LMFDB - Embedded newform 185.2.p.a.97.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] 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("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.p (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:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.8
Character	$\chi$	$=$	185.97
Dual form			185.2.p.a.103.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.183474 + 0.317786i) q^{2} +(-0.0494608 + 0.184590i) q^{3} +(0.932675 + 1.61544i) q^{4} +(1.13941 - 1.92399i) q^{5} +(-0.0495854 - 0.0495854i) q^{6} +(0.511509 - 1.90898i) q^{7} -1.41838 q^{8} +(2.56645 + 1.48174i) q^{9} +(0.402364 + 0.715091i) q^{10} +3.45234i q^{11} +(-0.344325 + 0.0922616i) q^{12} +(-1.54894 - 2.68284i) q^{13} +(0.512798 + 0.512798i) q^{14} +(0.298793 + 0.305486i) q^{15} +(-1.60511 + 2.78014i) q^{16} +(6.45506 + 3.72683i) q^{17} +(-0.941752 + 0.543721i) q^{18} +(-7.19086 - 1.92679i) q^{19} +(4.17079 + 0.0461969i) q^{20} +(0.327079 + 0.188839i) q^{21} +(-1.09710 - 0.633414i) q^{22} +1.31718 q^{23} +(0.0701542 - 0.261819i) q^{24} +(-2.40348 - 4.38444i) q^{25} +1.13676 q^{26} +(-0.805841 + 0.805841i) q^{27} +(3.56091 - 0.954144i) q^{28} +(-2.20635 - 2.20635i) q^{29} +(-0.151900 + 0.0389035i) q^{30} +(4.00610 - 4.00610i) q^{31} +(-2.00737 - 3.47687i) q^{32} +(-0.637268 - 0.170755i) q^{33} +(-2.36867 + 1.36755i) q^{34} +(-3.09004 - 3.15925i) q^{35} +5.52793i q^{36} +(-5.20549 - 3.14689i) q^{37} +(1.93164 - 1.93164i) q^{38} +(0.571837 - 0.153223i) q^{39} +(-1.61612 + 2.72895i) q^{40} +(-5.80754 + 3.35298i) q^{41} +(-0.120021 + 0.0692941i) q^{42} -12.5857 q^{43} +(-5.57705 + 3.21991i) q^{44} +(5.77510 - 3.24951i) q^{45} +(-0.241668 + 0.418582i) q^{46} +(-1.95542 - 1.95542i) q^{47} +(-0.433796 - 0.433796i) q^{48} +(2.67962 + 1.54708i) q^{49} +(1.83429 + 0.0406392i) q^{50} +(-1.00721 + 1.00721i) q^{51} +(2.88931 - 5.00443i) q^{52} +(-1.22993 - 4.59015i) q^{53} +(-0.108234 - 0.403936i) q^{54} +(6.64227 + 3.93364i) q^{55} +(-0.725515 + 2.70766i) q^{56} +(0.711331 - 1.23206i) q^{57} +(1.10595 - 0.296339i) q^{58} +(-1.37883 - 5.14585i) q^{59} +(-0.214818 + 0.767602i) q^{60} +(9.38781 + 2.51546i) q^{61} +(0.538068 + 2.00810i) q^{62} +(4.14137 - 4.14137i) q^{63} -4.94725 q^{64} +(-6.92664 - 0.0767214i) q^{65} +(0.171186 - 0.171186i) q^{66} +(4.77781 + 1.28021i) q^{67} +13.9037i q^{68} +(-0.0651488 + 0.243139i) q^{69} +(1.57091 - 0.402329i) q^{70} +(2.33213 + 4.03937i) q^{71} +(-3.64020 - 2.10167i) q^{72} +(-6.43715 - 6.43715i) q^{73} +(1.95511 - 1.07686i) q^{74} +(0.928202 - 0.226800i) q^{75} +(-3.59413 - 13.4135i) q^{76} +(6.59044 + 1.76590i) q^{77} +(-0.0562249 + 0.209834i) q^{78} +(-8.42204 - 2.25668i) q^{79} +(3.52007 + 6.25595i) q^{80} +(4.33633 + 7.51074i) q^{81} -2.46074i q^{82} +(3.51999 + 13.1368i) q^{83} +0.704502i q^{84} +(14.5254 - 8.17307i) q^{85} +(2.30915 - 3.99956i) q^{86} +(0.516397 - 0.298142i) q^{87} -4.89673i q^{88} +(14.7909 - 3.96321i) q^{89} +(-0.0269314 + 2.43144i) q^{90} +(-5.91378 + 1.58459i) q^{91} +(1.22850 + 2.12783i) q^{92} +(0.541342 + 0.937632i) q^{93} +(0.980175 - 0.262637i) q^{94} +(-11.9005 + 11.6397i) q^{95} +(0.741082 - 0.198572i) q^{96} +4.35591i q^{97} +(-0.983280 + 0.567697i) q^{98} +(-5.11547 + 8.86025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100}) $ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.183474	+	0.317786i	−0.129736	+	0.224709i	−0.923574	−	0.383420i	$-0.874746\pi$
$2$	−0.183474	+	0.317786i	−0.129736	+	0.224709i	0.793839	+	0.608129i	$0.208080\pi$
$3$	−0.0494608	+	0.184590i	−0.0285562	+	0.106573i	−0.978733	−	0.205138i	$-0.934236\pi$
$3$	−0.0494608	+	0.184590i	−0.0285562	+	0.106573i	0.950177	+	0.311711i	$0.100902\pi$
$4$	0.932675	+	1.61544i	0.466337	+	0.807720i
$5$	1.13941	−	1.92399i	0.509561	−	0.860434i
$5$	1.13941	−	1.92399i	0.509561	−	0.860434i
$6$	−0.0495854	−	0.0495854i	−0.0202431	−	0.0202431i
$7$	0.511509	−	1.90898i	0.193332	−	0.721526i	−0.799360	−	0.600853i	$-0.794828\pi$
$7$	0.511509	−	1.90898i	0.193332	−	0.721526i	0.992692	−	0.120674i	$-0.0385054\pi$
$8$	−1.41838			−0.501473
$9$	2.56645	+	1.48174i	0.855483	+	0.493913i
$10$	0.402364	+	0.715091i	0.127239	+	0.226132i
$11$			3.45234i			1.04092i	0.853886	+	0.520460i	$0.174239\pi$
$11$			3.45234i			1.04092i	−0.853886	+	0.520460i	$0.825761\pi$
$12$	−0.344325	+	0.0922616i	−0.0993981	+	0.0266336i
$13$	−1.54894	−	2.68284i	−0.429598	−	0.744086i	0.567239	−	0.823553i	$-0.308011\pi$
$13$	−1.54894	−	2.68284i	−0.429598	−	0.744086i	−0.996837	+	0.0794671i	$0.974678\pi$
$14$	0.512798	+	0.512798i	0.137051	+	0.137051i
$15$	0.298793	+	0.305486i	0.0771481	+	0.0788763i
$16$	−1.60511	+	2.78014i	−0.401278	+	0.695035i
$17$	6.45506	+	3.72683i	1.56558	+	0.903889i	0.996674	+	0.0814869i	$0.0259669\pi$
$17$	6.45506	+	3.72683i	1.56558	+	0.903889i	0.568907	+	0.822402i	$0.307366\pi$
$18$	−0.941752	+	0.543721i	−0.221973	+	0.128156i
$19$	−7.19086	−	1.92679i	−1.64970	−	0.442035i	−0.690169	−	0.723648i	$-0.742464\pi$
$19$	−7.19086	−	1.92679i	−1.64970	−	0.442035i	−0.959528	+	0.281614i	$0.909130\pi$
$20$	4.17079	+	0.0461969i	0.932618	+	0.0103299i
$21$	0.327079	+	0.188839i	0.0713745	+	0.0412081i
$22$	−1.09710	−	0.633414i	−0.233904	−	0.135044i
$23$	1.31718			0.274651			0.137326	−	0.990526i	$-0.456149\pi$
$23$	1.31718			0.274651			0.137326	+	0.990526i	$0.456149\pi$
$24$	0.0701542	−	0.261819i	0.0143202	−	0.0534436i
$25$	−2.40348	−	4.38444i	−0.480695	−	0.876888i
$26$	1.13676			0.222937
$27$	−0.805841	+	0.805841i	−0.155084	+	0.155084i
$28$	3.56091	−	0.954144i	0.672949	−	0.180316i
$29$	−2.20635	−	2.20635i	−0.409708	−	0.409708i	0.471929	−	0.881637i	$-0.343558\pi$
$29$	−2.20635	−	2.20635i	−0.409708	−	0.409708i	−0.881637	+	0.471929i	$0.843558\pi$
$30$	−0.151900	+	0.0389035i	−0.0277330	+	0.00710278i
$31$	4.00610	−	4.00610i	0.719518	−	0.719518i	−0.248989	−	0.968506i	$-0.580098\pi$
$31$	4.00610	−	4.00610i	0.719518	−	0.719518i	0.968506	+	0.248989i	$0.0800982\pi$
$32$	−2.00737	−	3.47687i	−0.354857	−	0.614630i
$33$	−0.637268	−	0.170755i	−0.110934	−	0.0297247i
$34$	−2.36867	+	1.36755i	−0.406223	+	0.234533i
$35$	−3.09004	−	3.15925i	−0.522311	−	0.534011i
$36$			5.52793i			0.921321i
$37$	−5.20549	−	3.14689i	−0.855777	−	0.517345i
$37$	−5.20549	−	3.14689i	−0.855777	−	0.517345i
$38$	1.93164	−	1.93164i	0.313353	−	0.313353i
$39$	0.571837	−	0.153223i	0.0915673	−	0.0245354i
$40$	−1.61612	+	2.72895i	−0.255531	+	0.431485i
$41$	−5.80754	+	3.35298i	−0.906985	+	0.523648i	−0.879460	−	0.475973i	$-0.842096\pi$
$41$	−5.80754	+	3.35298i	−0.906985	+	0.523648i	−0.0275253	+	0.999621i	$0.508763\pi$
$42$	−0.120021	+	0.0692941i	−0.0185196	+	0.0106923i
$43$	−12.5857			−1.91930			−0.959652	−	0.281191i	$-0.909270\pi$
$43$	−12.5857			−1.91930			−0.959652	+	0.281191i	$0.909270\pi$
$44$	−5.57705	+	3.21991i	−0.840772	+	0.485420i
$45$	5.77510	−	3.24951i	0.860901	−	0.484408i
$46$	−0.241668	+	0.418582i	−0.0356320	+	0.0617165i
$47$	−1.95542	−	1.95542i	−0.285228	−	0.285228i	0.549962	−	0.835190i	$-0.314642\pi$
$47$	−1.95542	−	1.95542i	−0.285228	−	0.285228i	−0.835190	+	0.549962i	$0.814642\pi$
$48$	−0.433796	−	0.433796i	−0.0626131	−	0.0626131i
$49$	2.67962	+	1.54708i	0.382803	+	0.221011i
$50$	1.83429	+	0.0406392i	0.259407	+	0.00574724i
$51$	−1.00721	+	1.00721i	−0.141037	+	0.141037i
$52$	2.88931	−	5.00443i	0.400675	−	0.693990i
$53$	−1.22993	−	4.59015i	−0.168943	−	0.630506i	−0.997504	−	0.0706065i	$-0.977507\pi$
$53$	−1.22993	−	4.59015i	−0.168943	−	0.630506i	0.828561	−	0.559899i	$-0.189160\pi$
$54$	−0.108234	−	0.403936i	−0.0147288	−	0.0549687i
$55$	6.64227	+	3.93364i	0.895643	+	0.530412i
$56$	−0.725515	+	2.70766i	−0.0969510	+	0.361826i
$57$	0.711331	−	1.23206i	0.0942181	−	0.163191i
$58$	1.10595	−	0.296339i	0.145219	−	0.0389112i
$59$	−1.37883	−	5.14585i	−0.179508	−	0.669933i	−0.995740	−	0.0922082i	$-0.970607\pi$
$59$	−1.37883	−	5.14585i	−0.179508	−	0.669933i	0.816232	−	0.577725i	$-0.196059\pi$
$60$	−0.214818	+	0.767602i	−0.0277329	+	0.0990970i
$61$	9.38781	+	2.51546i	1.20199	+	0.322071i	0.803613	−	0.595152i	$-0.202908\pi$
$61$	9.38781	+	2.51546i	1.20199	+	0.322071i	0.398373	+	0.917223i	$0.369575\pi$
$62$	0.538068	+	2.00810i	0.0683348	+	0.255029i
$63$	4.14137	−	4.14137i	0.521764	−	0.521764i
$64$	−4.94725			−0.618407
$65$	−6.92664	−	0.0767214i	−0.859144	−	0.00951612i
$66$	0.171186	−	0.171186i	0.0210715	−	0.0210715i
$67$	4.77781	+	1.28021i	0.583703	+	0.156403i	0.538574	−	0.842578i	$-0.318963\pi$
$67$	4.77781	+	1.28021i	0.583703	+	0.156403i	0.0451292	+	0.998981i	$0.485630\pi$
$68$			13.9037i			1.68607i
$69$	−0.0651488	+	0.243139i	−0.00784300	+	0.0292705i
$70$	1.57091	−	0.402329i	0.187759	−	0.0480876i
$71$	2.33213	+	4.03937i	0.276773	+	0.479385i	0.970581	−	0.240775i	$-0.0774016\pi$
$71$	2.33213	+	4.03937i	0.276773	+	0.479385i	−0.693808	+	0.720160i	$0.744068\pi$
$72$	−3.64020	−	2.10167i	−0.429002	−	0.247684i
$73$	−6.43715	−	6.43715i	−0.753412	−	0.753412i	0.221702	−	0.975114i	$-0.428839\pi$
$73$	−6.43715	−	6.43715i	−0.753412	−	0.753412i	−0.975114	+	0.221702i	$0.928839\pi$
$74$	1.95511	−	1.07686i	0.227276	−	0.125182i
$75$	0.928202	−	0.226800i	0.107180	−	0.0261886i
$76$	−3.59413	−	13.4135i	−0.412275	−	1.53863i
