LMFDB - Embedded newform 840.2.dj.a.67.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(67,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.dj (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.17
Character	$\chi$	$=$	840.67
Dual form			840.2.dj.a.163.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19136 + 0.762012i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.838675 - 1.81566i) q^{4} +(1.67469 - 1.48169i) q^{5} +(-1.04439 - 0.953542i) q^{6} +(2.57507 + 0.607466i) q^{7} +(0.384392 + 2.80219i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.866099 + 3.04136i) q^{10} +(2.35319 - 4.07584i) q^{11} +(1.97086 + 0.340171i) q^{12} +(1.44964 + 1.44964i) q^{13} +(-3.53073 + 1.23852i) q^{14} +(1.86464 + 1.23414i) q^{15} +(-2.59325 - 3.04550i) q^{16} +(2.50853 - 0.672160i) q^{17} +(0.650742 - 1.25560i) q^{18} +(-5.85686 + 3.38146i) q^{19} +(-1.28572 - 4.28333i) q^{20} +(0.0797100 + 2.64455i) q^{21} +(0.302347 + 6.64895i) q^{22} +(1.39288 - 5.19831i) q^{23} +(-2.60722 + 1.09655i) q^{24} +(0.609203 - 4.96275i) q^{25} +(-2.83168 - 0.622398i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.26260 - 4.16599i) q^{28} +5.50415 q^{29} +(-3.16189 - 0.0494257i) q^{30} +(-2.13639 - 1.23344i) q^{31} +(5.41020 + 1.65220i) q^{32} +(4.54601 + 1.21810i) q^{33} +(-2.47637 + 2.71232i) q^{34} +(5.21253 - 2.79813i) q^{35} +(0.181516 + 1.99175i) q^{36} +(-7.14437 - 1.91433i) q^{37} +(4.40091 - 8.49153i) q^{38} +(-1.02505 + 1.77544i) q^{39} +(4.79570 + 4.12326i) q^{40} -2.96457 q^{41} +(-2.11014 - 3.08987i) q^{42} +(1.62218 - 1.62218i) q^{43} +(-5.42679 - 7.69090i) q^{44} +(-0.709484 + 2.12053i) q^{45} +(2.30175 + 7.25446i) q^{46} +(4.88880 + 1.30995i) q^{47} +(2.27054 - 3.29312i) q^{48} +(6.26197 + 3.12853i) q^{49} +(3.05589 + 6.37664i) q^{50} +(1.29851 + 2.24909i) q^{51} +(3.84782 - 1.41627i) q^{52} +(8.75023 - 2.34462i) q^{53} +(1.38124 + 0.303595i) q^{54} +(-2.09825 - 10.3125i) q^{55} +(-0.712397 + 7.44933i) q^{56} +(-4.78211 - 4.78211i) q^{57} +(-6.55742 + 4.19423i) q^{58} +(-11.4335 - 6.60111i) q^{59} +(3.80461 - 2.35052i) q^{60} +(8.44371 - 4.87498i) q^{61} +(3.48510 - 0.158478i) q^{62} +(-2.53381 + 0.761454i) q^{63} +(-7.70449 + 2.15427i) q^{64} +(4.57561 + 0.279790i) q^{65} +(-6.34414 + 2.01292i) q^{66} +(-11.1212 + 2.97990i) q^{67} +(0.883432 - 5.11837i) q^{68} +5.38169 q^{69} +(-4.07779 + 7.30559i) q^{70} +14.5259i q^{71} +(-1.73399 - 2.23457i) q^{72} +(3.44791 + 12.8678i) q^{73} +(9.97026 - 3.16344i) q^{74} +(4.95132 - 0.696009i) q^{75} +(1.22758 + 13.4700i) q^{76} +(8.53556 - 9.06610i) q^{77} +(-0.131702 - 2.89628i) q^{78} +(6.51800 + 11.2895i) q^{79} +(-8.85538 - 1.25790i) q^{80} +(0.500000 - 0.866025i) q^{81} +(3.53187 - 2.25904i) q^{82} +(-3.03652 + 3.03652i) q^{83} +(4.86846 + 2.07319i) q^{84} +(3.20510 - 4.84253i) q^{85} +(-0.696480 + 3.16872i) q^{86} +(1.42458 + 5.31660i) q^{87} +(12.3258 + 5.02735i) q^{88} +(-0.0534045 + 0.0308331i) q^{89} +(-0.770616 - 3.06694i) q^{90} +(2.85231 + 4.61352i) q^{91} +(-8.27020 - 6.88870i) q^{92} +(0.638477 - 2.38283i) q^{93} +(-6.82251 + 2.16470i) q^{94} +(-4.79818 + 14.3410i) q^{95} +(-0.195639 + 5.65347i) q^{96} +(8.57024 + 8.57024i) q^{97} +(-9.84424 + 1.04449i) q^{98} +4.70638i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) $ 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.19136	+	0.762012i	−0.842418	+	0.538824i
$2$	−1.19136	+	0.762012i	−0.842418	+	0.538824i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.838675	−	1.81566i	0.419338	−	0.907830i
$5$	1.67469	−	1.48169i	0.748946	−	0.662631i
$5$	1.67469	−	1.48169i	0.748946	−	0.662631i
$6$	−1.04439	−	0.953542i	−0.426372	−	0.389282i
$7$	2.57507	+	0.607466i	0.973285	+	0.229601i
$7$	2.57507	+	0.607466i	0.973285	+	0.229601i
$8$	0.384392	+	2.80219i	0.135903	+	0.990722i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−0.866099	+	3.04136i	−0.273885	+	0.961763i
$11$	2.35319	−	4.07584i	0.709513	−	1.22891i	−0.255525	−	0.966803i	$-0.582248\pi$
$11$	2.35319	−	4.07584i	0.709513	−	1.22891i	0.965038	−	0.262110i	$-0.0844185\pi$
$12$	1.97086	+	0.340171i	0.568938	+	0.0981988i
$13$	1.44964	+	1.44964i	0.402057	+	0.402057i	0.878957	−	0.476900i	$-0.158240\pi$
$13$	1.44964	+	1.44964i	0.402057	+	0.402057i	−0.476900	+	0.878957i	$0.658240\pi$
$14$	−3.53073	+	1.23852i	−0.943627	+	0.331009i
$15$	1.86464	+	1.23414i	0.481449	+	0.318654i
$16$	−2.59325	−	3.04550i	−0.648312	−	0.761375i
$17$	2.50853	−	0.672160i	0.608409	−	0.163023i	0.0585560	−	0.998284i	$-0.481350\pi$
$17$	2.50853	−	0.672160i	0.608409	−	0.163023i	0.549853	+	0.835261i	$0.314684\pi$
$18$	0.650742	−	1.25560i	0.153381	−	0.295948i
$19$	−5.85686	+	3.38146i	−1.34366	+	0.775760i	−0.987342	−	0.158606i	$-0.949300\pi$
$19$	−5.85686	+	3.38146i	−1.34366	+	0.775760i	−0.356314	+	0.934366i	$0.615967\pi$
$20$	−1.28572	−	4.28333i	−0.287495	−	0.957782i
$21$	0.0797100	+	2.64455i	0.0173942	+	0.577088i
$22$	0.302347	+	6.64895i	0.0644606	+	1.41756i
$23$	1.39288	−	5.19831i	0.290436	−	1.08392i	−0.654338	−	0.756202i	$-0.727053\pi$
$23$	1.39288	−	5.19831i	0.290436	−	1.08392i	0.944774	−	0.327721i	$-0.106281\pi$
$24$	−2.60722	+	1.09655i	−0.532196	+	0.223833i
$25$	0.609203	−	4.96275i	0.121841	−	0.992550i
$26$	−2.83168	−	0.622398i	−0.555338	−	0.122062i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	3.26260	−	4.16599i	0.616573	−	0.787297i
$29$	5.50415			1.02209			0.511047	−	0.859553i	$-0.329258\pi$
$29$	5.50415			1.02209			0.511047	+	0.859553i	$0.329258\pi$
$30$	−3.16189	−	0.0494257i	−0.577280	−	0.00902386i
$31$	−2.13639	−	1.23344i	−0.383706	−	0.221533i	0.295723	−	0.955274i	$-0.404439\pi$
$31$	−2.13639	−	1.23344i	−0.383706	−	0.221533i	−0.679430	+	0.733741i	$0.737773\pi$
$32$	5.41020	+	1.65220i	0.956397	+	0.292070i
$33$	4.54601	+	1.21810i	0.791359	+	0.212044i
$34$	−2.47637	+	2.71232i	−0.424694	+	0.465159i
$35$	5.21253	−	2.79813i	0.881078	−	0.472970i
$36$	0.181516	+	1.99175i	0.0302527	+	0.331958i
$37$	−7.14437	−	1.91433i	−1.17453	−	0.314714i	−0.381774	−	0.924256i	$-0.624687\pi$
$37$	−7.14437	−	1.91433i	−1.17453	−	0.314714i	−0.792754	+	0.609542i	$0.791353\pi$
$38$	4.40091	−	8.49153i	0.713923	−	1.37751i
$39$	−1.02505	+	1.77544i	−0.164139	+	0.284297i
$40$	4.79570	+	4.12326i	0.758267	+	0.651944i
$41$	−2.96457			−0.462988			−0.231494	−	0.972836i	$-0.574361\pi$
$41$	−2.96457			−0.462988			−0.231494	+	0.972836i	$0.574361\pi$
$42$	−2.11014	−	3.08987i	−0.325602	−	0.476777i
$43$	1.62218	−	1.62218i	0.247380	−	0.247380i	−0.572514	−	0.819895i	$-0.694032\pi$
$43$	1.62218	−	1.62218i	0.247380	−	0.247380i	0.819895	+	0.572514i	$0.194032\pi$
$44$	−5.42679	−	7.69090i	−0.818119	−	1.15945i
$45$	−0.709484	+	2.12053i	−0.105764	+	0.316109i
$46$	2.30175	+	7.25446i	0.339375	+	1.06961i
$47$	4.88880	+	1.30995i	0.713104	+	0.191076i	0.597093	−	0.802172i	$-0.296322\pi$
$47$	4.88880	+	1.30995i	0.713104	+	0.191076i	0.116011	+	0.993248i	$0.462989\pi$
$48$	2.27054	−	3.29312i	0.327725	−	0.475321i
$49$	6.26197	+	3.12853i	0.894567	+	0.446934i
$50$	3.05589	+	6.37664i	0.432169	+	0.901793i
$51$	1.29851	+	2.24909i	0.181828	+	0.314936i
$52$	3.84782	−	1.41627i	0.533597	−	0.196402i
$53$	8.75023	−	2.34462i	1.20194	−	0.322058i	0.398343	−	0.917237i	$-0.369585\pi$
$53$	8.75023	−	2.34462i	1.20194	−	0.322058i	0.803593	+	0.595179i	$0.202919\pi$
$54$	1.38124	+	0.303595i	0.187963	+	0.0413140i
$55$	−2.09825	−	10.3125i	−0.282929	−	1.39054i
$56$	−0.712397	+	7.44933i	−0.0951981	+	0.995458i
$57$	−4.78211	−	4.78211i	−0.633406	−	0.633406i
$58$	−6.55742	+	4.19423i	−0.861031	+	0.550729i
$59$	−11.4335	−	6.60111i	−1.48851	−	0.859392i	−0.488596	−	0.872510i	$-0.662491\pi$
$59$	−11.4335	−	6.60111i	−1.48851	−	0.859392i	−0.999914	+	0.0131180i	$0.995824\pi$
$60$	3.80461	−	2.35052i	0.491173	−	0.303450i
$61$	8.44371	−	4.87498i	1.08111	−	0.624177i	0.149911	−	0.988699i	$-0.452101\pi$
$61$	8.44371	−	4.87498i	1.08111	−	0.624177i	0.931194	+	0.364523i	$0.118768\pi$
$62$	3.48510	−	0.158478i	0.442609	−	0.0201267i
$63$	−2.53381	+	0.761454i	−0.319230	+	0.0959342i
$64$	−7.70449	+	2.15427i	−0.963061	+	0.269284i
$65$	4.57561	+	0.279790i	0.567534	+	0.0347036i
$66$	−6.34414	+	2.01292i	−0.780910	+	0.247773i
$67$	−11.1212	+	2.97990i	−1.35867	+	0.364053i	−0.863326	−	0.504646i	$-0.831623\pi$
$67$	−11.1212	+	2.97990i	−1.35867	+	0.364053i	−0.495339	+	0.868700i	$0.664956\pi$
$68$	0.883432	−	5.11837i	0.107132	−	0.620694i
$69$	5.38169			0.647879
$70$	−4.07779	+	7.30559i	−0.487389	+	0.873185i
$71$			14.5259i			1.72391i	0.506984	+	0.861955i	$0.330760\pi$
$71$			14.5259i			1.72391i	−0.506984	+	0.861955i	$0.669240\pi$
$72$	−1.73399	−	2.23457i	−0.204352	−	0.263346i
$73$	3.44791	+	12.8678i	0.403547	+	1.50606i	0.806720	+	0.590934i	$0.201241\pi$
$73$	3.44791	+	12.8678i	0.403547	+	1.50606i	−0.403173	+	0.915124i	$0.632093\pi$
$74$	9.97026	−	3.16344i	1.15902	−	0.367743i
$75$	4.95132	−	0.696009i	0.571729	−	0.0803682i
$76$	1.22758	+	13.4700i	0.140813	+	1.54512i
$77$	8.53556	−	9.06610i	0.972718	−	1.03318i
$78$	−0.131702	−	2.89628i	−0.0149124	−	0.327939i
$79$	6.51800	+	11.2895i	0.733332	+	1.27017i	0.955451	+	0.295149i	$0.0953692\pi$
$79$	6.51800	+	11.2895i	0.733332	+	1.27017i	−0.222119	+	0.975020i	$0.571297\pi$
$80$	−8.85538	−	1.25790i	−0.990061	−	0.140637i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	3.53187	−	2.25904i	0.390029	−	0.249469i
