LMFDB - Embedded newform 336.2.w.b.85.12

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			85.12
Character	$\chi$	$=$	336.85
Dual form			336.2.w.b.253.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25104 + 0.659465i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.13021 + 1.65004i) q^{4} +(2.66347 + 2.66347i) q^{5} +(-1.35093 + 0.418308i) q^{6} -1.00000i q^{7} +(0.325801 + 2.80960i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(1.25104 + 0.659465i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.13021 + 1.65004i) q^{4} +(2.66347 + 2.66347i) q^{5} +(-1.35093 + 0.418308i) q^{6} -1.00000i q^{7} +(0.325801 + 2.80960i) q^{8} -1.00000i q^{9} +(1.57565 + 5.08857i) q^{10} +(-4.19750 - 4.19750i) q^{11} +(-1.96593 - 0.367572i) q^{12} +(0.146713 - 0.146713i) q^{13} +(0.659465 - 1.25104i) q^{14} -3.76671 q^{15} +(-1.44524 + 3.72978i) q^{16} -1.52402 q^{17} +(0.659465 - 1.25104i) q^{18} +(5.84565 - 5.84565i) q^{19} +(-1.38454 + 7.40510i) q^{20} +(0.707107 + 0.707107i) q^{21} +(-2.48314 - 8.01935i) q^{22} +5.92811i q^{23} +(-2.21706 - 1.75631i) q^{24} +9.18812i q^{25} +(0.280297 - 0.0867922i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.65004 - 1.13021i) q^{28} +(1.34452 - 1.34452i) q^{29} +(-4.71232 - 2.48401i) q^{30} -0.0732661 q^{31} +(-4.26772 + 3.71303i) q^{32} +5.93616 q^{33} +(-1.90661 - 1.00504i) q^{34} +(2.66347 - 2.66347i) q^{35} +(1.65004 - 1.13021i) q^{36} +(-4.05921 - 4.05921i) q^{37} +(11.1681 - 3.45815i) q^{38} +0.207484i q^{39} +(-6.61552 + 8.35104i) q^{40} -1.55315i q^{41} +(0.418308 + 1.35093i) q^{42} +(-3.52682 - 3.52682i) q^{43} +(2.18196 - 11.6701i) q^{44} +(2.66347 - 2.66347i) q^{45} +(-3.90938 + 7.41632i) q^{46} +9.26038 q^{47} +(-1.61541 - 3.65929i) q^{48} -1.00000 q^{49} +(-6.05924 + 11.4947i) q^{50} +(1.07764 - 1.07764i) q^{51} +(0.407900 + 0.0762652i) q^{52} +(1.23085 + 1.23085i) q^{53} +(0.418308 + 1.35093i) q^{54} -22.3598i q^{55} +(2.80960 - 0.325801i) q^{56} +8.26699i q^{57} +(2.56872 - 0.795389i) q^{58} +(0.548474 + 0.548474i) q^{59} +(-4.25718 - 6.21521i) q^{60} +(5.91897 - 5.91897i) q^{61} +(-0.0916590 - 0.0483164i) q^{62} -1.00000 q^{63} +(-7.78771 + 1.83074i) q^{64} +0.781533 q^{65} +(7.42638 + 3.91469i) q^{66} +(-1.40166 + 1.40166i) q^{67} +(-1.72247 - 2.51469i) q^{68} +(-4.19181 - 4.19181i) q^{69} +(5.08857 - 1.57565i) q^{70} -4.40942i q^{71} +(2.80960 - 0.325801i) q^{72} -10.3664i q^{73} +(-2.40133 - 7.75514i) q^{74} +(-6.49698 - 6.49698i) q^{75} +(16.2523 + 3.03871i) q^{76} +(-4.19750 + 4.19750i) q^{77} +(-0.136828 + 0.259571i) q^{78} -12.1074 q^{79} +(-13.7835 + 6.08480i) q^{80} -1.00000 q^{81} +(1.02425 - 1.94306i) q^{82} +(-9.09062 + 9.09062i) q^{83} +(-0.367572 + 1.96593i) q^{84} +(-4.05918 - 4.05918i) q^{85} +(-2.08639 - 6.73802i) q^{86} +1.90144i q^{87} +(10.4257 - 13.1608i) q^{88} +12.6372i q^{89} +(5.08857 - 1.57565i) q^{90} +(-0.146713 - 0.146713i) q^{91} +(-9.78161 + 6.70003i) q^{92} +(0.0518070 - 0.0518070i) q^{93} +(11.5851 + 6.10690i) q^{94} +31.1394 q^{95} +(0.392226 - 5.64324i) q^{96} -0.580917 q^{97} +(-1.25104 - 0.659465i) q^{98} +(-4.19750 + 4.19750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) $ 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.25104	+	0.659465i	0.884620	+	0.466312i
$2$	1.25104	+	0.659465i	0.884620	+	0.466312i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.13021	+	1.65004i	0.565106	+	0.825018i
$5$	2.66347	+	2.66347i	1.19114	+	1.19114i	0.976748	+	0.214391i	$0.0687767\pi$
$5$	2.66347	+	2.66347i	1.19114	+	1.19114i	0.214391	+	0.976748i	$0.431223\pi$
$6$	−1.35093	+	0.418308i	−0.551516	+	0.170774i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.325801	+	2.80960i	0.115188	+	0.993344i
$9$		−	1.00000i		−	0.333333i
$10$	1.57565	+	5.08857i	0.498263	+	1.60915i
$11$	−4.19750	−	4.19750i	−1.26559	−	1.26559i	−0.948341	−	0.317252i	$-0.897240\pi$
$11$	−4.19750	−	4.19750i	−1.26559	−	1.26559i	−0.317252	−	0.948341i	$-0.602760\pi$
$12$	−1.96593	−	0.367572i	−0.567516	−	0.106109i
$13$	0.146713	−	0.146713i	0.0406910	−	0.0406910i	−0.686469	−	0.727160i	$-0.740840\pi$
$13$	0.146713	−	0.146713i	0.0406910	−	0.0406910i	0.727160	+	0.686469i	$0.240840\pi$
$14$	0.659465	−	1.25104i	0.176249	−	0.334355i
$15$	−3.76671			−0.972561
$16$	−1.44524	+	3.72978i	−0.361310	+	0.932446i
$17$	−1.52402			−0.369629			−0.184815	−	0.982773i	$-0.559168\pi$
$17$	−1.52402			−0.369629			−0.184815	+	0.982773i	$0.559168\pi$
$18$	0.659465	−	1.25104i	0.155437	−	0.294873i
$19$	5.84565	−	5.84565i	1.34108	−	1.34108i	0.446100	−	0.894983i	$-0.352812\pi$
$19$	5.84565	−	5.84565i	1.34108	−	1.34108i	0.894983	−	0.446100i	$-0.147188\pi$
$20$	−1.38454	+	7.40510i	−0.309592	+	1.65583i
$21$	0.707107	+	0.707107i	0.154303	+	0.154303i
$22$	−2.48314	−	8.01935i	−0.529408	−	1.70973i
$23$			5.92811i			1.23610i	0.786140	+	0.618049i	$0.212077\pi$
$23$			5.92811i			1.23610i	−0.786140	+	0.618049i	$0.787923\pi$
$24$	−2.21706	−	1.75631i	−0.452556	−	0.358506i
$25$			9.18812i			1.83762i
$26$	0.280297	−	0.0867922i	0.0549707	−	0.0170214i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.65004	−	1.13021i	0.311828	−	0.213590i
$29$	1.34452	−	1.34452i	0.249672	−	0.249672i	−0.571164	−	0.820836i	$-0.693508\pi$
$29$	1.34452	−	1.34452i	0.249672	−	0.249672i	0.820836	+	0.571164i	$0.193508\pi$
$30$	−4.71232	−	2.48401i	−0.860347	−	0.453517i
$31$	−0.0732661			−0.0131590			−0.00657949	−	0.999978i	$-0.502094\pi$
$31$	−0.0732661			−0.0131590			−0.00657949	+	0.999978i	$0.502094\pi$
$32$	−4.26772	+	3.71303i	−0.754433	+	0.656377i
$33$	5.93616			1.03335
$34$	−1.90661	−	1.00504i	−0.326981	−	0.172363i
$35$	2.66347	−	2.66347i	0.450208	−	0.450208i
$36$	1.65004	−	1.13021i	0.275006	−	0.188369i
$37$	−4.05921	−	4.05921i	−0.667329	−	0.667329i	0.289768	−	0.957097i	$-0.406422\pi$
$37$	−4.05921	−	4.05921i	−0.667329	−	0.667329i	−0.957097	+	0.289768i	$0.906422\pi$
$38$	11.1681	−	3.45815i	1.81171	−	0.560986i
$39$			0.207484i			0.0332240i
$40$	−6.61552	+	8.35104i	−1.04601	+	1.32042i
$41$		−	1.55315i		−	0.242561i	−0.992618	−	0.121281i	$-0.961300\pi$
$41$		−	1.55315i		−	0.242561i	0.992618	−	0.121281i	$-0.0387001\pi$
$42$	0.418308	+	1.35093i	0.0645463	+	0.208453i
$43$	−3.52682	−	3.52682i	−0.537835	−	0.537835i	0.385057	−	0.922893i	$-0.374182\pi$
$43$	−3.52682	−	3.52682i	−0.537835	−	0.537835i	−0.922893	+	0.385057i	$0.874182\pi$
$44$	2.18196	−	11.6701i	0.328943	−	1.75933i
$45$	2.66347	−	2.66347i	0.397046	−	0.397046i
$46$	−3.90938	+	7.41632i	−0.576407	+	1.09348i
$47$	9.26038			1.35077			0.675383	−	0.737468i	$-0.263979\pi$
$47$	9.26038			1.35077			0.675383	+	0.737468i	$0.263979\pi$
$48$	−1.61541	−	3.65929i	−0.233165	−	0.528174i
$49$	−1.00000			−0.142857
$50$	−6.05924	+	11.4947i	−0.856907	+	1.62560i
$51$	1.07764	−	1.07764i	0.150900	−	0.150900i
$52$	0.407900	+	0.0762652i	0.0565655	+	0.0105761i
$53$	1.23085	+	1.23085i	0.169070	+	0.169070i	0.786570	−	0.617501i	$-0.211855\pi$
$53$	1.23085	+	1.23085i	0.169070	+	0.169070i	−0.617501	+	0.786570i	$0.711855\pi$
$54$	0.418308	+	1.35093i	0.0569245	+	0.183839i
$55$		−	22.3598i		−	3.01499i
$56$	2.80960	−	0.325801i	0.375449	−	0.0435370i
$57$			8.26699i			1.09499i
$58$	2.56872	−	0.795389i	0.337290	−	0.104440i
$59$	0.548474	+	0.548474i	0.0714052	+	0.0714052i	0.741907	−	0.670502i	$-0.233921\pi$
$59$	0.548474	+	0.548474i	0.0714052	+	0.0714052i	−0.670502	+	0.741907i	$0.733921\pi$
$60$	−4.25718	−	6.21521i	−0.549600	−	0.802381i
$61$	5.91897	−	5.91897i	0.757847	−	0.757847i	−0.218083	−	0.975930i	$-0.569981\pi$
$61$	5.91897	−	5.91897i	0.757847	−	0.757847i	0.975930	+	0.218083i	$0.0699805\pi$
$62$	−0.0916590	−	0.0483164i	−0.0116407	−	0.00613619i
$63$	−1.00000			−0.125988
$64$	−7.78771	+	1.83074i	−0.973463	+	0.228843i
$65$	0.781533			0.0969372
$66$	7.42638	+	3.91469i	0.914125	+	0.481865i
$67$	−1.40166	+	1.40166i	−0.171241	+	0.171241i	−0.787524	−	0.616284i	$-0.788637\pi$
$67$	−1.40166	+	1.40166i	−0.171241	+	0.171241i	0.616284	+	0.787524i	$0.288637\pi$
$68$	−1.72247	−	2.51469i	−0.208880	−	0.304951i
$69$	−4.19181	−	4.19181i	−0.504635	−	0.504635i
$70$	5.08857	−	1.57565i	0.608201	−	0.188326i
$71$		−	4.40942i		−	0.523302i	−0.965163	−	0.261651i	$-0.915733\pi$
$71$		−	4.40942i		−	0.523302i	0.965163	−	0.261651i	$-0.0842670\pi$
$72$	2.80960	−	0.325801i	0.331115	−	0.0383960i
$73$		−	10.3664i		−	1.21329i	−0.794972	−	0.606647i	$-0.792514\pi$
$73$		−	10.3664i		−	1.21329i	0.794972	−	0.606647i	$-0.207486\pi$
$74$	−2.40133	−	7.75514i	−0.279149	−	0.901517i
$75$	−6.49698	−	6.49698i	−0.750207	−	0.750207i
$76$	16.2523	+	3.03871i	1.86427	+	0.348564i
$77$	−4.19750	+	4.19750i	−0.478349	+	0.478349i
$78$	−0.136828	+	0.259571i	−0.0154928	+	0.0293907i
