LMFDB - Embedded newform 670.2.h.c.439.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(29,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("670.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.h (of order $6$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.5
Character	$\chi$	$=$	670.439
Dual form			670.2.h.c.29.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} -0.719082i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.192333 + 2.22778i) q^{5} +(0.359541 + 0.622744i) q^{6} +(-3.77588 - 2.18000i) q^{7} +1.00000i q^{8} +2.48292 q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} -0.719082i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.192333 + 2.22778i) q^{5} +(0.359541 + 0.622744i) q^{6} +(-3.77588 - 2.18000i) q^{7} +1.00000i q^{8} +2.48292 q^{9} +(-1.28046 - 1.83315i) q^{10} +(-2.13241 + 3.69343i) q^{11} +(-0.622744 - 0.359541i) q^{12} +(1.72113 - 0.993696i) q^{13} +4.36001 q^{14} +(1.60196 - 0.138303i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.11848 + 0.645754i) q^{17} +(-2.15027 + 1.24146i) q^{18} +(-2.20028 - 3.81100i) q^{19} +(2.02548 + 0.947326i) q^{20} +(-1.56760 + 2.71517i) q^{21} -4.26481i q^{22} +(-8.07540 + 4.66233i) q^{23} +0.719082 q^{24} +(-4.92602 + 0.856950i) q^{25} +(-0.993696 + 1.72113i) q^{26} -3.94267i q^{27} +(-3.77588 + 2.18000i) q^{28} +(-3.50823 + 6.07644i) q^{29} +(-1.31818 + 0.920753i) q^{30} +(3.21624 - 5.57069i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.65588 + 1.53338i) q^{33} +(0.645754 - 1.11848i) q^{34} +(4.13035 - 8.83111i) q^{35} +(1.24146 - 2.15027i) q^{36} +(-1.57530 + 0.909501i) q^{37} +(3.81100 + 2.20028i) q^{38} +(-0.714549 - 1.23764i) q^{39} +(-2.22778 + 0.192333i) q^{40} +(-3.64451 + 6.31247i) q^{41} -3.13520i q^{42} +8.93363i q^{43} +(2.13241 + 3.69343i) q^{44} +(0.477546 + 5.53140i) q^{45} +(4.66233 - 8.07540i) q^{46} +(-2.52546 - 1.45808i) q^{47} +(-0.622744 + 0.359541i) q^{48} +(6.00483 + 10.4007i) q^{49} +(3.83758 - 3.20515i) q^{50} +(0.464350 + 0.804278i) q^{51} -1.98739i q^{52} -6.63793i q^{53} +(1.97134 + 3.41445i) q^{54} +(-8.63829 - 4.04016i) q^{55} +(2.18000 - 3.77588i) q^{56} +(-2.74043 + 1.58219i) q^{57} -7.01646i q^{58} -10.1956 q^{59} +(0.681205 - 1.45649i) q^{60} +(-6.19683 - 10.7332i) q^{61} +6.43248i q^{62} +(-9.37520 - 5.41278i) q^{63} -1.00000 q^{64} +(2.54477 + 3.64318i) q^{65} -3.06675 q^{66} +(-3.09421 + 7.57799i) q^{67} +1.29151i q^{68} +(3.35260 + 5.80688i) q^{69} +(0.838571 + 9.71314i) q^{70} +(-4.43279 + 7.67782i) q^{71} +2.48292i q^{72} +(-2.54171 + 1.46746i) q^{73} +(0.909501 - 1.57530i) q^{74} +(0.616217 + 3.54221i) q^{75} -4.40057 q^{76} +(16.1034 - 9.29730i) q^{77} +(1.23764 + 0.714549i) q^{78} +(-3.98697 + 6.90563i) q^{79} +(1.83315 - 1.28046i) q^{80} +4.61366 q^{81} -7.28902i q^{82} +(6.13533 - 3.54224i) q^{83} +(1.56760 + 2.71517i) q^{84} +(-1.65372 - 2.36753i) q^{85} +(-4.46682 - 7.73675i) q^{86} +(4.36946 + 2.52271i) q^{87} +(-3.69343 - 2.13241i) q^{88} -5.47498 q^{89} +(-3.17927 - 4.55156i) q^{90} -8.66504 q^{91} +9.32467i q^{92} +(-4.00578 - 2.31274i) q^{93} +2.91615 q^{94} +(8.06690 - 5.63473i) q^{95} +(0.359541 - 0.622744i) q^{96} +(9.00867 - 5.20116i) q^{97} +(-10.4007 - 6.00483i) q^{98} +(-5.29459 + 9.17051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	$ 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) $ 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		−	0.719082i		−	0.415162i	−0.978218	−	0.207581i	$-0.933441\pi$
$3$		−	0.719082i		−	0.415162i	0.978218	−	0.207581i	$-0.0665591\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.192333	+	2.22778i	0.0860137	+	0.996294i
$5$	0.192333	+	2.22778i	0.0860137	+	0.996294i
$6$	0.359541	+	0.622744i	0.146782	+	0.254234i
$7$	−3.77588	−	2.18000i	−1.42715	−	0.823964i	−0.430253	−	0.902709i	$-0.641575\pi$
$7$	−3.77588	−	2.18000i	−1.42715	−	0.823964i	−0.996895	+	0.0787447i	$0.974909\pi$
$8$			1.00000i			0.353553i
$9$	2.48292			0.827640
$10$	−1.28046	−	1.83315i	−0.404916	−	0.579693i
$11$	−2.13241	+	3.69343i	−0.642944	+	1.11361i	0.341828	+	0.939763i	$0.388954\pi$
$11$	−2.13241	+	3.69343i	−0.642944	+	1.11361i	−0.984772	+	0.173850i	$0.944379\pi$
$12$	−0.622744	−	0.359541i	−0.179771	−	0.103791i
$13$	1.72113	−	0.993696i	0.477356	−	0.275602i	−0.241958	−	0.970287i	$-0.577790\pi$
$13$	1.72113	−	0.993696i	0.477356	−	0.275602i	0.719314	+	0.694685i	$0.244456\pi$
$14$	4.36001			1.16526
$15$	1.60196	−	0.138303i	0.413624	−	0.0357097i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.11848	+	0.645754i	−0.271271	+	0.156618i	−0.629465	−	0.777029i	$-0.716726\pi$
$17$	−1.11848	+	0.645754i	−0.271271	+	0.156618i	0.358194	+	0.933647i	$0.383393\pi$
$18$	−2.15027	+	1.24146i	−0.506824	+	0.292615i
$19$	−2.20028	−	3.81100i	−0.504780	−	0.874304i	−0.999985	−	0.00552814i	$-0.998240\pi$
$19$	−2.20028	−	3.81100i	−0.504780	−	0.874304i	0.495205	−	0.868776i	$-0.335093\pi$
$20$	2.02548	+	0.947326i	0.452911	+	0.211828i
$21$	−1.56760	+	2.71517i	−0.342079	+	0.592498i
$22$		−	4.26481i		−	0.909261i
$23$	−8.07540	+	4.66233i	−1.68384	+	0.972164i	−0.724767	+	0.688994i	$0.758052\pi$
$23$	−8.07540	+	4.66233i	−1.68384	+	0.972164i	−0.959070	+	0.283169i	$0.908614\pi$
$24$	0.719082			0.146782
$25$	−4.92602	+	0.856950i	−0.985203	+	0.171390i
$26$	−0.993696	+	1.72113i	−0.194880	+	0.337542i
$27$		−	3.94267i		−	0.758767i
$28$	−3.77588	+	2.18000i	−0.713574	+	0.411982i
$29$	−3.50823	+	6.07644i	−0.651462	+	1.12837i	0.331306	+	0.943523i	$0.392511\pi$
$29$	−3.50823	+	6.07644i	−0.651462	+	1.12837i	−0.982768	+	0.184842i	$0.940823\pi$
$30$	−1.31818	+	0.920753i	−0.240667	+	0.168106i
$31$	3.21624	−	5.57069i	0.577654	−	1.00053i	−0.418094	−	0.908404i	$-0.637302\pi$
$31$	3.21624	−	5.57069i	0.577654	−	1.00053i	0.995748	−	0.0921217i	$-0.0293649\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	2.65588	+	1.53338i	0.462330	+	0.266926i
$34$	0.645754	−	1.11848i	0.110746	−	0.191818i
$35$	4.13035	−	8.83111i	0.698156	−	1.49273i
$36$	1.24146	−	2.15027i	0.206910	−	0.358379i
$37$	−1.57530	+	0.909501i	−0.258978	+	0.149521i	−0.623868	−	0.781530i	$-0.714440\pi$
$37$	−1.57530	+	0.909501i	−0.258978	+	0.149521i	0.364890	+	0.931051i	$0.381106\pi$
$38$	3.81100	+	2.20028i	0.618227	+	0.356933i
$39$	−0.714549	−	1.23764i	−0.114419	−	0.198180i
$40$	−2.22778	+	0.192333i	−0.352243	+	0.0304104i
$41$	−3.64451	+	6.31247i	−0.569177	+	0.985843i	0.427471	+	0.904029i	$0.359405\pi$
$41$	−3.64451	+	6.31247i	−0.569177	+	0.985843i	−0.996648	+	0.0818137i	$0.973929\pi$
$42$		−	3.13520i		−	0.483772i
$43$			8.93363i			1.36237i	0.732113	+	0.681183i	$0.238534\pi$
$43$			8.93363i			1.36237i	−0.732113	+	0.681183i	$0.761466\pi$
$44$	2.13241	+	3.69343i	0.321472	+	0.556806i
$45$	0.477546	+	5.53140i	0.0711884	+	0.824573i
$46$	4.66233	−	8.07540i	0.687423	−	1.19065i
$47$	−2.52546	−	1.45808i	−0.368376	−	0.212682i	0.304373	−	0.952553i	$-0.401553\pi$
$47$	−2.52546	−	1.45808i	−0.368376	−	0.212682i	−0.672749	+	0.739871i	$0.734887\pi$
$48$	−0.622744	+	0.359541i	−0.0898853	+	0.0518953i
$49$	6.00483	+	10.4007i	0.857833	+	1.48581i
$50$	3.83758	−	3.20515i	0.542716	−	0.453276i
$51$	0.464350	+	0.804278i	0.0650220	+	0.112621i
$52$		−	1.98739i		−	0.275602i
$53$		−	6.63793i		−	0.911790i	−0.890033	−	0.455895i	$-0.849319\pi$
$53$		−	6.63793i		−	0.911790i	0.890033	−	0.455895i	$-0.150681\pi$
$54$	1.97134	+	3.41445i	0.268265	+	0.464648i
$55$	−8.63829	−	4.04016i	−1.16479	−	0.544776i
$56$	2.18000	−	3.77588i	0.291315	−	0.504573i
$57$	−2.74043	+	1.58219i	−0.362978	+	0.209566i
$58$		−	7.01646i		−	0.921307i
$59$	−10.1956			−1.32735			−0.663677	−	0.748020i	$-0.731005\pi$
$59$	−10.1956			−1.32735			−0.663677	+	0.748020i	$0.731005\pi$
$60$	0.681205	−	1.45649i	0.0879432	−	0.188032i
$61$	−6.19683	−	10.7332i	−0.793423	−	1.37425i	−0.923836	−	0.382789i	$-0.874964\pi$
$61$	−6.19683	−	10.7332i	−0.793423	−	1.37425i	0.130413	−	0.991460i	$-0.458370\pi$
$62$			6.43248i			0.816926i
$63$	−9.37520	−	5.41278i	−1.18116	−	0.681946i
$64$	−1.00000			−0.125000
$65$	2.54477	+	3.64318i	0.315639	+	0.451881i
$66$	−3.06675			−0.377491
$67$	−3.09421	+	7.57799i	−0.378018	+	0.925798i
$67$	−3.09421	+	7.57799i	−0.378018	+	0.925798i
$68$			1.29151i			0.156618i
$69$	3.35260	+	5.80688i	0.403606	+	0.699066i
$70$	0.838571	+	9.71314i	0.100228	+	1.16094i
$71$	−4.43279	+	7.67782i	−0.526076	+	0.911190i	0.473463	+	0.880814i	$0.343004\pi$
$71$	−4.43279	+	7.67782i	−0.526076	+	0.911190i	−0.999539	+	0.0303759i	$0.990330\pi$
$72$			2.48292i			0.292615i
$73$	−2.54171	+	1.46746i	−0.297484	+	0.171753i	−0.641312	−	0.767280i	$-0.721610\pi$
$73$	−2.54171	+	1.46746i	−0.297484	+	0.171753i	0.343828	+	0.939033i	$0.388276\pi$
$74$	0.909501	−	1.57530i	0.105727	−	0.183125i
$75$	0.616217	+	3.54221i	0.0711546	+	0.409019i
$76$	−4.40057			−0.504780
$77$	16.1034	−	9.29730i	1.83515	−	1.05953i
