LMFDB - Embedded newform 845.2.m.j.316.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(316,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("845.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.18
Character	$\chi$	$=$	845.316
Dual form			845.2.m.j.361.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.41570 + 1.39471i) q^{2} +(0.907309 - 1.57151i) q^{3} +(2.89042 + 5.00635i) q^{4} -1.00000i q^{5} +(4.38358 - 2.53086i) q^{6} +(0.233481 - 0.134800i) q^{7} +10.5463i q^{8} +(-0.146421 - 0.253609i) q^{9} +O(q^{10})$	\(q+(2.41570 + 1.39471i) q^{2} +(0.907309 - 1.57151i) q^{3} +(2.89042 + 5.00635i) q^{4} -1.00000i q^{5} +(4.38358 - 2.53086i) q^{6} +(0.233481 - 0.134800i) q^{7} +10.5463i q^{8} +(-0.146421 - 0.253609i) q^{9} +(1.39471 - 2.41570i) q^{10} +(-1.56820 - 0.905401i) q^{11} +10.4900 q^{12} +0.752028 q^{14} +(-1.57151 - 0.907309i) q^{15} +(-8.92820 + 15.4641i) q^{16} +(-0.368683 - 0.638578i) q^{17} -0.816858i q^{18} +(1.88763 - 1.08983i) q^{19} +(5.00635 - 2.89042i) q^{20} -0.489222i q^{21} +(-2.52554 - 4.37436i) q^{22} +(-1.37558 + 2.38258i) q^{23} +(16.5736 + 9.56878i) q^{24} -1.00000 q^{25} +4.91246 q^{27} +(1.34972 + 0.779259i) q^{28} +(3.60627 - 6.24624i) q^{29} +(-2.53086 - 4.38358i) q^{30} -6.19428i q^{31} +(-24.8690 + 14.3581i) q^{32} +(-2.84569 + 1.64296i) q^{33} -2.05682i q^{34} +(-0.134800 - 0.233481i) q^{35} +(0.846436 - 1.46607i) q^{36} +(-6.63727 - 3.83203i) q^{37} +6.07995 q^{38} +10.5463 q^{40} +(-7.25640 - 4.18948i) q^{41} +(0.682322 - 1.18182i) q^{42} +(-0.584581 - 1.01252i) q^{43} -10.4679i q^{44} +(-0.253609 + 0.146421i) q^{45} +(-6.64600 + 3.83707i) q^{46} -0.121132i q^{47} +(16.2013 + 28.0615i) q^{48} +(-3.46366 + 5.99923i) q^{49} +(-2.41570 - 1.39471i) q^{50} -1.33804 q^{51} +3.85022 q^{53} +(11.8671 + 6.85145i) q^{54} +(-0.905401 + 1.56820i) q^{55} +(1.42165 + 2.46237i) q^{56} -3.95524i q^{57} +(17.4233 - 10.0594i) q^{58} +(-9.20651 + 5.31538i) q^{59} -10.4900i q^{60} +(2.12190 + 3.67524i) q^{61} +(8.63921 - 14.9635i) q^{62} +(-0.0683730 - 0.0394752i) q^{63} -44.3888 q^{64} -9.16578 q^{66} +(-8.27136 - 4.77547i) q^{67} +(2.13130 - 3.69151i) q^{68} +(2.49616 + 4.32347i) q^{69} -0.752028i q^{70} +(-7.03296 + 4.06048i) q^{71} +(2.67464 - 1.54420i) q^{72} -0.692889i q^{73} +(-10.6891 - 18.5141i) q^{74} +(-0.907309 + 1.57151i) q^{75} +(10.9121 + 6.30010i) q^{76} -0.488193 q^{77} +6.65811 q^{79} +(15.4641 + 8.92820i) q^{80} +(4.89638 - 8.48079i) q^{81} +(-11.6862 - 20.2411i) q^{82} +9.19337i q^{83} +(2.44922 - 1.41406i) q^{84} +(-0.638578 + 0.368683i) q^{85} -3.26128i q^{86} +(-6.54400 - 11.3345i) q^{87} +(9.54865 - 16.5388i) q^{88} +(5.69120 + 3.28581i) q^{89} -0.816858 q^{90} -15.9040 q^{92} +(-9.73434 - 5.62013i) q^{93} +(0.168944 - 0.292620i) q^{94} +(-1.08983 - 1.88763i) q^{95} +52.1091i q^{96} +(15.1037 - 8.72012i) q^{97} +(-16.7343 + 9.66158i) q^{98} +0.530279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 14 q^{3} + 34 q^{4} - 32 q^{9}+O(q^{10}) $ 36 * q - 14 * q^3 + 34 * q^4 - 32 * q^9	$ 36 q - 14 q^{3} + 34 q^{4} - 32 q^{9} + 6 q^{10} - 48 q^{12} - 8 q^{14} - 74 q^{16} - 2 q^{17} - 24 q^{22} + 28 q^{23} - 36 q^{25} + 88 q^{27} - 24 q^{29} - 4 q^{30} - 14 q^{35} + 6 q^{36} + 188 q^{38} + 48 q^{40} + 22 q^{42} + 78 q^{43} + 6 q^{48} + 32 q^{49} - 172 q^{51} - 32 q^{53} + 18 q^{55} - 58 q^{56} + 6 q^{61} - 20 q^{62} - 136 q^{64} - 196 q^{66} + 40 q^{68} - 26 q^{69} + 30 q^{74} + 14 q^{75} + 16 q^{77} + 156 q^{79} - 58 q^{81} - 8 q^{82} - 32 q^{87} + 84 q^{88} + 40 q^{90} - 108 q^{92} - 32 q^{94} - 8 q^{95}+O(q^{100}) $ 36 * q - 14 * q^3 + 34 * q^4 - 32 * q^9 + 6 * q^10 - 48 * q^12 - 8 * q^14 - 74 * q^16 - 2 * q^17 - 24 * q^22 + 28 * q^23 - 36 * q^25 + 88 * q^27 - 24 * q^29 - 4 * q^30 - 14 * q^35 + 6 * q^36 + 188 * q^38 + 48 * q^40 + 22 * q^42 + 78 * q^43 + 6 * q^48 + 32 * q^49 - 172 * q^51 - 32 * q^53 + 18 * q^55 - 58 * q^56 + 6 * q^61 - 20 * q^62 - 136 * q^64 - 196 * q^66 + 40 * q^68 - 26 * q^69 + 30 * q^74 + 14 * q^75 + 16 * q^77 + 156 * q^79 - 58 * q^81 - 8 * q^82 - 32 * q^87 + 84 * q^88 + 40 * q^90 - 108 * q^92 - 32 * q^94 - 8 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	2.41570	+	1.39471i	1.70816	+	0.986207i	0.936838	+	0.349763i	$0.113738\pi$
$2$	2.41570	+	1.39471i	1.70816	+	0.986207i	0.771323	+	0.636444i	$0.219595\pi$
$3$	0.907309	−	1.57151i	0.523835	−	0.907309i	−0.475780	−	0.879565i	$-0.657834\pi$
$3$	0.907309	−	1.57151i	0.523835	−	0.907309i	0.999615	−	0.0277450i	$-0.00883264\pi$
$4$	2.89042	+	5.00635i	1.44521	+	2.50318i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	4.38358	−	2.53086i	1.78959	−	1.03322i
$7$	0.233481	−	0.134800i	0.0882475	−	0.0509497i	−0.455227	−	0.890375i	$-0.650442\pi$
$7$	0.233481	−	0.134800i	0.0882475	−	0.0509497i	0.543474	+	0.839426i	$0.317109\pi$
$8$			10.5463i			3.72869i
$9$	−0.146421	−	0.253609i	−0.0488070	−	0.0845362i
$10$	1.39471	−	2.41570i	0.441045	−	0.763913i
$11$	−1.56820	−	0.905401i	−0.472830	−	0.272989i	0.244594	−	0.969626i	$-0.421345\pi$
$11$	−1.56820	−	0.905401i	−0.472830	−	0.272989i	−0.717424	+	0.696637i	$0.754679\pi$
$12$	10.4900			3.02821
$13$		0			0
$13$		0			0
$14$	0.752028			0.200988
$15$	−1.57151	−	0.907309i	−0.405761	−	0.234266i
$16$	−8.92820	+	15.4641i	−2.23205	+	3.86603i
$17$	−0.368683	−	0.638578i	−0.0894188	−	0.154878i	0.817847	−	0.575436i	$-0.195168\pi$
$17$	−0.368683	−	0.638578i	−0.0894188	−	0.154878i	−0.907266	+	0.420558i	$0.861834\pi$
$18$		−	0.816858i		−	0.192535i
$19$	1.88763	−	1.08983i	0.433053	−	0.250023i	−0.267594	−	0.963532i	$-0.586228\pi$
$19$	1.88763	−	1.08983i	0.433053	−	0.250023i	0.700646	+	0.713509i	$0.252895\pi$
$20$	5.00635	−	2.89042i	1.11945	−	0.646317i
$21$		−	0.489222i		−	0.106757i
$22$	−2.52554	−	4.37436i	−0.538447	−	0.932617i
$23$	−1.37558	+	2.38258i	−0.286829	+	0.496802i	−0.973051	−	0.230590i	$-0.925934\pi$
$23$	−1.37558	+	2.38258i	−0.286829	+	0.496802i	0.686222	+	0.727392i	$0.259268\pi$
$24$	16.5736	+	9.56878i	3.38308	+	1.95322i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	4.91246			0.945403
$28$	1.34972	+	0.779259i	0.255072	+	0.147266i
$29$	3.60627	−	6.24624i	0.669667	−	1.15990i	−0.308331	−	0.951279i	$-0.599770\pi$
$29$	3.60627	−	6.24624i	0.669667	−	1.15990i	0.977997	−	0.208618i	$-0.0668964\pi$
$30$	−2.53086	−	4.38358i	−0.462070	−	0.800329i
$31$		−	6.19428i		−	1.11253i	−0.831007	−	0.556263i	$-0.812235\pi$
$31$		−	6.19428i		−	1.11253i	0.831007	−	0.556263i	$-0.187765\pi$
$32$	−24.8690	+	14.3581i	−4.39627	+	2.53819i
$33$	−2.84569	+	1.64296i	−0.495370	+	0.286002i
$34$		−	2.05682i		−	0.352742i
$35$	−0.134800	−	0.233481i	−0.0227854	−	0.0394655i
$36$	0.846436	−	1.46607i	0.141073	−	0.244345i
$37$	−6.63727	−	3.83203i	−1.09116	−	0.629982i	−0.157275	−	0.987555i	$-0.550271\pi$
$37$	−6.63727	−	3.83203i	−1.09116	−	0.629982i	−0.933885	+	0.357573i	$0.883604\pi$
$38$	6.07995			0.986299
$39$		0			0
$40$	10.5463			1.66752
$41$	−7.25640	−	4.18948i	−1.13326	−	0.654287i	−0.188507	−	0.982072i	$-0.560365\pi$
$41$	−7.25640	−	4.18948i	−1.13326	−	0.654287i	−0.944753	+	0.327785i	$0.893698\pi$
$42$	0.682322	−	1.18182i	0.105285	−	0.182358i
$43$	−0.584581	−	1.01252i	−0.0891478	−	0.154408i	0.818003	−	0.575213i	$-0.195081\pi$
$43$	−0.584581	−	1.01252i	−0.0891478	−	0.154408i	−0.907151	+	0.420805i	$0.861748\pi$
$44$		−	10.4679i		−	1.57810i
$45$	−0.253609	+	0.146421i	−0.0378058	+	0.0218272i
$46$	−6.64600	+	3.83707i	−0.979899	+	0.565745i
$47$		−	0.121132i		−	0.0176690i	−0.999961	−	0.00883449i	$-0.997188\pi$
$47$		−	0.121132i		−	0.0176690i	0.999961	−	0.00883449i	$-0.00281214\pi$
$48$	16.2013	+	28.0615i	2.33845	+	4.05032i
$49$	−3.46366	+	5.99923i	−0.494808	+	0.857033i
$50$	−2.41570	−	1.39471i	−0.341632	−	0.197241i
$51$	−1.33804			−0.187363
$52$		0			0
$53$	3.85022			0.528868			0.264434	−	0.964404i	$-0.414815\pi$
$53$	3.85022			0.528868			0.264434	+	0.964404i	$0.414815\pi$
$54$	11.8671	+	6.85145i	1.61490	+	0.932364i
$55$	−0.905401	+	1.56820i	−0.122084	+	0.211456i
$56$	1.42165	+	2.46237i	0.189976	+	0.329048i
$57$		−	3.95524i		−	0.523884i
$58$	17.4233	−	10.0594i	2.28780	−	1.32086i
$59$	−9.20651	+	5.31538i	−1.19859	+	0.692003i	−0.960240	−	0.279177i	$-0.909938\pi$
$59$	−9.20651	+	5.31538i	−1.19859	+	0.692003i	−0.238346	+	0.971180i	$0.576605\pi$
$60$		−	10.4900i		−	1.35426i
$61$	2.12190	+	3.67524i	0.271681	+	0.470566i	0.969293	−	0.245911i	$-0.0790869\pi$
$61$	2.12190	+	3.67524i	0.271681	+	0.470566i	−0.697611	+	0.716477i	$0.745754\pi$
$62$	8.63921	−	14.9635i	1.09718	−	1.90037i
