.668226	+	1.15740i
$531$	−12.2084	−	7.04849i	−0.529797	−	0.305879i
$532$	−2.25386	−	2.00737i	−0.0977174	−	0.0870306i
$533$	1.30136	−	38.9531i	0.0563682	−	1.68725i
$534$	−13.8559	+	23.9991i	−0.599602	+	1.03854i
$535$		−	36.0443i		−	1.55833i
$536$	−4.32320			−0.186734
$537$	−37.4547			−1.61629
$538$			8.15043i			0.351390i
$539$	−2.49109	+	5.76240i	−0.107299	+	0.248204i
$540$	−6.02493	+	3.47849i	−0.259272	+	0.149691i
$541$	5.52995	+	3.19272i	0.237751	+	0.137266i	0.614143	−	0.789195i	$-0.289502\pi$
$541$	5.52995	+	3.19272i	0.237751	+	0.137266i	−0.376392	+	0.926461i	$0.622835\pi$
$542$	0.242515	−	0.420048i	0.0104169	−	0.0180426i
$543$	−50.7062			−2.17601
$544$	−3.23740	+	1.86911i	−0.138802	+	0.0801375i
$545$	3.26177			0.139719
$546$	−15.0197	−	14.3045i	−0.642786	−	0.612178i
$547$	33.4717			1.43115			0.715573	−	0.698537i	$-0.246165\pi$
$547$	33.4717			1.43115			0.715573	+	0.698537i	$0.246165\pi$
$548$	11.2799	−	6.51244i	0.481853	−	0.278198i
$549$	−18.3643			−0.783767
$550$	−0.593505	+	1.02798i	−0.0253072	+	0.0438333i
$551$	6.99359	+	4.03775i	0.297937	+	0.172014i
$552$	−4.49297	+	2.59402i	−0.191234	+	0.110409i
$553$	20.5901	−	23.1184i	0.875579	−	0.983094i
$554$			2.97227i			0.126280i
$555$	−25.0061			−1.06145
$556$	−11.4458			−0.485412
$557$			25.0743i			1.06243i	0.847237	+	0.531216i	$0.178265\pi$
$557$			25.0743i			1.06243i	−0.847237	+	0.531216i	$0.821735\pi$
$558$	−4.43618	+	7.68370i	−0.187799	+	0.325277i
$559$	−17.9318	+	28.7935i	−0.758432	+	1.21784i
$560$	1.34798	−	6.51521i	0.0569625	−	0.275318i
$561$	−6.31286	−	3.64473i	−0.266529	−	0.153881i
$562$	−0.447391	−	0.774904i	−0.0188720	−	0.0326873i
$563$	−4.39232	+	7.60773i	−0.185114	+	0.320627i	−0.943615	−	0.331045i	$-0.892599\pi$
$563$	−4.39232	+	7.60773i	−0.185114	+	0.320627i	0.758501	+	0.651672i	$0.225932\pi$
$564$	0.950461	−	0.548749i	0.0400216	−	0.0231065i
$565$			33.3164i			1.40163i
$566$	8.51769	−	4.91769i	0.358025	−	0.206706i
$567$	29.0132	+	6.00275i	1.21844	+	0.252092i
$568$	−1.22469	−	2.12122i	−0.0513867	−	0.0890043i
$569$	−9.81154	−	16.9941i	−0.411321	−	0.712429i	0.583713	−	0.811960i	$-0.301599\pi$
$569$	−9.81154	−	16.9941i	−0.411321	−	0.712429i	−0.995035	+	0.0995304i	$0.968266\pi$
$570$			6.23733i			0.261253i
$571$	20.1968	+	34.9819i	0.845209	+	1.46395i	0.885439	+	0.464755i	$0.153858\pi$
$571$	20.1968	+	34.9819i	0.845209	+	1.46395i	−0.0402301	+	0.999190i	$0.512809\pi$
$572$	0.107968	−	3.23176i	0.00451436	−	0.135127i
$573$	−18.4666			−0.771455
$574$	−28.0066	−	5.79449i	−1.16897	−	0.241857i
$575$	−1.57906	+	2.73500i	−0.0658511	+	0.114058i
$576$	−1.72761			−0.0719838
$577$	−13.4211	+	7.74870i	−0.558729	+	0.322582i	−0.752635	−	0.658438i	$-0.771218\pi$
$577$	−13.4211	+	7.74870i	−0.558729	+	0.322582i	0.193906	+	0.981020i	$0.437884\pi$
$578$	2.62031	+	1.51284i	0.108991	+	0.0629258i
$579$		−	31.5559i		−	1.31142i
$580$			17.8014i			0.739162i
$581$	3.50703	−	16.9506i	0.145496	−	0.703229i
$582$	19.3943	−	33.5918i	0.803918	−	1.39243i
$583$	9.50278	−	5.48643i	0.393565	−	0.227225i
$584$	−4.88381	−	8.45901i	−0.202094	−	0.350036i
$585$	−0.523012	+	15.6551i	−0.0216239	+	0.647260i
$586$	5.45879	−	9.45490i	0.225500	−	0.390578i
$587$	8.47466	+	4.89285i	0.349787	+	0.201950i	0.664591	−	0.747207i	$-0.268606\pi$
$587$	8.47466	+	4.89285i	0.349787	+	0.201950i	−0.314805	+	0.949157i	$0.601939\pi$
$588$	−12.2156	+	9.07915i	−0.503765	+	0.374418i
$589$	−2.92927	−	5.07365i	−0.120699	−	0.209056i
$590$	17.7702	+	10.2596i	0.731587	+	0.422382i
$591$	−19.0417	−	10.9937i	−0.783271	−	0.452221i
$592$	3.96072	+	2.28672i	0.162785	+	0.0939837i
$593$	15.4021	+	8.89242i	0.632490	+	0.365168i	0.781716	−	0.623635i	$-0.214345\pi$
$593$	15.4021	+	8.89242i	0.632490	+	0.365168i	−0.149226	+	0.988803i	$0.547678\pi$
$594$	1.24057	+	2.14872i	0.0509010	+	0.0881632i
$595$	23.6118	−	7.81371i	0.967991	−	0.320331i
$596$	1.16465	+	0.672411i	0.0477059	+	0.0275430i
$597$	−11.4510	+	19.8338i	−0.468660	+	0.811743i
$598$	0.287254	−	8.59828i	0.0117467	−	0.351610i
$599$	18.9868	+	32.8860i	0.775778	+	1.34369i	0.934356	+	0.356341i	$0.115976\pi$
$599$	18.9868	+	32.8860i	0.775778	+	1.34369i	−0.158578	+	0.987346i	$0.550691\pi$
