LMFDB - Embedded newform 336.2.w.b.85.11

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			85.11
Character	$\chi$	$=$	336.85
Dual form			336.2.w.b.253.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.919506 - 1.07448i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.309018 - 1.97598i) q^{4} +(-1.77267 - 1.77267i) q^{5} +(-0.109584 - 1.40996i) q^{6} -1.00000i q^{7} +(-2.40730 - 1.48489i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.919506 - 1.07448i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.309018 - 1.97598i) q^{4} +(-1.77267 - 1.77267i) q^{5} +(-0.109584 - 1.40996i) q^{6} -1.00000i q^{7} +(-2.40730 - 1.48489i) q^{8} -1.00000i q^{9} +(-3.53468 + 0.274720i) q^{10} +(2.61271 + 2.61271i) q^{11} +(-1.61574 - 1.17872i) q^{12} +(-3.33586 + 3.33586i) q^{13} +(-1.07448 - 0.919506i) q^{14} -2.50694 q^{15} +(-3.80902 + 1.22123i) q^{16} +5.10041 q^{17} +(-1.07448 - 0.919506i) q^{18} +(0.678188 - 0.678188i) q^{19} +(-2.95498 + 4.05056i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(5.20971 - 0.404905i) q^{22} -7.10530i q^{23} +(-2.75220 + 0.652239i) q^{24} +1.28473i q^{25} +(0.516974 + 6.65165i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.97598 + 0.309018i) q^{28} +(7.37355 - 7.37355i) q^{29} +(-2.30514 + 2.69365i) q^{30} -0.578298 q^{31} +(-2.19023 + 5.21564i) q^{32} +3.69493 q^{33} +(4.68986 - 5.48029i) q^{34} +(-1.77267 + 1.77267i) q^{35} +(-1.97598 + 0.309018i) q^{36} +(6.93521 + 6.93521i) q^{37} +(-0.105102 - 1.35230i) q^{38} +4.71761i q^{39} +(1.63512 + 6.89958i) q^{40} -4.09322i q^{41} +(-1.40996 + 0.109584i) q^{42} +(3.04549 + 3.04549i) q^{43} +(4.35530 - 5.97005i) q^{44} +(-1.77267 + 1.77267i) q^{45} +(-7.63450 - 6.53336i) q^{46} -7.82190 q^{47} +(-1.82984 + 3.55692i) q^{48} -1.00000 q^{49} +(1.38041 + 1.18131i) q^{50} +(3.60654 - 3.60654i) q^{51} +(7.62243 + 5.56076i) q^{52} +(9.06508 + 9.06508i) q^{53} +(-1.40996 + 0.109584i) q^{54} -9.26295i q^{55} +(-1.48489 + 2.40730i) q^{56} -0.959103i q^{57} +(-1.14272 - 14.7028i) q^{58} +(-0.0513263 - 0.0513263i) q^{59} +(0.774688 + 4.95366i) q^{60} +(-7.18025 + 7.18025i) q^{61} +(-0.531749 + 0.621370i) q^{62} -1.00000 q^{63} +(3.59018 + 7.14917i) q^{64} +11.8268 q^{65} +(3.39751 - 3.97013i) q^{66} +(-7.45132 + 7.45132i) q^{67} +(-1.57612 - 10.0783i) q^{68} +(-5.02420 - 5.02420i) q^{69} +(0.274720 + 3.53468i) q^{70} -2.82386i q^{71} +(-1.48489 + 2.40730i) q^{72} +3.61089i q^{73} +(13.8287 - 1.07478i) q^{74} +(0.908439 + 0.908439i) q^{75} +(-1.54966 - 1.13052i) q^{76} +(2.61271 - 2.61271i) q^{77} +(5.06899 + 4.33787i) q^{78} -6.07405 q^{79} +(8.91697 + 4.58730i) q^{80} -1.00000 q^{81} +(-4.39808 - 3.76374i) q^{82} +(-2.13918 + 2.13918i) q^{83} +(-1.17872 + 1.61574i) q^{84} +(-9.04135 - 9.04135i) q^{85} +(6.07267 - 0.471975i) q^{86} -10.4278i q^{87} +(-2.40998 - 10.1692i) q^{88} +13.6149i q^{89} +(0.274720 + 3.53468i) q^{90} +(3.33586 + 3.33586i) q^{91} +(-14.0399 + 2.19566i) q^{92} +(-0.408919 + 0.408919i) q^{93} +(-7.19228 + 8.40448i) q^{94} -2.40441 q^{95} +(2.13929 + 5.23674i) q^{96} +10.1515 q^{97} +(-0.919506 + 1.07448i) q^{98} +(2.61271 - 2.61271i) 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 $

$2$	0.919506	−	1.07448i	0.650189	−	0.759773i
$2$	0.919506	−	1.07448i	0.650189	−	0.759773i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	−0.309018	−	1.97598i	−0.154509	−	0.987991i
$5$	−1.77267	−	1.77267i	−0.792763	−	0.792763i	0.189180	−	0.981942i	$-0.439417\pi$
$5$	−1.77267	−	1.77267i	−0.792763	−	0.792763i	−0.981942	+	0.189180i	$0.939417\pi$
$6$	−0.109584	−	1.40996i	−0.0447374	−	0.575614i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.40730	−	1.48489i	−0.851109	−	0.524989i
$9$		−	1.00000i		−	0.333333i
$10$	−3.53468	+	0.274720i	−1.11776	+	0.0868740i
$11$	2.61271	+	2.61271i	0.787762	+	0.787762i	0.981127	−	0.193365i	$-0.0619402\pi$
$11$	2.61271	+	2.61271i	0.787762	+	0.787762i	−0.193365	+	0.981127i	$0.561940\pi$
$12$	−1.61574	−	1.17872i	−0.466424	−	0.340268i
$13$	−3.33586	+	3.33586i	−0.925200	+	0.925200i	−0.997391	−	0.0721907i	$-0.977001\pi$
$13$	−3.33586	+	3.33586i	−0.925200	+	0.925200i	0.0721907	+	0.997391i	$0.477001\pi$
$14$	−1.07448	−	0.919506i	−0.287167	−	0.245748i
$15$	−2.50694			−0.647288
$16$	−3.80902	+	1.22123i	−0.952254	+	0.305307i
$17$	5.10041			1.23703			0.618516	−	0.785772i	$-0.287734\pi$
$17$	5.10041			1.23703			0.618516	+	0.785772i	$0.287734\pi$
$18$	−1.07448	−	0.919506i	−0.253258	−	0.216730i
$19$	0.678188	−	0.678188i	0.155587	−	0.155587i	−0.625021	−	0.780608i	$-0.714910\pi$
$19$	0.678188	−	0.678188i	0.155587	−	0.155587i	0.780608	+	0.625021i	$0.214910\pi$
$20$	−2.95498	+	4.05056i	−0.660754	+	0.905732i
$21$	−0.707107	−	0.707107i	−0.154303	−	0.154303i
$22$	5.20971	−	0.404905i	1.11071	−	0.0863259i
$23$		−	7.10530i		−	1.48156i	−0.671749	−	0.740778i	$-0.734457\pi$
$23$		−	7.10530i		−	1.48156i	0.671749	−	0.740778i	$-0.265543\pi$
$24$	−2.75220	+	0.652239i	−0.561790	+	0.133138i
$25$			1.28473i			0.256945i
$26$	0.516974	+	6.65165i	0.101387	+	1.30450i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.97598	+	0.309018i	−0.373426	+	0.0583989i
$29$	7.37355	−	7.37355i	1.36923	−	1.36923i	0.507700	−	0.861534i	$-0.330496\pi$
$29$	7.37355	−	7.37355i	1.36923	−	1.36923i	0.861534	−	0.507700i	$-0.169504\pi$
$30$	−2.30514	+	2.69365i	−0.420859	+	0.491792i
$31$	−0.578298			−0.103865			−0.0519327	−	0.998651i	$-0.516538\pi$
$31$	−0.578298			−0.103865			−0.0519327	+	0.998651i	$0.516538\pi$
$32$	−2.19023	+	5.21564i	−0.387181	+	0.922004i
$33$	3.69493			0.643205
$34$	4.68986	−	5.48029i	0.804304	−	0.939863i
$35$	−1.77267	+	1.77267i	−0.299636	+	0.299636i
$36$	−1.97598	+	0.309018i	−0.329330	+	0.0515030i
$37$	6.93521	+	6.93521i	1.14014	+	1.14014i	0.988424	+	0.151718i	$0.0484807\pi$
$37$	6.93521	+	6.93521i	1.14014	+	1.14014i	0.151718	+	0.988424i	$0.451519\pi$
$38$	−0.105102	−	1.35230i	−0.0170498	−	0.219372i
$39$			4.71761i			0.755423i
$40$	1.63512	+	6.89958i	0.258535	+	1.09092i
$41$		−	4.09322i		−	0.639253i	−0.947544	−	0.319627i	$-0.896443\pi$
$41$		−	4.09322i		−	0.639253i	0.947544	−	0.319627i	$-0.103557\pi$
$42$	−1.40996	+	0.109584i	−0.217562	+	0.0169091i
$43$	3.04549	+	3.04549i	0.464433	+	0.464433i	0.900105	−	0.435672i	$-0.143489\pi$
$43$	3.04549	+	3.04549i	0.464433	+	0.464433i	−0.435672	+	0.900105i	$0.643489\pi$
$44$	4.35530	−	5.97005i	0.656586	−	0.900018i
$45$	−1.77267	+	1.77267i	−0.264254	+	0.264254i
$46$	−7.63450	−	6.53336i	−1.12565	−	0.963292i
$47$	−7.82190			−1.14094			−0.570470	−	0.821318i	$-0.693239\pi$
$47$	−7.82190			−1.14094			−0.570470	+	0.821318i	$0.693239\pi$
$48$	−1.82984	+	3.55692i	−0.264115	+	0.513397i
$49$	−1.00000			−0.142857
$50$	1.38041	+	1.18131i	0.195220	+	0.167063i
$51$	3.60654	−	3.60654i	0.505016	−	0.505016i
$52$	7.62243	+	5.56076i	1.05704	+	0.771138i
$53$	9.06508	+	9.06508i	1.24518	+	1.24518i	0.957822	+	0.287362i	$0.0927782\pi$
$53$	9.06508	+	9.06508i	1.24518	+	1.24518i	0.287362	+	0.957822i	$0.407222\pi$
$54$	−1.40996	+	0.109584i	−0.191871	+	0.0149125i
$55$		−	9.26295i		−	1.24902i
$56$	−1.48489	+	2.40730i	−0.198427	+	0.321689i
$57$		−	0.959103i		−	0.127036i
$58$	−1.14272	−	14.7028i	−0.150046	−	1.93057i
$59$	−0.0513263	−	0.0513263i	−0.00668211	−	0.00668211i	0.703758	−	0.710440i	$-0.251504\pi$
$59$	−0.0513263	−	0.0513263i	−0.00668211	−	0.00668211i	−0.710440	+	0.703758i	$0.751504\pi$
$60$	0.774688	+	4.95366i	0.100012	+	0.639515i
$61$	−7.18025	+	7.18025i	−0.919337	+	0.919337i	−0.996981	−	0.0776442i	$-0.975260\pi$
$61$	−7.18025	+	7.18025i	−0.919337	+	0.919337i	0.0776442	+	0.996981i	$0.475260\pi$
$62$	−0.531749	+	0.621370i	−0.0675321	+	0.0789141i
$63$	−1.00000			−0.125988
$64$	3.59018	+	7.14917i	0.448772	+	0.893646i
$65$	11.8268			1.46693
$66$	3.39751	−	3.97013i	0.418205	−	0.488689i
$67$	−7.45132	+	7.45132i	−0.910324	+	0.910324i	−0.996297	−	0.0859737i	$-0.972600\pi$
$67$	−7.45132	+	7.45132i	−0.910324	+	0.910324i	0.0859737	+	0.996297i	$0.472600\pi$
$68$	−1.57612	−	10.0783i	−0.191132	−	1.22218i
$69$	−5.02420	−	5.02420i	−0.604843	−	0.604843i
$70$	0.274720	+	3.53468i	0.0328353	+	0.422475i
$71$		−	2.82386i		−	0.335130i	−0.985861	−	0.167565i	$-0.946410\pi$
$71$		−	2.82386i		−	0.335130i	0.985861	−	0.167565i	$-0.0535904\pi$
$72$	−1.48489	+	2.40730i	−0.174996	+	0.283703i
$73$			3.61089i			0.422623i	0.977419	+	0.211312i	$0.0677735\pi$
$73$			3.61089i			0.422623i	−0.977419	+	0.211312i	$0.932227\pi$
$74$	13.8287	−	1.07478i	1.60756	−	0.124941i
$75$	0.908439	+	0.908439i	0.104897	+	0.104897i
$76$	−1.54966	−	1.13052i	−0.177758	−	0.129679i
$77$	2.61271	−	2.61271i	0.297746	−	0.297746i
