LMFDB - Embedded newform 845.2.m.j.361.18

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			361.18
Character	$\chi$	$=$	845.361
Dual form			845.2.m.j.316.18

$q$-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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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	0.771323	−	0.636444i	$-0.219595\pi$
$2$	2.41570	−	1.39471i	1.70816	−	0.986207i	0.936838	−	0.349763i	$-0.113738\pi$
$3$	0.907309	+	1.57151i	0.523835	+	0.907309i	0.999615	+	0.0277450i	$0.00883264\pi$
$3$	0.907309	+	1.57151i	0.523835	+	0.907309i	−0.475780	+	0.879565i	$0.657834\pi$
$4$	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	0.543474	−	0.839426i	$-0.317109\pi$
$7$	0.233481	+	0.134800i	0.0882475	+	0.0509497i	−0.455227	+	0.890375i	$0.650442\pi$
$8$		−	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	−0.717424	−	0.696637i	$-0.754679\pi$
$11$	−1.56820	+	0.905401i	−0.472830	+	0.272989i	0.244594	+	0.969626i	$0.421345\pi$
$12$	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	−0.907266	−	0.420558i	$-0.861834\pi$
$17$	−0.368683	+	0.638578i	−0.0894188	+	0.154878i	0.817847	+	0.575436i	$0.195168\pi$
$18$			0.816858i			0.192535i
$19$	1.88763	+	1.08983i	0.433053	+	0.250023i	0.700646	−	0.713509i	$-0.252895\pi$
$19$	1.88763	+	1.08983i	0.433053	+	0.250023i	−0.267594	+	0.963532i	$0.586228\pi$
$20$	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	0.686222	−	0.727392i	$-0.259268\pi$
$23$	−1.37558	−	2.38258i	−0.286829	−	0.496802i	−0.973051	+	0.230590i	$0.925934\pi$
$24$	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	0.977997	+	0.208618i	$0.0668964\pi$
$29$	3.60627	+	6.24624i	0.669667	+	1.15990i	−0.308331	+	0.951279i	$0.599770\pi$
$30$	−2.53086	+	4.38358i	−0.462070	+	0.800329i
$31$			6.19428i			1.11253i	0.831007	+	0.556263i	$0.187765\pi$
$31$			6.19428i			1.11253i	−0.831007	+	0.556263i	$0.812235\pi$
$32$	−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	−0.933885	−	0.357573i	$-0.883604\pi$
$37$	−6.63727	+	3.83203i	−1.09116	+	0.629982i	−0.157275	+	0.987555i	$0.550271\pi$
$38$	6.07995			0.986299
$39$		0			0
$40$	10.5463			1.66752
$41$	−7.25640	+	4.18948i	−1.13326	+	0.654287i	−0.944753	−	0.327785i	$-0.893698\pi$
$41$	−7.25640	+	4.18948i	−1.13326	+	0.654287i	−0.188507	+	0.982072i	$0.560365\pi$
$42$	0.682322	+	1.18182i	0.105285	+	0.182358i
$43$	−0.584581	+	1.01252i	−0.0891478	+	0.154408i	−0.907151	−	0.420805i	$-0.861748\pi$
$43$	−0.584581	+	1.01252i	−0.0891478	+	0.154408i	0.818003	+	0.575213i	$0.195081\pi$
$44$			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	$0.00281214\pi$
$47$			0.121132i			0.0176690i	−0.999961	+	0.00883449i	$0.997188\pi$
$48$	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	−0.238346	−	0.971180i	$-0.576605\pi$
$59$	−9.20651	−	5.31538i	−1.19859	−	0.692003i	−0.960240	+	0.279177i	$0.909938\pi$
$60$			10.4900i			1.35426i
$61$	2.12190	−	3.67524i	0.271681	−	0.470566i	−0.697611	−	0.716477i	$-0.745754\pi$
$61$	2.12190	−	3.67524i	0.271681	−	0.470566i	0.969293	+	0.245911i	$0.0790869\pi$
$62$	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	−0.911340	−	0.411654i	$-0.864951\pi$
$67$	−8.27136	+	4.77547i	−1.01051	+	0.583417i	−0.0991674	+	0.995071i	$0.531618\pi$
$68$	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	0.0207860	−	0.999784i	$-0.493383\pi$
$71$	−7.03296	−	4.06048i	−0.834659	−	0.481891i	−0.855445	+	0.517893i	$0.826716\pi$
