LMFDB - Embedded newform 950.2.l.j.701.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			701.3
Character	$\chi$	$=$	950.701
Dual form			950.2.l.j.351.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.654394 + 0.549102i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.654394 + 0.549102i) q^{6} +(-1.39086 - 2.40903i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.394226 - 2.23577i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.654394 + 0.549102i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.654394 + 0.549102i) q^{6} +(-1.39086 - 2.40903i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.394226 - 2.23577i) q^{9} +(-1.58300 + 2.74184i) q^{11} +(-0.427125 - 0.739803i) q^{12} +(-3.68105 + 3.08877i) q^{13} +(2.61395 - 0.951401i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.235648 - 1.33642i) q^{17} +2.27026 q^{18} +(4.15700 - 1.31125i) q^{19} +(0.412636 - 2.34018i) q^{21} +(-2.42530 - 2.03507i) q^{22} +(-5.66623 - 2.06234i) q^{23} +(0.802733 - 0.292171i) q^{24} +(-2.40263 - 4.16148i) q^{26} +(2.25106 - 3.89895i) q^{27} +(0.483039 + 2.73945i) q^{28} +(-1.81040 - 10.2673i) q^{29} +(-3.80232 - 6.58582i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-2.54146 + 0.925014i) q^{33} +(1.27520 + 0.464135i) q^{34} +(-0.394226 + 2.23577i) q^{36} -10.9693 q^{37} +(0.569469 + 4.32154i) q^{38} -4.10490 q^{39} +(2.86803 + 2.40656i) q^{41} +(2.23297 + 0.812735i) q^{42} +(-1.44447 + 0.525743i) q^{43} +(2.42530 - 2.03507i) q^{44} +(3.01494 - 5.22203i) q^{46} +(-0.516096 - 2.92693i) q^{47} +(0.148339 + 0.841273i) q^{48} +(-0.368957 + 0.639053i) q^{49} +(0.888040 - 0.745154i) q^{51} +(4.51548 - 1.64350i) q^{52} +(4.04911 + 1.47376i) q^{53} +(3.44882 + 2.89391i) q^{54} -2.78171 q^{56} +(3.44032 + 1.42454i) q^{57} +10.4257 q^{58} +(0.714103 - 4.04988i) q^{59} +(3.98274 + 1.44960i) q^{61} +(7.14603 - 2.60094i) q^{62} +(-4.83772 + 4.05933i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.469642 - 2.66347i) q^{66} +(0.992825 + 5.63059i) q^{67} +(-0.678520 + 1.17523i) q^{68} +(-2.57551 - 4.46092i) q^{69} +(-0.844623 + 0.307418i) q^{71} +(-2.13334 - 0.776473i) q^{72} +(8.01712 + 6.72716i) q^{73} +(1.90480 - 10.8027i) q^{74} +(-4.35477 - 0.189610i) q^{76} +8.80690 q^{77} +(0.712809 - 4.04254i) q^{78} +(-1.71509 - 1.43913i) q^{79} +(-2.78603 + 1.01403i) q^{81} +(-2.86803 + 2.40656i) q^{82} +(-4.16812 - 7.21939i) q^{83} +(-1.18814 + 2.05792i) q^{84} +(-0.266927 - 1.51382i) q^{86} +(4.45307 - 7.71295i) q^{87} +(1.58300 + 2.74184i) q^{88} +(-7.26679 + 6.09756i) q^{89} +(12.5607 + 4.57174i) q^{91} +(4.61915 + 3.87593i) q^{92} +(1.12807 - 6.39758i) q^{93} +2.97208 q^{94} -0.854251 q^{96} +(-0.456661 + 2.58985i) q^{97} +(-0.565276 - 0.474323i) q^{98} +(6.75417 + 2.45832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) $ 24 * q - 3 * q^7 + 12 * q^8	$ 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 12 * q^8 - 6 * q^11 + 3 * q^12 - 24 * q^13 - 15 * q^14 + 9 * q^17 - 30 * q^18 - 15 * q^19 - 18 * q^21 - 12 * q^23 - 9 * q^26 + 21 * q^27 - 12 * q^28 - 12 * q^29 + 9 * q^31 + 42 * q^33 - 9 * q^34 - 66 * q^37 - 6 * q^38 + 66 * q^39 + 18 * q^41 - 9 * q^42 + 3 * q^43 - 3 * q^46 + 12 * q^47 - 27 * q^49 - 3 * q^51 + 12 * q^52 + 45 * q^53 + 27 * q^54 - 6 * q^56 + 27 * q^57 + 18 * q^58 + 36 * q^59 + 12 * q^61 + 24 * q^62 + 63 * q^63 - 12 * q^64 + 48 * q^66 + 54 * q^67 - 3 * q^68 + 21 * q^69 - 39 * q^71 - 48 * q^73 + 18 * q^74 + 6 * q^76 - 48 * q^77 + 12 * q^78 - 42 * q^79 - 36 * q^81 - 18 * q^82 + 3 * q^83 + 9 * q^84 - 39 * q^86 + 24 * q^87 + 6 * q^88 - 36 * q^89 + 12 * q^91 + 15 * q^92 + 6 * q^93 + 12 * q^94 + 6 * q^96 + 54 * q^97 - 3 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	0.654394	+	0.549102i	0.377815	+	0.317024i	0.811844	−	0.583875i	$-0.198464\pi$
$3$	0.654394	+	0.549102i	0.377815	+	0.317024i	−0.434029	+	0.900899i	$0.642909\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	−0.654394	+	0.549102i	−0.267155	+	0.224170i
$7$	−1.39086	−	2.40903i	−0.525694	−	0.910529i	−0.999552	−	0.0299274i	$-0.990472\pi$
$7$	−1.39086	−	2.40903i	−0.525694	−	0.910529i	0.473858	−	0.880601i	$-0.342861\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.394226	−	2.23577i	−0.131409	−	0.745255i
$10$		0			0
$11$	−1.58300	+	2.74184i	−0.477293	+	0.826695i	−0.999661	−	0.0260244i	$-0.991715\pi$
$11$	−1.58300	+	2.74184i	−0.477293	+	0.826695i	0.522368	+	0.852720i	$0.325049\pi$
$12$	−0.427125	−	0.739803i	−0.123300	−	0.213563i
$13$	−3.68105	+	3.08877i	−1.02094	+	0.856670i	−0.989745	−	0.142844i	$-0.954375\pi$
$13$	−3.68105	+	3.08877i	−1.02094	+	0.856670i	−0.0311941	+	0.999513i	$0.509931\pi$
$14$	2.61395	−	0.951401i	0.698608	−	0.254273i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	0.235648	−	1.33642i	0.0571530	−	0.324131i	−0.942805	−	0.333346i	$-0.891822\pi$
$17$	0.235648	−	1.33642i	0.0571530	−	0.324131i	0.999958	+	0.00921543i	$0.00293340\pi$
$18$	2.27026			0.535104
$19$	4.15700	−	1.31125i	0.953681	−	0.300820i
$19$	4.15700	−	1.31125i	0.953681	−	0.300820i
$20$		0			0
$21$	0.412636	−	2.34018i	0.0900447	−	0.510669i
$22$	−2.42530	−	2.03507i	−0.517075	−	0.433878i
$23$	−5.66623	−	2.06234i	−1.18149	−	0.430027i	−0.324762	−	0.945796i	$-0.605284\pi$
$23$	−5.66623	−	2.06234i	−1.18149	−	0.430027i	−0.856728	+	0.515768i	$0.827507\pi$
$24$	0.802733	−	0.292171i	0.163857	−	0.0596392i
$25$		0			0
$26$	−2.40263	−	4.16148i	−0.471195	−	0.816134i
$27$	2.25106	−	3.89895i	0.433217	−	0.750353i
$28$	0.483039	+	2.73945i	0.0912858	+	0.517707i
$29$	−1.81040	−	10.2673i	−0.336183	−	1.90659i	−0.415229	−	0.909717i	$-0.636298\pi$
$29$	−1.81040	−	10.2673i	−0.336183	−	1.90659i	0.0790458	−	0.996871i	$-0.474813\pi$
$30$		0			0
$31$	−3.80232	−	6.58582i	−0.682917	−	1.18285i	−0.974086	−	0.226176i	$-0.927378\pi$
$31$	−3.80232	−	6.58582i	−0.682917	−	1.18285i	0.291169	−	0.956672i	$-0.405956\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−2.54146	+	0.925014i	−0.442411	+	0.161024i
$34$	1.27520	+	0.464135i	0.218695	+	0.0795986i
$35$		0			0
$36$	−0.394226	+	2.23577i	−0.0657043	+	0.372628i
$37$	−10.9693			−1.80335			−0.901673	−	0.432419i	$-0.857660\pi$
$37$	−10.9693			−1.80335			−0.901673	+	0.432419i	$0.857660\pi$
$38$	0.569469	+	4.32154i	0.0923801	+	0.701046i
$39$	−4.10490			−0.657311
$40$		0			0
$41$	2.86803	+	2.40656i	0.447910	+	0.375841i	0.838660	−	0.544656i	$-0.183340\pi$
$41$	2.86803	+	2.40656i	0.447910	+	0.375841i	−0.390749	+	0.920497i	$0.627784\pi$
$42$	2.23297	+	0.812735i	0.344555	+	0.125408i
$43$	−1.44447	+	0.525743i	−0.220279	+	0.0801750i	−0.449802	−	0.893128i	$-0.648506\pi$
$43$	−1.44447	+	0.525743i	−0.220279	+	0.0801750i	0.229523	+	0.973303i	$0.426283\pi$
$44$	2.42530	−	2.03507i	0.365628	−	0.306798i
$45$		0			0
$46$	3.01494	−	5.22203i	0.444528	−	0.769946i
$47$	−0.516096	−	2.92693i	−0.0752804	−	0.426936i	−0.999034	−	0.0439484i	$-0.986006\pi$
$47$	−0.516096	−	2.92693i	−0.0752804	−	0.426936i	0.923753	−	0.382988i	$-0.125105\pi$
$48$	0.148339	+	0.841273i	0.0214109	+	0.121427i
$49$	−0.368957	+	0.639053i	−0.0527082	+	0.0912933i
$50$		0			0
$51$	0.888040	−	0.745154i	0.124350	−	0.104342i
$52$	4.51548	−	1.64350i	0.626184	−	0.227912i
$53$	4.04911	+	1.47376i	0.556188	+	0.202436i	0.604794	−	0.796382i	$-0.293255\pi$
$53$	4.04911	+	1.47376i	0.556188	+	0.202436i	−0.0486055	+	0.998818i	$0.515478\pi$
$54$	3.44882	+	2.89391i	0.469326	+	0.393811i
$55$		0			0
$56$	−2.78171			−0.371722
$57$	3.44032	+	1.42454i	0.455682	+	0.188686i
$58$	10.4257			1.36896
$59$	0.714103	−	4.04988i	0.0929682	−	0.527249i	−0.902383	−	0.430935i	$-0.858184\pi$
$59$	0.714103	−	4.04988i	0.0929682	−	0.527249i	0.995351	−	0.0963137i	$-0.0307052\pi$
$60$		0			0
$61$	3.98274	+	1.44960i	0.509937	+	0.185602i	0.584158	−	0.811640i	$-0.301425\pi$
$61$	3.98274	+	1.44960i	0.509937	+	0.185602i	−0.0742210	+	0.997242i	$0.523647\pi$
$62$	7.14603	−	2.60094i	0.907547	−	0.330320i
$63$	−4.83772	+	4.05933i	−0.609495	+	0.511427i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−0.469642	−	2.66347i	−0.0578089	−	0.327851i
$67$	0.992825	+	5.63059i	0.121293	+	0.687886i	0.983441	+	0.181230i	$0.0580077\pi$
$67$	0.992825	+	5.63059i	0.121293	+	0.687886i	−0.862148	+	0.506657i	$0.830881\pi$
$68$	−0.678520	+	1.17523i	−0.0822827	+	0.142518i
$69$	−2.57551	−	4.46092i	−0.310055	−	0.537032i
$70$		0			0
$71$	−0.844623	+	0.307418i	−0.100238	+	0.0364838i	−0.391652	−	0.920113i	$-0.628096\pi$
$71$	−0.844623	+	0.307418i	−0.100238	+	0.0364838i	0.291414	+	0.956597i	$0.405874\pi$