$83$	−3.03652	+	3.03652i	−0.333301	+	0.333301i	−0.853839	−	0.520537i	$-0.825732\pi$
$83$	−3.03652	+	3.03652i	−0.333301	+	0.333301i	0.520537	+	0.853839i	$0.325732\pi$
$84$	4.86846	+	2.07319i	0.531192	+	0.226204i
$85$	3.20510	−	4.84253i	0.347642	−	0.525246i
$86$	−0.696480	+	3.16872i	−0.0751034	+	0.341692i
$87$	1.42458	+	5.31660i	0.152731	+	0.569999i
$88$	12.3258	+	5.02735i	1.31394	+	0.535918i
$89$	−0.0534045	+	0.0308331i	−0.00566087	+	0.00326830i	−0.502828	−	0.864387i	$-0.667707\pi$
$89$	−0.0534045	+	0.0308331i	−0.00566087	+	0.00326830i	0.497167	+	0.867655i	$0.334374\pi$
$90$	−0.770616	−	3.06694i	−0.0812301	−	0.323284i
$91$	2.85231	+	4.61352i	0.299004	+	0.483629i
$92$	−8.27020	−	6.88870i	−0.862228	−	0.718197i
$93$	0.638477	−	2.38283i	0.0662070	−	0.247088i
$94$	−6.82251	+	2.16470i	−0.703688	+	0.223272i
$95$	−4.79818	+	14.3410i	−0.492283	+	1.47135i
$96$	−0.195639	+	5.65347i	−0.0199674	+	0.577005i
$97$	8.57024	+	8.57024i	0.870176	+	0.870176i	0.992491	−	0.122316i	$-0.0390320\pi$
$97$	8.57024	+	8.57024i	0.870176	+	0.870176i	−0.122316	+	0.992491i	$0.539032\pi$
$98$	−9.84424	+	1.04449i	−0.994418	+	0.105509i
$99$			4.70638i			0.473009i
$100$	−8.49974	−	5.26824i	−0.849974	−	0.526824i
$101$	1.82908	+	1.05602i	0.182000	+	0.105078i	0.588232	−	0.808692i	$-0.299824\pi$
$101$	1.82908	+	1.05602i	0.182000	+	0.105078i	−0.406232	+	0.913770i	$0.633157\pi$
$102$	−3.26083	−	1.68999i	−0.322870	−	0.167334i
$103$	−1.23422	+	4.60616i	−0.121611	+	0.453858i	−0.999696	−	0.0246459i	$-0.992154\pi$
$103$	−1.23422	+	4.60616i	−0.121611	+	0.453858i	0.878085	+	0.478504i	$0.158821\pi$
$104$	−3.50492	+	4.61938i	−0.343686	+	0.452968i
$105$	4.05189	+	4.31071i	0.395424	+	0.420682i
$106$	−8.63804	+	9.46106i	−0.839001	+	0.918939i
$107$	0.271567	−	1.01350i	0.0262534	−	0.0979790i	−0.951556	−	0.307475i	$-0.900516\pi$
$107$	0.271567	−	1.01350i	0.0262534	−	0.0979790i	0.977809	+	0.209496i	$0.0671825\pi$
$108$	−1.87690	+	0.690833i	−0.180605	+	0.0664754i
$109$	−1.86809	+	3.23562i	−0.178930	+	0.309916i	−0.941514	−	0.336973i	$-0.890597\pi$
$109$	−1.86809	+	3.23562i	−0.178930	+	0.309916i	0.762584	+	0.646889i	$0.223930\pi$
$110$	10.3580	+	10.6870i	0.987598	+	1.01896i
$111$		−	7.39640i		−	0.702035i
$112$	−4.82776	−	9.41768i	−0.456180	−	0.889887i
$113$	0.228114	−	0.228114i	0.0214591	−	0.0214591i	−0.696296	−	0.717755i	$-0.745170\pi$
$113$	0.228114	−	0.228114i	0.0214591	−	0.0214591i	0.717755	+	0.696296i	$0.245170\pi$
$114$	9.34123	+	2.05319i	0.874887	+	0.192298i
$115$	−5.36962	−	10.7694i	−0.500720	−	1.00425i
$116$	4.61619	−	9.99367i	0.428603	−	0.927889i
$117$	−1.98024	−	0.530604i	−0.183073	−	0.0490544i
$118$	18.6515	−	0.848138i	1.71701	−	0.0780774i
$119$	6.86797	−	0.207009i	0.629585	−	0.0189765i
$120$	−2.74154	+	5.69947i	−0.250267	+	0.520288i
$121$	−5.57500	−	9.65618i	−0.506818	−	0.877835i
$122$	−6.34470	+	12.2421i	−0.574422	+	1.10834i
$123$	−0.767287	−	2.86355i	−0.0691839	−	0.258198i
$124$	−4.03125	+	2.84449i	−0.362017	+	0.255443i
$125$	−6.33302	−	9.21374i	−0.566442	−	0.824102i
$126$	2.43844	−	2.83796i	0.217234	−	0.252825i
$127$	11.7532	−	11.7532i	1.04293	−	1.04293i	0.0438900	−	0.999036i	$-0.486025\pi$
$127$	11.7532	−	11.7532i	1.04293	−	1.04293i	0.999036	−	0.0438900i	$-0.0139751\pi$
$128$	7.53723	−	8.43742i	0.666203	−	0.745770i
$129$	1.98676	+	1.14706i	0.174924	+	0.100993i
$130$	−5.66440	+	3.15334i	−0.496801	+	0.276566i
$131$	−2.27304	−	3.93702i	−0.198596	−	0.343979i	0.749477	−	0.662030i	$-0.230305\pi$
$131$	−2.27304	−	3.93702i	−0.198596	−	0.343979i	−0.948073	+	0.318051i	$0.896972\pi$
$132$	6.02429	−	7.23243i	0.524347	−	0.629502i
$133$	−17.1360	+	5.14965i	−1.48588	+	0.446532i
$134$	10.9786	−	12.0246i	0.948404	−	1.03877i
$135$	−2.23190	−	0.136476i	−0.192091	−	0.0117460i
$136$	2.84778	+	6.77101i	0.244195	+	0.580609i
$137$	−5.65872	+	1.51625i	−0.483457	+	0.129542i	−0.492312	−	0.870419i	$-0.663848\pi$
$137$	−5.65872	+	1.51625i	−0.483457	+	0.129542i	0.00885501	+	0.999961i	$0.497181\pi$
$138$	−6.41153	+	4.10091i	−0.545786	+	0.349093i
$139$			20.8393i			1.76757i	0.467896	+	0.883784i	$0.345012\pi$
$139$			20.8393i			1.76757i	−0.467896	+	0.883784i	$0.654988\pi$
$140$	−0.708834	−	11.8109i	−0.0599074	−	0.998204i
$141$			5.06125i			0.426234i
$142$	−11.0689	−	17.3056i	−0.928884	−	1.45225i
$143$	9.31976	−	2.49722i	0.779358	−	0.208828i
$144$	3.76857	+	1.34086i	0.314047	+	0.111738i
$145$	9.21777	−	8.15543i	0.765494	−	0.677272i
$146$	−13.9131	−	12.7028i	−1.15146	−	1.05129i
$147$	−1.40122	+	6.85832i	−0.115570	+	0.565665i
$148$	−9.46758	+	11.3663i	−0.778230	+	0.934301i
$149$	−3.15549	−	5.46546i	−0.258507	−	0.447748i	0.707335	−	0.706879i	$-0.249897\pi$
$149$	−3.15549	−	5.46546i	−0.258507	−	0.447748i	−0.965842	+	0.259131i	$0.916564\pi$
$150$	−5.36844	+	4.60216i	−0.438331	+	0.375765i
$151$	−15.5775	−	8.99367i	−1.26768	−	0.731895i	−0.293130	−	0.956072i	$-0.594697\pi$
$151$	−15.5775	−	8.99367i	−1.26768	−	0.731895i	−0.974548	+	0.224178i	$0.928030\pi$
$152$	−11.7268	−	15.1122i	−0.951170	−	1.22576i
$153$	−1.83637	+	1.83637i	−0.148462	+	0.148462i
$154$	−3.26045	+	17.3052i	−0.262734	+	1.39449i
$155$	−5.40537	+	1.09982i	−0.434170	+	0.0883394i
$156$	2.36391	+	3.35015i	0.189264	+	0.268227i
$157$	−3.72103	−	13.8871i	−0.296970	−	1.10831i	−0.939640	−	0.342165i	$-0.888840\pi$
$157$	−3.72103	−	13.8871i	−0.296970	−	1.10831i	0.642670	−	0.766143i	$-0.277827\pi$
$158$	−16.3680	−	8.48307i	−1.30217	−	0.674876i
$159$	4.52945	+	7.84524i	0.359209	+	0.622168i
$160$	11.5085	−	5.24930i	0.909825	−	0.414993i
$161$	6.74457	−	12.5399i	0.531547	−	0.988282i
$162$	0.0642420	+	1.41275i	0.00504733	+	0.110996i
$163$	18.8703	+	5.05628i	1.47804	+	0.396039i	0.905679	−	0.423965i	$-0.139362\pi$
$163$	18.8703	+	5.05628i	1.47804	+	0.396039i	0.572358	+	0.820004i	$0.306029\pi$
$164$	−2.48631	+	5.38265i	−0.194148	+	0.420314i
$165$	9.41803	−	4.69583i	0.733192	−	0.365569i
$166$	1.30372	−	5.93145i	0.101188	−	0.460370i
$167$	−2.13748	+	2.13748i	−0.165403	+	0.165403i	−0.784955	−	0.619552i	$-0.787314\pi$
$167$	−2.13748	+	2.13748i	−0.165403	+	0.165403i	0.619552	+	0.784955i	$0.287314\pi$
$168$	−7.37988	+	1.23991i	−0.569370	+	0.0956608i
$169$		−	8.79710i		−	0.676700i
$170$	−0.128360	+	8.21151i	−0.00984476	+	0.629794i
$171$	3.38146	−	5.85686i	0.258587	−	0.447885i
$172$	−1.58485	−	4.30582i	−0.120844	−	0.328315i
$173$	4.12015	−	15.3766i	0.313249	−	1.16906i	−0.612359	−	0.790580i	$-0.709779\pi$
$173$	4.12015	−	15.3766i	0.313249	−	1.16906i	0.925608	−	0.378483i	$-0.123554\pi$
$174$	−5.74850	−	5.24844i	−0.435793	−	0.397883i
$175$	4.58344	−	12.4094i	0.346476	−	0.938059i
$176$	−18.5154	+	3.40303i	−1.39565	+	0.256513i
$177$	3.41699	−	12.7524i	0.256837	−	0.958527i
$178$	0.0401288	−	0.0774282i	0.00300778	−	0.00580349i
$179$	−9.28847	−	5.36270i	−0.694253	−	0.400827i	0.110950	−	0.993826i	$-0.464611\pi$
$179$	−9.28847	−	5.36270i	−0.694253	−	0.400827i	−0.805203	+	0.592999i	$0.797944\pi$
$180$	3.25513	+	3.06662i	0.242623	+	0.228572i
$181$			3.28428i			0.244118i	0.992523	+	0.122059i	$0.0389498\pi$
$181$			3.28428i			0.244118i	−0.992523	+	0.122059i	$0.961050\pi$
$182$	−6.91369	−	3.32287i	−0.512477	−	0.246307i
$183$	6.89426	+	6.89426i	0.509638	+	0.509638i
$184$	15.1021	+	1.90493i	1.11334	+	0.140433i
$185$	−14.8011	+	7.37981i	−1.08820	+	0.542575i
$186$	1.05509	+	3.32533i	0.0773629	+	0.243825i
$187$	3.16344	−	11.8061i	0.231334	−	0.863349i
$188$	6.47853	−	7.77777i	0.472496	−	0.567252i
$189$	−1.39131	−	2.25039i	−0.101203	−	0.163692i
$190$	−5.21162	−	20.7415i	−0.378090	−	1.50475i
$191$	0.546315	−	0.315415i	0.0395299	−	0.0228226i	−0.480105	−	0.877211i	$-0.659401\pi$
$191$	0.546315	−	0.315415i	0.0395299	−	0.0228226i	0.519635	+	0.854389i	$0.326068\pi$
$192$	−4.07494	−	6.88440i	−0.294083	−	0.496838i
$193$	0.881651	+	3.29037i	0.0634627	+	0.236846i	0.990370	−	0.138444i	$-0.0442100\pi$
$193$	0.881651	+	3.29037i	0.0634627	+	0.236846i	−0.926908	+	0.375289i	$0.877543\pi$
$194$	−16.7409	−	3.67961i	−1.20192	−	0.264181i
$195$	0.913999	+	4.49211i	0.0654528	+	0.321687i
$196$	10.9321	−	8.74579i	0.780866	−	0.624699i
$197$	−8.07539	+	8.07539i	−0.575347	+	0.575347i	−0.933618	−	0.358270i	$-0.883367\pi$
$197$	−8.07539	+	8.07539i	−0.575347	+	0.575347i	0.358270	+	0.933618i	$0.383367\pi$
$198$	−3.58632	−	5.60699i	−0.254868	−	0.398471i
$199$	−8.10365	+	14.0359i	−0.574453	+	0.994981i	0.421648	+	0.906760i	$0.361452\pi$
$199$	−8.10365	+	14.0359i	−0.574453	+	0.994981i	−0.996101	+	0.0882217i	$0.971882\pi$
$200$	14.1407	−	0.200539i	0.999899	−	0.0141803i
$201$	−5.75673	−	9.97095i	−0.406049	−	0.703297i
$202$	−2.98379	+	0.135682i	−0.209939	+	0.00954654i
$203$	14.1736	+	3.34358i	0.994789	+	0.234674i
$204$	5.17262	−	0.471403i	0.362156	−	0.0330048i
$205$	−4.96475	+	4.39256i	−0.346753	+	0.306790i
$206$	−2.03955	−	6.42808i	−0.142102	−	0.447866i
$207$	1.39288	+	5.19831i	0.0968121	+	0.361308i
$208$	0.655601	−	8.17414i	0.0454578	−	0.566774i
$209$			31.8289i			2.20165i
$210$	−8.11207	−	2.04802i	−0.559786	−	0.141327i
$211$	−17.6704			−1.21648			−0.608241	−	0.793753i	$-0.708124\pi$
$211$	−17.6704			−1.21648			−0.608241	+	0.793753i	$0.708124\pi$
$212$	3.08157	−	17.8538i	0.211643	−	1.22620i
$213$	−14.0310	+	3.75959i	−0.961386	+	0.257603i
$214$	0.448767	+	1.41438i	0.0306771	+	0.0966853i
$215$	0.313092	−	5.12023i	0.0213527	−	0.349197i
$216$	1.70964	−	2.25325i	0.116326	−	0.153314i