$600$	−2.49228	+	1.43892i	−0.101747	+	0.0587436i
$601$	5.04087	−	8.73104i	0.205621	−	0.356146i	−0.744709	−	0.667389i	$-0.767412\pi$
$601$	5.04087	−	8.73104i	0.205621	−	0.356146i	0.950330	+	0.311243i	$0.100745\pi$
$602$	18.5876	+	16.5548i	0.757575	+	0.674723i
$603$		−	7.46882i		−	0.304154i
$604$		−	0.502703i		−	0.0204547i
$605$	−22.2039	−	12.8194i	−0.902715	−	0.521183i
$606$	−8.32971	+	4.80916i	−0.338371	+	0.195359i
$607$	−25.3489			−1.02888			−0.514439	−	0.857527i	$-0.672000\pi$
$607$	−25.3489			−1.02888			−0.514439	+	0.857527i	$0.672000\pi$
$608$	0.570383	−	0.987933i	0.0231321	−	0.0400660i
$609$	27.0847	−	30.4105i	1.09753	−	1.23230i
$610$	26.7306			1.08229
$611$	−0.0607669	+	1.81891i	−0.00245837	+	0.0735854i
$612$	−3.22910	−	5.59297i	−0.130529	−	0.226082i
$613$		−	34.6843i		−	1.40088i	−0.713709	−	0.700442i	$-0.752986\pi$
$613$		−	34.6843i		−	1.40088i	0.713709	−	0.700442i	$-0.247014\pi$
$614$	3.05688	+	5.29467i	0.123366	+	0.213676i
$615$	29.5519	+	51.1853i	1.19165	+	2.06399i
$616$	−2.32357	−	0.480741i	−0.0936195	−	0.0193696i
$617$	36.6492	−	21.1594i	1.47544	−	0.851846i	0.475823	−	0.879541i	$-0.342150\pi$
$617$	36.6492	−	21.1594i	1.47544	−	0.851846i	0.999616	+	0.0276953i	$0.00881680\pi$
$618$			32.4599i			1.30573i
$619$	−24.8773	+	14.3629i	−0.999902	+	0.577294i	−0.908219	−	0.418495i	$-0.862558\pi$
$619$	−24.8773	+	14.3629i	−0.999902	+	0.577294i	−0.0916826	+	0.995788i	$0.529225\pi$
$620$	6.45720	−	11.1842i	0.259327	−	0.449168i
$621$	3.30060	+	5.71680i	0.132448	+	0.229407i
$622$	−27.1860	−	15.6959i	−1.09006	−	0.629347i
$623$	−32.0130	+	10.5938i	−1.28257	+	0.424433i
$624$	4.14429	−	6.65461i	0.165905	−	0.266397i
$625$	14.9330	−	25.8647i	0.597320	−	1.03459i
$626$			2.10968i			0.0843200i
$627$	2.22447			0.0888369
$628$	9.44573			0.376926
$629$			17.0966i			0.681685i
$630$	11.2557	+	2.32878i	0.448440	+	0.0927810i
$631$	37.0469	−	21.3890i	1.47481	−	0.851484i	0.475216	−	0.879869i	$-0.342370\pi$
$631$	37.0469	−	21.3890i	1.47481	−	0.851484i	0.999597	+	0.0283852i	$0.00903650\pi$
$632$	10.1335	+	5.85055i	0.403087	+	0.232722i
$633$	19.9251	−	34.5112i	0.791950	−	1.37170i
$634$	−31.6607			−1.25741
$635$	−17.3287	+	10.0048i	−0.687670	+	0.397027i
$636$	26.6030			1.05488
$637$	−2.07143	−	25.1537i	−0.0820730	−	0.996626i
$638$	6.34866			0.251346
$639$	3.66464	−	2.11578i	0.144971	−	0.0836990i
$640$	2.51467			0.0994011
$641$	1.12936	−	1.95611i	0.0446071	−	0.0772618i	−0.842860	−	0.538133i	$-0.819130\pi$
$641$	1.12936	−	1.95611i	0.0446071	−	0.0772618i	0.887467	+	0.460871i	$0.152463\pi$
$642$	−26.9902	−	15.5828i	−1.06522	−	0.615005i
$643$	−40.6516	+	23.4702i	−1.60314	+	0.925574i	−0.612288	+	0.790635i	$0.709751\pi$
$643$	−40.6516	+	23.4702i	−1.60314	+	0.925574i	−0.990854	+	0.134939i	$0.956916\pi$
$644$	−6.18200	−	1.27904i	−0.243605	−	0.0504012i
$645$		−	51.4393i		−	2.02542i
$646$	4.26444			0.167782
$647$	11.1916			0.439988			0.219994	−	0.975501i	$-0.429396\pi$
$647$	11.1916			0.439988			0.219994	+	0.975501i	$0.429396\pi$
$648$			11.1982i			0.439907i
$649$	3.65898	−	6.33753i	0.143627	−	0.248770i
$650$	0.159342	−	4.76952i	0.00624990	−	0.187076i
$651$	−28.0477	+	9.28165i	−1.09928	+	0.363776i
$652$	−19.1287	−	11.0439i	−0.749136	−	0.432514i
$653$	−11.0284	−	19.1017i	−0.431574	−	0.747508i	0.565435	−	0.824793i	$-0.308708\pi$
$653$	−11.0284	−	19.1017i	−0.431574	−	0.747508i	−0.997009	+	0.0772845i	$0.975375\pi$
$654$	1.41014	−	2.44244i	0.0551410	−	0.0955070i
$655$	−22.7374	+	13.1274i	−0.888422	+	0.512931i
$656$		−	10.8097i		−	0.422047i
$657$	14.6139	−	8.43733i	0.570142	−	0.329172i
$658$	1.30777	+	0.270573i	0.0509820	+	0.0105480i
$659$	19.7826	+	34.2645i	0.770621	+	1.33476i	0.937223	+	0.348731i	$0.113387\pi$
$659$	19.7826	+	34.2645i	0.770621	+	1.33476i	−0.166601	+	0.986024i	$0.553279\pi$
$660$	2.45178	+	4.24661i	0.0954354	+	0.165299i
$661$			40.4934i			1.57501i	0.616307	+	0.787506i	$0.288628\pi$
$661$			40.4934i			1.57501i	−0.616307	+	0.787506i	$0.711372\pi$
$662$	−0.796561	−	1.37968i	−0.0309592	−	0.0536230i
$663$	29.2898	+	0.978522i	1.13752	+	0.0380027i
$664$	6.54241			0.253895
$665$	−5.04788	+	5.66772i	−0.195748	+	0.219785i
