LMFDB - Embedded newform 336.2.w.a.253.7

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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 16 x^{17} + 35 x^{16} - 56 x^{15} + 64 x^{14} - 84 x^{13} + 125 x^{12} + \cdots + 1024 $ x^20 - 4x^19 + 8x^18 - 16x^17 + 35x^16 - 56x^15 + 64x^14 - 84x^13 + 125x^12 - 120x^11 + 100x^10 - 240x^9 + 500x^8 - 672x^7 + 1024x^6 - 1792x^5 + 2240x^4 - 2048x^3 + 2048x^2 - 2048*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.7
Root			$-0.545677 + 1.30470i$ of defining polynomial
Character	$\chi$	$=$	336.253
Dual form			336.2.w.a.85.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.783676 - 1.17722i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.771704 - 1.84512i) q^{4} +(0.134119 - 0.134119i) q^{5} +(-1.38656 + 0.278279i) q^{6} -1.00000i q^{7} +(-2.77688 - 0.537511i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.783676 - 1.17722i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.771704 - 1.84512i) q^{4} +(0.134119 - 0.134119i) q^{5} +(-1.38656 + 0.278279i) q^{6} -1.00000i q^{7} +(-2.77688 - 0.537511i) q^{8} +1.00000i q^{9} +(-0.0527819 - 0.262993i) q^{10} +(2.78707 - 2.78707i) q^{11} +(-0.759021 + 1.85037i) q^{12} +(-3.77686 - 3.77686i) q^{13} +(-1.17722 - 0.783676i) q^{14} -0.189672 q^{15} +(-2.80895 + 2.84777i) q^{16} -6.01433 q^{17} +(1.17722 + 0.783676i) q^{18} +(3.25357 + 3.25357i) q^{19} +(-0.350965 - 0.143965i) q^{20} +(-0.707107 + 0.707107i) q^{21} +(-1.09684 - 5.46517i) q^{22} -3.03186i q^{23} +(1.58348 + 2.34363i) q^{24} +4.96402i q^{25} +(-7.40605 + 1.48637i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.84512 + 0.771704i) q^{28} +(2.55533 + 2.55533i) q^{29} +(-0.148642 + 0.223287i) q^{30} +8.87021 q^{31} +(1.15116 + 5.53849i) q^{32} -3.94152 q^{33} +(-4.71329 + 7.08020i) q^{34} +(-0.134119 - 0.134119i) q^{35} +(1.84512 - 0.771704i) q^{36} +(6.76289 - 6.76289i) q^{37} +(6.37992 - 1.28043i) q^{38} +5.34129i q^{39} +(-0.444522 + 0.300342i) q^{40} -7.47741i q^{41} +(0.278279 + 1.38656i) q^{42} +(6.64643 - 6.64643i) q^{43} +(-7.29328 - 2.99169i) q^{44} +(0.134119 + 0.134119i) q^{45} +(-3.56917 - 2.37599i) q^{46} -6.53561 q^{47} +(3.99991 - 0.0274543i) q^{48} -1.00000 q^{49} +(5.84376 + 3.89019i) q^{50} +(4.25278 + 4.25278i) q^{51} +(-4.05415 + 9.88339i) q^{52} +(0.936484 - 0.936484i) q^{53} +(-0.278279 - 1.38656i) q^{54} -0.747597i q^{55} +(-0.537511 + 2.77688i) q^{56} -4.60125i q^{57} +(5.01074 - 1.00564i) q^{58} +(-0.924030 + 0.924030i) q^{59} +(0.146371 + 0.349969i) q^{60} +(4.61909 + 4.61909i) q^{61} +(6.95137 - 10.4422i) q^{62} +1.00000 q^{63} +(7.42216 + 2.98521i) q^{64} -1.01310 q^{65} +(-3.08887 + 4.64004i) q^{66} +(7.37751 + 7.37751i) q^{67} +(4.64128 + 11.0972i) q^{68} +(-2.14385 + 2.14385i) q^{69} +(-0.262993 + 0.0527819i) q^{70} -10.6232i q^{71} +(0.537511 - 2.77688i) q^{72} +10.9907i q^{73} +(-2.66151 - 13.2613i) q^{74} +(3.51010 - 3.51010i) q^{75} +(3.49244 - 8.51403i) q^{76} +(-2.78707 - 2.78707i) q^{77} +(6.28789 + 4.18584i) q^{78} +4.66256 q^{79} +(0.00520732 + 0.758672i) q^{80} -1.00000 q^{81} +(-8.80257 - 5.85987i) q^{82} +(-0.636613 - 0.636613i) q^{83} +(1.85037 + 0.759021i) q^{84} +(-0.806634 + 0.806634i) q^{85} +(-2.61567 - 13.0330i) q^{86} -3.61378i q^{87} +(-9.23746 + 6.24129i) q^{88} +13.9870i q^{89} +(0.262993 - 0.0527819i) q^{90} +(-3.77686 + 3.77686i) q^{91} +(-5.59415 + 2.33970i) q^{92} +(-6.27218 - 6.27218i) q^{93} +(-5.12180 + 7.69386i) q^{94} +0.872729 q^{95} +(3.10231 - 4.73029i) q^{96} -9.78344 q^{97} +(-0.783676 + 1.17722i) q^{98} +(2.78707 + 2.78707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4}+O(q^{10}) $ 20 * q + 4 * q^4	$ 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	0.783676	−	1.17722i	0.554143	−	0.832422i
$2$	0.783676	−	1.17722i	0.554143	−	0.832422i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−0.771704	−	1.84512i	−0.385852	−	0.922561i
$5$	0.134119	−	0.134119i	0.0599797	−	0.0599797i	−0.676481	−	0.736460i	$-0.736496\pi$
$5$	0.134119	−	0.134119i	0.0599797	−	0.0599797i	0.736460	+	0.676481i	$0.236496\pi$
$6$	−1.38656	+	0.278279i	−0.566063	+	0.113607i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.77688	−	0.537511i	−0.981777	−	0.190039i
$9$			1.00000i			0.333333i
$10$	−0.0527819	−	0.262993i	−0.0166911	−	0.0831657i
$11$	2.78707	−	2.78707i	0.840334	−	0.840334i	−0.148568	−	0.988902i	$-0.547466\pi$
$11$	2.78707	−	2.78707i	0.840334	−	0.840334i	0.988902	+	0.148568i	$0.0474664\pi$
$12$	−0.759021	+	1.85037i	−0.219111	+	0.534157i
$13$	−3.77686	−	3.77686i	−1.04751	−	1.04751i	−0.998813	−	0.0487003i	$-0.984492\pi$
$13$	−3.77686	−	3.77686i	−1.04751	−	1.04751i	−0.0487003	−	0.998813i	$-0.515508\pi$
$14$	−1.17722	−	0.783676i	−0.314626	−	0.209446i
$15$	−0.189672			−0.0489732
$16$	−2.80895	+	2.84777i	−0.702237	+	0.711943i
$17$	−6.01433			−1.45869			−0.729345	−	0.684146i	$-0.760175\pi$
$17$	−6.01433			−1.45869			−0.729345	+	0.684146i	$0.760175\pi$
$18$	1.17722	+	0.783676i	0.277474	+	0.184714i
$19$	3.25357	+	3.25357i	0.746421	+	0.746421i	0.973805	−	0.227385i	$-0.0730174\pi$
$19$	3.25357	+	3.25357i	0.746421	+	0.746421i	−0.227385	+	0.973805i	$0.573017\pi$
$20$	−0.350965	−	0.143965i	−0.0784782	−	0.0321916i
$21$	−0.707107	+	0.707107i	−0.154303	+	0.154303i
$22$	−1.09684	−	5.46517i	−0.233847	−	1.16518i
$23$		−	3.03186i		−	0.632186i	−0.948728	−	0.316093i	$-0.897629\pi$
$23$		−	3.03186i		−	0.632186i	0.948728	−	0.316093i	$-0.102371\pi$
$24$	1.58348	+	2.34363i	0.323226	+	0.478392i
$25$			4.96402i			0.992805i
$26$	−7.40605	+	1.48637i	−1.45245	+	0.291501i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−1.84512	+	0.771704i	−0.348695	+	0.145838i
$29$	2.55533	+	2.55533i	0.474513	+	0.474513i	0.903372	−	0.428859i	$-0.141084\pi$
$29$	2.55533	+	2.55533i	0.474513	+	0.474513i	−0.428859	+	0.903372i	$0.641084\pi$
$30$	−0.148642	+	0.223287i	−0.0271381	+	0.0407664i
$31$	8.87021			1.59314			0.796568	−	0.604549i	$-0.206646\pi$
$31$	8.87021			1.59314			0.796568	+	0.604549i	$0.206646\pi$
$32$	1.15116	+	5.53849i	0.203498	+	0.979075i
$33$	−3.94152			−0.686130
$34$	−4.71329	+	7.08020i	−0.808322	+	1.21425i
$35$	−0.134119	−	0.134119i	−0.0226702	−	0.0226702i
$36$	1.84512	−	0.771704i	0.307520	−	0.128617i
$37$	6.76289	−	6.76289i	1.11181	−	1.11181i	0.118907	−	0.992905i	$-0.462061\pi$
$37$	6.76289	−	6.76289i	1.11181	−	1.11181i	0.992905	−	0.118907i	$-0.0379390\pi$
$38$	6.37992	−	1.28043i	1.03496	−	0.207713i
$39$			5.34129i			0.855291i
$40$	−0.444522	+	0.300342i	−0.0702851	+	0.0474882i
$41$		−	7.47741i		−	1.16778i	−0.811835	−	0.583888i	$-0.801531\pi$
$41$		−	7.47741i		−	1.16778i	0.811835	−	0.583888i	$-0.198469\pi$
$42$	0.278279	+	1.38656i	0.0429394	+	0.213952i
$43$	6.64643	−	6.64643i	1.01357	−	1.01357i	0.0136640	−	0.999907i	$-0.495650\pi$
$43$	6.64643	−	6.64643i	1.01357	−	1.01357i	0.999907	−	0.0136640i	$-0.00434953\pi$
$44$	−7.29328	−	2.99169i	−1.09950	−	0.451015i
$45$	0.134119	+	0.134119i	0.0199932	+	0.0199932i
$46$	−3.56917	−	2.37599i	−0.526245	−	0.350321i
$47$	−6.53561			−0.953316			−0.476658	−	0.879089i	$-0.658152\pi$
$47$	−6.53561			−0.953316			−0.476658	+	0.879089i	$0.658152\pi$
$48$	3.99991	−	0.0274543i	0.577337	−	0.00396268i
$49$	−1.00000			−0.142857
$50$	5.84376	+	3.89019i	0.826432	+	0.550156i
$51$	4.25278	+	4.25278i	0.595508	+	0.595508i
$52$	−4.05415	+	9.88339i	−0.562210	+	1.37058i
$53$	0.936484	−	0.936484i	0.128636	−	0.128636i	−0.639858	−	0.768494i	$-0.721007\pi$
$53$	0.936484	−	0.936484i	0.128636	−	0.128636i	0.768494	+	0.639858i	$0.221007\pi$
$54$	−0.278279	−	1.38656i	−0.0378690	−	0.188688i
$55$		−	0.747597i		−	0.100806i
$56$	−0.537511	+	2.77688i	−0.0718280	+	0.371077i
$57$		−	4.60125i		−	0.609450i
$58$	5.01074	−	1.00564i	0.657943	−	0.132047i
$59$	−0.924030	+	0.924030i	−0.120298	+	0.120298i	−0.764693	−	0.644395i	$-0.777109\pi$
$59$	−0.924030	+	0.924030i	−0.120298	+	0.120298i	0.644395	+	0.764693i	$0.277109\pi$
$60$	0.146371	+	0.349969i	0.0188964	+	0.0451808i
$61$	4.61909	+	4.61909i	0.591414	+	0.591414i	0.938013	−	0.346600i	$-0.112664\pi$
$61$	4.61909	+	4.61909i	0.591414	+	0.591414i	−0.346600	+	0.938013i	$0.612664\pi$
$62$	6.95137	−	10.4422i	0.882825	−	1.32616i
$63$	1.00000			0.125988
$64$	7.42216	+	2.98521i	0.927770	+	0.373152i
$65$	−1.01310			−0.125659
$66$	−3.08887	+	4.64004i	−0.380214	+	0.571149i
$67$	7.37751	+	7.37751i	0.901306	+	0.901306i	0.995549	−	0.0942435i	$-0.0300432\pi$
$67$	7.37751	+	7.37751i	0.901306	+	0.901306i	−0.0942435	+	0.995549i	$0.530043\pi$
$68$	4.64128	+	11.0972i	0.562838	+	1.34573i
$69$	−2.14385	+	2.14385i	−0.258089	+	0.258089i
$70$	−0.262993	+	0.0527819i	−0.0314337	+	0.00630864i
$71$		−	10.6232i		−	1.26074i	−0.776295	−	0.630370i	$-0.782903\pi$
$71$		−	10.6232i		−	1.26074i	0.776295	−	0.630370i	$-0.217097\pi$
$72$	0.537511	−	2.77688i	0.0633463	−	0.327259i
$73$			10.9907i			1.28637i	0.765711	+	0.643185i	$0.222387\pi$
$73$			10.9907i			1.28637i	−0.765711	+	0.643185i	$0.777613\pi$
