LMFDB - Embedded newform 385.2.i.a.331.4

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.4
Root			$-1.03075 - 1.78531i$ of defining polynomial
Character	$\chi$	$=$	385.331
Dual form			385.2.i.a.221.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28821 - 2.23124i) q^{2} +(0.257458 + 0.445930i) q^{3} +(-2.31896 - 4.01655i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.32664 q^{6} +(1.46157 - 2.20541i) q^{7} -6.79636 q^{8} +(1.36743 - 2.36846i) q^{9} +O(q^{10})$	\(q+(1.28821 - 2.23124i) q^{2} +(0.257458 + 0.445930i) q^{3} +(-2.31896 - 4.01655i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.32664 q^{6} +(1.46157 - 2.20541i) q^{7} -6.79636 q^{8} +(1.36743 - 2.36846i) q^{9} +(1.28821 + 2.23124i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.19407 - 2.06819i) q^{12} -1.97017 q^{13} +(-3.03798 - 6.10213i) q^{14} -0.514916 q^{15} +(-4.11721 + 7.13121i) q^{16} +(1.19407 + 2.06819i) q^{17} +(-3.52307 - 6.10213i) q^{18} +(-2.27048 + 3.93259i) q^{19} +4.63791 q^{20} +(1.35975 + 0.0839592i) q^{21} -2.57641 q^{22} +(1.35739 - 2.35106i) q^{23} +(-1.74978 - 3.03070i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.53798 + 4.39592i) q^{26} +2.95297 q^{27} +(-12.2474 - 0.756231i) q^{28} +1.93472 q^{29} +(-0.663319 + 1.14890i) q^{30} +(1.79544 + 3.10980i) q^{31} +(3.81128 + 6.60132i) q^{32} +(0.257458 - 0.445930i) q^{33} +6.15283 q^{34} +(1.17915 + 2.36846i) q^{35} -12.6841 q^{36} +(-3.06873 + 5.31520i) q^{37} +(5.84971 + 10.1320i) q^{38} +(-0.507236 - 0.878558i) q^{39} +(3.39818 - 5.88582i) q^{40} +8.20275 q^{41} +(1.93897 - 2.92577i) q^{42} +9.15756 q^{43} +(-2.31896 + 4.01655i) q^{44} +(1.36743 + 2.36846i) q^{45} +(-3.49719 - 6.05731i) q^{46} +(3.72482 - 6.45157i) q^{47} -4.24003 q^{48} +(-2.72763 - 6.44671i) q^{49} -2.57641 q^{50} +(-0.614845 + 1.06494i) q^{51} +(4.56873 + 7.91328i) q^{52} +(6.14072 + 10.6360i) q^{53} +(3.80404 - 6.58879i) q^{54} +1.00000 q^{55} +(-9.93336 + 14.9887i) q^{56} -2.33822 q^{57} +(2.49232 - 4.31682i) q^{58} +(-0.929903 - 1.61064i) q^{59} +(1.19407 + 2.06819i) q^{60} +(0.466442 - 0.807902i) q^{61} +9.25161 q^{62} +(-3.22482 - 6.47741i) q^{63} +3.17003 q^{64} +(0.985084 - 1.70622i) q^{65} +(-0.663319 - 1.14890i) q^{66} +(5.77846 + 10.0086i) q^{67} +(5.53798 - 9.59207i) q^{68} +1.39788 q^{69} +(6.80360 + 0.420095i) q^{70} -12.4842 q^{71} +(-9.29355 + 16.0969i) q^{72} +(3.58365 + 6.20706i) q^{73} +(7.90633 + 13.6942i) q^{74} +(0.257458 - 0.445930i) q^{75} +21.0606 q^{76} +(-2.64072 - 0.163054i) q^{77} -2.61370 q^{78} +(0.410115 - 0.710340i) q^{79} +(-4.11721 - 7.13121i) q^{80} +(-3.34203 - 5.78856i) q^{81} +(10.5668 - 18.3023i) q^{82} -9.83688 q^{83} +(-2.81598 - 5.65620i) q^{84} -2.38814 q^{85} +(11.7968 - 20.4327i) q^{86} +(0.498109 + 0.862750i) q^{87} +(3.39818 + 5.88582i) q^{88} +(-5.29979 + 9.17950i) q^{89} +7.04614 q^{90} +(-2.87954 + 4.34502i) q^{91} -12.5909 q^{92} +(-0.924502 + 1.60129i) q^{93} +(-9.59668 - 16.6219i) q^{94} +(-2.27048 - 3.93259i) q^{95} +(-1.96249 + 3.39913i) q^{96} -7.02009 q^{97} +(-17.8979 - 2.21871i) q^{98} -2.73486 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9} + 3 q^{10} - 4 q^{11} + 3 q^{12} - 12 q^{13} + q^{14} - 6 q^{15} - 5 q^{16} + 3 q^{17} - q^{18} + 3 q^{19} + 6 q^{20} - 18 q^{21} - 6 q^{22} + 6 q^{23} + 4 q^{24} - 4 q^{25} + 5 q^{26} + 6 q^{27} - 20 q^{28} - 16 q^{29} - 7 q^{30} - 10 q^{31} - 4 q^{32} + 3 q^{33} + 20 q^{34} + q^{35} - 16 q^{36} + 9 q^{37} + 23 q^{38} + 13 q^{39} + 9 q^{40} + 30 q^{41} - 16 q^{42} - 4 q^{43} - 3 q^{44} + q^{45} - 16 q^{46} + 15 q^{47} - 2 q^{48} - 19 q^{49} - 6 q^{50} - q^{51} + 3 q^{52} + 30 q^{53} + 13 q^{54} + 8 q^{55} - 24 q^{56} - 12 q^{57} + q^{58} - 17 q^{59} + 3 q^{60} + 32 q^{62} - 11 q^{63} + 10 q^{64} + 6 q^{65} - 7 q^{66} + 25 q^{67} + 19 q^{68} + 12 q^{69} + q^{70} - 26 q^{71} - 26 q^{72} - 3 q^{73} + 16 q^{74} + 3 q^{75} + 80 q^{76} - 2 q^{77} - 10 q^{78} + 4 q^{79} - 5 q^{80} + 16 q^{81} + 27 q^{82} + 36 q^{83} - 24 q^{84} - 6 q^{85} + 10 q^{86} - 20 q^{87} + 9 q^{88} - 25 q^{89} + 2 q^{90} - 3 q^{91} - 52 q^{92} - 10 q^{93} - 23 q^{94} + 3 q^{95} + 7 q^{96} - 46 q^{97} - 60 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9 + 3 * q^10 - 4 * q^11 + 3 * q^12 - 12 * q^13 + q^14 - 6 * q^15 - 5 * q^16 + 3 * q^17 - q^18 + 3 * q^19 + 6 * q^20 - 18 * q^21 - 6 * q^22 + 6 * q^23 + 4 * q^24 - 4 * q^25 + 5 * q^26 + 6 * q^27 - 20 * q^28 - 16 * q^29 - 7 * q^30 - 10 * q^31 - 4 * q^32 + 3 * q^33 + 20 * q^34 + q^35 - 16 * q^36 + 9 * q^37 + 23 * q^38 + 13 * q^39 + 9 * q^40 + 30 * q^41 - 16 * q^42 - 4 * q^43 - 3 * q^44 + q^45 - 16 * q^46 + 15 * q^47 - 2 * q^48 - 19 * q^49 - 6 * q^50 - q^51 + 3 * q^52 + 30 * q^53 + 13 * q^54 + 8 * q^55 - 24 * q^56 - 12 * q^57 + q^58 - 17 * q^59 + 3 * q^60 + 32 * q^62 - 11 * q^63 + 10 * q^64 + 6 * q^65 - 7 * q^66 + 25 * q^67 + 19 * q^68 + 12 * q^69 + q^70 - 26 * q^71 - 26 * q^72 - 3 * q^73 + 16 * q^74 + 3 * q^75 + 80 * q^76 - 2 * q^77 - 10 * q^78 + 4 * q^79 - 5 * q^80 + 16 * q^81 + 27 * q^82 + 36 * q^83 - 24 * q^84 - 6 * q^85 + 10 * q^86 - 20 * q^87 + 9 * q^88 - 25 * q^89 + 2 * q^90 - 3 * q^91 - 52 * q^92 - 10 * q^93 - 23 * q^94 + 3 * q^95 + 7 * q^96 - 46 * q^97 - 60 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.28821	−	2.23124i	0.910900	−	1.57773i	0.0981049	−	0.995176i	$-0.468722\pi$
$2$	1.28821	−	2.23124i	0.910900	−	1.57773i	0.812795	−	0.582549i	$-0.197945\pi$
$3$	0.257458	+	0.445930i	0.148643	+	0.257458i	0.930726	−	0.365716i	$-0.119176\pi$
$3$	0.257458	+	0.445930i	0.148643	+	0.257458i	−0.782083	+	0.623174i	$0.785843\pi$
$4$	−2.31896	−	4.01655i	−1.15948	−	2.00828i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	1.32664			0.541597
$7$	1.46157	−	2.20541i	0.552422	−	0.833565i
$7$	1.46157	−	2.20541i	0.552422	−	0.833565i
$8$	−6.79636			−2.40288
$9$	1.36743	−	2.36846i	0.455810	−	0.789486i
$10$	1.28821	+	2.23124i	0.407367	+	0.705580i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	1.19407	−	2.06819i	0.344698	−	0.597034i
$13$	−1.97017			−0.546426			−0.273213	−	0.961954i	$-0.588086\pi$
$13$	−1.97017			−0.546426			−0.273213	+	0.961954i	$0.588086\pi$
$14$	−3.03798	−	6.10213i	−0.811936	−	1.63086i
$15$	−0.514916			−0.132951
$16$	−4.11721	+	7.13121i	−1.02930	+	1.78280i
$17$	1.19407	+	2.06819i	0.289604	+	0.501609i	0.973715	−	0.227769i	$-0.0731430\pi$
$17$	1.19407	+	2.06819i	0.289604	+	0.501609i	−0.684111	+	0.729378i	$0.739810\pi$
$18$	−3.52307	−	6.10213i	−0.830395	−	1.43829i
$19$	−2.27048	+	3.93259i	−0.520885	+	0.902198i	0.478821	+	0.877913i	$0.341064\pi$
$19$	−2.27048	+	3.93259i	−0.520885	+	0.902198i	−0.999705	+	0.0242857i	$0.992269\pi$
$20$	4.63791			1.03707
$21$	1.35975	+	0.0839592i	0.296722	+	0.0183214i
$22$	−2.57641			−0.549294
$23$	1.35739	−	2.35106i	0.283035	−	0.490231i	−0.689096	−	0.724670i	$-0.741992\pi$
$23$	1.35739	−	2.35106i	0.283035	−	0.490231i	0.972131	+	0.234440i	$0.0753255\pi$
$24$	−1.74978	−	3.03070i	−0.357172	−	0.618640i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.53798	+	4.39592i	−0.497740	+	0.862111i
$27$	2.95297			0.568300
$28$	−12.2474	−	0.756231i	−2.31455	−	0.142914i
$29$	1.93472			0.359268			0.179634	−	0.983733i	$-0.442509\pi$
$29$	1.93472			0.359268			0.179634	+	0.983733i	$0.442509\pi$
$30$	−0.663319	+	1.14890i	−0.121105	+	0.209760i
$31$	1.79544	+	3.10980i	0.322471	+	0.558536i	0.980997	−	0.194022i	$-0.0621532\pi$
$31$	1.79544	+	3.10980i	0.322471	+	0.558536i	−0.658526	+	0.752558i	$0.728820\pi$
$32$	3.81128	+	6.60132i	0.673745	+	1.16696i
$33$	0.257458	−	0.445930i	0.0448177	−	0.0776265i
$34$	6.15283			1.05520
$35$	1.17915	+	2.36846i	0.199313	+	0.400343i
$36$	−12.6841			−2.11401
$37$	−3.06873	+	5.31520i	−0.504497	+	0.873814i	0.495490	+	0.868614i	$0.334989\pi$
$37$	−3.06873	+	5.31520i	−0.504497	+	0.873814i	−0.999986	+	0.00520029i	$0.998345\pi$
$38$	5.84971	+	10.1320i	0.948948	+	1.64363i
$39$	−0.507236	−	0.878558i	−0.0812227	−	0.140682i
$40$	3.39818	−	5.88582i	0.537299	−	0.930630i
$41$	8.20275			1.28105			0.640527	−	0.767936i	$-0.278716\pi$
$41$	8.20275			1.28105			0.640527	+	0.767936i	$0.278716\pi$
$42$	1.93897	−	2.92577i	0.299190	−	0.451457i
$43$	9.15756			1.39651			0.698257	−	0.715847i	$-0.253959\pi$
$43$	9.15756			1.39651			0.698257	+	0.715847i	$0.253959\pi$
$44$	−2.31896	+	4.01655i	−0.349596	+	0.605518i
$45$	1.36743	+	2.36846i	0.203845	+	0.353069i
$46$	−3.49719	−	6.05731i	−0.515633	−	0.893102i
$47$	3.72482	−	6.45157i	0.543320	−	0.941059i	−0.455390	−	0.890292i	$-0.650500\pi$
$47$	3.72482	−	6.45157i	0.543320	−	0.941059i	0.998711	−	0.0507667i	$-0.0161665\pi$
$48$	−4.24003			−0.611996
$49$	−2.72763	−	6.44671i	−0.389661	−	0.920958i
$50$	−2.57641			−0.364360
$51$	−0.614845	+	1.06494i	−0.0860955	+	0.149122i
$52$	4.56873	+	7.91328i	0.633569	+	1.09737i
$53$	6.14072	+	10.6360i	0.843493	+	1.46097i	0.886923	+	0.461916i	$0.152838\pi$
$53$	6.14072	+	10.6360i	0.843493	+	1.46097i	−0.0434304	+	0.999056i	$0.513829\pi$
$54$	3.80404	−	6.58879i	0.517664	−	0.896621i
