LMFDB - Embedded newform 403.2.l.c.129.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.26
Character	$\chi$	$=$	403.129
Dual form			403.2.l.c.25.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.84455i q^{2} +(-1.26208 + 2.18598i) q^{3} -1.40238 q^{4} +(3.26306 - 1.88393i) q^{5} +(-4.03216 - 2.32797i) q^{6} +(1.26392 + 0.729726i) q^{7} +1.10234i q^{8} +(-1.68567 - 2.91967i) q^{9} +O(q^{10})$	\(q+1.84455i q^{2} +(-1.26208 + 2.18598i) q^{3} -1.40238 q^{4} +(3.26306 - 1.88393i) q^{5} +(-4.03216 - 2.32797i) q^{6} +(1.26392 + 0.729726i) q^{7} +1.10234i q^{8} +(-1.68567 - 2.91967i) q^{9} +(3.47501 + 6.01889i) q^{10} +(-5.25125 + 3.03181i) q^{11} +(1.76991 - 3.06558i) q^{12} +(-3.59287 + 0.302144i) q^{13} +(-1.34602 + 2.33137i) q^{14} +9.51064i q^{15} -4.83809 q^{16} +(-0.00325426 + 0.00563654i) q^{17} +(5.38549 - 3.10931i) q^{18} +(3.85044 + 2.22305i) q^{19} +(-4.57605 + 2.64198i) q^{20} +(-3.19033 + 1.84194i) q^{21} +(-5.59234 - 9.68621i) q^{22} +4.95595 q^{23} +(-2.40970 - 1.39124i) q^{24} +(4.59837 - 7.96461i) q^{25} +(-0.557320 - 6.62724i) q^{26} +0.937324 q^{27} +(-1.77250 - 1.02335i) q^{28} +0.860193 q^{29} -17.5429 q^{30} +(-0.183683 + 5.56473i) q^{31} -6.71944i q^{32} -15.3055i q^{33} +(-0.0103969 - 0.00600266i) q^{34} +5.49901 q^{35} +(2.36395 + 4.09449i) q^{36} +(5.71667 + 3.30052i) q^{37} +(-4.10054 + 7.10235i) q^{38} +(3.87399 - 8.23527i) q^{39} +(2.07673 + 3.59700i) q^{40} +(-0.392528 + 0.226626i) q^{41} +(-3.39756 - 5.88474i) q^{42} +(2.15806 - 3.73786i) q^{43} +(7.36425 - 4.25175i) q^{44} +(-11.0009 - 6.35137i) q^{45} +9.14152i q^{46} -8.08647i q^{47} +(6.10604 - 10.5760i) q^{48} +(-2.43500 - 4.21754i) q^{49} +(14.6912 + 8.48194i) q^{50} +(-0.00821425 - 0.0142275i) q^{51} +(5.03857 - 0.423720i) q^{52} +(-0.367881 - 0.637188i) q^{53} +1.72895i q^{54} +(-11.4234 + 19.7859i) q^{55} +(-0.804407 + 1.39327i) q^{56} +(-9.71910 + 5.61133i) q^{57} +1.58667i q^{58} +(7.33401 + 4.23429i) q^{59} -13.3375i q^{60} +9.39041 q^{61} +(-10.2645 - 0.338814i) q^{62} -4.92031i q^{63} +2.71819 q^{64} +(-11.1545 + 7.75462i) q^{65} +28.2318 q^{66} +(12.5249 - 7.23126i) q^{67} +(0.00456371 - 0.00790458i) q^{68} +(-6.25479 + 10.8336i) q^{69} +10.1432i q^{70} +(-11.6748 + 6.74046i) q^{71} +(3.21847 - 1.85818i) q^{72} +(4.05332 - 2.34019i) q^{73} +(-6.08799 + 10.5447i) q^{74} +(11.6070 + 20.1039i) q^{75} +(-5.39979 - 3.11757i) q^{76} -8.84957 q^{77} +(15.1904 + 7.14579i) q^{78} +(2.85074 - 4.93762i) q^{79} +(-15.7870 + 9.11461i) q^{80} +(3.87404 - 6.71003i) q^{81} +(-0.418025 - 0.724040i) q^{82} +(2.45139 - 1.41531i) q^{83} +(4.47406 - 2.58310i) q^{84} +0.0245232i q^{85} +(6.89469 + 3.98065i) q^{86} +(-1.08563 + 1.88037i) q^{87} +(-3.34209 - 5.78867i) q^{88} +8.26914i q^{89} +(11.7154 - 20.2917i) q^{90} +(-4.76159 - 2.23993i) q^{91} -6.95013 q^{92} +(-11.9326 - 7.42464i) q^{93} +14.9159 q^{94} +16.7523 q^{95} +(14.6886 + 8.48044i) q^{96} +5.36866i q^{97} +(7.77948 - 4.49149i) q^{98} +(17.7038 + 10.2213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.84455i			1.30430i	0.758091	+	0.652148i	$0.226132\pi$
$2$			1.84455i			1.30430i	−0.758091	+	0.652148i	$0.773868\pi$
$3$	−1.26208	+	2.18598i	−0.728660	+	1.26208i	0.228790	+	0.973476i	$0.426523\pi$
$3$	−1.26208	+	2.18598i	−0.728660	+	1.26208i	−0.957450	+	0.288600i	$0.906810\pi$
$4$	−1.40238			−0.701190
$5$	3.26306	−	1.88393i	1.45928	−	0.842518i	0.460308	−	0.887759i	$-0.347739\pi$
$5$	3.26306	−	1.88393i	1.45928	−	0.842518i	0.998976	+	0.0452409i	$0.0144055\pi$
$6$	−4.03216	−	2.32797i	−1.64612	−	0.950389i
$7$	1.26392	+	0.729726i	0.477718	+	0.275811i	0.719465	−	0.694529i	$-0.244387\pi$
$7$	1.26392	+	0.729726i	0.477718	+	0.275811i	−0.241747	+	0.970339i	$0.577720\pi$
$8$			1.10234i			0.389736i
$9$	−1.68567	−	2.91967i	−0.561890	−	0.973223i
$10$	3.47501	+	6.01889i	1.09889	+	1.90334i
$11$	−5.25125	+	3.03181i	−1.58331	+	0.914125i	−0.588939	+	0.808177i	$0.700454\pi$
$11$	−5.25125	+	3.03181i	−1.58331	+	0.914125i	−0.994372	+	0.105948i	$0.966212\pi$
$12$	1.76991	−	3.06558i	0.510929	−	0.884955i
$13$	−3.59287	+	0.302144i	−0.996483	+	0.0837995i
$13$	−3.59287	+	0.302144i	−0.996483	+	0.0837995i
$14$	−1.34602	+	2.33137i	−0.359739	+	0.623086i
$15$			9.51064i			2.45564i
$16$	−4.83809			−1.20952
$17$	−0.00325426	+	0.00563654i	−0.000789274	+	0.00136706i	−0.866420	−	0.499316i	$-0.833585\pi$
$17$	−0.00325426	+	0.00563654i	−0.000789274	+	0.00136706i	0.865630	+	0.500683i	$0.166918\pi$
$18$	5.38549	−	3.10931i	1.26937	−	0.732872i
$19$	3.85044	+	2.22305i	0.883352	+	0.510004i	0.871762	−	0.489929i	$-0.162977\pi$
$19$	3.85044	+	2.22305i	0.883352	+	0.510004i	0.0115898	+	0.999933i	$0.496311\pi$
$20$	−4.57605	+	2.64198i	−1.02324	+	0.590766i
$21$	−3.19033	+	1.84194i	−0.696188	+	0.401944i
$22$	−5.59234	−	9.68621i	−1.19229	−	2.06511i
$23$	4.95595			1.03339			0.516694	−	0.856170i	$-0.327163\pi$
$23$	4.95595			1.03339			0.516694	+	0.856170i	$0.327163\pi$
$24$	−2.40970	−	1.39124i	−0.491877	−	0.283985i
$25$	4.59837	−	7.96461i	0.919674	−	1.59292i
$26$	−0.557320	−	6.62724i	−0.109299	−	1.29971i
$27$	0.937324			0.180388
$28$	−1.77250	−	1.02335i	−0.334971	−	0.193396i
$29$	0.860193			0.159734			0.0798670	−	0.996806i	$-0.474550\pi$
$29$	0.860193			0.159734			0.0798670	+	0.996806i	$0.474550\pi$
$30$	−17.5429			−3.20288
$31$	−0.183683	+	5.56473i	−0.0329905	+	0.999456i
$31$	−0.183683	+	5.56473i	−0.0329905	+	0.999456i
$32$		−	6.71944i		−	1.18784i
$33$		−	15.3055i		−	2.66434i
$34$	−0.0103969	−	0.00600266i	−0.00178306	−	0.00102945i
$35$	5.49901			0.929502
$36$	2.36395	+	4.09449i	0.393992	+	0.682414i
$37$	5.71667	+	3.30052i	0.939815	+	0.542602i	0.889902	−	0.456151i	$-0.150772\pi$
$37$	5.71667	+	3.30052i	0.939815	+	0.542602i	0.0499126	+	0.998754i	$0.484106\pi$
$38$	−4.10054	+	7.10235i	−0.665196	+	1.15215i
$39$	3.87399	−	8.23527i	0.620336	−	1.31870i
$40$	2.07673	+	3.59700i	0.328360	+	0.568736i
$41$	−0.392528	+	0.226626i	−0.0613026	+	0.0353931i	−0.530338	−	0.847786i	$-0.677935\pi$
$41$	−0.392528	+	0.226626i	−0.0613026	+	0.0353931i	0.469035	+	0.883179i	$0.344602\pi$
$42$	−3.39756	−	5.88474i	−0.524255	−	0.908036i
$43$	2.15806	−	3.73786i	0.329100	−	0.570019i	−0.653233	−	0.757157i	$-0.726588\pi$
$43$	2.15806	−	3.73786i	0.329100	−	0.570019i	0.982334	+	0.187138i	$0.0599212\pi$
$44$	7.36425	−	4.25175i	1.11020	−	0.640976i
$45$	−11.0009	−	6.35137i	−1.63992	−	0.946806i
$46$			9.14152i			1.34784i
$47$		−	8.08647i		−	1.17953i	−0.807574	−	0.589766i	$-0.799220\pi$
$47$		−	8.08647i		−	1.17953i	0.807574	−	0.589766i	$-0.200780\pi$
$48$	6.10604	−	10.5760i	0.881330	−	1.52651i
$49$	−2.43500	−	4.21754i	−0.347857	−	0.602506i
$50$	14.6912	+	8.48194i	2.07764	+	1.19953i
$51$	−0.00821425	−	0.0142275i	−0.00115022	−	0.00199225i
$52$	5.03857	−	0.423720i	0.698724	−	0.0587594i
$53$	−0.367881	−	0.637188i	−0.0505323	−	0.0875245i	0.839653	−	0.543123i	$-0.182758\pi$
$53$	−0.367881	−	0.637188i	−0.0505323	−	0.0875245i	−0.890185	+	0.455599i	$0.849425\pi$
$54$			1.72895i			0.235280i
$55$	−11.4234	+	19.7859i	−1.54033	+	2.66794i
$56$	−0.804407	+	1.39327i	−0.107493	+	0.186184i
$57$	−9.71910	+	5.61133i	−1.28733	+	0.743238i
$58$			1.58667i			0.208340i
$59$	7.33401	+	4.23429i	0.954807	+	0.551258i	0.894571	−	0.446926i	$-0.147481\pi$
$59$	7.33401	+	4.23429i	0.954807	+	0.551258i	0.0602361	+	0.998184i	$0.480815\pi$
$60$		−	13.3375i		−	1.72187i
$61$	9.39041			1.20232			0.601159	−	0.799129i	$-0.294706\pi$
$61$	9.39041			1.20232			0.601159	+	0.799129i	$0.294706\pi$
$62$	−10.2645	−	0.338814i	−1.30359	−	0.0430294i
$63$		−	4.92031i		−	0.619901i
$64$	2.71819			0.339773
$65$	−11.1545	+	7.75462i	−1.38355	+	0.961842i
$66$	28.2318			3.47510
$67$	12.5249	−	7.23126i	1.53016	−	0.883440i	0.530809	−	0.847492i	$-0.321888\pi$
$67$	12.5249	−	7.23126i	1.53016	−	0.883440i	0.999354	−	0.0359478i	$-0.0114450\pi$
$68$	0.00456371	−	0.00790458i	0.000553431	−	0.000958571i
$69$	−6.25479	+	10.8336i	−0.752988	+	1.30421i
$70$			10.1432i			1.21235i
$71$	−11.6748	+	6.74046i	−1.38555	+	0.799945i	−0.992809	−	0.119706i	$-0.961805\pi$
$71$	−11.6748	+	6.74046i	−1.38555	+	0.799945i	−0.392736	+	0.919651i	$0.628471\pi$
$72$	3.21847	−	1.85818i	0.379300	−	0.218989i
$73$	4.05332	−	2.34019i	0.474406	−	0.273898i	−0.243676	−	0.969857i	$-0.578354\pi$
$73$	4.05332	−	2.34019i	0.474406	−	0.273898i	0.718082	+	0.695958i	$0.245020\pi$
$74$	−6.08799	+	10.5447i	−0.707715	+	1.22580i
$75$	11.6070	+	20.1039i	1.34026	+	2.32140i
$76$	−5.39979	−	3.11757i	−0.619398	−	0.357610i
$77$	−8.84957			−1.00850
