LMFDB - Embedded newform 802.2.e.b.45.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [802,2,Mod(45,802)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(802, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("802.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 802 = 2 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	802.e (of order $8$, degree $4$, 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:	$6.40400224211$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			45.7
Character	$\chi$	$=$	802.45
Dual form			802.2.e.b.303.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.865572 - 0.358532i) q^{3} +1.00000i q^{4} +1.42002 q^{5} +(-0.358532 - 0.865572i) q^{6} +(2.24756 - 2.24756i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.50065 - 1.50065i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.865572 - 0.358532i) q^{3} +1.00000i q^{4} +1.42002 q^{5} +(-0.358532 - 0.865572i) q^{6} +(2.24756 - 2.24756i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.50065 - 1.50065i) q^{9} +(1.00411 + 1.00411i) q^{10} +(-3.65510 - 3.65510i) q^{11} +(0.358532 - 0.865572i) q^{12} +(3.29666 - 1.36552i) q^{13} +3.17853 q^{14} +(-1.22913 - 0.509123i) q^{15} -1.00000 q^{16} +(-0.654431 + 0.271074i) q^{17} -2.12224i q^{18} +(-1.63536 - 3.94810i) q^{19} +1.42002i q^{20} +(-2.75125 + 1.13960i) q^{21} -5.16909i q^{22} +(-0.0235309 - 0.0568085i) q^{23} +(0.865572 - 0.358532i) q^{24} -2.98354 q^{25} +(3.29666 + 1.36552i) q^{26} +(1.83649 + 4.43367i) q^{27} +(2.24756 + 2.24756i) q^{28} +5.55835 q^{29} +(-0.509123 - 1.22913i) q^{30} +(-1.78381 - 4.30651i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.85328 + 4.47422i) q^{33} +(-0.654431 - 0.271074i) q^{34} +(3.19158 - 3.19158i) q^{35} +(1.50065 - 1.50065i) q^{36} +(-2.74132 - 1.13549i) q^{37} +(1.63536 - 3.94810i) q^{38} -3.34308 q^{39} +(-1.00411 + 1.00411i) q^{40} +9.21559 q^{41} +(-2.75125 - 1.13960i) q^{42} +(-1.30996 + 1.30996i) q^{43} +(3.65510 - 3.65510i) q^{44} +(-2.13095 - 2.13095i) q^{45} +(0.0235309 - 0.0568085i) q^{46} +(3.88185 + 3.88185i) q^{47} +(0.865572 + 0.358532i) q^{48} -3.10304i q^{49} +(-2.10968 - 2.10968i) q^{50} +0.663646 q^{51} +(1.36552 + 3.29666i) q^{52} +(-1.79209 + 4.32650i) q^{53} +(-1.83649 + 4.43367i) q^{54} +(-5.19032 - 5.19032i) q^{55} +3.17853i q^{56} +4.00369i q^{57} +(3.93035 + 3.93035i) q^{58} +(11.9049 - 4.93119i) q^{59} +(0.509123 - 1.22913i) q^{60} +(2.83604 + 6.84680i) q^{61} +(1.78381 - 4.30651i) q^{62} -6.74560 q^{63} -1.00000i q^{64} +(4.68132 - 1.93907i) q^{65} +(-1.85328 + 4.47422i) q^{66} +(0.0912961 - 0.220408i) q^{67} +(-0.271074 - 0.654431i) q^{68} +0.0576084i q^{69} +4.51358 q^{70} +(0.496715 - 1.19918i) q^{71} +2.12224 q^{72} +(3.80337 - 3.80337i) q^{73} +(-1.13549 - 2.74132i) q^{74} +(2.58247 + 1.06969i) q^{75} +(3.94810 - 1.63536i) q^{76} -16.4301 q^{77} +(-2.36391 - 2.36391i) q^{78} +(-2.07129 - 5.00053i) q^{79} -1.42002 q^{80} +1.87062i q^{81} +(6.51641 + 6.51641i) q^{82} +4.63500 q^{83} +(-1.13960 - 2.75125i) q^{84} +(-0.929306 + 0.384931i) q^{85} -1.85256 q^{86} +(-4.81115 - 1.99285i) q^{87} +5.16909 q^{88} +(9.55629 - 9.55629i) q^{89} -3.01363i q^{90} +(4.34034 - 10.4785i) q^{91} +(0.0568085 - 0.0235309i) q^{92} +4.36715i q^{93} +5.48977i q^{94} +(-2.32224 - 5.60638i) q^{95} +(0.358532 + 0.865572i) q^{96} +(-0.752224 - 1.81603i) q^{97} +(2.19418 - 2.19418i) q^{98} +10.9701i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) $ 68 * q + 4 * q^6 + 20 * q^9	$ 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) $ 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/802\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{8}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.865572	−	0.358532i	−0.499738	−	0.206998i	0.118553	−	0.992948i	$-0.462175\pi$
$3$	−0.865572	−	0.358532i	−0.499738	−	0.206998i	−0.618291	+	0.785949i	$0.712175\pi$
$4$			1.00000i			0.500000i
$5$	1.42002			0.635053			0.317526	−	0.948249i	$-0.397148\pi$
$5$	1.42002			0.635053			0.317526	+	0.948249i	$0.397148\pi$
$6$	−0.358532	−	0.865572i	−0.146370	−	0.353368i
$7$	2.24756	−	2.24756i	0.849497	−	0.849497i	−0.140573	−	0.990070i	$-0.544894\pi$
$7$	2.24756	−	2.24756i	0.849497	−	0.849497i	0.990070	+	0.140573i	$0.0448945\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.50065	−	1.50065i	−0.500217	−	0.500217i
$10$	1.00411	+	1.00411i	0.317526	+	0.317526i
$11$	−3.65510	−	3.65510i	−1.10205	−	1.10205i	−0.994163	−	0.107891i	$-0.965590\pi$
$11$	−3.65510	−	3.65510i	−1.10205	−	1.10205i	−0.107891	−	0.994163i	$-0.534410\pi$
$12$	0.358532	−	0.865572i	0.103499	−	0.249869i
$13$	3.29666	−	1.36552i	0.914328	−	0.378727i	0.124616	−	0.992205i	$-0.460230\pi$
$13$	3.29666	−	1.36552i	0.914328	−	0.378727i	0.789712	+	0.613478i	$0.210230\pi$
$14$	3.17853			0.849497
$15$	−1.22913	−	0.509123i	−0.317360	−	0.131455i
$16$	−1.00000			−0.250000
$17$	−0.654431	+	0.271074i	−0.158723	+	0.0657451i	−0.460630	−	0.887592i	$-0.652377\pi$
$17$	−0.654431	+	0.271074i	−0.158723	+	0.0657451i	0.301908	+	0.953337i	$0.402377\pi$
$18$		−	2.12224i		−	0.500217i
$19$	−1.63536	−	3.94810i	−0.375176	−	0.905755i	−0.992855	−	0.119325i	$-0.961927\pi$
$19$	−1.63536	−	3.94810i	−0.375176	−	0.905755i	0.617679	−	0.786430i	$-0.288073\pi$
$20$			1.42002i			0.317526i
$21$	−2.75125	+	1.13960i	−0.600371	+	0.248682i
$22$		−	5.16909i		−	1.10205i
$23$	−0.0235309	−	0.0568085i	−0.00490652	−	0.0118454i	0.921407	−	0.388598i	$-0.127041\pi$
$23$	−0.0235309	−	0.0568085i	−0.00490652	−	0.0118454i	−0.926314	+	0.376753i	$0.877041\pi$
$24$	0.865572	−	0.358532i	0.176684	−	0.0731850i
$25$	−2.98354			−0.596708
$26$	3.29666	+	1.36552i	0.646527	+	0.267800i
$27$	1.83649	+	4.43367i	0.353432	+	0.853260i
$28$	2.24756	+	2.24756i	0.424749	+	0.424749i
$29$	5.55835			1.03216			0.516080	−	0.856540i	$-0.327391\pi$
$29$	5.55835			1.03216			0.516080	+	0.856540i	$0.327391\pi$
$30$	−0.509123	−	1.22913i	−0.0929526	−	0.224408i
$31$	−1.78381	−	4.30651i	−0.320383	−	0.773472i	−0.999232	−	0.0391941i	$-0.987521\pi$
$31$	−1.78381	−	4.30651i	−0.320383	−	0.773472i	0.678849	−	0.734278i	$-0.262479\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.85328	+	4.47422i	0.322615	+	0.778862i
$34$	−0.654431	−	0.271074i	−0.112234	−	0.0464888i
$35$	3.19158	−	3.19158i	0.539476	−	0.539476i
$36$	1.50065	−	1.50065i	0.250108	−	0.250108i
$37$	−2.74132	−	1.13549i	−0.450671	−	0.186674i	0.145791	−	0.989315i	$-0.453427\pi$
$37$	−2.74132	−	1.13549i	−0.450671	−	0.186674i	−0.596462	+	0.802641i	$0.703427\pi$
$38$	1.63536	−	3.94810i	0.265290	−	0.640466i
$39$	−3.34308			−0.535321
$40$	−1.00411	+	1.00411i	−0.158763	+	0.158763i
$41$	9.21559			1.43923			0.719617	−	0.694371i	$-0.244317\pi$
$41$	9.21559			1.43923			0.719617	+	0.694371i	$0.244317\pi$
$42$	−2.75125	−	1.13960i	−0.424526	−	0.175845i
$43$	−1.30996	+	1.30996i	−0.199767	+	0.199767i	−0.799900	−	0.600133i	$-0.795114\pi$
$43$	−1.30996	+	1.30996i	−0.199767	+	0.199767i	0.600133	+	0.799900i	$0.295114\pi$
$44$	3.65510	−	3.65510i	0.551027	−	0.551027i
$45$	−2.13095	−	2.13095i	−0.317664	−	0.317664i
$46$	0.0235309	−	0.0568085i	0.00346944	−	0.00837596i
$47$	3.88185	+	3.88185i	0.566227	+	0.566227i	0.931069	−	0.364843i	$-0.118877\pi$
$47$	3.88185	+	3.88185i	0.566227	+	0.566227i	−0.364843	+	0.931069i	$0.618877\pi$
$48$	0.865572	+	0.358532i	0.124935	+	0.0517496i
$49$		−	3.10304i		−	0.443292i
$50$	−2.10968	−	2.10968i	−0.298354	−	0.298354i
$51$	0.663646			0.0929290
$52$	1.36552	+	3.29666i	0.189363	+	0.457164i
$53$	−1.79209	+	4.32650i	−0.246163	+	0.594290i	−0.997872	−	0.0652051i	$-0.979230\pi$
$53$	−1.79209	+	4.32650i	−0.246163	+	0.594290i	0.751709	+	0.659495i	$0.229230\pi$
$54$	−1.83649	+	4.43367i	−0.249914	+	0.603346i
$55$	−5.19032	−	5.19032i	−0.699862	−	0.699862i
$56$			3.17853i			0.424749i
$57$			4.00369i			0.530302i
$58$	3.93035	+	3.93035i	0.516080	+	0.516080i
$59$	11.9049	−	4.93119i	1.54989	−	0.641986i	0.566594	−	0.823997i	$-0.308261\pi$
$59$	11.9049	−	4.93119i	1.54989	−	0.641986i	0.983296	+	0.182011i	$0.0582606\pi$
$60$	0.509123	−	1.22913i	0.0657274	−	0.158680i
$61$	2.83604	+	6.84680i	0.363117	+	0.876643i	0.994841	+	0.101449i	$0.0323479\pi$
$61$	2.83604	+	6.84680i	0.363117	+	0.876643i	−0.631723	+	0.775194i	$0.717652\pi$
$62$	1.78381	−	4.30651i	0.226545	−	0.546927i
$63$	−6.74560			−0.849866
$64$		−	1.00000i		−	0.125000i
$65$	4.68132	−	1.93907i	0.580646	−	0.240512i
$66$	−1.85328	+	4.47422i	−0.228123	+	0.550739i
$67$	0.0912961	−	0.220408i	0.0111536	−	0.0269272i	−0.918205	−	0.396106i	$-0.870361\pi$
$67$	0.0912961	−	0.220408i	0.0111536	−	0.0269272i	0.929358	+	0.369179i	$0.120361\pi$
$68$	−0.271074	−	0.654431i	−0.0328726	−	0.0793614i
$69$			0.0576084i			0.00693524i
$70$	4.51358			0.539476
$71$	0.496715	−	1.19918i	0.0589492	−	0.142316i	−0.891661	−	0.452705i	$-0.850459\pi$
$71$	0.496715	−	1.19918i	0.0589492	−	0.142316i	0.950610	+	0.310389i	$0.100459\pi$
$72$	2.12224			0.250108
$73$	3.80337	−	3.80337i	0.445151	−	0.445151i	−0.448588	−	0.893739i	$-0.648073\pi$