$55$	1.00000			0.134840
$56$	−9.93336	+	14.9887i	−1.32740	+	2.00295i
$57$	−2.33822			−0.309704
$58$	2.49232	−	4.31682i	0.327258	−	0.566827i
$59$	−0.929903	−	1.61064i	−0.121063	−	0.209687i	0.799124	−	0.601166i	$-0.205297\pi$
$59$	−0.929903	−	1.61064i	−0.121063	−	0.209687i	−0.920187	+	0.391479i	$0.871964\pi$
$60$	1.19407	+	2.06819i	0.154154	+	0.267002i
$61$	0.466442	−	0.807902i	0.0597218	−	0.103441i	−0.834619	−	0.550828i	$-0.814312\pi$
$61$	0.466442	−	0.807902i	0.0597218	−	0.103441i	0.894341	+	0.447387i	$0.147645\pi$
$62$	9.25161			1.17496
$63$	−3.22482	−	6.47741i	−0.406289	−	0.816077i
$64$	3.17003			0.396253
$65$	0.985084	−	1.70622i	0.122185	−	0.211630i
$66$	−0.663319	−	1.14890i	−0.0816489	−	0.141420i
$67$	5.77846	+	10.0086i	0.705952	+	1.22274i	0.966347	+	0.257242i	$0.0828138\pi$
$67$	5.77846	+	10.0086i	0.705952	+	1.22274i	−0.260395	+	0.965502i	$0.583853\pi$
$68$	5.53798	−	9.59207i	0.671579	−	1.16321i
$69$	1.39788			0.168285
$70$	6.80360	+	0.420095i	0.813185	+	0.0502110i
$71$	−12.4842			−1.48160			−0.740801	−	0.671725i	$-0.765554\pi$
$71$	−12.4842			−1.48160			−0.740801	+	0.671725i	$0.765554\pi$
$72$	−9.29355	+	16.0969i	−1.09526	+	1.89704i
$73$	3.58365	+	6.20706i	0.419435	+	0.726482i	0.995883	−	0.0906518i	$-0.0288950\pi$
$73$	3.58365	+	6.20706i	0.419435	+	0.726482i	−0.576448	+	0.817134i	$0.695562\pi$
$74$	7.90633	+	13.6942i	0.919093	+	1.59191i
$75$	0.257458	−	0.445930i	0.0297287	−	0.0514916i
$76$	21.0606			2.41582
$77$	−2.64072	−	0.163054i	−0.300938	−	0.0185817i
$78$	−2.61370			−0.295943
$79$	0.410115	−	0.710340i	0.0461416	−	0.0799195i	−0.842032	−	0.539427i	$-0.818641\pi$
$79$	0.410115	−	0.710340i	0.0461416	−	0.0799195i	0.888174	+	0.459508i	$0.151974\pi$
$80$	−4.11721	−	7.13121i	−0.460318	−	0.797294i
$81$	−3.34203	−	5.78856i	−0.371336	−	0.643173i
$82$	10.5668	−	18.3023i	1.16691	−	2.02115i
$83$	−9.83688			−1.07974			−0.539869	−	0.841749i	$-0.681526\pi$
$83$	−9.83688			−1.07974			−0.539869	+	0.841749i	$0.681526\pi$
$84$	−2.81598	−	5.65620i	−0.307248	−	0.617142i
$85$	−2.38814			−0.259030
$86$	11.7968	−	20.4327i	1.27209	−	2.20332i
$87$	0.498109	+	0.862750i	0.0534029	+	0.0924965i
$88$	3.39818	+	5.88582i	0.362247	+	0.627431i
$89$	−5.29979	+	9.17950i	−0.561776	+	0.973025i	0.435565	+	0.900157i	$0.356548\pi$
$89$	−5.29979	+	9.17950i	−0.561776	+	0.973025i	−0.997342	+	0.0728679i	$0.976785\pi$
$90$	7.04614			0.742728
$91$	−2.87954	+	4.34502i	−0.301858	+	0.455482i
$92$	−12.5909			−1.31269
$93$	−0.924502	+	1.60129i	−0.0958664	+	0.166046i
$94$	−9.59668	−	16.6219i	−0.989821	−	1.71442i
$95$	−2.27048	−	3.93259i	−0.232947	−	0.403475i
$96$	−1.96249	+	3.39913i	−0.200296	+	0.346922i
$97$	−7.02009			−0.712782			−0.356391	−	0.934337i	$-0.615993\pi$
$97$	−7.02009			−0.712782			−0.356391	+	0.934337i	$0.615993\pi$
$98$	−17.8979	−	2.21871i	−1.80796	−	0.224123i
$99$	−2.73486			−0.274864
$100$	−2.31896	+	4.01655i	−0.231896	+	0.401655i
$101$	−8.29728	−	14.3713i	−0.825610	−	1.43000i	−0.901452	−	0.432879i	$-0.857498\pi$
$101$	−8.29728	−	14.3713i	−0.825610	−	1.43000i	0.0758422	−	0.997120i	$-0.475835\pi$
$102$	1.58410	+	2.74373i	0.156849	+	0.271670i
$103$	−8.02469	+	13.8992i	−0.790696	+	1.36953i	0.134841	+	0.990867i	$0.456948\pi$
$103$	−8.02469	+	13.8992i	−0.790696	+	1.36953i	−0.925537	+	0.378658i	$0.876386\pi$
$104$	13.3900			1.31299
$105$	−0.752586	+	1.13560i	−0.0734449	+	0.110823i
$106$	31.6421			3.07335
$107$	2.71043	−	4.69460i	0.262027	−	0.453844i	−0.704753	−	0.709452i	$-0.748942\pi$
$107$	2.71043	−	4.69460i	0.262027	−	0.453844i	0.966780	+	0.255608i	$0.0822757\pi$
$108$	−6.84782	−	11.8608i	−0.658931	−	1.14130i
$109$	1.29887	+	2.24971i	0.124409	+	0.215483i	0.921502	−	0.388374i	$-0.126963\pi$
$109$	1.29887	+	2.24971i	0.124409	+	0.215483i	−0.797093	+	0.603857i	$0.793630\pi$
$110$	1.28821	−	2.23124i	0.122826	−	0.212740i
$111$	−3.16028			−0.299961
$112$	9.70963	+	19.5029i	0.917474	+	1.84285i
$113$	−12.9031			−1.21382			−0.606909	−	0.794772i	$-0.707591\pi$
$113$	−12.9031			−1.21382			−0.606909	+	0.794772i	$0.707591\pi$
$114$	−3.01211	+	5.21712i	−0.282110	+	0.488628i
$115$	1.35739	+	2.35106i	0.126577	+	0.219238i
$116$	−4.48653	−	7.77090i	−0.416564	−	0.721510i
$117$	−2.69407	+	4.66626i	−0.249067	+	0.431396i
$118$	−4.79163			−0.441106
$119$	6.30640	+	0.389395i	0.578107	+	0.0356958i
$120$	3.49956			0.319464
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.20175	−	2.08149i	−0.108801	−	0.188449i
$123$	2.11186	+	3.65786i	0.190420	+	0.329818i
$124$	8.32711	−	14.4230i	0.747797	−	1.29522i
$125$	1.00000			0.0894427
$126$	−18.6069	−	1.14890i	−1.65763	−	0.102352i
$127$	14.3787			1.27591			0.637953	−	0.770075i	$-0.279781\pi$
$127$	14.3787			1.27591			0.637953	+	0.770075i	$0.279781\pi$
$128$	−3.53890	+	6.12956i	−0.312798	+	0.541782i
$129$	2.35769	+	4.08363i	0.207583	+	0.359544i
$130$	−2.53798	−	4.39592i	−0.222596	−	0.385548i
$131$	10.8824	−	18.8488i	0.950797	−	1.64683i	0.207093	−	0.978321i	$-0.433600\pi$
$131$	10.8824	−	18.8488i	0.950797	−	1.64683i	0.743705	−	0.668508i	$-0.233067\pi$
$132$	−2.38814			−0.207861
$133$	5.35449	+	10.7551i	0.464293	+	0.932585i
$134$	29.7754			2.57221
$135$	−1.47649	+	2.55735i	−0.127076	+	0.220102i
$136$	−8.11532	−	14.0561i	−0.695883	−	1.20530i
$137$	−6.09272	−	10.5529i	−0.520536	−	0.901595i	−0.999715	−	0.0238778i	$-0.992399\pi$
$137$	−6.09272	−	10.5529i	−0.520536	−	0.901595i	0.479179	−	0.877717i	$-0.340935\pi$
$138$	1.80076	−	3.11901i	0.153291	−	0.265508i
$139$	12.6389			1.07201			0.536007	−	0.844214i	$-0.319932\pi$
$139$	12.6389			1.07201			0.536007	+	0.844214i	$0.319932\pi$
$140$	6.77864	−	10.2285i	0.572899	−	0.864464i
$141$	3.83594			0.323044
$142$	−16.0822	+	27.8552i	−1.34959	+	2.33756i
$143$	0.985084	+	1.70622i	0.0823769	+	0.142681i
$144$	11.2600	+	19.5029i	0.938333	+	1.62524i
$145$	−0.967360	+	1.67552i	−0.0803348	+	0.139144i
$146$	18.4659			1.52825
$147$	2.17253	−	2.87609i	0.179188	−	0.237216i
$148$	28.4651			2.33981
$149$	2.08593	−	3.61294i	0.170886	−	0.295983i	−0.767844	−	0.640637i	$-0.778670\pi$
$149$	2.08593	−	3.61294i	0.170886	−	0.295983i	0.938730	+	0.344654i	$0.112004\pi$
$150$	−0.663319	−	1.14890i	−0.0541597	−	0.0938074i
$151$	−2.37809	−	4.11898i	−0.193526	−	0.335198i	0.752890	−	0.658146i	$-0.228659\pi$
$151$	−2.37809	−	4.11898i	−0.193526	−	0.335198i	−0.946416	+	0.322949i	$0.895326\pi$
$152$	15.4310	−	26.7273i	1.25162	−	2.16787i
$153$	6.53122			0.528018
$154$	−3.76561	+	5.68204i	−0.303442	+	0.457872i
$155$	−3.59089			−0.288427
$156$	−2.35251	+	4.07467i	−0.188352	+	0.326235i
$157$	8.11721	+	14.0594i	0.647824	+	1.12206i	0.983642	+	0.180137i	$0.0576540\pi$
$157$	8.11721	+	14.0594i	0.647824	+	1.12206i	−0.335818	+	0.941927i	$0.609013\pi$
$158$	−1.05663	−	1.83013i	−0.0840607	−	0.145597i
$159$	−3.16196	+	5.47667i	−0.250759	+	0.434328i
$160$	−7.62255			−0.602616
$161$	−3.20113	−	6.42983i	−0.252284	−	0.506742i
$162$	−17.2209			−1.35300
$163$	−1.40967	+	2.44162i	−0.110414	+	0.191242i	−0.915937	−	0.401322i	$-0.868551\pi$
$163$	−1.40967	+	2.44162i	−0.110414	+	0.191242i	0.805523	+	0.592564i	$0.201884\pi$
$164$	−19.0218	−	32.9468i	−1.48535	−	2.57271i
$165$	0.257458	+	0.445930i	0.0200431	+	0.0347156i
$166$	−12.6719	+	21.9485i	−0.983534	+	1.70353i
$167$	−10.5853			−0.819113			−0.409556	−	0.912285i	$-0.634316\pi$
$167$	−10.5853			−0.819113			−0.409556	+	0.912285i	$0.634316\pi$
$168$	−9.24135	−	0.570617i	−0.712986	−	0.0440240i
$169$	−9.11844			−0.701418
$170$	−3.07641	+	5.32851i	−0.235950	+	0.408678i
$171$	6.20946	+	10.7551i	0.474849	+	0.822463i
$172$	−21.2360	−	36.7818i	−1.61923	−	2.80459i
$173$	−8.09996	+	14.0295i	−0.615828	+	1.06665i	0.374410	+	0.927263i	$0.377845\pi$
$173$	−8.09996	+	14.0295i	−0.615828	+	1.06665i	−0.990239	+	0.139383i	$0.955488\pi$
$174$	2.56667			0.194579
$175$	−2.64072	−	0.163054i	−0.199620	−	0.0123257i
$176$	8.23442			0.620692
$177$	0.478822	−	0.829344i	0.0359905	−	0.0623373i
$178$	13.6544	+	23.6502i	1.02344	+	1.77266i
$179$	12.6395	+	21.8923i	0.944723	+	1.63631i	0.756305	+	0.654219i	$0.227003\pi$
$179$	12.6395	+	21.8923i	0.944723	+	1.63631i	0.188418	+	0.982089i	$0.439664\pi$
$180$	6.34203	−	10.9847i	0.472707	−	0.818752i
$181$	−23.8993			−1.77642			−0.888211	−	0.459435i	$-0.848052\pi$
$181$	−23.8993			−1.77642			−0.888211	+	0.459435i	$0.848052\pi$
$182$	5.98534	+	12.0222i	0.443663	+	0.891147i
$183$	0.480357			0.0355090
$184$	−9.22529	+	15.9787i	−0.680097	+	1.17796i
$185$	−3.06873	−	5.31520i	−0.225618	−	0.390782i
$186$	2.38190	+	4.12557i	0.174650	+	0.302502i
$187$	1.19407	−	2.06819i	0.0873189	−	0.151241i
$188$	−34.5508			−2.51987
$189$	4.31598	−	6.51250i	0.313941	−	0.473715i
$190$	−11.6994			−0.848765
$191$	10.4030	−	18.0185i	0.752734	−	1.30377i	−0.193758	−	0.981049i	$-0.562068\pi$
$191$	10.4030	−	18.0185i	0.752734	−	1.30377i	0.946493	−	0.322725i	$-0.104599\pi$
$192$	0.816149	+	1.41361i	0.0589004	+	0.102019i
$193$	2.61567	+	4.53048i	0.188280	+	0.326111i	0.944677	−	0.328002i	$-0.106375\pi$
