LMFDB - Embedded newform 968.2.o.h.565.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$968 = 2^{3} \cdot 11^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	968.o (of order $10$ , degree $4$ , 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:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			565.5
Character	$\chi$	$=$	968.565
Dual form			968.2.o.h.245.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.110755 + 1.40987i) q^{2} +(2.23784 + 0.727117i) q^{3} +(-1.97547 - 0.312301i) q^{4} +(2.44985 + 3.37193i) q^{5} +(-1.27299 + 3.07453i) q^{6} +(-0.288382 - 0.887547i) q^{7} +(0.659097 - 2.75056i) q^{8} +(2.05216 + 1.49098i) q^{9} +(-5.02532 + 3.08051i) q^{10} +(-4.19369 - 2.13527i) q^{12} +(-1.72410 + 2.37303i) q^{13} +(1.28327 - 0.308280i) q^{14} +(3.03058 + 9.32717i) q^{15} +(3.80494 + 1.23388i) q^{16} +(1.97907 - 1.43788i) q^{17} +(-2.32938 + 2.72815i) q^{18} +(2.55153 + 0.829041i) q^{19} +(-3.78654 - 7.42623i) q^{20} -2.19587i q^{21} -3.47129 q^{23} +(3.47493 - 5.67607i) q^{24} +(-3.82307 + 11.7662i) q^{25} +(-3.15471 - 2.69359i) q^{26} +(-0.640892 - 0.882112i) q^{27} +(0.292506 + 1.84338i) q^{28} +(-4.34866 + 1.41296i) q^{29} +(-13.4857 + 3.23969i) q^{30} +(2.95923 + 2.15001i) q^{31} +(-2.16103 + 5.22781i) q^{32} +(1.80803 + 2.94948i) q^{34} +(2.28626 - 3.14676i) q^{35} +(-3.58834 - 3.58628i) q^{36} +(4.31595 - 1.40234i) q^{37} +(-1.45143 + 3.50550i) q^{38} +(-5.58373 + 4.05682i) q^{39} +(10.8894 - 4.51604i) q^{40} +(-1.27506 + 3.92423i) q^{41} +(3.09590 + 0.243205i) q^{42} -11.4650i q^{43} +10.5724i q^{45} +(0.384463 - 4.89406i) q^{46} +(1.00821 - 3.10297i) q^{47} +(7.61765 + 5.52786i) q^{48} +(4.95854 - 3.60259i) q^{49} +(-16.1654 - 6.69320i) q^{50} +(5.47434 - 1.77872i) q^{51} +(4.14701 - 4.14940i) q^{52} +(0.382138 - 0.525968i) q^{53} +(1.31464 - 0.805875i) q^{54} +(-2.63133 + 0.208231i) q^{56} +(5.10709 + 3.71052i) q^{57} +(-1.51046 - 6.28753i) q^{58} +(-2.76724 + 0.899131i) q^{59} +(-3.07392 - 19.3720i) q^{60} +(6.29283 + 8.66134i) q^{61} +(-3.35898 + 3.93401i) q^{62} +(0.731513 - 2.25136i) q^{63} +(-7.13118 - 3.62578i) q^{64} -12.2255 q^{65} -5.42623i q^{67} +(-4.35863 + 2.22241i) q^{68} +(-7.76817 - 2.52403i) q^{69} +(4.18331 + 3.57185i) q^{70} +(6.27093 - 4.55610i) q^{71} +(5.45362 - 4.66190i) q^{72} +(-4.03732 - 12.4256i) q^{73} +(1.49910 + 6.24025i) q^{74} +(-17.1108 + 23.5510i) q^{75} +(-4.78154 - 2.43459i) q^{76} +(-5.10116 - 8.32165i) q^{78} +(3.91294 + 2.84292i) q^{79} +(5.16097 + 15.8528i) q^{80} +(-3.14438 - 9.67741i) q^{81} +(-5.39144 - 2.23230i) q^{82} +(0.387741 + 0.533679i) q^{83} +(-0.685774 + 4.33787i) q^{84} +(9.69685 + 3.15070i) q^{85} +(16.1641 + 1.26981i) q^{86} -10.7590 q^{87} -2.74629 q^{89} +(-14.9058 - 1.17095i) q^{90} +(2.60337 + 0.845887i) q^{91} +(6.85741 + 1.08409i) q^{92} +(5.05897 + 6.96307i) q^{93} +(4.26311 + 1.76512i) q^{94} +(3.45539 + 10.6346i) q^{95} +(-8.63726 + 10.1277i) q^{96} +(-1.47973 - 1.07509i) q^{97} +(4.53000 + 7.38991i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$40 q + 4 q^{4} + 2 q^{6} + 10 q^{9} - 40 q^{10} - 16 q^{12} + 12 q^{14} - 8 q^{15} - 4 q^{17} - 10 q^{18} - 12 q^{20} - 48 q^{23} + 6 q^{25} + 20 q^{26} - 12 q^{28} + 18 q^{30} + 4 q^{31} + 80 q^{32} - 32 q^{36}+ \cdots - 96 q^{98}+O(q^{100})$ 40 * q + 4 * q^4 + 2 * q^6 + 10 * q^9 - 40 * q^10 - 16 * q^12 + 12 * q^14 - 8 * q^15 - 4 * q^17 - 10 * q^18 - 12 * q^20 - 48 * q^23 + 6 * q^25 + 20 * q^26 - 12 * q^28 + 18 * q^30 + 4 * q^31 + 80 * q^32 - 32 * q^36 - 8 * q^38 + 24 * q^39 + 20 * q^40 + 4 * q^41 - 20 * q^42 + 2 * q^46 + 4 * q^47 - 32 * q^48 + 6 * q^49 - 6 * q^50 - 20 * q^52 + 152 * q^54 - 32 * q^56 + 16 * q^57 - 36 * q^58 + 4 * q^60 + 22 * q^62 - 40 * q^63 + 16 * q^64 - 64 * q^65 - 28 * q^68 - 28 * q^70 + 12 * q^71 - 4 * q^72 - 4 * q^73 - 14 * q^74 - 176 * q^76 - 32 * q^78 + 16 * q^79 + 56 * q^80 + 6 * q^81 + 4 * q^82 - 52 * q^84 + 20 * q^86 - 128 * q^87 - 16 * q^89 - 36 * q^90 + 36 * q^92 + 24 * q^95 + 60 * q^96 + 20 * q^97 - 96 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$ .

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.110755	+	1.40987i	−0.0783158	+	0.996929i
$2$	−0.110755	+	1.40987i	−0.0783158	+	0.996929i
$3$	2.23784	+	0.727117i	1.29202	+	0.419801i	0.872797	−	0.488084i	$-0.162304\pi$
$3$	2.23784	+	0.727117i	1.29202	+	0.419801i	0.419219	+	0.907885i	$0.362304\pi$
$4$	−1.97547	−	0.312301i	−0.987733	−	0.156151i
$5$	2.44985	+	3.37193i	1.09561	+	1.50797i	0.841082	+	0.540908i	$0.181919\pi$
$5$	2.44985	+	3.37193i	1.09561	+	1.50797i	0.254526	+	0.967066i	$0.418081\pi$
$6$	−1.27299	+	3.07453i	−0.519697	+	1.25517i
$7$	−0.288382	−	0.887547i	−0.108998	−	0.335461i	0.881650	−	0.471904i	$-0.156433\pi$
$7$	−0.288382	−	0.887547i	−0.108998	−	0.335461i	−0.990648	+	0.136443i	$0.956433\pi$
$8$	0.659097	−	2.75056i	0.233026	−	0.972470i
$9$	2.05216	+	1.49098i	0.684054	+	0.496995i
$10$	−5.02532	+	3.08051i	−1.58915	+	0.974144i
$11$		0			0
$11$		0			0
$12$	−4.19369	−	2.13527i	−1.21061	−	0.616401i
$13$	−1.72410	+	2.37303i	−0.478181	+	0.658159i	−0.978154	−	0.207882i	$-0.933343\pi$
$13$	−1.72410	+	2.37303i	−0.478181	+	0.658159i	0.499973	+	0.866041i	$0.333343\pi$
$14$	1.28327	−	0.308280i	0.342967	−	0.0823913i
$15$	3.03058	+	9.32717i	0.782492	+	2.40826i
$16$	3.80494	+	1.23388i	0.951234	+	0.308470i
$17$	1.97907	−	1.43788i	0.479995	−	0.348736i	−0.321329	−	0.946968i	$-0.604130\pi$
$17$	1.97907	−	1.43788i	0.479995	−	0.348736i	0.801324	+	0.598231i	$0.204130\pi$
$18$	−2.32938	+	2.72815i	−0.549040	+	0.643031i
$19$	2.55153	+	0.829041i	0.585360	+	0.190195i	0.586700	−	0.809804i	$-0.300427\pi$
$19$	2.55153	+	0.829041i	0.585360	+	0.190195i	−0.00134028	+	0.999999i	$0.500427\pi$
$20$	−3.78654	−	7.42623i	−0.846697	−	1.66056i
$21$		−	2.19587i		−	0.479179i
$22$		0			0
$23$	−3.47129			−0.723813			−0.361907	−	0.932214i	$-0.617874\pi$
$23$	−3.47129			−0.723813			−0.361907	+	0.932214i	$0.617874\pi$
$24$	3.47493	−	5.67607i	0.709318	−	1.15862i
$25$	−3.82307	+	11.7662i	−0.764614	+	2.35324i
$26$	−3.15471	−	2.69359i	−0.618689	−	0.528256i
$27$	−0.640892	−	0.882112i	−0.123340	−	0.169762i
$28$	0.292506	+	1.84338i	0.0552785	+	0.348366i
$29$	−4.34866	+	1.41296i	−0.807525	+	0.262381i	−0.683549	−	0.729904i	$-0.739565\pi$
$29$	−4.34866	+	1.41296i	−0.807525	+	0.262381i	−0.123976	+	0.992285i	$0.539565\pi$
$30$	−13.4857	+	3.23969i	−2.46215	+	0.591484i
$31$	2.95923	+	2.15001i	0.531493	+	0.386153i	0.820916	−	0.571049i	$-0.193463\pi$
$31$	2.95923	+	2.15001i	0.531493	+	0.386153i	−0.289423	+	0.957201i	$0.593463\pi$
$32$	−2.16103	+	5.22781i	−0.382019	+	0.924154i
$33$		0			0
$34$	1.80803	+	2.94948i	0.310074	+	0.505832i
$35$	2.28626	−	3.14676i	0.386448	−	0.531900i
$36$	−3.58834	−	3.58628i	−0.598057	−	0.597714i
$37$	4.31595	−	1.40234i	0.709539	−	0.230543i	0.0680569	−	0.997681i	$-0.478320\pi$
$37$	4.31595	−	1.40234i	0.709539	−	0.230543i	0.641482	+	0.767138i	$0.278320\pi$
$38$	−1.45143	+	3.50550i	−0.235454	+	0.568667i
$39$	−5.58373	+	4.05682i	−0.894113	+	0.649611i
$40$	10.8894	−	4.51604i	1.72177	−	0.714048i
$41$	−1.27506	+	3.92423i	−0.199131	+	0.612862i	0.800772	+	0.598969i	$0.204423\pi$
$41$	−1.27506	+	3.92423i	−0.199131	+	0.612862i	−0.999903	+	0.0138937i	$0.995577\pi$
$42$	3.09590	+	0.243205i	0.477707	+	0.0375273i
$43$		−	11.4650i		−	1.74839i	−0.485573	−	0.874196i	$-0.661389\pi$
$43$		−	11.4650i		−	1.74839i	0.485573	−	0.874196i	$-0.338611\pi$
$44$		0			0
$45$			10.5724i			1.57605i
$46$	0.384463	−	4.89406i	0.0566860	−	0.721590i
$47$	1.00821	−	3.10297i	0.147063	−	0.452614i	−0.850207	−	0.526448i	$-0.823523\pi$
$47$	1.00821	−	3.10297i	0.147063	−	0.452614i	0.997271	+	0.0738340i	$0.0235235\pi$
$48$	7.61765	+	5.52786i	1.09951	+	0.797878i
$49$	4.95854	−	3.60259i	0.708363	−	0.514656i
$50$	−16.1654	−	6.69320i	−2.28613	−	0.946561i
$51$	5.47434	−	1.77872i	0.766561	−	0.249071i
$52$	4.14701	−	4.14940i	0.575087	−	0.575418i
$53$	0.382138	−	0.525968i	0.0524907	−	0.0722472i	−0.781965	−	0.623323i	$-0.785782\pi$
$53$	0.382138	−	0.525968i	0.0524907	−	0.0722472i	0.834455	+	0.551075i	$0.185782\pi$
$54$	1.31464	−	0.805875i	0.178901	−	0.109666i
$55$		0			0
$56$	−2.63133	+	0.208231i	−0.351626	+	0.0278261i
$57$	5.10709	+	3.71052i	0.676450	+	0.491470i
$58$	−1.51046	−	6.28753i	−0.198333	−	0.825593i
$59$	−2.76724	+	0.899131i	−0.360264	+	0.117057i	−0.483556	−	0.875314i	$-0.660655\pi$
$59$	−2.76724	+	0.899131i	−0.360264	+	0.117057i	0.123292	+	0.992370i	$0.460655\pi$
$60$	−3.07392	−	19.3720i	−0.396842	−	2.50091i
$61$	6.29283	+	8.66134i	0.805714	+	1.10897i	0.991971	+	0.126469i	$0.0403646\pi$
$61$	6.29283	+	8.66134i	0.805714	+	1.10897i	−0.186256	+	0.982501i	$0.559635\pi$
