LMFDB - Embedded newform 403.2.l.c.25.9

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			25.9
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.26

$q$-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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

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

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	$-0.773868\pi$
$2$		−	1.84455i		−	1.30430i	0.758091	−	0.652148i	$-0.226132\pi$
$3$	−1.26208	−	2.18598i	−0.728660	−	1.26208i	−0.957450	−	0.288600i	$-0.906810\pi$
$3$	−1.26208	−	2.18598i	−0.728660	−	1.26208i	0.228790	−	0.973476i	$-0.426523\pi$
$4$	−1.40238			−0.701190
$5$	3.26306	+	1.88393i	1.45928	+	0.842518i	0.998976	−	0.0452409i	$-0.0144055\pi$
$5$	3.26306	+	1.88393i	1.45928	+	0.842518i	0.460308	+	0.887759i	$0.347739\pi$
$6$	−4.03216	+	2.32797i	−1.64612	+	0.950389i
$7$	1.26392	−	0.729726i	0.477718	−	0.275811i	−0.241747	−	0.970339i	$-0.577720\pi$
$7$	1.26392	−	0.729726i	0.477718	−	0.275811i	0.719465	+	0.694529i	$0.244387\pi$
$8$		−	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	−0.994372	−	0.105948i	$-0.966212\pi$
$11$	−5.25125	−	3.03181i	−1.58331	−	0.914125i	−0.588939	−	0.808177i	$-0.700454\pi$
$12$	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	0.865630	−	0.500683i	$-0.166918\pi$
$17$	−0.00325426	−	0.00563654i	−0.000789274	−	0.00136706i	−0.866420	+	0.499316i	$0.833585\pi$
$18$	5.38549	+	3.10931i	1.26937	+	0.732872i
$19$	3.85044	−	2.22305i	0.883352	−	0.510004i	0.0115898	−	0.999933i	$-0.496311\pi$
$19$	3.85044	−	2.22305i	0.883352	−	0.510004i	0.871762	+	0.489929i	$0.162977\pi$
$20$	−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	0.0499126	−	0.998754i	$-0.484106\pi$
$37$	5.71667	−	3.30052i	0.939815	−	0.542602i	0.889902	+	0.456151i	$0.150772\pi$
$38$	−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	0.469035	−	0.883179i	$-0.344602\pi$
$41$	−0.392528	−	0.226626i	−0.0613026	−	0.0353931i	−0.530338	+	0.847786i	$0.677935\pi$
$42$	−3.39756	+	5.88474i	−0.524255	+	0.908036i
$43$	2.15806	+	3.73786i	0.329100	+	0.570019i	0.982334	−	0.187138i	$-0.0599212\pi$
$43$	2.15806	+	3.73786i	0.329100	+	0.570019i	−0.653233	+	0.757157i	$0.726588\pi$
$44$	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	$0.200780\pi$
$47$			8.08647i			1.17953i	−0.807574	+	0.589766i	$0.799220\pi$
$48$	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	−0.890185	−	0.455599i	$-0.849425\pi$
$53$	−0.367881	+	0.637188i	−0.0505323	+	0.0875245i	0.839653	+	0.543123i	$0.182758\pi$
$54$		−	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	0.0602361	−	0.998184i	$-0.480815\pi$
$59$	7.33401	−	4.23429i	0.954807	−	0.551258i	0.894571	+	0.446926i	$0.147481\pi$
$60$			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	0.999354	+	0.0359478i	$0.0114450\pi$
$67$	12.5249	+	7.23126i	1.53016	+	0.883440i	0.530809	+	0.847492i	$0.321888\pi$
$68$	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	−0.392736	−	0.919651i	$-0.628471\pi$
$71$	−11.6748	−	6.74046i	−1.38555	−	0.799945i	−0.992809	+	0.119706i	$0.961805\pi$
$72$	3.21847	+	1.85818i	0.379300	+	0.218989i
$73$	4.05332	+	2.34019i	0.474406	+	0.273898i	0.718082	−	0.695958i	$-0.245020\pi$
$73$	4.05332	+	2.34019i	0.474406	+	0.273898i	−0.243676	+	0.969857i	$0.578354\pi$
