LMFDB - Embedded newform 213.2.l.a.23.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [213,2,Mod(23,213)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(213, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("213.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 213 = 3 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	213.l (of order $14$, degree $6$, 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:	$1.70081356305$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	213.23
Dual form			213.2.l.a.176.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.74810 + 1.39407i) q^{2} +(1.11251 + 1.32753i) q^{3} +(0.667405 - 2.92409i) q^{4} +3.11868i q^{5} +(-3.79544 - 0.769744i) q^{6} +(-0.583477 - 0.465307i) q^{7} +(0.969434 + 2.01305i) q^{8} +(-0.524652 + 2.95377i) q^{9} +(-4.34764 - 5.45177i) q^{10} +(0.989742 + 0.476634i) q^{11} +(4.62430 - 2.36708i) q^{12} +(0.661360 + 1.37333i) q^{13} +1.66865 q^{14} +(-4.14012 + 3.46955i) q^{15} +(0.903532 + 0.435118i) q^{16} -4.02082 q^{17} +(-3.20060 - 5.89489i) q^{18} +(-0.268615 - 1.17688i) q^{19} +(9.11929 + 2.08142i) q^{20} +(-0.0314150 - 1.29224i) q^{21} +(-2.39463 + 0.546559i) q^{22} +(4.50361 - 5.64734i) q^{23} +(-1.59387 + 3.52649i) q^{24} -4.72614 q^{25} +(-3.07064 - 1.47874i) q^{26} +(-4.50488 + 2.58960i) q^{27} +(-1.75002 + 1.39559i) q^{28} +(-7.71970 - 1.76197i) q^{29} +(2.40058 - 11.8367i) q^{30} +(-0.942357 - 1.95682i) q^{31} +(-6.54265 + 1.49332i) q^{32} +(0.468351 + 1.84417i) q^{33} +(7.02882 - 5.60530i) q^{34} +(1.45114 - 1.81968i) q^{35} +(8.28693 + 3.50549i) q^{36} +(5.68251 + 7.12564i) q^{37} +(2.11022 + 1.68284i) q^{38} +(-1.08736 + 2.40581i) q^{39} +(-6.27806 + 3.02335i) q^{40} +(10.0782 - 4.85341i) q^{41} +(1.85638 + 2.21517i) q^{42} +(6.38361 + 8.00479i) q^{43} +(2.05428 - 2.57599i) q^{44} +(-9.21184 - 1.63622i) q^{45} +16.1505i q^{46} +(1.66069 + 7.27597i) q^{47} +(0.427556 + 1.68353i) q^{48} +(-1.43371 - 6.28150i) q^{49} +(8.26179 - 6.58856i) q^{50} +(-4.47320 - 5.33775i) q^{51} +(4.45713 - 1.01731i) q^{52} +(2.61274 + 11.4472i) q^{53} +(4.26493 - 10.8070i) q^{54} +(-1.48647 + 3.08668i) q^{55} +(0.371045 - 1.62565i) q^{56} +(1.26350 - 1.66588i) q^{57} +(15.9511 - 7.68167i) q^{58} +(3.98872 + 1.92086i) q^{59} +(7.38215 + 14.4217i) q^{60} +(-1.55092 + 1.23682i) q^{61} +(4.37528 + 2.10702i) q^{62} +(1.68053 - 1.47933i) q^{63} +(8.10492 - 10.1633i) q^{64} +(-4.28297 + 2.06257i) q^{65} +(-3.38962 - 2.57088i) q^{66} +(-0.366683 - 0.0836929i) q^{67} +(-2.68352 + 11.7573i) q^{68} +(12.5073 - 0.304059i) q^{69} +5.20397i q^{70} +(7.44224 - 3.95133i) q^{71} +(-6.45470 + 1.80733i) q^{72} +(-1.25106 - 1.56878i) q^{73} +(-19.8672 - 4.53456i) q^{74} +(-5.25787 - 6.27408i) q^{75} -3.62058 q^{76} +(-0.355710 - 0.738639i) q^{77} +(-1.45304 - 5.72146i) q^{78} +(1.53996 - 0.741603i) q^{79} +(-1.35699 + 2.81782i) q^{80} +(-8.44948 - 3.09940i) q^{81} +(-10.8518 + 22.5340i) q^{82} +(-3.58377 + 7.44178i) q^{83} +(-3.79959 - 0.770586i) q^{84} -12.5397i q^{85} +(-22.3184 - 5.09403i) q^{86} +(-6.24917 - 12.2083i) q^{87} +2.45447i q^{88} +(10.3399 - 2.36001i) q^{89} +(18.3843 - 9.98164i) q^{90} +(0.253131 - 1.10904i) q^{91} +(-13.5076 - 16.9380i) q^{92} +(1.54936 - 3.42799i) q^{93} +(-13.0462 - 10.4040i) q^{94} +(3.67031 - 0.837724i) q^{95} +(-9.26117 - 7.02421i) q^{96} +(1.55893 - 3.23715i) q^{97} +(11.2631 + 8.98203i) q^{98} +(-1.92714 + 2.67340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 10 q^{3} + 10 q^{4} - 15 q^{6} - 14 q^{7} - 14 q^{9} + 2 q^{10} + 20 q^{12} - 14 q^{13} + 22 q^{15} - 30 q^{16} + 8 q^{18} - 14 q^{19} - 28 q^{21} - 14 q^{22} + 8 q^{24} - 84 q^{25} - 7 q^{27} - 42 q^{28}+ \cdots + 49 q^{99}+O(q^{100}) $ 132 * q - 10 * q^3 + 10 * q^4 - 15 * q^6 - 14 * q^7 - 14 * q^9 + 2 * q^10 + 20 * q^12 - 14 * q^13 + 22 * q^15 - 30 * q^16 + 8 * q^18 - 14 * q^19 - 28 * q^21 - 14 * q^22 + 8 * q^24 - 84 * q^25 - 7 * q^27 - 42 * q^28 - 5 * q^30 + 14 * q^31 - 7 * q^33 - 42 * q^34 - 43 * q^36 + 22 * q^37 - 35 * q^39 + 64 * q^40 - 28 * q^42 + 16 * q^43 - 50 * q^45 + 55 * q^48 + 12 * q^49 - 98 * q^51 - 168 * q^52 - 38 * q^54 + 70 * q^55 + 48 * q^57 + 86 * q^58 + 116 * q^60 + 14 * q^61 + 105 * q^63 + 2 * q^64 - 42 * q^67 - 28 * q^69 + 266 * q^72 - 62 * q^73 + 18 * q^75 - 120 * q^76 + 21 * q^78 - 74 * q^79 - 22 * q^81 - 182 * q^82 + 42 * q^84 - 2 * q^87 + 15 * q^90 - 22 * q^91 + 14 * q^94 - 210 * q^96 - 42 * q^97 + 49 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/213\mathbb{Z}\right)^\times$.

$n$	$7$	$143$
$\chi(n)$	$e\left(\frac{3}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.74810	+	1.39407i	−1.23610	+	0.985754i	−0.236195	+	0.971706i	$0.575900\pi$
$2$	−1.74810	+	1.39407i	−1.23610	+	0.985754i	−0.999901	+	0.0140481i	$0.995528\pi$
$3$	1.11251	+	1.32753i	0.642307	+	0.766448i
$3$	1.11251	+	1.32753i	0.642307	+	0.766448i
$4$	0.667405	−	2.92409i	0.333702	−	1.46205i
$5$			3.11868i			1.39471i	0.716724	+	0.697357i	$0.245641\pi$
$5$			3.11868i			1.39471i	−0.716724	+	0.697357i	$0.754359\pi$
$6$	−3.79544	−	0.769744i	−1.54948	−	0.314247i
$7$	−0.583477	−	0.465307i	−0.220534	−	0.175870i	0.506991	−	0.861951i	$-0.330758\pi$
$7$	−0.583477	−	0.465307i	−0.220534	−	0.175870i	−0.727524	+	0.686082i	$0.759329\pi$
$8$	0.969434	+	2.01305i	0.342747	+	0.711721i
$9$	−0.524652	+	2.95377i	−0.174884	+	0.984589i
$10$	−4.34764	−	5.45177i	−1.37485	−	1.72400i
$11$	0.989742	+	0.476634i	0.298418	+	0.143711i	0.577102	−	0.816672i	$-0.304184\pi$
$11$	0.989742	+	0.476634i	0.298418	+	0.143711i	−0.278683	+	0.960383i	$0.589898\pi$
$12$	4.62430	−	2.36708i	1.33492	−	0.683316i
$13$	0.661360	+	1.37333i	0.183428	+	0.380893i	0.972325	−	0.233633i	$-0.0750615\pi$
$13$	0.661360	+	1.37333i	0.183428	+	0.380893i	−0.788896	+	0.614526i	$0.789347\pi$
$14$	1.66865			0.445965
$15$	−4.14012	+	3.46955i	−1.06898	+	0.895835i
$16$	0.903532	+	0.435118i	0.225883	+	0.108780i
$17$	−4.02082			−0.975193			−0.487597	−	0.873069i	$-0.662126\pi$
$17$	−4.02082			−0.975193			−0.487597	+	0.873069i	$0.662126\pi$
$18$	−3.20060	−	5.89489i	−0.754389	−	1.38944i
$19$	−0.268615	−	1.17688i	−0.0616246	−	0.269995i	0.934724	−	0.355375i	$-0.115647\pi$
$19$	−0.268615	−	1.17688i	−0.0616246	−	0.269995i	−0.996348	+	0.0853798i	$0.972790\pi$
$20$	9.11929	+	2.08142i	2.03914	+	0.465419i
$21$	−0.0314150	−	1.29224i	−0.00685533	−	0.281990i
$22$	−2.39463	+	0.546559i	−0.510537	+	0.116527i
$23$	4.50361	−	5.64734i	0.939067	−	1.17755i	−0.0448625	−	0.998993i	$-0.514285\pi$
$23$	4.50361	−	5.64734i	0.939067	−	1.17755i	0.983929	−	0.178559i	$-0.0571436\pi$
$24$	−1.59387	+	3.52649i	−0.325348	+	0.719841i
$25$	−4.72614			−0.945229
$26$	−3.07064	−	1.47874i	−0.602201	−	0.290005i
$27$	−4.50488	+	2.58960i	−0.866965	+	0.498369i
$28$	−1.75002	+	1.39559i	−0.330722	+	0.263742i
$29$	−7.71970	−	1.76197i	−1.43351	−	0.327190i	−0.565918	−	0.824462i	$-0.691478\pi$
$29$	−7.71970	−	1.76197i	−1.43351	−	0.327190i	−0.867595	+	0.497272i	$0.834335\pi$
$30$	2.40058	−	11.8367i	0.438284	−	2.16108i
$31$	−0.942357	−	1.95682i	−0.169252	−	0.351456i	0.799039	−	0.601279i	$-0.205342\pi$
$31$	−0.942357	−	1.95682i	−0.169252	−	0.351456i	−0.968292	+	0.249823i	$0.919628\pi$
$32$	−6.54265	+	1.49332i	−1.15659	+	0.263984i
$33$	0.468351	+	1.84417i	0.0815294	+	0.321028i
$34$	7.02882	−	5.60530i	1.20543	−	0.961300i
$35$	1.45114	−	1.81968i	0.245288	−	0.307581i
$36$	8.28693	+	3.50549i	1.38115	+	0.584248i
$37$	5.68251	+	7.12564i	0.934198	+	1.17145i	0.984968	+	0.172737i	$0.0552611\pi$
$37$	5.68251	+	7.12564i	0.934198	+	1.17145i	−0.0507698	+	0.998710i	$0.516167\pi$
$38$	2.11022	+	1.68284i	0.342323	+	0.272993i
$39$	−1.08736	+	2.40581i	−0.174117	+	0.385238i
$40$	−6.27806	+	3.02335i	−0.992648	+	0.478034i
$41$	10.0782	−	4.85341i	1.57395	−	0.757976i	0.575734	−	0.817637i	$-0.304716\pi$
$41$	10.0782	−	4.85341i	1.57395	−	0.757976i	0.998219	+	0.0596617i	$0.0190022\pi$
$42$	1.85638	+	2.21517i	0.286446	+	0.341809i
$43$	6.38361	+	8.00479i	0.973491	+	1.22072i	0.975337	+	0.220721i	$0.0708410\pi$
$43$	6.38361	+	8.00479i	0.973491	+	1.22072i	−0.00184600	+	0.999998i	$0.500588\pi$
$44$	2.05428	−	2.57599i	0.309694	−	0.388344i
$45$	−9.21184	−	1.63622i	−1.37322	−	0.243913i
$46$			16.1505i			2.38126i
$47$	1.66069	+	7.27597i	0.242237	+	1.06131i	0.938975	+	0.343984i	$0.111777\pi$
$47$	1.66069	+	7.27597i	0.242237	+	1.06131i	−0.696739	+	0.717325i	$0.745366\pi$
$48$	0.427556	+	1.68353i	0.0617124	+	0.242997i
$49$	−1.43371	−	6.28150i	−0.204816	−	0.897358i
$50$	8.26179	−	6.58856i	1.16839	−	0.931763i
$51$	−4.47320	−	5.33775i	−0.626373	−	0.747435i
$52$	4.45713	−	1.01731i	0.618093	−	0.141076i
$53$	2.61274	+	11.4472i	0.358888	+	1.57239i	0.755969	+	0.654608i	$0.227166\pi$
$53$	2.61274	+	11.4472i	0.358888	+	1.57239i	−0.397081	+	0.917784i	$0.629977\pi$
$54$	4.26493	−	10.8070i	0.580383	−	1.47065i
$55$	−1.48647	+	3.08668i	−0.200435	+	0.416208i
$56$	0.371045	−	1.62565i	0.0495830	−	0.217237i
$57$	1.26350	−	1.66588i	0.167355	−	0.220652i
$58$	15.9511	−	7.68167i	2.09449	−	1.00865i
$59$	3.98872	+	1.92086i	0.519287	+	0.250075i	0.675120	−	0.737708i	$-0.264092\pi$
$59$	3.98872	+	1.92086i	0.519287	+	0.250075i	−0.155833	+	0.987783i	$0.549806\pi$
$60$	7.38215	+	14.4217i	0.953031	+	1.86183i
$61$	−1.55092	+	1.23682i	−0.198575	+	0.158359i	−0.717729	−	0.696322i	$-0.754819\pi$
$61$	−1.55092	+	1.23682i	−0.198575	+	0.158359i	0.519154	+	0.854681i	$0.326247\pi$
