LMFDB - Embedded newform 336.2.w.b.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (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:	$2.68297350792$
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			85.2
Character	$\chi$	$=$	336.85
Dual form			336.2.w.b.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40007 - 0.199481i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.92041 + 0.558576i) q^{4} +(1.25389 + 1.25389i) q^{5} +(-1.13106 + 0.848947i) q^{6} -1.00000i q^{7} +(-2.57730 - 1.16513i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.40007 - 0.199481i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.92041 + 0.558576i) q^{4} +(1.25389 + 1.25389i) q^{5} +(-1.13106 + 0.848947i) q^{6} -1.00000i q^{7} +(-2.57730 - 1.16513i) q^{8} -1.00000i q^{9} +(-1.50541 - 2.00566i) q^{10} +(4.50476 + 4.50476i) q^{11} +(1.75291 - 0.962965i) q^{12} +(2.23466 - 2.23466i) q^{13} +(-0.199481 + 1.40007i) q^{14} +1.77326 q^{15} +(3.37598 + 2.14540i) q^{16} -5.71385 q^{17} +(-0.199481 + 1.40007i) q^{18} +(-0.286290 + 0.286290i) q^{19} +(1.70759 + 3.10837i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(-5.40838 - 7.20561i) q^{22} +5.63920i q^{23} +(-2.64630 + 0.998550i) q^{24} -1.85554i q^{25} +(-3.57446 + 2.68291i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.558576 - 1.92041i) q^{28} +(5.63098 - 5.63098i) q^{29} +(-2.48270 - 0.353732i) q^{30} +9.37136 q^{31} +(-4.29866 - 3.67716i) q^{32} +6.37069 q^{33} +(7.99981 + 1.13980i) q^{34} +(1.25389 - 1.25389i) q^{35} +(0.558576 - 1.92041i) q^{36} +(1.10676 + 1.10676i) q^{37} +(0.457937 - 0.343718i) q^{38} -3.16028i q^{39} +(-1.77069 - 4.69259i) q^{40} +0.0881503i q^{41} +(0.848947 + 1.13106i) q^{42} +(-3.83305 - 3.83305i) q^{43} +(6.13475 + 11.1672i) q^{44} +(1.25389 - 1.25389i) q^{45} +(1.12491 - 7.89530i) q^{46} +3.18014 q^{47} +(3.90421 - 0.870157i) q^{48} -1.00000 q^{49} +(-0.370144 + 2.59789i) q^{50} +(-4.04030 + 4.04030i) q^{51} +(5.53970 - 3.04324i) q^{52} +(-2.81843 - 2.81843i) q^{53} +(0.848947 + 1.13106i) q^{54} +11.2969i q^{55} +(-1.16513 + 2.57730i) q^{56} +0.404875i q^{57} +(-9.00707 + 6.76052i) q^{58} +(-8.62389 - 8.62389i) q^{59} +(3.40540 + 0.990503i) q^{60} +(-4.88503 + 4.88503i) q^{61} +(-13.1206 - 1.86941i) q^{62} -1.00000 q^{63} +(5.28492 + 6.00580i) q^{64} +5.60402 q^{65} +(-8.91943 - 1.27083i) q^{66} +(-9.19959 + 9.19959i) q^{67} +(-10.9730 - 3.19162i) q^{68} +(3.98752 + 3.98752i) q^{69} +(-2.00566 + 1.50541i) q^{70} +3.04149i q^{71} +(-1.16513 + 2.57730i) q^{72} -4.95758i q^{73} +(-1.32877 - 1.77032i) q^{74} +(-1.31206 - 1.31206i) q^{75} +(-0.709710 + 0.389881i) q^{76} +(4.50476 - 4.50476i) q^{77} +(-0.630417 + 4.42463i) q^{78} -1.57254 q^{79} +(1.54302 + 6.92319i) q^{80} -1.00000 q^{81} +(0.0175843 - 0.123417i) q^{82} +(-7.63884 + 7.63884i) q^{83} +(-0.962965 - 1.75291i) q^{84} +(-7.16452 - 7.16452i) q^{85} +(4.60193 + 6.13117i) q^{86} -7.96341i q^{87} +(-6.36145 - 16.8587i) q^{88} +2.16431i q^{89} +(-2.00566 + 1.50541i) q^{90} +(-2.23466 - 2.23466i) q^{91} +(-3.14992 + 10.8296i) q^{92} +(6.62655 - 6.62655i) q^{93} +(-4.45243 - 0.634377i) q^{94} -0.717950 q^{95} +(-5.63976 + 0.439469i) q^{96} -4.52728 q^{97} +(1.40007 + 0.199481i) q^{98} +(4.50476 - 4.50476i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) $ 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$1$

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 $

$2$	−1.40007	−	0.199481i	−0.990002	−	0.141054i
$2$	−1.40007	−	0.199481i	−0.990002	−	0.141054i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.92041	+	0.558576i	0.960207	+	0.279288i
$5$	1.25389	+	1.25389i	0.560755	+	0.560755i	0.929522	−	0.368767i	$-0.120220\pi$
$5$	1.25389	+	1.25389i	0.560755	+	0.560755i	−0.368767	+	0.929522i	$0.620220\pi$
$6$	−1.13106	+	0.848947i	−0.461752	+	0.346581i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.57730	−	1.16513i	−0.911212	−	0.411937i
$9$		−	1.00000i		−	0.333333i
$10$	−1.50541	−	2.00566i	−0.476052	−	0.634246i
$11$	4.50476	+	4.50476i	1.35824	+	1.35824i	0.876093	+	0.482142i	$0.160141\pi$
$11$	4.50476	+	4.50476i	1.35824	+	1.35824i	0.482142	+	0.876093i	$0.339859\pi$
$12$	1.75291	−	0.962965i	0.506022	−	0.277984i
$13$	2.23466	−	2.23466i	0.619783	−	0.619783i	−0.325693	−	0.945476i	$-0.605598\pi$
$13$	2.23466	−	2.23466i	0.619783	−	0.619783i	0.945476	+	0.325693i	$0.105598\pi$
$14$	−0.199481	+	1.40007i	−0.0533135	+	0.374186i
$15$	1.77326			0.457855
$16$	3.37598	+	2.14540i	0.843996	+	0.536349i
$17$	−5.71385			−1.38581			−0.692906	−	0.721028i	$-0.743670\pi$
$17$	−5.71385			−1.38581			−0.692906	+	0.721028i	$0.743670\pi$
$18$	−0.199481	+	1.40007i	−0.0470181	+	0.330001i
$19$	−0.286290	+	0.286290i	−0.0656794	+	0.0656794i	−0.739184	−	0.673504i	$-0.764788\pi$
$19$	−0.286290	+	0.286290i	−0.0656794	+	0.0656794i	0.673504	+	0.739184i	$0.264788\pi$
$20$	1.70759	+	3.10837i	0.381829	+	0.695054i
$21$	−0.707107	−	0.707107i	−0.154303	−	0.154303i
$22$	−5.40838	−	7.20561i	−1.15307	−	1.53624i
$23$			5.63920i			1.17585i	0.808914	+	0.587927i	$0.200056\pi$
$23$			5.63920i			1.17585i	−0.808914	+	0.587927i	$0.799944\pi$
$24$	−2.64630	+	0.998550i	−0.540174	+	0.203828i
$25$		−	1.85554i		−	0.371107i
$26$	−3.57446	+	2.68291i	−0.701009	+	0.526163i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	0.558576	−	1.92041i	0.105561	−	0.362924i
$29$	5.63098	−	5.63098i	1.04565	−	1.04565i	0.0467404	−	0.998907i	$-0.485117\pi$
$29$	5.63098	−	5.63098i	1.04565	−	1.04565i	0.998907	−	0.0467404i	$-0.0148834\pi$
$30$	−2.48270	−	0.353732i	−0.453277	−	0.0645824i
$31$	9.37136			1.68315			0.841573	−	0.540143i	$-0.181630\pi$
$31$	9.37136			1.68315			0.841573	+	0.540143i	$0.181630\pi$
$32$	−4.29866	−	3.67716i	−0.759903	−	0.650036i
$33$	6.37069			1.10899
$34$	7.99981	+	1.13980i	1.37196	+	0.195475i
$35$	1.25389	−	1.25389i	0.211946	−	0.211946i
$36$	0.558576	−	1.92041i	0.0930961	−	0.320069i
$37$	1.10676	+	1.10676i	0.181950	+	0.181950i	0.792205	−	0.610255i	$-0.208933\pi$
$37$	1.10676	+	1.10676i	0.181950	+	0.181950i	−0.610255	+	0.792205i	$0.708933\pi$
$38$	0.457937	−	0.343718i	0.0742871	−	0.0557584i
$39$		−	3.16028i		−	0.506050i
$40$	−1.77069	−	4.69259i	−0.279971	−	0.741963i
$41$			0.0881503i			0.0137668i	0.999976	+	0.00688338i	$0.00219106\pi$
$41$			0.0881503i			0.0137668i	−0.999976	+	0.00688338i	$0.997809\pi$
$42$	0.848947	+	1.13106i	0.130995	+	0.174526i
$43$	−3.83305	−	3.83305i	−0.584535	−	0.584535i	0.351611	−	0.936146i	$-0.385634\pi$
$43$	−3.83305	−	3.83305i	−0.584535	−	0.584535i	−0.936146	+	0.351611i	$0.885634\pi$
$44$	6.13475	+	11.1672i	0.924848	+	1.68353i
$45$	1.25389	−	1.25389i	0.186918	−	0.186918i
$46$	1.12491	−	7.89530i	0.165859	−	1.16410i
$47$	3.18014			0.463871			0.231935	−	0.972731i	$-0.425494\pi$
$47$	3.18014			0.463871			0.231935	+	0.972731i	$0.425494\pi$
$48$	3.90421	−	0.870157i	0.563524	−	0.125596i
$49$	−1.00000			−0.142857
$50$	−0.370144	+	2.59789i	−0.0523463	+	0.367397i
$51$	−4.04030	+	4.04030i	−0.565755	+	0.565755i
$52$	5.53970	−	3.04324i	0.768218	−	0.422022i
$53$	−2.81843	−	2.81843i	−0.387141	−	0.387141i	0.486526	−	0.873666i	$-0.338264\pi$
$53$	−2.81843	−	2.81843i	−0.387141	−	0.387141i	−0.873666	+	0.486526i	$0.838264\pi$
$54$	0.848947	+	1.13106i	0.115527	+	0.153917i
$55$			11.2969i			1.52327i
$56$	−1.16513	+	2.57730i	−0.155698	+	0.344406i
$57$			0.404875i			0.0536270i
$58$	−9.00707	+	6.76052i	−1.18269	+	0.887700i
$59$	−8.62389	−	8.62389i	−1.12274	−	1.12274i	−0.991329	−	0.131407i	$-0.958051\pi$
$59$	−8.62389	−	8.62389i	−1.12274	−	1.12274i	−0.131407	−	0.991329i	$-0.541949\pi$
$60$	3.40540	+	0.990503i	0.439635	+	0.127873i
$61$	−4.88503	+	4.88503i	−0.625464	+	0.625464i	−0.946923	−	0.321459i	$-0.895827\pi$
$61$	−4.88503	+	4.88503i	−0.625464	+	0.625464i	0.321459	+	0.946923i	$0.395827\pi$
$62$	−13.1206	−	1.86941i	−1.66632	−	0.237415i
$63$	−1.00000			−0.125988
$64$	5.28492	+	6.00580i	0.660615	+	0.750725i
$65$	5.60402			0.695093
$66$	−8.91943	−	1.27083i	−1.09791	−	0.156429i
$67$	−9.19959	+	9.19959i	−1.12391	+	1.12391i	−0.132761	+	0.991148i	$0.542384\pi$
$67$	−9.19959	+	9.19959i	−1.12391	+	1.12391i	−0.991148	+	0.132761i	$0.957616\pi$
$68$	−10.9730	−	3.19162i	−1.33067	−	0.387041i
$69$	3.98752	+	3.98752i	0.480041	+	0.480041i
$70$	−2.00566	+	1.50541i	−0.239722	+	0.179931i
$71$			3.04149i			0.360958i	0.983579	+	0.180479i	$0.0577648\pi$
$71$			3.04149i			0.360958i	−0.983579	+	0.180479i	$0.942235\pi$
$72$	−1.16513	+	2.57730i	−0.137312	+	0.303737i
$73$		−	4.95758i		−	0.580241i	−0.956990	−	0.290120i	$-0.906305\pi$
$73$		−	4.95758i		−	0.580241i	0.956990	−	0.290120i	$-0.0936953\pi$
$74$	−1.32877	−	1.77032i	−0.154466	−	0.205796i
