LMFDB - Embedded newform 483.2.i.f.277.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
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} - x^{11} + 8 x^{10} - 3 x^{9} + 42 x^{8} - 15 x^{7} + 101 x^{6} + 6 x^{5} + 150 x^{4} - 28 x^{3} + \cdots + 4 $ x^12 - x^11 + 8x^10 - 3x^9 + 42x^8 - 15x^7 + 101x^6 + 6x^5 + 150x^4 - 28x^3 + 40x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.4
Root			$0.296764 - 0.514011i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.f.415.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.296764 + 0.514011i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.823862 - 1.42697i) q^{4} +(1.57560 + 2.72902i) q^{5} +0.593528 q^{6} +(-1.69175 - 2.03420i) q^{7} +2.16503 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.296764 + 0.514011i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.823862 - 1.42697i) q^{4} +(1.57560 + 2.72902i) q^{5} +0.593528 q^{6} +(-1.69175 - 2.03420i) q^{7} +2.16503 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.935165 + 1.61975i) q^{10} +(3.27267 - 5.66843i) q^{11} +(-0.823862 - 1.42697i) q^{12} -0.692965 q^{13} +(0.543550 - 1.47326i) q^{14} +3.15120 q^{15} +(-1.00522 - 1.74109i) q^{16} +(-3.42208 + 5.92722i) q^{17} +(0.296764 - 0.514011i) q^{18} +(1.45831 + 2.52587i) q^{19} +5.19231 q^{20} +(-2.60755 + 0.447998i) q^{21} +3.88485 q^{22} +(0.500000 + 0.866025i) q^{23} +(1.08251 - 1.87497i) q^{24} +(-2.46504 + 4.26958i) q^{25} +(-0.205647 - 0.356192i) q^{26} -1.00000 q^{27} +(-4.29652 + 0.738178i) q^{28} +2.94619 q^{29} +(0.935165 + 1.61975i) q^{30} +(0.269666 - 0.467076i) q^{31} +(2.76166 - 4.78333i) q^{32} +(-3.27267 - 5.66843i) q^{33} -4.06221 q^{34} +(2.88586 - 7.82192i) q^{35} -1.64772 q^{36} +(1.44806 + 2.50812i) q^{37} +(-0.865550 + 1.49918i) q^{38} +(-0.346483 + 0.600126i) q^{39} +(3.41122 + 5.90841i) q^{40} +9.26871 q^{41} +(-1.00410 - 1.20736i) q^{42} -4.27043 q^{43} +(-5.39246 - 9.34001i) q^{44} +(1.57560 - 2.72902i) q^{45} +(-0.296764 + 0.514011i) q^{46} +(-5.23372 - 9.06507i) q^{47} -2.01044 q^{48} +(-1.27596 + 6.88273i) q^{49} -2.92615 q^{50} +(3.42208 + 5.92722i) q^{51} +(-0.570908 + 0.988841i) q^{52} +(-6.28744 + 10.8902i) q^{53} +(-0.296764 - 0.514011i) q^{54} +20.6257 q^{55} +(-3.66269 - 4.40410i) q^{56} +2.91662 q^{57} +(0.874324 + 1.51437i) q^{58} +(-3.35163 + 5.80519i) q^{59} +(2.59616 - 4.49668i) q^{60} +(-2.65091 - 4.59152i) q^{61} +0.320109 q^{62} +(-0.915795 + 2.48220i) q^{63} -0.742642 q^{64} +(-1.09184 - 1.89112i) q^{65} +(1.94242 - 3.36437i) q^{66} +(1.36814 - 2.36969i) q^{67} +(5.63865 + 9.76643i) q^{68} +1.00000 q^{69} +(4.87697 - 0.837905i) q^{70} -0.587217 q^{71} +(-1.08251 - 1.87497i) q^{72} +(-5.26330 + 9.11630i) q^{73} +(-0.859467 + 1.48864i) q^{74} +(2.46504 + 4.26958i) q^{75} +4.80579 q^{76} +(-17.0673 + 2.93230i) q^{77} -0.411295 q^{78} +(6.69351 + 11.5935i) q^{79} +(3.16766 - 5.48654i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.75062 + 4.76422i) q^{82} -9.77501 q^{83} +(-1.50898 + 4.08998i) q^{84} -21.5674 q^{85} +(-1.26731 - 2.19505i) q^{86} +(1.47310 - 2.55148i) q^{87} +(7.08542 - 12.2723i) q^{88} +(-1.46470 - 2.53693i) q^{89} +1.87033 q^{90} +(1.17232 + 1.40963i) q^{91} +1.64772 q^{92} +(-0.269666 - 0.467076i) q^{93} +(3.10636 - 5.38037i) q^{94} +(-4.59544 + 7.95953i) q^{95} +(-2.76166 - 4.78333i) q^{96} -8.14170 q^{97} +(-3.91645 + 1.38669i) q^{98} -6.54534 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} - q^{14} - 6 q^{15} + 7 q^{16} - 15 q^{17} + q^{18} + q^{19} + 34 q^{20} - 4 q^{21} - 12 q^{22} + 6 q^{23} - 3 q^{24} - 9 q^{25} + 15 q^{26} - 12 q^{27} - 2 q^{28} - 12 q^{29} - 3 q^{30} + 11 q^{31} - 3 q^{32} - 14 q^{33} + 30 q^{34} - q^{35} + 6 q^{36} + 5 q^{37} - 14 q^{38} + 17 q^{40} + 36 q^{41} - 17 q^{42} - 74 q^{43} + 10 q^{44} - 3 q^{45} - q^{46} - 3 q^{47} + 14 q^{48} - 6 q^{49} - 60 q^{50} + 15 q^{51} + 7 q^{52} + 15 q^{53} - q^{54} - 4 q^{55} - 21 q^{56} + 2 q^{57} - 4 q^{58} + 2 q^{59} + 17 q^{60} + 12 q^{61} + 72 q^{62} - 2 q^{63} - 46 q^{64} + 17 q^{65} - 6 q^{66} + 10 q^{67} + q^{68} + 12 q^{69} - 56 q^{70} - 42 q^{71} + 3 q^{72} + 8 q^{73} + 16 q^{74} + 9 q^{75} + 36 q^{76} - 40 q^{77} + 30 q^{78} + 17 q^{79} - 3 q^{80} - 6 q^{81} + 48 q^{82} + 24 q^{83} - 25 q^{84} - 26 q^{85} - 22 q^{86} - 6 q^{87} + 2 q^{88} - 18 q^{89} - 6 q^{90} + 22 q^{91} - 6 q^{92} - 11 q^{93} - 3 q^{94} + 16 q^{95} + 3 q^{96} - 4 q^{97} - 62 q^{98} - 28 q^{99}+O(q^{100}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 - q^14 - 6 * q^15 + 7 * q^16 - 15 * q^17 + q^18 + q^19 + 34 * q^20 - 4 * q^21 - 12 * q^22 + 6 * q^23 - 3 * q^24 - 9 * q^25 + 15 * q^26 - 12 * q^27 - 2 * q^28 - 12 * q^29 - 3 * q^30 + 11 * q^31 - 3 * q^32 - 14 * q^33 + 30 * q^34 - q^35 + 6 * q^36 + 5 * q^37 - 14 * q^38 + 17 * q^40 + 36 * q^41 - 17 * q^42 - 74 * q^43 + 10 * q^44 - 3 * q^45 - q^46 - 3 * q^47 + 14 * q^48 - 6 * q^49 - 60 * q^50 + 15 * q^51 + 7 * q^52 + 15 * q^53 - q^54 - 4 * q^55 - 21 * q^56 + 2 * q^57 - 4 * q^58 + 2 * q^59 + 17 * q^60 + 12 * q^61 + 72 * q^62 - 2 * q^63 - 46 * q^64 + 17 * q^65 - 6 * q^66 + 10 * q^67 + q^68 + 12 * q^69 - 56 * q^70 - 42 * q^71 + 3 * q^72 + 8 * q^73 + 16 * q^74 + 9 * q^75 + 36 * q^76 - 40 * q^77 + 30 * q^78 + 17 * q^79 - 3 * q^80 - 6 * q^81 + 48 * q^82 + 24 * q^83 - 25 * q^84 - 26 * q^85 - 22 * q^86 - 6 * q^87 + 2 * q^88 - 18 * q^89 - 6 * q^90 + 22 * q^91 - 6 * q^92 - 11 * q^93 - 3 * q^94 + 16 * q^95 + 3 * q^96 - 4 * q^97 - 62 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.296764	+	0.514011i	0.209844	+	0.363460i	0.951665	−	0.307137i	$-0.0993711\pi$
$2$	0.296764	+	0.514011i	0.209844	+	0.363460i	−0.741821	+	0.670598i	$0.766038\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.823862	−	1.42697i	0.411931	−	0.713485i
$5$	1.57560	+	2.72902i	0.704631	+	1.22046i	0.966825	+	0.255441i	$0.0822206\pi$
$5$	1.57560	+	2.72902i	0.704631	+	1.22046i	−0.262194	+	0.965015i	$0.584446\pi$
$6$	0.593528			0.242307
$7$	−1.69175	−	2.03420i	−0.639422	−	0.768856i
$7$	−1.69175	−	2.03420i	−0.639422	−	0.768856i
$8$	2.16503			0.765453
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.935165	+	1.61975i	−0.295725	+	0.512211i
$11$	3.27267	−	5.66843i	0.986747	−	1.70910i	0.352847	−	0.935681i	$-0.385214\pi$
$11$	3.27267	−	5.66843i	0.986747	−	1.70910i	0.633900	−	0.773415i	$-0.281453\pi$
$12$	−0.823862	−	1.42697i	−0.237828	−	0.411931i
$13$	−0.692965			−0.192194			−0.0960970	−	0.995372i	$-0.530636\pi$
$13$	−0.692965			−0.192194			−0.0960970	+	0.995372i	$0.530636\pi$
$14$	0.543550	−	1.47326i	0.145270	−	0.393744i
$15$	3.15120			0.813637
$16$	−1.00522	−	1.74109i	−0.251305	−	0.435273i
$17$	−3.42208	+	5.92722i	−0.829977	+	1.43756i	0.0680776	+	0.997680i	$0.478313\pi$
$17$	−3.42208	+	5.92722i	−0.829977	+	1.43756i	−0.898055	+	0.439883i	$0.855020\pi$
$18$	0.296764	−	0.514011i	0.0699480	−	0.121153i
$19$	1.45831	+	2.52587i	0.334560	+	0.579475i	0.983400	−	0.181450i	$-0.0580791\pi$
$19$	1.45831	+	2.52587i	0.334560	+	0.579475i	−0.648840	+	0.760925i	$0.724746\pi$
$20$	5.19231			1.16104
$21$	−2.60755	+	0.447998i	−0.569013	+	0.0977613i
$22$	3.88485			0.828252
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	1.08251	−	1.87497i	0.220967	−	0.382726i
$25$	−2.46504	+	4.26958i	−0.493009	+	0.853916i
$26$	−0.205647	−	0.356192i	−0.0403308	−	0.0698549i
$27$	−1.00000			−0.192450
$28$	−4.29652	+	0.738178i	−0.811965	+	0.139502i
$29$	2.94619			0.547094			0.273547	−	0.961859i	$-0.411803\pi$
$29$	2.94619			0.547094			0.273547	+	0.961859i	$0.411803\pi$
$30$	0.935165	+	1.61975i	0.170737	+	0.295725i
$31$	0.269666	−	0.467076i	0.0484335	−	0.0838893i	−0.840792	−	0.541358i	$-0.817910\pi$
$31$	0.269666	−	0.467076i	0.0484335	−	0.0838893i	0.889226	+	0.457469i	$0.151244\pi$
$32$	2.76166	−	4.78333i	0.488196	−	0.845581i
$33$	−3.27267	−	5.66843i	−0.569699	−	0.986747i
$34$	−4.06221			−0.696663
$35$	2.88586	−	7.82192i	0.487799	−	1.32215i
$36$	−1.64772			−0.274621
$37$	1.44806	+	2.50812i	0.238060	+	0.412332i	0.960158	−	0.279459i	$-0.0901551\pi$
$37$	1.44806	+	2.50812i	0.238060	+	0.412332i	−0.722097	+	0.691791i	$0.756822\pi$
$38$	−0.865550	+	1.49918i	−0.140411	+	0.243198i
$39$	−0.346483	+	0.600126i	−0.0554816	+	0.0960970i
$40$	3.41122	+	5.90841i	0.539362	+	0.934202i
$41$	9.26871			1.44753			0.723765	−	0.690047i	$-0.242410\pi$
$41$	9.26871			1.44753			0.723765	+	0.690047i	$0.242410\pi$
$42$	−1.00410	−	1.20736i	−0.154936	−	0.186299i
$43$	−4.27043			−0.651235			−0.325617	−	0.945502i	$-0.605572\pi$
$43$	−4.27043			−0.651235			−0.325617	+	0.945502i	$0.605572\pi$
$44$	−5.39246	−	9.34001i	−0.812943	−	1.40806i
$45$	1.57560	−	2.72902i	0.234877	−	0.406819i
$46$	−0.296764	+	0.514011i	−0.0437555	+	0.0757867i
$47$	−5.23372	−	9.06507i	−0.763416	−	1.32228i	−0.941080	−	0.338184i	$-0.890187\pi$
$47$	−5.23372	−	9.06507i	−0.763416	−	1.32228i	0.177664	−	0.984091i	$-0.443146\pi$
$48$	−2.01044			−0.290182
$49$	−1.27596	+	6.88273i	−0.182279	+	0.983247i
$50$	−2.92615			−0.413820
$51$	3.42208	+	5.92722i	0.479188	+	0.829977i
$52$	−0.570908	+	0.988841i	−0.0791707	+	0.137128i