$77$	6.59044	+	1.76590i	0.751051	+	0.201243i
$78$	−0.0562249	+	0.209834i	−0.00636622	+	0.0237591i
$79$	−8.42204	−	2.25668i	−0.947554	−	0.253896i	−0.248230	−	0.968701i	$-0.579849\pi$
$79$	−8.42204	−	2.25668i	−0.947554	−	0.253896i	−0.699324	+	0.714805i	$0.746515\pi$
$80$	3.52007	+	6.25595i	0.393556	+	0.699436i
$81$	4.33633	+	7.51074i	0.481814	+	0.834527i
$82$		−	2.46074i		−	0.271743i
$83$	3.51999	+	13.1368i	0.386369	+	1.44195i	0.835998	+	0.548733i	$0.184889\pi$
$83$	3.51999	+	13.1368i	0.386369	+	1.44195i	−0.449629	+	0.893215i	$0.648444\pi$
$84$			0.704502i			0.0768675i
$85$	14.5254	−	8.17307i	1.57550	−	0.886494i
$86$	2.30915	−	3.99956i	0.249002	−	0.431284i
$87$	0.516397	−	0.298142i	0.0553636	−	0.0319642i
$88$		−	4.89673i		−	0.521993i
$89$	14.7909	−	3.96321i	1.56783	−	0.420100i	0.632701	−	0.774397i	$-0.281946\pi$
$89$	14.7909	−	3.96321i	1.56783	−	0.420100i	0.935133	+	0.354297i	$0.115280\pi$
$90$	−0.0269314	+	2.43144i	−0.00283881	+	0.256297i
$91$	−5.91378	+	1.58459i	−0.619933	+	0.166110i
$92$	1.22850	+	2.12783i	0.128080	+	0.221841i
$93$	0.541342	+	0.937632i	0.0561346	+	0.0972279i
$94$	0.980175	−	0.262637i	0.101097	−	0.0270890i
$95$	−11.9005	+	11.6397i	−1.22096	+	1.19421i
$96$	0.741082	−	0.198572i	0.0756364	−	0.0202667i
$97$			4.35591i			0.442276i	0.975243	+	0.221138i	$0.0709770\pi$
$97$			4.35591i			0.442276i	−0.975243	+	0.221138i	$0.929023\pi$
$98$	−0.983280	+	0.567697i	−0.0993263	+	0.0573461i
$99$	−5.11547	+	8.86025i	−0.514124	+	0.890489i
$100$	4.84114	−	7.97193i	0.484114	−	0.797193i
$101$			0.191058i			0.0190110i	0.999955	+	0.00950548i	$0.00302573\pi$
$101$			0.191058i			0.0190110i	−0.999955	+	0.00950548i	$0.996974\pi$
$102$	−0.135280	−	0.504873i	−0.0133947	−	0.0499898i
$103$		−	2.11028i		−	0.207932i	−0.994581	−	0.103966i	$-0.966847\pi$
$103$		−	2.11028i		−	0.207932i	0.994581	−	0.103966i	$-0.0331532\pi$
$104$	2.19698	+	3.80529i	0.215432	+	0.373139i
$105$	0.736003	−	0.414131i	0.0718265	−	0.0404150i
$106$	1.68434	+	0.451319i	0.163598	+	0.0438359i
$107$	−2.54999	+	9.51668i	−0.246517	+	0.920012i	0.726099	+	0.687591i	$0.241332\pi$
$107$	−2.54999	+	9.51668i	−0.246517	+	0.920012i	−0.972615	+	0.232422i	$0.925335\pi$
$108$	−2.05338	−	0.550200i	−0.197586	−	0.0529431i
$109$	4.09076	+	15.2669i	0.391824	+	1.46231i	0.827123	+	0.562020i	$0.189976\pi$
$109$	4.09076	+	15.2669i	0.391824	+	1.46231i	−0.435300	+	0.900286i	$0.643358\pi$
$110$	−2.46874	+	1.38910i	−0.235385	+	0.132445i
$111$	0.838351	−	0.805234i	0.0795728	−	0.0764295i
$112$	4.48619	+	4.48619i	0.423906	+	0.423906i
$113$	−5.40479	−	3.12046i	−0.508440	−	0.293548i	0.223752	−	0.974646i	$-0.428169\pi$
$113$	−5.40479	−	3.12046i	−0.508440	−	0.293548i	−0.732192	+	0.681098i	$0.761503\pi$
$114$	0.261021	+	0.452102i	0.0244469	+	0.0423432i
$115$	1.50081	−	2.53424i	0.139952	−	0.236320i
$116$	1.50642	−	5.62203i	0.139867	−	0.521992i
$117$		−	9.18050i		−	0.848737i
$118$	1.88826	+	0.505957i	0.173828	+	0.0465771i
$119$	10.4163	−	10.4163i	0.954857	−	0.954857i
$120$	−0.423803	−	0.433296i	−0.0386877	−	0.0395543i
$121$	−0.918652			−0.0835138
$122$	−2.52179	+	2.52179i	−0.228312	+	0.228312i
$123$	−0.331682	−	1.23786i	−0.0299068	−	0.111614i
$124$	10.2080	+	2.73523i	0.916707	+	0.245631i
$125$	−11.1742	−	0.371426i	−0.999448	−	0.0332214i
$126$	0.556237	+	2.07590i	0.0495535	+	0.184936i
$127$	−3.86342	+	1.03520i	−0.342823	+	0.0918592i	−0.426123	−	0.904665i	$-0.640121\pi$
$127$	−3.86342	+	1.03520i	−0.342823	+	0.0918592i	0.0832996	+	0.996525i	$0.473454\pi$
$128$	4.92244	−	8.52591i	0.435086	−	0.753591i
$129$	0.622499	−	2.32320i	0.0548080	−	0.204546i
$130$	1.29524	−	2.18711i	0.113600	−	0.191822i
$131$	0.918927	+	3.42948i	0.0802870	+	0.299635i	0.994380	−	0.105869i	$-0.0337625\pi$
$131$	0.918927	+	3.42948i	0.0802870	+	0.299635i	−0.914093	+	0.405505i	$0.867096\pi$
$132$	−0.318519	−	1.18873i	−0.0277235	−	0.103465i
$133$	−7.35638	+	12.7416i	−0.637879	+	1.10484i
$134$	−1.28344	+	1.28344i	−0.110872	+	0.110872i
$135$	0.632244	+	2.46862i	0.0544149	+	0.212465i
$136$	−9.15573	−	5.28606i	−0.785097	−	0.453276i
$137$	−1.62038	−	1.62038i	−0.138438	−	0.138438i	0.634492	−	0.772930i	$-0.281210\pi$
$137$	−1.62038	−	1.62038i	−0.138438	−	0.138438i	−0.772930	+	0.634492i	$0.781210\pi$
$138$	−0.0653130	−	0.0653130i	−0.00555981	−	0.00555981i
$139$	3.18045	−	5.50870i	0.269762	−	0.467241i	−0.699038	−	0.715084i	$-0.746388\pi$
$139$	3.18045	−	5.50870i	0.269762	−	0.467241i	0.968800	+	0.247843i	$0.0797216\pi$
$140$	2.22159	−	7.93832i	0.187758	−	0.670911i
$141$	0.457669	−	0.264235i	0.0385427	−	0.0222526i
$142$	−1.71154			−0.143629
$143$	9.26208	−	5.34746i	0.774534	−	0.447177i
$144$	−8.23889	+	4.75672i	−0.686574	+	0.396394i
$145$	−6.75893	+	1.73105i	−0.561299	+	0.143756i
$146$	3.22669	−	0.864588i	0.267042	−	0.0715538i
$147$	−0.418112	+	0.418112i	−0.0344853	+	0.0344853i
$148$	0.228577	−	11.3442i	0.0187889	−	0.932485i
$149$		−	18.0198i		−	1.47624i	−0.674668	−	0.738121i	$-0.735713\pi$
$149$		−	18.0198i		−	1.47624i	0.674668	−	0.738121i	$-0.264287\pi$
$150$	−0.0982269	+	0.336581i	−0.00802019	+	0.0274818i
$151$	−0.277285	+	0.160091i	−0.0225651	+	0.0130280i	−0.511240	−	0.859438i	$-0.670814\pi$
$151$	−0.277285	+	0.160091i	−0.0225651	+	0.0130280i	0.488675	+	0.872466i	$0.337480\pi$
$152$	10.1994	+	2.73291i	0.827279	+	0.221669i
$153$	11.0444	+	19.1294i	0.892885	+	1.54652i
$154$	−1.77035	+	1.77035i	−0.142659	+	0.142659i
$155$	−3.14310	−	12.2723i	−0.252460	−	0.985736i
$156$	0.780862	+	0.780862i	0.0625190	+	0.0625190i
$157$	−1.13930	+	0.305275i	−0.0909263	+	0.0243636i	−0.303995	−	0.952674i	$-0.598321\pi$
$157$	−1.13930	+	0.305275i	−0.0909263	+	0.0243636i	0.213069	+	0.977037i	$0.431654\pi$
$158$	2.26236	−	2.26236i	0.179984	−	0.179984i
$159$	0.908129			0.0720194
$160$	−8.97669	−	0.0994284i	−0.709670	−	0.00786050i
$161$	0.673751	−	2.51447i	0.0530990	−	0.198168i
$162$	−3.18241			−0.250034
$163$	7.96311	+	4.59750i	0.623719	+	0.360104i	0.778315	−	0.627873i	$-0.216074\pi$
$163$	7.96311	+	4.59750i	0.623719	+	0.360104i	−0.154597	+	0.987978i	$0.549408\pi$
$164$	−10.8331	−	6.25449i	−0.845922	−	0.488393i
$165$	−1.05464	+	1.03154i	−0.0821039	+	0.0803050i
$166$	−4.82051	−	1.29165i	−0.374144	−	0.100252i
$167$	−18.8329	+	10.8732i	−1.45733	+	0.841392i	−0.998879	−	0.0473268i	$-0.984930\pi$
$167$	−18.8329	+	10.8732i	−1.45733	+	0.841392i	−0.458454	+	0.888718i	$0.651596\pi$
$168$	−0.463922	−	0.267846i	−0.0357924	−	0.0206647i
$169$	1.70158	−	2.94722i	0.130891	−	0.226709i
$170$	−0.0677370	+	6.11550i	−0.00519519	+	0.469037i
$171$	−15.6000	−	15.6000i	−1.19296	−	1.19296i
$172$	−11.7384	−	20.3315i	−0.895043	−	1.55026i
$173$	3.34723	−	0.896886i	0.254485	−	0.0681890i	−0.129321	−	0.991603i	$-0.541280\pi$
$173$	3.34723	−	0.896886i	0.254485	−	0.0681890i	0.383806	+	0.923414i	$0.374613\pi$
$174$			0.218805i			0.0165876i
$175$	−9.59920	+	2.34550i	−0.725631	+	0.177303i
$176$	−9.59798	−	5.54140i	−0.723475	−	0.417699i
$177$	1.01807			0.0765229
$178$	−1.45429	+	5.42749i	−0.109004	+	0.406807i
$179$	10.5340	+	10.5340i	0.787350	+	0.787350i	0.981059	−	0.193709i	$-0.0620517\pi$
$179$	10.5340	+	10.5340i	0.787350	+	0.787350i	−0.193709	+	0.981059i	$0.562052\pi$
$180$	10.6357	+	6.29859i	0.792736	+	0.469469i
$181$	−0.0475195	−	0.0823062i	−0.00353210	−	0.00611777i	0.864254	−	0.503056i	$-0.167791\pi$
$181$	−0.0475195	−	0.0823062i	−0.00353210	−	0.00611777i	−0.867786	+	0.496938i	$0.834458\pi$
$182$	0.581462	−	2.17005i	0.0431009	−	0.160855i
$183$	−0.928657	+	1.60848i	−0.0686483	+	0.118902i
$184$	−1.86827			−0.137730
$185$	−11.9858	+	6.42971i	−0.881212	+	0.472721i
$186$	−0.397288			−0.0291306
$187$	−12.8663	+	22.2851i	−0.940876	+	1.62964i
$188$	1.33510	−	4.98265i	0.0973719	−	0.363397i
$189$	1.12614	+	1.95053i	0.0819145	+	0.141880i
$190$	−1.51552	−	5.91739i	−0.109947	−	0.429293i
$191$	6.76075	+	6.76075i	0.489190	+	0.489190i	0.908051	−	0.418860i	$-0.137570\pi$
$191$	6.76075	+	6.76075i	0.489190	+	0.489190i	−0.418860	+	0.908051i	$0.637570\pi$
$192$	0.244695	−	0.913214i	0.0176593	−	0.0659056i
$193$	−0.988625			−0.0711628			−0.0355814	−	0.999367i	$-0.511328\pi$
$193$	−0.988625			−0.0711628			−0.0355814	+	0.999367i	$0.511328\pi$
$194$	−1.38425	−	0.799195i	−0.0993831	−	0.0573789i
$195$	0.356759	−	1.27479i	0.0255480	−	0.0912899i
$196$			5.77169i			0.412263i
$197$	7.91972	−	2.12208i	0.564257	−	0.151192i	0.0345956	−	0.999401i	$-0.488986\pi$
$197$	7.91972	−	2.12208i	0.564257	−	0.151192i	0.529661	+	0.848209i	$0.322319\pi$
$198$	−1.87711	−	3.25125i	−0.133400	−	0.231056i
$199$	−0.311060	−	0.311060i	−0.0220505	−	0.0220505i	0.695996	−	0.718046i	$-0.254963\pi$
$199$	−0.311060	−	0.311060i	−0.0220505	−	0.0220505i	−0.718046	+	0.695996i	$0.754963\pi$
$200$	3.40904	+	6.21880i	0.241056	+	0.439736i
$201$	−0.472629	+	0.818617i	−0.0333367	+	0.0577408i
$202$	−0.0607155	−	0.0350541i	−0.00427192	−	0.00246640i
$203$	−5.34044	+	3.08330i	−0.374825	+	0.216405i
$204$	−2.56648	−	0.687687i	−0.179690	−	0.0481477i
$205$	−0.166079	+	14.9941i	−0.0115994	+	1.04723i
$206$	0.670616	+	0.387180i	0.0467240	+	0.0269761i
$207$	3.38048	+	1.95172i	0.234960	+	0.135654i
$208$	9.94489			0.689554
$209$	6.65192	−	24.8253i	0.460123	−	1.71720i
$210$	−0.00343224	+	0.309873i	−0.000236847	+	0.0213833i
