LMFDB - Embedded newform 197.2.e.a.93.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,2,Mod(6,197)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("197.6"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	197.e (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.57305291982$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{14})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			93.1
Root			$0.900969 + 0.433884i$ of defining polynomial
Character	$\chi$	$=$	197.93
Dual form			197.2.e.a.161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.846011 - 1.75676i) q^{2} +(-0.376510 - 0.781831i) q^{3} +(-1.12349 - 1.40881i) q^{4} +(-1.82640 - 1.45650i) q^{5} -1.69202 q^{6} +(0.623490 - 0.300257i) q^{7} +(0.376510 - 0.0859360i) q^{8} +(1.40097 - 1.75676i) q^{9} +(-4.10388 + 1.97632i) q^{10} +(-1.73341 + 3.59945i) q^{11} +(-0.678448 + 1.40881i) q^{12} +(-4.94989 - 1.12978i) q^{13} -1.34934i q^{14} +(-0.451083 + 1.97632i) q^{15} +(0.969501 - 4.24766i) q^{16} +(1.82640 + 1.45650i) q^{17} +(-1.90097 - 3.94740i) q^{18} +4.98792 q^{19} +4.20941i q^{20} +(-0.469501 - 0.374414i) q^{21} +(4.85690 + 6.09035i) q^{22} +(8.11745 + 3.90916i) q^{23} +(-0.208947 - 0.262012i) q^{24} +(0.101720 + 0.445662i) q^{25} +(-6.17241 + 7.73995i) q^{26} +(-4.43900 - 1.01317i) q^{27} +(-1.12349 - 0.541044i) q^{28} +(4.42543 + 2.13117i) q^{29} +(3.09030 + 2.46443i) q^{30} +(4.02930 - 8.36693i) q^{31} +(-6.03803 - 4.81517i) q^{32} +3.46681 q^{33} +(4.10388 - 1.97632i) q^{34} +(-1.57606 - 0.359726i) q^{35} -4.04892 q^{36} +(1.20895 + 5.29674i) q^{37} +(4.21983 - 8.76257i) q^{38} +(0.980386 + 4.29535i) q^{39} +(-0.812823 - 0.391435i) q^{40} +(-2.88740 + 3.62068i) q^{41} +(-1.05496 + 0.508041i) q^{42} +(-7.31551 - 3.52296i) q^{43} +(7.01842 - 1.60191i) q^{44} +(-5.11745 + 1.16802i) q^{45} +(13.7349 - 10.9532i) q^{46} +(0.306782 + 1.34410i) q^{47} +(-3.68598 + 0.841301i) q^{48} +(-4.06584 + 5.09841i) q^{49} +(0.868977 + 0.198338i) q^{50} +(0.451083 - 1.97632i) q^{51} +(3.96950 + 8.24275i) q^{52} +(6.27144 + 7.86413i) q^{53} +(-5.53534 + 6.94110i) q^{54} +(8.40850 - 4.04932i) q^{55} +(0.208947 - 0.166630i) q^{56} +(-1.87800 - 3.89971i) q^{57} +(7.48792 - 5.97142i) q^{58} +(0.425428 + 0.204875i) q^{59} +(3.29105 - 1.58489i) q^{60} +(1.46466 + 0.705341i) q^{61} +(-11.2899 - 14.1570i) q^{62} +(0.346011 - 1.51597i) q^{63} +(-5.71648 + 2.75291i) q^{64} +(7.39493 + 9.27295i) q^{65} +(2.93296 - 6.09035i) q^{66} +(-11.1969 + 2.55561i) q^{67} -4.20941i q^{68} -7.81831i q^{69} +(-1.96532 + 2.46443i) q^{70} +(3.18329 + 2.53859i) q^{71} +(0.376510 - 0.781831i) q^{72} +(-9.50484 + 2.16942i) q^{73} +(10.3279 + 2.35727i) q^{74} +(0.310134 - 0.247324i) q^{75} +(-5.60388 - 7.02704i) q^{76} +2.76469i q^{77} +(8.37531 + 1.91161i) q^{78} +(4.75571 - 3.79255i) q^{79} +(-7.95742 + 6.34583i) q^{80} +(-0.620801 - 2.71991i) q^{81} +(3.91789 + 8.13559i) q^{82} -7.48188 q^{83} +1.08209i q^{84} +(-1.21432 - 5.32030i) q^{85} +(-12.3780 + 9.87113i) q^{86} -4.26235i q^{87} +(-0.343322 + 1.50419i) q^{88} +(1.91939 + 3.98565i) q^{89} +(-2.27748 + 9.97829i) q^{90} +(-3.42543 + 0.781831i) q^{91} +(-3.61260 - 15.8279i) q^{92} -8.05861 q^{93} +(2.62080 + 0.598181i) q^{94} +(-9.10992 - 7.26492i) q^{95} +(-1.49127 + 6.53368i) q^{96} +(-4.19537 + 5.26083i) q^{97} +(5.51693 + 11.4560i) q^{98} +(3.89493 + 8.08790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 7 q^{3} - 2 q^{4} + 7 q^{5} - q^{7} + 7 q^{8} + 4 q^{9} - 7 q^{10} - 7 q^{11} - 7 q^{13} - 21 q^{15} - 4 q^{16} - 7 q^{17} - 7 q^{18} - 8 q^{19} + 7 q^{21} + 21 q^{22} + 25 q^{23} - 7 q^{24} + 2 q^{25}+ \cdots + 49 q^{98}+O(q^{100}) $ 6 * q - 7 * q^3 - 2 * q^4 + 7 * q^5 - q^7 + 7 * q^8 + 4 * q^9 - 7 * q^10 - 7 * q^11 - 7 * q^13 - 21 * q^15 - 4 * q^16 - 7 * q^17 - 7 * q^18 - 8 * q^19 + 7 * q^21 + 21 * q^22 + 25 * q^23 - 7 * q^24 + 2 * q^25 - 14 * q^26 - 7 * q^27 - 2 * q^28 + 13 * q^29 + 7 * q^30 - 7 * q^31 - 21 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 - 6 * q^36 + 13 * q^37 + 28 * q^38 - 7 * q^39 + 7 * q^40 - 19 * q^41 - 7 * q^42 - 29 * q^43 + 14 * q^44 - 7 * q^45 + 35 * q^46 - 29 * q^47 + 7 * q^48 - 22 * q^49 + 35 * q^50 + 21 * q^51 + 14 * q^52 + 19 * q^53 - 21 * q^54 + 21 * q^55 + 7 * q^56 + 28 * q^57 + 7 * q^58 - 11 * q^59 + 14 * q^60 + 21 * q^61 - 21 * q^62 - 3 * q^63 - 15 * q^64 + 21 * q^65 - 21 * q^66 - 35 * q^67 - 49 * q^70 - 7 * q^71 + 7 * q^72 - 35 * q^73 - 7 * q^75 - 16 * q^76 + 14 * q^78 + 35 * q^79 - 2 * q^81 + 35 * q^82 + 12 * q^83 - 7 * q^85 - 35 * q^86 - 21 * q^89 - 14 * q^90 - 7 * q^91 - 20 * q^92 + 14 * q^93 + 14 * q^94 - 56 * q^95 + 7 * q^96 - 37 * q^97 + 49 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

Coefficient data

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

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

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

$2$	0.846011	−	1.75676i	0.598220	−	1.24222i	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	0.846011	−	1.75676i	0.598220	−	1.24222i	0.951773	−	0.306802i	$-0.0992590\pi$
$3$	−0.376510	−	0.781831i	−0.217378	−	0.451391i	0.763553	−	0.645745i	$-0.223453\pi$
$3$	−0.376510	−	0.781831i	−0.217378	−	0.451391i	−0.980931	+	0.194354i	$0.937739\pi$
$4$	−1.12349	−	1.40881i	−0.561745	−	0.704406i
$5$	−1.82640	−	1.45650i	−0.816789	−	0.651368i	0.123272	−	0.992373i	$-0.460661\pi$
$5$	−1.82640	−	1.45650i	−0.816789	−	0.651368i	−0.940061	+	0.341005i	$0.889233\pi$
$6$	−1.69202			−0.690765
$7$	0.623490	−	0.300257i	0.235657	−	0.113486i	−0.312329	−	0.949974i	$-0.601109\pi$
$7$	0.623490	−	0.300257i	0.235657	−	0.113486i	0.547986	+	0.836488i	$0.315395\pi$
$8$	0.376510	−	0.0859360i	0.133116	−	0.0303830i
$9$	1.40097	−	1.75676i	0.466990	−	0.585586i
$10$	−4.10388	+	1.97632i	−1.29776	+	0.624968i
$11$	−1.73341	+	3.59945i	−0.522642	+	1.08528i	0.457907	+	0.889000i	$0.348599\pi$
$11$	−1.73341	+	3.59945i	−0.522642	+	1.08528i	−0.980549	+	0.196276i	$0.937115\pi$
$12$	−0.678448	+	1.40881i	−0.195851	+	0.406689i
$13$	−4.94989	−	1.12978i	−1.37285	−	0.313344i	−0.528409	−	0.848990i	$-0.677211\pi$
$13$	−4.94989	−	1.12978i	−1.37285	−	0.313344i	−0.844443	+	0.535646i	$0.820068\pi$
$14$		−	1.34934i		−	0.360627i
$15$	−0.451083	+	1.97632i	−0.116469	+	0.510284i
$16$	0.969501	−	4.24766i	0.242375	−	1.06191i
$17$	1.82640	+	1.45650i	0.442966	+	0.353254i	0.819432	−	0.573177i	$-0.194289\pi$
$17$	1.82640	+	1.45650i	0.442966	+	0.353254i	−0.376465	+	0.926431i	$0.622861\pi$
$18$	−1.90097	−	3.94740i	−0.448063	−	0.930412i
$19$	4.98792			1.14431			0.572153	−	0.820147i	$-0.306108\pi$
$19$	4.98792			1.14431			0.572153	+	0.820147i	$0.306108\pi$
$20$			4.20941i			0.941254i
$21$	−0.469501	−	0.374414i	−0.102453	−	0.0817039i
$22$	4.85690	+	6.09035i	1.03549	+	1.29847i
$23$	8.11745	+	3.90916i	1.69261	+	0.815116i	0.995137	+	0.0984998i	$0.0314044\pi$
$23$	8.11745	+	3.90916i	1.69261	+	0.815116i	0.697468	+	0.716616i	$0.254310\pi$
$24$	−0.208947	−	0.262012i	−0.0426512	−	0.0534829i
$25$	0.101720	+	0.445662i	0.0203439	+	0.0891325i
$26$	−6.17241	+	7.73995i	−1.21051	+	1.51793i
$27$	−4.43900	−	1.01317i	−0.854286	−	0.194985i
$28$	−1.12349	−	0.541044i	−0.212320	−	0.102248i
$29$	4.42543	+	2.13117i	0.821781	+	0.395749i	0.797026	−	0.603945i	$-0.206405\pi$