$78$	15.1904	+	7.14579i	1.71997	+	0.809102i
$79$	2.85074	−	4.93762i	0.320733	−	0.555526i	−0.659907	−	0.751348i	$-0.729404\pi$
$79$	2.85074	−	4.93762i	0.320733	−	0.555526i	0.980639	+	0.195822i	$0.0627375\pi$
$80$	−15.7870	+	9.11461i	−1.76504	+	1.01904i
$81$	3.87404	−	6.71003i	0.430449	−	0.745559i
$82$	−0.418025	−	0.724040i	−0.0461631	−	0.0799568i
$83$	2.45139	−	1.41531i	0.269075	−	0.155350i	−0.359392	−	0.933187i	$-0.617016\pi$
$83$	2.45139	−	1.41531i	0.269075	−	0.155350i	0.628467	+	0.777836i	$0.283683\pi$
$84$	4.47406	−	2.58310i	0.488160	−	0.281839i
$85$			0.0245232i			0.00265991i
$86$	6.89469	+	3.98065i	0.743473	+	0.429245i
$87$	−1.08563	+	1.88037i	−0.116392	+	0.201596i
$88$	−3.34209	−	5.78867i	−0.356268	−	0.617074i
$89$			8.26914i			0.876528i	0.898846	+	0.438264i	$0.144406\pi$
$89$			8.26914i			0.876528i	−0.898846	+	0.438264i	$0.855594\pi$
$90$	11.7154	−	20.2917i	1.23492	−	2.13894i
$91$	−4.76159	−	2.23993i	−0.499151	−	0.234808i
$92$	−6.95013			−0.724601
$93$	−11.9326	−	7.42464i	−1.23735	−	0.769900i
$94$	14.9159			1.53846
$95$	16.7523			1.71875
$96$	14.6886	+	8.48044i	1.49914	+	0.865531i
$97$			5.36866i			0.545105i	0.962141	+	0.272553i	$0.0878678\pi$
$97$			5.36866i			0.545105i	−0.962141	+	0.272553i	$0.912132\pi$
$98$	7.77948	−	4.49149i	0.785847	−	0.453709i
$99$	17.7038	+	10.2213i	1.77929	+	1.02728i
$100$	−6.44867	+	11.1694i	−0.644867	+	1.11694i
$101$	9.17334			0.912782			0.456391	−	0.889779i	$-0.349142\pi$
$101$	9.17334			0.912782			0.456391	+	0.889779i	$0.349142\pi$
$102$	0.0262434	−	0.0151516i	0.00259848	−	0.00150023i
$103$	−2.26560	−	3.92413i	−0.223236	−	0.386656i	0.732553	−	0.680710i	$-0.238329\pi$
$103$	−2.26560	−	3.92413i	−0.223236	−	0.386656i	−0.955789	+	0.294054i	$0.904995\pi$
$104$	−0.333065	−	3.96057i	−0.0326597	−	0.388366i
$105$	−6.94017	+	12.0207i	−0.677291	+	1.17310i
$106$	1.17533	−	0.678576i	0.114158	−	0.0659091i
$107$	−4.24679	+	7.35566i	−0.410553	+	0.711099i	−0.994950	−	0.100369i	$-0.967998\pi$
$107$	−4.24679	+	7.35566i	−0.410553	+	0.711099i	0.584397	+	0.811468i	$0.301331\pi$
$108$	−1.31449			−0.126486
$109$			7.23969i			0.693436i	0.937969	+	0.346718i	$0.112704\pi$
$109$			7.23969i			0.693436i	−0.937969	+	0.346718i	$0.887296\pi$
$110$	−36.4963	−	21.0711i	−3.47978	−	2.00905i
$111$	−14.4297	+	8.33102i	−1.36961	+	0.790745i
$112$	−6.11497	−	3.53048i	−0.577811	−	0.333599i
$113$	−8.67717	−	15.0293i	−0.816280	−	1.41384i	−0.908405	−	0.418091i	$-0.862699\pi$
$113$	−8.67717	−	15.0293i	−0.816280	−	1.41384i	0.0921256	−	0.995747i	$-0.470634\pi$
$114$	−10.3504	−	17.9274i	−0.969403	−	1.67906i
$115$	16.1716	−	9.33666i	1.50801	−	0.870648i
$116$	−1.20632			−0.112004
$117$	6.93855	+	9.98067i	0.641470	+	0.922713i
$118$	−7.81038	+	13.5280i	−0.719004	+	1.24535i
$119$	−0.00822627	+	0.00474944i	−0.000754101	+	0.000435380i
$120$	−10.4840			−0.957051
$121$	12.8837	−	22.3153i	1.17125	−	2.02866i
$122$			17.3211i			1.56818i
$123$		−	1.14408i		−	0.103158i
$124$	0.257594	−	7.80388i	0.0231326	−	0.700809i
$125$		−	15.8127i		−	1.41433i
$126$	9.07579			0.808535
$127$	1.25273	−	2.16980i	0.111162	−	0.192539i	−0.805077	−	0.593170i	$-0.797876\pi$
$127$	1.25273	−	2.16980i	0.111162	−	0.192539i	0.916239	+	0.400632i	$0.131209\pi$
$128$		−	8.42503i		−	0.744674i
$129$	5.44726	+	9.43493i	0.479604	+	0.830699i
$130$	−14.3038	−	20.5751i	−1.25453	−	1.80456i
$131$	−5.70997	+	9.88996i	−0.498882	+	0.864090i	−0.999999	−	0.00129000i	$-0.999589\pi$
$131$	−5.70997	+	9.88996i	−0.498882	+	0.864090i	0.501117	+	0.865380i	$0.332923\pi$
$132$			21.4641i			1.86821i
$133$	3.24444	+	5.61954i	0.281329	+	0.487276i
$134$	13.3385	+	23.1029i	1.15227	+	1.99579i
$135$	3.05854	−	1.76585i	0.263238	−	0.151980i
$136$	−0.00621339	−	0.00358731i	−0.000532794	−	0.000307609i
$137$	−4.30508	+	2.48554i	−0.367808	+	0.212354i	−0.672500	−	0.740097i	$-0.734780\pi$
$137$	−4.30508	+	2.48554i	−0.367808	+	0.212354i	0.304693	+	0.952451i	$0.401446\pi$
$138$	−19.9832	−	11.5373i	−1.70108	−	0.982120i
$139$	7.37172			0.625261			0.312631	−	0.949875i	$-0.398790\pi$
$139$	7.37172			0.625261			0.312631	+	0.949875i	$0.398790\pi$
$140$	−7.71170			−0.651758
$141$	17.6769	+	10.2057i	1.48866	+	0.859478i
$142$	−12.4331	−	21.5348i	−1.04337	−	1.80716i
$143$	17.9510	−	12.4795i	1.50114	−	1.04359i
$144$	8.15543	+	14.1256i	0.679619	+	1.17713i
$145$	2.80686	−	1.62054i	0.233097	−	0.134579i
$146$	4.31660	+	7.47658i	0.357245	+	0.618766i
$147$	12.2926			1.01388
$148$	−8.01695	−	4.62859i	−0.658989	−	0.380468i
$149$	−4.37357	−	2.52508i	−0.358297	−	0.206863i	0.310037	−	0.950725i	$-0.399659\pi$
$149$	−4.37357	−	2.52508i	−0.358297	−	0.206863i	−0.668333	+	0.743862i	$0.732992\pi$
$150$	−37.0827	+	21.4097i	−3.02779	+	1.74810i
$151$		−	18.9378i		−	1.54113i	−0.637359	−	0.770567i	$-0.719973\pi$
$151$		−	18.9378i		−	1.54113i	0.637359	−	0.770567i	$-0.280027\pi$
$152$	−2.45056	+	4.24450i	−0.198767	+	0.344274i
$153$	0.0219425			0.00177394
$154$		−	16.3235i		−	1.31539i
$155$	9.88419	+	18.5041i	0.793917	+	1.48629i
$156$	−5.43281	+	11.5490i	−0.434973	+	0.924658i
$157$	−11.0000			−0.877893			−0.438946	−	0.898513i	$-0.644648\pi$
$157$	−11.0000			−0.877893			−0.438946	+	0.898513i	$0.644648\pi$
$158$	9.10771	+	5.25834i	0.724571	+	0.418331i
$159$	1.85717			0.147283
$160$	−12.6589	−	21.9259i	−1.00078	−	1.73340i
$161$	6.26394	+	3.61649i	0.493668	+	0.285019i
$162$	12.3770	+	7.14588i	0.972430	+	0.561433i
$163$		−	11.1946i		−	0.876829i	−0.898773	−	0.438414i	$-0.855540\pi$
$163$		−	11.1946i		−	0.876829i	0.898773	−	0.438414i	$-0.144460\pi$
$164$	0.550474	−	0.317816i	0.0429848	−	0.0248173i
$165$	−28.8345	−	49.9427i	−2.24476	−	3.88804i
$166$	2.61061	+	4.52172i	0.202623	+	0.350953i
$167$	−6.43455	−	3.71499i	−0.497920	−	0.287474i	0.229934	−	0.973206i	$-0.426149\pi$
$167$	−6.43455	−	3.71499i	−0.497920	−	0.287474i	−0.727854	+	0.685732i	$0.759482\pi$
$168$	−2.03045	−	3.51684i	−0.156652	−	0.271330i
$169$	12.8174	−	2.17112i	0.985955	−	0.167010i
$170$	−0.0452343			−0.00346931
$171$		−	14.9894i		−	1.14626i
$172$	−3.02642	+	5.24190i	−0.230762	+	0.399691i
$173$	6.28007	+	10.8774i	0.477465	+	0.826993i	0.999666	−	0.0258288i	$-0.00822248\pi$
$173$	6.28007	+	10.8774i	0.477465	+	0.826993i	−0.522202	+	0.852822i	$0.674889\pi$
$174$	−3.46844	−	2.00250i	−0.262941	−	0.151809i
$175$	11.6240	−	6.71110i	0.878690	−	0.507312i
$176$	25.4060	−	14.6682i	1.91505	−	1.10565i
$177$	−18.5122	+	10.6880i	−1.39146	+	0.803359i
$178$	−15.2529			−1.14325
$179$	−9.51037	+	16.4725i	−0.710839	+	1.23121i	0.253704	+	0.967282i	$0.418351\pi$
$179$	−9.51037	+	16.4725i	−0.710839	+	1.23121i	−0.964543	+	0.263927i	$0.914982\pi$
$180$	15.4274	+	8.90703i	1.14989	+	0.663891i
$181$	−5.39144	−	9.33826i	−0.400743	−	0.694107i	0.593073	−	0.805149i	$-0.297915\pi$
$181$	−5.39144	−	9.33826i	−0.400743	−	0.694107i	−0.993816	+	0.111042i	$0.964581\pi$
$182$	4.13166	−	8.78302i	0.306259	−	0.651041i
$183$	−11.8514	+	20.5272i	−0.876081	+	1.51742i
$184$			5.46315i			0.402749i
$185$	24.8718			1.82861
$186$	13.6952	−	22.0103i	1.00418	−	1.61387i
$187$		−	0.0394652i		−	0.00288598i
$188$			11.3403i			0.827077i
$189$	1.18471	+	0.683990i	0.0861747	+	0.0497530i
$190$			30.9005i			2.24176i
$191$	10.6337	+	18.4181i	0.769428	+	1.33269i	0.937873	+	0.346977i	$0.112792\pi$
$191$	10.6337	+	18.4181i	0.769428	+	1.33269i	−0.168445	+	0.985711i	$0.553875\pi$
$192$	−3.43056	+	5.94190i	−0.247579	+	0.428820i
$193$	22.0760	+	12.7456i	1.58907	+	0.917448i	0.993461	+	0.114172i	$0.0364215\pi$
$193$	22.0760	+	12.7456i	1.58907	+	0.917448i	0.595606	+	0.803277i	$0.296912\pi$
$194$	−9.90279			−0.710979
$195$	−2.87358	−	34.1705i	−0.205781	−	2.44700i
$196$	3.41480	+	5.91460i	0.243914	+	0.422471i
$197$	15.7130	−	9.07192i	1.11951	−	0.646347i	0.178232	−	0.983989i	$-0.442962\pi$
$197$	15.7130	−	9.07192i	1.11951	−	0.646347i	0.941275	+	0.337641i	$0.109629\pi$
$198$	−18.8537	+	32.6555i	−1.33987	+	2.32073i
$199$	−2.26858	−	3.92929i	−0.160815	−	0.278540i	0.774346	−	0.632762i	$-0.218079\pi$
$199$	−2.26858	−	3.92929i	−0.160815	−	0.278540i	−0.935161	+	0.354222i	$0.884746\pi$
$200$	8.77972	+	5.06897i	0.620820	+	0.358430i
$201$			36.5056i			2.57491i
$202$			16.9207i			1.19054i
$203$	1.08722	+	0.627706i	0.0763078	+	0.0440563i
$204$	0.0115195	+	0.0199524i	0.000806526	+	0.00139694i
$205$	−0.853895	+	1.47899i	−0.0596386	+	0.103297i
$206$	7.23827	−	4.17902i	0.504314	−	0.291166i
$207$	−8.35411	−	14.4697i	−0.580651	−	1.00572i
$208$	17.3826	−	1.46180i	1.20527	−	0.101357i
$209$	−26.9595			−1.86483