$211$	1.21043			0.0833298			0.0416649	−	0.999132i	$-0.486734\pi$
$211$	1.21043			0.0833298			0.0416649	+	0.999132i	$0.486734\pi$
$212$	6.26799	−	6.26799i	0.430487	−	0.430487i
$213$	−0.860977	+	0.230698i	−0.0589932	+	0.0158072i
$214$	−2.55641	−	2.55641i	−0.174753	−	0.174753i
$215$	−14.3403	+	24.2148i	−0.978002	+	1.65143i
$216$	1.14299	−	1.14299i	0.0777706	−	0.0777706i
$217$	−5.59841	−	9.69673i	−0.380045	−	0.658257i
$218$	−5.60216	−	1.50109i	−0.379426	−	0.101667i
$219$	1.50662	−	0.869849i	0.101808	−	0.0587789i
$220$	−0.159487	+	14.3990i	−0.0107526	+	0.970780i
$221$		−	23.0905i		−	1.55324i
$222$	0.102077	+	0.414156i	0.00685094	+	0.0277963i
$223$	13.8676	−	13.8676i	0.928645	−	0.928645i	−0.0689736	−	0.997618i	$-0.521972\pi$
$223$	13.8676	−	13.8676i	0.928645	−	0.928645i	0.997618	+	0.0689736i	$0.0219724\pi$
$224$	−7.66406	+	2.05358i	−0.512077	+	0.137211i
$225$	0.328203	−	14.8138i	0.0218802	−	0.987584i
$226$	1.98328	−	1.14504i	0.131926	−	0.0761672i
$227$	17.3295	−	10.0052i	1.15020	−	0.664066i	0.201261	−	0.979538i	$-0.435496\pi$
$227$	17.3295	−	10.0052i	1.15020	−	0.664066i	0.948935	+	0.315471i	$0.102163\pi$
$228$	2.65376			0.175750
$229$	3.19465	−	1.84443i	0.211108	−	0.121883i	−0.390718	−	0.920510i	$-0.627773\pi$
$229$	3.19465	−	1.84443i	0.211108	−	0.121883i	0.601826	+	0.798627i	$0.294440\pi$
$230$	0.529987	+	0.941905i	0.0349463	+	0.0621074i
$231$	−0.651937	+	1.12919i	−0.0428943	+	0.0742951i
$232$	3.12944	+	3.12944i	0.205458	+	0.205458i
$233$	9.61670	+	9.61670i	0.630011	+	0.630011i	0.948071	−	0.318060i	$-0.103031\pi$
$233$	9.61670	+	9.61670i	0.630011	+	0.630011i	−0.318060	+	0.948071i	$0.603031\pi$
$234$	2.91743	+	1.68438i	0.190719	+	0.110111i
$235$	−5.99025	+	1.53418i	−0.390761	+	0.100079i
$236$	7.02682	−	7.02682i	0.457407	−	0.457407i
$237$	0.833121	−	1.44301i	0.0541171	−	0.0937335i
$238$	1.39903	+	5.22125i	0.0906856	+	0.338443i
$239$	−3.51998	−	13.1367i	−0.227689	−	0.849745i	−0.981310	−	0.192436i	$-0.938361\pi$
$239$	−3.51998	−	13.1367i	−0.227689	−	0.849745i	0.753621	−	0.657309i	$-0.228305\pi$
$240$	−1.32889	+	0.340346i	−0.0857796	+	0.0219693i
$241$	6.11044	−	22.8045i	0.393608	−	1.46897i	−0.430530	−	0.902576i	$-0.641673\pi$
$241$	6.11044	−	22.8045i	0.393608	−	1.46897i	0.824138	−	0.566389i	$-0.191660\pi$
$242$	0.168548	−	0.291935i	0.0108347	−	0.0187663i
$243$	−4.90329	+	1.31383i	−0.314546	+	0.0842823i
$244$	4.69221	+	17.5115i	0.300388	+	1.12106i
$245$	6.02976	−	3.39280i	0.385227	−	0.216758i
$246$	0.454228	+	0.121710i	0.0289605	+	0.00775995i
$247$	5.96894	+	22.2764i	0.379795	+	1.41741i
$248$	−5.68218	+	5.68218i	−0.360819	+	0.360819i
$249$	−2.59902			−0.164706
$250$	2.16820	−	3.48285i	0.137129	−	0.220275i
$251$	0.401654	−	0.401654i	0.0253522	−	0.0253522i	−0.694317	−	0.719669i	$-0.744293\pi$
$251$	0.401654	−	0.401654i	0.0253522	−	0.0253522i	0.719669	+	0.694317i	$0.244293\pi$
$252$	10.5527	+	2.82759i	0.664757	+	0.178121i
$253$			4.54736i			0.285890i
$254$	0.379864	−	1.41767i	0.0238348	−	0.0889527i
$255$	0.790232	+	3.08548i	0.0494862	+	0.193221i
$256$	−3.14098	−	5.44033i	−0.196311	−	0.340021i
$257$	14.1687	+	8.18028i	0.883817	+	0.510272i	0.871915	−	0.489657i	$-0.162878\pi$
$257$	14.1687	+	8.18028i	0.883817	+	0.510272i	0.0119019	+	0.999929i	$0.496211\pi$
$258$	0.624067	+	0.624067i	0.0388527	+	0.0388527i
$259$	−8.66999	+	8.32751i	−0.538727	+	0.517446i
$260$	−6.33636	−	11.2611i	−0.392964	−	0.698385i
$261$	−2.39324	−	8.93171i	−0.148138	−	0.552859i
$262$	−1.25844	−	0.337198i	−0.0777467	−	0.0208322i
$263$	−4.59860	+	17.1622i	−0.283562	+	1.05827i	0.666322	+	0.745664i	$0.267868\pi$
$263$	−4.59860	+	17.1622i	−0.283562	+	1.05827i	−0.949884	+	0.312603i	$0.898799\pi$
$264$	0.903888	+	0.242196i	0.0556305	+	0.0149061i
$265$	−10.2328	−	2.86371i	−0.628596	−	0.175916i
$266$	−2.69941	−	4.67551i	−0.165511	−	0.286674i
$267$			2.92628i			0.179085i
$268$	2.38804	+	8.91229i	0.145873	+	0.544405i
$269$			23.2463i			1.41735i	0.705533	+	0.708677i	$0.250708\pi$
$269$			23.2463i			1.41735i	−0.705533	+	0.708677i	$0.749292\pi$
$270$	−0.900492	−	0.252008i	−0.0548022	−	0.0153367i
$271$	−8.50840	+	14.7370i	−0.516848	+	0.895208i	0.482960	+	0.875642i	$0.339562\pi$
$271$	−8.50840	+	14.7370i	−0.516848	+	0.895208i	−0.999809	+	0.0195654i	$0.993772\pi$
$272$	−20.7222	+	11.9640i	−1.25647	+	0.725422i
$273$		−	1.17000i		−	0.0708117i
$274$	0.812229	−	0.217636i	0.0490686	−	0.0131479i
$275$	15.1366	−	8.29761i	0.912770	−	0.500365i
$276$	−0.453539	+	0.121525i	−0.0272998	+	0.00731497i
$277$	0.776108	+	1.34426i	0.0466318	+	0.0807686i	0.888399	−	0.459072i	$-0.151818\pi$
$277$	0.776108	+	1.34426i	0.0466318	+	0.0807686i	−0.841767	+	0.539840i	$0.818485\pi$
$278$	1.16706	+	2.02140i	0.0699954	+	0.121236i
$279$	16.2175	−	4.34546i	0.970914	−	0.260156i
$280$	4.38285	+	4.48102i	0.261925	+	0.267792i
$281$	9.62089	−	2.57791i	0.573934	−	0.153785i	0.0398338	−	0.999206i	$-0.487317\pi$
$281$	9.62089	−	2.57791i	0.573934	−	0.153785i	0.534100	+	0.845421i	$0.320650\pi$
$282$			0.193921i			0.0115478i
$283$	21.5075	−	12.4174i	1.27849	−	0.738137i	0.301919	−	0.953333i	$-0.402373\pi$
$283$	21.5075	−	12.4174i	1.27849	−	0.738137i	0.976571	+	0.215197i	$0.0690393\pi$
$284$	−4.35024	+	7.53484i	−0.258139	+	0.447110i
$285$	−1.55997	−	2.77242i	−0.0924049	−	0.164224i
$286$			3.92448i			0.232059i
$287$	3.43016	+	12.8015i	0.202476	+	0.755652i
$288$		−	11.8976i		−	0.701074i
$289$	19.2785	+	33.3914i	1.13403	+	1.96420i
$290$	0.689984	−	2.46549i	0.0405172	−	0.144779i
$291$	−0.804058	−	0.215447i	−0.0471347	−	0.0126297i
$292$	4.39507	−	16.4026i	0.257202	−	0.959890i
$293$	−6.40278	−	1.71562i	−0.374054	−	0.100227i	0.0668940	−	0.997760i	$-0.478691\pi$
$293$	−6.40278	−	1.71562i	−0.374054	−	0.100227i	−0.440948	+	0.897533i	$0.645358\pi$
$294$	−0.0561575	−	0.209583i	−0.00327517	−	0.0122231i
$295$	−11.4716	−	3.21040i	−0.667903	−	0.186917i
$296$	7.38336	+	4.46348i	0.429149	+	0.259435i
$297$	−2.78204	−	2.78204i	−0.161430	−	0.161430i
$298$	5.72645	+	3.30617i	0.331724	+	0.191521i
$299$	−2.04023	−	3.53379i	−0.117990	−	0.204364i
$300$	1.23209	+	1.28792i	0.0711349	+	0.0743583i
$301$	−6.43771	+	24.0259i	−0.371063	+	1.38483i
$302$		−	0.117490i		−	0.00676077i
$303$	−0.0352674	−	0.00944986i	−0.00202606	−	0.000542881i
$304$	16.8989	−	16.8989i	0.969217	−	0.969217i
$305$	15.5363	−	15.1959i	0.889606	−	0.870115i
$306$	−8.10542			−0.463356
$307$	9.43347	−	9.43347i	0.538396	−	0.538396i	−0.384661	−	0.923058i	$-0.625682\pi$
$307$	9.43347	−	9.43347i	0.538396	−	0.538396i	0.923058	+	0.384661i	$0.125682\pi$
$308$	3.29403	+	12.2935i	0.187695	+	0.700486i
$309$	0.389536	+	0.104376i	0.0221599	+	0.00593773i
$310$	4.47664	+	1.25282i	0.254256	+	0.0711552i
$311$	−2.04001	−	7.61341i	−0.115678	−	0.431717i	0.883659	−	0.468132i	$-0.155073\pi$
$311$	−2.04001	−	7.61341i	−0.115678	−	0.431717i	−0.999337	+	0.0364152i	$0.988406\pi$
$312$	−0.811083	+	0.217329i	−0.0459185	+	0.0123038i
$313$	−1.15066	+	1.99301i	−0.0650393	+	0.112651i	−0.896711	−	0.442616i	$-0.854051\pi$
$313$	−1.15066	+	1.99301i	−0.0650393	+	0.112651i	0.831672	+	0.555267i	$0.187384\pi$
$314$	0.112020	−	0.418065i	0.00632166	−	0.0235927i
$315$	−3.24922	−	12.6867i	−0.183073	−	0.714814i
$316$	−4.20950	−	15.7101i	−0.236803	−	0.883759i
$317$	−2.10279	−	7.84772i	−0.118104	−	0.440772i	0.881396	−	0.472378i	$-0.156604\pi$
$317$	−2.10279	−	7.84772i	−0.118104	−	0.440772i	−0.999500	+	0.0316064i	$0.989938\pi$
$318$	−0.166618	+	0.288591i	−0.00934347	+	0.0161834i
$319$	7.61706	−	7.61706i	0.426473	−	0.426473i
$320$	−5.63697	+	9.51847i	−0.315116	+	0.532099i
$321$	−1.63056	−	0.941405i	−0.0910091	−	0.0525441i
$322$	0.675448	+	0.675448i	0.0376413	+	0.0376413i
$323$	−39.2366	−	39.2366i	−2.18318	−	2.18318i
$324$	−8.08877	+	14.0102i	−0.449376	+	0.778342i
$325$	−8.03991	+	13.2394i	−0.445974	+	0.734388i
$326$	−2.92204	+	1.68704i	−0.161837	+	0.0934366i
$327$	−3.02046			−0.167032
$328$	8.23730	−	4.75581i	0.454829	−	0.262596i
$329$	−4.73308	+	2.73265i	−0.260943	+	0.150656i
$330$	−0.134308	−	0.524411i	−0.00739343	−	0.0288678i
$331$	−23.6164	+	6.32799i	−1.29807	+	0.347818i	−0.840722	−	0.541468i	$-0.817869\pi$
$331$	−23.6164	+	6.32799i	−1.29807	+	0.347818i	−0.457352	+	0.889285i	$0.651202\pi$
$332$	−17.9387	+	17.9387i	−0.984512	+	0.984512i
$333$	−8.69676	−	15.7895i	−0.476579	−	0.865259i
$334$		−	7.97977i		−	0.436634i
$335$	7.90702	−	7.73378i	0.432007	−	0.422541i
$336$	−1.05000	+	0.606217i	−0.0572821	+	0.0330718i
$337$	−18.7623	−	5.02735i	−1.02205	−	0.273857i	−0.291394	−	0.956603i	$-0.594119\pi$
$337$	−18.7623	−	5.02735i	−1.02205	−	0.273857i	−0.730656	+	0.682746i	$0.760786\pi$
$338$	0.624391	+	1.08148i	0.0339624	+	0.0588245i
$339$	0.843331	−	0.843331i	0.0458035	−	0.0458035i
$340$	26.7505	+	15.8420i	1.45075	+	0.859155i
$341$	13.8304	+	13.8304i	0.748960	+	0.748960i
$342$	7.81964	−	2.09527i	0.422838	−	0.113299i
$343$	14.1063	−	14.1063i	0.761667	−	0.761667i
$344$	17.8513			0.962479
$345$	0.393565	+	0.402381i	0.0211888	+	0.0216635i
$346$	−0.329110	+	1.22826i	−0.0176931	+	0.0660315i
$347$	3.39588			0.182300			0.0911501	−	0.995837i	$-0.470946\pi$
$347$	3.39588			0.182300			0.0911501	+	0.995837i	$0.470946\pi$
$348$	0.963262	+	0.556139i	0.0516363	+	0.0298122i
