LMFDB - Embedded newform 315.2.be.b.236.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.3
Character	$\chi$	$=$	315.236
Dual form			315.2.be.b.311.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57665 + 0.910280i) q^{2} +(-0.582275 - 1.63124i) q^{3} +(0.657218 - 1.13833i) q^{4} +1.00000 q^{5} +(2.40293 + 2.04187i) q^{6} +(-0.602558 + 2.57622i) q^{7} -1.24811i q^{8} +(-2.32191 + 1.89966i) q^{9} +O(q^{10})$	\(q+(-1.57665 + 0.910280i) q^{2} +(-0.582275 - 1.63124i) q^{3} +(0.657218 - 1.13833i) q^{4} +1.00000 q^{5} +(2.40293 + 2.04187i) q^{6} +(-0.602558 + 2.57622i) q^{7} -1.24811i q^{8} +(-2.32191 + 1.89966i) q^{9} +(-1.57665 + 0.910280i) q^{10} +0.279033i q^{11} +(-2.23958 - 0.409259i) q^{12} +(2.20610 - 1.27369i) q^{13} +(-1.39506 - 4.61030i) q^{14} +(-0.582275 - 1.63124i) q^{15} +(2.45057 + 4.24450i) q^{16} +(-1.04150 - 1.80393i) q^{17} +(1.93162 - 5.10870i) q^{18} +(6.77701 + 3.91271i) q^{19} +(0.657218 - 1.13833i) q^{20} +(4.55330 - 0.517151i) q^{21} +(-0.253998 - 0.439938i) q^{22} -1.79678i q^{23} +(-2.03597 + 0.726743i) q^{24} +1.00000 q^{25} +(-2.31883 + 4.01634i) q^{26} +(4.45081 + 2.68148i) q^{27} +(2.53659 + 2.37905i) q^{28} +(6.88216 + 3.97342i) q^{29} +(2.40293 + 2.04187i) q^{30} +(7.17091 + 4.14013i) q^{31} +(-5.56558 - 3.21329i) q^{32} +(0.455171 - 0.162474i) q^{33} +(3.28416 + 1.89611i) q^{34} +(-0.602558 + 2.57622i) q^{35} +(0.636452 + 3.89161i) q^{36} +(-0.516727 + 0.894997i) q^{37} -14.2466 q^{38} +(-3.36226 - 2.85705i) q^{39} -1.24811i q^{40} +(-2.77745 - 4.81068i) q^{41} +(-6.70821 + 4.96014i) q^{42} +(-1.32175 + 2.28933i) q^{43} +(0.317633 + 0.183386i) q^{44} +(-2.32191 + 1.89966i) q^{45} +(1.63557 + 2.83289i) q^{46} +(4.48674 + 7.77126i) q^{47} +(5.49692 - 6.46894i) q^{48} +(-6.27385 - 3.10465i) q^{49} +(-1.57665 + 0.910280i) q^{50} +(-2.33621 + 2.74932i) q^{51} -3.34838i q^{52} +(6.17152 - 3.56313i) q^{53} +(-9.45826 - 0.176275i) q^{54} +0.279033i q^{55} +(3.21541 + 0.752059i) q^{56} +(2.43650 - 13.3332i) q^{57} -14.4677 q^{58} +(1.07890 - 1.86871i) q^{59} +(-2.23958 - 0.409259i) q^{60} +(-2.94853 + 1.70233i) q^{61} -15.0747 q^{62} +(-3.49487 - 7.12642i) q^{63} +1.89770 q^{64} +(2.20610 - 1.27369i) q^{65} +(-0.569749 + 0.670498i) q^{66} +(5.98441 - 10.3653i) q^{67} -2.73797 q^{68} +(-2.93098 + 1.04622i) q^{69} +(-1.39506 - 4.61030i) q^{70} +4.67203i q^{71} +(2.37099 + 2.89800i) q^{72} +(-1.03587 + 0.598059i) q^{73} -1.88146i q^{74} +(-0.582275 - 1.63124i) q^{75} +(8.90795 - 5.14301i) q^{76} +(-0.718852 - 0.168134i) q^{77} +(7.90182 + 1.44397i) q^{78} +(-5.63869 - 9.76650i) q^{79} +(2.45057 + 4.24450i) q^{80} +(1.78255 - 8.82171i) q^{81} +(8.75813 + 5.05651i) q^{82} +(-7.70913 + 13.3526i) q^{83} +(2.40382 - 5.52306i) q^{84} +(-1.04150 - 1.80393i) q^{85} -4.81263i q^{86} +(2.47430 - 13.5401i) q^{87} +0.348264 q^{88} +(2.67584 - 4.63470i) q^{89} +(1.93162 - 5.10870i) q^{90} +(1.95201 + 6.45088i) q^{91} +(-2.04533 - 1.18087i) q^{92} +(2.57812 - 14.1082i) q^{93} +(-14.1480 - 8.16838i) q^{94} +(6.77701 + 3.91271i) q^{95} +(-2.00096 + 10.9498i) q^{96} +(-7.63783 - 4.40971i) q^{97} +(12.7178 - 0.816012i) q^{98} +(-0.530069 - 0.647891i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	$ 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) $ 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.57665	+	0.910280i	−1.11486	+	0.643665i	−0.940084	−	0.340943i	$-0.889254\pi$
$2$	−1.57665	+	0.910280i	−1.11486	+	0.643665i	−0.174776	+	0.984608i	$0.555920\pi$
$3$	−0.582275	−	1.63124i	−0.336177	−	0.941799i
$3$	−0.582275	−	1.63124i	−0.336177	−	0.941799i
$4$	0.657218	−	1.13833i	0.328609	−	0.569167i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	2.40293	+	2.04187i	0.980993	+	0.833589i
$7$	−0.602558	+	2.57622i	−0.227746	+	0.973721i
$7$	−0.602558	+	2.57622i	−0.227746	+	0.973721i
$8$		−	1.24811i		−	0.441274i
$9$	−2.32191	+	1.89966i	−0.773971	+	0.633221i
$10$	−1.57665	+	0.910280i	−0.498581	+	0.287856i
$11$			0.279033i			0.0841317i	0.999115	+	0.0420658i	$0.0133939\pi$
$11$			0.279033i			0.0841317i	−0.999115	+	0.0420658i	$0.986606\pi$
$12$	−2.23958	−	0.409259i	−0.646512	−	0.118143i
$13$	2.20610	−	1.27369i	0.611862	−	0.353259i	−0.161832	−	0.986818i	$-0.551740\pi$
$13$	2.20610	−	1.27369i	0.611862	−	0.353259i	0.773694	+	0.633560i	$0.218407\pi$
$14$	−1.39506	−	4.61030i	−0.372845	−	1.23215i
$15$	−0.582275	−	1.63124i	−0.150343	−	0.421185i
$16$	2.45057	+	4.24450i	0.612641	+	1.06113i
$17$	−1.04150	−	1.80393i	−0.252600	−	0.437517i	0.711641	−	0.702544i	$-0.247952\pi$
$17$	−1.04150	−	1.80393i	−0.252600	−	0.437517i	−0.964241	+	0.265027i	$0.914619\pi$
$18$	1.93162	−	5.10870i	0.455287	−	1.20413i
$19$	6.77701	+	3.91271i	1.55475	+	0.897637i	0.997744	+	0.0671307i	$0.0213844\pi$
$19$	6.77701	+	3.91271i	1.55475	+	0.897637i	0.557009	+	0.830506i	$0.311949\pi$
$20$	0.657218	−	1.13833i	0.146958	−	0.254539i
$21$	4.55330	−	0.517151i	0.993612	−	0.112852i
$22$	−0.253998	−	0.439938i	−0.0541526	−	0.0937951i
$23$		−	1.79678i		−	0.374654i	−0.982298	−	0.187327i	$-0.940018\pi$
$23$		−	1.79678i		−	0.374654i	0.982298	−	0.187327i	$-0.0599824\pi$
$24$	−2.03597	+	0.726743i	−0.415591	+	0.148346i
$25$	1.00000			0.200000
$26$	−2.31883	+	4.01634i	−0.454761	+	0.787669i
$27$	4.45081	+	2.68148i	0.856558	+	0.516051i
$28$	2.53659	+	2.37905i	0.479371	+	0.449599i
$29$	6.88216	+	3.97342i	1.27799	+	0.737845i	0.976478	−	0.215619i	$-0.0691768\pi$
$29$	6.88216	+	3.97342i	1.27799	+	0.737845i	0.301508	+	0.953464i	$0.402510\pi$
$30$	2.40293	+	2.04187i	0.438713	+	0.372792i
$31$	7.17091	+	4.14013i	1.28793	+	0.743589i	0.978285	−	0.207263i	$-0.0664554\pi$
$31$	7.17091	+	4.14013i	1.28793	+	0.743589i	0.309648	+	0.950851i	$0.399789\pi$
$32$	−5.56558	−	3.21329i	−0.983865	−	0.568035i
$33$	0.455171	−	0.162474i	0.0792351	−	0.0282831i
$34$	3.28416	+	1.89611i	0.563228	+	0.325180i
$35$	−0.602558	+	2.57622i	−0.101851	+	0.435461i
$36$	0.636452	+	3.89161i	0.106075	+	0.648601i
$37$	−0.516727	+	0.894997i	−0.0849493	+	0.147137i	−0.905370	−	0.424624i	$-0.860406\pi$
$37$	−0.516727	+	0.894997i	−0.0849493	+	0.147137i	0.820420	+	0.571761i	$0.193740\pi$
$38$	−14.2466			−2.31111
$39$	−3.36226	−	2.85705i	−0.538393	−	0.457494i
$40$		−	1.24811i		−	0.197344i
$41$	−2.77745	−	4.81068i	−0.433764	−	0.751302i	0.563429	−	0.826164i	$-0.309482\pi$
$41$	−2.77745	−	4.81068i	−0.433764	−	0.751302i	−0.997194	+	0.0748621i	$0.976148\pi$
$42$	−6.70821	+	4.96014i	−1.03510	+	0.765367i
$43$	−1.32175	+	2.28933i	−0.201564	+	0.349120i	−0.949033	−	0.315178i	$-0.897936\pi$
$43$	−1.32175	+	2.28933i	−0.201564	+	0.349120i	0.747468	+	0.664297i	$0.231269\pi$
$44$	0.317633	+	0.183386i	0.0478850	+	0.0276464i
$45$	−2.32191	+	1.89966i	−0.346130	+	0.283185i
$46$	1.63557	+	2.83289i	0.241152	+	0.417687i
$47$	4.48674	+	7.77126i	0.654458	+	1.13356i	0.982029	+	0.188729i	$0.0604367\pi$
$47$	4.48674	+	7.77126i	0.654458	+	1.13356i	−0.327571	+	0.944827i	$0.606230\pi$
$48$	5.49692	−	6.46894i	0.793412	−	0.933711i
$49$	−6.27385	−	3.10465i	−0.896264	−	0.443521i
$50$	−1.57665	+	0.910280i	−0.222972	+	0.128733i
$51$	−2.33621	+	2.74932i	−0.327135	+	0.384982i
$52$		−	3.34838i		−	0.464336i
$53$	6.17152	−	3.56313i	0.847723	−	0.489433i	−0.0121589	−	0.999926i	$-0.503870\pi$
$53$	6.17152	−	3.56313i	0.847723	−	0.489433i	0.859882	+	0.510493i	$0.170537\pi$
$54$	−9.45826	−	0.176275i	−1.28711	−	0.0239879i
$55$			0.279033i			0.0376248i
$56$	3.21541	+	0.752059i	0.429677	+	0.100498i
$57$	2.43650	−	13.3332i	0.322722	−	1.76603i
$58$	−14.4677			−1.89970
$59$	1.07890	−	1.86871i	0.140461	−	0.243286i	−0.787209	−	0.616686i	$-0.788475\pi$
$59$	1.07890	−	1.86871i	0.140461	−	0.243286i	0.927670	+	0.373400i	$0.121808\pi$
$60$	−2.23958	−	0.409259i	−0.289129	−	0.0528351i
$61$	−2.94853	+	1.70233i	−0.377520	+	0.217961i	−0.676739	−	0.736223i	$-0.736607\pi$
$61$	−2.94853	+	1.70233i	−0.377520	+	0.217961i	0.299219	+	0.954185i	$0.403274\pi$
$62$	−15.0747			−1.91449
$63$	−3.49487	−	7.12642i	−0.440312	−	0.897845i
$64$	1.89770			0.237213
$65$	2.20610	−	1.27369i	0.273633	−	0.157982i
$66$	−0.569749	+	0.670498i	−0.0701313	+	0.0825326i
$67$	5.98441	−	10.3653i	0.731113	−	1.26632i	−0.225295	−	0.974291i	$-0.572335\pi$
$67$	5.98441	−	10.3653i	0.731113	−	1.26632i	0.956408	−	0.292034i	$-0.0943319\pi$
$68$	−2.73797			−0.332027
$69$	−2.93098	+	1.04622i	−0.352849	+	0.125950i
$70$	−1.39506	−	4.61030i	−0.166742	−	0.551036i
$71$			4.67203i			0.554467i	0.960803	+	0.277234i	$0.0894176\pi$
$71$			4.67203i			0.554467i	−0.960803	+	0.277234i	$0.910582\pi$
$72$	2.37099	+	2.89800i	0.279424	+	0.341533i
$73$	−1.03587	+	0.598059i	−0.121239	+	0.0699975i	−0.559393	−	0.828902i	$-0.688966\pi$
$73$	−1.03587	+	0.598059i	−0.121239	+	0.0699975i	0.438154	+	0.898900i	$0.355632\pi$
$74$		−	1.88146i		−	0.218716i
$75$	−0.582275	−	1.63124i	−0.0672353	−	0.188360i
$76$	8.90795	−	5.14301i	1.02181	−	0.589943i
$77$	−0.718852	−	0.168134i	−0.0819208	−	0.0191606i
$78$	7.90182	+	1.44397i	0.894705	+	0.163497i
$79$	−5.63869	−	9.76650i	−0.634403	−	1.09882i	−0.986641	−	0.162907i	$-0.947913\pi$
$79$	−5.63869	−	9.76650i	−0.634403	−	1.09882i	0.352239	−	0.935910i	$-0.385421\pi$