$210$	−22.1729	−	12.8015i	−1.53007	−	0.883388i
$211$	−3.08388	+	5.34144i	−0.212303	+	0.367720i	−0.952435	−	0.304742i	$-0.901430\pi$
$211$	−3.08388	+	5.34144i	−0.212303	+	0.367720i	0.740132	+	0.672462i	$0.234763\pi$
$212$	0.515909	+	0.893580i	0.0354328	+	0.0613713i
$213$		−	34.0279i		−	2.33155i
$214$	−13.5679	−	7.83344i	−0.927484	−	0.535483i
$215$		−	16.2625i		−	1.10909i
$216$			1.03325i			0.0703038i
$217$	−4.29289	+	6.89936i	−0.291421	+	0.468359i
$218$	−13.3540			−0.904447
$219$			11.8140i			0.798315i
$220$	16.0200	−	27.7474i	1.08007	−	1.87073i
$221$	0.00998909	−	0.0212346i	0.000671939	−	0.00142840i
$222$	−15.3670	−	26.6164i	−1.03137	−	1.78638i
$223$	−14.5274	−	8.38740i	−0.972826	−	0.561662i	−0.0727296	−	0.997352i	$-0.523171\pi$
$223$	−14.5274	−	8.38740i	−0.972826	−	0.561662i	−0.900097	+	0.435690i	$0.856504\pi$
$224$	4.90335	−	8.49285i	0.327619	−	0.567453i
$225$	−31.0054			−2.06702
$226$	27.7224	−	16.0055i	1.84406	−	1.06467i
$227$	−23.1535	+	13.3677i	−1.53675	+	0.887243i	−0.537724	+	0.843121i	$0.680716\pi$
$227$	−23.1535	+	13.3677i	−1.53675	+	0.887243i	−0.999026	+	0.0441224i	$0.985951\pi$
$228$	13.6299	−	7.86921i	0.902661	−	0.521151i
$229$	−11.5032	−	6.64135i	−0.760150	−	0.438873i	0.0691997	−	0.997603i	$-0.477955\pi$
$229$	−11.5032	−	6.64135i	−0.760150	−	0.438873i	−0.829350	+	0.558730i	$0.811289\pi$
$230$	17.2220	+	29.8293i	1.13558	+	1.96689i
$231$	11.1688	−	19.3450i	0.734855	−	1.27281i
$232$			0.948227i			0.0622541i
$233$	4.74614			0.310930			0.155465	−	0.987841i	$-0.450312\pi$
$233$	4.74614			0.310930			0.155465	+	0.987841i	$0.450312\pi$
$234$	−18.4099	+	12.7985i	−1.20349	+	0.836667i
$235$	−15.2343	−	26.3866i	−0.993778	−	1.72127i
$236$	−10.2851	−	5.93809i	−0.669501	−	0.386537i
$237$	7.19569	+	12.4633i	0.467410	+	0.809579i
$238$	−0.00876060	−	0.0151738i	−0.000567865	−	0.000983571i
$239$	−17.6328	+	10.1803i	−1.14057	+	0.658508i	−0.946572	−	0.322494i	$-0.895479\pi$
$239$	−17.6328	+	10.1803i	−1.14057	+	0.658508i	−0.193998	+	0.981002i	$0.562146\pi$
$240$		−	46.0133i		−	2.97015i
$241$	−14.8743	−	8.58771i	−0.958141	−	0.553183i	−0.0625404	−	0.998042i	$-0.519920\pi$
$241$	−14.8743	−	8.58771i	−0.958141	−	0.553183i	−0.895600	+	0.444860i	$0.853254\pi$
$242$	41.1618	+	23.7648i	2.64598	+	1.52766i
$243$	11.1846	+	19.3724i	0.717496	+	1.24274i
$244$	−13.1689			−0.843054
$245$	−15.8911	−	9.17473i	−1.01524	−	0.586152i
$246$	2.11032			0.134549
$247$	−14.5058	−	6.82376i	−0.922983	−	0.434185i
$248$	−6.13424	−	0.202482i	−0.389524	−	0.0128576i
$249$			7.14491i			0.452790i
$250$	29.1674			1.84471
$251$	6.35149	−	11.0011i	0.400903	−	0.694384i	−0.592932	−	0.805252i	$-0.702030\pi$
$251$	6.35149	−	11.0011i	0.400903	−	0.694384i	0.993835	+	0.110868i	$0.0353632\pi$
$252$			6.90015i			0.434669i
$253$	−26.0249	+	15.0255i	−1.63617	+	0.944645i
$254$	4.00231	+	2.31074i	0.251127	+	0.144989i
$255$	−0.0536071	−	0.0309501i	−0.00335701	−	0.00193817i
$256$	20.9768			1.31105
$257$	−8.05542	−	13.9524i	−0.502483	−	0.870326i	−0.999996	−	0.00286970i	$-0.999087\pi$
$257$	−8.05542	−	13.9524i	−0.502483	−	0.870326i	0.497513	−	0.867457i	$-0.334247\pi$
$258$	−17.4032	+	10.0478i	−1.08348	+	0.625547i
$259$	4.81696	+	8.34321i	0.299311	+	0.518422i
$260$	15.6429	−	10.8749i	0.970131	−	0.674434i
$261$	−1.45000	−	2.51148i	−0.0897529	−	0.155457i
$262$	−18.2426	−	10.5324i	−1.12703	−	0.650691i
$263$	−4.79915			−0.295928			−0.147964	−	0.988993i	$-0.547272\pi$
$263$	−4.79915			−0.295928			−0.147964	+	0.988993i	$0.547272\pi$
$264$	16.8719			1.03839
$265$	−2.40083	−	1.38612i	−0.147482	−	0.0851488i
$266$	−10.3655	+	5.98455i	−0.635552	+	0.366936i
$267$	−18.0762	−	10.4363i	−1.10624	−	0.638690i
$268$	−17.5647	+	10.1410i	−1.07293	+	0.619459i
$269$	−6.82814	−	11.8267i	−0.416319	−	0.721086i	0.579247	−	0.815152i	$-0.303347\pi$
$269$	−6.82814	−	11.8267i	−0.416319	−	0.721086i	−0.995566	+	0.0940666i	$0.970013\pi$
$270$	3.25721	+	5.64165i	0.198227	+	0.343340i
$271$		−	1.75331i		−	0.106506i	−0.998581	−	0.0532529i	$-0.983041\pi$
$271$		−	1.75331i		−	0.106506i	0.998581	−	0.0532529i	$-0.0169590\pi$
$272$	0.0157444	−	0.0272701i	0.000954645	−	0.00165349i
$273$	10.9059	−	7.58179i	0.660056	−	0.458871i
$274$	−4.58471	−	7.94095i	−0.276972	−	0.479730i
$275$			55.7655i			3.36279i
$276$	8.77159	−	15.1928i	0.527988	−	0.914502i
$277$	−3.01250			−0.181004			−0.0905019	−	0.995896i	$-0.528847\pi$
$277$	−3.01250			−0.181004			−0.0905019	+	0.995896i	$0.528847\pi$
$278$			13.5975i			0.815526i
$279$	16.5568	−	8.84402i	0.991230	−	0.529477i
$280$			6.06178i			0.362261i
$281$			1.71530i			0.102326i	0.998690	+	0.0511632i	$0.0162929\pi$
$281$			1.71530i			0.102326i	−0.998690	+	0.0511632i	$0.983707\pi$
$282$	−18.8250	+	32.6059i	−1.12101	+	1.94165i
$283$	7.35168			0.437012			0.218506	−	0.975836i	$-0.429882\pi$
$283$	7.35168			0.437012			0.218506	+	0.975836i	$0.429882\pi$
$284$	16.3725	−	9.45269i	0.971531	−	0.560914i
$285$	−21.1427	+	36.6202i	−1.25238	+	2.16919i
$286$	23.0192	+	33.1116i	1.36115	+	1.95793i
$287$	−0.661501			−0.0390472
$288$	−19.6185	+	11.3268i	−1.15603	+	0.667436i
$289$	8.49998	+	14.7224i	0.499999	+	0.866023i
$290$	2.98918	+	5.17741i	0.175531	+	0.304028i
$291$	−11.7358	−	6.77566i	−0.687964	−	0.397196i
$292$	−5.68430	+	3.28183i	−0.332649	+	0.192055i
$293$	−8.14501	−	4.70252i	−0.475837	−	0.274724i	0.242843	−	0.970066i	$-0.421920\pi$
$293$	−8.14501	−	4.70252i	−0.475837	−	0.274724i	−0.718680	+	0.695341i	$0.755253\pi$
$294$			22.6744i			1.32240i
$295$	31.9084			1.85778
$296$	−3.63830	+	6.30172i	−0.211472	+	0.366280i
$297$	−4.92212	+	2.84179i	−0.285611	+	0.164897i
$298$	4.65765	−	8.06729i	0.269811	−	0.467326i
$299$	−17.8061	+	1.49741i	−1.02975	+	0.0865974i
$300$	−16.2774	−	28.1933i	−0.939777	−	1.62774i
$301$	5.45523	−	3.14958i	0.314434	−	0.181539i
$302$	34.9317			2.01010
$303$	−11.5775	+	20.0527i	−0.665107	+	1.15200i
$304$	−18.6288	−	10.7553i	−1.06843	−	0.616861i
$305$	30.6415	−	17.6909i	1.75452	−	1.01298i
$306$			0.0404740i			0.00231375i
$307$	17.8619	+	10.3126i	1.01943	+	0.588570i	0.913940	−	0.405849i	$-0.133024\pi$
$307$	17.8619	+	10.3126i	1.01943	+	0.588570i	0.105494	+	0.994420i	$0.466358\pi$
$308$	12.4105			0.707152
$309$	11.4374			0.650652
$310$	−34.1318	+	18.2319i	−1.93856	+	1.03550i
$311$	−21.0994			−1.19644			−0.598220	−	0.801332i	$-0.704125\pi$
$311$	−21.0994			−1.19644			−0.598220	+	0.801332i	$0.704125\pi$
$312$	9.07807	+	4.27046i	0.513945	+	0.241767i
$313$	2.46526	−	4.26996i	0.139345	−	0.241352i	−0.787904	−	0.615798i	$-0.788834\pi$
$313$	2.46526	−	4.26996i	0.139345	−	0.241352i	0.927249	+	0.374446i	$0.122167\pi$
$314$		−	20.2900i		−	1.14503i
$315$	−9.26952	−	16.0553i	−0.522278	−	0.904612i
$316$	−3.99782	+	6.92442i	−0.224895	+	0.389529i
$317$	−2.97665	−	1.71857i	−0.167185	−	0.0965245i	0.414073	−	0.910244i	$-0.364106\pi$
$317$	−2.97665	−	1.71857i	−0.167185	−	0.0965245i	−0.581258	+	0.813719i	$0.697439\pi$
$318$			3.42566i			0.192101i
$319$	−4.51709	+	2.60794i	−0.252908	+	0.146017i
$320$	8.86961	−	5.12087i	0.495826	−	0.286265i
$321$	−10.7196	−	18.5668i	−0.598307	−	1.03630i
$322$	−6.67081	+	11.5542i	−0.371750	+	0.643889i
$323$	−0.0250607	+	0.0144688i	−0.00139441	+	0.000805065i
$324$	−5.43288	+	9.41002i	−0.301827	+	0.522779i
$325$	−14.1149	+	30.0052i	−0.782953	+	1.66439i
$326$	20.6490			1.14364
$327$	−15.8258	−	9.13703i	−0.875169	−	0.505279i
$328$	−0.249820	−	0.432700i	−0.0137940	−	0.0238919i
$329$	5.90091	−	10.2207i	0.325328	−	0.563484i
$330$	92.1221	−	53.1867i	5.07115	−	2.92783i
$331$	24.4806	−	14.1339i	1.34558	−	0.776869i	0.357957	−	0.933738i	$-0.383474\pi$
$331$	24.4806	−	14.1339i	1.34558	−	0.776869i	0.987619	+	0.156870i	$0.0501402\pi$
$332$	−3.43778	+	1.98480i	−0.188673	+	0.108930i
$333$		−	22.2544i		−	1.21953i
$334$	6.85249	−	11.8689i	0.374952	−	0.649436i
$335$	27.2464	−	47.1921i	1.48863	−	2.57838i
$336$	15.4351	−	8.91147i	0.842055	−	0.486161i
$337$	31.7427			1.72914			0.864568	−	0.502515i	$-0.167592\pi$
$337$	31.7427			1.72914			0.864568	+	0.502515i	$0.167592\pi$
$338$	4.00476	+	23.6424i	0.217830	+	1.28598i
$339$	43.8050			2.37916
$340$		−	0.0343908i		−	0.00186510i
$341$	−15.9066	−	29.7787i	−0.861393	−	1.61261i
$342$	27.6487			1.49507
$343$		−	17.3237i		−	0.935392i
$344$	4.12040	+	2.37891i	0.222157	+	0.128262i
$345$			47.1343i			2.53762i
$346$	−20.0640	+	11.5839i	−1.07864	+	0.622756i
$347$	6.05701	−	10.4911i	0.325157	−	0.563189i	−0.656387	−	0.754425i	$-0.727916\pi$
$347$	6.05701	−	10.4911i	0.325157	−	0.563189i	0.981544	+	0.191235i	$0.0612494\pi$