$666$	−3.95057	+	6.84259i	−0.153082	+	0.265145i
$667$	16.8910			0.654021
$668$	6.77796	−	3.91326i	0.262247	−	0.151408i
$669$	41.3010	+	23.8452i	1.59679	+	0.921907i
$670$			10.8714i			0.420000i
$671$		−	9.53315i		−	0.368023i
$672$	−4.29587	−	3.82606i	−0.165717	−	0.147594i
$673$	16.0421	−	27.7857i	0.618378	−	1.07106i	−0.371404	−	0.928471i	$-0.621124\pi$
$673$	16.0421	−	27.7857i	0.618378	−	1.07106i	0.989782	−	0.142590i	$-0.0455431\pi$
$674$	−5.80816	+	3.35334i	−0.223722	+	0.129166i
$675$	1.83086	+	3.17115i	0.0704699	+	0.122057i
$676$	5.73410	+	11.6671i	0.220542	+	0.448733i
$677$	−4.38388	+	7.59310i	−0.168486	+	0.291827i	−0.937888	−	0.346939i	$-0.887221\pi$
$677$	−4.38388	+	7.59310i	−0.168486	+	0.291827i	0.769402	+	0.638765i	$0.220555\pi$
$678$	24.9476	+	14.4035i	0.958106	+	0.553163i
$679$	44.8090	−	14.8284i	1.71961	−	0.569060i
$680$	4.70020	+	8.14099i	0.180244	+	0.312193i
$681$	20.5513	+	11.8653i	0.787527	+	0.454679i
$682$	−3.98872	−	2.30289i	−0.152736	−	0.0881821i
$683$	−12.4647	−	7.19652i	−0.476950	−	0.275367i	0.242194	−	0.970228i	$-0.422133\pi$
$683$	−12.4647	−	7.19652i	−0.476950	−	0.275367i	−0.719145	+	0.694860i	$0.755466\pi$
$684$	1.70677	+	0.985401i	0.0652598	+	0.0376778i
$685$	−16.3766	−	28.3652i	−0.625720	−	1.08378i
$686$	−18.4478	−	1.63612i	−0.704342	−	0.0624673i
$687$	30.0085	+	17.3254i	1.14490	+	0.661006i
$688$	−4.70395	+	8.14749i	−0.179337	+	0.310620i
$689$	−23.3206	+	37.4466i	−0.888445	+	1.42660i
$690$	6.52310	+	11.2983i	0.248330	+	0.430120i
$691$	−22.6474	+	13.0755i	−0.861548	+	0.497415i	−0.864530	−	0.502580i	$-0.832384\pi$
$691$	−22.6474	+	13.0755i	−0.861548	+	0.497415i	0.00298221	+	0.999996i	$0.499051\pi$
$692$	1.66390	−	2.88195i	0.0632518	−	0.109555i
$693$	0.830535	−	4.01424i	0.0315494	−	0.152488i
$694$			5.06180i			0.192143i
$695$			28.7825i			1.09178i
$696$	13.3298	+	7.69597i	0.505265	+	0.291715i
$697$	34.9952	−	20.2045i	1.32554	−	0.765300i
$698$	−6.71411			−0.254133
$699$	4.70372	−	8.14709i	0.177911	−	0.308151i
$700$	−3.42920	−	0.709492i	−0.129611	−	0.0268163i
$701$	−7.94716			−0.300160			−0.150080	−	0.988674i	$-0.547953\pi$
$701$	−7.94716			−0.300160			−0.150080	+	0.988674i	$0.547953\pi$
$702$	−8.46724	−	5.27315i	−0.319575	−	0.199022i
$703$	−2.60862	−	4.51826i	−0.0983859	−	0.170409i
$704$		−	0.896829i		−	0.0338005i
$705$	−1.37992	−	2.39010i	−0.0519709	−	0.0900162i
$706$	11.5036	+	19.9248i	0.432943	+	0.749879i
$707$	−11.4611	−	2.37127i	−0.431038	−	0.0891806i
$708$	15.3650	−	8.87097i	0.577451	−	0.333391i
$709$		−	44.0462i		−	1.65419i	−0.562061	−	0.827096i	$-0.689991\pi$
$709$		−	44.0462i		−	1.65419i	0.562061	−	0.827096i	$-0.310009\pi$
$710$	−5.33416	+	3.07968i	−0.200188	+	0.115578i
$711$	−10.1075	+	17.5067i	−0.379060	+	0.656552i
$712$	−6.37254	−	11.0376i	−0.238821	−	0.413650i
$713$	−10.6122	−	6.12696i	−0.397431	−	0.229457i
$714$	4.35701	−	21.0588i	0.163057	−	0.788105i
$715$	−8.12681	−	0.271503i	−0.303925	−	0.0101536i
$716$	8.61302	−	14.9182i	0.321884	−	0.557519i
$717$			20.0265i			0.747905i
$718$	−12.7587			−0.476150
$719$	−19.2640			−0.718426			−0.359213	−	0.933256i	$-0.616955\pi$
$719$	−19.2640			−0.718426			−0.359213	+	0.933256i	$0.616955\pi$
$720$			4.34437i			0.161905i
$721$	−26.2698	+	29.4956i	−0.978340	+	1.09847i
$722$	15.3275	−	8.84933i	0.570430	−	0.329338i
$723$	11.7859	+	6.80459i	0.438322	+	0.253065i
$724$	11.6603	−	20.1962i	0.433352	−	0.750588i
$725$	9.36953			0.347975
$726$	−19.1986	+	11.0843i	−0.712525	+	0.411377i
$727$	−27.3156			−1.01308			−0.506540	−	0.862217i	$-0.669076\pi$
$727$	−27.3156			−1.01308			−0.506540	+	0.862217i	$0.669076\pi$
$728$	9.15141	−	2.69291i	0.339174	−	0.0998059i
$729$	−1.30007			−0.0481507
$730$	−21.2716	+	12.2812i	−0.787298	+	0.454547i
$731$	−35.1689			−1.30077
$732$	11.5563	−	20.0161i	0.427132	−	0.739815i
$733$	17.9894	+	10.3862i	0.664454	+	0.383622i	0.793972	−	0.607955i	$-0.208010\pi$
$733$	17.9894	+	10.3862i	0.664454	+	0.383622i	−0.129518	+	0.991577i	$0.541343\pi$
$734$	6.22238	−	3.59249i	0.229672	−	0.132601i
$735$	22.8311	+	30.7183i	0.842136	+	1.13306i
$736$		−	2.38606i		−	0.0879515i
$737$	3.87717			0.142818
$738$	18.6749			0.687434