$75$	−1.31206	−	1.31206i	−0.151504	−	0.151504i
$76$	−0.709710	+	0.389881i	−0.0814094	+	0.0447224i
$77$	4.50476	−	4.50476i	0.513365	−	0.513365i
$78$	−0.630417	+	4.42463i	−0.0713806	+	0.500991i
$79$	−1.57254			−0.176924			−0.0884622	−	0.996080i	$-0.528195\pi$
$79$	−1.57254			−0.176924			−0.0884622	+	0.996080i	$0.528195\pi$
$80$	1.54302	+	6.92319i	0.172515	+	0.774036i
$81$	−1.00000			−0.111111
$82$	0.0175843	−	0.123417i	0.00194186	−	0.0136291i
$83$	−7.63884	+	7.63884i	−0.838471	+	0.838471i	−0.988658	−	0.150186i	$-0.952013\pi$
$83$	−7.63884	+	7.63884i	−0.838471	+	0.838471i	0.150186	+	0.988658i	$0.452013\pi$
$84$	−0.962965	−	1.75291i	−0.105068	−	0.191258i
$85$	−7.16452	−	7.16452i	−0.777101	−	0.777101i
$86$	4.60193	+	6.13117i	0.496239	+	0.661141i
$87$		−	7.96341i		−	0.853768i
$88$	−6.36145	−	16.8587i	−0.678133	−	1.79715i
$89$			2.16431i			0.229416i	0.993399	+	0.114708i	$0.0365932\pi$
$89$			2.16431i			0.229416i	−0.993399	+	0.114708i	$0.963407\pi$
$90$	−2.00566	+	1.50541i	−0.211415	+	0.158684i
$91$	−2.23466	−	2.23466i	−0.234256	−	0.234256i
$92$	−3.14992	+	10.8296i	−0.328402	+	1.12906i
$93$	6.62655	−	6.62655i	0.687142	−	0.687142i
$94$	−4.45243	−	0.634377i	−0.459233	−	0.0654310i
$95$	−0.717950			−0.0736602
$96$	−5.63976	+	0.439469i	−0.575605	+	0.0448532i
$97$	−4.52728			−0.459676			−0.229838	−	0.973229i	$-0.573820\pi$
$97$	−4.52728			−0.459676			−0.229838	+	0.973229i	$0.573820\pi$
$98$	1.40007	+	0.199481i	0.141429	+	0.0201506i
$99$	4.50476	−	4.50476i	0.452745	−	0.452745i
$100$	1.03646	−	3.56340i	0.103646	−	0.356340i
$101$	−12.7835	−	12.7835i	−1.27201	−	1.27201i	−0.945032	−	0.326977i	$-0.893970\pi$
$101$	−12.7835	−	12.7835i	−1.27201	−	1.27201i	−0.326977	−	0.945032i	$-0.606030\pi$
$102$	6.46269	−	4.85076i	0.639901	−	0.480297i
$103$			3.35143i			0.330226i	0.986275	+	0.165113i	$0.0527989\pi$
$103$			3.35143i			0.330226i	−0.986275	+	0.165113i	$0.947201\pi$
$104$	−8.36305	+	3.15570i	−0.820065	+	0.309442i
$105$		−	1.77326i		−	0.173053i
$106$	3.38378	+	4.50823i	0.328662	+	0.437878i
$107$	12.2186	+	12.2186i	1.18122	+	1.18122i	0.979429	+	0.201788i	$0.0646752\pi$
$107$	12.2186	+	12.2186i	1.18122	+	1.18122i	0.201788	+	0.979429i	$0.435325\pi$
$108$	−0.962965	−	1.75291i	−0.0926614	−	0.168674i
$109$	−4.09852	+	4.09852i	−0.392567	+	0.392567i	−0.875602	−	0.483034i	$-0.839535\pi$
$109$	−4.09852	+	4.09852i	−0.392567	+	0.392567i	0.483034	+	0.875602i	$0.339535\pi$
$110$	2.25352	−	15.8165i	0.214865	−	1.50804i
$111$	1.56519			0.148562
$112$	2.14540	−	3.37598i	0.202721	−	0.319001i
$113$	−15.9696			−1.50229			−0.751147	−	0.660135i	$-0.770499\pi$
$113$	−15.9696			−1.50229			−0.751147	+	0.660135i	$0.770499\pi$
$114$	0.0807649	−	0.566855i	0.00756433	−	0.0530909i
$115$	−7.07092	+	7.07092i	−0.659366	+	0.659366i
$116$	13.9592	−	7.66849i	1.29608	−	0.712001i
$117$	−2.23466	−	2.23466i	−0.206594	−	0.206594i
$118$	10.3538	+	13.7944i	0.953143	+	1.26988i
$119$			5.71385i			0.523788i
$120$	−4.57023	−	2.06609i	−0.417203	−	0.188607i
$121$			29.5857i			2.68960i
$122$	7.81388	−	5.86494i	0.707436	−	0.530986i
$123$	0.0623316	+	0.0623316i	0.00562025	+	0.00562025i
$124$	17.9969	+	5.23462i	1.61617	+	0.470083i
$125$	8.59607	−	8.59607i	0.768855	−	0.768855i
$126$	1.40007	+	0.199481i	0.124729	+	0.0177712i
$127$	−0.401114			−0.0355931			−0.0177965	−	0.999842i	$-0.505665\pi$
$127$	−0.401114			−0.0355931			−0.0177965	+	0.999842i	$0.505665\pi$
$128$	−6.20124	−	9.46280i	−0.548117	−	0.836401i
$129$	−5.42075			−0.477270
$130$	−7.84604	−	1.11789i	−0.688143	−	0.0980459i
$131$	−6.96066	+	6.96066i	−0.608156	+	0.608156i	−0.942464	−	0.334308i	$-0.891497\pi$
$131$	−6.96066	+	6.96066i	−0.608156	+	0.608156i	0.334308	+	0.942464i	$0.391497\pi$
$132$	12.2344	+	3.55852i	1.06486	+	0.309729i
$133$	0.286290	+	0.286290i	0.0248245	+	0.0248245i
$134$	14.7152	−	11.0450i	1.27120	−	0.954139i
$135$		−	1.77326i		−	0.152618i
$136$	14.7263	+	6.65740i	1.26277	+	0.570868i
$137$		−	5.03628i		−	0.430279i	−0.976583	−	0.215139i	$-0.930979\pi$
$137$		−	5.03628i		−	0.430279i	0.976583	−	0.215139i	$-0.0690205\pi$
$138$	−4.78738	−	6.37825i	−0.407529	−	0.542953i
$139$	−13.6994	−	13.6994i	−1.16197	−	1.16197i	−0.984043	−	0.177928i	$-0.943061\pi$
$139$	−13.6994	−	13.6994i	−1.16197	−	1.16197i	−0.177928	−	0.984043i	$-0.556939\pi$
$140$	3.10837	−	1.70759i	0.262706	−	0.144318i
$141$	2.24870	−	2.24870i	0.189374	−	0.189374i
$142$	0.606719	−	4.25830i	0.0509147	−	0.357349i
$143$	20.1332			1.68362
$144$	2.14540	−	3.37598i	0.178783	−	0.281332i
$145$	14.1212			1.17270
$146$	−0.988943	+	6.94098i	−0.0818455	+	0.574439i
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$	1.50723	+	2.74365i	0.123893	+	0.225526i
$149$	−10.7481	−	10.7481i	−0.880516	−	0.880516i	0.113071	−	0.993587i	$-0.463931\pi$
$149$	−10.7481	−	10.7481i	−0.880516	−	0.880516i	−0.993587	+	0.113071i	$0.963931\pi$
$150$	1.57525	+	2.09872i	0.128619	+	0.171359i
$151$			14.3218i			1.16549i	0.812654	+	0.582746i	$0.198022\pi$
$151$			14.3218i			1.16549i	−0.812654	+	0.582746i	$0.801978\pi$
$152$	1.07142	−	0.404288i	0.0869037	−	0.0327921i
$153$			5.71385i			0.461937i
$154$	−7.20561	+	5.40838i	−0.580644	+	0.435820i
$155$	11.7506	+	11.7506i	0.943833	+	0.943833i
$156$	1.76526	−	6.06905i	0.141334	−	0.485913i
$157$	4.24676	−	4.24676i	0.338929	−	0.338929i	−0.517035	−	0.855964i	$-0.672964\pi$
$157$	4.24676	−	4.24676i	0.338929	−	0.338929i	0.855964	+	0.517035i	$0.172964\pi$
$158$	2.20167	+	0.313691i	0.175155	+	0.0249560i
$159$	−3.98586			−0.316099
$160$	−0.779295	−	10.0008i	−0.0616087	−	0.790631i
$161$	5.63920			0.444431
$162$	1.40007	+	0.199481i	0.110000	+	0.0156727i
$163$	4.59500	−	4.59500i	0.359908	−	0.359908i	−0.503871	−	0.863779i	$-0.668091\pi$
$163$	4.59500	−	4.59500i	0.359908	−	0.359908i	0.863779	+	0.503871i	$0.168091\pi$
$164$	−0.0492387	+	0.169285i	−0.00384489	+	0.0132189i
$165$	7.98812	+	7.98812i	0.621874	+	0.621874i
$166$	12.2187	−	9.17113i	0.948358	−	0.711818i
$167$		−	22.5799i		−	1.74729i	−0.486568	−	0.873643i	$-0.661751\pi$
$167$		−	22.5799i		−	1.74729i	0.486568	−	0.873643i	$-0.338249\pi$
$168$	0.998550	+	2.64630i	0.0770398	+	0.204166i
$169$			3.01261i			0.231739i
$170$	8.60167	+	11.4600i	0.659718	+	0.878945i
$171$	0.286290	+	0.286290i	0.0218931	+	0.0218931i
$172$	−5.21999	−	9.50210i	−0.398021	−	0.724528i
$173$	9.76393	−	9.76393i	0.742338	−	0.742338i	−0.230689	−	0.973027i	$-0.574098\pi$
$173$	9.76393	−	9.76393i	0.742338	−	0.742338i	0.973027	+	0.230689i	$0.0740981\pi$
$174$	−1.58855	+	11.1494i	−0.120428	+	0.845231i
$175$	−1.85554			−0.140265
$176$	5.54350	+	24.8725i	0.417857	+	1.87483i
$177$	−12.1960			−0.916710
$178$	0.431738	−	3.03019i	0.0323601	−	0.227122i
$179$	1.69623	−	1.69623i	0.126783	−	0.126783i	−0.640868	−	0.767651i	$-0.721426\pi$
$179$	1.69623	−	1.69623i	0.126783	−	0.126783i	0.767651	+	0.640868i	$0.221426\pi$
$180$	3.10837	−	1.70759i	0.231685	−	0.127276i
$181$	4.89950	+	4.89950i	0.364177	+	0.364177i	0.865348	−	0.501171i	$-0.167097\pi$
$181$	4.89950	+	4.89950i	0.364177	+	0.364177i	−0.501171	+	0.865348i	$0.667097\pi$
$182$	2.68291	+	3.57446i	0.198871	+	0.264956i
$183$			6.90848i			0.510690i
$184$	6.57043	−	14.5339i	0.484378	−	1.07145i
$185$			2.77550i			0.204059i
$186$	−10.5995	+	7.95579i	−0.777196	+	0.583347i
$187$	−25.7395	−	25.7395i	−1.88226	−	1.88226i
$188$	6.10718	+	1.77635i	0.445412	+	0.129554i
$189$	−0.707107	+	0.707107i	−0.0514344	+	0.0514344i
$190$	1.00518	+	0.143217i	0.0729237	+	0.0103901i
$191$	−4.36750			−0.316021			−0.158010	−	0.987437i	$-0.550508\pi$
$191$	−4.36750			−0.316021			−0.158010	+	0.987437i	$0.550508\pi$
$192$	7.98374	+	0.509735i	0.576177	+	0.0367870i
$193$	0.132339			0.00952596			0.00476298	−	0.999989i	$-0.498484\pi$
$193$	0.132339			0.00952596			0.00476298	+	0.999989i	$0.498484\pi$
$194$	6.33853	+	0.903107i	0.455080	+	0.0648393i
$195$	3.96264	−	3.96264i	0.283770	−	0.283770i
$196$	−1.92041	−	0.558576i	−0.137172	−	0.0398983i
$197$	0.0572708	+	0.0572708i	0.00408038	+	0.00408038i	0.709144	−	0.705064i	$-0.249082\pi$
$197$	0.0572708	+	0.0572708i	0.00408038	+	0.00408038i	−0.705064	+	0.709144i	$0.749082\pi$
$198$	−7.20561	+	5.40838i	−0.512080	+	0.384357i
$199$			1.71520i			0.121587i	0.998150	+	0.0607937i	$0.0193632\pi$
$199$			1.71520i			0.121587i	−0.998150	+	0.0607937i	$0.980637\pi$
$200$	−2.16195	+	4.78227i	−0.152873	+	0.338157i
$201$			13.0102i			0.917668i
$202$	15.3478	+	20.4480i	1.07987	+	1.43871i
$203$	−5.63098	−	5.63098i	−0.395218	−	0.395218i
$204$	−10.0159	+	5.50224i	−0.701251	+	0.385234i
$205$	−0.110530	+	0.110530i	−0.00771978	+	0.00771978i
$206$	0.668547	−	4.69225i	0.0465799	−	0.326925i
$207$	5.63920			0.391951
$208$	12.3384	−	2.74994i	0.855514	−	0.190674i
$209$	−2.57933			−0.178416
