LMFDB - Embedded newform 222.2.g.a.179.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [222,2,Mod(179,222)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(222, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("222.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 222 = 2 \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	222.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.77267892487$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			179.13
Character	$\chi$	$=$	222.179
Dual form			222.2.g.a.191.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.16395 - 1.28266i) q^{3} -1.00000i q^{4} +(0.266957 + 0.266957i) q^{5} +(-0.0839450 - 1.73002i) q^{6} -1.78781 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.290452 - 2.98591i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.16395 - 1.28266i) q^{3} -1.00000i q^{4} +(0.266957 + 0.266957i) q^{5} +(-0.0839450 - 1.73002i) q^{6} -1.78781 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.290452 - 2.98591i) q^{9} +0.377534 q^{10} +4.12119 q^{11} +(-1.28266 - 1.16395i) q^{12} +(-1.12529 + 1.12529i) q^{13} +(-1.26417 + 1.26417i) q^{14} +(0.653140 - 0.0316921i) q^{15} -1.00000 q^{16} +(1.26417 + 1.26417i) q^{17} +(-2.31674 - 1.90597i) q^{18} +(-5.39058 + 5.39058i) q^{19} +(0.266957 - 0.266957i) q^{20} +(-2.08092 + 2.29316i) q^{21} +(2.91412 - 2.91412i) q^{22} +(3.99326 + 3.99326i) q^{23} +(-1.73002 + 0.0839450i) q^{24} -4.85747i q^{25} +1.59140i q^{26} +(-4.16799 - 3.10289i) q^{27} +1.78781i q^{28} +(0.163784 - 0.163784i) q^{29} +(0.439430 - 0.484249i) q^{30} +(1.13043 + 1.13043i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.79684 - 5.28610i) q^{33} +1.78781 q^{34} +(-0.477268 - 0.477268i) q^{35} +(-2.98591 + 0.290452i) q^{36} +(4.38956 + 4.21091i) q^{37} +7.62343i q^{38} +(0.133590 + 2.75315i) q^{39} -0.377534i q^{40} -0.931119 q^{41} +(0.150078 + 3.09294i) q^{42} +(0.410276 - 0.410276i) q^{43} -4.12119i q^{44} +(0.719570 - 0.874646i) q^{45} +5.64732 q^{46} +10.2781i q^{47} +(-1.16395 + 1.28266i) q^{48} -3.80373 q^{49} +(-3.43475 - 3.43475i) q^{50} +(3.09294 - 0.150078i) q^{51} +(1.12529 + 1.12529i) q^{52} -6.30007i q^{53} +(-5.14128 + 0.753139i) q^{54} +(1.10018 + 1.10018i) q^{55} +(1.26417 + 1.26417i) q^{56} +(0.639949 + 13.1887i) q^{57} -0.231626i q^{58} +(-5.62756 - 5.62756i) q^{59} +(-0.0316921 - 0.653140i) q^{60} +(-1.08562 - 1.08562i) q^{61} +1.59867 q^{62} +(0.519274 + 5.33823i) q^{63} +1.00000i q^{64} -0.600808 q^{65} +(-0.345953 - 7.12972i) q^{66} -5.69230i q^{67} +(1.26417 - 1.26417i) q^{68} +(9.76994 - 0.474064i) q^{69} -0.674959 q^{70} +3.48288i q^{71} +(-1.90597 + 2.31674i) q^{72} -8.48345i q^{73} +(6.08145 - 0.126325i) q^{74} +(-6.23050 - 5.65384i) q^{75} +(5.39058 + 5.39058i) q^{76} -7.36790 q^{77} +(2.04123 + 1.85231i) q^{78} +(-7.58011 + 7.58011i) q^{79} +(-0.266957 - 0.266957i) q^{80} +(-8.83127 + 1.73453i) q^{81} +(-0.658401 + 0.658401i) q^{82} +9.27148i q^{83} +(2.29316 + 2.08092i) q^{84} +0.674959i q^{85} -0.580218i q^{86} +(-0.0194438 - 0.400716i) q^{87} +(-2.91412 - 2.91412i) q^{88} +(-2.03028 + 2.03028i) q^{89} +(-0.109656 - 1.12728i) q^{90} +(2.01180 - 2.01180i) q^{91} +(3.99326 - 3.99326i) q^{92} +(2.76572 - 0.134200i) q^{93} +(7.26774 + 7.26774i) q^{94} -2.87810 q^{95} +(0.0839450 + 1.73002i) q^{96} +(12.8316 - 12.8316i) q^{97} +(-2.68965 + 2.68965i) q^{98} +(-1.19701 - 12.3055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 8 q^{9}+O(q^{10}) $ 28 * q - 8 * q^9	$ 28 q - 8 q^{9} + 8 q^{12} + 20 q^{13} - 28 q^{16} - 20 q^{19} + 8 q^{22} + 12 q^{31} - 36 q^{37} - 8 q^{39} + 8 q^{42} - 28 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 20 q^{52} + 16 q^{55} + 8 q^{57} + 44 q^{61} + 16 q^{66} + 8 q^{69} - 16 q^{70} - 100 q^{75} + 20 q^{76} - 28 q^{79} + 8 q^{81} - 16 q^{82} - 76 q^{87} - 8 q^{88} + 60 q^{90} - 8 q^{91} + 84 q^{93} - 16 q^{94} + 28 q^{97}+O(q^{100}) $ 28 * q - 8 * q^9 + 8 * q^12 + 20 * q^13 - 28 * q^16 - 20 * q^19 + 8 * q^22 + 12 * q^31 - 36 * q^37 - 8 * q^39 + 8 * q^42 - 28 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 20 * q^52 + 16 * q^55 + 8 * q^57 + 44 * q^61 + 16 * q^66 + 8 * q^69 - 16 * q^70 - 100 * q^75 + 20 * q^76 - 28 * q^79 + 8 * q^81 - 16 * q^82 - 76 * q^87 - 8 * q^88 + 60 * q^90 - 8 * q^91 + 84 * q^93 - 16 * q^94 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/222\mathbb{Z}\right)^\times$.

$n$	$149$	$187$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.16395	−	1.28266i	0.672005	−	0.740546i
$3$	1.16395	−	1.28266i	0.672005	−	0.740546i
$4$		−	1.00000i		−	0.500000i
$5$	0.266957	+	0.266957i	0.119387	+	0.119387i	0.764276	−	0.644889i	$-0.223097\pi$
$5$	0.266957	+	0.266957i	0.119387	+	0.119387i	−0.644889	+	0.764276i	$0.723097\pi$
$6$	−0.0839450	−	1.73002i	−0.0342704	−	0.706276i
$7$	−1.78781			−0.675729			−0.337864	−	0.941195i	$-0.609705\pi$
$7$	−1.78781			−0.675729			−0.337864	+	0.941195i	$0.609705\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.290452	−	2.98591i	−0.0968175	−	0.995302i
$10$	0.377534			0.119387
$11$	4.12119			1.24258			0.621292	−	0.783579i	$-0.286608\pi$
$11$	4.12119			1.24258			0.621292	+	0.783579i	$0.286608\pi$
$12$	−1.28266	−	1.16395i	−0.370273	−	0.336003i
$13$	−1.12529	+	1.12529i	−0.312099	+	0.312099i	−0.845722	−	0.533623i	$-0.820830\pi$
$13$	−1.12529	+	1.12529i	−0.312099	+	0.312099i	0.533623	+	0.845722i	$0.320830\pi$
$14$	−1.26417	+	1.26417i	−0.337864	+	0.337864i
$15$	0.653140	−	0.0316921i	0.168640	−	0.00818287i
$16$	−1.00000			−0.250000
$17$	1.26417	+	1.26417i	0.306607	+	0.306607i	0.843592	−	0.536985i	$-0.180437\pi$
$17$	1.26417	+	1.26417i	0.306607	+	0.306607i	−0.536985	+	0.843592i	$0.680437\pi$
$18$	−2.31674	−	1.90597i	−0.546060	−	0.449242i
$19$	−5.39058	+	5.39058i	−1.23668	+	1.23668i	−0.275335	+	0.961348i	$0.588789\pi$
$19$	−5.39058	+	5.39058i	−1.23668	+	1.23668i	−0.961348	+	0.275335i	$0.911211\pi$
$20$	0.266957	−	0.266957i	0.0596934	−	0.0596934i
$21$	−2.08092	+	2.29316i	−0.454093	+	0.500408i
$22$	2.91412	−	2.91412i	0.621292	−	0.621292i
$23$	3.99326	+	3.99326i	0.832651	+	0.832651i	0.987879	−	0.155227i	$-0.0496111\pi$
$23$	3.99326	+	3.99326i	0.832651	+	0.832651i	−0.155227	+	0.987879i	$0.549611\pi$
$24$	−1.73002	+	0.0839450i	−0.353138	+	0.0171352i
$25$		−	4.85747i		−	0.971494i
$26$			1.59140i			0.312099i
$27$	−4.16799	−	3.10289i	−0.802129	−	0.597151i
$28$			1.78781i			0.337864i
$29$	0.163784	−	0.163784i	0.0304139	−	0.0304139i	−0.691736	−	0.722150i	$-0.743154\pi$
$29$	0.163784	−	0.163784i	0.0304139	−	0.0304139i	0.722150	+	0.691736i	$0.243154\pi$
$30$	0.439430	−	0.484249i	0.0802285	−	0.0884114i
$31$	1.13043	+	1.13043i	0.203031	+	0.203031i	0.801297	−	0.598266i	$-0.204144\pi$
$31$	1.13043	+	1.13043i	0.203031	+	0.203031i	−0.598266	+	0.801297i	$0.704144\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	4.79684	−	5.28610i	0.835023	−	0.920191i
$34$	1.78781			0.306607
$35$	−0.477268	−	0.477268i	−0.0806730	−	0.0806730i
$36$	−2.98591	+	0.290452i	−0.497651	+	0.0484087i
$37$	4.38956	+	4.21091i	0.721639	+	0.692269i
$37$	4.38956	+	4.21091i	0.721639	+	0.692269i
$38$			7.62343i			1.23668i
$39$	0.133590	+	2.75315i	0.0213915	+	0.440856i
$40$		−	0.377534i		−	0.0596934i
$41$	−0.931119			−0.145416			−0.0727082	−	0.997353i	$-0.523164\pi$
$41$	−0.931119			−0.145416			−0.0727082	+	0.997353i	$0.523164\pi$
$42$	0.150078	+	3.09294i	0.0231575	+	0.477251i
$43$	0.410276	−	0.410276i	0.0625665	−	0.0625665i	−0.675131	−	0.737698i	$-0.735913\pi$
$43$	0.410276	−	0.410276i	0.0625665	−	0.0625665i	0.737698	+	0.675131i	$0.235913\pi$
$44$		−	4.12119i		−	0.621292i
$45$	0.719570	−	0.874646i	0.107267	−	0.130385i
$46$	5.64732			0.832651
$47$			10.2781i			1.49922i	0.661879	+	0.749611i	$0.269759\pi$
$47$			10.2781i			1.49922i	−0.661879	+	0.749611i	$0.730241\pi$
$48$	−1.16395	+	1.28266i	−0.168001	+	0.185137i
$49$	−3.80373			−0.543391
$50$	−3.43475	−	3.43475i	−0.485747	−	0.485747i
$51$	3.09294	−	0.150078i	0.433098	−	0.0210151i
$52$	1.12529	+	1.12529i	0.156050	+	0.156050i
$53$		−	6.30007i		−	0.865381i	−0.901542	−	0.432691i	$-0.857564\pi$
$53$		−	6.30007i		−	0.865381i	0.901542	−	0.432691i	$-0.142436\pi$
$54$	−5.14128	+	0.753139i	−0.699640	+	0.102489i
$55$	1.10018	+	1.10018i	0.148348	+	0.148348i
$56$	1.26417	+	1.26417i	0.168932	+	0.168932i
$57$	0.639949	+	13.1887i	0.0847633	+	1.74688i
$58$		−	0.231626i		−	0.0304139i
$59$	−5.62756	−	5.62756i	−0.732646	−	0.732646i	0.238498	−	0.971143i	$-0.423345\pi$
$59$	−5.62756	−	5.62756i	−0.732646	−	0.732646i	−0.971143	+	0.238498i	$0.923345\pi$
$60$	−0.0316921	−	0.653140i	−0.00409143	−	0.0843200i
$61$	−1.08562	−	1.08562i	−0.138999	−	0.138999i	0.634183	−	0.773183i	$-0.281336\pi$
$61$	−1.08562	−	1.08562i	−0.138999	−	0.138999i	−0.773183	+	0.634183i	$0.781336\pi$
