LMFDB - Embedded newform 968.2.o.h.245.5

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			245.5
Character	$\chi$	$=$	968.245
Dual form			968.2.o.h.565.5

$q$ -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 $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$ .

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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	0.419219	−	0.907885i	$-0.362304\pi$
$3$	2.23784	−	0.727117i	1.29202	−	0.419801i	0.872797	+	0.488084i	$0.162304\pi$
$4$	−1.97547	+	0.312301i	−0.987733	+	0.156151i
$5$	2.44985	−	3.37193i	1.09561	−	1.50797i	0.254526	−	0.967066i	$-0.418081\pi$
$5$	2.44985	−	3.37193i	1.09561	−	1.50797i	0.841082	−	0.540908i	$-0.181919\pi$
$6$	−1.27299	−	3.07453i	−0.519697	−	1.25517i
$7$	−0.288382	+	0.887547i	−0.108998	+	0.335461i	−0.990648	−	0.136443i	$-0.956433\pi$
$7$	−0.288382	+	0.887547i	−0.108998	+	0.335461i	0.881650	+	0.471904i	$0.156433\pi$
$8$	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	0.499973	−	0.866041i	$-0.333343\pi$
$13$	−1.72410	−	2.37303i	−0.478181	−	0.658159i	−0.978154	+	0.207882i	$0.933343\pi$
$14$	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	0.801324	−	0.598231i	$-0.204130\pi$
$17$	1.97907	+	1.43788i	0.479995	+	0.348736i	−0.321329	+	0.946968i	$0.604130\pi$
$18$	−2.32938	−	2.72815i	−0.549040	−	0.643031i
$19$	2.55153	−	0.829041i	0.585360	−	0.190195i	−0.00134028	−	0.999999i	$-0.500427\pi$
$19$	2.55153	−	0.829041i	0.585360	−	0.190195i	0.586700	+	0.809804i	$0.300427\pi$
$20$	−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	−0.123976	−	0.992285i	$-0.539565\pi$
$29$	−4.34866	−	1.41296i	−0.807525	−	0.262381i	−0.683549	+	0.729904i	$0.739565\pi$
$30$	−13.4857	−	3.23969i	−2.46215	−	0.591484i
$31$	2.95923	−	2.15001i	0.531493	−	0.386153i	−0.289423	−	0.957201i	$-0.593463\pi$
$31$	2.95923	−	2.15001i	0.531493	−	0.386153i	0.820916	+	0.571049i	$0.193463\pi$
$32$	−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	0.641482	−	0.767138i	$-0.278320\pi$
$37$	4.31595	+	1.40234i	0.709539	+	0.230543i	0.0680569	+	0.997681i	$0.478320\pi$
$38$	−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	−0.999903	−	0.0138937i	$-0.995577\pi$
$41$	−1.27506	−	3.92423i	−0.199131	−	0.612862i	0.800772	−	0.598969i	$-0.204423\pi$
$42$	3.09590	−	0.243205i	0.477707	−	0.0375273i
$43$			11.4650i			1.74839i	0.485573	+	0.874196i	$0.338611\pi$
$43$			11.4650i			1.74839i	−0.485573	+	0.874196i	$0.661389\pi$
$44$		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	0.997271	−	0.0738340i	$-0.0235235\pi$
$47$	1.00821	+	3.10297i	0.147063	+	0.452614i	−0.850207	+	0.526448i	$0.823523\pi$
$48$	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	0.834455	−	0.551075i	$-0.185782\pi$
$53$	0.382138	+	0.525968i	0.0524907	+	0.0722472i	−0.781965	+	0.623323i	$0.785782\pi$
$54$	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	0.123292	−	0.992370i	$-0.460655\pi$
$59$	−2.76724	−	0.899131i	−0.360264	−	0.117057i	−0.483556	+	0.875314i	$0.660655\pi$
$60$	−3.07392	+	19.3720i	−0.396842	+	2.50091i
$61$	6.29283	−	8.66134i	0.805714	−	1.10897i	−0.186256	−	0.982501i	$-0.559635\pi$
$61$	6.29283	−	8.66134i	0.805714	−	1.10897i	0.991971	−	0.126469i	$-0.0403646\pi$
$62$	−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	$0.107541\pi$
$67$			5.42623i			0.662919i	−0.943469	+	0.331460i	$0.892459\pi$
$68$	−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	0.894031	−	0.448006i	$-0.147866\pi$
$71$	6.27093	+	4.55610i	0.744222	+	0.540709i	−0.149808	+	0.988715i	$0.547866\pi$
$72$	5.45362	+	4.66190i	0.642715	+	0.549410i
$73$	−4.03732	+	12.4256i	−0.472533	+	1.45431i	0.376724	+	0.926326i	$0.377051\pi$
$73$	−4.03732	+	12.4256i	−0.472533	+	1.45431i	−0.849256	+	0.527981i	$0.822949\pi$
$74$	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	−0.345490	−	0.938422i	$-0.612287\pi$
