LMFDB - Embedded newform 385.2.i.b.221.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.i (of order $3$, 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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 12 x^{9} + 49 x^{8} - 38 x^{7} + 136 x^{6} - 34 x^{5} + 113 x^{4} + \cdots + 4 $ x^12 - 3x^11 + 13x^10 - 12x^9 + 49x^8 - 38x^7 + 136x^6 - 34x^5 + 113x^4 - 72x^3 + 58x^2 - 16*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.5
Root			$-0.528400 - 0.915215i$ of defining polynomial
Character	$\chi$	$=$	385.221
Dual form			385.2.i.b.331.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02840 + 1.78124i) q^{2} +(0.831041 - 1.43941i) q^{3} +(-1.11521 + 1.93160i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.41857 q^{6} +(-1.49699 + 2.18152i) q^{7} -0.473937 q^{8} +(0.118742 + 0.205667i) q^{9} +O(q^{10})$	\(q+(1.02840 + 1.78124i) q^{2} +(0.831041 - 1.43941i) q^{3} +(-1.11521 + 1.93160i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.41857 q^{6} +(-1.49699 + 2.18152i) q^{7} -0.473937 q^{8} +(0.118742 + 0.205667i) q^{9} +(-1.02840 + 1.78124i) q^{10} +(0.500000 - 0.866025i) q^{11} +(1.85357 + 3.21048i) q^{12} +1.53780 q^{13} +(-5.42531 - 0.423016i) q^{14} +1.66208 q^{15} +(1.74303 + 3.01901i) q^{16} +(0.944440 - 1.63582i) q^{17} +(-0.244228 + 0.423016i) q^{18} +(-1.54334 - 2.67314i) q^{19} -2.23042 q^{20} +(1.89604 + 3.96770i) q^{21} +2.05680 q^{22} +(-0.476369 - 0.825095i) q^{23} +(-0.393861 + 0.682188i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.58147 + 2.73919i) q^{26} +5.38096 q^{27} +(-2.54438 - 5.32444i) q^{28} -8.17403 q^{29} +(1.70928 + 2.96057i) q^{30} +(1.88999 - 3.27355i) q^{31} +(-4.05900 + 7.03039i) q^{32} +(-0.831041 - 1.43941i) q^{33} +3.88505 q^{34} +(-2.63775 - 0.205667i) q^{35} -0.529690 q^{36} +(-1.20410 - 2.08557i) q^{37} +(3.17434 - 5.49812i) q^{38} +(1.27797 - 2.21351i) q^{39} +(-0.236969 - 0.410442i) q^{40} +2.20800 q^{41} +(-5.11755 + 7.45768i) q^{42} -3.36988 q^{43} +(1.11521 + 1.93160i) q^{44} +(-0.118742 + 0.205667i) q^{45} +(0.979796 - 1.69706i) q^{46} +(-3.84444 - 6.65876i) q^{47} +5.79411 q^{48} +(-2.51807 - 6.53141i) q^{49} -2.05680 q^{50} +(-1.56974 - 2.71886i) q^{51} +(-1.71497 + 2.97041i) q^{52} +(-0.824497 + 1.42807i) q^{53} +(5.53378 + 9.58479i) q^{54} +1.00000 q^{55} +(0.709477 - 1.03390i) q^{56} -5.13031 q^{57} +(-8.40617 - 14.5599i) q^{58} +(3.66244 - 6.34354i) q^{59} +(-1.85357 + 3.21048i) q^{60} +(-5.53570 - 9.58811i) q^{61} +7.77465 q^{62} +(-0.626422 - 0.0488426i) q^{63} -9.72497 q^{64} +(0.768898 + 1.33177i) q^{65} +(1.70928 - 2.96057i) q^{66} +(1.95919 - 3.39342i) q^{67} +(2.10650 + 3.64857i) q^{68} -1.58353 q^{69} +(-2.34631 - 4.90997i) q^{70} -9.15592 q^{71} +(-0.0562762 - 0.0974733i) q^{72} +(-4.71466 + 8.16602i) q^{73} +(2.47660 - 4.28960i) q^{74} +(0.831041 + 1.43941i) q^{75} +6.88461 q^{76} +(1.14076 + 2.38719i) q^{77} +5.25706 q^{78} +(-3.22604 - 5.58766i) q^{79} +(-1.74303 + 3.01901i) q^{80} +(4.11557 - 7.12838i) q^{81} +(2.27071 + 3.93299i) q^{82} +10.8285 q^{83} +(-9.77851 - 0.762439i) q^{84} +1.88888 q^{85} +(-3.46558 - 6.00256i) q^{86} +(-6.79295 + 11.7657i) q^{87} +(-0.236969 + 0.410442i) q^{88} +(6.09894 + 10.5637i) q^{89} -0.488457 q^{90} +(-2.30206 + 3.35473i) q^{91} +2.12501 q^{92} +(-3.14131 - 5.44091i) q^{93} +(7.90723 - 13.6957i) q^{94} +(1.54334 - 2.67314i) q^{95} +(6.74638 + 11.6851i) q^{96} +12.1284 q^{97} +(9.04444 - 11.2022i) q^{98} +0.237484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9 - 3 * q^10 + 6 * q^11 - 9 * q^12 + 28 * q^13 - 3 * q^14 - 2 * q^15 - 11 * q^16 - 3 * q^17 + 9 * q^18 + 3 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^22 + 10 * q^23 + 10 * q^24 - 6 * q^25 + 17 * q^26 + 2 * q^27 - 10 * q^28 - 32 * q^29 - 5 * q^30 - 2 * q^31 + 26 * q^32 + q^33 + 60 * q^34 - 3 * q^35 + 16 * q^36 - 5 * q^37 - q^38 - 3 * q^39 - 9 * q^40 - 18 * q^41 - 56 * q^42 - 40 * q^43 + 5 * q^44 - q^45 + 20 * q^46 - q^47 + 82 * q^48 + 15 * q^49 - 6 * q^50 + 5 * q^51 - 23 * q^52 + 24 * q^53 + 7 * q^54 + 12 * q^55 - 66 * q^56 - 60 * q^57 - 31 * q^58 + 7 * q^59 + 9 * q^60 + 14 * q^61 + 48 * q^62 - 13 * q^63 + 30 * q^64 + 14 * q^65 - 5 * q^66 - q^67 + 25 * q^68 - 8 * q^69 - 15 * q^70 - 18 * q^71 + 26 * q^72 - 13 * q^73 + 40 * q^74 - q^75 - 20 * q^76 - 66 * q^78 + 4 * q^79 + 11 * q^80 + 26 * q^81 + 27 * q^82 + 16 * q^83 - 90 * q^84 - 6 * q^85 - 36 * q^86 + 2 * q^87 - 9 * q^88 + 13 * q^89 + 18 * q^90 + 17 * q^91 - 36 * q^92 + 36 * q^93 + q^94 - 3 * q^95 + 89 * q^96 - 6 * q^97 + 18 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.02840	+	1.78124i	0.727188	+	1.25953i	0.958067	+	0.286545i	$0.0925067\pi$
$2$	1.02840	+	1.78124i	0.727188	+	1.25953i	−0.230878	+	0.972983i	$0.574160\pi$
$3$	0.831041	−	1.43941i	0.479802	−	0.831041i	−0.519930	−	0.854209i	$-0.674042\pi$
$3$	0.831041	−	1.43941i	0.479802	−	0.831041i	0.999732	+	0.0231680i	$0.00737527\pi$
$4$	−1.11521	+	1.93160i	−0.557606	+	0.965802i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	3.41857			1.39563
$7$	−1.49699	+	2.18152i	−0.565807	+	0.824537i
$7$	−1.49699	+	2.18152i	−0.565807	+	0.824537i
$8$	−0.473937			−0.167562
$9$	0.118742	+	0.205667i	0.0395807	+	0.0685557i
$10$	−1.02840	+	1.78124i	−0.325209	+	0.563278i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	1.85357	+	3.21048i	0.535081	+	0.926787i
$13$	1.53780			0.426508			0.213254	−	0.976997i	$-0.431594\pi$
$13$	1.53780			0.426508			0.213254	+	0.976997i	$0.431594\pi$
$14$	−5.42531	−	0.423016i	−1.44998	−	0.113056i
$15$	1.66208			0.429148
$16$	1.74303	+	3.01901i	0.435757	+	0.754753i
$17$	0.944440	−	1.63582i	0.229060	−	0.396744i	−0.728470	−	0.685078i	$-0.759768\pi$
$17$	0.944440	−	1.63582i	0.229060	−	0.396744i	0.957530	+	0.288334i	$0.0931014\pi$
$18$	−0.244228	+	0.423016i	−0.0575652	+	0.0997058i
$19$	−1.54334	−	2.67314i	−0.354066	−	0.613261i	0.632891	−	0.774241i	$-0.281868\pi$
$19$	−1.54334	−	2.67314i	−0.354066	−	0.613261i	−0.986958	+	0.160980i	$0.948535\pi$
$20$	−2.23042			−0.498738
$21$	1.89604	+	3.96770i	0.413749	+	0.865824i
$22$	2.05680			0.438511
$23$	−0.476369	−	0.825095i	−0.0993298	−	0.172044i	0.812078	−	0.583549i	$-0.198337\pi$
$23$	−0.476369	−	0.825095i	−0.0993298	−	0.172044i	−0.911407	+	0.411505i	$0.865003\pi$
$24$	−0.393861	+	0.682188i	−0.0803966	+	0.139251i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.58147	+	2.73919i	0.310152	+	0.537198i
$27$	5.38096			1.03557
$28$	−2.54438	−	5.32444i	−0.480842	−	1.00623i
$29$	−8.17403			−1.51788			−0.758939	−	0.651161i	$-0.774282\pi$
$29$	−8.17403			−1.51788			−0.758939	+	0.651161i	$0.774282\pi$
$30$	1.70928	+	2.96057i	0.312071	+	0.540523i
$31$	1.88999	−	3.27355i	0.339452	−	0.587948i	−0.644878	−	0.764286i	$-0.723092\pi$
$31$	1.88999	−	3.27355i	0.339452	−	0.587948i	0.984330	+	0.176338i	$0.0564251\pi$
$32$	−4.05900	+	7.03039i	−0.717536	+	1.24281i
$33$	−0.831041	−	1.43941i	−0.144666	−	0.250568i
$34$	3.88505			0.666280
$35$	−2.63775	−	0.205667i	−0.445860	−	0.0347641i
$36$	−0.529690			−0.0882817
$37$	−1.20410	−	2.08557i	−0.197953	−	0.342865i	0.749911	−	0.661538i	$-0.230096\pi$
$37$	−1.20410	−	2.08557i	−0.197953	−	0.342865i	−0.947865	+	0.318673i	$0.896763\pi$
$38$	3.17434	−	5.49812i	0.514946	−	0.891913i
$39$	1.27797	−	2.21351i	0.204639	−	0.354446i
$40$	−0.236969	−	0.410442i	−0.0374680	−	0.0648965i
$41$	2.20800			0.344832			0.172416	−	0.985024i	$-0.444843\pi$
$41$	2.20800			0.344832			0.172416	+	0.985024i	$0.444843\pi$
$42$	−5.11755	+	7.45768i	−0.789655	+	1.15075i
$43$	−3.36988			−0.513901			−0.256951	−	0.966425i	$-0.582718\pi$
$43$	−3.36988			−0.513901			−0.256951	+	0.966425i	$0.582718\pi$
$44$	1.11521	+	1.93160i	0.168125	+	0.291200i
$45$	−0.118742	+	0.205667i	−0.0177010	+	0.0306590i
$46$	0.979796	−	1.69706i	0.144463	−	0.250217i
$47$	−3.84444	−	6.65876i	−0.560769	−	0.971280i	−0.997430	−	0.0716536i	$-0.977172\pi$
$47$	−3.84444	−	6.65876i	−0.560769	−	0.971280i	0.436661	−	0.899626i	$-0.356161\pi$
$48$	5.79411			0.836308
$49$	−2.51807	−	6.53141i	−0.359724	−	0.933059i
$50$	−2.05680			−0.290875
$51$	−1.56974	−	2.71886i	−0.219807	−	0.380717i
$52$	−1.71497	+	2.97041i	−0.237823	+	0.411922i
$53$	−0.824497	+	1.42807i	−0.113253	+	0.196161i	−0.917080	−	0.398703i	$-0.869461\pi$
$53$	−0.824497	+	1.42807i	−0.113253	+	0.196161i	0.803827	+	0.594863i	$0.202794\pi$
$54$	5.53378	+	9.58479i	0.753052	+	1.30432i
$55$	1.00000			0.134840
$56$	0.709477	−	1.03390i	0.0948079	−	0.138161i
$57$	−5.13031			−0.679527
$58$	−8.40617	−	14.5599i	−1.10378	−	1.91181i
$59$	3.66244	−	6.34354i	0.476810	−	0.825859i	−0.522837	−	0.852433i	$-0.675126\pi$
$59$	3.66244	−	6.34354i	0.476810	−	0.825859i	0.999647	+	0.0265740i	$0.00845977\pi$
$60$	−1.85357	+	3.21048i	−0.239295	+	0.414472i
$61$	−5.53570	−	9.58811i	−0.708774	−	1.22763i	−0.965312	−	0.261098i	$-0.915915\pi$
$61$	−5.53570	−	9.58811i	−0.708774	−	1.22763i	0.256539	−	0.966534i	$-0.417418\pi$
$62$	7.77465			0.987382
