LMFDB - Embedded newform 399.2.ck.a.10.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [399,2,Mod(10,399)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("399.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(399, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 17])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [78] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			10.5
Character	$\chi$	$=$	399.10
Dual form			399.2.ck.a.40.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.763835 - 0.910304i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.102088 - 0.578971i) q^{4} +(-3.42867 + 0.604567i) q^{5} +(-0.763835 + 0.910304i) q^{6} +(-2.05773 - 1.66305i) q^{7} +(-2.66324 + 1.53762i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(3.16928 + 2.65934i) q^{10} +4.48406 q^{11} -0.587903 q^{12} +(0.722417 + 0.606180i) q^{13} +(0.0578863 + 3.14346i) q^{14} +(1.19077 + 3.27160i) q^{15} +(2.32909 + 0.847719i) q^{16} +(-1.81604 + 4.98954i) q^{17} +(1.02911 + 0.594159i) q^{18} +(3.15422 + 3.00847i) q^{19} +2.04682i q^{20} +(-1.28046 + 2.31526i) q^{21} +(-3.42508 - 4.08185i) q^{22} +(-4.47144 - 3.75198i) q^{23} +(1.97673 + 2.35578i) q^{24} +(6.69183 - 2.43563i) q^{25} -1.12064i q^{26} +(0.500000 + 0.866025i) q^{27} +(-1.17293 + 1.02159i) q^{28} +(-2.00359 - 0.353287i) q^{29} +(2.06860 - 3.58292i) q^{30} +(-2.83146 - 4.90423i) q^{31} +(1.09623 + 3.01188i) q^{32} +(-0.778648 - 4.41593i) q^{33} +(5.92915 - 2.15803i) q^{34} +(8.06071 + 4.45802i) q^{35} +(0.102088 + 0.578971i) q^{36} +(-3.43396 + 1.98259i) q^{37} +(0.329311 - 5.16928i) q^{38} +(0.471524 - 0.816703i) q^{39} +(8.20179 - 6.88212i) q^{40} +(-8.45583 + 7.09529i) q^{41} +(3.08565 - 0.602863i) q^{42} +(-6.85723 - 2.49583i) q^{43} +(0.457769 - 2.59614i) q^{44} +(3.01512 - 1.74078i) q^{45} +6.93626i q^{46} +(2.75737 + 7.57582i) q^{47} +(0.430398 - 2.44091i) q^{48} +(1.46852 + 6.84423i) q^{49} +(-7.32861 - 4.23118i) q^{50} +(5.22909 + 0.922029i) q^{51} +(0.424711 - 0.356375i) q^{52} +(-4.77895 - 0.842659i) q^{53} +(0.406428 - 1.11665i) q^{54} +(-15.3744 + 2.71091i) q^{55} +(8.03739 + 1.26509i) q^{56} +(2.41504 - 3.62872i) q^{57} +(1.20882 + 2.09373i) q^{58} +(3.75467 + 1.36659i) q^{59} +(2.01573 - 0.355427i) q^{60} +(-4.32989 + 5.16017i) q^{61} +(-2.30157 + 6.32351i) q^{62} +(2.50243 + 0.858972i) q^{63} +(4.38295 - 7.59149i) q^{64} +(-2.84341 - 1.64164i) q^{65} +(-3.42508 + 4.08185i) q^{66} +(7.84425 - 9.34841i) q^{67} +(2.70340 + 1.56081i) q^{68} +(-2.91852 + 5.05503i) q^{69} +(-2.09891 - 10.7429i) q^{70} +(0.343637 - 0.944136i) q^{71} +(1.97673 - 2.35578i) q^{72} +(-8.21615 + 1.44873i) q^{73} +(4.42774 + 1.61157i) q^{74} +(-3.56065 - 6.16722i) q^{75} +(2.06382 - 1.51907i) q^{76} +(-9.22698 - 7.45722i) q^{77} +(-1.10361 + 0.194597i) q^{78} +(-2.66334 + 7.31746i) q^{79} +(-8.49819 - 1.49846i) q^{80} +(0.766044 - 0.642788i) q^{81} +(12.9177 + 2.27774i) q^{82} +(-11.6723 - 6.73898i) q^{83} +(1.20975 + 0.977712i) q^{84} +(3.21010 - 18.2054i) q^{85} +(2.96583 + 8.14856i) q^{86} +2.03450i q^{87} +(-11.9421 + 6.89479i) q^{88} +(2.67971 - 15.1974i) q^{89} +(-3.88770 - 1.41501i) q^{90} +(-0.478432 - 2.44877i) q^{91} +(-2.62877 + 2.20580i) q^{92} +(-4.33805 + 3.64005i) q^{93} +(4.79012 - 8.29672i) q^{94} +(-12.6336 - 8.40811i) q^{95} +(2.77576 - 1.60259i) q^{96} +(2.13453 + 12.1055i) q^{97} +(5.10862 - 6.56466i) q^{98} +(-4.21363 + 1.53364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q - 6 q^{7} + 12 q^{10} + 6 q^{11} + 72 q^{12} + 3 q^{13} - 15 q^{14} + 18 q^{19} + 9 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{24} + 18 q^{25} + 39 q^{27} - 9 q^{28} - 6 q^{29} - 18 q^{31} - 51 q^{32} - 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) $ 78 * q - 6 * q^7 + 12 * q^10 + 6 * q^11 + 72 * q^12 + 3 * q^13 - 15 * q^14 + 18 * q^19 + 9 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^24 + 18 * q^25 + 39 * q^27 - 9 * q^28 - 6 * q^29 - 18 * q^31 - 51 * q^32 - 12 * q^33 + 30 * q^34 + 33 * q^35 + 18 * q^37 - 57 * q^38 - 18 * q^40 - 63 * q^41 - 27 * q^42 - 51 * q^43 - 36 * q^44 + 9 * q^45 - 84 * q^47 + 18 * q^49 - 27 * q^50 - 18 * q^51 + 18 * q^52 - 45 * q^53 + 30 * q^55 + 33 * q^56 - 6 * q^57 - 18 * q^58 - 24 * q^59 + 66 * q^61 + 171 * q^62 + 6 * q^63 + 18 * q^64 - 99 * q^65 - 12 * q^66 - 24 * q^67 - 12 * q^69 - 150 * q^70 - 66 * q^71 - 9 * q^72 + 3 * q^73 + 18 * q^74 - 36 * q^75 - 12 * q^76 + 21 * q^77 + 75 * q^78 + 45 * q^79 + 78 * q^80 - 24 * q^82 - 72 * q^83 - 9 * q^84 + 60 * q^85 - 9 * q^86 - 108 * q^88 + 48 * q^89 - 33 * q^90 - 54 * q^91 - 102 * q^92 + 9 * q^93 - 66 * q^94 - 84 * q^95 + 75 * q^97 - 39 * q^98 - 6 * q^99

Character values

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

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.763835	−	0.910304i	−0.540113	−	0.643682i	0.425100	−	0.905146i	$-0.360239\pi$
$2$	−0.763835	−	0.910304i	−0.540113	−	0.643682i	−0.965213	+	0.261465i	$0.915795\pi$
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.102088	−	0.578971i	0.0510441	−	0.289486i
$5$	−3.42867	+	0.604567i	−1.53335	+	0.270371i	−0.875663	−	0.482922i	$-0.839575\pi$
$5$	−3.42867	+	0.604567i	−1.53335	+	0.270371i	−0.657685	+	0.753293i	$0.728464\pi$
$6$	−0.763835	+	0.910304i	−0.311835	+	0.371630i
$7$	−2.05773	−	1.66305i	−0.777749	−	0.628574i
$7$	−2.05773	−	1.66305i	−0.777749	−	0.628574i
$8$	−2.66324	+	1.53762i	−0.941599	+	0.543632i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	3.16928	+	2.65934i	1.00221	+	0.840958i
$11$	4.48406			1.35199			0.675997	−	0.736905i	$-0.263713\pi$
$11$	4.48406			1.35199			0.675997	+	0.736905i	$0.263713\pi$
$12$	−0.587903			−0.169713
$13$	0.722417	+	0.606180i	0.200362	+	0.168124i	0.737448	−	0.675404i	$-0.236031\pi$
$13$	0.722417	+	0.606180i	0.200362	+	0.168124i	−0.537086	+	0.843527i	$0.680475\pi$
$14$	0.0578863	+	3.14346i	0.0154708	+	0.840125i
$15$	1.19077	+	3.27160i	0.307454	+	0.844724i
$16$	2.32909	+	0.847719i	0.582272	+	0.211930i
$17$	−1.81604	+	4.98954i	−0.440455	+	1.21014i	0.498739	+	0.866752i	$0.333797\pi$
$17$	−1.81604	+	4.98954i	−0.440455	+	1.21014i	−0.939194	+	0.343388i	$0.888425\pi$
$18$	1.02911	+	0.594159i	0.242564	+	0.140045i
$19$	3.15422	+	3.00847i	0.723628	+	0.690190i
$19$	3.15422	+	3.00847i	0.723628	+	0.690190i
$20$			2.04682i			0.457683i
$21$	−1.28046	+	2.31526i	−0.279420	+	0.505230i
$22$	−3.42508	−	4.08185i	−0.730230	−	0.870254i
$23$	−4.47144	−	3.75198i	−0.932359	−	0.782342i	0.0438803	−	0.999037i	$-0.486028\pi$
$23$	−4.47144	−	3.75198i	−0.932359	−	0.782342i	−0.976239	+	0.216695i	$0.930472\pi$
$24$	1.97673	+	2.35578i	0.403499	+	0.480871i
$25$	6.69183	−	2.43563i	1.33837	−	0.487125i
$26$		−	1.12064i		−	0.219776i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−1.17293	+	1.02159i	−0.221663	+	0.193062i
$29$	−2.00359	−	0.353287i	−0.372058	−	0.0656038i	−0.0155070	−	0.999880i	$-0.504936\pi$
$29$	−2.00359	−	0.353287i	−0.372058	−	0.0656038i	−0.356551	+	0.934276i	$0.616047\pi$
$30$	2.06860	−	3.58292i	0.377673	−	0.654149i
$31$	−2.83146	−	4.90423i	−0.508545	−	0.880826i	−0.999951	−	0.00989531i	$-0.996850\pi$
$31$	−2.83146	−	4.90423i	−0.508545	−	0.880826i	0.491406	−	0.870931i	$-0.336483\pi$
$32$	1.09623	+	3.01188i	0.193789	+	0.532430i
$33$	−0.778648	−	4.41593i	−0.135545	−	0.768715i
$34$	5.92915	−	2.15803i	1.01684	−	0.370100i
$35$	8.06071	+	4.45802i	1.36251	+	0.753543i
$36$	0.102088	+	0.578971i	0.0170147	+	0.0964952i
$37$	−3.43396	+	1.98259i	−0.564539	+	0.325937i	−0.754965	−	0.655765i	$-0.772346\pi$
$37$	−3.43396	+	1.98259i	−0.564539	+	0.325937i	0.190426	+	0.981701i	$0.439013\pi$
$38$	0.329311	−	5.16928i	0.0534213	−	0.838567i
$39$	0.471524	−	0.816703i	0.0755043	−	0.130777i
$40$	8.20179	−	6.88212i	1.29682	−	1.08816i
$41$	−8.45583	+	7.09529i	−1.32058	+	1.10810i	−0.334398	+	0.942432i	$0.608533\pi$
$41$	−8.45583	+	7.09529i	−1.32058	+	1.10810i	−0.986182	+	0.165666i	$0.947023\pi$
$42$	3.08565	−	0.602863i	0.476126	−	0.0930237i
$43$	−6.85723	−	2.49583i	−1.04572	−	0.380610i	−0.238673	−	0.971100i	$-0.576712\pi$
$43$	−6.85723	−	2.49583i	−1.04572	−	0.380610i	−0.807045	+	0.590490i	$0.798934\pi$
$44$	0.457769	−	2.59614i	0.0690113	−	0.391383i
$45$	3.01512	−	1.74078i	0.449468	−	0.259501i
$46$			6.93626i			1.02270i
$47$	2.75737	+	7.57582i	0.402204	+	1.10505i	0.961194	+	0.275872i	$0.0889667\pi$
$47$	2.75737	+	7.57582i	0.402204	+	1.10505i	−0.558990	+	0.829174i	$0.688811\pi$
$48$	0.430398	−	2.44091i	0.0621227	−	0.352315i
$49$	1.46852	+	6.84423i	0.209788	+	0.977747i
$50$	−7.32861	−	4.23118i	−1.03642	−	0.598379i
$51$	5.22909	+	0.922029i	0.732219	+	0.129110i
$52$	0.424711	−	0.356375i	0.0588968	−	0.0494203i
$53$	−4.77895	−	0.842659i	−0.656440	−	0.115748i	−0.164500	−	0.986377i	$-0.552601\pi$
$53$	−4.77895	−	0.842659i	−0.656440	−	0.115748i	−0.491940	+	0.870629i	$0.663712\pi$
$54$	0.406428	−	1.11665i	0.0553079	−	0.151957i
$55$	−15.3744	+	2.71091i	−2.07308	+	0.365539i
$56$	8.03739	+	1.26509i	1.07404	+	0.169055i
$57$	2.41504	−	3.62872i	0.319879	−	0.480635i
$58$	1.20882	+	2.09373i	0.158725	+	0.274920i
$59$	3.75467	+	1.36659i	0.488816	+	0.177915i	0.574657	−	0.818394i	$-0.305135\pi$
$59$	3.75467	+	1.36659i	0.488816	+	0.177915i	−0.0858409	+	0.996309i	$0.527358\pi$
$60$	2.01573	−	0.355427i	0.260229	−	0.0458854i
$61$	−4.32989	+	5.16017i	−0.554386	+	0.660691i	−0.968348	−	0.249603i	$-0.919700\pi$
$61$	−4.32989	+	5.16017i	−0.554386	+	0.660691i	0.413962	+	0.910294i	$0.364144\pi$
$62$	−2.30157	+	6.32351i	−0.292300	+	0.803087i