$74$	−2.66151	−	13.2613i	−0.309394	−	1.54160i
$75$	3.51010	−	3.51010i	0.405311	−	0.405311i
$76$	3.49244	−	8.51403i	0.400611	−	0.976626i
$77$	−2.78707	−	2.78707i	−0.317616	−	0.317616i
$78$	6.28789	+	4.18584i	0.711963	+	0.473953i
$79$	4.66256			0.524579			0.262290	−	0.964989i	$-0.415522\pi$
$79$	4.66256			0.524579			0.262290	+	0.964989i	$0.415522\pi$
$80$	0.00520732	+	0.758672i	0.000582196	+	0.0848221i
$81$	−1.00000			−0.111111
$82$	−8.80257	−	5.85987i	−0.972081	−	0.647114i
$83$	−0.636613	−	0.636613i	−0.0698773	−	0.0698773i	0.671304	−	0.741182i	$-0.265734\pi$
$83$	−0.636613	−	0.636613i	−0.0698773	−	0.0698773i	−0.741182	+	0.671304i	$0.765734\pi$
$84$	1.85037	+	0.759021i	0.201892	+	0.0828160i
$85$	−0.806634	+	0.806634i	−0.0874918	+	0.0874918i
$86$	−2.61567	−	13.0330i	−0.282055	−	1.40538i
$87$		−	3.61378i		−	0.387438i
$88$	−9.23746	+	6.24129i	−0.984717	+	0.665324i
$89$			13.9870i			1.48262i	0.671163	+	0.741310i	$0.265795\pi$
$89$			13.9870i			1.48262i	−0.671163	+	0.741310i	$0.734205\pi$
$90$	0.262993	−	0.0527819i	0.0277219	−	0.00556370i
$91$	−3.77686	+	3.77686i	−0.395923	+	0.395923i
$92$	−5.59415	+	2.33970i	−0.583230	+	0.243930i
$93$	−6.27218	−	6.27218i	−0.650395	−	0.650395i
$94$	−5.12180	+	7.69386i	−0.528273	+	0.793561i
$95$	0.872729			0.0895402
$96$	3.10231	−	4.73029i	0.316628	−	0.482783i
$97$	−9.78344			−0.993358			−0.496679	−	0.867934i	$-0.665447\pi$
$97$	−9.78344			−0.993358			−0.496679	+	0.867934i	$0.665447\pi$
$98$	−0.783676	+	1.17722i	−0.0791632	+	0.118917i
$99$	2.78707	+	2.78707i	0.280111	+	0.280111i
$100$	9.15923	−	3.83075i	0.915923	−	0.383075i
$101$	7.69946	−	7.69946i	0.766125	−	0.766125i	−0.211297	−	0.977422i	$-0.567769\pi$
$101$	7.69946	−	7.69946i	0.766125	−	0.766125i	0.977422	+	0.211297i	$0.0677687\pi$
$102$	8.33926	−	1.67366i	0.825710	−	0.165717i
$103$			8.50167i			0.837694i	0.908057	+	0.418847i	$0.137566\pi$
$103$			8.50167i			0.837694i	−0.908057	+	0.418847i	$0.862434\pi$
$104$	8.45781	+	12.5180i	0.829356	+	1.22749i
$105$			0.189672i			0.0185101i
$106$	−0.368549	−	1.83635i	−0.0357967	−	0.178362i
$107$	1.26436	−	1.26436i	0.122231	−	0.122231i	−0.643345	−	0.765576i	$-0.722454\pi$
$107$	1.26436	−	1.26436i	0.122231	−	0.122231i	0.765576	+	0.643345i	$0.222454\pi$
$108$	−1.85037	−	0.759021i	−0.178052	−	0.0730369i
$109$	−7.93923	−	7.93923i	−0.760441	−	0.760441i	0.215961	−	0.976402i	$-0.430712\pi$
$109$	−7.93923	−	7.93923i	−0.760441	−	0.760441i	−0.976402	+	0.215961i	$0.930712\pi$
$110$	−0.880088	−	0.585874i	−0.0839131	−	0.0558609i
$111$	−9.56417			−0.907791
$112$	2.84777	+	2.80895i	0.269089	+	0.265421i
$113$	−1.35750			−0.127703			−0.0638517	−	0.997959i	$-0.520338\pi$
$113$	−1.35750			−0.127703			−0.0638517	+	0.997959i	$0.520338\pi$
$114$	−5.41669	−	3.60589i	−0.507319	−	0.337722i
$115$	−0.406629	−	0.406629i	−0.0379183	−	0.0379183i
$116$	2.74294	−	6.68686i	0.254675	−	0.620859i
$117$	3.77686	−	3.77686i	0.349171	−	0.349171i
$118$	0.363648	+	1.81193i	0.0334765	+	0.166802i
$119$			6.01433i			0.551333i
$120$	0.526698	+	0.101951i	0.0480808	+	0.00930682i
$121$		−	4.53555i		−	0.412323i
$122$	9.05756	−	1.81782i	0.820033	−	0.164578i
$123$	−5.28733	+	5.28733i	−0.476742	+	0.476742i
$124$	−6.84517	−	16.3666i	−0.614715	−	1.46977i
$125$	1.33636	+	1.33636i	0.119528	+	0.119528i
$126$	0.783676	−	1.17722i	0.0698154	−	0.104875i
$127$	−5.01632			−0.445127			−0.222563	−	0.974918i	$-0.571442\pi$
$127$	−5.01632			−0.445127			−0.222563	+	0.974918i	$0.571442\pi$
$128$	9.33083	−	6.39809i	0.824737	−	0.565517i
$129$	−9.39947			−0.827577
$130$	−0.793939	+	1.19264i	−0.0696331	+	0.104601i
$131$	3.00106	+	3.00106i	0.262204	+	0.262204i	0.825949	−	0.563745i	$-0.190640\pi$
$131$	3.00106	+	3.00106i	0.262204	+	0.262204i	−0.563745	+	0.825949i	$0.690640\pi$
$132$	3.04168	+	7.27258i	0.264744	+	0.632997i
$133$	3.25357	−	3.25357i	0.282120	−	0.282120i
$134$	14.4665	−	2.90339i	1.24972	−	0.250814i
$135$		−	0.189672i		−	0.0163244i
$136$	16.7011	+	3.23277i	1.43211	+	0.277208i
$137$			21.3315i			1.82247i	0.411883	+	0.911237i	$0.364871\pi$
$137$			21.3315i			1.82247i	−0.411883	+	0.911237i	$0.635129\pi$
$138$	0.843702	+	4.20387i	0.0718207	+	0.357857i
$139$	−2.25618	+	2.25618i	−0.191367	+	0.191367i	−0.796287	−	0.604920i	$-0.793205\pi$
$139$	−2.25618	+	2.25618i	−0.191367	+	0.191367i	0.604920	+	0.796287i	$0.293205\pi$
$140$	−0.143965	+	0.350965i	−0.0121673	+	0.0296620i
$141$	4.62137	+	4.62137i	0.389190	+	0.389190i
$142$	−12.5058	−	8.32513i	−1.04947	−	0.698630i
$143$	−21.0528			−1.76052
$144$	−2.84777	−	2.80895i	−0.237314	−	0.234079i
$145$	0.685435			0.0569223
$146$	12.9386	+	8.61319i	1.07080	+	0.712832i
$147$	0.707107	+	0.707107i	0.0583212	+	0.0583212i
$148$	−17.6973	−	7.25941i	−1.45471	−	0.596720i
$149$	−6.91022	+	6.91022i	−0.566107	+	0.566107i	−0.931036	−	0.364928i	$-0.881093\pi$
$149$	−6.91022	+	6.91022i	−0.566107	+	0.566107i	0.364928	+	0.931036i	$0.381093\pi$
$150$	−1.38138	−	6.88294i	−0.112790	−	0.561990i
$151$			2.52324i			0.205338i	0.994716	+	0.102669i	$0.0327383\pi$
$151$			2.52324i			0.205338i	−0.994716	+	0.102669i	$0.967262\pi$
$152$	−7.28596	−	10.7836i	−0.590969	−	0.874667i
$153$		−	6.01433i		−	0.486230i
$154$	−5.46517	+	1.09684i	−0.440396	+	0.0883860i
$155$	1.18966	−	1.18966i	0.0955558	−	0.0955558i
$156$	9.85534	−	4.12189i	0.789058	−	0.330016i
$157$	−4.76403	−	4.76403i	−0.380211	−	0.380211i	0.490967	−	0.871178i	$-0.336644\pi$
$157$	−4.76403	−	4.76403i	−0.380211	−	0.380211i	−0.871178	+	0.490967i	$0.836644\pi$
$158$	3.65394	−	5.48887i	0.290692	−	0.436671i
$159$	−1.32439			−0.105031
$160$	0.897206	+	0.588423i	0.0709304	+	0.0465189i
$161$	−3.03186			−0.238944
$162$	−0.783676	+	1.17722i	−0.0615714	+	0.0924913i
$163$	14.9505	+	14.9505i	1.17101	+	1.17101i	0.981969	+	0.189043i	$0.0605385\pi$
$163$	14.9505	+	14.9505i	1.17101	+	1.17101i	0.189043	+	0.981969i	$0.439462\pi$
$164$	−13.7967	+	5.77034i	−1.07734	+	0.450588i
$165$	−0.528631	+	0.528631i	−0.0411539	+	0.0411539i
$166$	−1.24833	+	0.250536i	−0.0968894	+	0.0194454i
$167$		−	14.3385i		−	1.10955i	−0.832002	−	0.554773i	$-0.812805\pi$
$167$		−	14.3385i		−	1.10955i	0.832002	−	0.554773i	$-0.187195\pi$
$168$	2.34363	−	1.58348i	0.180815	−	0.122168i
$169$			15.5294i			1.19457i
$170$	0.317448	+	1.58173i	0.0243471	+	0.121313i
$171$	−3.25357	+	3.25357i	−0.248807	+	0.248807i
$172$	−17.3925	−	7.13440i	−1.32617	−	0.543993i
$173$	−6.14911	−	6.14911i	−0.467508	−	0.467508i	0.433598	−	0.901106i	$-0.357244\pi$
$173$	−6.14911	−	6.14911i	−0.467508	−	0.467508i	−0.901106	+	0.433598i	$0.857244\pi$
$174$	−4.25423	−	2.83204i	−0.322512	−	0.214696i
$175$	4.96402			0.375245
$176$	0.108211	+	15.7657i	0.00815674	+	1.18838i
$177$	1.30678			0.0982233
$178$	16.4658	+	10.9613i	1.23416	+	0.821583i
$179$	−0.669641	−	0.669641i	−0.0500513	−	0.0500513i	0.681638	−	0.731689i	$-0.261268\pi$
$179$	−0.669641	−	0.669641i	−0.0500513	−	0.0500513i	−0.731689	+	0.681638i	$0.761268\pi$
$180$	0.143965	−	0.350965i	0.0107305	−	0.0261594i
$181$	7.13665	−	7.13665i	0.530463	−	0.530463i	−0.390247	−	0.920710i	$-0.627611\pi$
$181$	7.13665	−	7.13665i	0.530463	−	0.530463i	0.920710	+	0.390247i	$0.127611\pi$
$182$	1.48637	+	7.40605i	0.110177	+	0.548973i
$183$		−	6.53238i		−	0.482887i
$184$	−1.62966	+	8.41912i	−0.120140	+	0.620665i
$185$		−	1.81406i		−	0.133372i
$186$	−12.2991	+	2.46839i	−0.901815	+	0.180991i
$187$	−16.7624	+	16.7624i	−1.22579	+	1.22579i
$188$	5.04355	+	12.0590i	0.367839	+	0.879492i
$189$	−0.707107	−	0.707107i	−0.0514344	−	0.0514344i
$190$	0.683937	−	1.02740i	0.0496180	−	0.0745352i
$191$	−18.2954			−1.32381			−0.661904	−	0.749589i	$-0.730251\pi$
$191$	−18.2954			−1.32381			−0.661904	+	0.749589i	$0.730251\pi$
$192$	−3.13740	−	7.35913i	−0.226422	−	0.531099i
$193$	4.60418			0.331416			0.165708	−	0.986175i	$-0.447009\pi$
$193$	4.60418			0.331416			0.165708	+	0.986175i	$0.447009\pi$
$194$	−7.66705	+	11.5173i	−0.550462	+	0.826893i
$195$	0.716367	+	0.716367i	0.0513001	+	0.0513001i
$196$	0.771704	+	1.84512i	0.0551217	+	0.131794i
$197$	−12.7368	+	12.7368i	−0.907461	+	0.907461i	−0.996067	−	0.0886055i	$-0.971759\pi$
$197$	−12.7368	+	12.7368i	−0.907461	+	0.907461i	0.0886055	+	0.996067i	$0.471759\pi$
$198$	5.46517	−	1.09684i	0.388392	−	0.0779491i
$199$		−	12.9031i		−	0.914676i	−0.889293	−	0.457338i	$-0.848803\pi$
$199$		−	12.9031i		−	0.914676i	0.889293	−	0.457338i	$-0.151197\pi$
$200$	2.66822	−	13.7845i	0.188672	−	0.974713i
$201$		−	10.4334i		−	0.735913i
$202$	−3.03009	−	15.0979i	−0.213197	−	1.06228i
$203$	2.55533	−	2.55533i	0.179349	−	0.179349i
$204$	4.56501	−	11.1288i	0.319614	−	0.779170i
$205$	−1.00286	−	1.00286i	−0.0700428	−	0.0700428i
$206$	10.0083	+	6.66255i	0.697315	+	0.464202i
$207$	3.03186			0.210729
$208$	21.3647	−	0.146641i	1.48137	−	0.0101677i
$209$	18.1359			1.25449
$210$	0.223287	+	0.148642i	0.0154082	+	0.0102573i
$211$	−17.4399	−	17.4399i	−1.20061	−	1.20061i	−0.973981	−	0.226628i	$-0.927230\pi$