$63$	−0.626422	−	0.0488426i	−0.0789218	−	0.00615359i
$64$	−9.72497			−1.21562
$65$	0.768898	+	1.33177i	0.0953701	+	0.165186i
$66$	1.70928	−	2.96057i	0.210398	−	0.364421i
$67$	1.95919	−	3.39342i	0.239353	−	0.414572i	−0.721176	−	0.692752i	$-0.756398\pi$
$67$	1.95919	−	3.39342i	0.239353	−	0.414572i	0.960529	+	0.278180i	$0.0897313\pi$
$68$	2.10650	+	3.64857i	0.255451	+	0.442454i
$69$	−1.58353			−0.190634
$70$	−2.34631	−	4.90997i	−0.280438	−	0.586853i
$71$	−9.15592			−1.08661			−0.543304	−	0.839536i	$-0.682827\pi$
$71$	−9.15592			−1.08661			−0.543304	+	0.839536i	$0.682827\pi$
$72$	−0.0562762	−	0.0974733i	−0.00663222	−	0.0114873i
$73$	−4.71466	+	8.16602i	−0.551809	+	0.955761i	0.446335	+	0.894866i	$0.352729\pi$
$73$	−4.71466	+	8.16602i	−0.551809	+	0.955761i	−0.998144	+	0.0608951i	$0.980605\pi$
$74$	2.47660	−	4.28960i	0.287899	−	0.498655i
$75$	0.831041	+	1.43941i	0.0959603	+	0.166208i
$76$	6.88461			0.789719
$77$	1.14076	+	2.38719i	0.130002	+	0.272045i
$78$	5.25706			0.595245
$79$	−3.22604	−	5.58766i	−0.362958	−	0.628661i	0.625489	−	0.780233i	$-0.284900\pi$
$79$	−3.22604	−	5.58766i	−0.362958	−	0.628661i	−0.988446	+	0.151572i	$0.951566\pi$
$80$	−1.74303	+	3.01901i	−0.194876	+	0.337536i
$81$	4.11557	−	7.12838i	0.457286	−	0.792043i
$82$	2.27071	+	3.93299i	0.250758	+	0.434326i
$83$	10.8285			1.18859			0.594293	−	0.804249i	$-0.297432\pi$
$83$	10.8285			1.18859			0.594293	+	0.804249i	$0.297432\pi$
$84$	−9.77851	−	0.762439i	−1.06692	−	0.0831889i
$85$	1.88888			0.204878
$86$	−3.46558	−	6.00256i	−0.373703	−	0.647273i
$87$	−6.79295	+	11.7657i	−0.728281	+	1.26142i
$88$	−0.236969	+	0.410442i	−0.0252609	+	0.0437532i
$89$	6.09894	+	10.5637i	0.646486	+	1.11975i	0.983956	+	0.178411i	$0.0570955\pi$
$89$	6.09894	+	10.5637i	0.646486	+	1.11975i	−0.337470	+	0.941336i	$0.609571\pi$
$90$	−0.488457			−0.0514879
$91$	−2.30206	+	3.35473i	−0.241321	+	0.351672i
$92$	2.12501			0.221548
$93$	−3.14131	−	5.44091i	−0.325739	−	0.564197i
$94$	7.90723	−	13.6957i	0.815569	−	1.41261i
$95$	1.54334	−	2.67314i	0.158343	−	0.274259i
$96$	6.74638	+	11.6851i	0.688550	+	1.19260i
$97$	12.1284			1.23145			0.615725	−	0.787961i	$-0.288863\pi$
$97$	12.1284			1.23145			0.615725	+	0.787961i	$0.288863\pi$
$98$	9.04444	−	11.2022i	0.913626	−	1.13159i
$99$	0.237484			0.0238680
$100$	−1.11521	−	1.93160i	−0.111521	−	0.193160i
$101$	−6.08195	+	10.5342i	−0.605177	+	1.04820i	0.386847	+	0.922144i	$0.373564\pi$
$101$	−6.08195	+	10.5342i	−0.605177	+	1.04820i	−0.992024	+	0.126053i	$0.959769\pi$
$102$	3.22863	−	5.59216i	0.319682	−	0.553706i
$103$	0.903516	+	1.56494i	0.0890261	+	0.154198i	0.907100	−	0.420916i	$-0.138291\pi$
$103$	0.903516	+	1.56494i	0.0890261	+	0.154198i	−0.818074	+	0.575113i	$0.804958\pi$
$104$	−0.728819			−0.0714666
$105$	−2.48811	+	3.62587i	−0.242815	+	0.353848i
$106$	−3.39165			−0.329426
$107$	5.41115	+	9.37238i	0.523115	+	0.906063i	0.999638	+	0.0269004i	$0.00856369\pi$
$107$	5.41115	+	9.37238i	0.523115	+	0.906063i	−0.476523	+	0.879162i	$0.658103\pi$
$108$	−6.00092	+	10.3939i	−0.577438	+	1.00015i
$109$	−8.52069	+	14.7583i	−0.816134	+	1.41359i	0.0923760	+	0.995724i	$0.470554\pi$
$109$	−8.52069	+	14.7583i	−0.816134	+	1.41359i	−0.908510	+	0.417862i	$0.862780\pi$
$110$	1.02840	+	1.78124i	0.0980541	+	0.169835i
$111$	−4.00264			−0.379913
$112$	−9.19533	−	0.716967i	−0.868877	−	0.0677470i
$113$	17.2417			1.62196			0.810980	−	0.585074i	$-0.198935\pi$
$113$	17.2417			1.62196			0.810980	+	0.585074i	$0.198935\pi$
$114$	−5.27601	−	9.13832i	−0.494144	−	0.855883i
$115$	0.476369	−	0.825095i	0.0444216	−	0.0769406i
$116$	9.11577	−	15.7890i	0.846378	−	1.46597i
$117$	0.182601	+	0.316274i	0.0168815	+	0.0292396i
$118$	15.0658			1.38692
$119$	2.15476	+	4.50911i	0.197526	+	0.413349i
$120$	−0.787722			−0.0719089
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	11.3858	−	19.7208i	1.03082	−	1.78544i
$123$	1.83494	−	3.17821i	0.165451	−	0.286570i
$124$	4.21547	+	7.30142i	0.378561	+	0.655686i
$125$	−1.00000			−0.0894427
$126$	−0.557212	−	1.16604i	−0.0496404	−	0.103879i
$127$	5.39923			0.479104			0.239552	−	0.970884i	$-0.422999\pi$
$127$	5.39923			0.479104			0.239552	+	0.970884i	$0.422999\pi$
$128$	−1.88317	−	3.26174i	−0.166450	−	0.288300i
$129$	−2.80050	+	4.85062i	−0.246571	+	0.427073i
$130$	−1.58147	+	2.73919i	−0.138704	+	0.240242i
$131$	−6.96872	−	12.0702i	−0.608860	−	1.05458i	−0.991429	−	0.130649i	$-0.958294\pi$
$131$	−6.96872	−	12.0702i	−0.608860	−	1.05458i	0.382569	−	0.923927i	$-0.375040\pi$
$132$	3.70715			0.322666
$133$	8.14188	+	0.634829i	0.705990	+	0.0550466i
$134$	8.05932			0.696219
$135$	2.69048	+	4.66005i	0.231560	+	0.401073i
$136$	−0.447605	+	0.775275i	−0.0383818	+	0.0664793i
$137$	8.36109	−	14.4818i	0.714336	−	1.23727i	−0.248879	−	0.968535i	$-0.580062\pi$
$137$	8.36109	−	14.4818i	0.714336	−	1.23727i	0.963215	−	0.268732i	$-0.0866046\pi$
$138$	−1.62850	−	2.82065i	−0.138627	−	0.240109i
$139$	−14.5504			−1.23414			−0.617072	−	0.786906i	$-0.711681\pi$
$139$	−14.5504			−1.23414			−0.617072	+	0.786906i	$0.711681\pi$
$140$	3.33891	−	4.86572i	0.282190	−	0.411228i
$141$	−12.7795			−1.07623
$142$	−9.41595	−	16.3089i	−0.790169	−	1.36861i
$143$	0.768898	−	1.33177i	0.0642985	−	0.111368i
$144$	−0.413941	+	0.716967i	−0.0344951	+	0.0597472i
$145$	−4.08701	−	7.07891i	−0.339408	−	0.587872i
$146$	−19.3942			−1.60508
$147$	−11.4940	−	1.80335i	−0.948006	−	0.148738i
$148$	5.37132			0.441520
$149$	10.5806	+	18.3261i	0.866794	+	1.50133i	0.865255	+	0.501333i	$0.167157\pi$
$149$	10.5806	+	18.3261i	0.866794	+	1.50133i	0.00153970	+	0.999999i	$0.499510\pi$
$150$	−1.70928	+	2.96057i	−0.139563	+	0.241729i
$151$	4.30195	−	7.45119i	0.350087	−	0.606369i	−0.636177	−	0.771543i	$-0.719485\pi$
$151$	4.30195	−	7.45119i	0.350087	−	0.606369i	0.986264	+	0.165174i	$0.0528186\pi$
$152$	0.731446	+	1.26690i	0.0593281	+	0.102759i
$153$	0.448578			0.0362654
$154$	−3.07900	+	4.48695i	−0.248113	+	0.361569i
$155$	3.77997			0.303615
$156$	2.85042	+	4.93707i	0.228216	+	0.395282i
$157$	−2.70799	+	4.69037i	−0.216121	+	0.374332i	−0.953619	−	0.301017i	$-0.902674\pi$
$157$	−2.70799	+	4.69037i	−0.216121	+	0.374332i	0.737498	+	0.675349i	$0.236007\pi$
$158$	6.63531	−	11.4927i	0.527877	−	0.914310i
$159$	1.37038	+	2.37357i	0.108678	+	0.188236i
$160$	−8.11799			−0.641784
$161$	2.51308	+	0.195947i	0.198059	+	0.0154428i
$162$	16.9298			1.33013
$163$	−3.10470	−	5.37750i	−0.243179	−	0.421198i	0.718439	−	0.695590i	$-0.244857\pi$
$163$	−3.10470	−	5.37750i	−0.243179	−	0.421198i	−0.961618	+	0.274391i	$0.911524\pi$
$164$	−2.46239	+	4.26499i	−0.192281	+	0.333040i
$165$	0.831041	−	1.43941i	0.0646964	−	0.112058i
$166$	11.1361	+	19.2882i	0.864326	+	1.49706i
$167$	2.53431			0.196110			0.0980552	−	0.995181i	$-0.468738\pi$
$167$	2.53431			0.196110			0.0980552	+	0.995181i	$0.468738\pi$
$168$	−0.898602	−	1.88044i	−0.0693286	−	0.145079i
$169$	−10.6352			−0.818091
$170$	1.94252	+	3.36455i	0.148985	+	0.258049i
$171$	0.366518	−	0.634829i	0.0280284	−	0.0485466i
$172$	3.75813	−	6.50927i	0.286554	−	0.496327i
$173$	11.1649	+	19.3381i	0.848848	+	1.47025i	0.882237	+	0.470805i	$0.156037\pi$
$173$	11.1649	+	19.3381i	0.848848	+	1.47025i	−0.0333894	+	0.999442i	$0.510630\pi$
$174$	−27.9435			−2.11839
$175$	−1.14076	−	2.38719i	−0.0862333	−	0.180454i
$176$	3.48606			0.262771
$177$	−6.08728	−	10.5435i	−0.457548	−	0.792497i
$178$	−12.5443	+	21.7274i	−0.940235	+	1.62853i
$179$	−10.9455	+	18.9581i	−0.818104	+	1.41700i	0.0889740	+	0.996034i	$0.471641\pi$
$179$	−10.9455	+	18.9581i	−0.818104	+	1.41700i	−0.907078	+	0.420963i	$0.861692\pi$
$180$	−0.264845	−	0.458725i	−0.0197404	−	0.0341913i
$181$	−20.9562			−1.55766			−0.778829	−	0.627236i	$-0.784186\pi$
$181$	−20.9562			−1.55766			−0.778829	+	0.627236i	$0.784186\pi$
$182$	−8.34303	−	0.650512i	−0.618426	−	0.0482192i
$183$	−18.4016			−1.36028
$184$	0.225769	+	0.391043i	0.0166439	+	0.0288281i
$185$	1.20410	−	2.08557i	0.0885274	−	0.153334i
$186$	6.46105	−	11.1909i	0.473747	−	0.820554i
$187$	−0.944440	−	1.63582i	−0.0690643	−	0.119623i
$188$	17.1494			1.25075
$189$	−8.05522	+	11.7387i	−0.585931	+	0.853864i
$190$	6.34868			0.460582
$191$	1.24053	+	2.14865i	0.0897613	+	0.155471i	0.907410	−	0.420246i	$-0.138056\pi$
$191$	1.24053	+	2.14865i	0.0897613	+	0.155471i	−0.817649	+	0.575717i	$0.804723\pi$
$192$	−8.08185	+	13.9982i	−0.583257	+	1.01023i
$193$	−8.16449	+	14.1413i	−0.587693	+	1.01791i	0.406841	+	0.913499i	$0.366630\pi$
$193$	−8.16449	+	14.1413i	−0.587693	+	1.01791i	−0.994534	+	0.104415i	$0.966703\pi$
$194$	12.4728	+	21.6035i	0.895496	+	1.55104i
$195$	2.55594			0.183035
$196$	15.4243	+	2.42000i	1.10173	+	0.172857i
$197$	−24.9926			−1.78065			−0.890326	−	0.455324i	$-0.849523\pi$
$197$	−24.9926			−1.78065			−0.890326	+	0.455324i	$0.849523\pi$
$198$	0.244228	+	0.423016i	0.0173566	+	0.0300624i
$199$	6.65246	−	11.5224i	0.471581	−	0.816802i	−0.527891	−	0.849312i	$-0.677017\pi$