$73$	3.80337	−	3.80337i	0.445151	−	0.445151i	0.893739	+	0.448588i	$0.148073\pi$
$74$	−1.13549	−	2.74132i	−0.131998	−	0.318673i
$75$	2.58247	+	1.06969i	0.298198	+	0.123518i
$76$	3.94810	−	1.63536i	0.452878	−	0.187588i
$77$	−16.4301			−1.87238
$78$	−2.36391	−	2.36391i	−0.267660	−	0.267660i
$79$	−2.07129	−	5.00053i	−0.233038	−	0.562604i	0.763494	−	0.645815i	$-0.223482\pi$
$79$	−2.07129	−	5.00053i	−0.233038	−	0.562604i	−0.996532	+	0.0832114i	$0.973482\pi$
$80$	−1.42002			−0.158763
$81$			1.87062i			0.207847i
$82$	6.51641	+	6.51641i	0.719617	+	0.719617i
$83$	4.63500			0.508758			0.254379	−	0.967105i	$-0.418129\pi$
$83$	4.63500			0.508758			0.254379	+	0.967105i	$0.418129\pi$
$84$	−1.13960	−	2.75125i	−0.124341	−	0.300185i
$85$	−0.929306	+	0.384931i	−0.100797	+	0.0417516i
$86$	−1.85256			−0.199767
$87$	−4.81115	−	1.99285i	−0.515810	−	0.213655i
$88$	5.16909			0.551027
$89$	9.55629	−	9.55629i	1.01296	−	1.01296i	0.0130494	−	0.999915i	$-0.495846\pi$
$89$	9.55629	−	9.55629i	1.01296	−	1.01296i	0.999915	−	0.0130494i	$-0.00415388\pi$
$90$		−	3.01363i		−	0.317664i
$91$	4.34034	−	10.4785i	0.454992	−	1.09845i
$92$	0.0568085	−	0.0235309i	0.00592270	−	0.00245326i
$93$			4.36715i			0.452852i
$94$			5.48977i			0.566227i
$95$	−2.32224	−	5.60638i	−0.238257	−	0.575202i
$96$	0.358532	+	0.865572i	0.0365925	+	0.0883421i
$97$	−0.752224	−	1.81603i	−0.0763767	−	0.184390i	0.881080	−	0.472968i	$-0.156817\pi$
$97$	−0.752224	−	1.81603i	−0.0763767	−	0.184390i	−0.957456	+	0.288578i	$0.906817\pi$
$98$	2.19418	−	2.19418i	0.221646	−	0.221646i
$99$			10.9701i			1.10253i
$100$		−	2.98354i		−	0.298354i
$101$	−4.73085	+	11.4213i	−0.470737	+	1.13646i	0.493101	+	0.869972i	$0.335863\pi$
$101$	−4.73085	+	11.4213i	−0.470737	+	1.13646i	−0.963838	+	0.266488i	$0.914137\pi$
$102$	0.469268	+	0.469268i	0.0464645	+	0.0464645i
$103$	−4.20170	+	4.20170i	−0.414006	+	0.414006i	−0.883132	−	0.469125i	$-0.844569\pi$
$103$	−4.20170	+	4.20170i	−0.414006	+	0.414006i	0.469125	+	0.883132i	$0.344569\pi$
$104$	−1.36552	+	3.29666i	−0.133900	+	0.323264i
$105$	−3.90683	+	1.61826i	−0.381267	+	0.157926i
$106$	−4.32650	+	1.79209i	−0.420226	+	0.174063i
$107$	−9.68131	+	4.01013i	−0.935928	+	0.387674i	−0.797924	−	0.602758i	$-0.794069\pi$
$107$	−9.68131	+	4.01013i	−0.935928	+	0.387674i	−0.138003	+	0.990432i	$0.544069\pi$
$108$	−4.43367	+	1.83649i	−0.426630	+	0.176716i
$109$	−4.62122	−	4.62122i	−0.442632	−	0.442632i	0.450263	−	0.892896i	$-0.351330\pi$
$109$	−4.62122	−	4.62122i	−0.442632	−	0.442632i	−0.892896	+	0.450263i	$0.851330\pi$
$110$		−	7.34022i		−	0.699862i
$111$	1.96570	+	1.96570i	0.186576	+	0.186576i
$112$	−2.24756	+	2.24756i	−0.212374	+	0.212374i
$113$			17.8074i			1.67518i	0.546301	+	0.837589i	$0.316036\pi$
$113$			17.8074i			1.67518i	−0.546301	+	0.837589i	$0.683964\pi$
$114$	−2.83104	+	2.83104i	−0.265151	+	0.265151i
$115$	−0.0334143	−	0.0806693i	−0.00311590	−	0.00752245i
$116$			5.55835i			0.516080i
$117$	−6.99629	−	2.89796i	−0.646808	−	0.267917i
$118$	11.9049	+	4.93119i	1.09594	+	0.453953i
$119$	−0.861617	+	2.08013i	−0.0789843	+	0.190685i
$120$	1.22913	−	0.509123i	0.112204	−	0.0464763i
$121$			15.7195i			1.42905i
$122$	−2.83604	+	6.84680i	−0.256763	+	0.619880i
$123$	−7.97676	−	3.30408i	−0.719240	−	0.297919i
$124$	4.30651	−	1.78381i	0.386736	−	0.160191i
$125$	−11.3368			−1.01399
$126$	−4.76986	−	4.76986i	−0.424933	−	0.424933i
$127$	1.75076	+	4.22670i	0.155355	+	0.375059i	0.982324	−	0.187187i	$-0.0599372\pi$
$127$	1.75076	+	4.22670i	0.155355	+	0.375059i	−0.826970	+	0.562247i	$0.809937\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.60353	−	0.664202i	0.141183	−	0.0584797i
$130$	4.68132	+	1.93907i	0.410579	+	0.170067i
$131$	−0.217258	+	0.524508i	−0.0189819	+	0.0458264i	−0.933086	−	0.359653i	$-0.882895\pi$
$131$	−0.217258	+	0.524508i	−0.0189819	+	0.0458264i	0.914104	+	0.405479i	$0.132895\pi$
$132$	−4.47422	+	1.85328i	−0.389431	+	0.161308i
$133$	−12.5491	−	5.19802i	−1.08815	−	0.450726i
$134$	0.220408	−	0.0912961i	0.0190404	−	0.00788678i
$135$	2.60785	+	6.29590i	0.224448	+	0.541865i
$136$	0.271074	−	0.654431i	0.0232444	−	0.0561170i
$137$	−3.62145	−	1.50005i	−0.309401	−	0.128158i	0.222580	−	0.974914i	$-0.428552\pi$
$137$	−3.62145	−	1.50005i	−0.309401	−	0.128158i	−0.531981	+	0.846756i	$0.678552\pi$
$138$	−0.0407353	+	0.0407353i	−0.00346762	+	0.00346762i
$139$	−11.0998	+	4.59769i	−0.941473	+	0.389971i	−0.800019	−	0.599974i	$-0.795178\pi$
$139$	−11.0998	+	4.59769i	−0.941473	+	0.389971i	−0.141453	+	0.989945i	$0.545178\pi$
$140$	3.19158	+	3.19158i	0.269738	+	0.269738i
$141$	−1.96826	−	4.75179i	−0.165757	−	0.400173i
$142$	1.19918	−	0.496715i	0.100633	−	0.0416834i
$143$	−17.0407	−	7.05850i	−1.42502	−	0.590261i
$144$	1.50065	+	1.50065i	0.125054	+	0.125054i
$145$	7.89298			0.655476
$146$	5.37878			0.445151
$147$	−1.11254	+	2.68591i	−0.0917606	+	0.221530i
$148$	1.13549	−	2.74132i	0.0933370	−	0.225336i
$149$			13.0329i			1.06770i	0.845580	+	0.533849i	$0.179255\pi$
$149$			13.0329i			1.06770i	−0.845580	+	0.533849i	$0.820745\pi$
$150$	1.06969	+	2.58247i	0.0873401	+	0.210858i
$151$	−7.99946	−	7.99946i	−0.650987	−	0.650987i	0.302244	−	0.953231i	$-0.402264\pi$
$151$	−7.99946	−	7.99946i	−0.650987	−	0.650987i	−0.953231	+	0.302244i	$0.902264\pi$
$152$	3.94810	+	1.63536i	0.320233	+	0.132645i
$153$	1.38886	+	0.575284i	0.112283	+	0.0465090i
$154$	−11.6178	−	11.6178i	−0.936192	−	0.936192i
$155$	−2.53305	−	6.11533i	−0.203460	−	0.491195i
$156$		−	3.34308i		−	0.267660i
$157$	−4.55123	+	1.88518i	−0.363228	+	0.150454i	−0.556831	−	0.830626i	$-0.687983\pi$
$157$	−4.55123	+	1.88518i	−0.363228	+	0.150454i	0.193603	+	0.981080i	$0.437983\pi$
$158$	2.07129	−	5.00053i	0.164783	−	0.397821i
$159$	3.10237	−	3.10237i	0.246034	−	0.246034i
$160$	−1.00411	−	1.00411i	−0.0793816	−	0.0793816i
$161$	−0.180567	−	0.0747935i	−0.0142307	−	0.00589455i
$162$	−1.32273	+	1.32273i	−0.103923	+	0.103923i
$163$	11.2606	−	4.66428i	0.881996	−	0.365335i	0.104725	−	0.994501i	$-0.466604\pi$
$163$	11.2606	−	4.66428i	0.881996	−	0.365335i	0.777271	+	0.629166i	$0.216604\pi$
$164$			9.21559i			0.719617i
$165$	2.63170	+	6.35349i	0.204878	+	0.494618i
$166$	3.27744	+	3.27744i	0.254379	+	0.254379i
$167$	7.57251	+	18.2817i	0.585979	+	1.41468i	0.887317	+	0.461160i	$0.152567\pi$
$167$	7.57251	+	18.2817i	0.585979	+	1.41468i	−0.301338	+	0.953517i	$0.597433\pi$
$168$	1.13960	−	2.75125i	0.0879223	−	0.212263i
$169$	−0.189092	+	0.189092i	−0.0145455	+	0.0145455i
$170$	−0.929306	−	0.384931i	−0.0712745	−	0.0295229i
$171$	−3.47062	+	8.37881i	−0.265405	+	0.640743i
$172$	−1.30996	−	1.30996i	−0.0998834	−	0.0998834i
$173$	−1.01450			−0.0771311			−0.0385656	−	0.999256i	$-0.512279\pi$
$173$	−1.01450			−0.0771311			−0.0385656	+	0.999256i	$0.512279\pi$
$174$	−1.99285	−	4.81115i	−0.151077	−	0.364733i
$175$	−6.70568	+	6.70568i	−0.506902	+	0.506902i
$176$	3.65510	+	3.65510i	0.275513	+	0.275513i
$177$	−12.0726			−0.907430
$178$	13.5146			1.01296
$179$		−	16.8191i		−	1.25712i	−0.777761	−	0.628561i	$-0.783644\pi$
$179$		−	16.8191i		−	1.25712i	0.777761	−	0.628561i	$-0.216356\pi$
$180$	2.13095	−	2.13095i	0.158832	−	0.158832i
$181$	−5.36725	+	5.36725i	−0.398945	+	0.398945i	−0.877861	−	0.478916i	$-0.841030\pi$
$181$	−5.36725	+	5.36725i	−0.398945	+	0.398945i	0.478916	+	0.877861i	$0.341030\pi$
$182$	10.4785	−	4.34034i	0.776719	−	0.321728i
$183$		−	6.94321i		−	0.513257i
$184$	0.0568085	+	0.0235309i	0.00418798	+	0.00173472i
$185$	−3.89274	−	1.61243i	−0.286200	−	0.118548i
$186$	−3.08804	+	3.08804i	−0.226426	+	0.226426i
$187$	3.38281	+	1.40121i	0.247376	+	0.102466i
$188$	−3.88185	+	3.88185i	−0.283113	+	0.283113i
$189$	14.0925	+	5.83732i	1.02508	+	0.424603i
$190$	2.32224	−	5.60638i	0.168473	−	0.406730i
$191$	8.07486	+	3.34472i	0.584276	+	0.242015i	0.655186	−	0.755468i	$-0.272590\pi$
$191$	8.07486	+	3.34472i	0.584276	+	0.242015i	−0.0709098	+	0.997483i	$0.522590\pi$
$192$	−0.358532	+	0.865572i	−0.0258748	+	0.0624673i
$193$	19.6551	−	8.14141i	1.41480	−	0.586031i	0.461255	−	0.887268i	$-0.347399\pi$
$193$	19.6551	−	8.14141i	1.41480	−	0.586031i	0.953549	+	0.301236i	$0.0973993\pi$
$194$	0.752224	−	1.81603i	0.0540065	−	0.130383i
$195$	−4.74724			−0.339957
$196$	3.10304			0.221646
$197$			19.7655i			1.40823i	0.710084	+	0.704117i	$0.248657\pi$
$197$			19.7655i			1.40823i	−0.710084	+	0.704117i	$0.751343\pi$
$198$	−7.75700	+	7.75700i	−0.551266	+	0.551266i
$199$	−0.796526	+	0.329932i	−0.0564643	+	0.0233883i	−0.410737	−	0.911754i	$-0.634729\pi$
$199$	−0.796526	+	0.329932i	−0.0564643	+	0.0233883i	0.354273	+	0.935142i	$0.384729\pi$
$200$	2.10968	−	2.10968i	0.149177	−	0.149177i
$201$	−0.158047	+	0.158047i	−0.0111478	+	0.0111478i
$202$	−11.4213	+	4.73085i	−0.803599	+	0.332862i
$203$	12.4927	−	12.4927i	0.876817	−	0.876817i
$204$			0.663646i			0.0464645i
$205$	13.0863			0.913989
$206$	−5.94211			−0.414006
$207$	−0.0499381	+	0.120561i	−0.00347094	+	0.00837959i
$208$	−3.29666	+	1.36552i	−0.228582	+	0.0946817i