$62$	1.59867			0.203031
$63$	0.519274	+	5.33823i	0.0654224	+	0.672554i
$64$			1.00000i			0.125000i
$65$	−0.600808			−0.0745210
$66$	−0.345953	−	7.12972i	−0.0425839	−	0.877607i
$67$		−	5.69230i		−	0.695425i	−0.937601	−	0.347712i	$-0.886959\pi$
$67$		−	5.69230i		−	0.695425i	0.937601	−	0.347712i	$-0.113041\pi$
$68$	1.26417	−	1.26417i	0.153303	−	0.153303i
$69$	9.76994	−	0.474064i	1.17616	−	0.0570706i
$70$	−0.674959			−0.0806730
$71$			3.48288i			0.413342i	0.978410	+	0.206671i	$0.0662630\pi$
$71$			3.48288i			0.413342i	−0.978410	+	0.206671i	$0.933737\pi$
$72$	−1.90597	+	2.31674i	−0.224621	+	0.273030i
$73$		−	8.48345i		−	0.992912i	−0.868062	−	0.496456i	$-0.834634\pi$
$73$		−	8.48345i		−	0.992912i	0.868062	−	0.496456i	$-0.165366\pi$
$74$	6.08145	−	0.126325i	0.706954	−	0.0146850i
$75$	−6.23050	−	5.65384i	−0.719436	−	0.652849i
$76$	5.39058	+	5.39058i	0.618342	+	0.618342i
$77$	−7.36790			−0.839650
$78$	2.04123	+	1.85231i	0.231124	+	0.209732i
$79$	−7.58011	+	7.58011i	−0.852829	+	0.852829i	−0.990481	−	0.137651i	$-0.956045\pi$
$79$	−7.58011	+	7.58011i	−0.852829	+	0.852829i	0.137651	+	0.990481i	$0.456045\pi$
$80$	−0.266957	−	0.266957i	−0.0298467	−	0.0298467i
$81$	−8.83127	+	1.73453i	−0.981253	+	0.192725i
$82$	−0.658401	+	0.658401i	−0.0727082	+	0.0727082i
$83$			9.27148i			1.01768i	0.860862	+	0.508838i	$0.169925\pi$
$83$			9.27148i			1.01768i	−0.860862	+	0.508838i	$0.830075\pi$
$84$	2.29316	+	2.08092i	0.250204	+	0.227047i
$85$			0.674959i			0.0732096i
$86$		−	0.580218i		−	0.0625665i
$87$	−0.0194438	−	0.400716i	−0.00208460	−	0.0429612i
$88$	−2.91412	−	2.91412i	−0.310646	−	0.310646i
$89$	−2.03028	+	2.03028i	−0.215210	+	0.215210i	−0.806476	−	0.591266i	$-0.798628\pi$
$89$	−2.03028	+	2.03028i	−0.215210	+	0.215210i	0.591266	+	0.806476i	$0.298628\pi$
$90$	−0.109656	−	1.12728i	−0.0115587	−	0.118826i
$91$	2.01180	−	2.01180i	0.210894	−	0.210894i
$92$	3.99326	−	3.99326i	0.416326	−	0.416326i
$93$	2.76572	−	0.134200i	0.286792	−	0.0139159i
$94$	7.26774	+	7.26774i	0.749611	+	0.749611i
$95$	−2.87810			−0.295287
$96$	0.0839450	+	1.73002i	0.00856761	+	0.176569i
$97$	12.8316	−	12.8316i	1.30285	−	1.30285i	0.376393	−	0.926460i	$-0.377164\pi$
$97$	12.8316	−	12.8316i	1.30285	−	1.30285i	0.926460	−	0.376393i	$-0.122836\pi$
$98$	−2.68965	+	2.68965i	−0.271695	+	0.271695i
$99$	−1.19701	−	12.3055i	−0.120304	−	1.23675i
$100$	−4.85747			−0.485747
$101$	5.47731			0.545013			0.272507	−	0.962154i	$-0.412147\pi$
$101$	5.47731			0.545013			0.272507	+	0.962154i	$0.412147\pi$
$102$	2.08092	−	2.29316i	0.206042	−	0.227057i
$103$	−13.9500	−	13.9500i	−1.37453	−	1.37453i	−0.853595	−	0.520937i	$-0.825583\pi$
$103$	−13.9500	−	13.9500i	−1.37453	−	1.37453i	−0.520937	−	0.853595i	$-0.674417\pi$
$104$	1.59140			0.156050
$105$	−1.16769	+	0.0566595i	−0.113955	+	0.00552940i
$106$	−4.45482	−	4.45482i	−0.432691	−	0.432691i
$107$		−	16.6241i		−	1.60711i	−0.595231	−	0.803555i	$-0.702939\pi$
$107$		−	16.6241i		−	1.60711i	0.595231	−	0.803555i	$-0.297061\pi$
$108$	−3.10289	+	4.16799i	−0.298575	+	0.401065i
$109$	−5.35931	+	5.35931i	−0.513329	+	0.513329i	−0.915545	−	0.402216i	$-0.868240\pi$
$109$	−5.35931	+	5.35931i	−0.513329	+	0.513329i	0.402216	+	0.915545i	$0.368240\pi$
$110$	1.55589			0.148348
$111$	10.5104	−	0.729052i	0.997603	−	0.0691986i
$112$	1.78781			0.168932
$113$	7.74344	−	7.74344i	0.728442	−	0.728442i	−0.241867	−	0.970309i	$-0.577760\pi$
$113$	7.74344	−	7.74344i	0.728442	−	0.728442i	0.970309	+	0.241867i	$0.0777599\pi$
$114$	9.77830	+	8.87327i	0.915821	+	0.831058i
$115$			2.13205i			0.198815i
$116$	−0.163784	−	0.163784i	−0.0152070	−	0.0152070i
$117$	3.68685	+	3.03317i	0.340850	+	0.280416i
$118$	−7.95857			−0.732646
$119$	−2.26010	−	2.26010i	−0.207183	−	0.207183i
$120$	−0.484249	−	0.439430i	−0.0442057	−	0.0401143i
$121$	5.98417			0.544016
$122$	−1.53530			−0.138999
$123$	−1.08377	+	1.19431i	−0.0977206	+	0.107688i
$124$	1.13043	−	1.13043i	0.101515	−	0.101515i
$125$	2.63152	−	2.63152i	0.235370	−	0.235370i
$126$	4.14188	+	3.40752i	0.368988	+	0.303566i
$127$	−17.2399			−1.52979			−0.764895	−	0.644155i	$-0.777209\pi$
$127$	−17.2399			−1.52979			−0.764895	+	0.644155i	$0.777209\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−0.0487064	−	1.00379i	−0.00428836	−	0.0883785i
$130$	−0.424835	+	0.424835i	−0.0372605	+	0.0372605i
$131$	−7.49571	+	7.49571i	−0.654903	+	0.654903i	−0.954170	−	0.299267i	$-0.903258\pi$
$131$	−7.49571	+	7.49571i	−0.654903	+	0.654903i	0.299267	+	0.954170i	$0.403258\pi$
$132$	−5.28610	−	4.79684i	−0.460096	−	0.417512i
$133$	9.63733	−	9.63733i	0.835663	−	0.835663i
$134$	−4.02506	−	4.02506i	−0.347712	−	0.347712i
$135$	−0.284336	−	1.94101i	−0.0244717	−	0.167055i
$136$		−	1.78781i		−	0.153303i
$137$		−	16.6562i		−	1.42304i	−0.702666	−	0.711520i	$-0.748007\pi$
$137$		−	16.6562i		−	1.42304i	0.702666	−	0.711520i	$-0.251993\pi$
$138$	6.57318	−	7.24361i	0.559546	−	0.616617i
$139$			3.87912i			0.329022i	0.986375	+	0.164511i	$0.0526046\pi$
$139$			3.87912i			0.329022i	−0.986375	+	0.164511i	$0.947395\pi$
$140$	−0.477268	+	0.477268i	−0.0403365	+	0.0403365i
$141$	13.1834	+	11.9632i	1.11024	+	1.00748i
$142$	2.46277	+	2.46277i	0.206671	+	0.206671i
$143$	−4.63753	+	4.63753i	−0.387810	+	0.387810i
$144$	0.290452	+	2.98591i	0.0242044	+	0.248826i
$145$	0.0874465			0.00726204
$146$	−5.99870	−	5.99870i	−0.496456	−	0.496456i
$147$	−4.42735	+	4.87891i	−0.365161	+	0.402406i
$148$	4.21091	−	4.38956i	0.346135	−	0.360820i
$149$		−	8.87655i		−	0.727195i	−0.931556	−	0.363598i	$-0.881548\pi$
$149$		−	8.87655i		−	0.727195i	0.931556	−	0.363598i	$-0.118452\pi$
$150$	−8.40349	+	0.407760i	−0.686142	+	0.0332935i
$151$			3.91814i			0.318854i	0.987210	+	0.159427i	$0.0509646\pi$
$151$			3.91814i			0.318854i	−0.987210	+	0.159427i	$0.949035\pi$
$152$	7.62343			0.618342
$153$	3.40752	−	4.14188i	0.275482	−	0.334851i
$154$	−5.20989	+	5.20989i	−0.419825	+	0.419825i
$155$			0.603551i			0.0484784i
$156$	2.75315	−	0.133590i	0.220428	−	0.0106958i
$157$	−12.0497			−0.961671			−0.480835	−	0.876811i	$-0.659667\pi$
$157$	−12.0497			−0.961671			−0.480835	+	0.876811i	$0.659667\pi$
$158$			10.7199i			0.852829i
$159$	−8.08087	−	7.33295i	−0.640855	−	0.581541i
$160$	−0.377534			−0.0298467
$161$	−7.13918	−	7.13918i	−0.562646	−	0.562646i
$162$	−5.01816	+	7.47115i	−0.394264	+	0.586989i
$163$	10.3806	+	10.3806i	0.813075	+	0.813075i	0.985094	−	0.172019i	$-0.0550289\pi$
$163$	10.3806	+	10.3806i	0.813075	+	0.813075i	−0.172019	+	0.985094i	$0.555029\pi$
$164$			0.931119i			0.0727082i
$165$	2.69171	−	0.130609i	0.209549	−	0.0101679i
$166$	6.55592	+	6.55592i	0.508838	+	0.508838i
$167$	−16.6075	−	16.6075i	−1.28513	−	1.28513i	−0.937712	−	0.347414i	$-0.887060\pi$
$167$	−16.6075	−	16.6075i	−1.28513	−	1.28513i	−0.347414	−	0.937712i	$-0.612940\pi$
$168$	3.09294	−	0.150078i	0.238625	−	0.0115788i
$169$			10.4674i			0.805188i
$170$	0.477268	+	0.477268i	0.0366048	+	0.0366048i
$171$	17.6615	+	14.5301i	1.35061	+	1.11114i
$172$	−0.410276	−	0.410276i	−0.0312833	−	0.0312833i
$173$	20.1505			1.53201			0.766006	−	0.642834i	$-0.222241\pi$
$173$	20.1505			1.53201			0.766006	+	0.642834i	$0.222241\pi$
$174$	−0.297098	−	0.269600i	−0.0225229	−	0.0204383i
$175$			8.68423i			0.656466i
$176$	−4.12119			−0.310646
$177$	−13.7684	+	0.668082i	−1.03490	+	0.0502161i
$178$			2.87126i			0.215210i
$179$	−0.605620	+	0.605620i	−0.0452662	+	0.0452662i	−0.729378	−	0.684111i	$-0.760190\pi$
$179$	−0.605620	+	0.605620i	−0.0452662	+	0.0452662i	0.684111	+	0.729378i	$0.260190\pi$
$180$	−0.874646	−	0.719570i	−0.0651923	−	0.0536336i
$181$	9.50527			0.706521			0.353260	−	0.935525i	$-0.385073\pi$
$181$	9.50527			0.706521			0.353260	+	0.935525i	$0.385073\pi$
$182$		−	2.84512i		−	0.210894i
$183$	−2.65609	+	0.128881i	−0.196344	+	0.00952713i
$184$		−	5.64732i		−	0.416326i
$185$	0.0476920	+	2.29595i	0.00350639	+	0.168802i
$186$	1.86076	−	2.05055i	0.136438	−	0.150354i
$187$	5.20989	+	5.20989i	0.380985	+	0.380985i
$188$	10.2781			0.749611
$189$	7.45157	+	5.54737i	0.542022	+	0.403512i
$190$	−2.03513	+	2.03513i	−0.147644	+	0.147644i
$191$	5.30286	+	5.30286i	0.383701	+	0.383701i	0.872434	−	0.488733i	$-0.162541\pi$
$191$	5.30286	+	5.30286i	0.383701	+	0.383701i	−0.488733	+	0.872434i	$0.662541\pi$
$192$	1.28266	+	1.16395i	0.0925683	+	0.0840007i
$193$	1.65938	−	1.65938i	0.119445	−	0.119445i	−0.644858	−	0.764303i	$-0.723083\pi$
$193$	1.65938	−	1.65938i	0.119445	−	0.119445i	0.764303	+	0.644858i	$0.223083\pi$
$194$		−	18.1466i		−	1.30285i
$195$	−0.699308	+	0.770634i	−0.0500785	+	0.0551862i
$196$			3.80373i			0.271695i
$197$			17.6848i			1.25999i	0.776599	+	0.629995i	$0.216943\pi$
$197$			17.6848i			1.25999i	−0.776599	+	0.629995i	$0.783057\pi$
