LMFDB - Embedded newform 861.2.i.g.247.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [861,2,Mod(247,861)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(861, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("861.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 861 = 3 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	861.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.87511961403$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.8
Character	$\chi$	$=$	861.247
Dual form			861.2.i.g.739.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.221125 - 0.383000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.902207 + 1.56267i) q^{4} +(-2.14637 + 3.71763i) q^{5} +0.442251 q^{6} +(0.504334 + 2.59724i) q^{7} +1.68250 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.221125 - 0.383000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.902207 + 1.56267i) q^{4} +(-2.14637 + 3.71763i) q^{5} +0.442251 q^{6} +(0.504334 + 2.59724i) q^{7} +1.68250 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.949235 + 1.64412i) q^{10} +(1.10606 + 1.91575i) q^{11} +(-0.902207 + 1.56267i) q^{12} +3.11687 q^{13} +(1.10626 + 0.381155i) q^{14} -4.29274 q^{15} +(-1.43237 + 2.48094i) q^{16} +(-3.46198 - 5.99633i) q^{17} +(0.221125 + 0.383000i) q^{18} +(3.86244 - 6.68994i) q^{19} -7.74589 q^{20} +(-1.99711 + 1.73539i) q^{21} +0.978311 q^{22} +(-0.0190846 + 0.0330555i) q^{23} +(0.841252 + 1.45709i) q^{24} +(-6.71383 - 11.6287i) q^{25} +(0.689218 - 1.19376i) q^{26} -1.00000 q^{27} +(-3.60361 + 3.13135i) q^{28} +2.66709 q^{29} +(-0.949235 + 1.64412i) q^{30} +(2.34980 + 4.06997i) q^{31} +(2.31597 + 4.01138i) q^{32} +(-1.10606 + 1.91575i) q^{33} -3.06213 q^{34} +(-10.7381 - 3.69971i) q^{35} -1.80441 q^{36} +(0.0150359 - 0.0260429i) q^{37} +(-1.70816 - 2.95863i) q^{38} +(1.55843 + 2.69928i) q^{39} +(-3.61128 + 6.25492i) q^{40} +1.00000 q^{41} +(0.223042 + 1.14863i) q^{42} +11.0093 q^{43} +(-1.99579 + 3.45681i) q^{44} +(-2.14637 - 3.71763i) q^{45} +(0.00844018 + 0.0146188i) q^{46} +(-1.89054 + 3.27451i) q^{47} -2.86474 q^{48} +(-6.49129 + 2.61975i) q^{49} -5.93839 q^{50} +(3.46198 - 5.99633i) q^{51} +(2.81206 + 4.87063i) q^{52} +(0.273068 + 0.472968i) q^{53} +(-0.221125 + 0.383000i) q^{54} -9.49606 q^{55} +(0.848545 + 4.36987i) q^{56} +7.72487 q^{57} +(0.589761 - 1.02150i) q^{58} +(-4.77954 - 8.27841i) q^{59} +(-3.87295 - 6.70814i) q^{60} +(3.01039 - 5.21414i) q^{61} +2.07840 q^{62} +(-2.50144 - 0.861853i) q^{63} -3.68100 q^{64} +(-6.68995 + 11.5873i) q^{65} +(0.489155 + 0.847242i) q^{66} +(4.48837 + 7.77408i) q^{67} +(6.24685 - 10.8199i) q^{68} -0.0381692 q^{69} +(-3.79145 + 3.29458i) q^{70} +15.6199 q^{71} +(-0.841252 + 1.45709i) q^{72} +(-1.21150 - 2.09837i) q^{73} +(-0.00664964 - 0.0115175i) q^{74} +(6.71383 - 11.6287i) q^{75} +13.9389 q^{76} +(-4.41784 + 3.83888i) q^{77} +1.37844 q^{78} +(-1.08068 + 1.87180i) q^{79} +(-6.14880 - 10.6500i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.221125 - 0.383000i) q^{82} -17.0488 q^{83} +(-4.51364 - 1.55514i) q^{84} +29.7228 q^{85} +(2.43443 - 4.21656i) q^{86} +(1.33354 + 2.30977i) q^{87} +(1.86095 + 3.22326i) q^{88} +(-4.34597 + 7.52744i) q^{89} -1.89847 q^{90} +(1.57194 + 8.09524i) q^{91} -0.0688730 q^{92} +(-2.34980 + 4.06997i) q^{93} +(0.836092 + 1.44815i) q^{94} +(16.5805 + 28.7182i) q^{95} +(-2.31597 + 4.01138i) q^{96} -0.216724 q^{97} +(-0.432024 + 3.06546i) q^{98} -2.21212 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9} - 3 q^{10} + 16 q^{11} + 14 q^{12} + 42 q^{13} - 14 q^{14} - 20 q^{15} - 22 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{19} + 80 q^{20} + 2 q^{22} + 7 q^{23} - 6 q^{24} - 22 q^{25} - 2 q^{26} - 28 q^{27} - 59 q^{28} - 32 q^{29} + 3 q^{30} - 8 q^{31} + 19 q^{32} - 16 q^{33} + 66 q^{34} - 8 q^{35} + 28 q^{36} - q^{37} - 32 q^{38} + 21 q^{39} + 13 q^{40} + 28 q^{41} - 10 q^{42} + 28 q^{43} + 36 q^{44} - 10 q^{45} + 12 q^{46} - 12 q^{47} - 44 q^{48} + 8 q^{49} - 2 q^{50} + 12 q^{51} - 60 q^{52} + 20 q^{53} - 2 q^{54} - 22 q^{55} + q^{56} - 4 q^{57} - 21 q^{58} - 25 q^{59} + 40 q^{60} - 26 q^{61} - 66 q^{62} + 84 q^{64} + 8 q^{65} + q^{66} + 22 q^{67} - 15 q^{68} + 14 q^{69} - 120 q^{70} - 72 q^{71} + 6 q^{72} - 31 q^{73} + 65 q^{74} + 22 q^{75} - 4 q^{76} - 18 q^{77} - 4 q^{78} - 12 q^{79} - 112 q^{80} - 14 q^{81} + 2 q^{82} + 40 q^{83} - 37 q^{84} + 80 q^{85} + 9 q^{86} - 16 q^{87} + 54 q^{88} - 39 q^{89} + 6 q^{90} - 17 q^{91} + 126 q^{92} + 8 q^{93} - 14 q^{94} + 55 q^{95} - 19 q^{96} + 36 q^{97} - 19 q^{98} - 32 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9 - 3 * q^10 + 16 * q^11 + 14 * q^12 + 42 * q^13 - 14 * q^14 - 20 * q^15 - 22 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^19 + 80 * q^20 + 2 * q^22 + 7 * q^23 - 6 * q^24 - 22 * q^25 - 2 * q^26 - 28 * q^27 - 59 * q^28 - 32 * q^29 + 3 * q^30 - 8 * q^31 + 19 * q^32 - 16 * q^33 + 66 * q^34 - 8 * q^35 + 28 * q^36 - q^37 - 32 * q^38 + 21 * q^39 + 13 * q^40 + 28 * q^41 - 10 * q^42 + 28 * q^43 + 36 * q^44 - 10 * q^45 + 12 * q^46 - 12 * q^47 - 44 * q^48 + 8 * q^49 - 2 * q^50 + 12 * q^51 - 60 * q^52 + 20 * q^53 - 2 * q^54 - 22 * q^55 + q^56 - 4 * q^57 - 21 * q^58 - 25 * q^59 + 40 * q^60 - 26 * q^61 - 66 * q^62 + 84 * q^64 + 8 * q^65 + q^66 + 22 * q^67 - 15 * q^68 + 14 * q^69 - 120 * q^70 - 72 * q^71 + 6 * q^72 - 31 * q^73 + 65 * q^74 + 22 * q^75 - 4 * q^76 - 18 * q^77 - 4 * q^78 - 12 * q^79 - 112 * q^80 - 14 * q^81 + 2 * q^82 + 40 * q^83 - 37 * q^84 + 80 * q^85 + 9 * q^86 - 16 * q^87 + 54 * q^88 - 39 * q^89 + 6 * q^90 - 17 * q^91 + 126 * q^92 + 8 * q^93 - 14 * q^94 + 55 * q^95 - 19 * q^96 + 36 * q^97 - 19 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/861\mathbb{Z}\right)^\times$.

$n$	$211$	$493$	$575$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.221125	−	0.383000i	0.156359	−	0.270822i	−0.777194	−	0.629261i	$-0.783358\pi$
$2$	0.221125	−	0.383000i	0.156359	−	0.270822i	0.933553	+	0.358439i	$0.116691\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.902207	+	1.56267i	0.451104	+	0.781334i
$5$	−2.14637	+	3.71763i	−0.959887	+	1.66257i	−0.237121	+	0.971480i	$0.576204\pi$
$5$	−2.14637	+	3.71763i	−0.959887	+	1.66257i	−0.722766	+	0.691093i	$0.757130\pi$
$6$	0.442251			0.180548
$7$	0.504334	+	2.59724i	0.190620	+	0.981664i
$7$	0.504334	+	2.59724i	0.190620	+	0.981664i
$8$	1.68250			0.594855
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.949235	+	1.64412i	0.300174	+	0.519917i
$11$	1.10606	+	1.91575i	0.333489	+	0.577621i	0.983193	−	0.182567i	$-0.0584405\pi$
$11$	1.10606	+	1.91575i	0.333489	+	0.577621i	−0.649704	+	0.760187i	$0.725107\pi$
$12$	−0.902207	+	1.56267i	−0.260445	+	0.451104i
$13$	3.11687			0.864463			0.432231	−	0.901763i	$-0.357726\pi$
$13$	3.11687			0.864463			0.432231	+	0.901763i	$0.357726\pi$
$14$	1.10626	+	0.381155i	0.295662	+	0.101868i
$15$	−4.29274			−1.10838
$16$	−1.43237	+	2.48094i	−0.358092	+	0.620234i
$17$	−3.46198	−	5.99633i	−0.839654	−	1.45432i	−0.890184	−	0.455601i	$-0.849425\pi$
$17$	−3.46198	−	5.99633i	−0.839654	−	1.45432i	0.0505305	−	0.998723i	$-0.483909\pi$
$18$	0.221125	+	0.383000i	0.0521197	+	0.0902740i
$19$	3.86244	−	6.68994i	0.886104	−	1.53478i	0.0416600	−	0.999132i	$-0.486735\pi$
$19$	3.86244	−	6.68994i	0.886104	−	1.53478i	0.844444	−	0.535645i	$-0.179931\pi$
$20$	−7.74589			−1.73203
$21$	−1.99711	+	1.73539i	−0.435805	+	0.378692i
$22$	0.978311			0.208577
$23$	−0.0190846	+	0.0330555i	−0.00397941	+	0.00689255i	−0.868008	−	0.496550i	$-0.834600\pi$
$23$	−0.0190846	+	0.0330555i	−0.00397941	+	0.00689255i	0.864029	+	0.503442i	$0.167933\pi$
$24$	0.841252	+	1.45709i	0.171720	+	0.297428i
$25$	−6.71383	−	11.6287i	−1.34277	−	2.32574i
$26$	0.689218	−	1.19376i	0.135167	−	0.234116i
$27$	−1.00000			−0.192450
$28$	−3.60361	+	3.13135i	−0.681018	+	0.591770i
$29$	2.66709			0.495266			0.247633	−	0.968854i	$-0.420347\pi$
$29$	2.66709			0.495266			0.247633	+	0.968854i	$0.420347\pi$
$30$	−0.949235	+	1.64412i	−0.173306	+	0.300174i
$31$	2.34980	+	4.06997i	0.422036	+	0.730987i	0.996138	−	0.0877959i	$-0.0279823\pi$
$31$	2.34980	+	4.06997i	0.422036	+	0.730987i	−0.574103	+	0.818783i	$0.694649\pi$
$32$	2.31597	+	4.01138i	0.409410	+	0.709119i
$33$	−1.10606	+	1.91575i	−0.192540	+	0.333489i
$34$	−3.06213			−0.525151
$35$	−10.7381	−	3.69971i	−1.81506	−	0.625366i
$36$	−1.80441			−0.300736
$37$	0.0150359	−	0.0260429i	0.00247189	−	0.00428143i	−0.864787	−	0.502139i	$-0.832547\pi$
$37$	0.0150359	−	0.0260429i	0.00247189	−	0.00428143i	0.867259	+	0.497858i	$0.165880\pi$
$38$	−1.70816	−	2.95863i	−0.277101	−	0.479953i
$39$	1.55843	+	2.69928i	0.249549	+	0.432231i
$40$	−3.61128	+	6.25492i	−0.570994	+	0.988990i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	0.223042	+	1.14863i	0.0344162	+	0.177238i
$43$	11.0093			1.67890			0.839449	−	0.543438i	$-0.182878\pi$
$43$	11.0093			1.67890			0.839449	+	0.543438i	$0.182878\pi$
$44$	−1.99579	+	3.45681i	−0.300877	+	0.521133i
$45$	−2.14637	−	3.71763i	−0.319962	−	0.554191i
$46$	0.00844018	+	0.0146188i	0.00124444	+	0.00215543i
$47$	−1.89054	+	3.27451i	−0.275763	+	0.477636i	−0.970327	−	0.241795i	$-0.922264\pi$