$209$	−8.45330	+	20.4081i	−0.584727	+	1.41166i
$210$	−3.90683	−	1.61826i	−0.269597	−	0.111671i
$211$	7.72488	−	18.6495i	0.531802	−	1.28388i	−0.398526	−	0.917157i	$-0.630478\pi$
$211$	7.72488	−	18.6495i	0.531802	−	1.28388i	0.930328	−	0.366728i	$-0.119522\pi$
$212$	−4.32650	−	1.79209i	−0.297145	−	0.123081i
$213$	−0.859885	+	0.859885i	−0.0589183	+	0.0589183i
$214$	−9.68131	−	4.01013i	−0.661801	−	0.274127i
$215$	−1.86017	+	1.86017i	−0.126863	+	0.126863i
$216$	−4.43367	−	1.83649i	−0.301673	−	0.124957i
$217$	−13.6884	−	5.66990i	−0.929226	−	0.384898i
$218$		−	6.53539i		−	0.442632i
$219$	−4.65572	+	1.92846i	−0.314604	+	0.130313i
$220$	5.19032	−	5.19032i	0.349931	−	0.349931i
$221$	−1.78728	+	1.78728i	−0.120225	+	0.120225i
$222$			2.77993i			0.186576i
$223$	12.7094			0.851083			0.425542	−	0.904939i	$-0.360084\pi$
$223$	12.7094			0.851083			0.425542	+	0.904939i	$0.360084\pi$
$224$	−3.17853			−0.212374
$225$	4.47725	+	4.47725i	0.298483	+	0.298483i
$226$	−12.5917	+	12.5917i	−0.837589	+	0.837589i
$227$	−4.64884	−	11.2233i	−0.308555	−	0.744917i	−0.999752	−	0.0222511i	$-0.992917\pi$
$227$	−4.64884	−	11.2233i	−0.308555	−	0.744917i	0.691198	−	0.722666i	$-0.257083\pi$
$228$	−4.00369			−0.265151
$229$	−11.3857	−	11.3857i	−0.752386	−	0.752386i	0.222538	−	0.974924i	$-0.428566\pi$
$229$	−11.3857	−	11.3857i	−0.752386	−	0.752386i	−0.974924	+	0.222538i	$0.928566\pi$
$230$	0.0334143	−	0.0806693i	0.00220327	−	0.00531917i
$231$	14.2214	+	5.89071i	0.935702	+	0.387580i
$232$	−3.93035	+	3.93035i	−0.258040	+	0.258040i
$233$	3.86301	−	9.32613i	0.253074	−	0.610975i	−0.745375	−	0.666645i	$-0.767730\pi$
$233$	3.86301	−	9.32613i	0.253074	−	0.610975i	0.998449	+	0.0556703i	$0.0177296\pi$
$234$	−2.89796	−	6.99629i	−0.189446	−	0.457362i
$235$	5.51231	+	5.51231i	0.359584	+	0.359584i
$236$	4.93119	+	11.9049i	0.320993	+	0.774945i
$237$			5.07094i			0.329393i
$238$	−2.08013	+	0.861617i	−0.134835	+	0.0558503i
$239$	1.63548	−	1.63548i	0.105790	−	0.105790i	−0.652230	−	0.758021i	$-0.726167\pi$
$239$	1.63548	−	1.63548i	0.105790	−	0.105790i	0.758021	+	0.652230i	$0.226167\pi$
$240$	1.22913	+	0.509123i	0.0793400	+	0.0328637i
$241$	19.2299	+	19.2299i	1.23871	+	1.23871i	0.960529	+	0.278179i	$0.0897307\pi$
$241$	19.2299	+	19.2299i	1.23871	+	1.23871i	0.278179	+	0.960529i	$0.410269\pi$
$242$	−11.1154	+	11.1154i	−0.714523	+	0.714523i
$243$	6.18013	−	14.9202i	0.396456	−	0.957129i
$244$	−6.84680	+	2.83604i	−0.438322	+	0.181559i
$245$		−	4.40638i		−	0.281513i
$246$	−3.30408	−	7.97676i	−0.210661	−	0.508580i
$247$	−10.7824	−	10.7824i	−0.686068	−	0.686068i
$248$	4.30651	+	1.78381i	0.273464	+	0.113272i
$249$	−4.01193	−	1.66180i	−0.254246	−	0.105312i
$250$	−8.01632	−	8.01632i	−0.506997	−	0.506997i
$251$	−6.71466	−	16.2106i	−0.423826	−	1.02321i	−0.981209	−	0.192950i	$-0.938194\pi$
$251$	−6.71466	−	16.2106i	−0.423826	−	1.02321i	0.557383	−	0.830256i	$-0.311806\pi$
$252$		−	6.74560i		−	0.424933i
$253$	−0.121633	+	0.293648i	−0.00764701	+	0.0184615i
$254$	−1.75076	+	4.22670i	−0.109852	+	0.265207i
$255$	0.942391			0.0590148
$256$	1.00000			0.0625000
$257$	3.81063	+	3.81063i	0.237700	+	0.237700i	0.815897	−	0.578197i	$-0.196243\pi$
$257$	3.81063	+	3.81063i	0.237700	+	0.237700i	−0.578197	+	0.815897i	$0.696243\pi$
$258$	1.60353	+	0.664202i	0.0998312	+	0.0413514i
$259$	−8.71338	+	3.60920i	−0.541423	+	0.224265i
$260$	1.93907	+	4.68132i	0.120256	+	0.290323i
$261$	−8.34114	−	8.34114i	−0.516304	−	0.516304i
$262$	−0.524508	+	0.217258i	−0.0324042	+	0.0134223i
$263$	20.7512	−	20.7512i	1.27957	−	1.27957i	0.338667	−	0.940906i	$-0.390024\pi$
$263$	20.7512	−	20.7512i	1.27957	−	1.27957i	0.940906	−	0.338667i	$-0.109976\pi$
$264$	−4.47422	−	1.85328i	−0.275369	−	0.114062i
$265$	−2.54481	+	6.14372i	−0.156326	+	0.377405i
$266$	−5.19802	−	12.5491i	−0.318711	−	0.769437i
$267$	−11.6979	+	4.84542i	−0.715899	+	0.296535i
$268$	0.220408	+	0.0912961i	0.0134636	+	0.00557680i
$269$	−6.07570	+	2.51664i	−0.370442	+	0.153442i	−0.560135	−	0.828401i	$-0.689251\pi$
$269$	−6.07570	+	2.51664i	−0.370442	+	0.153442i	0.189693	+	0.981843i	$0.439251\pi$
$270$	−2.60785	+	6.29590i	−0.158709	+	0.383156i
$271$	−14.3410	−	5.94022i	−0.871151	−	0.360843i	−0.0980925	−	0.995177i	$-0.531274\pi$
$271$	−14.3410	−	5.94022i	−0.871151	−	0.360843i	−0.773059	+	0.634335i	$0.781274\pi$
$272$	0.654431	−	0.271074i	0.0396807	−	0.0164363i
$273$	−7.51376	+	7.51376i	−0.454753	+	0.454753i
$274$	−1.50005	−	3.62145i	−0.0906215	−	0.218780i
$275$	10.9051	+	10.9051i	0.657604	+	0.657604i
$276$	−0.0576084			−0.00346762
$277$	13.0375	−	5.40031i	0.783348	−	0.324473i	0.0450819	−	0.998983i	$-0.485645\pi$
$277$	13.0375	−	5.40031i	0.783348	−	0.324473i	0.738266	+	0.674510i	$0.235645\pi$
$278$	−11.0998	−	4.59769i	−0.665722	−	0.275751i
$279$	−3.78568	+	9.13945i	−0.226643	+	0.547164i
$280$			4.51358i			0.269738i
$281$	17.8710	−	7.40241i	1.06609	−	0.441591i	0.220484	−	0.975391i	$-0.429236\pi$
$281$	17.8710	−	7.40241i	1.06609	−	0.441591i	0.845611	+	0.533800i	$0.179236\pi$
$282$	1.96826	−	4.75179i	0.117208	−	0.282965i
$283$	−7.60425	−	3.14978i	−0.452026	−	0.187235i	0.145043	−	0.989425i	$-0.453668\pi$
$283$	−7.60425	−	3.14978i	−0.452026	−	0.187235i	−0.597069	+	0.802190i	$0.703668\pi$
$284$	1.19918	+	0.496715i	0.0711580	+	0.0294746i
$285$			5.68532i			0.336769i
$286$	−7.05850	−	17.0407i	−0.417378	−	1.00764i
$287$	20.7126	−	20.7126i	1.22263	−	1.22263i
$288$			2.12224i			0.125054i
$289$	−11.6660	+	11.6660i	−0.686236	+	0.686236i
$290$	5.58118	+	5.58118i	0.327738	+	0.327738i
$291$			1.84160i			0.107956i
$292$	3.80337	+	3.80337i	0.222575	+	0.222575i
$293$	15.0993	−	6.25432i	0.882109	−	0.365381i	0.104795	−	0.994494i	$-0.466581\pi$
$293$	15.0993	−	6.25432i	0.882109	−	0.365381i	0.777314	+	0.629112i	$0.216581\pi$
$294$	−2.68591	+	1.11254i	−0.156645	+	0.0648846i
$295$	16.9053	−	7.00239i	0.984262	−	0.407695i
$296$	2.74132	−	1.13549i	0.159336	−	0.0659992i
$297$	9.49296	−	22.9180i	0.550837	−	1.32984i
$298$	−9.21566	+	9.21566i	−0.533849	+	0.533849i
$299$	−0.155146	−	0.155146i	−0.00897234	−	0.00897234i
$300$	−1.06969	+	2.58247i	−0.0617588	+	0.149099i
$301$			5.88842i			0.339403i
$302$		−	11.3129i		−	0.650987i
$303$	8.18979	−	8.18979i	0.470491	−	0.470491i
$304$	1.63536	+	3.94810i	0.0937940	+	0.226439i
$305$	4.02723	+	9.72260i	0.230599	+	0.556715i
$306$	0.575284	+	1.38886i	0.0328868	+	0.0793958i
$307$			12.6519i			0.722083i	0.932550	+	0.361041i	$0.117579\pi$
$307$			12.6519i			0.722083i	−0.932550	+	0.361041i	$0.882421\pi$
$308$		−	16.4301i		−	0.936192i
$309$	5.14332	−	2.13043i	0.292593	−	0.121196i
$310$	2.53305	−	6.11533i	0.143868	−	0.347328i
$311$		−	15.9833i		−	0.906331i	−0.891427	−	0.453165i	$-0.850295\pi$
$311$		−	15.9833i		−	0.906331i	0.891427	−	0.453165i	$-0.149705\pi$
$312$	2.36391	−	2.36391i	0.133830	−	0.133830i
$313$	7.42276			0.419559			0.209780	−	0.977749i	$-0.432725\pi$
$313$	7.42276			0.419559			0.209780	+	0.977749i	$0.432725\pi$
$314$	−4.55123	−	1.88518i	−0.256841	−	0.106387i
$315$	−9.57889			−0.539709
$316$	5.00053	−	2.07129i	0.281302	−	0.116519i
$317$	−4.32458	−	10.4405i	−0.242893	−	0.586395i	0.754675	−	0.656099i	$-0.227795\pi$
$317$	−4.32458	−	10.4405i	−0.242893	−	0.586395i	−0.997568	+	0.0697039i	$0.977795\pi$
$318$	4.38742			0.246034
$319$	−20.3163	−	20.3163i	−1.13750	−	1.13750i
$320$		−	1.42002i		−	0.0793816i
$321$	9.81763			0.547967
$322$	−0.0747935	−	0.180567i	−0.00416808	−	0.0100626i
$323$	2.14045	+	2.14045i	0.119098	+	0.119098i
$324$	−1.87062			−0.103923
$325$	−9.83571	+	4.07408i	−0.545587	+	0.225989i
$326$	11.2606	+	4.66428i	0.623665	+	0.258331i
$327$	2.34314	+	5.65685i	0.129576	+	0.312825i
$328$	−6.51641	+	6.51641i	−0.359808	+	0.359808i
$329$	17.4494			0.962016
$330$	−2.63170	+	6.35349i	−0.144870	+	0.349748i
$331$	−4.55971			−0.250624			−0.125312	−	0.992117i	$-0.539993\pi$
$331$	−4.55971			−0.250624			−0.125312	+	0.992117i	$0.539993\pi$
$332$			4.63500i			0.254379i
$333$	2.40979	+	5.81775i	0.132056	+	0.318811i
$334$	−7.57251	+	18.2817i	−0.414349	+	1.00033i
$335$	0.129642	−	0.312984i	0.00708312	−	0.0171002i
$336$	2.75125	−	1.13960i	0.150093	−	0.0621704i
$337$			15.4791i			0.843198i	0.906782	+	0.421599i	$0.138531\pi$
$337$			15.4791i			0.843198i	−0.906782	+	0.421599i	$0.861469\pi$
$338$	−0.267416			−0.0145455
$339$	6.38451	−	15.4136i	0.346759	−	0.837151i
$340$	−0.384931	−	0.929306i	−0.0208758	−	0.0503987i
$341$	−9.22070	+	22.2607i	−0.499329	+	1.20549i
$342$	−8.37881	+	3.47062i	−0.453074	+	0.187669i
$343$	8.75865	+	8.75865i	0.472922	+	0.472922i
$344$		−	1.85256i		−	0.0998834i
$345$			0.0818052i			0.00440424i
$346$	−0.717361	−	0.717361i	−0.0385656	−	0.0385656i
$347$	−13.5113	+	32.6191i	−0.725323	+	1.75109i	−0.0677411	+	0.997703i	$0.521579\pi$
$347$	−13.5113	+	32.6191i	−0.725323	+	1.75109i	−0.657582	+	0.753383i	$0.728421\pi$
$348$	1.99285	−	4.81115i	0.106828	−	0.257905i
$349$	5.03444	+	12.1542i	0.269487	+	0.650600i	0.999459	−	0.0328770i	$-0.0104669\pi$
$349$	5.03444	+	12.1542i	0.269487	+	0.650600i	−0.729972	+	0.683477i	$0.760467\pi$