$62$	4.37528	+	2.10702i	0.555661	+	0.267592i
$63$	1.68053	−	1.47933i	0.211727	−	0.186378i
$64$	8.10492	−	10.1633i	1.01312	−	1.27041i
$65$	−4.28297	+	2.06257i	−0.531237	+	0.255830i
$66$	−3.38962	−	2.57088i	−0.417233	−	0.316454i
$67$	−0.366683	−	0.0836929i	−0.0447974	−	0.0102247i	0.200063	−	0.979783i	$-0.435885\pi$
$67$	−0.366683	−	0.0836929i	−0.0447974	−	0.0102247i	−0.244861	+	0.969558i	$0.578742\pi$
$68$	−2.68352	+	11.7573i	−0.325424	+	1.42578i
$69$	12.5073	−	0.304059i	1.50570	−	0.0366044i
$70$			5.20397i			0.621994i
$71$	7.44224	−	3.95133i	0.883232	−	0.468937i
$71$	7.44224	−	3.95133i	0.883232	−	0.468937i
$72$	−6.45470	+	1.80733i	−0.760694	+	0.212996i
$73$	−1.25106	−	1.56878i	−0.146426	−	0.183612i	0.703210	−	0.710983i	$-0.251750\pi$
$73$	−1.25106	−	1.56878i	−0.146426	−	0.183612i	−0.849636	+	0.527370i	$0.823178\pi$
$74$	−19.8672	−	4.53456i	−2.30952	−	0.527132i
$75$	−5.25787	−	6.27408i	−0.607127	−	0.724468i
$76$	−3.62058			−0.415309
$77$	−0.355710	−	0.738639i	−0.0405369	−	0.0841758i
$78$	−1.45304	−	5.72146i	−0.164524	−	0.647828i
$79$	1.53996	−	0.741603i	0.173258	−	0.0834369i	−0.345244	−	0.938513i	$-0.612204\pi$
$79$	1.53996	−	0.741603i	0.173258	−	0.0834369i	0.518503	+	0.855076i	$0.326490\pi$
$80$	−1.35699	+	2.81782i	−0.151716	+	0.315042i
$81$	−8.44948	−	3.09940i	−0.938831	−	0.344378i
$82$	−10.8518	+	22.5340i	−1.19838	+	2.48846i
$83$	−3.58377	+	7.44178i	−0.393370	+	0.816841i	0.606395	+	0.795164i	$0.292615\pi$
$83$	−3.58377	+	7.44178i	−0.393370	+	0.816841i	−0.999765	+	0.0216776i	$0.993099\pi$
$84$	−3.79959	−	0.770586i	−0.414569	−	0.0840778i
$85$		−	12.5397i		−	1.36012i
$86$	−22.3184	−	5.09403i	−2.40666	−	0.549304i
$87$	−6.24917	−	12.2083i	−0.669981	−	1.30887i
$88$			2.45447i			0.261647i
$89$	10.3399	−	2.36001i	1.09602	−	0.250160i	0.363973	−	0.931410i	$-0.381420\pi$
$89$	10.3399	−	2.36001i	1.09602	−	0.250160i	0.732052	+	0.681249i	$0.238563\pi$
$90$	18.3843	−	9.98164i	1.93787	−	1.05216i
$91$	0.253131	−	1.10904i	0.0265354	−	0.116259i
$92$	−13.5076	−	16.9380i	−1.40827	−	1.76591i
$93$	1.54936	−	3.42799i	0.160661	−	0.355466i
$94$	−13.0462	−	10.4040i	−1.34562	−	1.07309i
$95$	3.67031	−	0.837724i	0.376566	−	0.0859487i
$96$	−9.26117	−	7.02421i	−0.945214	−	0.716906i
$97$	1.55893	−	3.23715i	0.158285	−	0.328683i	−0.806711	−	0.590946i	$-0.798755\pi$
$97$	1.55893	−	3.23715i	0.158285	−	0.328683i	0.964996	+	0.262263i	$0.0844689\pi$
$98$	11.2631	+	8.98203i	1.13775	+	0.907322i
$99$	−1.92714	+	2.67340i	−0.193685	+	0.268687i
$100$	−3.15425	+	13.8197i	−0.315425	+	1.38197i
$101$	−4.74724	−	9.85774i	−0.472368	−	0.980881i	−0.991970	−	0.126473i	$-0.959634\pi$
$101$	−4.74724	−	9.85774i	−0.472368	−	0.980881i	0.519602	−	0.854408i	$-0.326080\pi$
$102$	15.2608	+	3.09501i	1.51104	+	0.306451i
$103$	2.77046	+	12.1382i	0.272981	+	1.19601i	0.906475	+	0.422260i	$0.138763\pi$
$103$	2.77046	+	12.1382i	0.272981	+	1.19601i	−0.633493	+	0.773748i	$0.718380\pi$
$104$	−2.12344	+	2.66270i	−0.208220	+	0.261100i
$105$	4.03008	−	0.0979734i	0.393295	−	0.00956122i
$106$	−20.5255	−	16.3685i	−1.99361	−	1.58985i
$107$	−3.38602	−	2.70026i	−0.327339	−	0.261044i	0.446006	−	0.895030i	$-0.352846\pi$
$107$	−3.38602	−	2.70026i	−0.327339	−	0.261044i	−0.773344	+	0.633986i	$0.781418\pi$
$108$	4.56565	+	14.9010i	0.439329	+	1.43385i
$109$	−4.66641	+	5.85149i	−0.446961	+	0.560471i	−0.953363	−	0.301826i	$-0.902404\pi$
$109$	−4.66641	+	5.85149i	−0.446961	+	0.560471i	0.506402	+	0.862297i	$0.330975\pi$
$110$	−1.70454	−	7.46808i	−0.162522	−	0.712053i
$111$	−3.13764	+	15.4710i	−0.297811	+	1.46844i
$112$	−0.324726	−	0.674301i	−0.0306838	−	0.0637155i
$113$	4.02187	−	17.6210i	0.378346	−	1.65764i	−0.324190	−	0.945992i	$-0.605092\pi$
$113$	4.02187	−	17.6210i	0.378346	−	1.65764i	0.702536	−	0.711648i	$-0.252051\pi$
$114$	0.113616	+	4.67355i	0.0106412	+	0.437718i
$115$	17.6122	+	14.0453i	1.64235	+	1.30973i
$116$	−10.3043	+	21.3972i	−0.956733	+	1.98668i
$117$	−4.40348	+	1.23298i	−0.407102	+	0.113989i
$118$	−9.65050	+	2.20266i	−0.888401	+	0.202772i
$119$	2.34606	+	1.87092i	0.215063	+	0.171507i
$120$	−10.9980	−	4.97078i	−1.00397	−	0.453768i
$121$	−6.10598	−	7.65666i	−0.555089	−	0.696060i
$122$	0.986966	−	4.32418i	0.0893557	−	0.391493i
$123$	17.6551	+	7.97963i	1.59191	+	0.719499i
$124$	−6.35086	+	1.44954i	−0.570324	+	0.130173i
$125$			0.854073i			0.0763906i
$126$	−0.875459	+	4.92880i	−0.0779921	+	0.439092i
$127$	−12.5169	−	2.85690i	−1.11069	−	0.253509i	−0.372456	−	0.928050i	$-0.621484\pi$
$127$	−12.5169	−	2.85690i	−1.11069	−	0.253509i	−0.738237	+	0.674541i	$0.764342\pi$
$128$			15.6434i			1.38269i
$129$	−3.52476	+	17.3798i	−0.310337	+	1.53021i
$130$	4.61171	−	9.57632i	0.404474	−	0.839899i
$131$	−0.138636	+	0.287880i	−0.0121127	+	0.0251522i	−0.906937	−	0.421265i	$-0.861586\pi$
$131$	−0.138636	+	0.287880i	−0.0121127	+	0.0251522i	0.894825	+	0.446418i	$0.147300\pi$
$132$	5.70509	−	0.138694i	0.496564	−	0.0120718i
$133$	−0.390880	+	0.811672i	−0.0338936	+	0.0703809i
$134$	0.757673	−	0.364876i	0.0654530	−	0.0315205i
$135$	−8.07613	−	14.0493i	−0.695082	−	1.20917i
$136$	−3.89793	−	8.09413i	−0.334244	−	0.694066i
$137$	−2.82227			−0.241123			−0.120561	−	0.992706i	$-0.538469\pi$
$137$	−2.82227			−0.241123			−0.120561	+	0.992706i	$0.538469\pi$
$138$	−21.4402	+	17.9675i	−1.82511	+	1.52950i
$139$	11.2720	+	2.57276i	0.956079	+	0.218219i	0.671974	−	0.740574i	$-0.265446\pi$
$139$	11.2720	+	2.57276i	0.956079	+	0.218219i	0.284105	+	0.958793i	$0.408304\pi$
$140$	−4.35240	−	5.45773i	−0.367845	−	0.461263i
$141$	−7.81151	+	10.2992i	−0.657848	+	0.867348i
$142$	−7.50140	+	17.2823i	−0.629503	+	1.45030i
$143$			1.67447i			0.140026i
$144$	−1.75928	+	2.44054i	−0.146606	+	0.203378i
$145$	5.49502	−	24.0753i	0.456337	−	1.99934i
$146$	4.37398	+	0.998332i	0.361993	+	0.0826226i
$147$	6.74384	−	8.89151i	0.556223	−	0.733360i
$148$	24.6285	−	11.8605i	2.02445	−	0.974925i
$149$	8.05532	−	10.1010i	0.659917	−	0.827510i	−0.333417	−	0.942779i	$-0.608202\pi$
$149$	8.05532	−	10.1010i	0.659917	−	0.827510i	0.993334	+	0.115269i	$0.0367732\pi$
$150$	17.9378	+	3.63792i	1.46461	+	0.297035i
$151$	9.92785	+	4.78100i	0.807917	+	0.389072i	0.791787	−	0.610798i	$-0.209151\pi$
$151$	9.92785	+	4.78100i	0.807917	+	0.389072i	0.0161301	+	0.999870i	$0.494865\pi$
$152$	2.10872	−	1.68165i	0.171040	−	0.136399i
$153$	2.10953	−	11.8766i	0.170546	−	0.960165i
$154$	1.65153	+	0.795335i	0.133084	+	0.0640899i
$155$	6.10270	−	2.93891i	0.490181	−	0.236059i
$156$	6.30910	+	4.78519i	0.505132	+	0.383122i
$157$	−0.157307	+	0.689207i	−0.0125545	+	0.0550047i	−0.980817	−	0.194930i	$-0.937552\pi$
$157$	−0.157307	+	0.689207i	−0.0125545	+	0.0550047i	0.968263	+	0.249935i	$0.0804092\pi$
$158$	−1.65816	+	3.44320i	−0.131916	+	0.273926i
$159$	−12.2897	+	16.2036i	−0.974639	+	1.28503i
$160$	−4.65717	−	20.4044i	−0.368182	−	1.61311i
$161$	−5.25550	+	1.19953i	−0.414191	+	0.0945365i
$162$	19.0913	−	6.36106i	1.49996	−	0.499772i
$163$	13.9789	−	11.1478i	1.09491	−	0.873164i	0.102333	−	0.994750i	$-0.467369\pi$
$163$	13.9789	−	11.1478i	1.09491	−	0.873164i	0.992581	+	0.121586i	$0.0387980\pi$
$164$	−7.46557	−	32.7088i	−0.582963	−	2.55413i
$165$	−5.75136	+	1.46063i	−0.447743	+	0.113710i
$166$	−4.10953	−	18.0050i	−0.318961	−	1.39746i
$167$		−	16.1452i		−	1.24936i	−0.780882	−	0.624678i	$-0.785230\pi$
$167$		−	16.1452i		−	1.24936i	0.780882	−	0.624678i	$-0.214770\pi$
$168$	2.57089	−	1.31598i	0.198348	−	0.101530i
$169$	6.65673	−	8.34728i	0.512056	−	0.642098i
$170$	17.4811	+	21.9206i	1.34074	+	1.68123i
$171$	3.61716	−	0.175974i	0.276611	−	0.0134571i
$172$	27.6672	−	13.3238i	2.10960	−	1.01593i
$173$	2.65312	−	1.27768i	0.201713	−	0.0971400i	−0.330300	−	0.943876i	$-0.607150\pi$
$173$	2.65312	−	1.27768i	0.201713	−	0.0971400i	0.532013	+	0.846736i	$0.321436\pi$
$174$	27.9434	+	12.6297i	2.11838	+	0.957451i
$175$	2.75760	+	2.19911i	0.208455	+	0.166237i
$176$	0.686871	+	0.861309i	0.0517748	+	0.0649236i
$177$	1.88748	+	7.43210i	0.141872	+	0.558631i
$178$	−14.7852	+	18.5400i	−1.10820	+	1.38963i
$179$	8.74061	−	6.97041i	0.653304	−	0.520993i	−0.239812	−	0.970819i	$-0.577086\pi$
$179$	8.74061	−	6.97041i	0.653304	−	0.520993i	0.893116	+	0.449827i	$0.148514\pi$
$180$	−10.9325	+	25.8442i	−0.814859	+	1.92632i
$181$	−21.5406	+	4.91649i	−1.60110	+	0.365440i	−0.927549	−	0.373703i	$-0.878088\pi$
$181$	−21.5406	+	4.91649i	−1.60110	+	0.365440i	−0.673549	+	0.739143i	$0.735231\pi$
$182$	1.10358	+	2.29160i	0.0818026	+	0.169865i
$183$	−3.36733	−	0.682919i	−0.248920	−	0.0504829i
$184$	15.7343	+	3.59126i	1.15995	+	0.264751i
$185$	−22.2226	+	17.7219i	−1.63383	+	1.30294i
$186$	2.07041	+	8.15238i	0.151809	+	0.597762i
$187$	−3.97958	−	1.91646i	−0.291016	−	0.140146i
$188$	22.3839			1.63252
$189$	3.83346	+	0.585183i	0.278843	+	0.0425658i
$190$	−5.24824	+	6.58109i	−0.380747	+	0.477442i
$191$	−14.5233	+	3.31486i	−1.05087	+	0.239855i	−0.712874	−	0.701292i	$-0.752607\pi$
$191$	−14.5233	+	3.31486i	−1.05087	+	0.239855i	−0.337998	+	0.941147i	$0.609750\pi$
$192$	22.5088	−	0.547201i	1.62443	−	0.0394908i
$193$	−9.74528	−	2.22430i	−0.701481	−	0.160108i	−0.143118	−	0.989706i	$-0.545713\pi$
$193$	−9.74528	−	2.22430i	−0.701481	−	0.160108i	−0.558362	+	0.829597i	$0.688570\pi$
$194$	1.78763	+	7.83213i	0.128345	+	0.562314i
$195$	−7.50295	−	3.39113i	−0.537297	−	0.242844i
$196$	−19.3245			−1.38032
$197$	−9.67529	−	4.65938i	−0.689336	−	0.331967i	0.0562118	−	0.998419i	$-0.482098\pi$