$74$	−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	0.980639	−	0.195822i	$-0.0627375\pi$
$79$	2.85074	+	4.93762i	0.320733	+	0.555526i	−0.659907	+	0.751348i	$0.729404\pi$
$80$	−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	0.628467	−	0.777836i	$-0.283683\pi$
$83$	2.45139	+	1.41531i	0.269075	+	0.155350i	−0.359392	+	0.933187i	$0.617016\pi$
$84$	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	$-0.855594\pi$
$89$		−	8.26914i		−	0.876528i	0.898846	−	0.438264i	$-0.144406\pi$
$90$	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	$-0.912132\pi$
$97$		−	5.36866i		−	0.545105i	0.962141	−	0.272553i	$-0.0878678\pi$
$98$	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	−0.955789	−	0.294054i	$-0.904995\pi$
$103$	−2.26560	+	3.92413i	−0.223236	+	0.386656i	0.732553	+	0.680710i	$0.238329\pi$
$104$	−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	0.584397	−	0.811468i	$-0.301331\pi$
$107$	−4.24679	−	7.35566i	−0.410553	−	0.711099i	−0.994950	+	0.100369i	$0.967998\pi$
$108$	−1.31449			−0.126486
$109$		−	7.23969i		−	0.693436i	−0.937969	−	0.346718i	$-0.887296\pi$
$109$		−	7.23969i		−	0.693436i	0.937969	−	0.346718i	$-0.112704\pi$
$110$	−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	0.0921256	+	0.995747i	$0.470634\pi$
$113$	−8.67717	+	15.0293i	−0.816280	+	1.41384i	−0.908405	+	0.418091i	$0.862699\pi$
$114$	−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	0.916239	−	0.400632i	$-0.131209\pi$
$127$	1.25273	+	2.16980i	0.111162	+	0.192539i	−0.805077	+	0.593170i	$0.797876\pi$
$128$			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	0.501117	−	0.865380i	$-0.332923\pi$
$131$	−5.70997	−	9.88996i	−0.498882	−	0.864090i	−0.999999	+	0.00129000i	$0.999589\pi$
$132$		−	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	0.304693	−	0.952451i	$-0.401446\pi$
$137$	−4.30508	−	2.48554i	−0.367808	−	0.212354i	−0.672500	+	0.740097i	$0.734780\pi$
$138$	−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	−0.668333	−	0.743862i	$-0.732992\pi$
$149$	−4.37357	+	2.52508i	−0.358297	+	0.206863i	0.310037	+	0.950725i	$0.399659\pi$
$150$	−37.0827	−	21.4097i	−3.02779	−	1.74810i
$151$			18.9378i			1.54113i	0.637359	+	0.770567i	$0.280027\pi$
$151$			18.9378i			1.54113i	−0.637359	+	0.770567i	$0.719973\pi$
$152$	−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	$0.144460\pi$
$163$			11.1946i			0.876829i	−0.898773	+	0.438414i	$0.855540\pi$
$164$	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	−0.727854	−	0.685732i	$-0.759482\pi$
$167$	−6.43455	+	3.71499i	−0.497920	+	0.287474i	0.229934	+	0.973206i	$0.426149\pi$
$168$	−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	−0.522202	−	0.852822i	$-0.674889\pi$
$173$	6.28007	−	10.8774i	0.477465	−	0.826993i	0.999666	+	0.0258288i	$0.00822248\pi$
$174$	−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	−0.964543	−	0.263927i	$-0.914982\pi$
$179$	−9.51037	−	16.4725i	−0.710839	−	1.23121i	0.253704	−	0.967282i	$-0.418351\pi$
$180$	15.4274	−	8.90703i	1.14989	−	0.663891i
$181$	−5.39144	+	9.33826i	−0.400743	+	0.694107i	−0.993816	−	0.111042i	$-0.964581\pi$
$181$	−5.39144	+	9.33826i	−0.400743	+	0.694107i	0.593073	+	0.805149i	$0.297915\pi$
$182$	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	−0.168445	−	0.985711i	$-0.553875\pi$