$350$	−9.48327			−0.506902
$351$	12.1085	+	12.1085i	0.646305	+	0.646305i
$352$			5.16909i			0.275513i
$353$	10.7385	+	4.44804i	0.571554	+	0.236745i	0.649693	−	0.760197i	$-0.274898\pi$
$353$	10.7385	+	4.44804i	0.571554	+	0.236745i	−0.0781384	+	0.996943i	$0.524898\pi$
$354$	−8.53660	−	8.53660i	−0.453715	−	0.453715i
$355$	0.705345	−	1.70285i	0.0374358	−	0.0903781i
$356$	9.55629	+	9.55629i	0.506482	+	0.506482i
$357$	1.49158	−	1.49158i	0.0789429	−	0.0789429i
$358$	11.8929	−	11.8929i	0.628561	−	0.628561i
$359$	2.71985	+	1.12660i	0.143548	+	0.0594596i	0.453301	−	0.891358i	$-0.350246\pi$
$359$	2.71985	+	1.12660i	0.143548	+	0.0594596i	−0.309753	+	0.950817i	$0.600246\pi$
$360$	3.01363			0.158832
$361$	0.521950	−	0.521950i	0.0274710	−	0.0274710i
$362$	−7.59044			−0.398945
$363$	5.63594	−	13.6064i	0.295810	−	0.714149i
$364$	10.4785	+	4.34034i	0.549223	+	0.227496i
$365$	5.40086	−	5.40086i	0.282694	−	0.282694i
$366$	4.90959	−	4.90959i	0.256628	−	0.256628i
$367$	3.62548	+	1.50172i	0.189248	+	0.0783893i	0.475295	−	0.879826i	$-0.342341\pi$
$367$	3.62548	+	1.50172i	0.189248	+	0.0783893i	−0.286047	+	0.958216i	$0.592341\pi$
$368$	0.0235309	+	0.0568085i	0.00122663	+	0.00296135i
$369$	−13.8294	−	13.8294i	−0.719929	−	0.719929i
$370$	−1.61243	−	3.89274i	−0.0838260	−	0.202374i
$371$	5.69622	+	13.7519i	0.295733	+	0.713962i
$372$	−4.36715			−0.226426
$373$	−12.0180	−	12.0180i	−0.622268	−	0.622268i	0.323843	−	0.946111i	$-0.395025\pi$
$373$	−12.0180	−	12.0180i	−0.622268	−	0.622268i	−0.946111	+	0.323843i	$0.895025\pi$
$374$	1.40121	+	3.38281i	0.0724547	+	0.174921i
$375$	9.81281	+	4.06460i	0.506732	+	0.209895i
$376$	−5.48977			−0.283113
$377$	18.3240	−	7.59004i	0.943733	−	0.390907i
$378$	5.83732	+	14.0925i	0.300239	+	0.724842i
$379$			31.2646i			1.60595i	0.596011	+	0.802976i	$0.296752\pi$
$379$			31.2646i			1.60595i	−0.596011	+	0.802976i	$0.703248\pi$
$380$	5.60638	−	2.32224i	0.287601	−	0.119128i
$381$		−	4.28622i		−	0.219590i
$382$	3.34472	+	8.07486i	0.171131	+	0.413146i
$383$			13.9933i			0.715026i	0.933908	+	0.357513i	$0.116375\pi$
$383$			13.9933i			0.715026i	−0.933908	+	0.357513i	$0.883625\pi$
$384$	−0.865572	+	0.358532i	−0.0441710	+	0.0182962i
$385$	−23.3311			−1.18906
$386$	19.6551	+	8.14141i	1.00042	+	0.414387i
$387$	3.93158			0.199853
$388$	1.81603	−	0.752224i	0.0921949	−	0.0381884i
$389$	3.31087	−	7.99316i	0.167868	−	0.405269i	−0.817450	−	0.576000i	$-0.804613\pi$
$389$	3.31087	−	7.99316i	0.167868	−	0.405269i	0.985318	+	0.170731i	$0.0546128\pi$
$390$	−3.35680	−	3.35680i	−0.169978	−	0.169978i
$391$	0.0307986	+	0.0307986i	0.00155755	+	0.00155755i
$392$	2.19418	+	2.19418i	0.110823	+	0.110823i
$393$	0.376105	−	0.376105i	0.0189720	−	0.0189720i
$394$	−13.9763	+	13.9763i	−0.704117	+	0.704117i
$395$	−2.94127	−	7.10086i	−0.147991	−	0.357283i
$396$	−10.9701			−0.551266
$397$		−	12.2897i		−	0.616800i	−0.951257	−	0.308400i	$-0.900207\pi$
$397$		−	12.2897i		−	0.616800i	0.951257	−	0.308400i	$-0.0997935\pi$
$398$	−0.796526	−	0.329932i	−0.0399263	−	0.0165380i
$399$	8.99853	+	8.99853i	0.450490	+	0.450490i
$400$	2.98354			0.149177
$401$	−19.1023	−	6.00843i	−0.953924	−	0.300047i
$401$	−19.1023	−	6.00843i	−0.953924	−	0.300047i
$402$	−0.223512			−0.0111478
$403$	−11.7612	−	11.7612i	−0.585869	−	0.585869i
$404$	−11.4213	−	4.73085i	−0.568230	−	0.235369i
$405$			2.65632i			0.131994i
$406$	17.6674			0.876817
$407$	5.86947	+	14.1702i	0.290939	+	0.702389i
$408$	−0.469268	+	0.469268i	−0.0232322	+	0.0232322i
$409$	−16.4564	+	16.4564i	−0.813715	+	0.813715i	−0.985189	−	0.171474i	$-0.945147\pi$
$409$	−16.4564	+	16.4564i	−0.813715	+	0.813715i	0.171474	+	0.985189i	$0.445147\pi$
$410$	9.25344	+	9.25344i	0.456995	+	0.456995i
$411$	2.59681	+	2.59681i	0.128091	+	0.128091i
$412$	−4.20170	−	4.20170i	−0.207003	−	0.207003i
$413$	15.6739	−	37.8402i	0.771263	−	1.86199i
$414$	−0.120561	+	0.0499381i	−0.00592526	+	0.00245432i
$415$	6.58180			0.323088
$416$	−3.29666	−	1.36552i	−0.161632	−	0.0669501i
$417$	11.2561			0.551213
$418$	−20.4081	+	8.45330i	−0.998191	+	0.413464i
$419$		−	14.1930i		−	0.693375i	−0.937981	−	0.346688i	$-0.887306\pi$
$419$		−	14.1930i		−	0.693375i	0.937981	−	0.346688i	$-0.112694\pi$
$420$	−1.61826	−	3.90683i	−0.0789630	−	0.190634i
$421$		−	30.9210i		−	1.50700i	−0.657449	−	0.753499i	$-0.728364\pi$
$421$		−	30.9210i		−	1.50700i	0.657449	−	0.753499i	$-0.271636\pi$
$422$	18.6495	−	7.72488i	0.907843	−	0.376041i
$423$		−	11.6506i		−	0.566472i
$424$	−1.79209	−	4.32650i	−0.0870317	−	0.210113i
$425$	1.95252	−	0.808761i	0.0947112	−	0.0392307i
$426$	−1.21606			−0.0589183
$427$	21.7628	+	9.01443i	1.05317	+	0.436239i
$428$	−4.01013	−	9.68131i	−0.193837	−	0.467964i
$429$	12.2193	+	12.2193i	0.589952	+	0.589952i
$430$	−2.63068			−0.126863
$431$	8.72777	+	21.0707i	0.420402	+	1.01494i	0.982229	+	0.187685i	$0.0600984\pi$
$431$	8.72777	+	21.0707i	0.420402	+	1.01494i	−0.561828	+	0.827254i	$0.689902\pi$
$432$	−1.83649	−	4.43367i	−0.0883579	−	0.213315i
$433$	−14.4514	−	14.4514i	−0.694488	−	0.694488i	0.268728	−	0.963216i	$-0.413397\pi$
$433$	−14.4514	−	14.4514i	−0.694488	−	0.694488i	−0.963216	+	0.268728i	$0.913397\pi$
$434$	−5.66990	−	13.6884i	−0.272164	−	0.657062i
$435$	−6.83194	−	2.82988i	−0.327566	−	0.135682i
$436$	4.62122	−	4.62122i	0.221316	−	0.221316i
$437$	−0.185804	+	0.185804i	−0.00888822	+	0.00888822i
$438$	−4.65572	−	1.92846i	−0.222459	−	0.0921455i
$439$	−10.6679	+	25.7547i	−0.509153	+	1.22920i	0.435219	+	0.900325i	$0.356671\pi$
$439$	−10.6679	+	25.7547i	−0.509153	+	1.22920i	−0.944372	+	0.328879i	$0.893329\pi$
$440$	7.34022			0.349931
$441$	−4.65658	+	4.65658i	−0.221742	+	0.221742i
$442$	−2.52759			−0.120225
$443$	26.2358	+	10.8672i	1.24650	+	0.516317i	0.905740	−	0.423833i	$-0.139316\pi$
$443$	26.2358	+	10.8672i	1.24650	+	0.516317i	0.340760	+	0.940150i	$0.389316\pi$
$444$	−1.96570	+	1.96570i	−0.0932882	+	0.0932882i
$445$	13.5701	−	13.5701i	0.643286	−	0.643286i
$446$	8.98689	+	8.98689i	0.425542	+	0.425542i
$447$	4.67271	−	11.2809i	0.221012	−	0.533569i
$448$	−2.24756	−	2.24756i	−0.106187	−	0.106187i
$449$	37.9960	+	15.7385i	1.79314	+	0.742744i	0.988927	+	0.148405i	$0.0474140\pi$
$449$	37.9960	+	15.7385i	1.79314	+	0.742744i	0.804215	+	0.594338i	$0.202586\pi$
$450$			6.33179i			0.298483i
$451$	−33.6839	−	33.6839i	−1.58611	−	1.58611i
$452$	−17.8074			−0.837589
$453$	4.05605	+	9.79217i	0.190570	+	0.460076i
$454$	4.64884	−	11.2233i	0.218181	−	0.526736i
$455$	6.16338	−	14.8797i	0.288944	−	0.697572i
$456$	−2.83104	−	2.83104i	−0.132575	−	0.132575i
$457$		−	8.95641i		−	0.418963i	−0.977813	−	0.209482i	$-0.932822\pi$
$457$		−	8.95641i		−	0.418963i	0.977813	−	0.209482i	$-0.0671776\pi$
$458$		−	16.1018i		−	0.752386i
$459$	−2.40371	−	2.40371i	−0.112195	−	0.112195i
$460$	0.0806693	−	0.0334143i	0.00376122	−	0.00155795i
$461$	−13.8701	+	33.4854i	−0.645996	+	1.55957i	0.172469	+	0.985015i	$0.444826\pi$
$461$	−13.8701	+	33.4854i	−0.645996	+	1.55957i	−0.818464	+	0.574557i	$0.805174\pi$
$462$	5.89071	+	14.2214i	0.274061	+	0.661641i
$463$	12.3312	−	29.7702i	0.573080	−	1.38354i	−0.325839	−	0.945425i	$-0.605647\pi$
$463$	12.3312	−	29.7702i	0.573080	−	1.38354i	0.898920	−	0.438113i	$-0.144353\pi$
$464$	−5.55835			−0.258040
$465$			6.20144i			0.287585i
$466$	9.32613	−	3.86301i	0.432025	−	0.178950i
$467$	−0.122472	+	0.295674i	−0.00566733	+	0.0136821i	−0.926688	−	0.375832i	$-0.877357\pi$
$467$	−0.122472	+	0.295674i	−0.00566733	+	0.0136821i	0.921021	+	0.389514i	$0.127357\pi$
$468$	2.89796	−	6.99629i	0.133958	−	0.323404i
$469$	−0.290187	−	0.700574i	−0.0133996	−	0.0323495i
$470$			7.79559i			0.359584i
$471$	4.61532			0.212663
$472$	−4.93119	+	11.9049i	−0.226976	+	0.547969i
$473$	9.57606			0.440308
$474$	−3.58570	+	3.58570i	−0.164697	+	0.164697i
$475$	4.87915	+	11.7793i	0.223871	+	0.540472i
$476$	−2.08013	−	0.861617i	−0.0953425	−	0.0394921i
$477$	9.18186	−	3.80325i	0.420409	−	0.174139i
$478$	2.31292			0.105790
$479$	25.9822	+	25.9822i	1.18716	+	1.18716i	0.977849	+	0.209309i	$0.0671216\pi$
$479$	25.9822	+	25.9822i	1.18716	+	1.18716i	0.209309	+	0.977849i	$0.432878\pi$
$480$	0.509123	+	1.22913i	0.0232382	+	0.0561019i
$481$	−10.5877			−0.482760
$482$			27.1952i			1.23871i
$483$	0.129478	+	0.129478i	0.00589147	+	0.00589147i
$484$	−15.7195			−0.714523
$485$	−1.06817	−	2.57880i	−0.0485033	−	0.117097i
$486$	14.9202	−	6.18013i	0.676792	−	0.280337i
$487$	−7.56386			−0.342751			−0.171376	−	0.985206i	$-0.554821\pi$
$487$	−7.56386			−0.342751			−0.171376	+	0.985206i	$0.554821\pi$
$488$	−6.84680	−	2.83604i	−0.309940	−	0.128381i
$489$	−11.4191			−0.516391
$490$	3.11578	−	3.11578i	0.140757	−	0.140757i
$491$			16.8522i			0.760531i	0.924877	+	0.380266i	$0.124167\pi$
$491$			16.8522i			0.760531i	−0.924877	+	0.380266i	$0.875833\pi$
$492$	3.30408	−	7.97676i	0.148960	−	0.359620i
$493$	−3.63756	+	1.50673i	−0.163827	+	0.0678595i
$494$		−	15.2486i		−	0.686068i
$495$			15.5777i			0.700166i
$496$	1.78381	+	4.30651i	0.0800956	+	0.193368i