$349$	0.334598	+	0.193180i	0.0179106	+	0.0103407i	0.508929	−	0.860809i	$-0.330042\pi$
$349$	0.334598	+	0.193180i	0.0179106	+	0.0103407i	−0.491018	+	0.871149i	$0.663375\pi$
$350$	1.01583	−	3.48083i	0.0542986	−	0.186058i
$351$	3.41014	+	0.913745i	0.182020	+	0.0487721i
$352$	12.0033	−	6.93013i	0.639780	−	0.369377i
$353$	3.67390	+	2.12113i	0.195542	+	0.112896i	0.594574	−	0.804041i	$-0.297321\pi$
$353$	3.67390	+	2.12113i	0.195542	+	0.112896i	−0.399032	+	0.916937i	$0.630654\pi$
$354$	−0.186789	+	0.323529i	−0.00992774	+	0.0171954i
$355$	10.4290	+	0.115514i	0.553512	+	0.00613086i
$356$	20.1974	+	20.1974i	1.07046	+	1.07046i
$357$	1.40754	+	2.43793i	0.0744950	+	0.129029i
$358$	−5.28028	+	1.41485i	−0.279072	+	0.0747770i
$359$		−	18.8723i		−	0.996040i	−0.867166	−	0.498020i	$-0.834061\pi$
$359$		−	18.8723i		−	0.996040i	0.867166	−	0.498020i	$-0.165939\pi$
$360$	−8.19129	+	4.60904i	−0.431719	+	0.242918i
$361$	31.5415	+	18.2105i	1.66008	+	0.958447i
$362$	0.0348743			0.00183296
$363$	0.0454372	−	0.169574i	0.00238484	−	0.00890033i
$364$	−8.07545	−	8.07545i	−0.423268	−	0.423268i
$365$	−19.7196	+	5.05044i	−1.03217	+	0.264352i
$366$	−0.340768	−	0.590228i	−0.0178122	−	0.0308517i
$367$	3.44218	−	12.8464i	0.179680	−	0.670576i	−0.816027	−	0.578014i	$-0.803828\pi$
$367$	3.44218	−	12.8464i	0.179680	−	0.670576i	0.995707	−	0.0925616i	$-0.0295055\pi$
$368$	−2.11423	+	3.66195i	−0.110212	+	0.190892i
$369$	−19.8730			−1.03455
$370$	0.155806	−	4.98859i	0.00809998	−	0.259345i
$371$	−9.39162			−0.487588
$372$	−1.00979	+	1.74901i	−0.0523553	+	0.0906820i
$373$	−5.10346	+	19.0464i	−0.264247	+	0.986183i	0.698463	+	0.715646i	$0.253868\pi$
$373$	−5.10346	+	19.0464i	−0.264247	+	0.986183i	−0.962710	+	0.270536i	$0.912799\pi$
$374$	−4.72125	−	8.17745i	−0.244130	−	0.422846i
$375$	0.621245	−	2.04427i	0.0320809	−	0.105566i
$376$	2.77354	+	2.77354i	0.143034	+	0.143034i
$377$	−2.50178	+	9.33677i	−0.128848	+	0.480868i
$378$	−0.826467			−0.0425089
$379$	−9.48304	−	5.47504i	−0.487111	−	0.281234i	0.236264	−	0.971689i	$-0.424077\pi$
$379$	−9.48304	−	5.47504i	−0.487111	−	0.281234i	−0.723375	+	0.690455i	$0.757410\pi$
$380$	−29.9026	−	8.36842i	−1.53397	−	0.429291i
$381$		−	0.764351i		−	0.0391589i
$382$	−3.38889	+	0.908050i	−0.173391	+	0.0464599i
$383$	8.51460	+	14.7477i	0.435076	+	0.753574i	0.997302	−	0.0734101i	$-0.0233882\pi$
$383$	8.51460	+	14.7477i	0.435076	+	0.753574i	−0.562226	+	0.826984i	$0.690055\pi$
$384$	1.33033	+	1.33033i	0.0678882	+	0.0678882i
$385$	10.9068	−	10.6679i	0.555863	−	0.543684i
$386$	0.181387	−	0.314171i	0.00923234	−	0.0159909i
$387$	−32.3006	−	18.6488i	−1.64193	−	0.947970i
$388$	−7.03671	+	4.06265i	−0.357235	+	0.206250i
$389$	−12.4581	−	3.33813i	−0.631649	−	0.169250i	−0.0712310	−	0.997460i	$-0.522693\pi$
$389$	−12.4581	−	3.33813i	−0.631649	−	0.169250i	−0.560418	+	0.828210i	$0.689359\pi$
$390$	0.339656	+	0.347264i	0.0171991	+	0.0175844i
$391$	8.50248	+	4.90891i	0.429989	+	0.248254i
$392$	−3.80072	−	2.19435i	−0.191965	−	0.110831i
$393$	−0.678499			−0.0342258
$394$	−0.778693	+	2.90612i	−0.0392300	+	0.146408i
$395$	−13.9380	+	13.6326i	−0.701298	+	0.685932i
$396$	−19.0843			−0.959021
$397$	−21.7674	+	21.7674i	−1.09248	+	1.09248i	−0.0972114	+	0.995264i	$0.530992\pi$
$397$	−21.7674	+	21.7674i	−1.09248	+	1.09248i	−0.995264	+	0.0972114i	$0.969008\pi$
$398$	0.155922	−	0.0417791i	0.00781566	−	0.00209420i
$399$	−1.98813	−	1.98813i	−0.0995308	−	0.0995308i
$400$	16.0472	+	0.355530i	0.802360	+	0.0177765i
$401$	−0.609043	+	0.609043i	−0.0304142	+	0.0304142i	−0.722150	−	0.691736i	$-0.756846\pi$
$401$	−0.609043	+	0.609043i	−0.0304142	+	0.0304142i	0.691736	+	0.722150i	$0.256846\pi$
$402$	−0.173430	−	0.300389i	−0.00864990	−	0.0149821i
$403$	−16.9529	−	4.54253i	−0.844486	−	0.226279i
$404$	−0.308642	+	0.178195i	−0.0153555	+	0.00886552i
$405$	19.3915	+	0.214785i	0.963569	+	0.0106728i
$406$		−	2.26282i		−	0.112302i
$407$	10.8641	−	17.9711i	0.538514	−	0.890795i
$408$	1.42860	−	1.42860i	0.0707264	−	0.0707264i
$409$	−27.7946	+	7.44753i	−1.37435	+	0.368257i	−0.869067	−	0.494695i	$-0.835280\pi$
$409$	−27.7946	+	7.44753i	−1.37435	+	0.368257i	−0.505286	+	0.862952i	$0.668613\pi$
$410$	−4.73444	−	2.80380i	−0.233817	−	0.138470i
$411$	0.379251	−	0.218960i	0.0187071	−	0.0108005i
$412$	3.40902	−	1.96820i	0.167951	−	0.0969663i
$413$	−10.5286			−0.518079
$414$	−1.24046	+	0.716179i	−0.0609652	+	0.0351983i
$415$	29.2857	+	8.19579i	1.43758	+	0.402316i
$416$	−6.21859	+	10.7709i	−0.304892	+	0.528088i
$417$	0.859544	+	0.859544i	0.0420920	+	0.0420920i
$418$	6.66868	+	6.66868i	0.326176	+	0.326176i
$419$	−1.88268	−	1.08696i	−0.0919747	−	0.0531016i	0.453307	−	0.891354i	$-0.350244\pi$
$419$	−1.88268	−	1.08696i	−0.0919747	−	0.0531016i	−0.545282	+	0.838253i	$0.683577\pi$
$420$	1.35545	+	0.802719i	0.0661394	+	0.0391687i
$421$	16.3854	−	16.3854i	0.798575	−	0.798575i	−0.184296	−	0.982871i	$-0.559000\pi$
$421$	16.3854	−	16.3854i	0.798575	−	0.798575i	0.982871	+	0.184296i	$0.0590004\pi$
$422$	−0.222083	+	0.384659i	−0.0108108	+	0.0187249i
$423$	−2.12107	−	7.91593i	−0.103130	−	0.384886i
$424$	1.74450	+	6.51058i	0.0847206	+	0.316182i
$425$	0.825487	−	37.2591i	0.0400420	−	1.80733i
$426$	0.0846541	−	0.315933i	0.00410150	−	0.0153070i
$427$	9.60390	−	16.6345i	0.464766	−	0.804997i
$428$	−17.7519	+	4.75662i	−0.858072	+	0.229920i
$429$	0.528979	+	1.97418i	0.0255394	+	0.0953142i
$430$	−5.06404	−	8.99993i	−0.244210	−	0.434015i
$431$	−6.06172	−	1.62423i	−0.291983	−	0.0782366i	0.109854	−	0.993948i	$-0.464962\pi$
$431$	−6.06172	−	1.62423i	−0.291983	−	0.0782366i	−0.401837	+	0.915711i	$0.631628\pi$
$432$	−0.946883	−	3.53382i	−0.0455570	−	0.170021i
$433$	−12.5346	+	12.5346i	−0.602376	+	0.602376i	−0.940942	−	0.338567i	$-0.890058\pi$
$433$	−12.5346	+	12.5346i	−0.602376	+	0.602376i	0.338567	+	0.940942i	$0.390058\pi$
$434$	4.10864			0.197221
$435$	0.0147675	−	1.33325i	0.000708045	−	0.0639245i
$436$	−20.8474	+	20.8474i	−0.998412	+	0.998412i
$437$	−9.47167	−	2.53793i	−0.453091	−	0.121405i
$438$			0.638378i			0.0305029i
$439$	7.05673	−	26.3361i	0.336799	−	1.25695i	−0.565106	−	0.825018i	$-0.691165\pi$
$439$	7.05673	−	26.3361i	0.336799	−	1.25695i	0.901905	−	0.431934i	$-0.142169\pi$
$440$	−9.42126	−	5.57940i	−0.449141	−	0.265987i
$441$	4.58474	+	7.94100i	0.218321	+	0.378143i
$442$	7.33784	+	4.23650i	0.349025	+	0.201510i
$443$	−14.0595	−	14.0595i	−0.667985	−	0.667985i	0.289264	−	0.957249i	$-0.406589\pi$
$443$	−14.0595	−	14.0595i	−0.667985	−	0.667985i	−0.957249	+	0.289264i	$0.906589\pi$
$444$	2.08272	+	0.603285i	0.0988414	+	0.0286306i
$445$	9.22778	−	32.9733i	0.437439	−	1.56308i
$446$	1.86259	+	6.95128i	0.0881962	+	0.329153i
$447$	3.32628	+	0.891275i	0.157328	+	0.0421559i
$448$	−2.53057	+	9.44420i	−0.119558	+	0.446197i
$449$	−12.8304	−	3.43788i	−0.605502	−	0.162244i	−0.0569734	−	0.998376i	$-0.518145\pi$
$449$	−12.8304	−	3.43788i	−0.605502	−	0.162244i	−0.548528	+	0.836132i	$0.684812\pi$
$450$	4.64739	+	2.82224i	0.219080	+	0.133041i
$451$	−11.5756	−	20.0496i	−0.545076	−	0.944099i
$452$		−	11.6415i		−	0.547570i
$453$	−0.0158364	−	0.0591023i	−0.000744059	−	0.00277687i
$454$			7.34274i			0.344612i
$455$	−3.68950	+	13.1836i	−0.172966	+	0.618055i
$456$	−1.00894	+	1.74753i	−0.0472479	+	0.0818357i
$457$	13.0505	−	7.53471i	0.610477	−	0.352459i	−0.162675	−	0.986680i	$-0.552012\pi$
$457$	13.0505	−	7.53471i	0.610477	−	0.352459i	0.773152	+	0.634221i	$0.218679\pi$
$458$			1.35362i			0.0632504i
$459$	−8.20498	+	2.19852i	−0.382976	+	0.102618i
$460$	5.49369	+	0.0608497i	0.256145	+	0.00283713i
$461$	12.5579	−	3.36489i	0.584882	−	0.156719i	0.0457688	−	0.998952i	$-0.485426\pi$
$461$	12.5579	−	3.36489i	0.584882	−	0.156719i	0.539113	+	0.842233i	$0.318760\pi$
$462$	−0.239227	−	0.414353i	−0.0111298	−	0.0192774i
$463$	13.9799	+	24.2140i	0.649703	+	1.12532i	0.983194	+	0.182565i	$0.0584402\pi$
$463$	13.9799	+	24.2140i	0.649703	+	1.12532i	−0.333491	+	0.942753i	$0.608227\pi$
$464$	9.67539	−	2.59251i	0.449169	−	0.120354i
$465$	2.42081	+	0.0268135i	0.112262	+	0.00124345i
$466$	−4.82046	+	1.29164i	−0.223304	+	0.0598340i
$467$		−	1.30129i		−	0.0602165i	−0.999547	−	0.0301083i	$-0.990415\pi$
$467$		−	1.30129i		−	0.0602165i	0.999547	−	0.0301083i	$-0.00958521\pi$
$468$	14.8305	−	8.56242i	0.685542	−	0.395798i
$469$	4.88779	−	8.46590i	0.225697	−	0.390919i
$470$	0.611513	−	2.18510i	0.0282070	−	0.100791i
$471$		−	0.225403i		−	0.0103860i
$472$	1.95570	+	7.29877i	0.0900184	+	0.335953i
$473$		−	43.4502i		−	1.99784i
$474$	0.305712	+	0.529508i	0.0140418	+	0.0243211i
$475$	8.83518	+	36.1589i	0.405386	+	1.65908i
$476$	26.5418	+	7.11186i	1.21654	+	0.325972i
$477$	3.64486	−	13.6028i	0.166887	−	0.622830i
$478$	4.82050	+	1.29165i	0.220484	+	0.0590786i
$479$	−1.00395	−	3.74678i	−0.0458715	−	0.171195i	0.939190	−	0.343398i	$-0.111578\pi$
$479$	−1.00395	−	3.74678i	−0.0458715	−	0.171195i	−0.985061	+	0.172203i	$0.944911\pi$
$480$	0.462348	−	1.65209i	0.0211032	−	0.0754073i
$481$	−0.379608	+	18.8398i	−0.0173087	+	0.859022i
$482$	6.12584	+	6.12584i	0.279024	+	0.279024i
$483$	0.430822	+	0.248735i	0.0196031	+	0.0113179i
$484$	−0.856803	−	1.48403i	−0.0389456	−	0.0674558i
$485$	8.38072	+	4.96318i	0.380549	+	0.225366i