$63$	2.50243	+	0.858972i	0.315277	+	0.108220i
$64$	4.38295	−	7.59149i	0.547869	−	0.948936i
$65$	−2.84341	−	1.64164i	−0.352681	−	0.203621i
$66$	−3.42508	+	4.08185i	−0.421598	+	0.502441i
$67$	7.84425	−	9.34841i	0.958327	−	1.14209i	−0.0314551	−	0.999505i	$-0.510014\pi$
$67$	7.84425	−	9.34841i	0.958327	−	1.14209i	0.989783	−	0.142585i	$-0.0455414\pi$
$68$	2.70340	+	1.56081i	0.327835	+	0.189276i
$69$	−2.91852	+	5.05503i	−0.351349	+	0.608554i
$70$	−2.09891	−	10.7429i	−0.250867	−	1.28402i
$71$	0.343637	−	0.944136i	0.0407822	−	0.112048i	−0.917630	−	0.397436i	$-0.869900\pi$
$71$	0.343637	−	0.944136i	0.0407822	−	0.112048i	0.958412	+	0.285388i	$0.0921223\pi$
$72$	1.97673	−	2.35578i	0.232960	−	0.277631i
$73$	−8.21615	+	1.44873i	−0.961627	+	0.169561i	−0.632359	−	0.774676i	$-0.717913\pi$
$73$	−8.21615	+	1.44873i	−0.961627	+	0.169561i	−0.329268	+	0.944236i	$0.606802\pi$
$74$	4.42774	+	1.61157i	0.514714	+	0.187341i
$75$	−3.56065	−	6.16722i	−0.411148	−	0.712129i
$76$	2.06382	−	1.51907i	0.236737	−	0.174250i
$77$	−9.22698	−	7.45722i	−1.05151	−	0.849829i
$78$	−1.10361	+	0.194597i	−0.124960	+	0.0220338i
$79$	−2.66334	+	7.31746i	−0.299649	+	0.823279i	0.694909	+	0.719097i	$0.255444\pi$
$79$	−2.66334	+	7.31746i	−0.299649	+	0.823279i	−0.994558	+	0.104181i	$0.966778\pi$
$80$	−8.49819	−	1.49846i	−0.950126	−	0.167533i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	12.9177	+	2.27774i	1.42653	+	0.251535i
$83$	−11.6723	−	6.73898i	−1.28120	−	0.739699i	−0.304130	−	0.952631i	$-0.598366\pi$
$83$	−11.6723	−	6.73898i	−1.28120	−	0.739699i	−0.977067	+	0.212931i	$0.931699\pi$
$84$	1.20975	+	0.977712i	0.131994	+	0.106677i
$85$	3.21010	−	18.2054i	0.348185	−	1.97465i
$86$	2.96583	+	8.14856i	0.319814	+	0.878682i
$87$			2.03450i			0.218121i
$88$	−11.9421	+	6.89479i	−1.27304	+	0.734987i
$89$	2.67971	−	15.1974i	0.284048	−	1.61092i	−0.424617	−	0.905373i	$-0.639591\pi$
$89$	2.67971	−	15.1974i	0.284048	−	1.61092i	0.708666	−	0.705545i	$-0.249298\pi$
$90$	−3.88770	−	1.41501i	−0.409799	−	0.149155i
$91$	−0.478432	−	2.44877i	−0.0501533	−	0.256701i
$92$	−2.62877	+	2.20580i	−0.274068	+	0.229971i
$93$	−4.33805	+	3.64005i	−0.449835	+	0.377456i
$94$	4.79012	−	8.29672i	0.494063	−	0.855742i
$95$	−12.6336	−	8.40811i	−1.29618	−	0.862654i
$96$	2.77576	−	1.60259i	0.283300	−	0.163563i
$97$	2.13453	+	12.1055i	0.216729	+	1.22913i	0.877881	+	0.478878i	$0.158956\pi$
$97$	2.13453	+	12.1055i	0.216729	+	1.22913i	−0.661153	+	0.750251i	$0.729933\pi$
$98$	5.10862	−	6.56466i	0.516048	−	0.663131i
$99$	−4.21363	+	1.53364i	−0.423486	+	0.154136i
$100$	−0.727000	−	4.12302i	−0.0727000	−	0.412302i
$101$	−5.20319	−	14.2956i	−0.517736	−	1.42247i	−0.873008	−	0.487706i	$-0.837834\pi$
$101$	−5.20319	−	14.2956i	−0.517736	−	1.42247i	0.355271	−	0.934763i	$-0.384388\pi$
$102$	−3.15484	−	5.46434i	−0.312375	−	0.541050i
$103$	−4.35387	+	7.54112i	−0.428999	+	0.743049i	−0.996785	−	0.0801280i	$-0.974467\pi$
$103$	−4.35387	+	7.54112i	−0.428999	+	0.743049i	0.567785	+	0.823177i	$0.307800\pi$
$104$	−2.85605	−	0.503598i	−0.280059	−	0.0493819i
$105$	2.99057	−	8.71238i	0.291849	−	0.850241i
$106$	2.88326	+	4.99395i	0.280047	+	0.485056i
$107$			7.33833i			0.709423i	0.934976	+	0.354712i	$0.115421\pi$
$107$			7.33833i			0.709423i	−0.934976	+	0.354712i	$0.884579\pi$
$108$	0.552448	−	0.201075i	0.0531593	−	0.0193484i
$109$	2.47899	+	2.95435i	0.237444	+	0.282975i	0.871587	−	0.490241i	$-0.163091\pi$
$109$	2.47899	+	2.95435i	0.237444	+	0.282975i	−0.634143	+	0.773216i	$0.718647\pi$
$110$	14.2112	+	11.9246i	1.35499	+	1.13697i
$111$	2.54877	+	3.03751i	0.241919	+	0.288308i
$112$	−3.38284	−	5.61777i	−0.319648	−	0.530830i
$113$		−	1.02928i		−	0.0968265i	−0.998827	−	0.0484133i	$-0.984584\pi$
$113$		−	1.02928i		−	0.0968265i	0.998827	−	0.0484133i	$-0.0154164\pi$
$114$	−5.14793	+	0.573327i	−0.482147	+	0.0536970i
$115$	17.5994	+	10.1610i	1.64115	+	0.947521i
$116$	−0.409086	+	1.12396i	−0.0379827	+	0.104357i
$117$	−0.886175	−	0.322541i	−0.0819269	−	0.0298190i
$118$	−1.62394	−	4.46174i	−0.149496	−	0.410736i
$119$	12.0348	−	7.24695i	1.10323	−	0.664327i
$120$	−8.20179	−	6.88212i	−0.748718	−	0.628249i
$121$	9.10675			0.827886
$122$	8.00464			0.724706
$123$	8.45583	+	7.09529i	0.762437	+	0.639761i
$124$	−3.12847	+	1.13867i	−0.280945	+	0.102255i
$125$	−6.39596	+	3.69271i	−0.572072	+	0.330286i
$126$	−1.12952	−	2.93409i	−0.100626	−	0.261389i
$127$	−1.93283	+	2.30346i	−0.171511	+	0.204399i	−0.844952	−	0.534842i	$-0.820371\pi$
$127$	−1.93283	+	2.30346i	−0.171511	+	0.204399i	0.673441	+	0.739241i	$0.264816\pi$
$128$	−3.94545	+	0.695689i	−0.348732	+	0.0614908i
$129$	−1.26716	+	7.18645i	−0.111568	+	0.632731i
$130$	0.677502	+	3.84231i	0.0594209	+	0.336993i
$131$	−9.93911	−	11.8450i	−0.868384	−	1.03490i	−0.999055	−	0.0434744i	$-0.986157\pi$
$131$	−9.93911	−	11.8450i	−0.868384	−	1.03490i	0.130670	−	0.991426i	$-0.458287\pi$
$132$	−2.63619			−0.229451
$133$	−1.48731	−	11.4363i	−0.128966	−	0.991649i
$134$	−14.5016			−1.25275
$135$	−2.23791	−	2.66703i	−0.192608	−	0.229542i
$136$	−2.83547	−	16.0807i	−0.243139	−	1.37891i
$137$	2.72773	−	15.4697i	0.233045	−	1.32167i	−0.613646	−	0.789581i	$-0.710298\pi$
$137$	2.72773	−	15.4697i	0.233045	−	1.32167i	0.846691	−	0.532085i	$-0.178591\pi$
$138$	6.83088	−	1.20447i	0.581484	−	0.102531i
$139$	−6.48747	+	7.73146i	−0.550260	+	0.655774i	−0.967455	−	0.253043i	$-0.918569\pi$
$139$	−6.48747	+	7.73146i	−0.550260	+	0.655774i	0.417195	+	0.908817i	$0.363013\pi$
$140$	3.40397	−	4.21181i	0.287688	−	0.355963i
$141$	6.98191	−	4.03101i	0.587983	−	0.339472i
$142$	−1.12193	+	0.408350i	−0.0941505	+	0.0342680i
$143$	3.23936	+	2.71814i	0.270889	+	0.227302i
$144$	−2.47857			−0.206547
$145$	7.08325			0.588232
$146$	7.59457	+	6.37260i	0.628531	+	0.527400i
$147$	6.48524	−	2.63470i	0.534894	−	0.217306i
$148$	0.797299	+	2.19056i	0.0655375	+	0.180063i
$149$	−1.19010	−	0.433161i	−0.0974968	−	0.0354859i	0.292811	−	0.956170i	$-0.405409\pi$
$149$	−1.19010	−	0.433161i	−0.0974968	−	0.0354859i	−0.390308	+	0.920684i	$0.627631\pi$
$150$	−2.89430	+	7.95201i	−0.236318	+	0.649279i
$151$	−1.98920	−	1.14846i	−0.161879	−	0.0934606i	0.416872	−	0.908965i	$-0.363126\pi$
$151$	−1.98920	−	1.14846i	−0.161879	−	0.0934606i	−0.578751	+	0.815504i	$0.696460\pi$
$152$	−13.0264	−	3.16227i	−1.05658	−	0.256494i
$153$		−	5.30975i		−	0.429268i
$154$	0.259565	+	14.0954i	0.0209164	+	1.13584i
$155$	12.6731	+	15.1032i	1.01793	+	1.21312i
$156$	−0.424711	−	0.356375i	−0.0340041	−	0.0285328i
$157$	−2.91238	−	3.47084i	−0.232433	−	0.277003i	0.637203	−	0.770696i	$-0.280091\pi$
$157$	−2.91238	−	3.47084i	−0.232433	−	0.277003i	−0.869636	+	0.493693i	$0.835647\pi$
$158$	8.69546	−	3.16489i	0.691774	−	0.251785i
$159$			4.85268i			0.384842i
$160$	−5.57951	−	9.66400i	−0.441099	−	0.764006i
$161$	2.96128	+	15.1568i	0.233381	+	1.19452i
$162$	−1.17026	−	0.206349i	−0.0919446	−	0.0162123i
$163$	−8.79433	+	15.2322i	−0.688825	+	1.19308i	0.283393	+	0.959004i	$0.408540\pi$
$163$	−8.79433	+	15.2322i	−0.688825	+	1.19308i	−0.972218	+	0.234076i	$0.924793\pi$
$164$	3.24473	+	5.62003i	0.253370	+	0.438851i
$165$	5.33946	+	14.6700i	0.415676	+	1.14206i
$166$	2.78117	+	15.7728i	0.215860	+	1.22420i
$167$	22.7036	−	8.26343i	1.75686	−	0.639444i	0.756955	−	0.653467i	$-0.226686\pi$
$167$	22.7036	−	8.26343i	1.75686	−	0.639444i	0.999902	+	0.0140230i	$0.00446380\pi$
$168$	−0.149804	−	8.13496i	−0.0115576	−	0.627626i
$169$	−2.10299	−	11.9267i	−0.161769	−	0.917436i
$170$	−19.0244	+	10.9838i	−1.45911	+	0.842416i
$171$	−3.99296	−	1.74823i	−0.305349	−	0.133690i
$172$	−2.14505	+	3.71534i	−0.163559	+	0.283292i
$173$	−13.7781	+	11.5612i	−1.04753	+	0.878983i	−0.992832	−	0.119520i	$-0.961864\pi$
$173$	−13.7781	+	11.5612i	−1.04753	+	0.878983i	−0.0546989	+	0.998503i	$0.517420\pi$
$174$	1.85201	−	1.55402i	0.140401	−	0.117810i
$175$	−17.8206	−	6.11699i	−1.34711	−	0.462401i
$176$	10.4438	+	3.80122i	0.787228	+	0.286528i
$177$	0.693835	−	3.93493i	0.0521518	−	0.295768i
$178$	−15.8811	+	9.16894i	−1.19034	+	0.687241i
$179$			10.8917i			0.814085i	0.913409	+	0.407042i	$0.133440\pi$
$179$			10.8917i			0.814085i	−0.913409	+	0.407042i	$0.866560\pi$
$180$	−0.700054	−	1.92338i	−0.0521789	−	0.143360i
$181$	−1.23468	+	7.00224i	−0.0917733	+	0.520472i	0.903915	+	0.427712i	$0.140680\pi$
$181$	−1.23468	+	7.00224i	−0.0917733	+	0.520472i	−0.995688	+	0.0927604i	$0.970431\pi$
$182$	−1.86368	+	2.30598i	−0.138145	+	0.170930i
$183$	5.83365	+	3.36806i	0.431236	+	0.248974i
$184$	17.6777	+	3.11705i	1.30321	+	0.229792i
$185$	10.5753	−	8.87373i	0.777511	−	0.652409i
$186$	6.62711	+	1.16854i	0.485923	+	0.0856814i
$187$	−8.14324	+	22.3734i	−0.595492	+	1.63610i
$188$	4.66767	−	0.823037i	0.340425	−	0.0600261i
$189$	0.411379	−	2.61357i	0.0299234	−	0.190110i
$190$	1.99607	+	17.9228i	0.144810	+	1.30026i
$191$	−0.304223	−	0.526929i	−0.0220128	−	0.0381272i	0.854809	−	0.518942i	$-0.173674\pi$
$191$	−0.304223	−	0.526929i	−0.0220128	−	0.0381272i	−0.876822	+	0.480815i	$0.840341\pi$
$192$	−8.23725	−	2.99811i	−0.594472	−	0.216370i
$193$	20.8677	−	3.67953i	1.50209	−	0.264859i	0.638722	−	0.769438i	$-0.279463\pi$
$193$	20.8677	−	3.67953i	1.50209	−	0.264859i	0.863365	+	0.504579i	$0.168352\pi$
$194$	9.38927	−	11.1897i	0.674110	−	0.803373i
$195$	−1.12295	+	3.08528i	−0.0804160	+	0.220941i
$196$	4.11253	−	0.151515i	0.293752	−	0.0108225i
$197$	−0.402272	+	0.696756i	−0.0286607	+	0.0496418i	−0.880000	−	0.474974i	$-0.842458\pi$
$197$	−0.402272	+	0.696756i	−0.0286607	+	0.0496418i	0.851339	+	0.524616i	$0.175791\pi$