$199$	6.65246	−	11.5224i	0.471581	−	0.816802i	0.999471	+	0.0325106i	$0.0103503\pi$
$200$	0.236969	−	0.410442i	0.0167562	−	0.0290226i
$201$	−3.25633	−	5.64013i	−0.229684	−	0.397824i
$202$	−25.0187			−1.76031
$203$	12.2364	−	17.8318i	0.858827	−	1.25155i
$204$	7.00236			0.490263
$205$	1.10400	+	1.91219i	0.0771069	+	0.133553i
$206$	−1.85835	+	3.21876i	−0.129477	+	0.224262i
$207$	0.113130	−	0.195947i	0.00786308	−	0.0136193i
$208$	2.68042	+	4.64263i	0.185854	+	0.321908i
$209$	−3.08668			−0.213510
$210$	−9.01732	−	0.703087i	−0.622254	−	0.0485176i
$211$	1.59145			0.109560			0.0547800	−	0.998498i	$-0.482554\pi$
$211$	1.59145			0.109560			0.0547800	+	0.998498i	$0.482554\pi$
$212$	−1.83898	−	3.18520i	−0.126302	−	0.218761i
$213$	−7.60894	+	13.1791i	−0.521356	+	0.903015i
$214$	−11.1296	+	19.2771i	−0.760807	+	1.31776i
$215$	−1.68494	−	2.91840i	−0.114912	−	0.199033i
$216$	−2.55024			−0.173522
$217$	4.31204	+	9.02351i	0.292721	+	0.612556i
$218$	−35.0507			−2.37393
$219$	7.83614	+	13.5726i	0.529518	+	0.917151i
$220$	−1.11521	+	1.93160i	−0.0751876	+	0.130229i
$221$	1.45236	−	2.51555i	0.0976960	−	0.169214i
$222$	−4.11631	−	7.12966i	−0.276269	−	0.478511i
$223$	4.68366			0.313641			0.156821	−	0.987627i	$-0.449876\pi$
$223$	4.68366			0.313641			0.156821	+	0.987627i	$0.449876\pi$
$224$	−9.26068	−	19.3792i	−0.618755	−	1.29483i
$225$	−0.237484			−0.0158323
$226$	17.7313	+	30.7116i	1.17947	+	2.04290i
$227$	−0.709867	+	1.22953i	−0.0471155	+	0.0816065i	−0.888621	−	0.458641i	$-0.848336\pi$
$227$	−0.709867	+	1.22953i	−0.0471155	+	0.0816065i	0.841506	+	0.540248i	$0.181670\pi$
$228$	5.72139	−	9.90974i	0.378908	−	0.656288i
$229$	−6.50021	−	11.2587i	−0.429546	−	0.743996i	0.567287	−	0.823520i	$-0.307993\pi$
$229$	−6.50021	−	11.2587i	−0.429546	−	0.743996i	−0.996833	+	0.0795247i	$0.974660\pi$
$230$	1.95959			0.129212
$231$	4.38415	+	0.341836i	0.288456	+	0.0224911i
$232$	3.87397			0.254339
$233$	9.79161	+	16.9596i	0.641470	+	1.11106i	0.985105	+	0.171955i	$0.0550084\pi$
$233$	9.79161	+	16.9596i	0.641470	+	1.11106i	−0.343635	+	0.939103i	$0.611658\pi$
$234$	−0.375574	+	0.650512i	−0.0245520	+	0.0425253i
$235$	3.84444	−	6.65876i	0.250783	−	0.434370i
$236$	8.16881	+	14.1488i	0.531744	+	0.921008i
$237$	−10.7239			−0.696591
$238$	−5.81586	+	8.47531i	−0.376986	+	0.549373i
$239$	5.73323			0.370852			0.185426	−	0.982658i	$-0.440634\pi$
$239$	5.73323			0.370852			0.185426	+	0.982658i	$0.440634\pi$
$240$	2.89705	+	5.01785i	0.187004	+	0.323901i
$241$	9.07810	−	15.7237i	0.584772	−	1.01285i	−0.410132	−	0.912026i	$-0.634517\pi$
$241$	9.07810	−	15.7237i	0.584772	−	1.01285i	0.994904	−	0.100828i	$-0.0321492\pi$
$242$	1.02840	−	1.78124i	0.0661080	−	0.114502i
$243$	1.23102	+	2.13219i	0.0789701	+	0.136780i
$244$	24.6939			1.58087
$245$	4.39733	−	5.44642i	0.280935	−	0.347959i
$246$	7.54822			0.481257
$247$	−2.37334	−	4.11075i	−0.151012	−	0.261561i
$248$	−0.895735	+	1.55146i	−0.0568792	+	0.0985177i
$249$	8.99895	−	15.5866i	0.570285	−	0.987763i
$250$	−1.02840	−	1.78124i	−0.0650417	−	0.112656i
$251$	−0.546995			−0.0345260			−0.0172630	−	0.999851i	$-0.505495\pi$
$251$	−0.546995			−0.0345260			−0.0172630	+	0.999851i	$0.505495\pi$
$252$	0.792938	−	1.15553i	0.0499504	−	0.0727915i
$253$	−0.952738			−0.0598981
$254$	5.55256	+	9.61732i	0.348399	+	0.603444i
$255$	1.56974	−	2.71886i	0.0983007	−	0.170262i
$256$	−5.85167	+	10.1354i	−0.365730	+	0.633462i
$257$	3.61529	+	6.26187i	0.225516	+	0.390605i	0.956474	−	0.291817i	$-0.0942600\pi$
$257$	3.61529	+	6.26187i	0.225516	+	0.390605i	−0.730958	+	0.682422i	$0.760927\pi$
$258$	−11.5202			−0.717213
$259$	6.35224	+	0.495289i	0.394709	+	0.0307758i
$260$	−3.42994			−0.212716
$261$	−0.970600	−	1.68113i	−0.0600786	−	0.104059i
$262$	14.3333	−	24.8259i	0.885512	−	1.53375i
$263$	11.5262	−	19.9640i	0.710736	−	1.23103i	−0.253846	−	0.967245i	$-0.581695\pi$
$263$	11.5262	−	19.9640i	0.710736	−	1.23103i	0.964581	−	0.263786i	$-0.0849712\pi$
$264$	0.393861	+	0.682188i	0.0242405	+	0.0419857i
$265$	−1.64899			−0.101297
$266$	7.24232	+	15.1555i	0.444055	+	0.929243i
$267$	20.2739			1.24074
$268$	4.36982	+	7.56876i	0.266930	+	0.462335i
$269$	10.9211	−	18.9159i	0.665873	−	1.15333i	−0.313175	−	0.949695i	$-0.601393\pi$
$269$	10.9211	−	18.9159i	0.665873	−	1.15333i	0.979048	−	0.203630i	$-0.0652740\pi$
$270$	−5.53378	+	9.58479i	−0.336775	+	0.583312i
$271$	1.03545	+	1.79346i	0.0628993	+	0.108945i	0.895760	−	0.444538i	$-0.146632\pi$
$271$	1.03545	+	1.79346i	0.0628993	+	0.108945i	−0.832861	+	0.553482i	$0.813299\pi$
$272$	6.58474			0.399258
$273$	2.91572	+	6.10152i	0.176467	+	0.369281i
$274$	34.3942			2.07783
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	1.76597	−	3.05875i	0.106299	−	0.184115i
$277$	5.98891	−	10.3731i	0.359839	−	0.623259i	−0.628095	−	0.778137i	$-0.716165\pi$
$277$	5.98891	−	10.3731i	0.359839	−	0.623259i	0.987934	+	0.154878i	$0.0494984\pi$
$278$	−14.9636	−	25.9177i	−0.897456	−	1.55444i
$279$	0.897683			0.0537429
$280$	1.25013	+	0.0974733i	0.0747093	+	0.00582514i
$281$	−17.8620			−1.06556			−0.532779	−	0.846255i	$-0.678852\pi$
$281$	−17.8620			−1.06556			−0.532779	+	0.846255i	$0.678852\pi$
$282$	−13.1425	−	22.7634i	−0.782623	−	1.35554i
$283$	−4.32034	+	7.48304i	−0.256817	+	0.444821i	−0.965388	−	0.260820i	$-0.916007\pi$
$283$	−4.32034	+	7.48304i	−0.256817	+	0.444821i	0.708570	+	0.705640i	$0.249341\pi$
$284$	10.2108	−	17.6856i	0.605899	−	1.04945i
$285$	−2.56516	−	4.44298i	−0.151947	−	0.263180i
$286$	3.16294			0.187028
$287$	−3.30535	+	4.81681i	−0.195109	+	0.284327i
$288$	−1.92789			−0.113602
$289$	6.71607	+	11.6326i	0.395063	+	0.684269i
$290$	8.40617	−	14.5599i	0.493627	−	0.854987i
$291$	10.0792	−	17.4576i	0.590852	−	1.02338i
$292$	−10.5157	−	18.2137i	−0.615384	−	1.06588i
$293$	15.1338			0.884128			0.442064	−	0.896984i	$-0.354246\pi$
$293$	15.1338			0.884128			0.442064	+	0.896984i	$0.354246\pi$
$294$	−8.60819	−	22.3281i	−0.502040	−	1.30220i
$295$	7.32489			0.426472
$296$	0.570669	+	0.988428i	0.0331695	+	0.0574512i
$297$	2.69048	−	4.66005i	0.156118	−	0.270404i
$298$	−21.7621	+	37.6931i	−1.26065	+	2.18350i
$299$	−0.732559	−	1.26883i	−0.0423650	−	0.0733783i
$300$	−3.70715			−0.214032
$301$	5.04466	−	7.35145i	0.290769	−	0.423731i
$302$	17.6965			1.01832
$303$	10.1087	+	17.5088i	0.580730	+	1.00585i
$304$	5.38017	−	9.31872i	0.308574	−	0.534466i
$305$	5.53570	−	9.58811i	0.316973	−	0.549014i
$306$	0.461318	+	0.799026i	0.0263718	+	0.0456773i
$307$	−14.4369			−0.823959			−0.411979	−	0.911193i	$-0.635162\pi$
$307$	−14.4369			−0.823959			−0.411979	+	0.911193i	$0.635162\pi$
$308$	−5.88329	−	0.458725i	−0.335232	−	0.0261383i
$309$	3.00343			0.170859
$310$	3.88733	+	6.73304i	0.220785	+	0.382411i
$311$	−13.6171	+	23.5855i	−0.772155	+	1.33741i	0.164225	+	0.986423i	$0.447488\pi$
$311$	−13.6171	+	23.5855i	−0.772155	+	1.33741i	−0.936380	+	0.350989i	$0.885846\pi$
$312$	−0.605678	+	1.04907i	−0.0342898	+	0.0593916i
$313$	−3.77096	−	6.53149i	−0.213147	−	0.369182i	0.739551	−	0.673101i	$-0.235038\pi$
$313$	−3.77096	−	6.53149i	−0.213147	−	0.369182i	−0.952698	+	0.303919i	$0.901705\pi$
$314$	−11.1396			−0.628642
$315$	−0.270912	−	0.566919i	−0.0152642	−	0.0319423i
$316$	14.3909			0.809550
$317$	14.5166	+	25.1434i	0.815331	+	1.41220i	0.909090	+	0.416600i	$0.136779\pi$
$317$	14.5166	+	25.1434i	0.815331	+	1.41220i	−0.0937585	+	0.995595i	$0.529888\pi$
$318$	−2.81860	+	4.88196i	−0.158059	+	0.273767i
$319$	−4.08701	+	7.07891i	−0.228829	+	0.396343i
$320$	−4.86249	−	8.42207i	−0.271821	−	0.470808i
$321$	17.9875			1.00397
$322$	2.23542	+	4.67791i	0.124575	+	0.260690i
$323$	−5.83037			−0.324410
$324$	9.17948	+	15.8993i	0.509971	+	0.883296i
$325$	−0.768898	+	1.33177i	−0.0426508	+	0.0738733i
$326$	6.38575	−	11.0604i	0.353674	−	0.612581i
$327$	14.1621	+	24.5295i	0.783165	+	1.35648i
$328$	−1.04646			−0.0577808
$329$	20.2813	+	1.58135i	1.11814	+	0.0871826i
$330$	3.41857			0.188186
$331$	5.04134	+	8.73185i	0.277097	+	0.479946i	0.970662	−	0.240448i	$-0.0772943\pi$
$331$	5.04134	+	8.73185i	0.277097	+	0.479946i	−0.693565	+	0.720394i	$0.743961\pi$
$332$	−12.0761	+	20.9164i	−0.662763	+	1.14794i
$333$	0.285955	−	0.495289i	0.0156702	−	0.0271417i
$334$	2.60628	+	4.51421i	0.142609	+	0.247006i
$335$	3.91838			0.214084
$336$	−8.67370	+	12.6400i	−0.473189	+	0.689567i
$337$	−32.3875			−1.76426			−0.882131	−	0.471004i	$-0.843892\pi$
$337$	−32.3875			−1.76426			−0.882131	+	0.471004i	$0.843892\pi$
$338$	−10.9372	−	18.9438i	−0.594906	−	1.03041i
$339$	14.3285	−	24.8177i	0.778219	−	1.34791i
$340$	−2.10650	+	3.64857i	−0.114241	+	0.197871i
$341$	−1.88999	−	3.27355i	−0.102349	−	0.177273i
$342$	1.50771			0.0815276
$343$	18.0179	+	4.28421i	0.972876	+	0.231326i
$344$	1.59711			0.0861104
$345$	−0.791764	−	1.37138i	−0.0426272	−	0.0738324i
$346$	−22.9639	+	39.7746i	−1.23454	+	2.13829i
$347$	12.9879	−	22.4957i	0.697227	−	1.20763i	−0.272197	−	0.962241i	$-0.587750\pi$
$347$	12.9879	−	22.4957i	0.697227	−	1.20763i	0.969424	−	0.245391i	$-0.0789163\pi$
