LMFDB - Embedded newform 950.2.l.l.101.4

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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	950.101
Dual form			950.2.l.l.301.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.845354 + 0.307684i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.845354 + 0.307684i) q^{6} +(1.06731 - 1.84863i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.67818 - 1.40816i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.845354 + 0.307684i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.845354 + 0.307684i) q^{6} +(1.06731 - 1.84863i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.67818 - 1.40816i) q^{9} +(-0.575411 - 0.996641i) q^{11} +(0.449804 - 0.779083i) q^{12} +(2.12509 - 0.773468i) q^{13} +(0.370673 + 2.10219i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(0.0280660 - 0.0235502i) q^{17} +2.19071 q^{18} +(-3.00691 + 3.15571i) q^{19} +(1.47105 - 1.23436i) q^{21} +(1.08142 + 0.393604i) q^{22} +(1.40659 - 7.97719i) q^{23} +(0.156215 + 0.885940i) q^{24} +(-1.13073 + 1.95849i) q^{26} +(-2.33480 - 4.04399i) q^{27} +(-1.63521 - 1.37211i) q^{28} +(-4.74371 - 3.98044i) q^{29} +(2.21180 - 3.83095i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.179776 - 1.01956i) q^{33} +(-0.00636204 + 0.0360809i) q^{34} +(-1.67818 + 1.40816i) q^{36} +5.64857 q^{37} +(0.274975 - 4.35022i) q^{38} +2.03443 q^{39} +(-7.81864 - 2.84575i) q^{41} +(-0.333460 + 1.89115i) q^{42} +(0.121234 + 0.687551i) q^{43} +(-1.08142 + 0.393604i) q^{44} +(4.05013 + 7.01502i) q^{46} +(5.57985 + 4.68205i) q^{47} +(-0.689139 - 0.578256i) q^{48} +(1.22170 + 2.11605i) q^{49} +(0.0309717 - 0.0112728i) q^{51} +(-0.392700 - 2.22711i) q^{52} +(2.05103 - 11.6320i) q^{53} +(4.38799 + 1.59710i) q^{54} +2.13462 q^{56} +(-3.51286 + 1.74252i) q^{57} +6.19247 q^{58} +(1.27093 - 1.06644i) q^{59} +(-1.03441 + 5.86645i) q^{61} +(0.768149 + 4.35639i) q^{62} +(-4.39431 + 1.59940i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.793077 + 0.665470i) q^{66} +(-7.48620 - 6.28167i) q^{67} +(-0.0183188 - 0.0317290i) q^{68} +(3.64352 - 6.31077i) q^{69} +(-1.70377 - 9.66255i) q^{71} +(0.380412 - 2.15742i) q^{72} +(5.53912 + 2.01607i) q^{73} +(-4.32706 + 3.63083i) q^{74} +(2.58562 + 3.50921i) q^{76} -2.45657 q^{77} +(-1.55847 + 1.30771i) q^{78} +(8.50752 + 3.09648i) q^{79} +(0.411775 + 2.33529i) q^{81} +(7.81864 - 2.84575i) q^{82} +(-2.73497 + 4.73712i) q^{83} +(-0.960160 - 1.66305i) q^{84} +(-0.534820 - 0.448767i) q^{86} +(-2.78540 - 4.82445i) q^{87} +(0.575411 - 0.996641i) q^{88} +(6.65071 - 2.42066i) q^{89} +(0.838265 - 4.75404i) q^{91} +(-7.61175 - 2.77045i) q^{92} +(3.04847 - 2.55797i) q^{93} -7.28398 q^{94} +0.899607 q^{96} +(6.34610 - 5.32501i) q^{97} +(-2.29604 - 0.835691i) q^{98} +(-0.437787 + 2.48281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) $ 30 * q - 12 * q^7 + 15 * q^8	$ 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) $ 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	0.845354	+	0.307684i	0.488066	+	0.177641i	0.574319	−	0.818632i	$-0.305267\pi$
$3$	0.845354	+	0.307684i	0.488066	+	0.177641i	−0.0862529	+	0.996273i	$0.527489\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−0.845354	+	0.307684i	−0.345114	+	0.125611i
$7$	1.06731	−	1.84863i	0.403405	−	0.698718i	−0.590729	−	0.806870i	$-0.701160\pi$
$7$	1.06731	−	1.84863i	0.403405	−	0.698718i	0.994134	+	0.108152i	$0.0344932\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−1.67818	−	1.40816i	−0.559393	−	0.469386i
$10$		0			0
$11$	−0.575411	−	0.996641i	−0.173493	−	0.300499i	0.766146	−	0.642667i	$-0.222172\pi$
$11$	−0.575411	−	0.996641i	−0.173493	−	0.300499i	−0.939639	+	0.342168i	$0.888839\pi$
$12$	0.449804	−	0.779083i	0.129847	−	0.224902i
$13$	2.12509	−	0.773468i	0.589393	−	0.214521i	−0.0300696	−	0.999548i	$-0.509573\pi$
$13$	2.12509	−	0.773468i	0.589393	−	0.214521i	0.619462	+	0.785026i	$0.287351\pi$
$14$	0.370673	+	2.10219i	0.0990665	+	0.561834i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.0280660	−	0.0235502i	0.00680700	−	0.00571175i	−0.639378	−	0.768893i	$-0.720808\pi$
$17$	0.0280660	−	0.0235502i	0.00680700	−	0.00571175i	0.646185	+	0.763181i	$0.276364\pi$
$18$	2.19071			0.516354
$19$	−3.00691	+	3.15571i	−0.689832	+	0.723969i
$19$	−3.00691	+	3.15571i	−0.689832	+	0.723969i
$20$		0			0
$21$	1.47105	−	1.23436i	0.321009	−	0.269359i
$22$	1.08142	+	0.393604i	0.230559	+	0.0839167i
$23$	1.40659	−	7.97719i	0.293295	−	1.66336i	−0.380757	−	0.924675i	$-0.624336\pi$
$23$	1.40659	−	7.97719i	0.293295	−	1.66336i	0.674052	−	0.738684i	$-0.264552\pi$
$24$	0.156215	+	0.885940i	0.0318873	+	0.180842i
$25$		0			0
$26$	−1.13073	+	1.95849i	−0.221755	+	0.384091i
$27$	−2.33480	−	4.04399i	−0.449332	−	0.778266i
$28$	−1.63521	−	1.37211i	−0.309026	−	0.259304i
$29$	−4.74371	−	3.98044i	−0.880884	−	0.739150i	0.0854764	−	0.996340i	$-0.472759\pi$
$29$	−4.74371	−	3.98044i	−0.880884	−	0.739150i	−0.966361	+	0.257191i	$0.917203\pi$
$30$		0			0
$31$	2.21180	−	3.83095i	0.397251	−	0.688058i	−0.596135	−	0.802884i	$-0.703298\pi$
$31$	2.21180	−	3.83095i	0.397251	−	0.688058i	0.993386	+	0.114826i	$0.0366311\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.179776	−	1.01956i	−0.0312950	−	0.177483i
$34$	−0.00636204	+	0.0360809i	−0.00109108	+	0.00618783i
$35$		0			0
$36$	−1.67818	+	1.40816i	−0.279696	+	0.234693i
$37$	5.64857			0.928619			0.464310	−	0.885673i	$-0.346302\pi$
$37$	5.64857			0.928619			0.464310	+	0.885673i	$0.346302\pi$
$38$	0.274975	−	4.35022i	0.0446068	−	0.705698i
$39$	2.03443			0.325770
$40$		0			0
$41$	−7.81864	−	2.84575i	−1.22107	−	0.444432i	−0.350537	−	0.936549i	$-0.614001\pi$
$41$	−7.81864	−	2.84575i	−1.22107	−	0.444432i	−0.870529	+	0.492117i	$0.836223\pi$
$42$	−0.333460	+	1.89115i	−0.0514540	+	0.291810i
$43$	0.121234	+	0.687551i	0.0184880	+	0.104851i	0.992655	−	0.120977i	$-0.0386026\pi$
$43$	0.121234	+	0.687551i	0.0184880	+	0.104851i	−0.974167	+	0.225827i	$0.927492\pi$
$44$	−1.08142	+	0.393604i	−0.163030	+	0.0593381i
$45$		0			0
$46$	4.05013	+	7.01502i	0.597159	+	1.03431i
$47$	5.57985	+	4.68205i	0.813905	+	0.682947i	0.951536	−	0.307536i	$-0.0995045\pi$
$47$	5.57985	+	4.68205i	0.813905	+	0.682947i	−0.137632	+	0.990483i	$0.543949\pi$
$48$	−0.689139	−	0.578256i	−0.0994687	−	0.0834641i
$49$	1.22170	+	2.11605i	0.174528	+	0.302292i
$50$		0			0
$51$	0.0309717	−	0.0112728i	0.00433691	−	0.00157850i
$52$	−0.392700	−	2.22711i	−0.0544577	−	0.308845i
$53$	2.05103	−	11.6320i	0.281730	−	1.59777i	−0.435006	−	0.900428i	$-0.643254\pi$
$53$	2.05103	−	11.6320i	0.281730	−	1.59777i	0.716736	−	0.697344i	$-0.245635\pi$
$54$	4.38799	+	1.59710i	0.597129	+	0.217337i
$55$		0			0
$56$	2.13462			0.285251
$57$	−3.51286	+	1.74252i	−0.465290	+	0.230802i
$58$	6.19247			0.813111
$59$	1.27093	−	1.06644i	0.165462	−	0.138839i	−0.556297	−	0.830983i	$-0.687778\pi$
$59$	1.27093	−	1.06644i	0.165462	−	0.138839i	0.721759	+	0.692145i	$0.243334\pi$
$60$		0			0
$61$	−1.03441	+	5.86645i	−0.132443	+	0.751122i	0.844163	+	0.536086i	$0.180098\pi$
$61$	−1.03441	+	5.86645i	−0.132443	+	0.751122i	−0.976606	+	0.215035i	$0.931013\pi$
$62$	0.768149	+	4.35639i	0.0975550	+	0.553262i
$63$	−4.39431	+	1.59940i	−0.553631	+	0.201505i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$		0			0
$66$	0.793077	+	0.665470i	0.0976210	+	0.0819137i
$67$	−7.48620	−	6.28167i	−0.914585	−	0.767428i	0.0584009	−	0.998293i	$-0.481400\pi$
$67$	−7.48620	−	6.28167i	−0.914585	−	0.767428i	−0.972986	+	0.230865i	$0.925844\pi$
$68$	−0.0183188	−	0.0317290i	−0.00222148	−	0.00384771i
$69$	3.64352	−	6.31077i	0.438629	−	0.759727i
$70$		0			0
$71$	−1.70377	−	9.66255i	−0.202200	−	1.14673i	−0.901785	−	0.432184i	$-0.857743\pi$
$71$	−1.70377	−	9.66255i	−0.202200	−	1.14673i	0.699585	−	0.714549i	$-0.253368\pi$
$72$	0.380412	−	2.15742i	0.0448320	−	0.254255i
$73$	5.53912	+	2.01607i	0.648305	+	0.235964i	0.645179	−	0.764031i	$-0.276783\pi$
$73$	5.53912	+	2.01607i	0.648305	+	0.235964i	0.00312576	+	0.999995i	$0.499005\pi$
$74$	−4.32706	+	3.63083i	−0.503010	+	0.422076i
$75$		0			0
$76$	2.58562	+	3.50921i	0.296591	+	0.402534i
$77$	−2.45657			−0.279952
$78$	−1.55847	+	1.30771i	−0.176462	+	0.148069i
$79$	8.50752	+	3.09648i	0.957170	+	0.348382i	0.772924	−	0.634499i	$-0.218793\pi$
$79$	8.50752	+	3.09648i	0.957170	+	0.348382i	0.184246	+	0.982880i	$0.441016\pi$
$80$		0			0