$193$	2.61567	+	4.53048i	0.188280	+	0.326111i	−0.756397	+	0.654113i	$0.773042\pi$
$194$	−9.04333	+	15.6635i	−0.649273	+	1.12457i
$195$	1.01447			0.0726478
$196$	−19.5683	+	25.9053i	−1.39773	+	1.85038i
$197$	−26.8975			−1.91637			−0.958183	−	0.286155i	$-0.907623\pi$
$197$	−26.8975			−1.91637			−0.958183	+	0.286155i	$0.907623\pi$
$198$	−3.52307	+	6.10213i	−0.250374	+	0.433660i
$199$	−13.7206	−	23.7649i	−0.972631	−	1.68465i	−0.687541	−	0.726145i	$-0.741310\pi$
$199$	−13.7206	−	23.7649i	−0.972631	−	1.68465i	−0.285089	−	0.958501i	$-0.592023\pi$
$200$	3.39818	+	5.88582i	0.240288	+	0.416190i
$201$	−2.97542	+	5.15358i	−0.209870	+	0.363506i
$202$	−42.7545			−3.00819
$203$	2.82773	−	4.26684i	0.198468	−	0.299473i
$204$	5.70319			0.399303
$205$	−4.10137	+	7.10379i	−0.286452	+	0.496150i
$206$	20.6749	+	35.8100i	1.44049	+	2.49500i
$207$	−3.71226	−	6.42983i	−0.258020	−	0.446904i
$208$	8.11159	−	14.0497i	0.562438	−	0.974171i
$209$	4.54097			0.314105
$210$	1.56431	+	3.14209i	0.107947	+	0.216825i
$211$	−11.1901			−0.770359			−0.385180	−	0.922842i	$-0.625860\pi$
$211$	−11.1901			−0.770359			−0.385180	+	0.922842i	$0.625860\pi$
$212$	28.4801	−	49.3290i	1.95602	−	3.38793i
$213$	−3.21416	−	5.56708i	−0.220230	−	0.381450i
$214$	−6.98319	−	12.0952i	−0.477361	−	0.826814i
$215$	−4.57878	+	7.93068i	−0.312270	+	0.540868i
$216$	−20.0695			−1.36555
$217$	9.48253	+	0.585509i	0.643716	+	0.0397469i
$218$	6.69285			0.453297
$219$	−1.84528	+	3.19612i	−0.124692	+	0.215974i
$220$	−2.31896	−	4.01655i	−0.156344	−	0.270796i
$221$	−2.35251	−	4.07467i	−0.158247	−	0.274092i
$222$	−4.07110	+	7.05135i	−0.273234	+	0.473256i
$223$	17.0992			1.14505			0.572523	−	0.819889i	$-0.305965\pi$
$223$	17.0992			1.14505			0.572523	+	0.819889i	$0.305965\pi$
$224$	20.1290	+	1.24289i	1.34493	+	0.0830440i
$225$	−2.73486			−0.182324
$226$	−16.6218	+	28.7898i	−1.10567	+	1.91507i
$227$	1.76416	+	3.05562i	0.117092	+	0.202809i	0.918614	−	0.395156i	$-0.129310\pi$
$227$	1.76416	+	3.05562i	0.117092	+	0.202809i	−0.801522	+	0.597965i	$0.795976\pi$
$228$	5.42222	+	9.39157i	0.359095	+	0.621972i
$229$	−6.62255	+	11.4706i	−0.437631	+	0.757998i	−0.997506	−	0.0705782i	$-0.977516\pi$
$229$	−6.62255	+	11.4706i	−0.437631	+	0.757998i	0.559876	+	0.828577i	$0.310849\pi$
$230$	6.99438			0.461196
$231$	−0.607164	−	1.21956i	−0.0399485	−	0.0802410i
$232$	−13.1490			−0.863277
$233$	6.16051	−	10.6703i	0.403588	−	0.699036i	−0.590568	−	0.806988i	$-0.701096\pi$
$233$	6.16051	−	10.6703i	0.403588	−	0.699036i	0.994156	+	0.107952i	$0.0344294\pi$
$234$	6.94104	+	12.0222i	0.453750	+	0.785918i
$235$	3.72482	+	6.45157i	0.242980	+	0.420854i
$236$	−4.31281	+	7.47001i	−0.280740	+	0.486256i
$237$	0.422350			0.0274346
$238$	8.99279	−	13.5695i	0.582916	−	0.879579i
$239$	15.7503			1.01880			0.509400	−	0.860530i	$-0.329867\pi$
$239$	15.7503			1.01880			0.509400	+	0.860530i	$0.329867\pi$
$240$	2.12002	−	3.67198i	0.136846	−	0.237025i
$241$	8.04711	+	13.9380i	0.518360	+	0.897826i	0.999772	+	0.0213317i	$0.00679061\pi$
$241$	8.04711	+	13.9380i	0.518360	+	0.897826i	−0.481412	+	0.876494i	$0.659876\pi$
$242$	1.28821	+	2.23124i	0.0828091	+	0.143430i
$243$	6.15032	−	10.6527i	0.394543	−	0.683369i
$244$	−4.32664			−0.276985
$245$	6.94683	+	0.861161i	0.443816	+	0.0550176i
$246$	10.8821			0.693816
$247$	4.47323	−	7.74787i	0.284625	−	0.492985i
$248$	−12.2025	−	21.1353i	−0.774858	−	1.34209i
$249$	−2.53258	−	4.38656i	−0.160496	−	0.277987i
$250$	1.28821	−	2.23124i	0.0814734	−	0.141116i
$251$	−21.2232			−1.33960			−0.669798	−	0.742544i	$-0.733619\pi$
$251$	−21.2232			−1.33960			−0.669798	+	0.742544i	$0.733619\pi$
$252$	−18.5386	+	27.9735i	−1.16782	+	1.76216i
$253$	−2.71477			−0.170676
$254$	18.5228	−	32.0824i	1.16222	−	2.01303i
$255$	−0.614845	−	1.06494i	−0.0385031	−	0.0666893i
$256$	12.2877	+	21.2829i	0.767982	+	1.33018i
$257$	0.296360	−	0.513311i	0.0184864	−	0.0320195i	−0.856634	−	0.515924i	$-0.827449\pi$
$257$	0.296360	−	0.513311i	0.0184864	−	0.0320195i	0.875121	+	0.483905i	$0.160782\pi$
$258$	12.1488			0.756349
$259$	7.23701	+	14.5363i	0.449686	+	0.903245i
$260$	−9.13747			−0.566682
$261$	2.64559	−	4.58230i	0.163758	−	0.283637i
$262$	−28.0375	−	48.5624i	−1.73216	−	3.00019i
$263$	5.61919	+	9.73272i	0.346494	+	0.600145i	0.985624	−	0.168953i	$-0.0540388\pi$
$263$	5.61919	+	9.73272i	0.346494	+	0.600145i	−0.639130	+	0.769099i	$0.720705\pi$
$264$	−1.74978	+	3.03070i	−0.107691	+	0.186527i
$265$	−12.2814			−0.754443
$266$	30.8949	+	1.90764i	1.89429	+	0.116965i
$267$	−5.45789			−0.334017
$268$	26.8000	−	46.4190i	1.63707	−	2.83549i
$269$	−1.92748	−	3.33850i	−0.117521	−	0.203552i	0.801264	−	0.598311i	$-0.204161\pi$
$269$	−1.92748	−	3.33850i	−0.117521	−	0.203552i	−0.918785	+	0.394759i	$0.870828\pi$
$270$	3.80404	+	6.58879i	0.231507	+	0.400981i
$271$	5.79149	−	10.0312i	0.351808	−	0.609349i	−0.634758	−	0.772711i	$-0.718900\pi$
$271$	5.79149	−	10.0312i	0.351808	−	0.609349i	0.986566	+	0.163362i	$0.0522337\pi$
$272$	−19.6649			−1.19236
$273$	−2.67894	−	0.165414i	−0.162137	−	0.0100113i
$274$	−31.3948			−1.89663
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−3.24162	−	5.61466i	−0.195123	−	0.337963i
$277$	−1.96689	−	3.40675i	−0.118179	−	0.204692i	0.800867	−	0.598842i	$-0.204372\pi$
$277$	−1.96689	−	3.40675i	−0.118179	−	0.204692i	−0.919046	+	0.394150i	$0.871039\pi$
$278$	16.2815	−	28.2003i	0.976498	−	1.69134i
$279$	9.82058			0.587942
$280$	−8.01394	−	16.0969i	−0.478925	−	0.961974i
$281$	−22.6119			−1.34891			−0.674455	−	0.738316i	$-0.735621\pi$
$281$	−22.6119			−1.34891			−0.674455	+	0.738316i	$0.735621\pi$
$282$	4.94148	−	8.55890i	0.294261	−	0.509675i
$283$	6.45613	+	11.1823i	0.383777	+	0.664721i	0.991599	−	0.129352i	$-0.0412899\pi$
$283$	6.45613	+	11.1823i	0.383777	+	0.664721i	−0.607822	+	0.794073i	$0.707957\pi$
$284$	28.9503	+	50.1434i	1.71788	+	2.97546i
$285$	1.16911	−	2.02495i	0.0692520	−	0.119948i
$286$	5.07597			0.300148
$287$	11.9889	−	18.0904i	0.707682	−	1.06784i
$288$	20.8466			1.22840
$289$	5.64840	−	9.78332i	0.332259	−	0.575489i
$290$	2.49232	+	4.31682i	0.146354	+	0.253493i
$291$	−1.80738	−	3.13047i	−0.105950	−	0.183511i
$292$	16.6207	−	28.7878i	0.972651	−	1.68468i
$293$	−9.52755			−0.556606			−0.278303	−	0.960493i	$-0.589772\pi$
$293$	−9.52755			−0.556606			−0.278303	+	0.960493i	$0.589772\pi$
$294$	−3.61857	−	8.55245i	−0.211039	−	0.498789i
$295$	1.85981			0.108282
$296$	20.8562	−	36.1240i	1.21224	−	2.09967i
$297$	−1.47649	−	2.55735i	−0.0856744	−	0.148392i
$298$	−5.37422	−	9.30842i	−0.311320	−	0.539223i
$299$	−2.67428	+	4.63199i	−0.154658	+	0.267875i
$300$	−2.38814			−0.137879
$301$	13.3844	−	20.1961i	0.771465	−	1.16409i
$302$	−12.2539			−0.705133
$303$	4.27240	−	7.40002i	0.245443	−	0.425120i
$304$	−18.6961	−	32.3826i	−1.07230	−	1.85727i
$305$	0.466442	+	0.807902i	0.0267084	+	0.0462603i
$306$	8.41357	−	14.5727i	0.480972	−	0.833067i
$307$	26.4909			1.51192			0.755959	−	0.654619i	$-0.227171\pi$
$307$	26.4909			1.51192			0.755959	+	0.654619i	$0.227171\pi$
$308$	5.46881	+	10.9847i	0.311614	+	0.625912i
$309$	−8.26408			−0.470127
$310$	−4.62581	+	8.01213i	−0.262728	+	0.455058i
$311$	−11.5757	−	20.0498i	−0.656400	−	1.13692i	−0.981541	−	0.191253i	$-0.938745\pi$
$311$	−11.5757	−	20.0498i	−0.656400	−	1.13692i	0.325141	−	0.945666i	$-0.394588\pi$
$312$	3.44736	+	5.97099i	0.195168	+	0.338041i
$313$	−13.1669	+	22.8058i	−0.744240	+	1.28906i	0.206309	+	0.978487i	$0.433855\pi$
$313$	−13.1669	+	22.8058i	−0.744240	+	1.28906i	−0.950549	+	0.310574i	$0.899479\pi$
$314$	41.8266			2.36041
$315$	7.22201	+	0.445930i	0.406914	+	0.0251253i
$316$	−3.80416			−0.214001
$317$	9.09514	−	15.7532i	0.510834	−	0.884790i	−0.489087	−	0.872235i	$-0.662670\pi$
$317$	9.09514	−	15.7532i	0.510834	−	0.884790i	0.999921	−	0.0125555i	$-0.00399665\pi$
$318$	8.14651	+	14.1102i	0.456834	+	0.791259i
$319$	−0.967360	−	1.67552i	−0.0541617	−	0.0938109i
$320$	−1.58501	+	2.74532i	−0.0886049	+	0.153468i
$321$	2.79129			0.155795
$322$	−18.4702	−	1.14046i	−1.02931	−	0.0635555i
$323$	−10.8444			−0.603401
$324$	−15.5000	+	26.8468i	−0.861113	+	1.49149i
$325$	0.985084	+	1.70622i	0.0546426	+	0.0946438i
$326$	3.63190	+	6.29063i	0.201152	+	0.348406i
$327$	−0.668809	+	1.15841i	−0.0369852	+	0.0640602i
$328$	−55.7488			−3.07821
$329$	−8.78425	−	17.6442i	−0.484292	−	0.972754i
$330$	1.32664			0.0730290
$331$	8.08203	−	13.9985i	0.444229	−	0.769427i	−0.553769	−	0.832670i	$-0.686811\pi$
$331$	8.08203	−	13.9985i	0.444229	−	0.769427i	0.997998	+	0.0632434i	$0.0201445\pi$
$332$	22.8113	+	39.5103i	1.25193	+	2.16841i
$333$	8.39256	+	14.5363i	0.459910	+	0.796587i
$334$	−13.6360	+	23.6183i	−0.746130	+	1.29234i
$335$	−11.5569			−0.631422
$336$	−6.19711	+	9.35099i	−0.338080	+	0.510138i
$337$	11.0763			0.603365			0.301683	−	0.953408i	$-0.402452\pi$
$337$	11.0763			0.603365			0.301683	+	0.953408i	$0.402452\pi$
$338$	−11.7464	+	20.3454i	−0.638922	+	1.10665i
$339$	−3.32199	−	5.75386i	−0.180426	−	0.312507i
$340$	5.53798	+	9.59207i	0.300339	+	0.520203i