$72$	−2.13334	−	0.776473i	−0.251417	−	0.0915082i
$73$	8.01712	+	6.72716i	0.938333	+	0.787355i	0.977294	−	0.211886i	$-0.0679604\pi$
$73$	8.01712	+	6.72716i	0.938333	+	0.787355i	−0.0389612	+	0.999241i	$0.512405\pi$
$74$	1.90480	−	10.8027i	0.221429	−	1.25579i
$75$		0			0
$76$	−4.35477	−	0.189610i	−0.499527	−	0.0217497i
$77$	8.80690			1.00364
$78$	0.712809	−	4.04254i	0.0807097	−	0.457728i
$79$	−1.71509	−	1.43913i	−0.192963	−	0.161915i	0.541187	−	0.840902i	$-0.317975\pi$
$79$	−1.71509	−	1.43913i	−0.192963	−	0.161915i	−0.734151	+	0.678987i	$0.762419\pi$
$80$		0			0
$81$	−2.78603	+	1.01403i	−0.309558	+	0.112670i
$82$	−2.86803	+	2.40656i	−0.316720	+	0.265760i
$83$	−4.16812	−	7.21939i	−0.457510	−	0.792431i	0.541319	−	0.840818i	$-0.317925\pi$
$83$	−4.16812	−	7.21939i	−0.457510	−	0.792431i	−0.998829	+	0.0483869i	$0.984592\pi$
$84$	−1.18814	+	2.05792i	−0.129637	+	0.224537i
$85$		0			0
$86$	−0.266927	−	1.51382i	−0.0287834	−	0.163239i
$87$	4.45307	−	7.71295i	0.477420	−	0.826915i
$88$	1.58300	+	2.74184i	0.168748	+	0.292281i
$89$	−7.26679	+	6.09756i	−0.770278	+	0.646340i	−0.940780	−	0.339017i	$-0.889906\pi$
$89$	−7.26679	+	6.09756i	−0.770278	+	0.646340i	0.170502	+	0.985357i	$0.445461\pi$
$90$		0			0
$91$	12.5607	+	4.57174i	1.31672	+	0.479248i
$92$	4.61915	+	3.87593i	0.481580	+	0.404094i
$93$	1.12807	−	6.39758i	0.116975	−	0.663398i
$94$	2.97208			0.306547
$95$		0			0
$96$	−0.854251			−0.0871866
$97$	−0.456661	+	2.58985i	−0.0463669	+	0.262960i	−0.999175	−	0.0406138i	$-0.987069\pi$
$97$	−0.456661	+	2.58985i	−0.0463669	+	0.262960i	0.952808	+	0.303573i	$0.0981798\pi$
$98$	−0.565276	−	0.474323i	−0.0571015	−	0.0479138i
$99$	6.75417	+	2.45832i	0.678819	+	0.247070i
$100$		0			0
$101$	13.2133	−	11.0873i	1.31477	−	1.10323i	0.327387	−	0.944890i	$-0.393832\pi$
$101$	13.2133	−	11.0873i	1.31477	−	1.10323i	0.987386	−	0.158335i	$-0.0506125\pi$
$102$	0.579627	+	1.00394i	0.0573916	+	0.0994051i
$103$	−6.08058	+	10.5319i	−0.599137	+	1.03774i	0.393811	+	0.919191i	$0.371156\pi$
$103$	−6.08058	+	10.5319i	−0.599137	+	1.03774i	−0.992949	+	0.118545i	$0.962177\pi$
$104$	0.834426	+	4.73227i	0.0818222	+	0.464037i
$105$		0			0
$106$	−2.15449	+	3.73168i	−0.209262	+	0.362453i
$107$	−6.97556	−	12.0820i	−0.674353	−	1.16801i	−0.976658	−	0.214802i	$-0.931090\pi$
$107$	−6.97556	−	12.0820i	−0.674353	−	1.16801i	0.302305	−	0.953211i	$-0.402244\pi$
$108$	−3.44882	+	2.89391i	−0.331863	+	0.278466i
$109$	−15.9616	+	5.80955i	−1.52884	+	0.556454i	−0.963338	−	0.268291i	$-0.913541\pi$
$109$	−15.9616	+	5.80955i	−1.52884	+	0.556454i	−0.565506	+	0.824744i	$0.691319\pi$
$110$		0			0
$111$	−7.17826	−	6.02328i	−0.681330	−	0.571704i
$112$	0.483039	−	2.73945i	0.0456429	−	0.258854i
$113$	−0.218859			−0.0205885			−0.0102943	−	0.999947i	$-0.503277\pi$
$113$	−0.218859			−0.0205885			−0.0102943	+	0.999947i	$0.503277\pi$
$114$	−2.00031	+	3.14069i	−0.187346	+	0.294152i
$115$		0			0
$116$	−1.81040	+	10.2673i	−0.168091	+	0.953294i
$117$	8.35692	+	7.01229i	0.772598	+	0.648286i
$118$	3.86435	+	1.40651i	0.355742	+	0.129480i
$119$	−3.54724	+	1.29109i	−0.325175	+	0.118354i
$120$		0			0
$121$	0.488214	+	0.845612i	0.0443831	+	0.0768738i
$122$	−2.11917	+	3.67051i	−0.191861	+	0.332312i
$123$	0.555373	+	3.14968i	0.0500763	+	0.283997i
$124$	1.32053	+	7.48911i	0.118587	+	0.672542i
$125$		0			0
$126$	−3.15760	−	5.46912i	−0.281301	−	0.487228i
$127$	−9.62855	+	8.07931i	−0.854396	+	0.716923i	−0.960753	−	0.277405i	$-0.910526\pi$
$127$	−9.62855	+	8.07931i	−0.854396	+	0.716923i	0.106357	+	0.994328i	$0.466081\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−1.23394	−	0.449116i	−0.108642	−	0.0395425i
$130$		0			0
$131$	−2.41452	+	13.6934i	−0.210958	+	1.19640i	0.676827	+	0.736143i	$0.263355\pi$
$131$	−2.41452	+	13.6934i	−0.210958	+	1.19640i	−0.887785	+	0.460259i	$0.847756\pi$
$132$	2.70456			0.235402
$133$	−8.94062	−	8.19059i	−0.775250	−	0.710214i
$134$	−5.71745			−0.493913
$135$		0			0
$136$	−1.03955	−	0.872289i	−0.0891410	−	0.0747982i
$137$	−5.81017	−	2.11473i	−0.496397	−	0.180674i	0.0816760	−	0.996659i	$-0.473973\pi$
$137$	−5.81017	−	2.11473i	−0.496397	−	0.180674i	−0.578073	+	0.815985i	$0.696195\pi$
$138$	4.84038	−	1.76175i	0.412041	−	0.149971i
$139$	6.72241	−	5.64077i	0.570188	−	0.478444i	−0.311521	−	0.950239i	$-0.600838\pi$
$139$	6.72241	−	5.64077i	0.570188	−	0.478444i	0.881708	+	0.471795i	$0.156394\pi$
$140$		0			0
$141$	1.26945	−	2.19875i	0.106907	−	0.185168i
$142$	−0.156080	−	0.885174i	−0.0130979	−	0.0742822i
$143$	−2.64180	−	14.9824i	−0.220918	−	1.25289i
$144$	1.13513	−	1.96610i	0.0945940	−	0.163842i
$145$		0			0
$146$	−8.01712	+	6.72716i	−0.663502	+	0.556744i
$147$	−0.592349	+	0.215597i	−0.0488561	+	0.0177822i
$148$	10.3078	+	3.75173i	0.847295	+	0.308390i
$149$	12.6163	+	10.5864i	1.03357	+	0.867268i	0.991271	−	0.131837i	$-0.0420875\pi$
$149$	12.6163	+	10.5864i	1.03357	+	0.867268i	0.0422987	+	0.999105i	$0.486532\pi$
$150$		0			0
$151$	14.7347			1.19909			0.599547	−	0.800340i	$-0.295347\pi$
$151$	14.7347			1.19909			0.599547	+	0.800340i	$0.295347\pi$
$152$	0.942928	−	4.25569i	0.0764815	−	0.345182i
$153$	−3.08083			−0.249070
$154$	−1.52930	+	8.67311i	−0.123235	+	0.698899i
$155$		0			0
$156$	3.85735	+	1.40396i	0.308835	+	0.112407i
$157$	8.62832	−	3.14045i	0.688615	−	0.250635i	0.0260727	−	0.999660i	$-0.491700\pi$
$157$	8.62832	−	3.14045i	0.688615	−	0.250635i	0.662542	+	0.749025i	$0.269478\pi$
$158$	1.71509	−	1.43913i	0.136446	−	0.114491i
$159$	1.84047	+	3.18779i	0.145959	+	0.252808i
$160$		0			0
$161$	2.91267	+	16.5185i	0.229550	+	1.30184i
$162$	−0.514837	−	2.91978i	−0.0404494	−	0.229400i
$163$	8.18335	−	14.1740i	0.640970	−	1.11019i	−0.344247	−	0.938879i	$-0.611866\pi$
$163$	8.18335	−	14.1740i	0.640970	−	1.11019i	0.985217	−	0.171313i	$-0.0548010\pi$
$164$	−1.87197	−	3.24235i	−0.146176	−	0.253185i
$165$		0			0
$166$	7.83349	−	2.85116i	0.607997	−	0.221293i
$167$	−12.3025	−	4.47774i	−0.951994	−	0.346498i	−0.181103	−	0.983464i	$-0.557967\pi$
$167$	−12.3025	−	4.47774i	−0.951994	−	0.346498i	−0.770891	+	0.636967i	$0.780189\pi$
$168$	−1.82034	−	1.52744i	−0.140442	−	0.117845i
$169$	1.75222	−	9.93731i	0.134786	−	0.764408i
$170$		0			0
$171$	−4.57043	−	8.77715i	−0.349510	−	0.671205i
$172$	1.53717			0.117208
$173$	2.98366	−	16.9212i	0.226843	−	1.28649i	−0.632286	−	0.774735i	$-0.717883\pi$
$173$	2.98366	−	16.9212i	0.226843	−	1.28649i	0.859130	−	0.511758i	$-0.171006\pi$
$174$	6.82250	+	5.72476i	0.517213	+	0.433993i
$175$		0			0
$176$	−2.97507	+	1.08284i	−0.224254	+	0.0816219i
$177$	2.69110	−	2.25810i	0.202275	−	0.169729i
$178$	−4.74306	−	8.21522i	−0.355507	−	0.615757i
$179$	0.234505	−	0.406174i	0.0175277	−	0.0303589i	−0.857129	−	0.515103i	$-0.827754\pi$
$179$	0.234505	−	0.406174i	0.0175277	−	0.0303589i	0.874656	+	0.484744i	$0.161087\pi$
$180$		0			0
$181$	2.91687	+	16.5424i	0.216809	+	1.22958i	0.877740	+	0.479138i	$0.159051\pi$
$181$	2.91687	+	16.5424i	0.216809	+	1.22958i	−0.660931	+	0.750447i	$0.729838\pi$
$182$	−6.68343	+	11.5760i	−0.495409	+	0.858074i
$183$	1.81030	+	3.13554i	0.133821	+	0.231785i
$184$	−4.61915	+	3.87593i	−0.340528	+	0.285737i
$185$		0			0
$186$	6.10450	+	2.22186i	0.447604	+	0.162914i
$187$	3.29123	+	2.76167i	0.240679	+	0.201953i
$188$	−0.516096	+	2.92693i	−0.0376402	+	0.213468i
$189$	−12.5236			−0.910958
$190$		0			0
$191$	−18.1568			−1.31378			−0.656891	−	0.753985i	$-0.728129\pi$
$191$	−18.1568			−1.31378			−0.656891	+	0.753985i	$0.728129\pi$
$192$	0.148339	−	0.841273i	0.0107055	−	0.0607136i
$193$	3.41781	+	2.86788i	0.246019	+	0.206435i	0.757456	−	0.652886i	$-0.226442\pi$
$193$	3.41781	+	2.86788i	0.246019	+	0.206435i	−0.511437	+	0.859321i	$0.670887\pi$
$194$	−2.47121	−	0.899446i	−0.177422	−	0.0645765i
$195$		0			0
$196$	0.565276	−	0.474323i	0.0403768	−	0.0338802i
$197$	10.2342	+	17.7262i	0.729160	+	1.26294i	0.957239	+	0.289299i	$0.0934223\pi$
$197$	10.2342	+	17.7262i	0.729160	+	1.26294i	−0.228079	+	0.973643i	$0.573244\pi$
$198$	−3.59382	+	6.22467i	−0.255401	+	0.442368i
$199$	1.40764	+	7.98310i	0.0997847	+	0.565907i	0.993176	+	0.116627i	$0.0372083\pi$
$199$	1.40764	+	7.98310i	0.0997847	+	0.565907i	−0.893391	+	0.449280i	$0.851681\pi$
$200$		0			0
$201$	−2.44207	+	4.22979i	−0.172250	+	0.298346i
$202$	8.62437	+	14.9378i	0.606808	+	1.05102i
$203$	−22.2162	+	18.6416i	−1.55927	+	1.30839i
$204$	−1.08934	+	0.396488i	−0.0762692	+	0.0277597i
$205$		0			0
$206$	−9.31599	−	7.81704i	−0.649076	−	0.544639i
$207$	−2.37713	+	13.4814i	−0.165222	+	0.937021i
$208$	−4.80527			−0.333185