$198$	−9.54770	−	7.85487i	−0.678525	−	0.558221i
$199$	17.6422	+	17.6422i	1.25062	+	1.25062i	0.955441	+	0.295181i	$0.0953799\pi$
$199$	17.6422	+	17.6422i	1.25062	+	1.25062i	0.295181	+	0.955441i	$0.404620\pi$
$200$	−3.43475	+	3.43475i	−0.242873	+	0.242873i
$201$	−7.30130	−	6.62554i	−0.514994	−	0.467329i
$202$	3.87305	−	3.87305i	0.272507	−	0.272507i
$203$	−0.292815	+	0.292815i	−0.0205516	+	0.0205516i
$204$	−0.150078	−	3.09294i	−0.0105075	−	0.216549i
$205$	−0.248569	−	0.248569i	−0.0173608	−	0.0173608i
$206$	−19.7282			−1.37453
$207$	10.7636	−	13.0833i	0.748124	−	0.909355i
$208$	1.12529	−	1.12529i	0.0780248	−	0.0780248i
$209$	−22.2156	+	22.2156i	−1.53668	+	1.53668i
$210$	−0.785617	+	0.865745i	−0.0542127	+	0.0597421i
$211$	3.10412			0.213697			0.106848	−	0.994275i	$-0.465924\pi$
$211$	3.10412			0.213697			0.106848	+	0.994275i	$0.465924\pi$
$212$	−6.30007			−0.432691
$213$	4.46737	+	4.05389i	0.306099	+	0.277768i
$214$	−11.7550	−	11.7550i	−0.803555	−	0.803555i
$215$	0.219052			0.0149392
$216$	0.753139	+	5.14128i	0.0512446	+	0.349820i
$217$	−2.02099	−	2.02099i	−0.137194	−	0.137194i
$218$			7.57921i			0.513329i
$219$	−10.8814	−	9.87429i	−0.735297	−	0.667242i
$220$	1.10018	−	1.10018i	0.0741740	−	0.0741740i
$221$	−2.84512			−0.191384
$222$	6.91646	−	7.94749i	0.464202	−	0.533401i
$223$	17.1643			1.14941			0.574703	−	0.818362i	$-0.305117\pi$
$223$	17.1643			1.14941			0.574703	+	0.818362i	$0.305117\pi$
$224$	1.26417	−	1.26417i	0.0844661	−	0.0844661i
$225$	−14.5039	+	1.41086i	−0.966930	+	0.0940576i
$226$		−	10.9509i		−	0.728442i
$227$	14.9899	+	14.9899i	0.994914	+	0.994914i	0.999987	−	0.00507333i	$-0.00161490\pi$
$227$	14.9899	+	14.9899i	0.994914	+	0.994914i	−0.00507333	+	0.999987i	$0.501615\pi$
$228$	13.1887	−	0.639949i	0.873440	−	0.0423817i
$229$	−24.5488			−1.62223			−0.811116	−	0.584885i	$-0.801139\pi$
$229$	−24.5488			−1.62223			−0.811116	+	0.584885i	$0.801139\pi$
$230$	1.50759	+	1.50759i	0.0994075	+	0.0994075i
$231$	−8.57585	+	9.45054i	−0.564249	+	0.621800i
$232$	−0.231626			−0.0152070
$233$	−14.1417			−0.926451			−0.463225	−	0.886241i	$-0.653308\pi$
$233$	−14.1417			−0.926451			−0.463225	+	0.886241i	$0.653308\pi$
$234$	4.75177	−	0.462226i	0.310633	−	0.0302167i
$235$	−2.74382	+	2.74382i	−0.178987	+	0.178987i
$236$	−5.62756	+	5.62756i	−0.366323	+	0.366323i
$237$	0.899882	+	18.5456i	0.0584536	+	1.20467i
$238$	−3.19627			−0.207183
$239$	2.98846	+	2.98846i	0.193308	+	0.193308i	0.797124	−	0.603816i	$-0.206354\pi$
$239$	2.98846	+	2.98846i	0.193308	+	0.193308i	−0.603816	+	0.797124i	$0.706354\pi$
$240$	−0.653140	+	0.0316921i	−0.0421600	+	0.00204572i
$241$	−3.25700	+	3.25700i	−0.209802	+	0.209802i	−0.804183	−	0.594382i	$-0.797397\pi$
$241$	−3.25700	+	3.25700i	−0.209802	+	0.209802i	0.594382	+	0.804183i	$0.297397\pi$
$242$	4.23145	−	4.23145i	0.272008	−	0.272008i
$243$	−8.05432	+	13.3465i	−0.516685	+	0.856175i
$244$	−1.08562	+	1.08562i	−0.0694997	+	0.0694997i
$245$	−1.01543	−	1.01543i	−0.0648736	−	0.0648736i
$246$	0.0781628	+	1.61085i	0.00498348	+	0.102704i
$247$		−	12.1319i		−	0.771936i
$248$		−	1.59867i		−	0.101515i
$249$	11.8922	+	10.7915i	0.753637	+	0.683884i
$250$		−	3.72153i		−	0.235370i
$251$	10.8271	−	10.8271i	0.683402	−	0.683402i	−0.277363	−	0.960765i	$-0.589461\pi$
$251$	10.8271	−	10.8271i	0.683402	−	0.683402i	0.960765	+	0.277363i	$0.0894606\pi$
$252$	5.33823	−	0.519274i	0.336277	−	0.0327112i
$253$	16.4569	+	16.4569i	1.03464	+	1.03464i
$254$	−12.1904	+	12.1904i	−0.764895	+	0.764895i
$255$	0.865745	+	0.785617i	0.0542151	+	0.0491972i
$256$	1.00000			0.0625000
$257$	−3.52547	−	3.52547i	−0.219913	−	0.219913i	0.588549	−	0.808462i	$-0.299700\pi$
$257$	−3.52547	−	3.52547i	−0.219913	−	0.219913i	−0.808462	+	0.588549i	$0.799700\pi$
$258$	−0.744225	−	0.675344i	−0.0463334	−	0.0420451i
$259$	−7.84770	−	7.52831i	−0.487632	−	0.467786i
$260$			0.600808i			0.0372605i
$261$	−0.536615	−	0.441472i	−0.0332156	−	0.0273264i
$262$			10.6005i			0.654903i
$263$	22.4639			1.38518			0.692591	−	0.721331i	$-0.256469\pi$
$263$	22.4639			1.38518			0.692591	+	0.721331i	$0.256469\pi$
$264$	−7.12972	+	0.345953i	−0.438804	+	0.0212919i
$265$	1.68185	−	1.68185i	0.103315	−	0.103315i
$266$		−	13.6292i		−	0.835663i
$267$	0.241028	+	4.96732i	0.0147507	+	0.303995i
$268$	−5.69230			−0.347712
$269$			16.2029i			0.987911i	0.869487	+	0.493955i	$0.164449\pi$
$269$			16.2029i			0.987911i	−0.869487	+	0.493955i	$0.835551\pi$
$270$	−1.57356	−	1.17144i	−0.0957636	−	0.0712918i
$271$	−6.40228			−0.388911			−0.194456	−	0.980911i	$-0.562294\pi$
$271$	−6.40228			−0.388911			−0.194456	+	0.980911i	$0.562294\pi$
$272$	−1.26417	−	1.26417i	−0.0766517	−	0.0766517i
$273$	−0.238834	−	4.92210i	−0.0144549	−	0.297899i
$274$	−11.7777	−	11.7777i	−0.711520	−	0.711520i
$275$		−	20.0185i		−	1.20716i
$276$	−0.474064	−	9.76994i	−0.0285353	−	0.588081i
$277$	−7.93152	−	7.93152i	−0.476559	−	0.476559i	0.427471	−	0.904029i	$-0.359405\pi$
$277$	−7.93152	−	7.93152i	−0.476559	−	0.476559i	−0.904029	+	0.427471i	$0.859405\pi$
$278$	2.74295	+	2.74295i	0.164511	+	0.164511i
$279$	3.04702	−	3.70369i	0.182420	−	0.221734i
$280$			0.674959i			0.0403365i
$281$	18.6265	+	18.6265i	1.11117	+	1.11117i	0.992993	+	0.118174i	$0.0377040\pi$
$281$	18.6265	+	18.6265i	1.11117	+	1.11117i	0.118174	+	0.992993i	$0.462296\pi$
$282$	17.7813	−	0.862799i	1.05886	−	0.0513789i
$283$	13.7871	+	13.7871i	0.819556	+	0.819556i	0.986044	−	0.166488i	$-0.0532425\pi$
$283$	13.7871	+	13.7871i	0.819556	+	0.819556i	−0.166488	+	0.986044i	$0.553243\pi$
$284$	3.48288			0.206671
$285$	−3.34996	+	3.69164i	−0.198435	+	0.218674i
$286$			6.55846i			0.387810i
$287$	1.66466			0.0982620
$288$	2.31674	+	1.90597i	0.136515	+	0.112311i
$289$		−	13.8037i		−	0.811984i
$290$	0.0618340	−	0.0618340i	0.00363102	−	0.00363102i
$291$	−1.52332	−	31.3940i	−0.0892986	−	1.84035i
$292$	−8.48345			−0.496456
$293$		−	3.84343i		−	0.224536i	−0.993678	−	0.112268i	$-0.964189\pi$
$293$		−	3.84343i		−	0.224536i	0.993678	−	0.112268i	$-0.0358115\pi$
$294$	0.319305	+	6.58052i	0.0186222	+	0.383784i
$295$		−	3.00463i		−	0.174936i
$296$	−0.126325	−	6.08145i	−0.00734250	−	0.353477i
$297$	−17.1770	−	12.7876i	−0.996713	−	0.742010i
$298$	−6.27667	−	6.27667i	−0.363598	−	0.363598i
$299$	−8.98714			−0.519740
$300$	−5.65384	+	6.23050i	−0.326424	+	0.359718i
$301$	−0.733496	+	0.733496i	−0.0422780	+	0.0422780i
$302$	2.77054	+	2.77054i	0.159427	+	0.159427i
$303$	6.37531	−	7.02555i	0.366252	−	0.403607i
$304$	5.39058	−	5.39058i	0.309171	−	0.309171i
$305$		−	0.579627i		−	0.0331894i
$306$	−0.519274	−	5.33823i	−0.0296849	−	0.305167i
$307$			7.88639i			0.450100i	0.974347	+	0.225050i	$0.0722546\pi$
$307$			7.88639i			0.450100i	−0.974347	+	0.225050i	$0.927745\pi$
$308$			7.36790i			0.419825i
$309$	−34.1302	+	1.65609i	−1.94160	+	0.0942116i
$310$	0.426775	+	0.426775i	0.0242392	+	0.0242392i
$311$	1.07324	−	1.07324i	0.0608580	−	0.0608580i	−0.676023	−	0.736881i	$-0.736298\pi$
$311$	1.07324	−	1.07324i	0.0608580	−	0.0608580i	0.736881	+	0.676023i	$0.236298\pi$
$312$	1.85231	−	2.04123i	0.104866	−	0.115562i
$313$	14.3512	−	14.3512i	0.811179	−	0.811179i	−0.173631	−	0.984811i	$-0.555550\pi$
$313$	14.3512	−	14.3512i	0.811179	−	0.811179i	0.984811	+	0.173631i	$0.0555501\pi$
$314$	−8.52042	+	8.52042i	−0.480835	+	0.480835i
$315$	−1.28645	+	1.56370i	−0.0724835	+	0.0881046i
$316$	7.58011	+	7.58011i	0.426415	+	0.426415i
$317$	27.1932			1.52732			0.763662	−	0.645616i	$-0.223399\pi$
$317$	27.1932			1.52732			0.763662	+	0.645616i	$0.223399\pi$
$318$	−10.8992	+	0.528860i	−0.611198	+	0.0296570i
$319$	0.674984	−	0.674984i	0.0377919	−	0.0377919i
$320$	−0.266957	+	0.266957i	−0.0149233	+	0.0149233i
$321$	−21.3231	−	19.3495i	−1.19014	−	1.07999i
$322$	−10.0963			−0.562646
$323$	−13.6292			−0.758352
$324$	1.73453	+	8.83127i	0.0963626	+	0.490626i
$325$	5.46606	+	5.46606i	0.303202	+	0.303202i
$326$	14.6805			0.813075
$327$	0.636237	+	13.1121i	0.0351840	+	0.725104i
$328$	0.658401	+	0.658401i	0.0363541	+	0.0363541i
$329$		−	18.3754i		−	1.01307i
$330$	1.81097	−	1.99568i	0.0996907	−	0.109859i
$331$	6.34651	−	6.34651i	0.348836	−	0.348836i	−0.510840	−	0.859676i	$-0.670666\pi$
$331$	6.34651	−	6.34651i	0.348836	−	0.348836i	0.859676	+	0.510840i	$0.170666\pi$
$332$	9.27148			0.508838
$333$	11.2984	−	14.3299i	0.619150	−	0.785273i
$334$	−23.4865			−1.28513
$335$	1.51960	−	1.51960i	0.0830245	−	0.0830245i
$336$	2.08092	−	2.29316i	0.113523	−	0.125102i
$337$		−	11.0789i		−	0.603505i	−0.953386	−	0.301752i	$-0.902428\pi$
$337$		−	11.0789i		−	0.603505i	0.953386	−	0.301752i	$-0.0975715\pi$
$338$	7.40160	+	7.40160i	0.402594	+	0.402594i
$339$	−0.919272	−	18.9452i	−0.0499280	−	1.02896i
$340$	0.674959			0.0366048
$341$	4.65871	+	4.65871i	0.252283	+	0.252283i
