LMFDB - Embedded newform 950.2.u.h.99.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.4
Character	$\chi$	$=$	950.99
Dual form			950.2.u.h.499.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 + 0.939693i) q^{2} +(2.51497 - 0.443457i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.443457 + 2.51497i) q^{6} +(-3.95328 - 2.28243i) q^{7} +(0.866025 - 0.500000i) q^{8} +(3.30934 - 1.20450i) q^{9} +O(q^{10})$	\(q+(-0.342020 + 0.939693i) q^{2} +(2.51497 - 0.443457i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.443457 + 2.51497i) q^{6} +(-3.95328 - 2.28243i) q^{7} +(0.866025 - 0.500000i) q^{8} +(3.30934 - 1.20450i) q^{9} +(-1.71245 - 2.96606i) q^{11} +(-2.21163 - 1.27688i) q^{12} +(0.803603 + 0.141697i) q^{13} +(3.49688 - 2.93423i) q^{14} +(0.173648 + 0.984808i) q^{16} +(1.45386 - 3.99445i) q^{17} +3.52173i q^{18} +(-4.31207 + 0.637234i) q^{19} +(-10.9545 - 3.98712i) q^{21} +(3.37288 - 0.594729i) q^{22} +(3.10687 - 3.70262i) q^{23} +(1.95630 - 1.64153i) q^{24} +(-0.408000 + 0.706677i) q^{26} +(1.15386 - 0.666183i) q^{27} +(1.56127 + 4.28956i) q^{28} +(2.25311 - 0.820065i) q^{29} +(3.45137 - 5.97794i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-5.62209 - 6.70015i) q^{33} +(3.25630 + 2.73236i) q^{34} +(-3.30934 - 1.20450i) q^{36} -3.82859i q^{37} +(0.876010 - 4.26997i) q^{38} +2.08387 q^{39} +(2.12597 + 12.0570i) q^{41} +(7.49334 - 8.93022i) q^{42} +(-2.83718 - 3.38122i) q^{43} +(-0.594729 + 3.37288i) q^{44} +(2.41672 + 4.18588i) q^{46} +(-2.54364 - 6.98859i) q^{47} +(0.873440 + 2.39976i) q^{48} +(6.91895 + 11.9840i) q^{49} +(1.88505 - 10.6906i) q^{51} +(-0.524515 - 0.625092i) q^{52} +(7.25628 - 8.64770i) q^{53} +(0.231363 + 1.31212i) q^{54} -4.56485 q^{56} +(-10.5621 + 3.51484i) q^{57} +2.39771i q^{58} +(-5.29935 - 1.92881i) q^{59} +(7.36453 + 6.17958i) q^{61} +(4.43699 + 5.28780i) q^{62} +(-15.8319 - 2.79160i) q^{63} +(0.500000 - 0.866025i) q^{64} +(8.21895 - 2.99145i) q^{66} +(1.92774 + 5.29642i) q^{67} +(-3.68130 + 2.12540i) q^{68} +(6.17173 - 10.6898i) q^{69} +(-11.7667 + 9.87343i) q^{71} +(2.26372 - 2.69780i) q^{72} +(-9.16200 + 1.61551i) q^{73} +(3.59769 + 1.30945i) q^{74} +(3.71284 + 2.28359i) q^{76} +15.6342i q^{77} +(-0.712727 + 1.95820i) q^{78} +(0.376083 + 2.13287i) q^{79} +(-5.48689 + 4.60405i) q^{81} +(-12.0570 - 2.12597i) q^{82} +(-0.416134 - 0.240255i) q^{83} +(5.82879 + 10.0958i) q^{84} +(4.14768 - 1.50963i) q^{86} +(5.30284 - 3.06159i) q^{87} +(-2.96606 - 1.71245i) q^{88} +(0.474094 - 2.68872i) q^{89} +(-2.85346 - 2.39433i) q^{91} +(-4.76000 + 0.839317i) q^{92} +(6.02912 - 16.5649i) q^{93} +7.43710 q^{94} -2.55377 q^{96} +(0.682176 - 1.87426i) q^{97} +(-13.6277 + 2.40292i) q^{98} +(-9.23972 - 7.75304i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$2$	−0.342020	+	0.939693i	−0.241845	+	0.664463i
$3$	2.51497	−	0.443457i	1.45202	−	0.256030i	0.608681	−	0.793415i	$-0.291699\pi$
$3$	2.51497	−	0.443457i	1.45202	−	0.256030i	0.843337	+	0.537385i	$0.180588\pi$
$4$	−0.766044	−	0.642788i	−0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.443457	+	2.51497i	−0.181041	+	1.02673i
$7$	−3.95328	−	2.28243i	−1.49420	−	0.862676i	−0.494221	−	0.869336i	$-0.664547\pi$
$7$	−3.95328	−	2.28243i	−1.49420	−	0.862676i	−0.999978	+	0.00665977i	$0.997880\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	3.30934	−	1.20450i	1.10311	−	0.401500i
$10$		0			0
$11$	−1.71245	−	2.96606i	−0.516324	−	0.894300i	−0.999820	−	0.0189536i	$-0.993967\pi$
$11$	−1.71245	−	2.96606i	−0.516324	−	0.894300i	0.483496	−	0.875347i	$-0.339367\pi$
$12$	−2.21163	−	1.27688i	−0.638442	−	0.368605i
$13$	0.803603	+	0.141697i	0.222879	+	0.0392997i	0.283973	−	0.958832i	$-0.408348\pi$
$13$	0.803603	+	0.141697i	0.222879	+	0.0392997i	−0.0610931	+	0.998132i	$0.519459\pi$
$14$	3.49688	−	2.93423i	0.934581	−	0.784206i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.45386	−	3.99445i	0.352613	−	0.968796i	−0.628915	−	0.777474i	$-0.716501\pi$
$17$	1.45386	−	3.99445i	0.352613	−	0.968796i	0.981527	−	0.191321i	$-0.0612773\pi$
$18$			3.52173i			0.830079i
$19$	−4.31207	+	0.637234i	−0.989256	+	0.146191i
$19$	−4.31207	+	0.637234i	−0.989256	+	0.146191i
$20$		0			0
$21$	−10.9545	−	3.98712i	−2.39048	−	0.870062i
$22$	3.37288	−	0.594729i	0.719100	−	0.126797i
$23$	3.10687	−	3.70262i	0.647827	−	0.772051i	−0.337757	−	0.941233i	$-0.609668\pi$
$23$	3.10687	−	3.70262i	0.647827	−	0.772051i	0.985585	+	0.169183i	$0.0541128\pi$
$24$	1.95630	−	1.64153i	0.399328	−	0.335076i
$25$		0			0
$26$	−0.408000	+	0.706677i	−0.0800154	+	0.138591i
$27$	1.15386	−	0.666183i	0.222061	−	0.128207i
$28$	1.56127	+	4.28956i	0.295053	+	0.810651i
$29$	2.25311	−	0.820065i	0.418392	−	0.152282i	−0.124241	−	0.992252i	$-0.539650\pi$
$29$	2.25311	−	0.820065i	0.418392	−	0.152282i	0.542633	+	0.839970i	$0.317427\pi$
$30$		0			0
$31$	3.45137	−	5.97794i	0.619884	−	1.07367i	−0.369623	−	0.929182i	$-0.620513\pi$
$31$	3.45137	−	5.97794i	0.619884	−	1.07367i	0.989506	−	0.144488i	$-0.0461536\pi$
$32$	−0.984808	−	0.173648i	−0.174091	−	0.0306970i
$33$	−5.62209	−	6.70015i	−0.978680	−	1.16635i
$34$	3.25630	+	2.73236i	0.558451	+	0.468596i
$35$		0			0
$36$	−3.30934	−	1.20450i	−0.551557	−	0.200750i
$37$		−	3.82859i		−	0.629416i	−0.949189	−	0.314708i	$-0.898093\pi$
$37$		−	3.82859i		−	0.629416i	0.949189	−	0.314708i	$-0.101907\pi$
$38$	0.876010	−	4.26997i	0.142108	−	0.692680i
$39$	2.08387			0.333687
$40$		0			0
$41$	2.12597	+	12.0570i	0.332020	+	1.88298i	0.454874	+	0.890556i	$0.349684\pi$
$41$	2.12597	+	12.0570i	0.332020	+	1.88298i	−0.122853	+	0.992425i	$0.539204\pi$
$42$	7.49334	−	8.93022i	1.15625	−	1.37796i
$43$	−2.83718	−	3.38122i	−0.432666	−	0.515631i	0.505024	−	0.863106i	$-0.331484\pi$
$43$	−2.83718	−	3.38122i	−0.432666	−	0.515631i	−0.937689	+	0.347474i	$0.887039\pi$
$44$	−0.594729	+	3.37288i	−0.0896588	+	0.508480i
$45$		0			0
$46$	2.41672	+	4.18588i	0.356325	+	0.617174i
$47$	−2.54364	−	6.98859i	−0.371028	−	1.01939i	−0.974965	−	0.222358i	$-0.928625\pi$
$47$	−2.54364	−	6.98859i	−0.371028	−	1.01939i	0.603937	−	0.797032i	$-0.293598\pi$
$48$	0.873440	+	2.39976i	0.126070	+	0.346375i
$49$	6.91895	+	11.9840i	0.988421	+	1.71200i
$50$		0			0
$51$	1.88505	−	10.6906i	0.263960	−	1.49699i
$52$	−0.524515	−	0.625092i	−0.0727371	−	0.0866847i
$53$	7.25628	−	8.64770i	0.996727	−	1.18785i	0.0145501	−	0.999894i	$-0.495368\pi$
$53$	7.25628	−	8.64770i	0.996727	−	1.18785i	0.982177	−	0.187959i	$-0.0601871\pi$
$54$	0.231363	+	1.31212i	0.0314845	+	0.178558i
$55$		0			0
$56$	−4.56485			−0.610004
$57$	−10.5621	+	3.51484i	−1.39899	+	0.465552i
$58$			2.39771i			0.314835i
$59$	−5.29935	−	1.92881i	−0.689917	−	0.251109i	−0.0268173	−	0.999640i	$-0.508537\pi$
$59$	−5.29935	−	1.92881i	−0.689917	−	0.251109i	−0.663100	+	0.748531i	$0.730759\pi$
$60$		0			0
$61$	7.36453	+	6.17958i	0.942932	+	0.791214i	0.978093	−	0.208168i	$-0.0667501\pi$
$61$	7.36453	+	6.17958i	0.942932	+	0.791214i	−0.0351615	+	0.999382i	$0.511195\pi$
$62$	4.43699	+	5.28780i	0.563499	+	0.671551i
$63$	−15.8319	−	2.79160i	−1.99464	−	0.351708i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	8.21895	−	2.99145i	1.01168	−	0.368222i
$67$	1.92774	+	5.29642i	0.235511	+	0.647061i	0.999997	+	0.00242072i	$0.000770541\pi$
$67$	1.92774	+	5.29642i	0.235511	+	0.647061i	−0.764486	+	0.644640i	$0.777007\pi$
$68$	−3.68130	+	2.12540i	−0.446424	+	0.257743i
$69$	6.17173	−	10.6898i	0.742989	−	1.28689i
$70$		0			0
$71$	−11.7667	+	9.87343i	−1.39645	+	1.17176i	−0.433800	+	0.901009i	$0.642828\pi$
$71$	−11.7667	+	9.87343i	−1.39645	+	1.17176i	−0.962649	+	0.270751i	$0.912728\pi$
$72$	2.26372	−	2.69780i	0.266782	−	0.317939i
$73$	−9.16200	+	1.61551i	−1.07233	+	0.189081i	−0.681822	−	0.731518i	$-0.738812\pi$
$73$	−9.16200	+	1.61551i	−1.07233	+	0.189081i	−0.390509	+	0.920599i	$0.627701\pi$
$74$	3.59769	+	1.30945i	0.418223	+	0.152221i
$75$		0			0
$76$	3.71284	+	2.28359i	0.425892	+	0.261946i
$77$			15.6342i			1.78168i
$78$	−0.712727	+	1.95820i	−0.0807004	+	0.221723i
$79$	0.376083	+	2.13287i	0.0423127	+	0.239967i	0.998628	−	0.0523710i	$-0.0166778\pi$
$79$	0.376083	+	2.13287i	0.0423127	+	0.239967i	−0.956315	+	0.292338i	$0.905567\pi$
$80$		0			0
