LMFDB - Embedded newform 153.2.n.a.115.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,2,Mod(4,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.n (of order $12$, degree $4$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.8
Character	$\chi$	$=$	153.115
Dual form			153.2.n.a.4.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.218953 - 0.126413i) q^{2} +(0.963283 + 1.43947i) q^{3} +(-0.968040 - 1.67669i) q^{4} +(1.02659 - 3.83129i) q^{5} +(-0.0289461 - 0.436949i) q^{6} +(-0.551719 - 2.05904i) q^{7} +0.995142i q^{8} +(-1.14417 + 2.77324i) q^{9} +(-0.709099 + 0.709099i) q^{10} +(-0.307889 - 1.14906i) q^{11} +(1.48106 - 3.00860i) q^{12} +(3.09696 + 5.36409i) q^{13} +(-0.139489 + 0.520578i) q^{14} +(6.50393 - 2.21286i) q^{15} +(-1.81028 + 3.13550i) q^{16} +(2.45336 - 3.31376i) q^{17} +(0.601094 - 0.462573i) q^{18} +5.66168i q^{19} +(-7.41767 + 1.98756i) q^{20} +(2.43248 - 2.77762i) q^{21} +(-0.0778423 + 0.290512i) q^{22} +(0.703082 + 0.188390i) q^{23} +(-1.43248 + 0.958603i) q^{24} +(-9.29474 - 5.36632i) q^{25} -1.56598i q^{26} +(-5.09417 + 1.02441i) q^{27} +(-2.91830 + 2.91830i) q^{28} +(2.98504 - 0.799838i) q^{29} +(-1.70379 - 0.337667i) q^{30} +(-0.0116316 + 0.0434097i) q^{31} +(2.51637 - 1.45283i) q^{32} +(1.35746 - 1.55007i) q^{33} +(-0.956073 + 0.415424i) q^{34} -8.45517 q^{35} +(5.75748 - 0.766182i) q^{36} +(1.68986 + 1.68986i) q^{37} +(0.715709 - 1.23964i) q^{38} +(-4.73822 + 9.62513i) q^{39} +(3.81267 + 1.02160i) q^{40} +(0.650890 + 0.174405i) q^{41} +(-0.883726 + 0.300674i) q^{42} +(0.442424 + 0.255434i) q^{43} +(-1.62857 + 1.62857i) q^{44} +(9.45049 + 7.23063i) q^{45} +(-0.130127 - 0.130127i) q^{46} +(-4.74104 + 8.21172i) q^{47} +(-6.25728 + 0.414520i) q^{48} +(2.12692 - 1.22798i) q^{49} +(1.35674 + 2.34995i) q^{50} +(7.13336 + 0.339453i) q^{51} +(5.99596 - 10.3853i) q^{52} -7.10456i q^{53} +(1.24488 + 0.419670i) q^{54} -4.71845 q^{55} +(2.04904 - 0.549038i) q^{56} +(-8.14985 + 5.45380i) q^{57} +(-0.754693 - 0.202219i) q^{58} +(-7.91388 + 4.56908i) q^{59} +(-10.0064 - 8.76297i) q^{60} +(1.49801 + 5.59065i) q^{61} +(0.00803432 - 0.00803432i) q^{62} +(6.34148 + 0.825848i) q^{63} +6.50650 q^{64} +(23.7307 - 6.35862i) q^{65} +(-0.493168 + 0.167793i) q^{66} +(-1.68697 - 2.92191i) q^{67} +(-7.93112 - 0.905676i) q^{68} +(0.406084 + 1.19354i) q^{69} +(1.85129 + 1.06884i) q^{70} +(2.32488 + 2.32488i) q^{71} +(-2.75977 - 1.13861i) q^{72} +(-8.24518 - 8.24518i) q^{73} +(-0.156381 - 0.583622i) q^{74} +(-1.22879 - 18.5488i) q^{75} +(9.49291 - 5.48073i) q^{76} +(-2.19609 + 1.26791i) q^{77} +(2.25419 - 1.50848i) q^{78} +(0.0332596 + 0.124126i) q^{79} +(10.1546 + 10.1546i) q^{80} +(-6.38174 - 6.34613i) q^{81} +(-0.120467 - 0.120467i) q^{82} +(-5.37265 - 3.10190i) q^{83} +(-7.01196 - 1.38967i) q^{84} +(-10.1774 - 12.8014i) q^{85} +(-0.0645802 - 0.111856i) q^{86} +(4.02678 + 3.52641i) q^{87} +(1.14348 - 0.306394i) q^{88} +8.09524 q^{89} +(-1.15517 - 2.77783i) q^{90} +(9.33624 - 9.33624i) q^{91} +(-0.364738 - 1.36122i) q^{92} +(-0.0736917 + 0.0250724i) q^{93} +(2.07613 - 1.19866i) q^{94} +(21.6915 + 5.81223i) q^{95} +(4.51528 + 2.22277i) q^{96} +(-3.94729 + 1.05767i) q^{97} -0.620928 q^{98} +(3.53890 + 0.460869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30}+ \cdots + 6 q^{99}+O(q^{100}) $ 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7 - 16 * q^10 - 24 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^17 - 8 * q^18 + 18 * q^20 - 16 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 - 10 * q^29 - 36 * q^30 - 2 * q^31 + 12 * q^33 + 20 * q^34 - 128 * q^35 - 8 * q^37 - 24 * q^38 + 34 * q^39 - 20 * q^40 + 32 * q^41 + 20 * q^44 + 20 * q^45 - 40 * q^46 - 64 * q^47 + 62 * q^48 + 48 * q^50 + 40 * q^51 + 36 * q^52 - 46 * q^54 - 16 * q^55 + 12 * q^56 + 72 * q^57 - 10 * q^58 - 2 * q^61 - 28 * q^62 + 64 * q^63 - 8 * q^64 + 8 * q^65 - 4 * q^67 - 60 * q^68 - 24 * q^69 - 84 * q^71 + 72 * q^72 - 44 * q^73 - 14 * q^74 + 46 * q^75 - 56 * q^78 + 10 * q^79 + 204 * q^80 + 44 * q^81 - 52 * q^82 - 60 * q^84 + 22 * q^85 + 32 * q^86 + 16 * q^88 + 128 * q^89 - 66 * q^90 + 44 * q^91 + 136 * q^92 + 4 * q^95 - 2 * q^96 - 44 * q^97 + 208 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.218953	−	0.126413i	−0.154823	−	0.0893873i	0.420587	−	0.907252i	$-0.361824\pi$
$2$	−0.218953	−	0.126413i	−0.154823	−	0.0893873i	−0.575410	+	0.817865i	$0.695158\pi$
$3$	0.963283	+	1.43947i	0.556152	+	0.831081i
$3$	0.963283	+	1.43947i	0.556152	+	0.831081i
$4$	−0.968040	−	1.67669i	−0.484020	−	0.838347i
$5$	1.02659	−	3.83129i	0.459105	−	1.71340i	−0.216626	−	0.976255i	$-0.569505\pi$
$5$	1.02659	−	3.83129i	0.459105	−	1.71340i	0.675731	−	0.737149i	$-0.263828\pi$
$6$	−0.0289461	−	0.436949i	−0.0118172	−	0.178384i
$7$	−0.551719	−	2.05904i	−0.208530	−	0.778245i	−0.988344	−	0.152234i	$-0.951353\pi$
$7$	−0.551719	−	2.05904i	−0.208530	−	0.778245i	0.779814	−	0.626011i	$-0.215313\pi$
$8$			0.995142i			0.351836i
$9$	−1.14417	+	2.77324i	−0.381391	+	0.924414i
$10$	−0.709099	+	0.709099i	−0.224237	+	0.224237i
$11$	−0.307889	−	1.14906i	−0.0928322	−	0.346454i	0.903850	−	0.427850i	$-0.140729\pi$
$11$	−0.307889	−	1.14906i	−0.0928322	−	0.346454i	−0.996682	+	0.0813958i	$0.974062\pi$
$12$	1.48106	−	3.00860i	0.427546	−	0.868508i
$13$	3.09696	+	5.36409i	0.858942	+	1.48773i	0.872939	+	0.487829i	$0.162211\pi$
$13$	3.09696	+	5.36409i	0.858942	+	1.48773i	−0.0139970	+	0.999902i	$0.504456\pi$
$14$	−0.139489	+	0.520578i	−0.0372799	+	0.139130i
$15$	6.50393	−	2.21286i	1.67931	−	0.571359i
$16$	−1.81028	+	3.13550i	−0.452570	+	0.783874i
$17$	2.45336	−	3.31376i	0.595027	−	0.803706i
$17$	2.45336	−	3.31376i	0.595027	−	0.803706i
$18$	0.601094	−	0.462573i	0.141679	−	0.109029i
$19$			5.66168i			1.29888i	0.760413	+	0.649440i	$0.224996\pi$
$19$			5.66168i			1.29888i	−0.760413	+	0.649440i	$0.775004\pi$
$20$	−7.41767	+	1.98756i	−1.65864	+	0.444432i
$21$	2.43248	−	2.77762i	0.530810	−	0.606127i
$22$	−0.0778423	+	0.290512i	−0.0165960	+	0.0619373i
$23$	0.703082	+	0.188390i	0.146603	+	0.0392821i	0.331374	−	0.943499i	$-0.392488\pi$
$23$	0.703082	+	0.188390i	0.146603	+	0.0392821i	−0.184771	+	0.982782i	$0.559154\pi$
$24$	−1.43248	+	0.958603i	−0.292404	+	0.195674i
$25$	−9.29474	−	5.36632i	−1.85895	−	1.07326i
$26$		−	1.56598i		−	0.307114i
$27$	−5.09417	+	1.02441i	−0.980374	+	0.197148i
$28$	−2.91830	+	2.91830i	−0.551506	+	0.551506i
$29$	2.98504	−	0.799838i	0.554307	−	0.148526i	0.0292175	−	0.999573i	$-0.490698\pi$
$29$	2.98504	−	0.799838i	0.554307	−	0.148526i	0.525090	+	0.851047i	$0.324032\pi$
$30$	−1.70379	−	0.337667i	−0.311069	−	0.0616492i
$31$	−0.0116316	+	0.0434097i	−0.00208910	+	0.00779661i	−0.966963	−	0.254919i	$-0.917951\pi$
$31$	−0.0116316	+	0.0434097i	−0.00208910	+	0.00779661i	0.964873	+	0.262715i	$0.0846180\pi$
$32$	2.51637	−	1.45283i	0.444836	−	0.256826i
$33$	1.35746	−	1.55007i	0.236303	−	0.269832i
$34$	−0.956073	+	0.415424i	−0.163965	+	0.0712446i
$35$	−8.45517			−1.42918
$36$	5.75748	−	0.766182i	0.959580	−	0.127697i
$37$	1.68986	+	1.68986i	0.277812	+	0.277812i	0.832235	−	0.554423i	$-0.187061\pi$
$37$	1.68986	+	1.68986i	0.277812	+	0.277812i	−0.554423	+	0.832235i	$0.687061\pi$
$38$	0.715709	−	1.23964i	0.116103	−	0.201097i
$39$	−4.73822	+	9.62513i	−0.758723	+	1.54125i
$40$	3.81267	+	1.02160i	0.602836	+	0.161530i
$41$	0.650890	+	0.174405i	0.101652	+	0.0272375i	0.309286	−	0.950969i	$-0.399910\pi$
$41$	0.650890	+	0.174405i	0.101652	+	0.0272375i	−0.207635	+	0.978206i	$0.566576\pi$
$42$	−0.883726	+	0.300674i	−0.136362	+	0.0463950i
$43$	0.442424	+	0.255434i	0.0674691	+	0.0389533i	0.533355	−	0.845891i	$-0.320931\pi$
$43$	0.442424	+	0.255434i	0.0674691	+	0.0389533i	−0.465886	+	0.884845i	$0.654264\pi$
$44$	−1.62857	+	1.62857i	−0.245516	+	0.245516i
$45$	9.45049	+	7.23063i	1.40880	+	1.07788i
$46$	−0.130127	−	0.130127i	−0.0191862	−	0.0191862i
$47$	−4.74104	+	8.21172i	−0.691551	+	1.19780i	0.279778	+	0.960065i	$0.409739\pi$
$47$	−4.74104	+	8.21172i	−0.691551	+	1.19780i	−0.971330	+	0.237737i	$0.923594\pi$
$48$	−6.25728	+	0.414520i	−0.903161	+	0.0598308i
$49$	2.12692	−	1.22798i	0.303845	−	0.175425i
$50$	1.35674	+	2.34995i	0.191873	+	0.332333i
$51$	7.13336	+	0.339453i	0.998870	+	0.0475330i
$52$	5.99596	−	10.3853i	0.831490	−	1.44018i
$53$		−	7.10456i		−	0.975886i	−0.872875	−	0.487943i	$-0.837747\pi$
$53$		−	7.10456i		−	0.975886i	0.872875	−	0.487943i	$-0.162253\pi$
$54$	1.24488	+	0.419670i	0.169407	+	0.0571099i
$55$	−4.71845			−0.636236
$56$	2.04904	−	0.549038i	0.273814	−	0.0733683i
$57$	−8.14985	+	5.45380i	−1.07947	+	0.722374i
$58$	−0.754693	−	0.202219i	−0.0990961	−	0.0265527i
$59$	−7.91388	+	4.56908i	−1.03030	+	0.594844i	−0.917070	−	0.398725i	$-0.869453\pi$
$59$	−7.91388	+	4.56908i	−1.03030	+	0.594844i	−0.113229	+	0.993569i	$0.536119\pi$
$60$	−10.0064	−	8.76297i	−1.29182	−	1.13129i
$61$	1.49801	+	5.59065i	0.191800	+	0.715809i	0.993072	+	0.117508i	$0.0374906\pi$
$61$	1.49801	+	5.59065i	0.191800	+	0.715809i	−0.801271	+	0.598301i	$0.795843\pi$
$62$	0.00803432	−	0.00803432i	0.00102036	−	0.00102036i
$63$	6.34148	+	0.825848i	0.798952	+	0.104047i
$64$	6.50650			0.813312
$65$	23.7307	−	6.35862i	2.94343	−	0.788689i
$66$	−0.493168	+	0.167793i	−0.0607048	+	0.0206539i
$67$	−1.68697	−	2.92191i	−0.206096	−	0.356968i	0.744386	−	0.667750i	$-0.232742\pi$
$67$	−1.68697	−	2.92191i	−0.206096	−	0.356968i	−0.950481	+	0.310782i	$0.899409\pi$