$62$	−3.35898	+	3.93401i	−0.426591	+	0.499619i
$63$	0.731513	−	2.25136i	0.0921619	−	0.283645i
$64$	−7.13118	−	3.62578i	−0.891398	−	0.453222i
$65$	−12.2255			−1.51639
$66$		0			0
$67$		−	5.42623i		−	0.662919i	−0.943469	−	0.331460i	$-0.892459\pi$
$67$		−	5.42623i		−	0.662919i	0.943469	−	0.331460i	$-0.107541\pi$
$68$	−4.35863	+	2.22241i	−0.528562	+	0.269507i
$69$	−7.76817	−	2.52403i	−0.935178	−	0.303858i
$70$	4.18331	+	3.57185i	0.500001	+	0.426917i
$71$	6.27093	−	4.55610i	0.744222	−	0.540709i	−0.149808	−	0.988715i	$-0.547866\pi$
$71$	6.27093	−	4.55610i	0.744222	−	0.540709i	0.894031	+	0.448006i	$0.147866\pi$
$72$	5.45362	−	4.66190i	0.642715	−	0.549410i
$73$	−4.03732	−	12.4256i	−0.472533	−	1.45431i	−0.849256	−	0.527981i	$-0.822949\pi$
$73$	−4.03732	−	12.4256i	−0.472533	−	1.45431i	0.376724	−	0.926326i	$-0.377051\pi$
$74$	1.49910	+	6.24025i	0.174267	+	0.725414i
$75$	−17.1108	+	23.5510i	−1.97579	+	2.71944i
$76$	−4.78154	−	2.43459i	−0.548481	−	0.279266i
$77$		0			0
$78$	−5.10116	−	8.32165i	−0.577593	−	0.942242i
$79$	3.91294	+	2.84292i	0.440240	+	0.319853i	0.785730	−	0.618569i	$-0.212287\pi$
$79$	3.91294	+	2.84292i	0.440240	+	0.319853i	−0.345490	+	0.938422i	$0.612287\pi$
$80$	5.16097	+	15.8528i	0.577014	+	1.77240i
$81$	−3.14438	−	9.67741i	−0.349376	−	1.07527i
$82$	−5.39144	−	2.23230i	−0.595385	−	0.246516i
$83$	0.387741	+	0.533679i	0.0425601	+	0.0585789i	0.829767	−	0.558110i	$-0.188473\pi$
$83$	0.387741	+	0.533679i	0.0425601	+	0.0585789i	−0.787207	+	0.616689i	$0.788473\pi$
$84$	−0.685774	+	4.33787i	−0.0748241	+	0.473301i
$85$	9.69685	+	3.15070i	1.05177	+	0.341741i
$86$	16.1641	+	1.26981i	1.74302	+	0.136927i
$87$	−10.7590			−1.15348
$88$		0			0
$89$	−2.74629			−0.291107			−0.145553	−	0.989350i	$-0.546496\pi$
$89$	−2.74629			−0.291107			−0.145553	+	0.989350i	$0.546496\pi$
$90$	−14.9058	−	1.17095i	−1.57121	−	0.123429i
$91$	2.60337	+	0.845887i	0.272908	+	0.0886731i
$92$	6.85741	+	1.08409i	0.714934	+	0.113024i
$93$	5.05897	+	6.96307i	0.524591	+	0.722037i
$94$	4.26311	+	1.76512i	0.439706	+	0.182058i
$95$	3.45539	+	10.6346i	0.354516	+	1.09109i
$96$	−8.63726	+	10.1277i	−0.881536	+	1.03365i
$97$	−1.47973	−	1.07509i	−0.150244	−	0.109159i	0.510124	−	0.860101i	$-0.329600\pi$
$97$	−1.47973	−	1.07509i	−0.150244	−	0.109159i	−0.660368	+	0.750942i	$0.729600\pi$
$98$	4.53000	+	7.38991i	0.457599	+	0.746493i
$99$		0			0
$100$	11.2269	−	22.0498i	1.12269	−	2.20498i
$101$	−7.45377	+	10.2592i	−0.741677	+	1.02083i	0.256843	+	0.966453i	$0.417318\pi$
$101$	−7.45377	+	10.2592i	−0.741677	+	1.02083i	−0.998520	+	0.0543782i	$0.982682\pi$
$102$	1.90145	+	7.91511i	0.188272	+	0.783712i
$103$	−1.19480	−	3.67721i	−0.117727	−	0.362326i	0.874779	−	0.484522i	$-0.161006\pi$
$103$	−1.19480	−	3.67721i	−0.117727	−	0.362326i	−0.992506	+	0.122196i	$0.961006\pi$
$104$	5.39080	+	6.30631i	0.528612	+	0.618385i
$105$	7.40434	−	5.37957i	0.722589	−	0.524992i
$106$	0.699222	+	0.597019i	0.0679145	+	0.0579876i
$107$	12.1565	+	3.94990i	1.17522	+	0.381851i	0.830588	−	0.556888i	$-0.188005\pi$
$107$	12.1565	+	3.94990i	1.17522	+	0.381851i	0.344629	+	0.938739i	$0.388005\pi$
$108$	0.990576	+	1.94273i	0.0953182	+	0.186940i
$109$		−	1.85065i		−	0.177260i	−0.996065	−	0.0886299i	$-0.971751\pi$
$109$		−	1.85065i		−	0.177260i	0.996065	−	0.0886299i	$-0.0282489\pi$
$110$		0			0
$111$	10.6781			1.01352
$112$	−0.00214582	−	3.73289i	−0.000202761	−	0.352725i
$113$	5.15487	−	15.8651i	0.484929	−	1.49246i	−0.347154	−	0.937808i	$-0.612852\pi$
$113$	5.15487	−	15.8651i	0.484929	−	1.49246i	0.832083	−	0.554651i	$-0.187148\pi$
$114$	−5.79698	+	6.78937i	−0.542937	+	0.635883i
$115$	−8.50414	−	11.7049i	−0.793015	−	1.09149i
$116$	9.03189	−	1.43317i	0.838590	−	0.133067i
$117$	−7.07629	+	2.29923i	−0.654203	+	0.212563i
$118$	−0.961171	−	4.00103i	−0.0884830	−	0.368325i
$119$	−1.84691	−	1.34186i	−0.169306	−	0.123008i
$120$	27.6524	−	2.18829i	2.52431	−	0.199762i
$121$		0			0
$122$	−12.9083	+	7.91278i	−1.16866	+	0.716390i
$123$	−5.70676	+	7.85468i	−0.514561	+	0.708232i
$124$	−5.17441	−	5.17144i	−0.464676	−	0.464409i
$125$	−29.2211	+	9.49450i	−2.61361	+	0.849214i
$126$	3.09311	+	1.28069i	0.275556	+	0.114093i
$127$	−5.26680	+	3.82656i	−0.467353	+	0.339552i	−0.796409	−	0.604758i	$-0.793270\pi$
$127$	−5.26680	+	3.82656i	−0.467353	+	0.339552i	0.329056	+	0.944311i	$0.393270\pi$
$128$	5.90169	−	9.65246i	0.521641	−	0.853165i
$129$	8.33638	−	25.6567i	0.733977	−	2.25895i
$130$	1.35404	−	17.2364i	0.118757	−	1.51173i
$131$			6.91569i			0.604227i	0.953272	+	0.302114i	$0.0976922\pi$
$131$			6.91569i			0.604227i	−0.953272	+	0.302114i	$0.902308\pi$
$132$		0			0
$133$		−	2.50368i		−	0.217097i
$134$	7.65027	+	0.600983i	0.660883	+	0.0519171i
$135$	1.40433	−	4.32209i	0.120866	−	0.371986i
$136$	−2.65057	−	6.39125i	−0.227285	−	0.548045i
$137$	−4.70809	+	3.42063i	−0.402239	+	0.292244i	−0.770453	−	0.637497i	$-0.779970\pi$
$137$	−4.70809	+	3.42063i	−0.402239	+	0.292244i	0.368213	+	0.929741i	$0.379970\pi$
$138$	4.41892	−	10.6726i	0.376164	−	0.908509i
$139$	9.06860	−	2.94657i	0.769188	−	0.249924i	0.101971	−	0.994787i	$-0.467485\pi$
$139$	9.06860	−	2.94657i	0.769188	−	0.249924i	0.667217	+	0.744863i	$0.267485\pi$
$140$	−5.49916	+	5.50233i	−0.464764	+	0.465031i
$141$	4.51244	−	6.21084i	0.380016	−	0.523047i
$142$	5.72896	+	9.34580i	0.480764	+	0.784282i
$143$		0			0
$144$	5.96865	+	8.20522i	0.497388	+	0.683769i
$145$	−15.4180	−	11.2018i	−1.28039	−	0.930261i
$146$	17.9656	−	4.31590i	1.48685	−	0.357186i
$147$	13.7159	−	4.45657i	1.13127	−	0.367572i
$148$	−8.96398	+	1.42240i	−0.736834	+	0.116920i
$149$	−8.18322	−	11.2632i	−0.670396	−	0.922721i	0.329373	−	0.944200i	$-0.393162\pi$
$149$	−8.18322	−	11.2632i	−0.670396	−	0.922721i	−0.999769	+	0.0214790i	$0.993162\pi$
$150$	−31.3087	−	26.7324i	−2.55635	−	2.18269i
$151$	−4.70404	+	14.4775i	−0.382809	+	1.17816i	0.555248	+	0.831685i	$0.312623\pi$
$151$	−4.70404	+	14.4775i	−0.382809	+	1.17816i	−0.938057	+	0.346480i	$0.887377\pi$
$152$	3.96203	−	6.47171i	0.321363	−	0.524925i
$153$	6.20522			0.501662
$154$		0			0
$155$			15.2455i			1.22455i
$156$	12.2974	−	6.27031i	0.984582	−	0.502026i
$157$	−0.831166	−	0.270062i	−0.0663343	−	0.0215533i	0.275662	−	0.961255i	$-0.411103\pi$
$157$	−0.831166	−	0.270062i	−0.0663343	−	0.0215533i	−0.341996	+	0.939701i	$0.611103\pi$
$158$	−4.44152	+	5.20186i	−0.353348	+	0.413838i
$159$	1.23760	−	0.899171i	0.0981483	−	0.0713089i
$160$	−22.9220	+	5.52051i	−1.81214	+	0.436435i
$161$	1.00105	+	3.08093i	0.0788942	+	0.242811i
$162$	13.9921	−	3.36134i	1.09933	−	0.264092i
$163$	4.42418	−	6.08936i	0.346528	−	0.476955i	−0.599806	−	0.800146i	$-0.704755\pi$
$163$	4.42418	−	6.08936i	0.346528	−	0.476955i	0.946334	+	0.323190i	$0.104755\pi$
$164$	3.74438	−	7.35399i	0.292387	−	0.574250i
$165$		0			0
$166$	−0.795363	+	0.487556i	−0.0617321	+	0.0378417i
$167$	0.115612	+	0.0839969i	0.00894631	+	0.00649988i	0.592249	−	0.805755i	$-0.298240\pi$
$167$	0.115612	+	0.0839969i	0.00894631	+	0.00649988i	−0.583303	+	0.812255i	$0.698240\pi$
$168$	−6.03989	−	1.44729i	−0.465987	−	0.111661i
$169$	1.35850	+	4.18104i	0.104500	+	0.321618i
$170$	−5.51605	+	13.3223i	−0.423062	+	1.02178i
$171$	4.00006	+	5.50561i	0.305892	+	0.421025i
$172$	−3.58052	+	22.6487i	−0.273012	+	1.72694i
$173$	1.07383	+	0.348910i	0.0816421	+	0.0265271i	0.349553	−	0.936916i	$-0.386333\pi$
$173$	1.07383	+	0.348910i	0.0816421	+	0.0265271i	−0.267911	+	0.963444i	$0.586333\pi$
$174$	1.19161	−	15.1687i	0.0903360	−	1.14994i
$175$	11.5456			0.872762
$176$		0			0
$177$	−6.84641			−0.514608
$178$	0.304167	−	3.87192i	0.0227983	−	0.290213i
$179$	−14.4199	−	4.68532i	−1.07780	−	0.350197i	−0.284277	−	0.958742i	$-0.591754\pi$
$179$	−14.4199	−	4.68532i	−1.07780	−	0.350197i	−0.793519	+	0.608545i	$0.791754\pi$
$180$	3.30179	−	20.8855i	0.246101	−	1.55671i
$181$	9.94596	+	13.6894i	0.739278	+	1.01753i	0.998660	+	0.0517537i	$0.0164811\pi$
$181$	9.94596	+	13.6894i	0.739278	+	1.01753i	−0.259382	+	0.965775i	$0.583519\pi$
$182$	−1.48093	+	3.57673i	−0.109774	+	0.265125i
$183$	7.78452	+	23.9583i	0.575448	+	1.77105i
$184$	−2.28792	+	9.54799i	−0.168667	+	0.703887i
$185$	15.3020	+	11.1176i	1.12503	+	0.817381i
$186$	−10.3773	+	6.36129i	−0.760903	+	0.466432i
$187$		0			0
$188$	−2.96075	+	5.81494i	−0.215935	+	0.424098i
$189$	−0.598095	+	0.823206i	−0.0435050	+	0.0598795i
$190$	−15.3761	+	3.69381i	−1.11550	+	0.267977i
$191$	−5.15195	−	15.8561i	−0.372782	−	1.14730i	−0.944963	−	0.327177i	$-0.893903\pi$
$191$	−5.15195	−	15.8561i	−0.372782	−	1.14730i	0.572181	−	0.820127i	$-0.306097\pi$
$192$	−13.3221	−	13.2991i	−0.961437	−	0.959780i
$193$	0.146189	−	0.106213i	0.0105229	−	0.00764537i	−0.582511	−	0.812823i	$-0.697930\pi$