$81$	−5.48689	+	4.60405i	−0.609654	+	0.511561i
$82$	−12.0570	−	2.12597i	−1.33147	−	0.234774i
$83$	−0.416134	−	0.240255i	−0.0456767	−	0.0263714i	0.476988	−	0.878910i	$-0.341729\pi$
$83$	−0.416134	−	0.240255i	−0.0456767	−	0.0263714i	−0.522664	+	0.852538i	$0.675062\pi$
$84$	5.82879	+	10.0958i	0.635973	+	1.10154i
$85$		0			0
$86$	4.14768	−	1.50963i	0.447256	−	0.162788i
$87$	5.30284	−	3.06159i	0.568524	−	0.328237i
$88$	−2.96606	−	1.71245i	−0.316183	−	0.182548i
$89$	0.474094	−	2.68872i	0.0502539	−	0.285004i	−0.949316	−	0.314323i	$-0.898223\pi$
$89$	0.474094	−	2.68872i	0.0502539	−	0.285004i	0.999570	+	0.0293186i	$0.00933373\pi$
$90$		0			0
$91$	−2.85346	−	2.39433i	−0.299123	−	0.250994i
$92$	−4.76000	+	0.839317i	−0.496265	+	0.0875048i
$93$	6.02912	−	16.5649i	0.625191	−	1.71770i
$94$	7.43710			0.767078
$95$		0			0
$96$	−2.55377			−0.260643
$97$	0.682176	−	1.87426i	0.0692645	−	0.190303i	−0.900231	−	0.435414i	$-0.856602\pi$
$97$	0.682176	−	1.87426i	0.0692645	−	0.190303i	0.969495	+	0.245111i	$0.0788244\pi$
$98$	−13.6277	+	2.40292i	−1.37660	+	0.242732i
$99$	−9.23972	−	7.75304i	−0.928626	−	0.779210i
$100$		0			0
$101$	−0.698250	+	3.95997i	−0.0694784	+	0.394032i	0.930160	+	0.367154i	$0.119668\pi$
$101$	−0.698250	+	3.95997i	−0.0694784	+	0.394032i	−0.999639	+	0.0268781i	$0.991443\pi$
$102$	9.40119	+	5.42778i	0.930856	+	0.537430i
$103$	4.36328	−	2.51914i	0.429926	−	0.248218i	−0.269389	−	0.963031i	$-0.586822\pi$
$103$	4.36328	−	2.51914i	0.429926	−	0.248218i	0.699315	+	0.714813i	$0.253488\pi$
$104$	0.766789	−	0.279088i	0.0751899	−	0.0273669i
$105$		0			0
$106$	5.64439	+	9.77636i	0.548231	+	0.949564i
$107$	4.00990	+	2.31512i	0.387651	+	0.223811i	0.681142	−	0.732151i	$-0.261484\pi$
$107$	4.00990	+	2.31512i	0.387651	+	0.223811i	−0.293491	+	0.955962i	$0.594817\pi$
$108$	−1.31212	−	0.231363i	−0.126259	−	0.0222629i
$109$	13.7948	−	11.5752i	1.32130	−	1.10870i	0.335275	−	0.942120i	$-0.391171\pi$
$109$	13.7948	−	11.5752i	1.32130	−	1.10870i	0.986027	−	0.166584i	$-0.0532736\pi$
$110$		0			0
$111$	−1.69781	−	9.62878i	−0.161149	−	0.913923i
$112$	1.56127	−	4.28956i	0.147526	−	0.405325i
$113$			3.77177i			0.354818i	0.984137	+	0.177409i	$0.0567716\pi$
$113$			3.77177i			0.354818i	−0.984137	+	0.177409i	$0.943228\pi$
$114$	0.309593	−	11.1273i	0.0289960	−	1.04217i
$115$		0			0
$116$	−2.25311	−	0.820065i	−0.209196	−	0.0761411i
$117$	2.83007	−	0.499018i	0.261640	−	0.0461342i
$118$	3.62497	−	4.32007i	0.333706	−	0.397695i
$119$	−14.8645	+	12.4728i	−1.36263	+	1.14338i
$120$		0			0
$121$	−0.365002	+	0.632201i	−0.0331820	+	0.0574728i
$122$	−8.32572	+	4.80686i	−0.753775	+	0.435192i
$123$	10.6935	+	29.3801i	0.964199	+	2.64912i
$124$	−6.48645	+	2.36087i	−0.582500	+	0.212013i
$125$		0			0
$126$	8.03808	−	13.9224i	0.716089	−	1.24030i
$127$	17.4286	+	3.07313i	1.54653	+	0.272696i	0.880798	−	0.473491i	$-0.157006\pi$
$127$	17.4286	+	3.07313i	1.54653	+	0.272696i	0.665736	+	0.746187i	$0.268118\pi$
$128$	0.642788	+	0.766044i	0.0568149	+	0.0677094i
$129$	−8.63485	−	7.24550i	−0.760256	−	0.637930i
$130$		0			0
$131$	4.37918	+	1.59389i	0.382611	+	0.139259i	0.526163	−	0.850384i	$-0.323630\pi$
$131$	4.37918	+	1.59389i	0.382611	+	0.139259i	−0.143552	+	0.989643i	$0.545852\pi$
$132$			8.74642i			0.761278i
$133$	18.5013	+	7.32282i	1.60426	+	0.634969i
$134$	−5.63633			−0.486905
$135$		0			0
$136$	−0.738144	−	4.18622i	−0.0632953	−	0.358966i
$137$	4.51269	−	5.37802i	0.385546	−	0.459475i	−0.538011	−	0.842938i	$-0.680824\pi$
$137$	4.51269	−	5.37802i	0.385546	−	0.459475i	0.923556	+	0.383463i	$0.125269\pi$
$138$	7.93422	+	9.45564i	0.675406	+	0.804918i
$139$	−3.36353	+	19.0755i	−0.285291	+	1.61797i	0.418953	+	0.908008i	$0.362397\pi$
$139$	−3.36353	+	19.0755i	−0.285291	+	1.61797i	−0.704244	+	0.709958i	$0.748714\pi$
$140$		0			0
$141$	−9.49631	−	16.4481i	−0.799733	−	1.38518i
$142$	−5.25354	−	14.4340i	−0.440867	−	1.21127i
$143$	−0.955853	−	2.62618i	−0.0799324	−	0.219613i
$144$	1.76086	+	3.04990i	0.146739	+	0.254159i
$145$		0			0
$146$	1.61551	−	9.16200i	0.133700	−	0.758252i
$147$	22.7153	+	27.0711i	1.87353	+	2.23278i
$148$	−2.46097	+	2.93287i	−0.202290	+	0.241080i
$149$	3.31009	+	18.7725i	0.271173	+	1.53790i	0.750861	+	0.660461i	$0.229639\pi$
$149$	3.31009	+	18.7725i	0.271173	+	1.53790i	−0.479687	+	0.877440i	$0.659250\pi$
$150$		0			0
$151$	18.2844			1.48796			0.743980	−	0.668202i	$-0.232936\pi$
$151$	18.2844			1.48796			0.743980	+	0.668202i	$0.232936\pi$
$152$	−3.41574	+	2.70789i	−0.277053	+	0.219639i
$153$		−	14.9702i		−	1.21027i
$154$	−14.6914	−	5.34721i	−1.18386	−	0.430891i
$155$		0			0
$156$	−1.59634	−	1.33949i	−0.127810	−	0.107245i
$157$	−7.75898	−	9.24679i	−0.619234	−	0.737974i	0.361705	−	0.932293i	$-0.382195\pi$
$157$	−7.75898	−	9.24679i	−0.619234	−	0.737974i	−0.980938	+	0.194319i	$0.937750\pi$
$158$	−2.13287	−	0.376083i	−0.169682	−	0.0299196i
$159$	14.4144	−	24.9666i	1.14314	−	1.97998i
$160$		0			0
$161$	−20.7333	+	7.54630i	−1.63401	+	0.594732i
$162$	−2.44976	−	6.73067i	−0.192471	−	0.528811i
$163$	12.9257	−	7.46264i	1.01242	−	0.584519i	0.100519	−	0.994935i	$-0.467950\pi$
$163$	12.9257	−	7.46264i	1.01242	−	0.584519i	0.911898	+	0.410416i	$0.134616\pi$
$164$	6.12148	−	10.6027i	0.478007	−	0.827933i
$165$		0			0
$166$	0.368092	−	0.308866i	0.0285695	−	0.0239727i
$167$	−7.55738	+	9.00653i	−0.584807	+	0.696946i	−0.974599	−	0.223957i	$-0.928103\pi$
$167$	−7.55738	+	9.00653i	−0.584807	+	0.696946i	0.389792	+	0.920903i	$0.372547\pi$
$168$	−11.4805	+	2.02432i	−0.885737	+	0.156179i
$169$	−11.5903	−	4.21853i	−0.891562	−	0.324502i
$170$		0			0
$171$	−13.5026	+	7.30272i	−1.03257	+	0.558453i
$172$			4.41387i			0.336554i
$173$	2.62950	−	7.22448i	0.199917	−	0.549267i	−0.798706	−	0.601721i	$-0.794482\pi$
$173$	2.62950	−	7.22448i	0.199917	−	0.549267i	0.998623	+	0.0524536i	$0.0167042\pi$
$174$	1.06328	+	6.03016i	0.0806071	+	0.457146i
$175$		0			0
$176$	2.62363	−	2.20149i	0.197764	−	0.165943i
$177$	−14.1831	−	2.50085i	−1.06606	−	0.187976i
$178$	2.36442	+	1.36510i	0.177221	+	0.102319i
$179$	−10.2549	−	17.7620i	−0.766488	−	1.32760i	−0.939456	−	0.342669i	$-0.888669\pi$
$179$	−10.2549	−	17.7620i	−0.766488	−	1.32760i	0.172968	−	0.984928i	$-0.444664\pi$
$180$		0			0
$181$	24.9617	−	9.08531i	1.85539	−	0.675306i	0.873211	−	0.487342i	$-0.162033\pi$
$181$	24.9617	−	9.08531i	1.85539	−	0.675306i	0.982176	−	0.187964i	$-0.0601888\pi$
$182$	3.22588	−	1.86246i	0.239118	−	0.138055i
$183$	21.2619	+	12.2756i	1.57173	+	0.907438i
$184$	0.839317	−	4.76000i	0.0618753	−	0.350912i
$185$		0			0
$186$	13.5038	+	11.3310i	0.990148	+	0.830832i
$187$	−14.3374	+	2.52808i	−1.04846	+	0.184871i
$188$	−2.54364	+	6.98859i	−0.185514	+	0.509695i
$189$	−6.08206			−0.442405
$190$		0			0
$191$	17.6682			1.27842			0.639212	−	0.769031i	$-0.279261\pi$
$191$	17.6682			1.27842			0.639212	+	0.769031i	$0.279261\pi$
$192$	0.873440	−	2.39976i	0.0630351	−	0.173187i
$193$	14.5092	−	2.55837i	1.04440	−	0.184156i	0.374974	−	0.927036i	$-0.377652\pi$
$193$	14.5092	−	2.55837i	1.04440	−	0.184156i	0.669425	+	0.742880i	$0.266541\pi$
$194$	1.52791	+	1.28207i	0.109698	+	0.0920474i
$195$		0			0
$196$	2.40292	−	13.6277i	0.171637	−	0.973405i
$197$	−4.99412	−	2.88336i	−0.355816	−	0.205431i	0.311428	−	0.950270i	$-0.399193\pi$
$197$	−4.99412	−	2.88336i	−0.355816	−	0.205431i	−0.667244	+	0.744839i	$0.732526\pi$
$198$	10.4456	−	6.03080i	0.742340	−	0.428590i
$199$	−4.99379	+	1.81759i	−0.354000	+	0.128846i	−0.512898	−	0.858449i	$-0.671428\pi$
$199$	−4.99379	+	1.81759i	−0.354000	+	0.128846i	0.158898	+	0.987295i	$0.449206\pi$
$200$		0			0
$201$	7.19694	+	12.4655i	0.507633	+	0.879246i
$202$	−3.48234	−	2.01053i	−0.245017	−	0.141460i
$203$	−10.7789	−	1.90061i	−0.756531	−	0.133397i
$204$	−8.31584	+	6.97782i	−0.582225	+	0.488545i
$205$		0			0
$206$	0.874888	+	4.96174i	0.0609563	+	0.345700i
$207$	5.82188	−	15.9955i	0.404648	−	1.11176i
$208$			0.816000i			0.0565794i
$209$	9.27429	+	11.6986i	0.641516	+	0.809210i
$210$		0			0
$211$	−17.6700	−	6.43135i	−1.21645	−	0.442752i	−0.347515	−	0.937675i	$-0.612974\pi$
$211$	−17.6700	−	6.43135i	−1.21645	−	0.442752i	−0.868937	+	0.494922i	$0.835196\pi$
$212$	−11.1173	+	1.96027i	−0.763537	+	0.134632i