$80$	2.45057	+	4.24450i	0.273982	+	0.474550i
$81$	1.78255	−	8.82171i	0.198061	−	0.980190i
$82$	8.75813	+	5.05651i	0.967174	+	0.558398i
$83$	−7.70913	+	13.3526i	−0.846187	+	1.46564i	0.0384001	+	0.999262i	$0.487774\pi$
$83$	−7.70913	+	13.3526i	−0.846187	+	1.46564i	−0.884587	+	0.466376i	$0.845559\pi$
$84$	2.40382	−	5.52306i	0.262278	−	0.602616i
$85$	−1.04150	−	1.80393i	−0.112966	−	0.195663i
$86$		−	4.81263i		−	0.518959i
$87$	2.47430	−	13.5401i	0.265273	−	1.45165i
$88$	0.348264			0.0371251
$89$	2.67584	−	4.63470i	0.283639	−	0.491277i	−0.688639	−	0.725104i	$-0.741792\pi$
$89$	2.67584	−	4.63470i	0.283639	−	0.491277i	0.972278	+	0.233827i	$0.0751249\pi$
$90$	1.93162	−	5.10870i	0.203610	−	0.538504i
$91$	1.95201	+	6.45088i	0.204627	+	0.676236i
$92$	−2.04533	−	1.18087i	−0.213241	−	0.123115i
$93$	2.57812	−	14.1082i	0.267338	−	1.46295i
$94$	−14.1480	−	8.16838i	−1.45926	−	0.842504i
$95$	6.77701	+	3.91271i	0.695307	+	0.401436i
$96$	−2.00096	+	10.9498i	−0.204222	+	1.11756i
$97$	−7.63783	−	4.40971i	−0.775505	−	0.447738i	0.0593302	−	0.998238i	$-0.481104\pi$
$97$	−7.63783	−	4.40971i	−0.775505	−	0.447738i	−0.834835	+	0.550501i	$0.814437\pi$
$98$	12.7178	−	0.816012i	1.28469	−	0.0824296i
$99$	−0.530069	−	0.647891i	−0.0532740	−	0.0651155i
$100$	0.657218	−	1.13833i	0.0657218	−	0.113833i
$101$	−18.2702			−1.81795			−0.908977	−	0.416847i	$-0.863135\pi$
$101$	−18.2702			−1.81795			−0.908977	+	0.416847i	$0.863135\pi$
$102$	1.18073	−	6.46132i	0.116910	−	0.639766i
$103$			13.1835i			1.29901i	0.760356	+	0.649506i	$0.225024\pi$
$103$			13.1835i			1.29901i	−0.760356	+	0.649506i	$0.774976\pi$
$104$	−1.58971	−	2.75346i	−0.155884	−	0.269999i
$105$	4.55330	−	0.517151i	0.444357	−	0.0504687i
$106$	−6.48688	+	11.2356i	−0.630062	+	1.09130i
$107$	6.07964	+	3.51008i	0.587741	+	0.339332i	0.764204	−	0.644975i	$-0.223132\pi$
$107$	6.07964	+	3.51008i	0.587741	+	0.339332i	−0.176463	+	0.984307i	$0.556466\pi$
$108$	5.97757	−	3.30419i	0.575192	−	0.317946i
$109$	−5.11031	−	8.85131i	−0.489479	−	0.847802i	0.510448	−	0.859909i	$-0.329480\pi$
$109$	−5.11031	−	8.85131i	−0.489479	−	0.847802i	−0.999927	+	0.0121066i	$0.996146\pi$
$110$	−0.253998	−	0.439938i	−0.0242178	−	0.0419464i
$111$	1.76084	+	0.321773i	0.167131	+	0.0305413i
$112$	−12.4114	+	3.75564i	−1.17277	+	0.354875i
$113$	−9.97275	+	5.75777i	−0.938157	+	0.541645i	−0.889382	−	0.457165i	$-0.848865\pi$
$113$	−9.97275	+	5.75777i	−0.938157	+	0.541645i	−0.0487750	+	0.998810i	$0.515532\pi$
$114$	8.29546	+	23.2397i	0.776941	+	2.17660i
$115$		−	1.79678i		−	0.167550i
$116$	9.04616	−	5.22280i	0.839915	−	0.484925i
$117$	−2.70278	+	7.14825i	−0.249872	+	0.660856i
$118$			3.92841i			0.361640i
$119$	5.27488	−	1.59616i	0.483548	−	0.146320i
$120$	−2.03597	+	0.726743i	−0.185858	+	0.0663423i
$121$	10.9221			0.992922
$122$	3.09920	−	5.36797i	0.280588	−	0.485993i
$123$	−6.23015	+	7.33183i	−0.561754	+	0.661089i
$124$	9.42570	−	5.44193i	0.846453	−	0.488700i
$125$	1.00000			0.0894427
$126$	11.9972	+	8.05456i	1.06880	+	0.717558i
$127$	−14.5854			−1.29424			−0.647121	−	0.762387i	$-0.724027\pi$
$127$	−14.5854			−1.29424			−0.647121	+	0.762387i	$0.724027\pi$
$128$	8.13914	−	4.69914i	0.719405	−	0.415349i
$129$	4.50408	+	0.823070i	0.396562	+	0.0724672i
$130$	−2.31883	+	4.01634i	−0.203375	+	0.352256i
$131$	−3.31113			−0.289295			−0.144648	−	0.989483i	$-0.546205\pi$
$131$	−3.31113			−0.289295			−0.144648	+	0.989483i	$0.546205\pi$
$132$	0.114197	−	0.624918i	0.00993956	−	0.0543921i
$133$	−14.1636	+	15.1015i	−1.22814	+	1.30946i
$134$			21.7900i			1.88237i
$135$	4.45081	+	2.68148i	0.383064	+	0.230785i
$136$	−2.25150	+	1.29990i	−0.193065	+	0.111466i
$137$		−	9.58511i		−	0.818911i	−0.912330	−	0.409456i	$-0.865719\pi$
$137$		−	9.58511i		−	0.818911i	0.912330	−	0.409456i	$-0.134281\pi$
$138$	3.66878	−	4.31753i	0.312308	−	0.367533i
$139$	−1.53543	+	0.886482i	−0.130234	+	0.0751904i	−0.563701	−	0.825979i	$-0.690623\pi$
$139$	−1.53543	+	0.886482i	−0.130234	+	0.0751904i	0.433468	+	0.901169i	$0.357290\pi$
$140$	2.53659	+	2.37905i	0.214381	+	0.201067i
$141$	10.0643	−	11.8440i	0.847568	−	0.997443i
$142$	−4.25285	−	7.36615i	−0.356891	−	0.618154i
$143$	0.355403	+	0.615575i	0.0297203	+	0.0514770i
$144$	−13.7531	−	5.20011i	−1.14609	−	0.433343i
$145$	6.88216	+	3.97342i	0.571532	+	0.329974i
$146$	1.08880	−	1.88586i	0.0901099	−	0.156075i
$147$	−1.41133	+	12.0419i	−0.116405	+	0.993202i
$148$	0.679204	+	1.17642i	0.0558302	+	0.0967008i
$149$			11.3297i			0.928169i	0.885791	+	0.464084i	$0.153617\pi$
$149$			11.3297i			0.928169i	−0.885791	+	0.464084i	$0.846383\pi$
$150$	2.40293	+	2.04187i	0.196199	+	0.166718i
$151$	18.0711			1.47061			0.735304	−	0.677737i	$-0.237039\pi$
$151$	18.0711			1.47061			0.735304	+	0.677737i	$0.237039\pi$
$152$	4.88349	−	8.45846i	0.396104	−	0.686072i
$153$	5.84512	+	2.21006i	0.472550	+	0.178673i
$154$	1.28643	−	0.389268i	0.103663	−	0.0313681i
$155$	7.17091	+	4.14013i	0.575981	+	0.332543i
$156$	−5.46202	+	1.94967i	−0.437311	+	0.156099i
$157$	17.7971	+	10.2752i	1.42036	+	0.820047i	0.996330	−	0.0855994i	$-0.0272805\pi$
$157$	17.7971	+	10.2752i	1.42036	+	0.820047i	0.424034	+	0.905646i	$0.360614\pi$
$158$	17.7805	+	10.2656i	1.41454	+	0.816685i
$159$	−9.40585	−	7.99253i	−0.745932	−	0.633849i
$160$	−5.56558	−	3.21329i	−0.439998	−	0.254033i
$161$	4.62890	+	1.08266i	0.364808	+	0.0853258i
$162$	5.21976	+	15.5314i	0.410103	+	1.22026i
$163$	−0.386774	+	0.669912i	−0.0302945	+	0.0524716i	−0.880775	−	0.473535i	$-0.842978\pi$
$163$	−0.386774	+	0.669912i	−0.0302945	+	0.0524716i	0.850481	+	0.526006i	$0.176311\pi$
$164$	−7.30155			−0.570156
$165$	0.455171	−	0.162474i	0.0354350	−	0.0126486i
$166$		−	28.0698i		−	2.17864i
$167$	4.90398	+	8.49395i	0.379482	+	0.657282i	0.990987	−	0.133959i	$-0.0427690\pi$
$167$	4.90398	+	8.49395i	0.379482	+	0.657282i	−0.611505	+	0.791240i	$0.709436\pi$
$168$	−0.645461	−	5.68302i	−0.0497984	−	0.438455i
$169$	−3.25541	+	5.63854i	−0.250416	+	0.433734i
$170$	3.28416	+	1.89611i	0.251883	+	0.145425i
$171$	−23.1685	+	3.78908i	−1.77174	+	0.289758i
$172$	1.73735	+	3.00918i	0.132472	+	0.229448i
$173$	−1.48675	−	2.57513i	−0.113036	−	0.195783i	0.803957	−	0.594687i	$-0.202724\pi$
$173$	−1.48675	−	2.57513i	−0.113036	−	0.195783i	−0.916993	+	0.398904i	$0.869391\pi$
$174$	8.42417	+	23.6003i	0.638635	+	1.78914i
$175$	−0.602558	+	2.57622i	−0.0455491	+	0.194744i
$176$	−1.18436	+	0.683789i	−0.0892743	+	0.0515425i
$177$	−3.67654	−	0.671848i	−0.276346	−	0.0504992i
$178$			9.74307i			0.730274i
$179$	−9.60988	+	5.54827i	−0.718276	+	0.414697i	−0.814118	−	0.580700i	$-0.802779\pi$
$179$	−9.60988	+	5.54827i	−0.718276	+	0.414697i	0.0958418	+	0.995397i	$0.469446\pi$
$180$	0.636452	+	3.89161i	0.0474383	+	0.290063i
$181$		−	17.3072i		−	1.28644i	−0.765683	−	0.643218i	$-0.777599\pi$
$181$		−	17.3072i		−	1.28644i	0.765683	−	0.643218i	$-0.222401\pi$
$182$	−8.94975	−	8.39391i	−0.663399	−	0.622198i
$183$	4.49377	+	3.81854i	0.332189	+	0.282275i
$184$	−2.24258			−0.165325
$185$	−0.516727	+	0.894997i	−0.0379905	+	0.0658015i
$186$	8.77761	+	24.5905i	0.643606	+	1.80306i
$187$	0.503356	−	0.290613i	0.0368090	−	0.0212517i
$188$	11.7951			0.860244
$189$	−9.58995	+	9.85052i	−0.697566	+	0.716520i
$190$	−14.2466			−1.03356
$191$	9.40312	−	5.42889i	0.680386	−	0.392821i	−0.119615	−	0.992820i	$-0.538166\pi$
$191$	9.40312	−	5.42889i	0.680386	−	0.392821i	0.800000	+	0.600000i	$0.204833\pi$
$192$	−1.10499	−	3.09562i	−0.0797454	−	0.223407i
$193$	3.14169	−	5.44157i	0.226144	−	0.391693i	−0.730518	−	0.682893i	$-0.760721\pi$
$193$	3.14169	−	5.44157i	0.226144	−	0.391693i	0.956662	+	0.291200i	$0.0940546\pi$
$194$	16.0563			1.15277
$195$	−3.36226	−	2.85705i	−0.240776	−	0.204598i
$196$	−7.65741	+	5.10131i	−0.546958	+	0.364379i
$197$		−	20.0865i		−	1.43110i	−0.698561	−	0.715551i	$-0.746176\pi$
$197$		−	20.0865i		−	1.43110i	0.698561	−	0.715551i	$-0.253824\pi$
$198$	1.42550	+	0.538986i	0.101306	+	0.0383040i
$199$	19.3323	−	11.1615i	1.37043	−	0.791220i	0.379451	−	0.925212i	$-0.376113\pi$
$199$	19.3323	−	11.1615i	1.37043	−	0.791220i	0.990982	+	0.133991i	$0.0427795\pi$
$200$		−	1.24811i		−	0.0882547i
$201$	−20.3929	−	3.72658i	−1.43841	−	0.262853i
$202$	28.8057	−	16.6310i	2.02676	−	1.17015i
$203$	−14.3833	+	15.3358i	−1.00951	+	1.07636i
$204$	1.59425	+	4.46629i	0.111620	+	0.312703i
$205$	−2.77745	−	4.81068i	−0.193985	−	0.335993i
$206$	−12.0007	−	20.7858i	−0.836129	−	1.44822i
$207$	3.41327	+	4.17196i	0.237239	+	0.289971i
$208$	10.8124	+	6.24253i	0.749704	+	0.432842i
$209$	−1.09178	+	1.89101i	−0.0755197	+	0.130804i
$210$	−6.70821	+	4.96014i	−0.462911	+	0.342282i
$211$	−0.255337	−	0.442257i	−0.0175781	−	0.0304462i	0.857103	−	0.515146i	$-0.172262\pi$
$211$	−0.255337	−	0.442257i	−0.0175781	−	0.0304462i	−0.874681	+	0.484700i	$0.838929\pi$
$212$		−	9.36700i		−	0.643328i
$213$	7.62121	−	2.72040i	0.522197	−	0.186399i
$214$	−12.7806			−0.873665
$215$	−1.32175	+	2.28933i	−0.0901423	+	0.156131i
$216$	3.34678	−	5.55510i	0.227719	−	0.377976i
$217$	−14.9868	+	15.9792i	−1.01737	+	1.08474i
$218$	16.1143	+	9.30362i	1.09140	+	0.630121i
$219$	1.57874	+	1.34152i	0.106681	+	0.0906515i