$497$	−1.57882	−	3.81161i	−0.0708198	−	0.170974i
$498$	−1.66180	−	4.01193i	−0.0744668	−	0.179779i
$499$	10.3044	−	10.3044i	0.461289	−	0.461289i	−0.437789	−	0.899078i	$-0.644238\pi$
$499$	10.3044	−	10.3044i	0.461289	−	0.461289i	0.899078	+	0.437789i	$0.144238\pi$
$500$		−	11.3368i		−	0.506997i
$501$		−	18.5391i		−	0.828265i
$502$	6.71466	−	16.2106i	0.299690	−	0.723516i
$503$	−7.46512	−	7.46512i	−0.332853	−	0.332853i	0.520816	−	0.853669i	$-0.325628\pi$
$503$	−7.46512	−	7.46512i	−0.332853	−	0.332853i	−0.853669	+	0.520816i	$0.825628\pi$
$504$	4.76986	−	4.76986i	0.212466	−	0.212466i
$505$	−6.71791	+	16.2185i	−0.298943	+	0.721712i
$506$	−0.293648	+	0.121633i	−0.0130543	+	0.00540725i
$507$	0.231468	−	0.0958772i	0.0102799	−	0.00425805i
$508$	−4.22670	+	1.75076i	−0.187530	+	0.0776773i
$509$	13.8009	−	5.71651i	0.611713	−	0.253380i	−0.0552476	−	0.998473i	$-0.517595\pi$
$509$	13.8009	−	5.71651i	0.611713	−	0.253380i	0.666961	+	0.745093i	$0.267595\pi$
$510$	0.666371	+	0.666371i	0.0295074	+	0.0295074i
$511$		−	17.0966i		−	0.756309i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	14.5012	−	14.5012i	0.640246	−	0.640246i
$514$			5.38904i			0.237700i
$515$	−5.96651	+	5.96651i	−0.262916	+	0.262916i
$516$	0.664202	+	1.60353i	0.0292399	+	0.0705913i
$517$		−	28.3771i		−	1.24802i
$518$	−8.71338	−	3.60920i	−0.382844	−	0.158579i
$519$	0.878124	+	0.363731i	0.0385454	+	0.0159660i
$520$	−1.93907	+	4.68132i	−0.0850337	+	0.205289i
$521$	−23.4654	+	9.71967i	−1.02804	+	0.425827i	−0.832003	−	0.554771i	$-0.812806\pi$
$521$	−23.4654	+	9.71967i	−1.02804	+	0.425827i	−0.196033	+	0.980597i	$0.562806\pi$
$522$		−	11.7962i		−	0.516304i
$523$	1.03204	−	2.49157i	0.0451280	−	0.108949i	−0.899708	−	0.436492i	$-0.856221\pi$
$523$	1.03204	−	2.49157i	0.0451280	−	0.108949i	0.944836	+	0.327543i	$0.106221\pi$
$524$	−0.524508	−	0.217258i	−0.0229132	−	0.00949097i
$525$	8.20845	−	3.40005i	0.358246	−	0.148390i
$526$	29.3466			1.27957
$527$	2.33477	+	2.33477i	0.101704	+	0.101704i
$528$	−1.85328	−	4.47422i	−0.0806538	−	0.194715i
$529$	16.2608	−	16.2608i	0.706991	−	0.706991i
$530$	−6.14372	+	2.54481i	−0.266866	+	0.110539i
$531$	−25.2651	−	10.4652i	−1.09641	−	0.454149i
$532$	5.19802	−	12.5491i	0.225363	−	0.544074i
$533$	30.3806	−	12.5841i	1.31593	−	0.545077i
$534$	−11.6979	−	4.84542i	−0.506217	−	0.209682i
$535$	−13.7477	+	5.69447i	−0.594363	+	0.246193i
$536$	0.0912961	+	0.220408i	0.00394339	+	0.00952019i
$537$	−6.03019	+	14.5582i	−0.260222	+	0.628232i
$538$	−6.07570	−	2.51664i	−0.261942	−	0.108500i
$539$	−11.3419	+	11.3419i	−0.488531	+	0.488531i
$540$	−6.29590	+	2.60785i	−0.270932	+	0.112224i
$541$	20.6897	+	20.6897i	0.889518	+	0.889518i	0.994477	−	0.104959i	$-0.0334710\pi$
$541$	20.6897	+	20.6897i	0.889518	+	0.889518i	−0.104959	+	0.994477i	$0.533471\pi$
$542$	−5.94022	−	14.3410i	−0.255154	−	0.615997i
$543$	6.57007	−	2.72141i	0.281949	−	0.116787i
$544$	0.654431	+	0.271074i	0.0280585	+	0.0116222i
$545$	−6.56223	−	6.56223i	−0.281095	−	0.281095i
$546$	−10.6261			−0.454753
$547$	−37.3411			−1.59659			−0.798296	−	0.602266i	$-0.794265\pi$
$547$	−37.3411			−1.59659			−0.798296	+	0.602266i	$0.794265\pi$
$548$	1.50005	−	3.62145i	0.0640791	−	0.154701i
$549$	6.01875	−	14.5306i	0.256874	−	0.620149i
$550$			15.4222i			0.657604i
$551$	−9.08988	−	21.9449i	−0.387242	−	0.934884i
$552$	−0.0407353	−	0.0407353i	−0.00173381	−	0.00173381i
$553$	−15.8943	−	6.58365i	−0.675896	−	0.279965i
$554$	13.0375	+	5.40031i	0.553910	+	0.229437i
$555$	2.79134	+	2.79134i	0.118486	+	0.118486i
$556$	−4.59769	−	11.0998i	−0.194985	−	0.470736i
$557$			10.2448i			0.434086i	0.976162	+	0.217043i	$0.0696411\pi$
$557$			10.2448i			0.434086i	−0.976162	+	0.217043i	$0.930359\pi$
$558$	−9.13945	+	3.78568i	−0.386904	+	0.160261i
$559$	−2.52971	+	6.10726i	−0.106995	+	0.258310i
$560$	−3.19158	+	3.19158i	−0.134869	+	0.134869i
$561$	−2.42569	−	2.42569i	−0.102413	−	0.102413i
$562$	17.8710	+	7.40241i	0.753843	+	0.312252i
$563$	−15.3273	+	15.3273i	−0.645967	+	0.645967i	−0.952016	−	0.306049i	$-0.900993\pi$
$563$	−15.3273	+	15.3273i	−0.645967	+	0.645967i	0.306049	+	0.952016i	$0.400993\pi$
$564$	4.75179	−	1.96826i	0.200087	−	0.0828786i
$565$			25.2869i			1.06383i
$566$	−3.14978	−	7.60425i	−0.132395	−	0.319631i
$567$	4.20433	+	4.20433i	0.176565	+	0.176565i
$568$	0.496715	+	1.19918i	0.0208417	+	0.0503163i
$569$	5.60716	−	13.5369i	0.235064	−	0.567496i	−0.761695	−	0.647936i	$-0.775633\pi$
$569$	5.60716	−	13.5369i	0.235064	−	0.567496i	0.996759	+	0.0804400i	$0.0256325\pi$
$570$	−4.02013	+	4.02013i	−0.168385	+	0.168385i
$571$	−37.9449	−	15.7173i	−1.58794	−	0.657747i	−0.598296	−	0.801275i	$-0.704155\pi$
$571$	−37.9449	−	15.7173i	−1.58794	−	0.657747i	−0.989646	+	0.143527i	$0.954155\pi$
$572$	7.05850	−	17.0407i	0.295131	−	0.712508i
$573$	−5.79018	−	5.79018i	−0.241888	−	0.241888i
$574$	29.2920			1.22263
$575$	0.0702053	+	0.169490i	0.00292776	+	0.00706824i
$576$	−1.50065	+	1.50065i	−0.0625271	+	0.0625271i
$577$	21.6376	+	21.6376i	0.900784	+	0.900784i	0.995504	−	0.0947200i	$-0.0301956\pi$
$577$	21.6376	+	21.6376i	0.900784	+	0.900784i	−0.0947200	+	0.995504i	$0.530196\pi$
$578$	−16.4982			−0.686236
$579$	−19.9319			−0.828340
$580$			7.89298i			0.327738i
$581$	10.4174	−	10.4174i	0.432188	−	0.432188i
$582$	−1.30221	+	1.30221i	−0.0539782	+	0.0539782i
$583$	22.3641	−	9.26349i	0.926224	−	0.383655i
$584$			5.37878i			0.222575i
$585$	−9.93489	−	4.11516i	−0.410757	−	0.170141i
$586$	15.0993	+	6.25432i	0.623745	+	0.258364i
$587$	6.39845	−	6.39845i	0.264092	−	0.264092i	−0.562622	−	0.826714i	$-0.690207\pi$
$587$	6.39845	−	6.39845i	0.264092	−	0.264092i	0.826714	+	0.562622i	$0.190207\pi$
$588$	−2.68591	−	1.11254i	−0.110765	−	0.0458803i
$589$	−14.0853	+	14.0853i	−0.580376	+	0.580376i
$590$	16.9053	+	7.00239i	0.695979	+	0.288284i
$591$	7.08656	−	17.1085i	0.291502	−	0.703749i
$592$	2.74132	+	1.13549i	0.112668	+	0.0466685i
$593$	12.2901	−	29.6709i	0.504693	−	1.21844i	−0.442209	−	0.896912i	$-0.645805\pi$
$593$	12.2901	−	29.6709i	0.504693	−	1.21844i	0.946902	−	0.321524i	$-0.104195\pi$
$594$	22.9180	−	9.49296i	0.940338	−	0.389501i
$595$	−1.22351	+	2.95382i	−0.0501592	+	0.121095i
$596$	−13.0329			−0.533849
$597$	0.807742			0.0330587
$598$		−	0.219410i		−	0.00897234i
$599$	−31.5705	+	31.5705i	−1.28994	+	1.28994i	−0.355113	+	0.934824i	$0.615557\pi$
$599$	−31.5705	+	31.5705i	−1.28994	+	1.28994i	−0.934824	+	0.355113i	$0.884443\pi$
$600$	−2.58247	+	1.06969i	−0.105429	+	0.0436701i
$601$	18.8093	−	18.8093i	0.767247	−	0.767247i	−0.210374	−	0.977621i	$-0.567468\pi$
$601$	18.8093	−	18.8093i	0.767247	−	0.767247i	0.977621	+	0.210374i	$0.0674681\pi$
$602$	−4.16374	+	4.16374i	−0.169701	+	0.169701i
$603$	−0.467759	+	0.193752i	−0.0190486	+	0.00789020i
$604$	7.99946	−	7.99946i	0.325494	−	0.325494i
$605$			22.3220i			0.907520i
$606$	11.5821			0.470491
$607$	35.5951			1.44476			0.722380	−	0.691497i	$-0.243048\pi$
$607$	35.5951			1.44476			0.722380	+	0.691497i	$0.243048\pi$
$608$	−1.63536	+	3.94810i	−0.0663224	+	0.160116i
$609$	−15.2924	+	6.33431i	−0.619679	+	0.256679i
$610$	−4.02723	+	9.72260i	−0.163058	+	0.393657i
$611$	18.0979	+	7.49639i	0.732162	+	0.303271i
$612$	−0.575284	+	1.38886i	−0.0232545	+	0.0561413i
$613$	−21.9484	−	9.09133i	−0.886488	−	0.367195i	−0.107479	−	0.994207i	$-0.534278\pi$
$613$	−21.9484	−	9.09133i	−0.886488	−	0.367195i	−0.779010	+	0.627012i	$0.784278\pi$
$614$	−8.94625	+	8.94625i	−0.361041	+	0.361041i
$615$	−11.3272	−	4.69187i	−0.456756	−	0.189194i
$616$	11.6178	−	11.6178i	0.468096	−	0.468096i
$617$	27.7907	+	11.5113i	1.11881	+	0.463426i	0.863963	−	0.503555i	$-0.167975\pi$
$617$	27.7907	+	11.5113i	1.11881	+	0.463426i	0.254847	+	0.966981i	$0.417975\pi$
$618$	5.14332	+	2.13043i	0.206895	+	0.0856986i
$619$		−	29.7255i		−	1.19477i	−0.801955	−	0.597384i	$-0.796207\pi$
$619$		−	29.7255i		−	1.19477i	0.801955	−	0.597384i	$-0.203793\pi$
$620$	6.11533	−	2.53305i	0.245598	−	0.101730i
$621$	0.208656	−	0.208656i	0.00837308	−	0.00837308i
$622$	11.3019	−	11.3019i	0.453165	−	0.453165i
$623$		−	42.9566i		−	1.72102i
$624$	3.34308			0.133830
$625$	−1.18079			−0.0472315
$626$	5.24868	+	5.24868i	0.209780	+	0.209780i
$627$	14.6339	−	14.6339i	0.584421	−	0.584421i
$628$	−1.88518	−	4.55123i	−0.0752270	−	0.181614i
$629$	2.10181			0.0838047
$630$	−6.77330	−	6.77330i	−0.269855	−	0.269855i
$631$	−7.47789	+	18.0532i	−0.297690	+	0.718687i	0.702287	+	0.711894i	$0.252162\pi$
$631$	−7.47789	+	18.0532i	−0.297690	+	0.718687i	−0.999977	+	0.00679338i	$0.997838\pi$
$632$	5.00053	+	2.07129i	0.198910	+	0.0823914i
$633$	−13.3729	+	13.3729i	−0.531524	+	0.531524i
$634$	4.32458	−	10.4405i	0.171751	−	0.414644i
$635$	2.48611	+	6.00200i	0.0986583	+	0.238182i
$636$	3.10237	+	3.10237i	0.123017	+	0.123017i
$637$	−4.23726	−	10.2297i	−0.167886	−	0.405314i
$638$		−	28.7316i		−	1.13750i
$639$	−2.54494	+	1.05415i	−0.100676	+	0.0417014i
$640$	1.00411	−	1.00411i	0.0396908	−	0.0396908i
$641$	−4.95057	−	2.05059i	−0.195536	−	0.0809935i	0.282767	−	0.959189i	$-0.408748\pi$