$47$	−1.89054	+	3.27451i	−0.275763	+	0.477636i	0.694564	+	0.719431i	$0.255597\pi$
$48$	−2.86474			−0.413490
$49$	−6.49129	+	2.61975i	−0.927328	+	0.374250i
$50$	−5.93839			−0.839815
$51$	3.46198	−	5.99633i	0.484774	−	0.839654i
$52$	2.81206	+	4.87063i	0.389962	+	0.675435i
$53$	0.273068	+	0.472968i	0.0375088	+	0.0649672i	0.884170	−	0.467165i	$-0.154724\pi$
$53$	0.273068	+	0.472968i	0.0375088	+	0.0649672i	−0.846662	+	0.532132i	$0.821391\pi$
$54$	−0.221125	+	0.383000i	−0.0300913	+	0.0521197i
$55$	−9.49606			−1.28045
$56$	0.848545	+	4.36987i	0.113392	+	0.583948i
$57$	7.72487			1.02318
$58$	0.589761	−	1.02150i	0.0774394	−	0.134129i
$59$	−4.77954	−	8.27841i	−0.622243	−	1.07776i	−0.989067	−	0.147467i	$-0.952888\pi$
$59$	−4.77954	−	8.27841i	−0.622243	−	1.07776i	0.366824	−	0.930291i	$-0.380445\pi$
$60$	−3.87295	−	6.70814i	−0.499995	−	0.866017i
$61$	3.01039	−	5.21414i	0.385441	−	0.667603i	−0.606390	−	0.795168i	$-0.707383\pi$
$61$	3.01039	−	5.21414i	0.385441	−	0.667603i	0.991830	+	0.127565i	$0.0407161\pi$
$62$	2.07840			0.263957
$63$	−2.50144	−	0.861853i	−0.315152	−	0.108583i
$64$	−3.68100			−0.460125
$65$	−6.68995	+	11.5873i	−0.829787	+	1.43723i
$66$	0.489155	+	0.847242i	0.0602109	+	0.104288i
$67$	4.48837	+	7.77408i	0.548341	+	0.949755i	0.998388	+	0.0567502i	$0.0180739\pi$
$67$	4.48837	+	7.77408i	0.548341	+	0.949755i	−0.450047	+	0.893005i	$0.648593\pi$
$68$	6.24685	−	10.8199i	0.757542	−	1.31210i
$69$	−0.0381692			−0.00459503
$70$	−3.79145	+	3.29458i	−0.453165	+	0.393777i
$71$	15.6199			1.85374			0.926868	−	0.375386i	$-0.122490\pi$
$71$	15.6199			1.85374			0.926868	+	0.375386i	$0.122490\pi$
$72$	−0.841252	+	1.45709i	−0.0991426	+	0.171720i
$73$	−1.21150	−	2.09837i	−0.141795	−	0.245596i	0.786378	−	0.617746i	$-0.211954\pi$
$73$	−1.21150	−	2.09837i	−0.141795	−	0.245596i	−0.928173	+	0.372150i	$0.878621\pi$
$74$	−0.00664964	−	0.0115175i	−0.000773005	−	0.00133888i
$75$	6.71383	−	11.6287i	0.775246	−	1.34277i
$76$	13.9389			1.59890
$77$	−4.41784	+	3.83888i	−0.503459	+	0.437481i
$78$	1.37844			0.156077
$79$	−1.08068	+	1.87180i	−0.121586	+	0.210593i	−0.920393	−	0.390994i	$-0.872131\pi$
$79$	−1.08068	+	1.87180i	−0.121586	+	0.210593i	0.798807	+	0.601587i	$0.205465\pi$
$80$	−6.14880	−	10.6500i	−0.687457	−	1.19071i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.221125	−	0.383000i	0.0244192	−	0.0422953i
$83$	−17.0488			−1.87135			−0.935675	−	0.352862i	$-0.885208\pi$
$83$	−17.0488			−1.87135			−0.935675	+	0.352862i	$0.885208\pi$
$84$	−4.51364	−	1.55514i	−0.492478	−	0.169680i
$85$	29.7228			3.22389
$86$	2.43443	−	4.21656i	0.262511	−	0.454683i
$87$	1.33354	+	2.30977i	0.142971	+	0.247633i
$88$	1.86095	+	3.22326i	0.198378	+	0.343601i
$89$	−4.34597	+	7.52744i	−0.460672	+	0.797907i	−0.998995	−	0.0448320i	$-0.985725\pi$
$89$	−4.34597	+	7.52744i	−0.460672	+	0.797907i	0.538323	+	0.842739i	$0.319058\pi$
$90$	−1.89847			−0.200116
$91$	1.57194	+	8.09524i	0.164784	+	0.848612i
$92$	−0.0688730			−0.00718051
$93$	−2.34980	+	4.06997i	−0.243662	+	0.422036i
$94$	0.836092	+	1.44815i	0.0862363	+	0.149366i
$95$	16.5805	+	28.7182i	1.70112	+	2.94642i
$96$	−2.31597	+	4.01138i	−0.236373	+	0.409410i
$97$	−0.216724			−0.0220050			−0.0110025	−	0.999939i	$-0.503502\pi$
$97$	−0.216724			−0.0220050			−0.0110025	+	0.999939i	$0.503502\pi$
$98$	−0.432024	+	3.06546i	−0.0436410	+	0.309658i
$99$	−2.21212			−0.222326
$100$	12.1145	−	20.9830i	1.21145	−	2.09830i
$101$	−1.26663	−	2.19387i	−0.126034	−	0.218298i	0.796102	−	0.605162i	$-0.206892\pi$
$101$	−1.26663	−	2.19387i	−0.126034	−	0.218298i	−0.922137	+	0.386864i	$0.873558\pi$
$102$	−1.53106	−	2.65188i	−0.151598	−	0.262575i
$103$	−0.354817	+	0.614561i	−0.0349612	+	0.0605545i	−0.882977	−	0.469417i	$-0.844464\pi$
$103$	−0.354817	+	0.614561i	−0.0349612	+	0.0605545i	0.848015	+	0.529972i	$0.177797\pi$
$104$	5.24414			0.514230
$105$	−2.16498	−	11.1493i	−0.211280	−	1.08806i
$106$	0.241529			0.0234594
$107$	−3.21045	+	5.56066i	−0.310366	+	0.537569i	−0.978441	−	0.206524i	$-0.933785\pi$
$107$	−3.21045	+	5.56066i	−0.310366	+	0.537569i	0.668076	+	0.744093i	$0.267118\pi$
$108$	−0.902207	−	1.56267i	−0.0868149	−	0.150368i
$109$	1.26224	+	2.18627i	0.120901	+	0.209407i	0.920123	−	0.391629i	$-0.128088\pi$
$109$	1.26224	+	2.18627i	0.120901	+	0.209407i	−0.799222	+	0.601036i	$0.794755\pi$
$110$	−2.09982	+	3.63699i	−0.200210	+	0.346774i
$111$	0.0300718			0.00285429
$112$	−7.16598	−	2.46898i	−0.677121	−	0.233297i
$113$	1.71911			0.161721			0.0808603	−	0.996725i	$-0.474233\pi$
$113$	1.71911			0.161721			0.0808603	+	0.996725i	$0.474233\pi$
$114$	1.70816	−	2.95863i	0.159984	−	0.277101i
$115$	−0.0819253	−	0.141899i	−0.00763957	−	0.0132321i
$116$	2.40627	+	4.16777i	0.223416	+	0.386968i
$117$	−1.55843	+	2.69928i	−0.144077	+	0.249549i
$118$	−4.22751			−0.389174
$119$	13.8279	−	12.0157i	1.26760	−	1.10148i
$120$	−7.22256			−0.659327
$121$	3.05327	−	5.28841i	0.277570	−	0.480765i
$122$	−1.33135	−	2.30596i	−0.120534	−	0.208772i
$123$	0.500000	+	0.866025i	0.0450835	+	0.0780869i
$124$	−4.24001	+	7.34390i	−0.380764	+	0.659502i
$125$	36.1778			3.23584
$126$	−0.883222	+	0.767475i	−0.0786837	+	0.0683721i
$127$	−18.8770			−1.67506			−0.837529	−	0.546392i	$-0.816001\pi$
$127$	−18.8770			−1.67506			−0.837529	+	0.546392i	$0.816001\pi$
$128$	−5.44591	+	9.43258i	−0.481355	+	0.833731i
$129$	5.50464	+	9.53431i	0.484656	+	0.839449i
$130$	2.95864	+	5.12451i	0.259490	+	0.449449i
$131$	−4.84610	+	8.39369i	−0.423406	+	0.733360i	−0.996270	−	0.0862900i	$-0.972499\pi$
$131$	−4.84610	+	8.39369i	−0.423406	+	0.733360i	0.572864	+	0.819650i	$0.305832\pi$
$132$	−3.99158			−0.347422
$133$	19.3233	+	6.65770i	1.67554	+	0.577296i
$134$	3.96997			0.342953
$135$	2.14637	−	3.71763i	0.184730	−	0.319962i
$136$	−5.82480	−	10.0889i	−0.499473	−	0.865112i
$137$	−3.02923	−	5.24677i	−0.258804	−	0.448262i	0.707118	−	0.707096i	$-0.249995\pi$
$137$	−3.02923	−	5.24677i	−0.258804	−	0.448262i	−0.965922	+	0.258834i	$0.916662\pi$
$138$	−0.00844018	+	0.0146188i	−0.000718475	+	0.00124444i
$139$	−1.67013			−0.141658			−0.0708291	−	0.997488i	$-0.522565\pi$
$139$	−1.67013			−0.141658			−0.0708291	+	0.997488i	$0.522565\pi$
$140$	−3.90652	−	20.1179i	−0.330161	−	1.70027i
$141$	−3.78108			−0.318424
$142$	3.45395	−	5.98241i	0.289849	−	0.502033i
$143$	3.44744	+	5.97114i	0.288289	+	0.499332i
$144$	−1.43237	−	2.48094i	−0.119364	−	0.206745i
$145$	−5.72456	+	9.91523i	−0.475399	+	0.823415i
$146$	−1.07157			−0.0886837
$147$	−5.51442	−	4.31175i	−0.454822	−	0.355627i
$148$	0.0542620			0.00446031
$149$	−1.34771	+	2.33430i	−0.110409	+	0.191234i	−0.915935	−	0.401326i	$-0.868549\pi$
$149$	−1.34771	+	2.33430i	−0.110409	+	0.191234i	0.805526	+	0.592560i	$0.201883\pi$
$150$	−2.96920	−	5.14280i	−0.242434	−	0.419908i
$151$	0.852902	+	1.47727i	0.0694082	+	0.120219i	0.898641	−	0.438685i	$-0.144556\pi$
$151$	0.852902	+	1.47727i	0.0694082	+	0.120219i	−0.829233	+	0.558903i	$0.811222\pi$
$152$	6.49857	−	11.2558i	0.527103	−	0.912970i
$153$	6.92396			0.559769
$154$	0.493396	+	2.54091i	0.0397590	+	0.204752i
$155$	−20.1741			−1.62043
$156$	−2.81206	+	4.87063i	−0.225145	+	0.389962i
$157$	−5.84248	−	10.1195i	−0.466281	−	0.807622i	0.532977	−	0.846130i	$-0.321073\pi$
$157$	−5.84248	−	10.1195i	−0.466281	−	0.807622i	−0.999258	+	0.0385071i	$0.987740\pi$
$158$	0.477932	+	0.827803i	0.0380223	+	0.0658565i
$159$	−0.273068	+	0.472968i	−0.0216557	+	0.0375088i
$160$	−19.8837			−1.57195
$161$	−0.0954780	−	0.0328962i	−0.00752472	−	0.00259259i
$162$	−0.442251			−0.0347465
$163$	6.16659	−	10.6808i	0.483005	−	0.836589i	−0.516805	−	0.856103i	$-0.672879\pi$
$163$	6.16659	−	10.6808i	0.483005	−	0.836589i	0.999810	+	0.0195146i	$0.00621209\pi$
$164$	0.902207	+	1.56267i	0.0704505	+	0.122024i
$165$	−4.74803	−	8.22383i	−0.369634	−	0.640224i
$166$	−3.76992	+	6.52970i	−0.292603	+	0.506803i
$167$	6.35364			0.491659			0.245830	−	0.969313i	$-0.420940\pi$
$167$	6.35364			0.491659			0.245830	+	0.969313i	$0.420940\pi$
$168$	−3.36014	+	2.91979i	−0.259241	+	0.225267i
$169$	−3.28515			−0.252704
$170$	6.57247	−	11.3838i	0.504085	−	0.873101i
$171$	3.86244	+	6.68994i	0.295368	+	0.511592i
$172$	9.93265	+	17.2038i	0.757357	+	1.31178i
$173$	0.289519	−	0.501462i	0.0220117	−	0.0381254i	−0.854810	−	0.518942i	$-0.826326\pi$
$173$	0.289519	−	0.501462i	0.0220117	−	0.0381254i	0.876821	+	0.480816i	$0.159660\pi$
$174$	1.17952			0.0894193
$175$	26.8165	−	23.3022i	2.02713	−	1.76148i
$176$	−6.33714			−0.477680
$177$	4.77954	−	8.27841i	0.359252	−	0.622243i
$178$	1.92201	+	3.32901i	0.144061	+	0.249520i
$179$	−10.6454	−	18.4383i	−0.795672	−	1.37814i	−0.922411	−	0.386209i	$-0.873784\pi$
$179$	−10.6454	−	18.4383i	−0.795672	−	1.37814i	0.126739	−	0.991936i	$-0.459549\pi$
$180$	3.87295	−	6.70814i	0.288672	−	0.499995i
$181$	−21.3004			−1.58325			−0.791623	−	0.611010i	$-0.790763\pi$
$181$	−21.3004			−1.58325			−0.791623	+	0.611010i	$0.790763\pi$
$182$	3.44808	+	1.18801i	0.255588	+	0.0880611i
$183$	6.02077			0.445068
$184$	−0.0321099	+	0.0556160i	−0.00236717	+	0.00410007i
$185$	0.0645453	+	0.111796i	0.00474546	+	0.00821938i
$186$	1.03920	+	1.79995i	0.0761978	+	0.131978i
$187$	7.65831	−	13.2646i	0.560031	−	0.970003i
$188$	−6.82263			−0.497591