$486$	0.482107	−	1.79925i	0.0218688	−	0.0816156i
$487$			17.7036i			0.802228i	0.916028	+	0.401114i	$0.131377\pi$
$487$			17.7036i			0.802228i	−0.916028	+	0.401114i	$0.868623\pi$
$488$	−13.3155	−	3.56787i	−0.602764	−	0.161510i
$489$	−1.24252	+	1.24252i	−0.0561885	+	0.0561885i
$490$	−0.0281189	+	2.53866i	−0.00127028	+	0.114685i
$491$	28.1151			1.26882			0.634408	−	0.772998i	$-0.281244\pi$
$491$	28.1151			1.26882			0.634408	+	0.772998i	$0.281244\pi$
$492$	1.69033	−	1.69033i	0.0762059	−	0.0762059i
$493$	−6.01942	−	22.4648i	−0.271101	−	1.01176i
$494$	−8.17427	−	2.19029i	−0.367778	−	0.0985458i
$495$	11.2184	+	19.9376i	0.504230	+	0.896129i
$496$	4.70727	+	17.5678i	0.211363	+	0.788817i
$497$	8.90398	−	2.38581i	0.399398	−	0.107018i
$498$	0.476852	−	0.825932i	0.0213682	−	0.0370109i
$499$	−7.95975	+	29.7062i	−0.356327	+	1.32983i	0.522479	+	0.852652i	$0.325007\pi$
$499$	−7.95975	+	29.7062i	−0.356327	+	1.32983i	−0.878806	+	0.477179i	$0.841659\pi$
$500$	−9.82185	−	18.3976i	−0.439246	−	0.822767i
$501$	−1.07559	−	4.01416i	−0.0480539	−	0.179340i
$502$	0.0539470	+	0.201333i	0.00240777	+	0.00898593i
$503$	−10.1676	+	17.6108i	−0.453351	+	0.785227i	−0.998592	−	0.0530522i	$-0.983105\pi$
$503$	−10.1676	+	17.6108i	−0.453351	+	0.785227i	0.545240	+	0.838280i	$0.316438\pi$
$504$	−5.87404	+	5.87404i	−0.261651	+	0.261651i
$505$	0.367593	+	0.217694i	0.0163577	+	0.00968724i
$506$	−1.44509	−	0.834321i	−0.0642419	−	0.0370901i
$507$	0.459867	+	0.459867i	0.0204234	+	0.0204234i
$508$	−5.27562	−	5.27562i	−0.234068	−	0.234068i
$509$	−3.95875	+	6.85676i	−0.175469	+	0.303921i	−0.940323	−	0.340282i	$-0.889477\pi$
$509$	−3.95875	+	6.85676i	−0.175469	+	0.303921i	0.764855	+	0.644203i	$0.222811\pi$
$510$	−1.12551	−	0.314981i	−0.0498384	−	0.0139476i
$511$	−15.5811	+	8.99573i	−0.689265	+	0.397948i
$512$	21.9949			0.972046
$513$	7.34738	−	4.24201i	0.324395	−	0.187289i
$514$	−5.19916	+	3.00173i	−0.229325	+	0.132401i
$515$	−4.06015	−	2.40448i	−0.178912	−	0.105954i
$516$	4.33358	−	1.16118i	0.190775	−	0.0511180i
$517$	6.75079	−	6.75079i	0.296899	−	0.296899i
$518$	−1.05565	−	4.28308i	−0.0463825	−	0.188188i
$519$			0.662225i			0.0290685i
$520$	9.82461	+	0.108820i	0.430838	+	0.00477208i
$521$	−22.5608	+	13.0255i	−0.988406	+	0.570657i	−0.904798	−	0.425842i	$-0.859978\pi$
$521$	−22.5608	+	13.0255i	−0.988406	+	0.570657i	−0.0836089	+	0.996499i	$0.526645\pi$
$522$	3.27747	+	0.878195i	0.143451	+	0.0384376i
$523$	−1.66547	−	2.88468i	−0.0728259	−	0.126138i	0.827313	−	0.561741i	$-0.189868\pi$
$523$	−1.66547	−	2.88468i	−0.0728259	−	0.126138i	−0.900139	+	0.435603i	$0.856535\pi$
$524$	−4.68306	+	4.68306i	−0.204581	+	0.204581i
$525$	0.0418276	−	1.88793i	0.00182550	−	0.0823959i
$526$	−4.61019	−	4.61019i	−0.201014	−	0.201014i
$527$	40.7897	−	10.9296i	1.77683	−	0.476099i
$528$	1.49761	−	1.49761i	0.0651752	−	0.0651752i
$529$	−21.2650			−0.924567
$530$	2.78750	−	2.72642i	0.121081	−	0.118428i
$531$	4.08613	−	15.2496i	0.177323	−	0.661777i
$532$	−27.4445			−1.18987
$533$	17.9910	+	10.3871i	0.779278	+	0.449917i
$534$	−0.929930	−	0.536896i	−0.0402420	−	0.0232337i
$535$	15.4045	+	15.7496i	0.665995	+	0.680914i
$536$	−6.77676	−	1.81583i	−0.292711	−	0.0784318i
$537$	−2.46550	+	1.42346i	−0.106394	+	0.0614267i
$538$	−7.38736	−	4.26509i	−0.318492	−	0.183881i
$539$	−5.34104	+	9.25096i	−0.230055	+	0.398467i
$540$	−3.39822	+	3.32377i	−0.146236	+	0.143032i
$541$	−6.36223	−	6.36223i	−0.273534	−	0.273534i	0.556987	−	0.830521i	$-0.311957\pi$
$541$	−6.36223	−	6.36223i	−0.273534	−	0.273534i	−0.830521	+	0.556987i	$0.811957\pi$
$542$	−3.12214	−	5.40770i	−0.134107	−	0.232281i
$543$	0.0175433	−	0.00470071i	0.000752854	−	0.000201727i
$544$		−	29.9245i		−	1.28300i
$545$	34.0345	+	9.52475i	1.45788	+	0.407996i
$546$	0.371810	+	0.214664i	0.0159120	+	0.00918679i
$547$	10.6102			0.453658			0.226829	−	0.973935i	$-0.427164\pi$
$547$	10.6102			0.453658			0.226829	+	0.973935i	$0.427164\pi$
$548$	1.10634	−	4.12891i	0.0472604	−	0.176378i
$549$	20.3661	+	20.3661i	0.869203	+	0.869203i
$550$	−0.140300	+	6.33258i	−0.00598242	+	0.270022i
$551$	11.6144	+	20.1167i	0.494789	+	0.857000i
$552$	0.0924058	−	0.344863i	0.00393305	−	0.0146784i
$553$	−8.61591	+	14.9232i	−0.366386	+	0.634598i
$554$	−0.569582			−0.0241992
$555$	−0.594034	−	2.53047i	−0.0252154	−	0.107413i
$556$	11.8653			0.503200
$557$	−18.0586	+	31.2784i	−0.765166	+	1.32531i	0.174992	+	0.984570i	$0.444010\pi$
$557$	−18.0586	+	31.2784i	−0.765166	+	1.32531i	−0.940159	+	0.340737i	$0.889323\pi$
$558$	−1.59455	+	5.95096i	−0.0675029	+	0.251924i
$559$	19.4945	+	33.7655i	0.824529	+	1.42813i
$560$	13.7430	−	3.51976i	0.580749	−	0.148737i
$561$	−3.47722	−	3.47722i	−0.146809	−	0.146809i
$562$	−0.945957	+	3.53036i	−0.0399028	+	0.148919i
$563$	28.0509			1.18220			0.591102	−	0.806597i	$-0.298693\pi$
$563$	28.0509			1.18220			0.591102	+	0.806597i	$0.298693\pi$
$564$	0.853712	+	0.492891i	0.0359478	+	0.0207545i
$565$	−12.1620	+	6.84328i	−0.511660	+	0.287899i
$566$			9.11305i			0.383050i
$567$	16.5559	−	4.43614i	0.695283	−	0.186301i
$568$	−3.30785	−	5.72936i	−0.138794	−	0.240399i
$569$	1.69141	+	1.69141i	0.0709076	+	0.0709076i	0.741671	−	0.670764i	$-0.234033\pi$
$569$	1.69141	+	1.69141i	0.0709076	+	0.0709076i	−0.670764	+	0.741671i	$0.734033\pi$
$570$	1.16725	+	0.0129288i	0.0488908	+	0.000541528i
$571$	4.18372	−	7.24641i	0.175083	−	0.303253i	−0.765107	−	0.643903i	$-0.777314\pi$
$571$	4.18372	−	7.24641i	0.175083	−	0.303253i	0.940190	+	0.340650i	$0.110647\pi$
$572$	17.2770	+	9.97489i	0.722388	+	0.417071i
$573$	−1.58236	+	0.913575i	−0.0661040	+	0.0381651i
$574$	−4.69750	−	1.25869i	−0.196070	−	0.0525367i
$575$	−3.16581	−	5.77510i	−0.132024	−	0.240838i
$576$	−12.6969	−	7.33054i	−0.529037	−	0.305439i
$577$	−17.7050	−	10.2220i	−0.737067	−	0.425546i	0.0839349	−	0.996471i	$-0.473251\pi$
$577$	−17.7050	−	10.2220i	−0.737067	−	0.425546i	−0.821002	+	0.570925i	$0.806585\pi$
$578$	−14.1484			−0.588496
$579$	0.0488982	−	0.182490i	0.00203214	−	0.00758404i
$580$	−9.10029	−	9.30414i	−0.377869	−	0.386333i
$581$	26.8783			1.11510
$582$	0.215989	−	0.215989i	0.00895305	−	0.00895305i
$583$	15.8468	−	4.24613i	0.656306	−	0.175857i
$584$	9.13033	+	9.13033i	0.377816	+	0.377816i
$585$	−17.6632	−	10.4604i	−0.730283	−	0.432483i
$586$	1.71994	−	1.71994i	0.0710501	−	0.0710501i
$587$	−19.7052	−	34.1304i	−0.813320	−	1.40871i	−0.910528	−	0.413448i	$-0.864324\pi$
$587$	−19.7052	−	34.1304i	−0.813320	−	1.40871i	0.0972074	−	0.995264i	$-0.469009\pi$
$588$	−1.06540	−	0.285472i	−0.0439362	−	0.0117727i
$589$	−36.5262	+	21.0884i	−1.50504	+	0.868934i
$590$	3.12496	−	3.05649i	0.128653	−	0.125834i
$591$			1.56686i			0.0644521i
$592$	17.1042	−	9.42087i	0.702977	−	0.387195i
$593$	−29.8968	+	29.8968i	−1.22771	+	1.22771i	−0.262886	+	0.964827i	$0.584674\pi$
$593$	−29.8968	+	29.8968i	−1.22771	+	1.22771i	−0.964827	+	0.262886i	$0.915326\pi$
$594$	1.39452	−	0.373661i	0.0572180	−	0.0153315i
$595$	−8.17235	−	31.9092i	−0.335034	−	1.30815i
$596$	29.1100	−	16.8066i	1.19239	−	0.688427i
$597$	0.0728039	−	0.0420333i	0.00297966	−	0.00172031i
$598$	1.49732			0.0612299
$599$	20.3437	−	11.7455i	0.831222	−	0.479906i	−0.0230489	−	0.999734i	$-0.507337\pi$
$599$	20.3437	−	11.7455i	0.831222	−	0.479906i	0.854271	+	0.519828i	$0.174004\pi$
$600$	−1.31654	+	0.321689i	−0.0537477	+	0.0131329i
$601$	−5.10765	+	8.84671i	−0.208345	+	0.360865i	−0.951193	−	0.308595i	$-0.900141\pi$
$601$	−5.10765	+	8.84671i	−0.208345	+	0.360865i	0.742848	+	0.669460i	$0.233474\pi$
$602$	−6.45393	−	6.45393i	−0.263042	−	0.263042i
$603$	10.3651	+	10.3651i	0.422098	+	0.422098i
$604$	−0.517233	−	0.298625i	−0.0210459	−	0.0121509i
$605$	−1.04672	+	1.76748i	−0.0425554	+	0.0718581i
$606$	0.00947367	−	0.00947367i	0.000384842	−	0.000384842i
$607$	0.780718	−	1.35224i	0.0316884	−	0.0548859i	−0.849746	−	0.527192i	$-0.823245\pi$
$607$	0.780718	−	1.35224i	0.0316884	−	0.0548859i	0.881435	+	0.472306i	$0.156578\pi$
$608$	7.73555	+	28.8695i	0.313718	+	1.17081i
$609$	−0.305005	−	1.13829i	−0.0123594	−	0.0461260i
$610$	1.97854	+	7.72527i	0.0801088	+	0.312787i
$611$	−2.21726	+	8.27492i	−0.0897007	+	0.334768i
$612$	−20.6016	+	35.6831i	−0.832772	+	1.44240i
$613$	1.48419	−	0.397688i	0.0599460	−	0.0160625i	−0.228721	−	0.973492i	$-0.573454\pi$
$613$	1.48419	−	0.397688i	0.0599460	−	0.0160625i	0.288667	+	0.957429i	$0.406788\pi$
$614$	1.26703	+	4.72862i	0.0511331	+	0.190831i
$615$	−2.75954	−	0.772275i	−0.111276	−	0.0311411i
$616$	−9.34776	−	2.50472i	−0.376632	−	0.100918i
$617$	−1.04297	−	3.89243i	−0.0419886	−	0.156703i	0.941749	−	0.336318i	$-0.109182\pi$
$617$	−1.04297	−	3.89243i	−0.0419886	−	0.156703i	−0.983737	+	0.179614i	$0.942515\pi$
$618$	−0.104639	+	0.104639i	−0.00420919	+	0.00420919i
$619$	24.1544			0.970846			0.485423	−	0.874279i	$-0.338666\pi$
$619$	24.1544			0.970846			0.485423	+	0.874279i	$0.338666\pi$
$620$	16.8937	−	16.5236i	0.678467	−	0.663602i
$621$	−1.06144	+	1.06144i	−0.0425941	+	0.0425941i
$622$	2.79372	+	0.748575i	0.112018	+	0.0300151i
$623$		−	30.2628i		−	1.21245i
$624$	−0.491882	+	1.83573i	−0.0196910	+	0.0734880i
$625$	−13.4466	+	21.0758i	−0.537865	+	0.843031i
$626$	−0.422233	−	0.731329i	−0.0168758	−	0.0292298i