$348$	−15.1512	−	26.2426i	−0.812188	−	1.40675i
$349$	−34.1782			−1.82952			−0.914758	−	0.404002i	$-0.867619\pi$
$349$	−34.1782			−1.82952			−0.914758	+	0.404002i	$0.867619\pi$
$350$	3.07900	−	4.48695i	0.164579	−	0.239838i
$351$	8.27482			0.441677
$352$	4.05900	+	7.03039i	0.216345	+	0.374721i
$353$	0.353201	−	0.611763i	0.0187990	−	0.0325608i	−0.856473	−	0.516192i	$-0.827349\pi$
$353$	0.353201	−	0.611763i	0.0187990	−	0.0325608i	0.875272	+	0.483631i	$0.160682\pi$
$354$	12.5203	−	21.6858i	0.665447	−	1.15259i
$355$	−4.57796	−	7.92926i	−0.242973	−	0.420841i
$356$	−27.2064			−1.44194
$357$	8.28113	+	0.645686i	0.438284	+	0.0341733i
$358$	−45.0253			−2.37966
$359$	13.4217	+	23.2471i	0.708373	+	1.22694i	0.965461	+	0.260549i	$0.0839037\pi$
$359$	13.4217	+	23.2471i	0.708373	+	1.22694i	−0.257088	+	0.966388i	$0.582763\pi$
$360$	0.0562762	−	0.0974733i	0.00296602	−	0.00513729i
$361$	4.73620	−	8.20335i	0.249274	−	0.431755i
$362$	−21.5513	−	37.3280i	−1.13271	−	1.96191i
$363$	−1.66208			−0.0872367
$364$	−3.91274	−	8.18791i	−0.205083	−	0.429163i
$365$	−9.42931			−0.493553
$366$	−18.9242	−	32.7776i	−0.989182	−	1.71331i
$367$	−7.47596	+	12.9487i	−0.390242	+	0.675919i	−0.992481	−	0.122397i	$-0.960942\pi$
$367$	−7.47596	+	12.9487i	−0.390242	+	0.675919i	0.602239	+	0.798316i	$0.294275\pi$
$368$	1.66065	−	2.87633i	0.0865673	−	0.149939i
$369$	0.262183	+	0.454114i	0.0136487	+	0.0236402i
$370$	4.95320			0.257505
$371$	−1.88111	−	3.93646i	−0.0976621	−	0.204371i
$372$	14.0129			0.726536
$373$	−1.28156	−	2.21972i	−0.0663566	−	0.114933i	0.830938	−	0.556364i	$-0.187804\pi$
$373$	−1.28156	−	2.21972i	−0.0663566	−	0.114933i	−0.897295	+	0.441432i	$0.854471\pi$
$374$	1.94252	−	3.36455i	0.100445	−	0.173977i
$375$	−0.831041	+	1.43941i	−0.0429148	+	0.0743306i
$376$	1.82202	+	3.15583i	0.0939636	+	0.162750i
$377$	−12.5700			−0.647387
$378$	−29.1934	−	2.27623i	−1.50155	−	0.117077i
$379$	12.0592			0.619438			0.309719	−	0.950828i	$-0.399765\pi$
$379$	12.0592			0.619438			0.309719	+	0.950828i	$0.399765\pi$
$380$	3.44230	+	5.96224i	0.176586	+	0.305857i
$381$	4.48698	−	7.77167i	0.229875	−	0.398155i
$382$	−2.55151	+	4.41935i	−0.130547	+	0.226114i
$383$	−13.5544	−	23.4769i	−0.692598	−	1.19961i	−0.970984	−	0.239145i	$-0.923133\pi$
$383$	−13.5544	−	23.4769i	−0.692598	−	1.19961i	0.278386	−	0.960469i	$-0.410201\pi$
$384$	−6.25995			−0.319452
$385$	−1.49699	+	2.18152i	−0.0762935	+	0.111181i
$386$	−33.5854			−1.70945
$387$	−0.400146	−	0.693073i	−0.0203405	−	0.0352309i
$388$	−13.5257	+	23.4272i	−0.686664	+	1.18934i
$389$	−10.5248	+	18.2295i	−0.533628	+	0.924271i	0.465600	+	0.884995i	$0.345839\pi$
$389$	−10.5248	+	18.2295i	−0.533628	+	0.924271i	−0.999228	+	0.0392761i	$0.987495\pi$
$390$	2.62853	+	4.55275i	0.133101	+	0.230537i
$391$	−1.79961			−0.0910101
$392$	1.19341	+	3.09548i	0.0602761	+	0.156345i
$393$	−23.1652			−1.16853
$394$	−25.7024	−	44.5179i	−1.29487	−	2.24278i
$395$	3.22604	−	5.58766i	0.162320	−	0.281146i
$396$	−0.264845	+	0.458725i	−0.0133090	+	0.0230518i
$397$	5.71023	+	9.89041i	0.286588	+	0.496385i	0.972993	−	0.230834i	$-0.0741455\pi$
$397$	5.71023	+	9.89041i	0.286588	+	0.496385i	−0.686405	+	0.727220i	$0.740812\pi$
$398$	27.3656			1.37171
$399$	7.68001	−	11.1919i	0.384481	−	0.560295i
$400$	−3.48606			−0.174303
$401$	−3.95890	−	6.85702i	−0.197698	−	0.342423i	0.750084	−	0.661343i	$-0.230013\pi$
$401$	−3.95890	−	6.85702i	−0.197698	−	0.342423i	−0.947782	+	0.318920i	$0.896680\pi$
$402$	6.69763	−	11.6006i	0.334047	−	0.578587i
$403$	2.90642	−	5.03406i	0.144779	−	0.250764i
$404$	−13.5653	−	23.4958i	−0.674900	−	1.16896i
$405$	8.23115			0.409009
$406$	44.3467	+	3.45774i	2.20089	+	0.171605i
$407$	−2.40821			−0.119370
$408$	0.743956	+	1.28857i	0.0368313	+	0.0637937i
$409$	12.6021	−	21.8275i	0.623134	−	1.07930i	−0.365764	−	0.930707i	$-0.619192\pi$
$409$	12.6021	−	21.8275i	0.623134	−	1.07930i	0.988899	−	0.148592i	$-0.0474742\pi$
$410$	−2.27071	+	3.93299i	−0.112142	+	0.194236i
$411$	−13.8968	−	24.0700i	−0.685480	−	1.18729i
$412$	−4.03045			−0.198566
$413$	8.35594	+	17.4859i	0.411169	+	0.860424i
$414$	0.465372			0.0228718
$415$	5.41427	+	9.37778i	0.265776	+	0.460337i
$416$	−6.24191	+	10.8113i	−0.306035	+	0.530068i
$417$	−12.0919	+	20.9439i	−0.592145	+	1.02562i
$418$	−3.17434	−	5.49812i	−0.155262	−	0.268922i
$419$	21.9670			1.07316			0.536580	−	0.843849i	$-0.319716\pi$
$419$	21.9670			1.07316			0.536580	+	0.843849i	$0.319716\pi$
$420$	−4.22897	−	8.84966i	−0.206352	−	0.431819i
$421$	22.7516			1.10884			0.554422	−	0.832235i	$-0.312939\pi$
$421$	22.7516			1.10884			0.554422	+	0.832235i	$0.312939\pi$
$422$	1.63665	+	2.83475i	0.0796707	+	0.137994i
$423$	0.912992	−	1.58135i	0.0443912	−	0.0768878i
$424$	0.390760	−	0.676816i	0.0189770	−	0.0328691i
$425$	0.944440	+	1.63582i	0.0458121	+	0.0793488i
$426$	−31.3001			−1.51650
$427$	29.2035	+	2.27702i	1.41326	+	0.110193i
$428$	−24.1383			−1.16677
$429$	−1.27797	−	2.21351i	−0.0617010	−	0.106869i
$430$	3.46558	−	6.00256i	0.167125	−	0.289469i
$431$	13.7206	−	23.7648i	0.660898	−	1.14471i	−0.319482	−	0.947592i	$-0.603509\pi$
$431$	13.7206	−	23.7648i	0.660898	−	1.14471i	0.980380	−	0.197117i	$-0.0631578\pi$
$432$	9.37917	+	16.2452i	0.451255	+	0.781597i
$433$	11.5414			0.554646			0.277323	−	0.960777i	$-0.410553\pi$
$433$	11.5414			0.554646			0.277323	+	0.960777i	$0.410553\pi$
$434$	−11.6385	+	16.9606i	−0.558668	+	0.814133i
$435$	−13.5859			−0.651394
$436$	−19.0048	−	32.9172i	−0.910163	−	1.57645i
$437$	−1.47040	+	2.54681i	−0.0703387	+	0.121830i
$438$	−16.1174	+	27.9161i	−0.770118	+	1.33388i
$439$	3.25267	+	5.63379i	0.155241	+	0.268886i	0.933147	−	0.359495i	$-0.117051\pi$
$439$	3.25267	+	5.63379i	0.155241	+	0.268886i	−0.777905	+	0.628381i	$0.783718\pi$
$440$	−0.473937			−0.0225941
$441$	1.04430	−	1.29344i	0.0497284	−	0.0615922i
$442$	5.97441			0.284174
$443$	−9.56743	−	16.5713i	−0.454562	−	0.787325i	0.544101	−	0.839020i	$-0.316871\pi$
$443$	−9.56743	−	16.5713i	−0.454562	−	0.787325i	−0.998663	+	0.0516952i	$0.983538\pi$
$444$	4.46379	−	7.73151i	0.211842	−	0.366921i
$445$	−6.09894	+	10.5637i	−0.289117	+	0.500766i
$446$	4.81668	+	8.34273i	0.228076	+	0.395040i
$447$	35.1716			1.66356
$448$	14.5581	−	21.2152i	0.687808	−	1.00233i
$449$	−37.8605			−1.78675			−0.893373	−	0.449315i	$-0.851668\pi$
$449$	−37.8605			−1.78675			−0.893373	+	0.449315i	$0.851668\pi$
$450$	−0.244228	−	0.423016i	−0.0115130	−	0.0199412i
$451$	1.10400	−	1.91219i	0.0519854	−	0.0900414i
$452$	−19.2281	+	33.3041i	−0.904415	+	1.56649i
$453$	−7.15019	−	12.3845i	−0.335945	−	0.581874i
$454$	−2.92011			−0.137047
$455$	−4.05631	−	0.316274i	−0.190163	−	0.0148272i
$456$	2.43145			0.113863
$457$	4.61128	+	7.98697i	0.215707	+	0.373615i	0.953491	−	0.301422i	$-0.0974612\pi$
$457$	4.61128	+	7.98697i	0.215707	+	0.373615i	−0.737784	+	0.675037i	$0.764128\pi$
$458$	13.3696	−	23.1569i	0.624722	−	1.08205i
$459$	5.08199	−	8.80227i	0.237207	−	0.410855i
$460$	1.06251	+	1.84031i	0.0495396	+	0.0858050i
$461$	−32.8271			−1.52891			−0.764455	−	0.644677i	$-0.776992\pi$
$461$	−32.8271			−1.52891			−0.764455	+	0.644677i	$0.776992\pi$
$462$	3.89977	+	8.16077i	0.181434	+	0.379673i
$463$	13.0795			0.607856			0.303928	−	0.952695i	$-0.401702\pi$
$463$	13.0795			0.607856			0.303928	+	0.952695i	$0.401702\pi$
$464$	−14.2476	−	24.6775i	−0.661426	−	1.14562i
$465$	3.14131	−	5.44091i	0.145675	−	0.252316i
$466$	−20.1394	+	34.8824i	−0.932939	+	1.61590i
$467$	13.0651	+	22.6294i	0.604580	+	1.04716i	0.992118	+	0.125310i	$0.0399925\pi$
$467$	13.0651	+	22.6294i	0.604580	+	1.04716i	−0.387537	+	0.921854i	$0.626674\pi$
$468$	−0.814555			−0.0376528
$469$	4.46993	+	9.35391i	0.206402	+	0.431923i
$470$	15.8145			0.729467
$471$	4.50090	+	7.79578i	0.207390	+	0.359211i
$472$	−1.73577	+	3.00644i	−0.0798952	+	0.138383i
$473$	−1.68494	+	2.91840i	−0.0774735	+	0.134188i
$474$	−11.0284	−	19.1018i	−0.506553	−	0.877375i
$475$	3.08668			0.141627
$476$	−11.1128	−	0.866476i	−0.509356	−	0.0397149i
$477$	−0.391610			−0.0179306
$478$	5.89605	+	10.2123i	0.269679	+	0.467098i
$479$	8.65671	−	14.9939i	0.395535	−	0.685087i	−0.597634	−	0.801769i	$-0.703893\pi$
$479$	8.65671	−	14.9939i	0.395535	−	0.685087i	0.993169	+	0.116682i	$0.0372258\pi$
$480$	−6.74638	+	11.6851i	−0.307929	+	0.533348i
$481$	−1.85167	−	3.20718i	−0.0844287	−	0.146235i
$482$	37.3436			1.70096
$483$	2.37052	−	3.45450i	0.107862	−	0.157185i
$484$	2.23042			0.101383
$485$	6.06419	+	10.5035i	0.275360	+	0.476938i
$486$	−2.53197	+	4.38550i	−0.114852	+	0.198930i
$487$	−15.0465	+	26.0612i	−0.681820	+	1.18095i	0.292605	+	0.956234i	$0.405478\pi$
$487$	−15.0465	+	26.0612i	−0.681820	+	1.18095i	−0.974425	+	0.224714i	$0.927855\pi$
$488$	2.62357	+	4.54416i	0.118764	+	0.205705i
$489$	−10.3205			−0.466711
$490$	14.2236	+	2.23162i	0.642557	+	0.100814i
$491$	17.1429			0.773647			0.386823	−	0.922154i	$-0.373572\pi$