$193$	0.146189	−	0.106213i	0.0105229	−	0.00764537i	0.593034	+	0.805177i	$0.297930\pi$
$194$	1.67963	−	1.96716i	0.120590	−	0.141234i
$195$	−27.3587	−	8.88937i	−1.95919	−	0.636581i
$196$	−10.9205	+	5.56824i	−0.780038	+	0.397732i
$197$			8.38885i			0.597681i	0.954303	+	0.298840i	$0.0965998\pi$
$197$			8.38885i			0.597681i	−0.954303	+	0.298840i	$0.903400\pi$
$198$		0			0
$199$	22.0996			1.56660			0.783298	−	0.621646i	$-0.213536\pi$
$199$	22.0996			1.56660			0.783298	+	0.621646i	$0.213536\pi$
$200$	29.8439	+	18.2707i	2.11028	+	1.29193i
$201$	3.94550	−	12.1430i	0.278294	−	0.856502i
$202$	−13.6386	−	11.6451i	−0.959611	−	0.819347i
$203$	2.50814	+	3.45216i	0.176037	+	0.242294i
$204$	−11.3699	+	1.80416i	−0.796050	+	0.126316i
$205$	−16.3560	+	5.31438i	−1.14235	+	0.371172i
$206$	5.31671	−	1.27724i	0.370433	−	0.0889894i
$207$	−7.12364	−	5.17563i	−0.495128	−	0.359731i
$208$	−9.48814	+	6.90187i	−0.657884	+	0.478559i
$209$		0			0
$210$	6.76442	+	11.0350i	0.466789	+	0.761485i
$211$	8.83969	−	12.1668i	0.608549	−	0.837596i	−0.387908	−	0.921698i	$-0.626802\pi$
$211$	8.83969	−	12.1668i	0.608549	−	0.837596i	0.996457	+	0.0841019i	$0.0268021\pi$
$212$	−0.919161	+	0.919690i	−0.0631282	+	0.0631645i
$213$	17.3461	−	5.63610i	1.18854	−	0.386179i
$214$	−6.91524	+	16.7017i	−0.472716	+	1.14170i
$215$	38.6591	−	28.0875i	2.63653	−	1.91555i
$216$	−2.84871	+	1.18141i	−0.193830	+	0.0803851i
$217$	1.05485	−	3.24648i	0.0716076	−	0.220385i
$218$	2.60917	+	0.204969i	0.176715	+	0.0138823i
$219$		−	30.7421i		−	2.07736i
$220$		0			0
$221$			7.17543i			0.482672i
$222$	−1.18265	+	15.0547i	−0.0793744	+	1.01040i
$223$	−3.17564	+	9.77362i	−0.212657	+	0.654490i	0.786655	+	0.617393i	$0.211811\pi$
$223$	−3.17564	+	9.77362i	−0.212657	+	0.654490i	−0.999312	+	0.0370972i	$0.988189\pi$
$224$	5.26313	+	0.410412i	0.351657	+	0.0274218i
$225$	−25.3888	+	18.4460i	−1.69258	+	1.22973i
$226$	21.7967	+	9.02483i	1.44990	+	0.600323i
$227$	14.9020	−	4.84194i	0.989077	−	0.321371i	0.230585	−	0.973052i	$-0.425936\pi$
$227$	14.9020	−	4.84194i	0.989077	−	0.321371i	0.758493	+	0.651682i	$0.225936\pi$
$228$	−8.93008	−	8.92495i	−0.591409	−	0.591069i
$229$	8.27290	−	11.3867i	0.546689	−	0.752453i	−0.442869	−	0.896586i	$-0.646039\pi$
$229$	8.27290	−	11.3867i	0.546689	−	0.752453i	0.989558	+	0.144134i	$0.0460395\pi$
$230$	17.4443	−	10.6933i	1.15024	−	0.705098i
$231$		0			0
$232$	1.02026	+	12.8925i	0.0669831	+	0.846436i
$233$	−9.78854	−	7.11179i	−0.641269	−	0.465909i	0.219017	−	0.975721i	$-0.429715\pi$
$233$	−9.78854	−	7.11179i	−0.641269	−	0.465909i	−0.860286	+	0.509812i	$0.829715\pi$
$234$	−2.45787	−	10.2313i	−0.160676	−	0.668841i
$235$	12.9330	−	4.20218i	0.843654	−	0.274120i
$236$	5.74739	−	0.911991i	0.374123	−	0.0593656i
$237$	6.68938	+	9.20714i	0.434522	+	0.598068i
$238$	2.09640	−	2.45529i	0.135890	−	0.159153i
$239$	6.72046	−	20.6835i	0.434711	−	1.33790i	−0.458672	−	0.888606i	$-0.651675\pi$
$239$	6.72046	−	20.6835i	0.434711	−	1.33790i	0.893383	−	0.449296i	$-0.148325\pi$
$240$	0.0225503	+	39.2286i	0.00145561	+	2.53220i
$241$	6.93967			0.447024			0.223512	−	0.974701i	$-0.428248\pi$
$241$	6.93967			0.447024			0.223512	+	0.974701i	$0.428248\pi$
$242$		0			0
$243$		−	20.6718i		−	1.32609i
$244$	−9.72633	−	19.0754i	−0.622664	−	1.22118i
$245$	24.2954	+	7.89405i	1.55218	+	0.504333i
$246$	−10.4420	−	8.91573i	−0.665759	−	0.568446i
$247$	−6.36643	+	4.62549i	−0.405087	+	0.294313i
$248$	7.86415	−	6.72248i	0.499374	−	0.426878i
$249$	0.479653	+	1.47622i	0.0303968	+	0.0935517i
$250$	−10.1496	−	42.2495i	−0.641918	−	2.67209i
$251$	−10.4202	+	14.3421i	−0.657715	+	0.905268i	−0.999403	−	0.0345459i	$-0.989001\pi$
$251$	−10.4202	+	14.3421i	−0.657715	+	0.905268i	0.341688	+	0.939814i	$0.389001\pi$
$252$	−2.14818	+	4.21904i	−0.135323	+	0.265775i
$253$		0			0
$254$	−4.81162	−	7.84932i	−0.301908	−	0.492510i
$255$	19.4090	+	14.1015i	1.21544	+	0.883070i
$256$	12.9551	+	9.38968i	0.809692	+	0.586855i
$257$	5.48645	+	16.8855i	0.342235	+	1.05329i	0.963047	+	0.269332i	$0.0868029\pi$
$257$	5.48645	+	16.8855i	0.342235	+	1.05329i	−0.620812	+	0.783959i	$0.713197\pi$
$258$	35.2494	+	14.5948i	2.19453	+	0.908634i
$259$	−2.48928	−	3.42621i	−0.154677	−	0.212894i
$260$	24.1510	+	3.81803i	1.49778	+	0.236784i
$261$	−11.0309	−	3.58414i	−0.682793	−	0.221853i
$262$	−9.75023	−	0.765950i	−0.602371	−	0.0473205i
$263$	27.6424			1.70450			0.852252	−	0.523132i	$-0.175237\pi$
$263$	27.6424			1.70450			0.852252	+	0.523132i	$0.175237\pi$
$264$		0			0
$265$	2.70971			0.166456
$266$	3.52986	+	0.277296i	0.216430	+	0.0170021i
$267$	−6.14576	−	1.99688i	−0.376114	−	0.122207i
$268$	−1.69462	+	10.7193i	−0.103515	+	0.654787i
$269$	−6.24717	−	8.59849i	−0.380897	−	0.524259i	0.574925	−	0.818206i	$-0.305031\pi$
$269$	−6.24717	−	8.59849i	−0.380897	−	0.524259i	−0.955822	+	0.293947i	$0.905031\pi$
$270$	5.93804	+	2.45862i	0.361378	+	0.149627i
$271$	−6.10249	−	18.7815i	−0.370700	−	1.14090i	−0.946334	−	0.323189i	$-0.895245\pi$
$271$	−6.10249	−	18.7815i	−0.370700	−	1.14090i	0.575635	−	0.817707i	$-0.304755\pi$
$272$	9.30440	−	3.02910i	0.564162	−	0.183666i
$273$	5.21087	+	3.78592i	0.315376	+	0.229134i
$274$	−4.30120	−	7.01665i	−0.259845	−	0.423891i
$275$		0			0
$276$	14.5575	+	7.41215i	0.876259	+	0.446159i
$277$	−7.36805	+	10.1413i	−0.442703	+	0.609329i	−0.970810	−	0.239849i	$-0.922902\pi$
$277$	−7.36805	+	10.1413i	−0.442703	+	0.609329i	0.528107	+	0.849178i	$0.322902\pi$
$278$	3.14988	+	13.1119i	0.188917	+	0.786399i
$279$	2.86720	+	8.82433i	0.171655	+	0.528299i
$280$	−7.14850	−	8.36252i	−0.427205	−	0.499756i
$281$	−19.2576	+	13.9915i	−1.14881	+	0.834663i	−0.988323	−	0.152375i	$-0.951308\pi$
$281$	−19.2576	+	13.9915i	−1.14881	+	0.834663i	−0.160492	+	0.987037i	$0.551308\pi$
$282$	8.25670	+	7.04984i	0.491679	+	0.419812i
$283$	26.3723	+	8.56886i	1.56767	+	0.509366i	0.958843	−	0.283938i	$-0.0916411\pi$
$283$	26.3723	+	8.56886i	1.56767	+	0.509366i	0.608825	+	0.793304i	$0.291641\pi$
$284$	−13.8109	+	7.04200i	−0.819525	+	0.417866i
$285$			26.3110i			1.55853i
$286$		0			0
$287$	3.85065			0.227297
$288$	−12.2294	+	7.50625i	−0.720622	+	0.442310i
$289$	−3.40407	+	10.4766i	−0.200239	+	0.616273i
$290$	17.5007	−	20.4967i	1.02768	−	1.20361i
$291$	−2.52969	−	3.48182i	−0.148293	−	0.204108i
$292$	4.09507	+	25.8072i	0.239646	+	1.51025i
$293$	5.33913	−	1.73479i	0.311915	−	0.101347i	−0.148876	−	0.988856i	$-0.547566\pi$
$293$	5.33913	−	1.73479i	0.311915	−	0.101347i	0.460792	+	0.887508i	$0.347566\pi$
$294$	4.76408	+	19.8312i	0.277847	+	1.15658i
$295$	−9.81114	−	7.12821i	−0.571227	−	0.415021i
$296$	−1.01258	−	12.7956i	−0.0588553	−	0.743728i
$297$		0			0
$298$	16.7860	−	10.2898i	0.972389	−	0.596073i
$299$	5.98486	−	8.23745i	0.346113	−	0.476384i
$300$	41.1568	−	41.1805i	2.37619	−	2.37756i
$301$	−10.1757	+	3.30629i	−0.586518	+	0.190571i
$302$	−19.8904	−	8.23554i	−1.14457	−	0.473902i
$303$	−24.1400	+	17.5387i	−1.38681	+	1.00757i
$304$	8.68545	+	6.30273i	0.498145	+	0.361486i
$305$	−13.7889	+	42.4380i	−0.789553	+	2.42999i
$306$	−0.687261	+	8.74856i	−0.0392881	+	0.500122i
$307$			27.8554i			1.58979i	0.606747	+	0.794895i	$0.292474\pi$
$307$			27.8554i			1.58979i	−0.606747	+	0.794895i	$0.707526\pi$
$308$		0			0
$309$		−	9.09775i		−	0.517553i
$310$	−21.4942	−	1.68852i	−1.22079	−	0.0959017i
$311$	−7.54235	+	23.2130i	−0.427687	+	1.31629i	0.472710	+	0.881218i	$0.343276\pi$
$311$	−7.54235	+	23.2130i	−0.427687	+	1.31629i	−0.900398	+	0.435068i	$0.856724\pi$
$312$	7.47831	+	18.0322i	0.423376	+	1.02087i
$313$	−7.39048	+	5.36950i	−0.417735	+	0.303502i	−0.776726	−	0.629839i	$-0.783121\pi$
$313$	−7.39048	+	5.36950i	−0.417735	+	0.303502i	0.358991	+	0.933341i	$0.383121\pi$
$314$	0.472809	−	1.14193i	0.0266821	−	0.0644426i
$315$	9.38355	−	3.04890i	0.528703	−	0.171786i
$316$	−6.84203	−	6.83810i	−0.384894	−	0.384673i
$317$	−10.5508	+	14.5219i	−0.592591	+	0.815632i	−0.995005	−	0.0998262i	$-0.968171\pi$
$317$	−10.5508	+	14.5219i	−0.592591	+	0.815632i	0.402414	+	0.915458i	$0.368171\pi$
$318$	1.13064	+	1.84445i	0.0634033	+	0.103431i
$319$		0			0
$320$	−5.24447	−	32.9285i	−0.293175	−	1.84076i
$321$	24.3323	+	17.6785i	1.35810	+	0.986715i
$322$	−4.45458	+	1.07013i	−0.248244	+	0.0596359i
$323$	6.24170	−	2.02805i	0.347298	−	0.112844i
$324$	3.18935	+	20.0994i	0.177186	+	1.11663i
$325$	−21.3301	−	29.3584i	−1.18318	−	1.62851i
$326$	8.09520	+	6.91194i	0.448352	+	0.382817i
$327$	1.34564	−	4.14145i	0.0744139	−	0.229023i
$328$	9.95346	+	6.09359i	0.549588	+	0.336462i
$329$	−3.04478			−0.167864
$330$		0			0
$331$		−	13.1934i		−	0.725173i	−0.931950	−	0.362586i	$-0.881894\pi$
$331$		−	13.1934i		−	0.725173i	0.931950	−	0.362586i	$-0.118106\pi$