$63$	−0.0683730	−	0.0394752i	−0.00861419	−	0.00497341i
$64$	−44.3888			−5.54860
$65$		0			0
$66$	−9.16578			−1.12823
$67$	−8.27136	−	4.77547i	−1.01051	−	0.583417i	−0.0991674	−	0.995071i	$-0.531618\pi$
$67$	−8.27136	−	4.77547i	−1.01051	−	0.583417i	−0.911340	+	0.411654i	$0.864951\pi$
$68$	2.13130	−	3.69151i	0.258458	−	0.447662i
$69$	2.49616	+	4.32347i	0.300502	+	0.520485i
$70$		−	0.752028i		−	0.0898845i
$71$	−7.03296	+	4.06048i	−0.834659	+	0.481891i	−0.855445	−	0.517893i	$-0.826716\pi$
$71$	−7.03296	+	4.06048i	−0.834659	+	0.481891i	0.0207860	+	0.999784i	$0.493383\pi$
$72$	2.67464	−	1.54420i	0.315209	−	0.181986i
$73$		−	0.692889i		−	0.0810966i	−0.999178	−	0.0405483i	$-0.987090\pi$
$73$		−	0.692889i		−	0.0810966i	0.999178	−	0.0405483i	$-0.0129105\pi$
$74$	−10.6891	−	18.5141i	−1.24259	−	2.15222i
$75$	−0.907309	+	1.57151i	−0.104767	+	0.181462i
$76$	10.9121	+	6.30010i	1.25170	+	0.722672i
$77$	−0.488193			−0.0556348
$78$		0			0
$79$	6.65811			0.749096			0.374548	−	0.927207i	$-0.377798\pi$
$79$	6.65811			0.749096			0.374548	+	0.927207i	$0.377798\pi$
$80$	15.4641	+	8.92820i	1.72894	+	0.998204i
$81$	4.89638	−	8.48079i	0.544043	−	0.942310i
$82$	−11.6862	−	20.2411i	−1.29053	−	2.23526i
$83$			9.19337i			1.00910i	0.863381	+	0.504552i	$0.168342\pi$
$83$			9.19337i			1.00910i	−0.863381	+	0.504552i	$0.831658\pi$
$84$	2.44922	−	1.41406i	0.267232	−	0.154286i
$85$	−0.638578	+	0.368683i	−0.0692635	+	0.0399893i
$86$		−	3.26128i		−	0.351673i
$87$	−6.54400	−	11.3345i	−0.701590	−	1.21519i
$88$	9.54865	−	16.5388i	1.01789	−	1.76304i
$89$	5.69120	+	3.28581i	0.603266	+	0.348296i	0.770325	−	0.637651i	$-0.220094\pi$
$89$	5.69120	+	3.28581i	0.603266	+	0.348296i	−0.167059	+	0.985947i	$0.553427\pi$
$90$	−0.816858			−0.0861044
$91$		0			0
$92$	−15.9040			−1.65811
$93$	−9.73434	−	5.62013i	−1.00940	−	0.582780i
$94$	0.168944	−	0.292620i	0.0174253	−	0.0301815i
$95$	−1.08983	−	1.88763i	−0.111814	−	0.193667i
$96$			52.1091i			5.31836i
$97$	15.1037	−	8.72012i	1.53355	−	0.885394i	0.534354	−	0.845261i	$-0.320555\pi$
$97$	15.1037	−	8.72012i	1.53355	−	0.885394i	0.999194	−	0.0401336i	$-0.0127784\pi$
$98$	−16.7343	+	9.66158i	−1.69042	+	0.975967i
$99$			0.530279i			0.0532950i
$100$	−2.89042	−	5.00635i	−0.289042	−	0.500635i
$101$	−5.90035	+	10.2197i	−0.587107	+	1.01690i	0.407502	+	0.913204i	$0.366400\pi$
$101$	−5.90035	+	10.2197i	−0.587107	+	1.01690i	−0.994609	+	0.103695i	$0.966933\pi$
$102$	−3.23230	−	1.86617i	−0.320046	−	0.184779i
$103$	8.03859			0.792066			0.396033	−	0.918236i	$-0.370387\pi$
$103$	8.03859			0.792066			0.396033	+	0.918236i	$0.370387\pi$
$104$		0			0
$105$	−0.489222			−0.0477432
$106$	9.30099	+	5.36993i	0.903392	+	0.521574i
$107$	−8.64884	+	14.9802i	−0.836115	+	1.44819i	0.0570036	+	0.998374i	$0.481845\pi$
$107$	−8.64884	+	14.9802i	−0.836115	+	1.44819i	−0.893119	+	0.449820i	$0.851488\pi$
$108$	14.1991	+	24.5935i	1.36631	+	2.36651i
$109$			15.1297i			1.44916i	0.689189	+	0.724581i	$0.257967\pi$
$109$			15.1297i			1.44916i	−0.689189	+	0.724581i	$0.742033\pi$
$110$	−4.37436	+	2.52554i	−0.417079	+	0.240801i
$111$	−12.0441	+	6.95368i	−1.14318	+	0.660014i
$112$			4.81410i			0.454889i
$113$	−6.23428	−	10.7981i	−0.586472	−	1.01580i	−0.994690	−	0.102915i	$-0.967183\pi$
$113$	−6.23428	−	10.7981i	−0.586472	−	1.01580i	0.408218	−	0.912884i	$-0.366150\pi$
$114$	5.51640	−	9.55468i	0.516658	−	0.894878i
$115$	2.38258	+	1.37558i	0.222177	+	0.128274i
$116$	41.6945			3.87123
$117$		0			0
$118$	−29.6536			−2.72984
$119$	−0.172161	−	0.0993971i	−0.0157820	−	0.00911172i
$120$	9.56878	−	16.5736i	0.873506	−	1.51296i
$121$	−3.86050	−	6.68658i	−0.350954	−	0.607871i
$122$			11.8377i			1.07174i
$123$	−13.1676	+	7.60232i	−1.18728	+	0.685478i
$124$	31.0107	−	17.9041i	2.78485	−	1.60783i
$125$			1.00000i			0.0894427i
$126$	−0.110113	−	0.190721i	−0.00980962	−	0.0169908i
$127$	5.94378	−	10.2949i	0.527425	−	0.913528i	−0.472064	−	0.881564i	$-0.656491\pi$
$127$	5.94378	−	10.2949i	0.527425	−	0.913528i	0.999489	−	0.0319632i	$-0.0101759\pi$
$128$	−57.4922	−	33.1932i	−5.08164	−	2.93389i
$129$	−2.12158			−0.186795
$130$		0			0
$131$	13.7794			1.20391			0.601955	−	0.798530i	$-0.294389\pi$
$131$	13.7794			1.20391			0.601955	+	0.798530i	$0.294389\pi$
$132$	−16.4504	−	9.49767i	−1.43183	−	0.826666i
$133$	0.293818	−	0.508907i	0.0254772	−	0.0441278i
$134$	−13.3208	−	23.0723i	−1.15074	−	1.99314i
$135$		−	4.91246i		−	0.422797i
$136$	6.73465	−	3.88825i	0.577491	−	0.333415i
$137$	12.2633	−	7.08021i	1.04772	−	0.604903i	0.125712	−	0.992067i	$-0.459878\pi$
$137$	12.2633	−	7.08021i	1.04772	−	0.604903i	0.922011	+	0.387163i	$0.126545\pi$
$138$			13.9256i			1.18543i
$139$	−2.26822	−	3.92868i	−0.192388	−	0.333226i	0.753653	−	0.657273i	$-0.228290\pi$
$139$	−2.26822	−	3.92868i	−0.192388	−	0.333226i	−0.946041	+	0.324046i	$0.894957\pi$
$140$	0.779259	−	1.34972i	0.0658594	−	0.114072i
$141$	−0.190360	−	0.109905i	−0.0160312	−	0.00925564i
$142$	−22.6527			−1.90098
$143$		0			0
$144$	5.22911			0.435759
$145$	−6.24624	−	3.60627i	−0.518722	−	0.299484i
$146$	0.966378	−	1.67382i	0.0799780	−	0.138526i
$147$	6.28522	+	10.8863i	0.518396	+	0.897888i
$148$		−	44.3047i		−	3.64182i
$149$	3.04772	−	1.75960i	0.249679	−	0.144152i	−0.369938	−	0.929056i	$-0.620621\pi$
$149$	3.04772	−	1.75960i	0.249679	−	0.144152i	0.619617	+	0.784904i	$0.287288\pi$
$150$	−4.38358	+	2.53086i	−0.357918	+	0.206644i
$151$		−	4.49258i		−	0.365601i	−0.983150	−	0.182801i	$-0.941484\pi$
$151$		−	4.49258i		−	0.365601i	0.983150	−	0.182801i	$-0.0585162\pi$
$152$	11.4937	+	19.9076i	0.932259	+	1.61472i
$153$	−0.107966	+	0.187002i	−0.00872852	+	0.0151182i
$154$	−1.17933	−	0.680887i	−0.0950331	−	0.0548674i
$155$	−6.19428			−0.497536
$156$		0			0
$157$	10.2430			0.817480			0.408740	−	0.912651i	$-0.365968\pi$
$157$	10.2430			0.817480			0.408740	+	0.912651i	$0.365968\pi$
$158$	16.0840	+	9.28612i	1.27958	+	0.738764i
$159$	3.49334	−	6.05064i	0.277040	−	0.479847i
$160$	14.3581	+	24.8690i	1.13511	+	1.96607i
$161$			0.741716i			0.0584554i
$162$	23.6564	−	13.6581i	1.85863	−	1.07308i
$163$	−1.46202	+	0.844097i	−0.114514	+	0.0661147i	−0.556163	−	0.831073i	$-0.687727\pi$
$163$	−1.46202	+	0.844097i	−0.114514	+	0.0661147i	0.441649	+	0.897188i	$0.354394\pi$
$164$		−	48.4374i		−	3.78233i
$165$	1.64296	+	2.84569i	0.127904	+	0.221536i
$166$	−12.8221	+	22.2085i	−0.995185	+	1.72371i
$167$	3.72277	+	2.14934i	0.288077	+	0.166321i	0.637074	−	0.770802i	$-0.280144\pi$
$167$	3.72277	+	2.14934i	0.288077	+	0.166321i	−0.348997	+	0.937124i	$0.613478\pi$
$168$	5.15950			0.398064
$169$		0			0
$170$	−2.05682			−0.157751
$171$	−0.552778	−	0.319147i	−0.0422720	−	0.0244058i
$172$	3.37937	−	5.85324i	0.257674	−	0.446305i
$173$	−5.59562	−	9.69190i	−0.425427	−	0.736862i	0.571033	−	0.820927i	$-0.306543\pi$
$173$	−5.59562	−	9.69190i	−0.425427	−	0.736862i	−0.996460	+	0.0840654i	$0.973210\pi$
$174$		−	36.5079i		−	2.76765i
$175$	−0.233481	+	0.134800i	−0.0176495	+	0.0101899i
$176$	28.0024	−	16.1672i	2.11076	−	1.21865i
$177$			19.2908i			1.44998i
$178$	9.16550	+	15.8751i	0.686983	+	1.18989i
$179$	3.84100	−	6.65282i	0.287090	−	0.497255i	−0.686024	−	0.727579i	$-0.740645\pi$
$179$	3.84100	−	6.65282i	0.287090	−	0.497255i	0.973114	+	0.230324i	$0.0739787\pi$
$180$	−1.46607	−	0.846436i	−0.109274	−	0.0630896i
$181$	−6.44731			−0.479225			−0.239612	−	0.970869i	$-0.577020\pi$
$181$	−6.44731			−0.479225			−0.239612	+	0.970869i	$0.577020\pi$
$182$		0			0
$183$	7.70088			0.569266
$184$	−25.1274	−	14.5073i	−1.85242	−	1.06950i
$185$	−3.83203	+	6.63727i	−0.281736	+	0.487982i
$186$	−15.6769	−	27.1531i	−1.14948	−	1.99096i
$187$			1.33522i			0.0976412i
$188$	0.606432	−	0.350124i	0.0442286	−	0.0255354i
$189$	1.14697	−	0.662201i	0.0834295	−	0.0481680i
$190$		−	6.07995i		−	0.441086i
$191$	9.26601	+	16.0492i	0.670465	+	1.16128i	0.977772	+	0.209669i	$0.0672386\pi$
$191$	9.26601	+	16.0492i	0.670465	+	1.16128i	−0.307308	+	0.951610i	$0.599428\pi$
$192$	−40.2744	+	69.7573i	−2.90655	+	5.03430i
$193$	−3.43730	−	1.98453i	−0.247422	−	0.142849i	0.371161	−	0.928569i	$-0.378960\pi$
$193$	−3.43730	−	1.98453i	−0.247422	−	0.142849i	−0.618583	+	0.785719i	$0.712293\pi$
$194$	48.6481			3.49273
$195$		0			0
$196$	−40.0457			−2.86041
$197$	1.48598	+	0.857931i	0.105872	+	0.0611251i	0.552001	−	0.833843i	$-0.313864\pi$
$197$	1.48598	+	0.857931i	0.105872	+	0.0611251i	−0.446129	+	0.894969i	$0.647198\pi$
$198$	−0.739584	+	1.28100i	−0.0525600	+	0.0910365i
$199$	10.1256	+	17.5381i	0.717787	+	1.24324i	0.961875	+	0.273490i	$0.0881782\pi$