$217$	−4.75207	−	4.47399i	−0.322592	−	0.303714i
$218$	−0.240019	−	5.27829i	−0.0162561	−	0.357491i
$219$	−11.5369	+	6.66084i	−0.779593	+	0.450098i
$220$	−20.4837	−	4.83911i	−1.38101	−	0.326253i
$221$	4.61085	+	2.66208i	0.310160	+	0.179071i
$222$	5.63615	+	8.81177i	0.378273	+	0.591407i
$223$	3.05117	+	3.05117i	0.204321	+	0.204321i	0.801849	−	0.597527i	$-0.203850\pi$
$223$	3.05117	+	3.05117i	0.204321	+	0.204321i	−0.597527	+	0.801849i	$0.703850\pi$
$224$	12.9280	+	7.54104i	0.863787	+	0.503857i
$225$	1.95379	+	4.60247i	0.130253	+	0.306831i
$226$	−0.0979401	+	0.445591i	−0.00651488	+	0.0296403i
$227$	−21.6340	+	5.79680i	−1.43590	+	0.384747i	−0.891095	−	0.453818i	$-0.850062\pi$
$227$	−21.6340	+	5.79680i	−1.43590	+	0.384747i	−0.544802	+	0.838565i	$0.683395\pi$
$228$	−12.6933	+	4.67205i	−0.840636	+	0.309414i
$229$	−9.07263	−	15.7143i	−0.599536	−	1.03843i	−0.992890	−	0.119040i	$-0.962018\pi$
$229$	−9.07263	−	15.7143i	−0.599536	−	1.03843i	0.393353	−	0.919387i	$-0.371315\pi$
$230$	14.6036	+	8.73852i	0.962931	+	0.576201i
$231$	10.9663	+	5.89824i	0.721533	+	0.388076i
$232$	2.11575	+	15.4236i	0.138906	+	1.01261i
$233$	9.09270	+	2.43638i	0.595683	+	0.159613i	0.544049	−	0.839053i	$-0.316891\pi$
$233$	9.09270	+	2.43638i	0.595683	+	0.159613i	0.0516337	+	0.998666i	$0.483557\pi$
$234$	2.76351	−	0.876828i	0.180656	−	0.0573200i
$235$	10.1282	−	5.04990i	0.660689	−	0.329419i
$236$	−21.5743	+	15.2231i	−1.40437	+	0.990940i
$237$	−9.21784	+	9.21784i	−0.598763	+	0.598763i
$238$	−8.02447	+	5.48010i	−0.520149	+	0.355222i
$239$	−1.86371			−0.120553			−0.0602766	−	0.998182i	$-0.519198\pi$
$239$	−1.86371			−0.120553			−0.0602766	+	0.998182i	$0.519198\pi$
$240$	−1.07690	−	8.87920i	−0.0695139	−	0.573150i
$241$	−6.72470	+	11.6475i	−0.433176	+	0.750283i	−0.997145	−	0.0755134i	$-0.975940\pi$
$241$	−6.72470	+	11.6475i	−0.433176	+	0.750283i	0.563969	+	0.825796i	$0.309274\pi$
$242$	14.0000	+	7.25577i	0.899951	+	0.466418i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−1.76977	−	19.4194i	−0.113298	−	1.24320i
$245$	15.1224	−	4.03894i	0.966135	−	0.258039i
$246$	3.09618	+	2.82684i	0.197405	+	0.180233i
$247$	−13.3922	−	3.58843i	−0.852126	−	0.228327i
$248$	2.63513	−	6.46068i	0.167331	−	0.410253i
$249$	−3.71896	−	2.14714i	−0.235680	−	0.136070i
$250$	14.5659	+	6.15104i	0.921227	+	0.389026i
$251$	−16.8761			−1.06521			−0.532605	−	0.846364i	$-0.678787\pi$
$251$	−16.8761			−1.06521			−0.532605	+	0.846364i	$0.678787\pi$
$252$	−0.742501	+	5.23915i	−0.0467732	+	0.330035i
$253$	−17.9098	−	17.9098i	−1.12598	−	1.12598i
$254$	−5.04620	+	22.9583i	−0.316627	+	1.44053i
$255$	5.50706	+	1.84255i	0.344866	+	0.115385i
$256$	−2.55013	+	15.7955i	−0.159383	+	0.987217i
$257$	−2.31323	+	8.63309i	−0.144295	+	0.538517i	0.855491	+	0.517818i	$0.173256\pi$
$257$	−2.31323	+	8.63309i	−0.144295	+	0.538517i	−0.999786	+	0.0206986i	$0.993411\pi$
$258$	−3.24102	+	0.147378i	−0.201777	+	0.00917538i
$259$	−17.2344	−	9.26950i	−1.07089	−	0.575978i
$260$	4.34545	−	8.07310i	0.269494	−	0.500672i
$261$	−4.76673	+	2.75207i	−0.295053	+	0.170349i
$262$	5.70806	+	2.95832i	0.352645	+	0.182766i
$263$	−11.0715	+	2.96660i	−0.682699	+	0.182929i	−0.583468	−	0.812136i	$-0.698305\pi$
$263$	−11.0715	+	2.96660i	−0.682699	+	0.182929i	−0.0992305	+	0.995064i	$0.531638\pi$
$264$	−1.66589	+	13.2070i	−0.102529	+	0.812834i
$265$	11.1800	−	16.8916i	0.686780	−	1.03764i
$266$	16.4910	−	19.1929i	1.01113	−	1.17679i
$267$	−0.0436046	−	0.0436046i	−0.00266856	−	0.00266856i
$268$	−3.91654	+	22.6914i	−0.239241	+	1.38610i
$269$	−0.662600	+	1.14766i	−0.0403994	+	0.0699739i	−0.885518	−	0.464605i	$-0.846196\pi$
$269$	−0.662600	+	1.14766i	−0.0403994	+	0.0699739i	0.845119	+	0.534579i	$0.179530\pi$
$270$	2.76299	−	1.53814i	0.168150	−	0.0936083i
$271$	6.85052	−	3.95515i	0.416140	−	0.240258i	−0.277285	−	0.960788i	$-0.589435\pi$
$271$	6.85052	−	3.95515i	0.416140	−	0.240258i	0.693424	+	0.720530i	$0.256101\pi$
$272$	−8.55231	−	5.89666i	−0.518560	−	0.357538i
$273$	−3.71809	+	3.94919i	−0.225029	+	0.239016i
$274$	5.58617	−	6.11841i	0.337473	−	0.369626i
$275$	−18.7938	−	14.1613i	−1.13331	−	0.853959i
$276$	4.51349	−	9.77132i	0.271680	−	0.588165i
$277$	−2.94895	−	11.0056i	−0.177186	−	0.661265i	−0.996169	−	0.0874483i	$-0.972129\pi$
$277$	−2.94895	−	11.0056i	−0.177186	−	0.661265i	0.818984	−	0.573817i	$-0.194538\pi$
$278$	−15.8798	−	24.8271i	−0.952408	−	1.48903i
$279$	2.46689			0.147689
$280$	9.84453	+	13.5309i	0.588323	+	0.808626i
$281$	24.1127			1.43844			0.719221	−	0.694782i	$-0.244499\pi$
$281$	24.1127			1.43844			0.719221	+	0.694782i	$0.244499\pi$
$282$	−3.85674	−	6.02977i	−0.229665	−	0.359068i
$283$	−3.01073	−	11.2362i	−0.178969	−	0.667923i	−0.995841	−	0.0911039i	$-0.970960\pi$
$283$	−3.01073	−	11.2362i	−0.178969	−	0.667923i	0.816872	−	0.576819i	$-0.195706\pi$
$284$	26.3742	+	12.1825i	1.56502	+	0.722901i
$285$	−15.0942	−	0.922979i	−0.894101	−	0.0546725i
$286$	−9.20028	+	10.0769i	−0.544024	+	0.595857i
$287$	−7.63397	−	1.80087i	−0.450619	−	0.106302i
$288$	−5.51147	+	1.27425i	−0.324766	+	0.0750861i
$289$	−8.88148	+	5.12773i	−0.522440	+	0.301631i
$290$	−4.76714	+	16.7401i	−0.279936	+	0.983012i
$291$	−6.06007	+	10.4964i	−0.355248	+	0.615307i
$292$	26.2552	+	4.53164i	1.53647	+	0.265194i
$293$	13.9145	+	13.9145i	0.812895	+	0.812895i	0.985067	−	0.172172i	$-0.0550785\pi$
$293$	13.9145	+	13.9145i	0.812895	+	0.812895i	−0.172172	+	0.985067i	$0.555078\pi$
$294$	−3.55677	−	9.23847i	−0.207435	−	0.538799i
$295$	−28.9284	+	5.88598i	−1.68427	+	0.342695i
$296$	2.61807	−	20.7557i	0.152172	−	1.20640i
$297$	−4.54601	+	1.21810i	−0.263786	+	0.0706814i
$298$	7.92406	+	4.10681i	0.459029	+	0.237901i
$299$	9.55485	−	5.51649i	0.552571	−	0.319027i
$300$	2.88883	−	9.57364i	0.166787	−	0.552735i
$301$	5.16265	−	3.19181i	0.297570	−	0.183973i
$302$	25.4117	−	1.15554i	1.46228	−	0.0664940i
$303$	−0.546636	+	2.04008i	−0.0314034	+	0.117199i
$304$	25.4865	+	9.06810i	1.46175	+	0.520091i
$305$	6.91743	−	20.6750i	0.396091	−	1.18385i
$306$	0.788443	−	3.58712i	0.0450723	−	0.205062i
$307$	18.3419	+	18.3419i	1.04683	+	1.04683i	0.998848	+	0.0479780i	$0.0152777\pi$
$307$	18.3419	+	18.3419i	1.04683	+	1.04683i	0.0479780	+	0.998848i	$0.484722\pi$
$308$	−9.30239	−	23.1012i	−0.530053	−	1.31631i
$309$	−4.76865			−0.271279
$310$	5.60167	−	5.42924i	0.318153	−	0.308360i
$311$	−9.77084	−	5.64120i	−0.554054	−	0.319883i	0.196702	−	0.980463i	$-0.436977\pi$
$311$	−9.77084	−	5.64120i	−0.554054	−	0.319883i	−0.750755	+	0.660580i	$0.770310\pi$
$312$	−5.36912	−	2.18991i	−0.303967	−	0.123979i
$313$	15.6892	+	4.20392i	0.886808	+	0.237619i	0.673342	−	0.739331i	$-0.264858\pi$
$313$	15.6892	+	4.20392i	0.886808	+	0.237619i	0.213466	+	0.976951i	$0.431525\pi$
$314$	15.0152	+	13.7090i	0.847356	+	0.773644i
$315$	−3.11512	+	5.02952i	−0.175517	+	0.283381i
$316$	25.9644	−	2.36625i	1.46061	−	0.133112i
$317$	−8.22414	−	2.20365i	−0.461914	−	0.123769i	0.0203549	−	0.999793i	$-0.493520\pi$
$317$	−8.22414	−	2.20365i	−0.461914	−	0.123769i	−0.482269	+	0.876023i	$0.660187\pi$
$318$	−11.3744	−	5.89500i	−0.637843	−	0.330575i
$319$	12.9523	−	22.4340i	0.725190	−	1.25607i
$320$	−9.71070	+	15.0234i	−0.542845	+	0.839833i
$321$	1.04925			0.0585637
$322$	1.52034	+	20.0790i	0.0847251	+	1.11896i
$323$	−12.4193	+	12.4193i	−0.691026	+	0.691026i
$324$	−1.15307	−	1.63414i	−0.0640595	−	0.0907858i
$325$	8.07731	−	6.31106i	0.448048	−	0.350075i
$326$	−26.3343	+	8.35555i	−1.45852	+	0.462771i
$327$	−3.60886	−	0.966992i	−0.199571	−	0.0534748i
$328$	−1.13955	−	8.30727i	−0.0629214	−	0.458692i
$329$	11.7932	+	6.34299i	0.650182	+	0.349700i
$330$	−7.64198	+	12.7711i	−0.420677	+	0.703024i
$331$	−9.67989	−	16.7661i	−0.532055	−	0.921546i	−0.999300	−	0.0374180i	$-0.988087\pi$
$331$	−9.67989	−	16.7661i	−0.532055	−	0.921546i	0.467245	−	0.884128i	$-0.345247\pi$
$332$	2.96664	+	8.05994i	0.162815	+	0.442347i
$333$	7.14437	−	1.91433i	0.391509	−	0.104905i
$334$	0.917722	−	4.17529i	0.0502155	−	0.228462i
$335$	−14.2092	+	21.4685i	−0.776334	+	1.17295i
$336$	7.84727	−	7.10073i	0.428104	−	0.387377i
$337$	−18.3464	−	18.3464i	−0.999393	−	0.999393i	0.000606956	−	1.00000i	$-0.499807\pi$
$337$	−18.3464	−	18.3464i	−0.999393	−	0.999393i	−1.00000		0.000606956i	$0.999807\pi$
$338$	6.70350	+	10.4805i	0.364622	+	0.570065i
$339$	0.279381	+	0.161301i	0.0151739	+	0.00876066i
$340$	−6.10435	−	9.88068i	−0.331055	−	0.535855i
$341$	−10.0546	+	5.80505i	−0.544490	+	0.314361i
$342$	0.434464	+	9.55434i	0.0234931	+	0.516640i
$343$	14.2245	+	11.8601i	0.768053	+	0.640387i
$344$	5.16921	+	3.92210i	0.278705	+	0.211466i
$345$	9.01269	−	7.97398i	0.485227	−	0.429305i
$346$	6.80859	+	21.4587i	0.366032	+	1.15363i
$347$	−14.8109	+	3.96856i	−0.795089	+	0.213044i	−0.633427	−	0.773803i	$-0.718352\pi$
$347$	−14.8109	+	3.96856i	−0.795089	+	0.213044i	−0.161663	+	0.986846i	$0.551686\pi$
$348$	10.8479	+	1.87235i	0.581508	+	0.100368i
$349$	3.60952			0.193213			0.0966065	−	0.995323i	$-0.469201\pi$
$349$	3.60952			0.193213			0.0966065	+	0.995323i	$0.469201\pi$
$350$	3.99555	+	18.2766i	0.213571	+	0.976928i
$351$		−	2.05010i		−	0.109426i
$352$	19.4653	−	18.1632i	1.03751	−	0.968101i
$353$	6.34100	+	23.6649i	0.337497	+	1.25956i	0.901136	+	0.433536i	$0.142734\pi$
$353$	6.34100	+	23.6649i	0.337497	+	1.25956i	−0.563639	+	0.826021i	$0.690599\pi$
$354$	5.64660	+	17.7964i	0.300113	+	0.945871i