$79$	3.91294	−	2.84292i	0.440240	−	0.319853i	0.785730	+	0.618569i	$0.212287\pi$
$80$	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	−0.787207	−	0.616689i	$-0.788473\pi$
$83$	0.387741	−	0.533679i	0.0425601	−	0.0585789i	0.829767	+	0.558110i	$0.188473\pi$
$84$	−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	−0.660368	−	0.750942i	$-0.729600\pi$
$97$	−1.47973	+	1.07509i	−0.150244	+	0.109159i	0.510124	+	0.860101i	$0.329600\pi$
$98$	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	−0.998520	−	0.0543782i	$-0.982682\pi$
$101$	−7.45377	−	10.2592i	−0.741677	−	1.02083i	0.256843	−	0.966453i	$-0.417318\pi$
$102$	1.90145	−	7.91511i	0.188272	−	0.783712i
$103$	−1.19480	+	3.67721i	−0.117727	+	0.362326i	−0.992506	−	0.122196i	$-0.961006\pi$
$103$	−1.19480	+	3.67721i	−0.117727	+	0.362326i	0.874779	+	0.484522i	$0.161006\pi$
$104$	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	0.344629	−	0.938739i	$-0.388005\pi$
$107$	12.1565	−	3.94990i	1.17522	−	0.381851i	0.830588	+	0.556888i	$0.188005\pi$
$108$	0.990576	−	1.94273i	0.0953182	−	0.186940i
$109$			1.85065i			0.177260i	0.996065	+	0.0886299i	$0.0282489\pi$
$109$			1.85065i			0.177260i	−0.996065	+	0.0886299i	$0.971751\pi$
$110$		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	0.832083	+	0.554651i	$0.187148\pi$
$113$	5.15487	+	15.8651i	0.484929	+	1.49246i	−0.347154	+	0.937808i	$0.612852\pi$
$114$	−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	0.329056	−	0.944311i	$-0.393270\pi$
$127$	−5.26680	−	3.82656i	−0.467353	−	0.339552i	−0.796409	+	0.604758i	$0.793270\pi$
$128$	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	$-0.902308\pi$
$131$		−	6.91569i		−	0.604227i	0.953272	−	0.302114i	$-0.0976922\pi$
$132$		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	0.368213	−	0.929741i	$-0.379970\pi$
$137$	−4.70809	−	3.42063i	−0.402239	−	0.292244i	−0.770453	+	0.637497i	$0.779970\pi$
$138$	4.41892	+	10.6726i	0.376164	+	0.908509i
$139$	9.06860	+	2.94657i	0.769188	+	0.249924i	0.667217	−	0.744863i	$-0.267485\pi$
$139$	9.06860	+	2.94657i	0.769188	+	0.249924i	0.101971	+	0.994787i	$0.467485\pi$
$140$	−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	−0.999769	−	0.0214790i	$-0.993162\pi$
$149$	−8.18322	+	11.2632i	−0.670396	+	0.922721i	0.329373	+	0.944200i	$0.393162\pi$
$150$	−31.3087	+	26.7324i	−2.55635	+	2.18269i
$151$	−4.70404	−	14.4775i	−0.382809	−	1.17816i	−0.938057	−	0.346480i	$-0.887377\pi$
$151$	−4.70404	−	14.4775i	−0.382809	−	1.17816i	0.555248	−	0.831685i	$-0.312623\pi$
$152$	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	−0.341996	−	0.939701i	$-0.611103\pi$
$157$	−0.831166	+	0.270062i	−0.0663343	+	0.0215533i	0.275662	+	0.961255i	$0.411103\pi$
$158$	−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	0.946334	−	0.323190i	$-0.104755\pi$
$163$	4.42418	+	6.08936i	0.346528	+	0.476955i	−0.599806	+	0.800146i	$0.704755\pi$
$164$	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	−0.583303	−	0.812255i	$-0.698240\pi$
$167$	0.115612	−	0.0839969i	0.00894631	−	0.00649988i	0.592249	+	0.805755i	$0.298240\pi$
$168$	−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	−0.267911	−	0.963444i	$-0.586333\pi$
$173$	1.07383	−	0.348910i	0.0816421	−	0.0265271i	0.349553	+	0.936916i	$0.386333\pi$
$174$	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	−0.793519	−	0.608545i	$-0.791754\pi$
$179$	−14.4199	+	4.68532i	−1.07780	+	0.350197i	−0.284277	+	0.958742i	$0.591754\pi$
$180$	3.30179	+	20.8855i	0.246101	+	1.55671i
$181$	9.94596	−	13.6894i	0.739278	−	1.01753i	−0.259382	−	0.965775i	$-0.583519\pi$
$181$	9.94596	−	13.6894i	0.739278	−	1.01753i	0.998660	−	0.0517537i	$-0.0164811\pi$
$182$	−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	0.572181	+	0.820127i	$0.306097\pi$
$191$	−5.15195	+	15.8561i	−0.372782	+	1.14730i	−0.944963	+	0.327177i	$0.893903\pi$