$72$	2.67464	+	1.54420i	0.315209	+	0.181986i
$73$			0.692889i			0.0810966i	0.999178	+	0.0405483i	$0.0129105\pi$
$73$			0.692889i			0.0810966i	−0.999178	+	0.0405483i	$0.987090\pi$
$74$	−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	$-0.831658\pi$
$83$		−	9.19337i		−	1.00910i	0.863381	−	0.504552i	$-0.168342\pi$
$84$	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	−0.167059	−	0.985947i	$-0.553427\pi$
$89$	5.69120	−	3.28581i	0.603266	−	0.348296i	0.770325	+	0.637651i	$0.220094\pi$
$90$	−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	0.999194	+	0.0401336i	$0.0127784\pi$
$97$	15.1037	+	8.72012i	1.53355	+	0.885394i	0.534354	+	0.845261i	$0.320555\pi$
$98$	−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	−0.994609	−	0.103695i	$-0.966933\pi$
$101$	−5.90035	−	10.2197i	−0.587107	−	1.01690i	0.407502	−	0.913204i	$-0.366400\pi$
$102$	−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	−0.893119	−	0.449820i	$-0.851488\pi$
$107$	−8.64884	−	14.9802i	−0.836115	−	1.44819i	0.0570036	−	0.998374i	$-0.481845\pi$
$108$	14.1991	−	24.5935i	1.36631	−	2.36651i
$109$		−	15.1297i		−	1.44916i	−0.689189	−	0.724581i	$-0.742033\pi$
$109$		−	15.1297i		−	1.44916i	0.689189	−	0.724581i	$-0.257967\pi$
$110$	−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	0.408218	+	0.912884i	$0.366150\pi$
$113$	−6.23428	+	10.7981i	−0.586472	+	1.01580i	−0.994690	+	0.102915i	$0.967183\pi$
$114$	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	0.999489	+	0.0319632i	$0.0101759\pi$
$127$	5.94378	+	10.2949i	0.527425	+	0.913528i	−0.472064	+	0.881564i	$0.656491\pi$
$128$	−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	0.922011	−	0.387163i	$-0.126545\pi$
$137$	12.2633	+	7.08021i	1.04772	+	0.604903i	0.125712	+	0.992067i	$0.459878\pi$
$138$		−	13.9256i		−	1.18543i
$139$	−2.26822	+	3.92868i	−0.192388	+	0.333226i	−0.946041	−	0.324046i	$-0.894957\pi$
$139$	−2.26822	+	3.92868i	−0.192388	+	0.333226i	0.753653	+	0.657273i	$0.228290\pi$
$140$	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	0.619617	−	0.784904i	$-0.287288\pi$
$149$	3.04772	+	1.75960i	0.249679	+	0.144152i	−0.369938	+	0.929056i	$0.620621\pi$
$150$	−4.38358	−	2.53086i	−0.357918	−	0.206644i
$151$			4.49258i			0.365601i	0.983150	+	0.182801i	$0.0585162\pi$
$151$			4.49258i			0.365601i	−0.983150	+	0.182801i	$0.941484\pi$
$152$	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	0.441649	−	0.897188i	$-0.354394\pi$
$163$	−1.46202	−	0.844097i	−0.114514	−	0.0661147i	−0.556163	+	0.831073i	$0.687727\pi$
$164$			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	−0.348997	−	0.937124i	$-0.613478\pi$
$167$	3.72277	−	2.14934i	0.288077	−	0.166321i	0.637074	+	0.770802i	$0.280144\pi$
$168$	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	−0.996460	−	0.0840654i	$-0.973210\pi$
$173$	−5.59562	+	9.69190i	−0.425427	+	0.736862i	0.571033	+	0.820927i	$0.306543\pi$
$174$			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	0.973114	−	0.230324i	$-0.0739787\pi$
$179$	3.84100	+	6.65282i	0.287090	+	0.497255i	−0.686024	+	0.727579i	$0.740645\pi$
$180$	−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	−0.307308	−	0.951610i	$-0.599428\pi$
$191$	9.26601	−	16.0492i	0.670465	−	1.16128i	0.977772	−	0.209669i	$-0.0672386\pi$
$192$	−40.2744	−	69.7573i	−2.90655	−	5.03430i
$193$	−3.43730	+	1.98453i	−0.247422	+	0.142849i	−0.618583	−	0.785719i	$-0.712293\pi$