$739$		−	44.6154i		−	1.64120i	−0.571500	−	0.820602i	$-0.693638\pi$
$739$		−	44.6154i		−	1.64120i	0.571500	−	0.820602i	$-0.306362\pi$
$740$	5.75035	−	9.95991i	0.211387	−	0.366133i
$741$	−7.88996	+	4.21047i	−0.289845	+	0.154675i
$742$	24.1736	+	21.5299i	0.887440	+	0.790386i
$743$	−23.3733	−	13.4946i	−0.857485	−	0.495069i	0.00568443	−	0.999984i	$-0.498191\pi$
$743$	−23.3733	−	13.4946i	−0.857485	−	0.495069i	−0.863169	+	0.504915i	$0.831524\pi$
$744$	−5.58321	−	9.67041i	−0.204691	−	0.354534i
$745$	1.69089	−	2.92871i	0.0619495	−	0.107300i
$746$	17.6362	−	10.1822i	0.645706	−	0.372799i
$747$			11.3027i			0.413546i
$748$	2.90339	−	1.67627i	0.106158	−	0.0612906i
$749$	−11.9142	−	36.0030i	−0.435336	−	1.31552i
$750$	−10.0508	−	17.4084i	−0.367002	−	0.635666i
$751$	5.53412	+	9.58538i	0.201943	+	0.349775i	0.949154	−	0.314811i	$-0.101941\pi$
$751$	5.53412	+	9.58538i	0.201943	+	0.349775i	−0.747212	+	0.664586i	$0.768608\pi$
$752$			0.504758i			0.0184066i
$753$	−7.31755	−	12.6744i	−0.266667	−	0.461880i
$754$	−22.5180	+	12.0167i	−0.820057	+	0.437622i
$755$	−1.26413			−0.0460065
$756$	−4.86823	+	5.46602i	−0.177056	+	0.198797i
$757$	−19.3178	+	33.4595i	−0.702119	+	1.21611i	0.265602	+	0.964083i	$0.414429\pi$
$757$	−19.3178	+	33.4595i	−0.702119	+	1.21611i	−0.967721	+	0.252023i	$0.918904\pi$
$758$	−6.30959			−0.229175
$759$	4.02943	−	2.32639i	0.146259	−	0.0844426i
$760$	−2.48433	−	1.43433i	−0.0901159	−	0.0520285i
$761$		−	20.0417i		−	0.726512i	−0.931689	−	0.363256i	$-0.881665\pi$
$761$		−	20.0417i		−	0.726512i	0.931689	−	0.363256i	$-0.118335\pi$
$762$			17.3012i			0.626757i
$763$	3.25803	−	1.07816i	0.117949	−	0.0390320i
$764$	4.24656	−	7.35525i	0.153635	−	0.266104i
$765$	−14.0645	+	8.12012i	−0.508502	+	0.293584i
$766$	0.0122049	+	0.0211395i	0.000440980	+	0.000763800i
$767$	−0.982346	+	29.4042i	−0.0354705	+	1.06172i
$768$	1.08715	−	1.88301i	0.0392293	−	0.0679471i
$769$	−42.6924	−	24.6485i	−1.53953	−	0.888846i	−0.998866	−	0.0476053i	$-0.984841\pi$
$769$	−42.6924	−	24.6485i	−1.53953	−	0.888846i	−0.540660	−	0.841241i	$-0.681826\pi$
$770$	−1.20891	+	5.84302i	−0.0435660	+	0.210568i
$771$	21.5891	+	37.3935i	0.777513	+	1.34669i
$772$	12.5687	+	7.25654i	0.452357	+	0.261168i
$773$	14.7936	+	8.54108i	0.532088	+	0.307201i	0.741867	−	0.670548i	$-0.233941\pi$
$773$	14.7936	+	8.54108i	0.532088	+	0.307201i	−0.209778	+	0.977749i	$0.567274\pi$
$774$	−14.0757	−	8.12661i	−0.505940	−	0.292105i
$775$	−5.88666	−	3.39867i	−0.211455	−	0.122084i
$776$	8.91974	+	15.4494i	0.320200	+	0.554603i
$777$	−24.9774	+	8.26562i	−0.896061	+	0.296527i
$778$	−5.64153	−	3.25714i	−0.202259	−	0.116774i
$779$	−6.16566	+	10.6792i	−0.220908	+	0.382623i
$780$	−16.7341	−	10.4215i	−0.599178	−	0.373151i
$781$	1.09833	+	1.90237i	0.0393015	+	0.0680721i
$782$	7.72464	−	4.45982i	0.276232	−	0.159483i
$783$	9.79226	−	16.9607i	0.349947	−	0.606126i
$784$	−0.807130	−	6.95331i	−0.0288261	−	0.248333i
$785$		−	23.7529i		−	0.847777i
$786$			22.7012i			0.809726i
$787$	−2.24263	−	1.29478i	−0.0799410	−	0.0461540i	0.459497	−	0.888179i	$-0.348030\pi$
$787$	−2.24263	−	1.29478i	−0.0799410	−	0.0461540i	−0.539438	+	0.842026i	$0.681363\pi$
$788$	8.75759	−	5.05620i	0.311976	−	0.180120i
$789$	61.8601			2.20228
$790$	14.7122	−	25.4823i	0.523437	−	0.906619i
$791$	11.0125	+	33.2782i	0.391561	+	1.18324i
$792$	1.54937			0.0550546
$793$	18.0443	+	33.8130i	0.640771	+	1.20074i
$794$	9.10271	+	15.7664i	0.323043	+	0.559527i
$795$		−	66.8979i		−	2.37262i
$796$	−5.26652	−	9.12189i	−0.186667	−	0.323317i
$797$	−0.192040	−	0.332624i	−0.00680242	−	0.0117821i	0.862604	−	0.505879i	$-0.168832\pi$
$797$	−0.192040	−	0.332624i	−0.00680242	−	0.0117821i	−0.869407	+	0.494097i	$0.835499\pi$
$798$	2.06171	+	6.23019i	0.0729839	+	0.220546i
$799$	−1.63410	+	0.943448i	−0.0578103	+	0.0333768i
$800$		−	1.32356i		−	0.0467951i
$801$	19.0686	−	11.0093i	0.673757	−	0.388994i
$802$	−9.69737	+	16.7963i	−0.342426	+	0.593099i
$803$	4.37994	+	7.58628i	0.154565	+	0.267714i
$804$	8.14061	+	4.69999i	0.287097	+	0.165756i
$805$	−3.21636	+	15.5457i	−0.113362	+	0.547914i
$806$	18.5064	+	0.618269i	0.651861	+	0.0217776i
$807$	8.86077	−	15.3473i	0.311914	−	0.540251i