$210$	−0.353732	+	2.48270i	−0.0244099	+	0.171323i
$211$	13.9352	−	13.9352i	0.959338	−	0.959338i	−0.0398669	−	0.999205i	$-0.512693\pi$
$211$	13.9352	−	13.9352i	0.959338	−	0.959338i	0.999205	+	0.0398669i	$0.0126934\pi$
$212$	−3.83824	−	6.98685i	−0.263611	−	0.479859i
$213$	2.15066	+	2.15066i	0.147360	+	0.147360i
$214$	−14.6696	−	19.5443i	−1.00279	−	1.33602i
$215$		−	9.61242i		−	0.655562i
$216$	0.998550	+	2.64630i	0.0679427	+	0.180058i
$217$		−	9.37136i		−	0.636170i
$218$	6.55581	−	4.92066i	0.444016	−	0.333269i
$219$	−3.50554	−	3.50554i	−0.236882	−	0.236882i
$220$	−6.31019	+	21.6947i	−0.425433	+	1.46266i
$221$	−12.7685	+	12.7685i	−0.858902	+	0.858902i
$222$	−2.19139	−	0.312226i	−0.147076	−	0.0209553i
$223$	−2.21498			−0.148326			−0.0741629	−	0.997246i	$-0.523628\pi$
$223$	−2.21498			−0.148326			−0.0741629	+	0.997246i	$0.523628\pi$
$224$	−3.67716	+	4.29866i	−0.245691	+	0.287216i
$225$	−1.85554			−0.123702
$226$	22.3586	+	3.18563i	1.48727	+	0.211905i
$227$	10.9316	−	10.9316i	0.725556	−	0.725556i	−0.244175	−	0.969731i	$-0.578517\pi$
$227$	10.9316	−	10.9316i	0.725556	−	0.725556i	0.969731	+	0.244175i	$0.0785173\pi$
$228$	−0.226154	+	0.777528i	−0.0149774	+	0.0514931i
$229$	−4.77065	−	4.77065i	−0.315254	−	0.315254i	0.531687	−	0.846941i	$-0.321558\pi$
$229$	−4.77065	−	4.77065i	−0.315254	−	0.315254i	−0.846941	+	0.531687i	$0.821558\pi$
$230$	11.3103	−	8.48929i	0.745781	−	0.559767i
$231$		−	6.37069i		−	0.419160i
$232$	−21.0736	+	7.95187i	−1.38355	+	0.522066i
$233$			17.5396i			1.14906i	0.818485	+	0.574528i	$0.194814\pi$
$233$			17.5396i			1.14906i	−0.818485	+	0.574528i	$0.805186\pi$
$234$	2.68291	+	3.57446i	0.175388	+	0.233670i
$235$	3.98753	+	3.98753i	0.260118	+	0.260118i
$236$	−11.7443	−	21.3786i	−0.764492	−	1.39163i
$237$	−1.11195	+	1.11195i	−0.0722291	+	0.0722291i
$238$	1.13980	−	7.99981i	0.0738826	−	0.518551i
$239$	11.0342			0.713740			0.356870	−	0.934154i	$-0.383844\pi$
$239$	11.0342			0.713740			0.356870	+	0.934154i	$0.383844\pi$
$240$	5.98651	+	3.80435i	0.386428	+	0.245570i
$241$	16.6652			1.07350			0.536751	−	0.843741i	$-0.319651\pi$
$241$	16.6652			1.07350			0.536751	+	0.843741i	$0.319651\pi$
$242$	5.90178	−	41.4221i	0.379381	−	2.66271i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−12.1100	+	6.65263i	−0.775260	+	0.425891i
$245$	−1.25389	−	1.25389i	−0.0801079	−	0.0801079i
$246$	−0.0748349	−	0.0997029i	−0.00477130	−	0.00635682i
$247$			1.27952i			0.0814139i
$248$	−24.1528	−	10.9189i	−1.53370	−	0.693351i
$249$			10.8029i			0.684609i
$250$	−13.7499	+	10.3204i	−0.869619	+	0.652718i
$251$	−2.25958	−	2.25958i	−0.142623	−	0.142623i	0.632190	−	0.774813i	$-0.282156\pi$
$251$	−2.25958	−	2.25958i	−0.142623	−	0.142623i	−0.774813	+	0.632190i	$0.782156\pi$
$252$	−1.92041	−	0.558576i	−0.120975	−	0.0351870i
$253$	−25.4032	+	25.4032i	−1.59709	+	1.59709i
$254$	0.561589	+	0.0800146i	0.0352372	+	0.00502056i
$255$	−10.1322			−0.634501
$256$	6.79455	+	14.4857i	0.424659	+	0.905353i
$257$	−9.14858			−0.570673			−0.285337	−	0.958427i	$-0.592105\pi$
$257$	−9.14858			−0.570673			−0.285337	+	0.958427i	$0.592105\pi$
$258$	7.58945	+	1.08134i	0.472499	+	0.0673211i
$259$	1.10676	−	1.10676i	0.0687707	−	0.0687707i
$260$	10.7620	+	3.13027i	0.667433	+	0.194131i
$261$	−5.63098	−	5.63098i	−0.348549	−	0.348549i
$262$	11.1340	−	8.35692i	0.687858	−	0.516292i
$263$			24.3635i			1.50232i	0.660122	+	0.751158i	$0.270505\pi$
$263$			24.3635i			1.50232i	−0.660122	+	0.751158i	$0.729495\pi$
$264$	−16.4192	−	7.42271i	−1.01053	−	0.456836i
$265$		−	7.06797i		−	0.434182i
$266$	−0.343718	−	0.457937i	−0.0210747	−	0.0280779i
$267$	1.53040	+	1.53040i	0.0936587	+	0.0936587i
$268$	−22.8057	+	12.5284i	−1.39308	+	0.765291i
$269$	−6.56160	+	6.56160i	−0.400068	+	0.400068i	−0.878257	−	0.478189i	$-0.841293\pi$
$269$	−6.56160	+	6.56160i	−0.400068	+	0.400068i	0.478189	+	0.878257i	$0.341293\pi$
$270$	−0.353732	+	2.48270i	−0.0215275	+	0.151092i
$271$	−23.1972			−1.40913			−0.704565	−	0.709639i	$-0.748858\pi$
$271$	−23.1972			−1.40913			−0.704565	+	0.709639i	$0.748858\pi$
$272$	−19.2899	−	12.2585i	−1.16962	−	0.743279i
$273$	−3.16028			−0.191269
$274$	−1.00464	+	7.05117i	−0.0606927	+	0.425977i
$275$	8.35874	−	8.35874i	0.504051	−	0.504051i
$276$	5.43035	+	9.88502i	0.326869	+	0.595008i
$277$	14.2232	+	14.2232i	0.854591	+	0.854591i	0.990695	−	0.136103i	$-0.0434579\pi$
$277$	14.2232	+	14.2232i	0.854591	+	0.854591i	−0.136103	+	0.990695i	$0.543458\pi$
$278$	16.4475	+	21.9130i	0.986453	+	1.31426i
$279$		−	9.37136i		−	0.561049i
$280$	−4.69259	+	1.77069i	−0.280436	+	0.105819i
$281$			0.659932i			0.0393682i	0.999806	+	0.0196841i	$0.00626605\pi$
$281$			0.659932i			0.0393682i	−0.999806	+	0.0196841i	$0.993734\pi$
$282$	−3.59692	+	2.69977i	−0.214193	+	0.160769i
$283$	3.69227	+	3.69227i	0.219483	+	0.219483i	0.808280	−	0.588798i	$-0.200399\pi$
$283$	3.69227	+	3.69227i	0.219483	+	0.219483i	−0.588798	+	0.808280i	$0.700399\pi$
$284$	−1.69890	+	5.84091i	−0.100811	+	0.346594i
$285$	−0.507668	+	0.507668i	−0.0300716	+	0.0300716i
$286$	−28.1879	−	4.01619i	−1.66679	−	0.237482i
$287$	0.0881503			0.00520334
$288$	−3.67716	+	4.29866i	−0.216679	+	0.253301i
$289$	15.6481			0.920476
$290$	−19.7708	−	2.81692i	−1.16098	−	0.165415i
$291$	−3.20127	+	3.20127i	−0.187662	+	0.187662i
$292$	2.76919	−	9.52061i	0.162054	−	0.557151i
$293$	−6.58657	−	6.58657i	−0.384792	−	0.384792i	0.488033	−	0.872825i	$-0.337714\pi$
$293$	−6.58657	−	6.58657i	−0.384792	−	0.384792i	−0.872825	+	0.488033i	$0.837714\pi$
$294$	1.13106	−	0.848947i	0.0659645	−	0.0495116i
$295$		−	21.6268i		−	1.25916i
$296$	−1.56292	−	4.14197i	−0.0908431	−	0.240747i
$297$		−	6.37069i		−	0.369665i
$298$	12.9041	+	17.1921i	0.747512	+	0.995913i
$299$	12.6017	+	12.6017i	0.728774	+	0.728774i
$300$	−1.78682	−	3.25259i	−0.103162	−	0.187788i
$301$	−3.83305	+	3.83305i	−0.220933	+	0.220933i
$302$	2.85693	−	20.0516i	0.164398	−	1.15384i
$303$	−18.0786			−1.03859
$304$	−1.58072	+	0.352305i	−0.0906603	+	0.0202061i
$305$	−12.2506			−0.701465
$306$	1.13980	−	7.99981i	0.0651583	−	0.457319i
$307$	8.67092	−	8.67092i	0.494875	−	0.494875i	−0.414963	−	0.909838i	$-0.636205\pi$
$307$	8.67092	−	8.67092i	0.494875	−	0.494875i	0.909838	+	0.414963i	$0.136205\pi$
$308$	11.1672	−	6.13475i	0.636313	−	0.349560i
$309$	2.36982	+	2.36982i	0.134814	+	0.134814i
$310$	−14.1077	−	18.7958i	−0.801265	−	1.06753i
$311$		−	8.54796i		−	0.484710i	−0.970188	−	0.242355i	$-0.922080\pi$
$311$		−	8.54796i		−	0.484710i	0.970188	−	0.242355i	$-0.0779199\pi$
$312$	−3.68216	+	8.14499i	−0.208461	+	0.461119i
$313$		−	5.96877i		−	0.337375i	−0.985670	−	0.168688i	$-0.946047\pi$
$313$		−	5.96877i		−	0.337375i	0.985670	−	0.168688i	$-0.0539529\pi$
$314$	−6.79293	+	5.09864i	−0.383347	+	0.287733i
$315$	−1.25389	−	1.25389i	−0.0706485	−	0.0706485i
$316$	−3.01992	−	0.878383i	−0.169884	−	0.0494129i
$317$	8.48813	−	8.48813i	0.476741	−	0.476741i	−0.427347	−	0.904088i	$-0.640552\pi$
$317$	8.48813	−	8.48813i	0.476741	−	0.476741i	0.904088	+	0.427347i	$0.140552\pi$
$318$	5.58049	+	0.795103i	0.312939	+	0.0445871i
$319$	50.7324			2.84047
$320$	−0.903895	+	14.1573i	−0.0505292	+	0.791416i
$321$	17.2797			0.964460
$322$	−7.89530	−	1.12491i	−0.439988	−	0.0626890i
$323$	1.63582	−	1.63582i	0.0910194	−	0.0910194i
$324$	−1.92041	−	0.558576i	−0.106690	−	0.0310320i
$325$	−4.14649	−	4.14649i	−0.230006	−	0.230006i
$326$	−7.34996	+	5.51673i	−0.407077	+	0.305543i
$327$			5.79619i			0.320530i
$328$	0.102707	−	0.227189i	0.00567104	−	0.0125444i
$329$		−	3.18014i		−	0.175327i
$330$	−9.59048	−	12.7774i	−0.527939	−	0.703375i
$331$	−0.0421742	−	0.0421742i	−0.00231810	−	0.00231810i	0.705947	−	0.708265i	$-0.250522\pi$
$331$	−0.0421742	−	0.0421742i	−0.00231810	−	0.00231810i	−0.708265	+	0.705947i	$0.750522\pi$
$332$	−18.9366	+	10.4029i	−1.03928	+	0.570931i
$333$	1.10676	−	1.10676i	0.0606500	−	0.0606500i
$334$	−4.50426	+	31.6135i	−0.246462	+	1.72982i
$335$	−23.0705			−1.26048
$336$	−0.870157	−	3.90421i	−0.0474710	−	0.212992i
$337$	−9.93708			−0.541307			−0.270654	−	0.962677i	$-0.587240\pi$
$337$	−9.93708			−0.541307			−0.270654	+	0.962677i	$0.587240\pi$
$338$	0.600959	−	4.21788i	0.0326878	−	0.229422i
$339$	−11.2922	+	11.2922i	−0.613309	+	0.613309i
$340$	−9.75692	−	17.7608i	−0.529143	−	0.963214i
$341$	42.2157	+	42.2157i	2.28611	+	2.28611i
$342$	−0.343718	−	0.457937i	−0.0185861	−	0.0247624i
$343$			1.00000i			0.0539949i
$344$	5.41289	+	14.3449i	0.291843	+	0.773427i
$345$			9.99979i			0.538370i
$346$	−15.6179	+	11.7225i	−0.839626	+	0.630206i
$347$	−13.7948	−	13.7948i	−0.740543	−	0.740543i	0.232139	−	0.972683i	$-0.425427\pi$
$347$	−13.7948	−	13.7948i	−0.740543	−	0.740543i	−0.972683	+	0.232139i	$0.925427\pi$