$189$	−0.504334	−	2.59724i	−0.0366849	−	0.188921i
$190$	14.6654			1.06394
$191$	1.12974	−	1.95676i	0.0817448	−	0.141586i	−0.822255	−	0.569120i	$-0.807284\pi$
$191$	1.12974	−	1.95676i	0.0817448	−	0.141586i	0.903999	+	0.427534i	$0.140617\pi$
$192$	−1.84050	−	3.18784i	−0.132827	−	0.230062i
$193$	9.93874	+	17.2144i	0.715406	+	1.23912i	0.962803	+	0.270205i	$0.0870916\pi$
$193$	9.93874	+	17.2144i	0.715406	+	1.23912i	−0.247397	+	0.968914i	$0.579575\pi$
$194$	−0.0479232	+	0.0830054i	−0.00344068	+	0.00595944i
$195$	−13.3799			−0.958155
$196$	−9.95030	−	7.78018i	−0.710735	−	0.555727i
$197$	−7.13650			−0.508455			−0.254227	−	0.967144i	$-0.581821\pi$
$197$	−7.13650			−0.508455			−0.254227	+	0.967144i	$0.581821\pi$
$198$	−0.489155	+	0.847242i	−0.0347628	+	0.0602109i
$199$	6.98525	+	12.0988i	0.495172	+	0.857662i	0.999985	−	0.00556644i	$-0.00177186\pi$
$199$	6.98525	+	12.0988i	0.495172	+	0.857662i	−0.504813	+	0.863229i	$0.668439\pi$
$200$	−11.2961	−	19.5653i	−0.798751	−	1.38348i
$201$	−4.48837	+	7.77408i	−0.316585	+	0.548341i
$202$	−1.12034			−0.0788265
$203$	1.34510	+	6.92706i	0.0944077	+	0.486184i
$204$	12.4937			0.874734
$205$	−2.14637	+	3.71763i	−0.149909	+	0.259650i
$206$	0.156918	+	0.271790i	0.0109330	+	0.0189365i
$207$	−0.0190846	−	0.0330555i	−0.00132647	−	0.00229752i
$208$	−4.46450	+	7.73275i	−0.309558	+	0.536170i
$209$	17.0883			1.18202
$210$	−4.74891	−	1.63620i	−0.327706	−	0.112909i
$211$	23.3091			1.60466			0.802332	−	0.596878i	$-0.203592\pi$
$211$	23.3091			1.60466			0.802332	+	0.596878i	$0.203592\pi$
$212$	−0.492728	+	0.853430i	−0.0338407	+	0.0586138i
$213$	7.80993	+	13.5272i	0.535128	+	0.926868i
$214$	1.41982	+	2.45920i	0.0970570	+	0.168108i
$215$	−23.6300	+	40.9284i	−1.61155	+	2.79129i
$216$	−1.68250			−0.114480
$217$	−9.38559	+	8.15560i	−0.637135	+	0.553638i
$218$	1.11646			0.0756159
$219$	1.21150	−	2.09837i	0.0818653	−	0.141795i
$220$	−8.56741	−	14.8392i	−0.577615	−	1.00046i
$221$	−10.7905	−	18.6897i	−0.725850	−	1.25721i
$222$	0.00664964	−	0.0115175i	0.000446294	−	0.000773005i
$223$	24.6795			1.65266			0.826330	−	0.563186i	$-0.190425\pi$
$223$	24.6795			1.65266			0.826330	+	0.563186i	$0.190425\pi$
$224$	−9.25049	+	8.03821i	−0.618074	+	0.537075i
$225$	13.4277			0.895177
$226$	0.380140	−	0.658421i	0.0252865	−	0.0437975i
$227$	−5.87036	−	10.1678i	−0.389630	−	0.674858i	0.602770	−	0.797915i	$-0.294064\pi$
$227$	−5.87036	−	10.1678i	−0.389630	−	0.674858i	−0.992400	+	0.123057i	$0.960730\pi$
$228$	6.96943	+	12.0714i	0.461562	+	0.799449i
$229$	7.72053	−	13.3724i	0.510187	−	0.883670i	−0.489743	−	0.871867i	$-0.662909\pi$
$229$	7.72053	−	13.3724i	0.510187	−	0.883670i	0.999930	−	0.0118035i	$-0.00375725\pi$
$230$	−0.0724630			−0.00477807
$231$	−5.53348	−	1.90652i	−0.364077	−	0.125440i
$232$	4.48739			0.294611
$233$	3.62058	−	6.27103i	0.237192	−	0.410829i	−0.722715	−	0.691146i	$-0.757106\pi$
$233$	3.62058	−	6.27103i	0.237192	−	0.410829i	0.959907	+	0.280317i	$0.0904396\pi$
$234$	0.689218	+	1.19376i	0.0450556	+	0.0780386i
$235$	−8.11560	−	14.0566i	−0.529403	−	0.916953i
$236$	8.62428	−	14.9377i	0.561393	−	0.972360i
$237$	−2.16136			−0.140396
$238$	−1.54434	−	7.95307i	−0.100104	−	0.515521i
$239$	−13.7858			−0.891726			−0.445863	−	0.895101i	$-0.647103\pi$
$239$	−13.7858			−0.891726			−0.445863	+	0.895101i	$0.647103\pi$
$240$	6.14880	−	10.6500i	0.396903	−	0.687457i
$241$	−1.75450	−	3.03888i	−0.113017	−	0.195752i	0.803968	−	0.594672i	$-0.202718\pi$
$241$	−1.75450	−	3.03888i	−0.113017	−	0.195752i	−0.916985	+	0.398921i	$0.869385\pi$
$242$	−1.35031	−	2.33880i	−0.0868012	−	0.150344i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	10.8640			0.695494
$245$	4.19347	−	29.7552i	0.267911	−	1.90099i
$246$	0.442251			0.0281969
$247$	12.0387	−	20.8516i	0.766004	−	1.32676i
$248$	3.95354	+	6.84774i	0.251050	+	0.434832i
$249$	−8.52441	−	14.7647i	−0.540212	−	0.935675i
$250$	7.99983	−	13.8561i	0.505953	−	0.876337i
$251$	14.8746			0.938876			0.469438	−	0.882965i	$-0.344457\pi$
$251$	14.8746			0.938876			0.469438	+	0.882965i	$0.344457\pi$
$252$	−0.910028	−	4.68649i	−0.0573264	−	0.295221i
$253$	−0.0844348			−0.00530837
$254$	−4.17417	+	7.22988i	−0.261911	+	0.453643i
$255$	14.8614	+	25.7407i	0.930657	+	1.61195i
$256$	−1.27254	−	2.20411i	−0.0795340	−	0.137757i
$257$	10.8779	−	18.8411i	0.678547	−	1.17528i	−0.296871	−	0.954917i	$-0.595943\pi$
$257$	10.8779	−	18.8411i	0.678547	−	1.17528i	0.975418	−	0.220361i	$-0.0707234\pi$
$258$	4.86886			0.303122
$259$	0.0752228	+	0.0259175i	0.00467412	+	0.00161043i
$260$	−24.1429			−1.49728
$261$	−1.33354	+	2.30977i	−0.0825443	+	0.142971i
$262$	2.14319	+	3.71212i	0.132407	+	0.229335i
$263$	−1.13900	−	1.97281i	−0.0702340	−	0.121649i	0.828770	−	0.559590i	$-0.189041\pi$
$263$	−1.13900	−	1.97281i	−0.0702340	−	0.121649i	−0.899004	+	0.437941i	$0.855708\pi$
$264$	−1.86095	+	3.22326i	−0.114534	+	0.198378i
$265$	−2.34442			−0.144017
$266$	6.82278	−	5.92865i	0.418331	−	0.363509i
$267$	−8.69193			−0.531938
$268$	−8.09887	+	14.0277i	−0.494717	+	0.856876i
$269$	−1.01547	−	1.75884i	−0.0619141	−	0.107238i	0.833407	−	0.552660i	$-0.186387\pi$
$269$	−1.01547	−	1.75884i	−0.0619141	−	0.107238i	−0.895321	+	0.445422i	$0.853054\pi$
$270$	−0.949235	−	1.64412i	−0.0577686	−	0.100058i
$271$	−7.92177	+	13.7209i	−0.481214	+	0.833486i	−0.999768	−	0.0215586i	$-0.993137\pi$
$271$	−7.92177	+	13.7209i	−0.481214	+	0.833486i	0.518554	+	0.855045i	$0.326470\pi$
$272$	19.8354			1.20269
$273$	−6.22471	+	5.40896i	−0.376737	+	0.327365i
$274$	−2.67935			−0.161866
$275$	14.8518	−	25.7240i	0.895596	−	1.55122i
$276$	−0.0344365	−	0.0596458i	−0.00207283	−	0.00359025i
$277$	1.75000	+	3.03109i	0.105147	+	0.182120i	0.913798	−	0.406168i	$-0.133135\pi$
$277$	1.75000	+	3.03109i	0.105147	+	0.182120i	−0.808651	+	0.588289i	$0.799802\pi$
$278$	−0.369307	+	0.639659i	−0.0221496	+	0.0383642i
$279$	−4.69959			−0.281357
$280$	−18.0668	−	6.22479i	−1.07970	−	0.372002i
$281$	26.7164			1.59377			0.796883	−	0.604134i	$-0.206481\pi$
$281$	26.7164			1.59377			0.796883	+	0.604134i	$0.206481\pi$
$282$	−0.836092	+	1.44815i	−0.0497885	+	0.0862363i
$283$	−7.84585	−	13.5894i	−0.466387	−	0.807806i	0.532876	−	0.846193i	$-0.321111\pi$
$283$	−7.84585	−	13.5894i	−0.466387	−	0.807806i	−0.999263	+	0.0383873i	$0.987778\pi$
$284$	14.0924	+	24.4087i	0.836227	+	1.44839i
$285$	−16.5805	+	28.7182i	−0.982141	+	1.70112i
$286$	3.04926			0.180307
$287$	0.504334	+	2.59724i	0.0297699	+	0.153310i
$288$	−4.63194			−0.272940
$289$	−15.4706	+	26.7959i	−0.910037	+	1.57623i
$290$	2.53169	+	4.38502i	0.148666	+	0.257497i
$291$	−0.108362	−	0.187689i	−0.00635230	−	0.0110025i
$292$	2.18604	−	3.78633i	0.127928	−	0.221578i
$293$	14.4844			0.846189			0.423095	−	0.906085i	$-0.360944\pi$
$293$	14.4844			0.846189			0.423095	+	0.906085i	$0.360944\pi$
$294$	−2.87078	+	1.15859i	−0.167427	+	0.0675702i
$295$	41.0347			2.38913
$296$	0.0252980	−	0.0438174i	0.00147041	−	0.00254683i
$297$	−1.10606	−	1.91575i	−0.0641801	−	0.111163i
$298$	0.596026	+	1.03235i	0.0345268	+	0.0598022i
$299$	−0.0594841	+	0.103030i	−0.00344005	+	0.00595835i
$300$	24.2291			1.39887
$301$	5.55235	+	28.5937i	0.320032	+	1.64811i
$302$	0.754393			0.0434105
$303$	1.26663	−	2.19387i	0.0727660	−	0.126034i
$304$	11.0649	+	19.1649i	0.634614	+	1.09918i
$305$	12.9228	+	22.3830i	0.739959	+	1.28165i
$306$	1.53106	−	2.65188i	0.0875251	−	0.151598i
$307$	−19.7492			−1.12715			−0.563573	−	0.826066i	$-0.690574\pi$
$307$	−19.7492			−1.12715			−0.563573	+	0.826066i	$0.690574\pi$
$308$	−9.98470	−	3.44015i	−0.568931	−	0.196021i
$309$	−0.709634			−0.0403697
$310$	−4.46102	+	7.72671i	−0.253369	+	0.438847i
$311$	−9.06774	−	15.7058i	−0.514184	−	0.890594i	−0.999865	−	0.0164570i	$-0.994761\pi$
$311$	−9.06774	−	15.7058i	−0.514184	−	0.890594i	0.485680	−	0.874137i	$-0.338572\pi$
$312$	2.62207	+	4.54156i	0.148446	+	0.257115i
$313$	1.64119	−	2.84262i	0.0927653	−	0.160674i	−0.815908	−	0.578181i	$-0.803763\pi$
$313$	1.64119	−	2.84262i	0.0927653	−	0.160674i	0.908674	+	0.417507i	$0.137096\pi$
$314$	−5.16769			−0.291629
$315$	8.57307	−	7.44957i	0.483038	−	0.419736i
$316$	−3.90000			−0.219392
$317$	0.220350	−	0.381658i	0.0123761	−	0.0214360i	−0.859771	−	0.510680i	$-0.829394\pi$
$317$	0.220350	−	0.381658i	0.0123761	−	0.0214360i	0.872147	+	0.489244i	$0.162727\pi$
$318$	0.120765	+	0.209170i	0.00677214	+	0.0117297i
$319$	2.94996	+	5.10947i	0.165166	+	0.286076i
$320$	7.90080	−	13.6846i	0.441668	−	0.764991i
$321$	−6.42089			−0.358379
$322$	−0.0337119	+	0.0292939i	−0.00187869	+	0.00163249i
$323$	−53.4867			−2.97608
$324$	0.902207	−	1.56267i	0.0501226	−	0.0868149i
$325$	−20.9261	−	36.2451i	−1.16077	−	2.01051i
$326$	−2.72718	−	4.72361i	−0.151044	−	0.261617i
$327$	−1.26224	+	2.18627i	−0.0698022	+	0.120901i
$328$	1.68250			0.0929008
$329$	−9.45814	−	3.25873i	−0.521444	−	0.179660i
$330$	−4.19964			−0.231183
$331$	1.63403	−	2.83021i	0.0898141	−	0.155563i	−0.817618	−	0.575761i	$-0.804706\pi$
$331$	1.63403	−	2.83021i	0.0898141	−	0.155563i	0.907432	+	0.420198i	$0.138039\pi$
$332$	−15.3816	−	26.6416i	−0.844173	−	1.46215i
$333$	0.0150359	+	0.0260429i	0.000823962	+	0.00142714i
$334$	1.40495	−	2.43345i	0.0768755	−	0.133152i