$213$	−25.2144	+	30.0494i	−1.72766	+	2.05895i
$214$	−3.54696	+	2.97625i	−0.242465	+	0.203453i
$215$		0			0
$216$	0.666183	−	1.15386i	0.0453280	−	0.0785105i
$217$	−27.2884	+	15.7550i	−1.85246	+	1.06952i
$218$	6.15904	+	16.9218i	0.417143	+	1.14609i
$219$	−22.3257	+	8.12590i	−1.50863	+	0.549098i
$220$		0			0
$221$	1.73433	−	3.00394i	0.116663	−	0.202067i
$222$	9.62878	+	1.69781i	0.646241	+	0.113950i
$223$	−6.91157	−	8.23688i	−0.462833	−	0.551583i	0.483261	−	0.875476i	$-0.339452\pi$
$223$	−6.91157	−	8.23688i	−0.462833	−	0.551583i	−0.946093	+	0.323894i	$0.895008\pi$
$224$	3.49688	+	2.93423i	0.233645	+	0.196052i
$225$		0			0
$226$	−3.54430	−	1.29002i	−0.235764	−	0.0858109i
$227$			20.8415i			1.38330i	0.722235	+	0.691648i	$0.243115\pi$
$227$			20.8415i			1.38330i	−0.722235	+	0.691648i	$0.756885\pi$
$228$	10.3504	+	4.09669i	0.685469	+	0.271310i
$229$	−19.1888			−1.26803			−0.634015	−	0.773321i	$-0.718594\pi$
$229$	−19.1888			−1.26803			−0.634015	+	0.773321i	$0.718594\pi$
$230$		0			0
$231$	6.93310	+	39.3196i	0.456164	+	2.58704i
$232$	1.54122	−	1.83675i	0.101186	−	0.120589i
$233$	13.5744	+	16.1774i	0.889290	+	1.05981i	0.997838	+	0.0657234i	$0.0209355\pi$
$233$	13.5744	+	16.1774i	0.889290	+	1.05981i	−0.108548	+	0.994091i	$0.534620\pi$
$234$	−0.499018	+	2.83007i	−0.0326218	+	0.185007i
$235$		0			0
$236$	2.81973	+	4.88391i	0.183549	+	0.317915i
$237$	1.89168	+	5.19734i	0.122878	+	0.337603i
$238$	−6.63666	−	18.2341i	−0.430191	−	1.18194i
$239$	−3.07893	−	5.33286i	−0.199159	−	0.344954i	0.749097	−	0.662461i	$-0.230488\pi$
$239$	−3.07893	−	5.33286i	−0.199159	−	0.344954i	−0.948256	+	0.317507i	$0.897154\pi$
$240$		0			0
$241$	3.98528	−	22.6017i	0.256715	−	1.45590i	−0.534918	−	0.844904i	$-0.679657\pi$
$241$	3.98528	−	22.6017i	0.256715	−	1.45590i	0.791633	−	0.610997i	$-0.209231\pi$
$242$	−0.469237	−	0.559215i	−0.0301637	−	0.0359477i
$243$	−14.3269	+	17.0742i	−0.919074	+	1.09531i
$244$	−1.66940	−	9.46766i	−0.106873	−	0.606105i
$245$		0			0
$246$	−31.2657			−1.99343
$247$	−3.55549	−	0.0989236i	−0.226230	−	0.00629436i
$248$		−	6.90273i		−	0.438324i
$249$	−1.15311	−	0.419697i	−0.0730753	−	0.0265972i
$250$		0			0
$251$	−12.4104	−	10.4136i	−0.783341	−	0.657301i	0.160747	−	0.986996i	$-0.448610\pi$
$251$	−12.4104	−	10.4136i	−0.783341	−	0.657301i	−0.944088	+	0.329695i	$0.893054\pi$
$252$	10.3336	+	12.3151i	0.650953	+	0.775776i
$253$	−16.3026	−	2.87458i	−1.02493	−	0.180724i
$254$	−8.84871	+	15.3264i	−0.555218	+	0.961665i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−1.14814	−	3.15450i	−0.0716192	−	0.196772i	0.898718	−	0.438526i	$-0.144499\pi$
$257$	−1.14814	−	3.15450i	−0.0716192	−	0.196772i	−0.970338	+	0.241754i	$0.922277\pi$
$258$	9.76183	−	5.63600i	0.607745	−	0.350882i
$259$	−8.73847	+	15.1355i	−0.542982	+	0.940472i
$260$		0			0
$261$	6.46853	−	5.42775i	0.400392	−	0.335969i
$262$	−2.99554	+	3.56994i	−0.185065	+	0.220552i
$263$	−20.5327	+	3.62047i	−1.26610	+	0.223248i	−0.766068	−	0.642760i	$-0.777789\pi$
$263$	−20.5327	+	3.62047i	−1.26610	+	0.223248i	−0.500032	+	0.866007i	$0.666678\pi$
$264$	−8.21895	−	2.99145i	−0.505841	−	0.184111i
$265$		0			0
$266$	−13.2090	+	14.8809i	−0.809896	+	0.912409i
$267$		−	6.97230i		−	0.426698i
$268$	1.92774	−	5.29642i	0.117755	−	0.323530i
$269$	1.97588	+	11.2058i	0.120472	+	0.683228i	0.983895	+	0.178748i	$0.0572048\pi$
$269$	1.97588	+	11.2058i	0.120472	+	0.683228i	−0.863423	+	0.504480i	$0.831684\pi$
$270$		0			0
$271$	4.51353	−	3.78730i	0.274177	−	0.230062i	−0.495322	−	0.868709i	$-0.664950\pi$
$271$	4.51353	−	3.78730i	0.274177	−	0.230062i	0.769500	+	0.638647i	$0.220506\pi$
$272$	4.18622	+	0.738144i	0.253827	+	0.0447566i
$273$	−8.23814	−	4.75629i	−0.498595	−	0.287864i
$274$	3.51025	+	6.07994i	0.212062	+	0.367302i
$275$		0			0
$276$	−11.5991	+	4.22171i	−0.698181	+	0.254117i
$277$	−11.0025	+	6.35228i	−0.661075	+	0.381672i	−0.792686	−	0.609630i	$-0.791318\pi$
$277$	−11.0025	+	6.35228i	−0.661075	+	0.381672i	0.131612	+	0.991301i	$0.457985\pi$
$278$	−16.7747	−	9.68490i	−1.00608	−	0.580862i
$279$	4.22131	−	23.9402i	0.252723	−	1.43326i
$280$		0			0
$281$	10.0997	+	8.47462i	0.602495	+	0.505554i	0.892247	−	0.451548i	$-0.149128\pi$
$281$	10.0997	+	8.47462i	0.602495	+	0.505554i	−0.289751	+	0.957102i	$0.593573\pi$
$282$	18.7041	−	3.29803i	1.11381	−	0.196395i
$283$	−5.72532	+	15.7302i	−0.340335	+	0.935062i	0.644963	+	0.764214i	$0.276873\pi$
$283$	−5.72532	+	15.7302i	−0.340335	+	0.935062i	−0.985297	+	0.170848i	$0.945349\pi$
$284$	15.3603			0.911468
$285$		0			0
$286$	2.79473			0.165256
$287$	19.1146	−	52.5169i	1.12830	−	3.09997i
$288$	−3.46822	+	0.611541i	−0.204367	+	0.0360354i
$289$	−0.819145	−	0.687345i	−0.0481850	−	0.0404320i
$290$		0			0
$291$	0.884497	−	5.01623i	0.0518502	−	0.294057i
$292$	8.05693	+	4.65167i	0.471496	+	0.272218i
$293$	−5.92659	+	3.42172i	−0.346235	+	0.199899i	−0.663026	−	0.748597i	$-0.730728\pi$
$293$	−5.92659	+	3.42172i	−0.346235	+	0.199899i	0.316791	+	0.948495i	$0.397395\pi$
$294$	−33.2076	+	12.0866i	−1.93670	+	0.704903i
$295$		0			0
$296$	−1.91429	−	3.31565i	−0.111266	−	0.192718i
$297$	−3.95188	−	2.28162i	−0.229311	−	0.132393i
$298$	−18.7725	−	3.31009i	−1.08746	−	0.191748i
$299$	3.02134	−	2.53521i	0.174729	−	0.146615i
$300$		0			0
$301$	3.49878	+	19.8426i	0.201666	+	1.14371i
$302$	−6.25362	+	17.1817i	−0.359855	+	0.988694i
$303$			10.2688i			0.589930i
$304$	−1.37634	−	4.13590i	−0.0789383	−	0.237210i
$305$		0			0
$306$	14.0673	+	5.12010i	0.804177	+	0.292696i
$307$	24.3733	−	4.29767i	1.39106	−	0.245281i	0.572594	−	0.819839i	$-0.305937\pi$
$307$	24.3733	−	4.29767i	1.39106	−	0.245281i	0.818464	+	0.574558i	$0.194826\pi$
$308$	10.0495	−	11.9765i	0.572622	−	0.682424i
$309$	9.85638	−	8.27048i	0.560710	−	0.470491i
$310$		0			0
$311$	5.82580	−	10.0906i	0.330351	−	0.572184i	−0.652230	−	0.758021i	$-0.726166\pi$
$311$	5.82580	−	10.0906i	0.330351	−	0.572184i	0.982581	+	0.185837i	$0.0594997\pi$
$312$	1.80469	−	1.04194i	0.102170	−	0.0589881i
$313$	−5.29514	−	14.5483i	−0.299299	−	0.822317i	−0.994617	−	0.103615i	$-0.966959\pi$
$313$	−5.29514	−	14.5483i	−0.299299	−	0.822317i	0.695319	−	0.718702i	$-0.255263\pi$
$314$	11.3429	−	4.12847i	0.640115	−	0.232983i
$315$		0			0
$316$	1.08289	−	1.87562i	0.0609173	−	0.105512i
$317$	7.44843	+	1.31336i	0.418346	+	0.0737656i	0.378859	−	0.925454i	$-0.376317\pi$
$317$	7.44843	+	1.31336i	0.418346	+	0.0737656i	0.0394868	+	0.999220i	$0.487428\pi$
$318$	18.5309	+	22.0842i	1.03916	+	1.23842i
$319$	−6.29071	−	5.27853i	−0.352212	−	0.295541i
$320$		0			0
$321$	11.1114	+	4.04423i	0.620179	+	0.225727i
$322$		−	22.0639i		−	1.22957i
$323$	−3.72375	+	18.1508i	−0.207195	+	1.00994i
$324$	7.16262			0.397924
$325$		0			0
$326$	2.59175	+	14.6985i	0.143544	+	0.814077i
$327$	29.5604	−	35.2287i	1.63469	−	1.94815i
$328$	7.86962	+	9.37865i	0.434527	+	0.517849i
$329$	−5.89523	+	33.4335i	−0.325014	+	1.84325i
$330$		0			0
$331$	−4.69302	−	8.12854i	−0.257952	−	0.446785i	0.707741	−	0.706472i	$-0.249714\pi$
$331$	−4.69302	−	8.12854i	−0.257952	−	0.446785i	−0.965693	+	0.259686i	$0.916381\pi$
$332$	0.164344	+	0.451532i	0.00901956	+	0.0247811i
$333$	−4.61154	−	12.6701i	−0.252711	−	0.694317i
$334$	−5.87860	−	10.1820i	−0.321662	−	0.557136i
$335$		0			0
$336$	2.02432	−	11.4805i	0.110436	−	0.626311i
$337$	5.47636	+	6.52647i	0.298316	+	0.355520i	0.894293	−	0.447482i	$-0.147679\pi$
$337$	5.47636	+	6.52647i	0.298316	+	0.355520i	−0.595976	+	0.803002i	$0.703235\pi$
$338$	7.92823	−	9.44850i	0.431239	−	0.513931i
$339$	1.67262	+	9.48589i	0.0908441	+	0.515203i
$340$		0			0
$341$	−23.6412			−1.28024
$342$	−2.24416	−	15.1859i	−0.121350	−	0.821161i
$343$		−	31.2140i		−	1.68540i
$344$	−4.14768	−	1.50963i	−0.223628	−	0.0813939i
$345$		0			0
$346$	5.88945	+	4.94184i	0.316619	+	0.265675i
$347$	4.37307	+	5.21162i	0.234759	+	0.279774i	0.870543	−	0.492092i	$-0.163768\pi$
$347$	4.37307	+	5.21162i	0.234759	+	0.279774i	−0.635784	+	0.771867i	$0.719323\pi$
$348$	−6.03016	−	1.06328i	−0.323251	−	0.0569978i
$349$	−1.90811	+	3.30495i	−0.102139	+	0.176910i	−0.912566	−	0.408930i	$-0.865902\pi$
$349$	−1.90811	+	3.30495i	−0.102139	+	0.176910i	0.810427	+	0.585840i	$0.199235\pi$