$78$	5.06899	+	4.33787i	0.573950	+	0.491167i
$79$	−6.07405			−0.683384			−0.341692	−	0.939812i	$-0.611000\pi$
$79$	−6.07405			−0.683384			−0.341692	+	0.939812i	$0.611000\pi$
$80$	8.91697	+	4.58730i	0.996947	+	0.512875i
$81$	−1.00000			−0.111111
$82$	−4.39808	−	3.76374i	−0.485687	−	0.415635i
$83$	−2.13918	+	2.13918i	−0.234806	+	0.234806i	−0.814695	−	0.579889i	$-0.803096\pi$
$83$	−2.13918	+	2.13918i	−0.234806	+	0.234806i	0.579889	+	0.814695i	$0.303096\pi$
$84$	−1.17872	+	1.61574i	−0.128609	+	0.176292i
$85$	−9.04135	−	9.04135i	−0.980672	−	0.980672i
$86$	6.07267	−	0.471975i	0.654833	−	0.0508944i
$87$		−	10.4278i		−	1.11797i
$88$	−2.40998	−	10.1692i	−0.256905	−	1.08404i
$89$			13.6149i			1.44318i	0.692323	+	0.721588i	$0.256588\pi$
$89$			13.6149i			1.44318i	−0.692323	+	0.721588i	$0.743412\pi$
$90$	0.274720	+	3.53468i	0.0289580	+	0.372588i
$91$	3.33586	+	3.33586i	0.349693	+	0.349693i
$92$	−14.0399	+	2.19566i	−1.46377	+	0.228914i
$93$	−0.408919	+	0.408919i	−0.0424029	+	0.0424029i
$94$	−7.19228	+	8.40448i	−0.741827	+	0.866856i
$95$	−2.40441			−0.246687
$96$	2.13929	+	5.23674i	0.218340	+	0.534472i
$97$	10.1515			1.03073			0.515365	−	0.856971i	$-0.327657\pi$
$97$	10.1515			1.03073			0.515365	+	0.856971i	$0.327657\pi$
$98$	−0.919506	+	1.07448i	−0.0928841	+	0.108539i
$99$	2.61271	−	2.61271i	0.262587	−	0.262587i
$100$	2.53860	−	0.397004i	0.253860	−	0.0397004i
$101$	2.71273	+	2.71273i	0.269926	+	0.269926i	0.829070	−	0.559144i	$-0.188870\pi$
$101$	2.71273	+	2.71273i	0.269926	+	0.269926i	−0.559144	+	0.829070i	$0.688870\pi$
$102$	−0.558923	−	7.19138i	−0.0553416	−	0.712053i
$103$		−	5.88978i		−	0.580337i	−0.956976	−	0.290169i	$-0.906289\pi$
$103$		−	5.88978i		−	0.580337i	0.956976	−	0.290169i	$-0.0937114\pi$
$104$	12.9838	−	3.07701i	1.27317	−	0.301726i
$105$			2.50694i			0.244652i
$106$	18.0756	−	1.40486i	1.75566	−	0.136452i
$107$	−0.487701	−	0.487701i	−0.0471478	−	0.0471478i	0.683140	−	0.730288i	$-0.260614\pi$
$107$	−0.487701	−	0.487701i	−0.0471478	−	0.0471478i	−0.730288	+	0.683140i	$0.760614\pi$
$108$	−1.17872	+	1.61574i	−0.113423	+	0.155475i
$109$	2.87978	−	2.87978i	0.275833	−	0.275833i	−0.555610	−	0.831443i	$-0.687515\pi$
$109$	2.87978	−	2.87978i	0.275833	−	0.275833i	0.831443	+	0.555610i	$0.187515\pi$
$110$	−9.95287	−	8.51734i	−0.948968	−	0.812097i
$111$	9.80787			0.930922
$112$	1.22123	+	3.80902i	0.115395	+	0.359918i
$113$	11.5452			1.08609			0.543043	−	0.839705i	$-0.317272\pi$
$113$	11.5452			1.08609			0.543043	+	0.839705i	$0.317272\pi$
$114$	−1.03054	−	0.881901i	−0.0965187	−	0.0825976i
$115$	−12.5954	+	12.5954i	−1.17452	+	1.17452i
$116$	−16.8486	−	12.2914i	−1.56435	−	1.14123i
$117$	3.33586	+	3.33586i	0.308400	+	0.308400i
$118$	−0.102344	+	0.00795428i	−0.00942152	+	0.000732251i
$119$		−	5.10041i		−	0.467554i
$120$	6.03494	+	3.72253i	0.550913	+	0.339819i
$121$			2.65251i			0.241137i
$122$	1.11276	+	14.3173i	0.100744	+	1.29623i
$123$	−2.89434	−	2.89434i	−0.260974	−	0.260974i
$124$	0.178704	+	1.14271i	0.0160481	+	0.102618i
$125$	−6.58596	+	6.58596i	−0.589066	+	0.589066i
$126$	−0.919506	+	1.07448i	−0.0819161	+	0.0957224i
$127$	3.13665			0.278332			0.139166	−	0.990269i	$-0.455558\pi$
$127$	3.13665			0.278332			0.139166	+	0.990269i	$0.455558\pi$
$128$	10.9828	+	2.71612i	0.970755	+	0.240074i
$129$	4.30698			0.379208
$130$	10.8748	−	12.7076i	0.953780	−	1.11453i
$131$	4.27459	−	4.27459i	0.373473	−	0.373473i	−0.495268	−	0.868740i	$-0.664930\pi$
$131$	4.27459	−	4.27459i	0.373473	−	0.373473i	0.868740	+	0.495268i	$0.164930\pi$
$132$	−1.14180	−	7.30112i	−0.0993809	−	0.635481i
$133$	−0.678188	−	0.678188i	−0.0588064	−	0.0588064i
$134$	1.15477	+	14.8578i	0.0997567	+	1.28352i
$135$			2.50694i			0.215763i
$136$	−12.2782	−	7.57357i	−1.05285	−	0.649428i
$137$			0.234016i			0.0199933i	0.999950	+	0.00999666i	$0.00318209\pi$
$137$			0.234016i			0.0199933i	−0.999950	+	0.00999666i	$0.996818\pi$
$138$	−10.0182	+	0.778626i	−0.852805	+	0.0662810i
$139$	−11.3997	−	11.3997i	−0.966908	−	0.966908i	0.0325622	−	0.999470i	$-0.489633\pi$
$139$	−11.3997	−	11.3997i	−0.966908	−	0.966908i	−0.999470	+	0.0325622i	$0.989633\pi$
$140$	4.05056	+	2.95498i	0.342334	+	0.249741i
$141$	−5.53092	+	5.53092i	−0.465787	+	0.465787i
$142$	−3.03418	−	2.59655i	−0.254623	−	0.217898i
$143$	−17.4313			−1.45767
$144$	1.22123	+	3.80902i	0.101769	+	0.317418i
$145$	−26.1418			−2.17095
$146$	3.87984	+	3.32024i	0.321097	+	0.274785i
$147$	−0.707107	+	0.707107i	−0.0583212	+	0.0583212i
$148$	11.5608	−	15.8470i	0.950289	−	1.30261i
$149$	−14.1300	−	14.1300i	−1.15757	−	1.15757i	−0.984996	−	0.172576i	$-0.944791\pi$
$149$	−14.1300	−	14.1300i	−1.15757	−	1.15757i	−0.172576	−	0.984996i	$-0.555209\pi$
$150$	1.81142	−	0.140785i	0.147901	−	0.0114951i
$151$			10.8320i			0.881496i	0.897631	+	0.440748i	$0.145287\pi$
$151$			10.8320i			0.881496i	−0.897631	+	0.440748i	$0.854713\pi$
$152$	−2.63964	+	0.625564i	−0.214103	+	0.0507400i
$153$		−	5.10041i		−	0.412344i
$154$	−0.404905	−	5.20971i	−0.0326281	−	0.419810i
$155$	1.02513	+	1.02513i	0.0823406	+	0.0823406i
$156$	9.32192	−	1.45783i	0.746351	−	0.116720i
$157$	−9.02649	+	9.02649i	−0.720392	+	0.720392i	−0.968685	−	0.248293i	$-0.920130\pi$
$157$	−9.02649	+	9.02649i	−0.720392	+	0.720392i	0.248293	+	0.968685i	$0.420130\pi$
$158$	−5.58512	+	6.52645i	−0.444329	+	0.519217i
$159$	12.8200			1.01669
$160$	13.1282	−	5.36307i	1.03787	−	0.423988i
$161$	−7.10530			−0.559976
$162$	−0.919506	+	1.07448i	−0.0722432	+	0.0844192i
$163$	8.46602	−	8.46602i	0.663110	−	0.663110i	−0.293002	−	0.956112i	$-0.594654\pi$
$163$	8.46602	−	8.46602i	0.663110	−	0.663110i	0.956112	+	0.293002i	$0.0946542\pi$
$164$	−8.08813	+	1.26488i	−0.631577	+	0.0987704i
$165$	−6.54990	−	6.54990i	−0.509909	−	0.509909i
$166$	0.331520	+	4.26550i	0.0257309	+	0.331067i
$167$			11.7115i			0.906267i	0.891443	+	0.453133i	$0.149694\pi$
$167$			11.7115i			0.906267i	−0.891443	+	0.453133i	$0.850306\pi$
$168$	0.652239	+	2.75220i	0.0503213	+	0.212337i
$169$		−	9.25588i		−	0.711991i
$170$	−18.0283	+	1.40118i	−1.38271	+	0.107466i
$171$	−0.678188	−	0.678188i	−0.0518624	−	0.0518624i
$172$	5.07673	−	6.95895i	0.387097	−	0.530615i
$173$	−3.58553	+	3.58553i	−0.272602	+	0.272602i	−0.830147	−	0.557545i	$-0.811744\pi$
$173$	−3.58553	+	3.58553i	−0.272602	+	0.272602i	0.557545	+	0.830147i	$0.311744\pi$
$174$	−11.2044	−	9.58840i	−0.849407	−	0.726895i
$175$	1.28473			0.0971162
$176$	−13.1426	−	6.76114i	−0.990659	−	0.509640i
$177$	−0.0725863			−0.00545592
$178$	14.6289	+	12.5190i	1.09649	+	0.938337i
$179$	−13.3866	+	13.3866i	−1.00056	+	1.00056i	−0.000564656		1.00000i	$0.500180\pi$
$179$	−13.3866	+	13.3866i	−1.00056	+	1.00056i	−1.00000		0.000564656i	$0.999820\pi$
$180$	4.05056	+	2.95498i	0.301911	+	0.220251i
$181$	0.420573	+	0.420573i	0.0312610	+	0.0312610i	0.722564	−	0.691304i	$-0.242963\pi$
$181$	0.420573	+	0.420573i	0.0312610	+	0.0312610i	−0.691304	+	0.722564i	$0.742963\pi$
$182$	6.65165	−	0.516974i	0.493053	−	0.0383207i
$183$			10.1544i			0.750635i
$184$	−10.5506	+	17.1046i	−0.777801	+	1.26097i
$185$		−	24.5877i		−	1.80772i
$186$	0.0633721	+	0.815378i	0.00464667	+	0.0597864i
$187$	13.3259	+	13.3259i	0.974486	+	0.974486i
$188$	2.41711	+	15.4559i	0.176286	+	1.12724i
$189$	−0.707107	+	0.707107i	−0.0514344	+	0.0514344i
$190$	−2.21087	+	2.58349i	−0.160393	+	0.187426i
$191$	5.00614			0.362232			0.181116	−	0.983462i	$-0.442029\pi$
$191$	5.00614			0.362232			0.181116	+	0.983462i	$0.442029\pi$
$192$	7.59387	+	2.51658i	0.548040	+	0.181619i
$193$	0.554572			0.0399190			0.0199595	−	0.999801i	$-0.493646\pi$
$193$	0.554572			0.0399190			0.0199595	+	0.999801i	$0.493646\pi$
$194$	9.33437	−	10.9076i	0.670169	−	0.783120i
$195$	8.36278	−	8.36278i	0.598871	−	0.598871i
$196$	0.309018	+	1.97598i	0.0220727	+	0.141142i
$197$	−7.75562	−	7.75562i	−0.552565	−	0.552565i	0.374615	−	0.927180i	$-0.377775\pi$
$197$	−7.75562	−	7.75562i	−0.552565	−	0.552565i	−0.927180	+	0.374615i	$0.877775\pi$
$198$	−0.404905	−	5.20971i	−0.0287753	−	0.370238i
$199$		−	23.6723i		−	1.67809i	−0.544065	−	0.839043i	$-0.683116\pi$
$199$		−	23.6723i		−	1.67809i	0.544065	−	0.839043i	$-0.316884\pi$
$200$	1.90768	−	3.09272i	0.134894	−	0.218688i
$201$			10.5378i			0.743276i
$202$	5.40914	−	0.420404i	0.380586	−	0.0295796i
$203$	−7.37355	−	7.37355i	−0.517522	−	0.517522i
$204$	−8.24094	−	6.01197i	−0.576981	−	0.420922i
$205$	−7.25593	+	7.25593i	−0.506776	+	0.506776i
$206$	−6.32846	−	5.41569i	−0.440924	−	0.377329i
$207$	−7.10530			−0.493852
$208$	8.63249	−	16.7802i	0.598555	−	1.16350i
$209$	3.54382			0.245131
$210$	2.69365	+	2.30514i	0.185880	+	0.159070i
$211$	−16.5001	+	16.5001i	−1.13591	+	1.13591i	−0.146736	+	0.989176i	$0.546877\pi$