$53$	−6.28744	+	10.8902i	−0.863647	+	1.49588i	0.00473784	+	0.999989i	$0.498492\pi$
$53$	−6.28744	+	10.8902i	−0.863647	+	1.49588i	−0.868385	+	0.495891i	$0.834841\pi$
$54$	−0.296764	−	0.514011i	−0.0403845	−	0.0699480i
$55$	20.6257			2.78117
$56$	−3.66269	−	4.40410i	−0.489447	−	0.588523i
$57$	2.91662			0.386316
$58$	0.874324	+	1.51437i	0.114804	+	0.198847i
$59$	−3.35163	+	5.80519i	−0.436345	+	0.755772i	−0.997404	−	0.0720038i	$-0.977061\pi$
$59$	−3.35163	+	5.80519i	−0.436345	+	0.755772i	0.561059	+	0.827776i	$0.310394\pi$
$60$	2.59616	−	4.49668i	0.335162	−	0.580518i
$61$	−2.65091	−	4.59152i	−0.339415	−	0.587884i	0.644908	−	0.764260i	$-0.276896\pi$
$61$	−2.65091	−	4.59152i	−0.339415	−	0.587884i	−0.984323	+	0.176377i	$0.943562\pi$
$62$	0.320109			0.0406539
$63$	−0.915795	+	2.48220i	−0.115379	+	0.312728i
$64$	−0.742642			−0.0928303
$65$	−1.09184	−	1.89112i	−0.135426	−	0.234564i
$66$	1.94242	−	3.36437i	0.239096	−	0.414126i
$67$	1.36814	−	2.36969i	0.167145	−	0.289504i	−0.770270	−	0.637718i	$-0.779878\pi$
$67$	1.36814	−	2.36969i	0.167145	−	0.289504i	0.937415	+	0.348214i	$0.113212\pi$
$68$	5.63865	+	9.76643i	0.683787	+	1.18435i
$69$	1.00000			0.120386
$70$	4.87697	−	0.837905i	0.582909	−	0.100149i
$71$	−0.587217			−0.0696899			−0.0348449	−	0.999393i	$-0.511094\pi$
$71$	−0.587217			−0.0696899			−0.0348449	+	0.999393i	$0.511094\pi$
$72$	−1.08251	−	1.87497i	−0.127575	−	0.220967i
$73$	−5.26330	+	9.11630i	−0.616023	+	1.06698i	0.374181	+	0.927356i	$0.377924\pi$
$73$	−5.26330	+	9.11630i	−0.616023	+	1.06698i	−0.990204	+	0.139627i	$0.955410\pi$
$74$	−0.859467	+	1.48864i	−0.0999110	+	0.173051i
$75$	2.46504	+	4.26958i	0.284639	+	0.493009i
$76$	4.80579			0.551262
$77$	−17.0673	+	2.93230i	−1.94500	+	0.334167i
$78$	−0.411295			−0.0465699
$79$	6.69351	+	11.5935i	0.753078	+	1.30437i	0.946324	+	0.323219i	$0.104765\pi$
$79$	6.69351	+	11.5935i	0.753078	+	1.30437i	−0.193246	+	0.981150i	$0.561902\pi$
$80$	3.16766	−	5.48654i	0.354155	−	0.613414i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.75062	+	4.76422i	0.303755	+	0.526120i
$83$	−9.77501			−1.07295			−0.536473	−	0.843917i	$-0.680244\pi$
$83$	−9.77501			−1.07295			−0.536473	+	0.843917i	$0.680244\pi$
$84$	−1.50898	+	4.08998i	−0.164643	+	0.446254i
$85$	−21.5674			−2.33931
$86$	−1.26731	−	2.19505i	−0.136658	−	0.236698i
$87$	1.47310	−	2.55148i	0.157932	−	0.273547i
$88$	7.08542	−	12.2723i	0.755308	−	1.30823i
$89$	−1.46470	−	2.53693i	−0.155258	−	0.268914i	0.777895	−	0.628394i	$-0.216287\pi$
$89$	−1.46470	−	2.53693i	−0.155258	−	0.268914i	−0.933153	+	0.359480i	$0.882954\pi$
$90$	1.87033			0.197150
$91$	1.17232	+	1.40963i	0.122893	+	0.147770i
$92$	1.64772			0.171787
$93$	−0.269666	−	0.467076i	−0.0279631	−	0.0484335i
$94$	3.10636	−	5.38037i	0.320397	−	0.554943i
$95$	−4.59544	+	7.95953i	−0.471482	+	0.816631i
$96$	−2.76166	−	4.78333i	−0.281860	−	0.488196i
$97$	−8.14170			−0.826664			−0.413332	−	0.910580i	$-0.635635\pi$
$97$	−8.14170			−0.826664			−0.413332	+	0.910580i	$0.635635\pi$
$98$	−3.91645	+	1.38669i	−0.395622	+	0.140077i
$99$	−6.54534			−0.657831
$100$	4.06171	+	7.03509i	0.406171	+	0.703509i
$101$	0.0666245	−	0.115397i	0.00662939	−	0.0114824i	−0.862692	−	0.505730i	$-0.831223\pi$
$101$	0.0666245	−	0.115397i	0.00662939	−	0.0114824i	0.869321	+	0.494248i	$0.164556\pi$
$102$	−2.03110	+	3.51798i	−0.201109	+	0.348332i
$103$	5.50533	+	9.53551i	0.542456	+	0.939562i	0.998762	+	0.0497387i	$0.0158389\pi$
$103$	5.50533	+	9.53551i	0.542456	+	0.939562i	−0.456306	+	0.889823i	$0.650828\pi$
$104$	−1.50029			−0.147115
$105$	−5.33105	−	6.41019i	−0.520258	−	0.625570i
$106$	−7.46355			−0.724924
$107$	4.28755	+	7.42625i	0.414493	+	0.717923i	0.995375	−	0.0960649i	$-0.0306256\pi$
$107$	4.28755	+	7.42625i	0.414493	+	0.717923i	−0.580882	+	0.813988i	$0.697292\pi$
$108$	−0.823862	+	1.42697i	−0.0792762	+	0.137310i
$109$	−5.64113	+	9.77072i	−0.540322	+	0.935865i	0.458563	+	0.888662i	$0.348364\pi$
$109$	−5.64113	+	9.77072i	−0.540322	+	0.935865i	−0.998885	+	0.0472034i	$0.984969\pi$
$110$	6.12097	+	10.6018i	0.583612	+	1.01084i
$111$	2.89613			0.274888
$112$	−1.84115	+	4.99032i	−0.173973	+	0.471541i
$113$	3.14165			0.295541			0.147771	−	0.989022i	$-0.452790\pi$
$113$	3.14165			0.295541			0.147771	+	0.989022i	$0.452790\pi$
$114$	0.865550	+	1.49918i	0.0810662	+	0.140411i
$115$	−1.57560	+	2.72902i	−0.146926	+	0.254483i
$116$	2.42726	−	4.20413i	0.225365	−	0.390344i
$117$	0.346483	+	0.600126i	0.0320323	+	0.0554816i
$118$	−3.97858			−0.366258
$119$	17.8465	−	3.06618i	1.63598	−	0.281076i
$120$	6.82244			0.622801
$121$	−15.9207	−	27.5755i	−1.44734	−	2.50687i
$122$	1.57339	−	2.72520i	0.142448	−	0.246728i
$123$	4.63435	−	8.02694i	0.417866	−	0.723765i
$124$	−0.444336	−	0.769612i	−0.0399025	−	0.0691132i
$125$	0.220311			0.0197052
$126$	−1.54765	+	0.265900i	−0.137876	+	0.0236882i
$127$	−12.9337			−1.14768			−0.573841	−	0.818967i	$-0.694547\pi$
$127$	−12.9337			−1.14768			−0.573841	+	0.818967i	$0.694547\pi$
$128$	−5.74370	−	9.94838i	−0.507676	−	0.879321i
$129$	−2.13522	+	3.69830i	−0.187995	+	0.325617i
$130$	0.648037	−	1.12243i	0.0568366	−	0.0984438i
$131$	−3.07333	−	5.32317i	−0.268518	−	0.465088i	0.699961	−	0.714181i	$-0.253201\pi$
$131$	−3.07333	−	5.32317i	−0.268518	−	0.465088i	−0.968479	+	0.249094i	$0.919867\pi$
$132$	−10.7849			−0.938706
$133$	2.67103	−	7.23965i	0.231608	−	0.627757i
$134$	1.62406			0.140298
$135$	−1.57560	−	2.72902i	−0.135606	−	0.234877i
$136$	−7.40891	+	12.8326i	−0.635309	+	1.10039i
$137$	9.80611	−	16.9847i	0.837792	−	1.45110i	−0.0539443	−	0.998544i	$-0.517179\pi$
$137$	9.80611	−	16.9847i	0.837792	−	1.45110i	0.891737	−	0.452555i	$-0.149487\pi$
$138$	0.296764	+	0.514011i	0.0252622	+	0.0437555i
$139$	−11.8453			−1.00470			−0.502352	−	0.864663i	$-0.667532\pi$
$139$	−11.8453			−1.00470			−0.502352	+	0.864663i	$0.667532\pi$
$140$	−8.78410	−	10.5622i	−0.742392	−	0.892670i
$141$	−10.4674			−0.881517
$142$	−0.174265	−	0.301836i	−0.0146240	−	0.0253295i
$143$	−2.26785	+	3.92803i	−0.189647	+	0.328478i
$144$	−1.00522	+	1.74109i	−0.0837684	+	0.145091i
$145$	4.64203	+	8.04023i	0.385499	+	0.667704i
$146$	−6.24784			−0.517075
$147$	5.32264	+	4.54637i	0.439004	+	0.374979i
$148$	4.77202			0.392258
$149$	2.58687	+	4.48059i	0.211925	+	0.367064i	0.952317	−	0.305111i	$-0.0986935\pi$
$149$	2.58687	+	4.48059i	0.211925	+	0.367064i	−0.740392	+	0.672175i	$0.765360\pi$
$150$	−1.46307	+	2.53412i	−0.119459	+	0.206910i
$151$	2.52507	−	4.37355i	0.205487	−	0.355914i	−0.744801	−	0.667287i	$-0.767455\pi$
$151$	2.52507	−	4.37355i	0.205487	−	0.355914i	0.950288	+	0.311373i	$0.100789\pi$
$152$	3.15729	+	5.46858i	0.256090	+	0.443560i
$153$	6.84417			0.553318
$154$	−6.57219	−	7.90256i	−0.529602	−	0.636806i
$155$	1.69955			0.136511
$156$	0.570908	+	0.988841i	0.0457092	+	0.0791707i
$157$	4.82407	−	8.35553i	0.385003	−	0.666844i	−0.606767	−	0.794880i	$-0.707534\pi$
$157$	4.82407	−	8.35553i	0.385003	−	0.666844i	0.991770	+	0.128036i	$0.0408672\pi$
$158$	−3.97279	+	6.88107i	−0.316058	+	0.547428i
$159$	6.28744	+	10.8902i	0.498627	+	0.863647i
$160$	17.4051			1.37599
$161$	0.915795	−	2.48220i	0.0721748	−	0.195625i
$162$	−0.593528			−0.0466320
$163$	−11.9663	−	20.7262i	−0.937271	−	1.62340i	−0.770534	−	0.637399i	$-0.780010\pi$
$163$	−11.9663	−	20.7262i	−0.937271	−	1.62340i	−0.166737	−	0.986001i	$-0.553323\pi$
$164$	7.63614	−	13.2262i	0.596282	−	1.03279i
$165$	10.3129	−	17.8624i	0.802854	−	1.39058i
$166$	−2.90087	−	5.02446i	−0.225151	−	0.389974i
$167$	12.0368			0.931435			0.465718	−	0.884933i	$-0.345796\pi$
$167$	12.0368			0.931435			0.465718	+	0.884933i	$0.345796\pi$
$168$	−5.64541	+	0.969929i	−0.435553	+	0.0748317i
$169$	−12.5198			−0.963061
$170$	−6.40043	−	11.0859i	−0.490890	−	0.850247i
$171$	1.45831	−	2.52587i	0.111520	−	0.193158i
$172$	−3.51825	+	6.09378i	−0.268264	+	0.464647i
$173$	8.30191	+	14.3793i	0.631182	+	1.09324i	0.987310	+	0.158803i	$0.0507634\pi$
$173$	8.30191	+	14.3793i	0.631182	+	1.09324i	−0.356128	+	0.934437i	$0.615903\pi$
$174$	1.74865			0.132565
$175$	12.8554	−	2.20867i	0.971779	−	0.166960i
$176$	−13.1590			−0.991899
$177$	3.35163	+	5.80519i	0.251924	+	0.436345i
$178$	0.869340	−	1.50574i	0.0651598	−	0.112860i
$179$	−1.62269	+	2.81058i	−0.121285	+	0.210073i	−0.920275	−	0.391273i	$-0.872035\pi$
$179$	−1.62269	+	2.81058i	−0.121285	+	0.210073i	0.798989	+	0.601345i	$0.205368\pi$
$180$	−2.59616	−	4.49668i	−0.193506	−	0.335162i
$181$	14.3797			1.06883			0.534417	−	0.845221i	$-0.320531\pi$
$181$	14.3797			1.06883			0.534417	+	0.845221i	$0.320531\pi$
$182$	−0.376662	+	1.02092i	−0.0279200	+	0.0756753i
$183$	−5.30183			−0.391923
$184$	1.08251	+	1.87497i	0.0798040	+	0.138225i
$185$	−4.56314	+	7.90360i	−0.335489	+	0.581084i
$186$	0.160055	−	0.277223i	0.0117358	−	0.0203270i
$187$	22.3987	+	38.7957i	1.63796	+	2.83702i
$188$	−17.2474			−1.25790
$189$	1.69175	+	2.03420i	0.123057	+	0.147966i
$190$	−5.45505			−0.395751
$191$	4.94456	+	8.56423i	0.357776	+	0.619686i	0.987589	−	0.157061i	$-0.0502019\pi$
$191$	4.94456	+	8.56423i	0.357776	+	0.619686i	−0.629813	+	0.776747i	$0.716869\pi$