$81$	0.411775	+	2.33529i	0.0457527	+	0.259477i
$82$	7.81864	−	2.84575i	0.863424	−	0.314261i
$83$	−2.73497	+	4.73712i	−0.300203	+	0.519966i	−0.976182	−	0.216955i	$-0.930388\pi$
$83$	−2.73497	+	4.73712i	−0.300203	+	0.519966i	0.675979	+	0.736921i	$0.263721\pi$
$84$	−0.960160	−	1.66305i	−0.104762	−	0.181453i
$85$		0			0
$86$	−0.534820	−	0.448767i	−0.0576711	−	0.0483918i
$87$	−2.78540	−	4.82445i	−0.298626	−	0.517235i
$88$	0.575411	−	0.996641i	0.0613390	−	0.106242i
$89$	6.65071	−	2.42066i	0.704974	−	0.256589i	0.0354408	−	0.999372i	$-0.488716\pi$
$89$	6.65071	−	2.42066i	0.704974	−	0.256589i	0.669533	+	0.742782i	$0.266494\pi$
$90$		0			0
$91$	0.838265	−	4.75404i	0.0878740	−	0.498358i
$92$	−7.61175	−	2.77045i	−0.793580	−	0.288839i
$93$	3.04847	−	2.55797i	0.316112	−	0.265249i
$94$	−7.28398			−0.751285
$95$		0			0
$96$	0.899607			0.0918158
$97$	6.34610	−	5.32501i	0.644349	−	0.540673i	−0.261002	−	0.965338i	$-0.584053\pi$
$97$	6.34610	−	5.32501i	0.644349	−	0.540673i	0.905350	+	0.424666i	$0.139608\pi$
$98$	−2.29604	−	0.835691i	−0.231935	−	0.0844176i
$99$	−0.437787	+	2.48281i	−0.0439992	+	0.249532i
$100$		0			0
$101$	−0.354959	+	0.129194i	−0.0353197	+	0.0128553i	−0.359620	−	0.933099i	$-0.617094\pi$
$101$	−0.354959	+	0.129194i	−0.0353197	+	0.0128553i	0.324300	+	0.945954i	$0.394871\pi$
$102$	−0.0164797	+	0.0285437i	−0.00163173	+	0.00282624i
$103$	6.90619	+	11.9619i	0.680487	+	1.17864i	0.974832	+	0.222939i	$0.0715652\pi$
$103$	6.90619	+	11.9619i	0.680487	+	1.17864i	−0.294345	+	0.955699i	$0.595102\pi$
$104$	1.73239	+	1.45364i	0.169874	+	0.142542i
$105$		0			0
$106$	5.90570	+	10.2290i	0.573612	+	0.993525i
$107$	−3.23875	+	5.60969i	−0.313102	+	0.542309i	−0.979032	−	0.203705i	$-0.934702\pi$
$107$	−3.23875	+	5.60969i	−0.313102	+	0.542309i	0.665930	+	0.746014i	$0.268035\pi$
$108$	−4.38799	+	1.59710i	−0.422234	+	0.153681i
$109$	−0.298211	−	1.69124i	−0.0285634	−	0.161991i	0.967190	−	0.254056i	$-0.0817646\pi$
$109$	−0.298211	−	1.69124i	−0.0285634	−	0.161991i	−0.995753	+	0.0920643i	$0.970653\pi$
$110$		0			0
$111$	4.77504	+	1.73797i	0.453227	+	0.164961i
$112$	−1.63521	+	1.37211i	−0.154513	+	0.129652i
$113$	6.92537			0.651484			0.325742	−	0.945459i	$-0.394386\pi$
$113$	6.92537			0.651484			0.325742	+	0.945459i	$0.394386\pi$
$114$	1.57094	−	3.59287i	0.147132	−	0.336503i
$115$		0			0
$116$	−4.74371	+	3.98044i	−0.440442	+	0.369575i
$117$	−4.65544	−	1.69444i	−0.430395	−	0.156651i
$118$	−0.288097	+	1.63388i	−0.0265215	+	0.150411i
$119$	−0.0135805	−	0.0770191i	−0.00124493	−	0.00706033i
$120$		0			0
$121$	4.83780	−	8.37932i	0.439800	−	0.761757i
$122$	−2.97847	−	5.15887i	−0.269658	−	0.467062i
$123$	−5.73393	−	4.81134i	−0.517011	−	0.433824i
$124$	−3.38867	−	2.84343i	−0.304312	−	0.255348i
$125$		0			0
$126$	2.33816	−	4.04982i	0.208300	−	0.360786i
$127$	13.7727	−	5.01285i	1.22213	−	0.444818i	0.351234	−	0.936288i	$-0.385762\pi$
$127$	13.7727	−	5.01285i	1.22213	−	0.444818i	0.870895	+	0.491470i	$0.163540\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−0.109063	+	0.618526i	−0.00960245	+	0.0544582i
$130$		0			0
$131$	3.95429	−	3.31804i	0.345488	−	0.289899i	−0.453487	−	0.891263i	$-0.649820\pi$
$131$	3.95429	−	3.31804i	0.345488	−	0.289899i	0.798975	+	0.601364i	$0.205376\pi$
$132$	−1.03529			−0.0901103
$133$	2.62445	+	8.92680i	0.227569	+	0.774051i
$134$	9.77254			0.844219
$135$		0			0
$136$	0.0344280	+	0.0125308i	0.00295218	+	0.00107451i
$137$	−2.64600	+	15.0062i	−0.226063	+	1.28207i	0.634580	+	0.772857i	$0.281173\pi$
$137$	−2.64600	+	15.0062i	−0.226063	+	1.28207i	−0.860643	+	0.509209i	$0.829938\pi$
$138$	1.26538	+	7.17634i	0.107717	+	0.610891i
$139$	9.21476	−	3.35390i	0.781586	−	0.284474i	0.0797522	−	0.996815i	$-0.474587\pi$
$139$	9.21476	−	3.35390i	0.781586	−	0.284474i	0.701834	+	0.712341i	$0.252365\pi$
$140$		0			0
$141$	3.27636	+	5.67482i	0.275919	+	0.477906i
$142$	7.51613	+	6.30678i	0.630740	+	0.529253i
$143$	−1.99367	−	1.67289i	−0.166719	−	0.139894i
$144$	1.09535	+	1.89721i	0.0912794	+	0.158101i
$145$		0			0
$146$	−5.53912	+	2.01607i	−0.458421	+	0.166851i
$147$	0.381696	+	2.16471i	0.0314817	+	0.178542i
$148$	0.980864	−	5.56276i	0.0806265	−	0.457256i
$149$	−20.8349	−	7.58328i	−1.70686	−	0.621246i	−0.710283	−	0.703917i	$-0.751433\pi$
$149$	−20.8349	−	7.58328i	−1.70686	−	0.621246i	−0.996577	+	0.0826704i	$0.973655\pi$
$150$		0			0
$151$	−17.5102			−1.42496			−0.712482	−	0.701691i	$-0.752429\pi$
$151$	−17.5102			−1.42496			−0.712482	+	0.701691i	$0.752429\pi$
$152$	−4.23638	−	1.02620i	−0.343616	−	0.0832362i
$153$	−0.0802621			−0.00648881
$154$	1.88184	−	1.57905i	0.151643	−	0.127244i
$155$		0			0
$156$	0.353276	−	2.00353i	0.0282847	−	0.160410i
$157$	3.67952	+	20.8676i	0.293657	+	1.66541i	0.672610	+	0.739997i	$0.265173\pi$
$157$	3.67952	+	20.8676i	0.293657	+	1.66541i	−0.378952	+	0.925416i	$0.623716\pi$
$158$	−8.50752	+	3.09648i	−0.676822	+	0.246343i
$159$	5.31281	−	9.20206i	0.421333	−	0.729771i
$160$		0			0
$161$	−13.2456	−	11.1144i	−1.04390	−	0.875939i
$162$	−1.81653	−	1.52425i	−0.142720	−	0.119757i
$163$	−4.80181	−	8.31699i	−0.376107	−	0.651437i	0.614385	−	0.789006i	$-0.289404\pi$
$163$	−4.80181	−	8.31699i	−0.376107	−	0.651437i	−0.990492	+	0.137570i	$0.956071\pi$
$164$	−4.16021	+	7.20569i	−0.324858	+	0.562670i
$165$		0			0
$166$	−0.949847	−	5.38685i	−0.0737224	−	0.418101i
$167$	−1.24764	+	7.07571i	−0.0965451	+	0.547535i	0.897718	+	0.440571i	$0.145224\pi$
$167$	−1.24764	+	7.07571i	−0.0965451	+	0.547535i	−0.994263	+	0.106964i	$0.965887\pi$
$168$	1.80451	+	0.656788i	0.139221	+	0.0506723i
$169$	−6.04084	+	5.06887i	−0.464680	+	0.389913i
$170$		0			0
$171$	9.48987	−	1.06164i	0.725708	−	0.0811855i
$172$	0.698158			0.0532340
$173$	−19.4568	+	16.3262i	−1.47927	+	1.24126i	−0.572316	+	0.820033i	$0.693955\pi$
$173$	−19.4568	+	16.3262i	−1.47927	+	1.24126i	−0.906957	+	0.421224i	$0.861601\pi$
$174$	5.23483	+	1.90532i	0.396852	+	0.144442i
$175$		0			0
$176$	0.199838	+	1.13334i	0.0150634	+	0.0854286i
$177$	1.40252	−	0.510474i	0.105420	−	0.0383696i
$178$	−3.53877	+	6.12933i	−0.265242	+	0.459412i
$179$	5.27690	+	9.13986i	0.394414	+	0.683145i	0.993026	−	0.117894i	$-0.0376143\pi$
$179$	5.27690	+	9.13986i	0.394414	+	0.683145i	−0.598612	+	0.801039i	$0.704281\pi$
$180$		0			0
$181$	−0.332674	−	0.279147i	−0.0247275	−	0.0207488i	0.630340	−	0.776319i	$-0.282915\pi$
$181$	−0.332674	−	0.279147i	−0.0247275	−	0.0207488i	−0.655068	+	0.755570i	$0.727360\pi$
$182$	2.41369	+	4.18063i	0.178914	+	0.309889i
$183$	−2.67946	+	4.64096i	−0.198071	+	0.343069i
$184$	7.61175	−	2.77045i	0.561145	−	0.204240i
$185$		0			0
$186$	−0.691033	+	3.91904i	−0.0506690	+	0.287358i
$187$	−0.0396205	−	0.0144207i	−0.00289734	−	0.00105455i
$188$	5.57985	−	4.68205i	0.406952	−	0.341474i
$189$	−9.96782			−0.725052
$190$		0			0
$191$	26.4706			1.91534			0.957672	−	0.287861i	$-0.0929443\pi$
$191$	26.4706			1.91534			0.957672	+	0.287861i	$0.0929443\pi$
$192$	−0.689139	+	0.578256i	−0.0497343	+	0.0417321i
$193$	−11.2801	−	4.10561i	−0.811957	−	0.295528i	−0.0975250	−	0.995233i	$-0.531093\pi$
$193$	−11.2801	−	4.10561i	−0.811957	−	0.295528i	−0.714432	+	0.699705i	$0.753315\pi$
$194$	−1.43854	+	8.15839i	−0.103281	+	0.585738i
$195$		0			0
$196$	2.29604	−	0.835691i	0.164003	−	0.0596922i
$197$	12.1859	−	21.1067i	0.868212	−	1.50379i	0.00438927	−	0.999990i	$-0.498603\pi$
$197$	12.1859	−	21.1067i	0.868212	−	1.50379i	0.863822	−	0.503796i	$-0.168064\pi$
$198$	−1.26056	−	2.18335i	−0.0895839	−	0.155164i
$199$	0.197234	+	0.165499i	0.0139815	+	0.0117319i	0.649752	−	0.760147i	$-0.274873\pi$
$199$	0.197234	+	0.165499i	0.0139815	+	0.0117319i	−0.635770	+	0.771878i	$0.719317\pi$
$200$		0			0
$201$	−4.39572	−	7.61362i	−0.310050	−	0.537023i
$202$	0.188870	−	0.327132i	0.0132888	−	0.0230169i
$203$	−12.4214	+	4.52102i	−0.871811	+	0.317313i
$204$	−0.00572334	−	0.0324587i	−0.000400714	−	0.00227256i
$205$		0			0
$206$	−12.9794	−	4.72411i	−0.904317	−	0.329145i
$207$	−13.5937	+	11.4064i	−0.944825	+	0.792803i
$208$	−2.26147			−0.156805
$209$	4.87532	+	1.18098i	0.337233	+	0.0816900i
$210$		0			0
$211$	2.05853	−	1.72731i	0.141715	−	0.118913i	−0.569175	−	0.822217i	$-0.692737\pi$
$211$	2.05853	−	1.72731i	0.141715	−	0.118913i	0.710889	+	0.703304i	$0.248293\pi$
$212$	−11.0991	−	4.03974i	−0.762288	−	0.277450i
$213$	1.53272	−	8.69250i	0.105020	−	0.595600i
$214$	−1.12481	−	6.37910i	−0.0768903	−	0.436066i