$192$	−13.3221	+	13.2991i	−0.961437	+	0.959780i
$193$	0.146189	+	0.106213i	0.0105229	+	0.00764537i	0.593034	−	0.805177i	$-0.297930\pi$
$193$	0.146189	+	0.106213i	0.0105229	+	0.00764537i	−0.582511	+	0.812823i	$0.697930\pi$
$194$	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	$-0.903400\pi$
$197$		−	8.38885i		−	0.597681i	0.954303	−	0.298840i	$-0.0965998\pi$
$198$		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	0.996457	−	0.0841019i	$-0.0268021\pi$
$211$	8.83969	+	12.1668i	0.608549	+	0.837596i	−0.387908	+	0.921698i	$0.626802\pi$
$212$	−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	−0.999312	−	0.0370972i	$-0.988189\pi$
$223$	−3.17564	−	9.77362i	−0.212657	−	0.654490i	0.786655	−	0.617393i	$-0.211811\pi$
$224$	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	0.758493	−	0.651682i	$-0.225936\pi$
$227$	14.9020	+	4.84194i	0.989077	+	0.321371i	0.230585	+	0.973052i	$0.425936\pi$
$228$	−8.93008	+	8.92495i	−0.591409	+	0.591069i
$229$	8.27290	+	11.3867i	0.546689	+	0.752453i	0.989558	−	0.144134i	$-0.0460395\pi$
$229$	8.27290	+	11.3867i	0.546689	+	0.752453i	−0.442869	+	0.896586i	$0.646039\pi$
$230$	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	−0.860286	−	0.509812i	$-0.829715\pi$
$233$	−9.78854	+	7.11179i	−0.641269	+	0.465909i	0.219017	+	0.975721i	$0.429715\pi$
$234$	−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	0.893383	+	0.449296i	$0.148325\pi$
$239$	6.72046	+	20.6835i	0.434711	+	1.33790i	−0.458672	+	0.888606i	$0.651675\pi$
$240$	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	0.341688	−	0.939814i	$-0.389001\pi$
$251$	−10.4202	−	14.3421i	−0.657715	−	0.905268i	−0.999403	+	0.0345459i	$0.989001\pi$
$252$	−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	−0.620812	−	0.783959i	$-0.713197\pi$
$257$	5.48645	−	16.8855i	0.342235	−	1.05329i	0.963047	−	0.269332i	$-0.0868029\pi$
$258$	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	−0.955822	−	0.293947i	$-0.905031\pi$
$269$	−6.24717	+	8.59849i	−0.380897	+	0.524259i	0.574925	+	0.818206i	$0.305031\pi$
$270$	5.93804	−	2.45862i	0.361378	−	0.149627i
$271$	−6.10249	+	18.7815i	−0.370700	+	1.14090i	0.575635	+	0.817707i	$0.304755\pi$
$271$	−6.10249	+	18.7815i	−0.370700	+	1.14090i	−0.946334	+	0.323189i	$0.895245\pi$
$272$	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	0.528107	−	0.849178i	$-0.322902\pi$
$277$	−7.36805	−	10.1413i	−0.442703	−	0.609329i	−0.970810	+	0.239849i	$0.922902\pi$
$278$	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	−0.160492	−	0.987037i	$-0.551308\pi$
$281$	−19.2576	−	13.9915i	−1.14881	−	0.834663i	−0.988323	+	0.152375i	$0.951308\pi$
$282$	8.25670	−	7.04984i	0.491679	−	0.419812i
$283$	26.3723	−	8.56886i	1.56767	−	0.509366i	0.608825	−	0.793304i	$-0.291641\pi$
$283$	26.3723	−	8.56886i	1.56767	−	0.509366i	0.958843	+	0.283938i	$0.0916411\pi$
$284$	−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	0.460792	−	0.887508i	$-0.347566\pi$
$293$	5.33913	+	1.73479i	0.311915	+	0.101347i	−0.148876	+	0.988856i	$0.547566\pi$
$294$	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	$-0.707526\pi$
$307$		−	27.8554i		−	1.58979i	0.606747	−	0.794895i	$-0.292474\pi$
$308$		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	−0.900398	−	0.435068i	$-0.856724\pi$
$311$	−7.54235	−	23.2130i	−0.427687	−	1.31629i	0.472710	−	0.881218i	$-0.343276\pi$
$312$	7.47831	−	18.0322i	0.423376	−	1.02087i
$313$	−7.39048	−	5.36950i	−0.417735	−	0.303502i	0.358991	−	0.933341i	$-0.383121\pi$
$313$	−7.39048	−	5.36950i	−0.417735	−	0.303502i	−0.776726	+	0.629839i	$0.783121\pi$
$314$	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	0.402414	−	0.915458i	$-0.368171\pi$
$317$	−10.5508	−	14.5219i	−0.592591	−	0.815632i	−0.995005	+	0.0998262i	$0.968171\pi$
$318$	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	$0.118106\pi$
