LMFDB - Embedded newform 399.2.ci.b.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [399,2,Mod(17,399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(399, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 3, 10]))

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

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

chi := DirichletCharacter("399.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.ci (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	399.17
Dual form			399.2.ci.b.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.683230 - 1.87716i) q^{2} +(1.56993 + 0.731654i) q^{3} +(-1.52483 + 1.27949i) q^{4} +(-0.743891 - 0.624199i) q^{5} +(0.300807 - 3.44690i) q^{6} +(2.28326 + 1.33668i) q^{7} +(-0.0163842 - 0.00945940i) q^{8} +(1.92936 + 2.29729i) q^{9} +(-0.663472 + 1.82287i) q^{10} +(4.39836 - 2.53939i) q^{11} +(-3.33003 + 0.893056i) q^{12} +(-0.462503 - 0.551190i) q^{13} +(0.949176 - 5.19930i) q^{14} +(-0.711160 - 1.52422i) q^{15} +(-0.697866 + 3.95780i) q^{16} +(0.467300 + 0.392111i) q^{17} +(2.99418 - 5.19130i) q^{18} +(3.20172 - 2.95787i) q^{19} +1.93297 q^{20} +(2.60657 + 3.76906i) q^{21} +(-7.77194 - 6.52143i) q^{22} +(-7.49114 + 1.32089i) q^{23} +(-0.0188010 - 0.0268381i) q^{24} +(-0.704491 - 3.99537i) q^{25} +(-0.718675 + 1.24478i) q^{26} +(1.34815 + 5.01822i) q^{27} +(-5.19186 + 0.883182i) q^{28} +(6.46337 - 1.13967i) q^{29} +(-2.37532 + 2.37635i) q^{30} -5.92510i q^{31} +(7.86895 - 1.38751i) q^{32} +(8.76308 - 0.768595i) q^{33} +(0.416782 - 1.14510i) q^{34} +(-0.864141 - 2.41956i) q^{35} +(-5.88132 - 1.03439i) q^{36} +(3.65034 + 6.32257i) q^{37} +(-7.73991 - 3.98922i) q^{38} +(-0.322818 - 1.20372i) q^{39} +(0.00628349 + 0.0172637i) q^{40} +(-2.38849 - 2.00418i) q^{41} +(5.29423 - 7.46808i) q^{42} +(-6.52509 + 2.37494i) q^{43} +(-3.45765 + 9.49980i) q^{44} +(-0.00127032 - 2.91324i) q^{45} +(7.59769 + 13.1596i) q^{46} +(-7.21130 + 6.05100i) q^{47} +(-3.99134 + 5.70287i) q^{48} +(3.42655 + 6.10399i) q^{49} +(-7.01861 + 4.05220i) q^{50} +(0.446739 + 0.957489i) q^{51} +(1.41048 + 0.248706i) q^{52} +(-1.46315 - 1.74371i) q^{53} +(8.49890 - 5.95928i) q^{54} +(-4.85699 - 0.856418i) q^{55} +(-0.0247651 - 0.0434987i) q^{56} +(7.19061 - 2.30111i) q^{57} +(-6.55530 - 11.3541i) q^{58} +(-7.76831 - 6.51839i) q^{59} +(3.03462 + 1.41426i) q^{60} +(-9.33499 + 1.64601i) q^{61} +(-11.1224 + 4.04821i) q^{62} +(1.33449 + 7.82427i) q^{63} +(-3.96203 - 6.86243i) q^{64} +0.698719i q^{65} +(-7.42997 - 15.9246i) q^{66} +(11.0170 + 4.00986i) q^{67} -1.21426 q^{68} +(-12.7270 - 3.40722i) q^{69} +(-3.95149 + 3.27524i) q^{70} +(1.71503 + 4.71202i) q^{71} +(-0.00988001 - 0.0558898i) q^{72} +(0.375240 + 1.03096i) q^{73} +(9.37445 - 11.1720i) q^{74} +(1.81722 - 6.78789i) q^{75} +(-1.09752 + 8.60682i) q^{76} +(13.4370 + 0.0811195i) q^{77} +(-2.03902 + 1.42840i) q^{78} +(-2.08858 + 11.8449i) q^{79} +(2.98959 - 2.50856i) q^{80} +(-1.55510 + 8.86463i) q^{81} +(-2.13028 + 5.85290i) q^{82} +(4.70792 + 8.15436i) q^{83} +(-8.79705 - 2.41211i) q^{84} +(-0.102865 - 0.583376i) q^{85} +(8.91628 + 10.6260i) q^{86} +(10.9809 + 2.93975i) q^{87} -0.0960846 q^{88} +(-11.3178 - 4.11934i) q^{89} +(-5.46775 + 1.99280i) q^{90} +(-0.319248 - 1.87673i) q^{91} +(9.73268 - 11.5990i) q^{92} +(4.33513 - 9.30200i) q^{93} +(16.2857 + 9.40254i) q^{94} +(-4.22803 + 0.201829i) q^{95} +(13.3689 + 3.57906i) q^{96} +(5.51859 + 0.973076i) q^{97} +(9.11704 - 10.6026i) q^{98} +(14.3198 + 5.20490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 9 q^{3} - 6 q^{4} - 6 q^{7} - 3 q^{9} - 18 q^{10} - 27 q^{12} - 36 q^{13} - 15 q^{15} + 6 q^{16} - 18 q^{18} - 72 q^{19} + 12 q^{21} - 9 q^{24} + 18 q^{25} + 27 q^{27} - 108 q^{28} - 6 q^{30} - 9 q^{33}+ \cdots - 24 q^{99}+O(q^{100}) $ 288 * q - 9 * q^3 - 6 * q^4 - 6 * q^7 - 3 * q^9 - 18 * q^10 - 27 * q^12 - 36 * q^13 - 15 * q^15 + 6 * q^16 - 18 * q^18 - 72 * q^19 + 12 * q^21 - 9 * q^24 + 18 * q^25 + 27 * q^27 - 108 * q^28 - 6 * q^30 - 9 * q^33 + 36 * q^34 - 84 * q^36 - 24 * q^39 - 144 * q^40 + 39 * q^42 + 12 * q^43 - 6 * q^46 + 63 * q^48 - 30 * q^49 - 3 * q^51 + 90 * q^52 + 9 * q^54 - 90 * q^55 - 66 * q^57 + 24 * q^58 + 42 * q^60 + 54 * q^61 + 60 * q^63 + 54 * q^64 - 27 * q^66 + 102 * q^67 + 60 * q^70 - 39 * q^72 + 36 * q^73 - 63 * q^75 - 87 * q^78 + 6 * q^79 + 45 * q^81 - 18 * q^82 - 117 * q^84 + 36 * q^85 - 9 * q^87 - 204 * q^88 + 144 * q^90 - 198 * q^91 - 60 * q^93 - 180 * q^94 - 243 * q^96 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{5}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.683230	−	1.87716i	−0.483117	−	1.32735i	−0.906807	−	0.421545i	$-0.861488\pi$
$2$	−0.683230	−	1.87716i	−0.483117	−	1.32735i	0.423691	−	0.905807i	$-0.360734\pi$
$3$	1.56993	+	0.731654i	0.906400	+	0.422421i
$3$	1.56993	+	0.731654i	0.906400	+	0.422421i
$4$	−1.52483	+	1.27949i	−0.762417	+	0.639744i
$5$	−0.743891	−	0.624199i	−0.332678	−	0.279150i	0.461112	−	0.887342i	$-0.347451\pi$
$5$	−0.743891	−	0.624199i	−0.332678	−	0.279150i	−0.793790	+	0.608192i	$0.791895\pi$
$6$	0.300807	−	3.44690i	0.122804	−	1.40719i
$7$	2.28326	+	1.33668i	0.862991	+	0.505219i
$7$	2.28326	+	1.33668i	0.862991	+	0.505219i
$8$	−0.0163842	−	0.00945940i	−0.00579267	−	0.00334440i
$9$	1.92936	+	2.29729i	0.643122	+	0.765764i
$10$	−0.663472	+	1.82287i	−0.209808	+	0.576443i
$11$	4.39836	−	2.53939i	1.32616	−	0.765656i	0.341453	−	0.939899i	$-0.389081\pi$
$11$	4.39836	−	2.53939i	1.32616	−	0.765656i	0.984703	+	0.174243i	$0.0557477\pi$
$12$	−3.33003	+	0.893056i	−0.961296	+	0.257803i
$13$	−0.462503	−	0.551190i	−0.128275	−	0.152873i	0.698084	−	0.716016i	$-0.254036\pi$
$13$	−0.462503	−	0.551190i	−0.128275	−	0.152873i	−0.826359	+	0.563144i	$0.809592\pi$
$14$	0.949176	−	5.19930i	0.253678	−	1.38957i
$15$	−0.711160	−	1.52422i	−0.183621	−	0.393552i
$16$	−0.697866	+	3.95780i	−0.174467	+	0.989449i
$17$	0.467300	+	0.392111i	0.113337	+	0.0951009i	0.697695	−	0.716395i	$-0.254209\pi$
$17$	0.467300	+	0.392111i	0.113337	+	0.0951009i	−0.584358	+	0.811496i	$0.698654\pi$
$18$	2.99418	−	5.19130i	0.705736	−	1.22360i
$19$	3.20172	−	2.95787i	0.734524	−	0.678583i
$19$	3.20172	−	2.95787i	0.734524	−	0.678583i
$20$	1.93297			0.432224
$21$	2.60657	+	3.76906i	0.568800	+	0.822476i
$22$	−7.77194	−	6.52143i	−1.65698	−	1.39037i
$23$	−7.49114	+	1.32089i	−1.56201	+	0.275424i	−0.886783	−	0.462186i	$-0.847065\pi$
$23$	−7.49114	+	1.32089i	−1.56201	+	0.275424i	−0.675227	+	0.737610i	$0.735954\pi$
$24$	−0.0188010	−	0.0268381i	−0.00383773	−	0.00547831i
$25$	−0.704491	−	3.99537i	−0.140898	−	0.799073i
$26$	−0.718675	+	1.24478i	−0.140944	+	0.244122i
$27$	1.34815	+	5.01822i	0.259451	+	0.965756i
$28$	−5.19186	+	0.883182i	−0.981170	+	0.166906i
$29$	6.46337	−	1.13967i	1.20022	−	0.211631i	0.462425	−	0.886659i	$-0.346980\pi$
$29$	6.46337	−	1.13967i	1.20022	−	0.211631i	0.737792	+	0.675028i	$0.235868\pi$
$30$	−2.37532	+	2.37635i	−0.433672	+	0.433861i
$31$		−	5.92510i		−	1.06418i	−0.846688	−	0.532090i	$-0.821407\pi$
$31$		−	5.92510i		−	1.06418i	0.846688	−	0.532090i	$-0.178593\pi$
$32$	7.86895	−	1.38751i	1.39105	−	0.245279i
$33$	8.76308	−	0.768595i	1.52546	−	0.133795i
$34$	0.416782	−	1.14510i	0.0714775	−	0.196383i
$35$	−0.864141	−	2.41956i	−0.146066	−	0.408980i
$36$	−5.88132	−	1.03439i	−0.980220	−	0.172398i
$37$	3.65034	+	6.32257i	0.600112	+	1.03942i	0.992804	+	0.119754i	$0.0382105\pi$
$37$	3.65034	+	6.32257i	0.600112	+	1.03942i	−0.392692	+	0.919670i	$0.628456\pi$
$38$	−7.73991	−	3.98922i	−1.25558	−	0.647137i
$39$	−0.322818	−	1.20372i	−0.0516922	−	0.192750i
$40$	0.00628349	+	0.0172637i	0.000993507	+	0.00272964i
$41$	−2.38849	−	2.00418i	−0.373020	−	0.313001i	0.436935	−	0.899493i	$-0.356064\pi$
$41$	−2.38849	−	2.00418i	−0.373020	−	0.313001i	−0.809955	+	0.586492i	$0.800508\pi$
$42$	5.29423	−	7.46808i	0.816918	−	1.15235i
$43$	−6.52509	+	2.37494i	−0.995067	+	0.362175i	−0.787680	−	0.616084i	$-0.788718\pi$
$43$	−6.52509	+	2.37494i	−0.995067	+	0.362175i	−0.207387	+	0.978259i	$0.566496\pi$
$44$	−3.45765	+	9.49980i	−0.521260	+	1.43215i
$45$	−0.00127032	−	2.91324i	−0.000189369	−	0.434281i
$46$	7.59769	+	13.1596i	1.12022	+	1.94027i
$47$	−7.21130	+	6.05100i	−1.05188	+	0.882629i	−0.993290	−	0.115653i	$-0.963104\pi$
$47$	−7.21130	+	6.05100i	−1.05188	+	0.882629i	−0.0585869	+	0.998282i	$0.518659\pi$
$48$	−3.99134	+	5.70287i	−0.576100	+	0.823138i
$49$	3.42655	+	6.10399i	0.489507	+	0.871999i
$50$	−7.01861	+	4.05220i	−0.992581	+	0.573067i
$51$	0.446739	+	0.957489i	0.0625559	+	0.134075i
$52$	1.41048	+	0.248706i	0.195598	+	0.0344893i
$53$	−1.46315	−	1.74371i	−0.200979	−	0.239517i	0.656136	−	0.754643i	$-0.272190\pi$
$53$	−1.46315	−	1.74371i	−0.200979	−	0.239517i	−0.857115	+	0.515125i	$0.827745\pi$
$54$	8.49890	−	5.95928i	1.15655	−	0.810955i
$55$	−4.85699	−	0.856418i	−0.654916	−	0.115479i
$56$	−0.0247651	−	0.0434987i	−0.00330937	−	0.00581276i
$57$	7.19061	−	2.30111i	0.952420	−	0.304789i
$58$	−6.55530	−	11.3541i	−0.860753	−	1.49087i
$59$	−7.76831	−	6.51839i	−1.01135	−	0.848622i	−0.0228324	−	0.999739i	$-0.507268\pi$
$59$	−7.76831	−	6.51839i	−1.01135	−	0.848622i	−0.988516	+	0.151117i	$0.951713\pi$
$60$	3.03462	+	1.41426i	0.391768	+	0.182580i
$61$	−9.33499	+	1.64601i	−1.19522	+	0.210750i	−0.735632	−	0.677381i	$-0.763115\pi$
$61$	−9.33499	+	1.64601i	−1.19522	+	0.210750i	−0.459590	+	0.888131i	$0.652004\pi$
$62$	−11.1224	+	4.04821i	−1.41254	+	0.514123i
$63$	1.33449	+	7.82427i	0.168130	+	0.985765i
$64$	−3.96203	−	6.86243i	−0.495254	−	0.857804i
$65$			0.698719i			0.0866655i
$66$	−7.42997	−	15.9246i	−0.914567	−	1.96018i