$198$	4.61460	+	2.66424i	0.327945	+	0.189339i
$199$	−0.722648	+	0.861219i	−0.0512272	+	0.0610502i	−0.791050	−	0.611752i	$-0.790465\pi$
$199$	−0.722648	+	0.861219i	−0.0512272	+	0.0610502i	0.739822	+	0.672802i	$0.234909\pi$
$200$	−14.0769	+	16.7762i	−0.995386	+	1.18626i
$201$	−10.5685	−	6.10174i	−0.745446	−	0.430384i
$202$	−9.03899	+	15.6560i	−0.635981	+	1.10155i
$203$	3.53532	+	4.05905i	0.248131	+	0.284889i
$204$	1.06766	−	2.93336i	0.0747509	−	0.205376i
$205$	24.7027	−	29.4395i	1.72531	−	2.05615i
$206$	10.1903	−	1.79683i	0.709995	−	0.125191i
$207$	5.48503	+	1.99639i	0.381236	+	0.138759i
$208$	1.16870	+	2.02425i	0.0810350	+	0.140357i
$209$	14.1437	+	13.4901i	0.978341	+	0.933132i
$210$	−10.2152	+	3.93250i	−0.704917	+	0.271368i
$211$	−1.21859	+	0.214870i	−0.0838909	+	0.0147922i	−0.215436	−	0.976518i	$-0.569117\pi$
$211$	−1.21859	+	0.214870i	−0.0838909	+	0.0147922i	0.131545	+	0.991310i	$0.458006\pi$
$212$	−0.975750	+	2.68085i	−0.0670148	+	0.184122i
$213$	−0.989464	−	0.174469i	−0.0677970	−	0.0119544i
$214$	6.68011	−	5.60528i	0.456643	−	0.383169i
$215$	25.0201	+	4.41172i	1.70636	+	0.300877i
$216$	−2.66324	−	1.53762i	−0.181211	−	0.104622i
$217$	−2.32961	+	14.8005i	−0.158144	+	1.00472i
$218$	0.795811	−	4.51327i	0.0538991	−	0.305677i
$219$	2.85344	+	7.83976i	0.192817	+	0.529762i
$220$			9.17806i			0.618785i
$221$	−4.33649	+	2.50368i	−0.291704	+	0.168415i
$222$	0.818213	−	4.64032i	0.0549149	−	0.311438i
$223$	−8.38537	−	3.05203i	−0.561526	−	0.204379i	0.0456341	−	0.998958i	$-0.485469\pi$
$223$	−8.38537	−	3.05203i	−0.561526	−	0.204379i	−0.607160	+	0.794579i	$0.707691\pi$
$224$	2.75316	−	8.02074i	0.183953	−	0.535908i
$225$	−5.45523	+	4.57748i	−0.363682	+	0.305165i
$226$	−0.936957	+	0.786201i	−0.0623255	+	0.0522973i
$227$	0.298468	−	0.516961i	0.0198100	−	0.0343119i	−0.855950	−	0.517058i	$-0.827027\pi$
$227$	0.298468	−	0.516961i	0.0198100	−	0.0343119i	0.875760	+	0.482746i	$0.160361\pi$
$228$	−1.85438	−	1.76869i	−0.122809	−	0.117134i
$229$	4.28245	−	2.47247i	0.282992	−	0.163386i	−0.351785	−	0.936081i	$-0.614425\pi$
$229$	4.28245	−	2.47247i	0.282992	−	0.163386i	0.634777	+	0.772695i	$0.281092\pi$
$230$	−4.19344	−	23.7822i	−0.276507	−	1.56815i
$231$	−5.74167	+	10.3817i	−0.377774	+	0.683068i
$232$	5.87928	−	2.13988i	0.385994	−	0.140490i
$233$	0.0820665	+	0.465422i	0.00537636	+	0.0304908i	0.987378	−	0.158382i	$-0.0506277\pi$
$233$	0.0820665	+	0.465422i	0.00537636	+	0.0304908i	−0.982002	+	0.188873i	$0.939517\pi$
$234$	0.383281	+	1.05306i	0.0250559	+	0.0688405i
$235$	−14.0342	−	24.3080i	−0.915491	−	1.58568i
$236$	1.17452	−	2.03433i	0.0764549	−	0.132424i
$237$	7.66878	+	1.35221i	0.498141	+	0.0878356i
$238$	−15.7895	−	5.41983i	−1.02348	−	0.351315i
$239$	−7.09199	−	12.2837i	−0.458743	−	0.794565i	0.540152	−	0.841567i	$-0.318367\pi$
$239$	−7.09199	−	12.2837i	−0.458743	−	0.794565i	−0.998895	+	0.0470019i	$0.985033\pi$
$240$			8.62929i			0.557018i
$241$	−0.979097	+	0.356362i	−0.0630692	+	0.0229553i	−0.373362	−	0.927686i	$-0.621795\pi$
$241$	−0.979097	+	0.356362i	−0.0630692	+	0.0229553i	0.310293	+	0.950641i	$0.399573\pi$
$242$	−6.95606	−	8.28991i	−0.447152	−	0.532895i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	2.54556	+	3.03367i	0.162962	+	0.194211i
$245$	−9.17286	−	22.5788i	−0.586033	−	1.44251i
$246$		−	13.1170i		−	0.836310i
$247$	0.454992	+	4.08539i	0.0289504	+	0.259947i
$248$	15.0817	+	8.70744i	0.957691	+	0.552923i
$249$	−4.60973	+	12.6651i	−0.292130	+	0.802621i
$250$	8.24695	+	3.00165i	0.521583	+	0.189841i
$251$	−1.21355	−	3.33419i	−0.0765983	−	0.210452i	0.895483	−	0.445095i	$-0.146830\pi$
$251$	−1.21355	−	3.33419i	−0.0765983	−	0.210452i	−0.972082	+	0.234643i	$0.924608\pi$
$252$	0.752789	−	1.36114i	0.0474212	−	0.0857441i
$253$	−20.0502	−	16.8241i	−1.26054	−	1.05772i
$254$	3.57322			0.224203
$255$	−18.4863			−1.15765
$256$	−9.78317	−	8.20906i	−0.611448	−	0.513066i
$257$	7.21260	−	2.62517i	0.449909	−	0.163754i	−0.107121	−	0.994246i	$-0.534163\pi$
$257$	7.21260	−	2.62517i	0.449909	−	0.163754i	0.557030	+	0.830492i	$0.311941\pi$
$258$	7.50975	−	4.33576i	0.467537	−	0.269933i
$259$	10.3633	+	1.63120i	0.643945	+	0.101358i
$260$	−1.24074	+	1.47866i	−0.0769475	+	0.0917024i
$261$	2.00359	−	0.353287i	0.124019	−	0.0218679i
$262$	−3.19068	+	18.0952i	−0.197121	+	1.11793i
$263$	−3.94969	−	22.3998i	−0.243548	−	1.38123i	−0.823841	−	0.566821i	$-0.808173\pi$
$263$	−3.94969	−	22.3998i	−0.243548	−	1.38123i	0.580293	−	0.814408i	$-0.302938\pi$
$264$	8.86377	+	10.5634i	0.545528	+	0.650134i
$265$	16.8949			1.03785
$266$	−9.27441	+	10.0893i	−0.568650	+	0.618616i
$267$	−15.4318			−0.944411
$268$	−4.61165	−	5.49596i	−0.281702	−	0.335719i
$269$	3.30397	+	18.7377i	0.201447	+	1.14246i	0.902934	+	0.429778i	$0.141408\pi$
$269$	3.30397	+	18.7377i	0.201447	+	1.14246i	−0.701488	+	0.712681i	$0.747481\pi$
$270$	−0.718418	+	4.07435i	−0.0437215	+	0.247957i
$271$	14.1597	−	2.49673i	0.860139	−	0.151666i	0.273855	−	0.961771i	$-0.411701\pi$
$271$	14.1597	−	2.49673i	0.860139	−	0.151666i	0.586285	+	0.810105i	$0.300590\pi$
$272$	−8.45945	+	10.0816i	−0.512930	+	0.611286i
$273$	−2.32849	+	0.896388i	−0.140927	+	0.0542519i
$274$	−16.1657	+	9.33325i	−0.976603	+	0.563842i
$275$	30.0065	−	10.9215i	1.80946	−	0.658590i
$276$	2.62877	+	2.20580i	0.158233	+	0.132774i
$277$	0.283984			0.0170629			0.00853147	−	0.999964i	$-0.497284\pi$
$277$	0.283984			0.0170629			0.00853147	+	0.999964i	$0.497284\pi$
$278$	11.9933			0.719313
$279$	4.33805	+	3.64005i	0.259712	+	0.217924i
$280$	−28.3224	+	0.521553i	−1.69259	+	0.0311688i
$281$	9.49394	+	26.0844i	0.566361	+	1.55606i	0.810142	+	0.586234i	$0.199390\pi$
$281$	9.49394	+	26.0844i	0.566361	+	1.55606i	−0.243781	+	0.969830i	$0.578388\pi$
$282$	−9.00247	−	3.27663i	−0.536089	−	0.195121i
$283$	−9.01396	+	24.7656i	−0.535824	+	1.47216i	0.316216	+	0.948687i	$0.397588\pi$
$283$	−9.01396	+	24.7656i	−0.535824	+	1.47216i	−0.852040	+	0.523477i	$0.824635\pi$
$284$	−0.511546	−	0.295341i	−0.0303547	−	0.0175253i
$285$	−6.08656	+	13.9017i	−0.360537	+	0.823468i
$286$		−	5.02501i		−	0.297135i
$287$	29.1997	−	0.537708i	1.72360	−	0.0317399i
$288$	−2.06025	−	2.45531i	−0.121401	−	0.144680i
$289$	−8.57471	−	7.19503i	−0.504394	−	0.423237i
$290$	−5.41044	−	6.44791i	−0.317712	−	0.378634i
$291$	11.5510	−	4.20420i	0.677129	−	0.246455i
$292$			4.90481i			0.287032i
$293$	−6.33251	−	10.9682i	−0.369949	−	0.640770i	0.619608	−	0.784911i	$-0.287291\pi$
$293$	−6.33251	−	10.9682i	−0.369949	−	0.640770i	−0.989557	+	0.144141i	$0.953958\pi$
$294$	−7.35203	−	3.89107i	−0.428779	−	0.226932i
$295$	−13.6997	−	2.41563i	−0.797628	−	0.140643i
$296$	6.09697	−	10.5603i	0.354379	−	0.613803i
$297$	2.24203	+	3.88331i	0.130096	+	0.225332i
$298$	0.514732	+	1.41422i	0.0298177	+	0.0819233i
$299$	−0.955866	−	5.42099i	−0.0552792	−	0.313504i
$300$	−3.93414	+	1.43191i	−0.227138	+	0.0826714i
$301$	9.95965	+	16.5397i	0.574064	+	0.953331i
$302$	0.473969	+	2.68801i	0.0272738	+	0.154678i
$303$	−13.1749	+	7.60655i	−0.756880	+	0.436985i
$304$	4.79613	+	9.68089i	0.275077	+	0.555237i
$305$	11.7261	−	20.3102i	0.671435	−	1.16296i
$306$	−4.83349	+	4.05578i	−0.276312	+	0.231853i
$307$	−1.13867	+	0.955458i	−0.0649874	+	0.0545309i	−0.674703	−	0.738090i	$-0.735728\pi$
$307$	−1.13867	+	0.955458i	−0.0649874	+	0.0545309i	0.609715	+	0.792620i	$0.291284\pi$
$308$	−5.25948	+	4.58086i	−0.299687	+	0.261019i
$309$	8.18260	+	2.97822i	0.465492	+	0.169425i
$310$	4.06834	−	23.0727i	0.231066	−	1.31044i
$311$	1.01730	−	0.587339i	0.0576859	−	0.0333049i	−0.470880	−	0.882197i	$-0.656063\pi$
$311$	1.01730	−	0.587339i	0.0576859	−	0.0333049i	0.528566	+	0.848892i	$0.322730\pi$
$312$			2.90011i			0.164186i
$313$	−6.36266	−	17.4813i	−0.359639	−	0.988099i	−0.979155	−	0.203115i	$-0.934893\pi$
$313$	−6.36266	−	17.4813i	−0.359639	−	0.988099i	0.619516	−	0.784984i	$-0.287329\pi$
$314$	−0.934939	+	5.30230i	−0.0527616	+	0.299226i
$315$	−9.09933	−	1.43224i	−0.512689	−	0.0806978i
$316$	3.96470	+	2.28902i	0.223032	+	0.128768i
$317$	−20.0347	−	3.53267i	−1.12526	−	0.198414i	−0.420113	−	0.907472i	$-0.638010\pi$
$317$	−20.0347	−	3.53267i	−1.12526	−	0.198414i	−0.705151	+	0.709058i	$0.749121\pi$
$318$	4.41741	−	3.70665i	0.247716	−	0.207858i
$319$	−8.98422	−	1.58416i	−0.503020	−	0.0886959i
$320$	−10.4381	+	28.6785i	−0.583509	+	1.60318i
$321$	7.22685	−	1.27429i	0.403363	−	0.0711238i
$322$	11.5354	−	14.2730i	0.642841	−	0.795401i
$323$	−20.7391	+	10.2746i	−1.15395	+	0.571694i
$324$	−0.293951	−	0.509139i	−0.0163306	−	0.0282855i
$325$	6.31071	+	2.29691i	0.350055	+	0.127410i
$326$	20.5834	−	3.62940i	1.14001	−	0.201014i
$327$	2.47899	−	2.95435i	0.137089	−	0.163376i
$328$	11.6101	−	31.8984i	0.641058	−	1.76129i
$329$	6.92504	−	20.1746i	0.381790	−	1.11226i
$330$	9.27572	−	16.0660i	0.510612	−	0.884405i
$331$	−5.82822	−	3.36492i	−0.320348	−	0.184953i	0.331200	−	0.943561i	$-0.392547\pi$
$331$	−5.82822	−	3.36492i	−0.320348	−	0.184953i	−0.651548	+	0.758608i	$0.725880\pi$
$332$	−5.09328	+	6.06993i	−0.279530	+	0.333131i
$333$	2.54877	−	3.03751i	0.139672	−	0.166455i
$334$	−24.8640	−	14.3553i	−1.36050	−	0.785485i
$335$	−21.2436	+	36.7950i	−1.16066	+	2.01033i
$336$	−4.94500	+	4.30696i	−0.269772	+	0.234964i
$337$	8.35118	−	22.9447i	0.454918	−	1.24988i	−0.474307	−	0.880360i	$-0.657301\pi$
$337$	8.35118	−	22.9447i	0.454918	−	1.24988i	0.929224	−	0.369516i	$-0.120477\pi$
$338$	−9.25055	+	11.0244i	−0.503164	+	0.599647i
$339$	−1.01364	+	0.178733i	−0.0550535	+	0.00970742i
