LMFDB - Embedded newform 294.2.j.a.251.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(41,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("294.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.j (of order $14$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			251.19
Character	$\chi$	$=$	294.251
Dual form			294.2.j.a.41.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.781831 + 0.623490i) q^{2} +(1.52314 + 0.824644i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.59923 + 1.25172i) q^{5} +(0.676684 + 1.59440i) q^{6} +(-2.01156 - 1.71861i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(1.63993 + 2.51210i) q^{9} +(1.25172 + 2.59923i) q^{10} +(-3.63779 - 2.90104i) q^{11} +(-0.465037 + 1.66845i) q^{12} +(-1.88273 - 1.50143i) q^{13} +(-0.501162 - 2.59785i) q^{14} +(2.92677 + 4.04999i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(1.66757 - 7.30612i) q^{17} +(-0.284124 + 2.98652i) q^{18} +2.97594i q^{19} +(-0.641956 + 2.81259i) q^{20} +(-1.64665 - 4.27651i) q^{21} +(-1.03537 - 4.53625i) q^{22} +(-4.11077 + 0.938257i) q^{23} +(-1.40385 + 1.01450i) q^{24} +(2.07173 + 2.59786i) q^{25} +(-0.535854 - 2.34773i) q^{26} +(0.426252 + 5.17864i) q^{27} +(1.22791 - 2.34355i) q^{28} +(5.21333 + 1.18991i) q^{29} +(-0.236886 + 4.99122i) q^{30} +6.11012i q^{31} +(-0.974928 - 0.222521i) q^{32} +(-3.14855 - 7.41858i) q^{33} +(5.85905 - 4.67244i) q^{34} +(-3.07727 - 6.98498i) q^{35} +(-2.08420 + 2.15780i) q^{36} +(-0.628266 + 2.75262i) q^{37} +(-1.85547 + 2.32669i) q^{38} +(-1.62953 - 3.83948i) q^{39} +(-2.25553 + 1.79872i) q^{40} +(-0.953462 - 0.459163i) q^{41} +(1.37896 - 4.37018i) q^{42} +(4.51390 - 2.17378i) q^{43} +(2.01882 - 4.19213i) q^{44} +(1.11809 + 8.58225i) q^{45} +(-3.79892 - 1.82947i) q^{46} +(0.950670 - 1.19210i) q^{47} +(-1.73010 - 0.0821117i) q^{48} +(1.09274 + 6.91418i) q^{49} +3.32279i q^{50} +(8.56490 - 9.75310i) q^{51} +(1.04484 - 2.16963i) q^{52} +(10.0766 - 2.29992i) q^{53} +(-2.89557 + 4.31459i) q^{54} +(-5.82415 - 12.0940i) q^{55} +(2.42120 - 1.06667i) q^{56} +(-2.45409 + 4.53278i) q^{57} +(3.33405 + 4.18076i) q^{58} +(-7.30136 + 3.51615i) q^{59} +(-3.29718 + 3.75460i) q^{60} +(-11.6609 - 2.66153i) q^{61} +(-3.80960 + 4.77708i) q^{62} +(1.01852 - 7.87163i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-3.01428 - 6.25922i) q^{65} +(2.16378 - 7.76317i) q^{66} -12.2733 q^{67} +7.49401 q^{68} +(-7.03502 - 1.96082i) q^{69} +(1.94916 - 7.37972i) q^{70} +(12.9562 - 2.95718i) q^{71} +(-2.97486 + 0.387562i) q^{72} +(-0.233828 + 0.186472i) q^{73} +(-2.20743 + 1.76036i) q^{74} +(1.01322 + 5.66535i) q^{75} +(-2.90133 + 0.662209i) q^{76} +(2.33186 + 12.0876i) q^{77} +(1.11986 - 4.01782i) q^{78} +8.33881 q^{79} -2.88492 q^{80} +(-3.62129 + 8.23931i) q^{81} +(-0.459163 - 0.953462i) q^{82} +(-8.04620 - 10.0896i) q^{83} +(3.80288 - 2.55697i) q^{84} +(13.4796 - 16.9029i) q^{85} +(4.88444 + 1.11484i) q^{86} +(6.95939 + 6.11154i) q^{87} +(4.19213 - 2.01882i) q^{88} +(1.18218 + 1.48241i) q^{89} +(-4.47679 + 7.40699i) q^{90} +(1.20685 + 6.25591i) q^{91} +(-1.82947 - 3.79892i) q^{92} +(-5.03867 + 9.30658i) q^{93} +(1.48653 - 0.339290i) q^{94} +(-3.72505 + 7.73515i) q^{95} +(-1.30145 - 1.14290i) q^{96} +5.44330i q^{97} +(-3.45659 + 6.08704i) q^{98} +(1.32200 - 13.8960i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) $ 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

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 $

$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$2$	0.781831	+	0.623490i	0.552838	+	0.440874i
$3$	1.52314	+	0.824644i	0.879387	+	0.476108i
$3$	1.52314	+	0.824644i	0.879387	+	0.476108i
$4$	0.222521	+	0.974928i	0.111260	+	0.487464i
$5$	2.59923	+	1.25172i	1.16241	+	0.559787i	0.912739	−	0.408544i	$-0.133963\pi$
$5$	2.59923	+	1.25172i	1.16241	+	0.559787i	0.249671	+	0.968331i	$0.419678\pi$
$6$	0.676684	+	1.59440i	0.276255	+	0.650910i
$7$	−2.01156	−	1.71861i	−0.760298	−	0.649575i
$7$	−2.01156	−	1.71861i	−0.760298	−	0.649575i
$8$	−0.433884	+	0.900969i	−0.153401	+	0.318541i
$9$	1.63993	+	2.51210i	0.546642	+	0.837367i
$10$	1.25172	+	2.59923i	0.395829	+	0.821948i
$11$	−3.63779	−	2.90104i	−1.09684	−	0.874697i	−0.104047	−	0.994572i	$-0.533179\pi$
$11$	−3.63779	−	2.90104i	−1.09684	−	0.874697i	−0.992789	+	0.119875i	$0.961751\pi$
$12$	−0.465037	+	1.66845i	−0.134245	+	0.481641i
$13$	−1.88273	−	1.50143i	−0.522177	−	0.416422i	0.326609	−	0.945160i	$-0.394094\pi$
$13$	−1.88273	−	1.50143i	−0.522177	−	0.416422i	−0.848785	+	0.528738i	$0.822666\pi$
$14$	−0.501162	−	2.59785i	−0.133941	−	0.694305i
$15$	2.92677	+	4.04999i	0.755688	+	1.04570i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	1.66757	−	7.30612i	0.404446	−	1.77199i	−0.204586	−	0.978849i	$-0.565585\pi$
$17$	1.66757	−	7.30612i	0.404446	−	1.77199i	0.609032	−	0.793145i	$-0.291558\pi$
$18$	−0.284124	+	2.98652i	−0.0669686	+	0.703928i
$19$			2.97594i			0.682728i	0.939931	+	0.341364i	$0.110889\pi$
$19$			2.97594i			0.682728i	−0.939931	+	0.341364i	$0.889111\pi$
$20$	−0.641956	+	2.81259i	−0.143546	+	0.628915i
$21$	−1.64665	−	4.27651i	−0.359328	−	0.933211i
$22$	−1.03537	−	4.53625i	−0.220742	−	0.967132i
$23$	−4.11077	+	0.938257i	−0.857155	+	0.195640i	−0.628444	−	0.777854i	$-0.716308\pi$
$23$	−4.11077	+	0.938257i	−0.857155	+	0.195640i	−0.228710	+	0.973494i	$0.573451\pi$
$24$	−1.40385	+	1.01450i	−0.286559	+	0.207085i
$25$	2.07173	+	2.59786i	0.414345	+	0.519573i
$26$	−0.535854	−	2.34773i	−0.105090	−	0.460428i
$27$	0.426252	+	5.17864i	0.0820321	+	0.996630i
$28$	1.22791	−	2.34355i	0.232053	−	0.442890i
$29$	5.21333	+	1.18991i	0.968090	+	0.220960i	0.677202	−	0.735797i	$-0.263192\pi$
$29$	5.21333	+	1.18991i	0.968090	+	0.220960i	0.290888	+	0.956757i	$0.406049\pi$
$30$	−0.236886	+	4.99122i	−0.0432493	+	0.911268i
$31$			6.11012i			1.09741i	0.836016	+	0.548705i	$0.184879\pi$
$31$			6.11012i			1.09741i	−0.836016	+	0.548705i	$0.815121\pi$
$32$	−0.974928	−	0.222521i	−0.172345	−	0.0393365i
$33$	−3.14855	−	7.41858i	−0.548092	−	1.29141i
$34$	5.85905	−	4.67244i	1.00482	−	0.801317i
$35$	−3.07727	−	6.98498i	−0.520154	−	1.18068i
$36$	−2.08420	+	2.15780i	−0.347366	+	0.359634i
$37$	−0.628266	+	2.75262i	−0.103286	+	0.452527i	0.896665	+	0.442709i	$0.145982\pi$
$37$	−0.628266	+	2.75262i	−0.103286	+	0.452527i	−0.999952	+	0.00981833i	$0.996875\pi$
$38$	−1.85547	+	2.32669i	−0.300997	+	0.377438i
$39$	−1.62953	−	3.83948i	−0.260933	−	0.614808i
$40$	−2.25553	+	1.79872i	−0.356630	+	0.284403i
$41$	−0.953462	−	0.459163i	−0.148906	−	0.0717092i	0.357947	−	0.933742i	$-0.383477\pi$
$41$	−0.953462	−	0.459163i	−0.148906	−	0.0717092i	−0.506853	+	0.862033i	$0.669191\pi$
$42$	1.37896	−	4.37018i	0.212779	−	0.674333i
$43$	4.51390	−	2.17378i	0.688363	−	0.331498i	−0.0567950	−	0.998386i	$-0.518088\pi$
$43$	4.51390	−	2.17378i	0.688363	−	0.331498i	0.745158	+	0.666888i	$0.232374\pi$
$44$	2.01882	−	4.19213i	0.304349	−	0.631987i
$45$	1.11809	+	8.58225i	0.166675	+	1.27937i
$46$	−3.79892	−	1.82947i	−0.560121	−	0.269740i
$47$	0.950670	−	1.19210i	0.138669	−	0.173886i	−0.707647	−	0.706566i	$-0.750243\pi$
$47$	0.950670	−	1.19210i	0.138669	−	0.173886i	0.846317	+	0.532680i	$0.178815\pi$
$48$	−1.73010	−	0.0821117i	−0.249719	−	0.0118518i
$49$	1.09274	+	6.91418i	0.156105	+	0.987740i
$50$			3.32279i			0.469914i
$51$	8.56490	−	9.75310i	1.19933	−	1.36571i
$52$	1.04484	−	2.16963i	0.144893	−	0.300874i
$53$	10.0766	−	2.29992i	1.38413	−	0.315918i	0.535332	−	0.844642i	$-0.320186\pi$
$53$	10.0766	−	2.29992i	1.38413	−	0.315918i	0.848794	+	0.528724i	$0.177329\pi$
$54$	−2.89557	+	4.31459i	−0.394037	+	0.587141i
$55$	−5.82415	−	12.0940i	−0.785328	−	1.63075i
$56$	2.42120	−	1.06667i	0.323546	−	0.142540i
$57$	−2.45409	+	4.53278i	−0.325052	+	0.600382i
$58$	3.33405	+	4.18076i	0.437782	+	0.548961i
$59$	−7.30136	+	3.51615i	−0.950556	+	0.457764i	−0.843881	−	0.536530i	$-0.819735\pi$
$59$	−7.30136	+	3.51615i	−0.950556	+	0.457764i	−0.106675	+	0.994294i	$0.534020\pi$
$60$	−3.29718	+	3.75460i	−0.425664	+	0.484716i
$61$	−11.6609	−	2.66153i	−1.49303	−	0.340774i	−0.603394	−	0.797444i	$-0.706185\pi$
$61$	−11.6609	−	2.66153i	−1.49303	−	0.340774i	−0.889637	+	0.456669i	$0.849042\pi$
$62$	−3.80960	+	4.77708i	−0.483819	+	0.606690i
$63$	1.01852	−	7.87163i	0.128322	−	0.991733i
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−3.01428	−	6.25922i	−0.373876	−	0.776361i
$66$	2.16378	−	7.76317i	0.266343	−	0.955580i
$67$	−12.2733			−1.49942			−0.749712	−	0.661764i	$-0.769808\pi$
$67$	−12.2733			−1.49942			−0.749712	+	0.661764i	$0.769808\pi$
$68$	7.49401			0.908782
$69$	−7.03502	−	1.96082i	−0.846916	−	0.236055i
$70$	1.94916	−	7.37972i	0.232969	−	0.882046i
$71$	12.9562	−	2.95718i	1.53762	−	0.350952i	0.631977	−	0.774988i	$-0.282244\pi$
$71$	12.9562	−	2.95718i	1.53762	−	0.350952i	0.905646	+	0.424035i	$0.139387\pi$
$72$	−2.97486	+	0.387562i	−0.350591	+	0.0456746i
$73$	−0.233828	+	0.186472i	−0.0273676	+	0.0218249i	−0.637078	−	0.770799i	$-0.719857\pi$
$73$	−0.233828	+	0.186472i	−0.0273676	+	0.0218249i	0.609711	+	0.792624i	$0.291286\pi$
$74$	−2.20743	+	1.76036i	−0.256608	+	0.204638i
$75$	1.01322	+	5.66535i	0.116997	+	0.654178i
$76$	−2.90133	+	0.662209i	−0.332805	+	0.0759606i
$77$	2.33186	+	12.0876i	0.265740	+	1.37751i
$78$	1.11986	−	4.01782i	0.126799	−	0.454928i