$67$	11.0170	+	4.00986i	1.34594	+	0.489883i	0.911679	−	0.410903i	$-0.134787\pi$
$67$	11.0170	+	4.00986i	1.34594	+	0.489883i	0.434263	+	0.900786i	$0.357009\pi$
$68$	−1.21426			−0.147250
$69$	−12.7270	−	3.40722i	−1.53215	−	0.410181i
$70$	−3.95149	+	3.27524i	−0.472293	+	0.391466i
$71$	1.71503	+	4.71202i	0.203537	+	0.559213i	0.998899	−	0.0469220i	$-0.0149412\pi$
$71$	1.71503	+	4.71202i	0.203537	+	0.559213i	−0.795362	+	0.606135i	$0.792719\pi$
$72$	−0.00988001	−	0.0558898i	−0.00116437	−	0.00658668i
$73$	0.375240	+	1.03096i	0.0439185	+	0.120665i	0.959713	−	0.280982i	$-0.0906601\pi$
$73$	0.375240	+	1.03096i	0.0439185	+	0.120665i	−0.915795	+	0.401647i	$0.868438\pi$
$74$	9.37445	−	11.1720i	1.08976	−	1.29872i
$75$	1.81722	−	6.78789i	0.209835	−	0.783798i
$76$	−1.09752	+	8.60682i	−0.125894	+	0.987270i
$77$	13.4370	+	0.0811195i	1.53128	+	0.00924442i
$78$	−2.03902	+	1.42840i	−0.230873	+	0.161734i
$79$	−2.08858	+	11.8449i	−0.234984	+	1.33266i	0.607665	+	0.794194i	$0.292106\pi$
$79$	−2.08858	+	11.8449i	−0.234984	+	1.33266i	−0.842648	+	0.538464i	$0.819005\pi$
$80$	2.98959	−	2.50856i	0.334246	−	0.280466i
$81$	−1.55510	+	8.86463i	−0.172789	+	0.984959i
$82$	−2.13028	+	5.85290i	−0.235250	+	0.646345i
$83$	4.70792	+	8.15436i	0.516762	+	0.895057i	0.999811	+	0.0194639i	$0.00619594\pi$
$83$	4.70792	+	8.15436i	0.516762	+	0.895057i	−0.483049	+	0.875593i	$0.660471\pi$
$84$	−8.79705	−	2.41211i	−0.959837	−	0.263183i
$85$	−0.102865	−	0.583376i	−0.0111573	−	0.0632760i
$86$	8.91628	+	10.6260i	0.961467	+	1.14583i
$87$	10.9809	+	2.93975i	1.17727	+	0.315174i
$88$	−0.0960846			−0.0102426
$89$	−11.3178	−	4.11934i	−1.19968	−	0.436649i	−0.336570	−	0.941658i	$-0.609267\pi$
$89$	−11.3178	−	4.11934i	−1.19968	−	0.436649i	−0.863114	+	0.505009i	$0.831489\pi$
$90$	−5.46775	+	1.99280i	−0.576352	+	0.210060i
$91$	−0.319248	−	1.87673i	−0.0334663	−	0.196735i
$92$	9.73268	−	11.5990i	1.01470	−	1.20927i
$93$	4.33513	−	9.30200i	0.449532	−	0.964573i
$94$	16.2857	+	9.40254i	1.67974	+	0.969798i
$95$	−4.22803	+	0.201829i	−0.433787	+	0.0207072i
$96$	13.3689	+	3.57906i	1.36446	+	0.365286i
$97$	5.51859	+	0.973076i	0.560327	+	0.0988009i	0.446637	−	0.894715i	$-0.352622\pi$
$97$	5.51859	+	0.973076i	0.560327	+	0.0988009i	0.113691	+	0.993516i	$0.463733\pi$
$98$	9.11704	−	10.6026i	0.920960	−	1.07103i
$99$	14.3198	+	5.20490i	1.43919	+	0.523112i
$100$	6.18625	+	5.19088i	0.618625	+	0.519088i
$101$	2.95218	+	16.7426i	0.293753	+	1.66595i	0.672229	+	0.740343i	$0.265337\pi$
$101$	2.95218	+	16.7426i	0.293753	+	1.66595i	−0.378476	+	0.925611i	$0.623552\pi$
$102$	1.49213	−	1.49279i	0.147743	−	0.147808i
$103$		−	11.2269i		−	1.10622i	−0.833109	−	0.553109i	$-0.813441\pi$
$103$		−	11.2269i		−	1.10622i	0.833109	−	0.553109i	$-0.186559\pi$
$104$	0.00236380	+	0.0134058i	0.000231790	+	0.00131454i
$105$	0.413637	−	4.43079i	0.0403668	−	0.432401i
$106$	−2.27356	+	3.93792i	−0.220827	+	0.382484i
$107$	5.10879	+	2.94956i	0.493886	+	0.285145i	0.726185	−	0.687499i	$-0.241292\pi$
$107$	5.10879	+	2.94956i	0.493886	+	0.285145i	−0.232299	+	0.972644i	$0.574625\pi$
$108$	−8.47645	−	5.92701i	−0.815646	−	0.570327i
$109$	0.823618	−	4.67097i	0.0788883	−	0.447398i	−0.919621	−	0.392808i	$-0.871504\pi$
$109$	0.823618	−	4.67097i	0.0788883	−	0.447398i	0.998509	−	0.0545899i	$-0.0173852\pi$
$110$	1.71081	+	9.70247i	0.163119	+	0.925095i
$111$	1.10484	+	12.5968i	0.104867	+	1.19563i
$112$	−6.88373	+	8.10385i	−0.650452	+	0.765742i
$113$		−	8.50325i		−	0.799918i	−0.916533	−	0.399959i	$-0.869024\pi$
$113$		−	8.50325i		−	0.799918i	0.916533	−	0.399959i	$-0.130976\pi$
$114$	−9.23239	−	11.9257i	−0.864692	−	1.11695i
$115$	6.39709	+	3.69336i	0.596532	+	0.344408i
$116$	−8.39737	+	10.0076i	−0.779676	+	0.929182i
$117$	0.373907	−	2.12595i	0.0345677	−	0.196544i
$118$	−6.92851	+	19.0359i	−0.637821	+	1.75240i
$119$	0.542838	+	1.51992i	0.0497619	+	0.139331i
$120$	−0.00276645	+	0.0317002i	−0.000252541	+	0.00289382i
$121$	7.39705	−	12.8121i	0.672459	−	1.16473i
$122$	9.46777	+	16.3987i	0.857171	+	1.48466i
$123$	−2.28340	−	4.89398i	−0.205887	−	0.441275i
$124$	7.58110	+	9.03480i	0.680803	+	0.811349i
$125$	−4.39754	+	7.61677i	−0.393328	+	0.681264i
$126$	13.7756	−	7.85082i	1.22723	−	0.699407i
$127$	−5.45908	+	4.58072i	−0.484415	+	0.406473i	−0.852020	−	0.523509i	$-0.824622\pi$
$127$	−5.45908	+	4.58072i	−0.484415	+	0.406473i	0.367604	+	0.929982i	$0.380178\pi$
$128$	0.0972850	−	0.115940i	0.00859886	−	0.0102477i
$129$	−11.9816	−	1.04562i	−1.05492	−	0.0920617i
$130$	1.31161	−	0.477386i	0.115036	−	0.0418695i
$131$	−7.02623	+	2.55734i	−0.613884	+	0.223436i	−0.630202	−	0.776431i	$-0.717028\pi$
$131$	−7.02623	+	2.55734i	−0.613884	+	0.223436i	0.0163177	+	0.999867i	$0.494806\pi$
$132$	−12.3788	+	12.3842i	−1.07744	+	1.07791i
$133$	11.2641	−	2.47391i	0.976721	−	0.214515i
$134$		−	23.4203i		−	2.02321i
$135$	2.12949	−	4.57452i	0.183278	−	0.393712i
$136$	−0.00394718	−	0.0108448i	−0.000338468	−	0.000929933i
$137$	7.92730	+	9.44739i	0.677275	+	0.807145i	0.989755	−	0.142780i	$-0.0456040\pi$
$137$	7.92730	+	9.44739i	0.677275	+	0.807145i	−0.312479	+	0.949925i	$0.601160\pi$
$138$	2.29958	+	26.2185i	0.195753	+	2.23187i
$139$	−1.89684	−	2.26056i	−0.160888	−	0.191739i	0.679578	−	0.733603i	$-0.262163\pi$
$139$	−1.89684	−	2.26056i	−0.160888	−	0.191739i	−0.840466	+	0.541865i	$0.817719\pi$
$140$	4.41346	+	2.58376i	0.373006	+	0.218368i
$141$	−15.7485	+	4.22347i	−1.32626	+	0.355681i
$142$	7.67344	−	6.43878i	0.643941	−	0.540330i
$143$	−3.43394	−	1.24985i	−0.287161	−	0.104518i
$144$	−10.4387	+	6.03283i	−0.869888	+	0.502736i
$145$	−5.51942	−	3.18664i	−0.458363	−	0.264636i
$146$	1.67891	−	1.40877i	0.138947	−	0.116591i
$147$	0.913438	+	12.0899i	0.0753391	+	0.997158i
$148$	−13.6558	−	4.97031i	−1.12250	−	0.408557i
$149$	−5.37806	−	0.948298i	−0.440588	−	0.0776876i	−0.0510462	−	0.998696i	$-0.516256\pi$
$149$	−5.37806	−	0.948298i	−0.440588	−	0.0776876i	−0.389542	+	0.921009i	$0.627367\pi$
$150$	−13.9835	+	1.22647i	−1.14175	+	0.100141i
$151$	2.97604	−	5.15465i	0.242187	−	0.419480i	−0.719150	−	0.694855i	$-0.755469\pi$
$151$	2.97604	−	5.15465i	0.242187	−	0.419480i	0.961337	+	0.275375i	$0.0888020\pi$
$152$	−0.0804371	+	0.0181760i	−0.00652431	+	0.00147427i
$153$	0.000797996		1.83005i	6.45141e−5		0.147951i
$154$	−9.02827	−	25.2787i	−0.727518	−	2.03702i
$155$	−3.69844	+	4.40763i	−0.297066	+	0.354030i
$156$	2.03239	+	1.42243i	0.162721	+	0.113886i
$157$	−10.3496	−	1.82492i	−0.825990	−	0.145644i	−0.255354	−	0.966848i	$-0.582192\pi$
$157$	−10.3496	−	1.82492i	−0.825990	−	0.145644i	−0.570636	+	0.821203i	$0.693303\pi$
$158$	23.6618	−	4.17221i	1.88243	−	0.331923i
$159$	−1.02125	−	3.80802i	−0.0809901	−	0.301996i
$160$	−6.71973	−	3.87964i	−0.531241	−	0.306712i
$161$	−18.8698	−	6.99735i	−1.48715	−	0.551468i
$162$	17.7028	−	3.13740i	1.39086	−	0.246498i
$163$	−5.83650			−0.457150			−0.228575	−	0.973526i	$-0.573407\pi$
$163$	−5.83650			−0.457150			−0.228575	+	0.973526i	$0.573407\pi$
$164$	6.20639			0.484637
$165$	−6.99854	−	4.89815i	−0.544835	−	0.381321i
$166$	12.0904	−	14.4088i	0.938400	−	1.11834i
$167$	−7.81313	−	2.84375i	−0.604598	−	0.220056i	0.0215398	−	0.999768i	$-0.493143\pi$
$167$	−7.81313	−	2.84375i	−0.604598	−	0.220056i	−0.626138	+	0.779712i	$0.715365\pi$
$168$	−0.00705344	−	0.0864094i	−0.000544184	−	0.00666663i
$169$	2.16753	−	12.2926i	0.166733	−	0.945588i
$170$	−1.02481	+	0.591674i	−0.0785993	+	0.0453793i
$171$	12.9724	+	1.64846i	0.992023	+	0.126061i
$172$	6.91098	−	11.9702i	0.526957	−	0.912716i
$173$	−6.03111	+	2.19515i	−0.458537	+	0.166894i	−0.560953	−	0.827848i	$-0.689565\pi$
$173$	−6.03111	+	2.19515i	−0.458537	+	0.166894i	0.102416	+	0.994742i	$0.467343\pi$
$174$	−1.98408	−	22.6214i	−0.150413	−	1.71492i
$175$	3.73201	−	10.0641i	0.282113	−	0.760778i
$176$	6.98094	+	19.1800i	0.526208	+	1.44574i
$177$	−7.42651	−	15.9171i	−0.558211	−	1.19641i
$178$			24.0598i			1.80336i
$179$	−8.29976	+	4.79187i	−0.620353	+	0.358161i	−0.777007	−	0.629493i	$-0.783263\pi$
$179$	−8.29976	+	4.79187i	−0.620353	+	0.358161i	0.156653	+	0.987654i	$0.449929\pi$
$180$	3.72940	+	4.44059i	0.277973	+	0.330982i
$181$	−4.77715	+	0.842340i	−0.355082	+	0.0626106i	−0.348344	−	0.937367i	$-0.613256\pi$
$181$	−4.77715	+	0.842340i	−0.355082	+	0.0626106i	−0.00673819	+	0.999977i	$0.502145\pi$
$182$	−3.30480	+	1.88152i	−0.244968	+	0.139467i
$183$	−15.8596	−	4.24586i	−1.17238	−	0.313863i
$184$	0.135231	+	0.0492200i	0.00996934	+	0.00362854i
$185$	1.23109	−	6.98184i	0.0905113	−	0.513315i
$186$	−20.4232	−	1.78231i	−1.49750	−	0.130686i
$187$	3.05108	+	0.537987i	0.223117	+	0.0393415i
$188$	3.25386	−	18.4535i	0.237312	−	1.34586i
$189$	−3.62960	+	13.2599i	−0.264015	+	0.964519i
$190$	3.26758	+	7.79879i	0.237055	+	0.565784i
$191$	−0.0187913	+	0.0108491i	−0.00135969	+	0.000785016i	−0.500680	−	0.865633i	$-0.666917\pi$
$191$	−0.0187913	+	0.0108491i	−0.00135969	+	0.000785016i	0.499320	+	0.866418i	$0.333583\pi$
$192$	−1.19918	−	13.6724i	−0.0865435	−	0.986719i
$193$	−10.3051	+	3.75074i	−0.741775	+	0.269984i	−0.685141	−	0.728411i	$-0.740259\pi$
$193$	−10.3051	+	3.75074i	−0.741775	+	0.269984i	−0.0566348	+	0.998395i	$0.518037\pi$
$194$	−1.94385	−	11.0241i	−0.139560	−	0.791484i
$195$	−0.511221	+	1.09694i	−0.0366093	+	0.0785536i
$196$	−13.0349	−	4.92335i	−0.931065	−	0.351668i
$197$	−4.72688	+	2.72907i	−0.336776	+	0.194438i	−0.658846	−	0.752278i	$-0.728955\pi$
$197$	−4.72688	+	2.72907i	−0.336776	+	0.194438i	0.322069	+	0.946716i	$0.395622\pi$
$198$	−0.0132719	−	30.4366i	−0.000943195	−	2.16304i
$199$	2.17035	−	5.96298i	0.153852	−	0.422704i	−0.838690	−	0.544609i	$-0.816678\pi$