$191$	10.6337	−	18.4181i	0.769428	−	1.33269i	0.937873	−	0.346977i	$-0.112792\pi$
$192$	−3.43056	−	5.94190i	−0.247579	−	0.428820i
$193$	22.0760	−	12.7456i	1.58907	−	0.917448i	0.595606	−	0.803277i	$-0.296912\pi$
$193$	22.0760	−	12.7456i	1.58907	−	0.917448i	0.993461	−	0.114172i	$-0.0364215\pi$
$194$	−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	0.941275	−	0.337641i	$-0.109629\pi$
$197$	15.7130	+	9.07192i	1.11951	+	0.646347i	0.178232	+	0.983989i	$0.442962\pi$
$198$	−18.8537	−	32.6555i	−1.33987	−	2.32073i
$199$	−2.26858	+	3.92929i	−0.160815	+	0.278540i	−0.935161	−	0.354222i	$-0.884746\pi$
$199$	−2.26858	+	3.92929i	−0.160815	+	0.278540i	0.774346	+	0.632762i	$0.218079\pi$
$200$	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	0.740132	−	0.672462i	$-0.234763\pi$
$211$	−3.08388	−	5.34144i	−0.212303	−	0.367720i	−0.952435	+	0.304742i	$0.901430\pi$
$212$	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	−0.900097	−	0.435690i	$-0.856504\pi$
$223$	−14.5274	+	8.38740i	−0.972826	+	0.561662i	−0.0727296	+	0.997352i	$0.523171\pi$
$224$	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	−0.999026	−	0.0441224i	$-0.985951\pi$
$227$	−23.1535	−	13.3677i	−1.53675	−	0.887243i	−0.537724	−	0.843121i	$-0.680716\pi$
$228$	13.6299	+	7.86921i	0.902661	+	0.521151i
$229$	−11.5032	+	6.64135i	−0.760150	+	0.438873i	−0.829350	−	0.558730i	$-0.811289\pi$
$229$	−11.5032	+	6.64135i	−0.760150	+	0.438873i	0.0691997	+	0.997603i	$0.477955\pi$
$230$	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	−0.193998	−	0.981002i	$-0.562146\pi$
$239$	−17.6328	−	10.1803i	−1.14057	−	0.658508i	−0.946572	+	0.322494i	$0.895479\pi$
$240$			46.0133i			2.97015i
$241$	−14.8743	+	8.58771i	−0.958141	+	0.553183i	−0.895600	−	0.444860i	$-0.853254\pi$
$241$	−14.8743	+	8.58771i	−0.958141	+	0.553183i	−0.0625404	+	0.998042i	$0.519920\pi$
$242$	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	0.993835	−	0.110868i	$-0.0353632\pi$
$251$	6.35149	+	11.0011i	0.400903	+	0.694384i	−0.592932	+	0.805252i	$0.702030\pi$
$252$		−	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	0.497513	+	0.867457i	$0.334247\pi$
$257$	−8.05542	+	13.9524i	−0.502483	+	0.870326i	−0.999996	+	0.00286970i	$0.999087\pi$
$258$	−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	−0.995566	−	0.0940666i	$-0.970013\pi$
$269$	−6.82814	+	11.8267i	−0.416319	+	0.721086i	0.579247	+	0.815152i	$0.303347\pi$
$270$	3.25721	−	5.64165i	0.198227	−	0.343340i
$271$			1.75331i			0.106506i	0.998581	+	0.0532529i	$0.0169590\pi$
$271$			1.75331i			0.106506i	−0.998581	+	0.0532529i	$0.983041\pi$
$272$	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	$-0.983707\pi$
$281$		−	1.71530i		−	0.102326i	0.998690	−	0.0511632i	$-0.0162929\pi$
$282$	−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	−0.718680	−	0.695341i	$-0.755253\pi$
$293$	−8.14501	+	4.70252i	−0.475837	+	0.274724i	0.242843	+	0.970066i	$0.421920\pi$
$294$		−	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	0.105494	−	0.994420i	$-0.466358\pi$
$307$	17.8619	−	10.3126i	1.01943	−	0.588570i	0.913940	+	0.405849i	$0.133024\pi$
$308$	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	0.927249	−	0.374446i	$-0.122167\pi$
$313$	2.46526	+	4.26996i	0.139345	+	0.241352i	−0.787904	+	0.615798i	$0.788834\pi$