$341$	1.79544	−	3.10980i	0.0972287	−	0.168405i
$342$	31.9963			1.73016
$343$	−18.2042	−	3.40680i	−0.982936	−	0.183950i
$344$	−62.2381			−3.35565
$345$	−0.698940	+	1.21060i	−0.0376297	+	0.0651765i
$346$	20.8688	+	36.1459i	1.12192	+	1.94322i
$347$	7.42585	+	12.8619i	0.398640	+	0.690466i	0.993558	−	0.113321i	$-0.0361488\pi$
$347$	7.42585	+	12.8619i	0.398640	+	0.690466i	−0.594918	+	0.803786i	$0.702815\pi$
$348$	2.31019	−	4.00136i	0.123839	−	0.214495i
$349$	−0.178880			−0.00957522			−0.00478761	−	0.999989i	$-0.501524\pi$
$349$	−0.178880			−0.00957522			−0.00478761	+	0.999989i	$0.501524\pi$
$350$	−3.76561	+	5.68204i	−0.201280	+	0.303718i
$351$	−5.81785			−0.310534
$352$	3.81128	−	6.60132i	0.203142	−	0.351852i
$353$	13.7946	+	23.8929i	0.734210	+	1.27169i	0.955069	+	0.296383i	$0.0957806\pi$
$353$	13.7946	+	23.8929i	0.734210	+	1.27169i	−0.220859	+	0.975306i	$0.570886\pi$
$354$	−1.23364	−	2.13673i	−0.0655675	−	0.113566i
$355$	6.24210	−	10.8116i	0.331296	−	0.573822i
$356$	49.1599			2.60547
$357$	1.44999	+	2.91247i	0.0767417	+	0.154144i
$358$	65.1294			3.44219
$359$	−4.09089	+	7.08562i	−0.215909	+	0.373965i	−0.953553	−	0.301224i	$-0.902605\pi$
$359$	−4.09089	+	7.08562i	−0.215909	+	0.373965i	0.737645	+	0.675189i	$0.235938\pi$
$360$	−9.29355	−	16.0969i	−0.489813	−	0.848381i
$361$	−0.810186	−	1.40328i	−0.0426414	−	0.0738570i
$362$	−30.7873	+	53.3251i	−1.61814	+	2.80271i
$363$	−0.514916			−0.0270261
$364$	24.1295	+	1.48990i	1.26473	+	0.0780921i
$365$	−7.16730			−0.375154
$366$	0.618800	−	1.07179i	0.0323452	−	0.0560235i
$367$	4.02833	+	6.97727i	0.210277	+	0.364211i	0.951801	−	0.306716i	$-0.0992300\pi$
$367$	4.02833	+	6.97727i	0.210277	+	0.364211i	−0.741524	+	0.670926i	$0.765897\pi$
$368$	11.1773	+	19.3596i	0.582656	+	1.00919i
$369$	11.2167	−	19.4279i	0.583918	−	1.01138i
$370$	−15.8127			−0.822061
$371$	32.4319	+	2.00254i	1.68378	+	0.103967i
$372$	8.57552			0.444620
$373$	12.9350	−	22.4040i	0.669748	−	1.16004i	−0.308227	−	0.951313i	$-0.599736\pi$
$373$	12.9350	−	22.4040i	0.669748	−	1.16004i	0.977975	−	0.208724i	$-0.0669311\pi$
$374$	−3.07641	−	5.32851i	−0.159078	−	0.275531i
$375$	0.257458	+	0.445930i	0.0132951	+	0.0230277i
$376$	−25.3152	+	43.8472i	−1.30553	+	2.26125i
$377$	−3.81172			−0.196314
$378$	−8.97109	−	18.0194i	−0.461423	−	0.926820i
$379$	−14.7314			−0.756702			−0.378351	−	0.925662i	$-0.623509\pi$
$379$	−14.7314			−0.756702			−0.378351	+	0.925662i	$0.623509\pi$
$380$	−10.5303	+	18.2390i	−0.540193	+	0.935642i
$381$	3.70192	+	6.41192i	0.189655	+	0.328492i
$382$	−26.8024	−	46.4232i	−1.37133	−	2.37522i
$383$	5.63221	−	9.75528i	0.287793	−	0.498471i	−0.685490	−	0.728082i	$-0.740412\pi$
$383$	5.63221	−	9.75528i	0.287793	−	0.498471i	0.973283	+	0.229611i	$0.0737453\pi$
$384$	−3.64448			−0.185981
$385$	1.46157	−	2.20541i	0.0744885	−	0.112398i
$386$	13.4781			0.686018
$387$	12.5223	−	21.6893i	0.636546	−	1.10253i
$388$	16.2793	+	28.1965i	0.826455	+	1.43146i
$389$	−4.36760	−	7.56491i	−0.221446	−	0.383556i	0.733801	−	0.679364i	$-0.237744\pi$
$389$	−4.36760	−	7.56491i	−0.221446	−	0.383556i	−0.955247	+	0.295808i	$0.904411\pi$
$390$	1.30685	−	2.26353i	0.0661749	−	0.114618i
$391$	6.48325			0.327872
$392$	18.5379	+	43.8142i	0.936307	+	2.21295i
$393$	11.2070			0.565319
$394$	−34.6495	+	60.0148i	−1.74562	+	3.02350i
$395$	0.410115	+	0.710340i	0.0206351	+	0.0357411i
$396$	6.34203	+	10.9847i	0.318699	+	0.552002i
$397$	−15.3358	+	26.5624i	−0.769681	+	1.33313i	0.168054	+	0.985778i	$0.446252\pi$
$397$	−15.3358	+	26.5624i	−0.769681	+	1.33313i	−0.937736	+	0.347349i	$0.887082\pi$
$398$	−70.7002			−3.54388
$399$	−3.41747	+	5.15671i	−0.171087	+	0.258159i
$400$	8.23442			0.411721
$401$	1.67885	−	2.90786i	0.0838379	−	0.145211i	−0.821058	−	0.570845i	$-0.806616\pi$
$401$	1.67885	−	2.90786i	0.0838379	−	0.145211i	0.904895	+	0.425634i	$0.139949\pi$
$402$	7.66593	+	13.2778i	0.382342	+	0.662235i
$403$	−3.53732	−	6.12683i	−0.176207	−	0.305199i
$404$	−38.4821	+	66.6529i	−1.91455	+	3.31610i
$405$	6.68405			0.332133
$406$	−5.87765	−	11.8059i	−0.291703	−	0.585918i
$407$	6.13747			0.304223
$408$	4.17871	−	7.23773i	0.206877	−	0.358321i
$409$	0.440953	+	0.763754i	0.0218037	+	0.0377652i	0.876721	−	0.480999i	$-0.159726\pi$
$409$	0.440953	+	0.763754i	0.0218037	+	0.0377652i	−0.854918	+	0.518764i	$0.826392\pi$
$410$	10.5668	+	18.3023i	0.521859	+	0.903887i
$411$	3.13724	−	5.43386i	0.154749	−	0.268032i
$412$	74.4356			3.66718
$413$	−4.91123	−	0.303249i	−0.241666	−	0.0149219i
$414$	−19.1287			−0.940123
$415$	4.91844	−	8.51899i	0.241437	−	0.418181i
$416$	−7.50885	−	13.0057i	−0.368152	−	0.637658i
$417$	3.25398	+	5.63605i	0.159348	+	0.275999i
$418$	5.84971	−	10.1320i	0.286118	−	0.495572i
$419$	16.8636			0.823843			0.411921	−	0.911219i	$-0.364858\pi$
$419$	16.8636			0.823843			0.411921	+	0.911219i	$0.364858\pi$
$420$	6.30640	+	0.389395i	0.307721	+	0.0190006i
$421$	−38.1275			−1.85822			−0.929111	−	0.369801i	$-0.879426\pi$
$421$	−38.1275			−1.85822			−0.929111	+	0.369801i	$0.879426\pi$
$422$	−14.4152	+	24.9678i	−0.701720	+	1.21542i
$423$	−10.1869	−	17.6442i	−0.495302	−	0.857888i
$424$	−41.7346	−	72.2864i	−2.02681	−	3.51054i
$425$	1.19407	−	2.06819i	0.0579208	−	0.100322i
$426$	−16.5620			−0.802431
$427$	−1.10001	−	2.20950i	−0.0532333	−	0.106925i
$428$	−25.1415			−1.21526
$429$	−0.507236	+	0.878558i	−0.0244896	+	0.0424172i
$430$	11.7968	+	20.4327i	0.568894	+	0.985353i
$431$	0.196132	+	0.339710i	0.00944734	+	0.0163633i	0.870710	−	0.491796i	$-0.163659\pi$
$431$	0.196132	+	0.339710i	0.00944734	+	0.0163633i	−0.861263	+	0.508159i	$0.830326\pi$
$432$	−12.1580	+	21.0583i	−0.584952	+	1.01317i
$433$	−6.86253			−0.329792			−0.164896	−	0.986311i	$-0.552729\pi$
$433$	−6.86253			−0.329792			−0.164896	+	0.986311i	$0.552729\pi$
$434$	13.5219	−	20.4036i	0.649071	−	0.979402i
$435$	−0.996218			−0.0477650
$436$	6.02404	−	10.4339i	0.288499	−	0.499695i
$437$	6.16385	+	10.6761i	0.294857	+	0.510707i
$438$	4.75420	+	8.23452i	0.227165	+	0.393461i
$439$	0.766528	−	1.32767i	0.0365844	−	0.0633660i	−0.847153	−	0.531348i	$-0.821686\pi$
$439$	0.766528	−	1.32767i	0.0365844	−	0.0633660i	0.883738	+	0.467982i	$0.155019\pi$
$440$	−6.79636			−0.324004
$441$	−18.9986	−	2.35516i	−0.904696	−	0.112150i
$442$	−12.1221			−0.576590
$443$	8.37422	−	14.5046i	0.397871	−	0.689133i	−0.595592	−	0.803287i	$-0.703082\pi$
$443$	8.37422	−	14.5046i	0.397871	−	0.689133i	0.993463	+	0.114154i	$0.0364157\pi$
$444$	7.32856	+	12.6934i	0.347798	+	0.602404i
$445$	−5.29979	−	9.17950i	−0.251234	−	0.435150i
$446$	22.0273	−	38.1524i	1.04302	−	1.80657i
$447$	2.14816			0.101604
$448$	4.63321	−	6.99119i	0.218899	−	0.330303i
$449$	11.8164			0.557653			0.278826	−	0.960342i	$-0.410055\pi$
$449$	11.8164			0.557653			0.278826	+	0.960342i	$0.410055\pi$
$450$	−3.52307	+	6.10213i	−0.166079	+	0.287657i
$451$	−4.10137	−	7.10379i	−0.193126	−	0.334504i
$452$	29.9216	+	51.8258i	1.40739	+	2.43768i
$453$	1.22452	−	2.12093i	0.0575329	−	0.0996499i
$454$	9.09044			0.426636
$455$	−2.32313	−	4.66626i	−0.108910	−	0.218758i
$456$	15.8914			0.744181
$457$	8.92255	−	15.4543i	0.417380	−	0.722923i	−0.578295	−	0.815827i	$-0.696282\pi$
$457$	8.92255	−	15.4543i	0.417380	−	0.722923i	0.995675	+	0.0929049i	$0.0296152\pi$
$458$	17.0624	+	29.5530i	0.797276	+	1.38092i
$459$	3.52605	+	6.10730i	0.164582	+	0.285064i
$460$	6.29544	−	10.9040i	0.293527	−	0.508403i
$461$	−15.5475			−0.724121			−0.362060	−	0.932155i	$-0.617927\pi$
$461$	−15.5475			−0.724121			−0.362060	+	0.932155i	$0.617927\pi$
$462$	−3.50328	−	0.216314i	−0.162987	−	0.0100638i
$463$	−10.2066			−0.474340			−0.237170	−	0.971468i	$-0.576220\pi$
$463$	−10.2066			−0.474340			−0.237170	+	0.971468i	$0.576220\pi$
$464$	−7.96564	+	13.7969i	−0.369796	+	0.640505i
$465$	−0.924502	−	1.60129i	−0.0428728	−	0.0742578i
$466$	−15.8720	−	27.4912i	−0.735258	−	1.27350i
$467$	−1.84717	+	3.19939i	−0.0854768	+	0.148050i	−0.905594	−	0.424145i	$-0.860575\pi$
$467$	−1.84717	+	3.19939i	−0.0854768	+	0.148050i	0.820117	+	0.572195i	$0.193908\pi$
$468$	24.9897			1.15515
$469$	30.5186	+	1.88440i	1.40922	+	0.0870137i
$470$	19.1934			0.885323
$471$	−4.17968	+	7.23942i	−0.192590	+	0.333575i
$472$	6.31996	+	10.9465i	0.290900	+	0.503853i
$473$	−4.57878	−	7.93068i	−0.210532	−	0.364653i
$474$	0.544074	−	0.942364i	0.0249901	−	0.0432842i
$475$	4.54097			0.208354
$476$	−13.0603	−	26.2330i	−0.598616	−	1.20239i
$477$	33.5880			1.53789
$478$	20.2896	−	35.1427i	0.928026	−	1.60739i
$479$	−6.38976	−	11.0674i	−0.291955	−	0.505682i	0.682317	−	0.731057i	$-0.260973\pi$
$479$	−6.38976	−	11.0674i	−0.291955	−	0.505682i	−0.974272	+	0.225375i	$0.927639\pi$
$480$	−1.96249	−	3.39913i	−0.0895749	−	0.155148i
$481$	6.04592	−	10.4718i	0.275670	−	0.477475i
$482$	41.4654			1.88870
$483$	2.04310	−	3.08289i	0.0929643	−	0.140277i
$484$	4.63791			0.210814
$485$	3.51004	−	6.07957i	0.159383	−	0.276059i
$486$	−15.8458	−	27.4457i	−0.718779	−	1.24496i