$342$	22.7628	−	2.21424i	1.23087	−	0.119733i
$343$	19.3150			1.04291
$344$	−0.580218			−0.0312833
$345$	2.73471	+	2.48160i	0.147232	+	0.133605i
$346$	14.2485	−	14.2485i	0.766006	−	0.766006i
$347$	20.6322	−	20.6322i	1.10759	−	1.10759i	0.114129	−	0.993466i	$-0.463592\pi$
$347$	20.6322	−	20.6322i	1.10759	−	1.10759i	0.993466	−	0.114129i	$-0.0364077\pi$
$348$	−0.400716	+	0.0194438i	−0.0214806	+	0.00104230i
$349$	−10.5547			−0.564981			−0.282490	−	0.959270i	$-0.591161\pi$
$349$	−10.5547			−0.564981			−0.282490	+	0.959270i	$0.591161\pi$
$350$	6.14068	+	6.14068i	0.328233	+	0.328233i
$351$	8.18184	−	1.19855i	0.436714	−	0.0639736i
$352$	−2.91412	+	2.91412i	−0.155323	+	0.155323i
$353$	−17.8245	+	17.8245i	−0.948704	+	0.948704i	−0.998747	−	0.0500430i	$-0.984064\pi$
$353$	−17.8245	+	17.8245i	−0.948704	+	0.948704i	0.0500430	+	0.998747i	$0.484064\pi$
$354$	−9.26336	+	10.2082i	−0.492342	+	0.542558i
$355$	−0.929779	+	0.929779i	−0.0493475	+	0.0493475i
$356$	2.03028	+	2.03028i	0.107605	+	0.107605i
$357$	−5.52959	+	0.268311i	−0.292657	+	0.0142005i
$358$			0.856476i			0.0452662i
$359$		−	36.1572i		−	1.90830i	−0.299324	−	0.954152i	$-0.596761\pi$
$359$		−	36.1572i		−	1.90830i	0.299324	−	0.954152i	$-0.403239\pi$
$360$	−1.12728	+	0.109656i	−0.0594129	+	0.00577936i
$361$		−	39.1167i		−	2.05877i
$362$	6.72124	−	6.72124i	0.353260	−	0.353260i
$363$	6.96526	−	7.67568i	0.365582	−	0.402869i
$364$	−2.01180	−	2.01180i	−0.105447	−	0.105447i
$365$	2.26471	−	2.26471i	0.118541	−	0.118541i
$366$	−1.78701	+	1.96927i	−0.0934083	+	0.102935i
$367$	−33.8582			−1.76739			−0.883693	−	0.468068i	$-0.844950\pi$
$367$	−33.8582			−1.76739			−0.883693	+	0.468068i	$0.844950\pi$
$368$	−3.99326	−	3.99326i	−0.208163	−	0.208163i
$369$	0.270446	+	2.78023i	0.0140788	+	0.144733i
$370$	1.65721	+	1.58976i	0.0861541	+	0.0826478i
$371$			11.2633i			0.584763i
$372$	−0.134200	−	2.76572i	−0.00695795	−	0.143396i
$373$		−	3.27926i		−	0.169794i	−0.996390	−	0.0848969i	$-0.972944\pi$
$373$		−	3.27926i		−	0.169794i	0.996390	−	0.0848969i	$-0.0270561\pi$
$374$	7.36790			0.380985
$375$	−0.312404	−	6.43830i	−0.0161325	−	0.332472i
$376$	7.26774	−	7.26774i	0.374805	−	0.374805i
$377$			0.368609i			0.0189843i
$378$	9.19164	−	1.34647i	0.472767	−	0.0692549i
$379$	25.2117			1.29504			0.647518	−	0.762050i	$-0.275807\pi$
$379$	25.2117			1.29504			0.647518	+	0.762050i	$0.275807\pi$
$380$			2.87810i			0.147644i
$381$	−20.0663	+	22.1129i	−1.02803	+	1.13288i
$382$	7.49937			0.383701
$383$	11.5399	+	11.5399i	0.589663	+	0.589663i	0.937540	−	0.347877i	$-0.113097\pi$
$383$	11.5399	+	11.5399i	0.589663	+	0.589663i	−0.347877	+	0.937540i	$0.613097\pi$
$384$	1.73002	−	0.0839450i	0.0882845	−	0.00428380i
$385$	−1.96691	−	1.96691i	−0.100243	−	0.100243i
$386$		−	2.34672i		−	0.119445i
$387$	−1.34421	−	1.10588i	−0.0683302	−	0.0562151i
$388$	−12.8316	−	12.8316i	−0.651426	−	0.651426i
$389$	6.37516	+	6.37516i	0.323233	+	0.323233i	0.850006	−	0.526773i	$-0.176598\pi$
$389$	6.37516	+	6.37516i	0.323233	+	0.323233i	−0.526773	+	0.850006i	$0.676598\pi$
$390$	0.0504348	+	1.03941i	0.00255387	+	0.0526324i
$391$			10.0963i			0.510593i
$392$	2.68965	+	2.68965i	0.135848	+	0.135848i
$393$	0.889862	+	18.3391i	0.0448876	+	0.925084i
$394$	12.5050	+	12.5050i	0.629995	+	0.629995i
$395$	−4.04713			−0.203633
$396$	−12.3055	+	1.19701i	−0.618373	+	0.0601519i
$397$		−	15.1056i		−	0.758131i	−0.925370	−	0.379065i	$-0.876246\pi$
$397$		−	15.1056i		−	0.758131i	0.925370	−	0.379065i	$-0.123754\pi$
$398$	24.9498			1.25062
$399$	−1.14411	−	23.5788i	−0.0572770	−	1.18042i
$400$			4.85747i			0.242873i
$401$	−14.7763	+	14.7763i	−0.737892	+	0.737892i	−0.972170	−	0.234277i	$-0.924728\pi$
$401$	−14.7763	+	14.7763i	−0.737892	+	0.737892i	0.234277	+	0.972170i	$0.424728\pi$
$402$	−9.84776	+	0.477840i	−0.491162	+	0.0238325i
$403$	−2.54412			−0.126732
$404$		−	5.47731i		−	0.272507i
$405$	−2.82061	−	1.89453i	−0.140157	−	0.0941397i
$406$			0.414103i			0.0205516i
$407$	18.0902	+	17.3539i	0.896698	+	0.860203i
$408$	−2.29316	−	2.08092i	−0.113528	−	0.103021i
$409$	3.74510	+	3.74510i	0.185183	+	0.185183i	0.793610	−	0.608427i	$-0.208199\pi$
$409$	3.74510	+	3.74510i	0.185183	+	0.185183i	−0.608427	+	0.793610i	$0.708199\pi$
$410$	−0.351529			−0.0173608
$411$	−21.3644	−	19.3870i	−1.05383	−	0.956290i
$412$	−13.9500	+	13.9500i	−0.687266	+	0.687266i
$413$	10.0610	+	10.0610i	0.495070	+	0.495070i
$414$	−1.64028	−	16.8624i	−0.0806152	−	0.828740i
$415$	−2.47508	+	2.47508i	−0.121497	+	0.121497i
$416$		−	1.59140i		−	0.0780248i
$417$	4.97560	+	4.51509i	0.243656	+	0.221105i
$418$			31.4176i			1.53668i
$419$			37.4361i			1.82887i	0.404731	+	0.914436i	$0.367365\pi$
$419$			37.4361i			1.82887i	−0.404731	+	0.914436i	$0.632635\pi$
$420$	0.0566595	+	1.16769i	0.00276470	+	0.0569774i
$421$	3.26967	+	3.26967i	0.159354	+	0.159354i	0.782280	−	0.622926i	$-0.214056\pi$
$421$	3.26967	+	3.26967i	0.159354	+	0.159354i	−0.622926	+	0.782280i	$0.714056\pi$
$422$	2.19495	−	2.19495i	0.106848	−	0.106848i
$423$	30.6896	−	2.98531i	1.49218	−	0.145151i
$424$	−4.45482	+	4.45482i	−0.216345	+	0.216345i
$425$	6.14068	−	6.14068i	0.297867	−	0.297867i
$426$	6.02544	−	0.292371i	0.291933	−	0.0141654i
$427$	1.94088	+	1.94088i	0.0939259	+	0.0939259i
$428$	−16.6241			−0.803555
$429$	0.550550	+	11.3462i	0.0265808	+	0.547801i
$430$	0.154893	−	0.154893i	0.00746961	−	0.00746961i
$431$	−14.0245	+	14.0245i	−0.675536	+	0.675536i	−0.958987	−	0.283451i	$-0.908521\pi$
$431$	−14.0245	+	14.0245i	−0.675536	+	0.675536i	0.283451	+	0.958987i	$0.408521\pi$
$432$	4.16799	+	3.10289i	0.200532	+	0.149288i
$433$	−26.7687			−1.28642			−0.643210	−	0.765690i	$-0.722398\pi$
$433$	−26.7687			−1.28642			−0.643210	+	0.765690i	$0.722398\pi$
$434$	−2.85811			−0.137194
$435$	0.101783	−	0.112164i	0.00488013	−	0.00537787i
$436$	5.35931	+	5.35931i	0.256664	+	0.256664i
$437$	−43.0519			−2.05945
$438$	−14.6765	+	0.712143i	−0.701270	+	0.0340275i
$439$	10.2456	+	10.2456i	0.488994	+	0.488994i	0.907989	−	0.418995i	$-0.137617\pi$
$439$	10.2456	+	10.2456i	0.488994	+	0.488994i	−0.418995	+	0.907989i	$0.637617\pi$
$440$		−	1.55589i		−	0.0741740i
$441$	1.10480	+	11.3576i	0.0526097	+	0.540838i
$442$	−2.01180	+	2.01180i	−0.0956918	+	0.0956918i
$443$	−24.9989			−1.18773			−0.593866	−	0.804564i	$-0.702399\pi$
$443$	−24.9989			−1.18773			−0.593866	+	0.804564i	$0.702399\pi$
$444$	−0.729052	−	10.5104i	−0.0345993	−	0.498801i
$445$	−1.08400			−0.0513864
$446$	12.1370	−	12.1370i	0.574703	−	0.574703i
$447$	−11.3856	−	10.3318i	−0.538522	−	0.488679i
$448$		−	1.78781i		−	0.0844661i
$449$	−21.5090	−	21.5090i	−1.01507	−	1.01507i	−0.999885	−	0.0151870i	$-0.995166\pi$
$449$	−21.5090	−	21.5090i	−1.01507	−	1.01507i	−0.0151870	−	0.999885i	$-0.504834\pi$
$450$	−9.25821	+	11.2535i	−0.436436	+	0.530494i
$451$	−3.83731			−0.180692
$452$	−7.74344	−	7.74344i	−0.364221	−	0.364221i
$453$	5.02566	+	4.56051i	0.236126	+	0.214271i
$454$	21.1989			0.994914
$455$	1.07413			0.0503560
$456$	8.87327	−	9.77830i	0.415529	−	0.457911i
$457$	−4.59131	+	4.59131i	−0.214772	+	0.214772i	−0.806291	−	0.591519i	$-0.798529\pi$
$457$	−4.59131	+	4.59131i	−0.214772	+	0.214772i	0.591519	+	0.806291i	$0.298529\pi$
$458$	−17.3586	+	17.3586i	−0.811116	+	0.811116i
$459$	−1.34647	−	9.19164i	−0.0628478	−	0.429029i
$460$	2.13205			0.0994075
$461$	9.71160	+	9.71160i	0.452314	+	0.452314i	0.896122	−	0.443808i	$-0.146373\pi$
$461$	9.71160	+	9.71160i	0.452314	+	0.452314i	−0.443808	+	0.896122i	$0.646373\pi$
$462$	0.618499	+	12.7466i	0.0287752	+	0.593024i
$463$	−6.90017	+	6.90017i	−0.320678	+	0.320678i	−0.849027	−	0.528349i	$-0.822811\pi$
$463$	−6.90017	+	6.90017i	−0.320678	+	0.320678i	0.528349	+	0.849027i	$0.322811\pi$
$464$	−0.163784	+	0.163784i	−0.00760348	+	0.00760348i
$465$	0.774153	+	0.702502i	0.0359005	+	0.0325777i
$466$	−9.99966	+	9.99966i	−0.463225	+	0.463225i
$467$	18.6536	+	18.6536i	0.863188	+	0.863188i	0.991707	−	0.128519i	$-0.0410225\pi$
$467$	18.6536	+	18.6536i	0.863188	+	0.863188i	−0.128519	+	0.991707i	$0.541022\pi$
$468$	3.03317	−	3.68685i	0.140208	−	0.170425i
$469$			10.1767i			0.469919i
$470$			3.88035i			0.178987i
$471$	−14.0252	+	15.4557i	−0.646248	+	0.712162i
$472$			7.95857i			0.366323i
$473$	1.69082	−	1.69082i	0.0777442	−	0.0777442i
$474$	13.7500	+	12.4774i	0.631560	+	0.573106i
$475$	26.1846	+	26.1846i	1.20143	+	1.20143i
$476$	−2.26010	+	2.26010i	−0.103592	+	0.103592i
$477$	−18.8114	+	1.82987i	−0.861316	+	0.0837840i
$478$	4.22633			0.193308
$479$	−28.7903	−	28.7903i	−1.31546	−	1.31546i	−0.917325	−	0.398139i	$-0.869656\pi$
$479$	−28.7903	−	28.7903i	−1.31546	−	1.31546i	−0.398139	−	0.917325i	$-0.630344\pi$
$480$	−0.439430	+	0.484249i	−0.0200571	+	0.0221028i
$481$	−9.67802	+	0.201034i	−0.441280	+	0.00916635i