$348$	4.44818	−	15.2931i	0.238447	−	0.819794i
$349$	4.91302	−	4.91302i	0.262988	−	0.262988i	−0.563279	−	0.826267i	$-0.690460\pi$
$349$	4.91302	−	4.91302i	0.262988	−	0.262988i	0.826267	+	0.563279i	$0.190460\pi$
$350$	2.59789	+	0.370144i	0.138863	+	0.0197850i
$351$	−3.16028			−0.168683
$352$	−2.79972	−	35.9291i	−0.149226	−	1.91503i
$353$	−17.3926			−0.925717			−0.462858	−	0.886432i	$-0.653176\pi$
$353$	−17.3926			−0.925717			−0.462858	+	0.886432i	$0.653176\pi$
$354$	17.0753	+	2.43288i	0.907544	+	0.129306i
$355$	−3.81368	+	3.81368i	−0.202409	+	0.202409i
$356$	−1.20893	+	4.15636i	−0.0640732	+	0.220287i
$357$	4.04030	+	4.04030i	0.213835	+	0.213835i
$358$	−2.71322	+	2.03649i	−0.143398	+	0.107632i
$359$		−	3.69545i		−	0.195039i	−0.995234	−	0.0975193i	$-0.968909\pi$
$359$		−	3.69545i		−	0.195039i	0.995234	−	0.0975193i	$-0.0310908\pi$
$360$	−4.69259	+	1.77069i	−0.247321	+	0.0933237i
$361$			18.8361i			0.991372i
$362$	−5.88231	−	7.83702i	−0.309167	−	0.411905i
$363$	20.9202	+	20.9202i	1.09803	+	1.09803i
$364$	−3.04324	−	5.53970i	−0.159509	−	0.290359i
$365$	6.21624	−	6.21624i	0.325373	−	0.325373i
$366$	1.37811	−	9.67238i	0.0720350	−	0.505584i
$367$	22.6986			1.18486			0.592430	−	0.805622i	$-0.298169\pi$
$367$	22.6986			1.18486			0.592430	+	0.805622i	$0.298169\pi$
$368$	−12.0983	+	19.0379i	−0.630669	+	0.992417i
$369$	0.0881503			0.00458892
$370$	0.553660	−	3.88591i	0.0287834	−	0.202019i
$371$	−2.81843	+	2.81843i	−0.146325	+	0.146325i
$372$	16.4272	−	9.02429i	0.851709	−	0.467888i
$373$	8.78680	+	8.78680i	0.454963	+	0.454963i	0.896998	−	0.442035i	$-0.145743\pi$
$373$	8.78680	+	8.78680i	0.454963	+	0.454963i	−0.442035	+	0.896998i	$0.645743\pi$
$374$	30.9027	+	41.1717i	1.59794	+	2.12894i
$375$		−	12.1567i		−	0.627768i
$376$	−8.19616	−	3.70529i	−0.422685	−	0.191086i
$377$		−	25.1666i		−	1.29615i
$378$	1.13106	−	0.848947i	0.0581753	−	0.0436651i
$379$	6.55494	+	6.55494i	0.336705	+	0.336705i	0.855126	−	0.518421i	$-0.173480\pi$
$379$	6.55494	+	6.55494i	0.336705	+	0.336705i	−0.518421	+	0.855126i	$0.673480\pi$
$380$	−1.37876	−	0.401030i	−0.0707290	−	0.0205724i
$381$	−0.283630	+	0.283630i	−0.0145308	+	0.0145308i
$382$	6.11482	+	0.871233i	0.312861	+	0.0445761i
$383$	23.3083			1.19100			0.595499	−	0.803356i	$-0.296954\pi$
$383$	23.3083			1.19100			0.595499	+	0.803356i	$0.296954\pi$
$384$	−11.0762	−	2.30627i	−0.565227	−	0.117691i
$385$	11.2969			0.575744
$386$	−0.185284	−	0.0263991i	−0.00943072	−	0.00134368i
$387$	−3.83305	+	3.83305i	−0.194845	+	0.194845i
$388$	−8.69426	−	2.52883i	−0.441384	−	0.128382i
$389$	9.48823	+	9.48823i	0.481073	+	0.481073i	0.905474	−	0.424402i	$-0.139515\pi$
$389$	9.48823	+	9.48823i	0.481073	+	0.481073i	−0.424402	+	0.905474i	$0.639515\pi$
$390$	−6.33846	+	4.75751i	−0.320960	+	0.240906i
$391$		−	32.2215i		−	1.62951i
$392$	2.57730	+	1.16513i	0.130173	+	0.0588482i
$393$			9.84386i			0.496557i
$394$	−0.0687590	−	0.0916079i	−0.00346403	−	0.00461514i
$395$	−1.97178	−	1.97178i	−0.0992112	−	0.0992112i
$396$	11.1672	−	6.13475i	0.561175	−	0.308283i
$397$	4.23702	−	4.23702i	0.212650	−	0.212650i	−0.592742	−	0.805392i	$-0.701955\pi$
$397$	4.23702	−	4.23702i	0.212650	−	0.212650i	0.805392	+	0.592742i	$0.201955\pi$
$398$	0.342150	−	2.40141i	0.0171504	−	0.120372i
$399$	0.404875			0.0202691
$400$	3.98086	−	6.26426i	0.199043	−	0.313213i
$401$	8.83591			0.441244			0.220622	−	0.975359i	$-0.429191\pi$
$401$	8.83591			0.441244			0.220622	+	0.975359i	$0.429191\pi$
$402$	2.59528	−	18.2152i	0.129441	−	0.908493i
$403$	20.9418	−	20.9418i	1.04318	−	1.04318i
$404$	−17.4091	−	31.6903i	−0.866135	−	1.57665i
$405$	−1.25389	−	1.25389i	−0.0623061	−	0.0623061i
$406$	6.76052	+	9.00707i	0.335519	+	0.447013i
$407$			9.97136i			0.494262i
$408$	15.1206	−	5.70556i	0.748579	−	0.282468i
$409$		−	15.5230i		−	0.767561i	−0.923424	−	0.383781i	$-0.874622\pi$
$409$		−	15.5230i		−	0.767561i	0.923424	−	0.383781i	$-0.125378\pi$
$410$	0.176800	−	0.132702i	0.00873151	−	0.00655369i
$411$	−3.56119	−	3.56119i	−0.175660	−	0.175660i
$412$	−1.87203	+	6.43613i	−0.0922283	+	0.317086i
$413$	−8.62389	+	8.62389i	−0.424354	+	0.424354i
$414$	−7.89530	−	1.12491i	−0.388033	−	0.0552865i
$415$	−19.1565			−0.940354
$416$	−17.8232	+	1.38885i	−0.873856	+	0.0680939i
$417$	−19.3739			−0.948746
$418$	3.61126	+	0.514528i	0.176632	+	0.0251664i
$419$	2.34025	−	2.34025i	0.114329	−	0.114329i	−0.647628	−	0.761957i	$-0.724239\pi$
$419$	2.34025	−	2.34025i	0.114329	−	0.114329i	0.761957	+	0.647628i	$0.224239\pi$
$420$	0.990503	−	3.40540i	0.0483316	−	0.166167i
$421$	−27.4171	−	27.4171i	−1.33623	−	1.33623i	−0.899681	−	0.436548i	$-0.856201\pi$
$421$	−27.4171	−	27.4171i	−1.33623	−	1.33623i	−0.436548	−	0.899681i	$-0.643799\pi$
$422$	−22.2901	+	16.7305i	−1.08507	+	0.814428i
$423$		−	3.18014i		−	0.154624i
$424$	3.98008	+	10.5478i	0.193290	+	0.512245i
$425$			10.6023i			0.514285i
$426$	−2.58206	−	3.44009i	−0.125101	−	0.166673i
$427$	4.88503	+	4.88503i	0.236403	+	0.236403i
$428$	16.6398	+	30.2898i	0.804313	+	1.46411i
$429$	14.2363	−	14.2363i	0.687335	−	0.687335i
$430$	−1.91750	+	13.4581i	−0.0924698	+	0.649007i
$431$	−28.2047			−1.35857			−0.679287	−	0.733872i	$-0.737711\pi$
$431$	−28.2047			−1.35857			−0.679287	+	0.733872i	$0.737711\pi$
$432$	−0.870157	−	3.90421i	−0.0418655	−	0.187841i
$433$	21.9056			1.05272			0.526359	−	0.850262i	$-0.323557\pi$
$433$	21.9056			1.05272			0.526359	+	0.850262i	$0.323557\pi$
$434$	−1.86941	+	13.1206i	−0.0897345	+	0.629809i
$435$	9.98522	−	9.98522i	0.478755	−	0.478755i
$436$	−10.1602	+	5.58153i	−0.486586	+	0.267307i
$437$	−1.61445	−	1.61445i	−0.0772294	−	0.0772294i
$438$	4.20872	+	5.60730i	0.201101	+	0.267927i
$439$			15.1464i			0.722897i	0.932392	+	0.361449i	$0.117718\pi$
$439$			15.1464i			0.722897i	−0.932392	+	0.361449i	$0.882282\pi$
$440$	13.1624	−	29.1155i	0.627494	−	1.38803i
$441$			1.00000i			0.0476190i
$442$	20.4239	−	15.3298i	0.971467	−	0.729163i
$443$	−1.48378	−	1.48378i	−0.0704965	−	0.0704965i	0.670979	−	0.741476i	$-0.265874\pi$
$443$	−1.48378	−	1.48378i	−0.0704965	−	0.0704965i	−0.741476	+	0.670979i	$0.765874\pi$
$444$	3.00582	+	0.874280i	0.142650	+	0.0414915i
$445$	−2.71379	+	2.71379i	−0.128646	+	0.128646i
$446$	3.10113	+	0.441846i	0.146843	+	0.0209220i
$447$	−15.2001			−0.718938
$448$	6.00580	−	5.28492i	0.283747	−	0.249689i
$449$	1.26628			0.0597593			0.0298796	−	0.999554i	$-0.490488\pi$
$449$	1.26628			0.0597593			0.0298796	+	0.999554i	$0.490488\pi$
$450$	2.59789	+	0.370144i	0.122466	+	0.0174488i
$451$	−0.397095	+	0.397095i	−0.0186985	+	0.0186985i
$452$	−30.6682	−	8.92024i	−1.44251	−	0.419573i
$453$	10.1270	+	10.1270i	0.475810	+	0.475810i
$454$	−17.4857	+	13.1244i	−0.820644	+	0.615959i
$455$		−	5.60402i		−	0.262720i
$456$	0.471734	−	1.04348i	0.0220910	−	0.0488656i
$457$		−	33.9888i		−	1.58993i	−0.606655	−	0.794965i	$-0.707489\pi$
$457$		−	33.9888i		−	1.58993i	0.606655	−	0.794965i	$-0.292511\pi$
$458$	5.72761	+	7.63092i	0.267634	+	0.356570i
$459$	4.04030	+	4.04030i	0.188585	+	0.188585i
$460$	−17.5287	+	9.62945i	−0.817282	+	0.448975i
$461$	7.31824	−	7.31824i	0.340845	−	0.340845i	−0.515840	−	0.856685i	$-0.672520\pi$
$461$	7.31824	−	7.31824i	0.340845	−	0.340845i	0.856685	+	0.515840i	$0.172520\pi$
$462$	−1.27083	+	8.91943i	−0.0591244	+	0.414970i
$463$	5.42568			0.252153			0.126076	−	0.992021i	$-0.459762\pi$
$463$	5.42568			0.252153			0.126076	+	0.992021i	$0.459762\pi$
$464$	31.0908	−	6.92942i	1.44335	−	0.321690i
$465$	16.6179			0.770636
$466$	3.49881	−	24.5567i	0.162079	−	1.13757i
$467$	−16.7291	+	16.7291i	−0.774133	+	0.774133i	−0.978826	−	0.204693i	$-0.934380\pi$
$467$	−16.7291	+	16.7291i	−0.774133	+	0.774133i	0.204693	+	0.978826i	$0.434380\pi$
$468$	−3.04324	−	5.53970i	−0.140674	−	0.256073i
$469$	9.19959	+	9.19959i	0.424798	+	0.424798i
$470$	−4.78740	−	6.37828i	−0.220827	−	0.294208i
$471$		−	6.00583i		−	0.276734i
$472$	12.1783	+	32.2743i	0.560554	+	1.48555i
$473$		−	34.5339i		−	1.58787i
$474$	1.77863	−	1.33500i	0.0816951	−	0.0613187i
$475$	0.531221	+	0.531221i	0.0243741	+	0.0243741i
$476$	−3.19162	+	10.9730i	−0.146288	+	0.502945i
$477$	−2.81843	+	2.81843i	−0.129047	+	0.129047i
$478$	−15.4486	−	2.20110i	−0.706604	−	0.100676i
$479$	22.8060			1.04203			0.521017	−	0.853547i	$-0.325553\pi$
$479$	22.8060			1.04203			0.521017	+	0.853547i	$0.325553\pi$
$480$	−7.62266	−	6.52057i	−0.347925	−	0.297622i
$481$	4.94645			0.225539
$482$	−23.3326	−	3.32440i	−1.06277	−	0.151422i
$483$	3.98752	−	3.98752i	0.181438	−	0.181438i
$484$	−16.5258	+	56.8167i	−0.751175	+	2.58258i
$485$	−5.67670	−	5.67670i	−0.257766	−	0.257766i
$486$	1.13106	−	0.848947i	0.0513058	−	0.0385090i