$199$	10.1256	+	17.5381i	0.717787	+	1.24324i	−0.244088	+	0.969753i	$0.578488\pi$
$200$		−	10.5463i		−	0.745738i
$201$	−15.0094	+	8.66566i	−1.05868	+	0.611229i
$202$	−28.5070	+	16.4585i	−2.00575	+	1.15802i
$203$		−	1.94450i		−	0.136477i
$204$	−3.86749	−	6.69869i	−0.270779	−	0.469002i
$205$	−4.18948	+	7.25640i	−0.292606	+	0.506809i
$206$	19.4189	+	11.2115i	1.35298	+	0.781141i
$207$	0.805657			0.0559970
$208$		0			0
$209$	−3.94692			−0.273014
$210$	−1.18182	−	0.682322i	−0.0815531	−	0.0470847i
$211$	−3.38891	+	5.86976i	−0.233302	+	0.404091i	−0.958778	−	0.284157i	$-0.908286\pi$
$211$	−3.38891	+	5.86976i	−0.233302	+	0.404091i	0.725476	+	0.688248i	$0.241620\pi$
$212$	11.1287	+	19.2755i	0.764325	+	1.32385i
$213$			14.7365i			1.00973i
$214$	−41.7861	+	24.1252i	−2.85644	+	1.64917i
$215$	−1.01252	+	0.584581i	−0.0690536	+	0.0398681i
$216$			51.8084i			3.52512i
$217$	−0.834990	−	1.44625i	−0.0566828	−	0.0981776i
$218$	−21.1015	+	36.5489i	−1.42917	+	2.47540i
$219$	−1.08888	−	0.628665i	−0.0735797	−	0.0424812i
$220$	−10.4679			−0.705749
$221$		0			0
$222$	−38.7934			−2.60364
$223$	8.84491	+	5.10661i	0.592299	+	0.341964i	0.766006	−	0.642833i	$-0.222241\pi$
$223$	8.84491	+	5.10661i	0.592299	+	0.341964i	−0.173707	+	0.984797i	$0.555575\pi$
$224$	−3.87096	+	6.70471i	−0.258640	+	0.447977i
$225$	0.146421	+	0.253609i	0.00976140	+	0.0169072i
$226$		−	34.7800i		−	2.31353i
$227$	7.87387	−	4.54598i	0.522607	−	0.301727i	−0.215394	−	0.976527i	$-0.569103\pi$
$227$	7.87387	−	4.54598i	0.522607	−	0.301727i	0.738001	+	0.674800i	$0.235770\pi$
$228$	19.8013	−	11.4323i	1.31137	−	0.757122i
$229$			7.80962i			0.516074i	0.966135	+	0.258037i	$0.0830757\pi$
$229$			7.80962i			0.516074i	−0.966135	+	0.258037i	$0.916924\pi$
$230$	3.83707	+	6.64600i	0.253009	+	0.438224i
$231$	−0.442942	+	0.767199i	−0.0291435	+	0.0504780i
$232$	65.8748	+	38.0329i	4.32489	+	2.49698i
$233$	3.62746			0.237643			0.118821	−	0.992916i	$-0.462088\pi$
$233$	3.62746			0.237643			0.118821	+	0.992916i	$0.462088\pi$
$234$		0			0
$235$	−0.121132			−0.00790181
$236$	−53.2213	−	30.7273i	−3.46441	−	2.00018i
$237$	6.04097	−	10.4633i	0.392403	−	0.679662i
$238$	−0.277260	−	0.480228i	−0.0179721	−	0.0311286i
$239$			19.0089i			1.22959i	0.788688	+	0.614793i	$0.210761\pi$
$239$			19.0089i			1.22959i	−0.788688	+	0.614793i	$0.789239\pi$
$240$	28.0615	−	16.2013i	1.81136	−	1.04579i
$241$	8.78654	−	5.07291i	0.565991	−	0.326775i	−0.189556	−	0.981870i	$-0.560705\pi$
$241$	8.78654	−	5.07291i	0.565991	−	0.326775i	0.755547	+	0.655095i	$0.227371\pi$
$242$		−	21.5371i		−	1.38446i
$243$	−1.51638	−	2.62645i	−0.0972760	−	0.168487i
$244$	−12.2664	+	21.2460i	−0.785273	+	1.36013i
$245$	5.99923	+	3.46366i	0.383277	+	0.221285i
$246$	−42.4120			−2.70409
$247$		0			0
$248$	65.3269			4.14826
$249$	14.4474	+	8.34123i	0.915569	+	0.528604i
$250$	−1.39471	+	2.41570i	−0.0882091	+	0.152783i
$251$	0.0643811	+	0.111511i	0.00406370	+	0.00703853i	0.868050	−	0.496477i	$-0.165373\pi$
$251$	0.0643811	+	0.111511i	0.00406370	+	0.00703853i	−0.863986	+	0.503515i	$0.832040\pi$
$252$		−	0.456399i		−	0.0287505i
$253$	4.31438	−	2.49091i	0.271243	−	0.156602i
$254$	28.7168	−	16.5797i	1.80186	−	1.04030i
$255$			1.33804i			0.0837912i
$256$	−48.2007	−	83.4860i	−3.01254	−	5.21787i
$257$	3.36934	−	5.83587i	0.210174	−	0.364032i	−0.741595	−	0.670848i	$-0.765930\pi$
$257$	3.36934	−	5.83587i	0.210174	−	0.364032i	0.951769	+	0.306816i	$0.0992637\pi$
$258$	−5.12512	−	2.95899i	−0.319076	−	0.184219i
$259$	−2.06624			−0.128390
$260$		0			0
$261$	−2.11213			−0.130738
$262$	33.2869	+	19.2182i	2.05647	+	1.18730i
$263$	−8.90337	+	15.4211i	−0.549005	+	0.950905i	0.449338	+	0.893362i	$0.351660\pi$
$263$	−8.90337	+	15.4211i	−0.549005	+	0.950905i	−0.998343	+	0.0575429i	$0.981673\pi$
$264$	−17.3272	−	30.0115i	−1.06641	−	1.84708i
$265$		−	3.85022i		−	0.236517i
$266$	1.41955	−	0.819579i	0.0870384	−	0.0502516i
$267$	10.3274	−	5.96250i	0.632024	−	0.364899i
$268$		−	55.2125i		−	3.37264i
$269$	0.102557	+	0.177634i	0.00625302	+	0.0108305i	0.869135	−	0.494575i	$-0.164676\pi$
$269$	0.102557	+	0.177634i	0.00625302	+	0.0108305i	−0.862882	+	0.505405i	$0.831343\pi$
$270$	6.85145	−	11.8671i	0.416966	−	0.722206i
$271$	−23.0300	−	13.2964i	−1.39898	−	0.807699i	−0.404690	−	0.914454i	$-0.632621\pi$
$271$	−23.0300	−	13.2964i	−1.39898	−	0.807699i	−0.994285	+	0.106755i	$0.965954\pi$
$272$	13.1667			0.798349
$273$		0			0
$274$	39.4993			2.38624
$275$	1.56820	+	0.905401i	0.0945660	+	0.0545977i
$276$	−14.4299	+	24.9933i	−0.868577	+	1.50442i
$277$	12.6075	+	21.8368i	0.757510	+	1.31205i	0.944117	+	0.329611i	$0.106917\pi$
$277$	12.6075	+	21.8368i	0.757510	+	1.31205i	−0.186607	+	0.982435i	$0.559749\pi$
$278$		−	12.6540i		−	0.758939i
$279$	−1.57092	+	0.906973i	−0.0940487	+	0.0542990i
$280$	2.46237	−	1.42165i	0.147155	−	0.0849597i
$281$		−	12.7906i		−	0.763025i	−0.924364	−	0.381513i	$-0.875403\pi$
$281$		−	12.7906i		−	0.763025i	0.924364	−	0.381513i	$-0.124597\pi$
$282$	−0.306570	−	0.530994i	−0.0182560	−	0.0316203i
$283$	11.2368	−	19.4628i	0.667961	−	1.15694i	−0.310512	−	0.950569i	$-0.600500\pi$
$283$	11.2368	−	19.4628i	0.667961	−	1.15694i	0.978473	−	0.206373i	$-0.0661662\pi$
$284$	−40.6564	−	23.4730i	−2.41251	−	1.39287i
$285$	−3.95524			−0.234288
$286$		0			0
$287$	−2.25897			−0.133343
$288$	7.28270	+	4.20467i	0.429137	+	0.247762i
$289$	8.22815	−	14.2516i	0.484009	−	0.838327i
$290$	−10.0594	−	17.4233i	−0.590707	−	1.02313i
$291$		−	31.6474i		−	1.85520i
$292$	3.46885	−	2.00274i	0.202999	−	0.117201i
$293$	16.8092	−	9.70479i	0.982003	−	0.566960i	0.0791289	−	0.996864i	$-0.474786\pi$
$293$	16.8092	−	9.70479i	0.982003	−	0.566960i	0.902874	+	0.429905i	$0.141453\pi$
$294$			35.0642i			2.04498i
$295$	5.31538	+	9.20651i	0.309473	+	0.536024i
$296$	40.4138	−	69.9988i	2.34901	−	4.06860i
$297$	−7.70372	−	4.44775i	−0.447015	−	0.258084i
$298$	9.81653			0.568656
$299$		0			0
$300$	−10.4900			−0.605641
$301$	−0.272977	−	0.157603i	−0.0157341	−	0.00908411i
$302$	6.26584	−	10.8527i	0.360558	−	0.624505i
$303$	10.7069	+	18.5449i	0.615095	+	1.06538i
$304$			38.9207i			2.23226i
$305$	3.67524	−	2.12190i	0.210444	−	0.121500i
$306$	−0.521627	+	0.301162i	−0.0298195	+	0.0172163i
$307$			20.9899i			1.19796i	0.800765	+	0.598978i	$0.204426\pi$
$307$			20.9899i			1.19796i	−0.800765	+	0.598978i	$0.795574\pi$
$308$	−1.41108	−	2.44407i	−0.0804039	−	0.139264i
$309$	7.29349	−	12.6327i	0.414912	−	0.718649i
$310$	−14.9635	−	8.63921i	−0.849872	−	0.490674i
$311$	−12.5265			−0.710311			−0.355155	−	0.934807i	$-0.615572\pi$
$311$	−12.5265			−0.710311			−0.355155	+	0.934807i	$0.615572\pi$
$312$		0			0
$313$	−8.46526			−0.478485			−0.239242	−	0.970960i	$-0.576899\pi$
$313$	−8.46526			−0.478485			−0.239242	+	0.970960i	$0.576899\pi$
$314$	24.7440	+	14.2860i	1.39639	+	0.806205i
$315$	−0.0394752	+	0.0683730i	−0.00222418	+	0.00385238i
$316$	19.2447	+	33.3329i	1.08260	+	1.87512i
$317$			15.3660i			0.863043i	0.902103	+	0.431522i	$0.142023\pi$
$317$			15.3660i			0.863043i	−0.902103	+	0.431522i	$0.857977\pi$
$318$	16.8777	−	9.74437i	0.946457	−	0.546437i
$319$	−11.3107	+	6.53023i	−0.633277	+	0.365623i
$320$			44.3888i			2.48141i
$321$	15.6944	+	27.1834i	0.875974	+	1.51723i
$322$	−1.03448	+	1.79177i	−0.0576491	+	0.0998512i
$323$	−1.39188	−	0.803600i	−0.0774461	−	0.0447135i
$324$	56.6104			3.14502
$325$		0			0
$326$	−4.70907			−0.260811
$327$	23.7764	+	13.7273i	1.31484	+	0.759123i
$328$	44.1837	−	76.5283i	2.43963	−	4.22557i
$329$	−0.0163287	−	0.0282821i	−0.000900230	−	0.00155924i
$330$			9.16578i			0.504560i
$331$	−5.96314	+	3.44282i	−0.327764	+	0.189234i	−0.654848	−	0.755761i	$-0.727267\pi$
$331$	−5.96314	+	3.44282i	−0.327764	+	0.189234i	0.327084	+	0.944995i	$0.393934\pi$
$332$	−46.0253	+	26.5727i	−2.52596	+	1.45837i
$333$			2.24436i			0.122990i
$334$	5.99541	+	10.3844i	0.328054	+	0.568207i
$335$	−4.77547	+	8.27136i	−0.260912	+	0.451913i
$336$	7.56538	+	4.36788i	0.412726	+	0.238287i
$337$	12.4209			0.676609			0.338305	−	0.941037i	$-0.390147\pi$
$337$	12.4209			0.676609			0.338305	+	0.941037i	$0.390147\pi$
$338$		0			0
$339$	−22.6257			−1.22886
$340$	−3.69151	−	2.13130i	−0.200200	−	0.115586i
$341$	−5.60830	+	9.71387i	−0.303707	+	0.526035i
$342$	−0.890233	−	1.54193i	−0.0481383	−	0.0833780i
$343$			3.75481i			0.202741i
$344$	10.6784	−	6.16518i	0.575741	−	0.332404i
$345$	4.32347	−	2.49616i	0.232768	−	0.134389i
$346$		−	31.2170i		−	1.67824i
$347$	−11.7441	−	20.3413i	−0.630455	−	1.09198i	−0.987459	−	0.157877i	$-0.949535\pi$