$220$	0.317633	+	0.183386i	0.0214148	+	0.0123639i
$221$	−4.59530	−	2.65310i	−0.309113	−	0.178467i
$222$	−3.06912	+	1.09553i	−0.205986	+	0.0735271i
$223$	−15.5316	−	8.96717i	−1.04007	−	0.600486i	−0.120219	−	0.992747i	$-0.538360\pi$
$223$	−15.5316	−	8.96717i	−1.04007	−	0.600486i	−0.919854	+	0.392261i	$0.871693\pi$
$224$	11.6317	−	12.4020i	0.777178	−	0.828642i
$225$	−2.32191	+	1.89966i	−0.154794	+	0.126644i
$226$	10.4824	−	18.1560i	0.697276	−	1.20772i
$227$	11.0635			0.734307			0.367154	−	0.930160i	$-0.380332\pi$
$227$	11.0635			0.734307			0.367154	+	0.930160i	$0.380332\pi$
$228$	−13.5764	−	11.5364i	−0.899117	−	0.764016i
$229$		−	26.7146i		−	1.76535i	−0.469982	−	0.882676i	$-0.655739\pi$
$229$		−	26.7146i		−	1.76535i	0.469982	−	0.882676i	$-0.344261\pi$
$230$	1.63557	+	2.83289i	0.107846	+	0.186795i
$231$	0.144302	+	1.27052i	0.00949439	+	0.0835942i
$232$	4.95926	−	8.58970i	0.325592	−	0.563941i
$233$	0.00408712	+	0.00235970i	0.000267756	+	0.000154589i	0.500134	−	0.865948i	$-0.333284\pi$
$233$	0.00408712	+	0.00235970i	0.000267756	+	0.000154589i	−0.499866	+	0.866103i	$0.666617\pi$
$234$	−2.24557	−	13.7306i	−0.146797	−	0.897597i
$235$	4.48674	+	7.77126i	0.292683	+	0.506941i
$236$	−1.41815	−	2.45630i	−0.0923136	−	0.159892i
$237$	−12.6483	+	14.8849i	−0.821594	+	0.966876i
$238$	−6.86369	+	7.31821i	−0.444907	+	0.474369i
$239$	13.1415	−	7.58726i	0.850054	−	0.490779i	−0.0106152	−	0.999944i	$-0.503379\pi$
$239$	13.1415	−	7.58726i	0.850054	−	0.490779i	0.860669	+	0.509165i	$0.170046\pi$
$240$	5.49692	−	6.46894i	0.354824	−	0.417568i
$241$			9.68357i			0.623774i	0.950119	+	0.311887i	$0.100961\pi$
$241$			9.68357i			0.623774i	−0.950119	+	0.311887i	$0.899039\pi$
$242$	−17.2204	+	9.94220i	−1.10697	+	0.639109i
$243$	−15.4283	+	2.22888i	−0.989725	+	0.142983i
$244$			4.47522i			0.286496i
$245$	−6.27385	−	3.10465i	−0.400821	−	0.198349i
$246$	3.14876	−	17.2309i	0.200758	−	1.09860i
$247$	19.9344			1.26839
$248$	5.16733	−	8.95009i	0.328126	−	0.568331i
$249$	26.2702	+	4.80058i	1.66480	+	0.304225i
$250$	−1.57665	+	0.910280i	−0.0997161	+	0.0575711i
$251$	−28.0986			−1.77357			−0.886784	−	0.462183i	$-0.847066\pi$
$251$	−28.0986			−1.77357			−0.886784	+	0.462183i	$0.847066\pi$
$252$	−10.4091	−	0.705277i	−0.655714	−	0.0444283i
$253$	0.501361			0.0315203
$254$	22.9960	−	13.2768i	1.44290	−	0.833058i
$255$	−2.33621	+	2.74932i	−0.146299	+	0.172169i
$256$	−10.4528	+	18.1047i	−0.653297	+	1.13154i
$257$	8.13814			0.507643			0.253822	−	0.967251i	$-0.418312\pi$
$257$	8.13814			0.507643			0.253822	+	0.967251i	$0.418312\pi$
$258$	−7.85058	+	2.80227i	−0.488755	+	0.174462i
$259$	−1.99435	−	1.87049i	−0.123923	−	0.116227i
$260$		−	3.34838i		−	0.207657i
$261$	−23.5279	+	3.84787i	−1.45634	+	0.238177i
$262$	5.22050	−	3.01406i	0.322524	−	0.186209i
$263$		−	0.512706i		−	0.0316148i	−0.999875	−	0.0158074i	$-0.994968\pi$
$263$		−	0.512706i		−	0.0316148i	0.999875	−	0.0158074i	$-0.00503186\pi$
$264$	−0.202785	−	0.568104i	−0.0124806	−	0.0349644i
$265$	6.17152	−	3.56313i	0.379113	−	0.218881i
$266$	8.58443	−	36.7025i	0.526345	−	2.25038i
$267$	−9.11840	−	1.66629i	−0.558037	−	0.101975i
$268$	−7.86613	−	13.6245i	−0.480500	−	0.832251i
$269$	−0.187109	−	0.324082i	−0.0114082	−	0.0197596i	0.860265	−	0.509847i	$-0.170298\pi$
$269$	−0.187109	−	0.324082i	−0.0114082	−	0.0197596i	−0.871673	+	0.490088i	$0.836965\pi$
$270$	−9.45826	−	0.176275i	−0.575611	−	0.0107277i
$271$	−5.62493	−	3.24755i	−0.341690	−	0.197275i	0.319329	−	0.947644i	$-0.396542\pi$
$271$	−5.62493	−	3.24755i	−0.341690	−	0.197275i	−0.661019	+	0.750369i	$0.729876\pi$
$272$	5.10452	−	8.84128i	0.309507	−	0.536082i
$273$	9.38635	−	6.94039i	0.568088	−	0.420052i
$274$	8.72513	+	15.1124i	0.527104	+	0.912971i
$275$			0.279033i			0.0168263i
$276$	−0.735347	+	4.02403i	−0.0442627	+	0.242218i
$277$	−3.64780			−0.219175			−0.109588	−	0.993977i	$-0.534953\pi$
$277$	−3.64780			−0.219175			−0.109588	+	0.993977i	$0.534953\pi$
$278$	1.61389	−	2.79534i	0.0967949	−	0.167654i
$279$	−24.5151	+	4.00931i	−1.46768	+	0.240031i
$280$	3.21541	+	0.752059i	0.192157	+	0.0449441i
$281$	−2.85480	−	1.64822i	−0.170303	−	0.0983244i	0.412426	−	0.910991i	$-0.364682\pi$
$281$	−2.85480	−	1.64822i	−0.170303	−	0.0983244i	−0.582729	+	0.812667i	$0.698015\pi$
$282$	−5.08656	+	27.8352i	−0.302900	+	1.65756i
$283$	−12.0752	−	6.97164i	−0.717799	−	0.414421i	0.0961433	−	0.995368i	$-0.469349\pi$
$283$	−12.0752	−	6.97164i	−0.717799	−	0.414421i	−0.813942	+	0.580946i	$0.802683\pi$
$284$	5.31833	+	3.07054i	0.315585	+	0.182203i
$285$	2.43650	−	13.3332i	0.144326	−	0.789792i
$286$	−1.12069	−	0.647032i	−0.0662679	−	0.0382598i
$287$	14.0670	−	4.25661i	0.830346	−	0.251260i
$288$	19.0270	−	3.11176i	1.12117	−	0.183362i
$289$	6.33056	−	10.9649i	0.372386	−	0.644992i
$290$	−14.4677			−0.849572
$291$	−2.74599	+	15.0268i	−0.160973	+	0.880888i
$292$			1.57222i			0.0920073i
$293$	14.4552	+	25.0371i	0.844482	+	1.46269i	0.886070	+	0.463551i	$0.153425\pi$
$293$	14.4552	+	25.0371i	0.844482	+	1.46269i	−0.0415885	+	0.999135i	$0.513242\pi$
$294$	−8.73635	−	20.2706i	−0.509514	−	1.18221i
$295$	1.07890	−	1.86871i	0.0628161	−	0.108801i
$296$	1.11705	+	0.644932i	0.0649275	+	0.0374859i
$297$	−0.748221	+	1.24192i	−0.0434162	+	0.0720637i
$298$	−10.3132	−	17.8630i	−0.597430	−	1.03478i
$299$	−2.28854	−	3.96387i	−0.132350	−	0.229237i
$300$	−2.23958	−	0.409259i	−0.129302	−	0.0236286i
$301$	−5.10140	−	4.78457i	−0.294040	−	0.275778i
$302$	−28.4919	+	16.4498i	−1.63952	+	0.946579i
$303$	10.6383	+	29.8032i	0.611153	+	1.71215i
$304$			38.3534i			2.19972i
$305$	−2.94853	+	1.70233i	−0.168832	+	0.0974753i
$306$	−11.2275	+	1.83620i	−0.641833	+	0.104968i
$307$			9.62077i			0.549086i	0.961575	+	0.274543i	$0.0885266\pi$
$307$			9.62077i			0.549086i	−0.961575	+	0.274543i	$0.911473\pi$
$308$	−0.663835	+	0.707793i	−0.0378255	+	0.0403303i
$309$	21.5056	−	7.67644i	1.22341	−	0.436697i
$310$	−15.0747			−0.856185
$311$	−1.52947	+	2.64912i	−0.0867284	+	0.150218i	−0.906126	−	0.423007i	$-0.860975\pi$
$311$	−1.52947	+	2.64912i	−0.0867284	+	0.150218i	0.819398	+	0.573225i	$0.194308\pi$
$312$	−3.56591	+	4.19647i	−0.201880	+	0.237578i
$313$	2.97744	−	1.71902i	0.168295	−	0.0971650i	−0.413487	−	0.910510i	$-0.635689\pi$
$313$	2.97744	−	1.71902i	0.168295	−	0.0971650i	0.581781	+	0.813345i	$0.302356\pi$
$314$	−37.4131			−2.11134
$315$	−3.49487	−	7.12642i	−0.196914	−	0.401528i
$316$	−14.8234			−0.833882
$317$	−4.45259	+	2.57070i	−0.250082	+	0.144385i	−0.619802	−	0.784758i	$-0.712787\pi$
$317$	−4.45259	+	2.57070i	−0.250082	+	0.144385i	0.369720	+	0.929143i	$0.379454\pi$
$318$	22.1052	+	4.03947i	1.23960	+	0.226522i
$319$	−1.10872	+	1.92035i	−0.0620762	+	0.107519i
$320$	1.89770			0.106085
$321$	2.18578	−	11.9612i	0.121998	−	0.667609i
$322$	−8.28368	+	2.50661i	−0.461632	+	0.139688i
$323$		−	16.3003i		−	0.906974i
$324$	−8.87053	−	7.82692i	−0.492807	−	0.434829i
$325$	2.20610	−	1.27369i	0.122372	−	0.0706518i
$326$		−	1.40829i		−	0.0779980i
$327$	−11.4630	+	13.4901i	−0.633908	+	0.746002i
$328$	−6.00426	+	3.46656i	−0.331530	+	0.191409i
$329$	−22.7240	+	6.87621i	−1.25282	+	0.379098i
$330$	−0.569749	+	0.670498i	−0.0313637	+	0.0369097i
$331$	−5.74999	−	9.95927i	−0.316048	−	0.547411i	0.663612	−	0.748077i	$-0.269023\pi$
$331$	−5.74999	−	9.95927i	−0.316048	−	0.547411i	−0.979660	+	0.200666i	$0.935689\pi$
$332$	10.1332	+	17.5511i	0.556129	+	0.963244i
$333$	−0.500400	−	3.05971i	−0.0274217	−	0.167671i
$334$	−15.4637	−	8.92799i	−0.846138	−	0.488518i
$335$	5.98441	−	10.3653i	0.326964	−	0.566317i
$336$	13.3532	+	18.0592i	0.728477	+	0.985210i
$337$	8.53664	+	14.7859i	0.465020	+	0.805439i	0.999202	−	0.0399304i	$-0.0127136\pi$
$337$	8.53664	+	14.7859i	0.465020	+	0.805439i	−0.534182	+	0.845370i	$0.679380\pi$
$338$		−	11.8533i		−	0.644737i
$339$	15.1992	+	12.9154i	0.825507	+	0.701467i
$340$	−2.73797			−0.148487
$341$	−1.15523	+	2.00092i	−0.0625594	+	0.108356i
$342$	33.0794	−	27.0638i	1.78873	−	1.46344i
$343$	11.7786	−	14.2921i	0.635986	−	0.771701i
$344$	2.85734	+	1.64968i	0.154057	+	0.0889450i
$345$	−2.93098	+	1.04622i	−0.157799	+	0.0563265i
$346$	4.68818	+	2.70672i	0.252038	+	0.145514i
$347$	−3.82126	−	2.20621i	−0.205136	−	0.118435i	0.393913	−	0.919148i	$-0.371121\pi$
$347$	−3.82126	−	2.20621i	−0.205136	−	0.118435i	−0.599049	+	0.800712i	$0.704454\pi$
$348$	−13.7870	−	11.7154i	−0.739062	−	0.628011i
$349$	15.3333	+	8.85267i	0.820771	+	0.473873i	0.850682	−	0.525680i	$-0.176189\pi$
$349$	15.3333	+	8.85267i	0.820771	+	0.473873i	−0.0299110	+	0.999553i	$0.509522\pi$
$350$	−1.39506	−	4.61030i	−0.0745691	−	0.246431i
$351$	13.2343	+	0.246649i	0.706395	+	0.0131652i
$352$	0.896614	−	1.55298i	0.0477897	−	0.0827742i
$353$	−3.11419			−0.165752			−0.0828759	−	0.996560i	$-0.526410\pi$
$353$	−3.11419			−0.165752			−0.0828759	+	0.996560i	$0.526410\pi$
$354$	6.40820	−	2.28741i	0.340592	−	0.121575i
$355$			4.67203i			0.247965i
$356$	−3.51723	−	6.09201i	−0.186413	−	0.322876i
$357$	−5.67516	−	7.67522i	−0.300361	−	0.406215i
$358$	10.1009	−	17.4954i	0.533852	−	0.924658i
$359$	−9.45069	−	5.45636i	−0.498788	−	0.287975i	0.229425	−	0.973326i	$-0.426315\pi$