$79$	−12.1074			−1.36219			−0.681094	−	0.732196i	$-0.738496\pi$
$79$	−12.1074			−1.36219			−0.681094	+	0.732196i	$0.738496\pi$
$80$	−13.7835	+	6.08480i	−1.54104	+	0.680301i
$81$	−1.00000			−0.111111
$82$	1.02425	−	1.94306i	0.113109	−	0.214575i
$83$	−9.09062	+	9.09062i	−0.997825	+	0.997825i	−0.999998	−	0.00217245i	$-0.999308\pi$
$83$	−9.09062	+	9.09062i	−0.997825	+	0.997825i	0.00217245	+	0.999998i	$0.499308\pi$
$84$	−0.367572	+	1.96593i	−0.0401053	+	0.214501i
$85$	−4.05918	−	4.05918i	−0.440280	−	0.440280i
$86$	−2.08639	−	6.73802i	−0.224981	−	0.726579i
$87$			1.90144i			0.203856i
$88$	10.4257	−	13.1608i	1.11139	−	1.40295i
$89$			12.6372i			1.33954i	0.742569	+	0.669770i	$0.233607\pi$
$89$			12.6372i			1.33954i	−0.742569	+	0.669770i	$0.766393\pi$
$90$	5.08857	−	1.57565i	0.536383	−	0.166088i
$91$	−0.146713	−	0.146713i	−0.0153797	−	0.0153797i
$92$	−9.78161	+	6.70003i	−1.01980	+	0.698526i
$93$	0.0518070	−	0.0518070i	0.00537213	−	0.00537213i
$94$	11.5851	+	6.10690i	1.19491	+	0.629878i
$95$	31.1394			3.19483
$96$	0.392226	−	5.64324i	0.0400314	−	0.575961i
$97$	−0.580917			−0.0589832			−0.0294916	−	0.999565i	$-0.509389\pi$
$97$	−0.580917			−0.0589832			−0.0294916	+	0.999565i	$0.509389\pi$
$98$	−1.25104	−	0.659465i	−0.126374	−	0.0666160i
$99$	−4.19750	+	4.19750i	−0.421864	+	0.421864i
$100$	−15.1607	+	10.3845i	−1.51607	+	1.03845i
$101$	2.37738	+	2.37738i	0.236558	+	0.236558i	0.815423	−	0.578865i	$-0.196504\pi$
$101$	2.37738	+	2.37738i	0.236558	+	0.236558i	−0.578865	+	0.815423i	$0.696504\pi$
$102$	2.05885	−	0.637510i	0.203856	−	0.0631229i
$103$			13.6973i			1.34964i	0.737983	+	0.674819i	$0.235778\pi$
$103$			13.6973i			1.34964i	−0.737983	+	0.674819i	$0.764222\pi$
$104$	0.460005	+	0.364407i	0.0451072	+	0.0357330i
$105$			3.76671i			0.367593i
$106$	0.728141	+	2.35154i	0.0707233	+	0.228402i
$107$	−0.673478	−	0.673478i	−0.0651075	−	0.0651075i	0.673803	−	0.738911i	$-0.264660\pi$
$107$	−0.673478	−	0.673478i	−0.0651075	−	0.0651075i	−0.738911	+	0.673803i	$0.764660\pi$
$108$	−0.367572	+	1.96593i	−0.0353696	+	0.189172i
$109$	9.67641	−	9.67641i	0.926832	−	0.926832i	−0.0706683	−	0.997500i	$-0.522513\pi$
$109$	9.67641	−	9.67641i	0.926832	−	0.926832i	0.997500	+	0.0706683i	$0.0225132\pi$
$110$	14.7455	−	27.9730i	1.40593	−	2.66713i
$111$	5.74058			0.544872
$112$	3.72978	+	1.44524i	0.352431	+	0.136563i
$113$	10.5062			0.988340			0.494170	−	0.869365i	$-0.335472\pi$
$113$	10.5062			0.988340			0.494170	+	0.869365i	$0.335472\pi$
$114$	−5.45179	+	10.3424i	−0.510607	+	0.968650i
$115$	−15.7893	+	15.7893i	−1.47236	+	1.47236i
$116$	3.73811	+	0.698917i	0.347075	+	0.0648928i
$117$	−0.146713	−	0.146713i	−0.0135637	−	0.0135637i
$118$	0.324465	+	1.04786i	0.0298694	+	0.0964636i
$119$			1.52402i			0.139707i
$120$	−1.22720	−	10.5830i	−0.112027	−	0.966087i
$121$			24.2380i			2.20345i
$122$	11.3082	−	3.50153i	1.02380	−	0.317013i
$123$	1.09824	+	1.09824i	0.0990253	+	0.0990253i
$124$	−0.0828062	−	0.120892i	−0.00743622	−	0.0108564i
$125$	−11.1549	+	11.1549i	−0.997727	+	0.997727i
$126$	−1.25104	−	0.659465i	−0.111452	−	0.0587498i
$127$	−11.9443			−1.05989			−0.529945	−	0.848032i	$-0.677787\pi$
$127$	−11.9443			−1.05989			−0.529945	+	0.848032i	$0.677787\pi$
$128$	−10.9501	−	2.84538i	−0.967858	−	0.251499i
$129$	4.98768			0.439141
$130$	0.977730	+	0.515393i	0.0857526	+	0.0452030i
$131$	−9.19810	+	9.19810i	−0.803642	+	0.803642i	−0.983663	−	0.180021i	$-0.942384\pi$
$131$	−9.19810	+	9.19810i	−0.803642	+	0.803642i	0.180021	+	0.983663i	$0.442384\pi$
$132$	6.70912	+	9.79488i	0.583954	+	0.852535i
$133$	−5.84565	−	5.84565i	−0.506882	−	0.506882i
$134$	−2.67789	+	0.829192i	−0.231334	+	0.0716313i
$135$			3.76671i			0.324187i
$136$	−0.496528	−	4.28189i	−0.0425769	−	0.367169i
$137$			2.42423i			0.207116i	0.994623	+	0.103558i	$0.0330227\pi$
$137$			2.42423i			0.207116i	−0.994623	+	0.103558i	$0.966977\pi$
$138$	−2.47978	−	8.00848i	−0.211093	−	0.681727i
$139$	−12.5811	−	12.5811i	−1.06712	−	1.06712i	−0.997579	−	0.0695400i	$-0.977847\pi$
$139$	−12.5811	−	12.5811i	−1.06712	−	1.06712i	−0.0695400	−	0.997579i	$-0.522153\pi$
$140$	7.40510	+	1.38454i	0.625845	+	0.117015i
$141$	−6.54808	+	6.54808i	−0.551448	+	0.551448i
$142$	2.90786	−	5.51637i	0.244022	−	0.462924i
$143$	−1.23166			−0.102996
$144$	3.72978	+	1.44524i	0.310815	+	0.120437i
$145$	7.16219			0.594788
$146$	6.83626	−	12.9688i	0.565773	−	1.07330i
$147$	0.707107	−	0.707107i	0.0583212	−	0.0583212i
$148$	2.11008	−	11.2856i	0.173447	−	0.927671i
$149$	−16.9548	−	16.9548i	−1.38899	−	1.38899i	−0.827445	−	0.561546i	$-0.810207\pi$
$149$	−16.9548	−	16.9548i	−1.38899	−	1.38899i	−0.561546	−	0.827445i	$-0.689793\pi$
$150$	−3.84347	−	12.4125i	−0.313818	−	1.01348i
$151$		−	14.7780i		−	1.20262i	−0.799016	−	0.601310i	$-0.794646\pi$
$151$		−	14.7780i		−	1.20262i	0.799016	−	0.601310i	$-0.205354\pi$
$152$	18.3284	+	14.5194i	1.48663	+	1.17768i
$153$			1.52402i			0.123210i
$154$	−8.01935	+	2.48314i	−0.646218	+	0.200097i
$155$	−0.195142	−	0.195142i	−0.0156742	−	0.0156742i
$156$	−0.342356	+	0.234501i	−0.0274104	+	0.0187751i
$157$	5.72313	−	5.72313i	0.456755	−	0.456755i	−0.440833	−	0.897589i	$-0.645317\pi$
$157$	5.72313	−	5.72313i	0.456755	−	0.456755i	0.897589	+	0.440833i	$0.145317\pi$
$158$	−15.1469	−	7.98440i	−1.20502	−	0.635205i
$159$	−1.74068			−0.138045
$160$	−21.2565	−	1.47740i	−1.68047	−	0.116799i
$161$	5.92811			0.467201
$162$	−1.25104	−	0.659465i	−0.0982911	−	0.0518125i
$163$	3.97999	−	3.97999i	0.311737	−	0.311737i	−0.533845	−	0.845582i	$-0.679254\pi$
$163$	3.97999	−	3.97999i	0.311737	−	0.311737i	0.845582	+	0.533845i	$0.179254\pi$
$164$	2.56276	−	1.75539i	0.200118	−	0.137073i
$165$	15.8108	+	15.8108i	1.23087	+	1.23087i
$166$	−17.3677	+	5.37780i	−1.34799	+	0.417398i
$167$			4.37824i			0.338799i	0.985548	+	0.169399i	$0.0541827\pi$
$167$			4.37824i			0.338799i	−0.985548	+	0.169399i	$0.945817\pi$
$168$	−1.75631	+	2.21706i	−0.135502	+	0.171050i
$169$			12.9570i			0.996688i
$170$	−2.40132	−	7.75509i	−0.184173	−	0.594788i
$171$	−5.84565	−	5.84565i	−0.447028	−	0.447028i
$172$	1.83333	−	9.80544i	0.139790	−	0.747658i
$173$	−2.29897	+	2.29897i	−0.174788	+	0.174788i	−0.789079	−	0.614291i	$-0.789442\pi$
$173$	−2.29897	+	2.29897i	−0.174788	+	0.174788i	0.614291	+	0.789079i	$0.289442\pi$
$174$	−1.25394	+	2.37879i	−0.0950606	+	0.180335i
$175$	9.18812			0.694557
$176$	21.7222	−	9.58935i	1.63737	−	0.722825i
$177$	−0.775659			−0.0583021
$178$	−8.33379	+	15.8097i	−0.624644	+	1.18498i
$179$	−13.0003	+	13.0003i	−0.971690	+	0.971690i	−0.999610	−	0.0279201i	$-0.991112\pi$
$179$	−13.0003	+	13.0003i	−0.971690	+	0.971690i	0.0279201	+	0.999610i	$0.491112\pi$
$180$	7.40510	+	1.38454i	0.551944	+	0.103197i
$181$	10.9054	+	10.9054i	0.810592	+	0.810592i	0.984723	−	0.174130i	$-0.0557114\pi$
$181$	10.9054	+	10.9054i	0.810592	+	0.810592i	−0.174130	+	0.984723i	$0.555711\pi$
$182$	−0.0867922	−	0.280297i	−0.00643347	−	0.0207770i
$183$			8.37069i			0.618779i
$184$	−16.6556	+	1.93139i	−1.22787	+	0.142384i
$185$		−	21.6231i		−	1.58976i
$186$	0.0989775	−	0.0306478i	0.00725739	−	0.00224721i
$187$	6.39707	+	6.39707i	0.467800	+	0.467800i
$188$	10.4662	+	15.2800i	0.763325	+	1.11441i
$189$	0.707107	−	0.707107i	0.0514344	−	0.0514344i
$190$	38.9567	+	20.5353i	2.82621	+	1.48979i
$191$	10.9853			0.794870			0.397435	−	0.917630i	$-0.369900\pi$
$191$	10.9853			0.794870			0.397435	+	0.917630i	$0.369900\pi$
$192$	4.21221	−	6.80127i	0.303990	−	0.490839i
$193$	−2.00804			−0.144542			−0.0722711	−	0.997385i	$-0.523025\pi$
$193$	−2.00804			−0.144542			−0.0722711	+	0.997385i	$0.523025\pi$
$194$	−0.726752	−	0.383095i	−0.0521777	−	0.0275046i
$195$	−0.552627	+	0.552627i	−0.0395744	+	0.0395744i
$196$	−1.13021	−	1.65004i	−0.0807294	−	0.117860i
$197$	−9.89580	−	9.89580i	−0.705047	−	0.705047i	0.260443	−	0.965489i	$-0.416131\pi$
$197$	−9.89580	−	9.89580i	−0.705047	−	0.705047i	−0.965489	+	0.260443i	$0.916131\pi$
$198$	−8.01935	+	2.48314i	−0.569910	+	0.176469i
$199$			13.0600i			0.925796i	0.886412	+	0.462898i	$0.153190\pi$
$199$			13.0600i			0.925796i	−0.886412	+	0.462898i	$0.846810\pi$
$200$	−25.8149	+	2.99350i	−1.82539	+	0.211672i
$201$		−	1.98225i		−	0.139817i
$202$	1.40640	+	4.54200i	0.0989542	+	0.319574i
$203$	−1.34452	−	1.34452i	−0.0943671	−	0.0943671i
$204$	2.99612	+	0.560186i	0.209770	+	0.0392209i
$205$	4.13677	−	4.13677i	0.288924	−	0.288924i
$206$	−9.03291	+	17.1359i	−0.629352	+	1.19392i
$207$	5.92811			0.412032
$208$	0.335173	+	0.759245i	0.0232400	+	0.0526442i
$209$	−49.0742			−3.39453
$210$	−2.48401	+	4.71232i	−0.171413	+	0.325181i
$211$	−5.30933	+	5.30933i	−0.365510	+	0.365510i	−0.865837	−	0.500327i	$-0.833213\pi$