$335$	−38.5348			−2.10538
$336$	−1.44479	−	7.44041i	−0.0788196	−	0.405908i
$337$	−18.8129			−1.02481			−0.512403	−	0.858745i	$-0.671244\pi$
$337$	−18.8129			−1.02481			−0.512403	+	0.858745i	$0.671244\pi$
$338$	−0.726430	+	1.25821i	−0.0395126	+	0.0684378i
$339$	0.859557	+	1.48880i	0.0466847	+	0.0808603i
$340$	26.8161	+	46.4469i	1.45431	+	2.51894i
$341$	−5.19803	+	9.00325i	−0.281489	+	0.487553i
$342$	3.41633			0.184734
$343$	−10.0779	−	15.5382i	−0.544156	−	0.838984i
$344$	18.5232			0.998702
$345$	0.0819253	−	0.141899i	0.00441071	−	0.00763957i
$346$	−0.128040	−	0.221772i	−0.00688347	−	0.0119225i
$347$	12.4399	+	21.5466i	0.667809	+	1.15668i	0.978515	+	0.206174i	$0.0661012\pi$
$347$	12.4399	+	21.5466i	0.667809	+	1.15668i	−0.310706	+	0.950506i	$0.600566\pi$
$348$	−2.40627	+	4.16777i	−0.128989	+	0.223416i
$349$	34.7651			1.86094			0.930468	−	0.366374i	$-0.119401\pi$
$349$	34.7651			1.86094			0.930468	+	0.366374i	$0.119401\pi$
$350$	−2.99493	−	15.4234i	−0.160086	−	0.824416i
$351$	−3.11687			−0.166366
$352$	−5.12320	+	8.87365i	−0.273068	+	0.472967i
$353$	8.31474	+	14.4015i	0.442549	+	0.766517i	0.997878	−	0.0651138i	$-0.0207410\pi$
$353$	8.31474	+	14.4015i	0.442549	+	0.766517i	−0.555329	+	0.831631i	$0.687408\pi$
$354$	−2.11376	−	3.66113i	−0.112345	−	0.194587i
$355$	−33.5260	+	58.0688i	−1.77938	+	3.08197i
$356$	−15.6839			−0.831242
$357$	17.3199	+	5.96744i	0.916666	+	0.315830i
$358$	−9.41584			−0.497643
$359$	12.6386	−	21.8907i	0.667041	−	1.15535i	−0.311687	−	0.950185i	$-0.600894\pi$
$359$	12.6386	−	21.8907i	0.667041	−	1.15535i	0.978728	−	0.205164i	$-0.0657728\pi$
$360$	−3.61128	−	6.25492i	−0.190331	−	0.329663i
$361$	−20.3368	−	35.2244i	−1.07036	−	1.85392i
$362$	−4.71006	+	8.15805i	−0.247555	+	0.428778i
$363$	6.10653			0.320510
$364$	−11.2320	+	9.76001i	−0.588715	+	0.511564i
$365$	10.4013			0.544428
$366$	1.33135	−	2.30596i	0.0695906	−	0.120534i
$367$	−16.6092	−	28.7679i	−0.866992	−	1.50167i	−0.865056	−	0.501676i	$-0.832717\pi$
$367$	−16.6092	−	28.7679i	−0.866992	−	1.50167i	−0.00193616	−	0.999998i	$-0.500616\pi$
$368$	−0.0546724	−	0.0946954i	−0.00285000	−	0.00493634i
$369$	−0.500000	+	0.866025i	−0.0260290	+	0.0450835i
$370$	0.0570904			0.00296799
$371$	−1.09069	+	0.947757i	−0.0566260	+	0.0492051i
$372$	−8.48001			−0.439668
$373$	−12.9904	+	22.5001i	−0.672619	+	1.16501i	0.304539	+	0.952500i	$0.401498\pi$
$373$	−12.9904	+	22.5001i	−0.672619	+	1.16501i	−0.977159	+	0.212511i	$0.931836\pi$
$374$	−3.38689	−	5.86627i	−0.175132	−	0.303338i
$375$	18.0889	+	31.3309i	0.934107	+	1.61792i
$376$	−3.18084	+	5.50938i	−0.164039	+	0.284124i
$377$	8.31295			0.428139
$378$	−1.10626	−	0.381155i	−0.0569001	−	0.0196045i
$379$	10.2601			0.527028			0.263514	−	0.964656i	$-0.415118\pi$
$379$	10.2601			0.527028			0.263514	+	0.964656i	$0.415118\pi$
$380$	−29.9180	+	51.8195i	−1.53476	+	2.65828i
$381$	−9.43848	−	16.3479i	−0.483548	−	0.837529i
$382$	−0.499627	−	0.865379i	−0.0255631	−	0.0442766i
$383$	1.29594	−	2.24463i	0.0662194	−	0.114695i	−0.831015	−	0.556250i	$-0.812240\pi$
$383$	1.29594	−	2.24463i	0.0662194	−	0.114695i	0.897234	+	0.441555i	$0.145573\pi$
$384$	−10.8918			−0.555820
$385$	−4.78919	−	24.6635i	−0.244080	−	1.25697i
$386$	8.79083			0.447441
$387$	−5.50464	+	9.53431i	−0.279816	+	0.484656i
$388$	−0.195530	−	0.338668i	−0.00992653	−	0.0171933i
$389$	4.32704	+	7.49465i	0.219390	+	0.379994i	0.954621	−	0.297822i	$-0.0962601\pi$
$389$	4.32704	+	7.49465i	0.219390	+	0.379994i	−0.735232	+	0.677816i	$0.762927\pi$
$390$	−2.95864	+	5.12451i	−0.149816	+	0.259490i
$391$	0.264282			0.0133653
$392$	−10.9216	+	4.40775i	−0.551626	+	0.222625i
$393$	−9.69220			−0.488907
$394$	−1.57806	+	2.73328i	−0.0795016	+	0.137701i
$395$	−4.63909	−	8.03514i	−0.233418	−	0.404292i
$396$	−1.99579	−	3.45681i	−0.100292	−	0.173711i
$397$	−15.0214	+	26.0178i	−0.753902	+	1.30580i	0.192017	+	0.981392i	$0.438497\pi$
$397$	−15.0214	+	26.0178i	−0.753902	+	1.30580i	−0.945919	+	0.324404i	$0.894836\pi$
$398$	6.17847			0.309699
$399$	3.89592	+	20.0633i	0.195040	+	1.00442i
$400$	38.4667			1.92334
$401$	−6.04710	+	10.4739i	−0.301978	+	0.523040i	−0.976584	−	0.215137i	$-0.930980\pi$
$401$	−6.04710	+	10.4739i	−0.301978	+	0.523040i	0.674606	+	0.738178i	$0.264313\pi$
$402$	1.98498	+	3.43809i	0.0990020	+	0.171476i
$403$	7.32400	+	12.6855i	0.364834	+	0.631912i
$404$	2.28552	−	3.95865i	0.113709	−	0.196950i
$405$	4.29274			0.213308
$406$	2.95050	+	1.01657i	0.146431	+	0.0504517i
$407$	0.0665224			0.00329739
$408$	5.82480	−	10.0889i	0.288371	−	0.499473i
$409$	6.75698	+	11.7034i	0.334111	+	0.578697i	0.983314	−	0.181918i	$-0.0582306\pi$
$409$	6.75698	+	11.7034i	0.334111	+	0.578697i	−0.649203	+	0.760616i	$0.724897\pi$
$410$	0.949235	+	1.64412i	0.0468794	+	0.0811974i
$411$	3.02923	−	5.24677i	0.149421	−	0.258804i
$412$	−1.28047			−0.0630844
$413$	19.0905	−	16.5887i	0.939383	−	0.816276i
$414$	−0.0168804			−0.000829624
$415$	36.5931	−	63.3811i	1.79628	−	3.11126i
$416$	7.21857	+	12.5029i	0.353920	+	0.613007i
$417$	−0.835063	−	1.44637i	−0.0408932	−	0.0708291i
$418$	3.77866	−	6.54484i	0.184820	−	0.320118i
$419$	32.1763			1.57191			0.785957	−	0.618281i	$-0.212171\pi$
$419$	32.1763			1.57191			0.785957	+	0.618281i	$0.212171\pi$
$420$	15.4694	−	13.4421i	0.754828	−	0.655908i
$421$	−32.2673			−1.57261			−0.786307	−	0.617836i	$-0.788010\pi$
$421$	−32.2673			−1.57261			−0.786307	+	0.617836i	$0.788010\pi$
$422$	5.15423	−	8.92739i	0.250904	−	0.434579i
$423$	−1.89054	−	3.27451i	−0.0919211	−	0.159212i
$424$	0.459439	+	0.795771i	0.0223123	+	0.0386461i
$425$	−46.4863	+	80.5166i	−2.25492	+	3.90563i
$426$	6.90790			0.334689
$427$	15.0606	+	5.18902i	0.728834	+	0.251114i
$428$	−11.5859			−0.560028
$429$	−3.44744	+	5.97114i	−0.166444	+	0.288289i
$430$	10.4504	+	18.1006i	0.503962	+	0.872888i
$431$	−5.22409	−	9.04838i	−0.251635	−	0.435845i	0.712341	−	0.701834i	$-0.247635\pi$
$431$	−5.22409	−	9.04838i	−0.251635	−	0.435845i	−0.963976	+	0.265988i	$0.914302\pi$
$432$	1.43237	−	2.48094i	0.0689149	−	0.119364i
$433$	3.79123			0.182195			0.0910975	−	0.995842i	$-0.470963\pi$
$433$	3.79123			0.182195			0.0910975	+	0.995842i	$0.470963\pi$
$434$	1.04821	+	5.39809i	0.0503156	+	0.259117i
$435$	−11.4491			−0.548943
$436$	−2.27761	+	3.94494i	−0.109078	+	0.188928i
$437$	0.147426	+	0.255349i	0.00705234	+	0.0122150i
$438$	−0.535785	−	0.928007i	−0.0256008	−	0.0443419i
$439$	2.24634	−	3.89078i	0.107212	−	0.185697i	−0.807428	−	0.589966i	$-0.799141\pi$
$439$	2.24634	−	3.89078i	0.107212	−	0.185697i	0.914640	+	0.404270i	$0.132474\pi$
$440$	−15.9772			−0.761682
$441$	0.976875	−	6.93150i	0.0465179	−	0.330072i
$442$	−9.54424			−0.453973
$443$	4.09954	−	7.10061i	0.194775	−	0.337360i	−0.752052	−	0.659104i	$-0.770936\pi$
$443$	4.09954	−	7.10061i	0.194775	−	0.337360i	0.946827	+	0.321744i	$0.104269\pi$
$444$	0.0271310	+	0.0469923i	0.00128758	+	0.00223015i
$445$	−18.6561	−	32.3134i	−0.884385	−	1.53180i
$446$	5.45726	−	9.45225i	0.258409	−	0.447577i
$447$	−2.69542			−0.127489
$448$	−1.85645	−	9.56043i	−0.0877092	−	0.451688i
$449$	32.0190			1.51107			0.755535	−	0.655109i	$-0.227377\pi$
$449$	32.0190			1.51107			0.755535	+	0.655109i	$0.227377\pi$
$450$	2.96920	−	5.14280i	0.139969	−	0.242434i
$451$	1.10606	+	1.91575i	0.0520823	+	0.0902092i
$452$	1.55100	+	2.68641i	0.0729528	+	0.126358i
$453$	−0.852902	+	1.47727i	−0.0400729	+	0.0694082i
$454$	−5.19234			−0.243689
$455$	−33.4691	−	11.5315i	−1.56905	−	0.540606i
$456$	12.9971			0.608647
$457$	−1.96190	+	3.39810i	−0.0917736	+	0.158957i	−0.908258	−	0.418412i	$-0.862587\pi$
$457$	−1.96190	+	3.39810i	−0.0917736	+	0.158957i	0.816484	+	0.577368i	$0.195920\pi$
$458$	−3.41441	−	5.91393i	−0.159545	−	0.276340i
$459$	3.46198	+	5.99633i	0.161591	+	0.279885i
$460$	0.147827	−	0.256044i	0.00689248	−	0.0119381i
$461$	26.4099			1.23003			0.615016	−	0.788514i	$-0.289149\pi$
$461$	26.4099			1.23003			0.615016	+	0.788514i	$0.289149\pi$
$462$	−1.95379	+	1.69775i	−0.0908986	+	0.0789863i
$463$	5.27988			0.245377			0.122688	−	0.992445i	$-0.460848\pi$
$463$	5.27988			0.245377			0.122688	+	0.992445i	$0.460848\pi$
$464$	−3.82026	+	6.61688i	−0.177351	+	0.307181i
$465$	−10.0871	−	17.4713i	−0.467777	−	0.810213i
$466$	−1.60120	−	2.77337i	−0.0741744	−	0.128474i
$467$	−10.0518	+	17.4102i	−0.465140	+	0.805646i	−0.999208	−	0.0397958i	$-0.987329\pi$
$467$	−10.0518	+	17.4102i	−0.465140	+	0.805646i	0.534068	+	0.845441i	$0.320663\pi$
$468$	−5.62412			−0.259975
$469$	−17.9275	+	15.5781i	−0.827815	+	0.719330i
$470$	−7.17826			−0.331108
$471$	5.84248	−	10.1195i	0.269207	−	0.466281i
$472$	−8.04160	−	13.9285i	−0.370145	−	0.641110i
$473$	12.1769	+	21.0910i	0.559895	+	0.969766i
$474$	−0.477932	+	0.827803i	−0.0219522	+	0.0380223i
$475$	−103.727			−4.75932
$476$	31.2523	+	10.7677i	1.43244	+	0.493538i
$477$	−0.546137			−0.0250059
$478$	−3.04838	+	5.27995i	−0.139430	+	0.241499i
$479$	11.7276	+	20.3128i	0.535848	+	0.928115i	0.999122	+	0.0419004i	$0.0133412\pi$
$479$	11.7276	+	20.3128i	0.535848	+	0.928115i	−0.463274	+	0.886215i	$0.653325\pi$
$480$	−9.94187	−	17.2198i	−0.453782	−	0.785974i
$481$	0.0468649	−	0.0811723i	0.00213685	−	0.00370114i
$482$	−1.55186			−0.0706852