$359$	−9.45069	−	5.45636i	−0.498788	−	0.287975i	−0.728213	+	0.685351i	$0.759649\pi$
$360$	2.37099	+	2.89800i	0.124962	+	0.152738i
$361$	21.1186	+	36.5785i	1.11150	+	1.92518i
$362$	15.7544	+	27.2875i	0.828034	+	1.43420i
$363$	−6.35969	−	17.8167i	−0.333797	−	0.935133i
$364$	8.62616	+	2.01759i	0.452134	+	0.105750i
$365$	−1.03587	+	0.598059i	−0.0542199	+	0.0313039i
$366$	−10.5611	−	1.92991i	−0.552035	−	0.100878i
$367$			4.67691i			0.244133i	0.992522	+	0.122066i	$0.0389520\pi$
$367$			4.67691i			0.244133i	−0.992522	+	0.122066i	$0.961048\pi$
$368$	7.62643	−	4.40312i	0.397555	−	0.229529i
$369$	15.5877	+	5.89376i	0.811462	+	0.306817i
$370$		−	1.88146i		−	0.0978126i
$371$	5.46071	+	18.0462i	0.283506	+	0.936912i
$372$	−14.3655	−	12.2069i	−0.744815	−	0.632899i
$373$	−31.4719			−1.62955			−0.814775	−	0.579777i	$-0.803140\pi$
$373$	−31.4719			−1.62955			−0.814775	+	0.579777i	$0.803140\pi$
$374$	−0.529077	+	0.916389i	−0.0273579	+	0.0473853i
$375$	−0.582275	−	1.63124i	−0.0300685	−	0.0842371i
$376$	9.69939	−	5.59995i	0.500208	−	0.288795i
$377$	20.2437			1.04260
$378$	6.15327	−	24.2604i	0.316490	−	1.24782i
$379$	−7.31121			−0.375551			−0.187776	−	0.982212i	$-0.560128\pi$
$379$	−7.31121			−0.375551			−0.187776	+	0.982212i	$0.560128\pi$
$380$	8.90795	−	5.14301i	0.456968	−	0.263831i
$381$	8.49270	+	23.7923i	0.435094	+	1.21892i
$382$	−9.88362	+	17.1189i	−0.505690	+	0.875881i
$383$	−34.3022			−1.75276			−0.876380	−	0.481620i	$-0.840049\pi$
$383$	−34.3022			−1.75276			−0.876380	+	0.481620i	$0.840049\pi$
$384$	−12.4047	−	10.5407i	−0.633022	−	0.537905i
$385$	−0.718852	−	0.168134i	−0.0366361	−	0.00856889i
$386$			11.4393i			0.582244i
$387$	−1.27998	−	7.82650i	−0.0650652	−	0.397843i
$388$	−10.0394	+	5.79628i	−0.509676	+	0.294261i
$389$		−	28.2765i		−	1.43367i	−0.697241	−	0.716837i	$-0.745589\pi$
$389$		−	28.2765i		−	1.43367i	0.697241	−	0.716837i	$-0.254411\pi$
$390$	7.90182	+	1.44397i	0.400124	+	0.0731183i
$391$	−3.24126	+	1.87134i	−0.163917	+	0.0946378i
$392$	−3.87494	+	7.83045i	−0.195714	+	0.395498i
$393$	1.92799	+	5.40126i	0.0972542	+	0.272458i
$394$	18.2843	+	31.6693i	0.921150	+	1.59548i
$395$	−5.63869	−	9.76650i	−0.283713	−	0.491406i
$396$	−1.08589	+	0.177591i	−0.0545679	+	0.00892430i
$397$	−3.85562	−	2.22604i	−0.193508	−	0.111722i	0.400116	−	0.916465i	$-0.368970\pi$
$397$	−3.85562	−	2.22604i	−0.193508	−	0.111722i	−0.593624	+	0.804743i	$0.702303\pi$
$398$	−20.3202	+	35.1957i	−1.01856	+	1.76420i
$399$	32.8812	+	14.3110i	1.64612	+	0.716447i
$400$	2.45057	+	4.24450i	0.122528	+	0.212225i
$401$			14.6559i			0.731881i	0.930638	+	0.365940i	$0.119253\pi$
$401$			14.6559i			0.731881i	−0.930638	+	0.365940i	$0.880747\pi$
$402$	35.5447	−	12.6877i	1.77281	−	0.632807i
$403$	21.0930			1.05072
$404$	−12.0075	+	20.7976i	−0.597396	+	1.03472i
$405$	1.78255	−	8.82171i	0.0885756	−	0.438354i
$406$	8.71762	−	37.2720i	0.432648	−	1.84978i
$407$	−0.249734	−	0.144184i	−0.0123788	−	0.00714693i
$408$	3.43145	+	2.91584i	0.169882	+	0.144356i
$409$	11.4931	+	6.63552i	0.568295	+	0.328105i	0.756468	−	0.654031i	$-0.226923\pi$
$409$	11.4931	+	6.63552i	0.568295	+	0.328105i	−0.188173	+	0.982136i	$0.560257\pi$
$410$	8.75813	+	5.05651i	0.432533	+	0.249723i
$411$	−15.6356	+	5.58117i	−0.771250	+	0.275299i
$412$	15.0073	+	8.66445i	0.739355	+	0.426867i
$413$	4.16412	+	3.90550i	0.204903	+	0.192177i
$414$	−9.17919	−	3.47069i	−0.451133	−	0.170575i
$415$	−7.70913	+	13.3526i	−0.378426	+	0.655453i
$416$	−16.3710			−0.802653
$417$	2.34011	+	1.98849i	0.114596	+	0.0973766i
$418$		−	3.97529i		−	0.194438i
$419$	18.8571	+	32.6614i	0.921227	+	1.59561i	0.797519	+	0.603294i	$0.206145\pi$
$419$	18.8571	+	32.6614i	0.921227	+	1.59561i	0.123708	+	0.992319i	$0.460521\pi$
$420$	2.40382	−	5.52306i	0.117294	−	0.269498i
$421$	17.0455	−	29.5237i	0.830749	−	1.43890i	−0.0666970	−	0.997773i	$-0.521246\pi$
$421$	17.0455	−	29.5237i	0.830749	−	1.43890i	0.897446	−	0.441125i	$-0.145421\pi$
$422$	0.805155	+	0.464856i	0.0391943	+	0.0226288i
$423$	−25.1806	−	9.52089i	−1.22432	−	0.462921i
$424$	−4.44718	−	7.70273i	−0.215974	−	0.374078i
$425$	−1.04150	−	1.80393i	−0.0505201	−	0.0875034i
$426$	−9.53966	+	11.2266i	−0.462198	+	0.543929i
$427$	−2.60893	−	8.62182i	−0.126255	−	0.417239i
$428$	7.99129	−	4.61377i	0.386274	−	0.223015i
$429$	0.797212	−	0.938182i	0.0384897	−	0.0452959i
$430$		−	4.81263i		−	0.232086i
$431$	−23.9166	+	13.8082i	−1.15202	+	0.665119i	−0.949379	−	0.314134i	$-0.898286\pi$
$431$	−23.9166	+	13.8082i	−1.15202	+	0.665119i	−0.202642	+	0.979253i	$0.564953\pi$
$432$	−0.474549	+	25.4626i	−0.0228317	+	1.22507i
$433$			7.35963i			0.353681i	0.984239	+	0.176841i	$0.0565877\pi$
$433$			7.35963i			0.353681i	−0.984239	+	0.176841i	$0.943412\pi$
$434$	9.08338	−	38.8358i	0.436016	−	1.86418i
$435$	2.47430	−	13.5401i	0.118634	−	0.649198i
$436$	−13.4343			−0.643388
$437$	7.03027	−	12.1768i	0.336303	−	0.582495i
$438$	−3.71028	−	0.678012i	−0.177284	−	0.0323967i
$439$	−3.91072	+	2.25786i	−0.186649	+	0.107762i	−0.590413	−	0.807102i	$-0.701035\pi$
$439$	−3.91072	+	2.25786i	−0.186649	+	0.107762i	0.403764	+	0.914863i	$0.367702\pi$
$440$	0.348264			0.0166028
$441$	20.4651	−	4.70949i	0.974529	−	0.224261i
$442$	9.66024			0.459491
$443$	27.4070	−	15.8234i	1.30215	−	0.751795i	0.321375	−	0.946952i	$-0.395855\pi$
$443$	27.4070	−	15.8234i	1.30215	−	0.751795i	0.980772	+	0.195157i	$0.0625218\pi$
$444$	1.52354	−	1.79294i	0.0723039	−	0.0850894i
$445$	2.67584	−	4.63470i	0.126847	−	0.219706i
$446$	32.6505			1.54605
$447$	18.4816	−	6.59703i	0.874149	−	0.312029i
$448$	−1.14348	+	4.88891i	−0.0540242	+	0.230979i
$449$		−	33.1966i		−	1.56664i	−0.621617	−	0.783322i	$-0.713524\pi$
$449$		−	33.1966i		−	1.56664i	0.621617	−	0.783322i	$-0.286476\pi$
$450$	1.93162	−	5.10870i	0.0910573	−	0.240826i
$451$	1.34234	−	0.775000i	0.0632083	−	0.0364933i
$452$			15.1364i			0.711958i
$453$	−10.5224	−	29.4784i	−0.494384	−	1.38502i
$454$	−17.4432	+	10.0708i	−0.818650	+	0.472648i
$455$	1.95201	+	6.45088i	0.0915118	+	0.302422i
$456$	−16.6413	−	3.04102i	−0.779302	−	0.142409i
$457$	−4.03284	−	6.98509i	−0.188648	−	0.326749i	0.756151	−	0.654397i	$-0.227077\pi$
$457$	−4.03284	−	6.98509i	−0.188648	−	0.326749i	−0.944800	+	0.327648i	$0.893744\pi$
$458$	24.3178	+	42.1196i	1.13630	+	1.96812i
$459$	0.201685	−	10.8217i	0.00941384	−	0.505113i
$460$	−2.04533	−	1.18087i	−0.0953642	−	0.0550586i
$461$	7.24840	−	12.5546i	0.337592	−	0.584726i	−0.646388	−	0.763009i	$-0.723721\pi$
$461$	7.24840	−	12.5546i	0.337592	−	0.584726i	0.983979	+	0.178284i	$0.0570544\pi$
$462$	−1.38404	−	1.87181i	−0.0643916	−	0.0870847i
$463$	−20.4326	−	35.3903i	−0.949583	−	1.64473i	−0.746304	−	0.665606i	$-0.768173\pi$
$463$	−20.4326	−	35.3903i	−0.949583	−	1.64473i	−0.203280	−	0.979121i	$-0.565160\pi$
$464$			38.9485i			1.80814i
$465$	2.57812	−	14.1082i	0.119557	−	0.654252i
$466$	−0.00859194			−0.000398014
$467$	−6.08030	+	10.5314i	−0.281363	+	0.487334i	−0.971721	−	0.236134i	$-0.924120\pi$
$467$	−6.08030	+	10.5314i	−0.281363	+	0.487334i	0.690358	+	0.723468i	$0.257453\pi$
$468$	6.36079	+	7.77463i	0.294028	+	0.359383i
$469$	23.0974	+	21.6629i	1.06654	+	1.00030i
$470$	−14.1480	−	8.16838i	−0.652601	−	0.376779i
$471$	6.39849	−	35.0144i	0.294827	−	1.61338i
$472$	−2.33236	−	1.34659i	−0.107356	−	0.0619818i
$473$	−0.638799	−	0.368811i	−0.0293720	−	0.0169579i
$474$	6.39252	−	34.9817i	0.293618	−	1.60676i
$475$	6.77701	+	3.91271i	0.310951	+	0.179527i
$476$	1.64978	−	7.05361i	0.0756177	−	0.323302i
$477$	−7.56097	+	19.9971i	−0.346193	+	0.915603i
$478$	−13.8130	+	23.9249i	−0.631794	+	1.09430i
$479$	−23.7488			−1.08511			−0.542556	−	0.840020i	$-0.682543\pi$
$479$	−23.7488			−1.08511			−0.542556	+	0.840020i	$0.682543\pi$
$480$	−2.00096	+	10.9498i	−0.0913309	+	0.499789i
$481$			2.63260i			0.120036i
$482$	−8.81476	−	15.2676i	−0.401501	−	0.695420i
$483$	−0.929205	−	8.18127i	−0.0422803	−	0.372261i
$484$	7.17823	−	12.4331i	0.326283	−	0.565139i
$485$	−7.63783	−	4.40971i	−0.346816	−	0.200234i
$486$	22.2961	−	17.5582i	1.01137	−	0.796457i
$487$	−14.7059	−	25.4713i	−0.666386	−	1.15422i	−0.978907	−	0.204304i	$-0.934507\pi$
$487$	−14.7059	−	25.4713i	−0.666386	−	1.15422i	0.312521	−	0.949911i	$-0.398827\pi$
$488$	2.12470	+	3.68009i	0.0961806	+	0.166590i
$489$	1.31800	+	0.240850i	0.0596020	+	0.0108916i
$490$	12.7178	−	0.816012i	0.574530	−	0.0368636i
$491$	−24.5640	+	14.1821i	−1.10856	+	0.640027i	−0.938456	−	0.345399i	$-0.887744\pi$
$491$	−24.5640	+	14.1821i	−1.10856	+	0.640027i	−0.170103	+	0.985426i	$0.554410\pi$
$492$	4.25151	+	11.9106i	0.191673	+	0.536972i
$493$		−	16.5532i		−	0.745520i
$494$	−31.4295	+	18.1458i	−1.41408	+	0.816420i
$495$	−0.530069	−	0.647891i	−0.0238249	−	0.0291205i
$496$			40.5826i			1.82221i
$497$	−12.0362	−	2.81517i	−0.539896	−	0.126277i
$498$	−45.7888	+	16.3444i	−2.05184	+	0.732408i
$499$	−33.3694			−1.49382			−0.746909	−	0.664926i	$-0.768463\pi$
$499$	−33.3694			−1.49382			−0.746909	+	0.664926i	$0.768463\pi$
$500$	0.657218	−	1.13833i	0.0293917	−	0.0509079i
$501$	11.0002	−	12.9454i	0.491454	−	0.578358i
$502$	44.3017	−	25.5776i	1.97728	−	1.14158i