$314$			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	−0.581258	−	0.813719i	$-0.697439\pi$
$317$	−2.97665	+	1.71857i	−0.167185	+	0.0965245i	0.414073	+	0.910244i	$0.364106\pi$
$318$		−	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	0.987619	−	0.156870i	$-0.0501402\pi$
$331$	24.4806	+	14.1339i	1.34558	+	0.776869i	0.357957	+	0.933738i	$0.383474\pi$
$332$	−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	0.981544	−	0.191235i	$-0.0612494\pi$
$347$	6.05701	+	10.4911i	0.325157	+	0.563189i	−0.656387	+	0.754425i	$0.727916\pi$
$348$	1.52247	+	2.63699i	0.0816127	+	0.141357i
$349$		−	12.2402i		−	0.655203i	−0.944816	−	0.327601i	$-0.893760\pi$
$349$		−	12.2402i		−	0.655203i	0.944816	−	0.327601i	$-0.106240\pi$
$350$	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	−0.651036	−	0.759047i	$-0.725665\pi$
$353$	−5.99723	+	3.46251i	−0.319201	+	0.184291i	0.331836	+	0.943337i	$0.392332\pi$
$354$	−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	0.255797	−	0.966730i	$-0.417662\pi$
$359$	−8.59293	−	4.96113i	−0.453517	−	0.261838i	−0.709314	+	0.704892i	$0.750995\pi$
$360$	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	−0.887277	−	0.461238i	$-0.847405\pi$
$367$	−0.846646	+	1.46643i	−0.0441946	+	0.0765472i	0.843082	+	0.537785i	$0.180739\pi$
$368$	−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	−0.941201	−	0.337848i	$-0.890301\pi$
$379$	−21.7888	+	12.5798i	−1.11922	+	0.646180i	−0.178016	+	0.984028i	$0.556968\pi$
$380$	−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	0.935138	−	0.354285i	$-0.115276\pi$
$383$	21.4469	+	12.3824i	1.09589	+	0.632711i	0.160749	+	0.986995i	$0.448609\pi$
$384$	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	0.803802	−	0.594896i	$-0.202807\pi$
$389$	−2.23451	−	3.87028i	−0.113294	−	0.196231i	−0.917097	+	0.398665i	$0.869474\pi$
$390$	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	−0.709390	−	0.704816i	$-0.751029\pi$
$397$	−9.03983	+	5.21915i	−0.453696	+	0.261941i	0.255694	+	0.966758i	$0.417696\pi$
$398$	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	$0.252822\pi$
$401$			28.5696i			1.42670i	−0.700809	+	0.713349i	$0.747178\pi$
$402$	−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	−0.199618	−	0.979874i	$-0.563970\pi$
$409$	11.1062	−	6.41219i	0.549168	−	0.317063i	0.748787	+	0.662811i	$0.230637\pi$
$410$	−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	0.292730	−	0.956195i	$-0.405436\pi$
$421$	−7.98149	−	4.60812i	−0.388994	−	0.224586i	−0.681724	+	0.731609i	$0.738770\pi$
$422$	−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	0.0343193	−	0.999411i	$-0.489074\pi$
$431$	19.0373	−	10.9912i	0.916994	−	0.529427i	0.882675	+	0.469984i	$0.155740\pi$
$432$	−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	0.348296	+	0.937384i	$0.386760\pi$
$439$	−13.3603	+	23.1407i	−0.637651	+	1.10444i	−0.985947	+	0.167059i	$0.946573\pi$
$440$	−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	−0.896456	−	0.443133i	$-0.853867\pi$
$443$	−1.35680	+	2.35005i	−0.0644637	+	0.111654i	0.831992	+	0.554787i	$0.187200\pi$
$444$	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	$-0.901103\pi$
$449$		−	12.9562i		−	0.611441i	0.952121	−	0.305720i	$-0.0988973\pi$