$487$	9.60645	+	16.6389i	0.435310	+	0.753978i	0.997321	−	0.0731512i	$-0.0233056\pi$
$487$	9.60645	+	16.6389i	0.435310	+	0.753978i	−0.562011	+	0.827130i	$0.689972\pi$
$488$	−3.17011	+	5.49079i	−0.143504	+	0.248556i
$489$	−1.45172			−0.0656492
$490$	10.8704	−	14.3907i	0.491075	−	0.650105i
$491$	13.0183			0.587508			0.293754	−	0.955881i	$-0.405095\pi$
$491$	13.0183			0.587508			0.293754	+	0.955881i	$0.405095\pi$
$492$	9.79464	−	16.9648i	0.441577	−	0.764833i
$493$	2.31019	+	4.00136i	0.104046	+	0.180212i
$494$	−11.5249	−	19.9617i	−0.518530	−	0.898120i
$495$	1.36743	−	2.36846i	0.0614614	−	0.106454i
$496$	−29.5689			−1.32768
$497$	−18.2465	+	27.5327i	−0.818468	+	1.23501i
$498$	−13.0500			−0.584783
$499$	10.1432	−	17.5685i	0.454071	−	0.786473i	−0.544564	−	0.838720i	$-0.683305\pi$
$499$	10.1432	−	17.5685i	0.454071	−	0.786473i	0.998634	+	0.0522462i	$0.0166380\pi$
$500$	−2.31896	−	4.01655i	−0.103707	−	0.179626i
$501$	−2.72526	−	4.72029i	−0.121756	−	0.210887i
$502$	−27.3399	+	47.3540i	−1.22024	+	2.11351i
$503$	20.6614			0.921247			0.460624	−	0.887596i	$-0.347626\pi$
$503$	20.6614			0.921247			0.460624	+	0.887596i	$0.347626\pi$
$504$	21.9170	+	44.0228i	0.976262	+	1.96093i
$505$	16.5946			0.738448
$506$	−3.49719	+	6.05731i	−0.155469	+	0.269280i
$507$	−2.34762	−	4.06619i	−0.104261	−	0.180586i
$508$	−33.3437	−	57.7529i	−1.47939	−	2.56237i
$509$	5.89418	−	10.2090i	0.261255	−	0.452507i	−0.705321	−	0.708888i	$-0.749197\pi$
$509$	5.89418	−	10.2090i	0.261255	−	0.452507i	0.966576	+	0.256381i	$0.0825303\pi$
$510$	−3.16819			−0.140290
$511$	18.9269	+	1.16866i	0.837275	+	0.0516984i
$512$	49.1608			2.17262
$513$	−6.70467	+	11.6128i	−0.296019	+	0.512719i
$514$	−0.763547	−	1.32250i	−0.0336786	−	0.0583331i
$515$	−8.02469	−	13.8992i	−0.353610	−	0.612470i
$516$	10.9347	−	18.9395i	0.481375	−	0.833767i
$517$	−7.44964			−0.327635
$518$	41.7569	+	2.57832i	1.83469	+	0.113285i
$519$	−8.34159			−0.366155
$520$	−6.69499	+	11.5961i	−0.293595	+	0.508521i
$521$	13.8494	+	23.9879i	0.606755	+	1.05093i	0.991772	+	0.128020i	$0.0408623\pi$
$521$	13.8494	+	23.9879i	0.606755	+	1.05093i	−0.385017	+	0.922910i	$0.625804\pi$
$522$	−6.81615	−	11.8059i	−0.298335	−	0.516731i
$523$	−10.8334	+	18.7640i	−0.473713	+	0.820495i	−0.999547	−	0.0300925i	$-0.990420\pi$
$523$	−10.8334	+	18.7640i	−0.473713	+	0.820495i	0.525834	+	0.850587i	$0.323753\pi$
$524$	−100.943			−4.40972
$525$	−0.607164	−	1.21956i	−0.0264988	−	0.0532259i
$526$	28.9547			1.26249
$527$	−4.28776	+	7.42662i	−0.186778	+	0.323509i
$528$	2.12002	+	3.67198i	0.0922619	+	0.159802i
$529$	7.81500	+	13.5360i	0.339783	+	0.588521i
$530$	−15.8210	+	27.4029i	−0.687222	+	1.19030i
$531$	−5.08631			−0.220727
$532$	30.7816	−	46.4472i	1.33455	−	2.01374i
$533$	−16.1608			−0.700002
$534$	−7.03089	+	12.1779i	−0.304257	+	0.526988i
$535$	2.71043	+	4.69460i	0.117182	+	0.202965i
$536$	−39.2725	−	68.0220i	−1.69631	−	2.93810i
$537$	−6.50830	+	11.2727i	−0.280854	+	0.486453i
$538$	−9.93199			−0.428199
$539$	−4.21920	+	5.58555i	−0.181734	+	0.240587i
$540$	13.6956			0.589366
$541$	−16.6244	+	28.7943i	−0.714738	+	1.23796i	0.248322	+	0.968678i	$0.420121\pi$
$541$	−16.6244	+	28.7943i	−0.714738	+	1.23796i	−0.963060	+	0.269285i	$0.913212\pi$
$542$	−14.9213	−	25.8444i	−0.640924	−	1.11011i
$543$	−6.15307	−	10.6574i	−0.264054	−	0.457354i
$544$	−9.10185	+	15.7649i	−0.390238	+	0.675913i
$545$	−2.59774			−0.111275
$546$	−3.82010	+	5.76426i	−0.163485	+	0.246688i
$547$	8.82697			0.377414			0.188707	−	0.982033i	$-0.439570\pi$
$547$	8.82697			0.377414			0.188707	+	0.982033i	$0.439570\pi$
$548$	−28.2575	+	48.9434i	−1.20710	+	2.09076i
$549$	−1.27565	−	2.20950i	−0.0544436	−	0.0942991i
$550$	1.28821	+	2.23124i	0.0549294	+	0.0951404i
$551$	−4.39275	+	7.60846i	−0.187137	+	0.324131i
$552$	−9.50050			−0.404368
$553$	−0.967176	−	1.94268i	−0.0411285	−	0.0826112i
$554$	−10.1350			−0.430596
$555$	1.58014	−	2.73688i	0.0670732	−	0.116174i
$556$	−29.3090	−	50.7646i	−1.24298	−	2.15290i
$557$	1.98021	+	3.42983i	0.0839043	+	0.145326i	0.904924	−	0.425574i	$-0.139928\pi$
$557$	1.98021	+	3.42983i	0.0839043	+	0.145326i	−0.821020	+	0.570900i	$0.806594\pi$
$558$	12.6509	−	21.9121i	0.535557	−	0.927612i
$559$	−18.0419			−0.763092
$560$	−21.7448	−	1.34266i	−0.918886	−	0.0567375i
$561$	1.22969			0.0519175
$562$	−29.1288	+	50.4525i	−1.22872	+	2.12821i
$563$	−14.3436	−	24.8438i	−0.604510	−	1.04704i	−0.992129	−	0.125222i	$-0.960036\pi$
$563$	−14.3436	−	24.8438i	−0.604510	−	1.04704i	0.387619	−	0.921820i	$-0.373298\pi$
$564$	−8.89537	−	15.4072i	−0.374563	−	0.648762i
$565$	6.45153	−	11.1744i	0.271418	−	0.470109i
$566$	33.2673			1.39833
$567$	−17.6507	−	1.08986i	−0.741261	−	0.0457699i
$568$	84.8471			3.56010
$569$	−2.67862	+	4.63950i	−0.112294	+	0.194498i	−0.916695	−	0.399589i	$-0.869153\pi$
$569$	−2.67862	+	4.63950i	−0.112294	+	0.194498i	0.804401	+	0.594087i	$0.202486\pi$
$570$	−3.01211	−	5.21712i	−0.126163	−	0.218521i
$571$	−6.04708	−	10.4739i	−0.253063	−	0.438317i	0.711305	−	0.702884i	$-0.248105\pi$
$571$	−6.04708	−	10.4739i	−0.253063	−	0.438317i	−0.964367	+	0.264566i	$0.914771\pi$
$572$	4.56873	−	7.91328i	0.191028	−	0.330871i
$573$	10.7133			0.447556
$574$	−24.9198	−	50.0543i	−1.04013	−	2.08923i
$575$	−2.71477			−0.113214
$576$	4.33479	−	7.50808i	0.180616	−	0.312837i
$577$	−6.67150	−	11.5554i	−0.277738	−	0.481057i	0.693084	−	0.720857i	$-0.256251\pi$
$577$	−6.67150	−	11.5554i	−0.277738	−	0.481057i	−0.970822	+	0.239800i	$0.922918\pi$
$578$	−14.5526	−	25.2059i	−0.605310	−	1.04843i
$579$	−1.34685	+	2.33282i	−0.0559733	+	0.0969485i
$580$	8.97306			0.372586
$581$	−14.3773	+	21.6943i	−0.596471	+	0.900032i
$582$	−9.31311			−0.386041
$583$	6.14072	−	10.6360i	0.254323	−	0.440500i
$584$	−24.3558	−	42.1854i	−1.00785	−	1.74565i
$585$	−2.69407	−	4.66626i	−0.111386	−	0.192926i
$586$	−12.2735	+	21.2583i	−0.507012	+	0.878171i
$587$	−2.31418			−0.0955164			−0.0477582	−	0.998859i	$-0.515208\pi$
$587$	−2.31418			−0.0955164			−0.0477582	+	0.998859i	$0.515208\pi$
$588$	−16.5900	−	2.05657i	−0.684159	−	0.0848115i
$589$	−16.3061			−0.671881
$590$	2.39582	−	4.14968i	0.0986342	−	0.170839i
$591$	−6.92497	−	11.9944i	−0.284855	−	0.493384i
$592$	−25.2692	−	43.7676i	−1.03856	−	1.79884i
$593$	16.2272	−	28.1063i	0.666370	−	1.15419i	−0.312541	−	0.949904i	$-0.601180\pi$
$593$	16.2272	−	28.1063i	0.666370	−	1.15419i	0.978912	−	0.204283i	$-0.0654864\pi$
$594$	−7.60808			−0.312163
$595$	−3.49043	+	5.26681i	−0.143094	+	0.215918i
$596$	−19.3487			−0.792555
$597$	7.06498	−	12.2369i	0.289150	−	0.500823i
$598$	6.89005	+	11.9339i	0.281755	+	0.488014i
$599$	3.22724	+	5.58974i	0.131861	+	0.228391i	0.924394	−	0.381439i	$-0.124571\pi$
$599$	3.22724	+	5.58974i	0.131861	+	0.228391i	−0.792533	+	0.609829i	$0.791238\pi$
$600$	−1.74978	+	3.03070i	−0.0714344	+	0.123728i
$601$	−10.1597			−0.414422			−0.207211	−	0.978296i	$-0.566439\pi$
$601$	−10.1597			−0.414422			−0.207211	+	0.978296i	$0.566439\pi$
$602$	−27.8205	−	55.8806i	−1.13388	−	2.27752i
$603$	31.6066			1.28712
$604$	−11.0294	+	19.1035i	−0.448779	+	0.777309i
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	−11.0075	−	19.0655i	−0.447148	−	0.774484i
$607$	−11.8079	+	20.4519i	−0.479268	+	0.830116i	−0.999717	−	0.0237764i	$-0.992431\pi$
$607$	−11.8079	+	20.4519i	−0.479268	+	0.830116i	0.520450	+	0.853892i	$0.325764\pi$
$608$	−34.6138			−1.40377
$609$	2.63073	+	0.162437i	0.106603	+	0.00658230i
$610$	2.40350			0.0973148
$611$	−7.33852	+	12.7107i	−0.296885	+	0.514219i
$612$	−15.1456	−	26.2330i	−0.612225	−	1.06041i
$613$	2.75091	+	4.76472i	0.111108	+	0.192445i	0.916217	−	0.400682i	$-0.131227\pi$
$613$	2.75091	+	4.76472i	0.111108	+	0.192445i	−0.805109	+	0.593127i	$0.797893\pi$
$614$	34.1258	−	59.1077i	1.37721	−	2.38539i
$615$	−4.22373			−0.170317
$616$	17.9473	+	1.10817i	0.723117	+	0.0446496i
$617$	32.6648			1.31504			0.657518	−	0.753439i	$-0.271606\pi$
$617$	32.6648			1.31504			0.657518	+	0.753439i	$0.271606\pi$
$618$	−10.6459	+	18.4392i	−0.428239	+	0.741732i
$619$	11.6993	+	20.2637i	0.470233	+	0.814468i	0.999421	−	0.0340371i	$-0.0108365\pi$
$619$	11.6993	+	20.2637i	0.470233	+	0.814468i	−0.529187	+	0.848505i	$0.677503\pi$
$620$	8.32711	+	14.4230i	0.334425	+	0.579241i
$621$	4.00833	−	6.94262i	0.160849	−	0.278598i
$622$	−59.6478			−2.39166
$623$	12.4985	+	25.1047i	0.500742	+	1.00580i
$624$	8.35358			0.334411
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	33.9235	+	58.7572i	1.35586	+	2.34841i
$627$	1.16911	+	2.02495i	0.0466897	+	0.0808689i
$628$	37.6469	−	65.2064i	1.50228	−	2.60202i
$629$	−14.6571			−0.584417
$630$	10.2984	−	15.5396i	0.410299	−	0.619112i
$631$	−5.72328			−0.227840			−0.113920	−	0.993490i	$-0.536341\pi$
$631$	−5.72328			−0.227840			−0.113920	+	0.993490i	$0.536341\pi$
$632$	−2.78729	+	4.82773i	−0.110872	+	0.192037i
$633$	−2.88098	−	4.99001i	−0.114509	−	0.198335i
$634$	−23.4329	−	40.5869i	−0.930638	−	1.61191i
$635$	−7.18937	+	12.4524i	−0.285301	+	0.494157i
$636$	29.3298			1.16300
$637$	5.37388	+	12.7011i	0.212921	+	0.503236i