$332$	−0.599300	−	1.17536i	−0.0328909	−	0.0645061i
$333$	10.9479	+	3.55719i	0.599942	+	0.194933i
$334$	−0.131229	+	0.153695i	−0.00718055	+	0.00840979i
$335$	18.2969	−	13.2935i	0.999665	−	0.726299i
$336$	2.70945	−	8.35516i	0.147812	−	0.455811i
$337$	−7.37660	−	22.7028i	−0.401829	−	1.23670i	−0.923514	−	0.383564i	$-0.874697\pi$
$337$	−7.37660	−	22.7028i	−0.401829	−	1.23670i	0.521686	−	0.853138i	$-0.325303\pi$
$338$	−6.04518	+	1.45224i	−0.328815	+	0.0789914i
$339$	23.0715	−	31.7552i	1.25307	−	1.72471i
$340$	−18.1718	−	9.25244i	−0.985506	−	0.501784i
$341$		0			0
$342$	−8.20522	+	5.02979i	−0.443688	+	0.271980i
$343$	−9.91237	−	7.20176i	−0.535218	−	0.388859i
$344$	−31.5351	−	7.55653i	−1.70026	−	0.407421i
$345$	−10.5200	−	32.3773i	−0.566378	−	1.74313i
$346$	−0.610850	+	1.47532i	−0.0328395	+	0.0793138i
$347$	21.8780	+	30.1124i	1.17447	+	1.61652i	0.622215	+	0.782846i	$0.286233\pi$
$347$	21.8780	+	30.1124i	1.17447	+	1.61652i	0.552256	+	0.833675i	$0.313767\pi$
$348$	21.2540	+	3.36004i	1.13933	+	0.180117i
$349$	−27.0233	−	8.78041i	−1.44652	−	0.470004i	−0.522600	−	0.852578i	$-0.675038\pi$
$349$	−27.0233	−	8.78041i	−1.44652	−	0.470004i	−0.923925	+	0.382574i	$0.875038\pi$
$350$	−1.27873	+	16.2777i	−0.0683511	+	0.870082i
$351$	3.19824			0.170709
$352$		0			0
$353$	−6.72158			−0.357754			−0.178877	−	0.983871i	$-0.557246\pi$
$353$	−6.72158			−0.357754			−0.178877	+	0.983871i	$0.557246\pi$
$354$	0.758276	−	9.65255i	0.0403019	−	0.513027i
$355$	30.7257	+	9.98338i	1.63075	+	0.529863i
$356$	5.42521	+	0.857671i	0.287536	+	0.0454565i
$357$	−3.15740	−	4.34578i	−0.167107	−	0.230003i
$358$	8.20278	−	19.8113i	0.433530	−	1.04706i
$359$	−6.12657	−	18.8556i	−0.323348	−	0.995163i	−0.972181	−	0.234232i	$-0.924743\pi$
$359$	−6.12657	−	18.8556i	−0.323348	−	0.995163i	0.648833	−	0.760931i	$-0.275257\pi$
$360$	29.0802	+	6.96827i	1.53266	+	0.367260i
$361$	−9.54835	−	6.93728i	−0.502545	−	0.365120i
$362$	−20.4019	+	12.5063i	−1.07230	+	0.657319i
$363$		0			0
$364$	−4.87871	−	2.48406i	−0.255714	−	0.130200i
$365$	32.0074	−	44.0545i	1.67535	−	2.30592i
$366$	−34.6402	+	8.32165i	−1.81067	+	0.434980i
$367$	1.40548	+	4.32561i	0.0733653	+	0.225795i	0.981014	−	0.193934i	$-0.0621249\pi$
$367$	1.40548	+	4.32561i	0.0733653	+	0.225795i	−0.907649	+	0.419730i	$0.862125\pi$
$368$	−13.2080	−	4.28315i	−0.688516	−	0.223275i
$369$	−8.46760	+	6.15207i	−0.440806	+	0.320264i
$370$	−17.3691	+	20.3426i	−0.902978	+	1.05756i
$371$	−0.577023	−	0.187486i	−0.0299575	−	0.00973379i
$372$	−7.81925	−	15.3352i	−0.405409	−	0.795095i
$373$		−	33.3992i		−	1.72934i	−0.502336	−	0.864672i	$-0.667526\pi$
$373$		−	33.3992i		−	1.72934i	0.502336	−	0.864672i	$-0.332474\pi$
$374$		0			0
$375$	−72.2956			−3.73333
$376$	−7.87039	−	4.81831i	−0.405884	−	0.248486i
$377$	4.14454	−	12.7556i	0.213455	−	0.656945i
$378$	−1.09437	−	0.934410i	−0.0562884	−	0.0480609i
$379$	−5.43609	−	7.48213i	−0.279233	−	0.384331i	0.646247	−	0.763129i	$-0.276338\pi$
$379$	−5.43609	−	7.48213i	−0.279233	−	0.384331i	−0.925480	+	0.378797i	$0.876338\pi$
$380$	−3.50481	−	22.0874i	−0.179793	−	1.13306i
$381$	−14.5686	+	4.73363i	−0.746372	+	0.242511i
$382$	22.9256	−	5.50743i	1.17298	−	0.281785i
$383$	−25.5714	−	18.5787i	−1.30664	−	0.949328i	−0.306642	−	0.951825i	$-0.599205\pi$
$383$	−25.5714	−	18.5787i	−1.30664	−	0.949328i	−0.999997	+	0.00249665i	$0.999205\pi$
$384$	20.2255	−	17.3094i	1.03213	−	0.883318i
$385$		0			0
$386$	0.133555	+	0.217872i	0.00679777	+	0.0110894i
$387$	17.0941	−	23.5280i	0.868941	−	1.19600i
$388$	2.58741	+	2.58593i	0.131356	+	0.131281i
$389$	−4.75093	+	1.54367i	−0.240882	+	0.0782673i	−0.426970	−	0.904266i	$-0.640419\pi$
$389$	−4.75093	+	1.54367i	−0.240882	+	0.0782673i	0.186088	+	0.982533i	$0.440419\pi$
$390$	15.5630	−	37.5876i	0.788061	−	1.90332i
$391$	−6.86991	+	4.99128i	−0.347426	+	0.252420i
$392$	−6.64099	−	16.0132i	−0.335421	−	0.808791i
$393$	−5.02852	+	15.4762i	−0.253655	+	0.780671i
$394$	−11.8272	−	0.929109i	−0.595845	−	0.0468078i
$395$			20.1589i			1.01430i
$396$		0			0
$397$			17.7950i			0.893107i	0.894757	+	0.446553i	$0.147349\pi$
$397$			17.7950i			0.893107i	−0.894757	+	0.446553i	$0.852651\pi$
$398$	−2.44764	+	31.1575i	−0.122689	+	1.56178i
$399$	1.82047	−	5.60283i	0.0911374	−	0.280492i
$400$	−29.0646	+	40.0524i	−1.45323	+	2.00262i
$401$	9.84887	−	7.15562i	0.491829	−	0.357335i	−0.314058	−	0.949404i	$-0.601689\pi$
$401$	9.84887	−	7.15562i	0.491829	−	0.357335i	0.805887	+	0.592069i	$0.201689\pi$
$402$	16.6831	+	6.90755i	0.832076	+	0.344517i
$403$	−10.2040	+	3.31550i	−0.508300	+	0.165157i
$404$	17.9286	−	17.9389i	0.891983	−	0.892496i
$405$	24.9283	−	34.3109i	1.23870	−	1.70492i
$406$	−5.14489	+	3.15381i	−0.255337	+	0.156521i
$407$		0			0
$408$	−1.28436	−	16.2299i	−0.0635852	−	0.803497i
$409$	0.475699	+	0.345616i	0.0235218	+	0.0170896i	0.599484	−	0.800387i	$-0.295372\pi$
$409$	0.475699	+	0.345616i	0.0235218	+	0.0170896i	−0.575962	+	0.817476i	$0.695372\pi$
$410$	−5.68107	−	23.6484i	−0.280568	−	1.16791i
$411$	−13.0231	+	4.23147i	−0.642384	+	0.208723i
$412$	1.21189	+	7.63734i	0.0597053	+	0.376265i
$413$	1.59604	+	2.19676i	0.0785361	+	0.108096i
$414$	8.08595	−	9.47018i	0.397403	−	0.465434i
$415$	−0.849623	+	2.61487i	−0.0417064	+	0.128359i
$416$	−8.67988	−	14.1415i	−0.425566	−	0.693342i
$417$	22.4365			1.09872
$418$		0			0
$419$		−	11.1507i		−	0.544748i	−0.962191	−	0.272374i	$-0.912191\pi$
$419$		−	11.1507i		−	0.544748i	0.962191	−	0.272374i	$-0.0878088\pi$
$420$	−16.3071	+	8.31477i	−0.795703	+	0.405719i
$421$	−33.1346	−	10.7661i	−1.61488	−	0.524708i	−0.644157	−	0.764893i	$-0.722792\pi$
$421$	−33.1346	−	10.7661i	−1.61488	−	0.524708i	−0.970727	+	0.240186i	$0.922792\pi$
$422$	16.1745	+	13.8103i	0.787365	+	0.672277i
$423$	6.69549	−	4.86456i	0.325546	−	0.236523i
$424$	−1.19484	−	1.39776i	−0.0580266	−	0.0678811i
$425$	9.35223	+	28.7832i	0.453650	+	1.39619i
$426$	6.02499	+	25.0800i	0.291912	+	1.21513i
$427$	5.87261	−	8.08295i	0.284196	−	0.391162i
$428$	−22.7813	−	11.5994i	−1.10117	−	0.560678i
$429$		0			0
$430$	35.3180	+	57.6152i	1.70319	+	2.77845i
$431$	−20.1160	−	14.6151i	−0.968953	−	0.703986i	−0.0137403	−	0.999906i	$-0.504374\pi$
$431$	−20.1160	−	14.6151i	−0.968953	−	0.703986i	−0.955213	+	0.295920i	$0.904374\pi$
$432$	−1.35013	−	4.14716i	−0.0649582	−	0.199530i
$433$	−0.169250	−	0.520897i	−0.00813362	−	0.0250327i	0.946907	−	0.321507i	$-0.104189\pi$
$433$	−0.169250	−	0.520897i	−0.00813362	−	0.0250327i	−0.955041	+	0.296474i	$0.904189\pi$
$434$	4.46028	+	1.84676i	0.214100	+	0.0886473i
$435$	−26.3579	−	36.2785i	−1.26376	−	1.73942i
$436$	−0.577959	+	3.65589i	−0.0276792	+	0.175085i
$437$	−8.85707	−	2.87784i	−0.423691	−	0.137666i
$438$	43.3423	+	3.40485i	2.07098	+	0.162690i
$439$	−27.5308			−1.31397			−0.656987	−	0.753902i	$-0.728169\pi$
$439$	−27.5308			−1.31397			−0.656987	+	0.753902i	$0.728169\pi$
$440$		0			0
$441$	15.5471			0.740340
$442$	−10.1164	−	0.794717i	−0.481189	−	0.0378008i
$443$	−7.66033	−	2.48899i	−0.363953	−	0.118256i	0.121331	−	0.992612i	$-0.461284\pi$
$443$	−7.66033	−	2.48899i	−0.363953	−	0.118256i	−0.485284	+	0.874357i	$0.661284\pi$
$444$	−21.0942	−	3.33477i	−1.00108	−	0.158261i
$445$	−6.72802	−	9.26032i	−0.318939	−	0.438981i
$446$	−13.4278	−	5.55972i	−0.635826	−	0.263261i
$447$	−10.1230	−	31.1555i	−0.478803	−	1.47360i
$448$	−1.16155	+	7.37487i	−0.0548779	+	0.348430i
$449$	27.3209	+	19.8498i	1.28935	+	0.936771i	0.999792	−	0.0203882i	$-0.00649023\pi$
$449$	27.3209	+	19.8498i	1.28935	+	0.936771i	0.289562	+	0.957159i	$0.406490\pi$
$450$	−23.1945	−	37.8379i	−1.09340	−	1.78369i
$451$		0			0
$452$	−15.1379	+	29.7310i	−0.712029	+	1.39843i
$453$	−21.0537	+	28.9780i	−0.989190	+	1.36150i
$454$	5.17603	+	21.5461i	0.242923	+	1.01121i
$455$	3.52561	+	10.8507i	0.165283	+	0.508689i
$456$	13.5721	−	11.6018i	0.635571	−	0.543303i
$457$	−3.10031	+	2.25251i	−0.145026	+	0.105368i	−0.657933	−	0.753077i	$-0.728569\pi$
$457$	−3.10031	+	2.25251i	−0.145026	+	0.105368i	0.512906	+	0.858445i	$0.328569\pi$
$458$	15.1375	+	12.9249i	0.707327	+	0.603939i
$459$	−2.53674	−	0.824236i	−0.118405	−	0.0384720i
$460$	13.1442	+	25.7786i	0.612850	+	1.20193i
$461$			15.8380i			0.737649i	0.929499	+	0.368825i	$0.120240\pi$
$461$			15.8380i			0.737649i	−0.929499	+	0.368825i	$0.879760\pi$
$462$		0			0
$463$	30.4131			1.41341			0.706707	−	0.707506i	$-0.250180\pi$
$463$	30.4131			1.41341			0.706707	+	0.707506i	$0.250180\pi$
$464$	−18.2898	+	0.0105137i	−0.849082	+	0.000488088i
$465$	−11.0853	+	34.1170i	−0.514068	+	1.58214i
$466$	11.1108	−	13.0129i	0.514700	−	0.602811i
$467$	−11.8624	−	16.3271i	−0.548925	−	0.755530i	0.440941	−	0.897536i	$-0.354645\pi$
$467$	−11.8624	−	16.3271i	−0.548925	−	0.755530i	−0.989866	+	0.142006i	$0.954645\pi$