$641$	−4.95057	−	2.05059i	−0.195536	−	0.0809935i	−0.478303	+	0.878195i	$0.658748\pi$
$642$	6.94211	+	6.94211i	0.273983	+	0.273983i
$643$	−11.5781	+	11.5781i	−0.456597	+	0.456597i	−0.897537	−	0.440940i	$-0.854645\pi$
$643$	−11.5781	+	11.5781i	−0.456597	+	0.456597i	0.440940	+	0.897537i	$0.354645\pi$
$644$	0.0747935	−	0.180567i	0.00294728	−	0.00711535i
$645$	2.27704	−	0.943181i	0.0896584	−	0.0371377i
$646$			3.02706i			0.119098i
$647$	−4.26100	−	10.2870i	−0.167517	−	0.404422i	0.817720	−	0.575616i	$-0.195238\pi$
$647$	−4.26100	−	10.2870i	−0.167517	−	0.404422i	−0.985237	+	0.171194i	$0.945238\pi$
$648$	−1.32273	−	1.32273i	−0.0519617	−	0.0519617i
$649$	−61.5377	−	25.4898i	−2.41557	−	1.00056i
$650$	−9.83571	−	4.07408i	−0.385788	−	0.159799i
$651$	9.81542	+	9.81542i	0.384697	+	0.384697i
$652$	4.66428	+	11.2606i	0.182667	+	0.440998i
$653$			27.5470i			1.07800i	0.842307	+	0.538998i	$0.181197\pi$
$653$			27.5470i			1.07800i	−0.842307	+	0.538998i	$0.818803\pi$
$654$	−2.34314	+	5.65685i	−0.0916242	+	0.221200i
$655$	−0.308511	+	0.744812i	−0.0120545	+	0.0291022i
$656$	−9.21559			−0.359808
$657$	−11.4151			−0.445344
$658$	12.3386	+	12.3386i	0.481008	+	0.481008i
$659$	32.5165	+	13.4688i	1.26666	+	0.524669i	0.911948	−	0.410305i	$-0.134578\pi$
$659$	32.5165	+	13.4688i	1.26666	+	0.524669i	0.354716	+	0.934974i	$0.384578\pi$
$660$	−6.35349	+	2.63170i	−0.247309	+	0.102439i
$661$	−12.9621	−	31.2934i	−0.504169	−	1.21717i	−0.947194	−	0.320662i	$-0.896095\pi$
$661$	−12.9621	−	31.2934i	−0.504169	−	1.21717i	0.443025	−	0.896509i	$-0.353905\pi$
$662$	−3.22420	−	3.22420i	−0.125312	−	0.125312i
$663$	2.18781	−	0.906221i	0.0849676	−	0.0351947i
$664$	−3.27744	+	3.27744i	−0.127189	+	0.127189i
$665$	−17.8200	−	7.38130i	−0.691031	−	0.286235i
$666$	−2.40979	+	5.81775i	−0.0933775	+	0.225433i
$667$	−0.130793	−	0.315762i	−0.00506432	−	0.0122263i
$668$	−18.2817	+	7.57251i	−0.707339	+	0.292989i
$669$	−11.0009	−	4.55672i	−0.425319	−	0.176173i
$670$	0.312984	−	0.129642i	0.0120916	−	0.00500852i
$671$	14.6597	−	35.3917i	0.565933	−	1.36628i
$672$	2.75125	+	1.13960i	0.106132	+	0.0439611i
$673$	−7.87860	+	3.26342i	−0.303698	+	0.125796i	−0.529328	−	0.848417i	$-0.677556\pi$
$673$	−7.87860	+	3.26342i	−0.303698	+	0.125796i	0.225630	+	0.974213i	$0.427556\pi$
$674$	−10.9453	+	10.9453i	−0.421599	+	0.421599i
$675$	−5.47923	−	13.2280i	−0.210896	−	0.509147i
$676$	−0.189092	−	0.189092i	−0.00727276	−	0.00727276i
$677$	−50.4403			−1.93858			−0.969289	−	0.245926i	$-0.920908\pi$
$677$	−50.4403			−1.93858			−0.969289	+	0.245926i	$0.920908\pi$
$678$	15.4136	−	6.38451i	0.591955	−	0.245196i
$679$	−5.77230	−	2.39096i	−0.221520	−	0.0917568i
$680$	0.384931	−	0.929306i	0.0147614	−	0.0356372i
$681$			11.3813i			0.436134i
$682$	−22.2607	+	9.22070i	−0.852408	+	0.353079i
$683$	4.17317	−	10.0749i	0.159682	−	0.385506i	−0.823707	−	0.567015i	$-0.808098\pi$
$683$	4.17317	−	10.0749i	0.159682	−	0.385506i	0.983389	+	0.181509i	$0.0580981\pi$
$684$	−8.37881	−	3.47062i	−0.320372	−	0.132702i
$685$	−5.14253	−	2.13011i	−0.196486	−	0.0813872i
$686$			12.3866i			0.472922i
$687$	5.77300	+	13.9372i	0.220254	+	0.531739i
$688$	1.30996	−	1.30996i	0.0499417	−	0.0499417i
$689$			16.7101i			0.636604i
$690$	−0.0578450	+	0.0578450i	−0.00220212	+	0.00220212i
$691$	5.43950	+	5.43950i	0.206928	+	0.206928i	0.802960	−	0.596032i	$-0.203257\pi$
$691$	5.43950	+	5.43950i	0.206928	+	0.206928i	−0.596032	+	0.802960i	$0.703257\pi$
$692$		−	1.01450i		−	0.0385656i
$693$	24.6558	+	24.6558i	0.936598	+	0.936598i
$694$	−32.6191	+	13.5113i	−1.23820	+	0.512881i
$695$	−15.7619	+	6.52881i	−0.597885	+	0.247652i
$696$	4.81115	−	1.99285i	0.182366	−	0.0755386i
$697$	−6.03097	+	2.49811i	−0.228439	+	0.0946226i
$698$	−5.03444	+	12.1542i	−0.190556	+	0.460044i
$699$	−6.68743	+	6.68743i	−0.252942	+	0.252942i
$700$	−6.70568	−	6.70568i	−0.253451	−	0.253451i
$701$	−18.8237	+	45.4445i	−0.710962	+	1.71642i	−0.0133800	+	0.999910i	$0.504259\pi$
$701$	−18.8237	+	45.4445i	−0.710962	+	1.71642i	−0.697582	+	0.716505i	$0.745741\pi$
$702$			17.1240i			0.646305i
$703$			12.6800i			0.478233i
$704$	−3.65510	+	3.65510i	−0.137757	+	0.137757i
$705$	−2.79497	−	6.74765i	−0.105265	−	0.254131i
$706$	4.44804	+	10.7385i	0.167404	+	0.404150i
$707$	15.0371	+	36.3029i	0.565530	+	1.36531i
$708$		−	12.0726i		−	0.453715i
$709$			24.8987i			0.935089i	0.883970	+	0.467544i	$0.154861\pi$
$709$			24.8987i			0.935089i	−0.883970	+	0.467544i	$0.845139\pi$
$710$	1.70285	−	0.705345i	0.0639070	−	0.0264711i
$711$	−4.39577	+	10.6123i	−0.164854	+	0.397993i
$712$			13.5146i			0.506482i
$713$	−0.202672	+	0.202672i	−0.00759011	+	0.00759011i
$714$	2.10942			0.0789429
$715$	−24.1982	−	10.0232i	−0.904960	−	0.374847i
$716$	16.8191			0.628561
$717$	−2.00200	+	0.829255i	−0.0747660	+	0.0309691i
$718$	1.12660	+	2.71985i	0.0420443	+	0.101504i
$719$	−30.6332			−1.14243			−0.571213	−	0.820802i	$-0.693527\pi$
$719$	−30.6332			−1.14243			−0.571213	+	0.820802i	$0.693527\pi$
$720$	2.13095	+	2.13095i	0.0794160	+	0.0794160i
$721$			18.8872i			0.703394i
$722$	0.738149			0.0274710
$723$	−9.75035	−	23.5394i	−0.362619	−	0.875440i
$724$	−5.36725	−	5.36725i	−0.199472	−	0.199472i
$725$	−16.5836			−0.615898
$726$	13.6064	−	5.63594i	0.504980	−	0.209169i
$727$	−6.25749	−	2.59194i	−0.232077	−	0.0961296i	0.263614	−	0.964628i	$-0.415085\pi$
$727$	−6.25749	−	2.59194i	−0.232077	−	0.0961296i	−0.495692	+	0.868499i	$0.665085\pi$
$728$	4.34034	+	10.4785i	0.160864	+	0.388360i
$729$	−6.73051	+	6.73051i	−0.249278	+	0.249278i
$730$	7.63798			0.282694
$731$	0.502182	−	1.21237i	0.0185739	−	0.0448413i
$732$	6.94321			0.256628
$733$			3.35990i			0.124101i	0.998073	+	0.0620504i	$0.0197640\pi$
$733$			3.35990i			0.124101i	−0.998073	+	0.0620504i	$0.980236\pi$
$734$	1.50172	+	3.62548i	0.0554296	+	0.133819i
$735$	−1.57983	+	3.81404i	−0.0582728	+	0.140683i
$736$	−0.0235309	+	0.0568085i	−0.000867359	+	0.00209399i
$737$	−1.13931	+	0.471918i	−0.0419671	+	0.0173833i
$738$		−	19.5577i		−	0.719929i
$739$	−8.64853			−0.318141			−0.159071	−	0.987267i	$-0.550850\pi$
$739$	−8.64853			−0.318141			−0.159071	+	0.987267i	$0.550850\pi$
$740$	1.61243	−	3.89274i	0.0592739	−	0.143100i
$741$	5.46712	+	13.1988i	0.200840	+	0.484869i
$742$	−5.69622	+	13.7519i	−0.209115	+	0.504848i
$743$	16.7063	−	6.91998i	0.612895	−	0.253870i	−0.0545705	−	0.998510i	$-0.517379\pi$
$743$	16.7063	−	6.91998i	0.612895	−	0.253870i	0.667466	+	0.744640i	$0.267379\pi$
$744$	−3.08804	−	3.08804i	−0.113213	−	0.113213i
$745$			18.5070i			0.678044i
$746$		−	16.9960i		−	0.622268i
$747$	−6.95552	−	6.95552i	−0.254489	−	0.254489i
$748$	−1.40121	+	3.38281i	−0.0512332	+	0.123688i
$749$	−12.7463	+	30.7723i	−0.465740	+	1.12440i
$750$	4.06460	+	9.81281i	0.148418	+	0.358313i
$751$	27.1868			0.992062			0.496031	−	0.868305i	$-0.334790\pi$
$751$	27.1868			0.992062			0.496031	+	0.868305i	$0.334790\pi$
$752$	−3.88185	−	3.88185i	−0.141557	−	0.141557i
$753$			16.4389i			0.599067i
$754$	18.3240	+	7.59004i	0.667320	+	0.276413i
$755$	−11.3594	−	11.3594i	−0.413411	−	0.413411i
$756$	−5.83732	+	14.0925i	−0.212301	+	0.512541i
$757$	24.2594	+	24.2594i	0.881722	+	0.881722i	0.993710	−	0.111988i	$-0.0357218\pi$
$757$	24.2594	+	24.2594i	0.881722	+	0.881722i	−0.111988	+	0.993710i	$0.535722\pi$
$758$	−22.1074	+	22.1074i	−0.802976	+	0.802976i
$759$	0.210565	−	0.210565i	0.00764301	−	0.00764301i
$760$	5.60638	+	2.32224i	0.203365	+	0.0842364i
$761$	7.66714			0.277934			0.138967	−	0.990297i	$-0.455622\pi$
$761$	7.66714			0.277934			0.138967	+	0.990297i	$0.455622\pi$
$762$	3.03081	−	3.03081i	0.109795	−	0.109795i
$763$	−20.7729			−0.752030
$764$	−3.34472	+	8.07486i	−0.121008	+	0.292138i
$765$	1.97221	+	0.816916i	0.0713054	+	0.0295357i
$766$	−9.89478	+	9.89478i	−0.357513	+	0.357513i
$767$	32.5129	−	32.5129i	1.17397	−	1.17397i
$768$	−0.865572	−	0.358532i	−0.0312336	−	0.0129374i
$769$	−14.2831	−	34.4825i	−0.515062	−	1.24347i	−0.940904	−	0.338672i	$-0.890022\pi$
$769$	−14.2831	−	34.4825i	−0.515062	−	1.24347i	0.425843	−	0.904797i	$-0.359978\pi$
$770$	−16.4976	−	16.4976i	−0.594531	−	0.594531i
$771$	−1.93214	−	4.66460i	−0.0695844	−	0.167992i
$772$	8.14141	+	19.6551i	0.293016	+	0.707402i
$773$	−1.67578			−0.0602734			−0.0301367	−	0.999546i	$-0.509594\pi$
$773$	−1.67578			−0.0602734			−0.0301367	+	0.999546i	$0.509594\pi$
$774$	2.78005	+	2.78005i	0.0999267	+	0.0999267i
$775$	5.32208	+	12.8486i	0.191175	+	0.461537i
$776$	1.81603	+	0.752224i	0.0651916	+	0.0270033i
$777$	8.83607			0.316992
$778$	7.99316	−	3.31087i	0.286569	−	0.118701i
$779$	−15.0708	−	36.3841i	−0.539966	−	1.30359i
$780$		−	4.74724i		−	0.169978i
$781$	−6.19865	+	2.56756i	−0.221805	+	0.0918747i
$782$			0.0435558i			0.00155755i
$783$	10.2078	+	24.6439i	0.364798	+	0.880701i
$784$			3.10304i			0.110823i
$785$	−6.46285	+	2.67700i	−0.230669	+	0.0955462i
$786$	0.531893			0.0189720
$787$	10.2309	+	4.23778i	0.364693	+	0.151061i	0.557502	−	0.830176i	$-0.311760\pi$