$638$	−4.98464			−0.197344
$639$	−17.0713	+	29.5683i	−0.675329	+	1.16970i
$640$	−3.53890	−	6.12956i	−0.139887	−	0.242292i
$641$	10.3949	+	18.0045i	0.410574	+	0.711135i	0.994953	−	0.100346i	$-0.0319951\pi$
$641$	10.3949	+	18.0045i	0.410574	+	0.711135i	−0.584379	+	0.811481i	$0.698662\pi$
$642$	3.59576	−	6.22804i	0.141913	−	0.245801i
$643$	−29.4788			−1.16253			−0.581264	−	0.813715i	$-0.697442\pi$
$643$	−29.4788			−1.16253			−0.581264	+	0.813715i	$0.697442\pi$
$644$	−18.4025	+	27.7680i	−0.725159	+	1.09421i
$645$	−4.71537			−0.185668
$646$	−13.9699	+	24.1966i	−0.549638	+	0.952001i
$647$	−12.5030	−	21.6557i	−0.491542	−	0.851375i	0.508411	−	0.861115i	$-0.330233\pi$
$647$	−12.5030	−	21.6557i	−0.491542	−	0.851375i	−0.999953	+	0.00973935i	$0.996900\pi$
$648$	22.7136	+	39.3411i	0.892275	+	1.54547i
$649$	−0.929903	+	1.61064i	−0.0365019	+	0.0632231i
$650$	5.07597			0.199096
$651$	2.18026	+	4.37929i	0.0854510	+	0.171638i
$652$	13.0759			0.512090
$653$	−10.9886	+	19.0329i	−0.430018	+	0.744813i	−0.996874	−	0.0790037i	$-0.974826\pi$
$653$	−10.9886	+	19.0329i	−0.430018	+	0.744813i	0.566856	+	0.823817i	$0.308159\pi$
$654$	1.72313	+	2.98455i	0.0673796	+	0.116705i
$655$	10.8824	+	18.8488i	0.425210	+	0.736485i
$656$	−33.7724	+	58.4956i	−1.31859	+	2.28387i
$657$	19.6016			0.764730
$658$	−50.6843	−	3.12955i	−1.97588	−	0.122003i
$659$	27.4501			1.06931			0.534653	−	0.845072i	$-0.320442\pi$
$659$	27.4501			1.06931			0.534653	+	0.845072i	$0.320442\pi$
$660$	1.19407	−	2.06819i	0.0464790	−	0.0805041i
$661$	16.5687	+	28.6979i	0.644449	+	1.11622i	0.984428	+	0.175786i	$0.0562466\pi$
$661$	16.5687	+	28.6979i	0.644449	+	1.11622i	−0.339979	+	0.940433i	$0.610420\pi$
$662$	−20.8227	−	36.0659i	−0.809296	−	1.40174i
$663$	1.21135	−	2.09812i	0.0470448	−	0.0814841i
$664$	66.8550			2.59448
$665$	−11.9914	−	0.740423i	−0.465008	−	0.0287124i
$666$	43.2455			1.67573
$667$	2.62616	−	4.54865i	0.101685	−	0.176124i
$668$	24.5468	+	42.5163i	0.949744	+	1.64500i
$669$	4.40232	+	7.62504i	0.170204	+	0.294801i
$670$	−14.8877	+	25.7863i	−0.575163	+	0.996211i
$671$	−0.932884			−0.0360136
$672$	4.62814	+	9.29614i	0.178534	+	0.358607i
$673$	−34.7534			−1.33965			−0.669823	−	0.742521i	$-0.733630\pi$
$673$	−34.7534			−1.33965			−0.669823	+	0.742521i	$0.733630\pi$
$674$	14.2686	−	24.7139i	0.549606	−	0.951945i
$675$	−1.47649	−	2.55735i	−0.0568300	−	0.0984324i
$676$	21.1453	+	36.6247i	0.813279	+	1.40864i
$677$	5.66402	−	9.81037i	0.217686	−	0.377043i	−0.736414	−	0.676531i	$-0.763482\pi$
$677$	5.66402	−	9.81037i	0.217686	−	0.377043i	0.954100	+	0.299488i	$0.0968158\pi$
$678$	−17.1177			−0.657400
$679$	−10.2604	+	15.4821i	−0.393756	+	0.594150i
$680$	16.2306			0.622416
$681$	−0.908397	+	1.57339i	−0.0348098	+	0.0602924i
$682$	−4.62581	−	8.01213i	−0.177131	−	0.306800i
$683$	−20.9600	−	36.3037i	−0.802011	−	1.38912i	−0.918291	−	0.395907i	$-0.870430\pi$
$683$	−20.9600	−	36.3037i	−0.802011	−	1.38912i	0.116280	−	0.993217i	$-0.462903\pi$
$684$	28.7989	−	49.8812i	1.10115	−	1.90726i
$685$	12.1854			0.465582
$686$	−31.0522	+	36.2293i	−1.18558	+	1.38324i
$687$	−6.82012			−0.260204
$688$	−37.7036	+	65.3045i	−1.43744	+	2.48971i
$689$	−12.0983	−	20.9548i	−0.460907	−	0.798314i
$690$	1.80076	+	3.11901i	0.0685538	+	0.118739i
$691$	−4.05855	+	7.02961i	−0.154394	+	0.267419i	−0.932838	−	0.360295i	$-0.882676\pi$
$691$	−4.05855	+	7.02961i	−0.154394	+	0.267419i	0.778444	+	0.627714i	$0.216009\pi$
$692$	75.1338			2.85616
$693$	−3.99719	+	6.03148i	−0.151841	+	0.229117i
$694$	38.2641			1.45249
$695$	−6.31943	+	10.9456i	−0.239710	+	0.415189i
$696$	−3.38533	−	5.86356i	−0.128321	−	0.222258i
$697$	9.79464	+	16.9648i	0.370999	+	0.642588i
$698$	−0.230434	+	0.399124i	−0.00872207	+	0.0151071i
$699$	6.34429			0.239963
$700$	5.46881	+	10.9847i	0.206701	+	0.415183i
$701$	−18.0131			−0.680347			−0.340174	−	0.940363i	$-0.610486\pi$
$701$	−18.0131			−0.680347			−0.340174	+	0.940363i	$0.610486\pi$
$702$	−7.49460	+	12.9810i	−0.282865	+	0.489937i
$703$	−13.9350	−	24.1362i	−0.525569	−	0.910313i
$704$	−1.58501	−	2.74532i	−0.0597374	−	0.103468i
$705$	−1.91797	+	3.32202i	−0.0722349	+	0.125114i
$706$	71.0810			2.67517
$707$	−43.8216	−	2.70581i	−1.64808	−	0.101762i
$708$	−4.44147			−0.166921
$709$	3.50573	−	6.07211i	0.131661	−	0.228043i	−0.792656	−	0.609669i	$-0.791302\pi$
$709$	3.50573	−	6.07211i	0.131661	−	0.228043i	0.924317	+	0.381626i	$0.124636\pi$
$710$	−16.0822	−	27.8552i	−0.603555	−	1.04539i
$711$	−1.12161	−	1.94268i	−0.0420636	−	0.0728563i
$712$	36.0193	−	62.3872i	1.34988	−	2.33806i
$713$	9.74844			0.365082
$714$	8.36631	+	0.516587i	0.313101	+	0.0193328i
$715$	−1.97017			−0.0736801
$716$	58.6211	−	101.535i	2.19077	−	3.79453i
$717$	4.05504	+	7.02353i	0.151438	+	0.262298i
$718$	10.5398	+	18.2555i	0.393343	+	0.681289i
$719$	11.5406	−	19.9889i	0.430391	−	0.745459i	−0.566516	−	0.824051i	$-0.691709\pi$
$719$	11.5406	−	19.9889i	0.430391	−	0.745459i	0.996907	+	0.0785918i	$0.0250424\pi$
$720$	−22.5200			−0.839270
$721$	18.9247	+	38.0123i	0.704791	+	1.41565i
$722$	−4.17475			−0.155368
$723$	−4.14359	+	7.17690i	−0.154102	+	0.266912i
$724$	55.4215	+	95.9929i	2.05972	+	3.56755i
$725$	−0.967360	−	1.67552i	−0.0359268	−	0.0622271i
$726$	−0.663319	+	1.14890i	−0.0246181	+	0.0426397i
$727$	−43.1087			−1.59881			−0.799407	−	0.600789i	$-0.794853\pi$
$727$	−43.1087			−1.59881			−0.799407	+	0.600789i	$0.794853\pi$
$728$	19.5704	−	29.5303i	0.725327	−	1.09447i
$729$	−13.7184			−0.508087
$730$	−9.23297	+	15.9920i	−0.341728	+	0.591890i
$731$	10.9347	+	18.9395i	0.404436	+	0.700504i
$732$	−1.11393	−	1.92938i	−0.0411719	−	0.0713119i
$733$	6.21394	−	10.7629i	0.229517	−	0.397535i	−0.728148	−	0.685420i	$-0.759619\pi$
$733$	6.21394	−	10.7629i	0.229517	−	0.397535i	0.957665	+	0.287885i	$0.0929520\pi$
$734$	20.7573			0.766166
$735$	1.40450	+	3.31951i	0.0518057	+	0.122442i
$736$	20.6935			0.762773
$737$	5.77846	−	10.0086i	0.212852	−	0.368671i
$738$	−28.8989	−	50.0543i	−1.06378	−	1.84252i
$739$	2.16674	+	3.75291i	0.0797050	+	0.138053i	0.903123	−	0.429383i	$-0.141269\pi$
$739$	2.16674	+	3.75291i	0.0797050	+	0.138053i	−0.823418	+	0.567436i	$0.807936\pi$
$740$	−14.2325	+	24.6515i	−0.523198	+	0.906206i
$741$	4.60668			0.169231
$742$	46.2471	−	69.7836i	1.69779	−	2.56184i
$743$	12.0397			0.441695			0.220848	−	0.975308i	$-0.429118\pi$
$743$	12.0397			0.441695			0.220848	+	0.975308i	$0.429118\pi$
$744$	6.28325	−	10.8829i	0.230355	−	0.398987i
$745$	2.08593	+	3.61294i	0.0764226	+	0.132368i
$746$	−33.3259	−	57.7221i	−1.22015	−	2.11336i
$747$	−13.4513	+	23.2983i	−0.492156	+	0.852439i
$748$	−11.0760			−0.404978
$749$	−6.39202	−	12.8391i	−0.233559	−	0.469130i
$750$	1.32664			0.0484419
$751$	−15.5400	+	26.9161i	−0.567063	+	0.982183i	0.429791	+	0.902928i	$0.358587\pi$
$751$	−15.5400	+	26.9161i	−0.567063	+	0.982183i	−0.996854	+	0.0792542i	$0.974746\pi$
$752$	30.6717	+	53.1249i	1.11848	+	1.93727i
$753$	−5.46408	−	9.46406i	−0.199122	−	0.344890i
$754$	−4.91029	+	8.50487i	−0.178822	+	0.309729i
$755$	4.75618			0.173095
$756$	−36.1664	−	2.23313i	−1.31536	−	0.0812181i
$757$	11.6643			0.423947			0.211973	−	0.977275i	$-0.432011\pi$
$757$	11.6643			0.423947			0.211973	+	0.977275i	$0.432011\pi$
$758$	−18.9771	+	32.8694i	−0.689280	+	1.19387i
$759$	−0.698940	−	1.21060i	−0.0253699	−	0.0439420i
$760$	15.4310	+	26.7273i	0.559742	+	0.969502i
$761$	14.7117	−	25.4814i	0.533299	−	0.923702i	−0.465944	−	0.884814i	$-0.654285\pi$
$761$	14.7117	−	25.4814i	0.533299	−	0.923702i	0.999244	−	0.0388876i	$-0.0123814\pi$
$762$	19.0754			0.691028
$763$	6.85990	+	0.423572i	0.248345	+	0.0153343i
$764$	−96.4964			−3.49112
$765$	−3.26561	+	5.65620i	−0.118068	+	0.204500i
$766$	−14.5109	−	25.1336i	−0.524301	−	0.908116i
$767$	1.83207	+	3.17323i	0.0661521	+	0.114579i
$768$	−6.32714	+	10.9589i	−0.228311	+	0.395446i
$769$	−14.5119			−0.523314			−0.261657	−	0.965161i	$-0.584269\pi$
$769$	−14.5119			−0.523314			−0.261657	+	0.965161i	$0.584269\pi$
$770$	−3.03798	−	6.10213i	−0.109481	−	0.219906i
$771$	0.305201			0.0109916
$772$	12.1313	−	21.0120i	0.436614	−	0.756237i
$773$	−5.34759	−	9.26229i	−0.192339	−	0.333141i	0.753686	−	0.657235i	$-0.228274\pi$
$773$	−5.34759	−	9.26229i	−0.192339	−	0.333141i	−0.946025	+	0.324094i	$0.894941\pi$
$774$	−32.2627	−	55.8806i	−1.15966	−	2.00859i
$775$	1.79544	−	3.10980i	0.0644942	−	0.111707i
$776$	47.7110			1.71273
$777$	−4.61897	+	6.96970i	−0.165705	+	0.250037i
$778$	−22.5055			−0.806862
$779$	−18.6242	+	32.2581i	−0.667281	+	1.15577i
$780$	−2.35251	−	4.07467i	−0.0842335	−	0.145897i
$781$	6.24210	+	10.8116i	0.223360	+	0.386871i
$782$	8.35177	−	14.4657i	0.298659	−	0.517292i
$783$	5.71317			0.204172
$784$	57.2031	+	7.09116i	2.04297	+	0.253256i
$785$	−16.2344			−0.579431
$786$	14.4370	−	25.0056i	0.514949	−	0.891919i
$787$	−0.960998	−	1.66450i	−0.0342559	−	0.0593329i	0.848389	−	0.529373i	$-0.177573\pi$
$787$	−0.960998	−	1.66450i	−0.0342559	−	0.0593329i	−0.882645	+	0.470040i	$0.844239\pi$