$347$	−11.7441	−	20.3413i	−0.630455	−	1.09198i	0.357004	−	0.934103i	$-0.383798\pi$
$348$	37.8298	−	65.5231i	2.02789	−	3.51241i
$349$	−15.1798	−	8.76406i	−0.812556	−	0.469129i	0.0352867	−	0.999377i	$-0.488766\pi$
$349$	−15.1798	−	8.76406i	−0.812556	−	0.469129i	−0.847843	+	0.530248i	$0.822099\pi$
$350$	−0.752028			−0.0401976
$351$		0			0
$352$	51.9995			2.77158
$353$	3.47485	+	2.00621i	0.184948	+	0.106780i	0.589615	−	0.807684i	$-0.299279\pi$
$353$	3.47485	+	2.00621i	0.184948	+	0.106780i	−0.404667	+	0.914464i	$0.632613\pi$
$354$	−26.9050	+	46.6008i	−1.42998	+	2.47681i
$355$	4.06048	+	7.03296i	0.215508	+	0.373271i
$356$			37.9895i			2.01344i
$357$	−0.312406	+	0.180368i	−0.0165343	+	0.00954608i
$358$	18.5575	−	10.7142i	0.980792	−	0.566261i
$359$		−	5.71225i		−	0.301481i	−0.988573	−	0.150740i	$-0.951834\pi$
$359$		−	5.71225i		−	0.301481i	0.988573	−	0.150740i	$-0.0481658\pi$
$360$	−1.54420	−	2.67464i	−0.0813867	−	0.140966i
$361$	−7.12456	+	12.3401i	−0.374977	+	0.649479i
$362$	−15.5748	−	8.99211i	−0.818593	−	0.472615i
$363$	−14.0107			−0.735369
$364$		0			0
$365$	−0.692889			−0.0362675
$366$	18.6031	+	10.7405i	0.972397	+	0.561414i
$367$	−2.21827	+	3.84215i	−0.115793	+	0.200559i	−0.918096	−	0.396357i	$-0.870274\pi$
$367$	−2.21827	+	3.84215i	−0.115793	+	0.200559i	0.802304	+	0.596916i	$0.203607\pi$
$368$	−24.5630	−	42.5443i	−1.28043	−	2.21777i
$369$			2.45371i			0.127735i
$370$	−18.5141	+	10.6891i	−0.962503	+	0.555701i
$371$	0.898952	−	0.519010i	0.0466713	−	0.0269457i
$372$		−	64.9781i		−	3.36896i
$373$	3.74571	+	6.48776i	0.193946	+	0.335924i	0.946554	−	0.322544i	$-0.104538\pi$
$373$	3.74571	+	6.48776i	0.193946	+	0.335924i	−0.752609	+	0.658468i	$0.771205\pi$
$374$	−1.86225	+	3.22551i	−0.0962945	+	0.166787i
$375$	1.57151	+	0.907309i	0.0811522	+	0.0468533i
$376$	1.27750			0.0658822
$377$		0			0
$378$	3.69431			0.190015
$379$	10.0178	+	5.78381i	0.514582	+	0.297094i	0.734715	−	0.678376i	$-0.237316\pi$
$379$	10.0178	+	5.78381i	0.514582	+	0.297094i	−0.220133	+	0.975470i	$0.570649\pi$
$380$	6.30010	−	10.9121i	0.323189	−	0.559779i
$381$	−10.7857	−	18.6814i	−0.552568	−	0.957076i
$382$			51.6935i			2.64487i
$383$	−23.0073	+	13.2833i	−1.17562	+	0.678744i	−0.954997	−	0.296616i	$-0.904142\pi$
$383$	−23.0073	+	13.2833i	−1.17562	+	0.678744i	−0.220622	+	0.975359i	$0.570809\pi$
$384$	−104.326	+	60.2329i	−5.32389	+	3.07375i
$385$			0.488193i			0.0248806i
$386$	−5.53567	−	9.58806i	−0.281758	−	0.488019i
$387$	−0.171190	+	0.296510i	−0.00870207	+	0.0150724i
$388$	87.3120	+	50.4096i	4.43260	+	2.55916i
$389$	−32.0328			−1.62413			−0.812063	−	0.583570i	$-0.801656\pi$
$389$	−32.0328			−1.62413			−0.812063	+	0.583570i	$0.801656\pi$
$390$		0			0
$391$	2.02862			0.102591
$392$	−63.2698	−	36.5289i	−3.19561	−	1.84499i
$393$	12.5022	−	21.6544i	0.630651	−	1.09232i
$394$	2.39313	+	4.14502i	0.120564	+	0.208823i
$395$		−	6.65811i		−	0.335006i
$396$	−2.65476	+	1.53273i	−0.133407	+	0.0770225i
$397$	32.8856	−	18.9865i	1.65048	−	0.952905i	0.673607	−	0.739090i	$-0.264744\pi$
$397$	32.8856	−	18.9865i	1.65048	−	0.952905i	0.976874	−	0.213815i	$-0.0685891\pi$
$398$			56.4892i			2.83155i
$399$	−0.533167	−	0.923472i	−0.0266917	−	0.0462314i
$400$	8.92820	−	15.4641i	0.446410	−	0.773205i
$401$	25.1807	+	14.5381i	1.25746	+	0.725997i	0.972581	−	0.232565i	$-0.0747118\pi$
$401$	25.1807	+	14.5381i	1.25746	+	0.725997i	0.284883	+	0.958562i	$0.408045\pi$
$402$	−48.3443			−2.41119
$403$		0			0
$404$	−68.2180			−3.39397
$405$	−8.48079	−	4.89638i	−0.421414	−	0.243303i
$406$	2.71201	−	4.69734i	0.134595	−	0.233125i
$407$	6.93905	+	12.0188i	0.343956	+	0.595749i
$408$		−	14.1114i		−	0.698618i
$409$	23.1421	−	13.3611i	1.14430	−	0.660663i	0.196809	−	0.980442i	$-0.436942\pi$
$409$	23.1421	−	13.3611i	1.14430	−	0.660663i	0.947492	+	0.319779i	$0.103609\pi$
$410$	−20.2411	+	11.6862i	−0.999637	+	0.577141i
$411$		−	25.6958i		−	1.26748i
$412$	23.2349	+	40.2440i	1.14470	+	1.98268i
$413$	−1.43303	+	2.48208i	−0.0705148	+	0.122135i
$414$	1.94623	+	1.12366i	0.0956519	+	0.0552247i
$415$	9.19337			0.451285
$416$		0			0
$417$	−8.23193			−0.403119
$418$	−9.53458	−	5.50479i	−0.466352	−	0.269248i
$419$	−17.6931	+	30.6453i	−0.864363	+	1.49712i	0.00331518	+	0.999995i	$0.498945\pi$
$419$	−17.6931	+	30.6453i	−0.864363	+	1.49712i	−0.867678	+	0.497126i	$0.834389\pi$
$420$	−1.41406	−	2.44922i	−0.0689989	−	0.119510i
$421$			14.1178i			0.688058i	0.938959	+	0.344029i	$0.111792\pi$
$421$			14.1178i			0.688058i	−0.938959	+	0.344029i	$0.888208\pi$
$422$	−16.3732	+	9.45307i	−0.797035	+	0.460168i
$423$	−0.0307202	+	0.0177363i	−0.00149367	+	0.000862371i
$424$			40.6057i			1.97198i
$425$	0.368683	+	0.638578i	0.0178838	+	0.0309756i
$426$	−20.5531	+	35.5989i	−0.995799	+	1.72477i
$427$	0.990847	+	0.572066i	0.0479504	+	0.0276842i
$428$	−99.9951			−4.83345
$429$		0			0
$430$	−3.26128			−0.157273
$431$	−12.2528	−	7.07413i	−0.590195	−	0.340749i	0.174980	−	0.984572i	$-0.444014\pi$
$431$	−12.2528	−	7.07413i	−0.590195	−	0.340749i	−0.765174	+	0.643823i	$0.777347\pi$
$432$	−43.8594	+	75.9668i	−2.11019	+	3.65495i
$433$	−12.4280	−	21.5260i	−0.597253	−	1.03447i	−0.993225	−	0.116210i	$-0.962926\pi$
$433$	−12.4280	−	21.5260i	−0.597253	−	1.03447i	0.395972	−	0.918263i	$-0.370408\pi$
$434$		−	4.65827i		−	0.223604i
$435$	−11.3345	+	6.54400i	−0.543449	+	0.313761i
$436$	−75.7446	+	43.7312i	−3.62751	+	2.09434i
$437$			5.99658i			0.286855i
$438$	−1.75361	−	3.03734i	−0.0837906	−	0.145130i
$439$	4.88111	−	8.45433i	0.232963	−	0.403503i	−0.725716	−	0.687995i	$-0.758491\pi$
$439$	4.88111	−	8.45433i	0.232963	−	0.403503i	0.958679	+	0.284491i	$0.0918246\pi$
$440$	−16.5388	−	9.54865i	−0.788454	−	0.455214i
$441$	2.02861			0.0966005
$442$		0			0
$443$	−32.5970			−1.54873			−0.774365	−	0.632740i	$-0.781930\pi$
$443$	−32.5970			−1.54873			−0.774365	+	0.632740i	$0.781930\pi$
$444$	−69.6251	−	40.1981i	−3.30426	−	1.90772i
$445$	3.28581	−	5.69120i	0.155763	−	0.269789i
$446$	14.2445	+	24.6721i	0.674495	+	1.16826i
$447$		−	6.38602i		−	0.302048i
$448$	−10.3639	+	5.98363i	−0.489650	+	0.282700i
$449$	10.5532	−	6.09290i	0.498037	−	0.287542i	−0.229866	−	0.973222i	$-0.573829\pi$
$449$	10.5532	−	6.09290i	0.498037	−	0.287542i	0.727902	+	0.685681i	$0.240495\pi$
$450$			0.816858i			0.0385071i
$451$	7.58632	+	13.1399i	0.357226	+	0.618734i
$452$	36.0394	−	62.4220i	1.69515	−	2.93609i
$453$	−7.06012	−	4.07616i	−0.331713	−	0.191515i
$454$	25.3613			1.19026
$455$		0			0
$456$	41.7132			1.95340
$457$	26.1079	+	15.0734i	1.22128	+	0.705105i	0.965190	−	0.261548i	$-0.0842331\pi$
$457$	26.1079	+	15.0734i	1.22128	+	0.705105i	0.256088	+	0.966654i	$0.417566\pi$
$458$	−10.8921	+	18.8657i	−0.508956	+	0.881538i
$459$	−1.81114	−	3.13699i	−0.0845368	−	0.146422i
$460$			15.9040i			0.741530i
$461$	−27.5727	+	15.9191i	−1.28419	+	0.741427i	−0.977611	−	0.210419i	$-0.932517\pi$
$461$	−27.5727	+	15.9191i	−1.28419	+	0.741427i	−0.306578	+	0.951846i	$0.599184\pi$
$462$	−2.14004	+	1.23555i	−0.0995635	+	0.0574830i
$463$		−	15.5796i		−	0.724045i	−0.932169	−	0.362023i	$-0.882086\pi$
$463$		−	15.5796i		−	0.724045i	0.932169	−	0.362023i	$-0.117914\pi$
$464$	64.3950	+	111.535i	2.98946	+	5.17790i
$465$	−5.62013	+	9.73434i	−0.260627	+	0.451419i
$466$	8.76288	+	5.05925i	0.405932	+	0.234365i
$467$	29.7598			1.37712			0.688560	−	0.725179i	$-0.258243\pi$
$467$	29.7598			1.37712			0.688560	+	0.725179i	$0.258243\pi$
$468$		0			0
$469$	−2.57494			−0.118900
$470$	−0.292620	−	0.168944i	−0.0134976	−	0.00779282i
$471$	9.29356	−	16.0969i	0.428225	−	0.741707i
$472$	−56.0577	−	97.0948i	−2.58027	−	4.46915i
$473$			2.11712i			0.0973453i
$474$	29.1864	−	16.8508i	1.34058	−	0.773982i
$475$	−1.88763	+	1.08983i	−0.0866106	+	0.0500046i
$476$		−	1.14920i		−	0.0526734i
$477$	−0.563753	−	0.976449i	−0.0258125	−	0.0447085i
$478$	−26.5119	+	45.9200i	−1.21263	+	2.10033i
$479$	13.0803	+	7.55192i	0.597654	+	0.345056i	0.768118	−	0.640308i	$-0.221193\pi$
$479$	13.0803	+	7.55192i	0.597654	+	0.345056i	−0.170464	+	0.985364i	$0.554527\pi$
$480$	52.1091			2.37844
$481$		0			0
$482$	28.3009			1.28907
$483$	1.16561	+	0.672966i	0.0530371	+	0.0306210i
$484$	22.3169	−	38.6540i	1.01441	−	1.75700i
$485$	−8.72012	−	15.1037i	−0.395960	−	0.685824i
$486$		−	8.45964i		−	0.383737i
$487$	−6.05414	+	3.49536i	−0.274339	+	0.158390i	−0.630858	−	0.775898i	$-0.717297\pi$
$487$	−6.05414	+	3.49536i	−0.274339	+	0.158390i	0.356519	+	0.934288i	$0.383964\pi$
$488$	−38.7603	+	22.3783i	−1.75460	+	1.01302i
$489$			3.06343i			0.138533i