$340$	−10.2127	−	3.71711i	−0.553861	−	0.201589i
$341$	−12.6964	−	21.9908i	−0.687550	−	1.19087i
$342$	1.45854	+	4.97016i	0.0788691	+	0.268756i
$343$	8.36049	−	16.5258i	0.451424	−	0.892310i
$344$	22.1001	−	3.89685i	1.19156	−	0.210104i
$345$	6.95055	−	19.0965i	0.374205	−	1.02812i
$346$	21.0484	+	3.71141i	1.13157	+	0.199526i
$347$	−17.8819	+	15.0047i	−0.959950	+	0.805493i	−0.980945	−	0.194286i	$-0.937761\pi$
$347$	−17.8819	+	15.0047i	−0.959950	+	0.805493i	0.0209954	+	0.999780i	$0.493316\pi$
$348$	1.17792	+	0.207699i	0.0631430	+	0.0111338i
$349$	−12.6620	−	7.31042i	−0.677782	−	0.391318i	0.121237	−	0.992624i	$-0.461314\pi$
$349$	−12.6620	−	7.31042i	−0.677782	−	0.391318i	−0.799019	+	0.601306i	$0.794647\pi$
$350$	8.04365	+	20.8945i	0.429951	+	1.11686i
$351$	−0.163759	+	0.928721i	−0.00874078	+	0.0495715i
$352$	4.91558	+	13.5054i	0.262001	+	0.719842i
$353$		−	19.3777i		−	1.03137i	−0.856777	−	0.515686i	$-0.827537\pi$
$353$		−	19.3777i		−	1.03137i	0.856777	−	0.515686i	$-0.172463\pi$
$354$	−4.11196	+	2.37404i	−0.218548	+	0.126179i
$355$	−0.607426	+	3.44488i	−0.0322388	+	0.182835i
$356$	−8.52527	−	3.10294i	−0.451838	−	0.164456i
$357$	−9.22667	−	10.5935i	−0.488327	−	0.560669i
$358$	9.91477	−	8.31948i	0.524012	−	0.439698i
$359$	−19.0622	+	15.9950i	−1.00606	+	0.844186i	−0.987813	−	0.155647i	$-0.950254\pi$
$359$	−19.0622	+	15.9950i	−1.00606	+	0.844186i	−0.0182493	+	0.999833i	$0.505809\pi$
$360$	−5.35334	+	9.27226i	−0.282146	+	0.488691i
$361$	0.898249	+	18.9788i	0.0472762	+	0.998882i
$362$	7.31726	−	4.22462i	0.384586	−	0.222041i
$363$	−1.58137	−	8.96840i	−0.0830004	−	0.470719i
$364$	−1.46661	+	0.0270074i	−0.0768712	+	0.00141557i
$365$	27.2946	−	9.93443i	1.42867	−	0.519992i
$366$	−1.38999	−	7.88303i	−0.0726560	−	0.412053i
$367$	7.21016	+	19.8097i	0.376367	+	1.03406i	0.972850	+	0.231435i	$0.0743419\pi$
$367$	7.21016	+	19.8097i	0.376367	+	1.03406i	−0.596483	+	0.802625i	$0.703436\pi$
$368$	−7.23375	−	12.5292i	−0.377085	−	0.653131i
$369$	5.51915	−	9.55946i	0.287316	−	0.497645i
$370$	−16.1556	−	2.84866i	−0.839888	−	0.148095i
$371$	8.43242	+	9.68161i	0.437789	+	0.502644i
$372$	1.66462	+	2.88321i	0.0863066	+	0.149487i
$373$		−	29.0997i		−	1.50673i	−0.657604	−	0.753364i	$-0.728430\pi$
$373$		−	29.0997i		−	1.50673i	0.657604	−	0.753364i	$-0.271570\pi$
$374$	26.5866	−	9.67675i	1.37476	−	0.500373i
$375$	4.74726	+	5.65756i	0.245147	+	0.292155i
$376$	−18.9923	−	15.9364i	−0.979454	−	0.821859i
$377$	−1.23327	−	1.46976i	−0.0635168	−	0.0756964i
$378$	−2.69337	+	1.62186i	−0.138532	+	0.0834195i
$379$			10.0355i			0.515487i	0.966213	+	0.257743i	$0.0829789\pi$
$379$			10.0355i			0.515487i	−0.966213	+	0.257743i	$0.917021\pi$
$380$	−6.15779	+	6.45613i	−0.315888	+	0.331193i
$381$	2.60410	+	1.50348i	0.133412	+	0.0770255i
$382$	−0.247289	+	0.679422i	−0.0126524	+	0.0347622i
$383$	5.50129	+	2.00230i	0.281103	+	0.102313i	0.478724	−	0.877965i	$-0.341099\pi$
$383$	5.50129	+	2.00230i	0.281103	+	0.102313i	−0.197621	+	0.980278i	$0.563322\pi$
$384$	1.37024	+	3.76470i	0.0699247	+	0.192117i
$385$	36.1447	+	19.9900i	1.84210	+	1.01879i
$386$	−19.2890	−	16.1854i	−0.981782	−	0.823813i
$387$	7.29731			0.370943
$388$	7.22666			0.366878
$389$	−8.43097	−	7.07442i	−0.427467	−	0.358687i	0.403528	−	0.914967i	$-0.367784\pi$
$389$	−8.43097	−	7.07442i	−0.427467	−	0.358687i	−0.830995	+	0.556280i	$0.812228\pi$
$390$	3.66629	−	1.33442i	0.185650	−	0.0675709i
$391$	26.8410	−	15.4966i	1.35741	−	0.783699i
$392$	−14.4349	−	15.9698i	−0.729071	−	0.806598i
$393$	−9.93911	+	11.8450i	−0.501362	+	0.597500i
$394$	0.941530	−	0.166017i	0.0474336	−	0.00836382i
$395$	4.70781	−	26.6993i	0.236876	−	1.34339i
$396$	0.457769	+	2.59614i	0.0230038	+	0.130461i
$397$	−19.2216	−	22.9074i	−0.964703	−	1.14969i	−0.988690	−	0.149975i	$-0.952081\pi$
$397$	−19.2216	−	22.9074i	−0.964703	−	1.14969i	0.0239871	−	0.999712i	$-0.492364\pi$
$398$	1.33595			0.0669654
$399$	−11.0042	+	3.45060i	−0.550901	+	0.172746i
$400$	17.6506			0.882530
$401$	−2.82800	−	3.37028i	−0.141223	−	0.168304i	0.690797	−	0.723049i	$-0.257260\pi$
$401$	−2.82800	−	3.37028i	−0.141223	−	0.168304i	−0.832020	+	0.554746i	$0.812816\pi$
$402$	2.51818	+	14.2813i	0.125595	+	0.712286i
$403$	0.927351	−	5.25927i	0.0461947	−	0.261983i
$404$	−8.80794	+	1.55308i	−0.438212	+	0.0772685i
$405$	−2.23791	+	2.66703i	−0.111202	+	0.132526i
$406$	0.994564	−	6.31866i	0.0493594	−	0.313590i
$407$	−15.3980	+	8.89006i	−0.763253	+	0.440664i
$408$	−15.3441	+	5.58478i	−0.759644	+	0.276488i
$409$	−8.80729	−	7.39020i	−0.435493	−	0.365422i	0.398527	−	0.917157i	$-0.369522\pi$
$409$	−8.80729	−	7.39020i	−0.435493	−	0.365422i	−0.834019	+	0.551735i	$0.813966\pi$
$410$	−45.6677			−2.25537
$411$	−15.7083			−0.774836
$412$	3.92161	+	3.29062i	0.193204	+	0.162117i
$413$	−5.45339	−	9.05628i	−0.268344	−	0.445630i
$414$	−2.37234	−	6.51795i	−0.116594	−	0.320340i
$415$	44.0945	+	16.0491i	2.16451	+	0.787819i
$416$	−1.03380	+	2.84035i	−0.0506863	+	0.139259i
$417$	8.74054	+	5.04636i	0.428026	+	0.247121i
$418$	1.47665	−	23.1793i	0.0722253	−	1.13374i
$419$		−	26.6341i		−	1.30116i	−0.759438	−	0.650580i	$-0.774526\pi$
$419$		−	26.6341i		−	1.30116i	0.759438	−	0.650580i	$-0.225474\pi$
$420$	−4.73891	−	2.62088i	−0.231235	−	0.127886i
$421$	−0.698017	−	0.831864i	−0.0340193	−	0.0405426i	0.748767	−	0.662834i	$-0.230646\pi$
$421$	−0.698017	−	0.831864i	−0.0340193	−	0.0405426i	−0.782786	+	0.622291i	$0.786202\pi$
$422$	1.12640	+	0.945158i	0.0548321	+	0.0460096i
$423$	−5.18216	−	6.17586i	−0.251965	−	0.300281i
$424$	14.0232	−	5.10403i	0.681027	−	0.247874i
$425$			37.8123i			1.83417i
$426$	0.596968	+	1.03398i	0.0289232	+	0.0500964i
$427$	17.4914	−	3.41740i	0.846467	−	0.165380i
$428$	4.24868	+	0.749157i	0.205368	+	0.0362119i
$429$	2.11434	−	3.66214i	0.102081	−	0.176810i
$430$	−15.0952	−	26.1457i	−0.727956	−	1.26086i
$431$	8.98964	+	24.6988i	0.433016	+	1.18970i	0.943952	+	0.330082i	$0.107076\pi$
$431$	8.98964	+	24.6988i	0.433016	+	1.18970i	−0.510937	+	0.859618i	$0.670701\pi$
$432$	0.430398	+	2.44091i	0.0207076	+	0.117438i
$433$	−4.47632	+	1.62925i	−0.215118	+	0.0782967i	−0.447331	−	0.894368i	$-0.647626\pi$
$433$	−4.47632	+	1.62925i	−0.215118	+	0.0782967i	0.232213	+	0.972665i	$0.425403\pi$
$434$	15.2523	−	9.18446i	0.732136	−	0.440868i
$435$	−1.22999	−	6.97564i	−0.0589737	−	0.334456i
$436$	1.96356	−	1.13366i	0.0940373	−	0.0542925i
$437$	−2.81620	−	25.2868i	−0.134717	−	1.20963i
$438$	4.95700	−	8.58578i	0.236855	−	0.410244i
$439$	−16.7785	+	14.0789i	−0.800795	+	0.671947i	−0.948392	−	0.317100i	$-0.897291\pi$
$439$	−16.7785	+	14.0789i	−0.800795	+	0.671947i	0.147596	+	0.989048i	$0.452846\pi$
$440$	36.7773	−	30.8598i	1.75329	−	1.47118i
$441$	−3.72082	−	5.92921i	−0.177182	−	0.282343i
$442$	5.59147	+	2.03513i	0.265959	+	0.0968013i
$443$	−2.72358	+	15.4462i	−0.129401	+	0.733871i	0.849195	+	0.528080i	$0.177088\pi$
$443$	−2.72358	+	15.4462i	−0.129401	+	0.733871i	−0.978596	+	0.205791i	$0.934023\pi$
$444$	2.01883	−	1.16557i	0.0958095	−	0.0553156i
$445$			53.7268i			2.54690i
$446$	3.62677	+	9.96448i	0.171733	+	0.471832i
$447$	−0.219922	+	1.24724i	−0.0104019	+	0.0589923i
$448$	−21.6440	+	8.33218i	−1.02258	+	0.393658i
$449$	28.4806	+	16.4433i	1.34408	+	0.776007i	0.987404	−	0.158220i	$-0.0505756\pi$
$449$	28.4806	+	16.4433i	1.34408	+	0.776007i	0.356679	+	0.934227i	$0.383909\pi$
$450$	8.33379	+	1.46947i	0.392859	+	0.0692716i
$451$	−37.9164	+	31.8157i	−1.78541	+	1.49814i
$452$	−0.595923	−	0.105077i	−0.0280299	−	0.00494242i
$453$	−0.785595	+	2.15841i	−0.0369105	+	0.101411i
$454$	−0.698572	+	0.123177i	−0.0327856	+	0.00578099i
$455$	3.12083	+	8.10679i	0.146307	+	0.380052i
$456$	−0.852225	+	13.3776i	−0.0399091	+	0.626463i
$457$	6.20139	+	10.7411i	0.290089	+	0.502448i	0.973830	−	0.227276i	$-0.0729818\pi$
$457$	6.20139	+	10.7411i	0.290089	+	0.502448i	−0.683742	+	0.729724i	$0.739649\pi$
$458$	−5.52179	−	2.00977i	−0.258016	−	0.0939102i
$459$	−5.22909	+	0.922029i	−0.244073	+	0.0430366i
$460$	7.67963	−	9.15223i	0.358065	−	0.426725i
$461$	−0.703017	+	1.93152i	−0.0327428	+	0.0899600i	−0.954987	−	0.296648i	$-0.904131\pi$
$461$	−0.703017	+	1.93152i	−0.0327428	+	0.0899600i	0.922244	+	0.386608i	$0.126353\pi$
$462$	13.8362	−	2.70327i	0.643720	−	0.125767i
$463$	11.2957	−	19.5648i	0.524958	−	0.909253i	−0.474620	−	0.880191i	$-0.657414\pi$
$463$	11.2957	−	19.5648i	0.524958	−	0.909253i	0.999578	−	0.0290625i	$-0.00925218\pi$
$464$	−4.36706	−	2.52132i	−0.202736	−	0.117049i
$465$	12.6731	−	15.1032i	0.587700	−	0.700394i
$466$	0.360990	−	0.430212i	0.0167226	−	0.0199292i
$467$	19.3142	+	11.1511i	0.893755	+	0.516010i	0.875169	−	0.483818i	$-0.160750\pi$
$467$	19.3142	+	11.1511i	0.893755	+	0.516010i	0.0185859	+	0.999827i	$0.494084\pi$
$468$	−0.277210	+	0.480142i	−0.0128140	+	0.0221946i
$469$	−31.6882	+	6.19113i	−1.46323	+	0.285880i
$470$	−11.4078	+	31.3427i	−0.526203	+	1.44573i
$471$	−2.91238	+	3.47084i	−0.134195	+	0.159928i
$472$	−12.1009	+	2.13371i	−0.556989	+	0.0982121i
$473$	−30.7482	−	11.1914i	−1.41380	−	0.514582i
$474$	−4.62676	−	8.01378i	−0.212514	−	0.368085i
$475$	28.4350	+	12.4496i	1.30469	+	0.571228i
$476$	−2.96717	−	7.70762i	−0.136000	−	0.353278i
$477$	4.77895	−	0.842659i	0.218813	−	0.0385827i
$478$	−5.76477	+	15.8386i	−0.263674	+	0.724440i
$479$	2.70186	+	0.476411i	0.123451	+	0.0217678i	0.235032	−	0.971988i	$-0.424480\pi$
$479$	2.70186	+	0.476411i	0.123451	+	0.0217678i	−0.111581	+	0.993755i	$0.535591\pi$
$480$	−8.54831	+	7.17289i	−0.390175	+	0.327396i