$199$	2.17035	−	5.96298i	0.153852	−	0.422704i	0.992542	+	0.121905i	$0.0389002\pi$
$200$	−0.0262513	+	0.0721248i	−0.00185624	+	0.00509999i
$201$	14.3621	+	14.3558i	1.01303	+	1.01258i
$202$	29.4116	−	16.9808i	2.06939	−	1.19476i
$203$	16.2809	+	6.03732i	1.14270	+	0.423737i
$204$	−1.90630	−	0.888415i	−0.133468	−	0.0622015i
$205$	0.525770	+	2.98179i	0.0367214	+	0.208257i
$206$	−21.0746	+	7.67054i	−1.46834	+	0.534432i
$207$	−17.4876	−	14.6609i	−1.21547	−	1.01900i
$208$	2.50426	−	1.44584i	0.173639	−	0.100251i
$209$	6.57109	−	21.1402i	0.454532	−	1.46230i
$210$	−8.59990	+	2.25078i	−0.593450	+	0.155319i
$211$	4.84025	−	27.4504i	0.333216	−	1.88976i	−0.110960	−	0.993825i	$-0.535393\pi$
$211$	4.84025	−	27.4504i	0.333216	−	1.88976i	0.444177	−	0.895939i	$-0.353496\pi$
$212$	4.46211	+	0.786791i	0.306459	+	0.0540370i
$213$	−0.755082	+	8.65235i	−0.0517373	+	0.592849i
$214$	2.04632	−	11.6053i	0.139883	−	0.793319i
$215$	6.33639	+	2.30626i	0.432139	+	0.157286i
$216$	0.0253811	−	0.0949719i	0.00172696	−	0.00646202i
$217$	7.91999	−	13.5286i	0.537644	−	0.918378i
$218$	−9.33088	+	1.64529i	−0.631967	+	0.111433i
$219$	−0.165208	+	1.89309i	−0.0111637	+	0.127923i
$220$	8.50188	−	4.90856i	0.573197	−	0.330935i
$221$		−	0.438923i		−	0.0295252i
$222$	22.8913	−	10.6805i	1.53636	−	0.716826i
$223$	1.00634	+	2.76488i	0.0673892	+	0.185150i	0.968816	−	0.247781i	$-0.0797014\pi$
$223$	1.00634	+	2.76488i	0.0673892	+	0.185150i	−0.901427	+	0.432932i	$0.857479\pi$
$224$	19.8215	+	7.35026i	1.32438	+	0.491110i
$225$	7.81930	−	9.32694i	0.521287	−	0.621796i
$226$	−15.9620	+	5.80968i	−1.06177	+	0.386454i
$227$	2.65212	−	4.59361i	0.176028	−	0.304889i	−0.764489	−	0.644637i	$-0.777009\pi$
$227$	2.65212	−	4.59361i	0.176028	−	0.304889i	0.940516	+	0.339748i	$0.110342\pi$
$228$	−8.02025	+	12.7091i	−0.531154	+	0.841681i
$229$	−21.5777	+	12.4579i	−1.42589	+	0.823239i	−0.996793	−	0.0800186i	$-0.974502\pi$
$229$	−21.5777	+	12.4579i	−1.42589	+	0.823239i	−0.429099	+	0.903258i	$0.641169\pi$
$230$	2.56234	−	14.5318i	0.168956	−	0.958197i
$231$	21.0358	+	9.95856i	1.38405	+	0.655225i
$232$	−0.116677	−	0.0424671i	−0.00766024	−	0.00278810i
$233$	−1.67372	+	1.99466i	−0.109649	+	0.130674i	−0.818077	−	0.575108i	$-0.804960\pi$
$233$	−1.67372	+	1.99466i	−0.109649	+	0.130674i	0.708429	+	0.705782i	$0.249404\pi$
$234$	−4.24621	+	0.750631i	−0.277584	+	0.0490703i
$235$	9.14146			0.596323
$236$	20.1856			1.31397
$237$	−11.9453	+	17.0676i	−0.775931	+	1.10866i
$238$	2.48226	−	2.05745i	0.160901	−	0.133365i
$239$	9.78409	+	5.64885i	0.632880	+	0.365394i	0.781867	−	0.623446i	$-0.214268\pi$
$239$	9.78409	+	5.64885i	0.632880	+	0.365394i	−0.148986	+	0.988839i	$0.547601\pi$
$240$	6.52885	−	1.75093i	0.421435	−	0.113022i
$241$	−22.1050	+	3.89771i	−1.42391	+	0.251073i	−0.831930	−	0.554881i	$-0.812764\pi$
$241$	−22.1050	+	3.89771i	−1.42391	+	0.251073i	−0.591978	+	0.805954i	$0.701653\pi$
$242$	−29.1042	−	5.13185i	−1.87089	−	0.329888i
$243$	−8.92725	+	12.7791i	−0.572683	+	0.819777i
$244$	12.1283	−	14.4539i	0.776432	−	0.925316i
$245$	1.26112	−	6.67956i	0.0805703	−	0.426741i
$246$	−7.62669	+	7.63002i	−0.486260	+	0.486472i
$247$	−3.11115	−	0.396727i	−0.197958	−	0.0252431i
$248$	−0.0560479	+	0.0970778i	−0.00355905	+	0.00616445i
$249$	1.42494	+	16.2463i	0.0903019	+	1.02957i
$250$	17.3024	+	3.05088i	1.09430	+	0.192955i
$251$	−10.7683	−	3.91936i	−0.679692	−	0.247388i	−0.0209767	−	0.999780i	$-0.506678\pi$
$251$	−10.7683	−	3.91936i	−0.679692	−	0.247388i	−0.658715	+	0.752392i	$0.728900\pi$
$252$	−12.0459	−	10.2232i	−0.758822	−	0.644004i
$253$	−29.5945	+	24.8327i	−1.86059	+	1.56122i
$254$	12.3285	+	7.11789i	0.773562	+	0.446616i
$255$	0.265339	−	0.991122i	0.0166162	−	0.0620665i
$256$	−15.1765	−	5.52378i	−0.948529	−	0.345236i
$257$	5.21056	−	4.37218i	0.325026	−	0.272729i	−0.465644	−	0.884972i	$-0.654177\pi$
$257$	5.21056	−	4.37218i	0.325026	−	0.272729i	0.790669	+	0.612243i	$0.209733\pi$
$258$	6.22338	+	23.2057i	0.387451	+	1.44473i
$259$	−0.116608	+	19.3154i	−0.00724566	+	1.20020i
$260$	−0.894003	−	1.06543i	−0.0554437	−	0.0660752i
$261$	15.0883	+	12.6494i	0.933945	+	0.782979i
$262$	9.60106	+	11.4421i	0.593155	+	0.706895i
$263$	3.67488	+	10.0966i	0.226603	+	0.622586i	0.999935	−	0.0114153i	$-0.00363367\pi$
$263$	3.67488	+	10.0966i	0.226603	+	0.622586i	−0.773332	+	0.634001i	$0.781411\pi$
$264$	−0.150846	−	0.0703007i	−0.00928394	−	0.00432671i
$265$			2.21043i			0.135785i
$266$	−12.3399	−	19.4542i	−0.756607	−	1.19282i
$267$	−14.7542	−	14.7478i	−0.902944	−	0.902551i
$268$	−21.9297	+	7.98175i	−1.33957	+	0.487563i
$269$	22.4406	−	8.16771i	1.36823	−	0.497994i	0.449640	−	0.893210i	$-0.351552\pi$
$269$	22.4406	−	8.16771i	1.36823	−	0.497994i	0.918588	+	0.395216i	$0.129330\pi$
$270$	−10.0420	−	0.871946i	−0.611139	−	0.0530649i
$271$	20.9353	−	24.9497i	1.27173	−	1.51559i	0.523728	−	0.851885i	$-0.324541\pi$
$271$	20.9353	−	24.9497i	1.27173	−	1.51559i	0.747999	−	0.663700i	$-0.231015\pi$
$272$	−1.87801	+	1.57584i	−0.113871	+	0.0955491i
$273$	0.871919	−	3.17991i	0.0527709	−	0.192457i
$274$	12.3181	−	21.3355i	0.744163	−	1.28893i
$275$	−13.2444	−	15.7841i	−0.798668	−	0.951816i
$276$	23.7660	−	11.0886i	1.43055	−	0.667455i
$277$	−0.0727697	−	0.126041i	−0.00437231	−	0.00757306i	0.863831	−	0.503782i	$-0.168058\pi$
$277$	−0.0727697	−	0.126041i	−0.00437231	−	0.00757306i	−0.868203	+	0.496209i	$0.834725\pi$
$278$	−2.94746	+	5.10515i	−0.176777	+	0.306187i
$279$	13.6117	−	11.4317i	0.814911	−	0.684397i
$280$	−0.00872933	+	0.0478166i	−0.000521677	+	0.00285759i
$281$	5.75673	−	15.8165i	0.343418	−	0.943532i	−0.640978	−	0.767560i	$-0.721471\pi$
$281$	5.75673	−	15.8165i	0.343418	−	0.943532i	0.984395	−	0.175972i	$-0.0563069\pi$
$282$	18.6880	+	26.6768i	1.11285	+	1.58858i
$283$	−16.6018	+	19.7852i	−0.986873	+	1.17611i	−0.00250336	+	0.999997i	$0.500797\pi$
$283$	−16.6018	+	19.7852i	−0.986873	+	1.17611i	−0.984370	+	0.176113i	$0.943648\pi$
$284$	−8.64411	−	4.99068i	−0.512933	−	0.296142i
$285$	−6.78538	−	2.77660i	−0.401932	−	0.164471i
$286$			7.29999i			0.431658i
$287$	−2.77459	−	7.76873i	−0.163779	−	0.458574i
$288$	18.3696	+	15.4003i	1.08244	+	0.907470i
$289$	−2.88740	−	16.3753i	−0.169847	−	0.963251i
$290$	−2.21079	+	12.5380i	−0.129822	+	0.736259i
$291$	7.95184	+	5.56536i	0.466145	+	0.326247i
$292$	−1.89128	−	1.09193i	−0.110679	−	0.0639005i
$293$	−3.90771	+	6.76836i	−0.228291	+	0.395412i	−0.957302	−	0.289091i	$-0.906647\pi$
$293$	−3.90771	+	6.76836i	−0.228291	+	0.395412i	0.729011	+	0.684502i	$0.239980\pi$
$294$	22.0706	−	9.97485i	1.28718	−	0.581745i
$295$	1.71001	+	9.69795i	0.0995606	+	0.564636i
$296$		−	0.138120i		−	0.00802806i
$297$	18.6729	+	18.6485i	1.08351	+	1.08209i
$298$	1.89435	+	10.7434i	0.109737	+	0.622348i
$299$	4.19273	+	3.51812i	0.242472	+	0.203458i
$300$	5.91406	+	12.6755i	0.341448	+	0.731822i
$301$	−18.0730	−	3.29938i	−1.04171	−	0.190173i
$302$	−11.7094	−	2.06469i	−0.673802	−	0.118809i
$303$	−7.61510	+	28.4447i	−0.437476	+	1.63411i
$304$	9.47229	+	14.7359i	0.543273	+	0.845164i
$305$	7.97166	+	4.60244i	0.456456	+	0.263535i
$306$	3.43475	−	1.25184i	0.196352	−	0.0715631i
$307$	8.60145	−	10.2508i	0.490911	−	0.585045i	−0.462538	−	0.886599i	$-0.653061\pi$
$307$	8.60145	−	10.2508i	0.490911	−	0.585045i	0.953449	+	0.301555i	$0.0975056\pi$
$308$	−20.5929	+	17.0687i	−1.17339	+	0.972582i
$309$	8.21419	−	17.6254i	0.467289	−	1.00268i
$310$	10.8007	+	3.93114i	0.613440	+	0.223274i
$311$	21.8053			1.23646			0.618232	−	0.785995i	$-0.287849\pi$
$311$	21.8053			1.23646			0.618232	+	0.785995i	$0.287849\pi$
$312$	−0.00609739	+	0.0227756i	−0.000345197	+	0.00128942i
$313$	8.60346	+	10.2532i	0.486296	+	0.579545i	0.952271	−	0.305253i	$-0.0987409\pi$
$313$	8.60346	+	10.2532i	0.486296	+	0.579545i	−0.465975	+	0.884798i	$0.654296\pi$
$314$	3.64551	+	20.6747i	0.205728	+	1.16674i
$315$	3.89119	−	6.65339i	0.219243	−	0.374876i
$316$	−11.9707	−	20.7339i	−0.673404	−	1.16637i
$317$	−0.0826020	+	0.226947i	−0.00463939	+	0.0127466i	−0.941991	−	0.335639i	$-0.891048\pi$
$317$	−0.0826020	+	0.226947i	−0.00463939	+	0.0127466i	0.937351	+	0.348386i	$0.113270\pi$
$318$	−6.45052	+	4.51880i	−0.361727	+	0.253402i
$319$	25.5342	−	21.4257i	1.42964	−	1.19961i
$320$	−1.33621	+	7.57800i	−0.0746962	+	0.423623i
$321$	5.86239	+	8.36848i	0.327207	+	0.467083i
$322$	−0.242704	+	40.2025i	−0.0135253	+	2.24040i
$323$	2.65598	−	0.126786i	0.147782	−	0.00705454i
$324$	−8.97091	−	15.5068i	−0.498384	−	0.861490i
$325$	−1.87638	+	2.23618i	−0.104083	+	0.124041i
$326$	3.98767	+	10.9560i	0.220857	+	0.606799i
$327$	4.71056	−	6.73050i	0.260494	−	0.372197i
$328$	0.0201751	+	0.0554306i	0.00111398	+	0.00306064i
$329$	−24.5536	+	4.17678i	−1.35368	+	0.230273i
$330$	−4.41300	+	16.4839i	−0.242928	+	0.907411i
$331$	13.1711			0.723949			0.361975	−	0.932188i	$-0.382103\pi$
$331$	13.1711			0.723949			0.361975	+	0.932188i	$0.382103\pi$
$332$	−17.6122	−	6.41032i	−0.966595	−	0.351812i
$333$	−7.48196	+	20.5844i	−0.410009	+	1.12802i
$334$			16.6094i			0.908827i
$335$	−5.69251	−	9.85971i	−0.311015	−	0.538694i
$336$	−16.7362	+	7.68597i	−0.913034	+	0.419304i
$337$	0.785852	−	0.286027i	0.0428081	−	0.0155809i	−0.320527	−	0.947239i	$-0.603860\pi$
$337$	0.785852	−	0.286027i	0.0428081	−	0.0155809i	0.363335	+	0.931658i	$0.381638\pi$
$338$	−24.5562	+	4.32992i	−1.33568	+	0.235516i
$339$	6.22144	−	13.3495i	0.337902	−	0.725046i
$340$	0.903275	+	0.757938i	0.0489870	+	0.0411049i
$341$	−15.0462	−	26.0607i	−0.814796	−	1.41127i
$342$	−5.76870	−	25.4775i	−0.311935	−	1.37767i
$343$	−0.335400	+	18.5172i	−0.0181099	+	0.999836i
$344$	0.129374	+	0.0228121i	0.00697536	+	0.00122994i