$211$	−16.5001	+	16.5001i	−1.13591	+	1.13591i	−0.989176	+	0.146736i	$0.953123\pi$
$212$	15.1112	−	20.7137i	1.03784	−	1.42262i
$213$	−1.99677	−	1.99677i	−0.136816	−	0.136816i
$214$	−0.972469	+	0.0755814i	−0.0664766	+	0.00516664i
$215$		−	10.7973i		−	0.736370i
$216$	0.652239	+	2.75220i	0.0443792	+	0.187263i
$217$			0.578298i			0.0392574i
$218$	−0.446293	−	5.74224i	−0.0302268	−	0.388913i
$219$	2.55329	+	2.55329i	0.172535	+	0.172535i
$220$	−18.3034	+	2.86242i	−1.23402	+	0.192984i
$221$	−17.0142	+	17.0142i	−1.14450	+	1.14450i
$222$	9.01840	−	10.5384i	0.605275	−	0.707289i
$223$	16.7379			1.12085			0.560427	−	0.828204i	$-0.310637\pi$
$223$	16.7379			1.12085			0.560427	+	0.828204i	$0.310637\pi$
$224$	5.21564	+	2.19023i	0.348485	+	0.146341i
$225$	1.28473			0.0856484
$226$	10.6159	−	12.4051i	0.706160	−	0.825178i
$227$	1.57831	−	1.57831i	0.104756	−	0.104756i	−0.652786	−	0.757542i	$-0.726400\pi$
$227$	1.57831	−	1.57831i	0.104756	−	0.104756i	0.757542	+	0.652786i	$0.226400\pi$
$228$	−1.89517	+	0.296380i	−0.125511	+	0.0196282i
$229$	11.4540	+	11.4540i	0.756899	+	0.756899i	0.975757	−	0.218858i	$-0.0702331\pi$
$229$	11.4540	+	11.4540i	0.756899	+	0.756899i	−0.218858	+	0.975757i	$0.570233\pi$
$230$	1.95196	+	25.1150i	0.128709	+	1.65603i
$231$		−	3.69493i		−	0.243109i
$232$	−28.6993	+	6.80140i	−1.88420	+	0.446534i
$233$		−	11.4871i		−	0.752546i	−0.926509	−	0.376273i	$-0.877206\pi$
$233$		−	11.4871i		−	0.752546i	0.926509	−	0.376273i	$-0.122794\pi$
$234$	6.65165	−	0.516974i	0.434832	−	0.0337957i
$235$	13.8656	+	13.8656i	0.904495	+	0.904495i
$236$	−0.0855591	+	0.117281i	−0.00556942	+	0.00763431i
$237$	−4.29500	+	4.29500i	−0.278990	+	0.278990i
$238$	−5.48029	−	4.68986i	−0.355235	−	0.303998i
$239$	−16.9827			−1.09852			−0.549260	−	0.835652i	$-0.685090\pi$
$239$	−16.9827			−1.09852			−0.549260	+	0.835652i	$0.685090\pi$
$240$	9.54896	−	3.06154i	0.616383	−	0.197622i
$241$	−10.3821			−0.668767			−0.334383	−	0.942437i	$-0.608528\pi$
$241$	−10.3821			−0.668767			−0.334383	+	0.942437i	$0.608528\pi$
$242$	2.85007	+	2.43900i	0.183210	+	0.156785i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	16.4069	+	11.9692i	1.05034	+	0.766251i
$245$	1.77267	+	1.77267i	0.113252	+	0.113252i
$246$	−5.77128	+	0.448551i	−0.367963	+	0.0285985i
$247$			4.52468i			0.287898i
$248$	1.39214	+	0.858711i	0.0884008	+	0.0545282i
$249$			3.02526i			0.191718i
$250$	1.02066	+	13.1323i	0.0645521	+	0.830560i
$251$	−15.2558	−	15.2558i	−0.962940	−	0.962940i	0.0363971	−	0.999337i	$-0.488412\pi$
$251$	−15.2558	−	15.2558i	−0.962940	−	0.962940i	−0.999337	+	0.0363971i	$0.988412\pi$
$252$	0.309018	+	1.97598i	0.0194663	+	0.124475i
$253$	18.5641	−	18.5641i	1.16711	−	1.16711i
$254$	2.88416	−	3.37027i	0.180969	−	0.211469i
$255$	−12.7864			−0.800716
$256$	13.0172	−	9.30335i	0.813575	−	0.581460i
$257$	10.9124			0.680698			0.340349	−	0.940299i	$-0.389455\pi$
$257$	10.9124			0.680698			0.340349	+	0.940299i	$0.389455\pi$
$258$	3.96029	−	4.62776i	0.246557	−	0.288112i
$259$	6.93521	−	6.93521i	0.430933	−	0.430933i
$260$	−3.65468	−	23.3695i	−0.226654	−	1.44931i
$261$	−7.37355	−	7.37355i	−0.456411	−	0.456411i
$262$	−0.662454	−	8.52347i	−0.0409266	−	0.526582i
$263$			3.94477i			0.243245i	0.992576	+	0.121622i	$0.0388097\pi$
$263$			3.94477i			0.243245i	−0.992576	+	0.121622i	$0.961190\pi$
$264$	−8.89480	−	5.48658i	−0.547437	−	0.337676i
$265$		−	32.1388i		−	1.97427i
$266$	−1.35230	+	0.105102i	−0.0829147	+	0.00644423i
$267$	9.62719	+	9.62719i	0.589174	+	0.589174i
$268$	17.0263	+	12.4211i	1.04005	+	0.758739i
$269$	20.9774	−	20.9774i	1.27901	−	1.27901i	0.337795	−	0.941220i	$-0.390319\pi$
$269$	20.9774	−	20.9774i	1.27901	−	1.27901i	0.941220	−	0.337795i	$-0.109681\pi$
$270$	2.69365	+	2.30514i	0.163931	+	0.140286i
$271$	2.40623			0.146168			0.0730841	−	0.997326i	$-0.476716\pi$
$271$	2.40623			0.146168			0.0730841	+	0.997326i	$0.476716\pi$
$272$	−19.4275	+	6.22877i	−1.17797	+	0.377674i
$273$	4.71761			0.285523
$274$	0.251445	+	0.215179i	0.0151904	+	0.0129994i
$275$	−3.35662	+	3.35662i	−0.202412	+	0.202412i
$276$	−8.37517	+	11.4803i	−0.504126	+	0.691033i
$277$	6.77517	+	6.77517i	0.407080	+	0.407080i	0.880719	−	0.473639i	$-0.157060\pi$
$277$	6.77517	+	6.77517i	0.407080	+	0.407080i	−0.473639	+	0.880719i	$0.657060\pi$
$278$	−22.7308	+	1.76666i	−1.36330	+	0.105957i
$279$			0.578298i			0.0346218i
$280$	6.89958	−	1.63512i	0.412329	−	0.0977172i
$281$		−	8.47751i		−	0.505726i	−0.967502	−	0.252863i	$-0.918628\pi$
$281$		−	8.47751i		−	0.505726i	0.967502	−	0.252863i	$-0.0813722\pi$
$282$	0.857153	+	11.0286i	0.0510427	+	0.656742i
$283$	21.7418	+	21.7418i	1.29241	+	1.29241i	0.933290	+	0.359123i	$0.116924\pi$
$283$	21.7418	+	21.7418i	1.29241	+	1.29241i	0.359123	+	0.933290i	$0.383076\pi$
$284$	−5.57989	+	0.872623i	−0.331106	+	0.0517806i
$285$	−1.70017	+	1.70017i	−0.100710	+	0.100710i
$286$	−16.0281	+	18.7295i	−0.947764	+	1.10750i
$287$	−4.09322			−0.241615
$288$	5.21564	+	2.19023i	0.307335	+	0.129060i
$289$	9.01419			0.530247
$290$	−24.0375	+	28.0888i	−1.41153	+	1.64943i
$291$	7.17820	−	7.17820i	0.420793	−	0.420793i
$292$	7.13506	−	1.11583i	0.417548	−	0.0652991i
$293$	0.294588	+	0.294588i	0.0172100	+	0.0172100i	0.715659	−	0.698449i	$-0.246126\pi$
$293$	0.294588	+	0.294588i	0.0172100	+	0.0172100i	−0.698449	+	0.715659i	$0.746126\pi$
$294$	0.109584	+	1.40996i	0.00639106	+	0.0822306i
$295$			0.181969i			0.0105947i
$296$	−6.39708	−	26.9932i	−0.371823	−	1.56895i
$297$		−	3.69493i		−	0.214402i
$298$	−28.1750	+	2.18979i	−1.63213	+	0.126851i
$299$	23.7023	+	23.7023i	1.37074	+	1.37074i
$300$	1.51434	−	2.07578i	0.0874302	−	0.119845i
$301$	3.04549	−	3.04549i	0.175539	−	0.175539i
$302$	11.6388	+	9.96009i	0.669736	+	0.573139i
$303$	3.83637			0.220394
$304$	−1.75501	+	3.41145i	−0.100657	+	0.195660i
$305$	25.4564			1.45763
$306$	−5.48029	−	4.68986i	−0.313288	−	0.268101i
$307$	6.21494	−	6.21494i	0.354705	−	0.354705i	−0.507152	−	0.861857i	$-0.669302\pi$
$307$	6.21494	−	6.21494i	0.354705	−	0.354705i	0.861857	+	0.507152i	$0.169302\pi$
$308$	−5.97005	−	4.35530i	−0.340175	−	0.248166i
$309$	−4.16470	−	4.16470i	−0.236922	−	0.236922i
$310$	2.04410	−	0.158870i	0.116097	−	0.00902320i
$311$			27.4267i			1.55523i	0.628743	+	0.777613i	$0.283570\pi$
$311$			27.4267i			1.55523i	−0.628743	+	0.777613i	$0.716430\pi$
$312$	7.00516	−	11.3567i	0.396589	−	0.642947i
$313$		−	8.16652i		−	0.461599i	−0.973001	−	0.230800i	$-0.925866\pi$
$313$		−	8.16652i		−	0.461599i	0.973001	−	0.230800i	$-0.0741342\pi$
$314$	1.39888	+	17.9987i	0.0789433	+	1.01573i
$315$	1.77267	+	1.77267i	0.0998787	+	0.0998787i
$316$	1.87699	+	12.0022i	0.105589	+	0.675178i
$317$	−15.2299	+	15.2299i	−0.855397	+	0.855397i	−0.990792	−	0.135395i	$-0.956770\pi$
$317$	−15.2299	+	15.2299i	−0.855397	+	0.855397i	0.135395	+	0.990792i	$0.456770\pi$
$318$	11.7880	−	13.7748i	0.661039	−	0.772452i
$319$	38.5299			2.15726
$320$	6.30892	−	19.0373i	0.352679	−	1.06422i
$321$	−0.689713			−0.0384960
$322$	−6.53336	+	7.63450i	−0.364090	+	0.425454i
$323$	3.45904	−	3.45904i	0.192466	−	0.192466i
$324$	0.309018	+	1.97598i	0.0171677	+	0.109777i
$325$	−4.28566	−	4.28566i	−0.237726	−	0.237726i
$326$	−1.31202	−	16.8811i	−0.0726661	−	0.934959i
$327$		−	4.07262i		−	0.225216i
$328$	−6.07800	+	9.85360i	−0.335601	+	0.544074i
$329$			7.82190i			0.431235i
$330$	−13.0604	+	1.01507i	−0.718952	+	0.0558778i
$331$	2.53222	+	2.53222i	0.139183	+	0.139183i	0.773266	−	0.634082i	$-0.218622\pi$
$331$	2.53222	+	2.53222i	0.139183	+	0.139183i	−0.634082	+	0.773266i	$0.718622\pi$
$332$	4.88803	+	3.56594i	0.268266	+	0.195706i
$333$	6.93521	−	6.93521i	0.380047	−	0.380047i
$334$	12.5838	+	10.7688i	0.688557	+	0.589244i
$335$	26.4175			1.44334
$336$	3.55692	+	1.82984i	0.194046	+	0.0998261i
$337$	−16.5519			−0.901637			−0.450819	−	0.892616i	$-0.648868\pi$
$337$	−16.5519			−0.901637			−0.450819	+	0.892616i	$0.648868\pi$
$338$	−9.94526	−	8.51083i	−0.540951	−	0.462928i
$339$	8.16372	−	8.16372i	0.443392	−	0.443392i
$340$	−15.0716	+	20.6595i	−0.817373	+	1.12042i
$341$	−1.51093	−	1.51093i	−0.0818212	−	0.0818212i
$342$	−1.35230	+	0.105102i	−0.0731239	+	0.00568327i
$343$			1.00000i			0.0539949i
$344$	−2.80918	−	11.8536i	−0.151461	−	0.639106i
$345$			17.8125i			0.958994i
$346$	0.555667	+	7.14949i	0.0298728	+	0.384359i
$347$	−4.81546	−	4.81546i	−0.258508	−	0.258508i	0.565939	−	0.824447i	$-0.308514\pi$
$347$	−4.81546	−	4.81546i	−0.258508	−	0.258508i	−0.824447	+	0.565939i	$0.808514\pi$
$348$	−20.6051	+	3.22237i	−1.10455	+	0.172737i
$349$	−9.35951	+	9.35951i	−0.501003	+	0.501003i	−0.911750	−	0.410747i	$-0.865268\pi$