$487$			23.1892i			1.05080i	0.850854	+	0.525402i	$0.176085\pi$
$487$			23.1892i			1.05080i	−0.850854	+	0.525402i	$0.823915\pi$
$488$	18.2819	−	6.89846i	0.827583	−	0.312279i
$489$		−	6.49831i		−	0.293864i
$490$	1.50541	+	2.00566i	0.0680074	+	0.0906065i
$491$	21.1571	+	21.1571i	0.954805	+	0.954805i	0.999022	−	0.0442174i	$-0.0140794\pi$
$491$	21.1571	+	21.1571i	0.954805	+	0.954805i	−0.0442174	+	0.999022i	$0.514079\pi$
$492$	0.0848856	+	0.154520i	0.00382694	+	0.00696628i
$493$	−32.1746	+	32.1746i	−1.44907	+	1.44907i
$494$	0.255240	−	1.79142i	0.0114838	−	0.0805999i
$495$	11.2969			0.507758
$496$	31.6376	+	20.1053i	1.42057	+	0.902754i
$497$	3.04149			0.136429
$498$	2.15498	−	15.1249i	0.0965671	−	0.677764i
$499$	−13.4046	+	13.4046i	−0.600074	+	0.600074i	−0.940332	−	0.340258i	$-0.889485\pi$
$499$	−13.4046	+	13.4046i	−0.600074	+	0.600074i	0.340258	+	0.940332i	$0.389485\pi$
$500$	21.3096	−	11.7065i	0.952993	−	0.523528i
$501$	−15.9664	−	15.9664i	−0.713326	−	0.713326i
$502$	2.71284	+	3.61432i	0.121080	+	0.161315i
$503$			16.9580i			0.756118i	0.925781	+	0.378059i	$0.123408\pi$
$503$			16.9580i			0.756118i	−0.925781	+	0.378059i	$0.876592\pi$
$504$	2.57730	+	1.16513i	0.114802	+	0.0518992i
$505$		−	32.0582i		−	1.42657i
$506$	40.6338	−	30.4989i	1.80639	−	1.35584i
$507$	2.13024	+	2.13024i	0.0946071	+	0.0946071i
$508$	−0.770305	−	0.224053i	−0.0341767	−	0.00994073i
$509$	−25.6479	+	25.6479i	−1.13682	+	1.13682i	−0.147807	+	0.989016i	$0.547221\pi$
$509$	−25.6479	+	25.6479i	−1.13682	+	1.13682i	−0.989016	+	0.147807i	$0.952779\pi$
$510$	14.1858	+	2.02117i	0.628157	+	0.0894991i
$511$	−4.95758			−0.219310
$512$	−6.62325	−	21.6364i	−0.292709	−	0.956201i
$513$	0.404875			0.0178757
$514$	12.8087	+	1.82497i	0.564967	+	0.0804959i
$515$	−4.20231	+	4.20231i	−0.185176	+	0.185176i
$516$	−10.4101	−	3.02790i	−0.458279	−	0.133296i
$517$	14.3257	+	14.3257i	0.630046	+	0.630046i
$518$	−1.77032	+	1.32877i	−0.0777835	+	0.0583827i
$519$		−	13.8083i		−	0.606116i
$520$	−14.4432	−	6.52943i	−0.633377	−	0.286335i
$521$		−	4.86163i		−	0.212992i	−0.994313	−	0.106496i	$-0.966037\pi$
$521$		−	4.86163i		−	0.212992i	0.994313	−	0.106496i	$-0.0339631\pi$
$522$	6.76052	+	9.00707i	0.295900	+	0.394229i
$523$	−1.52369	−	1.52369i	−0.0666265	−	0.0666265i	0.673008	−	0.739635i	$-0.265002\pi$
$523$	−1.52369	−	1.52369i	−0.0666265	−	0.0666265i	−0.739635	+	0.673008i	$0.765002\pi$
$524$	−17.2554	+	9.47930i	−0.753806	+	0.414105i
$525$	−1.31206	+	1.31206i	−0.0572631	+	0.0572631i
$526$	4.86005	−	34.1107i	0.211908	−	1.48730i
$527$	−53.5466			−2.33252
$528$	21.5073	+	13.6677i	0.935987	+	0.594808i
$529$	−8.80057			−0.382634
$530$	−1.40993	+	9.89569i	−0.0612433	+	0.429841i
$531$	−8.62389	+	8.62389i	−0.374245	+	0.374245i
$532$	0.389881	+	0.709710i	0.0169035	+	0.0307698i
$533$	0.196986	+	0.196986i	0.00853240	+	0.00853240i
$534$	−1.83738	−	2.44795i	−0.0795113	−	0.105933i
$535$			30.6415i			1.32475i
$536$	34.4288	−	12.9913i	1.48710	−	0.561139i
$537$		−	2.39884i		−	0.103518i
$538$	10.4956	−	7.87781i	0.452499	−	0.339636i
$539$	−4.50476	−	4.50476i	−0.194034	−	0.194034i
$540$	0.990503	−	3.40540i	0.0426245	−	0.146545i
$541$	24.4546	−	24.4546i	1.05139	−	1.05139i	0.0527792	−	0.998606i	$-0.483192\pi$
$541$	24.4546	−	24.4546i	1.05139	−	1.05139i	0.998606	−	0.0527792i	$-0.0168079\pi$
$542$	32.4778	+	4.62740i	1.39504	+	0.198764i
$543$	6.92894			0.297349
$544$	24.5619	+	21.0107i	1.05308	+	0.900828i
$545$	−10.2782			−0.440268
$546$	4.42463	+	0.630417i	0.189357	+	0.0269793i
$547$	21.2494	−	21.2494i	0.908560	−	0.908560i	−0.0875965	−	0.996156i	$-0.527919\pi$
$547$	21.2494	−	21.2494i	0.908560	−	0.908560i	0.996156	+	0.0875965i	$0.0279186\pi$
$548$	2.81315	−	9.67175i	0.120172	−	0.413157i
$549$	4.88503	+	4.88503i	0.208488	+	0.208488i
$550$	−13.3703	+	10.0354i	−0.570110	+	0.427913i
$551$			3.22419i			0.137355i
$552$	−5.63102	−	14.9230i	−0.239672	−	0.635165i
$553$			1.57254i			0.0668711i
$554$	−17.0763	−	22.7508i	−0.725503	−	0.966591i
$555$	1.96258	+	1.96258i	0.0833067	+	0.0833067i
$556$	−18.6564	−	33.9608i	−0.791209	−	1.44026i
$557$	−3.36666	+	3.36666i	−0.142650	+	0.142650i	−0.774825	−	0.632175i	$-0.782162\pi$
$557$	−3.36666	+	3.36666i	−0.142650	+	0.142650i	0.632175	+	0.774825i	$0.282162\pi$
$558$	−1.86941	+	13.1206i	−0.0791384	+	0.555439i
$559$	−17.1311			−0.724569
$560$	6.92319	−	1.54302i	0.292558	−	0.0652044i
$561$	−36.4012			−1.53686
$562$	0.131644	−	0.923954i	0.00555306	−	0.0389746i
$563$	−22.0115	+	22.0115i	−0.927674	+	0.927674i	−0.997555	−	0.0698813i	$-0.977738\pi$
$563$	−22.0115	+	22.0115i	−0.927674	+	0.927674i	0.0698813	+	0.997555i	$0.477738\pi$
$564$	5.57450	−	3.06236i	0.234729	−	0.128949i
$565$	−20.0241	−	20.0241i	−0.842419	−	0.842419i
$566$	−4.43291	−	5.90599i	−0.186329	−	0.248247i
$567$			1.00000i			0.0419961i
$568$	3.54374	−	7.83881i	0.148692	−	0.328909i
$569$			31.4982i			1.32048i	0.751057	+	0.660238i	$0.229544\pi$
$569$			31.4982i			1.32048i	−0.751057	+	0.660238i	$0.770456\pi$
$570$	0.812042	−	0.609502i	0.0340127	−	0.0255292i
$571$	−20.5439	−	20.5439i	−0.859737	−	0.859737i	0.131570	−	0.991307i	$-0.457998\pi$
$571$	−20.5439	−	20.5439i	−0.859737	−	0.859737i	−0.991307	+	0.131570i	$0.957998\pi$
$572$	38.6640	+	11.2459i	1.61662	+	0.470215i
$573$	−3.08829	+	3.08829i	−0.129015	+	0.129015i
$574$	−0.123417	−	0.0175843i	−0.00515132	−	0.000733955i
$575$	10.4637			0.436368
$576$	6.00580	−	5.28492i	0.250242	−	0.220205i
$577$	29.5367			1.22963			0.614814	−	0.788672i	$-0.289231\pi$
$577$	29.5367			1.22963			0.614814	+	0.788672i	$0.289231\pi$
$578$	−21.9085	−	3.12150i	−0.911273	−	0.129837i
$579$	0.0935777	−	0.0935777i	0.00388896	−	0.00388896i
$580$	27.1186	+	7.88779i	1.12604	+	0.327523i
$581$	7.63884	+	7.63884i	0.316912	+	0.316912i
$582$	5.12061	−	3.84343i	0.212256	−	0.159315i
$583$		−	25.3926i		−	1.05166i
$584$	−5.77625	+	12.7772i	−0.239023	+	0.528722i
$585$		−	5.60402i		−	0.231698i
$586$	7.90779	+	10.5356i	0.326668	+	0.435221i
$587$	6.07789	+	6.07789i	0.250861	+	0.250861i	0.821324	−	0.570462i	$-0.193236\pi$
$587$	6.07789	+	6.07789i	0.250861	+	0.250861i	−0.570462	+	0.821324i	$0.693236\pi$
$588$	−1.75291	+	0.962965i	−0.0722888	+	0.0397120i
$589$	−2.68293	+	2.68293i	−0.110548	+	0.110548i
$590$	−4.31413	+	30.2791i	−0.177610	+	1.24657i
$591$	0.0809932			0.00333162
$592$	1.36196	+	6.11084i	0.0559764	+	0.251154i
$593$	25.7745			1.05843			0.529216	−	0.848487i	$-0.322486\pi$
$593$	25.7745			1.05843			0.529216	+	0.848487i	$0.322486\pi$
$594$	−1.27083	+	8.91943i	−0.0521428	+	0.365969i
$595$	−7.16452	+	7.16452i	−0.293717	+	0.293717i
$596$	−14.6371	−	26.6444i	−0.599560	−	1.09140i
$597$	1.21283	+	1.21283i	0.0496379	+	0.0496379i
$598$	−15.1295	−	20.1571i	−0.618691	−	0.824284i
$599$		−	23.7727i		−	0.971325i	−0.874146	−	0.485663i	$-0.838578\pi$
$599$		−	23.7727i		−	0.971325i	0.874146	−	0.485663i	$-0.161422\pi$
$600$	1.85285	+	4.91030i	0.0756421	+	0.200462i
$601$			35.6063i			1.45241i	0.687477	+	0.726206i	$0.258718\pi$
$601$			35.6063i			1.45241i	−0.687477	+	0.726206i	$0.741282\pi$
$602$	6.13117	−	4.60193i	0.249888	−	0.187561i
$603$	9.19959	+	9.19959i	0.374636	+	0.374636i
$604$	−7.99982	+	27.5038i	−0.325508	+	1.11911i
$605$	−37.0971	+	37.0971i	−1.50821	+	1.50821i
$606$	25.3114	+	3.60635i	1.02821	+	0.146498i
$607$	23.0247			0.934544			0.467272	−	0.884114i	$-0.345237\pi$
$607$	23.0247			0.934544			0.467272	+	0.884114i	$0.345237\pi$
$608$	2.28340	−	0.177930i	0.0926040	−	0.00721602i
$609$	−7.96341			−0.322694
$610$	17.1517	+	2.44375i	0.694452	+	0.0989447i
$611$	7.10652	−	7.10652i	0.287499	−	0.287499i
$612$	−3.19162	+	10.9730i	−0.129014	+	0.443556i
$613$	6.96604	+	6.96604i	0.281356	+	0.281356i	0.833650	−	0.552294i	$-0.186247\pi$
$613$	6.96604	+	6.96604i	0.281356	+	0.281356i	−0.552294	+	0.833650i	$0.686247\pi$
$614$	−13.8696	+	10.4102i	−0.559732	+	0.420123i
$615$			0.156314i			0.00630317i
$616$	−16.8587	+	6.36145i	−0.679258	+	0.256310i
$617$			4.74756i			0.191130i	0.995423	+	0.0955648i	$0.0304657\pi$
$617$			4.74756i			0.191130i	−0.995423	+	0.0955648i	$0.969534\pi$
$618$	−2.84519	−	3.79066i	−0.114450	−	0.152483i
$619$	−23.1554	−	23.1554i	−0.930696	−	0.930696i	0.0670537	−	0.997749i	$-0.478640\pi$
$619$	−23.1554	−	23.1554i	−0.930696	−	0.930696i	−0.997749	+	0.0670537i	$0.978640\pi$
$620$	16.0025	+	29.1297i	0.642674	+	1.16988i
$621$	3.98752	−	3.98752i	0.160014	−	0.160014i
$622$	−1.70516	+	11.9678i	−0.0683705	+	0.479864i
$623$	2.16431			0.0867111
$624$	6.78006	−	10.6691i	0.271420	−	0.427105i
$625$	12.2793			0.491172
$626$	−1.19066	+	8.35672i	−0.0475882	+	0.334002i
$627$	−1.82386	+	1.82386i	−0.0728381	+	0.0728381i
$628$	10.5277	−	5.78341i	0.420101	−	0.230783i
$629$	−6.32385	−	6.32385i	−0.252149	−	0.252149i