$331$			13.1934i			0.725173i	−0.931950	+	0.362586i	$0.881894\pi$
$332$	−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	0.521686	+	0.853138i	$0.325303\pi$
$337$	−7.37660	+	22.7028i	−0.401829	+	1.23670i	−0.923514	+	0.383564i	$0.874697\pi$
$338$	−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	0.552256	−	0.833675i	$-0.313767\pi$
$347$	21.8780	−	30.1124i	1.17447	−	1.61652i	0.622215	−	0.782846i	$-0.286233\pi$
$348$	21.2540	−	3.36004i	1.13933	−	0.180117i
$349$	−27.0233	+	8.78041i	−1.44652	+	0.470004i	−0.923925	−	0.382574i	$-0.875038\pi$
$349$	−27.0233	+	8.78041i	−1.44652	+	0.470004i	−0.522600	+	0.852578i	$0.675038\pi$
$350$	−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	0.648833	+	0.760931i	$0.275257\pi$
$359$	−6.12657	+	18.8556i	−0.323348	+	0.995163i	−0.972181	+	0.234232i	$0.924743\pi$
$360$	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	−0.907649	−	0.419730i	$-0.862125\pi$
$367$	1.40548	−	4.32561i	0.0733653	−	0.225795i	0.981014	+	0.193934i	$0.0621249\pi$
$368$	−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	$0.332474\pi$
$373$			33.3992i			1.72934i	−0.502336	+	0.864672i	$0.667526\pi$
$374$		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	−0.925480	−	0.378797i	$-0.876338\pi$
$379$	−5.43609	+	7.48213i	−0.279233	+	0.384331i	0.646247	+	0.763129i	$0.276338\pi$
$380$	−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	−0.999997	−	0.00249665i	$-0.999205\pi$
$383$	−25.5714	+	18.5787i	−1.30664	+	0.949328i	−0.306642	+	0.951825i	$0.599205\pi$
$384$	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	0.186088	−	0.982533i	$-0.440419\pi$
$389$	−4.75093	−	1.54367i	−0.240882	−	0.0782673i	−0.426970	+	0.904266i	$0.640419\pi$
$390$	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	$-0.852651\pi$
$397$		−	17.7950i		−	0.893107i	0.894757	−	0.446553i	$-0.147349\pi$
$398$	−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	0.805887	−	0.592069i	$-0.201689\pi$
$401$	9.84887	+	7.15562i	0.491829	+	0.357335i	−0.314058	+	0.949404i	$0.601689\pi$
$402$	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	−0.575962	−	0.817476i	$-0.695372\pi$
$409$	0.475699	−	0.345616i	0.0235218	−	0.0170896i	0.599484	+	0.800387i	$0.295372\pi$
$410$	−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	$0.0878088\pi$
$419$			11.1507i			0.544748i	−0.962191	+	0.272374i	$0.912191\pi$
$420$	−16.3071	−	8.31477i	−0.795703	−	0.405719i
$421$	−33.1346	+	10.7661i	−1.61488	+	0.524708i	−0.970727	−	0.240186i	$-0.922792\pi$
$421$	−33.1346	+	10.7661i	−1.61488	+	0.524708i	−0.644157	+	0.764893i	$0.722792\pi$
$422$	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	−0.955213	−	0.295920i	$-0.904374\pi$
$431$	−20.1160	+	14.6151i	−0.968953	+	0.703986i	−0.0137403	+	0.999906i	$0.504374\pi$
$432$	−1.35013	+	4.14716i	−0.0649582	+	0.199530i
$433$	−0.169250	+	0.520897i	−0.00813362	+	0.0250327i	−0.955041	−	0.296474i	$-0.904189\pi$
$433$	−0.169250	+	0.520897i	−0.00813362	+	0.0250327i	0.946907	+	0.321507i	$0.104189\pi$
$434$	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	−0.485284	−	0.874357i	$-0.661284\pi$
$443$	−7.66033	+	2.48899i	−0.363953	+	0.118256i	0.121331	+	0.992612i	$0.461284\pi$
$444$	−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	0.289562	−	0.957159i	$-0.406490\pi$
$449$	27.3209	−	19.8498i	1.28935	−	0.936771i	0.999792	+	0.0203882i	$0.00649023\pi$
$450$	−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	0.512906	−	0.858445i	$-0.328569\pi$
$457$	−3.10031	−	2.25251i	−0.145026	−	0.105368i	−0.657933	+	0.753077i	$0.728569\pi$
$458$	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	$-0.879760\pi$
$461$		−	15.8380i		−	0.737649i	0.929499	−	0.368825i	$-0.120240\pi$
$462$		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	−0.989866	−	0.142006i	$-0.954645\pi$
$467$	−11.8624	+	16.3271i	−0.548925	+	0.755530i	0.440941	+	0.897536i	$0.354645\pi$