$450$			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	$-0.810093\pi$
$457$		−	24.0216i		−	1.12368i	0.827245	−	0.561841i	$-0.189907\pi$
$458$	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	$0.0229870\pi$
$461$			3.09838i			0.144306i	−0.997394	+	0.0721529i	$0.977013\pi$
$462$	35.6828	−	20.6015i	1.66012	−	0.958469i
$463$			34.5600i			1.60614i	0.595885	+	0.803070i	$0.296802\pi$
$463$			34.5600i			1.60614i	−0.595885	+	0.803070i	$0.703198\pi$
$464$	−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	−0.999462	−	0.0327969i	$-0.989559\pi$
$479$	−32.1898	+	18.5848i	−1.47079	+	0.849161i	−0.471328	+	0.881958i	$0.656225\pi$
$480$	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	−0.426186	−	0.904636i	$-0.640143\pi$
$487$	−31.3966	−	18.1268i	−1.42272	−	0.821405i	−0.996530	+	0.0832302i	$0.973476\pi$
$488$		−	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	−0.871792	−	0.489877i	$-0.837042\pi$
$491$	−0.258148	+	0.447125i	−0.0116500	+	0.0201785i	0.860142	+	0.510055i	$0.170375\pi$
$492$		−	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	0.0110038	−	0.999939i	$-0.496497\pi$
$499$	19.7131	−	11.3814i	0.882479	−	0.509499i	0.871475	+	0.490440i	$0.163164\pi$
$500$		−	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	0.765930	+	0.642924i	$0.222279\pi$
$503$	21.0765	+	36.5055i	0.939754	+	1.62770i	0.173824	+	0.984777i	$0.444388\pi$
$504$	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	0.260100	−	0.965582i	$-0.416245\pi$
$509$	−10.0638	−	5.81032i	−0.446069	−	0.257538i	−0.706169	+	0.708044i	$0.749578\pi$
$510$	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	0.918746	−	0.394849i	$-0.129203\pi$
$521$	2.68024	+	4.64232i	0.117424	+	0.203384i	−0.801322	+	0.598233i	$0.795870\pi$
$522$	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	0.269053	−	0.963125i	$-0.413289\pi$
$541$	28.7875	−	16.6205i	1.23767	−	0.714570i	0.968618	+	0.248556i	$0.0799559\pi$
$542$	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	−0.554683	−	0.832061i	$-0.687161\pi$
$547$	10.3666	−	17.9555i	0.443245	−	0.767722i	0.997928	+	0.0643392i	$0.0204940\pi$
$548$	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	$-0.960613\pi$
$557$		−	5.82569i		−	0.246842i	0.992354	−	0.123421i	$-0.0393866\pi$
$558$	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	−0.656231	−	0.754560i	$-0.727850\pi$
$563$	7.71984	−	13.3712i	0.325353	−	0.563527i	0.981584	+	0.191033i	$0.0611837\pi$
$564$	−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	−0.997635	−	0.0687359i	$-0.978103\pi$
$569$	−10.4787	+	18.1497i	−0.439290	+	0.760873i	0.558345	+	0.829609i	$0.311437\pi$
$570$	−67.5479	+	38.9988i	−2.82927	+	1.63348i
$571$	−1.30982	+	2.26867i	−0.0548142	+	0.0949410i	−0.892130	−	0.451778i	$-0.850790\pi$
$571$	−1.30982	+	2.26867i	−0.0548142	+	0.0949410i	0.837316	+	0.546719i	$0.184123\pi$
$572$	−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	−0.968874	−	0.247554i	$-0.920373\pi$
$577$	−29.7600	+	17.1819i	−1.23892	+	0.715293i	−0.270049	+	0.962846i	$0.587040\pi$
$578$	−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	$0.0804552\pi$
$587$			12.1177i			0.500149i	−0.968227	+	0.250075i	$0.919545\pi$
$588$	−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	$-0.991400\pi$
$593$		−	1.31568i		−	0.0540284i	0.999635	−	0.0270142i	$-0.00859993\pi$