$193$	−3.43730	+	1.98453i	−0.247422	+	0.142849i	0.371161	+	0.928569i	$0.378960\pi$
$194$	48.6481			3.49273
$195$		0			0
$196$	−40.0457			−2.86041
$197$	1.48598	−	0.857931i	0.105872	−	0.0611251i	−0.446129	−	0.894969i	$-0.647198\pi$
$197$	1.48598	−	0.857931i	0.105872	−	0.0611251i	0.552001	+	0.833843i	$0.313864\pi$
$198$	−0.739584	−	1.28100i	−0.0525600	−	0.0910365i
$199$	10.1256	−	17.5381i	0.717787	−	1.24324i	−0.244088	−	0.969753i	$-0.578488\pi$
$199$	10.1256	−	17.5381i	0.717787	−	1.24324i	0.961875	−	0.273490i	$-0.0881782\pi$
$200$			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	0.725476	−	0.688248i	$-0.241620\pi$
$211$	−3.38891	−	5.86976i	−0.233302	−	0.404091i	−0.958778	+	0.284157i	$0.908286\pi$
$212$	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	−0.173707	−	0.984797i	$-0.555575\pi$
$223$	8.84491	−	5.10661i	0.592299	−	0.341964i	0.766006	+	0.642833i	$0.222241\pi$
$224$	−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	0.738001	−	0.674800i	$-0.235770\pi$
$227$	7.87387	+	4.54598i	0.522607	+	0.301727i	−0.215394	+	0.976527i	$0.569103\pi$
$228$	19.8013	+	11.4323i	1.31137	+	0.757122i
$229$		−	7.80962i		−	0.516074i	−0.966135	−	0.258037i	$-0.916924\pi$
$229$		−	7.80962i		−	0.516074i	0.966135	−	0.258037i	$-0.0830757\pi$
$230$	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	$-0.789239\pi$
$239$		−	19.0089i		−	1.22959i	0.788688	−	0.614793i	$-0.210761\pi$
$240$	28.0615	+	16.2013i	1.81136	+	1.04579i
$241$	8.78654	+	5.07291i	0.565991	+	0.326775i	0.755547	−	0.655095i	$-0.227371\pi$
$241$	8.78654	+	5.07291i	0.565991	+	0.326775i	−0.189556	+	0.981870i	$0.560705\pi$
$242$			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	−0.863986	−	0.503515i	$-0.832040\pi$
$251$	0.0643811	−	0.111511i	0.00406370	−	0.00703853i	0.868050	+	0.496477i	$0.165373\pi$
$252$			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	0.951769	−	0.306816i	$-0.0992637\pi$
$257$	3.36934	+	5.83587i	0.210174	+	0.364032i	−0.741595	+	0.670848i	$0.765930\pi$
$258$	−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	−0.998343	−	0.0575429i	$-0.981673\pi$
$263$	−8.90337	−	15.4211i	−0.549005	−	0.950905i	0.449338	−	0.893362i	$-0.351660\pi$
$264$	−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	−0.862882	−	0.505405i	$-0.831343\pi$
$269$	0.102557	−	0.177634i	0.00625302	−	0.0108305i	0.869135	+	0.494575i	$0.164676\pi$
$270$	6.85145	+	11.8671i	0.416966	+	0.722206i
$271$	−23.0300	+	13.2964i	−1.39898	+	0.807699i	−0.994285	−	0.106755i	$-0.965954\pi$
$271$	−23.0300	+	13.2964i	−1.39898	+	0.807699i	−0.404690	+	0.914454i	$0.632621\pi$
$272$	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	−0.186607	−	0.982435i	$-0.559749\pi$
$277$	12.6075	−	21.8368i	0.757510	−	1.31205i	0.944117	−	0.329611i	$-0.106917\pi$
$278$			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	$0.124597\pi$
$281$			12.7906i			0.763025i	−0.924364	+	0.381513i	$0.875403\pi$
$282$	−0.306570	+	0.530994i	−0.0182560	+	0.0316203i
$283$	11.2368	+	19.4628i	0.667961	+	1.15694i	0.978473	+	0.206373i	$0.0661662\pi$
$283$	11.2368	+	19.4628i	0.667961	+	1.15694i	−0.310512	+	0.950569i	$0.600500\pi$
$284$	−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	0.902874	−	0.429905i	$-0.141453\pi$
$293$	16.8092	+	9.70479i	0.982003	+	0.566960i	0.0791289	+	0.996864i	$0.474786\pi$
$294$		−	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	$-0.795574\pi$