$211$	−17.4399	−	17.4399i	−1.20061	−	1.20061i	−0.226628	−	0.973981i	$-0.572770\pi$
$212$	−2.45061	−	1.00524i	−0.168309	−	0.0690401i
$213$	−7.51172	+	7.51172i	−0.514695	+	0.514695i
$214$	−0.497586	−	2.47929i	−0.0340143	−	0.169481i
$215$		−	1.78282i		−	0.121587i
$216$	−2.34363	+	1.58348i	−0.159464	+	0.107742i
$217$		−	8.87021i		−	0.602149i
$218$	−15.5680	+	3.12445i	−1.05440	+	0.211615i
$219$	7.77163	−	7.77163i	0.525158	−	0.525158i
$220$	−1.37941	+	0.576923i	−0.0929996	+	0.0388962i
$221$	22.7153	+	22.7153i	1.52800	+	1.52800i
$222$	−7.49521	+	11.2592i	−0.503046	+	0.755665i
$223$	−5.42439			−0.363244			−0.181622	−	0.983368i	$-0.558135\pi$
$223$	−5.42439			−0.363244			−0.181622	+	0.983368i	$0.558135\pi$
$224$	5.53849	−	1.15116i	0.370056	−	0.0769149i
$225$	−4.96402			−0.330935
$226$	−1.06384	+	1.59808i	−0.0707659	+	0.106303i
$227$	−2.25166	−	2.25166i	−0.149448	−	0.149448i	0.628424	−	0.777871i	$-0.283700\pi$
$227$	−2.25166	−	2.25166i	−0.149448	−	0.149448i	−0.777871	+	0.628424i	$0.783700\pi$
$228$	−8.48986	+	3.55080i	−0.562255	+	0.235157i
$229$	5.67660	−	5.67660i	0.375121	−	0.375121i	−0.494218	−	0.869338i	$-0.664545\pi$
$229$	5.67660	−	5.67660i	0.375121	−	0.375121i	0.869338	+	0.494218i	$0.164545\pi$
$230$	−0.797358	+	0.160027i	−0.0525762	+	0.0105519i
$231$			3.94152i			0.259333i
$232$	−5.72234	−	8.46938i	−0.375690	−	0.556042i
$233$		−	25.2049i		−	1.65123i	−0.564235	−	0.825614i	$-0.690829\pi$
$233$		−	25.2049i		−	1.65123i	0.564235	−	0.825614i	$-0.309171\pi$
$234$	−1.48637	−	7.40605i	−0.0971670	−	0.484148i
$235$	−0.876547	+	0.876547i	−0.0571796	+	0.0571796i
$236$	2.41802	+	0.991870i	0.157400	+	0.0645653i
$237$	−3.29693	−	3.29693i	−0.214159	−	0.214159i
$238$	7.08020	+	4.71329i	0.458941	+	0.305517i
$239$	−10.5973			−0.685481			−0.342741	−	0.939430i	$-0.611355\pi$
$239$	−10.5973			−0.685481			−0.342741	+	0.939430i	$0.611355\pi$
$240$	0.532780	−	0.540144i	0.0343908	−	0.0348662i
$241$	−15.1391			−0.975193			−0.487597	−	0.873069i	$-0.662126\pi$
$241$	−15.1391			−0.975193			−0.487597	+	0.873069i	$0.662126\pi$
$242$	−5.33935	−	3.55440i	−0.343227	−	0.228486i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	4.95821	−	12.0873i	0.317417	−	0.773813i
$245$	−0.134119	+	0.134119i	−0.00856853	+	0.00856853i
$246$	2.08081	+	10.3679i	0.132667	+	0.661034i
$247$		−	24.5766i		−	1.56377i
$248$	−24.6315	−	4.76784i	−1.56410	−	0.302758i
$249$			0.900306i			0.0570546i
$250$	2.62047	−	0.525920i	0.165733	−	0.0332621i
$251$	5.19866	−	5.19866i	0.328136	−	0.328136i	−0.523741	−	0.851877i	$-0.675464\pi$
$251$	5.19866	−	5.19866i	0.328136	−	0.328136i	0.851877	+	0.523741i	$0.175464\pi$
$252$	−0.771704	−	1.84512i	−0.0486128	−	0.116232i
$253$	−8.45001	−	8.45001i	−0.531248	−	0.531248i
$254$	−3.93117	+	5.90533i	−0.246664	+	0.370533i
$255$	1.14075			0.0714367
$256$	−0.219629	−	15.9985i	−0.0137268	−	0.999906i
$257$	14.5239			0.905976			0.452988	−	0.891517i	$-0.350358\pi$
$257$	14.5239			0.905976			0.452988	+	0.891517i	$0.350358\pi$
$258$	−7.36614	+	11.0653i	−0.458596	+	0.688893i
$259$	−6.76289	−	6.76289i	−0.420225	−	0.420225i
$260$	0.781810	+	1.86929i	0.0484858	+	0.115928i
$261$	−2.55533	+	2.55533i	−0.158171	+	0.158171i
$262$	5.88478	−	1.18106i	0.363563	−	0.0729659i
$263$			19.1065i			1.17816i	0.808075	+	0.589080i	$0.200510\pi$
$263$			19.1065i			1.17816i	−0.808075	+	0.589080i	$0.799490\pi$
$264$	10.9451	+	2.11861i	0.673626	+	0.130391i
$265$		−	0.251200i		−	0.0154311i
$266$	−1.28043	−	6.37992i	−0.0785082	−	0.391178i
$267$	9.89030	−	9.89030i	0.605277	−	0.605277i
$268$	7.91915	−	19.3056i	0.483739	−	1.17928i
$269$	12.7078	+	12.7078i	0.774809	+	0.774809i	0.978943	−	0.204134i	$-0.0654378\pi$
$269$	12.7078	+	12.7078i	0.774809	+	0.774809i	−0.204134	+	0.978943i	$0.565438\pi$
$270$	−0.223287	−	0.148642i	−0.0135888	−	0.00904605i
$271$	22.6859			1.37807			0.689035	−	0.724728i	$-0.258035\pi$
$271$	22.6859			1.37807			0.689035	+	0.724728i	$0.258035\pi$
$272$	16.8939	−	17.1275i	1.02435	−	1.03850i
$273$	5.34129			0.323270
$274$	25.1119	+	16.7170i	1.51707	+	1.00991i
$275$	13.8351	+	13.8351i	0.834288	+	0.834288i
$276$	5.61007	+	2.30124i	0.337687	+	0.138519i
$277$	4.59745	−	4.59745i	0.276234	−	0.276234i	−0.555370	−	0.831604i	$-0.687423\pi$
$277$	4.59745	−	4.59745i	0.276234	−	0.276234i	0.831604	+	0.555370i	$0.187423\pi$
$278$	0.887912	+	4.42415i	0.0532534	+	0.265343i
$279$			8.87021i			0.531046i
$280$	0.300342	+	0.444522i	0.0179488	+	0.0265653i
$281$			20.5961i			1.22866i	0.789049	+	0.614330i	$0.210574\pi$
$281$			20.5961i			1.22866i	−0.789049	+	0.614330i	$0.789426\pi$
$282$	9.06204	−	1.81872i	0.539637	−	0.108303i
$283$	3.35466	−	3.35466i	0.199414	−	0.199414i	−0.600335	−	0.799749i	$-0.704966\pi$
$283$	3.35466	−	3.35466i	0.199414	−	0.199414i	0.799749	+	0.600335i	$0.204966\pi$
$284$	−19.6011	+	8.19795i	−1.16311	+	0.486459i
$285$	−0.617113	−	0.617113i	−0.0365546	−	0.0365546i
$286$	−16.4986	+	24.7838i	−0.975581	+	1.46550i
$287$	−7.47741			−0.441377
$288$	−5.53849	+	1.15116i	−0.326358	+	0.0678326i
$289$	19.1722			1.12778
$290$	0.537159	−	0.806910i	0.0315431	−	0.0473834i
$291$	6.91794	+	6.91794i	0.405537	+	0.405537i
$292$	20.2793	−	8.48160i	1.18675	−	0.496348i
$293$	8.50873	−	8.50873i	0.497085	−	0.497085i	−0.413444	−	0.910529i	$-0.635674\pi$
$293$	8.50873	−	8.50873i	0.497085	−	0.497085i	0.910529	+	0.413444i	$0.135674\pi$
$294$	1.38656	−	0.278279i	0.0808661	−	0.0162296i
$295$			0.247859i			0.0144309i
$296$	−22.4149	+	15.1446i	−1.30284	+	0.880263i
$297$		−	3.94152i		−	0.228710i
$298$	2.71949	+	13.5502i	0.157536	+	0.784944i
$299$	−11.4509	+	11.4509i	−0.662224	+	0.662224i
$300$	−9.18531	−	3.76780i	−0.530314	−	0.217534i
$301$	−6.64643	−	6.64643i	−0.383094	−	0.383094i
$302$	2.97041	+	1.97740i	0.170928	+	0.113787i
$303$	−10.8887			−0.625538
$304$	−18.4045	+	0.126324i	−1.05557	+	0.00724516i
$305$	1.23901			0.0709456
$306$	−7.08020	−	4.71329i	−0.404748	−	0.269441i
$307$	4.32701	+	4.32701i	0.246955	+	0.246955i	0.819720	−	0.572765i	$-0.194129\pi$
$307$	4.32701	+	4.32701i	0.246955	+	0.246955i	−0.572765	+	0.819720i	$0.694129\pi$
$308$	−2.99169	+	7.29328i	−0.170468	+	0.415573i
$309$	6.01159	−	6.01159i	0.341987	−	0.341987i
$310$	−0.468186	−	2.33280i	−0.0265912	−	0.132494i
$311$		−	12.7184i		−	0.721196i	−0.932721	−	0.360598i	$-0.882573\pi$
$311$		−	12.7184i		−	0.721196i	0.932721	−	0.360598i	$-0.117427\pi$
$312$	2.87101	−	14.8321i	0.162539	−	0.839705i
$313$			21.0967i			1.19246i	0.802815	+	0.596229i	$0.203335\pi$
$313$			21.0967i			1.19246i	−0.802815	+	0.596229i	$0.796665\pi$
$314$	−9.34178	+	1.87487i	−0.527187	+	0.105805i
$315$	0.134119	−	0.134119i	0.00755673	−	0.00755673i
$316$	−3.59812	−	8.60300i	−0.202410	−	0.483956i
$317$	17.5940	+	17.5940i	0.988178	+	0.988178i	0.999931	−	0.0117526i	$-0.00374106\pi$
$317$	17.5940	+	17.5940i	0.988178	+	0.988178i	−0.0117526	+	0.999931i	$0.503741\pi$
$318$	−1.03789	+	1.55910i	−0.0582020	+	0.0874299i
$319$	14.2438			0.797499
$320$	1.39582	−	0.595078i	0.0780289	−	0.0332659i
$321$	−1.78808			−0.0998010
$322$	−2.37599	+	3.56917i	−0.132409	+	0.198902i
$323$	−19.5681	−	19.5681i	−1.08880	−	1.08880i
$324$	0.771704	+	1.84512i	0.0428724	+	0.102507i
$325$	18.7484	−	18.7484i	1.03998	−	1.03998i
$326$	29.3164	−	5.88370i	1.62368	−	0.325868i
$327$			11.2278i			0.620897i
$328$	−4.01919	+	20.7639i	−0.221923	+	1.14649i
$329$			6.53561i			0.360320i
$330$	0.208041	+	1.03659i	0.0114523	+	0.0570625i
$331$	−8.93792	+	8.93792i	−0.491272	+	0.491272i	−0.908707	−	0.417435i	$-0.862929\pi$
$331$	−8.93792	+	8.93792i	−0.491272	+	0.491272i	0.417435	+	0.908707i	$0.362929\pi$
$332$	−0.683352	+	1.66590i	−0.0375038	+	0.0914284i
$333$	6.76289	+	6.76289i	0.370604	+	0.370604i
$334$	−16.8796	−	11.2367i	−0.923610	−	0.614846i
$335$	1.97892			0.108120
$336$	−0.0274543	−	3.99991i	−0.00149775	−	0.218213i
$337$	25.0411			1.36408			0.682039	−	0.731316i	$-0.261093\pi$
$337$	25.0411			1.36408			0.682039	+	0.731316i	$0.261093\pi$
$338$	18.2816	+	12.1700i	0.994386	+	0.661962i
$339$	0.959901	+	0.959901i	0.0521347	+	0.0521347i
$340$	2.11082	+	0.865856i	0.114475	+	0.0469576i
$341$	24.7219	−	24.7219i	1.33877	−	1.33877i
$342$	1.28043	+	6.37992i	0.0692377	+	0.344987i
$343$			1.00000i			0.0539949i
$344$	−22.0289	+	14.8838i	−1.18772	+	0.802482i
$345$			0.575060i			0.0309602i
$346$	−12.0578	+	2.41996i	−0.648230	+	0.130098i
$347$	12.8314	−	12.8314i	0.688827	−	0.688827i	−0.273145	−	0.961973i	$-0.588064\pi$
$347$	12.8314	−	12.8314i	0.688827	−	0.688827i	0.961973	+	0.273145i	$0.0880640\pi$
$348$	−6.66787	+	2.78877i	−0.357435	+	0.149494i
$349$	−17.7348	−	17.7348i	−0.949320	−	0.949320i	0.0494565	−	0.998776i	$-0.484251\pi$
$349$	−17.7348	−	17.7348i	−0.949320	−	0.949320i	−0.998776	+	0.0494565i	$0.984251\pi$
$350$	3.89019	−	5.84376i	0.207939	−	0.312362i
$351$	−5.34129			−0.285097
$352$	18.6445	+	12.2278i	0.993757	+	0.651744i
$353$	8.06386			0.429196			0.214598	−	0.976702i	$-0.431156\pi$
$353$	8.06386			0.429196			0.214598	+	0.976702i	$0.431156\pi$