$483$	−0.0192500	−	0.0991345i	−0.000875907	−	0.00451078i
$484$	11.0187			0.500851
$485$	0.465171	−	0.805699i	0.0211223	−	0.0365849i
$486$	−0.221125	−	0.383000i	−0.0100304	−	0.0173732i
$487$	−19.8399	−	34.3637i	−0.899030	−	1.55717i	−0.828736	−	0.559640i	$-0.810939\pi$
$487$	−19.8399	−	34.3637i	−0.899030	−	1.55717i	−0.0702946	−	0.997526i	$-0.522394\pi$
$488$	5.06499	−	8.77282i	0.229281	−	0.397127i
$489$	12.3332			0.557726
$490$	−10.4690	−	8.18572i	−0.472939	−	0.369793i
$491$	42.0432			1.89738			0.948691	−	0.316204i	$-0.102408\pi$
$491$	42.0432			1.89738			0.948691	+	0.316204i	$0.102408\pi$
$492$	−0.902207	+	1.56267i	−0.0406746	+	0.0704505i
$493$	−9.23341	−	15.9927i	−0.415852	−	0.720276i
$494$	−5.32412	−	9.22165i	−0.239543	−	0.414901i
$495$	4.74803	−	8.22383i	0.213408	−	0.369634i
$496$	−13.4631			−0.604511
$497$	7.87763	+	40.5685i	0.353360	+	1.81975i
$498$	−7.53985			−0.337869
$499$	2.85467	−	4.94443i	0.127793	−	0.221343i	−0.795028	−	0.606572i	$-0.792544\pi$
$499$	2.85467	−	4.94443i	0.127793	−	0.221343i	0.922821	+	0.385229i	$0.125877\pi$
$500$	32.6399	+	56.5339i	1.45970	+	2.52827i
$501$	3.17682	+	5.50241i	0.141930	+	0.245830i
$502$	3.28915	−	5.69697i	0.146802	−	0.254268i
$503$	5.71736			0.254924			0.127462	−	0.991843i	$-0.459317\pi$
$503$	5.71736			0.254924			0.127462	+	0.991843i	$0.459317\pi$
$504$	−4.20869	−	1.45007i	−0.187470	−	0.0645913i
$505$	10.8746			0.483915
$506$	−0.0186707	+	0.0323385i	−0.000830012	+	0.00143762i
$507$	−1.64258	−	2.84502i	−0.0729493	−	0.126352i
$508$	−17.0309	−	29.4984i	−0.755625	−	1.30878i
$509$	−17.7196	+	30.6912i	−0.785407	+	1.36036i	0.143349	+	0.989672i	$0.454213\pi$
$509$	−17.7196	+	30.6912i	−0.785407	+	1.36036i	−0.928756	+	0.370692i	$0.879120\pi$
$510$	13.1449			0.582067
$511$	4.83897	−	4.20482i	0.214064	−	0.186010i
$512$	−22.9092			−1.01245
$513$	−3.86244	+	6.68994i	−0.170531	+	0.295368i
$514$	−4.81078	−	8.33251i	−0.212194	−	0.367531i
$515$	−1.52314	−	2.63815i	−0.0671175	−	0.116251i
$516$	−9.93265	+	17.2038i	−0.437260	+	0.757357i
$517$	−8.36419			−0.367857
$518$	0.0265601	−	0.0230794i	0.00116698	−	0.00101405i
$519$	0.579038			0.0254170
$520$	−11.2559	+	19.4958i	−0.493603	+	0.854945i
$521$	2.10534	+	3.64656i	0.0922368	+	0.159759i	0.908452	−	0.417989i	$-0.137265\pi$
$521$	2.10534	+	3.64656i	0.0922368	+	0.159759i	−0.816215	+	0.577748i	$0.803932\pi$
$522$	0.589761	+	1.02150i	0.0258131	+	0.0447096i
$523$	−6.20559	+	10.7484i	−0.271352	+	0.469995i	−0.969208	−	0.246243i	$-0.920804\pi$
$523$	−6.20559	+	10.7484i	−0.271352	+	0.469995i	0.697857	+	0.716237i	$0.254137\pi$
$524$	−17.4887			−0.763999
$525$	33.5885	+	11.5727i	1.46592	+	0.505073i
$526$	−1.00745			−0.0439269
$527$	16.2699	−	28.1803i	0.708728	−	1.22755i
$528$	−3.16857	−	5.48813i	−0.137894	−	0.238840i
$529$	11.4993	+	19.9173i	0.499968	+	0.865971i
$530$	−0.518412	+	0.897916i	−0.0225184	+	0.0390030i
$531$	9.55909			0.414829
$532$	7.02985	+	36.2026i	0.304783	+	1.56958i
$533$	3.11687			0.135006
$534$	−1.92201	+	3.32901i	−0.0831734	+	0.144061i
$535$	−13.7816	−	23.8705i	−0.595832	−	1.03201i
$536$	7.55170	+	13.0799i	0.326184	+	0.564967i
$537$	10.6454	−	18.4383i	0.459382	−	0.795672i
$538$	−0.898182			−0.0387234
$539$	−12.1985	−	9.53810i	−0.525429	−	0.410835i
$540$	7.74589			0.333330
$541$	−14.8665	+	25.7496i	−0.639162	+	1.10706i	0.346455	+	0.938066i	$0.387385\pi$
$541$	−14.8665	+	25.7496i	−0.639162	+	1.10706i	−0.985617	+	0.168994i	$0.945948\pi$
$542$	3.50341	+	6.06808i	0.150484	+	0.260647i
$543$	−10.6502	−	18.4467i	−0.457044	−	0.791623i
$544$	16.0357	−	27.7746i	0.687525	−	1.19083i
$545$	−10.8370			−0.464205
$546$	0.695192	+	3.58013i	0.0297515	+	0.153215i
$547$	−1.76774			−0.0755829			−0.0377915	−	0.999286i	$-0.512032\pi$
$547$	−1.76774			−0.0755829			−0.0377915	+	0.999286i	$0.512032\pi$
$548$	5.46598	−	9.46735i	0.233495	−	0.404425i
$549$	3.01039	+	5.21414i	0.128480	+	0.222534i
$550$	−6.56821	−	11.3765i	−0.280070	−	0.485095i
$551$	10.3015	−	17.8426i	0.438857	−	0.760122i
$552$	−0.0642198			−0.00273338
$553$	−5.40653	−	1.86278i	−0.229909	−	0.0792134i
$554$	1.54788			0.0657630
$555$	−0.0645453	+	0.111796i	−0.00273979	+	0.00474546i
$556$	−1.50680	−	2.60985i	−0.0639025	−	0.110682i
$557$	18.7731	+	32.5160i	0.795442	+	1.37775i	0.922558	+	0.385859i	$0.126095\pi$
$557$	18.7731	+	32.5160i	0.795442	+	1.37775i	−0.127115	+	0.991888i	$0.540572\pi$
$558$	−1.03920	+	1.79995i	−0.0439928	+	0.0761978i
$559$	34.3144			1.45135
$560$	24.5596	−	21.3411i	1.03783	−	0.901825i
$561$	15.3166			0.646668
$562$	5.90767	−	10.2324i	0.249200	−	0.431627i
$563$	3.75196	+	6.49859i	0.158126	+	0.273883i	0.934193	−	0.356768i	$-0.116121\pi$
$563$	3.75196	+	6.49859i	0.158126	+	0.273883i	−0.776067	+	0.630651i	$0.782788\pi$
$564$	−3.41131	−	5.90857i	−0.143642	−	0.248796i
$565$	−3.68986	+	6.39102i	−0.155234	+	0.268872i
$566$	−6.93966			−0.291696
$567$	1.99711	−	1.73539i	0.0838706	−	0.0728793i
$568$	26.2805			1.10271
$569$	1.46412	−	2.53593i	0.0613790	−	0.106312i	−0.833703	−	0.552213i	$-0.813784\pi$
$569$	1.46412	−	2.53593i	0.0613790	−	0.106312i	0.895082	+	0.445902i	$0.147117\pi$
$570$	7.33272	+	12.7006i	0.307134	+	0.531971i
$571$	−7.16981	−	12.4185i	−0.300047	−	0.519697i	0.676099	−	0.736811i	$-0.263669\pi$
$571$	−7.16981	−	12.4185i	−0.300047	−	0.519697i	−0.976146	+	0.217113i	$0.930336\pi$
$572$	−6.22061	+	10.7744i	−0.260097	+	0.450500i
$573$	2.25947			0.0943908
$574$	1.10626	+	0.381155i	0.0461746	+	0.0159091i
$575$	0.512523			0.0213737
$576$	1.84050	−	3.18784i	0.0766875	−	0.132827i
$577$	7.66307	+	13.2728i	0.319018	+	0.552555i	0.980283	−	0.197597i	$-0.0633137\pi$
$577$	7.66307	+	13.2728i	0.319018	+	0.552555i	−0.661266	+	0.750152i	$0.729980\pi$
$578$	6.84190	+	11.8505i	0.284585	+	0.492916i
$579$	−9.93874	+	17.2144i	−0.413040	+	0.715406i
$580$	−20.6590			−0.857817
$581$	−8.59830	−	44.2798i	−0.356718	−	1.83704i
$582$	−0.0958464			−0.00397296
$583$	−0.604059	+	1.04626i	−0.0250176	+	0.0433317i
$584$	−2.03835	−	3.53052i	−0.0843474	−	0.146094i
$585$	−6.68995	−	11.5873i	−0.276596	−	0.479078i
$586$	3.20287	−	5.54754i	0.132310	−	0.229167i
$587$	−18.1300			−0.748306			−0.374153	−	0.927367i	$-0.622066\pi$
$587$	−18.1300			−0.748306			−0.374153	+	0.927367i	$0.622066\pi$
$588$	1.76269	−	12.5073i	0.0726920	−	0.515792i
$589$	36.3037			1.49587
$590$	9.07382	−	15.7163i	0.373563	−	0.647030i
$591$	−3.56825	−	6.18039i	−0.146778	−	0.254227i
$592$	0.0430739	+	0.0746062i	0.00177033	+	0.00306630i
$593$	7.32606	−	12.6891i	0.300845	−	0.521080i	−0.675482	−	0.737376i	$-0.736065\pi$
$593$	7.32606	−	12.6891i	0.300845	−	0.521080i	0.976328	+	0.216297i	$0.0693978\pi$
$594$	−0.978311			−0.0401406
$595$	14.9902	+	77.1972i	0.614539	+	3.16478i
$596$	−4.86366			−0.199223
$597$	−6.98525	+	12.0988i	−0.285887	+	0.495172i
$598$	0.0263069	+	0.0455649i	0.00107577	+	0.00186329i
$599$	−2.29131	−	3.96867i	−0.0936205	−	0.162155i	0.815412	−	0.578882i	$-0.196511\pi$
$599$	−2.29131	−	3.96867i	−0.0936205	−	0.162155i	−0.909032	+	0.416726i	$0.863177\pi$
$600$	11.2961	−	19.5653i	0.461159	−	0.798751i
$601$	0.579777			0.0236496			0.0118248	−	0.999930i	$-0.496236\pi$
$601$	0.579777			0.0236496			0.0118248	+	0.999930i	$0.496236\pi$
$602$	12.1792	+	4.19624i	0.496386	+	0.171026i
$603$	−8.97673			−0.365561
$604$	−1.53899	+	2.66561i	−0.0626206	+	0.108462i
$605$	13.1069	+	22.7018i	0.532871	+	0.922960i
$606$	−0.560168	−	0.970239i	−0.0227553	−	0.0394133i
$607$	−5.63388	+	9.75817i	−0.228672	+	0.396072i	−0.957415	−	0.288716i	$-0.906772\pi$
$607$	−5.63388	+	9.75817i	−0.228672	+	0.396072i	0.728743	+	0.684788i	$0.240105\pi$
$608$	35.7812			1.45112
$609$	−5.32646	+	4.62842i	−0.215839	+	0.187553i
$610$	11.4303			0.462798
$611$	−5.89255	+	10.2062i	−0.238387	+	0.412899i
$612$	6.24685	+	10.8199i	0.252514	+	0.437367i
$613$	−20.8159	−	36.0541i	−0.840745	−	1.45621i	−0.889266	−	0.457391i	$-0.848784\pi$
$613$	−20.8159	−	36.0541i	−0.840745	−	1.45621i	0.0485206	−	0.998822i	$-0.484549\pi$
$614$	−4.36705	+	7.56395i	−0.176240	+	0.305256i
$615$	−4.29274			−0.173100
$616$	−7.43303	+	6.45893i	−0.299485	+	0.260238i
$617$	−14.5914			−0.587427			−0.293713	−	0.955894i	$-0.594891\pi$
$617$	−14.5914			−0.587427			−0.293713	+	0.955894i	$0.594891\pi$
$618$	−0.156918	+	0.271790i	−0.00631217	+	0.0109330i
$619$	−10.1878	−	17.6458i	−0.409482	−	0.709244i	0.585349	−	0.810781i	$-0.300957\pi$
$619$	−10.1878	−	17.6458i	−0.409482	−	0.709244i	−0.994832	+	0.101537i	$0.967624\pi$
$620$	−18.2013	−	31.5255i	−0.730980	−	1.26609i
$621$	0.0190846	−	0.0330555i	0.000765838	−	0.00132647i
$622$	−8.02043			−0.321590
$623$	−21.7424	−	7.49117i	−0.871089	−	0.300127i
$624$	−8.92901			−0.357446
$625$	−44.0819	+	76.3520i	−1.76327	+	3.05408i
$626$	−0.725816	−	1.25715i	−0.0290094	−	0.0502458i
$627$	8.54416	+	14.7989i	0.341221	+	0.591012i
$628$	10.5423	−	18.2597i	0.420682	−	0.728643i
$629$	−0.208216			−0.00830212
$630$	−0.957463	−	4.93078i	−0.0381462	−	0.196447i
$631$	9.23277			0.367551			0.183775	−	0.982968i	$-0.441168\pi$
$631$	9.23277			0.367551			0.183775	+	0.982968i	$0.441168\pi$
$632$	−1.81825	+	3.14931i	−0.0723262	+	0.125273i
$633$	11.6545	+	20.1863i	0.463227	+	0.802332i
$634$	−0.0974500	−	0.168788i	−0.00387023	−	0.00670344i