$79$	8.33881			0.938189			0.469095	−	0.883148i	$-0.344580\pi$
$79$	8.33881			0.938189			0.469095	+	0.883148i	$0.344580\pi$
$80$	−2.88492			−0.322544
$81$	−3.62129	+	8.23931i	−0.402366	+	0.915479i
$82$	−0.459163	−	0.953462i	−0.0507061	−	0.105292i
$83$	−8.04620	−	10.0896i	−0.883185	−	1.10748i	−0.993528	−	0.113585i	$-0.963766\pi$
$83$	−8.04620	−	10.0896i	−0.883185	−	1.10748i	0.110343	−	0.993894i	$-0.464805\pi$
$84$	3.80288	−	2.55697i	0.414928	−	0.278989i
$85$	13.4796	−	16.9029i	1.46207	−	1.83338i
$86$	4.88444	+	1.11484i	0.526703	+	0.120216i
$87$	6.95939	+	6.11154i	0.746125	+	0.655225i
$88$	4.19213	−	2.01882i	0.446882	−	0.215207i
$89$	1.18218	+	1.48241i	0.125311	+	0.157135i	0.840529	−	0.541766i	$-0.182244\pi$
$89$	1.18218	+	1.48241i	0.125311	+	0.157135i	−0.715218	+	0.698901i	$0.753673\pi$
$90$	−4.47679	+	7.40699i	−0.471895	+	0.780765i
$91$	1.20685	+	6.25591i	0.126512	+	0.655797i
$92$	−1.82947	−	3.79892i	−0.190735	−	0.396065i
$93$	−5.03867	+	9.30658i	−0.522486	+	0.965047i
$94$	1.48653	−	0.339290i	0.153324	−	0.0349951i
$95$	−3.72505	+	7.73515i	−0.382182	+	0.793610i
$96$	−1.30145	−	1.14290i	−0.132829	−	0.116647i
$97$			5.44330i			0.552683i	0.961059	+	0.276342i	$0.0891221\pi$
$97$			5.44330i			0.552683i	−0.961059	+	0.276342i	$0.910878\pi$
$98$	−3.45659	+	6.08704i	−0.349168	+	0.614883i
$99$	1.32200	−	13.8960i	0.132866	−	1.39660i
$100$	−2.07173	+	2.59786i	−0.207173	+	0.259786i
$101$	−0.422700	−	0.203561i	−0.0420602	−	0.0202551i	0.412735	−	0.910851i	$-0.364573\pi$
$101$	−0.422700	−	0.203561i	−0.0420602	−	0.0202551i	−0.454796	+	0.890596i	$0.650288\pi$
$102$	12.7773	−	2.28516i	1.26514	−	0.226264i
$103$	−0.0868796	+	0.180407i	−0.00856050	+	0.0177761i	−0.905205	−	0.424975i	$-0.860283\pi$
$103$	−0.0868796	+	0.180407i	−0.00856050	+	0.0177761i	0.896645	+	0.442751i	$0.145997\pi$
$104$	2.16963	−	1.04484i	0.212750	−	0.102455i
$105$	1.07300	−	13.1768i	0.104714	−	1.28592i
$106$	9.31217	+	4.48450i	0.904478	+	0.435574i
$107$	3.49879	−	2.79020i	0.338241	−	0.269738i	−0.439607	−	0.898190i	$-0.644882\pi$
$107$	3.49879	−	2.79020i	0.338241	−	0.269738i	0.777849	+	0.628452i	$0.216311\pi$
$108$	−4.95395	+	1.56792i	−0.476694	+	0.150873i
$109$	−5.21135	+	6.53483i	−0.499157	+	0.625923i	−0.966039	−	0.258397i	$-0.916806\pi$
$109$	−5.21135	+	6.53483i	−0.499157	+	0.625923i	0.466882	+	0.884320i	$0.345377\pi$
$110$	2.98697	−	13.0867i	0.284796	−	1.24777i
$111$	−3.22687	+	3.67453i	−0.306281	+	0.348771i
$112$	2.55803	+	0.675635i	0.241711	+	0.0638415i
$113$	6.77014	−	5.39901i	0.636881	−	0.507896i	−0.250989	−	0.967990i	$-0.580756\pi$
$113$	6.77014	−	5.39901i	0.636881	−	0.507896i	0.887870	+	0.460094i	$0.152184\pi$
$114$	−4.74483	+	2.01377i	−0.444394	+	0.188607i
$115$	−11.8593	−	2.70680i	−1.10588	−	0.252410i
$116$			5.34740i			0.496493i
$117$	0.684200	−	7.19185i	0.0632543	−	0.664887i
$118$	−7.90071	−	1.80329i	−0.727320	−	0.166006i
$119$	−15.9108	+	11.8308i	−1.45854	+	1.08452i
$120$	−4.91879	+	0.879704i	−0.449022	+	0.0803056i
$121$	2.36976	+	10.3826i	0.215432	+	0.943871i
$122$	−7.45745	−	9.35135i	−0.675166	−	0.846631i
$123$	−1.07361	−	1.48564i	−0.0968043	−	0.133955i
$124$	−5.95692	+	1.35963i	−0.534947	+	0.122098i
$125$	−1.07669	−	4.71731i	−0.0963025	−	0.421929i
$126$	5.70420	−	5.51925i	0.508170	−	0.491694i
$127$	−3.93570	+	17.2434i	−0.349237	+	1.53011i	0.429682	+	0.902981i	$0.358626\pi$
$127$	−3.93570	+	17.2434i	−0.349237	+	1.53011i	−0.778918	+	0.627126i	$0.784231\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	8.66791	+	0.411384i	0.763167	+	0.0362204i
$130$	1.54590	−	6.77303i	0.135584	−	0.594034i
$131$	−16.1430	+	7.77407i	−1.41042	+	0.679223i	−0.975246	−	0.221122i	$-0.929028\pi$
$131$	−16.1430	+	7.77407i	−1.41042	+	0.679223i	−0.435176	+	0.900346i	$0.643314\pi$
$132$	6.53197	−	4.72040i	0.568535	−	0.410858i
$133$	5.11449	−	5.98628i	0.443483	−	0.519076i
$134$	−9.59567	−	7.65229i	−0.828939	−	0.661057i
$135$	−5.37429	+	13.9940i	−0.462545	+	1.20441i
$136$	5.85905	+	4.67244i	0.502410	+	0.400658i
$137$	0.289063	+	0.600245i	0.0246963	+	0.0512824i	0.912952	−	0.408067i	$-0.133797\pi$
$137$	0.289063	+	0.600245i	0.0246963	+	0.0512824i	−0.888256	+	0.459349i	$0.848083\pi$
$138$	−4.27764	−	5.91929i	−0.364137	−	0.503884i
$139$	5.46640	−	11.3511i	0.463654	−	0.962787i	−0.529754	−	0.848152i	$-0.677716\pi$
$139$	5.46640	−	11.3511i	0.463654	−	0.962787i	0.993408	−	0.114636i	$-0.0365701\pi$
$140$	6.12509	−	4.55442i	0.517665	−	0.384919i
$141$	2.43107	−	1.03178i	0.204733	−	0.0868914i
$142$	11.9734	+	5.76607i	1.00478	+	0.483878i
$143$	2.49328	+	10.9238i	0.208499	+	0.913493i
$144$	−2.56748	−	1.55179i	−0.213957	−	0.129316i
$145$	12.0612	+	9.61847i	1.00163	+	0.798771i
$146$	−0.299078			−0.0247519
$147$	−4.03735	+	11.4324i	−0.332995	+	0.942929i
$148$	−2.82340			−0.232082
$149$	−0.178248	−	0.142148i	−0.0146027	−	0.0116452i	0.616161	−	0.787620i	$-0.288687\pi$
$149$	−0.178248	−	0.142148i	−0.0146027	−	0.0116452i	−0.630764	+	0.775975i	$0.717258\pi$
$150$	−2.74012	+	5.06108i	−0.223730	+	0.413236i
$151$	2.82839	+	12.3920i	0.230171	+	1.00845i	0.949498	+	0.313774i	$0.101594\pi$
$151$	2.82839	+	12.3920i	0.230171	+	1.00845i	−0.719326	+	0.694672i	$0.755549\pi$
$152$	−2.68123	−	1.29121i	−0.217477	−	0.104731i
$153$	21.0884	−	7.79237i	1.70490	−	0.629976i
$154$	−5.71336	+	10.9043i	−0.460396	+	0.878697i
$155$	−7.64817	+	15.8816i	−0.614316	+	1.27564i
$156$	3.38061	−	2.44304i	0.270665	−	0.195599i
$157$	6.13153	+	12.7323i	0.489350	+	1.01614i	0.988723	+	0.149758i	$0.0478494\pi$
$157$	6.13153	+	12.7323i	0.489350	+	1.01614i	−0.499373	+	0.866387i	$0.666436\pi$
$158$	6.51954	+	5.19916i	0.518667	+	0.413623i
$159$	17.2447	+	4.80650i	1.36759	+	0.381180i
$160$	−2.25553	−	1.79872i	−0.178315	−	0.142201i
$161$	9.88156	+	5.17747i	0.778776	+	0.408042i
$162$	−7.96837	+	4.18391i	−0.626054	+	0.328719i
$163$	9.00713	−	4.33761i	0.705493	−	0.339747i	−0.0465003	−	0.998918i	$-0.514807\pi$
$163$	9.00713	−	4.33761i	0.705493	−	0.339747i	0.751993	+	0.659171i	$0.229093\pi$
$164$	0.235486	−	1.03173i	0.0183883	−	0.0805645i
$165$	1.10221	−	23.2237i	0.0858070	−	1.80796i
$166$		−	12.9051i		−	1.00163i
$167$	0.736547	−	3.22702i	0.0569957	−	0.249715i	−0.938402	−	0.345546i	$-0.887694\pi$
$167$	0.736547	−	3.22702i	0.0569957	−	0.249715i	0.995398	+	0.0958312i	$0.0305509\pi$
$168$	4.56746	+	0.371933i	0.352387	+	0.0286952i
$169$	−1.60238	−	7.02047i	−0.123260	−	0.540036i
$170$	21.0776	−	4.81083i	1.61658	−	0.368973i
$171$	−7.47586	+	4.88032i	−0.571694	+	0.373208i
$172$	3.12372	+	3.91702i	0.238181	+	0.298670i
$173$	5.27591	+	23.1153i	0.401120	+	1.75742i	0.622878	+	0.782319i	$0.285963\pi$
$173$	5.27591	+	23.1153i	0.401120	+	1.75742i	−0.221758	+	0.975102i	$0.571180\pi$
$174$	1.63059	+	9.11730i	0.123615	+	0.691181i
$175$	0.297323	−	8.78625i	0.0224755	−	0.664178i
$176$	4.53625	+	1.03537i	0.341933	+	0.0780440i
$177$	−14.0206	−	0.665425i	−1.05385	−	0.0500164i
$178$			1.89607i			0.142117i
$179$	12.0722	+	2.75541i	0.902322	+	0.205949i	0.648422	−	0.761281i	$-0.275429\pi$
$179$	12.0722	+	2.75541i	0.902322	+	0.205949i	0.253900	+	0.967230i	$0.418287\pi$
$180$	−8.11828	+	2.99978i	−0.605101	+	0.223591i
$181$	−7.05221	+	5.62395i	−0.524186	+	0.418025i	−0.849506	−	0.527579i	$-0.823100\pi$
$181$	−7.05221	+	5.62395i	−0.524186	+	0.418025i	0.325319	+	0.945604i	$0.394528\pi$
$182$	−2.95694	+	5.64353i	−0.219183	+	0.418326i
$183$	−15.5665	−	13.6700i	−1.15071	−	1.01052i
$184$	0.938257	−	4.11077i	0.0691692	−	0.303050i
$185$	−5.07852	+	6.36826i	−0.373380	+	0.468204i
$186$	−9.74195	+	4.13462i	−0.714314	+	0.303165i
$187$	−27.2617	+	21.7404i	−1.99357	+	1.58982i
$188$	1.37376	+	0.661567i	0.100192	+	0.0482497i
$189$	8.04265	−	11.1497i	0.585017	−	0.811021i
$190$	−7.73515	+	3.72505i	−0.561167	+	0.270244i
$191$	3.52413	−	7.31792i	0.254997	−	0.529506i	−0.733693	−	0.679481i	$-0.762205\pi$
$191$	3.52413	−	7.31792i	0.254997	−	0.529506i	0.988690	+	0.149975i	$0.0479193\pi$
$192$	−0.304931	−	1.70500i	−0.0220065	−	0.123048i
$193$	10.4257	+	5.02073i	0.750455	+	0.361400i	0.769692	−	0.638415i	$-0.220410\pi$
$193$	10.4257	+	5.02073i	0.750455	+	0.361400i	−0.0192375	+	0.999815i	$0.506124\pi$
$194$	−3.39384	+	4.25574i	−0.243664	+	0.305544i
$195$	0.570447	−	12.0194i	0.0408506	−	0.860726i
$196$	−6.49767	+	2.60389i	−0.464120	+	0.185992i
$197$			13.9770i			0.995822i	0.867228	+	0.497911i	$0.165899\pi$
$197$			13.9770i			0.995822i	−0.867228	+	0.497911i	$0.834101\pi$
$198$	9.69759	−	10.0401i	0.689178	−	0.713517i
$199$	0.920359	−	1.91114i	0.0652425	−	0.135477i	−0.865798	−	0.500394i	$-0.833188\pi$
$199$	0.920359	−	1.91114i	0.0652425	−	0.135477i	0.931040	+	0.364917i	$0.118903\pi$
$200$	−3.23948	+	0.739391i	−0.229066	+	0.0522828i
$201$	−18.6940	−	10.1211i	−1.31857	−	0.713889i
$202$	−0.203561	−	0.422700i	−0.0143225	−	0.0297410i
$203$	−8.44192	−	11.3533i	−0.592507	−	0.796843i
$204$	11.4144	+	6.17989i	0.799171	+	0.432679i
$205$	−1.90352	−	2.38694i	−0.132948	−	0.166711i
$206$	−0.180407	+	0.0868796i	−0.0125696	+	0.00605319i
$207$	−9.09835	−	8.78800i	−0.632379	−	0.610808i
$208$	2.34773	+	0.535854i	0.162786	+	0.0371548i
$209$	8.63334	−	10.8259i	0.597180	−	0.748840i
$210$	9.05449	−	9.63301i	0.624819	−	0.664741i
$211$	−17.3525	−	21.7593i	−1.19459	−	1.49797i	−0.821527	−	0.570170i	$-0.806878\pi$