$349$	−9.35951	+	9.35951i	−0.501003	+	0.501003i	0.410747	+	0.911750i	$0.365268\pi$
$350$	1.18131	−	1.38041i	0.0631439	−	0.0737862i
$351$	4.71761			0.251808
$352$	−19.3494	+	7.90453i	−1.03133	+	0.421313i
$353$	−16.7584			−0.891958			−0.445979	−	0.895044i	$-0.647144\pi$
$353$	−16.7584			−0.891958			−0.445979	+	0.895044i	$0.647144\pi$
$354$	−0.0667435	+	0.0779926i	−0.00354738	+	0.00414526i
$355$	−5.00577	+	5.00577i	−0.265679	+	0.265679i
$356$	26.9028	−	4.20725i	1.42585	−	0.222984i
$357$	−3.60654	−	3.60654i	−0.190878	−	0.190878i
$358$	2.07459	+	26.6928i	0.109646	+	1.41076i
$359$			19.2222i			1.01451i	0.861797	+	0.507253i	$0.169339\pi$
$359$			19.2222i			1.01451i	−0.861797	+	0.507253i	$0.830661\pi$
$360$	6.89958	−	1.63512i	0.363640	−	0.0861785i
$361$			18.0801i			0.951585i
$362$	0.838618	−	0.0651783i	0.0440768	−	0.00342570i
$363$	1.87561	+	1.87561i	0.0984440	+	0.0984440i
$364$	5.56076	−	7.62243i	0.291463	−	0.399524i
$365$	6.40093	−	6.40093i	0.335040	−	0.335040i
$366$	10.9107	+	9.33704i	0.570312	+	0.488055i
$367$	−1.54024			−0.0803997			−0.0401999	−	0.999192i	$-0.512799\pi$
$367$	−1.54024			−0.0803997			−0.0401999	+	0.999192i	$0.512799\pi$
$368$	8.67719	+	27.0642i	0.452330	+	1.41082i
$369$	−4.09322			−0.213084
$370$	−26.4190	−	22.6085i	−1.37346	−	1.17536i
$371$	9.06508	−	9.06508i	0.470635	−	0.470635i
$372$	0.934379	+	0.681653i	0.0484453	+	0.0353421i
$373$	19.1581	+	19.1581i	0.991968	+	0.991968i	0.999968	−	0.00799989i	$-0.00254647\pi$
$373$	19.1581	+	19.1581i	0.991968	+	0.991968i	−0.00799989	+	0.999968i	$0.502546\pi$
$374$	26.5717	−	2.06518i	1.37399	−	0.106788i
$375$			9.31395i			0.480970i
$376$	18.8296	+	11.6147i	0.971065	+	0.598982i
$377$			49.1942i			2.53363i
$378$	0.109584	+	1.40996i	0.00563638	+	0.0725206i
$379$	−25.1766	−	25.1766i	−1.29323	−	1.29323i	−0.932775	−	0.360459i	$-0.882620\pi$
$379$	−25.1766	−	25.1766i	−1.29323	−	1.29323i	−0.360459	−	0.932775i	$-0.617380\pi$
$380$	0.743006	+	4.75107i	0.0381154	+	0.243725i
$381$	2.21794	−	2.21794i	0.113629	−	0.113629i
$382$	4.60318	−	5.37900i	0.235519	−	0.275214i
$383$	7.24184			0.370041			0.185020	−	0.982735i	$-0.440765\pi$
$383$	7.24184			0.370041			0.185020	+	0.982735i	$0.440765\pi$
$384$	9.68663	−	5.84545i	0.494319	−	0.298299i
$385$	−9.26295			−0.472084
$386$	0.509932	−	0.595877i	0.0259549	−	0.0303293i
$387$	3.04549	−	3.04549i	0.154811	−	0.154811i
$388$	−3.13700	−	20.0592i	−0.159257	−	1.01835i
$389$	−10.8915	−	10.8915i	−0.552219	−	0.552219i	0.374861	−	0.927081i	$-0.377690\pi$
$389$	−10.8915	−	10.8915i	−0.552219	−	0.552219i	−0.927081	+	0.374861i	$0.877690\pi$
$390$	−1.29602	−	16.6753i	−0.0656266	−	0.844385i
$391$		−	36.2399i		−	1.83273i
$392$	2.40730	+	1.48489i	0.121587	+	0.0749985i
$393$		−	6.04518i		−	0.304939i
$394$	−15.4646	+	1.20193i	−0.779096	+	0.0605522i
$395$	10.7673	+	10.7673i	0.541761	+	0.541761i
$396$	−5.97005	−	4.35530i	−0.300006	−	0.218862i
$397$	6.61435	−	6.61435i	0.331965	−	0.331965i	−0.521367	−	0.853332i	$-0.674578\pi$
$397$	6.61435	−	6.61435i	0.331965	−	0.331965i	0.853332	+	0.521367i	$0.174578\pi$
$398$	−25.4354	−	21.7668i	−1.27496	−	1.09107i
$399$	−0.959103			−0.0480152
$400$	−1.56894	−	4.89354i	−0.0784472	−	0.244677i
$401$	13.4671			0.672513			0.336256	−	0.941770i	$-0.390839\pi$
$401$	13.4671			0.672513			0.336256	+	0.941770i	$0.390839\pi$
$402$	11.3226	+	9.68953i	0.564721	+	0.483270i
$403$	1.92912	−	1.92912i	0.0960963	−	0.0960963i
$404$	4.52202	−	6.19858i	0.224979	−	0.308391i
$405$	1.77267	+	1.77267i	0.0880847	+	0.0880847i
$406$	−14.7028	+	1.14272i	−0.729686	+	0.0567120i
$407$			36.2394i			1.79632i
$408$	−14.0373	+	3.32669i	−0.694952	+	0.164696i
$409$		−	33.3014i		−	1.64665i	−0.567572	−	0.823324i	$-0.692117\pi$
$409$		−	33.3014i		−	1.64665i	0.567572	−	0.823324i	$-0.307883\pi$
$410$	1.12449	+	14.4682i	0.0555345	+	0.714535i
$411$	0.165474	+	0.165474i	0.00816224	+	0.00816224i
$412$	−11.6381	+	1.82005i	−0.573368	+	0.0896673i
$413$	−0.0513263	+	0.0513263i	−0.00252560	+	0.00252560i
$414$	−6.53336	+	7.63450i	−0.321097	+	0.375215i
$415$	7.58413			0.372290
$416$	−10.0923	−	24.7049i	−0.494818	−	1.21126i
$417$	−16.1216			−0.789477
$418$	3.25856	−	3.80777i	0.159381	−	0.186244i
$419$	28.0784	−	28.0784i	1.37172	−	1.37172i	0.513825	−	0.857895i	$-0.328228\pi$
$419$	28.0784	−	28.0784i	1.37172	−	1.37172i	0.857895	−	0.513825i	$-0.171772\pi$
$420$	4.95366	−	0.774688i	0.241714	−	0.0378009i
$421$	14.5632	+	14.5632i	0.709765	+	0.709765i	0.966486	−	0.256721i	$-0.0826421\pi$
$421$	14.5632	+	14.5632i	0.709765	+	0.709765i	−0.256721	+	0.966486i	$0.582642\pi$
$422$	2.55710	+	32.9009i	0.124478	+	1.60159i
$423$			7.82190i			0.380314i
$424$	−8.36167	−	35.2830i	−0.406079	−	1.71350i
$425$			6.55263i			0.317849i
$426$	−3.98153	+	0.309449i	−0.192906	+	0.0149929i
$427$	7.18025	+	7.18025i	0.347477	+	0.347477i
$428$	−0.812980	+	1.11440i	−0.0392969	+	0.0538664i
$429$	−12.3258	+	12.3258i	−0.595093	+	0.595093i
$430$	−11.6015	−	9.92819i	−0.559474	−	0.478780i
$431$	−20.6763			−0.995945			−0.497972	−	0.867193i	$-0.665922\pi$
$431$	−20.6763			−0.995945			−0.497972	+	0.867193i	$0.665922\pi$
$432$	3.55692	+	1.82984i	0.171132	+	0.0880383i
$433$	−21.5770			−1.03693			−0.518463	−	0.855100i	$-0.673496\pi$
$433$	−21.5770			−1.03693			−0.518463	+	0.855100i	$0.673496\pi$
$434$	0.621370	+	0.531749i	0.0298267	+	0.0255247i
$435$	−18.4850	+	18.4850i	−0.886289	+	0.886289i
$436$	−6.58029	−	4.80049i	−0.315139	−	0.229902i
$437$	−4.81873	−	4.81873i	−0.230511	−	0.230511i
$438$	5.09122	−	0.395695i	0.243268	−	0.0189071i
$439$		−	33.8178i		−	1.61404i	−0.590526	−	0.807019i	$-0.701080\pi$
$439$		−	33.8178i		−	1.61404i	0.590526	−	0.807019i	$-0.298920\pi$
$440$	−13.7545	+	22.2987i	−0.655720	+	1.06305i
$441$			1.00000i			0.0476190i
$442$	2.63678	+	33.9262i	0.125419	+	1.61370i
$443$	−11.7292	−	11.7292i	−0.557270	−	0.557270i	0.371259	−	0.928529i	$-0.378926\pi$
$443$	−11.7292	−	11.7292i	−0.557270	−	0.557270i	−0.928529	+	0.371259i	$0.878926\pi$
$444$	−3.03081	−	19.3802i	−0.143836	−	0.919743i
$445$	24.1347	−	24.1347i	1.14410	−	1.14410i
$446$	15.3906	−	17.9846i	0.728766	−	0.851593i
$447$	−19.9828			−0.945154
$448$	7.14917	−	3.59018i	0.337766	−	0.169620i
$449$	−2.54577			−0.120142			−0.0600712	−	0.998194i	$-0.519133\pi$
$449$	−2.54577			−0.120142			−0.0600712	+	0.998194i	$0.519133\pi$
$450$	1.18131	−	1.38041i	0.0556877	−	0.0650733i
$451$	10.6944	−	10.6944i	0.503579	−	0.503579i
$452$	−3.56769	−	22.8132i	−0.167810	−	1.07304i
$453$	7.65938	+	7.65938i	0.359869	+	0.359869i
$454$	−0.244598	−	3.14713i	−0.0114796	−	0.147702i
$455$		−	11.8268i		−	0.554447i
$456$	−1.42417	+	2.30885i	−0.0666927	+	0.108122i
$457$			26.9308i			1.25977i	0.776689	+	0.629885i	$0.216898\pi$
$457$			26.9308i			1.25977i	−0.776689	+	0.629885i	$0.783102\pi$
$458$	22.8390	−	1.77508i	1.06720	−	0.0829439i
$459$	−3.60654	−	3.60654i	−0.168339	−	0.168339i
$460$	28.7804	+	20.9960i	1.34189	+	0.978944i
$461$	−1.88433	+	1.88433i	−0.0877619	+	0.0877619i	−0.749625	−	0.661863i	$-0.769766\pi$
$461$	−1.88433	+	1.88433i	−0.0877619	+	0.0877619i	0.661863	+	0.749625i	$0.269766\pi$
$462$	−3.97013	−	3.39751i	−0.184707	−	0.158066i
$463$	−4.84091			−0.224976			−0.112488	−	0.993653i	$-0.535882\pi$
$463$	−4.84091			−0.224976			−0.112488	+	0.993653i	$0.535882\pi$
$464$	−19.0812	+	37.0908i	−0.885822	+	1.72190i
$465$	1.44976			0.0672308
$466$	−12.3427	−	10.5625i	−0.571764	−	0.489297i
$467$	4.33750	−	4.33750i	0.200716	−	0.200716i	−0.599591	−	0.800307i	$-0.704670\pi$
$467$	4.33750	−	4.33750i	0.200716	−	0.200716i	0.800307	+	0.599591i	$0.204670\pi$
$468$	5.56076	−	7.62243i	0.257046	−	0.352347i
$469$	7.45132	+	7.45132i	0.344070	+	0.344070i
$470$	27.6479	−	2.14883i	1.27530	−	0.0991180i
$471$			12.7654i			0.588198i
$472$	0.0473436	+	0.199772i	0.00217917	+	0.00919524i
$473$			15.9140i			0.731725i
$474$	0.665618	+	8.56418i	0.0305728	+	0.393366i
$475$	0.871287	+	0.871287i	0.0399774	+	0.0399774i
$476$	−10.0783	+	1.57612i	−0.461939	+	0.0722413i
$477$	9.06508	−	9.06508i	0.415061	−	0.415061i
$478$	−15.6157	+	18.2476i	−0.714245	+	0.834625i
$479$	24.0485			1.09880			0.549401	−	0.835559i	$-0.314856\pi$
$479$	24.0485			1.09880			0.549401	+	0.835559i	$0.314856\pi$
$480$	5.49076	−	13.0753i	0.250618	−	0.596802i
$481$	−46.2698			−2.10972
$482$	−9.54636	+	11.1553i	−0.434825	+	0.508111i
$483$	−5.02420	+	5.02420i	−0.228609	+	0.228609i
$484$	5.24132	−	0.819674i	0.238242	−	0.0372579i
$485$	−17.9953	−	17.9953i	−0.817124	−	0.817124i
$486$	0.109584	+	1.40996i	0.00497082	+	0.0639572i
$487$		−	17.4797i		−	0.792079i	−0.918233	−	0.396040i	$-0.870384\pi$
$487$		−	17.4797i		−	0.792079i	0.918233	−	0.396040i	$-0.129616\pi$