$482$			4.60609i			0.209802i
$483$	−17.4668	+	0.847537i	−0.794767	+	0.0385643i
$484$		−	5.98417i		−	0.272008i
$485$	6.85097			0.311087
$486$	3.74210	+	15.1326i	0.169745	+	0.686430i
$487$	−2.09513	+	2.09513i	−0.0949395	+	0.0949395i	−0.752981	−	0.658042i	$-0.771385\pi$
$487$	−2.09513	+	2.09513i	−0.0949395	+	0.0949395i	0.658042	+	0.752981i	$0.271385\pi$
$488$			1.53530i			0.0694997i
$489$	25.3974	−	1.23235i	1.14851	−	0.0557289i
$490$	−1.43604			−0.0648736
$491$			16.4327i			0.741597i	0.928713	+	0.370799i	$0.120916\pi$
$491$			16.4327i			0.741597i	−0.928713	+	0.370799i	$0.879084\pi$
$492$	1.19431	+	1.08377i	0.0538438	+	0.0488603i
$493$	0.414103			0.0186502
$494$	−8.57857	−	8.57857i	−0.385968	−	0.385968i
$495$	2.96548	−	3.60458i	0.133288	−	0.162014i
$496$	−1.13043	−	1.13043i	−0.0507577	−	0.0507577i
$497$		−	6.22673i		−	0.279307i
$498$	16.0398	−	0.778294i	0.718760	−	0.0348762i
$499$	−24.6519	−	24.6519i	−1.10357	−	1.10357i	−0.993976	−	0.109594i	$-0.965045\pi$
$499$	−24.6519	−	24.6519i	−1.10357	−	1.10357i	−0.109594	−	0.993976i	$-0.534955\pi$
$500$	−2.63152	−	2.63152i	−0.117685	−	0.117685i
$501$	−40.6321	+	1.97158i	−1.81531	+	0.0880836i
$502$		−	15.3119i		−	0.683402i
$503$	−22.5640	−	22.5640i	−1.00608	−	1.00608i	−0.999981	−	0.00609878i	$-0.998059\pi$
$503$	−22.5640	−	22.5640i	−1.00608	−	1.00608i	−0.00609878	−	0.999981i	$-0.501941\pi$
$504$	3.40752	−	4.14188i	0.151783	−	0.184494i
$505$	1.46221	+	1.46221i	0.0650673	+	0.0650673i
$506$	23.2736			1.03464
$507$	13.4262	+	12.1836i	0.596279	+	0.541091i
$508$			17.2399i			0.764895i
$509$	14.7908			0.655593			0.327796	−	0.944748i	$-0.393694\pi$
$509$	14.7908			0.655593			0.327796	+	0.944748i	$0.393694\pi$
$510$	1.16769	−	0.0566595i	0.0517062	−	0.00250892i
$511$			15.1668i			0.670939i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	39.1942	−	5.74150i	1.73047	−	0.253494i
$514$	−4.98577			−0.219913
$515$		−	7.44808i		−	0.328202i
$516$	−1.00379	+	0.0487064i	−0.0441892	+	0.00214418i
$517$			42.3581i			1.86291i
$518$	−10.8725	+	0.225845i	−0.477709	+	0.00992308i
$519$	23.4541	−	25.8463i	1.02952	−	1.13453i
$520$	0.424835	+	0.424835i	0.0186303	+	0.0186303i
$521$	3.29897			0.144531			0.0722653	−	0.997385i	$-0.476977\pi$
$521$	3.29897			0.144531			0.0722653	+	0.997385i	$0.476977\pi$
$522$	−0.691612	+	0.0672762i	−0.0302710	+	0.00294460i
$523$	29.3282	−	29.3282i	1.28243	−	1.28243i	0.343152	−	0.939280i	$-0.388505\pi$
$523$	29.3282	−	29.3282i	1.28243	−	1.28243i	0.939280	−	0.343152i	$-0.111495\pi$
$524$	7.49571	+	7.49571i	0.327451	+	0.327451i
$525$	11.1389	+	10.1080i	0.486144	+	0.441149i
$526$	15.8844	−	15.8844i	0.692591	−	0.692591i
$527$			2.85811i			0.124501i
$528$	−4.79684	+	5.28610i	−0.208756	+	0.230048i
$529$			8.89217i			0.386616i
$530$		−	2.37849i		−	0.103315i
$531$	−15.1688	+	18.4379i	−0.658271	+	0.800137i
$532$	−9.63733	−	9.63733i	−0.417831	−	0.417831i
$533$	1.04778	−	1.04778i	0.0453843	−	0.0453843i
$534$	3.68286	+	3.34199i	0.159373	+	0.144622i
$535$	4.43791	−	4.43791i	0.191867	−	0.191867i
$536$	−4.02506	+	4.02506i	−0.173856	+	0.173856i
$537$	0.0718969	+	1.48172i	0.00310258	+	0.0639408i
$538$	11.4572	+	11.4572i	0.493955	+	0.493955i
$539$	−15.6759			−0.675209
$540$	−1.94101	+	0.284336i	−0.0835277	+	0.0122359i
$541$	14.6931	−	14.6931i	0.631704	−	0.631704i	−0.316791	−	0.948495i	$-0.602605\pi$
$541$	14.6931	−	14.6931i	0.631704	−	0.631704i	0.948495	+	0.316791i	$0.102605\pi$
$542$	−4.52710	+	4.52710i	−0.194456	+	0.194456i
$543$	11.0636	−	12.1921i	0.474786	−	0.523211i
$544$	−1.78781			−0.0766517
$545$	−2.86141			−0.122569
$546$	−3.64933	−	3.31157i	−0.156177	−	0.141722i
$547$	30.5971	+	30.5971i	1.30824	+	1.30824i	0.922686	+	0.385553i	$0.125989\pi$
$547$	30.5971	+	30.5971i	1.30824	+	1.30824i	0.385553	+	0.922686i	$0.374011\pi$
$548$	−16.6562			−0.711520
$549$	−2.92624	+	3.55688i	−0.124889	+	0.151804i
$550$	−14.1552	−	14.1552i	−0.603581	−	0.603581i
$551$			1.76578i			0.0752248i
$552$	−7.24361	−	6.57318i	−0.308308	−	0.279773i
$553$	13.5518	−	13.5518i	0.576281	−	0.576281i
$554$	−11.2169			−0.476559
$555$	3.00045	+	2.61120i	0.127362	+	0.110839i
$556$	3.87912			0.164511
$557$	26.8651	−	26.8651i	1.13831	−	1.13831i	0.149559	−	0.988753i	$-0.452215\pi$
$557$	26.8651	−	26.8651i	1.13831	−	1.13831i	0.988753	−	0.149559i	$-0.0477854\pi$
$558$	−0.464337	−	4.77347i	−0.0196569	−	0.202077i
$559$			0.923359i			0.0390539i
$560$	0.477268	+	0.477268i	0.0201683	+	0.0201683i
$561$	12.7466	−	0.618499i	0.538161	−	0.0261130i
$562$	26.3419			1.11117
$563$	−7.01868	−	7.01868i	−0.295802	−	0.295802i	0.543565	−	0.839367i	$-0.317074\pi$
$563$	−7.01868	−	7.01868i	−0.295802	−	0.295802i	−0.839367	+	0.543565i	$0.817074\pi$
$564$	11.9632	−	13.1834i	0.503742	−	0.555121i
$565$	4.13433			0.173933
$566$	19.4979			0.819556
$567$	15.7886	−	3.10101i	0.663061	−	0.130230i
$568$	2.46277	−	2.46277i	0.103336	−	0.103336i
$569$	−27.4108	+	27.4108i	−1.14912	+	1.14912i	−0.162395	+	0.986726i	$0.551922\pi$
$569$	−27.4108	+	27.4108i	−1.14912	+	1.14912i	−0.986726	+	0.162395i	$0.948078\pi$
$570$	0.241603	+	4.97916i	0.0101196	+	0.208554i
$571$	−25.6469			−1.07329			−0.536644	−	0.843809i	$-0.680308\pi$
$571$	−25.6469			−1.07329			−0.536644	+	0.843809i	$0.680308\pi$
$572$	4.63753	+	4.63753i	0.193905	+	0.193905i
$573$	12.9740	−	0.629535i	0.541998	−	0.0262992i
$574$	1.17710	−	1.17710i	0.0491310	−	0.0491310i
$575$	19.3971	−	19.3971i	0.808915	−	0.808915i
$576$	2.98591	−	0.290452i	0.124413	−	0.0121022i
$577$	4.49347	−	4.49347i	0.187066	−	0.187066i	−0.607361	−	0.794426i	$-0.707772\pi$
$577$	4.49347	−	4.49347i	0.187066	−	0.187066i	0.794426	+	0.607361i	$0.207772\pi$
$578$	−9.76071	−	9.76071i	−0.405992	−	0.405992i
$579$	−0.196996	−	4.05986i	−0.00818685	−	0.168722i
$580$		−	0.0874465i		−	0.00363102i
$581$		−	16.5756i		−	0.687673i
$582$	−23.2760	−	21.1217i	−0.964823	−	0.875524i
$583$		−	25.9638i		−	1.07531i
$584$	−5.99870	+	5.99870i	−0.248228	+	0.248228i
$585$	0.174506	+	1.79396i	0.00721494	+	0.0741709i
$586$	−2.71772	−	2.71772i	−0.112268	−	0.112268i
$587$	3.75308	−	3.75308i	0.154906	−	0.154906i	−0.625399	−	0.780305i	$-0.715064\pi$
$587$	3.75308	−	3.75308i	0.154906	−	0.154906i	0.780305	+	0.625399i	$0.215064\pi$
$588$	4.87891	+	4.42735i	0.201203	+	0.182581i
$589$	−12.1873			−0.502170
$590$	−2.12459	−	2.12459i	−0.0874682	−	0.0874682i
$591$	22.6837	+	20.5842i	0.933081	+	0.846720i
$592$	−4.38956	−	4.21091i	−0.180410	−	0.173067i
$593$			26.8493i			1.10257i	0.834318	+	0.551284i	$0.185862\pi$
$593$			26.8493i			1.10257i	−0.834318	+	0.551284i	$0.814138\pi$
$594$	−21.1882	+	3.10383i	−0.869362	+	0.127352i
$595$		−	1.20670i		−	0.0494698i
$596$	−8.87655			−0.363598
$597$	43.1636	−	2.09441i	1.76657	−	0.0857187i
$598$	−6.35487	+	6.35487i	−0.259870	+	0.259870i
$599$		−	33.1030i		−	1.35255i	−0.736649	−	0.676276i	$-0.763593\pi$
$599$		−	33.1030i		−	1.35255i	0.736649	−	0.676276i	$-0.236407\pi$
$600$	0.407760	+	8.40349i	0.0166467	+	0.343071i
$601$	−31.1316			−1.26989			−0.634943	−	0.772559i	$-0.718976\pi$
$601$	−31.1316			−1.26989			−0.634943	+	0.772559i	$0.718976\pi$
$602$			1.03732i			0.0422780i
$603$	−16.9967	+	1.65334i	−0.692158	+	0.0673293i
$604$	3.91814			0.159427
$605$	1.59752	+	1.59752i	0.0649483	+	0.0649483i
$606$	−0.459793	−	9.47584i	−0.0186778	−	0.384930i
$607$	−17.7393	−	17.7393i	−0.720017	−	0.720017i	0.248591	−	0.968608i	$-0.420032\pi$
$607$	−17.7393	−	17.7393i	−0.720017	−	0.720017i	−0.968608	+	0.248591i	$0.920032\pi$
$608$		−	7.62343i		−	0.309171i
$609$	0.0347619	+	0.716404i	0.00140862	+	0.0290301i
$610$	−0.409858	−	0.409858i	−0.0165947	−	0.0165947i
$611$	−11.5659	−	11.5659i	−0.467906	−	0.467906i
$612$	−4.14188	−	3.40752i	−0.167426	−	0.137741i
$613$			46.7890i			1.88979i	0.327371	+	0.944896i	$0.393837\pi$
$613$			46.7890i			1.88979i	−0.327371	+	0.944896i	$0.606163\pi$
$614$	5.57652	+	5.57652i	0.225050	+	0.225050i
$615$	−0.608151	+	0.0295091i	−0.0245230	+	0.00118992i
$616$	5.20989	+	5.20989i	0.209912	+	0.209912i
$617$	22.2310			0.894985			0.447492	−	0.894288i	$-0.352317\pi$
$617$	22.2310			0.894985			0.447492	+	0.894288i	$0.352317\pi$
$618$	−22.9626	+	25.3047i	−0.923693	+	1.01790i
$619$			3.27875i			0.131784i	0.997827	+	0.0658920i	$0.0209893\pi$
$619$			3.27875i			0.131784i	−0.997827	+	0.0658920i	$0.979011\pi$
$620$	0.603551			0.0242392
$621$	−4.25321	−	29.0344i	−0.170676	−	1.16511i
$622$		−	1.51779i		−	0.0608580i
$623$	3.62976	−	3.62976i	0.145423	−	0.145423i
$624$	−0.133590	−	2.75315i	−0.00534789	−	0.110214i
$625$	−22.8823			−0.915293
$626$		−	20.2957i		−	0.811179i
$627$	2.63735	+	54.3529i	0.105326	+	2.17065i
$628$			12.0497i			0.480835i
$629$	0.225845	+	10.8725i	0.00900504	+	0.433514i
$630$	0.196043	+	2.01536i	0.00781056	+	0.0802940i