$78$	1.23764	+	0.714549i	0.140135	+	0.0809067i
$79$	−3.98697	+	6.90563i	−0.448569	+	0.776944i	−0.998293	−	0.0584021i	$-0.981399\pi$
$79$	−3.98697	+	6.90563i	−0.448569	+	0.776944i	0.549724	+	0.835346i	$0.314733\pi$
$80$	1.83315	−	1.28046i	0.204952	−	0.143159i
$81$	4.61366			0.512629
$82$		−	7.28902i		−	0.804937i
$83$	6.13533	−	3.54224i	0.673440	−	0.388811i	−0.123939	−	0.992290i	$-0.539553\pi$
$83$	6.13533	−	3.54224i	0.673440	−	0.388811i	0.797379	+	0.603479i	$0.206219\pi$
$84$	1.56760	+	2.71517i	0.171039	+	0.296249i
$85$	−1.65372	−	2.36753i	−0.179371	−	0.256794i
$86$	−4.46682	−	7.73675i	−0.481669	−	0.834275i
$87$	4.36946	+	2.52271i	0.468455	+	0.270463i
$88$	−3.69343	−	2.13241i	−0.393721	−	0.227315i
$89$	−5.47498			−0.580347			−0.290174	−	0.956974i	$-0.593713\pi$
$89$	−5.47498			−0.580347			−0.290174	+	0.956974i	$0.593713\pi$
$90$	−3.17927	−	4.55156i	−0.335124	−	0.479777i
$91$	−8.66504			−0.908343
$92$			9.32467i			0.972164i
$93$	−4.00578	−	2.31274i	−0.415380	−	0.239820i
$94$	2.91615			0.300778
$95$	8.06690	−	5.63473i	0.827646	−	0.578111i
$96$	0.359541	−	0.622744i	0.0366955	−	0.0635585i
$97$	9.00867	−	5.20116i	0.914691	−	0.528097i	0.0327537	−	0.999463i	$-0.489572\pi$
$97$	9.00867	−	5.20116i	0.914691	−	0.528097i	0.881938	+	0.471366i	$0.156239\pi$
$98$	−10.4007	−	6.00483i	−1.05063	−	0.606580i
$99$	−5.29459	+	9.17051i	−0.532127	+	0.921670i
$100$	−1.72087	+	4.69453i	−0.172087	+	0.469453i
$101$	2.59521	−	4.49503i	0.258233	−	0.447272i	−0.707536	−	0.706677i	$-0.750193\pi$
$101$	2.59521	−	4.49503i	0.258233	−	0.447272i	0.965769	+	0.259405i	$0.0835266\pi$
$102$	−0.804278	−	0.464350i	−0.0796354	−	0.0459775i
$103$	7.03881	+	4.06386i	0.693555	+	0.400424i	0.804942	−	0.593353i	$-0.202196\pi$
$103$	7.03881	+	4.06386i	0.693555	+	0.400424i	−0.111388	+	0.993777i	$0.535530\pi$
$104$	0.993696	+	1.72113i	0.0974399	+	0.168771i
$105$	−6.35030	−	2.97006i	−0.619726	−	0.289848i
$106$	3.31897	+	5.74862i	0.322367	+	0.558355i
$107$		−	14.3863i		−	1.39078i	−0.718635	−	0.695388i	$-0.755233\pi$
$107$		−	14.3863i		−	1.39078i	0.718635	−	0.695388i	$-0.244767\pi$
$108$	−3.41445	−	1.97134i	−0.328556	−	0.189692i
$109$	−0.991414			−0.0949602			−0.0474801	−	0.998872i	$-0.515119\pi$
$109$	−0.991414			−0.0949602			−0.0474801	+	0.998872i	$0.515119\pi$
$110$	9.50106	−	0.820262i	0.905891	−	0.0782089i
$111$	0.654006	+	1.13277i	0.0620755	+	0.107518i
$112$			4.36001i			0.411982i
$113$	11.1297	+	6.42571i	1.04699	+	0.604480i	0.921805	−	0.387653i	$-0.126714\pi$
$113$	11.1297	+	6.42571i	1.04699	+	0.604480i	0.125185	+	0.992133i	$0.460047\pi$
$114$	1.58219	−	2.74043i	0.148185	−	0.256664i
$115$	−11.9398	−	17.0935i	−1.11339	−	1.59398i
$116$	3.50823	+	6.07644i	0.325731	+	0.564183i
$117$	4.27343	−	2.46727i	0.395079	−	0.228099i
$118$	8.82964	−	5.09780i	0.812835	−	0.469290i
$119$	5.63098			0.516191
$120$	0.138303	+	1.60196i	0.0126253	+	0.146238i
$121$	−3.59431	−	6.22552i	−0.326755	−	0.565956i
$122$	10.7332	+	6.19683i	0.971740	+	0.561035i
$123$	4.53919	+	2.62070i	0.409285	+	0.236301i
$124$	−3.21624	−	5.57069i	−0.288827	−	0.500263i
$125$	−2.85653	−	10.8093i	−0.255496	−	0.966810i
$126$	10.8256			0.964417
$127$	−5.19117	−	2.99713i	−0.460642	−	0.265952i	0.251672	−	0.967813i	$-0.419020\pi$
$127$	−5.19117	−	2.99713i	−0.460642	−	0.265952i	−0.712314	+	0.701861i	$0.752353\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	6.42402			0.565603
$130$	−4.02542	−	1.88271i	−0.353053	−	0.165124i
$131$	−5.04072			−0.440410			−0.220205	−	0.975454i	$-0.570673\pi$
$131$	−5.04072			−0.440410			−0.220205	+	0.975454i	$0.570673\pi$
$132$	2.65588	−	1.53338i	0.231165	−	0.133463i
$133$			19.1865i			1.66368i
$134$	−1.10933	−	8.10983i	−0.0958315	−	0.700583i
$135$	8.78341	−	0.758304i	0.755955	−	0.0652644i
$136$	−0.645754	−	1.11848i	−0.0553729	−	0.0959088i
$137$			8.91411i			0.761584i	0.924661	+	0.380792i	$0.124349\pi$
$137$			8.91411i			0.761584i	−0.924661	+	0.380792i	$0.875651\pi$
$138$	−5.80688	−	3.35260i	−0.494314	−	0.285392i
$139$	20.0776			1.70296			0.851482	−	0.524384i	$-0.175705\pi$
$139$	20.0776			1.70296			0.851482	+	0.524384i	$0.175705\pi$
$140$	−5.58279	−	7.99254i	−0.471832	−	0.675493i
$141$	−1.04848	+	1.81601i	−0.0882976	+	0.152936i
$142$		−	8.86558i		−	0.743983i
$143$			8.47585i			0.708786i
$144$	−1.24146	−	2.15027i	−0.103455	−	0.179189i
$145$	−14.2117	−	6.64688i	−1.18022	−	0.551993i
$146$	1.46746	−	2.54171i	0.121447	−	0.210353i
$147$	7.47894	−	4.31797i	0.616853	−	0.356140i
$148$			1.81900i			0.149521i
$149$	3.59429			0.294456			0.147228	−	0.989103i	$-0.452965\pi$
$149$	3.59429			0.294456			0.147228	+	0.989103i	$0.452965\pi$
$150$	−2.30477	−	2.75954i	−0.188183	−	0.225315i
$151$	−8.61765	−	14.9262i	−0.701294	−	1.21468i	−0.968012	−	0.250903i	$-0.919273\pi$
$151$	−8.61765	−	14.9262i	−0.701294	−	1.21468i	0.266718	−	0.963775i	$-0.414061\pi$
$152$	3.81100	−	2.20028i	0.309113	−	0.178467i
$153$	−2.77709	+	1.60336i	−0.224515	+	0.129624i
$154$	−9.29730	+	16.1034i	−0.749198	+	1.29765i
$155$	13.0289	+	6.09365i	1.04650	+	0.489454i
$156$	−1.42910			−0.114419
$157$	8.38054	−	4.83851i	0.668840	−	0.386155i	−0.126797	−	0.991929i	$-0.540470\pi$
$157$	8.38054	−	4.83851i	0.668840	−	0.386155i	0.795637	+	0.605774i	$0.207136\pi$
$158$		−	7.97393i		−	0.634372i
$159$	−4.77322			−0.378541
$160$	−0.947326	+	2.02548i	−0.0748927	+	0.160128i
$161$	40.6556			3.20411
$162$	−3.99554	+	2.30683i	−0.313920	+	0.181242i
$163$	16.4575	+	9.50176i	1.28905	+	0.744235i	0.978485	−	0.206316i	$-0.0661476\pi$
$163$	16.4575	+	9.50176i	1.28905	+	0.744235i	0.310567	+	0.950551i	$0.399481\pi$
$164$	3.64451	+	6.31247i	0.284588	+	0.492921i
$165$	−2.90521	+	6.21164i	−0.226170	+	0.483576i
$166$	−3.54224	+	6.13533i	−0.274931	+	0.476194i
$167$	8.47859	+	4.89512i	0.656093	+	0.378795i	0.790787	−	0.612092i	$-0.209672\pi$
$167$	8.47859	+	4.89512i	0.656093	+	0.378795i	−0.134694	+	0.990887i	$0.543005\pi$
$168$	−2.71517	−	1.56760i	−0.209480	−	0.120943i
$169$	−4.52514	+	7.83777i	−0.348088	+	0.602905i
$170$	2.61593	+	1.22348i	0.200632	+	0.0938365i
$171$	−5.46313	−	9.46242i	−0.417776	−	0.723609i
$172$	7.73675	+	4.46682i	0.589922	+	0.340592i
$173$	9.27306	−	5.35380i	0.705018	−	0.407042i	−0.104196	−	0.994557i	$-0.533227\pi$
$173$	9.27306	−	5.35380i	0.705018	−	0.407042i	0.809214	+	0.587515i	$0.199894\pi$
$174$	−5.04541			−0.382492
$175$	20.4682	+	7.50300i	1.54725	+	0.567173i
$176$	4.26481			0.321472
$177$			7.33147i			0.551067i
$178$	4.74147	−	2.73749i	0.355389	−	0.205184i
$179$	17.0961			1.27783			0.638913	−	0.769279i	$-0.279385\pi$
$179$	17.0961			1.27783			0.638913	+	0.769279i	$0.279385\pi$
$180$	5.02911	+	2.35213i	0.374848	+	0.175318i
$181$	−7.40979	+	12.8341i	−0.550766	+	0.953954i	0.447454	+	0.894307i	$0.352331\pi$
$181$	−7.40979	+	12.8341i	−0.550766	+	0.953954i	−0.998220	+	0.0596470i	$0.981002\pi$
$182$	7.50414	−	4.33252i	0.556244	−	0.321148i
$183$	−7.71807	+	4.45603i	−0.570536	+	0.329399i
$184$	−4.66233	−	8.07540i	−0.343712	−	0.595326i
$185$	−2.32915	−	3.33450i	−0.171243	−	0.245157i
$186$	4.62548			0.339157
$187$		−	5.50804i		−	0.402788i
$188$	−2.52546	+	1.45808i	−0.184188	+	0.106341i
$189$	−8.59504	+	14.8870i	−0.625197	+	1.08287i
$190$	−4.16877	+	8.91327i	−0.302434	+	0.646637i
$191$	1.27714	+	2.21208i	0.0924110	+	0.160060i	0.908525	−	0.417830i	$-0.137209\pi$
$191$	1.27714	+	2.21208i	0.0924110	+	0.160060i	−0.816114	+	0.577891i	$0.803876\pi$
$192$			0.719082i			0.0518953i
$193$		−	10.4563i		−	0.752659i	−0.926486	−	0.376330i	$-0.877186\pi$
$193$		−	10.4563i		−	0.752659i	0.926486	−	0.376330i	$-0.122814\pi$
$194$	−5.20116	+	9.00867i	−0.373421	+	0.646784i
$195$	2.61975	−	1.82990i	0.187604	−	0.131042i
$196$	12.0097			0.857833
$197$	−16.8025	−	9.70090i	−1.19713	−	0.691161i	−0.237212	−	0.971458i	$-0.576234\pi$
$197$	−16.8025	−	9.70090i	−1.19713	−	0.691161i	−0.959913	+	0.280297i	$0.909567\pi$
$198$		−	10.5892i		−	0.752541i
$199$	8.29222	+	14.3625i	0.587820	+	1.01813i	0.994517	+	0.104571i	$0.0333470\pi$
$199$	8.29222	+	14.3625i	0.587820	+	1.01813i	−0.406698	+	0.913563i	$0.633320\pi$
$200$	−0.856950	−	4.92602i	−0.0605955	−	0.348322i
$201$	5.44920	+	2.22499i	0.384357	+	0.156939i
$202$			5.19041i			0.365196i
$203$	26.4933	−	15.2959i	1.85947	−	1.07356i
$204$	0.928701			0.0650220
$205$	−14.7638	−	6.90507i	−1.03115	−	0.482271i
$206$	−8.12772			−0.566285
$207$	−20.0506	+	11.5762i	−1.39361	+	0.804602i
$208$	−1.72113	−	0.993696i	−0.119339	−	0.0689004i
$209$	18.7676			1.29818
$210$	6.98455	−	0.603002i	0.481980	−	0.0416111i
$211$	7.17273	+	12.4235i	0.493791	+	0.855271i	0.999974	−	0.00715468i	$-0.00227742\pi$
$211$	7.17273	+	12.4235i	0.493791	+	0.855271i	−0.506183	+	0.862426i	$0.668944\pi$
$212$	−5.74862	−	3.31897i	−0.394817	−	0.227948i
$213$	5.52099	+	3.18754i	0.378292	+	0.218407i
$214$	7.19315	+	12.4589i	0.491713	+	0.851672i