$355$	21.5229	+	24.3265i	1.14232	+	1.29112i
$356$	0.0111934	+	0.122823i	0.000593250	+	0.00650963i
$357$	1.97752	+	6.58037i	0.104661	+	0.348270i
$358$	15.1524	−	0.689021i	0.800827	−	0.0364159i
$359$	−15.4916	−	26.8322i	−0.817615	−	1.41615i	−0.907435	−	0.420193i	$-0.861962\pi$
$359$	−15.4916	−	26.8322i	−0.817615	−	1.41615i	0.0898196	−	0.995958i	$-0.471371\pi$
$360$	−6.21483	−	1.17299i	−0.327550	−	0.0618222i
$361$	13.3686	−	23.1550i	0.703608	−	1.21868i
$362$	−2.50266	−	3.91276i	−0.131537	−	0.205650i
$363$	7.88424	−	7.88424i	0.413815	−	0.413815i
$364$	10.7688	−	1.30958i	0.564436	−	0.0686408i
$365$	24.8402	+	16.4408i	1.30020	+	0.860553i
$366$	−13.4670	−	2.96003i	−0.703934	−	0.154723i
$367$	5.34077	+	19.9320i	0.278786	+	1.04044i	0.953262	+	0.302146i	$0.0977030\pi$
$367$	5.34077	+	19.9320i	0.278786	+	1.04044i	−0.674476	+	0.738297i	$0.735630\pi$
$368$	−19.4436	+	9.23849i	−1.01357	+	0.481589i
$369$	2.56739	−	1.48228i	0.133653	−	0.0771646i
$370$	12.0099	−	20.0706i	0.624365	−	1.04342i
$371$	23.9567	−	0.722085i	1.24377	−	0.0374888i
$372$	−3.79094	−	3.15768i	−0.196551	−	0.163718i
$373$	−6.39202	+	23.8553i	−0.330966	+	1.23518i	0.577210	+	0.816595i	$0.304141\pi$
$373$	−6.39202	+	23.8553i	−0.330966	+	1.23518i	−0.908177	+	0.418587i	$0.862525\pi$
$374$	5.22761	+	16.4759i	0.270313	+	0.851949i
$375$	7.26068	−	8.50191i	0.374940	−	0.439037i
$376$	−1.79151	+	14.2028i	−0.0923900	+	0.732456i
$377$	7.97902	+	7.97902i	0.410940	+	0.410940i
$378$	3.37237	+	1.62083i	0.173456	+	0.0833668i
$379$		−	15.7998i		−	0.811582i	−0.913966	−	0.405791i	$-0.866996\pi$
$379$		−	15.7998i		−	0.811582i	0.913966	−	0.405791i	$-0.133004\pi$
$380$	22.0142	+	20.7393i	1.12930	+	1.06390i
$381$	14.3947	+	8.31076i	0.737460	+	0.425773i
$382$	−0.410507	+	0.792071i	−0.0210034	+	0.0405259i
$383$	−5.52205	+	20.6086i	−0.282164	+	1.05305i	0.668724	+	0.743511i	$0.266841\pi$
$383$	−5.52205	+	20.6086i	−0.282164	+	1.05305i	−0.950887	+	0.309538i	$0.899826\pi$
$384$	10.1007	+	5.09664i	0.515449	+	0.260087i
$385$	0.861332	−	27.8300i	0.0438975	−	1.41835i
$386$	−3.55766	−	3.24818i	−0.181080	−	0.165328i
$387$	−0.593760	+	2.21594i	−0.0301825	+	0.112643i
$388$	22.7483	−	8.37300i	1.15487	−	0.425075i
$389$	−5.03830	+	8.72660i	−0.255452	+	0.442456i	−0.965018	−	0.262183i	$-0.915558\pi$
$389$	−5.03830	+	8.72660i	−0.255452	+	0.442456i	0.709566	+	0.704639i	$0.248891\pi$
$390$	−4.51195	−	4.65524i	−0.228471	−	0.235727i
$391$		−	13.9764i		−	0.706816i
$392$	−6.35969	+	18.7498i	−0.321213	+	0.947007i
$393$	3.21456	−	3.21456i	0.162153	−	0.162153i
$394$	3.46715	−	15.7742i	0.174672	−	0.794694i
$395$	27.6432	+	9.24883i	1.39088	+	0.465359i
$396$	8.54519	+	3.94712i	0.429412	+	0.198350i
$397$	−14.9386	−	4.00278i	−0.749746	−	0.200894i	−0.136340	−	0.990662i	$-0.543534\pi$
$397$	−14.9386	−	4.00278i	−0.749746	−	0.200894i	−0.613405	+	0.789768i	$0.710201\pi$
$398$	−1.04119	−	22.8969i	−0.0521901	−	1.14772i
$399$	−9.40929	−	15.2192i	−0.471054	−	0.761914i
$400$	−16.6939	+	11.0143i	−0.834693	+	0.550715i
$401$	8.30512	+	14.3849i	0.414738	+	0.718347i	0.995401	−	0.0957969i	$-0.0305399\pi$
$401$	8.30512	+	14.3849i	0.414738	+	0.718347i	−0.580663	+	0.814144i	$0.697207\pi$
$402$	14.4563	+	7.49229i	0.721016	+	0.373682i
$403$	−1.30894	−	4.88503i	−0.0652030	−	0.243341i
$404$	3.45138	−	2.43533i	0.171713	−	0.121162i
$405$	−0.445832	−	2.19117i	−0.0221536	−	0.108880i
$406$	−19.4337	+	6.81702i	−0.964477	+	0.338323i
$407$	−24.6146	+	24.6146i	−1.22010	+	1.22010i
$408$	−5.80323	+	4.50321i	−0.287303	+	0.222942i
$409$	−18.7964	−	10.8521i	−0.929422	−	0.536602i	−0.0427934	−	0.999084i	$-0.513626\pi$
$409$	−18.7964	−	10.8521i	−0.929422	−	0.536602i	−0.886629	+	0.462482i	$0.846959\pi$
$410$	2.56761	−	9.01632i	0.126805	−	0.445284i
$411$	−2.92917	−	5.07347i	−0.144485	−	0.250256i
$412$	7.32811	+	6.10399i	0.361030	+	0.300722i
$413$	−25.4320	−	23.9438i	−1.25143	−	1.17820i
$414$	−5.62060	−	5.13167i	−0.276238	−	0.252208i
$415$	−0.586069	+	9.58442i	−0.0287690	+	0.470481i
$416$	5.44773	+	10.2379i	0.267097	+	0.501955i
$417$	−20.1292	+	5.39361i	−0.985733	+	0.264126i
$418$	−24.2540	−	37.9196i	−1.18630	−	1.85471i
$419$		−	6.43493i		−	0.314367i	−0.987569	−	0.157183i	$-0.949759\pi$
$419$		−	6.43493i		−	0.314367i	0.987569	−	0.157183i	$-0.0502414\pi$
$420$	11.2250	−	3.74157i	0.547724	−	0.182570i
$421$			14.3531i			0.699525i	0.936838	+	0.349763i	$0.113738\pi$
$421$			14.3531i			0.699525i	−0.936838	+	0.349763i	$0.886262\pi$
$422$	21.0518	−	13.4651i	1.02479	−	0.655469i
$423$	−4.88880	+	1.30995i	−0.237701	+	0.0636919i
$424$	9.93356	+	23.6185i	0.482416	+	1.14702i
$425$	−1.80755	−	12.8587i	−0.0876792	−	0.623739i
$426$	13.8511	−	15.1708i	0.671087	−	0.735027i
$427$	24.7045	−	7.42414i	1.19554	−	0.359279i
$428$	−1.61242	−	1.34307i	−0.0779393	−	0.0649199i
$429$	4.82427	+	8.35587i	0.232918	+	0.403425i
$430$	3.52867	+	6.33861i	0.170168	+	0.305675i
$431$	−11.0037	−	6.35298i	−0.530029	−	0.306012i	0.210999	−	0.977486i	$-0.432328\pi$
$431$	−11.0037	−	6.35298i	−0.530029	−	0.306012i	−0.741028	+	0.671474i	$0.765662\pi$
$432$	−0.319790	+	3.98720i	−0.0153859	+	0.191834i
$433$	−17.7077	+	17.7077i	−0.850976	+	0.850976i	−0.990253	−	0.139277i	$-0.955522\pi$
$433$	−17.7077	+	17.7077i	−0.850976	+	0.850976i	0.139277	+	0.990253i	$0.455522\pi$
$434$	9.07066	+	1.70899i	0.435405	+	0.0820342i
$435$	10.2633	+	6.79290i	0.492086	+	0.325695i
$436$	4.30807	+	6.10544i	0.206319	+	0.292398i
$437$	9.41996	+	35.1558i	0.450618	+	1.68173i
$438$	8.66898	−	16.7267i	0.414220	−	0.799234i
$439$	2.30467	+	3.99180i	0.109996	+	0.190518i	0.915768	−	0.401707i	$-0.131583\pi$
$439$	2.30467	+	3.99180i	0.109996	+	0.190518i	−0.805773	+	0.592225i	$0.798250\pi$
$440$	28.0909	−	9.84373i	1.33918	−	0.469281i
$441$	−6.98729	+	0.421594i	−0.332728	+	0.0200759i
$442$	−7.52172	+	0.342034i	−0.357772	+	0.0162689i
$443$	18.2069	+	4.87852i	0.865035	+	0.231786i	0.663940	−	0.747786i	$-0.268883\pi$
$443$	18.2069	+	4.87852i	0.865035	+	0.231786i	0.201096	+	0.979572i	$0.435550\pi$
$444$	−13.4294	−	6.20318i	−0.637329	−	0.294390i
$445$	−0.0437512	+	0.130765i	−0.00207401	+	0.00619885i
$446$	−5.96006	−	1.31001i	−0.282217	−	0.0620308i
$447$	4.46253	−	4.46253i	0.211070	−	0.211070i
$448$	−21.1482	+	0.867189i	−0.999160	+	0.0409708i
$449$		−	36.7871i		−	1.73609i	−0.496485	−	0.868045i	$-0.665376\pi$
$449$		−	36.7871i		−	1.73609i	0.496485	−	0.868045i	$-0.334624\pi$
$450$	−5.83480	−	3.99438i	−0.275055	−	0.188297i
$451$	−6.97619	+	12.0831i	−0.328496	+	0.568972i
$452$	−0.222864	−	0.605491i	−0.0104826	−	0.0284799i
$453$	4.65547	−	17.3744i	0.218733	−	0.816322i
$454$	21.3566	−	23.3914i	1.00231	−	1.09781i
$455$	11.6126	+	3.50000i	0.544405	+	0.164083i
$456$	11.5622	−	15.2386i	0.541447	−	0.713611i
$457$	−4.31639	+	16.1090i	−0.201912	+	0.753547i	0.788456	+	0.615091i	$0.210881\pi$
$457$	−4.31639	+	16.1090i	−0.201912	+	0.753547i	−0.990369	+	0.138456i	$0.955786\pi$
$458$	22.7832	+	11.8079i	1.06459	+	0.551746i
$459$	−2.24909	−	1.29851i	−0.104979	−	0.0606094i
$460$	−24.0570	+	0.717379i	−1.12166	+	0.0334480i
$461$			11.0189i			0.513203i	0.966517	+	0.256602i	$0.0826028\pi$
$461$			11.0189i			0.513203i	−0.966517	+	0.256602i	$0.917397\pi$
$462$	−17.5594	+	1.32956i	−0.816937	+	0.0618568i
$463$	−16.6328	−	16.6328i	−0.772994	−	0.772994i	0.205635	−	0.978629i	$-0.434074\pi$
$463$	−16.6328	−	16.6328i	−0.772994	−	0.772994i	−0.978629	+	0.205635i	$0.934074\pi$
$464$	−14.2736	−	16.7629i	−0.662636	−	0.778197i
$465$	−2.46136	−	4.93654i	−0.114143	−	0.228926i
$466$	−12.6892	+	4.02614i	−0.587817	+	0.186507i
$467$	8.32922	−	31.0851i	0.385430	−	1.43845i	−0.452057	−	0.891989i	$-0.649310\pi$
$467$	8.32922	−	31.0851i	0.385430	−	1.43845i	0.837487	−	0.546457i	$-0.184024\pi$
$468$	−2.62418	+	3.15044i	−0.121303	+	0.145629i
$469$	−30.4479	+	0.917739i	−1.40596	+	0.0423772i
$470$	−8.21821	+	13.7340i	−0.379078	+	0.633504i
$471$	12.4508	−	7.18847i	0.573702	−	0.331227i
$472$	14.1026	−	34.5761i	0.649126	−	1.59149i
$473$	−2.79446	−	10.4291i	−0.128489	−	0.479529i
$474$	3.95766	−	18.0059i	0.181781	−	0.827037i
$475$	13.2133	+	31.1261i	0.606269	+	1.42816i
$476$	5.38414	−	12.6435i	0.246781	−	0.579514i
$477$	−6.40561	+	6.40561i	−0.293293	+	0.293293i
$478$	2.22035	−	1.42017i	0.101556	−	0.0649569i
$479$	9.65123	−	16.7164i	0.440976	−	0.763793i	−0.556786	−	0.830656i	$-0.687966\pi$
$479$	9.65123	−	16.7164i	0.440976	−	0.763793i	0.997762	+	0.0668630i	$0.0212991\pi$
$480$	8.04904	+	9.75771i	0.367387	+	0.445377i
$481$	−7.58167	−	13.1318i	−0.345694	−	0.598760i
$482$	−0.864016	−	19.0007i	−0.0393549	−	0.865457i
$483$	13.8582	+	3.26919i	0.630571	+	0.148753i
$484$	−22.2080	+	2.02391i	−1.00945	+	0.0919957i
$485$	27.0509	+	1.65411i	1.22832	+	0.0751094i
$486$	−1.34799	+	0.427701i	−0.0611460	+	0.0194009i
$487$	3.56697	+	13.3121i	0.161635	+	0.603229i	0.998445	+	0.0557369i	$0.0177508\pi$
$487$	3.56697	+	13.3121i	0.161635	+	0.603229i	−0.836811	+	0.547492i	$0.815583\pi$
$488$	16.9063	+	21.7869i	0.765311	+	0.986248i
$489$			19.5360i			0.883448i
$490$	−14.9385	+	16.3353i	−0.674852	+	0.737953i
$491$	−23.0455			−1.04003			−0.520015	−	0.854157i	$-0.674074\pi$
$491$	−23.0455			−1.04003			−0.520015	+	0.854157i	$0.674074\pi$
$492$	−5.84274	−	1.00846i	−0.263411	−	0.0454648i
$493$	13.8073	−	3.69967i	0.621852	−	0.166625i
$494$	18.6894	−	5.92992i	0.840875	−	0.266800i