$68$	−7.93112	−	0.905676i	−0.961789	−	0.109829i
$69$	0.406084	+	1.19354i	0.0488868	+	0.143685i
$70$	1.85129	+	1.06884i	0.221271	+	0.127751i
$71$	2.32488	+	2.32488i	0.275912	+	0.275912i	0.831475	−	0.555563i	$-0.187497\pi$
$71$	2.32488	+	2.32488i	0.275912	+	0.275912i	−0.555563	+	0.831475i	$0.687497\pi$
$72$	−2.75977	−	1.13861i	−0.325242	−	0.134187i
$73$	−8.24518	−	8.24518i	−0.965026	−	0.965026i	0.0343828	−	0.999409i	$-0.489053\pi$
$73$	−8.24518	−	8.24518i	−0.965026	−	0.965026i	−0.999409	+	0.0343828i	$0.989053\pi$
$74$	−0.156381	−	0.583622i	−0.0181789	−	0.0678447i
$75$	−1.22879	−	18.5488i	−0.141888	−	2.14183i
$76$	9.49291	−	5.48073i	1.08891	−	0.628683i
$77$	−2.19609	+	1.26791i	−0.250268	+	0.144492i
$78$	2.25419	−	1.50848i	0.255237	−	0.170802i
$79$	0.0332596	+	0.124126i	0.00374199	+	0.0139653i	0.967772	−	0.251830i	$-0.0810323\pi$
$79$	0.0332596	+	0.124126i	0.00374199	+	0.0139653i	−0.964030	+	0.265795i	$0.914366\pi$
$80$	10.1546	+	10.1546i	1.13532	+	1.13532i
$81$	−6.38174	−	6.34613i	−0.709082	−	0.705126i
$82$	−0.120467	−	0.120467i	−0.0133034	−	0.0133034i
$83$	−5.37265	−	3.10190i	−0.589725	−	0.340478i	0.175264	−	0.984522i	$-0.443922\pi$
$83$	−5.37265	−	3.10190i	−0.589725	−	0.340478i	−0.764989	+	0.644043i	$0.777256\pi$
$84$	−7.01196	−	1.38967i	−0.765068	−	0.151625i
$85$	−10.1774	−	12.8014i	−1.10389	−	1.38851i
$86$	−0.0645802	−	0.111856i	−0.00696386	−	0.0120618i
$87$	4.02678	+	3.52641i	0.431716	+	0.378071i
$88$	1.14348	−	0.306394i	0.121895	−	0.0326617i
$89$	8.09524			0.858094			0.429047	−	0.903282i	$-0.358850\pi$
$89$	8.09524			0.858094			0.429047	+	0.903282i	$0.358850\pi$
$90$	−1.15517	−	2.77783i	−0.121766	−	0.292809i
$91$	9.33624	−	9.33624i	0.978704	−	0.978704i
$92$	−0.364738	−	1.36122i	−0.0380266	−	0.141917i
$93$	−0.0736917	+	0.0250724i	−0.00764147	+	0.00259989i
$94$	2.07613	−	1.19866i	0.214137	−	0.123632i
$95$	21.6915	+	5.81223i	2.22550	+	0.596322i
$96$	4.51528	+	2.22277i	0.460839	+	0.226860i
$97$	−3.94729	+	1.05767i	−0.400786	+	0.107390i	−0.453581	−	0.891215i	$-0.649854\pi$
$97$	−3.94729	+	1.05767i	−0.400786	+	0.107390i	0.0527947	+	0.998605i	$0.483187\pi$
$98$	−0.620928			−0.0627232
$99$	3.53890	+	0.460869i	0.355673	+	0.0463191i
$100$			20.7792i			2.07792i
$101$	−3.57539	+	6.19276i	−0.355765	+	0.616203i	−0.987249	−	0.159186i	$-0.949113\pi$
$101$	−3.57539	+	6.19276i	−0.355765	+	0.616203i	0.631484	+	0.775389i	$0.282446\pi$
$102$	−1.51896	−	0.976072i	−0.150400	−	0.0966455i
$103$	5.50590	+	9.53649i	0.542512	+	0.939658i	0.998759	+	0.0498052i	$0.0158601\pi$
$103$	5.50590	+	9.53649i	0.542512	+	0.939658i	−0.456247	+	0.889853i	$0.650807\pi$
$104$	−5.33803	+	3.08191i	−0.523437	+	0.302206i
$105$	−8.14472	−	12.1710i	−0.794843	−	1.18777i
$106$	−0.898107	+	1.55557i	−0.0872319	+	0.151090i
$107$	5.42949	+	5.42949i	0.524889	+	0.524889i	0.919044	−	0.394155i	$-0.128963\pi$
$107$	5.42949	+	5.42949i	0.524889	+	0.524889i	−0.394155	+	0.919044i	$0.628963\pi$
$108$	6.64898	+	7.54969i	0.639799	+	0.726470i
$109$	−7.35646	+	7.35646i	−0.704621	+	0.704621i	−0.965399	−	0.260778i	$-0.916021\pi$
$109$	−7.35646	+	7.35646i	−0.704621	+	0.704621i	0.260778	+	0.965399i	$0.416021\pi$
$110$	1.03312	+	0.596473i	0.0985042	+	0.0568714i
$111$	−0.804698	+	4.06033i	−0.0763786	+	0.385390i
$112$	7.45489	+	1.99753i	0.704421	+	0.188749i
$113$	−13.3551	−	3.57848i	−1.25634	−	0.336635i	−0.431557	−	0.902085i	$-0.642036\pi$
$113$	−13.3551	−	3.57848i	−1.25634	−	0.336635i	−0.824782	+	0.565450i	$0.808702\pi$
$114$	2.47387	−	0.163884i	0.231699	−	0.0153491i
$115$	1.44355	−	2.50031i	0.134612	−	0.233155i
$116$	−4.23072	−	4.23072i	−0.392812	−	0.392812i
$117$	−18.4194	+	2.45118i	−1.70287	+	0.226611i
$118$	2.31036			0.212686
$119$	−8.17674	−	3.22330i	−0.749561	−	0.295480i
$120$	2.20211	+	6.47234i	0.201024	+	0.590841i
$121$	8.30074	−	4.79243i	0.754613	−	0.435676i
$122$	0.378735	−	1.41346i	0.0342891	−	0.127969i
$123$	0.375939	+	1.10494i	0.0338973	+	0.0996291i
$124$	0.0840446	−	0.0225197i	0.00754743	−	0.00202233i
$125$	−16.0783	+	16.0783i	−1.43809	+	1.43809i
$126$	−1.28409	−	0.982467i	−0.114396	−	0.0875251i
$127$		−	10.1096i		−	0.897084i	−0.893762	−	0.448542i	$-0.851944\pi$
$127$		−	10.1096i		−	0.897084i	0.893762	−	0.448542i	$-0.148056\pi$
$128$	−6.45736	−	3.72816i	−0.570755	−	0.329526i
$129$	0.0584895	+	0.882914i	0.00514971	+	0.0777362i
$130$	−5.99972	−	1.60762i	−0.526211	−	0.140998i
$131$	2.18549	−	8.15638i	0.190948	−	0.712626i	−0.802331	−	0.596879i	$-0.796407\pi$
$131$	2.18549	−	8.15638i	0.190948	−	0.712626i	0.993279	−	0.115747i	$-0.0369261\pi$
$132$	−3.91306	−	0.775511i	−0.340588	−	0.0674996i
$133$	11.6576	−	3.12366i	1.01085	−	0.270855i
$134$			0.853016i			0.0736893i
$135$	−1.30481	+	20.5689i	−0.112300	+	1.77029i
$136$	3.29766	+	2.44144i	0.282772	+	0.209352i
$137$	−1.44676	+	2.50586i	−0.123605	+	0.214090i	−0.921187	−	0.389121i	$-0.872779\pi$
$137$	−1.44676	+	2.50586i	−0.123605	+	0.214090i	0.797582	+	0.603211i	$0.206112\pi$
$138$	0.0619654	−	0.312664i	0.00527485	−	0.0266157i
$139$	1.21808	−	4.54595i	0.103316	−	0.385582i	−0.894832	−	0.446402i	$-0.852705\pi$
$139$	1.21808	−	4.54595i	0.103316	−	0.385582i	0.998149	+	0.0608202i	$0.0193716\pi$
$140$	8.18494	+	14.1767i	0.691754	+	1.19815i
$141$	−16.3875	+	1.08561i	−1.38008	+	0.0914246i
$142$	−0.215146	−	0.802934i	−0.0180546	−	0.0673807i
$143$	5.21014	−	5.21014i	0.435694	−	0.435694i
$144$	−6.62422	−	8.60789i	−0.552019	−	0.717325i
$145$		−	12.2576i		−	1.01794i
$146$	0.763014	+	2.84761i	0.0631475	+	0.235670i
$147$	3.81646	+	1.87875i	0.314777	+	0.154957i
$148$	1.19753	−	4.46924i	0.0984363	−	0.367369i
$149$	−5.25356	−	9.09944i	−0.430389	−	0.745455i	0.566518	−	0.824049i	$-0.308290\pi$
$149$	−5.25356	−	9.09944i	−0.430389	−	0.745455i	−0.996907	+	0.0785942i	$0.974957\pi$
$150$	−2.07576	+	4.21666i	−0.169485	+	0.344289i
$151$	0.878252	+	0.507059i	0.0714711	+	0.0412639i	0.535310	−	0.844656i	$-0.320195\pi$
$151$	0.878252	+	0.507059i	0.0714711	+	0.0412639i	−0.463839	+	0.885920i	$0.653528\pi$
$152$	−5.63418			−0.456992
$153$	6.38281	+	10.5953i	0.516019	+	0.856577i
$154$	0.641123			0.0516631
$155$	0.154374	+	0.0891280i	0.0123996	+	0.00715893i
$156$	20.7252	−	1.37296i	1.65934	−	0.109925i
$157$	0.417298	+	0.722782i	0.0333040	+	0.0576843i	0.882197	−	0.470881i	$-0.156064\pi$
$157$	0.417298	+	0.722782i	0.0333040	+	0.0576843i	−0.848893	+	0.528565i	$0.822730\pi$
$158$	0.00840887	−	0.0313823i	0.000668974	−	0.00249664i
$159$	10.2268	−	6.84370i	0.811040	−	0.542741i
$160$	−2.98292	−	11.1324i	−0.235820	−	0.880093i
$161$		−	1.55161i		−	0.122284i
$162$	0.595072	+	2.19624i	0.0467533	+	0.172553i
$163$	−17.8094	+	17.8094i	−1.39494	+	1.39494i	−0.581114	+	0.813822i	$0.697383\pi$
$163$	−17.8094	+	17.8094i	−1.39494	+	1.39494i	−0.813822	+	0.581114i	$0.802617\pi$
$164$	−0.337663	−	1.26017i	−0.0263670	−	0.0984031i
$165$	−4.54520	−	6.79209i	−0.353844	−	0.528763i
$166$	0.784240	+	1.35834i	0.0608689	+	0.105428i
$167$	0.699072	−	2.60897i	0.0540958	−	0.201888i	−0.933589	−	0.358346i	$-0.883341\pi$
$167$	0.699072	−	2.60897i	0.0540958	−	0.201888i	0.987685	+	0.156458i	$0.0500075\pi$
$168$	2.76413	+	2.42066i	0.213257	+	0.186758i
$169$	−12.6823	+	21.9664i	−0.975563	+	1.68972i
$170$	0.610113	+	4.08946i	0.0467935	+	0.313647i
$171$	−15.7012	−	6.47794i	−1.20070	−	0.495380i
$172$		−	0.989080i		−	0.0754167i
$173$	9.95002	−	2.66610i	0.756486	−	0.202700i	0.140093	−	0.990138i	$-0.455260\pi$
$173$	9.95002	−	2.66610i	0.756486	−	0.202700i	0.616393	+	0.787438i	$0.288593\pi$
$174$	−0.435894	−	1.28116i	−0.0330450	−	0.0971242i
$175$	−5.92140	+	22.0990i	−0.447616	+	1.67052i
$176$	4.16024	+	1.11473i	0.313590	+	0.0840261i
$177$	−14.2004	−	6.99051i	−1.06737	−	0.525439i
$178$	−1.77248	−	1.02334i	−0.132853	−	0.0767027i
$179$		−	9.03233i		−	0.675108i	−0.941306	−	0.337554i	$-0.890400\pi$
$179$		−	9.03233i		−	0.675108i	0.941306	−	0.337554i	$-0.109600\pi$
$180$	2.97511	−	22.8451i	0.221752	−	1.70277i
$181$	15.5693	−	15.5693i	1.15726	−	1.15726i	0.172196	−	0.985063i	$-0.444914\pi$
$181$	15.5693	−	15.5693i	1.15726	−	1.15726i	0.985063	−	0.172196i	$-0.0550863\pi$
$182$	−3.22442	+	0.863981i	−0.239010	+	0.0640425i
$183$	−6.60459	+	7.54172i	−0.488225	+	0.557500i
$184$	−0.187475	+	0.699666i	−0.0138208	+	0.0515801i
$185$	8.20915	−	4.73955i	0.603549	−	0.348459i
$186$	0.0193045	+	0.00382587i	0.00141548	+	0.000280527i
$187$	−4.56307	−	1.79878i	−0.333685	−	0.131540i
$188$	18.3580			1.33890
$189$	4.91985	+	9.92393i	0.357867	+	0.721859i
$190$	−4.01469	−	4.01469i	−0.291257	−	0.291257i
$191$	−11.6017	+	20.0948i	−0.839472	+	1.45401i	0.0508643	+	0.998706i	$0.483802\pi$
$191$	−11.6017	+	20.0948i	−0.839472	+	1.45401i	−0.890337	+	0.455303i	$0.849531\pi$
$192$	6.26760	+	9.36594i	0.452325	+	0.675928i
$193$	−16.7418	−	4.48595i	−1.20510	−	0.322906i	−0.400263	−	0.916400i	$-0.631081\pi$
$193$	−16.7418	−	4.48595i	−1.20510	−	0.322906i	−0.804838	+	0.593494i	$0.797748\pi$
$194$	0.997976	+	0.267407i	0.0716505	+	0.0191987i
$195$	32.0124	+	28.0346i	2.29246	+	2.00760i
$196$	−4.11788	−	2.37746i	−0.294134	−	0.169819i
$197$	−2.14303	+	2.14303i	−0.152685	+	0.152685i	−0.779316	−	0.626631i	$-0.784433\pi$
$197$	−2.14303	+	2.14303i	−0.152685	+	0.152685i	0.626631	+	0.779316i	$0.284433\pi$
$198$	−0.716594	−	0.548271i	−0.0509261	−	0.0389639i
$199$	2.45708	+	2.45708i	0.174178	+	0.174178i	0.788812	−	0.614634i	$-0.210696\pi$
$199$	2.45708	+	2.45708i	0.174178	+	0.174178i	−0.614634	+	0.788812i	$0.710696\pi$