$215$		0			0
$216$	2.33480	−	4.04399i	0.158863	−	0.275159i
$217$	−4.72135	−	8.17761i	−0.320506	−	0.555132i
$218$	1.31555	+	1.10388i	0.0891003	+	0.0747640i
$219$	4.06220	+	3.40859i	0.274498	+	0.230331i
$220$		0			0
$221$	0.0414273	−	0.0717542i	0.00278670	−	0.00482671i
$222$	−4.77504	+	1.73797i	−0.320480	+	0.116645i
$223$	1.06235	+	6.02489i	0.0711403	+	0.403457i	0.999495	+	0.0317623i	$0.0101120\pi$
$223$	1.06235	+	6.02489i	0.0711403	+	0.403457i	−0.928355	+	0.371694i	$0.878777\pi$
$224$	0.370673	−	2.10219i	0.0247666	−	0.140458i
$225$		0			0
$226$	−5.30514	+	4.45154i	−0.352893	+	0.296112i
$227$	−0.981843			−0.0651672			−0.0325836	−	0.999469i	$-0.510374\pi$
$227$	−0.981843			−0.0651672			−0.0325836	+	0.999469i	$0.510374\pi$
$228$	1.10604	+	3.76208i	0.0732493	+	0.249150i
$229$	−20.0859			−1.32731			−0.663657	−	0.748037i	$-0.730997\pi$
$229$	−20.0859			−1.32731			−0.663657	+	0.748037i	$0.730997\pi$
$230$		0			0
$231$	−2.07667	−	0.755846i	−0.136635	−	0.0497310i
$232$	1.07531	−	6.09839i	0.0705976	−	0.400379i
$233$	2.79441	+	15.8479i	0.183068	+	1.03823i	0.928413	+	0.371550i	$0.121174\pi$
$233$	2.79441	+	15.8479i	0.183068	+	1.03823i	−0.745345	+	0.666679i	$0.767715\pi$
$234$	4.65544	−	1.69444i	0.304336	−	0.110769i
$235$		0			0
$236$	−0.829543	−	1.43681i	−0.0539987	−	0.0935284i
$237$	6.23913	+	5.23525i	0.405275	+	0.340066i
$238$	0.0599102	+	0.0502706i	0.00388340	+	0.00325856i
$239$	4.29381	+	7.43711i	0.277744	+	0.481066i	0.970824	−	0.239794i	$-0.0770800\pi$
$239$	4.29381	+	7.43711i	0.277744	+	0.481066i	−0.693080	+	0.720861i	$0.743747\pi$
$240$		0			0
$241$	−11.1897	+	4.07273i	−0.720793	+	0.262347i	−0.676263	−	0.736661i	$-0.736401\pi$
$241$	−11.1897	+	4.07273i	−0.720793	+	0.262347i	−0.0445308	+	0.999008i	$0.514179\pi$
$242$	1.68015	+	9.52861i	0.108004	+	0.612523i
$243$	−2.80304	+	15.8968i	−0.179815	+	1.01978i
$244$	5.59770	+	2.03740i	0.358356	+	0.130431i
$245$		0			0
$246$	7.48511			0.477233
$247$	−3.94910	+	9.03190i	−0.251275	+	0.574686i
$248$	4.42359			0.280899
$249$	−3.76956	+	3.16303i	−0.238886	+	0.200449i
$250$		0			0
$251$	−3.11493	+	17.6657i	−0.196613	+	1.11505i	0.713490	+	0.700665i	$0.247113\pi$
$251$	−3.11493	+	17.6657i	−0.196613	+	1.11505i	−0.910103	+	0.414382i	$0.863998\pi$
$252$	0.812035	+	4.60528i	0.0511534	+	0.290105i
$253$	−8.75977	+	3.18829i	−0.550722	+	0.200446i
$254$	−7.32829	+	12.6930i	−0.459818	+	0.796428i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−20.8725	−	17.5141i	−1.30199	−	1.09250i	−0.989797	−	0.142485i	$-0.954491\pi$
$257$	−20.8725	−	17.5141i	−1.30199	−	1.09250i	−0.312197	−	0.950018i	$-0.601065\pi$
$258$	−0.314034	−	0.543923i	−0.0195509	−	0.0338632i
$259$	6.02878	−	10.4421i	0.374610	−	0.648843i
$260$		0			0
$261$	2.35569	+	13.3598i	0.145814	+	0.826950i
$262$	−0.896365	+	5.08354i	−0.0553776	+	0.314062i
$263$	0.470923	+	0.171402i	0.0290384	+	0.0105691i	0.356498	−	0.934296i	$-0.383970\pi$
$263$	0.470923	+	0.171402i	0.0290384	+	0.0105691i	−0.327460	+	0.944865i	$0.606193\pi$
$264$	0.793077	−	0.665470i	0.0488105	−	0.0409569i
$265$		0			0
$266$	−7.74848	−	5.15136i	−0.475090	−	0.315850i
$267$	6.36700			0.389654
$268$	−7.48620	+	6.28167i	−0.457292	+	0.383714i
$269$	−19.3314	−	7.03604i	−1.17865	−	0.428995i	−0.322928	−	0.946424i	$-0.604667\pi$
$269$	−19.3314	−	7.03604i	−1.17865	−	0.428995i	−0.855726	+	0.517429i	$0.826889\pi$
$270$		0			0
$271$	1.87357	+	10.6255i	0.113811	+	0.645456i	0.987332	+	0.158669i	$0.0507202\pi$
$271$	1.87357	+	10.6255i	0.113811	+	0.645456i	−0.873521	+	0.486787i	$0.838169\pi$
$272$	−0.0344280	+	0.0125308i	−0.00208751	+	0.000759790i
$273$	2.17137	−	3.76093i	0.131417	−	0.227622i
$274$	−7.61885	−	13.1962i	−0.460272	−	0.797214i
$275$		0			0
$276$	−5.58220	−	4.68402i	−0.336009	−	0.281945i
$277$	−10.0957	−	17.4863i	−0.606594	−	1.05065i	−0.991797	−	0.127820i	$-0.959202\pi$
$277$	−10.0957	−	17.4863i	−0.606594	−	1.05065i	0.385203	−	0.922832i	$-0.374131\pi$
$278$	−4.90307	+	8.49237i	−0.294067	+	0.509339i
$279$	−9.10637	+	3.31445i	−0.545184	+	0.198431i
$280$		0			0
$281$	−0.196386	+	1.11376i	−0.0117154	+	0.0664415i	−0.990105	−	0.140329i	$-0.955184\pi$
$281$	−0.196386	+	1.11376i	−0.0117154	+	0.0664415i	0.978390	+	0.206770i	$0.0662952\pi$
$282$	−6.15754	−	2.24116i	−0.366676	−	0.133459i
$283$	5.78772	−	4.85647i	0.344044	−	0.288687i	−0.454349	−	0.890824i	$-0.650128\pi$
$283$	5.78772	−	4.85647i	0.344044	−	0.288687i	0.798393	+	0.602136i	$0.205684\pi$
$284$	−9.81161			−0.582212
$285$		0			0
$286$	2.60255			0.153892
$287$	−13.6057	+	11.4165i	−0.803117	+	0.673895i
$288$	−2.05859	−	0.749266i	−0.121304	−	0.0441509i
$289$	−2.95179	+	16.7404i	−0.173634	+	0.984730i
$290$		0			0
$291$	7.00312	−	2.54893i	0.410530	−	0.149421i
$292$	2.94730	−	5.10488i	0.172478	−	0.298740i
$293$	8.42459	+	14.5918i	0.492170	+	0.852463i	0.999959	−	0.00901811i	$-0.00287059\pi$
$293$	8.42459	+	14.5918i	0.492170	+	0.852463i	−0.507790	+	0.861481i	$0.669537\pi$
$294$	−1.68384	−	1.41291i	−0.0982036	−	0.0824026i
$295$		0			0
$296$	2.82429	+	4.89181i	0.164158	+	0.284330i
$297$	−2.68694	+	4.65391i	−0.155912	+	0.270047i
$298$	20.8349	−	7.58328i	1.20693	−	0.439287i
$299$	−3.18097	−	18.0402i	−0.183960	−	1.04329i
$300$		0			0
$301$	1.40043	+	0.509713i	0.0807192	+	0.0293794i
$302$	13.4136	−	11.2554i	0.771867	−	0.647674i
$303$	−0.339817			−0.0195220
$304$	3.90489	−	1.93697i	0.223961	−	0.111093i
$305$		0			0
$306$	0.0614843	−	0.0515915i	0.00351483	−	0.00294929i
$307$	18.3440	+	6.67668i	1.04695	+	0.381058i	0.807511	−	0.589853i	$-0.200814\pi$
$307$	18.3440	+	6.67668i	1.04695	+	0.381058i	0.239439	+	0.970911i	$0.423037\pi$
$308$	−0.426578	+	2.41925i	−0.0243066	+	0.137849i
$309$	2.15770	+	12.2369i	0.122747	+	0.696136i
$310$		0			0
$311$	−16.0432	+	27.7876i	−0.909725	+	1.57569i	−0.0952788	+	0.995451i	$0.530374\pi$
$311$	−16.0432	+	27.7876i	−0.909725	+	1.57569i	−0.814446	+	0.580239i	$0.802959\pi$
$312$	1.01722	+	1.76187i	0.0575886	+	0.0997463i
$313$	4.98909	+	4.18634i	0.282000	+	0.236626i	0.772805	−	0.634643i	$-0.218853\pi$
$313$	4.98909	+	4.18634i	0.282000	+	0.236626i	−0.490805	+	0.871269i	$0.663297\pi$
$314$	−16.2321	−	13.6203i	−0.916030	−	0.768640i
$315$		0			0
$316$	4.52676	−	7.84057i	0.254650	−	0.441067i
$317$	−7.23292	+	2.63257i	−0.406241	+	0.147860i	−0.537055	−	0.843547i	$-0.680463\pi$
$317$	−7.23292	+	2.63257i	−0.406241	+	0.147860i	0.130814	+	0.991407i	$0.458241\pi$
$318$	1.84512	+	10.4642i	0.103469	+	0.586803i
$319$	−1.23749	+	7.01816i	−0.0692862	+	0.392942i
$320$		0			0
$321$	−4.46391	+	3.74566i	−0.249151	+	0.209062i
$322$	17.2910			0.963588
$323$	−0.0100744	+	0.159381i	−0.000560554	+	0.00886821i
$324$	2.37131			0.131740
$325$		0			0
$326$	9.02446	+	3.28463i	0.499819	+	0.181919i
$327$	0.268273	−	1.52145i	0.0148355	−	0.0841364i
$328$	−1.44483	−	8.19401i	−0.0797771	−	0.452439i
$329$	14.6108	−	5.31791i	0.805521	−	0.293186i
$330$		0			0
$331$	10.0884	+	17.4736i	0.554508	+	0.960436i	0.997942	+	0.0641290i	$0.0204269\pi$
$331$	10.0884	+	17.4736i	0.554508	+	0.960436i	−0.443433	+	0.896307i	$0.646240\pi$
$332$	4.19022	+	3.51602i	0.229968	+	0.192966i
$333$	−9.47931	−	7.95409i	−0.519463	−	0.435881i
$334$	−3.59243	−	6.22227i	−0.196569	−	0.340468i
$335$		0			0
$336$	−1.80451	+	0.656788i	−0.0984441	+	0.0358307i
$337$	1.24455	+	7.05822i	0.0677952	+	0.384486i	0.999759	+	0.0219353i	$0.00698280\pi$
$337$	1.24455	+	7.05822i	0.0677952	+	0.384486i	−0.931964	+	0.362550i	$0.881906\pi$
$338$	1.36935	−	7.76596i	0.0744827	−	0.422412i
$339$	5.85439	+	2.13083i	0.317967	+	0.115731i
$340$		0			0
$341$	−5.09077			−0.275681
$342$	−6.58725	+	6.91323i	−0.356198	+	0.373825i
$343$	20.1581			1.08843
$344$	−0.534820	+	0.448767i	−0.0288356	+	0.0241959i
$345$		0			0
$346$	4.41050	−	25.0132i	0.237110	−	1.34472i
$347$	−1.29390	−	7.33806i	−0.0694601	−	0.393928i	−0.999640	−	0.0268241i	$-0.991461\pi$
$347$	−1.29390	−	7.33806i	−0.0694601	−	0.393928i	0.930180	−	0.367104i	$-0.119651\pi$
$348$	−5.23483	+	1.90532i	−0.280616	+	0.102136i
$349$	−13.0654	+	22.6299i	−0.699373	+	1.21135i	0.269311	+	0.963053i	$0.413204\pi$
$349$	−13.0654	+	22.6299i	−0.699373	+	1.21135i	−0.968684	+	0.248297i	$0.920129\pi$
$350$		0			0
$351$	−8.08954	−	6.78793i	−0.431788	−	0.362313i
$352$	−0.881581	−	0.739734i	−0.0469884	−	0.0394280i
$353$	−7.03480	−	12.1846i	−0.374425	−	0.648523i	0.615816	−	0.787890i	$-0.288826\pi$