$307$		−	20.9899i		−	1.19796i	0.800765	−	0.598978i	$-0.204426\pi$
$308$	−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	$-0.857977\pi$
$317$		−	15.3660i		−	0.863043i	0.902103	−	0.431522i	$-0.142023\pi$
$318$	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	0.327084	−	0.944995i	$-0.393934\pi$
$331$	−5.96314	−	3.44282i	−0.327764	−	0.189234i	−0.654848	+	0.755761i	$0.727267\pi$
$332$	−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	0.357004	+	0.934103i	$0.383798\pi$
$347$	−11.7441	+	20.3413i	−0.630455	+	1.09198i	−0.987459	+	0.157877i	$0.949535\pi$
$348$	37.8298	+	65.5231i	2.02789	+	3.51241i
$349$	−15.1798	+	8.76406i	−0.812556	+	0.469129i	−0.847843	−	0.530248i	$-0.822099\pi$
$349$	−15.1798	+	8.76406i	−0.812556	+	0.469129i	0.0352867	+	0.999377i	$0.488766\pi$
$350$	−0.752028			−0.0401976
$351$		0			0
$352$	51.9995			2.77158
$353$	3.47485	−	2.00621i	0.184948	−	0.106780i	−0.404667	−	0.914464i	$-0.632613\pi$
$353$	3.47485	−	2.00621i	0.184948	−	0.106780i	0.589615	+	0.807684i	$0.299279\pi$
$354$	−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	$0.0481658\pi$
$359$			5.71225i			0.301481i	−0.988573	+	0.150740i	$0.951834\pi$
$360$	−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	0.802304	−	0.596916i	$-0.203607\pi$
$367$	−2.21827	−	3.84215i	−0.115793	−	0.200559i	−0.918096	+	0.396357i	$0.870274\pi$
$368$	−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	−0.752609	−	0.658468i	$-0.771205\pi$
$373$	3.74571	−	6.48776i	0.193946	−	0.335924i	0.946554	+	0.322544i	$0.104538\pi$
$374$	−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	−0.220133	−	0.975470i	$-0.570649\pi$
$379$	10.0178	−	5.78381i	0.514582	−	0.297094i	0.734715	+	0.678376i	$0.237316\pi$
$380$	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	−0.220622	−	0.975359i	$-0.570809\pi$
$383$	−23.0073	−	13.2833i	−1.17562	−	0.678744i	−0.954997	+	0.296616i	$0.904142\pi$
$384$	−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	0.976874	+	0.213815i	$0.0685891\pi$
$397$	32.8856	+	18.9865i	1.65048	+	0.952905i	0.673607	+	0.739090i	$0.264744\pi$
$398$		−	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	0.284883	−	0.958562i	$-0.408045\pi$
$401$	25.1807	−	14.5381i	1.25746	−	0.725997i	0.972581	+	0.232565i	$0.0747118\pi$
$402$	−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	0.947492	−	0.319779i	$-0.103609\pi$
$409$	23.1421	+	13.3611i	1.14430	+	0.660663i	0.196809	+	0.980442i	$0.436942\pi$
$410$	−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	−0.867678	−	0.497126i	$-0.834389\pi$
$419$	−17.6931	−	30.6453i	−0.864363	−	1.49712i	0.00331518	−	0.999995i	$-0.498945\pi$
$420$	−1.41406	+	2.44922i	−0.0689989	+	0.119510i
$421$		−	14.1178i		−	0.688058i	−0.938959	−	0.344029i	$-0.888208\pi$
$421$		−	14.1178i		−	0.688058i	0.938959	−	0.344029i	$-0.111792\pi$
$422$	−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	−0.765174	−	0.643823i	$-0.777347\pi$
$431$	−12.2528	+	7.07413i	−0.590195	+	0.340749i	0.174980	+	0.984572i	$0.444014\pi$
$432$	−43.8594	−	75.9668i	−2.11019	−	3.65495i
$433$	−12.4280	+	21.5260i	−0.597253	+	1.03447i	0.395972	+	0.918263i	$0.370408\pi$
$433$	−12.4280	+	21.5260i	−0.597253	+	1.03447i	−0.993225	+	0.116210i	$0.962926\pi$
$434$			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	0.958679	−	0.284491i	$-0.0918246\pi$
$439$	4.88111	+	8.45433i	0.232963	+	0.403503i	−0.725716	+	0.687995i	$0.758491\pi$