$481$	−3.68255	−	0.649334i	−0.167910	−	0.0296071i
$482$	1.07227	+	0.619073i	0.0488404	+	0.0281980i
$483$	14.4123	−	5.54824i	0.655783	−	0.252454i
$484$	0.929692	−	5.27254i	0.0422587	−	0.239661i
$485$	−14.6372	−	40.2154i	−0.664641	−	1.82609i
$486$			1.18832i			0.0539032i
$487$	0.186950	−	0.107935i	0.00847150	−	0.00489102i	−0.495758	−	0.868461i	$-0.665110\pi$
$487$	0.186950	−	0.107935i	0.00847150	−	0.00489102i	0.504230	+	0.863570i	$0.331776\pi$
$488$	3.59716	−	20.4005i	0.162836	−	0.923488i
$489$	16.5279	+	6.01568i	0.747419	+	0.272038i
$490$	−13.5470	+	25.5966i	−0.611991	+	1.15634i
$491$	1.17125	−	0.982798i	0.0528579	−	0.0443531i	−0.615976	−	0.787765i	$-0.711238\pi$
$491$	1.17125	−	0.982798i	0.0528579	−	0.0443531i	0.668834	+	0.743412i	$0.266794\pi$
$492$	4.97121	−	4.17134i	0.224119	−	0.188058i
$493$	5.40135	−	9.35541i	0.243265	−	0.421347i
$494$	3.37141	−	3.53475i	0.151687	−	0.159036i
$495$	13.5200	−	7.80576i	0.607678	−	0.350843i
$496$	−2.43731	−	13.8227i	−0.109438	−	0.620657i
$497$	−2.27726	+	1.37129i	−0.102149	+	0.0615108i
$498$	15.0502	−	5.47783i	0.674416	−	0.245467i
$499$	−2.81149	−	15.9448i	−0.125860	−	0.713786i	−0.980794	−	0.195049i	$-0.937513\pi$
$499$	−2.81149	−	15.9448i	−0.125860	−	0.713786i	0.854934	−	0.518737i	$-0.173598\pi$
$500$	1.48502	+	4.08006i	0.0664121	+	0.182466i
$501$	−12.0803	−	20.9237i	−0.539709	−	0.934804i
$502$	−2.10817	+	3.65147i	−0.0940924	+	0.162973i
$503$	−1.03321	−	0.182182i	−0.0460684	−	0.00812309i	0.150566	−	0.988600i	$-0.451890\pi$
$503$	−1.03321	−	0.182182i	−0.0460684	−	0.00812309i	−0.196635	+	0.980477i	$0.563001\pi$
$504$	−7.98536	+	1.56015i	−0.355696	+	0.0694946i
$505$	26.4827	+	45.8694i	1.17846	+	2.04116i
$506$			31.1026i			1.38268i
$507$	−11.3803	+	4.14209i	−0.505417	+	0.183957i
$508$	1.13632	+	1.35421i	0.0504159	+	0.0600834i
$509$	11.9423	+	10.0208i	0.529332	+	0.444163i	0.867871	−	0.496790i	$-0.165488\pi$
$509$	11.9423	+	10.0208i	0.529332	+	0.444163i	−0.338538	+	0.940953i	$0.609933\pi$
$510$	14.1205	+	16.8281i	0.625264	+	0.745161i
$511$	19.3159	+	10.6828i	0.854487	+	0.472578i
$512$			23.1886i			1.02480i
$513$	−1.02830	+	4.23587i	−0.0454004	+	0.187018i
$514$	−7.89894	−	4.56045i	−0.348407	−	0.201153i
$515$	10.3689	−	28.4882i	0.456907	−	1.25534i
$516$	4.03138	+	1.46730i	0.177472	+	0.0645944i
$517$	12.3642	+	33.9704i	0.543777	+	1.49402i
$518$	−6.43098	−	10.6797i	−0.282561	−	0.469240i
$519$	13.7781	+	11.5612i	0.604792	+	0.507481i
$520$	10.0969			0.442779
$521$	16.0096			0.701393			0.350696	−	0.936489i	$-0.385945\pi$
$521$	16.0096			0.701393			0.350696	+	0.936489i	$0.385945\pi$
$522$	−1.85201	−	1.55402i	−0.0810604	−	0.0680178i
$523$	14.1641	−	5.15532i	0.619354	−	0.225426i	−0.0132371	−	0.999912i	$-0.504214\pi$
$523$	14.1641	−	5.15532i	0.619354	−	0.225426i	0.632591	+	0.774486i	$0.281991\pi$
$524$	−7.87256	+	4.54523i	−0.343915	+	0.198559i
$525$	−2.92955	+	18.6120i	−0.127856	+	0.812295i
$526$	−17.3737	+	20.7052i	−0.757529	+	0.902788i
$527$	29.6119	−	5.22138i	1.28991	−	0.227447i
$528$	1.92993	−	10.9452i	0.0839894	−	0.476328i
$529$	1.92248	+	10.9029i	0.0835860	+	0.474040i
$530$	−12.9049	−	15.3795i	−0.560554	−	0.668043i
$531$	−3.99563			−0.173396
$532$	−6.77310	−	0.306398i	−0.293651	−	0.0132841i
$533$	−10.4097			−0.450892
$534$	11.7874	+	14.0476i	0.510089	+	0.607900i
$535$	−4.43652	−	25.1607i	−0.191807	−	1.08779i
$536$	−6.51680	+	36.9586i	−0.281483	+	1.59637i
$537$	10.7262	−	1.89133i	0.462872	−	0.0816168i
$538$	14.5333	−	17.3202i	0.626577	−	0.746725i
$539$	6.58492	+	30.6899i	0.283632	+	1.32191i
$540$	−1.77260	+	1.02341i	−0.0762805	+	0.0440406i
$541$	−29.7926	+	10.8436i	−1.28089	+	0.466204i	−0.890725	−	0.454543i	$-0.849803\pi$
$541$	−29.7926	+	10.8436i	−1.28089	+	0.466204i	−0.390160	+	0.920747i	$0.627580\pi$
$542$	−13.0885	−	10.9825i	−0.562197	−	0.471739i
$543$	7.11026			0.305130
$544$	−17.0187			−0.729671
$545$	−10.2858	−	8.63077i	−0.440593	−	0.369702i
$546$	2.59457	+	1.43494i	0.111037	+	0.0614098i
$547$	12.5502	+	34.4813i	0.536606	+	1.47431i	0.851074	+	0.525046i	$0.175952\pi$
$547$	12.5502	+	34.4813i	0.536606	+	1.47431i	−0.314468	+	0.949268i	$0.601826\pi$
$548$	−8.67804	−	3.15855i	−0.370708	−	0.134927i
$549$	2.30389	−	6.32988i	0.0983275	−	0.270153i
$550$	−32.8619	−	18.9728i	−1.40124	−	0.809004i
$551$	−5.25692	−	7.14209i	−0.223953	−	0.304263i
$552$		−	17.9504i		−	0.764019i
$553$	17.6497	−	10.6281i	0.750544	−	0.451953i
$554$	−0.216917	−	0.258512i	−0.00921592	−	0.0109831i
$555$	−10.5753	−	8.87373i	−0.448896	−	0.376669i
$556$	3.81400	+	4.54535i	0.161750	+	0.192766i
$557$	13.6224	−	4.95814i	0.577199	−	0.210083i	−0.0368909	−	0.999319i	$-0.511745\pi$
$557$	13.6224	−	4.95814i	0.577199	−	0.210083i	0.614090	+	0.789236i	$0.289523\pi$
$558$		−	6.72934i		−	0.284876i
$559$	−3.44086	−	5.95974i	−0.145533	−	0.252070i
$560$	14.9950	+	17.2164i	0.633653	+	0.727524i
$561$	23.4475	+	4.13443i	0.989955	+	0.174556i
$562$	16.4929	−	28.5666i	0.695711	−	1.20501i
$563$	−16.6439	−	28.8282i	−0.701459	−	1.21496i	−0.967954	−	0.251126i	$-0.919199\pi$
$563$	−16.6439	−	28.8282i	−0.701459	−	1.21496i	0.266495	−	0.963836i	$-0.414134\pi$
$564$	−1.62107	−	4.45384i	−0.0682592	−	0.187541i
$565$	0.622269	+	3.52906i	0.0261791	+	0.148469i
$566$	29.4294	−	10.7114i	1.23701	−	0.450235i
$567$	−2.64530	+	0.0487129i	−0.111092	+	0.00204575i
$568$	0.536536	+	3.04285i	0.0225126	+	0.127675i
$569$	10.8900	−	6.28734i	0.456532	−	0.263579i	−0.254053	−	0.967190i	$-0.581764\pi$
$569$	10.8900	−	6.28734i	0.456532	−	0.263579i	0.710585	+	0.703611i	$0.248430\pi$
$570$	17.3039	−	5.07802i	0.724782	−	0.212695i
$571$	−18.8074	+	32.5754i	−0.787066	+	1.36324i	0.140692	+	0.990053i	$0.455067\pi$
$571$	−18.8074	+	32.5754i	−0.787066	+	1.36324i	−0.927757	+	0.373184i	$0.878266\pi$
$572$	1.90443	−	1.59800i	0.0796280	−	0.0668159i
$573$	−0.466096	+	0.391101i	−0.0194714	+	0.0163385i
$574$	−22.7932	−	26.1698i	−0.951371	−	1.09231i
$575$	−39.0605	−	14.2169i	−1.62894	−	0.592884i
$576$	−1.52218	+	8.63272i	−0.0634242	+	0.359697i
$577$	−22.1806	+	12.8060i	−0.923392	+	0.533121i	−0.884716	−	0.466131i	$-0.845648\pi$
$577$	−22.1806	+	12.8060i	−0.923392	+	0.533121i	−0.0386767	+	0.999252i	$0.512314\pi$
$578$			13.3014i			0.553266i
$579$	−7.24726	−	19.9117i	−0.301186	−	0.827502i
$580$	0.723116	−	4.10100i	0.0300258	−	0.170285i
$581$	12.8111	+	33.2786i	0.531494	+	1.38063i
$582$	−12.6501	−	7.30356i	−0.524365	−	0.302742i
$583$	−21.4291	−	3.77853i	−0.887502	−	0.156491i
$584$	19.6540	−	16.4917i	0.813288	−	0.682430i
$585$	3.23340	+	0.570136i	0.133685	+	0.0235722i
$586$	−5.14742	+	14.1424i	−0.212638	+	0.584218i
$587$	−10.7975	+	1.90389i	−0.445660	+	0.0785819i	−0.391975	−	0.919976i	$-0.628208\pi$
$587$	−10.7975	+	1.90389i	−0.445660	+	0.0785819i	−0.0536853	+	0.998558i	$0.517097\pi$
$588$	−0.863346	−	4.02374i	−0.0356038	−	0.165936i
$589$	5.82317	−	23.9874i	0.239939	−	0.988383i
$590$	8.26537	+	14.3160i	0.340280	+	0.589382i
$591$	0.756025	+	0.275171i	0.0310987	+	0.0113190i
$592$	−9.67867	+	1.70661i	−0.397791	+	0.0701413i
$593$	−17.2225	+	20.5250i	−0.707244	+	0.842860i	−0.993325	−	0.115345i	$-0.963203\pi$
$593$	−17.2225	+	20.5250i	−0.707244	+	0.842860i	0.286082	+	0.958205i	$0.407647\pi$
$594$	1.82245	−	5.00713i	0.0747759	−	0.205445i
$595$	−36.8821	+	32.1233i	−1.51202	+	1.31693i
$596$	−0.372283	+	0.644813i	−0.0152493	+	0.0264126i
$597$	0.973621	+	0.562121i	0.0398477	+	0.0230061i
$598$	−4.20462	+	5.01087i	−0.171940	+	0.204910i
$599$	−9.99655	+	11.9134i	−0.408448	+	0.486769i	−0.930577	−	0.366097i	$-0.880694\pi$
$599$	−9.99655	+	11.9134i	−0.408448	+	0.486769i	0.522129	+	0.852867i	$0.325138\pi$
$600$	18.9657	+	10.9499i	0.774273	+	0.447027i
$601$	−4.83113	+	8.36775i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$601$	−4.83113	+	8.36775i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$602$	7.44859	−	21.6999i	0.303582	−	0.884421i
$603$	−4.17384	+	11.4675i	−0.169972	+	0.466994i
$604$	−0.868001	+	1.03444i	−0.0353185	+	0.0420909i
$605$	−31.2241	+	5.50564i	−1.26944	+	0.223836i
$606$	16.9878	+	6.18304i	0.690080	+	0.251169i
$607$	−10.6792	−	18.4970i	−0.433457	−	0.750769i	0.563711	−	0.825972i	$-0.309373\pi$
$607$	−10.6792	−	18.4970i	−0.433457	−	0.750769i	−0.997168	+	0.0752026i	$0.976040\pi$
$608$	−5.60337	+	12.7981i	−0.227247	+	0.519033i
$609$	3.38348	−	4.18646i	0.137106	−	0.169644i
$610$	−27.4453	+	4.83935i	−1.11123	+	0.195939i
$611$	−2.60033	+	7.14436i	−0.105198	+	0.289030i
$612$	−3.07419	−	0.542063i	−0.124267	−	0.0219116i
$613$	13.5139	−	11.3395i	0.545821	−	0.457998i	−0.327702	−	0.944781i	$-0.606274\pi$
$613$	13.5139	−	11.3395i	0.545821	−	0.457998i	0.873523	+	0.486783i	$0.161830\pi$
$614$	1.73951	+	0.306723i	0.0702011	+	0.0123783i
$615$	−33.2819	−	19.2153i	−1.34205	−	0.774835i
$616$	36.0401	+	5.67275i	1.45210	+	0.228562i
$617$	−4.01524	+	22.7715i	−0.161647	+	0.916748i	0.790807	+	0.612066i	$0.209661\pi$
$617$	−4.01524	+	22.7715i	−0.161647	+	0.916748i	−0.952454	+	0.304682i	$0.901450\pi$
$618$	−3.53907	−	9.72352i	−0.142362	−	0.391137i
$619$		−	42.8557i		−	1.72252i	−0.508168	−	0.861258i	$-0.669677\pi$
$619$		−	42.8557i		−	1.72252i	0.508168	−	0.861258i	$-0.330323\pi$
$620$	10.0381	−	5.79549i	0.403139	−	0.232752i
$621$	1.01359	−	5.74837i	0.0406741	−	0.230674i
$622$	−1.31171	−	0.477423i	−0.0525947	−	0.0191429i
$623$	−30.7881	+	26.8156i	−1.23350	+	1.07434i
$624$	1.79056	−	1.50246i	0.0716796	−	0.0601464i
$625$	−7.57897	+	6.35951i	−0.303159	+	0.254380i
$626$	−11.0532	+	19.1448i	−0.441776	+	0.765178i