$354$	1.02409	−	1.53837i	0.0544297	−	0.0817632i
$355$	−1.42477	−	1.42477i	−0.0756188	−	0.0756188i
$356$	25.8077	−	10.7938i	1.36781	−	0.572071i
$357$	4.25278	−	4.25278i	0.225081	−	0.225081i
$358$	−1.31310	+	0.263535i	−0.0693994	+	0.0139282i
$359$			26.1988i			1.38272i	0.722512	+	0.691359i	$0.242988\pi$
$359$			26.1988i			1.38272i	−0.722512	+	0.691359i	$0.757012\pi$
$360$	−0.300342	−	0.444522i	−0.0158294	−	0.0234284i
$361$			2.17146i			0.114287i
$362$	−2.80860	−	13.9942i	−0.147617	−	0.735521i
$363$	−3.20712	+	3.20712i	−0.168330	+	0.168330i
$364$	9.88339	+	4.05415i	0.518031	+	0.212495i
$365$	1.47406	+	1.47406i	0.0771561	+	0.0771561i
$366$	−7.69006	−	5.11927i	−0.401966	−	0.267588i
$367$	−1.67280			−0.0873195			−0.0436598	−	0.999046i	$-0.513902\pi$
$367$	−1.67280			−0.0873195			−0.0436598	+	0.999046i	$0.513902\pi$
$368$	8.63404	+	8.51633i	0.450081	+	0.443944i
$369$	7.47741			0.389258
$370$	−2.13555	−	1.42164i	−0.111022	−	0.0739073i
$371$	−0.936484	−	0.936484i	−0.0486198	−	0.0486198i
$372$	−6.73268	+	16.4132i	−0.349073	+	0.850985i
$373$	−17.9995	+	17.9995i	−0.931977	+	0.931977i	−0.997829	−	0.0658519i	$-0.979023\pi$
$373$	−17.9995	+	17.9995i	−0.931977	+	0.931977i	0.0658519	+	0.997829i	$0.479023\pi$
$374$	6.59677	+	32.8693i	0.341111	+	1.69963i
$375$		−	1.88990i		−	0.0975941i
$376$	18.1486	+	3.51296i	0.935944	+	0.181167i
$377$		−	19.3023i		−	0.994118i
$378$	−1.38656	+	0.278279i	−0.0713172	+	0.0143131i
$379$	−13.7305	+	13.7305i	−0.705288	+	0.705288i	−0.965540	−	0.260253i	$-0.916194\pi$
$379$	−13.7305	+	13.7305i	−0.705288	+	0.705288i	0.260253	+	0.965540i	$0.416194\pi$
$380$	−0.673488	−	1.61029i	−0.0345492	−	0.0826062i
$381$	3.54708	+	3.54708i	0.181722	+	0.181722i
$382$	−14.3377	+	21.5377i	−0.733578	+	1.10197i
$383$	12.4305			0.635169			0.317585	−	0.948230i	$-0.397128\pi$
$383$	12.4305			0.635169			0.317585	+	0.948230i	$0.397128\pi$
$384$	−11.1220	−	2.07376i	−0.567569	−	0.105826i
$385$	−0.747597			−0.0381011
$386$	3.60819	−	5.42014i	0.183652	−	0.275878i
$387$	6.64643	+	6.64643i	0.337857	+	0.337857i
$388$	7.54992	+	18.0516i	0.383289	+	0.916433i
$389$	−12.4721	+	12.4721i	−0.632358	+	0.632358i	−0.948659	−	0.316301i	$-0.897559\pi$
$389$	−12.4721	+	12.4721i	−0.632358	+	0.632358i	0.316301	+	0.948659i	$0.397559\pi$
$390$	1.40472	−	0.281923i	0.0711309	−	0.0142757i
$391$			18.2346i			0.922163i
$392$	2.77688	+	0.537511i	0.140254	+	0.0271484i
$393$		−	4.24414i		−	0.214089i
$394$	5.01253	+	24.9756i	0.252527	+	1.25825i
$395$	0.625337	−	0.625337i	0.0314641	−	0.0314641i
$396$	2.99169	−	7.29328i	0.150338	−	0.366501i
$397$	8.43957	+	8.43957i	0.423570	+	0.423570i	0.886431	−	0.462861i	$-0.153177\pi$
$397$	8.43957	+	8.43957i	0.423570	+	0.423570i	−0.462861	+	0.886431i	$0.653177\pi$
$398$	−15.1898	−	10.1118i	−0.761396	−	0.506861i
$399$	−4.60125			−0.230350
$400$	−14.1364	−	13.9437i	−0.706821	−	0.697184i
$401$	−1.69845			−0.0848166			−0.0424083	−	0.999100i	$-0.513503\pi$
$401$	−1.69845			−0.0848166			−0.0424083	+	0.999100i	$0.513503\pi$
$402$	−12.2824	−	8.17638i	−0.612590	−	0.407801i
$403$	−33.5016	−	33.5016i	−1.66883	−	1.66883i
$404$	−20.1481	−	8.26474i	−1.00241	−	0.411186i
$405$	−0.134119	+	0.134119i	−0.00666441	+	0.00666441i
$406$	−1.00564	−	5.01074i	−0.0499091	−	0.248679i
$407$		−	37.6973i		−	1.86859i
$408$	−9.52355	−	14.0954i	−0.471486	−	0.697825i
$409$			23.7533i			1.17452i	0.809397	+	0.587262i	$0.199794\pi$
$409$			23.7533i			1.17452i	−0.809397	+	0.587262i	$0.800206\pi$
$410$	−1.96651	+	0.394672i	−0.0971188	+	0.0194914i
$411$	15.0837	−	15.0837i	0.744022	−	0.744022i
$412$	15.6866	−	6.56077i	0.772824	−	0.323226i
$413$	0.924030	+	0.924030i	0.0454685	+	0.0454685i
$414$	2.37599	−	3.56917i	0.116774	−	0.175415i
$415$	−0.170763			−0.00838244
$416$	16.5704	−	25.2659i	0.812428	−	1.23876i
$417$	3.19073			0.156251
$418$	14.2127	−	21.3500i	0.695164	−	1.04426i
$419$	12.2409	+	12.2409i	0.598006	+	0.598006i	0.939782	−	0.341775i	$-0.111028\pi$
$419$	12.2409	+	12.2409i	0.598006	+	0.598006i	−0.341775	+	0.939782i	$0.611028\pi$
$420$	0.349969	−	0.146371i	0.0170767	−	0.00714217i
$421$	−17.0973	+	17.0973i	−0.833274	+	0.833274i	−0.987963	−	0.154689i	$-0.950562\pi$
$421$	−17.0973	+	17.0973i	−0.833274	+	0.833274i	0.154689	+	0.987963i	$0.450562\pi$
$422$	−34.1978	+	6.86338i	−1.66472	+	0.334104i
$423$		−	6.53561i		−	0.317772i
$424$	−3.10388	+	2.09714i	−0.150738	+	0.101846i
$425$		−	29.8553i		−	1.44819i
$426$	2.95621	+	14.7297i	0.143229	+	0.713658i
$427$	4.61909	−	4.61909i	0.223533	−	0.223533i
$428$	−3.30862	−	1.35719i	−0.159928	−	0.0656024i
$429$	14.8866	+	14.8866i	0.718731	+	0.718731i
$430$	−2.09878	−	1.39715i	−0.101212	−	0.0673767i
$431$	27.3527			1.31753			0.658766	−	0.752348i	$-0.271079\pi$
$431$	27.3527			1.31753			0.658766	+	0.752348i	$0.271079\pi$
$432$	0.0274543	+	3.99991i	0.00132089	+	0.192446i
$433$	15.8911			0.763676			0.381838	−	0.924229i	$-0.375291\pi$
$433$	15.8911			0.763676			0.381838	+	0.924229i	$0.375291\pi$
$434$	−10.4422	−	6.95137i	−0.501242	−	0.333676i
$435$	−0.484676	−	0.484676i	−0.0232384	−	0.0232384i
$436$	−8.52212	+	20.7756i	−0.408135	+	0.994970i
$437$	9.86437	−	9.86437i	0.471877	−	0.471877i
$438$	−3.05849	−	15.2394i	−0.146141	−	0.728166i
$439$			22.6973i			1.08328i	0.840609	+	0.541642i	$0.182197\pi$
$439$			22.6973i			1.08328i	−0.840609	+	0.541642i	$0.817803\pi$
$440$	−0.401842	+	2.07599i	−0.0191571	+	0.0989689i
$441$		−	1.00000i		−	0.0476190i
$442$	44.5424	−	8.93952i	2.11867	−	0.425210i
$443$	−24.1622	+	24.1622i	−1.14798	+	1.14798i	−0.161031	+	0.986949i	$0.551482\pi$
$443$	−24.1622	+	24.1622i	−1.14798	+	1.14798i	−0.986949	+	0.161031i	$0.948518\pi$
$444$	7.38070	+	17.6471i	0.350273	+	0.837492i
$445$	1.87592	+	1.87592i	0.0889270	+	0.0889270i
$446$	−4.25097	+	6.38572i	−0.201289	+	0.302372i
$447$	9.77253			0.462225
$448$	2.98521	−	7.42216i	0.141038	−	0.350664i
$449$	−4.44242			−0.209651			−0.104825	−	0.994491i	$-0.533428\pi$
$449$	−4.44242			−0.209651			−0.104825	+	0.994491i	$0.533428\pi$
$450$	−3.89019	+	5.84376i	−0.183385	+	0.275477i
$451$	−20.8401	−	20.8401i	−0.981321	−	0.981321i
$452$	1.04759	+	2.50476i	0.0492745	+	0.117814i
$453$	1.78420	−	1.78420i	0.0838290	−	0.0838290i
$454$	−4.41527	+	0.886131i	−0.207219	+	0.0415882i
$455$			1.01310i			0.0474947i
$456$	−2.47322	+	12.7771i	−0.115819	+	0.598344i
$457$		−	34.2838i		−	1.60373i	−0.597506	−	0.801864i	$-0.703842\pi$
$457$		−	34.2838i		−	1.60373i	0.597506	−	0.801864i	$-0.296158\pi$
$458$	−2.23400	−	11.1312i	−0.104388	−	0.520129i
$459$	−4.25278	+	4.25278i	−0.198503	+	0.198503i
$460$	−0.436483	+	1.06408i	−0.0203511	+	0.0496128i
$461$	−0.574771	−	0.574771i	−0.0267698	−	0.0267698i	0.693595	−	0.720365i	$-0.256026\pi$
$461$	−0.574771	−	0.574771i	−0.0267698	−	0.0267698i	−0.720365	+	0.693595i	$0.756026\pi$
$462$	4.64004	+	3.08887i	0.215874	+	0.143707i
$463$	9.24114			0.429472			0.214736	−	0.976672i	$-0.431111\pi$
$463$	9.24114			0.429472			0.214736	+	0.976672i	$0.431111\pi$
$464$	−14.4548	+	0.0992138i	−0.671047	+	0.00460588i
$465$	−1.68243			−0.0780210
$466$	−29.6718	−	19.7525i	−1.37452	−	0.915016i
$467$	−21.1636	−	21.1636i	−0.979337	−	0.979337i	0.0204539	−	0.999791i	$-0.493489\pi$
$467$	−21.1636	−	21.1636i	−0.979337	−	0.979337i	−0.999791	+	0.0204539i	$0.993489\pi$
$468$	−9.88339	−	4.05415i	−0.456860	−	0.187403i
$469$	7.37751	−	7.37751i	0.340662	−	0.340662i
$470$	0.344962	+	1.71882i	0.0159119	+	0.0792832i
$471$			6.73736i			0.310441i
$472$	3.06260	−	2.06925i	0.140968	−	0.0952448i
$473$		−	37.0482i		−	1.70348i
$474$	−6.46494	+	1.29749i	−0.296945	+	0.0595958i
$475$	−16.1508	+	16.1508i	−0.741050	+	0.741050i
$476$	11.0972	−	4.64128i	0.508638	−	0.212733i
$477$	0.936484	+	0.936484i	0.0428786	+	0.0428786i
$478$	−8.30484	+	12.4754i	−0.379854	+	0.570609i
$479$	32.9689			1.50639			0.753194	−	0.657798i	$-0.228512\pi$
$479$	32.9689			1.50639			0.753194	+	0.657798i	$0.228512\pi$
$480$	−0.218343	−	1.05050i	−0.00996594	−	0.0479485i
$481$	−51.0850			−2.32928
$482$	−11.8641	+	17.8220i	−0.540396	+	0.811772i
$483$	2.14385	+	2.14385i	0.0975484	+	0.0975484i
$484$	−8.36864	+	3.50010i	−0.380393	+	0.159096i
$485$	−1.31214	+	1.31214i	−0.0595813	+	0.0595813i
$486$	1.38656	−	0.278279i	0.0628958	−	0.0126230i
$487$			4.73293i			0.214470i	0.994234	+	0.107235i	$0.0341997\pi$
$487$			4.73293i			0.214470i	−0.994234	+	0.107235i	$0.965800\pi$
$488$	−10.3439	−	15.3095i	−0.468244	−	0.693028i
$489$		−	21.1432i		−	0.956127i
$490$	0.0527819	+	0.262993i	0.00238444	+	0.0118808i
$491$	28.5380	−	28.5380i	1.28790	−	1.28790i	0.351841	−	0.936060i	$-0.385556\pi$
$491$	28.5380	−	28.5380i	1.28790	−	1.28790i	0.936060	−	0.351841i	$-0.114444\pi$
$492$	13.8360	+	5.67551i	0.623775	+	0.255872i
$493$	−15.3686	−	15.3686i	−0.692167	−	0.692167i
$494$	−28.9321	−	19.2601i	−1.30172	−	0.866553i
$495$	0.747597			0.0336020
$496$	−24.9160	+	25.2603i	−1.11876	+	1.13422i
$497$	−10.6232			−0.476515