$29$	4.42543	+	2.13117i	0.821781	+	0.395749i	0.0247549	+	0.999694i	$0.492119\pi$
$30$	3.09030	+	2.46443i	0.564209	+	0.449942i
$31$	4.02930	−	8.36693i	0.723684	−	1.50275i	−0.135334	−	0.990800i	$-0.543211\pi$
$31$	4.02930	−	8.36693i	0.723684	−	1.50275i	0.859018	−	0.511946i	$-0.171075\pi$
$32$	−6.03803	−	4.81517i	−1.06738	−	0.851210i
$33$	3.46681			0.603495
$34$	4.10388	−	1.97632i	0.703809	−	0.338936i
$35$	−1.57606	−	0.359726i	−0.266404	−	0.0608049i
$36$	−4.04892			−0.674820
$37$	1.20895	+	5.29674i	0.198750	+	0.870779i	0.971682	+	0.236291i	$0.0759319\pi$
$37$	1.20895	+	5.29674i	0.198750	+	0.870779i	−0.772933	+	0.634488i	$0.781211\pi$
$38$	4.21983	−	8.76257i	0.684547	−	1.42148i
$39$	0.980386	+	4.29535i	0.156987	+	0.687807i
$40$	−0.812823	−	0.391435i	−0.128519	−	0.0618913i
$41$	−2.88740	+	3.62068i	−0.450935	+	0.565455i	−0.954389	−	0.298567i	$-0.903491\pi$
$41$	−2.88740	+	3.62068i	−0.450935	+	0.565455i	0.503453	+	0.864023i	$0.332063\pi$
$42$	−1.05496	+	0.508041i	−0.162784	+	0.0783924i
$43$	−7.31551	−	3.52296i	−1.11561	−	0.537247i	−0.217073	−	0.976155i	$-0.569651\pi$
$43$	−7.31551	−	3.52296i	−1.11561	−	0.537247i	−0.898532	+	0.438908i	$0.855365\pi$
$44$	7.01842	−	1.60191i	1.05807	−	0.241497i
$45$	−5.11745	+	1.16802i	−0.762864	+	0.174119i
$46$	13.7349	−	10.9532i	2.02510	−	1.61496i
$47$	0.306782	+	1.34410i	0.0447488	+	0.196057i	0.992361	−	0.123365i	$-0.0393685\pi$
$47$	0.306782	+	1.34410i	0.0447488	+	0.196057i	−0.947613	+	0.319422i	$0.896511\pi$
$48$	−3.68598	+	0.841301i	−0.532025	+	0.121431i
$49$	−4.06584	+	5.09841i	−0.580835	+	0.728344i
$50$	0.868977	+	0.198338i	0.122892	+	0.0280493i
$51$	0.451083	−	1.97632i	0.0631642	−	0.276740i
$52$	3.96950	+	8.24275i	0.550471	+	1.14306i
$53$	6.27144	+	7.86413i	0.861448	+	1.08022i	0.996003	+	0.0893159i	$0.0284681\pi$
$53$	6.27144	+	7.86413i	0.861448	+	1.08022i	−0.134555	+	0.990906i	$0.542961\pi$
$54$	−5.53534	+	6.94110i	−0.753265	+	0.944564i
$55$	8.40850	−	4.04932i	1.13380	−	0.546010i
$56$	0.208947	−	0.166630i	0.0279218	−	0.0222669i
$57$	−1.87800	−	3.89971i	−0.248747	−	0.516529i
$58$	7.48792	−	5.97142i	0.983212	−	0.784085i
$59$	0.425428	+	0.204875i	0.0553859	+	0.0266725i	0.461372	−	0.887207i	$-0.347357\pi$
$59$	0.425428	+	0.204875i	0.0553859	+	0.0266725i	−0.405986	+	0.913879i	$0.633072\pi$
$60$	3.29105	−	1.58489i	0.424873	−	0.204608i
$61$	1.46466	+	0.705341i	0.187530	+	0.0903097i	0.525293	−	0.850922i	$-0.323956\pi$
$61$	1.46466	+	0.705341i	0.187530	+	0.0903097i	−0.337763	+	0.941231i	$0.609670\pi$
$62$	−11.2899	−	14.1570i	−1.43381	−	1.79794i
$63$	0.346011	−	1.51597i	0.0435933	−	0.190995i
$64$	−5.71648	+	2.75291i	−0.714560	+	0.344114i
$65$	7.39493	+	9.27295i	0.917228	+	1.15017i
$66$	2.93296	−	6.09035i	0.361022	−	0.749671i
$67$	−11.1969	+	2.55561i	−1.36791	+	0.312218i	−0.842531	−	0.538648i	$-0.818935\pi$
$67$	−11.1969	+	2.55561i	−1.36791	+	0.312218i	−0.525384	+	0.850865i	$0.676078\pi$
$68$		−	4.20941i		−	0.510466i
$69$		−	7.81831i		−	0.941214i
$70$	−1.96532	+	2.46443i	−0.234901	+	0.294556i
$71$	3.18329	+	2.53859i	0.377787	+	0.301275i	0.793913	−	0.608032i	$-0.208041\pi$
$71$	3.18329	+	2.53859i	0.377787	+	0.301275i	−0.416125	+	0.909307i	$0.636612\pi$
$72$	0.376510	−	0.781831i	0.0443722	−	0.0921397i
$73$	−9.50484	+	2.16942i	−1.11246	+	0.253911i	−0.738980	−	0.673728i	$-0.764692\pi$
$73$	−9.50484	+	2.16942i	−1.11246	+	0.253911i	−0.373478	+	0.927639i	$0.621835\pi$
$74$	10.3279	+	2.35727i	1.20059	+	0.274027i
$75$	0.310134	−	0.247324i	0.0358112	−	0.0285585i
$76$	−5.60388	−	7.02704i	−0.642809	−	0.806056i
$77$			2.76469i			0.315066i
$78$	8.37531	+	1.91161i	0.948318	+	0.216447i
$79$	4.75571	−	3.79255i	0.535059	−	0.426695i	−0.318322	−	0.947983i	$-0.603119\pi$
$79$	4.75571	−	3.79255i	0.535059	−	0.426695i	0.853381	+	0.521287i	$0.174548\pi$
$80$	−7.95742	+	6.34583i	−0.889666	+	0.709485i
$81$	−0.620801	−	2.71991i	−0.0689779	−	0.302212i
$82$	3.91789	+	8.13559i	0.432659	+	0.898426i
$83$	−7.48188			−0.821243			−0.410621	−	0.911806i	$-0.634688\pi$
$83$	−7.48188			−0.821243			−0.410621	+	0.911806i	$0.634688\pi$
$84$			1.08209i			0.118066i
$85$	−1.21432	−	5.32030i	−0.131712	−	0.577068i
$86$	−12.3780	+	9.87113i	−1.33475	+	1.06443i
$87$		−	4.26235i		−	0.456972i
$88$	−0.343322	+	1.50419i	−0.0365983	+	0.160348i
$89$	1.91939	+	3.98565i	0.203455	+	0.422478i	0.977583	−	0.210551i	$-0.0675258\pi$
$89$	1.91939	+	3.98565i	0.203455	+	0.422478i	−0.774128	+	0.633029i	$0.781811\pi$
$90$	−2.27748	+	9.97829i	−0.240067	+	1.05180i
$91$	−3.42543	+	0.781831i	−0.359082	+	0.0819582i
$92$	−3.61260	−	15.8279i	−0.376640	−	1.65017i
$93$	−8.05861			−0.835639
$94$	2.62080	+	0.598181i	0.270315	+	0.0616976i
$95$	−9.10992	−	7.26492i	−0.934658	−	0.745365i
$96$	−1.49127	+	6.53368i	−0.152202	+	0.666841i
$97$	−4.19537	+	5.26083i	−0.425976	+	0.534157i	−0.947787	−	0.318904i	$-0.896685\pi$
$97$	−4.19537	+	5.26083i	−0.425976	+	0.534157i	0.521811	+	0.853061i	$0.325257\pi$
$98$	5.51693	+	11.4560i	0.557294	+	1.15723i
$99$	3.89493	+	8.08790i	0.391455	+	0.812865i
$100$	0.513574	−	0.644001i	0.0513574	−	0.0644001i
$101$	0.0108851	−	0.0476909i	0.00108311	−	0.00474542i	−0.974383	−	0.224893i	$-0.927797\pi$
$101$	0.0108851	−	0.0476909i	0.00108311	−	0.00474542i	0.975467	+	0.220148i	$0.0706539\pi$
$102$	−3.09030	−	2.46443i	−0.305985	−	0.244015i
$103$	4.94989	+	1.12978i	0.487727	+	0.111320i	0.459311	−	0.888276i	$-0.348096\pi$
$103$	4.94989	+	1.12978i	0.487727	+	0.111320i	0.0284162	+	0.999596i	$0.490954\pi$
$104$	−1.96077			−0.192269
$105$	0.312159	+	1.36766i	0.0304636	+	0.133470i
$106$	19.1211	−	4.36427i	1.85721	−	0.423895i
$107$	−2.30678	+	10.1067i	−0.223005	+	0.977049i	0.732197	+	0.681093i	$0.238495\pi$
$107$	−2.30678	+	10.1067i	−0.223005	+	0.977049i	−0.955202	+	0.295956i	$0.904362\pi$
$108$	3.55980	+	7.39201i	0.342542	+	0.711296i
$109$	−0.367781	+	1.61135i	−0.0352270	+	0.154340i	−0.989482	−	0.144653i	$-0.953793\pi$
$109$	−0.367781	+	1.61135i	−0.0352270	+	0.154340i	0.954255	+	0.298993i	$0.0966506\pi$
$110$		−	18.1975i		−	1.73506i
$111$	3.68598	−	2.93947i	0.349858	−	0.279002i
$112$	−0.670915	−	2.93947i	−0.0633955	−	0.277754i
$113$		−	12.9379i		−	1.21710i	−0.793516	−	0.608550i	$-0.791752\pi$
$113$		−	12.9379i		−	1.21710i	0.793516	−	0.608550i	$-0.208248\pi$
$114$	−8.43967			−0.790447
$115$	−9.13198	−	18.9628i	−0.851562	−	1.76829i
$116$	−1.96950	−	8.62895i	−0.182864	−	0.801177i
$117$	−8.91939	+	7.11297i	−0.824598	+	0.657595i
$118$	0.719833	−	0.574047i	0.0662660	−	0.0528453i
$119$	1.57606	+	0.359726i	0.144478	+	0.0329761i
$120$			0.782870i			0.0714659i
$121$	−3.09299	−	3.87849i	−0.281181	−	0.352590i
$122$	2.47823	−	1.97632i	0.224368	−	0.178928i
$123$	3.91789	+	0.894234i	0.353265	+	0.0806304i
$124$	−16.3143	+	3.72364i	−1.46507	+	0.334392i
$125$	−4.60454	+	9.56142i	−0.411843	+	0.855200i
$126$	−2.37047	−	1.89039i	−0.211178	−	0.168409i
$127$	−4.96346	+	6.22398i	−0.440436	+	0.552289i	−0.951658	−	0.307160i	$-0.900621\pi$
$127$	−4.96346	+	6.22398i	−0.440436	+	0.552289i	0.511222	+	0.859449i	$0.329193\pi$
$128$		−	3.07439i		−	0.271741i
$129$			7.04593i			0.620359i
$130$	22.5465	−	5.14610i	1.97746	−	0.451343i
$131$	8.12953	−	16.8811i	0.710280	−	1.47491i	−0.162454	−	0.986716i	$-0.551941\pi$
$131$	8.12953	−	16.8811i	0.710280	−	1.47491i	0.872734	−	0.488196i	$-0.162345\pi$
$132$	−3.89493	−	4.88409i	−0.339010	−	0.425105i