$440$	−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	0.727902	−	0.685681i	$-0.240495\pi$
$449$	10.5532	+	6.09290i	0.498037	+	0.287542i	−0.229866	+	0.973222i	$0.573829\pi$
$450$		−	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	0.256088	−	0.966654i	$-0.417566\pi$
$457$	26.1079	−	15.0734i	1.22128	−	0.705105i	0.965190	+	0.261548i	$0.0842331\pi$
$458$	−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	−0.306578	−	0.951846i	$-0.599184\pi$
$461$	−27.5727	−	15.9191i	−1.28419	−	0.741427i	−0.977611	+	0.210419i	$0.932517\pi$
$462$	−2.14004	−	1.23555i	−0.0995635	−	0.0574830i
$463$			15.5796i			0.724045i	0.932169	+	0.362023i	$0.117914\pi$
$463$			15.5796i			0.724045i	−0.932169	+	0.362023i	$0.882086\pi$
$464$	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	−0.170464	−	0.985364i	$-0.554527\pi$
$479$	13.0803	−	7.55192i	0.597654	−	0.345056i	0.768118	+	0.640308i	$0.221193\pi$
$480$	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	0.356519	−	0.934288i	$-0.383964\pi$
$487$	−6.05414	−	3.49536i	−0.274339	−	0.158390i	−0.630858	+	0.775898i	$0.717297\pi$
$488$	−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	0.579029	−	0.815307i	$-0.303432\pi$
$491$	−9.23041	−	15.9875i	−0.416563	−	0.721508i	−0.995591	+	0.0937997i	$0.970099\pi$
$492$	−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	$-0.930683\pi$
$499$		−	9.65233i		−	0.432097i	0.976383	−	0.216049i	$-0.0693170\pi$
$500$	−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	−0.932253	−	0.361807i	$-0.882160\pi$
$503$	−3.42677	+	5.93533i	−0.152792	+	0.264643i	0.779461	+	0.626451i	$0.215493\pi$
$504$	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	−0.980250	−	0.197764i	$-0.936632\pi$
$509$	−29.3092	+	16.9217i	−1.29911	+	0.750039i	−0.318856	+	0.947803i	$0.603299\pi$
$510$	−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	−0.966870	−	0.255270i	$-0.917836\pi$
$523$	−16.1115	−	27.9059i	−0.704505	−	1.22024i	0.262365	−	0.964969i	$-0.415498\pi$
$524$	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	$-0.933244\pi$
$541$		−	9.68462i		−	0.416375i	0.978089	−	0.208187i	$-0.0667564\pi$
$542$	−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	0.191423	−	0.981508i	$-0.438690\pi$
$557$	26.8376	−	15.4947i	1.13715	−	0.656531i	0.945722	+	0.324976i	$0.105356\pi$
$558$	−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	−0.975152	−	0.221538i	$-0.928892\pi$
$563$	−7.01670	+	12.1533i	−0.295719	+	0.512199i	0.679433	+	0.733737i	$0.262226\pi$
$564$			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	0.993438	−	0.114374i	$-0.0364863\pi$
$569$	9.48586	+	16.4300i	0.397668	+	0.688781i	−0.595770	+	0.803155i	$0.703153\pi$
$570$	−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	$0.0709931\pi$
$577$			10.6262i			0.442374i	−0.975231	+	0.221187i	$0.929007\pi$
$578$	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	−0.733213	−	0.680000i	$-0.761980\pi$
$587$	−12.3787	+	7.14682i	−0.510922	+	0.294981i	0.222291	+	0.974980i	$0.428647\pi$
$588$	−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	$-0.996899\pi$
$593$		−	0.474392i		−	0.0194809i	0.999953	−	0.00974047i	$-0.00310054\pi$
$594$	−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	0.591803	−	0.806083i	$-0.298416\pi$
$601$	−9.85973	−	17.0776i	−0.402187	−	0.696608i	−0.993990	+	0.109475i	$0.965083\pi$
$602$	−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	−0.999914	−	0.0130936i	$-0.995832\pi$