$211$	−17.3525	−	21.7593i	−1.19459	−	1.49797i	−0.373067	−	0.927804i	$-0.621694\pi$
$212$	4.48450	+	9.31217i	0.307997	+	0.639562i
$213$	22.1728	+	6.18008i	1.51926	+	0.423452i
$214$	4.47513			0.305913
$215$	14.4536			0.985729
$216$	−4.85074	−	1.86289i	−0.330051	−	0.126753i
$217$	10.5009	−	12.2909i	0.712849	−	0.834358i
$218$	−8.14879	+	1.85991i	−0.551906	+	0.125969i
$219$	−0.509927	+	0.0911982i	−0.0344577	+	0.00616260i
$220$	10.4948	−	8.36929i	0.707556	−	0.564257i
$221$	−14.1092	+	11.2517i	−0.949089	+	0.756873i
$222$	−4.81390	+	0.860944i	−0.323088	+	0.0577828i
$223$	3.50751	−	0.800567i	0.234881	−	0.0536100i	−0.103460	−	0.994634i	$-0.532991\pi$
$223$	3.50751	−	0.800567i	0.234881	−	0.0536100i	0.338341	+	0.941024i	$0.390134\pi$
$224$	1.57870	+	2.12314i	0.105481	+	0.141858i
$225$	−3.12861	+	9.46468i	−0.208574	+	0.630979i
$226$	8.65933			0.576010
$227$	14.7267			0.977448			0.488724	−	0.872438i	$-0.337462\pi$
$227$	14.7267			0.977448			0.488724	+	0.872438i	$0.337462\pi$
$228$	−4.96522	−	1.38392i	−0.328830	−	0.0916526i
$229$	−6.82289	−	14.1679i	−0.450869	−	0.936239i	−0.995245	−	0.0973984i	$-0.968948\pi$
$229$	−6.82289	−	14.1679i	−0.450869	−	0.936239i	0.544376	−	0.838841i	$-0.316766\pi$
$230$	−7.58428	−	9.51039i	−0.500093	−	0.627097i
$231$	−6.41619	+	20.3341i	−0.422154	+	1.33788i
$232$	−3.33405	+	4.18076i	−0.218891	+	0.274481i
$233$	−10.0999	−	2.30524i	−0.661667	−	0.151021i	−0.121516	−	0.992589i	$-0.538776\pi$
$233$	−10.0999	−	2.30524i	−0.661667	−	0.151021i	−0.540151	+	0.841568i	$0.681633\pi$
$234$	5.01897	−	5.19622i	0.328101	−	0.339688i
$235$	3.96319	−	1.90857i	0.258530	−	0.124501i
$236$	−5.05270	−	6.33588i	−0.328903	−	0.412431i
$237$	12.7012	+	6.87655i	0.825031	+	0.446680i
$238$	−19.8159	−	0.670564i	−1.28448	−	0.0434662i
$239$	−1.82199	−	3.78341i	−0.117855	−	0.244728i	0.833693	−	0.552228i	$-0.186222\pi$
$239$	−1.82199	−	3.78341i	−0.117855	−	0.244728i	−0.951548	+	0.307499i	$0.900508\pi$
$240$	−4.39415	−	2.37904i	−0.283641	−	0.153566i
$241$	−14.6559	+	3.34511i	−0.944068	+	0.215477i	−0.666734	−	0.745296i	$-0.732308\pi$
$241$	−14.6559	+	3.34511i	−0.944068	+	0.215477i	−0.277334	+	0.960774i	$0.589451\pi$
$242$	−4.62068	+	9.59495i	−0.297029	+	0.616786i
$243$	−12.3102	+	9.56337i	−0.789702	+	0.613490i
$244$		−	11.9608i		−	0.765713i
$245$	−5.81437	+	19.3393i	−0.371466	+	1.23554i
$246$	0.0868958	−	1.83090i	0.00554027	−	0.116734i
$247$	4.46817	−	5.60291i	0.284303	−	0.356505i
$248$	−5.50502	−	2.65108i	−0.349569	−	0.168344i
$249$	−3.93517	−	22.0032i	−0.249381	−	1.39439i
$250$	2.09940	−	4.35945i	0.132778	−	0.275716i
$251$	9.61968	−	4.63260i	0.607189	−	0.292407i	−0.104915	−	0.994481i	$-0.533457\pi$
$251$	9.61968	−	4.63260i	0.607189	−	0.292407i	0.712104	+	0.702074i	$0.247743\pi$
$252$	7.90092	−	0.758616i	0.497711	−	0.0477883i
$253$	17.6761	+	8.51234i	1.11128	+	0.535166i
$254$	−13.8281	+	11.0276i	−0.867655	+	0.691932i
$255$	34.4703	−	14.6297i	2.15861	−	0.916145i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	5.20624	−	22.8100i	0.324756	−	1.42285i	−0.504224	−	0.863573i	$-0.668221\pi$
$257$	5.20624	−	22.8100i	0.324756	−	1.42285i	0.828980	−	0.559278i	$-0.188921\pi$
$258$	6.52035	+	5.72599i	0.405939	+	0.356484i
$259$	5.99448	−	4.45730i	0.372479	−	0.276963i
$260$	5.43155	−	4.33151i	0.336850	−	0.268629i
$261$	5.56030	+	15.0478i	0.344174	+	0.931433i
$262$	−17.4682	−	3.98700i	−1.07919	−	0.246317i
$263$			6.88819i			0.424744i	0.977189	+	0.212372i	$0.0681189\pi$
$263$			6.88819i			0.424744i	−0.977189	+	0.212372i	$0.931881\pi$
$264$	8.05002	+	0.382059i	0.495444	+	0.0235141i
$265$	29.0702	+	6.63508i	1.78577	+	0.407590i
$266$	7.73106	−	1.49143i	0.474022	−	0.0914453i
$267$	0.578172	+	3.23280i	0.0353835	+	0.197844i
$268$	−2.73107	−	11.9656i	−0.166827	−	0.730915i
$269$	−14.1801	−	17.7812i	−0.864574	−	1.08414i	−0.995687	−	0.0927745i	$-0.970426\pi$
$269$	−14.1801	−	17.7812i	−0.864574	−	1.08414i	0.131113	−	0.991367i	$-0.458145\pi$
$270$	−12.9269	+	7.59014i	−0.786707	+	0.461921i
$271$	10.5677	−	2.41201i	0.641942	−	0.146519i	0.110855	−	0.993837i	$-0.464641\pi$
$271$	10.5677	−	2.41201i	0.641942	−	0.146519i	0.531087	+	0.847318i	$0.321784\pi$
$272$	1.66757	+	7.30612i	0.101112	+	0.442998i
$273$	−3.32069	+	10.5239i	−0.200977	+	0.636933i
$274$	−0.148248	+	0.649518i	−0.00895600	+	0.0392388i
$275$		−	15.4607i		−	0.932312i
$276$	0.346223	−	7.29496i	0.0208402	−	0.439105i
$277$	2.45017	−	10.7349i	0.147217	−	0.644998i	−0.846435	−	0.532493i	$-0.821255\pi$
$277$	2.45017	−	10.7349i	0.147217	−	0.644998i	0.993651	−	0.112505i	$-0.0358875\pi$
$278$	11.3511	−	5.46640i	0.680793	−	0.327853i
$279$	−15.3492	+	10.0201i	−0.918934	+	0.599890i
$280$	7.62843	+	0.258143i	0.455886	+	0.0154270i
$281$	4.52326	+	3.60718i	0.269835	+	0.215186i	0.749054	−	0.662509i	$-0.230508\pi$
$281$	4.52326	+	3.60718i	0.269835	+	0.215186i	−0.479219	+	0.877696i	$0.659080\pi$
$282$	2.54399	+	0.709069i	0.151492	+	0.0422244i
$283$	−25.0068	−	19.9423i	−1.48650	−	1.18544i	−0.936692	−	0.350153i	$-0.886130\pi$
$283$	−25.0068	−	19.9423i	−1.48650	−	1.18544i	−0.549808	−	0.835291i	$-0.685299\pi$
$284$	5.76607	+	11.9734i	0.342153	+	0.710488i
$285$	−12.0525	+	8.70989i	−0.713930	+	0.515930i
$286$	−4.86154	+	10.0951i	−0.287469	+	0.596936i
$287$	1.12882	+	2.56226i	0.0666321	+	0.151246i
$288$	−1.03981	−	2.81403i	−0.0612716	−	0.165819i
$289$	−35.2821	−	16.9910i	−2.07542	−	0.999468i
$290$	3.43279	+	15.0401i	0.201581	+	0.883182i
$291$	−4.48878	+	8.29092i	−0.263137	+	0.486022i
$292$	−0.233828	−	0.186472i	−0.0136838	−	0.0109124i
$293$	9.91912			0.579481			0.289741	−	0.957105i	$-0.406431\pi$
$293$	9.91912			0.579481			0.289741	+	0.957105i	$0.406431\pi$
$294$	−10.2845	+	6.42097i	−0.599805	+	0.374478i
$295$	−23.3791			−1.36119
$296$	−2.20743	−	1.76036i	−0.128304	−	0.102319i
$297$	13.4728	−	20.0754i	0.781774	−	1.16489i
$298$	−0.0507321	−	0.222272i	−0.00293883	−	0.0128759i
$299$	9.14822	+	4.40555i	0.529055	+	0.254779i
$300$	−5.29785	+	2.24848i	−0.305871	+	0.129816i
$301$	−12.8159	−	3.38497i	−0.738694	−	0.195106i
$302$	−5.51496	+	11.4519i	−0.317350	+	0.658985i
$303$	−0.475966	−	0.658630i	−0.0273435	−	0.0378373i
$304$	−1.29121	−	2.68123i	−0.0740561	−	0.153779i
$305$	−26.9779	−	21.5142i	−1.54475	−	1.23190i
$306$	21.3460	+	7.05608i	1.22027	+	0.403369i
$307$	5.98865	+	4.77579i	0.341790	+	0.272569i	0.779308	−	0.626641i	$-0.215571\pi$
$307$	5.98865	+	4.77579i	0.341790	+	0.272569i	−0.437518	+	0.899210i	$0.644142\pi$
$308$	−11.2656	+	4.96314i	−0.641919	+	0.282801i
$309$	−0.281102	+	0.203141i	−0.0159913	+	0.0115563i
$310$	−15.8816	+	7.64817i	−0.902013	+	0.434387i
$311$	−3.66299	+	16.0486i	−0.207709	+	0.910034i	0.758377	+	0.651816i	$0.225992\pi$
$311$	−3.66299	+	16.0486i	−0.207709	+	0.910034i	−0.966087	+	0.258218i	$0.916865\pi$
$312$	4.16627	+	0.197734i	0.235869	+	0.0111945i
$313$		−	25.1309i		−	1.42048i	−0.703957	−	0.710242i	$-0.748585\pi$
$313$		−	25.1309i		−	1.42048i	0.703957	−	0.710242i	$-0.251415\pi$
$314$	−3.14461	+	13.7774i	−0.177460	+	0.777505i
$315$	12.5005	−	19.1853i	0.704322	−	1.08097i
$316$	1.85556	+	8.12974i	0.104383	+	0.457333i
$317$	−11.5423	+	2.63445i	−0.648278	+	0.147965i	−0.534001	−	0.845484i	$-0.679312\pi$
$317$	−11.5423	+	2.63445i	−0.648278	+	0.147965i	−0.114277	+	0.993449i	$0.536455\pi$
$318$	10.4856	+	14.5098i	0.588005	+	0.813667i
$319$	−15.5130	−	19.4527i	−0.868563	−	1.08914i
$320$	−0.641956	−	2.81259i	−0.0358864	−	0.157229i
$321$	7.63008	−	1.36461i	0.425870	−	0.0761649i
$322$	4.49761	+	10.2090i	0.250642	+	0.568923i
$323$	21.7426	+	4.96260i	1.20979	+	0.276127i
$324$	−8.83855	−	1.69708i	−0.491030	−	0.0942822i
$325$		−	8.00164i		−	0.443851i
$326$	9.74651	+	2.22458i	0.539809	+	0.123208i
$327$	−13.3265	+	5.65596i	−0.736959	+	0.312775i
$328$	0.827383	−	0.659816i	0.0456846	−	0.0364322i
$329$	−3.96109	+	0.764150i	−0.218382	+	0.0421289i
$330$	15.3415	−	17.4698i	0.844521	−	0.961681i
$331$	−3.53714	+	15.4972i	−0.194419	+	0.851803i	0.779770	+	0.626066i	$0.215336\pi$
$331$	−3.53714	+	15.4972i	−0.194419	+	0.851803i	−0.974188	+	0.225737i	$0.927521\pi$
$332$	8.04620	−	10.0896i	0.441592	−	0.553739i
$333$	−7.94515	+	2.93581i	−0.435392	+	0.160882i
$334$	2.58787	−	2.06376i	0.141602	−	0.112924i
$335$	−31.9011	−	15.3628i	−1.74295	−	0.839359i
$336$	3.33909	+	3.13855i	0.182162	+	0.171222i
$337$	3.25821	−	1.56907i	0.177486	−	0.0854727i	−0.343031	−	0.939324i	$-0.611454\pi$
$337$	3.25821	−	1.56907i	0.177486	−	0.0854727i	0.520517	+	0.853851i	$0.325739\pi$
$338$	3.12440	−	6.48789i	0.169945	−	0.352895i
$339$	14.7641	−	2.64050i	0.801878	−	0.143412i
$340$	19.4786	+	9.38042i	1.05638	+	0.508724i
$341$	17.7257	−	22.2273i	0.959901	−	1.20368i
$342$	−8.88770	−	0.845535i	−0.480592	−	0.0457213i
$343$	9.68471	−	15.7863i	0.522925	−	0.852379i
$344$			5.01005i			0.270124i
$345$	−15.8312	−	13.9025i	−0.852323	−	0.748486i
$346$	−10.2873	+	21.3617i	−0.553046	+	1.14841i
$347$	26.0935	−	5.95567i	1.40077	−	0.319717i	0.545593	−	0.838050i	$-0.316304\pi$
$347$	26.0935	−	5.95567i	1.40077	−	0.319717i	0.855179	+	0.518333i	$0.173447\pi$
$348$	−4.40970	+	8.14485i	−0.236385	+	0.436610i
$349$	10.2383	+	21.2600i	0.548041	+	1.13802i	0.972571	+	0.232605i	$0.0747251\pi$
$349$	10.2383	+	21.2600i	0.548041	+	1.13802i	−0.424530	+	0.905414i	$0.639561\pi$
$350$	5.71059	−	6.68399i	0.305244	−	0.357274i