$133$	3.10992	−	1.49766i	0.269664	−	0.129863i
$134$	−4.98307	+	21.8323i	−0.430472	+	1.88602i
$135$	6.63169	+	8.31587i	0.570765	+	0.715716i
$136$	0.812823	+	0.391435i	0.0696990	+	0.0335653i
$137$	−13.2545	+	6.38304i	−1.13241	+	0.545340i	−0.903705	−	0.428156i	$-0.859163\pi$
$137$	−13.2545	+	6.38304i	−1.13241	+	0.545340i	−0.228705	+	0.973496i	$0.573449\pi$
$138$	−13.7349	−	6.61438i	−1.16919	−	0.563053i
$139$	10.3693	−	8.26922i	0.879510	−	0.701386i	−0.0757582	−	0.997126i	$-0.524138\pi$
$139$	10.3693	−	8.26922i	0.879510	−	0.701386i	0.955268	+	0.295740i	$0.0955663\pi$
$140$	1.26391	+	2.62453i	0.106820	+	0.221813i
$141$	0.935353	−	0.745919i	0.0787709	−	0.0628177i
$142$	7.15279	−	3.44460i	0.600249	−	0.289065i
$143$	12.6468	−	15.8585i	1.05757	−	1.32616i
$144$	−6.10388	−	7.65402i	−0.508656	−	0.637835i
$145$	−4.97853	−	10.3380i	−0.413444	−	0.858525i
$146$	−4.23005	+	18.5331i	−0.350082	+	1.53381i
$147$	5.51693	+	1.25920i	0.455028	+	0.103857i
$148$	6.10388	−	7.65402i	0.501735	−	0.629156i
$149$	−10.2947	+	2.34970i	−0.843375	+	0.192495i	−0.622316	−	0.782766i	$-0.713808\pi$
$149$	−10.2947	+	2.34970i	−0.843375	+	0.192495i	−0.221058	+	0.975261i	$0.570951\pi$
$150$	−0.172112	−	0.754070i	−0.0140529	−	0.0615696i
$151$	6.26175	−	4.99358i	0.509574	−	0.406372i	−0.334666	−	0.942337i	$-0.608624\pi$
$151$	6.26175	−	4.99358i	0.509574	−	0.406372i	0.844240	+	0.535965i	$0.180052\pi$
$152$	1.87800	−	0.428642i	0.152326	−	0.0347674i
$153$	5.11745	−	1.16802i	0.413721	−	0.0944292i
$154$	4.85690	+	2.33896i	0.391380	+	0.188479i
$155$	−19.5456	+	9.41265i	−1.56994	+	0.756042i
$156$	4.94989	−	6.20696i	0.396308	−	0.496955i
$157$	9.18814	+	4.42477i	0.733293	+	0.353135i	0.762978	−	0.646424i	$-0.223736\pi$
$157$	9.18814	+	4.42477i	0.733293	+	0.353135i	−0.0296853	+	0.999559i	$0.509451\pi$
$158$	−2.63922	−	11.5632i	−0.209965	−	0.919917i
$159$	3.78717	−	7.86413i	0.300342	−	0.623666i
$160$	4.01453	+	17.5888i	0.317377	+	1.39052i
$161$	6.23490			0.491379
$162$	−5.30343	−	1.21047i	−0.416677	−	0.0951038i
$163$	21.7974	−	10.4971i	1.70730	−	0.822194i	0.714891	−	0.699235i	$-0.246476\pi$
$163$	21.7974	−	10.4971i	1.70730	−	0.822194i	0.992412	−	0.122958i	$-0.0392382\pi$
$164$	8.34481			0.651621
$165$	−6.33177	−	5.04942i	−0.492928	−	0.393097i
$166$	−6.32975	+	13.1439i	−0.491284	+	1.02016i
$167$	−1.55765	−	1.24218i	−0.120534	−	0.0961229i	0.561367	−	0.827567i	$-0.310275\pi$
$167$	−1.55765	−	1.24218i	−0.120534	−	0.0961229i	−0.681902	+	0.731444i	$0.738847\pi$
$168$	−0.208947	−	0.100624i	−0.0161206	−	0.00776329i
$169$	11.5124	+	5.54407i	0.885567	+	0.426467i
$170$	−10.3738	−	2.36776i	−0.795636	−	0.181599i
$171$	6.98792	−	8.76257i	0.534379	−	0.670091i
$172$	3.25571	+	14.2642i	0.248245	+	1.08763i
$173$	−11.9363	−	14.9677i	−0.907501	−	1.13797i	−0.989956	−	0.141376i	$-0.954847\pi$
$173$	−11.9363	−	14.9677i	−0.907501	−	1.13797i	0.0824550	−	0.996595i	$-0.473724\pi$
$174$	−7.48792	−	3.60599i	−0.567658	−	0.273370i
$175$	0.197234	+	0.247324i	0.0149095	+	0.0186959i
$176$	13.6087	+	10.8526i	1.02580	+	0.818045i
$177$		−	0.409750i		−	0.0307987i
$178$	8.62565			0.646519
$179$	−2.56920	−	5.33499i	−0.192031	−	0.398756i	0.782616	−	0.622505i	$-0.213885\pi$
$179$	−2.56920	−	5.33499i	−0.192031	−	0.398756i	−0.974647	+	0.223749i	$0.928171\pi$
$180$	7.39493	+	5.89726i	0.551185	+	0.439556i
$181$	−4.64191	+	20.3375i	−0.345030	+	1.51168i	0.443271	+	0.896387i	$0.353818\pi$
$181$	−4.64191	+	20.3375i	−0.345030	+	1.51168i	−0.788302	+	0.615289i	$0.789039\pi$
$182$	−1.52446	+	6.67909i	−0.113000	+	0.495087i
$183$		−	1.41068i		−	0.104281i
$184$	3.39224	+	0.774257i	0.250079	+	0.0570790i
$185$	5.50670	−	11.4348i	0.404861	−	0.840703i
$186$	−6.81767	+	14.1570i	−0.499896	+	1.03804i
$187$	−8.40850	+	4.04932i	−0.614891	+	0.296116i
$188$	1.54892	−	1.94228i	0.112966	−	0.141655i
$189$	−3.07188	+	0.701137i	−0.223447	+	0.0510002i
$190$	−20.4698	+	9.85773i	−1.48504	+	0.715155i
$191$	−3.70171			−0.267846			−0.133923	−	0.990992i	$-0.542758\pi$
$191$	−3.70171			−0.267846			−0.133923	+	0.990992i	$0.542758\pi$
$192$	4.30463	+	3.43282i	0.310660	+	0.247743i
$193$	−12.4031	−	15.5530i	−0.892796	−	1.11953i	−0.992221	−	0.124486i	$-0.960272\pi$
$193$	−12.4031	−	15.5530i	−0.892796	−	1.11953i	0.0994249	−	0.995045i	$-0.468300\pi$
$194$	5.69269	+	11.8210i	0.408711	+	0.848697i
$195$	4.46562	−	9.27295i	0.319789	−	0.664049i
$196$	11.7506			0.839331
$197$	14.0315	−	0.343744i	0.999700	−	0.0244907i
$197$	14.0315	−	0.343744i	0.999700	−	0.0244907i
$198$	17.5036			1.24393
$199$	−8.85301	+	18.3835i	−0.627573	+	1.30317i	0.308453	+	0.951240i	$0.400189\pi$
$199$	−8.85301	+	18.3835i	−0.627573	+	1.30317i	−0.936026	+	0.351930i	$0.885526\pi$
$200$	0.0765969	+	0.159055i	0.00541622	+	0.0112469i
$201$	6.21379	+	7.79185i	0.438287	+	0.549595i
$202$	−0.0745725	−	0.0594696i	−0.00524690	−	0.00418426i
$203$	3.39911			0.238571
$204$	−3.29105	+	1.58489i	−0.230420	+	0.110964i
$205$	10.5471	−	2.40730i	0.736638	−	0.168133i
$206$	6.17241	−	7.73995i	0.430052	−	0.539268i
$207$	18.2397	−	8.78380i	1.26775	−	0.610516i
$208$	−9.59783	+	19.9301i	−0.665490	+	1.38190i
$209$	−8.64609	+	17.9538i	−0.598062	+	1.24189i
$210$	2.66673	+	0.608665i	0.184022	+	0.0420019i
$211$			20.8903i			1.43815i	0.694932	+	0.719075i	$0.255434\pi$
$211$			20.8903i			1.43815i	−0.694932	+	0.719075i	$0.744566\pi$
$212$	4.03319	−	17.6706i	0.277000	−	1.21362i
$213$	0.786208	−	3.44460i	0.0538701	−	0.236020i
$214$	15.8034	+	12.6028i	1.08030	+	0.861511i
$215$	8.22982	+	17.0894i	0.561269	+	1.16549i
$216$	−1.75840			−0.119644
$217$		−	6.42652i		−	0.436261i
$218$	2.51961	+	2.00933i	0.170650	+	0.136089i
$219$	5.27479	+	6.61438i	0.356437	+	0.446958i
$220$	−15.1516	−	7.29662i	−1.02152	−	0.491938i
$221$	−7.39493	−	9.27295i	−0.497437	−	0.623766i
$222$	−2.04556	−	8.96221i	−0.137289	−	0.601504i
$223$	8.28650	−	10.3909i	0.554905	−	0.695829i	−0.422702	−	0.906269i	$-0.638918\pi$
$223$	8.28650	−	10.3909i	0.554905	−	0.695829i	0.977607	+	0.210440i	$0.0674896\pi$
$224$	−5.21044	−	1.18925i	−0.348137	−	0.0794600i
$225$	0.925428	+	0.445662i	0.0616952	+	0.0297108i
$226$	−22.7289	−	10.9456i	−1.51190	−	0.728093i
$227$	−4.75571	−	3.79255i	−0.315647	−	0.251720i	0.452831	−	0.891597i	$-0.350414\pi$
$227$	−4.75571	−	3.79255i	−0.315647	−	0.251720i	−0.768478	+	0.639876i	$0.778986\pi$
$228$	−3.38404	+	7.02704i	−0.224114	+	0.465377i
$229$	−5.29321	−	4.22119i	−0.349785	−	0.278944i	0.432797	−	0.901491i	$-0.357527\pi$
$229$	−5.29321	−	4.22119i	−0.349785	−	0.278944i	−0.782582	+	0.622547i	$0.786098\pi$
$230$	−41.0388			−2.70602
$231$	2.16152	−	1.04093i	0.142218	−	0.0684884i
$232$	1.84936	+	0.422105i	0.121417	+	0.0277126i
$233$	4.14138			0.271311			0.135655	−	0.990756i	$-0.456686\pi$
$233$	4.14138			0.271311			0.135655	+	0.990756i	$0.456686\pi$
$234$	4.94989	+	21.6869i	0.323584	+	1.41771i
$235$	1.39738	−	2.90169i	0.0911550	−	0.189285i
$236$	−0.189333	−	0.829522i	−0.0123245	−	0.0539973i
$237$	−4.75571	−	2.29023i	−0.308916	−	0.148766i
$238$	1.96532	−	2.46443i	0.127393	−	0.159746i
$239$	19.5993	−	9.43854i	1.26778	−	0.610528i	0.325555	−	0.945523i	$-0.394449\pi$
$239$	19.5993	−	9.43854i	1.26778	−	0.610528i	0.942220	+	0.334995i	$0.108735\pi$
$240$	7.95742	+	3.83209i	0.513649	+	0.247360i
$241$	21.3654	−	4.87651i	1.37627	−	0.314124i	0.530503	−	0.847683i	$-0.322003\pi$