$468$	14.6970	−	2.33211i	0.679370	−	0.107802i
$469$	−4.81603	+	1.56482i	−0.222384	+	0.0722569i
$470$	4.49213	+	18.6992i	0.207206	+	0.862531i
$471$	−1.66365	−	1.20871i	−0.0766568	−	0.0556945i
$472$	0.649234	+	8.20408i	0.0298834	+	0.377624i
$473$		0			0
$474$	−13.7218	+	8.41142i	−0.630261	+	0.386349i
$475$	−19.5093	+	26.8523i	−0.895149	+	1.23207i
$476$	3.22945	+	3.22759i	0.148021	+	0.147936i
$477$	1.56842	−	0.509610i	0.0718130	−	0.0233334i
$478$	28.4167	+	11.7658i	1.29975	+	0.538154i
$479$	10.1616	−	7.38284i	0.464296	−	0.337331i	−0.330918	−	0.943659i	$-0.607358\pi$
$479$	10.1616	−	7.38284i	0.464296	−	0.337331i	0.795214	+	0.606329i	$0.207358\pi$
$480$	−55.3098	−	4.31299i	−2.52453	−	0.196860i
$481$	−4.11337	+	12.6597i	−0.187554	+	0.577231i
$482$	−0.768605	+	9.78403i	−0.0350090	+	0.445651i
$483$			7.62250i			0.346836i
$484$		0			0
$485$		−	7.62338i		−	0.346160i
$486$	29.1445	+	2.28951i	1.32202	+	0.103854i
$487$	4.40407	−	13.5543i	0.199568	−	0.614206i	−0.800325	−	0.599566i	$-0.795340\pi$
$487$	4.40407	−	13.5543i	0.199568	−	0.614206i	0.999893	−	0.0146398i	$-0.00466015\pi$
$488$	27.9711	−	11.6002i	1.26619	−	0.525114i
$489$	14.3283	−	10.4101i	0.647947	−	0.470761i
$490$	−13.8204	+	33.3790i	−0.624344	+	1.50791i
$491$	−19.4060	+	6.30538i	−0.875779	+	0.284558i	−0.712204	−	0.701973i	$-0.752303\pi$
$491$	−19.4060	+	6.30538i	−0.875779	+	0.284558i	−0.163576	+	0.986531i	$0.552303\pi$
$492$	13.7265	−	13.7344i	0.618840	−	0.619196i
$493$	−6.57462	+	9.04918i	−0.296106	+	0.407555i
$494$	−5.81622	−	9.48814i	−0.261684	−	0.426892i
$495$		0			0
$496$	8.60683	+	11.8320i	0.386458	+	0.531271i
$497$	−5.85217	−	4.25185i	−0.262506	−	0.190722i
$498$	−2.13440	+	0.512749i	−0.0956449	+	0.0229768i
$499$	−31.7416	+	10.3135i	−1.42095	+	0.461694i	−0.915904	−	0.401398i	$-0.868524\pi$
$499$	−31.7416	+	10.3135i	−1.42095	+	0.461694i	−0.505046	+	0.863093i	$0.668524\pi$
$500$	60.6904	−	9.63029i	2.71416	−	0.430680i
$501$	0.197645	+	0.272035i	0.00883012	+	0.0121536i
$502$	−19.0665	−	16.2796i	−0.850978	−	0.726592i
$503$	−4.57804	+	14.0898i	−0.204125	+	0.628231i	0.795624	+	0.605791i	$0.207143\pi$
$503$	−4.57804	+	14.0898i	−0.204125	+	0.628231i	−0.999748	+	0.0224396i	$0.992857\pi$
$504$	−5.71038	−	3.49594i	−0.254360	−	0.155721i
$505$	−52.8541			−2.35197
$506$		0			0
$507$			10.3443i			0.459405i
$508$	11.5994	−	5.91441i	0.514642	−	0.262409i
$509$	−22.7743	−	7.39983i	−1.00945	−	0.327992i	−0.242817	−	0.970072i	$-0.578072\pi$
$509$	−22.7743	−	7.39983i	−1.00945	−	0.327992i	−0.766637	+	0.642080i	$0.778072\pi$
$510$	−22.0309	+	25.8024i	−0.975546	+	1.14255i
$511$	−9.86402	+	7.16663i	−0.436358	+	0.317033i
$512$	−14.6731	+	17.2250i	−0.648464	+	0.761245i
$513$	−0.903945	−	2.78206i	−0.0399101	−	0.122831i
$514$	−24.4141	+	5.86501i	−1.07686	+	0.258695i
$515$	9.47222	−	13.0374i	0.417396	−	0.574496i
$516$	−24.4809	+	48.0806i	−1.07771	+	2.11663i
$517$		0			0
$518$	5.10621	−	3.13010i	0.224354	−	0.137529i
$519$	2.14937	+	1.56161i	0.0943467	+	0.0685469i
$520$	−8.05779	+	33.6270i	−0.353357	+	1.47464i
$521$	6.37059	+	19.6067i	0.279101	+	0.858983i	0.988105	+	0.153780i	$0.0491445\pi$
$521$	6.37059	+	19.6067i	0.279101	+	0.858983i	−0.709005	+	0.705204i	$0.750855\pi$
$522$	6.27490	−	15.1551i	0.274645	−	0.663321i
$523$	−13.2848	−	18.2849i	−0.580903	−	0.799545i	0.412891	−	0.910781i	$-0.364519\pi$
$523$	−13.2848	−	18.2849i	−0.580903	−	0.799545i	−0.993794	+	0.111236i	$0.964519\pi$
$524$	2.15978	−	13.6617i	0.0943504	−	0.596815i
$525$	25.8371	+	8.39497i	1.12762	+	0.366387i
$526$	−3.06154	+	38.9722i	−0.133490	+	1.69927i
$527$	8.94797			0.389779
$528$		0			0
$529$	−10.9502			−0.476095
$530$	−0.300115	+	3.82034i	−0.0130362	+	0.165945i
$531$	−7.01942	−	2.28075i	−0.304617	−	0.0989760i
$532$	−0.781902	+	4.94594i	−0.0338998	+	0.214434i
$533$	−7.11397	−	9.79154i	−0.308140	−	0.424119i
$534$	3.49601	−	8.44356i	0.151287	−	0.365388i
$535$	16.4629	+	50.6677i	0.711755	+	2.19056i
$536$	−14.9252	−	3.57641i	−0.644669	−	0.154477i
$537$	−28.8627	−	20.9700i	−1.24552	−	0.904921i
$538$	12.8147	−	7.85537i	0.552479	−	0.338669i
$539$		0			0
$540$	−4.12400	+	8.09956i	−0.177469	+	0.348550i
$541$	−3.08829	+	4.25066i	−0.132776	+	0.182750i	−0.870228	−	0.492649i	$-0.836029\pi$
$541$	−3.08829	+	4.25066i	−0.132776	+	0.182750i	0.737452	+	0.675399i	$0.236029\pi$
$542$	27.1554	−	6.52356i	1.16642	−	0.280211i
$543$	12.3036	+	37.8666i	0.527999	+	1.62501i
$544$	3.24012	+	13.4535i	0.138919	+	0.576813i
$545$	6.24026	−	4.53381i	0.267303	−	0.194207i
$546$	−5.91478	+	6.92733i	−0.253129	+	0.296463i
$547$	−29.8979	−	9.71442i	−1.27834	−	0.415359i	−0.410346	−	0.911930i	$-0.634592\pi$
$547$	−29.8979	−	9.71442i	−1.27834	−	0.415359i	−0.867996	+	0.496571i	$0.834592\pi$
$548$	10.3689	−	5.28699i	0.442939	−	0.225849i
$549$			27.1570i			1.15903i
$550$		0			0
$551$	−12.2671			−0.522596
$552$	−12.0625	+	19.7033i	−0.513414	+	0.838626i
$553$	1.39480	−	4.29276i	0.0593130	−	0.182547i
$554$	−13.4818	−	11.5112i	−0.572787	−	0.489064i
$555$	26.1597	+	36.0057i	1.11042	+	1.52836i
$556$	−18.8349	+	2.98871i	−0.798779	+	0.126749i
$557$	−13.2107	+	4.29241i	−0.559755	+	0.181875i	−0.575211	−	0.818005i	$-0.695080\pi$
$557$	−13.2107	+	4.29241i	−0.559755	+	0.181875i	0.0154561	+	0.999881i	$0.495080\pi$
$558$	−12.7587	+	3.06504i	−0.540119	+	0.129753i
$559$	27.2067	+	19.7668i	1.15072	+	0.836047i
$560$	12.5818	−	9.15226i	0.531678	−	0.386754i
$561$		0			0
$562$	−17.5933	−	28.7004i	−0.742129	−	1.21065i
$563$	−12.0590	+	16.5978i	−0.508227	+	0.699514i	−0.983619	−	0.180260i	$-0.942306\pi$
$563$	−12.0590	+	16.5978i	−0.508227	+	0.699514i	0.475392	+	0.879774i	$0.342306\pi$
$564$	−10.8538	+	10.8601i	−0.457028	+	0.457291i
$565$	66.1246	−	21.4852i	2.78188	−	0.903888i
$566$	−15.0019	+	36.2324i	−0.630575	+	1.52296i
$567$	−7.68238	+	5.58158i	−0.322630	+	0.234404i
$568$	−8.39867	−	20.2515i	−0.352400	−	0.849733i
$569$	6.46796	−	19.9063i	0.271151	−	0.834517i	−0.719061	−	0.694947i	$-0.755428\pi$
$569$	6.46796	−	19.9063i	0.271151	−	0.834517i	0.990212	−	0.139570i	$-0.0445720\pi$
$570$	−37.0951	−	2.91408i	−1.55374	−	0.122057i
$571$		−	6.00582i		−	0.251336i	−0.992072	−	0.125668i	$-0.959893\pi$
$571$		−	6.00582i		−	0.251336i	0.992072	−	0.125668i	$-0.0401074\pi$
$572$		0			0
$573$		−	39.2293i		−	1.63883i
$574$	−0.426480	+	5.42891i	−0.0178009	+	0.226598i
$575$	13.2710	−	40.8438i	0.553437	−	1.70331i
$576$	−9.22837	−	18.0732i	−0.384516	−	0.753048i
$577$	36.7465	−	26.6979i	1.52978	−	1.11145i	0.573417	−	0.819264i	$-0.305618\pi$
$577$	36.7465	−	26.6979i	1.52978	−	1.11145i	0.956362	−	0.292185i	$-0.0943824\pi$
$578$	−14.3937	−	5.95964i	−0.598699	−	0.247888i
$579$	0.404377	−	0.131390i	0.0168053	−	0.00546039i
$580$	26.9594	+	26.9439i	1.11943	+	1.11878i
$581$	0.361848	−	0.498042i	0.0150120	−	0.0206622i
$582$	5.18909	−	3.18090i	0.215095	−	0.131853i
$583$		0			0
$584$	−36.8384	+	2.91522i	−1.52438	+	0.120633i
$585$	−25.0887	−	18.2280i	−1.03729	−	0.753635i
$586$	1.85449	+	7.71962i	0.0766083	+	0.318894i
$587$	4.70991	−	1.53034i	0.194399	−	0.0631641i	−0.210199	−	0.977659i	$-0.567411\pi$
$587$	4.70991	−	1.53034i	0.194399	−	0.0631641i	0.404598	+	0.914494i	$0.367411\pi$
$588$	−28.4871	+	4.52031i	−1.17479	+	0.186414i
$589$	5.76811	+	7.93912i	0.237671	+	0.327126i
$590$	11.1365	−	13.0430i	0.458482	−	0.536970i
$591$	−6.09967	+	18.7729i	−0.250907	+	0.772213i
$592$	18.1523	−	0.0104347i	0.746053	−	0.000428862i
$593$	17.6332			0.724110			0.362055	−	0.932157i	$-0.382075\pi$
$593$	17.6332			0.724110			0.362055	+	0.932157i	$0.382075\pi$
$594$		0			0
$595$		−	9.51502i		−	0.390078i
$596$	12.6482	+	24.8058i	0.518089	+	1.01608i
$597$	49.4552	+	16.0690i	2.02407	+	0.657659i
$598$	10.9509	+	9.35022i	0.447815	+	0.382359i
$599$	−36.5298	+	26.5404i	−1.49257	+	1.08441i	−0.519338	+	0.854569i	$0.673822\pi$
$599$	−36.5298	+	26.5404i	−1.49257	+	1.08441i	−0.973228	+	0.229844i	$0.926178\pi$
$600$	53.5008	+	62.5867i	2.18416	+	2.55509i
$601$	4.83225	+	14.8721i	0.197112	+	0.606647i	0.999945	+	0.0104444i	$0.00332461\pi$
$601$	4.83225	+	14.8721i	0.197112	+	0.606647i	−0.802834	+	0.596203i	$0.796675\pi$
$602$	−3.53442	−	14.7126i	−0.144052	−	0.599641i
$603$	8.09042	−	11.1355i	0.329467	−	0.453473i
$604$	13.8140	−	27.1308i	0.562084	−	1.10394i
$605$		0			0
$606$	−22.0537	−	35.9767i	−0.895869	−	1.46145i
$607$	−33.9235	−	24.6469i	−1.37691	−	1.00039i	−0.997161	−	0.0752967i	$-0.976010\pi$
$607$	−33.9235	−	24.6469i	−1.37691	−	1.00039i	−0.379751	−	0.925089i	$-0.623990\pi$
$608$	−9.84798	+	11.5473i	−0.399389	+	0.468305i
$609$	3.10269	+	9.54910i	0.125727	+	0.386949i
$610$	−58.3049	−	24.1408i	−2.36069	−	0.977434i
$611$	5.62515	+	7.74236i	0.227569	+	0.313222i