$787$	10.2309	+	4.23778i	0.364693	+	0.151061i	−0.192809	+	0.981236i	$0.561760\pi$
$788$	−19.7655			−0.704117
$789$	−25.4016	+	10.5217i	−0.904321	+	0.374582i
$790$	2.94127	−	7.10086i	0.104646	−	0.252637i
$791$	40.0231	+	40.0231i	1.42306	+	1.42306i
$792$	−7.75700	−	7.75700i	−0.275633	−	0.275633i
$793$	18.6989	+	18.6989i	0.664017	+	0.664017i
$794$	8.69009	−	8.69009i	0.308400	−	0.308400i
$795$	4.40543	−	4.40543i	0.156245	−	0.156245i
$796$	−0.329932	−	0.796526i	−0.0116941	−	0.0282321i
$797$	24.2263			0.858141			0.429070	−	0.903271i	$-0.358841\pi$
$797$	24.2263			0.858141			0.429070	+	0.903271i	$0.358841\pi$
$798$			12.7258i			0.450490i
$799$	−3.59268	−	1.48814i	−0.127100	−	0.0526464i
$800$	2.10968	+	2.10968i	0.0745885	+	0.0745885i
$801$	−28.6813			−1.01340
$802$	−9.25878	−	17.7560i	−0.326939	−	0.626986i
$803$	−27.8034			−0.981160
$804$	−0.158047	−	0.158047i	−0.00557388	−	0.00557388i
$805$	−0.256410	−	0.106208i	−0.00903725	−	0.00374335i
$806$		−	16.6329i		−	0.585869i
$807$	6.16125			0.216886
$808$	−4.73085	−	11.4213i	−0.166431	−	0.401800i
$809$	21.7651	−	21.7651i	0.765221	−	0.765221i	−0.212040	−	0.977261i	$-0.568011\pi$
$809$	21.7651	−	21.7651i	0.765221	−	0.765221i	0.977261	+	0.212040i	$0.0680106\pi$
$810$	−1.87830	+	1.87830i	−0.0659969	+	0.0659969i
$811$	−25.2939	−	25.2939i	−0.888187	−	0.888187i	0.106161	−	0.994349i	$-0.466144\pi$
$811$	−25.2939	−	25.2939i	−0.888187	−	0.888187i	−0.994349	+	0.106161i	$0.966144\pi$
$812$	12.4927	+	12.4927i	0.438409	+	0.438409i
$813$	10.2834	+	10.2834i	0.360654	+	0.360654i
$814$	−5.86947	+	14.1702i	−0.205725	+	0.496664i
$815$	15.9902	−	6.62338i	0.560114	−	0.232007i
$816$	−0.663646			−0.0232322
$817$	7.31409	+	3.02960i	0.255888	+	0.105992i
$818$	−23.2728			−0.813715
$819$	−22.2379	+	9.21125i	−0.777056	+	0.321867i
$820$			13.0863i			0.456995i
$821$	−12.2488	−	29.5712i	−0.427486	−	1.03204i	−0.980082	−	0.198593i	$-0.936363\pi$
$821$	−12.2488	−	29.5712i	−0.427486	−	1.03204i	0.552597	−	0.833449i	$-0.313637\pi$
$822$			3.67244i			0.128091i
$823$	−0.630546	+	0.261181i	−0.0219794	+	0.00910418i	−0.393646	−	0.919262i	$-0.628786\pi$
$823$	−0.630546	+	0.261181i	−0.0219794	+	0.00910418i	0.371667	+	0.928366i	$0.378786\pi$
$824$		−	5.94211i		−	0.207003i
$825$	−5.52935	−	13.3490i	−0.192507	−	0.464753i
$826$	37.8402	−	15.6739i	1.31663	−	0.545365i
$827$	17.8781			0.621683			0.310842	−	0.950462i	$-0.399389\pi$
$827$	17.8781			0.621683			0.310842	+	0.950462i	$0.399389\pi$
$828$	−0.120561	−	0.0499381i	−0.00418979	−	0.00173547i
$829$	15.8165	+	38.1844i	0.549330	+	1.32620i	0.917978	+	0.396631i	$0.129821\pi$
$829$	15.8165	+	38.1844i	0.549330	+	1.32620i	−0.368648	+	0.929569i	$0.620179\pi$
$830$	4.65404	+	4.65404i	0.161544	+	0.161544i
$831$	−13.2211			−0.458634
$832$	−1.36552	−	3.29666i	−0.0473409	−	0.114291i
$833$	0.841154	+	2.03073i	0.0291443	+	0.0703605i
$834$	7.95926	+	7.95926i	0.275607	+	0.275607i
$835$	10.7531	+	25.9603i	0.372127	+	0.898395i
$836$	−20.4081	−	8.45330i	−0.705828	−	0.292363i
$837$	15.8177	−	15.8177i	0.546739	−	0.546739i
$838$	10.0360	−	10.0360i	0.346688	−	0.346688i
$839$	−18.3436	−	7.59818i	−0.633292	−	0.262318i	0.0428591	−	0.999081i	$-0.486353\pi$
$839$	−18.3436	−	7.59818i	−0.633292	−	0.262318i	−0.676151	+	0.736763i	$0.736353\pi$
$840$	1.61826	−	3.90683i	0.0558353	−	0.134798i
$841$	1.89527			0.0653540
$842$	21.8645	−	21.8645i	0.753499	−	0.753499i
$843$	−18.1226			−0.624177
$844$	18.6495	+	7.72488i	0.641942	+	0.265901i
$845$	−0.268514	+	0.268514i	−0.00923717	+	0.00923717i
$846$	8.23823	−	8.23823i	0.283236	−	0.283236i
$847$	35.3305	+	35.3305i	1.21397	+	1.21397i
$848$	1.79209	−	4.32650i	0.0615407	−	0.148572i
$849$	5.45273	+	5.45273i	0.187137	+	0.187137i
$850$	1.95252	+	0.808761i	0.0669709	+	0.0277403i
$851$			0.182450i			0.00625430i
$852$	−0.859885	−	0.859885i	−0.0294592	−	0.0294592i
$853$	48.8779			1.67355			0.836773	−	0.547550i	$-0.184439\pi$
$853$	48.8779			1.67355			0.836773	+	0.547550i	$0.184439\pi$
$854$	9.01443	+	21.7628i	0.308467	+	0.744706i
$855$	−4.92835	+	11.8981i	−0.168546	+	0.406906i
$856$	4.01013	−	9.68131i	0.137063	−	0.330900i
$857$	−6.32460	−	6.32460i	−0.216044	−	0.216044i	0.590785	−	0.806829i	$-0.298818\pi$
$857$	−6.32460	−	6.32460i	−0.216044	−	0.216044i	−0.806829	+	0.590785i	$0.798818\pi$
$858$			17.2807i			0.589952i
$859$			47.3913i			1.61697i	0.588516	+	0.808485i	$0.299712\pi$
$859$			47.3913i			1.61697i	−0.588516	+	0.808485i	$0.700288\pi$
$860$	−1.86017	−	1.86017i	−0.0634313	−	0.0634313i
$861$	−25.3544	+	10.5021i	−0.864074	+	0.357911i
$862$	−8.72777	+	21.0707i	−0.297269	+	0.717671i
$863$	−12.3499	−	29.8153i	−0.420396	−	1.01493i	−0.982231	−	0.187677i	$-0.939904\pi$
$863$	−12.3499	−	29.8153i	−0.420396	−	1.01493i	0.561835	−	0.827250i	$-0.310096\pi$
$864$	1.83649	−	4.43367i	0.0624785	−	0.150836i
$865$	−1.44061			−0.0489823
$866$		−	20.4373i		−	0.694488i
$867$	14.2804	−	5.91514i	0.484988	−	0.200889i
$868$	5.66990	−	13.6884i	0.192449	−	0.464613i
$869$	−10.7067	+	25.8482i	−0.363199	+	0.876840i
$870$	−2.82988	−	6.83194i	−0.0959420	−	0.231624i
$871$		−	0.851277i		−	0.0288444i
$872$	6.53539			0.221316
$873$	−1.59640	+	3.85405i	−0.0540299	+	0.130440i
$874$	−0.262767			−0.00888822
$875$	−25.4801	+	25.4801i	−0.861385	+	0.861385i
$876$	−1.92846	−	4.65572i	−0.0651567	−	0.157302i
$877$	−35.9077	−	14.8735i	−1.21252	−	0.502241i	−0.317494	−	0.948260i	$-0.602841\pi$
$877$	−35.9077	−	14.8735i	−1.21252	−	0.502241i	−0.895024	+	0.446019i	$0.852841\pi$
$878$	−25.7547	+	10.6679i	−0.869178	+	0.360025i
$879$	−15.3119			−0.516457
$880$	5.19032	+	5.19032i	0.174966	+	0.174966i
$881$	−13.1392	−	31.7207i	−0.442669	−	1.06870i	−0.975009	−	0.222167i	$-0.928687\pi$
$881$	−13.1392	−	31.7207i	−0.442669	−	1.06870i	0.532339	−	0.846531i	$-0.321313\pi$
$882$	−6.58540			−0.221742
$883$			20.4559i			0.688397i	0.938897	+	0.344198i	$0.111849\pi$
$883$			20.4559i			0.688397i	−0.938897	+	0.344198i	$0.888151\pi$
$884$	−1.78728	−	1.78728i	−0.0601126	−	0.0601126i
$885$	−17.1433			−0.576266
$886$	10.8672	+	26.2358i	0.365091	+	0.881409i
$887$	−14.1547	+	5.86308i	−0.475269	+	0.196863i	−0.607442	−	0.794364i	$-0.707804\pi$
$887$	−14.1547	+	5.86308i	−0.475269	+	0.196863i	0.132173	+	0.991227i	$0.457804\pi$
$888$	−2.77993			−0.0932882
$889$	13.4347	+	5.56483i	0.450585	+	0.186638i
$890$	19.1911			0.643286
$891$	6.83731	−	6.83731i	0.229058	−	0.229058i
$892$			12.7094i			0.425542i
$893$	8.97773	−	21.6741i	0.300428	−	0.725298i
$894$	11.2809	−	4.67271i	0.377290	−	0.156279i
$895$		−	23.8835i		−	0.798338i
$896$		−	3.17853i		−	0.106187i
$897$	0.0786654	+	0.189915i	0.00262656	+	0.00634108i
$898$	15.7385	+	37.9960i	0.525199	+	1.26794i
$899$	−9.91507	−	23.9371i	−0.330686	−	0.798347i
$900$	−4.47725	+	4.47725i	−0.149242	+	0.149242i
$901$		−	3.31718i		−	0.110511i
$902$		−	47.6362i		−	1.58611i
$903$	2.11119	−	5.09685i	0.0702558	−	0.169613i
$904$	−12.5917	−	12.5917i	−0.418795	−	0.418795i
$905$	−7.62161	+	7.62161i	−0.253351	+	0.253351i
$906$	−4.05605	+	9.79217i	−0.134753	+	0.325323i
$907$	−37.1668	+	15.3950i	−1.23410	+	0.511182i	−0.901867	−	0.432015i	$-0.857803\pi$
$907$	−37.1668	+	15.3950i	−1.23410	+	0.511182i	−0.332235	+	0.943197i	$0.607803\pi$
$908$	11.2233	−	4.64884i	0.372458	−	0.154277i
$909$	24.2387	−	10.0400i	0.803947	−	0.333006i
$910$	14.8797	−	6.16338i	0.493258	−	0.204314i
$911$	26.9777	+	26.9777i	0.893811	+	0.893811i	0.994880	−	0.101068i	$-0.0322260\pi$
$911$	26.9777	+	26.9777i	0.893811	+	0.893811i	−0.101068	+	0.994880i	$0.532226\pi$
$912$		−	4.00369i		−	0.132575i
$913$	−16.9414	−	16.9414i	−0.560678	−	0.560678i
$914$	6.33314	−	6.33314i	0.209482	−	0.209482i
$915$		−	9.85951i		−	0.325945i
$916$	11.3857	−	11.3857i	0.376193	−	0.376193i
$917$	0.690561	+	1.66716i	0.0228043	+	0.0550545i
$918$		−	3.39935i		−	0.112195i
$919$	6.74355	+	2.79327i	0.222449	+	0.0921414i	0.491125	−	0.871089i	$-0.336586\pi$
$919$	6.74355	+	2.79327i	0.222449	+	0.0921414i	−0.268676	+	0.963231i	$0.586586\pi$
$920$	0.0806693	+	0.0334143i	0.00265959	+	0.00110164i
$921$	4.53611	−	10.9511i	0.149470	−	0.360852i
$922$	−33.4854	+	13.8701i	−1.10278	+	0.456788i
$923$		−	4.63154i		−	0.152449i
$924$	−5.89071	+	14.2214i	−0.193790	+	0.467851i
$925$	8.17885	+	3.38779i	0.268919	+	0.111390i
$926$	29.7702	−	12.3312i	0.978309	−	0.405229i
$927$	12.6106			0.414186
$928$	−3.93035	−	3.93035i	−0.129020	−	0.129020i
$929$	−3.41427	−	8.24277i	−0.112019	−	0.270437i	0.857921	−	0.513781i	$-0.171756\pi$
$929$	−3.41427	−	8.24277i	−0.112019	−	0.270437i	−0.969940	+	0.243344i	$0.921756\pi$
$930$	−4.38508	+	4.38508i	−0.143793	+	0.143793i
$931$	−12.2511	+	5.07457i	−0.401514	+	0.166312i
$932$	9.32613	+	3.86301i	0.305487	+	0.126537i
$933$	−5.73052	+	13.8347i	−0.187609	+	0.452928i
$934$	−0.295674	+	0.122472i	−0.00967473	+	0.00400741i
$935$	4.80367	+	1.98974i	0.157097	+	0.0650716i
$936$	6.99629	−	2.89796i	0.228681	−	0.0947228i
$937$	−8.40159	−	20.2832i	−0.274468	−	0.662624i	0.725196	−	0.688542i	$-0.241749\pi$
$937$	−8.40159	−	20.2832i	−0.274468	−	0.662624i	−0.999664	+	0.0259181i	$0.991749\pi$