$241$	21.3654	−	4.87651i	1.37627	−	0.314124i	0.845763	+	0.533559i	$0.179146\pi$
$242$	−9.43027	+	2.15240i	−0.606201	+	0.138361i
$243$	−12.5722	+	10.0260i	−0.806506	+	0.643167i
$244$	−0.651833	−	2.85587i	−0.0417294	−	0.182828i
$245$	14.8517	−	3.38980i	0.948839	−	0.216566i
$246$	4.88553	−	6.12627i	0.311490	−	0.390597i
$247$	−24.6896	−	5.63525i	−1.57096	−	0.358562i
$248$	0.798053	−	3.49650i	0.0506764	−	0.222028i
$249$	2.81700	+	5.84957i	0.178520	+	0.370701i
$250$	12.9016	+	16.1781i	0.815971	+	1.02320i
$251$	−4.08546	+	5.12300i	−0.257872	+	0.323361i	−0.893867	−	0.448332i	$-0.852018\pi$
$251$	−4.08546	+	5.12300i	−0.257872	+	0.323361i	0.635995	+	0.771693i	$0.280590\pi$
$252$	−2.52446	+	1.21572i	−0.159026	+	0.0765829i
$253$	−28.1417	+	22.4422i	−1.76925	+	1.41093i
$254$	6.73490	+	13.9852i	0.422585	+	0.877507i
$255$	−3.70237	+	2.95254i	−0.231852	+	0.184896i
$256$	−16.8339	−	8.10679i	−1.05212	−	0.506675i
$257$	−10.3959	+	5.00640i	−0.648478	+	0.312290i	−0.729052	−	0.684458i	$-0.760039\pi$
$257$	−10.3959	+	5.00640i	−0.648478	+	0.312290i	0.0805744	+	0.996749i	$0.474325\pi$
$258$	12.3780	+	5.96093i	0.770621	+	0.371111i
$259$	2.34415	+	2.93947i	0.145658	+	0.182650i
$260$	4.75571	−	20.8361i	0.294937	−	1.29220i
$261$	9.94385	−	4.78870i	0.615509	−	0.296413i
$262$	−22.7784	−	28.5633i	−1.40726	−	1.76464i
$263$	2.40366	−	4.99125i	0.148216	−	0.307773i	−0.813622	−	0.581395i	$-0.802507\pi$
$263$	2.40366	−	4.99125i	0.148216	−	0.307773i	0.961837	+	0.273621i	$0.0882215\pi$
$264$	1.30529	−	0.297924i	0.0803351	−	0.0183360i
$265$		−	23.4974i		−	1.44343i
$266$		−	6.73041i		−	0.412668i
$267$	2.39344	−	3.00127i	0.146476	−	0.183675i
$268$	16.1799	+	12.9031i	0.988347	+	0.788181i
$269$	1.66703	−	3.46162i	0.101641	−	0.211059i	−0.843947	−	0.536427i	$-0.819774\pi$
$269$	1.66703	−	3.46162i	0.101641	−	0.211059i	0.945588	+	0.325368i	$0.105488\pi$
$270$	20.2195	−	4.61496i	1.23052	−	0.280858i
$271$	−7.43176	−	1.69625i	−0.451448	−	0.103040i	−0.00924914	−	0.999957i	$-0.502944\pi$
$271$	−7.43176	−	1.69625i	−0.451448	−	0.103040i	−0.442198	+	0.896917i	$0.645801\pi$
$272$	7.95742	−	6.34583i	0.482489	−	0.384772i
$273$	1.90097	+	2.38374i	0.115052	+	0.144270i
$274$			28.6851i			1.73293i
$275$	−1.78046	−	0.406379i	−0.107366	−	0.0245056i
$276$	−11.0145	+	8.78380i	−0.662997	+	0.528722i
$277$	−1.67725	+	1.33756i	−0.100776	+	0.0803664i	−0.672582	−	0.740023i	$-0.734815\pi$
$277$	−1.67725	+	1.33756i	−0.100776	+	0.0803664i	0.571805	+	0.820389i	$0.306243\pi$
$278$	−5.75451	−	25.2122i	−0.345133	−	1.51213i
$279$	−9.05376	−	18.8003i	−0.542035	−	1.12555i
$280$	−0.624318			−0.0373101
$281$			13.1968i			0.787255i	0.919270	+	0.393627i	$0.128780\pi$
$281$			13.1968i			0.787255i	−0.919270	+	0.393627i	$0.871220\pi$
$282$	−0.519082	−	2.27425i	−0.0309109	−	0.135429i
$283$	11.7557	−	9.37486i	0.698804	−	0.557278i	−0.208361	−	0.978052i	$-0.566813\pi$
$283$	11.7557	−	9.37486i	0.698804	−	0.557278i	0.907165	+	0.420774i	$0.138241\pi$
$284$		−	7.33674i		−	0.435355i
$285$	−2.24996	+	9.85773i	−0.133276	+	0.583922i
$286$	−17.1603	−	35.6338i	−1.01471	−	2.10707i
$287$	−0.713128	+	3.12442i	−0.0420946	+	0.184428i
$288$	−16.9182	+	3.86147i	−0.996914	+	0.227539i
$289$	−2.56853	−	11.2535i	−0.151090	−	0.661969i
$290$	−22.3733			−1.31380
$291$	5.69269	+	1.29932i	0.333711	+	0.0761674i
$292$	13.7349	+	10.9532i	0.803774	+	0.640988i
$293$	1.37316	−	6.01620i	0.0802207	−	0.351470i	−0.918848	−	0.394611i	$-0.870879\pi$
$293$	1.37316	−	6.01620i	0.0802207	−	0.351470i	0.999069	+	0.0431410i	$0.0137365\pi$
$294$	6.87949	−	8.62661i	0.401220	−	0.503114i
$295$	−0.478598	−	0.993819i	−0.0278651	−	0.0578624i
$296$	0.910362	+	1.89039i	0.0529137	+	0.109876i
$297$	11.3415	−	14.2217i	0.658098	−	0.825229i
$298$	−4.58157	+	20.0732i	−0.265403	+	1.16281i
$299$	−35.7640	−	28.5208i	−2.06828	−	1.64940i
$300$	−0.696866	−	0.159055i	−0.0402336	−	0.00918305i
$301$	−5.61894			−0.323870
$302$	−3.47501	−	15.2250i	−0.199964	−	0.876101i
$303$	−0.0413846	+	0.00944576i	−0.00237748	+	0.000542645i
$304$	4.83579	−	21.1870i	0.277352	−	1.21516i
$305$	−1.64771	−	3.42151i	−0.0943477	−	0.195915i
$306$	2.27748	−	9.97829i	0.130195	−	0.570421i
$307$			13.0909i			0.747139i	0.927602	+	0.373569i	$0.121866\pi$
$307$			13.0909i			0.747139i	−0.927602	+	0.373569i	$0.878134\pi$
$308$	3.89493	−	3.10610i	0.221934	−	0.176987i
$309$	−0.980386	−	4.29535i	−0.0557722	−	0.244354i
$310$			42.3001i			2.40248i
$311$	−10.3961			−0.589510			−0.294755	−	0.955573i	$-0.595238\pi$
$311$	−10.3961			−0.589510			−0.294755	+	0.955573i	$0.595238\pi$
$312$	0.738250	+	1.53299i	0.0417952	+	0.0867886i
$313$	−6.40462	−	28.0605i	−0.362010	−	1.58607i	−0.748085	−	0.663603i	$-0.769026\pi$
$313$	−6.40462	−	28.0605i	−0.362010	−	1.58607i	0.386074	−	0.922468i	$-0.373831\pi$
$314$	15.5465	−	12.3979i	0.877341	−	0.699656i
$315$	−2.83997	+	2.26480i	−0.160014	+	0.127607i
$316$	−10.6860	−	2.43901i	−0.601133	−	0.137205i
$317$			20.9113i			1.17450i	0.809407	+	0.587248i	$0.199789\pi$
$317$			20.9113i			1.17450i	−0.809407	+	0.587248i	$0.800211\pi$
$318$	−10.6114	−	13.3063i	−0.595058	−	0.746179i
$319$	−15.3421	+	12.2349i	−0.858994	+	0.685025i
$320$	14.4502	+	3.29816i	0.807790	+	0.184373i
$321$	8.77024	−	2.00175i	0.489507	−	0.111727i
$322$	5.27479	−	10.9532i	0.293953	−	0.610399i
$323$	9.10992	+	7.26492i	0.506889	+	0.404231i
$324$	−3.13437	+	3.93038i	−0.174132	+	0.218355i
$325$		−	2.32090i		−	0.128740i
$326$		−	47.1734i		−	2.61269i
$327$	1.39828	−	0.319148i	0.0773251	−	0.0176489i
$328$	−0.775987	+	1.61135i	−0.0428467	+	0.0889721i
$329$	0.594851	+	0.745919i	0.0327952	+	0.0411239i
$330$	−14.2274	+	6.85154i	−0.783191	+	0.377165i
$331$	−2.00120	+	8.76781i	−0.109996	+	0.481923i	0.889683	+	0.456579i	$0.150925\pi$
$331$	−2.00120	+	8.76781i	−0.109996	+	0.481923i	−0.999679	+	0.0253441i	$0.991932\pi$
$332$	8.40581	+	10.5406i	0.461329	+	0.578488i
$333$	10.9988	+	5.29674i	0.602731	+	0.290260i
$334$	−3.50000	+	1.68551i	−0.191511	+	0.0922271i
$335$	24.1722	+	11.6407i	1.32067	+	0.636000i
$336$	−2.04556	+	1.63128i	−0.111595	+	0.0889938i
$337$	−4.04570	−	8.40098i	−0.220383	−	0.457630i	0.761237	−	0.648473i	$-0.224592\pi$
$337$	−4.04570	−	8.40098i	−0.220383	−	0.457630i	−0.981621	+	0.190843i	$0.938878\pi$
$338$	19.4792	−	15.5341i	1.05953	−	0.844946i
$339$	−10.1153	+	4.87127i	−0.549387	+	0.264571i
$340$	−6.13102	+	7.68806i	−0.332501	+	0.416944i
$341$	23.1320	+	29.0066i	1.25267	+	1.57079i
$342$	−9.48188	−	19.6893i	−0.512721	−	1.06468i
$343$	−2.08211	+	9.12230i	−0.112423	+	0.492558i
$344$	−3.05711	−	0.697766i	−0.164829	−	0.0376210i
$345$	−11.3874	+	14.2793i	−0.613077	+	0.768774i
$346$	−36.3928	+	8.30643i	−1.95649	+	0.446556i
$347$	1.92035	+	8.41359i	0.103090	+	0.451665i	0.999956	+	0.00936379i	$0.00298063\pi$
$347$	1.92035	+	8.41359i	0.103090	+	0.451665i	−0.896867	+	0.442301i	$0.854162\pi$
$348$	−6.00484	+	4.78870i	−0.321893	+	0.256701i
$349$	−3.62983	+	0.828484i	−0.194300	+	0.0443477i	−0.318563	−	0.947902i	$-0.603200\pi$
$349$	−3.62983	+	0.828484i	−0.194300	+	0.0443477i	0.124263	+	0.992249i	$0.460343\pi$
$350$	0.601351	−	0.137254i	0.0321436	−	0.00733656i
$351$	20.8279	+	10.0302i	1.11171	+	0.535372i
$352$	27.7983	−	13.3870i	1.48166	−	0.713528i
$353$	−19.6109	+	24.5913i	−1.04378	+	1.30886i	−0.0941276	+	0.995560i	$0.530006\pi$