$635$	40.5170	−	70.1775i	1.60787	−	2.78491i
$636$	−0.985457			−0.0390759
$637$	−20.2325	+	8.16542i	−0.801640	+	0.323526i
$638$	2.60924			0.103301
$639$	−7.80993	+	13.5272i	−0.308956	+	0.535128i
$640$	−23.3779	−	40.4917i	−0.924092	−	1.60057i
$641$	−2.56164	−	4.43690i	−0.101179	−	0.175247i	0.810992	−	0.585058i	$-0.198928\pi$
$641$	−2.56164	−	4.43690i	−0.101179	−	0.175247i	−0.912171	+	0.409811i	$0.865595\pi$
$642$	−1.41982	+	2.45920i	−0.0560359	+	0.0970570i
$643$	15.5518			0.613302			0.306651	−	0.951822i	$-0.400792\pi$
$643$	15.5518			0.613302			0.306651	+	0.951822i	$0.400792\pi$
$644$	−0.0347350	−	0.178880i	−0.00136875	−	0.00704885i
$645$	−47.2600			−1.86086
$646$	−11.8273	+	20.4854i	−0.465338	+	0.805989i
$647$	−10.2733	−	17.7938i	−0.403884	−	0.699548i	0.590307	−	0.807179i	$-0.299007\pi$
$647$	−10.2733	−	17.7938i	−0.403884	−	0.699548i	−0.994191	+	0.107631i	$0.965673\pi$
$648$	−0.841252	−	1.45709i	−0.0330475	−	0.0572400i
$649$	10.5729	−	18.3128i	0.415023	−	0.718841i
$650$	−18.5092			−0.725989
$651$	−11.7558	−	4.05036i	−0.460744	−	0.158746i
$652$	22.2542			0.871540
$653$	−11.3343	+	19.6316i	−0.443546	+	0.768244i	−0.997950	−	0.0640040i	$-0.979613\pi$
$653$	−11.3343	+	19.6316i	−0.443546	+	0.768244i	0.554404	+	0.832248i	$0.312946\pi$
$654$	0.558228	+	0.966879i	0.0218284	+	0.0378080i
$655$	−20.8031	−	36.0320i	−0.812843	−	1.40789i
$656$	−1.43237	+	2.48094i	−0.0559246	+	0.0968643i
$657$	2.42299			0.0945299
$658$	−3.33953	+	2.90188i	−0.130188	+	0.113127i
$659$	−38.2328			−1.48934			−0.744669	−	0.667434i	$-0.767393\pi$
$659$	−38.2328			−1.48934			−0.744669	+	0.667434i	$0.767393\pi$
$660$	8.56741	−	14.8392i	0.333486	−	0.577615i
$661$	−12.9051	−	22.3523i	−0.501951	−	0.869405i	−0.999997	−	0.00225444i	$-0.999282\pi$
$661$	−12.9051	−	22.3523i	−0.501951	−	0.869405i	0.498046	−	0.867150i	$-0.334051\pi$
$662$	−0.722649	−	1.25166i	−0.0280865	−	0.0486473i
$663$	10.7905	−	18.6897i	0.419069	−	0.725850i
$664$	−28.6847			−1.11318
$665$	−66.2259	+	57.5469i	−2.56813	+	2.23157i
$666$	0.0132993			0.000515336
$667$	−0.0509003	+	0.0881619i	−0.00197087	+	0.00341364i
$668$	5.73230	+	9.92863i	0.221789	+	0.384150i
$669$	12.3397	+	21.3731i	0.477082	+	0.826330i
$670$	−8.52103	+	14.7589i	−0.329196	+	0.570184i
$671$	13.3187			0.514161
$672$	−11.5865	−	3.99205i	−0.446960	−	0.153997i
$673$	−7.21950			−0.278291			−0.139146	−	0.990272i	$-0.544436\pi$
$673$	−7.21950			−0.278291			−0.139146	+	0.990272i	$0.544436\pi$
$674$	−4.16002	+	7.20536i	−0.160238	+	0.277540i
$675$	6.71383	+	11.6287i	0.258415	+	0.447589i
$676$	−2.96389	−	5.13360i	−0.113996	−	0.197446i
$677$	−5.89490	+	10.2103i	−0.226560	+	0.392413i	−0.956786	−	0.290792i	$-0.906081\pi$
$677$	−5.89490	+	10.2103i	−0.226560	+	0.392413i	0.730227	+	0.683205i	$0.239414\pi$
$678$	0.760279			0.0291983
$679$	−0.109301	−	0.562884i	−0.00419460	−	0.0216015i
$680$	50.0088			1.91775
$681$	5.87036	−	10.1678i	0.224953	−	0.389630i
$682$	2.29883	+	3.98169i	0.0880268	+	0.152467i
$683$	−13.5717	−	23.5069i	−0.519307	−	0.899467i	−0.999748	−	0.0224396i	$-0.992857\pi$
$683$	−13.5717	−	23.5069i	−0.519307	−	0.899467i	0.480441	−	0.877027i	$-0.340477\pi$
$684$	−6.96943	+	12.0714i	−0.266483	+	0.461562i
$685$	26.0074			0.993691
$686$	−8.17962	+	0.423949i	−0.312299	+	0.0161864i
$687$	15.4411			0.589114
$688$	−15.7694	+	27.3133i	−0.601201	+	1.04131i
$689$	0.851117	+	1.47418i	0.0324250	+	0.0561617i
$690$	−0.0362315	−	0.0627548i	−0.00137931	−	0.00238904i
$691$	1.13478	−	1.96549i	0.0431690	−	0.0747709i	−0.843634	−	0.536919i	$-0.819588\pi$
$691$	1.13478	−	1.96549i	0.0431690	−	0.0747709i	0.886803	+	0.462148i	$0.152921\pi$
$692$	1.04482			0.0397183
$693$	−1.11565	−	5.74540i	−0.0423799	−	0.218250i
$694$	11.0031			0.417673
$695$	3.58471	−	6.20890i	0.135976	−	0.235517i
$696$	2.24369	+	3.88619i	0.0850470	+	0.147306i
$697$	−3.46198	−	5.99633i	−0.131132	−	0.227127i
$698$	7.68745	−	13.3151i	0.290974	−	0.503982i
$699$	7.24116			0.273886
$700$	60.6076	+	20.8819i	2.29075	+	0.789261i
$701$	31.9632			1.20723			0.603616	−	0.797275i	$-0.293726\pi$
$701$	31.9632			1.20723			0.603616	+	0.797275i	$0.293726\pi$
$702$	−0.689218	+	1.19376i	−0.0260129	+	0.0450556i
$703$	−0.116150	−	0.201178i	−0.00438069	−	0.00758759i
$704$	−4.07140	−	7.05188i	−0.153447	−	0.265778i
$705$	8.11560	−	14.0566i	0.305651	−	0.529403i
$706$	7.35440			0.276786
$707$	5.05919	−	4.39618i	0.190270	−	0.165335i
$708$	17.2486			0.648240
$709$	8.73117	−	15.1228i	0.327906	−	0.567950i	−0.654190	−	0.756330i	$-0.726990\pi$
$709$	8.73117	−	15.1228i	0.327906	−	0.567950i	0.982096	+	0.188380i	$0.0603237\pi$
$710$	14.8269	+	25.6810i	0.556444	+	0.963790i
$711$	−1.08068	−	1.87180i	−0.0405287	−	0.0701978i
$712$	−7.31211	+	12.6649i	−0.274033	+	0.474639i
$713$	−0.179380			−0.00671782
$714$	6.11540	−	5.31397i	0.228863	−	0.198870i
$715$	−29.5979			−1.10690
$716$	19.2087	−	33.2704i	0.717861	−	1.24337i
$717$	−6.89288	−	11.9388i	−0.257419	−	0.445863i
$718$	−5.58944	−	9.68119i	−0.208596	−	0.361299i
$719$	7.91889	−	13.7159i	0.295325	−	0.511517i	−0.679736	−	0.733457i	$-0.737906\pi$
$719$	7.91889	−	13.7159i	0.295325	−	0.511517i	0.975060	+	0.221940i	$0.0712388\pi$
$720$	12.2976			0.458304
$721$	−1.77511	−	0.611600i	−0.0661085	−	0.0227772i
$722$	−17.9879			−0.669442
$723$	1.75450	−	3.03888i	0.0652506	−	0.113017i
$724$	−19.2174	−	33.2854i	−0.714208	−	1.23704i
$725$	−17.9064	−	31.0147i	−0.665026	−	1.15186i
$726$	1.35031	−	2.33880i	0.0501147	−	0.0868012i
$727$	−14.3866			−0.533568			−0.266784	−	0.963756i	$-0.585961\pi$
$727$	−14.3866			−0.533568			−0.266784	+	0.963756i	$0.585961\pi$
$728$	2.64480	+	13.6203i	0.0980228	+	0.504801i
$729$	1.00000			0.0370370
$730$	2.29999	−	3.98370i	0.0851264	−	0.147443i
$731$	−38.1139	−	66.0152i	−1.40969	−	2.44166i
$732$	5.43199	+	9.40847i	0.200772	+	0.347747i
$733$	−21.6705	+	37.5343i	−0.800416	+	1.38636i	0.118926	+	0.992903i	$0.462055\pi$
$733$	−21.6705	+	37.5343i	−0.800416	+	1.38636i	−0.919342	+	0.393459i	$0.871278\pi$
$734$	−14.6908			−0.542249
$735$	27.8655	−	11.2459i	1.02783	−	0.414812i
$736$	−0.176798			−0.00651684
$737$	−9.92880	+	17.1972i	−0.365732	+	0.633466i
$738$	0.221125	+	0.383000i	0.00813974	+	0.0140984i
$739$	−3.86781	−	6.69925i	−0.142280	−	0.246436i	0.786075	−	0.618131i	$-0.212110\pi$
$739$	−3.86781	−	6.69925i	−0.142280	−	0.246436i	−0.928355	+	0.371695i	$0.878777\pi$
$740$	−0.116466	+	0.201726i	−0.00428139	+	0.00741559i
$741$	24.0774			0.884505
$742$	0.121811	+	0.627309i	0.00447184	+	0.0230292i
$743$	29.4859			1.08173			0.540867	−	0.841108i	$-0.318096\pi$
$743$	29.4859			1.08173			0.540867	+	0.841108i	$0.318096\pi$
$744$	−3.95354	+	6.84774i	−0.144944	+	0.251050i
$745$	−5.78538	−	10.0206i	−0.211960	−	0.367125i
$746$	5.74503	+	9.95068i	0.210340	+	0.364320i
$747$	8.52441	−	14.7647i	0.311892	−	0.540212i
$748$	27.6375			1.01053
$749$	−16.0615	−	5.53386i	−0.586874	−	0.202203i
$750$	15.9997			0.584225
$751$	8.17919	−	14.1668i	0.298463	−	0.516953i	−0.677322	−	0.735687i	$-0.736859\pi$
$751$	8.17919	−	14.1668i	0.298463	−	0.516953i	0.975784	+	0.218734i	$0.0701928\pi$
$752$	−5.41590	−	9.38061i	−0.197498	−	0.342076i
$753$	7.43730	+	12.8818i	0.271030	+	0.469438i
$754$	1.83820	−	3.18386i	0.0669434	−	0.115949i
$755$	−7.32259			−0.266496
$756$	3.60361	−	3.13135i	0.131062	−	0.113886i
$757$	−47.1225			−1.71270			−0.856349	−	0.516397i	$-0.827273\pi$
$757$	−47.1225			−1.71270			−0.856349	+	0.516397i	$0.827273\pi$
$758$	2.26878	−	3.92964i	0.0824057	−	0.142731i
$759$	−0.0422174	−	0.0731226i	−0.00153239	−	0.00265418i
$760$	27.8967	+	48.3185i	1.01192	+	1.75270i
$761$	19.6418	−	34.0205i	0.712013	−	1.23324i	−0.252087	−	0.967705i	$-0.581117\pi$
$761$	19.6418	−	34.0205i	0.712013	−	1.23324i	0.964100	−	0.265538i	$-0.0855497\pi$
$762$	−8.34835			−0.302429
$763$	−5.04167	+	4.38096i	−0.182521	+	0.158601i
$764$	4.07702			0.147502
$765$	−14.8614	+	25.7407i	−0.537315	+	0.930657i
$766$	−0.573130	−	0.992691i	−0.0207080	−	0.0358674i
$767$	−14.8972	−	25.8027i	−0.537906	−	0.931681i
$768$	1.27254	−	2.20411i	0.0459190	−	0.0795340i
$769$	−25.4482			−0.917687			−0.458843	−	0.888517i	$-0.651736\pi$
$769$	−25.4482			−0.917687			−0.458843	+	0.888517i	$0.651736\pi$
$770$	−10.5052	−	3.61947i	−0.378579	−	0.130437i
$771$	21.7559			0.783519
$772$	−17.9336	+	31.0619i	−0.645445	+	1.11794i
$773$	−0.887524	−	1.53724i	−0.0319220	−	0.0552905i	0.849623	−	0.527390i	$-0.176829\pi$
$773$	−0.887524	−	1.53724i	−0.0319220	−	0.0552905i	−0.881545	+	0.472100i	$0.843496\pi$
$774$	2.43443	+	4.21656i	0.0875038	+	0.151561i
$775$	31.5523	−	54.6501i	1.13339	−	1.96309i
$776$	−0.364639			−0.0130898
$777$	0.0151662	+	0.0781036i	0.000544086	+	0.00280195i
$778$	3.82727			0.137214
$779$	3.86244	−	6.68994i	0.138386	−	0.239692i
$780$	−12.0714	−	20.9084i	−0.432227	−	0.748639i
$781$	17.2765	+	29.9238i	0.618202	+	1.07076i
$782$	0.0584395	−	0.101220i	0.00208979	−	0.00361962i
$783$	−2.66709			−0.0953139
$784$	2.79849	−	19.8569i	0.0999462	−	0.709177i
$785$	50.1606			1.79031
$786$	−2.14319	+	3.71212i	−0.0764451	+	0.132407i
$787$	−24.3880	−	42.2413i	−0.869338	−	1.50574i	−0.862674	−	0.505760i	$-0.831212\pi$
$787$	−24.3880	−	42.2413i	−0.869338	−	1.50574i	−0.00666413	−	0.999978i	$-0.502121\pi$