$488$	27.9469	−	6.62310i	1.26510	−	0.299814i
$489$		−	11.9728i		−	0.541427i
$490$	3.53468	−	0.274720i	0.159681	−	0.0124106i
$491$	−26.3886	−	26.3886i	−1.19090	−	1.19090i	−0.976815	−	0.214085i	$-0.931323\pi$
$491$	−26.3886	−	26.3886i	−1.19090	−	1.19090i	−0.214085	−	0.976815i	$-0.568677\pi$
$492$	−4.82477	+	6.61358i	−0.217517	+	0.298163i
$493$	37.6081	−	37.6081i	1.69379	−	1.69379i
$494$	4.86168	+	4.16047i	0.218737	+	0.187188i
$495$	−9.26295			−0.416339
$496$	2.20275	−	0.706234i	0.0989063	−	0.0317108i
$497$	−2.82386			−0.126667
$498$	3.25058	+	2.78174i	0.145662	+	0.124653i
$499$	2.93443	−	2.93443i	0.131363	−	0.131363i	−0.638368	−	0.769731i	$-0.720390\pi$
$499$	2.93443	−	2.93443i	0.131363	−	0.131363i	0.769731	+	0.638368i	$0.220390\pi$
$500$	15.0489	+	10.9786i	0.673008	+	0.490976i
$501$	8.28131	+	8.28131i	0.369982	+	0.369982i
$502$	−30.4199	+	2.36427i	−1.35771	+	0.105523i
$503$			34.0266i			1.51717i	0.651575	+	0.758585i	$0.274109\pi$
$503$			34.0266i			1.51717i	−0.651575	+	0.758585i	$0.725891\pi$
$504$	2.40730	+	1.48489i	0.107230	+	0.0661424i
$505$		−	9.61754i		−	0.427975i
$506$	−2.87697	−	37.0165i	−0.127897	−	1.64559i
$507$	−6.54489	−	6.54489i	−0.290669	−	0.290669i
$508$	−0.969280	−	6.19796i	−0.0430048	−	0.274990i
$509$	17.5157	−	17.5157i	0.776372	−	0.776372i	−0.202840	−	0.979212i	$-0.565017\pi$
$509$	17.5157	−	17.5157i	0.776372	−	0.776372i	0.979212	+	0.202840i	$0.0650172\pi$
$510$	−11.7572	+	13.7387i	−0.520616	+	0.608362i
$511$	3.61089			0.159737
$512$	1.97312	−	22.5412i	0.0872004	−	0.996191i
$513$	−0.959103			−0.0423454
$514$	10.0340	−	11.7252i	0.442582	−	0.517175i
$515$	−10.4406	+	10.4406i	−0.460070	+	0.460070i
$516$	−1.33093	−	8.51051i	−0.0585910	−	0.374654i
$517$	−20.4363	−	20.4363i	−0.898790	−	0.898790i
$518$	−1.07478	−	13.8287i	−0.0472233	−	0.607599i
$519$			5.07070i			0.222579i
$520$	−28.4705	−	17.5615i	−1.24852	−	0.770122i
$521$		−	10.7174i		−	0.469537i	−0.972051	−	0.234769i	$-0.924567\pi$
$521$		−	10.7174i		−	0.469537i	0.972051	−	0.234769i	$-0.0754333\pi$
$522$	−14.7028	+	1.14272i	−0.643522	+	0.0500153i
$523$	−32.0081	−	32.0081i	−1.39962	−	1.39962i	−0.801138	−	0.598480i	$-0.795772\pi$
$523$	−32.0081	−	32.0081i	−1.39962	−	1.39962i	−0.598480	−	0.801138i	$-0.704228\pi$
$524$	−9.76744	−	7.12559i	−0.426693	−	0.311283i
$525$	0.908439	−	0.908439i	0.0396475	−	0.0396475i
$526$	4.23858	+	3.62724i	0.184811	+	0.158155i
$527$	−2.94956			−0.128485
$528$	−14.0740	+	4.51235i	−0.612494	+	0.196375i
$529$	−27.4852			−1.19501
$530$	−34.5325	−	29.5518i	−1.50000	−	1.28365i
$531$	−0.0513263	+	0.0513263i	−0.00222737	+	0.00222737i
$532$	−1.13052	+	1.54966i	−0.0490141	+	0.0671863i
$533$	13.6544	+	13.6544i	0.591437	+	0.591437i
$534$	19.1965	−	1.49197i	0.830713	−	0.0645640i
$535$			1.72907i			0.0747540i
$536$	29.0020	−	6.87314i	1.25269	−	0.296874i
$537$			18.9316i			0.816957i
$538$	−3.25097	−	41.8286i	−0.140159	−	1.80336i
$539$	−2.61271	−	2.61271i	−0.112537	−	0.112537i
$540$	4.95366	−	0.774688i	0.213172	−	0.0333373i
$541$	−17.3428	+	17.3428i	−0.745624	+	0.745624i	−0.973654	−	0.228030i	$-0.926772\pi$
$541$	−17.3428	+	17.3428i	−0.745624	+	0.745624i	0.228030	+	0.973654i	$0.426772\pi$
$542$	2.21254	−	2.58545i	0.0950369	−	0.111055i
$543$	0.594781			0.0255245
$544$	−11.1711	+	26.6019i	−0.478955	+	1.14055i
$545$	−10.2098			−0.437340
$546$	4.33787	−	5.06899i	0.185644	−	0.216933i
$547$	−3.18694	+	3.18694i	−0.136264	+	0.136264i	−0.771949	−	0.635685i	$-0.780718\pi$
$547$	−3.18694	+	3.18694i	−0.136264	+	0.136264i	0.635685	+	0.771949i	$0.280718\pi$
$548$	0.462411	−	0.0723151i	0.0197532	−	0.00308915i
$549$	7.18025	+	7.18025i	0.306446	+	0.306446i
$550$	0.520192	+	6.69305i	0.0221810	+	0.285393i
$551$		−	10.0013i		−	0.426070i
$552$	4.63435	+	19.5552i	0.197251	+	0.832323i
$553$			6.07405i			0.258295i
$554$	13.5096	−	1.04998i	0.573968	−	0.0446094i
$555$	−17.3861	−	17.3861i	−0.738000	−	0.738000i
$556$	−19.0029	+	26.0483i	−0.805900	+	1.10469i
$557$	17.1583	−	17.1583i	0.727019	−	0.727019i	−0.243006	−	0.970025i	$-0.578133\pi$
$557$	17.1583	−	17.1583i	0.727019	−	0.727019i	0.970025	+	0.243006i	$0.0781334\pi$
$558$	0.621370	+	0.531749i	0.0263047	+	0.0225107i
$559$	−20.3186			−0.859387
$560$	4.58730	−	8.91697i	0.193849	−	0.376811i
$561$	18.8457			0.795665
$562$	−9.10893	−	7.79512i	−0.384237	−	0.328817i
$563$	−30.5052	+	30.5052i	−1.28564	+	1.28564i	−0.348235	+	0.937407i	$0.613219\pi$
$563$	−30.5052	+	30.5052i	−1.28564	+	1.28564i	−0.937407	+	0.348235i	$0.886781\pi$
$564$	12.6381	+	9.21984i	0.532162	+	0.388225i
$565$	−20.4659	−	20.4659i	−0.861008	−	0.861008i
$566$	43.3528	−	3.36943i	1.82225	−	0.141628i
$567$			1.00000i			0.0419961i
$568$	−4.19313	+	6.79787i	−0.175940	+	0.285232i
$569$		−	28.6701i		−	1.20191i	−0.799282	−	0.600956i	$-0.794787\pi$
$569$		−	28.6701i		−	1.20191i	0.799282	−	0.600956i	$-0.205213\pi$
$570$	0.263484	+	3.39012i	0.0110361	+	0.141997i
$571$	2.68672	+	2.68672i	0.112436	+	0.112436i	0.761086	−	0.648651i	$-0.224666\pi$
$571$	2.68672	+	2.68672i	0.112436	+	0.112436i	−0.648651	+	0.761086i	$0.724666\pi$
$572$	5.38657	+	34.4439i	0.225224	+	1.44017i
$573$	3.53988	−	3.53988i	0.147880	−	0.147880i
$574$	−3.76374	+	4.39808i	−0.157095	+	0.183573i
$575$	9.12836			0.380679
$576$	7.14917	−	3.59018i	0.297882	−	0.149591i
$577$	25.4928			1.06128			0.530640	−	0.847597i	$-0.321952\pi$
$577$	25.4928			1.06128			0.530640	+	0.847597i	$0.321952\pi$
$578$	8.28860	−	9.68558i	0.344760	−	0.402867i
$579$	0.392142	−	0.392142i	0.0162969	−	0.0162969i
$580$	8.07827	+	51.6557i	0.335432	+	2.14488i
$581$	2.13918	+	2.13918i	0.0887482	+	0.0887482i
$582$	−1.11244	−	14.3132i	−0.0461121	−	0.593302i
$583$			47.3688i			1.96182i
$584$	5.36179	−	8.69250i	0.221873	−	0.359698i
$585$		−	11.8268i		−	0.488976i
$586$	0.587405	−	0.0456538i	0.0242655	−	0.00188594i
$587$	−18.3619	−	18.3619i	−0.757875	−	0.757875i	0.218061	−	0.975935i	$-0.430027\pi$
$587$	−18.3619	−	18.3619i	−0.757875	−	0.757875i	−0.975935	+	0.218061i	$0.930027\pi$
$588$	1.61574	+	1.17872i	0.0666320	+	0.0486097i
$589$	−0.392195	+	0.392195i	−0.0161601	+	0.0161601i
$590$	0.195522	+	0.167322i	0.00804953	+	0.00688853i
$591$	−10.9681			−0.451168
$592$	−34.8858	−	17.9469i	−1.43380	−	0.737612i
$593$	6.05686			0.248725			0.124363	−	0.992237i	$-0.460311\pi$
$593$	6.05686			0.248725			0.124363	+	0.992237i	$0.460311\pi$
$594$	−3.97013	−	3.39751i	−0.162896	−	0.139402i
$595$	−9.04135	+	9.04135i	−0.370659	+	0.370659i
$596$	−23.5542	+	32.2870i	−0.964816	+	1.32253i
$597$	−16.7389	−	16.7389i	−0.685076	−	0.685076i
$598$	47.2620	−	3.67325i	1.93269	−	0.150211i
$599$		−	43.2639i		−	1.76772i	−0.467755	−	0.883858i	$-0.654937\pi$
$599$		−	43.2639i		−	1.76772i	0.467755	−	0.883858i	$-0.345063\pi$
$600$	−0.837949	−	3.53582i	−0.0342091	−	0.144349i
$601$			42.4545i			1.73176i	0.500255	+	0.865878i	$0.333240\pi$
$601$			42.4545i			1.73176i	−0.500255	+	0.865878i	$0.666760\pi$
$602$	−0.471975	−	6.07267i	−0.0192363	−	0.247504i
$603$	7.45132	+	7.45132i	0.303441	+	0.303441i
$604$	21.4038	−	3.34728i	0.870910	−	0.136199i
$605$	4.70203	−	4.70203i	0.191165	−	0.191165i
$606$	3.52757	−	4.12211i	0.143298	−	0.167449i
$607$	−18.2870			−0.742244			−0.371122	−	0.928584i	$-0.621027\pi$
$607$	−18.2870			−0.742244			−0.371122	+	0.928584i	$0.621027\pi$
$608$	2.05180	+	5.02257i	0.0832115	+	0.203692i
$609$	−10.4278			−0.422555
$610$	23.4074	−	27.3525i	0.947736	−	1.10747i
$611$	26.0927	−	26.0927i	1.05560	−	1.05560i
$612$	−10.0783	+	1.57612i	−0.407392	+	0.0637108i
$613$	8.87432	+	8.87432i	0.358430	+	0.358430i	0.863234	−	0.504804i	$-0.168435\pi$
$613$	8.87432	+	8.87432i	0.358430	+	0.358430i	−0.504804	+	0.863234i	$0.668435\pi$
$614$	−0.963159	−	12.3925i	−0.0388699	−	0.500121i
$615$			10.2614i			0.413781i
$616$	−10.1692	+	2.40998i	−0.409728	+	0.0971008i
$617$			18.4768i			0.743848i	0.928263	+	0.371924i	$0.121302\pi$
$617$			18.4768i			0.743848i	−0.928263	+	0.371924i	$0.878698\pi$
$618$	−8.30436	+	0.645425i	−0.334051	+	0.0259628i
$619$	3.83595	+	3.83595i	0.154180	+	0.154180i	0.779982	−	0.625802i	$-0.215228\pi$
$619$	3.83595	+	3.83595i	0.154180	+	0.154180i	−0.625802	+	0.779982i	$0.715228\pi$
$620$	1.70886	−	2.34243i	0.0686295	−	0.0940742i
$621$	−5.02420	+	5.02420i	−0.201614	+	0.201614i
$622$	29.4695	+	25.2190i	1.18162	+	1.01119i
$623$	13.6149			0.545469
$624$	−5.76128	−	17.9695i	−0.230636	−	0.719354i
$625$	29.7731			1.19092
$626$	−8.77477	−	7.50917i	−0.350710	−	0.300127i
$627$	2.50586	−	2.50586i	0.100074	−	0.100074i
$628$	20.6255	+	15.0468i	0.823048	+	0.600434i
$629$	35.3724	+	35.3724i	1.41039	+	1.41039i
$630$	3.53468	−	0.274720i	0.140825	−	0.0109451i