$197$	−9.67529	−	4.65938i	−0.689336	−	0.331967i	−0.745548	+	0.666452i	$0.767812\pi$
$198$	−0.358060	−	7.35994i	−0.0254462	−	0.523048i
$199$	−19.7710			−1.40153			−0.700764	−	0.713393i	$-0.747158\pi$
$199$	−19.7710			−1.40153			−0.700764	+	0.713393i	$0.747158\pi$
$200$	−4.58169	−	9.51397i	−0.323974	−	0.672739i
$201$	−0.296833	−	0.579890i	−0.0209370	−	0.0409023i
$202$	22.0410	+	10.6144i	1.55080	+	0.746826i
$203$	3.68441	+	4.62010i	0.258595	+	0.324268i
$204$	−18.5935	+	9.51760i	−1.30181	+	0.666365i
$205$	15.1362	+	31.4307i	1.05716	+	2.19521i
$206$	−21.7644	−	17.3566i	−1.51640	−	1.20929i
$207$	14.3181	+	16.2655i	0.995177	+	1.13053i
$208$			1.52862i			0.105990i
$209$	0.295082	−	1.29284i	0.0204113	−	0.0894276i
$210$	−6.90841	+	5.78946i	−0.476726	+	0.399511i
$211$	19.5906	−	15.6230i	1.34867	−	1.07553i	0.358827	−	0.933404i	$-0.383177\pi$
$211$	19.5906	−	15.6230i	1.34867	−	1.07553i	0.989848	−	0.142128i	$-0.0453945\pi$
$212$	35.2163			2.41867
$213$	13.5251	+	5.48389i	0.926721	+	0.375750i
$214$	9.68345			0.661947
$215$	−24.9644	+	19.9084i	−1.70255	+	1.35774i
$216$	−9.58019	−	6.55811i	−0.651849	−	0.446223i
$217$	−0.360681	+	1.58025i	−0.0244846	+	0.107274i
$218$		−	16.7343i		−	1.13339i
$219$	0.690784	−	3.40611i	0.0466789	−	0.230163i
$220$	8.03367	+	6.40663i	0.541630	+	0.431935i
$221$	−2.65921	−	5.52191i	−0.178878	−	0.371444i
$222$	−16.0827	−	31.4190i	−1.07940	−	2.10870i
$223$	−2.04781	−	2.56788i	−0.137132	−	0.171958i	0.708524	−	0.705687i	$-0.249362\pi$
$223$	−2.04781	−	2.56788i	−0.137132	−	0.171958i	−0.845655	+	0.533729i	$0.820790\pi$
$224$	4.51234	+	2.17303i	0.301493	+	0.145191i
$225$	2.47958	−	13.9599i	0.165305	−	0.930662i
$226$	17.5341	+	36.4100i	1.16635	+	2.42196i
$227$	8.69416			0.577052			0.288526	−	0.957472i	$-0.406835\pi$
$227$	8.69416			0.577052			0.288526	+	0.957472i	$0.406835\pi$
$228$	−4.02793	−	4.80642i	−0.266756	−	0.318313i
$229$	−12.5409	−	6.03940i	−0.828729	−	0.399095i	−0.0290906	−	0.999577i	$-0.509261\pi$
$229$	−12.5409	−	6.03940i	−0.828729	−	0.399095i	−0.799638	+	0.600482i	$0.794975\pi$
$230$	−50.3681			−3.32117
$231$	0.584833	−	1.29396i	0.0384792	−	0.0851361i
$232$	−3.93681	−	17.2483i	−0.258464	−	1.13240i
$233$	−8.93425	−	2.03919i	−0.585302	−	0.133591i	−0.0803922	−	0.996763i	$-0.525617\pi$
$233$	−8.93425	−	2.03919i	−0.585302	−	0.133591i	−0.504910	+	0.863172i	$0.668474\pi$
$234$	5.97887	−	8.29412i	0.390851	−	0.542204i
$235$	−22.6914	+	5.17916i	−1.48022	+	0.337851i
$236$	8.27887	−	10.3814i	0.538908	−	0.675770i
$237$	2.69771	+	1.21929i	0.175235	+	0.0792015i
$238$	−6.70934			−0.434902
$239$	22.8486	+	11.0033i	1.47795	+	0.711745i	0.987190	−	0.159548i	$-0.0510036\pi$
$239$	22.8486	+	11.0033i	1.47795	+	0.711745i	0.490764	+	0.871293i	$0.336718\pi$
$240$	−5.25040	+	1.33341i	−0.338912	+	0.0860711i
$241$	−4.05244	+	3.23171i	−0.261041	+	0.208173i	−0.745261	−	0.666773i	$-0.767675\pi$
$241$	−4.05244	+	3.23171i	−0.261041	+	0.208173i	0.484220	+	0.874946i	$0.339103\pi$
$242$	21.3478	+	4.87249i	1.37229	+	0.313216i
$243$	−5.28558	−	14.6650i	−0.339070	−	0.940761i
$244$	2.58148	+	5.36050i	0.165262	+	0.343171i
$245$	19.5900	−	4.47128i	1.25156	−	0.285660i
$246$	−41.9871	+	10.6632i	−2.67700	+	0.679860i
$247$	1.43859	−	1.14724i	0.0915354	−	0.0729971i
$248$	3.02563	−	3.79403i	0.192128	−	0.240921i
$249$	−13.8661	+	3.52149i	−0.878730	+	0.223165i
$250$	−1.19063	−	1.49301i	−0.0753023	−	0.0944261i
$251$	−5.78819	−	4.61593i	−0.365347	−	0.291355i	0.423559	−	0.905869i	$-0.360781\pi$
$251$	−5.78819	−	4.61593i	−0.365347	−	0.291355i	−0.788906	+	0.614514i	$0.789352\pi$
$252$	−3.20410	−	5.90134i	−0.201839	−	0.371749i
$253$	7.14912	−	3.44284i	0.449462	−	0.216449i
$254$	25.8635	−	12.4552i	1.62282	−	0.781510i
$255$	16.6467	−	13.9505i	1.04246	−	0.873612i
$256$	−5.59810	−	7.01980i	−0.349881	−	0.438737i
$257$	−13.9733	+	17.5219i	−0.871628	+	1.09299i	0.123298	+	0.992370i	$0.460653\pi$
$257$	−13.9733	+	17.5219i	−0.871628	+	1.09299i	−0.994925	+	0.100617i	$0.967918\pi$
$258$	−18.0670	−	35.2954i	−1.12480	−	2.19740i
$259$		−	6.80176i		−	0.422641i
$260$	3.17266	+	13.9003i	0.196760	+	0.862063i
$261$	9.25461	−	21.8778i	0.572846	−	1.35420i
$262$	−0.158974	−	0.696512i	−0.00982147	−	0.0430307i
$263$	10.1054	−	8.05881i	0.623127	−	0.496927i	−0.260280	−	0.965533i	$-0.583815\pi$
$263$	10.1054	−	8.05881i	0.623127	−	0.496927i	0.883407	+	0.468606i	$0.155243\pi$
$264$	−3.25837	+	2.73061i	−0.200539	+	0.168058i
$265$	−35.7001	+	8.14830i	−2.19304	+	0.500546i
$266$	−0.448224	−	1.96380i	−0.0274824	−	0.120408i
$267$	14.6362	+	11.1009i	0.895719	+	0.679366i
$268$	−0.489451	+	1.01636i	−0.0298980	+	0.0620838i
$269$	−3.55103	+	15.5581i	−0.216510	+	0.948593i	0.743524	+	0.668710i	$0.233153\pi$
$269$	−3.55103	+	15.5581i	−0.216510	+	0.948593i	−0.960034	+	0.279884i	$0.909704\pi$
$270$	33.7035	+	13.3009i	2.05113	+	0.809469i
$271$	19.9339	−	9.59966i	1.21090	−	0.583138i	0.284135	−	0.958784i	$-0.408294\pi$
$271$	19.9339	−	9.59966i	1.21090	−	0.583138i	0.926763	+	0.375647i	$0.122579\pi$
$272$	−3.63294	−	1.74953i	−0.220280	−	0.106081i
$273$	1.75389	−	0.897779i	0.106150	−	0.0543360i
$274$	4.93362	−	3.93443i	0.298051	−	0.237688i
$275$	−4.67766	−	2.25264i	−0.282073	−	0.135839i
$276$	7.45833	−	36.7754i	0.448939	−	2.21362i
$277$	−5.96294	+	7.47729i	−0.358278	+	0.449267i	−0.928005	−	0.372567i	$-0.878478\pi$
$277$	−5.96294	+	7.47729i	−0.358278	+	0.449267i	0.569727	+	0.821834i	$0.307049\pi$
$278$	−23.2912	+	11.2165i	−1.39692	+	0.672719i
$279$	6.27441	−	1.75685i	0.375639	−	0.105180i
$280$	5.06989	+	1.15717i	0.302984	+	0.0691541i
$281$	0.575435	−	2.52115i	0.0343276	−	0.150399i	−0.954860	−	0.297058i	$-0.903995\pi$
$281$	0.575435	−	2.52115i	0.0343276	−	0.150399i	0.989187	+	0.146658i	$0.0468518\pi$
$282$	−0.702425	−	28.8938i	−0.0418288	−	1.72060i
$283$		−	12.0550i		−	0.716596i	−0.933607	−	0.358298i	$-0.883357\pi$
$283$		−	12.0550i		−	0.716596i	0.933607	−	0.358298i	$-0.116643\pi$
$284$	−6.58706	−	24.3989i	−0.390870	−	1.44781i
$285$	5.19535	+	3.94046i	0.307746	+	0.233413i
$286$	−2.33432	−	2.92714i	−0.138031	−	0.173086i
$287$	−8.13873	−	1.85761i	−0.480414	−	0.109651i
$288$	−0.978297	−	20.1089i	−0.0576467	−	1.18493i
$289$	−0.832970			−0.0489982
$290$	23.9566	+	49.7465i	1.40678	+	2.92121i
$291$	6.03173	−	1.53184i	0.353586	−	0.0897978i
$292$	−5.42223	+	2.61121i	−0.317312	+	0.152809i
$293$	2.82393	−	5.86396i	0.164976	−	0.342576i	−0.802049	−	0.597259i	$-0.796257\pi$
$293$	2.82393	−	5.86396i	0.164976	−	0.342576i	0.967025	+	0.254682i	$0.0819709\pi$
$294$	0.606418	+	24.9447i	0.0353670	+	1.45480i
$295$	−5.99055	+	12.4395i	−0.348784	+	0.724257i
$296$	−8.83546	+	18.3470i	−0.513550	+	1.06640i
$297$	−5.69296	+	0.415853i	−0.330339	+	0.0241302i
$298$			28.8873i			1.67340i
$299$	10.7342	+	2.45000i	0.620773	+	0.141687i
$300$	−21.8551	+	11.1871i	−1.26180	+	0.645890i
$301$		−	7.64095i		−	0.440417i
$302$	−24.0199	+	5.48240i	−1.38219	+	0.315476i
$303$	7.80507	−	17.2689i	0.448389	−	0.992072i
$304$	0.269380	−	1.18023i	0.0154500	−	0.0676908i
$305$	−3.85724	−	4.83683i	−0.220865	−	0.276956i
$306$	12.8691	+	23.7023i	0.735675	+	1.35497i
$307$	9.36201	+	7.46596i	0.534318	+	0.426105i	0.853118	−	0.521717i	$-0.174708\pi$
$307$	9.36201	+	7.46596i	0.534318	+	0.426105i	−0.318800	+	0.947822i	$0.603280\pi$
$308$	−2.39725	+	0.547157i	−0.136596	+	0.0311771i
$309$	−13.0316	+	17.1817i	−0.741340	+	0.977430i
$310$	−6.57113	+	13.6451i	−0.373215	+	0.774989i
$311$	5.01852	+	4.00214i	0.284574	+	0.226940i	0.755365	−	0.655305i	$-0.227460\pi$
$311$	5.01852	+	4.00214i	0.284574	+	0.226940i	−0.470790	+	0.882245i	$0.656031\pi$
$312$	−5.89715	+	0.143363i	−0.333860	+	0.00811633i
$313$	3.18381	−	13.9492i	0.179960	−	0.788455i	−0.801687	−	0.597744i	$-0.796064\pi$
$313$	3.18381	−	13.9492i	0.179960	−	0.788455i	0.981646	−	0.190710i	$-0.0610791\pi$
$314$	−0.685812	−	1.42410i	−0.0387026	−	0.0803668i
$315$	4.61355	+	5.24104i	0.259944	+	0.295299i
$316$	−1.14074	−	4.99792i	−0.0641717	−	0.281155i
$317$	6.12366	−	7.67883i	0.343939	−	0.431286i	−0.579535	−	0.814948i	$-0.696766\pi$
$317$	6.12366	−	7.67883i	0.343939	−	0.431286i	0.923474	+	0.383662i	$0.125337\pi$
$318$	−1.10511	−	45.4582i	−0.0619718	−	2.54917i
$319$	−6.80069	−	5.42337i	−0.380766	−	0.303651i
$320$	31.6959	+	25.2766i	1.77185	+	1.41301i
$321$	−0.182307	−	7.49908i	−0.0101754	−	0.418558i
$322$	7.51493	−	9.42343i	0.418791	−	0.525147i
$323$	1.08006	+	4.73203i	0.0600959	+	0.263297i
$324$	−14.7021	+	22.6385i	−0.816786	+	1.25769i
$325$	−3.12568	−	6.49055i	−0.173382	−	0.360031i
$326$	−8.89581	+	38.9751i	−0.492693	+	2.15863i
$327$	−12.9594	+	0.315051i	−0.716657	+	0.0174223i
$328$	19.5403	+	15.5829i	1.07893	+	0.860421i
$329$	2.41659	−	5.01809i	0.133231	−	0.276656i
$330$	8.01776	−	10.5711i	0.441363	−	0.581921i
$331$	−28.0110	+	6.39332i	−1.53962	+	0.351409i	−0.906352	−	0.422523i	$-0.861145\pi$
$331$	−28.0110	+	6.39332i	−1.53962	+	0.351409i	−0.633269	+	0.773931i	$0.718287\pi$
$332$	19.3686	+	15.4459i	1.06299	+	0.847706i
$333$	−24.0288	+	13.0463i	−1.31677	+	0.714934i
$334$	22.5075	+	28.2236i	1.23156	+	1.54433i
$335$	0.261011	−	1.14356i	0.0142606	−	0.0624796i
$336$	0.533892	−	1.18125i	0.0291262	−	0.0644424i
$337$	18.1478	−	4.14211i	0.988571	−	0.225635i	0.302484	−	0.953154i	$-0.402184\pi$
$337$	18.1478	−	4.14211i	0.988571	−	0.225635i	0.686087	+	0.727520i	$0.259327\pi$
$338$			23.8718i			1.29846i
$339$	27.8666	−	14.2643i	1.51351	−	0.774732i