$345$	7.34073	+	10.4788i	0.395211	+	0.564159i
$346$	8.24127	+	9.82157i	0.443054	+	0.528011i
$347$	18.2453	+	3.21714i	0.979460	+	0.172705i	0.640385	−	0.768054i	$-0.278775\pi$
$347$	18.2453	+	3.21714i	0.979460	+	0.172705i	0.339075	+	0.940759i	$0.389886\pi$
$348$	−20.5054	+	9.56726i	−1.09920	+	0.512859i
$349$	1.03188	−	0.595754i	0.0552351	−	0.0318900i	−0.472128	−	0.881530i	$-0.656514\pi$
$349$	1.03188	−	0.595754i	0.0552351	−	0.0318900i	0.527363	+	0.849640i	$0.323181\pi$
$350$	−21.4418	−	0.129445i	−1.14611	−	0.00691913i
$351$	2.14247	−	3.06402i	0.114356	−	0.163546i
$352$	31.0871	−	26.0851i	1.65695	−	1.39034i
$353$	−1.80063	−	3.11878i	−0.0958379	−	0.165996i	0.814120	−	0.580697i	$-0.197220\pi$
$353$	−1.80063	−	3.11878i	−0.0958379	−	0.165996i	−0.909958	+	0.414700i	$0.863886\pi$
$354$	−24.8050	+	24.8158i	−1.31837	+	1.31895i
$355$	1.66544	−	4.57575i	0.0883922	−	0.242856i
$356$	22.5284	−	8.19967i	1.19400	−	0.434582i
$357$	−0.259840	+	2.78335i	−0.0137522	+	0.147310i
$358$	14.6657	+	12.3060i	0.775109	+	0.650394i
$359$	4.58160	+	12.5878i	0.241808	+	0.664361i	0.999925	+	0.0122430i	$0.00389718\pi$
$359$	4.58160	+	12.5878i	0.241808	+	0.664361i	−0.758117	+	0.652118i	$0.773881\pi$
$360$	−0.0275367	+	0.0477431i	−0.00145131	+	0.00251628i
$361$	1.50197	−	18.9405i	0.0790509	−	0.996871i
$362$	4.84509	+	8.39195i	0.254653	+	0.441071i
$363$	20.9868	−	14.7020i	1.10152	−	0.771653i
$364$	2.88805	+	2.45323i	0.151375	+	0.128584i
$365$	0.364388	−	1.00115i	0.0190730	−	0.0524025i
$366$	2.86560	+	32.6719i	0.149787	+	1.70779i
$367$	3.31918	−	0.585261i	0.173260	−	0.0305504i	−0.0863452	−	0.996265i	$-0.527519\pi$
$367$	3.31918	−	0.585261i	0.173260	−	0.0305504i	0.259605	+	0.965715i	$0.416408\pi$
$368$		−	30.5702i		−	1.59358i
$369$	−0.00407877	−	9.35387i	−0.000212332	−	0.486943i
$370$	−13.9471	+	2.45926i	−0.725078	+	0.127851i
$371$	−1.00996	−	5.93711i	−0.0524343	−	0.308240i
$372$	5.29145	+	19.7307i	0.274349	+	1.02299i
$373$	13.8597	−	24.0058i	0.717630	−	1.24297i	−0.244306	−	0.969698i	$-0.578560\pi$
$373$	13.8597	−	24.0058i	0.717630	−	1.24297i	0.961936	−	0.273274i	$-0.0881065\pi$
$374$	−1.07470	−	6.09493i	−0.0555714	−	0.315161i
$375$	−12.4767	+	8.74032i	−0.644293	+	0.451348i
$376$	0.175390	−	0.0309260i	0.00904505	−	0.00159489i
$377$	−3.61750	−	3.03544i	−0.186311	−	0.156333i
$378$	27.3709	−	2.24625i	1.40781	−	0.115534i
$379$	0.0207978			0.00106831			0.000534157	−	1.00000i	$-0.499830\pi$
$379$	0.0207978			0.00106831			0.000534157		1.00000i	$0.499830\pi$
$380$	6.18881	−	5.71747i	0.317479	−	0.293300i
$381$	−11.9219	+	3.19724i	−0.610777	+	0.163800i
$382$	0.0332043	+	0.0278617i	0.00169888	+	0.00142553i
$383$	−4.20898	+	23.8703i	−0.215069	+	1.21972i	0.665718	+	0.746203i	$0.268125\pi$
$383$	−4.20898	+	23.8703i	−0.215069	+	1.21972i	−0.880787	+	0.473513i	$0.842986\pi$
$384$	0.237559	−	0.110838i	0.0121229	−	0.00565620i
$385$	−9.94501	−	8.44769i	−0.506845	−	0.430534i
$386$	14.0815	+	16.7816i	0.716728	+	0.854163i
$387$	−18.0452	−	10.4079i	−0.917290	−	0.529064i
$388$	−9.65996	+	5.57718i	−0.490410	+	0.283139i
$389$	6.19986	−	17.0340i	0.314346	−	0.863657i	−0.677421	−	0.735596i	$-0.736902\pi$
$389$	6.19986	−	17.0340i	0.314346	−	0.863657i	0.991766	−	0.128061i	$-0.0408755\pi$
$390$	2.40841	+	0.210180i	0.121955	+	0.0106429i
$391$	−4.01854	−	2.32011i	−0.203226	−	0.117333i
$392$	0.00159893	−	0.132422i	8.07582e−5	−	0.00668832i
$393$	−12.9018	−	1.12592i	−0.650808	−	0.0567954i
$394$	8.35244	+	7.00853i	0.420790	+	0.353084i
$395$	8.94727	−	7.50765i	0.450186	−	0.377751i
$396$	−28.4949	+	10.3854i	−1.43192	+	0.521884i
$397$	−9.83363	−	27.0177i	−0.493536	−	1.35598i	−0.897424	−	0.441170i	$-0.854564\pi$
$397$	−9.83363	−	27.0177i	−0.493536	−	1.35598i	0.403888	−	0.914809i	$-0.367659\pi$
$398$	−12.6763			−0.635406
$399$	19.4939	+	4.35755i	0.975915	+	0.218150i
$400$	16.3045			0.815224
$401$	3.21519	+	8.83365i	0.160559	+	0.441132i	0.993720	−	0.111899i	$-0.0356934\pi$
$401$	3.21519	+	8.83365i	0.160559	+	0.441132i	−0.833161	+	0.553031i	$0.813471\pi$
$402$	17.1356	−	36.7683i	0.854645	−	1.83384i
$403$	−3.26586	+	2.74038i	−0.162684	+	0.136508i
$404$	−25.9236	−	21.7525i	−1.28975	−	1.08223i
$405$	6.69012	−	5.62363i	0.332435	−	0.279440i
$406$	0.209405	−	34.6868i	0.0103926	−	1.72147i
$407$	32.1110	+	18.5393i	1.59168	+	0.918959i
$408$	0.00173783	−	0.0199135i	8.60356e−5	−	0.000985867i
$409$	−5.24922	+	14.4221i	−0.259557	+	0.713128i	0.739637	+	0.673006i	$0.234997\pi$
$409$	−5.24922	+	14.4221i	−0.259557	+	0.713128i	−0.999195	+	0.0401224i	$0.987225\pi$
$410$	5.23807	−	3.02420i	0.258690	−	0.149355i
$411$	5.53309	+	20.6318i	0.272927	+	1.01769i
$412$	14.3647	+	17.1191i	0.707696	+	0.843399i
$413$	−9.02405	−	25.2670i	−0.444045	−	1.24331i
$414$	−15.5727	+	42.8437i	−0.765356	+	2.10566i
$415$	1.58776	−	9.00464i	0.0779401	−	0.442020i
$416$	−4.40420	−	3.69556i	−0.215933	−	0.181190i
$417$	−1.32395	−	4.93676i	−0.0648343	−	0.241754i
$418$	−44.1731	+	2.10864i	−2.16058	+	0.103137i
$419$	9.04835			0.442041			0.221021	−	0.975269i	$-0.429061\pi$
$419$	9.04835			0.442041			0.221021	+	0.975269i	$0.429061\pi$
$420$	5.03841	+	7.28546i	0.245849	+	0.355494i
$421$	0.671329	+	0.563312i	0.0327186	+	0.0274542i	0.659000	−	0.752143i	$-0.270980\pi$
$421$	0.671329	+	0.563312i	0.0327186	+	0.0274542i	−0.626282	+	0.779597i	$0.715424\pi$
$422$	−54.8358	+	9.66903i	−2.66936	+	0.470681i
$423$	−27.8142	−	4.89188i	−1.35237	−	0.237851i
$424$	0.00747798	+	0.0424097i	0.000363163	+	0.00205960i
$425$	1.23742	−	2.14327i	0.0600236	−	0.103964i
$426$	16.7577	−	4.49414i	0.811915	−	0.217742i
$427$	−23.5144	−	8.71966i	−1.13794	−	0.421974i
$428$	−11.5640	+	2.03904i	−0.558967	+	0.0985609i
$429$	−4.47659	−	4.47464i	−0.216132	−	0.216038i
$430$		−	13.4701i		−	0.649587i
$431$	−9.49913	+	1.67495i	−0.457557	+	0.0806796i	−0.397676	−	0.917526i	$-0.630183\pi$
$431$	−9.49913	+	1.67495i	−0.457557	+	0.0806796i	−0.0598808	+	0.998206i	$0.519072\pi$
$432$	−20.8019	+	1.83364i	−1.00083	+	0.0882211i
$433$	1.29175	−	3.54906i	0.0620777	−	0.170557i	−0.904776	−	0.425887i	$-0.859962\pi$
$433$	1.29175	−	3.54906i	0.0620777	−	0.170557i	0.966854	+	0.255330i	$0.0821842\pi$
$434$	−30.8064	−	5.62397i	−1.47876	−	0.269959i
$435$	−6.33359	−	9.04111i	−0.303672	−	0.433488i
$436$	4.72057	+	8.17626i	0.226074	+	0.391572i
$437$	−20.0775	+	26.3869i	−0.960435	+	1.26226i
$438$	3.66650	−	0.983292i	0.175192	−	0.0469835i
$439$	9.74650	+	26.7783i	0.465175	+	1.27806i	0.921546	+	0.388268i	$0.126927\pi$
$439$	9.74650	+	26.7783i	0.465175	+	1.27806i	−0.456372	+	0.889789i	$0.650851\pi$
$440$	0.0714765	+	0.0599759i	0.00340751	+	0.00285924i
$441$	−7.41159	+	19.6486i	−0.352933	+	0.935649i
$442$	−0.823929	+	0.299886i	−0.0391903	+	0.0142641i
$443$	13.3254	−	36.6111i	0.633107	−	1.73945i	−0.0392598	−	0.999229i	$-0.512500\pi$
$443$	13.3254	−	36.6111i	0.633107	−	1.73945i	0.672367	−	0.740218i	$-0.265278\pi$
$444$	−17.8021	−	17.7944i	−0.844851	−	0.844483i
$445$	5.84793	+	10.1289i	0.277218	+	0.480156i
$446$	4.50257	−	3.77810i	0.213203	−	0.178898i
$447$	−7.74936	−	5.42364i	−0.366532	−	0.256530i
$448$	0.126565	−	20.9647i	0.00597962	−	0.990489i
$449$	−2.86899	+	1.65641i	−0.135396	+	0.0781708i	−0.566168	−	0.824290i	$-0.691575\pi$
$449$	−2.86899	+	1.65641i	−0.135396	+	0.0781708i	0.430772	+	0.902461i	$0.358241\pi$
$450$	−22.8505	−	8.30563i	−1.07718	−	0.391531i
$451$	−15.5949	−	2.74980i	−0.734334	−	0.129483i
$452$	10.8798	+	12.9660i	0.511743	+	0.609871i
$453$	8.44360	−	5.91502i	0.396715	−	0.277912i
$454$	−10.4349	−	1.83996i	−0.489736	−	0.0863537i
$455$	−0.933967	+	1.59536i	−0.0437850	+	0.0747915i
$456$	−0.139579	−	0.0303171i	−0.00653640	−	0.00141973i
$457$	−13.0112	−	22.5361i	−0.608640	−	1.05420i	−0.991465	−	0.130375i	$-0.958382\pi$
$457$	−13.0112	−	22.5361i	−0.608640	−	1.05420i	0.382824	−	0.923821i	$-0.374951\pi$
$458$	38.1279	+	31.9931i	1.78160	+	1.49494i
$459$	−1.33771	+	2.87364i	−0.0624390	+	0.134130i
$460$	−14.4801	+	2.55323i	−0.675139	+	0.119045i
$461$	−3.97743	+	1.44766i	−0.185247	+	0.0674245i	−0.432978	−	0.901404i	$-0.642537\pi$
$461$	−3.97743	+	1.44766i	−0.185247	+	0.0674245i	0.247731	+	0.968829i	$0.420315\pi$
$462$	4.32155	−	46.2914i	0.201057	−	2.15367i
$463$	13.0632	+	22.6261i	0.607099	+	1.05153i	0.991716	+	0.128450i	$0.0410001\pi$
$463$	13.0632	+	22.6261i	0.607099	+	1.05153i	−0.384617	+	0.923076i	$0.625667\pi$
$464$			26.3760i			1.22448i
$465$	−9.03116	+	4.21370i	−0.418810	+	0.195406i
$466$	4.88782	+	1.77902i	0.226424	+	0.0824116i
$467$	−1.38689			−0.0641776			−0.0320888	−	0.999485i	$-0.510216\pi$
$467$	−1.38689			−0.0641776			−0.0320888	+	0.999485i	$0.510216\pi$
$468$	2.14998	+	3.72013i	0.0993829	+	0.171963i
$469$	19.7948	+	23.8818i	0.914038	+	1.10276i
$470$	−6.24572	−	17.1600i	−0.288093	−	0.791530i
$471$	−14.9130	−	10.4373i	−0.687154	−	0.480927i
$472$	0.0656172	+	0.180282i	0.00302028	+	0.00829815i
$473$	−22.6688	+	27.0156i	−1.04231	+	1.24218i
$474$	40.2000	+	10.7622i	1.84645	+	0.494322i
$475$	−14.0734	−	10.7082i	−0.645730	−	0.491327i
$476$	−2.77246	−	1.62308i	−0.127076	−	0.0743936i
$477$	1.18287	−	6.72553i	0.0541599	−	0.307941i
$478$	3.91900	−	22.2258i	0.179251	−	1.01658i
$479$	6.33594	−	5.31649i	0.289497	−	0.242916i	−0.486460	−	0.873703i	$-0.661712\pi$
$479$	6.33594	−	5.31649i	0.289497	−	0.242916i	0.775957	+	0.630786i	$0.217268\pi$
$480$	−7.71096	−	11.0073i	−0.351955	−	0.502411i
$481$	1.79664	−	4.93624i	0.0819199	−	0.225073i
$482$	22.4194	+	38.8316i	1.02118	+	1.76873i
$483$	−24.5047	−	24.7915i	−1.11500	−	1.12805i
$484$	5.11361	+	29.0007i	0.232437	+	1.31821i
$485$	−3.49784	−	4.16856i	−0.158829	−	0.189284i
$486$	30.0877	+	8.02683i	1.36481	+	0.364104i