$200$	5.34025	−	9.24958i	0.377613	−	0.654044i
$201$	2.58099	−	5.24297i	0.182049	−	0.369810i
$202$	1.56569	−	0.903950i	0.110161	−	0.0636017i
$203$	−3.29380	−	5.70503i	−0.231179	−	0.400414i
$204$	−6.33621	−	12.2891i	−0.443624	−	0.860406i
$205$	1.33639	−	2.31470i	0.0933378	−	0.161666i
$206$		−	2.78406i		−	0.193975i
$207$	−1.32690	+	1.73427i	−0.0922258	+	0.120540i
$208$	−22.4255			−1.55493
$209$	6.50561	−	1.74317i	0.450002	−	0.120578i
$210$	0.244744	+	3.69448i	0.0168890	+	0.254943i
$211$	9.33859	+	2.50227i	0.642895	+	0.172263i	0.565514	−	0.824738i	$-0.308678\pi$
$211$	9.33859	+	2.50227i	0.642895	+	0.172263i	0.0773805	+	0.997002i	$0.475344\pi$
$212$	−11.9122	+	6.87749i	−0.818131	+	0.472348i
$213$	−1.10709	+	5.58612i	−0.0758563	+	0.382754i
$214$	−0.502448	−	1.87516i	−0.0343467	−	0.128183i
$215$	1.43283	−	1.43283i	0.0977181	−	0.0977181i
$216$	−1.01943	−	5.06942i	−0.0693637	−	0.344930i
$217$	0.0957998			0.00650331
$218$	2.54067	−	0.680771i	0.172076	−	0.0461076i
$219$	3.92628	−	19.8112i	0.265314	−	1.33872i
$220$	4.56765	+	7.91140i	0.307951	+	0.533386i
$221$	25.3733	+	2.89745i	1.70679	+	0.194903i
$222$	0.689469	−	0.787299i	0.0462742	−	0.0528401i
$223$	−2.31875	−	1.33873i	−0.155275	−	0.0896480i	0.420349	−	0.907362i	$-0.361908\pi$
$223$	−2.31875	−	1.33873i	−0.155275	−	0.0896480i	−0.575624	+	0.817714i	$0.695241\pi$
$224$	−4.37976	−	4.37976i	−0.292635	−	0.292635i
$225$	25.5169	−	19.6366i	1.70113	−	1.30911i
$226$	2.47177	+	2.47177i	0.164420	+	0.164420i
$227$	−5.24113	−	19.5602i	−0.347866	−	1.29825i	−0.889228	−	0.457465i	$-0.848758\pi$
$227$	−5.24113	−	19.5602i	−0.347866	−	1.29825i	0.541361	−	0.840790i	$-0.317909\pi$
$228$	17.0337	+	8.38530i	1.12809	+	0.555330i
$229$	2.37683	−	1.37227i	0.157066	−	0.0906819i	−0.419407	−	0.907798i	$-0.637762\pi$
$229$	2.37683	−	1.37227i	0.157066	−	0.0906819i	0.576473	+	0.817116i	$0.304429\pi$
$230$	−0.632142	+	0.364967i	−0.0416822	+	0.0240652i
$231$	−3.94059	−	1.93986i	−0.259272	−	0.127633i
$232$	0.795952	+	2.97053i	0.0522568	+	0.195025i
$233$	−7.71254	−	7.71254i	−0.505266	−	0.505266i	0.407804	−	0.913070i	$-0.366295\pi$
$233$	−7.71254	−	7.71254i	−0.505266	−	0.505266i	−0.913070	+	0.407804i	$0.866295\pi$
$234$	4.34285	+	1.79175i	0.283901	+	0.117130i
$235$	26.5943	+	26.5943i	1.73482	+	1.73482i
$236$	15.3219	+	8.84610i	0.997371	+	0.575832i
$237$	−0.146638	+	0.167445i	−0.00952519	+	0.0108767i
$238$	1.38286	+	1.73940i	0.0896374	+	0.112748i
$239$	−10.8739	−	18.8341i	−0.703371	−	1.21827i	−0.967276	−	0.253726i	$-0.918344\pi$
$239$	−10.8739	−	18.8341i	−0.703371	−	1.21827i	0.263905	−	0.964549i	$-0.414990\pi$
$240$	−4.83552	+	24.3990i	−0.312131	+	1.57495i
$241$	5.63618	−	1.51021i	0.363059	−	0.0972812i	−0.0726781	−	0.997355i	$-0.523155\pi$
$241$	5.63618	−	1.51021i	0.363059	−	0.0972812i	0.435737	+	0.900074i	$0.356488\pi$
$242$	−2.42330			−0.155776
$243$	2.98767	−	15.2995i	0.191659	−	0.981462i
$244$	7.92367	−	7.92367i	0.507261	−	0.507261i
$245$	−2.52126	−	9.40946i	−0.161077	−	0.601148i
$246$	0.0573655	−	0.289454i	0.00365749	−	0.0184549i
$247$	−30.3698	+	17.5340i	−1.93238	+	1.11566i
$248$	−0.0431988	−	0.0115751i	−0.00274313	−	0.000735019i
$249$	−0.710277	−	10.7218i	−0.0450119	−	0.679467i
$250$	5.55291	−	1.48790i	0.351197	−	0.0941029i
$251$	−0.160391			−0.0101238			−0.00506188	−	0.999987i	$-0.501611\pi$
$251$	−0.160391			−0.0101238			−0.00506188	+	0.999987i	$0.501611\pi$
$252$	−4.75411	−	11.4322i	−0.299481	−	0.720160i
$253$		−	0.865886i		−	0.0544378i
$254$	−1.27799	+	2.21354i	−0.0801879	+	0.138890i
$255$	8.62358	−	26.9815i	0.540029	−	1.68964i
$256$	−5.56393	−	9.63700i	−0.347745	−	0.602313i
$257$	−15.7573	+	9.09748i	−0.982913	+	0.567485i	−0.903148	−	0.429329i	$-0.858750\pi$
$257$	−15.7573	+	9.09748i	−0.982913	+	0.567485i	−0.0797648	+	0.996814i	$0.525417\pi$
$258$	0.0988051	−	0.200711i	0.00615134	−	0.0124957i
$259$	2.54717	−	4.41183i	0.158274	−	0.274138i
$260$	−33.6337	−	33.6337i	−2.08587	−	2.08587i
$261$	−1.19725	+	9.19338i	−0.0741079	+	0.569056i
$262$	−1.50959	+	1.50959i	−0.0932629	+	0.0932629i
$263$	−15.2224	−	8.78864i	−0.938651	−	0.541930i	−0.0491139	−	0.998793i	$-0.515640\pi$
$263$	−15.2224	−	8.78864i	−0.938651	−	0.541930i	−0.889537	+	0.456863i	$0.848973\pi$
$264$	1.54254	+	1.35086i	0.0949366	+	0.0831398i
$265$	−27.2196	−	7.29347i	−1.67209	−	0.448034i
$266$	−2.94735	−	0.789740i	−0.180714	−	0.0484221i
$267$	7.79801	+	11.6529i	0.477230	+	0.713145i
$268$	−3.26610	+	5.65705i	−0.199509	+	0.345559i
$269$	−12.6878	−	12.6878i	−0.773588	−	0.773588i	0.205143	−	0.978732i	$-0.434234\pi$
$269$	−12.6878	−	12.6878i	−0.773588	−	0.773588i	−0.978732	+	0.205143i	$0.934234\pi$
$270$	2.88586	−	4.33868i	0.175628	−	0.264044i
$271$	20.3520			1.23630			0.618148	−	0.786062i	$-0.287883\pi$
$271$	20.3520			1.23630			0.618148	+	0.786062i	$0.287883\pi$
$272$	5.94903	+	13.6913i	0.360713	+	0.830160i
$273$	22.4327	+	4.44583i	1.35769	+	0.269074i
$274$	0.633545	−	0.365778i	0.0382739	−	0.0220974i
$275$	−3.30447	+	12.3324i	−0.199267	+	0.743674i
$276$	1.60810	−	1.83627i	0.0967961	−	0.110531i
$277$	25.0631	−	6.71563i	1.50589	−	0.403503i	0.590824	−	0.806800i	$-0.298803\pi$
$277$	25.0631	−	6.71563i	1.50589	−	0.403503i	0.915069	+	0.403297i	$0.132136\pi$
$278$	−0.841369	+	0.841369i	−0.0504620	+	0.0504620i
$279$	−0.107077	−	0.0819254i	−0.00641054	−	0.00490474i
$280$		−	8.41409i		−	0.502838i
$281$	−1.48219	−	0.855744i	−0.0884202	−	0.0510494i	0.455138	−	0.890421i	$-0.349590\pi$
$281$	−1.48219	−	0.855744i	−0.0884202	−	0.0510494i	−0.543558	+	0.839372i	$0.682923\pi$
$282$	3.72534	+	1.83389i	0.221840	+	0.109207i
$283$	2.68605	+	0.719725i	0.159669	+	0.0427832i	0.337768	−	0.941229i	$-0.390328\pi$
$283$	2.68605	+	0.719725i	0.159669	+	0.0427832i	−0.178099	+	0.984013i	$0.556995\pi$
$284$	1.64753	−	6.14868i	0.0977632	−	0.364857i
$285$	12.5285	+	36.8232i	0.742126	+	2.18122i
$286$	−1.79941	+	0.482149i	−0.106401	+	0.0285101i
$287$		−	1.43643i		−	0.0847899i
$288$	1.14988	+	8.64079i	0.0677574	+	0.509163i
$289$	−4.96207	−	16.2597i	−0.291886	−	0.956453i
$290$	−1.54952	+	2.68385i	−0.0909910	+	0.157601i
$291$	−5.32485	−	4.66318i	−0.312148	−	0.273361i
$292$	−5.84298	+	21.8063i	−0.341935	+	1.27612i
$293$	3.16748	+	5.48624i	0.185046	+	0.320509i	0.943592	−	0.331110i	$-0.107423\pi$
$293$	3.16748	+	5.48624i	0.185046	+	0.320509i	−0.758546	+	0.651620i	$0.774090\pi$
$294$	−0.598129	−	0.893809i	−0.0348836	−	0.0521280i
$295$	9.38115	+	35.0109i	0.546192	+	2.03841i
$296$	−1.68165	+	1.68165i	−0.0977441	+	0.0977441i
$297$	2.74555	+	5.53810i	0.159313	+	0.321353i
$298$			2.65647i			0.153885i
$299$	1.16687	+	4.35483i	0.0674820	+	0.251846i
$300$	−29.9112	+	20.0163i	−1.72692	+	1.15564i
$301$	0.281855	−	1.05190i	0.0162459	−	0.0606304i
$302$	−0.128197	−	0.222044i	−0.00737693	−	0.0127772i
$303$	−12.3584	+	0.818696i	−0.709973	+	0.0470329i
$304$	−17.7522	−	10.2492i	−1.01816	−	0.587834i
$305$	22.9572			1.31453
$306$	−0.0581591	−	3.12674i	−0.00332474	−	0.178744i
$307$	−6.06447			−0.346118			−0.173059	−	0.984911i	$-0.555365\pi$
$307$	−6.06447			−0.346118			−0.173059	+	0.984911i	$0.555365\pi$
$308$	4.25181	+	2.45478i	0.242269	+	0.139874i
$309$	−8.42380	+	17.1119i	−0.479213	+	0.973464i
$310$	−0.0225338	−	0.0390297i	−0.00127984	−	0.00221674i
$311$	−1.95336	+	7.29002i	−0.110765	+	0.413379i	−0.998935	−	0.0461346i	$-0.985310\pi$
$311$	−1.95336	+	7.29002i	−0.110765	+	0.413379i	0.888171	+	0.459514i	$0.151976\pi$
$312$	−9.57837	−	4.71520i	−0.542268	−	0.266946i
$313$	4.66185	+	17.3983i	0.263503	+	0.983407i	0.963160	+	0.268928i	$0.0866695\pi$
$313$	4.66185	+	17.3983i	0.263503	+	0.983407i	−0.699657	+	0.714479i	$0.746664\pi$
$314$		−	0.211007i		−	0.0119078i
$315$	9.67417	−	23.4482i	0.545077	−	1.32116i
$316$	0.175925	−	0.175925i	0.00989658	−	0.00989658i
$317$	5.49818	+	20.5195i	0.308809	+	1.15249i	0.929617	+	0.368527i	$0.120138\pi$
$317$	5.49818	+	20.5195i	0.308809	+	1.15249i	−0.620809	+	0.783962i	$0.713196\pi$
$318$	−3.10433	+	0.205649i	−0.174082	+	0.0115322i
$319$	−1.83812	−	3.18372i	−0.102915	−	0.178254i
$320$	6.67951	−	24.9283i	0.373396	−	1.39353i
$321$	−2.58548	+	13.0457i	−0.144307	+	0.728143i
$322$	−0.196144	+	0.339731i	−0.0109307	+	0.0189325i
$323$	18.7615	+	13.8901i	1.04392	+	0.772868i
$324$	−4.46274	+	16.8435i	−0.247930	+	0.935752i
$325$		−	66.4771i		−	3.68749i
$326$	6.15075	−	1.64809i	0.340658	−	0.0912791i
$327$	−17.6758	−	3.50308i	−0.977473	−	0.193721i
$328$	−0.173558	+	0.647727i	−0.00958314	+	0.0357648i
$329$	19.5240	+	5.23144i	1.07639	+	0.288418i
$330$	0.136581	+	2.06172i	0.00751853	+	0.113494i
$331$	3.80655	+	2.19772i	0.209227	+	0.120797i	0.600952	−	0.799285i	$-0.294788\pi$
$331$	3.80655	+	2.19772i	0.209227	+	0.120797i	−0.391725	+	0.920082i	$0.628122\pi$
$332$			12.0111i			0.659193i
$333$	−6.61990	+	2.75291i	−0.362768	+	0.150858i
$334$	−0.482872	+	0.482872i	−0.0264216	+	0.0264216i
$335$	−12.9265	+	3.46364i	−0.706250	+	0.189239i
$336$	4.30577	+	12.6553i	0.234899	+	0.690404i
$337$	−6.87510	+	25.6582i	−0.374511	+	1.39769i	0.479548	+	0.877516i	$0.340801\pi$
$337$	−6.87510	+	25.6582i	−0.374511	+	1.39769i	−0.854058	+	0.520177i	$0.825866\pi$
$338$	5.55367	−	3.20641i	0.302080	−	0.174406i
$339$	−7.71359	−	22.6714i	−0.418944	−	1.23134i
$340$	−11.6119	+	29.4566i	−0.629744	+	1.59751i
$341$	0.0534616			0.00289511
$342$	2.61894	+	3.40320i	0.141616	+	0.184024i
$343$	−14.2532	−	14.2532i	−0.769599	−	0.769599i
$344$	−0.254193	+	0.440275i	−0.0137052	+	0.0237380i