$630$	1.50541	+	2.00566i	0.0599769	+	0.0799074i
$631$			15.6800i			0.624210i	0.950048	+	0.312105i	$0.101034\pi$
$631$			15.6800i			0.624210i	−0.950048	+	0.312105i	$0.898966\pi$
$632$	4.05290	+	1.83222i	0.161216	+	0.0728817i
$633$		−	19.7073i		−	0.783296i
$634$	−13.5772	+	10.1908i	−0.539221	+	0.404728i
$635$	−0.502951	−	0.502951i	−0.0199590	−	0.0199590i
$636$	−7.65450	−	2.22641i	−0.303520	−	0.0882827i
$637$	−2.23466	+	2.23466i	−0.0885404	+	0.0885404i
$638$	−71.0291	−	10.1202i	−2.81207	−	0.400661i
$639$	3.04149			0.120319
$640$	4.08963	−	19.6409i	0.161657	−	0.776376i
$641$	38.1727			1.50773			0.753866	−	0.657028i	$-0.228187\pi$
$641$	38.1727			1.50773			0.753866	+	0.657028i	$0.228187\pi$
$642$	−24.1929	−	3.44698i	−0.954817	−	0.136041i
$643$	28.1560	−	28.1560i	1.11036	−	1.11036i	0.117263	−	0.993101i	$-0.462588\pi$
$643$	28.1560	−	28.1560i	1.11036	−	1.11036i	0.993101	−	0.117263i	$-0.0374121\pi$
$644$	10.8296	+	3.14992i	0.426746	+	0.124124i
$645$	−6.79701	−	6.79701i	−0.267632	−	0.267632i
$646$	−2.61658	+	1.96395i	−0.102948	+	0.0772707i
$647$		−	35.6292i		−	1.40073i	−0.713786	−	0.700364i	$-0.753021\pi$
$647$		−	35.6292i		−	1.40073i	0.713786	−	0.700364i	$-0.246979\pi$
$648$	2.57730	+	1.16513i	0.101246	+	0.0457708i
$649$		−	77.6971i		−	3.04988i
$650$	4.97824	+	6.63254i	0.195263	+	0.260149i
$651$	−6.62655	−	6.62655i	−0.259715	−	0.259715i
$652$	11.3910	−	6.25765i	0.446105	−	0.245068i
$653$	19.5363	−	19.5363i	0.764514	−	0.764514i	−0.212621	−	0.977135i	$-0.568200\pi$
$653$	19.5363	−	19.5363i	0.764514	−	0.764514i	0.977135	+	0.212621i	$0.0682000\pi$
$654$	1.15623	−	8.11509i	0.0452122	−	0.317325i
$655$	−17.4558			−0.682053
$656$	−0.189117	+	0.297594i	−0.00738379	+	0.0116191i
$657$	−4.95758			−0.193414
$658$	−0.634377	+	4.45243i	−0.0247306	+	0.173574i
$659$	7.55948	−	7.55948i	0.294475	−	0.294475i	−0.544370	−	0.838845i	$-0.683231\pi$
$659$	7.55948	−	7.55948i	0.294475	−	0.294475i	0.838845	+	0.544370i	$0.183231\pi$
$660$	10.8785	+	19.8025i	0.423446	+	0.770810i
$661$	12.5551	+	12.5551i	0.488336	+	0.488336i	0.907781	−	0.419445i	$-0.137775\pi$
$661$	12.5551	+	12.5551i	0.488336	+	0.488336i	−0.419445	+	0.907781i	$0.637775\pi$
$662$	0.0506341	+	0.0674600i	0.00196795	+	0.00262191i
$663$			18.0574i			0.701291i
$664$	28.5878	−	10.7873i	1.10942	−	0.418628i
$665$			0.717950i			0.0278409i
$666$	−1.77032	+	1.32877i	−0.0685986	+	0.0514887i
$667$	31.7542	+	31.7542i	1.22953	+	1.22953i
$668$	12.6126	−	43.3628i	0.487996	−	1.67776i
$669$	−1.56622	+	1.56622i	−0.0605537	+	0.0605537i
$670$	32.3004	+	4.60212i	1.24787	+	0.177796i
$671$	−44.0118			−1.69906
$672$	0.439469	+	5.63976i	0.0169529	+	0.217558i
$673$	−28.3557			−1.09303			−0.546517	−	0.837448i	$-0.684046\pi$
$673$	−28.3557			−1.09303			−0.546517	+	0.837448i	$0.684046\pi$
$674$	13.9127	+	1.98226i	0.535895	+	0.0763538i
$675$	−1.31206	+	1.31206i	−0.0505013	+	0.0505013i
$676$	−1.68277	+	5.78546i	−0.0647220	+	0.222518i
$677$	−11.8533	−	11.8533i	−0.455561	−	0.455561i	0.441634	−	0.897195i	$-0.354399\pi$
$677$	−11.8533	−	11.8533i	−0.455561	−	0.455561i	−0.897195	+	0.441634i	$0.854399\pi$
$678$	18.0625	−	13.5573i	0.693686	−	0.520667i
$679$			4.52728i			0.173741i
$680$	10.1175	+	26.8127i	0.387987	+	1.02822i
$681$		−	15.4596i		−	0.592414i
$682$	−50.6839	−	67.5263i	−1.94079	−	2.58572i
$683$	30.5129	+	30.5129i	1.16754	+	1.16754i	0.982784	+	0.184758i	$0.0591502\pi$
$683$	30.5129	+	30.5129i	1.16754	+	1.16754i	0.184758	+	0.982784i	$0.440850\pi$
$684$	0.389881	+	0.709710i	0.0149075	+	0.0271365i
$685$	6.31493	−	6.31493i	0.241281	−	0.241281i
$686$	0.199481	−	1.40007i	0.00761622	−	0.0534551i
$687$	−6.74672			−0.257403
$688$	−4.71691	−	21.1637i	−0.179830	−	0.806860i
$689$	−12.5964			−0.479886
$690$	1.99477	−	14.0004i	0.0759395	−	0.532988i
$691$	−29.2562	+	29.2562i	−1.11296	+	1.11296i	−0.120211	+	0.992748i	$0.538357\pi$
$691$	−29.2562	+	29.2562i	−1.11296	+	1.11296i	−0.992748	+	0.120211i	$0.961643\pi$
$692$	24.2047	−	13.2969i	0.920125	−	0.505472i
$693$	−4.50476	−	4.50476i	−0.171122	−	0.171122i
$694$	16.5619	+	22.0655i	0.628682	+	0.837596i
$695$		−	34.3551i		−	1.30316i
$696$	−9.27845	+	20.5241i	−0.351699	+	0.777963i
$697$		−	0.503677i		−	0.0190781i
$698$	−7.85865	+	5.89854i	−0.297454	+	0.223263i
$699$	12.4024	+	12.4024i	0.469100	+	0.469100i
$700$	−3.56340	−	1.03646i	−0.134684	−	0.0391745i
$701$	5.03573	−	5.03573i	0.190197	−	0.190197i	−0.605584	−	0.795781i	$-0.707061\pi$
$701$	5.03573	−	5.03573i	0.190197	−	0.190197i	0.795781	+	0.605584i	$0.207061\pi$
$702$	4.42463	+	0.630417i	0.166997	+	0.0237935i
$703$	−0.633708			−0.0239008
$704$	−3.24736	+	50.8619i	−0.122390	+	1.91693i
$705$	5.63922			0.212385
$706$	24.3510	+	3.46950i	0.916461	+	0.130576i
$707$	−12.7835	+	12.7835i	−0.480774	+	0.480774i
$708$	−23.4214	−	6.81241i	−0.880231	−	0.256026i
$709$	−27.4748	−	27.4748i	−1.03184	−	1.03184i	−0.999476	−	0.0323629i	$-0.989697\pi$
$709$	−27.4748	−	27.4748i	−1.03184	−	1.03184i	−0.0323629	−	0.999476i	$-0.510303\pi$
$710$	6.10019	−	4.57868i	0.228936	−	0.171835i
$711$			1.57254i			0.0589748i
$712$	2.52171	−	5.57806i	0.0945050	−	0.209047i
$713$			52.8470i			1.97914i
$714$	−4.85076	−	6.46269i	−0.181535	−	0.241860i
$715$	25.2447	+	25.2447i	0.944099	+	0.944099i
$716$	4.20495	−	2.31000i	0.157146	−	0.0863287i
$717$	7.80232	−	7.80232i	0.291383	−	0.291383i
$718$	−0.737173	+	5.17391i	−0.0275110	+	0.193088i
$719$	−40.1704			−1.49810			−0.749052	−	0.662511i	$-0.769491\pi$
$719$	−40.1704			−1.49810			−0.749052	+	0.662511i	$0.769491\pi$
$720$	6.92319	−	1.54302i	0.258012	−	0.0575049i
$721$	3.35143			0.124814
$722$	3.75744	−	26.3719i	0.139837	−	0.981461i
$723$	11.7841	−	11.7841i	0.438255	−	0.438255i
$724$	6.67233	+	12.1458i	0.247975	+	0.451396i
$725$	−10.4485	−	10.4485i	−0.388047	−	0.388047i
$726$	−25.1167	−	33.4630i	−0.932167	−	1.24193i
$727$			48.6502i			1.80434i	0.431383	+	0.902169i	$0.358026\pi$
$727$			48.6502i			1.80434i	−0.431383	+	0.902169i	$0.641974\pi$
$728$	3.15570	+	8.36305i	0.116958	+	0.309955i
$729$			1.00000i			0.0370370i
$730$	−9.94322	+	7.46318i	−0.368015	+	0.276225i
$731$	21.9015	+	21.9015i	0.810055	+	0.810055i
$732$	−3.85891	+	13.2671i	−0.142630	+	0.490368i
$733$	−24.4218	+	24.4218i	−0.902041	+	0.902041i	−0.995613	−	0.0935714i	$-0.970172\pi$
$733$	−24.4218	+	24.4218i	−0.902041	+	0.902041i	0.0935714	+	0.995613i	$0.470172\pi$
$734$	−31.7798	−	4.52795i	−1.17301	−	0.167130i
$735$	−1.77326			−0.0654078
$736$	20.7362	−	24.2410i	0.764348	−	0.893536i
$737$	−82.8838			−3.05306
$738$	−0.123417	−	0.0175843i	−0.00454304	−	0.000647287i
$739$	−1.20752	+	1.20752i	−0.0444192	+	0.0444192i	−0.728967	−	0.684548i	$-0.759999\pi$
$739$	−1.20752	+	1.20752i	−0.0444192	+	0.0444192i	0.684548	+	0.728967i	$0.259999\pi$
$740$	−1.55033	+	5.33011i	−0.0569912	+	0.195939i
$741$	0.904757	+	0.904757i	0.0332371	+	0.0332371i
$742$	4.50823	−	3.38378i	0.165502	−	0.124223i
$743$			7.13676i			0.261822i	0.991394	+	0.130911i	$0.0417903\pi$
$743$			7.13676i			0.261822i	−0.991394	+	0.130911i	$0.958210\pi$
$744$	−24.7994	+	9.35777i	−0.909191	+	0.343073i
$745$		−	26.9537i		−	0.987508i
$746$	−10.5494	−	14.0550i	−0.386240	−	0.514589i
$747$	7.63884	+	7.63884i	0.279490	+	0.279490i
$748$	−35.0530	−	63.8080i	−1.28167	−	2.33305i
$749$	12.2186	−	12.2186i	0.446458	−	0.446458i
$750$	−2.42503	+	17.0202i	−0.0885494	+	0.621491i
$751$	−35.1201			−1.28155			−0.640775	−	0.767729i	$-0.721387\pi$
$751$	−35.1201			−1.28155			−0.640775	+	0.767729i	$0.721387\pi$
$752$	10.7361	+	6.82266i	0.391505	+	0.248797i
$753$	−3.19553			−0.116452
$754$	−5.02027	+	35.2352i	−0.182827	+	1.28319i
$755$	−17.9579	+	17.9579i	−0.653556	+	0.653556i
$756$	−1.75291	+	0.962965i	−0.0637528	+	0.0350227i
$757$	4.94770	+	4.94770i	0.179827	+	0.179827i	0.791281	−	0.611453i	$-0.209415\pi$
$757$	4.94770	+	4.94770i	0.179827	+	0.179827i	−0.611453	+	0.791281i	$0.709415\pi$
$758$	−7.86982	−	10.4850i	−0.285845	−	0.380832i
$759$			35.9256i			1.30402i
$760$	1.85037	+	0.836509i	0.0671200	+	0.0303434i
$761$		−	39.0600i		−	1.41592i	−0.706251	−	0.707962i	$-0.749615\pi$
$761$		−	39.0600i		−	1.41592i	0.706251	−	0.707962i	$-0.250385\pi$
$762$	0.453682	−	0.340525i	0.0164352	−	0.0123359i
$763$	4.09852	+	4.09852i	0.148377	+	0.148377i
$764$	−8.38740	−	2.43958i	−0.303446	−	0.0882609i
$765$	−7.16452	+	7.16452i	−0.259034	+	0.259034i
$766$	−32.6333	−	4.64956i	−1.17909	−	0.167996i
$767$	−38.5429			−1.39170
$768$	15.0474	+	5.43843i	0.542975	+	0.196243i
$769$	−42.3802			−1.52827			−0.764134	−	0.645057i	$-0.776833\pi$
$769$	−42.3802			−1.52827			−0.764134	+	0.645057i	$0.776833\pi$
$770$	−15.8165	−	2.25352i	−0.569987	−	0.0812112i
$771$	−6.46903	+	6.46903i	−0.232976	+	0.232976i