$498$	1.05986	+	0.705549i	0.0474935	+	0.0316164i
$499$	−8.41828	−	8.41828i	−0.376854	−	0.376854i	0.493112	−	0.869966i	$-0.335859\pi$
$499$	−8.41828	−	8.41828i	−0.376854	−	0.376854i	−0.869966	+	0.493112i	$0.835859\pi$
$500$	1.43447	−	3.49702i	0.0641517	−	0.156392i
$501$	−10.1388	+	10.1388i	−0.452970	+	0.452970i
$502$	−2.04591	−	10.1940i	−0.0913134	−	0.454982i
$503$			21.9738i			0.979763i	0.871789	+	0.489881i	$0.162960\pi$
$503$			21.9738i			0.979763i	−0.871789	+	0.489881i	$0.837040\pi$
$504$	−2.77688	−	0.537511i	−0.123692	−	0.0239427i
$505$		−	2.06528i		−	0.0919039i
$506$	−16.5696	+	3.32547i	−0.736609	+	0.147835i
$507$	10.9810	−	10.9810i	0.487681	−	0.487681i
$508$	3.87112	+	9.25573i	0.171753	+	0.410657i
$509$	−16.4205	−	16.4205i	−0.727827	−	0.727827i	0.242359	−	0.970187i	$-0.422079\pi$
$509$	−16.4205	−	16.4205i	−0.727827	−	0.727827i	−0.970187	+	0.242359i	$0.922079\pi$
$510$	0.893981	−	1.34292i	0.0395861	−	0.0594655i
$511$	10.9907			0.486202
$512$	−19.0059	−	12.2791i	−0.839950	−	0.542664i
$513$	4.60125			0.203150
$514$	11.3820	−	17.0979i	0.502040	−	0.754154i
$515$	1.14023	+	1.14023i	0.0502446	+	0.0502446i
$516$	7.25360	+	17.3432i	0.319322	+	0.763490i
$517$	−18.2152	+	18.2152i	−0.801104	+	0.801104i
$518$	−13.2613	+	2.66151i	−0.582670	+	0.116940i
$519$			8.69615i			0.381719i
$520$	2.81325	+	0.544551i	0.123369	+	0.0238801i
$521$			15.4897i			0.678614i	0.940676	+	0.339307i	$0.110193\pi$
$521$			15.4897i			0.678614i	−0.940676	+	0.339307i	$0.889807\pi$
$522$	1.00564	+	5.01074i	0.0440157	+	0.219314i
$523$	−10.9552	+	10.9552i	−0.479036	+	0.479036i	−0.904823	−	0.425787i	$-0.859997\pi$
$523$	−10.9552	+	10.9552i	−0.479036	+	0.479036i	0.425787	+	0.904823i	$0.359997\pi$
$524$	3.22139	−	7.85325i	0.140727	−	0.343071i
$525$	−3.51010	−	3.51010i	−0.153193	−	0.153193i
$526$	22.4926	+	14.9733i	0.980726	+	0.652869i
$527$	−53.3484			−2.32389
$528$	11.0715	−	11.2245i	0.481826	−	0.488486i
$529$	13.8078			0.600341
$530$	−0.295718	−	0.196859i	−0.0128452	−	0.00855102i
$531$	−0.924030	−	0.924030i	−0.0400995	−	0.0400995i
$532$	−8.51403	−	3.49244i	−0.369130	−	0.151417i
$533$	−28.2412	+	28.2412i	−1.22326	+	1.22326i
$534$	−3.89229	−	19.3939i	−0.168436	−	0.839255i
$535$		−	0.339150i		−	0.0146627i
$536$	−16.5210	−	24.4520i	−0.713598	−	1.05616i
$537$			0.947016i			0.0408668i
$538$	24.9187	−	5.00111i	1.07432	−	0.215613i
$539$	−2.78707	+	2.78707i	−0.120048	+	0.120048i
$540$	−0.349969	+	0.146371i	−0.0150603	+	0.00629880i
$541$	−7.15374	−	7.15374i	−0.307563	−	0.307563i	0.536400	−	0.843964i	$-0.319784\pi$
$541$	−7.15374	−	7.15374i	−0.307563	−	0.307563i	−0.843964	+	0.536400i	$0.819784\pi$
$542$	17.7784	−	26.7063i	0.763648	−	1.14714i
$543$	−10.0927			−0.433121
$544$	−6.92344	−	33.3103i	−0.296840	−	1.42817i
$545$	−2.12960			−0.0912220
$546$	4.18584	−	6.28789i	0.179138	−	0.269097i
$547$	13.6151	+	13.6151i	0.582141	+	0.582141i	0.935491	−	0.353350i	$-0.114958\pi$
$547$	13.6151	+	13.6151i	0.582141	+	0.582141i	−0.353350	+	0.935491i	$0.614958\pi$
$548$	39.3592	−	16.4616i	1.68134	−	0.703205i
$549$	−4.61909	+	4.61909i	−0.197138	+	0.197138i
$550$	27.1292	−	5.44475i	1.15679	−	0.232165i
$551$			16.6279i			0.708373i
$552$	7.10556	−	4.80087i	0.302433	−	0.204339i
$553$		−	4.66256i		−	0.198272i
$554$	−1.80931	−	9.01513i	−0.0768701	−	0.383016i
$555$	−1.28273	+	1.28273i	−0.0544490	+	0.0544490i
$556$	5.90404	+	2.42183i	0.250387	+	0.102708i
$557$	−9.87510	−	9.87510i	−0.418421	−	0.418421i	0.466238	−	0.884659i	$-0.345609\pi$
$557$	−9.87510	−	9.87510i	−0.418421	−	0.418421i	−0.884659	+	0.466238i	$0.845609\pi$
$558$	10.4422	+	6.95137i	0.442054	+	0.294275i
$559$	−50.2053			−2.12346
$560$	0.758672	−	0.00520732i	0.0320597	−	0.000220049i
$561$	23.7056			1.00085
$562$	24.2462	+	16.1407i	1.02276	+	0.680853i
$563$	−27.0945	−	27.0945i	−1.14190	−	1.14190i	−0.988103	−	0.153796i	$-0.950850\pi$
$563$	−27.0945	−	27.0945i	−1.14190	−	1.14190i	−0.153796	−	0.988103i	$-0.549150\pi$
$564$	4.96066	−	12.0933i	0.208882	−	0.509221i
$565$	−0.182067	+	0.182067i	−0.00765961	+	0.00765961i
$566$	−1.32021	−	6.57814i	−0.0554926	−	0.276500i
$567$			1.00000i			0.0419961i
$568$	−5.71008	+	29.4993i	−0.239590	+	1.23776i
$569$			8.15974i			0.342074i	0.985265	+	0.171037i	$0.0547118\pi$
$569$			8.15974i			0.342074i	−0.985265	+	0.171037i	$0.945288\pi$
$570$	−1.21010	+	0.242862i	−0.0506853	+	0.0101724i
$571$	0.546419	−	0.546419i	0.0228669	−	0.0228669i	−0.695581	−	0.718448i	$-0.744853\pi$
$571$	0.546419	−	0.546419i	0.0228669	−	0.0228669i	0.718448	+	0.695581i	$0.244853\pi$
$572$	16.2465	+	38.8450i	0.679301	+	1.62419i
$573$	12.9368	+	12.9368i	0.540442	+	0.540442i
$574$	−5.85987	+	8.80257i	−0.244586	+	0.367412i
$575$	15.0502			0.627637
$576$	−2.98521	+	7.42216i	−0.124384	+	0.309257i
$577$	−1.28756			−0.0536018			−0.0268009	−	0.999641i	$-0.508532\pi$
$577$	−1.28756			−0.0536018			−0.0268009	+	0.999641i	$0.508532\pi$
$578$	15.0248	−	22.5699i	0.624949	−	0.938785i
$579$	−3.25565	−	3.25565i	−0.135300	−	0.135300i
$580$	−0.528953	−	1.26471i	−0.0219636	−	0.0525143i
$581$	−0.636613	+	0.636613i	−0.0264111	+	0.0264111i
$582$	13.5654	−	2.72253i	0.562303	−	0.112852i
$583$		−	5.22010i		−	0.216194i
$584$	5.90765	−	30.5200i	0.244460	−	1.26293i
$585$		−	1.01310i		−	0.0418864i
$586$	−3.34858	−	16.6847i	−0.138328	−	0.689241i
$587$	26.3145	−	26.3145i	1.08611	−	1.08611i	0.0901895	−	0.995925i	$-0.471253\pi$
$587$	26.3145	−	26.3145i	1.08611	−	1.08611i	0.995925	−	0.0901895i	$-0.0287473\pi$
$588$	0.759021	−	1.85037i	0.0313015	−	0.0763082i
$589$	28.8599	+	28.8599i	1.18915	+	1.18915i
$590$	0.291785	+	0.194241i	0.0120126	+	0.00799679i
$591$	18.0126			0.740939
$592$	0.262577	+	38.2558i	0.0107919	+	1.57230i
$593$	−14.3677			−0.590011			−0.295006	−	0.955496i	$-0.595322\pi$
$593$	−14.3677			−0.590011			−0.295006	+	0.955496i	$0.595322\pi$
$594$	−4.64004	−	3.08887i	−0.190383	−	0.126738i
$595$	0.806634	+	0.806634i	0.0330688	+	0.0330688i
$596$	18.0828	+	7.41755i	0.740702	+	0.303835i
$597$	−9.12387	+	9.12387i	−0.373415	+	0.373415i
$598$	4.50646	+	22.4541i	0.184283	+	0.918216i
$599$		−	25.3817i		−	1.03707i	−0.855058	−	0.518533i	$-0.826478\pi$
$599$		−	25.3817i		−	1.03707i	0.855058	−	0.518533i	$-0.173522\pi$
$600$	−11.6338	+	7.86041i	−0.474950	+	0.320900i
$601$			9.76191i			0.398197i	0.979980	+	0.199098i	$0.0638013\pi$
$601$			9.76191i			0.398197i	−0.979980	+	0.199098i	$0.936199\pi$
$602$	−13.0330	+	2.61567i	−0.531184	+	0.106607i
$603$	−7.37751	+	7.37751i	−0.300435	+	0.300435i
$604$	4.65568	−	1.94719i	0.189437	−	0.0792301i
$605$	−0.608302	−	0.608302i	−0.0247310	−	0.0247310i
$606$	−8.53320	+	12.8184i	−0.346638	+	0.520712i
$607$	23.0454			0.935383			0.467691	−	0.883892i	$-0.345086\pi$
$607$	23.0454			0.935383			0.467691	+	0.883892i	$0.345086\pi$
$608$	−14.2745	+	21.7652i	−0.578907	+	0.882697i
$609$	−3.61378			−0.146438
$610$	0.970984	−	1.45859i	0.0393140	−	0.0590567i
$611$	24.6841	+	24.6841i	0.998612	+	0.998612i
$612$	−11.0972	+	4.64128i	−0.448577	+	0.187613i
$613$	22.0312	−	22.0312i	0.889833	−	0.889833i	−0.104674	−	0.994507i	$-0.533380\pi$
$613$	22.0312	−	22.0312i	0.889833	−	0.889833i	0.994507	+	0.104674i	$0.0333799\pi$
$614$	8.48482	−	1.70288i	0.342420	−	0.0687225i
$615$			1.41826i			0.0571897i
$616$	6.24129	+	9.23746i	0.251469	+	0.372188i
$617$			0.578847i			0.0233035i	0.999932	+	0.0116517i	$0.00370895\pi$
$617$			0.578847i			0.0233035i	−0.999932	+	0.0116517i	$0.996291\pi$
$618$	−2.36584	−	11.7881i	−0.0951678	−	0.474187i
$619$	16.5197	−	16.5197i	0.663983	−	0.663983i	−0.292333	−	0.956316i	$-0.594432\pi$
$619$	16.5197	−	16.5197i	0.663983	−	0.663983i	0.956316	+	0.292333i	$0.0944317\pi$
$620$	−3.11313	−	1.27700i	−0.125026	−	0.0512857i
$621$	−2.14385	−	2.14385i	−0.0860296	−	0.0860296i
$622$	−14.9724	−	9.96713i	−0.600339	−	0.399646i
$623$	13.9870			0.560377
$624$	−15.2108	−	15.0034i	−0.608919	−	0.600617i
$625$	−24.4617			−0.978466
$626$	24.8355	+	16.5330i	0.992628	+	0.660792i
$627$	−12.8240	−	12.8240i	−0.512141	−	0.512141i
$628$	−5.11380	+	12.4666i	−0.204063	+	0.497473i
$629$	−40.6743	+	40.6743i	−1.62179	+	1.62179i
$630$	−0.0527819	−	0.262993i	−0.00210288	−	0.0104779i
$631$		−	11.3095i		−	0.450224i	−0.974333	−	0.225112i	$-0.927725\pi$
$631$		−	11.3095i		−	0.450224i	0.974333	−	0.225112i	$-0.0722747\pi$
$632$	−12.9474	−	2.50618i	−0.515020	−	0.0996905i
$633$			24.6637i			0.980293i
$634$	34.5001	−	6.92405i	1.37017	−	0.274989i
$635$	−0.672783	+	0.672783i	−0.0266986	+	0.0266986i
$636$	1.02203	+	2.44366i	0.0405263	+	0.0968973i
$637$	3.77686	+	3.77686i	0.149645	+	0.149645i
$638$	11.1625	−	16.7681i	0.441928	−	0.663856i
$639$	10.6232			0.420247
$640$	0.393335	−	2.10954i	0.0155479	−	0.0833870i
$641$	−8.85114			−0.349599			−0.174799	−	0.984604i	$-0.555928\pi$
$641$	−8.85114			−0.349599			−0.174799	+	0.984604i	$0.555928\pi$
$642$	−1.40128	+	2.10497i	−0.0553040	+	0.0830765i
$643$	16.1621	+	16.1621i	0.637372	+	0.637372i	0.949906	−	0.312535i	$-0.101178\pi$