$491$	17.1429			0.773647			0.386823	+	0.922154i	$0.373572\pi$
$492$	4.09270	+	7.08877i	0.184513	+	0.319586i
$493$	−7.71987	+	13.3712i	−0.347686	+	0.602209i
$494$	4.88149	−	8.45499i	0.219629	−	0.380408i
$495$	0.118742	+	0.205667i	0.00533705	+	0.00924405i
$496$	13.1772			0.591674
$497$	13.7063	−	19.9738i	0.614811	−	0.895949i
$498$	37.0181			1.65882
$499$	−0.642884	−	1.11351i	−0.0287794	−	0.0498475i	0.851277	−	0.524717i	$-0.175829\pi$
$499$	−0.642884	−	1.11351i	−0.0287794	−	0.0498475i	−0.880056	+	0.474869i	$0.842495\pi$
$500$	1.11521	−	1.93160i	0.0498738	−	0.0863840i
$501$	2.10611	−	3.64789i	0.0940941	−	0.162976i
$502$	−0.562529	−	0.974329i	−0.0251069	−	0.0434864i
$503$	−1.47083			−0.0655812			−0.0327906	−	0.999462i	$-0.510439\pi$
$503$	−1.47083			−0.0655812			−0.0327906	+	0.999462i	$0.510439\pi$
$504$	0.296885	+	0.0231483i	0.0132243	+	0.00103111i
$505$	−12.1639			−0.541286
$506$	−0.979796	−	1.69706i	−0.0435572	−	0.0754433i
$507$	−8.83827	+	15.3083i	−0.392521	+	0.679867i
$508$	−6.02128	+	10.4292i	−0.267151	+	0.462720i
$509$	−12.2001	−	21.1312i	−0.540760	−	0.936623i	−0.998861	−	0.0477230i	$-0.984804\pi$
$509$	−12.2001	−	21.1312i	−0.540760	−	0.936623i	0.458101	−	0.888900i	$-0.348530\pi$
$510$	6.45726			0.285932
$511$	−10.7566	−	22.5095i	−0.475843	−	0.995764i
$512$	−31.6041			−1.39672
$513$	−8.30466	−	14.3841i	−0.366659	−	0.635073i
$514$	−7.43593	+	12.8794i	−0.327985	+	0.568086i
$515$	−0.903516	+	1.56494i	−0.0398137	+	0.0689593i
$516$	−6.24631	−	10.8189i	−0.274979	−	0.476277i
$517$	−7.68887			−0.338156
$518$	5.65041	+	11.8242i	0.248265	+	0.519526i
$519$	37.1138			1.62911
$520$	−0.364409	−	0.631176i	−0.0159804	−	0.0276789i
$521$	−6.67954	+	11.5693i	−0.292636	+	0.506860i	−0.974432	−	0.224682i	$-0.927866\pi$
$521$	−6.67954	+	11.5693i	−0.292636	+	0.506860i	0.681796	+	0.731542i	$0.261199\pi$
$522$	1.99633	−	3.45774i	0.0873770	−	0.151341i
$523$	−14.2851	−	24.7425i	−0.624644	−	1.08191i	−0.988610	−	0.150502i	$-0.951911\pi$
$523$	−14.2851	−	24.7425i	−0.624644	−	1.08191i	0.363966	−	0.931412i	$-0.381422\pi$
$524$	31.0864			1.35802
$525$	−4.38415	−	0.341836i	−0.191340	−	0.0149189i
$526$	47.4142			2.06736
$527$	−3.56996	−	6.18335i	−0.155510	−	0.269351i
$528$	2.89705	−	5.01785i	0.126078	−	0.218374i
$529$	11.0461	−	19.1325i	0.480267	−	0.831847i
$530$	−1.69582	−	2.93725i	−0.0736619	−	0.127586i
$531$	1.73954			0.0754898
$532$	−10.3062	+	15.0189i	−0.446829	+	0.651152i
$533$	3.39546			0.147074
$534$	20.8496	+	36.1126i	0.902252	+	1.56275i
$535$	−5.41115	+	9.37238i	−0.233944	+	0.405204i
$536$	−0.928533	+	1.60827i	−0.0401065	+	0.0694665i
$537$	18.1923	+	31.5100i	0.785055	+	1.35976i
$538$	44.9251			1.93686
$539$	−6.91540	−	1.08500i	−0.297867	−	0.0467340i
$540$	−12.0018			−0.516477
$541$	−15.1907	−	26.3111i	−0.653099	−	1.13120i	−0.982367	−	0.186964i	$-0.940135\pi$
$541$	−15.1907	−	26.3111i	−0.653099	−	1.13120i	0.329268	−	0.944237i	$-0.393198\pi$
$542$	−2.12972	+	3.68878i	−0.0914793	+	0.158447i
$543$	−17.4154	+	30.1644i	−0.747367	+	1.29448i
$544$	7.66695	+	13.2796i	0.328718	+	0.569356i
$545$	−17.0414			−0.729973
$546$	−7.86975	+	11.4684i	−0.336794	+	0.490802i
$547$	18.4132			0.787291			0.393646	−	0.919262i	$-0.371214\pi$
$547$	18.4132			0.787291			0.393646	+	0.919262i	$0.371214\pi$
$548$	18.6488	+	32.3006i	0.796637	+	1.37982i
$549$	1.31464	−	2.27702i	0.0561074	−	0.0971809i
$550$	−1.02840	+	1.78124i	−0.0438511	+	0.0759524i
$551$	12.6153	+	21.8503i	0.537430	+	0.930856i
$552$	0.750493			0.0319431
$553$	17.0189	+	1.32698i	0.723719	+	0.0564289i
$554$	24.6360			1.04668
$555$	−2.00132	−	3.46639i	−0.0849512	−	0.147140i
$556$	16.2267	−	28.1055i	0.688167	−	1.19194i
$557$	−8.45681	+	14.6476i	−0.358327	+	0.620640i	−0.987681	−	0.156478i	$-0.949986\pi$
$557$	−8.45681	+	14.6476i	−0.358327	+	0.620640i	0.629355	+	0.777118i	$0.283319\pi$
$558$	0.923177	+	1.59899i	0.0390812	+	0.0676906i
$559$	−5.18218			−0.219183
$560$	−3.97675	−	8.32187i	−0.168048	−	0.351663i
$561$	−3.13947			−0.132549
$562$	−18.3693	−	31.8165i	−0.774861	−	1.34210i
$563$	10.6690	−	18.4793i	0.449646	−	0.778809i	−0.548717	−	0.836008i	$-0.684884\pi$
$563$	10.6690	−	18.4793i	0.449646	−	0.778809i	0.998363	+	0.0571987i	$0.0182169\pi$
$564$	14.2519	−	24.6850i	0.600113	−	1.03943i
$565$	8.62083	+	14.9317i	0.362681	+	0.628182i
$566$	−17.7721			−0.747019
$567$	9.38976	+	19.6493i	0.394333	+	0.825193i
$568$	4.33933			0.182074
$569$	12.6630	+	21.9329i	0.530859	+	0.919475i	0.999352	+	0.0360077i	$0.0114641\pi$
$569$	12.6630	+	21.9329i	0.530859	+	0.919475i	−0.468492	+	0.883468i	$0.655203\pi$
$570$	5.27601	−	9.13832i	0.220988	−	0.382762i
$571$	−12.5542	+	21.7446i	−0.525379	+	0.909983i	0.474184	+	0.880426i	$0.342743\pi$
$571$	−12.5542	+	21.7446i	−0.525379	+	0.909983i	−0.999563	+	0.0295573i	$0.990590\pi$
$572$	1.71497	+	2.97041i	0.0717065	+	0.124199i
$573$	4.12371			0.172271
$574$	−11.9791	−	0.934021i	−0.499999	−	0.0389853i
$575$	0.952738			0.0397319
$576$	−1.15476	−	2.00011i	−0.0481151	−	0.0833378i
$577$	5.86116	−	10.1518i	0.244003	−	0.422626i	−0.717848	−	0.696200i	$-0.754873\pi$
$577$	5.86116	−	10.1518i	0.244003	−	0.422626i	0.961851	+	0.273574i	$0.0882059\pi$
$578$	−13.8136	+	23.9259i	−0.574570	+	0.995185i
$579$	13.5700	+	23.5040i	0.563952	+	0.976793i
$580$	18.2315			0.757024
$581$	−16.2102	+	23.6227i	−0.672511	+	0.980033i
$582$	41.4617			1.71864
$583$	0.824497	+	1.42807i	0.0341472	+	0.0591446i
$584$	2.23445	−	3.87018i	0.0924622	−	0.160149i
$585$	−0.182601	+	0.316274i	−0.00754962	+	0.0130763i
$586$	15.5636	+	26.9570i	0.642927	+	1.11358i
$587$	−28.2807			−1.16727			−0.583634	−	0.812017i	$-0.698370\pi$
$587$	−28.2807			−1.16727			−0.583634	+	0.812017i	$0.698370\pi$
$588$	16.3016	−	20.1907i	0.672265	−	0.832649i
$589$	−11.6676			−0.480754
$590$	7.53291	+	13.0474i	0.310125	+	0.537153i
$591$	−20.7699	+	35.9745i	−0.854360	+	1.47979i
$592$	4.19757	−	7.27041i	0.172519	−	0.298812i
$593$	12.3375	+	21.3691i	0.506639	+	0.877525i	0.999970	+	0.00768348i	$0.00244575\pi$
$593$	12.3375	+	21.3691i	0.506639	+	0.877525i	−0.493331	+	0.869842i	$0.664221\pi$
$594$	11.0676			0.454108
$595$	−2.82763	+	4.12063i	−0.115921	+	0.168929i
$596$	−47.1983			−1.93332
$597$	−11.0569	−	19.1512i	−0.452530	−	0.783806i
$598$	1.50673	−	2.60973i	0.0616146	−	0.106720i
$599$	−2.13362	+	3.69554i	−0.0871774	+	0.150996i	−0.906317	−	0.422599i	$-0.861118\pi$
$599$	−2.13362	+	3.69554i	−0.0871774	+	0.150996i	0.819140	+	0.573594i	$0.194451\pi$
$600$	−0.393861	−	0.682188i	−0.0160793	−	0.0278502i
$601$	29.4863			1.20277			0.601385	−	0.798959i	$-0.294616\pi$
$601$	29.4863			1.20277			0.601385	+	0.798959i	$0.294616\pi$
$602$	18.2826	+	1.42551i	0.745145	+	0.0580995i
$603$	0.930552			0.0378950
$604$	9.59516	+	16.6193i	0.390422	+	0.676230i
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$	−20.7916	+	36.0120i	−0.844600	+	1.46289i
$607$	−17.0268	−	29.4914i	−0.691098	−	1.19702i	−0.971478	−	0.237128i	$-0.923794\pi$
$607$	−17.0268	−	29.4914i	−0.691098	−	1.19702i	0.280380	−	0.959889i	$-0.409539\pi$
$608$	25.0576			1.01622
$609$	−15.4982	−	32.4321i	−0.628021	−	1.31421i
$610$	22.7716			0.921997
$611$	−5.91196	−	10.2398i	−0.239172	−	0.414259i
$612$	−0.500260	+	0.866476i	−0.0202218	+	0.0350252i
$613$	−7.84473	+	13.5875i	−0.316846	+	0.548793i	−0.979828	−	0.199842i	$-0.935957\pi$
$613$	−7.84473	+	13.5875i	−0.316846	+	0.548793i	0.662983	+	0.748635i	$0.269290\pi$
$614$	−14.8469	−	25.7156i	−0.599173	−	1.03780i
$615$	3.66988			0.147984
$616$	−0.540648	−	1.13138i	−0.0217833	−	0.0455845i
$617$	−17.9888			−0.724200			−0.362100	−	0.932139i	$-0.617940\pi$
$617$	−17.9888			−0.724200			−0.362100	+	0.932139i	$0.617940\pi$
$618$	3.08873	+	5.34984i	0.124247	+	0.215202i
$619$	4.70238	−	8.14476i	0.189005	−	0.327365i	−0.755914	−	0.654671i	$-0.772807\pi$
$619$	4.70238	−	8.14476i	0.189005	−	0.327365i	0.944919	+	0.327305i	$0.106141\pi$
$620$	−4.21547	+	7.30142i	−0.169298	+	0.293232i
$621$	−2.56332	−	4.43981i	−0.102863	−	0.178163i
$622$	−56.0153			−2.24601
$623$	−32.1749	−	2.50870i	−1.28906	−	0.100509i
$624$	8.91016			0.356692
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.75610	−	13.4340i	0.309996	−	0.536929i
$627$	−2.56516	+	4.44298i	−0.102443	+	0.177436i
$628$	−6.03996	−	10.4615i	−0.241021	−	0.417460i
$629$	−4.54881			−0.181373
$630$	0.731213	−	1.06558i	0.0291322	−	0.0424537i
$631$	41.7606			1.66246			0.831231	−	0.555927i	$-0.187637\pi$
$631$	41.7606			1.66246			0.831231	+	0.555927i	$0.187637\pi$
$632$	1.52894	+	2.64820i	0.0608179	+	0.105340i
$633$	1.32256	−	2.29074i	0.0525670	−	0.0910488i
$634$	−29.8577	+	51.7150i	−1.18580	+	2.05386i
$635$	2.69961	+	4.67587i	0.107131	+	0.185556i
$636$	−6.11306			−0.242399
$637$	−3.87227	−	10.0440i	−0.153425	−	0.397957i
$638$	−16.8123			−0.665607
$639$	−1.08719	−	1.88307i	−0.0430086	−	0.0744932i
$640$	1.88317	−	3.26174i	0.0744387	−	0.128932i
$641$	−5.43432	+	9.41252i	−0.214643	+	0.371772i	−0.953162	−	0.302460i	$-0.902192\pi$