$353$	−19.6109	+	24.5913i	−1.04378	+	1.30886i	−0.949654	+	0.313301i	$0.898565\pi$
$354$	−0.719833	−	0.346653i	−0.0382587	−	0.0184244i
$355$	−2.11649	−	9.27295i	−0.112332	−	0.492157i
$356$	3.45862	−	7.18189i	0.183306	−	0.380639i
$357$	−0.312159	−	1.36766i	−0.0165212	−	0.0723841i
$358$	−11.5459			−0.610218
$359$	−4.16003	−	0.949500i	−0.219558	−	0.0501127i	0.111327	−	0.993784i	$-0.464490\pi$
$359$	−4.16003	−	0.949500i	−0.219558	−	0.0501127i	−0.330885	+	0.943671i	$0.607347\pi$
$360$	−1.82640	+	0.879546i	−0.0962595	+	0.0463562i
$361$	5.87933			0.309438
$362$	31.8010	+	25.3605i	1.67143	+	1.33292i
$363$	−1.86778	+	3.87849i	−0.0980331	+	0.203568i
$364$	4.94989	+	3.94740i	0.259445	+	0.206900i
$365$	20.5194	+	9.88161i	1.07403	+	0.517227i
$366$	−2.47823	−	1.19345i	−0.129539	−	0.0623828i
$367$	21.3949	+	4.88325i	1.11681	+	0.254904i	0.740808	−	0.671717i	$-0.234443\pi$
$367$	21.3949	+	4.88325i	1.11681	+	0.254904i	0.375998	+	0.926620i	$0.377300\pi$
$368$	24.4746	−	30.6902i	1.27583	−	1.59984i
$369$	2.31551	+	10.1449i	0.120541	+	0.528123i
$370$	−15.4294	−	19.3479i	−0.802139	−	1.00585i
$371$	6.27144	+	3.02017i	0.325597	+	0.156799i
$372$	9.05376	+	11.3531i	0.469416	+	0.588629i
$373$	−20.7533	−	16.5502i	−1.07457	−	0.856938i	−0.0843437	−	0.996437i	$-0.526879\pi$
$373$	−20.7533	−	16.5502i	−1.07457	−	0.856938i	−0.990222	+	0.139499i	$0.955451\pi$
$374$			18.1975i			0.940969i
$375$	9.20908			0.475555
$376$	0.231013	+	0.479704i	0.0119136	+	0.0247388i
$377$	−19.4976	−	15.5488i	−1.00418	−	0.800805i
$378$	−1.36712	+	5.98973i	−0.0703169	+	0.308079i
$379$	−1.27532	+	5.58756i	−0.0655089	+	0.287013i	−0.997063	−	0.0765903i	$-0.975597\pi$
$379$	−1.27532	+	5.58756i	−0.0655089	+	0.287013i	0.931554	+	0.363604i	$0.118454\pi$
$380$			20.9962i			1.07708i
$381$	6.73490	+	1.53720i	0.345039	+	0.0787530i
$382$	−3.13169	+	6.50301i	−0.160231	+	0.332723i
$383$	−7.74847	+	16.0899i	−0.395928	+	0.822154i	0.603759	+	0.797167i	$0.293669\pi$
$383$	−7.74847	+	16.0899i	−0.395928	+	0.822154i	−0.999688	+	0.0249872i	$0.992046\pi$
$384$	−2.40366	+	1.15754i	−0.122661	+	0.0590705i
$385$	4.02678	−	5.04942i	0.205224	−	0.257342i
$386$	−37.8161	+	8.63128i	−1.92479	+	0.439321i
$387$	−16.4378	+	7.91603i	−0.835581	+	0.402394i
$388$	12.1250			0.615553
$389$	1.30529	+	1.04093i	0.0661808	+	0.0527775i	0.656022	−	0.754742i	$-0.272238\pi$
$389$	1.30529	+	1.04093i	0.0661808	+	0.0527775i	−0.589841	+	0.807520i	$0.700809\pi$
$390$	−12.5124	−	15.6900i	−0.633589	−	0.794495i
$391$	9.13198	+	18.9628i	0.461824	+	0.958988i
$392$	−1.09269	+	2.26900i	−0.0551894	+	0.114602i
$393$	−16.2591			−0.820161
$394$	11.2669	−	24.9407i	0.567618	−	1.25649i
$395$	−14.2097			−0.714966
$396$	7.01842	−	14.5739i	0.352689	−	0.732366i
$397$	−13.7267	−	28.5038i	−0.688923	−	1.43056i	−0.892291	−	0.451462i	$-0.850903\pi$
$397$	−13.7267	−	28.5038i	−0.688923	−	1.43056i	0.203367	−	0.979103i	$-0.434811\pi$
$398$	24.8056	+	31.1052i	1.24339	+	1.55916i
$399$	−2.34183	−	1.86755i	−0.117238	−	0.0934943i
$400$	1.99164			0.0995820
$401$	26.7756	−	12.8945i	1.33711	−	0.643919i	0.377699	−	0.925928i	$-0.376715\pi$
$401$	26.7756	−	12.8945i	1.33711	−	0.643919i	0.959412	+	0.282010i	$0.0910011\pi$
$402$	18.9453	−	4.32415i	0.944908	−	0.215669i
$403$	−29.3974	+	36.8631i	−1.46439	+	1.83628i
$404$	−0.0794168	+	0.0382451i	−0.00395113	+	0.00190277i
$405$	−2.82772	+	5.87183i	−0.140511	+	0.291774i
$406$	2.87568	−	5.97142i	0.142718	−	0.296356i
$407$	−21.1610	−	4.82986i	−1.04891	−	0.239407i
$408$		−	0.782870i		−	0.0387578i
$409$	−7.94989	+	34.8307i	−0.393097	+	1.72227i	0.260543	+	0.965462i	$0.416099\pi$
$409$	−7.94989	+	34.8307i	−0.393097	+	1.72227i	−0.653639	+	0.756806i	$0.726759\pi$
$410$	4.69388	−	20.5652i	0.231814	−	1.01564i
$411$	9.98092	+	7.95952i	0.492322	+	0.392614i
$412$	−3.96950	−	8.24275i	−0.195563	−	0.406091i
$413$	0.326765			0.0160790
$414$		−	39.4740i		−	1.94004i
$415$	13.6649	+	10.8974i	0.670782	+	0.534931i
$416$	24.4475	+	30.6562i	1.19864	+	1.50304i
$417$	−10.3693	−	4.99358i	−0.507785	−	0.244537i
$418$	24.2258	+	30.3782i	1.18492	+	1.48585i
$419$	2.22641	+	9.75452i	0.108767	+	0.476540i	0.999747	+	0.0224967i	$0.00716154\pi$
$419$	2.22641	+	9.75452i	0.108767	+	0.476540i	−0.890980	+	0.454043i	$0.849981\pi$
$420$	1.57606	−	1.97632i	0.0769041	−	0.0964347i
$421$	15.1020	+	3.44694i	0.736027	+	0.167993i	0.574072	−	0.818805i	$-0.305363\pi$
$421$	15.1020	+	3.44694i	0.736027	+	0.167993i	0.161955	+	0.986798i	$0.448220\pi$
$422$	36.6993	+	17.6735i	1.78649	+	0.860331i
$423$	2.79105	+	1.34410i	0.135706	+	0.0653524i
$424$	3.03707	+	2.42198i	0.147493	+	0.117622i
$425$	−0.463328	+	0.962111i	−0.0224747	+	0.0466692i
$426$	−5.38620	−	4.29535i	−0.260962	−	0.208110i
$427$	1.12498			0.0544417
$428$	16.8300	−	8.10492i	0.813511	−	0.391766i
$429$	−17.1603	−	3.91673i	−0.828508	−	0.189102i
$430$	36.9845			1.78355
$431$	0.651596	+	2.85483i	0.0313863	+	0.137512i	0.988194	−	0.153211i	$-0.0489613\pi$
$431$	0.651596	+	2.85483i	0.0313863	+	0.137512i	−0.956807	+	0.290723i	$0.906104\pi$
$432$	−8.60723	+	17.8731i	−0.414115	+	0.859920i
$433$	−7.10978	−	31.1500i	−0.341674	−	1.49697i	−0.795539	−	0.605903i	$-0.792812\pi$
$433$	−7.10978	−	31.1500i	−0.341674	−	1.49697i	0.453864	−	0.891071i	$-0.350045\pi$
$434$	−11.2899	−	5.43691i	−0.541930	−	0.260980i
$435$	−6.20812	+	7.78474i	−0.297657	+	0.373249i
$436$	2.68329	−	1.29221i	0.128506	−	0.0618854i
$437$	40.4892	+	19.4986i	1.93686	+	0.932743i
$438$	16.0824	−	3.67070i	0.768447	−	0.175393i
$439$	−13.2240	+	3.01829i	−0.631148	+	0.144055i	−0.526115	−	0.850413i	$-0.676352\pi$
$439$	−13.2240	+	3.01829i	−0.631148	+	0.144055i	−0.105033	+	0.994469i	$0.533495\pi$
$440$	2.81790	−	2.24720i	0.134338	−	0.107131i
$441$	3.26055	+	14.2854i	0.155264	+	0.680258i
$442$	−22.5465	+	5.14610i	−1.07243	+	0.244775i
$443$	−12.6773	+	15.8968i	−0.602314	+	0.755278i	−0.985737	−	0.168295i	$-0.946174\pi$
$443$	−12.6773	+	15.8968i	−0.602314	+	0.755278i	0.383422	+	0.923573i	$0.374745\pi$
$444$	−8.28232	−	1.89039i	−0.393062	−	0.0897138i
$445$	2.29954	−	10.0750i	0.109009	−	0.477599i
$446$	−11.2439	−	23.3482i	−0.532415	−	1.10557i
$447$	5.71313	+	7.16404i	0.270222	+	0.338847i
$448$	−2.73759	+	3.43282i	−0.129339	+	0.162186i
$449$	−21.5896	+	10.3970i	−1.01888	+	0.490666i	−0.867303	−	0.497780i	$-0.834149\pi$
$449$	−21.5896	+	10.3970i	−1.01888	+	0.490666i	−0.151575	+	0.988446i	$0.548434\pi$
$450$	1.56584	−	1.24872i	0.0738146	−	0.0588651i
$451$	−8.02744	−	16.6692i	−0.377998	−	0.784920i
$452$	−18.2271	+	14.5356i	−0.857332	+	0.683699i
$453$	−6.26175	−	3.01550i	−0.294203	−	0.141681i
$454$	−10.6860	+	5.14610i	−0.501518	+	0.241518i
$455$	7.39493	+	3.56121i	0.346680	+	0.166952i
$456$	−1.04221	−	1.30689i	−0.0488061	−	0.0612009i
$457$	1.51693	−	6.64609i	0.0709588	−	0.310891i	−0.926976	−	0.375120i	$-0.877602\pi$
$457$	1.51693	−	6.64609i	0.0709588	−	0.310891i	0.997935	+	0.0642288i	$0.0204588\pi$
$458$	−11.8937	+	5.72772i	−0.555758	+	0.267639i
$459$	−6.63169	−	8.31587i	−0.309541	−	0.388152i
$460$	−16.4553	+	34.1697i	−0.767231	+	1.59317i
$461$	−22.1552	+	5.05679i	−1.03187	+	0.235518i	−0.704744	−	0.709462i	$-0.748938\pi$
$461$	−22.1552	+	5.05679i	−1.03187	+	0.235518i	−0.327129	+	0.944980i	$0.606081\pi$
$462$		−	4.67792i		−	0.217636i
$463$		−	6.76819i		−	0.314545i	−0.987555	−	0.157272i	$-0.949730\pi$