$350$		0			0
$351$	1.02164	−	0.371848i	0.0545313	−	0.0198478i
$352$	1.17139	+	3.21836i	0.0624352	+	0.171539i
$353$	−3.25685	+	1.88034i	−0.173345	+	0.100081i	−0.584162	−	0.811637i	$-0.698577\pi$
$353$	−3.25685	+	1.88034i	−0.173345	+	0.100081i	0.410817	+	0.911718i	$0.365243\pi$
$354$	7.20092	−	12.4724i	0.382725	−	0.662899i
$355$		0			0
$356$	−2.09146	+	1.75494i	−0.110847	+	0.0930116i
$357$	−31.8527	+	37.9606i	−1.68582	+	2.00909i
$358$	20.1982	−	3.56149i	1.06751	−	0.188231i
$359$	−13.6016	−	4.95058i	−0.717865	−	0.261281i	−0.0428458	−	0.999082i	$-0.513642\pi$
$359$	−13.6016	−	4.95058i	−0.717865	−	0.261281i	−0.675019	+	0.737800i	$0.735865\pi$
$360$		0			0
$361$	18.1879	−	5.49559i	0.957256	−	0.289242i
$362$			26.5637i			1.39616i
$363$	−0.637614	+	1.75183i	−0.0334660	+	0.0919472i
$364$	0.646826	+	3.66833i	0.0339029	+	0.192273i
$365$		0			0
$366$	−18.8073	+	15.7812i	−0.983073	+	0.824896i
$367$	−8.66431	−	1.52775i	−0.452273	−	0.0797479i	−0.0571284	−	0.998367i	$-0.518194\pi$
$367$	−8.66431	−	1.52775i	−0.452273	−	0.0797479i	−0.395145	+	0.918619i	$0.629306\pi$
$368$	4.18588	+	2.41672i	0.218204	+	0.125980i
$369$	21.5582	+	37.3399i	1.12227	+	1.94383i
$370$		0			0
$371$	−48.4239	+	17.6248i	−2.51404	+	0.915036i
$372$	−15.2663	+	8.81399i	−0.791519	+	0.456984i
$373$	−5.80859	−	3.35359i	−0.300757	−	0.173642i	0.342026	−	0.939691i	$-0.388887\pi$
$373$	−5.80859	−	3.35359i	−0.300757	−	0.173642i	−0.642783	+	0.766048i	$0.722220\pi$
$374$	2.52808	−	14.3374i	0.130724	−	0.741371i
$375$		0			0
$376$	−5.69715	−	4.78047i	−0.293808	−	0.246534i
$377$	1.92681	−	0.339748i	0.0992356	−	0.0174979i
$378$	2.08019	−	5.71527i	0.106993	−	0.293962i
$379$	16.8707			0.866591			0.433295	−	0.901252i	$-0.357351\pi$
$379$	16.8707			0.866591			0.433295	+	0.901252i	$0.357351\pi$
$380$		0			0
$381$	45.1951			2.31542
$382$	−6.04287	+	16.6026i	−0.309180	+	0.849465i
$383$	6.88419	−	1.21387i	0.351766	−	0.0620258i	0.00502655	−	0.999987i	$-0.498400\pi$
$383$	6.88419	−	1.21387i	0.351766	−	0.0620258i	0.346739	+	0.937962i	$0.387289\pi$
$384$	1.95630	+	1.64153i	0.0998320	+	0.0837690i
$385$		0			0
$386$	−2.55837	+	14.5092i	−0.130218	+	0.738501i
$387$	−13.4619	−	7.77222i	−0.684306	−	0.395084i
$388$	−1.72733	+	0.997275i	−0.0876920	+	0.0506290i
$389$	11.1144	−	4.04531i	0.563523	−	0.205106i	−0.0445218	−	0.999008i	$-0.514176\pi$
$389$	11.1144	−	4.04531i	0.563523	−	0.205106i	0.608045	+	0.793903i	$0.291954\pi$
$390$		0			0
$391$	−10.2730	−	17.7933i	−0.519527	−	0.899847i
$392$	11.9840	+	6.91895i	0.605282	+	0.349460i
$393$	11.7203	+	2.06661i	0.591212	+	0.104247i
$394$	4.41756	−	3.70677i	0.222553	−	0.186744i
$395$		0			0
$396$	2.09447	+	11.8783i	0.105251	+	0.596909i
$397$	10.1873	−	27.9894i	0.511286	−	1.40475i	−0.368612	−	0.929583i	$-0.620167\pi$
$397$	10.1873	−	27.9894i	0.511286	−	1.40475i	0.879898	−	0.475163i	$-0.157611\pi$
$398$		−	5.31428i		−	0.266381i
$399$	49.7774	+	10.2122i	2.49199	+	0.511247i
$400$		0			0
$401$	−17.1199	−	6.23113i	−0.854927	−	0.311168i	−0.122879	−	0.992422i	$-0.539213\pi$
$401$	−17.1199	−	6.23113i	−0.854927	−	0.311168i	−0.732047	+	0.681254i	$0.761435\pi$
$402$	−14.1752	+	2.49947i	−0.706995	+	0.124662i
$403$	3.62059	−	4.31485i	0.180354	−	0.214938i
$404$	3.08031	−	2.58469i	0.153251	−	0.128593i
$405$		0			0
$406$	5.47259	−	9.47881i	0.271600	−	0.470426i
$407$	−11.3558	+	6.55628i	−0.562887	+	0.324983i
$408$	−3.71282	−	10.2009i	−0.183812	−	0.505019i
$409$	17.3500	−	6.31489i	0.857903	−	0.312251i	0.124645	−	0.992201i	$-0.460221\pi$
$409$	17.3500	−	6.31489i	0.857903	−	0.312251i	0.733258	+	0.679950i	$0.237999\pi$
$410$		0			0
$411$	8.96437	−	15.5267i	0.442180	−	0.765878i
$412$	−4.96174	−	0.874888i	−0.244447	−	0.0431026i
$413$	16.5475	+	19.7205i	0.814247	+	0.970382i
$414$	13.0396	+	10.9415i	0.640863	+	0.537748i
$415$		0			0
$416$	−0.766789	−	0.279088i	−0.0375949	−	0.0136834i
$417$			49.4660i			2.42236i
$418$	−14.1651	+	4.71382i	−0.692837	+	0.230561i
$419$	38.4546			1.87863			0.939314	−	0.343057i	$-0.111463\pi$
$419$	38.4546			1.87863			0.939314	+	0.343057i	$0.111463\pi$
$420$		0			0
$421$	1.36999	+	7.76960i	0.0667692	+	0.378667i	0.999821	+	0.0189248i	$0.00602430\pi$
$421$	1.36999	+	7.76960i	0.0667692	+	0.378667i	−0.933052	+	0.359742i	$0.882865\pi$
$422$	12.0870	−	14.4047i	0.588385	−	0.701210i
$423$	−16.8355	−	20.0638i	−0.818571	−	0.975535i
$424$	1.96027	−	11.1173i	0.0951993	−	0.539902i
$425$		0			0
$426$	−19.6134	−	33.9713i	−0.950270	−	1.64592i
$427$	−15.0096	−	41.2386i	−0.726366	−	1.99568i
$428$	−1.58363	−	4.35099i	−0.0765477	−	0.210313i
$429$	−3.56854	−	6.18089i	−0.172291	−	0.298416i
$430$		0			0
$431$	0.372953	−	2.11512i	0.0179645	−	0.101882i	−0.974507	−	0.224357i	$-0.927972\pi$
$431$	0.372953	−	2.11512i	0.0179645	−	0.101882i	0.992472	+	0.122475i	$0.0390831\pi$
$432$	0.856429	+	1.02065i	0.0412049	+	0.0491061i
$433$	−5.64524	+	6.72774i	−0.271293	+	0.323314i	−0.884440	−	0.466655i	$-0.845459\pi$
$433$	−5.64524	+	6.72774i	−0.271293	+	0.323314i	0.613147	+	0.789969i	$0.289904\pi$
$434$	−5.47165	−	31.0313i	−0.262648	−	1.48955i
$435$		0			0
$436$	−18.0078			−0.862419
$437$	−11.0376	+	17.9458i	−0.528000	+	0.858463i
$438$		−	23.7586i		−	1.13523i
$439$	2.27368	+	0.827552i	0.108517	+	0.0394969i	0.395708	−	0.918376i	$-0.370499\pi$
$439$	2.27368	+	0.827552i	0.108517	+	0.0394969i	−0.287191	+	0.957873i	$0.592721\pi$
$440$		0			0
$441$	37.3318	+	31.3251i	1.77771	+	1.49167i
$442$	2.22961	+	2.65714i	0.106052	+	0.126387i
$443$	32.4737	+	5.72598i	1.54287	+	0.272050i	0.879375	−	0.476130i	$-0.157961\pi$
$443$	32.4737	+	5.72598i	1.54287	+	0.272050i	0.663496	+	0.748180i	$0.269072\pi$
$444$	−4.88866	+	8.46740i	−0.232005	+	0.401845i
$445$		0			0
$446$	10.1040	−	3.67757i	0.478440	−	0.174138i
$447$	16.6496	+	45.7443i	0.787497	+	2.16363i
$448$	−3.95328	+	2.28243i	−0.186775	+	0.107835i
$449$	−9.54580	+	16.5338i	−0.450494	+	0.780279i	−0.998417	−	0.0562503i	$-0.982086\pi$
$449$	−9.54580	+	16.5338i	−0.450494	+	0.780279i	0.547923	+	0.836529i	$0.315419\pi$
$450$		0			0
$451$	32.1210	−	26.9527i	1.51252	−	1.26916i
$452$	2.42445	−	2.88934i	0.114036	−	0.135903i
$453$	45.9846	−	8.10833i	2.16054	−	0.380962i
$454$	−19.5846	−	7.12820i	−0.919149	−	0.334543i
$455$		0			0
$456$	−7.38966	+	8.32501i	−0.346052	+	0.389854i
$457$		−	17.3344i		−	0.810867i	−0.914125	−	0.405434i	$-0.867121\pi$
$457$		−	17.3344i		−	0.810867i	0.914125	−	0.405434i	$-0.132879\pi$
$458$	6.56294	−	18.0315i	0.306666	−	0.842559i
$459$	−0.983478	−	5.57758i	−0.0459048	−	0.260339i
$460$		0			0
$461$	9.33023	−	7.82900i	0.434552	−	0.364633i	−0.399114	−	0.916901i	$-0.630682\pi$
$461$	9.33023	−	7.82900i	0.434552	−	0.364633i	0.833666	+	0.552269i	$0.186238\pi$
$462$	−39.3196	−	6.93310i	−1.82931	−	0.322557i
$463$	7.19217	+	4.15240i	0.334249	+	0.192979i	0.657726	−	0.753257i	$-0.271519\pi$
$463$	7.19217	+	4.15240i	0.334249	+	0.192979i	−0.323477	+	0.946236i	$0.604852\pi$
$464$	1.19885	+	2.07648i	0.0556554	+	0.0963980i
$465$		0			0
$466$	−19.8445	+	7.22280i	−0.919278	+	0.334590i
$467$	−7.02421	+	4.05543i	−0.325042	+	0.187663i	−0.653638	−	0.756808i	$-0.726758\pi$
$467$	−7.02421	+	4.05543i	−0.325042	+	0.187663i	0.328596	+	0.944471i	$0.393425\pi$
$468$	−2.48872	−	1.43686i	−0.115041	−	0.0664191i
$469$	4.46780	−	25.3382i	0.206304	−	1.17001i
$470$		0			0
$471$	−23.6142	−	19.8146i	−1.08808	−	0.913010i
$472$	−5.55378	+	0.979281i	−0.255633	+	0.0450750i
$473$	−5.17035	+	14.2054i	−0.237733	+	0.653166i
$474$	−5.53089			−0.254042
$475$		0			0
$476$	19.4043			0.889394
$477$	13.5973	−	37.3584i	0.622579	−	1.71052i
$478$	6.06431	−	1.06930i	0.277375	−	0.0489087i
$479$	−24.1256	−	20.2438i	−1.10233	−	0.924962i	−0.104747	−	0.994499i	$-0.533403\pi$
$479$	−24.1256	−	20.2438i	−1.10233	−	0.924962i	−0.997579	+	0.0695374i	$0.977848\pi$
$480$		0			0
$481$	0.542499	−	3.07666i	0.0247358	−	0.140284i
$482$	19.8756	+	11.4752i	0.905308	+	0.522680i
$483$	−48.7972	+	28.1731i	−2.22035	+	1.28192i
$484$	0.685978	−	0.249676i	0.0311808	−	0.0113489i
$485$		0			0
$486$	−11.1444	−	19.3026i	−0.505520	−	0.875586i
$487$	−13.5725	−	7.83611i	−0.615030	−	0.355088i	0.159901	−	0.987133i	$-0.448882\pi$