$351$	6.97285	−	10.3900i	0.372183	−	0.554577i
$352$	2.90104	+	3.63779i	0.154626	+	0.193895i
$353$	−2.87388	+	1.38399i	−0.152961	+	0.0736621i	−0.508798	−	0.860886i	$-0.669910\pi$
$353$	−2.87388	+	1.38399i	−0.152961	+	0.0736621i	0.355837	+	0.934548i	$0.384196\pi$
$354$	−10.5468	−	9.26194i	−0.560558	−	0.492266i
$355$	37.3778	+	8.53123i	1.98381	+	0.452791i
$356$	−1.18218	+	1.48241i	−0.0626555	+	0.0785675i
$357$	−33.9906	+	4.89919i	−1.79897	+	0.259293i
$358$	7.72049	+	9.68119i	0.408040	+	0.511667i
$359$	−13.3455	−	27.7123i	−0.704350	−	1.46260i	−0.878432	−	0.477867i	$-0.841410\pi$
$359$	−13.3455	−	27.7123i	−0.704350	−	1.46260i	0.174083	−	0.984731i	$-0.444304\pi$
$360$	−8.21746	−	2.71634i	−0.433098	−	0.143163i
$361$	10.1438			0.533883
$362$	−9.02011			−0.474087
$363$	−4.95245	+	17.7683i	−0.259936	+	0.932596i
$364$	−5.83051	+	2.56866i	−0.305602	+	0.134635i
$365$	−0.841184	+	0.191995i	−0.0440296	+	0.0100495i
$366$	−3.64723	−	20.3932i	−0.190644	−	1.06597i
$367$	17.0204	−	13.5733i	0.888458	−	0.708521i	−0.0688394	−	0.997628i	$-0.521930\pi$
$367$	17.0204	−	13.5733i	0.888458	−	0.708521i	0.957297	+	0.289106i	$0.0933582\pi$
$368$	3.29658	−	2.62894i	0.171846	−	0.137043i
$369$	−0.410142	−	3.14818i	−0.0213512	−	0.163888i
$370$	−7.94109	+	1.81250i	−0.412838	+	0.0942275i
$371$	−24.2223	−	12.6913i	−1.25756	−	0.658902i
$372$	−10.1945	−	2.84143i	−0.528558	−	0.147321i
$373$	36.3483			1.88204			0.941022	−	0.338346i	$-0.109867\pi$
$373$	36.3483			1.88204			0.941022	+	0.338346i	$0.109867\pi$
$374$	−34.8690			−1.80303
$375$	2.25014	−	8.07302i	0.116197	−	0.416889i
$376$	0.661567	+	1.37376i	0.0341177	+	0.0708462i
$377$	−8.02874	−	10.0677i	−0.413501	−	0.518514i
$378$	13.2397	−	3.70267i	0.680978	−	0.190445i
$379$	−6.17065	+	7.73775i	−0.316965	+	0.397462i	−0.914635	−	0.404281i	$-0.867522\pi$
$379$	−6.17065	+	7.73775i	−0.316965	+	0.397462i	0.597670	+	0.801742i	$0.296093\pi$
$380$	−8.37012	−	1.91042i	−0.429378	−	0.0980027i
$381$	−20.2143	+	23.0186i	−1.03561	+	1.17928i
$382$	7.31792	−	3.52413i	0.374417	−	0.180310i
$383$	−1.97469	−	2.47619i	−0.100902	−	0.126527i	0.728817	−	0.684709i	$-0.240071\pi$
$383$	−1.97469	−	2.47619i	−0.100902	−	0.126527i	−0.829719	+	0.558182i	$0.811499\pi$
$384$	0.824644	−	1.52314i	0.0420824	−	0.0777275i
$385$	−9.06925	+	34.3372i	−0.462212	+	1.74999i
$386$	5.02073	+	10.4257i	0.255548	+	0.530652i
$387$	12.8632	+	7.77453i	0.653874	+	0.395202i
$388$	−5.30682	+	1.21125i	−0.269413	+	0.0614918i
$389$	−7.31815	+	15.1963i	−0.371045	+	0.770482i	−0.999976	−	0.00697892i	$-0.997779\pi$
$389$	−7.31815	+	15.1963i	−0.371045	+	0.770482i	0.628931	+	0.777461i	$0.283493\pi$
$390$	7.93996	−	9.04147i	0.402056	−	0.457833i
$391$			31.5984i			1.59800i
$392$	−6.70358	−	2.01543i	−0.338582	−	0.101795i
$393$	−30.9989	−	1.47123i	−1.56369	−	0.0742137i
$394$	−8.71454	+	10.9277i	−0.439032	+	0.550529i
$395$	21.6745	+	10.4379i	1.09056	+	0.525186i
$396$	13.8418	−	1.80329i	0.695575	−	0.0906188i
$397$	−14.6638	+	30.4498i	−0.735957	+	1.52823i	0.109382	+	0.994000i	$0.465113\pi$
$397$	−14.6638	+	30.4498i	−0.735957	+	1.52823i	−0.845339	+	0.534231i	$0.820601\pi$
$398$	1.91114	−	0.920359i	0.0957970	−	0.0461334i
$399$	12.7267	−	4.90032i	0.637130	−	0.245323i
$400$	−2.99373	−	1.44170i	−0.149687	−	0.0720852i
$401$	6.79065	−	5.41536i	0.339109	−	0.270430i	−0.439097	−	0.898440i	$-0.644702\pi$
$401$	6.79065	−	5.41536i	0.339109	−	0.270430i	0.778206	+	0.628010i	$0.216130\pi$
$402$	−8.30515	−	19.5685i	−0.414223	−	0.975990i
$403$	9.17391	−	11.5037i	0.456985	−	0.573041i
$404$	0.104398	−	0.457398i	0.00519400	−	0.0227564i
$405$	−19.7259	+	16.8830i	−0.980187	+	0.838923i
$406$	0.478485	−	14.1398i	0.0237468	−	0.701746i
$407$	10.2710	−	8.19082i	0.509112	−	0.406004i
$408$	5.07107	+	11.9484i	0.251056	+	0.591535i
$409$	9.82743	+	2.24305i	0.485935	+	0.110912i	0.458468	−	0.888711i	$-0.348399\pi$
$409$	9.82743	+	2.24305i	0.485935	+	0.110912i	0.0274677	+	0.999623i	$0.491256\pi$
$410$		−	3.05301i		−	0.150777i
$411$	−0.0547046	+	1.15263i	−0.00269838	+	0.0568551i
$412$	−0.195217	−	0.0445569i	−0.00961763	−	0.00219516i
$413$	20.7300	+	5.47527i	1.02006	+	0.269421i
$414$	−1.63415	−	12.5435i	−0.0803141	−	0.616477i
$415$	−8.28451	−	36.2968i	−0.406670	−	1.78174i
$416$	1.50143	+	1.88273i	0.0736137	+	0.0923086i
$417$	17.6867	−	12.7815i	0.866122	−	0.625913i
$418$	13.4996	−	3.08120i	0.660288	−	0.150707i
$419$	2.80952	+	12.3093i	0.137254	+	0.601350i	0.996032	+	0.0890008i	$0.0283674\pi$
$419$	2.80952	+	12.3093i	0.137254	+	0.601350i	−0.858777	+	0.512349i	$0.828775\pi$
$420$	13.0852	−	1.88601i	0.638491	−	0.0920280i
$421$	−3.48180	+	15.2548i	−0.169693	+	0.743473i	0.816429	+	0.577446i	$0.195951\pi$
$421$	−3.48180	+	15.2548i	−0.169693	+	0.743473i	−0.986121	+	0.166026i	$0.946906\pi$
$422$		−	27.8312i		−	1.35480i
$423$	4.55371	+	0.433219i	0.221409	+	0.0210638i
$424$	−2.29992	+	10.0766i	−0.111694	+	0.489362i
$425$	22.4350	−	10.8041i	1.08826	−	0.524078i
$426$	13.4822	+	18.6563i	0.653214	+	0.903901i
$427$	18.8825	+	25.3945i	0.913789	+	1.22892i
$428$	3.49879	+	2.79020i	0.169121	+	0.134869i
$429$	−5.21061	+	18.6946i	−0.251571	+	0.902581i
$430$	11.3003	+	9.01169i	0.544949	+	0.434582i
$431$	12.0545	+	25.0315i	0.580646	+	1.20572i	0.959877	+	0.280422i	$0.0904746\pi$
$431$	12.0545	+	25.0315i	0.580646	+	1.20572i	−0.379230	+	0.925302i	$0.623811\pi$
$432$	−2.63097	−	4.48085i	−0.126582	−	0.215585i
$433$	3.65350	−	7.58657i	0.175576	−	0.364587i	−0.794546	−	0.607204i	$-0.792291\pi$
$433$	3.65350	−	7.58657i	0.175576	−	0.364587i	0.970122	+	0.242616i	$0.0780055\pi$
$434$	15.8732	−	3.06216i	0.761937	−	0.146988i
$435$	10.4391	+	24.5965i	0.500516	+	1.17931i
$436$	−7.53062	−	3.62655i	−0.360651	−	0.173680i
$437$	−2.79220	−	12.2334i	−0.133569	−	0.585204i
$438$	−0.455538	−	0.246633i	−0.0217665	−	0.0117846i
$439$	6.53855	+	5.21432i	0.312068	+	0.248866i	0.766981	−	0.641670i	$-0.221758\pi$
$439$	6.53855	+	5.21432i	0.312068	+	0.248866i	−0.454913	+	0.890536i	$0.650330\pi$
$440$	13.4233			0.639931
$441$	−15.5771	+	14.0838i	−0.741767	+	0.670657i
$442$	−18.0464			−0.858379
$443$	9.66699	+	7.70917i	0.459293	+	0.366274i	0.825633	−	0.564207i	$-0.190818\pi$
$443$	9.66699	+	7.70917i	0.459293	+	0.366274i	−0.366341	+	0.930481i	$0.619390\pi$
$444$	−4.30045	−	2.32830i	−0.204090	−	0.110496i
$445$	1.21720	+	5.33288i	0.0577006	+	0.252803i
$446$	3.24143	+	1.56099i	0.153486	+	0.0739151i
$447$	−0.154276	−	0.363503i	−0.00729699	−	0.0171931i
$448$	−0.0894800	+	2.64424i	−0.00422753	+	0.124928i
$449$	4.88794	−	10.1499i	0.230676	−	0.479004i	−0.753215	−	0.657775i	$-0.771498\pi$
$449$	4.88794	−	10.1499i	0.230676	−	0.479004i	0.983891	+	0.178771i	$0.0572122\pi$
$450$	−8.34718	+	5.44913i	−0.393490	+	0.256874i
$451$	2.13644	+	4.43637i	0.100601	+	0.208901i
$452$	6.77014	+	5.39901i	0.318441	+	0.253948i
$453$	−5.91094	+	21.2072i	−0.277720	+	0.996401i
$454$	11.5138	+	9.18197i	0.540371	+	0.430931i
$455$	−4.69378	+	17.7712i	−0.220048	+	0.833125i
$456$	−3.01911	−	4.17776i	−0.141383	−	0.195642i
$457$	−36.4383	+	17.5478i	−1.70451	+	0.820849i	−0.711519	+	0.702667i	$0.751993\pi$
$457$	−36.4383	+	17.5478i	−1.70451	+	0.820849i	−0.992992	+	0.118183i	$0.962293\pi$
$458$	3.49918	−	15.3309i	0.163506	−	0.716366i
$459$	38.5466	+	5.52152i	1.79920	+	0.257722i
$460$		−	12.1642i		−	0.567161i
$461$	−1.96475	+	8.60814i	−0.0915076	+	0.400921i	−0.999850	−	0.0173058i	$-0.994491\pi$
$461$	−1.96475	+	8.60814i	−0.0915076	+	0.400921i	0.908343	+	0.418227i	$0.137348\pi$
$462$	−17.6945	+	11.8974i	−0.823221	+	0.553516i
$463$	−2.13150	−	9.33871i	−0.0990592	−	0.434007i	−1.00000		6.47049e-5i	$-0.999979\pi$
$463$	−2.13150	−	9.33871i	−0.0990592	−	0.434007i	0.900941	−	0.433942i	$-0.142878\pi$
$464$	−5.21333	+	1.18991i	−0.242023	+	0.0552401i
$465$	−24.7459	+	17.8829i	−1.14756	+	0.829299i
$466$	−6.45914	−	8.09950i	−0.299214	−	0.375202i
$467$	−1.91183	−	8.37626i	−0.0884688	−	0.387607i	0.911236	−	0.411884i	$-0.135129\pi$
$467$	−1.91183	−	8.37626i	−0.0884688	−	0.387607i	−0.999705	+	0.0242765i	$0.992272\pi$
$468$	7.16378	−	0.933291i	0.331146	−	0.0431414i
$469$	24.6885	+	21.0931i	1.14001	+	0.973989i
$470$	4.28852	+	0.978827i	0.197815	+	0.0451499i
$471$	−1.16038	+	24.4494i	−0.0534676	+	1.12657i
$472$		−	8.10390i		−	0.373012i
$473$	−22.7269	−	5.18726i	−1.04498	−	0.238510i
$474$	5.64273	+	13.2954i	0.259179	+	0.610676i
$475$	−7.73109	+	6.16534i	−0.354727	+	0.282885i
$476$	−15.0746	−	12.8793i	−0.690945	−	0.590322i
$477$	22.3025	+	21.5417i	1.02116	+	0.986327i
$478$	0.934425	−	4.09398i	0.0427396	−	0.187254i
$479$	−1.46111	+	1.83217i	−0.0667596	+	0.0837139i	−0.814090	−	0.580739i	$-0.802764\pi$
$479$	−1.46111	+	1.83217i	−0.0667596	+	0.0837139i	0.747330	+	0.664453i	$0.231335\pi$
$480$	−1.95218	−	4.59971i	−0.0891045	−	0.209947i
$481$	5.31572	−	4.23914i	0.242376	−	0.193288i
$482$	−13.5441	−	6.52248i	−0.616915	−	0.297091i
$483$	10.7814	+	16.0348i	0.490573	+	0.729608i
$484$	−9.59495	+	4.62068i	−0.436134	+	0.210031i
$485$	−6.81350	+	14.1484i	−0.309385	+	0.642444i
$486$	−15.5872	−	0.198367i	−0.707050	−	0.00899812i
$487$	−4.19737	−	2.02135i	−0.190201	−	0.0915960i	0.336359	−	0.941734i	$-0.390804\pi$
$487$	−4.19737	−	2.02135i	−0.190201	−	0.0915960i	−0.526560	+	0.850138i	$0.676519\pi$
$488$	7.45745	−	9.35135i	0.337583	−	0.423316i