$607$	−12.0383	+	20.8509i	−0.488618	+	0.846311i	0.511297	+	0.859404i	$0.329165\pi$
$608$	−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	−0.718551	−	0.695474i	$-0.755194\pi$
$613$	−11.7735	+	6.79744i	−0.475528	+	0.274546i	0.243023	+	0.970021i	$0.421861\pi$
$614$	−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	0.457329	−	0.889297i	$-0.348806\pi$
$617$	−2.09050	−	1.20695i	−0.0841602	−	0.0485899i	−0.541489	+	0.840708i	$0.682139\pi$
$618$	35.2378	+	20.3446i	1.41747	+	0.818379i
$619$			11.6882i			0.469790i	0.972021	+	0.234895i	$0.0754747\pi$
$619$			11.6882i			0.469790i	−0.972021	+	0.234895i	$0.924525\pi$
$620$	−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	−0.349526	−	0.936927i	$-0.613657\pi$
$631$	−33.5522	−	19.3714i	−1.33569	−	0.771162i	−0.986165	+	0.165765i	$0.946991\pi$
$632$		−	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	0.222828	+	0.974858i	$0.428471\pi$
$641$	−18.5540	+	32.1364i	−0.732838	+	1.26931i	−0.955666	+	0.294454i	$0.904862\pi$
$642$		−	87.5562i		−	3.45557i
$643$	33.3930	+	19.2794i	1.31689	+	0.760307i	0.983227	−	0.182385i	$-0.0583819\pi$
$643$	33.3930	+	19.2794i	1.31689	+	0.760307i	0.333663	+	0.942692i	$0.391715\pi$
$644$	−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	−0.913420	−	0.407018i	$-0.866568\pi$
$647$	−20.5829	−	35.6507i	−0.809198	−	1.40157i	0.104222	−	0.994554i	$-0.466765\pi$
$648$	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	0.928813	−	0.370548i	$-0.120830\pi$
$653$	3.66706	+	6.35153i	0.143503	+	0.248555i	−0.785310	+	0.619102i	$0.787497\pi$
$654$	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	0.376010	+	0.926616i	$0.377296\pi$
$659$	−15.7740	+	27.3214i	−0.614468	+	1.06429i	−0.990478	+	0.137674i	$0.956037\pi$
$660$	−9.49767	−	16.4504i	−0.369696	−	0.640333i
$661$	4.86551	−	2.80911i	0.189247	−	0.109262i	−0.402383	−	0.915471i	$-0.631818\pi$
$661$	4.86551	−	2.80911i	0.189247	−	0.109262i	0.591630	+	0.806210i	$0.298485\pi$
$662$	−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	0.670770	+	0.741666i	$0.265964\pi$
$673$	25.3634	+	43.9306i	0.977686	+	1.69340i	0.306916	+	0.951737i	$0.400703\pi$
$674$	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	0.212790	−	0.977098i	$-0.431745\pi$
$683$	−13.7730	−	7.95182i	−0.527007	−	0.304268i	−0.739797	+	0.672830i	$0.765078\pi$
$684$			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	−0.784174	−	0.620541i	$-0.786913\pi$
$691$	−16.7936	+	9.69578i	−0.638858	+	0.368845i	0.145317	+	0.989385i	$0.453580\pi$
$692$	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	0.191590	−	0.981475i	$-0.438636\pi$
$709$	−14.9803	−	8.64889i	−0.562598	−	0.324816i	−0.754187	+	0.656659i	$0.771969\pi$
$710$		−	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	−0.999497	−	0.0317202i	$-0.989901\pi$
$719$	−12.6637	+	21.9342i	−0.472278	+	0.818009i	0.527219	+	0.849730i	$0.323235\pi$
$720$			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	$0.264218\pi$
$733$			39.9598i			1.47595i	−0.674828	+	0.737975i	$0.735782\pi$
$734$	−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	−0.666140	−	0.745827i	$-0.732055\pi$
$739$	−9.60444	+	5.54513i	−0.353305	+	0.203981i	0.312835	+	0.949808i	$0.398721\pi$
$740$	−44.3047			−1.62867
$741$		0			0
$742$	2.89547			0.106296
$743$	17.2066	−	9.93424i	0.631249	−	0.364452i	−0.149986	−	0.988688i	$-0.547923\pi$