$353$	−7.03480	−	12.1846i	−0.374425	−	0.648523i	−0.990241	+	0.139367i	$0.955493\pi$
$354$	−0.746263	+	1.29257i	−0.0396634	+	0.0686991i
$355$		0			0
$356$	−1.22900	−	6.97001i	−0.0651369	−	0.369410i
$357$	0.0122172	−	0.0692869i	0.000646600	−	0.00366705i
$358$	−9.91733	−	3.60961i	−0.524147	−	0.190774i
$359$	21.4311	−	17.9828i	1.13109	−	0.949097i	0.131979	−	0.991252i	$-0.457867\pi$
$359$	21.4311	−	17.9828i	1.13109	−	0.949097i	0.999111	+	0.0421551i	$0.0134224\pi$
$360$		0			0
$361$	−0.917004	−	18.9779i	−0.0482634	−	0.998835i
$362$	0.434275			0.0228250
$363$	6.66784	−	5.59498i	0.349971	−	0.293660i
$364$	−4.53625	−	1.65106i	−0.237764	−	0.0865390i
$365$		0			0
$366$	−0.930566	−	5.27750i	−0.0486414	−	0.275859i
$367$	23.8004	−	8.66262i	1.24237	−	0.452185i	0.364552	−	0.931183i	$-0.381222\pi$
$367$	23.8004	−	8.66262i	1.24237	−	0.452185i	0.877816	+	0.478998i	$0.159000\pi$
$368$	−4.05013	+	7.01502i	−0.211127	+	0.365683i
$369$	9.11380	+	15.7856i	0.474445	+	0.821763i
$370$		0			0
$371$	−19.3142	−	16.2065i	−1.00274	−	0.841400i
$372$	−1.98975	−	3.44635i	−0.103164	−	0.178685i
$373$	10.6981	−	18.5296i	0.553925	−	0.959427i	−0.444061	−	0.895997i	$-0.646463\pi$
$373$	10.6981	−	18.5296i	0.553925	−	0.959427i	0.997986	−	0.0634302i	$-0.0202040\pi$
$374$	0.0396205	−	0.0144207i	0.00204873	−	0.000745676i
$375$		0			0
$376$	−1.26485	+	7.17332i	−0.0652296	+	0.369936i
$377$	−13.1595	−	4.78968i	−0.677750	−	0.246681i
$378$	7.63579	−	6.40719i	0.392743	−	0.329550i
$379$	37.8831			1.94592			0.972961	−	0.230968i	$-0.0741894\pi$
$379$	37.8831			1.94592			0.972961	+	0.230968i	$0.0741894\pi$
$380$		0			0
$381$	13.1852			0.675497
$382$	−20.2776	+	17.0150i	−1.03749	+	0.870561i
$383$	−3.09921	−	1.12802i	−0.158362	−	0.0576391i	0.261623	−	0.965170i	$-0.415742\pi$
$383$	−3.09921	−	1.12802i	−0.158362	−	0.0576391i	−0.419985	+	0.907531i	$0.637965\pi$
$384$	0.156215	−	0.885940i	0.00797182	−	0.0452105i
$385$		0			0
$386$	11.2801	−	4.10561i	0.574140	−	0.208970i
$387$	0.764730	−	1.32455i	0.0388734	−	0.0673307i
$388$	−4.14212	−	7.17436i	−0.210284	−	0.364223i
$389$	3.32824	+	2.79272i	0.168748	+	0.141597i	0.723251	−	0.690585i	$-0.242647\pi$
$389$	3.32824	+	2.79272i	0.168748	+	0.141597i	−0.554503	+	0.832182i	$0.687091\pi$
$390$		0			0
$391$	−0.148387	−	0.257013i	−0.00750424	−	0.0129977i
$392$	−1.22170	+	2.11605i	−0.0617051	+	0.106876i
$393$	4.36368	−	1.58825i	0.220119	−	0.0801167i
$394$	4.23213	+	24.0016i	0.213212	+	1.20918i
$395$		0			0
$396$	2.36907	+	0.862272i	0.119050	+	0.0433308i
$397$	19.8582	−	16.6630i	0.996654	−	0.836292i	0.0101368	−	0.999949i	$-0.496773\pi$
$397$	19.8582	−	16.6630i	0.996654	−	0.836292i	0.986517	+	0.163656i	$0.0523289\pi$
$398$	−0.257470			−0.0129058
$399$	−0.528039	+	8.35381i	−0.0264350	+	0.418213i
$400$		0			0
$401$	2.96077	−	2.48438i	0.147854	−	0.124064i	−0.565861	−	0.824501i	$-0.691456\pi$
$401$	2.96077	−	2.48438i	0.147854	−	0.124064i	0.713714	+	0.700437i	$0.247011\pi$
$402$	8.26126	+	3.00685i	0.412034	+	0.149968i
$403$	1.73715	−	9.85184i	0.0865334	−	0.490755i
$404$	0.0655937	+	0.372001i	0.00326341	+	0.0185077i
$405$		0			0
$406$	6.60928	−	11.4476i	0.328013	−	0.568136i
$407$	−3.25025	−	5.62960i	−0.161109	−	0.279049i
$408$	0.0252484	+	0.0211859i	0.00124998	+	0.00104886i
$409$	−6.68991	−	5.61350i	−0.330795	−	0.277570i	0.462229	−	0.886761i	$-0.347050\pi$
$409$	−6.68991	−	5.61350i	−0.330795	−	0.277570i	−0.793024	+	0.609191i	$0.791494\pi$
$410$		0			0
$411$	−6.85398	+	11.8714i	−0.338082	+	0.585575i
$412$	12.9794	−	4.72411i	0.639449	−	0.232740i
$413$	−0.614978	−	3.48772i	−0.0302611	−	0.171619i
$414$	3.08143	−	17.4757i	0.151444	−	0.858883i
$415$		0			0
$416$	1.73239	−	1.45364i	0.0849372	−	0.0712708i
$417$	8.82168			0.432000
$418$	−4.49383	+	2.22911i	−0.219800	+	0.109029i
$419$	1.35441			0.0661673			0.0330836	−	0.999453i	$-0.489467\pi$
$419$	1.35441			0.0661673			0.0330836	+	0.999453i	$0.489467\pi$
$420$		0			0
$421$	2.38379	+	0.867629i	0.116179	+	0.0422856i	0.399455	−	0.916753i	$-0.369199\pi$
$421$	2.38379	+	0.867629i	0.116179	+	0.0422856i	−0.283277	+	0.959038i	$0.591421\pi$
$422$	−0.466630	+	2.64639i	−0.0227152	+	0.128824i
$423$	−2.77091	−	15.7146i	−0.134726	−	0.764072i
$424$	11.0991	−	4.03974i	0.539019	−	0.196187i
$425$		0			0
$426$	4.41330	+	7.64406i	0.213825	+	0.370356i
$427$	9.74088	+	8.17357i	0.471394	+	0.395547i
$428$	4.96206	+	4.16366i	0.239850	+	0.201258i
$429$	−1.17064	−	2.02760i	−0.0565188	−	0.0978935i
$430$		0			0
$431$	13.9605	−	5.08122i	0.672455	−	0.244754i	0.0168504	−	0.999858i	$-0.494636\pi$
$431$	13.9605	−	5.08122i	0.672455	−	0.244754i	0.655605	+	0.755104i	$0.272414\pi$
$432$	0.810867	+	4.59866i	0.0390129	+	0.221253i
$433$	−0.474466	+	2.69083i	−0.0228014	+	0.129313i	−0.994084	−	0.108617i	$-0.965358\pi$
$433$	−0.474466	+	2.69083i	−0.0228014	+	0.129313i	0.971282	+	0.237930i	$0.0764689\pi$
$434$	8.87323	+	3.22959i	0.425929	+	0.155025i
$435$		0			0
$436$	−1.71733			−0.0822451
$437$	20.9442	+	28.4255i	1.00190	+	1.35978i
$438$	−5.30283			−0.253379
$439$	22.0695	−	18.5185i	1.05332	−	0.883839i	0.0598800	−	0.998206i	$-0.480928\pi$
$439$	22.0695	−	18.5185i	1.05332	−	0.883839i	0.993439	+	0.114366i	$0.0364837\pi$
$440$		0			0
$441$	0.929499	−	5.27145i	0.0442618	−	0.251021i
$442$	0.0143876	+	0.0815959i	0.000684346	+	0.00388112i
$443$	12.8763	−	4.68659i	0.611772	−	0.222667i	−0.0175066	−	0.999847i	$-0.505573\pi$
$443$	12.8763	−	4.68659i	0.611772	−	0.222667i	0.629278	+	0.777180i	$0.283351\pi$
$444$	2.54075	−	4.40070i	0.120579	−	0.208848i
$445$		0			0
$446$	−4.68654	−	3.93247i	−0.221914	−	0.186208i
$447$	−15.2796	−	12.8211i	−0.722700	−	0.606418i
$448$	1.06731	+	1.84863i	0.0504257	+	0.0873398i
$449$	10.4586	−	18.1148i	0.493572	−	0.854891i	−0.506401	−	0.862298i	$-0.669024\pi$
$449$	10.4586	−	18.1148i	0.493572	−	0.854891i	0.999973	+	0.00740712i	$0.00235778\pi$
$450$		0			0
$451$	1.66274	+	9.42985i	0.0782952	+	0.444034i
$452$	1.20258	−	6.82016i	0.0565645	−	0.320793i
$453$	−14.8024	−	5.38762i	−0.695476	−	0.253132i
$454$	0.752136	−	0.631117i	0.0352995	−	0.0296198i
$455$		0			0
$456$	−3.26549	−	2.17097i	−0.152921	−	0.101665i
$457$	40.8499			1.91088			0.955438	−	0.295190i	$-0.0953831\pi$
$457$	40.8499			1.91088			0.955438	+	0.295190i	$0.0953831\pi$
$458$	15.3867	−	12.9110i	0.718973	−	0.603290i
$459$	−0.160765	−	0.0585137i	−0.00750387	−	0.00273118i
$460$		0			0
$461$	5.01978	+	28.4686i	0.233794	+	1.32591i	0.845138	+	0.534548i	$0.179518\pi$
$461$	5.01978	+	28.4686i	0.233794	+	1.32591i	−0.611344	+	0.791365i	$0.709371\pi$
$462$	2.07667	−	0.755846i	0.0966154	−	0.0351651i
$463$	16.0908	−	27.8701i	0.747803	−	1.29523i	−0.201071	−	0.979577i	$-0.564442\pi$
$463$	16.0908	−	27.8701i	0.747803	−	1.29523i	0.948874	−	0.315656i	$-0.102224\pi$
$464$	3.09623	+	5.36284i	0.143739	+	0.248963i
$465$		0			0
$466$	−12.3275	−	10.3440i	−0.571059	−	0.479175i
$467$	−18.4169	−	31.8990i	−0.852232	−	1.47611i	−0.879189	−	0.476472i	$-0.841915\pi$
$467$	−18.4169	−	31.8990i	−0.852232	−	1.47611i	0.0269574	−	0.999637i	$-0.491418\pi$
$468$	−2.47711	+	4.29048i	−0.114504	+	0.198327i
$469$	−19.6026	+	7.13476i	−0.905164	+	0.329453i
$470$		0			0
$471$	−3.31012	+	18.7726i	−0.152522	+	0.864997i
$472$	1.55903	+	0.567441i	0.0717602	+	0.0261186i
$473$	0.615483	−	0.516451i	0.0282999	−	0.0237465i
$474$	−8.14460			−0.374094
$475$		0			0
$476$	−0.0782072			−0.00358462
$477$	−19.8216	+	16.6323i	−0.907570	+	0.761542i
$478$	−8.06973	−	2.93714i	−0.369101	−	0.134342i
$479$	−1.28216	+	7.27148i	−0.0585833	+	0.332242i	−0.999987	−	0.00503861i	$-0.998396\pi$
$479$	−1.28216	+	7.27148i	−0.0585833	+	0.332242i	0.941404	+	0.337281i	$0.109507\pi$
$480$		0			0
$481$	12.0037	−	4.36899i	0.547321	−	0.199209i
$482$	5.95393	−	10.3125i	0.271194	−	0.469722i
$483$	−7.77754	−	13.4711i	−0.353890	−	0.612956i
$484$	−7.41195	−	6.21936i	−0.336907	−	0.282698i
$485$		0			0
$486$	−8.07102	−	13.9794i	−0.366109	−	0.634119i
$487$	−13.2286	+	22.9127i	−0.599446	+	1.03827i	0.393457	+	0.919343i	$0.371279\pi$
$487$	−13.2286	+	22.9127i	−0.599446	+	1.03827i	−0.992903	+	0.118928i	$0.962054\pi$
$488$	−5.59770	+	2.03740i	−0.253396	+	0.0922286i
$489$	−1.50023	−	8.50824i	−0.0678429	−	0.384756i
$490$		0			0
$491$	7.54434	+	2.74591i	0.340471	+	0.123921i	0.506596	−	0.862183i	$-0.330903\pi$
$491$	7.54434	+	2.74591i	0.340471	+	0.123921i	−0.166125	+	0.986105i	$0.553126\pi$