$348$	1.52247	−	2.63699i	0.0816127	−	0.141357i
$349$			12.2402i			0.655203i	0.944816	+	0.327601i	$0.106240\pi$
$349$			12.2402i			0.655203i	−0.944816	+	0.327601i	$0.893760\pi$
$350$	12.3790	+	21.4410i	0.661685	+	1.14607i
$351$	−3.36768	+	0.283206i	−0.179754	+	0.0151164i
$352$	20.3721	+	35.2854i	1.08583	+	1.88072i
$353$	−5.99723	−	3.46251i	−0.319201	−	0.184291i	0.331836	−	0.943337i	$-0.392332\pi$
$353$	−5.99723	−	3.46251i	−0.319201	−	0.184291i	−0.651036	+	0.759047i	$0.725665\pi$
$354$	−19.7146	−	34.1467i	−1.04782	−	1.81488i
$355$	−25.3971	+	43.9890i	−1.34794	+	2.33469i
$356$		−	11.5965i		−	0.614613i
$357$		−	0.0239766i		−	0.00126898i
$358$	−30.3843	−	17.5424i	−1.60586	−	0.927145i
$359$	−8.59293	+	4.96113i	−0.453517	+	0.261838i	−0.709314	−	0.704892i	$-0.750995\pi$
$359$	−8.59293	+	4.96113i	−0.453517	+	0.261838i	0.255797	+	0.966730i	$0.417662\pi$
$360$	7.00137	−	12.1267i	0.369005	−	0.639135i
$361$	0.383936	+	0.664997i	0.0202072	+	0.0349998i
$362$	17.2249	−	9.94481i	0.905322	−	0.522688i
$363$	32.5205	+	56.3272i	1.70688	+	2.95641i
$364$	6.67757	+	3.14123i	0.350000	+	0.164645i
$365$	8.81749	−	15.2723i	0.461529	−	0.799391i
$366$	−37.8636	−	21.8606i	−1.97916	−	1.14267i
$367$	−0.846646	−	1.46643i	−0.0441946	−	0.0765472i	0.843082	−	0.537785i	$-0.180739\pi$
$367$	−0.846646	−	1.46643i	−0.0441946	−	0.0765472i	−0.887277	+	0.461238i	$0.847405\pi$
$368$	−23.9773			−1.24991
$369$	1.32335	+	0.764035i	0.0688907	+	0.0397741i
$370$			45.8773i			2.38505i
$371$		−	1.07381i		−	0.0557494i
$372$	16.7340	+	10.4122i	0.867618	+	0.539846i
$373$	19.0784			0.987842			0.493921	−	0.869507i	$-0.335563\pi$
$373$	19.0784			0.987842			0.493921	+	0.869507i	$0.335563\pi$
$374$	0.0727957			0.00376418
$375$	34.5663	+	19.9568i	1.78499	+	1.03057i
$376$	8.91405			0.459707
$377$	−3.09056	+	0.259902i	−0.159172	+	0.0133856i
$378$	−1.26166	+	2.18525i	−0.0648927	+	0.112397i
$379$	−21.7888	−	12.5798i	−1.11922	−	0.646180i	−0.178016	−	0.984028i	$-0.556968\pi$
$379$	−21.7888	−	12.5798i	−1.11922	−	0.646180i	−0.941201	+	0.337848i	$0.890301\pi$
$380$	−23.4931			−1.20517
$381$	3.16209	+	5.47690i	0.161999	+	0.280590i
$382$	−33.9732	+	19.6145i	−1.73822	+	1.00356i
$383$	21.4469	−	12.3824i	1.09589	−	0.632711i	0.160749	−	0.986995i	$-0.448609\pi$
$383$	21.4469	−	12.3824i	1.09589	−	0.632711i	0.935138	+	0.354285i	$0.115276\pi$
$384$	18.4169	+	10.6330i	0.939836	+	0.542614i
$385$	−28.8767	+	16.6719i	−1.47169	+	0.849681i
$386$	−23.5100	+	40.7204i	−1.19663	+	2.07262i
$387$	−14.5511			−0.739673
$388$		−	7.52891i		−	0.382222i
$389$	−2.23451	+	3.87028i	−0.113294	+	0.196231i	−0.917097	−	0.398665i	$-0.869474\pi$
$389$	−2.23451	+	3.87028i	−0.113294	+	0.196231i	0.803802	+	0.594896i	$0.202807\pi$
$390$	63.0293	−	5.30047i	3.19161	−	0.268400i
$391$	−0.0161280	+	0.0279344i	−0.000815626	+	0.00141271i
$392$	4.64917	−	2.68420i	0.234819	−	0.135573i
$393$	−14.4128	−	24.9638i	−0.727031	−	1.25925i
$394$	16.7336	+	28.9835i	0.843029	+	1.46017i
$395$		−	21.4823i		−	1.08089i
$396$	−24.8274	−	14.3341i	−1.24762	−	0.720316i
$397$	−9.03983	−	5.21915i	−0.453696	−	0.261941i	0.255694	−	0.966758i	$-0.417696\pi$
$397$	−9.03983	−	5.21915i	−0.453696	−	0.261941i	−0.709390	+	0.704816i	$0.751029\pi$
$398$	7.24779	−	4.18451i	0.363299	−	0.209751i
$399$	−16.3789			−0.819972
$400$	−22.2473	+	38.5335i	−1.11237	+	1.92667i
$401$		−	28.5696i		−	1.42670i	−0.700809	−	0.713349i	$-0.747178\pi$
$401$		−	28.5696i		−	1.42670i	0.700809	−	0.713349i	$-0.252822\pi$
$402$	−67.3366			−3.35844
$403$	−1.02140	−	20.0489i	−0.0508794	−	0.998705i
$404$	−12.8645			−0.640034
$405$		−	29.1936i		−	1.45064i
$406$	−1.15784	+	2.00543i	−0.0574625	+	0.0995280i
$407$	−40.0262			−1.98403
$408$	0.0156836	−	0.00905490i	0.000776452	−	0.000448284i
$409$	11.1062	+	6.41219i	0.549168	+	0.317063i	0.748787	−	0.662811i	$-0.230637\pi$
$409$	11.1062	+	6.41219i	0.549168	+	0.317063i	−0.199618	+	0.979874i	$0.563970\pi$
$410$	−2.72808	−	1.57506i	−0.134730	−	0.0777865i
$411$		−	12.5477i		−	0.618935i
$412$	3.17723	+	5.50312i	0.156531	+	0.271119i
$413$	6.17975	+	10.7036i	0.304086	+	0.526692i
$414$	26.6902	−	15.4096i	1.31175	−	0.757341i
$415$	5.33268	−	9.23647i	0.261771	−	0.453401i
$416$	2.03023	+	24.1421i	0.0995404	+	1.18366i
$417$	−9.30367	+	16.1144i	−0.455603	+	0.789127i
$418$		−	49.7283i		−	2.43229i
$419$	−21.1787			−1.03465			−0.517323	−	0.855790i	$-0.673071\pi$
$419$	−21.1787			−1.03465			−0.517323	+	0.855790i	$0.673071\pi$
$420$	9.73275	−	16.8576i	0.474910	−	0.822568i
$421$	−7.98149	+	4.60812i	−0.388994	+	0.224586i	−0.681724	−	0.731609i	$-0.738770\pi$
$421$	−7.98149	+	4.60812i	−0.388994	+	0.224586i	0.292730	+	0.956195i	$0.405436\pi$
$422$	−9.85258	−	5.68839i	−0.479616	−	0.276906i
$423$	−23.6098	+	13.6311i	−1.14795	+	0.662768i
$424$	0.702399	−	0.405530i	0.0341115	−	0.0196943i
$425$	0.0299286	+	0.0518378i	0.00145175	+	0.00251450i
$426$	62.7663			3.04104
$427$	11.8688	+	6.85243i	0.574369	+	0.331612i
$428$	5.95562	−	10.3154i	0.287876	−	0.498616i
$429$	4.62446	+	54.9906i	0.223271	+	2.65497i
$430$	29.9970			1.44659
$431$	19.0373	+	10.9912i	0.916994	+	0.529427i	0.882675	−	0.469984i	$-0.155740\pi$
$431$	19.0373	+	10.9912i	0.916994	+	0.529427i	0.0343193	+	0.999411i	$0.489074\pi$
$432$	−4.53486			−0.218184
$433$	8.05251			0.386979			0.193490	−	0.981102i	$-0.438019\pi$
$433$	8.05251			0.386979			0.193490	+	0.981102i	$0.438019\pi$
$434$	−12.7262	−	7.91848i	−0.610879	−	0.380099i
$435$			8.18099i			0.392248i
$436$		−	10.1528i		−	0.486231i
$437$	19.0826	+	11.0173i	0.912845	+	0.527031i
$438$	−21.7915			−1.04124
$439$	−13.3603	−	23.1407i	−0.637651	−	1.10444i	−0.985947	−	0.167059i	$-0.946573\pi$
$439$	−13.3603	−	23.1407i	−0.637651	−	1.10444i	0.348296	−	0.937384i	$-0.386760\pi$
$440$	−21.8109	−	12.5925i	−1.03979	−	0.600324i
$441$	−8.20921	+	14.2188i	−0.390915	+	0.677085i
$442$	0.0391684	+	0.0184254i	0.00186305	+	0.000876408i
$443$	−1.35680	−	2.35005i	−0.0644637	−	0.111654i	0.831992	−	0.554787i	$-0.187200\pi$
$443$	−1.35680	−	2.35005i	−0.0644637	−	0.111654i	−0.896456	+	0.443133i	$0.853867\pi$
$444$	20.2360	−	11.6833i	0.960358	−	0.554463i
$445$	15.5785	+	26.9827i	0.738490	+	1.27910i
$446$	15.4710	−	26.7966i	0.732573	−	1.26885i
$447$	11.0396	−	6.37369i	0.522153	−	0.301465i
$448$	3.43558	+	1.98353i	0.162316	+	0.0937131i
$449$			12.9562i			0.611441i	0.952121	+	0.305720i	$0.0988973\pi$
$449$			12.9562i			0.611441i	−0.952121	+	0.305720i	$0.901103\pi$
$450$		−	57.1911i		−	2.69601i
$451$	1.37418	−	2.38014i	0.0647074	−	0.112077i
$452$	12.1687	+	21.0768i	0.572368	+	0.991370i
$453$	41.3976	+	23.9009i	1.94503	+	1.12296i
$454$	−24.6574	−	42.7078i	−1.15723	−	2.00438i
$455$	−19.7572	+	1.66149i	−0.926233	+	0.0778918i
$456$	−6.18560	−	10.7138i	−0.289667	−	0.501718i
$457$			24.0216i			1.12368i	0.827245	+	0.561841i	$0.189907\pi$
$457$			24.0216i			1.12368i	−0.827245	+	0.561841i	$0.810093\pi$
$458$	12.2503	−	21.2182i	0.572420	−	0.991461i
$459$	−0.00305030	+	0.00528327i	−0.000142376	+	0.000246602i
$460$	−22.6787	+	13.0935i	−1.05740	+	0.610490i
$461$		−	3.09838i		−	0.144306i	−0.997394	−	0.0721529i	$-0.977013\pi$
$461$		−	3.09838i		−	0.144306i	0.997394	−	0.0721529i	$-0.0229870\pi$
$462$	35.6828	+	20.6015i	1.66012	+	0.958469i
$463$		−	34.5600i		−	1.60614i	−0.595885	−	0.803070i	$-0.703198\pi$
$463$		−	34.5600i		−	1.60614i	0.595885	−	0.803070i	$-0.296802\pi$
$464$	−4.16169			−0.193202
$465$	−52.9242	−	1.74695i	−2.45430	−	0.0810127i
$466$			8.75452i			0.405545i
$467$	−0.115305			−0.00533569			−0.00266784	−	0.999996i	$-0.500849\pi$
$467$	−0.115305			−0.00533569			−0.00266784	+	0.999996i	$0.500849\pi$
$468$	−9.73050	−	13.9967i	−0.449792	−	0.646998i
$469$	21.1074			0.974648
$470$	48.6716	−	28.1005i	2.24505	−	1.29618i
$471$	13.8828	−	24.0457i	0.639685	−	1.10797i
$472$	−4.66764	+	8.08458i	−0.214845	+	0.372123i
$473$			26.1713i			1.20336i
$474$	−22.9892	+	13.2728i	−1.05593	+	0.609642i
$475$	35.4115	−	20.4448i	1.62479	−	0.938074i
$476$	0.0115364	−	0.00666052i	0.000528768	−	0.000305285i
$477$	−1.24025	+	2.14818i	−0.0567872	+	0.0983584i
$478$	−18.7781	−	32.5246i	−0.858890	−	1.48764i
$479$	−32.1898	−	18.5848i	−1.47079	−	0.849161i	−0.471328	−	0.881958i	$-0.656225\pi$
$479$	−32.1898	−	18.5848i	−1.47079	−	0.849161i	−0.999462	+	0.0327969i	$0.989559\pi$
$480$	63.9062			2.91690
$481$	−21.5365	−	10.1311i	−0.981979	−	0.461938i
$482$	15.8405	−	27.4365i	0.721515	−	1.24970i
$483$	−15.8111	+	9.12857i	−0.719432	+	0.415364i
$484$	−18.0679	+	31.2945i	−0.821269	+	1.42248i