$808$		−	4.42362i		−	0.155623i
$809$	−9.48209			−0.333372			−0.166686	−	0.986010i	$-0.553307\pi$
$809$	−9.48209			−0.333372			−0.166686	+	0.986010i	$0.553307\pi$
$810$	28.1598			0.989433
$811$		−	19.3479i		−	0.679397i	−0.940534	−	0.339699i	$-0.889675\pi$
$811$		−	19.3479i		−	0.679397i	0.940534	−	0.339699i	$-0.110325\pi$
$812$	5.88414	+	17.7810i	0.206493	+	0.623990i
$813$	−0.913313	+	0.527302i	−0.0320313	+	0.0184933i
$814$	−3.55209	−	2.05080i	−0.124501	−	0.0718805i
$815$	−27.7718	+	48.1023i	−0.972805	+	1.68495i
$816$	8.12805			0.284539
$817$	9.29438	−	5.36611i	0.325169	−	0.187737i
$818$	1.10374			0.0385915
$819$	4.65230	+	15.8101i	0.162565	+	0.552449i
$820$	−27.1828			−0.949264
$821$	15.8970	−	9.17813i	0.554809	−	0.320319i	−0.196251	−	0.980554i	$-0.562877\pi$
$821$	15.8970	−	9.17813i	0.554809	−	0.320319i	0.751059	+	0.660235i	$0.229543\pi$
$822$	−28.3201			−0.987777
$823$	−10.9831	+	19.0233i	−0.382848	+	0.663112i	−0.991468	−	0.130350i	$-0.958390\pi$
$823$	−10.9831	+	19.0233i	−0.382848	+	0.663112i	0.608620	+	0.793462i	$0.291723\pi$
$824$	−12.9288	−	7.46443i	−0.450395	−	0.260036i
$825$	2.23515	−	1.29046i	0.0778179	−	0.0449282i
$826$	21.1411	+	4.37403i	0.735592	+	0.152192i
$827$			27.4660i			0.955085i	0.878609	+	0.477543i	$0.158472\pi$
$827$			27.4660i			0.955085i	−0.878609	+	0.477543i	$0.841528\pi$
$828$	4.12219			0.143256
$829$	14.4009			0.500165			0.250083	−	0.968224i	$-0.419542\pi$
$829$	14.4009			0.500165			0.250083	+	0.968224i	$0.419542\pi$
$830$		−	16.4520i		−	0.571057i
$831$	3.23131	−	5.59679i	0.112093	−	0.194151i
$832$	1.69751	+	3.18095i	0.0588506	+	0.110280i
$833$	21.0020	−	15.6095i	0.727677	−	0.540838i
$834$	21.5526	+	12.4434i	0.746305	+	0.430879i
$835$	−9.84055	−	17.0443i	−0.340546	−	0.589843i
$836$	−0.511536	+	0.886007i	−0.0176918	+	0.0306432i
$837$	−12.3045	+	7.10401i	−0.425306	+	0.245551i
$838$		−	18.2996i		−	0.632151i
$839$	16.0335	−	9.25696i	0.553539	−	0.319586i	−0.197009	−	0.980402i	$-0.563123\pi$
$839$	16.0335	−	9.25696i	0.553539	−	0.319586i	0.750548	+	0.660816i	$0.229790\pi$
$840$	−9.62128	+	10.8027i	−0.331966	+	0.372729i
$841$	−10.5562	−	18.2839i	−0.364007	−	0.630478i
$842$	−4.46177	−	7.72802i	−0.153763	−	0.266325i
$843$			1.94553i			0.0670076i
$844$	9.16386	+	15.8723i	0.315433	+	0.546346i
$845$	29.3388	−	14.4194i	1.00928	−	0.496041i
$846$	−0.872025			−0.0299808
$847$	−26.4158	−	5.46536i	−0.907658	−	0.187792i
$848$	−6.11759	+	10.5960i	−0.210079	+	0.363867i
$849$	−21.3851			−0.733936
$850$	4.28490	−	2.47389i	0.146971	−	0.0848538i
$851$	−9.45053	−	5.45627i	−0.323960	−	0.187038i
$852$			5.32569i			0.182455i
$853$			26.8958i			0.920895i	0.887687	+	0.460447i	$0.152311\pi$
$853$			26.8958i			0.920895i	−0.887687	+	0.460447i	$0.847689\pi$
$854$	26.6999	−	8.83564i	0.913653	−	0.302349i
$855$	2.47796	−	4.29195i	0.0847444	−	0.146782i
$856$	12.4133	−	7.16680i	0.424276	−	0.244956i
$857$	11.5717	+	20.0428i	0.395282	+	0.684648i	0.993137	−	0.116956i	$-0.0373137\pi$
$857$	11.5717	+	20.0428i	0.395282	+	0.684648i	−0.597856	+	0.801604i	$0.703980\pi$
$858$	−3.71672	+	5.96804i	−0.126887	+	0.203746i
$859$	21.0988	−	36.5443i	0.719883	−	1.24687i	−0.241163	−	0.970485i	$-0.577529\pi$
$859$	21.0988	−	36.5443i	0.719883	−	1.24687i	0.961046	−	0.276389i	$-0.0891379\pi$
$860$	20.4882	+	11.8289i	0.698643	+	0.403362i
$861$	46.4370	+	41.3585i	1.58257	+	1.40949i
$862$	−15.2071	−	26.3395i	−0.517956	−	0.897126i
$863$	30.4881	+	17.6023i	1.03783	+	0.599189i	0.919217	−	0.393752i	$-0.128823\pi$
$863$	30.4881	+	17.6023i	1.03783	+	0.599189i	0.118610	+	0.992941i	$0.462156\pi$
$864$	−2.39591	−	1.38328i	−0.0815106	−	0.0470602i
$865$	−7.24716	−	4.18415i	−0.246411	−	0.142265i
$866$	8.44916	+	4.87813i	0.287114	+	0.165765i
$867$	−3.28938	−	5.69737i	−0.111713	−	0.193493i
$868$	2.75293	−	13.3058i	0.0934406	−	0.451628i
$869$	−9.08797	−	5.24694i	−0.308288	−	0.177990i
$870$	19.3528	−	33.5201i	0.656122	−	1.13644i
$871$	−13.7519	+	7.33869i	−0.465965	+	0.248662i
$872$	0.648548	+	1.12332i	0.0219626	+	0.0380404i
$873$	−26.6906	+	15.4099i	−0.903342	+	0.521545i
$874$	−1.36097	+	2.35727i	−0.0460355	+	0.0797359i
$875$	4.95576	−	23.9527i	0.167535	−	0.809750i