$340$	−36.6671	−	8.36902i	−1.98855	−	0.453874i
$341$		−	2.38591i		−	0.129204i
$342$	−6.07785	+	5.35019i	−0.328653	+	0.289305i
$343$	−4.35293	+	9.03895i	−0.235036	+	0.488057i
$344$	−9.92557	+	20.6106i	−0.535151	+	1.11125i
$345$	0.948262	+	39.0062i	0.0510527	+	2.10002i
$346$	−2.85677	+	5.93214i	−0.153581	+	0.318914i
$347$	−17.4560	+	8.40635i	−0.937086	+	0.451277i	−0.839140	−	0.543915i	$-0.816941\pi$
$347$	−17.4560	+	8.40635i	−0.937086	+	0.451277i	−0.0979454	+	0.995192i	$0.531227\pi$
$348$	−39.8689	+	10.1252i	−2.13720	+	0.542770i
$349$	11.4148	+	23.7030i	0.611018	+	1.26879i	0.945264	+	0.326306i	$0.105804\pi$
$349$	11.4148	+	23.7030i	0.611018	+	1.26879i	−0.334246	+	0.942486i	$0.608482\pi$
$350$	−7.88627			−0.421539
$351$	−6.53572	−	4.47403i	−0.348851	−	0.238806i
$352$	−7.18730	−	1.64045i	−0.383084	−	0.0874365i
$353$	−20.7571	−	26.0286i	−1.10479	−	1.38536i	−0.914960	−	0.403545i	$-0.867778\pi$
$353$	−20.7571	−	26.0286i	−1.10479	−	1.38536i	−0.189830	−	0.981817i	$-0.560794\pi$
$354$	−13.6604	−	10.3608i	−0.726040	−	0.550671i
$355$	12.3229	+	23.2099i	0.654033	+	1.23186i
$356$		−	31.8098i		−	1.68592i
$357$	0.126314	+	5.19587i	0.00668527	+	0.274994i
$358$	−5.56229	+	24.3700i	−0.293976	+	1.28799i
$359$	22.4055	+	5.11391i	1.18252	+	0.269902i	0.768188	−	0.640225i	$-0.221159\pi$
$359$	22.4055	+	5.11391i	1.18252	+	0.269902i	0.414330	+	0.910127i	$0.364016\pi$
$360$	−5.63648	−	20.1301i	−0.297069	−	1.06095i
$361$	15.8055	−	7.61153i	0.831869	−	0.400607i
$362$	30.8012	−	38.6235i	1.61888	−	2.03001i
$363$	3.37146	−	16.6239i	0.176956	−	0.872531i
$364$	−3.07400	−	1.48036i	−0.161121	−	0.0775919i
$365$	4.89253	−	3.90166i	0.256087	−	0.204222i
$366$	6.83847	−	3.50046i	0.357453	−	0.182972i
$367$	−16.2722	−	7.83629i	−0.849403	−	0.409051i	−0.0420471	−	0.999116i	$-0.513388\pi$
$367$	−16.2722	−	7.83629i	−0.849403	−	0.409051i	−0.807356	+	0.590065i	$0.799102\pi$
$368$	6.52641	−	3.14295i	0.340213	−	0.163838i
$369$	9.04829	+	32.3150i	0.471035	+	1.68225i
$370$	14.1418	−	61.9594i	0.735199	−	3.22112i
$371$	3.80198	−	7.89490i	0.197389	−	0.409883i
$372$	−8.98969	−	6.81831i	−0.466094	−	0.353513i
$373$	−4.18401	−	18.3313i	−0.216640	−	0.949161i	−0.959941	−	0.280204i	$-0.909598\pi$
$373$	−4.18401	−	18.3313i	−0.216640	−	0.949161i	0.743301	−	0.668957i	$-0.233259\pi$
$374$	9.62839	−	2.19762i	0.497872	−	0.113636i
$375$	−1.13380	+	0.950163i	−0.0585494	+	0.0490662i
$376$	−13.0370	+	10.3966i	−0.672330	+	0.536166i
$377$	−2.68574	−	11.7670i	−0.138323	−	0.606031i
$378$	−7.51706	+	4.32113i	−0.386636	+	0.222255i
$379$	−6.48104	−	28.3953i	−0.332909	−	1.45857i	−0.813470	−	0.581607i	$-0.802424\pi$
$379$	−6.48104	−	28.3953i	−0.332909	−	1.45857i	0.480561	−	0.876961i	$-0.340433\pi$
$380$		−	11.2914i		−	0.579238i
$381$	−10.1325	−	19.7948i	−0.519105	−	1.01412i
$382$	20.7672	−	26.0412i	1.06254	−	1.33239i
$383$	11.4375	+	14.3422i	0.584429	+	0.732851i	0.982861	−	0.184347i	$-0.0590170\pi$
$383$	11.4375	+	14.3422i	0.584429	+	0.732851i	−0.398432	+	0.917198i	$0.630446\pi$
$384$	−20.7670	+	17.4034i	−1.05976	+	0.888114i
$385$	2.30358	−	1.10934i	0.117401	−	0.0565374i
$386$	20.1366	−	9.69727i	1.02492	−	0.493578i
$387$	−26.9935	+	14.6560i	−1.37215	+	0.745004i
$388$	−8.42529	−	6.71894i	−0.427729	−	0.341103i
$389$	−3.47698	−	4.36000i	−0.176290	−	0.221061i	0.685834	−	0.727758i	$-0.259438\pi$
$389$	−3.47698	−	4.36000i	−0.176290	−	0.221061i	−0.862124	+	0.506697i	$0.830866\pi$
$390$	17.8434	−	4.53156i	0.903535	−	0.229465i
$391$	−18.1082	+	22.7070i	−0.915771	+	1.14834i
$392$	11.2551	−	8.97564i	0.568468	−	0.453338i
$393$	−0.536402	+	0.136226i	−0.0270579	+	0.00687171i
$394$	23.4089	−	5.34293i	1.17932	−	0.269173i
$395$	2.31282	+	4.80262i	0.116371	+	0.241646i
$396$	6.53108	+	7.41936i	0.328199	+	0.372837i
$397$	3.57035	+	0.814910i	0.179191	+	0.0408992i	0.311175	−	0.950353i	$-0.399278\pi$
$397$	3.57035	+	0.814910i	0.179191	+	0.0408992i	−0.131984	+	0.991252i	$0.542135\pi$
$398$	34.5618	−	27.5621i	1.73242	−	1.38156i
$399$	−1.51237	+	0.384087i	−0.0757134	+	0.0192284i
$400$	−4.27022	−	2.05643i	−0.213511	−	0.102821i
$401$	19.8139			0.989461			0.494730	−	0.869047i	$-0.335267\pi$
$401$	19.8139			0.989461			0.494730	+	0.869047i	$0.335267\pi$
$402$	1.32730	+	0.599903i	0.0661997	+	0.0299205i
$403$	2.06413	−	2.58833i	0.102821	−	0.128934i
$404$	−31.9932	+	7.30225i	−1.59172	+	0.363300i
$405$	9.66602	−	26.3512i	0.480309	−	1.30940i
$406$	−12.8815	−	2.94011i	−0.639296	−	0.145915i
$407$	2.22789	+	9.76102i	0.110432	+	0.483836i
$408$	6.40869	−	14.1794i	0.317278	−	0.701984i
$409$	−14.1955			−0.701925			−0.350962	−	0.936390i	$-0.614145\pi$
$409$	−14.1955			−0.701925			−0.350962	+	0.936390i	$0.614145\pi$
$410$	−70.2761	−	33.8432i	−3.47069	−	1.67140i
$411$	−3.13980	−	3.74664i	−0.154875	−	0.184808i
$412$	37.3421			1.83971
$413$	−1.43353	−	2.97676i	−0.0705395	−	0.146477i
$414$	−47.7047	−	8.47337i	−2.34456	−	0.416444i
$415$	−23.2085	−	11.1766i	−1.13926	−	0.548639i
$416$	−6.37786	−	7.99759i	−0.312700	−	0.392114i
$417$	9.12479	+	17.8261i	0.446843	+	0.872948i
$418$	1.28647	+	2.67138i	0.0629233	+	0.130662i
$419$	9.19147	+	7.32995i	0.449033	+	0.358091i	0.821745	−	0.569855i	$-0.193001\pi$
$419$	9.19147	+	7.32995i	0.449033	+	0.358091i	−0.372712	+	0.927947i	$0.621572\pi$
$420$	2.40321	−	11.8497i	0.117265	−	0.578206i
$421$			7.27047i			0.354341i	0.984180	+	0.177170i	$0.0566944\pi$
$421$			7.27047i			0.354341i	−0.984180	+	0.177170i	$0.943306\pi$
$422$	−12.4670	+	54.6213i	−0.606882	+	2.65892i
$423$	−22.3628	+	1.08795i	−1.08732	+	0.0528978i
$424$	−20.5109	+	16.3569i	−0.996096	+	0.794360i
$425$	19.0030			0.921780
$426$	−31.2881	+	9.26841i	−1.51591	+	0.449056i
$427$	1.48043			0.0716430
$428$	−10.1556	+	8.09885i	−0.490891	+	0.391473i
$429$	−2.22290	+	1.86286i	−0.107323	+	0.0899396i
$430$	15.8866	−	69.6039i	0.766122	−	3.35660i
$431$			15.1601i			0.730237i	0.930961	+	0.365119i	$0.118972\pi$
$431$			15.1601i			0.730237i	−0.930961	+	0.365119i	$0.881028\pi$
$432$	−5.19709	+	0.379631i	−0.250045	+	0.0182650i
$433$	15.1948	+	12.1174i	0.730214	+	0.582326i	0.916436	−	0.400182i	$-0.131053\pi$
$433$	15.1948	+	12.1174i	0.730214	+	0.582326i	−0.186222	+	0.982508i	$0.559624\pi$
$434$	−1.57246	−	3.26525i	−0.0754806	−	0.156737i
$435$	38.0738	−	19.4891i	1.82550	−	0.934432i
$436$	13.9959	+	17.5503i	0.670282	+	0.840507i
$437$	−7.85599	−	3.78324i	−0.375803	−	0.180977i
$438$	3.54077	+	6.91722i	0.169185	+	0.330518i
$439$	−0.939085	−	1.95003i	−0.0448201	−	0.0930699i	0.877356	−	0.479840i	$-0.159305\pi$
$439$	−0.939085	−	1.95003i	−0.0448201	−	0.0930699i	−0.922176	+	0.386770i	$0.873591\pi$
$440$	−7.65469			−0.364923
$441$	19.3063	−	0.939249i	0.919347	−	0.0447261i
$442$	12.3465	+	5.94576i	0.587263	+	0.282811i
$443$	−5.23668			−0.248802			−0.124401	−	0.992232i	$-0.539701\pi$
$443$	−5.23668			−0.248802			−0.124401	+	0.992232i	$0.539701\pi$
$444$	43.1445	+	19.5002i	2.04755	+	0.925436i
$445$	7.36010	+	32.2467i	0.348902	+	1.52864i
$446$	7.15958	+	1.63413i	0.339016	+	0.0773782i
$447$	22.3710	−	0.543852i	1.05811	−	0.0257233i
$448$	−9.45807	+	2.15874i	−0.446852	+	0.101991i
$449$	−7.45840	+	9.35254i	−0.351984	+	0.441374i	−0.926030	−	0.377449i	$-0.876801\pi$
$449$	−7.45840	+	9.35254i	−0.351984	+	0.441374i	0.574047	+	0.818823i	$0.305373\pi$
$450$	15.1265	+	27.8601i	0.713070	+	1.31334i
$451$	12.2881			0.578625
$452$	−48.8411	−	23.5206i	−2.29729	−	1.10632i
$453$	4.69791	+	18.4984i	0.220727	+	0.869130i
$454$	−15.1983	+	12.1202i	−0.713292	+	0.568831i
$455$	3.45874	+	0.789435i	0.162148	+	0.0370093i
$456$	4.57839	+	0.928533i	0.214403	+	0.0434825i
$457$	−6.47755	−	13.4508i	−0.303007	−	0.629201i	0.692754	−	0.721174i	$-0.256397\pi$
$457$	−6.47755	−	13.4508i	−0.303007	−	0.629201i	−0.995762	+	0.0919728i	$0.970683\pi$
$458$	30.3422	−	6.92541i	1.41780	−	0.323603i
$459$	18.1133	−	10.4123i	0.845458	−	0.486006i
$460$	52.8242	−	42.1259i	2.46294	−	1.96413i
$461$	−22.8815	+	28.6925i	−1.06570	+	1.33634i	−0.126885	+	0.991917i	$0.540498\pi$
$461$	−22.8815	+	28.6925i	−1.06570	+	1.33634i	−0.938813	+	0.344426i	$0.888073\pi$
$462$	0.781512	+	3.07727i	0.0363592	+	0.143167i
$463$	8.25919	+	10.3567i	0.383837	+	0.481316i	0.935790	−	0.352559i	$-0.114688\pi$
$463$	8.25919	+	10.3567i	0.383837	+	0.481316i	−0.551953	+	0.833876i	$0.686117\pi$
$464$	−6.20833	−	4.95098i	−0.288215	−	0.229843i
$465$	10.6908	+	4.83194i	0.495773	+	0.224076i
$466$	18.4608	−	8.89024i	0.855178	−	0.411832i
$467$	8.56134	−	4.12293i	0.396172	−	0.190786i	−0.225182	−	0.974317i	$-0.572298\pi$
$467$	8.56134	−	4.12293i	0.396172	−	0.190786i	0.621353	+	0.783531i	$0.286583\pi$
$468$	0.666457	+	13.6991i	0.0308070	+	0.633239i
$469$	0.175008	+	0.219453i	0.00808112	+	0.0101334i
$470$	32.4468	−	40.6870i	1.49666	−	1.87675i
$471$	−1.08995	+	0.557920i	−0.0502221	+	0.0257076i
$472$			9.89164i			0.455300i
$473$	2.50276	+	10.9653i	0.115077	+	0.504186i
$474$	−6.41565	+	1.62934i	−0.294681	+	0.0748380i
$475$	1.26951	+	5.56211i	0.0582493	+	0.255207i
$476$	7.03651	−	5.61143i	0.322518	−	0.257199i
$477$	−35.1831	+	1.71165i	−1.61092	+	0.0783712i
$478$	−55.2811	+	12.6175i	−2.52850	+	0.577113i
$479$	−0.524602	−	2.29843i	−0.0239697	−	0.105018i	0.961528	−	0.274707i	$-0.0885809\pi$
$479$	−0.524602	−	2.29843i	−0.0239697	−	0.105018i	−0.985498	+	0.169689i	$0.945724\pi$
$480$	21.9062	−	28.8826i	0.999879	−	1.31830i
$481$	−6.02766	+	12.5166i	−0.274837	+	0.570706i