$487$	22.8894			1.03722			0.518609	−	0.855012i	$-0.326450\pi$
$487$	22.8894			1.03722			0.518609	+	0.855012i	$0.326450\pi$
$488$	0.168516	+	0.0613349i	0.00762837	+	0.00277650i
$489$	−9.16290	−	4.27030i	−0.414361	−	0.193110i
$490$	−13.4002	+	2.19635i	−0.605361	+	0.0992208i
$491$	−16.2163	+	19.3259i	−0.731833	+	0.872165i	−0.995723	−	0.0923880i	$-0.970550\pi$
$491$	−16.2163	+	19.3259i	−0.731833	+	0.872165i	0.263890	+	0.964553i	$0.414994\pi$
$492$	9.74359	+	4.54093i	0.439275	+	0.204721i
$493$	3.46721	+	2.00179i	0.156155	+	0.0901562i
$494$	1.38091	+	6.11118i	0.0621302	+	0.274955i
$495$	−7.40346	−	12.8103i	−0.332761	−	0.575779i
$496$	23.4504	+	4.13493i	1.05295	+	0.185664i
$497$	−2.38261	+	13.0512i	−0.106875	+	0.585427i
$498$	29.5234	−	13.7748i	1.32298	−	0.617265i
$499$	28.5798	+	23.9813i	1.27941	+	1.07355i	0.993325	+	0.115345i	$0.0367975\pi$
$499$	28.5798	+	23.9813i	1.27941	+	1.07355i	0.286082	+	0.958205i	$0.407647\pi$
$500$	−3.04004	−	17.2409i	−0.135955	−	0.771037i
$501$	−10.1854	−	10.1810i	−0.455052	−	0.454853i
$502$			22.8917i			1.02171i
$503$	−1.29251	−	7.33019i	−0.0576302	−	0.326837i	0.942339	−	0.334659i	$-0.108621\pi$
$503$	−1.29251	−	7.33019i	−0.0576302	−	0.326837i	−0.999969	+	0.00782215i	$0.997510\pi$
$504$	0.0521484	−	0.140817i	0.00232287	−	0.00627251i
$505$	8.25464	−	14.2974i	0.367326	−	0.636228i
$506$	66.8347	+	38.5871i	2.97117	+	1.71540i
$507$	12.3968	−	17.7127i	0.550563	−	0.786650i
$508$	2.46323	−	13.9697i	0.109288	−	0.619803i
$509$	−7.55692	−	42.8574i	−0.334954	−	1.89962i	−0.427682	−	0.903929i	$-0.640670\pi$
$509$	−7.55692	−	42.8574i	−0.334954	−	1.89962i	0.0927272	−	0.995692i	$-0.470442\pi$
$510$	−2.04178	+	0.179081i	−0.0904116	+	0.00792985i
$511$	−0.521301	+	2.85553i	−0.0230610	+	0.126321i
$512$			31.9599i			1.41244i
$513$	19.1596	+	12.0793i	0.845918	+	0.533312i
$514$	−11.7673	−	6.79384i	−0.519032	−	0.299664i
$515$	−7.00781	+	8.35158i	−0.308801	+	0.368015i
$516$	19.6078	−	13.7359i	0.863184	−	0.604688i
$517$	−16.3520	+	44.9268i	−0.719161	+	1.97588i
$518$	36.3378	−	12.9780i	1.59659	−	0.570220i
$519$	−11.0745	−	0.966461i	−0.486117	−	0.0424229i
$520$	0.00660946	−	0.0114479i	0.000289844	−	0.000502025i
$521$	−1.21038	−	2.09645i	−0.0530279	−	0.0918470i	0.838293	−	0.545220i	$-0.183554\pi$
$521$	−1.21038	−	2.09645i	−0.0530279	−	0.0918470i	−0.891321	+	0.453373i	$0.850221\pi$
$522$	13.4362	−	36.9657i	0.588084	−	1.61794i
$523$	−12.3832	−	14.7578i	−0.541481	−	0.645311i	0.424038	−	0.905644i	$-0.360612\pi$
$523$	−12.3832	−	14.7578i	−0.541481	−	0.645311i	−0.965519	+	0.260333i	$0.916168\pi$
$524$	7.44175	−	12.8895i	0.325094	−	0.563080i
$525$	13.2225	−	13.0695i	0.577075	−	0.570398i
$526$	16.4422	−	13.7967i	0.716915	−	0.601563i
$527$	2.32330	−	2.76880i	0.101204	−	0.120611i
$528$	−3.07351	+	35.2189i	−0.133757	+	1.53270i
$529$	32.7594	−	11.9235i	1.42432	−	0.518411i
$530$	4.14932	−	1.51023i	0.180235	−	0.0656002i
$531$	−0.0132657	−	30.4224i	−0.000575684	−	1.32022i
$532$	−14.0105	+	18.1846i	−0.607433	+	0.788401i
$533$			2.24345i			0.0971748i
$534$	−17.6034	+	37.7722i	−0.761775	+	1.63456i
$535$	−1.95927	−	5.38306i	−0.0847068	−	0.232730i
$536$	−0.142574	−	0.169913i	−0.00615824	−	0.00733910i
$537$	−16.5360	+	1.45035i	−0.713583	+	0.0625872i
$538$	−30.6642	−	36.5442i	−1.32203	−	1.57553i
$539$	30.5717	+	18.1462i	1.31681	+	0.781612i
$540$	2.60592	+	9.70004i	0.112141	+	0.417423i
$541$	−25.6985	+	21.5636i	−1.10486	+	0.927090i	−0.997742	−	0.0671560i	$-0.978607\pi$
$541$	−25.6985	+	21.5636i	−1.10486	+	0.927090i	−0.107120	+	0.994246i	$0.534163\pi$
$542$	−61.1381	−	22.2525i	−2.62611	−	0.955825i
$543$	−8.11609	−	2.17280i	−0.348295	−	0.0932439i
$544$	4.22122	+	2.43712i	0.180983	+	0.104491i
$545$	−3.52830	+	2.96059i	−0.151136	+	0.126818i
$546$	−6.56493	+	0.535883i	−0.280953	+	0.0229337i
$547$	26.3363	+	9.58562i	1.12606	+	0.409852i	0.836860	−	0.547418i	$-0.184389\pi$
$547$	26.3363	+	9.58562i	1.12606	+	0.409852i	0.289198	+	0.957269i	$0.406611\pi$
$548$	−24.1756	−	4.26282i	−1.03273	−	0.182099i
$549$	−21.7920	−	18.2694i	−0.930058	−	0.779721i
$550$	−20.5802	+	35.6460i	−0.877545	+	1.51995i
$551$	17.3229	−	22.7667i	0.737979	−	0.969894i
$552$	0.176291	+	0.176214i	0.00750344	+	0.00750017i
$553$	−20.6017	+	24.2533i	−0.876073	+	1.03135i
$554$	−0.186880	+	0.222715i	−0.00793978	+	0.00946227i
$555$	7.04101	−	10.0603i	0.298874	−	0.427035i
$556$	5.78473	+	1.02000i	0.245327	+	0.0432578i
$557$	25.1979	−	4.44308i	1.06767	−	0.188259i	0.387913	−	0.921696i	$-0.373196\pi$
$557$	25.1979	−	4.44308i	1.06767	−	0.188259i	0.679758	+	0.733437i	$0.262085\pi$
$558$	−30.7590	−	17.7408i	−1.30213	−	0.751030i
$559$	4.32692	+	2.49815i	0.183009	+	0.105660i
$560$	10.1792	−	1.73157i	0.430148	−	0.0731720i
$561$	4.39636	+	3.07694i	0.185614	+	0.129908i
$562$	−33.6232			−1.41831
$563$	36.5013			1.53835			0.769173	−	0.639040i	$-0.220668\pi$
$563$	36.5013			1.53835			0.769173	+	0.639040i	$0.220668\pi$
$564$	18.6099	−	26.5901i	0.783620	−	1.11964i
$565$	−5.30772	+	6.32550i	−0.223297	+	0.266116i
$566$	48.4829	+	17.6463i	2.03789	+	0.741730i
$567$	−15.3999	+	18.1616i	−0.646736	+	0.762714i
$568$	0.0164735	−	0.0934256i	0.000691211	−	0.00392005i
$569$	22.0182	−	12.7122i	0.923051	−	0.532924i	0.0384440	−	0.999261i	$-0.487760\pi$
$569$	22.0182	−	12.7122i	0.923051	−	0.532924i	0.884607	+	0.466337i	$0.154427\pi$
$570$	−0.576138	+	14.6343i	−0.0241318	+	0.612963i
$571$	−8.88510	+	15.3894i	−0.371830	+	0.644028i	−0.989847	−	0.142136i	$-0.954603\pi$
$571$	−8.88510	+	15.3894i	−0.371830	+	0.644028i	0.618017	+	0.786165i	$0.287936\pi$
$572$	6.83536	−	2.48787i	0.285801	−	0.104023i
$573$	−0.0374388	+	0.00328370i	−0.00156403	+	0.000137178i
$574$	−12.6875	+	10.5162i	−0.529565	+	0.438937i
$575$	10.5549	+	28.9993i	0.440169	+	1.20935i
$576$	8.12082	−	22.3421i	0.338367	−	0.930920i
$577$		−	19.4682i		−	0.810472i	−0.914212	−	0.405236i	$-0.867189\pi$
$577$		−	19.4682i		−	0.810472i	0.914212	−	0.405236i	$-0.132811\pi$
$578$	−28.7662	+	16.6082i	−1.19652	+	0.690809i
$579$	−18.9225	−	1.65135i	−0.786392	−	0.0686276i
$580$	12.4935	−	2.20294i	0.518763	−	0.0914719i
$581$	−0.150392	+	24.9115i	−0.00623930	+	1.03350i
$582$	5.01412	−	18.7293i	0.207842	−	0.776354i
$583$	−10.8634	−	3.95396i	−0.449917	−	0.163756i
$584$	0.00360430	−	0.0204410i	0.000149147	−	0.000845854i
$585$	−1.60516	+	1.34808i	−0.0663653	+	0.0557364i
$586$	15.3751	+	2.71105i	0.635142	+	0.111993i
$587$	−1.64894	+	9.35163i	−0.0680592	+	0.385983i	0.931683	+	0.363273i	$0.118341\pi$
$587$	−1.64894	+	9.35163i	−0.0680592	+	0.385983i	−0.999742	+	0.0227104i	$0.992770\pi$
$588$	−16.8617	−	17.2664i	−0.695365	−	0.712052i
$589$	−17.5257	−	18.9705i	−0.722134	−	0.781666i
$590$	17.0363	−	9.83589i	0.701372	−	0.404937i
$591$	−9.41761	+	0.826003i	−0.387389	+	0.0339772i
$592$	−27.5709	+	10.0350i	−1.13316	+	0.412435i
$593$	1.45883	+	8.27345i	0.0599071	+	0.339750i	0.999999	−	0.00117026i	$-0.000372507\pi$
$593$	1.45883	+	8.27345i	0.0599071	+	0.339750i	−0.940092	+	0.340920i	$0.889261\pi$
$594$	22.2482	−	47.7931i	0.912857	−	1.96098i
$595$	0.544922	−	1.46950i	0.0223396	−	0.0602435i
$596$	9.41399	−	5.43517i	0.385612	−	0.222633i
$597$	7.77013	−	7.77352i	0.318010	−	0.318149i
$598$	3.73947	−	10.2741i	0.152918	−	0.420140i
$599$	6.92917	−	19.0377i	0.283118	−	0.777861i	−0.713868	−	0.700280i	$-0.753058\pi$
$599$	6.92917	−	19.0377i	0.283118	−	0.777861i	0.996986	−	0.0775805i	$-0.0247195\pi$
$600$	−0.0939830	+	0.0940240i	−0.00383684	+	0.00383852i
$601$	12.7065	−	7.33608i	0.518307	−	0.299245i	−0.217935	−	0.975963i	$-0.569932\pi$
$601$	12.7065	−	7.33608i	0.518307	−	0.299245i	0.736242	+	0.676719i	$0.236599\pi$
$602$	6.15457	+	36.1802i	0.250841	+	1.47459i
$603$	12.0440	+	33.0458i	0.490470	+	1.34573i
$604$	2.05735	+	11.6678i	0.0837123	+	0.474756i
$605$	−13.4999	+	4.91355i	−0.548848	+	0.199764i
$606$	58.5982	−	5.13955i	2.38039	−	0.208780i
$607$	−23.1110	+	13.3431i	−0.938047	+	0.541582i	−0.889347	−	0.457232i	$-0.848841\pi$
$607$	−23.1110	+	13.3431i	−0.938047	+	0.541582i	−0.0486992	+	0.998813i	$0.515508\pi$
$608$	21.0901	−	27.7178i	0.855316	−	1.12410i
$609$	21.1427	+	21.3902i	0.856745	+	0.866774i
$610$	3.19303	−	18.1086i	0.129282	−	0.733196i
$611$	6.67050	+	1.17619i	0.269859	+	0.0475835i
$612$	−2.34274	−	2.78950i	−0.0946998	−	0.112759i
$613$	−5.79494	+	32.8648i	−0.234056	+	1.32740i	0.610538	+	0.791987i	$0.290953\pi$
$613$	−5.79494	+	32.8648i	−0.234056	+	1.32740i	−0.844594	+	0.535408i	$0.820158\pi$
$614$	−25.1192	−	9.14263i	−1.01373	−	0.368967i
$615$	−1.35622	+	5.06589i	−0.0546879	+	0.204276i
$616$	−0.219386	−	0.128435i	−0.00883932	−	0.00517478i
$617$	30.8006	−	5.43097i	1.23998	−	0.218643i	0.485075	−	0.874472i	$-0.338792\pi$
$617$	30.8006	−	5.43097i	1.23998	−	0.218643i	0.754909	+	0.655830i	$0.227681\pi$
$618$	−38.6979	−	3.37713i	−1.55666	−	0.135848i
$619$	29.4636	−	17.0108i	1.18424	−	0.683722i	0.227249	−	0.973837i	$-0.427027\pi$
$619$	29.4636	−	17.0108i	1.18424	−	0.683722i	0.956992	+	0.290115i	$0.0936936\pi$
$620$		−	11.4530i		−	0.459964i
$621$	−16.7277	−	35.8114i	−0.671258	−	1.43706i
$622$	−14.8980	−	40.9320i	−0.597357	−	1.64122i
$623$	−20.3352	−	24.5339i	−0.814713	−	0.982928i
$624$	4.98937	−	0.437609i	0.199735	−	0.0175184i
$625$	−11.0360	+	4.01677i	−0.441440	+	0.160671i
$626$	13.3687	−	23.1553i	0.534323	−	0.925474i
$627$	25.7835	−	28.3809i	1.02969	−	1.13342i
$628$	18.1164	−	10.4595i	0.722924	−	0.417380i
$629$	−0.773348	+	4.38587i	−0.0308354	+	0.174876i
$630$	−15.1480	−	2.75858i	−0.603513	−	0.109904i
$631$	21.6203	+	7.86916i	0.860692	+	0.313266i	0.734392	−	0.678726i	$-0.237468\pi$