$627$	4.25350	+	2.45576i	0.169868	+	0.0980735i
$628$	−1.55575	−	1.55575i	−0.0620813	−	0.0620813i
$629$	−21.8738	−	39.7133i	−0.872166	−	1.58347i
$630$	4.62780	+	1.29512i	0.184376	+	0.0515987i
$631$	−4.33716	−	16.1865i	−0.172660	−	0.644374i	−0.996938	−	0.0781902i	$-0.975086\pi$
$631$	−4.33716	−	16.1865i	−0.172660	−	0.644374i	0.824279	−	0.566184i	$-0.191581\pi$
$632$	11.9457	+	3.20083i	0.475173	+	0.127322i
$633$	−0.0598690	+	0.223434i	−0.00237958	+	0.00888071i
$634$	2.87970	+	0.771614i	0.114368	+	0.0306447i
$635$	−2.41032	+	8.61270i	−0.0956505	+	0.341785i
$636$	0.846989	+	1.46703i	0.0335853	+	0.0581715i
$637$		−	9.58532i		−	0.379784i
$638$	1.02306	+	3.81812i	0.0405035	+	0.151161i
$639$			13.8224i			0.546808i
$640$	−10.7951	−	19.1853i	−0.426713	−	0.758364i
$641$	−13.1598	+	22.7934i	−0.519779	+	0.900283i	0.479957	+	0.877292i	$0.340652\pi$
$641$	−13.1598	+	22.7934i	−0.519779	+	0.900283i	−0.999736	+	0.0229913i	$0.992681\pi$
$642$	0.598330	−	0.345446i	0.0236142	−	0.0136337i
$643$		−	34.2404i		−	1.35031i	−0.737675	−	0.675155i	$-0.764077\pi$
$643$		−	34.2404i		−	1.35031i	0.737675	−	0.675155i	$-0.235923\pi$
$644$	4.69037	−	1.25678i	0.184826	−	0.0495241i
$645$	−3.76053	−	3.84477i	−0.148071	−	0.151387i
$646$	19.6677	−	5.26995i	0.773817	−	0.207344i
$647$	16.4706	+	28.5278i	0.647524	+	1.12155i	0.983712	+	0.179750i	$0.0575290\pi$
$647$	16.4706	+	28.5278i	0.647524	+	1.12155i	−0.336188	+	0.941795i	$0.609138\pi$
$648$	−6.15056	−	10.6531i	−0.241617	−	0.418493i
$649$	17.7652	−	4.76018i	0.697346	−	0.186853i
$650$	−2.73217	−	4.98405i	−0.107165	−	0.195490i
$651$	2.06682	−	0.553803i	0.0810051	−	0.0217053i
$652$			17.1519i			0.671720i
$653$	−18.9744	+	10.9549i	−0.742526	+	0.428698i	−0.822987	−	0.568060i	$-0.807694\pi$
$653$	−18.9744	+	10.9549i	−0.742526	+	0.428698i	0.0804608	+	0.996758i	$0.474361\pi$
$654$	0.554174	−	0.959858i	0.0216699	−	0.0375334i
$655$	7.64533	+	2.13959i	0.298728	+	0.0836007i
$656$		−	21.5277i		−	0.840515i
$657$	−6.98244	−	26.0588i	−0.272411	−	1.01665i
$658$		−	2.00548i		−	0.0781816i
$659$	−4.76225	−	8.24846i	−0.185511	−	0.321314i	0.758238	−	0.651978i	$-0.226061\pi$
$659$	−4.76225	−	8.24846i	−0.185511	−	0.321314i	−0.943749	+	0.330664i	$0.892727\pi$
$660$	−2.65002	−	0.741625i	−0.103152	−	0.0288677i
$661$	4.49979	+	1.20572i	0.175022	+	0.0468969i	0.345265	−	0.938505i	$-0.387789\pi$
$661$	4.49979	+	1.20572i	0.175022	+	0.0468969i	−0.170244	+	0.985402i	$0.554456\pi$
$662$	2.32204	−	8.66598i	0.0902487	−	0.336813i
$663$	4.26228	+	1.14207i	0.165533	+	0.0443545i
$664$	−4.99268	−	18.6329i	−0.193754	−	0.723098i
$665$	16.1328	+	28.6716i	0.625604	+	1.11184i
$666$	6.61331	+	0.133253i	0.256260	+	0.00516346i
$667$	−2.90616	−	2.90616i	−0.112527	−	0.112527i
$668$	−35.1299	−	20.2823i	−1.35922	−	0.784745i
$669$	1.87392	+	3.24573i	0.0724501	+	0.125487i
$670$	1.00695	+	3.93168i	0.0389020	+	0.151894i
$671$	−8.68421	+	32.4099i	−0.335250	+	1.25117i
$672$		−	1.51628i		−	0.0584919i
$673$	−14.3592	−	3.84754i	−0.553507	−	0.148312i	−0.0287852	−	0.999586i	$-0.509164\pi$
$673$	−14.3592	−	3.84754i	−0.553507	−	0.148312i	−0.524722	+	0.851274i	$0.675831\pi$
$674$	5.04002	−	5.04002i	0.194134	−	0.194134i
$675$	5.46998	+	1.59634i	0.210540	+	0.0614433i
$676$	6.34808			0.244157
$677$	7.15203	−	7.15203i	0.274875	−	0.274875i	−0.556184	−	0.831059i	$-0.687735\pi$
$677$	7.15203	−	7.15203i	0.274875	−	0.274875i	0.831059	+	0.556184i	$0.187735\pi$
$678$	0.113270	+	0.422728i	0.00435009	+	0.0162348i
$679$	8.31534	+	2.22809i	0.319113	+	0.0855062i
$680$	−20.6025	+	11.5925i	−0.790069	+	0.444553i
$681$	0.989727	+	3.69371i	0.0379264	+	0.141543i
$682$	−6.93264	+	1.85759i	−0.265464	+	0.0711310i
$683$	−8.68491	+	15.0427i	−0.332319	+	0.575593i	−0.982966	−	0.183787i	$-0.941164\pi$
$683$	−8.68491	+	15.0427i	−0.332319	+	0.575593i	0.650647	+	0.759380i	$0.274498\pi$
$684$	10.6511	−	39.7505i	0.407256	−	1.51990i
$685$	−4.96387	+	1.27131i	−0.189660	+	0.0485743i
$686$	1.89464	+	7.07091i	0.0723378	+	0.269969i
$687$	0.182454	+	0.680927i	0.00696105	+	0.0259790i
$688$	20.2015	−	34.9900i	0.770175	−	1.33398i
$689$	−10.4096	+	10.4096i	−0.396573	+	0.396573i
$690$	−0.200080	+	0.0512430i	−0.00761691	+	0.00195079i
$691$	0.688714	+	0.397629i	0.0261999	+	0.0151265i	0.513043	−	0.858363i	$-0.328518\pi$
$691$	0.688714	+	0.397629i	0.0261999	+	0.0151265i	−0.486843	+	0.873490i	$0.661852\pi$
$692$	4.57074	+	4.57074i	0.173753	+	0.173753i
$693$	14.2974	+	14.2974i	0.543114	+	0.543114i
$694$	−0.623054	+	1.07916i	−0.0236508	+	0.0409644i
$695$	−6.97483	−	12.3958i	−0.264570	−	0.470201i
$696$	−0.732448	+	0.422879i	−0.0277634	+	0.0160292i
$697$	−49.9840			−1.89328
$698$	−0.122780	+	0.0708869i	−0.00464728	+	0.00268311i
$699$	−2.25080	+	1.29950i	−0.0851329	+	0.0491515i
$700$	−12.7419	−	13.3193i	−0.481600	−	0.503424i
$701$	−7.03789	+	1.88580i	−0.265817	+	0.0712255i	−0.389266	−	0.921125i	$-0.627271\pi$
$701$	−7.03789	+	1.88580i	−0.265817	+	0.0712255i	0.123449	+	0.992351i	$0.460605\pi$
$702$	−0.916047	+	0.916047i	−0.0345740	+	0.0345740i
$703$	31.3686	+	32.6587i	1.18309	+	1.23175i
$704$		−	17.0796i		−	0.643712i
$705$	0.0130880	−	1.18162i	0.000492922	−	0.0445025i
$706$	−1.34813	+	0.778343i	−0.0507375	+	0.0292933i
$707$	0.364725	+	0.0977278i	0.0137169	+	0.00367543i
$708$	0.949529	+	1.64463i	0.0356855	+	0.0618091i
$709$	−0.492179	+	0.492179i	−0.0184842	+	0.0184842i	−0.716288	−	0.697804i	$-0.754161\pi$
$709$	−0.492179	+	0.492179i	−0.0184842	+	0.0184842i	0.697804	+	0.716288i	$0.254161\pi$
$710$	−1.95015	+	3.29299i	−0.0731879	+	0.123584i
$711$	−18.2709	−	18.2709i	−0.685213	−	0.685213i
$712$	−20.9791	+	5.62134i	−0.786227	+	0.210669i
$713$	5.27677	−	5.27677i	0.197617	−	0.197617i
$714$	−1.03299			−0.0386586
$715$	0.264868	−	23.9131i	0.00990551	−	0.894300i
$716$	−7.19227	+	26.8419i	−0.268788	+	1.00313i
$717$	2.59901			0.0970620
$718$	5.99734	+	3.46257i	0.223819	+	0.129222i
$719$	−10.8743	−	6.27829i	−0.405543	−	0.234141i	0.283330	−	0.959023i	$-0.408561\pi$
$719$	−10.8743	−	6.27829i	−0.405543	−	0.234141i	−0.688873	+	0.724882i	$0.741894\pi$
$720$	−0.235608	+	21.2714i	−0.00878059	+	0.792739i
$721$	−4.02847	−	1.07943i	−0.150028	−	0.0401999i
$722$	−11.5741	+	6.68230i	−0.430742	+	0.248689i
$723$	3.90725	+	2.25585i	0.145312	+	0.0838961i
$724$	0.0886405	−	0.153530i	0.00329430	−	0.00570589i
$725$	−4.37069	+	14.9765i	−0.162324	+	0.556213i
$726$	0.0455517	+	0.0455517i	0.00169058	+	0.00169058i
$727$	0.227219	+	0.393556i	0.00842710	+	0.0145962i	0.870208	−	0.492684i	$-0.163984\pi$
$727$	0.227219	+	0.393556i	0.00842710	+	0.0145962i	−0.861781	+	0.507280i	$0.830651\pi$
$728$	8.38799	−	2.24756i	0.310880	−	0.0832999i
$729$			25.0479i			0.927699i
$730$	2.01307	−	7.19323i	0.0745071	−	0.266234i
$731$	−81.2415	−	46.9048i	−3.00483	−	1.73484i
$732$	−3.46454			−0.128053
$733$	0.0722495	−	0.269639i	0.00266859	−	0.00995933i	−0.964579	−	0.263795i	$-0.915026\pi$
$733$	0.0722495	−	0.269639i	0.00266859	−	0.00995933i	0.967247	+	0.253836i	$0.0816923\pi$
$734$	3.45085	+	3.45085i	0.127373	+	0.127373i
$735$	0.328041	+	1.28084i	0.0121000	+	0.0472447i
$736$	−2.64408	−	4.57967i	−0.0974619	−	0.168809i
$737$	−4.41972	+	16.4946i	−0.162803	+	0.607588i
$738$	3.64617	−	6.31536i	0.134218	−	0.232472i
$739$	20.7632			0.763786			0.381893	−	0.924207i	$-0.375272\pi$
$739$	20.7632			0.763786			0.381893	+	0.924207i	$0.375272\pi$
$740$	−21.5656	−	13.3655i	−0.792769	−	0.491325i
$741$	−4.40723			−0.161904
$742$	1.72312	−	2.98452i	0.0632576	−	0.109565i
$743$	4.93760	−	18.4274i	0.181143	−	0.676035i	−0.814280	−	0.580472i	$-0.802868\pi$
$743$	4.93760	−	18.4274i	0.181143	−	0.676035i	0.995423	−	0.0955632i	$-0.0304652\pi$
$744$	−0.767829	−	1.32992i	−0.0281500	−	0.0487572i
$745$	−34.6700	−	20.5320i	−1.27021	−	0.752236i
$746$	−5.11631	−	5.11631i	−0.187322	−	0.187322i
$747$	−10.4314	+	38.9306i	−0.381665	+	1.42439i
$748$	−48.0002			−1.75506
$749$	16.8628	+	9.73574i	0.616153	+	0.355736i
$750$	0.535658	+	0.572493i	0.0195595	+	0.0209045i
$751$		−	32.9736i		−	1.20322i	−0.798788	−	0.601612i	$-0.794525\pi$
$751$		−	32.9736i		−	1.20322i	0.798788	−	0.601612i	$-0.205475\pi$
$752$	8.57503	−	2.29767i	0.312699	−	0.0837875i
$753$	0.0542752	+	0.0940075i	0.00197790	+	0.00342582i
$754$	−2.50808	−	2.50808i	−0.0913390	−	0.0913390i
$755$	−0.00792954	+	0.715903i	−0.000288586	+	0.0260544i
$756$	−2.10064	+	3.63842i	−0.0763996	+	0.132328i
$757$	−44.1108	−	25.4674i	−1.60323	−	0.925628i	−0.990835	−	0.135079i	$-0.956871\pi$
$757$	−44.1108	−	25.4674i	−1.60323	−	0.925628i	−0.612399	−	0.790549i	$-0.709795\pi$
$758$	3.47978	−	2.00905i	0.126391	−	0.0729720i
$759$	−0.839398	−	0.224916i	−0.0304682	−	0.00816393i
$760$	16.8794	−	16.5096i	0.612280	−	0.598865i
$761$	3.27486	+	1.89074i	0.118714	+	0.0685394i	0.558181	−	0.829719i	$-0.311499\pi$
$761$	3.27486	+	1.89074i	0.118714	+	0.0685394i	−0.439467	+	0.898259i	$0.644833\pi$
$762$	0.242900	+	0.140238i	0.00879934	+	0.00508030i
$763$	31.2367			1.13084
$764$	−4.61600	+	17.2272i	−0.167001	+	0.623257i
$765$	49.3890	+	0.547046i	1.78566	+	0.0197785i
$766$	−6.24883			−0.225779
$767$	−11.6698	+	11.6698i	−0.421371	+	0.421371i
$768$	1.15959	−	0.310710i	0.0418430	−	0.0112118i
$769$	1.69910	+	1.69910i	0.0612712	+	0.0612712i	0.737078	−	0.675807i	$-0.236205\pi$