$468$	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	0.795214	−	0.606329i	$-0.207358\pi$
$479$	10.1616	+	7.38284i	0.464296	+	0.337331i	−0.330918	+	0.943659i	$0.607358\pi$
$480$	−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	0.999893	+	0.0146398i	$0.00466015\pi$
$487$	4.40407	+	13.5543i	0.199568	+	0.614206i	−0.800325	+	0.599566i	$0.795340\pi$
$488$	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	−0.163576	−	0.986531i	$-0.552303\pi$
$491$	−19.4060	−	6.30538i	−0.875779	−	0.284558i	−0.712204	+	0.701973i	$0.752303\pi$
$492$	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	−0.505046	−	0.863093i	$-0.668524\pi$
$499$	−31.7416	−	10.3135i	−1.42095	−	0.461694i	−0.915904	+	0.401398i	$0.868524\pi$
$500$	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	−0.999748	−	0.0224396i	$-0.992857\pi$
$503$	−4.57804	−	14.0898i	−0.204125	−	0.628231i	0.795624	−	0.605791i	$-0.207143\pi$
$504$	−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	−0.766637	−	0.642080i	$-0.778072\pi$
$509$	−22.7743	+	7.39983i	−1.00945	+	0.327992i	−0.242817	+	0.970072i	$0.578072\pi$
$510$	−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	−0.709005	−	0.705204i	$-0.750855\pi$
$521$	6.37059	−	19.6067i	0.279101	−	0.858983i	0.988105	−	0.153780i	$-0.0491445\pi$
$522$	6.27490	+	15.1551i	0.274645	+	0.663321i
$523$	−13.2848	+	18.2849i	−0.580903	+	0.799545i	−0.993794	−	0.111236i	$-0.964519\pi$
$523$	−13.2848	+	18.2849i	−0.580903	+	0.799545i	0.412891	+	0.910781i	$0.364519\pi$
$524$	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	0.737452	−	0.675399i	$-0.236029\pi$
$541$	−3.08829	−	4.25066i	−0.132776	−	0.182750i	−0.870228	+	0.492649i	$0.836029\pi$
$542$	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	−0.867996	−	0.496571i	$-0.834592\pi$
$547$	−29.8979	+	9.71442i	−1.27834	+	0.415359i	−0.410346	+	0.911930i	$0.634592\pi$
$548$	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	0.0154561	−	0.999881i	$-0.495080\pi$
$557$	−13.2107	−	4.29241i	−0.559755	−	0.181875i	−0.575211	+	0.818005i	$0.695080\pi$
$558$	−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	0.475392	−	0.879774i	$-0.342306\pi$
$563$	−12.0590	−	16.5978i	−0.508227	−	0.699514i	−0.983619	+	0.180260i	$0.942306\pi$
$564$	−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	0.990212	+	0.139570i	$0.0445720\pi$
$569$	6.46796	+	19.9063i	0.271151	+	0.834517i	−0.719061	+	0.694947i	$0.755428\pi$
$570$	−37.0951	+	2.91408i	−1.55374	+	0.122057i
$571$			6.00582i			0.251336i	0.992072	+	0.125668i	$0.0401074\pi$
$571$			6.00582i			0.251336i	−0.992072	+	0.125668i	$0.959893\pi$
$572$		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	0.956362	+	0.292185i	$0.0943824\pi$
$577$	36.7465	+	26.6979i	1.52978	+	1.11145i	0.573417	+	0.819264i	$0.305618\pi$
$578$	−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	0.404598	−	0.914494i	$-0.367411\pi$
$587$	4.70991	+	1.53034i	0.194399	+	0.0631641i	−0.210199	+	0.977659i	$0.567411\pi$
$588$	−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	−0.973228	−	0.229844i	$-0.926178\pi$
$599$	−36.5298	−	26.5404i	−1.49257	−	1.08441i	−0.519338	−	0.854569i	$-0.673822\pi$
$600$	53.5008	−	62.5867i	2.18416	−	2.55509i
$601$	4.83225	−	14.8721i	0.197112	−	0.606647i	−0.802834	−	0.596203i	$-0.796675\pi$
$601$	4.83225	−	14.8721i	0.197112	−	0.606647i	0.999945	−	0.0104444i	$-0.00332461\pi$
$602$	−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	−0.379751	+	0.925089i	$0.623990\pi$
$607$	−33.9235	+	24.6469i	−1.37691	+	1.00039i	−0.997161	+	0.0752967i	$0.976010\pi$
$608$	−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	−0.791028	−	0.611780i	$-0.790454\pi$
$613$	−26.5263	+	8.61893i	−1.07139	+	0.348115i	−0.280360	+	0.959895i	$0.590454\pi$
$614$	−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	−0.405264	−	0.914200i	$-0.632820\pi$