$938$	0.290187	−	0.700574i	0.00947495	−	0.0228746i
$939$	−6.42493	−	2.66129i	−0.209670	−	0.0868481i
$940$	−5.51231	+	5.51231i	−0.179792	+	0.179792i
$941$	−26.1609	+	10.8362i	−0.852821	+	0.353250i	−0.765896	−	0.642965i	$-0.777704\pi$
$941$	−26.1609	+	10.8362i	−0.852821	+	0.353250i	−0.0869255	+	0.996215i	$0.527704\pi$
$942$	3.26352	+	3.26352i	0.106331	+	0.106331i
$943$	−0.216851	−	0.523524i	−0.00706163	−	0.0170483i
$944$	−11.9049	+	4.93119i	−0.387473	+	0.160496i
$945$	20.0117	+	8.28912i	0.650981	+	0.269645i
$946$	6.77130	+	6.77130i	0.220154	+	0.220154i
$947$	−52.5221			−1.70674			−0.853370	−	0.521306i	$-0.825445\pi$
$947$	−52.5221			−1.70674			−0.853370	+	0.521306i	$0.825445\pi$
$948$	−5.07094			−0.164697
$949$	7.34483	−	17.7320i	0.238423	−	0.575604i
$950$	−4.87915	+	11.7793i	−0.158300	+	0.382171i
$951$			10.5875i			0.343322i
$952$	−0.861617	−	2.08013i	−0.0279252	−	0.0674173i
$953$	38.4175	+	38.4175i	1.24446	+	1.24446i	0.958130	+	0.286333i	$0.0924364\pi$
$953$	38.4175	+	38.4175i	1.24446	+	1.24446i	0.286333	+	0.958130i	$0.407564\pi$
$954$	9.18186	+	3.80325i	0.297274	+	0.123135i
$955$	11.4665	+	4.74957i	0.371046	+	0.153692i
$956$	1.63548	+	1.63548i	0.0528952	+	0.0528952i
$957$	10.3012	+	24.8693i	0.332990	+	0.803910i
$958$			36.7444i			1.18716i
$959$	−11.5109	+	4.76796i	−0.371705	+	0.153965i
$960$	−0.509123	+	1.22913i	−0.0164319	+	0.0396700i
$961$	6.55628	−	6.55628i	0.211493	−	0.211493i
$962$	−7.48667	−	7.48667i	−0.241380	−	0.241380i
$963$	20.5461	+	8.51046i	0.662088	+	0.274246i
$964$	−19.2299	+	19.2299i	−0.619354	+	0.619354i
$965$	27.9106	−	11.5610i	0.898475	−	0.372161i
$966$			0.183110i			0.00589147i
$967$	−2.89960	−	7.00024i	−0.0932447	−	0.225113i	0.870375	−	0.492389i	$-0.163876\pi$
$967$	−2.89960	−	7.00024i	−0.0932447	−	0.225113i	−0.963620	+	0.267276i	$0.913876\pi$
$968$	−11.1154	−	11.1154i	−0.357262	−	0.357262i
$969$	−1.08530	−	2.62014i	−0.0348647	−	0.0841709i
$970$	1.06817	−	2.57880i	0.0342970	−	0.0828002i
$971$	−30.9160	+	30.9160i	−0.992142	+	0.992142i	−0.999969	−	0.00782771i	$-0.997508\pi$
$971$	−30.9160	+	30.9160i	−0.992142	+	0.992142i	0.00782771	+	0.999969i	$0.497508\pi$
$972$	14.9202	+	6.18013i	0.478564	+	0.198228i
$973$	−14.6139	+	35.2810i	−0.468499	+	1.13106i
$974$	−5.34846	−	5.34846i	−0.171376	−	0.171376i
$975$	9.97420			0.319430
$976$	−2.83604	−	6.84680i	−0.0907794	−	0.219161i
$977$	2.76247	−	2.76247i	0.0883794	−	0.0883794i	−0.661535	−	0.749914i	$-0.730095\pi$
$977$	2.76247	−	2.76247i	0.0883794	−	0.0883794i	0.749914	+	0.661535i	$0.230095\pi$
$978$	−8.07454	−	8.07454i	−0.258195	−	0.258195i
$979$	−69.8584			−2.23268
$980$	4.40638			0.140757
$981$			13.8697i			0.442824i
$982$	−11.9163	+	11.9163i	−0.380266	+	0.380266i
$983$	−29.0239	+	29.0239i	−0.925720	+	0.925720i	−0.997426	−	0.0717058i	$-0.977156\pi$
$983$	−29.0239	+	29.0239i	−0.925720	+	0.925720i	0.0717058	+	0.997426i	$0.477156\pi$
$984$	7.97676	−	3.30408i	0.254290	−	0.105330i
$985$			28.0675i			0.894303i
$986$	−3.63756	−	1.50673i	−0.115843	−	0.0479839i
$987$	−15.1037	−	6.25616i	−0.480756	−	0.199136i
$988$	10.7824	−	10.7824i	0.343034	−	0.343034i
$989$	0.105241	+	0.0435924i	0.00334648	+	0.00138616i
$990$	−11.0151	+	11.0151i	−0.350083	+	0.350083i
$991$	21.0320	+	8.71175i	0.668104	+	0.276738i	0.690844	−	0.723004i	$-0.257239\pi$
$991$	21.0320	+	8.71175i	0.668104	+	0.276738i	−0.0227401	+	0.999741i	$0.507239\pi$
$992$	−1.78381	+	4.30651i	−0.0566362	+	0.136732i
$993$	3.94676	+	1.63480i	0.125247	+	0.0518788i
$994$	1.57882	−	3.81161i	0.0500772	−	0.120897i
$995$	−1.13108	+	0.468510i	−0.0358578	+	0.0148528i
$996$	1.66180	−	4.01193i	0.0526560	−	0.127123i
$997$	−32.4007			−1.02614			−0.513071	−	0.858346i	$-0.671492\pi$
$997$	−32.4007			−1.02614			−0.513071	+	0.858346i	$0.671492\pi$
$998$	14.5727			0.461289
$999$		−	14.2394i		−	0.450516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	802.2.e.b.45.7	✓	68
401.303	even	8	inner	802.2.e.b.303.7	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
802.2.e.b.45.7	✓	68	1.1	even	1	trivial
802.2.e.b.303.7	yes	68	401.303	even	8	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:	\( N \)	\(=\)	\( 802 = 2 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	802.e (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.865572 - 0.358532i) q^{3} +1.00000i q^{4} +1.42002 q^{5} +(-0.358532 - 0.865572i) q^{6} +(2.24756 - 2.24756i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.50065 - 1.50065i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.865572 - 0.358532i) q^{3} +1.00000i q^{4} +1.42002 q^{5} +(-0.358532 - 0.865572i) q^{6} +(2.24756 - 2.24756i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.50065 - 1.50065i) q^{9} +(1.00411 + 1.00411i) q^{10} +(-3.65510 - 3.65510i) q^{11} +(0.358532 - 0.865572i) q^{12} +(3.29666 - 1.36552i) q^{13} +3.17853 q^{14} +(-1.22913 - 0.509123i) q^{15} -1.00000 q^{16} +(-0.654431 + 0.271074i) q^{17} -2.12224i q^{18} +(-1.63536 - 3.94810i) q^{19} +1.42002i q^{20} +(-2.75125 + 1.13960i) q^{21} -5.16909i q^{22} +(-0.0235309 - 0.0568085i) q^{23} +(0.865572 - 0.358532i) q^{24} -2.98354 q^{25} +(3.29666 + 1.36552i) q^{26} +(1.83649 + 4.43367i) q^{27} +(2.24756 + 2.24756i) q^{28} +5.55835 q^{29} +(-0.509123 - 1.22913i) q^{30} +(-1.78381 - 4.30651i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.85328 + 4.47422i) q^{33} +(-0.654431 - 0.271074i) q^{34} +(3.19158 - 3.19158i) q^{35} +(1.50065 - 1.50065i) q^{36} +(-2.74132 - 1.13549i) q^{37} +(1.63536 - 3.94810i) q^{38} -3.34308 q^{39} +(-1.00411 + 1.00411i) q^{40} +9.21559 q^{41} +(-2.75125 - 1.13960i) q^{42} +(-1.30996 + 1.30996i) q^{43} +(3.65510 - 3.65510i) q^{44} +(-2.13095 - 2.13095i) q^{45} +(0.0235309 - 0.0568085i) q^{46} +(3.88185 + 3.88185i) q^{47} +(0.865572 + 0.358532i) q^{48} -3.10304i q^{49} +(-2.10968 - 2.10968i) q^{50} +0.663646 q^{51} +(1.36552 + 3.29666i) q^{52} +(-1.79209 + 4.32650i) q^{53} +(-1.83649 + 4.43367i) q^{54} +(-5.19032 - 5.19032i) q^{55} +3.17853i q^{56} +4.00369i q^{57} +(3.93035 + 3.93035i) q^{58} +(11.9049 - 4.93119i) q^{59} +(0.509123 - 1.22913i) q^{60} +(2.83604 + 6.84680i) q^{61} +(1.78381 - 4.30651i) q^{62} -6.74560 q^{63} -1.00000i q^{64} +(4.68132 - 1.93907i) q^{65} +(-1.85328 + 4.47422i) q^{66} +(0.0912961 - 0.220408i) q^{67} +(-0.271074 - 0.654431i) q^{68} +0.0576084i q^{69} +4.51358 q^{70} +(0.496715 - 1.19918i) q^{71} +2.12224 q^{72} +(3.80337 - 3.80337i) q^{73} +(-1.13549 - 2.74132i) q^{74} +(2.58247 + 1.06969i) q^{75} +(3.94810 - 1.63536i) q^{76} -16.4301 q^{77} +(-2.36391 - 2.36391i) q^{78} +(-2.07129 - 5.00053i) q^{79} -1.42002 q^{80} +1.87062i q^{81} +(6.51641 + 6.51641i) q^{82} +4.63500 q^{83} +(-1.13960 - 2.75125i) q^{84} +(-0.929306 + 0.384931i) q^{85} -1.85256 q^{86} +(-4.81115 - 1.99285i) q^{87} +5.16909 q^{88} +(9.55629 - 9.55629i) q^{89} -3.01363i q^{90} +(4.34034 - 10.4785i) q^{91} +(0.0568085 - 0.0235309i) q^{92} +4.36715i q^{93} +5.48977i q^{94} +(-2.32224 - 5.60638i) q^{95} +(0.358532 + 0.865572i) q^{96} +(-0.752224 - 1.81603i) q^{97} +(2.19418 - 2.19418i) q^{98} +10.9701i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{6} + 20 q^{9}+O(q^{10}) \) 68 * q + 4 * q^6 + 20 * q^9	\( 68 q + 4 q^{6} + 20 q^{9} - 4 q^{10} + 12 q^{11} - 4 q^{12} - 8 q^{13} + 8 q^{14} - 4 q^{15} - 68 q^{16} + 4 q^{17} + 20 q^{19} - 40 q^{21} - 16 q^{23} + 20 q^{25} - 8 q^{26} - 12 q^{27} + 16 q^{29} - 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{35} - 20 q^{36} + 12 q^{37} - 20 q^{38} + 40 q^{39} + 4 q^{40} + 24 q^{41} - 40 q^{42} + 40 q^{43} - 12 q^{44} + 28 q^{45} + 16 q^{46} + 4 q^{47} - 8 q^{50} + 24 q^{51} + 4 q^{52} + 12 q^{53} + 12 q^{54} - 24 q^{55} - 4 q^{58} + 4 q^{59} + 4 q^{60} - 20 q^{61} + 8 q^{62} - 16 q^{63} + 36 q^{65} - 8 q^{66} + 48 q^{67} + 8 q^{68} - 16 q^{71} - 68 q^{72} + 40 q^{73} - 8 q^{74} - 96 q^{75} - 16 q^{77} + 32 q^{78} + 28 q^{79} - 16 q^{82} + 16 q^{83} - 4 q^{84} + 16 q^{85} - 32 q^{86} + 8 q^{87} + 8 q^{88} - 20 q^{89} - 4 q^{91} + 8 q^{92} - 24 q^{95} - 4 q^{96} + 24 q^{97} + 24 q^{98}+O(q^{100}) \) 68 * q + 4 * q^6 + 20 * q^9 - 4 * q^10 + 12 * q^11 - 4 * q^12 - 8 * q^13 + 8 * q^14 - 4 * q^15 - 68 * q^16 + 4 * q^17 + 20 * q^19 - 40 * q^21 - 16 * q^23 + 20 * q^25 - 8 * q^26 - 12 * q^27 + 16 * q^29 - 4 * q^30 - 8 * q^31 + 8 * q^33 + 4 * q^34 + 16 * q^35 - 20 * q^36 + 12 * q^37 - 20 * q^38 + 40 * q^39 + 4 * q^40 + 24 * q^41 - 40 * q^42 + 40 * q^43 - 12 * q^44 + 28 * q^45 + 16 * q^46 + 4 * q^47 - 8 * q^50 + 24 * q^51 + 4 * q^52 + 12 * q^53 + 12 * q^54 - 24 * q^55 - 4 * q^58 + 4 * q^59 + 4 * q^60 - 20 * q^61 + 8 * q^62 - 16 * q^63 + 36 * q^65 - 8 * q^66 + 48 * q^67 + 8 * q^68 - 16 * q^71 - 68 * q^72 + 40 * q^73 - 8 * q^74 - 96 * q^75 - 16 * q^77 + 32 * q^78 + 28 * q^79 - 16 * q^82 + 16 * q^83 - 4 * q^84 + 16 * q^85 - 32 * q^86 + 8 * q^87 + 8 * q^88 - 20 * q^89 - 4 * q^91 + 8 * q^92 - 24 * q^95 - 4 * q^96 + 24 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more