$788$	−6.43860	−	11.1520i	−0.229366	−	0.397273i
$789$	1.13900	−	1.97281i	0.0405496	−	0.0702340i
$790$	−4.10328			−0.145988
$791$	0.867008	+	4.46495i	0.0308273	+	0.158755i
$792$	−3.72190			−0.132252
$793$	9.38297	−	16.2518i	0.333199	−	0.577118i
$794$	6.64322	+	11.5064i	0.235759	+	0.408346i
$795$	−1.17221	−	2.03033i	−0.0415741	−	0.0720084i
$796$	−12.6043	+	21.8313i	−0.446747	+	0.773789i
$797$	12.9486			0.458665			0.229332	−	0.973348i	$-0.426346\pi$
$797$	12.9486			0.458665			0.229332	+	0.973348i	$0.426346\pi$
$798$	8.54575	+	2.94437i	0.302516	+	0.104230i
$799$	26.1800			0.926183
$800$	31.0981	−	53.8634i	1.09948	−	1.90436i
$801$	−4.34597	−	7.52744i	−0.153557	−	0.265969i
$802$	2.67433	+	4.63208i	0.0944340	+	0.163564i
$803$	2.67997	−	4.64185i	0.0945742	−	0.163807i
$804$	−16.1977			−0.571251
$805$	0.327227	−	0.284344i	0.0115332	−	0.0100218i
$806$	6.47809			0.228181
$807$	1.01547	−	1.75884i	0.0357461	−	0.0619141i
$808$	−2.13111	−	3.69119i	−0.0749722	−	0.129856i
$809$	17.1358	+	29.6801i	0.602464	+	1.04350i	0.992447	+	0.122676i	$0.0391475\pi$
$809$	17.1358	+	29.6801i	0.602464	+	1.04350i	−0.389983	+	0.920822i	$0.627519\pi$
$810$	0.949235	−	1.64412i	0.0333527	−	0.0577686i
$811$	39.7411			1.39550			0.697749	−	0.716342i	$-0.254185\pi$
$811$	39.7411			1.39550			0.697749	+	0.716342i	$0.254185\pi$
$812$	−9.61114	+	8.35159i	−0.337285	+	0.293084i
$813$	−15.8435			−0.555657
$814$	0.0147098	−	0.0254781i	0.000515578	−	0.000893007i
$815$	26.4716	+	45.8502i	0.927260	+	1.60606i
$816$	9.91768	+	17.1779i	0.347188	+	0.601347i
$817$	42.5226	−	73.6513i	1.48768	−	2.57673i
$818$	5.97656			0.208965
$819$	−7.79666	−	2.68628i	−0.272437	−	0.0938662i
$820$	−7.74589			−0.270498
$821$	21.3153	−	36.9191i	0.743908	−	1.28849i	−0.206795	−	0.978384i	$-0.566303\pi$
$821$	21.3153	−	36.9191i	0.743908	−	1.28849i	0.950703	−	0.310102i	$-0.100363\pi$
$822$	−1.33968	−	2.32039i	−0.0467266	−	0.0809328i
$823$	−5.93802	−	10.2850i	−0.206986	−	0.358511i	0.743777	−	0.668427i	$-0.233032\pi$
$823$	−5.93802	−	10.2850i	−0.206986	−	0.358511i	−0.950764	+	0.309916i	$0.899699\pi$
$824$	−0.596981	+	1.03400i	−0.0207968	+	0.0360212i
$825$	29.7036			1.03415
$826$	−2.13208	−	10.9799i	−0.0741845	−	0.382038i
$827$	−18.5702			−0.645751			−0.322875	−	0.946442i	$-0.604649\pi$
$827$	−18.5702			−0.645751			−0.322875	+	0.946442i	$0.604649\pi$
$828$	0.0344365	−	0.0596458i	0.00119675	−	0.00207283i
$829$	22.7738	+	39.4453i	0.790966	+	1.36999i	0.925369	+	0.379066i	$0.123755\pi$
$829$	22.7738	+	39.4453i	0.790966	+	1.36999i	−0.134404	+	0.990927i	$0.542912\pi$
$830$	−16.1833	−	28.0303i	−0.561731	−	0.972947i
$831$	−1.75000	+	3.03109i	−0.0607068	+	0.105147i
$832$	−11.4732			−0.397761
$833$	38.1816	+	29.8544i	1.32292	+	1.03439i
$834$	−0.738614			−0.0255761
$835$	−13.6373	+	23.6205i	−0.471937	+	0.817419i
$836$	15.4172	+	26.7034i	0.533215	+	0.923556i
$837$	−2.34980	−	4.06997i	−0.0812208	−	0.140679i
$838$	7.11499	−	12.3235i	0.245783	−	0.425709i
$839$	−0.520222			−0.0179601			−0.00898004	−	0.999960i	$-0.502858\pi$
$839$	−0.520222			−0.0179601			−0.00898004	+	0.999960i	$0.502858\pi$
$840$	−3.64259	−	18.7587i	−0.125681	−	0.647237i
$841$	−21.8866			−0.754712
$842$	−7.13513	+	12.3584i	−0.245893	+	0.425899i
$843$	13.3582	+	23.1371i	0.460081	+	0.796883i
$844$	21.0296	+	36.4244i	0.723870	+	1.25378i
$845$	7.05116	−	12.2130i	0.242567	−	0.420139i
$846$	−1.67218			−0.0574909
$847$	15.2751	+	5.26293i	0.524860	+	0.180837i
$848$	−1.56454			−0.0537265
$849$	7.84585	−	13.5894i	0.269269	−	0.466387i
$850$	20.5586	+	35.6085i	0.705154	+	1.22136i
$851$	0.000573908	0	0.000994038i	1.96733e−5	0	3.40752e-5i
$852$	−14.0924	+	24.4087i	−0.482796	+	0.836227i
$853$	−26.2375			−0.898356			−0.449178	−	0.893442i	$-0.648283\pi$
$853$	−26.2375			−0.898356			−0.449178	+	0.893442i	$0.648283\pi$
$854$	5.31768	−	4.62080i	0.181967	−	0.158120i
$855$	−33.1609			−1.13408
$856$	−5.40159	+	9.35583i	−0.184623	+	0.319776i
$857$	18.8160	+	32.5903i	0.642742	+	1.11326i	0.984818	+	0.173590i	$0.0555366\pi$
$857$	18.8160	+	32.5903i	0.642742	+	1.11326i	−0.342076	+	0.939672i	$0.611130\pi$
$858$	1.52463	+	2.64074i	0.0520501	+	0.0901534i
$859$	10.8225	−	18.7451i	0.369259	−	0.639575i	−0.620191	−	0.784451i	$-0.712945\pi$
$859$	10.8225	−	18.7451i	0.369259	−	0.639575i	0.989450	+	0.144876i	$0.0462783\pi$
$860$	−85.2766			−2.90791
$861$	−1.99711	+	1.73539i	−0.0680612	+	0.0591418i
$862$	−4.62071			−0.157382
$863$	16.5685	−	28.6974i	0.563998	−	0.976873i	−0.433145	−	0.901324i	$-0.642596\pi$
$863$	16.5685	−	28.6974i	0.563998	−	0.976873i	0.997142	−	0.0755481i	$-0.0240706\pi$
$864$	−2.31597	−	4.01138i	−0.0787909	−	0.136470i
$865$	1.24283	+	2.15265i	0.0422575	+	0.0731922i
$866$	0.838338	−	1.45204i	0.0284879	−	0.0493424i
$867$	−30.9413			−1.05082
$868$	−21.2123	−	7.30852i	−0.719991	−	0.248067i
$869$	−4.78119			−0.162191
$870$	−2.53169	+	4.38502i	−0.0858324	+	0.148666i
$871$	13.9896	+	24.2308i	0.474021	+	0.821028i
$872$	2.12373	+	3.67841i	0.0719186	+	0.124567i
$873$	0.108362	−	0.187689i	0.00366750	−	0.00635230i
$874$	0.130399			0.00441080
$875$	18.2457	+	93.9623i	0.616817	+	3.17651i
$876$	4.37208			0.147719
$877$	−1.45977	+	2.52839i	−0.0492929	+	0.0853777i	−0.889619	−	0.456703i	$-0.849030\pi$
$877$	−1.45977	+	2.52839i	−0.0492929	+	0.0853777i	0.840326	+	0.542081i	$0.182363\pi$
$878$	−0.993446	−	1.72070i	−0.0335272	−	0.0580708i
$879$	7.24221	+	12.5439i	0.244274	+	0.423095i
$880$	13.6019	−	23.5591i	0.458519	−	0.794178i
$881$	−24.7028			−0.832258			−0.416129	−	0.909306i	$-0.636613\pi$
$881$	−24.7028			−0.832258			−0.416129	+	0.909306i	$0.636613\pi$
$882$	−2.43876	−	1.90687i	−0.0821172	−	0.0642078i
$883$	6.69015			0.225141			0.112571	−	0.993644i	$-0.464092\pi$
$883$	6.69015			0.225141			0.112571	+	0.993644i	$0.464092\pi$
$884$	19.4706	−	33.7240i	0.654867	−	1.13426i
$885$	20.5174	+	35.5371i	0.689683	+	1.19457i
$886$	−1.81302	−	3.14025i	−0.0609097	−	0.105499i
$887$	4.70380	−	8.14722i	0.157938	−	0.273557i	−0.776187	−	0.630503i	$-0.782849\pi$
$887$	4.70380	−	8.14722i	0.157938	−	0.273557i	0.934125	+	0.356946i	$0.116182\pi$
$888$	0.0505959			0.00169789
$889$	−9.52029	−	49.0279i	−0.319300	−	1.64434i
$890$	−16.5014			−0.553127
$891$	1.10606	−	1.91575i	0.0370544	−	0.0641801i
$892$	22.2660	+	38.5658i	0.745521	+	1.29128i
$893$	14.6042	+	25.2952i	0.488710	+	0.846470i
$894$	−0.596026	+	1.03235i	−0.0199341	+	0.0345268i
$895$	91.3957			3.05502
$896$	−27.2452	−	9.38714i	−0.910199	−	0.313602i
$897$	−0.118968			−0.00397223
$898$	7.08021	−	12.2633i	0.236270	−	0.409231i
$899$	6.26711	+	10.8550i	0.209020	+	0.362033i
$900$	12.1145	+	20.9830i	0.403818	+	0.699433i
$901$	1.89071	−	3.27481i	0.0629888	−	0.109100i
$902$	0.978311			0.0325742
$903$	−21.9867	+	19.1053i	−0.731672	+	0.635786i
$904$	2.89242			0.0962004
$905$	45.7186	−	79.1869i	1.51974	−	2.63226i
$906$	0.377197	+	0.653324i	0.0125315	+	0.0217052i
$907$	−10.8784	−	18.8419i	−0.361210	−	0.625635i	0.626950	−	0.779060i	$-0.284303\pi$
$907$	−10.8784	−	18.8419i	−0.361210	−	0.625635i	−0.988160	+	0.153425i	$0.950970\pi$
$908$	10.5926	−	18.3469i	0.351527	−	0.608862i
$909$	2.53326			0.0840229
$910$	−11.8174	+	10.2687i	−0.391744	+	0.340406i
$911$	−38.9801			−1.29147			−0.645734	−	0.763562i	$-0.723449\pi$
$911$	−38.9801			−1.29147			−0.645734	+	0.763562i	$0.723449\pi$
$912$	−11.0649	+	19.1649i	−0.366395	+	0.634614i
$913$	−18.8570	−	32.6613i	−0.624076	−	1.08093i
$914$	0.867650	+	1.50281i	0.0286993	+	0.0497087i
$915$	−12.9228	+	22.3830i	−0.427215	+	0.739959i
$916$	27.8621			0.920589
$917$	−24.2445	−	8.35325i	−0.800623	−	0.275849i
$918$	3.06213			0.101065
$919$	28.6955	−	49.7020i	0.946576	−	1.63952i	0.194012	−	0.980999i	$-0.437850\pi$
$919$	28.6955	−	49.7020i	0.946576	−	1.63952i	0.752564	−	0.658519i	$-0.228817\pi$
$920$	−0.137840	−	0.238745i	−0.00454444	−	0.00787120i
$921$	−9.87460	−	17.1033i	−0.325379	−	0.563573i
$922$	5.83990	−	10.1150i	0.192327	−	0.333120i
$923$	48.6850			1.60249
$924$	−2.01309	−	10.3671i	−0.0662258	−	0.341052i
$925$	−0.403794			−0.0132767
$926$	1.16751	−	2.02219i	0.0383669	−	0.0664534i
$927$	−0.354817	−	0.614561i	−0.0116537	−	0.0201848i
$928$	6.17690	+	10.6987i	0.202767	+	0.351202i
$929$	17.6972	−	30.6525i	0.580627	−	1.00567i	−0.414778	−	0.909922i	$-0.636141\pi$
$929$	17.6972	−	30.6525i	0.580627	−	1.00567i	0.995405	−	0.0957525i	$-0.0305257\pi$
$930$	−8.92203			−0.292565
$931$	−7.54623	+	53.5450i	−0.247318	+	1.75487i
$932$	13.0661			0.427993
$933$	9.06774	−	15.7058i	0.296865	−	0.514184i
$934$	4.44540	+	7.69965i	0.145458	+	0.251940i
$935$	32.8752	+	56.9415i	1.07513	+	1.86219i
$936$	−2.62207	+	4.54156i	−0.0857051	+	0.148446i
$937$	−33.9294			−1.10842			−0.554212	−	0.832376i	$-0.686980\pi$
$937$	−33.9294			−1.10842			−0.554212	+	0.832376i	$0.686980\pi$
$938$	2.00219	+	10.3110i	0.0653738	+	0.336664i
$939$	3.28237			0.107116
$940$	14.6439	−	25.3640i	0.477631	−	0.827282i
$941$	9.00263	+	15.5930i	0.293477	+	0.508318i	0.974630	−	0.223824i	$-0.0718542\pi$
$941$	9.00263	+	15.5930i	0.293477	+	0.508318i	−0.681152	+	0.732142i	$0.738521\pi$
$942$	−2.58384	−	4.47535i	−0.0841861	−	0.145815i
$943$	−0.0190846	+	0.0330555i	−0.000621480	+	0.00107643i