$489$	17.2961	+	0.820884i	0.782158	+	0.0371217i
$490$	−16.6037	+	11.4949i	−0.750080	+	0.519287i
$491$		−	15.2995i		−	0.690456i	−0.938519	−	0.345228i	$-0.887802\pi$
$491$		−	15.2995i		−	0.690456i	0.938519	−	0.345228i	$-0.112198\pi$
$492$	1.20949	−	1.37728i	0.0545279	−	0.0620925i
$493$	17.3872	−	36.1049i	0.783081	−	1.62608i
$494$	6.98671	−	1.59467i	0.314347	−	0.0717477i
$495$	20.8301	−	34.4641i	0.936243	−	1.54904i
$496$	−2.65108	−	5.50502i	−0.119037	−	0.247183i
$497$	−31.1445	−	16.3182i	−1.39702	−	0.731973i
$498$	10.6421	−	19.6563i	0.476884	−	0.880820i
$499$	7.46190	+	9.35693i	0.334041	+	0.418874i	0.920278	−	0.391266i	$-0.127963\pi$
$499$	7.46190	+	9.35693i	0.334041	+	0.418874i	−0.586237	+	0.810140i	$0.699391\pi$
$500$	4.35945	−	2.09940i	0.194960	−	0.0938880i
$501$	3.78301	−	4.30783i	0.169013	−	0.192460i
$502$	10.4093	+	2.37587i	0.464592	+	0.106040i
$503$	11.9928	−	15.0386i	0.534735	−	0.670536i	−0.438930	−	0.898521i	$-0.644642\pi$
$503$	11.9928	−	15.0386i	0.534735	−	0.670536i	0.973665	+	0.227985i	$0.0732138\pi$
$504$	6.65018	+	4.33303i	0.296222	+	0.193009i
$505$	−0.843890	−	1.05820i	−0.0375526	−	0.0470895i
$506$	8.51234	+	17.6761i	0.378420	+	0.785796i
$507$	3.34874	−	12.0146i	0.148723	−	0.533586i
$508$	−17.6869			−0.784728
$509$	−4.99446			−0.221376			−0.110688	−	0.993855i	$-0.535305\pi$
$509$	−4.99446			−0.221376			−0.110688	+	0.993855i	$0.535305\pi$
$510$	36.0714	+	10.0539i	1.59727	+	0.445196i
$511$	0.790833	+	0.0267615i	0.0349844	+	0.00118386i
$512$	0.974928	−	0.222521i	0.0430861	−	0.00983413i
$513$	−15.4113	+	1.26850i	−0.680427	+	0.0560056i
$514$	18.2922	−	14.5876i	0.806835	−	0.643430i
$515$	−0.451639	+	0.360170i	−0.0199016	+	0.0158710i
$516$	1.52772	+	8.54213i	0.0672542	+	0.376046i
$517$	−6.91668	+	1.57869i	−0.304195	+	0.0694306i
$518$	7.46575	+	0.252638i	0.328026	+	0.0111003i
$519$	−11.0259	+	39.5586i	−0.483983	+	1.73643i
$520$	6.94721			0.304655
$521$	−31.3151			−1.37194			−0.685970	−	0.727630i	$-0.740622\pi$
$521$	−31.3151			−1.37194			−0.685970	+	0.727630i	$0.740622\pi$
$522$	−5.03491	+	15.2316i	−0.220372	+	0.666669i
$523$	−3.64913	−	7.57751i	−0.159566	−	0.331341i	0.805823	−	0.592156i	$-0.201723\pi$
$523$	−3.64913	−	7.57751i	−0.159566	−	0.331341i	−0.965389	+	0.260815i	$0.916009\pi$
$524$	−11.1713	−	14.0084i	−0.488021	−	0.611959i
$525$	7.69839	−	13.1375i	0.335985	−	0.573368i
$526$	−4.29472	+	5.38541i	−0.187259	+	0.234815i
$527$	44.6412	+	10.1891i	1.94460	+	0.443843i
$528$	6.05555	+	5.31781i	0.263534	+	0.231428i
$529$	−4.70417	+	2.26541i	−0.204529	+	0.0984961i
$530$	18.5911	+	23.3125i	0.807545	+	1.01263i
$531$	−20.8066	−	12.5755i	−0.902929	−	0.545731i
$532$	6.97428	+	3.65419i	0.302373	+	0.158429i
$533$	1.10571	+	2.29604i	0.0478938	+	0.0994524i
$534$	−1.56358	+	2.88799i	−0.0676629	+	0.124975i
$535$	12.5867	−	2.87283i	0.544171	−	0.124203i
$536$	5.32519	−	11.0579i	0.230013	−	0.477628i
$537$	16.1155	+	14.1522i	0.695436	+	0.610712i
$538$		−	22.7431i		−	0.980523i
$539$	16.0832	−	28.3224i	0.692752	−	1.21993i
$540$	−14.8390	−	2.12559i	−0.638571	−	0.0914707i
$541$	10.3931	−	13.0326i	0.446836	−	0.560314i	−0.506495	−	0.862243i	$-0.669059\pi$
$541$	10.3931	−	13.0326i	0.446836	−	0.560314i	0.953330	+	0.301929i	$0.0976305\pi$
$542$	9.76602	+	4.70307i	0.419486	+	0.202014i
$543$	−15.3793	+	2.75051i	−0.659988	+	0.118036i
$544$	−3.25153	+	6.75187i	−0.139408	+	0.289484i
$545$	−21.7253	+	10.4623i	−0.930608	+	0.448157i
$546$	−9.15774	+	6.15747i	−0.391915	+	0.263515i
$547$	7.40451	+	3.56582i	0.316594	+	0.152464i	0.585431	−	0.810722i	$-0.300925\pi$
$547$	7.40451	+	3.56582i	0.316594	+	0.152464i	−0.268837	+	0.963186i	$0.586639\pi$
$548$	−0.520873	+	0.415382i	−0.0222506	+	0.0177443i
$549$	−12.4370	−	33.6582i	−0.530799	−	1.43650i
$550$	9.63956	−	12.0876i	0.411032	−	0.515418i
$551$	−3.54110	+	15.5146i	−0.150856	+	0.660942i
$552$	4.81902	−	5.48756i	0.205111	−	0.233566i
$553$	−16.7740	−	14.3312i	−0.713303	−	0.609424i
$554$	8.60872	−	6.86523i	0.365750	−	0.291676i
$555$	−12.9868	+	5.51180i	−0.551261	+	0.233963i
$556$	12.2829	+	2.80349i	0.520910	+	0.118894i
$557$		−	23.1690i		−	0.981704i	−0.871243	−	0.490852i	$-0.836686\pi$
$557$		−	23.1690i		−	0.981704i	0.871243	−	0.490852i	$-0.163314\pi$
$558$	−18.2480	−	1.73603i	−0.772498	−	0.0734919i
$559$	−11.7623	−	2.68466i	−0.497490	−	0.113549i
$560$	5.80319	+	4.95807i	0.245230	+	0.209517i
$561$	−59.4515	+	10.6326i	−2.51004	+	0.448910i
$562$	1.28739	+	5.64042i	0.0543052	+	0.237927i
$563$	−15.3693	−	19.2725i	−0.647738	−	0.812238i	0.344208	−	0.938893i	$-0.388147\pi$
$563$	−15.3693	−	19.2725i	−0.647738	−	0.812238i	−0.991947	+	0.126655i	$0.959576\pi$
$564$	1.54687	+	2.14052i	0.0651351	+	0.0901322i
$565$	24.3552	−	5.55891i	1.02463	−	0.233865i
$566$	−7.11731	−	31.1830i	−0.299163	−	1.31072i
$567$	21.4446	−	10.3503i	0.900590	−	0.434670i
$568$	−2.95718	+	12.9562i	−0.124080	+	0.543632i
$569$			38.6428i			1.61999i	0.586437	+	0.809995i	$0.300530\pi$
$569$			38.6428i			1.61999i	−0.586437	+	0.809995i	$0.699470\pi$
$570$	−14.8536	−	0.704960i	−0.622148	−	0.0295275i
$571$	5.19670	−	22.7682i	0.217475	−	0.952821i	−0.741861	−	0.670554i	$-0.766057\pi$
$571$	5.19670	−	22.7682i	0.217475	−	0.952821i	0.959336	−	0.282267i	$-0.0910863\pi$
$572$	−10.0951	+	4.86154i	−0.422097	+	0.203271i
$573$	11.4024	−	8.24009i	0.476343	−	0.344235i
$574$	−0.714999	+	2.70707i	−0.0298435	+	0.112991i
$575$	−10.9539	−	8.73541i	−0.456807	−	0.364292i
$576$	0.941562	−	2.84841i	0.0392318	−	0.118684i
$577$	−15.8979	−	12.6781i	−0.661837	−	0.527797i	0.233968	−	0.972244i	$-0.424829\pi$
$577$	−15.8979	−	12.6781i	−0.661837	−	0.527797i	−0.895805	+	0.444447i	$0.853400\pi$
$578$	−16.9910	−	35.2821i	−0.706731	−	1.46754i
$579$	11.7394	+	16.2447i	0.487874	+	0.675108i
$580$	−6.69345	+	13.8991i	−0.277931	+	0.577129i
$581$	−1.15475	+	34.1241i	−0.0479070	+	1.41571i
$582$	−8.67877	+	3.68339i	−0.359747	+	0.152681i
$583$	−43.3287	−	20.8660i	−1.79449	−	0.864181i
$584$	−0.0665511	−	0.291579i	−0.00275390	−	0.0120656i
$585$	10.7806	−	17.8368i	0.445722	−	0.737462i
$586$	7.75508	+	6.18447i	0.320359	+	0.255478i
$587$	−6.17869			−0.255022			−0.127511	−	0.991837i	$-0.540699\pi$
$587$	−6.17869			−0.255022			−0.127511	+	0.991837i	$0.540699\pi$
$588$	−12.0442	−	1.39217i	−0.496693	−	0.0574123i
$589$	−18.1834			−0.749232
$590$	−18.2785	−	14.5766i	−0.752516	−	0.600111i
$591$	−11.5261	+	21.2890i	−0.474119	+	0.875713i
$592$	−0.628266	−	2.75262i	−0.0258216	−	0.113132i
$593$	3.75428	+	1.80797i	0.154170	+	0.0742442i	0.509378	−	0.860543i	$-0.329876\pi$
$593$	3.75428	+	1.80797i	0.154170	+	0.0742442i	−0.355208	+	0.934787i	$0.615590\pi$
$594$	23.0503	−	7.29539i	0.945765	−	0.299334i
$595$	−56.1647	+	10.8349i	−2.30253	+	0.444189i
$596$	0.0989203	−	0.205410i	0.00405193	−	0.00841393i
$597$	2.97785	−	2.15198i	0.121875	−	0.0880746i
$598$	4.40555	+	9.14822i	0.180156	+	0.374098i
$599$	9.06415	+	7.22842i	0.370351	+	0.295345i	0.790925	−	0.611913i	$-0.209600\pi$
$599$	9.06415	+	7.22842i	0.370351	+	0.295345i	−0.420574	+	0.907258i	$0.638171\pi$
$600$	−5.54393	−	1.54522i	−0.226330	−	0.0630834i
$601$	−4.10413	−	3.27294i	−0.167411	−	0.133506i	0.536201	−	0.844091i	$-0.319859\pi$
$601$	−4.10413	−	3.27294i	−0.167411	−	0.133506i	−0.703612	+	0.710585i	$0.748430\pi$
$602$	−7.90935	−	10.6370i	−0.322361	−	0.433533i
$603$	−20.1273	−	30.8318i	−0.819648	−	1.25557i
$604$	−11.4519	+	5.51496i	−0.465972	+	0.224401i
$605$	−6.83657	+	29.9530i	−0.277946	+	1.21776i
$606$	0.0385236	−	0.811697i	0.00156492	−	0.0329730i
$607$		−	16.1724i		−	0.656416i	−0.944605	−	0.328208i	$-0.893555\pi$
$607$		−	16.1724i		−	0.656416i	0.944605	−	0.328208i	$-0.106445\pi$
$608$	0.662209	−	2.90133i	0.0268561	−	0.117664i
$609$	−3.49585	−	24.2542i	−0.141659	−	0.982830i
$610$	−7.67832	−	33.6409i	−0.310886	−	1.36208i
$611$	−3.57972	+	0.817047i	−0.144820	+	0.0330542i
$612$	12.2896	+	18.8257i	0.496778	+	0.760984i
$613$	16.9833	+	21.2964i	0.685951	+	0.860155i	0.995887	−	0.0906023i	$-0.0288792\pi$
$613$	16.9833	+	21.2964i	0.685951	+	0.860155i	−0.309936	+	0.950757i	$0.600308\pi$
$614$	1.70446	+	7.46773i	0.0687864	+	0.301373i
$615$	−0.930957	−	5.20537i	−0.0375398	−	0.209901i
$616$	−11.9023	−	3.14367i	−0.479557	−	0.126662i
$617$	−9.89497	−	2.25846i	−0.398356	−	0.0909223i	0.0186493	−	0.999826i	$-0.494063\pi$
$617$	−9.89497	−	2.25846i	−0.398356	−	0.0909223i	−0.417006	+	0.908904i	$0.636921\pi$
$618$	−0.346431	−	0.0164418i	−0.0139355	−	0.000661387i
$619$			1.05891i			0.0425611i	0.999774	+	0.0212806i	$0.00677432\pi$
$619$			1.05891i			0.0425611i	−0.999774	+	0.0212806i	$0.993226\pi$
$620$	−17.1853	−	3.92243i	−0.690177	−	0.157528i
$621$	−6.61111	−	20.8883i	−0.265295	−	0.838217i
$622$	−12.8700	+	10.2635i	−0.516040	+	0.411528i
$623$	0.169661	−	5.01367i	0.00679731	−	0.200868i
$624$	3.13404	+	2.75222i	0.125462	+	0.110177i
$625$	6.80314	−	29.8065i	0.272125	−	1.19226i
$626$	15.6689	−	19.6482i	0.626255	−	0.785298i
$627$	22.0773	−	9.36990i	0.881682	−	0.374198i
$628$	−11.0486	+	8.81100i	−0.440889	+	0.351597i
$629$	19.0633	+	9.18038i	0.760102	+	0.366046i
$630$	21.7351	−	7.20572i	0.865946	−	0.287083i
$631$	36.2353	−	17.4500i	1.44250	−	0.694673i	0.461227	−	0.887282i	$-0.347409\pi$
$631$	36.2353	−	17.4500i	1.44250	−	0.694673i	0.981275	+	0.192609i	$0.0616950\pi$
$632$	−3.61807	+	7.51301i	−0.143919	+	0.298851i