$631$	−12.1222	−	12.1222i	−0.482576	−	0.482576i	0.423377	−	0.905954i	$-0.360845\pi$
$631$	−12.1222	−	12.1222i	−0.482576	−	0.482576i	−0.905954	+	0.423377i	$0.860845\pi$
$632$	10.7199			0.426415
$633$	3.61304	−	3.98155i	0.143605	−	0.158252i
$634$	19.2285	−	19.2285i	0.763662	−	0.763662i
$635$	−4.60230	−	4.60230i	−0.182637	−	0.182637i
$636$	−7.33295	+	8.08087i	−0.290770	+	0.320427i
$637$	4.28030	−	4.28030i	0.169592	−	0.169592i
$638$		−	0.954572i		−	0.0377919i
$639$	10.3996	−	1.01161i	0.411400	−	0.0400187i
$640$			0.377534i			0.0149233i
$641$		−	42.9426i		−	1.69613i	−0.529891	−	0.848066i	$-0.677767\pi$
$641$		−	42.9426i		−	1.69613i	0.529891	−	0.848066i	$-0.322233\pi$
$642$	−28.7599	+	1.39551i	−1.13506	+	0.0550763i
$643$	−0.613731	−	0.613731i	−0.0242032	−	0.0242032i	0.694902	−	0.719105i	$-0.255448\pi$
$643$	−0.613731	−	0.613731i	−0.0242032	−	0.0242032i	−0.719105	+	0.694902i	$0.755448\pi$
$644$	−7.13918	+	7.13918i	−0.281323	+	0.281323i
$645$	0.254965	−	0.280970i	0.0100392	−	0.0110632i
$646$	−9.63733	+	9.63733i	−0.379176	+	0.379176i
$647$	7.60238	−	7.60238i	0.298880	−	0.298880i	−0.541695	−	0.840575i	$-0.682217\pi$
$647$	7.60238	−	7.60238i	0.298880	−	0.298880i	0.840575	+	0.541695i	$0.182217\pi$
$648$	7.47115	+	5.01816i	0.293495	+	0.197132i
$649$	−23.1922	−	23.1922i	−0.910374	−	0.910374i
$650$	7.73017			0.303202
$651$	−4.94458	+	0.239924i	−0.193793	+	0.00940338i
$652$	10.3806	−	10.3806i	0.406538	−	0.406538i
$653$	19.8914	−	19.8914i	0.778411	−	0.778411i	−0.201150	−	0.979560i	$-0.564468\pi$
$653$	19.8914	−	19.8914i	0.778411	−	0.778411i	0.979560	+	0.201150i	$0.0644678\pi$
$654$	9.72158	+	8.82180i	0.380144	+	0.344960i
$655$	−4.00206			−0.156373
$656$	0.931119			0.0363541
$657$	−25.3308	+	2.46404i	−0.988248	+	0.0961313i
$658$	−12.9933	−	12.9933i	−0.506533	−	0.506533i
$659$	6.18576			0.240963			0.120481	−	0.992716i	$-0.461556\pi$
$659$	6.18576			0.240963			0.120481	+	0.992716i	$0.461556\pi$
$660$	−0.130609	−	2.69171i	−0.00508395	−	0.104775i
$661$	−0.112967	−	0.112967i	−0.00439392	−	0.00439392i	0.704906	−	0.709300i	$-0.250989\pi$
$661$	−0.112967	−	0.112967i	−0.00439392	−	0.00439392i	−0.709300	+	0.704906i	$0.750989\pi$
$662$		−	8.97533i		−	0.348836i
$663$	−3.31157	+	3.64933i	−0.128611	+	0.141728i
$664$	6.55592	−	6.55592i	0.254419	−	0.254419i
$665$	5.14550			0.199534
$666$	−2.14357	−	18.1220i	−0.0830615	−	0.702211i
$667$	1.30806			0.0506484
$668$	−16.6075	+	16.6075i	−0.642563	+	0.642563i
$669$	19.9783	−	22.0160i	0.772407	−	0.851189i
$670$		−	2.14904i		−	0.0830245i
$671$	−4.47404	−	4.47404i	−0.172718	−	0.172718i
$672$	−0.150078	−	3.09294i	−0.00578938	−	0.119313i
$673$	−7.32561			−0.282382			−0.141191	−	0.989982i	$-0.545093\pi$
$673$	−7.32561			−0.282382			−0.141191	+	0.989982i	$0.545093\pi$
$674$	−7.83394	−	7.83394i	−0.301752	−	0.301752i
$675$	−15.0722	+	20.2459i	−0.580128	+	0.779263i
$676$	10.4674			0.402594
$677$	−4.91261			−0.188807			−0.0944034	−	0.995534i	$-0.530094\pi$
$677$	−4.91261			−0.188807			−0.0944034	+	0.995534i	$0.530094\pi$
$678$	−14.0463	−	12.7463i	−0.539445	−	0.489517i
$679$	−22.9405	+	22.9405i	−0.880375	+	0.880375i
$680$	0.477268	−	0.477268i	0.0183024	−	0.0183024i
$681$	36.6744	−	1.77954i	1.40537	−	0.0681922i
$682$	6.58840			0.252283
$683$	11.0526	+	11.0526i	0.422916	+	0.422916i	0.886207	−	0.463290i	$-0.153331\pi$
$683$	11.0526	+	11.0526i	0.422916	+	0.422916i	−0.463290	+	0.886207i	$0.653331\pi$
$684$	14.5301	−	17.6615i	0.555571	−	0.675303i
$685$	4.44650	−	4.44650i	0.169892	−	0.169892i
$686$	13.6578	−	13.6578i	0.521457	−	0.521457i
$687$	−28.5735	+	31.4879i	−1.09015	+	1.20134i
$688$	−0.410276	+	0.410276i	−0.0156416	+	0.0156416i
$689$	7.08941	+	7.08941i	0.270085	+	0.270085i
$690$	3.68849	−	0.178975i	0.140418	−	0.00681347i
$691$		−	6.41978i		−	0.244220i	−0.992517	−	0.122110i	$-0.961034\pi$
$691$		−	6.41978i		−	0.244220i	0.992517	−	0.122110i	$-0.0389661\pi$
$692$		−	20.1505i		−	0.766006i
$693$	2.14002	+	21.9999i	0.0812928	+	0.835705i
$694$		−	29.1783i		−	1.10759i
$695$	−1.03556	+	1.03556i	−0.0392809	+	0.0392809i
$696$	−0.269600	+	0.297098i	−0.0102192	+	0.0112615i
$697$	−1.17710	−	1.17710i	−0.0445857	−	0.0445857i
$698$	−7.46331	+	7.46331i	−0.282490	+	0.282490i
$699$	−16.4601	+	18.1390i	−0.622580	+	0.686080i
$700$	8.68423			0.328233
$701$	−3.53270	−	3.53270i	−0.133428	−	0.133428i	0.637238	−	0.770667i	$-0.280077\pi$
$701$	−3.53270	−	3.53270i	−0.133428	−	0.133428i	−0.770667	+	0.637238i	$0.780077\pi$
$702$	4.93793	−	6.63293i	0.186370	−	0.250344i
$703$	−46.3615	+	0.963031i	−1.74856	+	0.0363214i
$704$			4.12119i			0.155323i
$705$	0.325736	+	6.71306i	0.0122679	+	0.252829i
$706$			25.2077i			0.948704i
$707$	−9.79240			−0.368281
$708$	0.668082	+	13.7684i	0.0251081	+	0.517450i
$709$	−1.55430	+	1.55430i	−0.0583731	+	0.0583731i	−0.735691	−	0.677318i	$-0.763142\pi$
$709$	−1.55430	+	1.55430i	−0.0583731	+	0.0583731i	0.677318	+	0.735691i	$0.263142\pi$
$710$			1.31491i			0.0493475i
$711$	24.8352	+	20.4318i	0.931392	+	0.766254i
$712$	2.87126			0.107605
$713$			9.02818i			0.338108i
$714$	−3.72029	+	4.09973i	−0.139228	+	0.153429i
$715$	−2.47604			−0.0925986
$716$	0.605620	+	0.605620i	0.0226331	+	0.0226331i
$717$	7.31161	−	0.354779i	0.273057	−	0.0132495i
$718$	−25.5670	−	25.5670i	−0.954152	−	0.954152i
$719$			41.5403i			1.54919i	0.632457	+	0.774595i	$0.282046\pi$
$719$			41.5403i			1.54919i	−0.632457	+	0.774595i	$0.717954\pi$
$720$	−0.719570	+	0.874646i	−0.0268168	+	0.0325961i
$721$	24.9399	+	24.9399i	0.928811	+	0.928811i
$722$	−27.6597	−	27.6597i	−1.02939	−	1.02939i
$723$	0.386659	+	7.96861i	0.0143800	+	0.296356i
$724$		−	9.50527i		−	0.353260i
$725$	−0.795576	−	0.795576i	−0.0295469	−	0.0295469i
$726$	−0.502342	−	10.3527i	−0.0186437	−	0.384225i
$727$	2.66970	+	2.66970i	0.0990136	+	0.0990136i	0.754878	−	0.655865i	$-0.227696\pi$
$727$	2.66970	+	2.66970i	0.0990136	+	0.0990136i	−0.655865	+	0.754878i	$0.727696\pi$
$728$	−2.84512			−0.105447
$729$	7.74420	+	25.8656i	0.286822	+	0.957984i
$730$		−	3.20279i		−	0.118541i
$731$	1.03732			0.0383667
$732$	0.128881	+	2.65609i	0.00476357	+	0.0981719i
$733$		−	20.6215i		−	0.761673i	−0.924642	−	0.380837i	$-0.875636\pi$
$733$		−	20.6215i		−	0.761673i	0.924642	−	0.380837i	$-0.124364\pi$
$734$	−23.9414	+	23.9414i	−0.883693	+	0.883693i
$735$	−2.48437	+	0.120548i	−0.0916373	+	0.00444649i
$736$	−5.64732			−0.208163
$737$		−	23.4590i		−	0.864124i
$738$	2.15716	+	1.77469i	0.0794060	+	0.0653272i
$739$		−	29.4267i		−	1.08248i	−0.840869	−	0.541239i	$-0.817955\pi$
$739$		−	29.4267i		−	1.08248i	0.840869	−	0.541239i	$-0.182045\pi$
$740$	2.29595	−	0.0476920i	0.0844009	−	0.00175319i
$741$	−15.5612	−	14.1209i	−0.571654	−	0.518745i
$742$	7.96438	+	7.96438i	0.292382	+	0.292382i
$743$	1.84245			0.0675930			0.0337965	−	0.999429i	$-0.489240\pi$
$743$	1.84245			0.0675930			0.0337965	+	0.999429i	$0.489240\pi$
$744$	−2.05055	−	1.86076i	−0.0751769	−	0.0682189i
$745$	2.36966	−	2.36966i	0.0868175	−	0.0868175i
$746$	−2.31879	−	2.31879i	−0.0848969	−	0.0848969i
$747$	27.6838	−	2.69292i	1.01290	−	0.0985289i
$748$	5.20989	−	5.20989i	0.190492	−	0.190492i
$749$			29.7207i			1.08597i
$750$	−4.77347	−	4.33166i	−0.174302	−	0.158170i
$751$		−	37.8400i		−	1.38080i	−0.723428	−	0.690400i	$-0.757435\pi$
$751$		−	37.8400i		−	1.38080i	0.723428	−	0.690400i	$-0.242565\pi$
$752$		−	10.2781i		−	0.374805i
$753$	−1.28535	−	26.4897i	−0.0468409	−	0.965340i
$754$	0.260646	+	0.260646i	0.00949216	+	0.00949216i
$755$	−1.04597	+	1.04597i	−0.0380669	+	0.0380669i
$756$	5.54737	−	7.45157i	0.201756	−	0.271011i
$757$	7.62240	−	7.62240i	0.277041	−	0.277041i	−0.554886	−	0.831927i	$-0.687238\pi$
$757$	7.62240	−	7.62240i	0.277041	−	0.277041i	0.831927	+	0.554886i	$0.187238\pi$
$758$	17.8273	−	17.8273i	0.647518	−	0.647518i
$759$	40.2638	−	1.95371i	1.46148	−	0.0709151i
$760$	2.03513	+	2.03513i	0.0738218	+	0.0738218i
$761$	3.97250			0.144003			0.0720016	−	0.997405i	$-0.477061\pi$
$761$	3.97250			0.144003			0.0720016	+	0.997405i	$0.477061\pi$
$762$	1.44720	+	29.8252i	0.0524265	+	1.08045i
$763$	9.58143	−	9.58143i	0.346871	−	0.346871i
$764$	5.30286	−	5.30286i	0.191851	−	0.191851i
$765$	2.01536	−	0.196043i	0.0728657	−	0.00708797i
$766$	16.3199			0.589663
$767$	12.6653			0.457316
$768$	1.16395	−	1.28266i	0.0420003	−	0.0462841i
$769$	24.3617	+	24.3617i	0.878504	+	0.878504i	0.993380	−	0.114876i	$-0.0366470\pi$
$769$	24.3617	+	24.3617i	0.878504	+	0.878504i	−0.114876	+	0.993380i	$0.536647\pi$
$770$	−2.78163			−0.100243
$771$	−8.62547	+	0.418531i	−0.310639	+	0.0150730i
$772$	−1.65938	−	1.65938i	−0.0597225	−	0.0597225i
$773$		−	33.2429i		−	1.19567i	−0.801621	−	0.597833i	$-0.796029\pi$
$773$		−	33.2429i		−	1.19567i	0.801621	−	0.597833i	$-0.203971\pi$
$774$	−1.73248	+	0.168526i	−0.0622726	+	0.00605754i