$631$			31.9301i			1.27112i	0.772053	+	0.635558i	$0.219230\pi$
$631$			31.9301i			1.27112i	−0.772053	+	0.635558i	$0.780770\pi$
$632$	14.6221	+	9.01932i	0.581634	+	0.358769i
$633$			23.3346i			0.927468i
$634$	2.36025	+	30.3682i	0.0937377	+	1.20608i
$635$	−5.56024	−	5.56024i	−0.220651	−	0.220651i
$636$	−3.96159	−	25.3320i	−0.157087	−	1.00448i
$637$	3.33586	−	3.33586i	0.132171	−	0.132171i
$638$	35.4285	−	41.3996i	1.40263	−	1.63903i
$639$	−2.82386			−0.111710
$640$	−14.6542	−	24.2837i	−0.579257	−	0.959899i
$641$	−12.3796			−0.488965			−0.244482	−	0.969654i	$-0.578618\pi$
$641$	−12.3796			−0.488965			−0.244482	+	0.969654i	$0.578618\pi$
$642$	−0.634195	+	0.741083i	−0.0250297	+	0.0292482i
$643$	−29.5599	+	29.5599i	−1.16573	+	1.16573i	−0.182530	+	0.983200i	$0.558429\pi$
$643$	−29.5599	+	29.5599i	−1.16573	+	1.16573i	−0.983200	+	0.182530i	$0.941571\pi$
$644$	2.19566	+	14.0399i	0.0865213	+	0.553251i
$645$	−7.63485	−	7.63485i	−0.300622	−	0.300622i
$646$	−0.536064	−	6.89728i	−0.0210912	−	0.271370i
$647$		−	8.33949i		−	0.327859i	−0.986472	−	0.163930i	$-0.947583\pi$
$647$		−	8.33949i		−	0.327859i	0.986472	−	0.163930i	$-0.0524170\pi$
$648$	2.40730	+	1.48489i	0.0945676	+	0.0583321i
$649$		−	0.268201i		−	0.0105278i
$650$	−8.54556	+	0.664170i	−0.335184	+	0.0260509i
$651$	0.408919	+	0.408919i	0.0160268	+	0.0160268i
$652$	−19.3449	−	14.1126i	−0.757603	−	0.552690i
$653$	−32.4395	+	32.4395i	−1.26946	+	1.26946i	−0.323088	+	0.946369i	$0.604721\pi$
$653$	−32.4395	+	32.4395i	−1.26946	+	1.26946i	−0.946369	+	0.323088i	$0.895279\pi$
$654$	−4.37595	−	3.74480i	−0.171113	−	0.146433i
$655$	−15.1549			−0.592150
$656$	4.99875	+	15.5911i	0.195169	+	0.608732i
$657$	3.61089			0.140874
$658$	8.40448	+	7.19228i	0.327641	+	0.280384i
$659$	9.58661	−	9.58661i	0.373441	−	0.373441i	−0.495288	−	0.868729i	$-0.664937\pi$
$659$	9.58661	−	9.58661i	0.373441	−	0.373441i	0.868729	+	0.495288i	$0.164937\pi$
$660$	−10.9184	+	14.9665i	−0.425000	+	0.582571i
$661$	32.4153	+	32.4153i	1.26081	+	1.26081i	0.950701	+	0.310108i	$0.100365\pi$
$661$	32.4153	+	32.4153i	1.26081	+	1.26081i	0.310108	+	0.950701i	$0.399635\pi$
$662$	5.04921	−	0.392430i	0.196243	−	0.0152522i
$663$			24.0618i			0.934482i
$664$	8.32611	−	1.97319i	0.323116	−	0.0765747i
$665$			2.40441i			0.0932390i
$666$	−1.07478	−	13.8287i	−0.0416470	−	0.535852i
$667$	−52.3913	−	52.3913i	−2.02860	−	2.02860i
$668$	23.1418	−	3.61908i	0.895384	−	0.140026i
$669$	11.8355	−	11.8355i	0.457586	−	0.457586i
$670$	24.2910	−	28.3851i	0.938444	−	1.09661i
$671$	−37.5198			−1.44844
$672$	5.23674	−	2.13929i	0.202012	−	0.0825249i
$673$	20.4273			0.787416			0.393708	−	0.919236i	$-0.371192\pi$
$673$	20.4273			0.787416			0.393708	+	0.919236i	$0.371192\pi$
$674$	−15.2195	+	17.7847i	−0.586235	+	0.685040i
$675$	0.908439	−	0.908439i	0.0349658	−	0.0349658i
$676$	−18.2895	+	2.86023i	−0.703441	+	0.110009i
$677$	12.1223	+	12.1223i	0.465899	+	0.465899i	0.900583	−	0.434684i	$-0.143140\pi$
$677$	12.1223	+	12.1223i	0.465899	+	0.465899i	−0.434684	+	0.900583i	$0.643140\pi$
$678$	−1.26517	−	16.2783i	−0.0485886	−	0.625166i
$679$		−	10.1515i		−	0.389579i
$680$	8.33979	+	35.1907i	0.319816	+	1.34950i
$681$		−	2.23207i		−	0.0855330i
$682$	−3.01277	+	0.234156i	−0.115365	+	0.00896628i
$683$	23.8282	+	23.8282i	0.911759	+	0.911759i	0.996411	−	0.0846513i	$-0.0269776\pi$
$683$	23.8282	+	23.8282i	0.911759	+	0.911759i	−0.0846513	+	0.996411i	$0.526978\pi$
$684$	−1.13052	+	1.54966i	−0.0432264	+	0.0592528i
$685$	0.414833	−	0.414833i	0.0158500	−	0.0158500i
$686$	1.07448	+	0.919506i	0.0410239	+	0.0351069i
$687$	16.1983			0.618005
$688$	−15.3196	−	7.88109i	−0.584053	−	0.300464i
$689$	−60.4796			−2.30409
$690$	19.1392	+	16.3787i	0.728617	+	0.623527i
$691$	11.9711	−	11.9711i	0.455402	−	0.455402i	−0.441741	−	0.897143i	$-0.645639\pi$
$691$	11.9711	−	11.9711i	0.455402	−	0.455402i	0.897143	+	0.441741i	$0.145639\pi$
$692$	8.19293	+	5.97695i	0.311448	+	0.227209i
$693$	−2.61271	−	2.61271i	−0.0992487	−	0.0992487i
$694$	−9.60197	+	0.746276i	−0.364486	+	0.0283283i
$695$			40.4157i			1.53306i
$696$	−15.4841	+	25.1028i	−0.586925	+	0.951518i
$697$		−	20.8771i		−	0.790776i
$698$	1.45049	+	18.6627i	0.0549018	+	0.706395i
$699$	−8.12262	−	8.12262i	−0.307226	−	0.307226i
$700$	−0.397004	−	2.53860i	−0.0150053	−	0.0959500i
$701$	−0.0601154	+	0.0601154i	−0.00227053	+	0.00227053i	−0.708241	−	0.705971i	$-0.750511\pi$
$701$	−0.0601154	+	0.0601154i	−0.00227053	+	0.00227053i	0.705971	+	0.708241i	$0.250511\pi$
$702$	4.33787	−	5.06899i	0.163722	−	0.191317i
$703$	9.40676			0.354783
$704$	−9.29861	+	28.0588i	−0.350454	+	1.05751i
$705$	19.6090			0.738517
$706$	−15.4094	+	18.0065i	−0.579941	+	0.677685i
$707$	2.71273	−	2.71273i	0.102023	−	0.102023i
$708$	0.0224305	+	0.143429i	0.000842989	+	0.00539040i
$709$	8.33174	+	8.33174i	0.312905	+	0.312905i	0.846034	−	0.533129i	$-0.178984\pi$
$709$	8.33174	+	8.33174i	0.312905	+	0.312905i	−0.533129	+	0.846034i	$0.678984\pi$
$710$	0.775769	+	9.98144i	0.0291141	+	0.374597i
$711$			6.07405i			0.227795i
$712$	20.2167	−	32.7751i	0.757652	−	1.22830i
$713$			4.10898i			0.153883i
$714$	−7.19138	+	0.558923i	−0.269131	+	0.0209171i
$715$	30.8999	+	30.8999i	1.15559	+	1.15559i
$716$	30.5885	+	22.3151i	1.14315	+	0.833953i
$717$	−12.0086	+	12.0086i	−0.448469	+	0.448469i
$718$	20.6538	+	17.6749i	0.770795	+	0.659621i
$719$	0.782061			0.0291659			0.0145830	−	0.999894i	$-0.495358\pi$
$719$	0.782061			0.0291659			0.0145830	+	0.999894i	$0.495358\pi$
$720$	4.58730	−	8.91697i	0.170958	−	0.332316i
$721$	−5.88978			−0.219347
$722$	19.4267	+	16.6248i	0.722989	+	0.618710i
$723$	−7.34122	+	7.34122i	−0.273023	+	0.273023i
$724$	0.701081	−	0.961011i	0.0260555	−	0.0357157i
$725$	9.47300	+	9.47300i	0.351818	+	0.351818i
$726$	3.73994	−	0.290672i	0.138802	−	0.0107879i
$727$			30.5823i			1.13423i	0.823637	+	0.567117i	$0.191941\pi$
$727$			30.5823i			1.13423i	−0.823637	+	0.567117i	$0.808059\pi$
$728$	−3.07701	−	12.9838i	−0.114042	−	0.481212i
$729$			1.00000i			0.0370370i
$730$	−0.991983	−	12.7634i	−0.0367149	−	0.472393i
$731$	15.5333	+	15.5333i	0.574518	+	0.574518i
$732$	20.0649	−	3.13789i	0.741621	−	0.115980i
$733$	14.6059	−	14.6059i	0.539481	−	0.539481i	−0.383895	−	0.923377i	$-0.625418\pi$
$733$	14.6059	−	14.6059i	0.539481	−	0.539481i	0.923377	+	0.383895i	$0.125418\pi$
$734$	−1.41626	+	1.65496i	−0.0522750	+	0.0610855i
$735$	2.50694			0.0924697
$736$	37.0587	+	15.5622i	1.36600	+	0.573631i
$737$	−38.9363			−1.43424
$738$	−3.76374	+	4.39808i	−0.138545	+	0.161896i
$739$	−18.2187	+	18.2187i	−0.670186	+	0.670186i	−0.957759	−	0.287572i	$-0.907152\pi$
$739$	−18.2187	+	18.2187i	−0.670186	+	0.670186i	0.287572	+	0.957759i	$0.407152\pi$
$740$	−48.5849	+	7.59804i	−1.78602	+	0.279310i
$741$	3.19943	+	3.19943i	0.117534	+	0.117534i
$742$	−1.40486	−	18.0756i	−0.0515740	−	0.663578i
$743$		−	13.9676i		−	0.512420i	−0.966621	−	0.256210i	$-0.917526\pi$
$743$		−	13.9676i		−	0.512420i	0.966621	−	0.256210i	$-0.0824739\pi$
$744$	1.59159	−	0.377189i	0.0583505	−	0.0138284i
$745$			50.0956i			1.83536i
$746$	38.2010	−	2.96902i	1.39864	−	0.108704i
$747$	2.13918	+	2.13918i	0.0782686	+	0.0782686i
$748$	22.2138	−	30.4497i	0.812217	−	1.11335i
$749$	−0.487701	+	0.487701i	−0.0178202	+	0.0178202i
$750$	10.0077	+	8.56423i	0.365428	+	0.312722i
$751$	25.2109			0.919959			0.459979	−	0.887930i	$-0.347857\pi$
$751$	25.2109			0.919959			0.459979	+	0.887930i	$0.347857\pi$
$752$	29.7937	−	9.55232i	1.08647	−	0.348337i
$753$	−21.5750			−0.786238
$754$	52.8582	+	45.2344i	1.92498	+	1.64734i
$755$	19.2016	−	19.2016i	0.698817	−	0.698817i
$756$	1.61574	+	1.17872i	0.0587639	+	0.0428697i
$757$	−1.53592	−	1.53592i	−0.0558240	−	0.0558240i	0.678644	−	0.734468i	$-0.262568\pi$
$757$	−1.53592	−	1.53592i	−0.0558240	−	0.0558240i	−0.734468	+	0.678644i	$0.762568\pi$
$758$	−50.2018	+	3.90174i	−1.82341	+	0.141718i
$759$		−	26.2536i		−	0.952945i
$760$	5.78813	+	3.57029i	0.209958	+	0.129508i
$761$		−	12.8849i		−	0.467077i	−0.972348	−	0.233539i	$-0.924969\pi$
$761$		−	12.8849i		−	0.467077i	0.972348	−	0.233539i	$-0.0750305\pi$
$762$	−0.343726	−	4.42255i	−0.0124519	−	0.160212i
$763$	−2.87978	−	2.87978i	−0.104255	−	0.104255i
$764$	−1.54699	−	9.89205i	−0.0559681	−	0.357882i
$765$	−9.04135	+	9.04135i	−0.326891	+	0.326891i
$766$	6.65892	−	7.78122i	0.240596	−	0.281147i
$767$	0.342434			0.0123646
$768$	2.62609	−	15.7830i	0.0947608	−	0.569521i
$769$	45.7669			1.65040			0.825198	−	0.564844i	$-0.191064\pi$
$769$	45.7669			1.65040			0.825198	+	0.564844i	$0.191064\pi$
$770$	−8.51734	+	9.95287i	−0.306944	+	0.358676i
$771$	7.71624	−	7.71624i	0.277894	−	0.277894i