$643$	16.1621	+	16.1621i	0.637372	+	0.637372i	−0.312535	+	0.949906i	$0.601178\pi$
$644$	2.33970	+	5.59415i	0.0921969	+	0.220440i
$645$	−1.26064	+	1.26064i	−0.0496378	+	0.0496378i
$646$	−38.3710	+	7.70093i	−1.50969	+	0.302989i
$647$			44.3267i			1.74266i	0.490695	+	0.871331i	$0.336743\pi$
$647$			44.3267i			1.74266i	−0.490695	+	0.871331i	$0.663257\pi$
$648$	2.77688	+	0.537511i	0.109086	+	0.0211154i
$649$			5.15068i			0.202182i
$650$	−7.37838	−	36.7638i	−0.289404	−	1.44199i
$651$	−6.27218	+	6.27218i	−0.245826	+	0.245826i
$652$	16.0481	−	39.1228i	0.628493	−	1.53217i
$653$	−23.2993	−	23.2993i	−0.911771	−	0.911771i	0.0846406	−	0.996412i	$-0.473026\pi$
$653$	−23.2993	−	23.2993i	−0.911771	−	0.911771i	−0.996412	+	0.0846406i	$0.973026\pi$
$654$	13.2176	+	8.79894i	0.516848	+	0.344066i
$655$	0.804997			0.0314538
$656$	21.2940	+	21.0036i	0.831390	+	0.820055i
$657$	−10.9907			−0.428790
$658$	7.69386	+	5.12180i	0.299938	+	0.199669i
$659$	25.3797	+	25.3797i	0.988653	+	0.988653i	0.999936	−	0.0112831i	$-0.00359161\pi$
$659$	25.3797	+	25.3797i	0.988653	+	0.988653i	−0.0112831	+	0.999936i	$0.503592\pi$
$660$	1.38333	+	0.567442i	0.0538462	+	0.0220877i
$661$	−9.71743	+	9.71743i	−0.377964	+	0.377964i	−0.870367	−	0.492403i	$-0.836119\pi$
$661$	−9.71743	+	9.71743i	−0.377964	+	0.377964i	0.492403	+	0.870367i	$0.336119\pi$
$662$	3.51748	+	17.5263i	0.136711	+	0.681181i
$663$		−	32.1243i		−	1.24760i
$664$	1.42561	+	2.10999i	0.0553245	+	0.0818833i
$665$		−	0.872729i		−	0.0338430i
$666$	13.2613	−	2.66151i	0.513866	−	0.103131i
$667$	7.74740	−	7.74740i	0.299981	−	0.299981i
$668$	−26.4562	+	11.0651i	−1.02362	+	0.428120i
$669$	3.83563	+	3.83563i	0.148294	+	0.148294i
$670$	1.55083	−	2.32963i	0.0599140	−	0.0900015i
$671$	25.7475			0.993970
$672$	−4.73029	−	3.10231i	−0.182475	−	0.119674i
$673$	−33.2565			−1.28194			−0.640971	−	0.767565i	$-0.721468\pi$
$673$	−33.2565			−1.28194			−0.640971	+	0.767565i	$0.721468\pi$
$674$	19.6241	−	29.4790i	0.755894	−	1.13549i
$675$	3.51010	+	3.51010i	0.135104	+	0.135104i
$676$	28.6537	−	11.9841i	1.10206	−	0.460927i
$677$	−10.3549	+	10.3549i	−0.397971	+	0.397971i	−0.877517	−	0.479546i	$-0.840801\pi$
$677$	−10.3549	+	10.3549i	−0.397971	+	0.397971i	0.479546	+	0.877517i	$0.340801\pi$
$678$	1.88227	−	0.377765i	0.0722881	−	0.0145080i
$679$			9.78344i			0.375454i
$680$	2.67350	−	1.80635i	0.102524	−	0.0692705i
$681$			3.18432i			0.122024i
$682$	−9.72921	−	48.4772i	−0.372551	−	1.85629i
$683$	−10.7131	+	10.7131i	−0.409925	+	0.409925i	−0.881713	−	0.471787i	$-0.843609\pi$
$683$	−10.7131	+	10.7131i	−0.409925	+	0.409925i	0.471787	+	0.881713i	$0.343609\pi$
$684$	8.51403	+	3.49244i	0.325542	+	0.133537i
$685$	2.86095	+	2.86095i	0.109311	+	0.109311i
$686$	1.17722	+	0.783676i	0.0449465	+	0.0299209i
$687$	−8.02793			−0.306285
$688$	0.258055	+	37.5970i	0.00983827	+	1.43337i
$689$	−7.07394			−0.269496
$690$	0.676973	+	0.450661i	0.0257719	+	0.0171564i
$691$	−2.45093	−	2.45093i	−0.0932379	−	0.0932379i	0.658949	−	0.752187i	$-0.271001\pi$
$691$	−2.45093	−	2.45093i	−0.0932379	−	0.0932379i	−0.752187	+	0.658949i	$0.771001\pi$
$692$	−6.60057	+	16.0911i	−0.250916	+	0.611694i
$693$	2.78707	−	2.78707i	0.105872	−	0.105872i
$694$	−5.04976	−	25.1611i	−0.191686	−	0.955103i
$695$			0.605193i			0.0229563i
$696$	−1.94245	+	10.0351i	−0.0736284	+	0.380378i
$697$			44.9716i			1.70342i
$698$	−34.7761	+	6.97944i	−1.31629	+	0.264176i
$699$	−17.8226	+	17.8226i	−0.674111	+	0.674111i
$700$	−3.83075	−	9.15923i	−0.144789	−	0.346186i
$701$	6.58762	+	6.58762i	0.248811	+	0.248811i	0.820482	−	0.571672i	$-0.193705\pi$
$701$	6.58762	+	6.58762i	0.248811	+	0.248811i	−0.571672	+	0.820482i	$0.693705\pi$
$702$	−4.18584	+	6.28789i	−0.157984	+	0.237321i
$703$	44.0071			1.65976
$704$	29.0061	−	12.3661i	1.09321	−	0.466065i
$705$	1.23962			0.0466870
$706$	6.31945	−	9.49295i	0.237836	−	0.357272i
$707$	−7.69946	−	7.69946i	−0.289568	−	0.289568i
$708$	−1.00844	−	2.41116i	−0.0378996	−	0.0906169i
$709$	−24.5140	+	24.5140i	−0.920644	+	0.920644i	−0.997075	−	0.0764305i	$-0.975648\pi$
$709$	−24.5140	+	24.5140i	−0.920644	+	0.920644i	0.0764305	+	0.997075i	$0.475648\pi$
$710$	−2.79382	+	0.560711i	−0.104850	+	0.0210431i
$711$			4.66256i			0.174860i
$712$	7.51817	−	38.8403i	0.281755	−	1.45560i
$713$		−	26.8932i		−	1.00716i
$714$	−1.67366	−	8.33926i	−0.0626352	−	0.312089i
$715$	−2.82357	+	2.82357i	−0.105596	+	0.105596i
$716$	−0.718805	+	1.75233i	−0.0268630	+	0.0654878i
$717$	7.49341	+	7.49341i	0.279846	+	0.279846i
$718$	30.8418	+	20.5313i	1.15100	+	0.766223i
$719$	9.85761			0.367627			0.183813	−	0.982961i	$-0.441156\pi$
$719$	9.85761			0.367627			0.183813	+	0.982961i	$0.441156\pi$
$720$	−0.758672	+	0.00520732i	−0.0282740	+	0.000194065i
$721$	8.50167			0.316619
$722$	2.55629	+	1.70172i	0.0951352	+	0.0633315i
$723$	10.7049	+	10.7049i	0.398121	+	0.398121i
$724$	−18.6754	−	7.66060i	−0.694064	−	0.284704i
$725$	−12.6847	+	12.6847i	−0.471099	+	0.471099i
$726$	1.26215	+	6.28883i	0.0468427	+	0.233401i
$727$		−	0.782266i		−	0.0290126i	−0.999895	−	0.0145063i	$-0.995382\pi$
$727$		−	0.782266i		−	0.0290126i	0.999895	−	0.0145063i	$-0.00461767\pi$
$728$	12.5180	−	8.45781i	0.463949	−	0.313467i
$729$		−	1.00000i		−	0.0370370i
$730$	2.89049	−	0.580112i	0.106982	−	0.0214709i
$731$	−39.9738	+	39.9738i	−1.47849	+	1.47849i
$732$	−12.0530	+	5.04106i	−0.445493	+	0.186323i
$733$	−29.3506	−	29.3506i	−1.08409	−	1.08409i	−0.996124	−	0.0879655i	$-0.971963\pi$
$733$	−29.3506	−	29.3506i	−1.08409	−	1.08409i	−0.0879655	−	0.996124i	$-0.528037\pi$
$734$	−1.31093	+	1.96926i	−0.0483875	+	0.0726867i
$735$	0.189672			0.00699617
$736$	16.7919	−	3.49014i	0.618958	−	0.128648i
$737$	41.1233			1.51480
$738$	5.85987	−	8.80257i	0.215705	−	0.324027i
$739$	−12.9910	−	12.9910i	−0.477881	−	0.477881i	0.426573	−	0.904453i	$-0.359721\pi$
$739$	−12.9910	−	12.9910i	−0.477881	−	0.477881i	−0.904453	+	0.426573i	$0.859721\pi$
$740$	−3.34716	+	1.39992i	−0.123044	+	0.0514619i
$741$	−17.3783	+	17.3783i	−0.638407	+	0.638407i
$742$	−1.83635	+	0.368549i	−0.0674145	+	0.0135299i
$743$			21.8475i			0.801509i	0.916186	+	0.400754i	$0.131252\pi$
$743$			21.8475i			0.801509i	−0.916186	+	0.400754i	$0.868748\pi$
$744$	14.0458	+	20.7885i	0.514942	+	0.762143i
$745$			1.85358i			0.0679099i
$746$	7.08362	+	35.2951i	0.259350	+	1.29225i
$747$	0.636613	−	0.636613i	0.0232924	−	0.0232924i
$748$	43.8642	+	17.9930i	1.60383	+	0.657891i
$749$	−1.26436	−	1.26436i	−0.0461989	−	0.0461989i
$750$	−2.22483	−	1.48107i	−0.0812394	−	0.0540810i
$751$	25.3170			0.923832			0.461916	−	0.886924i	$-0.347162\pi$
$751$	25.3170			0.923832			0.461916	+	0.886924i	$0.347162\pi$
$752$	18.3582	−	18.6119i	0.669454	−	0.678707i
$753$	−7.35201			−0.267922
$754$	−22.7231	−	15.1267i	−0.827525	−	0.550883i
$755$	0.338413	+	0.338413i	0.0123161	+	0.0123161i
$756$	−0.759021	+	1.85037i	−0.0276053	+	0.0672975i
$757$	−18.3979	+	18.3979i	−0.668684	+	0.668684i	−0.957411	−	0.288727i	$-0.906768\pi$
$757$	−18.3979	+	18.3979i	−0.668684	+	0.668684i	0.288727	+	0.957411i	$0.406768\pi$
$758$	5.40358	+	26.9241i	0.196267	+	0.977927i
$759$			11.9501i			0.433762i
$760$	−2.42347	−	0.469102i	−0.0879084	−	0.0170161i
$761$		−	51.2094i		−	1.85634i	−0.372159	−	0.928169i	$-0.621382\pi$
$761$		−	51.2094i		−	1.85634i	0.372159	−	0.928169i	$-0.378618\pi$
$762$	6.95546	−	1.39594i	0.251970	−	0.0505695i
$763$	−7.93923	+	7.93923i	−0.287420	+	0.287420i
$764$	14.1186	+	33.7572i	0.510794	+	1.22129i
$765$	−0.806634	−	0.806634i	−0.0291639	−	0.0291639i
$766$	9.74149	−	14.6335i	0.351974	−	0.528728i
$767$	6.97987			0.252029
$768$	−11.1573	+	11.4679i	−0.402606	+	0.413814i
$769$	40.3794			1.45612			0.728060	−	0.685514i	$-0.240422\pi$
$769$	40.3794			1.45612			0.728060	+	0.685514i	$0.240422\pi$
$770$	−0.585874	+	0.880088i	−0.0211134	+	0.0317162i
$771$	−10.2700	−	10.2700i	−0.369863	−	0.369863i
$772$	−3.55306	−	8.49528i	−0.127878	−	0.305752i
$773$	34.3666	−	34.3666i	1.23608	−	1.23608i	0.274491	−	0.961590i	$-0.411491\pi$
$773$	34.3666	−	34.3666i	1.23608	−	1.23608i	0.961590	−	0.274491i	$-0.0885092\pi$
$774$	13.0330	−	2.61567i	0.468460	−	0.0940185i
$775$			44.0319i			1.58167i
$776$	27.1675	+	5.25871i	0.975256	+	0.188777i
$777$			9.56417i			0.343113i
$778$	4.90833	+	24.4564i	0.175972	+	0.876806i
$779$	24.3283	−	24.3283i	0.871651	−	0.871651i
$780$	0.768961	−	1.87461i	0.0275332	−	0.0671217i
$781$	−29.6076	−	29.6076i	−1.05944	−	1.05944i
$782$	21.4662	+	14.2900i	0.767629	+	0.511010i
$783$	3.61378			0.129146
$784$	2.80895	−	2.84777i	0.100320	−	0.101706i
$785$	−1.27789			−0.0456099
$786$	−4.99630	−	3.32603i	−0.178212	−	0.118636i
$787$	−29.0184	−	29.0184i	−1.03439	−	1.03439i	−0.999387	−	0.0350069i	$-0.988855\pi$
$787$	−29.0184	−	29.0184i	−1.03439	−	1.03439i	−0.0350069	−	0.999387i	$-0.511145\pi$
$788$	33.3300	+	13.6719i	1.18733	+	0.487043i
$789$	13.5104	−	13.5104i	0.480982	−	0.480982i
$790$	−0.246099	−	1.22622i	−0.00875580	−	0.0436270i