$482$	2.57886	−	11.2987i	0.117464	−	0.514643i
$483$	−7.43920	−	5.64232i	−0.338495	−	0.256735i
$484$	−26.4639	+	12.7443i	−1.20291	+	0.579289i
$485$	10.0956	+	4.86180i	0.458419	+	0.220763i
$486$	29.6837	+	18.2675i	1.34648	+	0.828632i
$487$	−5.72646	+	4.56670i	−0.259491	+	0.206937i	−0.744590	−	0.667522i	$-0.767355\pi$
$487$	−5.72646	+	4.56670i	−0.259491	+	0.206937i	0.485099	+	0.874459i	$0.338784\pi$
$488$	−3.99330	−	1.92307i	−0.180768	−	0.0870534i
$489$	30.3507	+	6.15535i	1.37251	+	0.278354i
$490$	−28.0120	+	35.1260i	−1.26546	+	1.58683i
$491$	5.09796	−	2.45505i	0.230068	−	0.110795i	−0.315299	−	0.948992i	$-0.602105\pi$
$491$	5.09796	−	2.45505i	0.230068	−	0.110795i	0.545367	+	0.838198i	$0.316390\pi$
$492$	35.1163	−	46.2995i	1.58316	−	2.08734i
$493$	31.0396	+	7.08458i	1.39795	+	0.319073i
$494$	−0.915482	+	4.01099i	−0.0411895	+	0.180463i
$495$	−8.33747	−	6.01012i	−0.374741	−	0.270135i
$496$		−	2.17809i		−	0.0977991i
$497$	−6.18096	−	1.15742i	−0.277254	−	0.0519174i
$498$	19.3302	−	25.4862i	0.866209	−	1.14207i
$499$	−25.7409	−	32.2780i	−1.15232	−	1.44496i	−0.874960	−	0.484196i	$-0.839112\pi$
$499$	−25.7409	−	32.2780i	−1.15232	−	1.44496i	−0.277359	−	0.960766i	$-0.589459\pi$
$500$	2.49739	+	0.570012i	0.111686	+	0.0254917i
$501$	21.4332	−	17.9617i	0.957567	−	0.802470i
$502$	16.5533			0.738809
$503$	2.82432	+	5.86475i	0.125930	+	0.261496i	0.954396	−	0.298543i	$-0.0965005\pi$
$503$	2.82432	+	5.86475i	0.125930	+	0.261496i	−0.828466	+	0.560039i	$0.810786\pi$
$504$	4.60713	+	1.94888i	0.205218	+	0.0868101i
$505$	30.7431	−	14.8051i	1.36805	−	0.658818i
$506$	−7.69787	+	15.9848i	−0.342212	+	0.710611i
$507$	18.4869	−	0.449427i	0.821032	−	0.0199597i
$508$	−16.7076	+	34.6938i	−0.741282	+	1.53929i
$509$	−11.1579	+	23.1697i	−0.494566	+	1.02698i	0.493037	+	0.870008i	$0.335887\pi$
$509$	−11.1579	+	23.1697i	−0.494566	+	1.02698i	−0.987603	+	0.156969i	$0.949828\pi$
$510$	−9.65232	+	47.5935i	−0.427412	+	2.10747i
$511$			1.49748i			0.0662446i
$512$	−10.9303	−	2.49476i	−0.483054	−	0.110254i
$513$	4.25773	+	4.60610i	0.187983	+	0.203364i
$514$		−	50.1098i		−	2.21025i
$515$	−37.8550	+	8.64016i	−1.66809	+	0.380731i
$516$	48.4677	+	21.9061i	2.13367	+	0.964361i
$517$	−1.82432	+	7.99287i	−0.0802336	+	0.351526i
$518$	9.48210	+	11.8902i	0.416620	+	0.522424i
$519$	4.64777	+	2.10066i	0.204014	+	0.0922090i
$520$	−8.30411	−	6.62231i	−0.364159	−	0.290407i
$521$	11.0206	−	2.51538i	0.482821	−	0.110201i	0.0258193	−	0.999667i	$-0.491781\pi$
$521$	11.0206	−	2.51538i	0.482821	−	0.110201i	0.457001	+	0.889466i	$0.348923\pi$
$522$	14.3211	+	51.1462i	0.626816	+	2.23861i
$523$	−5.32925	+	11.0663i	−0.233032	+	0.483896i	−0.984390	−	0.175998i	$-0.943685\pi$
$523$	−5.32925	+	11.0663i	−0.233032	+	0.483896i	0.751359	+	0.659894i	$0.229399\pi$
$524$	0.749262	+	0.597516i	0.0327317	+	0.0261026i
$525$	0.148472	+	6.10731i	0.00647985	+	0.266545i
$526$	−6.43082	+	28.1753i	−0.280397	+	1.22850i
$527$	3.78905	+	7.86805i	0.165054	+	0.342738i
$528$	−0.379261	+	1.87005i	−0.0165052	+	0.0813836i
$529$	−6.49204	−	28.4435i	−0.282262	−	1.23667i
$530$	51.0481	−	64.0123i	2.21739	−	2.78052i
$531$	−7.76647	+	10.7740i	−0.337036	+	0.467550i
$532$	2.11253	+	1.68468i	0.0915896	+	0.0730403i
$533$	13.3307	+	10.6308i	0.577415	+	0.460473i
$534$	−41.0610	+	0.998215i	−1.77688	+	0.0431970i
$535$	8.42123	−	10.5599i	0.364082	−	0.456544i
$536$	−0.186997	−	0.819286i	−0.00807703	−	0.0353878i
$537$	18.9774	+	3.84876i	0.818935	+	0.166086i
$538$	−15.4814	−	32.1475i	−0.667452	−	1.38598i
$539$	1.57498	−	6.90042i	0.0678390	−	0.297222i
$540$	−46.4714	+	14.2388i	−1.99981	+	0.612739i
$541$	−17.7948	−	14.1909i	−0.765060	−	0.610115i	0.161234	−	0.986916i	$-0.448453\pi$
$541$	−17.7948	−	14.1909i	−0.765060	−	0.610115i	−0.926294	+	0.376801i	$0.877024\pi$
$542$	−21.4640	+	44.5704i	−0.921956	+	1.91446i
$543$	−30.4908	−	23.1260i	−1.30849	−	0.992433i
$544$	26.3068	−	6.00437i	1.12790	−	0.257435i
$545$	−18.2489	−	14.5530i	−0.781697	−	0.623382i
$546$	−1.81442	+	4.01445i	−0.0776501	+	0.171803i
$547$	4.77268	+	5.98475i	0.204065	+	0.255889i	0.873324	−	0.487140i	$-0.161960\pi$
$547$	4.77268	+	5.98475i	0.204065	+	0.255889i	−0.669259	+	0.743029i	$0.733388\pi$
$548$	−1.88360	+	8.25258i	−0.0804633	+	0.352533i
$549$	−2.83958	−	5.22997i	−0.121191	−	0.223210i
$550$	11.3174	−	2.58312i	0.482574	−	0.110144i
$551$			9.55846i			0.407204i
$552$	12.7371	+	24.8831i	0.542126	+	1.05909i
$553$	−1.24360	−	0.283844i	−0.0528833	−	0.0120703i
$554$		−	21.3838i		−	0.908511i
$555$	−48.2491	−	9.78527i	−2.04806	−	0.415362i
$556$	15.0460	−	31.2433i	0.638092	−	1.32501i
$557$	8.29986	−	17.2348i	0.351676	−	0.730264i	−0.647827	−	0.761788i	$-0.724322\pi$
$557$	8.29986	−	17.2348i	0.351676	−	0.730264i	0.999503	+	0.0315242i	$0.0100361\pi$
$558$	−8.51916	+	11.8181i	−0.360645	+	0.500300i
$559$	−6.77134	+	14.0608i	−0.286397	+	0.594710i
$560$	2.10293	−	1.01272i	0.0888649	−	0.0427951i
$561$	−1.88316	−	7.41507i	−0.0795069	−	0.313065i
$562$	2.50873	+	5.20942i	0.105824	+	0.219746i
$563$	−37.9690			−1.60020			−0.800101	−	0.599866i	$-0.795221\pi$
$563$	−37.9690			−1.60020			−0.800101	+	0.599866i	$0.795221\pi$
$564$	24.9023	+	29.7153i	1.04858	+	1.25124i
$565$	54.9541	+	12.5429i	2.31194	+	0.527684i
$566$	16.8055	+	21.0734i	0.706387	+	0.885782i
$567$	3.48790	+	5.74003i	0.146478	+	0.241059i
$568$	15.1690	+	11.1511i	0.636477	+	0.467888i
$569$		−	11.9181i		−	0.499633i	−0.968293	−	0.249817i	$-0.919630\pi$
$569$		−	11.9181i		−	0.499633i	0.968293	−	0.249817i	$-0.0803704\pi$
$570$	−14.5753	+	0.354333i	−0.610491	+	0.0148414i
$571$	4.65208	−	20.3821i	0.194683	−	0.852964i	−0.779355	−	0.626582i	$-0.784453\pi$
$571$	4.65208	−	20.3821i	0.194683	−	0.852964i	0.974039	−	0.226381i	$-0.0726896\pi$
$572$	4.89629	+	1.11755i	0.204724	+	0.0467270i
$573$	−20.5579	−	15.5923i	−0.858819	−	0.651379i
$574$	16.8170	−	8.09863i	0.701927	−	0.338030i
$575$	−21.2847	+	26.6901i	−0.887633	+	1.11306i
$576$	25.7676	+	29.2722i	1.07365	+	1.21968i
$577$	4.46869	+	2.15201i	0.186034	+	0.0895892i	0.524582	−	0.851360i	$-0.324222\pi$
$577$	4.46869	+	2.15201i	0.186034	+	0.0895892i	−0.338548	+	0.940949i	$0.609936\pi$
$578$	1.45612	−	1.16122i	0.0605665	−	0.0483002i
$579$	−7.88889	−	15.4117i	−0.327851	−	0.640487i
$580$	−66.7308	−	32.1359i	−2.77085	−	1.33437i
$581$	5.55376	−	2.67455i	0.230409	−	0.110959i
$582$	−8.40860	+	11.0864i	−0.348548	+	0.459548i
$583$	−2.87018	+	12.5751i	−0.118871	+	0.520806i
$584$	1.94522	−	4.03929i	0.0804937	−	0.167147i
$585$	−3.84528	−	13.7330i	−0.158983	−	0.567790i
$586$	3.23822	+	14.1876i	0.133770	+	0.586083i
$587$	−24.1010	+	5.50089i	−0.994753	+	0.227046i	−0.688761	−	0.724988i	$-0.741845\pi$
$587$	−24.1010	+	5.50089i	−0.994753	+	0.227046i	−0.305992	+	0.952034i	$0.598988\pi$
$588$	−21.4987	−	25.6538i	−0.886592	−	1.05795i
$589$	−2.04982	+	1.63468i	−0.0844613	+	0.0673556i
$590$	−6.86940	−	30.0968i	−0.282809	−	1.23907i
$591$	−4.57840	−	18.0278i	−0.188330	−	0.741565i
$592$	2.03383	+	8.91080i	0.0835900	+	0.366232i
$593$		−	3.79186i		−	0.155713i	−0.996965	−	0.0778564i	$-0.975192\pi$
$593$		−	3.79186i		−	0.155713i	0.996965	−	0.0778564i	$-0.0248076\pi$
$594$	9.37216	−	8.66332i	0.384545	−	0.355460i
$595$	−5.83479	+	7.31660i	−0.239203	+	0.299951i
$596$	−24.1602	−	30.2960i	−0.989641	−	1.24097i
$597$	−21.9954	−	26.2465i	−0.900211	−	1.07420i
$598$	−22.1799	+	10.6813i	−0.907003	+	0.436790i
$599$	−11.8494	+	5.70636i	−0.484152	+	0.233155i	−0.660005	−	0.751261i	$-0.729446\pi$
$599$	−11.8494	+	5.70636i	−0.484152	+	0.233155i	0.175853	+	0.984416i	$0.443732\pi$
$600$	7.53288	−	16.6667i	0.307529	−	0.680414i
$601$	23.6284	+	18.8430i	0.963821	+	0.768622i	0.972874	−	0.231337i	$-0.0743101\pi$
$601$	23.6284	+	18.8430i	0.963821	+	0.768622i	−0.00905252	+	0.999959i	$0.502882\pi$
$602$	10.6520	+	13.3572i	0.434143	+	0.544398i
$603$	0.439590	−	1.03919i	0.0179015	−	0.0423189i
$604$	20.6060	−	25.8391i	0.838445	−	1.05138i
$605$	23.8786	−	19.0426i	0.970805	−	0.774191i
$606$	10.4299	+	41.0686i	0.423686	+	1.66830i
$607$	−6.54351	+	1.49351i	−0.265593	+	0.0606199i	−0.353243	−	0.935531i	$-0.614921\pi$
$607$	−6.54351	+	1.49351i	−0.265593	+	0.0606199i	0.0876505	+	0.996151i	$0.472064\pi$
$608$	3.51491	+	7.29879i	0.142549	+	0.296005i
$609$	−2.03437	+	10.0311i	−0.0824370	+	0.406479i
$610$	13.4857	+	3.07803i	0.546021	+	0.124626i
$611$	−8.89398	+	7.09271i	−0.359812	+	0.286940i
$612$	−33.3203	−	14.0949i	−1.34689	−	0.569755i
$613$	0.944818	+	0.455000i	0.0381608	+	0.0183773i	0.452867	−	0.891578i	$-0.350401\pi$
$613$	0.944818	+	0.455000i	0.0381608	+	0.0183773i	−0.414706	+	0.909955i	$0.636116\pi$
$614$	−26.7738			−1.08050
$615$	−24.8859	+	55.0606i	−1.00350	+	2.22026i
$616$	1.14208	−	1.43212i	0.0460158	−	0.0577019i
$617$	31.6306	−	7.21948i	1.27340	−	0.290645i	0.468187	−	0.883630i	$-0.344908\pi$
$617$	31.6306	−	7.21948i	1.27340	−	0.290645i	0.805214	+	0.592984i	$0.202050\pi$
$618$	−1.17182	−	48.2022i	−0.0471376	−	1.93898i
$619$	23.4440	+	5.35094i	0.942294	+	0.215072i	0.665958	−	0.745989i	$-0.268023\pi$
$619$	23.4440	+	5.35094i	0.942294	+	0.215072i	0.276335	+	0.961061i	$0.410880\pi$
$620$	−4.52066	−	19.8063i	−0.181554	−	0.795440i
$621$	−5.66386	+	37.1032i	−0.227283	+	1.48890i
$622$	−14.3521			−0.575468
$623$	−7.13121	−	3.43421i	−0.285706	−	0.137589i
$624$	−2.02928	+	1.70060i	−0.0812361	+	0.0680784i
$625$	−26.2943			−1.05177
$626$	13.8805	+	28.8231i	0.554775	+	1.15200i