$215$	−19.9022	+	1.71823i	−1.35732	+	0.117182i
$216$	3.94267			0.268265
$217$	−24.2882	+	14.0228i	−1.64879	+	0.951931i
$218$	0.858590	−	0.495707i	0.0581510	−	0.0335735i
$219$	1.05522	+	1.82770i	0.0713052	+	0.123504i
$220$	−7.81803	+	5.46090i	−0.527092	+	0.368174i
$221$	−1.28337	+	2.22285i	−0.0863285	+	0.149525i
$222$	−1.13277	−	0.654006i	−0.0760266	−	0.0438940i
$223$			5.05374i			0.338424i	0.985580	+	0.169212i	$0.0541222\pi$
$223$			5.05374i			0.338424i	−0.985580	+	0.169212i	$0.945878\pi$
$224$	−2.18000	−	3.77588i	−0.145658	−	0.252286i
$225$	−12.2309	+	2.12774i	−0.815394	+	0.141849i
$226$	−12.8514			−0.854864
$227$	−20.0355	−	11.5675i	−1.32980	−	0.767763i	−0.344535	−	0.938773i	$-0.611964\pi$
$227$	−20.0355	−	11.5675i	−1.32980	−	0.767763i	−0.985269	+	0.171010i	$0.945297\pi$
$228$			3.16437i			0.209566i
$229$	2.46042	+	4.26157i	0.162589	+	0.281612i	0.935796	−	0.352541i	$-0.114682\pi$
$229$	2.46042	+	4.26157i	0.162589	+	0.281612i	−0.773208	+	0.634153i	$0.781349\pi$
$230$	18.8869	+	8.83349i	1.24537	+	0.582463i
$231$	−6.68553	−	11.5797i	−0.439875	−	0.761886i
$232$	−6.07644	−	3.50823i	−0.398938	−	0.230327i
$233$	2.91434	+	1.68260i	0.190925	+	0.110231i	0.592416	−	0.805633i	$-0.298174\pi$
$233$	2.91434	+	1.68260i	0.190925	+	0.110231i	−0.401491	+	0.915863i	$0.631508\pi$
$234$	−2.46727	+	4.27343i	−0.161290	+	0.279363i
$235$	2.76254	−	5.90661i	0.180209	−	0.385305i
$236$	−5.09780	+	8.82964i	−0.331838	+	0.574761i
$237$	4.96572	+	2.86696i	0.322558	+	0.186229i
$238$	−4.87658	+	2.81549i	−0.316101	+	0.182501i
$239$	9.14925	−	15.8470i	0.591816	−	1.02505i	−0.402172	−	0.915564i	$-0.631745\pi$
$239$	9.14925	−	15.8470i	0.591816	−	1.02505i	0.993988	−	0.109491i	$-0.0349220\pi$
$240$	−0.920753	−	1.31818i	−0.0594343	−	0.0850885i
$241$	1.53395			0.0988102			0.0494051	−	0.998779i	$-0.484267\pi$
$241$	1.53395			0.0988102			0.0494051	+	0.998779i	$0.484267\pi$
$242$	6.22552	+	3.59431i	0.400192	+	0.231051i
$243$		−	15.1456i		−	0.971592i
$244$	−12.3937			−0.793423
$245$	−22.0155	+	15.3778i	−1.40652	+	0.982454i
$246$	−5.24140			−0.334180
$247$	−7.57396	−	4.37283i	−0.481919	−	0.278236i
$248$	5.57069	+	3.21624i	0.353739	+	0.204231i
$249$	−2.54716	−	4.41181i	−0.161420	−	0.279587i
$250$	7.87846	+	7.93283i	0.498278	+	0.501717i
$251$	−11.7688	−	20.3841i	−0.742837	−	1.28663i	−0.951198	−	0.308580i	$-0.900146\pi$
$251$	−11.7688	−	20.3841i	−0.742837	−	1.28663i	0.208361	−	0.978052i	$-0.433187\pi$
$252$	−9.37520	+	5.41278i	−0.590582	+	0.340973i
$253$		−	39.7679i		−	2.50019i
$254$	5.99425			0.376113
$255$	−1.70245	+	1.18916i	−0.106611	+	0.0744681i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.25605	−	0.725182i	−0.0783504	−	0.0452356i	0.460313	−	0.887757i	$-0.347737\pi$
$257$	−1.25605	−	0.725182i	−0.0783504	−	0.0452356i	−0.538663	+	0.842521i	$0.681071\pi$
$258$	−5.56336	+	3.21201i	−0.346360	+	0.199971i
$259$	7.93086			0.492800
$260$	4.42747	−	0.382240i	0.274580	−	0.0237055i
$261$	−8.71066	+	15.0873i	−0.539176	+	0.933881i
$262$	4.36539	−	2.52036i	0.269695	−	0.155708i
$263$		−	3.63154i		−	0.223930i	−0.993712	−	0.111965i	$-0.964285\pi$
$263$		−	3.63154i		−	0.223930i	0.993712	−	0.111965i	$-0.0357145\pi$
$264$	−1.53338	+	2.65588i	−0.0943727	+	0.163458i
$265$	14.7879	−	1.27669i	0.908411	−	0.0784265i
$266$	−9.59326	−	16.6160i	−0.588200	−	1.01879i
$267$			3.93696i			0.240938i
$268$	5.01562	+	6.46866i	0.306378	+	0.395136i
$269$	−11.1787			−0.681579			−0.340790	−	0.940140i	$-0.610694\pi$
$269$	−11.1787			−0.681579			−0.340790	+	0.940140i	$0.610694\pi$
$270$	−7.22750	+	5.04841i	−0.439852	+	0.307237i
$271$	1.22628			0.0744913			0.0372456	−	0.999306i	$-0.488142\pi$
$271$	1.22628			0.0744913			0.0372456	+	0.999306i	$0.488142\pi$
$272$	1.11848	+	0.645754i	0.0678177	+	0.0391546i
$273$			6.23088i			0.377110i
$274$	−4.45705	−	7.71984i	−0.269260	−	0.466373i
$275$	7.33918	−	20.0213i	0.442569	−	1.20733i
$276$	6.70520			0.403606
$277$		−	24.5655i		−	1.47600i	−0.674801	−	0.738000i	$-0.735771\pi$
$277$		−	24.5655i		−	1.47600i	0.674801	−	0.738000i	$-0.264229\pi$
$278$	−17.3877	+	10.0388i	−1.04285	+	0.602088i
$279$	7.98567	−	13.8316i	0.478089	−	0.828075i
$280$	8.83111	+	4.13035i	0.527760	+	0.246835i
$281$	−8.28466	−	14.3495i	−0.494221	−	0.856017i	0.505756	−	0.862676i	$-0.331213\pi$
$281$	−8.28466	−	14.3495i	−0.494221	−	0.856017i	−0.999978	+	0.00665969i	$0.997880\pi$
$282$		−	2.09695i		−	0.124872i
$283$			20.8933i			1.24198i	0.783819	+	0.620989i	$0.213269\pi$
$283$			20.8933i			1.24198i	−0.783819	+	0.620989i	$0.786731\pi$
$284$	4.43279	+	7.67782i	0.263038	+	0.455595i
$285$	−4.05184	−	5.80076i	−0.240010	−	0.343608i
$286$	−4.23792	−	7.34030i	−0.250594	−	0.434041i
$287$	27.5224	−	15.8901i	1.62460	−	0.937962i
$288$	2.15027	+	1.24146i	0.126706	+	0.0731538i
$289$	−7.66600	+	13.2779i	−0.450941	+	0.781053i
$290$	15.6311	−	1.34949i	0.917892	−	0.0792450i
$291$	−3.74006	−	6.47797i	−0.219246	−	0.379745i
$292$			2.93491i			0.171753i
$293$			20.6330i			1.20539i	0.797971	+	0.602695i	$0.205907\pi$
$293$			20.6330i			1.20539i	−0.797971	+	0.602695i	$0.794093\pi$
$294$	−4.31797	+	7.47894i	−0.251829	+	0.436181i
$295$	−1.96094	−	22.7136i	−0.114171	−	1.32243i
$296$	−0.909501	−	1.57530i	−0.0528636	−	0.0915625i
$297$	14.5620	+	8.40737i	0.844973	+	0.487845i
$298$	−3.11275	+	1.79714i	−0.180316	+	0.104106i
$299$	−9.26588	+	16.0490i	−0.535860	+	0.928136i
$300$	3.37575	+	1.23745i	0.194899	+	0.0714440i
$301$	19.4753	−	33.7323i	1.12254	−	1.94430i
$302$	14.9262	+	8.61765i	0.858906	+	0.495890i
$303$	−3.23230	−	1.86617i	−0.185690	−	0.107208i
$304$	−2.20028	+	3.81100i	−0.126195	+	0.218576i
$305$	22.7194	−	15.8695i	1.30091	−	0.908686i
$306$	1.60336	−	2.77709i	0.0916578	−	0.158756i
$307$	−25.1949	+	14.5463i	−1.43795	+	0.830201i	−0.997707	−	0.0676767i	$-0.978441\pi$
$307$	−25.1949	+	14.5463i	−1.43795	+	0.830201i	−0.440244	+	0.897878i	$0.645108\pi$
$308$		−	18.5946i		−	1.05953i
$309$	2.92225	−	5.06148i	0.166241	−	0.287938i
$310$	−14.3302	+	1.23717i	−0.813898	+	0.0702668i
$311$	18.8614			1.06953			0.534767	−	0.845000i	$-0.320400\pi$
$311$	18.8614			1.06953			0.534767	+	0.845000i	$0.320400\pi$
$312$	1.23764	−	0.714549i	0.0700673	−	0.0404534i
$313$			32.1011i			1.81446i	0.420635	+	0.907230i	$0.361807\pi$
$313$			32.1011i			1.81446i	−0.420635	+	0.907230i	$0.638193\pi$
$314$	−4.83851	+	8.38054i	−0.273053	+	0.472941i
$315$	10.2553	−	21.9270i	0.577822	−	1.23544i
$316$	3.98697	+	6.90563i	0.224284	+	0.388472i
$317$	−20.2266	+	11.6778i	−1.13604	+	0.655893i	−0.945447	−	0.325776i	$-0.894374\pi$
$317$	−20.2266	+	11.6778i	−1.13604	+	0.655893i	−0.190593	+	0.981669i	$0.561041\pi$
$318$	4.13373	−	2.38661i	0.231808	−	0.133834i
$319$	−14.9619	−	25.9148i	−0.837708	−	1.45095i
$320$	−0.192333	−	2.22778i	−0.0107517	−	0.124537i
$321$	−10.3449			−0.577398
$322$	−35.2088	+	20.3278i	−1.96211	+	1.13282i
$323$	4.92194	+	2.84168i	0.273864	+	0.158116i
$324$	2.30683	−	3.99554i	0.128157	−	0.221975i
$325$	−7.62677	+	6.36988i	−0.423057	+	0.353338i
$326$	−19.0035			−1.05251
$327$			0.712908i			0.0394239i
$328$	−6.31247	−	3.64451i	−0.348548	−	0.201234i
$329$	6.35722	+	11.0110i	0.350485	+	0.607058i
$330$	−0.589836	−	6.83205i	−0.0324694	−	0.376092i
$331$	3.47546	−	6.01967i	0.191028	−	0.330871i	−0.754563	−	0.656228i	$-0.772151\pi$
$331$	3.47546	−	6.01967i	0.191028	−	0.330871i	0.945591	+	0.325357i	$0.105484\pi$
$332$		−	7.08447i		−	0.388811i
$333$	−3.91135	+	2.25822i	−0.214341	+	0.123750i
$334$	−9.79023			−0.535698
$335$	−17.4772	−	5.43573i	−0.954882	−	0.296985i
$336$	3.13520			0.171039
$337$	−4.30213	+	2.48384i	−0.234352	+	0.135303i	−0.612578	−	0.790410i	$-0.709868\pi$
$337$	−4.30213	+	2.48384i	−0.234352	+	0.135303i	0.378226	+	0.925713i	$0.376534\pi$
$338$		−	9.05028i		−	0.492270i
$339$	4.62062	−	8.00314i	0.250957	−	0.434671i
$340$	−2.87720	+	0.248399i	−0.156038	+	0.0134713i
$341$	13.7167	+	23.7579i	0.742798	+	1.28656i
$342$	9.46242	+	5.46313i	0.511669	+	0.295412i
$343$		−	21.8422i		−	1.17937i
$344$	−8.93363			−0.481669
$345$	−12.2916	+	8.58571i	−0.661759	+	0.462239i
$346$	−5.35380	+	9.27306i	−0.287822	+	0.498523i
$347$	−5.38181	−	3.10719i	−0.288911	−	0.166803i	0.348540	−	0.937294i	$-0.386678\pi$
$347$	−5.38181	−	3.10719i	−0.288911	−	0.166803i	−0.637451	+	0.770491i	$0.720011\pi$
$348$	4.36946	−	2.52271i	0.234227	−	0.135231i
$349$	−6.05640			−0.324192			−0.162096	−	0.986775i	$-0.551825\pi$
$349$	−6.05640			−0.324192			−0.162096	+	0.986775i	$0.551825\pi$
$350$	−21.4775	+	3.73631i	−1.14802	+	0.199714i
$351$	−3.91782	−	6.78585i	−0.209118	−	0.362202i
$352$	−3.69343	+	2.13241i	−0.196861	+	0.113658i
$353$	−20.7468	+	11.9781i	−1.10424	+	0.637532i	−0.937331	−	0.348440i	$-0.886711\pi$
$353$	−20.7468	+	11.9781i	−1.10424	+	0.637532i	−0.166907	+	0.985973i	$0.553378\pi$
$354$	−3.66574	−	6.34924i	−0.194832	−	0.337458i