$495$	6.97338	+	7.88175i	0.313430	+	0.354258i
$496$	1.78373	+	9.70499i	0.0800918	+	0.435767i
$497$	−8.82401	+	37.4053i	−0.395811	+	1.67786i
$498$	6.06677	−	0.275874i	0.271858	−	0.0123622i
$499$	−34.8573	+	20.1248i	−1.56043	+	0.900912i	−0.563212	+	0.826313i	$0.690434\pi$
$499$	−34.8573	+	20.1248i	−1.56043	+	0.900912i	−0.997214	+	0.0745993i	$0.976232\pi$
$500$	−22.0404	+	3.77127i	−0.985675	+	0.168657i
$501$	−2.61787	−	1.51143i	−0.116958	−	0.0675256i
$502$	20.1055	−	12.8598i	0.897353	−	0.573961i
$503$	15.4889	+	15.4889i	0.690616	+	0.690616i	0.962368	−	0.271751i	$-0.0876027\pi$
$503$	15.4889	+	15.4889i	0.690616	+	0.690616i	−0.271751	+	0.962368i	$0.587603\pi$
$504$	−3.10771	−	6.80751i	−0.138428	−	0.303230i
$505$	4.62785	−	0.941616i	0.205936	−	0.0419013i
$506$	34.9845	+	7.68952i	1.55525	+	0.341841i
$507$	8.49735	−	2.27686i	0.377381	−	0.101119i
$508$	−11.4827	−	31.1969i	−0.509462	−	1.38414i
$509$	21.4785	+	37.2019i	0.952020	+	1.64895i	0.741045	+	0.671455i	$0.234331\pi$
$509$	21.4785	+	37.2019i	0.952020	+	1.64895i	0.210975	+	0.977491i	$0.432336\pi$
$510$	−7.96494	+	2.00131i	−0.352693	+	0.0886195i
$511$	1.06187	+	35.2299i	0.0469744	+	1.55848i
$512$	−8.99821	−	20.7613i	−0.397669	−	0.917529i
$513$	6.53248	+	1.75037i	0.288416	+	0.0772808i
$514$	−3.82263	−	12.0478i	−0.168609	−	0.531406i
$515$	4.75795	+	9.54263i	0.209660	+	0.420499i
$516$	3.74891	−	2.64527i	0.165037	−	0.116452i
$517$	16.8434	−	16.8434i	0.740772	−	0.740772i
$518$	27.5958	−	2.08950i	1.21249	−	0.0918072i
$519$	15.9190			0.698769
$520$	0.974803	+	12.9293i	0.0427479	+	0.566985i
$521$	8.22536	−	14.2467i	0.360359	−	0.624161i	−0.627661	−	0.778487i	$-0.715987\pi$
$521$	8.22536	−	14.2467i	0.360359	−	0.624161i	0.988020	+	0.154326i	$0.0493207\pi$
$522$	3.58178	−	6.91102i	0.156770	−	0.302487i
$523$	6.28304	+	1.68353i	0.274738	+	0.0736158i	0.393557	−	0.919300i	$-0.371244\pi$
$523$	6.28304	+	1.68353i	0.274738	+	0.0736158i	−0.118819	+	0.992916i	$0.537911\pi$
$524$	−9.05462	+	0.825186i	−0.395553	+	0.0360484i
$525$	13.1728	+	1.21549i	0.574908	+	0.0530482i
$526$	10.9296	−	11.9709i	0.476552	−	0.521957i
$527$	−6.18827	−	1.65814i	−0.269565	−	0.0722298i
$528$	−8.07921	−	17.0037i	−0.351603	−	0.739992i
$529$	−5.16376	−	2.98130i	−0.224511	−	0.129622i
$530$	−0.447743	+	28.6433i	−0.0194487	+	1.24418i
$531$	13.2022			0.572928
$532$	−5.02148	+	35.4320i	−0.217709	+	1.53617i
$533$	−4.29755	−	4.29755i	−0.186147	−	0.186147i
$534$	0.0851760	+	0.0187215i	0.00368593	+	0.000810160i
$535$	−1.04690	−	2.09968i	−0.0452615	−	0.0907773i
$536$	−12.6251	−	30.0181i	−0.545322	−	1.29658i
$537$	2.77594	−	10.3599i	0.119791	−	0.447065i
$538$	−0.0851335	−	1.87218i	−0.00367037	−	0.0807154i
$539$	27.4870	−	18.1608i	1.18395	−	0.782240i
$540$	−2.11963	+	3.93791i	−0.0912145	+	0.169461i
$541$	−18.7758	+	10.8402i	−0.807235	+	0.466058i	−0.845995	−	0.533191i	$-0.820993\pi$
$541$	−18.7758	+	10.8402i	−0.807235	+	0.466058i	0.0387595	+	0.999249i	$0.487659\pi$
$542$	−5.14756	+	9.93219i	−0.221107	+	0.426624i
$543$	−3.17237	+	0.850034i	−0.136139	+	0.0364784i
$544$	14.6822	+	0.508081i	0.629495	+	0.0217838i
$545$	1.66570	+	8.18659i	0.0713509	+	0.350675i
$546$	1.42025	−	7.53813i	0.0607811	−	0.322602i
$547$	8.51539	+	8.51539i	0.364092	+	0.364092i	0.865317	−	0.501225i	$-0.167117\pi$
$547$	8.51539	+	8.51539i	0.364092	+	0.364092i	−0.501225	+	0.865317i	$0.667117\pi$
$548$	−1.99283	+	11.5459i	−0.0851296	+	0.493218i
$549$	−4.87498	+	8.44371i	−0.208059	+	0.360369i
$550$	33.1813	+	2.55009i	1.41485	+	0.108736i
$551$	−32.2370	+	18.6121i	−1.37334	+	0.792901i
$552$	2.06868	+	15.0805i	0.0880487	+	0.641868i
$553$	9.92631	+	33.0307i	0.422110	+	1.40461i
$554$	11.8997	+	10.8645i	0.505570	+	0.461590i
$555$	−10.9592	−	12.3867i	−0.465190	−	0.525787i
$556$	37.8371	+	17.4774i	1.60465	+	0.741208i
$557$	−2.34727	−	8.76015i	−0.0994572	−	0.371179i	0.898200	−	0.439586i	$-0.144875\pi$
$557$	−2.34727	−	8.76015i	−0.0994572	−	0.371179i	−0.997657	+	0.0684071i	$0.978208\pi$
$558$	−2.93895	+	1.87980i	−0.124416	+	0.0795782i
$559$	4.70315			0.198922
$560$	−22.0391	−	8.61851i	−0.931321	−	0.364199i
$561$	12.2226			0.516038
$562$	−28.7269	+	18.3741i	−1.21177	+	0.775067i
$563$	−5.46578	−	20.3986i	−0.230355	−	0.859698i	−0.980188	−	0.198070i	$-0.936533\pi$
$563$	−5.46578	−	20.3986i	−0.230355	−	0.859698i	0.749833	−	0.661628i	$-0.230134\pi$
$564$	9.18952	+	4.24475i	0.386949	+	0.178736i
$565$	0.0440275	−	0.720015i	0.00185225	−	0.0302912i
$566$	12.1490	+	11.0921i	0.510660	+	0.466238i
$567$	1.81362	−	1.92634i	0.0761647	−	0.0808988i
$568$	−40.7043	+	5.58364i	−1.70792	+	0.234285i
$569$	−11.3988	+	6.58113i	−0.477865	+	0.275895i	−0.719526	−	0.694465i	$-0.755641\pi$
$569$	−11.3988	+	6.58113i	−0.477865	+	0.275895i	0.241662	+	0.970361i	$0.422308\pi$
$570$	18.6859	−	10.4023i	0.782666	−	0.435706i
$571$	−5.49773	+	9.52235i	−0.230073	+	0.398498i	−0.957829	−	0.287338i	$-0.907230\pi$
$571$	−5.49773	+	9.52235i	−0.230073	+	0.398498i	0.727756	+	0.685836i	$0.240563\pi$
$572$	3.28215	−	19.0159i	0.137233	−	0.795094i
$573$	0.446064	+	0.446064i	0.0186346	+	0.0186346i
$574$	10.4671	−	3.67169i	0.436888	−	0.153253i
$575$	−24.9494	−	10.0794i	−1.04046	−	0.420338i
$576$	5.59514	−	5.71790i	0.233131	−	0.238246i
$577$	8.34364	−	2.23567i	0.347350	−	0.0930722i	−0.0809259	−	0.996720i	$-0.525788\pi$
$577$	8.34364	−	2.23567i	0.347350	−	0.0930722i	0.428276	+	0.903648i	$0.359121\pi$
$578$	6.67365	−	12.8768i	0.277587	−	0.535603i
$579$	−2.95006	+	1.70322i	−0.122600	+	0.0707834i
$580$	−7.07678	−	23.5761i	−0.293847	−	0.978944i
$581$	−9.66383	+	5.97467i	−0.400923	+	0.247871i
$582$	−0.778623	−	17.1228i	−0.0322749	−	0.709762i
$583$	11.0346	−	41.1819i	0.457008	−	1.70558i
$584$	−34.7325	+	14.6079i	−1.43724	+	0.604480i
$585$	−4.10249	+	2.04550i	−0.169617	+	0.0845710i
$586$	−27.1802	−	5.97417i	−1.12280	−	0.246790i
$587$	2.36935	+	2.36935i	0.0977935	+	0.0977935i	0.754311	−	0.656517i	$-0.227971\pi$
$587$	2.36935	+	2.36935i	0.0977935	+	0.0977935i	−0.656517	+	0.754311i	$0.727971\pi$
$588$	11.2772	+	8.29604i	0.465065	+	0.342123i
$589$	16.6834			0.687426
$590$	29.9789	−	29.0561i	1.23421	−	1.19622i
$591$	−9.89029	−	5.71016i	−0.406832	−	0.234885i
$592$	12.6970	+	26.7225i	0.521845	+	1.09829i
$593$	−13.6306	−	3.65232i	−0.559743	−	0.149983i	−0.0321547	−	0.999483i	$-0.510237\pi$
$593$	−13.6306	−	3.65232i	−0.559743	−	0.149983i	−0.527588	+	0.849500i	$0.676904\pi$
$594$	4.48773	−	4.91531i	0.184134	−	0.201678i
$595$	11.1950	−	10.5229i	0.458951	−	0.431395i
$596$	−12.5698	+	1.14554i	−0.514881	+	0.0469233i
$597$	−15.6551	−	4.19476i	−0.640719	−	0.171680i
$598$	−7.17962	+	13.8530i	−0.293597	+	0.566493i
$599$	7.71996	−	13.3714i	0.315429	−	0.546339i	−0.664099	−	0.747644i	$-0.731185\pi$
$599$	7.71996	−	13.3714i	0.315429	−	0.546339i	0.979529	+	0.201305i	$0.0645182\pi$
$600$	3.85359	+	13.6070i	0.157322	+	0.555503i
$601$	3.24967			0.132557			0.0662785	−	0.997801i	$-0.478887\pi$
$601$	3.24967			0.132557			0.0662785	+	0.997801i	$0.478887\pi$
$602$	−3.71838	+	7.73660i	−0.151550	+	0.315320i
$603$	8.14125	−	8.14125i	0.331537	−	0.331537i
$604$	−29.3939	+	20.7407i	−1.19602	+	0.843926i
$605$	−23.6439	−	7.91075i	−0.961260	−	0.321618i
$606$	−0.903321	−	2.84701i	−0.0366949	−	0.115652i
$607$	−11.0059	−	2.94901i	−0.446714	−	0.119697i	0.0284473	−	0.999595i	$-0.490944\pi$
$607$	−11.0059	−	2.94901i	−0.446714	−	0.119697i	−0.475162	+	0.879899i	$0.657610\pi$
$608$	−37.2736	+	8.61767i	−1.51165	+	0.349493i
$609$	0.438736	+	14.5560i	0.0177785	+	0.589839i
$610$	7.51347	+	29.9026i	0.304211	+	1.21072i
$611$	5.18803	+	8.98593i	0.209885	+	0.363532i
$612$	1.79411	+	4.87436i	0.0725227	+	0.197034i
$613$	15.2356	−	4.08237i	0.615360	−	0.164885i	0.0623425	−	0.998055i	$-0.480143\pi$
$613$	15.2356	−	4.08237i	0.615360	−	0.164885i	0.553018	+	0.833170i	$0.313476\pi$
$614$	−35.8285	−	7.87504i	−1.44592	−	0.317811i
$615$	−5.52786	−	3.65870i	−0.222905	−	0.147533i
$616$	28.6859	+	20.4333i	1.15579	+	0.823281i
$617$	0.236797	+	0.236797i	0.00953310	+	0.00953310i	0.711857	−	0.702324i	$-0.247854\pi$
$617$	0.236797	+	0.236797i	0.00953310	+	0.00953310i	−0.702324	+	0.711857i	$0.747854\pi$
$618$	5.68117	−	3.63377i	0.228530	−	0.146172i
$619$	−11.5244	−	6.65359i	−0.463203	−	0.267430i	0.250187	−	0.968198i	$-0.419508\pi$
$619$	−11.5244	−	6.65359i	−0.463203	−	0.267430i	−0.713390	+	0.700767i	$0.752841\pi$
$620$	−2.53646	+	10.7367i	−0.101867	+	0.431197i
$621$	−4.66068	+	2.69085i	−0.187027	+	0.107980i
$622$	15.9392	−	0.724804i	0.639106	−	0.0290620i
$623$	−0.156250	+	0.0469560i	−0.00626004	+	0.00188125i
$624$	8.06529	−	1.48236i	0.322870	−	0.0593419i
$625$	−24.2577	−	6.04664i	−0.970310	−	0.241866i
$626$	−21.8950	+	6.94701i	−0.875098	+	0.277658i
$627$	−30.7443	+	8.23792i	−1.22781	+	0.328991i
$628$	−28.3349	−	4.89061i	−1.13069	−	0.195157i
$629$	−19.2086			−0.765899
$630$	−0.121326	−	8.36572i	−0.00483373	−	0.333298i
$631$		−	34.1624i		−	1.35998i	−0.733220	−	0.679991i	$-0.761983\pi$
$631$		−	34.1624i		−	1.35998i	0.733220	−	0.679991i	$-0.238017\pi$
$632$	−29.1298	+	22.6042i	−1.15872	+	0.899148i
$633$	−4.57344	−	17.0683i	−0.181778	−	0.678404i
$634$	11.4771	−	3.64155i	0.455814	−	0.144624i
$635$	2.26844	−	37.0975i	0.0900204	−	1.47217i
$636$	18.0430	−	1.64434i	0.715453	−	0.0652022i
$637$	4.54234	+	13.6128i	0.179974	+	0.539360i
$638$	1.66416	+	36.5968i	0.0658849	+	1.44888i
$639$	−7.26296	−	12.5798i	−0.287318	−	0.497650i