$876$			21.2378i			0.717559i
$877$		−	3.38906i		−	0.114441i	−0.998362	−	0.0572203i	$-0.981776\pi$
$877$		−	3.38906i		−	0.114441i	0.998362	−	0.0572203i	$-0.0182237\pi$
$878$	−0.904247	−	0.522067i	−0.0305169	−	0.0176189i
$879$	−20.5578	+	11.8691i	−0.693399	+	0.400334i
$880$	−2.25523			−0.0760237
$881$	0.550385	−	0.953295i	0.0185430	−	0.0321173i	−0.856605	−	0.515973i	$-0.827431\pi$
$881$	0.550385	−	0.953295i	0.0185430	−	0.0321173i	0.875148	+	0.483855i	$0.160764\pi$
$882$	12.0126	−	1.39441i	0.404486	−	0.0469521i
$883$	−23.9125			−0.804719			−0.402360	−	0.915482i	$-0.631810\pi$
$883$	−23.9125			−0.804719			−0.402360	+	0.915482i	$0.631810\pi$
$884$	−7.12517	+	11.4411i	−0.239645	+	0.384805i
$885$	−22.3076	−	38.6378i	−0.749860	−	1.29880i
$886$			20.2207i			0.679328i
$887$	2.77342	+	4.80370i	0.0931223	+	0.161292i	0.908823	−	0.417181i	$-0.136982\pi$
$887$	2.77342	+	4.80370i	0.0931223	+	0.161292i	−0.815701	+	0.578474i	$0.803649\pi$
$888$	−4.97204	−	8.61182i	−0.166851	−	0.288994i
$889$	−14.0019	+	15.7212i	−0.469608	+	0.527273i
$890$	−27.7558	+	16.0248i	−0.930377	+	0.537154i
$891$		−	10.0429i		−	0.336449i
$892$	−18.9950	+	10.9668i	−0.636001	+	0.367195i
$893$	0.287905	−	0.498667i	0.00963438	−	0.0166872i
$894$	−1.46203	−	2.53231i	−0.0488976	−	0.0846930i
$895$	−37.5143	−	21.6589i	−1.25397	−	0.723978i
$896$	2.51179	−	0.831210i	0.0839130	−	0.0277688i
$897$	−9.88855	+	15.8783i	−0.330169	+	0.530162i
$898$	0.518441	−	0.897966i	0.0173006	−	0.0299655i
$899$			36.3551i			1.21251i
$900$	2.28661			0.0762202
$901$	−45.7379			−1.52375
$902$			9.69443i			0.322789i
$903$	−17.0030	−	51.3804i	−0.565823	−	1.70983i
$904$	−11.4738	+	6.62441i	−0.381613	+	0.220324i
$905$	−50.7869	−	29.3218i	−1.68821	−	0.974691i
$906$	−0.546516	+	0.946593i	−0.0181568	+	0.0314485i
$907$	−3.07483			−0.102098			−0.0510490	−	0.998696i	$-0.516256\pi$
$907$	−3.07483			−0.102098			−0.0510490	+	0.998696i	$0.516256\pi$
$908$	−9.45188	+	5.45704i	−0.313671	+	0.181098i
$909$	7.64231			0.253479
$910$	−6.77178	−	23.0128i	−0.224482	−	0.762866i
$911$	−25.1389			−0.832890			−0.416445	−	0.909161i	$-0.636724\pi$
$911$	−25.1389			−0.832890			−0.416445	+	0.909161i	$0.636724\pi$
$912$	−2.14807	+	1.24019i	−0.0711297	+	0.0410667i
$913$	−5.86742			−0.194183
$914$	12.2964	−	21.2980i	0.406730	−	0.704477i
$915$	−50.3338	−	29.0602i	−1.66398	−	0.960701i
$916$	−13.8014	+	7.96824i	−0.456011	+	0.263278i
$917$	−18.3721	+	20.6281i	−0.606701	+	0.681200i
$918$		−	10.3420i		−	0.341338i
$919$	−59.4855			−1.96224			−0.981122	−	0.193388i	$-0.938052\pi$
$919$	−59.4855			−1.96224			−0.981122	+	0.193388i	$0.938052\pi$
$920$	−6.00016			−0.197820
$921$		−	13.2932i		−	0.438026i
$922$	12.9639	−	22.4541i	0.426942	−	0.739485i
$923$	−7.49646	−	4.66857i	−0.246749	−	0.153668i
$924$	3.85266	+	3.43132i	0.126743	+	0.112882i
$925$	−5.24227	−	3.02663i	−0.172365	−	0.0995149i
$926$	0.855731	+	1.48217i	0.0281211	+	0.0487071i
$927$	12.8956	−	22.3359i	0.423548	−	0.733607i
$928$	−6.13060	+	3.53950i	−0.201247	+	0.116190i
$929$		−	45.7142i		−	1.49983i	−0.661532	−	0.749917i	$-0.730094\pi$
$929$		−	45.7142i		−	1.49983i	0.661532	−	0.749917i	$-0.269906\pi$
$930$	−24.3179	+	14.0399i	−0.797415	+	0.460388i
$931$	−3.16866	+	7.32978i	−0.103849	+	0.240224i
$932$	2.16332	+	3.74698i	0.0708619	+	0.122736i
$933$	34.1276	+	59.1108i	1.11729	+	1.93520i
$934$		−	29.2913i		−	0.958439i
$935$	−4.21527	−	7.30107i	−0.137854	−	0.238771i
$936$	−5.49545	+	2.93264i	−0.179624	+	0.0958564i
$937$	−51.9091			−1.69580			−0.847898	−	0.530159i	$-0.822132\pi$
$937$	−51.9091			−1.69580			−0.847898	+	0.530159i	$0.822132\pi$
$938$	3.59349	+	10.8590i	0.117332	+	0.354558i
$939$	2.29355	−	3.97255i	0.0748472	−	0.129639i
$940$	1.26930			0.0414000
$941$	29.2227	−	16.8717i	0.952632	−	0.550002i	0.0587341	−	0.998274i	$-0.481294\pi$
$941$	29.2227	−	16.8717i	0.952632	−	0.550002i	0.893897	+	0.448272i	$0.147960\pi$
$942$	−17.7864	−	10.2690i	−0.579511	−	0.334581i
$943$			25.7926i			0.839922i
$944$			8.15981i			0.265579i
$945$	13.7452	+	12.2420i	0.447132	+	0.398232i
$946$	4.21864	−	7.30690i	0.137160	−	0.237568i