$355$	−17.9571	−	8.39859i	−0.953062	−	0.445751i
$356$	−2.73749	+	4.74147i	−0.145087	+	0.251298i
$357$		−	4.04914i		−	0.214303i
$358$	−14.8057	+	8.54807i	−0.782505	+	0.451779i
$359$	−13.9745			−0.737545			−0.368772	−	0.929520i	$-0.620222\pi$
$359$	−13.9745			−0.737545			−0.368772	+	0.929520i	$0.620222\pi$
$360$	−5.53140	+	0.477546i	−0.291531	+	0.0251689i
$361$	−0.182503	+	0.316105i	−0.00960543	+	0.0166371i
$362$		−	14.8196i		−	0.778900i
$363$	−4.47666	+	2.58460i	−0.234964	+	0.135656i
$364$	−4.33252	+	7.50414i	−0.227086	+	0.393324i
$365$	−3.75802	−	5.38013i	−0.196704	−	0.281609i
$366$	4.45603	−	7.71807i	0.232920	−	0.403430i
$367$	15.6474	+	9.03405i	0.816790	+	0.471574i	0.849308	−	0.527897i	$-0.177019\pi$
$367$	15.6474	+	9.03405i	0.816790	+	0.471574i	−0.0325185	+	0.999471i	$0.510353\pi$
$368$	8.07540	+	4.66233i	0.420959	+	0.243041i
$369$	−9.04902	+	15.6734i	−0.471073	+	0.815923i
$370$	3.68435	+	1.72319i	0.191540	+	0.0895842i
$371$	−14.4707	+	25.0640i	−0.751282	+	1.30126i
$372$	−4.00578	+	2.31274i	−0.207690	+	0.119910i
$373$	−15.1584	−	8.75168i	−0.784870	−	0.453145i	0.0532835	−	0.998579i	$-0.483031\pi$
$373$	−15.1584	−	8.75168i	−0.784870	−	0.453145i	−0.838153	+	0.545435i	$0.816365\pi$
$374$	2.75402	+	4.77010i	0.142407	+	0.246656i
$375$	−7.77275	+	2.05408i	−0.401383	+	0.106072i
$376$	1.45808	−	2.52546i	0.0751945	−	0.130241i
$377$			13.9445i			0.718176i
$378$		−	17.1901i		−	0.884162i
$379$	1.24586	+	2.15789i	0.0639954	+	0.110843i	0.896248	−	0.443553i	$-0.146282\pi$
$379$	1.24586	+	2.15789i	0.0639954	+	0.110843i	−0.832253	+	0.554397i	$0.812949\pi$
$380$	−0.846373	−	9.80350i	−0.0434180	−	0.502909i
$381$	−2.15518	+	3.73288i	−0.110413	+	0.191241i
$382$	−2.21208	−	1.27714i	−0.113180	−	0.0653444i
$383$	−9.40498	+	5.42997i	−0.480572	+	0.277458i	−0.720655	−	0.693294i	$-0.756159\pi$
$383$	−9.40498	+	5.42997i	−0.480572	+	0.277458i	0.240083	+	0.970752i	$0.422825\pi$
$384$	−0.359541	−	0.622744i	−0.0183478	−	0.0317792i
$385$	23.8096	+	34.0867i	1.21345	+	1.73722i
$386$	5.22814	+	9.05540i	0.266105	+	0.460908i
$387$			22.1815i			1.12755i
$388$		−	10.4023i		−	0.528097i
$389$	−8.95560	−	15.5116i	−0.454067	−	0.786467i	0.544567	−	0.838717i	$-0.316694\pi$
$389$	−8.95560	−	15.5116i	−0.454067	−	0.786467i	−0.998634	+	0.0522502i	$0.983361\pi$
$390$	−1.35382	+	2.89461i	−0.0685534	+	0.146574i
$391$	6.02144	−	10.4294i	0.304517	−	0.527439i
$392$	−10.4007	+	6.00483i	−0.525313	+	0.303290i
$393$			3.62469i			0.182842i
$394$	19.4018			0.977449
$395$	−16.1511	−	7.55391i	−0.812648	−	0.380079i
$396$	5.29459	+	9.17051i	0.266063	+	0.460835i
$397$			8.60853i			0.432050i	0.976388	+	0.216025i	$0.0693092\pi$
$397$			8.60853i			0.432050i	−0.976388	+	0.216025i	$0.930691\pi$
$398$	−14.3625	−	8.29222i	−0.719929	−	0.415651i
$399$	13.7967			0.690698
$400$	3.20515	+	3.83758i	0.160257	+	0.191879i
$401$	4.66690			0.233054			0.116527	−	0.993188i	$-0.462824\pi$
$401$	4.66690			0.233054			0.116527	+	0.993188i	$0.462824\pi$
$402$	−5.83164	+	0.797700i	−0.290856	+	0.0397856i
$403$		−	12.7839i		−	0.636809i
$404$	−2.59521	−	4.49503i	−0.129116	−	0.223636i
$405$	0.887356	+	10.2782i	0.0440931	+	0.510729i
$406$	−15.2959	+	26.4933i	−0.759124	+	1.31484i
$407$		−	7.75770i		−	0.384535i
$408$	−0.804278	+	0.464350i	−0.0398177	+	0.0229888i
$409$	12.1282	−	21.0067i	0.599701	−	1.03871i	−0.393164	−	0.919468i	$-0.628619\pi$
$409$	12.1282	−	21.0067i	0.599701	−	1.03871i	0.992865	−	0.119244i	$-0.0380472\pi$
$410$	16.2383	−	1.40192i	0.801954	−	0.0692357i
$411$	6.40998			0.316181
$412$	7.03881	−	4.06386i	0.346777	−	0.200212i
$413$	38.4973	+	22.2264i	1.89433	+	1.09369i
$414$	11.5762	−	20.0506i	0.568939	−	0.985432i
$415$	9.07135	+	12.9869i	0.445295	+	0.637501i
$416$	1.98739			0.0974399
$417$		−	14.4375i		−	0.707006i
$418$	−16.2532	+	9.38380i	−0.794971	+	0.458977i
$419$	9.51164	+	16.4746i	0.464674	+	0.804839i	0.999187	−	0.0403213i	$-0.0128381\pi$
$419$	9.51164	+	16.4746i	0.464674	+	0.804839i	−0.534513	+	0.845160i	$0.679505\pi$
$420$	−5.74730	+	4.01449i	−0.280439	+	0.195887i
$421$	−7.08680	−	12.2747i	−0.345389	−	0.598232i	0.640035	−	0.768346i	$-0.278920\pi$
$421$	−7.08680	−	12.2747i	−0.345389	−	0.598232i	−0.985424	+	0.170114i	$0.945586\pi$
$422$	−12.4235	−	7.17273i	−0.604768	−	0.349163i
$423$	−6.27052	−	3.62029i	−0.304883	−	0.176024i
$424$	6.63793			0.322367
$425$	4.95627	−	4.13947i	0.240414	−	0.200794i
$426$	−6.37508			−0.308874
$427$			54.0364i			2.61501i
$428$	−12.4589	−	7.19315i	−0.602223	−	0.347694i
$429$	6.09483			0.294261
$430$	16.3767	−	11.4391i	0.789753	−	0.551643i
$431$	−14.4033	+	24.9473i	−0.693784	+	1.20167i	0.276805	+	0.960926i	$0.410724\pi$
$431$	−14.4033	+	24.9473i	−0.693784	+	1.20167i	−0.970589	+	0.240743i	$0.922609\pi$
$432$	−3.41445	+	1.97134i	−0.164278	+	0.0948459i
$433$	1.69237	+	0.977090i	0.0813301	+	0.0469560i	0.540114	−	0.841592i	$-0.318381\pi$
$433$	1.69237	+	0.977090i	0.0813301	+	0.0469560i	−0.458783	+	0.888548i	$0.651715\pi$
$434$	14.0228	−	24.2882i	0.673117	−	1.16587i
$435$	−4.77965	+	10.2194i	−0.229167	+	0.489982i
$436$	−0.495707	+	0.858590i	−0.0237401	+	0.0411190i
$437$	35.5363	+	20.5169i	1.69993	+	0.981457i
$438$	−1.82770	−	1.05522i	−0.0873307	−	0.0504204i
$439$	−13.1169	−	22.7191i	−0.626034	−	1.08432i	−0.988340	−	0.152263i	$-0.951344\pi$
$439$	−13.1169	−	22.7191i	−0.626034	−	1.08432i	0.362306	−	0.932059i	$-0.381989\pi$
$440$	4.04016	−	8.63829i	0.192607	−	0.411815i
$441$	14.9095	+	25.8240i	0.709977	+	1.22972i
$442$		−	2.56673i		−	0.122087i
$443$	30.3351	+	17.5140i	1.44126	+	0.832114i	0.997934	−	0.0642446i	$-0.0204638\pi$
$443$	30.3351	+	17.5140i	1.44126	+	0.832114i	0.443330	+	0.896359i	$0.353797\pi$
$444$	1.30801			0.0620755
$445$	−1.05302	−	12.1971i	−0.0499178	−	0.578196i
$446$	−2.52687	−	4.37667i	−0.119651	−	0.207241i
$447$		−	2.58459i		−	0.122247i
$448$	3.77588	+	2.18000i	0.178393	+	0.102995i
$449$	−14.4152	+	24.9678i	−0.680294	+	1.17830i	0.294597	+	0.955622i	$0.404815\pi$
$449$	−14.4152	+	24.9678i	−0.680294	+	1.17830i	−0.974891	+	0.222683i	$0.928519\pi$
$450$	9.52841	−	7.95813i	0.449173	−	0.375150i
$451$	−15.5431	−	26.9215i	−0.731898	−	1.26768i
$452$	11.1297	−	6.42571i	0.523495	−	0.302240i
$453$	−10.7332	+	6.19680i	−0.504288	+	0.291151i
$454$	23.1350			1.08578
$455$	−1.66657	−	19.3038i	−0.0781300	−	0.904977i
$456$	−1.58219	−	2.74043i	−0.0740926	−	0.128332i
$457$	7.06118	+	4.07677i	0.330308	+	0.190703i	0.655978	−	0.754780i	$-0.272256\pi$
$457$	7.06118	+	4.07677i	0.330308	+	0.190703i	−0.325670	+	0.945484i	$0.605590\pi$
$458$	−4.26157	−	2.46042i	−0.199130	−	0.114968i
$459$	2.54600	+	4.40979i	0.118837	+	0.205832i
$460$	−20.7733	+	1.79344i	−0.968561	+	0.0836194i
$461$	−0.777681			−0.0362202			−0.0181101	−	0.999836i	$-0.505765\pi$
$461$	−0.777681			−0.0362202			−0.0181101	+	0.999836i	$0.505765\pi$
$462$	11.5797	+	6.68553i	0.538735	+	0.311039i
$463$	17.5724	−	10.1455i	0.816660	−	0.471499i	−0.0326031	−	0.999468i	$-0.510380\pi$
$463$	17.5724	−	10.1455i	0.816660	−	0.471499i	0.849263	+	0.527969i	$0.177046\pi$
$464$	7.01646			0.325731
$465$	4.38184	−	9.36883i	0.203203	−	0.434469i
$466$	−3.36519			−0.155890
$467$	−24.3988	+	14.0867i	−1.12904	+	0.651853i	−0.943694	−	0.330819i	$-0.892675\pi$
$467$	−24.3988	+	14.0867i	−1.12904	+	0.651853i	−0.185349	+	0.982673i	$0.559342\pi$
$468$		−	4.93453i		−	0.228099i
$469$	28.2034	−	21.8682i	1.30231	−	1.00978i
$470$	0.560871	+	6.49655i	0.0258710	+	0.299663i
$471$	−3.47928	−	6.02630i	−0.160317	−	0.277677i
$472$		−	10.1956i		−	0.469290i
$473$	−32.9958	−	19.0501i	−1.51715	−	0.875926i
$474$	−5.73392			−0.263367
$475$	14.1045	+	16.8875i	0.647158	+	0.774853i
$476$	2.81549	−	4.87658i	0.129048	−	0.223517i
$477$		−	16.4815i		−	0.754634i
$478$			18.2985i			0.836954i
$479$	−7.77686	−	13.4699i	−0.355334	−	0.615456i	0.631841	−	0.775098i	$-0.282299\pi$
$479$	−7.77686	−	13.4699i	−0.355334	−	0.615456i	−0.987175	+	0.159642i	$0.948966\pi$
$480$	1.45649	+	0.681205i	0.0664793	+	0.0310926i
$481$	−1.80753	+	3.13074i	−0.0824164	+	0.142749i
$482$	−1.32844	+	0.766974i	−0.0605087	+	0.0349347i
$483$		−	29.2347i		−	1.33023i
$484$	−7.18861			−0.326755
$485$	13.3197	+	19.0690i	0.604816	+	0.865878i
$486$	7.57281	+	13.1165i	0.343509	+	0.594976i
$487$	−24.8721	+	14.3599i	−1.12706	+	0.650711i	−0.943195	−	0.332240i	$-0.892196\pi$
$487$	−24.8721	+	14.3599i	−1.12706	+	0.650711i	−0.183869	+	0.982951i	$0.558862\pi$
$488$	10.7332	−	6.19683i	0.485870	−	0.280517i
$489$	6.83254	−	11.8343i	0.308978	−	0.535166i
$490$	11.3771	−	24.3253i	0.513963	−	1.09891i
$491$	19.3458			0.873066			0.436533	−	0.899688i	$-0.356206\pi$
$491$	19.3458			0.873066			0.436533	+	0.899688i	$0.356206\pi$
$492$	4.53919	−	2.62070i	0.204642	−	0.118150i
$493$		−	9.06182i		−	0.408124i
$494$	8.74565			0.393485
$495$	−21.4482	−	10.0314i	−0.964025	−	0.450878i