$640$	0.120931	−	25.2979i	0.00478020	−	0.999989i
$641$	−5.79023	+	10.0290i	−0.228700	+	0.396121i	−0.957423	−	0.288688i	$-0.906781\pi$
$641$	−5.79023	+	10.0290i	−0.228700	+	0.396121i	0.728723	+	0.684809i	$0.240114\pi$
$642$	−1.25004	+	0.799545i	−0.0493351	+	0.0315555i
$643$	1.02318	−	1.02318i	0.0403504	−	0.0403504i	−0.686644	−	0.726994i	$-0.740917\pi$
$643$	1.02318	−	1.02318i	0.0403504	−	0.0403504i	0.726994	+	0.686644i	$0.240917\pi$
$644$	−17.1117	−	22.7628i	−0.674295	−	0.896978i
$645$	5.02679	−	1.02279i	0.197930	−	0.0402723i
$646$	5.33218	−	24.2594i	0.209792	−	0.954474i
$647$	4.85554	+	18.1211i	0.190891	+	0.712415i	0.993292	+	0.115630i	$0.0368887\pi$
$647$	4.85554	+	18.1211i	0.190891	+	0.712415i	−0.802401	+	0.596785i	$0.796445\pi$
$648$	2.61896	+	1.06820i	0.102882	+	0.0419629i
$649$	−53.8102	+	31.0673i	−2.11224	+	1.21950i
$650$	−4.81387	+	13.6738i	−0.188816	+	0.536329i
$651$	3.09161	−	5.74810i	0.121170	−	0.225286i
$652$	25.0066	−	30.0215i	0.979333	−	1.17573i
$653$	−1.70512	+	6.36358i	−0.0667263	+	0.249026i	−0.991230	−	0.132147i	$-0.957813\pi$
$653$	−1.70512	+	6.36358i	−0.0667263	+	0.249026i	0.924504	+	0.381173i	$0.124480\pi$
$654$	5.03631	−	1.59796i	0.196935	−	0.0624853i
$655$	−9.64007	−	3.22537i	−0.376669	−	0.126026i
$656$	7.68786	+	9.02859i	0.300160	+	0.352507i
$657$	−9.41985	−	9.41985i	−0.367504	−	0.367504i
$658$	−18.8834	+	1.42981i	−0.736152	+	0.0557399i
$659$		−	41.1503i		−	1.60299i	−0.598002	−	0.801494i	$-0.704039\pi$
$659$		−	41.1503i		−	1.60299i	0.598002	−	0.801494i	$-0.295961\pi$
$660$	−0.627360	−	21.0382i	−0.0244199	−	0.818911i
$661$	3.09722	+	1.78818i	0.120468	+	0.0695522i	0.559023	−	0.829152i	$-0.311176\pi$
$661$	3.09722	+	1.78818i	0.120468	+	0.0695522i	−0.438555	+	0.898704i	$0.644510\pi$
$662$	24.3082	+	12.5982i	0.944764	+	0.489643i
$663$	−1.37799	+	5.14274i	−0.0535168	+	0.199727i
$664$	−9.67610	−	7.34168i	−0.375506	−	0.284912i
$665$	−21.0673	+	34.0142i	−0.816955	+	1.31902i
$666$	−7.05278	+	7.72475i	−0.273290	+	0.299328i
$667$	7.66664	−	28.6123i	0.296854	−	1.10787i
$668$	2.08829	+	5.67359i	0.0807983	+	0.219518i
$669$	−2.15750	+	3.73690i	−0.0834138	+	0.144477i
$670$	0.569061	−	36.4043i	0.0219848	−	1.40642i
$671$		−	45.8870i		−	1.77145i
$672$	−3.93808	+	14.4392i	−0.151915	+	0.557006i
$673$	12.1451	−	12.1451i	0.468158	−	0.468158i	−0.433159	−	0.901317i	$-0.642601\pi$
$673$	12.1451	−	12.1451i	0.468158	−	0.468158i	0.901317	+	0.433159i	$0.142601\pi$
$674$	35.8374	+	7.87699i	1.38040	+	0.303410i
$675$	−3.93996	+	3.07842i	−0.151649	+	0.118489i
$676$	−15.9726	−	7.37791i	−0.614329	−	0.283766i
$677$	33.4130	+	8.95299i	1.28417	+	0.344092i	0.835442	−	0.549578i	$-0.185212\pi$
$677$	33.4130	+	8.95299i	1.28417	+	0.344092i	0.448725	+	0.893670i	$0.351878\pi$
$678$	−0.455757	+	0.0207246i	−0.0175032	+	0.000795923i
$679$	16.8628	+	27.2751i	0.647136	+	1.04672i
$680$	14.8017	+	7.11985i	0.567618	+	0.273034i
$681$	−11.1986	−	19.3965i	−0.429130	−	0.743275i
$682$	7.55518	−	14.5777i	0.289303	−	0.558208i
$683$	−9.58985	−	35.7898i	−0.366946	−	1.36946i	−0.864764	−	0.502178i	$-0.832532\pi$
$683$	−9.58985	−	35.7898i	−0.366946	−	1.36946i	0.497819	−	0.867281i	$-0.334135\pi$
$684$	−7.79813	−	11.0516i	−0.298169	−	0.422568i
$685$	−7.23001	+	10.9237i	−0.276245	+	0.417373i
$686$	−25.9841	−	3.29041i	−0.992077	−	0.125629i
$687$	12.8306	−	12.8306i	0.489519	−	0.489519i
$688$	−9.14707	−	0.733635i	−0.348729	−	0.0279696i
$689$	16.0835	+	9.28581i	0.612732	+	0.353761i
$690$	−4.66108	+	16.3677i	−0.177444	+	0.623106i
$691$	14.3894	+	24.9231i	0.547398	+	0.948121i	0.998452	+	0.0556242i	$0.0177149\pi$
$691$	14.3894	+	24.9231i	0.547398	+	0.948121i	−0.451054	+	0.892497i	$0.648952\pi$
$692$	−24.4633	−	20.3768i	−0.929953	−	0.774609i
$693$	−2.85896	+	12.1193i	−0.108603	+	0.460372i
$694$	14.6210	−	16.0141i	0.555005	−	0.607885i
$695$	30.8774	+	34.8995i	1.17124	+	1.32381i
$696$	−14.3505	+	6.03559i	−0.543954	+	0.228778i
$697$	−7.43672	+	1.99266i	−0.281686	+	0.0754775i
$698$	−4.30023	+	2.75050i	−0.162766	+	0.104108i
$699$			9.41346i			0.356050i
$700$	−18.6872	−	18.7294i	−0.706308	−	0.707904i
$701$		−	24.7798i		−	0.935921i	−0.883749	−	0.467960i	$-0.844989\pi$
$701$		−	24.7798i		−	0.935921i	0.883749	−	0.467960i	$-0.155011\pi$
$702$	1.56220	+	2.44240i	0.0589614	+	0.0921825i
$703$	48.3168	−	12.9465i	1.82230	−	0.488285i
$704$	−9.34964	+	36.4717i	−0.352378	+	1.37458i
$705$	7.49920	+	8.47605i	0.282436	+	0.319227i
$706$	−25.5874	−	23.3615i	−0.962993	−	0.879222i
$707$	4.06852	+	3.83043i	0.153012	+	0.144058i
$708$	−20.2882	−	16.8992i	−0.762479	−	0.635111i
$709$	−6.98171	−	12.0927i	−0.262204	−	0.454150i	0.704624	−	0.709581i	$-0.251116\pi$
$709$	−6.98171	−	12.0927i	−0.262204	−	0.454150i	−0.966827	+	0.255431i	$0.917783\pi$
$710$	−44.1786	−	12.5809i	−1.65799	−	0.472153i
$711$	−11.2895	−	6.51800i	−0.423389	−	0.244444i
$712$	−0.106928	−	0.137797i	−0.00400731	−	0.00516417i
$713$	−9.38756	+	9.38756i	−0.351567	+	0.351567i
$714$	−7.37025	−	6.33269i	−0.275825	−	0.236995i
$715$	11.9077	−	17.9911i	0.445321	−	0.672828i
$716$	−17.5269	+	12.3671i	−0.655009	+	0.462182i
$717$	−0.482363	−	1.80020i	−0.0180142	−	0.0672298i
$718$	38.9025	+	20.1621i	1.45183	+	0.752441i
$719$	3.97223	+	6.88011i	0.148139	+	0.256585i	0.930540	−	0.366191i	$-0.119338\pi$
$719$	3.97223	+	6.88011i	0.148139	+	0.256585i	−0.782400	+	0.622776i	$0.786005\pi$
$720$	8.29793	−	3.33832i	0.309246	−	0.124412i
$721$	−5.97628	+	11.1114i	−0.222568	+	0.413812i
$722$	1.71765	+	37.7729i	0.0639241	+	1.40576i
$723$	−12.9911	−	3.48096i	−0.483145	−	0.129458i
$724$	5.96313	+	2.75444i	0.221618	+	0.102368i
$725$	3.35314	−	27.3157i	0.124533	−	1.01448i
$726$	−3.38508	+	15.4008i	−0.125632	+	0.571579i
$727$	12.8465	−	12.8465i	0.476449	−	0.476449i	−0.427545	−	0.903994i	$-0.640621\pi$
$727$	12.8465	−	12.8465i	0.476449	−	0.476449i	0.903994	+	0.427545i	$0.140621\pi$
$728$	−11.8315	+	9.76611i	−0.438506	+	0.361956i
$729$			1.00000i			0.0370370i
$730$	−42.1217	−	0.658434i	−1.55899	−	0.0243697i
$731$	2.97893	−	5.15967i	0.110180	−	0.190837i
$732$	18.2997	−	6.73559i	0.676375	−	0.248955i
$733$	−5.49176	+	20.4955i	−0.202843	+	0.757020i	0.787253	+	0.616630i	$0.211502\pi$
$733$	−5.49176	+	20.4955i	−0.202843	+	0.757020i	−0.990096	+	0.140390i	$0.955164\pi$
$734$	−21.5512	−	19.6765i	−0.795470	−	0.726272i
$735$	7.81529	+	13.5618i	0.288271	+	0.500233i
$736$	16.1244	−	25.8226i	0.594354	−	0.951833i
$737$	−14.0246	+	52.3404i	−0.516601	+	1.92798i
$738$	−1.92917	+	3.72232i	−0.0710136	+	0.137020i
$739$	34.7517	+	20.0639i	1.27836	+	0.738062i	0.976547	−	0.215305i	$-0.0690745\pi$
$739$	34.7517	+	20.0639i	1.27836	+	0.738062i	0.301814	+	0.953367i	$0.402408\pi$
$740$	0.985939	+	33.0630i	0.0362438	+	1.21542i
$741$		−	13.8646i		−	0.509330i
$742$	−27.9908	+	19.1156i	−1.02758	+	0.701755i
$743$	−10.5715	−	10.5715i	−0.387831	−	0.387831i	0.486082	−	0.873913i	$-0.338426\pi$
$743$	−10.5715	−	10.5715i	−0.387831	−	0.387831i	−0.873913	+	0.486082i	$0.838426\pi$
$744$	6.92256	+	0.873192i	0.253793	+	0.0320128i
$745$	−13.3826	−	4.47753i	−0.490300	−	0.164044i
$746$	−10.5629	−	33.2911i	−0.386734	−	1.21887i
$747$	1.11144	−	4.14796i	0.0406656	−	0.151766i
$748$	−18.7828	−	15.6452i	−0.686767	−	0.572046i
$749$	1.31497	−	2.44487i	0.0480481	−	0.0893337i
$750$	−2.17152	+	15.6616i	−0.0792927	+	0.571879i
$751$	−1.96504	+	1.13452i	−0.0717054	+	0.0413991i	−0.535424	−	0.844583i	$-0.679848\pi$
$751$	−1.96504	+	1.13452i	−0.0717054	+	0.0413991i	0.463719	+	0.885983i	$0.346515\pi$
$752$	−8.68841	−	18.2858i	−0.316834	−	0.666816i
$753$	−4.36786	−	16.3011i	−0.159174	−	0.594044i
$754$	−15.5860	−	3.42577i	−0.567608	−	0.124759i
$755$	−39.4134	+	8.01933i	−1.43440	+	0.291853i
$756$	−5.25280	+	0.638791i	−0.191043	+	0.0232326i
$757$	8.49357	−	8.49357i	0.308704	−	0.308704i	−0.535703	−	0.844407i	$-0.679953\pi$
$757$	8.49357	−	8.49357i	0.308704	−	0.308704i	0.844407	+	0.535703i	$0.179953\pi$
$758$	12.0397	+	18.8233i	0.437300	+	0.683692i
$759$	12.6641	−	21.9349i	0.459679	−	0.796187i
$760$	−42.0304	−	7.93286i	−1.52460	−	0.287755i
$761$	0.811300	+	1.40521i	0.0294096	+	0.0509389i	0.880356	−	0.474314i	$-0.157304\pi$
$761$	0.811300	+	1.40521i	0.0294096	+	0.0509389i	−0.850946	+	0.525253i	$0.823971\pi$
$762$	−23.4821	+	1.06780i	−0.850667	+	0.0386823i
$763$	−6.77598	+	7.19714i	−0.245307	+	0.260554i
$764$	−0.114506	−	1.25645i	−0.00414268	−	0.0454569i
$765$	−0.354433	+	5.79630i	−0.0128145	+	0.209566i
$766$	−9.12523	−	28.7601i	−0.329708	−	1.03914i
$767$	−7.00516	−	26.1436i	−0.252942	−	0.943991i
$768$	−15.9173	+	1.62493i	−0.574365	+	0.0586345i
$769$		−	0.380100i		−	0.0137068i	−0.999977	−	0.00685338i	$-0.997818\pi$
$769$		−	0.380100i		−	0.0137068i	0.999977	−	0.00685338i	$-0.00218151\pi$
$770$	20.1806	+	33.8119i	0.727259	+	1.21849i
$771$	−8.93763			−0.321881
$772$	6.71361	+	1.15877i	0.241628	+	0.0417051i
$773$	−41.5592	+	11.1358i	−1.49478	+	0.400525i	−0.911348	−	0.411636i	$-0.864957\pi$
$773$	−41.5592	+	11.1358i	−1.49478	+	0.400525i	−0.583433	+	0.812162i	$0.698291\pi$
$774$	−0.981193	−	3.09244i	−0.0352683	−	0.111155i
$775$	−7.42276	+	9.85093i	−0.266633	+	0.353856i
$776$	−20.7211	+	27.3097i	−0.743843	+	0.980362i
$777$	4.49306	−	19.0462i	0.161188	−	0.683280i
$778$	−0.647341	−	14.2358i	−0.0232083	−	0.510377i
$779$	17.3631	−	10.0246i	0.622096	−	0.359167i
$780$	8.92270	+	2.10791i	0.319484	+	0.0754754i