$743$	17.2066	−	9.93424i	0.631249	−	0.364452i	0.781236	+	0.624236i	$0.214590\pi$
$744$	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	0.926326	−	0.376722i	$-0.122949\pi$
$751$	3.75199	+	6.49863i	0.136912	+	0.237138i	−0.789414	+	0.613861i	$0.789616\pi$
$752$	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	0.991804	+	0.127767i	$0.0407809\pi$
$757$	16.6884	+	28.9052i	0.606551	+	1.05058i	−0.385253	+	0.922811i	$0.625886\pi$
$758$	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	0.269439	−	0.963017i	$-0.413162\pi$
$761$	−11.8576	−	6.84601i	−0.429839	−	0.248168i	−0.699278	+	0.714850i	$0.746495\pi$
$762$			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	0.00618377	−	0.999981i	$-0.498032\pi$
$769$	24.2724	−	14.0137i	0.875285	−	0.505346i	0.869101	+	0.494635i	$0.164698\pi$
$770$	−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	0.694975	−	0.719034i	$-0.255415\pi$
$773$	11.6706	+	6.73801i	0.419761	+	0.242349i	−0.275214	+	0.961383i	$0.588749\pi$
$774$	−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	0.213836	−	0.976870i	$-0.431404\pi$
$787$	−14.7348	−	8.50715i	−0.525240	−	0.303247i	−0.739076	+	0.673622i	$0.764737\pi$
$788$		−	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	−0.563374	−	0.826202i	$-0.690497\pi$
$797$	12.2474	−	21.2131i	0.433825	−	0.751407i	0.997199	+	0.0747953i	$0.0238303\pi$
$798$			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	0.950107	−	0.311923i	$-0.100973\pi$
$809$	5.82854	+	10.0953i	0.204920	+	0.354933i	−0.745187	+	0.666856i	$0.767640\pi$
$810$	−13.6581	+	23.6564i	−0.479895	+	0.831203i
$811$			40.2610i			1.41376i	0.707335	+	0.706878i	$0.249897\pi$
$811$			40.2610i			1.41376i	−0.707335	+	0.706878i	$0.750103\pi$
$812$	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	−0.751191	−	0.660085i	$-0.770520\pi$
$821$	−15.9064	+	9.18355i	−0.555136	+	0.320508i	0.196055	+	0.980593i	$0.437187\pi$
$822$	35.8381	+	62.0734i	1.25000	+	2.16506i
$823$	10.4039	−	18.0200i	0.362656	−	0.628138i	−0.625741	−	0.780031i	$-0.715203\pi$
$823$	10.4039	−	18.0200i	0.362656	−	0.628138i	0.988397	+	0.151892i	$0.0485367\pi$
$824$		−	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	$0.147924\pi$
$827$			25.7766i			0.896341i	−0.893948	+	0.448171i	$0.852076\pi$
$828$	2.32869	−	4.03340i	0.0809274	−	0.140170i
$829$	23.3144	+	40.3817i	0.809743	+	1.40252i	0.913042	+	0.407866i	$0.133727\pi$
$829$	23.3144	+	40.3817i	0.809743	+	1.40252i	−0.103299	+	0.994650i	$0.532940\pi$
$830$	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	0.361986	−	0.932183i	$-0.382099\pi$
$839$	−7.65602	−	4.42021i	−0.264315	−	0.152602i	−0.626301	+	0.779581i	$0.715432\pi$
$840$			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	$-0.848580\pi$
$853$		−	26.7505i		−	0.915920i	0.888973	−	0.457960i	$-0.151420\pi$
$854$	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	$0.0656254\pi$
$863$			12.0275i			0.409422i	−0.978822	+	0.204711i	$0.934375\pi$
$864$	−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	0.704460	−	0.709744i	$-0.251189\pi$
$877$	13.0905	+	7.55779i	0.442034	+	0.255208i	−0.262426	+	0.964952i	$0.584523\pi$
$878$	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	0.975737	−	0.218944i	$-0.0702613\pi$
$881$	8.85277	+	15.3334i	0.298257	+	0.516597i	−0.677480	+	0.735541i	$0.736928\pi$
$882$	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	0.769342	−	0.638837i	$-0.220584\pi$