$211$	−5.30933	+	5.30933i	−0.365510	+	0.365510i	0.500327	+	0.865837i	$0.333213\pi$
$212$	−0.639825	+	3.42206i	−0.0439434	+	0.235028i
$213$	3.11793	+	3.11793i	0.213637	+	0.213637i
$214$	−0.398414	−	1.28668i	−0.0272350	−	0.0879559i
$215$		−	18.7872i		−	1.28127i
$216$	−1.75631	+	2.21706i	−0.119502	+	0.150852i
$217$			0.0732661i			0.00497363i
$218$	18.4868	−	5.72434i	1.25209	−	0.387701i
$219$	7.33014	+	7.33014i	0.495325	+	0.495325i
$220$	36.8945	−	25.2713i	2.48743	−	1.70379i
$221$	−0.223594	+	0.223594i	−0.0150406	+	0.0150406i
$222$	7.18171	+	3.78571i	0.482005	+	0.254080i
$223$	1.49216			0.0999223			0.0499611	−	0.998751i	$-0.484090\pi$
$223$	1.49216			0.0999223			0.0499611	+	0.998751i	$0.484090\pi$
$224$	3.71303	+	4.26772i	0.248087	+	0.285149i
$225$	9.18812			0.612541
$226$	13.1437	+	6.92847i	0.874305	+	0.460875i
$227$	16.0345	−	16.0345i	1.06425	−	1.06425i	0.0664559	−	0.997789i	$-0.478831\pi$
$227$	16.0345	−	16.0345i	1.06425	−	1.06425i	0.997789	−	0.0664559i	$-0.0211692\pi$
$228$	−13.6408	+	9.34345i	−0.903387	+	0.618785i
$229$	−2.93674	−	2.93674i	−0.194065	−	0.194065i	0.603385	−	0.797450i	$-0.293818\pi$
$229$	−2.93674	−	2.93674i	−0.194065	−	0.194065i	−0.797450	+	0.603385i	$0.793818\pi$
$230$	−30.1656	+	9.34061i	−1.98906	+	0.615902i
$231$		−	5.93616i		−	0.390571i
$232$	4.21562	+	3.33953i	0.276769	+	0.219251i
$233$			18.4388i			1.20796i	0.796998	+	0.603982i	$0.206420\pi$
$233$			18.4388i			1.20796i	−0.796998	+	0.603982i	$0.793580\pi$
$234$	−0.0867922	−	0.280297i	−0.00567379	−	0.0183236i
$235$	24.6647	+	24.6647i	1.60895	+	1.60895i
$236$	−0.285110	+	1.52489i	−0.0185591	+	0.0992621i
$237$	8.56122	−	8.56122i	0.556111	−	0.556111i
$238$	−1.00504	+	1.90661i	−0.0651469	+	0.123587i
$239$	−13.3974			−0.866605			−0.433302	−	0.901249i	$-0.642652\pi$
$239$	−13.3974			−0.866605			−0.433302	+	0.901249i	$0.642652\pi$
$240$	5.44381	−	14.0490i	0.351396	−	0.906860i
$241$	−21.7644			−1.40197			−0.700985	−	0.713176i	$-0.747256\pi$
$241$	−21.7644			−1.40197			−0.700985	+	0.713176i	$0.747256\pi$
$242$	−15.9841	+	30.3227i	−1.02750	+	1.94922i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	16.4562	+	3.07683i	1.05350	+	0.196974i
$245$	−2.66347	−	2.66347i	−0.170163	−	0.170163i
$246$	0.649696	+	2.09820i	0.0414231	+	0.133776i
$247$		−	1.71527i		−	0.109140i
$248$	−0.0238702	−	0.205848i	−0.00151576	−	0.0130714i
$249$		−	12.8561i		−	0.814721i
$250$	−21.3116	+	6.59900i	−1.34786	+	0.417357i
$251$	12.8418	+	12.8418i	0.810566	+	0.810566i	0.984719	−	0.174153i	$-0.0557187\pi$
$251$	12.8418	+	12.8418i	0.810566	+	0.810566i	−0.174153	+	0.984719i	$0.555719\pi$
$252$	−1.13021	−	1.65004i	−0.0711967	−	0.103943i
$253$	24.8832	−	24.8832i	1.56440	−	1.56440i
$254$	−14.9429	−	7.87688i	−0.937599	−	0.494239i
$255$	5.74055			0.359487
$256$	−11.8226	−	10.7809i	−0.738909	−	0.673805i
$257$	−17.4641			−1.08938			−0.544691	−	0.838637i	$-0.683353\pi$
$257$	−17.4641			−1.08938			−0.544691	+	0.838637i	$0.683353\pi$
$258$	6.23980	+	3.28920i	0.388473	+	0.204777i
$259$	−4.05921	+	4.05921i	−0.252227	+	0.252227i
$260$	0.883298	+	1.28956i	0.0547798	+	0.0799750i
$261$	−1.34452	−	1.34452i	−0.0832239	−	0.0832239i
$262$	−17.5730	+	5.44139i	−1.08567	+	0.336170i
$263$			28.9791i			1.78693i	0.449135	+	0.893464i	$0.351732\pi$
$263$			28.9791i			1.78693i	−0.449135	+	0.893464i	$0.648268\pi$
$264$	1.93401	+	16.6782i	0.119030	+	1.02647i
$265$			6.55665i			0.402772i
$266$	−3.45815	−	11.1681i	−0.212033	−	0.684763i
$267$	−8.93585	−	8.93585i	−0.546865	−	0.546865i
$268$	−3.89698	−	0.728620i	−0.238046	−	0.0445075i
$269$	−7.86881	+	7.86881i	−0.479770	+	0.479770i	−0.905058	−	0.425288i	$-0.860173\pi$
$269$	−7.86881	+	7.86881i	−0.479770	+	0.479770i	0.425288	+	0.905058i	$0.360173\pi$
$270$	−2.48401	+	4.71232i	−0.151172	+	0.286782i
$271$	17.6682			1.07326			0.536632	−	0.843816i	$-0.319696\pi$
$271$	17.6682			1.07326			0.536632	+	0.843816i	$0.319696\pi$
$272$	2.20258	−	5.68426i	0.133551	−	0.344659i
$273$	0.207484			0.0125575
$274$	−1.59869	+	3.03281i	−0.0965806	+	0.183219i
$275$	38.5671	−	38.5671i	2.32568	−	2.32568i
$276$	2.17901	−	11.6543i	0.131161	−	0.701505i
$277$	8.93230	+	8.93230i	0.536690	+	0.536690i	0.922555	−	0.385865i	$-0.126097\pi$
$277$	8.93230	+	8.93230i	0.536690	+	0.536690i	−0.385865	+	0.922555i	$0.626097\pi$
$278$	−7.44272	−	24.0364i	−0.446385	−	1.44161i
$279$			0.0732661i			0.00438633i
$280$	8.35104	+	6.61552i	0.499070	+	0.395353i
$281$		−	28.7979i		−	1.71794i	−0.512028	−	0.858969i	$-0.671106\pi$
$281$		−	28.7979i		−	1.71794i	0.512028	−	0.858969i	$-0.328894\pi$
$282$	−12.5101	+	3.87369i	−0.744968	+	0.230675i
$283$	5.32568	+	5.32568i	0.316579	+	0.316579i	0.847451	−	0.530873i	$-0.178136\pi$
$283$	5.32568	+	5.32568i	0.316579	+	0.316579i	−0.530873	+	0.847451i	$0.678136\pi$
$284$	7.27571	−	4.98358i	0.431734	−	0.295721i
$285$	−22.0189	+	22.0189i	−1.30429	+	1.30429i
$286$	−1.54086	−	0.812235i	−0.0911127	−	0.0480285i
$287$	−1.55315			−0.0916796
$288$	3.71303	+	4.26772i	0.218792	+	0.251478i
$289$	−14.6774			−0.863374
$290$	8.96020	+	4.72321i	0.526161	+	0.277357i
$291$	0.410771	−	0.410771i	0.0240798	−	0.0240798i
$292$	17.1049	−	11.7162i	1.00099	−	0.685639i
$293$	−6.34091	−	6.34091i	−0.370440	−	0.370440i	0.497197	−	0.867637i	$-0.334362\pi$
$293$	−6.34091	−	6.34091i	−0.370440	−	0.370440i	−0.867637	+	0.497197i	$0.834362\pi$
$294$	1.35093	−	0.418308i	0.0787880	−	0.0243962i
$295$			2.92169i			0.170107i
$296$	10.0823	−	12.7272i	0.586019	−	0.739756i
$297$		−	5.93616i		−	0.344451i
$298$	−10.0301	−	32.3923i	−0.581026	−	1.87643i
$299$	0.869734	+	0.869734i	0.0502980	+	0.0502980i
$300$	3.37729	−	18.0632i	0.194988	−	1.04288i
$301$	−3.52682	+	3.52682i	−0.203283	+	0.203283i
$302$	9.74560	−	18.4880i	0.560796	−	1.06386i
$303$	−3.36212			−0.193149
$304$	13.3546	+	30.2514i	0.765940	+	1.73503i
$305$	31.5300			1.80540
$306$	−1.00504	+	1.90661i	−0.0574542	+	0.108994i
$307$	0.705377	−	0.705377i	0.0402580	−	0.0402580i	−0.686691	−	0.726949i	$-0.740938\pi$
$307$	0.705377	−	0.705377i	0.0402580	−	0.0402580i	0.726949	+	0.686691i	$0.240938\pi$
$308$	−11.6701	−	2.18196i	−0.664965	−	0.124329i
$309$	−9.68547	−	9.68547i	−0.550987	−	0.550987i
$310$	−0.115441	−	0.372820i	−0.00655663	−	0.0211747i
$311$		−	12.0031i		−	0.680634i	−0.940311	−	0.340317i	$-0.889466\pi$
$311$		−	12.0031i		−	0.680634i	0.940311	−	0.340317i	$-0.110534\pi$
$312$	−0.582947	+	0.0675985i	−0.0330029	+	0.00382701i
$313$		−	6.69748i		−	0.378564i	−0.981923	−	0.189282i	$-0.939384\pi$
$313$		−	6.69748i		−	0.378564i	0.981923	−	0.189282i	$-0.0606160\pi$
$314$	10.9341	−	3.38567i	0.617046	−	0.191064i
$315$	−2.66347	−	2.66347i	−0.150069	−	0.150069i
$316$	−13.6839	−	19.9776i	−0.769781	−	1.12383i
$317$	−0.358883	+	0.358883i	−0.0201569	+	0.0201569i	−0.717113	−	0.696957i	$-0.754537\pi$
$317$	−0.358883	+	0.358883i	−0.0201569	+	0.0201569i	0.696957	+	0.717113i	$0.254537\pi$
$318$	−2.17767	−	1.14792i	−0.122117	−	0.0643721i
$319$	−11.2873			−0.631966
$320$	−25.6184	−	15.8662i	−1.43211	−	0.886947i
$321$	0.952441			0.0531601
$322$	7.41632	+	3.90938i	0.413295	+	0.217861i
$323$	−8.90888	+	8.90888i	−0.495703	+	0.495703i
$324$	−1.13021	−	1.65004i	−0.0627896	−	0.0916687i
$325$	1.34802	+	1.34802i	0.0747747	+	0.0747747i
$326$	7.60379	−	2.35447i	0.421135	−	0.130402i
$327$			13.6845i			0.756755i
$328$	4.36373	−	0.506018i	0.240947	−	0.0279402i
$329$		−	9.26038i		−	0.510541i
$330$	9.35329	+	30.2066i	0.514881	+	1.66282i
$331$	1.96758	+	1.96758i	0.108148	+	0.108148i	0.759110	−	0.650962i	$-0.225634\pi$
$331$	1.96758	+	1.96758i	0.108148	+	0.108148i	−0.650962	+	0.759110i	$0.725634\pi$
$332$	−25.2742	−	4.72553i	−1.38710	−	0.259347i
$333$	−4.05921	+	4.05921i	−0.222443	+	0.222443i
$334$	−2.88730	+	5.47737i	−0.157986	+	0.299708i
$335$	−7.46658			−0.407943
$336$	−3.65929	+	1.61541i	−0.199631	+	0.0881281i
$337$	28.1821			1.53518			0.767588	−	0.640943i	$-0.221457\pi$
$337$	28.1821			1.53518			0.767588	+	0.640943i	$0.221457\pi$
$338$	−8.54465	+	16.2097i	−0.464768	+	0.881691i
$339$	−7.42900	+	7.42900i	−0.403488	+	0.403488i
$340$	2.11006	−	11.2855i	0.114434	−	0.612044i
$341$	0.307534	+	0.307534i	0.0166539	+	0.0166539i
$342$	−3.45815	−	11.1681i	−0.186995	−	0.603904i
$343$			1.00000i			0.0539949i
$344$	8.75992	−	11.0580i	0.472303	−	0.596207i
$345$		−	22.3295i		−	1.20218i
$346$	−4.39221	+	1.36002i	−0.236127	+	0.0731152i
$347$	−0.476477	−	0.476477i	−0.0255786	−	0.0255786i	0.694202	−	0.719780i	$-0.255758\pi$
$347$	−0.476477	−	0.476477i	−0.0255786	−	0.0255786i	−0.719780	+	0.694202i	$0.755758\pi$
$348$	−3.13745	+	2.14903i	−0.168185	+	0.115200i
$349$	5.73485	−	5.73485i	0.306980	−	0.306980i	−0.536757	−	0.843737i	$-0.680351\pi$