$769$	1.69910	+	1.69910i	0.0612712	+	0.0612712i	−0.675807	+	0.737078i	$0.736205\pi$
$770$	1.38898	+	5.42330i	0.0500553	+	0.195442i
$771$	−2.21079	+	2.21079i	−0.0796197	+	0.0796197i
$772$	−0.922066	−	1.59706i	−0.0331859	−	0.0574796i
$773$	29.0946	+	7.79586i	1.04646	+	0.280398i	0.740787	−	0.671740i	$-0.234453\pi$
$773$	29.0946	+	7.79586i	1.04646	+	0.280398i	0.305671	+	0.952137i	$0.401119\pi$
$774$	11.8526	−	6.84312i	0.426034	−	0.245971i
$775$	−27.1931	−	7.93595i	−0.976805	−	0.285068i
$776$		−	6.17834i		−	0.221789i
$777$	−1.10835	−	2.01228i	−0.0397619	−	0.0721901i
$778$	3.34654	−	3.34654i	0.119979	−	0.119979i
$779$	48.2217	−	12.9210i	1.72772	−	0.462941i
$780$	2.39209	−	0.612646i	0.0856507	−	0.0219362i
$781$	−13.9453	+	8.05131i	−0.499001	+	0.288099i
$782$	−3.11997	+	1.80131i	−0.111570	+	0.0644148i
$783$	3.55593			0.127079
$784$	−8.60219	+	4.96648i	−0.307221	+	0.177374i
$785$	−0.710790	+	2.53984i	−0.0253692	+	0.0906509i
$786$	0.124487	−	0.215618i	0.00444030	−	0.00769082i
$787$	−15.3527	−	15.3527i	−0.547265	−	0.547265i	0.378384	−	0.925649i	$-0.376480\pi$
$787$	−15.3527	−	15.3527i	−0.547265	−	0.547265i	−0.925649	+	0.378384i	$0.876480\pi$
$788$	10.8146	+	10.8146i	0.385255	+	0.385255i
$789$	−2.94052	−	1.69771i	−0.104685	−	0.0604402i
$790$	−1.77500	−	6.93054i	−0.0631516	−	0.246577i
$791$	−8.72149	+	8.72149i	−0.310101	+	0.310101i
$792$	7.25568	−	12.5672i	0.257819	−	0.446556i
$793$	−7.79257	−	29.0823i	−0.276722	−	1.03274i
$794$	−2.92363	−	10.9111i	−0.103756	−	0.387221i
$795$	1.03473	−	1.74723i	0.0366983	−	0.0619679i
$796$	0.212381	−	0.792617i	0.00752765	−	0.0280936i
$797$	−18.7203	+	32.4245i	−0.663106	+	1.14853i	0.316689	+	0.948529i	$0.397429\pi$
$797$	−18.7203	+	32.4245i	−0.663106	+	1.14853i	−0.979795	+	0.200004i	$0.935904\pi$
$798$	0.996568	−	0.267030i	0.0352781	−	0.00945274i
$799$	−5.33484	−	19.9099i	−0.188733	−	0.704362i
$800$	−10.4195	+	17.1578i	−0.368384	+	0.606619i
$801$	43.8326	+	11.7449i	1.54875	+	0.414986i
$802$	−0.0818019	−	0.305289i	−0.00288853	−	0.0107801i
$803$	22.2232	−	22.2232i	0.784241	−	0.784241i
$804$	−1.76324			−0.0621845
$805$	−4.07014	−	4.16131i	−0.143454	−	0.146667i
$806$	4.55397	−	4.55397i	0.160407	−	0.160407i
$807$	−4.29104	−	1.14978i	−0.151052	−	0.0404742i
$808$		−	0.270993i		−	0.00953349i
$809$	−11.2061	+	41.8217i	−0.393985	+	1.47037i	0.429517	+	0.903059i	$0.358684\pi$
$809$	−11.2061	+	41.8217i	−0.393985	+	1.47037i	−0.823502	+	0.567313i	$0.807983\pi$
$810$	−3.62608	+	6.12292i	−0.127407	+	0.215138i
$811$	6.94395	+	12.0273i	0.243835	+	0.422335i	0.961803	−	0.273741i	$-0.0882611\pi$
$811$	6.94395	+	12.0273i	0.243835	+	0.422335i	−0.717968	+	0.696076i	$0.754928\pi$
$812$	−9.96178	−	5.75144i	−0.349590	−	0.201836i
$813$	−2.29947	−	2.29947i	−0.0806459	−	0.0806459i
$814$	3.71769	+	6.74969i	0.130305	+	0.236577i
$815$	17.9188	−	10.0825i	0.627669	−	0.353174i
$816$	−1.18349	−	4.41686i	−0.0414306	−	0.154621i
$817$	90.5021	+	24.2500i	3.16627	+	0.848399i
$818$	2.73285	−	10.1991i	0.0955520	−	0.356605i
$819$	−17.5254	−	4.69591i	−0.612386	−	0.164088i
$820$	−24.3769	+	13.7163i	−0.851280	+	0.478994i
$821$	−5.62408	−	9.74120i	−0.196282	−	0.339970i	0.751038	−	0.660259i	$-0.229553\pi$
$821$	−5.62408	−	9.74120i	−0.196282	−	0.339970i	−0.947320	+	0.320289i	$0.896220\pi$
$822$			0.160694i			0.00560485i
$823$	8.48178	+	31.6544i	0.295656	+	1.10340i	0.940695	+	0.339254i	$0.110175\pi$
$823$	8.48178	+	31.6544i	0.295656	+	1.10340i	−0.645038	+	0.764150i	$0.723159\pi$
$824$			2.99317i			0.104272i
$825$	0.782991	+	3.20447i	0.0272602	+	0.111565i
$826$	1.93172	−	3.34584i	0.0672132	−	0.116417i
$827$	28.5291	−	16.4713i	0.992054	−	0.572763i	0.0861665	−	0.996281i	$-0.472538\pi$
$827$	28.5291	−	16.4713i	0.992054	−	0.572763i	0.905888	+	0.423518i	$0.139205\pi$
$828$			7.28128i			0.253042i
$829$	−4.10251	+	1.09926i	−0.142486	+	0.0381790i	−0.329357	−	0.944205i	$-0.606832\pi$
$829$	−4.10251	+	1.09926i	−0.142486	+	0.0381790i	0.186871	+	0.982384i	$0.440165\pi$
$830$	−7.97767	+	7.80288i	−0.276909	+	0.270842i
$831$	−0.286524	+	0.0767738i	−0.00993940	+	0.00266325i
$832$	7.66299	+	13.2727i	0.265666	+	0.460148i
$833$	11.5314	+	19.9730i	0.399539	+	0.692023i
$834$	−0.430854	+	0.115447i	−0.0149193	+	0.00399761i
$835$	−0.538566	+	48.6233i	−0.0186378	+	1.68268i
$836$	46.3079	−	12.4082i	1.60159	−	0.429145i
$837$			6.45657i			0.223172i
$838$	0.690843	−	0.398859i	0.0238648	−	0.0137783i
$839$	1.39115	−	2.40954i	0.0480278	−	0.0831865i	−0.841012	−	0.541016i	$-0.818040\pi$
$839$	1.39115	−	2.40954i	0.0480278	−	0.0831865i	0.889040	+	0.457830i	$0.151373\pi$
$840$	−1.04393	+	0.587395i	−0.0360191	+	0.0202671i
$841$		−	19.2641i		−	0.664278i
$842$	2.20076	+	8.21333i	0.0758431	+	0.283050i
$843$			1.90343i			0.0655575i
$844$	1.12894	+	1.95538i	0.0388598	+	0.0673071i
$845$	−3.73162	−	6.63193i	−0.128372	−	0.228145i
$846$	2.90473	+	0.778320i	0.0998667	+	0.0267592i
$847$	−0.469899	+	1.75369i	−0.0161459	+	0.0602574i
$848$	14.7354	+	3.94835i	0.506017	+	0.135587i
$849$	1.22835	+	4.58425i	0.0421567	+	0.157331i
$850$	11.6890	+	7.09840i	0.400929	+	0.243473i
$851$	−6.85658	−	4.14502i	−0.235040	−	0.142089i
$852$	−1.17569	−	1.17569i	−0.0402785	−	0.0402785i
$853$	−18.5940	−	10.7353i	−0.636648	−	0.367569i	0.146674	−	0.989185i	$-0.453143\pi$
$853$	−18.5940	−	10.7353i	−0.636648	−	0.367569i	−0.783322	+	0.621616i	$0.786476\pi$
$854$	3.52413	+	6.10397i	0.120593	+	0.208874i
$855$	−47.7890	+	12.2394i	−1.63435	+	0.418578i
$856$	3.61685	−	13.4983i	0.123621	−	0.461362i
$857$		−	19.7692i		−	0.675302i	−0.941271	−	0.337651i	$-0.890368\pi$
$857$		−	19.7692i		−	0.675302i	0.941271	−	0.337651i	$-0.109632\pi$
$858$	−0.724420	−	0.194108i	−0.0247313	−	0.00662673i
$859$	−14.4663	+	14.4663i	−0.493582	+	0.493582i	−0.909433	−	0.415851i	$-0.863484\pi$
$859$	−14.4663	+	14.4663i	−0.493582	+	0.493582i	0.415851	+	0.909433i	$0.363484\pi$
$860$	−52.4924	−	0.581421i	−1.78998	−	0.0198263i
$861$	−2.53270			−0.0863141
$862$	1.62833	−	1.62833i	0.0554610	−	0.0554610i
$863$	13.9291	+	51.9841i	0.474152	+	1.76956i	0.624603	+	0.780943i	$0.285261\pi$
$863$	13.9291	+	51.9841i	0.474152	+	1.76956i	−0.150450	+	0.988618i	$0.548072\pi$
$864$	4.41943	+	1.18418i	0.150352	+	0.0402867i
$865$	2.08827	−	7.46195i	0.0710034	−	0.253714i
$866$	−1.68355	−	6.28310i	−0.0572094	−	0.213509i
$867$	−7.11724	+	1.90706i	−0.241714	+	0.0647672i
$868$	10.4430	−	18.0878i	0.354458	−	0.613939i
$869$	7.79082	−	29.0758i	0.264286	−	0.986327i
$870$	0.420979	+	0.249309i	0.0142725	+	0.00845238i
$871$	−3.96594	−	14.8011i	−0.134381	−	0.501515i
$872$	−5.80225	−	21.6543i	−0.196489	−	0.733307i
$873$	−6.45432	+	11.1792i	−0.218446	+	0.378359i
$874$	2.54432	−	2.54432i	0.0860629	−	0.0860629i
$875$	−6.42474	+	21.1413i	−0.217196	+	0.714705i
$876$	2.81038	+	1.62257i	0.0949538	+	0.0548216i
$877$	12.5701	+	12.5701i	0.424462	+	0.424462i	0.886737	−	0.462275i	$-0.152967\pi$
$877$	12.5701	+	12.5701i	0.424462	+	0.424462i	−0.462275	+	0.886737i	$0.652967\pi$
$878$	7.07451	+	7.07451i	0.238753	+	0.238753i
$879$	0.633372	−	1.09703i	0.0213631	−	0.0370020i
$880$	−21.5977	+	12.1525i	−0.728057	+	0.409660i
$881$	45.1002	−	26.0386i	1.51946	−	0.877263i	0.519727	−	0.854333i	$-0.326034\pi$
$881$	45.1002	−	26.0386i	1.51946	−	0.877263i	0.999737	−	0.0229301i	$-0.00729951\pi$
$882$	−3.36472			−0.113296
$883$	−27.5003	+	15.8773i	−0.925459	+	0.534314i	−0.885372	−	0.464882i	$-0.846097\pi$
$883$	−27.5003	+	15.8773i	−0.925459	+	0.534314i	−0.0400864	+	0.999196i	$0.512763\pi$
$884$	37.3013	−	21.5359i	1.25458	−	0.724332i
$885$	1.16000	−	1.95876i	0.0389931	−	0.0658430i
$886$	7.04744	−	1.88835i	0.236763	−	0.0634405i
$887$	−8.37990	+	8.37990i	−0.281370	+	0.281370i	−0.833655	−	0.552285i	$-0.813756\pi$
$887$	−8.37990	+	8.37990i	−0.281370	+	0.281370i	0.552285	+	0.833655i	$0.313756\pi$
$888$	−1.18910	+	1.14213i	−0.0399036	+	0.0383273i
$889$			7.90470i			0.265115i
$890$	8.78540	+	8.98219i	0.294487	+	0.301084i
$891$	−25.9296	+	14.9705i	−0.868675	+	0.501530i
$892$	35.3363	+	9.46833i	1.18315	+	0.317023i
$893$	10.2935	+	17.8289i	0.344459	+	0.596620i
$894$	−0.893520	+	0.893520i	−0.0298838	+	0.0298838i
$895$	32.2700	−	8.26475i	1.07867	−	0.276260i
$896$	−13.7579	−	13.7579i	−0.459620	−	0.459620i
$897$	0.753214	−	0.201823i	0.0251491	−	0.00673868i
$898$	3.44654	−	3.44654i	0.115013	−	0.115013i
$899$	−17.6777			−0.589585
$900$	24.2369	−	13.2862i	0.807895	−	0.442874i
$901$	9.16745	−	34.2134i	0.305412	−	1.13981i
$902$	8.49531			0.282863
$903$	−4.11652	−	2.37668i	−0.136989	−	0.0790908i
$904$	7.66605	+	4.42600i	0.254969	+	0.147207i
$905$	−0.212501	−	0.00235372i	−0.00706376	−	7.82402e-5i
$906$	0.0216874	+	0.00581113i	0.000720517	+	0.000193062i
$907$	42.9187	−	24.7791i	1.42509	−	0.822777i	0.428364	−	0.903606i	$-0.359090\pi$
$907$	42.9187	−	24.7791i	1.42509	−	0.822777i	0.996728	+	0.0808295i	$0.0257569\pi$
$908$	32.3255	+	18.6631i	1.07276	+	0.619358i
$909$	−0.283098	+	0.490340i	−0.00938977	+	0.0162636i
$910$	−3.51262	−	3.59131i	−0.116442	−	0.119051i
$911$	−31.0017	−	31.0017i	−1.02713	−	1.02713i	−0.999621	−	0.0275118i	$-0.991242\pi$
$911$	−31.0017	−	31.0017i	−1.02713	−	1.02713i	−0.0275118	−	0.999621i	$-0.508758\pi$