$209$	−2.98531	+	13.4735i	−0.206498	+	0.931983i
$210$		0			0
$211$	4.24189	−	24.0570i	0.292024	−	1.65615i	−0.387035	−	0.922065i	$-0.626501\pi$
$211$	4.24189	−	24.0570i	0.292024	−	1.65615i	0.679059	−	0.734084i	$-0.262388\pi$
$212$	−3.30087	−	2.76976i	−0.226704	−	0.190228i
$213$	−0.721520	−	0.262612i	−0.0494377	−	0.0179939i
$214$	13.1098	−	4.77156i	0.896165	−	0.326177i
$215$		0			0
$216$	−2.25106	−	3.89895i	−0.153165	−	0.265290i
$217$	−10.5770	+	18.3198i	−0.718011	+	1.24363i
$218$	−2.94958	−	16.7279i	−0.199771	−	1.13296i
$219$	1.55246	+	8.80443i	0.104905	+	0.594949i
$220$		0			0
$221$	3.26047	+	5.64730i	0.219323	+	0.379879i
$222$	7.17826	−	6.02328i	0.481773	−	0.404256i
$223$	23.3511	−	8.49912i	1.56371	−	0.569143i	0.592126	−	0.805846i	$-0.298289\pi$
$223$	23.3511	−	8.49912i	1.56371	−	0.569143i	0.971582	+	0.236703i	$0.0760667\pi$
$224$	2.61395	+	0.951401i	0.174652	+	0.0635682i
$225$		0			0
$226$	0.0380045	−	0.215534i	0.00252802	−	0.0143371i
$227$	−8.33013			−0.552890			−0.276445	−	0.961030i	$-0.589156\pi$
$227$	−8.33013			−0.552890			−0.276445	+	0.961030i	$0.589156\pi$
$228$	−2.74562	−	2.51529i	−0.181833	−	0.166579i
$229$	0.699318			0.0462123			0.0231061	−	0.999733i	$-0.492644\pi$
$229$	0.699318			0.0462123			0.0231061	+	0.999733i	$0.492644\pi$
$230$		0			0
$231$	5.76319	+	4.83589i	0.379190	+	0.318178i
$232$	−9.79693	−	3.56579i	−0.643200	−	0.234106i
$233$	−2.41623	+	0.879436i	−0.158293	+	0.0576138i	−0.419951	−	0.907547i	$-0.637953\pi$
$233$	−2.41623	+	0.879436i	−0.158293	+	0.0576138i	0.261659	+	0.965160i	$0.415731\pi$
$234$	−8.35692	+	7.01229i	−0.546309	+	0.458408i
$235$		0			0
$236$	−2.05618	+	3.56140i	−0.133846	+	0.231828i
$237$	−0.332116	−	1.88352i	−0.0215732	−	0.122348i
$238$	−0.655504	−	3.71755i	−0.0424900	−	0.240973i
$239$	−8.86697	+	15.3580i	−0.573557	+	0.993430i	0.422640	+	0.906298i	$0.361104\pi$
$239$	−8.86697	+	15.3580i	−0.573557	+	0.993430i	−0.996197	+	0.0871319i	$0.972230\pi$
$240$		0			0
$241$	−6.92980	+	5.81479i	−0.446387	+	0.374564i	−0.838093	−	0.545527i	$-0.816330\pi$
$241$	−6.92980	+	5.81479i	−0.446387	+	0.374564i	0.391706	+	0.920091i	$0.371885\pi$
$242$	−0.917543	+	0.333958i	−0.0589819	+	0.0214676i
$243$	−15.0718	−	5.48568i	−0.966856	−	0.351907i
$244$	−3.24676	−	2.72435i	−0.207852	−	0.174409i
$245$		0			0
$246$	−3.19827			−0.203914
$247$	−11.2520	+	17.6668i	−0.715947	+	1.12411i
$248$	−7.60465			−0.482896
$249$	1.23659	−	7.01304i	0.0783656	−	0.444434i
$250$		0			0
$251$	6.34305	+	2.30868i	0.400370	+	0.145723i	0.534354	−	0.845261i	$-0.320555\pi$
$251$	6.34305	+	2.30868i	0.400370	+	0.145723i	−0.133984	+	0.990983i	$0.542777\pi$
$252$	5.93434	−	2.15992i	0.373828	−	0.136062i
$253$	14.6242	−	12.2712i	0.919419	−	0.771484i
$254$	−6.28459	−	10.8852i	−0.394330	−	0.683000i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−0.561448	−	3.18413i	−0.0350222	−	0.198621i	0.962277	−	0.272073i	$-0.0877093\pi$
$257$	−0.561448	−	3.18413i	−0.0350222	−	0.198621i	−0.997299	+	0.0734526i	$0.976598\pi$
$258$	0.656564	−	1.13720i	0.0408759	−	0.0707991i
$259$	15.2567	+	26.4255i	0.948008	+	1.64200i
$260$		0			0
$261$	−22.2415	+	8.09526i	−1.37672	+	0.501084i
$262$	−13.0661	−	4.75568i	−0.807228	−	0.293807i
$263$	0.784511	+	0.658282i	0.0483750	+	0.0405914i	0.666655	−	0.745367i	$-0.267726\pi$
$263$	0.784511	+	0.658282i	0.0483750	+	0.0405914i	−0.618280	+	0.785958i	$0.712170\pi$
$264$	−0.469642	+	2.66347i	−0.0289045	+	0.163925i
$265$		0			0
$266$	9.61868	−	7.38251i	0.589759	−	0.452650i
$267$	−8.10353			−0.495928
$268$	0.992825	−	5.63059i	0.0606465	−	0.343943i
$269$	−7.15929	−	6.00736i	−0.436509	−	0.366275i	0.397892	−	0.917432i	$-0.369742\pi$
$269$	−7.15929	−	6.00736i	−0.436509	−	0.366275i	−0.834401	+	0.551157i	$0.814186\pi$
$270$		0			0
$271$	−9.09509	+	3.31034i	−0.552487	+	0.201089i	−0.603151	−	0.797627i	$-0.706088\pi$
$271$	−9.09509	+	3.31034i	−0.552487	+	0.201089i	0.0506640	+	0.998716i	$0.483866\pi$
$272$	1.03955	−	0.872289i	0.0630322	−	0.0528903i
$273$	5.70933	+	9.88885i	0.345544	+	0.598500i
$274$	3.09153	−	5.35468i	0.186766	−	0.323488i
$275$		0			0
$276$	0.894466	+	5.07277i	0.0538405	+	0.305345i
$277$	1.30482	−	2.26001i	0.0783990	−	0.135791i	−0.824160	−	0.566357i	$-0.808353\pi$
$277$	1.30482	−	2.26001i	0.0783990	−	0.135791i	0.902559	+	0.430566i	$0.141686\pi$
$278$	4.38774	+	7.59980i	0.263159	+	0.455805i
$279$	−13.2254	+	11.0974i	−0.791782	+	0.664384i
$280$		0			0
$281$	−28.4175	−	10.3431i	−1.69524	−	0.617018i	−0.699974	−	0.714169i	$-0.746805\pi$
$281$	−28.4175	−	10.3431i	−1.69524	−	0.617018i	−0.995270	+	0.0971504i	$0.969027\pi$
$282$	1.94491	+	1.63197i	0.115818	+	0.0971827i
$283$	3.30904	−	18.7665i	0.196702	−	1.11555i	−0.713272	−	0.700887i	$-0.752788\pi$
$283$	3.30904	−	18.7665i	0.196702	−	1.11555i	0.909974	−	0.414665i	$-0.136101\pi$
$284$	0.898829			0.0533357
$285$		0			0
$286$	15.2135			0.899593
$287$	1.80847	−	10.2563i	0.106751	−	0.605413i
$288$	1.73912	+	1.45929i	0.102478	+	0.0859896i
$289$	14.2443	+	5.18449i	0.837898	+	0.304970i
$290$		0			0
$291$	−1.72093	+	1.44403i	−0.100883	+	0.0846506i
$292$	−5.23281	−	9.06348i	−0.306227	−	0.530400i
$293$	−0.314058	+	0.543964i	−0.0183474	+	0.0317787i	−0.875053	−	0.484026i	$-0.839174\pi$
$293$	−0.314058	+	0.543964i	−0.0183474	+	0.0317787i	0.856706	+	0.515805i	$0.172507\pi$
$294$	−0.109462	−	0.620788i	−0.00638393	−	0.0362051i
$295$		0			0
$296$	−5.48466	+	9.49971i	−0.318789	+	0.552160i
$297$	7.12686	+	12.3441i	0.413542	+	0.716277i
$298$	−12.6163	+	10.5864i	−0.730844	+	0.613251i
$299$	27.2278	−	9.91009i	1.57462	−	0.573115i
$300$		0			0
$301$	3.27558	+	2.74853i	0.188801	+	0.158423i
$302$	−2.55866	+	14.5109i	−0.147234	+	0.835006i
$303$	14.7347			0.846489
$304$	4.02730	+	1.66760i	0.230981	+	0.0956431i
$305$		0			0
$306$	0.534980	−	3.03402i	0.0305828	−	0.173444i
$307$	−16.3205	−	13.6945i	−0.931460	−	0.781588i	0.0446192	−	0.999004i	$-0.485793\pi$
$307$	−16.3205	−	13.6945i	−0.931460	−	0.781588i	−0.976079	+	0.217417i	$0.930237\pi$
$308$	−8.27578	−	3.01214i	−0.471556	−	0.171633i
$309$	−9.76217	+	3.55314i	−0.555350	+	0.202131i
$310$		0			0
$311$	−16.4799	−	28.5440i	−0.934490	−	1.61858i	−0.775541	−	0.631298i	$-0.782523\pi$
$311$	−16.4799	−	28.5440i	−0.934490	−	1.61858i	−0.158950	−	0.987287i	$-0.550811\pi$
$312$	−2.05245	+	3.55495i	−0.116197	+	0.201259i
$313$	4.95291	+	28.0894i	0.279955	+	1.58770i	0.722768	+	0.691090i	$0.242869\pi$
$313$	4.95291	+	28.0894i	0.279955	+	1.58770i	−0.442813	+	0.896614i	$0.646020\pi$
$314$	1.59445	+	9.04257i	0.0899799	+	0.510302i
$315$		0			0
$316$	1.11945	+	1.93894i	0.0629739	+	0.109074i
$317$	23.4843	−	19.7057i	1.31901	−	1.10678i	0.332494	−	0.943105i	$-0.392110\pi$
$317$	23.4843	−	19.7057i	1.31901	−	1.10678i	0.986514	−	0.163674i	$-0.0523346\pi$
$318$	−3.45896	+	1.25896i	−0.193969	+	0.0705988i
$319$	31.0171	+	11.2893i	1.73663	+	0.632080i
$320$		0			0
$321$	2.06950	−	11.7367i	0.115508	−	0.655078i
$322$	−16.7734			−0.934743
$323$	−0.772793	−	5.86451i	−0.0429993	−	0.326310i
$324$	2.96483			0.164713
$325$		0			0
$326$	12.5376	+	10.5203i	0.694395	+	0.582666i
$327$	−13.6352	−	4.96281i	−0.754029	−	0.274444i
$328$	3.51815	−	1.28050i	0.194258	−	0.0707040i
$329$	−6.33325	+	5.31422i	−0.349163	+	0.292983i
$330$		0			0
$331$	−3.90181	+	6.75813i	−0.214463	+	0.371460i	−0.953106	−	0.302636i	$-0.902133\pi$
$331$	−3.90181	+	6.75813i	−0.214463	+	0.371460i	0.738644	+	0.674096i	$0.235467\pi$
$332$	1.44757	+	8.20958i	0.0794458	+	0.450559i
$333$	4.32439	+	24.5248i	0.236975	+	1.34395i
$334$	6.54601	−	11.3380i	0.358182	−	0.620389i
$335$		0			0
$336$	1.82034	−	1.52744i	0.0993074	−	0.0833288i
$337$	3.37565	−	1.22864i	0.183883	−	0.0669280i	−0.248437	−	0.968648i	$-0.579917\pi$
$337$	3.37565	−	1.22864i	0.183883	−	0.0669280i	0.432321	+	0.901720i	$0.357695\pi$
$338$	9.48207	+	3.45119i	0.515756	+	0.187720i
$339$	−0.143220	−	0.120176i	−0.00777865	−	0.00652706i
$340$		0			0
$341$	24.0763			1.30381
$342$	9.43745	−	2.97686i	0.510319	−	0.160970i
$343$	−17.4193			−0.940554
$344$	−0.266927	+	1.51382i	−0.0143917	+	0.0816195i
$345$		0			0
$346$	16.1460	+	5.87666i	0.868014	+	0.315931i
$347$	14.4497	−	5.25926i	0.775701	−	0.282332i	0.0763220	−	0.997083i	$-0.475682\pi$
$347$	14.4497	−	5.25926i	0.775701	−	0.282332i	0.699379	+	0.714751i	$0.253460\pi$
$348$	−6.82250	+	5.72476i	−0.365725	+	0.306879i
$349$	−16.4988	−	28.5767i	−0.883159	−	1.52968i	−0.847809	−	0.530301i	$-0.822079\pi$
$349$	−16.4988	−	28.5767i	−0.883159	−	1.52968i	−0.0353493	−	0.999375i	$-0.511254\pi$
$350$		0			0
$351$	3.75669	+	21.3052i	0.200517	+	1.13719i