$594$	−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	−0.0113771	−	0.999935i	$-0.503622\pi$
$599$	21.0549	−	36.4682i	0.860281	−	1.49005i	0.871658	−	0.490115i	$-0.163045\pi$
$600$	−22.1613	−	12.7949i	−0.904733	−	0.522348i
$601$	−14.0503	−	24.3358i	−0.573124	−	0.992680i	−0.996243	−	0.0866054i	$-0.972398\pi$
$601$	−14.0503	−	24.3358i	−0.573124	−	0.992680i	0.423119	−	0.906074i	$-0.360935\pi$
$602$	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	−0.881182	−	0.472777i	$-0.843252\pi$
$607$	−0.767548	+	1.32943i	−0.0311538	+	0.0539600i	0.850028	+	0.526737i	$0.176585\pi$
$608$	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	−0.782008	−	0.623268i	$-0.785805\pi$
$613$	−15.6784	+	9.05195i	−0.633246	+	0.365605i	0.148762	+	0.988873i	$0.452471\pi$
$614$	−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	−0.935437	−	0.353494i	$-0.884994\pi$
$617$	−27.2494	+	15.7325i	−1.09702	+	0.633365i	−0.161584	+	0.986859i	$0.551660\pi$
$618$		−	21.0970i		−	0.848644i
$619$			20.8783i			0.839168i	0.907716	+	0.419584i	$0.137824\pi$
$619$			20.8783i			0.839168i	−0.907716	+	0.419584i	$0.862176\pi$
$620$	−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	0.0256984	−	0.999670i	$-0.491819\pi$
$631$	−20.7788	−	11.9967i	−0.827192	−	0.477579i	−0.852890	+	0.522090i	$0.825152\pi$
$632$	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	−0.758498	−	0.651676i	$-0.774066\pi$
$641$	4.68683	−	8.11783i	0.185119	−	0.320635i	0.943617	+	0.331041i	$0.107400\pi$
$642$	34.2475	+	19.7728i	1.35164	+	0.780370i
$643$		−	23.3392i		−	0.920408i	−0.887813	−	0.460204i	$-0.847776\pi$
$643$		−	23.3392i		−	0.920408i	0.887813	−	0.460204i	$-0.152224\pi$
$644$	−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	0.227941	−	0.973675i	$-0.426801\pi$
$661$	−12.8888	−	7.44134i	−0.501316	−	0.289435i	−0.729257	+	0.684240i	$0.760134\pi$
$662$	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	0.434010	+	0.900908i	$0.357098\pi$
$673$	−14.6108	+	25.3066i	−0.563204	+	0.975499i	−0.997214	+	0.0745904i	$0.976235\pi$
$674$		−	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	−0.966717	−	0.255850i	$-0.917645\pi$
$677$	−6.81146	+	11.7978i	−0.261786	+	0.453426i	0.704931	+	0.709276i	$0.250978\pi$
$678$		−	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	$0.134124\pi$
$683$			21.3781i			0.818009i	−0.912532	+	0.409005i	$0.865876\pi$
$684$		−	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	0.163221	−	0.986589i	$-0.447812\pi$
$691$	−16.0239	−	9.25143i	−0.609580	−	0.351941i	−0.772801	+	0.634649i	$0.781145\pi$
$692$	−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	0.948644	−	0.316346i	$-0.102456\pi$
$701$	5.30476	+	9.18811i	0.200358	+	0.347030i	−0.748286	+	0.663376i	$0.769123\pi$
$702$	−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	$-0.898429\pi$
$709$		−	16.7061i		−	0.627412i	0.949520	−	0.313706i	$-0.101571\pi$
$710$	−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	0.979286	−	0.202481i	$-0.0649006\pi$
$719$	8.42740	+	14.5967i	0.314289	+	0.544365i	−0.664997	+	0.746846i	$0.731567\pi$
$720$	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	0.907979	+	0.419016i	$0.137625\pi$
$727$	22.0252	+	38.1487i	0.816868	+	1.41486i	−0.0911112	+	0.995841i	$0.529042\pi$