$345$	4.98968	−	0.330546i	0.268635	−	0.0177960i
$346$	−2.51562	−	0.674058i	−0.135241	−	0.0362376i
$347$	15.3681	+	4.11787i	0.825003	+	0.221059i	0.646533	−	0.762886i	$-0.276218\pi$
$347$	15.3681	+	4.11787i	0.825003	+	0.221059i	0.178470	+	0.983945i	$0.442885\pi$
$348$	2.01463	−	10.1654i	0.107995	−	0.544922i
$349$	19.6887	+	11.3673i	1.05391	+	0.608477i	0.923743	−	0.383014i	$-0.125114\pi$
$349$	19.6887	+	11.3673i	1.05391	+	0.608477i	0.130171	+	0.991492i	$0.458447\pi$
$350$	4.09010	−	4.09010i	0.218625	−	0.218625i
$351$	−21.2715	−	24.1530i	−1.13539	−	1.28919i
$352$	−2.44415	−	2.44415i	−0.130274	−	0.130274i
$353$	7.45918	−	12.9197i	0.397012	−	0.687645i	−0.596343	−	0.802729i	$-0.703380\pi$
$353$	7.45918	−	12.9197i	0.397012	−	0.687645i	0.993356	+	0.115084i	$0.0367137\pi$
$354$	2.22553	+	3.32571i	0.118286	+	0.176759i
$355$	11.2940	−	6.52058i	0.599422	−	0.346076i
$356$	−7.83651	−	13.5732i	−0.415334	−	0.719380i
$357$	−3.23666	−	14.8752i	−0.171302	−	0.787277i
$358$	−1.14180	+	1.97766i	−0.0603461	+	0.104523i
$359$			25.3903i			1.34005i	0.742339	+	0.670024i	$0.233716\pi$
$359$			25.3903i			1.34005i	−0.742339	+	0.670024i	$0.766284\pi$
$360$	−7.19550	+	9.40457i	−0.379236	+	0.495665i
$361$	−13.0547			−0.687087
$362$	−5.37712	+	1.44079i	−0.282615	+	0.0757265i
$363$	14.8945	+	7.33223i	0.781761	+	0.384842i
$364$	−24.6919	−	6.61617i	−1.29421	−	0.346781i
$365$	−40.0541	+	23.1252i	−2.09653	+	1.21043i
$366$	2.39947	−	0.816381i	0.125422	−	0.0426729i
$367$	−2.68585	−	10.0237i	−0.140200	−	0.523235i	−0.999922	−	0.0124724i	$-0.996030\pi$
$367$	−2.68585	−	10.0237i	−0.140200	−	0.523235i	0.859722	−	0.510762i	$-0.170637\pi$
$368$	−1.86347	+	1.86347i	−0.0971402	+	0.0971402i
$369$	−1.22840	+	1.60553i	−0.0639478	+	0.0835803i
$370$	−2.39656			−0.124591
$371$	−14.6286	+	3.91972i	−0.759478	+	0.203502i
$372$	0.113375	+	0.0992872i	0.00587823	+	0.00514780i
$373$	−14.6963	−	25.4548i	−0.760946	−	1.31800i	−0.942363	−	0.334591i	$-0.891402\pi$
$373$	−14.6963	−	25.4548i	−0.760946	−	1.31800i	0.181418	−	0.983406i	$-0.441931\pi$
$374$	0.771712	+	0.970680i	0.0399043	+	0.0501927i
$375$	−38.6323	−	7.65636i	−1.99496	−	0.395373i
$376$	−8.17182	−	4.71800i	−0.421429	−	0.243312i
$377$	13.5349	+	13.5349i	0.697085	+	0.697085i
$378$	0.177292	−	2.79481i	0.00911893	−	0.143750i
$379$	23.3276	+	23.3276i	1.19826	+	1.19826i	0.974688	+	0.223569i	$0.0717708\pi$
$379$	23.3276	+	23.3276i	1.19826	+	1.19826i	0.223569	+	0.974688i	$0.428229\pi$
$380$	−11.2529	−	41.9965i	−0.577263	−	2.15438i
$381$	14.5525	−	9.73842i	0.745549	−	0.498915i
$382$	5.08048	−	2.93322i	0.259940	−	0.150076i
$383$	−9.43624	+	5.44802i	−0.482169	+	0.278381i	−0.721320	−	0.692602i	$-0.756464\pi$
$383$	−9.43624	+	5.44802i	−0.482169	+	0.278381i	0.239151	+	0.970982i	$0.423131\pi$
$384$	−0.853677	−	12.8865i	−0.0435640	−	0.657610i
$385$	2.60326	+	9.71549i	0.132674	+	0.495147i
$386$	3.09859	+	3.09859i	0.157714	+	0.157714i
$387$	−1.21459	+	0.934690i	−0.0617411	+	0.0475130i
$388$	5.59453	+	5.59453i	0.284019	+	0.284019i
$389$	21.5125	+	12.4202i	1.09073	+	0.629730i	0.933769	−	0.357875i	$-0.116499\pi$
$389$	21.5125	+	12.4202i	1.09073	+	0.629730i	0.156956	+	0.987606i	$0.449832\pi$
$390$	−3.46530	−	10.1850i	−0.175472	−	0.515740i
$391$	2.34919	−	1.86766i	0.118804	−	0.0944515i
$392$	1.22201	+	2.11658i	0.0617208	+	0.106904i
$393$	13.8461	−	4.71094i	0.698445	−	0.237635i
$394$	0.740131	−	0.198318i	0.0372873	−	0.00999110i
$395$	0.509708			0.0256462
$396$	−2.65306	−	6.37979i	−0.133321	−	0.320596i
$397$	4.48358	−	4.48358i	0.225025	−	0.225025i	−0.585586	−	0.810610i	$-0.699135\pi$
$397$	4.48358	−	4.48358i	0.225025	−	0.225025i	0.810610	+	0.585586i	$0.199135\pi$
$398$	−0.227379	−	0.848592i	−0.0113975	−	0.0425361i
$399$	15.7260	+	13.7719i	0.787286	+	0.689458i
$400$	33.6522	−	19.4291i	1.68261	−	0.971455i
$401$	11.5880	+	3.10500i	0.578678	+	0.155056i	0.536274	−	0.844044i	$-0.319831\pi$
$401$	11.5880	+	3.10500i	0.578678	+	0.155056i	0.0424047	+	0.999101i	$0.486498\pi$
$402$	−1.22789	+	0.821696i	−0.0612418	+	0.0409825i
$403$	−0.268876	+	0.0720452i	−0.0133937	+	0.00358883i
$404$	13.8445			0.688789
$405$	−30.8653	+	17.9354i	−1.53371	+	0.891218i
$406$			1.66551i			0.0826580i
$407$	1.42146	−	2.46204i	0.0704593	−	0.122039i
$408$	−0.337804	+	7.09870i	−0.0167238	+	0.351438i
$409$	12.5735	+	21.7779i	0.621718	+	1.07685i	0.989166	+	0.146803i	$0.0468985\pi$
$409$	12.5735	+	21.7779i	0.621718	+	1.07685i	−0.367447	+	0.930044i	$0.619768\pi$
$410$	−0.585216	+	0.337875i	−0.0289018	+	0.0166864i
$411$	−5.00076	+	0.331280i	−0.246669	+	0.0163408i
$412$	10.6599	−	18.4634i	0.525173	−	0.909627i
$413$	13.7742	+	13.7742i	0.677782	+	0.677782i
$414$	0.509762	−	0.211986i	0.0250534	−	0.0104186i
$415$	−17.3998	+	17.3998i	−0.854122	+	0.854122i
$416$	15.5862	+	8.99869i	0.764176	+	0.441197i
$417$	7.71713	−	2.62564i	0.377910	−	0.128578i
$418$	−1.64478	−	0.440719i	−0.0804490	−	0.0215563i
$419$	20.8431	+	5.58490i	1.01825	+	0.272840i	0.729074	−	0.684435i	$-0.239951\pi$
$419$	20.8431	+	5.58490i	1.01825	+	0.272840i	0.289179	+	0.957275i	$0.406618\pi$
$420$	−12.5226	+	25.4382i	−0.611041	+	1.24126i
$421$	9.29851	−	16.1055i	0.453182	−	0.784934i	−0.545400	−	0.838176i	$-0.683622\pi$
$421$	9.29851	−	16.1055i	0.453182	−	0.784934i	0.998582	+	0.0532420i	$0.0169555\pi$
$422$	−1.72840	−	1.72840i	−0.0841370	−	0.0841370i
$423$	−17.3485	−	22.5437i	−0.843514	−	1.09611i
$424$	7.07004			0.343352
$425$	−40.5861	+	17.6351i	−1.96871	+	0.855427i
$426$	0.948557	−	1.08315i	0.0459577	−	0.0524788i
$427$	10.6849	−	6.16893i	0.517078	−	0.298535i
$428$	3.84763	−	14.3596i	0.185982	−	0.694095i
$429$	12.5187	+	2.48102i	0.604408	+	0.119785i
$430$	−0.494851	+	0.132595i	−0.0238638	+	0.00639429i
$431$	−7.41836	+	7.41836i	−0.357330	+	0.357330i	−0.862828	−	0.505498i	$-0.831309\pi$
$431$	−7.41836	+	7.41836i	−0.357330	+	0.357330i	0.505498	+	0.862828i	$0.331309\pi$
$432$	6.00984	−	17.8272i	0.289149	−	0.857713i
$433$			11.6239i			0.558607i	0.960203	+	0.279303i	$0.0901035\pi$
$433$			11.6239i			0.558607i	−0.960203	+	0.279303i	$0.909897\pi$
$434$	−0.0209757	−	0.0121103i	−0.00100687	−	0.000581314i
$435$	17.6445	−	11.8076i	0.845991	−	0.566130i
$436$	19.4559	+	5.21319i	0.931767	+	0.249666i
$437$	−1.06661	+	3.98063i	−0.0510227	+	0.190419i
$438$	−3.36406	+	3.84139i	−0.160741	+	0.183549i
$439$	19.2729	−	5.16416i	0.919846	−	0.246472i	0.232326	−	0.972638i	$-0.425366\pi$
$439$	19.2729	−	5.16416i	0.919846	−	0.246472i	0.687520	+	0.726166i	$0.258700\pi$
$440$		−	4.69553i		−	0.223850i
$441$	0.971917	+	7.30347i	0.0462817	+	0.347784i
$442$	−5.18929	−	3.84191i	−0.246829	−	0.182741i
$443$	17.7015	−	30.6600i	0.841025	−	1.45670i	−0.0480033	−	0.998847i	$-0.515286\pi$
$443$	17.7015	−	30.6600i	0.841025	−	1.45670i	0.889029	−	0.457852i	$-0.151381\pi$
$444$	7.58691	−	2.58133i	0.360059	−	0.122504i
$445$	8.31049	−	31.0152i	0.393955	−	1.47026i
$446$	0.338465	+	0.586239i	0.0160268	+	0.0277592i
$447$	8.03774	−	16.3277i	0.380172	−	0.772274i
$448$	−3.58976	−	13.3972i	−0.169600	−	0.632956i
$449$	−25.6708	+	25.6708i	−1.21148	+	1.21148i	−0.240938	+	0.970540i	$0.577455\pi$
$449$	−25.6708	+	25.6708i	−1.21148	+	1.21148i	−0.970540	+	0.240938i	$0.922545\pi$
$450$	−8.06932	+	1.07383i	−0.380392	+	0.0506210i
$451$		−	0.801608i		−	0.0377463i
$452$	6.92822	+	25.8565i	0.325876	+	1.21619i
$453$	0.116107	+	1.75266i	0.00545517	+	0.0823472i
$454$	−1.32509	+	4.94531i	−0.0621897	+	0.232095i
$455$	−26.1853	−	45.3543i	−1.22759	−	2.12624i
$456$	−5.42731	−	8.11025i	−0.254157	−	0.379797i
$457$	18.2026	+	10.5093i	0.851484	+	0.491604i	0.861151	−	0.508349i	$-0.169744\pi$
$457$	18.2026	+	10.5093i	0.851484	+	0.491604i	−0.00966751	+	0.999953i	$0.503077\pi$
$458$	−0.693888			−0.0324232
$459$	−9.10317	+	19.3941i	−0.424900	+	0.905240i
$460$	−5.58967			−0.260620
$461$	4.21083	+	2.43113i	0.196118	+	0.113229i	0.594844	−	0.803842i	$-0.297214\pi$
$461$	4.21083	+	2.43113i	0.196118	+	0.113229i	−0.398725	+	0.917070i	$0.630547\pi$
$462$	0.617582	+	0.922879i	0.0287325	+	0.0429362i
$463$	−11.4905	−	19.9022i	−0.534010	−	0.924933i	−0.999211	−	0.0397274i	$-0.987351\pi$
$463$	−11.4905	−	19.9022i	−0.534010	−	0.924933i	0.465200	−	0.885205i	$-0.345982\pi$
$464$	−2.89586	+	10.8075i	−0.134437	+	0.501726i
$465$	0.0204086	+	0.308073i	0.000946426	+	0.0142865i
$466$	0.713723	+	2.66365i	0.0330626	+	0.123391i
$467$		−	42.0080i		−	1.94390i	−0.235193	−	0.971949i	$-0.575572\pi$
$467$		−	42.0080i		−	1.94390i	0.235193	−	0.971949i	$-0.424428\pi$
$468$	21.9406	+	28.5108i	1.01420	+	1.31791i
$469$	−5.08560	+	5.08560i	−0.234831	+	0.234831i
$470$	−2.46106	−	9.18478i	−0.113520	−	0.423662i
$471$	−0.638449	+	1.29693i	−0.0294182	+	0.0597595i
$472$	−4.54688	−	7.87543i	−0.209287	−	0.362496i
$473$	0.157291	−	0.587017i	0.00723224	−	0.0269911i
$474$	0.0532742	−	0.0181257i	0.00244696	−	0.000832542i
$475$	30.3824	−	52.6239i	1.39404	−	2.41455i
$476$	2.51092	+	16.8302i	0.115088	+	0.771410i
$477$	19.7027	+	8.12884i	0.902123	+	0.372194i
$478$			5.49838i			0.251490i
$479$	−27.9894	+	7.49972i	−1.27887	+	0.342671i	−0.833421	−	0.552638i	$-0.813621\pi$
$479$	−27.9894	+	7.49972i	−1.27887	+	0.342671i	−0.445445	+	0.895309i	$0.646954\pi$
$480$	13.1514	−	15.0175i	0.600276	−	0.685451i
$481$	−3.83114	+	14.2980i	−0.174685	+	0.651934i
$482$	−1.42497	−	0.381820i	−0.0649057	−	0.0173914i
$483$	2.23351	−	1.49464i	0.101628	−	0.0680086i
$484$	−16.0709	−	9.27853i	−0.730495	−	0.421751i
$485$			16.2090i			0.736012i