$772$	−0.171373	−	1.09582i	−0.00616784	−	0.0394396i
$773$	−13.9432	−	13.9432i	−0.501501	−	0.501501i	0.410403	−	0.911904i	$-0.365388\pi$
$773$	−13.9432	−	13.9432i	−0.501501	−	0.501501i	−0.911904	+	0.410403i	$0.865388\pi$
$774$	−0.471975	−	6.07267i	−0.0169648	−	0.218278i
$775$		−	0.742955i		−	0.0266877i
$776$	−24.4377	−	15.0739i	−0.877263	−	0.541122i
$777$		−	9.80787i		−	0.351856i
$778$	−21.7174	+	1.68790i	−0.778608	+	0.0605143i
$779$	−2.77597	−	2.77597i	−0.0994595	−	0.0994595i
$780$	−19.1090	−	13.9405i	−0.684210	−	0.499148i
$781$	7.37792	−	7.37792i	0.264003	−	0.264003i
$782$	−38.9391	−	33.3228i	−1.39246	−	1.19162i
$783$	−10.4278			−0.372658
$784$	3.80902	−	1.22123i	0.136036	−	0.0436153i
$785$	32.0020			1.14220
$786$	−6.49543	−	5.55858i	−0.231684	−	0.198268i
$787$	−8.90507	+	8.90507i	−0.317432	+	0.317432i	−0.847780	−	0.530348i	$-0.822061\pi$
$787$	−8.90507	+	8.90507i	−0.317432	+	0.317432i	0.530348	+	0.847780i	$0.322061\pi$
$788$	−12.9283	+	17.7216i	−0.460553	+	0.631306i
$789$	2.78937	+	2.78937i	0.0993043	+	0.0993043i
$790$	21.4698	−	1.66866i	0.763863	−	0.0593683i
$791$		−	11.5452i		−	0.410502i
$792$	−10.1692	+	2.40998i	−0.361346	+	0.0856348i
$793$		−	47.9046i		−	1.70114i
$794$	−1.02506	−	13.1889i	−0.0363780	−	0.468058i
$795$	−22.7256	−	22.7256i	−0.805993	−	0.805993i
$796$	−46.7761	+	7.31517i	−1.65793	+	0.259279i
$797$	−4.00907	+	4.00907i	−0.142009	+	0.142009i	−0.774537	−	0.632528i	$-0.782017\pi$
$797$	−4.00907	+	4.00907i	−0.142009	+	0.142009i	0.632528	+	0.774537i	$0.282017\pi$
$798$	−0.881901	+	1.03054i	−0.0312190	+	0.0364806i
$799$	−39.8949			−1.41138
$800$	−6.70067	−	2.81384i	−0.236905	−	0.0994843i
$801$	13.6149			0.481059
$802$	12.3830	−	14.4701i	0.437260	−	0.510957i
$803$	−9.43422	+	9.43422i	−0.332926	+	0.332926i
$804$	20.8224	−	3.25636i	0.734350	−	0.114843i
$805$	12.5954	+	12.5954i	0.443928	+	0.443928i
$806$	−0.298965	−	3.84664i	−0.0105306	−	0.135492i
$807$		−	29.6665i		−	1.04431i
$808$	−2.50223	−	10.5585i	−0.0880282	−	0.371445i
$809$			9.38878i			0.330092i	0.986286	+	0.165046i	$0.0527772\pi$
$809$			9.38878i			0.330092i	−0.986286	+	0.165046i	$0.947223\pi$
$810$	3.53468	−	0.274720i	0.124196	−	0.00965266i
$811$	25.9151	+	25.9151i	0.910004	+	0.910004i	0.996272	−	0.0862681i	$-0.0274942\pi$
$811$	25.9151	+	25.9151i	0.910004	+	0.910004i	−0.0862681	+	0.996272i	$0.527494\pi$
$812$	−12.2914	+	16.8486i	−0.431345	+	0.591269i
$813$	1.70146	−	1.70146i	0.0596729	−	0.0596729i
$814$	38.9386	+	33.3224i	1.36480	+	1.16795i
$815$	−30.0149			−1.05138
$816$	−9.33295	+	18.1418i	−0.326719	+	0.635088i
$817$	4.13083			0.144520
$818$	−35.7817	−	30.6208i	−1.25108	−	1.07063i
$819$	3.33586	−	3.33586i	0.116564	−	0.116564i
$820$	16.5798	+	12.0954i	0.578992	+	0.422389i
$821$	8.51099	+	8.51099i	0.297036	+	0.297036i	0.839852	−	0.542816i	$-0.182642\pi$
$821$	8.51099	+	8.51099i	0.297036	+	0.297036i	−0.542816	+	0.839852i	$0.682642\pi$
$822$	0.329953	−	0.0256443i	0.0115084	−	0.000894449i
$823$			14.3855i			0.501447i	0.968059	+	0.250723i	$0.0806685\pi$
$823$			14.3855i			0.501447i	−0.968059	+	0.250723i	$0.919332\pi$
$824$	−8.74570	+	14.1785i	−0.304671	+	0.493930i
$825$			4.74698i			0.165268i
$826$	0.00795428	+	0.102344i	0.000276765	+	0.00356100i
$827$	−12.4276	−	12.4276i	−0.432151	−	0.432151i	0.457209	−	0.889359i	$-0.348849\pi$
$827$	−12.4276	−	12.4276i	−0.432151	−	0.432151i	−0.889359	+	0.457209i	$0.848849\pi$
$828$	2.19566	+	14.0399i	0.0763046	+	0.487922i
$829$	−6.80383	+	6.80383i	−0.236307	+	0.236307i	−0.815319	−	0.579012i	$-0.803438\pi$
$829$	−6.80383	+	6.80383i	−0.236307	+	0.236307i	0.579012	+	0.815319i	$0.303438\pi$
$830$	6.97365	−	8.14900i	0.242059	−	0.282856i
$831$	9.58153			0.332380
$832$	−35.8249	−	11.8723i	−1.24201	−	0.411597i
$833$	−5.10041			−0.176719
$834$	−14.8239	+	17.3223i	−0.513309	+	0.599823i
$835$	20.7607	−	20.7607i	0.718454	−	0.718454i
$836$	−1.09510	−	7.00253i	−0.0378749	−	0.242187i
$837$	0.408919	+	0.408919i	0.0141343	+	0.0141343i
$838$	−4.35145	−	55.9880i	−0.150318	−	1.93407i
$839$			5.33066i			0.184035i	0.995757	+	0.0920173i	$0.0293315\pi$
$839$			5.33066i			0.184035i	−0.995757	+	0.0920173i	$0.970668\pi$
$840$	3.72253	−	6.03494i	0.128440	−	0.208225i
$841$		−	79.7385i		−	2.74960i
$842$	29.0387	−	2.25692i	1.00074	−	0.0777787i
$843$	−5.99451	−	5.99451i	−0.206462	−	0.206462i
$844$	37.7027	+	27.5050i	1.29778	+	0.946763i
$845$	−16.4076	+	16.4076i	−0.564440	+	0.564440i
$846$	8.40448	+	7.19228i	0.288952	+	0.247276i
$847$	2.65251			0.0911414
$848$	−45.5995	−	23.4585i	−1.56589	−	0.805568i
$849$	30.7475			1.05525
$850$	7.04068	+	6.02519i	0.241493	+	0.206662i
$851$	49.2768	−	49.2768i	1.68919	−	1.68919i
$852$	−3.32854	+	4.56262i	−0.114034	+	0.156313i
$853$	−35.7856	−	35.7856i	−1.22527	−	1.22527i	−0.965732	−	0.259542i	$-0.916428\pi$
$853$	−35.7856	−	35.7856i	−1.22527	−	1.22527i	−0.259542	−	0.965732i	$-0.583572\pi$
$854$	14.3173	−	1.11276i	0.489929	−	0.0380778i
$855$			2.40441i			0.0822291i
$856$	0.449858	+	1.89823i	0.0153758	+	0.0648800i
$857$			19.6814i			0.672305i	0.941808	+	0.336152i	$0.109126\pi$
$857$			19.6814i			0.672305i	−0.941808	+	0.336152i	$0.890874\pi$
$858$	1.91018	+	24.5774i	0.0652126	+	0.839059i
$859$	−38.1660	−	38.1660i	−1.30221	−	1.30221i	−0.926901	−	0.375306i	$-0.877538\pi$
$859$	−38.1660	−	38.1660i	−1.30221	−	1.30221i	−0.375306	−	0.926901i	$-0.622462\pi$
$860$	−21.3353	+	3.33656i	−0.727528	+	0.113776i
$861$	−2.89434	+	2.89434i	−0.0986389	+	0.0986389i
$862$	−19.0120	+	22.2163i	−0.647552	+	0.756691i
$863$	32.1316			1.09377			0.546886	−	0.837207i	$-0.315813\pi$
$863$	32.1316			1.09377			0.546886	+	0.837207i	$0.315813\pi$
$864$	5.23674	−	2.13929i	0.178157	−	0.0727802i
$865$	12.7119			0.432218
$866$	−19.8402	+	23.1841i	−0.674198	+	0.787828i
$867$	6.37400	−	6.37400i	0.216472	−	0.216472i
$868$	1.14271	−	0.178704i	0.0387860	−	0.00606563i
$869$	−15.8697	−	15.8697i	−0.538344	−	0.538344i
$870$	2.86471	+	36.8589i	0.0971229	+	1.24963i
$871$		−	49.7131i		−	1.68446i
$872$	−11.2087	+	2.65632i	−0.379573	+	0.0899544i
$873$		−	10.1515i		−	0.343576i
$874$	−9.60848	+	0.746782i	−0.325012	+	0.0252603i
$875$	6.58596	+	6.58596i	0.222646	+	0.222646i
$876$	4.25624	−	5.83426i	0.143805	−	0.197121i
$877$	−8.28244	+	8.28244i	−0.279678	+	0.279678i	−0.832980	−	0.553302i	$-0.813367\pi$
$877$	−8.28244	+	8.28244i	−0.279678	+	0.279678i	0.553302	+	0.832980i	$0.313367\pi$
$878$	−36.3366	−	31.0957i	−1.22630	−	1.04943i
$879$	0.416610			0.0140519
$880$	11.3122	+	35.2827i	0.381333	+	1.18938i
$881$	−27.5183			−0.927116			−0.463558	−	0.886067i	$-0.653427\pi$
$881$	−27.5183			−0.927116			−0.463558	+	0.886067i	$0.653427\pi$
$882$	1.07448	+	0.919506i	0.0361796	+	0.0309614i
$883$	−12.1588	+	12.1588i	−0.409176	+	0.409176i	−0.881451	−	0.472275i	$-0.843433\pi$
$883$	−12.1588	+	12.1588i	−0.409176	+	0.409176i	0.472275	+	0.881451i	$0.343433\pi$
$884$	38.8775	+	28.3621i	1.30759	+	0.953922i
$885$	0.128672	+	0.128672i	0.00432525	+	0.00432525i
$886$	−23.3878	+	1.81773i	−0.785730	+	0.0610678i
$887$		−	14.4004i		−	0.483518i	−0.970336	−	0.241759i	$-0.922276\pi$
$887$		−	14.4004i		−	0.483518i	0.970336	−	0.241759i	$-0.0777243\pi$
$888$	−23.6105	−	14.5637i	−0.792316	−	0.488724i
$889$		−	3.13665i		−	0.105200i
$890$	−3.74028	−	48.1243i	−0.125374	−	1.61313i
$891$	−2.61271	−	2.61271i	−0.0875291	−	0.0875291i
$892$	−5.17231	−	33.0738i	−0.173182	−	1.10739i
$893$	−5.30472	+	5.30472i	−0.177516	+	0.177516i
$894$	−18.3743	+	21.4711i	−0.614528	+	0.718102i
$895$	47.4602			1.58642
$896$	2.71612	−	10.9828i	0.0907393	−	0.366911i
$897$	33.5200			1.11920
$898$	−2.34085	+	2.73539i	−0.0781153	+	0.0912810i
$899$	−4.26411	+	4.26411i	−0.142216	+	0.142216i
$900$	−0.397004	−	2.53860i	−0.0132335	−	0.0846199i
$901$	46.2356	+	46.2356i	1.54033	+	1.54033i
$902$	−1.65736	−	21.3245i	−0.0551842	−	0.710028i
$903$		−	4.30698i		−	0.143327i
$904$	−27.7929	−	17.1435i	−0.924377	−	0.570183i
$905$		−	1.49108i		−	0.0495651i
$906$	15.2727	−	1.18701i	0.507402	−	0.0394358i
$907$	4.24263	+	4.24263i	0.140874	+	0.140874i	0.774027	−	0.633153i	$-0.218239\pi$
$907$	4.24263	+	4.24263i	0.140874	+	0.140874i	−0.633153	+	0.774027i	$0.718239\pi$
$908$	−3.60644	−	2.63099i	−0.119684	−	0.0873123i
$909$	2.71273	−	2.71273i	0.0899754	−	0.0899754i
$910$	−12.7076	−	10.8748i	−0.421253	−	0.360495i
$911$	23.9378			0.793093			0.396547	−	0.918015i	$-0.370208\pi$
$911$	23.9378			0.793093			0.396547	+	0.918015i	$0.370208\pi$
$912$	1.17128	+	3.65324i	0.0387851	+	0.120971i
$913$	−11.1781			−0.369942
$914$	28.9366	+	24.7630i	0.957138	+	0.819088i
$915$	18.0004	−	18.0004i	0.595076	−	0.595076i
$916$	19.0933	−	26.1723i	0.630862	−	0.864757i