$349$	5.73485	−	5.73485i	0.306980	−	0.306980i	0.843737	+	0.536757i	$0.180351\pi$
$350$	11.4947	+	6.05924i	0.614419	+	0.323880i
$351$	0.207484			0.0110747
$352$	33.4992	+	2.32832i	1.78551	+	0.124100i
$353$	0.824211			0.0438683			0.0219342	−	0.999759i	$-0.493018\pi$
$353$	0.824211			0.0438683			0.0219342	+	0.999759i	$0.493018\pi$
$354$	−0.970382	−	0.511520i	−0.0515752	−	0.0271870i
$355$	11.7444	−	11.7444i	0.623326	−	0.623326i
$356$	−20.8518	+	14.2827i	−1.10514	+	0.756982i
$357$	−1.07764	−	1.07764i	−0.0570350	−	0.0570350i
$358$	−24.8372	+	7.69069i	−1.31269	+	0.406466i
$359$			9.05922i			0.478127i	0.971004	+	0.239064i	$0.0768405\pi$
$359$			9.05922i			0.478127i	−0.971004	+	0.239064i	$0.923160\pi$
$360$	8.35104	+	6.61552i	0.440139	+	0.348668i
$361$		−	49.3432i		−	2.59701i
$362$	6.45139	+	20.8348i	0.339077	+	1.09506i
$363$	−17.1388	−	17.1388i	−0.899556	−	0.899556i
$364$	0.0762652	−	0.407900i	0.00399738	−	0.0213797i
$365$	27.6105	−	27.6105i	1.44520	−	1.44520i
$366$	−5.52018	+	10.4721i	−0.288544	+	0.547385i
$367$	3.23474			0.168852			0.0844259	−	0.996430i	$-0.473094\pi$
$367$	3.23474			0.168852			0.0844259	+	0.996430i	$0.473094\pi$
$368$	−22.1106	−	8.56756i	−1.15259	−	0.446615i
$369$	−1.55315			−0.0808538
$370$	14.2597	−	27.0514i	0.741326	−	1.40634i
$371$	1.23085	−	1.23085i	0.0639024	−	0.0639024i
$372$	0.144036	+	0.0269305i	0.00746793	+	0.00139628i
$373$	6.57461	+	6.57461i	0.340421	+	0.340421i	0.856525	−	0.516105i	$-0.172619\pi$
$373$	6.57461	+	6.57461i	0.340421	+	0.340421i	−0.516105	+	0.856525i	$0.672619\pi$
$374$	3.78436	+	12.2216i	0.195685	+	0.631966i
$375$		−	15.7755i		−	0.814641i
$376$	3.01704	+	26.0180i	0.155592	+	1.34177i
$377$		−	0.394519i		−	0.0203188i
$378$	1.35093	−	0.418308i	0.0694845	−	0.0215154i
$379$	−4.69610	−	4.69610i	−0.241223	−	0.241223i	0.576133	−	0.817356i	$-0.304561\pi$
$379$	−4.69610	−	4.69610i	−0.241223	−	0.241223i	−0.817356	+	0.576133i	$0.804561\pi$
$380$	35.1941	+	51.3811i	1.80542	+	2.63580i
$381$	8.44593	−	8.44593i	0.432698	−	0.432698i
$382$	13.7431	+	7.24443i	0.703158	+	0.370657i
$383$	7.63826			0.390297			0.195148	−	0.980774i	$-0.437481\pi$
$383$	7.63826			0.390297			0.195148	+	0.980774i	$0.437481\pi$
$384$	9.75485	−	5.73087i	0.497800	−	0.292452i
$385$	−22.3598			−1.13956
$386$	−2.51215	−	1.32423i	−0.127865	−	0.0674018i
$387$	−3.52682	+	3.52682i	−0.179278	+	0.179278i
$388$	−0.656560	−	0.958535i	−0.0333318	−	0.0486622i
$389$	−23.2180	−	23.2180i	−1.17720	−	1.17720i	−0.980455	−	0.196745i	$-0.936963\pi$
$389$	−23.2180	−	23.2180i	−1.17720	−	1.17720i	−0.196745	−	0.980455i	$-0.563037\pi$
$390$	−1.05580	+	0.326921i	−0.0534624	+	0.0165543i
$391$		−	9.03457i		−	0.456898i
$392$	−0.325801	−	2.80960i	−0.0164554	−	0.141906i
$393$		−	13.0081i		−	0.656171i
$394$	−5.85413	−	18.9060i	−0.294927	−	0.952470i
$395$	−32.2477	−	32.2477i	−1.62256	−	1.62256i
$396$	−11.6701	−	2.18196i	−0.586444	−	0.109648i
$397$	−13.7846	+	13.7846i	−0.691828	+	0.691828i	−0.962634	−	0.270806i	$-0.912710\pi$
$397$	−13.7846	+	13.7846i	−0.691828	+	0.691828i	0.270806	+	0.962634i	$0.412710\pi$
$398$	−8.61258	+	16.3386i	−0.431710	+	0.818978i
$399$	8.26699			0.413867
$400$	−34.2697	−	13.2791i	−1.71348	−	0.663953i
$401$	15.9198			0.794997			0.397499	−	0.917603i	$-0.369878\pi$
$401$	15.9198			0.794997			0.397499	+	0.917603i	$0.369878\pi$
$402$	1.30723	−	2.47988i	0.0651985	−	0.123685i
$403$	−0.0107491	+	0.0107491i	−0.000535452	+	0.000535452i
$404$	−1.23582	+	6.60971i	−0.0614844	+	0.328845i
$405$	−2.66347	−	2.66347i	−0.132349	−	0.132349i
$406$	−0.795389	−	2.56872i	−0.0394745	−	0.127484i
$407$			34.0770i			1.68913i
$408$	3.37885	+	2.67665i	0.167278	+	0.132514i
$409$			8.36888i			0.413814i	0.978361	+	0.206907i	$0.0663398\pi$
$409$			8.36888i			0.413814i	−0.978361	+	0.206907i	$0.933660\pi$
$410$	7.90332	−	2.44722i	0.390317	−	0.120859i
$411$	−1.71419	−	1.71419i	−0.0845547	−	0.0845547i
$412$	−22.6011	+	15.4809i	−1.11348	+	0.762688i
$413$	0.548474	−	0.548474i	0.0269886	−	0.0269886i
$414$	7.41632	+	3.90938i	0.364492	+	0.192136i
$415$	−48.4251			−2.37710
$416$	−0.0813806	+	1.17088i	−0.00399001	+	0.0574072i
$417$	17.7924			0.871299
$418$	−61.3939	−	32.3627i	−3.00287	−	1.58291i
$419$	10.6166	−	10.6166i	0.518657	−	0.518657i	−0.398508	−	0.917165i	$-0.630472\pi$
$419$	10.6166	−	10.6166i	0.518657	−	0.518657i	0.917165	+	0.398508i	$0.130472\pi$
$420$	−6.21521	+	4.25718i	−0.303271	+	0.207729i
$421$	−0.605437	−	0.605437i	−0.0295072	−	0.0295072i	0.692199	−	0.721706i	$-0.256642\pi$
$421$	−0.605437	−	0.605437i	−0.0295072	−	0.0295072i	−0.721706	+	0.692199i	$0.756642\pi$
$422$	−10.1435	+	3.14088i	−0.493779	+	0.152896i
$423$		−	9.26038i		−	0.450255i
$424$	−3.05718	+	3.85920i	−0.148470	+	0.187419i
$425$		−	14.0029i		−	0.679240i
$426$	1.84450	+	5.95683i	0.0893662	+	0.288609i
$427$	−5.91897	−	5.91897i	−0.286439	−	0.286439i
$428$	0.350090	−	1.87244i	0.0169223	−	0.0905076i
$429$	0.870914	−	0.870914i	0.0420481	−	0.0420481i
$430$	12.3895	−	23.5035i	0.597473	−	1.13344i
$431$	4.10210			0.197591			0.0987957	−	0.995108i	$-0.468501\pi$
$431$	4.10210			0.197591			0.0987957	+	0.995108i	$0.468501\pi$
$432$	−3.65929	+	1.61541i	−0.176058	+	0.0777216i
$433$	6.26338			0.300999			0.150500	−	0.988610i	$-0.451912\pi$
$433$	6.26338			0.300999			0.150500	+	0.988610i	$0.451912\pi$
$434$	−0.0483164	+	0.0916590i	−0.00231926	+	0.00439977i
$435$	−5.06443	+	5.06443i	−0.242821	+	0.242821i
$436$	26.9028	+	5.03003i	1.28841	+	0.240895i
$437$	34.6537	+	34.6537i	1.65771	+	1.65771i
$438$	4.33634	+	14.0043i	0.207198	+	0.669150i
$439$		−	23.3245i		−	1.11322i	−0.830775	−	0.556609i	$-0.812102\pi$
$439$		−	23.3245i		−	1.11322i	0.830775	−	0.556609i	$-0.187898\pi$
$440$	62.8221	−	7.28485i	2.99493	−	0.347292i
$441$			1.00000i			0.0476190i
$442$	−0.427178	+	0.132273i	−0.0203188	+	0.00629159i
$443$	21.8261	+	21.8261i	1.03699	+	1.03699i	0.999289	+	0.0376998i	$0.0120030\pi$
$443$	21.8261	+	21.8261i	1.03699	+	1.03699i	0.0376998	+	0.999289i	$0.487997\pi$
$444$	6.48808	+	9.47217i	0.307910	+	0.449529i
$445$	−33.6588	+	33.6588i	−1.59558	+	1.59558i
$446$	1.86675	+	0.984026i	0.0883932	+	0.0465950i
$447$	23.9777			1.13411
$448$	1.83074	+	7.78771i	0.0864944	+	0.367935i
$449$	−4.92487			−0.232419			−0.116209	−	0.993225i	$-0.537074\pi$
$449$	−4.92487			−0.232419			−0.116209	+	0.993225i	$0.537074\pi$
$450$	11.4947	+	6.05924i	0.541867	+	0.285636i
$451$	−6.51935	+	6.51935i	−0.306984	+	0.306984i
$452$	11.8742	+	17.3356i	0.558517	+	0.815398i
$453$	10.4497	+	10.4497i	0.490968	+	0.490968i
$454$	30.6340	−	9.48562i	1.43772	−	0.445182i
$455$		−	0.781533i		−	0.0366388i
$456$	−23.2269	+	2.69340i	−1.08770	+	0.126130i
$457$			36.1163i			1.68945i	0.535201	+	0.844724i	$0.320236\pi$
$457$			36.1163i			1.68945i	−0.535201	+	0.844724i	$0.679764\pi$
$458$	−1.73731	−	5.61065i	−0.0811790	−	0.262169i
$459$	−1.07764	−	1.07764i	−0.0503002	−	0.0503002i
$460$	−43.8983	−	8.20769i	−2.04677	−	0.382686i
$461$	8.45692	−	8.45692i	0.393878	−	0.393878i	−0.482189	−	0.876067i	$-0.660158\pi$
$461$	8.45692	−	8.45692i	0.393878	−	0.393878i	0.876067	+	0.482189i	$0.160158\pi$
$462$	3.91469	−	7.42638i	0.182128	−	0.345507i
$463$	7.69593			0.357660			0.178830	−	0.983880i	$-0.442769\pi$
$463$	7.69593			0.357660			0.178830	+	0.983880i	$0.442769\pi$
$464$	3.07162	+	6.95794i	0.142596	+	0.323014i
$465$	0.275972			0.0127979
$466$	−12.1597	+	23.0677i	−0.563288	+	1.06859i
$467$	22.3393	−	22.3393i	1.03374	−	1.03374i	0.0343283	−	0.999411i	$-0.489071\pi$
$467$	22.3393	−	22.3393i	1.03374	−	1.03374i	0.999411	−	0.0343283i	$-0.0109292\pi$
$468$	0.0762652	−	0.407900i	0.00352536	−	0.0188552i
$469$	1.40166	+	1.40166i	0.0647228	+	0.0647228i
$470$	14.5911	+	47.1221i	0.673036	+	2.17358i
$471$			8.09373i			0.372939i
$472$	−1.36230	+	1.71969i	−0.0627049	+	0.0791550i
$473$			29.6077i			1.36136i
$474$	16.3563	−	5.06462i	0.751268	−	0.232626i
$475$	53.7105	+	53.7105i	2.46441	+	2.46441i
$476$	−2.51469	+	1.72247i	−0.115261	+	0.0789491i
$477$	1.23085	−	1.23085i	0.0563566	−	0.0563566i
$478$	−16.7607	−	8.83510i	−0.766616	−	0.404108i
$479$	−13.6640			−0.624326			−0.312163	−	0.950029i	$-0.601053\pi$
$479$	−13.6640			−0.624326			−0.312163	+	0.950029i	$0.601053\pi$
$480$	16.0753	−	13.9859i	0.733732	−	0.638366i
$481$	−1.19108			−0.0543085
$482$	−27.2282	−	14.3529i	−1.24021	−	0.653756i
$483$	−4.19181	+	4.19181i	−0.190734	+	0.190734i
$484$	−39.9935	+	27.3940i	−1.81789	+	1.24518i
$485$	−1.54725	−	1.54725i	−0.0702572	−	0.0702572i
$486$	1.35093	−	0.418308i	0.0612795	−	0.0189748i
$487$			15.3319i			0.694754i	0.937725	+	0.347377i	$0.112928\pi$
$487$			15.3319i			0.694754i	−0.937725	+	0.347377i	$0.887072\pi$