$486$	−2.58821	+	2.97219i	−0.117404	+	0.134821i
$487$	14.3249	−	14.3249i	0.649122	−	0.649122i	−0.303658	−	0.952781i	$-0.598208\pi$
$487$	14.3249	−	14.3249i	0.649122	−	0.649122i	0.952781	+	0.303658i	$0.0982082\pi$
$488$	−5.56349	+	1.49073i	−0.251847	+	0.0674822i
$489$	−42.7915	−	8.48066i	−1.93510	−	0.383509i
$490$	−0.637438	+	2.37895i	−0.0287965	+	0.107470i
$491$	−24.6487	+	14.2310i	−1.11238	+	0.642234i	−0.939445	−	0.342699i	$-0.888659\pi$
$491$	−24.6487	+	14.2310i	−1.11238	+	0.642234i	−0.172937	+	0.984933i	$0.555326\pi$
$492$	1.48872	−	1.69996i	0.0671168	−	0.0766402i
$493$	4.67289	−	11.8540i	0.210456	−	0.533877i
$494$	8.86609			0.398904
$495$	5.39872	−	13.0854i	0.242654	−	0.588145i
$496$	−0.115055	−	0.115055i	−0.00516610	−	0.00516610i
$497$	3.50434	−	6.06970i	0.157191	−	0.272263i
$498$	−1.19986	+	2.43736i	−0.0537668	+	0.109221i
$499$	−4.87968	−	1.30751i	−0.218445	−	0.0585320i	0.147937	−	0.988997i	$-0.452737\pi$
$499$	−4.87968	−	1.30751i	−0.218445	−	0.0585320i	−0.366381	+	0.930465i	$0.619403\pi$
$500$	42.5229	+	11.3940i	1.90168	+	0.509554i
$501$	4.42895	−	1.50688i	0.197871	−	0.0673226i
$502$	0.0351181	+	0.0202754i	0.00156740	+	0.000904936i
$503$	13.3944	−	13.3944i	0.597227	−	0.597227i	−0.342346	−	0.939574i	$-0.611222\pi$
$503$	13.3944	−	13.3944i	0.597227	−	0.597227i	0.939574	+	0.342346i	$0.111222\pi$
$504$	−0.821836	+	6.31067i	−0.0366075	+	0.281100i
$505$	20.0558	+	20.0558i	0.892470	+	0.892470i
$506$	−0.109459	+	0.189589i	−0.00486605	+	0.00842824i
$507$	−43.8368	+	2.90401i	−1.94686	+	0.128972i
$508$	−16.9507	+	9.78651i	−0.752067	+	0.434206i
$509$	−10.9921	−	19.0388i	−0.487214	−	0.843880i	0.512677	−	0.858581i	$-0.328654\pi$
$509$	−10.9921	−	19.0388i	−0.487214	−	0.843880i	−0.999892	+	0.0147010i	$0.995320\pi$
$510$	−5.29896	+	4.81755i	−0.234642	+	0.213325i
$511$	−12.4282	+	21.5262i	−0.549789	+	0.952263i
$512$			17.7260i			0.783388i
$513$	−5.79989	−	28.8416i	−0.256071	−	1.27339i
$514$	4.60015			0.202904
$515$	42.1893	−	11.3046i	1.85908	−	0.498140i
$516$	1.42376	−	0.952764i	0.0626773	−	0.0419431i
$517$	10.8955	+	2.91943i	0.479182	+	0.128396i
$518$	−1.11542	+	0.643990i	−0.0490089	+	0.0282953i
$519$	13.4225	+	11.7546i	0.589181	+	0.515969i
$520$	6.32772	+	23.6154i	0.277489	+	1.03560i
$521$	2.16814	−	2.16814i	0.0949880	−	0.0949880i	−0.658016	−	0.753004i	$-0.728604\pi$
$521$	2.16814	−	2.16814i	0.0949880	−	0.0949880i	0.753004	+	0.658016i	$0.228604\pi$
$522$	1.42430	−	1.86157i	0.0623400	−	0.0814789i
$523$	−8.39511			−0.367093			−0.183546	−	0.983011i	$-0.558758\pi$
$523$	−8.39511			−0.367093			−0.183546	+	0.983011i	$0.558758\pi$
$524$	−15.7914	+	4.23129i	−0.689850	+	0.184845i
$525$	−37.5149	+	12.7639i	−1.63728	+	0.557060i
$526$	2.22199	+	3.84860i	0.0968835	+	0.167807i
$527$	0.115313	+	0.145044i	0.00502312	+	0.00631821i
$528$	2.40286	+	7.06236i	0.104571	+	0.307350i
$529$	−19.4598	−	11.2351i	−0.846076	−	0.488482i
$530$	5.03784	+	5.03784i	0.218830	+	0.218830i
$531$	−3.61633	−	27.1749i	−0.156935	−	1.17929i
$532$	−16.5225	−	16.5225i	−0.716340	−	0.716340i
$533$	1.08025	+	4.03156i	0.0467909	+	0.174626i
$534$	−0.234326	−	3.53721i	−0.0101403	−	0.153070i
$535$	26.3758	−	15.2281i	1.14033	−	0.658367i
$536$	2.90771	−	1.67877i	0.125594	−	0.0725118i
$537$	13.0018	−	8.70069i	0.561069	−	0.375463i
$538$	1.17414	+	4.38193i	0.0506206	+	0.188919i
$539$	−2.06587	−	2.06587i	−0.0889834	−	0.0889834i
$540$	35.7508	−	17.7237i	1.53847	−	0.762707i
$541$	−9.57793	−	9.57793i	−0.411787	−	0.411787i	0.470574	−	0.882361i	$-0.344047\pi$
$541$	−9.57793	−	9.57793i	−0.411787	−	0.411787i	−0.882361	+	0.470574i	$0.844047\pi$
$542$	−4.45614	−	2.57275i	−0.191408	−	0.110509i
$543$	37.4093	+	7.41397i	1.60539	+	0.318164i
$544$	1.35923	−	11.9030i	0.0582766	−	0.510335i
$545$	20.6326	+	35.7368i	0.883805	+	1.53080i
$546$	−4.34971	−	3.80921i	−0.186150	−	0.163019i
$547$	−33.3422	+	8.93403i	−1.42561	+	0.381991i	−0.887471	−	0.460864i	$-0.847540\pi$
$547$	−33.3422	+	8.93403i	−1.42561	+	0.381991i	−0.538141	+	0.842855i	$0.680873\pi$
$548$	5.60208			0.239309
$549$	−17.2182	−	2.24232i	−0.734855	−	0.0956998i
$550$	2.28250	−	2.28250i	0.0973263	−	0.0973263i
$551$	4.52843	+	16.9003i	0.192918	+	0.719978i
$552$	−1.18774	+	0.404111i	−0.0505537	+	0.0172001i
$553$	0.237232	−	0.136966i	0.0100881	−	0.00582437i
$554$	−6.33658	−	1.69788i	−0.269216	−	0.0721361i
$555$	14.7302	+	7.25133i	0.625262	+	0.307802i
$556$	−8.80131	+	2.35831i	−0.373259	+	0.100014i
$557$	−1.00975			−0.0427845			−0.0213923	−	0.999771i	$-0.506810\pi$
$557$	−1.00975			−0.0427845			−0.0213923	+	0.999771i	$0.506810\pi$
$558$	0.0130885	+	0.0314738i	0.000554079	+	0.00133239i
$559$			3.16427i			0.133835i
$560$	15.3062	−	26.5112i	0.646806	−	1.12030i
$561$	−1.80623	−	8.30116i	−0.0762592	−	0.350475i
$562$	0.216354	+	0.374736i	0.00912634	+	0.0158073i
$563$	−18.4533	+	10.6540i	−0.777716	+	0.449014i	−0.835620	−	0.549308i	$-0.814891\pi$
$563$	−18.4533	+	10.6540i	−0.777716	+	0.449014i	0.0579043	+	0.998322i	$0.481558\pi$
$564$	17.6840	+	26.4259i	0.744630	+	1.11273i
$565$	−27.4204	+	47.4935i	−1.15358	+	1.99807i
$566$	−0.497137	−	0.497137i	−0.0208962	−	0.0208962i
$567$	−9.54602	+	16.6416i	−0.400895	+	0.698880i
$568$	−2.31358	+	2.31358i	−0.0970758	+	0.0970758i
$569$	15.8917	+	9.17509i	0.666215	+	0.384640i	0.794641	−	0.607079i	$-0.207659\pi$
$569$	15.8917	+	9.17509i	0.666215	+	0.384640i	−0.128426	+	0.991719i	$0.540992\pi$
$570$	1.91176	−	9.64633i	0.0800749	−	0.404040i
$571$	15.9345	+	4.26965i	0.666840	+	0.178679i	0.576331	−	0.817216i	$-0.304484\pi$
$571$	15.9345	+	4.26965i	0.666840	+	0.178679i	0.0905089	+	0.995896i	$0.471151\pi$
$572$	−13.7794	−	3.69219i	−0.576147	−	0.154378i
$573$	−40.1017	+	2.65658i	−1.67527	+	0.110980i
$574$	−0.181583	+	0.314512i	−0.00757914	+	0.0131275i
$575$	−5.52400	−	5.52400i	−0.230367	−	0.230367i
$576$	−7.44455	+	18.0441i	−0.310190	+	0.751837i
$577$	−12.1380			−0.505314			−0.252657	−	0.967556i	$-0.581304\pi$
$577$	−12.1380			−0.505314			−0.252657	+	0.967556i	$0.581304\pi$
$578$	−0.968973	+	4.18739i	−0.0403040	+	0.174172i
$579$	−9.66969	−	28.4206i	−0.401858	−	1.18112i
$580$	−20.5523	+	11.8659i	−0.853388	+	0.492704i
$581$	−3.42276	+	12.7739i	−0.142000	+	0.529951i
$582$	0.576408	+	1.69415i	0.0238929	+	0.0702247i
$583$	−8.16356	+	2.18742i	−0.338100	+	0.0905936i
$584$	8.20513	−	8.20513i	0.339531	−	0.339531i
$585$	−9.51799	+	73.0863i	−0.393521	+	3.02175i
$586$		−	1.60164i		−	0.0661631i
$587$	36.4005	+	21.0158i	1.50241	+	0.867416i	0.999996	+	0.00278844i	$0.000887590\pi$
$587$	36.4005	+	21.0158i	1.50241	+	0.867416i	0.502413	+	0.864628i	$0.332446\pi$
$588$	−0.544393	−	8.21775i	−0.0224504	−	0.338894i
$589$	−0.245772	−	0.0658544i	−0.0101269	−	0.00271348i
$590$	2.37179	−	8.85166i	0.0976452	−	0.364417i
$591$	−5.14919	−	1.02049i	−0.211809	−	0.0419775i
$592$	−8.35769	+	2.23944i	−0.343499	+	0.0920403i
$593$		−	45.7907i		−	1.88040i	−0.340627	−	0.940198i	$-0.610639\pi$
$593$		−	45.7907i		−	1.88040i	0.340627	−	0.940198i	$-0.389361\pi$
$594$	0.0989389	−	1.55966i	0.00405951	−	0.0639935i
$595$	−20.7436	+	28.0184i	−0.850403	+	1.14864i
$596$	−10.1713	+	17.6172i	−0.416633	+	0.721630i
$597$	−1.17004	+	5.90376i	−0.0478865	+	0.241625i
$598$	0.295016	−	1.10101i	0.0120641	−	0.0450238i
$599$	19.4601	+	33.7059i	0.795119	+	1.37719i	0.922764	+	0.385367i	$0.125925\pi$
$599$	19.4601	+	33.7059i	0.795119	+	1.37719i	−0.127644	+	0.991820i	$0.540742\pi$
$600$	18.4587	−	1.22282i	0.753574	−	0.0499212i
$601$	−8.27589	−	30.8860i	−0.337581	−	1.25987i	−0.901044	−	0.433727i	$-0.857198\pi$
$601$	−8.27589	−	30.8860i	−0.337581	−	1.25987i	0.563464	−	0.826141i	$-0.309468\pi$
$602$	−0.194687	+	0.194687i	−0.00793483	+	0.00793483i
$603$	10.0333	−	1.33520i	0.408589	−	0.0543734i
$604$		−	1.96341i		−	0.0798901i
$605$	−9.83973	−	36.7224i	−0.400042	−	1.49298i
$606$	2.80941	+	1.38301i	0.114125	+	0.0561808i
$607$	5.85959	−	21.8683i	0.237833	−	0.887606i	−0.739018	−	0.673686i	$-0.764710\pi$
$607$	5.85959	−	21.8683i	0.237833	−	0.887606i	0.976851	−	0.213920i	$-0.0686232\pi$
$608$	8.22544	+	14.2469i	0.333586	+	0.577788i
$609$	5.03938	−	10.2369i	0.204206	−	0.414820i
$610$	−5.02656	−	2.90209i	−0.203519	−	0.117502i
$611$	−58.7312			−2.37601
$612$	11.5862	−	20.9587i	0.468345	−	0.847203i
$613$	10.3407			0.417657			0.208829	−	0.977952i	$-0.433035\pi$
$613$	10.3407			0.417657			0.208829	+	0.977952i	$0.433035\pi$
$614$	1.32784	+	0.766627i	0.0535871	+	0.0309386i
$615$	4.61928	−	0.306009i	0.186267	−	0.0123395i
$616$	−1.26175	−	2.18542i	−0.0508375	−	0.0880532i
$617$	5.06113	−	18.8884i	0.203753	−	0.760418i	−0.786073	−	0.618134i	$-0.787889\pi$
$617$	5.06113	−	18.8884i	0.203753	−	0.760418i	0.989826	−	0.142283i	$-0.0454445\pi$
$618$	4.00759	−	2.68184i	0.161209	−	0.107879i
$619$	−0.649866	−	2.42533i	−0.0261203	−	0.0974824i	0.951635	−	0.307231i	$-0.0994023\pi$
$619$	−0.649866	−	2.42533i	−0.0261203	−	0.0974824i	−0.977755	+	0.209748i	$0.932736\pi$
$620$		−	0.345118i		−	0.0138603i
$621$	−3.77461	−	0.239447i	−0.151470	−	0.00960868i
$622$	1.34925	−	1.34925i	0.0540998	−	0.0540998i
$623$	−4.46629	−	16.6684i	−0.178938	−	0.667807i
$624$	−21.6021	−	32.2809i	−0.864775	−	1.29227i
$625$	18.2632	+	31.6328i	0.730529	+	1.26531i
$626$	1.17863	−	4.39872i	0.0471077	−	0.175808i
$627$	8.77599	+	7.68549i	0.350479	+	0.306929i
$628$	0.807922	−	1.39936i	0.0322396	−	0.0558406i
$629$	9.74565	−	1.45397i	0.388585	−	0.0579735i
$630$	−5.08235	+	3.91113i	−0.202486	+	0.155823i