$503$	22.5856			1.00704			0.503522	−	0.863983i	$-0.332037\pi$
$503$	22.5856			1.00704			0.503522	+	0.863983i	$0.332037\pi$
$504$	−8.89456	+	4.36199i	−0.396195	+	0.194298i
$505$	−18.2702			−0.813014
$506$	−0.790471	+	0.456378i	−0.0351407	+	0.0202885i
$507$	11.0934	+	2.02719i	0.492674	+	0.0900307i
$508$	−9.58577	+	16.6030i	−0.425300	+	0.736641i
$509$	−9.37499			−0.415539			−0.207769	−	0.978178i	$-0.566620\pi$
$509$	−9.37499			−0.415539			−0.207769	+	0.978178i	$0.566620\pi$
$510$	1.18073	−	6.46132i	0.0522838	−	0.286112i
$511$	−0.916563	−	3.02899i	−0.0405463	−	0.133995i
$512$		−	19.2632i		−	0.851321i
$513$	19.6713	+	35.5871i	0.868510	+	1.57121i
$514$	−12.8310	+	7.40798i	−0.565951	+	0.326752i
$515$			13.1835i			0.580936i
$516$	3.89709	−	4.58621i	0.171560	−	0.201897i
$517$	−2.16844	+	1.25195i	−0.0953679	+	0.0550607i
$518$	4.84707	+	1.13369i	0.212968	+	0.0498115i
$519$	−3.33497	+	3.92469i	−0.146389	+	0.172275i
$520$	−1.58971	−	2.75346i	−0.0697134	−	0.120747i
$521$	5.18548	+	8.98151i	0.227180	+	0.393487i	0.956971	−	0.290183i	$-0.0937161\pi$
$521$	5.18548	+	8.98151i	0.227180	+	0.393487i	−0.729791	+	0.683670i	$0.760383\pi$
$522$	33.5927	−	27.4837i	1.47031	−	1.20293i
$523$	20.2717	+	11.7039i	0.886419	+	0.511774i	0.872769	−	0.488133i	$-0.162322\pi$
$523$	20.2717	+	11.7039i	0.886419	+	0.511774i	0.0136495	+	0.999907i	$0.495655\pi$
$524$	−2.17614	+	3.76918i	−0.0950649	+	0.164657i
$525$	4.55330	−	0.517151i	0.198722	−	0.0225703i
$526$	0.466706	+	0.808358i	0.0203493	+	0.0352461i
$527$		−	17.2477i		−	0.751323i
$528$	1.80505	+	1.53382i	0.0785546	+	0.0667511i
$529$	19.7716			0.859634
$530$	−6.48688	+	11.2356i	−0.281772	+	0.488044i
$531$	1.04481	+	6.38854i	0.0453410	+	0.277239i
$532$	7.88197	+	26.0478i	0.341727	+	1.12932i
$533$	−12.2547	−	7.07523i	−0.530808	−	0.306462i
$534$	15.8933	−	5.67314i	0.687771	−	0.245501i
$535$	6.07964	+	3.51008i	0.262846	+	0.151754i
$536$	−12.9370	−	7.46921i	−0.558795	−	0.322621i
$537$	14.6462	+	12.4454i	0.632029	+	0.537060i
$538$	0.590011	+	0.340643i	0.0254372	+	0.0146862i
$539$	0.866300	−	1.75061i	0.0373142	−	0.0754042i
$540$	5.97757	−	3.30419i	0.257234	−	0.142190i
$541$	−0.818259	+	1.41727i	−0.0351797	+	0.0609330i	−0.883079	−	0.469224i	$-0.844534\pi$
$541$	−0.818259	+	1.41727i	−0.0351797	+	0.0609330i	0.847899	+	0.530157i	$0.177867\pi$
$542$	11.8247			0.507916
$543$	−28.2323	+	10.0776i	−1.21156	+	0.432470i
$544$			13.3865i			0.573943i
$545$	−5.11031	−	8.85131i	−0.218902	−	0.379149i
$546$	−8.48130	+	19.4868i	−0.362966	+	0.833957i
$547$	−2.64181	+	4.57574i	−0.112956	+	0.195645i	−0.916961	−	0.398978i	$-0.869365\pi$
$547$	−2.64181	+	4.57574i	−0.112956	+	0.195645i	0.804005	+	0.594622i	$0.202698\pi$
$548$	−10.9111	−	6.29950i	−0.466097	−	0.269102i
$549$	3.61236	−	9.55388i	0.154172	−	0.407750i
$550$	−0.253998	−	0.439938i	−0.0108305	−	0.0187590i
$551$	31.0937	+	53.8558i	1.32463	+	2.29433i
$552$	1.30580	+	3.65819i	0.0555784	+	0.155703i
$553$	28.5583	−	8.64165i	1.21442	−	0.367480i
$554$	5.75131	−	3.32052i	0.244350	−	0.141075i
$555$	1.76084	+	0.321773i	0.0747433	+	0.0136585i
$556$			2.33045i			0.0988330i
$557$	−33.7106	+	19.4628i	−1.42837	+	0.824667i	−0.996992	−	0.0775063i	$-0.975304\pi$
$557$	−33.7106	+	19.4628i	−1.42837	+	0.824667i	−0.431374	+	0.902173i	$0.641971\pi$
$558$	35.0021	−	28.6369i	1.48176	−	1.21229i
$559$			6.73399i			0.284818i
$560$	−12.4114	+	3.75564i	−0.524477	+	0.158705i
$561$	−0.767151	−	0.651880i	−0.0323892	−	0.0275224i
$562$	6.00135			0.253152
$563$	14.1036	−	24.4282i	0.594397	−	1.02953i	−0.399234	−	0.916849i	$-0.630724\pi$
$563$	14.1036	−	24.4282i	0.594397	−	1.02953i	0.993632	−	0.112678i	$-0.0359427\pi$
$564$	−6.86797	−	19.2406i	−0.289194	−	0.810177i
$565$	−9.97275	+	5.75777i	−0.419557	+	0.242231i
$566$	25.3846			1.06699
$567$	21.6526	+	9.90784i	0.909323	+	0.416090i
$568$	5.83120			0.244672
$569$	−30.0992	+	17.3778i	−1.26182	+	0.728514i	−0.973427	−	0.228997i	$-0.926455\pi$
$569$	−30.0992	+	17.3778i	−1.26182	+	0.728514i	−0.288397	+	0.957511i	$0.593122\pi$
$570$	8.29546	+	23.2397i	0.347459	+	0.973406i
$571$	−4.41700	+	7.65047i	−0.184846	+	0.320162i	−0.943525	−	0.331303i	$-0.892512\pi$
$571$	−4.41700	+	7.65047i	−0.184846	+	0.320162i	0.758679	+	0.651465i	$0.225845\pi$
$572$	0.934308			0.0390654
$573$	−14.3310	−	12.1777i	−0.598688	−	0.508729i
$574$	−18.3040	+	19.5161i	−0.763993	+	0.814584i
$575$		−	1.79678i		−	0.0749308i
$576$	−4.40630	+	3.60500i	−0.183596	+	0.150208i
$577$	−23.9018	+	13.7997i	−0.995047	+	0.574491i	−0.906779	−	0.421606i	$-0.861466\pi$
$577$	−23.9018	+	13.7997i	−0.995047	+	0.574491i	−0.0882679	+	0.996097i	$0.528133\pi$
$578$			23.0503i			0.958767i
$579$	−10.7059	−	1.95638i	−0.444920	−	0.0813043i
$580$	9.04616	−	5.22280i	0.375621	−	0.216865i
$581$	−29.7541	−	27.9061i	−1.23441	−	1.15774i
$582$	−9.34916	−	26.1917i	−0.387535	−	1.08568i
$583$	0.994231	+	1.72206i	0.0411768	+	0.0713204i
$584$	0.746444	+	1.29288i	0.0308881	+	0.0534997i
$585$	−2.70278	+	7.14825i	−0.111746	+	0.295544i
$586$	−45.5816	−	26.3166i	−1.88296	−	1.08713i
$587$	3.99098	−	6.91258i	0.164725	−	0.285313i	−0.771832	−	0.635826i	$-0.780660\pi$
$587$	3.99098	−	6.91258i	0.164725	−	0.285313i	0.936558	+	0.350513i	$0.113993\pi$
$588$	12.7802	+	9.52074i	0.527046	+	0.392629i
$589$	32.3982	+	56.1154i	1.33495	+	2.31219i
$590$			3.92841i			0.161730i
$591$	−32.7659	+	11.6958i	−1.34781	+	0.481103i
$592$	−5.06509			−0.208174
$593$	−3.87546	+	6.71249i	−0.159146	+	0.275649i	−0.934561	−	0.355803i	$-0.884207\pi$
$593$	−3.87546	+	6.71249i	−0.159146	+	0.275649i	0.775415	+	0.631452i	$0.217541\pi$
$594$	0.0491864	−	2.63917i	0.00201814	−	0.108286i
$595$	5.27488	−	1.59616i	0.216249	−	0.0654362i
$596$	12.8970	+	7.44611i	0.528283	+	0.305005i
$597$	−29.4639	−	25.0367i	−1.20588	−	1.02468i
$598$	7.21647	+	4.16643i	0.295103	+	0.170378i
$599$	21.2258	+	12.2547i	0.867263	+	0.500715i	0.866438	−	0.499285i	$-0.166404\pi$
$599$	21.2258	+	12.2547i	0.867263	+	0.500715i	0.000825408		1.00000i	$0.499737\pi$
$600$	−2.03597	+	0.726743i	−0.0831182	+	0.0296692i
$601$	−12.3323	−	7.12006i	−0.503046	−	0.290433i	0.226925	−	0.973912i	$-0.427133\pi$
$601$	−12.3323	−	7.12006i	−0.503046	−	0.290433i	−0.729970	+	0.683479i	$0.760466\pi$
$602$	12.3984	+	2.89989i	0.505322	+	0.118191i
$603$	5.79533	+	35.4357i	0.236004	+	1.44305i
$604$	11.8767	−	20.5710i	0.483255	−	0.837022i
$605$	10.9221			0.444048
$606$	−43.9021	−	37.3054i	−1.78340	−	1.51543i
$607$			2.61757i			0.106244i	0.998588	+	0.0531219i	$0.0169172\pi$
$607$			2.61757i			0.106244i	−0.998588	+	0.0531219i	$0.983083\pi$
$608$	−25.1453	−	43.5530i	−1.01978	−	1.76631i
$609$	33.3914	+	14.5331i	1.35309	+	0.588909i
$610$	3.09920	−	5.36797i	0.125483	−	0.217343i
$611$	19.7964	+	11.4295i	0.800877	+	0.462387i
$612$	6.35731	−	5.20121i	0.256979	−	0.210247i
$613$	−9.63669	−	16.6912i	−0.389222	−	0.674152i	0.603123	−	0.797648i	$-0.293923\pi$
$613$	−9.63669	−	16.6912i	−0.389222	−	0.674152i	−0.992345	+	0.123496i	$0.960589\pi$
$614$	−8.75759	−	15.1686i	−0.353428	−	0.612155i
$615$	−6.23015	+	7.33183i	−0.251224	+	0.295648i
$616$	−0.209849	+	0.897206i	−0.00845507	+	0.0361495i
$617$	12.9304	−	7.46538i	0.520559	−	0.300545i	−0.216604	−	0.976260i	$-0.569498\pi$
$617$	12.9304	−	7.46538i	0.520559	−	0.300545i	0.737163	+	0.675714i	$0.236165\pi$
$618$	−26.9190	+	31.6791i	−1.08284	+	1.27432i
$619$		−	3.14324i		−	0.126338i	−0.998003	−	0.0631688i	$-0.979879\pi$
$619$		−	3.14324i		−	0.126338i	0.998003	−	0.0631688i	$-0.0201207\pi$
$620$	9.42570	−	5.44193i	0.378545	−	0.218553i
$621$	4.81802	−	7.99711i	0.193340	−	0.320913i
$622$		−	5.56899i		−	0.223296i
$623$	10.3277	+	9.68625i	0.413769	+	0.388071i
$624$	3.88731	−	21.2725i	0.155617	−	0.851582i
$625$	1.00000			0.0400000
$626$	−3.12958	+	5.42060i	−0.125083	+	0.216651i
$627$	3.72041	+	0.679864i	0.148579	+	0.0271512i
$628$	23.3931	−	13.5060i	0.933488	−	0.538950i
$629$	2.15268			0.0858330
$630$	11.9972	+	8.05456i	0.477981	+	0.320902i
$631$	−4.71364			−0.187647			−0.0938235	−	0.995589i	$-0.529909\pi$
$631$	−4.71364			−0.187647			−0.0938235	+	0.995589i	$0.529909\pi$
$632$	−12.1897	+	7.03771i	−0.484879	+	0.279945i
$633$	−0.572752	+	0.674032i	−0.0227649	+	0.0267904i
$634$	4.68012	−	8.10620i	0.185871	−	0.321938i
$635$	−14.5854			−0.578803
$636$	−15.2799	+	5.45417i	−0.605886	+	0.216272i
$637$	−17.7951	+	1.14179i	−0.705068	+	0.0452394i
$638$		−	4.03697i		−	0.159825i
$639$	−8.87528	−	10.8480i	−0.351101	−	0.429142i
$640$	8.13914	−	4.69914i	0.321728	−	0.185750i
$641$		−	46.3694i		−	1.83148i	−0.401769	−	0.915741i	$-0.631604\pi$
$641$		−	46.3694i		−	1.83148i	0.401769	−	0.915741i	$-0.368396\pi$
$642$	7.44183	+	20.8483i	0.293706	+	0.822817i
$643$	15.9868	−	9.23001i	0.630460	−	0.363996i	−0.150470	−	0.988615i	$-0.548079\pi$
$643$	15.9868	−	9.23001i	0.630460	−	0.363996i	0.780930	+	0.624618i	$0.214745\pi$
$644$	4.27463	−	4.55769i	0.168444	−	0.179598i
$645$	4.50408	+	0.823070i	0.177348	+	0.0324083i
$646$	14.8378	+	25.6999i	0.583787	+	1.01115i
$647$	9.35740	+	16.2075i	0.367877	+	0.637182i	0.989233	−	0.146346i	$-0.0467513\pi$
$647$	9.35740	+	16.2075i	0.367877	+	0.637182i	−0.621356	+	0.783528i	$0.713418\pi$