$192$	−0.371321	+	0.643147i	−0.0267978	+	0.0464151i
$193$	1.79525	−	3.10947i	0.129225	−	0.223825i	−0.794151	−	0.607720i	$-0.792084\pi$
$193$	1.79525	−	3.10947i	0.129225	−	0.223825i	0.923377	+	0.383895i	$0.125418\pi$
$194$	−2.41616	−	4.18492i	−0.173471	−	0.300460i
$195$	−2.18368			−0.156376
$196$	8.77024	+	7.49117i	0.626446	+	0.535084i
$197$	8.21279			0.585137			0.292569	−	0.956245i	$-0.405490\pi$
$197$	8.21279			0.585137			0.292569	+	0.956245i	$0.405490\pi$
$198$	−1.94242	−	3.36437i	−0.138042	−	0.239096i
$199$	−1.12253	+	1.94429i	−0.0795743	+	0.137827i	−0.903066	−	0.429501i	$-0.858689\pi$
$199$	−1.12253	+	1.94429i	−0.0795743	+	0.137827i	0.823492	+	0.567328i	$0.192023\pi$
$200$	−5.33689	+	9.24376i	−0.377375	+	0.653633i
$201$	−1.36814	−	2.36969i	−0.0965013	−	0.167145i
$202$	0.0790871			0.00556455
$203$	−4.98422	−	5.99315i	−0.349824	−	0.420637i
$204$	11.2773			0.789569
$205$	14.6038	+	25.2945i	1.01997	+	1.76665i
$206$	−3.26757	+	5.65960i	−0.227662	+	0.394323i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	0.696583	+	1.20652i	0.0482994	+	0.0836570i
$209$	19.0903			1.32050
$210$	1.71284	−	4.64253i	0.118197	−	0.320365i
$211$	−23.0784			−1.58878			−0.794392	−	0.607406i	$-0.792210\pi$
$211$	−23.0784			−1.58878			−0.794392	+	0.607406i	$0.792210\pi$
$212$	10.3600	+	17.9440i	0.711526	+	1.23240i
$213$	−0.293609	+	0.508545i	−0.0201177	+	0.0348449i
$214$	−2.54478	+	4.40769i	−0.173958	+	0.301304i
$215$	−6.72850	−	11.6541i	−0.458880	−	0.794804i
$216$	−2.16503			−0.147311
$217$	−1.40634	+	0.241620i	−0.0954683	+	0.0164023i
$218$	−6.69634			−0.453533
$219$	5.26330	+	9.11630i	0.355661	+	0.616023i
$220$	16.9927	−	29.4323i	1.14565	−	1.98432i
$221$	2.37139	−	4.10736i	0.159517	−	0.276291i
$222$	0.859467	+	1.48864i	0.0576837	+	0.0999110i
$223$	4.28573			0.286993			0.143497	−	0.989651i	$-0.454165\pi$
$223$	4.28573			0.286993			0.143497	+	0.989651i	$0.454165\pi$
$224$	−14.4023	+	2.47443i	−0.962293	+	0.165330i
$225$	4.93009			0.328672
$226$	0.932328	+	1.61484i	0.0620175	+	0.107418i
$227$	−5.46669	+	9.46858i	−0.362837	+	0.628452i	−0.988427	−	0.151701i	$-0.951525\pi$
$227$	−5.46669	+	9.46858i	−0.362837	+	0.628452i	0.625590	+	0.780152i	$0.284858\pi$
$228$	2.40290	−	4.16194i	0.159136	−	0.275631i
$229$	−2.78875	−	4.83026i	−0.184286	−	0.319193i	0.759050	−	0.651033i	$-0.225664\pi$
$229$	−2.78875	−	4.83026i	−0.184286	−	0.319193i	−0.943336	+	0.331840i	$0.892331\pi$
$230$	−1.87033			−0.123326
$231$	−5.99419	+	16.2468i	−0.394389	+	1.06896i
$232$	6.37859			0.418775
$233$	11.1353	+	19.2869i	0.729497	+	1.26353i	0.957096	+	0.289772i	$0.0935793\pi$
$233$	11.1353	+	19.2869i	0.729497	+	1.26353i	−0.227598	+	0.973755i	$0.573087\pi$
$234$	−0.205647	+	0.356192i	−0.0134436	+	0.0232850i
$235$	16.4925	−	28.5659i	1.07585	−	1.86343i
$236$	5.52256	+	9.56536i	0.359488	+	0.622652i
$237$	13.3870			0.869580
$238$	6.87225	+	8.26335i	0.445462	+	0.535634i
$239$	13.3901			0.866134			0.433067	−	0.901362i	$-0.357431\pi$
$239$	13.3901			0.866134			0.433067	+	0.901362i	$0.357431\pi$
$240$	−3.16766	−	5.48654i	−0.204471	−	0.354155i
$241$	1.64322	−	2.84615i	0.105849	−	0.183336i	−0.808236	−	0.588859i	$-0.799577\pi$
$241$	1.64322	−	2.84615i	0.105849	−	0.183336i	0.914085	+	0.405523i	$0.132911\pi$
$242$	9.44941	−	16.3669i	0.607431	−	1.05210i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−8.73595			−0.559262
$245$	−20.7935	+	7.36233i	−1.32845	+	0.470362i
$246$	5.50124			0.350746
$247$	−1.01056	−	1.75034i	−0.0643004	−	0.111372i
$248$	0.583835	−	1.01123i	0.0370736	−	0.0642133i
$249$	−4.88750	+	8.46540i	−0.309733	+	0.536473i
$250$	0.0653804	+	0.113242i	0.00413502	+	0.00716207i
$251$	10.2769			0.648672			0.324336	−	0.945942i	$-0.394859\pi$
$251$	10.2769			0.648672			0.324336	+	0.945942i	$0.394859\pi$
$252$	2.78754	+	3.35180i	0.175598	+	0.211144i
$253$	6.54534			0.411502
$254$	−3.83827	−	6.64807i	−0.240834	−	0.417137i
$255$	−10.7837	+	18.6779i	−0.675301	+	1.16966i
$256$	2.66641	−	4.61835i	0.166650	−	0.288647i
$257$	−11.7035	−	20.2711i	−0.730046	−	1.26448i	−0.956863	−	0.290539i	$-0.906165\pi$
$257$	−11.7035	−	20.2711i	−0.730046	−	1.26448i	0.226817	−	0.973937i	$-0.427168\pi$
$258$	−2.53462			−0.157799
$259$	2.65226	−	7.18877i	0.164803	−	0.446688i
$260$	−3.59809			−0.223144
$261$	−1.47310	−	2.55148i	−0.0911824	−	0.157932i
$262$	1.82411	−	3.15945i	0.112694	−	0.195192i
$263$	13.6828	−	23.6993i	0.843719	−	1.46136i	−0.0430104	−	0.999075i	$-0.513695\pi$
$263$	13.6828	−	23.6993i	0.843719	−	1.46136i	0.886729	−	0.462289i	$-0.152972\pi$
$264$	−7.08542	−	12.2723i	−0.436078	−	0.755308i
$265$	−39.6260			−2.43421
$266$	4.51392	−	0.775530i	0.276766	−	0.0475508i
$267$	−2.92939			−0.179276
$268$	−2.25432	−	3.90460i	−0.137705	−	0.238511i
$269$	13.1885	−	22.8432i	0.804119	−	1.39277i	−0.112765	−	0.993622i	$-0.535971\pi$
$269$	13.1885	−	22.8432i	0.804119	−	1.39277i	0.916884	−	0.399153i	$-0.130696\pi$
$270$	0.935165	−	1.61975i	0.0569123	−	0.0985750i
$271$	−2.15218	−	3.72768i	−0.130736	−	0.226441i	0.793225	−	0.608929i	$-0.208401\pi$
$271$	−2.15218	−	3.72768i	−0.130736	−	0.226441i	−0.923960	+	0.382488i	$0.875067\pi$
$272$	13.7598			0.834311
$273$	1.80694	−	0.310447i	0.109361	−	0.0187891i
$274$	11.6404			0.703223
$275$	16.1345	+	27.9459i	0.972950	+	1.68520i
$276$	0.823862	−	1.42697i	0.0495907	−	0.0858935i
$277$	7.32466	−	12.6867i	0.440096	−	0.762269i	−0.557600	−	0.830110i	$-0.688278\pi$
$277$	7.32466	−	12.6867i	0.440096	−	0.762269i	0.997696	+	0.0678408i	$0.0216110\pi$
$278$	−3.51526	−	6.08861i	−0.210831	−	0.365171i
$279$	−0.539333			−0.0322890
$280$	6.24796	−	16.9347i	0.373387	−	1.01204i
$281$	17.0380			1.01640			0.508202	−	0.861238i	$-0.330310\pi$
$281$	17.0380			1.01640			0.508202	+	0.861238i	$0.330310\pi$
$282$	−3.10636	−	5.38037i	−0.184981	−	0.320397i
$283$	8.95641	−	15.5130i	0.532403	−	0.922150i	−0.466881	−	0.884320i	$-0.654622\pi$
$283$	8.95641	−	15.5130i	0.532403	−	0.922150i	0.999284	−	0.0378294i	$-0.0120443\pi$
$284$	−0.483786	+	0.837942i	−0.0287074	+	0.0497227i
$285$	4.59544	+	7.95953i	0.272210	+	0.471482i
$286$	−2.69206			−0.159185
$287$	−15.6803	−	18.8544i	−0.925582	−	1.11294i
$288$	−5.52331			−0.325464
$289$	−14.9213	−	25.8445i	−0.877725	−	1.52026i
$290$	−2.75517	+	4.77210i	−0.161789	+	0.280228i
$291$	−4.07085	+	7.05092i	−0.238637	+	0.413332i
$292$	8.67247	+	15.0212i	0.507518	+	0.879047i
$293$	−18.7699			−1.09655			−0.548273	−	0.836299i	$-0.684715\pi$
$293$	−18.7699			−1.09655			−0.548273	+	0.836299i	$0.684715\pi$
$294$	−0.757316	+	4.08509i	−0.0441676	+	0.238248i
$295$	−21.1233			−1.22985
$296$	3.13510	+	5.43015i	0.182224	+	0.315621i
$297$	−3.27267	+	5.66843i	−0.189900	+	0.328916i
$298$	−1.53538	+	2.65936i	−0.0889422	+	0.154052i
$299$	−0.346483	−	0.600126i	−0.0200376	−	0.0347062i
$300$	8.12342			0.469006
$301$	7.22451	+	8.68692i	0.416414	+	0.500706i
$302$	2.99740			0.172481
$303$	−0.0666245	−	0.115397i	−0.00382748	−	0.00662939i
$304$	2.93185	−	5.07812i	0.168153	−	0.291250i
$305$	8.35357	−	14.4688i	0.478324	−	0.828482i
$306$	2.03110	+	3.51798i	0.116111	+	0.201109i
$307$	−1.42373			−0.0812566			−0.0406283	−	0.999174i	$-0.512936\pi$
$307$	−1.42373			−0.0812566			−0.0406283	+	0.999174i	$0.512936\pi$
$308$	−9.87677	+	26.7703i	−0.562781	+	1.52538i
$309$	11.0107			0.626374
$310$	0.504365	+	0.873586i	0.0286460	+	0.0496164i
$311$	2.21236	−	3.83191i	0.125451	−	0.217288i	−0.796458	−	0.604694i	$-0.793295\pi$
$311$	2.21236	−	3.83191i	0.125451	−	0.217288i	0.921909	+	0.387406i	$0.126629\pi$
$312$	−0.750145	+	1.29929i	−0.0424686	+	0.0735577i
$313$	−10.8433	−	18.7811i	−0.612898	−	1.06157i	−0.990749	−	0.135704i	$-0.956670\pi$
$313$	−10.8433	−	18.7811i	−0.612898	−	1.06157i	0.377852	−	0.925866i	$-0.376663\pi$
$314$	5.72644			0.323162
$315$	−8.21691	+	1.41173i	−0.462970	+	0.0795422i
$316$	22.0581			1.24086
$317$	5.81349	+	10.0693i	0.326518	+	0.565546i	0.981818	−	0.189822i	$-0.0607912\pi$
$317$	5.81349	+	10.0693i	0.326518	+	0.565546i	−0.655300	+	0.755369i	$0.727458\pi$
$318$	−3.73178	+	6.46363i	−0.209268	+	0.362462i
$319$	9.64191	−	16.7003i	0.539844	−	0.935036i
$320$	−1.17011	−	2.02669i	−0.0654111	−	0.113295i
$321$	8.57510			0.478615
$322$	1.54765	−	0.265900i	0.0862473	−	0.0148180i
$323$	−19.9619			−1.11071
$324$	0.823862	+	1.42697i	0.0457701	+	0.0792762i
$325$	1.70819	−	2.95867i	0.0947533	−	0.164118i
$326$	7.10232	−	12.3016i	0.393361	−	0.681322i
$327$	5.64113	+	9.77072i	0.311955	+	0.540322i
$328$	20.0670			1.10802
$329$	−9.58603	+	25.9823i	−0.528495	+	1.43245i
$330$	12.2419			0.673897
$331$	−3.94742	−	6.83713i	−0.216970	−	0.375803i	0.736910	−	0.675991i	$-0.236284\pi$
$331$	−3.94742	−	6.83713i	−0.216970	−	0.375803i	−0.953880	+	0.300188i	$0.902951\pi$
$332$	−8.05326	+	13.9486i	−0.441980	+	0.765531i
$333$	1.44806	−	2.50812i	0.0793534	−	0.137444i
$334$	3.57209	+	6.18704i	0.195456	+	0.338540i
$335$	8.62259			0.471102
$336$	3.40117	+	4.08965i	0.185549	+	0.223108i
$337$	12.1596			0.662378			0.331189	−	0.943565i	$-0.392550\pi$
$337$	12.1596			0.662378			0.331189	+	0.943565i	$0.392550\pi$