$631$			36.9651i			1.47156i	0.677223	+	0.735778i	$0.263183\pi$
$631$			36.9651i			1.47156i	−0.677223	+	0.735778i	$0.736817\pi$
$632$	−0.123523	+	0.0330980i	−0.00491349	+	0.00131657i
$633$	5.39375	+	15.8530i	0.214382	+	0.630102i
$634$	1.39008	−	5.18785i	0.0552072	−	0.206036i
$635$	−38.7328	−	10.3784i	−1.53707	−	0.411856i
$636$	−21.3748	−	10.5223i	−0.847565	−	0.417236i
$637$	13.1740	+	7.60599i	0.521971	+	0.301360i
$638$			0.929449i			0.0367972i
$639$	−9.10751	+	3.78739i	−0.360287	+	0.149827i
$640$	−20.9127	+	20.9127i	−0.826647	+	0.826647i
$641$	−29.5311	+	7.91284i	−1.16641	+	0.312538i	−0.789523	−	0.613721i	$-0.789672\pi$
$641$	−29.5311	+	7.91284i	−1.16641	+	0.312538i	−0.376886	+	0.926260i	$0.623005\pi$
$642$	2.21525	−	2.52957i	0.0874289	−	0.0998343i
$643$	−8.76080	+	32.6957i	−0.345492	+	1.28939i	0.546544	+	0.837430i	$0.315943\pi$
$643$	−8.76080	+	32.6957i	−0.345492	+	1.28939i	−0.892036	+	0.451964i	$0.850724\pi$
$644$	−2.60158	+	1.50202i	−0.102517	+	0.0591880i
$645$	3.44274	+	0.682300i	0.135558	+	0.0268656i
$646$	−2.35200	−	5.41298i	−0.0925382	−	0.212971i
$647$	−45.5491			−1.79072			−0.895360	−	0.445343i	$-0.853082\pi$
$647$	−45.5491			−1.79072			−0.895360	+	0.445343i	$0.853082\pi$
$648$	6.31530	−	6.35074i	0.248088	−	0.249480i
$649$	7.68675	+	7.68675i	0.301731	+	0.301731i
$650$	−8.40356	+	14.5554i	−0.329615	+	0.570909i
$651$	0.0922823	+	0.137901i	0.00361683	+	0.00540478i
$652$	47.1010	+	12.6207i	1.84462	+	0.494264i
$653$	4.78256	+	1.28148i	0.187156	+	0.0501483i	0.351180	−	0.936308i	$-0.385781\pi$
$653$	4.78256	+	1.28148i	0.187156	+	0.0501483i	−0.164024	+	0.986456i	$0.552447\pi$
$654$	3.42734	+	3.00146i	0.134020	+	0.117366i
$655$	−29.0058	−	16.7465i	−1.13335	−	0.654340i
$656$	−1.72514	+	1.72514i	−0.0673554	+	0.0673554i
$657$	32.2998	−	13.4320i	1.26014	−	0.524032i
$658$	−3.61352	−	3.61352i	−0.140870	−	0.140870i
$659$	−10.5183	+	18.2183i	−0.409736	+	0.709683i	−0.994860	−	0.101260i	$-0.967712\pi$
$659$	−10.5183	+	18.2183i	−0.409736	+	0.709683i	0.585124	+	0.810944i	$0.301046\pi$
$660$	−6.98832	+	14.1959i	−0.272020	+	0.552576i
$661$	−26.7663	+	15.4535i	−1.04109	+	0.601073i	−0.920142	−	0.391586i	$-0.871927\pi$
$661$	−26.7663	+	15.4535i	−1.04109	+	0.601073i	−0.120948	+	0.992659i	$0.538593\pi$
$662$	−0.555639	−	0.962394i	−0.0215955	−	0.0374045i
$663$	20.2709	+	39.3153i	0.787255	+	1.52688i
$664$	3.08683	−	5.34655i	0.119792	−	0.207486i
$665$		−	47.8705i		−	1.85634i
$666$	1.79745	+	0.234081i	0.0696498	+	0.00907046i
$667$	2.24941			0.0870973
$668$	−5.05118	+	1.35346i	−0.195436	+	0.0523669i
$669$	−0.306544	−	4.62735i	−0.0118517	−	0.178904i
$670$	3.26815	+	0.875698i	0.126260	+	0.0338312i
$671$	5.96276	−	3.44260i	0.230190	−	0.132900i
$672$	2.08560	−	10.5235i	0.0804539	−	0.405953i
$673$	−4.42294	−	16.5067i	−0.170492	−	0.636285i	−0.997276	−	0.0737647i	$-0.976499\pi$
$673$	−4.42294	−	16.5067i	−0.170492	−	0.636285i	0.826784	−	0.562520i	$-0.190168\pi$
$674$	4.74885	−	4.74885i	0.182919	−	0.182919i
$675$	52.8463	+	17.8153i	2.03406	+	0.685712i
$676$	49.1080			1.88877
$677$	34.3071	−	9.19256i	1.31853	−	0.353299i	0.470103	−	0.882612i	$-0.344217\pi$
$677$	34.3071	−	9.19256i	1.31853	−	0.353299i	0.848427	+	0.529313i	$0.177550\pi$
$678$	−1.17704	+	5.93907i	−0.0452038	+	0.228089i
$679$	4.35559	+	7.54410i	0.167152	+	0.289516i
$680$	12.7392	−	10.1279i	0.488526	−	0.388389i
$681$	23.1077	−	26.3865i	0.885488	−	1.01113i
$682$	−0.0117056	−	0.00675823i	−0.000448230	−	0.000258786i
$683$	−21.8027	−	21.8027i	−0.834259	−	0.834259i	0.153837	−	0.988096i	$-0.450837\pi$
$683$	−21.8027	−	21.8027i	−0.834259	−	0.834259i	−0.988096	+	0.153837i	$0.950837\pi$
$684$	4.33788	+	32.5970i	0.165863	+	1.24638i
$685$	8.11544	+	8.11544i	0.310075	+	0.310075i
$686$	1.31900	+	4.92257i	0.0503596	+	0.187944i
$687$	4.26490	+	2.09951i	0.162716	+	0.0801013i
$688$	−1.60182	+	0.924814i	−0.0610690	+	0.0352582i
$689$	38.1095	−	22.0025i	1.45186	−	0.838230i
$690$	−1.13429	−	0.558385i	−0.0431818	−	0.0212574i
$691$	−9.42266	−	35.1659i	−0.358455	−	1.33777i	−0.876080	−	0.482165i	$-0.839851\pi$
$691$	−9.42266	−	35.1659i	−0.358455	−	1.33777i	0.517625	−	0.855607i	$-0.326816\pi$
$692$	−14.1023	−	14.1023i	−0.536087	−	0.536087i
$693$	−1.00353	−	7.54101i	−0.0381208	−	0.286459i
$694$	−2.84435	−	2.84435i	−0.107970	−	0.107970i
$695$	−16.1664	−	9.33365i	−0.613225	−	0.354046i
$696$	−3.50928	+	4.00722i	−0.133019	+	0.151893i
$697$	2.17480	−	1.72902i	0.0823766	−	0.0654912i
$698$	−2.87394	−	4.97782i	−0.108780	−	0.188413i
$699$	3.67265	−	18.5314i	0.138912	−	0.700921i
$700$	42.7853	−	11.4643i	1.61713	−	0.433310i
$701$	29.3060			1.10687			0.553435	−	0.832892i	$-0.313317\pi$
$701$	29.3060			1.10687			0.553435	+	0.832892i	$0.313317\pi$
$702$	1.60421	+	7.97738i	0.0605470	+	0.301087i
$703$	−9.56747	+	9.56747i	−0.360844	+	0.360844i
$704$	−2.00328	−	7.47635i	−0.0755015	−	0.281776i
$705$	−12.6640	+	63.8997i	−0.476953	+	2.40660i
$706$	−3.26643	+	1.88587i	−0.122934	+	0.0709757i
$707$	14.7238	+	3.94522i	0.553744	+	0.148375i
$708$	2.02559	+	30.5768i	0.0761263	+	1.14915i
$709$	−13.1884	+	3.53383i	−0.495302	+	0.132716i	−0.497819	−	0.867281i	$-0.665866\pi$
$709$	−13.1884	+	3.53383i	−0.495302	+	0.132716i	0.00251670	+	0.999997i	$0.499199\pi$
$710$	−3.29714			−0.123739
$711$	−0.382287	−	0.0497851i	−0.0143369	−	0.00186709i
$712$			8.05591i			0.301908i
$713$	−0.0163559	+	0.0283293i	−0.000612534	+	0.00106094i
$714$	−1.17173	+	3.66612i	−0.0438510	+	0.137201i
$715$	−14.6129	−	25.3102i	−0.546490	−	0.946548i
$716$	−15.1445	+	8.74366i	−0.565975	+	0.326766i
$717$	16.6366	−	33.7952i	0.621304	−	1.26210i
$718$	3.20966	−	5.55929i	0.119783	−	0.207471i
$719$	1.37014	+	1.37014i	0.0510976	+	0.0510976i	0.732194	−	0.681096i	$-0.238497\pi$
$719$	1.37014	+	1.37014i	0.0510976	+	0.0510976i	−0.681096	+	0.732194i	$0.738497\pi$
$720$	−39.7797	+	16.5425i	−1.48250	+	0.616503i
$721$	16.5983	−	16.5983i	0.618154	−	0.618154i
$722$	2.85836	+	1.65028i	0.106377	+	0.0614169i
$723$	7.60315	+	6.65838i	0.282764	+	0.247628i
$724$	−41.1767	−	11.0333i	−1.53032	−	0.410048i
$725$	−32.0373	−	8.58438i	−1.18984	−	0.318816i
$726$	−2.33432	−	3.48828i	−0.0866349	−	0.129462i
$727$	3.06673	−	5.31173i	0.113739	−	0.197001i	−0.803536	−	0.595256i	$-0.797051\pi$
$727$	3.06673	−	5.31173i	0.113739	−	0.197001i	0.917275	+	0.398255i	$0.130384\pi$
$728$	9.29088	+	9.29088i	0.344343	+	0.344343i
$729$	24.9012	−	10.4371i	0.922265	−	0.386557i
$730$	11.6933			0.432789
$731$	1.93187	−	0.839419i	0.0714529	−	0.0310470i
$732$	19.0387	+	3.77318i	0.703689	+	0.139461i
$733$	5.68407	−	3.28170i	0.209946	−	0.121212i	−0.391340	−	0.920246i	$-0.627988\pi$
$733$	5.68407	−	3.28170i	0.209946	−	0.121212i	0.601286	+	0.799034i	$0.294655\pi$
$734$	−0.679052	+	2.53426i	−0.0250643	+	0.0935411i
$735$	11.1160	−	12.6933i	0.410019	−	0.468198i
$736$	2.04291	−	0.547397i	0.0753027	−	0.0201773i
$737$	−2.83805	+	2.83805i	−0.104541	+	0.104541i
$738$	0.471921	−	0.196250i	0.0173716	−	0.00722406i
$739$		−	30.7767i		−	1.13214i	−0.824358	−	0.566069i	$-0.808464\pi$
$739$		−	30.7767i		−	1.13214i	0.824358	−	0.566069i	$-0.191536\pi$
$740$	−15.8936	−	9.17615i	−0.584259	−	0.337322i
$741$	−54.4944	−	26.8263i	−2.00190	−	0.985489i
$742$	3.69848	+	0.991005i	0.135775	+	0.0363809i
$743$	11.0741	−	41.3290i	0.406269	−	1.51622i	−0.395435	−	0.918494i	$-0.629406\pi$
$743$	11.0741	−	41.3290i	0.406269	−	1.51622i	0.801704	−	0.597722i	$-0.203927\pi$
$744$	−0.0249506	−	0.0733336i	−0.000914735	−	0.00268854i
$745$	−40.2558	+	10.7865i	−1.47486	+	0.395187i
$746$			7.43120i			0.272076i
$747$	14.7496	−	11.3506i	0.539658	−	0.415295i
$748$	1.40123	+	9.39217i	0.0512341	+	0.343412i
$749$	8.18400	−	14.1751i	0.299037	−	0.517947i
$750$	7.49081	+	6.56000i	0.273526	+	0.239537i
$751$	−4.03694	+	15.0661i	−0.147310	+	0.549768i	0.852332	+	0.523002i	$0.175188\pi$
$751$	−4.03694	+	15.0661i	−0.147310	+	0.549768i	−0.999642	+	0.0267667i	$0.991479\pi$
$752$	−17.1652	−	29.7310i	−0.625951	−	1.08418i
$753$	−0.154502	−	0.230878i	−0.00563035	−	0.00841367i
$754$	−1.25253	−	4.67451i	−0.0456145	−	0.170236i
$755$	2.84429	−	2.84429i	0.103514	−	0.103514i
$756$	11.8768	−	17.8558i	0.431954	−	0.649411i
$757$			35.5119i			1.29070i	0.763887	+	0.645350i	$0.223289\pi$
$757$			35.5119i			1.29070i	−0.763887	+	0.645350i	$0.776711\pi$
$758$	−2.15875	−	8.05656i	−0.0784092	−	0.292627i
$759$	1.24642	−	0.834093i	0.0452422	−	0.0302757i
$760$	−5.78399	+	21.5861i	−0.209807	+	0.783012i
$761$	−4.19687	−	7.26919i	−0.152136	−	0.263508i	0.779876	−	0.625934i	$-0.215282\pi$
$761$	−4.19687	−	7.26919i	−0.152136	−	0.263508i	−0.932013	+	0.362426i	$0.881949\pi$
$762$	−4.41739	+	0.292634i	−0.160025	+	0.0106010i
$763$	19.2060	+	11.0886i	0.695302	+	0.401433i
$764$	44.9238			1.62528
$765$	47.1460	−	13.5774i	1.70457	−	0.490890i
$766$	2.75480			0.0995348
$767$	−49.0179	−	28.3005i	−1.76994	−	1.02187i
$768$	8.51258	−	17.2923i	0.307171	−	0.623982i
$769$	6.89301	+	11.9390i	0.248568	+	0.430533i	0.963129	−	0.269041i	$-0.0867066\pi$
$769$	6.89301	+	11.9390i	0.248568	+	0.430533i	−0.714560	+	0.699574i	$0.753373\pi$
$770$	0.658170	−	2.45632i	0.0237188	−	0.0885198i
$771$	−28.2743	−	13.9188i	−1.01827	−	0.501272i
$772$	8.68516	+	32.4135i	0.312586	+	1.16659i
$773$			26.6931i			0.960083i	0.877246	+	0.480041i	$0.159378\pi$
$773$			26.6931i			0.960083i	−0.877246	+	0.480041i	$0.840622\pi$
$774$	0.384095	−	0.0511138i	0.0138060	−	0.00183725i
$775$	0.341063	−	0.341063i	0.0122513	−	0.0122513i