$631$	21.6203	+	7.86916i	0.860692	+	0.313266i	0.126300	+	0.991992i	$0.459690\pi$
$632$	0.146265	−	0.174312i	0.00581813	−	0.00693378i
$633$	27.6831	−	39.5539i	1.10030	−	1.57212i
$634$	0.482452			0.0191606
$635$	6.92024			0.274622
$636$	6.42955	+	4.49993i	0.254948	+	0.178434i
$637$	1.77967	−	4.71180i	0.0705130	−	0.186688i
$638$	−57.6651	−	33.2930i	−2.28298	−	1.31808i
$639$	−7.51595	+	13.0311i	−0.297326	+	0.515504i
$640$	−0.144739	+	0.0255214i	−0.00572131	+	0.00100882i
$641$	48.2783	+	8.51276i	1.90688	+	0.336234i	0.996917	−	0.0784613i	$-0.0250007\pi$
$641$	48.2783	+	8.51276i	1.90688	+	0.336234i	0.909960	+	0.414695i	$0.136112\pi$
$642$	11.7036	−	16.7222i	0.461905	−	0.659974i
$643$	−5.43184	+	6.47341i	−0.214211	+	0.255286i	−0.862441	−	0.506158i	$-0.831065\pi$
$643$	−5.43184	+	6.47341i	−0.214211	+	0.255286i	0.648230	+	0.761445i	$0.275510\pi$
$644$	37.7264	−	13.4739i	1.48663	−	0.530947i
$645$	8.26032	+	8.25672i	0.325250	+	0.325108i
$646$	−2.05264	−	4.89907i	−0.0807600	−	0.192751i
$647$	5.03320	−	8.71776i	0.197876	−	0.342730i	−0.749964	−	0.661479i	$-0.769929\pi$
$647$	5.03320	−	8.71776i	0.197876	−	0.342730i	0.947839	+	0.318748i	$0.103262\pi$
$648$	0.109333	−	0.130529i	0.00429501	−	0.00512767i
$649$	−50.7206	−	8.94341i	−1.99096	−	0.351060i
$650$	5.47966	+	1.99443i	0.214930	+	0.0782280i
$651$	22.3321	−	15.4442i	0.875262	−	0.605306i
$652$	8.89969	−	7.46773i	0.348539	−	0.292459i
$653$	−27.9704	−	16.1487i	−1.09457	−	0.631949i	−0.159779	−	0.987153i	$-0.551078\pi$
$653$	−27.9704	−	16.1487i	−1.09457	−	0.631949i	−0.934789	+	0.355204i	$0.884411\pi$
$654$	−15.8526	−	4.24399i	−0.619886	−	0.165953i
$655$	6.82304	+	2.48338i	0.266598	+	0.0970338i
$656$	9.59900	−	8.05452i	0.374778	−	0.314476i
$657$	−1.64445	+	2.85114i	−0.0641560	+	0.111234i
$658$	24.6162	+	43.2372i	0.959639	+	1.68556i
$659$	−11.3211	−	13.4919i	−0.441007	−	0.525572i	0.499057	−	0.866569i	$-0.333680\pi$
$659$	−11.3211	−	13.4919i	−0.441007	−	0.525572i	−0.940064	+	0.340997i	$0.889235\pi$
$660$	16.9387	−	1.48567i	0.659339	−	0.0578296i
$661$	−26.3990	−	31.4611i	−1.02680	−	1.22370i	−0.974342	−	0.225073i	$-0.927738\pi$
$661$	−26.3990	−	31.4611i	−1.02680	−	1.22370i	−0.0524612	−	0.998623i	$-0.516707\pi$
$662$	−8.99890	−	24.7243i	−0.349752	−	0.960936i
$663$	0.321140	−	0.689079i	0.0124720	−	0.0267616i
$664$		−	0.178136i		−	0.00691303i
$665$	−9.92348	−	5.19071i	−0.384816	−	0.201287i
$666$	43.7522	−	0.0190782i	1.69536	−	0.000739265i
$667$	−46.9126	+	17.0748i	−1.81646	+	0.661138i
$668$	15.5523	−	5.66056i	0.601735	−	0.219014i
$669$	−0.443062	+	5.07697i	−0.0171298	+	0.196287i
$670$	−14.6190	+	17.4222i	−0.564780	+	0.673078i
$671$	−36.8788	+	30.9450i	−1.42369	+	1.19462i
$672$	25.7406	+	26.0419i	0.992964	+	1.00459i
$673$	−6.21528	+	10.7652i	−0.239581	+	0.414967i	−0.960594	−	0.277955i	$-0.910344\pi$
$673$	−6.21528	+	10.7652i	−0.239581	+	0.414967i	0.721013	+	0.692922i	$0.243677\pi$
$674$	−1.07383	−	1.27975i	−0.0413626	−	0.0492940i
$675$	19.0999	−	8.92162i	0.735154	−	0.343393i
$676$	12.4232	+	21.5176i	0.477814	+	0.827599i
$677$	−1.90259	+	3.29538i	−0.0731223	+	0.126652i	−0.900268	−	0.435336i	$-0.856630\pi$
$677$	−1.90259	+	3.29538i	−0.0731223	+	0.126652i	0.827146	+	0.561987i	$0.189963\pi$
$678$	−29.3098	−	2.55784i	−1.12564	−	0.0982332i
$679$	11.2997	+	9.59839i	0.433642	+	0.368352i
$680$	−0.00383303	+	0.0105312i	−0.000146990	+	0.000403852i
$681$	7.52458	−	5.27121i	0.288343	−	0.201993i
$682$	−38.6402	+	46.0495i	−1.47961	+	1.76333i
$683$	22.8916	+	13.2165i	0.875922	+	0.505714i	0.869312	−	0.494265i	$-0.164563\pi$
$683$	22.8916	+	13.2165i	0.875922	+	0.505714i	0.00661011	+	0.999978i	$0.497896\pi$
$684$	−21.8899	+	14.0844i	−0.836981	+	0.538529i
$685$		−	11.9760i		−	0.457581i
$686$	34.9889	−	12.0219i	1.33588	−	0.458999i
$687$	−42.9903	+	3.77061i	−1.64018	+	0.143858i
$688$	−4.84588	−	27.4824i	−0.184748	−	1.04776i
$689$	−0.284405	+	1.61294i	−0.0108350	+	0.0614483i
$690$	14.6549	−	20.9391i	0.557904	−	0.797139i
$691$	−7.90236	−	4.56243i	−0.300620	−	0.173563i	0.342101	−	0.939663i	$-0.388861\pi$
$691$	−7.90236	−	4.56243i	−0.300620	−	0.173563i	−0.642721	+	0.766100i	$0.722195\pi$
$692$	6.38778	−	11.0640i	0.242827	−	0.420589i
$693$	25.7385	+	31.0251i	0.977723	+	1.17855i
$694$	−6.42667	−	36.4474i	−0.243953	−	1.38353i
$695$			2.86562i			0.108699i
$696$	−0.152104	−	0.152038i	−0.00576549	−	0.00576298i
$697$	−0.330280	−	1.87311i	−0.0125102	−	0.0709491i
$698$	−1.82334	−	1.52996i	−0.0690142	−	0.0579098i
$699$	−4.08702	+	1.90689i	−0.154585	+	0.0721253i
$700$	7.18625	+	20.1212i	0.271615	+	0.760510i
$701$	−8.79419	−	1.55065i	−0.332152	−	0.0585674i	0.00508522	−	0.999987i	$-0.498381\pi$
$701$	−8.79419	−	1.55065i	−0.332152	−	0.0585674i	−0.337237	+	0.941420i	$0.609492\pi$
$702$	−7.21546	−	1.92832i	−0.272330	−	0.0727797i
$703$	30.3887	+	9.44583i	1.14613	+	0.356256i
$704$	−34.8529	−	20.1223i	−1.31357	−	0.758388i
$705$	14.3515	+	6.68838i	0.540507	+	0.251899i
$706$	−4.62421	+	5.51092i	−0.174034	+	0.207406i
$707$	−15.6390	+	42.1739i	−0.588166	+	1.58611i
$708$	31.6900	+	14.7689i	1.19098	+	0.555048i
$709$	45.8590	+	16.6913i	1.72227	+	0.626855i	0.998033	−	0.0626967i	$-0.0199701\pi$
$709$	45.8590	+	16.6913i	1.72227	+	0.626855i	0.724237	+	0.689551i	$0.242192\pi$
$710$	−9.72729			−0.365059
$711$	−31.2409	+	18.0551i	−1.17162	+	0.677119i
$712$	0.146466	+	0.174552i	0.00548905	+	0.00654160i
$713$	7.82641	+	44.3858i	0.293101	+	1.66226i
$714$	5.40231	−	1.41390i	0.202176	−	0.0529140i
$715$	1.77432	+	3.07322i	0.0663559	+	0.114932i
$716$	6.52462	−	17.9262i	0.243837	−	0.669935i
$717$	11.2273	+	16.0269i	0.419293	+	0.598534i
$718$	20.4991	−	17.2008i	0.765020	−	0.641928i
$719$	−6.72749	+	38.1535i	−0.250893	+	1.42288i	0.555506	+	0.831512i	$0.312525\pi$
$719$	−6.72749	+	38.1535i	−0.250893	+	1.42288i	−0.806399	+	0.591372i	$0.798587\pi$
$720$	11.5309	+	2.02803i	0.429732	+	0.0755801i
$721$	15.0068	−	25.6339i	0.558882	−	0.954656i
$722$	−36.5806	+	10.1213i	−1.36139	+	0.376676i
$723$	−37.5551	−	10.0541i	−1.39669	−	0.373915i
$724$	6.20659	−	7.39673i	0.230666	−	0.274897i
$725$	−9.10676	−	25.0206i	−0.338217	−	0.929243i
$726$	−41.9368	−	29.3508i	−1.55642	−	1.08931i
$727$	6.11121	+	16.7904i	0.226652	+	0.622722i	0.999936	−	0.0113385i	$-0.00360923\pi$
$727$	6.11121	+	16.7904i	0.226652	+	0.622722i	−0.773283	+	0.634061i	$0.781387\pi$
$728$	−0.0125221	+	0.0337685i	−0.000464101	+	0.00125154i
$729$	−23.3650	+	13.5306i	−0.865371	+	0.501132i
$730$	−2.12828			−0.0787710
$731$	−3.98041	−	1.44875i	−0.147221	−	0.0535840i
$732$	29.6158	−	13.8179i	1.09463	−	0.510725i
$733$		−	42.4184i		−	1.56676i	−0.621543	−	0.783380i	$-0.713494\pi$
$733$		−	42.4184i		−	1.56676i	0.621543	−	0.783380i	$-0.286506\pi$
$734$	−3.36639	−	5.83076i	−0.124256	−	0.215217i
$735$	6.86700	−	9.56374i	0.253293	−	0.352764i
$736$	−57.1147	+	20.7880i	−2.10527	+	0.766257i
$737$	58.6394	−	10.3397i	2.16001	−	0.380868i
$738$	−17.5559	+	6.39850i	−0.646242	+	0.235532i
$739$	−1.60093	−	1.34334i	−0.0588913	−	0.0494157i	0.612867	−	0.790186i	$-0.290016\pi$
$739$	−1.60093	−	1.34334i	−0.0588913	−	0.0494157i	−0.671758	+	0.740770i	$0.734461\pi$
$740$	7.05598	+	12.2213i	0.259383	+	0.449264i
$741$	−4.59403	−	2.89912i	−0.168766	−	0.106502i
$742$	−10.4549	+	5.95226i	−0.383810	+	0.218514i
$743$	−16.1777	−	2.85257i	−0.593504	−	0.104651i	−0.131175	−	0.991359i	$-0.541875\pi$
$743$	−16.1777	−	2.85257i	−0.593504	−	0.104651i	−0.462329	+	0.886708i	$0.652986\pi$
$744$	−0.159019	+	0.111398i	−0.00582991	+	0.00408404i
$745$	3.40877	+	4.06241i	0.124888	+	0.148835i
$746$	−54.5321	−	9.61547i	−1.99656	−	0.352047i
$747$	−9.64965	+	26.5482i	−0.353062	+	0.971348i
$748$	−5.34074	+	3.08348i	−0.195277	+	0.112743i
$749$	7.72207	+	13.5635i	0.282158	+	0.495598i
$750$	24.9314	+	17.4491i	0.910366	+	0.637149i
$751$	−0.595965	+	0.500074i	−0.0217471	+	0.0182479i	−0.653596	−	0.756843i	$-0.726741\pi$
$751$	−0.595965	+	0.500074i	−0.0217471	+	0.0182479i	0.631849	+	0.775091i	$0.282296\pi$
$752$	−18.9161	−	32.7637i	−0.689799	−	1.19477i
$753$	−14.0379	−	14.0318i	−0.511571	−	0.511348i
$754$	−3.22642	+	8.86453i	−0.117499	+	0.322827i
$755$	−5.43138	+	1.97686i	−0.197668	+	0.0719453i
$756$	−11.4314	−	24.8632i	−0.415756	−	0.904267i
$757$	−20.9189	−	17.5531i	−0.760312	−	0.637978i	0.177896	−	0.984049i	$-0.443071\pi$
$757$	−20.9189	−	17.5531i	−0.760312	−	0.637978i	−0.938208	+	0.346072i	$0.887515\pi$
$758$	−0.0142097	−	0.0390409i	−0.000516120	−	0.00141803i
$759$	−64.6302	+	17.3327i	−2.34593	+	0.629137i
$760$	0.0711819	+	0.0366878i	0.00258204	+	0.00133081i
$761$	3.81709	+	6.61139i	0.138369	+	0.239663i	0.926880	−	0.375359i	$-0.122481\pi$
$761$	3.81709	+	6.61139i	0.138369	+	0.239663i	−0.788510	+	0.615022i	$0.789147\pi$
$762$	14.1471	+	20.1948i	0.512496	+	0.731581i
$763$	8.12415	−	9.56412i	0.294114	−	0.346245i
$764$	0.0147722	−	0.0405863i	0.000534440	−	0.00146836i
$765$	1.14172	−	1.36186i	0.0412790	−	0.0492380i
$766$	47.6841	−	8.40799i	1.72290	−	0.303793i
$767$			7.29659i			0.263465i
$768$	−19.7845	−	19.7759i	−0.713911	−	0.713600i
$769$	21.4702	−	3.78578i	0.774235	−	0.136519i	0.227448	−	0.973790i	$-0.426962\pi$
$769$	21.4702	−	3.78578i	0.774235	−	0.136519i	0.546787	+	0.837272i	$0.315851\pi$
$770$	−9.06292	+	24.4401i	−0.326605	+	0.880759i
$771$	11.3791	−	3.05169i	0.409810	−	0.109904i
$772$	10.9145	−	18.9045i	0.392821	−	0.680387i
$773$	1.23099	+	6.98128i	0.0442756	+	0.251099i	0.998910	−	0.0466816i	$-0.0148646\pi$
$773$	1.23099	+	6.98128i	0.0442756	+	0.251099i	−0.954634	+	0.297781i	$0.903754\pi$
$774$	−7.20829	+	40.9847i	−0.259097	+	1.47317i
$775$	−23.6730	+	4.17418i	−0.850358	+	0.149941i
$776$	−0.0812127	−	0.0681455i	−0.00291536	−	0.00244628i