$612$	−12.2582	−	1.93790i	−0.495509	−	0.0783349i
$613$	−26.5263	−	8.61893i	−1.07139	−	0.348115i	−0.280360	−	0.959895i	$-0.590454\pi$
$613$	−26.5263	−	8.61893i	−1.07139	−	0.348115i	−0.791028	+	0.611780i	$0.790454\pi$
$614$	−39.2724	−	3.08513i	−1.58491	−	0.124506i
$615$	−40.4662			−1.63175
$616$		0			0
$617$	−14.7471			−0.593697			−0.296849	−	0.954925i	$-0.595936\pi$
$617$	−14.7471			−0.593697			−0.296849	+	0.954925i	$0.595936\pi$
$618$	12.8266	+	1.00762i	0.515963	+	0.0405326i
$619$	−4.87084	−	1.58263i	−0.195776	−	0.0636113i	0.209488	−	0.977811i	$-0.432820\pi$
$619$	−4.87084	−	1.58263i	−0.195776	−	0.0636113i	−0.405264	+	0.914200i	$0.632820\pi$
$620$	4.76120	−	30.1170i	0.191214	−	1.20953i
$621$	2.22472	+	3.06206i	0.0892749	+	0.122876i
$622$	−31.8919	−	13.2047i	−1.27875	−	0.529460i
$623$	0.791981	+	2.43747i	0.0317300	+	0.0976550i
$624$	−26.2514	+	8.54628i	−1.05090	+	0.342125i
$625$	−53.5575	−	38.9118i	−2.14230	−	1.55647i
$626$	−6.75176	−	11.0143i	−0.269855	−	0.440221i
$627$		0			0
$628$	1.55760	+	0.793073i	0.0621550	+	0.0316471i
$629$	6.52518	−	8.98114i	0.260176	−	0.358101i
$630$	3.25927	+	13.5673i	0.129853	+	0.540533i
$631$	−14.9903	−	46.1355i	−0.596755	−	1.83662i	−0.545787	−	0.837924i	$-0.683769\pi$
$631$	−14.9903	−	46.1355i	−0.596755	−	1.83662i	−0.0509681	−	0.998700i	$-0.516231\pi$
$632$	10.3986	−	8.88902i	0.413635	−	0.353586i
$633$	28.6285	−	20.7998i	1.13788	−	0.826718i
$634$	−19.3054	−	16.4836i	−0.766717	−	0.654648i
$635$	−25.8058	−	8.38481i	−1.02407	−	0.332741i
$636$	−2.72565	+	1.38978i	−0.108079	+	0.0551083i
$637$			17.9780i			0.712314i
$638$		0			0
$639$	19.6620			0.777818
$640$	47.0057	−	3.74701i	1.85806	−	0.148114i
$641$	−2.23158	+	6.86810i	−0.0881422	+	0.271274i	−0.985406	−	0.170221i	$-0.945552\pi$
$641$	−2.23158	+	6.86810i	−0.0881422	+	0.271274i	0.897264	+	0.441495i	$0.145552\pi$
$642$	−27.6193	+	32.3474i	−1.09005	+	1.27665i
$643$	7.03032	+	9.67641i	0.277249	+	0.381600i	0.924820	−	0.380405i	$-0.124215\pi$
$643$	7.03032	+	9.67641i	0.277249	+	0.381600i	−0.647571	+	0.762005i	$0.724215\pi$
$644$	−1.01537	−	6.39891i	−0.0400113	−	0.252152i
$645$	106.936	−	34.7455i	4.21059	−	1.36810i
$646$	2.16799	+	9.02461i	0.0852983	+	0.355068i
$647$	21.1924	+	15.3972i	0.833158	+	0.605325i	0.920451	−	0.390858i	$-0.127822\pi$
$647$	21.1924	+	15.3972i	0.833158	+	0.605325i	−0.0872932	+	0.996183i	$0.527822\pi$
$648$	−28.6908	+	2.27046i	−1.12708	+	0.0891921i
$649$		0			0
$650$	43.7540	−	26.8211i	1.71617	−	1.05201i
$651$	4.72114	−	6.49810i	0.185036	−	0.254680i
$652$	−10.6415	+	10.6476i	−0.416754	+	0.416994i
$653$	−32.5433	+	10.5740i	−1.27352	+	0.413791i	−0.866292	−	0.499537i	$-0.833503\pi$
$653$	−32.5433	+	10.5740i	−1.27352	+	0.413791i	−0.407225	+	0.913328i	$0.633503\pi$
$654$	5.68986	+	2.35586i	0.222491	+	0.0921215i
$655$	−23.3193	+	16.9424i	−0.911159	+	0.661996i
$656$	−9.69356	+	13.3582i	−0.378470	+	0.521550i
$657$	10.2411	−	31.5189i	0.399544	−	1.22967i
$658$	0.337225	−	4.29274i	0.0131464	−	0.167349i
$659$			2.73052i			0.106366i	0.998585	+	0.0531831i	$0.0169367\pi$
$659$			2.73052i			0.106366i	−0.998585	+	0.0531831i	$0.983063\pi$
$660$		0			0
$661$		−	11.2478i		−	0.437488i	−0.975782	−	0.218744i	$-0.929804\pi$
$661$		−	11.2478i		−	0.437488i	0.975782	−	0.218744i	$-0.0701959\pi$
$662$	18.6009	+	1.46124i	0.722946	+	0.0567925i
$663$	−5.21738	+	16.0574i	−0.202626	+	0.623620i
$664$	1.72348	−	0.714758i	0.0668839	−	0.0277380i
$665$	8.44224	−	6.13365i	0.327376	−	0.237853i
$666$	−6.22771	+	15.0411i	−0.241319	+	0.582833i
$667$	15.0954	−	4.90480i	0.584497	−	0.189915i
$668$	−0.202155	−	0.202039i	−0.00782161	−	0.00781712i
$669$	−14.2131	+	19.5627i	−0.549512	+	0.756338i
$670$	16.7156	+	27.2685i	0.645779	+	1.05348i
$671$		0			0
$672$	11.4796	+	4.74534i	0.442835	+	0.183056i
$673$	−16.2153	−	11.7811i	−0.625054	−	0.454128i	0.229629	−	0.973278i	$-0.426249\pi$
$673$	−16.2153	−	11.7811i	−0.625054	−	0.454128i	−0.854683	+	0.519150i	$0.826249\pi$
$674$	32.8250	−	7.88558i	1.26437	−	0.303741i
$675$	12.8293	−	4.16848i	0.493799	−	0.160445i
$676$	−1.37793	−	8.68377i	−0.0529974	−	0.333991i
$677$	15.9533	+	21.9578i	0.613135	+	0.843908i	0.996831	−	0.0795517i	$-0.0253489\pi$
$677$	15.9533	+	21.9578i	0.613135	+	0.843908i	−0.383696	+	0.923460i	$0.625349\pi$
$678$	42.2154	+	36.0449i	1.62127	+	1.38430i
$679$	−0.527465	+	1.62337i	−0.0202423	+	0.0622993i
$680$	15.0574	−	24.5952i	0.577423	−	0.943182i
$681$	36.8688			1.41282
$682$		0			0
$683$			41.8019i			1.59951i	0.600330	+	0.799753i	$0.295036\pi$
$683$			41.8019i			1.59951i	−0.600330	+	0.799753i	$0.704964\pi$
$684$	−6.18258	−	12.1254i	−0.236397	−	0.463625i
$685$	−23.0683	−	7.49533i	−0.881393	−	0.286382i
$686$	11.2514	−	13.1775i	0.429580	−	0.503120i
$687$	26.7929	−	19.4661i	1.02221	−	0.742680i
$688$	14.1464	−	43.6235i	0.539327	−	1.66313i
$689$	0.589290	+	1.81365i	0.0224501	+	0.0690945i
$690$	46.8129	−	11.2459i	1.78214	−	0.428124i
$691$	−16.9137	+	23.2797i	−0.643427	+	0.885601i	−0.998793	−	0.0491260i	$-0.984356\pi$
$691$	−16.9137	+	23.2797i	−0.643427	+	0.885601i	0.355366	+	0.934727i	$0.384356\pi$
$692$	−2.01236	−	1.02462i	−0.0764984	−	0.0389502i
$693$		0			0
$694$	−44.8777	+	27.5100i	−1.70354	+	1.04426i
$695$	32.1523	+	23.3600i	1.21961	+	0.886097i
$696$	−7.09121	+	29.5932i	−0.268792	+	1.12173i
$697$	3.11913	+	9.59971i	0.118146	+	0.363615i
$698$	15.3722	−	37.1269i	0.581847	−	1.40527i
$699$	−16.7341	−	23.0325i	−0.632940	−	0.871167i
$700$	−22.8079	−	3.60569i	−0.862056	−	0.136282i
$701$	21.4773	+	6.97841i	0.811188	+	0.263571i	0.685101	−	0.728448i	$-0.259758\pi$
$701$	21.4773	+	6.97841i	0.811188	+	0.263571i	0.126087	+	0.992019i	$0.459758\pi$
$702$	−0.354222	+	4.50910i	−0.0133692	+	0.170185i
$703$	12.1749			0.459184
$704$		0			0
$705$	31.9973			1.20509
$706$	0.744450	−	9.47655i	0.0280178	−	0.356655i
$707$	11.2551	+	3.65700i	0.423291	+	0.137536i
$708$	13.5249	+	2.13814i	0.508295	+	0.0803563i
$709$	−8.54760	−	11.7648i	−0.321012	−	0.441835i	0.617764	−	0.786364i	$-0.288039\pi$
$709$	−8.54760	−	11.7648i	−0.321012	−	0.441835i	−0.938776	+	0.344529i	$0.888039\pi$
$710$	−17.4783	+	42.2135i	−0.655949	+	1.58425i
$711$	3.79124	+	11.6683i	0.142183	+	0.437594i
$712$	−1.81008	+	7.55385i	−0.0678355	+	0.283093i
$713$	−10.2723	−	7.46329i	−0.384702	−	0.279502i
$714$	6.47669	−	3.97020i	0.242384	−	0.148581i
$715$		0			0
$716$	27.0229	+	13.7591i	1.00989	+	0.514200i
$717$	30.0786	−	41.3996i	1.12331	−	1.54610i
$718$	27.2626	−	6.54930i	1.01743	−	0.244418i
$719$	−1.84920	−	5.69125i	−0.0689635	−	0.212248i	0.910635	−	0.413211i	$-0.135593\pi$
$719$	−1.84920	−	5.69125i	−0.0689635	−	0.212248i	−0.979599	+	0.200963i	$0.935593\pi$
$720$	−13.0451	+	40.2275i	−0.486164	+	1.49919i
$721$	−2.91914	+	2.12088i	−0.108714	+	0.0789856i
$722$	10.8382	−	12.6936i	0.403356	−	0.472406i
$723$	15.5299	+	5.04595i	0.577561	+	0.187661i
$724$	−15.3727	−	30.1492i	−0.571322	−	1.12049i
$725$		−	56.5690i		−	2.10092i
$726$		0			0
$727$	−13.7234			−0.508973			−0.254486	−	0.967076i	$-0.581906\pi$
$727$	−13.7234			−0.508973			−0.254486	+	0.967076i	$0.581906\pi$
$728$	4.04254	−	6.60322i	0.149827	−	0.244732i
$729$	5.59764	−	17.2278i	0.207320	−	0.638066i
$730$	58.5661	+	50.0056i	2.16763	+	1.85079i
$731$	−16.4852	−	22.6900i	−0.609728	−	0.839219i
$732$	−7.89586	−	49.7599i	−0.291839	−	1.83918i
$733$	44.1890	−	14.3579i	1.63216	−	0.530320i	0.657392	−	0.753549i	$-0.271660\pi$
$733$	44.1890	−	14.3579i	1.63216	−	0.530320i	0.974766	+	0.223228i	$0.0716596\pi$
$734$	−6.25422	+	1.50246i	−0.230847	+	0.0554566i
$735$	48.6292	+	35.3312i	1.79372	+	1.30321i
$736$	7.50155	−	18.1472i	0.276511	−	0.668915i
$737$		0			0
$738$	−7.73579	−	12.6196i	−0.284758	−	0.464534i
$739$	7.39311	−	10.1757i	0.271960	−	0.374321i	−0.651090	−	0.759000i	$-0.725688\pi$
$739$	7.39311	−	10.1757i	0.271960	−	0.374321i	0.923050	+	0.384680i	$0.125688\pi$
$740$	−26.7566	−	26.7413i	−0.983594	−	0.983029i
$741$	−17.6103	+	5.72194i	−0.646931	+	0.210201i
$742$	0.328239	−	0.792762i	0.0120500	−	0.0291032i
$743$	−7.57418	+	5.50297i	−0.277870	+	0.201884i	−0.717988	−	0.696056i	$-0.754937\pi$
$743$	−7.57418	+	5.50297i	−0.277870	+	0.201884i	0.440118	+	0.897940i	$0.354937\pi$
$744$	22.4867	−	9.32566i	0.824403	−	0.341895i
$745$	17.9312	−	55.1866i	0.656948	−	2.02188i
$746$	47.0885	+	3.69914i	1.72403	+	0.135435i
$747$			1.67331i			0.0612233i
$748$		0			0
$749$		−	11.9286i		−	0.435861i
$750$	8.00712	−	101.927i	0.292379	−	3.72186i
$751$	1.22435	−	3.76817i	0.0446773	−	0.137503i	−0.926230	−	0.376960i	$-0.876969\pi$
$751$	1.22435	−	3.76817i	0.0446773	−	0.137503i	0.970907	+	0.239457i	$0.0769695\pi$
$752$	7.66488	−	10.5626i	0.279509	−	0.385177i