$781$	59.2054	+	34.1823i	2.11854	+	1.22314i
$782$	10.6502	+	16.6509i	0.380850	+	0.595435i
$783$	−3.89202	−	3.89202i	−0.139089	−	0.139089i
$784$	−6.71089	−	27.1839i	−0.239675	−	0.970853i
$785$	−26.8079	−	17.7432i	−0.956814	−	0.633281i
$786$	−1.38016	+	6.27923i	−0.0492288	+	0.223973i
$787$	−15.0315	+	4.02768i	−0.535816	+	0.143571i	−0.516572	−	0.856243i	$-0.672792\pi$
$787$	−15.0315	+	4.02768i	−0.535816	+	0.143571i	−0.0192431	+	0.999815i	$0.506126\pi$
$788$	7.88953	+	21.4348i	0.281053	+	0.763583i
$789$	−5.73104	−	9.92645i	−0.204030	−	0.353391i
$790$	−39.9807	+	10.0457i	−1.42245	+	0.357412i
$791$	0.725981	−	0.448838i	0.0258129	−	0.0159588i
$792$	−13.1881	+	1.80909i	−0.468620	+	0.0642833i
$793$	19.3073	+	5.17336i	0.685621	+	0.183712i
$794$	20.8474	−	6.61463i	0.739846	−	0.234744i
$795$	19.2096	+	6.42714i	0.681296	+	0.227947i
$796$	18.6882	+	26.4851i	0.662385	+	0.938739i
$797$	21.9104	−	21.9104i	0.776105	−	0.776105i	−0.203061	−	0.979166i	$-0.565089\pi$
$797$	21.9104	−	21.9104i	0.776105	−	0.776105i	0.979166	+	0.203061i	$0.0650891\pi$
$798$	22.8071	+	10.9616i	0.807362	+	0.388036i
$799$	13.1442			0.465009
$800$	11.4954	−	25.8429i	0.406422	−	0.913685i
$801$	0.0308331	−	0.0534045i	0.00108943	−	0.00188696i
$802$	−20.8558	−	10.8090i	−0.736445	−	0.381678i
$803$	60.5606	+	16.2272i	2.13714	+	0.572644i
$804$	−22.9319	+	2.08988i	−0.808746	+	0.0737044i
$805$	−7.28511	−	30.9938i	−0.256766	−	1.09239i
$806$	5.28187	+	4.82240i	0.186046	+	0.169862i
$807$	−1.28004	−	0.342987i	−0.0450597	−	0.0120737i
$808$	−2.25608	+	5.53135i	−0.0793687	+	0.194592i
$809$	−42.6507	−	24.6244i	−1.49952	−	0.865748i	−0.499520	−	0.866302i	$-0.666490\pi$
$809$	−42.6507	−	24.6244i	−1.49952	−	0.865748i	−1.00000		0.000553784i	$0.999824\pi$
$810$	2.20085	+	2.27074i	0.0773298	+	0.0797858i
$811$	−22.7295			−0.798139			−0.399070	−	0.916921i	$-0.630667\pi$
$811$	−22.7295			−0.798139			−0.399070	+	0.916921i	$0.630667\pi$
$812$	17.9578	−	22.9302i	0.630196	−	0.804693i
$813$	5.59343	+	5.59343i	0.196170	+	0.196170i
$814$	10.5682	−	48.0814i	0.370415	−	1.68525i
$815$	39.0938	−	19.4922i	1.36940	−	0.682781i
$816$	3.48224	−	9.78707i	0.121903	−	0.342616i
$817$	−4.01555	+	14.9862i	−0.140486	+	0.524302i
$818$	30.6627	−	1.39432i	1.07210	−	0.0487513i
$819$	−4.77694	−	2.56927i	−0.166920	−	0.0897776i
$820$	3.81160	+	12.6982i	0.133107	+	0.443441i
$821$	35.2201	−	20.3343i	1.22919	−	0.709672i	0.262328	−	0.964979i	$-0.415510\pi$
$821$	35.2201	−	20.3343i	1.22919	−	0.709672i	0.966860	+	0.255306i	$0.0821763\pi$
$822$	7.35573	+	3.81226i	0.256561	+	0.132968i
$823$	6.28670	−	1.68452i	0.219141	−	0.0587186i	−0.147578	−	0.989050i	$-0.547148\pi$
$823$	6.28670	−	1.68452i	0.219141	−	0.0587186i	0.366719	+	0.930332i	$0.380481\pi$
$824$	−13.3817	−	1.68794i	−0.466175	−	0.0588020i
$825$	8.81457	−	21.8186i	0.306884	−	0.759628i
$826$	48.5441	+	9.14614i	1.68907	+	0.318235i
$827$	36.0435	+	36.0435i	1.25336	+	1.25336i	0.954206	+	0.299151i	$0.0967033\pi$
$827$	36.0435	+	36.0435i	1.25336	+	1.25336i	0.299151	+	0.954206i	$0.403297\pi$
$828$	10.6066	+	1.83069i	0.368603	+	0.0636210i
$829$	−20.3826	+	35.3037i	−0.707918	+	1.22615i	0.257711	+	0.966222i	$0.417032\pi$
$829$	−20.3826	+	35.3037i	−0.707918	+	1.22615i	−0.965628	+	0.259927i	$0.916301\pi$
$830$	−6.60522	−	11.8651i	−0.229271	−	0.411843i
$831$	9.86739	−	5.69694i	0.342296	−	0.197625i
$832$	−14.2916	−	8.04580i	−0.495473	−	0.278938i
$833$	17.8112	+	3.63899i	0.617123	+	0.126084i
$834$	19.8712	−	21.7644i	0.688082	−	0.753641i
$835$	−0.412548	+	6.74671i	−0.0142768	+	0.233479i
$836$	57.7904	+	26.6941i	1.99872	+	0.923234i
$837$	0.638477	+	2.38283i	0.0220690	+	0.0823626i
$838$	4.90349	+	7.66632i	0.169388	+	0.264829i
$839$	−10.0769			−0.347892			−0.173946	−	0.984755i	$-0.555652\pi$
$839$	−10.0769			−0.347892			−0.173946	+	0.984755i	$0.555652\pi$
$840$	−10.5219	+	13.0111i	−0.363040	+	0.448927i
$841$	1.29565			0.0446777
$842$	−10.9372	−	17.0997i	−0.376921	−	0.589293i
$843$	6.24082	+	23.2911i	0.214945	+	0.802187i
$844$	−14.8197	+	32.0835i	−0.510116	+	1.10436i
$845$	−13.0346	−	14.7325i	−0.448403	−	0.506812i
$846$	4.82612	−	5.28594i	0.165925	−	0.181734i
$847$	−8.49021	−	28.2520i	−0.291727	−	0.970749i
$848$	−29.8320	−	20.5686i	−1.02444	−	0.706330i
$849$	10.0741	−	5.81629i	0.345742	−	0.199614i
$850$	11.9519	+	13.9420i	0.409948	+	0.478206i
$851$	−19.9026	+	34.4723i	−0.682251	+	1.18169i
$852$	−4.94129	+	28.6286i	−0.169286	+	0.980798i
$853$	−17.0953	−	17.0953i	−0.585333	−	0.585333i	0.351031	−	0.936364i	$-0.385831\pi$
$853$	−17.0953	−	17.0953i	−0.585333	−	0.585333i	−0.936364	+	0.351031i	$0.885831\pi$
$854$	−23.7747	+	27.6700i	−0.813553	+	0.946846i
$855$	−3.01513	−	14.8187i	−0.103115	−	0.506790i
$856$	2.94441	+	0.371400i	0.100638	+	0.0126942i
$857$	−15.4573	+	4.14177i	−0.528011	+	0.141480i	−0.512970	−	0.858407i	$-0.671455\pi$
$857$	−15.4573	+	4.14177i	−0.528011	+	0.141480i	−0.0150413	+	0.999887i	$0.504788\pi$
$858$	−12.1147	−	6.27870i	−0.413589	−	0.214351i
$859$	41.9138	−	24.1989i	1.43008	−	0.825656i	0.432953	−	0.901417i	$-0.357472\pi$
$859$	41.9138	−	24.1989i	1.43008	−	0.825656i	0.997126	+	0.0757602i	$0.0241384\pi$
$860$	−9.03401	−	4.86268i	−0.308057	−	0.165816i
$861$	−0.236306	−	7.83995i	−0.00805328	−	0.267185i
$862$	17.9504	−	0.816256i	0.611393	−	0.0278018i
$863$	−1.24131	+	4.63262i	−0.0422546	+	0.157696i	−0.983830	−	0.179107i	$-0.942679\pi$
$863$	−1.24131	+	4.63262i	−0.0422546	+	0.157696i	0.941575	+	0.336803i	$0.109346\pi$
$864$	−2.65731	−	4.99387i	−0.0904034	−	0.169895i
$865$	−15.8834	−	31.8559i	−0.540050	−	1.08313i
$866$	7.60274	−	34.5897i	0.258352	−	1.17540i
$867$	−7.25170	−	7.25170i	−0.246281	−	0.246281i
$868$	−12.1087	+	4.87593i	−0.410995	+	0.165500i
$869$	61.3523			2.08124
$870$	−17.4035	−	0.272047i	−0.590035	−	0.00922324i
$871$	−20.4414	−	11.8019i	−0.692631	−	0.399891i
$872$	−9.78488	−	3.99098i	−0.331358	−	0.135152i
$873$	−11.7072	−	3.13692i	−0.396227	−	0.106169i
$874$	−38.0117	−	34.7051i	−1.28576	−	1.17392i
$875$	−10.7109	−	27.5731i	−0.362095	−	0.932141i
$876$	2.41810	+	26.5334i	0.0817001	+	0.896481i
$877$	42.7620	+	11.4581i	1.44397	+	0.386911i	0.893923	−	0.448221i	$-0.147942\pi$
$877$	42.7620	+	11.4581i	1.44397	+	0.386911i	0.550049	+	0.835132i	$0.314609\pi$
$878$	−5.78749	−	2.99949i	−0.195318	−	0.101228i
$879$	−9.83905	+	17.0417i	−0.331863	+	0.574804i
$880$	−25.9654	+	33.1331i	−0.875292	+	1.11692i
$881$	15.7780			0.531573			0.265787	−	0.964032i	$-0.414368\pi$
$881$	15.7780			0.531573			0.265787	+	0.964032i	$0.414368\pi$
$882$	8.00312	−	5.82667i	0.269479	−	0.196194i
$883$	−19.9690	+	19.9690i	−0.672010	+	0.672010i	−0.958179	−	0.286169i	$-0.907618\pi$
$883$	−19.9690	+	19.9690i	−0.672010	+	0.672010i	0.286169	+	0.958179i	$0.407618\pi$
$884$	8.70044	−	6.13913i	0.292627	−	0.206481i
$885$	−13.1726	−	26.4192i	−0.442793	−	0.888073i
$886$	−25.4084	+	8.06180i	−0.853613	+	0.270841i
$887$	4.60894	+	1.23496i	0.154753	+	0.0414660i	0.335364	−	0.942089i	$-0.391141\pi$
$887$	4.60894	+	1.23496i	0.154753	+	0.0414660i	−0.180611	+	0.983555i	$0.557807\pi$
$888$	20.7261	−	2.84311i	0.695522	−	0.0954086i
$889$	37.4049	−	23.1256i	1.25452	−	0.775608i
$890$	−0.0475210	−	0.189127i	−0.00159291	−	0.00633955i
$891$	−2.35319	−	4.07584i	−0.0788348	−	0.136546i
$892$	8.09882	−	2.98094i	0.271169	−	0.0998094i
$893$	−33.0625	+	8.85908i	−1.10640	+	0.296458i
$894$	−1.91598	+	8.71698i	−0.0640798	+	0.291539i
$895$	−23.5012	+	4.78173i	−0.785558	+	0.159836i
$896$	24.5343	−	17.1483i	0.819635	−	0.572886i
$897$	7.80150	+	7.80150i	0.260484	+	0.260484i
$898$	28.0322	+	43.8267i	0.935447	+	1.46251i
$899$	−11.7590	−	6.78906i	−0.392184	−	0.226428i
$900$	9.99511	+	0.312558i	0.333170	+	0.0104186i
$901$	20.3743	−	11.7631i	0.678766	−	0.391886i
$902$	−0.896329	−	19.7113i	−0.0298445	−	0.656314i
$903$	4.41925	+	4.16064i	0.147063	+	0.138457i
$904$	0.726902	+	0.551532i	0.0241764	+	0.0183437i
$905$	4.86627	+	5.50016i	0.161760	+	0.182832i
$906$	7.69320	+	24.2467i	0.255589	+	0.805544i
$907$	36.9586	−	9.90302i	1.22719	−	0.328824i	0.413705	−	0.910411i	$-0.364235\pi$
$907$	36.9586	−	9.90302i	1.22719	−	0.328824i	0.813484	+	0.581587i	$0.197568\pi$
$908$	−7.61884	+	44.1416i	−0.252840	+	1.46489i
$909$	−2.11204			−0.0700520
$910$	−16.5018	+	4.67914i	−0.547028	+	0.155112i
$911$		−	32.0730i		−	1.06262i	−0.847176	−	0.531312i	$-0.821699\pi$
$911$		−	32.0730i		−	1.06262i	0.847176	−	0.531312i	$-0.178301\pi$
$912$	−2.16272	+	26.9651i	−0.0716147	+	0.892904i
$913$	5.23087	+	19.5219i	0.173117	+	0.646080i
$914$	−7.13287	−	22.4807i	−0.235934	−	0.743597i
$915$	21.7609	+	1.33064i	0.719393	+	0.0439895i
$916$	−36.1407	+	3.29366i	−1.19412	+	0.108826i
$917$	−3.46163	−	11.5189i	−0.114313	−	0.380387i
$918$	3.66896	−	0.166838i	0.121094	−	0.00550648i
$919$	−21.4528	−	37.1573i	−0.707661	−	1.22570i	−0.965723	−	0.259576i	$-0.916417\pi$
$919$	−21.4528	−	37.1573i	−0.707661	−	1.22570i	0.258062	−	0.966128i	$-0.416916\pi$
$920$	28.1138	−	19.1863i	0.926886	−	0.632555i
$921$	−12.9697	+	22.4641i	−0.427365	+	0.740218i
$922$	−8.39656	−	13.1275i	−0.276526	−	0.432332i
$923$	−21.0573	+	21.0573i	−0.693110	+	0.693110i
$924$	19.9064	−	14.9645i	0.654873	−	0.492294i
$925$	−13.8527	+	34.2895i	−0.455474	+	1.12743i
$926$	32.4901	+	7.14127i	1.06769	+	0.234677i
$927$	−1.23422	−	4.60616i	−0.0405370	−	0.151286i