$496$	−6.43248			−0.288827
$497$	33.4754	−	19.3270i	1.50157	−	0.866935i
$498$	4.41181	+	2.54716i	0.197698	+	0.114141i
$499$	7.87663	+	13.6427i	0.352607	+	0.610732i	0.986705	−	0.162520i	$-0.0519621\pi$
$499$	7.87663	+	13.6427i	0.352607	+	0.610732i	−0.634099	+	0.773252i	$0.718629\pi$
$500$	−10.7894	−	2.93081i	−0.482515	−	0.131070i
$501$	3.51999	−	6.09680i	0.157262	−	0.272385i
$502$	20.3841	+	11.7688i	0.909786	+	0.525265i
$503$	−19.6248	−	11.3304i	−0.875028	−	0.505198i	−0.00601242	−	0.999982i	$-0.501914\pi$
$503$	−19.6248	−	11.3304i	−0.875028	−	0.505198i	−0.869016	+	0.494784i	$0.835247\pi$
$504$	5.41278	−	9.37520i	0.241104	−	0.417605i
$505$	10.5131	+	4.91701i	0.467826	+	0.218804i
$506$	19.8840	+	34.4400i	0.883950	+	1.53105i
$507$	5.63600	+	3.25395i	0.250304	+	0.144513i
$508$	−5.19117	+	2.99713i	−0.230321	+	0.132976i
$509$	−22.7155			−1.00685			−0.503424	−	0.864040i	$-0.667926\pi$
$509$	−22.7155			−1.00685			−0.503424	+	0.864040i	$0.667926\pi$
$510$	0.879782	−	1.88107i	0.0389574	−	0.0832950i
$511$	12.7962			0.566072
$512$		−	1.00000i		−	0.0441942i
$513$	−15.0255	+	8.67500i	−0.663394	+	0.383011i
$514$	1.45036			0.0639728
$515$	−7.69959	+	16.4625i	−0.339285	+	0.725426i
$516$	3.21201	−	5.56336i	0.141401	−	0.244913i
$517$	10.7706	−	6.21842i	0.473691	−	0.273486i
$518$	−6.86832	+	3.96543i	−0.301777	+	0.174231i
$519$	−3.84983	−	6.66809i	−0.168989	−	0.292697i
$520$	−3.64318	+	2.54477i	−0.159764	+	0.111595i
$521$	5.11132			0.223931			0.111965	−	0.993712i	$-0.464285\pi$
$521$	5.11132			0.223931			0.111965	+	0.993712i	$0.464285\pi$
$522$		−	17.4213i		−	0.762511i
$523$	−11.3540	+	6.55522i	−0.496474	+	0.286640i	−0.727256	−	0.686366i	$-0.759205\pi$
$523$	−11.3540	+	6.55522i	−0.496474	+	0.286640i	0.230782	+	0.973005i	$0.425872\pi$
$524$	−2.52036	+	4.36539i	−0.110102	+	0.190703i
$525$	5.39527	−	14.7183i	0.235469	−	0.642360i
$526$	1.81577	+	3.14501i	0.0791714	+	0.137129i
$527$			8.30760i			0.361885i
$528$		−	3.06675i		−	0.133463i
$529$	31.9747	−	55.3818i	1.39020	−	2.40790i
$530$	−12.1683	+	8.49958i	−0.528558	+	0.369198i
$531$	−25.3149			−1.09857
$532$	16.6160	+	9.59326i	0.720395	+	0.415920i
$533$			14.4861i			0.627464i
$534$	−1.96848	−	3.40951i	−0.0851845	−	0.147544i
$535$	32.0495	−	2.76695i	1.38562	−	0.119626i
$536$	−7.57799	−	3.09421i	−0.327319	−	0.133649i
$537$		−	12.2935i		−	0.530505i
$538$	9.68106	−	5.58937i	0.417380	−	0.240975i
$539$	−51.2189			−2.20616
$540$	3.73499	−	7.98581i	0.160729	−	0.343654i
$541$	4.14753			0.178316			0.0891581	−	0.996017i	$-0.471582\pi$
$541$	4.14753			0.178316			0.0891581	+	0.996017i	$0.471582\pi$
$542$	−1.06199	+	0.613140i	−0.0456164	+	0.0263366i
$543$	9.22880	+	5.32825i	0.396046	+	0.228657i
$544$	−1.29151			−0.0553729
$545$	−0.190681	−	2.20865i	−0.00816788	−	0.0946083i
$546$	−3.11544	−	5.39610i	−0.133328	−	0.230932i
$547$	−7.07068	−	4.08226i	−0.302321	−	0.174545i	0.341164	−	0.940004i	$-0.389179\pi$
$547$	−7.07068	−	4.08226i	−0.302321	−	0.174545i	−0.643485	+	0.765459i	$0.722512\pi$
$548$	7.71984	+	4.45705i	0.329775	+	0.190396i
$549$	−15.3862	−	26.6497i	−0.656669	−	1.13738i
$550$	3.65473	+	21.0085i	0.155838	+	0.895807i
$551$	30.8764			1.31538
$552$	−5.80688	+	3.35260i	−0.247157	+	0.142696i
$553$	30.1086	−	17.3832i	1.28035	−	0.739209i
$554$	12.2828	+	21.2744i	0.521845	+	0.903861i
$555$	−2.39778	+	1.67485i	−0.101780	+	0.0710934i
$556$	10.0388	−	17.3877i	0.425741	−	0.737405i
$557$	−26.1186	−	15.0796i	−1.10668	−	0.638943i	−0.168713	−	0.985665i	$-0.553961\pi$
$557$	−26.1186	−	15.0796i	−1.10668	−	0.638943i	−0.937968	+	0.346722i	$0.887295\pi$
$558$			15.9713i			0.676120i
$559$	8.87731	+	15.3760i	0.375470	+	0.650334i
$560$	−9.71314	+	0.838571i	−0.410455	+	0.0354361i
$561$	−3.96073			−0.167222
$562$	14.3495	+	8.28466i	0.605295	+	0.349467i
$563$		−	7.29395i		−	0.307403i	−0.988117	−	0.153702i	$-0.950881\pi$
$563$		−	7.29395i		−	0.307403i	0.988117	−	0.153702i	$-0.0491195\pi$
$564$	1.04848	+	1.81601i	0.0441488	+	0.0764680i
$565$	−12.1745	+	26.0303i	−0.512184	+	1.09510i
$566$	−10.4467	−	18.0941i	−0.439106	−	0.760553i
$567$	−17.4206	−	10.0578i	−0.731596	−	0.422387i
$568$	−7.67782	−	4.43279i	−0.322154	−	0.185996i
$569$	−23.4386	+	40.5968i	−0.982597	+	1.70191i	−0.330432	+	0.943830i	$0.607195\pi$
$569$	−23.4386	+	40.5968i	−0.982597	+	1.70191i	−0.652164	+	0.758078i	$0.726139\pi$
$570$	6.40937	+	2.99769i	0.268459	+	0.125559i
$571$	0.783406	−	1.35690i	0.0327845	−	0.0567844i	−0.849168	−	0.528123i	$-0.822896\pi$
$571$	0.783406	−	1.35690i	0.0327845	−	0.0567844i	0.881952	+	0.471339i	$0.156229\pi$
$572$	7.34030	+	4.23792i	0.306913	+	0.177197i
$573$	1.59067	−	0.918372i	0.0664511	−	0.0383655i
$574$	−15.8901	+	27.5224i	−0.663239	+	1.14876i
$575$	35.7842	−	29.8869i	1.49230	−	1.24637i
$576$	−2.48292			−0.103455
$577$	3.34989	+	1.93406i	0.139458	+	0.0805159i	0.568105	−	0.822956i	$-0.307677\pi$
$577$	3.34989	+	1.93406i	0.139458	+	0.0805159i	−0.428648	+	0.903472i	$0.641010\pi$
$578$		−	15.3320i		−	0.637727i
$579$	−7.51893			−0.312476
$580$	−12.8622	+	8.98427i	−0.534075	+	0.373051i
$581$	−30.8884			−1.28146
$582$	6.47797	+	3.74006i	0.268521	+	0.155030i
$583$	24.5168	+	14.1548i	1.01538	+	0.586231i
$584$	−1.46746	−	2.54171i	−0.0607237	−	0.105177i
$585$	6.31845	+	9.04574i	0.261236	+	0.373995i
$586$	−10.3165	−	17.8687i	−0.426170	−	0.738148i
$587$	19.3189	−	11.1538i	0.797375	−	0.460365i	−0.0451774	−	0.998979i	$-0.514385\pi$
$587$	19.3189	−	11.1538i	0.797375	−	0.460365i	0.842552	+	0.538614i	$0.181052\pi$
$588$		−	8.63594i		−	0.356140i
$589$	−28.3066			−1.16635
$590$	13.0550	+	18.6900i	0.537466	+	0.769457i
$591$	−6.97575	+	12.0823i	−0.286944	+	0.497001i
$592$	1.57530	+	0.909501i	0.0647445	+	0.0373802i
$593$	8.66635	−	5.00352i	0.355884	−	0.205470i	−0.311390	−	0.950282i	$-0.600794\pi$
$593$	8.66635	−	5.00352i	0.355884	−	0.205470i	0.667274	+	0.744812i	$0.267461\pi$
$594$	−16.8147			−0.689917
$595$	1.08302	+	12.5446i	0.0443996	+	0.514278i
$596$	1.79714	−	3.11275i	0.0736139	−	0.127503i
$597$	10.3279	−	5.96279i	0.422691	−	0.244041i
$598$		−	18.5318i		−	0.757820i
$599$	8.12267	−	14.0689i	0.331883	−	0.574838i	−0.650998	−	0.759079i	$-0.725649\pi$
$599$	8.12267	−	14.0689i	0.331883	−	0.574838i	0.982881	+	0.184241i	$0.0589827\pi$
$600$	−3.54221	+	0.616217i	−0.144610	+	0.0251570i
$601$	16.2363	+	28.1221i	0.662293	+	1.14712i	0.980012	+	0.198940i	$0.0637498\pi$
$601$	16.2363	+	28.1221i	0.662293	+	1.14712i	−0.317719	+	0.948185i	$0.602917\pi$
$602$			38.9507i			1.58751i
$603$	−7.68267	+	18.8155i	−0.312863	+	0.766228i
$604$	−17.2353			−0.701294
$605$	13.1778	−	9.20470i	0.535754	−	0.374224i
$606$	3.73233			0.151616
$607$	−2.74034	−	1.58213i	−0.111227	−	0.0642168i	0.443355	−	0.896346i	$-0.353788\pi$
$607$	−2.74034	−	1.58213i	−0.111227	−	0.0642168i	−0.554581	+	0.832129i	$0.687122\pi$
$608$		−	4.40057i		−	0.178467i
$609$	−10.9990	−	19.0509i	−0.445703	−	0.771980i
$610$	−11.7408	+	25.1031i	−0.475372	+	1.01640i
$611$	−5.79553			−0.234462
$612$			3.20671i			0.129624i
$613$	−4.25914	+	2.45902i	−0.172025	+	0.0993187i	−0.583540	−	0.812084i	$-0.698333\pi$
$613$	−4.25914	+	2.45902i	−0.172025	+	0.0993187i	0.411515	+	0.911403i	$0.365000\pi$
$614$	14.5463	−	25.1949i	0.587041	−	1.01679i
$615$	−4.96532	+	10.6164i	−0.200221	+	0.428093i
$616$	9.29730	+	16.1034i	0.374599	+	0.648825i
$617$		−	15.8714i		−	0.638957i	−0.947594	−	0.319478i	$-0.896492\pi$
$617$		−	15.8714i		−	0.638957i	0.947594	−	0.319478i	$-0.103508\pi$
$618$			5.84450i			0.235100i
$619$	18.0356	+	31.2385i	0.724910	+	1.25558i	0.959011	+	0.283369i	$0.0914521\pi$
$619$	18.0356	+	31.2385i	0.724910	+	1.25558i	−0.234101	+	0.972212i	$0.575215\pi$
$620$	11.7917	−	8.23650i	0.473566	−	0.330786i
$621$	18.3820	+	31.8386i	0.737646	+	1.27764i
$622$	−16.3345	+	9.43071i	−0.654953	+	0.378137i
$623$	20.6729	+	11.9355i	0.828241	+	0.478185i
$624$	−0.714549	+	1.23764i	−0.0286049	+	0.0495451i
$625$	23.5313	−	8.44270i	0.941251	−	0.337708i
$626$	−16.0505	−	27.8003i	−0.641509	−	1.11113i
$627$		−	13.4954i		−	0.538956i
$628$		−	9.67701i		−	0.386155i
$629$	1.17463	−	2.03451i	0.0468355	−	0.0811214i
$630$	2.08211	+	24.1170i	0.0829531	+	0.960843i
$631$	20.4480	+	35.4169i	0.814021	+	1.40993i	0.910029	+	0.414545i	$0.136059\pi$
$631$	20.4480	+	35.4169i	0.814021	+	1.40993i	−0.0960076	+	0.995381i	$0.530607\pi$
$632$	−6.90563	−	3.98697i	−0.274691	−	0.158593i
$633$	8.93354	−	5.15778i	0.355076	−	0.205003i
$634$	11.6778	−	20.2266i	0.463786	−	0.803302i
$635$	5.67851	−	12.1412i	0.225345	−	0.481811i
$636$	−2.38661	+	4.13373i	−0.0946353	+	0.163913i
$637$	20.6702	+	11.9339i	0.818983	+	0.472840i
$638$	25.9148	+	14.9619i	1.02598	+	0.592349i
$639$	−11.0063	+	19.0634i	−0.435401	+	0.754137i
$640$	1.28046	+	1.83315i	0.0506144	+	0.0724616i
$641$	2.33346	−	4.04167i	0.0921660	−	0.159636i	−0.816256	−	0.577690i	$-0.803954\pi$