$947$	39.2666	−	22.6706i	1.27599	−	0.736695i	0.299884	−	0.953976i	$-0.403052\pi$
$947$	39.2666	−	22.6706i	1.27599	−	0.736695i	0.976109	+	0.217281i	$0.0697187\pi$
$948$	−12.7209	−	22.0332i	−0.413156	−	0.715606i
$949$	−29.8944	−	18.6174i	−0.970414	−	0.604346i
$950$	−0.754939	+	1.30759i	−0.0244935	+	0.0424239i
$951$	59.6172	+	34.4200i	1.93322	+	1.11615i
$952$	7.38578	+	6.57804i	0.239374	+	0.213195i
$953$	3.50930	+	6.07828i	0.113677	+	0.196895i	0.917250	−	0.398311i	$-0.130404\pi$
$953$	3.50930	+	6.07828i	0.113677	+	0.196895i	−0.803573	+	0.595206i	$0.797070\pi$
$954$	−18.3057	−	10.5688i	−0.592670	−	0.342178i
$955$	−18.4960	−	10.6787i	−0.598517	−	0.345554i
$956$	−7.97656	−	4.60527i	−0.257980	−	0.148945i
$957$	−11.9546	−	6.90197i	−0.386436	−	0.223109i
$958$	−12.1796	−	21.0957i	−0.393505	−	0.681571i
$959$	−25.7338	−	22.9195i	−0.830989	−	0.740109i
$960$	−4.73514	−	2.73383i	−0.152826	−	0.0882341i
$961$	−2.31268	+	4.00568i	−0.0746026	+	0.129216i
$962$	16.4806	+	0.550590i	0.531356	+	0.0177517i
$963$	12.3814	+	21.4453i	0.398987	+	0.691065i
$964$	−5.42053	+	3.12954i	−0.174584	+	0.100796i
$965$	18.2478	−	31.6061i	0.587417	−	1.01744i
$966$	10.2502	+	9.12923i	0.329796	+	0.293728i
$967$			19.4023i			0.623937i	0.950092	+	0.311968i	$0.100988\pi$
$967$			19.4023i			0.623937i	−0.950092	+	0.311968i	$0.899012\pi$
$968$		−	10.1957i		−	0.327702i
$969$	−8.02997	−	4.63610i	−0.257960	−	0.148933i
$970$	38.8503	−	22.4302i	1.24741	−	0.720190i
$971$	−15.6039			−0.500752			−0.250376	−	0.968149i	$-0.580554\pi$
$971$	−15.6039			−0.500752			−0.250376	+	0.968149i	$0.580554\pi$
$972$	8.02431	−	13.8985i	0.257380	−	0.445795i
$973$	9.51390	+	28.7495i	0.305002	+	0.921668i
$974$	29.6786			0.950964
$975$	−5.48524	+	8.80780i	−0.175668	+	0.282075i
$976$	5.31492	+	9.20572i	0.170127	+	0.294668i
$977$			11.6723i			0.373429i	0.982414	+	0.186715i	$0.0597840\pi$
$977$			11.6723i			0.373429i	−0.982414	+	0.186715i	$0.940216\pi$
$978$	24.0129	+	41.5916i	0.767848	+	1.32995i
$979$	5.71508	+	9.89880i	0.182655	+	0.316367i
$980$	−17.4853	+	2.02967i	−0.558547	+	0.0648353i
$981$	−1.94066	+	1.12044i	−0.0619605	+	0.0357729i
$982$			28.5778i			0.911953i
$983$	52.0585	−	30.0560i	1.66041	−	0.958638i	0.687890	−	0.725815i	$-0.258537\pi$
$983$	52.0585	−	30.0560i	1.66041	−	0.958638i	0.972519	−	0.232822i	$-0.0747960\pi$
$984$	−11.7518	+	20.3547i	−0.374633	+	0.648884i
$985$	−12.7147	−	22.0224i	−0.405123	−	0.701694i
$986$	−22.9176	−	13.2315i	−0.729844	−	0.421376i
$987$	−2.16838	−	1.93123i	−0.0690201	−	0.0614718i
$988$	0.137335	−	4.11080i	0.00436921	−	0.130782i
$989$	11.2239	−	19.4404i	0.356900	−	0.618170i
$990$		−	3.89616i		−	0.123828i
$991$	37.2948			1.18471			0.592354	−	0.805678i	$-0.298199\pi$
$991$	37.2948			1.18471			0.592354	+	0.805678i	$0.298199\pi$
$992$	5.13562			0.163056
$993$			3.46394i			0.109925i
$994$	−4.31008	+	4.83933i	−0.136708	+	0.153494i
$995$	−22.9385	+	13.2436i	−0.727201	+	0.419849i
$996$	−12.3194	−	7.11260i	−0.390355	−	0.225371i
$997$	−3.58235	+	6.20481i	−0.113454	+	0.196508i	−0.917161	−	0.398518i	$-0.869525\pi$
$997$	−3.58235	+	6.20481i	−0.113454	+	0.196508i	0.803707	+	0.595026i	$0.202858\pi$
$998$	6.09255			0.192856
$999$	−10.9576	+	6.32636i	−0.346682	+	0.200157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.v.a.121.7	yes	20
3.2	odd	2		1638.2.cr.c.667.5		20
7.2	even	3		1274.2.m.g.589.4		20
7.3	odd	6		1274.2.o.h.459.7		20
7.4	even	3		182.2.o.a.95.9	yes	20
7.5	odd	6		1274.2.m.f.589.2		20
7.6	odd	2		1274.2.v.h.667.9		20
13.10	even	6		182.2.o.a.23.4	✓	20
21.11	odd	6		1638.2.dt.c.1369.1		20
39.23	odd	6		1638.2.dt.c.1297.6		20
91.10	odd	6		1274.2.v.h.361.9		20
91.23	even	6		1274.2.m.g.491.4		20
91.62	odd	6		1274.2.o.h.569.2		20
91.75	odd	6		1274.2.m.f.491.2		20
91.88	even	6	inner	182.2.v.a.179.7	yes	20
273.179	odd	6		1638.2.cr.c.361.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.o.a.23.4	✓	20	13.10	even	6
182.2.o.a.95.9	yes	20	7.4	even	3
182.2.v.a.121.7	yes	20	1.1	even	1	trivial
182.2.v.a.179.7	yes	20	91.88	even	6	inner
1274.2.m.f.491.2		20	91.75	odd	6
1274.2.m.f.589.2		20	7.5	odd	6
1274.2.m.g.491.4		20	91.23	even	6
1274.2.m.g.589.4		20	7.2	even	3
1274.2.o.h.459.7		20	7.3	odd	6