$641$	−5.43432	+	9.41252i	−0.214643	+	0.371772i	0.738519	+	0.674232i	$0.235525\pi$
$642$	18.4984	+	32.0401i	0.730073	+	1.26452i
$643$	−43.1506			−1.70169			−0.850846	−	0.525415i	$-0.823910\pi$
$643$	−43.1506			−1.70169			−0.850846	+	0.525415i	$0.823910\pi$
$644$	−3.18111	+	4.63576i	−0.125353	+	0.182674i
$645$	−5.60101			−0.220540
$646$	−5.99595	−	10.3853i	−0.235907	−	0.408604i
$647$	−4.43555	+	7.68260i	−0.174380	+	0.302034i	−0.939946	−	0.341322i	$-0.889125\pi$
$647$	−4.43555	+	7.68260i	−0.174380	+	0.302034i	0.765567	+	0.643356i	$0.222459\pi$
$648$	−1.95052	+	3.37841i	−0.0766238	+	0.132716i
$649$	−3.66244	−	6.34354i	−0.143764	−	0.249006i
$650$	−3.16294			−0.124061
$651$	16.5720	+	1.29213i	0.649507	+	0.0506426i
$652$	13.8496			0.542393
$653$	19.1540	+	33.1757i	0.749554	+	1.29827i	0.948037	+	0.318161i	$0.103065\pi$
$653$	19.1540	+	33.1757i	0.749554	+	1.29827i	−0.198483	+	0.980104i	$0.563601\pi$
$654$	−29.1286	+	50.4522i	−1.13902	+	1.97284i
$655$	6.96872	−	12.0702i	0.272290	−	0.471621i
$656$	3.84861	+	6.66599i	0.150263	+	0.260263i
$657$	−2.23931			−0.0873638
$658$	18.0405	+	37.7521i	0.703292	+	1.47173i
$659$	18.4905			0.720288			0.360144	−	0.932897i	$-0.382727\pi$
$659$	18.4905			0.720288			0.360144	+	0.932897i	$0.382727\pi$
$660$	1.85357	+	3.21048i	0.0721503	+	0.124968i
$661$	10.9394	−	18.9475i	0.425492	−	0.736973i	−0.570974	−	0.820968i	$-0.693434\pi$
$661$	10.9394	−	18.9475i	0.425492	−	0.736973i	0.996466	+	0.0839944i	$0.0267678\pi$
$662$	−10.3690	+	17.9597i	−0.403003	+	0.698022i
$663$	−2.41393	−	4.18106i	−0.0937494	−	0.162379i
$664$	−5.13204			−0.199162
$665$	3.52116	+	7.36849i	0.136545	+	0.285738i
$666$	1.17631			0.0455809
$667$	3.89385	+	6.74435i	0.150771	+	0.261142i
$668$	−2.82629	+	4.89528i	−0.109352	+	0.189404i
$669$	3.89231	−	6.74169i	0.150486	−	0.260649i
$670$	4.02966	+	6.97958i	0.155679	+	0.269645i
$671$	−11.0714			−0.427407
$672$	−35.5905	−	2.77502i	−1.37293	−	0.107049i
$673$	−20.2680			−0.781272			−0.390636	−	0.920545i	$-0.627745\pi$
$673$	−20.2680			−0.781272			−0.390636	+	0.920545i	$0.627745\pi$
$674$	−33.3073	−	57.6900i	−1.28295	−	2.22214i
$675$	−2.69048	+	4.66005i	−0.103557	+	0.179365i
$676$	11.8605	−	20.5430i	0.456173	−	0.790114i
$677$	11.6074	+	20.1046i	0.446108	+	0.772682i	0.998129	−	0.0611488i	$-0.0194764\pi$
$677$	11.6074	+	20.1046i	0.446108	+	0.772682i	−0.552021	+	0.833830i	$0.686143\pi$
$678$	58.9418			2.26365
$679$	−18.1560	+	26.4583i	−0.696763	+	1.01538i
$680$	−0.895210			−0.0343297
$681$	1.17986	+	2.04357i	0.0452122	+	0.0783099i
$682$	3.88733	−	6.73304i	0.148853	−	0.257822i
$683$	−7.64419	+	13.2401i	−0.292497	+	0.506620i	−0.974400	−	0.224823i	$-0.927819\pi$
$683$	−7.64419	+	13.2401i	−0.292497	+	0.506620i	0.681903	+	0.731443i	$0.261153\pi$
$684$	0.817492	+	1.41594i	0.0312576	+	0.0541397i
$685$	16.7222			0.638922
$686$	10.8984	+	36.5001i	0.416103	+	1.39358i
$687$	−21.6078			−0.824388
$688$	−5.87379	−	10.1737i	−0.223936	−	0.387869i
$689$	−1.26791	+	2.19608i	−0.0483035	+	0.0836640i
$690$	1.62850	−	2.82065i	0.0619960	−	0.107380i
$691$	−13.4955	−	23.3750i	−0.513394	−	0.889225i	−0.999879	−	0.0155361i	$-0.995054\pi$
$691$	−13.4955	−	23.3750i	−0.513394	−	0.889225i	0.486485	−	0.873689i	$-0.338279\pi$
$692$	−49.8047			−1.89329
$693$	−0.355510	+	0.518076i	−0.0135047	+	0.0196801i
$694$	53.4270			2.02806
$695$	−7.27518	−	12.6010i	−0.275963	−	0.477982i
$696$	3.21943	−	5.57622i	0.122032	−	0.211366i
$697$	2.08533	−	3.61189i	0.0789874	−	0.136810i
$698$	−35.1488	−	60.8796i	−1.33040	−	2.30433i
$699$	32.5489			1.23111
$700$	5.88329	+	0.458725i	0.222368	+	0.0173382i
$701$	49.9046			1.88487			0.942435	−	0.334390i	$-0.108530\pi$
$701$	49.9046			1.88487			0.942435	+	0.334390i	$0.108530\pi$
$702$	8.50983	+	14.7395i	0.321183	+	0.556305i
$703$	−3.71668	+	6.43748i	−0.140177	+	0.242794i
$704$	−4.86249	+	8.42207i	−0.183262	+	0.317419i
$705$	−6.38977	−	11.0674i	−0.240653	−	0.416822i
$706$	1.45293			0.0546817
$707$	−13.8761	−	29.0375i	−0.521864	−	1.09207i
$708$	27.1544			1.02053
$709$	−13.5871	−	23.5335i	−0.510273	−	0.883820i	−0.999929	−	0.0119037i	$-0.996211\pi$
$709$	−13.5871	−	23.5335i	−0.510273	−	0.883820i	0.489656	−	0.871916i	$-0.337122\pi$
$710$	9.41595	−	16.3089i	0.353374	−	0.612062i
$711$	0.766132	−	1.32698i	0.0287322	−	0.0497656i
$712$	−2.89051	−	5.00652i	−0.108327	−	0.187627i
$713$	−3.60133			−0.134871
$714$	7.36619	+	15.4147i	0.275673	+	0.576881i
$715$	1.53780			0.0575103
$716$	−24.4131	−	42.2847i	−0.912359	−	1.58025i
$717$	4.76455	−	8.25244i	0.177935	−	0.308193i
$718$	−27.6058	+	47.8147i	−1.03024	+	1.78443i
$719$	11.1329	+	19.2828i	0.415188	+	0.719126i	0.995448	−	0.0953047i	$-0.0303826\pi$
$719$	11.1329	+	19.2828i	0.415188	+	0.719126i	−0.580260	+	0.814431i	$0.697049\pi$
$720$	−0.827882			−0.0308533
$721$	−4.76649	−	0.371647i	−0.177513	−	0.0138409i
$722$	19.4828			0.725076
$723$	−15.0885	−	26.1341i	−0.561149	−	0.971938i
$724$	23.3706	−	40.4790i	0.868560	−	1.50439i
$725$	4.08701	−	7.07891i	0.151788	−	0.262904i
$726$	−1.70928	−	2.96057i	−0.0634375	−	0.109877i
$727$	−39.6395			−1.47015			−0.735074	−	0.677987i	$-0.762853\pi$
$727$	−39.6395			−1.47015			−0.735074	+	0.677987i	$0.762853\pi$
$728$	1.09103	−	1.58993i	0.0404363	−	0.0589268i
$729$	28.7856			1.06613
$730$	−9.69710	−	16.7959i	−0.358906	−	0.621643i
$731$	−3.18264	+	5.51250i	−0.117714	+	0.203887i
$732$	20.5217	−	35.5445i	0.758502	−	1.31376i
$733$	−17.7364	−	30.7204i	−0.655109	−	1.13468i	−0.981866	−	0.189574i	$-0.939289\pi$
$733$	−17.7364	−	30.7204i	−0.655109	−	1.13468i	0.326757	−	0.945108i	$-0.394044\pi$
$734$	−30.7531			−1.13512
$735$	−4.18523	−	10.8557i	−0.154375	−	0.400420i
$736$	7.73432			0.285091
$737$	−1.95919	−	3.39342i	−0.0721677	−	0.124998i
$738$	−0.539258	+	0.934021i	−0.0198503	+	0.0343818i
$739$	−1.83428	+	3.17707i	−0.0674751	+	0.116870i	−0.897789	−	0.440425i	$-0.854828\pi$
$739$	−1.83428	+	3.17707i	−0.0674751	+	0.116870i	0.830314	+	0.557296i	$0.188161\pi$
$740$	2.68566	+	4.65170i	0.0987269	+	0.171000i
$741$	−7.88938			−0.289824
$742$	5.07725	−	7.39896i	0.186392	−	0.271624i
$743$	27.6855			1.01568			0.507841	−	0.861451i	$-0.330444\pi$
$743$	27.6855			1.01568			0.507841	+	0.861451i	$0.330444\pi$
$744$	1.48879	+	2.57865i	0.0545815	+	0.0945380i
$745$	−10.5806	+	18.3261i	−0.387642	+	0.671416i
$746$	2.63591	−	4.56553i	0.0965074	−	0.167156i
$747$	1.28580	+	2.22707i	0.0470450	+	0.0814843i
$748$	4.21300			0.154043
$749$	−28.5465	−	2.22579i	−1.04307	−	0.0813286i
$750$	−3.41857			−0.124828
$751$	12.1408	+	21.0285i	0.443025	+	0.767342i	0.997912	−	0.0645837i	$-0.0205719\pi$
$751$	12.1408	+	21.0285i	0.443025	+	0.767342i	−0.554887	+	0.831926i	$0.687239\pi$
$752$	13.4019	−	23.2128i	0.488718	−	0.846484i
$753$	−0.454575	+	0.787347i	−0.0165656	+	0.0286925i
$754$	−12.9270	−	22.3902i	−0.470772	−	0.815402i
$755$	8.60389			0.313128
$756$	−13.6912	−	28.6506i	−0.497944	−	1.04201i
$757$	−30.4600			−1.10709			−0.553544	−	0.832820i	$-0.686725\pi$
$757$	−30.4600			−1.10709			−0.553544	+	0.832820i	$0.686725\pi$
$758$	12.4016	+	21.4803i	0.450448	+	0.780199i
$759$	−0.791764	+	1.37138i	−0.0287392	+	0.0497778i
$760$	−0.731446	+	1.26690i	−0.0265323	+	0.0459554i
$761$	13.8128	+	23.9244i	0.500712	+	0.867259i	1.00000		0.000822765i	$0.000261894\pi$
$761$	13.8128	+	23.9244i	0.500712	+	0.867259i	−0.499287	+	0.866436i	$0.666405\pi$
$762$	18.4576			0.668649
$763$	−19.4401	−	40.6810i	−0.703780	−	1.47275i
$764$	−5.53380			−0.200206
$765$	0.224289	+	0.388480i	0.00810919	+	0.0140455i
$766$	27.8787	−	48.2873i	1.00730	−	1.74469i
$767$	5.63209	−	9.75507i	0.203363	−	0.352235i
$768$	9.72596	+	16.8459i	0.350955	+	0.607873i
$769$	−24.7230			−0.891535			−0.445767	−	0.895149i	$-0.647069\pi$
$769$	−24.7230			−0.891535			−0.445767	+	0.895149i	$0.647069\pi$
$770$	−5.42531	−	0.423016i	−0.195515	−	0.0152444i
$771$	12.0178			0.432811
$772$	−18.2103	−	31.5411i	−0.655402	−	1.13519i
$773$	9.01692	−	15.6178i	0.324316	−	0.561732i	−0.657058	−	0.753840i	$-0.728199\pi$
$773$	9.01692	−	15.6178i	0.324316	−	0.561732i	0.981374	+	0.192108i	$0.0615325\pi$
$774$	0.823019	−	1.42551i	0.0295828	−	0.0512390i
$775$	1.88999	+	3.27355i	0.0678903	+	0.117590i
$776$	−5.74809			−0.206344
$777$	5.99189	−	8.73184i	0.214958	−	0.313253i
$778$	−43.2948			−1.55219
$779$	−3.40770	−	5.90231i	−0.122094	−	0.211472i
$780$	−2.85042	+	4.93707i	−0.102061	+	0.176775i
$781$	−4.57796	+	7.92926i	−0.163812	+	0.283731i
$782$	−1.85072	−	3.20553i	−0.0661815	−	0.114630i
$783$	−43.9841			−1.57186
$784$	15.3294	−	18.9865i	0.547477	−	0.678090i
$785$	−5.41597			−0.193304
$786$	−23.8231	−	41.2627i	−0.849740	−	1.47179i
$787$	12.2948	−	21.2952i	0.438262	−	0.759092i	−0.559294	−	0.828970i	$-0.688928\pi$
$787$	12.2948	−	21.2952i	0.438262	−	0.759092i	0.997556	+	0.0698777i	$0.0222609\pi$
$788$	27.8721	−	48.2759i	0.992902	−	1.71976i
$789$	−19.1575	−	33.1817i	−0.682024	−	1.18130i
$790$	13.2706			0.472148
$791$	−25.8105	+	37.6131i	−0.917717	+	1.33737i