$487$	−13.5725	−	7.83611i	−0.615030	−	0.355088i	−0.774932	+	0.632045i	$0.782216\pi$
$488$	9.46766	+	1.66940i	0.428581	+	0.0755704i
$489$	29.1983	−	24.5003i	1.32039	−	1.10794i
$490$		0			0
$491$	−2.50123	−	14.1852i	−0.112879	−	0.640168i	−0.987779	−	0.155864i	$-0.950184\pi$
$491$	−2.50123	−	14.1852i	−0.112879	−	0.640168i	0.874900	−	0.484304i	$-0.160927\pi$
$492$	10.6935	−	29.3801i	0.482100	−	1.32456i
$493$		−	10.1922i		−	0.459033i
$494$	1.30901	−	3.30723i	0.0588949	−	0.148799i
$495$		0			0
$496$	6.48645	+	2.36087i	0.291250	+	0.106006i
$497$	69.0524	−	12.1758i	3.09742	−	0.546159i
$498$	0.788772	−	0.940022i	0.0353457	−	0.0421234i
$499$	17.3717	−	14.5766i	0.777666	−	0.652539i	−0.164994	−	0.986295i	$-0.552760\pi$
$499$	17.3717	−	14.5766i	0.777666	−	0.652539i	0.942660	+	0.333756i	$0.108316\pi$
$500$		0			0
$501$	−15.0126	+	26.0025i	−0.670712	+	1.16171i
$502$	14.0302	−	8.10035i	0.626199	−	0.361536i
$503$	−9.26902	−	25.4664i	−0.413285	−	1.13549i	−0.955433	−	0.295208i	$-0.904611\pi$
$503$	−9.26902	−	25.4664i	−0.413285	−	1.13549i	0.542148	−	0.840283i	$-0.317611\pi$
$504$	−15.1067	+	5.49837i	−0.672904	+	0.244917i
$505$		0			0
$506$	8.27704	−	14.3362i	0.367959	−	0.637324i
$507$	−31.0200	−	5.46966i	−1.37765	−	0.242916i
$508$	−11.3757	−	13.5570i	−0.504714	−	0.601495i
$509$	5.88641	+	4.93928i	0.260910	+	0.218930i	0.763853	−	0.645390i	$-0.223305\pi$
$509$	5.88641	+	4.93928i	0.260910	+	0.218930i	−0.502943	+	0.864320i	$0.667749\pi$
$510$		0			0
$511$	39.9072	+	14.5250i	1.76539	+	0.642550i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.55102	+	3.60791i	−0.200933	+	0.159293i
$514$	3.35695			0.148069
$515$		0			0
$516$	1.95736	+	11.1007i	0.0861680	+	0.488683i
$517$	−16.3727	+	19.5122i	−0.720070	+	0.858146i
$518$	−11.2340	−	13.3881i	−0.493592	−	0.588240i
$519$	3.40936	−	19.3354i	0.149654	−	0.848731i
$520$		0			0
$521$	−6.14900	−	10.6504i	−0.269393	−	0.466602i	0.699312	−	0.714816i	$-0.253490\pi$
$521$	−6.14900	−	10.6504i	−0.269393	−	0.466602i	−0.968705	+	0.248214i	$0.920156\pi$
$522$	2.88804	+	7.93483i	0.126406	+	0.347298i
$523$	−5.04254	−	13.8543i	−0.220495	−	0.605805i	0.779287	−	0.626667i	$-0.215581\pi$
$523$	−5.04254	−	13.8543i	−0.220495	−	0.605805i	−0.999782	+	0.0208617i	$0.993359\pi$
$524$	−2.33011	−	4.03588i	−0.101791	−	0.176308i
$525$		0			0
$526$	3.62047	−	20.5327i	0.157860	−	0.895268i
$527$	−18.8608	−	22.4774i	−0.821588	−	0.979131i
$528$	5.62209	−	6.70015i	0.244670	−	0.291586i
$529$	−0.0628742	−	0.356577i	−0.00273366	−	0.0155033i
$530$		0			0
$531$	−19.8606			−0.861877
$532$	−9.46576	−	17.5020i	−0.410393	−	0.758807i
$533$			9.99026i			0.432726i
$534$	6.55182	+	2.38467i	0.283525	+	0.103195i
$535$		0			0
$536$	4.31768	+	3.62297i	0.186495	+	0.156488i
$537$	−33.6675	−	40.1234i	−1.45286	−	1.73145i
$538$	−11.2058	−	1.97588i	−0.483115	−	0.0851863i
$539$	23.6968	−	41.0440i	1.02069	−	1.76789i
$540$		0			0
$541$	−30.4211	+	11.0724i	−1.30790	+	0.476038i	−0.899563	−	0.436791i	$-0.856115\pi$
$541$	−30.4211	+	11.0724i	−1.30790	+	0.476038i	−0.408341	+	0.912829i	$0.633893\pi$
$542$	2.01518	+	5.53666i	0.0865594	+	0.237820i
$543$	58.7489	−	33.9187i	2.52116	−	1.45559i
$544$	−2.12540	+	3.68130i	−0.0911258	+	0.157835i
$545$		0			0
$546$	7.28706	−	6.11457i	0.311857	−	0.261679i
$547$	20.0014	−	23.8367i	0.855196	−	1.01918i	−0.144364	−	0.989525i	$-0.546114\pi$
$547$	20.0014	−	23.8367i	0.855196	−	1.01918i	0.999560	−	0.0296585i	$-0.00944198\pi$
$548$	−6.91385	+	1.21910i	−0.295345	+	0.0520773i
$549$	31.8150	+	11.5797i	1.35783	+	0.494211i
$550$		0			0
$551$	−9.19299	+	4.97193i	−0.391634	+	0.211811i
$552$		−	12.3435i		−	0.525373i
$553$	3.38137	−	9.29023i	0.143790	−	0.395061i
$554$	−2.20612	−	12.5116i	−0.0937292	−	0.531565i
$555$		0			0
$556$	14.8381	−	12.4507i	0.629277	−	0.528026i
$557$	4.91297	+	0.866290i	0.208169	+	0.0367059i	0.276760	−	0.960939i	$-0.410739\pi$
$557$	4.91297	+	0.866290i	0.208169	+	0.0367059i	−0.0685909	+	0.997645i	$0.521850\pi$
$558$	21.0527	+	12.1548i	0.891231	+	0.514552i
$559$	−1.80086	−	3.11918i	−0.0761682	−	0.131927i
$560$		0			0
$561$	−34.9371	+	12.7161i	−1.47505	+	0.536873i
$562$	−11.4178	+	6.59209i	−0.481632	+	0.278070i
$563$	−22.5594	−	13.0247i	−0.950764	−	0.548924i	−0.0574458	−	0.998349i	$-0.518296\pi$
$563$	−22.5594	−	13.0247i	−0.950764	−	0.548924i	−0.893318	+	0.449425i	$0.851629\pi$
$564$	−3.29803	+	18.7041i	−0.138872	+	0.787584i
$565$		0			0
$566$	−12.8234	−	10.7601i	−0.539006	−	0.452280i
$567$	32.1996	−	5.67766i	1.35226	−	0.238439i
$568$	−5.25354	+	14.4340i	−0.220434	+	0.605637i
$569$	−33.8230			−1.41793			−0.708967	−	0.705242i	$-0.750838\pi$
$569$	−33.8230			−1.41793			−0.708967	+	0.705242i	$0.750838\pi$
$570$		0			0
$571$	41.6528			1.74312			0.871558	−	0.490293i	$-0.163110\pi$
$571$	41.6528			1.74312			0.871558	+	0.490293i	$0.163110\pi$
$572$	−0.955853	+	2.62618i	−0.0399662	+	0.109806i
$573$	44.4349	−	7.83507i	1.85630	−	0.327315i
$574$	42.8122	+	35.9237i	1.78695	+	1.49943i
$575$		0			0
$576$	0.611541	−	3.46822i	0.0254809	−	0.144509i
$577$	31.3403	+	18.0943i	1.30471	+	0.753276i	0.981208	−	0.192951i	$-0.0618058\pi$
$577$	31.3403	+	18.0943i	1.30471	+	0.753276i	0.323504	+	0.946227i	$0.395139\pi$
$578$	0.926057	−	0.534659i	0.0385189	−	0.0222389i
$579$	35.3558	−	12.8685i	1.46934	−	0.534795i
$580$		0			0
$581$	1.09673	+	1.89959i	0.0455000	+	0.0788084i
$582$	4.41120	+	2.54681i	0.182850	+	0.105569i
$583$	−38.0756	−	6.71376i	−1.57693	−	0.278056i
$584$	−7.12677	+	5.98007i	−0.294908	+	0.247457i
$585$		0			0
$586$	−1.18835	−	6.73947i	−0.0490903	−	0.278405i
$587$	−9.69163	+	26.6275i	−0.400016	+	1.09904i	0.562260	+	0.826961i	$0.309932\pi$
$587$	−9.69163	+	26.6275i	−0.400016	+	1.09904i	−0.962276	+	0.272075i	$0.912290\pi$
$588$		−	35.3388i		−	1.45735i
$589$	−11.0732	+	27.9766i	−0.456263	+	1.15276i
$590$		0			0
$591$	−13.8387	−	5.03687i	−0.569248	−	0.207189i
$592$	3.77042	−	0.664827i	0.154963	−	0.0273242i
$593$	−28.7061	+	34.2107i	−1.17882	+	1.40486i	−0.283773	+	0.958892i	$0.591586\pi$
$593$	−28.7061	+	34.2107i	−1.17882	+	1.40486i	−0.895047	+	0.445972i	$0.852858\pi$
$594$	3.49564	−	2.93319i	0.143428	−	0.120350i
$595$		0			0
$596$	9.53103	−	16.5082i	0.390406	−	0.676203i
$597$	−11.7532	+	6.78572i	−0.481027	+	0.277721i
$598$	1.34896	+	3.70622i	0.0551629	+	0.151559i
$599$	10.8852	−	3.96190i	0.444759	−	0.161879i	−0.109926	−	0.993940i	$-0.535061\pi$
$599$	10.8852	−	3.96190i	0.444759	−	0.161879i	0.554684	+	0.832061i	$0.312839\pi$
$600$		0			0
$601$	1.22575	−	2.12305i	0.0499992	−	0.0866012i	−0.839943	−	0.542675i	$-0.817411\pi$
$601$	1.22575	−	2.12305i	0.0499992	−	0.0866012i	0.889942	+	0.456074i	$0.150745\pi$
$602$	−19.8426	−	3.49878i	−0.808722	−	0.142600i
$603$	12.7591	+	15.2057i	0.519590	+	0.619224i
$604$	−14.0066	−	11.7530i	−0.569922	−	0.478221i
$605$		0			0
$606$	−9.64956	−	3.51215i	−0.391987	−	0.142671i
$607$		−	22.4395i		−	0.910790i	−0.890290	−	0.455395i	$-0.849498\pi$
$607$		−	22.4395i		−	0.910790i	0.890290	−	0.455395i	$-0.150502\pi$
$608$	4.35721	+	0.121230i	0.176708	+	0.00491652i
$609$	−27.9515			−1.13265
$610$		0			0
$611$	−1.05381	−	5.97648i	−0.0426328	−	0.241782i
$612$	−9.62263	+	11.4678i	−0.388972	+	0.463559i
$613$	14.8459	+	17.6927i	0.599622	+	0.714602i	0.977425	−	0.211284i	$-0.0677646\pi$
$613$	14.8459	+	17.6927i	0.599622	+	0.714602i	−0.377802	+	0.925886i	$0.623320\pi$
$614$	−4.29767	+	24.3733i	−0.173440	+	0.983626i
$615$		0			0
$616$	7.81711	+	13.5396i	0.314960	+	0.545527i
$617$	5.59562	+	15.3738i	0.225271	+	0.618928i	0.999909	−	0.0134772i	$-0.00429007\pi$
$617$	5.59562	+	15.3738i	0.225271	+	0.618928i	−0.774638	+	0.632405i	$0.782068\pi$
$618$	4.40063	+	12.0906i	0.177019	+	0.486357i
$619$	5.96422	+	10.3303i	0.239722	+	0.415211i	0.960635	−	0.277815i	$-0.0896103\pi$
$619$	5.96422	+	10.3303i	0.239722	+	0.415211i	−0.720912	+	0.693026i	$0.756277\pi$
$620$		0			0
$621$	1.11828	−	6.34207i	0.0448749	−	0.254498i
$622$	7.48950	+	8.92564i	0.300302	+	0.357886i
$623$	−8.01104	+	9.54719i	−0.320956	+	0.382500i
$624$	0.361861	+	2.05222i	0.0144860	+	0.0821544i
$625$		0			0
$626$	15.4819			0.618783
$627$	28.5124	+	25.3089i	1.13868	+	1.01074i
$628$			12.0708i			0.481678i
$629$	−15.2931	−	5.56623i	−0.609775	−	0.221940i