$917$	−4.27459	−	4.27459i	−0.141159	−	0.141159i
$918$	−7.19138	+	0.558923i	−0.237351	+	0.0184472i
$919$		−	8.85507i		−	0.292102i	−0.989277	−	0.146051i	$-0.953344\pi$
$919$		−	8.85507i		−	0.292102i	0.989277	−	0.146051i	$-0.0466563\pi$
$920$	49.0236	−	11.6180i	1.61626	−	0.383035i
$921$		−	8.78925i		−	0.289616i
$922$	0.292023	+	3.75732i	0.00961728	+	0.123741i
$923$	9.41998	+	9.41998i	0.310063	+	0.310063i
$924$	−7.30112	+	1.14180i	−0.240189	+	0.0375625i
$925$	−8.90985	+	8.90985i	−0.292954	+	0.292954i
$926$	−4.45125	+	5.20147i	−0.146277	+	0.170931i
$927$	−5.88978			−0.193446
$928$	22.3080	+	54.6075i	0.732297	+	1.79258i
$929$	−3.87678			−0.127193			−0.0635964	−	0.997976i	$-0.520257\pi$
$929$	−3.87678			−0.127193			−0.0635964	+	0.997976i	$0.520257\pi$
$930$	1.33306	−	1.55774i	0.0437127	−	0.0510802i
$931$	−0.678188	+	0.678188i	−0.0222267	+	0.0222267i
$932$	−22.6983	+	3.54972i	−0.743509	+	0.116275i
$933$	19.3936	+	19.3936i	0.634918	+	0.634918i
$934$	−0.672204	−	8.64892i	−0.0219952	−	0.283001i
$935$		−	47.2449i		−	1.54507i
$936$	−3.07701	−	12.9838i	−0.100575	−	0.424389i
$937$			39.9883i			1.30636i	0.757202	+	0.653181i	$0.226566\pi$
$937$			39.9883i			1.30636i	−0.757202	+	0.653181i	$0.773434\pi$
$938$	14.8578	−	1.15477i	0.485125	−	0.0377045i
$939$	−5.77460	−	5.77460i	−0.188447	−	0.188447i
$940$	23.1136	−	31.6830i	0.753881	−	1.03339i
$941$	26.1890	−	26.1890i	0.853737	−	0.853737i	−0.136854	−	0.990591i	$-0.543699\pi$
$941$	26.1890	−	26.1890i	0.853737	−	0.853737i	0.990591	+	0.136854i	$0.0436993\pi$
$942$	13.7162	+	11.7378i	0.446897	+	0.382440i
$943$	−29.0835			−0.947090
$944$	0.258184	+	0.132821i	0.00840316	+	0.00432297i
$945$	2.50694			0.0815506
$946$	17.0993	+	14.6330i	0.555945	+	0.475760i
$947$	−9.53230	+	9.53230i	−0.309758	+	0.309758i	−0.844816	−	0.535057i	$-0.820290\pi$
$947$	−9.53230	+	9.53230i	−0.309758	+	0.309758i	0.535057	+	0.844816i	$0.320290\pi$
$948$	9.81408	+	7.15962i	0.318747	+	0.232534i
$949$	−12.0454	−	12.0454i	−0.391011	−	0.391011i
$950$	1.73733	−	0.135028i	0.0563665	−	0.00438087i
$951$			21.5383i			0.698429i
$952$	−7.57357	+	12.2782i	−0.245461	+	0.397939i
$953$			15.4174i			0.499418i	0.968321	+	0.249709i	$0.0803350\pi$
$953$			15.4174i			0.499418i	−0.968321	+	0.249709i	$0.919665\pi$
$954$	−1.40486	−	18.0756i	−0.0454840	−	0.585220i
$955$	−8.87425	−	8.87425i	−0.287164	−	0.287164i
$956$	5.24796	+	33.5575i	0.169731	+	1.08533i
$957$	27.2448	−	27.2448i	0.880698	−	0.880698i
$958$	22.1127	−	25.8396i	0.714429	−	0.834840i
$959$	0.234016			0.00755676
$960$	−9.00035	−	17.9225i	−0.290485	−	0.578446i
$961$	−30.6656			−0.989212
$962$	−42.5453	+	49.7160i	−1.37172	+	1.60291i
$963$	−0.487701	+	0.487701i	−0.0157159	+	0.0157159i
$964$	3.20824	+	20.5148i	0.103330	+	0.660736i
$965$	−0.983074	−	0.983074i	−0.0316463	−	0.0316463i
$966$	0.778626	+	10.0182i	0.0250519	+	0.322330i
$967$			57.3334i			1.84372i	0.387526	+	0.921859i	$0.373330\pi$
$967$			57.3334i			1.84372i	−0.387526	+	0.921859i	$0.626670\pi$
$968$	3.93870	−	6.38539i	0.126595	−	0.205234i
$969$		−	4.89182i		−	0.157148i
$970$	−35.8823	+	2.78882i	−1.15211	+	0.0895435i
$971$	36.5508	+	36.5508i	1.17297	+	1.17297i	0.981498	+	0.191474i	$0.0613267\pi$
$971$	36.5508	+	36.5508i	1.17297	+	1.17297i	0.191474	+	0.981498i	$0.438673\pi$
$972$	1.61574	+	1.17872i	0.0518249	+	0.0378075i
$973$	−11.3997	+	11.3997i	−0.365457	+	0.365457i
$974$	−18.7816	−	16.0727i	−0.601800	−	0.515001i
$975$	−6.06084			−0.194102
$976$	18.5810	−	36.1184i	0.594762	−	1.15612i
$977$	−44.1265			−1.41173			−0.705866	−	0.708346i	$-0.749442\pi$
$977$	−44.1265			−1.41173			−0.705866	+	0.708346i	$0.749442\pi$
$978$	−12.8645	−	11.0090i	−0.411361	−	0.352030i
$979$	−35.5718	+	35.5718i	−1.13688	+	1.13688i
$980$	2.95498	−	4.05056i	0.0943934	−	0.129390i
$981$	−2.87978	−	2.87978i	−0.0919442	−	0.0919442i
$982$	−52.6185	+	4.08957i	−1.67912	+	0.130503i
$983$			17.4923i			0.557916i	0.960303	+	0.278958i	$0.0899891\pi$
$983$			17.4923i			0.557916i	−0.960303	+	0.278958i	$0.910011\pi$
$984$	2.66976	+	11.2653i	0.0851088	+	0.359126i
$985$			27.4963i			0.876106i
$986$	−5.82832	−	74.9901i	−0.185611	−	2.38817i
$987$	5.53092	+	5.53092i	0.176051	+	0.176051i
$988$	8.94068	−	1.39821i	0.284441	−	0.0444829i
$989$	21.6391	−	21.6391i	0.688084	−	0.688084i
$990$	−8.51734	+	9.95287i	−0.270699	+	0.316323i
$991$	−33.9097			−1.07718			−0.538589	−	0.842569i	$-0.681042\pi$
$991$	−33.9097			−1.07718			−0.538589	+	0.842569i	$0.681042\pi$
$992$	1.26660	−	3.01620i	0.0402147	−	0.0957643i
$993$	3.58109			0.113643
$994$	−2.59655	+	3.03418i	−0.0823577	+	0.0962384i
$995$	−41.9632	+	41.9632i	−1.33032	+	1.33032i
$996$	5.97786	−	0.934859i	0.189416	−	0.0296222i
$997$	26.9354	+	26.9354i	0.853052	+	0.853052i	0.990508	−	0.137456i	$-0.0438926\pi$
$997$	26.9354	+	26.9354i	0.853052	+	0.853052i	−0.137456	+	0.990508i	$0.543893\pi$
$998$	−0.454764	−	5.85122i	−0.0143953	−	0.185217i
$999$		−	9.80787i		−	0.310307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.85.11	✓	28
4.3	odd	2		1344.2.w.b.1009.1		28
8.3	odd	2		2688.2.w.c.2017.14		28
8.5	even	2		2688.2.w.d.2017.1		28
16.3	odd	4		1344.2.w.b.337.1		28
16.5	even	4		2688.2.w.d.673.1		28
16.11	odd	4		2688.2.w.c.673.14		28
16.13	even	4	inner	336.2.w.b.253.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.11	✓	28	1.1	even	1	trivial
336.2.w.b.253.11	yes	28	16.13	even	4	inner
1344.2.w.b.337.1		28	16.3	odd	4
1344.2.w.b.1009.1		28	4.3	odd	2
2688.2.w.c.673.14		28	16.11	odd	4
2688.2.w.c.2017.14		28	8.3	odd	2
2688.2.w.d.673.1		28	16.5	even	4
2688.2.w.d.2017.1		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)

\(f(q)\)	\(=\)	\(q+(0.919506 - 1.07448i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.309018 - 1.97598i) q^{4} +(-1.77267 - 1.77267i) q^{5} +(-0.109584 - 1.40996i) q^{6} -1.00000i q^{7} +(-2.40730 - 1.48489i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.919506 - 1.07448i) q^{2} +(0.707107 - 0.707107i) q^{3} +(-0.309018 - 1.97598i) q^{4} +(-1.77267 - 1.77267i) q^{5} +(-0.109584 - 1.40996i) q^{6} -1.00000i q^{7} +(-2.40730 - 1.48489i) q^{8} -1.00000i q^{9} +(-3.53468 + 0.274720i) q^{10} +(2.61271 + 2.61271i) q^{11} +(-1.61574 - 1.17872i) q^{12} +(-3.33586 + 3.33586i) q^{13} +(-1.07448 - 0.919506i) q^{14} -2.50694 q^{15} +(-3.80902 + 1.22123i) q^{16} +5.10041 q^{17} +(-1.07448 - 0.919506i) q^{18} +(0.678188 - 0.678188i) q^{19} +(-2.95498 + 4.05056i) q^{20} +(-0.707107 - 0.707107i) q^{21} +(5.20971 - 0.404905i) q^{22} -7.10530i q^{23} +(-2.75220 + 0.652239i) q^{24} +1.28473i q^{25} +(0.516974 + 6.65165i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.97598 + 0.309018i) q^{28} +(7.37355 - 7.37355i) q^{29} +(-2.30514 + 2.69365i) q^{30} -0.578298 q^{31} +(-2.19023 + 5.21564i) q^{32} +3.69493 q^{33} +(4.68986 - 5.48029i) q^{34} +(-1.77267 + 1.77267i) q^{35} +(-1.97598 + 0.309018i) q^{36} +(6.93521 + 6.93521i) q^{37} +(-0.105102 - 1.35230i) q^{38} +4.71761i q^{39} +(1.63512 + 6.89958i) q^{40} -4.09322i q^{41} +(-1.40996 + 0.109584i) q^{42} +(3.04549 + 3.04549i) q^{43} +(4.35530 - 5.97005i) q^{44} +(-1.77267 + 1.77267i) q^{45} +(-7.63450 - 6.53336i) q^{46} -7.82190 q^{47} +(-1.82984 + 3.55692i) q^{48} -1.00000 q^{49} +(1.38041 + 1.18131i) q^{50} +(3.60654 - 3.60654i) q^{51} +(7.62243 + 5.56076i) q^{52} +(9.06508 + 9.06508i) q^{53} +(-1.40996 + 0.109584i) q^{54} -9.26295i q^{55} +(-1.48489 + 2.40730i) q^{56} -0.959103i q^{57} +(-1.14272 - 14.7028i) q^{58} +(-0.0513263 - 0.0513263i) q^{59} +(0.774688 + 4.95366i) q^{60} +(-7.18025 + 7.18025i) q^{61} +(-0.531749 + 0.621370i) q^{62} -1.00000 q^{63} +(3.59018 + 7.14917i) q^{64} +11.8268 q^{65} +(3.39751 - 3.97013i) q^{66} +(-7.45132 + 7.45132i) q^{67} +(-1.57612 - 10.0783i) q^{68} +(-5.02420 - 5.02420i) q^{69} +(0.274720 + 3.53468i) q^{70} -2.82386i q^{71} +(-1.48489 + 2.40730i) q^{72} +3.61089i q^{73} +(13.8287 - 1.07478i) q^{74} +(0.908439 + 0.908439i) q^{75} +(-1.54966 - 1.13052i) q^{76} +(2.61271 - 2.61271i) q^{77} +(5.06899 + 4.33787i) q^{78} -6.07405 q^{79} +(8.91697 + 4.58730i) q^{80} -1.00000 q^{81} +(-4.39808 - 3.76374i) q^{82} +(-2.13918 + 2.13918i) q^{83} +(-1.17872 + 1.61574i) q^{84} +(-9.04135 - 9.04135i) q^{85} +(6.07267 - 0.471975i) q^{86} -10.4278i q^{87} +(-2.40998 - 10.1692i) q^{88} +13.6149i q^{89} +(0.274720 + 3.53468i) q^{90} +(3.33586 + 3.33586i) q^{91} +(-14.0399 + 2.19566i) q^{92} +(-0.408919 + 0.408919i) q^{93} +(-7.19228 + 8.40448i) q^{94} -2.40441 q^{95} +(2.13929 + 5.23674i) q^{96} +10.1515 q^{97} +(-0.919506 + 1.07448i) q^{98} +(2.61271 - 2.61271i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more