$772$	0.254146	+	0.0739214i	0.00914690	+	0.00266049i
$773$	9.70554	+	9.70554i	0.349084	+	0.349084i	0.859768	−	0.510684i	$-0.170608\pi$
$773$	9.70554	+	9.70554i	0.349084	+	0.349084i	−0.510684	+	0.859768i	$0.670608\pi$
$774$	6.13117	−	4.60193i	0.220380	−	0.165413i
$775$		−	17.3889i		−	0.624628i
$776$	11.6682	+	5.27489i	0.418862	+	0.189358i
$777$		−	1.56519i		−	0.0561510i
$778$	−11.3915	−	15.1770i	−0.408405	−	0.544120i
$779$	−0.0252365	−	0.0252365i	−0.000904193	−	0.000904193i
$780$	9.82334	−	5.39647i	0.351732	−	0.193225i
$781$	−13.7012	+	13.7012i	−0.490266	+	0.490266i
$782$	−6.42759	+	45.1125i	−0.229850	+	1.61322i
$783$	−7.96341			−0.284589
$784$	−3.37598	−	2.14540i	−0.120571	−	0.0766213i
$785$	10.6499			0.380112
$786$	1.96366	−	13.7821i	0.0700416	−	0.491593i
$787$	−5.33546	+	5.33546i	−0.190189	+	0.190189i	−0.795778	−	0.605589i	$-0.792938\pi$
$787$	−5.33546	+	5.33546i	−0.190189	+	0.190189i	0.605589	+	0.795778i	$0.292938\pi$
$788$	0.0779936	+	0.141974i	0.00277841	+	0.00505761i
$789$	17.2276	+	17.2276i	0.613318	+	0.613318i
$790$	2.36731	+	3.15398i	0.0842251	+	0.112213i
$791$			15.9696i			0.567813i
$792$	−16.8587	+	6.36145i	−0.599049	+	0.226044i
$793$			21.8328i			0.775304i
$794$	−6.77734	+	5.08693i	−0.240519	+	0.180529i
$795$	−4.99781	−	4.99781i	−0.177254	−	0.177254i
$796$	−0.958072	+	3.29390i	−0.0339579	+	0.116749i
$797$	23.0066	−	23.0066i	0.814937	−	0.814937i	−0.170432	−	0.985369i	$-0.554516\pi$
$797$	23.0066	−	23.0066i	0.814937	−	0.814937i	0.985369	+	0.170432i	$0.0545165\pi$
$798$	−0.566855	−	0.0807649i	−0.0200665	−	0.00285905i
$799$	−18.1708			−0.642838
$800$	−6.82310	+	7.97632i	−0.241233	+	0.282006i
$801$	2.16431			0.0764720
$802$	−12.3709	−	1.76260i	−0.436832	−	0.0622394i
$803$	22.3327	−	22.3327i	0.788103	−	0.788103i
$804$	−7.26718	+	24.9849i	−0.256294	+	0.881151i
$805$	7.07092	+	7.07092i	0.249217	+	0.249217i
$806$	−33.4975	+	25.1426i	−1.17990	+	0.885609i
$807$			9.27950i			0.326654i
$808$	18.0524	+	47.8415i	0.635082	+	1.68306i
$809$		−	39.0732i		−	1.37374i	−0.726780	−	0.686871i	$-0.758984\pi$
$809$		−	39.0732i		−	1.37374i	0.726780	−	0.686871i	$-0.241016\pi$
$810$	1.50541	+	2.00566i	0.0528946	+	0.0704717i
$811$	−11.1634	−	11.1634i	−0.392000	−	0.392000i	0.483399	−	0.875400i	$-0.339402\pi$
$811$	−11.1634	−	11.1634i	−0.392000	−	0.392000i	−0.875400	+	0.483399i	$0.839402\pi$
$812$	−7.66849	−	13.9592i	−0.269111	−	0.489870i
$813$	−16.4029	+	16.4029i	−0.575275	+	0.575275i
$814$	1.98910	−	13.9606i	0.0697178	−	0.489320i
$815$	11.5232			0.403641
$816$	−22.3081	+	4.97195i	−0.780938	+	0.174053i
$817$	2.19473			0.0767838
$818$	−3.09654	+	21.7333i	−0.108268	+	0.759887i
$819$	−2.23466	+	2.23466i	−0.0780853	+	0.0780853i
$820$	−0.274004	+	0.150525i	−0.00956863	+	0.00525655i
$821$	29.5463	+	29.5463i	1.03117	+	1.03117i	0.999498	+	0.0316759i	$0.0100844\pi$
$821$	29.5463	+	29.5463i	1.03117	+	1.03117i	0.0316759	+	0.999498i	$0.489916\pi$
$822$	4.27554	+	5.69632i	0.149127	+	0.198682i
$823$		−	7.74340i		−	0.269918i	−0.990851	−	0.134959i	$-0.956910\pi$
$823$		−	7.74340i		−	0.269918i	0.990851	−	0.134959i	$-0.0430903\pi$
$824$	3.90487	−	8.63763i	0.136032	−	0.300906i
$825$		−	11.8210i		−	0.411556i
$826$	13.7944	−	10.3538i	0.479968	−	0.360254i
$827$	−29.6004	−	29.6004i	−1.02931	−	1.02931i	−0.999557	−	0.0297490i	$-0.990529\pi$
$827$	−29.6004	−	29.6004i	−1.02931	−	1.02931i	−0.0297490	−	0.999557i	$-0.509471\pi$
$828$	10.8296	+	3.14992i	0.376355	+	0.109467i
$829$	37.7932	−	37.7932i	1.31261	−	1.31261i	0.393129	−	0.919483i	$-0.371393\pi$
$829$	37.7932	−	37.7932i	1.31261	−	1.31261i	0.919483	−	0.393129i	$-0.128607\pi$
$830$	26.8205	+	3.82135i	0.930952	+	0.132641i
$831$	20.1147			0.697771
$832$	25.2309	+	1.61091i	0.874724	+	0.0558481i
$833$	5.71385			0.197973
$834$	27.1250	+	3.86473i	0.939260	+	0.133825i
$835$	28.3126	−	28.3126i	0.979799	−	0.979799i
$836$	−4.95339	−	1.44075i	−0.171317	−	0.0498295i
$837$	−6.62655	−	6.62655i	−0.229047	−	0.229047i
$838$	−3.74336	+	2.80969i	−0.129312	+	0.0970591i
$839$			13.6704i			0.471954i	0.971759	+	0.235977i	$0.0758290\pi$
$839$			13.6704i			0.471954i	−0.971759	+	0.235977i	$0.924171\pi$
$840$	−2.06609	+	4.57023i	−0.0712869	+	0.157688i
$841$		−	34.4160i		−	1.18676i
$842$	32.9168	+	43.8552i	1.13439	+	1.51135i
$843$	0.466642	+	0.466642i	0.0160720	+	0.0160720i
$844$	34.5452	−	18.9775i	1.18910	−	0.653232i
$845$	−3.77747	+	3.77747i	−0.129949	+	0.129949i
$846$	−0.634377	+	4.45243i	−0.0218103	+	0.153078i
$847$	29.5857			1.01658
$848$	−3.46832	−	15.5616i	−0.119103	−	0.534388i
$849$	5.22166			0.179207
$850$	2.11495	−	14.8439i	0.0725421	−	0.509143i
$851$	−6.24123	+	6.24123i	−0.213947	+	0.213947i
$852$	2.92884	+	5.33145i	0.100341	+	0.182653i
$853$	−32.7033	−	32.7033i	−1.11974	−	1.11974i	−0.991779	−	0.127959i	$-0.959157\pi$
$853$	−32.7033	−	32.7033i	−1.11974	−	1.11974i	−0.127959	−	0.991779i	$-0.540843\pi$
$854$	−5.86494	−	7.81388i	−0.200694	−	0.267385i
$855$			0.717950i			0.0245534i
$856$	−17.2547	−	45.7273i	−0.589752	−	1.56293i
$857$			26.3226i			0.899164i	0.893239	+	0.449582i	$0.148427\pi$
$857$			26.3226i			0.899164i	−0.893239	+	0.449582i	$0.851573\pi$
$858$	−22.7718	+	17.0920i	−0.777415	+	0.583512i
$859$	−22.0749	−	22.0749i	−0.753187	−	0.753187i	0.221885	−	0.975073i	$-0.428779\pi$
$859$	−22.0749	−	22.0749i	−0.753187	−	0.753187i	−0.975073	+	0.221885i	$0.928779\pi$
$860$	5.36927	−	18.4598i	0.183091	−	0.629475i
$861$	0.0623316	−	0.0623316i	0.00212426	−	0.00212426i
$862$	39.4887	+	5.62631i	1.34499	+	0.191633i
$863$	46.8237			1.59390			0.796949	−	0.604047i	$-0.206446\pi$
$863$	46.8237			1.59390			0.796949	+	0.604047i	$0.206446\pi$
$864$	0.439469	+	5.63976i	0.0149511	+	0.191868i
$865$	24.4857			0.832540
$866$	−30.6695	−	4.36976i	−1.04219	−	0.148490i
$867$	11.0649	−	11.0649i	0.375783	−	0.375783i
$868$	5.23462	−	17.9969i	0.177675	−	0.610855i
$869$	−7.08390	−	7.08390i	−0.240305	−	0.240305i
$870$	−15.9719	+	11.9882i	−0.541498	+	0.406438i
$871$			41.1159i			1.39316i
$872$	15.3384	−	5.78778i	0.519425	−	0.195999i
$873$			4.52728i			0.153225i
$874$	1.93829	+	2.58240i	0.0655637	+	0.0873508i
$875$	−8.59607	−	8.59607i	−0.290600	−	0.290600i
$876$	−4.77398	−	8.69020i	−0.161298	−	0.293615i
$877$	−26.2035	+	26.2035i	−0.884829	+	0.884829i	−0.994021	−	0.109192i	$-0.965174\pi$
$877$	−26.2035	+	26.2035i	−0.884829	+	0.884829i	0.109192	+	0.994021i	$0.465174\pi$
$878$	3.02142	−	21.2061i	0.101968	−	0.715670i
$879$	−9.31482			−0.314181
$880$	−24.2363	+	38.1382i	−0.817007	+	1.28564i
$881$	59.1566			1.99304			0.996518	−	0.0833811i	$-0.0265719\pi$
$881$	59.1566			1.99304			0.996518	+	0.0833811i	$0.0265719\pi$
$882$	0.199481	−	1.40007i	0.00671688	−	0.0471429i
$883$	−39.0013	+	39.0013i	−1.31250	+	1.31250i	−0.392928	+	0.919569i	$0.628538\pi$
$883$	−39.0013	+	39.0013i	−1.31250	+	1.31250i	−0.919569	+	0.392928i	$0.871462\pi$
$884$	−31.6530	+	17.3886i	−1.06461	+	0.584843i
$885$	−15.2924	−	15.2924i	−0.514050	−	0.514050i
$886$	1.78142	+	2.37339i	0.0598478	+	0.0797355i
$887$			27.3020i			0.916711i	0.888769	+	0.458356i	$0.151561\pi$
$887$			27.3020i			0.916711i	−0.888769	+	0.458356i	$0.848439\pi$
$888$	−4.03397	−	1.82366i	−0.135371	−	0.0611981i
$889$			0.401114i			0.0134529i
$890$	4.34086	−	3.25816i	0.145506	−	0.109214i
$891$	−4.50476	−	4.50476i	−0.150915	−	0.150915i
$892$	−4.25367	−	1.23723i	−0.142423	−	0.0414256i
$893$	−0.910442	+	0.910442i	−0.0304668	+	0.0304668i
$894$	21.2812	+	3.03212i	0.711750	+	0.101409i
$895$	4.25377			0.142188
$896$	−9.46280	+	6.20124i	−0.316130	+	0.207169i
$897$	17.8215			0.595041
$898$	−1.77288	−	0.252598i	−0.0591618	−	0.00842931i
$899$	52.7700	−	52.7700i	1.75998	−	1.75998i
$900$	−3.56340	−	1.03646i	−0.118780	−	0.0345486i
$901$	16.1041	+	16.1041i	0.536504	+	0.536504i
$902$	0.635176	−	0.476750i	0.0211490	−	0.0158740i
$903$			5.42075i			0.180391i
$904$	41.1584	+	18.6067i	1.36891	+	0.618851i
$905$			12.2868i			0.408428i
$906$	−12.1585	−	16.1988i	−0.403938	−	0.538168i
$907$	23.3127	+	23.3127i	0.774086	+	0.774086i	0.978818	−	0.204732i	$-0.0656323\pi$
$907$	23.3127	+	23.3127i	0.774086	+	0.774086i	−0.204732	+	0.978818i	$0.565632\pi$
$908$	27.0993	−	14.8871i	0.899323	−	0.494045i
$909$	−12.7835	+	12.7835i	−0.424003	+	0.424003i
$910$	−1.11789	+	7.84604i	−0.0370579	+	0.260094i
$911$	−3.94366			−0.130659			−0.0653297	−	0.997864i	$-0.520810\pi$
$911$	−3.94366			−0.130659			−0.0653297	+	0.997864i	$0.520810\pi$
$912$	−0.868618	+	1.36685i	−0.0287628	+	0.0452610i
$913$	−68.8222			−2.27768
$914$	−6.78012	+	47.5869i	−0.224267	+	1.57403i
$915$	−8.66245	+	8.66245i	−0.286372	+	0.286372i
$916$	−6.49686	−	11.8264i	−0.214662	−	0.390755i
$917$	6.96066	+	6.96066i	0.229861	+	0.229861i