$728$	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	0.963416	−	0.268011i	$-0.0863664\pi$
$733$	32.8412	+	18.9609i	1.21302	+	0.700337i	0.249603	+	0.968348i	$0.419700\pi$
$734$	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	0.167017	−	0.985954i	$-0.446587\pi$
$739$	−16.4014	−	9.46937i	−0.603336	−	0.348336i	−0.770353	+	0.637618i	$0.779920\pi$
$740$	−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	$-0.852871\pi$
$743$		−	24.3107i		−	0.891873i	0.895065	−	0.445937i	$-0.147129\pi$
$744$	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	0.698073	−	0.716027i	$-0.254041\pi$
$751$	−7.42825	−	12.8661i	−0.271061	−	0.469491i	−0.969134	+	0.246536i	$0.920708\pi$
$752$		−	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	−0.805847	−	0.592124i	$-0.798289\pi$
$757$	3.02296	−	5.23593i	0.109871	−	0.190303i	0.915718	+	0.401821i	$0.131623\pi$
$758$	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	−0.203436	−	0.979088i	$-0.565211\pi$
$761$	14.9727	−	8.64451i	0.542761	−	0.313363i	0.746197	+	0.665725i	$0.231878\pi$
$762$	−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	−0.796692	−	0.604385i	$-0.793419\pi$
$769$	−18.6248	+	10.7530i	−0.671626	+	0.387763i	0.125067	+	0.992148i	$0.460086\pi$
$770$	−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	$0.251674\pi$
$773$			39.5254i			1.42163i	−0.703379	+	0.710815i	$0.748326\pi$
$774$			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	0.0201655	−	0.999797i	$-0.493581\pi$
$787$	25.1387	−	14.5138i	0.896098	−	0.517362i	0.875932	+	0.482434i	$0.160247\pi$
$788$	−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	−0.906175	−	0.422904i	$-0.861011\pi$
$797$	−2.45164	+	4.24637i	−0.0868417	+	0.150414i	0.819333	+	0.573318i	$0.194344\pi$
$798$			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	0.999422	+	0.0340075i	$0.0108270\pi$
$809$	15.0509	+	26.0690i	0.529162	+	0.916536i	−0.470259	+	0.882528i	$0.655840\pi$
$810$	53.8493			1.89207
$811$	9.77216	+	5.64196i	0.343147	+	0.198116i	0.661663	−	0.749802i	$-0.269851\pi$
$811$	9.77216	+	5.64196i	0.343147	+	0.198116i	−0.318516	+	0.947918i	$0.603184\pi$
$812$	−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	$-0.848202\pi$
$821$		−	26.3045i		−	0.918034i	0.888428	−	0.459017i	$-0.151798\pi$
$822$	23.1450			0.807275
$823$	−4.27919	−	7.41177i	−0.149163	−	0.258358i	0.781755	−	0.623585i	$-0.214325\pi$
$823$	−4.27919	−	7.41177i	−0.149163	−	0.258358i	−0.930918	+	0.365227i	$0.880991\pi$
$824$	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	0.987010	−	0.160659i	$-0.0513618\pi$
$827$	38.5749	+	22.2712i	1.34138	+	0.774447i	0.354371	+	0.935105i	$0.384695\pi$
$828$	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	$0.0430812\pi$
$839$			7.81667i			0.269861i	−0.990855	+	0.134931i	$0.956919\pi$
$840$	−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	$-0.802524\pi$
$853$		−	33.9582i		−	1.16271i	0.813652	−	0.581353i	$-0.197476\pi$
$854$	−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	−0.816106	−	0.577902i	$-0.803872\pi$
$857$	2.70568	−	4.68638i	0.0924244	−	0.160084i	0.908531	+	0.417818i	$0.137205\pi$
$858$	−101.433	−	8.53006i	−3.46287	−	0.291211i
$859$	14.4066	−	24.9530i	0.491548	−	0.851387i	−0.508404	−	0.861118i	$-0.669764\pi$
$859$	14.4066	−	24.9530i	0.491548	−	0.851387i	0.999953	+	0.00973182i	$0.00309778\pi$