$619$	−4.87084	+	1.58263i	−0.195776	+	0.0636113i	0.209488	+	0.977811i	$0.432820\pi$
$620$	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	−0.0509681	+	0.998700i	$0.516231\pi$
$631$	−14.9903	+	46.1355i	−0.596755	+	1.83662i	−0.545787	+	0.837924i	$0.683769\pi$
$632$	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	0.897264	−	0.441495i	$-0.145552\pi$
$641$	−2.23158	−	6.86810i	−0.0881422	−	0.271274i	−0.985406	+	0.170221i	$0.945552\pi$
$642$	−27.6193	−	32.3474i	−1.09005	−	1.27665i
$643$	7.03032	−	9.67641i	0.277249	−	0.381600i	−0.647571	−	0.762005i	$-0.724215\pi$
$643$	7.03032	−	9.67641i	0.277249	−	0.381600i	0.924820	+	0.380405i	$0.124215\pi$
$644$	−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	−0.0872932	−	0.996183i	$-0.527822\pi$
$647$	21.1924	−	15.3972i	0.833158	−	0.605325i	0.920451	+	0.390858i	$0.127822\pi$
$648$	−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	−0.407225	−	0.913328i	$-0.633503\pi$
$653$	−32.5433	−	10.5740i	−1.27352	−	0.413791i	−0.866292	+	0.499537i	$0.833503\pi$
$654$	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	$-0.983063\pi$
$659$		−	2.73052i		−	0.106366i	0.998585	−	0.0531831i	$-0.0169367\pi$
$660$		0			0
$661$			11.2478i			0.437488i	0.975782	+	0.218744i	$0.0701959\pi$
$661$			11.2478i			0.437488i	−0.975782	+	0.218744i	$0.929804\pi$
$662$	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	−0.854683	−	0.519150i	$-0.826249\pi$
$673$	−16.2153	+	11.7811i	−0.625054	+	0.454128i	0.229629	+	0.973278i	$0.426249\pi$
$674$	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	−0.383696	−	0.923460i	$-0.625349\pi$
$677$	15.9533	−	21.9578i	0.613135	−	0.843908i	0.996831	+	0.0795517i	$0.0253489\pi$
$678$	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	$-0.704964\pi$
$683$		−	41.8019i		−	1.59951i	0.600330	−	0.799753i	$-0.295036\pi$
$684$	−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	0.355366	−	0.934727i	$-0.384356\pi$
$691$	−16.9137	−	23.2797i	−0.643427	−	0.885601i	−0.998793	+	0.0491260i	$0.984356\pi$
$692$	−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	0.126087	−	0.992019i	$-0.459758\pi$
$701$	21.4773	−	6.97841i	0.811188	−	0.263571i	0.685101	+	0.728448i	$0.259758\pi$
$702$	−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	−0.938776	−	0.344529i	$-0.888039\pi$
$709$	−8.54760	+	11.7648i	−0.321012	+	0.441835i	0.617764	+	0.786364i	$0.288039\pi$
$710$	−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	−0.979599	−	0.200963i	$-0.935593\pi$
$719$	−1.84920	+	5.69125i	−0.0689635	+	0.212248i	0.910635	+	0.413211i	$0.135593\pi$
$720$	−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	0.974766	−	0.223228i	$-0.0716596\pi$
$733$	44.1890	+	14.3579i	1.63216	+	0.530320i	0.657392	+	0.753549i	$0.271660\pi$
$734$	−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	0.923050	−	0.384680i	$-0.125688\pi$
$739$	7.39311	+	10.1757i	0.271960	+	0.374321i	−0.651090	+	0.759000i	$0.725688\pi$
$740$	−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	0.440118	−	0.897940i	$-0.354937\pi$
$743$	−7.57418	−	5.50297i	−0.277870	−	0.201884i	−0.717988	+	0.696056i	$0.754937\pi$
$744$	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	0.970907	−	0.239457i	$-0.0769695\pi$
$751$	1.22435	+	3.76817i	0.0446773	+	0.137503i	−0.926230	+	0.376960i	$0.876969\pi$
$752$	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	0.769193	−	0.639017i	$-0.220658\pi$
$757$	−2.09768	−	2.88722i	−0.0762417	−	0.104938i	−0.845435	+	0.534079i	$0.820658\pi$
$758$	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	0.477306	−	0.878737i	$-0.341613\pi$
$761$	40.2905	−	29.2728i	1.46053	−	1.06114i	0.983224	−	0.182401i	$-0.0583868\pi$
$762$	−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	−0.688248	−	0.725476i	$-0.741620\pi$