$352$	−0.549771	−	3.11790i	−0.0293029	−	0.166185i
$353$	2.92362	−	5.06386i	0.155608	−	0.269522i	−0.777672	−	0.628670i	$-0.783600\pi$
$353$	2.92362	−	5.06386i	0.155608	−	0.269522i	0.933280	+	0.359149i	$0.116933\pi$
$354$	1.75649	+	3.04233i	0.0933564	+	0.161698i
$355$		0			0
$356$	8.91404	−	3.24444i	0.472443	−	0.171955i
$357$	−3.03023	−	1.10291i	−0.160377	−	0.0583724i
$358$	0.359282	+	0.301474i	0.0189887	+	0.0159334i
$359$	2.72021	−	15.4271i	0.143567	−	0.814209i	−0.824940	−	0.565221i	$-0.808791\pi$
$359$	2.72021	−	15.4271i	0.143567	−	0.814209i	0.968507	−	0.248988i	$-0.0800980\pi$
$360$		0			0
$361$	15.5613	−	10.9017i	0.819014	−	0.573773i
$362$	−16.7976			−0.882860
$363$	−0.144843	+	0.821443i	−0.00760226	+	0.0431146i
$364$	−10.2396	−	8.59206i	−0.536702	−	0.450346i
$365$		0			0
$366$	−3.40226	+	1.23832i	−0.177839	+	0.0647280i
$367$	10.7857	−	9.05031i	0.563011	−	0.472423i	−0.316307	−	0.948657i	$-0.602443\pi$
$367$	10.7857	−	9.05031i	0.563011	−	0.472423i	0.879318	+	0.476234i	$0.157999\pi$
$368$	−3.01494	−	5.22203i	−0.157164	−	0.272217i
$369$	4.24985	−	7.36096i	0.221238	−	0.383196i
$370$		0			0
$371$	−2.08140	−	11.8042i	−0.108061	−	0.612845i
$372$	−3.24814	+	5.62594i	−0.168408	+	0.291691i
$373$	1.70094	+	2.94612i	0.0880714	+	0.152544i	0.906696	−	0.421785i	$-0.138596\pi$
$373$	1.70094	+	2.94612i	0.0880714	+	0.152544i	−0.818624	+	0.574329i	$0.805263\pi$
$374$	−3.29123	+	2.76167i	−0.170185	+	0.142803i
$375$		0			0
$376$	−2.79284	−	1.01651i	−0.144030	−	0.0524226i
$377$	38.3774	+	32.2025i	1.97654	+	1.65851i
$378$	2.17470	−	12.3333i	0.111854	−	0.634358i
$379$	3.36412			0.172803			0.0864016	−	0.996260i	$-0.472463\pi$
$379$	3.36412			0.172803			0.0864016	+	0.996260i	$0.472463\pi$
$380$		0			0
$381$	−10.7372			−0.550085
$382$	3.15290	−	17.8810i	0.161316	−	0.914871i
$383$	1.33818	+	1.12286i	0.0683776	+	0.0573756i	0.676336	−	0.736593i	$-0.263567\pi$
$383$	1.33818	+	1.12286i	0.0683776	+	0.0573756i	−0.607958	+	0.793969i	$0.708011\pi$
$384$	0.802733	+	0.292171i	0.0409643	+	0.0149098i
$385$		0			0
$386$	−3.41781	+	2.86788i	−0.173962	+	0.145971i
$387$	1.74488	+	3.02223i	0.0886974	+	0.153628i
$388$	1.31490	−	2.27748i	0.0667540	−	0.115621i
$389$	−0.512989	−	2.90930i	−0.0260096	−	0.147508i	0.969037	−	0.246914i	$-0.0794166\pi$
$389$	−0.512989	−	2.90930i	−0.0260096	−	0.147508i	−0.995047	+	0.0994067i	$0.968306\pi$
$390$		0			0
$391$	−4.09139	+	7.08650i	−0.206911	+	0.358380i
$392$	0.368957	+	0.639053i	0.0186352	+	0.0322771i
$393$	−9.09915	+	7.63509i	−0.458991	+	0.385139i
$394$	−19.2341	+	7.00064i	−0.969000	+	0.352687i
$395$		0			0
$396$	−5.50605	−	4.62012i	−0.276689	−	0.232170i
$397$	−0.330922	+	1.87675i	−0.0166085	+	0.0941914i	−0.991985	−	0.126354i	$-0.959673\pi$
$397$	−0.330922	+	1.87675i	−0.0166085	+	0.0941914i	0.975377	+	0.220545i	$0.0707837\pi$
$398$	−8.10626			−0.406330
$399$	−1.35322	−	10.2692i	−0.0677456	−	0.514102i
$400$		0			0
$401$	0.443767	−	2.51673i	0.0221607	−	0.125679i	−0.971721	−	0.236134i	$-0.924120\pi$
$401$	0.443767	−	2.51673i	0.0221607	−	0.125679i	0.993881	+	0.110455i	$0.0352307\pi$
$402$	−3.74147	−	3.13946i	−0.186607	−	0.156582i
$403$	34.3386	+	12.4982i	1.71053	+	0.622581i
$404$	−16.2085	+	5.89942i	−0.806404	+	0.293507i
$405$		0			0
$406$	−14.5006	−	25.1158i	−0.719653	−	1.24648i
$407$	17.3645	−	30.0761i	0.860724	−	1.49082i
$408$	−0.201302	−	1.14164i	−0.00996594	−	0.0565197i
$409$	−0.172527	−	0.978451i	−0.00853092	−	0.0483813i	0.980245	−	0.197786i	$-0.0633752\pi$
$409$	−0.172527	−	0.978451i	−0.00853092	−	0.0483813i	−0.988776	+	0.149405i	$0.952264\pi$
$410$		0			0
$411$	−2.64094	−	4.57424i	−0.130268	−	0.225631i
$412$	9.31599	−	7.81704i	0.458966	−	0.385118i
$413$	−10.7495	+	3.91250i	−0.528948	+	0.192521i
$414$	−12.8638	−	4.68204i	−0.632221	−	0.230110i
$415$		0			0
$416$	0.834426	−	4.73227i	0.0409111	−	0.232018i
$417$	7.49647			0.367104
$418$	−12.7504	−	5.27961i	−0.623644	−	0.258234i
$419$	−14.8657			−0.726238			−0.363119	−	0.931743i	$-0.618288\pi$
$419$	−14.8657			−0.726238			−0.363119	+	0.931743i	$0.618288\pi$
$420$		0			0
$421$	29.8436	+	25.0418i	1.45449	+	1.22046i	0.929221	+	0.369526i	$0.120480\pi$
$421$	29.8436	+	25.0418i	1.45449	+	1.22046i	0.525269	+	0.850936i	$0.323965\pi$
$422$	22.9549	+	8.35489i	1.11743	+	0.406710i
$423$	−6.34046	+	2.30774i	−0.308284	+	0.112206i
$424$	3.30087	−	2.76976i	0.160304	−	0.134511i
$425$		0			0
$426$	0.383913	−	0.664957i	0.0186006	−	0.0322173i
$427$	−2.04728	−	11.6107i	−0.0990750	−	0.561882i
$428$	2.42259	+	13.7392i	0.117100	+	0.664108i
$429$	6.49807	−	11.2550i	0.313730	−	0.543396i
$430$		0			0
$431$	−20.8535	+	17.4982i	−1.00448	+	0.842857i	−0.987599	−	0.157000i	$-0.949818\pi$
$431$	−20.8535	+	17.4982i	−1.00448	+	0.842857i	−0.0168797	+	0.999858i	$0.505373\pi$
$432$	4.23061	−	1.53982i	0.203545	−	0.0740844i
$433$	31.3746	+	11.4194i	1.50777	+	0.548782i	0.958058	−	0.286574i	$-0.0925165\pi$
$433$	31.3746	+	11.4194i	1.50777	+	0.548782i	0.549709	+	0.835356i	$0.314739\pi$
$434$	−16.2048	−	13.5975i	−0.777858	−	0.652700i
$435$		0			0
$436$	16.9860			0.813481
$437$	−26.2587	−	1.14332i	−1.25613	−	0.0546926i
$438$	−8.94026			−0.427182
$439$	3.21620	−	18.2400i	0.153501	−	0.870546i	−0.806643	−	0.591039i	$-0.798718\pi$
$439$	3.21620	−	18.2400i	0.153501	−	0.870546i	0.960144	−	0.279507i	$-0.0901710\pi$
$440$		0			0
$441$	1.57423	+	0.572971i	0.0749631	+	0.0272843i
$442$	−6.12768	+	2.23029i	−0.291464	+	0.106084i
$443$	10.4056	−	8.73132i	0.494384	−	0.414838i	−0.361210	−	0.932484i	$-0.617636\pi$
$443$	10.4056	−	8.73132i	0.494384	−	0.414838i	0.855594	+	0.517647i	$0.173192\pi$
$444$	4.68528	+	8.11514i	0.222353	+	0.385127i
$445$		0			0
$446$	4.31512	+	24.4722i	0.204327	+	1.15879i
$447$	2.44306	+	13.8553i	0.115553	+	0.655333i
$448$	−1.39086	+	2.40903i	−0.0657117	+	0.113816i
$449$	−1.40297	−	2.43001i	−0.0662101	−	0.114679i	0.831020	−	0.556242i	$-0.187757\pi$
$449$	−1.40297	−	2.43001i	−0.0662101	−	0.114679i	−0.897230	+	0.441563i	$0.854424\pi$
$450$		0			0
$451$	−11.1385	+	4.05408i	−0.524491	+	0.190899i
$452$	0.205660	+	0.0748542i	0.00967345	+	0.00352085i
$453$	9.64231	+	8.09086i	0.453035	+	0.380142i
$454$	1.44651	−	8.20357i	0.0678881	−	0.385013i
$455$		0			0
$456$	2.95385	−	2.26713i	0.138327	−	0.106168i
$457$	18.8826			0.883289			0.441644	−	0.897190i	$-0.354395\pi$
$457$	18.8826			0.883289			0.441644	+	0.897190i	$0.354395\pi$
$458$	−0.121435	+	0.688694i	−0.00567430	+	0.0321806i
$459$	−4.68020	−	3.92715i	−0.218453	−	0.183304i
$460$		0			0
$461$	−5.14272	+	1.87180i	−0.239521	+	0.0871784i	−0.458991	−	0.888441i	$-0.651789\pi$
$461$	−5.14272	+	1.87180i	−0.239521	+	0.0871784i	0.219471	+	0.975619i	$0.429567\pi$
$462$	−5.76319	+	4.83589i	−0.268128	+	0.224986i
$463$	3.52956	+	6.11338i	0.164033	+	0.284113i	0.936311	−	0.351171i	$-0.114216\pi$
$463$	3.52956	+	6.11338i	0.164033	+	0.284113i	−0.772279	+	0.635284i	$0.780883\pi$
$464$	5.21284	−	9.02890i	0.242000	−	0.419156i
$465$		0			0
$466$	−0.446501	−	2.53223i	−0.0206838	−	0.117304i
$467$	4.75442	−	8.23490i	0.220008	−	0.381066i	−0.734802	−	0.678282i	$-0.762725\pi$
$467$	4.75442	−	8.23490i	0.220008	−	0.381066i	0.954810	+	0.297216i	$0.0960582\pi$
$468$	−5.45459	−	9.44763i	−0.252139	−	0.436717i
$469$	12.1834	−	10.2231i	0.562577	−	0.472058i
$470$		0			0
$471$	7.37075	+	2.68273i	0.339626	+	0.123614i
$472$	−3.15025	−	2.64337i	−0.145002	−	0.121671i
$473$	0.845090	−	4.79274i	0.0388573	−	0.220371i
$474$	1.91258			0.0878477
$475$		0			0
$476$	3.77490			0.173022
$477$	1.69871	−	9.63386i	0.0777786	−	0.441104i
$478$	−13.5850	−	11.3992i	−0.621363	−	0.521386i
$479$	−28.7966	−	10.4811i	−1.31575	−	0.478894i	−0.413657	−	0.910433i	$-0.635749\pi$
$479$	−28.7966	−	10.4811i	−1.31575	−	0.478894i	−0.902094	+	0.431539i	$0.857971\pi$
$480$		0			0
$481$	40.3786	−	33.8817i	1.84111	−	1.54487i
$482$	−4.52310	−	7.83425i	−0.206022	−	0.356840i
$483$	−7.16433	+	12.4090i	−0.325988	+	0.564628i
$484$	−0.169555	−	0.961594i	−0.00770705	−	0.0437088i
$485$		0			0
$486$	8.01953	−	13.8902i	0.363773	−	0.630074i
$487$	−14.4610	−	25.0472i	−0.655292	−	1.13500i	−0.981821	−	0.189811i	$-0.939212\pi$
$487$	−14.4610	−	25.0472i	−0.655292	−	1.13500i	0.326529	−	0.945187i	$-0.394121\pi$
$488$	3.24676	−	2.72435i	0.146974	−	0.123326i
$489$	13.1381	−	4.78188i	0.594125	−	0.216244i
$490$		0			0
$491$	−30.3092	−	25.4325i	−1.36784	−	1.14775i	−0.973475	−	0.228795i	$-0.926521\pi$
$491$	−30.3092	−	25.4325i	−1.36784	−	1.14775i	−0.394361	−	0.918955i	$-0.629034\pi$
$492$	0.555373	−	3.14968i	0.0250381	−	0.141998i