$490$	9.66158	+	16.7343i	0.436466	+	0.755981i
$491$	−9.23041	+	15.9875i	−0.416563	+	0.721508i	−0.995591	−	0.0937997i	$-0.970099\pi$
$491$	−9.23041	+	15.9875i	−0.416563	+	0.721508i	0.579029	+	0.815307i	$0.303432\pi$
$492$	−76.1197	−	43.9478i	−3.43174	−	1.98132i
$493$	−5.31827			−0.239523
$494$		0			0
$495$	0.530279			0.0238343
$496$	95.7889	+	55.3038i	4.30105	+	2.48321i
$497$	−1.09471	+	1.89609i	−0.0491044	+	0.0850513i
$498$	23.2672	+	40.2999i	1.04263	+	1.80588i
$499$			9.65233i			0.432097i	0.976383	+	0.216049i	$0.0693170\pi$
$499$			9.65233i			0.432097i	−0.976383	+	0.216049i	$0.930683\pi$
$500$	−5.00635	+	2.89042i	−0.223891	+	0.129263i
$501$	6.75541	−	3.90024i	0.301810	−	0.174250i
$502$			0.359171i			0.0160306i
$503$	−3.42677	−	5.93533i	−0.152792	−	0.264643i	0.779461	−	0.626451i	$-0.215493\pi$
$503$	−3.42677	−	5.93533i	−0.152792	−	0.264643i	−0.932253	+	0.361807i	$0.882160\pi$
$504$	0.416318	−	0.721084i	0.0185443	−	0.0321197i
$505$	10.2197	+	5.90035i	0.454771	+	0.262562i
$506$	13.8963			0.617768
$507$		0			0
$508$	68.7201			3.04896
$509$	−29.3092	−	16.9217i	−1.29911	−	0.750039i	−0.318856	−	0.947803i	$-0.603299\pi$
$509$	−29.3092	−	16.9217i	−1.29911	−	0.750039i	−0.980250	+	0.197764i	$0.936632\pi$
$510$	−1.86617	+	3.23230i	−0.0826355	+	0.143129i
$511$	−0.0934017	−	0.161776i	−0.00413185	−	0.00715657i
$512$		−	136.131i		−	6.01618i
$513$	9.27292	−	5.35372i	0.409410	−	0.236373i
$514$	16.2787	−	9.39850i	0.718021	−	0.414550i
$515$		−	8.03859i		−	0.354223i
$516$	−6.13226	−	10.6214i	−0.269958	−	0.467581i
$517$	−0.109673	+	0.189960i	−0.00482343	+	0.00835443i
$518$	−4.99141	−	2.88179i	−0.219310	−	0.126619i
$519$	−20.3078			−0.891416
$520$		0			0
$521$	−36.7411			−1.60966			−0.804828	−	0.593508i	$-0.797742\pi$
$521$	−36.7411			−1.60966			−0.804828	+	0.593508i	$0.797742\pi$
$522$	−5.10229	−	2.94581i	−0.223321	−	0.128935i
$523$	−16.1115	+	27.9059i	−0.704505	+	1.22024i	0.262365	+	0.964969i	$0.415498\pi$
$523$	−16.1115	+	27.9059i	−0.704505	+	1.22024i	−0.966870	+	0.255270i	$0.917836\pi$
$524$	39.8282	+	68.9844i	1.73990	+	3.01360i
$525$			0.489222i			0.0213514i
$526$	−43.0158	+	24.8352i	−1.87558	+	1.08287i
$527$	−3.95553	+	2.28372i	−0.172305	+	0.0994806i
$528$		−	58.6746i		−	2.55349i
$529$	7.71555	+	13.3637i	0.335459	+	0.581031i
$530$	5.36993	−	9.30099i	0.233255	−	0.404009i
$531$	2.69605	+	1.55657i	0.116999	+	0.0675492i
$532$	3.39702			0.147280
$533$		0			0
$534$	33.2638			1.43946
$535$	14.9802	+	8.64884i	0.647652	+	0.373922i
$536$	50.3637	−	87.2325i	2.17538	−	3.76787i
$537$	−6.96996	−	12.0723i	−0.300776	−	0.520959i
$538$			0.572149i			0.0246671i
$539$	10.8634	−	6.27200i	0.467921	−	0.270154i
$540$	24.5935	−	14.1991i	1.05834	−	0.611031i
$541$			9.68462i			0.416375i	0.978089	+	0.208187i	$0.0667564\pi$
$541$			9.68462i			0.416375i	−0.978089	+	0.208187i	$0.933244\pi$
$542$	−37.0892	−	64.2404i	−1.59312	−	2.75936i
$543$	−5.84971	+	10.1320i	−0.251035	+	0.434805i
$544$	18.3376	+	10.5872i	0.786217	+	0.453923i
$545$	15.1297			0.648085
$546$		0			0
$547$	−5.81447			−0.248609			−0.124304	−	0.992244i	$-0.539670\pi$
$547$	−5.81447			−0.248609			−0.124304	+	0.992244i	$0.539670\pi$
$548$	70.8921	+	40.9296i	3.02836	+	1.74842i
$549$	0.621382	−	1.07626i	0.0265199	−	0.0459339i
$550$	2.52554	+	4.37436i	0.107689	+	0.186523i
$551$		−	15.7208i		−	0.669729i
$552$	−45.5967	+	26.3253i	−1.94073	+	1.12048i
$553$	1.55454	−	0.897515i	0.0661059	−	0.0381662i
$554$			70.3350i			2.98825i
$555$	6.95368	+	12.0441i	0.295167	+	0.511244i
$556$	13.1122	−	22.7111i	0.556083	−	0.963164i
$557$	26.8376	+	15.4947i	1.13715	+	0.656531i	0.945722	−	0.324976i	$-0.105356\pi$
$557$	26.8376	+	15.4947i	1.13715	+	0.656531i	0.191423	+	0.981508i	$0.438690\pi$
$558$	−5.05985			−0.214200
$559$		0			0
$560$	4.81410			0.203433
$561$	2.09831	+	1.21146i	0.0885908	+	0.0511479i
$562$	17.8392	−	30.8984i	0.752501	−	1.30337i
$563$	−7.01670	−	12.1533i	−0.295719	−	0.512199i	0.679433	−	0.733737i	$-0.262226\pi$
$563$	−7.01670	−	12.1533i	−0.295719	−	0.512199i	−0.975152	+	0.221538i	$0.928892\pi$
$564$		−	1.27068i		−	0.0535054i
$565$	−10.7981	+	6.23428i	−0.454279	+	0.262278i
$566$	54.2898	−	31.3442i	2.28197	−	1.31750i
$567$		−	2.64014i		−	0.110875i
$568$	−42.8232	−	74.1719i	−1.79682	−	3.11219i
$569$	9.48586	−	16.4300i	0.397668	−	0.688781i	−0.595770	−	0.803155i	$-0.703153\pi$
$569$	9.48586	−	16.4300i	0.397668	−	0.688781i	0.993438	+	0.114374i	$0.0364863\pi$
$570$	−9.55468	−	5.51640i	−0.400202	−	0.231057i
$571$	−18.6462			−0.780318			−0.390159	−	0.920748i	$-0.627580\pi$
$571$	−18.6462			−0.780318			−0.390159	+	0.920748i	$0.627580\pi$
$572$		0			0
$573$	33.6285			1.40485
$574$	−5.45701	−	3.15061i	−0.227771	−	0.131504i
$575$	1.37558	−	2.38258i	0.0573657	−	0.0993604i
$576$	6.49946	+	11.2574i	0.270811	+	0.469058i
$577$		−	10.6262i		−	0.442374i	−0.975231	−	0.221187i	$-0.929007\pi$
$577$		−	10.6262i		−	0.442374i	0.975231	−	0.221187i	$-0.0709931\pi$
$578$	39.7535	−	22.9517i	1.65353	−	0.954666i
$579$	−6.23739	+	3.60116i	−0.259217	+	0.149659i
$580$		−	41.6945i		−	1.73127i
$581$	1.23927	+	2.14648i	0.0514136	+	0.0890509i
$582$	44.1389	−	76.4508i	1.82962	−	3.16899i
$583$	−6.03791	−	3.48599i	−0.250065	−	0.144375i
$584$	7.30744			0.302384
$585$		0			0
$586$	54.1414			2.23656
$587$	−12.3787	−	7.14682i	−0.510922	−	0.294981i	0.222291	−	0.974980i	$-0.428647\pi$
$587$	−12.3787	−	7.14682i	−0.510922	−	0.294981i	−0.733213	+	0.680000i	$0.761980\pi$
$588$	−36.3338	+	62.9320i	−1.49838	+	2.59527i
$589$	−6.75068	−	11.6925i	−0.278157	−	0.481782i
$590$			29.6536i			1.22082i
$591$	2.69649	−	1.55682i	0.110919	−	0.0640390i
$592$	118.518	−	68.4263i	4.87105	−	2.81230i
$593$			0.474392i			0.0194809i	0.999953	+	0.00974047i	$0.00310054\pi$
$593$			0.474392i			0.0194809i	−0.999953	+	0.00974047i	$0.996899\pi$
$594$	−12.4066	−	21.4889i	−0.509049	−	0.881699i
$595$	−0.0993971	+	0.172161i	−0.00407489	+	0.00705791i
$596$	17.6184	+	10.1720i	0.721677	+	0.416660i
$597$	36.7483			1.50401
$598$		0			0
$599$	−32.2915			−1.31940			−0.659698	−	0.751531i	$-0.729316\pi$
$599$	−32.2915			−1.31940			−0.659698	+	0.751531i	$0.729316\pi$
$600$	−16.5736	−	9.56878i	−0.676615	−	0.390644i
$601$	−9.85973	+	17.0776i	−0.402187	+	0.696608i	−0.993990	−	0.109475i	$-0.965083\pi$
$601$	−9.85973	+	17.0776i	−0.402187	+	0.696608i	0.591803	+	0.806083i	$0.298416\pi$
$602$	−0.439621	−	0.761446i	−0.0179176	−	0.0310342i
$603$			2.79692i			0.113899i
$604$	22.4914	−	12.9854i	0.915164	−	0.528370i
$605$	−6.68658	+	3.86050i	−0.271848	+	0.156952i
$606$			59.7319i			2.42644i
$607$	−12.0383	−	20.8509i	−0.488618	−	0.846311i	0.511297	−	0.859404i	$-0.329165\pi$
$607$	−12.0383	−	20.8509i	−0.488618	−	0.846311i	−0.999914	+	0.0130936i	$0.995832\pi$
$608$	−31.2957	+	54.2058i	−1.26921	+	2.19834i
$609$	−3.05580	−	1.76427i	−0.123827	−	0.0714917i
$610$	11.8377			0.479295
$611$		0			0
$612$	−1.24827			−0.0504582
$613$	−11.7735	−	6.79744i	−0.475528	−	0.274546i	0.243023	−	0.970021i	$-0.421861\pi$
$613$	−11.7735	−	6.79744i	−0.475528	−	0.274546i	−0.718551	+	0.695474i	$0.755194\pi$
$614$	−29.2748	+	50.7054i	−1.18143	+	2.04630i
$615$	7.60232	+	13.1676i	0.306555	+	0.530969i
$616$		−	5.14864i		−	0.207445i
$617$	−2.09050	+	1.20695i	−0.0841602	+	0.0485899i	−0.541489	−	0.840708i	$-0.682139\pi$
$617$	−2.09050	+	1.20695i	−0.0841602	+	0.0485899i	0.457329	+	0.889297i	$0.348806\pi$
$618$	35.2378	−	20.3446i	1.41747	−	0.818379i
$619$		−	11.6882i		−	0.469790i	−0.972021	−	0.234895i	$-0.924525\pi$
$619$		−	11.6882i		−	0.469790i	0.972021	−	0.234895i	$-0.0754747\pi$
$620$	−17.9041	−	31.0107i	−0.719044	−	1.24542i
$621$	−6.75749	+	11.7043i	−0.271169	+	0.469678i
$622$	−30.2602	−	17.4708i	−1.21333	−	0.700514i
$623$	1.77172			0.0709823
$624$		0			0
$625$	1.00000			0.0400000
$626$	−20.4496	−	11.8066i	−0.817329	−	0.471885i
$627$	−3.58107	+	6.20260i	−0.143014	+	0.247708i
$628$	29.6065	+	51.2800i	1.18143	+	2.04630i
$629$			5.65122i			0.225329i
$630$	−0.190721	+	0.110113i	−0.00759850	+	0.00438700i
$631$	−33.5522	+	19.3714i	−1.33569	+	0.771162i	−0.986165	−	0.165765i	$-0.946991\pi$
$631$	−33.5522	+	19.3714i	−1.33569	+	0.771162i	−0.349526	+	0.936927i	$0.613657\pi$
$632$			70.2186i			2.79315i
$633$	6.14958	+	10.6514i	0.244424	+	0.423354i
$634$	−21.4311	+	37.1198i	−0.851139	+	1.47422i
$635$	−10.2949	−	5.94378i	−0.408542	−	0.235872i
$636$	40.3889			1.60152
$637$		0			0
$638$	−36.4311			−1.44232
$639$	2.05955	+	1.18908i	0.0814745	+	0.0470393i
$640$	−33.1932	+	57.4922i	−1.31207	+	2.27258i