$912$	2.28353	+	3.95520i	0.0756154	+	0.130970i
$913$	−45.3526	+	12.1522i	−1.50095	+	0.402179i
$914$			5.52969i			0.182906i
$915$	2.03658	+	3.61945i	0.0673272	+	0.119655i
$916$	5.95913	+	3.44051i	0.196895	+	0.113678i
$917$	7.01685			0.231717
$918$	0.806741	−	3.01080i	0.0266264	−	0.0993712i
$919$	−25.3860	−	25.3860i	−0.837407	−	0.837407i	0.151110	−	0.988517i	$-0.451715\pi$
$919$	−25.3860	−	25.3860i	−0.837407	−	0.837407i	−0.988517	+	0.151110i	$0.951715\pi$
$920$	−2.12873	+	3.59452i	−0.0701820	+	0.118508i
$921$	1.27474	+	2.20791i	0.0420041	+	0.0727532i
$922$	−1.23474	+	4.60811i	−0.0406639	+	0.151760i
$923$	7.22466	−	12.5135i	0.237802	−	0.411886i
$924$	−2.43218			−0.0800129
$925$	−1.28607	+	30.3866i	−0.0422856	+	0.999106i
$926$	−10.2598			−0.337158
$927$	3.12688	−	5.41591i	0.102700	−	0.177882i
$928$	−3.24222	+	12.1001i	−0.106431	+	0.397207i
$929$	−9.74401	−	16.8771i	−0.319691	−	0.553720i	0.660733	−	0.750621i	$-0.270246\pi$
$929$	−9.74401	−	16.8771i	−0.319691	−	0.553720i	−0.980423	+	0.196901i	$0.936912\pi$
$930$	−0.452676	+	0.764379i	−0.0148438	+	0.0250650i
$931$	−16.2879	−	16.2879i	−0.533814	−	0.533814i
$932$	−6.56595	+	24.5044i	−0.215075	+	0.802670i
$933$	1.50626			0.0493127
$934$	0.413532	+	0.238753i	0.0135312	+	0.00781223i
$935$	28.2162	+	50.1465i	0.922769	+	1.63997i
$936$			13.0214i			0.425619i
$937$	41.8686	−	11.2187i	1.36779	−	0.366498i	0.501118	−	0.865379i	$-0.332922\pi$
$937$	41.8686	−	11.2187i	1.36779	−	0.366498i	0.866670	+	0.498881i	$0.166256\pi$
$938$	1.79356	+	3.10654i	0.0585619	+	0.101432i
$939$	−0.310977	−	0.310977i	−0.0101483	−	0.0101483i
$940$	−8.06533	−	8.24600i	−0.263062	−	0.268955i
$941$	−1.14543	+	1.98394i	−0.0373398	+	0.0646745i	−0.884091	−	0.467314i	$-0.845222\pi$
$941$	−1.14543	+	1.98394i	−0.0373398	+	0.0646745i	0.846752	+	0.531989i	$0.178555\pi$
$942$	0.0716300	+	0.0413556i	0.00233383	+	0.00134744i
$943$	−7.64958	+	4.41649i	−0.249105	+	0.143821i
$944$	16.5194	+	4.42635i	0.537659	+	0.144065i
$945$	5.03593	+	0.0557794i	0.163819	+	0.00181450i
$946$	13.8078	+	7.97197i	0.448932	+	0.259191i
$947$	−52.1263	−	30.0952i	−1.69388	−	0.977961i	−0.951333	−	0.308165i	$-0.900285\pi$
$947$	−52.1263	−	30.0952i	−1.69388	−	0.977961i	−0.742545	−	0.669796i	$-0.766382\pi$
$948$	3.10813			0.100947
$949$	−7.29910	+	27.2406i	−0.236939	+	0.884268i
$950$	−13.1118	−	3.82651i	−0.425403	−	0.124148i
$951$	1.55262			0.0503471
$952$	−14.7742	+	14.7742i	−0.478835	+	0.478835i
$953$	16.8063	−	4.50324i	0.544410	−	0.145874i	0.0238757	−	0.999715i	$-0.492399\pi$
$953$	16.8063	−	4.50324i	0.544410	−	0.145874i	0.520534	+	0.853841i	$0.325733\pi$
$954$	3.65405	+	3.65405i	0.118304	+	0.118304i
$955$	20.7109	−	5.30432i	0.670189	−	0.171644i
$956$	17.9386	−	17.9386i	0.580177	−	0.580177i
$957$	1.02929	+	1.78278i	0.0332722	+	0.0576291i
$958$	1.37487	+	0.368395i	0.0444201	+	0.0119023i
$959$	−3.92210	+	2.26443i	−0.126651	+	0.0731221i
$960$	−1.47821	−	1.51132i	−0.0477089	−	0.0487776i
$961$		−	1.09774i		−	0.0354111i
$962$	−5.91738	−	3.57725i	−0.190784	−	0.115335i
$963$	−20.6457	+	20.6457i	−0.665297	+	0.665297i
$964$	42.5383	−	11.3981i	1.37007	−	0.367108i
$965$	−1.12645	+	1.90210i	−0.0362618	+	0.0612309i
$966$	−0.158089	+	0.0912729i	−0.00508644	+	0.00293666i
$967$	41.2531	−	23.8175i	1.32661	−	0.765918i	0.341836	−	0.939760i	$-0.388951\pi$
$967$	41.2531	−	23.8175i	1.32661	−	0.765918i	0.984774	+	0.173841i	$0.0556180\pi$
$968$	1.30300			0.0418799
$969$	9.18337	−	5.30202i	0.295012	−	0.170325i
$970$	−3.11487	+	1.75266i	−0.100013	+	0.0562746i
$971$	17.9256	−	31.0481i	0.575261	−	0.996382i	−0.420752	−	0.907176i	$-0.638234\pi$
$971$	17.9256	−	31.0481i	0.575261	−	0.996382i	0.996013	−	0.0892060i	$-0.0284329\pi$
$972$	−6.69559	−	6.69559i	−0.214761	−	0.214761i
$973$	−8.88915	−	8.88915i	−0.284973	−	0.284973i
$974$	−5.62597	−	3.24815i	−0.180268	−	0.104078i
$975$	−2.04620	−	2.13892i	−0.0655307	−	0.0685002i
$976$	−22.0618	+	22.0618i	−0.706182	+	0.706182i
$977$	−9.90840	+	17.1619i	−0.316998	+	0.549056i	−0.979860	−	0.199685i	$-0.936008\pi$
$977$	−9.90840	+	17.1619i	−0.316998	+	0.549056i	0.662862	+	0.748741i	$0.269341\pi$
$978$	−0.166885	−	0.622823i	−0.00533639	−	0.0199157i
$979$	13.6824	+	51.0633i	0.437290	+	1.63199i
$980$	11.1047	+	6.57634i	0.354726	+	0.210073i
$981$	−12.1229	+	45.2432i	−0.387054	+	1.44450i
$982$	−5.15838	+	8.93458i	−0.164611	+	0.285114i
$983$	48.9652	−	13.1202i	1.56175	−	0.418469i	0.628532	−	0.777784i	$-0.283656\pi$
$983$	48.9652	−	13.1202i	1.56175	−	0.418469i	0.933216	+	0.359315i	$0.116990\pi$
$984$	0.470452	+	1.75575i	0.0149975	+	0.0559713i
$985$	4.94097	−	17.6554i	0.157432	−	0.562548i
$986$	8.24339	+	2.20881i	0.262523	+	0.0703429i
$987$	−0.270318	−	1.00884i	−0.00860430	−	0.0321117i
$988$	−30.4191	+	30.4191i	−0.967761	+	0.967761i
$989$	−16.5777			−0.527139
$990$	−8.39417	−	0.0929762i	−0.266784	−	0.00295498i
$991$	24.1350	−	24.1350i	0.766673	−	0.766673i	−0.210846	−	0.977519i	$-0.567622\pi$
$991$	24.1350	−	24.1350i	0.766673	−	0.766673i	0.977519	+	0.210846i	$0.0676220\pi$
$992$	−21.9705	−	5.88697i	−0.697563	−	0.186911i
$993$		−	4.67234i		−	0.148272i
$994$	−0.875468	+	3.26729i	−0.0277682	+	0.103632i
$995$	−0.952902	+	0.244051i	−0.0302090	+	0.00773692i
$996$	−2.42404	−	4.19856i	−0.0768086	−	0.133036i
$997$	−45.2668	−	26.1348i	−1.43361	−	0.827697i	−0.436219	−	0.899840i	$-0.643683\pi$
$997$	−45.2668	−	26.1348i	−1.43361	−	0.827697i	−0.997394	+	0.0721432i	$0.977016\pi$
$998$	−7.97980	−	7.97980i	−0.252596	−	0.252596i
$999$	6.73069	−	1.65891i	0.212950	−	0.0524855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.97.8	✓	68
5.2	odd	4		925.2.y.b.393.8		68
5.3	odd	4		185.2.u.a.23.10	yes	68
5.4	even	2		925.2.t.b.282.10		68
37.29	odd	12		185.2.u.a.177.10	yes	68
185.29	odd	12		925.2.y.b.732.8		68
185.103	even	12	inner	185.2.p.a.103.8	yes	68
185.177	even	12		925.2.t.b.843.10		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.8	✓	68	1.1	even	1	trivial
185.2.p.a.103.8	yes	68	185.103	even	12	inner
185.2.u.a.23.10	yes	68	5.3	odd	4
185.2.u.a.177.10	yes	68	37.29	odd	12
925.2.t.b.282.10		68	5.4	even	2
925.2.t.b.843.10		68	185.177	even	12
925.2.y.b.393.8		68	5.2	odd	4
925.2.y.b.732.8		68	185.29	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.183474 + 0.317786i) q^{2} +(-0.0494608 + 0.184590i) q^{3} +(0.932675 + 1.61544i) q^{4} +(1.13941 - 1.92399i) q^{5} +(-0.0495854 - 0.0495854i) q^{6} +(0.511509 - 1.90898i) q^{7} -1.41838 q^{8} +(2.56645 + 1.48174i) q^{9} +(0.402364 + 0.715091i) q^{10} +3.45234i q^{11} +(-0.344325 + 0.0922616i) q^{12} +(-1.54894 - 2.68284i) q^{13} +(0.512798 + 0.512798i) q^{14} +(0.298793 + 0.305486i) q^{15} +(-1.60511 + 2.78014i) q^{16} +(6.45506 + 3.72683i) q^{17} +(-0.941752 + 0.543721i) q^{18} +(-7.19086 - 1.92679i) q^{19} +(4.17079 + 0.0461969i) q^{20} +(0.327079 + 0.188839i) q^{21} +(-1.09710 - 0.633414i) q^{22} +1.31718 q^{23} +(0.0701542 - 0.261819i) q^{24} +(-2.40348 - 4.38444i) q^{25} +1.13676 q^{26} +(-0.805841 + 0.805841i) q^{27} +(3.56091 - 0.954144i) q^{28} +(-2.20635 - 2.20635i) q^{29} +(-0.151900 + 0.0389035i) q^{30} +(4.00610 - 4.00610i) q^{31} +(-2.00737 - 3.47687i) q^{32} +(-0.637268 - 0.170755i) q^{33} +(-2.36867 + 1.36755i) q^{34} +(-3.09004 - 3.15925i) q^{35} +5.52793i q^{36} +(-5.20549 - 3.14689i) q^{37} +(1.93164 - 1.93164i) q^{38} +(0.571837 - 0.153223i) q^{39} +(-1.61612 + 2.72895i) q^{40} +(-5.80754 + 3.35298i) q^{41} +(-0.120021 + 0.0692941i) q^{42} -12.5857 q^{43} +(-5.57705 + 3.21991i) q^{44} +(5.77510 - 3.24951i) q^{45} +(-0.241668 + 0.418582i) q^{46} +(-1.95542 - 1.95542i) q^{47} +(-0.433796 - 0.433796i) q^{48} +(2.67962 + 1.54708i) q^{49} +(1.83429 + 0.0406392i) q^{50} +(-1.00721 + 1.00721i) q^{51} +(2.88931 - 5.00443i) q^{52} +(-1.22993 - 4.59015i) q^{53} +(-0.108234 - 0.403936i) q^{54} +(6.64227 + 3.93364i) q^{55} +(-0.725515 + 2.70766i) q^{56} +(0.711331 - 1.23206i) q^{57} +(1.10595 - 0.296339i) q^{58} +(-1.37883 - 5.14585i) q^{59} +(-0.214818 + 0.767602i) q^{60} +(9.38781 + 2.51546i) q^{61} +(0.538068 + 2.00810i) q^{62} +(4.14137 - 4.14137i) q^{63} -4.94725 q^{64} +(-6.92664 - 0.0767214i) q^{65} +(0.171186 - 0.171186i) q^{66} +(4.77781 + 1.28021i) q^{67} +13.9037i q^{68} +(-0.0651488 + 0.243139i) q^{69} +(1.57091 - 0.402329i) q^{70} +(2.33213 + 4.03937i) q^{71} +(-3.64020 - 2.10167i) q^{72} +(-6.43715 - 6.43715i) q^{73} +(1.95511 - 1.07686i) q^{74} +(0.928202 - 0.226800i) q^{75} +(-3.59413 - 13.4135i) q^{76} +(6.59044 + 1.76590i) q^{77} +(-0.0562249 + 0.209834i) q^{78} +(-8.42204 - 2.25668i) q^{79} +(3.52007 + 6.25595i) q^{80} +(4.33633 + 7.51074i) q^{81} -2.46074i q^{82} +(3.51999 + 13.1368i) q^{83} +0.704502i q^{84} +(14.5254 - 8.17307i) q^{85} +(2.30915 - 3.99956i) q^{86} +(0.516397 - 0.298142i) q^{87} -4.89673i q^{88} +(14.7909 - 3.96321i) q^{89} +(-0.0269314 + 2.43144i) q^{90} +(-5.91378 + 1.58459i) q^{91} +(1.22850 + 2.12783i) q^{92} +(0.541342 + 0.937632i) q^{93} +(0.980175 - 0.262637i) q^{94} +(-11.9005 + 11.6397i) q^{95} +(0.741082 - 0.198572i) q^{96} +4.35591i q^{97} +(-0.983280 + 0.567697i) q^{98} +(-5.11547 + 8.86025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100}) \) 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more