$633$	−8.48661	−	47.4522i	−0.337312	−	1.88605i
$634$	−10.6667	−	5.13679i	−0.423627	−	0.204008i
$635$	−31.8137	+	39.8932i	−1.26249	+	1.58311i
$636$	−0.848685	+	17.8819i	−0.0336525	+	0.709063i
$637$	8.32384	−	14.6582i	0.329802	−	0.580780i
$638$		−	24.8810i		−	0.985047i
$639$	28.6760	+	27.6978i	1.13440	+	1.09571i
$640$	1.25172	−	2.59923i	0.0494787	−	0.102743i
$641$	25.5641	−	5.83483i	1.00972	−	0.230462i	0.314499	−	0.949258i	$-0.398164\pi$
$641$	25.5641	−	5.83483i	1.00972	−	0.230462i	0.695221	+	0.718796i	$0.255306\pi$
$642$	6.81625	+	3.69039i	0.269016	+	0.145648i
$643$	5.00892	+	10.4011i	0.197533	+	0.410181i	0.976082	−	0.217403i	$-0.0697584\pi$
$643$	5.00892	+	10.4011i	0.197533	+	0.410181i	−0.778549	+	0.627583i	$0.784044\pi$
$644$	−2.84881	+	10.7859i	−0.112259	+	0.425024i
$645$	22.0149	+	11.9191i	0.866837	+	0.469314i
$646$	13.9049	+	17.4362i	0.547081	+	0.686018i
$647$	−12.4504	+	5.99580i	−0.489476	+	0.235719i	−0.662307	−	0.749232i	$-0.730423\pi$
$647$	−12.4504	+	5.99580i	−0.489476	+	0.235719i	0.172831	+	0.984951i	$0.444708\pi$
$648$	−5.85214	−	6.83757i	−0.229894	−	0.268605i
$649$	36.7613	+	8.39053i	1.44301	+	0.329357i
$650$	4.98894	−	6.25593i	0.195682	−	0.245378i
$651$	26.1300	−	10.0612i	1.02411	−	0.394329i
$652$	6.23313	+	7.81610i	0.244108	+	0.306102i
$653$	−6.57768	−	13.6587i	−0.257405	−	0.534506i	0.731717	−	0.681609i	$-0.238719\pi$
$653$	−6.57768	−	13.6587i	−0.257405	−	0.534506i	−0.989121	+	0.147103i	$0.953005\pi$
$654$	−13.9455	−	3.88695i	−0.545314	−	0.151992i
$655$	−51.6903			−2.01971
$656$	1.05826			0.0413182
$657$	−0.851897	−	0.281600i	−0.0332357	−	0.0109863i
$658$	−3.57335	−	1.87226i	−0.139304	−	0.0729885i
$659$	−12.7651	+	2.91356i	−0.497260	+	0.113496i	−0.463793	−	0.885944i	$-0.653512\pi$
$659$	−12.7651	+	2.91356i	−0.497260	+	0.113496i	−0.0334665	+	0.999440i	$0.510655\pi$
$660$	22.8867	−	4.09318i	0.890863	−	0.159327i
$661$	−17.8131	+	14.2055i	−0.692849	+	0.552529i	−0.905368	−	0.424628i	$-0.860405\pi$
$661$	−17.8131	+	14.2055i	−0.692849	+	0.552529i	0.212519	+	0.977157i	$0.431833\pi$
$662$	−12.4278	+	9.91083i	−0.483020	+	0.385196i
$663$	−30.7690	+	5.50290i	−1.19497	+	0.213715i
$664$	12.5815	−	2.87165i	0.488258	−	0.111442i
$665$	20.7869	−	9.15778i	0.806081	−	0.355124i
$666$	−8.04222	−	2.65841i	−0.311630	−	0.103011i
$667$	−22.5472			−0.873032
$668$	3.31001			0.128068
$669$	6.00263	+	1.67307i	0.232075	+	0.0646847i
$670$	−15.3628	−	31.9011i	−0.593516	−	1.23245i
$671$	34.6989	+	43.5110i	1.33953	+	1.67972i
$672$	0.653747	+	4.53570i	0.0252189	+	0.174969i
$673$	25.5398	−	32.0258i	0.984485	−	1.23451i	0.0123891	−	0.999923i	$-0.496056\pi$
$673$	25.5398	−	32.0258i	0.984485	−	1.23451i	0.972096	−	0.234582i	$-0.0753722\pi$
$674$	3.52567	+	0.804711i	0.135804	+	0.0309963i
$675$	−12.5703	+	11.8361i	−0.483832	+	0.455570i
$676$	6.48789	−	3.12440i	0.249534	−	0.120169i
$677$	−18.6187	−	23.3471i	−0.715575	−	0.897303i	0.282503	−	0.959266i	$-0.408835\pi$
$677$	−18.6187	−	23.3471i	−0.715575	−	0.897303i	−0.998078	+	0.0619633i	$0.980264\pi$
$678$	13.1894	+	7.14086i	0.506536	+	0.274243i
$679$	9.35493	−	10.9495i	0.359009	−	0.420204i
$680$	9.38042	+	19.4786i	0.359723	+	0.746971i
$681$	22.4309	+	12.1443i	0.859555	+	0.465371i
$682$	27.7170	−	6.32623i	1.06134	−	0.242244i
$683$	3.59068	−	7.45612i	0.137393	−	0.285300i	−0.820908	−	0.571061i	$-0.806532\pi$
$683$	3.59068	−	7.45612i	0.137393	−	0.285300i	0.958301	+	0.285761i	$0.0922462\pi$
$684$	−6.42150	−	6.20245i	−0.245532	−	0.237157i
$685$			1.92200i			0.0734358i
$686$	17.4144	−	6.30389i	0.664885	−	0.240684i
$687$	1.29122	−	27.2061i	0.0492631	−	1.03798i
$688$	−3.12372	+	3.91702i	−0.119091	+	0.149335i
$689$	−22.4247	−	10.7992i	−0.854313	−	0.411416i
$690$	−3.70926	−	20.7400i	−0.141209	−	0.789559i
$691$	−12.0684	+	25.0603i	−0.459105	+	0.953340i	0.534994	+	0.844856i	$0.320314\pi$
$691$	−12.0684	+	25.0603i	−0.459105	+	0.953340i	−0.994098	+	0.108484i	$0.965400\pi$
$692$	−21.3617	+	10.2873i	−0.812050	+	0.391063i
$693$	−26.5411	+	25.6806i	−1.00821	+	0.975525i
$694$	24.1140	+	11.6127i	0.915356	+	0.440812i
$695$	28.4168	−	22.6617i	1.07791	−	0.859606i
$696$	−8.52587	+	3.61850i	−0.323172	+	0.137159i
$697$	−4.94467	+	6.20041i	−0.187293	+	0.234857i
$698$	−5.25078	+	23.0051i	−0.198745	+	0.870758i
$699$	−13.4826	−	11.8400i	−0.509959	−	0.447831i
$700$	8.63212	−	1.66526i	0.326263	−	0.0629407i
$701$	−19.7551	+	15.7542i	−0.746140	+	0.595027i	−0.920998	−	0.389567i	$-0.872625\pi$
$701$	−19.7551	+	15.7542i	−0.746140	+	0.595027i	0.174858	+	0.984594i	$0.444053\pi$
$702$	11.9296	−	3.77572i	0.450255	−	0.142505i
$703$	−8.19162	−	1.86968i	−0.308953	−	0.0705165i
$704$			4.65291i			0.175363i
$705$	7.61039	+	0.361194i	0.286624	+	0.0136033i
$706$	−3.10979	−	0.709789i	−0.117038	−	0.0267132i
$707$	0.500442	+	1.13593i	0.0188210	+	0.0427212i
$708$	−2.47113	−	13.8171i	−0.0928708	−	0.519279i
$709$	−4.75092	−	20.8151i	−0.178424	−	0.781728i	−0.982358	−	0.187009i	$-0.940120\pi$
$709$	−4.75092	−	20.8151i	−0.178424	−	0.781728i	0.803934	−	0.594719i	$-0.202737\pi$
$710$	23.9040	+	29.9746i	0.897100	+	1.12493i
$711$	13.6750	+	20.9479i	0.512853	+	0.785608i
$712$	−1.84853	+	0.421916i	−0.0692768	+	0.0158120i
$713$	−5.73286	−	25.1173i	−0.214697	−	0.940650i
$714$	−29.6295	−	17.3625i	−1.10886	−	0.649774i
$715$	−7.19293	+	31.5143i	−0.269000	+	1.17857i
$716$			12.3827i			0.462763i
$717$	0.344809	−	7.26517i	0.0128771	−	0.271323i
$718$	6.84436	−	29.9871i	0.255429	−	1.11911i
$719$	−2.37615	+	1.14429i	−0.0886153	+	0.0426749i	−0.477666	−	0.878541i	$-0.658517\pi$
$719$	−2.37615	+	1.14429i	−0.0886153	+	0.0426749i	0.389051	+	0.921216i	$0.372803\pi$
$720$	−4.73106	−	7.24722i	−0.176316	−	0.270088i
$721$	0.484814	−	0.213587i	0.0180554	−	0.00795441i
$722$	7.93072	+	6.32454i	0.295151	+	0.235375i
$723$	−25.0815	−	6.99080i	−0.932791	−	0.259991i
$724$	−7.05221	−	5.62395i	−0.262093	−	0.209012i
$725$	7.70937	+	16.0087i	0.286319	+	0.594547i
$726$	−14.9504	+	10.8040i	−0.554860	+	0.400976i
$727$	4.40261	−	9.14211i	0.163284	−	0.339062i	−0.803233	−	0.595665i	$-0.796889\pi$
$727$	4.40261	−	9.14211i	0.163284	−	0.339062i	0.966517	+	0.256602i	$0.0826031\pi$
$728$	−6.16001	−	1.62700i	−0.228305	−	0.0603007i
$729$	−26.6366	+	4.41481i	−0.986541	+	0.163511i
$730$	−0.777371	−	0.374362i	−0.0287718	−	0.0138558i
$731$	−8.35463	−	36.6040i	−0.309007	−	1.35385i
$732$	9.86342	−	18.2180i	0.364562	−	0.673358i
$733$	21.5704	+	17.2018i	0.796722	+	0.635364i	0.934847	−	0.355050i	$-0.115536\pi$
$733$	21.5704	+	17.2018i	0.796722	+	0.635364i	−0.138126	+	0.990415i	$0.544108\pi$
$734$	21.7699			0.803542
$735$	−24.8042	+	24.6618i	−0.914916	+	0.909663i
$736$	4.21649			0.155422
$737$	44.6478	+	35.6054i	1.64462	+	1.31154i
$738$	1.64220	−	2.71707i	0.0604501	−	0.100017i
$739$	2.63231	+	11.5329i	0.0968310	+	0.424244i	0.999987	−	0.00506793i	$-0.00161318\pi$
$739$	2.63231	+	11.5329i	0.0968310	+	0.424244i	−0.903156	+	0.429312i	$0.858756\pi$
$740$	−7.33867	−	3.53412i	−0.269775	−	0.129917i
$741$	11.4261	−	4.84938i	0.419747	−	0.178146i
$742$	−11.0248	−	25.0249i	−0.404735	−	0.918692i
$743$	13.7067	−	28.4622i	0.502849	−	1.04418i	−0.482857	−	0.875699i	$-0.660401\pi$
$743$	13.7067	−	28.4622i	0.502849	−	1.04418i	0.985706	−	0.168477i	$-0.0538848\pi$
$744$	−6.19874	−	8.57766i	−0.227257	−	0.314472i
$745$	−0.285378	−	0.592593i	−0.0104554	−	0.0217109i
$746$	28.4182	+	22.6628i	1.04047	+	0.829744i
$747$	12.1510	−	36.7591i	0.444580	−	1.34494i
$748$	−27.2617	−	21.7404i	−0.996785	−	0.794909i
$749$	−11.8333	−	0.400434i	−0.432379	−	0.0146315i
$750$	6.79268	−	4.90880i	0.248033	−	0.179244i
$751$	−0.647311	+	0.311729i	−0.0236207	+	0.0113751i	−0.445657	−	0.895204i	$-0.647030\pi$
$751$	−0.647311	+	0.311729i	−0.0236207	+	0.0113751i	0.422036	+	0.906579i	$0.361316\pi$
$752$	−0.339290	+	1.48653i	−0.0123726	+	0.0542081i
$753$	18.4724	+	0.876711i	0.673171	+	0.0319491i
$754$		−	12.8771i		−	0.468957i
$755$	−8.15970	+	35.7500i	−0.296962	+	1.30108i
$756$	12.6598	+	5.35996i	0.460433	+	0.194940i
$757$	6.13618	+	26.8844i	0.223023	+	0.977129i	0.955188	+	0.296001i	$0.0956531\pi$
$757$	6.13618	+	26.8844i	0.223023	+	0.977129i	−0.732164	+	0.681128i	$0.761490\pi$
$758$	−9.64882	+	2.20228i	−0.350461	+	0.0799904i
$759$	19.9035	+	27.5420i	0.722451	+	0.999710i
$760$	−5.35289	−	6.71231i	−0.194170	−	0.243481i
$761$	−2.00081	−	8.76612i	−0.0725293	−	0.317772i	0.925629	−	0.378432i	$-0.123537\pi$
$761$	−2.00081	−	8.76612i	−0.0725293	−	0.317772i	−0.998158	+	0.0606602i	$0.980679\pi$
$762$	−30.1561	+	5.39328i	−1.09244	+	0.195378i
$763$	21.7138	−	4.18889i	0.786091	−	0.151648i
$764$	7.91864	+	1.80738i	0.286486	+	0.0653886i
$765$	64.5674	+	6.14265i	2.33444	+	0.222088i
$766$		−	3.16716i		−	0.114434i
$767$	19.0258	+	4.34251i	0.686981	+	0.156799i
$768$	1.59440	−	0.676684i	0.0575328	−	0.0244177i
$769$	15.0334	−	11.9888i	0.542120	−	0.432326i	−0.313759	−	0.949503i	$-0.601588\pi$
$769$	15.0334	−	11.9888i	0.542120	−	0.432326i	0.855879	+	0.517177i	$0.173017\pi$
$770$	−28.4995	+	21.1913i	−1.02705	+	0.763682i
$771$	26.7400	−	30.4496i	0.963017	−	1.09662i
$772$	−2.57492	+	11.2815i	−0.0926735	+	0.406029i
$773$	12.8114	−	16.0650i	0.460795	−	0.577819i	−0.496095	−	0.868268i	$-0.665233\pi$
$773$	12.8114	−	16.0650i	0.460795	−	0.577819i	0.956890	+	0.290449i	$0.0938048\pi$