$492$	−5.73393	+	4.81134i	−0.258505	+	0.216912i
$493$	−0.226877			−0.0102180
$494$	−2.78041	−	9.45727i	−0.125096	−	0.425503i
$495$		0			0
$496$	−3.38867	+	2.84343i	−0.152156	+	0.127674i
$497$	−19.6810	−	7.16329i	−0.882812	−	0.321317i
$498$	0.854489	−	4.84605i	0.0382906	−	0.217157i
$499$	3.76753	+	21.3667i	0.168658	+	0.956506i	0.945212	+	0.326456i	$0.105854\pi$
$499$	3.76753	+	21.3667i	0.168658	+	0.956506i	−0.776555	+	0.630050i	$0.783034\pi$
$500$		0			0
$501$	−3.23178	+	5.59760i	−0.144385	+	0.250082i
$502$	−8.96909	−	15.5349i	−0.400310	−	0.693358i
$503$	15.1058	+	12.6753i	0.673536	+	0.565164i	0.914110	−	0.405467i	$-0.132891\pi$
$503$	15.1058	+	12.6753i	0.673536	+	0.565164i	−0.240574	+	0.970631i	$0.577336\pi$
$504$	−3.58227	−	3.00588i	−0.159567	−	0.133893i
$505$		0			0
$506$	4.66097	−	8.07304i	0.207206	−	0.358891i
$507$	−6.66626	+	2.42632i	−0.296059	+	0.107757i
$508$	−2.54509	−	14.4339i	−0.112920	−	0.640402i
$509$	0.901498	−	5.11265i	0.0399582	−	0.226614i	−0.958289	−	0.285802i	$-0.907740\pi$
$509$	0.901498	−	5.11265i	0.0399582	−	0.226614i	0.998247	+	0.0591880i	$0.0188511\pi$
$510$		0			0
$511$	9.63894	−	8.08803i	0.426402	−	0.357793i
$512$	−1.00000			−0.0441942
$513$	19.7822	+	4.79196i	0.873405	+	0.211570i
$514$	27.2472			1.20182
$515$		0			0
$516$	0.590191	+	0.214812i	0.0259817	+	0.00945657i
$517$	1.45562	−	8.25521i	0.0640179	−	0.363064i
$518$	2.09377	+	11.8744i	0.0919951	+	0.521730i
$519$	−21.4712	+	7.81487i	−0.942481	+	0.343035i
$520$		0			0
$521$	−14.6395	−	25.3563i	−0.641366	−	1.11088i	−0.985128	−	0.171822i	$-0.945035\pi$
$521$	−14.6395	−	25.3563i	−0.641366	−	1.11088i	0.343762	−	0.939057i	$-0.388299\pi$
$522$	−10.3921	−	8.71998i	−0.454849	−	0.381663i
$523$	−1.39649	−	1.17180i	−0.0610643	−	0.0512390i	0.611745	−	0.791055i	$-0.290468\pi$
$523$	−1.39649	−	1.17180i	−0.0610643	−	0.0512390i	−0.672809	+	0.739816i	$0.734912\pi$
$524$	−2.58098	−	4.47039i	−0.112751	−	0.195290i
$525$		0			0
$526$	−0.470923	+	0.171402i	−0.0205332	+	0.00747348i
$527$	−0.0281431	−	0.159607i	−0.00122593	−	0.00695261i
$528$	−0.179776	+	1.01956i	−0.00782374	+	0.0443706i
$529$	−40.0441	−	14.5749i	−1.74105	−	0.633690i
$530$		0			0
$531$	−3.63457			−0.157727
$532$	9.24691	−	1.03446i	0.400904	−	0.0448495i
$533$	−18.8164			−0.815027
$534$	−4.87741	+	4.09263i	−0.211066	+	0.177106i
$535$		0			0
$536$	1.69698	−	9.62407i	0.0732985	−	0.415697i
$537$	1.64866	+	9.35004i	0.0711451	+	0.403484i
$538$	19.3314	−	7.03604i	0.833434	−	0.303345i
$539$	1.40596	−	2.43519i	0.0605589	−	0.104891i
$540$		0			0
$541$	9.50497	+	7.97562i	0.408651	+	0.342899i	0.823826	−	0.566843i	$-0.191835\pi$
$541$	9.50497	+	7.97562i	0.408651	+	0.342899i	−0.415175	+	0.909741i	$0.636280\pi$
$542$	−8.26521	−	6.93533i	−0.355021	−	0.297898i
$543$	−0.195339	−	0.338336i	−0.00838278	−	0.0145194i
$544$	0.0183188	−	0.0317290i	0.000785411	−	0.00136037i
$545$		0			0
$546$	0.754109	+	4.27677i	0.0322729	+	0.183029i
$547$	6.88009	−	39.0189i	0.294171	−	1.66833i	−0.376380	−	0.926465i	$-0.622831\pi$
$547$	6.88009	−	39.0189i	0.294171	−	1.66833i	0.670551	−	0.741863i	$-0.266058\pi$
$548$	14.3188	+	5.21160i	0.611667	+	0.222629i
$549$	9.99682	−	8.38833i	0.426654	−	0.358005i
$550$		0			0
$551$	26.8250	−	3.00093i	1.14278	−	0.127844i
$552$	7.28705			0.310157
$553$	14.8044	−	12.4224i	0.629548	−	0.528254i
$554$	18.9738	+	6.90589i	0.806119	+	0.293403i
$555$		0			0
$556$	−1.70282	−	9.65717i	−0.0722156	−	0.409555i
$557$	−37.8354	+	13.7710i	−1.60314	+	0.583495i	−0.980066	−	0.198670i	$-0.936338\pi$
$557$	−37.8354	+	13.7710i	−1.60314	+	0.583495i	−0.623072	+	0.782165i	$0.714116\pi$
$558$	4.84540	−	8.39248i	0.205122	−	0.355282i
$559$	0.789431	+	1.36733i	0.0333894	+	0.0578321i
$560$		0			0
$561$	−0.0290564	−	0.0243812i	−0.00122676	−	0.00102937i
$562$	−0.565472	−	0.979426i	−0.0238530	−	0.0413146i
$563$	4.61587	−	7.99492i	0.194536	−	0.336946i	−0.752213	−	0.658921i	$-0.771013\pi$
$563$	4.61587	−	7.99492i	0.194536	−	0.336946i	0.946748	+	0.321975i	$0.104347\pi$
$564$	6.15754	−	2.24116i	0.259279	−	0.0943699i
$565$		0			0
$566$	−1.31197	+	7.44055i	−0.0551462	+	0.312750i
$567$	4.75659	+	1.73126i	0.199758	+	0.0727059i
$568$	7.51613	−	6.30678i	0.315370	−	0.264627i
$569$	1.97117			0.0826355			0.0413178	−	0.999146i	$-0.486844\pi$
$569$	1.97117			0.0826355			0.0413178	+	0.999146i	$0.486844\pi$
$570$		0			0
$571$	−13.6836			−0.572642			−0.286321	−	0.958134i	$-0.592432\pi$
$571$	−13.6836			−0.572642			−0.286321	+	0.958134i	$0.592432\pi$
$572$	−1.99367	+	1.67289i	−0.0833594	+	0.0699469i
$573$	22.3770	+	8.14457i	0.934814	+	0.340244i
$574$	3.08415	−	17.4911i	0.128730	−	0.730064i
$575$		0			0
$576$	2.05859	−	0.749266i	0.0857746	−	0.0312194i
$577$	11.7284	−	20.3142i	0.488260	−	0.845692i	−0.511649	−	0.859195i	$-0.670965\pi$
$577$	11.7284	−	20.3142i	0.488260	−	0.845692i	0.999909	+	0.0135033i	$0.00429835\pi$
$578$	−8.49933	−	14.7213i	−0.353525	−	0.612324i
$579$	−8.27243	−	6.94139i	−0.343790	−	0.288474i
$580$		0			0
$581$	5.83813	+	10.1119i	0.242207	+	0.419514i
$582$	−3.72628	+	6.45411i	−0.154459	+	0.267532i
$583$	−12.7731	+	4.64902i	−0.529006	+	0.192543i
$584$	1.02359	+	5.80505i	0.0423564	+	0.240215i
$585$		0			0
$586$	−15.8330	−	5.76276i	−0.654057	−	0.238057i
$587$	13.5997	−	11.4115i	0.561320	−	0.471004i	−0.317432	−	0.948281i	$-0.602821\pi$
$587$	13.5997	−	11.4115i	0.561320	−	0.471004i	0.878753	+	0.477277i	$0.158376\pi$
$588$	2.19810			0.0906481
$589$	5.43868	+	18.4991i	0.224097	+	0.762242i
$590$		0			0
$591$	16.7956	−	14.0932i	0.690879	−	0.579716i
$592$	−5.30792	−	1.93193i	−0.218154	−	0.0794016i
$593$	−7.21492	+	40.9178i	−0.296281	+	1.68029i	0.365668	+	0.930746i	$0.380841\pi$
$593$	−7.21492	+	40.9178i	−0.296281	+	1.68029i	−0.661949	+	0.749549i	$0.730270\pi$
$594$	−0.933164	−	5.29223i	−0.0382882	−	0.217143i
$595$		0			0
$596$	−11.0860	+	19.2015i	−0.454101	+	0.786525i
$597$	0.115811	+	0.200591i	0.00473983	+	0.00820963i
$598$	14.0328	+	11.7749i	0.573842	+	0.481511i
$599$	20.4270	+	17.1403i	0.834624	+	0.700333i	0.956348	−	0.292231i	$-0.0943978\pi$
$599$	20.4270	+	17.1403i	0.834624	+	0.700333i	−0.121724	+	0.992564i	$0.538842\pi$
$600$		0			0
$601$	7.11077	−	12.3162i	0.290054	−	0.502389i	−0.683768	−	0.729699i	$-0.739660\pi$
$601$	7.11077	−	12.3162i	0.290054	−	0.502389i	0.973822	+	0.227311i	$0.0729933\pi$
$602$	−1.40043	+	0.509713i	−0.0570771	+	0.0207744i
$603$	3.71759	+	21.0835i	0.151392	+	0.858587i
$604$	−3.04062	+	17.2442i	−0.123721	+	0.701658i
$605$		0			0
$606$	0.260315	−	0.218430i	0.0105746	−	0.00887312i
$607$	14.9537			0.606953			0.303476	−	0.952839i	$-0.401853\pi$
$607$	14.9537			0.606953			0.303476	+	0.952839i	$0.401853\pi$
$608$	−1.74625	+	3.99382i	−0.0708199	+	0.161971i
$609$	−11.8915			−0.481869
$610$		0			0
$611$	15.4791	+	5.63392i	0.626216	+	0.227924i
$612$	−0.0139374	+	0.0790427i	−0.000563385	+	0.00319511i
$613$	0.854395	+	4.84551i	0.0345087	+	0.195708i	0.997188	−	0.0749346i	$-0.0238748\pi$
$613$	0.854395	+	4.84551i	0.0345087	+	0.195708i	−0.962680	+	0.270643i	$0.912764\pi$
$614$	−18.3440	+	6.67668i	−0.740305	+	0.269449i
$615$		0			0
$616$	−1.22828	−	2.12745i	−0.0494890	−	0.0857174i
$617$	17.3980	+	14.5987i	0.700419	+	0.587721i	0.921893	−	0.387445i	$-0.126642\pi$
$617$	17.3980	+	14.5987i	0.700419	+	0.587721i	−0.221474	+	0.975166i	$0.571087\pi$
$618$	−9.51865	−	7.98710i	−0.382896	−	0.321288i
$619$	−6.64360	−	11.5071i	−0.267029	−	0.462508i	0.701064	−	0.713098i	$-0.252709\pi$
$619$	−6.64360	−	11.5071i	−0.267029	−	0.462508i	−0.968093	+	0.250590i	$0.919375\pi$
$620$		0			0
$621$	−35.5438	+	12.9369i	−1.42632	+	0.519139i
$622$	−5.57174	−	31.5989i	−0.223406	−	1.26700i
$623$	2.62345	−	14.8783i	0.105106	−	0.596088i
$624$	−1.91174	−	0.695817i	−0.0765309	−	0.0278550i
$625$		0			0
$626$	−6.51280			−0.260304
$627$	3.75800	+	2.49840i	0.150080	+	0.0997766i
$628$	21.1895			0.845553
$629$	0.158533	−	0.133025i	0.00632111	−	0.00530404i
$630$		0			0
$631$	−6.43164	+	36.4757i	−0.256040	+	1.45207i	0.537350	+	0.843359i	$0.319425\pi$
$631$	−6.43164	+	36.4757i	−0.256040	+	1.45207i	−0.793390	+	0.608714i	$0.791686\pi$
$632$	1.57213	+	8.91597i	0.0625358	+	0.354658i
$633$	2.27165	−	0.826812i	0.0902899	−	0.0328628i
$634$	3.84856	−	6.66590i	0.152846	−	0.264737i
$635$		0			0
$636$	−8.13970	−	6.83002i	−0.322760	−	0.270828i
$637$	4.23291	+	3.55183i	0.167714	+	0.140729i
$638$	−3.56322	−	6.17167i	−0.141069	−	0.244339i