$775$	5.49102	−	5.49102i	0.197243	−	0.197243i
$776$	−18.1466			−0.651426
$777$	−18.7906	+	1.30341i	−0.674109	+	0.0467595i
$778$	9.01584			0.323233
$779$	5.01927	−	5.01927i	0.179834	−	0.179834i
$780$	0.770634	+	0.699308i	0.0275931	+	0.0250393i
$781$			14.3536i			0.513612i
$782$	7.13918	+	7.13918i	0.255297	+	0.255297i
$783$	−1.19085	+	0.174446i	−0.0425576	+	0.00623420i
$784$	3.80373			0.135848
$785$	−3.21675	−	3.21675i	−0.114811	−	0.114811i
$786$	13.5969	+	12.3385i	0.484986	+	0.440098i
$787$	−4.51606			−0.160980			−0.0804901	−	0.996755i	$-0.525649\pi$
$787$	−4.51606			−0.160980			−0.0804901	+	0.996755i	$0.525649\pi$
$788$	17.6848			0.629995
$789$	26.1468	−	28.8136i	0.930850	−	1.02579i
$790$	−2.86175	+	2.86175i	−0.101816	+	0.101816i
$791$	−13.8438	+	13.8438i	−0.492229	+	0.492229i
$792$	−7.85487	+	9.54770i	−0.279111	+	0.339263i
$793$	2.44327			0.0867632
$794$	−10.6813	−	10.6813i	−0.379065	−	0.379065i
$795$	−0.199663	−	4.11483i	−0.00708130	−	0.145938i
$796$	17.6422	−	17.6422i	0.625311	−	0.625311i
$797$	−27.0639	+	27.0639i	−0.958653	+	0.958653i	−0.999179	−	0.0405251i	$-0.987097\pi$
$797$	−27.0639	+	27.0639i	−0.958653	+	0.958653i	0.0405251	+	0.999179i	$0.487097\pi$
$798$	−17.4817	−	15.8637i	−0.618847	−	0.561570i
$799$	−12.9933	+	12.9933i	−0.459672	+	0.459672i
$800$	3.43475	+	3.43475i	0.121437	+	0.121437i
$801$	6.65194	+	5.47254i	0.235035	+	0.193363i
$802$			20.8968i			0.737892i
$803$		−	34.9619i		−	1.23378i
$804$	−6.62554	+	7.30130i	−0.233665	+	0.257497i
$805$		−	3.81171i		−	0.134345i
$806$	−1.79896	+	1.79896i	−0.0633658	+	0.0633658i
$807$	20.7829	+	18.8594i	0.731593	+	0.663881i
$808$	−3.87305	−	3.87305i	−0.136253	−	0.136253i
$809$	−0.847014	+	0.847014i	−0.0297794	+	0.0297794i	−0.721840	−	0.692060i	$-0.756703\pi$
$809$	−0.847014	+	0.847014i	−0.0297794	+	0.0297794i	0.692060	+	0.721840i	$0.256703\pi$
$810$	−3.33411	+	0.654843i	−0.117149	+	0.0230088i
$811$	30.7161			1.07859			0.539294	−	0.842117i	$-0.318691\pi$
$811$	30.7161			1.07859			0.539294	+	0.842117i	$0.318691\pi$
$812$	0.292815	+	0.292815i	0.0102758	+	0.0102758i
$813$	−7.45192	+	8.21198i	−0.261350	+	0.288007i
$814$	25.0628	−	0.520609i	0.878450	−	0.0182473i
$815$			5.54237i			0.194141i
$816$	−3.09294	+	0.150078i	−0.108275	+	0.00525377i
$817$			4.42325i			0.154750i
$818$	5.29637			0.185183
$819$	−6.59139	−	5.42273i	−0.230322	−	0.189485i
$820$	−0.248569	+	0.248569i	−0.00868039	+	0.00868039i
$821$		−	4.17744i		−	0.145794i	−0.997339	−	0.0728969i	$-0.976776\pi$
$821$		−	4.17744i		−	0.145794i	0.997339	−	0.0728969i	$-0.0232244\pi$
$822$	−28.8156	+	1.39821i	−1.00506	+	0.0487681i
$823$	−9.86955			−0.344031			−0.172015	−	0.985094i	$-0.555028\pi$
$823$	−9.86955			−0.344031			−0.172015	+	0.985094i	$0.555028\pi$
$824$			19.7282i			0.687266i
$825$	−25.6770	−	23.3005i	−0.893960	−	0.811220i
$826$	14.2284			0.495070
$827$	36.0691	+	36.0691i	1.25424	+	1.25424i	0.953799	+	0.300446i	$0.0971354\pi$
$827$	36.0691	+	36.0691i	1.25424	+	1.25424i	0.300446	+	0.953799i	$0.402865\pi$
$828$	−13.0833	−	10.7636i	−0.454677	−	0.374062i
$829$	13.4650	+	13.4650i	0.467657	+	0.467657i	0.901155	−	0.433497i	$-0.142721\pi$
$829$	13.4650	+	13.4650i	0.467657	+	0.467657i	−0.433497	+	0.901155i	$0.642721\pi$
$830$			3.50030i			0.121497i
$831$	−19.4053	+	0.941600i	−0.673164	+	0.0326637i
$832$	−1.12529	−	1.12529i	−0.0390124	−	0.0390124i
$833$	−4.80858	−	4.80858i	−0.166607	−	0.166607i
$834$	6.71093	−	0.325632i	0.232380	−	0.0112757i
$835$		−	8.86696i		−	0.306854i
$836$	22.2156	+	22.2156i	0.768342	+	0.768342i
$837$	−1.20402	−	8.21920i	−0.0416170	−	0.284097i
$838$	26.4713	+	26.4713i	0.914436	+	0.914436i
$839$	−4.61221			−0.159231			−0.0796156	−	0.996826i	$-0.525369\pi$
$839$	−4.61221			−0.159231			−0.0796156	+	0.996826i	$0.525369\pi$
$840$	0.865745	+	0.785617i	0.0298711	+	0.0271064i
$841$			28.9463i			0.998150i
$842$	4.62401			0.159354
$843$	45.5719	−	2.21127i	1.56958	−	0.0761603i
$844$		−	3.10412i		−	0.106848i
$845$	−2.79436	+	2.79436i	−0.0961288	+	0.0961288i
$846$	19.5899	−	23.8117i	0.673514	−	0.818664i
$847$	−10.6986			−0.367607
$848$			6.30007i			0.216345i
$849$	33.7316	−	1.63675i	1.15767	−	0.0561731i
$850$		−	8.68423i		−	0.297867i
$851$	0.713398	+	34.3439i	0.0244550	+	1.17729i
$852$	4.05389	−	4.46737i	0.138884	−	0.153049i
$853$	−14.7450	−	14.7450i	−0.504861	−	0.504861i	0.408084	−	0.912945i	$-0.366197\pi$
$853$	−14.7450	−	14.7450i	−0.504861	−	0.504861i	−0.912945	+	0.408084i	$0.866197\pi$
$854$	2.74482			0.0939259
$855$	0.835952	+	8.59375i	0.0285890	+	0.293900i
$856$	−11.7550	+	11.7550i	−0.401777	+	0.401777i
$857$	−13.0251	−	13.0251i	−0.444929	−	0.444929i	0.448735	−	0.893665i	$-0.351875\pi$
$857$	−13.0251	−	13.0251i	−0.444929	−	0.444929i	−0.893665	+	0.448735i	$0.851875\pi$
$858$	8.41229	+	7.63370i	0.287191	+	0.260610i
$859$	−13.2686	+	13.2686i	−0.452719	+	0.452719i	−0.896256	−	0.443537i	$-0.853723\pi$
$859$	−13.2686	+	13.2686i	−0.452719	+	0.452719i	0.443537	+	0.896256i	$0.353723\pi$
$860$		−	0.219052i		−	0.00746961i
$861$	1.93758	−	2.13520i	0.0660326	−	0.0727676i
$862$			19.8336i			0.675536i
$863$			41.1886i			1.40208i	0.713123	+	0.701039i	$0.247280\pi$
$863$			41.1886i			1.40208i	−0.713123	+	0.701039i	$0.752720\pi$
$864$	5.14128	−	0.753139i	0.174910	−	0.0256223i
$865$	5.37930	+	5.37930i	0.182902	+	0.182902i
$866$	−18.9283	+	18.9283i	−0.643210	+	0.643210i
$867$	−17.7055	−	16.0668i	−0.601312	−	0.545658i
$868$	−2.02099	+	2.02099i	−0.0685969	+	0.0685969i
$869$	−31.2391	+	31.2391i	−1.05971	+	1.05971i
$870$	−0.00734070	−	0.151284i	−0.000248873	−	0.00512900i
$871$	6.40548	+	6.40548i	0.217042	+	0.217042i
$872$	7.57921			0.256664
$873$	−42.0410	−	34.5870i	−1.42287	−	1.17059i
$874$	−30.4423	+	30.4423i	−1.02973	+	1.02973i
$875$	−4.70466	+	4.70466i	−0.159046	+	0.159046i
$876$	−9.87429	+	10.8814i	−0.333621	+	0.367649i
$877$	−4.95595			−0.167350			−0.0836752	−	0.996493i	$-0.526666\pi$
$877$	−4.95595			−0.167350			−0.0836752	+	0.996493i	$0.526666\pi$
$878$	14.4894			0.488994
$879$	−4.92983	−	4.47355i	−0.166279	−	0.150889i
$880$	−1.10018	−	1.10018i	−0.0370870	−	0.0370870i
$881$	−33.0643			−1.11396			−0.556982	−	0.830525i	$-0.688041\pi$
$881$	−33.0643			−1.11396			−0.556982	+	0.830525i	$0.688041\pi$
$882$	8.81225	+	7.24982i	0.296724	+	0.244114i
$883$	3.42652	+	3.42652i	0.115311	+	0.115311i	0.762408	−	0.647097i	$-0.224017\pi$
$883$	3.42652	+	3.42652i	0.115311	+	0.115311i	−0.647097	+	0.762408i	$0.724017\pi$
$884$			2.84512i			0.0956918i
$885$	−3.85393	−	3.49723i	−0.129548	−	0.117558i
$886$	−17.6769	+	17.6769i	−0.593866	+	0.593866i
$887$	11.3232			0.380196			0.190098	−	0.981765i	$-0.439119\pi$
$887$	11.3232			0.380196			0.190098	+	0.981765i	$0.439119\pi$
$888$	−7.94749	−	6.91646i	−0.266700	−	0.232101i
$889$	30.8216			1.03372
$890$	−0.766501	+	0.766501i	−0.0256932	+	0.0256932i
$891$	−36.3953	+	7.14831i	−1.21929	+	0.239477i
$892$		−	17.1643i		−	0.574703i
$893$	−55.4051	−	55.4051i	−1.85406	−	1.85406i
$894$	−15.3566	+	0.745142i	−0.513601	+	0.0249213i
$895$	−0.323349			−0.0108084
$896$	−1.26417	−	1.26417i	−0.0422330	−	0.0422330i
$897$	−10.4606	+	11.5275i	−0.349268	+	0.384891i
$898$	−30.4183			−1.01507
$899$	0.370292			0.0123499
$900$	1.41086	+	14.5039i	0.0470288	+	0.483465i
$901$	7.96438	−	7.96438i	0.265332	−	0.265332i
$902$	−2.71339	+	2.71339i	−0.0903460	+	0.0903460i
$903$	0.0870779	+	1.79458i	0.00289777	+	0.0597199i
$904$	−10.9509			−0.364221
$905$	2.53750	+	2.53750i	0.0843492	+	0.0843492i
$906$	6.77844	−	0.328909i	0.225199	−	0.0109273i
$907$	−26.0829	+	26.0829i	−0.866069	+	0.866069i	−0.992035	−	0.125966i	$-0.959797\pi$
$907$	−26.0829	+	26.0829i	−0.866069	+	0.866069i	0.125966	+	0.992035i	$0.459797\pi$
$908$	14.9899	−	14.9899i	0.497457	−	0.497457i
$909$	−1.59090	−	16.3547i	−0.0527668	−	0.542453i
$910$	0.759524	−	0.759524i	0.0251780	−	0.0251780i
$911$	−23.4966	−	23.4966i	−0.778476	−	0.778476i	0.201096	−	0.979572i	$-0.435550\pi$
$911$	−23.4966	−	23.4966i	−0.778476	−	0.778476i	−0.979572	+	0.201096i	$0.935550\pi$
$912$	−0.639949	−	13.1887i	−0.0211908	−	0.436720i
$913$			38.2095i			1.26455i
$914$			6.49309i			0.214772i
$915$	−0.743467	−	0.674656i	−0.0245783	−	0.0223034i
$916$			24.5488i			0.811116i
$917$	13.4009	−	13.4009i	0.442537	−	0.442537i
$918$	−7.45157	−	5.54737i	−0.245938	−	0.183091i
$919$	−18.7152	−	18.7152i	−0.617357	−	0.617357i	0.327496	−	0.944853i	$-0.393795\pi$
$919$	−18.7152	−	18.7152i	−0.617357	−	0.617357i	−0.944853	+	0.327496i	$0.893795\pi$
$920$	1.50759	−	1.50759i	0.0497037	−	0.0497037i
$921$	10.1156	+	9.17935i	0.333320	+	0.302470i
$922$	13.7343			0.452314
$923$	−3.91925	−	3.91925i	−0.129004	−	0.129004i
$924$	9.45054	+	8.57585i	0.310900	+	0.282125i
$925$	20.4544	−	21.3221i	0.672535	−	0.701068i