$792$	−0.112552			−0.00399938
$793$	−8.51278	−	14.7446i	−0.302298	−	0.523595i
$794$	−11.7448	+	20.3426i	−0.416807	+	0.721931i
$795$	−1.37038	+	2.37357i	−0.0486024	+	0.0841819i
$796$	14.8378	+	25.6999i	0.525913	+	0.910907i
$797$	36.9099			1.30742			0.653708	−	0.756747i	$-0.273212\pi$
$797$	36.9099			1.30742			0.653708	+	0.756747i	$0.273212\pi$
$798$	27.8336	+	2.17021i	0.985298	+	0.0768244i
$799$	−14.5234			−0.513799
$800$	−4.05900	−	7.03039i	−0.143507	−	0.248562i
$801$	−1.44840	+	2.50870i	−0.0511767	+	0.0886406i
$802$	8.14266	−	14.1035i	0.287527	−	0.498012i
$803$	4.71466	+	8.16602i	0.166377	+	0.288173i
$804$	14.5260			0.512293
$805$	1.08685	+	2.27437i	0.0383063	+	0.0801608i
$806$	11.9558			0.421126
$807$	−18.1518	−	31.4399i	−0.638974	−	1.10674i
$808$	2.88246	−	4.99257i	0.101405	−	0.175638i
$809$	−12.5083	+	21.6651i	−0.439769	+	0.761703i	−0.997671	−	0.0682041i	$-0.978273\pi$
$809$	−12.5083	+	21.6651i	−0.439769	+	0.761703i	0.557902	+	0.829907i	$0.311606\pi$
$810$	8.46491	+	14.6617i	0.297427	+	0.515158i
$811$	−35.5675			−1.24894			−0.624471	−	0.781048i	$-0.714686\pi$
$811$	−35.5675			−1.24894			−0.624471	+	0.781048i	$0.714686\pi$
$812$	20.7978	+	43.5221i	0.729860	+	1.52733i
$813$	3.44202			0.120717
$814$	−2.47660	−	4.28960i	−0.0868048	−	0.150350i
$815$	3.10470	−	5.37750i	0.108753	−	0.188366i
$816$	5.47219	−	9.47811i	0.191565	−	0.331800i
$817$	5.20086	+	9.00816i	0.181955	+	0.315156i
$818$	51.8400			1.81254
$819$	−0.963310	−	0.0751100i	−0.0336608	−	0.00262456i
$820$	−4.92479			−0.171981
$821$	3.02560	+	5.24049i	0.105594	+	0.182894i	0.913981	−	0.405758i	$-0.132992\pi$
$821$	3.02560	+	5.24049i	0.105594	+	0.182894i	−0.808387	+	0.588652i	$0.799659\pi$
$822$	28.5830	−	49.5072i	0.996946	−	1.72676i
$823$	16.4704	−	28.5276i	0.574123	−	0.994410i	−0.422013	−	0.906590i	$-0.638676\pi$
$823$	16.4704	−	28.5276i	0.574123	−	0.994410i	0.996136	−	0.0878206i	$-0.0279902\pi$
$824$	−0.428210	−	0.741681i	−0.0149174	−	0.0258377i
$825$	1.66208			0.0578663
$826$	−22.5533	+	32.8664i	−0.784731	+	1.14357i
$827$	−41.1297			−1.43022			−0.715110	−	0.699012i	$-0.753624\pi$
$827$	−41.1297			−1.43022			−0.715110	+	0.699012i	$0.753624\pi$
$828$	0.252328	+	0.437045i	0.00876900	+	0.0151884i
$829$	1.42759	−	2.47266i	0.0495823	−	0.0858791i	−0.840169	−	0.542325i	$-0.817544\pi$
$829$	1.42759	−	2.47266i	0.0495823	−	0.0858791i	0.889751	+	0.456445i	$0.150878\pi$
$830$	−11.1361	+	19.2882i	−0.386538	+	0.669504i
$831$	−9.95405	−	17.2409i	−0.345302	−	0.598081i
$832$	−14.9550			−0.518472
$833$	−13.0624	−	2.04942i	−0.452584	−	0.0710084i
$834$	−49.7414			−1.72240
$835$	1.26715	+	2.19477i	0.0438516	+	0.0759532i
$836$	3.44230	−	5.96224i	0.119055	−	0.206209i
$837$	10.1700	−	17.6149i	0.351525	−	0.608859i
$838$	22.5909	+	39.1286i	0.780390	+	1.35168i
$839$	−45.8337			−1.58235			−0.791177	−	0.611587i	$-0.790532\pi$
$839$	−45.8337			−1.58235			−0.791177	+	0.611587i	$0.790532\pi$
$840$	1.17921	−	1.71843i	0.0406866	−	0.0592916i
$841$	37.8147			1.30396
$842$	23.3977	+	40.5261i	0.806339	+	1.39662i
$843$	−14.8441	+	25.7106i	−0.511256	+	0.885522i
$844$	−1.77480	+	3.07405i	−0.0610913	+	0.105813i
$845$	−5.31759	−	9.21034i	−0.182931	−	0.316845i
$846$	3.75568			0.129123
$847$	2.63775	+	0.205667i	0.0906340	+	0.00706681i
$848$	−5.74848			−0.197404
$849$	7.18075	+	12.4374i	0.246443	+	0.426852i
$850$	−1.94252	+	3.36455i	−0.0666280	+	0.115403i
$851$	−1.14720	+	1.98700i	−0.0393253	+	0.0681135i
$852$	−16.9712	−	29.3949i	−0.581423	−	1.00705i
$853$	1.37150			0.0469593			0.0234797	−	0.999724i	$-0.492526\pi$
$853$	1.37150			0.0469593			0.0234797	+	0.999724i	$0.492526\pi$
$854$	25.9770	+	54.3602i	0.888914	+	1.86017i
$855$	0.733037			0.0250693
$856$	−2.56454	−	4.44192i	−0.0876543	−	0.151822i
$857$	−6.56199	+	11.3657i	−0.224153	+	0.388245i	−0.956065	−	0.293155i	$-0.905295\pi$
$857$	−6.56199	+	11.3657i	−0.224153	+	0.388245i	0.731912	+	0.681399i	$0.238628\pi$
$858$	2.62853	−	4.55275i	0.0897366	−	0.155428i
$859$	−24.6165	−	42.6371i	−0.839905	−	1.45476i	−0.889974	−	0.456012i	$-0.849277\pi$
$859$	−24.6165	−	42.6371i	−0.839905	−	1.45476i	0.0500687	−	0.998746i	$-0.484056\pi$
$860$	7.51625			0.256302
$861$	4.18646	+	8.76070i	0.142674	+	0.298564i
$862$	56.4411			1.92239
$863$	0.472060	+	0.817632i	0.0160691	+	0.0278325i	0.873948	−	0.486019i	$-0.161551\pi$
$863$	0.472060	+	0.817632i	0.0160691	+	0.0278325i	−0.857879	+	0.513852i	$0.828218\pi$
$864$	−21.8413	+	37.8303i	−0.743056	+	1.28701i
$865$	−11.1649	+	19.3381i	−0.379616	+	0.657515i
$866$	11.8692	+	20.5581i	0.403332	+	0.698592i
$867$	22.3253			0.758207
$868$	−22.2387	−	1.73397i	−0.754831	−	0.0588547i
$869$	−6.45208			−0.218872
$870$	−13.9717	−	24.1998i	−0.473686	−	0.820449i
$871$	3.01283	−	5.21838i	0.102086	−	0.176818i
$872$	4.03827	−	6.99449i	0.136753	−	0.236863i
$873$	1.44015	+	2.49441i	0.0487416	+	0.0844229i
$874$	−6.04863			−0.204598
$875$	1.49699	−	2.18152i	0.0506074	−	0.0737489i
$876$	−34.9559			−1.18105
$877$	−2.61776	−	4.53409i	−0.0883954	−	0.153105i	0.818438	−	0.574595i	$-0.194841\pi$
$877$	−2.61776	−	4.53409i	−0.0883954	−	0.153105i	−0.906833	+	0.421490i	$0.861507\pi$
$878$	−6.69009	+	11.5876i	−0.225780	+	0.391062i
$879$	12.5768	−	21.7837i	0.424206	−	0.734746i
$880$	1.74303	+	3.01901i	0.0587575	+	0.101771i
$881$	30.6327			1.03204			0.516022	−	0.856576i	$-0.327412\pi$
$881$	30.6327			1.03204			0.516022	+	0.856576i	$0.327412\pi$
$882$	3.37788	+	0.529973i	0.113739	+	0.0178451i
$883$	22.4867			0.756738			0.378369	−	0.925655i	$-0.376485\pi$
$883$	22.4867			0.756738			0.378369	+	0.925655i	$0.376485\pi$
$884$	3.23937	+	5.61075i	0.108952	+	0.188710i
$885$	6.08728	−	10.5435i	0.204622	−	0.354415i
$886$	19.6783	−	34.0838i	0.661105	−	1.14507i
$887$	4.05804	+	7.02872i	0.136256	+	0.236001i	0.926076	−	0.377336i	$-0.123160\pi$
$887$	4.05804	+	7.02872i	0.136256	+	0.236001i	−0.789821	+	0.613338i	$0.789827\pi$
$888$	1.89700			0.0636591
$889$	−8.08256	+	11.7785i	−0.271080	+	0.395039i
$890$	−25.0886			−0.840971
$891$	−4.11557	−	7.12838i	−0.137877	−	0.238810i
$892$	−5.22328	+	9.04698i	−0.174888	+	0.302915i
$893$	−11.8665	+	20.5535i	−0.397099	+	0.687795i
$894$	36.1704	+	62.6490i	1.20972	+	2.09530i
$895$	−21.8910			−0.731734
$896$	9.93463	+	0.774611i	0.331893	+	0.0258779i
$897$	−2.43514			−0.0813071
$898$	−38.9357	−	67.4386i	−1.29930	−	2.25046i
$899$	−15.4488	+	26.7581i	−0.515247	+	0.892433i
$900$	0.264845	−	0.458725i	0.00882817	−	0.0152908i
$901$	1.55738	+	2.69745i	0.0518837	+	0.0898652i
$902$	4.54142			0.151213
$903$	−6.38941	−	13.3707i	−0.212626	−	0.444948i
$904$	−8.17147			−0.271779
$905$	−10.4781	−	18.1486i	−0.348303	−	0.603279i
$906$	14.7065	−	25.4724i	0.488591	−	0.846264i
$907$	9.46779	−	16.3987i	0.314373	−	0.544510i	−0.664931	−	0.746905i	$-0.731539\pi$
$907$	9.46779	−	16.3987i	0.314373	−	0.544510i	0.979304	+	0.202395i	$0.0648725\pi$
$908$	−1.58330	−	2.74236i	−0.0525438	−	0.0910086i
$909$	−2.88873			−0.0958131
$910$	−3.60815	−	7.55053i	−0.119609	−	0.250298i
$911$	−4.96615			−0.164536			−0.0822680	−	0.996610i	$-0.526216\pi$
$911$	−4.96615			−0.164536			−0.0822680	+	0.996610i	$0.526216\pi$
$912$	−8.94228	−	15.4885i	−0.296108	−	0.512875i
$913$	5.41427	−	9.37778i	0.179186	−	0.310359i
$914$	−9.48448	+	16.4276i	−0.313719	+	0.543377i
$915$	−9.20078	−	15.9362i	−0.304169	−	0.526835i
$916$	28.9965			0.958070
$917$	36.7634	+	2.86647i	1.21404	+	0.0946593i
$918$	20.9053			0.689977
$919$	27.5914	+	47.7897i	0.910156	+	1.57644i	0.813843	+	0.581085i	$0.197372\pi$
$919$	27.5914	+	47.7897i	0.910156	+	1.57644i	0.0963133	+	0.995351i	$0.469295\pi$
$920$	−0.225769	+	0.391043i	−0.00744338	+	0.0128923i
$921$	−11.9977	+	20.7806i	−0.395337	+	0.684743i
$922$	−33.7594	−	58.4729i	−1.11181	−	1.92570i
$923$	−14.0799			−0.463447
$924$	−5.54955	+	8.08722i	−0.182567	+	0.266050i
$925$	2.40821			0.0791813
$926$	13.4509	+	23.2977i	0.442026	+	0.765611i
$927$	−0.214570	+	0.371647i	−0.00704742	+	0.0122065i
$928$	33.1783	−	57.4666i	1.08913	−	1.88643i
$929$	10.6238	+	18.4010i	0.348557	+	0.603718i	0.985993	−	0.166785i	$-0.0533386\pi$
$929$	10.6238	+	18.4010i	0.348557	+	0.603718i	−0.637437	+	0.770503i	$0.720005\pi$
$930$	12.9221			0.423733
$931$	−13.5732	+	16.8113i	−0.444842	+	0.550970i
$932$	−43.6789			−1.43075
$933$	22.6327	+	39.2010i	0.740963	+	1.28338i
$934$	−26.8723	+	46.5441i	−0.879288	+	1.52297i
$935$	0.944440	−	1.63582i	0.0308865	−	0.0534969i
$936$	−0.0865414	−	0.149894i	−0.00282869	−	0.00489944i
$937$	−16.2888			−0.532133			−0.266067	−	0.963955i	$-0.585724\pi$
$937$	−16.2888			−0.532133			−0.266067	+	0.963955i	$0.585724\pi$
$938$	−12.0647	+	17.5816i	−0.393926	+	0.574059i
$939$	−12.5353			−0.409073
$940$	8.57472	+	14.8519i	0.279677	+	0.484414i
$941$	14.5002	−	25.1151i	0.472693	−	0.818728i	−0.526819	−	0.849978i	$-0.676615\pi$
$941$	14.5002	−	25.1151i	0.472693	−	0.818728i	0.999512	+	0.0312497i	$0.00994872\pi$
$942$	−9.25744	+	16.0344i	−0.301624	+	0.522428i