$918$	−4.85076	−	6.46269i	−0.160099	−	0.213300i
$919$			13.9321i			0.459577i	0.973241	+	0.229789i	$0.0738035\pi$
$919$			13.9321i			0.459577i	−0.973241	+	0.229789i	$0.926196\pi$
$920$	26.4624	−	9.98529i	0.872440	−	0.329205i
$921$		−	12.2625i		−	0.404064i
$922$	−11.7059	+	8.78623i	−0.385514	+	0.289359i
$923$	6.79668	+	6.79668i	0.223715	+	0.223715i
$924$	3.55852	−	12.2344i	0.117067	−	0.402481i
$925$	2.05363	−	2.05363i	0.0675230	−	0.0675230i
$926$	−7.59636	−	1.08232i	−0.249632	−	0.0355673i
$927$	3.35143			0.110075
$928$	−44.9117	+	3.49968i	−1.47430	+	0.114883i
$929$	43.4737			1.42632			0.713162	−	0.700999i	$-0.247262\pi$
$929$	43.4737			1.42632			0.713162	+	0.700999i	$0.247262\pi$
$930$	−23.2663	−	3.31496i	−0.762932	−	0.108702i
$931$	0.286290	−	0.286290i	0.00938278	−	0.00938278i
$932$	−9.79719	+	33.6833i	−0.320918	+	1.10333i
$933$	−6.04432	−	6.04432i	−0.197882	−	0.197882i
$934$	26.7592	−	20.0849i	0.875588	−	0.657198i
$935$		−	64.5488i		−	2.11097i
$936$	3.15570	+	8.36305i	0.103147	+	0.273355i
$937$			44.1011i			1.44072i	0.693600	+	0.720360i	$0.256023\pi$
$937$			44.1011i			1.44072i	−0.693600	+	0.720360i	$0.743977\pi$
$938$	−11.0450	−	14.7152i	−0.360631	−	0.480470i
$939$	−4.22056	−	4.22056i	−0.137733	−	0.137733i
$940$	5.43038	+	9.88506i	0.177119	+	0.322415i
$941$	−2.96444	+	2.96444i	−0.0966380	+	0.0966380i	−0.753773	−	0.657135i	$-0.771768\pi$
$941$	−2.96444	+	2.96444i	−0.0966380	+	0.0966380i	0.657135	+	0.753773i	$0.271768\pi$
$942$	−1.19805	+	8.40861i	−0.0390346	+	0.273967i
$943$	−0.497097			−0.0161877
$944$	−10.6125	−	47.6158i	−0.345406	−	1.54976i
$945$	−1.77326			−0.0576843
$946$	−6.88886	+	48.3500i	−0.223976	+	1.57199i
$947$	38.7078	−	38.7078i	1.25783	−	1.25783i	0.305708	−	0.952125i	$-0.401107\pi$
$947$	38.7078	−	38.7078i	1.25783	−	1.25783i	0.952125	−	0.305708i	$-0.0988931\pi$
$948$	−2.75652	+	1.51430i	−0.0895276	+	0.0491821i
$949$	−11.0785	−	11.0785i	−0.359623	−	0.359623i
$950$	−0.637781	−	0.849718i	−0.0206923	−	0.0275685i
$951$		−	12.0040i		−	0.389257i
$952$	6.65740	−	14.7263i	0.215768	−	0.477282i
$953$			5.80693i			0.188105i	0.995567	+	0.0940525i	$0.0299821\pi$
$953$			5.80693i			0.188105i	−0.995567	+	0.0940525i	$0.970018\pi$
$954$	4.50823	−	3.38378i	0.145959	−	0.109554i
$955$	−5.47635	−	5.47635i	−0.177210	−	0.177210i
$956$	21.1901	+	6.16342i	0.685338	+	0.199339i
$957$	35.8732	−	35.8732i	1.15962	−	1.15962i
$958$	−31.9301	−	4.54937i	−1.03161	−	0.146983i
$959$	−5.03628			−0.162630
$960$	9.37156	+	10.6499i	0.302466	+	0.343723i
$961$	56.8224			1.83298
$962$	−6.92540	−	0.986724i	−0.223284	−	0.0318133i
$963$	12.2186	−	12.2186i	0.393739	−	0.393739i
$964$	32.0042	+	9.30881i	1.03078	+	0.299816i
$965$	0.165938	+	0.165938i	0.00534173	+	0.00534173i
$966$	−6.37825	+	4.78738i	−0.205217	+	0.154032i
$967$		−	4.60493i		−	0.148084i	−0.997255	−	0.0740422i	$-0.976410\pi$
$967$		−	4.60493i		−	0.148084i	0.997255	−	0.0740422i	$-0.0235900\pi$
$968$	34.4713	−	76.2510i	1.10795	−	2.45080i
$969$		−	2.31340i		−	0.0743170i
$970$	6.81541	+	9.08020i	0.218830	+	0.291548i
$971$	−34.1315	−	34.1315i	−1.09533	−	1.09533i	−0.994949	−	0.100382i	$-0.967994\pi$
$971$	−34.1315	−	34.1315i	−1.09533	−	1.09533i	−0.100382	−	0.994949i	$-0.532006\pi$
$972$	−1.75291	+	0.962965i	−0.0562247	+	0.0308871i
$973$	−13.6994	+	13.6994i	−0.439184	+	0.439184i
$974$	4.62581	−	32.4666i	0.148220	−	1.04030i
$975$	−5.86402			−0.187799
$976$	−26.9721	+	6.01146i	−0.863357	+	0.192422i
$977$	35.6172			1.13949			0.569747	−	0.821820i	$-0.307041\pi$
$977$	35.6172			1.13949			0.569747	+	0.821820i	$0.307041\pi$
$978$	−1.29629	+	9.09812i	−0.0414508	+	0.290926i
$979$	−9.74967	+	9.74967i	−0.311601	+	0.311601i
$980$	−1.70759	−	3.10837i	−0.0545470	−	0.0992934i
$981$	4.09852	+	4.09852i	0.130856	+	0.130856i
$982$	−25.4010	−	33.8419i	−0.810579	−	1.07994i
$983$			9.18421i			0.292931i	0.989216	+	0.146465i	$0.0467897\pi$
$983$			9.18421i			0.292931i	−0.989216	+	0.146465i	$0.953210\pi$
$984$	−0.0880224	−	0.233272i	−0.00280605	−	0.00743644i
$985$			0.143622i			0.00457619i
$986$	51.4650	−	38.6286i	1.63898	−	1.23019i
$987$	−2.24870	−	2.24870i	−0.0715768	−	0.0715768i
$988$	−0.714710	+	2.45721i	−0.0227379	+	0.0781742i
$989$	21.6153	−	21.6153i	0.687328	−	0.687328i
$990$	−15.8165	−	2.25352i	−0.502682	−	0.0716215i
$991$	49.0701			1.55876			0.779382	−	0.626549i	$-0.215533\pi$
$991$	49.0701			1.55876			0.779382	+	0.626549i	$0.215533\pi$
$992$	−40.2843	−	34.4600i	−1.27903	−	1.09411i
$993$	−0.0596433			−0.00189272
$994$	−4.25830	−	0.606719i	−0.135065	−	0.0192439i
$995$	−2.15067	+	2.15067i	−0.0681808	+	0.0681808i
$996$	−6.03427	+	20.7461i	−0.191203	+	0.657367i
$997$	33.8969	+	33.8969i	1.07353	+	1.07353i	0.997073	+	0.0764518i	$0.0243591\pi$
$997$	33.8969	+	33.8969i	1.07353	+	1.07353i	0.0764518	+	0.997073i	$0.475641\pi$
$998$	21.4414	−	16.0935i	0.678717	−	0.509431i
$999$		−	1.56519i		−	0.0495205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.85.2	✓	28
4.3	odd	2		1344.2.w.b.1009.5		28
8.3	odd	2		2688.2.w.c.2017.10		28
8.5	even	2		2688.2.w.d.2017.5		28
16.3	odd	4		1344.2.w.b.337.5		28
16.5	even	4		2688.2.w.d.673.5		28
16.11	odd	4		2688.2.w.c.673.10		28
16.13	even	4	inner	336.2.w.b.253.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.2	✓	28	1.1	even	1	trivial
336.2.w.b.253.2	yes	28	16.13	even	4	inner
1344.2.w.b.337.5		28	16.3	odd	4
1344.2.w.b.1009.5		28	4.3	odd	2
2688.2.w.c.673.10		28	16.11	odd	4
2688.2.w.c.2017.10		28	8.3	odd	2
2688.2.w.d.673.5		28	16.5	even	4
2688.2.w.d.2017.5		28	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40007 - 0.199481i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.92041 + 0.558576i) q^{4} +(1.25389 + 1.25389i) q^{5} +(-1.13106 + 0.848947i) q^{6} -1.00000i q^{7} +(-2.57730 - 1.16513i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.40007 - 0.199481i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.92041 + 0.558576i) q^{4} +(1.25389 + 1.25389i) q^{5} +(-1.13106 + 0.848947i) q^{6} -1.00000i q^{7} +(-2.57730 - 1.16513i) q^{8} -1.00000i q^{9} +(-1.50541 - 2.00566i) q^{10} +(4.50476 + 4.50476i) q^{11} +(1.75291 - 0.962965i) q^{12} +(2.23466 - 2.23466i) q^{13} +(-0.199481 + 1.40007i) q^{14} +1.77326 q^{15} +(3.37598 + 2.14540i) q^{16} -5.71385 q^{17} +(-0.199481 + 1.40007i) q^{18} +(-0.286290 + 0.286290i) q^{19} +(1.70759 + 3.10837i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(-5.40838 - 7.20561i) q^{22} +5.63920i q^{23} +(-2.64630 + 0.998550i) q^{24} -1.85554i q^{25} +(-3.57446 + 2.68291i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.558576 - 1.92041i) q^{28} +(5.63098 - 5.63098i) q^{29} +(-2.48270 - 0.353732i) q^{30} +9.37136 q^{31} +(-4.29866 - 3.67716i) q^{32} +6.37069 q^{33} +(7.99981 + 1.13980i) q^{34} +(1.25389 - 1.25389i) q^{35} +(0.558576 - 1.92041i) q^{36} +(1.10676 + 1.10676i) q^{37} +(0.457937 - 0.343718i) q^{38} -3.16028i q^{39} +(-1.77069 - 4.69259i) q^{40} +0.0881503i q^{41} +(0.848947 + 1.13106i) q^{42} +(-3.83305 - 3.83305i) q^{43} +(6.13475 + 11.1672i) q^{44} +(1.25389 - 1.25389i) q^{45} +(1.12491 - 7.89530i) q^{46} +3.18014 q^{47} +(3.90421 - 0.870157i) q^{48} -1.00000 q^{49} +(-0.370144 + 2.59789i) q^{50} +(-4.04030 + 4.04030i) q^{51} +(5.53970 - 3.04324i) q^{52} +(-2.81843 - 2.81843i) q^{53} +(0.848947 + 1.13106i) q^{54} +11.2969i q^{55} +(-1.16513 + 2.57730i) q^{56} +0.404875i q^{57} +(-9.00707 + 6.76052i) q^{58} +(-8.62389 - 8.62389i) q^{59} +(3.40540 + 0.990503i) q^{60} +(-4.88503 + 4.88503i) q^{61} +(-13.1206 - 1.86941i) q^{62} -1.00000 q^{63} +(5.28492 + 6.00580i) q^{64} +5.60402 q^{65} +(-8.91943 - 1.27083i) q^{66} +(-9.19959 + 9.19959i) q^{67} +(-10.9730 - 3.19162i) q^{68} +(3.98752 + 3.98752i) q^{69} +(-2.00566 + 1.50541i) q^{70} +3.04149i q^{71} +(-1.16513 + 2.57730i) q^{72} -4.95758i q^{73} +(-1.32877 - 1.77032i) q^{74} +(-1.31206 - 1.31206i) q^{75} +(-0.709710 + 0.389881i) q^{76} +(4.50476 - 4.50476i) q^{77} +(-0.630417 + 4.42463i) q^{78} -1.57254 q^{79} +(1.54302 + 6.92319i) q^{80} -1.00000 q^{81} +(0.0175843 - 0.123417i) q^{82} +(-7.63884 + 7.63884i) q^{83} +(-0.962965 - 1.75291i) q^{84} +(-7.16452 - 7.16452i) q^{85} +(4.60193 + 6.13117i) q^{86} -7.96341i q^{87} +(-6.36145 - 16.8587i) q^{88} +2.16431i q^{89} +(-2.00566 + 1.50541i) q^{90} +(-2.23466 - 2.23466i) q^{91} +(-3.14992 + 10.8296i) q^{92} +(6.62655 - 6.62655i) q^{93} +(-4.45243 - 0.634377i) q^{94} -0.717950 q^{95} +(-5.63976 + 0.439469i) q^{96} -4.52728 q^{97} +(1.40007 + 0.199481i) q^{98} +(4.50476 - 4.50476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) \) 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

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