$773$	−22.7602	+	7.39524i	−0.818628	+	0.265988i	−0.130380	+	0.991464i	$0.541620\pi$
$774$	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	−0.643832	−	0.765167i	$-0.722656\pi$
$787$	7.93466	−	10.9211i	0.282840	−	0.389296i	0.926672	+	0.375871i	$0.122656\pi$
$788$	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	−0.484367	−	0.874865i	$-0.660950\pi$
$797$	14.0410	−	19.3257i	0.497357	−	0.684553i	0.981724	+	0.190312i	$0.0609500\pi$
$798$	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	0.836612	−	0.547796i	$-0.184533\pi$
$809$	16.3306	+	11.8649i	0.574155	+	0.417148i	−0.262457	+	0.964944i	$0.584533\pi$
$810$	45.6129	−	38.9458i	1.60268	−	1.36842i
$811$	3.59503	−	1.16810i	0.126238	−	0.0410174i	−0.245216	−	0.969468i	$-0.578859\pi$
$811$	3.59503	−	1.16810i	0.126238	−	0.0410174i	0.371455	+	0.928451i	$0.378859\pi$
$812$	−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	−0.285097	−	0.958499i	$-0.592026\pi$
$821$	−30.9206	−	10.0467i	−1.07914	−	0.350633i	−0.794040	+	0.607866i	$0.792026\pi$
$822$	−4.52345	+	18.8296i	−0.157773	+	0.656757i
$823$	−16.7993	+	12.2054i	−0.585587	+	0.425454i	−0.840734	−	0.541448i	$-0.817876\pi$
$823$	−16.7993	+	12.2054i	−0.585587	+	0.425454i	0.255147	+	0.966902i	$0.417876\pi$
$824$	−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	0.908093	−	0.418768i	$-0.137538\pi$
$827$	6.59140	+	9.07228i	0.229205	+	0.315474i	−0.678888	+	0.734242i	$0.737538\pi$
$828$	12.4562	−	12.4490i	0.432882	−	0.432633i
$829$	6.48815	+	2.10813i	0.225343	+	0.0732183i	0.419512	−	0.907750i	$-0.362201\pi$
$829$	6.48815	+	2.10813i	0.225343	+	0.0732183i	−0.194169	+	0.980968i	$0.562201\pi$
$830$	−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	−0.999641	−	0.0268038i	$-0.991467\pi$
$839$	−5.98628	−	18.4239i	−0.206669	−	0.636063i	0.792971	−	0.609259i	$-0.208533\pi$
$840$	−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	−0.906347	−	0.422534i	$-0.861141\pi$
$853$	−6.55434	+	9.02128i	−0.224416	+	0.308883i	0.681931	+	0.731417i	$0.261141\pi$
$854$	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	$0.157228\pi$
$859$			27.7908i			0.948210i	−0.880468	+	0.474105i	$0.842772\pi$
$860$	−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	0.584727	−	0.811230i	$-0.301202\pi$
$863$	−0.179462	−	0.130387i	−0.00610896	−	0.00443842i	−0.590836	+	0.806792i	$0.701202\pi$
$864$	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	−0.547826	−	0.836592i	$-0.684544\pi$
$877$	−14.7861	+	4.80428i	−0.499290	+	0.162229i	0.0485360	+	0.998821i	$0.484544\pi$
$878$	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	−0.528337	−	0.849035i	$-0.677184\pi$
$883$	−13.5716	+	4.40968i	−0.456720	+	0.148397i	0.0716166	+	0.997432i	$0.477184\pi$
$884$	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	0.750659	+	0.660690i	$0.229736\pi$
$887$	−7.29616	+	22.4553i	−0.244981	+	0.753974i	−0.995640	+	0.0932837i	$0.970264\pi$
$888$	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	−0.0914327	−	0.995811i	$-0.529145\pi$
$907$	26.6198	−	36.6389i	0.883894	−	1.21658i	0.975327	−	0.220765i	$-0.0708554\pi$
$908$	−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	−0.244683	−	0.969603i	$-0.578684\pi$
$911$	18.1656	−	13.1981i	0.601853	−	0.437272i	0.846536	+	0.532331i	$0.178684\pi$
$912$	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	0.982409	−	0.186741i	$-0.0597925\pi$
$919$	33.6008	+	24.4124i	1.10839	+	0.805292i	0.125980	+	0.992033i	$0.459793\pi$
$920$	−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	0.959931	−	0.280236i	$-0.0904128\pi$
$929$	30.1761	+	21.9242i	0.990046	+	0.719310i	0.0301145	+	0.999546i	$0.490413\pi$
$930$	−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	−0.399684	−	0.916653i	$-0.630880\pi$
$937$	10.6707	−	7.75270i	0.348596	−	0.253270i	0.748280	+	0.663383i	$0.230880\pi$
$938$	−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	−0.504351	−	0.863499i	$-0.668268\pi$