$485$	10.1142	+	17.5183i	0.459261	+	0.795463i
$486$	−35.7334	+	20.6307i	−1.62090	+	0.935827i
$487$	−31.3966	+	18.1268i	−1.42272	+	0.821405i	−0.996530	−	0.0832302i	$-0.973476\pi$
$487$	−31.3966	+	18.1268i	−1.42272	+	0.821405i	−0.426186	+	0.904636i	$0.640143\pi$
$488$			10.3514i			0.468587i
$489$	24.4712	+	14.1284i	1.10662	+	0.638910i
$490$	16.9233	−	29.3120i	0.764516	−	1.32418i
$491$	−0.258148	−	0.447125i	−0.0116500	−	0.0201785i	0.860142	−	0.510055i	$-0.170375\pi$
$491$	−0.258148	−	0.447125i	−0.0116500	−	0.0201785i	−0.871792	+	0.489877i	$0.837042\pi$
$492$			1.60443i			0.0723335i
$493$	−0.00279929	+	0.00484852i	−0.000126074	+	0.000218366i
$494$	12.5868	−	26.7568i	0.566306	−	1.20384i
$495$	77.0245			3.46200
$496$	0.888677	−	26.9227i	0.0399028	−	1.20886i
$497$	−19.6748			−0.882533
$498$	−13.1792			−0.590573
$499$	19.7131	+	11.3814i	0.882479	+	0.509499i	0.871475	−	0.490440i	$-0.163164\pi$
$499$	19.7131	+	11.3814i	0.882479	+	0.509499i	0.0110038	+	0.999939i	$0.496497\pi$
$500$			22.1754i			0.991716i
$501$	16.2418	−	9.37719i	0.725629	−	0.418942i
$502$	20.2921	+	11.7157i	0.905683	+	0.522896i
$503$	21.0765	−	36.5055i	0.939754	−	1.62770i	0.173824	−	0.984777i	$-0.444388\pi$
$503$	21.0765	−	36.5055i	0.939754	−	1.62770i	0.765930	−	0.642924i	$-0.222279\pi$
$504$	5.42387			0.241598
$505$	29.9332	−	17.2819i	1.33201	−	0.769035i
$506$	−27.7154	−	48.0044i	−1.23210	−	2.13406i
$507$	−11.4305	+	30.7587i	−0.507647	+	1.36604i
$508$	−1.75681	+	3.04289i	−0.0779459	+	0.135006i
$509$	−10.0638	+	5.81032i	−0.446069	+	0.257538i	−0.706169	−	0.708044i	$-0.749578\pi$
$509$	−10.0638	+	5.81032i	−0.446069	+	0.257538i	0.260100	+	0.965582i	$0.416245\pi$
$510$	0.0570891	−	0.0988813i	0.00252795	−	0.00437854i
$511$	6.83079			0.302176
$512$			21.8428i			0.965324i
$513$	3.60911	+	2.08372i	0.159346	+	0.0919986i
$514$	25.7359	−	14.8587i	1.13516	−	0.655387i
$515$	−14.7856	−	8.53645i	−0.651530	−	0.376161i
$516$	−7.63913	−	13.2314i	−0.336294	−	0.582478i
$517$	24.5166	+	42.4640i	1.07824	+	1.86757i
$518$	−15.3895	+	8.88514i	−0.676176	+	0.390390i
$519$	−31.7037			−1.39164
$520$	−8.54824	−	12.2961i	−0.374865	−	0.539219i
$521$	2.68024	−	4.64232i	0.117424	−	0.203384i	−0.801322	−	0.598233i	$-0.795870\pi$
$521$	2.68024	−	4.64232i	0.117424	−	0.203384i	0.918746	+	0.394849i	$0.129203\pi$
$522$	4.63256	−	2.67461i	0.202762	−	0.117064i
$523$	−44.3905			−1.94106			−0.970530	−	0.240980i	$-0.922531\pi$
$523$	−44.3905			−1.94106			−0.970530	+	0.240980i	$0.922531\pi$
$524$	8.00755	−	13.8695i	0.349812	−	0.605891i
$525$			33.8797i			1.47863i
$526$		−	8.85229i		−	0.385978i
$527$	−0.0307681	−	0.0191444i	−0.00134028	−	0.000833945i
$528$			74.0494i			3.22258i
$529$	1.56147			0.0678898
$530$	2.55678	−	4.42847i	0.111059	−	0.192360i
$531$		−	28.5505i		−	1.23899i
$532$	−4.54994	−	7.88073i	−0.197265	−	0.341673i
$533$	1.34183	−	0.932839i	0.0581211	−	0.0404057i
$534$	19.2503	−	33.3425i	0.833042	−	1.44287i
$535$			32.0026i			1.38359i
$536$	7.97132	+	13.8067i	0.344309	+	0.596360i
$537$	−24.0056	−	41.5790i	−1.03592	−	1.79427i
$538$	21.8150	−	12.5949i	0.940510	−	0.543003i
$539$	25.5736	+	14.7649i	1.10153	+	0.635970i
$540$	−4.28924	+	2.47640i	−0.184580	+	0.106567i
$541$	28.7875	+	16.6205i	1.23767	+	0.714570i	0.968618	−	0.248556i	$-0.0799559\pi$
$541$	28.7875	+	16.6205i	1.23767	+	0.714570i	0.269053	+	0.963125i	$0.413289\pi$
$542$	3.23407			0.138915
$543$	27.2176			1.16802
$544$	0.0378744	+	0.0218668i	0.00162385	+	0.000937531i
$545$	13.6390	+	23.6235i	0.584233	+	1.01192i
$546$	13.9850	+	20.1166i	0.598504	+	0.860910i
$547$	10.3666	+	17.9555i	0.443245	+	0.767722i	0.997928	−	0.0643392i	$-0.0204940\pi$
$547$	10.3666	+	17.9555i	0.443245	+	0.767722i	−0.554683	+	0.832061i	$0.687161\pi$
$548$	6.03736	−	3.48567i	0.257903	−	0.148900i
$549$	−15.8291	−	27.4169i	−0.675571	−	1.17012i
$550$	−102.863			−4.38607
$551$	3.31212	+	1.91226i	0.141101	+	0.0814649i
$552$	−11.9423	−	6.89491i	−0.508300	−	0.293467i
$553$	7.20622	−	4.16052i	0.306440	−	0.176923i
$554$		−	5.55672i		−	0.236083i
$555$	−31.3901	+	54.3692i	−1.33243	+	2.30784i
$556$	−10.3380			−0.438427
$557$			5.82569i			0.246842i	0.992354	+	0.123421i	$0.0393866\pi$
$557$			5.82569i			0.246842i	−0.992354	+	0.123421i	$0.960613\pi$
$558$	16.3133	+	30.5399i	0.690596	+	1.29286i
$559$	−6.62424	+	14.0817i	−0.280175	+	0.595592i
$560$	−26.6047			−1.12425
$561$	0.0862701	+	0.0498081i	0.00364233	+	0.00210290i
$562$	−3.16397			−0.133464
$563$	7.71984	+	13.3712i	0.325353	+	0.563527i	0.981584	−	0.191033i	$-0.0611837\pi$
$563$	7.71984	+	13.3712i	0.325353	+	0.563527i	−0.656231	+	0.754560i	$0.727850\pi$
$564$	−24.7897	−	14.3123i	−1.04383	−	0.602658i
$565$	−56.6283	−	32.6943i	−2.38237	−	1.37546i
$566$			13.5606i			0.569994i
$567$	9.79298	−	5.65398i	0.411266	−	0.237445i
$568$	−7.43028	−	12.8696i	−0.311768	−	0.539998i
$569$	−10.4787	−	18.1497i	−0.439290	−	0.760873i	0.558345	−	0.829609i	$-0.311437\pi$
$569$	−10.4787	−	18.1497i	−0.439290	−	0.760873i	−0.997635	+	0.0687359i	$0.978103\pi$
$570$	−67.5479	−	38.9988i	−2.82927	−	1.63348i
$571$	−1.30982	−	2.26867i	−0.0548142	−	0.0949410i	0.837316	−	0.546719i	$-0.184123\pi$
$571$	−1.30982	−	2.26867i	−0.0548142	−	0.0949410i	−0.892130	+	0.451778i	$0.850790\pi$
$572$	−25.1741	+	17.5010i	−1.05258	+	0.731756i
$573$	−53.6822			−2.24261
$574$		−	1.22017i		−	0.0509291i
$575$	22.7893	−	39.4722i	0.950380	−	1.64611i
$576$	−4.58197	−	7.93620i	−0.190915	−	0.330675i
$577$	−29.7600	−	17.1819i	−1.23892	−	0.715293i	−0.270049	−	0.962846i	$-0.587040\pi$
$577$	−29.7600	−	17.1819i	−1.23892	−	0.715293i	−0.968874	+	0.247554i	$0.920373\pi$
$578$	−27.1563	+	15.6787i	−1.12955	+	0.652147i
$579$	−55.7232	+	32.1718i	−2.31578	+	1.33702i
$580$	−3.93629	+	2.27262i	−0.163446	+	0.0943653i
$581$	4.13115			0.171389
$582$	12.4981	−	21.6473i	0.518062	−	0.897309i
$583$	3.86367	+	2.23069i	0.160017	+	0.0923857i
$584$	2.57969	+	4.46815i	0.106748	+	0.184893i
$585$	41.4438	+	19.4958i	1.71349	+	0.806051i
$586$	8.67406	−	15.0239i	0.358322	−	0.620632i
$587$		−	12.1177i		−	0.500149i	−0.968227	−	0.250075i	$-0.919545\pi$
$587$		−	12.1177i		−	0.500149i	0.968227	−	0.250075i	$-0.0804552\pi$
$588$	−17.2389			−0.710921
$589$	−13.0780	+	21.0183i	−0.538868	+	0.866046i
$590$			58.8568i			2.42310i
$591$			45.7978i			1.88387i
$592$	−27.6578	−	15.9682i	−1.13673	−	0.656290i
$593$			1.31568i			0.0540284i	0.999635	+	0.0270142i	$0.00859993\pi$
$593$			1.31568i			0.0540284i	−0.999635	+	0.0270142i	$0.991400\pi$
$594$	−5.24183	−	9.07912i	−0.215075	−	0.372521i
$595$	−0.0178952	+	0.0309954i	−0.000733632	+	0.00127069i
$596$	6.13341	+	3.54113i	0.251234	+	0.145050i
$597$	11.4525			0.468718
$598$	−2.76205	−	32.8443i	−0.112949	−	1.34310i
$599$	21.0549	+	36.4682i	0.860281	+	1.49005i	0.871658	+	0.490115i	$0.163045\pi$
$599$	21.0549	+	36.4682i	0.860281	+	1.49005i	−0.0113771	+	0.999935i	$0.503622\pi$
$600$	−22.1613	+	12.7949i	−0.904733	+	0.522348i
$601$	−14.0503	+	24.3358i	−0.573124	+	0.992680i	0.423119	+	0.906074i	$0.360935\pi$
$601$	−14.0503	+	24.3358i	−0.573124	+	0.992680i	−0.996243	+	0.0866054i	$0.972398\pi$
$602$	5.80957	+	10.0625i	0.236780	+	0.410116i
$603$	−42.2258	−	24.3791i	−1.71957	−	0.992792i
$604$			26.5580i			1.08063i
$605$		−	97.0882i		−	3.94719i
$606$	−36.9884	−	21.3552i	−1.50255	−	0.867497i
$607$	−0.767548	−	1.32943i	−0.0311538	−	0.0539600i	0.850028	−	0.526737i	$-0.176585\pi$
$607$	−0.767548	−	1.32943i	−0.0311538	−	0.0539600i	−0.881182	+	0.472777i	$0.843252\pi$
$608$	14.9377	−	25.8728i	0.605803	−	1.04928i
$609$	−2.74430	+	1.58442i	−0.111205	+	0.0642041i
$610$	32.6317	+	56.5198i	1.32122	+	2.28842i
$611$	2.44327	+	29.0536i	0.0988443	+	1.17538i
$612$	−0.0307717			−0.00124387
$613$	−15.6784	−	9.05195i	−0.633246	−	0.365605i	0.148762	−	0.988873i	$-0.452471\pi$
$613$	−15.6784	−	9.05195i	−0.633246	−	0.365605i	−0.782008	+	0.623268i	$0.785805\pi$
$614$	−19.0221	+	32.9473i	−0.767671	+	1.32964i
$615$	−2.15536	−	3.73320i	−0.0869126	−	0.150537i
$616$		−	9.75524i		−	0.393050i
$617$	−27.2494	−	15.7325i	−1.09702	−	0.633365i	−0.161584	−	0.986859i	$-0.551660\pi$
$617$	−27.2494	−	15.7325i	−1.09702	−	0.633365i	−0.935437	+	0.353494i	$0.884994\pi$
$618$			21.0970i			0.848644i
$619$		−	20.8783i		−	0.839168i	−0.907716	−	0.419584i	$-0.862176\pi$
$619$		−	20.8783i		−	0.839168i	0.907716	−	0.419584i	$-0.137824\pi$
$620$	−13.8614	−	25.9498i	−0.556687	−	1.04217i
$621$	4.64534			0.186411
$622$		−	38.9191i		−	1.56051i
$623$	−6.03421	+	10.4516i	−0.241756	+	0.418733i
$624$	−18.7427	+	39.8430i	−0.750310	+	1.59499i