$928$	29.7785	+	9.09395i	0.977528	+	0.298523i
$929$	42.0632	−	24.2852i	1.38005	−	0.796772i	0.387885	−	0.921708i	$-0.373206\pi$
$929$	42.0632	−	24.2852i	1.38005	−	0.796772i	0.992165	+	0.124935i	$0.0398723\pi$
$930$	6.69406	+	4.00561i	0.219507	+	0.131349i
$931$	−47.2545	+	2.85121i	−1.54870	+	0.0934446i
$932$	12.0495	−	14.4659i	0.394694	−	0.473847i
$933$	2.92010	−	10.8980i	0.0955998	−	0.356783i
$934$	13.7641	+	43.3805i	0.450375	+	1.41945i
$935$	−12.1952	−	24.4589i	−0.398825	−	0.799890i
$936$	0.725663	−	5.75296i	0.0237190	−	0.188041i
$937$	20.1049	+	20.1049i	0.656798	+	0.656798i	0.954621	−	0.297823i	$-0.0962605\pi$
$937$	20.1049	+	20.1049i	0.656798	+	0.656798i	−0.297823	+	0.954621i	$0.596261\pi$
$938$	35.5751	−	24.2951i	1.16157	−	0.793262i
$939$			16.2427i			0.530060i
$940$	−0.674665	−	22.6246i	−0.0220051	−	0.737932i
$941$	−32.8063	−	18.9407i	−1.06946	−	0.617451i	−0.141423	−	0.989949i	$-0.545168\pi$
$941$	−32.8063	−	18.9407i	−1.06946	−	0.617451i	−0.928033	+	0.372498i	$0.878501\pi$
$942$	−9.35567	+	18.0517i	−0.304824	+	0.588156i
$943$	−4.12930	+	15.4108i	−0.134468	+	0.501843i
$944$	9.54612	+	51.9389i	0.310700	+	1.69047i
$945$	−5.66439	−	1.70724i	−0.184263	−	0.0555365i
$946$	11.2763	+	10.2954i	0.366623	+	0.334731i
$947$	−14.4397	+	53.8897i	−0.469227	+	1.75118i	0.173254	+	0.984877i	$0.444572\pi$
$947$	−14.4397	+	53.8897i	−0.469227	+	1.75118i	−0.642481	+	0.766302i	$0.722095\pi$
$948$	9.00570	+	24.4672i	0.292491	+	0.794659i
$949$	−13.6554	+	23.6518i	−0.443272	+	0.767770i
$950$	−39.4603	−	27.0137i	−1.28026	−	0.876440i
$951$		−	8.51426i		−	0.276094i
$952$	3.22007	+	19.1657i	0.104363	+	0.621165i
$953$	−28.4799	+	28.4799i	−0.922554	+	0.922554i	−0.997209	−	0.0746556i	$-0.976214\pi$
$953$	−28.4799	+	28.4799i	−0.922554	+	0.922554i	0.0746556	+	0.997209i	$0.476214\pi$
$954$	2.75023	−	12.5125i	0.0890421	−	0.405108i
$955$	0.447564	−	1.33769i	0.0144828	−	0.0432867i
$956$	−1.56305	+	3.38386i	−0.0505525	+	0.109442i
$957$	25.0219	+	6.70461i	0.808844	+	0.216729i
$958$	1.24003	+	27.2696i	0.0400635	+	0.881042i
$959$	−15.4927	+	0.466968i	−0.500284	+	0.0150792i
$960$	−17.0248	−	5.49148i	−0.549473	−	0.177237i
$961$	−12.4572	−	21.5766i	−0.401846	−	0.696018i
$962$	19.0391	+	9.86741i	0.613845	+	0.318138i
$963$	0.271567	+	1.01350i	0.00875113	+	0.0326597i
$964$	15.5081	+	21.9783i	0.499482	+	0.707872i
$965$	6.35179	+	4.20403i	0.204471	+	0.135332i
$966$	−19.0013	+	6.66535i	−0.611357	+	0.214454i
$967$	27.6005	−	27.6005i	0.887571	−	0.887571i	−0.106718	−	0.994289i	$-0.534034\pi$
$967$	27.6005	−	27.6005i	0.887571	−	0.887571i	0.994289	+	0.106718i	$0.0340343\pi$
$968$	24.9154	−	19.3339i	0.800812	−	0.621416i
$969$	−15.2104	−	8.78174i	−0.488629	−	0.282110i
$970$	−33.4879	+	18.6425i	−1.07523	+	0.598575i
$971$	7.55464	+	13.0850i	0.242440	+	0.419919i	0.961409	−	0.275124i	$-0.0887189\pi$
$971$	7.55464	+	13.0850i	0.242440	+	0.419919i	−0.718969	+	0.695042i	$0.755386\pi$
$972$	1.28003	−	1.53673i	0.0410568	−	0.0492906i
$973$	−12.6592	+	53.6627i	−0.405834	+	1.72035i
$974$	−14.3935	−	13.1414i	−0.461198	−	0.421079i
$975$	8.18658	+	6.16866i	0.262180	+	0.197555i
$976$	−36.7434	−	13.0733i	−1.17613	−	0.418466i
$977$	15.8388	−	4.24400i	0.506729	−	0.135778i	0.00360797	−	0.999993i	$-0.498852\pi$
$977$	15.8388	−	4.24400i	0.506729	−	0.135778i	0.503121	+	0.864216i	$0.332185\pi$
$978$	−14.8867	−	23.2744i	−0.476023	−	0.744233i
$979$			0.290225i			0.00927562i
$980$	5.34943	−	30.8445i	0.170881	−	0.985292i
$981$		−	3.73617i		−	0.119287i
$982$	27.4555	−	17.5610i	0.876141	−	0.560394i
$983$	40.2927	−	10.7964i	1.28514	−	0.344351i	0.449326	−	0.893368i	$-0.351664\pi$
$983$	40.2927	−	10.7964i	1.28514	−	0.344351i	0.835811	+	0.549017i	$0.184998\pi$
$984$	7.72927	−	3.25080i	0.246400	−	0.103632i
$985$	−1.55860	+	25.4890i	−0.0496612	+	0.812147i
$986$	−13.6303	+	14.9290i	−0.434078	+	0.475436i
$987$	−3.07454	+	13.0331i	−0.0978637	+	0.414848i
$988$	−17.7471	+	21.3062i	−0.564610	+	0.677840i
$989$	−6.17310	−	10.6921i	−0.196293	−	0.339990i
$990$	−14.3138	−	4.07619i	−0.454922	−	0.129550i
$991$	29.5256	+	17.0466i	0.937911	+	0.541503i	0.889305	−	0.457315i	$-0.151189\pi$
$991$	29.5256	+	17.0466i	0.937911	+	0.541503i	0.0486061	+	0.998818i	$0.484522\pi$
$992$	−9.52038	−	10.2029i	−0.302272	−	0.323943i
$993$	13.6894	−	13.6894i	0.434421	−	0.434421i
$994$	−17.9907	−	51.2871i	−0.570631	−	1.62673i
$995$	7.22574	+	35.5130i	0.229071	+	1.12584i
$996$	−7.01749	+	4.95162i	−0.222358	+	0.156898i
$997$	−3.27315	−	12.2156i	−0.103662	−	0.386871i	0.894528	−	0.447012i	$-0.147512\pi$
$997$	−3.27315	−	12.2156i	−0.103662	−	0.386871i	−0.998190	+	0.0601405i	$0.980845\pi$
$998$	26.1922	−	50.5376i	0.829098	−	1.59974i
$999$	3.69820	+	6.40547i	0.117006	+	0.202660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.dj.a.67.17	✓	384
5.3	odd	4	inner	840.2.dj.a.403.67	yes	384
7.2	even	3	inner	840.2.dj.a.667.81	yes	384
8.3	odd	2	inner	840.2.dj.a.67.63	yes	384
35.23	odd	12	inner	840.2.dj.a.163.63	yes	384
40.3	even	4	inner	840.2.dj.a.403.81	yes	384
56.51	odd	6	inner	840.2.dj.a.667.67	yes	384
280.163	even	12	inner	840.2.dj.a.163.17	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.dj.a.67.17	✓	384	1.1	even	1	trivial
840.2.dj.a.67.63	yes	384	8.3	odd	2	inner
840.2.dj.a.163.17	yes	384	280.163	even	12	inner
840.2.dj.a.163.63	yes	384	35.23	odd	12	inner
840.2.dj.a.403.67	yes	384	5.3	odd	4	inner
840.2.dj.a.403.81	yes	384	40.3	even	4	inner
840.2.dj.a.667.67	yes	384	56.51	odd	6	inner
840.2.dj.a.667.81	yes	384	7.2	even	3	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.dj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19136 + 0.762012i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.838675 - 1.81566i) q^{4} +(1.67469 - 1.48169i) q^{5} +(-1.04439 - 0.953542i) q^{6} +(2.57507 + 0.607466i) q^{7} +(0.384392 + 2.80219i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.866099 + 3.04136i) q^{10} +(2.35319 - 4.07584i) q^{11} +(1.97086 + 0.340171i) q^{12} +(1.44964 + 1.44964i) q^{13} +(-3.53073 + 1.23852i) q^{14} +(1.86464 + 1.23414i) q^{15} +(-2.59325 - 3.04550i) q^{16} +(2.50853 - 0.672160i) q^{17} +(0.650742 - 1.25560i) q^{18} +(-5.85686 + 3.38146i) q^{19} +(-1.28572 - 4.28333i) q^{20} +(0.0797100 + 2.64455i) q^{21} +(0.302347 + 6.64895i) q^{22} +(1.39288 - 5.19831i) q^{23} +(-2.60722 + 1.09655i) q^{24} +(0.609203 - 4.96275i) q^{25} +(-2.83168 - 0.622398i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(3.26260 - 4.16599i) q^{28} +5.50415 q^{29} +(-3.16189 - 0.0494257i) q^{30} +(-2.13639 - 1.23344i) q^{31} +(5.41020 + 1.65220i) q^{32} +(4.54601 + 1.21810i) q^{33} +(-2.47637 + 2.71232i) q^{34} +(5.21253 - 2.79813i) q^{35} +(0.181516 + 1.99175i) q^{36} +(-7.14437 - 1.91433i) q^{37} +(4.40091 - 8.49153i) q^{38} +(-1.02505 + 1.77544i) q^{39} +(4.79570 + 4.12326i) q^{40} -2.96457 q^{41} +(-2.11014 - 3.08987i) q^{42} +(1.62218 - 1.62218i) q^{43} +(-5.42679 - 7.69090i) q^{44} +(-0.709484 + 2.12053i) q^{45} +(2.30175 + 7.25446i) q^{46} +(4.88880 + 1.30995i) q^{47} +(2.27054 - 3.29312i) q^{48} +(6.26197 + 3.12853i) q^{49} +(3.05589 + 6.37664i) q^{50} +(1.29851 + 2.24909i) q^{51} +(3.84782 - 1.41627i) q^{52} +(8.75023 - 2.34462i) q^{53} +(1.38124 + 0.303595i) q^{54} +(-2.09825 - 10.3125i) q^{55} +(-0.712397 + 7.44933i) q^{56} +(-4.78211 - 4.78211i) q^{57} +(-6.55742 + 4.19423i) q^{58} +(-11.4335 - 6.60111i) q^{59} +(3.80461 - 2.35052i) q^{60} +(8.44371 - 4.87498i) q^{61} +(3.48510 - 0.158478i) q^{62} +(-2.53381 + 0.761454i) q^{63} +(-7.70449 + 2.15427i) q^{64} +(4.57561 + 0.279790i) q^{65} +(-6.34414 + 2.01292i) q^{66} +(-11.1212 + 2.97990i) q^{67} +(0.883432 - 5.11837i) q^{68} +5.38169 q^{69} +(-4.07779 + 7.30559i) q^{70} +14.5259i q^{71} +(-1.73399 - 2.23457i) q^{72} +(3.44791 + 12.8678i) q^{73} +(9.97026 - 3.16344i) q^{74} +(4.95132 - 0.696009i) q^{75} +(1.22758 + 13.4700i) q^{76} +(8.53556 - 9.06610i) q^{77} +(-0.131702 - 2.89628i) q^{78} +(6.51800 + 11.2895i) q^{79} +(-8.85538 - 1.25790i) q^{80} +(0.500000 - 0.866025i) q^{81} +(3.53187 - 2.25904i) q^{82} +(-3.03652 + 3.03652i) q^{83} +(4.86846 + 2.07319i) q^{84} +(3.20510 - 4.84253i) q^{85} +(-0.696480 + 3.16872i) q^{86} +(1.42458 + 5.31660i) q^{87} +(12.3258 + 5.02735i) q^{88} +(-0.0534045 + 0.0308331i) q^{89} +(-0.770616 - 3.06694i) q^{90} +(2.85231 + 4.61352i) q^{91} +(-8.27020 - 6.88870i) q^{92} +(0.638477 - 2.38283i) q^{93} +(-6.82251 + 2.16470i) q^{94} +(-4.79818 + 14.3410i) q^{95} +(-0.195639 + 5.65347i) q^{96} +(8.57024 + 8.57024i) q^{97} +(-9.84424 + 1.04449i) q^{98} +4.70638i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + 24 q^{8} - 16 q^{16} + 32 q^{26} + 44 q^{28} + 48 q^{35} + 12 q^{38} + 20 q^{40} - 20 q^{42} - 48 q^{46} - 32 q^{48} - 72 q^{50} + 4 q^{52} + 32 q^{56} + 8 q^{58} + 20 q^{60} - 144 q^{62} - 24 q^{66}+ \cdots - 80 q^{98}+O(q^{100}) \) 384 * q + 24 * q^8 - 16 * q^16 + 32 * q^26 + 44 * q^28 + 48 * q^35 + 12 * q^38 + 20 * q^40 - 20 * q^42 - 48 * q^46 - 32 * q^48 - 72 * q^50 + 4 * q^52 + 32 * q^56 + 8 * q^58 + 20 * q^60 - 144 * q^62 - 24 * q^66 + 48 * q^67 + 44 * q^68 - 40 * q^70 + 12 * q^72 + 96 * q^76 - 48 * q^78 + 36 * q^80 + 192 * q^81 - 44 * q^82 + 32 * q^86 + 68 * q^88 + 24 * q^90 - 64 * q^91 - 72 * q^92 + 32 * q^97 - 80 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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