$493$	−14.1481			−0.637197
$494$	−15.4445	−	14.1488i	−0.694880	−	0.636587i
$495$		0			0
$496$	1.32053	−	7.48911i	0.0592937	−	0.336271i
$497$	1.91533	+	1.60715i	0.0859142	+	0.0720906i
$498$	6.69177	+	2.43560i	0.299865	+	0.109142i
$499$	−2.87074	+	1.04486i	−0.128512	+	0.0467745i	−0.405476	−	0.914106i	$-0.632894\pi$
$499$	−2.87074	+	1.04486i	−0.128512	+	0.0467745i	0.276964	+	0.960880i	$0.410672\pi$
$500$		0			0
$501$	−5.59194	−	9.68552i	−0.249829	−	0.432717i
$502$	−3.37507	+	5.84579i	−0.150637	+	0.260910i
$503$	−5.70366	−	32.3470i	−0.254313	−	1.44228i	−0.797829	−	0.602884i	$-0.794018\pi$
$503$	−5.70366	−	32.3470i	−0.254313	−	1.44228i	0.543515	−	0.839399i	$-0.317093\pi$
$504$	1.09662	+	6.21925i	0.0488474	+	0.277028i
$505$		0			0
$506$	9.54530	+	16.5329i	0.424340	+	0.734979i
$507$	6.60323	−	5.54077i	0.293260	−	0.246074i
$508$	11.8112	−	4.29891i	0.524036	−	0.190733i
$509$	19.0237	+	6.92408i	0.843213	+	0.306904i	0.727270	−	0.686352i	$-0.240789\pi$
$509$	19.0237	+	6.92408i	0.843213	+	0.306904i	0.115943	+	0.993256i	$0.463011\pi$
$510$		0			0
$511$	5.05530	−	28.6700i	0.223633	−	1.26829i
$512$	−1.00000			−0.0441942
$513$	4.24517	−	19.1596i	0.187429	−	0.845918i
$514$	3.23325			0.142613
$515$		0			0
$516$	1.00591	+	0.844062i	0.0442829	+	0.0371578i
$517$	8.84214	+	3.21828i	0.388877	+	0.141540i
$518$	−28.6733	+	10.4362i	−1.25983	+	0.458541i
$519$	11.2439	−	9.43478i	0.493554	−	0.414141i
$520$		0			0
$521$	7.47243	−	12.9426i	0.327373	−	0.567027i	−0.654617	−	0.755961i	$-0.727170\pi$
$521$	7.47243	−	12.9426i	0.327373	−	0.567027i	0.981990	+	0.188934i	$0.0605032\pi$
$522$	−4.11007	−	23.3094i	−0.179893	−	1.02022i
$523$	4.90745	+	27.8315i	0.214588	+	1.21699i	0.881620	+	0.471960i	$0.156453\pi$
$523$	4.90745	+	27.8315i	0.214588	+	1.21699i	−0.667032	+	0.745029i	$0.732436\pi$
$524$	6.95234	−	12.0418i	0.303715	−	0.526049i
$525$		0			0
$526$	−0.784511	+	0.658282i	−0.0342063	+	0.0287025i
$527$	−9.69745	+	3.52958i	−0.422428	+	0.153751i
$528$	−2.54146	−	0.925014i	−0.110603	−	0.0402561i
$529$	10.2339	+	8.58726i	0.444952	+	0.373359i
$530$		0			0
$531$	−9.33609			−0.405152
$532$	5.60008	+	10.7545i	0.242794	+	0.466267i
$533$	−17.9906			−0.779261
$534$	1.40716	−	7.98042i	0.0608939	−	0.345346i
$535$		0			0
$536$	5.37265	+	1.95548i	0.232063	+	0.0844640i
$537$	0.376490	−	0.137031i	0.0162467	−	0.00591333i
$538$	7.15929	−	6.00736i	0.308659	−	0.258995i
$539$	−1.16812	−	2.02324i	−0.0503145	−	0.0871473i
$540$		0			0
$541$	3.81672	+	21.6457i	0.164093	+	0.930620i	0.949994	+	0.312267i	$0.101088\pi$
$541$	3.81672	+	21.6457i	0.164093	+	0.930620i	−0.785901	+	0.618353i	$0.787800\pi$
$542$	−1.68070	−	9.53175i	−0.0721924	−	0.409424i
$543$	−7.17466	+	12.4269i	−0.307894	+	0.533289i
$544$	0.678520	+	1.17523i	0.0290913	+	0.0503877i
$545$		0			0
$546$	−10.7300	+	3.90541i	−0.459203	+	0.167136i
$547$	−26.1305	−	9.51074i	−1.11726	−	0.406650i	−0.283609	−	0.958940i	$-0.591532\pi$
$547$	−26.1305	−	9.51074i	−1.11726	−	0.406650i	−0.833652	+	0.552290i	$0.813754\pi$
$548$	4.73650	+	3.97439i	0.202333	+	0.169778i
$549$	1.67086	−	9.47593i	0.0713107	−	0.404423i
$550$		0			0
$551$	−20.9888	−	40.3072i	−0.894151	−	1.71715i
$552$	−5.15103			−0.219242
$553$	−1.08147	+	6.13335i	−0.0459890	+	0.260816i
$554$	1.99910	+	1.67744i	0.0849336	+	0.0712677i
$555$		0			0
$556$	−8.24626	+	3.00139i	−0.349719	+	0.127287i
$557$	−11.9805	+	10.0528i	−0.507630	+	0.425952i	−0.860294	−	0.509798i	$-0.829720\pi$
$557$	−11.9805	+	10.0528i	−0.507630	+	0.425952i	0.352664	+	0.935750i	$0.385276\pi$
$558$	−8.63224	−	14.9515i	−0.365432	−	0.632947i
$559$	3.69325	−	6.39690i	0.156208	−	0.270560i
$560$		0			0
$561$	0.637323	+	3.61444i	0.0269078	+	0.152602i
$562$	15.1206	−	26.1897i	0.637825	−	1.10474i
$563$	15.9429	+	27.6140i	0.671914	+	1.16379i	0.977361	+	0.211580i	$0.0678610\pi$
$563$	15.9429	+	27.6140i	0.671914	+	1.16379i	−0.305446	+	0.952209i	$0.598806\pi$
$564$	−1.94491	+	1.63197i	−0.0818955	+	0.0687185i
$565$		0			0
$566$	17.9068	+	6.51754i	0.752679	+	0.273953i
$567$	6.31779	+	5.30126i	0.265322	+	0.222632i
$568$	−0.156080	+	0.885174i	−0.00654897	+	0.0371411i
$569$	16.2946			0.683104			0.341552	−	0.939863i	$-0.389047\pi$
$569$	16.2946			0.683104			0.341552	+	0.939863i	$0.389047\pi$
$570$		0			0
$571$	45.9474			1.92284			0.961418	−	0.275090i	$-0.0887077\pi$
$571$	45.9474			1.92284			0.961418	+	0.275090i	$0.0887077\pi$
$572$	−2.64180	+	14.9824i	−0.110459	+	0.626444i
$573$	−11.8817	−	9.96995i	−0.496366	−	0.416501i
$574$	9.78649	+	3.56199i	0.408480	+	0.148675i
$575$		0			0
$576$	−1.73912	+	1.45929i	−0.0724632	+	0.0608038i
$577$	21.0732	+	36.4998i	0.877288	+	1.51951i	0.854305	+	0.519771i	$0.173983\pi$
$577$	21.0732	+	36.4998i	0.877288	+	1.51951i	0.0229826	+	0.999736i	$0.492684\pi$
$578$	−7.57922	+	13.1276i	−0.315254	+	0.546036i
$579$	0.661834	+	3.75345i	0.0275049	+	0.155988i
$580$		0			0
$581$	−11.5945	+	20.0822i	−0.481021	+	0.833152i
$582$	−1.12326	−	1.94554i	−0.0465605	−	0.0806451i
$583$	−10.4506	+	8.76906i	−0.432818	+	0.363177i
$584$	9.83446	−	3.57945i	0.406953	−	0.148119i
$585$		0			0
$586$	−0.481164	−	0.403745i	−0.0198767	−	0.0166785i
$587$	3.63466	−	20.6132i	0.150019	−	0.850797i	−0.813181	−	0.582011i	$-0.802266\pi$
$587$	3.63466	−	20.6132i	0.150019	−	0.850797i	0.963200	−	0.268787i	$-0.0866227\pi$
$588$	0.630364			0.0259958
$589$	−24.4419	−	22.3915i	−1.00711	−	0.922624i
$590$		0			0
$591$	−3.03628	+	17.2196i	−0.124896	+	0.708319i
$592$	−8.40299	−	7.05094i	−0.345361	−	0.289792i
$593$	32.4706	+	11.8183i	1.33341	+	0.485320i	0.907730	−	0.419555i	$-0.137814\pi$
$593$	32.4706	+	11.8183i	1.33341	+	0.485320i	0.425676	+	0.904875i	$0.360036\pi$
$594$	−13.3941	+	4.87506i	−0.549567	+	0.200026i
$595$		0			0
$596$	−8.23473	−	14.2630i	−0.337307	−	0.584234i
$597$	−3.46239	+	5.99703i	−0.141706	+	0.245442i
$598$	5.03149	+	28.5350i	0.205753	+	1.16688i
$599$	−0.508878	−	2.88599i	−0.0207922	−	0.117918i	0.972645	−	0.232296i	$-0.0746238\pi$
$599$	−0.508878	−	2.88599i	−0.0207922	−	0.117918i	−0.993437	+	0.114378i	$0.963513\pi$
$600$		0			0
$601$	−16.1662	−	28.0006i	−0.659432	−	1.14217i	−0.980763	−	0.195202i	$-0.937464\pi$
$601$	−16.1662	−	28.0006i	−0.659432	−	1.14217i	0.321331	−	0.946967i	$-0.395870\pi$
$602$	−3.27558	+	2.74853i	−0.133502	+	0.112022i
$603$	12.1973	−	4.43945i	0.496712	−	0.180788i
$604$	−13.8461	−	5.03957i	−0.563390	−	0.205057i
$605$		0			0
$606$	−2.55866	+	14.5109i	−0.103939	+	0.589465i
$607$	−12.3695			−0.502063			−0.251031	−	0.967979i	$-0.580770\pi$
$607$	−12.3695			−0.502063			−0.251031	+	0.967979i	$0.580770\pi$
$608$	−2.34159	+	3.67654i	−0.0949642	+	0.149103i
$609$	−24.7743			−1.00391
$610$		0			0
$611$	10.9404	+	9.18006i	0.442600	+	0.371385i
$612$	2.89503	+	1.05371i	0.117025	+	0.0425935i
$613$	14.5146	−	5.28288i	0.586239	−	0.213373i	−0.0318356	−	0.999493i	$-0.510135\pi$
$613$	14.5146	−	5.28288i	0.586239	−	0.213373i	0.618074	+	0.786120i	$0.287913\pi$
$614$	16.3205	−	13.6945i	0.658641	−	0.552666i
$615$		0			0
$616$	4.40345	−	7.62700i	0.177420	−	0.307301i
$617$	−7.72363	−	43.8029i	−0.310942	−	1.76344i	−0.594126	−	0.804372i	$-0.702502\pi$
$617$	−7.72363	−	43.8029i	−0.310942	−	1.76344i	0.283185	−	0.959065i	$-0.408609\pi$
$618$	−1.80398	−	10.2309i	−0.0725666	−	0.411545i
$619$	1.83161	−	3.17245i	0.0736187	−	0.127511i	−0.826866	−	0.562399i	$-0.809879\pi$
$619$	1.83161	−	3.17245i	0.0736187	−	0.127511i	0.900485	+	0.434888i	$0.143212\pi$
$620$		0			0
$621$	−20.7960	+	17.4499i	−0.834514	+	0.700240i
$622$	30.9721	−	11.2729i	1.24187	−	0.452003i
$623$	24.7963	+	9.02511i	0.993442	+	0.361583i
$624$	−3.14454	−	2.63858i	−0.125882	−	0.105628i
$625$		0			0
$626$	−28.5227			−1.14000
$627$	−9.35191	+	7.17775i	−0.373479	+	0.286652i
$628$	−9.18206			−0.366404
$629$	−2.58490	+	14.6597i	−0.103067	+	0.584519i
$630$		0			0
$631$	−13.5764	−	4.94141i	−0.540468	−	0.196714i	0.0573381	−	0.998355i	$-0.481739\pi$
$631$	−13.5764	−	4.94141i	−0.540468	−	0.196714i	−0.597807	+	0.801640i	$0.703961\pi$
$632$	−2.10387	+	0.765748i	−0.0836876	+	0.0304598i
$633$	15.9856	−	13.4135i	0.635370	−	0.533139i
$634$	15.3283	+	26.5494i	0.608764	+	1.05441i
$635$		0			0
$636$	−0.639190	−	3.62502i	−0.0253455	−	0.143742i
$637$	−0.615736	−	3.49201i	−0.0243963	−	0.138358i
$638$	−16.5039	+	28.5855i	−0.653394	+	1.13171i
$639$	1.02029	+	1.76719i	0.0403619	+	0.0699089i
$640$		0			0
$641$	−3.70070	+	1.34695i	−0.146169	+	0.0532011i	−0.414069	−	0.910246i	$-0.635893\pi$
$641$	−3.70070	+	1.34695i	−0.146169	+	0.0532011i	0.267900	+	0.963447i	$0.413670\pi$