$463$		−	6.76819i		−	0.314545i	0.987555	−	0.157272i	$-0.0502700\pi$
$464$	13.3430	−	16.7315i	0.619431	−	0.776742i
$465$	14.7182	+	11.7374i	0.682541	+	0.544308i
$466$	3.50365	−	7.27540i	0.162303	−	0.337026i
$467$	19.9717	−	4.55840i	0.924178	−	0.210938i	0.266151	−	0.963931i	$-0.414248\pi$
$467$	19.9717	−	4.55840i	0.924178	−	0.210938i	0.658028	+	0.752994i	$0.271391\pi$
$468$	20.0417	+	4.57438i	0.926427	+	0.211451i
$469$	−6.21379	+	4.95533i	−0.286926	+	0.228816i
$470$	−3.91537	−	4.90972i	−0.180603	−	0.226468i
$471$		−	8.84955i		−	0.407766i
$472$	0.177784	+	0.0405780i	0.00818317	+	0.00186776i
$473$	25.3615	−	20.2251i	1.16612	−	0.929952i
$474$	−8.04676	+	6.41708i	−0.369600	+	0.294746i
$475$	0.507369	+	2.22293i	0.0232797	+	0.101995i
$476$	−1.26391	−	2.62453i	−0.0579310	−	0.120295i
$477$	22.6015			1.03485
$478$		−	42.4164i		−	1.94008i
$479$	−5.40030	−	23.6603i	−0.246746	−	1.08107i	−0.934735	−	0.355345i	$-0.884363\pi$
$479$	−5.40030	−	23.6603i	−0.246746	−	1.08107i	0.687989	−	0.725721i	$-0.258494\pi$
$480$	12.2400	−	9.76106i	0.558676	−	0.445529i
$481$		−	27.5841i		−	1.25773i
$482$	9.50849	−	41.6594i	0.433100	−	1.89753i
$483$	−2.34750	−	4.87464i	−0.106815	−	0.221804i
$484$	−1.98911	+	8.71488i	−0.0904143	+	0.396131i
$485$	15.3248	−	3.49779i	0.695865	−	0.158827i
$486$	6.97703	+	30.5684i	0.316485	+	1.38661i
$487$	10.4203			0.472188			0.236094	−	0.971730i	$-0.424133\pi$
$487$	10.4203			0.472188			0.236094	+	0.971730i	$0.424133\pi$
$488$	0.612072	+	0.139701i	0.0277072	+	0.00632399i
$489$	−16.4139	−	13.0896i	−0.742261	−	0.591934i
$490$	6.60962	−	28.9586i	0.298592	−	1.30822i
$491$	14.8264	−	18.5917i	0.669106	−	0.839032i	−0.325194	−	0.945647i	$-0.605430\pi$
$491$	14.8264	−	18.5917i	0.669106	−	0.839032i	0.994300	+	0.106615i	$0.0340012\pi$
$492$	−3.14191	−	6.52424i	−0.141648	−	0.294135i
$493$	4.97853	+	10.3380i	0.224221	+	0.465601i
$494$	−30.7875	+	38.6063i	−1.38519	+	1.73698i
$495$	4.66637	−	20.4447i	0.209738	−	0.918920i
$496$	−31.6335	−	25.2269i	−1.42038	−	1.13272i
$497$	2.74698	+	0.626980i	0.123219	+	0.0281239i
$498$	12.6595			0.567286
$499$	−8.59060	−	37.6379i	−0.384568	−	1.68490i	−0.682957	−	0.730458i	$-0.739307\pi$
$499$	−8.59060	−	37.6379i	−0.384568	−	1.68490i	0.298390	−	0.954444i	$-0.403551\pi$
$500$	18.6434	−	4.25523i	0.833758	−	0.190300i
$501$	−0.384707	+	1.68551i	−0.0171874	+	0.0753031i
$502$	5.54354	+	11.5113i	0.247420	+	0.513774i
$503$	−0.0162619	+	0.0712482i	−0.000725084	+	0.00317680i	−0.975289	−	0.220932i	$-0.929090\pi$
$503$	−0.0162619	+	0.0712482i	−0.000725084	+	0.00317680i	0.974564	+	0.224109i	$0.0719472\pi$
$504$		−	0.600514i		−	0.0267490i
$505$	−0.0893425	+	0.0712482i	−0.00397569	+	0.00317050i
$506$	15.6174	+	68.4245i	0.694280	+	3.04184i
$507$		−	11.0881i		−	0.492441i
$508$	14.3448			0.636448
$509$	5.08791	+	10.5652i	0.225518	+	0.468292i	0.982771	−	0.184830i	$-0.0591733\pi$
$509$	5.08791	+	10.5652i	0.225518	+	0.468292i	−0.757253	+	0.653122i	$0.773459\pi$
$510$	2.05466	+	9.00207i	0.0909820	+	0.398618i
$511$	−5.27479	+	4.20651i	−0.233343	+	0.186085i
$512$	−23.6761	+	18.8810i	−1.04634	+	0.834431i
$513$	−22.1414	−	5.05362i	−0.977566	−	0.223123i
$514$			22.4985i			0.992368i
$515$	−7.39493	−	9.27295i	−0.325859	−	0.408615i
$516$	9.92639	−	7.91603i	0.436985	−	0.348484i
$517$	−5.36981	−	1.22562i	−0.236164	−	0.0539028i
$518$	7.14712	−	1.63128i	0.314026	−	0.0716745i
$519$	−7.20805	+	14.9677i	−0.316398	+	0.657007i
$520$	3.58115	+	2.85587i	0.157044	+	0.125238i
$521$	−6.19537	+	7.76875i	−0.271424	+	0.340355i	−0.898798	−	0.438363i	$-0.855558\pi$
$521$	−6.19537	+	7.76875i	−0.271424	+	0.340355i	0.627374	+	0.778718i	$0.284130\pi$
$522$		−	21.5202i		−	0.941915i
$523$		−	8.80969i		−	0.385221i	−0.981275	−	0.192610i	$-0.938305\pi$
$523$		−	8.80969i		−	0.385221i	0.981275	−	0.192610i	$-0.0616953\pi$
$524$	−32.9158	+	7.51282i	−1.43793	+	0.328199i
$525$	0.119105	−	0.247324i	0.00519817	−	0.0107941i
$526$	−6.73490	−	8.44529i	−0.293656	−	0.368232i
$527$	19.5456	−	9.41265i	0.851418	−	0.410021i
$528$	3.36108	−	14.7258i	0.146272	−	0.640860i
$529$	36.2712	+	45.4826i	1.57701	+	1.97751i
$530$	−41.2793	−	19.8790i	−1.79306	−	0.863491i
$531$	0.955927	−	0.460350i	0.0414837	−	0.0199775i
$532$	−5.60388	−	2.69868i	−0.242959	−	0.117003i
$533$	18.3828	−	14.6598i	0.796249	−	0.634988i
$534$	−3.24764	−	6.74380i	−0.140539	−	0.291833i
$535$	18.9335	−	15.0990i	0.818566	−	0.652785i
$536$	−3.99612	+	1.92443i	−0.172606	+	0.0831226i
$537$	−3.20373	+	4.01736i	−0.138251	+	0.173362i
$538$	−4.67092	−	5.85714i	−0.201377	−	0.252519i
$539$	−11.3037	−	23.4724i	−0.486886	−	1.01103i
$540$	4.26487	−	18.6856i	0.183531	−	0.804100i
$541$	−40.7930	−	9.31073i	−1.75383	−	0.400300i	−0.779673	−	0.626186i	$-0.784615\pi$
$541$	−40.7930	−	9.31073i	−1.75383	−	0.400300i	−0.974154	+	0.225887i	$0.927472\pi$
$542$	−9.26726	+	11.6208i	−0.398063	+	0.499155i
$543$	17.6482	−	4.02810i	0.757359	−	0.172862i
$544$	−4.01453	−	17.5888i	−0.172122	−	0.754114i
$545$	3.01865	−	2.40730i	0.129305	−	0.103117i
$546$	5.79590	−	1.32288i	0.248041	−	0.0566139i
$547$	−11.2796	+	2.57450i	−0.482282	+	0.110078i	−0.456748	−	0.889596i	$-0.650986\pi$
$547$	−11.2796	+	2.57450i	−0.482282	+	0.110078i	−0.0255344	+	0.999674i	$0.508129\pi$
$548$	23.8838	+	11.5018i	1.02027	+	0.491334i
$549$	3.29105	−	1.58489i	0.140459	−	0.0676413i
$550$	−2.22020	+	2.78404i	−0.0946697	+	0.118712i
$551$	22.0737	+	10.6301i	0.940370	+	0.452858i
$552$	−0.671875	−	2.94368i	−0.0285969	−	0.125291i
$553$	1.82640	−	3.79255i	0.0776663	−	0.161276i
$554$	0.930804	+	4.07812i	0.0395461	+	0.173263i
$555$	−11.0134			−0.467493
$556$	−23.2995	−	5.31797i	−0.988121	−	0.225532i
$557$	24.6603	−	11.8758i	1.04489	−	0.503193i	0.168957	−	0.985623i	$-0.445960\pi$
$557$	24.6603	−	11.8758i	1.04489	−	0.503193i	0.875934	+	0.482430i	$0.160246\pi$
$558$	−40.6872			−1.72243
$559$	32.2308	+	25.7032i	1.36322	+	1.08713i
$560$	−3.05599	+	6.34583i	−0.129139	+	0.268160i
$561$	6.33177	+	5.04942i	0.267328	+	0.213187i
$562$	23.1836	+	11.1646i	0.977941	+	0.470951i
$563$	−7.36443	−	3.54652i	−0.310374	−	0.149468i	0.272212	−	0.962237i	$-0.412245\pi$
$563$	−7.36443	−	3.54652i	−0.310374	−	0.149468i	−0.582586	+	0.812769i	$0.697959\pi$
$564$	−2.10172	−	0.479704i	−0.0884984	−	0.0201992i
$565$	−18.8442	+	23.6298i	−0.792779	+	0.994114i
$566$	−6.52393	−	28.5832i	−0.274221	−	1.20144i
$567$	−1.20373	−	1.50944i	−0.0505521	−	0.0633903i
$568$	1.41670	+	0.682246i	0.0594433	+	0.0286264i
$569$	20.3233	+	25.4847i	0.851999	+	1.06837i	0.996881	+	0.0789236i	$0.0251483\pi$
$569$	20.3233	+	25.4847i	0.851999	+	1.06837i	−0.144882	+	0.989449i	$0.546280\pi$
$570$	15.4142	+	12.2924i	0.645629	+	0.514872i
$571$			0.963149i			0.0403065i	0.999797	+	0.0201533i	$0.00641542\pi$
$571$			0.963149i			0.0403065i	−0.999797	+	0.0201533i	$0.993585\pi$
$572$	−36.5502			−1.52824
$573$	1.39373	+	2.89411i	0.0582240	+	0.120903i
$574$	4.88553	+	3.89608i	0.203918	+	0.162619i
$575$	−0.916461	+	4.01528i	−0.0382191	+	0.167449i
$576$	−3.17241	+	13.8992i	−0.132184	+	0.579134i
$577$			23.4738i			0.977229i	0.872500	+	0.488614i	$0.162497\pi$
$577$			23.4738i			0.977229i	−0.872500	+	0.488614i	$0.837503\pi$
$578$	−21.9426	−	5.00827i	−0.912694	−	0.208316i
$579$	−7.48994	+	15.5530i	−0.311271	+	0.646362i
$580$	−8.97099	+	18.6285i	−0.372500	+	0.773505i