$944$	27.3843			0.891283
$945$	10.7381	+	3.69971i	0.349309	+	0.120352i
$946$	10.7705			0.350179
$947$	14.3206	−	24.8040i	0.465357	−	0.806022i	−0.533861	−	0.845572i	$-0.679259\pi$
$947$	14.3206	−	24.8040i	0.465357	−	0.806022i	0.999218	+	0.0395508i	$0.0125927\pi$
$948$	−1.95000	−	3.37750i	−0.0633330	−	0.109696i
$949$	−3.77607	−	6.54034i	−0.122576	−	0.212309i
$950$	−22.9367	+	39.7275i	−0.744163	+	1.28893i
$951$	0.440700			0.0142907
$952$	23.2655	−	20.2165i	0.754039	−	0.655222i
$953$	10.2041			0.330544			0.165272	−	0.986248i	$-0.447150\pi$
$953$	10.2041			0.330544			0.165272	+	0.986248i	$0.447150\pi$
$954$	−0.120765	+	0.209170i	−0.00390990	+	0.00677214i
$955$	4.84967	+	8.39987i	0.156932	+	0.271813i
$956$	−12.4376	−	21.5426i	−0.402261	−	0.696736i
$957$	−2.94996	+	5.10947i	−0.0953585	+	0.165166i
$958$	10.3731			0.335139
$959$	12.0994	−	10.5137i	0.390709	−	0.339507i
$960$	15.8016			0.509994
$961$	4.45692	−	7.71961i	0.143772	−	0.249020i
$962$	−0.0207260	−	0.0358985i	−0.000668234	−	0.00115741i
$963$	−3.21045	−	5.56066i	−0.103455	−	0.179190i
$964$	3.16585	−	5.48341i	0.101965	−	0.176609i
$965$	−85.3289			−2.74684
$966$	−0.0422252	−	0.0145484i	−0.00135857	−	0.000468086i
$967$	−49.6045			−1.59517			−0.797587	−	0.603204i	$-0.793891\pi$
$967$	−49.6045			−1.59517			−0.797587	+	0.603204i	$0.793891\pi$
$968$	5.13714	−	8.89778i	0.165114	−	0.285985i
$969$	−26.7434	−	46.3209i	−0.859121	−	1.48804i
$970$	−0.205722	−	0.356321i	−0.00660534	−	0.0114408i
$971$	−13.1515	+	22.7790i	−0.422051	+	0.731014i	−0.996140	−	0.0877792i	$-0.972023\pi$
$971$	−13.1515	+	22.7790i	−0.422051	+	0.731014i	0.574089	+	0.818793i	$0.305356\pi$
$972$	1.80441			0.0578766
$973$	−0.842302	−	4.33772i	−0.0270030	−	0.139061i
$974$	−17.5484			−0.562287
$975$	20.9261	−	36.2451i	0.670172	−	1.16077i
$976$	8.62398	+	14.9372i	0.276047	+	0.478127i
$977$	−16.4132	−	28.4286i	−0.525106	−	0.909510i	−0.999573	−	0.0292366i	$-0.990692\pi$
$977$	−16.4132	−	28.4286i	−0.525106	−	0.909510i	0.474467	−	0.880273i	$-0.342641\pi$
$978$	2.72718	−	4.72361i	0.0872056	−	0.151044i
$979$	−19.2276			−0.614516
$980$	50.2809	−	20.2923i	1.60616	−	0.648214i
$981$	−2.52449			−0.0806006
$982$	9.29681	−	16.1026i	0.296673	−	0.513853i
$983$	6.34590	+	10.9914i	0.202403	+	0.350572i	0.949302	−	0.314365i	$-0.101792\pi$
$983$	6.34590	+	10.9914i	0.202403	+	0.350572i	−0.746899	+	0.664937i	$0.768458\pi$
$984$	0.841252	+	1.45709i	0.0268181	+	0.0464504i
$985$	15.3176	−	26.5308i	0.488059	−	0.845343i
$986$	−8.16696			−0.260089
$987$	−1.90693	−	9.82036i	−0.0606981	−	0.312585i
$988$	43.4456			1.38219
$989$	−0.210108	+	0.363917i	−0.00668103	+	0.0115719i
$990$	−2.09982	−	3.63699i	−0.0667366	−	0.115591i
$991$	26.2514	+	45.4687i	0.833902	+	1.44436i	0.894921	+	0.446224i	$0.147232\pi$
$991$	26.2514	+	45.4687i	0.833902	+	1.44436i	−0.0610191	+	0.998137i	$0.519435\pi$
$992$	−10.8841	+	18.8518i	−0.345571	+	0.598547i
$993$	3.26805			0.103708
$994$	17.2797	+	5.95359i	0.548079	+	0.188836i
$995$	−59.9718			−1.90123
$996$	15.3816	−	26.6416i	0.487383	−	0.844173i
$997$	−12.3567	−	21.4025i	−0.391341	−	0.677823i	0.601285	−	0.799034i	$-0.294655\pi$
$997$	−12.3567	−	21.4025i	−0.391341	−	0.677823i	−0.992627	+	0.121211i	$0.961322\pi$
$998$	−1.26248	−	2.18668i	−0.0399631	−	0.0692181i
$999$	−0.0150359	+	0.0260429i	−0.000475715	+	0.000823962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	861.2.i.g.247.8	✓	28
7.2	even	3		6027.2.a.bj.1.7		14
7.4	even	3	inner	861.2.i.g.739.8	yes	28
7.5	odd	6		6027.2.a.bk.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.g.247.8	✓	28	1.1	even	1	trivial
861.2.i.g.739.8	yes	28	7.4	even	3	inner
6027.2.a.bj.1.7		14	7.2	even	3
6027.2.a.bk.1.7		14	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 861 = 3 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	861.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.221125 - 0.383000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.902207 + 1.56267i) q^{4} +(-2.14637 + 3.71763i) q^{5} +0.442251 q^{6} +(0.504334 + 2.59724i) q^{7} +1.68250 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.221125 - 0.383000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.902207 + 1.56267i) q^{4} +(-2.14637 + 3.71763i) q^{5} +0.442251 q^{6} +(0.504334 + 2.59724i) q^{7} +1.68250 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.949235 + 1.64412i) q^{10} +(1.10606 + 1.91575i) q^{11} +(-0.902207 + 1.56267i) q^{12} +3.11687 q^{13} +(1.10626 + 0.381155i) q^{14} -4.29274 q^{15} +(-1.43237 + 2.48094i) q^{16} +(-3.46198 - 5.99633i) q^{17} +(0.221125 + 0.383000i) q^{18} +(3.86244 - 6.68994i) q^{19} -7.74589 q^{20} +(-1.99711 + 1.73539i) q^{21} +0.978311 q^{22} +(-0.0190846 + 0.0330555i) q^{23} +(0.841252 + 1.45709i) q^{24} +(-6.71383 - 11.6287i) q^{25} +(0.689218 - 1.19376i) q^{26} -1.00000 q^{27} +(-3.60361 + 3.13135i) q^{28} +2.66709 q^{29} +(-0.949235 + 1.64412i) q^{30} +(2.34980 + 4.06997i) q^{31} +(2.31597 + 4.01138i) q^{32} +(-1.10606 + 1.91575i) q^{33} -3.06213 q^{34} +(-10.7381 - 3.69971i) q^{35} -1.80441 q^{36} +(0.0150359 - 0.0260429i) q^{37} +(-1.70816 - 2.95863i) q^{38} +(1.55843 + 2.69928i) q^{39} +(-3.61128 + 6.25492i) q^{40} +1.00000 q^{41} +(0.223042 + 1.14863i) q^{42} +11.0093 q^{43} +(-1.99579 + 3.45681i) q^{44} +(-2.14637 - 3.71763i) q^{45} +(0.00844018 + 0.0146188i) q^{46} +(-1.89054 + 3.27451i) q^{47} -2.86474 q^{48} +(-6.49129 + 2.61975i) q^{49} -5.93839 q^{50} +(3.46198 - 5.99633i) q^{51} +(2.81206 + 4.87063i) q^{52} +(0.273068 + 0.472968i) q^{53} +(-0.221125 + 0.383000i) q^{54} -9.49606 q^{55} +(0.848545 + 4.36987i) q^{56} +7.72487 q^{57} +(0.589761 - 1.02150i) q^{58} +(-4.77954 - 8.27841i) q^{59} +(-3.87295 - 6.70814i) q^{60} +(3.01039 - 5.21414i) q^{61} +2.07840 q^{62} +(-2.50144 - 0.861853i) q^{63} -3.68100 q^{64} +(-6.68995 + 11.5873i) q^{65} +(0.489155 + 0.847242i) q^{66} +(4.48837 + 7.77408i) q^{67} +(6.24685 - 10.8199i) q^{68} -0.0381692 q^{69} +(-3.79145 + 3.29458i) q^{70} +15.6199 q^{71} +(-0.841252 + 1.45709i) q^{72} +(-1.21150 - 2.09837i) q^{73} +(-0.00664964 - 0.0115175i) q^{74} +(6.71383 - 11.6287i) q^{75} +13.9389 q^{76} +(-4.41784 + 3.83888i) q^{77} +1.37844 q^{78} +(-1.08068 + 1.87180i) q^{79} +(-6.14880 - 10.6500i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.221125 - 0.383000i) q^{82} -17.0488 q^{83} +(-4.51364 - 1.55514i) q^{84} +29.7228 q^{85} +(2.43443 - 4.21656i) q^{86} +(1.33354 + 2.30977i) q^{87} +(1.86095 + 3.22326i) q^{88} +(-4.34597 + 7.52744i) q^{89} -1.89847 q^{90} +(1.57194 + 8.09524i) q^{91} -0.0688730 q^{92} +(-2.34980 + 4.06997i) q^{93} +(0.836092 + 1.44815i) q^{94} +(16.5805 + 28.7182i) q^{95} +(-2.31597 + 4.01138i) q^{96} -0.216724 q^{97} +(-0.432024 + 3.06546i) q^{98} -2.21212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9	\( 28 q + 2 q^{2} + 14 q^{3} - 14 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} - 14 q^{9} - 3 q^{10} + 16 q^{11} + 14 q^{12} + 42 q^{13} - 14 q^{14} - 20 q^{15} - 22 q^{16} - 12 q^{17} + 2 q^{18} - 2 q^{19} + 80 q^{20} + 2 q^{22} + 7 q^{23} - 6 q^{24} - 22 q^{25} - 2 q^{26} - 28 q^{27} - 59 q^{28} - 32 q^{29} + 3 q^{30} - 8 q^{31} + 19 q^{32} - 16 q^{33} + 66 q^{34} - 8 q^{35} + 28 q^{36} - q^{37} - 32 q^{38} + 21 q^{39} + 13 q^{40} + 28 q^{41} - 10 q^{42} + 28 q^{43} + 36 q^{44} - 10 q^{45} + 12 q^{46} - 12 q^{47} - 44 q^{48} + 8 q^{49} - 2 q^{50} + 12 q^{51} - 60 q^{52} + 20 q^{53} - 2 q^{54} - 22 q^{55} + q^{56} - 4 q^{57} - 21 q^{58} - 25 q^{59} + 40 q^{60} - 26 q^{61} - 66 q^{62} + 84 q^{64} + 8 q^{65} + q^{66} + 22 q^{67} - 15 q^{68} + 14 q^{69} - 120 q^{70} - 72 q^{71} + 6 q^{72} - 31 q^{73} + 65 q^{74} + 22 q^{75} - 4 q^{76} - 18 q^{77} - 4 q^{78} - 12 q^{79} - 112 q^{80} - 14 q^{81} + 2 q^{82} + 40 q^{83} - 37 q^{84} + 80 q^{85} + 9 q^{86} - 16 q^{87} + 54 q^{88} - 39 q^{89} + 6 q^{90} - 17 q^{91} + 126 q^{92} + 8 q^{93} - 14 q^{94} + 55 q^{95} - 19 q^{96} + 36 q^{97} - 19 q^{98} - 32 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 + 14 * q^3 - 14 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 - 14 * q^9 - 3 * q^10 + 16 * q^11 + 14 * q^12 + 42 * q^13 - 14 * q^14 - 20 * q^15 - 22 * q^16 - 12 * q^17 + 2 * q^18 - 2 * q^19 + 80 * q^20 + 2 * q^22 + 7 * q^23 - 6 * q^24 - 22 * q^25 - 2 * q^26 - 28 * q^27 - 59 * q^28 - 32 * q^29 + 3 * q^30 - 8 * q^31 + 19 * q^32 - 16 * q^33 + 66 * q^34 - 8 * q^35 + 28 * q^36 - q^37 - 32 * q^38 + 21 * q^39 + 13 * q^40 + 28 * q^41 - 10 * q^42 + 28 * q^43 + 36 * q^44 - 10 * q^45 + 12 * q^46 - 12 * q^47 - 44 * q^48 + 8 * q^49 - 2 * q^50 + 12 * q^51 - 60 * q^52 + 20 * q^53 - 2 * q^54 - 22 * q^55 + q^56 - 4 * q^57 - 21 * q^58 - 25 * q^59 + 40 * q^60 - 26 * q^61 - 66 * q^62 + 84 * q^64 + 8 * q^65 + q^66 + 22 * q^67 - 15 * q^68 + 14 * q^69 - 120 * q^70 - 72 * q^71 + 6 * q^72 - 31 * q^73 + 65 * q^74 + 22 * q^75 - 4 * q^76 - 18 * q^77 - 4 * q^78 - 12 * q^79 - 112 * q^80 - 14 * q^81 + 2 * q^82 + 40 * q^83 - 37 * q^84 + 80 * q^85 + 9 * q^86 - 16 * q^87 + 54 * q^88 - 39 * q^89 + 6 * q^90 - 17 * q^91 + 126 * q^92 + 8 * q^93 - 14 * q^94 + 55 * q^95 - 19 * q^96 + 36 * q^97 - 19 * q^98 - 32 * q^99

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