$776$	−1.05253	−	3.92811i	−0.0377838	−	0.141011i
$777$	8.80436	−	0.583254i	0.315855	−	0.0209241i
$778$	−3.14015	−	5.43890i	−0.112580	−	0.194994i
$779$	−0.987428	+	3.68513i	−0.0353783	+	0.132034i
$780$	16.0161	−	80.8136i	0.573467	−	2.89359i
$781$	1.95562	−	3.38723i	0.0699775	−	0.121205i
$782$	−0.750460	+	0.111962i	−0.0268364	+	0.00400376i
$783$	−14.3869	+	7.13241i	−0.514147	+	0.254892i
$784$			8.89193i			0.317569i
$785$	3.19758	−	0.856788i	0.114126	−	0.0305801i
$786$	−3.62718	−	0.718854i	−0.129377	−	0.0256407i
$787$	10.1380	−	37.8357i	0.361382	−	1.34870i	−0.510878	−	0.859654i	$-0.670679\pi$
$787$	10.1380	−	37.8357i	0.361382	−	1.34870i	0.872260	−	0.489043i	$-0.162654\pi$
$788$	5.66775	+	1.51867i	0.201905	+	0.0541004i
$789$	−2.01243	−	30.3781i	−0.0716444	−	1.08149i
$790$	−0.111602	−	0.0644336i	−0.00397063	−	0.00229244i
$791$			29.4730i			1.04794i
$792$	−0.458630	+	3.52170i	−0.0162967	+	0.125138i
$793$	−25.3495	+	25.3495i	−0.900186	+	0.900186i
$794$	−1.54848	+	0.414913i	−0.0549534	+	0.0147247i
$795$	−15.7214	−	46.2076i	−0.557581	−	1.63881i
$796$	1.74122	−	6.49832i	0.0617159	−	0.230327i
$797$	24.2216	−	13.9843i	0.857972	−	0.495350i	−0.00536065	−	0.999986i	$-0.501706\pi$
$797$	24.2216	−	13.9843i	0.857972	−	0.495350i	0.863333	+	0.504635i	$0.168373\pi$
$798$	−1.70232	−	5.00338i	−0.0602615	−	0.177118i
$799$	15.5802	+	35.8570i	0.551189	+	1.26853i
$800$	−31.1853			−1.10257
$801$	−9.26234	+	22.4501i	−0.327269	+	0.793234i
$802$	−2.14473	−	2.14473i	−0.0757329	−	0.0757329i
$803$	−6.93560	+	12.0128i	−0.244752	+	0.423923i
$804$	−11.2894	+	0.747874i	−0.398145	+	0.0263755i
$805$	−5.94468	−	1.59287i	−0.209522	−	0.0561413i
$806$	0.0679788	+	0.0182149i	0.00239445	+	0.000641591i
$807$	6.04182	−	30.4857i	0.212682	−	1.07315i
$808$	−6.16267	−	3.55802i	−0.216802	−	0.125171i
$809$	−22.5970	+	22.5970i	−0.794469	+	0.794469i	−0.982217	−	0.187748i	$-0.939881\pi$
$809$	−22.5970	+	22.5970i	−0.794469	+	0.794469i	0.187748	+	0.982217i	$0.439881\pi$
$810$	9.02532	−	0.0252523i	0.317117	−	0.000887274i
$811$	−24.4577	−	24.4577i	−0.858827	−	0.858827i	0.132373	−	0.991200i	$-0.457740\pi$
$811$	−24.4577	−	24.4577i	−0.858827	−	0.858827i	−0.991200	+	0.132373i	$0.957740\pi$
$812$	−6.37706	+	11.0454i	−0.223791	+	0.387617i
$813$	19.6047	+	29.2962i	0.687568	+	1.02746i
$814$	−0.622468	+	0.359382i	−0.0218175	+	0.0125963i
$815$	49.9498	+	86.5156i	1.74967	+	3.03051i
$816$	−13.9777	+	21.7521i	−0.489318	+	0.761476i
$817$	−1.44619	+	2.50487i	−0.0505956	+	0.0876342i
$818$		−	6.35779i		−	0.222295i
$819$	15.2094	+	36.5739i	0.531459	+	1.27800i
$820$	−5.17473			−0.180709
$821$	31.6509	−	8.48084i	1.10462	−	0.295983i	0.339978	−	0.940433i	$-0.389580\pi$
$821$	31.6509	−	8.48084i	1.10462	−	0.295983i	0.764646	+	0.644450i	$0.222914\pi$
$822$	1.13681	+	0.559625i	0.0396508	+	0.0195192i
$823$	9.09521	+	2.43706i	0.317039	+	0.0849504i	0.413830	−	0.910354i	$-0.364191\pi$
$823$	9.09521	+	2.43706i	0.317039	+	0.0849504i	−0.0967903	+	0.995305i	$0.530858\pi$
$824$	−9.49016	+	5.47915i	−0.330605	+	0.190875i
$825$	−20.9354	+	7.12294i	−0.728876	+	0.247989i
$826$	−1.27467	−	4.75713i	−0.0443514	−	0.165522i
$827$	35.7044	−	35.7044i	1.24156	−	1.24156i	0.282213	−	0.959352i	$-0.408932\pi$
$827$	35.7044	−	35.7044i	1.24156	−	1.24156i	0.959352	−	0.282213i	$-0.0910685\pi$
$828$	4.19232	+	0.545964i	0.145693	+	0.0189736i
$829$	17.1199			0.594599			0.297300	−	0.954784i	$-0.403914\pi$
$829$	17.1199			0.594599			0.297300	+	0.954784i	$0.403914\pi$
$830$	6.00930	−	1.61019i	0.208586	−	0.0558904i
$831$	33.8098	+	29.6086i	1.17285	+	1.02711i
$832$	20.1504	+	34.9015i	0.698588	+	1.20999i
$833$	1.14887	−	10.0608i	0.0398059	−	0.348585i
$834$	−2.02161	−	0.400653i	−0.0700025	−	0.0138735i
$835$	−9.27806	−	5.35669i	−0.321081	−	0.185376i
$836$	−9.22045	−	9.22045i	−0.318896	−	0.318896i
$837$	0.0147840	−	0.233052i	0.000511008	−	0.00805546i
$838$	−3.85767	−	3.85767i	−0.133261	−	0.133261i
$839$	12.2012	+	45.5353i	0.421231	+	1.57205i	0.772019	+	0.635600i	$0.219247\pi$
$839$	12.2012	+	45.5353i	0.421231	+	1.57205i	−0.350788	+	0.936455i	$0.614086\pi$
$840$	12.1119	−	8.10515i	0.417899	−	0.279654i
$841$	−16.8440	+	9.72491i	−0.580829	+	0.335342i
$842$	−4.07188	+	2.35090i	−0.140326	+	0.0810174i
$843$	−0.195949	−	2.95790i	−0.00674884	−	0.101875i
$844$	−4.84459	−	18.0802i	−0.166758	−	0.622348i
$845$	71.1401	+	71.1401i	2.44729	+	2.44729i
$846$	0.948710	+	7.12908i	0.0326173	+	0.245103i
$847$	−14.4475	−	14.4475i	−0.496422	−	0.496422i
$848$	22.2763	+	12.8612i	0.764972	+	0.441657i
$849$	1.55140	+	4.55980i	0.0532439	+	0.156492i
$850$	11.1158	+	1.26934i	0.381267	+	0.0435379i
$851$	0.869759	+	1.50647i	0.0298149	+	0.0516410i
$852$	10.4379	−	3.55134i	0.357597	−	0.121667i
$853$	−24.2910	+	6.50876i	−0.831709	+	0.222856i	−0.649459	−	0.760397i	$-0.725005\pi$
$853$	−24.2910	+	6.50876i	−0.831709	+	0.222856i	−0.182250	+	0.983252i	$0.558338\pi$
$854$	−3.11933			−0.106741
$855$	−40.9376	+	53.5057i	−1.40003	+	1.82986i
$856$	−5.40311	+	5.40311i	−0.184675	+	0.184675i
$857$	0.830409	+	3.09913i	0.0283662	+	0.105864i	0.978658	−	0.205498i	$-0.0658814\pi$
$857$	0.830409	+	3.09913i	0.0283662	+	0.105864i	−0.950291	+	0.311362i	$0.899215\pi$
$858$	−2.42738	−	2.12575i	−0.0828693	−	0.0725719i
$859$	39.2004	−	22.6324i	1.33750	−	0.772206i	0.351064	−	0.936351i	$-0.385820\pi$
$859$	39.2004	−	22.6324i	1.33750	−	0.772206i	0.986436	+	0.164145i	$0.0524865\pi$
$860$	−3.78945	−	1.01538i	−0.129219	−	0.0346242i
$861$	2.06771	−	1.38369i	0.0704673	−	0.0471560i
$862$	2.56205	−	0.686500i	0.0872638	−	0.0233823i
$863$	35.5005			1.20845			0.604226	−	0.796813i	$-0.293483\pi$
$863$	35.5005			1.20845			0.604226	+	0.796813i	$0.293483\pi$
$864$	−11.3305	+	9.97875i	−0.385472	+	0.339484i
$865$		−	40.8584i		−	1.38923i
$866$	1.46940	−	2.54508i	0.0499324	−	0.0864854i
$867$	18.6255	−	22.8055i	0.632557	−	0.774514i
$868$	−0.0927380	−	0.160627i	−0.00314773	−	0.00545203i
$869$	0.132388	−	0.0764344i	0.00449097	−	0.00259286i
$870$	−5.35596	+	0.354811i	−0.181584	+	0.0120292i
$871$	10.4489	−	18.0981i	0.354048	−	0.613230i
$872$	−7.32072	−	7.32072i	−0.247911	−	0.247911i
$873$	1.58319	−	12.1569i	0.0535830	−	0.411450i
$874$	0.736739	−	0.736739i	0.0249206	−	0.0249206i
$875$	41.9767	+	24.2352i	1.41907	+	0.819301i
$876$	−37.0181	+	12.5948i	−1.25072	+	0.425540i
$877$	35.2545	+	9.44642i	1.19046	+	0.318983i	0.799068	−	0.601241i	$-0.205327\pi$
$877$	35.2545	+	9.44642i	1.19046	+	0.318983i	0.391392	+	0.920224i	$0.371994\pi$
$878$	−4.87269	−	1.30563i	−0.164445	−	0.0440630i
$879$	−4.84612	+	9.84431i	−0.163455	+	0.332040i
$880$	8.54172	−	14.7947i	0.287941	−	0.498729i
$881$	−4.47095	−	4.47095i	−0.150630	−	0.150630i	0.627769	−	0.778399i	$-0.283968\pi$
$881$	−4.47095	−	4.47095i	−0.150630	−	0.150630i	−0.778399	+	0.627769i	$0.783968\pi$
$882$	0.710448	−	1.72198i	0.0239220	−	0.0579822i
$883$	−58.5316			−1.96974			−0.984872	−	0.173282i	$-0.944563\pi$
$883$	−58.5316			−1.96974			−0.984872	+	0.173282i	$0.944563\pi$
$884$	−19.7042	−	45.3481i	−0.662725	−	1.52522i
$885$	−41.3606	+	47.2293i	−1.39032	+	1.58760i
$886$	−7.75162	+	4.47540i	−0.260421	+	0.150354i
$887$	7.94483	−	29.6505i	0.266761	−	0.995566i	−0.694402	−	0.719587i	$-0.744331\pi$
$887$	7.94483	−	29.6505i	0.266761	−	0.995566i	0.961164	−	0.275979i	$-0.0890021\pi$
$888$	−4.04061	−	0.800789i	−0.135594	−	0.0268727i
$889$	−20.8161	+	5.57766i	−0.698151	+	0.187069i
$890$	−5.74033	+	5.74033i	−0.192416	+	0.192416i
$891$	−5.32721	+	9.28691i	−0.178468	+	0.311123i
$892$			5.18377i			0.173566i
$893$	−46.4921	−	26.8422i	−1.55580	−	0.898241i
$894$	−3.82392	+	2.55893i	−0.127891	+	0.0855835i
$895$	−34.6055	−	9.27250i	−1.15673	−	0.309946i
$896$	−4.11379	+	15.3529i	−0.137432	+	0.512903i
$897$	−5.14464	+	5.87462i	−0.171774	+	0.196148i
$898$	8.86582	−	2.37559i	0.295856	−	0.0792744i
$899$			0.138883i			0.00463200i
$900$	−57.6259	−	23.7750i	−1.92086	−	0.792501i
$901$	−23.5428	−	17.4300i	−0.784325	−	0.580678i
$902$	−0.101334	+	0.175515i	−0.00337404	+	0.00584401i
$903$	1.78569	−	0.607552i	0.0594239	−	0.0202181i
$904$	3.56110	−	13.2902i	0.118440	−	0.442025i
$905$	−43.6672	−	75.6339i	−1.45155	−	2.51415i
$906$	0.196137	−	0.398429i	0.00651621	−	0.0132369i
$907$	−7.93668	−	29.6201i	−0.263533	−	0.983519i	−0.963142	−	0.268993i	$-0.913309\pi$
$907$	−7.93668	−	29.6201i	−0.263533	−	0.983519i	0.699609	−	0.714526i	$-0.253358\pi$
$908$	−27.7228	+	27.7228i	−0.920014	+	0.920014i
$909$	−13.0832	−	17.0010i	−0.433941	−	0.563888i
$910$			13.2406i			0.438923i
$911$	0.0481892	+	0.179844i	0.00159658	+	0.00595851i	0.966720	−	0.255839i	$-0.0823516\pi$
$911$	0.0481892	+	0.179844i	0.00159658	+	0.00595851i	−0.965123	+	0.261797i	$0.915685\pi$
$912$	−2.34688	−	35.4267i	−0.0777129	−	1.17310i
$913$	−1.91009	+	7.12854i	−0.0632146	+	0.235920i
$914$	−2.65702	−	4.60209i	−0.0878864	−	0.152224i
$915$	22.1143	+	33.0463i	0.731076	+	1.09248i
$916$	−4.60174	−	2.65682i	−0.152046	−	0.0877836i
$917$	−18.0001			−0.594416
$918$	4.44484	−	3.09565i	0.146701	−	0.102172i
$919$	46.3030			1.52740			0.763698	−	0.645573i	$-0.223382\pi$
$919$	46.3030			1.52740			0.763698	+	0.645573i	$0.223382\pi$
$920$	2.48816	+	1.43654i	0.0820322	+	0.0473613i
$921$	−5.84181	−	8.72965i	−0.192494	−	0.287652i
$922$	−0.614651	−	1.06461i	−0.0202425	−	0.0350610i
$923$	−5.27080	+	19.6709i	−0.173491	+	0.647476i
$924$	0.562099	+	8.48502i	0.0184917	+	0.279137i
$925$	−6.63850	−	24.7752i	−0.218272	−	0.814604i