$642$	11.1990	+	4.07611i	0.441990	+	0.160871i
$643$	−32.0655	−	26.9061i	−1.26454	−	1.06107i	−0.995183	−	0.0980331i	$-0.968745\pi$
$643$	−32.0655	−	26.9061i	−1.26454	−	1.06107i	−0.269355	−	0.963041i	$-0.586811\pi$
$644$	2.91267	−	16.5185i	0.114775	−	0.650922i
$645$		0			0
$646$	5.90961	+	0.257308i	0.232510	+	0.0101237i
$647$	37.3768			1.46943			0.734716	−	0.678375i	$-0.237315\pi$
$647$	37.3768			1.46943			0.734716	+	0.678375i	$0.237315\pi$
$648$	−0.514837	+	2.91978i	−0.0202247	+	0.114700i
$649$	9.97368	+	8.36891i	0.391501	+	0.328509i
$650$		0			0
$651$	−16.9810	+	6.18056i	−0.665536	+	0.242235i
$652$	−12.5376	+	10.5203i	−0.491011	+	0.412007i
$653$	−15.4098	−	26.6905i	−0.603031	−	1.04448i	−0.992359	−	0.123381i	$-0.960626\pi$
$653$	−15.4098	−	26.6905i	−0.603031	−	1.04448i	0.389328	−	0.921099i	$-0.372707\pi$
$654$	7.25514	−	12.5663i	0.283698	−	0.491380i
$655$		0			0
$656$	0.650129	+	3.68706i	0.0253833	+	0.143956i
$657$	11.8798	−	20.5764i	0.463475	−	0.802763i
$658$	−4.13373	−	7.15983i	−0.161150	−	0.279119i
$659$	−5.21609	+	4.37682i	−0.203190	+	0.170497i	−0.738705	−	0.674029i	$-0.764562\pi$
$659$	−5.21609	+	4.37682i	−0.203190	+	0.170497i	0.535514	+	0.844526i	$0.320118\pi$
$660$		0			0
$661$	33.9368	+	12.3520i	1.31999	+	0.480437i	0.903455	−	0.428683i	$-0.141022\pi$
$661$	33.9368	+	12.3520i	1.31999	+	0.480437i	0.416535	+	0.909120i	$0.363244\pi$
$662$	−5.97791	−	5.01606i	−0.232338	−	0.194955i
$663$	−0.967311	+	5.48589i	−0.0375673	+	0.213054i
$664$	−8.33623			−0.323508
$665$		0			0
$666$	−24.9032			−0.964978
$667$	−10.9165	+	61.9105i	−0.422688	+	2.39718i
$668$	10.0291	+	8.41539i	0.388036	+	0.325601i
$669$	19.9477	+	7.26038i	0.771224	+	0.280702i
$670$		0			0
$671$	−10.2792	+	8.62530i	−0.396826	+	0.332976i
$672$	1.18814	+	2.05792i	0.0458335	+	0.0793859i
$673$	1.30856	−	2.26649i	0.0504412	−	0.0873667i	−0.839702	−	0.543047i	$-0.817271\pi$
$673$	1.30856	−	2.26649i	0.0504412	−	0.0873667i	0.890144	+	0.455680i	$0.150604\pi$
$674$	0.623795	+	3.53771i	0.0240277	+	0.136268i
$675$		0			0
$676$	−5.04530	+	8.73872i	−0.194050	+	0.336105i
$677$	0.634426	+	1.09886i	0.0243830	+	0.0422325i	0.877959	−	0.478735i	$-0.158905\pi$
$677$	0.634426	+	1.09886i	0.0243830	+	0.0422325i	−0.853576	+	0.520968i	$0.825571\pi$
$678$	0.143220	−	0.120176i	0.00550034	−	0.00461533i
$679$	6.87418	−	2.50200i	0.263807	−	0.0960179i
$680$		0			0
$681$	−5.45119	−	4.57409i	−0.208890	−	0.175279i
$682$	−4.18081	+	23.7106i	−0.160092	+	0.907924i
$683$	16.3670			0.626264			0.313132	−	0.949710i	$-0.398622\pi$
$683$	16.3670			0.626264			0.313132	+	0.949710i	$0.398622\pi$
$684$	1.29284	+	9.81100i	0.0494330	+	0.375133i
$685$		0			0
$686$	3.02483	−	17.1547i	0.115489	−	0.654968i
$687$	0.457630	+	0.383997i	0.0174597	+	0.0146504i
$688$	−1.44447	−	0.525743i	−0.0550698	−	0.0200438i
$689$	−19.4571	+	7.08180i	−0.741255	+	0.269795i
$690$		0			0
$691$	8.07725	+	13.9902i	0.307273	+	0.532213i	0.977765	−	0.209704i	$-0.0672501\pi$
$691$	8.07725	+	13.9902i	0.307273	+	0.532213i	−0.670492	+	0.741917i	$0.733917\pi$
$692$	−8.59110	+	14.8802i	−0.326585	+	0.565661i
$693$	−3.47191	−	19.6902i	−0.131887	−	0.747968i
$694$	2.67020	+	15.1434i	0.101359	+	0.574837i
$695$		0			0
$696$	−4.45307	−	7.71295i	−0.168793	−	0.292359i
$697$	3.89203	−	3.26580i	0.147421	−	0.123701i
$698$	31.0075	−	11.2858i	1.17365	−	0.427175i
$699$	−2.06407	−	0.751259i	−0.0780702	−	0.0284152i
$700$		0			0
$701$	3.90435	−	22.1427i	0.147465	−	0.836317i	−0.817889	−	0.575376i	$-0.804856\pi$
$701$	3.90435	−	22.1427i	0.147465	−	0.836317i	0.965355	−	0.260942i	$-0.0840331\pi$
$702$	−21.6339			−0.816519
$703$	−45.5995	+	14.3835i	−1.71982	+	0.542483i
$704$	3.16600			0.119323
$705$		0			0
$706$	4.47924	+	3.75853i	0.168579	+	0.141454i
$707$	−45.0874	−	16.4105i	−1.69569	−	0.617179i
$708$	−3.30112	+	1.20151i	−0.124064	+	0.0451555i
$709$	30.7633	−	25.8135i	1.15534	−	0.969447i	0.155511	−	0.987834i	$-0.450298\pi$
$709$	30.7633	−	25.8135i	1.15534	−	0.969447i	0.999831	+	0.0183876i	$0.00585328\pi$
$710$		0			0
$711$	−2.54143	+	4.40189i	−0.0953112	+	0.165084i
$712$	1.64725	+	9.34201i	0.0617332	+	0.350106i
$713$	7.96265	+	45.1584i	0.298204	+	1.69120i
$714$	1.61235	−	2.79268i	0.0603408	−	0.104513i
$715$		0			0
$716$	−0.359282	+	0.301474i	−0.0134270	+	0.0112666i
$717$	−14.2356	+	5.18134i	−0.531639	+	0.193501i
$718$	14.7203	+	5.35776i	0.549358	+	0.199950i
$719$	8.60668	+	7.22186i	0.320975	+	0.269330i	0.789011	−	0.614380i	$-0.210594\pi$
$719$	8.60668	+	7.22186i	0.320975	+	0.269330i	−0.468036	+	0.883710i	$0.655038\pi$
$720$		0			0
$721$	33.8288			1.25985
$722$	8.03388	+	17.2179i	0.298990	+	0.640785i
$723$	−7.72773			−0.287397
$724$	2.91687	−	16.5424i	0.108404	−	0.614792i
$725$		0			0
$726$	−0.783812	−	0.285284i	−0.0290900	−	0.0105879i
$727$	4.30407	−	1.56655i	0.159629	−	0.0581003i	−0.260970	−	0.965347i	$-0.584042\pi$
$727$	4.30407	−	1.56655i	0.159629	−	0.0581003i	0.420599	+	0.907247i	$0.361820\pi$
$728$	10.2396	−	8.59206i	0.379505	−	0.318443i
$729$	−2.40345	−	4.16290i	−0.0890167	−	0.154182i
$730$		0			0
$731$	0.362230	+	2.05431i	0.0133976	+	0.0759814i
$732$	−0.628711	−	3.56560i	−0.0232378	−	0.131788i
$733$	1.77436	−	3.07329i	0.0655376	−	0.113514i	−0.831395	−	0.555682i	$-0.812457\pi$
$733$	1.77436	−	3.07329i	0.0655376	−	0.113514i	0.896932	+	0.442168i	$0.145790\pi$
$734$	7.03989	+	12.1935i	0.259847	+	0.450069i
$735$		0			0
$736$	5.66623	−	2.06234i	0.208860	−	0.0760188i
$737$	−17.0098	−	6.19107i	−0.626565	−	0.228051i
$738$	6.51115	+	5.46351i	0.239679	+	0.201114i
$739$	−8.11900	+	46.0451i	−0.298662	+	1.69380i	0.353271	+	0.935521i	$0.385069\pi$
$739$	−8.11900	+	46.0451i	−0.298662	+	1.69380i	−0.651934	+	0.758276i	$0.726042\pi$
$740$		0			0
$741$	−17.0641	+	5.38254i	−0.626865	+	0.197732i
$742$	11.9863			0.440032
$743$	5.46514	−	30.9943i	0.200496	−	1.13707i	−0.703874	−	0.710324i	$-0.748548\pi$
$743$	5.46514	−	30.9943i	0.200496	−	1.13707i	0.904371	−	0.426747i	$-0.140341\pi$
$744$	−4.97644	−	4.17573i	−0.182445	−	0.153090i
$745$		0			0
$746$	−3.19672	+	1.16351i	−0.117040	+	0.0425992i
$747$	−14.4977	+	12.1650i	−0.530442	+	0.445094i
$748$	−2.14820	−	3.72079i	−0.0785459	−	0.136045i
$749$	−19.4040	+	33.6087i	−0.709006	+	1.22803i
$750$		0			0
$751$	1.07418	+	6.09197i	0.0391974	+	0.222299i	0.998114	−	0.0613890i	$-0.0195530\pi$
$751$	1.07418	+	6.09197i	0.0391974	+	0.222299i	−0.958917	+	0.283688i	$0.908442\pi$
$752$	1.48604	−	2.57390i	0.0541903	−	0.0938603i
$753$	2.88315	+	4.99377i	0.105068	+	0.181983i
$754$	−38.3774	+	32.2025i	−1.39762	+	1.17275i
$755$		0			0
$756$	11.7683	+	4.28332i	0.428010	+	0.155783i
$757$	−32.5924	−	27.3483i	−1.18459	−	0.993990i	−0.999937	−	0.0111858i	$-0.996439\pi$
$757$	−32.5924	−	27.3483i	−1.18459	−	0.993990i	−0.184653	−	0.982804i	$-0.559116\pi$
$758$	−0.584173	+	3.31301i	−0.0212181	+	0.120334i
$759$	16.3082			0.591949
$760$		0			0
$761$	9.05719			0.328323			0.164161	−	0.986433i	$-0.447508\pi$
$761$	9.05719			0.328323			0.164161	+	0.986433i	$0.447508\pi$
$762$	1.86450	−	10.5741i	0.0675437	−	0.383060i
$763$	36.1957	+	30.3718i	1.31037	+	1.09953i
$764$	17.0618	+	6.21000i	0.617276	+	0.224670i
$765$		0			0
$766$	−1.33818	+	1.12286i	−0.0483503	+	0.0405707i
$767$	9.88048	+	17.1135i	0.356763	+	0.617932i
$768$	−0.427125	+	0.739803i	−0.0154126	+	0.0266953i
$769$	−2.77743	−	15.7516i	−0.100157	−	0.568017i	−0.993045	−	0.117738i	$-0.962436\pi$
$769$	−2.77743	−	15.7516i	−0.100157	−	0.568017i	0.892888	−	0.450279i	$-0.148676\pi$
$770$		0			0
$771$	1.38100	−	2.39197i	0.0497357	−	0.0861447i
$772$	−2.23082	−	3.86389i	−0.0802888	−	0.139064i
$773$	−33.0004	+	27.6907i	−1.18694	+	0.995964i	−0.187036	+	0.982353i	$0.559888\pi$
$773$	−33.0004	+	27.6907i	−1.18694	+	0.995964i	−0.999907	+	0.0136105i	$0.995667\pi$
$774$	−3.27931	+	1.19357i	−0.117872	+	0.0429020i
$775$		0			0
$776$	2.01455	+	1.69041i	0.0723180	+	0.0606820i
$777$	−4.52634	+	25.6702i	−0.162382	+	0.920912i
$778$	2.95418			0.105913
$779$	15.0780	+	6.24338i	0.540224	+	0.223692i
$780$		0			0
$781$	0.494150	−	2.80246i	0.0176821	−	0.100280i
$782$	−6.26838	−	5.25979i	−0.224157	−	0.188090i
$783$	−44.1070	−	16.0536i	−1.57625	−	0.573710i
$784$	−0.693413	+	0.252382i	−0.0247648	+	0.00901364i
$785$		0			0
$786$	−5.93905	−	10.2867i	−0.211839	−	0.366915i
$787$	−0.505079	+	0.874822i	−0.0180041	+	0.0311840i	−0.874887	−	0.484327i	$-0.839065\pi$
$787$	−0.505079	+	0.874822i	−0.0180041	+	0.0311840i	0.856883	+	0.515511i	$0.172398\pi$
$788$	−3.55432	−	20.1575i	−0.126617	−	0.718082i