$627$	2.04456	−	1.04656i	0.0816518	−	0.0417958i
$628$	1.91032	+	0.919960i	0.0762300	+	0.0367104i
$629$	−22.8484	−	28.6509i	−0.911024	−	1.14239i
$630$	−15.3713	−	2.73027i	−0.612408	−	0.108777i
$631$	−1.40897	−	2.92575i	−0.0560902	−	0.116472i	0.871040	−	0.491213i	$-0.163446\pi$
$631$	−1.40897	−	2.92575i	−0.0560902	−	0.116472i	−0.927130	+	0.374740i	$0.877732\pi$
$632$	2.98577	+	2.38107i	0.118768	+	0.0947140i
$633$	42.5347	+	8.62636i	1.69060	+	0.342867i
$634$			21.9602i			0.872150i
$635$	8.90974	−	39.0361i	0.353572	−	1.54910i
$636$	39.1785	+	46.7506i	1.55353	+	1.85378i
$637$	7.67837	−	6.12329i	0.304228	−	0.242614i
$638$	19.4489			0.769988
$639$	7.76672	+	24.0557i	0.307247	+	0.951630i
$640$	−48.7867			−1.92846
$641$	−8.56376	+	6.82937i	−0.338248	+	0.269744i	−0.777851	−	0.628448i	$-0.783690\pi$
$641$	−8.56376	+	6.82937i	−0.338248	+	0.269744i	0.439603	+	0.898192i	$0.355119\pi$
$642$	10.7729	+	12.8550i	0.425173	+	0.507348i
$643$	−5.17483	+	22.6724i	−0.204075	+	0.894113i	0.764349	+	0.644803i	$0.223061\pi$
$643$	−5.17483	+	22.6724i	−0.204075	+	0.894113i	−0.968424	+	0.249309i	$0.919796\pi$
$644$			16.1681i			0.637114i
$645$	−54.2020	−	10.9926i	−2.13420	−	0.432832i
$646$	−8.48482	−	6.76641i	−0.333831	−	0.266221i
$647$	1.57332	+	3.26703i	0.0618536	+	0.128440i	0.929604	−	0.368560i	$-0.120149\pi$
$647$	1.57332	+	3.26703i	0.0618536	+	0.128440i	−0.867750	+	0.497000i	$0.834435\pi$
$648$	−1.95197	−	20.0139i	−0.0766805	−	0.786220i
$649$	3.03225	+	3.80232i	0.119026	+	0.149254i
$650$	14.5123	+	6.98874i	0.569218	+	0.274121i
$651$	−2.49908	+	1.27922i	−0.0979467	+	0.0501368i
$652$	−23.2676	−	48.3157i	−0.911231	−	1.89219i
$653$	1.09091			0.0426907			0.0213454	−	0.999772i	$-0.493205\pi$
$653$	1.09091			0.0426907			0.0213454	+	0.999772i	$0.493205\pi$
$654$	22.2152	−	18.6170i	0.868683	−	0.727983i
$655$	−0.897805	−	0.432360i	−0.0350802	−	0.0168937i
$656$	11.2178			0.437981
$657$	5.29020	−	2.87229i	0.206390	−	0.112059i
$658$	2.77111	+	12.1410i	0.108029	+	0.473307i
$659$	−5.80284	−	1.32446i	−0.226047	−	0.0515937i	0.107997	−	0.994151i	$-0.465556\pi$
$659$	−5.80284	−	1.32446i	−0.226047	−	0.0515937i	−0.334044	+	0.942558i	$0.608413\pi$
$660$	0.432542	+	17.7923i	0.0168367	+	0.692566i
$661$	9.04413	−	2.06426i	0.351776	−	0.0802905i	−0.0429818	−	0.999076i	$-0.513686\pi$
$661$	9.04413	−	2.06426i	0.351776	−	0.0802905i	0.394758	+	0.918785i	$0.370829\pi$
$662$	40.0534	−	50.2253i	1.55672	−	1.95206i
$663$	4.37209	−	9.67335i	0.169798	−	0.375682i
$664$	−18.4549			−0.716189
$665$	−2.53134	−	1.21903i	−0.0981612	−	0.0472719i
$666$	23.8174	−	56.3041i	0.922906	−	2.18174i
$667$	−44.7170	+	35.6606i	−1.73145	+	1.38078i
$668$	−47.2102	−	10.7754i	−1.82662	−	0.416913i
$669$	1.13071	−	5.57531i	0.0437160	−	0.215554i
$670$	1.13793	+	2.36294i	0.0439621	+	0.0912882i
$671$	−2.12452	+	0.484909i	−0.0820164	+	0.0187197i
$672$	2.13526	+	8.40776i	0.0823695	+	0.324336i
$673$	−18.4827	+	14.7394i	−0.712454	+	0.568163i	−0.911238	−	0.411880i	$-0.864872\pi$
$673$	−18.4827	+	14.7394i	−0.712454	+	0.568163i	0.198784	+	0.980043i	$0.436301\pi$
$674$	−25.9498	+	32.5400i	−0.999549	+	1.25339i
$675$	21.2907	−	12.2388i	0.819480	−	0.471072i
$676$	−19.9655	−	25.0359i	−0.767903	−	0.962919i
$677$	5.24572	+	4.18332i	0.201609	+	0.160778i	0.719090	−	0.694917i	$-0.244559\pi$
$677$	5.24572	+	4.18332i	0.201609	+	0.160778i	−0.517481	+	0.855695i	$0.673130\pi$
$678$	−28.8284	+	63.7835i	−1.10715	+	2.44959i
$679$	−2.41587	+	1.16342i	−0.0927126	+	0.0446480i
$680$	25.2430	−	12.1564i	0.968023	−	0.466175i
$681$	9.67233	+	11.5417i	0.370644	+	0.442280i
$682$	3.32612	+	4.17082i	0.127364	+	0.159709i
$683$	28.2751	−	35.4558i	1.08192	−	1.35668i	0.152223	−	0.988346i	$-0.451357\pi$
$683$	28.2751	−	35.4558i	1.08192	−	1.35668i	0.929694	−	0.368334i	$-0.120072\pi$
$684$	1.89954	−	10.6944i	0.0726309	−	0.408909i
$685$		−	8.80175i		−	0.336298i
$686$	−4.99152	−	21.8693i	−0.190577	−	0.834974i
$687$	−5.93444	−	23.3673i	−0.226413	−	0.891519i
$688$	2.28476	+	10.0102i	0.0871058	+	0.381636i
$689$	−13.9928	+	11.1589i	−0.533082	+	0.425119i
$690$	−56.0349	−	66.8650i	−2.13321	−	2.54551i
$691$	20.0904	−	4.58550i	0.764275	−	0.174441i	0.177423	−	0.984135i	$-0.443224\pi$
$691$	20.0904	−	4.58550i	0.764275	−	0.174441i	0.586852	+	0.809694i	$0.300367\pi$
$692$	−1.96534	−	8.61070i	−0.0747109	−	0.327330i
$693$	2.36839	−	0.663156i	0.0899678	−	0.0251912i
$694$	18.7958	−	39.0300i	0.713480	−	1.48156i
$695$	−8.02361	+	35.1537i	−0.304353	+	1.33346i
$696$	18.5178	−	24.4151i	0.701916	−	0.925450i
$697$	−40.5227	+	19.5147i	−1.53491	+	0.739173i
$698$	−52.9977	−	25.5224i	−2.00599	−	0.966036i
$699$	−7.23236	−	14.1291i	−0.273553	−	0.534410i
$700$	8.27082	−	6.59576i	0.312608	−	0.249296i
$701$	−44.6246	−	21.4901i	−1.68545	−	0.811668i	−0.996196	−	0.0871448i	$-0.972226\pi$
$701$	−44.6246	−	21.4901i	−1.68545	−	0.811668i	−0.689250	−	0.724523i	$-0.742060\pi$
$702$	17.6622	−	1.29017i	0.666617	−	0.0486943i
$703$	6.85962	−	8.60169i	0.258715	−	0.324419i
$704$	12.8659	−	6.19591i	0.484903	−	0.233517i
$705$	−32.1198	−	24.3616i	−1.20970	−	0.917510i
$706$	72.5712	+	16.5639i	2.73125	+	0.623390i
$707$	−1.81697	+	7.96069i	−0.0683344	+	0.299392i
$708$	22.9919	−	0.558945i	0.864087	−	0.0210064i
$709$		−	17.1523i		−	0.644167i	−0.946711	−	0.322084i	$-0.895617\pi$
$709$		−	17.1523i		−	0.644167i	0.946711	−	0.322084i	$-0.104383\pi$
$710$	−53.8980	−	23.3944i	−2.02275	−	0.877978i
$711$	1.38258	+	4.93775i	0.0518509	+	0.185180i
$712$	14.7746	+	18.5268i	0.553703	+	0.694322i
$713$	−15.2949	−	3.49095i	−0.572797	−	0.130737i
$714$	−7.46419	−	8.90682i	−0.279340	−	0.333330i
$715$	−5.22212			−0.195296
$716$	−14.5486	−	30.2104i	−0.543706	−	1.12902i
$717$	10.8121	+	42.5734i	0.403784	+	1.58993i
$718$	−46.2963	+	22.2951i	−1.72776	+	0.832047i
$719$	−4.52178	+	9.38957i	−0.168634	+	0.350172i	−0.968110	−	0.250526i	$-0.919396\pi$
$719$	−4.52178	+	9.38957i	−0.168634	+	0.350172i	0.799476	+	0.600698i	$0.205111\pi$
$720$	−7.61125	−	5.48662i	−0.283654	−	0.204474i
$721$	4.03148	−	8.37145i	0.150140	−	0.311769i
$722$	−17.0187	+	35.3397i	−0.633370	+	1.31521i
$723$	−8.79855	−	1.78441i	−0.327222	−	0.0663631i
$724$			66.2678i			2.46282i
$725$	36.4844	+	8.32733i	1.35500	+	0.309269i
$726$	17.2812	+	33.7604i	0.641366	+	1.25297i
$727$		−	27.1981i		−	1.00872i	−0.863493	−	0.504361i	$-0.831728\pi$
$727$		−	27.1981i		−	1.00872i	0.863493	−	0.504361i	$-0.168272\pi$
$728$	2.47795	−	0.565576i	0.0918390	−	0.0209616i
$729$	13.5879	−	23.3317i	0.503257	−	0.864137i
$730$	−3.11348	+	13.6410i	−0.115235	+	0.504877i
$731$	−25.6674	−	32.1859i	−0.949342	−	1.19044i
$732$	−4.24429	+	9.39058i	−0.156873	+	0.347086i
$733$	−1.97334	−	1.57368i	−0.0728869	−	0.0581254i	0.586369	−	0.810044i	$-0.300557\pi$
$733$	−1.97334	−	1.57368i	−0.0728869	−	0.0581254i	−0.659256	+	0.751919i	$0.729128\pi$
$734$	39.3698	−	8.98591i	1.45317	−	0.331676i
$735$	27.7298	+	21.0319i	1.02283	+	0.775772i
$736$	−21.0322	+	43.6739i	−0.775259	+	1.60984i
$737$	−0.323030	−	0.257608i	−0.0118990	−	0.00948911i
$738$	−60.8667	−	43.8761i	−2.24053	−	1.61510i
$739$	7.08444	−	31.0390i	0.260605	−	1.14179i	−0.659992	−	0.751273i	$-0.729440\pi$
$739$	7.08444	−	31.0390i	0.260605	−	1.14179i	0.920597	−	0.390514i	$-0.127703\pi$
$740$	36.9890	+	76.8084i	1.35974	+	2.82353i
$741$	3.12344	+	0.633456i	0.114742	+	0.0232706i
$742$	4.35975	+	19.1013i	0.160051	+	0.701231i
$743$	−24.6208	+	30.8735i	−0.903249	+	1.13264i	0.0873964	+	0.996174i	$0.472145\pi$
$743$	−24.6208	+	30.8735i	−0.903249	+	1.13264i	−0.990645	+	0.136464i	$0.956426\pi$
$744$	8.40271	−	0.204275i	0.308058	−	0.00748907i
$745$	31.5019	+	25.1219i	1.15414	+	0.920396i
$746$	32.8692	+	26.2123i	1.20343	+	0.959701i
$747$	−20.1010	−	14.4900i	−0.735459	−	0.530160i
$748$	−8.25990	+	10.3576i	−0.302012	+	0.378711i
$749$	0.719213	+	3.15108i	0.0262795	+	0.115138i
$750$	0.657417	−	3.24158i	0.0240055	−	0.118366i
$751$	2.19682	+	4.56175i	0.0801632	+	0.166461i	0.937198	−	0.348798i	$-0.113410\pi$
$751$	2.19682	+	4.56175i	0.0801632	+	0.166461i	−0.857035	+	0.515259i	$0.827696\pi$
$752$	−1.66542	+	7.29667i	−0.0607315	+	0.266082i
$753$	−0.311643	−	12.8192i	−0.0113569	−	0.467159i
$754$	21.0989	+	16.8258i	0.768377	+	0.612760i
$755$	−14.9104	+	30.9617i	−0.542645	+	1.12681i
$756$	4.26959	−	10.8188i	0.155284	−	0.393477i
$757$	43.5346	−	9.93648i	1.58229	−	0.361148i	0.661112	−	0.750287i	$-0.270085\pi$
$757$	43.5346	−	9.93648i	1.58229	−	0.361148i	0.921179	+	0.389140i	$0.127228\pi$
$758$	50.9145	+	40.6029i	1.84930	+	1.47476i
$759$	12.5239	+	5.66047i	0.454589	+	0.205462i
$760$	5.24451	+	6.57640i	0.190238	+	0.238551i
$761$	−7.15903	+	31.3657i	−0.259514	+	1.13701i	0.662258	+	0.749276i	$0.269598\pi$
$761$	−7.15903	+	31.3657i	−0.259514	+	1.13701i	−0.921772	+	0.387731i	$0.873259\pi$
$762$	45.3080	+	20.4780i	1.64134	+	0.741839i
$763$	5.44548	−	1.24290i	0.197140	−	0.0449958i
$764$			44.6799i			1.61646i
$765$	37.0392	+	6.57895i	1.33916	+	0.237863i
$766$	−39.9879	−	9.12697i	−1.44482	−	0.329771i
$767$			6.74820i			0.243663i
$768$	3.09103	−	15.2412i	0.111538	−	0.549970i
$769$	4.36887	−	9.07206i	0.157546	−	0.327147i	−0.807223	−	0.590247i	$-0.799031\pi$
$769$	4.36887	−	9.07206i	0.157546	−	0.327147i	0.964769	+	0.263100i	$0.0847448\pi$
$770$	−2.48039	+	5.15059i	−0.0893871	+	0.185614i
$771$	−38.8061	+	0.943399i	−1.39757	+	0.0339757i
$772$	−13.0081	+	27.0116i	−0.468171	+	0.972168i