$630$		0			0
$631$	21.5749	+	18.1035i	0.858883	+	0.720688i	0.961727	−	0.274009i	$-0.0883499\pi$
$631$	21.5749	+	18.1035i	0.858883	+	0.720688i	−0.102844	+	0.994697i	$0.532794\pi$
$632$	1.39214	+	1.65908i	0.0553762	+	0.0659947i
$633$	−47.2915	−	8.33877i	−1.87967	−	0.331436i
$634$	−3.78167	+	6.55004i	−0.150189	+	0.260135i
$635$		0			0
$636$	−27.0903	+	9.86006i	−1.07420	+	0.390977i
$637$	3.86200	+	10.6107i	0.153018	+	0.420413i
$638$	7.11174	−	4.10597i	0.281557	−	0.162557i
$639$	−27.0474	+	46.8475i	−1.06998	+	1.85326i
$640$		0			0
$641$	−9.66506	+	8.10994i	−0.381747	+	0.320324i	−0.813388	−	0.581722i	$-0.802379\pi$
$641$	−9.66506	+	8.10994i	−0.381747	+	0.320324i	0.431641	+	0.902045i	$0.357935\pi$
$642$	−7.60066	+	9.05811i	−0.299974	+	0.357495i
$643$	3.43350	−	0.605419i	0.135404	−	0.0238754i	−0.105535	−	0.994416i	$-0.533656\pi$
$643$	3.43350	−	0.605419i	0.135404	−	0.0238754i	0.240939	+	0.970540i	$0.422544\pi$
$644$	20.7333	+	7.54630i	0.817006	+	0.297366i
$645$		0			0
$646$	−15.7826	−	9.70711i	−0.620956	−	0.381921i
$647$		−	41.3497i		−	1.62562i	−0.582526	−	0.812812i	$-0.697936\pi$
$647$		−	41.3497i		−	1.62562i	0.582526	−	0.812812i	$-0.302064\pi$
$648$	−2.44976	+	6.73067i	−0.0962357	+	0.264405i
$649$	3.35395	+	19.0212i	0.131654	+	0.746647i
$650$		0			0
$651$	−61.6429	+	51.7246i	−2.41598	+	2.02725i
$652$	−14.6985	−	2.59175i	−0.575639	−	0.101501i
$653$	21.4517	+	12.3851i	0.839469	+	0.484668i	0.857084	−	0.515177i	$-0.172274\pi$
$653$	21.4517	+	12.3851i	0.839469	+	0.484668i	−0.0176147	+	0.999845i	$0.505607\pi$
$654$	22.9939	+	39.8266i	0.899133	+	1.55734i
$655$		0			0
$656$	−11.5046	+	4.18734i	−0.449180	+	0.163488i
$657$	−28.3743	+	16.3819i	−1.10699	+	0.639119i
$658$	−29.4009	−	16.9746i	−1.14617	−	0.661740i
$659$	−5.30246	+	30.0718i	−0.206555	+	1.17143i	0.688420	+	0.725312i	$0.258305\pi$
$659$	−5.30246	+	30.0718i	−0.206555	+	1.17143i	−0.894975	+	0.446117i	$0.852806\pi$
$660$		0			0
$661$	5.85365	+	4.91180i	0.227681	+	0.191047i	0.749491	−	0.662015i	$-0.230299\pi$
$661$	5.85365	+	4.91180i	0.227681	+	0.191047i	−0.521810	+	0.853062i	$0.674743\pi$
$662$	9.24344	−	1.62987i	0.359256	−	0.0633466i
$663$	3.02966	−	8.32393i	0.117662	−	0.323274i
$664$	−0.480511			−0.0186474
$665$		0			0
$666$	13.4832			0.522465
$667$	3.96373	−	10.8903i	0.153476	−	0.421672i
$668$	11.5786	−	2.04161i	0.447988	−	0.0789924i
$669$	−21.0351	−	17.6505i	−0.813263	−	0.682409i
$670$		0			0
$671$	5.71756	−	32.4259i	0.220724	−	1.25179i
$672$	10.0958	+	5.82879i	0.389452	+	0.224850i
$673$	−23.9670	+	13.8374i	−0.923861	+	0.533392i	−0.884865	−	0.465848i	$-0.845749\pi$
$673$	−23.9670	+	13.8374i	−0.923861	+	0.533392i	−0.0389966	+	0.999239i	$0.512416\pi$
$674$	−8.00591	+	2.91391i	−0.308376	+	0.112240i
$675$		0			0
$676$	6.16707	+	10.6817i	0.237195	+	0.410834i
$677$	−15.0710	−	8.70125i	−0.579226	−	0.334416i	0.181600	−	0.983373i	$-0.441872\pi$
$677$	−15.0710	−	8.70125i	−0.579226	−	0.334416i	−0.760826	+	0.648956i	$0.775206\pi$
$678$	−9.48589	−	1.67262i	−0.364303	−	0.0642365i
$679$	−6.97471	+	5.85247i	−0.267665	+	0.224597i
$680$		0			0
$681$	9.24229	+	52.4156i	0.354165	+	2.00857i
$682$	8.08578	−	22.2155i	0.309621	−	0.850675i
$683$			16.0345i			0.613545i	0.951783	+	0.306772i	$0.0992490\pi$
$683$			16.0345i			0.613545i	−0.951783	+	0.306772i	$0.900751\pi$
$684$	15.0376	+	3.08507i	0.574979	+	0.117961i
$685$		0			0
$686$	29.3315	+	10.6758i	1.11988	+	0.407604i
$687$	−48.2592	+	8.50939i	−1.84120	+	0.324654i
$688$	2.83718	−	3.38122i	0.108166	−	0.128908i
$689$	7.05652	−	5.92113i	0.268832	−	0.225577i
$690$		0			0
$691$	−22.9510	+	39.7524i	−0.873099	+	1.51225i	−0.0143239	+	0.999897i	$0.504560\pi$
$691$	−22.9510	+	39.7524i	−0.873099	+	1.51225i	−0.858775	+	0.512354i	$0.828774\pi$
$692$	−6.65812	+	3.84407i	−0.253104	+	0.146130i
$693$	18.8314	+	51.7389i	0.715347	+	1.96540i
$694$	−6.39300	+	2.32686i	−0.242675	+	0.0883264i
$695$		0			0
$696$	3.06159	−	5.30284i	0.116049	−	0.201004i
$697$	51.2518	+	9.03707i	1.94130	+	0.342303i
$698$	−2.45303	−	2.92340i	−0.0928484	−	0.110652i
$699$	41.3132	+	34.6659i	1.56261	+	1.31119i
$700$		0			0
$701$	−22.3326	−	8.12842i	−0.843492	−	0.307006i	−0.116108	−	0.993237i	$-0.537042\pi$
$701$	−22.3326	−	8.12842i	−0.843492	−	0.307006i	−0.727384	+	0.686231i	$0.759264\pi$
$702$			1.08721i			0.0410341i
$703$	2.43970	+	16.5091i	0.0920152	+	0.622653i
$704$	−3.42491			−0.129081
$705$		0			0
$706$	−0.653037	−	3.70356i	−0.0245774	−	0.139385i
$707$	11.7987	−	14.0612i	0.443737	−	0.528825i
$708$	9.25733	+	11.0325i	0.347912	+	0.414625i
$709$	2.18071	−	12.3674i	0.0818984	−	0.464469i	−0.916084	−	0.400985i	$-0.868668\pi$
$709$	2.18071	−	12.3674i	0.0818984	−	0.464469i	0.997983	−	0.0634836i	$-0.0202210\pi$
$710$		0			0
$711$	3.81364	+	6.60542i	0.143023	+	0.247722i
$712$	−0.933784	−	2.56555i	−0.0349950	−	0.0961480i
$713$	−11.4111	−	31.3518i	−0.427350	−	1.17413i
$714$	−24.7770	−	42.9151i	−0.927257	−	1.60606i
$715$		0			0
$716$	−3.56149	+	20.1982i	−0.133099	+	0.754844i
$717$	−10.1083	−	12.0466i	−0.377502	−	0.449889i
$718$	9.30404	−	11.0881i	0.347224	−	0.413805i
$719$	−1.20794	−	6.85055i	−0.0450485	−	0.255483i	0.953964	−	0.299922i	$-0.0969608\pi$
$719$	−1.20794	−	6.85055i	−0.0450485	−	0.255483i	−0.999012	+	0.0444399i	$0.985850\pi$
$720$		0			0
$721$	−22.9990			−0.856528
$722$	−1.05645	+	18.9706i	−0.0393169	+	0.706013i
$723$		−	58.6098i		−	2.17972i
$724$	−24.9617	−	9.08531i	−0.927694	−	0.337653i
$725$		0			0
$726$	−1.42810	−	1.19832i	−0.0530019	−	0.0444739i
$727$	33.5669	+	40.0035i	1.24493	+	1.48365i	0.813569	+	0.581468i	$0.197521\pi$
$727$	33.5669	+	40.0035i	1.24493	+	1.48365i	0.431359	+	0.902180i	$0.358034\pi$
$728$	−3.66833	−	0.646826i	−0.135957	−	0.0239730i
$729$	−17.7162	+	30.6854i	−0.656157	+	1.13650i
$730$		0			0
$731$	−17.6310	+	6.41715i	−0.652105	+	0.237347i
$732$	−8.39700	−	23.0706i	−0.310362	−	0.852713i
$733$	24.6540	−	14.2340i	0.910615	−	0.525744i	0.0299862	−	0.999550i	$-0.490454\pi$
$733$	24.6540	−	14.2340i	0.910615	−	0.525744i	0.880629	+	0.473806i	$0.157120\pi$
$734$	4.39898	−	7.61926i	0.162369	−	0.281232i
$735$		0			0
$736$	−3.70262	+	3.10687i	−0.136481	+	0.114521i
$737$	12.4083	−	14.7877i	0.457067	−	0.544711i
$738$	−42.4613	+	7.48707i	−1.56302	+	0.275603i
$739$	−7.54033	−	2.74446i	−0.277376	−	0.100956i	0.199587	−	0.979880i	$-0.436040\pi$
$739$	−7.54033	−	2.74446i	−0.277376	−	0.100956i	−0.476962	+	0.878924i	$0.658262\pi$
$740$		0			0
$741$	−8.98581	+	1.32792i	−0.330102	+	0.0487822i
$742$		−	51.5316i		−	1.89178i
$743$	5.87914	−	16.1528i	0.215685	−	0.592589i	−0.783915	−	0.620868i	$-0.786780\pi$
$743$	5.87914	−	16.1528i	0.215685	−	0.592589i	0.999600	+	0.0282789i	$0.00900266\pi$
$744$	−3.06107	−	17.3602i	−0.112224	−	0.636455i
$745$		0			0
$746$	5.13800	−	4.31129i	0.188115	−	0.157848i
$747$	−1.66652	−	0.293852i	−0.0609747	−	0.0107515i
$748$	12.6081	+	7.27931i	0.460999	+	0.266158i
$749$	−10.5682	−	18.3046i	−0.386152	−	0.668835i
$750$		0			0
$751$	39.3470	−	14.3211i	1.43579	−	0.522585i	0.497206	−	0.867633i	$-0.334359\pi$
$751$	39.3470	−	14.3211i	1.43579	−	0.522585i	0.938585	+	0.345048i	$0.112137\pi$
$752$	6.44072	−	3.71855i	0.234869	−	0.135602i
$753$	−35.8299	−	20.6864i	−1.30571	−	0.753854i
$754$	−0.339748	+	1.92681i	−0.0123729	+	0.0701701i
$755$		0			0
$756$	4.65913	+	3.90947i	0.169451	+	0.142186i
$757$	−40.1742	+	7.08380i	−1.46016	+	0.257465i	−0.846619	−	0.532200i	$-0.821365\pi$
$757$	−40.1742	+	7.08380i	−1.46016	+	0.257465i	−0.613538	+	0.789665i	$0.710254\pi$
$758$	−5.77013	+	15.8533i	−0.209580	+	0.575817i
$759$	−42.2752			−1.53449
$760$		0			0
$761$	28.2817			1.02521			0.512606	−	0.858624i	$-0.328680\pi$
$761$	28.2817			1.02521			0.512606	+	0.858624i	$0.328680\pi$
$762$	−15.4576	+	42.4695i	−0.559971	+	1.53851i
$763$	−80.9543	+	14.2744i	−2.93074	+	0.516769i
$764$	−13.5346	−	11.3569i	−0.489665	−	0.410878i
$765$		0			0
$766$	−1.21387	+	6.88419i	−0.0438589	+	0.248736i
$767$	−3.98527	−	2.30090i	−0.143900	−	0.0830806i
$768$	−2.21163	+	1.27688i	−0.0798052	+	0.0460756i
$769$	30.8544	−	11.2301i	1.11264	−	0.404967i	0.280678	−	0.959802i	$-0.409441\pi$
$769$	30.8544	−	11.2301i	1.11264	−	0.404967i	0.831961	+	0.554835i	$0.187218\pi$