$791$			1.35750i			0.0482673i
$792$	−6.24129	−	9.23746i	−0.221775	−	0.328239i
$793$		−	34.8913i		−	1.23903i
$794$	16.5491	−	3.32136i	0.587307	−	0.117871i
$795$	−0.177625	+	0.177625i	−0.00629971	+	0.00629971i
$796$	−23.8078	+	9.95737i	−0.843845	+	0.352929i
$797$	3.81255	+	3.81255i	0.135047	+	0.135047i	0.771399	−	0.636352i	$-0.219557\pi$
$797$	3.81255	+	3.81255i	0.135047	+	0.135047i	−0.636352	+	0.771399i	$0.719557\pi$
$798$	−3.60589	+	5.41669i	−0.127647	+	0.191749i
$799$	39.3073			1.39059
$800$	−27.4932	+	5.71437i	−0.972031	+	0.202034i
$801$	−13.9870			−0.494206
$802$	−1.33104	+	1.99946i	−0.0470005	+	0.0706032i
$803$	30.6320	+	30.6320i	1.08098	+	1.08098i
$804$	−19.2508	+	8.05147i	−0.678925	+	0.283953i
$805$	−0.406629	+	0.406629i	−0.0143318	+	0.0143318i
$806$	−65.6932	+	13.1844i	−2.31394	+	0.464401i
$807$		−	17.9716i		−	0.632629i
$808$	−25.5191	+	17.2420i	−0.897757	+	0.606570i
$809$			41.2180i			1.44915i	0.689196	+	0.724575i	$0.257964\pi$
$809$			41.2180i			1.44915i	−0.689196	+	0.724575i	$0.742036\pi$
$810$	0.0527819	+	0.262993i	0.00185457	+	0.00924063i
$811$	4.84442	−	4.84442i	0.170111	−	0.170111i	−0.616917	−	0.787028i	$-0.711619\pi$
$811$	4.84442	−	4.84442i	0.170111	−	0.170111i	0.787028	+	0.616917i	$0.211619\pi$
$812$	−6.68686	−	2.74294i	−0.234663	−	0.0962583i
$813$	−16.0414	−	16.0414i	−0.562595	−	0.562595i
$814$	−44.3781	−	29.5425i	−1.55545	−	1.03546i
$815$	4.01028			0.140474
$816$	−24.0568	+	0.165119i	−0.842155	+	0.00578032i
$817$	43.2493			1.51310
$818$	27.9629	+	18.6149i	0.977699	+	0.650854i
$819$	−3.77686	−	3.77686i	−0.131974	−	0.131974i
$820$	−1.07649	+	2.62431i	−0.0375926	+	0.0916449i
$821$	−34.1175	+	34.1175i	−1.19071	+	1.19071i	−0.213840	+	0.976869i	$0.568597\pi$
$821$	−34.1175	+	34.1175i	−1.19071	+	1.19071i	−0.976869	+	0.213840i	$0.931403\pi$
$822$	−5.93611	−	29.5775i	−0.207046	−	1.03163i
$823$		−	37.9543i		−	1.32301i	−0.749943	−	0.661503i	$-0.769919\pi$
$823$		−	37.9543i		−	1.32301i	0.749943	−	0.661503i	$-0.230081\pi$
$824$	4.56974	−	23.6081i	0.159195	−	0.822428i
$825$		−	19.5658i		−	0.681193i
$826$	1.81193	−	0.363648i	0.0630451	−	0.0126529i
$827$	28.8859	−	28.8859i	1.00446	−	1.00446i	0.00447096	−	0.999990i	$-0.498577\pi$
$827$	28.8859	−	28.8859i	1.00446	−	1.00446i	0.999990	−	0.00447096i	$-0.00142316\pi$
$828$	−2.33970	−	5.59415i	−0.0813100	−	0.194410i
$829$	16.2153	+	16.2153i	0.563181	+	0.563181i	0.930210	−	0.367029i	$-0.119625\pi$
$829$	16.2153	+	16.2153i	0.563181	+	0.563181i	−0.367029	+	0.930210i	$0.619625\pi$
$830$	−0.133823	+	0.201026i	−0.00464507	+	0.00697773i
$831$	−6.50177			−0.225544
$832$	−16.7578	−	39.3072i	−0.580971	−	1.36273i
$833$	6.01433			0.208384
$834$	2.50050	−	3.75619i	0.0865851	−	0.130066i
$835$	−1.92306	−	1.92306i	−0.0665502	−	0.0665502i
$836$	−13.9955	−	33.4629i	−0.484045	−	1.15734i
$837$	6.27218	−	6.27218i	0.216798	−	0.216798i
$838$	24.0031	−	4.81735i	0.829174	−	0.166413i
$839$		−	24.8586i		−	0.858216i	−0.903253	−	0.429108i	$-0.858828\pi$
$839$		−	24.8586i		−	0.858216i	0.903253	−	0.429108i	$-0.141172\pi$
$840$	0.101951	−	0.526698i	0.00351765	−	0.0181728i
$841$		−	15.9406i		−	0.549675i
$842$	6.72859	+	33.5262i	0.231883	+	1.15539i
$843$	14.5636	−	14.5636i	0.501599	−	0.501599i
$844$	−18.7203	+	45.6371i	−0.644378	+	1.57089i
$845$	2.08278	+	2.08278i	0.0716500	+	0.0716500i
$846$	−7.69386	−	5.12180i	−0.264520	−	0.176091i
$847$	−4.53555			−0.155843
$848$	0.0363601	+	5.29743i	0.00124861	+	0.181914i
$849$	−4.74420			−0.162821
$850$	−35.1463	−	23.3969i	−1.20551	−	0.802506i
$851$	−20.5041	−	20.5041i	−0.702872	−	0.702872i
$852$	19.6569	+	8.06322i	0.673433	+	0.276241i
$853$	20.4838	−	20.4838i	0.701354	−	0.701354i	−0.263347	−	0.964701i	$-0.584827\pi$
$853$	20.4838	−	20.4838i	0.701354	−	0.701354i	0.964701	+	0.263347i	$0.0848266\pi$
$854$	−1.81782	−	9.05756i	−0.0622046	−	0.309943i
$855$			0.872729i			0.0298467i
$856$	−4.19060	+	2.83138i	−0.143232	+	0.0967747i
$857$		−	30.9795i		−	1.05824i	−0.848548	−	0.529119i	$-0.822522\pi$
$857$		−	30.9795i		−	1.05824i	0.848548	−	0.529119i	$-0.177478\pi$
$858$	29.1911	−	5.85855i	0.996566	−	0.200008i
$859$	−3.04764	+	3.04764i	−0.103984	+	0.103984i	−0.757185	−	0.653201i	$-0.773426\pi$
$859$	−3.04764	+	3.04764i	−0.103984	+	0.103984i	0.653201	+	0.757185i	$0.273426\pi$
$860$	−3.28952	+	1.37581i	−0.112172	+	0.0469147i
$861$	5.28733	+	5.28733i	0.180192	+	0.180192i
$862$	21.4357	−	32.2002i	0.730101	−	1.09674i
$863$	8.08269			0.275138			0.137569	−	0.990492i	$-0.456071\pi$
$863$	8.08269			0.275138			0.137569	+	0.990492i	$0.456071\pi$
$864$	4.73029	+	3.10231i	0.160928	+	0.105543i
$865$	−1.64942			−0.0560820
$866$	12.4535	−	18.7073i	0.423185	−	0.635700i
$867$	−13.5568	−	13.5568i	−0.460413	−	0.460413i
$868$	−16.3666	+	6.84517i	−0.555519	+	0.232340i
$869$	12.9949	−	12.9949i	0.440822	−	0.440822i
$870$	−0.950400	+	0.190742i	−0.0322216	+	0.00646677i
$871$		−	55.7277i		−	1.88826i
$872$	17.7789	+	26.3138i	0.602070	+	0.891096i
$873$		−	9.78344i		−	0.331119i
$874$	−3.88208	−	19.3430i	−0.131313	−	0.654287i
$875$	1.33636	−	1.33636i	0.0451773	−	0.0451773i
$876$	−20.3370	−	8.34221i	−0.687124	−	0.281857i
$877$	21.9677	+	21.9677i	0.741798	+	0.741798i	0.972924	−	0.231126i	$-0.0742409\pi$
$877$	21.9677	+	21.9677i	0.741798	+	0.741798i	−0.231126	+	0.972924i	$0.574241\pi$
$878$	26.7198	+	17.7873i	0.901749	+	0.600294i
$879$	−12.0332			−0.405868
$880$	2.12899	+	2.09996i	0.0717681	+	0.0707897i
$881$	−50.0647			−1.68672			−0.843361	−	0.537348i	$-0.819426\pi$
$881$	−50.0647			−1.68672			−0.843361	+	0.537348i	$0.819426\pi$
$882$	−1.17722	−	0.783676i	−0.0396391	−	0.0263877i
$883$	6.11176	+	6.11176i	0.205677	+	0.205677i	0.802427	−	0.596750i	$-0.203542\pi$
$883$	6.11176	+	6.11176i	0.205677	+	0.205677i	−0.596750	+	0.802427i	$0.703542\pi$
$884$	24.3830	−	59.4420i	0.820090	−	1.99925i
$885$	0.175263	−	0.175263i	0.00589140	−	0.00589140i
$886$	9.50893	+	47.3796i	0.319459	+	1.59175i
$887$			42.6066i			1.43059i	0.698824	+	0.715294i	$0.253707\pi$
$887$			42.6066i			1.43059i	−0.698824	+	0.715294i	$0.746293\pi$
$888$	26.5586	+	5.14085i	0.891248	+	0.172516i
$889$			5.01632i			0.168242i
$890$	3.67848	−	0.738260i	0.123303	−	0.0247465i
$891$	−2.78707	+	2.78707i	−0.0933705	+	0.0933705i
$892$	4.18602	+	10.0087i	0.140158	+	0.335115i
$893$	−21.2641	−	21.2641i	−0.711575	−	0.711575i
$894$	7.65850	−	11.5044i	0.256138	−	0.384766i
$895$	−0.179623			−0.00600413
$896$	−6.39809	−	9.33083i	−0.213745	−	0.311721i
$897$	16.1940			0.540703
$898$	−3.48142	+	5.22972i	−0.116177	+	0.174518i
$899$	22.6663	+	22.6663i	0.755964	+	0.755964i
$900$	3.83075	+	9.15923i	0.127692	+	0.305308i
$901$	−5.63232	+	5.63232i	−0.187640	+	0.187640i
$902$	−40.8653	+	8.20153i	−1.36067	+	0.273081i
$903$			9.39947i			0.312795i
$904$	3.76963	+	0.729674i	0.125376	+	0.0242686i
$905$		−	1.91431i		−	0.0636340i
$906$	−0.702164	−	3.49863i	−0.0233278	−	0.116234i
$907$	21.8484	−	21.8484i	0.725464	−	0.725464i	−0.244249	−	0.969713i	$-0.578541\pi$
$907$	21.8484	−	21.8484i	0.725464	−	0.725464i	0.969713	+	0.244249i	$0.0785414\pi$
$908$	−2.41697	+	5.89219i	−0.0802100	+	0.195539i
$909$	7.69946	+	7.69946i	0.255375	+	0.255375i
$910$	1.19264	+	0.793939i	0.0395356	+	0.0263188i
$911$	−30.3818			−1.00659			−0.503297	−	0.864113i	$-0.667880\pi$
$911$	−30.3818			−1.00659			−0.503297	+	0.864113i	$0.667880\pi$
$912$	13.1033	+	12.9247i	0.433894	+	0.427978i
$913$	−3.54857			−0.117441
$914$	−40.3596	−	26.8674i	−1.33498	−	0.888694i
$915$	−0.876114	−	0.876114i	−0.0289634	−	0.0289634i
$916$	−14.8547	−	6.09337i	−0.490813	−	0.201331i
$917$	3.00106	−	3.00106i	0.0991038	−	0.0991038i
$918$	1.67366	+	8.33926i	0.0552391	+	0.275237i
$919$		−	19.9349i		−	0.657591i	−0.944401	−	0.328796i	$-0.893357\pi$
$919$		−	19.9349i		−	0.657591i	0.944401	−	0.328796i	$-0.106643\pi$
$920$	0.910593	+	1.34773i	0.0300214	+	0.0444333i
$921$		−	6.11931i		−	0.201638i
$922$	−1.12707	+	0.226199i	−0.0371180	+	0.00744947i
$923$	−40.1223	+	40.1223i	−1.32064	+	1.32064i
$924$	7.27258	−	3.04168i	0.239250	−	0.100064i
$925$	33.5711	+	33.5711i	1.10381	+	1.10381i
$926$	7.24206	−	10.8789i	0.237989	−	0.357502i
$927$	−8.50167			−0.279231
$928$	−11.2111	+	17.0943i	−0.368022	+	0.561146i
$929$	−36.3990			−1.19421			−0.597107	−	0.802162i	$-0.703683\pi$
$929$	−36.3990			−1.19421			−0.597107	+	0.802162i	$0.703683\pi$
$930$	−1.31848	+	1.98060i	−0.0432348	+	0.0649464i
$931$	−3.25357	−	3.25357i	−0.106632	−	0.106632i
$932$	−46.5061	+	19.4507i	−1.52336	+	0.637130i
$933$	−8.99329	+	8.99329i	−0.294427	+	0.294427i
$934$	−41.4998	+	8.32887i	−1.35791	+	0.272529i
$935$			4.49630i			0.147045i
$936$	−12.5180	+	8.45781i	−0.409164	+	0.276452i
$937$			13.3858i			0.437294i	0.975804	+	0.218647i	$0.0701644\pi$
$937$			13.3858i			0.437294i	−0.975804	+	0.218647i	$0.929836\pi$
$938$	−2.90339	−	14.4665i	−0.0947990	−	0.472349i
$939$	14.9176	−	14.9176i	0.486819	−	0.486819i
$940$	2.29377	+	0.940901i	0.0748145	+	0.0306888i