$788$	62.3741	+	108.035i	2.22199	+	3.84859i
$789$	−2.89341	+	5.01153i	−0.103008	+	0.178415i
$790$	2.11325			0.0751862
$791$	−18.8587	+	28.4565i	−0.670539	+	1.01180i
$792$	18.5871			0.660464
$793$	−0.918969	+	1.59170i	−0.0326336	+	0.0565230i
$794$	39.5114	+	68.4357i	1.40221	+	2.42869i
$795$	−3.16196	−	5.47667i	−0.112143	−	0.194237i
$796$	−63.6352	+	110.219i	−2.25549	+	3.90662i
$797$	−41.0591			−1.45439			−0.727193	−	0.686433i	$-0.759176\pi$
$797$	−41.0591			−1.45439			−0.727193	+	0.686433i	$0.759176\pi$
$798$	7.10347	+	14.2681i	0.251460	+	0.505086i
$799$	17.7907			0.629391
$800$	3.81128	−	6.60132i	0.134749	−	0.233392i
$801$	14.4942	+	25.1047i	0.512127	+	0.887030i
$802$	−4.32542	−	7.49185i	−0.152736	−	0.264546i
$803$	3.58365	−	6.20706i	0.126464	−	0.219043i
$804$	27.5995			0.973360
$805$	7.16896	+	0.442655i	0.252673	+	0.0156015i
$806$	−18.2272			−0.642027
$807$	0.992492	−	1.71905i	0.0349374	−	0.0605133i
$808$	56.3913	+	97.6726i	1.98384	+	3.43611i
$809$	14.0775	+	24.3830i	0.494939	+	0.857259i	0.999983	−	0.00583444i	$-0.00185717\pi$
$809$	14.0775	+	24.3830i	0.494939	+	0.857259i	−0.505044	+	0.863093i	$0.668524\pi$
$810$	8.61045	−	14.9137i	0.302540	−	0.524015i
$811$	11.4271			0.401261			0.200631	−	0.979667i	$-0.435701\pi$
$811$	11.4271			0.401261			0.200631	+	0.979667i	$0.435701\pi$
$812$	−23.6954	−	1.46309i	−0.831544	−	0.0513445i
$813$	5.96426			0.209176
$814$	7.90633	−	13.6942i	0.277117	−	0.479980i
$815$	−1.40967	−	2.44162i	−0.0493786	−	0.0855262i
$816$	−5.06289	−	8.76918i	−0.177237	−	0.306983i
$817$	−20.7921	+	36.0129i	−0.727423	+	1.25993i
$818$	2.27216			0.0794441
$819$	6.35343	+	12.7616i	0.222007	+	0.445926i
$820$	38.0436			1.32854
$821$	13.4642	−	23.3207i	0.469904	−	0.813898i	−0.529504	−	0.848308i	$-0.677622\pi$
$821$	13.4642	−	23.3207i	0.469904	−	0.813898i	0.999408	+	0.0344099i	$0.0109552\pi$
$822$	−8.08283	−	13.9999i	−0.281921	−	0.488302i
$823$	−14.4519	−	25.0314i	−0.503761	−	0.872540i	−0.999991	−	0.00434836i	$-0.998616\pi$
$823$	−14.4519	−	25.0314i	−0.503761	−	0.872540i	0.496229	−	0.868191i	$-0.334717\pi$
$824$	54.5387	−	94.4637i	1.89994	−	3.29080i
$825$	−0.514916			−0.0179271
$826$	−7.00331	+	10.5675i	−0.243676	+	0.367690i
$827$	46.7846			1.62686			0.813430	−	0.581663i	$-0.197598\pi$
$827$	46.7846			1.62686			0.813430	+	0.581663i	$0.197598\pi$
$828$	−17.2172	+	29.8210i	−0.598338	+	1.03635i
$829$	9.87523	+	17.1044i	0.342981	+	0.594060i	0.984985	−	0.172641i	$-0.0552301\pi$
$829$	9.87523	+	17.1044i	0.342981	+	0.594060i	−0.642004	+	0.766701i	$0.721897\pi$
$830$	−12.6719	−	21.9485i	−0.439850	−	0.761842i
$831$	1.01278	−	1.75419i	0.0351330	−	0.0608522i
$832$	−6.24548			−0.216523
$833$	10.0760	−	13.3390i	0.349114	−	0.462171i
$834$	16.7672			0.580600
$835$	5.29263	−	9.16711i	0.183159	−	0.317241i
$836$	−10.5303	−	18.2390i	−0.364198	−	0.630810i
$837$	5.30189	+	9.18315i	0.183260	+	0.317416i
$838$	21.7239	−	37.6268i	0.750439	−	1.29980i
$839$	−26.0530			−0.899449			−0.449725	−	0.893167i	$-0.648478\pi$
$839$	−26.0530			−0.899449			−0.449725	+	0.893167i	$0.648478\pi$
$840$	5.11484	−	7.71794i	0.176479	−	0.266294i
$841$	−25.2569			−0.870926
$842$	−49.1162	+	85.0717i	−1.69265	+	2.93176i
$843$	−5.82161	−	10.0833i	−0.200507	−	0.347288i
$844$	25.9494	+	44.9457i	0.893215	+	1.54709i
$845$	4.55922	−	7.89680i	0.156842	−	0.271658i
$846$	−52.4912			−1.80468
$847$	1.17915	+	2.36846i	0.0405161	+	0.0813812i
$848$	−101.131			−3.47284
$849$	−3.32436	+	5.75797i	−0.114092	+	0.197613i
$850$	−3.07641	−	5.32851i	−0.105520	−	0.182766i
$851$	8.33092	+	14.4296i	0.285580	+	0.494639i
$852$	−14.9070	+	25.8196i	−0.510705	+	0.884566i
$853$	9.81496			0.336058			0.168029	−	0.985782i	$-0.446260\pi$
$853$	9.81496			0.336058			0.168029	+	0.985782i	$0.446260\pi$
$854$	−6.34697	−	0.391900i	−0.217189	−	0.0134105i
$855$	−12.4189			−0.424718
$856$	−18.4211	+	31.9062i	−0.629619	+	1.09053i
$857$	−15.8253	−	27.4103i	−0.540583	−	0.936317i	−0.998871	−	0.0475132i	$-0.984870\pi$
$857$	−15.8253	−	27.4103i	−0.540583	−	0.936317i	0.458288	−	0.888804i	$-0.348463\pi$
$858$	1.30685	+	2.26353i	0.0446151	+	0.0772756i
$859$	−6.32781	+	10.9601i	−0.215902	+	0.373953i	−0.953551	−	0.301231i	$-0.902603\pi$
$859$	−6.32781	+	10.9601i	−0.215902	+	0.373953i	0.737649	+	0.675184i	$0.235936\pi$
$860$	42.4720			1.44828
$861$	11.1537	+	0.688696i	0.380117	+	0.0234707i
$862$	1.01063			0.0344223
$863$	−11.0652	+	19.1654i	−0.376663	+	0.652399i	−0.990574	−	0.136976i	$-0.956262\pi$
$863$	−11.0652	+	19.1654i	−0.376663	+	0.652399i	0.613912	+	0.789375i	$0.289595\pi$
$864$	11.2546	+	19.4935i	0.382889	+	0.663183i
$865$	−8.09996	−	14.0295i	−0.275407	−	0.477019i
$866$	−8.84036	+	15.3120i	−0.300408	+	0.520322i
$867$	5.81691			0.197552
$868$	−19.6379	−	39.4448i	−0.666552	−	1.33885i
$869$	−0.820230			−0.0278244
$870$	−1.28334	+	2.22280i	−0.0435091	+	0.0753600i
$871$	−11.3845	−	19.7186i	−0.385751	−	0.668139i
$872$	−8.82758	−	15.2898i	−0.298940	−	0.517779i
$873$	−9.59948	+	16.6268i	−0.324893	+	0.562732i
$874$	31.7613			1.07434
$875$	1.46157	−	2.20541i	0.0494101	−	0.0745563i
$876$	17.1165			0.578313
$877$	16.8579	−	29.1988i	0.569252	−	0.985974i	−0.427388	−	0.904068i	$-0.640566\pi$
$877$	16.8579	−	29.1988i	0.569252	−	0.985974i	0.996640	−	0.0819055i	$-0.0261006\pi$
$878$	−1.97489	−	3.42062i	−0.0666495	−	0.115440i
$879$	−2.45294	−	4.24863i	−0.0827358	−	0.143303i
$880$	−4.11721	+	7.13121i	−0.138791	+	0.240393i
$881$	−12.1303			−0.408679			−0.204340	−	0.978900i	$-0.565505\pi$
$881$	−12.1303			−0.408679			−0.204340	+	0.978900i	$0.565505\pi$
$882$	−29.7291	+	39.3565i	−1.00103	+	1.32520i
$883$	57.1051			1.92174			0.960871	−	0.276998i	$-0.0893395\pi$
$883$	57.1051			1.92174			0.960871	+	0.276998i	$0.0893395\pi$
$884$	−10.9108	+	18.8980i	−0.366969	+	0.635608i
$885$	0.478822	+	0.829344i	0.0160954	+	0.0278781i
$886$	−21.5755	−	37.3698i	−0.724842	−	1.25546i
$887$	2.42692	−	4.20355i	0.0814881	−	0.141141i	−0.822401	−	0.568908i	$-0.807366\pi$
$887$	2.42692	−	4.20355i	0.0814881	−	0.141141i	0.903889	+	0.427766i	$0.140699\pi$
$888$	21.4784			0.720768
$889$	21.0155	−	31.7109i	0.704838	−	1.06355i
$890$	−27.3089			−0.915396
$891$	−3.34203	+	5.78856i	−0.111962	+	0.193924i
$892$	−39.6523	−	68.6797i	−1.32766	−	2.29957i
$893$	16.9143	+	29.2964i	0.566014	+	0.980366i
$894$	2.76727	−	4.79306i	0.0925514	−	0.160304i
$895$	−25.2791			−0.844986
$896$	8.34581	+	16.7635i	0.278814	+	0.560029i
$897$	−2.75406			−0.0919554
$898$	15.2220	−	26.3653i	0.507966	−	0.879823i
$899$	3.47368	+	6.01659i	0.115854	+	0.200664i
$900$	6.34203	+	10.9847i	0.211401	+	0.366157i
$901$	−14.6649	+	25.4003i	−0.488558	+	0.846207i
$902$	−21.1337			−0.703675
$903$	12.4520	+	0.768861i	0.414376	+	0.0255861i
$904$	87.6938			2.91665
$905$	11.9497	−	20.6974i	0.397220	−	0.688006i
$906$	−3.15487	−	5.46439i	−0.104813	−	0.181542i
$907$	12.9796	+	22.4813i	0.430980	+	0.746479i	0.996958	−	0.0779411i	$-0.0248346\pi$
$907$	12.9796	+	22.4813i	0.430980	+	0.746479i	−0.565978	+	0.824420i	$0.691501\pi$
$908$	8.18204	−	14.1717i	0.271531	−	0.470305i
$909$	−45.3838			−1.50529
$910$	−13.4042	−	0.827658i	−0.444346	−	0.0274366i
$911$	−12.9871			−0.430283			−0.215142	−	0.976583i	$-0.569021\pi$
$911$	−12.9871			−0.430283			−0.215142	+	0.976583i	$0.569021\pi$
$912$	9.62692	−	16.6743i	0.318779	−	0.552142i
$913$	4.91844	+	8.51899i	0.162777	+	0.281937i
$914$	−22.9882	−	39.8167i	−0.760382	−	1.31702i
$915$	−0.240179	+	0.416001i	−0.00794006	+	0.0137526i
$916$	61.4297			2.02969
$917$	−25.6639	−	51.5489i	−0.847498	−	1.70230i
$918$	18.1691			0.599671
$919$	−3.64884	+	6.31998i	−0.120364	+	0.208477i	−0.919911	−	0.392126i	$-0.871740\pi$
$919$	−3.64884	+	6.31998i	−0.120364	+	0.208477i	0.799547	+	0.600603i	$0.205073\pi$
$920$	−9.22529	−	15.9787i	−0.304149	−	0.526801i
$921$	6.82030	+	11.8131i	0.224737	+	0.389255i
$922$	−20.0284	+	34.6903i	−0.659602	+	1.14246i
$923$	24.5960			0.809586
$924$	−3.49043	+	5.26681i	−0.114827	+	0.173265i
$925$	6.13747			0.201799
$926$	−13.1482	+	22.7734i	−0.432077	+	0.748379i
$927$	21.9464	+	38.0123i	0.720815	+	1.24849i
$928$	7.37375	+	12.7717i	0.242055	+	0.419252i
$929$	−18.1980	+	31.5198i	−0.597057	+	1.03413i	0.396196	+	0.918166i	$0.370330\pi$
$929$	−18.1980	+	31.5198i	−0.597057	+	1.03413i	−0.993253	+	0.115967i	$0.963003\pi$
$930$	−4.76380			−0.156211
$931$	31.5453	+	3.91050i	1.03386	+	0.128162i
$932$	−57.1438			−1.87181
$933$	5.96053	−	10.3239i	0.195139	−	0.337991i
$934$	4.75908	+	8.24296i	0.155722	+	0.269718i
$935$	1.19407	+	2.06819i	0.0390502	+	0.0676369i
$936$	18.3099	−	31.7136i	0.598476	−	1.03659i
$937$	47.8115			1.56193			0.780966	−	0.624573i	$-0.214727\pi$
$937$	47.8115			1.56193			0.780966	+	0.624573i	$0.214727\pi$
$938$	43.5189	−	65.6669i	1.42094	−	2.14410i
$939$	−13.5597			−0.442505
$940$	17.2754	−	29.9218i	0.563461	−	0.975943i
$941$	−4.99565	−	8.65271i	−0.162853	−	0.282070i	0.773038	−	0.634360i	$-0.218736\pi$
$941$	−4.99565	−	8.65271i	−0.162853	−	0.282070i	−0.935891	+	0.352290i	$0.885403\pi$