$887$	−5.02068	−	8.69607i	−0.168578	−	0.291985i	−0.937920	+	0.346851i	$0.887251\pi$
$888$	−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	0.896673	−	0.442693i	$-0.145977\pi$
$907$	1.95616	+	3.38817i	0.0649534	+	0.112503i	−0.831720	+	0.555195i	$0.812643\pi$
$908$	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	−0.996140	−	0.0877733i	$-0.972025\pi$
$919$	−12.7946	+	22.1610i	−0.422056	+	0.731023i	0.574084	+	0.818796i	$0.305358\pi$
$920$	−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	0.183544	−	0.983012i	$-0.441243\pi$
$929$	−17.5561	−	10.1360i	−0.575997	−	0.332552i	−0.759541	+	0.650459i	$0.774576\pi$
$930$	−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	$-0.706526\pi$
$941$		−	48.8847i		−	1.59359i	0.604247	−	0.796797i	$-0.293474\pi$
$942$	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	−0.0399427	−	0.999202i	$-0.512718\pi$
$947$	24.7855	−	14.3099i	0.805420	−	0.465010i	0.845363	+	0.534192i	$0.179384\pi$
$948$	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	0.289495	+	0.957179i	$0.406513\pi$
$953$	−21.1215	+	36.5836i	−0.684194	+	1.18506i	−0.973689	+	0.227879i	$0.926821\pi$
$954$			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	$-0.952948\pi$
$967$		−	9.15979i		−	0.294559i	0.989095	−	0.147280i	$-0.0470517\pi$
$968$	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	0.493382	+	0.869813i	$0.335761\pi$
$971$	−15.7858	+	27.3417i	−0.506589	+	0.877438i	−0.999971	+	0.00762547i	$0.997573\pi$
$972$	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	−0.612651	−	0.790354i	$-0.709897\pi$
$977$	−7.33008	+	4.23202i	−0.234510	+	0.135394i	0.378141	+	0.925748i	$0.376563\pi$
$978$	−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	$0.0294959\pi$
$983$			5.80225i			0.185063i	−0.995710	+	0.0925315i	$0.970504\pi$
$984$	−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	0.948934	+	0.315476i	$0.102164\pi$
$991$	23.5370	+	40.7673i	0.747677	+	1.29501i	−0.201257	+	0.979539i	$0.564503\pi$
$992$	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	−0.912635	−	0.408775i	$-0.865956\pi$
$997$	−3.23041	+	5.59524i	−0.102308	+	0.177203i	0.810327	+	0.585978i	$0.199289\pi$
$998$	−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.361.18		36
13.2	odd	12		845.2.a.o.1.9	yes	9
13.3	even	3		845.2.c.h.506.18		18
13.4	even	6	inner	845.2.m.j.316.18		36
13.5	odd	4		845.2.e.o.146.1		18
13.6	odd	12		845.2.e.o.191.1		18
13.7	odd	12		845.2.e.p.191.9		18
13.8	odd	4		845.2.e.p.146.9		18
13.9	even	3	inner	845.2.m.j.316.1		36
13.10	even	6		845.2.c.h.506.1		18
13.11	odd	12		845.2.a.n.1.1	✓	9
13.12	even	2	inner	845.2.m.j.361.1		36
39.2	even	12		7605.2.a.cp.1.1		9
39.11	even	12		7605.2.a.cs.1.9		9
65.24	odd	12		4225.2.a.bt.1.9		9
65.54	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	13.11	odd	12
845.2.a.o.1.9	yes	9	13.2	odd	12
845.2.c.h.506.1		18	13.10	even	6
845.2.c.h.506.18		18	13.3	even	3
845.2.e.o.146.1		18	13.5	odd	4
845.2.e.o.191.1		18	13.6	odd	12
845.2.e.p.146.9		18	13.8	odd	4
845.2.e.p.191.9		18	13.7	odd	12
845.2.m.j.316.1		36	13.9	even	3	inner
845.2.m.j.316.18		36	13.4	even	6	inner
845.2.m.j.361.1		36	13.12	even	2	inner
845.2.m.j.361.18		36	1.1	even	1	trivial
4225.2.a.bs.1.1		9	65.54	odd	12
4225.2.a.bt.1.9		9	65.24	odd	12
7605.2.a.cp.1.1		9	39.2	even	12
7605.2.a.cs.1.9		9	39.11	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

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