$338$	−3.71543	−	6.43531i	−0.202093	−	0.350035i
$339$	1.57082	−	2.72074i	0.0853154	−	0.147771i
$340$	−17.7685	+	30.7760i	−0.963634	+	1.66906i
$341$	−1.76506	−	3.05717i	−0.0955833	−	0.165555i
$342$	1.73110			0.0936071
$343$	16.1595	−	9.04831i	0.872529	−	0.488563i
$344$	−9.24561			−0.498490
$345$	1.57560	+	2.72902i	0.0848276	+	0.146926i
$346$	−4.92742	+	8.53454i	−0.264900	+	0.458820i
$347$	−7.00958	+	12.1409i	−0.376294	+	0.651760i	−0.990520	−	0.137370i	$-0.956135\pi$
$347$	−7.00958	+	12.1409i	−0.376294	+	0.651760i	0.614226	+	0.789130i	$0.289468\pi$
$348$	−2.42726	−	4.20413i	−0.130115	−	0.225365i
$349$	2.94132			0.157445			0.0787226	−	0.996897i	$-0.474916\pi$
$349$	2.94132			0.157445			0.0787226	+	0.996897i	$0.474916\pi$
$350$	4.95031	+	5.95237i	0.264605	+	0.318168i
$351$	0.692965			0.0369878
$352$	−18.0760	−	31.3085i	−0.963453	−	1.66875i
$353$	5.03670	−	8.72382i	0.268076	−	0.464322i	−0.700289	−	0.713860i	$-0.746945\pi$
$353$	5.03670	−	8.72382i	0.268076	−	0.464322i	0.968365	+	0.249538i	$0.0802787\pi$
$354$	−1.98929	+	3.44555i	−0.105729	+	0.183129i
$355$	−0.925221	−	1.60253i	−0.0491056	−	0.0850534i
$356$	−4.82683			−0.255822
$357$	6.26786	−	16.9886i	0.331730	−	0.899132i
$358$	−1.92622			−0.101804
$359$	16.2478	+	28.1420i	0.857526	+	1.48528i	0.874282	+	0.485418i	$0.161333\pi$
$359$	16.2478	+	28.1420i	0.857526	+	1.48528i	−0.0167563	+	0.999860i	$0.505334\pi$
$360$	3.41122	−	5.90841i	0.179787	−	0.311401i
$361$	5.24665	−	9.08747i	0.276140	−	0.478288i
$362$	4.26738	+	7.39132i	0.224289	+	0.388479i
$363$	−31.8415			−1.67124
$364$	2.97734	−	0.511532i	0.156055	−	0.0268115i
$365$	−33.1715			−1.73627
$366$	−1.57339	−	2.72520i	−0.0822426	−	0.142448i
$367$	−12.1371	+	21.0221i	−0.633552	+	1.09734i	0.353269	+	0.935522i	$0.385070\pi$
$367$	−12.1371	+	21.0221i	−0.633552	+	1.09734i	−0.986820	+	0.161821i	$0.948263\pi$
$368$	1.00522	−	1.74109i	0.0524008	−	0.0907608i
$369$	−4.63435	−	8.02694i	−0.241255	−	0.417866i
$370$	−5.41671			−0.281601
$371$	32.7896	−	5.63353i	1.70235	−	0.292478i
$372$	−0.888672			−0.0460755
$373$	11.0313	+	19.1069i	0.571181	+	0.989315i	0.996445	+	0.0842458i	$0.0268481\pi$
$373$	11.0313	+	19.1069i	0.571181	+	0.989315i	−0.425264	+	0.905070i	$0.639819\pi$
$374$	−13.2943	+	23.0264i	−0.687430	+	1.19066i
$375$	0.110155	−	0.190795i	0.00568840	−	0.00985261i
$376$	−11.3311	−	19.6261i	−0.584359	−	1.01214i
$377$	−2.04161			−0.105148
$378$	−0.543550	+	1.47326i	−0.0279572	+	0.0757761i
$379$	0.844591			0.0433837			0.0216919	−	0.999765i	$-0.493095\pi$
$379$	0.844591			0.0433837			0.0216919	+	0.999765i	$0.493095\pi$
$380$	7.57202	+	13.1151i	0.388436	+	0.672791i
$381$	−6.46686	+	11.2009i	−0.331307	+	0.573841i
$382$	−2.93474	+	5.08311i	−0.150154	+	0.260075i
$383$	−16.5176	−	28.6093i	−0.844009	−	1.46187i	−0.886479	−	0.462769i	$-0.846856\pi$
$383$	−16.5176	−	28.6093i	−0.844009	−	1.46187i	0.0424697	−	0.999098i	$-0.486477\pi$
$384$	−11.4874			−0.586214
$385$	−34.8936	−	41.9568i	−1.77834	−	2.13832i
$386$	2.13107			0.108469
$387$	2.13522	+	3.69830i	0.108539	+	0.187995i
$388$	−6.70763	+	11.6180i	−0.340529	+	0.589813i
$389$	−0.386406	+	0.669275i	−0.0195916	+	0.0339336i	−0.875655	−	0.482937i	$-0.839570\pi$
$389$	−0.386406	+	0.669275i	−0.0195916	+	0.0339336i	0.856063	+	0.516871i	$0.172903\pi$
$390$	−0.648037	−	1.12243i	−0.0328146	−	0.0568366i
$391$	−6.84417			−0.346125
$392$	−2.76248	+	14.9013i	−0.139526	+	0.752629i
$393$	−6.14667			−0.310058
$394$	2.43726	+	4.22146i	0.122788	+	0.212674i
$395$	−21.0926	+	36.5335i	−1.06128	+	1.83820i
$396$	−5.39246	+	9.34001i	−0.270981	+	0.469353i
$397$	10.5690	+	18.3061i	0.530444	+	0.918756i	0.999369	+	0.0355178i	$0.0113080\pi$
$397$	10.5690	+	18.3061i	0.530444	+	0.918756i	−0.468925	+	0.883238i	$0.655359\pi$
$398$	−1.33251			−0.0667928
$399$	−4.93420	−	5.93300i	−0.247019	−	0.297022i
$400$	9.91165			0.495583
$401$	−14.1572	−	24.5209i	−0.706975	−	1.22452i	−0.965974	−	0.258639i	$-0.916726\pi$
$401$	−14.1572	−	24.5209i	−0.706975	−	1.22452i	0.258999	−	0.965878i	$-0.416607\pi$
$402$	0.812031	−	1.40648i	0.0405004	−	0.0701488i
$403$	−0.186870	+	0.323668i	−0.00930863	+	0.0161230i
$404$	−0.109779	−	0.190142i	−0.00546170	−	0.00945994i
$405$	−3.15120			−0.156585
$406$	1.60140	−	4.34050i	0.0794763	−	0.215415i
$407$	18.9561			0.939621
$408$	7.40891	+	12.8326i	0.366796	+	0.635309i
$409$	11.1572	−	19.3248i	0.551688	−	0.955551i	−0.446465	−	0.894801i	$-0.647317\pi$
$409$	11.1572	−	19.3248i	0.551688	−	0.955551i	0.998153	−	0.0607502i	$-0.0193493\pi$
$410$	−8.66777	+	15.0130i	−0.428071	+	0.741440i
$411$	−9.80611	−	16.9847i	−0.483700	−	0.837792i
$412$	18.1425			0.893818
$413$	17.4791	−	3.00305i	0.860088	−	0.147770i
$414$	0.593528			0.0291703
$415$	−15.4015	−	26.6762i	−0.756031	−	1.30948i
$416$	−1.91373	+	3.31468i	−0.0938284	+	0.162516i
$417$	−5.92265	+	10.2583i	−0.290033	+	0.502352i
$418$	5.66532	+	9.81262i	0.277100	+	0.479951i
$419$	−5.99719			−0.292982			−0.146491	−	0.989212i	$-0.546798\pi$
$419$	−5.99719			−0.292982			−0.146491	+	0.989212i	$0.546798\pi$
$420$	−13.5392	+	2.32615i	−0.660645	+	0.113504i
$421$	12.4472			0.606638			0.303319	−	0.952889i	$-0.401905\pi$
$421$	12.4472			0.606638			0.303319	+	0.952889i	$0.401905\pi$
$422$	−6.84885	−	11.8626i	−0.333397	−	0.577460i
$423$	−5.23372	+	9.06507i	−0.254472	+	0.440759i
$424$	−13.6125	+	23.5775i	−0.661081	+	1.14503i
$425$	−16.8712	−	29.2217i	−0.818372	−	1.41746i
$426$	−0.348530			−0.0168863
$427$	−4.85539	+	13.1602i	−0.234969	+	0.636867i
$428$	14.1294			0.682970
$429$	2.26785	+	3.92803i	0.109493	+	0.189647i
$430$	3.99356	−	6.91704i	0.192586	−	0.333570i
$431$	−2.69497	+	4.66783i	−0.129812	+	0.224842i	−0.923604	−	0.383349i	$-0.874771\pi$
$431$	−2.69497	+	4.66783i	−0.129812	+	0.224842i	0.793791	+	0.608190i	$0.208104\pi$
$432$	1.00522	+	1.74109i	0.0483637	+	0.0837684i
$433$	−32.6738			−1.57020			−0.785102	−	0.619366i	$-0.787390\pi$
$433$	−32.6738			−1.57020			−0.785102	+	0.619366i	$0.787390\pi$
$434$	−0.541546	−	0.651167i	−0.0259950	−	0.0312570i
$435$	9.28405			0.445136
$436$	9.29502	+	16.0994i	0.445151	+	0.771024i
$437$	−1.45831	+	2.52587i	−0.0697605	+	0.120829i
$438$	−3.12392	+	5.41079i	−0.149267	+	0.258537i
$439$	−0.0144158	−	0.0249690i	−0.000688030	−	0.00119170i	0.865681	−	0.500596i	$-0.166886\pi$
$439$	−0.0144158	−	0.0249690i	−0.000688030	−	0.00119170i	−0.866369	+	0.499404i	$0.833552\pi$
$440$	44.6552			2.12885
$441$	6.59859	−	2.33635i	0.314219	−	0.111255i
$442$	2.81497			0.133894
$443$	−8.46637	−	14.6642i	−0.402249	−	0.696716i	0.591748	−	0.806123i	$-0.298438\pi$
$443$	−8.46637	−	14.6642i	−0.402249	−	0.696716i	−0.993997	+	0.109407i	$0.965105\pi$
$444$	2.38601	−	4.13269i	0.113235	−	0.196129i
$445$	4.61556	−	7.99438i	0.218799	−	0.378970i
$446$	1.27185	+	2.20291i	0.0602239	+	0.104311i
$447$	5.17374			0.244709
$448$	1.25637	+	1.51068i	0.0593577	+	0.0713731i
$449$	20.8257			0.982825			0.491412	−	0.870927i	$-0.336481\pi$
$449$	20.8257			0.982825			0.491412	+	0.870927i	$0.336481\pi$
$450$	1.46307	+	2.53412i	0.0689699	+	0.119459i
$451$	30.3334	−	52.5390i	1.42835	−	2.47397i
$452$	2.58828	−	4.48304i	0.121743	−	0.210864i
$453$	−2.52507	−	4.37355i	−0.118638	−	0.205487i
$454$	−6.48927			−0.304556
$455$	−1.99980	+	5.42032i	−0.0937520	+	0.254108i
$456$	6.31457			0.295707
$457$	7.17566	+	12.4286i	0.335663	+	0.581386i	0.983612	−	0.180298i	$-0.0577063\pi$
$457$	7.17566	+	12.4286i	0.335663	+	0.581386i	−0.647949	+	0.761684i	$0.724373\pi$
$458$	1.65520	−	2.86690i	0.0773426	−	0.133961i
$459$	3.42208	−	5.92722i	0.159729	−	0.276659i
$460$	2.59616	+	4.49668i	0.121046	+	0.209659i
$461$	−3.54822			−0.165257			−0.0826286	−	0.996580i	$-0.526332\pi$
$461$	−3.54822			−0.165257			−0.0826286	+	0.996580i	$0.526332\pi$
$462$	−10.1299	+	1.74040i	−0.471286	+	0.0809710i
$463$	12.2267			0.568223			0.284111	−	0.958791i	$-0.408301\pi$
$463$	12.2267			0.568223			0.284111	+	0.958791i	$0.408301\pi$
$464$	−2.96157	−	5.12960i	−0.137488	−	0.238136i
$465$	0.849774	−	1.47185i	0.0394073	−	0.0682555i
$466$	−6.60911	+	11.4473i	−0.306161	+	0.530287i
$467$	14.2930	+	24.7562i	0.661401	+	1.14558i	0.980248	+	0.197774i	$0.0633713\pi$
$467$	14.2930	+	24.7562i	0.661401	+	1.14558i	−0.318846	+	0.947806i	$0.603295\pi$
$468$	1.14182			0.0527804
$469$	−7.13499	+	1.22585i	−0.329463	+	0.0566045i
$470$	19.5776			0.903045
$471$	−4.82407	−	8.35553i	−0.222281	−	0.385003i
$472$	−7.25637	+	12.5684i	−0.334002	+	0.578508i
$473$	−13.9757	+	24.2066i	−0.642604	+	1.11302i
$474$	3.97279	+	6.88107i	0.182476	+	0.316058i
$475$	−14.3792			−0.659763
$476$	10.3277	−	27.9925i	0.473369	−	1.28304i
$477$	12.5749			0.575765
$478$	3.97370	+	6.88266i	0.181753	+	0.314805i
$479$	−15.1346	+	26.2138i	−0.691516	+	1.19774i	0.279825	+	0.960051i	$0.409724\pi$
$479$	−15.1346	+	26.2138i	−0.691516	+	1.19774i	−0.971341	+	0.237690i	$0.923610\pi$
$480$	8.70254	−	15.0732i	0.397215	−	0.687996i
$481$	−1.00346	−	1.73804i	−0.0457537	−	0.0792478i
$482$	1.95060			0.0888474
$483$	−1.69175	−	2.03420i	−0.0769773	−	0.0925594i
$484$	−52.4660			−2.38482
$485$	−12.8281	−	22.2189i	−0.582493	−	1.00891i