$941$	14.5016	−	19.9597i	0.472738	−	0.650668i	0.977089	+	0.212831i	$0.0682683\pi$
$942$	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	$-0.782440\pi$
$947$		−	38.8667i		−	1.26300i	0.775376	−	0.631500i	$-0.217560\pi$
$948$	−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	0.235326	+	0.971916i	$0.424384\pi$
$953$	−16.2483	+	50.0072i	−0.526335	+	1.61989i	−0.761661	+	0.647976i	$0.775616\pi$
$954$	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	−0.0702964	−	0.997526i	$-0.522395\pi$
$971$	14.3079	−	4.64893i	0.459164	−	0.149191i	0.529460	+	0.848335i	$0.322395\pi$
$972$	−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	−0.429938	−	0.902859i	$-0.641464\pi$
$977$	9.24812	−	6.71916i	0.295874	−	0.214965i	0.725811	+	0.687894i	$0.241464\pi$
$978$	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	−0.0713009	−	0.997455i	$-0.522715\pi$
$983$	17.9549	−	55.2595i	0.572672	−	1.76250i	0.643973	−	0.765048i	$-0.277285\pi$
$984$	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	0.503780	−	0.863832i	$-0.331942\pi$
$997$	12.7437	+	4.14069i	0.403598	+	0.131137i	−0.100181	+	0.994969i	$0.531942\pi$
$998$	−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.245.5		40
8.5	even	2	inner	968.2.o.h.245.9		40
11.2	odd	10		88.2.c.a.45.7	✓	10
11.3	even	5	inner	968.2.o.h.269.1		40
11.4	even	5	inner	968.2.o.h.565.9		40
11.5	even	5	inner	968.2.o.h.493.7		40
11.6	odd	10		968.2.o.g.493.4		40
11.7	odd	10		968.2.o.g.565.2		40
11.8	odd	10		968.2.o.g.269.10		40
11.9	even	5		968.2.c.d.485.4		10
11.10	odd	2		968.2.o.g.245.6		40
33.2	even	10		792.2.f.g.397.4		10
44.31	odd	10		3872.2.c.f.1937.9		10
44.35	even	10		352.2.c.a.177.9		10
88.5	even	10	inner	968.2.o.h.493.1		40
88.13	odd	10		88.2.c.a.45.8	yes	10
88.21	odd	2		968.2.o.g.245.2		40
88.29	odd	10		968.2.o.g.565.6		40
88.35	even	10		352.2.c.a.177.2		10
88.37	even	10	inner	968.2.o.h.565.5		40
88.53	even	10		968.2.c.d.485.3		10
88.61	odd	10		968.2.o.g.493.10		40
88.69	even	10	inner	968.2.o.h.269.7		40
88.75	odd	10		3872.2.c.f.1937.2		10
88.85	odd	10		968.2.o.g.269.4		40
132.35	odd	10		3168.2.f.g.1585.1		10
176.13	odd	20		2816.2.a.r.1.5		5
176.35	even	20		2816.2.a.q.1.1		5
176.101	odd	20		2816.2.a.o.1.1		5
176.123	even	20		2816.2.a.p.1.5		5
264.35	odd	10		3168.2.f.g.1585.10		10
264.101	even	10		792.2.f.g.397.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.c.a.45.7	✓	10	11.2	odd	10
88.2.c.a.45.8	yes	10	88.13	odd	10
352.2.c.a.177.2		10	88.35	even	10
352.2.c.a.177.9		10	44.35	even	10
792.2.f.g.397.3		10	264.101	even	10
792.2.f.g.397.4		10	33.2	even	10
968.2.c.d.485.3		10	88.53	even	10
968.2.c.d.485.4		10	11.9	even	5
968.2.o.g.245.2		40	88.21	odd	2
968.2.o.g.245.6		40	11.10	odd	2
968.2.o.g.269.4		40	88.85	odd	10
968.2.o.g.269.10		40	11.8	odd	10
968.2.o.g.493.4		40	11.6	odd	10
968.2.o.g.493.10		40	88.61	odd	10
968.2.o.g.565.2		40	11.7	odd	10
968.2.o.g.565.6		40	88.29	odd	10
968.2.o.h.245.5		40	1.1	even	1	trivial
968.2.o.h.245.9		40	8.5	even	2	inner
968.2.o.h.269.1		40	11.3	even	5	inner
968.2.o.h.269.7		40	88.69	even	10	inner
968.2.o.h.493.1		40	88.5	even	10	inner
968.2.o.h.493.7		40	11.5	even	5	inner
968.2.o.h.565.5		40	88.37	even	10	inner
968.2.o.h.565.9		40	11.4	even	5	inner
2816.2.a.o.1.1		5	176.101	odd	20
2816.2.a.p.1.5		5	176.123	even	20
2816.2.a.q.1.1		5	176.35	even	20
2816.2.a.r.1.5		5	176.13	odd	20
3168.2.f.g.1585.1		10	132.35	odd	10
3168.2.f.g.1585.10		10	264.35	odd	10
3872.2.c.f.1937.2		10	88.75	odd	10
3872.2.c.f.1937.9		10	44.31	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

Related objects

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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.245.5

Level	$968$
Weight	$2$
Character	968.245
Analytic conductor	$7.730$
Analytic rank	$0$
Dimension	$40$
Inner twists	$8$