$860$		−	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	0.568738	−	0.822519i	$-0.307432\pi$
$863$	4.13582	+	2.38782i	0.140785	+	0.0812822i	−0.427953	+	0.903801i	$0.640765\pi$
$864$			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	0.492767	−	0.870161i	$-0.335985\pi$
$877$	−0.427352	−	0.246732i	−0.0144307	−	0.00833154i	−0.507198	+	0.861830i	$0.669319\pi$
$878$	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	−0.662917	−	0.748693i	$-0.730682\pi$
$881$	9.40696	−	16.2933i	0.316928	−	0.548936i	0.979846	+	0.199757i	$0.0640152\pi$
$882$	−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	0.704424	−	0.709780i	$-0.251206\pi$
$887$	−7.81719	−	13.5398i	−0.262475	−	0.454621i	−0.966899	+	0.255159i	$0.917872\pi$
$888$	−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	−0.844922	−	0.534889i	$-0.820353\pi$
$911$	−26.7325	−	46.3021i	−0.885689	−	1.53406i	−0.0407661	−	0.999169i	$-0.512980\pi$
$912$	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	−0.747090	−	0.664723i	$-0.768550\pi$
$919$	6.12734	−	10.6129i	0.202122	−	0.350086i	0.949212	+	0.314637i	$0.101883\pi$
$920$	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	$-0.743781\pi$
$929$		−	43.9383i		−	1.44157i	0.693159	−	0.720785i	$-0.256219\pi$
$930$	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	0.954008	−	0.299782i	$-0.0969139\pi$
$937$	6.65426	+	11.5255i	0.217385	+	0.376522i	−0.736623	+	0.676304i	$0.763581\pi$
$938$		−	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	0.556020	−	0.831169i	$-0.312328\pi$
$941$	3.50370	+	2.02286i	0.114217	+	0.0659435i	−0.441803	+	0.897112i	$0.645661\pi$
$942$	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	−0.454910	−	0.890538i	$-0.650329\pi$
$947$	2.73462	−	1.57884i	0.0888633	−	0.0513053i	0.543773	+	0.839232i	$0.316995\pi$
$948$	−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	−0.922646	−	0.385648i	$-0.873978\pi$
$967$	−32.6511	+	18.8511i	−1.04999	+	0.606211i	−0.127342	+	0.991859i	$0.540645\pi$
$968$	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	−0.526232	−	0.850341i	$-0.676396\pi$
$971$	14.7485	−	25.5451i	0.473301	−	0.819782i	0.999533	+	0.0305593i	$0.00972884\pi$
$972$	−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	$0.272121\pi$
$977$			47.1668i			1.50900i	−0.656300	+	0.754500i	$0.727879\pi$
$978$	−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	−0.414076	−	0.910243i	$-0.635895\pi$
$983$	−44.1889	−	25.5125i	−1.40941	−	0.813721i	−0.995331	+	0.0965213i	$0.969228\pi$
$984$	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	0.171164	−	0.985243i	$-0.445247\pi$
$997$	29.6438	−	51.3445i	0.938827	−	1.62610i	0.767663	−	0.640854i	$-0.221420\pi$
$998$	−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.25.9	✓	68
13.12	even	2	inner	403.2.l.c.25.26	yes	68
31.5	even	3	inner	403.2.l.c.129.9	yes	68
403.129	even	6	inner	403.2.l.c.129.26	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.9	✓	68	1.1	even	1	trivial
403.2.l.c.25.26	yes	68	13.12	even	2	inner
403.2.l.c.129.9	yes	68	31.5	even	3	inner
403.2.l.c.129.26	yes	68	403.129	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
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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