$639$	−10.7472	+	18.6147i	−0.425152	+	0.736385i
$640$		0			0
$641$	−5.38419	−	30.5353i	−0.212663	−	1.20607i	−0.884917	−	0.465749i	$-0.845785\pi$
$641$	−5.38419	−	30.5353i	−0.212663	−	1.20607i	0.672254	−	0.740321i	$-0.265326\pi$
$642$	1.01189	−	5.73869i	0.0399359	−	0.226488i
$643$	−15.2806	−	5.56168i	−0.602608	−	0.219331i	0.0226580	−	0.999743i	$-0.492787\pi$
$643$	−15.2806	−	5.56168i	−0.602608	−	0.219331i	−0.625266	+	0.780412i	$0.715009\pi$
$644$	−13.2456	+	11.1144i	−0.521951	+	0.437969i
$645$		0			0
$646$	−0.0947309	−	0.128569i	−0.00372714	−	0.00505847i
$647$	47.0983			1.85162			0.925812	−	0.377985i	$-0.123383\pi$
$647$	47.0983			1.85162			0.925812	+	0.377985i	$0.123383\pi$
$648$	−1.81653	+	1.52425i	−0.0713601	+	0.0598783i
$649$	−1.79417	−	0.653024i	−0.0704272	−	0.0256334i
$650$		0			0
$651$	−1.47509	−	8.36566i	−0.0578134	−	0.327876i
$652$	−9.02446	+	3.28463i	−0.353425	+	0.128636i
$653$	13.1067	−	22.7015i	0.512906	−	0.888380i	−0.486982	−	0.873412i	$-0.661902\pi$
$653$	13.1067	−	22.7015i	0.512906	−	0.888380i	0.999888	−	0.0149675i	$-0.00476448\pi$
$654$	0.772461	+	1.33794i	0.0302056	+	0.0523176i
$655$		0			0
$656$	6.37381	+	5.34826i	0.248855	+	0.208815i
$657$	−6.45668	−	11.1833i	−0.251899	−	0.436302i
$658$	−7.77426	+	13.4654i	−0.303072	+	0.524937i
$659$	−7.18816	+	2.61628i	−0.280011	+	0.101916i	−0.478208	−	0.878246i	$-0.658714\pi$
$659$	−7.18816	+	2.61628i	−0.280011	+	0.101916i	0.198197	+	0.980162i	$0.436491\pi$
$660$		0			0
$661$	−8.35220	+	47.3677i	−0.324863	+	1.84239i	0.185772	+	0.982593i	$0.440521\pi$
$661$	−8.35220	+	47.3677i	−0.324863	+	1.84239i	−0.510635	+	0.859797i	$0.670590\pi$
$662$	−18.9600	−	6.90087i	−0.736900	−	0.268210i
$663$	0.0570984	−	0.0479112i	0.00221752	−	0.00186072i
$664$	−5.46995			−0.212275
$665$		0			0
$666$	12.3744			0.479497
$667$	−38.4252	+	32.2426i	−1.48783	+	1.24844i
$668$	6.75156	+	2.45737i	0.261226	+	0.0950784i
$669$	−0.955699	+	5.42004i	−0.0369495	+	0.209551i
$670$		0			0
$671$	6.44196	−	2.34468i	0.248689	−	0.0905154i
$672$	0.960160	−	1.66305i	0.0370390	−	0.0641534i
$673$	−22.2011	−	38.4534i	−0.855789	−	1.48227i	−0.875911	−	0.482473i	$-0.839739\pi$
$673$	−22.2011	−	38.4534i	−0.855789	−	1.48227i	0.0201219	−	0.999798i	$-0.493595\pi$
$674$	−5.49032	−	4.60693i	−0.211479	−	0.177452i
$675$		0			0
$676$	3.94288	+	6.82927i	0.151649	+	0.262664i
$677$	−1.53312	+	2.65544i	−0.0589226	+	0.102057i	−0.893982	−	0.448103i	$-0.852100\pi$
$677$	−1.53312	+	2.65544i	−0.0589226	+	0.102057i	0.835059	+	0.550160i	$0.185433\pi$
$678$	−5.85439	+	2.13083i	−0.224837	+	0.0818339i
$679$	−3.07074	−	17.4151i	−0.117844	−	0.668328i
$680$		0			0
$681$	−0.830006	−	0.302097i	−0.0318059	−	0.0115764i
$682$	3.89976	−	3.27228i	0.149329	−	0.125302i
$683$	31.7607			1.21529			0.607644	−	0.794210i	$-0.292115\pi$
$683$	31.7607			1.21529			0.607644	+	0.794210i	$0.292115\pi$
$684$	0.602389	−	9.53005i	0.0230329	−	0.364391i
$685$		0			0
$686$	−15.4420	+	12.9574i	−0.589577	+	0.494714i
$687$	−16.9797	−	6.18011i	−0.647816	−	0.235786i
$688$	0.121234	−	0.687551i	0.00462200	−	0.0262126i
$689$	−4.63833	−	26.3053i	−0.176706	−	1.00215i
$690$		0			0
$691$	6.89195	−	11.9372i	0.262182	−	0.454112i	−0.704640	−	0.709565i	$-0.748891\pi$
$691$	6.89195	−	11.9372i	0.262182	−	0.454112i	0.966821	+	0.255453i	$0.0822246\pi$
$692$	12.6995	+	21.9962i	0.482763	+	0.836171i
$693$	4.12256	+	3.45924i	0.156603	+	0.131406i
$694$	5.70800	+	4.78958i	0.216673	+	0.181810i
$695$		0			0
$696$	2.78540	−	4.82445i	0.105580	−	0.182870i
$697$	−0.286456	+	0.104261i	−0.0108503	+	0.00394918i
$698$	−4.53756	−	25.7338i	−0.171749	−	0.974037i
$699$	−2.51387	+	14.2569i	−0.0950833	+	0.539244i
$700$		0			0
$701$	−22.8905	+	19.2074i	−0.864562	+	0.725454i	−0.962946	−	0.269695i	$-0.913077\pi$
$701$	−22.8905	+	19.2074i	−0.864562	+	0.725454i	0.0983834	+	0.995149i	$0.468633\pi$
$702$	10.5601			0.398567
$703$	−16.9847	+	17.8252i	−0.640591	+	0.672292i
$704$	1.15082			0.0433732
$705$		0			0
$706$	13.2211	+	4.81209i	0.497583	+	0.181105i
$707$	−0.140018	+	0.794080i	−0.00526591	+	0.0298644i
$708$	−0.259175	−	1.46985i	−0.00974037	−	0.0552404i
$709$	24.2954	−	8.84281i	0.912433	−	0.332099i	0.157209	−	0.987565i	$-0.449750\pi$
$709$	24.2954	−	8.84281i	0.912433	−	0.332099i	0.755224	+	0.655467i	$0.227528\pi$
$710$		0			0
$711$	−9.91679	−	17.1764i	−0.371909	−	0.644165i
$712$	5.42171	+	4.54935i	0.203187	+	0.170494i
$713$	−27.4491	−	23.0325i	−1.02798	−	0.862574i
$714$	0.0351779	+	0.0609299i	0.00131650	+	0.00228024i
$715$		0			0
$716$	9.91733	−	3.60961i	0.370628	−	0.134898i
$717$	1.34152	+	7.60813i	0.0500999	+	0.284131i
$718$	−4.85804	+	27.5513i	−0.181300	+	1.02821i
$719$	17.7416	+	6.45741i	0.661650	+	0.240821i	0.650948	−	0.759122i	$-0.274371\pi$
$719$	17.7416	+	6.45741i	0.661650	+	0.240821i	0.0107012	+	0.999943i	$0.496594\pi$
$720$		0			0
$721$	29.4842			1.09805
$722$	12.9012	+	13.9484i	0.480133	+	0.519107i
$723$	−10.7124			−0.398398
$724$	−0.332674	+	0.279147i	−0.0123637	+	0.0103744i
$725$		0			0
$726$	−1.51148	+	8.57201i	−0.0560962	+	0.318137i
$727$	5.17269	+	29.3358i	0.191845	+	1.08800i	0.916841	+	0.399252i	$0.130730\pi$
$727$	5.17269	+	29.3358i	0.191845	+	1.08800i	−0.724997	+	0.688752i	$0.758159\pi$
$728$	4.53625	−	1.65106i	0.168125	−	0.0611923i
$729$	−3.70378	+	6.41513i	−0.137177	+	0.237598i
$730$		0			0
$731$	0.0195945	+	0.0164417i	0.000724728	+	0.000608119i
$732$	4.10517	+	3.44464i	0.151731	+	0.127318i
$733$	6.66338	+	11.5413i	0.246118	+	0.426288i	0.962445	−	0.271476i	$-0.0875117\pi$
$733$	6.66338	+	11.5413i	0.246118	+	0.426288i	−0.716328	+	0.697764i	$0.754178\pi$
$734$	−12.6639	+	21.9345i	−0.467433	+	0.809618i
$735$		0			0
$736$	−1.40659	−	7.97719i	−0.0518477	−	0.294043i
$737$	−1.95293	+	11.0756i	−0.0719370	+	0.407975i
$738$	−17.1283	−	6.23421i	−0.630503	−	0.229484i
$739$	−36.7309	+	30.8208i	−1.35117	+	1.13376i	−0.372563	+	0.928007i	$0.621521\pi$
$739$	−36.7309	+	30.8208i	−1.35117	+	1.13376i	−0.978603	+	0.205756i	$0.934035\pi$
$740$		0			0
$741$	−6.11736	+	6.42008i	−0.224727	+	0.235848i
$742$	25.2128			0.925592
$743$	−26.6169	+	22.3342i	−0.976478	+	0.819362i	−0.983554	−	0.180613i	$-0.942192\pi$
$743$	−26.6169	+	22.3342i	−0.976478	+	0.819362i	0.00707666	+	0.999975i	$0.497747\pi$
$744$	3.73951	+	1.36107i	0.137097	+	0.0498992i
$745$		0			0
$746$	3.71540	+	21.0711i	0.136031	+	0.771468i
$747$	11.2604	−	4.09845i	0.411996	−	0.149954i
$748$	−0.0210816	+	0.0365145i	−0.000770821	+	0.00133510i
$749$	6.91351	+	11.9745i	0.252614	+	0.437541i
$750$		0			0
$751$	−16.8228	−	14.1160i	−0.613873	−	0.515101i	0.281998	−	0.959415i	$-0.409003\pi$
$751$	−16.8228	−	14.1160i	−0.613873	−	0.515101i	−0.895871	+	0.444314i	$0.853447\pi$
$752$	−3.64199	−	6.30811i	−0.132810	−	0.230033i
$753$	−8.06866	+	13.9753i	−0.294038	+	0.509290i
$754$	13.1595	−	4.78968i	0.479242	−	0.174430i
$755$		0			0
$756$	−1.73089	+	9.81638i	−0.0629520	+	0.357018i
$757$	−8.72443	−	3.17543i	−0.317095	−	0.115413i	0.178569	−	0.983927i	$-0.442853\pi$
$757$	−8.72443	−	3.17543i	−0.317095	−	0.115413i	−0.495664	+	0.868514i	$0.665075\pi$
$758$	−29.0201	+	24.3508i	−1.05406	+	0.884460i
$759$	−8.38609			−0.304396
$760$		0			0
$761$	−13.5581			−0.491482			−0.245741	−	0.969336i	$-0.579031\pi$
$761$	−13.5581			−0.491482			−0.245741	+	0.969336i	$0.579031\pi$
$762$	−10.1004	+	8.47527i	−0.365900	+	0.307027i
$763$	−3.44477	−	1.25379i	−0.124709	−	0.0453903i
$764$	4.59657	−	26.0684i	0.166298	−	0.943123i
$765$		0			0
$766$	3.09921	−	1.12802i	0.111979	−	0.0407570i
$767$	1.87599	−	3.24930i	0.0677379	−	0.117326i
$768$	0.449804	+	0.779083i	0.0162309	+	0.0281127i
$769$	−15.1389	−	12.7031i	−0.545924	−	0.458085i	0.327634	−	0.944805i	$-0.393749\pi$
$769$	−15.1389	−	12.7031i	−0.545924	−	0.458085i	−0.873558	+	0.486720i	$0.838193\pi$
$770$		0			0
$771$	−12.2559	−	21.2278i	−0.441385	−	0.764501i
$772$	−6.00200	+	10.3958i	−0.216017	+	0.374152i
$773$	16.0490	−	5.84138i	0.577244	−	0.210100i	−0.0368657	−	0.999320i	$-0.511737\pi$
$773$	16.0490	−	5.84138i	0.577244	−	0.210100i	0.614110	+	0.789221i	$0.289515\pi$
$774$	0.265588	+	1.50622i	0.00954636	+	0.0541401i
$775$		0			0
$776$	7.78464	+	2.83338i	0.279452	+	0.101712i
$777$	8.30933	−	6.97236i	0.298096	−	0.250132i
$778$	−4.34471			−0.155765
$779$	32.4903	−	16.1164i	1.16409	−	0.577431i
$780$		0			0
$781$	−8.64973	+	7.25798i	−0.309512	+	0.259711i
$782$	0.278876	+	0.101502i	0.00997257	+	0.00362972i