$773$	40.1535	−	19.3369i	1.44422	−	0.695501i	0.462641	−	0.886546i	$-0.346902\pi$
$773$	40.1535	−	19.3369i	1.44422	−	0.695501i	0.981581	+	0.191045i	$0.0611876\pi$
$774$	26.7560	−	63.2508i	0.961724	−	2.27350i
$775$	4.45371	+	9.24823i	0.159982	+	0.332206i
$776$	8.02783			0.288182
$777$	9.02951	−	7.56701i	0.323932	−	0.271465i
$778$	12.1563	+	2.77459i	0.435823	+	0.0994737i
$779$	−8.41905	−	10.5572i	−0.301644	−	0.378249i
$780$	−14.9235	+	19.6760i	−0.534346	+	0.704515i
$781$	9.24924	−	0.363566i	0.330964	−	0.0130094i
$782$		−	64.9382i		−	2.32219i
$783$	39.3392	−	12.0535i	1.40587	−	0.430756i
$784$	1.43779	−	6.29937i	0.0513497	−	0.224978i
$785$	−2.14942	−	0.490590i	−0.0767159	−	0.0175099i
$786$	0.747778	−	0.985918i	0.0266724	−	0.0351665i
$787$	16.0193	−	7.71448i	0.571026	−	0.274992i	−0.126009	−	0.992029i	$-0.540217\pi$
$787$	16.0193	−	7.71448i	0.571026	−	0.274992i	0.697035	+	0.717037i	$0.254502\pi$
$788$	−20.0818	+	25.1817i	−0.715383	+	0.897062i
$789$	21.9406	+	4.44973i	0.781108	+	0.158415i
$790$	−10.7382	−	5.17126i	−0.382049	−	0.183985i
$791$	−10.5458	+	8.41002i	−0.374967	+	0.299026i
$792$	−7.24992	−	1.28774i	−0.257615	−	0.0457579i
$793$	−2.72428	−	1.31194i	−0.0967420	−	0.0465885i
$794$	−7.37739	+	3.55276i	−0.261814	+	0.126083i
$795$	−50.5337	−	38.3277i	−1.79225	−	1.35934i
$796$	−13.1953	+	57.8122i	−0.467693	+	2.04910i
$797$	23.1631	−	48.0986i	0.820478	−	1.70374i	0.116876	−	0.993147i	$-0.462712\pi$
$797$	23.1631	−	48.0986i	0.820478	−	1.70374i	0.703602	−	0.710594i	$-0.251574\pi$
$798$	2.10834	−	2.77977i	0.0746345	−	0.0984029i
$799$	−6.67735	−	29.2554i	−0.236228	−	1.03498i
$800$	30.9215	−	7.05763i	1.09324	−	0.249525i
$801$	1.54608	+	31.7798i	0.0546281	+	1.12288i
$802$	−34.6368	+	27.6219i	−1.22307	+	0.975365i
$803$	−0.490493	−	2.14899i	−0.0173091	−	0.0758363i
$804$	−1.89376	+	0.480945i	−0.0667877	+	0.0169616i
$805$	−3.74096	−	16.3902i	−0.131851	−	0.577679i
$806$			7.40220i			0.260731i
$807$	−24.6043	+	12.5944i	−0.866113	+	0.443344i
$808$	15.2420	−	19.1129i	0.536212	−	0.672388i
$809$	−31.8846	−	39.9820i	−1.12100	−	1.40569i	−0.902944	−	0.429759i	$-0.858599\pi$
$809$	−31.8846	−	39.9820i	−1.12100	−	1.40569i	−0.218060	−	0.975935i	$-0.569973\pi$
$810$	19.8381	+	59.5397i	0.697040	+	2.09201i
$811$	46.2530	−	22.2743i	1.62416	−	0.782155i	0.624162	−	0.781295i	$-0.285440\pi$
$811$	46.2530	−	22.2743i	1.62416	−	0.782155i	1.00000		0.000860359i	$-0.000273861\pi$
$812$	15.9686	−	7.69007i	0.560388	−	0.269869i
$813$	34.9204	+	15.7831i	1.22471	+	0.553536i
$814$	−17.5021	−	13.9574i	−0.613448	−	0.489208i
$815$	34.7664	+	43.5957i	1.21782	+	1.52709i
$816$	−1.71913	−	6.76920i	−0.0601815	−	0.236969i
$817$	7.70595	−	9.66296i	0.269597	−	0.338064i
$818$	24.8153	−	19.7895i	0.867646	−	0.691925i
$819$	3.14304	+	1.32955i	0.109827	+	0.0464583i
$820$	102.008	−	23.2827i	3.56228	−	0.813067i
$821$	−3.54972	−	7.37106i	−0.123886	−	0.257252i	0.829797	−	0.558065i	$-0.188456\pi$
$821$	−3.54972	−	7.37106i	−0.123886	−	0.257252i	−0.953683	+	0.300813i	$0.902742\pi$
$822$	10.7118	+	2.17243i	0.373616	+	0.0757721i
$823$	6.95582	+	1.58762i	0.242465	+	0.0553410i	0.342026	−	0.939690i	$-0.388887\pi$
$823$	6.95582	+	1.58762i	0.242465	+	0.0553410i	−0.0995615	+	0.995031i	$0.531744\pi$
$824$	−21.7490	+	17.3442i	−0.757661	+	0.604215i
$825$	−2.21349	−	8.71580i	−0.0770639	−	0.303445i
$826$	6.65576	+	3.20525i	0.231584	+	0.111525i
$827$	−4.96494			−0.172648			−0.0863239	−	0.996267i	$-0.527512\pi$
$827$	−4.96494			−0.172648			−0.0863239	+	0.996267i	$0.527512\pi$
$828$	57.1177	−	31.0118i	1.98498	−	1.07773i
$829$	−28.7158	+	36.0085i	−0.997341	+	1.25063i	−0.0293682	+	0.999569i	$0.509350\pi$
$829$	−28.7158	+	36.0085i	−0.997341	+	1.25063i	−0.967972	+	0.251057i	$0.919222\pi$
$830$	56.1518	−	12.8163i	1.94906	−	0.444860i
$831$	−16.5601	+	0.402586i	−0.574464	+	0.0139655i
$832$	19.3178	+	4.40915i	0.669723	+	0.152860i
$833$	5.76470	+	25.2568i	0.199735	+	0.875097i
$834$	−40.8019	−	18.4413i	−1.41285	−	0.638571i
$835$	50.3518			1.74250
$836$	−3.58344	−	1.72569i	−0.123936	−	0.0596844i
$837$	9.31260	+	6.37494i	0.321891	+	0.220350i
$838$	−26.2861			−0.908037
$839$	−8.24585	−	17.1227i	−0.284678	−	0.591141i	0.708768	−	0.705442i	$-0.249251\pi$
$839$	−8.24585	−	17.1227i	−0.284678	−	0.591141i	−0.993446	+	0.114301i	$0.963537\pi$
$840$	4.10412	+	8.01777i	0.141606	+	0.276639i
$841$	30.3612	+	14.6212i	1.04694	+	0.504178i
$842$	−10.1355	−	12.7095i	−0.349293	−	0.438000i
$843$	3.98707	−	2.04089i	0.137322	−	0.0702920i
$844$	−32.6082	−	67.7117i	−1.12242	−	2.33073i
$845$	26.0325	+	20.7602i	0.895544	+	0.714173i
$846$	37.5758	−	33.0771i	1.29188	−	1.13721i
$847$			7.30864i			0.251128i
$848$	−2.62018	+	11.4797i	−0.0899773	+	0.394216i
$849$	16.0033	−	13.4113i	0.549233	−	0.460274i
$850$	−33.2192	+	26.4914i	−1.13941	+	0.908649i
$851$	65.8327			2.25672
$852$	25.0621	−	35.8885i	0.858612	−	1.22952i
$853$	−32.3178			−1.10654			−0.553271	−	0.833001i	$-0.686621\pi$
$853$	−32.3178			−1.10654			−0.553271	+	0.833001i	$0.686621\pi$
$854$	−2.58795	+	2.06382i	−0.0885577	+	0.0706224i
$855$	0.548807	+	11.2808i	0.0187688	+	0.385794i
$856$	2.15324	−	9.43395i	0.0735961	−	0.322446i
$857$			15.1369i			0.517067i	0.966002	+	0.258533i	$0.0832392\pi$
$857$			15.1369i			0.517067i	−0.966002	+	0.258533i	$0.916761\pi$
$858$	1.28891	−	6.35534i	0.0440027	−	0.216968i
$859$	8.05874	+	6.42663i	0.274961	+	0.219274i	0.751255	−	0.660012i	$-0.229449\pi$
$859$	8.05874	+	6.42663i	0.274961	+	0.219274i	−0.476294	+	0.879286i	$0.658020\pi$
$860$	41.5527	+	86.2850i	1.41693	+	2.94229i
$861$	−6.58838	−	12.8710i	−0.224531	−	0.438642i
$862$	−21.1342	−	26.5015i	−0.719834	−	0.902643i
$863$	−23.8458	−	11.4835i	−0.811720	−	0.390904i	−0.0184923	−	0.999829i	$-0.505887\pi$
$863$	−23.8458	−	11.4835i	−0.811720	−	0.390904i	−0.793228	+	0.608925i	$0.791601\pi$
$864$	25.6068	−	23.6701i	0.871160	−	0.805272i
$865$	3.98466	+	8.27423i	0.135483	+	0.281332i
$866$	−43.4545			−1.47664
$867$	−0.926686	−	1.10579i	−0.0314719	−	0.0375546i
$868$	4.38007	+	2.10933i	0.148669	+	0.0715953i
$869$	1.87763			0.0636943
$870$	−39.3878	+	87.1464i	−1.33537	+	2.95454i
$871$	−0.127571	−	0.558927i	−0.00432259	−	0.0189385i
$872$	−16.3031	−	3.72108i	−0.552093	−	0.126012i
$873$	8.74390	+	6.30309i	0.295936	+	0.213327i
$874$	19.0072	−	4.33826i	0.642927	−	0.146744i
$875$	0.397406	−	0.498332i	0.0134348	−	0.0168467i
$876$	−9.49873	−	4.29316i	−0.320932	−	0.145053i
$877$	−6.56156			−0.221568			−0.110784	−	0.993845i	$-0.535336\pi$
$877$	−6.56156			−0.221568			−0.110784	+	0.993845i	$0.535336\pi$
$878$	4.36009	+	2.09971i	0.147146	+	0.0708618i
$879$	10.9262	−	2.77485i	0.368532	−	0.0935935i
$880$	−2.68614	+	2.14213i	−0.0905499	+	0.0722111i
$881$	−44.4743	−	10.1510i	−1.49838	−	0.341995i	−0.606798	−	0.794856i	$-0.707546\pi$
$881$	−44.4743	−	10.1510i	−1.49838	−	0.341995i	−0.891581	+	0.452861i	$0.850403\pi$
$882$	−32.4400	+	28.5562i	−1.09231	+	0.961536i
$883$	−8.82431	−	18.3239i	−0.296962	−	0.616647i	0.698090	−	0.716010i	$-0.254034\pi$
$883$	−8.82431	−	18.3239i	−0.296962	−	0.616647i	−0.995051	+	0.0993633i	$0.968319\pi$
$884$	−17.9213	+	4.09043i	−0.602760	+	0.137576i
$885$	−23.1783	+	5.88644i	−0.779131	+	0.197871i
$886$	9.15426	−	7.30028i	0.307543	−	0.245258i
$887$	23.0499	−	28.9036i	0.773938	−	0.970488i	−0.226055	−	0.974115i	$-0.572583\pi$
$887$	23.0499	−	28.9036i	0.773938	−	0.970488i	0.999993	+	0.00362661i	$0.00115439\pi$
$888$	−34.1857	+	8.68190i	−1.14720	+	0.291345i
$889$	5.97398	+	7.49113i	0.200361	+	0.251244i
$890$	−57.8203	−	46.1101i	−1.93814	−	1.54562i
$891$	−6.88552	−	7.09492i	−0.230674	−	0.237689i
$892$	−8.87542	+	4.27418i	−0.297171	+	0.143110i
$893$	8.11686	−	3.90887i	0.271620	−	0.130806i
$894$	−38.3487	+	32.1374i	−1.28257	+	1.07483i
$895$	21.7384	+	27.2591i	0.726636	+	0.911173i
$896$	7.27899	−	9.12757i	0.243174	−	0.304931i
$897$	8.68940	+	16.9755i	0.290131	+	0.566796i
$898$		−	26.7467i		−	0.892550i
$899$	3.82685	+	16.7665i	0.127632	+	0.559194i
$900$	−39.1652	−	16.5674i	−1.30551	−	0.552248i
$901$	−10.5054	−	46.0271i	−0.349985	−	1.53339i
$902$	−21.4809	+	17.1305i	−0.715237	+	0.570382i
$903$	10.1436	−	8.50062i	0.337557	−	0.282883i
$904$	39.3708	−	8.98614i	1.30945	−	0.298874i
$905$	−15.3330	−	67.1780i	−0.509685	−	2.23307i
$906$	−34.0004	−	25.7879i	−1.12959	−	0.856745i
$907$	−6.53009	+	13.5599i	−0.216828	+	0.450248i	−0.980804	−	0.194997i	$-0.937530\pi$
$907$	−6.53009	+	13.5599i	−0.216828	+	0.450248i	0.763976	+	0.645245i	$0.223245\pi$
$908$	5.80252	−	25.4225i	0.192564	−	0.843676i
$909$	31.6081	−	8.85035i	1.04837	−	0.293548i
$910$	−7.14676	+	3.44170i	−0.236913	+	0.114091i
$911$	21.4995	+	10.3536i	0.712312	+	0.343031i	0.754700	−	0.656070i	$-0.227782\pi$
$911$	21.4995	+	10.3536i	0.712312	+	0.343031i	−0.0423883	+	0.999101i	$0.513497\pi$
$912$	1.86647	−	0.955406i	0.0618051	−	0.0316366i
$913$	−7.09401	+	5.65729i	−0.234778	+	0.187229i
$914$	30.0747	+	14.4832i	0.994783	+	0.479062i
$915$	2.12980	−	10.5016i	0.0704092	−	0.347172i
$916$	−26.0296	+	32.6401i	−0.860043	+	1.07846i
$917$	0.214844	−	0.103463i	0.00709476	−	0.00341666i
$918$	−17.1485	+	43.4530i	−0.565986	+	1.43416i
$919$	−40.1415	−	9.16203i	−1.32415	−	0.302228i	−0.498732	−	0.866756i	$-0.666201\pi$
$919$	−40.1415	−	9.16203i	−1.32415	−	0.302228i	−0.825413	+	0.564529i	$0.809058\pi$
$920$	−11.2000	+	49.0703i	−0.369252	+	1.61780i
$921$	0.504061	+	20.7343i	0.0166094	+	0.683217i
$922$		−	82.0559i		−	2.70237i