$625$	−6.79816	−	11.7748i	−0.271926	−	0.470990i
$626$	7.87617	+	4.54731i	0.314795	+	0.181747i
$627$	34.0249	−	58.9329i	1.35883	−	2.35355i
$628$	15.4261			0.615570
$629$	−0.0372071	+	0.0214815i	−0.00148354	+	0.000856524i
$630$	29.6148	−	17.0981i	1.17988	−	0.681206i
$631$	−20.7788	+	11.9967i	−0.827192	+	0.477579i	−0.852890	−	0.522090i	$-0.825152\pi$
$631$	−20.7788	+	11.9967i	−0.827192	+	0.477579i	0.0256984	+	0.999670i	$0.491819\pi$
$632$	5.44294	+	3.14248i	0.216509	+	0.125001i
$633$	−7.78419	−	13.4826i	−0.309394	−	0.535886i
$634$	3.17000	−	5.49059i	0.125897	−	0.218059i
$635$		−	9.44025i		−	0.374625i
$636$	−2.60446			−0.103274
$637$	10.0229	+	14.4174i	0.397123	+	0.571236i
$638$	−4.81049	−	8.33202i	−0.190449	−	0.329868i
$639$	39.3598	+	22.7244i	1.55705	+	0.898963i
$640$	−15.8722	−	27.4914i	−0.627402	−	1.08669i
$641$	4.68683	+	8.11783i	0.185119	+	0.320635i	0.943617	−	0.331041i	$-0.107400\pi$
$641$	4.68683	+	8.11783i	0.185119	+	0.320635i	−0.758498	+	0.651676i	$0.774066\pi$
$642$	34.2475	−	19.7728i	1.35164	−	0.780370i
$643$			23.3392i			0.920408i	0.887813	+	0.460204i	$0.152224\pi$
$643$			23.3392i			0.920408i	−0.887813	+	0.460204i	$0.847776\pi$
$644$	−8.78443	−	5.07170i	−0.346155	−	0.199853i
$645$	35.5495	+	20.5245i	1.39976	+	0.808151i
$646$	−0.0266885	−	0.0462258i	−0.00105004	−	0.00181873i
$647$	−27.8988			−1.09682			−0.548408	−	0.836211i	$-0.684766\pi$
$647$	−27.8988			−1.09682			−0.548408	+	0.836211i	$0.684766\pi$
$648$	7.39675	+	4.27051i	0.290572	+	0.167762i
$649$	−51.3503			−2.01568
$650$	−55.3462	−	26.0357i	−2.17086	−	1.02120i
$651$	−9.66389	−	18.0917i	−0.378758	−	0.709069i
$652$			15.6991i			0.614824i
$653$	1.27131			0.0497502			0.0248751	−	0.999691i	$-0.492081\pi$
$653$	1.27131			0.0497502			0.0248751	+	0.999691i	$0.492081\pi$
$654$	16.8538	−	29.1916i	0.659034	−	1.14148i
$655$			43.0287i			1.68127i
$656$	1.89909	−	1.09644i	0.0741469	−	0.0428087i
$657$	−13.6651	−	7.88957i	−0.533128	−	0.307802i
$658$	18.8526	+	10.8845i	0.734950	+	0.424324i
$659$	28.6250			1.11507			0.557536	−	0.830153i	$-0.311747\pi$
$659$	28.6250			1.11507			0.557536	+	0.830153i	$0.311747\pi$
$660$	40.4369	+	70.0387i	1.57400	+	2.72625i
$661$	−12.8888	+	7.44134i	−0.501316	+	0.289435i	−0.729257	−	0.684240i	$-0.760134\pi$
$661$	−12.8888	+	7.44134i	−0.501316	+	0.289435i	0.227941	+	0.973675i	$0.426801\pi$
$662$	26.0707	+	45.1558i	1.01327	+	1.75503i
$663$	0.0338115	+	0.0486356i	0.00131313	+	0.00188885i
$664$	1.56015	+	2.70226i	0.0605457	+	0.104868i
$665$	21.1736	+	12.2246i	0.821077	+	0.474049i
$666$	41.0494			1.59063
$667$	4.26308			0.165067
$668$	9.02368	+	5.20983i	0.349137	+	0.201574i
$669$	36.6694	−	21.1711i	1.41772	−	0.818520i
$670$	87.0484	+	50.2574i	3.36297	+	1.94161i
$671$	−49.3114	+	28.4699i	−1.90364	+	1.09907i
$672$	12.3768	+	21.4372i	0.477445	+	0.826960i
$673$	−14.6108	−	25.3066i	−0.563204	−	0.975499i	−0.997214	−	0.0745904i	$-0.976235\pi$
$673$	−14.6108	−	25.3066i	−0.563204	−	0.975499i	0.434010	−	0.900908i	$-0.357098\pi$
$674$			58.5512i			2.25531i
$675$	4.31016	−	7.46542i	0.165898	−	0.287344i
$676$	−17.9749	+	3.04474i	−0.691342	+	0.117105i
$677$	−6.81146	−	11.7978i	−0.261786	−	0.453426i	0.704931	−	0.709276i	$-0.250978\pi$
$677$	−6.81146	−	11.7978i	−0.261786	−	0.453426i	−0.966717	+	0.255850i	$0.917645\pi$
$678$			80.8007i			3.10313i
$679$	−3.91765	+	6.78558i	−0.150346	+	0.260407i
$680$	−0.0270329			−0.00103666
$681$		−	67.4840i		−	2.58599i
$682$	54.9284	−	29.3407i	2.10332	−	1.12351i
$683$		−	21.3781i		−	0.818009i	−0.912532	−	0.409005i	$-0.865876\pi$
$683$		−	21.3781i		−	0.818009i	0.912532	−	0.409005i	$-0.134124\pi$
$684$			21.0208i			0.803749i
$685$	−9.36515	+	16.2209i	−0.357824	+	0.619769i
$686$	31.9545			1.22003
$687$	29.0357	−	16.7638i	1.10778	−	0.639578i
$688$	−10.4409	+	18.0841i	−0.398054	+	0.689450i
$689$	1.51427	+	2.17818i	0.0576891	+	0.0829821i
$690$	−86.9418			−3.30982
$691$	−16.0239	+	9.25143i	−0.609580	+	0.351941i	−0.772801	−	0.634649i	$-0.781145\pi$
$691$	−16.0239	+	9.25143i	−0.609580	+	0.351941i	0.163221	+	0.986589i	$0.447812\pi$
$692$	−8.80705	−	15.2543i	−0.334794	−	0.579880i
$693$	14.9175	+	25.8378i	0.566667	+	0.981497i
$694$	19.3513	+	11.1725i	0.734566	+	0.424102i
$695$	24.0544	−	13.8878i	0.912434	−	0.526794i
$696$	−2.07280	−	1.19673i	−0.0785694	−	0.0453621i
$697$		−	0.00295000i		−	0.000111739i
$698$	−22.5777			−0.854579
$699$	−5.98999	+	10.3750i	−0.226562	+	0.392417i
$700$	−16.3012	+	9.41152i	−0.616129	+	0.355722i
$701$	5.30476	−	9.18811i	0.200358	−	0.347030i	−0.748286	−	0.663376i	$-0.769123\pi$
$701$	5.30476	−	9.18811i	0.200358	−	0.347030i	0.948644	+	0.316346i	$0.102456\pi$
$702$	−0.522390	−	6.21188i	−0.0197163	−	0.234452i
$703$	14.6745	+	25.4169i	0.553458	+	0.958618i
$704$	−14.2739	+	8.24103i	−0.537967	+	0.310595i
$705$	76.9075			2.89650
$706$	6.38678	−	11.0622i	0.240370	−	0.416332i
$707$	11.5944	+	6.69403i	0.436052	+	0.251755i
$708$	25.9611	−	14.9886i	0.975678	−	0.563308i
$709$			16.7061i			0.627412i	0.949520	+	0.313706i	$0.101571\pi$
$709$			16.7061i			0.627412i	−0.949520	+	0.313706i	$0.898429\pi$
$710$	−81.1401	−	46.8463i	−3.04514	−	1.75811i
$711$	−19.2216			−0.720867
$712$	−9.11542			−0.341615
$713$	−0.910327	+	27.5786i	−0.0340920	+	1.03283i
$714$	0.0442262			0.00165512
$715$	35.0647	−	74.5398i	1.31134	−	2.78763i
$716$	13.3372	−	23.1006i	0.498433	−	0.863312i
$717$		−	51.3932i		−	1.91931i
$718$	−9.15107	−	15.8501i	−0.341515	−	0.591521i
$719$	8.42740	−	14.5967i	0.314289	−	0.544365i	−0.664997	−	0.746846i	$-0.731567\pi$
$719$	8.42740	−	14.5967i	0.314289	−	0.544365i	0.979286	+	0.202481i	$0.0649006\pi$
$720$	53.2233	+	30.7285i	1.98351	+	1.14518i
$721$		−	6.61307i		−	0.246283i
$722$	−1.22662	+	0.708191i	−0.0456502	+	0.0263561i
$723$	37.5451	−	21.6767i	1.39632	−	0.806164i
$724$	7.56086	+	13.0958i	0.280997	+	0.486701i
$725$	3.95549	−	6.85111i	0.146903	−	0.254444i
$726$	−103.899	+	59.9859i	−3.85604	+	2.22628i
$727$	22.0252	−	38.1487i	0.816868	−	1.41486i	−0.0911112	−	0.995841i	$-0.529042\pi$
$727$	22.0252	−	38.1487i	0.816868	−	1.41486i	0.907979	−	0.419016i	$-0.137625\pi$
$728$	2.46916	−	5.24890i	0.0915132	−	0.194537i
$729$	−33.2193			−1.23034
$730$	28.1707	+	16.2643i	1.04264	+	0.601970i
$731$	0.0140457	+	0.0243279i	0.000519501	+	0.000899802i
$732$	16.6202	−	28.7870i	0.614300	−	1.06400i
$733$	32.8412	−	18.9609i	1.21302	−	0.700337i	0.249603	−	0.968348i	$-0.419700\pi$
$733$	32.8412	−	18.9609i	1.21302	−	0.700337i	0.963416	+	0.268011i	$0.0863664\pi$
$734$	2.70492	−	1.56168i	0.0998403	−	0.0576428i
$735$	40.1115	−	23.1584i	1.47954	−	0.854210i
$736$		−	33.3012i		−	1.22750i
$737$	−43.8476	+	75.9463i	−1.61515	+	2.79752i
$738$	−1.40930	+	2.44099i	−0.0518772	+	0.0898539i
$739$	−16.4014	+	9.46937i	−0.603336	+	0.348336i	−0.770353	−	0.637618i	$-0.779920\pi$
$739$	−16.4014	+	9.46937i	−0.603336	+	0.348336i	0.167017	+	0.985954i	$0.446587\pi$
$740$	−34.8797			−1.28220
$741$	33.2240	−	23.0973i	1.22052	−	0.848501i
$742$	1.98070			0.0727138
$743$			24.3107i			0.891873i	0.895065	+	0.445937i	$0.147129\pi$
$743$			24.3107i			0.891873i	−0.895065	+	0.445937i	$0.852871\pi$
$744$	8.18449	−	13.1538i	0.300058	−	0.482240i
$745$	−19.0283			−0.697143
$746$			35.1911i			1.28844i
$747$	−8.26446	−	4.77149i	−0.302381	−	0.174580i
$748$			0.0553452i			0.00202362i
$749$	−10.7352	+	6.19799i	−0.392257	+	0.226470i
$750$	−36.8115	+	63.7594i	−1.34417	+	2.32816i
$751$	−7.42825	+	12.8661i	−0.271061	+	0.469491i	−0.969134	−	0.246536i	$-0.920708\pi$
$751$	−7.42825	+	12.8661i	−0.271061	+	0.469491i	0.698073	+	0.716027i	$0.254041\pi$
$752$			39.1231i			1.42667i
$753$	16.0321	+	27.7685i	0.584243	+	1.01194i
$754$	−0.479403	−	5.70071i	−0.0174588	−	0.207608i
$755$	−35.6774	−	61.7951i	−1.29843	−	2.24895i
$756$	−1.66141	−	0.959215i	−0.0604249	−	0.0348863i
$757$	3.02296	+	5.23593i	0.109871	+	0.190303i	0.915718	−	0.401821i	$-0.131623\pi$
$757$	3.02296	+	5.23593i	0.109871	+	0.190303i	−0.805847	+	0.592124i	$0.798289\pi$
$758$	23.2041	−	40.1907i	0.842811	−	1.45979i
$759$		−	75.8533i		−	2.75330i
$760$			18.4667i			0.669859i
$761$	14.9727	+	8.64451i	0.542761	+	0.313363i	0.746197	−	0.665725i	$-0.231878\pi$
$761$	14.9727	+	8.64451i	0.542761	+	0.313363i	−0.203436	+	0.979088i	$0.565211\pi$
$762$	−10.1024	+	5.83265i	−0.365973	+	0.211295i
$763$	−5.28299	+	9.15041i	−0.191257	+	0.331267i
$764$	−14.9125	−	25.8292i	−0.539516	−	0.934468i
$765$	0.0715995	−	0.0413380i	0.00258869	−	0.00149458i
$766$	22.8400	+	39.5600i	0.825242	+	1.42936i