$648$	−11.0105	−	2.22482i	−0.432532	−	0.0873992i
$649$	0.521433	+	0.301050i	0.0204680	+	0.0118172i
$650$	−2.31883	+	4.01634i	−0.0909521	+	0.157534i
$651$	34.7924	+	15.1428i	1.36362	+	0.593493i
$652$	0.508390	+	0.880557i	0.0199101	+	0.0344853i
$653$		−	28.6445i		−	1.12095i	−0.828172	−	0.560473i	$-0.810619\pi$
$653$		−	28.6445i		−	1.12095i	0.828172	−	0.560473i	$-0.189381\pi$
$654$	5.79349	−	31.7037i	0.226544	−	1.23971i
$655$	−3.31113			−0.129377
$656$	13.6126	−	23.5778i	0.531484	−	0.920557i
$657$	1.26908	−	3.35644i	0.0495117	−	0.130947i
$658$	29.5686	−	31.5266i	1.15270	−	1.22903i
$659$	−29.6315	−	17.1078i	−1.15428	−	0.666424i	−0.204354	−	0.978897i	$-0.565509\pi$
$659$	−29.6315	−	17.1078i	−1.15428	−	0.666424i	−0.949927	+	0.312473i	$0.898843\pi$
$660$	0.114197	−	0.624918i	0.00444510	−	0.0243249i
$661$	23.1824	+	13.3844i	0.901690	+	0.520591i	0.877748	−	0.479122i	$-0.159045\pi$
$661$	23.1824	+	13.3844i	0.901690	+	0.520591i	0.0239421	+	0.999713i	$0.492378\pi$
$662$	18.1314	+	10.4682i	0.704699	+	0.406858i
$663$	−1.65212	+	9.04089i	−0.0641631	+	0.351119i
$664$	16.6655	+	9.62184i	0.646747	+	0.373400i
$665$	−14.1636	+	15.1015i	−0.549239	+	0.585609i
$666$	3.57415	+	4.36859i	0.138495	+	0.169279i
$667$	7.13935	−	12.3657i	0.276437	−	0.478802i
$668$	12.8919			0.498804
$669$	−5.58398	+	30.5572i	−0.215889	+	1.18141i
$670$			21.7900i			0.841820i
$671$	−0.475008	−	0.822737i	−0.0183375	−	0.0317614i
$672$	−27.0035	−	11.7528i	−1.04168	−	0.453375i
$673$	−11.4116	+	19.7654i	−0.439884	+	0.761902i	−0.997680	−	0.0680765i	$-0.978314\pi$
$673$	−11.4116	+	19.7654i	−0.439884	+	0.761902i	0.557796	+	0.829978i	$0.311647\pi$
$674$	−26.9186	−	15.5415i	−1.03687	−	0.598635i
$675$	4.45081	+	2.68148i	0.171312	+	0.103210i
$676$	4.27903	+	7.41150i	0.164578	+	0.285058i
$677$	12.8886	+	22.3237i	0.495349	+	0.857969i	0.999986	−	0.00536256i	$-0.00170696\pi$
$677$	12.8886	+	22.3237i	0.495349	+	0.857969i	−0.504637	+	0.863332i	$0.668374\pi$
$678$	−35.7204	−	6.52751i	−1.37184	−	0.250688i
$679$	15.9626	−	17.0197i	0.612589	−	0.653155i
$680$	−2.25150	+	1.29990i	−0.0863411	+	0.0498491i
$681$	−6.44197	−	18.0472i	−0.246857	−	0.691570i
$682$		−	4.20634i		−	0.161069i
$683$	−15.4429	+	8.91598i	−0.590907	+	0.341161i	−0.765456	−	0.643488i	$-0.777487\pi$
$683$	−15.4429	+	8.91598i	−0.590907	+	0.341161i	0.174549	+	0.984649i	$0.444153\pi$
$684$	−10.9135	+	28.8637i	−0.417288	+	1.10363i
$685$		−	9.58511i		−	0.366228i
$686$	−5.56096	+	33.2555i	−0.212319	+	1.26970i
$687$	−43.5781	+	15.5553i	−1.66261	+	0.593470i
$688$	−12.9561			−0.493946
$689$	9.07666	−	15.7212i	0.345793	−	0.598931i
$690$	3.66878	−	4.31753i	0.139668	−	0.164366i
$691$	29.8677	−	17.2441i	1.13622	−	0.655998i	0.190730	−	0.981643i	$-0.438914\pi$
$691$	29.8677	−	17.2441i	1.13622	−	0.655998i	0.945492	+	0.325644i	$0.105581\pi$
$692$	−3.90848			−0.148578
$693$	1.98851	−	0.975185i	0.0755372	−	0.0370442i
$694$	8.03305			0.304931
$695$	−1.53543	+	0.886482i	−0.0582422	+	0.0336262i
$696$	−16.8995	−	3.08820i	−0.640576	−	0.117058i
$697$	−5.78541	+	10.0206i	−0.219138	+	0.379558i
$698$	−32.2336			−1.22006
$699$	0.00146942	−	0.00804107i	5.55784e−5	−	0.000304141i
$700$	2.53659	+	2.37905i	0.0958742	+	0.0899197i
$701$		−	18.2242i		−	0.688319i	−0.938911	−	0.344159i	$-0.888164\pi$
$701$		−	18.2242i		−	0.688319i	0.938911	−	0.344159i	$-0.111836\pi$
$702$	−21.0904	+	11.6580i	−0.796006	+	0.440004i
$703$	−7.00373	+	4.04360i	−0.264151	+	0.152507i
$704$			0.529522i			0.0199571i
$705$	10.0643	−	11.8440i	0.379044	−	0.446070i
$706$	4.90999	−	2.83479i	0.184790	−	0.106689i
$707$	11.0089	−	47.0681i	0.414031	−	1.77018i
$708$	−3.18108	+	3.74359i	−0.119552	+	0.140693i
$709$	−13.5259	−	23.4276i	−0.507977	−	0.879842i	−0.999957	−	0.00923576i	$-0.997060\pi$
$709$	−13.5259	−	23.4276i	−0.507977	−	0.879842i	0.491980	−	0.870606i	$-0.336273\pi$
$710$	−4.25285	−	7.36615i	−0.159607	−	0.276447i
$711$	31.6456	+	11.9653i	1.18680	+	0.448735i
$712$	−5.78461	−	3.33975i	−0.216788	−	0.125162i
$713$	7.43889	−	12.8845i	0.278589	−	0.482530i
$714$	15.9343	+	6.93515i	0.596327	+	0.259542i
$715$	0.355403	+	0.615575i	0.0132913	+	0.0230212i
$716$			14.5857i			0.545092i
$717$	−20.0286	−	17.0191i	−0.747983	−	0.635592i
$718$	19.8672			0.741439
$719$	4.20805	−	7.28856i	0.156934	−	0.271817i	−0.776828	−	0.629713i	$-0.783172\pi$
$719$	4.20805	−	7.28856i	0.156934	−	0.271817i	0.933761	+	0.357896i	$0.116506\pi$
$720$	−13.7531	−	5.20011i	−0.512549	−	0.193797i
$721$	−33.9637	−	7.94384i	−1.26488	−	0.295844i
$722$	−66.5933	−	38.4476i	−2.47835	−	1.43087i
$723$	15.7963	−	5.63850i	0.587469	−	0.209698i
$724$	−19.7014	−	11.3746i	−0.732198	−	0.422735i
$725$	6.88216	+	3.97342i	0.255597	+	0.147569i
$726$	26.2452	+	22.3016i	0.974049	+	0.827689i
$727$	−33.6074	−	19.4032i	−1.24643	−	0.719626i	−0.276034	−	0.961148i	$-0.589020\pi$
$727$	−33.6074	−	19.4032i	−1.24643	−	0.719626i	−0.970395	+	0.241522i	$0.922353\pi$
$728$	8.05141	−	2.43633i	0.298405	−	0.0902963i
$729$	12.6194	+	23.8695i	0.467384	+	0.884055i
$730$	1.08880	−	1.88586i	0.0402984	−	0.0697988i
$731$	5.50638			0.203661
$732$	7.30017	−	2.60581i	0.269822	−	0.0963133i
$733$			39.7960i			1.46990i	0.678121	+	0.734950i	$0.262794\pi$
$733$			39.7960i			1.46990i	−0.678121	+	0.734950i	$0.737206\pi$
$734$	−4.25729	−	7.37385i	−0.157140	−	0.272174i
$735$	−1.41133	+	12.0419i	−0.0520578	+	0.444173i
$736$	−5.77357	+	10.0001i	−0.212816	+	0.368609i
$737$	2.89227	+	1.66985i	0.106538	+	0.0615097i
$738$	−29.9413	+	4.89674i	−1.10215	+	0.180251i
$739$	−8.38375	−	14.5211i	−0.308401	−	0.534167i	0.669612	−	0.742712i	$-0.266461\pi$
$739$	−8.38375	−	14.5211i	−0.308401	−	0.534167i	−0.978013	+	0.208545i	$0.933127\pi$
$740$	0.679204	+	1.17642i	0.0249680	+	0.0432459i
$741$	−11.6073	−	32.5178i	−0.426404	−	1.19457i
$742$	−25.0367	−	23.4818i	−0.919127	−	0.862043i
$743$	29.7811	−	17.1941i	1.09256	−	0.630790i	0.158304	−	0.987390i	$-0.449397\pi$
$743$	29.7811	−	17.1941i	1.09256	−	0.630790i	0.934257	+	0.356600i	$0.116064\pi$
$744$	−17.6086	−	3.21777i	−0.645562	−	0.117969i
$745$			11.3297i			0.415090i
$746$	49.6201	−	28.6482i	1.81672	−	1.04888i
$747$	−7.46554	−	45.6483i	−0.273150	−	1.67018i
$748$		−	0.763983i		−	0.0279340i
$749$	−12.7061	+	13.5475i	−0.464270	+	0.495014i
$750$	2.40293	+	2.04187i	0.0877427	+	0.0745585i
$751$	−19.4900			−0.711200			−0.355600	−	0.934638i	$-0.615723\pi$
$751$	−19.4900			−0.711200			−0.355600	+	0.934638i	$0.615723\pi$
$752$	−21.9901	+	38.0880i	−0.801897	+	1.38893i
$753$	16.3611	+	45.8357i	0.596232	+	1.67035i
$754$	−31.9172	+	18.4274i	−1.16235	+	0.671086i
$755$	18.0711			0.657676
$756$	4.91050	+	17.3905i	0.178593	+	0.632487i
$757$	−11.6307			−0.422726			−0.211363	−	0.977408i	$-0.567790\pi$
$757$	−11.6307			−0.422726			−0.211363	+	0.977408i	$0.567790\pi$
$758$	11.5272	−	6.65524i	0.418687	−	0.241729i
$759$	−0.291930	−	0.817842i	−0.0105964	−	0.0296858i
$760$	4.88349	−	8.45846i	0.177143	−	0.306821i
$761$	18.4568			0.669058			0.334529	−	0.942385i	$-0.391423\pi$
$761$	18.4568			0.669058			0.334529	+	0.942385i	$0.391423\pi$
$762$	−35.0477	−	29.7814i	−1.26964	−	1.07887i
$763$	25.8822	−	7.83186i	0.936999	−	0.283532i
$764$		−	14.2719i		−	0.516338i
$765$	5.84512	+	2.21006i	0.211331	+	0.0799051i
$766$	54.0826	−	31.2246i	1.95408	−	1.12819i
$767$		−	5.49676i		−	0.198477i
$768$	35.6196	+	6.50908i	1.28531	+	0.234876i
$769$	−15.1013	+	8.71871i	−0.544565	+	0.314405i	−0.746927	−	0.664906i	$-0.768472\pi$
$769$	−15.1013	+	8.71871i	−0.544565	+	0.314405i	0.202362	+	0.979311i	$0.435138\pi$
$770$	1.28643	−	0.389268i	0.0463596	−	0.0140282i
$771$	−4.73863	−	13.2753i	−0.170658	−	0.478098i
$772$	−4.12955	−	7.15260i	−0.148626	−	0.257428i
$773$	−15.6712	−	27.1434i	−0.563655	−	0.976279i	−0.997173	−	0.0751342i	$-0.976061\pi$
$773$	−15.6712	−	27.1434i	−0.563655	−	0.976279i	0.433519	−	0.901145i	$-0.357272\pi$
$774$	9.14239	+	11.1745i	0.328616	+	0.401659i
$775$	7.17091	+	4.14013i	0.257587	+	0.148718i
$776$	−5.50380	+	9.53286i	−0.197575	+	0.342210i
$777$	−1.88996	+	4.34242i	−0.0678021	+	0.155783i
$778$	25.7395	+	44.5821i	0.922806	+	1.59835i
$779$		−	43.4694i		−	1.55745i
$780$	−5.46202	+	1.94967i	−0.195572	+	0.0698096i
$781$	−1.30365			−0.0466483
$782$	3.40689	−	5.90090i	0.121830	−	0.211016i
$783$	19.9765	+	36.1393i	0.713903	+	1.29151i
$784$	−2.19679	−	34.2375i	−0.0784566	−	1.22277i
$785$	17.7971	+	10.2752i	0.635206	+	0.366736i
$786$	−7.95643	−	6.76090i	−0.283796	−	0.241153i
$787$	0.182058	+	0.105111i	0.00648965	+	0.00374680i	0.503241	−	0.864146i	$-0.332141\pi$
$787$	0.182058	+	0.105111i	0.00648965	+	0.00374680i	−0.496752	+	0.867893i	$0.665474\pi$
$788$	−22.8651	−	13.2012i	−0.814536	−	0.470273i
$789$	−0.836349	+	0.298536i	−0.0297748	+	0.0106282i
$790$	17.7805	+	10.2656i	0.632602	+	0.365233i
$791$	−8.82413	−	29.1614i	−0.313750	−	1.03686i
$792$	−0.808639	+	0.661585i	−0.0287337	+	0.0235084i
$793$	−4.33650	+	7.51104i	−0.153994	+	0.266725i
$794$	8.10528			0.287646
$795$	−9.40585	−	7.99253i	−0.333591	−	0.283466i
$796$		−	29.3422i		−	1.04001i
$797$	−14.9432	−	25.8824i	−0.529315	−	0.916801i	−0.999415	−	0.0341878i	$-0.989116\pi$