$641$	2.33346	−	4.04167i	0.0921660	−	0.159636i	0.908422	+	0.418054i	$0.137288\pi$
$642$	8.95897	−	5.17246i	0.353582	−	0.204141i
$643$			18.8938i			0.745097i	0.928013	+	0.372549i	$0.121516\pi$
$643$			18.8938i			0.745097i	−0.928013	+	0.372549i	$0.878484\pi$
$644$	20.3278	−	35.2088i	0.801028	−	1.38742i
$645$	1.23555	+	14.3113i	0.0486496	+	0.563507i
$646$	−5.68337			−0.223609
$647$	30.8881	−	17.8332i	1.21434	−	0.701097i	0.250635	−	0.968082i	$-0.419361\pi$
$647$	30.8881	−	17.8332i	1.21434	−	0.701097i	0.963701	+	0.266985i	$0.0860274\pi$
$648$			4.61366i			0.181242i
$649$	21.7411	−	37.6568i	0.853414	−	1.47816i
$650$	3.42004	−	9.32987i	0.134145	−	0.365948i
$651$	10.0836	+	17.4652i	0.395206	+	0.684517i
$652$	16.4575	−	9.50176i	0.644526	−	0.372117i
$653$	−12.9107	+	7.45400i	−0.505235	+	0.291697i	−0.730873	−	0.682514i	$-0.760887\pi$
$653$	−12.9107	+	7.45400i	−0.505235	+	0.291697i	0.225638	+	0.974211i	$0.427553\pi$
$654$	−0.356454	−	0.617397i	−0.0139385	−	0.0241421i
$655$	−0.969494	−	11.2296i	−0.0378813	−	0.438777i
$656$	7.28902			0.284588
$657$	−6.31086	+	3.64358i	−0.246210	+	0.142149i
$658$	−11.0110	−	6.35722i	−0.429255	−	0.247830i
$659$	−1.79197	+	3.10379i	−0.0698053	+	0.120906i	−0.898816	−	0.438327i	$-0.855571\pi$
$659$	−1.79197	+	3.10379i	−0.0698053	+	0.120906i	0.829010	+	0.559233i	$0.188904\pi$
$660$	3.92684	+	5.62181i	0.152852	+	0.218829i
$661$	−49.3614			−1.91994			−0.959969	−	0.280107i	$-0.909630\pi$
$661$	−49.3614			−1.91994			−0.959969	+	0.280107i	$0.909630\pi$
$662$			6.95092i			0.270155i
$663$	1.59842	+	0.922846i	0.0620773	+	0.0358404i
$664$	3.54224	+	6.13533i	0.137465	+	0.238097i
$665$	−42.7433	+	3.69019i	−1.65752	+	0.143099i
$666$	2.25822	−	3.91135i	0.0875042	−	0.151562i
$667$		−	65.4262i		−	2.53331i
$668$	8.47859	−	4.89512i	0.328046	−	0.189398i
$669$	3.63406			0.140501
$670$	17.8536	−	4.03113i	0.689744	−	0.155736i
$671$	52.8566			2.04051
$672$	−2.71517	+	1.56760i	−0.104740	+	0.0604716i
$673$		−	11.4631i		−	0.441869i	−0.975289	−	0.220935i	$-0.929089\pi$
$673$		−	11.4631i		−	0.441869i	0.975289	−	0.220935i	$-0.0709107\pi$
$674$	2.48384	−	4.30213i	0.0956738	−	0.165712i
$675$	3.37867	+	19.4217i	0.130045	+	0.747540i
$676$	4.52514	+	7.83777i	0.174044	+	0.301453i
$677$	−1.20776	−	0.697301i	−0.0464180	−	0.0267994i	0.476611	−	0.879114i	$-0.341865\pi$
$677$	−1.20776	−	0.697301i	−0.0464180	−	0.0267994i	−0.523029	+	0.852315i	$0.675198\pi$
$678$			9.24123i			0.354907i
$679$	−45.3541			−1.74053
$680$	2.36753	−	1.65372i	0.0907905	−	0.0634172i
$681$	−8.31800	+	14.4072i	−0.318746	+	0.552085i
$682$	−23.7579	−	13.7167i	−0.909738	−	0.525238i
$683$	−19.1606	+	11.0624i	−0.733161	+	0.423290i	−0.819577	−	0.572969i	$-0.805792\pi$
$683$	−19.1606	+	11.0624i	−0.733161	+	0.423290i	0.0864168	+	0.996259i	$0.472458\pi$
$684$	−10.9263			−0.417776
$685$	−19.8587	+	1.71447i	−0.758761	+	0.0655066i
$686$	10.9211	+	18.9159i	0.416969	+	0.722211i
$687$	3.06442	−	1.76924i	0.116915	−	0.0675008i
$688$	7.73675	−	4.46682i	0.294961	−	0.170296i
$689$	−6.59609	−	11.4248i	−0.251291	−	0.435249i
$690$	6.35201	−	13.5813i	0.241817	−	0.517030i
$691$	23.1082	−	40.0247i	0.879079	−	1.52261i	0.0267261	−	0.999643i	$-0.491492\pi$
$691$	23.1082	−	40.0247i	0.879079	−	1.52261i	0.852353	−	0.522967i	$-0.175175\pi$
$692$		−	10.7076i		−	0.407042i
$693$	39.9835	−	23.0845i	1.51885	−	0.876906i
$694$	6.21438			0.235895
$695$	3.86158	+	44.7286i	0.146478	+	1.69665i
$696$	−2.52271	+	4.36946i	−0.0956230	+	0.165624i
$697$		−	9.41382i		−	0.356574i
$698$	5.24500	−	3.02820i	0.198526	−	0.114619i
$699$	1.20993	−	2.09565i	0.0457636	−	0.0792649i
$700$	16.7319	−	13.9745i	0.632406	−	0.528185i
$701$	−20.7843	+	35.9994i	−0.785011	+	1.35968i	0.143981	+	0.989580i	$0.454010\pi$
$701$	−20.7843	+	35.9994i	−0.785011	+	1.35968i	−0.928992	+	0.370099i	$0.879324\pi$
$702$	6.78585	+	3.91782i	0.256116	+	0.147868i
$703$	6.93222	+	4.00232i	0.261454	+	0.150950i
$704$	2.13241	−	3.69343i	0.0803681	−	0.139202i
$705$	−4.24734	−	1.98650i	−0.159964	−	0.0748158i
$706$	11.9781	−	20.7468i	0.450803	−	0.780814i
$707$	−19.5984	+	11.3151i	−0.737072	+	0.425549i
$708$	6.34924	+	3.66574i	0.238619	+	0.137767i
$709$	−2.95590	−	5.11977i	−0.111011	−	0.192277i	0.805167	−	0.593048i	$-0.202076\pi$
$709$	−2.95590	−	5.11977i	−0.111011	−	0.192277i	−0.916178	+	0.400771i	$0.868742\pi$
$710$	19.7506	−	1.70514i	0.741226	−	0.0639928i
$711$	−9.89932	+	17.1461i	−0.371254	+	0.643030i
$712$		−	5.47498i		−	0.205184i
$713$			59.9807i			2.24630i
$714$	2.02457	+	3.50666i	0.0757676	+	0.131233i
$715$	−18.8823	+	1.63018i	−0.706159	+	0.0609653i
$716$	8.54807	−	14.8057i	0.319456	−	0.553315i
$717$	−11.3953	−	6.57906i	−0.425564	−	0.245700i
$718$	12.1023	−	6.98724i	0.451652	−	0.260761i
$719$	−24.6986	−	42.7792i	−0.921103	−	1.59540i	−0.797712	−	0.603038i	$-0.793957\pi$
$719$	−24.6986	−	42.7792i	−0.921103	−	1.59540i	−0.123390	−	0.992358i	$-0.539377\pi$
$720$	4.55156	−	3.17927i	0.169627	−	0.118484i
$721$	−17.7185	−	30.6893i	−0.659870	−	1.14293i
$722$		−	0.365006i		−	0.0135841i
$723$		−	1.10303i		−	0.0410223i
$724$	7.40979	+	12.8341i	0.275383	+	0.476977i
$725$	12.0744	−	32.9390i	0.448432	−	1.22332i
$726$	2.58460	−	4.47666i	0.0959236	−	0.166145i
$727$	11.6403	−	6.72055i	0.431716	−	0.249251i	−0.268362	−	0.963318i	$-0.586482\pi$
$727$	11.6403	−	6.72055i	0.431716	−	0.249251i	0.700077	+	0.714067i	$0.253149\pi$
$728$		−	8.66504i		−	0.321148i
$729$	2.95003			0.109260
$730$	5.94461	+	2.78032i	0.220020	+	0.102904i
$731$	−5.76893	−	9.99208i	−0.213372	−	0.369570i
$732$			8.91206i			0.329399i
$733$	−38.3474	−	22.1399i	−1.41640	−	0.817756i	−0.420415	−	0.907332i	$-0.638116\pi$
$733$	−38.3474	−	22.1399i	−1.41640	−	0.817756i	−0.995980	+	0.0895756i	$0.971449\pi$
$734$	−18.0681			−0.666906
$735$	11.0579	+	15.8310i	0.407878	+	0.583934i
$736$	−9.32467			−0.343712
$737$	−21.3907	−	27.5876i	−0.787936	−	1.01620i
$738$		−	18.0980i		−	0.666198i
$739$	−11.8154	−	20.4649i	−0.434638	−	0.752814i	0.562628	−	0.826710i	$-0.309790\pi$
$739$	−11.8154	−	20.4649i	−0.434638	−	0.752814i	−0.997266	+	0.0738955i	$0.976457\pi$
$740$	−4.05234	+	0.349853i	−0.148967	+	0.0128609i
$741$	−3.14442	+	5.44630i	−0.115513	+	0.200075i
$742$		−	28.9414i		−	1.06247i
$743$	17.2571	−	9.96339i	0.633101	−	0.365521i	−0.148851	−	0.988860i	$-0.547557\pi$
$743$	17.2571	−	9.96339i	0.633101	−	0.365521i	0.781952	+	0.623338i	$0.214224\pi$
$744$	2.31274	−	4.00578i	0.0847892	−	0.146859i
$745$	0.691299	+	8.00729i	0.0253272	+	0.293364i
$746$	17.5034			0.640844
$747$	15.2335	−	8.79509i	0.557366	−	0.321796i
$748$	−4.77010	−	2.75402i	−0.174412	−	0.100697i
$749$	−31.3622	+	54.3209i	−1.14595	+	1.98484i
$750$	5.70436	−	5.66526i	0.208294	−	0.206866i
$751$	14.5377			0.530487			0.265244	−	0.964181i	$-0.414548\pi$
$751$	14.5377			0.530487			0.265244	+	0.964181i	$0.414548\pi$
$752$			2.91615i			0.106341i
$753$	−14.6578	+	8.46270i	−0.534161	+	0.308398i
$754$	−6.97223	−	12.0763i	−0.253914	−	0.439791i
$755$	31.5949	−	22.0690i	1.14985	−	0.803174i
$756$	8.59504	+	14.8870i	0.312598	+	0.541436i
$757$	24.3957	+	14.0849i	0.886676	+	0.511923i	0.872854	−	0.487982i	$-0.162267\pi$
$757$	24.3957	+	14.0849i	0.886676	+	0.511923i	0.0138225	+	0.999904i	$0.495600\pi$
$758$	−2.15789	−	1.24586i	−0.0783780	−	0.0452516i
$759$	−28.5964			−1.03798
$760$	5.63473	+	8.06690i	0.204393	+	0.292617i
$761$	23.5769			0.854662			0.427331	−	0.904095i	$-0.359454\pi$
$761$	23.5769			0.854662			0.427331	+	0.904095i	$0.359454\pi$
$762$		−	4.31036i		−	0.156148i
$763$	3.74346	+	2.16129i	0.135522	+	0.0782438i
$764$	2.55429			0.0924110
$765$	−4.10605	−	5.87838i	−0.148455	−	0.212533i
$766$	5.42997	−	9.40498i	0.196193	−	0.339816i
$767$	−17.5480	+	10.1313i	−0.633620	+	0.365821i
$768$	0.622744	+	0.359541i	0.0224713	+	0.0129738i
$769$	−2.62353	+	4.54409i	−0.0946070	+	0.163864i	−0.909445	−	0.415825i	$-0.863493\pi$
$769$	−2.62353	+	4.54409i	−0.0946070	+	0.163864i	0.814838	+	0.579689i	$0.196826\pi$
$770$	−37.6630	−	17.6151i	−1.35728	−	0.634806i
$771$	−0.521466	+	0.903205i	−0.0187801	+	0.0325281i
$772$	−9.05540	−	5.22814i	−0.325911	−	0.188165i
$773$	−1.67437	−	0.966700i	−0.0602230	−	0.0347698i	0.469586	−	0.882887i	$-0.344403\pi$
$773$	−1.67437	−	0.966700i	−0.0602230	−	0.0347698i	−0.529809	+	0.848117i	$0.677736\pi$
$774$	−11.0907	−	19.2097i	−0.398649	−	0.690480i
$775$	−11.0694	+	30.1975i	−0.397626	+	1.08472i
$776$	5.20116	+	9.00867i	0.186711	+	0.323392i
$777$		−	5.70294i		−	0.204592i
$778$	15.5116	+	8.95560i	0.556116	+	0.321074i
$779$	32.0758			1.14924
$780$	−0.274862	−	3.18372i	−0.00984164	−	0.113995i
$781$	−18.9050	−	32.7445i	−0.676475	−	1.17169i
$782$			12.0429i			0.430653i
$783$	23.9574	+	13.8318i	0.856167	+	0.494308i
$784$	6.00483	−	10.4007i	0.214458	−	0.371453i
$785$	12.3910	+	17.7394i	0.442253	+	0.633146i
$786$	−1.81235	−	3.13908i	−0.0646442	−	0.111967i