$486$	−0.296764	+	0.514011i	−0.0134615	+	0.0233160i
$487$	−14.4684	+	25.0601i	−0.655627	+	1.13558i	0.326109	+	0.945332i	$0.394262\pi$
$487$	−14.4684	+	25.0601i	−0.655627	+	1.13558i	−0.981736	+	0.190247i	$0.939071\pi$
$488$	−5.73930	−	9.94077i	−0.259806	−	0.449997i
$489$	−23.9325			−1.08227
$490$	−9.95509	−	8.50322i	−0.449725	−	0.384136i
$491$	−11.9185			−0.537876			−0.268938	−	0.963158i	$-0.586673\pi$
$491$	−11.9185			−0.537876			−0.268938	+	0.963158i	$0.586673\pi$
$492$	−7.63614	−	13.2262i	−0.344264	−	0.596282i
$493$	−10.0821	+	17.4627i	−0.454076	+	0.786482i
$494$	0.599796	−	1.03888i	0.0269861	−	0.0467413i
$495$	−10.3129	−	17.8624i	−0.463528	−	0.802854i
$496$	−1.08430			−0.0486864
$497$	0.993426	+	1.19452i	0.0445612	+	0.0535815i
$498$	−5.80174			−0.259982
$499$	−5.18689	−	8.98396i	−0.232197	−	0.402177i	0.726257	−	0.687423i	$-0.241258\pi$
$499$	−5.18689	−	8.98396i	−0.232197	−	0.402177i	−0.958454	+	0.285246i	$0.907925\pi$
$500$	0.181506	−	0.314377i	0.00811719	−	0.0140594i
$501$	6.01840	−	10.4242i	0.268882	−	0.465718i
$502$	3.04982	+	5.28243i	0.136120	+	0.235767i
$503$	22.4429			1.00068			0.500340	−	0.865829i	$-0.333209\pi$
$503$	22.4429			1.00068			0.500340	+	0.865829i	$0.333209\pi$
$504$	−1.98272	+	5.37403i	−0.0883175	+	0.239378i
$505$	0.419895			0.0186851
$506$	1.94242	+	3.36437i	0.0863512	+	0.149565i
$507$	−6.25990	+	10.8425i	−0.278012	+	0.481531i
$508$	−10.6556	+	18.4560i	−0.472766	+	0.818855i
$509$	2.98190	+	5.16481i	0.132171	+	0.228926i	0.924513	−	0.381150i	$-0.124472\pi$
$509$	2.98190	+	5.16481i	0.132171	+	0.228926i	−0.792342	+	0.610077i	$0.791139\pi$
$510$	−12.8009			−0.566831
$511$	27.4486	−	4.71590i	1.21425	−	0.208619i
$512$	−19.8096			−0.875470
$513$	−1.45831	−	2.52587i	−0.0643861	−	0.111520i
$514$	6.94637	−	12.0315i	0.306391	−	0.530686i
$515$	−17.3484	+	30.0483i	−0.764462	+	1.32409i
$516$	3.51825	+	6.09378i	0.154882	+	0.268264i
$517$	−68.5129			−3.01319
$518$	4.48220	−	0.770080i	0.196937	−	0.0338354i
$519$	16.6038			0.728827
$520$	−2.36386	−	4.09432i	−0.103662	−	0.179548i
$521$	−0.510936	+	0.884968i	−0.0223845	+	0.0387711i	−0.877001	−	0.480489i	$-0.840459\pi$
$521$	−0.510936	+	0.884968i	−0.0223845	+	0.0387711i	0.854616	+	0.519260i	$0.173792\pi$
$522$	0.874324	−	1.51437i	0.0382681	−	0.0662824i
$523$	−2.49185	−	4.31600i	−0.108961	−	0.188726i	0.806389	−	0.591386i	$-0.201419\pi$
$523$	−2.49185	−	4.31600i	−0.108961	−	0.188726i	−0.915350	+	0.402660i	$0.868086\pi$
$524$	−10.1280			−0.442444
$525$	4.51495	−	12.2375i	0.197049	−	0.534087i
$526$	16.2423			0.708197
$527$	1.84564	+	3.19675i	0.0803975	+	0.139253i
$528$	−6.57951	+	11.3961i	−0.286337	+	0.495949i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−11.7596	−	20.3682i	−0.510804	−	0.884738i
$531$	6.70326			0.290897
$532$	−8.13020	−	9.77595i	−0.352489	−	0.423841i
$533$	−6.42289			−0.278206
$534$	−0.869340	−	1.50574i	−0.0376200	−	0.0651598i
$535$	−13.5109	+	23.4016i	−0.584129	+	1.01174i
$536$	2.96207	−	5.13045i	0.127942	−	0.221602i
$537$	1.62269	+	2.81058i	0.0700242	+	0.121285i
$538$	15.6555			0.674958
$539$	34.8385	+	29.7576i	1.50060	+	1.28175i
$540$	−5.19231			−0.223442
$541$	−7.66700	−	13.2796i	−0.329630	−	0.570936i	0.652808	−	0.757523i	$-0.273591\pi$
$541$	−7.66700	−	13.2796i	−0.329630	−	0.570936i	−0.982438	+	0.186587i	$0.940257\pi$
$542$	1.27738	−	2.21249i	0.0548681	−	0.0950344i
$543$	7.18985	−	12.4532i	0.308546	−	0.534417i
$544$	18.9012	+	32.7379i	0.810384	+	1.40363i
$545$	−35.5527			−1.52291
$546$	0.695808	+	0.836656i	0.0297778	+	0.0358056i
$547$	−6.89796			−0.294935			−0.147468	−	0.989067i	$-0.547112\pi$
$547$	−6.89796			−0.294935			−0.147468	+	0.989067i	$0.547112\pi$
$548$	−16.1578	−	27.9861i	−0.690225	−	1.19551i
$549$	−2.65091	+	4.59152i	−0.113138	+	0.195961i
$550$	−9.57631	+	16.5867i	−0.408335	+	0.707258i
$551$	4.29647	+	7.44170i	0.183036	+	0.317027i
$552$	2.16503			0.0921497
$553$	12.2598	−	33.2292i	0.521338	−	1.41305i
$554$	8.69479			0.369406
$555$	4.56314	+	7.90360i	0.193695	+	0.335489i
$556$	−9.75889	+	16.9029i	−0.413869	+	0.716842i
$557$	−14.7445	+	25.5382i	−0.624743	+	1.08209i	0.363847	+	0.931459i	$0.381463\pi$
$557$	−14.7445	+	25.5382i	−0.624743	+	1.08209i	−0.988590	+	0.150628i	$0.951870\pi$
$558$	−0.160055	−	0.277223i	−0.00677566	−	0.0117358i
$559$	2.95926			0.125163
$560$	−16.5196	+	2.83821i	−0.698081	+	0.119936i
$561$	44.7974			1.89135
$562$	5.05628	+	8.75773i	0.213286	+	0.369423i
$563$	3.61211	−	6.25636i	0.152232	−	0.263674i	−0.779815	−	0.626010i	$-0.784687\pi$
$563$	3.61211	−	6.25636i	0.152232	−	0.263674i	0.932048	+	0.362335i	$0.118020\pi$
$564$	−8.62372	+	14.9367i	−0.363124	+	0.628950i
$565$	4.94998	+	8.57362i	0.208247	+	0.360695i
$566$	10.6318			0.446887
$567$	2.60755	−	0.447998i	0.109507	−	0.0188142i
$568$	−1.27134			−0.0533443
$569$	1.80688	+	3.12960i	0.0757482	+	0.131200i	0.901411	−	0.432964i	$-0.142532\pi$
$569$	1.80688	+	3.12960i	0.0757482	+	0.131200i	−0.825663	+	0.564163i	$0.809199\pi$
$570$	−2.72752	+	4.72421i	−0.114243	+	0.197875i
$571$	1.26695	−	2.19442i	0.0530203	−	0.0918338i	−0.838297	−	0.545214i	$-0.816449\pi$
$571$	1.26695	−	2.19442i	0.0530203	−	0.0918338i	0.891317	+	0.453380i	$0.149782\pi$
$572$	3.73679	+	6.47230i	0.156243	+	0.270621i
$573$	9.88912			0.413124
$574$	5.03801	−	13.6552i	0.210283	−	0.569957i
$575$	−4.93009			−0.205599
$576$	0.371321	+	0.643147i	0.0154717	+	0.0267978i
$577$	1.05343	−	1.82459i	0.0438548	−	0.0759588i	−0.843265	−	0.537498i	$-0.819369\pi$
$577$	1.05343	−	1.82459i	0.0438548	−	0.0759588i	0.887120	+	0.461540i	$0.152703\pi$
$578$	8.85623	−	15.3394i	0.368371	−	0.638037i
$579$	−1.79525	−	3.10947i	−0.0746082	−	0.129225i
$580$	15.2976			0.635196
$581$	16.5369	+	19.8843i	0.686065	+	0.824941i
$582$	−4.83233			−0.200306
$583$	41.1535	+	71.2799i	1.70440	+	2.95211i
$584$	−11.3952	+	19.7371i	−0.471536	+	0.816725i
$585$	−1.09184	+	1.89112i	−0.0451419	+	0.0781881i
$586$	−5.57022	−	9.64791i	−0.230104	−	0.398551i
$587$	3.01620			0.124492			0.0622460	−	0.998061i	$-0.480174\pi$
$587$	3.01620			0.124492			0.0622460	+	0.998061i	$0.480174\pi$
$588$	10.8727	−	3.84967i	0.448381	−	0.158758i
$589$	1.57303			0.0648156
$590$	−6.26865	−	10.8576i	−0.258076	−	0.447001i
$591$	4.10640	−	7.11249i	0.168915	−	0.292569i
$592$	2.91125	−	5.04243i	0.119652	−	0.207243i
$593$	−5.22680	−	9.05308i	−0.214639	−	0.371765i	0.738522	−	0.674229i	$-0.235524\pi$
$593$	−5.22680	−	9.05308i	−0.214639	−	0.371765i	−0.953161	+	0.302464i	$0.902191\pi$
$594$	−3.88485			−0.159397
$595$	36.4866	+	43.8724i	1.49581	+	1.79859i
$596$	8.52489			0.349193
$597$	1.12253	+	1.94429i	0.0459423	+	0.0795743i
$598$	0.205647	−	0.356192i	0.00840954	−	0.0145658i
$599$	0.885052	−	1.53296i	0.0361623	−	0.0626349i	−0.847378	−	0.530990i	$-0.821820\pi$
$599$	0.885052	−	1.53296i	0.0361623	−	0.0626349i	0.883540	+	0.468356i	$0.155153\pi$
$600$	5.33689	+	9.24376i	0.217878	+	0.377375i
$601$	−37.1024			−1.51344			−0.756720	−	0.653739i	$-0.773199\pi$
$601$	−37.1024			−1.51344			−0.756720	+	0.653739i	$0.773199\pi$
$602$	−2.32120	+	6.29144i	−0.0946049	+	0.256420i
$603$	−2.73628			−0.111430
$604$	−4.16062	−	7.20640i	−0.169293	−	0.293224i
$605$	50.1695	−	86.8961i	2.03968	−	3.53283i
$606$	0.0395435	−	0.0684914i	0.00160635	−	0.00278227i
$607$	4.95018	+	8.57397i	0.200922	+	0.348007i	0.948826	−	0.315800i	$-0.102273\pi$
$607$	4.95018	+	8.57397i	0.200922	+	0.348007i	−0.747904	+	0.663807i	$0.768940\pi$
$608$	16.1094			0.653323
$609$	−7.68233	+	1.31989i	−0.311304	+	0.0534846i
$610$	9.91617			0.401494
$611$	3.62679	+	6.28178i	0.146724	+	0.254133i
$612$	5.63865	−	9.76643i	0.227929	−	0.394785i
$613$	16.6981	−	28.9220i	0.674430	−	1.16815i	−0.302205	−	0.953243i	$-0.597723\pi$
$613$	16.6981	−	28.9220i	0.674430	−	1.16815i	0.976635	−	0.214905i	$-0.0689441\pi$
$614$	−0.422512	−	0.731813i	−0.0170512	−	0.0295336i
$615$	29.2076			1.17776
$616$	−36.9511	+	6.34852i	−1.48880	+	0.255789i
$617$	−19.5997			−0.789054			−0.394527	−	0.918884i	$-0.629092\pi$
$617$	−19.5997			−0.789054			−0.394527	+	0.918884i	$0.629092\pi$
$618$	3.26757	+	5.65960i	0.131441	+	0.227662i
$619$	10.2341	−	17.7259i	0.411342	−	0.712466i	−0.583694	−	0.811973i	$-0.698393\pi$
$619$	10.2341	−	17.7259i	0.411342	−	0.712466i	0.995037	+	0.0995075i	$0.0317267\pi$
$620$	1.40019	−	2.42521i	0.0562331	−	0.0973986i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	2.62619			0.105301
$623$	−2.68273	+	7.27134i	−0.107481	+	0.291320i
$624$	1.39317			0.0557713
$625$	12.6723	+	21.9491i	0.506894	+	0.877965i
$626$	6.43579	−	11.1471i	0.257226	−	0.445528i
$627$	9.54515	−	16.5327i	0.381197	−	0.660252i
$628$	−7.94873	−	13.7676i	−0.317189	−	0.549387i
$629$	−19.8216			−0.790338
$630$	−3.16413	−	3.80463i	−0.126062	−	0.151580i
$631$	−16.9942			−0.676529			−0.338265	−	0.941051i	$-0.609840\pi$
$631$	−16.9942			−0.676529			−0.338265	+	0.941051i	$0.609840\pi$
$632$	14.4916	+	25.1002i	0.576446	+	0.998434i
$633$	−11.5392	+	19.9865i	−0.458642	+	0.794392i
$634$	−3.45047	+	5.97640i	−0.137036	+	0.237353i
$635$	−20.3784	−	35.2964i	−0.808692	−	1.40070i