$488$	18.5584	+	14.7015i	0.840097	+	0.665507i
$489$			5.62855i			0.254532i
$490$	−1.57565	−	5.08857i	−0.0711804	−	0.229878i
$491$	26.6653	+	26.6653i	1.20339	+	1.20339i	0.973129	+	0.230260i	$0.0739578\pi$
$491$	26.6653	+	26.6653i	1.20339	+	1.20339i	0.230260	+	0.973129i	$0.426042\pi$
$492$	−0.570894	+	3.05339i	−0.0257379	+	0.137657i
$493$	−2.04908	+	2.04908i	−0.0922860	+	0.0922860i
$494$	1.13116	−	2.14587i	0.0508933	−	0.0965474i
$495$	−22.3598			−1.00500
$496$	0.105887	−	0.273267i	0.00475448	−	0.0122700i
$497$	−4.40942			−0.197790
$498$	8.47813	−	16.0835i	0.379914	−	0.720719i
$499$	20.6885	−	20.6885i	0.926143	−	0.926143i	−0.0713114	−	0.997454i	$-0.522718\pi$
$499$	20.6885	−	20.6885i	0.926143	−	0.926143i	0.997454	+	0.0713114i	$0.0227184\pi$
$500$	−31.0135	−	5.79861i	−1.38696	−	0.259322i
$501$	−3.09589	−	3.09589i	−0.138314	−	0.138314i
$502$	7.59690	+	24.5343i	0.339066	+	1.09502i
$503$			14.0834i			0.627946i	0.949432	+	0.313973i	$0.101660\pi$
$503$			14.0834i			0.627946i	−0.949432	+	0.313973i	$0.898340\pi$
$504$	−0.325801	−	2.80960i	−0.0145123	−	0.125150i
$505$			12.6642i			0.563548i
$506$	47.5396	−	14.7204i	2.11339	−	0.654400i
$507$	−9.16195	−	9.16195i	−0.406896	−	0.406896i
$508$	−13.4996	−	19.7086i	−0.598950	−	0.874428i
$509$	−10.2117	+	10.2117i	−0.452625	+	0.452625i	−0.896225	−	0.443600i	$-0.853701\pi$
$509$	−10.2117	+	10.2117i	−0.452625	+	0.452625i	0.443600	+	0.896225i	$0.353701\pi$
$510$	7.18166	+	3.78569i	0.318009	+	0.167633i
$511$	−10.3664			−0.458582
$512$	−7.68090	−	21.2839i	−0.339451	−	0.940624i
$513$	8.26699			0.364997
$514$	−21.8483	−	11.5170i	−0.963689	−	0.507992i
$515$	−36.4824	+	36.4824i	−1.60761	+	1.60761i
$516$	5.63713	+	8.22985i	0.248161	+	0.362299i
$517$	−38.8704	−	38.8704i	−1.70952	−	1.70952i
$518$	−7.75514	+	2.40133i	−0.340741	+	0.105509i
$519$		−	3.25124i		−	0.142714i
$520$	0.254624	+	2.19579i	0.0111660	+	0.0962919i
$521$			19.2699i			0.844228i	0.906543	+	0.422114i	$0.138712\pi$
$521$			19.2699i			0.844228i	−0.906543	+	0.422114i	$0.861288\pi$
$522$	−0.795389	−	2.56872i	−0.0348132	−	0.112430i
$523$	19.3658	+	19.3658i	0.846808	+	0.846808i	0.989734	−	0.142925i	$-0.0456508\pi$
$523$	19.3658	+	19.3658i	0.846808	+	0.846808i	−0.142925	+	0.989734i	$0.545651\pi$
$524$	−25.5730	−	4.78140i	−1.11716	−	0.208877i
$525$	−6.49698	+	6.49698i	−0.283552	+	0.283552i
$526$	−19.1107	+	36.2541i	−0.833266	+	1.58075i
$527$	0.111659			0.00486394
$528$	−8.57919	+	22.1406i	−0.373361	+	0.963545i
$529$	−12.1425			−0.527936
$530$	−4.32388	+	8.20264i	−0.187817	+	0.356300i
$531$	0.548474	−	0.548474i	0.0238017	−	0.0238017i
$532$	3.03871	−	16.2523i	0.131745	−	0.704629i
$533$	−0.227868	−	0.227868i	−0.00987006	−	0.00987006i
$534$	−5.28624	−	17.0720i	−0.228758	−	0.738777i
$535$		−	3.58757i		−	0.155104i
$536$	−4.39478	−	3.48145i	−0.189826	−	0.150376i
$537$		−	18.3852i		−	0.793382i
$538$	−15.0334	+	4.65500i	−0.648136	+	0.200691i
$539$	4.19750	+	4.19750i	0.180799	+	0.180799i
$540$	−6.21521	+	4.25718i	−0.267460	+	0.183200i
$541$	12.2649	−	12.2649i	0.527311	−	0.527311i	−0.392459	−	0.919770i	$-0.628375\pi$
$541$	12.2649	−	12.2649i	0.527311	−	0.527311i	0.919770	+	0.392459i	$0.128375\pi$
$542$	22.1036	+	11.6515i	0.949431	+	0.500476i
$543$	−15.4226			−0.661846
$544$	6.50409	−	5.65873i	0.278861	−	0.242616i
$545$	51.5456			2.20797
$546$	0.259571	+	0.136828i	0.0111086	+	0.00585572i
$547$	−6.08878	+	6.08878i	−0.260338	+	0.260338i	−0.825191	−	0.564854i	$-0.808933\pi$
$547$	−6.08878	+	6.08878i	−0.260338	+	0.260338i	0.564854	+	0.825191i	$0.308933\pi$
$548$	−4.00007	+	2.73989i	−0.170874	+	0.117042i
$549$	−5.91897	−	5.91897i	−0.252616	−	0.252616i
$550$	73.6828	−	22.8154i	3.14184	−	0.972853i
$551$		−	15.7192i		−	0.669661i
$552$	10.4116	−	13.1430i	0.443148	−	0.559403i
$553$			12.1074i			0.514859i
$554$	5.28414	+	17.0652i	0.224502	+	0.725032i
$555$	15.2899	+	15.2899i	0.649018	+	0.649018i
$556$	6.53999	−	34.9787i	0.277357	−	1.48343i
$557$	20.7744	−	20.7744i	0.880239	−	0.880239i	−0.113320	−	0.993559i	$-0.536148\pi$
$557$	20.7744	−	20.7744i	0.880239	−	0.880239i	0.993559	+	0.113320i	$0.0361485\pi$
$558$	−0.0483164	+	0.0916590i	−0.00204540	+	0.00388023i
$559$	−1.03486			−0.0437701
$560$	6.08480	+	13.7835i	0.257130	+	0.582460i
$561$	−9.04682			−0.381957
$562$	18.9912	−	36.0274i	0.801095	−	1.51972i
$563$	−7.51558	+	7.51558i	−0.316744	+	0.316744i	−0.847515	−	0.530771i	$-0.821902\pi$
$563$	−7.51558	+	7.51558i	−0.316744	+	0.316744i	0.530771	+	0.847515i	$0.321902\pi$
$564$	−18.2053	−	3.40385i	−0.766581	−	0.143328i
$565$	27.9829	+	27.9829i	1.17725	+	1.17725i
$566$	3.15055	+	10.1747i	0.132427	+	0.427676i
$567$			1.00000i			0.0419961i
$568$	12.3887	−	1.43660i	0.519819	−	0.0602782i
$569$		−	6.86134i		−	0.287643i	−0.989604	−	0.143821i	$-0.954061\pi$
$569$		−	6.86134i		−	0.287643i	0.989604	−	0.143821i	$-0.0459390\pi$
$570$	−42.0672	+	13.0259i	−1.76200	+	0.545593i
$571$	−13.1701	−	13.1701i	−0.551153	−	0.551153i	0.375621	−	0.926774i	$-0.377430\pi$
$571$	−13.1701	−	13.1701i	−0.551153	−	0.551153i	−0.926774	+	0.375621i	$0.877430\pi$
$572$	−1.39203	−	2.03228i	−0.0582039	−	0.0849739i
$573$	−7.76779	+	7.76779i	−0.324504	+	0.324504i
$574$	−1.94306	−	1.02425i	−0.0811016	−	0.0427513i
$575$	−54.4682			−2.27148
$576$	1.83074	+	7.78771i	0.0762809	+	0.324488i
$577$	−6.17181			−0.256936			−0.128468	−	0.991714i	$-0.541006\pi$
$577$	−6.17181			−0.256936			−0.128468	+	0.991714i	$0.541006\pi$
$578$	−18.3620	−	9.67921i	−0.763758	−	0.402602i
$579$	1.41990	−	1.41990i	0.0590091	−	0.0590091i
$580$	8.09479	+	11.8179i	0.336118	+	0.490711i
$581$	9.09062	+	9.09062i	0.377142	+	0.377142i
$582$	0.784780	−	0.243002i	0.0325302	−	0.0100728i
$583$		−	10.3330i		−	0.427947i
$584$	29.1254	−	3.37738i	1.20522	−	0.139757i
$585$		−	0.781533i		−	0.0323124i
$586$	−3.75114	−	12.1144i	−0.154958	−	0.500439i
$587$	−8.56420	−	8.56420i	−0.353482	−	0.353482i	0.507921	−	0.861404i	$-0.330414\pi$
$587$	−8.56420	−	8.56420i	−0.353482	−	0.353482i	−0.861404	+	0.507921i	$0.830414\pi$
$588$	1.96593	+	0.367572i	0.0810737	+	0.0151584i
$589$	−0.428288	+	0.428288i	−0.0176473	+	0.0176473i
$590$	−1.92675	+	3.65515i	−0.0793230	+	0.150480i
$591$	13.9948			0.575668
$592$	21.0065	−	9.27342i	0.863361	−	0.381135i
$593$	−9.41187			−0.386499			−0.193249	−	0.981150i	$-0.561903\pi$
$593$	−9.41187			−0.386499			−0.193249	+	0.981150i	$0.561903\pi$
$594$	3.91469	−	7.42638i	0.160622	−	0.304708i
$595$	−4.05918	+	4.05918i	−0.166410	+	0.166410i
$596$	8.81353	−	47.1386i	0.361016	−	1.93087i
$597$	−9.23478	−	9.23478i	−0.377955	−	0.377955i
$598$	0.514514	+	1.66163i	0.0210401	+	0.0679492i
$599$		−	29.2723i		−	1.19603i	−0.801484	−	0.598017i	$-0.795956\pi$
$599$		−	29.2723i		−	1.19603i	0.801484	−	0.598017i	$-0.204044\pi$
$600$	16.1372	−	20.3707i	0.658798	−	0.831628i
$601$			41.2772i			1.68373i	0.539685	+	0.841867i	$0.318543\pi$
$601$			41.2772i			1.68373i	−0.539685	+	0.841867i	$0.681457\pi$
$602$	−6.73802	+	2.08639i	−0.274621	+	0.0850348i
$603$	1.40166	+	1.40166i	0.0570802	+	0.0570802i
$604$	24.3843	−	16.7023i	0.992184	−	0.679608i
$605$	−64.5571	+	64.5571i	−2.62462	+	2.62462i
$606$	−4.20616	−	2.21720i	−0.170864	−	0.0900677i
$607$	40.9346			1.66148			0.830741	−	0.556659i	$-0.187917\pi$
$607$	40.9346			1.66148			0.830741	+	0.556659i	$0.187917\pi$
$608$	−3.24253	+	46.6526i	−0.131502	+	1.89201i
$609$	1.90144			0.0770504
$610$	39.4453	+	20.7929i	1.59709	+	0.841881i
$611$	1.35862	−	1.35862i	0.0549639	−	0.0549639i
$612$	−2.51469	+	1.72247i	−0.101650	+	0.0696266i
$613$	16.3705	+	16.3705i	0.661200	+	0.661200i	0.955663	−	0.294463i	$-0.0951408\pi$
$613$	16.3705	+	16.3705i	0.661200	+	0.661200i	−0.294463	+	0.955663i	$0.595141\pi$
$614$	1.34763	−	0.417285i	0.0543859	−	0.0168403i
$615$			5.85027i			0.235906i
$616$	−13.1608	−	10.4257i	−0.530265	−	0.420065i
$617$		−	17.9004i		−	0.720642i	−0.932828	−	0.360321i	$-0.882667\pi$
$617$		−	17.9004i		−	0.720642i	0.932828	−	0.360321i	$-0.117333\pi$
$618$	−5.72970	−	18.5042i	−0.230482	−	0.744346i
$619$	−10.2626	−	10.2626i	−0.412490	−	0.412490i	0.470115	−	0.882605i	$-0.344212\pi$
$619$	−10.2626	−	10.2626i	−0.412490	−	0.412490i	−0.882605	+	0.470115i	$0.844212\pi$
$620$	0.101440	−	0.542543i	0.00407391	−	0.0217890i
$621$	−4.19181	+	4.19181i	−0.168212	+	0.168212i
$622$	7.91563	−	15.0164i	0.317388	−	0.602103i
$623$	12.6372			0.506298
$624$	−0.773870	−	0.299865i	−0.0309796	−	0.0120042i
$625$	−13.4810			−0.539239
$626$	4.41675	−	8.37882i	0.176529	−	0.334885i
$627$	34.7007	−	34.7007i	1.38581	−	1.38581i
$628$	15.9117	+	2.97502i	0.634947	+	0.118716i
$629$	6.18631	+	6.18631i	0.246664	+	0.246664i
$630$	−1.57565	−	5.08857i	−0.0627753	−	0.202734i