$783$	−5.02127	+	28.4770i	−0.179446	+	1.01769i
$784$	−0.424292	−	2.40628i	−0.0151533	−	0.0859385i
$785$		0			0
$786$	−2.32187	+	4.02159i	−0.0828183	+	0.143445i
$787$	12.5839	+	21.7960i	0.448568	+	0.776942i	0.998293	−	0.0584033i	$-0.0186009\pi$
$787$	12.5839	+	21.7960i	0.448568	+	0.776942i	−0.549725	+	0.835346i	$0.685268\pi$
$788$	−18.6699	−	15.6659i	−0.665089	−	0.558076i
$789$	0.345359	+	0.289791i	0.0122951	+	0.0103168i
$790$		0			0
$791$	7.39152	−	12.8025i	0.262812	−	0.455204i
$792$	−2.36907	+	0.862272i	−0.0841813	+	0.0306395i
$793$	2.33929	+	13.2668i	0.0830707	+	0.471117i
$794$	−4.50149	+	25.5292i	−0.159752	+	0.905997i
$795$		0			0
$796$	0.197234	−	0.165499i	0.00699076	−	0.00586594i
$797$	28.2917			1.00214			0.501071	−	0.865406i	$-0.332939\pi$
$797$	28.2917			1.00214			0.501071	+	0.865406i	$0.332939\pi$
$798$	−4.96522	−	6.73880i	−0.175767	−	0.238551i
$799$	0.266867			0.00944107
$800$		0			0
$801$	−14.5698	−	5.30296i	−0.514797	−	0.187371i
$802$	−0.671152	+	3.80629i	−0.0236992	+	0.134405i
$803$	−1.17797	−	6.68058i	−0.0415696	−	0.235753i
$804$	−8.26126	+	3.00685i	−0.291352	+	0.106044i
$805$		0			0
$806$	5.00191	+	8.66356i	0.176185	+	0.305161i
$807$	−14.1770	−	11.8959i	−0.499053	−	0.418755i
$808$	−0.289365	−	0.242806i	−0.0101798	−	0.00854189i
$809$	−1.15497	−	2.00046i	−0.0406064	−	0.0703324i	0.845008	−	0.534754i	$-0.179596\pi$
$809$	−1.15497	−	2.00046i	−0.0406064	−	0.0703324i	−0.885614	+	0.464421i	$0.846262\pi$
$810$		0			0
$811$	−12.1095	+	4.40751i	−0.425223	+	0.154769i	−0.545762	−	0.837940i	$-0.683760\pi$
$811$	−12.1095	+	4.40751i	−0.425223	+	0.154769i	0.120539	+	0.992709i	$0.461538\pi$
$812$	2.29538	+	13.0177i	0.0805521	+	0.456833i
$813$	−1.68548	+	9.55882i	−0.0591123	+	0.335242i
$814$	6.10847	+	2.22330i	0.214102	+	0.0779267i
$815$		0			0
$816$	−0.0329594			−0.00115381
$817$	−2.53425	−	1.68482i	−0.0886622	−	0.0589446i
$818$	8.73306			0.305344
$819$	−8.10120	+	6.79771i	−0.283079	+	0.237531i
$820$		0			0
$821$	2.54626	−	14.4405i	0.0888650	−	0.503978i	−0.907591	−	0.419856i	$-0.862080\pi$
$821$	2.54626	−	14.4405i	0.0888650	−	0.503978i	0.996455	−	0.0841217i	$-0.0268085\pi$
$822$	−2.38036	−	13.4997i	−0.0830246	−	0.470856i
$823$	31.3707	−	11.4180i	1.09351	−	0.398006i	0.268592	−	0.963254i	$-0.413442\pi$
$823$	31.3707	−	11.4180i	1.09351	−	0.398006i	0.824921	+	0.565248i	$0.191219\pi$
$824$	−6.90619	+	11.9619i	−0.240589	+	0.416712i
$825$		0			0
$826$	2.71296	+	2.27644i	0.0943960	+	0.0792076i
$827$	5.64874	+	4.73986i	0.196426	+	0.164821i	0.735696	−	0.677312i	$-0.236855\pi$
$827$	5.64874	+	4.73986i	0.196426	+	0.164821i	−0.539270	+	0.842133i	$0.681300\pi$
$828$	8.87264	+	15.3679i	0.308345	+	0.534070i
$829$	−3.66811	+	6.35335i	−0.127399	+	0.220661i	−0.922668	−	0.385595i	$-0.873996\pi$
$829$	−3.66811	+	6.35335i	−0.127399	+	0.220661i	0.795269	+	0.606256i	$0.207329\pi$
$830$		0			0
$831$	−3.15421	−	17.8884i	−0.109418	−	0.620543i
$832$	−0.392700	+	2.22711i	−0.0136144	+	0.0772112i
$833$	0.0841214	+	0.0306177i	0.00291463	+	0.00106084i
$834$	−6.75780	+	5.67047i	−0.234003	+	0.196352i
$835$		0			0
$836$	2.00963	−	4.59618i	0.0695044	−	0.158962i
$837$	−20.6564			−0.713990
$838$	−1.03754	+	0.870598i	−0.0358412	+	0.0300743i
$839$	−14.5357	−	5.29055i	−0.501827	−	0.182650i	0.0786886	−	0.996899i	$-0.474927\pi$
$839$	−14.5357	−	5.29055i	−0.501827	−	0.182650i	−0.580516	+	0.814249i	$0.697149\pi$
$840$		0			0
$841$	1.62303	+	9.20468i	0.0559667	+	0.317403i
$842$	−2.38379	+	0.867629i	−0.0821508	+	0.0299005i
$843$	−0.508702	+	0.881099i	−0.0175206	+	0.0303466i
$844$	−1.34361	−	2.32720i	−0.0462489	−	0.0801054i
$845$		0			0
$846$	12.2238	+	10.2570i	0.420263	+	0.352643i
$847$	−10.3269	−	17.8867i	−0.354836	−	0.614593i
$848$	−5.90570	+	10.2290i	−0.202802	+	0.351264i
$849$	6.38693	−	2.32465i	0.219199	−	0.0797819i
$850$		0			0
$851$	7.94525	−	45.0597i	0.272360	−	1.54463i
$852$	−8.29429	−	3.01887i	−0.284158	−	0.103425i
$853$	−29.8285	+	25.0291i	−1.02131	+	0.856980i	−0.989791	−	0.142523i	$-0.954478\pi$
$853$	−29.8285	+	25.0291i	−1.02131	+	0.856980i	−0.0315176	+	0.999503i	$0.510034\pi$
$854$	−12.7158			−0.435126
$855$		0			0
$856$	−6.47751			−0.221397
$857$	−40.6768	+	34.1319i	−1.38949	+	1.16592i	−0.423948	+	0.905687i	$0.639356\pi$
$857$	−40.6768	+	34.1319i	−1.38949	+	1.16592i	−0.965545	+	0.260236i	$0.916200\pi$
$858$	2.20008	+	0.800762i	0.0751093	+	0.0273376i
$859$	0.385392	−	2.18567i	0.0131494	−	0.0745740i	−0.977527	−	0.210811i	$-0.932390\pi$
$859$	0.385392	−	2.18567i	0.0131494	−	0.0745740i	0.990676	+	0.136237i	$0.0435008\pi$
$860$		0			0
$861$	−15.0143	+	5.46475i	−0.511685	+	0.186238i
$862$	−7.42824	+	12.8661i	−0.253007	+	0.438221i
$863$	−4.65949	−	8.07047i	−0.158611	−	0.274722i	0.775757	−	0.631032i	$-0.217368\pi$
$863$	−4.65949	−	8.07047i	−0.158611	−	0.274722i	−0.934368	+	0.356310i	$0.884035\pi$
$864$	−3.57712	−	3.00156i	−0.121696	−	0.102115i
$865$		0			0
$866$	−1.36617	−	2.36628i	−0.0464244	−	0.0804094i
$867$	−7.64606	+	13.2434i	−0.259674	+	0.449768i
$868$	−8.87323	+	3.22959i	−0.301177	+	0.109619i
$869$	−1.80924	−	10.2607i	−0.0613741	−	0.348070i
$870$		0			0
$871$	−20.7675	−	7.55874i	−0.703679	−	0.256118i
$872$	1.31555	−	1.10388i	0.0445501	−	0.0373820i
$873$	−18.1483			−0.614228
$874$	−34.3157	−	8.31251i	−1.16075	−	0.281175i
$875$		0			0
$876$	4.06220	−	3.40859i	0.137249	−	0.115166i
$877$	8.00218	+	2.91255i	0.270214	+	0.0983500i	0.473574	−	0.880754i	$-0.342964\pi$
$877$	8.00218	+	2.91255i	0.270214	+	0.0983500i	−0.203359	+	0.979104i	$0.565186\pi$
$878$	−5.00274	+	28.3720i	−0.168834	+	0.957508i
$879$	2.63210	+	14.9274i	0.0887784	+	0.503488i
$880$		0			0
$881$	18.8598	−	32.6661i	0.635402	−	1.10055i	−0.351027	−	0.936365i	$-0.614168\pi$
$881$	18.8598	−	32.6661i	0.635402	−	1.10055i	0.986430	−	0.164184i	$-0.0524991\pi$
$882$	2.67638	+	4.63563i	0.0901186	+	0.156090i
$883$	39.6674	+	33.2849i	1.33491	+	1.12012i	0.982902	+	0.184129i	$0.0589463\pi$
$883$	39.6674	+	33.2849i	1.33491	+	1.12012i	0.352011	+	0.935996i	$0.385498\pi$
$884$	−0.0634703	−	0.0532579i	−0.00213474	−	0.00179126i
$885$		0			0
$886$	−6.85134	+	11.8669i	−0.230175	+	0.398675i
$887$	−25.3400	+	9.22299i	−0.850833	+	0.309678i	−0.730380	−	0.683041i	$-0.760657\pi$
$887$	−25.3400	+	9.22299i	−0.850833	+	0.309678i	−0.120453	+	0.992719i	$0.538435\pi$
$888$	0.882393	+	5.00430i	0.0296112	+	0.167933i
$889$	5.43280	−	30.8109i	0.182210	−	1.03337i
$890$		0			0
$891$	2.09051	−	1.75414i	0.0700346	−	0.0587660i
$892$	6.11784			0.204840
$893$	−31.5533	+	3.52989i	−1.05589	+	0.118123i
$894$	19.9461			0.667098
$895$		0			0
$896$	−2.00589	−	0.730083i	−0.0670120	−	0.0243904i
$897$	2.86162	−	16.2291i	0.0955468	−	0.541873i
$898$	3.63223	+	20.5994i	0.121209	+	0.687411i
$899$	−25.7410	+	9.36895i	−0.858510	+	0.312472i
$900$		0			0
$901$	−0.216370	−	0.374764i	−0.00720834	−	0.0124852i
$902$	−7.33512	−	6.15490i	−0.244233	−	0.204936i
$903$	1.02703	+	0.861777i	0.0341773	+	0.0286781i
$904$	3.46269	+	5.99755i	0.115167	+	0.199476i
$905$		0			0
$906$	14.8024	−	5.38762i	0.491776	−	0.178992i
$907$	−5.76401	−	32.6893i	−0.191391	−	1.08543i	−0.917465	−	0.397815i	$-0.869768\pi$
$907$	−5.76401	−	32.6893i	−0.191391	−	1.08543i	0.726075	−	0.687616i	$-0.241343\pi$
$908$	−0.170495	+	0.966927i	−0.00565809	+	0.0320886i
$909$	0.777610	+	0.283027i	0.0257917	+	0.00938741i
$910$		0			0
$911$	18.6372			0.617476			0.308738	−	0.951147i	$-0.400093\pi$
$911$	18.6372			0.617476			0.308738	+	0.951147i	$0.400093\pi$
$912$	3.89699	−	0.435959i	0.129042	−	0.0144360i
$913$	6.29494			0.208332
$914$	−31.2928	+	26.2578i	−1.03507	+	0.868531i
$915$		0			0
$916$	−3.48788	+	19.7808i	−0.115243	+	0.653575i
$917$	−1.91340	−	10.8514i	−0.0631860	−	0.358345i
$918$	0.160765	−	0.0585137i	0.00530604	−	0.00193124i
$919$	25.8149	−	44.7127i	0.851555	−	1.47494i	−0.0282498	−	0.999601i	$-0.508993\pi$
$919$	25.8149	−	44.7127i	0.851555	−	1.47494i	0.879805	−	0.475335i	$-0.157673\pi$
$920$		0			0
$921$	13.4529	+	11.2883i	0.443288	+	0.371963i
$922$	−22.1446	−	18.5815i	−0.729294	−	0.611950i
$923$	−11.0943	−	19.2159i	−0.365174	−	0.632500i
$924$	−1.10497	+	1.91387i	−0.0363509	+	0.0629617i
$925$		0			0
$926$	5.58828	+	31.6927i	0.183642	+	1.04149i
$927$	5.25440	−	29.7992i	0.172577	−	0.978733i
$928$	−5.81902	−	2.11795i	−0.191019	−	0.0695251i
$929$	39.5095	−	33.1524i	1.29626	−	1.08770i	0.305487	−	0.952196i	$-0.401181\pi$