$636$	20.7199			0.821599
$637$	0.884193	−	4.76949i	0.0350330	−	0.188974i
$638$	11.4455			0.453132
$639$	0.293609	+	0.508545i	0.0116150	+	0.0201177i
$640$	18.0996	−	31.3494i	0.715448	−	1.23919i
$641$	−5.48164	+	9.49448i	−0.216512	+	0.375009i	−0.953739	−	0.300635i	$-0.902801\pi$
$641$	−5.48164	+	9.49448i	−0.216512	+	0.375009i	0.737227	+	0.675645i	$0.236135\pi$
$642$	2.54478	+	4.40769i	0.100435	+	0.173958i
$643$	11.7658			0.463996			0.231998	−	0.972716i	$-0.425474\pi$
$643$	11.7658			0.463996			0.231998	+	0.972716i	$0.425474\pi$
$644$	−2.78754	−	3.35180i	−0.109844	−	0.132080i
$645$	−13.4570			−0.529869
$646$	−5.92397	−	10.2606i	−0.233075	−	0.403699i
$647$	−0.884701	+	1.53235i	−0.0347812	+	0.0602428i	−0.882892	−	0.469576i	$-0.844407\pi$
$647$	−0.884701	+	1.53235i	−0.0347812	+	0.0602428i	0.848111	+	0.529819i	$0.177740\pi$
$648$	−1.08251	+	1.87497i	−0.0425252	+	0.0736557i
$649$	21.9376	+	37.9970i	0.861124	+	1.49151i
$650$	2.02772			0.0795337
$651$	−0.493918	+	1.33873i	−0.0193582	+	0.0524691i
$652$	−39.4342			−1.54436
$653$	−5.28392	−	9.15202i	−0.206776	−	0.358146i	0.743921	−	0.668267i	$-0.232964\pi$
$653$	−5.28392	−	9.15202i	−0.206776	−	0.358146i	−0.950697	+	0.310121i	$0.899630\pi$
$654$	−3.34817	+	5.79920i	−0.130924	+	0.226767i
$655$	9.68470	−	16.7744i	0.378413	−	0.655430i
$656$	−9.31710	−	16.1377i	−0.363772	−	0.630071i
$657$	10.5266			0.410682
$658$	−16.2000	+	2.78329i	−0.631540	+	0.108504i
$659$	−10.3840			−0.404504			−0.202252	−	0.979334i	$-0.564826\pi$
$659$	−10.3840			−0.404504			−0.202252	+	0.979334i	$0.564826\pi$
$660$	−16.9927	−	29.4323i	−0.661441	−	1.14565i
$661$	16.6734	−	28.8792i	0.648521	−	1.12327i	−0.334955	−	0.942234i	$-0.608721\pi$
$661$	16.6734	−	28.8792i	0.648521	−	1.12327i	0.983476	−	0.181037i	$-0.0579455\pi$
$662$	2.34291	−	4.05803i	0.0910596	−	0.157720i
$663$	−2.37139	−	4.10736i	−0.0920970	−	0.159517i
$664$	−21.1632			−0.821290
$665$	23.9656	−	4.11750i	0.929348	−	0.159670i
$666$	1.71893			0.0666073
$667$	1.47310	+	2.55148i	0.0570385	+	0.0987936i
$668$	9.91666	−	17.1762i	0.383687	−	0.664566i
$669$	2.14286	−	3.71155i	0.0828479	−	0.143497i
$670$	2.55888	+	4.43210i	0.0988580	+	0.171227i
$671$	−34.7023			−1.33967
$672$	−5.05822	+	13.7100i	−0.195125	+	0.528873i
$673$	11.0030			0.424134			0.212067	−	0.977255i	$-0.431980\pi$
$673$	11.0030			0.424134			0.212067	+	0.977255i	$0.431980\pi$
$674$	3.60855	+	6.25018i	0.138996	+	0.240748i
$675$	2.46504	−	4.26958i	0.0948796	−	0.164336i
$676$	−10.3146	+	17.8654i	−0.396715	+	0.687130i
$677$	−16.8484	−	29.1822i	−0.647536	−	1.12156i	−0.983710	−	0.179765i	$-0.942466\pi$
$677$	−16.8484	−	29.1822i	−0.647536	−	1.12156i	0.336174	−	0.941800i	$-0.390867\pi$
$678$	1.86466			0.0716117
$679$	13.7737	+	16.5619i	0.528587	+	0.635586i
$680$	−46.6940			−1.79063
$681$	5.46669	+	9.46858i	0.209484	+	0.362837i
$682$	1.04761	−	1.81452i	0.0401152	−	0.0694815i
$683$	23.5809	−	40.8433i	0.902297	−	1.56282i	0.0777918	−	0.996970i	$-0.475213\pi$
$683$	23.5809	−	40.8433i	0.902297	−	1.56282i	0.824505	−	0.565854i	$-0.191454\pi$
$684$	−2.40290	−	4.16194i	−0.0918770	−	0.159136i
$685$	61.8021			2.36134
$686$	9.44648	+	5.62092i	0.360668	+	0.214608i
$687$	−5.57751			−0.212795
$688$	4.29273	+	7.43522i	0.163659	+	0.283465i
$689$	4.35698	−	7.54651i	0.165988	−	0.287499i
$690$	−0.935165	+	1.61975i	−0.0356011	+	0.0616629i
$691$	−11.9250	−	20.6548i	−0.453650	−	0.785745i	0.544959	−	0.838462i	$-0.316545\pi$
$691$	−11.9250	−	20.6548i	−0.453650	−	0.785745i	−0.998609	+	0.0527174i	$0.983212\pi$
$692$	27.3585			1.04001
$693$	11.0731	+	13.3145i	0.420632	+	0.505778i
$694$	−8.32077			−0.315852
$695$	−18.6635	−	32.3261i	−0.707946	−	1.22620i
$696$	3.18929	−	5.52402i	0.120890	−	0.209387i
$697$	−31.7183	+	54.9377i	−1.20142	+	2.08091i
$698$	0.872879	+	1.51187i	0.0330390	+	0.0572251i
$699$	22.2706			0.842351
$700$	7.43939	−	20.1640i	0.281183	−	0.762126i
$701$	6.20352			0.234304			0.117152	−	0.993114i	$-0.462624\pi$
$701$	6.20352			0.234304			0.117152	+	0.993114i	$0.462624\pi$
$702$	0.205647	+	0.356192i	0.00776166	+	0.0134436i
$703$	−4.22346	+	7.31524i	−0.159291	+	0.275900i
$704$	−2.43042	+	4.20962i	−0.0916000	+	0.158656i
$705$	−16.4925	−	28.5659i	−0.621144	−	1.07585i
$706$	5.97885			0.225017
$707$	−0.347453	+	0.0596953i	−0.0130673	+	0.00224507i
$708$	11.0451			0.415101
$709$	−8.12457	−	14.0722i	−0.305124	−	0.528491i	0.672165	−	0.740402i	$-0.265365\pi$
$709$	−8.12457	−	14.0722i	−0.305124	−	0.528491i	−0.977289	+	0.211911i	$0.932031\pi$
$710$	0.549145	−	0.951147i	0.0206090	−	0.0356959i
$711$	6.69351	−	11.5935i	0.251026	−	0.434790i
$712$	−3.17111	−	5.49252i	−0.118842	−	0.205841i
$713$	0.539333			0.0201982
$714$	10.5924	−	1.81986i	0.396411	−	0.0681067i
$715$	−14.2929			−0.534524
$716$	2.67374	+	4.63106i	0.0999225	+	0.173071i
$717$	6.69505	−	11.5962i	0.250031	−	0.433067i
$718$	−9.64353	+	16.7031i	−0.359893	+	0.623353i
$719$	−20.0251	−	34.6845i	−0.746811	−	1.29351i	−0.949344	−	0.314239i	$-0.898251\pi$
$719$	−20.0251	−	34.6845i	−0.746811	−	1.29351i	0.202533	−	0.979275i	$-0.435083\pi$
$720$	−6.33531			−0.236103
$721$	10.0835	−	27.3307i	0.375529	−	1.01785i
$722$	6.22807			0.231785
$723$	−1.64322	−	2.84615i	−0.0611121	−	0.105849i
$724$	11.8469	−	20.5194i	0.440286	−	0.762598i
$725$	−7.26249	+	12.5790i	−0.269722	+	0.467172i
$726$	−9.44941	−	16.3669i	−0.350700	−	0.607431i
$727$	40.4544			1.50037			0.750185	−	0.661228i	$-0.229964\pi$
$727$	40.4544			1.50037			0.750185	+	0.661228i	$0.229964\pi$
$728$	2.53812	+	3.05189i	0.0940688	+	0.113111i
$729$	1.00000			0.0370370
$730$	−9.84411	−	17.0505i	−0.364347	−	0.631067i
$731$	14.6138	−	25.3118i	0.540510	−	0.936191i
$732$	−4.36798	+	7.56556i	−0.161445	+	0.279631i
$733$	26.5084	+	45.9139i	0.979110	+	1.69587i	0.665646	+	0.746268i	$0.268156\pi$
$733$	26.5084	+	45.9139i	0.979110	+	1.69587i	0.313464	+	0.949600i	$0.398510\pi$
$734$	−14.4074			−0.531788
$735$	−4.02080	+	21.6889i	−0.148309	+	0.800006i
$736$	5.52331			0.203592
$737$	−8.95496	−	15.5104i	−0.329860	−	0.571334i
$738$	2.75062	−	4.76422i	0.101252	−	0.175373i
$739$	−15.2758	+	26.4585i	−0.561930	+	0.973292i	0.435398	+	0.900238i	$0.356608\pi$
$739$	−15.2758	+	26.4585i	−0.561930	+	0.973292i	−0.997328	+	0.0730537i	$0.976726\pi$
$740$	7.51880	+	13.0229i	0.276397	+	0.478733i
$741$	−2.02112			−0.0742477
$742$	12.6265	+	15.1824i	0.463532	+	0.557363i
$743$	−49.1733			−1.80399			−0.901997	−	0.431743i	$-0.857899\pi$
$743$	−49.1733			−1.80399			−0.901997	+	0.431743i	$0.857899\pi$
$744$	−0.583835	−	1.01123i	−0.0214044	−	0.0370736i
$745$	−8.15175	+	14.1193i	−0.298657	+	0.517289i
$746$	−6.54742	+	11.3405i	−0.239718	+	0.415204i
$747$	4.88750	+	8.46540i	0.178824	+	0.309733i
$748$	73.8138			2.69890
$749$	7.85303	−	21.2851i	0.286943	−	0.777741i
$750$	0.130761			0.00477471
$751$	−20.7611	−	35.9592i	−0.757582	−	1.31217i	−0.944080	−	0.329715i	$-0.893047\pi$
$751$	−20.7611	−	35.9592i	−0.757582	−	1.31217i	0.186498	−	0.982455i	$-0.440286\pi$
$752$	−10.5221	+	18.2248i	−0.383701	+	0.664590i
$753$	5.13845	−	8.90005i	0.187255	−	0.324336i
$754$	−0.605877	−	1.04941i	−0.0220647	−	0.0382172i
$755$	15.9140			0.579170
$756$	4.29652	−	0.738178i	0.156263	−	0.0268473i
$757$	−26.7837			−0.973470			−0.486735	−	0.873550i	$-0.661812\pi$
$757$	−26.7837			−0.973470			−0.486735	+	0.873550i	$0.661812\pi$
$758$	0.250644	+	0.434129i	0.00910381	+	0.0157683i
$759$	3.27267	−	5.66843i	0.118790	−	0.205751i
$760$	−9.94925	+	17.2326i	−0.360897	+	0.625093i
$761$	11.8342	+	20.4974i	0.428988	+	0.743029i	0.996784	−	0.0801405i	$-0.0255369\pi$
$761$	11.8342	+	20.4974i	0.428988	+	0.743029i	−0.567795	+	0.823170i	$0.692204\pi$
$762$	−7.67653			−0.278091
$763$	29.4190	−	5.05443i	1.06504	−	0.182983i
$764$	16.2945			0.589516
$765$	10.7837	+	18.6779i	0.389885	+	0.675301i
$766$	9.80366	−	16.9804i	0.354221	−	0.613528i
$767$	2.32256	−	4.02280i	0.0838629	−	0.145255i
$768$	−2.66641	−	4.61835i	−0.0962157	−	0.166650i
$769$	−16.2072			−0.584448			−0.292224	−	0.956350i	$-0.594395\pi$
$769$	−16.2072			−0.584448			−0.292224	+	0.956350i	$0.594395\pi$
$770$	11.2111	−	30.3870i	0.404020	−	1.09507i
$771$	−23.4070			−0.842984
$772$	−2.95808	−	5.12355i	−0.106464	−	0.184401i
$773$	−21.9449	+	38.0098i	−0.789305	+	1.36712i	0.137089	+	0.990559i	$0.456225\pi$
$773$	−21.9449	+	38.0098i	−0.789305	+	1.36712i	−0.926393	+	0.376557i	$0.877108\pi$
$774$	−1.26731	+	2.19505i	−0.0455526	+	0.0788994i
$775$	1.32948	+	2.30273i	0.0477563	+	0.0827163i
$776$	−17.6270			−0.632773
$777$	−4.89953	−	5.89131i	−0.175770	−	0.211350i
$778$	−0.458686			−0.0164447
$779$	13.5167	+	23.4116i	0.484285	+	0.838806i
$780$	−1.79905	+	3.11604i	−0.0644162	+	0.111572i
$781$	−1.92177	+	3.32860i	−0.0687663	+	0.119107i
$782$	−2.03110	−	3.51798i	−0.0726322	−	0.125803i
$783$	−2.94619			−0.105288
$784$	13.2661	−	4.69710i	0.473789	−	0.167754i
$785$	30.4033			1.08514
$786$	−1.82411	−	3.15945i	−0.0650639	−	0.112694i
$787$	12.8675	−	22.2871i	0.458675	−	0.794449i	−0.540216	−	0.841527i	$-0.681657\pi$
$787$	12.8675	−	22.2871i	0.458675	−	0.794449i	0.998891	+	0.0470774i	$0.0149907\pi$