$942$	10.7686	+	18.6517i	0.350860	+	0.607707i
$943$	11.1343	−	19.2852i	0.362583	−	0.628012i
$944$	15.3144			0.498442
$945$	3.48200	+	6.99400i	0.113270	+	0.227515i
$946$	−23.5937			−0.767096
$947$	−24.6187	+	42.6409i	−0.800001	+	1.38564i	0.119614	+	0.992820i	$0.461834\pi$
$947$	−24.6187	+	42.6409i	−0.800001	+	1.38564i	−0.919615	+	0.392821i	$0.871499\pi$
$948$	−0.979411	−	1.69639i	−0.0318098	−	0.0550962i
$949$	−7.06039	−	12.2290i	−0.229190	−	0.396969i
$950$	5.84971	−	10.1320i	0.189790	−	0.328725i
$951$	9.36647			0.303729
$952$	−42.8606	−	2.64647i	−1.38912	−	0.0857726i
$953$	−27.0740			−0.877012			−0.438506	−	0.898728i	$-0.644492\pi$
$953$	−27.0740			−0.877012			−0.438506	+	0.898728i	$0.644492\pi$
$954$	43.2684	−	74.9430i	1.40087	−	2.42637i
$955$	10.4030	+	18.0185i	0.336633	+	0.583066i
$956$	−36.5242	−	63.2618i	−1.18128	−	2.04603i
$957$	0.498109	−	0.862750i	0.0161016	−	0.0278887i
$958$	−32.9253			−1.06377
$959$	−32.1784	−	1.98689i	−1.03909	−	0.0641599i
$960$	−1.63230			−0.0526822
$961$	9.05277	−	15.6799i	0.292025	−	0.505802i
$962$	−15.5768	−	26.9798i	−0.502216	−	0.869864i
$963$	−7.41265	−	12.8391i	−0.238869	−	0.413734i
$964$	37.3218	−	64.6433i	1.20205	−	2.08202i
$965$	−5.23135			−0.168403
$966$	−4.24674	−	8.53005i	−0.136637	−	0.274450i
$967$	43.2201			1.38987			0.694933	−	0.719075i	$-0.255434\pi$
$967$	43.2201			1.38987			0.694933	+	0.719075i	$0.255434\pi$
$968$	3.39818	−	5.88582i	0.109222	−	0.189177i
$969$	−2.79199	−	4.83587i	−0.0896916	−	0.155350i
$970$	−9.04333	−	15.6635i	−0.290364	−	0.502925i
$971$	8.24538	−	14.2814i	0.264607	−	0.458312i	−0.702854	−	0.711334i	$-0.748091\pi$
$971$	8.24538	−	14.2814i	0.264607	−	0.458312i	0.967461	+	0.253022i	$0.0814245\pi$
$972$	−57.0493			−1.82986
$973$	18.4726	−	27.8738i	0.592204	−	0.893593i
$974$	49.5004			1.58609
$975$	−0.507236	+	0.878558i	−0.0162445	+	0.0281364i
$976$	3.84088	+	6.65260i	0.122944	+	0.212944i
$977$	−15.4795	−	26.8113i	−0.495233	−	0.857769i	0.504752	−	0.863264i	$-0.331584\pi$
$977$	−15.4795	−	26.8113i	−0.495233	−	0.857769i	−0.999985	+	0.00549585i	$0.998251\pi$
$978$	−1.87012	+	3.23914i	−0.0597999	+	0.103576i
$979$	10.5996			0.338764
$980$	−12.6505	−	29.8993i	−0.404105	−	0.955097i
$981$	7.10445			0.226828
$982$	16.7703	−	29.0470i	0.535161	−	0.926926i
$983$	−8.92458	−	15.4578i	−0.284650	−	0.493028i	0.687874	−	0.725830i	$-0.258544\pi$
$983$	−8.92458	−	15.4578i	−0.284650	−	0.493028i	−0.972524	+	0.232802i	$0.925211\pi$
$984$	−14.3530	−	24.8601i	−0.457557	−	0.792511i
$985$	13.4487	−	23.2939i	0.428513	−	0.742206i
$986$	11.9040			0.379100
$987$	5.60649	−	8.45980i	0.178457	−	0.269278i
$988$	−41.4929			−1.32007
$989$	12.4303	−	21.5300i	0.395262	−	0.684614i
$990$	−3.52307	−	6.10213i	−0.111970	−	0.193939i
$991$	−24.9321	−	43.1836i	−0.791993	−	1.37177i	−0.924731	−	0.380621i	$-0.875710\pi$
$991$	−24.9321	−	43.1836i	−0.791993	−	1.37177i	0.132738	−	0.991151i	$-0.457623\pi$
$992$	−13.6859	+	23.7046i	−0.434526	+	0.752622i
$993$	8.32314			0.264127
$994$	37.9268	+	76.1802i	1.20296	+	2.41629i
$995$	27.4413			0.869947
$996$	−11.7459	+	20.3445i	−0.372183	+	0.644640i
$997$	−8.21670	−	14.2317i	−0.260225	−	0.450724i	0.706076	−	0.708136i	$-0.250464\pi$
$997$	−8.21670	−	14.2317i	−0.260225	−	0.450724i	−0.966302	+	0.257412i	$0.917130\pi$
$998$	−26.1330	−	45.2637i	−0.827226	−	1.43280i
$999$	−9.06189	+	15.6956i	−0.286705	+	0.496588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.a.331.4	yes	8
7.2	even	3		2695.2.a.j.1.1		4
7.4	even	3	inner	385.2.i.a.221.4	✓	8
7.5	odd	6		2695.2.a.k.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.a.221.4	✓	8	7.4	even	3	inner
385.2.i.a.331.4	yes	8	1.1	even	1	trivial
2695.2.a.j.1.1		4	7.2	even	3
2695.2.a.k.1.1		4	7.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(1.28821 - 2.23124i) q^{2} +(0.257458 + 0.445930i) q^{3} +(-2.31896 - 4.01655i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.32664 q^{6} +(1.46157 - 2.20541i) q^{7} -6.79636 q^{8} +(1.36743 - 2.36846i) q^{9} +O(q^{10})\)	\(q+(1.28821 - 2.23124i) q^{2} +(0.257458 + 0.445930i) q^{3} +(-2.31896 - 4.01655i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.32664 q^{6} +(1.46157 - 2.20541i) q^{7} -6.79636 q^{8} +(1.36743 - 2.36846i) q^{9} +(1.28821 + 2.23124i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(1.19407 - 2.06819i) q^{12} -1.97017 q^{13} +(-3.03798 - 6.10213i) q^{14} -0.514916 q^{15} +(-4.11721 + 7.13121i) q^{16} +(1.19407 + 2.06819i) q^{17} +(-3.52307 - 6.10213i) q^{18} +(-2.27048 + 3.93259i) q^{19} +4.63791 q^{20} +(1.35975 + 0.0839592i) q^{21} -2.57641 q^{22} +(1.35739 - 2.35106i) q^{23} +(-1.74978 - 3.03070i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.53798 + 4.39592i) q^{26} +2.95297 q^{27} +(-12.2474 - 0.756231i) q^{28} +1.93472 q^{29} +(-0.663319 + 1.14890i) q^{30} +(1.79544 + 3.10980i) q^{31} +(3.81128 + 6.60132i) q^{32} +(0.257458 - 0.445930i) q^{33} +6.15283 q^{34} +(1.17915 + 2.36846i) q^{35} -12.6841 q^{36} +(-3.06873 + 5.31520i) q^{37} +(5.84971 + 10.1320i) q^{38} +(-0.507236 - 0.878558i) q^{39} +(3.39818 - 5.88582i) q^{40} +8.20275 q^{41} +(1.93897 - 2.92577i) q^{42} +9.15756 q^{43} +(-2.31896 + 4.01655i) q^{44} +(1.36743 + 2.36846i) q^{45} +(-3.49719 - 6.05731i) q^{46} +(3.72482 - 6.45157i) q^{47} -4.24003 q^{48} +(-2.72763 - 6.44671i) q^{49} -2.57641 q^{50} +(-0.614845 + 1.06494i) q^{51} +(4.56873 + 7.91328i) q^{52} +(6.14072 + 10.6360i) q^{53} +(3.80404 - 6.58879i) q^{54} +1.00000 q^{55} +(-9.93336 + 14.9887i) q^{56} -2.33822 q^{57} +(2.49232 - 4.31682i) q^{58} +(-0.929903 - 1.61064i) q^{59} +(1.19407 + 2.06819i) q^{60} +(0.466442 - 0.807902i) q^{61} +9.25161 q^{62} +(-3.22482 - 6.47741i) q^{63} +3.17003 q^{64} +(0.985084 - 1.70622i) q^{65} +(-0.663319 - 1.14890i) q^{66} +(5.77846 + 10.0086i) q^{67} +(5.53798 - 9.59207i) q^{68} +1.39788 q^{69} +(6.80360 + 0.420095i) q^{70} -12.4842 q^{71} +(-9.29355 + 16.0969i) q^{72} +(3.58365 + 6.20706i) q^{73} +(7.90633 + 13.6942i) q^{74} +(0.257458 - 0.445930i) q^{75} +21.0606 q^{76} +(-2.64072 - 0.163054i) q^{77} -2.61370 q^{78} +(0.410115 - 0.710340i) q^{79} +(-4.11721 - 7.13121i) q^{80} +(-3.34203 - 5.78856i) q^{81} +(10.5668 - 18.3023i) q^{82} -9.83688 q^{83} +(-2.81598 - 5.65620i) q^{84} -2.38814 q^{85} +(11.7968 - 20.4327i) q^{86} +(0.498109 + 0.862750i) q^{87} +(3.39818 + 5.88582i) q^{88} +(-5.29979 + 9.17950i) q^{89} +7.04614 q^{90} +(-2.87954 + 4.34502i) q^{91} -12.5909 q^{92} +(-0.924502 + 1.60129i) q^{93} +(-9.59668 - 16.6219i) q^{94} +(-2.27048 - 3.93259i) q^{95} +(-1.96249 + 3.39913i) q^{96} -7.02009 q^{97} +(-17.8979 - 2.21871i) q^{98} -2.73486 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9	\( 8 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 4 q^{5} + 14 q^{6} + q^{7} - 18 q^{8} + q^{9} + 3 q^{10} - 4 q^{11} + 3 q^{12} - 12 q^{13} + q^{14} - 6 q^{15} - 5 q^{16} + 3 q^{17} - q^{18} + 3 q^{19} + 6 q^{20} - 18 q^{21} - 6 q^{22} + 6 q^{23} + 4 q^{24} - 4 q^{25} + 5 q^{26} + 6 q^{27} - 20 q^{28} - 16 q^{29} - 7 q^{30} - 10 q^{31} - 4 q^{32} + 3 q^{33} + 20 q^{34} + q^{35} - 16 q^{36} + 9 q^{37} + 23 q^{38} + 13 q^{39} + 9 q^{40} + 30 q^{41} - 16 q^{42} - 4 q^{43} - 3 q^{44} + q^{45} - 16 q^{46} + 15 q^{47} - 2 q^{48} - 19 q^{49} - 6 q^{50} - q^{51} + 3 q^{52} + 30 q^{53} + 13 q^{54} + 8 q^{55} - 24 q^{56} - 12 q^{57} + q^{58} - 17 q^{59} + 3 q^{60} + 32 q^{62} - 11 q^{63} + 10 q^{64} + 6 q^{65} - 7 q^{66} + 25 q^{67} + 19 q^{68} + 12 q^{69} + q^{70} - 26 q^{71} - 26 q^{72} - 3 q^{73} + 16 q^{74} + 3 q^{75} + 80 q^{76} - 2 q^{77} - 10 q^{78} + 4 q^{79} - 5 q^{80} + 16 q^{81} + 27 q^{82} + 36 q^{83} - 24 q^{84} - 6 q^{85} + 10 q^{86} - 20 q^{87} + 9 q^{88} - 25 q^{89} + 2 q^{90} - 3 q^{91} - 52 q^{92} - 10 q^{93} - 23 q^{94} + 3 q^{95} + 7 q^{96} - 46 q^{97} - 60 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 4 * q^5 + 14 * q^6 + q^7 - 18 * q^8 + q^9 + 3 * q^10 - 4 * q^11 + 3 * q^12 - 12 * q^13 + q^14 - 6 * q^15 - 5 * q^16 + 3 * q^17 - q^18 + 3 * q^19 + 6 * q^20 - 18 * q^21 - 6 * q^22 + 6 * q^23 + 4 * q^24 - 4 * q^25 + 5 * q^26 + 6 * q^27 - 20 * q^28 - 16 * q^29 - 7 * q^30 - 10 * q^31 - 4 * q^32 + 3 * q^33 + 20 * q^34 + q^35 - 16 * q^36 + 9 * q^37 + 23 * q^38 + 13 * q^39 + 9 * q^40 + 30 * q^41 - 16 * q^42 - 4 * q^43 - 3 * q^44 + q^45 - 16 * q^46 + 15 * q^47 - 2 * q^48 - 19 * q^49 - 6 * q^50 - q^51 + 3 * q^52 + 30 * q^53 + 13 * q^54 + 8 * q^55 - 24 * q^56 - 12 * q^57 + q^58 - 17 * q^59 + 3 * q^60 + 32 * q^62 - 11 * q^63 + 10 * q^64 + 6 * q^65 - 7 * q^66 + 25 * q^67 + 19 * q^68 + 12 * q^69 + q^70 - 26 * q^71 - 26 * q^72 - 3 * q^73 + 16 * q^74 + 3 * q^75 + 80 * q^76 - 2 * q^77 - 10 * q^78 + 4 * q^79 - 5 * q^80 + 16 * q^81 + 27 * q^82 + 36 * q^83 - 24 * q^84 - 6 * q^85 + 10 * q^86 - 20 * q^87 + 9 * q^88 - 25 * q^89 + 2 * q^90 - 3 * q^91 - 52 * q^92 - 10 * q^93 - 23 * q^94 + 3 * q^95 + 7 * q^96 - 46 * q^97 - 60 * q^98 - 2 * q^99

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