1274.2.o.h.569.2		20	91.62	odd	6
1274.2.v.h.361.9		20	91.10	odd	6
1274.2.v.h.667.9		20	7.6	odd	2
1638.2.cr.c.361.5		20	273.179	odd	6
1638.2.cr.c.667.5		20	3.2	odd	2
1638.2.dt.c.1297.6		20	39.23	odd	6
1638.2.dt.c.1369.1		20	21.11	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} -2.17431 q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.17777 - 1.25733i) q^{5} +(-1.88301 + 1.08715i) q^{6} +(-2.59088 - 0.536046i) q^{7} -1.00000i q^{8} +1.72761 q^{9} -2.51467 q^{10} +0.896829i q^{11} +(-1.08715 + 1.88301i) q^{12} +(-1.69751 - 3.18095i) q^{13} +(-2.51179 + 0.831210i) q^{14} +(4.73514 + 2.73383i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.86911 - 3.23740i) q^{17} +(1.49616 - 0.863806i) q^{18} +1.14077i q^{19} +(-2.17777 + 1.25733i) q^{20} +(5.63337 + 1.16553i) q^{21} +(0.448414 + 0.776676i) q^{22} +(1.19303 + 2.06639i) q^{23} +2.17431i q^{24} +(0.661782 + 1.14624i) q^{25} +(-3.06056 - 1.90603i) q^{26} +2.76656 q^{27} +(-1.75967 + 1.97574i) q^{28} +(3.53950 - 6.13060i) q^{29} +5.46767 q^{30} +(-4.44758 + 2.56781i) q^{31} +(-0.866025 - 0.500000i) q^{32} -1.94998i q^{33} -3.73822i q^{34} +(4.96834 + 4.42499i) q^{35} +(0.863806 - 1.49616i) q^{36} +(-3.96072 + 2.28672i) q^{37} +(0.570383 + 0.987933i) q^{38} +(3.69091 + 6.91637i) q^{39} +(-1.25733 + 2.17777i) q^{40} +(9.36146 + 5.40484i) q^{41} +(5.46140 - 1.80731i) q^{42} +(-4.70395 - 8.14749i) q^{43} +(0.776676 + 0.448414i) q^{44} +(-3.76234 - 2.17219i) q^{45} +(2.06639 + 1.19303i) q^{46} +(-0.437133 - 0.252379i) q^{47} +(1.08715 + 1.88301i) q^{48} +(6.42531 + 2.77766i) q^{49} +(1.14624 + 0.661782i) q^{50} +(-4.06402 + 7.03910i) q^{51} +(-3.60354 - 0.120388i) q^{52} +(-6.11759 - 10.5960i) q^{53} +(2.39591 - 1.38328i) q^{54} +(1.12761 - 1.95308i) q^{55} +(-0.536046 + 2.59088i) q^{56} -2.48038i q^{57} -7.07901i q^{58} +(-7.06660 - 4.07991i) q^{59} +(4.73514 - 2.73383i) q^{60} -10.6298 q^{61} +(-2.56781 + 4.44758i) q^{62} +(-4.47603 - 0.926080i) q^{63} -1.00000 q^{64} +(-0.302737 + 9.06172i) q^{65} +(-0.974991 - 1.68873i) q^{66} -4.32320i q^{67} +(-1.86911 - 3.23740i) q^{68} +(-2.59402 - 4.49297i) q^{69} +(6.51521 + 1.34798i) q^{70} +(2.12122 - 1.22469i) q^{71} -1.72761i q^{72} +(8.45901 - 4.88381i) q^{73} +(-2.28672 + 3.96072i) q^{74} +(-1.43892 - 2.49228i) q^{75} +(0.987933 + 0.570383i) q^{76} +(0.480741 - 2.32357i) q^{77} +(6.65461 + 4.14429i) q^{78} +(-5.85055 + 10.1335i) q^{79} +2.51467i q^{80} -11.1982 q^{81} +10.8097 q^{82} +6.54241i q^{83} +(3.82606 - 4.29587i) q^{84} +(-8.14099 + 4.70020i) q^{85} +(-8.14749 - 4.70395i) q^{86} +(-7.69597 + 13.3298i) q^{87} +0.896829 q^{88} +(11.0376 - 6.37254i) q^{89} -4.34437 q^{90} +(2.69291 + 9.15141i) q^{91} +2.38606 q^{92} +(9.67041 - 5.58321i) q^{93} -0.504758 q^{94} +(1.43433 - 2.48433i) q^{95} +(1.88301 + 1.08715i) q^{96} +(-15.4494 + 8.91974i) q^{97} +(6.95331 - 0.807130i) q^{98} +1.54937i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} + 10 q^{4} - 2 q^{7} + 32 q^{9} + 8 q^{10} - 2 q^{12} + 6 q^{13} - 4 q^{14} - 12 q^{15} - 10 q^{16} - 10 q^{17} - 24 q^{18} + 14 q^{21} + 2 q^{22} + 18 q^{25} - 6 q^{26} - 28 q^{27} - 4 q^{28}+ \cdots + 12 q^{98}+O(q^{100}) \) 20 * q - 4 * q^3 + 10 * q^4 - 2 * q^7 + 32 * q^9 + 8 * q^10 - 2 * q^12 + 6 * q^13 - 4 * q^14 - 12 * q^15 - 10 * q^16 - 10 * q^17 - 24 * q^18 + 14 * q^21 + 2 * q^22 + 18 * q^25 - 6 * q^26 - 28 * q^27 - 4 * q^28 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 36 * q^35 + 16 * q^36 - 36 * q^37 - 14 * q^38 - 26 * q^39 + 4 * q^40 + 18 * q^41 - 4 * q^42 + 8 * q^43 - 6 * q^44 - 60 * q^45 + 12 * q^46 - 18 * q^47 + 2 * q^48 - 12 * q^50 - 22 * q^51 - 4 * q^53 - 18 * q^54 + 2 * q^55 - 2 * q^56 - 12 * q^60 + 8 * q^61 - 24 * q^62 + 64 * q^63 - 20 * q^64 - 18 * q^65 + 32 * q^66 + 10 * q^68 - 34 * q^69 + 48 * q^70 - 18 * q^71 + 72 * q^73 + 12 * q^74 - 18 * q^75 + 24 * q^76 + 42 * q^77 + 20 * q^78 + 42 * q^79 + 4 * q^81 + 32 * q^82 + 16 * q^84 - 12 * q^85 - 42 * q^86 - 64 * q^87 + 4 * q^88 - 18 * q^89 + 52 * q^90 + 60 * q^91 + 60 * q^93 - 32 * q^94 - 12 * q^95 + 78 * q^97 + 12 * q^98

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