$581$	−4.66487	+	2.24649i	−0.193532	+	0.0931999i
$582$	7.09866	−	8.90144i	0.294249	−	0.368977i
$583$	−39.1775	+	8.94202i	−1.62257	+	0.370341i
$584$	−3.39224	+	1.63362i	−0.140372	+	0.0675995i
$585$	26.6504			1.10186
$586$	−9.40731	−	7.50208i	−0.388612	−	0.309908i
$587$	−3.14646	−	3.94553i	−0.129868	−	0.162850i	0.712646	−	0.701524i	$-0.247497\pi$
$587$	−3.14646	−	3.94553i	−0.129868	−	0.162850i	−0.842514	+	0.538675i	$0.818925\pi$
$588$	−4.42423	−	9.18701i	−0.182452	−	0.378866i
$589$	20.0978	−	41.7336i	0.828117	−	1.71960i
$590$	−2.15080			−0.0885471
$591$	−5.55174	−	10.8408i	−0.228368	−	0.445931i
$592$	23.6708			0.972866
$593$	−20.2220	+	41.9914i	−0.830418	+	1.72438i	−0.153726	+	0.988114i	$0.549127\pi$
$593$	−20.2220	+	41.9914i	−0.830418	+	1.72438i	−0.676692	+	0.736266i	$0.736587\pi$
$594$	−15.3892	−	31.9560i	−0.631426	−	1.31117i
$595$	−2.35458	−	2.95254i	−0.0965282	−	0.121043i
$596$	14.8763	+	11.8634i	0.609356	+	0.485945i
$597$	17.7060			0.724659
$598$	−80.3609	+	38.6998i	−3.28620	+	1.58255i
$599$	16.2066	−	3.69904i	0.662182	−	0.151139i	0.121795	−	0.992555i	$-0.461135\pi$
$599$	16.2066	−	3.69904i	0.662182	−	0.151139i	0.540387	+	0.841417i	$0.318278\pi$
$600$	0.0955148	−	0.119772i	0.00389937	−	0.00488966i
$601$	−0.217677	+	0.104828i	−0.00887921	+	0.00427600i	−0.438318	−	0.898820i	$-0.644426\pi$
$601$	−0.217677	+	0.104828i	−0.00887921	+	0.00427600i	0.429439	+	0.903096i	$0.358711\pi$
$602$	−4.75368	+	9.87113i	−0.193746	+	0.402317i
$603$	−11.1969	+	23.2505i	−0.455972	+	0.946835i
$604$	−14.0700	−	3.21139i	−0.572501	−	0.130670i
$605$			11.5886i			0.471144i
$606$	−0.0184179	+	0.0806940i	−0.000748175	+	0.00327797i
$607$	−7.23849	+	31.7139i	−0.293801	+	1.28723i	0.585388	+	0.810753i	$0.300942\pi$
$607$	−7.23849	+	31.7139i	−0.293801	+	1.28723i	−0.879189	+	0.476473i	$0.841915\pi$
$608$	−30.1172	−	24.0177i	−1.22141	−	0.974045i
$609$	−1.27980	−	2.65753i	−0.0518601	−	0.107689i
$610$	−7.40475			−0.299809
$611$		−	6.99974i		−	0.283179i
$612$	−7.39493	−	5.89726i	−0.298922	−	0.238383i
$613$	−19.6095	−	24.5896i	−0.792022	−	0.993164i	−0.999887	−	0.0150069i	$-0.995223\pi$
$613$	−19.6095	−	24.5896i	−0.792022	−	0.993164i	0.207865	−	0.978157i	$-0.433348\pi$
$614$	22.9976	+	11.0751i	0.928108	+	0.446953i
$615$	−5.85317	−	7.33965i	−0.236023	−	0.295963i
$616$	0.237586	+	1.04093i	0.00957263	+	0.0419404i
$617$	−24.1320	+	30.2605i	−0.971517	+	1.21824i	0.00437512	+	0.999990i	$0.498607\pi$
$617$	−24.1320	+	30.2605i	−0.971517	+	1.21824i	−0.975892	+	0.218253i	$0.929964\pi$
$618$	−8.37531	−	1.91161i	−0.336905	−	0.0768963i
$619$	−35.8560	−	17.2673i	−1.44117	−	0.694033i	−0.460136	−	0.887848i	$-0.652199\pi$
$619$	−35.8560	−	17.2673i	−1.44117	−	0.694033i	−0.981038	+	0.193816i	$0.937914\pi$
$620$	35.2199	+	16.9610i	1.41446	+	0.681170i
$621$	−32.0727	−	25.5771i	−1.28703	−	1.02638i
$622$	−8.79523	+	18.2635i	−0.352657	+	0.732299i
$623$	2.39344	+	1.90870i	0.0958910	+	0.0764705i
$624$	19.1957			0.768442
$625$	24.3952	−	11.7481i	0.975809	−	0.469925i
$626$	−54.7139	−	12.4881i	−2.18681	−	0.499124i
$627$	17.2922			0.690583
$628$	−4.08911	−	17.9155i	−0.163173	−	0.714908i
$629$	−5.50670	+	11.4348i	−0.219567	+	0.455935i
$630$	1.57606	+	6.90519i	0.0627919	+	0.275109i
$631$	−29.4816	−	14.1976i	−1.17365	−	0.565198i	−0.257592	−	0.966254i	$-0.582929\pi$
$631$	−29.4816	−	14.1976i	−1.17365	−	0.565198i	−0.916054	+	0.401056i	$0.868643\pi$
$632$	1.46466	−	1.83662i	0.0582609	−	0.0730569i
$633$	16.3327	−	7.86543i	0.649168	−	0.312623i
$634$	36.7362	+	17.6912i	1.45898	+	0.702607i
$635$	18.1305	−	4.13817i	0.719487	−	0.164218i
$636$	−15.3339	+	3.49987i	−0.608030	+	0.138779i
$637$	25.8855	−	20.6430i	1.02562	−	0.817906i
$638$	8.51424	+	37.3033i	0.337082	+	1.47685i
$639$	8.91939	−	2.03579i	0.352845	−	0.0805347i
$640$	−4.47786	+	5.61506i	−0.177003	+	0.221955i
$641$	25.9203	+	5.91615i	1.02379	+	0.233674i	0.701276	−	0.712890i	$-0.252614\pi$
$641$	25.9203	+	5.91615i	1.02379	+	0.233674i	0.322516	+	0.946564i	$0.395471\pi$
$642$	3.90312	−	17.1007i	0.154044	−	0.674911i
$643$	14.8476	+	30.8314i	0.585534	+	1.21587i	0.957717	+	0.287714i	$0.0928951\pi$
$643$	14.8476	+	30.8314i	0.585534	+	1.21587i	−0.372183	+	0.928159i	$0.621391\pi$
$644$	−7.00484	−	8.78380i	−0.276030	−	0.346130i
$645$	10.2624	−	12.8687i	0.404082	−	0.506703i
$646$	20.4698	−	9.85773i	0.805373	−	0.387847i
$647$	27.6410	−	22.0430i	1.08668	−	0.866598i	0.0950195	−	0.995475i	$-0.469709\pi$
$647$	27.6410	−	22.0430i	1.08668	−	0.866598i	0.991661	+	0.128877i	$0.0411372\pi$
$648$	−0.467476	−	0.970724i	−0.0183642	−	0.0381336i
$649$	−1.47488	+	1.17618i	−0.0578940	+	0.0461689i
$650$	−4.07726	−	1.96351i	−0.159923	−	0.0770150i
$651$	−5.02446	+	2.41965i	−0.196924	+	0.0948336i
$652$	−39.2775	−	18.9151i	−1.53823	−	0.740771i
$653$	−17.1253	−	21.4744i	−0.670164	−	0.840359i	0.324243	−	0.945974i	$-0.394890\pi$
$653$	−17.1253	−	21.4744i	−0.670164	−	0.840359i	−0.994407	+	0.105615i	$0.966319\pi$
$654$	0.622293	−	2.72645i	0.0243336	−	0.106612i
$655$	−39.4352	+	18.9910i	−1.54086	+	0.742039i
$656$	12.5801	+	15.7749i	0.491170	+	0.615907i
$657$	−9.50484	+	19.7370i	−0.370819	+	0.770014i
$658$	1.81365	−	0.413954i	0.0707035	−	0.0161376i
$659$		−	37.8129i		−	1.47298i	−0.676448	−	0.736491i	$-0.736481\pi$
$659$		−	37.8129i		−	1.47298i	0.676448	−	0.736491i	$-0.263519\pi$
$660$			14.5932i			0.568041i
$661$	1.86025	−	2.33268i	0.0723553	−	0.0907306i	−0.744337	−	0.667805i	$-0.767234\pi$
$661$	1.86025	−	2.33268i	0.0723553	−	0.0907306i	0.816692	+	0.577074i	$0.195806\pi$
$662$	13.7099	+	10.9333i	0.532851	+	0.424934i
$663$	−4.46562	+	9.27295i	−0.173430	+	0.360131i
$664$	−2.81700	+	0.642963i	−0.109321	+	0.0249518i
$665$	−7.86128	−	1.79429i	−0.304847	−	0.0695794i
$666$	18.6102	−	14.8411i	0.721131	−	0.575083i
$667$	27.5921	+	34.5994i	1.06837	+	1.33969i
$668$			3.59001i			0.138902i
$669$	−11.2439	−	2.56635i	−0.434715	−	0.0992209i
$670$	40.8998	−	32.6165i	1.58010	−	1.26009i
$671$	−5.07769	+	4.04932i	−0.196022	+	0.156322i
$672$	1.03199	+	4.52145i	0.0398099	+	0.174419i
$673$	6.27197	+	13.0239i	0.241767	+	0.502034i	0.986178	−	0.165687i	$-0.0529842\pi$
$673$	6.27197	+	13.0239i	0.241767	+	0.502034i	−0.744412	+	0.667721i	$0.767270\pi$
$674$	−18.1812			−0.700313
$675$		−	2.08136i		−	0.0801114i
$676$	−5.12349	−	22.4475i	−0.197057	−	0.863364i
$677$	5.41281	−	4.31657i	0.208031	−	0.165899i	−0.513932	−	0.857831i	$-0.671812\pi$
$677$	5.41281	−	4.31657i	0.208031	−	0.165899i	0.721963	+	0.691932i	$0.243240\pi$
$678$			21.8913i			0.840730i
$679$	−1.03617	+	4.53977i	−0.0397646	+	0.174220i
$680$	−0.914411	−	1.89879i	−0.0350661	−	0.0728154i
$681$	−1.17456	+	5.14610i	−0.0450094	+	0.197199i
$682$	70.5275	−	16.0974i	2.70064	−	0.616403i
$683$	−8.04234	−	35.2358i	−0.307732	−	1.34826i	−0.858162	−	0.513380i	$-0.828393\pi$
$683$	−8.04234	−	35.2358i	−0.307732	−	1.34826i	0.550430	−	0.834881i	$-0.314464\pi$
$684$	−20.1957			−0.772201
$685$	33.5049	+	7.64728i	1.28016	+	0.292187i
$686$	14.2642	+	11.3753i	0.544610	+	0.434312i
$687$	−1.30731	+	5.72772i	−0.0498772	+	0.218526i
$688$	−22.0567	+	27.6583i	−0.840906	+	1.05446i
$689$	−22.1582	−	46.0119i	−0.844159	−	1.75291i
$690$	15.4515	+	32.0854i	0.588229	+	1.22147i
$691$	26.9544	−	33.7997i	1.02539	−	1.28580i	0.0677925	−	0.997699i	$-0.478404\pi$
$691$	26.9544	−	33.7997i	1.02539	−	1.28580i	0.957600	−	0.288102i	$-0.0930241\pi$