$753$	−33.7471	+	24.5187i	−1.22981	+	0.893510i
$754$	17.5247	+	7.25601i	0.638211	+	0.264248i
$755$	−60.3415	+	19.6061i	−2.19605	+	0.713540i
$756$	1.43860	−	1.43943i	0.0523215	−	0.0523516i
$757$	−2.09768	+	2.88722i	−0.0762417	+	0.104938i	−0.845435	−	0.534079i	$-0.820658\pi$
$757$	−2.09768	+	2.88722i	−0.0762417	+	0.104938i	0.769193	+	0.639017i	$0.220658\pi$
$758$	11.1509	−	6.83549i	0.405019	−	0.248276i
$759$		0			0
$760$	31.5286	−	2.49503i	1.14366	−	0.0905042i
$761$	40.2905	+	29.2728i	1.46053	+	1.06114i	0.983224	+	0.182401i	$0.0583868\pi$
$761$	40.2905	+	29.2728i	1.46053	+	1.06114i	0.477306	+	0.878737i	$0.341613\pi$
$762$	−5.06025	−	21.0641i	−0.183313	−	0.763072i
$763$	−1.64254	+	0.533693i	−0.0594638	+	0.0193210i
$764$	5.22563	+	32.9321i	0.189057	+	1.19144i
$765$	15.2019	+	20.9236i	0.549625	+	0.756494i
$766$	29.0258	−	33.9947i	1.04874	−	1.22828i
$767$	2.63735	−	8.11694i	0.0952293	−	0.293086i
$768$	22.1639	+	30.4324i	0.799773	+	1.09814i
$769$	−30.5772			−1.10264			−0.551321	−	0.834293i	$-0.685876\pi$
$769$	−30.5772			−1.10264			−0.551321	+	0.834293i	$0.685876\pi$
$770$		0			0
$771$			41.7764i			1.50454i
$772$	−0.321963	+	0.164165i	−0.0115877	+	0.00590842i
$773$	−22.7602	−	7.39524i	−0.818628	−	0.265988i	−0.130380	−	0.991464i	$-0.541620\pi$
$773$	−22.7602	−	7.39524i	−0.818628	−	0.265988i	−0.688248	+	0.725476i	$0.741620\pi$
$774$	31.2781	+	26.7063i	1.12427	+	0.959938i
$775$	−36.6107	+	26.5993i	−1.31510	+	0.955474i
$776$	−3.93239	+	3.36151i	−0.141165	+	0.120671i
$777$	−3.07936	−	9.47729i	−0.110471	−	0.339996i
$778$	−1.65019	−	6.86917i	−0.0591620	−	0.246272i
$779$	−6.50670	+	8.95571i	−0.233127	+	0.320871i
$780$	51.2699	+	26.1048i	1.83576	+	0.934701i
$781$		0			0
$782$	−6.27618	−	10.2385i	−0.224436	−	0.366128i
$783$	4.03341	+	2.93044i	0.144142	+	0.104725i
$784$	23.3121	−	7.58938i	0.832575	−	0.271049i
$785$	−1.12560	−	3.46425i	−0.0401745	−	0.123644i
$786$	−21.2625	−	8.80363i	−0.758408	−	0.314015i
$787$	7.93466	+	10.9211i	0.282840	+	0.389296i	0.926672	−	0.375871i	$-0.122656\pi$
$787$	7.93466	+	10.9211i	0.282840	+	0.389296i	−0.643832	+	0.765167i	$0.722656\pi$
$788$	2.61985	−	16.5719i	0.0933282	−	0.590349i
$789$	61.8592	+	20.0993i	2.20224	+	0.715553i
$790$	−28.4214	−	2.23270i	−1.01119	−	0.0794360i
$791$	−15.5676			−0.553519
$792$		0			0
$793$	−31.4031			−1.11516
$794$	−25.0887	−	1.97089i	−0.890364	−	0.0699444i
$795$	6.06389	+	1.97028i	0.215064	+	0.0698785i
$796$	−43.6569	−	6.90172i	−1.54738	−	0.244625i
$797$	14.0410	+	19.3257i	0.497357	+	0.684553i	0.981724	−	0.190312i	$-0.0609500\pi$
$797$	14.0410	+	19.3257i	0.497357	+	0.684553i	−0.484367	+	0.874865i	$0.660950\pi$
$798$	7.69763	+	3.18717i	0.272493	+	0.112824i
$799$	−2.46636	−	7.59067i	−0.0872535	−	0.268539i
$800$	−53.2496	−	45.4133i	−1.88266	−	1.60560i
$801$	−5.63584	−	4.09468i	−0.199133	−	0.144678i
$802$	8.99768	+	14.6782i	0.317719	+	0.518304i
$803$		0			0
$804$	−11.5865	+	22.7559i	−0.408624	+	0.802540i
$805$	−7.93625	+	10.9233i	−0.279716	+	0.384996i
$806$	−3.54427	−	14.7536i	−0.124841	−	0.519673i
$807$	−7.72803	−	23.7844i	−0.272040	−	0.837252i
$808$	23.3059	+	27.2639i	0.819898	+	0.959140i
$809$	16.3306	−	11.8649i	0.574155	−	0.417148i	−0.262457	−	0.964944i	$-0.584533\pi$
$809$	16.3306	−	11.8649i	0.574155	−	0.417148i	0.836612	+	0.547796i	$0.184533\pi$
$810$	45.6129	+	38.9458i	1.60268	+	1.36842i
$811$	3.59503	+	1.16810i	0.126238	+	0.0410174i	0.371455	−	0.928451i	$-0.378859\pi$
$811$	3.59503	+	1.16810i	0.126238	+	0.0410174i	−0.245216	+	0.969468i	$0.578859\pi$
$812$	−3.87664	−	7.60293i	−0.136043	−	0.266811i
$813$		−	46.4672i		−	1.62968i
$814$		0			0
$815$	31.3715			1.09890
$816$	23.0242	−	0.0132353i	0.806009	−	0.000463328i
$817$	9.50493	−	29.2532i	0.332535	−	1.02344i
$818$	−0.539959	+	0.632395i	−0.0188792	+	0.0221112i
$819$	4.08134	+	5.61749i	0.142614	+	0.196291i
$820$	33.9703	−	5.39038i	1.18630	−	0.188240i
$821$	−30.9206	+	10.0467i	−1.07914	+	0.350633i	−0.794040	−	0.607866i	$-0.792026\pi$
$821$	−30.9206	+	10.0467i	−1.07914	+	0.350633i	−0.285097	+	0.958499i	$0.592026\pi$
$822$	−4.52345	−	18.8296i	−0.157773	−	0.656757i
$823$	−16.7993	−	12.2054i	−0.585587	−	0.425454i	0.255147	−	0.966902i	$-0.417876\pi$
$823$	−16.7993	−	12.2054i	−0.585587	−	0.425454i	−0.840734	+	0.541448i	$0.817876\pi$
$824$	−10.9019	+	0.862726i	−0.379785	+	0.0300545i
$825$		0			0
$826$	−3.27392	+	2.00691i	−0.113914	+	0.0698293i
$827$	6.59140	−	9.07228i	0.229205	−	0.315474i	−0.678888	−	0.734242i	$-0.737538\pi$
$827$	6.59140	−	9.07228i	0.229205	−	0.315474i	0.908093	+	0.418768i	$0.137538\pi$
$828$	12.4562	+	12.4490i	0.432882	+	0.432633i
$829$	6.48815	−	2.10813i	0.225343	−	0.0732183i	−0.194169	−	0.980968i	$-0.562201\pi$
$829$	6.48815	−	2.10813i	0.225343	−	0.0732183i	0.419512	+	0.907750i	$0.362201\pi$
$830$	−3.59253	−	1.48747i	−0.124698	−	0.0516308i
$831$	−23.8624	+	17.3370i	−0.827776	+	0.601415i
$832$	20.8990	−	10.6713i	0.724541	−	0.369960i
$833$	4.63321	−	14.2596i	0.160531	−	0.494064i
$834$	−2.48497	+	31.6326i	−0.0860473	+	1.09535i
$835$			0.595616i			0.0206121i
$836$		0			0
$837$		−	3.98829i		−	0.137856i
$838$	15.7211	+	1.23500i	0.543075	+	0.0426624i
$839$	−5.98628	+	18.4239i	−0.206669	+	0.636063i	0.792971	+	0.609259i	$0.208533\pi$
$839$	−5.98628	+	18.4239i	−0.206669	+	0.636063i	−0.999641	+	0.0268038i	$0.991467\pi$
$840$	−9.91665	−	23.9117i	−0.342157	−	0.825034i
$841$	−6.54716	+	4.75679i	−0.225764	+	0.164027i
$842$	18.8486	−	45.5231i	0.649567	−	1.56883i
$843$	−53.2689	+	17.3081i	−1.83468	+	0.596123i
$844$	−21.2622	+	21.2744i	−0.731876	+	0.732296i
$845$	−10.7701	+	14.8237i	−0.370501	+	0.509951i
$846$	6.11683	+	9.97855i	0.210301	+	0.343070i
$847$		0			0
$848$	2.10299	−	1.52976i	0.0722170	−	0.0525322i
$849$	52.7862	+	38.3514i	1.81162	+	1.31622i
$850$	−41.6164	+	9.99754i	−1.42743	+	0.342913i
$851$	−14.9819	+	4.86792i	−0.513573	+	0.166870i
$852$	−36.0269	+	5.71671i	−1.23426	+	0.195851i
$853$	−6.55434	−	9.02128i	−0.224416	−	0.308883i	0.681931	−	0.731417i	$-0.261141\pi$
$853$	−6.55434	−	9.02128i	−0.224416	−	0.308883i	−0.906347	+	0.422534i	$0.861141\pi$
$854$	10.7455	+	9.17485i	0.367703	+	0.313957i
$855$	−8.76499	+	26.9759i	−0.299756	+	0.922555i
$856$	18.8768	−	30.8339i	0.645195	−	1.05388i
$857$	30.4078			1.03871			0.519355	−	0.854558i	$-0.326172\pi$
$857$	30.4078			1.03871			0.519355	+	0.854558i	$0.326172\pi$
$858$		0			0
$859$		−	27.7908i		−	0.948210i	−0.880468	−	0.474105i	$-0.842772\pi$
$859$		−	27.7908i		−	0.948210i	0.880468	−	0.474105i	$-0.157228\pi$
$860$	−85.1416	+	43.4126i	−2.90330	+	1.48036i
$861$	8.61712	+	2.79987i	0.293671	+	0.0954194i
$862$	22.8334	−	26.7422i	0.777708	−	0.910844i
$863$	−0.179462	+	0.130387i	−0.00610896	+	0.00443842i	−0.590836	−	0.806792i	$-0.701202\pi$
$863$	−0.179462	+	0.130387i	−0.00610896	+	0.00443842i	0.584727	+	0.811230i	$0.301202\pi$
$864$	5.99649	−	1.44419i	0.204005	−	0.0491323i
$865$	1.45423	+	4.47567i	0.0494455	+	0.152177i
$866$	0.753143	−	0.180928i	0.0255928	−	0.00614818i
$867$	−15.2355	+	20.9699i	−0.517425	+	0.712174i
$868$	−3.09769	+	6.08388i	−0.105142	+	0.206500i
$869$		0			0
$870$	54.0673	−	33.1432i	1.83305	−	1.12366i
$871$	12.8766	+	9.35538i	0.436306	+	0.316995i
$872$	−5.09032	−	1.21976i	−0.172380	−	0.0413062i
$873$	−1.43371	−	4.41252i	−0.0485239	−	0.149341i
$874$	5.03835	−	12.1686i	0.170425	−	0.411609i
$875$	16.8536	+	23.1970i	0.569757	+	0.784203i
$876$	−9.60078	+	60.7299i	−0.324380	+	2.05187i
$877$	−14.7861	−	4.80428i	−0.499290	−	0.162229i	0.0485360	−	0.998821i	$-0.484544\pi$
$877$	−14.7861	−	4.80428i	−0.499290	−	0.162229i	−0.547826	+	0.836592i	$0.684544\pi$
$878$	3.04918	−	38.8149i	0.102905	−	1.30994i
$879$	13.2095			0.445545
$880$		0			0
$881$	21.4338			0.722125			0.361062	−	0.932542i	$-0.382414\pi$
$881$	21.4338			0.722125			0.361062	+	0.932542i	$0.382414\pi$
$882$	−1.72193	+	21.9195i	−0.0579804	+	0.738066i
$883$	−13.5716	−	4.40968i	−0.456720	−	0.148397i	0.0716166	−	0.997432i	$-0.477184\pi$
$883$	−13.5716	−	4.40968i	−0.456720	−	0.148397i	−0.528337	+	0.849035i	$0.677184\pi$
$884$	2.24090	−	14.1748i	0.0753695	−	0.476751i
$885$	−16.7727	−	23.0856i	−0.563808	−	0.776015i
$886$	4.35758	−	10.5244i	0.146396	−	0.353574i
$887$	−7.29616	−	22.4553i	−0.244981	−	0.753974i	−0.995640	−	0.0932837i	$-0.970264\pi$
$887$	−7.29616	−	22.4553i	−0.244981	−	0.753974i	0.750659	−	0.660690i	$-0.229736\pi$
$888$	7.03789	−	29.3707i	0.236176	−	0.985616i
$889$	4.91510	+	3.57103i	0.164847	+	0.119768i
$890$	13.8010	−	8.46000i	0.462611	−	0.283580i
$891$		0			0
$892$	9.32569	−	18.3157i	0.312247	−	0.613255i
$893$	5.14497	−	7.08144i	0.172170	−	0.236972i
$894$	45.0463	−	10.8215i	1.50657	−	0.361926i
$895$	−19.5281	−	60.1014i	−0.652753	−	2.00897i