$631$			2.27892i			0.0907222i	0.998971	+	0.0453611i	$0.0144438\pi$
$631$			2.27892i			0.0907222i	−0.998971	+	0.0453611i	$0.985556\pi$
$632$	−3.94460	−	34.0169i	−0.156908	−	1.35312i
$633$		−	7.50853i		−	0.298437i
$634$	−0.685648	+	0.212307i	−0.0272306	+	0.00843178i
$635$	−31.8134	−	31.8134i	−1.26248	−	1.26248i
$636$	−1.96734	−	2.87219i	−0.0780101	−	0.113890i
$637$	−0.146713	+	0.146713i	−0.00581300	+	0.00581300i
$638$	−14.1208	−	7.44356i	−0.559050	−	0.294693i
$639$	−4.40942			−0.174434
$640$	−21.5865	−	36.7437i	−0.853283	−	1.45242i
$641$	−3.30602			−0.130580			−0.0652901	−	0.997866i	$-0.520797\pi$
$641$	−3.30602			−0.130580			−0.0652901	+	0.997866i	$0.520797\pi$
$642$	1.19154	+	0.628102i	0.0470265	+	0.0247892i
$643$	33.0308	−	33.0308i	1.30261	−	1.30261i	0.375981	−	0.926627i	$-0.377306\pi$
$643$	33.0308	−	33.0308i	1.30261	−	1.30261i	0.926627	−	0.375981i	$-0.122694\pi$
$644$	6.70003	+	9.78161i	0.264018	+	0.385449i
$645$	13.2845	+	13.2845i	0.523078	+	0.523078i
$646$	−17.0205	+	5.27029i	−0.669662	+	0.207357i
$647$			28.5616i			1.12287i	0.827520	+	0.561436i	$0.189751\pi$
$647$			28.5616i			1.12287i	−0.827520	+	0.561436i	$0.810249\pi$
$648$	−0.325801	−	2.80960i	−0.0127987	−	0.110372i
$649$		−	4.60444i		−	0.180740i
$650$	0.797458	+	2.57540i	0.0312789	+	0.101016i
$651$	−0.0518070	−	0.0518070i	−0.00203047	−	0.00203047i
$652$	11.0654	+	2.06890i	0.433353	+	0.0810242i
$653$	4.94265	−	4.94265i	0.193421	−	0.193421i	−0.603752	−	0.797173i	$-0.706328\pi$
$653$	4.94265	−	4.94265i	0.193421	−	0.193421i	0.797173	+	0.603752i	$0.206328\pi$
$654$	−9.02445	+	17.1199i	−0.352884	+	0.669441i
$655$	−48.9977			−1.91450
$656$	5.79292	+	2.24468i	0.226175	+	0.0876400i
$657$	−10.3664			−0.404431
$658$	6.10690	−	11.5851i	0.238072	−	0.451635i
$659$	−11.7007	+	11.7007i	−0.455796	+	0.455796i	−0.897273	−	0.441477i	$-0.854455\pi$
$659$	−11.7007	+	11.7007i	−0.455796	+	0.455796i	0.441477	+	0.897273i	$0.354455\pi$
$660$	−8.21883	+	43.9579i	−0.319917	+	1.71106i
$661$	−9.28005	−	9.28005i	−0.360952	−	0.360952i	0.503211	−	0.864163i	$-0.332152\pi$
$661$	−9.28005	−	9.28005i	−0.360952	−	0.360952i	−0.864163	+	0.503211i	$0.832152\pi$
$662$	1.16397	+	3.75907i	0.0452392	+	0.146101i
$663$		−	0.316210i		−	0.0122806i
$664$	−28.5027	−	22.5793i	−1.10612	−	0.876246i
$665$		−	31.1394i		−	1.20753i
$666$	−7.75514	+	2.40133i	−0.300506	+	0.0930498i
$667$	7.97049	+	7.97049i	0.308619	+	0.308619i
$668$	−7.22426	+	4.94834i	−0.279515	+	0.191457i
$669$	−1.05511	+	1.05511i	−0.0407931	+	0.0407931i
$670$	−9.34100	−	4.92394i	−0.360874	−	0.190229i
$671$	−49.6897			−1.91825
$672$	−5.64324	−	0.392226i	−0.217693	−	0.0151304i
$673$	−3.86798			−0.149100			−0.0745499	−	0.997217i	$-0.523752\pi$
$673$	−3.86798			−0.149100			−0.0745499	+	0.997217i	$0.523752\pi$
$674$	35.2570	+	18.5851i	1.35805	+	0.715871i
$675$	−6.49698	+	6.49698i	−0.250069	+	0.250069i
$676$	−21.3794	+	14.6441i	−0.822286	+	0.563235i
$677$	10.5701	+	10.5701i	0.406243	+	0.406243i	0.880426	−	0.474183i	$-0.157257\pi$
$677$	10.5701	+	10.5701i	0.406243	+	0.406243i	−0.474183	+	0.880426i	$0.657257\pi$
$678$	−14.1932	+	4.39483i	−0.545085	+	0.168782i
$679$			0.580917i			0.0222936i
$680$	10.0822	−	12.7272i	0.386634	−	0.488064i
$681$			22.6762i			0.868953i
$682$	0.181930	+	0.587546i	0.00696647	+	0.0224983i
$683$	−28.3245	−	28.3245i	−1.08381	−	1.08381i	−0.996151	−	0.0876568i	$-0.972062\pi$
$683$	−28.3245	−	28.3245i	−1.08381	−	1.08381i	−0.0876568	−	0.996151i	$-0.527938\pi$
$684$	3.03871	−	16.2523i	0.116188	−	0.621424i
$685$	−6.45686	+	6.45686i	−0.246704	+	0.246704i
$686$	−0.659465	+	1.25104i	−0.0251785	+	0.0477650i
$687$	4.15317			0.158453
$688$	18.2514	−	8.05717i	0.695828	−	0.307177i
$689$	0.361164			0.0137592
$690$	14.7255	−	27.9351i	0.560591	−	1.06347i
$691$	−9.07023	+	9.07023i	−0.345048	+	0.345048i	−0.858261	−	0.513213i	$-0.828455\pi$
$691$	−9.07023	+	9.07023i	−0.345048	+	0.345048i	0.513213	+	0.858261i	$0.328455\pi$
$692$	−6.39172	−	1.19506i	−0.242977	−	0.0454295i
$693$	4.19750	+	4.19750i	0.159450	+	0.159450i
$694$	−0.281873	−	0.910313i	−0.0106997	−	0.0345550i
$695$		−	67.0190i		−	2.54217i
$696$	−5.34230	+	0.619493i	−0.202499	+	0.0234818i
$697$			2.36703i			0.0896578i
$698$	10.9565	−	3.39261i	0.414709	−	0.128412i
$699$	−13.0382	−	13.0382i	−0.493149	−	0.493149i
$700$	10.3845	+	15.1607i	0.392498	+	0.573022i
$701$	−30.0214	+	30.0214i	−1.13389	+	1.13389i	−0.144369	+	0.989524i	$0.546115\pi$
$701$	−30.0214	+	30.0214i	−1.13389	+	1.13389i	−0.989524	+	0.144369i	$0.953885\pi$
$702$	0.259571	+	0.136828i	0.00979688	+	0.00516426i
$703$	−47.4574			−1.78989
$704$	40.3734	+	25.0043i	1.52163	+	0.942387i
$705$	−34.8812			−1.31370
$706$	1.03112	+	0.543538i	0.0388068	+	0.0204563i
$707$	2.37738	−	2.37738i	0.0894106	−	0.0894106i
$708$	−0.876659	−	1.27987i	−0.0329469	−	0.0481003i
$709$	21.8954	+	21.8954i	0.822298	+	0.822298i	0.986437	−	0.164139i	$-0.0524847\pi$
$709$	21.8954	+	21.8954i	0.822298	+	0.822298i	−0.164139	+	0.986437i	$0.552485\pi$
$710$	22.4377	−	6.94769i	0.842071	−	0.260742i
$711$			12.1074i			0.454063i
$712$	−35.5055	+	4.11721i	−1.33062	+	0.154299i
$713$		−	0.434330i		−	0.0162658i
$714$	−0.637510	−	2.05885i	−0.0238582	−	0.0770505i
$715$	−3.28048	−	3.28048i	−0.122683	−	0.122683i
$716$	−36.1441	−	6.75789i	−1.35077	−	0.252554i
$717$	9.47338	−	9.47338i	0.353790	−	0.353790i
$718$	−5.97424	+	11.3335i	−0.222957	+	0.422961i
$719$	43.7925			1.63319			0.816593	−	0.577214i	$-0.195860\pi$
$719$	43.7925			1.63319			0.816593	+	0.577214i	$0.195860\pi$
$720$	6.08480	+	13.7835i	0.226767	+	0.513681i
$721$	13.6973			0.510115
$722$	32.5401	−	61.7304i	1.21102	−	2.29737i
$723$	15.3898	−	15.3898i	0.572352	−	0.572352i
$724$	−5.66890	+	30.3197i	−0.210683	+	1.12682i
$725$	12.3536	+	12.3536i	0.458803	+	0.458803i
$726$	−10.1389	−	32.7439i	−0.376291	−	1.21524i
$727$			4.00092i			0.148386i	0.997244	+	0.0741929i	$0.0236381\pi$
$727$			4.00092i			0.148386i	−0.997244	+	0.0741929i	$0.976362\pi$
$728$	0.364407	−	0.460005i	0.0135058	−	0.0170489i
$729$			1.00000i			0.0370370i
$730$	52.7501	−	16.3337i	1.95237	−	0.604539i
$731$	5.37495	+	5.37495i	0.198800	+	0.198800i
$732$	−13.8119	+	9.46065i	−0.510504	+	0.349676i
$733$	21.1300	−	21.1300i	0.780454	−	0.780454i	−0.199454	−	0.979907i	$-0.563917\pi$
$733$	21.1300	−	21.1300i	0.780454	−	0.780454i	0.979907	+	0.199454i	$0.0639168\pi$
$734$	4.04679	+	2.13320i	0.149370	+	0.0787377i
$735$	3.76671			0.138937
$736$	−22.0113	−	25.2995i	−0.811346	−	0.932553i
$737$	11.7670			0.433442
$738$	−1.94306	−	1.02425i	−0.0715249	−	0.0377031i
$739$	−21.0896	+	21.0896i	−0.775795	+	0.775795i	−0.979113	−	0.203318i	$-0.934827\pi$
$739$	−21.0896	+	21.0896i	−0.775795	+	0.775795i	0.203318	+	0.979113i	$0.434827\pi$
$740$	35.6790	−	24.4387i	1.31158	−	0.898385i
$741$	1.21288	+	1.21288i	0.0445562	+	0.0445562i
$742$	2.35154	−	0.728141i	0.0863279	−	0.0267309i
$743$		−	0.490458i		−	0.0179932i	−0.999960	−	0.00899658i	$-0.997136\pi$
$743$		−	0.490458i		−	0.0179932i	0.999960	−	0.00899658i	$-0.00286374\pi$
$744$	0.162436	+	0.128678i	0.00595518	+	0.00471757i
$745$		−	90.3171i		−	3.30896i
$746$	3.88939	+	12.5608i	0.142401	+	0.459885i
$747$	9.09062	+	9.09062i	0.332608	+	0.332608i
$748$	−3.32536	+	17.7854i	−0.121587	+	0.650300i
$749$	−0.673478	+	0.673478i	−0.0246083	+	0.0246083i
$750$	10.4034	−	19.7357i	0.379877	−	0.720648i
$751$	5.26831			0.192244			0.0961218	−	0.995370i	$-0.469356\pi$
$751$	5.26831			0.192244			0.0961218	+	0.995370i	$0.469356\pi$
$752$	−13.3835	+	34.5392i	−0.488046	+	1.25951i
$753$	−18.1610			−0.661824
$754$	0.260172	−	0.493560i	0.00947489	−	0.0179744i
$755$	39.3608	−	39.3608i	1.43249	−	1.43249i
$756$	1.96593	+	0.367572i	0.0715003	+	0.0133684i
$757$	16.8185	+	16.8185i	0.611280	+	0.611280i	0.943280	−	0.331999i	$-0.107723\pi$
$757$	16.8185	+	16.8185i	0.611280	+	0.611280i	−0.331999	+	0.943280i	$0.607723\pi$
$758$	−2.77811	−	8.97194i	−0.100905	−	0.325875i
$759$			35.1902i			1.27732i
$760$	10.1452	+	87.4892i	0.368007	+	3.17357i
$761$		−	8.50916i		−	0.308457i	−0.988035	−	0.154228i	$-0.950711\pi$
$761$		−	8.50916i		−	0.308457i	0.988035	−	0.154228i	$-0.0492892\pi$
$762$	16.1360	−	4.99642i	0.584546	−	0.181001i
$763$	−9.67641	−	9.67641i	−0.350309	−	0.350309i
$764$	12.4157	+	18.1262i	0.449186	+	0.655782i
$765$	−4.05918	+	4.05918i	−0.146760	+	0.146760i
$766$	9.55578	+	5.03716i	0.345264	+	0.182000i
$767$	0.160937			0.00581110
$768$	15.9830	−	0.736576i	0.576738	−	0.0265789i
$769$	27.6303			0.996372			0.498186	−	0.867070i	$-0.334000\pi$
$769$	27.6303			0.996372			0.498186	+	0.867070i	$0.334000\pi$
$770$	−27.9730	−	14.7455i	−1.00808	−	0.531391i
$771$	12.3490	−	12.3490i	0.444738	−	0.444738i