$797$	−14.9432	−	25.8824i	−0.529315	−	0.916801i	0.470100	−	0.882613i	$-0.344218\pi$
$798$	−64.8692	+	7.36766i	−2.29635	+	0.260812i
$799$	9.34587	−	16.1875i	0.330633	−	0.572673i
$800$	−5.56558	−	3.21329i	−0.196773	−	0.113607i
$801$	2.59130	+	15.8446i	0.0915590	+	0.559840i
$802$	−13.3410	−	23.1072i	−0.471086	−	0.815945i
$803$	−0.166878	−	0.289042i	−0.00588901	−	0.0102001i
$804$	−17.6447	+	20.7648i	−0.622280	+	0.732318i
$805$	4.62890	+	1.08266i	0.163147	+	0.0381589i
$806$	−33.2563	+	19.2005i	−1.17140	+	0.676310i
$807$	−0.419708	+	0.493925i	−0.0147744	+	0.0173870i
$808$			22.8032i			0.802215i
$809$	6.84767	−	3.95351i	0.240751	−	0.138998i	−0.374771	−	0.927118i	$-0.622279\pi$
$809$	6.84767	−	3.95351i	0.240751	−	0.138998i	0.615522	+	0.788120i	$0.288945\pi$
$810$	5.21976	+	15.5314i	0.183404	+	0.545717i
$811$			48.2315i			1.69364i	0.531883	+	0.846818i	$0.321485\pi$
$811$			48.2315i			1.69364i	−0.531883	+	0.846818i	$0.678515\pi$
$812$	8.00427	+	26.4520i	0.280895	+	0.928282i
$813$	−2.02230	+	11.0666i	−0.0709251	+	0.388123i
$814$	0.524991			0.0184009
$815$	−0.386774	+	0.669912i	−0.0135481	+	0.0234660i
$816$	−17.3945	−	3.17866i	−0.608930	−	0.111275i
$817$	−17.9150	+	10.3432i	−0.626765	+	0.361863i
$818$	−24.1607			−0.844759
$819$	−16.7869	−	11.2702i	−0.586582	−	0.393813i
$820$	−7.30155			−0.254981
$821$	−14.3914	+	8.30886i	−0.502262	+	0.289981i	−0.729647	−	0.683824i	$-0.760316\pi$
$821$	−14.3914	+	8.30886i	−0.502262	+	0.289981i	0.227385	+	0.973805i	$0.426982\pi$
$822$	19.5715	−	23.0324i	0.682635	−	0.803346i
$823$	23.4389	−	40.5973i	0.817028	−	1.41513i	−0.0908353	−	0.995866i	$-0.528954\pi$
$823$	23.4389	−	40.5973i	0.817028	−	1.41513i	0.907863	−	0.419267i	$-0.137713\pi$
$824$	16.4545			0.573220
$825$	0.455171	−	0.162474i	0.0158470	−	0.00565662i
$826$	−10.1205	−	2.36710i	−0.352136	−	0.0823618i
$827$		−	22.0393i		−	0.766381i	−0.923669	−	0.383191i	$-0.874825\pi$
$827$		−	22.0393i		−	0.766381i	0.923669	−	0.383191i	$-0.125175\pi$
$828$	6.99235	−	1.14356i	0.243001	−	0.0397416i
$829$	−35.2039	+	20.3250i	−1.22268	+	0.705915i	−0.965489	−	0.260445i	$-0.916131\pi$
$829$	−35.2039	+	20.3250i	−1.22268	+	0.705915i	−0.257192	+	0.966360i	$0.582797\pi$
$830$		−	28.0698i		−	0.974319i
$831$	2.12402	+	5.95045i	0.0736815	+	0.206419i
$832$	4.18653	−	2.41709i	0.145142	−	0.0837976i
$833$	0.933641	+	14.5511i	0.0323488	+	0.504164i
$834$	−5.49962	−	1.00499i	−0.190436	−	0.0348001i
$835$	4.90398	+	8.49395i	0.169709	+	0.293945i
$836$	1.43507	+	2.48561i	0.0496329	+	0.0859667i
$837$	20.8147	+	37.6555i	0.719460	+	1.30157i
$838$	−59.4620	−	34.3304i	−2.05408	−	1.18592i
$839$	21.5312	−	37.2932i	0.743341	−	1.28750i	−0.207625	−	0.978209i	$-0.566573\pi$
$839$	21.5312	−	37.2932i	0.743341	−	1.28750i	0.950966	−	0.309296i	$-0.100093\pi$
$840$	−0.645461	−	5.68302i	−0.0222705	−	0.196083i
$841$	17.0761	+	29.5767i	0.588831	+	1.01989i
$842$			62.0648i			2.13889i
$843$	−1.02637	+	5.61658i	−0.0353500	+	0.193445i
$844$	−0.671248			−0.0231053
$845$	−3.25541	+	5.63854i	−0.111990	+	0.193972i
$846$	48.3677	−	7.91028i	1.66292	−	0.271961i
$847$	−6.58122	+	28.1379i	−0.226134	+	0.966829i
$848$	30.2474	+	17.4633i	1.03870	+	0.599694i
$849$	−4.34134	+	23.7571i	−0.148994	+	0.815341i
$850$	3.28416	+	1.89611i	0.112646	+	0.0650360i
$851$	1.60811	+	0.928443i	0.0551253	+	0.0318266i
$852$	1.91207	−	10.4634i	0.0655064	−	0.358470i
$853$	−29.0793	−	16.7889i	−0.995655	−	0.574842i	−0.0886951	−	0.996059i	$-0.528270\pi$
$853$	−29.0793	−	16.7889i	−0.995655	−	0.574842i	−0.906960	+	0.421217i	$0.861603\pi$
$854$	11.9616	+	11.2187i	0.409319	+	0.383897i
$855$	−23.1685	+	3.78908i	−0.792345	+	0.129584i
$856$	4.38097	−	7.58806i	0.149738	−	0.259354i
$857$	5.80997			0.198465			0.0992324	−	0.995064i	$-0.468361\pi$
$857$	5.80997			0.198465			0.0992324	+	0.995064i	$0.468361\pi$
$858$	−0.402916	+	2.20487i	−0.0137553	+	0.0752731i
$859$		−	30.8353i		−	1.05209i	−0.850458	−	0.526043i	$-0.823675\pi$
$859$		−	30.8353i		−	1.05209i	0.850458	−	0.526043i	$-0.176325\pi$
$860$	1.73735	+	3.00918i	0.0592431	+	0.102612i
$861$	−15.1344	−	20.4681i	−0.515779	−	0.697552i
$862$	25.1387	−	43.5415i	0.856228	−	1.48303i
$863$	28.8588	+	16.6616i	0.982365	+	0.567169i	0.902983	−	0.429676i	$-0.141372\pi$
$863$	28.8588	+	16.6616i	0.982365	+	0.567169i	0.0793816	+	0.996844i	$0.474705\pi$
$864$	−16.1550	−	29.2257i	−0.549603	−	0.994279i
$865$	−1.48675	−	2.57513i	−0.0505511	−	0.0875570i
$866$	−6.69933	−	11.6036i	−0.227652	−	0.394305i
$867$	−21.5725	−	3.94213i	−0.732640	−	0.133882i
$868$	8.34009	+	27.5618i	0.283081	+	0.935508i
$869$	2.72518	−	1.57338i	0.0924454	−	0.0533734i
$870$	8.42417	+	23.6003i	0.285606	+	0.800126i
$871$		−	30.4892i		−	1.03309i
$872$	−11.0474	+	6.37823i	−0.374113	+	0.215994i
$873$	26.1113	−	4.27037i	0.883735	−	0.144530i
$874$			25.5980i			0.865867i
$875$	−0.602558	+	2.57622i	−0.0203702	+	0.0870922i
$876$	2.56468	−	0.915465i	0.0866524	−	0.0309307i
$877$	−7.04857			−0.238013			−0.119007	−	0.992893i	$-0.537971\pi$
$877$	−7.04857			−0.238013			−0.119007	+	0.992893i	$0.537971\pi$
$878$	4.11056	−	7.11970i	0.138725	−	0.240278i
$879$	32.4248	−	38.1585i	1.09366	−	1.28705i
$880$	−1.18436	+	0.683789i	−0.0399247	+	0.0230505i
$881$	49.3816			1.66371			0.831855	−	0.554993i	$-0.187279\pi$
$881$	49.3816			1.66371			0.831855	+	0.554993i	$0.187279\pi$
$882$	−27.9794	+	26.0542i	−0.942115	+	0.877290i
$883$	42.7741			1.43946			0.719732	−	0.694252i	$-0.244265\pi$
$883$	42.7741			1.43946			0.719732	+	0.694252i	$0.244265\pi$
$884$	−6.04023	+	3.48733i	−0.203155	+	0.117291i
$885$	−3.67654	−	0.671848i	−0.123586	−	0.0225839i
$886$	−28.8075	+	49.8961i	−0.967808	+	1.67629i
$887$	20.1380			0.676168			0.338084	−	0.941116i	$-0.390221\pi$
$887$	20.1380			0.676168			0.338084	+	0.941116i	$0.390221\pi$
$888$	0.401608	−	2.19772i	0.0134771	−	0.0737505i
$889$	8.78853	−	37.5752i	0.294758	−	1.26023i
$890$			9.74307i			0.326588i
$891$	2.46155	+	0.497391i	0.0824650	+	0.0166632i
$892$	−20.4153	+	11.7868i	−0.683554	+	0.394650i
$893$			70.2213i			2.34987i
$894$	−23.1338	+	27.2246i	−0.773712	+	0.910527i
$895$	−9.60988	+	5.54827i	−0.321223	+	0.185458i
$896$	7.20172	+	23.7997i	0.240592	+	0.795094i
$897$	−5.13348	+	6.04124i	−0.171402	+	0.201711i
$898$	30.2182	+	52.3394i	1.00839	+	1.74659i
$899$	32.9009	+	56.9860i	1.09731	+	1.90059i
$900$	0.636452	+	3.89161i	0.0212151	+	0.129720i
$901$	−12.8552	−	7.42198i	−0.428270	−	0.247262i
$902$	−1.41093	+	2.44381i	−0.0469790	+	0.0813699i
$903$	−4.83438	+	11.1076i	−0.160878	+	0.369636i
$904$	7.18633	+	12.4471i	0.239014	+	0.413984i
$905$		−	17.3072i		−	0.575312i
$906$	43.4237	+	36.8989i	1.44266	+	1.22588i
$907$	13.2596			0.440277			0.220138	−	0.975469i	$-0.429349\pi$
$907$	13.2596			0.440277			0.220138	+	0.975469i	$0.429349\pi$
$908$	7.27110	−	12.5939i	0.241300	−	0.417944i
$909$	42.4218	−	34.7073i	1.40704	−	1.15117i
$910$	−8.94975	−	8.39391i	−0.296681	−	0.278255i
$911$	35.4901	+	20.4902i	1.17584	+	0.678871i	0.955048	−	0.296450i	$-0.0958029\pi$
$911$	35.4901	+	20.4902i	1.17584	+	0.678871i	0.220791	+	0.975321i	$0.429136\pi$
$912$	62.5637	−	22.3322i	2.07169	−	0.739494i
$913$	−3.72582	−	2.15110i	−0.123307	−	0.0711911i
$914$	12.7168	+	7.34203i	0.420633	+	0.242853i
$915$	4.49377	+	3.81854i	0.148560	+	0.126237i
$916$	−30.4102	−	17.5573i	−1.00478	−	0.580111i
$917$	1.99515	−	8.53022i	0.0658856	−	0.281693i
$918$	9.53277	+	17.2456i	0.314628	+	0.569190i
$919$	17.2002	−	29.7915i	0.567381	−	0.982732i	−0.429443	−	0.903094i	$-0.641290\pi$
$919$	17.2002	−	29.7915i	0.567381	−	0.982732i	0.996824	−	0.0796385i	$-0.0253766\pi$
$920$	−2.24258			−0.0739356
$921$	15.6938	−	5.60193i	0.517129	−	0.184590i
$922$			26.3923i			0.869183i
$923$	5.95073	+	10.3070i	0.195871	+	0.339258i
$924$	1.54112	+	0.670746i	0.0506991	+	0.0220659i
$925$	−0.516727	+	0.894997i	−0.0169899	+	0.0294273i
$926$	64.4301	+	37.1988i	2.11731	+	1.22243i
$927$	−25.0443	−	30.6110i	−0.822562	−	1.00540i
$928$	−25.5355	−	44.2287i	−0.838243	−	1.45188i
$929$	−9.60425	−	16.6351i	−0.315105	−	0.545778i	0.664355	−	0.747418i	$-0.268707\pi$
$929$	−9.60425	−	16.6351i	−0.315105	−	0.545778i	−0.979460	+	0.201639i	$0.935373\pi$
$930$	8.77761	+	24.5905i	0.287829	+	0.806354i
$931$	−30.3704	−	45.5880i	−0.995348	−	1.49409i
$932$	0.00537225	−	0.00310167i	0.000175974	−	0.000101599i
$933$	5.21194	+	0.952423i	0.170631	+	0.0311809i
$934$		−	22.1391i		−	0.724413i
$935$	0.503356	−	0.290613i	0.0164615	−	0.00950405i
$936$	8.92181	+	3.37337i	0.291618	+	0.110262i
$937$			1.73959i			0.0568300i	0.999596	+	0.0284150i	$0.00904599\pi$
$937$			1.73959i			0.0568300i	−0.999596	+	0.0284150i	$0.990954\pi$
$938$	−56.1358	−	13.1297i	−1.83290	−	0.428700i
$939$	−4.53783	−	3.85598i	−0.148087	−	0.125835i
$940$	11.7951			0.384713
$941$	1.75755	−	3.04416i	0.0572944	−	0.0992367i	−0.835956	−	0.548797i	$-0.815086\pi$
$941$	1.75755	−	3.04416i	0.0572944	−	0.0992367i	0.893250	+	0.449560i	$0.148419\pi$
$942$	21.7847	+	61.0298i	0.709784	+	1.98846i
$943$	−8.64372	+	4.99046i	−0.281478	+	0.162512i
$944$	10.5757			0.344209
$945$	−9.58995	+	9.85052i	−0.311961	+	0.320438i
$946$	1.34288			0.0436609