$641$	−18.5540	−	32.1364i	−0.732838	−	1.26931i	−0.955666	−	0.294454i	$-0.904862\pi$
$641$	−18.5540	−	32.1364i	−0.732838	−	1.26931i	0.222828	−	0.974858i	$-0.428471\pi$
$642$			87.5562i			3.45557i
$643$	33.3930	−	19.2794i	1.31689	−	0.760307i	0.333663	−	0.942692i	$-0.391715\pi$
$643$	33.3930	−	19.2794i	1.31689	−	0.760307i	0.983227	+	0.182385i	$0.0583819\pi$
$644$	−3.71329	+	2.14387i	−0.146324	+	0.0844803i
$645$			2.12158i			0.0835373i
$646$	−2.24157	−	3.88252i	−0.0881936	−	0.152756i
$647$	−20.5829	+	35.6507i	−0.809198	+	1.40157i	0.104222	+	0.994554i	$0.466765\pi$
$647$	−20.5829	+	35.6507i	−0.809198	+	1.40157i	−0.913420	+	0.407018i	$0.866568\pi$
$648$	89.4412	+	51.6389i	3.51358	+	2.02857i
$649$	19.2502			0.755636
$650$		0			0
$651$	−3.03038			−0.118770
$652$	−8.45169	−	4.87959i	−0.330994	−	0.191099i
$653$	3.66706	−	6.35153i	0.143503	−	0.248555i	−0.785310	−	0.619102i	$-0.787497\pi$
$653$	3.66706	−	6.35153i	0.143503	−	0.248555i	0.928813	+	0.370548i	$0.120830\pi$
$654$	38.2912	+	66.3223i	1.49730	+	2.59341i
$655$		−	13.7794i		−	0.538405i
$656$	129.573	−	74.8091i	5.05898	−	2.92081i
$657$	−0.175723	+	0.101454i	−0.00685560	+	0.00395808i
$658$		−	0.0910950i		−	0.00355125i
$659$	−15.7740	−	27.3214i	−0.614468	−	1.06429i	−0.990478	−	0.137674i	$-0.956037\pi$
$659$	−15.7740	−	27.3214i	−0.614468	−	1.06429i	0.376010	−	0.926616i	$-0.377296\pi$
$660$	−9.49767	+	16.4504i	−0.369696	+	0.640333i
$661$	4.86551	+	2.80911i	0.189247	+	0.109262i	0.591630	−	0.806210i	$-0.298485\pi$
$661$	4.86551	+	2.80911i	0.189247	+	0.109262i	−0.402383	+	0.915471i	$0.631818\pi$
$662$	−19.2069			−0.746497
$663$		0			0
$664$	−96.9563			−3.76263
$665$	−0.508907	−	0.293818i	−0.0197346	−	0.0113938i
$666$	−3.13023	+	5.42171i	−0.121294	+	0.210087i
$667$	9.92143	+	17.1844i	0.384159	+	0.665383i
$668$			24.8500i			0.961476i
$669$	16.0501	−	9.26656i	0.620534	−	0.358266i
$670$	−23.0723	+	13.3208i	−0.891359	+	0.514627i
$671$		−	7.68468i		−	0.296664i
$672$	7.02432	+	12.1665i	0.270969	+	0.469332i
$673$	25.3634	−	43.9306i	0.977686	−	1.69340i	0.306916	−	0.951737i	$-0.400703\pi$
$673$	25.3634	−	43.9306i	0.977686	−	1.69340i	0.670770	−	0.741666i	$-0.265964\pi$
$674$	30.0052	+	17.3235i	1.15576	+	0.667277i
$675$	−4.91246			−0.189081
$676$		0			0
$677$	33.0566			1.27047			0.635234	−	0.772320i	$-0.280904\pi$
$677$	33.0566			1.27047			0.635234	+	0.772320i	$0.280904\pi$
$678$	−54.6570	−	31.5562i	−2.09909	−	1.21191i
$679$	2.35095	−	4.07197i	0.0902212	−	0.156268i
$680$	−3.88825	−	6.73465i	−0.149108	−	0.258262i
$681$		−	16.4984i		−	0.632222i
$682$	−27.0960	+	15.6439i	−1.03756	+	0.599035i
$683$	−13.7730	+	7.95182i	−0.527007	+	0.304268i	−0.739797	−	0.672830i	$-0.765078\pi$
$683$	−13.7730	+	7.95182i	−0.527007	+	0.304268i	0.212790	+	0.977098i	$0.431745\pi$
$684$		−	3.68987i		−	0.141086i
$685$	−7.08021	−	12.2633i	−0.270521	−	0.468556i
$686$	−5.23687	+	9.07052i	−0.199944	+	0.346314i
$687$	12.2729	+	7.08574i	0.468239	+	0.270338i
$688$	20.8770			0.795929
$689$		0			0
$690$	13.9256			0.530140
$691$	−16.7936	−	9.69578i	−0.638858	−	0.368845i	0.145317	−	0.989385i	$-0.453580\pi$
$691$	−16.7936	−	9.69578i	−0.638858	−	0.368845i	−0.784174	+	0.620541i	$0.786913\pi$
$692$	32.3474	−	56.0273i	1.22966	−	2.12984i
$693$	0.0714817	+	0.123810i	0.00271537	+	0.00470315i
$694$		−	65.5182i		−	2.48704i
$695$	−3.92868	+	2.26822i	−0.149023	+	0.0860387i
$696$	119.538	−	69.0151i	4.53107	−	2.61601i
$697$			6.17836i			0.234022i
$698$	−24.4466	−	42.3428i	−0.925318	−	1.60270i
$699$	3.29123	−	5.70058i	0.124486	−	0.215616i
$700$	−1.34972	−	0.779259i	−0.0510144	−	0.0294532i
$701$	−14.2486			−0.538162			−0.269081	−	0.963118i	$-0.586720\pi$
$701$	−14.2486			−0.538162			−0.269081	+	0.963118i	$0.586720\pi$
$702$		0			0
$703$	−16.7050			−0.630040
$704$	69.6106	+	40.1897i	2.62355	+	1.51471i
$705$	−0.109905	+	0.190360i	−0.00413925	+	0.00716939i
$706$	5.59614	+	9.69281i	0.210614	+	0.364794i
$707$			3.18148i			0.119652i
$708$	−96.5764	+	55.7584i	−3.62956	+	2.09553i
$709$	−14.9803	+	8.64889i	−0.562598	+	0.324816i	−0.754187	−	0.656659i	$-0.771969\pi$
$709$	−14.9803	+	8.64889i	−0.562598	+	0.324816i	0.191590	+	0.981475i	$0.438636\pi$
$710$			22.6527i			0.850143i
$711$	−0.974888	−	1.68856i	−0.0365611	−	0.0633258i
$712$	−34.6533	+	60.0212i	−1.29869	+	2.24939i
$713$	14.7584	+	8.52074i	0.552705	+	0.319104i
$714$	−1.00624			−0.0376577
$715$		0			0
$716$	44.4084			1.65962
$717$	29.8727	+	17.2470i	1.11562	+	0.644101i
$718$	7.96691	−	13.7991i	0.297323	−	0.514978i
$719$	−12.6637	−	21.9342i	−0.472278	−	0.818009i	0.527219	−	0.849730i	$-0.323235\pi$
$719$	−12.6637	−	21.9342i	−0.472278	−	0.818009i	−0.999497	+	0.0317202i	$0.989901\pi$
$720$		−	5.22911i		−	0.194877i
$721$	1.87686	−	1.08360i	0.0698978	−	0.0403555i
$722$	−34.4217	+	19.8734i	−1.28104	+	0.739610i
$723$		−	18.4108i		−	0.684705i
$724$	−18.6354	−	32.2775i	−0.692580	−	1.19958i
$725$	−3.60627	+	6.24624i	−0.133933	+	0.231979i
$726$	−33.8456	−	19.5408i	−1.25613	−	0.725227i
$727$	43.3262			1.60688			0.803439	−	0.595387i	$-0.203001\pi$
$727$	43.3262			1.60688			0.803439	+	0.595387i	$0.203001\pi$
$728$		0			0
$729$	23.8750			0.884259
$730$	−1.67382	−	0.966378i	−0.0619507	−	0.0357673i
$731$	−0.431050	+	0.746601i	−0.0159430	+	0.0276140i
$732$	22.2588	+	38.5533i	0.822708	+	1.42497i
$733$		−	39.9598i		−	1.47595i	−0.674828	−	0.737975i	$-0.735782\pi$
$733$		−	39.9598i		−	1.47595i	0.674828	−	0.737975i	$-0.264218\pi$
$734$	−10.7174	+	6.18767i	−0.395585	+	0.228391i
$735$	10.8863	−	6.28522i	0.401548	−	0.231834i
$736$		−	79.0032i		−	2.91210i
$737$	8.64743	+	14.9778i	0.318532	+	0.551714i
$738$	−3.42221	+	5.92745i	−0.125973	+	0.218192i
$739$	−9.60444	−	5.54513i	−0.353305	−	0.203981i	0.312835	−	0.949808i	$-0.398721\pi$
$739$	−9.60444	−	5.54513i	−0.353305	−	0.203981i	−0.666140	+	0.745827i	$0.732055\pi$
$740$	−44.3047			−1.62867
$741$		0			0
$742$	2.89547			0.106296
$743$	17.2066	+	9.93424i	0.631249	+	0.364452i	0.781236	−	0.624236i	$-0.214590\pi$
$743$	17.2066	+	9.93424i	0.631249	+	0.364452i	−0.149986	+	0.988688i	$0.547923\pi$
$744$	59.2717	−	102.662i	2.17301	−	3.76376i
$745$	−1.75960	−	3.04772i	−0.0644669	−	0.111660i
$746$			20.8967i			0.765082i
$747$	2.33152	−	1.34610i	0.0853058	−	0.0492513i
$748$	−6.68460	+	3.85935i	−0.244413	+	0.141112i
$749$			4.66347i			0.170399i
$750$	2.53086	+	4.38358i	0.0924140	+	0.160066i
$751$	3.75199	−	6.49863i	0.136912	−	0.237138i	−0.789414	−	0.613861i	$-0.789616\pi$
$751$	3.75199	−	6.49863i	0.136912	−	0.237138i	0.926326	+	0.376722i	$0.122949\pi$
$752$	1.87321	+	1.08150i	0.0683088	+	0.0394381i
$753$	0.233654			0.00851483
$754$		0			0
$755$	−4.49258			−0.163502
$756$	6.63042	+	3.82808i	0.241146	+	0.139226i
$757$	16.6884	−	28.9052i	0.606551	−	1.05058i	−0.385253	−	0.922811i	$-0.625886\pi$
$757$	16.6884	−	28.9052i	0.606551	−	1.05058i	0.991804	−	0.127767i	$-0.0407809\pi$
$758$	16.1334	+	27.9439i	0.585993	+	1.01497i
$759$		−	9.04009i		−	0.328135i
$760$	19.9076	−	11.4937i	0.722124	−	0.416919i
$761$	−11.8576	+	6.84601i	−0.429839	+	0.248168i	−0.699278	−	0.714850i	$-0.746495\pi$
$761$	−11.8576	+	6.84601i	−0.429839	+	0.248168i	0.269439	+	0.963017i	$0.413162\pi$
$762$		−	60.1716i		−	2.17979i
$763$	2.03949	+	3.53250i	0.0738344	+	0.127885i
$764$	−53.5653	+	92.7778i	−1.93792	+	3.35658i
$765$	0.187002	+	0.107966i	0.00676109	+	0.00390351i
$766$	−74.1051			−2.67753
$767$		0			0
$768$	−174.932			−6.31230
$769$	24.2724	+	14.0137i	0.875285	+	0.505346i	0.869101	−	0.494635i	$-0.164698\pi$
$769$	24.2724	+	14.0137i	0.875285	+	0.505346i	0.00618377	+	0.999981i	$0.498032\pi$
$770$	−0.680887	+	1.17933i	−0.0245375	+	0.0425001i
$771$	−6.11407	−	10.5899i	−0.220193	−	0.381385i
$772$		−	22.9445i		−	0.825789i
$773$	11.6706	−	6.73801i	0.419761	−	0.242349i	−0.275214	−	0.961383i	$-0.588749\pi$
$773$	11.6706	−	6.73801i	0.419761	−	0.242349i	0.694975	+	0.719034i	$0.255415\pi$
$774$	−0.827089	+	0.477520i	−0.0297291	+	0.0171641i
$775$			6.19428i			0.222505i
$776$	91.9653	+	159.289i	3.30136	+	5.71812i
$777$	−1.87471	+	3.24710i	−0.0672550	+	0.116489i
$778$	−77.3817	−	44.6764i	−2.77427	−	1.60173i
$779$	−18.2632			−0.654348
$780$		0			0
$781$	14.7055			0.526203
$782$	4.90053	+	2.82932i	0.175243	+	0.101176i
$783$	17.7156	−	30.6844i	0.633105	−	1.09657i
$784$	−61.8485	−	107.125i	−2.20887	−	3.82588i
$785$		−	10.2430i		−	0.365588i
$786$	60.4031	−	34.8737i	2.15451	−	1.24390i
$787$	−14.7348	+	8.50715i	−0.525240	+	0.303247i	−0.739076	−	0.673622i	$-0.764737\pi$
$787$	−14.7348	+	8.50715i	−0.525240	+	0.303247i	0.213836	+	0.976870i	$0.431404\pi$