$774$	5.20952	+	14.0985i	0.187252	+	0.506759i
$775$	−15.8732	+	12.6585i	−0.570184	+	0.454706i
$776$	−4.90424	−	2.36176i	−0.176052	−	0.0847822i
$777$	12.8061	−	1.84579i	0.459417	−	0.0662175i
$778$	−15.1963	+	7.31815i	−0.544813	+	0.262368i
$779$	1.36644	−	2.83745i	0.0489579	−	0.101662i
$780$	11.8450	−	2.11842i	0.424118	−	0.0758516i
$781$	−55.7110	−	26.8290i	−1.99350	−	0.960017i
$782$	−19.7013	+	24.7046i	−0.704516	+	0.883435i
$783$	−3.93991	+	27.5051i	−0.140801	+	0.982953i
$784$	−3.98447	−	5.75534i	−0.142303	−	0.205548i
$785$			40.7690i			1.45511i
$786$	−23.3187	−	20.4778i	−0.831749	−	0.730418i
$787$	−21.9609	+	45.6023i	−0.782822	+	1.62555i	−0.00263929	+	0.999997i	$0.500840\pi$
$787$	−21.9609	+	45.6023i	−0.782822	+	1.62555i	−0.780183	+	0.625551i	$0.784874\pi$
$788$	−13.6266	+	3.11018i	−0.485427	+	0.110796i
$789$	−5.68031	+	10.4917i	−0.202224	+	0.373514i
$790$	10.4379	+	21.6745i	0.371363	+	0.771143i
$791$	−22.8973	−	0.774837i	−0.814135	−	0.0275500i
$792$	11.9463	+	7.22033i	0.424492	+	0.256563i
$793$	17.9583	+	22.5190i	0.637719	+	0.799675i
$794$	−30.4498	+	14.6638i	−1.08062	+	0.520400i
$795$	38.8065	+	34.0787i	1.37632	+	1.20865i
$796$	2.06803	+	0.472014i	0.0732993	+	0.0167301i
$797$	20.0785	−	25.1776i	0.711216	−	0.891836i	−0.286590	−	0.958053i	$-0.592522\pi$
$797$	20.0785	−	25.1776i	0.711216	−	0.891836i	0.997805	+	0.0662173i	$0.0210930\pi$
$798$	13.0054	+	4.10371i	0.460386	+	0.145270i
$799$	−7.12433	−	8.93363i	−0.252041	−	0.316049i
$800$	−1.44170	−	2.99373i	−0.0509720	−	0.105844i
$801$	−1.78527	+	5.40080i	−0.0630794	+	0.190828i
$802$	8.68556			0.306698
$803$	1.39158			0.0491079
$804$	5.70755	−	20.4775i	0.201290	−	0.722185i
$805$	19.2037	+	25.8264i	0.676840	+	0.910260i
$806$	14.3449	−	3.27413i	0.505278	−	0.115326i
$807$	−6.93507	−	38.7769i	−0.244126	−	1.36501i
$808$	0.366805	−	0.292517i	0.0129042	−	0.0102907i
$809$	−7.50065	+	5.98157i	−0.263709	+	0.210301i	−0.746414	−	0.665482i	$-0.768226\pi$
$809$	−7.50065	+	5.98157i	−0.263709	+	0.210301i	0.482705	+	0.875783i	$0.339654\pi$
$810$	−25.9487	+	0.900766i	−0.911744	+	0.0316497i
$811$	41.5006	−	9.47224i	1.45728	−	0.332615i	0.580799	−	0.814047i	$-0.302740\pi$
$811$	41.5006	−	9.47224i	1.45728	−	0.332615i	0.876484	+	0.481432i	$0.159883\pi$
$812$	9.19011	−	10.7566i	0.322510	−	0.377483i
$813$	18.0852	+	5.04075i	0.634274	+	0.176787i
$814$	13.1370			0.460453
$815$	28.8411			1.01026
$816$	−3.48499	+	12.5034i	−0.121999	+	0.437707i
$817$	6.46904	+	13.4331i	0.226323	+	0.469965i
$818$	6.28488	+	7.88099i	0.219746	+	0.275552i
$819$	−13.7363	+	13.2910i	−0.479986	+	0.464423i
$820$	1.90352	−	2.38694i	0.0664738	−	0.0833555i
$821$	−27.7630	−	6.33673i	−0.968936	−	0.221153i	−0.291366	−	0.956612i	$-0.594110\pi$
$821$	−27.7630	−	6.33673i	−0.968936	−	0.221153i	−0.677570	+	0.735458i	$0.736967\pi$
$822$	−0.761424	+	0.867056i	−0.0265577	+	0.0302421i
$823$	−5.04639	+	2.43022i	−0.175906	+	0.0847120i	−0.519765	−	0.854310i	$-0.673980\pi$
$823$	−5.04639	+	2.43022i	−0.175906	+	0.0847120i	0.343858	+	0.939022i	$0.388266\pi$
$824$	−0.124846	−	0.156552i	−0.00434921	−	0.00545373i
$825$	12.7495	−	23.5488i	0.443882	−	0.819863i
$826$	12.7936	+	17.2057i	0.445146	+	0.598663i
$827$	2.95915	+	6.14473i	0.102900	+	0.213673i	0.946062	−	0.323986i	$-0.105023\pi$
$827$	2.95915	+	6.14473i	0.102900	+	0.213673i	−0.843162	+	0.537659i	$0.819309\pi$
$828$	6.54309	−	10.8257i	0.227388	−	0.376221i
$829$	−24.0573	+	5.49091i	−0.835543	+	0.190707i	−0.618827	−	0.785527i	$-0.712392\pi$
$829$	−24.0573	+	5.49091i	−0.835543	+	0.190707i	−0.216716	+	0.976235i	$0.569535\pi$
$830$	16.1536	−	33.5433i	0.560699	−	1.16430i
$831$	12.5844	−	14.3303i	0.436549	−	0.497111i
$832$			2.40811i			0.0834861i
$833$	52.3381	+	3.54626i	1.81341	+	0.122871i
$834$	21.7972	+	1.03451i	0.754774	+	0.0358220i
$835$	5.95379	−	7.46582i	0.206039	−	0.258365i
$836$	12.4755	+	6.00790i	0.431475	+	0.207788i
$837$	−31.6421	+	2.60445i	−1.09371	+	0.0900228i
$838$	−5.47816	+	11.3755i	−0.189240	+	0.392961i
$839$	−34.6081	+	16.6664i	−1.19481	+	0.575388i	−0.922191	−	0.386735i	$-0.873603\pi$
$839$	−34.6081	+	16.6664i	−1.19481	+	0.575388i	−0.272615	+	0.962123i	$0.587888\pi$
$840$	11.4063	+	6.68392i	0.393555	+	0.230617i
$841$	−0.365211	−	0.175876i	−0.0125935	−	0.00606470i
$842$	−12.2334	+	9.75580i	−0.421590	+	0.336207i
$843$	3.91493	+	9.22433i	0.134837	+	0.317703i
$844$	17.3525	−	21.7593i	0.597297	−	0.748987i
$845$	4.62274	−	20.2535i	0.159027	−	0.696743i
$846$	3.29012	+	3.17790i	0.113117	+	0.109258i
$847$	13.0767	−	24.9579i	0.449322	−	0.857562i
$848$	−8.08080	+	6.44422i	−0.277496	+	0.221295i
$849$	−21.6437	−	50.9966i	−0.742808	−	1.75020i
$850$	24.2767	+	5.54100i	0.832684	+	0.190055i
$851$		−	11.9048i		−	0.408093i
$852$	−1.09122	+	22.9921i	−0.0373845	+	0.787696i
$853$	−44.2321	−	10.0957i	−1.51448	−	0.345670i	−0.617083	−	0.786898i	$-0.711686\pi$
$853$	−44.2321	−	10.0957i	−1.51448	−	0.345670i	−0.897395	+	0.441228i	$0.854543\pi$
$854$	−1.07025	+	31.6273i	−0.0366233	+	1.08226i
$855$	−25.5403	+	3.32736i	−0.873459	+	0.113793i
$856$	0.995809	+	4.36293i	0.0340361	+	0.149122i
$857$	1.49189	+	1.87077i	0.0509621	+	0.0639044i	0.806659	−	0.591017i	$-0.201273\pi$
$857$	1.49189	+	1.87077i	0.0509621	+	0.0639044i	−0.755697	+	0.654921i	$0.772702\pi$
$858$	−15.7297	+	11.3672i	−0.537002	+	0.388071i
$859$	−31.2446	+	7.13139i	−1.06605	+	0.243320i	−0.719345	−	0.694653i	$-0.755558\pi$
$859$	−31.2446	+	7.13139i	−1.06605	+	0.243320i	−0.346709	+	0.937973i	$0.612701\pi$
$860$	3.21623	+	14.0912i	0.109673	+	0.480507i
$861$	−0.393602	+	4.83357i	−0.0134139	+	0.164728i
$862$	−6.18227	+	27.0863i	−0.210569	+	0.922563i
$863$		−	44.5268i		−	1.51571i	−0.652423	−	0.757855i	$-0.726247\pi$
$863$		−	44.5268i		−	1.51571i	0.652423	−	0.757855i	$-0.273753\pi$
$864$	0.736791	−	5.14365i	0.0250661	−	0.174991i
$865$	−15.2206	+	66.6858i	−0.517516	+	2.26738i
$866$	7.58657	−	3.65350i	0.257802	−	0.124151i
$867$	−39.7282	−	54.9748i	−1.34924	−	1.86704i
$868$	14.3194	+	7.50268i	0.486031	+	0.254657i
$869$	−30.3349	−	24.1912i	−1.02904	−	0.820632i
$870$	−7.17405	+	25.7390i	−0.243223	+	0.872633i
$871$	23.1074	+	18.4275i	0.782964	+	0.624393i
$872$	−3.62655	−	7.53062i	−0.122811	−	0.255019i
$873$	−13.6741	+	8.92660i	−0.462798	+	0.302120i
$874$	5.44438	−	11.3054i	0.184159	−	0.382410i
$875$	−5.94139	+	11.3396i	−0.200856	+	0.383347i
$876$	−0.202381	−	0.476849i	−0.00683782	−	0.0161112i
$877$	−25.3033	−	12.1854i	−0.854433	−	0.411473i	−0.0452119	−	0.998977i	$-0.514396\pi$
$877$	−25.3033	−	12.1854i	−0.854433	−	0.411473i	−0.809221	+	0.587504i	$0.800111\pi$
$878$	1.86097	+	8.15343i	0.0628046	+	0.275165i
$879$	15.1082	+	8.17974i	0.509588	+	0.275896i
$880$	10.4948	+	8.36929i	0.353778	+	0.282129i
$881$	0.634950			0.0213920			0.0106960	−	0.999943i	$-0.496595\pi$
$881$	0.634950			0.0213920			0.0106960	+	0.999943i	$0.496595\pi$
$882$	−20.9598	+	1.29899i	−0.705753	+	0.0437392i
$883$	15.3886			0.517867			0.258933	−	0.965895i	$-0.416629\pi$
$883$	15.3886			0.517867			0.258933	+	0.965895i	$0.416629\pi$
$884$	−14.1092	−	11.2517i	−0.474545	−	0.378437i
$885$	−35.6097	−	19.2795i	−1.19701	−	0.648072i
$886$	2.75137	+	12.0545i	0.0924341	+	0.404980i
$887$	2.88090	+	1.38737i	0.0967311	+	0.0465832i	0.481624	−	0.876378i	$-0.340047\pi$
$887$	2.88090	+	1.38737i	0.0967311	+	0.0465832i	−0.384893	+	0.922961i	$0.625762\pi$
$888$	−1.91055	−	4.50162i	−0.0641139	−	0.151065i
$889$	37.5517	−	27.9222i	1.25944	−	0.936481i
$890$	−2.37336	+	4.92832i	−0.0795551	+	0.165198i
$891$	37.0761	−	19.4674i	1.24210	−	0.652182i
$892$	1.56099	+	3.24143i	0.0522658	+	0.108531i
$893$	3.54763	+	2.82914i	0.118717	+	0.0946735i
$894$	0.106023	−	0.380388i	0.00354594	−	0.0127221i
$895$	27.9295	+	22.2730i	0.933580	+	0.744505i
$896$	−1.71861	+	2.01156i	−0.0574148	+	0.0672015i
$897$	10.3010	+	14.2543i	0.343941	+	0.475937i
$898$	10.1499	−	4.88794i	0.338707	−	0.163113i
$899$	−7.27047	+	31.8540i	−0.242484	+	1.06239i
$900$	−9.92357	−	0.944083i	−0.330786	−	0.0314694i
$901$		−	77.4560i		−	2.58043i
$902$	−1.09569	+	4.80055i	−0.0364826	+	0.159841i
$903$	−16.7290	−	15.7243i	−0.556706	−	0.523272i
$904$	1.92688	+	8.44222i	0.0640872	+	0.280784i
$905$	−25.3699	+	5.79052i	−0.843324	+	0.192483i
$906$	−17.8438	+	12.8950i	−0.592822	+	0.428409i
$907$	35.6060	+	44.6485i	1.18228	+	1.48253i	0.839708	+	0.543039i	$0.182726\pi$
$907$	35.6060	+	44.6485i	1.18228	+	1.48253i	0.342571	+	0.939492i	$0.388702\pi$
$908$	3.27701	+	14.3575i	0.108751	+	0.476471i
$909$	−0.181829	−	1.39569i	−0.00603089	−	0.0462921i
$910$	−14.7499	+	10.9675i	−0.488954	+	0.363570i
$911$	−41.8336	−	9.54825i	−1.38601	−	0.316348i	−0.536491	−	0.843906i	$-0.680251\pi$
$911$	−41.8336	−	9.54825i	−1.38601	−	0.316348i	−0.849519	+	0.527558i	$0.823108\pi$
$912$	0.244360	−	5.14869i	0.00809156	−	0.170490i
$913$			60.0463i			1.98724i
$914$	−39.4294	−	8.99951i	−1.30421	−	0.297677i
$915$	−23.3497	−	55.0163i	−0.771917	−	1.81878i
$916$	12.2944	−	9.80447i	0.406219	−	0.323949i
$917$	45.8332	+	12.1056i	1.51355	+	0.399763i
$918$	26.6943	+	28.3503i	0.881043	+	0.935699i
$919$	−3.93329	+	17.2329i	−0.129747	+	0.568461i	0.867702	+	0.497085i	$0.165596\pi$
$919$	−3.93329	+	17.2329i	−0.129747	+	0.568461i	−0.997449	+	0.0713759i	$0.977261\pi$
$920$	7.58428	−	9.51039i	0.250046	−	0.313548i
$921$	5.18324	+	12.2127i	0.170794	+	0.402423i