$772$	−2.26952	−	3.31335i	−0.0816816	−	0.119250i
$773$	25.0268	+	25.0268i	0.900151	+	0.900151i	0.995449	−	0.0952981i	$-0.0303804\pi$
$773$	25.0268	+	25.0268i	0.900151	+	0.900151i	−0.0952981	+	0.995449i	$0.530380\pi$
$774$	−6.73802	+	2.08639i	−0.242193	+	0.0749936i
$775$		−	0.673178i		−	0.0241813i
$776$	−0.189264	−	1.63215i	−0.00679416	−	0.0585906i
$777$		−	5.74058i		−	0.205942i
$778$	−13.7352	−	44.3582i	−0.492432	−	1.59032i
$779$	−9.07917	−	9.07917i	−0.325295	−	0.325295i
$780$	−1.53644	−	0.287269i	−0.0550134	−	0.0102859i
$781$	−18.5085	+	18.5085i	−0.662288	+	0.662288i
$782$	5.95798	−	11.3026i	0.213057	−	0.404181i
$783$	1.90144			0.0679521
$784$	1.44524	−	3.72978i	0.0516158	−	0.133207i
$785$	30.4867			1.08812
$786$	8.57838	−	16.2737i	0.305981	−	0.580462i
$787$	8.76714	−	8.76714i	0.312515	−	0.312515i	−0.533368	−	0.845883i	$-0.679074\pi$
$787$	8.76714	−	8.76714i	0.312515	−	0.312515i	0.845883	+	0.533368i	$0.179074\pi$
$788$	5.14408	−	27.5128i	0.183250	−	0.980102i
$789$	−20.4913	−	20.4913i	−0.729510	−	0.729510i
$790$	−19.0770	−	61.6094i	−0.678728	−	2.19196i
$791$		−	10.5062i		−	0.373557i
$792$	−13.1608	−	10.4257i	−0.467650	−	0.370463i
$793$		−	1.73678i		−	0.0616750i
$794$	−26.3355	+	8.15463i	−0.934612	+	0.289397i
$795$	−4.63625	−	4.63625i	−0.164431	−	0.164431i
$796$	−21.5494	+	14.7605i	−0.763799	+	0.523173i
$797$	−15.4398	+	15.4398i	−0.546907	+	0.546907i	−0.925545	−	0.378638i	$-0.876393\pi$
$797$	−15.4398	+	15.4398i	−0.546907	+	0.546907i	0.378638	+	0.925545i	$0.376393\pi$
$798$	10.3424	+	5.45179i	0.366115	+	0.192991i
$799$	−14.1130			−0.499282
$800$	−34.1158	−	39.2123i	−1.20617	−	1.38636i
$801$	12.6372			0.446513
$802$	19.9163	+	10.4986i	0.703271	+	0.370717i
$803$	−43.5129	+	43.5129i	−1.53554	+	1.53554i
$804$	3.27079	−	2.24037i	0.115352	−	0.0790116i
$805$	15.7893	+	15.7893i	0.556501	+	0.556501i
$806$	−0.0205363	+	0.00635893i	−0.000723359	+	0.000223984i
$807$		−	11.1282i		−	0.391730i
$808$	−5.90494	+	7.45404i	−0.207735	+	0.262232i
$809$		−	22.5646i		−	0.793329i	−0.917964	−	0.396664i	$-0.870168\pi$
$809$		−	22.5646i		−	0.793329i	0.917964	−	0.396664i	$-0.129832\pi$
$810$	−1.57565	−	5.08857i	−0.0553626	−	0.178794i
$811$	12.9168	+	12.9168i	0.453569	+	0.453569i	0.896537	−	0.442968i	$-0.146075\pi$
$811$	12.9168	+	12.9168i	0.453569	+	0.453569i	−0.442968	+	0.896537i	$0.646075\pi$
$812$	0.698917	−	3.73811i	0.0245272	−	0.131182i
$813$	−12.4933	+	12.4933i	−0.438158	+	0.438158i
$814$	−22.4726	+	42.6318i	−0.787664	+	1.49424i
$815$	21.2011			0.742643
$816$	2.46192	+	5.57684i	0.0861846	+	0.195228i
$817$	−41.2331			−1.44256
$818$	−5.51898	+	10.4698i	−0.192967	+	0.366069i
$819$	−0.146713	+	0.146713i	−0.00512658	+	0.00512658i
$820$	11.5012	+	2.15039i	0.401641	+	0.0750950i
$821$	21.0865	+	21.0865i	0.735922	+	0.735922i	0.971786	−	0.235864i	$-0.0757919\pi$
$821$	21.0865	+	21.0865i	0.735922	+	0.735922i	−0.235864	+	0.971786i	$0.575792\pi$
$822$	−1.01407	−	3.27497i	−0.0353699	−	0.114228i
$823$			7.62120i			0.265658i	0.991139	+	0.132829i	$0.0424062\pi$
$823$			7.62120i			0.265658i	−0.991139	+	0.132829i	$0.957594\pi$
$824$	−38.4840	+	4.46260i	−1.34065	+	0.155462i
$825$			54.5421i			1.89891i
$826$	1.04786	−	0.324465i	0.0364598	−	0.0112896i
$827$	−3.31841	−	3.31841i	−0.115393	−	0.115393i	0.647053	−	0.762445i	$-0.276001\pi$
$827$	−3.31841	−	3.31841i	−0.115393	−	0.115393i	−0.762445	+	0.647053i	$0.776001\pi$
$828$	6.70003	+	9.78161i	0.232842	+	0.339934i
$829$	38.3342	−	38.3342i	1.33140	−	1.33140i	0.427283	−	0.904118i	$-0.359471\pi$
$829$	38.3342	−	38.3342i	1.33140	−	1.33140i	0.904118	−	0.427283i	$-0.140529\pi$
$830$	−60.5819	−	31.9347i	−2.10283	−	1.10847i
$831$	−12.6322			−0.438206
$832$	−0.873966	+	1.41116i	−0.0302993	+	0.0489230i
$833$	1.52402			0.0528042
$834$	22.2591	+	11.7335i	0.770769	+	0.406297i
$835$	−11.6613	+	11.6613i	−0.403556	+	0.403556i
$836$	−55.4642	−	80.9742i	−1.91827	−	2.80055i
$837$	−0.0518070	−	0.0518070i	−0.00179071	−	0.00179071i
$838$	20.2832	−	6.28056i	0.700670	−	0.216958i
$839$			2.08420i			0.0719546i	0.999353	+	0.0359773i	$0.0114544\pi$
$839$			2.08420i			0.0719546i	−0.999353	+	0.0359773i	$0.988546\pi$
$840$	−10.5830	+	1.22720i	−0.365147	+	0.0423424i
$841$			25.3845i			0.875328i
$842$	−0.358163	−	1.15669i	−0.0123431	−	0.0398623i
$843$	20.3632	+	20.3632i	0.701345	+	0.701345i
$844$	−14.7613	−	2.75992i	−0.508104	−	0.0950005i
$845$	−34.5104	+	34.5104i	−1.18719	+	1.18719i
$846$	6.10690	−	11.5851i	0.209959	−	0.398305i
$847$	24.2380			0.832827
$848$	−6.36967	+	2.81192i	−0.218735	+	0.0965618i
$849$	−7.53164			−0.258485
$850$	9.23441	−	17.5182i	0.316738	−	0.600869i
$851$	24.0634	−	24.0634i	0.824884	−	0.824884i
$852$	−1.62078	+	8.66863i	−0.0555270	+	0.296982i
$853$	−2.17161	−	2.17161i	−0.0743547	−	0.0743547i	0.668951	−	0.743306i	$-0.266743\pi$
$853$	−2.17161	−	2.17161i	−0.0743547	−	0.0743547i	−0.743306	+	0.668951i	$0.766743\pi$
$854$	−3.50153	−	11.3082i	−0.119820	−	0.386960i
$855$		−	31.1394i		−	1.06494i
$856$	1.67278	−	2.11162i	0.0571746	−	0.0721738i
$857$		−	23.8443i		−	0.814504i	−0.913316	−	0.407252i	$-0.866487\pi$
$857$		−	23.8443i		−	0.814504i	0.913316	−	0.407252i	$-0.133513\pi$
$858$	1.66389	−	0.515213i	0.0568042	−	0.0175891i
$859$	−26.6248	−	26.6248i	−0.908426	−	0.908426i	0.0877197	−	0.996145i	$-0.472042\pi$
$859$	−26.6248	−	26.6248i	−0.908426	−	0.908426i	−0.996145	+	0.0877197i	$0.972042\pi$
$860$	30.9995	−	21.2335i	1.05707	−	0.724055i
$861$	1.09824	−	1.09824i	0.0374280	−	0.0374280i
$862$	5.13190	+	2.70519i	0.174793	+	0.0921392i
$863$	−34.9006			−1.18803			−0.594015	−	0.804454i	$-0.702458\pi$
$863$	−34.9006			−1.18803			−0.594015	+	0.804454i	$0.702458\pi$
$864$	−5.64324	−	0.392226i	−0.191987	−	0.0133438i
$865$	−12.2465			−0.416393
$866$	7.83576	+	4.13048i	0.266270	+	0.140360i
$867$	10.3785	−	10.3785i	0.352471	−	0.352471i
$868$	−0.120892	+	0.0828062i	−0.00410333	+	0.00281063i
$869$	50.8208	+	50.8208i	1.72398	+	1.72398i
$870$	−9.67564	+	2.99600i	−0.328035	+	0.101574i
$871$			0.411286i			0.0139359i
$872$	30.3394	+	24.0342i	1.02742	+	0.813902i
$873$			0.580917i			0.0196611i
$874$	20.5003	+	66.2061i	0.693433	+	2.23945i
$875$	11.1549	+	11.1549i	0.377105	+	0.377105i
$876$	−3.81039	+	20.3796i	−0.128741	+	0.688563i
$877$	9.68861	−	9.68861i	0.327161	−	0.327161i	−0.524345	−	0.851506i	$-0.675690\pi$
$877$	9.68861	−	9.68861i	0.327161	−	0.327161i	0.851506	+	0.524345i	$0.175690\pi$
$878$	15.3817	−	29.1799i	0.519107	−	0.984775i
$879$	8.96740			0.302463
$880$	83.3972	+	32.3153i	2.81132	+	1.08935i
$881$	11.0684			0.372904			0.186452	−	0.982464i	$-0.440301\pi$
$881$	11.0684			0.372904			0.186452	+	0.982464i	$0.440301\pi$
$882$	−0.659465	+	1.25104i	−0.0222053	+	0.0421248i
$883$	25.0415	−	25.0415i	0.842714	−	0.842714i	−0.146498	−	0.989211i	$-0.546800\pi$
$883$	25.0415	−	25.0415i	0.842714	−	0.842714i	0.989211	+	0.146498i	$0.0468000\pi$
$884$	−0.621647	−	0.116230i	−0.0209083	−	0.00390923i
$885$	−2.06594	−	2.06594i	−0.0694459	−	0.0694459i
$886$	12.9118	+	41.6989i	0.433781	+	1.40090i
$887$			23.0870i			0.775186i	0.921831	+	0.387593i	$0.126693\pi$
$887$			23.0870i			0.775186i	−0.921831	+	0.387593i	$0.873307\pi$
$888$	1.87029	+	16.1287i	0.0627628	+	0.541245i
$889$			11.9443i			0.400600i
$890$	−64.3053	+	19.9117i	−2.15552	+	0.667443i
$891$	4.19750	+	4.19750i	0.140621	+	0.140621i
$892$	1.68645	+	2.46211i	0.0564667	+	0.0824377i
$893$	54.1329	−	54.1329i	1.81149	−	1.81149i
$894$	29.9971	+	15.8125i	1.00325	+	0.528848i
$895$	−69.2519			−2.31484
$896$	−2.84538	+	10.9501i	−0.0950576	+	0.365816i
$897$	−1.22999			−0.0410681
$898$	−6.16121	−	3.24778i	−0.205602	−	0.108380i
$899$	−0.0985080	+	0.0985080i	−0.00328543	+	0.00328543i
$900$	10.3845	+	15.1607i	0.346151	+	0.505358i
$901$	−1.87584	−	1.87584i	−0.0624932	−	0.0624932i
$902$	−12.4553	+	3.85670i	−0.414715	+	0.128414i
$903$		−	4.98768i		−	0.165980i
$904$	3.42293	+	29.5182i	0.113845	+	0.981761i
$905$			58.0924i			1.93106i
$906$	6.18178	+	19.9641i	0.205376	+	0.663264i
$907$	−15.0563	−	15.0563i	−0.499936	−	0.499936i	0.411482	−	0.911418i	$-0.365011\pi$
$907$	−15.0563	−	15.0563i	−0.499936	−	0.499936i	−0.911418	+	0.411482i	$0.865011\pi$
$908$	44.5798	+	8.33511i	1.47943	+	0.276610i
$909$	2.37738	−	2.37738i	0.0788528	−	0.0788528i
$910$	0.515393	−	0.977730i	0.0170851	−	0.0324114i
$911$	16.2778			0.539309			0.269654	−	0.962957i	$-0.413091\pi$
$911$	16.2778			0.539309			0.269654	+	0.962957i	$0.413091\pi$
$912$	−30.8341	−	11.9478i	−1.02102	−	0.395631i
$913$	76.3157			2.52568
$914$	−23.8174	+	45.1830i	−0.787811	+	1.49452i
$915$	−22.2951	+	22.2951i	−0.737052	+	0.737052i
$916$	1.52659	−	8.16486i	0.0504399	−	0.269774i