$926$			5.81020i			0.190935i
$927$	−32.7467	+	4.35780i	−1.07554	+	0.143129i
$928$	6.34943	−	6.34943i	0.208430	−	0.208430i
$929$	1.74286	+	6.50445i	0.0571814	+	0.213404i	0.988605	−	0.150533i	$-0.0480990\pi$
$929$	1.74286	+	6.50445i	0.0571814	+	0.213404i	−0.931424	+	0.363937i	$0.881432\pi$
$930$	0.0344758	−	0.0700335i	0.00113051	−	0.00229649i
$931$	6.95241	+	12.0419i	0.227856	+	0.394658i
$932$	−5.46553	+	20.3976i	−0.179029	+	0.668146i
$933$	−12.3754	+	4.21055i	−0.405154	+	0.137847i
$934$	−5.31035	+	9.19779i	−0.173760	+	0.300961i
$935$	−11.5761	+	15.6358i	−0.378577	+	0.511346i
$936$	−2.43927	−	18.3299i	−0.0797300	−	0.599131i
$937$			21.6108i			0.705993i	0.935625	+	0.352996i	$0.114837\pi$
$937$			21.6108i			0.705993i	−0.935625	+	0.352996i	$0.885163\pi$
$938$	1.75640	−	0.470625i	0.0573483	−	0.0153664i
$939$	−20.5537	+	23.4700i	−0.670743	+	0.765916i
$940$	18.8462	−	70.3349i	0.614695	−	2.29407i
$941$	37.6735	+	10.0946i	1.22812	+	0.329074i	0.813848	−	0.581078i	$-0.197369\pi$
$941$	37.6735	+	10.0946i	1.22812	+	0.329074i	0.414274	+	0.910152i	$0.364035\pi$
$942$	0.303740	−	0.203260i	0.00989637	−	0.00662256i
$943$	0.424772	+	0.245242i	0.0138325	+	0.00798619i
$944$		−	33.0853i		−	1.07683i
$945$	43.0721	−	8.66157i	1.40113	−	0.281761i
$946$	−0.108646	+	0.108646i	−0.00353238	+	0.00353238i
$947$	−30.1587	+	8.08099i	−0.980025	+	0.262597i	−0.713055	−	0.701108i	$-0.752689\pi$
$947$	−30.1587	+	8.08099i	−0.980025	+	0.262597i	−0.266970	+	0.963705i	$0.586022\pi$
$948$	0.422706	+	0.0837741i	0.0137289	+	0.00272086i
$949$	18.6929	−	69.7629i	0.606798	−	2.26460i
$950$	−13.3047	+	7.68145i	−0.431660	+	0.249219i
$951$	−24.2410	+	27.6806i	−0.786067	+	0.897604i
$952$	3.20764	−	8.13702i	0.103960	−	0.263722i
$953$	−12.7689			−0.413626			−0.206813	−	0.978380i	$-0.566309\pi$
$953$	−12.7689			−0.413626			−0.206813	+	0.978380i	$0.566309\pi$
$954$	−3.28638	−	4.27050i	−0.106400	−	0.138263i
$955$	65.0787	+	65.0787i	2.10590	+	2.10590i
$956$	−21.0526	+	36.4643i	−0.680891	+	1.17934i
$957$	2.81225	−	5.71275i	0.0909072	−	0.184667i
$958$	7.07642	+	1.89612i	0.228629	+	0.0612609i
$959$	5.95787	+	1.59641i	0.192390	+	0.0515507i
$960$	42.3178	−	14.3980i	1.36580	−	0.464693i
$961$	26.8450	+	15.4990i	0.865969	+	0.499967i
$962$	2.64630	−	2.64630i	0.0853200	−	0.0853200i
$963$	−21.2696	+	8.84502i	−0.685402	+	0.285027i
$964$	−7.98821	−	7.98821i	−0.257283	−	0.257283i
$965$	−34.3740	+	59.5374i	−1.10654	+	1.91658i
$966$	−0.677976	+	0.0449132i	−0.0218135	+	0.00144506i
$967$	−2.47812	+	1.43074i	−0.0796909	+	0.0460095i	−0.539316	−	0.842104i	$-0.681317\pi$
$967$	−2.47812	+	1.43074i	−0.0796909	+	0.0460095i	0.459625	+	0.888113i	$0.347984\pi$
$968$	4.76915	+	8.26041i	0.153286	+	0.265500i
$969$	−1.92188	+	40.3868i	−0.0617396	+	1.29741i
$970$	2.04902	−	3.54901i	0.0657902	−	0.113952i
$971$		−	12.2706i		−	0.393782i	−0.980425	−	0.196891i	$-0.936915\pi$
$971$		−	12.2706i		−	0.393782i	0.980425	−	0.196891i	$-0.0630845\pi$
$972$	−28.5447	+	9.80109i	−0.915572	+	0.314370i
$973$	−10.0323			−0.321622
$974$	−4.94733	+	1.32563i	−0.158523	+	0.0424760i
$975$	95.6921	−	64.0363i	3.06460	−	2.05080i
$976$	−20.2413	−	5.42363i	−0.647908	−	0.173606i
$977$	−23.1580	+	13.3703i	−0.740890	+	0.427753i	−0.822393	−	0.568920i	$-0.807361\pi$
$977$	−23.1580	+	13.3703i	−0.740890	+	0.427753i	0.0815031	+	0.996673i	$0.474028\pi$
$978$	8.29729	+	7.26627i	0.265318	+	0.232350i
$979$	−2.49244	−	9.30191i	−0.0796587	−	0.297290i
$980$	−13.3361	+	13.3361i	−0.426006	+	0.426006i
$981$	−11.9842	−	28.8183i	−0.382626	−	0.920097i
$982$	7.19590			0.229630
$983$	24.4431	−	6.54950i	0.779613	−	0.208897i	0.152999	−	0.988226i	$-0.451107\pi$
$983$	24.4431	−	6.54950i	0.779613	−	0.208897i	0.626614	+	0.779330i	$0.284440\pi$
$984$	−1.09957	+	0.374112i	−0.0350531	+	0.0119263i
$985$	6.01056	+	10.4106i	0.191512	+	0.331709i
$986$	−2.52164	+	2.00476i	−0.0803054	+	0.0638445i
$987$	11.2766	+	33.1436i	0.358938	+	1.05497i
$988$	58.7983	+	33.9472i	1.87062	+	1.08001i
$989$	0.262939	+	0.262939i	0.00836098	+	0.00836098i
$990$	−2.83623	+	2.18263i	−0.0901413	+	0.0693684i
$991$	17.5471	+	17.5471i	0.557403	+	0.557403i	0.928567	−	0.371165i	$-0.121041\pi$
$991$	17.5471	+	17.5471i	0.557403	+	0.557403i	−0.371165	+	0.928567i	$0.621041\pi$
$992$	0.0337974	+	0.126134i	0.00107307	+	0.00400474i
$993$	0.503235	+	7.59646i	0.0159697	+	0.241066i
$994$	−1.53458	+	0.885987i	−0.0486738	+	0.0281018i
$995$	11.9362	−	6.89136i	0.378402	−	0.218471i
$996$	−17.2896	+	11.5700i	−0.547842	+	0.366611i
$997$	2.03716	+	7.60277i	0.0645174	+	0.240782i	0.990653	−	0.136410i	$-0.0435564\pi$
$997$	2.03716	+	7.60277i	0.0645174	+	0.240782i	−0.926135	+	0.377192i	$0.876890\pi$
$998$	0.903137	+	0.903137i	0.0285883	+	0.0285883i
$999$	−10.3396	−	6.87734i	−0.327130	−	0.217589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.n.a.115.8	yes	64
3.2	odd	2		459.2.o.a.370.9		64
9.4	even	3	inner	153.2.n.a.13.9	yes	64
9.5	odd	6		459.2.o.a.64.8		64
17.4	even	4	inner	153.2.n.a.106.9	yes	64
51.38	odd	4		459.2.o.a.208.8		64
153.4	even	12	inner	153.2.n.a.4.8	✓	64
153.140	odd	12		459.2.o.a.361.9		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.n.a.4.8	✓	64	153.4	even	12	inner
153.2.n.a.13.9	yes	64	9.4	even	3	inner
153.2.n.a.106.9	yes	64	17.4	even	4	inner
153.2.n.a.115.8	yes	64	1.1	even	1	trivial
459.2.o.a.64.8		64	9.5	odd	6
459.2.o.a.208.8		64	51.38	odd	4
459.2.o.a.361.9		64	153.140	odd	12
459.2.o.a.370.9		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.218953 - 0.126413i) q^{2} +(0.963283 + 1.43947i) q^{3} +(-0.968040 - 1.67669i) q^{4} +(1.02659 - 3.83129i) q^{5} +(-0.0289461 - 0.436949i) q^{6} +(-0.551719 - 2.05904i) q^{7} +0.995142i q^{8} +(-1.14417 + 2.77324i) q^{9} +(-0.709099 + 0.709099i) q^{10} +(-0.307889 - 1.14906i) q^{11} +(1.48106 - 3.00860i) q^{12} +(3.09696 + 5.36409i) q^{13} +(-0.139489 + 0.520578i) q^{14} +(6.50393 - 2.21286i) q^{15} +(-1.81028 + 3.13550i) q^{16} +(2.45336 - 3.31376i) q^{17} +(0.601094 - 0.462573i) q^{18} +5.66168i q^{19} +(-7.41767 + 1.98756i) q^{20} +(2.43248 - 2.77762i) q^{21} +(-0.0778423 + 0.290512i) q^{22} +(0.703082 + 0.188390i) q^{23} +(-1.43248 + 0.958603i) q^{24} +(-9.29474 - 5.36632i) q^{25} -1.56598i q^{26} +(-5.09417 + 1.02441i) q^{27} +(-2.91830 + 2.91830i) q^{28} +(2.98504 - 0.799838i) q^{29} +(-1.70379 - 0.337667i) q^{30} +(-0.0116316 + 0.0434097i) q^{31} +(2.51637 - 1.45283i) q^{32} +(1.35746 - 1.55007i) q^{33} +(-0.956073 + 0.415424i) q^{34} -8.45517 q^{35} +(5.75748 - 0.766182i) q^{36} +(1.68986 + 1.68986i) q^{37} +(0.715709 - 1.23964i) q^{38} +(-4.73822 + 9.62513i) q^{39} +(3.81267 + 1.02160i) q^{40} +(0.650890 + 0.174405i) q^{41} +(-0.883726 + 0.300674i) q^{42} +(0.442424 + 0.255434i) q^{43} +(-1.62857 + 1.62857i) q^{44} +(9.45049 + 7.23063i) q^{45} +(-0.130127 - 0.130127i) q^{46} +(-4.74104 + 8.21172i) q^{47} +(-6.25728 + 0.414520i) q^{48} +(2.12692 - 1.22798i) q^{49} +(1.35674 + 2.34995i) q^{50} +(7.13336 + 0.339453i) q^{51} +(5.99596 - 10.3853i) q^{52} -7.10456i q^{53} +(1.24488 + 0.419670i) q^{54} -4.71845 q^{55} +(2.04904 - 0.549038i) q^{56} +(-8.14985 + 5.45380i) q^{57} +(-0.754693 - 0.202219i) q^{58} +(-7.91388 + 4.56908i) q^{59} +(-10.0064 - 8.76297i) q^{60} +(1.49801 + 5.59065i) q^{61} +(0.00803432 - 0.00803432i) q^{62} +(6.34148 + 0.825848i) q^{63} +6.50650 q^{64} +(23.7307 - 6.35862i) q^{65} +(-0.493168 + 0.167793i) q^{66} +(-1.68697 - 2.92191i) q^{67} +(-7.93112 - 0.905676i) q^{68} +(0.406084 + 1.19354i) q^{69} +(1.85129 + 1.06884i) q^{70} +(2.32488 + 2.32488i) q^{71} +(-2.75977 - 1.13861i) q^{72} +(-8.24518 - 8.24518i) q^{73} +(-0.156381 - 0.583622i) q^{74} +(-1.22879 - 18.5488i) q^{75} +(9.49291 - 5.48073i) q^{76} +(-2.19609 + 1.26791i) q^{77} +(2.25419 - 1.50848i) q^{78} +(0.0332596 + 0.124126i) q^{79} +(10.1546 + 10.1546i) q^{80} +(-6.38174 - 6.34613i) q^{81} +(-0.120467 - 0.120467i) q^{82} +(-5.37265 - 3.10190i) q^{83} +(-7.01196 - 1.38967i) q^{84} +(-10.1774 - 12.8014i) q^{85} +(-0.0645802 - 0.111856i) q^{86} +(4.02678 + 3.52641i) q^{87} +(1.14348 - 0.306394i) q^{88} +8.09524 q^{89} +(-1.15517 - 2.77783i) q^{90} +(9.33624 - 9.33624i) q^{91} +(-0.364738 - 1.36122i) q^{92} +(-0.0736917 + 0.0250724i) q^{93} +(2.07613 - 1.19866i) q^{94} +(21.6915 + 5.81223i) q^{95} +(4.51528 + 2.22277i) q^{96} +(-3.94729 + 1.05767i) q^{97} -0.620928 q^{98} +(3.53890 + 0.460869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30}+ \cdots + 6 q^{99}+O(q^{100}) \) 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7 - 16 * q^10 - 24 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^17 - 8 * q^18 + 18 * q^20 - 16 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 - 10 * q^29 - 36 * q^30 - 2 * q^31 + 12 * q^33 + 20 * q^34 - 128 * q^35 - 8 * q^37 - 24 * q^38 + 34 * q^39 - 20 * q^40 + 32 * q^41 + 20 * q^44 + 20 * q^45 - 40 * q^46 - 64 * q^47 + 62 * q^48 + 48 * q^50 + 40 * q^51 + 36 * q^52 - 46 * q^54 - 16 * q^55 + 12 * q^56 + 72 * q^57 - 10 * q^58 - 2 * q^61 - 28 * q^62 + 64 * q^63 - 8 * q^64 + 8 * q^65 - 4 * q^67 - 60 * q^68 - 24 * q^69 - 84 * q^71 + 72 * q^72 - 44 * q^73 - 14 * q^74 + 46 * q^75 - 56 * q^78 + 10 * q^79 + 204 * q^80 + 44 * q^81 - 52 * q^82 - 60 * q^84 + 22 * q^85 + 32 * q^86 + 16 * q^88 + 128 * q^89 - 66 * q^90 + 44 * q^91 + 136 * q^92 + 4 * q^95 - 2 * q^96 - 44 * q^97 + 208 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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