$627$	10.8292	−	16.2714i	0.432475	−	0.649816i
$628$	−2.30684	+	1.33185i	−0.0920528	+	0.0531467i
$629$	−3.65602	−	20.7343i	−0.145775	−	0.826732i
$630$	5.64661	+	9.37715i	0.224966	+	0.373595i
$631$	28.5624	−	10.3959i	1.13705	−	0.413853i	0.296204	−	0.955125i	$-0.404279\pi$
$631$	28.5624	−	10.3959i	1.13705	−	0.413853i	0.840848	+	0.541272i	$0.182057\pi$
$632$	−4.15839	−	23.5834i	−0.165412	−	0.938097i
$633$	0.423210	+	1.16276i	0.0168211	+	0.0462156i
$634$	12.0875	+	20.9361i	0.480054	+	0.831478i
$635$	5.23445	−	9.06634i	0.207723	−	0.359787i
$636$	2.80956	+	0.495401i	0.111406	+	0.0196439i
$637$	−3.08795	+	5.83457i	−0.122349	+	0.231174i
$638$	5.42040	+	9.38841i	0.214596	+	0.371691i
$639$			1.00473i			0.0397464i
$640$	13.1071	−	4.77058i	0.518102	−	0.188574i
$641$	−12.5725	−	14.9834i	−0.496585	−	0.591807i	0.458294	−	0.888800i	$-0.348461\pi$
$641$	−12.5725	−	14.9834i	−0.496585	−	0.591807i	−0.954880	+	0.296993i	$0.904016\pi$
$642$	−6.68011	−	5.60528i	−0.263643	−	0.221223i
$643$	−9.45722	−	11.2707i	−0.372956	−	0.444472i	0.546622	−	0.837380i	$-0.315914\pi$
$643$	−9.45722	−	11.2707i	−0.372956	−	0.444472i	−0.919578	+	0.392908i	$0.871469\pi$
$644$	9.07766	−	0.167164i	0.357710	−	0.00658718i
$645$		−	25.4061i		−	1.00036i
$646$	25.1942	+	11.0307i	0.991254	+	0.433998i
$647$	0.758379	+	0.437850i	0.0298150	+	0.0172137i	0.514833	−	0.857290i	$-0.327854\pi$
$647$	0.758379	+	0.437850i	0.0298150	+	0.0172137i	−0.485018	+	0.874504i	$0.661187\pi$
$648$	−1.05180	+	2.88979i	−0.0413185	+	0.113522i
$649$	16.8361	+	6.12785i	0.660876	+	0.240539i
$650$	−2.72946	−	7.49913i	−0.107058	−	0.294140i
$651$	14.9801	−	0.275857i	0.587118	−	0.0108117i
$652$	7.92122	+	6.64669i	0.310219	+	0.260305i
$653$	−43.4554			−1.70054			−0.850271	−	0.526345i	$-0.823562\pi$
$653$	−43.4554			−1.70054			−0.850271	+	0.526345i	$0.823562\pi$
$654$	−4.58289			−0.179205
$655$	41.2391	+	34.6037i	1.61134	+	1.35208i
$656$	−25.7092	+	9.35739i	−1.00378	+	0.365345i
$657$	7.22516	−	4.17145i	0.281880	−	0.162744i
$658$	−23.6546	+	9.10622i	−0.922154	+	0.354997i
$659$	−12.9776	+	15.4661i	−0.505535	+	0.602473i	−0.957097	−	0.289766i	$-0.906422\pi$
$659$	−12.9776	+	15.4661i	−0.505535	+	0.602473i	0.451562	+	0.892240i	$0.350867\pi$
$660$	9.03862	−	1.59375i	0.351828	−	0.0620368i
$661$	7.99553	−	45.3449i	0.310990	−	1.76371i	−0.282883	−	0.959155i	$-0.591291\pi$
$661$	7.99553	−	45.3449i	0.310990	−	1.76371i	0.593873	−	0.804559i	$-0.297598\pi$
$662$	1.38870	+	7.87569i	0.0539732	+	0.306098i
$663$	3.21866	+	3.83585i	0.125003	+	0.148972i
$664$	41.4481			1.60850
$665$	12.0135	+	38.3120i	0.465863	+	1.48568i
$666$	−4.71190			−0.182583
$667$	7.63341	+	9.09714i	0.295567	+	0.352243i
$668$	−2.46652	−	13.9883i	−0.0954325	−	0.541224i
$669$	−1.54955	+	8.78796i	−0.0599092	+	0.339762i
$670$	49.7213	−	8.76720i	1.92090	−	0.338706i
$671$	−19.4155	+	23.1385i	−0.749526	+	0.893250i
$672$	−8.37696	−	1.31854i	−0.323148	−	0.0508639i
$673$	19.8251	−	11.4460i	0.764202	−	0.441212i	−0.0666001	−	0.997780i	$-0.521215\pi$
$673$	19.8251	−	11.4460i	0.764202	−	0.441212i	0.830803	+	0.556567i	$0.187882\pi$
$674$	−27.2655	+	9.92385i	−1.05023	+	0.382252i
$675$	5.45523	+	4.57748i	0.209972	+	0.176187i
$676$	−7.11989			−0.273842
$677$	−36.0701			−1.38629			−0.693144	−	0.720800i	$-0.743775\pi$
$677$	−36.0701			−1.38629			−0.693144	+	0.720800i	$0.743775\pi$
$678$	0.936957	+	0.786201i	0.0359836	+	0.0301938i
$679$	15.7398	−	28.4597i	0.604039	−	1.09218i
$680$	19.4438	+	53.4214i	0.745635	+	2.04862i
$681$	−0.560936	−	0.204164i	−0.0214951	−	0.00782358i
$682$	−10.3204	+	28.3550i	−0.395187	+	1.08577i
$683$	12.4741	+	7.20192i	0.477308	+	0.275574i	0.719294	−	0.694706i	$-0.244465\pi$
$683$	12.4741	+	7.20192i	0.477308	+	0.275574i	−0.241986	+	0.970280i	$0.577799\pi$
$684$	−1.41981	+	2.13333i	−0.0542877	+	0.0815700i
$685$			54.6896i			2.08958i
$686$	−21.4295	+	5.01241i	−0.818184	+	0.191375i
$687$	−3.17855	−	3.78805i	−0.121269	−	0.144523i
$688$	−13.8553	−	11.6260i	−0.528230	−	0.443237i
$689$	−2.94159	−	3.50565i	−0.112066	−	0.133555i
$690$	−22.6927	+	8.25946i	−0.863896	+	0.314432i
$691$		−	33.5827i		−	1.27754i	−0.769396	−	0.638772i	$-0.779443\pi$
$691$		−	33.5827i		−	1.27754i	0.769396	−	0.638772i	$-0.220557\pi$
$692$	5.28702	+	9.15739i	0.200982	+	0.348112i
$693$	11.2210	+	3.85168i	0.426252	+	0.146313i
$694$	27.3176	+	4.81683i	1.03696	+	0.182845i
$695$	17.5692	−	30.4308i	0.666438	−	1.15430i
$696$	−3.12830	−	5.41837i	−0.118578	−	0.205383i
$697$	−20.0460	−	55.0760i	−0.759298	−	2.08615i
$698$	3.01700	+	17.1102i	0.114195	+	0.647632i
$699$	0.444101	−	0.161639i	0.0167974	−	0.00611377i
$700$	−5.36083	+	9.69311i	−0.202620	+	0.366365i
$701$	−2.31169	−	13.1102i	−0.0873113	−	0.495167i	−0.996834	−	0.0795124i	$-0.974664\pi$
$701$	−2.31169	−	13.1102i	−0.0873113	−	0.495167i	0.909523	−	0.415654i	$-0.136447\pi$
$702$	0.970503	−	0.560320i	0.0366293	−	0.0211479i
$703$	−16.7960	−	4.07739i	−0.633474	−	0.153782i
$704$	19.6534	−	34.0407i	0.740715	−	1.28296i
$705$	−21.5017	+	18.0420i	−0.809800	+	0.679502i
$706$	−17.6396	+	14.8014i	−0.663876	+	0.557058i
$707$	−13.0676	+	38.0698i	−0.491459	+	1.43176i
$708$	−2.20738	−	0.803420i	−0.0829584	−	0.0301944i
$709$	−7.58737	+	43.0301i	−0.284950	+	1.61603i	0.420515	+	0.907286i	$0.361849\pi$
$709$	−7.58737	+	43.0301i	−0.284950	+	1.61603i	−0.705465	+	0.708745i	$0.749262\pi$
$710$	3.59986	−	2.07838i	0.135100	−	0.0780003i
$711$		−	7.78708i		−	0.292038i
$712$	16.2311	+	44.5947i	0.608287	+	1.67126i
$713$	−5.73989	+	32.5525i	−0.214961	+	1.21910i
$714$	−2.59567	+	16.4908i	−0.0971404	+	0.617152i
$715$	−12.7500	−	7.36121i	−0.476823	−	0.275294i
$716$	6.30599	+	1.11192i	0.235666	+	0.0415542i
$717$	−10.8656	+	9.11728i	−0.405782	+	0.340491i
$718$	29.1207	+	5.13477i	1.08677	+	0.191628i
$719$	−5.49178	+	15.0886i	−0.204809	+	0.562708i	−0.998988	−	0.0449757i	$-0.985679\pi$
$719$	−5.49178	+	15.0886i	−0.204809	+	0.562708i	0.794179	+	0.607684i	$0.207901\pi$
$720$	8.49819	−	1.49846i	0.316709	−	0.0558443i
$721$	21.5004	−	8.27690i	0.800716	−	0.308248i
$722$	16.5903	−	15.3143i	0.617428	−	0.569940i
$723$	0.520967	+	0.902340i	0.0193750	+	0.0335584i
$724$	3.92805	+	1.42969i	0.145985	+	0.0531341i
$725$	−14.2682	+	2.51586i	−0.529907	+	0.0934368i
$726$	−6.95606	+	8.28991i	−0.258164	+	0.307667i
$727$	10.5070	−	28.8678i	0.389684	−	1.07065i	−0.577460	−	0.816419i	$-0.695956\pi$
$727$	10.5070	−	28.8678i	0.389684	−	1.07065i	0.967144	−	0.254230i	$-0.0818219\pi$
$728$	5.03947	+	5.78603i	0.186775	+	0.214444i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−29.8919	−	17.2581i	−1.10635	−	0.638752i
$731$	24.9060	−	29.6819i	0.921183	−	1.09782i
$732$	2.54556	−	3.03367i	0.0940864	−	0.112128i
$733$	1.36159	+	0.786113i	0.0502914	+	0.0290358i	0.524935	−	0.851142i	$-0.324090\pi$
$733$	1.36159	+	0.786113i	0.0502914	+	0.0290358i	−0.474643	+	0.880178i	$0.657423\pi$
$734$	12.5255	−	21.6948i	0.462325	−	0.800770i
$735$	−20.6429	+	12.9543i	−0.761426	+	0.477826i
$736$	6.39877	−	17.5805i	0.235862	−	0.648025i
$737$	35.1740	−	41.9188i	1.29565	−	1.54410i
$738$	−12.9177	+	2.27774i	−0.475508	+	0.0838449i
$739$	32.5697	+	11.8544i	1.19810	+	0.436072i	0.862560	−	0.505955i	$-0.168860\pi$
$739$	32.5697	+	11.8544i	1.19810	+	0.436072i	0.335538	+	0.942027i	$0.391082\pi$
$740$	−4.05802	−	7.02869i	−0.149176	−	0.258380i
$741$	3.94432	−	1.15750i	0.144898	−	0.0425218i
$742$	2.37223	−	15.0712i	0.0870872	−	0.553282i
$743$	37.4279	−	6.59956i	1.37310	−	0.242114i	0.562055	−	0.827100i	$-0.310011\pi$
$743$	37.4279	−	6.59956i	1.37310	−	0.242114i	0.811043	+	0.584986i	$0.198900\pi$
$744$	5.95624	−	16.3646i	0.218366	−	0.599957i
$745$	4.34234	+	0.765671i	0.159091	+	0.0280520i
$746$	−26.4896	+	22.2274i	−0.969853	+	0.813803i
$747$	13.2732	+	2.34042i	0.485641	+	0.0856316i
$748$	12.1222	+	6.99875i	0.443231	+	0.255900i
$749$	12.2040	−	15.1003i	0.445925	−	0.551754i
$750$	1.52398	−	8.64289i	0.0556477	−	0.315594i
$751$	2.17651	+	5.97990i	0.0794219	+	0.218210i	0.973048	−	0.230602i	$-0.0740696\pi$
$751$	2.17651	+	5.97990i	0.0794219	+	0.218210i	−0.893626	+	0.448812i	$0.851847\pi$
$752$			19.9822i			0.728677i
$753$	−3.07280	+	1.77408i	−0.111979	+	0.0646512i
$754$	−0.395908	+	2.24531i	−0.0144181	+	0.0817692i
$755$	7.51463	+	2.73510i	0.273485	+	0.0995405i
$756$	−1.47119	−	0.504992i	−0.0535065	−	0.0183664i
$757$	9.85075	−	8.26576i	0.358031	−	0.300424i	−0.445974	−	0.895046i	$-0.647143\pi$
$757$	9.85075	−	8.26576i	0.358031	−	0.300424i	0.804006	+	0.594622i	$0.202698\pi$
$758$	9.13532	−	7.66544i	0.331810	−	0.278421i
$759$	−13.0868	+	22.6670i	−0.475021	+	0.822761i
$760$	46.5749	+	2.96708i	1.68945	+	0.107627i
$761$	−7.43956	+	4.29523i	−0.269684	+	0.155702i	−0.628744	−	0.777612i	$-0.716431\pi$
$761$	−7.43956	+	4.29523i	−0.269684	+	0.155702i	0.359060	+	0.933314i	$0.383097\pi$
$762$	−0.620482	−	3.51893i	−0.0224777	−	0.127477i
$763$	−0.187867	−	10.2019i	−0.00680125	−	0.369335i
$764$	−0.336134	+	0.122343i	−0.0121609	+	0.00442621i
$765$	3.21010	+	18.2054i	0.116062	+	0.658218i
$766$	−2.37937	−	6.53727i	−0.0859702	−	0.236201i
$767$	1.88404	+	3.26325i	0.0680286	+	0.117829i
$768$	−6.38551	+	11.0600i	−0.230417	+	0.399094i
$769$	−17.4672	−	3.07994i	−0.629884	−	0.111066i	−0.150413	−	0.988623i	$-0.548060\pi$
$769$	−17.4672	−	3.07994i	−0.629884	−	0.111066i	−0.479471	+	0.877558i	$0.659171\pi$
$770$	−9.41161	−	48.1717i	−0.339171	−	1.73599i
$771$	−3.83774	−	6.64716i	−0.138213	−	0.239392i
$772$		−	12.4574i		−	0.448352i