$896$	−10.2690	−	2.45444i	−0.343062	−	0.0819969i
$897$	19.3827	−	14.0824i	0.647171	−	0.470197i
$898$	−31.0116	+	36.3205i	−1.03487	+	1.21203i
$899$	−15.9066	−	5.16835i	−0.530513	−	0.172374i
$900$	55.9154	−	28.5106i	1.86385	−	0.950352i
$901$		−	1.59039i		−	0.0529837i
$902$		0			0
$903$	−25.1756			−0.837792
$904$	−40.2403	−	24.6354i	−1.33837	−	0.819361i
$905$	−21.7937	+	67.0743i	−0.724449	+	2.22962i
$906$	−38.5234	−	32.8925i	−1.27985	−	1.09278i
$907$	26.6198	+	36.6389i	0.883894	+	1.21658i	0.975327	+	0.220765i	$0.0708554\pi$
$907$	26.6198	+	36.6389i	0.883894	+	1.21658i	−0.0914327	+	0.995811i	$0.529145\pi$
$908$	−30.9505	+	4.91119i	−1.02713	+	0.162984i
$909$	−30.5927	+	9.94017i	−1.01470	+	0.329694i
$910$	−15.6886	+	3.76887i	−0.520071	+	0.124937i
$911$	18.1656	+	13.1981i	0.601853	+	0.437272i	0.846536	−	0.532331i	$-0.178684\pi$
$911$	18.1656	+	13.1981i	0.601853	+	0.437272i	−0.244683	+	0.969603i	$0.578684\pi$
$912$	14.8538	+	20.4198i	0.491859	+	0.676168i
$913$		0			0
$914$	−2.83237	−	4.62051i	−0.0936864	−	0.152833i
$915$	−61.7148	+	84.9431i	−2.04023	+	2.80813i
$916$	−19.8989	+	19.9104i	−0.657479	+	0.657857i
$917$	6.13801	−	1.99436i	0.202695	−	0.0658595i
$918$	1.44302	−	3.48518i	0.0476268	−	0.115028i
$919$	33.6008	−	24.4124i	1.10839	−	0.805292i	0.125980	−	0.992033i	$-0.459793\pi$
$919$	33.6008	−	24.4124i	1.10839	−	0.805292i	0.982409	+	0.186741i	$0.0597925\pi$
$920$	−37.8002	+	15.6765i	−1.24624	+	0.516838i
$921$	−20.2541	+	62.3358i	−0.667396	+	2.05403i
$922$	−22.3295	−	1.75414i	−0.735383	−	0.0577696i
$923$			22.7363i			0.748373i
$924$		0			0
$925$			56.1436i			1.84599i
$926$	−3.36841	+	42.8784i	−0.110693	+	1.40907i
$927$	3.03074	−	9.32765i	0.0995425	−	0.306360i
$928$	2.01087	−	25.7874i	0.0660100	−	0.846512i
$929$	30.1761	−	21.9242i	0.990046	−	0.719310i	0.0301145	−	0.999546i	$-0.490413\pi$
$929$	30.1761	−	21.9242i	0.990046	−	0.719310i	0.959931	+	0.280236i	$0.0904128\pi$
$930$	−46.8728	−	19.4074i	−1.53702	−	0.636395i
$931$	15.6385	−	5.08127i	0.512533	−	0.166532i
$932$	17.1159	+	17.1061i	0.560651	+	0.560328i
$933$	−33.7571	+	46.4626i	−1.10516	+	1.52112i
$934$	24.3330	−	14.9161i	0.796199	−	0.488069i
$935$		0			0
$936$	1.66020	+	20.9792i	0.0542653	+	0.685726i
$937$	10.6707	+	7.75270i	0.348596	+	0.253270i	0.748280	−	0.663383i	$-0.230880\pi$
$937$	10.6707	+	7.75270i	0.348596	+	0.253270i	−0.399684	+	0.916653i	$0.630880\pi$
$938$	−1.67280	−	6.96329i	−0.0546188	−	0.227360i
$939$	−20.4430	+	6.64232i	−0.667131	+	0.216764i
$940$	−26.8610	+	4.26228i	−0.876109	+	0.139020i
$941$	14.5016	+	19.9597i	0.472738	+	0.650668i	0.977089	−	0.212831i	$-0.0682683\pi$
$941$	14.5016	+	19.9597i	0.472738	+	0.650668i	−0.504351	+	0.863499i	$0.668268\pi$
$942$	1.88838	−	2.21166i	0.0615268	−	0.0720596i
$943$	4.42610	−	13.6221i	0.144134	−	0.443598i
$944$	−11.6386	+	0.00669035i	−0.378804	+	0.000217752i
$945$	−4.24104			−0.137961
$946$		0			0
$947$			38.8667i			1.26300i	0.775376	+	0.631500i	$0.217560\pi$
$947$			38.8667i			1.26300i	−0.775376	+	0.631500i	$0.782440\pi$
$948$	−10.3392	−	20.2775i	−0.335803	−	0.658583i
$949$	36.4470	+	11.8424i	1.18312	+	0.384419i
$950$	−35.6974	−	30.4796i	−1.15818	−	0.988890i
$951$	−34.1701	+	24.8260i	−1.10804	+	0.805038i
$952$	−4.90816	+	4.19563i	−0.159074	+	0.135981i
$953$	−16.2483	−	50.0072i	−0.526335	−	1.61989i	−0.761661	−	0.647976i	$-0.775616\pi$
$953$	−16.2483	−	50.0072i	−0.526335	−	1.61989i	0.235326	−	0.971916i	$-0.424384\pi$
$954$	0.544773	+	2.26771i	0.0176377	+	0.0734198i
$955$	40.8441	−	56.2170i	1.32168	−	1.81914i
$956$	−19.7355	+	38.7607i	−0.638292	+	1.25361i
$957$		0			0
$958$	9.28340	+	15.1442i	0.299933	+	0.489288i
$959$	4.39370	+	3.19221i	0.141880	+	0.103082i
$960$	12.2066	−	77.5019i	0.393966	−	2.50136i
$961$	−5.44501	−	16.7580i	−0.175646	−	0.540581i
$962$	−17.3929	−	7.20144i	−0.560769	−	0.232184i
$963$	19.0580	+	26.2310i	0.614134	+	0.845283i
$964$	−13.7091	−	2.16727i	−0.441540	−	0.0698030i
$965$	0.716285	+	0.232735i	0.0230580	+	0.00749201i
$966$	−10.7467	−	0.844233i	−0.345771	−	0.0271627i
$967$	2.98370			0.0959493			0.0479746	−	0.998849i	$-0.484723\pi$
$967$	2.98370			0.0959493			0.0479746	+	0.998849i	$0.484723\pi$
$968$		0			0
$969$	15.4425			0.496086
$970$	10.7480	+	0.844330i	0.345097	+	0.0271098i
$971$	14.3079	+	4.64893i	0.459164	+	0.149191i	0.529460	−	0.848335i	$-0.322395\pi$
$971$	14.3079	+	4.64893i	0.459164	+	0.149191i	−0.0702964	+	0.997526i	$0.522395\pi$
$972$	−6.45581	+	40.8364i	−0.207070	+	1.30983i
$973$	−5.23043	−	7.19907i	−0.167680	−	0.230792i
$974$	18.6221	+	7.71038i	0.596690	+	0.247057i
$975$	−26.3863	−	81.2088i	−0.845039	−	2.60076i
$976$	13.2568	+	40.7204i	0.424338	+	1.30343i
$977$	9.24812	+	6.71916i	0.295874	+	0.214965i	0.725811	−	0.687894i	$-0.241464\pi$
$977$	9.24812	+	6.71916i	0.295874	+	0.214965i	−0.429938	+	0.902859i	$0.641464\pi$
$978$	13.0899	+	21.3540i	0.418570	+	0.682824i
$979$		0			0
$980$	−45.5294	−	23.1819i	−1.45438	−	0.740519i
$981$	2.75929	−	3.79783i	0.0880972	−	0.121255i
$982$	−6.74045	−	28.0582i	−0.215097	−	0.895375i
$983$	17.9549	+	55.2595i	0.572672	+	1.76250i	0.643973	+	0.765048i	$0.277285\pi$
$983$	17.9549	+	55.2595i	0.572672	+	1.76250i	−0.0713009	+	0.997455i	$0.522715\pi$
$984$	17.8435	+	20.8738i	0.568829	+	0.665432i
$985$	−28.2866	+	20.5514i	−0.901287	+	0.654823i
$986$	−12.0300	−	10.2716i	−0.383113	−	0.327114i
$987$	−6.81372	−	2.21391i	−0.216883	−	0.0704696i
$988$	14.0212	−	7.14925i	0.446075	−	0.227448i
$989$			39.7982i			1.26551i
$990$		0			0
$991$	30.2307			0.960311			0.480156	−	0.877183i	$-0.340580\pi$
$991$	30.2307			0.960311			0.480156	+	0.877183i	$0.340580\pi$
$992$	−17.6348	+	10.8241i	−0.559905	+	0.343664i
$993$	9.59312	−	29.5246i	0.304429	−	0.936935i
$994$	6.64272	−	7.77988i	0.210694	−	0.246763i
$995$	54.1407	+	74.5182i	1.71637	+	2.36239i
$996$	−0.486513	−	3.06602i	−0.0154158	−	0.0971506i
$997$	12.7437	−	4.14069i	0.403598	−	0.131137i	−0.100181	−	0.994969i	$-0.531942\pi$
$997$	12.7437	−	4.14069i	0.403598	−	0.131137i	0.503780	+	0.863832i	$0.331942\pi$
$998$	−11.0251	−	45.8938i	−0.348994	−	1.45274i
$999$	−4.00308	−	2.90841i	−0.126652	−	0.0920179i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.h.565.5		40
8.5	even	2	inner	968.2.o.h.565.9		40
11.2	odd	10		968.2.o.g.269.4		40
11.3	even	5	inner	968.2.o.h.245.9		40
11.4	even	5	inner	968.2.o.h.493.1		40
11.5	even	5		968.2.c.d.485.3		10
11.6	odd	10		88.2.c.a.45.8	yes	10
11.7	odd	10		968.2.o.g.493.10		40
11.8	odd	10		968.2.o.g.245.2		40
11.9	even	5	inner	968.2.o.h.269.7		40
11.10	odd	2		968.2.o.g.565.6		40
33.17	even	10		792.2.f.g.397.3		10
44.27	odd	10		3872.2.c.f.1937.2		10
44.39	even	10		352.2.c.a.177.2		10
88.5	even	10		968.2.c.d.485.4		10
88.13	odd	10		968.2.o.g.269.10		40
88.21	odd	2		968.2.o.g.565.2		40
88.27	odd	10		3872.2.c.f.1937.9		10
88.29	odd	10		968.2.o.g.493.4		40
88.37	even	10	inner	968.2.o.h.493.7		40
88.53	even	10	inner	968.2.o.h.269.1		40
88.61	odd	10		88.2.c.a.45.7	✓	10
88.69	even	10	inner	968.2.o.h.245.5		40
88.83	even	10		352.2.c.a.177.9		10
88.85	odd	10		968.2.o.g.245.6		40
132.83	odd	10		3168.2.f.g.1585.10		10
176.61	odd	20		2816.2.a.o.1.1		5
176.83	even	20		2816.2.a.p.1.5		5
176.149	odd	20		2816.2.a.r.1.5		5
176.171	even	20		2816.2.a.q.1.1		5
264.83	odd	10		3168.2.f.g.1585.1		10
264.149	even	10		792.2.f.g.397.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.7	✓	10	88.61	odd	10
88.2.c.a.45.8	yes	10	11.6	odd	10
352.2.c.a.177.2		10	44.39	even	10
352.2.c.a.177.9		10	88.83	even	10
792.2.f.g.397.3		10	33.17	even	10
792.2.f.g.397.4		10	264.149	even	10
968.2.c.d.485.3		10	11.5	even	5
968.2.c.d.485.4		10	88.5	even	10
968.2.o.g.245.2		40	11.8	odd	10
968.2.o.g.245.6		40	88.85	odd	10
968.2.o.g.269.4		40	11.2	odd	10
968.2.o.g.269.10		40	88.13	odd	10
968.2.o.g.493.4		40	88.29	odd	10
968.2.o.g.493.10		40	11.7	odd	10
968.2.o.g.565.2		40	88.21	odd	2
968.2.o.g.565.6		40	11.10	odd	2
968.2.o.h.245.5		40	88.69	even	10	inner
968.2.o.h.245.9		40	11.3	even	5	inner
968.2.o.h.269.1		40	88.53	even	10	inner
968.2.o.h.269.7		40	11.9	even	5	inner
968.2.o.h.493.1		40	11.4	even	5	inner
968.2.o.h.493.7		40	88.37	even	10	inner
968.2.o.h.565.5		40	1.1	even	1	trivial
968.2.o.h.565.9		40	8.5	even	2	inner
2816.2.a.o.1.1		5	176.61	odd	20
2816.2.a.p.1.5		5	176.83	even	20
2816.2.a.q.1.1		5	176.171	even	20
2816.2.a.r.1.5		5	176.149	odd	20
3168.2.f.g.1585.1		10	264.83	odd	10
3168.2.f.g.1585.10		10	132.83	odd	10
3872.2.c.f.1937.2		10	44.27	odd	10
3872.2.c.f.1937.9		10	88.27	odd	10

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	968.2.o.h.565.5

Level	$968$
Weight	$2$
Character	968.565
Analytic conductor	$7.730$
Analytic rank	$0$
Dimension	$40$
Inner twists	$8$