$787$	−36.4002	+	21.0157i	−1.29753	+	0.749128i	−0.979977	−	0.199113i	$-0.936194\pi$
$787$	−36.4002	+	21.0157i	−1.29753	+	0.749128i	−0.317551	+	0.948241i	$0.602861\pi$
$788$	−16.8025	+	9.70090i	−0.598563	+	0.345580i
$789$	−2.61138			−0.0929675
$790$	17.7642	−	1.53365i	0.632021	−	0.0545647i
$791$	−28.0162	−	48.5254i	−0.996140	−	1.72536i
$792$	−9.17051	−	5.29459i	−0.325860	−	0.188135i
$793$	−21.3311	−	12.3155i	−0.757490	−	0.437337i
$794$	−4.30427	−	7.45521i	−0.152753	−	0.264575i
$795$	−0.918046	−	10.6337i	−0.0325597	−	0.377138i
$796$	16.5844			0.587820
$797$	−3.94158	−	2.27567i	−0.139618	−	0.0806084i	0.428564	−	0.903511i	$-0.359020\pi$
$797$	−3.94158	−	2.27567i	−0.139618	−	0.0806084i	−0.568182	+	0.822903i	$0.692353\pi$
$798$	−11.9483	+	6.89834i	−0.422964	+	0.244199i
$799$	3.76623			0.133240
$800$	−4.69453	−	1.72087i	−0.165977	−	0.0608419i
$801$	−13.5939			−0.480319
$802$	−4.04165	+	2.33345i	−0.142716	+	0.0823969i
$803$		−	12.5168i		−	0.441710i
$804$	4.65150	−	3.60665i	0.164046	−	0.127197i
$805$	7.81940	+	90.5718i	0.275598	+	3.19224i
$806$	6.39193	+	11.0711i	0.225146	+	0.389964i
$807$			8.03843i			0.282966i
$808$	4.49503	+	2.59521i	0.158135	+	0.0912990i
$809$	39.6718			1.39478			0.697392	−	0.716689i	$-0.254343\pi$
$809$	39.6718			1.39478			0.697392	+	0.716689i	$0.254343\pi$
$810$	−5.90758	−	8.45752i	−0.207571	−	0.297167i
$811$	−24.5793	+	42.5726i	−0.863096	+	1.49493i	0.00582938	+	0.999983i	$0.498144\pi$
$811$	−24.5793	+	42.5726i	−0.863096	+	1.49493i	−0.868925	+	0.494943i	$0.835189\pi$
$812$		−	30.5918i		−	1.07356i
$813$		−	0.881797i		−	0.0309260i
$814$	3.87885	+	6.71836i	0.135954	+	0.235478i
$815$	−18.0025	+	38.4913i	−0.630601	+	1.34829i
$816$	0.464350	−	0.804278i	0.0162555	−	0.0281554i
$817$	34.0461	−	19.6565i	1.19112	−	0.687695i
$818$			24.2564i			0.848106i
$819$	−21.5146			−0.751781
$820$	−13.3619	+	9.33326i	−0.466616	+	0.325932i
$821$	1.86791	+	3.23531i	0.0651904	+	0.112913i	0.896778	−	0.442480i	$-0.145901\pi$
$821$	1.86791	+	3.23531i	0.0651904	+	0.112913i	−0.831588	+	0.555393i	$0.812568\pi$
$822$	−5.55120	+	3.20499i	−0.193620	+	0.111787i
$823$	5.36947	−	3.10006i	0.187168	−	0.108061i	−0.403488	−	0.914985i	$-0.632202\pi$
$823$	5.36947	−	3.10006i	0.187168	−	0.108061i	0.590656	+	0.806923i	$0.298869\pi$
$824$	−4.06386	+	7.03881i	−0.141571	+	0.245209i
$825$	−14.3970	−	5.27747i	−0.501237	−	0.183738i
$826$	−44.4529			−1.54671
$827$	−29.9298	+	17.2800i	−1.04076	+	0.600883i	−0.920049	−	0.391804i	$-0.871851\pi$
$827$	−29.9298	+	17.2800i	−1.04076	+	0.600883i	−0.120712	+	0.992688i	$0.538518\pi$
$828$			23.1524i			0.804602i
$829$	31.1494			1.08186			0.540932	−	0.841067i	$-0.318072\pi$
$829$	31.1494			1.08186			0.540932	+	0.841067i	$0.318072\pi$
$830$	−14.3495	−	6.71130i	−0.498077	−	0.232953i
$831$	−17.6646			−0.612779
$832$	−1.72113	+	0.993696i	−0.0596695	+	0.0344502i
$833$	−13.4326	−	7.75529i	−0.465410	−	0.268705i
$834$	7.21874	+	12.5032i	0.249964	+	0.432951i
$835$	−9.27454	+	19.8299i	−0.320959	+	0.686243i
$836$	9.38380	−	16.2532i	0.324545	−	0.562129i
$837$	−21.9634	−	12.6806i	−0.759166	−	0.438305i
$838$	−16.4746	−	9.51164i	−0.569107	−	0.328574i
$839$	18.5613	−	32.1492i	0.640808	−	1.10991i	−0.344445	−	0.938807i	$-0.611933\pi$
$839$	18.5613	−	32.1492i	0.640808	−	1.10991i	0.985253	−	0.171106i	$-0.0547339\pi$
$840$	2.97006	−	6.35030i	0.102477	−	0.219106i
$841$	−10.1154	−	17.5203i	−0.348806	−	0.604150i
$842$	12.2747	+	7.08680i	0.423014	+	0.244227i
$843$	−10.3184	+	5.95735i	−0.355386	+	0.205182i
$844$	14.3455			0.493791
$845$	−18.3312	−	8.57356i	−0.630611	−	0.294939i
$846$	7.24057			0.248936
$847$			31.3424i			1.07694i
$848$	−5.74862	+	3.31897i	−0.197408	+	0.113974i
$849$	15.0240			0.515623
$850$	−2.22251	+	6.06302i	−0.0762316	+	0.207960i
$851$	8.48079	−	14.6892i	0.290718	−	0.503538i
$852$	5.52099	−	3.18754i	0.189146	−	0.109203i
$853$	19.4492	−	11.2290i	0.665928	−	0.384474i	−0.128604	−	0.991696i	$-0.541050\pi$
$853$	19.4492	−	11.2290i	0.665928	−	0.384474i	0.794532	+	0.607222i	$0.207716\pi$
$854$	−27.0182	−	46.7969i	−0.924544	−	1.60136i
$855$	20.0295	−	13.9906i	0.684993	−	0.478468i
$856$	14.3863			0.491713
$857$		−	17.8942i		−	0.611253i	−0.952152	−	0.305626i	$-0.901134\pi$
$857$		−	17.8942i		−	0.611253i	0.952152	−	0.305626i	$-0.0988659\pi$
$858$	−5.27828	+	3.04742i	−0.180197	+	0.104037i
$859$	0.777419	−	1.34653i	0.0265252	−	0.0459430i	−0.852458	−	0.522796i	$-0.824889\pi$
$859$	0.777419	−	1.34653i	0.0265252	−	0.0459430i	0.878983	+	0.476853i	$0.158222\pi$
$860$	−8.46306	+	18.0949i	−0.288588	+	0.617031i
$861$	−11.4263	−	19.7909i	−0.389406	−	0.674472i
$862$		−	28.8066i		−	0.981158i
$863$			42.6285i			1.45109i	0.688175	+	0.725545i	$0.258412\pi$
$863$			42.6285i			1.45109i	−0.688175	+	0.725545i	$0.741588\pi$
$864$	1.97134	−	3.41445i	0.0670662	−	0.116162i
$865$	13.7106	+	19.6286i	0.466175	+	0.667394i
$866$	−1.95418			−0.0664057
$867$	9.54791	+	5.51249i	0.324264	+	0.187214i
$868$			28.0457i			0.951931i
$869$	−17.0037	−	29.4512i	−0.576810	−	0.999064i
$870$	−0.970397	−	11.2401i	−0.0328996	−	0.381074i
$871$	2.20467	+	16.1174i	0.0747025	+	0.546118i
$872$		−	0.991414i		−	0.0335735i
$873$	22.3678	−	12.9141i	0.757035	−	0.437075i
$874$	−41.0338			−1.38799
$875$	−12.7783	+	47.0417i	−0.431987	+	1.59030i
$876$	2.11044			0.0713052
$877$	19.3537	−	11.1739i	0.653529	−	0.377315i	−0.136278	−	0.990671i	$-0.543514\pi$
$877$	19.3537	−	11.1739i	0.653529	−	0.377315i	0.789807	+	0.613355i	$0.210181\pi$
$878$	22.7191	+	13.1169i	0.766732	+	0.442673i
$879$	14.8368			0.500433
$880$	0.820262	+	9.50106i	0.0276510	+	0.320281i
$881$	14.3048	+	24.7766i	0.481941	+	0.834746i	0.999785	−	0.0207291i	$-0.00659875\pi$
$881$	14.3048	+	24.7766i	0.481941	+	0.834746i	−0.517844	+	0.855475i	$0.673265\pi$
$882$	−25.8240	−	14.9095i	−0.869541	−	0.502030i
$883$	−27.0967	−	15.6443i	−0.911877	−	0.526472i	−0.0308423	−	0.999524i	$-0.509819\pi$
$883$	−27.0967	−	15.6443i	−0.911877	−	0.526472i	−0.881035	+	0.473052i	$0.843152\pi$
$884$	1.28337	+	2.22285i	0.0431643	+	0.0747627i
$885$	−16.3329	+	1.41008i	−0.549025	+	0.0473993i
$886$	−35.0279			−1.17679
$887$	−5.04098	+	2.91041i	−0.169260	+	0.0977220i	−0.582237	−	0.813019i	$-0.697822\pi$
$887$	−5.04098	+	2.91041i	−0.169260	+	0.0977220i	0.412977	+	0.910741i	$0.364489\pi$
$888$	−1.13277	+	0.654006i	−0.0380133	+	0.0219470i
$889$	13.0675	+	22.6336i	0.438270	+	0.759105i
$890$	7.01047	+	10.0365i	0.234992	+	0.336423i
$891$	−9.83819	+	17.0402i	−0.329592	+	0.570870i
$892$	4.37667	+	2.52687i	0.146542	+	0.0846059i
$893$			12.8327i			0.429431i
$894$	1.29229	+	2.23832i	0.0432208	+	0.0748606i
$895$	3.28814	+	38.0864i	0.109911	+	1.27309i
$896$	−4.36001			−0.145658
$897$	11.5405	+	6.66293i	0.385327	+	0.222469i
$898$		−	28.8304i		−	0.962082i
$899$	22.5666	+	39.0865i	0.752639	+	1.30361i
$900$	−4.27278	+	11.6561i	−0.142426	+	0.388538i
$901$	4.28647	+	7.42439i	0.142803	+	0.247342i
$902$	26.9215	+	15.5431i	0.896388	+	0.517530i
$903$	−24.2563	−	14.0044i	−0.807199	−	0.466037i
$904$	−6.42571	+	11.1297i	−0.213716	+	0.370167i
$905$	−30.0168	−	14.0390i	−0.997792	−	0.466671i
$906$	6.19680	−	10.7332i	0.205875	−	0.356586i
$907$	−48.9701	−	28.2729i	−1.62603	−	0.938787i	−0.985263	−	0.171048i	$-0.945285\pi$
$907$	−48.9701	−	28.2729i	−1.62603	−	0.938787i	−0.640764	−	0.767738i	$-0.721382\pi$
$908$	−20.0355	+	11.5675i	−0.664902	+	0.383882i
$909$	6.44369	−	11.1608i	0.213724	−	0.370180i
$910$	11.0952	+	15.8843i	0.367802	+	0.526560i
$911$	2.72341			0.0902304			0.0451152	−	0.998982i	$-0.485635\pi$
$911$	2.72341			0.0902304			0.0451152	+	0.998982i	$0.485635\pi$
$912$	2.74043	+	1.58219i	0.0907446	+	0.0523914i
$913$			30.2139i			0.999935i
$914$	−8.15355			−0.269695
$915$	−11.4115	−	16.3371i	−0.377252	−	0.540089i
$916$	4.92083			0.162589
$917$	19.0331	+	10.9888i	0.628529	+	0.362882i
$918$	−4.40979	−	2.54600i	−0.145545	−	0.0840304i
$919$	18.6076	+	32.2293i	0.613808	+	1.06315i	0.990592	+	0.136846i	$0.0436966\pi$
$919$	18.6076	+	32.2293i	0.613808	+	1.06315i	−0.376784	+	0.926301i	$0.622970\pi$
$920$	17.0935	−	11.9398i	0.563556	−	0.393644i
$921$	10.4600	+	18.1172i	0.344668	+	0.596983i
$922$	0.673491	−	0.388840i	0.0221803	−	0.0128058i
$923$			17.6194i			0.579949i
$924$	−13.3711			−0.439875
$925$	6.98056	−	5.83017i	0.229520	−	0.191695i
$926$	−10.1455	+	17.5724i	−0.333400	+	0.577466i
$927$	17.4768	+	10.0902i	0.574014	+	0.331407i
$928$	−6.07644	+	3.50823i	−0.199469	+	0.115163i
$929$	11.9755			0.392904			0.196452	−	0.980513i	$-0.437058\pi$
$929$	11.9755			0.392904			0.196452	+	0.980513i	$0.437058\pi$
$930$	0.889631	+	10.3046i	0.0291721	+	0.337900i
$931$	26.4247	−	45.7689i	0.866034	−	1.50001i
$932$	2.91434	−	1.68260i	0.0954625	−	0.0551153i
$933$		−	13.5629i		−	0.444030i
$934$	14.0867	−	24.3988i	0.460930	−	0.798354i
$935$	12.2707	−	1.05937i	0.401295	−	0.0346453i