$788$	6.76621	−	11.7194i	0.241036	−	0.417487i
$789$	−13.6828	−	23.6993i	−0.487121	−	0.843719i
$790$	−25.0381			−0.890816
$791$	−5.31488	−	6.39074i	−0.188975	−	0.227229i
$792$	−14.1708			−0.503539
$793$	1.83699	+	3.18176i	0.0652335	+	0.112988i
$794$	−6.27301	+	10.8652i	−0.222621	+	0.385591i
$795$	−19.8130	+	34.3172i	−0.702695	+	1.21710i
$796$	1.84963	+	3.20365i	0.0655583	+	0.113550i
$797$	−0.541418			−0.0191780			−0.00958901	−	0.999954i	$-0.503052\pi$
$797$	−0.541418			−0.0191780			−0.00958901	+	0.999954i	$0.503052\pi$
$798$	1.58533	−	4.29694i	0.0561202	−	0.152110i
$799$	71.6409			2.53447
$800$	13.6152	+	23.5822i	0.481370	+	0.833757i
$801$	−1.46470	+	2.53693i	−0.0517525	+	0.0896380i
$802$	8.40268	−	14.5539i	0.296709	−	0.513915i
$803$	34.4501	+	59.6693i	1.21572	+	2.10568i
$804$	−4.50864			−0.159008
$805$	8.21691	−	1.41173i	0.289608	−	0.0497571i
$806$	−0.221825			−0.00781344
$807$	−13.1885	−	22.8432i	−0.464258	−	0.804119i
$808$	0.144244	−	0.249838i	0.00507448	−	0.00878926i
$809$	1.94860	−	3.37507i	0.0685091	−	0.118661i	−0.829736	−	0.558156i	$-0.811509\pi$
$809$	1.94860	−	3.37507i	0.0685091	−	0.118661i	0.898245	+	0.439495i	$0.144842\pi$
$810$	−0.935165	−	1.61975i	−0.0328583	−	0.0569123i
$811$	17.8242			0.625892			0.312946	−	0.949771i	$-0.398684\pi$
$811$	17.8242			0.625892			0.312946	+	0.949771i	$0.398684\pi$
$812$	−12.6584	+	2.17481i	−0.444221	+	0.0763210i
$813$	−4.30436			−0.150960
$814$	5.62550	+	9.74366i	0.197174	+	0.341515i
$815$	37.7082	−	65.3125i	1.32086	−	2.28780i
$816$	6.87990	−	11.9163i	0.240845	−	0.417155i
$817$	−6.22762	−	10.7866i	−0.217877	−	0.377374i
$818$	13.2442			0.463073
$819$	0.634614	−	1.72008i	0.0221752	−	0.0601044i
$820$	48.1261			1.68063
$821$	9.34489	+	16.1858i	0.326139	+	0.564889i	0.981742	−	0.190217i	$-0.0609190\pi$
$821$	9.34489	+	16.1858i	0.326139	+	0.564889i	−0.655603	+	0.755105i	$0.727586\pi$
$822$	5.82020	−	10.0809i	0.203003	−	0.351611i
$823$	−1.72465	+	2.98717i	−0.0601174	+	0.104126i	−0.894518	−	0.447033i	$-0.852481\pi$
$823$	−1.72465	+	2.98717i	−0.0601174	+	0.104126i	0.834400	+	0.551159i	$0.185814\pi$
$824$	11.9192	+	20.6446i	0.415225	+	0.719190i
$825$	32.2691			1.12347
$826$	6.73076	+	8.09323i	0.234193	+	0.281599i
$827$	55.4418			1.92790			0.963950	−	0.266085i	$-0.0857301\pi$
$827$	55.4418			1.92790			0.963950	+	0.266085i	$0.0857301\pi$
$828$	−0.823862	−	1.42697i	−0.0286312	−	0.0495907i
$829$	−18.3829	+	31.8402i	−0.638465	+	1.10585i	0.347304	+	0.937752i	$0.387097\pi$
$829$	−18.3829	+	31.8402i	−0.638465	+	1.10585i	−0.985770	+	0.168102i	$0.946236\pi$
$830$	9.14124	−	15.8331i	0.317297	−	0.549575i
$831$	−7.32466	−	12.6867i	−0.254090	−	0.440096i
$832$	0.514625			0.0178414
$833$	−36.4290	−	31.1162i	−1.26219	−	1.07811i
$834$	−7.03052			−0.243447
$835$	18.9652	+	32.8487i	0.656318	+	1.13678i
$836$	15.7278	−	27.2413i	0.543956	−	0.942160i
$837$	−0.269666	+	0.467076i	−0.00932104	+	0.0161445i
$838$	−1.77975	−	3.08262i	−0.0614805	−	0.106487i
$839$	−25.3306			−0.874508			−0.437254	−	0.899338i	$-0.644049\pi$
$839$	−25.3306			−0.874508			−0.437254	+	0.899338i	$0.644049\pi$
$840$	−11.5419	−	13.8782i	−0.398233	−	0.478844i
$841$	−20.3200			−0.700688
$842$	3.69387	+	6.39798i	0.127299	+	0.220489i
$843$	8.51902	−	14.7554i	0.293411	−	0.508202i
$844$	−19.0134	+	32.9322i	−0.654469	+	1.13357i
$845$	−19.7262	−	34.1668i	−0.678603	−	1.17537i
$846$	−6.21272			−0.213598
$847$	−29.1603	+	79.0369i	−1.00196	+	2.71574i
$848$	25.2811			0.868156
$849$	−8.95641	−	15.5130i	−0.307383	−	0.532403i
$850$	10.0135	−	17.3439i	0.343461	−	0.594892i
$851$	−1.44806	+	2.50812i	−0.0496390	+	0.0859772i
$852$	0.483786	+	0.837942i	0.0165742	+	0.0287074i
$853$	−51.3694			−1.75885			−0.879427	−	0.476034i	$-0.842074\pi$
$853$	−51.3694			−1.75885			−0.879427	+	0.476034i	$0.842074\pi$
$854$	−8.20539	+	1.40976i	−0.280783	+	0.0482408i
$855$	9.19088			0.314321
$856$	9.28266	+	16.0780i	0.317275	+	0.549536i
$857$	−4.77766	+	8.27515i	−0.163202	+	0.282674i	−0.936015	−	0.351960i	$-0.885515\pi$
$857$	−4.77766	+	8.27515i	−0.163202	+	0.282674i	0.772814	+	0.634633i	$0.218849\pi$
$858$	−1.34603	+	2.33140i	−0.0459528	+	0.0795925i
$859$	1.81712	+	3.14735i	0.0619994	+	0.107386i	0.895359	−	0.445345i	$-0.146919\pi$
$859$	1.81712	+	3.14735i	0.0619994	+	0.107386i	−0.833360	+	0.552731i	$0.813586\pi$
$860$	−22.1734			−0.756108
$861$	−24.1686	+	4.15237i	−0.823663	+	0.141512i
$862$	−3.19909			−0.108961
$863$	−4.28894	−	7.42866i	−0.145997	−	0.252875i	0.783747	−	0.621080i	$-0.213306\pi$
$863$	−4.28894	−	7.42866i	−0.145997	−	0.252875i	−0.929745	+	0.368205i	$0.879972\pi$
$864$	−2.76166	+	4.78333i	−0.0939534	+	0.162732i
$865$	−26.1610	+	45.3122i	−0.889501	+	1.54066i
$866$	−9.69643	−	16.7947i	−0.329498	−	0.570707i
$867$	−29.8427			−1.01351
$868$	−0.813841	+	2.20586i	−0.0276236	+	0.0748718i
$869$	87.6225			2.97239
$870$	2.75517	+	4.77210i	0.0934092	+	0.161789i
$871$	−0.948075	+	1.64211i	−0.0321243	+	0.0556409i
$872$	−12.2132	+	21.1539i	−0.413591	+	0.716361i
$873$	4.07085	+	7.05092i	0.137777	+	0.238637i
$874$	−1.73110			−0.0585553
$875$	−0.372711	−	0.448157i	−0.0125999	−	0.0151505i
$876$	17.3449			0.586031
$877$	−22.8156	−	39.5177i	−0.770427	−	1.33442i	−0.937329	−	0.348445i	$-0.886710\pi$
$877$	−22.8156	−	39.5177i	−0.770427	−	1.33442i	0.166902	−	0.985973i	$-0.446623\pi$
$878$	0.00855621	−	0.0148198i	0.000288758	−	0.000500144i
$879$	−9.38493	+	16.2552i	−0.316546	+	0.548273i
$880$	−20.7334	−	35.9113i	−0.698922	−	1.21057i
$881$	−17.3176			−0.583446			−0.291723	−	0.956503i	$-0.594229\pi$
$881$	−17.3176			−0.583446			−0.291723	+	0.956503i	$0.594229\pi$
$882$	3.15914	+	2.69840i	0.106374	+	0.0908599i
$883$	14.3872			0.484166			0.242083	−	0.970256i	$-0.422169\pi$
$883$	14.3872			0.484166			0.242083	+	0.970256i	$0.422169\pi$
$884$	−3.90739	−	6.76780i	−0.131420	−	0.227626i
$885$	−10.5617	+	18.2934i	−0.355027	+	0.614924i
$886$	5.02503	−	8.70361i	0.168819	−	0.292403i
$887$	−1.08599	−	1.88099i	−0.0364639	−	0.0631573i	0.847218	−	0.531246i	$-0.178276\pi$
$887$	−1.08599	−	1.88099i	−0.0364639	−	0.0631573i	−0.883681	+	0.468089i	$0.844943\pi$
$888$	6.27020			0.210414
$889$	21.8806	+	26.3098i	0.733853	+	0.882403i
$890$	5.47893			0.183654
$891$	3.27267	+	5.66843i	0.109639	+	0.189900i
$892$	3.53085	−	6.11561i	0.118222	−	0.204766i
$893$	15.2648	−	26.4394i	0.510817	−	0.884760i
$894$	1.53538	+	2.65936i	0.0513508	+	0.0889422i
$895$	−10.2268			−0.341846
$896$	−10.5201	+	28.5140i	−0.351452	+	0.952587i
$897$	−0.692965			−0.0231374
$898$	6.18032	+	10.7046i	0.206240	+	0.357218i
$899$	0.794489	−	1.37610i	0.0264977	−	0.0458954i
$900$	4.06171	−	7.03509i	0.135390	−	0.234503i
$901$	−43.0323	−	74.5342i	−1.43361	−	2.48309i
$902$	36.0075			1.19892
$903$	11.1354	−	1.91315i	0.370561	−	0.0636656i
$904$	6.80175			0.226223
$905$	22.6567	+	39.2425i	0.753134	+	1.30447i
$906$	1.49870	−	2.59582i	0.0497910	−	0.0862405i
$907$	6.43433	−	11.1446i	0.213648	−	0.370050i	−0.739205	−	0.673480i	$-0.764799\pi$
$907$	6.43433	−	11.1446i	0.213648	−	0.370050i	0.952854	+	0.303430i	$0.0981320\pi$
$908$	9.00759	+	15.6016i	0.298927	+	0.517757i
$909$	−0.133249			−0.00441959
$910$	−3.37957	+	0.580639i	−0.112032	+	0.0192480i
$911$	−4.61820			−0.153008			−0.0765039	−	0.997069i	$-0.524376\pi$
$911$	−4.61820			−0.153008			−0.0765039	+	0.997069i	$0.524376\pi$
$912$	−2.93185	−	5.07812i	−0.0970833	−	0.168153i
$913$	−31.9904	+	55.4089i	−1.05873	+	1.83377i
$914$	−4.25896	+	7.37673i	−0.140874	+	0.244001i
$915$	−8.35357	−	14.4688i	−0.276161	−	0.478324i
$916$	−9.19019			−0.303652
$917$	−5.62909	+	15.2573i	−0.185889	+	0.503839i
$918$	4.06221			0.134073
$919$	0.197692	+	0.342412i	0.00652124	+	0.0112951i	0.869268	−	0.494342i	$-0.164591\pi$
$919$	0.197692	+	0.342412i	0.00652124	+	0.0112951i	−0.862746	+	0.505637i	$0.831258\pi$
$920$	−3.41122	+	5.90841i	−0.112465	+	0.194795i
$921$	−0.711865	+	1.23299i	−0.0234568	+	0.0406283i
$922$	−1.05299	−	1.82382i	−0.0346782	−	0.0600644i
$923$	0.406921			0.0133940
$924$	18.2454	+	21.9387i	0.600229	+	0.721730i
$925$	−14.2782			−0.469463
$926$	3.62845	+	6.28465i	0.119238	+	0.206527i
$927$	5.50533	−	9.53551i	0.180819	−	0.313187i
$928$	8.13637	−	14.0926i	0.267089	−	0.462612i
$929$	18.3243	+	31.7387i	0.601202	+	1.04131i	0.992639	+	0.121107i	$0.0386445\pi$
$929$	18.3243	+	31.7387i	0.601202	+	1.04131i	−0.391438	+	0.920205i	$0.628022\pi$
$930$	1.00873			0.0330776
$931$	−19.2456	+	6.81427i	−0.630750	+	0.223329i
$932$	36.6958			1.20201
$933$	−2.21236	−	3.83191i	−0.0724293	−	0.125451i
$934$	−8.48330	+	14.6935i	−0.277582	+	0.480786i
$935$	−70.5829	+	122.253i	−2.30831	+	3.99811i
$936$	0.750145	+	1.29929i	0.0245192	+	0.0424686i
$937$	−37.1650			−1.21413			−0.607063	−	0.794654i	$-0.707652\pi$
$937$	−37.1650			−1.21413			−0.607063	+	0.794654i	$0.707652\pi$
$938$	−2.74751	−	3.30367i	−0.0897094	−	0.107869i
$939$	−21.6865			−0.707714
$940$	−27.1751	−	47.0687i	−0.886354	−	1.53521i
$941$	−10.6874	+	18.5111i	−0.348398	+	0.603443i	−0.985965	−	0.166952i	$-0.946608\pi$
$941$	−10.6874	+	18.5111i	−0.348398	+	0.603443i	0.637567	+	0.770395i	$0.279941\pi$