$917$	9.19810	+	9.19810i	0.303748	+	0.303748i
$918$	−0.637510	−	2.05885i	−0.0210410	−	0.0679521i
$919$			40.9288i			1.35012i	0.737764	+	0.675059i	$0.235882\pi$
$919$			40.9288i			1.35012i	−0.737764	+	0.675059i	$0.764118\pi$
$920$	−49.5059	−	39.2176i	−1.63216	−	1.29296i
$921$			0.997554i			0.0328705i
$922$	16.1570	−	5.00292i	0.532103	−	0.164762i
$923$	−0.646921	−	0.646921i	−0.0212937	−	0.0212937i
$924$	9.79488	−	6.70912i	0.322228	−	0.220714i
$925$	37.2965	−	37.2965i	1.22630	−	1.22630i
$926$	9.62793	+	5.07520i	0.316394	+	0.166781i
$927$	13.6973			0.449879
$928$	−0.745796	+	10.7303i	−0.0244819	+	0.352239i
$929$	−28.3854			−0.931296			−0.465648	−	0.884970i	$-0.654179\pi$
$929$	−28.3854			−0.931296			−0.465648	+	0.884970i	$0.654179\pi$
$930$	0.345253	+	0.181994i	0.0113213	+	0.00596782i
$931$	−5.84565	+	5.84565i	−0.191583	+	0.191583i
$932$	−30.4246	+	20.8397i	−0.996592	+	0.682628i
$933$	8.48748	+	8.48748i	0.277868	+	0.277868i
$934$	42.6794	−	13.2154i	1.39651	−	0.432421i
$935$			34.0768i			1.11443i
$936$	0.364407	−	0.460005i	0.0119110	−	0.0150357i
$937$		−	34.7730i		−	1.13598i	−0.823034	−	0.567991i	$-0.807721\pi$
$937$		−	34.7730i		−	1.13598i	0.823034	−	0.567991i	$-0.192279\pi$
$938$	0.829192	+	2.67789i	0.0270741	+	0.0874362i
$939$	4.73583	+	4.73583i	0.154548	+	0.154548i
$940$	−12.8213	+	68.5741i	−0.418186	+	2.23664i
$941$	38.4711	−	38.4711i	1.25412	−	1.25412i	0.300266	−	0.953856i	$-0.402925\pi$
$941$	38.4711	−	38.4711i	1.25412	−	1.25412i	0.953856	−	0.300266i	$-0.0970753\pi$
$942$	−5.33753	+	10.1256i	−0.173906	+	0.329910i
$943$	9.20726			0.299830
$944$	−2.83837	+	1.25301i	−0.0923809	+	0.0407820i
$945$	3.76671			0.122531
$946$	−19.5252	+	37.0404i	−0.634819	+	1.20429i
$947$	−24.6217	+	24.6217i	−0.800097	+	0.800097i	−0.983110	−	0.183013i	$-0.941415\pi$
$947$	−24.6217	+	24.6217i	−0.800097	+	0.800097i	0.183013	+	0.983110i	$0.441415\pi$
$948$	23.8023	+	4.45033i	0.773063	+	0.144540i
$949$	−1.52089	−	1.52089i	−0.0493701	−	0.0493701i
$950$	31.7739	+	102.614i	1.03088	+	3.32925i
$951$		−	0.507537i		−	0.0164580i
$952$	−4.28189	+	0.496528i	−0.138777	+	0.0160926i
$953$		−	36.3316i		−	1.17690i	−0.808535	−	0.588448i	$-0.799739\pi$
$953$		−	36.3316i		−	1.17690i	0.808535	−	0.588448i	$-0.200261\pi$
$954$	2.35154	−	0.728141i	0.0761340	−	0.0235744i
$955$	29.2590	+	29.2590i	0.946801	+	0.946801i
$956$	−15.1419	−	22.1062i	−0.489723	−	0.714965i
$957$	7.98131	−	7.98131i	0.257999	−	0.257999i
$958$	−17.0943	−	9.01095i	−0.552291	−	0.291131i
$959$	2.42423			0.0782824
$960$	29.3341	−	6.89588i	0.946752	−	0.222564i
$961$	−30.9946			−0.999827
$962$	−1.49009	−	0.785475i	−0.0480424	−	0.0253247i
$963$	−0.673478	+	0.673478i	−0.0217025	+	0.0217025i
$964$	−24.5984	−	35.9121i	−0.792262	−	1.15665i
$965$	−5.34836	−	5.34836i	−0.172170	−	0.172170i
$966$	−8.00848	+	2.47978i	−0.257669	+	0.0797856i
$967$		−	34.0003i		−	1.09338i	−0.837336	−	0.546688i	$-0.815888\pi$
$967$		−	34.0003i		−	1.09338i	0.837336	−	0.546688i	$-0.184112\pi$
$968$	−68.0990	+	7.89676i	−2.18879	+	0.253812i
$969$		−	12.5991i		−	0.404740i
$970$	−0.915320	−	2.95604i	−0.0293892	−	0.0949127i
$971$	−11.3730	−	11.3730i	−0.364978	−	0.364978i	0.500664	−	0.865642i	$-0.333089\pi$
$971$	−11.3730	−	11.3730i	−0.364978	−	0.364978i	−0.865642	+	0.500664i	$0.833089\pi$
$972$	1.96593	+	0.367572i	0.0630573	+	0.0117899i
$973$	−12.5811	+	12.5811i	−0.403333	+	0.403333i
$974$	−10.1108	+	19.1808i	−0.323972	+	0.614594i
$975$	−1.90639			−0.0610533
$976$	13.5221	+	30.6308i	0.432833	+	0.980469i
$977$	−41.6665			−1.33303			−0.666514	−	0.745492i	$-0.732214\pi$
$977$	−41.6665			−1.33303			−0.666514	+	0.745492i	$0.732214\pi$
$978$	−3.71183	+	7.04155i	−0.118691	+	0.225164i
$979$	53.0446	−	53.0446i	1.69531	−	1.69531i
$980$	1.38454	−	7.40510i	0.0442274	−	0.236547i
$981$	−9.67641	−	9.67641i	−0.308944	−	0.308944i
$982$	15.7746	+	50.9443i	0.503388	+	1.62570i
$983$		−	61.3506i		−	1.95678i	−0.206765	−	0.978391i	$-0.566294\pi$
$983$		−	61.3506i		−	1.95678i	0.206765	−	0.978391i	$-0.433706\pi$
$984$	−2.72782	+	3.44343i	−0.0869596	+	0.109773i
$985$		−	52.7143i		−	1.67962i
$986$	−3.91478	+	1.21219i	−0.124672	+	0.0386040i
$987$	6.54808	+	6.54808i	0.208428	+	0.208428i
$988$	2.83026	−	1.93862i	0.0900425	−	0.0616756i
$989$	20.9074	−	20.9074i	0.664817	−	0.664817i
$990$	−27.9730	−	14.7455i	−0.889042	−	0.468643i
$991$	24.3612			0.773861			0.386930	−	0.922109i	$-0.373535\pi$
$991$	24.3612			0.773861			0.386930	+	0.922109i	$0.373535\pi$
$992$	0.312679	−	0.272039i	0.00992757	−	0.00863725i
$993$	−2.78258			−0.0883024
$994$	−5.51637	−	2.90786i	−0.174969	−	0.0922317i
$995$	−34.7848	+	34.7848i	−1.10275	+	1.10275i
$996$	21.2130	−	14.5301i	0.672160	−	0.460404i
$997$	−2.63532	−	2.63532i	−0.0834613	−	0.0834613i	0.664144	−	0.747605i	$-0.268796\pi$
$997$	−2.63532	−	2.63532i	−0.0834613	−	0.0834613i	−0.747605	+	0.664144i	$0.768796\pi$
$998$	39.5254	−	12.2388i	1.25116	−	0.387413i
$999$		−	5.74058i		−	0.181624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.85.12	✓	28
4.3	odd	2		1344.2.w.b.1009.13		28
8.3	odd	2		2688.2.w.c.2017.2		28
8.5	even	2		2688.2.w.d.2017.13		28
16.3	odd	4		1344.2.w.b.337.13		28
16.5	even	4		2688.2.w.d.673.13		28
16.11	odd	4		2688.2.w.c.673.2		28
16.13	even	4	inner	336.2.w.b.253.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.12	✓	28	1.1	even	1	trivial
336.2.w.b.253.12	yes	28	16.13	even	4	inner
1344.2.w.b.337.13		28	16.3	odd	4
1344.2.w.b.1009.13		28	4.3	odd	2
2688.2.w.c.673.2		28	16.11	odd	4
2688.2.w.c.2017.2		28	8.3	odd	2
2688.2.w.d.673.13		28	16.5	even	4
2688.2.w.d.2017.13		28	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.25104 + 0.659465i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.13021 + 1.65004i) q^{4} +(2.66347 + 2.66347i) q^{5} +(-1.35093 + 0.418308i) q^{6} -1.00000i q^{7} +(0.325801 + 2.80960i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(1.25104 + 0.659465i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.13021 + 1.65004i) q^{4} +(2.66347 + 2.66347i) q^{5} +(-1.35093 + 0.418308i) q^{6} -1.00000i q^{7} +(0.325801 + 2.80960i) q^{8} -1.00000i q^{9} +(1.57565 + 5.08857i) q^{10} +(-4.19750 - 4.19750i) q^{11} +(-1.96593 - 0.367572i) q^{12} +(0.146713 - 0.146713i) q^{13} +(0.659465 - 1.25104i) q^{14} -3.76671 q^{15} +(-1.44524 + 3.72978i) q^{16} -1.52402 q^{17} +(0.659465 - 1.25104i) q^{18} +(5.84565 - 5.84565i) q^{19} +(-1.38454 + 7.40510i) q^{20} +(0.707107 + 0.707107i) q^{21} +(-2.48314 - 8.01935i) q^{22} +5.92811i q^{23} +(-2.21706 - 1.75631i) q^{24} +9.18812i q^{25} +(0.280297 - 0.0867922i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.65004 - 1.13021i) q^{28} +(1.34452 - 1.34452i) q^{29} +(-4.71232 - 2.48401i) q^{30} -0.0732661 q^{31} +(-4.26772 + 3.71303i) q^{32} +5.93616 q^{33} +(-1.90661 - 1.00504i) q^{34} +(2.66347 - 2.66347i) q^{35} +(1.65004 - 1.13021i) q^{36} +(-4.05921 - 4.05921i) q^{37} +(11.1681 - 3.45815i) q^{38} +0.207484i q^{39} +(-6.61552 + 8.35104i) q^{40} -1.55315i q^{41} +(0.418308 + 1.35093i) q^{42} +(-3.52682 - 3.52682i) q^{43} +(2.18196 - 11.6701i) q^{44} +(2.66347 - 2.66347i) q^{45} +(-3.90938 + 7.41632i) q^{46} +9.26038 q^{47} +(-1.61541 - 3.65929i) q^{48} -1.00000 q^{49} +(-6.05924 + 11.4947i) q^{50} +(1.07764 - 1.07764i) q^{51} +(0.407900 + 0.0762652i) q^{52} +(1.23085 + 1.23085i) q^{53} +(0.418308 + 1.35093i) q^{54} -22.3598i q^{55} +(2.80960 - 0.325801i) q^{56} +8.26699i q^{57} +(2.56872 - 0.795389i) q^{58} +(0.548474 + 0.548474i) q^{59} +(-4.25718 - 6.21521i) q^{60} +(5.91897 - 5.91897i) q^{61} +(-0.0916590 - 0.0483164i) q^{62} -1.00000 q^{63} +(-7.78771 + 1.83074i) q^{64} +0.781533 q^{65} +(7.42638 + 3.91469i) q^{66} +(-1.40166 + 1.40166i) q^{67} +(-1.72247 - 2.51469i) q^{68} +(-4.19181 - 4.19181i) q^{69} +(5.08857 - 1.57565i) q^{70} -4.40942i q^{71} +(2.80960 - 0.325801i) q^{72} -10.3664i q^{73} +(-2.40133 - 7.75514i) q^{74} +(-6.49698 - 6.49698i) q^{75} +(16.2523 + 3.03871i) q^{76} +(-4.19750 + 4.19750i) q^{77} +(-0.136828 + 0.259571i) q^{78} -12.1074 q^{79} +(-13.7835 + 6.08480i) q^{80} -1.00000 q^{81} +(1.02425 - 1.94306i) q^{82} +(-9.09062 + 9.09062i) q^{83} +(-0.367572 + 1.96593i) q^{84} +(-4.05918 - 4.05918i) q^{85} +(-2.08639 - 6.73802i) q^{86} +1.90144i q^{87} +(10.4257 - 13.1608i) q^{88} +12.6372i q^{89} +(5.08857 - 1.57565i) q^{90} +(-0.146713 - 0.146713i) q^{91} +(-9.78161 + 6.70003i) q^{92} +(0.0518070 - 0.0518070i) q^{93} +(11.5851 + 6.10690i) q^{94} +31.1394 q^{95} +(0.392226 - 5.64324i) q^{96} -0.580917 q^{97} +(-1.25104 - 0.659465i) q^{98} +(-4.19750 + 4.19750i) 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

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