$777$	−14.3153	+	30.2385i	−0.513557	+	1.08480i
$778$	−36.2114			−1.29824
$779$	−13.5754	+	0.648034i	−0.486389	+	0.0232182i
$780$	−0.623995	−	2.32675i	−0.0223426	−	0.0833111i
$781$	19.5090	+	16.3700i	0.698087	+	0.585764i
$782$	−1.60962	+	9.12861i	−0.0575599	+	0.326438i
$783$	14.4327	+	30.8981i	0.515781	+	1.10421i
$784$	−26.5496	+	9.30182i	−0.948201	+	0.332208i
$785$	6.55988	+	7.81776i	0.234132	+	0.279028i
$786$	6.70134	+	24.9879i	0.239029	+	0.891291i
$787$	12.4578	−	7.19253i	0.444074	−	0.256386i	−0.261250	−	0.965271i	$-0.584135\pi$
$787$	12.4578	−	7.19253i	0.444074	−	0.256386i	0.705324	+	0.708885i	$0.250801\pi$
$788$	3.71590	−	10.2094i	0.132374	−	0.363693i
$789$	−1.61795	+	18.5398i	−0.0576004	+	0.660033i
$790$	−20.2061	−	11.6660i	−0.718901	−	0.415057i
$791$	11.3662	−	19.4151i	0.404134	−	0.690323i
$792$	−0.185382	−	0.220734i	−0.00658727	−	0.00784345i
$793$	5.22472	+	4.38406i	0.185535	+	0.155683i
$794$	−43.9979	+	36.9186i	−1.56143	+	1.31019i
$795$	−1.61727	+	3.47022i	−0.0573586	+	0.123076i
$796$	4.32014	+	11.8695i	0.153123	+	0.420703i
$797$	−45.8995			−1.62584			−0.812921	−	0.582373i	$-0.802124\pi$
$797$	−45.8995			−1.62584			−0.812921	+	0.582373i	$0.802124\pi$
$798$	−5.13900	−	39.5703i	−0.181919	−	1.40077i
$799$	−5.74251			−0.203155
$800$	−11.0872	−	30.4619i	−0.391992	−	1.07699i
$801$	−12.3728	−	33.9480i	−0.437173	−	1.19949i
$802$	14.3855	−	12.0708i	0.507968	−	0.426236i
$803$	4.26846	+	3.58166i	0.150631	+	0.126394i
$804$	−40.2680	−	3.51414i	−1.42014	−	0.123934i
$805$	9.66936	+	16.9838i	0.340800	+	0.598600i
$806$	7.37546	+	4.25822i	0.259789	+	0.149989i
$807$	41.2061	+	3.59602i	1.45052	+	0.126586i
$808$	0.110006	−	0.302240i	0.00387001	−	0.0106328i
$809$	12.5318	−	7.23526i	0.440596	−	0.254378i	−0.263254	−	0.964726i	$-0.584796\pi$
$809$	12.5318	−	7.23526i	0.440596	−	0.254378i	0.703851	+	0.710348i	$0.251462\pi$
$810$	−15.1273	−	8.71619i	−0.531520	−	0.306256i
$811$	18.0304	+	21.4878i	0.633134	+	0.754540i	0.983269	−	0.182159i	$-0.0583087\pi$
$811$	18.0304	+	21.4878i	0.633134	+	0.754540i	−0.350135	+	0.936699i	$0.613864\pi$
$812$	−32.5504	+	11.6253i	−1.14229	+	0.407969i
$813$	51.1215	−	23.8519i	1.79291	−	0.836523i
$814$	12.8620	−	72.9440i	0.450813	−	2.55669i
$815$	4.34172	+	3.64314i	0.152084	+	0.127614i
$816$	−4.10131	+	1.09990i	−0.143575	+	0.0385043i
$817$	−13.8667	+	26.9043i	−0.485135	+	0.941261i
$818$	30.6590			1.07197
$819$	3.69545	−	4.35430i	0.129129	−	0.152152i
$820$	−4.61688	−	3.87402i	−0.161228	−	0.135287i
$821$	−21.9632	+	3.87270i	−0.766521	+	0.135158i	−0.543219	−	0.839591i	$-0.682795\pi$
$821$	−21.9632	+	3.87270i	−0.766521	+	0.135158i	−0.223302	+	0.974749i	$0.571684\pi$
$822$	34.9488	−	24.4828i	1.21898	−	0.853934i
$823$	−3.27969	−	18.6000i	−0.114323	−	0.648356i	−0.987083	−	0.160208i	$-0.948784\pi$
$823$	−3.27969	−	18.6000i	−0.114323	−	0.648356i	0.872761	−	0.488149i	$-0.162328\pi$
$824$	−0.106200	+	0.183943i	−0.00369964	+	0.00640796i
$825$	−9.24433	−	34.4702i	−0.321846	−	1.20010i
$826$	−41.2646	+	34.2027i	−1.43578	+	1.19007i
$827$	−16.4608	+	2.90248i	−0.572398	+	0.100929i	−0.452353	−	0.891839i	$-0.649415\pi$
$827$	−16.4608	+	2.90248i	−0.572398	+	0.100929i	−0.120045	+	0.992768i	$0.538304\pi$
$828$	45.4241	−	0.0198072i	1.57860	−	0.000688349i
$829$			14.4157i			0.500678i	0.968158	+	0.250339i	$0.0805421\pi$
$829$			14.4157i			0.500678i	−0.968158	+	0.250339i	$0.919458\pi$
$830$	−17.9879	+	3.17176i	−0.624371	+	0.110093i
$831$	−0.0220251	−	0.251118i	−0.000764043	−	0.00871118i
$832$	−1.95005	+	5.35773i	−0.0676059	+	0.185746i
$833$	−0.792217	+	4.19599i	−0.0274487	+	0.145382i
$834$	−8.36252	+	5.85822i	−0.289570	+	0.202853i
$835$	4.03706	+	6.99239i	0.139708	+	0.241982i
$836$	17.0288	+	40.6429i	0.588954	+	1.40567i
$837$	29.7335	−	7.98790i	1.02774	−	0.276102i
$838$	−6.18211	−	16.9852i	−0.213557	−	0.586744i
$839$	−12.7764	−	10.7206i	−0.441089	−	0.370118i	0.395028	−	0.918669i	$-0.370735\pi$
$839$	−12.7764	−	10.7206i	−0.441089	−	0.370118i	−0.836117	+	0.548552i	$0.815179\pi$
$840$	−0.0486897	+	0.0686820i	−0.00167995	+	0.00236975i
$841$	13.2252	−	4.81357i	0.456041	−	0.165985i
$842$	0.598754	−	1.64506i	0.0206344	−	0.0566926i
$843$	20.6099	−	20.6188i	0.709841	−	0.710151i
$844$	27.7419	+	48.0504i	0.954915	+	1.65396i
$845$	−9.28546	+	7.79143i	−0.319430	+	0.268033i
$846$	9.82063	+	55.5539i	0.337640	+	1.90998i
$847$	34.0151	−	19.3658i	1.16877	−	0.665415i
$848$	7.92234	−	4.57396i	0.272054	−	0.157071i
$849$	−40.5396	+	18.9147i	−1.39131	+	0.649150i
$850$	−4.86871	−	0.858484i	−0.166995	−	0.0294458i
$851$	−35.6966	−	42.5415i	−1.22366	−	1.45831i
$852$	−9.91920	−	14.1595i	−0.339826	−	0.485097i
$853$	−22.3229	−	3.93612i	−0.764320	−	0.134770i	−0.222120	−	0.975019i	$-0.571298\pi$
$853$	−22.3229	−	3.93612i	−0.764320	−	0.134770i	−0.542200	+	0.840249i	$0.682409\pi$
$854$	−0.302442	+	50.0978i	−0.0103494	+	1.71431i
$855$	−8.62107	−	9.32362i	−0.294835	−	0.318861i
$856$	−0.0558022	−	0.0966522i	−0.00190728	−	0.00330351i
$857$	−10.2229	−	8.57806i	−0.349209	−	0.293021i	0.451263	−	0.892391i	$-0.350973\pi$
$857$	−10.2229	−	8.57806i	−0.349209	−	0.293021i	−0.800472	+	0.599370i	$0.795418\pi$
$858$	−5.34107	+	11.4605i	−0.182341	+	0.391254i
$859$	32.5509	−	5.73961i	1.11062	−	0.195833i	0.411903	−	0.911228i	$-0.364864\pi$
$859$	32.5509	−	5.73961i	1.11062	−	0.195833i	0.698720	+	0.715395i	$0.253753\pi$
$860$	−12.6128	+	4.59068i	−0.430092	+	0.156541i
$861$	1.32811	−	14.2264i	0.0452619	−	0.484835i
$862$	9.63424	+	16.6870i	0.328143	+	0.568361i
$863$		−	20.4696i		−	0.696795i	−0.937347	−	0.348397i	$-0.886726\pi$
$863$		−	20.4696i		−	0.696795i	0.937347	−	0.348397i	$-0.113274\pi$
$864$	17.5713	+	37.6176i	0.597788	+	1.27978i
$865$	5.85670	+	2.13166i	0.199134	+	0.0724788i
$866$	−7.54472			−0.256380
$867$	7.44801	−	27.8206i	0.252948	−	0.944837i
$868$	5.23294	+	30.7623i	0.177618	+	1.04414i
$869$	20.8926	+	57.4020i	0.708733	+	1.94723i
$870$	−12.6443	+	18.0663i	−0.428682	+	0.612506i
$871$	−2.88521	−	7.92704i	−0.0977615	−	0.268597i
$872$	−0.0576789	+	0.0687390i	−0.00195325	+	0.00232780i
$873$	8.41193	+	14.5552i	0.284701	+	0.492620i
$874$	63.2500	+	19.6602i	2.13946	+	0.665018i
$875$	−20.2219	+	11.5129i	−0.683626	+	0.389208i
$876$	−2.17027	−	3.09802i	−0.0733265	−	0.104672i
$877$	−6.96784	+	39.5166i	−0.235287	+	1.33438i	0.606721	+	0.794915i	$0.292485\pi$
$877$	−6.96784	+	39.5166i	−0.235287	+	1.33438i	−0.842008	+	0.539465i	$0.818627\pi$
$878$	43.6080	−	36.5914i	1.47170	−	1.23490i
$879$	−11.0869	+	7.76676i	−0.373953	+	0.261966i
$880$	6.77906	−	18.6253i	0.228522	−	0.627859i
$881$	−11.0759	−	19.1840i	−0.373156	−	0.646326i	0.616893	−	0.787047i	$-0.288391\pi$
$881$	−11.0759	−	19.1840i	−0.373156	−	0.646326i	−0.990049	+	0.140722i	$0.955058\pi$
$882$	41.9474	+	0.488201i	1.41244	+	0.0164386i
$883$	−0.783037	−	4.44082i	−0.0263513	−	0.149446i	0.968793	−	0.247870i	$-0.0797307\pi$
$883$	−0.783037	−	4.44082i	−0.0263513	−	0.149446i	−0.995144	+	0.0984248i	$0.968620\pi$
$884$	0.561597	+	0.669285i	0.0188886	+	0.0225105i
$885$	−4.41095	+	16.4762i	−0.148272	+	0.553843i
$886$	−77.8292			−2.61472
$887$	25.4108	+	9.24878i	0.853211	+	0.310544i	0.731349	−	0.682003i	$-0.238891\pi$
$887$	25.4108	+	9.24878i	0.853211	+	0.310544i	0.121862	+	0.992547i	$0.461113\pi$
$888$	0.101056	−	0.216839i	0.00339122	−	0.00727663i
$889$	−18.5875	+	3.16189i	−0.623404	+	0.106047i
$890$	15.0181	−	17.8979i	0.503407	−	0.599938i
$891$	15.6709	+	42.9389i	0.524994	+	1.43851i
$892$	−5.07213	−	2.92840i	−0.169827	−	0.0980499i
$893$	−5.19044	+	40.7037i	−0.173692	+	1.36210i
$894$	−4.88645	+	18.2524i	−0.163427	+	0.610451i
$895$	9.16520	+	1.61607i	0.306359	+	0.0540193i
$896$	0.377102	−	0.134681i	0.0125981	−	0.00449939i
$897$	4.00825	+	8.59084i	0.133832	+	0.286840i
$898$	5.06952	+	4.25383i	0.169172	+	0.141952i
$899$	−6.75264	−	38.2961i	−0.225213	−	1.27725i
$900$	0.0105641	+	24.2267i	0.000352137	+	0.807558i
$901$		−	1.38855i		−	0.0462594i
$902$	5.49308	+	31.1528i	0.182899	+	1.03727i
$903$	−25.9594	−	18.4030i	−0.863874	−	0.612413i
$904$	−0.0804356	+	0.139319i	−0.00267525	+	0.00463367i
$905$	4.07947	+	2.35528i	0.135606	+	0.0782922i
$906$	−16.8723	−	11.8087i	−0.560546	−	0.392317i
$907$	2.93108	−	16.6230i	0.0973248	−	0.551956i	−0.896685	−	0.442669i	$-0.854032\pi$
$907$	2.93108	−	16.6230i	0.0973248	−	0.551956i	0.994010	−	0.109288i	$-0.0348571\pi$
$908$	1.83342	+	10.3979i	0.0608442	+	0.345065i
$909$	−32.7669	+	39.0847i	−1.08681	+	1.29636i
$910$	3.63285	+	0.663208i	0.120428	+	0.0219851i
$911$		−	47.5790i		−	1.57636i	−0.615443	−	0.788182i	$-0.711023\pi$
$911$		−	47.5790i		−	1.57636i	0.615443	−	0.788182i	$-0.288977\pi$
$912$	4.08923	+	30.0648i	0.135408	+	0.995546i
$913$	41.4143	+	23.9105i	1.37061	+	0.791323i
$914$	−33.4142	+	39.8215i	−1.10524	+	1.31718i
$915$	9.14756	+	13.0580i	0.302409	+	0.431684i
$916$	16.9627	−	46.6045i	0.560462	−	1.53986i
$917$	−19.4611	−	3.55278i	−0.642661	−	0.117323i
$918$	6.30823	+	0.547742i	0.208203	+	0.0180782i
$919$	−14.4228	+	24.9810i	−0.475763	+	0.824046i	−0.999615	−	0.0277639i	$-0.991161\pi$
$919$	−14.4228	+	24.9810i	−0.475763	+	0.824046i	0.523852	+	0.851810i	$0.324495\pi$
$920$	−0.0698740	−	0.121025i	−0.00230368	−	0.00399008i
$921$	21.0037	−	9.79977i	0.692096	−	0.322914i
$922$	5.43499	+	6.47717i	0.178992	+	0.213314i
$923$	1.80401	−	3.12463i	0.0593796	−	0.102848i
$924$	−44.8179	+	11.7298i	−1.47440	+	0.385883i
$925$	22.6893	−	19.0386i	0.746021	−	0.625986i
$926$	33.5477	−	39.9806i	1.10245	−	1.31384i
$927$	25.7914	−	21.6608i	0.847102	−	0.711432i
$928$	49.2786	−	17.9360i	1.61765	−	0.588777i