$923$	10.3485	+	7.60739i	0.340624	+	0.250400i
$924$	−3.39332	−	2.57370i	−0.111632	−	0.0846684i
$925$	−26.8563	−	33.6768i	−0.883031	−	1.10729i
$926$	−28.8758	−	6.59072i	−0.948919	−	0.216585i
$927$	−37.3068	+	1.81497i	−1.22532	+	0.0596115i
$928$	53.1385			1.74436
$929$	8.37619	+	17.3933i	0.274814	+	0.570657i	0.992002	−	0.126223i	$-0.0402855\pi$
$929$	8.37619	+	17.3933i	0.274814	+	0.570657i	−0.717188	+	0.696880i	$0.754571\pi$
$930$	−25.4246	+	6.45692i	−0.833707	+	0.211731i
$931$	−7.00746	+	3.37462i	−0.229660	+	0.110599i
$932$	−11.9255	+	24.7636i	−0.390633	+	0.811159i
$933$	0.270203	+	11.1146i	0.00884604	+	0.363876i
$934$	−9.21849	+	19.1424i	−0.301638	+	0.626358i
$935$	5.97683	−	12.4110i	0.195463	−	0.405884i
$936$	−6.75094	−	7.66913i	−0.220661	−	0.250673i
$937$			47.1315i			1.53972i	0.638214	+	0.769859i	$0.279673\pi$
$937$			47.1315i			1.53972i	−0.638214	+	0.769859i	$0.720327\pi$
$938$	−0.611864	−	0.139654i	−0.0199781	−	0.00455987i
$939$	22.0599	−	11.2920i	0.719899	−	0.368500i
$940$			69.8083i			2.27690i
$941$	18.6748	−	4.26239i	0.608780	−	0.138950i	0.0929926	−	0.995667i	$-0.470357\pi$
$941$	18.6748	−	4.26239i	0.608780	−	0.138950i	0.515787	+	0.856717i	$0.327500\pi$
$942$	1.12756	−	2.49476i	0.0367380	−	0.0812836i
$943$	17.9794	−	78.7730i	0.585490	−	2.56520i
$944$	2.76813	+	3.47112i	0.0900949	+	0.112975i
$945$	−1.82500	+	11.9553i	−0.0593671	+	0.388906i
$946$	−19.6615	−	15.6795i	−0.639250	−	0.509785i
$947$	−11.4187	+	2.60625i	−0.371059	+	0.0846919i	−0.403984	−	0.914766i	$-0.632375\pi$
$947$	−11.4187	+	2.60625i	−0.371059	+	0.0846919i	0.0329249	+	0.999458i	$0.489518\pi$
$948$	5.36578	−	7.07459i	0.174272	−	0.229772i
$949$	1.32705	−	2.75565i	0.0430779	−	0.0894523i
$950$	−9.97319	−	7.95335i	−0.323573	−	0.258041i
$951$	17.0065	−	0.413437i	0.551472	−	0.0134066i
$952$	−1.49191	+	6.53647i	−0.0483530	+	0.211848i
$953$	15.1049	+	31.3656i	0.489295	+	1.01603i	0.988734	+	0.149683i	$0.0478253\pi$
$953$	15.1049	+	31.3656i	0.489295	+	1.01603i	−0.499439	+	0.866349i	$0.666460\pi$
$954$	59.1175	−	52.0397i	1.91400	−	1.68485i
$955$	−10.3380	−	45.2936i	−0.334529	−	1.46567i
$956$	47.4239	−	59.4677i	1.53380	−	1.92332i
$957$	−0.366157	−	15.0616i	−0.0118362	−	0.486874i
$958$	4.12123	+	3.28657i	0.133151	+	0.106184i
$959$	1.64673	+	1.31322i	0.0531757	+	0.0424062i
$960$	1.70654	+	70.1976i	0.0550784	+	2.26562i
$961$	16.3871	−	20.5487i	0.528615	−	0.662862i
$962$	−6.91194	−	30.2832i	−0.222850	−	0.976369i
$963$	9.75241	−	8.58481i	0.314267	−	0.276642i
$964$	6.74520	+	14.0066i	0.217248	+	0.451121i
$965$	6.93686	−	30.3924i	0.223305	−	0.978365i
$966$	20.8703	−	0.507368i	0.671490	−	0.0163243i
$967$	−36.4535	−	29.0707i	−1.17227	−	0.934850i	−0.173515	−	0.984831i	$-0.555513\pi$
$967$	−36.4535	−	29.0707i	−1.17227	−	0.934850i	−0.998750	+	0.0499809i	$0.984084\pi$
$968$	9.49390	−	19.7143i	0.305145	−	0.633641i
$969$	−5.08033	+	6.69822i	−0.163204	+	0.215178i
$970$	−24.4259	+	5.57505i	−0.784268	+	0.179004i
$971$	−40.8066	−	32.5422i	−1.30955	−	1.04433i	−0.995484	−	0.0949252i	$-0.969739\pi$
$971$	−40.8066	−	32.5422i	−1.30955	−	1.04433i	−0.314061	−	0.949403i	$-0.601690\pi$
$972$	−46.4094	+	5.66802i	−1.48858	+	0.181802i
$973$	−5.37983	−	6.74610i	−0.172470	−	0.216270i
$974$	3.64417	−	15.9661i	0.116767	−	0.511588i
$975$	5.13902	−	11.3702i	0.164580	−	0.364138i
$976$	−1.93947	+	0.442672i	−0.0620810	+	0.0141696i
$977$			16.9870i			0.543463i	0.962373	+	0.271731i	$0.0875962\pi$
$977$			16.9870i			0.543463i	−0.962373	+	0.271731i	$0.912404\pi$
$978$	−61.6371	+	31.5507i	−1.97094	+	1.00888i
$979$	11.3587	+	2.59254i	0.363024	+	0.0828580i
$980$		−	60.2670i		−	1.92516i
$981$	−14.8357	−	16.8535i	−0.473667	−	0.538090i
$982$	−5.48927	+	11.3986i	−0.175170	+	0.363743i
$983$	−10.9858	+	22.8123i	−0.350393	+	0.727599i	−0.999451	−	0.0331405i	$-0.989449\pi$
$983$	−10.9858	+	22.8123i	−0.350393	+	0.727599i	0.649058	+	0.760739i	$0.275163\pi$
$984$	1.05207	+	43.2764i	0.0335389	+	1.37960i
$985$	14.5311	−	30.1741i	0.462999	−	0.961427i
$986$	−64.1368	+	30.8866i	−2.04253	+	0.983631i
$987$	9.35012	−	2.37459i	0.297618	−	0.0755839i
$988$	−2.39451	−	4.97225i	−0.0761794	−	0.158188i
$989$	73.9550			2.35163
$990$	22.9533	−	1.11667i	0.729502	−	0.0354902i
$991$	18.3551	+	4.18944i	0.583070	+	0.133082i	0.503874	−	0.863777i	$-0.331908\pi$
$991$	18.3551	+	4.18944i	0.583070	+	0.133082i	0.0791961	+	0.996859i	$0.474765\pi$
$992$	9.08767	+	11.3956i	0.288534	+	0.361810i
$993$	−39.6497	−	30.0727i	−1.25825	−	0.954327i
$994$	12.4185	−	6.59338i	0.393890	−	0.209129i
$995$		−	61.6593i		−	1.95473i
$996$	1.04283	+	42.8961i	0.0330432	+	1.35921i
$997$	−4.53729	+	19.8791i	−0.143697	+	0.629579i	0.850860	+	0.525392i	$0.176081\pi$
$997$	−4.53729	+	19.8791i	−0.143697	+	0.629579i	−0.994558	+	0.104187i	$0.966776\pi$
$998$	89.9954	+	20.5409i	2.84875	+	0.650209i
$999$	−44.0516	−	17.3847i	−1.39373	−	0.550029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	213.2.l.a.23.3	✓	132
3.2	odd	2	inner	213.2.l.a.23.20	yes	132
71.34	odd	14	inner	213.2.l.a.176.20	yes	132
213.176	even	14	inner	213.2.l.a.176.3	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.l.a.23.3	✓	132	1.1	even	1	trivial
213.2.l.a.23.20	yes	132	3.2	odd	2	inner
213.2.l.a.176.3	yes	132	213.176	even	14	inner
213.2.l.a.176.20	yes	132	71.34	odd	14	inner

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:	\( N \)	\(=\)	\( 213 = 3 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	213.l (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.74810 + 1.39407i) q^{2} +(1.11251 + 1.32753i) q^{3} +(0.667405 - 2.92409i) q^{4} +3.11868i q^{5} +(-3.79544 - 0.769744i) q^{6} +(-0.583477 - 0.465307i) q^{7} +(0.969434 + 2.01305i) q^{8} +(-0.524652 + 2.95377i) q^{9} +(-4.34764 - 5.45177i) q^{10} +(0.989742 + 0.476634i) q^{11} +(4.62430 - 2.36708i) q^{12} +(0.661360 + 1.37333i) q^{13} +1.66865 q^{14} +(-4.14012 + 3.46955i) q^{15} +(0.903532 + 0.435118i) q^{16} -4.02082 q^{17} +(-3.20060 - 5.89489i) q^{18} +(-0.268615 - 1.17688i) q^{19} +(9.11929 + 2.08142i) q^{20} +(-0.0314150 - 1.29224i) q^{21} +(-2.39463 + 0.546559i) q^{22} +(4.50361 - 5.64734i) q^{23} +(-1.59387 + 3.52649i) q^{24} -4.72614 q^{25} +(-3.07064 - 1.47874i) q^{26} +(-4.50488 + 2.58960i) q^{27} +(-1.75002 + 1.39559i) q^{28} +(-7.71970 - 1.76197i) q^{29} +(2.40058 - 11.8367i) q^{30} +(-0.942357 - 1.95682i) q^{31} +(-6.54265 + 1.49332i) q^{32} +(0.468351 + 1.84417i) q^{33} +(7.02882 - 5.60530i) q^{34} +(1.45114 - 1.81968i) q^{35} +(8.28693 + 3.50549i) q^{36} +(5.68251 + 7.12564i) q^{37} +(2.11022 + 1.68284i) q^{38} +(-1.08736 + 2.40581i) q^{39} +(-6.27806 + 3.02335i) q^{40} +(10.0782 - 4.85341i) q^{41} +(1.85638 + 2.21517i) q^{42} +(6.38361 + 8.00479i) q^{43} +(2.05428 - 2.57599i) q^{44} +(-9.21184 - 1.63622i) q^{45} +16.1505i q^{46} +(1.66069 + 7.27597i) q^{47} +(0.427556 + 1.68353i) q^{48} +(-1.43371 - 6.28150i) q^{49} +(8.26179 - 6.58856i) q^{50} +(-4.47320 - 5.33775i) q^{51} +(4.45713 - 1.01731i) q^{52} +(2.61274 + 11.4472i) q^{53} +(4.26493 - 10.8070i) q^{54} +(-1.48647 + 3.08668i) q^{55} +(0.371045 - 1.62565i) q^{56} +(1.26350 - 1.66588i) q^{57} +(15.9511 - 7.68167i) q^{58} +(3.98872 + 1.92086i) q^{59} +(7.38215 + 14.4217i) q^{60} +(-1.55092 + 1.23682i) q^{61} +(4.37528 + 2.10702i) q^{62} +(1.68053 - 1.47933i) q^{63} +(8.10492 - 10.1633i) q^{64} +(-4.28297 + 2.06257i) q^{65} +(-3.38962 - 2.57088i) q^{66} +(-0.366683 - 0.0836929i) q^{67} +(-2.68352 + 11.7573i) q^{68} +(12.5073 - 0.304059i) q^{69} +5.20397i q^{70} +(7.44224 - 3.95133i) q^{71} +(-6.45470 + 1.80733i) q^{72} +(-1.25106 - 1.56878i) q^{73} +(-19.8672 - 4.53456i) q^{74} +(-5.25787 - 6.27408i) q^{75} -3.62058 q^{76} +(-0.355710 - 0.738639i) q^{77} +(-1.45304 - 5.72146i) q^{78} +(1.53996 - 0.741603i) q^{79} +(-1.35699 + 2.81782i) q^{80} +(-8.44948 - 3.09940i) q^{81} +(-10.8518 + 22.5340i) q^{82} +(-3.58377 + 7.44178i) q^{83} +(-3.79959 - 0.770586i) q^{84} -12.5397i q^{85} +(-22.3184 - 5.09403i) q^{86} +(-6.24917 - 12.2083i) q^{87} +2.45447i q^{88} +(10.3399 - 2.36001i) q^{89} +(18.3843 - 9.98164i) q^{90} +(0.253131 - 1.10904i) q^{91} +(-13.5076 - 16.9380i) q^{92} +(1.54936 - 3.42799i) q^{93} +(-13.0462 - 10.4040i) q^{94} +(3.67031 - 0.837724i) q^{95} +(-9.26117 - 7.02421i) q^{96} +(1.55893 - 3.23715i) q^{97} +(11.2631 + 8.98203i) q^{98} +(-1.92714 + 2.67340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 10 q^{3} + 10 q^{4} - 15 q^{6} - 14 q^{7} - 14 q^{9} + 2 q^{10} + 20 q^{12} - 14 q^{13} + 22 q^{15} - 30 q^{16} + 8 q^{18} - 14 q^{19} - 28 q^{21} - 14 q^{22} + 8 q^{24} - 84 q^{25} - 7 q^{27} - 42 q^{28}+ \cdots + 49 q^{99}+O(q^{100}) \) 132 * q - 10 * q^3 + 10 * q^4 - 15 * q^6 - 14 * q^7 - 14 * q^9 + 2 * q^10 + 20 * q^12 - 14 * q^13 + 22 * q^15 - 30 * q^16 + 8 * q^18 - 14 * q^19 - 28 * q^21 - 14 * q^22 + 8 * q^24 - 84 * q^25 - 7 * q^27 - 42 * q^28 - 5 * q^30 + 14 * q^31 - 7 * q^33 - 42 * q^34 - 43 * q^36 + 22 * q^37 - 35 * q^39 + 64 * q^40 - 28 * q^42 + 16 * q^43 - 50 * q^45 + 55 * q^48 + 12 * q^49 - 98 * q^51 - 168 * q^52 - 38 * q^54 + 70 * q^55 + 48 * q^57 + 86 * q^58 + 116 * q^60 + 14 * q^61 + 105 * q^63 + 2 * q^64 - 42 * q^67 - 28 * q^69 + 266 * q^72 - 62 * q^73 + 18 * q^75 - 120 * q^76 + 21 * q^78 - 74 * q^79 - 22 * q^81 - 182 * q^82 + 42 * q^84 - 2 * q^87 + 15 * q^90 - 22 * q^91 + 14 * q^94 - 210 * q^96 - 42 * q^97 + 49 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more