$943$	−1.05183	−	1.82181i	−0.0342521	−	0.0593265i
$944$	25.5350			0.831092
$945$	−14.1936	−	1.10669i	−0.461718	−	0.0360005i
$946$	−6.93116			−0.225351
$947$	−21.6628	−	37.5211i	−0.703946	−	1.21927i	−0.967070	−	0.254509i	$-0.918086\pi$
$947$	−21.6628	−	37.5211i	−0.703946	−	1.21927i	0.263124	−	0.964762i	$-0.415247\pi$
$948$	11.9594	−	20.7143i	0.388423	−	0.672769i
$949$	−7.25018	+	12.5577i	−0.235351	+	0.407640i
$950$	3.17434	+	5.49812i	0.102989	+	0.178383i
$951$	48.2554			1.56479
$952$	−1.02122	−	2.13703i	−0.0330979	−	0.0692617i
$953$	24.9429			0.807980			0.403990	−	0.914763i	$-0.367623\pi$
$953$	24.9429			0.807980			0.403990	+	0.914763i	$0.367623\pi$
$954$	−0.402731	−	0.697551i	−0.0130389	−	0.0225840i
$955$	−1.24053	+	2.14865i	−0.0401425	+	0.0695288i
$956$	−6.39377	+	11.0743i	−0.206789	+	0.358169i
$957$	6.79295	+	11.7657i	0.219585	+	0.380332i
$958$	35.6102			1.15051
$959$	19.0760	+	39.9190i	0.615996	+	1.28905i
$960$	−16.1637			−0.521681
$961$	8.35590	+	14.4728i	0.269545	+	0.466866i
$962$	3.80850	−	6.59652i	0.122791	−	0.212680i
$963$	−1.28506	+	2.22579i	−0.0414105	+	0.0717251i
$964$	20.2480	+	35.0706i	0.652144	+	1.12955i
$965$	−16.3290			−0.525648
$966$	8.59114	+	0.669858i	0.276415	+	0.0215523i
$967$	9.28042			0.298438			0.149219	−	0.988804i	$-0.452324\pi$
$967$	9.28042			0.298438			0.149219	+	0.988804i	$0.452324\pi$
$968$	0.236969	+	0.410442i	0.00761646	+	0.0131921i
$969$	−4.84527	+	8.39226i	−0.155653	+	0.269598i
$970$	−12.4728	+	21.6035i	−0.400478	+	0.693648i
$971$	7.37082	+	12.7666i	0.236541	+	0.409701i	0.959719	−	0.280960i	$-0.0906529\pi$
$971$	7.37082	+	12.7666i	0.236541	+	0.409701i	−0.723178	+	0.690661i	$0.757320\pi$
$972$	−5.49141			−0.176137
$973$	21.7817	−	31.7419i	0.698288	−	1.01760i
$974$	−61.8951			−1.98325
$975$	1.27797	+	2.21351i	0.0409278	+	0.0708891i
$976$	19.2978	−	33.4247i	0.617706	−	1.06990i
$977$	3.55459	−	6.15673i	0.113721	−	0.196971i	−0.803546	−	0.595242i	$-0.797056\pi$
$977$	3.55459	−	6.15673i	0.113721	−	0.196971i	0.917268	+	0.398271i	$0.130390\pi$
$978$	−10.6136	−	18.3834i	−0.339387	−	0.587835i
$979$	12.1979			0.389846
$980$	5.61636	+	14.5678i	0.179408	+	0.465352i
$981$	−4.04706			−0.129213
$982$	17.6297	+	30.5356i	0.562587	+	0.974429i
$983$	−26.7764	+	46.3781i	−0.854035	+	1.47923i	0.0235022	+	0.999724i	$0.492518\pi$
$983$	−26.7764	+	46.3781i	−0.854035	+	1.47923i	−0.877537	+	0.479508i	$0.840815\pi$
$984$	−0.869647	+	1.50627i	−0.0277233	+	0.0480182i
$985$	−12.4963	−	21.6443i	−0.398166	−	0.689643i
$986$	−31.7565			−1.01133
$987$	19.1308	−	27.8788i	0.608939	−	0.887393i
$988$	10.5871			0.336821
$989$	1.60530	+	2.78047i	0.0510457	+	0.0884138i
$990$	−0.244228	+	0.423016i	−0.00776209	+	0.0134443i
$991$	30.3239	−	52.5226i	0.963271	−	1.66843i	0.249081	−	0.968483i	$-0.419871\pi$
$991$	30.3239	−	52.5226i	0.963271	−	1.66843i	0.714190	−	0.699952i	$-0.246795\pi$
$992$	15.3429	+	26.5747i	0.487138	+	0.843747i
$993$	16.7582			0.531806
$994$	49.6737	+	3.87310i	1.57556	+	0.122847i
$995$	13.3049			0.421795
$996$	20.0715	+	34.7648i	0.635989	+	1.10157i
$997$	17.7576	−	30.7571i	0.562390	−	0.974087i	−0.434898	−	0.900480i	$-0.643215\pi$
$997$	17.7576	−	30.7571i	0.562390	−	0.974087i	0.997287	−	0.0736075i	$-0.0234512\pi$
$998$	1.32228	−	2.29026i	0.0418562	−	0.0724970i
$999$	−6.47924	−	11.2224i	−0.204994	−	0.355060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.b.221.5	✓	12
7.2	even	3	inner	385.2.i.b.331.5	yes	12
7.3	odd	6		2695.2.a.q.1.2		6
7.4	even	3		2695.2.a.r.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.b.221.5	✓	12	1.1	even	1	trivial
385.2.i.b.331.5	yes	12	7.2	even	3	inner
2695.2.a.q.1.2		6	7.3	odd	6
2695.2.a.r.1.2		6	7.4	even	3

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02840 + 1.78124i) q^{2} +(0.831041 - 1.43941i) q^{3} +(-1.11521 + 1.93160i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.41857 q^{6} +(-1.49699 + 2.18152i) q^{7} -0.473937 q^{8} +(0.118742 + 0.205667i) q^{9} +O(q^{10})\)	\(q+(1.02840 + 1.78124i) q^{2} +(0.831041 - 1.43941i) q^{3} +(-1.11521 + 1.93160i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.41857 q^{6} +(-1.49699 + 2.18152i) q^{7} -0.473937 q^{8} +(0.118742 + 0.205667i) q^{9} +(-1.02840 + 1.78124i) q^{10} +(0.500000 - 0.866025i) q^{11} +(1.85357 + 3.21048i) q^{12} +1.53780 q^{13} +(-5.42531 - 0.423016i) q^{14} +1.66208 q^{15} +(1.74303 + 3.01901i) q^{16} +(0.944440 - 1.63582i) q^{17} +(-0.244228 + 0.423016i) q^{18} +(-1.54334 - 2.67314i) q^{19} -2.23042 q^{20} +(1.89604 + 3.96770i) q^{21} +2.05680 q^{22} +(-0.476369 - 0.825095i) q^{23} +(-0.393861 + 0.682188i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.58147 + 2.73919i) q^{26} +5.38096 q^{27} +(-2.54438 - 5.32444i) q^{28} -8.17403 q^{29} +(1.70928 + 2.96057i) q^{30} +(1.88999 - 3.27355i) q^{31} +(-4.05900 + 7.03039i) q^{32} +(-0.831041 - 1.43941i) q^{33} +3.88505 q^{34} +(-2.63775 - 0.205667i) q^{35} -0.529690 q^{36} +(-1.20410 - 2.08557i) q^{37} +(3.17434 - 5.49812i) q^{38} +(1.27797 - 2.21351i) q^{39} +(-0.236969 - 0.410442i) q^{40} +2.20800 q^{41} +(-5.11755 + 7.45768i) q^{42} -3.36988 q^{43} +(1.11521 + 1.93160i) q^{44} +(-0.118742 + 0.205667i) q^{45} +(0.979796 - 1.69706i) q^{46} +(-3.84444 - 6.65876i) q^{47} +5.79411 q^{48} +(-2.51807 - 6.53141i) q^{49} -2.05680 q^{50} +(-1.56974 - 2.71886i) q^{51} +(-1.71497 + 2.97041i) q^{52} +(-0.824497 + 1.42807i) q^{53} +(5.53378 + 9.58479i) q^{54} +1.00000 q^{55} +(0.709477 - 1.03390i) q^{56} -5.13031 q^{57} +(-8.40617 - 14.5599i) q^{58} +(3.66244 - 6.34354i) q^{59} +(-1.85357 + 3.21048i) q^{60} +(-5.53570 - 9.58811i) q^{61} +7.77465 q^{62} +(-0.626422 - 0.0488426i) q^{63} -9.72497 q^{64} +(0.768898 + 1.33177i) q^{65} +(1.70928 - 2.96057i) q^{66} +(1.95919 - 3.39342i) q^{67} +(2.10650 + 3.64857i) q^{68} -1.58353 q^{69} +(-2.34631 - 4.90997i) q^{70} -9.15592 q^{71} +(-0.0562762 - 0.0974733i) q^{72} +(-4.71466 + 8.16602i) q^{73} +(2.47660 - 4.28960i) q^{74} +(0.831041 + 1.43941i) q^{75} +6.88461 q^{76} +(1.14076 + 2.38719i) q^{77} +5.25706 q^{78} +(-3.22604 - 5.58766i) q^{79} +(-1.74303 + 3.01901i) q^{80} +(4.11557 - 7.12838i) q^{81} +(2.27071 + 3.93299i) q^{82} +10.8285 q^{83} +(-9.77851 - 0.762439i) q^{84} +1.88888 q^{85} +(-3.46558 - 6.00256i) q^{86} +(-6.79295 + 11.7657i) q^{87} +(-0.236969 + 0.410442i) q^{88} +(6.09894 + 10.5637i) q^{89} -0.488457 q^{90} +(-2.30206 + 3.35473i) q^{91} +2.12501 q^{92} +(-3.14131 - 5.44091i) q^{93} +(7.90723 - 13.6957i) q^{94} +(1.54334 - 2.67314i) q^{95} +(6.74638 + 11.6851i) q^{96} +12.1284 q^{97} +(9.04444 - 11.2022i) q^{98} +0.237484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9	\( 12 q + 3 q^{2} - q^{3} - 5 q^{4} + 6 q^{5} - 10 q^{6} - 3 q^{7} - 18 q^{8} + q^{9} - 3 q^{10} + 6 q^{11} - 9 q^{12} + 28 q^{13} - 3 q^{14} - 2 q^{15} - 11 q^{16} - 3 q^{17} + 9 q^{18} + 3 q^{19} - 10 q^{20} - 8 q^{21} + 6 q^{22} + 10 q^{23} + 10 q^{24} - 6 q^{25} + 17 q^{26} + 2 q^{27} - 10 q^{28} - 32 q^{29} - 5 q^{30} - 2 q^{31} + 26 q^{32} + q^{33} + 60 q^{34} - 3 q^{35} + 16 q^{36} - 5 q^{37} - q^{38} - 3 q^{39} - 9 q^{40} - 18 q^{41} - 56 q^{42} - 40 q^{43} + 5 q^{44} - q^{45} + 20 q^{46} - q^{47} + 82 q^{48} + 15 q^{49} - 6 q^{50} + 5 q^{51} - 23 q^{52} + 24 q^{53} + 7 q^{54} + 12 q^{55} - 66 q^{56} - 60 q^{57} - 31 q^{58} + 7 q^{59} + 9 q^{60} + 14 q^{61} + 48 q^{62} - 13 q^{63} + 30 q^{64} + 14 q^{65} - 5 q^{66} - q^{67} + 25 q^{68} - 8 q^{69} - 15 q^{70} - 18 q^{71} + 26 q^{72} - 13 q^{73} + 40 q^{74} - q^{75} - 20 q^{76} - 66 q^{78} + 4 q^{79} + 11 q^{80} + 26 q^{81} + 27 q^{82} + 16 q^{83} - 90 q^{84} - 6 q^{85} - 36 q^{86} + 2 q^{87} - 9 q^{88} + 13 q^{89} + 18 q^{90} + 17 q^{91} - 36 q^{92} + 36 q^{93} + q^{94} - 3 q^{95} + 89 q^{96} - 6 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - q^3 - 5 * q^4 + 6 * q^5 - 10 * q^6 - 3 * q^7 - 18 * q^8 + q^9 - 3 * q^10 + 6 * q^11 - 9 * q^12 + 28 * q^13 - 3 * q^14 - 2 * q^15 - 11 * q^16 - 3 * q^17 + 9 * q^18 + 3 * q^19 - 10 * q^20 - 8 * q^21 + 6 * q^22 + 10 * q^23 + 10 * q^24 - 6 * q^25 + 17 * q^26 + 2 * q^27 - 10 * q^28 - 32 * q^29 - 5 * q^30 - 2 * q^31 + 26 * q^32 + q^33 + 60 * q^34 - 3 * q^35 + 16 * q^36 - 5 * q^37 - q^38 - 3 * q^39 - 9 * q^40 - 18 * q^41 - 56 * q^42 - 40 * q^43 + 5 * q^44 - q^45 + 20 * q^46 - q^47 + 82 * q^48 + 15 * q^49 - 6 * q^50 + 5 * q^51 - 23 * q^52 + 24 * q^53 + 7 * q^54 + 12 * q^55 - 66 * q^56 - 60 * q^57 - 31 * q^58 + 7 * q^59 + 9 * q^60 + 14 * q^61 + 48 * q^62 - 13 * q^63 + 30 * q^64 + 14 * q^65 - 5 * q^66 - q^67 + 25 * q^68 - 8 * q^69 - 15 * q^70 - 18 * q^71 + 26 * q^72 - 13 * q^73 + 40 * q^74 - q^75 - 20 * q^76 - 66 * q^78 + 4 * q^79 + 11 * q^80 + 26 * q^81 + 27 * q^82 + 16 * q^83 - 90 * q^84 - 6 * q^85 - 36 * q^86 + 2 * q^87 - 9 * q^88 + 13 * q^89 + 18 * q^90 + 17 * q^91 - 36 * q^92 + 36 * q^93 + q^94 - 3 * q^95 + 89 * q^96 - 6 * q^97 + 18 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more