$773$	−7.33709	+	2.67048i	−0.263897	+	0.0960506i	−0.470580	−	0.882357i	$-0.655955\pi$
$773$	−7.33709	+	2.67048i	−0.263897	+	0.0960506i	0.206683	+	0.978408i	$0.433733\pi$
$774$	−5.57394	−	6.64277i	−0.200351	−	0.238769i
$775$	−30.8925	−	25.9219i	−1.10969	−	0.931142i
$776$	−24.2985	−	28.9578i	−0.872266	−	1.03953i
$777$	−0.193156	−	10.4891i	−0.00692942	−	0.376295i
$778$			13.0784i			0.468885i
$779$	−48.0175	−	3.05898i	−1.72041	−	0.109599i
$780$	1.67165	+	0.965125i	0.0598545	+	0.0345570i
$781$	1.54089	−	4.23356i	0.0551373	−	0.151489i
$782$	−34.6087	−	12.5965i	−1.23761	−	0.450452i
$783$	−0.695840	−	1.91181i	−0.0248673	−	0.0683224i
$784$	−2.38167	+	17.1857i	−0.0850598	+	0.613775i
$785$	12.0840	+	10.1396i	0.431295	+	0.361899i
$786$	18.3744			0.655392
$787$	36.5966			1.30453			0.652263	−	0.757992i	$-0.273820\pi$
$787$	36.5966			1.30453			0.652263	+	0.757992i	$0.273820\pi$
$788$	0.362334	+	0.304035i	0.0129076	+	0.0108308i
$789$	−21.3736	+	7.77936i	−0.760921	+	0.276953i
$790$	−27.9005	+	16.1084i	−0.992655	+	0.573110i
$791$	−1.71175	+	2.11798i	−0.0608627	+	0.0753068i
$792$	8.86377	−	10.5634i	0.314961	−	0.375355i
$793$	−6.25597	+	1.10310i	−0.222156	+	0.0391721i
$794$	−6.17055	+	34.9949i	−0.218985	+	1.24192i
$795$	−2.93377	−	16.6382i	−0.104050	−	0.590098i
$796$	0.424847	+	0.506313i	0.0150583	+	0.0179458i
$797$	28.5655			1.01184			0.505921	−	0.862580i	$-0.331153\pi$
$797$	28.5655			1.01184			0.505921	+	0.862580i	$0.331153\pi$
$798$	11.5465	+	7.38151i	0.408742	+	0.261303i
$799$	−42.8073			−1.51441
$800$	14.6716	+	17.4850i	0.518720	+	0.618187i
$801$	2.67971	+	15.1974i	0.0946827	+	0.536972i
$802$	−0.907850	+	5.14867i	−0.0320573	+	0.181806i
$803$	−36.8417	+	6.49618i	−1.30011	+	0.229245i
$804$	−4.61165	+	5.49596i	−0.162641	+	0.193827i
$805$	−19.3166	−	50.1774i	−0.680819	−	1.76852i
$806$	−5.49588	+	3.17305i	−0.193584	+	0.111766i
$807$	17.8793	−	6.50755i	0.629383	−	0.229077i
$808$	35.8387	+	30.0722i	1.26080	+	1.05794i
$809$	21.3874			0.751942			0.375971	−	0.926632i	$-0.377309\pi$
$809$	21.3874			0.751942			0.375971	+	0.926632i	$0.377309\pi$
$810$	4.13720			0.145366
$811$	−22.1628	−	18.5968i	−0.778243	−	0.653023i	0.164563	−	0.986367i	$-0.447379\pi$
$811$	−22.1628	−	18.5968i	−0.778243	−	0.653023i	−0.942805	+	0.333343i	$0.891823\pi$
$812$	2.71099	−	1.63247i	0.0951370	−	0.0572884i
$813$	−4.91761	−	13.5110i	−0.172468	−	0.473852i
$814$	19.8542	+	7.22635i	0.695890	+	0.253283i
$815$	20.9440	−	57.5431i	0.733635	−	2.01565i
$816$	11.3974	+	6.58029i	0.398988	+	0.230356i
$817$	−14.1206	−	28.5021i	−0.494018	−	0.997164i
$818$			13.6622i			0.477688i
$819$	1.28711	+	2.13746i	0.0449752	+	0.0746889i
$820$	−14.5228	−	17.3076i	−0.507158	−	0.604407i
$821$	35.3620	+	29.6722i	1.23414	+	1.03557i	0.997959	+	0.0638600i	$0.0203411\pi$
$821$	35.3620	+	29.6722i	1.23414	+	1.03557i	0.236184	+	0.971708i	$0.424103\pi$
$822$	11.9986	+	14.2994i	0.418499	+	0.498748i
$823$	40.7451	−	14.8300i	1.42028	−	0.516941i	0.486153	−	0.873874i	$-0.338400\pi$
$823$	40.7451	−	14.8300i	1.42028	−	0.516941i	0.934130	+	0.356933i	$0.116177\pi$
$824$		−	26.7785i		−	0.932872i
$825$	−15.9661	−	27.6542i	−0.555870	−	0.962794i
$826$	−4.07847	+	11.8817i	−0.141908	+	0.413419i
$827$	−34.8833	−	6.15087i	−1.21301	−	0.213887i	−0.469696	−	0.882828i	$-0.655636\pi$
$827$	−34.8833	−	6.15087i	−1.21301	−	0.213887i	−0.743315	+	0.668942i	$0.766748\pi$
$828$	1.71581	−	2.97187i	0.0596284	−	0.103279i
$829$	17.0922	+	29.6046i	0.593637	+	1.02821i	0.993738	+	0.111738i	$0.0356417\pi$
$829$	17.0922	+	29.6046i	0.593637	+	1.02821i	−0.400101	+	0.916471i	$0.631025\pi$
$830$	−19.0714	−	52.3983i	−0.661978	−	1.81877i
$831$	−0.0493133	−	0.279669i	−0.00171066	−	0.00970163i
$832$	7.76812	−	2.82736i	0.269311	−	0.0980212i
$833$	−36.8164	−	5.10218i	−1.27561	−	0.176780i
$834$	−2.08262	−	11.8111i	−0.0721153	−	0.408986i
$835$	−72.8474	+	42.0585i	−2.52099	+	1.45549i
$836$	9.25430	−	6.81162i	0.320067	−	0.235585i
$837$	2.83146	−	4.90423i	0.0978696	−	0.169515i
$838$	−24.2451	+	20.3441i	−0.837533	+	0.702774i
$839$	30.6351	−	25.7059i	1.05764	−	0.887467i	0.0637654	−	0.997965i	$-0.479689\pi$
$839$	30.6351	−	25.7059i	1.05764	−	0.887467i	0.993876	+	0.110498i	$0.0352446\pi$
$840$	5.43176	+	27.8016i	0.187414	+	0.959245i
$841$	−23.3615	−	8.50290i	−0.805569	−	0.293203i
$842$	−0.224079	+	1.27082i	−0.00772227	+	0.0437952i
$843$	24.0395	−	13.8792i	0.827964	−	0.478026i
$844$			0.727461i			0.0250403i
$845$	14.4210	+	39.6212i	0.496096	+	1.36301i
$846$	−1.66359	+	9.43468i	−0.0571954	+	0.324371i
$847$	−18.7392	−	15.1450i	−0.643888	−	0.520388i
$848$	−10.4163	−	6.01384i	−0.357696	−	0.206516i
$849$	25.9547	+	4.57651i	0.890761	+	0.157065i
$850$	34.4207	−	28.8824i	1.18062	−	0.990658i
$851$	22.7934	+	4.01909i	0.781347	+	0.137773i
$852$	−0.202025	+	0.555060i	−0.00692127	+	0.0190160i
$853$	27.6452	−	4.87460i	0.946554	−	0.166903i	0.320996	−	0.947081i	$-0.395982\pi$
$853$	27.6452	−	4.87460i	0.946554	−	0.166903i	0.625558	+	0.780177i	$0.284871\pi$
$854$	−16.4714	−	13.3121i	−0.563640	−	0.455532i
$855$	14.7475	+	3.58008i	0.504352	+	0.122436i
$856$	−11.2836	−	19.5438i	−0.385666	−	0.667992i
$857$	0.876291	+	0.318944i	0.0299335	+	0.0108949i	0.356944	−	0.934126i	$-0.383819\pi$
$857$	0.876291	+	0.318944i	0.0299335	+	0.0108949i	−0.327010	+	0.945021i	$0.606041\pi$
$858$	−4.94867	+	0.872584i	−0.168945	+	0.0297895i
$859$	−19.0856	+	22.7454i	−0.651193	+	0.776062i	−0.986093	−	0.166192i	$-0.946853\pi$
$859$	−19.0856	+	22.7454i	−0.651193	+	0.776062i	0.334900	+	0.942254i	$0.391297\pi$
$860$	5.10851	−	14.0355i	0.174199	−	0.478607i
$861$	−5.60001	−	28.6627i	−0.190848	−	0.976822i
$862$	15.6168	−	27.0491i	0.531911	−	0.921297i
$863$	37.8623	+	21.8598i	1.28885	+	0.744116i	0.978448	−	0.206491i	$-0.0662044\pi$
$863$	37.8623	+	21.8598i	1.28885	+	0.744116i	0.310398	+	0.950607i	$0.399538\pi$
$864$	−2.06025	+	2.45531i	−0.0700910	+	0.0835313i
$865$	40.2511	−	47.9694i	1.36858	−	1.63101i
$866$	4.90229	+	2.83034i	0.166586	+	0.0961787i
$867$	−5.59674	+	9.69384i	−0.190075	+	0.329220i
$868$	8.33121	+	2.85973i	0.282780	+	0.0970655i
$869$	−11.9426	+	32.8119i	−0.405123	+	1.11307i
$870$	−5.41044	+	6.44791i	−0.183431	+	0.218605i
$871$	11.3336	−	1.99842i	0.384025	−	0.0677140i
$872$	−11.1448	−	4.05639i	−0.377412	−	0.137367i
$873$	−6.14613	−	10.6454i	−0.208015	−	0.360293i
$874$	−20.8675	+	21.8785i	−0.705854	+	0.740052i
$875$	19.3023	+	3.03821i	0.652538	+	0.102710i
$876$	4.83029	−	0.851711i	0.163201	−	0.0287767i
$877$	−12.1687	+	33.4331i	−0.410907	+	1.12896i	0.545803	+	0.837913i	$0.316225\pi$
$877$	−12.1687	+	33.4331i	−0.410907	+	1.12896i	−0.956710	+	0.291043i	$0.905998\pi$
$878$	25.6321	+	4.51963i	0.865040	+	0.152530i
$879$	−9.70196	+	8.14091i	−0.327239	+	0.274586i
$880$	−38.1063	−	6.71918i	−1.28456	−	0.226503i
$881$	−12.9623	−	7.48376i	−0.436709	−	0.252134i	0.265491	−	0.964113i	$-0.414466\pi$
$881$	−12.9623	−	7.48376i	−0.436709	−	0.252134i	−0.702201	+	0.711979i	$0.747799\pi$
$882$	−2.55529	+	7.91601i	−0.0860409	+	0.266546i
$883$	5.27974	−	29.9429i	0.177677	−	1.00766i	−0.757331	−	0.653032i	$-0.773497\pi$
$883$	5.27974	−	29.9429i	0.177677	−	1.00766i	0.935008	−	0.354627i	$-0.115392\pi$
$884$	1.00685	+	2.76630i	0.0338641	+	0.0930407i
$885$			13.9111i			0.467615i
$886$	16.1411	−	9.31906i	0.542271	−	0.313080i
$887$	7.79490	−	44.2071i	0.261727	−	1.48433i	−0.516468	−	0.856306i	$-0.672754\pi$
$887$	7.79490	−	44.2071i	0.261727	−	1.48433i	0.778196	−	0.628022i	$-0.216135\pi$
$888$	−11.4586	−	4.17057i	−0.384524	−	0.139955i
$889$	7.80803	−	1.52550i	0.261873	−	0.0511637i
$890$	48.9077	−	41.0385i	1.63939	−	1.37561i
$891$	3.43499	−	2.88230i	0.115076	−	0.0965605i
$892$	−2.62308	+	4.54331i	−0.0878273	+	0.152121i
$893$	−14.0942	+	32.1913i	−0.471645	+	1.07724i
$894$	1.30335	−	0.752489i	0.0435905	−	0.0251670i
$895$	−6.58478	−	37.3441i	−0.220105	−	1.24828i
$896$	9.27564	+	5.12994i	0.309877	+	0.171379i
$897$	−5.17265	+	1.88269i	−0.172710	+	0.0628612i
$898$	−6.78611	−	38.4860i	−0.226456	−	1.28429i
$899$	3.94049	+	10.8264i	0.131423	+	0.361081i
$900$	2.09331	+	3.62573i	0.0697771	+	0.120858i
$901$	12.8833	−	22.3145i	0.429204	−	0.743403i
$902$	57.9238	+	10.2135i	1.92865	+	0.340073i
$903$	14.5589	−	12.6804i	0.484490	−	0.421978i
$904$	1.58265	+	2.74122i	0.0526380	+	0.0911717i
$905$		−	24.7548i		−	0.822878i
$906$	2.56487	−	0.933536i	0.0852121	−	0.0310147i
$907$	−29.3394	−	34.9653i	−0.974199	−	1.16101i	−0.986940	−	0.161087i	$-0.948500\pi$
$907$	−29.3394	−	34.9653i	−0.974199	−	1.16101i	0.0127411	−	0.999919i	$-0.495944\pi$
$908$	−0.268836	−	0.225580i	−0.00892163	−	0.00748613i
$909$	9.77879	+	11.6539i	0.324342	+	0.386536i
$910$	4.99584	−	9.03316i	0.165610	−	0.299446i
$911$		−	11.4719i		−	0.380079i	−0.981776	−	0.190040i	$-0.939138\pi$
$911$		−	11.4719i		−	0.380079i	0.981776	−	0.190040i	$-0.0608617\pi$
$912$	8.70097	−	6.40434i	0.288118	−	0.212069i
$913$	−52.3390	−	30.2180i	−1.73217	−	1.00007i
$914$	5.04084	−	13.8496i	0.166736	−	0.458104i
$915$	−22.0379	−	8.02113i	−0.728550	−	0.265171i
$916$	−0.994303	−	2.73182i	−0.0328527	−	0.0902620i
$917$	0.753223	+	40.9030i	0.0248736	+	1.35074i
$918$	4.83349	+	4.05578i	0.159529	+	0.133861i
$919$	5.32817			0.175760			0.0878801	−	0.996131i	$-0.471991\pi$
$919$	5.32817			0.175760			0.0878801	+	0.996131i	$0.471991\pi$
$920$	−62.4954			−2.06041
$921$	1.13867	+	0.955458i	0.0375205	+	0.0314834i
$922$	2.29526	−	0.835407i	0.0755904	−	0.0275127i
$923$	0.820565	−	0.473753i	0.0270092	−	0.0155938i
$924$	5.42457	+	4.38412i	0.178455	+	0.144227i