$942$	2.86322	−	4.95925i	0.0932888	−	0.161581i
$943$	4.63435	+	8.02694i	0.150915	+	0.261393i
$944$	13.4765			0.438623
$945$	−2.88586	+	7.82192i	−0.0938769	+	0.254447i
$946$	−16.5900			−0.539386
$947$	−29.0241	−	50.2713i	−0.943158	−	1.63360i	−0.759398	−	0.650626i	$-0.774506\pi$
$947$	−29.0241	−	50.2713i	−0.943158	−	1.63360i	−0.183760	−	0.982971i	$-0.558827\pi$
$948$	11.0290	−	19.1029i	0.358207	−	0.620432i
$949$	3.64728	−	6.31728i	0.118396	−	0.205068i
$950$	−4.26724	−	7.39107i	−0.138447	−	0.239798i
$951$	11.6270			0.377031
$952$	38.6381	−	6.63836i	1.25227	−	0.215150i
$953$	0.853059			0.0276333			0.0138166	−	0.999905i	$-0.495602\pi$
$953$	0.853059			0.0276333			0.0138166	+	0.999905i	$0.495602\pi$
$954$	3.73178	+	6.46363i	0.120821	+	0.209268i
$955$	−15.5813	+	26.9876i	−0.504200	+	0.873299i
$956$	11.0316	−	19.1073i	0.356787	−	0.617974i
$957$	−9.64191	−	16.7003i	−0.311679	−	0.539844i
$958$	−17.9656			−0.580442
$959$	−51.1398	+	8.78624i	−1.65139	+	0.283723i
$960$	−2.34022			−0.0755302
$961$	15.3546	+	26.5949i	0.495308	+	0.857899i
$962$	0.595581	−	1.03158i	0.0192023	−	0.0332594i
$963$	4.28755	−	7.42625i	0.138164	−	0.239308i
$964$	−2.70758	−	4.68966i	−0.0872052	−	0.151044i
$965$	11.3144			0.364224
$966$	0.543550	−	1.47326i	0.0174884	−	0.0474013i
$967$	38.6397			1.24257			0.621284	−	0.783585i	$-0.286611\pi$
$967$	38.6397			1.24257			0.621284	+	0.783585i	$0.286611\pi$
$968$	−34.4688	−	59.7018i	−1.10787	−	1.91889i
$969$	−9.98094	+	17.2875i	−0.320634	+	0.555354i
$970$	7.61383	−	13.1875i	0.244465	−	0.423426i
$971$	20.5682	+	35.6252i	0.660066	+	1.14327i	0.980598	+	0.196030i	$0.0628050\pi$
$971$	20.5682	+	35.6252i	0.660066	+	1.14327i	−0.320532	+	0.947238i	$0.603862\pi$
$972$	1.64772			0.0528508
$973$	20.0393	+	24.0957i	0.642430	+	0.772473i
$974$	−17.1748			−0.550318
$975$	−1.70819	−	2.95867i	−0.0547058	−	0.0947533i
$976$	−5.32951	+	9.23098i	−0.170593	+	0.295477i
$977$	−3.79942	+	6.58079i	−0.121554	+	0.210538i	−0.920381	−	0.391023i	$-0.872121\pi$
$977$	−3.79942	+	6.58079i	−0.121554	+	0.210538i	0.798827	+	0.601561i	$0.205454\pi$
$978$	−7.10232	−	12.3016i	−0.227107	−	0.393361i
$979$	−19.1739			−0.612800
$980$	−6.62517	+	35.7373i	−0.211633	+	1.14159i
$981$	11.2823			0.360215
$982$	−3.53699	−	6.12625i	−0.112870	−	0.195497i
$983$	−19.5315	+	33.8296i	−0.622959	+	1.07900i	0.365973	+	0.930626i	$0.380736\pi$
$983$	−19.5315	+	33.8296i	−0.622959	+	1.07900i	−0.988932	+	0.148371i	$0.952597\pi$
$984$	10.0335	−	17.3785i	0.319857	−	0.554008i
$985$	12.9401	+	22.4129i	0.412306	+	0.714134i
$986$	−11.9680			−0.381140
$987$	17.7083	+	21.2929i	0.563661	+	0.677760i
$988$	−3.33025			−0.105949
$989$	−2.13522	−	3.69830i	−0.0678959	−	0.117599i
$990$	6.12097	−	10.6018i	0.194537	−	0.336948i
$991$	−0.903144	+	1.56429i	−0.0286893	+	0.0496914i	−0.880014	−	0.474949i	$-0.842467\pi$
$991$	−0.903144	+	1.56429i	−0.0286893	+	0.0496914i	0.851324	+	0.524640i	$0.175800\pi$
$992$	−1.48945	−	2.57981i	−0.0472901	−	0.0819089i
$993$	−7.89484			−0.250535
$994$	−0.319182	+	0.865122i	−0.0101238	+	0.0274400i
$995$	−7.07467			−0.224282
$996$	8.05326	+	13.9486i	0.255177	+	0.441980i
$997$	19.7503	−	34.2086i	0.625499	−	1.08340i	−0.362945	−	0.931811i	$-0.618229\pi$
$997$	19.7503	−	34.2086i	0.625499	−	1.08340i	0.988444	−	0.151586i	$-0.0484381\pi$
$998$	3.07857	−	5.33224i	0.0974504	−	0.168789i
$999$	−1.44806	−	2.50812i	−0.0458147	−	0.0793534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.f.277.4	✓	12
7.2	even	3	inner	483.2.i.f.415.4	yes	12
7.3	odd	6		3381.2.a.bd.1.3		6
7.4	even	3		3381.2.a.bc.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.4	✓	12	1.1	even	1	trivial
483.2.i.f.415.4	yes	12	7.2	even	3	inner
3381.2.a.bc.1.3		6	7.4	even	3
3381.2.a.bd.1.3		6	7.3	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.296764 + 0.514011i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.823862 - 1.42697i) q^{4} +(1.57560 + 2.72902i) q^{5} +0.593528 q^{6} +(-1.69175 - 2.03420i) q^{7} +2.16503 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.296764 + 0.514011i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.823862 - 1.42697i) q^{4} +(1.57560 + 2.72902i) q^{5} +0.593528 q^{6} +(-1.69175 - 2.03420i) q^{7} +2.16503 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.935165 + 1.61975i) q^{10} +(3.27267 - 5.66843i) q^{11} +(-0.823862 - 1.42697i) q^{12} -0.692965 q^{13} +(0.543550 - 1.47326i) q^{14} +3.15120 q^{15} +(-1.00522 - 1.74109i) q^{16} +(-3.42208 + 5.92722i) q^{17} +(0.296764 - 0.514011i) q^{18} +(1.45831 + 2.52587i) q^{19} +5.19231 q^{20} +(-2.60755 + 0.447998i) q^{21} +3.88485 q^{22} +(0.500000 + 0.866025i) q^{23} +(1.08251 - 1.87497i) q^{24} +(-2.46504 + 4.26958i) q^{25} +(-0.205647 - 0.356192i) q^{26} -1.00000 q^{27} +(-4.29652 + 0.738178i) q^{28} +2.94619 q^{29} +(0.935165 + 1.61975i) q^{30} +(0.269666 - 0.467076i) q^{31} +(2.76166 - 4.78333i) q^{32} +(-3.27267 - 5.66843i) q^{33} -4.06221 q^{34} +(2.88586 - 7.82192i) q^{35} -1.64772 q^{36} +(1.44806 + 2.50812i) q^{37} +(-0.865550 + 1.49918i) q^{38} +(-0.346483 + 0.600126i) q^{39} +(3.41122 + 5.90841i) q^{40} +9.26871 q^{41} +(-1.00410 - 1.20736i) q^{42} -4.27043 q^{43} +(-5.39246 - 9.34001i) q^{44} +(1.57560 - 2.72902i) q^{45} +(-0.296764 + 0.514011i) q^{46} +(-5.23372 - 9.06507i) q^{47} -2.01044 q^{48} +(-1.27596 + 6.88273i) q^{49} -2.92615 q^{50} +(3.42208 + 5.92722i) q^{51} +(-0.570908 + 0.988841i) q^{52} +(-6.28744 + 10.8902i) q^{53} +(-0.296764 - 0.514011i) q^{54} +20.6257 q^{55} +(-3.66269 - 4.40410i) q^{56} +2.91662 q^{57} +(0.874324 + 1.51437i) q^{58} +(-3.35163 + 5.80519i) q^{59} +(2.59616 - 4.49668i) q^{60} +(-2.65091 - 4.59152i) q^{61} +0.320109 q^{62} +(-0.915795 + 2.48220i) q^{63} -0.742642 q^{64} +(-1.09184 - 1.89112i) q^{65} +(1.94242 - 3.36437i) q^{66} +(1.36814 - 2.36969i) q^{67} +(5.63865 + 9.76643i) q^{68} +1.00000 q^{69} +(4.87697 - 0.837905i) q^{70} -0.587217 q^{71} +(-1.08251 - 1.87497i) q^{72} +(-5.26330 + 9.11630i) q^{73} +(-0.859467 + 1.48864i) q^{74} +(2.46504 + 4.26958i) q^{75} +4.80579 q^{76} +(-17.0673 + 2.93230i) q^{77} -0.411295 q^{78} +(6.69351 + 11.5935i) q^{79} +(3.16766 - 5.48654i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.75062 + 4.76422i) q^{82} -9.77501 q^{83} +(-1.50898 + 4.08998i) q^{84} -21.5674 q^{85} +(-1.26731 - 2.19505i) q^{86} +(1.47310 - 2.55148i) q^{87} +(7.08542 - 12.2723i) q^{88} +(-1.46470 - 2.53693i) q^{89} +1.87033 q^{90} +(1.17232 + 1.40963i) q^{91} +1.64772 q^{92} +(-0.269666 - 0.467076i) q^{93} +(3.10636 - 5.38037i) q^{94} +(-4.59544 + 7.95953i) q^{95} +(-2.76166 - 4.78333i) q^{96} -8.14170 q^{97} +(-3.91645 + 1.38669i) q^{98} -6.54534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9	\( 12 q + q^{2} + 6 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 2 q^{7} - 6 q^{8} - 6 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} - q^{14} - 6 q^{15} + 7 q^{16} - 15 q^{17} + q^{18} + q^{19} + 34 q^{20} - 4 q^{21} - 12 q^{22} + 6 q^{23} - 3 q^{24} - 9 q^{25} + 15 q^{26} - 12 q^{27} - 2 q^{28} - 12 q^{29} - 3 q^{30} + 11 q^{31} - 3 q^{32} - 14 q^{33} + 30 q^{34} - q^{35} + 6 q^{36} + 5 q^{37} - 14 q^{38} + 17 q^{40} + 36 q^{41} - 17 q^{42} - 74 q^{43} + 10 q^{44} - 3 q^{45} - q^{46} - 3 q^{47} + 14 q^{48} - 6 q^{49} - 60 q^{50} + 15 q^{51} + 7 q^{52} + 15 q^{53} - q^{54} - 4 q^{55} - 21 q^{56} + 2 q^{57} - 4 q^{58} + 2 q^{59} + 17 q^{60} + 12 q^{61} + 72 q^{62} - 2 q^{63} - 46 q^{64} + 17 q^{65} - 6 q^{66} + 10 q^{67} + q^{68} + 12 q^{69} - 56 q^{70} - 42 q^{71} + 3 q^{72} + 8 q^{73} + 16 q^{74} + 9 q^{75} + 36 q^{76} - 40 q^{77} + 30 q^{78} + 17 q^{79} - 3 q^{80} - 6 q^{81} + 48 q^{82} + 24 q^{83} - 25 q^{84} - 26 q^{85} - 22 q^{86} - 6 q^{87} + 2 q^{88} - 18 q^{89} - 6 q^{90} + 22 q^{91} - 6 q^{92} - 11 q^{93} - 3 q^{94} + 16 q^{95} + 3 q^{96} - 4 q^{97} - 62 q^{98} - 28 q^{99}+O(q^{100}) \) 12 * q + q^2 + 6 * q^3 - 3 * q^4 - 3 * q^5 + 2 * q^6 - 2 * q^7 - 6 * q^8 - 6 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 - q^14 - 6 * q^15 + 7 * q^16 - 15 * q^17 + q^18 + q^19 + 34 * q^20 - 4 * q^21 - 12 * q^22 + 6 * q^23 - 3 * q^24 - 9 * q^25 + 15 * q^26 - 12 * q^27 - 2 * q^28 - 12 * q^29 - 3 * q^30 + 11 * q^31 - 3 * q^32 - 14 * q^33 + 30 * q^34 - q^35 + 6 * q^36 + 5 * q^37 - 14 * q^38 + 17 * q^40 + 36 * q^41 - 17 * q^42 - 74 * q^43 + 10 * q^44 - 3 * q^45 - q^46 - 3 * q^47 + 14 * q^48 - 6 * q^49 - 60 * q^50 + 15 * q^51 + 7 * q^52 + 15 * q^53 - q^54 - 4 * q^55 - 21 * q^56 + 2 * q^57 - 4 * q^58 + 2 * q^59 + 17 * q^60 + 12 * q^61 + 72 * q^62 - 2 * q^63 - 46 * q^64 + 17 * q^65 - 6 * q^66 + 10 * q^67 + q^68 + 12 * q^69 - 56 * q^70 - 42 * q^71 + 3 * q^72 + 8 * q^73 + 16 * q^74 + 9 * q^75 + 36 * q^76 - 40 * q^77 + 30 * q^78 + 17 * q^79 - 3 * q^80 - 6 * q^81 + 48 * q^82 + 24 * q^83 - 25 * q^84 - 26 * q^85 - 22 * q^86 - 6 * q^87 + 2 * q^88 - 18 * q^89 - 6 * q^90 + 22 * q^91 - 6 * q^92 - 11 * q^93 - 3 * q^94 + 16 * q^95 + 3 * q^96 - 4 * q^97 - 62 * q^98 - 28 * q^99

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