$929$	31.2890	−	11.3882i	1.02656	−	0.373636i	0.226788	−	0.973944i	$-0.427177\pi$
$929$	31.2890	−	11.3882i	1.02656	−	0.373636i	0.799769	+	0.600308i	$0.204955\pi$
$930$	14.0801	+	14.0740i	0.461706	+	0.461505i
$931$	29.0257	+	9.40794i	0.951279	+	0.308333i
$932$		−	5.18302i		−	0.169775i
$933$	34.2328	+	15.9539i	1.12073	+	0.522308i
$934$	0.947564	+	2.60341i	0.0310053	+	0.0851862i
$935$	−1.93386	−	2.30468i	−0.0632440	−	0.0753712i
$936$	−0.0262364	+	0.0312950i	−0.000857562	+	0.00102291i
$937$	−13.6277	−	16.2408i	−0.445197	−	0.530565i	0.496046	−	0.868296i	$-0.334785\pi$
$937$	−13.6277	−	16.2408i	−0.445197	−	0.530565i	−0.941242	+	0.337732i	$0.890340\pi$
$938$	31.3056	−	53.4747i	1.02216	−	1.74601i
$939$	6.00503	+	22.3916i	0.195967	+	0.730721i
$940$	−13.9392	+	11.6964i	−0.454647	+	0.381494i
$941$	−33.7892	−	12.2983i	−1.10150	−	0.400912i	−0.273628	−	0.961836i	$-0.588224\pi$
$941$	−33.7892	−	12.2983i	−1.10150	−	0.400912i	−0.827867	+	0.560924i	$0.810446\pi$
$942$	−9.40354	+	35.1251i	−0.306384	+	1.14444i
$943$	20.5398	+	11.8587i	0.668869	+	0.386172i
$944$	31.2197	−	26.1964i	1.01611	−	0.852621i
$945$	10.9769	−	7.59836i	0.357078	−	0.247175i
$946$	66.2006	+	24.0951i	2.15237	+	0.783398i
$947$	−51.4984	−	9.08055i	−1.67347	−	0.295078i	−0.745162	−	0.666884i	$-0.767628\pi$
$947$	−51.4984	−	9.08055i	−1.67347	−	0.295078i	−0.928311	+	0.371805i	$0.878739\pi$
$948$	−3.62316	−	41.3091i	−0.117675	−	1.34166i
$949$	0.394706	−	0.683652i	0.0128127	−	0.0221923i
$950$	−10.4857	+	33.7341i	−0.340201	+	1.09448i
$951$	−0.295726	+	0.295855i	−0.00958958	+	0.00959376i
$952$	0.00548361	−	0.0300376i	0.000177725	−	0.000973524i
$953$	−22.4227	+	26.7223i	−0.726342	+	0.865621i	−0.995231	−	0.0975507i	$-0.968899\pi$
$953$	−22.4227	+	26.7223i	−0.726342	+	0.865621i	0.268889	+	0.963171i	$0.413344\pi$
$954$	−13.4331	+	2.37465i	−0.434912	+	0.0768822i
$955$	0.0207507	+	0.00365891i	0.000671476	+	0.000118399i
$956$	−22.1467	+	3.90507i	−0.716277	+	0.126299i
$957$	55.7630	−	14.9547i	1.80256	−	0.483417i
$958$	−14.3088	−	8.26119i	−0.462296	−	0.266907i
$959$	5.47192	+	32.1671i	0.176697	+	1.03873i
$960$	−7.64223	+	10.9193i	−0.246652	+	0.352419i
$961$	−4.10685			−0.132479
$962$	−10.4936			−0.338328
$963$	3.08072	+	17.4272i	0.0992747	+	0.561583i
$964$	28.7194	−	34.2264i	0.924989	−	1.10236i
$965$	10.0071	+	3.64227i	0.322139	+	0.117249i
$966$	−29.7953	+	62.9375i	−0.958649	+	2.02498i
$967$	6.34214	−	35.9681i	0.203950	−	1.15666i	−0.695135	−	0.718879i	$-0.744655\pi$
$967$	6.34214	−	35.9681i	0.203950	−	1.15666i	0.899084	−	0.437776i	$-0.144234\pi$
$968$	−0.242389	+	0.139943i	−0.00779067	+	0.00449795i
$969$	4.26246	+	1.74421i	0.136930	+	0.0560321i
$970$	−5.43522	+	9.41408i	−0.174514	+	0.302268i
$971$	56.7006	−	20.6373i	1.81961	−	0.662284i	0.824232	−	0.566253i	$-0.191607\pi$
$971$	56.7006	−	20.6373i	1.81961	−	0.662284i	0.995378	−	0.0960309i	$-0.0306148\pi$
$972$	−2.73808	−	30.9082i	−0.0878238	−	0.991382i
$973$	−1.30932	−	7.69693i	−0.0419748	−	0.246752i
$974$	−15.6387	−	42.9670i	−0.501097	−	1.37675i
$975$	−4.58189	+	2.13779i	−0.146738	+	0.0684639i
$976$		−	38.0947i		−	1.21938i
$977$	−22.6618	+	13.0838i	−0.725016	+	0.418588i	−0.816596	−	0.577209i	$-0.804142\pi$
$977$	−22.6618	+	13.0838i	−0.725016	+	0.418588i	0.0915799	+	0.995798i	$0.470808\pi$
$978$	−1.75566	+	20.1178i	−0.0561399	+	0.643297i
$979$	−60.2404	+	10.6220i	−1.92529	+	0.339481i
$980$	6.62341	+	11.7988i	0.211577	+	0.376899i
$981$	12.3196	−	7.11991i	0.393336	−	0.227321i
$982$	47.3572	+	17.2366i	1.51123	+	0.550043i
$983$	3.19061	−	18.0949i	0.101765	−	0.577136i	−0.890699	−	0.454594i	$-0.849784\pi$
$983$	3.19061	−	18.0949i	0.101765	−	0.577136i	0.992463	−	0.122542i	$-0.0391046\pi$
$984$	−0.00888253	+	0.101783i	−0.000283165	+	0.00324473i
$985$	5.21977	+	0.920386i	0.166316	+	0.0293259i
$986$	1.38878	−	7.87618i	0.0442279	−	0.250829i
$987$	−41.6033	−	11.4075i	−1.32425	−	0.363103i
$988$	5.25160	−	3.37574i	0.167076	−	0.107397i
$989$	45.7433	−	26.4099i	1.45455	−	0.839786i
$990$	−18.9886	+	22.6498i	−0.603499	+	0.719859i
$991$	−8.00132	+	2.91224i	−0.254170	+	0.0925104i	−0.465963	−	0.884804i	$-0.654292\pi$
$991$	−8.00132	+	2.91224i	−0.254170	+	0.0925104i	0.211793	+	0.977315i	$0.432070\pi$
$992$	−8.22113	−	46.6244i	−0.261021	−	1.48032i
$993$	20.6777	+	9.63669i	0.656188	+	0.305811i
$994$	26.1271	−	4.44445i	0.828700	−	0.140969i
$995$	−5.33659	+	3.08108i	−0.169181	+	0.0976768i
$996$	−22.9598	−	22.9498i	−0.727509	−	0.727192i
$997$	2.15672	−	5.92555i	0.0683041	−	0.187664i	−0.900844	−	0.434143i	$-0.857051\pi$
$997$	2.15672	−	5.92555i	0.0683041	−	0.187664i	0.969148	+	0.246479i	$0.0792736\pi$
$998$	25.4901	−	70.0336i	0.806876	−	2.21687i
$999$	−26.8068	+	26.8419i	−0.848131	+	0.849241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.ci.b.17.8	yes	288
3.2	odd	2	inner	399.2.ci.b.17.41	yes	288
7.5	odd	6		399.2.cb.b.131.8	✓	288
19.9	even	9		399.2.cb.b.332.41	yes	288
21.5	even	6		399.2.cb.b.131.41	yes	288
57.47	odd	18		399.2.cb.b.332.8	yes	288
133.47	odd	18	inner	399.2.ci.b.47.41	yes	288
399.47	even	18	inner	399.2.ci.b.47.8	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.cb.b.131.8	✓	288	7.5	odd	6
399.2.cb.b.131.41	yes	288	21.5	even	6
399.2.cb.b.332.8	yes	288	57.47	odd	18
399.2.cb.b.332.41	yes	288	19.9	even	9
399.2.ci.b.17.8	yes	288	1.1	even	1	trivial
399.2.ci.b.17.41	yes	288	3.2	odd	2	inner
399.2.ci.b.47.8	yes	288	399.47	even	18	inner
399.2.ci.b.47.41	yes	288	133.47	odd	18	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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.ci (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.683230 - 1.87716i) q^{2} +(1.56993 + 0.731654i) q^{3} +(-1.52483 + 1.27949i) q^{4} +(-0.743891 - 0.624199i) q^{5} +(0.300807 - 3.44690i) q^{6} +(2.28326 + 1.33668i) q^{7} +(-0.0163842 - 0.00945940i) q^{8} +(1.92936 + 2.29729i) q^{9} +(-0.663472 + 1.82287i) q^{10} +(4.39836 - 2.53939i) q^{11} +(-3.33003 + 0.893056i) q^{12} +(-0.462503 - 0.551190i) q^{13} +(0.949176 - 5.19930i) q^{14} +(-0.711160 - 1.52422i) q^{15} +(-0.697866 + 3.95780i) q^{16} +(0.467300 + 0.392111i) q^{17} +(2.99418 - 5.19130i) q^{18} +(3.20172 - 2.95787i) q^{19} +1.93297 q^{20} +(2.60657 + 3.76906i) q^{21} +(-7.77194 - 6.52143i) q^{22} +(-7.49114 + 1.32089i) q^{23} +(-0.0188010 - 0.0268381i) q^{24} +(-0.704491 - 3.99537i) q^{25} +(-0.718675 + 1.24478i) q^{26} +(1.34815 + 5.01822i) q^{27} +(-5.19186 + 0.883182i) q^{28} +(6.46337 - 1.13967i) q^{29} +(-2.37532 + 2.37635i) q^{30} -5.92510i q^{31} +(7.86895 - 1.38751i) q^{32} +(8.76308 - 0.768595i) q^{33} +(0.416782 - 1.14510i) q^{34} +(-0.864141 - 2.41956i) q^{35} +(-5.88132 - 1.03439i) q^{36} +(3.65034 + 6.32257i) q^{37} +(-7.73991 - 3.98922i) q^{38} +(-0.322818 - 1.20372i) q^{39} +(0.00628349 + 0.0172637i) q^{40} +(-2.38849 - 2.00418i) q^{41} +(5.29423 - 7.46808i) q^{42} +(-6.52509 + 2.37494i) q^{43} +(-3.45765 + 9.49980i) q^{44} +(-0.00127032 - 2.91324i) q^{45} +(7.59769 + 13.1596i) q^{46} +(-7.21130 + 6.05100i) q^{47} +(-3.99134 + 5.70287i) q^{48} +(3.42655 + 6.10399i) q^{49} +(-7.01861 + 4.05220i) q^{50} +(0.446739 + 0.957489i) q^{51} +(1.41048 + 0.248706i) q^{52} +(-1.46315 - 1.74371i) q^{53} +(8.49890 - 5.95928i) q^{54} +(-4.85699 - 0.856418i) q^{55} +(-0.0247651 - 0.0434987i) q^{56} +(7.19061 - 2.30111i) q^{57} +(-6.55530 - 11.3541i) q^{58} +(-7.76831 - 6.51839i) q^{59} +(3.03462 + 1.41426i) q^{60} +(-9.33499 + 1.64601i) q^{61} +(-11.1224 + 4.04821i) q^{62} +(1.33449 + 7.82427i) q^{63} +(-3.96203 - 6.86243i) q^{64} +0.698719i q^{65} +(-7.42997 - 15.9246i) q^{66} +(11.0170 + 4.00986i) q^{67} -1.21426 q^{68} +(-12.7270 - 3.40722i) q^{69} +(-3.95149 + 3.27524i) q^{70} +(1.71503 + 4.71202i) q^{71} +(-0.00988001 - 0.0558898i) q^{72} +(0.375240 + 1.03096i) q^{73} +(9.37445 - 11.1720i) q^{74} +(1.81722 - 6.78789i) q^{75} +(-1.09752 + 8.60682i) q^{76} +(13.4370 + 0.0811195i) q^{77} +(-2.03902 + 1.42840i) q^{78} +(-2.08858 + 11.8449i) q^{79} +(2.98959 - 2.50856i) q^{80} +(-1.55510 + 8.86463i) q^{81} +(-2.13028 + 5.85290i) q^{82} +(4.70792 + 8.15436i) q^{83} +(-8.79705 - 2.41211i) q^{84} +(-0.102865 - 0.583376i) q^{85} +(8.91628 + 10.6260i) q^{86} +(10.9809 + 2.93975i) q^{87} -0.0960846 q^{88} +(-11.3178 - 4.11934i) q^{89} +(-5.46775 + 1.99280i) q^{90} +(-0.319248 - 1.87673i) q^{91} +(9.73268 - 11.5990i) q^{92} +(4.33513 - 9.30200i) q^{93} +(16.2857 + 9.40254i) q^{94} +(-4.22803 + 0.201829i) q^{95} +(13.3689 + 3.57906i) q^{96} +(5.51859 + 0.973076i) q^{97} +(9.11704 - 10.6026i) q^{98} +(14.3198 + 5.20490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 9 q^{3} - 6 q^{4} - 6 q^{7} - 3 q^{9} - 18 q^{10} - 27 q^{12} - 36 q^{13} - 15 q^{15} + 6 q^{16} - 18 q^{18} - 72 q^{19} + 12 q^{21} - 9 q^{24} + 18 q^{25} + 27 q^{27} - 108 q^{28} - 6 q^{30} - 9 q^{33}+ \cdots - 24 q^{99}+O(q^{100}) \) 288 * q - 9 * q^3 - 6 * q^4 - 6 * q^7 - 3 * q^9 - 18 * q^10 - 27 * q^12 - 36 * q^13 - 15 * q^15 + 6 * q^16 - 18 * q^18 - 72 * q^19 + 12 * q^21 - 9 * q^24 + 18 * q^25 + 27 * q^27 - 108 * q^28 - 6 * q^30 - 9 * q^33 + 36 * q^34 - 84 * q^36 - 24 * q^39 - 144 * q^40 + 39 * q^42 + 12 * q^43 - 6 * q^46 + 63 * q^48 - 30 * q^49 - 3 * q^51 + 90 * q^52 + 9 * q^54 - 90 * q^55 - 66 * q^57 + 24 * q^58 + 42 * q^60 + 54 * q^61 + 60 * q^63 + 54 * q^64 - 27 * q^66 + 102 * q^67 + 60 * q^70 - 39 * q^72 + 36 * q^73 - 63 * q^75 - 87 * q^78 + 6 * q^79 + 45 * q^81 - 18 * q^82 - 117 * q^84 + 36 * q^85 - 9 * q^87 - 204 * q^88 + 144 * q^90 - 198 * q^91 - 60 * q^93 - 180 * q^94 - 243 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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