$767$	−27.6295	−	12.9973i	−0.997644	−	0.469307i
$768$	−26.4743	+	45.8549i	−0.955310	+	1.65464i
$769$	−18.6248	−	10.7530i	−0.671626	−	0.387763i	0.125067	−	0.992148i	$-0.460086\pi$
$769$	−18.6248	−	10.7530i	−0.671626	−	0.387763i	−0.796692	+	0.604385i	$0.793419\pi$
$770$	−30.7523	−	53.2646i	−1.10824	−	1.91952i
$771$	40.6662			1.46456
$772$	−30.9590	−	17.8742i	−1.11424	−	0.643306i
$773$		−	39.5254i		−	1.42163i	−0.703379	−	0.710815i	$-0.748326\pi$
$773$		−	39.5254i		−	1.42163i	0.703379	−	0.710815i	$-0.251674\pi$
$774$		−	26.8403i		−	0.964754i
$775$	43.4763	+	27.0517i	1.56171	+	0.971725i
$776$	−5.91810			−0.212447
$777$	−24.3175			−0.872384
$778$	−7.13894	−	4.12167i	−0.255944	−	0.147769i
$779$	−2.01521			−0.0722024
$780$	4.02985	+	47.9200i	0.144292	+	1.71581i
$781$	40.8716	−	70.7916i	1.46250	−	2.53312i
$782$	−0.0515266	−	0.0297489i	−0.00184259	−	0.00106382i
$783$	0.806280			0.0288141
$784$	11.7807	+	20.4048i	0.420741	+	0.728744i
$785$	−35.8935	+	20.7231i	−1.28110	+	0.739641i
$786$	46.0470	−	26.5853i	1.64244	−	0.948265i
$787$	25.1387	+	14.5138i	0.896098	+	0.517362i	0.875932	−	0.482434i	$-0.160247\pi$
$787$	25.1387	+	14.5138i	0.896098	+	0.517362i	0.0201655	+	0.999797i	$0.493581\pi$
$788$	−22.0356	+	12.7223i	−0.784987	+	0.453213i
$789$	6.05689	−	10.4908i	0.215631	−	0.373484i
$790$	39.6253			1.40981
$791$		−	25.3278i		−	0.900555i
$792$	−11.2673	+	19.5156i	−0.400367	+	0.693456i
$793$	−33.7385	+	2.83725i	−1.19809	+	0.100754i
$794$	9.62700	−	16.6745i	0.341649	−	0.591754i
$795$	6.06007	−	3.49878i	0.214928	−	0.124089i
$796$	3.18141	+	5.51036i	0.112762	+	0.195310i
$797$	−2.45164	−	4.24637i	−0.0868417	−	0.150414i	0.819333	−	0.573318i	$-0.194344\pi$
$797$	−2.45164	−	4.24637i	−0.0868417	−	0.150414i	−0.906175	+	0.422904i	$0.861011\pi$
$798$		−	30.2118i		−	1.06949i
$799$	0.0455797	+	0.0263155i	0.00161249	+	0.000930974i
$800$	−53.5177	−	30.8985i	−1.89214	−	1.09243i
$801$	24.1432	−	13.9391i	0.853057	−	0.492512i
$802$	52.6982			1.86084
$803$	−14.1900	+	24.5778i	−0.500755	+	0.867332i
$804$		−	51.1948i		−	1.80550i
$805$	27.2528			0.960536
$806$	36.9812	−	1.88402i	1.30261	−	0.0663619i
$807$	34.4705			1.21342
$808$			10.1122i			0.355744i
$809$	15.0509	−	26.0690i	0.529162	−	0.916536i	−0.470259	−	0.882528i	$-0.655840\pi$
$809$	15.0509	−	26.0690i	0.529162	−	0.916536i	0.999422	−	0.0340075i	$-0.0108270\pi$
$810$	53.8493			1.89207
$811$	9.77216	−	5.64196i	0.343147	−	0.198116i	−0.318516	−	0.947918i	$-0.603184\pi$
$811$	9.77216	−	5.64196i	0.343147	−	0.198116i	0.661663	+	0.749802i	$0.269851\pi$
$812$	−1.52469	−	0.880283i	−0.0535063	−	0.0308919i
$813$	3.83270	+	2.21281i	0.134418	+	0.0776066i
$814$		−	73.8305i		−	2.58776i
$815$	−21.0898	−	36.5286i	−0.738744	−	1.27954i
$816$	0.0397413	+	0.0688339i	0.00139122	+	0.00240967i
$817$	16.6189	−	9.59495i	0.581423	−	0.335685i
$818$	−11.8276	+	20.4861i	−0.413544	+	0.716279i
$819$	1.48664	+	17.6780i	0.0519474	+	0.617721i
$820$	1.19749	−	2.07411i	0.0418180	−	0.0724310i
$821$			26.3045i			0.918034i	0.888428	+	0.459017i	$0.151798\pi$
$821$			26.3045i			0.918034i	−0.888428	+	0.459017i	$0.848202\pi$
$822$	23.1450			0.807275
$823$	−4.27919	+	7.41177i	−0.149163	+	0.258358i	−0.930918	−	0.365227i	$-0.880991\pi$
$823$	−4.27919	+	7.41177i	−0.149163	+	0.258358i	0.781755	+	0.623585i	$0.214325\pi$
$824$	4.32573	−	2.49746i	0.150694	−	0.0870032i
$825$	−121.902	−	70.3803i	−4.24409	−	2.45033i
$826$	−19.7435	+	11.3989i	−0.686963	+	0.396618i
$827$	38.5749	−	22.2712i	1.34138	−	0.774447i	0.354371	−	0.935105i	$-0.384695\pi$
$827$	38.5749	−	22.2712i	1.34138	−	0.774447i	0.987010	+	0.160659i	$0.0513618\pi$
$828$	11.7156	+	20.2921i	0.407147	+	0.705199i
$829$	24.1665			0.839336			0.419668	−	0.907678i	$-0.362147\pi$
$829$	24.1665			0.839336			0.419668	+	0.907678i	$0.362147\pi$
$830$	17.0372	+	9.83642i	0.591369	+	0.341427i
$831$	3.80201	−	6.58527i	0.131890	−	0.228440i
$832$	−9.76609	+	0.821283i	−0.338578	+	0.0284729i
$833$	0.0316965			0.00109822
$834$	−29.7240	−	17.1611i	−1.02926	−	0.594241i
$835$	−27.9951			−0.968809
$836$	37.8075			1.30760
$837$	−0.172171	+	5.21596i	−0.00595110	+	0.180290i
$838$		−	39.0652i		−	1.34949i
$839$		−	7.81667i		−	0.269861i	−0.990855	−	0.134931i	$-0.956919\pi$
$839$		−	7.81667i		−	0.269861i	0.990855	−	0.134931i	$-0.0430812\pi$
$840$	−13.2509	−	7.65043i	−0.457201	−	0.263965i
$841$	−28.2601			−0.974485
$842$	−8.49992	−	14.7223i	−0.292927	−	0.507364i
$843$	−3.74962	−	2.16484i	−0.129144	−	0.0745611i
$844$	4.32478	−	7.49073i	0.148865	−	0.257842i
$845$	37.7338	−	31.2316i	1.29808	−	1.07440i
$846$	−25.1433	−	43.5496i	−0.864446	−	1.49726i
$847$	32.5681	−	18.8032i	1.11905	−	0.646086i
$848$	1.77984	+	3.08277i	0.0611200	+	0.105863i
$849$	−9.27838	+	16.0706i	−0.318433	+	0.551542i
$850$	−0.0956177	+	0.0552049i	−0.00327966	+	0.00189351i
$851$	28.3315	+	16.3572i	0.971193	+	0.560719i
$852$			47.7200i			1.63486i
$853$			33.9582i			1.16271i	0.813652	+	0.581353i	$0.197476\pi$
$853$			33.9582i			1.16271i	−0.813652	+	0.581353i	$0.802524\pi$
$854$	−12.6397	+	21.8926i	−0.432521	+	0.749148i
$855$	−28.2389	−	48.9111i	−0.965749	−	1.67273i
$856$	−8.10845	−	4.68142i	−0.277141	−	0.160007i
$857$	2.70568	+	4.68638i	0.0924244	+	0.160084i	0.908531	−	0.417818i	$-0.137205\pi$
$857$	2.70568	+	4.68638i	0.0924244	+	0.160084i	−0.816106	+	0.577902i	$0.803872\pi$
$858$	−101.433	+	8.53006i	−3.46287	+	0.291211i
$859$	14.4066	+	24.9530i	0.491548	+	0.851387i	0.999953	−	0.00973182i	$-0.00309778\pi$
$859$	14.4066	+	24.9530i	0.491548	+	0.851387i	−0.508404	+	0.861118i	$0.669764\pi$
$860$			22.8062i			0.777685i
$861$	0.834864	−	1.44603i	0.0284521	−	0.0492805i
$862$	−20.2738	+	35.1153i	−0.690530	+	1.19603i
$863$	4.13582	−	2.38782i	0.140785	−	0.0812822i	−0.427953	−	0.903801i	$-0.640765\pi$
$863$	4.13582	−	2.38782i	0.140785	−	0.0812822i	0.568738	+	0.822519i	$0.307432\pi$
$864$		−	6.29829i		−	0.214272i
$865$	40.9845	+	23.6624i	1.39351	+	0.804546i
$866$			14.8533i			0.504736i
$867$	−42.9105			−1.45732
$868$	6.02027	−	9.67553i	0.204341	−	0.328409i
$869$			34.5716i			1.17276i
$870$	−15.0903			−0.511608
$871$	−42.8155	+	29.7653i	−1.45075	+	1.00856i
$872$	−7.98061			−0.270257
$873$	15.6747	−	9.04980i	0.530509	−	0.306289i
$874$	−20.3221	+	35.1989i	−0.687405	+	1.19062i
$875$	11.5390	−	19.9861i	0.390088	−	0.675652i
$876$		−	16.5677i		−	0.559771i
$877$	−0.427352	+	0.246732i	−0.0144307	+	0.00833154i	−0.507198	−	0.861830i	$-0.669319\pi$
$877$	−0.427352	+	0.246732i	−0.0144307	+	0.00833154i	0.492767	+	0.870161i	$0.335985\pi$
$878$	42.6842	−	24.6437i	1.44052	−	0.831686i
$879$	20.5592	−	11.8699i	0.693446	−	0.400361i
$880$	55.2675	−	95.7262i	1.86307	−	3.22693i
$881$	9.40696	+	16.2933i	0.316928	+	0.548936i	0.979846	−	0.199757i	$-0.0640152\pi$
$881$	9.40696	+	16.2933i	0.316928	+	0.548936i	−0.662917	+	0.748693i	$0.730682\pi$
$882$	−26.2273	−	15.1423i	−0.883119	−	0.509869i
$883$	−7.26725			−0.244562			−0.122281	−	0.992495i	$-0.539021\pi$
$883$	−7.26725			−0.244562			−0.122281	+	0.992495i	$0.539021\pi$
$884$	−0.0140085	+	0.0297790i	−0.000471157	+	0.00100158i
$885$	−40.2708	+	69.7512i	−1.35369	+	2.34466i
$886$	4.33480	−	2.50270i	0.145630	−	0.0840798i
$887$	−7.81719	+	13.5398i	−0.262475	+	0.454621i	−0.966899	−	0.255159i	$-0.917872\pi$
$887$	−7.81719	+	13.5398i	−0.262475	+	0.454621i	0.704424	+	0.709780i	$0.251206\pi$
$888$	−9.18362	−	15.9065i	−0.308182	−	0.533787i
$889$	3.16672	−	1.82831i	0.106208	−	0.0613194i
$890$	−49.7711	+	28.7353i	−1.66833	+	0.963211i
$891$			46.9814i			1.57394i
$892$	20.3729	+	11.7623i	0.682136	+	0.393832i
$893$	17.9767	−	31.1365i	0.601566	−	1.04194i
$894$	11.7566	+	20.3631i	0.393200	+	0.681043i
$895$			71.6674i			2.39558i
$896$	6.14797	−	10.6486i	0.205389	−	0.355744i
$897$	19.1993	−	40.8136i	0.641047	−	1.36273i
$898$	−23.8984			−0.797500
$899$	−0.158003	+	4.78675i	−0.00526971	+	0.159647i
$900$	43.4813			1.44938
$901$	0.00478872			0.000159535
$902$	4.39030	+	2.53474i	0.146181	+	0.0843977i
$903$			15.9000i			0.529120i
$904$	16.5674	−	9.56521i	0.551024	−	0.318134i
$905$	−35.1852	−	20.3142i	−1.16960	−	0.675266i
$906$	−44.0865	+	76.3601i	−1.46468	+	2.53689i
$907$	7.65201			0.254081			0.127040	−	0.991898i	$-0.459452\pi$
$907$	7.65201			0.254081			0.127040	+	0.991898i	$0.459452\pi$
$908$	32.4700	−	18.7466i	1.07755	−	0.622126i
$909$	−15.4632	−	26.7831i	−0.512883	−	0.888340i
$910$	−3.06471	−	36.4433i	−0.101594	−	1.20808i
$911$	−26.7325	+	46.3021i	−0.885689	+	1.53406i	−0.0407661	+	0.999169i	$0.512980\pi$