$770$		0			0
$771$	−4.28643	−	7.42431i	−0.154372	−	0.267380i
$772$	−12.7592	−	7.36654i	−0.459214	−	0.265127i
$773$	14.6230	+	2.57843i	0.525953	+	0.0927397i	0.430319	−	0.902677i	$-0.358401\pi$
$773$	14.6230	+	2.57843i	0.525953	+	0.0927397i	0.0956341	+	0.995417i	$0.469512\pi$
$774$	11.9077	−	9.99177i	0.428014	−	0.359147i
$775$		0			0
$776$	−0.346350	−	1.96425i	−0.0124332	−	0.0705124i
$777$	−15.2651	+	41.9404i	−0.547631	+	1.50460i
$778$			11.8277i			0.424044i
$779$	−16.8504	−	50.6357i	−0.603729	−	1.81421i
$780$		0			0
$781$	49.4351	+	17.9929i	1.76893	+	0.643837i
$782$	20.2338	−	3.56777i	0.723560	−	0.127583i
$783$	2.05347	−	2.44723i	0.0733849	−	0.0874567i
$784$	−10.6004	+	8.89483i	−0.378587	+	0.317672i
$785$		0			0
$786$	−5.95057	+	10.3067i	−0.212250	+	0.367627i
$787$	16.5221	−	9.53904i	0.588949	−	0.340030i	−0.175733	−	0.984438i	$-0.556229\pi$
$787$	16.5221	−	9.53904i	0.588949	−	0.340030i	0.764682	+	0.644408i	$0.222896\pi$
$788$	1.97233	+	5.41894i	0.0702614	+	0.193042i
$789$	−50.0336	+	18.2107i	−1.78124	+	0.648319i
$790$		0			0
$791$	8.60879	−	14.9109i	0.306093	−	0.530169i
$792$	−11.8783	−	2.09447i	−0.422079	−	0.0744239i
$793$	5.04253	+	6.00946i	0.179066	+	0.213402i
$794$	22.8171	+	19.1459i	0.809750	+	0.679461i
$795$		0			0
$796$	4.99379	+	1.81759i	0.177000	+	0.0644228i
$797$		−	5.02894i		−	0.178134i	−0.996026	−	0.0890672i	$-0.971611\pi$
$797$		−	5.02894i		−	0.178134i	0.996026	−	0.0890672i	$-0.0283886\pi$
$798$	−26.6212	+	43.2827i	−0.942379	+	1.53219i
$799$	−31.6136			−1.11841
$800$		0			0
$801$	−1.66963	−	9.46895i	−0.0589935	−	0.334569i
$802$	11.7107	−	13.9563i	0.413519	−	0.492813i
$803$	20.4812	+	24.4085i	0.722766	+	0.861359i
$804$	2.49947	−	14.1752i	0.0881496	−	0.499921i
$805$		0			0
$806$	2.81632	+	4.87800i	0.0992005	+	0.171820i
$807$	9.93856	+	27.3060i	0.349854	+	0.961216i
$808$	1.37528	+	3.77856i	0.0483823	+	0.132929i
$809$	−11.3894	−	19.7270i	−0.400429	−	0.693564i	0.593348	−	0.804946i	$-0.297806\pi$
$809$	−11.3894	−	19.7270i	−0.400429	−	0.693564i	−0.993778	+	0.111382i	$0.964472\pi$
$810$		0			0
$811$	4.11323	−	23.3273i	0.144435	−	0.819132i	−0.823384	−	0.567485i	$-0.807917\pi$
$811$	4.11323	−	23.3273i	0.144435	−	0.819132i	0.967819	−	0.251647i	$-0.0809723\pi$
$812$	7.03543	+	8.38450i	0.246895	+	0.294238i
$813$	9.67188	−	11.5265i	0.339208	−	0.404252i
$814$	−2.27697	−	12.9133i	−0.0798078	−	0.452613i
$815$		0			0
$816$	10.8556			0.380021
$817$	14.3887	+	12.7721i	0.503398	+	0.446839i
$818$			18.4635i			0.645561i
$819$	−12.3270	−	4.48667i	−0.430741	−	0.156777i
$820$		0			0
$821$	−4.27500	−	3.58715i	−0.149199	−	0.125192i	0.565133	−	0.825000i	$-0.308825\pi$
$821$	−4.27500	−	3.58715i	−0.149199	−	0.125192i	−0.714332	+	0.699807i	$0.753269\pi$
$822$	11.5244	+	13.7342i	0.401959	+	0.479036i
$823$	−0.337724	−	0.0595499i	−0.0117723	−	0.00207578i	0.167759	−	0.985828i	$-0.446347\pi$
$823$	−0.337724	−	0.0595499i	−0.0117723	−	0.00207578i	−0.179531	+	0.983752i	$0.557458\pi$
$824$	2.51914	−	4.36328i	0.0877584	−	0.152002i
$825$		0			0
$826$	−24.1908	+	8.80472i	−0.841705	+	0.306355i
$827$	−14.2632	−	39.1878i	−0.495980	−	1.36269i	−0.895129	−	0.445807i	$-0.852917\pi$
$827$	−14.2632	−	39.1878i	−0.495980	−	1.36269i	0.399149	−	0.916886i	$-0.369306\pi$
$828$	−14.7415	+	8.51101i	−0.512303	+	0.295778i
$829$	−2.81234	+	4.87112i	−0.0976766	+	0.169181i	−0.910723	−	0.413019i	$-0.864474\pi$
$829$	−2.81234	+	4.87112i	−0.0976766	+	0.169181i	0.813046	+	0.582200i	$0.197808\pi$
$830$		0			0
$831$	−24.8539	+	20.8549i	−0.862173	+	0.723449i
$832$	0.524515	−	0.625092i	0.0181843	−	0.0216712i
$833$	57.9285	−	10.2144i	2.00710	−	0.353907i
$834$	−46.4828	−	16.9184i	−1.60957	−	0.585835i
$835$		0			0
$836$	0.415201	−	14.9231i	0.0143600	−	0.516125i
$837$		−	9.19697i		−	0.317894i
$838$	−13.1522	+	36.1355i	−0.454337	+	1.24828i
$839$	5.64367	+	32.0068i	0.194841	+	1.10500i	0.912645	+	0.408753i	$0.134036\pi$
$839$	5.64367	+	32.0068i	0.194841	+	1.10500i	−0.717804	+	0.696245i	$0.754853\pi$
$840$		0			0
$841$	−17.8113	+	14.9455i	−0.614183	+	0.515360i
$842$	−7.76960	−	1.36999i	−0.267758	−	0.0472130i
$843$	29.1585	+	16.8347i	1.00427	+	0.579816i
$844$	9.40200	+	16.2847i	0.323630	+	0.560544i
$845$		0			0
$846$	24.6119	−	8.95799i	0.846174	−	0.307982i
$847$	2.88591	−	1.66618i	0.0991609	−	0.0572506i
$848$	9.77636	+	5.64439i	0.335722	+	0.193829i
$849$	−7.42334	+	42.0999i	−0.254768	+	1.44486i
$850$		0			0
$851$	−14.1758	−	11.8949i	−0.485941	−	0.407753i
$852$	38.6308	−	6.81165i	1.32347	−	0.233363i
$853$	2.11722	−	5.81701i	0.0724921	−	0.199170i	−0.898155	−	0.439679i	$-0.855092\pi$
$853$	2.11722	−	5.81701i	0.0724921	−	0.199170i	0.970647	+	0.240509i	$0.0773143\pi$
$854$	43.8852			1.50172
$855$		0			0
$856$	4.63023			0.158258
$857$	−9.29500	+	25.5378i	−0.317511	+	0.872355i	0.673573	+	0.739120i	$0.264759\pi$
$857$	−9.29500	+	25.5378i	−0.317511	+	0.872355i	−0.991085	+	0.133234i	$0.957464\pi$
$858$	7.02865	−	1.23934i	0.239954	−	0.0423104i
$859$	7.91500	+	6.64147i	0.270056	+	0.226604i	0.767751	−	0.640748i	$-0.221376\pi$
$859$	7.91500	+	6.64147i	0.270056	+	0.226604i	−0.497695	+	0.867352i	$0.665820\pi$
$860$		0			0
$861$	24.7836	−	140.555i	0.844624	−	4.79010i
$862$	1.86001	+	1.07388i	0.0633521	+	0.0365764i
$863$	−15.1734	+	8.76039i	−0.516510	+	0.298207i	−0.735505	−	0.677519i	$-0.763055\pi$
$863$	−15.1734	+	8.76039i	−0.516510	+	0.298207i	0.218996	+	0.975726i	$0.429722\pi$
$864$	−1.25202	+	0.455696i	−0.0425944	+	0.0155031i
$865$		0			0
$866$	−4.39122	−	7.60582i	−0.149220	−	0.258456i
$867$	−2.36493	−	1.36539i	−0.0803173	−	0.0463712i
$868$	31.0313	+	5.47165i	1.05327	+	0.185720i
$869$	5.68221	−	4.76794i	0.192756	−	0.161741i
$870$		0			0
$871$	0.798651	+	4.52938i	0.0270613	+	0.153472i
$872$	6.15904	−	16.9218i	0.208571	−	0.573045i
$873$		−	7.02426i		−	0.237735i
$874$	−13.0884	−	16.5098i	−0.442723	−	0.558451i
$875$		0			0
$876$	22.3257	+	8.12590i	0.754317	+	0.274549i
$877$	−29.6407	+	5.22646i	−1.00090	+	0.176485i	−0.650004	−	0.759931i	$-0.725233\pi$
$877$	−29.6407	+	5.22646i	−1.00090	+	0.176485i	−0.350892	+	0.936416i	$0.614122\pi$
$878$	−1.55529	+	1.85352i	−0.0524884	+	0.0625533i
$879$	−13.3878	+	11.2337i	−0.451560	+	0.378904i
$880$		0			0
$881$	−8.38802	+	14.5285i	−0.282600	+	0.489477i	−0.972024	−	0.234881i	$-0.924530\pi$
$881$	−8.38802	+	14.5285i	−0.282600	+	0.489477i	0.689425	+	0.724357i	$0.257863\pi$
$882$	−42.2042	+	24.3666i	−1.42109	+	0.820467i
$883$	−16.1287	−	44.3132i	−0.542774	−	1.49126i	−0.843278	−	0.537478i	$-0.819377\pi$
$883$	−16.1287	−	44.3132i	−0.542774	−	1.49126i	0.300504	−	0.953781i	$-0.402845\pi$
$884$	−3.25947	+	1.18635i	−0.109628	+	0.0399013i
$885$		0			0
$886$	−16.4873	+	28.5569i	−0.553902	+	0.959386i
$887$	−21.7305	−	3.83168i	−0.729640	−	0.128655i	−0.203526	−	0.979070i	$-0.565240\pi$
$887$	−21.7305	−	3.83168i	−0.729640	−	0.128655i	−0.526114	+	0.850414i	$0.676351\pi$
$888$	−6.28474	−	7.48986i	−0.210902	−	0.251343i
$889$	−61.8858	−	51.9283i	−2.07558	−	1.74162i
$890$		0			0
$891$	23.0519	+	8.39021i	0.772268	+	0.281083i
$892$			10.7525i			0.360020i
$893$	15.4217	+	28.5144i	0.516068	+	0.954197i
$894$	−48.6801			−1.62810
$895$		0			0
$896$	−0.792679	−	4.49550i	−0.0264815	−	0.150184i
$897$	6.47433	−	7.71580i	0.216172	−	0.257623i
$898$	−12.2718	−	14.6250i	−0.409517	−	0.488043i
$899$	2.87401	−	16.2993i	0.0958535	−	0.543612i
$900$		0			0
$901$	−23.9932	−	41.5574i	−0.799328	−	1.38448i
$902$	14.3413	+	39.4023i	0.477512	+	1.31195i
$903$	17.5986	+	48.3519i	0.585646	+	1.60905i
$904$	1.88589	+	3.26645i	0.0627236	+	0.108640i
$905$		0			0
$906$	−8.10833	+	45.9846i	−0.269381	+	1.52774i
$907$	20.8005	+	24.7890i	0.690668	+	0.823106i	0.991436	−	0.130591i	$-0.0416875\pi$
$907$	20.8005	+	24.7890i	0.690668	+	0.823106i	−0.300768	+	0.953697i	$0.597243\pi$
$908$	13.3966	−	15.9655i	0.444583	−	0.529833i
$909$	2.45904	+	13.9459i	0.0815613	+	0.462557i
$910$		0			0
$911$	0.987475			0.0327165			0.0163583	−	0.999866i	$-0.494793\pi$
$911$	0.987475			0.0327165			0.0163583	+	0.999866i	$0.494793\pi$
$912$	−5.29554	−	9.79133i	−0.175353	−	0.324223i
$913$			1.64571i			0.0544649i
$914$	16.2890	+	5.92870i	0.538791	+	0.196104i