$926$			9.75831i			0.320678i
$927$	−37.6015	+	45.7051i	−1.23500	+	1.50115i
$928$			0.231626i			0.00760348i
$929$	37.9435			1.24489			0.622443	−	0.782665i	$-0.286140\pi$
$929$	37.9435			1.24489			0.622443	+	0.782665i	$0.286140\pi$
$930$	1.04415	−	0.0506651i	0.0342391	−	0.00166137i
$931$	20.5043	−	20.5043i	0.672002	−	0.672002i
$932$			14.1417i			0.463225i
$933$	−0.127411	−	2.62581i	−0.00417126	−	0.0859651i
$934$	26.3802			0.863188
$935$			2.78163i			0.0909691i
$936$	−0.462226	−	4.75177i	−0.0151083	−	0.155317i
$937$	−3.74034			−0.122192			−0.0610958	−	0.998132i	$-0.519460\pi$
$937$	−3.74034			−0.122192			−0.0610958	+	0.998132i	$0.519460\pi$
$938$	7.19605	+	7.19605i	0.234959	+	0.234959i
$939$	−1.70372	−	35.1119i	−0.0555989	−	1.14583i
$940$	2.74382	+	2.74382i	0.0894935	+	0.0894935i
$941$			34.6365i			1.12912i	0.825393	+	0.564559i	$0.190954\pi$
$941$			34.6365i			1.12912i	−0.825393	+	0.564559i	$0.809046\pi$
$942$	1.01151	+	20.8462i	0.0329569	+	0.679205i
$943$	−3.71820	−	3.71820i	−0.121081	−	0.121081i
$944$	5.62756	+	5.62756i	0.183161	+	0.183161i
$945$	0.508338	+	3.47015i	0.0165362	+	0.112884i
$946$		−	2.39119i		−	0.0777442i
$947$	3.19196	+	3.19196i	0.103725	+	0.103725i	0.757065	−	0.653340i	$-0.226633\pi$
$947$	3.19196	+	3.19196i	0.103725	+	0.103725i	−0.653340	+	0.757065i	$0.726633\pi$
$948$	18.5456	−	0.899882i	0.602333	−	0.0292268i
$949$	9.54633	+	9.54633i	0.309887	+	0.309887i
$950$	37.0306			1.20143
$951$	31.6515	−	34.8798i	1.02637	−	1.13105i
$952$			3.19627i			0.103592i
$953$	28.2370			0.914685			0.457343	−	0.889291i	$-0.348801\pi$
$953$	28.2370			0.914685			0.457343	+	0.889291i	$0.348801\pi$
$954$	−12.0078	+	14.5956i	−0.388766	+	0.472550i
$955$			2.83127i			0.0916176i
$956$	2.98846	−	2.98846i	0.0966538	−	0.0966538i
$957$	−0.0801316	−	1.65142i	−0.00259029	−	0.0533830i
$958$	−40.7157			−1.31546
$959$			29.7782i			0.961588i
$960$	0.0316921	+	0.653140i	0.00102286	+	0.0210800i
$961$		−	28.4443i		−	0.917557i
$962$	−6.70124	+	6.98555i	−0.216057	+	0.225223i
$963$	−49.6379	+	4.82850i	−1.59956	+	0.155596i
$964$	3.25700	+	3.25700i	0.104901	+	0.104901i
$965$	0.885966			0.0285203
$966$	−11.7516	+	12.9502i	−0.378101	+	0.416666i
$967$	−15.7710	+	15.7710i	−0.507160	+	0.507160i	−0.913654	−	0.406493i	$-0.866751\pi$
$967$	−15.7710	+	15.7710i	−0.507160	+	0.507160i	0.406493	+	0.913654i	$0.366751\pi$
$968$	−4.23145	−	4.23145i	−0.136004	−	0.136004i
$969$	−15.8637	+	17.4817i	−0.509616	+	0.561594i
$970$	4.84437	−	4.84437i	0.155543	−	0.155543i
$971$		−	29.1654i		−	0.935962i	−0.883739	−	0.467981i	$-0.844982\pi$
$971$		−	29.1654i		−	0.935962i	0.883739	−	0.467981i	$-0.155018\pi$
$972$	13.3465	+	8.05432i	0.428088	+	0.258343i
$973$		−	6.93512i		−	0.222330i
$974$			2.96296i			0.0949395i
$975$	13.3733	−	0.648910i	0.428289	−	0.0207817i
$976$	1.08562	+	1.08562i	0.0347498	+	0.0347498i
$977$	23.5329	−	23.5329i	0.752885	−	0.752885i	−0.222132	−	0.975017i	$-0.571302\pi$
$977$	23.5329	−	23.5329i	0.752885	−	0.752885i	0.975017	+	0.222132i	$0.0713016\pi$
$978$	17.0873	−	18.8301i	0.546391	−	0.602120i
$979$	−8.36718	+	8.36718i	−0.267416	+	0.267416i
$980$	−1.01543	+	1.01543i	−0.0324368	+	0.0324368i
$981$	17.5590	+	14.4458i	0.560617	+	0.461218i
$982$	11.6197	+	11.6197i	0.370799	+	0.370799i
$983$	15.7355			0.501886			0.250943	−	0.968002i	$-0.419259\pi$
$983$	15.7355			0.501886			0.250943	+	0.968002i	$0.419259\pi$
$984$	1.61085	−	0.0781628i	0.0513520	−	0.00249174i
$985$	−4.72108	+	4.72108i	−0.150426	+	0.150426i
$986$	0.292815	−	0.292815i	0.00932512	−	0.00932512i
$987$	−23.5694	−	21.3880i	−0.750223	−	0.680786i
$988$	−12.1319			−0.385968
$989$	3.27668			0.104192
$990$	−0.451911	−	4.64573i	−0.0143627	−	0.147651i
$991$	−7.92576	−	7.92576i	−0.251770	−	0.251770i	0.569926	−	0.821696i	$-0.306972\pi$
$991$	−7.92576	−	7.92576i	−0.251770	−	0.251770i	−0.821696	+	0.569926i	$0.806972\pi$
$992$	−1.59867			−0.0507577
$993$	−0.753434	−	15.5275i	−0.0239095	−	0.492749i
$994$	−4.40296	−	4.40296i	−0.139654	−	0.139654i
$995$			9.41941i			0.298615i
$996$	10.7915	−	11.8922i	0.341942	−	0.376818i
$997$	−2.57513	+	2.57513i	−0.0815550	+	0.0815550i	−0.746708	−	0.665153i	$-0.768367\pi$
$997$	−2.57513	+	2.57513i	−0.0815550	+	0.0815550i	0.665153	+	0.746708i	$0.268367\pi$
$998$	−34.8631			−1.10357
$999$	−5.22965	−	31.1713i	−0.165459	−	0.986217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	222.2.g.a.179.13	yes	28
3.2	odd	2	inner	222.2.g.a.179.2	✓	28
37.6	odd	4	inner	222.2.g.a.191.2	yes	28
111.80	even	4	inner	222.2.g.a.191.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
222.2.g.a.179.2	✓	28	3.2	odd	2	inner
222.2.g.a.179.13	yes	28	1.1	even	1	trivial
222.2.g.a.191.2	yes	28	37.6	odd	4	inner
222.2.g.a.191.13	yes	28	111.80	even	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 222 = 2 \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	222.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.16395 - 1.28266i) q^{3} -1.00000i q^{4} +(0.266957 + 0.266957i) q^{5} +(-0.0839450 - 1.73002i) q^{6} -1.78781 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.290452 - 2.98591i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.16395 - 1.28266i) q^{3} -1.00000i q^{4} +(0.266957 + 0.266957i) q^{5} +(-0.0839450 - 1.73002i) q^{6} -1.78781 q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.290452 - 2.98591i) q^{9} +0.377534 q^{10} +4.12119 q^{11} +(-1.28266 - 1.16395i) q^{12} +(-1.12529 + 1.12529i) q^{13} +(-1.26417 + 1.26417i) q^{14} +(0.653140 - 0.0316921i) q^{15} -1.00000 q^{16} +(1.26417 + 1.26417i) q^{17} +(-2.31674 - 1.90597i) q^{18} +(-5.39058 + 5.39058i) q^{19} +(0.266957 - 0.266957i) q^{20} +(-2.08092 + 2.29316i) q^{21} +(2.91412 - 2.91412i) q^{22} +(3.99326 + 3.99326i) q^{23} +(-1.73002 + 0.0839450i) q^{24} -4.85747i q^{25} +1.59140i q^{26} +(-4.16799 - 3.10289i) q^{27} +1.78781i q^{28} +(0.163784 - 0.163784i) q^{29} +(0.439430 - 0.484249i) q^{30} +(1.13043 + 1.13043i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.79684 - 5.28610i) q^{33} +1.78781 q^{34} +(-0.477268 - 0.477268i) q^{35} +(-2.98591 + 0.290452i) q^{36} +(4.38956 + 4.21091i) q^{37} +7.62343i q^{38} +(0.133590 + 2.75315i) q^{39} -0.377534i q^{40} -0.931119 q^{41} +(0.150078 + 3.09294i) q^{42} +(0.410276 - 0.410276i) q^{43} -4.12119i q^{44} +(0.719570 - 0.874646i) q^{45} +5.64732 q^{46} +10.2781i q^{47} +(-1.16395 + 1.28266i) q^{48} -3.80373 q^{49} +(-3.43475 - 3.43475i) q^{50} +(3.09294 - 0.150078i) q^{51} +(1.12529 + 1.12529i) q^{52} -6.30007i q^{53} +(-5.14128 + 0.753139i) q^{54} +(1.10018 + 1.10018i) q^{55} +(1.26417 + 1.26417i) q^{56} +(0.639949 + 13.1887i) q^{57} -0.231626i q^{58} +(-5.62756 - 5.62756i) q^{59} +(-0.0316921 - 0.653140i) q^{60} +(-1.08562 - 1.08562i) q^{61} +1.59867 q^{62} +(0.519274 + 5.33823i) q^{63} +1.00000i q^{64} -0.600808 q^{65} +(-0.345953 - 7.12972i) q^{66} -5.69230i q^{67} +(1.26417 - 1.26417i) q^{68} +(9.76994 - 0.474064i) q^{69} -0.674959 q^{70} +3.48288i q^{71} +(-1.90597 + 2.31674i) q^{72} -8.48345i q^{73} +(6.08145 - 0.126325i) q^{74} +(-6.23050 - 5.65384i) q^{75} +(5.39058 + 5.39058i) q^{76} -7.36790 q^{77} +(2.04123 + 1.85231i) q^{78} +(-7.58011 + 7.58011i) q^{79} +(-0.266957 - 0.266957i) q^{80} +(-8.83127 + 1.73453i) q^{81} +(-0.658401 + 0.658401i) q^{82} +9.27148i q^{83} +(2.29316 + 2.08092i) q^{84} +0.674959i q^{85} -0.580218i q^{86} +(-0.0194438 - 0.400716i) q^{87} +(-2.91412 - 2.91412i) q^{88} +(-2.03028 + 2.03028i) q^{89} +(-0.109656 - 1.12728i) q^{90} +(2.01180 - 2.01180i) q^{91} +(3.99326 - 3.99326i) q^{92} +(2.76572 - 0.134200i) q^{93} +(7.26774 + 7.26774i) q^{94} -2.87810 q^{95} +(0.0839450 + 1.73002i) q^{96} +(12.8316 - 12.8316i) q^{97} +(-2.68965 + 2.68965i) q^{98} +(-1.19701 - 12.3055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 8 q^{9}+O(q^{10}) \) 28 * q - 8 * q^9	\( 28 q - 8 q^{9} + 8 q^{12} + 20 q^{13} - 28 q^{16} - 20 q^{19} + 8 q^{22} + 12 q^{31} - 36 q^{37} - 8 q^{39} + 8 q^{42} - 28 q^{43} - 16 q^{46} + 4 q^{49} - 8 q^{51} - 20 q^{52} + 16 q^{55} + 8 q^{57} + 44 q^{61} + 16 q^{66} + 8 q^{69} - 16 q^{70} - 100 q^{75} + 20 q^{76} - 28 q^{79} + 8 q^{81} - 16 q^{82} - 76 q^{87} - 8 q^{88} + 60 q^{90} - 8 q^{91} + 84 q^{93} - 16 q^{94} + 28 q^{97}+O(q^{100}) \) 28 * q - 8 * q^9 + 8 * q^12 + 20 * q^13 - 28 * q^16 - 20 * q^19 + 8 * q^22 + 12 * q^31 - 36 * q^37 - 8 * q^39 + 8 * q^42 - 28 * q^43 - 16 * q^46 + 4 * q^49 - 8 * q^51 - 20 * q^52 + 16 * q^55 + 8 * q^57 + 44 * q^61 + 16 * q^66 + 8 * q^69 - 16 * q^70 - 100 * q^75 + 20 * q^76 - 28 * q^79 + 8 * q^81 - 16 * q^82 - 76 * q^87 - 8 * q^88 + 60 * q^90 - 8 * q^91 + 84 * q^93 - 16 * q^94 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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