$925$	−18.1506	+	21.6310i	−0.596787	+	0.711223i
$926$	−26.4380	+	4.66173i	−0.868806	+	0.153194i
$927$	1.51208	−	8.57545i	0.0496633	−	0.281655i
$928$	−1.13235	−	6.42187i	−0.0371712	−	0.210808i
$929$	−9.74911	−	11.6185i	−0.319858	−	0.381192i	0.582026	−	0.813170i	$-0.302260\pi$
$929$	−9.74911	−	11.6185i	−0.319858	−	0.381192i	−0.901884	+	0.431978i	$0.857816\pi$
$930$	−23.4286			−0.768255
$931$	−15.9586	+	26.0062i	−0.523022	+	0.852319i
$932$	0.277844			0.00910109
$933$	−0.755069	−	0.899856i	−0.0247198	−	0.0294600i
$934$	−4.60202	−	26.0994i	−0.150583	−	0.853997i
$935$	14.3943	−	81.6340i	0.470743	−	2.66972i
$936$	2.85605	−	0.503598i	0.0933528	−	0.0164606i
$937$	−16.2535	+	19.3701i	−0.530977	+	0.632794i	−0.963140	−	0.269002i	$-0.913306\pi$
$937$	−16.2535	+	19.3701i	−0.530977	+	0.632794i	0.432163	+	0.901796i	$0.357751\pi$
$938$	29.8404	+	24.1169i	0.974324	+	0.787445i
$939$	−16.1108	+	9.30158i	−0.525757	+	0.303546i
$940$	−15.5063	+	5.64385i	−0.505761	+	0.184082i
$941$	13.8787	+	11.6456i	0.452434	+	0.379637i	0.840338	−	0.542062i	$-0.182356\pi$
$941$	13.8787	+	11.6456i	0.452434	+	0.379637i	−0.387904	+	0.921700i	$0.626801\pi$
$942$	5.38410			0.175423
$943$	64.4311			2.09817
$944$	7.58647	+	6.36581i	0.246919	+	0.207189i
$945$	0.169597	+	9.20979i	0.00551699	+	0.299595i
$946$	13.2990	+	36.5386i	0.432387	+	1.18797i
$947$	37.8521	+	13.7770i	1.23003	+	0.447694i	0.873607	−	0.486632i	$-0.161775\pi$
$947$	37.8521	+	13.7770i	1.23003	+	0.447694i	0.356421	+	0.934326i	$0.383997\pi$
$948$	1.56578	−	4.30195i	0.0508543	−	0.139721i
$949$	−6.81367	−	3.93387i	−0.221181	−	0.127699i
$950$	−10.3867	−	35.3940i	−0.336990	−	1.14833i
$951$			20.3438i			0.659693i
$952$	−20.9085	+	37.8054i	−0.677647	+	1.22528i
$953$	−16.3056	−	19.4322i	−0.528189	−	0.629472i	0.434307	−	0.900765i	$-0.356993\pi$
$953$	−16.3056	−	19.4322i	−0.528189	−	0.629472i	−0.962497	+	0.271293i	$0.912549\pi$
$954$	−4.41741	−	3.70665i	−0.143019	−	0.120007i
$955$	1.36164	+	1.62274i	0.0440617	+	0.0525107i
$956$	−7.83591	+	2.85204i	−0.253431	+	0.0922415i
$957$			9.12282i			0.294899i
$958$	−1.63010	−	2.82342i	−0.0526661	−	0.0912204i
$959$	−31.3398	+	27.2961i	−1.01202	+	0.881439i
$960$	30.0554	+	5.29957i	0.970033	+	0.171043i
$961$	−0.534324	+	0.925476i	−0.0172363	+	0.0298541i
$962$	2.22178	+	3.84823i	0.0716329	+	0.124072i
$963$	−2.50986	−	6.89578i	−0.0808790	−	0.222213i
$964$	0.106369	+	0.603249i	0.00342592	+	0.0194293i
$965$	−69.3238	+	25.2318i	−2.23161	+	0.812241i
$966$	−16.0592	−	8.88164i	−0.516697	−	0.285762i
$967$	9.95880	+	56.4792i	0.320254	+	1.81625i	0.541121	+	0.840944i	$0.318000\pi$
$967$	9.95880	+	56.4792i	0.320254	+	1.81625i	−0.220868	+	0.975304i	$0.570889\pi$
$968$	−24.2535	+	14.0028i	−0.779537	+	0.450066i
$969$	13.7198	+	18.6398i	0.440744	+	0.598797i
$970$	−25.4278	+	44.0422i	−0.816437	+	1.41411i
$971$	3.86156	−	3.24023i	0.123923	−	0.103984i	−0.578720	−	0.815526i	$-0.696448\pi$
$971$	3.86156	−	3.24023i	0.123923	−	0.103984i	0.702643	+	0.711542i	$0.252003\pi$
$972$	−0.450360	+	0.377897i	−0.0144453	+	0.0121210i
$973$	26.2073	−	5.12028i	0.840167	−	0.164149i
$974$	−0.241053	−	0.0877360i	−0.00772383	−	0.00281124i
$975$	1.16617	−	6.61369i	0.0373474	−	0.211808i
$976$	−14.4591	+	8.34795i	−0.462824	+	0.267211i
$977$			52.7554i			1.68779i	0.536505	+	0.843897i	$0.319744\pi$
$977$			52.7554i			1.68779i	−0.536505	+	0.843897i	$0.680256\pi$
$978$	−7.14853	−	19.6404i	−0.228585	−	0.628032i
$979$	12.0159	−	68.1458i	0.384031	−	2.17795i
$980$	−14.0089	+	3.00579i	−0.447498	+	0.0960166i
$981$	−3.33994	−	1.92831i	−0.106636	−	0.0615663i
$982$	−1.78929	−	0.315500i	−0.0570985	−	0.0100680i
$983$	17.1546	−	14.3944i	0.547145	−	0.459109i	−0.326828	−	0.945084i	$-0.605980\pi$
$983$	17.1546	−	14.3944i	0.547145	−	0.459109i	0.873973	+	0.485975i	$0.161535\pi$
$984$	−33.4298	−	5.89458i	−1.06570	−	0.187912i
$985$	0.958024	−	2.63215i	0.0305252	−	0.0838673i
$986$	−12.6420	+	2.22913i	−0.402604	+	0.0709899i
$987$	−21.0707	−	3.31655i	−0.670687	−	0.105567i
$988$	2.41177	+	0.153643i	0.0767287	+	0.00488804i
$989$	21.2974	+	36.8881i	0.677217	+	1.17297i
$990$	−17.4327	−	6.34497i	−0.554046	−	0.201656i
$991$	−39.8658	+	7.02941i	−1.26638	+	0.223297i	−0.766186	−	0.642618i	$-0.777848\pi$
$991$	−39.8658	+	7.02941i	−1.26638	+	0.223297i	−0.500191	+	0.865915i	$0.666737\pi$
$992$	11.6670	−	13.9042i	0.370428	−	0.441459i
$993$	−2.30174	+	6.32398i	−0.0730436	+	0.200686i
$994$	2.98774	+	1.02556i	0.0947655	+	0.0325287i
$995$	1.95706	−	3.38973i	0.0620429	−	0.107462i
$996$	6.86215	+	3.96186i	0.217436	+	0.125536i
$997$	−7.35640	+	8.76701i	−0.232979	+	0.277654i	−0.869850	−	0.493317i	$-0.835784\pi$
$997$	−7.35640	+	8.76701i	−0.232979	+	0.277654i	0.636870	+	0.770971i	$0.280229\pi$
$998$	−12.3671	+	14.7385i	−0.391473	+	0.466539i
$999$	−3.43396	−	1.98259i	−0.108646	−	0.0627265i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.ck.a.10.5	yes	78
7.5	odd	6		399.2.cd.a.124.5	✓	78
19.2	odd	18		399.2.cd.a.325.5	yes	78
133.40	even	18	inner	399.2.ck.a.40.5	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.cd.a.124.5	✓	78	7.5	odd	6
399.2.cd.a.325.5	yes	78	19.2	odd	18
399.2.ck.a.10.5	yes	78	1.1	even	1	trivial
399.2.ck.a.40.5	yes	78	133.40	even	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.763835 - 0.910304i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.102088 - 0.578971i) q^{4} +(-3.42867 + 0.604567i) q^{5} +(-0.763835 + 0.910304i) q^{6} +(-2.05773 - 1.66305i) q^{7} +(-2.66324 + 1.53762i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(3.16928 + 2.65934i) q^{10} +4.48406 q^{11} -0.587903 q^{12} +(0.722417 + 0.606180i) q^{13} +(0.0578863 + 3.14346i) q^{14} +(1.19077 + 3.27160i) q^{15} +(2.32909 + 0.847719i) q^{16} +(-1.81604 + 4.98954i) q^{17} +(1.02911 + 0.594159i) q^{18} +(3.15422 + 3.00847i) q^{19} +2.04682i q^{20} +(-1.28046 + 2.31526i) q^{21} +(-3.42508 - 4.08185i) q^{22} +(-4.47144 - 3.75198i) q^{23} +(1.97673 + 2.35578i) q^{24} +(6.69183 - 2.43563i) q^{25} -1.12064i q^{26} +(0.500000 + 0.866025i) q^{27} +(-1.17293 + 1.02159i) q^{28} +(-2.00359 - 0.353287i) q^{29} +(2.06860 - 3.58292i) q^{30} +(-2.83146 - 4.90423i) q^{31} +(1.09623 + 3.01188i) q^{32} +(-0.778648 - 4.41593i) q^{33} +(5.92915 - 2.15803i) q^{34} +(8.06071 + 4.45802i) q^{35} +(0.102088 + 0.578971i) q^{36} +(-3.43396 + 1.98259i) q^{37} +(0.329311 - 5.16928i) q^{38} +(0.471524 - 0.816703i) q^{39} +(8.20179 - 6.88212i) q^{40} +(-8.45583 + 7.09529i) q^{41} +(3.08565 - 0.602863i) q^{42} +(-6.85723 - 2.49583i) q^{43} +(0.457769 - 2.59614i) q^{44} +(3.01512 - 1.74078i) q^{45} +6.93626i q^{46} +(2.75737 + 7.57582i) q^{47} +(0.430398 - 2.44091i) q^{48} +(1.46852 + 6.84423i) q^{49} +(-7.32861 - 4.23118i) q^{50} +(5.22909 + 0.922029i) q^{51} +(0.424711 - 0.356375i) q^{52} +(-4.77895 - 0.842659i) q^{53} +(0.406428 - 1.11665i) q^{54} +(-15.3744 + 2.71091i) q^{55} +(8.03739 + 1.26509i) q^{56} +(2.41504 - 3.62872i) q^{57} +(1.20882 + 2.09373i) q^{58} +(3.75467 + 1.36659i) q^{59} +(2.01573 - 0.355427i) q^{60} +(-4.32989 + 5.16017i) q^{61} +(-2.30157 + 6.32351i) q^{62} +(2.50243 + 0.858972i) q^{63} +(4.38295 - 7.59149i) q^{64} +(-2.84341 - 1.64164i) q^{65} +(-3.42508 + 4.08185i) q^{66} +(7.84425 - 9.34841i) q^{67} +(2.70340 + 1.56081i) q^{68} +(-2.91852 + 5.05503i) q^{69} +(-2.09891 - 10.7429i) q^{70} +(0.343637 - 0.944136i) q^{71} +(1.97673 - 2.35578i) q^{72} +(-8.21615 + 1.44873i) q^{73} +(4.42774 + 1.61157i) q^{74} +(-3.56065 - 6.16722i) q^{75} +(2.06382 - 1.51907i) q^{76} +(-9.22698 - 7.45722i) q^{77} +(-1.10361 + 0.194597i) q^{78} +(-2.66334 + 7.31746i) q^{79} +(-8.49819 - 1.49846i) q^{80} +(0.766044 - 0.642788i) q^{81} +(12.9177 + 2.27774i) q^{82} +(-11.6723 - 6.73898i) q^{83} +(1.20975 + 0.977712i) q^{84} +(3.21010 - 18.2054i) q^{85} +(2.96583 + 8.14856i) q^{86} +2.03450i q^{87} +(-11.9421 + 6.89479i) q^{88} +(2.67971 - 15.1974i) q^{89} +(-3.88770 - 1.41501i) q^{90} +(-0.478432 - 2.44877i) q^{91} +(-2.62877 + 2.20580i) q^{92} +(-4.33805 + 3.64005i) q^{93} +(4.79012 - 8.29672i) q^{94} +(-12.6336 - 8.40811i) q^{95} +(2.77576 - 1.60259i) q^{96} +(2.13453 + 12.1055i) q^{97} +(5.10862 - 6.56466i) q^{98} +(-4.21363 + 1.53364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q - 6 q^{7} + 12 q^{10} + 6 q^{11} + 72 q^{12} + 3 q^{13} - 15 q^{14} + 18 q^{19} + 9 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{24} + 18 q^{25} + 39 q^{27} - 9 q^{28} - 6 q^{29} - 18 q^{31} - 51 q^{32} - 12 q^{33}+ \cdots - 6 q^{99}+O(q^{100}) \) 78 * q - 6 * q^7 + 12 * q^10 + 6 * q^11 + 72 * q^12 + 3 * q^13 - 15 * q^14 + 18 * q^19 + 9 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^24 + 18 * q^25 + 39 * q^27 - 9 * q^28 - 6 * q^29 - 18 * q^31 - 51 * q^32 - 12 * q^33 + 30 * q^34 + 33 * q^35 + 18 * q^37 - 57 * q^38 - 18 * q^40 - 63 * q^41 - 27 * q^42 - 51 * q^43 - 36 * q^44 + 9 * q^45 - 84 * q^47 + 18 * q^49 - 27 * q^50 - 18 * q^51 + 18 * q^52 - 45 * q^53 + 30 * q^55 + 33 * q^56 - 6 * q^57 - 18 * q^58 - 24 * q^59 + 66 * q^61 + 171 * q^62 + 6 * q^63 + 18 * q^64 - 99 * q^65 - 12 * q^66 - 24 * q^67 - 12 * q^69 - 150 * q^70 - 66 * q^71 - 9 * q^72 + 3 * q^73 + 18 * q^74 - 36 * q^75 - 12 * q^76 + 21 * q^77 + 75 * q^78 + 45 * q^79 + 78 * q^80 - 24 * q^82 - 72 * q^83 - 9 * q^84 + 60 * q^85 - 9 * q^86 - 108 * q^88 + 48 * q^89 - 33 * q^90 - 54 * q^91 - 102 * q^92 + 9 * q^93 - 66 * q^94 - 84 * q^95 + 75 * q^97 - 39 * q^98 - 6 * q^99

Introduction

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