$947$	5.28629	−	3.05204i	0.171781	−	0.0991780i	−0.411644	−	0.911345i	$-0.635045\pi$
$947$	5.28629	−	3.05204i	0.171781	−	0.0991780i	0.583426	+	0.812167i	$0.301712\pi$
$948$	8.63129	+	24.1806i	0.280331	+	0.785349i
$949$	−1.52349	+	2.63876i	−0.0494545	+	0.0856577i
$950$	−14.2466			−0.462222
$951$	6.78607	+	5.76640i	0.220053	+	0.186988i
$952$	−1.99218	−	6.58364i	−0.0645671	−	0.213377i
$953$		−	0.788320i		−	0.0255362i	−0.999918	−	0.0127681i	$-0.995936\pi$
$953$		−	0.788320i		−	0.0255362i	0.999918	−	0.0127681i	$-0.00406432\pi$
$954$	−6.28192	−	38.4110i	−0.203385	−	1.24360i
$955$	9.40312	−	5.42889i	0.304278	−	0.175675i
$956$		−	19.9459i		−	0.645097i
$957$	3.77814	+	0.690413i	0.122130	+	0.0223179i
$958$	37.4436	−	21.6181i	1.20975	−	0.698449i
$959$	24.6934	+	5.77558i	0.797391	+	0.186503i
$960$	−1.10499	−	3.09562i	−0.0356632	−	0.0999106i
$961$	18.7813	+	32.5302i	0.605848	+	1.04936i
$962$	−2.39641	−	4.15070i	−0.0772632	−	0.133824i
$963$	−20.7844	+	3.39917i	−0.669766	+	0.109537i
$964$	11.0231	+	6.36422i	0.355032	+	0.204978i
$965$	3.14169	−	5.44157i	0.101135	−	0.175170i
$966$	8.91228	+	12.0532i	0.286748	+	0.387804i
$967$	−9.70715	−	16.8133i	−0.312161	−	0.540679i	0.666669	−	0.745354i	$-0.267719\pi$
$967$	−9.70715	−	16.8133i	−0.312161	−	0.540679i	−0.978830	+	0.204675i	$0.934386\pi$
$968$		−	13.6320i		−	0.438150i
$969$	−26.5898	+	9.49127i	−0.854187	+	0.304903i
$970$	16.0563			0.515535
$971$	−18.5702	+	32.1645i	−0.595945	+	1.03221i	0.397468	+	0.917616i	$0.369889\pi$
$971$	−18.5702	+	32.1645i	−0.595945	+	1.03221i	−0.993413	+	0.114591i	$0.963444\pi$
$972$	−7.60253	+	19.0274i	−0.243851	+	0.610305i
$973$	−1.35859	−	4.48977i	−0.0435543	−	0.143935i
$974$	46.3720	+	26.7729i	1.48586	+	0.857859i
$975$	−3.36226	−	2.85705i	−0.107679	−	0.0914988i
$976$	−14.4511	−	8.34336i	−0.462569	−	0.267064i
$977$	39.1113	+	22.5809i	1.25128	+	0.722428i	0.971364	−	0.237596i	$-0.0763595\pi$
$977$	39.1113	+	22.5809i	1.25128	+	0.722428i	0.279918	+	0.960024i	$0.409693\pi$
$978$	−2.29726	+	0.820012i	−0.0734584	+	0.0262211i
$979$	1.29323	+	0.746650i	0.0413320	+	0.0238630i
$980$	−7.65741	+	5.10131i	−0.244607	+	0.162955i
$981$	28.6802	+	10.8441i	0.915689	+	0.346225i
$982$	25.8193	−	44.7203i	0.823926	−	1.42708i
$983$	−29.7135			−0.947713			−0.473857	−	0.880602i	$-0.657139\pi$
$983$	−29.7135			−0.947713			−0.473857	+	0.880602i	$0.657139\pi$
$984$	9.15094	+	7.77592i	0.291721	+	0.247887i
$985$		−	20.0865i		−	0.640008i
$986$	15.0681	+	26.0987i	0.479865	+	0.831151i
$987$	24.4484	+	33.0646i	0.778201	+	1.05246i
$988$	13.1012	−	22.6920i	0.416805	−	0.721928i
$989$	4.11342	+	2.37488i	0.130799	+	0.0755169i
$990$	1.42550	+	0.538986i	0.0453052	+	0.0171301i
$991$	−7.42230	−	12.8558i	−0.235777	−	0.408378i	0.723721	−	0.690093i	$-0.242430\pi$
$991$	−7.42230	−	12.8558i	−0.235777	−	0.408378i	−0.959498	+	0.281714i	$0.909097\pi$
$992$	−26.6068	−	46.0844i	−0.844768	−	1.46318i
$993$	−12.8979	+	15.1787i	−0.409303	+	0.481680i
$994$	21.5394	−	6.51775i	0.683189	−	0.206731i
$995$	19.3323	−	11.1615i	0.612877	−	0.353844i
$996$	22.7299	−	26.7492i	0.720224	−	0.847582i
$997$			39.9004i			1.26366i	0.775108	+	0.631828i	$0.217695\pi$
$997$			39.9004i			1.26366i	−0.775108	+	0.631828i	$0.782305\pi$
$998$	52.6118	−	30.3755i	1.66540	−	0.961518i
$999$	−4.69976	+	2.59787i	−0.148694	+	0.0821929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.b.236.3	yes	30
3.2	odd	2		945.2.be.b.656.13		30
7.3	odd	6		315.2.t.b.101.3	✓	30
9.4	even	3		945.2.t.b.341.3		30
9.5	odd	6		315.2.t.b.131.13	yes	30
21.17	even	6		945.2.t.b.521.13		30
63.31	odd	6		945.2.be.b.206.13		30
63.59	even	6	inner	315.2.be.b.311.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.b.101.3	✓	30	7.3	odd	6
315.2.t.b.131.13	yes	30	9.5	odd	6
315.2.be.b.236.3	yes	30	1.1	even	1	trivial
315.2.be.b.311.3	yes	30	63.59	even	6	inner
945.2.t.b.341.3		30	9.4	even	3
945.2.t.b.521.13		30	21.17	even	6
945.2.be.b.206.13		30	63.31	odd	6
945.2.be.b.656.13		30	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57665 + 0.910280i) q^{2} +(-0.582275 - 1.63124i) q^{3} +(0.657218 - 1.13833i) q^{4} +1.00000 q^{5} +(2.40293 + 2.04187i) q^{6} +(-0.602558 + 2.57622i) q^{7} -1.24811i q^{8} +(-2.32191 + 1.89966i) q^{9} +O(q^{10})\)	\(q+(-1.57665 + 0.910280i) q^{2} +(-0.582275 - 1.63124i) q^{3} +(0.657218 - 1.13833i) q^{4} +1.00000 q^{5} +(2.40293 + 2.04187i) q^{6} +(-0.602558 + 2.57622i) q^{7} -1.24811i q^{8} +(-2.32191 + 1.89966i) q^{9} +(-1.57665 + 0.910280i) q^{10} +0.279033i q^{11} +(-2.23958 - 0.409259i) q^{12} +(2.20610 - 1.27369i) q^{13} +(-1.39506 - 4.61030i) q^{14} +(-0.582275 - 1.63124i) q^{15} +(2.45057 + 4.24450i) q^{16} +(-1.04150 - 1.80393i) q^{17} +(1.93162 - 5.10870i) q^{18} +(6.77701 + 3.91271i) q^{19} +(0.657218 - 1.13833i) q^{20} +(4.55330 - 0.517151i) q^{21} +(-0.253998 - 0.439938i) q^{22} -1.79678i q^{23} +(-2.03597 + 0.726743i) q^{24} +1.00000 q^{25} +(-2.31883 + 4.01634i) q^{26} +(4.45081 + 2.68148i) q^{27} +(2.53659 + 2.37905i) q^{28} +(6.88216 + 3.97342i) q^{29} +(2.40293 + 2.04187i) q^{30} +(7.17091 + 4.14013i) q^{31} +(-5.56558 - 3.21329i) q^{32} +(0.455171 - 0.162474i) q^{33} +(3.28416 + 1.89611i) q^{34} +(-0.602558 + 2.57622i) q^{35} +(0.636452 + 3.89161i) q^{36} +(-0.516727 + 0.894997i) q^{37} -14.2466 q^{38} +(-3.36226 - 2.85705i) q^{39} -1.24811i q^{40} +(-2.77745 - 4.81068i) q^{41} +(-6.70821 + 4.96014i) q^{42} +(-1.32175 + 2.28933i) q^{43} +(0.317633 + 0.183386i) q^{44} +(-2.32191 + 1.89966i) q^{45} +(1.63557 + 2.83289i) q^{46} +(4.48674 + 7.77126i) q^{47} +(5.49692 - 6.46894i) q^{48} +(-6.27385 - 3.10465i) q^{49} +(-1.57665 + 0.910280i) q^{50} +(-2.33621 + 2.74932i) q^{51} -3.34838i q^{52} +(6.17152 - 3.56313i) q^{53} +(-9.45826 - 0.176275i) q^{54} +0.279033i q^{55} +(3.21541 + 0.752059i) q^{56} +(2.43650 - 13.3332i) q^{57} -14.4677 q^{58} +(1.07890 - 1.86871i) q^{59} +(-2.23958 - 0.409259i) q^{60} +(-2.94853 + 1.70233i) q^{61} -15.0747 q^{62} +(-3.49487 - 7.12642i) q^{63} +1.89770 q^{64} +(2.20610 - 1.27369i) q^{65} +(-0.569749 + 0.670498i) q^{66} +(5.98441 - 10.3653i) q^{67} -2.73797 q^{68} +(-2.93098 + 1.04622i) q^{69} +(-1.39506 - 4.61030i) q^{70} +4.67203i q^{71} +(2.37099 + 2.89800i) q^{72} +(-1.03587 + 0.598059i) q^{73} -1.88146i q^{74} +(-0.582275 - 1.63124i) q^{75} +(8.90795 - 5.14301i) q^{76} +(-0.718852 - 0.168134i) q^{77} +(7.90182 + 1.44397i) q^{78} +(-5.63869 - 9.76650i) q^{79} +(2.45057 + 4.24450i) q^{80} +(1.78255 - 8.82171i) q^{81} +(8.75813 + 5.05651i) q^{82} +(-7.70913 + 13.3526i) q^{83} +(2.40382 - 5.52306i) q^{84} +(-1.04150 - 1.80393i) q^{85} -4.81263i q^{86} +(2.47430 - 13.5401i) q^{87} +0.348264 q^{88} +(2.67584 - 4.63470i) q^{89} +(1.93162 - 5.10870i) q^{90} +(1.95201 + 6.45088i) q^{91} +(-2.04533 - 1.18087i) q^{92} +(2.57812 - 14.1082i) q^{93} +(-14.1480 - 8.16838i) q^{94} +(6.77701 + 3.91271i) q^{95} +(-2.00096 + 10.9498i) q^{96} +(-7.63783 - 4.40971i) q^{97} +(12.7178 - 0.816012i) q^{98} +(-0.530069 - 0.647891i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9	\( 30 q + 3 q^{2} - q^{3} + 15 q^{4} + 30 q^{5} + q^{6} + 6 q^{7} - 5 q^{9} + 3 q^{10} - 18 q^{12} + 12 q^{13} - 9 q^{14} - q^{15} - 21 q^{16} + 3 q^{17} - 22 q^{18} + 15 q^{20} - 10 q^{21} + 15 q^{22} + 2 q^{24} + 30 q^{25} - 24 q^{26} + 5 q^{27} + 27 q^{28} + q^{30} + 6 q^{31} + 9 q^{32} - 17 q^{33} - 48 q^{34} + 6 q^{35} + 21 q^{36} - 3 q^{37} - 60 q^{38} + 12 q^{39} + 18 q^{41} - 47 q^{42} + 12 q^{43} - 15 q^{44} - 5 q^{45} + 9 q^{46} - 30 q^{47} + 40 q^{48} - 24 q^{49} + 3 q^{50} + 33 q^{51} + 30 q^{53} + 13 q^{54} + 72 q^{56} - 21 q^{57} + 15 q^{59} - 18 q^{60} - 30 q^{61} - 12 q^{62} + 10 q^{63} - 138 q^{64} + 12 q^{65} + 44 q^{66} - 6 q^{67} - 42 q^{68} - 32 q^{69} - 9 q^{70} - 137 q^{72} + 6 q^{73} - q^{75} + 54 q^{76} - 21 q^{77} - 18 q^{78} - 12 q^{79} - 21 q^{80} - 17 q^{81} + 6 q^{82} + 6 q^{83} - 12 q^{84} + 3 q^{85} - 47 q^{87} + 96 q^{88} + 3 q^{89} - 22 q^{90} + 15 q^{91} - 3 q^{92} - 18 q^{93} + 3 q^{94} + 60 q^{96} - 36 q^{97} - 24 q^{98} - q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - q^3 + 15 * q^4 + 30 * q^5 + q^6 + 6 * q^7 - 5 * q^9 + 3 * q^10 - 18 * q^12 + 12 * q^13 - 9 * q^14 - q^15 - 21 * q^16 + 3 * q^17 - 22 * q^18 + 15 * q^20 - 10 * q^21 + 15 * q^22 + 2 * q^24 + 30 * q^25 - 24 * q^26 + 5 * q^27 + 27 * q^28 + q^30 + 6 * q^31 + 9 * q^32 - 17 * q^33 - 48 * q^34 + 6 * q^35 + 21 * q^36 - 3 * q^37 - 60 * q^38 + 12 * q^39 + 18 * q^41 - 47 * q^42 + 12 * q^43 - 15 * q^44 - 5 * q^45 + 9 * q^46 - 30 * q^47 + 40 * q^48 - 24 * q^49 + 3 * q^50 + 33 * q^51 + 30 * q^53 + 13 * q^54 + 72 * q^56 - 21 * q^57 + 15 * q^59 - 18 * q^60 - 30 * q^61 - 12 * q^62 + 10 * q^63 - 138 * q^64 + 12 * q^65 + 44 * q^66 - 6 * q^67 - 42 * q^68 - 32 * q^69 - 9 * q^70 - 137 * q^72 + 6 * q^73 - q^75 + 54 * q^76 - 21 * q^77 - 18 * q^78 - 12 * q^79 - 21 * q^80 - 17 * q^81 + 6 * q^82 + 6 * q^83 - 12 * q^84 + 3 * q^85 - 47 * q^87 + 96 * q^88 + 3 * q^89 - 22 * q^90 + 15 * q^91 - 3 * q^92 - 18 * q^93 + 3 * q^94 + 60 * q^96 - 36 * q^97 - 24 * q^98 - q^99

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