$789$	0.151915	+	0.861552i	0.00540831	+	0.0306721i
$790$		0			0
$791$	0.304401	+	0.527239i	0.0108233	+	0.0187465i
$792$	5.50605	−	4.62012i	0.195649	−	0.164169i
$793$	−19.1381	+	6.96570i	−0.679614	+	0.247359i
$794$	−1.79077	−	0.651789i	−0.0635522	−	0.0231311i
$795$		0			0
$796$	1.40764	−	7.98310i	0.0498924	−	0.282954i
$797$	38.3494			1.35841			0.679203	−	0.733951i	$-0.262326\pi$
$797$	38.3494			1.35841			0.679203	+	0.733951i	$0.262326\pi$
$798$	10.3482	+	0.450566i	0.366321	+	0.0159499i
$799$	−4.03323			−0.142686
$800$		0			0
$801$	16.4975	+	13.8430i	0.582909	+	0.489119i
$802$	2.40143	+	0.874050i	0.0847975	+	0.0308638i
$803$	−31.1359	+	11.3325i	−1.09876	+	0.399917i
$804$	3.74147	−	3.13946i	0.131951	−	0.110720i
$805$		0			0
$806$	−18.2712	+	31.6466i	−0.643575	+	1.11470i
$807$	−1.38635	−	7.86236i	−0.0488017	−	0.276768i
$808$	−2.99521	−	16.9867i	−0.105371	−	0.597590i
$809$	−26.9094	+	46.6085i	−0.946086	+	1.63867i	−0.192522	+	0.981293i	$0.561667\pi$
$809$	−26.9094	+	46.6085i	−0.946086	+	1.63867i	−0.753563	+	0.657376i	$0.771667\pi$
$810$		0			0
$811$	−33.3848	+	28.0132i	−1.17230	+	0.983676i	−0.999999	−	0.00136831i	$-0.999564\pi$
$811$	−33.3848	+	28.0132i	−1.17230	+	0.983676i	−0.172300	+	0.985044i	$0.555120\pi$
$812$	27.2522	−	9.91900i	0.956366	−	0.348089i
$813$	−7.76949	−	2.82786i	−0.272488	−	0.0991774i
$814$	26.6039	+	22.3233i	0.932466	+	0.782432i
$815$		0			0
$816$	1.15925			0.0405820
$817$	−5.31527	+	4.07956i	−0.185958	+	0.142726i
$818$	0.993545			0.0347385
$819$	5.26956	−	29.8852i	0.184133	−	1.04427i
$820$		0			0
$821$	22.1270	+	8.05358i	0.772239	+	0.281072i	0.697933	−	0.716163i	$-0.254103\pi$
$821$	22.1270	+	8.05358i	0.772239	+	0.281072i	0.0743065	+	0.997235i	$0.476326\pi$
$822$	4.96335	−	1.80651i	0.173117	−	0.0630093i
$823$	19.5518	−	16.4059i	0.681534	−	0.571875i	−0.234920	−	0.972015i	$-0.575483\pi$
$823$	19.5518	−	16.4059i	0.681534	−	0.571875i	0.916454	+	0.400140i	$0.131038\pi$
$824$	6.08058	+	10.5319i	0.211827	+	0.366895i
$825$		0			0
$826$	−1.98643	−	11.2656i	−0.0691166	−	0.391980i
$827$	1.04161	+	5.90726i	0.0362203	+	0.205416i	0.997547	−	0.0699935i	$-0.0222978\pi$
$827$	1.04161	+	5.90726i	0.0362203	+	0.205416i	−0.961327	+	0.275409i	$0.911187\pi$
$828$	6.84468	−	11.8553i	0.237869	−	0.412001i
$829$	4.83910	+	8.38157i	0.168069	+	0.291104i	0.937741	−	0.347336i	$-0.112914\pi$
$829$	4.83910	+	8.38157i	0.168069	+	0.291104i	−0.769672	+	0.638440i	$0.779580\pi$
$830$		0			0
$831$	2.09484	−	0.762460i	0.0726693	−	0.0264495i
$832$	4.51548	+	1.64350i	0.156546	+	0.0569781i
$833$	0.767102	+	0.643675i	0.0265785	+	0.0223020i
$834$	−1.30175	+	7.38258i	−0.0450758	+	0.255638i
$835$		0			0
$836$	7.41349	−	11.6399i	0.256401	−	0.402575i
$837$	−34.2370			−1.18340
$838$	2.58141	−	14.6399i	0.0891732	−	0.505726i
$839$	23.9478	+	20.0946i	0.826768	+	0.693741i	0.954547	−	0.298062i	$-0.0963402\pi$
$839$	23.9478	+	20.0946i	0.826768	+	0.693741i	−0.127778	+	0.991803i	$0.540785\pi$
$840$		0			0
$841$	−74.8886	+	27.2572i	−2.58237	+	0.939904i
$842$	−29.8436	+	25.0418i	−1.02848	+	0.862997i
$843$	−12.9168	−	22.3725i	−0.444878	−	0.770551i
$844$	−12.2140	+	21.1553i	−0.420424	+	0.728197i
$845$		0			0
$846$	−1.17167	−	6.64487i	−0.0402829	−	0.228455i
$847$	1.35807	−	2.35225i	0.0466639	−	0.0808242i
$848$	2.15449	+	3.73168i	0.0739854	+	0.128147i
$849$	12.4701	−	10.4637i	0.427974	−	0.359113i
$850$		0			0
$851$	62.1547	+	22.6225i	2.13064	+	0.775488i
$852$	0.588189	+	0.493549i	0.0201510	+	0.0169087i
$853$	7.36275	−	41.7562i	0.252096	−	1.42971i	−0.551324	−	0.834292i	$-0.685877\pi$
$853$	7.36275	−	41.7562i	0.252096	−	1.42971i	0.803419	−	0.595414i	$-0.203012\pi$
$854$	11.7898			0.403440
$855$		0			0
$856$	−13.9511			−0.476839
$857$	−6.27056	+	35.5621i	−0.214198	+	1.21478i	0.668094	+	0.744077i	$0.267110\pi$
$857$	−6.27056	+	35.5621i	−0.214198	+	1.21478i	−0.882292	+	0.470702i	$0.844001\pi$
$858$	9.95562	+	8.35376i	0.339879	+	0.285193i
$859$	−24.3549	−	8.86444i	−0.830977	−	0.302451i	−0.108717	−	0.994073i	$-0.534674\pi$
$859$	−24.3549	−	8.86444i	−0.830977	−	0.302451i	−0.722260	+	0.691622i	$0.756897\pi$
$860$		0			0
$861$	6.81523	−	5.71866i	0.232262	−	0.194891i
$862$	−13.6112	−	23.5752i	−0.463598	−	0.802975i
$863$	22.7413	−	39.3891i	0.774124	−	1.34082i	−0.161162	−	0.986928i	$-0.551524\pi$
$863$	22.7413	−	39.3891i	0.774124	−	1.34082i	0.935286	−	0.353894i	$-0.115143\pi$
$864$	0.781785	+	4.43372i	0.0265969	+	0.150838i
$865$		0			0
$866$	−16.6941	+	28.9150i	−0.567288	+	0.982571i
$867$	6.47455	+	11.2143i	0.219887	+	0.380856i
$868$	16.2048	−	13.5975i	0.550028	−	0.461529i
$869$	6.66087	−	2.42436i	0.225955	−	0.0822407i
$870$		0			0
$871$	−21.0462	−	17.6599i	−0.713124	−	0.598382i
$872$	−2.94958	+	16.7279i	−0.0998855	+	0.566479i
$873$	5.97033			0.202065
$874$	5.68574	−	25.6613i	0.192323	−	0.868006i
$875$		0			0
$876$	1.55246	−	8.80443i	0.0524527	−	0.297474i
$877$	−20.6745	−	17.3479i	−0.698127	−	0.585798i	0.223113	−	0.974793i	$-0.428378\pi$
$877$	−20.6745	−	17.3479i	−0.698127	−	0.585798i	−0.921240	+	0.388995i	$0.872822\pi$
$878$	17.4044	+	6.33467i	0.587369	+	0.213785i
$879$	−0.504209	+	0.183517i	−0.0170065	+	0.00618988i
$880$		0			0
$881$	−24.0249	−	41.6123i	−0.809419	−	1.40196i	−0.913267	−	0.407362i	$-0.866449\pi$
$881$	−24.0249	−	41.6123i	−0.809419	−	1.40196i	0.103847	−	0.994593i	$-0.466885\pi$
$882$	−0.837628	+	1.45081i	−0.0282044	+	0.0488514i
$883$	−3.54171	−	20.0861i	−0.119188	−	0.675949i	−0.984591	−	0.174873i	$-0.944049\pi$
$883$	−3.54171	−	20.0861i	−0.119188	−	0.675949i	0.865403	−	0.501077i	$-0.167063\pi$
$884$	−1.13235	−	6.42188i	−0.0380851	−	0.215991i
$885$		0			0
$886$	6.79176	+	11.7637i	0.228174	+	0.395208i
$887$	−20.0250	+	16.8029i	−0.672372	+	0.564187i	−0.913767	−	0.406240i	$-0.866840\pi$
$887$	−20.0250	+	16.8029i	−0.672372	+	0.564187i	0.241394	+	0.970427i	$0.422395\pi$
$888$	−8.80544	+	3.20492i	−0.295491	+	0.107550i
$889$	32.8553	+	11.9583i	1.10193	+	0.401070i
$890$		0			0
$891$	1.62997	−	9.24405i	0.0546062	−	0.309687i
$892$	−24.8498			−0.832031
$893$	−5.98333	−	11.4905i	−0.200224	−	0.384515i
$894$	−14.0690			−0.470539
$895$		0			0
$896$	−2.13091	−	1.78805i	−0.0711888	−	0.0597345i
$897$	23.2593	+	8.46570i	0.776606	+	0.282662i
$898$	2.63671	−	0.959686i	0.0879883	−	0.0320251i
$899$	−60.7348	+	50.9625i	−2.02562	+	1.69970i
$900$		0			0
$901$	2.92373	−	5.06405i	0.0974035	−	0.168708i
$902$	−2.05831	−	11.6733i	−0.0685342	−	0.388677i
$903$	0.634292	+	3.59725i	0.0211079	+	0.119709i
$904$	−0.109430	+	0.189538i	−0.00363957	+	0.00630393i
$905$		0			0
$906$	−9.64231	+	8.09086i	−0.320344	+	0.268801i
$907$	7.18433	−	2.61488i	0.238552	−	0.0868258i	−0.219978	−	0.975505i	$-0.570598\pi$
$907$	7.18433	−	2.61488i	0.238552	−	0.0868258i	0.458530	+	0.888679i	$0.348376\pi$
$908$	7.82776	+	2.84907i	0.259773	+	0.0945497i
$909$	−29.9976	−	25.1709i	−0.994956	−	0.834868i
$910$		0			0
$911$	25.2731			0.837335			0.418668	−	0.908140i	$-0.362497\pi$
$911$	25.2731			0.837335			0.418668	+	0.908140i	$0.362497\pi$
$912$	1.71976	+	3.30266i	0.0569470	+	0.109362i
$913$	26.3925			0.873465
$914$	−3.27892	+	18.5957i	−0.108457	+	0.615091i
$915$		0			0
$916$	−0.657144	−	0.239181i	−0.0217127	−	0.00790276i
$917$	36.3462	−	13.2289i	1.20026	−	0.436858i
$918$	4.68020	−	3.92715i	0.154469	−	0.129615i
$919$	−9.50216	−	16.4582i	−0.313447	−	0.542907i	0.665659	−	0.746256i	$-0.268151\pi$
$919$	−9.50216	−	16.4582i	−0.313447	−	0.542907i	−0.979106	+	0.203349i	$0.934817\pi$
$920$		0			0
$921$	−3.16035	−	17.9232i	−0.104137	−	0.590590i
$922$	−0.950337	−	5.38963i	−0.0312977	−	0.177498i
$923$	2.15956	−	3.74046i	0.0710827	−	0.123119i
$924$	−3.76165	−	6.51537i	−0.123749	−	0.214340i
$925$		0			0
$926$	−6.63341	+	2.41436i	−0.217987	+	0.0793409i
$927$	25.9439	+	9.44282i	0.852110	+	0.310143i
$928$	7.98653	+	6.70150i	0.262171	+	0.219987i
$929$	1.18404	−	6.71501i	0.0388470	−	0.220312i	−0.959204	−	0.282715i	$-0.908765\pi$
$929$	1.18404	−	6.71501i	0.0388470	−	0.220312i	0.998051	+	0.0624023i	$0.0198762\pi$
$930$		0			0
$931$	−0.695800	+	3.14034i	−0.0228039	+	0.102920i
$932$	2.57130			0.0842257
$933$	4.88923	−	27.7282i	0.160066	−	0.907781i
$934$	7.28419	+	6.11216i	0.238346	+	0.199996i
$935$		0			0
$936$	10.2513	−	3.73116i	0.335074	−	0.121957i
$937$	1.49929	−	1.25805i	0.0489796	−	0.0410988i	−0.617969	−	0.786202i	$-0.712044\pi$
$937$	1.49929	−	1.25805i	0.0489796	−	0.0410988i	0.666949	+	0.745104i	$0.267600\pi$
$938$	7.95215	+	13.7735i	0.259647	+	0.449722i
$939$	−12.1828	+	21.1012i	−0.397569	+	0.688610i
$940$		0			0