$911$	−26.7325	+	46.3021i	−0.885689	+	1.53406i	−0.844922	+	0.534889i	$0.820353\pi$
$912$	47.0219	−	27.1481i	1.55705	−	0.898963i
$913$	−8.58189	+	14.8643i	−0.284019	+	0.491936i
$914$	−44.3091			−1.46561
$915$			89.3088i			2.95246i
$916$	16.1318	+	9.31370i	0.533010	+	0.307733i
$917$	−14.4339	+	8.33343i	−0.476650	+	0.275194i
$918$	−0.00974528	−	0.00562644i	−0.000321642	−	0.000185700i
$919$	6.12734	+	10.6129i	0.202122	+	0.350086i	0.949212	−	0.314637i	$-0.101883\pi$
$919$	6.12734	+	10.6129i	0.202122	+	0.350086i	−0.747090	+	0.664723i	$0.768550\pi$
$920$	10.2922	+	17.8266i	0.339323	+	0.587725i
$921$	−45.0862	+	26.0305i	−1.48564	+	0.857735i
$922$	5.71512			0.188218
$923$	39.9095	−	27.7450i	1.31364	−	0.913239i
$924$	−15.6629	+	27.1290i	−0.515273	+	0.892479i
$925$	52.5747	−	30.3540i	1.72865	−	0.998035i
$926$	63.7478			2.09488
$927$	−7.63811	+	13.2296i	−0.250868	+	0.434517i
$928$		−	5.78002i		−	0.189738i
$929$			43.9383i			1.44157i	0.693159	+	0.720785i	$0.256219\pi$
$929$			43.9383i			1.44157i	−0.693159	+	0.720785i	$0.743781\pi$
$930$	3.22234	−	97.6215i	0.105665	−	3.20114i
$931$		−	21.6525i		−	0.709633i
$932$	−6.65590			−0.218021
$933$	26.6291	−	46.1229i	0.871797	−	1.51000i
$934$		−	0.212687i		−	0.00695932i
$935$	−0.0743496	−	0.128777i	−0.00243149	−	0.00421147i
$936$	−11.0021	+	7.64865i	−0.359615	+	0.250004i
$937$	6.65426	−	11.5255i	0.217385	−	0.376522i	−0.736623	−	0.676304i	$-0.763581\pi$
$937$	6.65426	−	11.5255i	0.217385	−	0.376522i	0.954008	+	0.299782i	$0.0969139\pi$
$938$			38.9337i			1.27123i
$939$	6.22270	+	10.7780i	0.203070	+	0.351728i
$940$	21.3643	+	37.0041i	0.696827	+	1.20694i
$941$	3.50370	−	2.02286i	0.114217	−	0.0659435i	−0.441803	−	0.897112i	$-0.645661\pi$
$941$	3.50370	−	2.02286i	0.114217	−	0.0659435i	0.556020	+	0.831169i	$0.312328\pi$
$942$	44.3536	+	25.6076i	1.44512	+	0.834340i
$943$	−1.94535	+	1.12315i	−0.0633494	+	0.0365748i
$944$	−35.4826	−	20.4859i	−1.15486	−	0.666759i
$945$	5.15435			0.167671
$946$	−48.2743			−1.56953
$947$	2.73462	+	1.57884i	0.0888633	+	0.0513053i	0.543773	−	0.839232i	$-0.316995\pi$
$947$	2.73462	+	1.57884i	0.0888633	+	0.0513053i	−0.454910	+	0.890538i	$0.650329\pi$
$948$	−10.0911	−	17.4783i	−0.327744	−	0.567669i
$949$	−13.8560	+	9.63267i	−0.449785	+	0.312690i
$950$	37.7116	+	65.3185i	1.22353	+	2.11921i
$951$	7.51352	−	4.33793i	0.243643	−	0.140667i
$952$	−0.00523550	−	0.00906816i	−0.000169684	−	0.000293901i
$953$	22.8000			0.738565			0.369282	−	0.929317i	$-0.379603\pi$
$953$	22.8000			0.738565			0.369282	+	0.929317i	$0.379603\pi$
$954$	−3.96243	−	2.28771i	−0.128289	−	0.0740674i
$955$	69.3968	+	40.0663i	2.24563	+	1.29651i
$956$	24.7279	−	14.2766i	0.799757	−	0.461740i
$957$		−	13.1657i		−	0.425586i
$958$	34.2807	−	59.3759i	1.10756	−	1.91835i
$959$	−7.25505			−0.234278
$960$			25.8517i			0.834360i
$961$	−30.9325	−	2.04430i	−0.997823	−	0.0659451i
$962$	18.6873	−	39.7252i	0.602504	−	1.28079i
$963$	28.6348			0.922743
$964$	20.8595	+	12.0432i	0.671839	+	0.387886i
$965$	96.0472			3.09187
$966$	−16.8381	−	29.1645i	−0.541758	−	0.938353i
$967$	−32.6511	−	18.8511i	−1.04999	−	0.606211i	−0.127342	−	0.991859i	$-0.540645\pi$
$967$	−32.6511	−	18.8511i	−1.04999	−	0.606211i	−0.922646	+	0.385648i	$0.873978\pi$
$968$	24.5991	+	14.2023i	0.790644	+	0.456478i
$969$		−	0.0730429i		−	0.00234647i
$970$	−32.3134	+	18.6561i	−1.03752	+	0.599013i
$971$	14.7485	+	25.5451i	0.473301	+	0.819782i	0.999533	−	0.0305593i	$-0.00972884\pi$
$971$	14.7485	+	25.5451i	0.473301	+	0.819782i	−0.526232	+	0.850341i	$0.676396\pi$
$972$	−15.6851	−	27.1675i	−0.503101	−	0.871396i
$973$	9.31729	+	5.37934i	0.298699	+	0.172454i
$974$	−33.4359	−	57.9127i	−1.07136	−	1.85564i
$975$	−47.7766	−	68.7237i	−1.53008	−	2.20092i
$976$	−45.4316			−1.45423
$977$		−	47.1668i		−	1.50900i	−0.656300	−	0.754500i	$-0.727879\pi$
$977$		−	47.1668i		−	1.50900i	0.656300	−	0.754500i	$-0.272121\pi$
$978$	−26.0607	+	45.1384i	−0.833328	+	1.44337i
$979$	−25.0705	−	43.4233i	−0.801256	−	1.38782i
$980$	22.2854	+	12.8665i	0.711880	+	0.411004i
$981$	21.1375	−	12.2037i	0.674868	−	0.389635i
$982$	0.824746	−	0.476167i	0.0263187	−	0.0151951i
$983$	−44.1889	+	25.5125i	−1.40941	+	0.813721i	−0.995331	−	0.0965213i	$-0.969228\pi$
$983$	−44.1889	+	25.5125i	−1.40941	+	0.813721i	−0.414076	+	0.910243i	$0.635895\pi$
$984$	1.26116			0.0402045
$985$	34.1817	−	59.2044i	1.08912	−	1.88641i
$986$	−0.00894336	−	0.00516345i	−0.000284814	−	0.000164438i
$987$	14.8948	+	25.7985i	0.474106	+	0.821176i
$988$	20.3427	+	9.56950i	0.647187	+	0.304446i
$989$	10.6952	−	18.5247i	0.340088	−	0.589050i
$990$			142.076i			4.51547i
$991$	51.3004			1.62961			0.814806	−	0.579734i	$-0.196843\pi$
$991$	51.3004			1.62961			0.814806	+	0.579734i	$0.196843\pi$
$992$	37.3919	+	1.23425i	1.18719	+	0.0391875i
$993$			71.3521i			2.26429i
$994$		−	36.2912i		−	1.15109i
$995$	−14.8050	−	8.54767i	−0.469350	−	0.270979i
$996$		−	10.0199i		−	0.317492i
$997$	29.6438	+	51.3445i	0.938827	+	1.62610i	0.767663	+	0.640854i	$0.221420\pi$
$997$	29.6438	+	51.3445i	0.938827	+	1.62610i	0.171164	+	0.985243i	$0.445247\pi$
$998$	−20.9935	+	36.3618i	−0.664538	+	1.15101i
$999$	5.35837	+	3.09366i	0.169531	+	0.0978790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.129.26	yes	68
13.12	even	2	inner	403.2.l.c.129.9	yes	68
31.25	even	3	inner	403.2.l.c.25.26	yes	68
403.25	even	6	inner	403.2.l.c.25.9	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.9	✓	68	403.25	even	6	inner
403.2.l.c.25.26	yes	68	31.25	even	3	inner
403.2.l.c.129.9	yes	68	13.12	even	2	inner
403.2.l.c.129.26	yes	68	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.84455i q^{2} +(-1.26208 + 2.18598i) q^{3} -1.40238 q^{4} +(3.26306 - 1.88393i) q^{5} +(-4.03216 - 2.32797i) q^{6} +(1.26392 + 0.729726i) q^{7} +1.10234i q^{8} +(-1.68567 - 2.91967i) q^{9} +O(q^{10})\)	\(q+1.84455i q^{2} +(-1.26208 + 2.18598i) q^{3} -1.40238 q^{4} +(3.26306 - 1.88393i) q^{5} +(-4.03216 - 2.32797i) q^{6} +(1.26392 + 0.729726i) q^{7} +1.10234i q^{8} +(-1.68567 - 2.91967i) q^{9} +(3.47501 + 6.01889i) q^{10} +(-5.25125 + 3.03181i) q^{11} +(1.76991 - 3.06558i) q^{12} +(-3.59287 + 0.302144i) q^{13} +(-1.34602 + 2.33137i) q^{14} +9.51064i q^{15} -4.83809 q^{16} +(-0.00325426 + 0.00563654i) q^{17} +(5.38549 - 3.10931i) q^{18} +(3.85044 + 2.22305i) q^{19} +(-4.57605 + 2.64198i) q^{20} +(-3.19033 + 1.84194i) q^{21} +(-5.59234 - 9.68621i) q^{22} +4.95595 q^{23} +(-2.40970 - 1.39124i) q^{24} +(4.59837 - 7.96461i) q^{25} +(-0.557320 - 6.62724i) q^{26} +0.937324 q^{27} +(-1.77250 - 1.02335i) q^{28} +0.860193 q^{29} -17.5429 q^{30} +(-0.183683 + 5.56473i) q^{31} -6.71944i q^{32} -15.3055i q^{33} +(-0.0103969 - 0.00600266i) q^{34} +5.49901 q^{35} +(2.36395 + 4.09449i) q^{36} +(5.71667 + 3.30052i) q^{37} +(-4.10054 + 7.10235i) q^{38} +(3.87399 - 8.23527i) q^{39} +(2.07673 + 3.59700i) q^{40} +(-0.392528 + 0.226626i) q^{41} +(-3.39756 - 5.88474i) q^{42} +(2.15806 - 3.73786i) q^{43} +(7.36425 - 4.25175i) q^{44} +(-11.0009 - 6.35137i) q^{45} +9.14152i q^{46} -8.08647i q^{47} +(6.10604 - 10.5760i) q^{48} +(-2.43500 - 4.21754i) q^{49} +(14.6912 + 8.48194i) q^{50} +(-0.00821425 - 0.0142275i) q^{51} +(5.03857 - 0.423720i) q^{52} +(-0.367881 - 0.637188i) q^{53} +1.72895i q^{54} +(-11.4234 + 19.7859i) q^{55} +(-0.804407 + 1.39327i) q^{56} +(-9.71910 + 5.61133i) q^{57} +1.58667i q^{58} +(7.33401 + 4.23429i) q^{59} -13.3375i q^{60} +9.39041 q^{61} +(-10.2645 - 0.338814i) q^{62} -4.92031i q^{63} +2.71819 q^{64} +(-11.1545 + 7.75462i) q^{65} +28.2318 q^{66} +(12.5249 - 7.23126i) q^{67} +(0.00456371 - 0.00790458i) q^{68} +(-6.25479 + 10.8336i) q^{69} +10.1432i q^{70} +(-11.6748 + 6.74046i) q^{71} +(3.21847 - 1.85818i) q^{72} +(4.05332 - 2.34019i) q^{73} +(-6.08799 + 10.5447i) q^{74} +(11.6070 + 20.1039i) q^{75} +(-5.39979 - 3.11757i) q^{76} -8.84957 q^{77} +(15.1904 + 7.14579i) q^{78} +(2.85074 - 4.93762i) q^{79} +(-15.7870 + 9.11461i) q^{80} +(3.87404 - 6.71003i) q^{81} +(-0.418025 - 0.724040i) q^{82} +(2.45139 - 1.41531i) q^{83} +(4.47406 - 2.58310i) q^{84} +0.0245232i q^{85} +(6.89469 + 3.98065i) q^{86} +(-1.08563 + 1.88037i) q^{87} +(-3.34209 - 5.78867i) q^{88} +8.26914i q^{89} +(11.7154 - 20.2917i) q^{90} +(-4.76159 - 2.23993i) q^{91} -6.95013 q^{92} +(-11.9326 - 7.42464i) q^{93} +14.9159 q^{94} +16.7523 q^{95} +(14.6886 + 8.48044i) q^{96} +5.36866i q^{97} +(7.77948 - 4.49149i) q^{98} +(17.7038 + 10.2213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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