$788$			9.91912i			0.353354i
$789$	16.1562	+	27.9834i	0.575177	+	0.996235i
$790$	9.28612	−	16.0840i	0.330385	−	0.572244i
$791$	−2.91117	−	1.68077i	−0.103509	−	0.0597612i
$792$	−5.59249			−0.198721
$793$		0			0
$794$	105.923			3.75905
$795$	−6.05064	−	3.49334i	−0.214594	−	0.123896i
$796$	−58.5346	+	101.385i	−2.07471	+	3.59349i
$797$	12.2474	+	21.2131i	0.433825	+	0.751407i	0.997199	−	0.0747953i	$-0.0238303\pi$
$797$	12.2474	+	21.2131i	0.433825	+	0.751407i	−0.563374	+	0.826202i	$0.690497\pi$
$798$		−	2.97445i		−	0.105294i
$799$	−0.0773525	+	0.0446595i	−0.00273653	+	0.00157994i
$800$	24.8690	−	14.3581i	0.879253	−	0.507637i
$801$		−	1.92445i		−	0.0679971i
$802$	40.5528	+	70.2394i	1.43197	+	2.48024i
$803$	−0.627342	+	1.08659i	−0.0221384	+	0.0383449i
$804$	−86.7667	−	50.0948i	−3.06003	−	1.76671i
$805$	0.741716			0.0261420
$806$		0			0
$807$	0.372204			0.0131022
$808$	−107.780	−	62.2270i	−3.79170	−	2.18914i
$809$	5.82854	−	10.0953i	0.204920	−	0.354933i	−0.745187	−	0.666856i	$-0.767640\pi$
$809$	5.82854	−	10.0953i	0.204920	−	0.354933i	0.950107	+	0.311923i	$0.100973\pi$
$810$	−13.6581	−	23.6564i	−0.479895	−	0.831203i
$811$		−	40.2610i		−	1.41376i	−0.707335	−	0.706878i	$-0.750103\pi$
$811$		−	40.2610i		−	1.41376i	0.707335	−	0.706878i	$-0.249897\pi$
$812$	9.73486	−	5.62043i	0.341627	−	0.197238i
$813$	−41.7908	+	24.1279i	−1.46567	+	0.846202i
$814$			38.7118i			1.35685i
$815$	0.844097	+	1.46202i	0.0295674	+	0.0512123i
$816$	11.9463	−	20.6916i	0.418203	−	0.724350i
$817$	−2.20695	−	1.27418i	−0.0772114	−	0.0445780i
$818$	74.5392			2.60620
$819$		0			0
$820$	−48.4374			−1.69151
$821$	−15.9064	−	9.18355i	−0.555136	−	0.320508i	0.196055	−	0.980593i	$-0.437187\pi$
$821$	−15.9064	−	9.18355i	−0.555136	−	0.320508i	−0.751191	+	0.660085i	$0.770520\pi$
$822$	35.8381	−	62.0734i	1.25000	−	2.16506i
$823$	10.4039	+	18.0200i	0.362656	+	0.628138i	0.988397	−	0.151892i	$-0.0485367\pi$
$823$	10.4039	+	18.0200i	0.362656	+	0.628138i	−0.625741	+	0.780031i	$0.715203\pi$
$824$			84.7776i			2.95337i
$825$	2.84569	−	1.64296i	0.0990741	−	0.0572004i
$826$	−6.92355	+	3.99731i	−0.240901	+	0.139084i
$827$		−	25.7766i		−	0.896341i	−0.893948	−	0.448171i	$-0.852076\pi$
$827$		−	25.7766i		−	0.896341i	0.893948	−	0.448171i	$-0.147924\pi$
$828$	2.32869	+	4.03340i	0.0809274	+	0.140170i
$829$	23.3144	−	40.3817i	0.809743	−	1.40252i	−0.103299	−	0.994650i	$-0.532940\pi$
$829$	23.3144	−	40.3817i	0.809743	−	1.40252i	0.913042	−	0.407866i	$-0.133727\pi$
$830$	22.2085	+	12.8221i	0.770867	+	0.445060i
$831$	45.7555			1.58724
$832$		0			0
$833$	5.10797			0.176981
$834$	−19.8859	−	11.4811i	−0.688592	−	0.397559i
$835$	2.14934	−	3.72277i	0.0743811	−	0.128832i
$836$	−11.4082	−	19.7597i	−0.394562	−	0.683402i
$837$		−	30.4291i		−	1.05178i
$838$	−85.4825	+	49.3533i	−2.95294	+	1.70488i
$839$	−7.65602	+	4.42021i	−0.264315	+	0.152602i	−0.626301	−	0.779581i	$-0.715432\pi$
$839$	−7.65602	+	4.42021i	−0.264315	+	0.152602i	0.361986	+	0.932183i	$0.382099\pi$
$840$		−	5.15950i		−	0.178020i
$841$	−11.5103	−	19.9364i	−0.396907	−	0.687463i
$842$	−19.6902	+	34.1043i	−0.678567	+	1.17531i
$843$	−20.1006	−	11.6051i	−0.692300	−	0.399700i
$844$	−39.1814			−1.34868
$845$		0			0
$846$	−0.0989481			−0.00340190
$847$	−1.80271	−	1.04079i	−0.0619417	−	0.0357621i
$848$	−34.3755	+	59.5402i	−1.18046	+	2.04462i
$849$	−20.3906	−	35.3176i	−0.699804	−	1.21210i
$850$			2.05682i			0.0705483i
$851$	18.2602	−	10.5425i	0.625953	−	0.361394i
$852$	−73.7759	+	42.5945i	−2.52752	+	1.45927i
$853$			26.7505i			0.915920i	0.888973	+	0.457960i	$0.151420\pi$
$853$			26.7505i			0.915920i	−0.888973	+	0.457960i	$0.848580\pi$
$854$	1.59573	+	2.76388i	0.0546047	+	0.0945781i
$855$	−0.319147	+	0.552778i	−0.0109146	+	0.0189046i
$856$	−157.986	−	91.2135i	−5.39987	−	3.11761i
$857$	14.3257			0.489356			0.244678	−	0.969604i	$-0.421318\pi$
$857$	14.3257			0.489356			0.244678	+	0.969604i	$0.421318\pi$
$858$		0			0
$859$	14.9290			0.509370			0.254685	−	0.967024i	$-0.418028\pi$
$859$	14.9290			0.509370			0.254685	+	0.967024i	$0.418028\pi$
$860$	−5.85324	−	3.37937i	−0.199594	−	0.115235i
$861$	−2.04959	+	3.54999i	−0.0698498	+	0.120983i
$862$	−19.7327	−	34.1780i	−0.672098	−	1.16411i
$863$		−	12.0275i		−	0.409422i	−0.978822	−	0.204711i	$-0.934375\pi$
$863$		−	12.0275i		−	0.409422i	0.978822	−	0.204711i	$-0.0656254\pi$
$864$	−122.168	+	70.5338i	−4.15624	+	2.39961i
$865$	−9.69190	+	5.59562i	−0.329535	+	0.190257i
$866$		−	69.3339i		−	2.35606i
$867$	−14.9309	−	25.8612i	−0.507082	−	0.878291i
$868$	4.82694	−	8.36051i	0.163837	−	0.283774i
$869$	−10.4413	−	6.02826i	−0.354195	−	0.204495i
$870$	−36.5079			−1.23773
$871$		0			0
$872$	−159.563			−5.40348
$873$	−4.42300	−	2.55362i	−0.149696	−	0.0864269i
$874$	−8.36347	+	14.4860i	−0.282899	+	0.489995i
$875$	0.134800	+	0.233481i	0.00455708	+	0.00789310i
$876$		−	7.26842i		−	0.245577i
$877$	13.0905	−	7.55779i	0.442034	−	0.255208i	−0.262426	−	0.964952i	$-0.584523\pi$
$877$	13.0905	−	7.55779i	0.442034	−	0.255208i	0.704460	+	0.709744i	$0.251189\pi$
$878$	23.5826	−	13.6154i	0.795876	−	0.459499i
$879$		−	35.2210i		−	1.18797i
$880$	−16.1672	−	28.0024i	−0.544996	−	0.943961i
$881$	8.85277	−	15.3334i	0.298257	−	0.516597i	−0.677480	−	0.735541i	$-0.736928\pi$
$881$	8.85277	−	15.3334i	0.298257	−	0.516597i	0.975737	+	0.218944i	$0.0702613\pi$
$882$	4.90052	+	2.82932i	0.165009	+	0.0952681i
$883$	−39.3891			−1.32555			−0.662775	−	0.748818i	$-0.730621\pi$
$883$	−39.3891			−1.32555			−0.662775	+	0.748818i	$0.730621\pi$
$884$		0			0
$885$	19.2908			0.648452
$886$	−78.7447	−	45.4633i	−2.64548	−	1.52737i
$887$	−5.02068	+	8.69607i	−0.168578	+	0.291985i	−0.937920	−	0.346851i	$-0.887251\pi$
$887$	−5.02068	+	8.69607i	−0.168578	+	0.291985i	0.769342	+	0.638837i	$0.220584\pi$
$888$	−73.3357	−	127.021i	−2.46099	−	4.26255i
$889$		−	3.20489i		−	0.107489i
$890$	15.8751	−	9.16550i	0.532135	−	0.307228i
$891$	−15.3570	+	8.86638i	−0.514480	+	0.297035i
$892$			59.0410i			1.97684i
$893$	−0.132013	−	0.228654i	−0.00441766	−	0.00765160i
$894$	8.90663	−	15.4267i	0.297882	−	0.515947i
$895$	−6.65282	−	3.84100i	−0.222379	−	0.128391i
$896$	−17.8978			−0.597923
$897$		0			0
$898$	33.9913			1.13430
$899$	−38.6909	−	22.3382i	−1.29041	−	0.745021i
$900$	−0.846436	+	1.46607i	−0.0282145	+	0.0488690i
$901$	−1.41951	−	2.45866i	−0.0472907	−	0.0819099i
$902$			42.3228i			1.40920i
$903$	−0.495349	+	0.285990i	−0.0164842	+	0.00951715i
$904$	113.880	−	65.7488i	3.78760	−	2.18677i
$905$			6.44731i			0.214316i
$906$	−11.3701	−	19.6936i	−0.377746	−	0.654276i
$907$	1.95616	−	3.38817i	0.0649534	−	0.112503i	−0.831720	−	0.555195i	$-0.812643\pi$
$907$	1.95616	−	3.38817i	0.0649534	−	0.112503i	0.896673	+	0.442693i	$0.145977\pi$
$908$	45.5176	+	26.2796i	1.51055	+	0.872119i
$909$	3.45574			0.114620
$910$		0			0
$911$	15.8817			0.526183			0.263092	−	0.964771i	$-0.415258\pi$
$911$	15.8817			0.526183			0.263092	+	0.964771i	$0.415258\pi$
$912$	61.1642	+	35.3132i	2.02535	+	1.16934i
$913$	8.32369	−	14.4170i	0.275474	−	0.477135i
$914$	42.0461	+	72.8259i	1.39076	+	2.40887i
$915$		−	7.70088i		−	0.254583i
$916$	−39.0977	+	22.5731i	−1.29182	+	0.745835i
$917$	3.21722	−	1.85746i	0.106242	−	0.0613389i
$918$		−	10.1040i		−	0.333483i
$919$	−12.7946	−	22.1610i	−0.422056	−	0.731023i	0.574084	−	0.818796i	$-0.305358\pi$
$919$	−12.7946	−	22.1610i	−0.422056	−	0.731023i	−0.996140	+	0.0877733i	$0.972025\pi$
$920$	−14.5073	+	25.1274i	−0.478293	+	0.828427i
$921$	32.9857	+	19.0443i	1.08692	+	0.627532i
$922$	−88.8100			−2.92480
$923$		0			0
$924$	−5.12115			−0.168474
$925$	6.63727	+	3.83203i	0.218232	+	0.125996i
$926$	21.7290	−	37.6357i	0.714059	−	1.23679i
$927$	−1.17702	−	2.03866i	−0.0386584	−	0.0669583i
$928$			207.117i			6.79895i
$929$	−17.5561	+	10.1360i	−0.575997	+	0.332552i	−0.759541	−	0.650459i	$-0.774576\pi$
$929$	−17.5561	+	10.1360i	−0.575997	+	0.332552i	0.183544	+	0.983012i	$0.441243\pi$
$930$	−27.1531	+	15.6769i	−0.890386	+	0.514065i
$931$			15.0991i			0.494854i
$932$	10.4849	+	18.1604i	0.343444	+	0.594862i
$933$	−11.3654	+	19.6854i	−0.372086	+	0.644472i
$934$	71.8909	+	41.5063i	2.35234	+	1.35813i
$935$	1.33522			0.0436665
$936$		0			0
$937$	8.15562			0.266433			0.133216	−	0.991087i	$-0.457470\pi$
$937$	8.15562			0.266433			0.133216	+	0.991087i	$0.457470\pi$
$938$	−6.22030	−	3.59129i	−0.203100	−	0.117260i
$939$	−7.68061	+	13.3032i	−0.250647	+	0.434134i
$940$	−0.350124	−	0.606432i	−0.0114198	−	0.0197796i
$941$			48.8847i			1.59359i	0.604247	+	0.796797i	$0.293474\pi$