$941$	−1.30211	−	7.38466i	−0.0424477	−	0.240733i	0.956200	−	0.292713i	$-0.0945580\pi$
$941$	−1.30211	−	7.38466i	−0.0424477	−	0.240733i	−0.998648	+	0.0519798i	$0.983447\pi$
$942$	−3.92189	+	6.79292i	−0.127782	+	0.221325i
$943$	−11.2878	−	19.5510i	−0.367580	−	0.636667i
$944$	3.15025	−	2.64337i	0.102532	−	0.0860343i
$945$		0			0
$946$	4.57318	+	1.66450i	0.148687	+	0.0541177i
$947$	0.549732	+	0.461280i	0.0178639	+	0.0149896i	0.651676	−	0.758498i	$-0.274066\pi$
$947$	0.549732	+	0.461280i	0.0178639	+	0.0149896i	−0.633812	+	0.773487i	$0.718511\pi$
$948$	−0.332116	+	1.88352i	−0.0107866	+	0.0611740i
$949$	−50.2901			−1.63248
$950$		0			0
$951$	26.1884			0.849217
$952$	−0.655504	+	3.71755i	−0.0212450	+	0.120486i
$953$	−37.5256	−	31.4877i	−1.21557	−	1.01999i	−0.999044	−	0.0437094i	$-0.986082\pi$
$953$	−37.5256	−	31.4877i	−1.21557	−	1.01999i	−0.216528	−	0.976277i	$-0.569473\pi$
$954$	9.19252	+	3.34580i	0.297619	+	0.108324i
$955$		0			0
$956$	13.5850	−	11.3992i	0.439370	−	0.368675i
$957$	14.0984	+	24.4192i	0.455738	+	0.789361i
$958$	15.3224	−	26.5391i	0.495043	−	0.857440i
$959$	2.98666	+	16.9382i	0.0964442	+	0.546962i
$960$		0			0
$961$	−13.4153	+	23.2360i	−0.432752	+	0.749549i
$962$	26.3553	+	45.6487i	0.849728	+	1.47177i
$963$	−24.2626	+	20.3587i	−0.781852	+	0.656052i
$964$	8.50065	−	3.09399i	0.273788	−	0.0996506i
$965$		0			0
$966$	−10.9764	−	9.21029i	−0.353160	−	0.296336i
$967$	−0.906194	+	5.13928i	−0.0291412	+	0.165268i	−0.995905	−	0.0904018i	$-0.971185\pi$
$967$	−0.906194	+	5.13928i	−0.0291412	+	0.165268i	0.966764	+	0.255670i	$0.0822960\pi$
$968$	0.976429			0.0313836
$969$	2.71450	−	4.26204i	0.0872023	−	0.136916i
$970$		0			0
$971$	0.747673	−	4.24027i	0.0239940	−	0.136077i	−0.970458	−	0.241272i	$-0.922436\pi$
$971$	0.747673	−	4.24027i	0.0239940	−	0.136077i	0.994452	+	0.105195i	$0.0335467\pi$
$972$	12.2866	+	10.3097i	0.394094	+	0.330684i
$973$	−22.9387	−	8.34901i	−0.735381	−	0.267657i
$974$	27.1778	−	9.89193i	0.870834	−	0.316958i
$975$		0			0
$976$	2.11917	+	3.67051i	0.0678330	+	0.117490i
$977$	10.0224	−	17.3593i	0.320645	−	0.555374i	−0.659976	−	0.751287i	$-0.729434\pi$
$977$	10.0224	−	17.3593i	0.320645	−	0.555374i	0.980621	+	0.195913i	$0.0627669\pi$
$978$	2.42782	+	13.7689i	0.0776332	+	0.440280i
$979$	−5.21519	−	29.5768i	−0.166678	−	0.945279i
$980$		0			0
$981$	19.2813	+	33.3961i	0.615603	+	1.06626i
$982$	30.3092	−	25.4325i	0.967206	−	0.811582i
$983$	−29.9674	+	10.9072i	−0.955812	+	0.347887i	−0.772391	−	0.635147i	$-0.780939\pi$
$983$	−29.9674	+	10.9072i	−0.955812	+	0.347887i	−0.183421	+	0.983034i	$0.558717\pi$
$984$	3.00539	+	1.09387i	0.0958082	+	0.0348713i
$985$		0			0
$986$	2.45679	−	13.9331i	0.0782400	−	0.443721i
$987$	−7.06249			−0.224801
$988$	16.6158	−	12.7529i	0.528619	−	0.405724i
$989$	9.26894			0.294735
$990$		0			0
$991$	28.4508	+	23.8730i	0.903768	+	0.758352i	0.970923	−	0.239391i	$-0.0769477\pi$
$991$	28.4508	+	23.8730i	0.903768	+	0.758352i	−0.0671549	+	0.997743i	$0.521392\pi$
$992$	7.14603	+	2.60094i	0.226887	+	0.0825800i
$993$	−6.26422	+	2.27999i	−0.198789	+	0.0723533i
$994$	−1.91533	+	1.60715i	−0.0607505	+	0.0509757i
$995$		0			0
$996$	−3.56062	+	6.16717i	−0.112822	+	0.195414i
$997$	9.74265	+	55.2533i	0.308553	+	1.74989i	0.606291	+	0.795243i	$0.292657\pi$
$997$	9.74265	+	55.2533i	0.308553	+	1.74989i	−0.297738	+	0.954648i	$0.596232\pi$
$998$	−0.530491	−	3.00856i	−0.0167924	−	0.0952344i
$999$	−24.6926	+	42.7688i	−0.781239	+	1.35315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.j.701.3	yes	24
5.2	odd	4		950.2.u.h.549.3		48
5.3	odd	4		950.2.u.h.549.6		48
5.4	even	2		950.2.l.k.701.2	yes	24
19.9	even	9	inner	950.2.l.j.351.3	✓	24
95.9	even	18		950.2.l.k.351.2	yes	24
95.28	odd	36		950.2.u.h.199.3		48
95.47	odd	36		950.2.u.h.199.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.351.3	✓	24	19.9	even	9	inner
950.2.l.j.701.3	yes	24	1.1	even	1	trivial
950.2.l.k.351.2	yes	24	95.9	even	18
950.2.l.k.701.2	yes	24	5.4	even	2
950.2.u.h.199.3		48	95.28	odd	36
950.2.u.h.199.6		48	95.47	odd	36
950.2.u.h.549.3		48	5.2	odd	4
950.2.u.h.549.6		48	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.654394 + 0.549102i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.654394 + 0.549102i) q^{6} +(-1.39086 - 2.40903i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.394226 - 2.23577i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.654394 + 0.549102i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.654394 + 0.549102i) q^{6} +(-1.39086 - 2.40903i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.394226 - 2.23577i) q^{9} +(-1.58300 + 2.74184i) q^{11} +(-0.427125 - 0.739803i) q^{12} +(-3.68105 + 3.08877i) q^{13} +(2.61395 - 0.951401i) q^{14} +(0.766044 + 0.642788i) q^{16} +(0.235648 - 1.33642i) q^{17} +2.27026 q^{18} +(4.15700 - 1.31125i) q^{19} +(0.412636 - 2.34018i) q^{21} +(-2.42530 - 2.03507i) q^{22} +(-5.66623 - 2.06234i) q^{23} +(0.802733 - 0.292171i) q^{24} +(-2.40263 - 4.16148i) q^{26} +(2.25106 - 3.89895i) q^{27} +(0.483039 + 2.73945i) q^{28} +(-1.81040 - 10.2673i) q^{29} +(-3.80232 - 6.58582i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-2.54146 + 0.925014i) q^{33} +(1.27520 + 0.464135i) q^{34} +(-0.394226 + 2.23577i) q^{36} -10.9693 q^{37} +(0.569469 + 4.32154i) q^{38} -4.10490 q^{39} +(2.86803 + 2.40656i) q^{41} +(2.23297 + 0.812735i) q^{42} +(-1.44447 + 0.525743i) q^{43} +(2.42530 - 2.03507i) q^{44} +(3.01494 - 5.22203i) q^{46} +(-0.516096 - 2.92693i) q^{47} +(0.148339 + 0.841273i) q^{48} +(-0.368957 + 0.639053i) q^{49} +(0.888040 - 0.745154i) q^{51} +(4.51548 - 1.64350i) q^{52} +(4.04911 + 1.47376i) q^{53} +(3.44882 + 2.89391i) q^{54} -2.78171 q^{56} +(3.44032 + 1.42454i) q^{57} +10.4257 q^{58} +(0.714103 - 4.04988i) q^{59} +(3.98274 + 1.44960i) q^{61} +(7.14603 - 2.60094i) q^{62} +(-4.83772 + 4.05933i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.469642 - 2.66347i) q^{66} +(0.992825 + 5.63059i) q^{67} +(-0.678520 + 1.17523i) q^{68} +(-2.57551 - 4.46092i) q^{69} +(-0.844623 + 0.307418i) q^{71} +(-2.13334 - 0.776473i) q^{72} +(8.01712 + 6.72716i) q^{73} +(1.90480 - 10.8027i) q^{74} +(-4.35477 - 0.189610i) q^{76} +8.80690 q^{77} +(0.712809 - 4.04254i) q^{78} +(-1.71509 - 1.43913i) q^{79} +(-2.78603 + 1.01403i) q^{81} +(-2.86803 + 2.40656i) q^{82} +(-4.16812 - 7.21939i) q^{83} +(-1.18814 + 2.05792i) q^{84} +(-0.266927 - 1.51382i) q^{86} +(4.45307 - 7.71295i) q^{87} +(1.58300 + 2.74184i) q^{88} +(-7.26679 + 6.09756i) q^{89} +(12.5607 + 4.57174i) q^{91} +(4.61915 + 3.87593i) q^{92} +(1.12807 - 6.39758i) q^{93} +2.97208 q^{94} -0.854251 q^{96} +(-0.456661 + 2.58985i) q^{97} +(-0.565276 - 0.474323i) q^{98} +(6.75417 + 2.45832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 12 q^{8}+O(q^{10}) \) 24 * q - 3 * q^7 + 12 * q^8	\( 24 q - 3 q^{7} + 12 q^{8} - 6 q^{11} + 3 q^{12} - 24 q^{13} - 15 q^{14} + 9 q^{17} - 30 q^{18} - 15 q^{19} - 18 q^{21} - 12 q^{23} - 9 q^{26} + 21 q^{27} - 12 q^{28} - 12 q^{29} + 9 q^{31} + 42 q^{33} - 9 q^{34} - 66 q^{37} - 6 q^{38} + 66 q^{39} + 18 q^{41} - 9 q^{42} + 3 q^{43} - 3 q^{46} + 12 q^{47} - 27 q^{49} - 3 q^{51} + 12 q^{52} + 45 q^{53} + 27 q^{54} - 6 q^{56} + 27 q^{57} + 18 q^{58} + 36 q^{59} + 12 q^{61} + 24 q^{62} + 63 q^{63} - 12 q^{64} + 48 q^{66} + 54 q^{67} - 3 q^{68} + 21 q^{69} - 39 q^{71} - 48 q^{73} + 18 q^{74} + 6 q^{76} - 48 q^{77} + 12 q^{78} - 42 q^{79} - 36 q^{81} - 18 q^{82} + 3 q^{83} + 9 q^{84} - 39 q^{86} + 24 q^{87} + 6 q^{88} - 36 q^{89} + 12 q^{91} + 15 q^{92} + 6 q^{93} + 12 q^{94} + 6 q^{96} + 54 q^{97} - 3 q^{98} + 51 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 12 * q^8 - 6 * q^11 + 3 * q^12 - 24 * q^13 - 15 * q^14 + 9 * q^17 - 30 * q^18 - 15 * q^19 - 18 * q^21 - 12 * q^23 - 9 * q^26 + 21 * q^27 - 12 * q^28 - 12 * q^29 + 9 * q^31 + 42 * q^33 - 9 * q^34 - 66 * q^37 - 6 * q^38 + 66 * q^39 + 18 * q^41 - 9 * q^42 + 3 * q^43 - 3 * q^46 + 12 * q^47 - 27 * q^49 - 3 * q^51 + 12 * q^52 + 45 * q^53 + 27 * q^54 - 6 * q^56 + 27 * q^57 + 18 * q^58 + 36 * q^59 + 12 * q^61 + 24 * q^62 + 63 * q^63 - 12 * q^64 + 48 * q^66 + 54 * q^67 - 3 * q^68 + 21 * q^69 - 39 * q^71 - 48 * q^73 + 18 * q^74 + 6 * q^76 - 48 * q^77 + 12 * q^78 - 42 * q^79 - 36 * q^81 - 18 * q^82 + 3 * q^83 + 9 * q^84 - 39 * q^86 + 24 * q^87 + 6 * q^88 - 36 * q^89 + 12 * q^91 + 15 * q^92 + 6 * q^93 + 12 * q^94 + 6 * q^96 + 54 * q^97 - 3 * q^98 + 51 * q^99

Introduction

L-functions

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