$929$	39.5095	−	33.1524i	1.29626	−	1.08770i	0.990777	−	0.135499i	$-0.0432637\pi$
$930$		0			0
$931$	−10.3512	−	2.50743i	−0.339246	−	0.0821776i
$932$	16.0924			0.527123
$933$	−22.1120	+	18.5541i	−0.723913	+	0.607435i
$934$	34.6124	+	12.5979i	1.13255	+	0.412216i
$935$		0			0
$936$	−0.860290	−	4.87895i	−0.0281195	−	0.159473i
$937$	−2.46321	+	0.896535i	−0.0804696	+	0.0292885i	−0.381941	−	0.924187i	$-0.624744\pi$
$937$	−2.46321	+	0.896535i	−0.0804696	+	0.0292885i	0.301472	+	0.953475i	$0.402522\pi$
$938$	10.4303	−	18.0659i	0.340562	−	0.589871i
$939$	2.92948	+	5.07401i	0.0955999	+	0.165584i
$940$		0			0
$941$	24.2663	+	20.3619i	0.791060	+	0.663778i	0.946008	−	0.324145i	$-0.105076\pi$
$941$	24.2663	+	20.3619i	0.791060	+	0.663778i	−0.154948	+	0.987923i	$0.549521\pi$
$942$	−9.53111	−	16.5084i	−0.310540	−	0.537872i
$943$	−33.6987	+	58.3679i	−1.09738	+	1.90072i
$944$	−1.55903	+	0.567441i	−0.0507421	+	0.0184686i
$945$		0			0
$946$	−0.139519	+	0.791249i	−0.00453614	+	0.0257257i
$947$	−45.3917	−	16.5212i	−1.47503	−	0.536868i	−0.525571	−	0.850750i	$-0.676148\pi$
$947$	−45.3917	−	16.5212i	−1.47503	−	0.536868i	−0.949462	+	0.313881i	$0.898371\pi$
$948$	6.23913	−	5.23525i	0.202637	−	0.170033i
$949$	13.3305			0.432725
$950$		0			0
$951$	−6.92438			−0.224538
$952$	0.0599102	−	0.0502706i	0.00194170	−	0.00162928i
$953$	32.4750	+	11.8199i	1.05197	+	0.382885i	0.809405	−	0.587251i	$-0.199790\pi$
$953$	32.4750	+	11.8199i	1.05197	+	0.382885i	0.242562	+	0.970136i	$0.422012\pi$
$954$	4.49320	−	25.4822i	0.145473	−	0.825017i
$955$		0			0
$956$	8.06973	−	2.93714i	0.260994	−	0.0949940i
$957$	−3.20549	+	5.55208i	−0.103619	+	0.179473i
$958$	−3.69183	−	6.39443i	−0.119278	−	0.206595i
$959$	24.9169	+	20.9078i	0.804609	+	0.675147i
$960$		0			0
$961$	5.71591	+	9.90024i	0.184384	+	0.319363i
$962$	−6.38703	+	11.0627i	−0.205926	+	0.356675i
$963$	13.3345	−	4.85338i	0.429700	−	0.156398i
$964$	2.06778	+	11.7269i	0.0665986	+	0.377699i
$965$		0			0
$966$	14.6170	+	5.32015i	0.470294	+	0.171173i
$967$	5.87837	−	4.93254i	0.189036	−	0.158620i	−0.543358	−	0.839501i	$-0.682847\pi$
$967$	5.87837	−	4.93254i	0.189036	−	0.158620i	0.732394	+	0.680881i	$0.238403\pi$
$968$	9.67561			0.310986
$969$	−0.0575555	+	0.131634i	−0.00184895	+	0.00422869i
$970$		0			0
$971$	38.0452	−	31.9237i	1.22093	−	1.02448i	0.222151	−	0.975012i	$-0.428692\pi$
$971$	38.0452	−	31.9237i	1.22093	−	1.02448i	0.998776	−	0.0494674i	$-0.0157524\pi$
$972$	15.1686	+	5.52090i	0.486532	+	0.177083i
$973$	3.63487	−	20.6144i	0.116529	−	0.660867i
$974$	−4.59425	−	26.0553i	−0.147209	−	0.834866i
$975$		0			0
$976$	2.97847	−	5.15887i	0.0953386	−	0.165131i
$977$	−12.5824	−	21.7934i	−0.402548	−	0.697233i	0.591485	−	0.806316i	$-0.298542\pi$
$977$	−12.5824	−	21.7934i	−0.402548	−	0.697233i	−0.994033	+	0.109083i	$0.965209\pi$
$978$	6.61824	+	5.55336i	0.211628	+	0.177577i
$979$	−6.23942	−	5.23550i	−0.199413	−	0.167327i
$980$		0			0
$981$	−1.88108	+	3.25813i	−0.0600583	+	0.104024i
$982$	−7.54434	+	2.74591i	−0.240749	+	0.0876256i
$983$	−2.23197	−	12.6581i	−0.0711888	−	0.403732i	−0.999491	−	0.0319049i	$-0.989843\pi$
$983$	−2.23197	−	12.6581i	−0.0711888	−	0.403732i	0.928302	−	0.371827i	$-0.121268\pi$
$984$	1.29978	−	7.37139i	0.0414353	−	0.234991i
$985$		0			0
$986$	0.173798	−	0.145834i	0.00553485	−	0.00464429i
$987$	13.9876			0.445229
$988$	8.20893	+	5.45747i	0.261161	+	0.173625i
$989$	5.65526			0.179827
$990$		0			0
$991$	−20.4702	−	7.45056i	−0.650259	−	0.236675i	−0.00423369	−	0.999991i	$-0.501348\pi$
$991$	−20.4702	−	7.45056i	−0.650259	−	0.236675i	−0.646025	+	0.763316i	$0.723570\pi$
$992$	0.768149	−	4.35639i	0.0243888	−	0.138316i
$993$	3.15192	+	17.8754i	0.100023	+	0.567260i
$994$	19.6810	−	7.16329i	0.624243	−	0.227206i
$995$		0			0
$996$	2.46040	+	4.26154i	0.0779609	+	0.135032i
$997$	−17.0267	−	14.2871i	−0.539240	−	0.452477i	0.332038	−	0.943266i	$-0.392264\pi$
$997$	−17.0267	−	14.2871i	−0.539240	−	0.452477i	−0.871278	+	0.490790i	$0.836708\pi$
$998$	−16.6204	−	13.9461i	−0.526108	−	0.441457i
$999$	−13.1883	−	22.8428i	−0.417259	−	0.722713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.l.101.4		30
5.2	odd	4		190.2.p.a.139.4	✓	60
5.3	odd	4		190.2.p.a.139.7	yes	60
5.4	even	2		950.2.l.m.101.2		30
19.16	even	9	inner	950.2.l.l.301.4		30
95.54	even	18		950.2.l.m.301.2		30
95.73	odd	36		190.2.p.a.149.4	yes	60
95.92	odd	36		190.2.p.a.149.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.p.a.139.4	✓	60	5.2	odd	4
190.2.p.a.139.7	yes	60	5.3	odd	4
190.2.p.a.149.4	yes	60	95.73	odd	36
190.2.p.a.149.7	yes	60	95.92	odd	36
950.2.l.l.101.4		30	1.1	even	1	trivial
950.2.l.l.301.4		30	19.16	even	9	inner
950.2.l.m.101.2		30	5.4	even	2
950.2.l.m.301.2		30	95.54	even	18

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)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.845354 + 0.307684i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.845354 + 0.307684i) q^{6} +(1.06731 - 1.84863i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.67818 - 1.40816i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.845354 + 0.307684i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.845354 + 0.307684i) q^{6} +(1.06731 - 1.84863i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.67818 - 1.40816i) q^{9} +(-0.575411 - 0.996641i) q^{11} +(0.449804 - 0.779083i) q^{12} +(2.12509 - 0.773468i) q^{13} +(0.370673 + 2.10219i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(0.0280660 - 0.0235502i) q^{17} +2.19071 q^{18} +(-3.00691 + 3.15571i) q^{19} +(1.47105 - 1.23436i) q^{21} +(1.08142 + 0.393604i) q^{22} +(1.40659 - 7.97719i) q^{23} +(0.156215 + 0.885940i) q^{24} +(-1.13073 + 1.95849i) q^{26} +(-2.33480 - 4.04399i) q^{27} +(-1.63521 - 1.37211i) q^{28} +(-4.74371 - 3.98044i) q^{29} +(2.21180 - 3.83095i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.179776 - 1.01956i) q^{33} +(-0.00636204 + 0.0360809i) q^{34} +(-1.67818 + 1.40816i) q^{36} +5.64857 q^{37} +(0.274975 - 4.35022i) q^{38} +2.03443 q^{39} +(-7.81864 - 2.84575i) q^{41} +(-0.333460 + 1.89115i) q^{42} +(0.121234 + 0.687551i) q^{43} +(-1.08142 + 0.393604i) q^{44} +(4.05013 + 7.01502i) q^{46} +(5.57985 + 4.68205i) q^{47} +(-0.689139 - 0.578256i) q^{48} +(1.22170 + 2.11605i) q^{49} +(0.0309717 - 0.0112728i) q^{51} +(-0.392700 - 2.22711i) q^{52} +(2.05103 - 11.6320i) q^{53} +(4.38799 + 1.59710i) q^{54} +2.13462 q^{56} +(-3.51286 + 1.74252i) q^{57} +6.19247 q^{58} +(1.27093 - 1.06644i) q^{59} +(-1.03441 + 5.86645i) q^{61} +(0.768149 + 4.35639i) q^{62} +(-4.39431 + 1.59940i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.793077 + 0.665470i) q^{66} +(-7.48620 - 6.28167i) q^{67} +(-0.0183188 - 0.0317290i) q^{68} +(3.64352 - 6.31077i) q^{69} +(-1.70377 - 9.66255i) q^{71} +(0.380412 - 2.15742i) q^{72} +(5.53912 + 2.01607i) q^{73} +(-4.32706 + 3.63083i) q^{74} +(2.58562 + 3.50921i) q^{76} -2.45657 q^{77} +(-1.55847 + 1.30771i) q^{78} +(8.50752 + 3.09648i) q^{79} +(0.411775 + 2.33529i) q^{81} +(7.81864 - 2.84575i) q^{82} +(-2.73497 + 4.73712i) q^{83} +(-0.960160 - 1.66305i) q^{84} +(-0.534820 - 0.448767i) q^{86} +(-2.78540 - 4.82445i) q^{87} +(0.575411 - 0.996641i) q^{88} +(6.65071 - 2.42066i) q^{89} +(0.838265 - 4.75404i) q^{91} +(-7.61175 - 2.77045i) q^{92} +(3.04847 - 2.55797i) q^{93} -7.28398 q^{94} +0.899607 q^{96} +(6.34610 - 5.32501i) q^{97} +(-2.29604 - 0.835691i) q^{98} +(-0.437787 + 2.48281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) 30 * q - 12 * q^7 + 15 * q^8	\( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) 30 * q - 12 * q^7 + 15 * q^8 + 6 * q^11 + 6 * q^14 - 30 * q^18 + 24 * q^19 + 24 * q^21 + 3 * q^22 + 3 * q^23 + 3 * q^26 - 18 * q^27 + 3 * q^28 + 12 * q^29 - 30 * q^33 + 24 * q^37 - 12 * q^38 - 24 * q^39 - 3 * q^41 + 12 * q^42 + 6 * q^43 - 3 * q^44 + 48 * q^47 + 15 * q^49 - 90 * q^51 - 18 * q^53 + 18 * q^54 - 24 * q^56 - 42 * q^57 + 36 * q^58 - 18 * q^59 - 60 * q^61 - 24 * q^62 - 21 * q^63 - 15 * q^64 - 78 * q^66 - 30 * q^67 - 12 * q^68 + 24 * q^69 + 30 * q^73 - 9 * q^74 - 3 * q^76 + 78 * q^77 - 6 * q^79 + 60 * q^81 + 3 * q^82 - 42 * q^83 - 6 * q^84 + 12 * q^86 - 54 * q^87 - 6 * q^88 - 30 * q^89 - 6 * q^91 - 6 * q^92 + 72 * q^93 - 78 * q^94 - 42 * q^97 + 6 * q^98 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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