$941$			48.8847i			1.59359i	−0.604247	+	0.796797i	$0.706526\pi$
$942$	44.9010	−	25.9236i	1.46295	−	0.844637i
$943$	19.9635	−	11.5260i	0.650103	−	0.375337i
$944$		−	189.827i		−	6.17835i
$945$	−0.662201	−	1.14697i	−0.0215414	−	0.0373108i
$946$	−2.95276	+	5.11434i	−0.0960026	+	0.166281i
$947$	24.7855	+	14.3099i	0.805420	+	0.465010i	0.845363	−	0.534192i	$-0.179384\pi$
$947$	24.7855	+	14.3099i	0.805420	+	0.465010i	−0.0399427	+	0.999202i	$0.512718\pi$
$948$	69.8437			2.26842
$949$		0			0
$950$	−6.07995			−0.197260
$951$	24.1478	+	13.9418i	0.783047	+	0.452093i
$952$	1.04827	−	1.81566i	0.0339748	−	0.0588460i
$953$	−21.1215	−	36.5836i	−0.684194	−	1.18506i	−0.973689	−	0.227879i	$-0.926821\pi$
$953$	−21.1215	−	36.5836i	−0.684194	−	1.18506i	0.289495	−	0.957179i	$-0.406513\pi$
$954$		−	3.14508i		−	0.101826i
$955$	16.0492	−	9.26601i	0.519340	−	0.299841i
$956$	−95.1655	+	54.9438i	−3.07787	+	1.77701i
$957$			23.6998i			0.766105i
$958$	21.0654	+	36.4864i	0.680593	+	1.17882i
$959$	1.90883	−	3.30619i	0.0616393	−	0.106762i
$960$	69.7573	+	40.2744i	2.25141	+	1.29985i
$961$	−7.36907			−0.237712
$962$		0			0
$963$	5.06549			0.163233
$964$	50.7936	+	29.3257i	1.63595	+	0.944517i
$965$	−1.98453	+	3.43730i	−0.0638842	+	0.110651i
$966$	1.87718	+	3.25137i	0.0603973	+	0.104611i
$967$			9.15979i			0.294559i	0.989095	+	0.147280i	$0.0470517\pi$
$967$			9.15979i			0.294559i	−0.989095	+	0.147280i	$0.952948\pi$
$968$	70.5189	−	40.7141i	2.26656	−	1.30860i
$969$	−2.52573	+	1.45823i	−0.0811380	+	0.0468450i
$970$		−	48.6481i		−	1.56200i
$971$	−15.7858	−	27.3417i	−0.506589	−	0.877438i	−0.999971	−	0.00762547i	$-0.997573\pi$
$971$	−15.7858	−	27.3417i	−0.506589	−	0.877438i	0.493382	−	0.869813i	$-0.335761\pi$
$972$	8.76596	−	15.1831i	0.281168	−	0.486998i
$973$	−1.05917	−	0.611515i	−0.0339556	−	0.0196043i
$974$	−19.5000			−0.624820
$975$		0			0
$976$	−75.7790			−2.42563
$977$	−7.33008	−	4.23202i	−0.234510	−	0.135394i	0.378141	−	0.925748i	$-0.376563\pi$
$977$	−7.33008	−	4.23202i	−0.234510	−	0.135394i	−0.612651	+	0.790354i	$0.709897\pi$
$978$	−4.27259	+	7.40034i	−0.136622	+	0.236637i
$979$	−5.94996	−	10.3056i	−0.190161	−	0.329369i
$980$			40.0457i			1.27921i
$981$	3.83702	−	2.21531i	0.122507	−	0.0707293i
$982$	−44.5959	+	25.7474i	−1.42311	+	0.821634i
$983$		−	5.80225i		−	0.185063i	−0.995710	−	0.0925315i	$-0.970504\pi$
$983$		−	5.80225i		−	0.185063i	0.995710	−	0.0925315i	$-0.0294959\pi$
$984$	−80.1765	−	138.870i	−2.55593	−	4.42701i
$985$	0.857931	−	1.48598i	0.0273360	−	0.0473473i
$986$	−12.8474	−	7.41744i	−0.409144	−	0.236219i
$987$	−0.0592607			−0.00188629
$988$		0			0
$989$	3.21656			0.102281
$990$	1.28100	+	0.739584i	0.0407128	+	0.0235055i
$991$	23.5370	−	40.7673i	0.747677	−	1.29501i	−0.201257	−	0.979539i	$-0.564503\pi$
$991$	23.5370	−	40.7673i	0.747677	−	1.29501i	0.948934	−	0.315476i	$-0.102164\pi$
$992$	88.9383	+	154.046i	2.82379	+	4.89096i
$993$			12.4948i			0.396511i
$994$	−5.28899	+	3.05360i	−0.167756	+	0.0968542i
$995$	17.5381	−	10.1256i	0.555995	−	0.321004i
$996$			96.4386i			3.05578i
$997$	−3.23041	−	5.59524i	−0.102308	−	0.177203i	0.810327	−	0.585978i	$-0.199289\pi$
$997$	−3.23041	−	5.59524i	−0.102308	−	0.177203i	−0.912635	+	0.408775i	$0.865956\pi$
$998$	−13.4622	+	23.3172i	−0.426138	+	0.738092i
$999$	−32.6053	−	18.8247i	−1.03159	−	0.595587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.m.j.316.18		36
13.2	odd	12		845.2.e.p.146.9		18
13.3	even	3	inner	845.2.m.j.361.1		36
13.4	even	6		845.2.c.h.506.18		18
13.5	odd	4		845.2.e.p.191.9		18
13.6	odd	12		845.2.a.n.1.1	✓	9
13.7	odd	12		845.2.a.o.1.9	yes	9
13.8	odd	4		845.2.e.o.191.1		18
13.9	even	3		845.2.c.h.506.1		18
13.10	even	6	inner	845.2.m.j.361.18		36
13.11	odd	12		845.2.e.o.146.1		18
13.12	even	2	inner	845.2.m.j.316.1		36
39.20	even	12		7605.2.a.cp.1.1		9
39.32	even	12		7605.2.a.cs.1.9		9
65.19	odd	12		4225.2.a.bt.1.9		9
65.59	odd	12		4225.2.a.bs.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.1	✓	9	13.6	odd	12
845.2.a.o.1.9	yes	9	13.7	odd	12
845.2.c.h.506.1		18	13.9	even	3
845.2.c.h.506.18		18	13.4	even	6
845.2.e.o.146.1		18	13.11	odd	12
845.2.e.o.191.1		18	13.8	odd	4
845.2.e.p.146.9		18	13.2	odd	12
845.2.e.p.191.9		18	13.5	odd	4
845.2.m.j.316.1		36	13.12	even	2	inner
845.2.m.j.316.18		36	1.1	even	1	trivial
845.2.m.j.361.1		36	13.3	even	3	inner
845.2.m.j.361.18		36	13.10	even	6	inner
4225.2.a.bs.1.1		9	65.59	odd	12
4225.2.a.bt.1.9		9	65.19	odd	12
7605.2.a.cp.1.1		9	39.20	even	12
7605.2.a.cs.1.9		9	39.32	even	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.41570 + 1.39471i) q^{2} +(0.907309 - 1.57151i) q^{3} +(2.89042 + 5.00635i) q^{4} -1.00000i q^{5} +(4.38358 - 2.53086i) q^{6} +(0.233481 - 0.134800i) q^{7} +10.5463i q^{8} +(-0.146421 - 0.253609i) q^{9} +O(q^{10})\)	\(q+(2.41570 + 1.39471i) q^{2} +(0.907309 - 1.57151i) q^{3} +(2.89042 + 5.00635i) q^{4} -1.00000i q^{5} +(4.38358 - 2.53086i) q^{6} +(0.233481 - 0.134800i) q^{7} +10.5463i q^{8} +(-0.146421 - 0.253609i) q^{9} +(1.39471 - 2.41570i) q^{10} +(-1.56820 - 0.905401i) q^{11} +10.4900 q^{12} +0.752028 q^{14} +(-1.57151 - 0.907309i) q^{15} +(-8.92820 + 15.4641i) q^{16} +(-0.368683 - 0.638578i) q^{17} -0.816858i q^{18} +(1.88763 - 1.08983i) q^{19} +(5.00635 - 2.89042i) q^{20} -0.489222i q^{21} +(-2.52554 - 4.37436i) q^{22} +(-1.37558 + 2.38258i) q^{23} +(16.5736 + 9.56878i) q^{24} -1.00000 q^{25} +4.91246 q^{27} +(1.34972 + 0.779259i) q^{28} +(3.60627 - 6.24624i) q^{29} +(-2.53086 - 4.38358i) q^{30} -6.19428i q^{31} +(-24.8690 + 14.3581i) q^{32} +(-2.84569 + 1.64296i) q^{33} -2.05682i q^{34} +(-0.134800 - 0.233481i) q^{35} +(0.846436 - 1.46607i) q^{36} +(-6.63727 - 3.83203i) q^{37} +6.07995 q^{38} +10.5463 q^{40} +(-7.25640 - 4.18948i) q^{41} +(0.682322 - 1.18182i) q^{42} +(-0.584581 - 1.01252i) q^{43} -10.4679i q^{44} +(-0.253609 + 0.146421i) q^{45} +(-6.64600 + 3.83707i) q^{46} -0.121132i q^{47} +(16.2013 + 28.0615i) q^{48} +(-3.46366 + 5.99923i) q^{49} +(-2.41570 - 1.39471i) q^{50} -1.33804 q^{51} +3.85022 q^{53} +(11.8671 + 6.85145i) q^{54} +(-0.905401 + 1.56820i) q^{55} +(1.42165 + 2.46237i) q^{56} -3.95524i q^{57} +(17.4233 - 10.0594i) q^{58} +(-9.20651 + 5.31538i) q^{59} -10.4900i q^{60} +(2.12190 + 3.67524i) q^{61} +(8.63921 - 14.9635i) q^{62} +(-0.0683730 - 0.0394752i) q^{63} -44.3888 q^{64} -9.16578 q^{66} +(-8.27136 - 4.77547i) q^{67} +(2.13130 - 3.69151i) q^{68} +(2.49616 + 4.32347i) q^{69} -0.752028i q^{70} +(-7.03296 + 4.06048i) q^{71} +(2.67464 - 1.54420i) q^{72} -0.692889i q^{73} +(-10.6891 - 18.5141i) q^{74} +(-0.907309 + 1.57151i) q^{75} +(10.9121 + 6.30010i) q^{76} -0.488193 q^{77} +6.65811 q^{79} +(15.4641 + 8.92820i) q^{80} +(4.89638 - 8.48079i) q^{81} +(-11.6862 - 20.2411i) q^{82} +9.19337i q^{83} +(2.44922 - 1.41406i) q^{84} +(-0.638578 + 0.368683i) q^{85} -3.26128i q^{86} +(-6.54400 - 11.3345i) q^{87} +(9.54865 - 16.5388i) q^{88} +(5.69120 + 3.28581i) q^{89} -0.816858 q^{90} -15.9040 q^{92} +(-9.73434 - 5.62013i) q^{93} +(0.168944 - 0.292620i) q^{94} +(-1.08983 - 1.88763i) q^{95} +52.1091i q^{96} +(15.1037 - 8.72012i) q^{97} +(-16.7343 + 9.66158i) q^{98} +0.530279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 14 q^{3} + 34 q^{4} - 32 q^{9}+O(q^{10}) \) 36 * q - 14 * q^3 + 34 * q^4 - 32 * q^9	\( 36 q - 14 q^{3} + 34 q^{4} - 32 q^{9} + 6 q^{10} - 48 q^{12} - 8 q^{14} - 74 q^{16} - 2 q^{17} - 24 q^{22} + 28 q^{23} - 36 q^{25} + 88 q^{27} - 24 q^{29} - 4 q^{30} - 14 q^{35} + 6 q^{36} + 188 q^{38} + 48 q^{40} + 22 q^{42} + 78 q^{43} + 6 q^{48} + 32 q^{49} - 172 q^{51} - 32 q^{53} + 18 q^{55} - 58 q^{56} + 6 q^{61} - 20 q^{62} - 136 q^{64} - 196 q^{66} + 40 q^{68} - 26 q^{69} + 30 q^{74} + 14 q^{75} + 16 q^{77} + 156 q^{79} - 58 q^{81} - 8 q^{82} - 32 q^{87} + 84 q^{88} + 40 q^{90} - 108 q^{92} - 32 q^{94} - 8 q^{95}+O(q^{100}) \) 36 * q - 14 * q^3 + 34 * q^4 - 32 * q^9 + 6 * q^10 - 48 * q^12 - 8 * q^14 - 74 * q^16 - 2 * q^17 - 24 * q^22 + 28 * q^23 - 36 * q^25 + 88 * q^27 - 24 * q^29 - 4 * q^30 - 14 * q^35 + 6 * q^36 + 188 * q^38 + 48 * q^40 + 22 * q^42 + 78 * q^43 + 6 * q^48 + 32 * q^49 - 172 * q^51 - 32 * q^53 + 18 * q^55 - 58 * q^56 + 6 * q^61 - 20 * q^62 - 136 * q^64 - 196 * q^66 + 40 * q^68 - 26 * q^69 + 30 * q^74 + 14 * q^75 + 16 * q^77 + 156 * q^79 - 58 * q^81 - 8 * q^82 - 32 * q^87 + 84 * q^88 + 40 * q^90 - 108 * q^92 - 32 * q^94 - 8 * q^95

Introduction

L-functions

Modular forms

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