$915$		0			0
$916$	14.6994	+	12.3343i	0.485683	+	0.407537i
$917$	−13.6742	−	16.2963i	−0.451561	−	0.538150i
$918$	5.57758	+	0.983478i	0.184088	+	0.0324596i
$919$	18.5503	−	32.1300i	0.611917	−	1.05987i	−0.379000	−	0.925396i	$-0.623732\pi$
$919$	18.5503	−	32.1300i	0.611917	−	1.05987i	0.990917	−	0.134474i	$-0.0429346\pi$
$920$		0			0
$921$	59.3923	−	21.6170i	1.95704	−	0.712305i
$922$	4.16572	+	11.4452i	0.137191	+	0.376928i
$923$	−10.8548	+	6.26702i	−0.357290	+	0.206281i
$924$	19.9631	−	34.5770i	0.656737	−	1.13750i
$925$		0			0
$926$	−6.36185	+	5.33823i	−0.209063	+	0.175425i
$927$	11.4053	−	13.5923i	0.374598	−	0.446428i
$928$	−2.36128	+	0.416358i	−0.0775129	+	0.0136676i
$929$	51.4497	+	18.7261i	1.68801	+	0.614385i	0.994372	−	0.105941i	$-0.0337854\pi$
$929$	51.4497	+	18.7261i	1.68801	+	0.614385i	0.693636	+	0.720326i	$0.256008\pi$
$930$		0			0
$931$	−37.4716	−	47.2667i	−1.22808	−	1.54910i
$932$		−	21.1181i		−	0.691745i
$933$	10.1770	−	27.9610i	0.333179	−	0.915402i
$934$	−1.40844	−	7.98763i	−0.0460854	−	0.261363i
$935$		0			0
$936$	2.20140	−	1.84720i	0.0719551	−	0.0603775i
$937$	18.1772	+	3.20513i	0.593822	+	0.104707i	0.462479	−	0.886630i	$-0.346960\pi$
$937$	18.1772	+	3.20513i	0.593822	+	0.104707i	0.131343	+	0.991337i	$0.458071\pi$
$938$	22.2820	+	12.8645i	0.727533	+	0.420041i
$939$	−19.7686	−	34.2403i	−0.645125	−	1.11739i
$940$		0			0
$941$	5.45017	−	1.98370i	0.177671	−	0.0646668i	−0.251653	−	0.967818i	$-0.580974\pi$
$941$	5.45017	−	1.98370i	0.177671	−	0.0646668i	0.429324	+	0.903151i	$0.358752\pi$
$942$	26.6962	−	15.4130i	0.869808	−	0.502184i
$943$	51.2475	+	29.5878i	1.66885	+	0.963510i
$944$	0.979281	−	5.55378i	0.0318729	−	0.180760i
$945$		0			0
$946$	−11.5804	−	9.71708i	−0.376510	−	0.315930i
$947$	−32.9262	+	5.80578i	−1.06996	+	0.188663i	−0.680771	−	0.732496i	$-0.738355\pi$
$947$	−32.9262	+	5.80578i	−1.06996	+	0.188663i	−0.389187	+	0.921159i	$0.627244\pi$
$948$	1.89168	−	5.19734i	0.0614388	−	0.168802i
$949$	−7.59152			−0.246431
$950$		0			0
$951$	19.3150			0.626332
$952$	−6.63666	+	18.2341i	−0.215095	+	0.590970i
$953$	−30.5937	+	5.39450i	−0.991027	+	0.174745i	−0.645579	−	0.763693i	$-0.723384\pi$
$953$	−30.5937	+	5.39450i	−0.991027	+	0.174745i	−0.345448	+	0.938438i	$0.612273\pi$
$954$	30.4548	+	25.5546i	0.986012	+	0.827362i
$955$		0			0
$956$	−1.06930	+	6.06431i	−0.0345837	+	0.196134i
$957$	−18.1617	−	10.4857i	−0.587086	−	0.338954i
$958$	27.2744	−	15.7469i	0.881195	−	0.508758i
$959$	−30.1149	+	10.9609i	−0.972460	+	0.353947i
$960$		0			0
$961$	−8.32387	−	14.4174i	−0.268512	−	0.465076i
$962$	2.70557	+	1.56206i	0.0872312	+	0.0503629i
$963$	16.0587	+	2.83158i	0.517483	+	0.0912463i
$964$	−17.5810	+	14.7522i	−0.566245	+	0.475136i
$965$		0			0
$966$	−9.78440	−	55.4901i	−0.314808	−	1.78536i
$967$	−4.88033	+	13.4086i	−0.156941	+	0.431191i	−0.993096	−	0.117301i	$-0.962576\pi$
$967$	−4.88033	+	13.4086i	−0.156941	+	0.431191i	0.836156	+	0.548492i	$0.184798\pi$
$968$			0.730003i			0.0234632i
$969$	−1.31602	+	47.3000i	−0.0422766	+	1.51949i
$970$		0			0
$971$	31.2960	+	11.3908i	1.00434	+	0.365549i	0.791255	−	0.611486i	$-0.209428\pi$
$971$	31.2960	+	11.3908i	1.00434	+	0.365549i	0.213081	+	0.977035i	$0.431650\pi$
$972$	21.9502	−	3.87040i	0.704052	−	0.124143i
$973$	56.8355	−	67.7339i	1.82206	−	2.17145i
$974$	12.0056	−	10.0739i	0.384685	−	0.322789i
$975$		0			0
$976$	−4.80686	+	8.32572i	−0.153864	+	0.266500i
$977$	10.9390	−	6.31564i	0.349970	−	0.202055i	−0.314702	−	0.949191i	$-0.601905\pi$
$977$	10.9390	−	6.31564i	0.349970	−	0.202055i	0.664672	+	0.747135i	$0.268571\pi$
$978$	13.0363	+	35.8170i	0.416856	+	1.14530i
$979$	−8.78678	+	3.19812i	−0.280827	+	0.102213i
$980$		0			0
$981$	31.7093	−	54.9222i	1.01240	−	1.75353i
$982$	14.1852	+	2.50123i	0.452667	+	0.0798174i
$983$	22.5864	+	26.9174i	0.720394	+	0.858532i	0.994669	−	0.103119i	$-0.0328824\pi$
$983$	22.5864	+	26.9174i	0.720394	+	0.858532i	−0.274275	+	0.961651i	$0.588438\pi$
$984$	23.9509	+	20.0972i	0.763526	+	0.640675i
$985$		0			0
$986$	9.57752	+	3.48593i	0.305010	+	0.111015i
$987$			86.6985i			2.75964i
$988$	2.66007	+	2.36120i	0.0846282	+	0.0751199i
$989$	−21.3341			−0.678386
$990$		0			0
$991$	6.83350	+	38.7547i	0.217073	+	1.23108i	0.877272	+	0.479993i	$0.159361\pi$
$991$	6.83350	+	38.7547i	0.217073	+	1.23108i	−0.660199	+	0.751091i	$0.729528\pi$
$992$	−4.43699	+	5.28780i	−0.140875	+	0.167888i
$993$	−15.4075	−	18.3619i	−0.488941	−	0.582697i
$994$	−12.1758	+	69.0524i	−0.386193	+	2.19021i
$995$		0			0
$996$	0.613556	+	1.06271i	0.0194413	+	0.0336733i
$997$	21.1388	+	58.0784i	0.669472	+	1.83936i	0.527637	+	0.849470i	$0.323078\pi$
$997$	21.1388	+	58.0784i	0.669472	+	1.83936i	0.141835	+	0.989890i	$0.454700\pi$
$998$	7.75605	+	21.3096i	0.245514	+	0.674543i
$999$	−2.55054	−	4.41766i	−0.0806955	−	0.139769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.h.99.4		48
5.2	odd	4		950.2.l.k.251.1	yes	24
5.3	odd	4		950.2.l.j.251.4	✓	24
5.4	even	2	inner	950.2.u.h.99.5		48
19.5	even	9	inner	950.2.u.h.499.5		48
95.24	even	18	inner	950.2.u.h.499.4		48
95.43	odd	36		950.2.l.j.651.4	yes	24
95.62	odd	36		950.2.l.k.651.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.251.4	✓	24	5.3	odd	4
950.2.l.j.651.4	yes	24	95.43	odd	36
950.2.l.k.251.1	yes	24	5.2	odd	4
950.2.l.k.651.1	yes	24	95.62	odd	36
950.2.u.h.99.4		48	1.1	even	1	trivial
950.2.u.h.99.5		48	5.4	even	2	inner
950.2.u.h.499.4		48	95.24	even	18	inner
950.2.u.h.499.5		48	19.5	even	9	inner

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 + 0.939693i) q^{2} +(2.51497 - 0.443457i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.443457 + 2.51497i) q^{6} +(-3.95328 - 2.28243i) q^{7} +(0.866025 - 0.500000i) q^{8} +(3.30934 - 1.20450i) q^{9} +O(q^{10})\)	\(q+(-0.342020 + 0.939693i) q^{2} +(2.51497 - 0.443457i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(-0.443457 + 2.51497i) q^{6} +(-3.95328 - 2.28243i) q^{7} +(0.866025 - 0.500000i) q^{8} +(3.30934 - 1.20450i) q^{9} +(-1.71245 - 2.96606i) q^{11} +(-2.21163 - 1.27688i) q^{12} +(0.803603 + 0.141697i) q^{13} +(3.49688 - 2.93423i) q^{14} +(0.173648 + 0.984808i) q^{16} +(1.45386 - 3.99445i) q^{17} +3.52173i q^{18} +(-4.31207 + 0.637234i) q^{19} +(-10.9545 - 3.98712i) q^{21} +(3.37288 - 0.594729i) q^{22} +(3.10687 - 3.70262i) q^{23} +(1.95630 - 1.64153i) q^{24} +(-0.408000 + 0.706677i) q^{26} +(1.15386 - 0.666183i) q^{27} +(1.56127 + 4.28956i) q^{28} +(2.25311 - 0.820065i) q^{29} +(3.45137 - 5.97794i) q^{31} +(-0.984808 - 0.173648i) q^{32} +(-5.62209 - 6.70015i) q^{33} +(3.25630 + 2.73236i) q^{34} +(-3.30934 - 1.20450i) q^{36} -3.82859i q^{37} +(0.876010 - 4.26997i) q^{38} +2.08387 q^{39} +(2.12597 + 12.0570i) q^{41} +(7.49334 - 8.93022i) q^{42} +(-2.83718 - 3.38122i) q^{43} +(-0.594729 + 3.37288i) q^{44} +(2.41672 + 4.18588i) q^{46} +(-2.54364 - 6.98859i) q^{47} +(0.873440 + 2.39976i) q^{48} +(6.91895 + 11.9840i) q^{49} +(1.88505 - 10.6906i) q^{51} +(-0.524515 - 0.625092i) q^{52} +(7.25628 - 8.64770i) q^{53} +(0.231363 + 1.31212i) q^{54} -4.56485 q^{56} +(-10.5621 + 3.51484i) q^{57} +2.39771i q^{58} +(-5.29935 - 1.92881i) q^{59} +(7.36453 + 6.17958i) q^{61} +(4.43699 + 5.28780i) q^{62} +(-15.8319 - 2.79160i) q^{63} +(0.500000 - 0.866025i) q^{64} +(8.21895 - 2.99145i) q^{66} +(1.92774 + 5.29642i) q^{67} +(-3.68130 + 2.12540i) q^{68} +(6.17173 - 10.6898i) q^{69} +(-11.7667 + 9.87343i) q^{71} +(2.26372 - 2.69780i) q^{72} +(-9.16200 + 1.61551i) q^{73} +(3.59769 + 1.30945i) q^{74} +(3.71284 + 2.28359i) q^{76} +15.6342i q^{77} +(-0.712727 + 1.95820i) q^{78} +(0.376083 + 2.13287i) q^{79} +(-5.48689 + 4.60405i) q^{81} +(-12.0570 - 2.12597i) q^{82} +(-0.416134 - 0.240255i) q^{83} +(5.82879 + 10.0958i) q^{84} +(4.14768 - 1.50963i) q^{86} +(5.30284 - 3.06159i) q^{87} +(-2.96606 - 1.71245i) q^{88} +(0.474094 - 2.68872i) q^{89} +(-2.85346 - 2.39433i) q^{91} +(-4.76000 + 0.839317i) q^{92} +(6.02912 - 16.5649i) q^{93} +7.43710 q^{94} -2.55377 q^{96} +(0.682176 - 1.87426i) q^{97} +(-13.6277 + 2.40292i) q^{98} +(-9.23972 - 7.75304i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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