$922$	−6.90319	+	5.50511i	−0.227344	+	0.181301i
$923$	−28.8331	−	13.8853i	−0.949054	−	0.457041i
$924$	−21.2520	−	1.73057i	−0.699139	−	0.0569316i
$925$	−8.45251	+	4.07052i	−0.277917	+	0.133838i
$926$	4.15612	−	8.63027i	0.136579	−	0.283608i
$927$	−0.595677	+	0.0776043i	−0.0195646	+	0.00254886i
$928$	−4.81784	−	2.32015i	−0.158153	−	0.0761626i
$929$	23.2399	−	29.1420i	0.762478	−	0.956117i	−0.237406	−	0.971411i	$-0.576297\pi$
$929$	23.2399	−	29.1420i	0.762478	−	0.956117i	0.999883	+	0.0152941i	$0.00486845\pi$
$930$	−30.4969	−	1.44740i	−1.00003	−	0.0474622i
$931$	−20.5762	+	3.25192i	−0.674358	+	0.106577i
$932$		−	10.3597i		−	0.339342i
$933$	−18.8137	+	21.4237i	−0.615932	+	0.701380i
$934$	3.72779	−	7.74083i	0.121977	−	0.253288i
$935$	−98.0722	+	22.3843i	−3.20730	+	0.732046i
$936$	6.18277	+	3.73687i	0.202090	+	0.122143i
$937$	−20.6904	−	42.9641i	−0.675927	−	1.40358i	−0.902975	−	0.429693i	$-0.858622\pi$
$937$	−20.6904	−	42.9641i	−0.675927	−	1.40358i	0.227048	−	0.973883i	$-0.427092\pi$
$938$	6.15092	+	31.8843i	0.200835	+	1.04106i
$939$	20.7241	−	38.2780i	0.676305	−	1.24916i
$940$	2.74261	+	3.43913i	0.0894541	+	0.112172i
$941$	14.5846	−	7.02355i	0.475443	−	0.228961i	−0.180787	−	0.983522i	$-0.557864\pi$
$941$	14.5846	−	7.02355i	0.475443	−	0.228961i	0.656230	+	0.754561i	$0.272150\pi$
$942$	−16.1512	+	18.3918i	−0.526233	+	0.599237i
$943$	4.35027	+	0.992922i	0.141664	+	0.0323340i
$944$	5.05270	−	6.33588i	0.164451	−	0.206215i
$945$	34.8610	−	18.9134i	1.13403	−	0.615254i
$946$	−14.5344	−	18.2255i	−0.472553	−	0.592563i
$947$	13.9762	+	29.0218i	0.454165	+	0.943083i	0.994802	+	0.101827i	$0.0324689\pi$
$947$	13.9762	+	29.0218i	0.454165	+	0.943083i	−0.540637	+	0.841256i	$0.681817\pi$
$948$	−3.87786	+	13.9129i	−0.125947	+	0.451871i
$949$	0.720212			0.0233791
$950$	−9.88843			−0.320823
$951$	−19.7530	−	5.50562i	−0.640534	−	0.178532i
$952$	−3.75571	−	19.4683i	−0.121723	−	0.630972i
$953$	52.8885	−	12.0715i	1.71323	−	0.391033i	0.750364	−	0.661025i	$-0.229878\pi$
$953$	52.8885	−	12.0715i	1.71323	−	0.391033i	0.962863	+	0.269992i	$0.0870210\pi$
$954$	4.00574	+	30.7473i	0.129691	+	0.995482i
$955$	18.3200	−	14.6097i	0.592822	−	0.472759i
$956$	3.28312	−	2.61820i	0.106184	−	0.0846787i
$957$	−7.58698	−	42.4220i	−0.245252	−	1.37131i
$958$	−2.28468	+	0.521462i	−0.0738145	+	0.0168477i
$959$	0.450122	−	1.70421i	0.0145352	−	0.0550320i
$960$	1.34160	−	4.81337i	0.0432999	−	0.155351i
$961$	−6.33352			−0.204307
$962$	6.79906			0.219210
$963$	12.7470	+	4.21361i	0.410767	+	0.135782i
$964$	−6.52248	−	13.5441i	−0.210075	−	0.436225i
$965$	20.8141	+	26.1000i	0.670029	+	0.840190i
$966$	−1.56825	+	19.2586i	−0.0504576	+	0.619636i
$967$	26.8752	−	33.7004i	0.864248	−	1.08373i	−0.131473	−	0.991320i	$-0.541971\pi$
$967$	26.8752	−	33.7004i	0.864248	−	1.08373i	0.995721	−	0.0924125i	$-0.0294579\pi$
$968$	−10.3826	−	2.36976i	−0.333709	−	0.0761668i
$969$	29.0247	+	25.4886i	0.932407	+	0.818813i
$970$	−14.1484	+	6.81350i	−0.454277	+	0.218768i
$971$	−1.64618	−	2.06424i	−0.0528284	−	0.0662447i	0.754715	−	0.656052i	$-0.227775\pi$
$971$	−1.64618	−	2.06424i	−0.0528284	−	0.0662447i	−0.807544	+	0.589808i	$0.799204\pi$
$972$	−12.0629	−	9.87355i	−0.386917	−	0.316694i
$973$	−30.5041	+	13.4388i	−0.977917	+	0.430827i
$974$	−2.02135	−	4.19737i	−0.0647682	−	0.134492i
$975$	6.59850	−	12.1876i	0.211321	−	0.390317i
$976$	11.6609	−	2.66153i	0.373258	−	0.0851936i
$977$	−0.531524	+	1.10372i	−0.0170050	+	0.0353112i	−0.909298	−	0.416145i	$-0.863381\pi$
$977$	−0.531524	+	1.10372i	−0.0170050	+	0.0353112i	0.892293	+	0.451456i	$0.149095\pi$
$978$	13.0108	+	11.4257i	0.416041	+	0.365355i
$979$		−	8.82226i		−	0.281961i
$980$	−20.1483	−	1.36518i	−0.643613	−	0.0436092i
$981$	−24.9624	−	2.37481i	−0.796987	−	0.0758217i
$982$	9.53907	−	11.9616i	0.304404	−	0.381711i
$983$	44.8504	+	21.5988i	1.43050	+	0.688895i	0.979091	−	0.203421i	$-0.0652059\pi$
$983$	44.8504	+	21.5988i	1.43050	+	0.688895i	0.451413	+	0.892315i	$0.350920\pi$
$984$	1.80434	−	0.322697i	0.0575201	−	0.0102872i
$985$	−17.4954	+	36.3295i	−0.557448	+	1.15755i
$986$	36.1049	−	17.3872i	1.14981	−	0.553722i
$987$	−6.66346	−	2.10258i	−0.212100	−	0.0669259i
$988$	6.45669	+	3.10938i	0.205415	+	0.0989225i
$989$	−16.5160	+	13.1711i	−0.525180	+	0.418817i
$990$	37.7736	−	13.9577i	1.20052	−	0.443606i
$991$	−13.1258	+	16.4592i	−0.416954	+	0.522844i	−0.945307	−	0.326181i	$-0.894238\pi$
$991$	−13.1258	+	16.4592i	−0.416954	+	0.522844i	0.528353	+	0.849025i	$0.322810\pi$
$992$	1.35963	−	5.95692i	0.0431683	−	0.189132i
$993$	−18.1672	+	20.6876i	−0.576520	+	0.656500i
$994$	−14.1755	−	32.1764i	−0.449619	−	1.02057i
$995$	4.78444	−	3.81547i	0.151677	−	0.120958i
$996$	20.5758	−	8.73267i	0.651970	−	0.276705i
$997$	14.5443	+	3.31963i	0.460621	+	0.105134i	0.446533	−	0.894767i	$-0.352658\pi$
$997$	14.5443	+	3.31963i	0.460621	+	0.105134i	0.0140879	+	0.999901i	$0.495516\pi$
$998$			11.9680i			0.378839i
$999$	−14.5226	−	2.08026i	−0.459475	−	0.0658165i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.j.a.251.19	yes	120
3.2	odd	2	inner	294.2.j.a.251.1	yes	120
49.41	odd	14	inner	294.2.j.a.41.1	✓	120
147.41	even	14	inner	294.2.j.a.41.19	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.j.a.41.1	✓	120	49.41	odd	14	inner
294.2.j.a.41.19	yes	120	147.41	even	14	inner
294.2.j.a.251.1	yes	120	3.2	odd	2	inner
294.2.j.a.251.19	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.781831 + 0.623490i) q^{2} +(1.52314 + 0.824644i) q^{3} +(0.222521 + 0.974928i) q^{4} +(2.59923 + 1.25172i) q^{5} +(0.676684 + 1.59440i) q^{6} +(-2.01156 - 1.71861i) q^{7} +(-0.433884 + 0.900969i) q^{8} +(1.63993 + 2.51210i) q^{9} +(1.25172 + 2.59923i) q^{10} +(-3.63779 - 2.90104i) q^{11} +(-0.465037 + 1.66845i) q^{12} +(-1.88273 - 1.50143i) q^{13} +(-0.501162 - 2.59785i) q^{14} +(2.92677 + 4.04999i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(1.66757 - 7.30612i) q^{17} +(-0.284124 + 2.98652i) q^{18} +2.97594i q^{19} +(-0.641956 + 2.81259i) q^{20} +(-1.64665 - 4.27651i) q^{21} +(-1.03537 - 4.53625i) q^{22} +(-4.11077 + 0.938257i) q^{23} +(-1.40385 + 1.01450i) q^{24} +(2.07173 + 2.59786i) q^{25} +(-0.535854 - 2.34773i) q^{26} +(0.426252 + 5.17864i) q^{27} +(1.22791 - 2.34355i) q^{28} +(5.21333 + 1.18991i) q^{29} +(-0.236886 + 4.99122i) q^{30} +6.11012i q^{31} +(-0.974928 - 0.222521i) q^{32} +(-3.14855 - 7.41858i) q^{33} +(5.85905 - 4.67244i) q^{34} +(-3.07727 - 6.98498i) q^{35} +(-2.08420 + 2.15780i) q^{36} +(-0.628266 + 2.75262i) q^{37} +(-1.85547 + 2.32669i) q^{38} +(-1.62953 - 3.83948i) q^{39} +(-2.25553 + 1.79872i) q^{40} +(-0.953462 - 0.459163i) q^{41} +(1.37896 - 4.37018i) q^{42} +(4.51390 - 2.17378i) q^{43} +(2.01882 - 4.19213i) q^{44} +(1.11809 + 8.58225i) q^{45} +(-3.79892 - 1.82947i) q^{46} +(0.950670 - 1.19210i) q^{47} +(-1.73010 - 0.0821117i) q^{48} +(1.09274 + 6.91418i) q^{49} +3.32279i q^{50} +(8.56490 - 9.75310i) q^{51} +(1.04484 - 2.16963i) q^{52} +(10.0766 - 2.29992i) q^{53} +(-2.89557 + 4.31459i) q^{54} +(-5.82415 - 12.0940i) q^{55} +(2.42120 - 1.06667i) q^{56} +(-2.45409 + 4.53278i) q^{57} +(3.33405 + 4.18076i) q^{58} +(-7.30136 + 3.51615i) q^{59} +(-3.29718 + 3.75460i) q^{60} +(-11.6609 - 2.66153i) q^{61} +(-3.80960 + 4.77708i) q^{62} +(1.01852 - 7.87163i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(-3.01428 - 6.25922i) q^{65} +(2.16378 - 7.76317i) q^{66} -12.2733 q^{67} +7.49401 q^{68} +(-7.03502 - 1.96082i) q^{69} +(1.94916 - 7.37972i) q^{70} +(12.9562 - 2.95718i) q^{71} +(-2.97486 + 0.387562i) q^{72} +(-0.233828 + 0.186472i) q^{73} +(-2.20743 + 1.76036i) q^{74} +(1.01322 + 5.66535i) q^{75} +(-2.90133 + 0.662209i) q^{76} +(2.33186 + 12.0876i) q^{77} +(1.11986 - 4.01782i) q^{78} +8.33881 q^{79} -2.88492 q^{80} +(-3.62129 + 8.23931i) q^{81} +(-0.459163 - 0.953462i) q^{82} +(-8.04620 - 10.0896i) q^{83} +(3.80288 - 2.55697i) q^{84} +(13.4796 - 16.9029i) q^{85} +(4.88444 + 1.11484i) q^{86} +(6.95939 + 6.11154i) q^{87} +(4.19213 - 2.01882i) q^{88} +(1.18218 + 1.48241i) q^{89} +(-4.47679 + 7.40699i) q^{90} +(1.20685 + 6.25591i) q^{91} +(-1.82947 - 3.79892i) q^{92} +(-5.03867 + 9.30658i) q^{93} +(1.48653 - 0.339290i) q^{94} +(-3.72505 + 7.73515i) q^{95} +(-1.30145 - 1.14290i) q^{96} +5.44330i q^{97} +(-3.45659 + 6.08704i) q^{98} +(1.32200 - 13.8960i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 20 q^{4} - 14 q^{6} + 4 q^{7} - 10 q^{9} + 12 q^{15} - 20 q^{16} - 8 q^{18} - 12 q^{21} - 10 q^{22} - 24 q^{25} + 42 q^{27} - 4 q^{28} + 8 q^{30} + 10 q^{36} - 58 q^{37} + 8 q^{39} - 14 q^{40} - 2 q^{42}+ \cdots - 224 q^{99}+O(q^{100}) \) 120 * q + 20 * q^4 - 14 * q^6 + 4 * q^7 - 10 * q^9 + 12 * q^15 - 20 * q^16 - 8 * q^18 - 12 * q^21 - 10 * q^22 - 24 * q^25 + 42 * q^27 - 4 * q^28 + 8 * q^30 + 10 * q^36 - 58 * q^37 + 8 * q^39 - 14 * q^40 - 2 * q^42 - 12 * q^43 + 14 * q^45 - 60 * q^46 - 36 * q^49 - 24 * q^51 - 42 * q^52 - 14 * q^55 + 34 * q^57 + 50 * q^58 - 12 * q^60 - 154 * q^61 + 20 * q^64 - 28 * q^67 + 28 * q^69 - 38 * q^70 + 8 * q^72 - 84 * q^75 - 16 * q^78 + 16 * q^79 + 22 * q^81 - 30 * q^84 - 32 * q^85 - 56 * q^87 - 4 * q^88 - 42 * q^90 + 88 * q^91 + 14 * q^93 + 112 * q^94 - 224 * q^99

Introduction

L-functions

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