$936$	2.46727	+	4.27343i	0.0806452	+	0.139682i
$937$		−	7.39015i		−	0.241426i	−0.992687	−	0.120713i	$-0.961482\pi$
$937$		−	7.39015i		−	0.241426i	0.992687	−	0.120713i	$-0.0385180\pi$
$938$	−13.4908	+	33.0401i	−0.440489	+	1.07880i
$939$	23.0833			0.753296
$940$	−3.73400	−	5.34574i	−0.121790	−	0.174359i
$941$	−18.2720			−0.595649			−0.297825	−	0.954621i	$-0.596261\pi$
$941$	−18.2720			−0.595649			−0.297825	+	0.954621i	$0.596261\pi$
$942$	6.02630	+	3.47928i	0.196347	+	0.113361i
$943$		−	67.9676i		−	2.21333i
$944$	5.09780	+	8.82964i	0.165919	+	0.287380i
$945$	−34.8182	−	16.2846i	−1.13264	−	0.529738i
$946$	38.1002			1.23875
$947$		−	2.45034i		−	0.0796254i	−0.999207	−	0.0398127i	$-0.987324\pi$
$947$		−	2.45034i		−	0.0796254i	0.999207	−	0.0398127i	$-0.0126761\pi$
$948$	4.96572	−	2.86696i	0.161279	−	0.0931145i
$949$	−2.91641	+	5.05137i	−0.0946706	+	0.163974i
$950$	−20.6586	−	7.57280i	−0.670254	−	0.245694i
$951$	8.39733	+	14.5446i	0.272302	+	0.471641i
$952$			5.63098i			0.182501i
$953$		−	24.2453i		−	0.785381i	−0.919671	−	0.392690i	$-0.871544\pi$
$953$		−	24.2453i		−	0.785381i	0.919671	−	0.392690i	$-0.128456\pi$
$954$	8.24073	+	14.2734i	0.266804	+	0.462117i
$955$	−4.68239	+	3.27065i	−0.151519	+	0.105836i
$956$	−9.14925	−	15.8470i	−0.295908	−	0.512527i
$957$	−18.6349	+	10.7589i	−0.602381	+	0.347785i
$958$	13.4699	+	7.77686i	0.435193	+	0.251259i
$959$	19.4328	−	33.6586i	0.627517	−	1.08689i
$960$	−1.60196	+	0.138303i	−0.0517030	+	0.00446371i
$961$	−5.18839	−	8.98655i	−0.167367	−	0.289889i
$962$		−	3.61507i		−	0.116554i
$963$		−	35.7200i		−	1.15106i
$964$	0.766974	−	1.32844i	0.0247026	−	0.0427861i
$965$	23.2943	−	2.01108i	0.749870	−	0.0647390i
$966$	14.6174	+	25.3180i	0.470306	+	0.814594i
$967$	6.60352	+	3.81254i	0.212355	+	0.122603i	0.602405	−	0.798190i	$-0.294209\pi$
$967$	6.60352	+	3.81254i	0.212355	+	0.122603i	−0.390051	+	0.920793i	$0.627542\pi$
$968$	6.22552	−	3.59431i	0.200096	−	0.115525i
$969$	2.04341	−	3.53928i	0.0656436	−	0.113698i
$970$	−21.0697	−	9.85438i	−0.676507	−	0.316405i
$971$	13.4155	−	23.2363i	0.430523	−	0.745688i	−0.566395	−	0.824134i	$-0.691662\pi$
$971$	13.4155	−	23.2363i	0.430523	−	0.745688i	0.996918	+	0.0784459i	$0.0249958\pi$
$972$	−13.1165	−	7.57281i	−0.420711	−	0.242898i
$973$	−75.8107	−	43.7693i	−2.43038	−	1.40318i
$974$	14.3599	−	24.8721i	0.460122	−	0.796955i
$975$	4.58047	+	5.48428i	0.146692	+	0.175637i
$976$	−6.19683	+	10.7332i	−0.198356	+	0.343562i
$977$	36.4630	−	21.0519i	1.16656	−	0.673511i	0.213689	−	0.976902i	$-0.431452\pi$
$977$	36.4630	−	21.0519i	1.16656	−	0.673511i	0.952866	+	0.303390i	$0.0981186\pi$
$978$			13.6651i			0.436961i
$979$	11.6749	−	20.2215i	0.373131	−	0.646282i
$980$	2.30985	+	26.7549i	0.0737854	+	0.854654i
$981$	−2.46160			−0.0785929
$982$	−16.7540	+	9.67292i	−0.534641	+	0.308675i
$983$			19.9069i			0.634930i	0.948270	+	0.317465i	$0.102832\pi$
$983$			19.9069i			0.634930i	−0.948270	+	0.317465i	$0.897168\pi$
$984$	−2.62070	+	4.53919i	−0.0835449	+	0.144704i
$985$	18.3798	−	39.2980i	0.585630	−	1.25214i
$986$	4.53091	+	7.84776i	0.144294	+	0.249924i
$987$	7.91783	−	4.57136i	0.252027	−	0.145508i
$988$	−7.57396	+	4.37283i	−0.240960	+	0.139118i
$989$	−41.6516	−	72.1426i	−1.32444	−	2.29400i
$990$	23.5904	−	2.03665i	0.749752	−	0.0647288i
$991$	−3.70394			−0.117660			−0.0588298	−	0.998268i	$-0.518737\pi$
$991$	−3.70394			−0.117660			−0.0588298	+	0.998268i	$0.518737\pi$
$992$	5.57069	−	3.21624i	0.176870	−	0.102116i
$993$	−4.32864	−	2.49914i	−0.137365	−	0.0793078i
$994$	−19.3270	+	33.4754i	−0.613015	+	1.06177i
$995$	−30.4017	+	21.2356i	−0.963800	+	0.673215i
$996$	−5.09432			−0.161420
$997$			11.0370i			0.349544i	0.984609	+	0.174772i	$0.0559188\pi$
$997$			11.0370i			0.349544i	−0.984609	+	0.174772i	$0.944081\pi$
$998$	−13.6427	−	7.87663i	−0.431853	−	0.249330i
$999$	3.58586	+	6.21090i	0.113452	+	0.196504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.h.c.439.5	yes	52
5.4	even	2	inner	670.2.h.c.439.22	yes	52
67.29	even	3	inner	670.2.h.c.29.18	yes	52
335.29	even	6	inner	670.2.h.c.29.9	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.h.c.29.9	✓	52	335.29	even	6	inner
670.2.h.c.29.18	yes	52	67.29	even	3	inner
670.2.h.c.439.5	yes	52	1.1	even	1	trivial
670.2.h.c.439.22	yes	52	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} -0.719082i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.192333 + 2.22778i) q^{5} +(0.359541 + 0.622744i) q^{6} +(-3.77588 - 2.18000i) q^{7} +1.00000i q^{8} +2.48292 q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} -0.719082i q^{3} +(0.500000 - 0.866025i) q^{4} +(0.192333 + 2.22778i) q^{5} +(0.359541 + 0.622744i) q^{6} +(-3.77588 - 2.18000i) q^{7} +1.00000i q^{8} +2.48292 q^{9} +(-1.28046 - 1.83315i) q^{10} +(-2.13241 + 3.69343i) q^{11} +(-0.622744 - 0.359541i) q^{12} +(1.72113 - 0.993696i) q^{13} +4.36001 q^{14} +(1.60196 - 0.138303i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.11848 + 0.645754i) q^{17} +(-2.15027 + 1.24146i) q^{18} +(-2.20028 - 3.81100i) q^{19} +(2.02548 + 0.947326i) q^{20} +(-1.56760 + 2.71517i) q^{21} -4.26481i q^{22} +(-8.07540 + 4.66233i) q^{23} +0.719082 q^{24} +(-4.92602 + 0.856950i) q^{25} +(-0.993696 + 1.72113i) q^{26} -3.94267i q^{27} +(-3.77588 + 2.18000i) q^{28} +(-3.50823 + 6.07644i) q^{29} +(-1.31818 + 0.920753i) q^{30} +(3.21624 - 5.57069i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.65588 + 1.53338i) q^{33} +(0.645754 - 1.11848i) q^{34} +(4.13035 - 8.83111i) q^{35} +(1.24146 - 2.15027i) q^{36} +(-1.57530 + 0.909501i) q^{37} +(3.81100 + 2.20028i) q^{38} +(-0.714549 - 1.23764i) q^{39} +(-2.22778 + 0.192333i) q^{40} +(-3.64451 + 6.31247i) q^{41} -3.13520i q^{42} +8.93363i q^{43} +(2.13241 + 3.69343i) q^{44} +(0.477546 + 5.53140i) q^{45} +(4.66233 - 8.07540i) q^{46} +(-2.52546 - 1.45808i) q^{47} +(-0.622744 + 0.359541i) q^{48} +(6.00483 + 10.4007i) q^{49} +(3.83758 - 3.20515i) q^{50} +(0.464350 + 0.804278i) q^{51} -1.98739i q^{52} -6.63793i q^{53} +(1.97134 + 3.41445i) q^{54} +(-8.63829 - 4.04016i) q^{55} +(2.18000 - 3.77588i) q^{56} +(-2.74043 + 1.58219i) q^{57} -7.01646i q^{58} -10.1956 q^{59} +(0.681205 - 1.45649i) q^{60} +(-6.19683 - 10.7332i) q^{61} +6.43248i q^{62} +(-9.37520 - 5.41278i) q^{63} -1.00000 q^{64} +(2.54477 + 3.64318i) q^{65} -3.06675 q^{66} +(-3.09421 + 7.57799i) q^{67} +1.29151i q^{68} +(3.35260 + 5.80688i) q^{69} +(0.838571 + 9.71314i) q^{70} +(-4.43279 + 7.67782i) q^{71} +2.48292i q^{72} +(-2.54171 + 1.46746i) q^{73} +(0.909501 - 1.57530i) q^{74} +(0.616217 + 3.54221i) q^{75} -4.40057 q^{76} +(16.1034 - 9.29730i) q^{77} +(1.23764 + 0.714549i) q^{78} +(-3.98697 + 6.90563i) q^{79} +(1.83315 - 1.28046i) q^{80} +4.61366 q^{81} -7.28902i q^{82} +(6.13533 - 3.54224i) q^{83} +(1.56760 + 2.71517i) q^{84} +(-1.65372 - 2.36753i) q^{85} +(-4.46682 - 7.73675i) q^{86} +(4.36946 + 2.52271i) q^{87} +(-3.69343 - 2.13241i) q^{88} -5.47498 q^{89} +(-3.17927 - 4.55156i) q^{90} -8.66504 q^{91} +9.32467i q^{92} +(-4.00578 - 2.31274i) q^{93} +2.91615 q^{94} +(8.06690 - 5.63473i) q^{95} +(0.359541 - 0.622744i) q^{96} +(9.00867 - 5.20116i) q^{97} +(-10.4007 - 6.00483i) q^{98} +(-5.29459 + 9.17051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9}+O(q^{10}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9	\( 52 q + 26 q^{4} - 16 q^{5} - 6 q^{6} - 48 q^{9} - 10 q^{10} + 24 q^{11} + 24 q^{14} + 28 q^{15} - 26 q^{16} - 24 q^{19} - 8 q^{20} + 4 q^{21} - 12 q^{24} - 28 q^{25} + 4 q^{26} - 20 q^{29} - 10 q^{30} - 30 q^{31} - 16 q^{34} - 14 q^{35} - 24 q^{36} - 8 q^{39} - 20 q^{40} - 10 q^{41} - 24 q^{44} - 16 q^{45} - 8 q^{46} + 14 q^{49} - 8 q^{50} - 44 q^{51} + 42 q^{54} + 16 q^{55} + 12 q^{56} + 80 q^{59} + 14 q^{60} - 20 q^{61} - 52 q^{64} + 10 q^{65} - 40 q^{66} - 4 q^{69} + 48 q^{70} - 74 q^{71} + 34 q^{74} - 16 q^{75} - 48 q^{76} + 32 q^{79} + 8 q^{80} + 4 q^{81} - 4 q^{84} + 20 q^{85} + 12 q^{86} + 84 q^{89} - 30 q^{90} - 16 q^{91} + 136 q^{94} + 2 q^{95} - 6 q^{96} - 96 q^{99}+O(q^{100}) \) 52 * q + 26 * q^4 - 16 * q^5 - 6 * q^6 - 48 * q^9 - 10 * q^10 + 24 * q^11 + 24 * q^14 + 28 * q^15 - 26 * q^16 - 24 * q^19 - 8 * q^20 + 4 * q^21 - 12 * q^24 - 28 * q^25 + 4 * q^26 - 20 * q^29 - 10 * q^30 - 30 * q^31 - 16 * q^34 - 14 * q^35 - 24 * q^36 - 8 * q^39 - 20 * q^40 - 10 * q^41 - 24 * q^44 - 16 * q^45 - 8 * q^46 + 14 * q^49 - 8 * q^50 - 44 * q^51 + 42 * q^54 + 16 * q^55 + 12 * q^56 + 80 * q^59 + 14 * q^60 - 20 * q^61 - 52 * q^64 + 10 * q^65 - 40 * q^66 - 4 * q^69 + 48 * q^70 - 74 * q^71 + 34 * q^74 - 16 * q^75 - 48 * q^76 + 32 * q^79 + 8 * q^80 + 4 * q^81 - 4 * q^84 + 20 * q^85 + 12 * q^86 + 84 * q^89 - 30 * q^90 - 16 * q^91 + 136 * q^94 + 2 * q^95 - 6 * q^96 - 96 * q^99

Introduction

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