$941$	0.359294	+	0.359294i	0.0117126	+	0.0117126i	0.712939	−	0.701226i	$-0.247364\pi$
$941$	0.359294	+	0.359294i	0.0117126	+	0.0117126i	−0.701226	+	0.712939i	$0.747364\pi$
$942$	7.93137	+	5.27991i	0.258418	+	0.172029i
$943$	−22.6704			−0.738251
$944$	−0.0358766	−	5.22698i	−0.00116768	−	0.170124i
$945$	−0.189672			−0.00617005
$946$	−43.6139	−	29.0338i	−1.41801	−	0.943969i
$947$	18.9214	+	18.9214i	0.614863	+	0.614863i	0.944209	−	0.329346i	$-0.106828\pi$
$947$	18.9214	+	18.9214i	0.614863	+	0.614863i	−0.329346	+	0.944209i	$0.606828\pi$
$948$	−3.53898	+	8.62749i	−0.114941	+	0.280208i
$949$	41.5106	−	41.5106i	1.34749	−	1.34749i
$950$	6.35609	+	31.6701i	0.206219	+	1.02751i
$951$		−	24.8817i		−	0.806844i
$952$	3.23277	−	16.7011i	0.104775	−	0.541286i
$953$		−	1.05352i		−	0.0341267i	−0.999854	−	0.0170634i	$-0.994568\pi$
$953$		−	1.05352i		−	0.0341267i	0.999854	−	0.0170634i	$-0.00543170\pi$
$954$	1.83635	−	0.368549i	0.0594540	−	0.0119322i
$955$	−2.45375	+	2.45375i	−0.0794016	+	0.0794016i
$956$	8.17796	+	19.5533i	0.264494	+	0.632398i
$957$	−10.0719	−	10.0719i	−0.325578	−	0.325578i
$958$	25.8370	−	38.8117i	0.834754	−	1.25395i
$959$	21.3315			0.688830
$960$	−1.40778	−	0.566213i	−0.0454359	−	0.0182744i
$961$	47.6806			1.53808
$962$	−40.0341	+	60.1384i	−1.29075	+	1.93894i
$963$	1.26436	+	1.26436i	0.0407436	+	0.0407436i
$964$	11.6829	+	27.9334i	0.376280	+	0.899675i
$965$	0.617507	−	0.617507i	0.0198782	−	0.0198782i
$966$	4.20387	−	0.843702i	0.135257	−	0.0271457i
$967$		−	10.9429i		−	0.351899i	−0.984399	−	0.175950i	$-0.943700\pi$
$967$		−	10.9429i		−	0.351899i	0.984399	−	0.175950i	$-0.0562996\pi$
$968$	−2.43791	+	12.5947i	−0.0783574	+	0.404809i
$969$			27.6734i			0.888998i
$970$	0.516388	+	2.57298i	0.0165802	+	0.0826133i
$971$	27.3759	−	27.3759i	0.878535	−	0.878535i	−0.114848	−	0.993383i	$-0.536638\pi$
$971$	27.3759	−	27.3759i	0.878535	−	0.878535i	0.993383	+	0.114848i	$0.0366381\pi$
$972$	0.759021	−	1.85037i	0.0243456	−	0.0593508i
$973$	2.25618	+	2.25618i	0.0723300	+	0.0723300i
$974$	5.57171	+	3.70909i	0.178529	+	0.118847i
$975$	−26.5143			−0.849137
$976$	−26.1289	+	0.179342i	−0.836365	+	0.00574058i
$977$	−34.7701			−1.11239			−0.556197	−	0.831051i	$-0.687740\pi$
$977$	−34.7701			−1.11239			−0.556197	+	0.831051i	$0.687740\pi$
$978$	−24.8902	−	16.5694i	−0.795901	−	0.529831i
$979$	38.9828	+	38.9828i	1.24590	+	1.24590i
$980$	0.350965	+	0.143965i	0.0112112	+	0.00459881i
$981$	7.93923	−	7.93923i	0.253480	−	0.253480i
$982$	−11.2310	−	55.9600i	−0.358396	−	1.78576i
$983$			35.3780i			1.12838i	0.825644	+	0.564192i	$0.190812\pi$
$983$			35.3780i			1.12838i	−0.825644	+	0.564192i	$0.809188\pi$
$984$	17.5243	−	11.8403i	0.558654	−	0.377455i
$985$			3.41649i			0.108859i
$986$	−30.1363	+	6.04825i	−0.959735	+	0.192616i
$987$	4.62137	−	4.62137i	0.147100	−	0.147100i
$988$	−45.3468	+	18.9658i	−1.44267	+	0.603384i
$989$	−20.1510	−	20.1510i	−0.640765	−	0.640765i
$990$	0.585874	−	0.880088i	0.0186203	−	0.0279710i
$991$	−32.6273			−1.03644			−0.518220	−	0.855248i	$-0.673405\pi$
$991$	−32.6273			−1.03644			−0.518220	+	0.855248i	$0.673405\pi$
$992$	10.2110	+	49.1275i	0.324200	+	1.55980i
$993$	12.6401			0.401122
$994$	−8.32513	+	12.5058i	−0.264057	+	0.396661i
$995$	−1.73055	−	1.73055i	−0.0548620	−	0.0548620i
$996$	1.66117	−	0.694770i	0.0526363	−	0.0220146i
$997$	−32.3612	+	32.3612i	−1.02489	+	1.02489i	−0.0252082	+	0.999682i	$0.508025\pi$
$997$	−32.3612	+	32.3612i	−1.02489	+	1.02489i	−0.999682	+	0.0252082i	$0.991975\pi$
$998$	−16.5074	+	3.31298i	−0.522532	+	0.104870i
$999$		−	9.56417i		−	0.302597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.a.253.7	yes	20
4.3	odd	2		1344.2.w.a.337.8		20
8.3	odd	2		2688.2.w.b.673.3		20
8.5	even	2		2688.2.w.a.673.8		20
16.3	odd	4		2688.2.w.b.2017.3		20
16.5	even	4	inner	336.2.w.a.85.7	✓	20
16.11	odd	4		1344.2.w.a.1009.8		20
16.13	even	4		2688.2.w.a.2017.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.a.85.7	✓	20	16.5	even	4	inner
336.2.w.a.253.7	yes	20	1.1	even	1	trivial
1344.2.w.a.337.8		20	4.3	odd	2
1344.2.w.a.1009.8		20	16.11	odd	4
2688.2.w.a.673.8		20	8.5	even	2
2688.2.w.a.2017.8		20	16.13	even	4
2688.2.w.b.673.3		20	8.3	odd	2
2688.2.w.b.2017.3		20	16.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.783676 - 1.17722i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.771704 - 1.84512i) q^{4} +(0.134119 - 0.134119i) q^{5} +(-1.38656 + 0.278279i) q^{6} -1.00000i q^{7} +(-2.77688 - 0.537511i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.783676 - 1.17722i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.771704 - 1.84512i) q^{4} +(0.134119 - 0.134119i) q^{5} +(-1.38656 + 0.278279i) q^{6} -1.00000i q^{7} +(-2.77688 - 0.537511i) q^{8} +1.00000i q^{9} +(-0.0527819 - 0.262993i) q^{10} +(2.78707 - 2.78707i) q^{11} +(-0.759021 + 1.85037i) q^{12} +(-3.77686 - 3.77686i) q^{13} +(-1.17722 - 0.783676i) q^{14} -0.189672 q^{15} +(-2.80895 + 2.84777i) q^{16} -6.01433 q^{17} +(1.17722 + 0.783676i) q^{18} +(3.25357 + 3.25357i) q^{19} +(-0.350965 - 0.143965i) q^{20} +(-0.707107 + 0.707107i) q^{21} +(-1.09684 - 5.46517i) q^{22} -3.03186i q^{23} +(1.58348 + 2.34363i) q^{24} +4.96402i q^{25} +(-7.40605 + 1.48637i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-1.84512 + 0.771704i) q^{28} +(2.55533 + 2.55533i) q^{29} +(-0.148642 + 0.223287i) q^{30} +8.87021 q^{31} +(1.15116 + 5.53849i) q^{32} -3.94152 q^{33} +(-4.71329 + 7.08020i) q^{34} +(-0.134119 - 0.134119i) q^{35} +(1.84512 - 0.771704i) q^{36} +(6.76289 - 6.76289i) q^{37} +(6.37992 - 1.28043i) q^{38} +5.34129i q^{39} +(-0.444522 + 0.300342i) q^{40} -7.47741i q^{41} +(0.278279 + 1.38656i) q^{42} +(6.64643 - 6.64643i) q^{43} +(-7.29328 - 2.99169i) q^{44} +(0.134119 + 0.134119i) q^{45} +(-3.56917 - 2.37599i) q^{46} -6.53561 q^{47} +(3.99991 - 0.0274543i) q^{48} -1.00000 q^{49} +(5.84376 + 3.89019i) q^{50} +(4.25278 + 4.25278i) q^{51} +(-4.05415 + 9.88339i) q^{52} +(0.936484 - 0.936484i) q^{53} +(-0.278279 - 1.38656i) q^{54} -0.747597i q^{55} +(-0.537511 + 2.77688i) q^{56} -4.60125i q^{57} +(5.01074 - 1.00564i) q^{58} +(-0.924030 + 0.924030i) q^{59} +(0.146371 + 0.349969i) q^{60} +(4.61909 + 4.61909i) q^{61} +(6.95137 - 10.4422i) q^{62} +1.00000 q^{63} +(7.42216 + 2.98521i) q^{64} -1.01310 q^{65} +(-3.08887 + 4.64004i) q^{66} +(7.37751 + 7.37751i) q^{67} +(4.64128 + 11.0972i) q^{68} +(-2.14385 + 2.14385i) q^{69} +(-0.262993 + 0.0527819i) q^{70} -10.6232i q^{71} +(0.537511 - 2.77688i) q^{72} +10.9907i q^{73} +(-2.66151 - 13.2613i) q^{74} +(3.51010 - 3.51010i) q^{75} +(3.49244 - 8.51403i) q^{76} +(-2.78707 - 2.78707i) q^{77} +(6.28789 + 4.18584i) q^{78} +4.66256 q^{79} +(0.00520732 + 0.758672i) q^{80} -1.00000 q^{81} +(-8.80257 - 5.85987i) q^{82} +(-0.636613 - 0.636613i) q^{83} +(1.85037 + 0.759021i) q^{84} +(-0.806634 + 0.806634i) q^{85} +(-2.61567 - 13.0330i) q^{86} -3.61378i q^{87} +(-9.23746 + 6.24129i) q^{88} +13.9870i q^{89} +(0.262993 - 0.0527819i) q^{90} +(-3.77686 + 3.77686i) q^{91} +(-5.59415 + 2.33970i) q^{92} +(-6.27218 - 6.27218i) q^{93} +(-5.12180 + 7.69386i) q^{94} +0.872729 q^{95} +(3.10231 - 4.73029i) q^{96} -9.78344 q^{97} +(-0.783676 + 1.17722i) q^{98} +(2.78707 + 2.78707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4}+O(q^{10}) \) 20 * q + 4 * q^4	\( 20 q + 4 q^{4} - 4 q^{10} + 12 q^{11} - 8 q^{12} + 4 q^{14} + 8 q^{15} - 4 q^{18} + 8 q^{19} + 28 q^{20} - 12 q^{22} + 8 q^{24} - 20 q^{26} - 4 q^{28} + 12 q^{29} + 8 q^{30} - 24 q^{33} - 44 q^{34} + 4 q^{36} + 12 q^{37} - 4 q^{38} + 16 q^{40} + 4 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{48} - 20 q^{49} + 48 q^{50} - 8 q^{51} + 16 q^{52} - 36 q^{53} - 4 q^{54} - 16 q^{56} + 16 q^{58} - 12 q^{60} + 8 q^{61} + 12 q^{62} + 20 q^{63} - 32 q^{64} + 16 q^{65} - 24 q^{66} - 12 q^{67} + 4 q^{68} - 16 q^{69} - 20 q^{70} + 16 q^{72} - 16 q^{74} - 16 q^{75} - 32 q^{76} - 12 q^{77} + 12 q^{78} + 24 q^{79} - 8 q^{80} - 20 q^{81} - 76 q^{82} + 40 q^{83} - 16 q^{85} - 84 q^{86} + 16 q^{88} + 20 q^{90} - 4 q^{92} - 32 q^{94} - 72 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 - 4 * q^10 + 12 * q^11 - 8 * q^12 + 4 * q^14 + 8 * q^15 - 4 * q^18 + 8 * q^19 + 28 * q^20 - 12 * q^22 + 8 * q^24 - 20 * q^26 - 4 * q^28 + 12 * q^29 + 8 * q^30 - 24 * q^33 - 44 * q^34 + 4 * q^36 + 12 * q^37 - 4 * q^38 + 16 * q^40 + 4 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^46 - 16 * q^48 - 20 * q^49 + 48 * q^50 - 8 * q^51 + 16 * q^52 - 36 * q^53 - 4 * q^54 - 16 * q^56 + 16 * q^58 - 12 * q^60 + 8 * q^61 + 12 * q^62 + 20 * q^63 - 32 * q^64 + 16 * q^65 - 24 * q^66 - 12 * q^67 + 4 * q^68 - 16 * q^69 - 20 * q^70 + 16 * q^72 - 16 * q^74 - 16 * q^75 - 32 * q^76 - 12 * q^77 + 12 * q^78 + 24 * q^79 - 8 * q^80 - 20 * q^81 - 76 * q^82 + 40 * q^83 - 16 * q^85 - 84 * q^86 + 16 * q^88 + 20 * q^90 - 4 * q^92 - 32 * q^94 - 72 * q^97 + 12 * q^99

Introduction

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