$692$	−7.67629	+	33.6320i	−0.291809	+	1.27850i
$693$	4.85690	+	3.87325i	0.184498	+	0.147132i
$694$	16.4053	+	3.74440i	0.622736	+	0.142135i
$695$	−30.9825			−1.17523
$696$	−0.366289	−	1.60482i	−0.0138842	−	0.0608304i
$697$	−10.5471	+	2.40730i	−0.399498	+	0.0911829i
$698$	−1.61542	+	7.07764i	−0.0611447	+	0.267893i
$699$	−1.55927	−	3.23786i	−0.0589770	−	0.122467i
$700$	0.126842	−	0.555732i	0.00479418	−	0.0210047i
$701$		−	44.4113i		−	1.67739i	−0.544600	−	0.838696i	$-0.683319\pi$
$701$		−	44.4113i		−	1.67739i	0.544600	−	0.838696i	$-0.316681\pi$
$702$	35.2412	−	28.1039i	1.33009	−	1.06072i
$703$	6.03013	+	26.4197i	0.227431	+	0.996439i
$704$		−	25.3481i		−	0.955343i
$705$	−2.79476			−0.105257
$706$	26.6099	+	55.2561i	1.00148	+	2.07959i
$707$	−0.00753275	−	0.0330031i	−0.000283298	−	0.00124121i
$708$	−0.577261	+	0.460350i	−0.0216948	+	0.0173010i
$709$	33.2309	−	26.5007i	1.24801	−	0.995256i	0.248366	−	0.968666i	$-0.420107\pi$
$709$	33.2309	−	26.5007i	1.24801	−	0.995256i	0.999646	−	0.0265899i	$-0.00846484\pi$
$710$	−18.0809	−	4.12685i	−0.678564	−	0.154878i
$711$		−	13.6679i		−	0.512586i
$712$	1.06518	+	1.33569i	0.0399193	+	0.0500572i
$713$	65.4153	−	52.1670i	2.44982	−	1.95367i
$714$	−2.66673	−	0.608665i	−0.0998000	−	0.0227787i
$715$	−46.1960	+	10.5439i	−1.72763	+	0.394321i
$716$	−4.62953	+	9.61332i	−0.173014	+	0.359267i
$717$	−14.7587	−	11.7697i	−0.551173	−	0.439546i
$718$	−5.18747	+	6.50488i	−0.193595	+	0.242760i
$719$			28.5955i			1.06643i	0.845979	+	0.533217i	$0.179017\pi$
$719$			28.5955i			1.06643i	−0.845979	+	0.533217i	$0.820983\pi$
$720$			22.8696i			0.852299i
$721$	3.42543	−	0.781831i	0.127570	−	0.0291169i
$722$	4.97398	−	10.3286i	0.185112	−	0.384390i
$723$	−11.8569	−	14.8681i	−0.440963	−	0.552950i
$724$	33.8669	−	16.3094i	1.25865	−	0.606135i
$725$	−0.499632	+	2.18903i	−0.0185558	+	0.0812985i
$726$	5.23341	+	6.56248i	0.194230	+	0.243557i
$727$	18.9780	+	9.13932i	0.703855	+	0.338959i	0.751342	−	0.659913i	$-0.229407\pi$
$727$	18.9780	+	9.13932i	0.703855	+	0.338959i	−0.0474870	+	0.998872i	$0.515121\pi$
$728$	−1.22252	+	0.588735i	−0.0453096	+	0.0218200i
$729$	5.03146	+	2.42302i	0.186350	+	0.0897416i
$730$	34.7192	−	27.6877i	1.28502	−	1.02477i
$731$	−8.22982	−	17.0894i	−0.304391	−	0.632074i
$732$	−1.98739	+	1.58489i	−0.0734559	+	0.0585791i
$733$	21.9955	−	10.5925i	0.812421	−	0.391241i	0.0189278	−	0.999821i	$-0.493975\pi$
$733$	21.9955	−	10.5925i	0.812421	−	0.391241i	0.793493	+	0.608580i	$0.208260\pi$
$734$	26.6790	−	33.4545i	0.984741	−	1.23483i
$735$	−8.24206	−	10.3352i	−0.304013	−	0.381220i
$736$	−30.1902	−	62.6905i	−1.11282	−	2.31080i
$737$	10.2099	−	44.7325i	0.376087	−	1.64774i
$738$	19.7811	+	4.51491i	0.728153	+	0.166196i
$739$	−14.6230	+	18.3366i	−0.537914	+	0.674523i	−0.974305	−	0.225234i	$-0.927685\pi$
$739$	−14.6230	+	18.3366i	−0.537914	+	0.674523i	0.436390	+	0.899757i	$0.356257\pi$
$740$	−22.2962	+	5.08896i	−0.819624	+	0.187074i
$741$	4.89008	+	21.4249i	0.179642	+	0.787062i
$742$	10.6114	−	8.46232i	0.389557	−	0.310661i
$743$	−12.6661	+	2.89095i	−0.464673	+	0.106059i	−0.448446	−	0.893810i	$-0.648022\pi$
$743$	−12.6661	+	2.89095i	−0.464673	+	0.106059i	−0.0162267	+	0.999868i	$0.505165\pi$
$744$	−3.03415	+	0.692524i	−0.111237	+	0.0253892i
$745$	22.2245	+	10.7028i	0.814244	+	0.392119i
$746$	−46.6323	+	22.4569i	−1.70733	+	0.822206i
$747$	−10.4819	+	13.1439i	−0.383512	+	0.480909i
$748$	15.1516	+	7.29662i	0.553997	+	0.266791i
$749$	1.59634	+	6.99403i	0.0583291	+	0.255556i
$750$	7.79098	−	16.1781i	0.284486	−	0.590742i
$751$	2.71499	+	11.8951i	0.0990713	+	0.434060i	1.00000		9.26386e-5i	$2.94878e-5\pi$
$751$	2.71499	+	11.8951i	0.0990713	+	0.434060i	−0.900929	+	0.433967i	$0.857113\pi$
$752$	6.00670			0.219042
$753$	5.54354	+	1.26528i	0.202018	+	0.0461093i
$754$	−43.8107	+	21.0981i	−1.59549	+	0.768349i
$755$	−18.7096			−0.680912
$756$	4.43900	+	3.53999i	0.161445	+	0.128748i
$757$	−14.2274	+	29.5434i	−0.517102	+	1.07377i	0.464980	+	0.885321i	$0.346062\pi$
$757$	−14.2274	+	29.5434i	−0.517102	+	1.07377i	−0.982082	+	0.188453i	$0.939653\pi$
$758$	8.73705	+	6.96757i	0.317344	+	0.253073i
$759$	28.1417	+	13.5523i	1.02148	+	0.491918i
$760$	−4.05429	−	1.95245i	−0.147065	−	0.0708226i
$761$	1.93780	+	0.442291i	0.0702454	+	0.0160330i	0.257499	−	0.966279i	$-0.417102\pi$
$761$	1.93780	+	0.442291i	0.0702454	+	0.0160330i	−0.187254	+	0.982312i	$0.559959\pi$
$762$	8.39828	−	10.5311i	0.304238	−	0.381502i
$763$	0.254512	+	1.11509i	0.00921397	+	0.0403690i
$764$	4.15883	+	5.21501i	0.150461	+	0.188673i
$765$	−11.0477	−	5.32030i	−0.399431	−	0.192356i
$766$	21.7107	+	27.2244i	0.784441	+	0.983658i
$767$	−1.87435	−	1.49475i	−0.0676790	−	0.0539722i
$768$			16.2136i			0.585057i
$769$	18.7681			0.676794			0.338397	−	0.941003i	$-0.390115\pi$
$769$	18.7681			0.676794			0.338397	+	0.941003i	$0.390115\pi$
$770$	−5.46392	−	11.3459i	−0.196906	−	0.408879i
$771$	7.82832	+	6.24287i	0.281930	+	0.224832i
$772$	−7.97650	+	34.9473i	−0.287081	+	1.25778i
$773$	8.33393	−	36.5133i	0.299751	−	1.31329i	−0.570749	−	0.821124i	$-0.693347\pi$
$773$	8.33393	−	36.5133i	0.299751	−	1.31329i	0.870500	−	0.492169i	$-0.163796\pi$
$774$			35.5743i			1.27869i
$775$	4.13869	+	0.944628i	0.148666	+	0.0339320i
$776$	−1.12751	+	2.34129i	−0.0404751	+	0.0840474i
$777$	1.41557	−	2.93947i	0.0507835	−	0.105453i
$778$	2.93296	−	1.41244i	0.105152	−	0.0506384i
$779$	−14.4021	+	18.0597i	−0.516009	+	0.647054i
$780$	−18.0809	+	4.12685i	−0.647400	+	0.147765i
$781$	−14.6555	+	7.05771i	−0.524414	+	0.252545i
$782$	41.0388			1.46754
$783$	−17.4852	−	13.9440i	−0.624871	−	0.498318i
$784$	17.7145	+	22.2132i	0.632659	+	0.793329i
$785$	−10.3365	−	21.4639i	−0.368925	−	0.766081i
$786$	−13.7553	+	28.5633i	−0.490637	+	1.01882i
$787$	−3.84309			−0.136991			−0.0684956	−	0.997651i	$-0.521820\pi$
$787$	−3.84309			−0.136991			−0.0684956	+	0.997651i	$0.521820\pi$
$788$	−16.2485	−	19.3815i	−0.578828	−	0.690437i
$789$	−4.80731			−0.171145
$790$	−12.0215	+	24.9630i	−0.427707	+	0.888143i
$791$	−3.88471	−	8.06668i	−0.138124	−	0.286818i
$792$	2.16152	+	2.71046i	0.0768063	+	0.0963121i
$793$	−6.45300	−	5.14610i	−0.229153	−	0.182743i
$794$	−61.6872			−2.18920
$795$	−18.3710	+	8.84701i	−0.651552	+	0.313771i
$796$	35.8451	−	8.18141i	1.27050	−	0.289982i
$797$	−22.3488	+	28.0245i	−0.791636	+	0.992680i	0.208257	+	0.978074i	$0.433221\pi$
$797$	−22.3488	+	28.0245i	−0.791636	+	0.992680i	−0.999893	+	0.0146063i	$0.995351\pi$
$798$	−5.26205	+	2.53407i	−0.186274	+	0.0897050i
$799$	−1.39738	+	2.90169i	−0.0494357	+	0.102654i
$800$	1.53175	−	3.18072i	0.0541557	−	0.112455i
$801$	9.69083	+	2.21187i	0.342408	+	0.0781525i
$802$		−	57.9472i		−	2.04619i
$803$	8.66703	−	37.9727i	0.305853	−	1.34003i
$804$	3.99612	−	17.5081i	0.140932	−	0.617464i
$805$	−11.3874	−	9.08114i	−0.401353	−	0.320068i
$806$	39.8892	+	82.8307i	1.40504	+	2.91759i
$807$	−3.33406			−0.117364
$808$		−	0.0188915i		−	0.000664602i
$809$	5.18090	+	4.13163i	0.182151	+	0.145260i	0.710320	−	0.703879i	$-0.248550\pi$
$809$	5.18090	+	4.13163i	0.182151	+	0.145260i	−0.528170	+	0.849139i	$0.677121\pi$
$810$	7.92311	+	9.93526i	0.278390	+	0.349090i
$811$	29.4991	+	14.2060i	1.03585	+	0.498841i	0.872954	−	0.487802i	$-0.162201\pi$
$811$	29.4991	+	14.2060i	1.03585	+	0.498841i	0.162899	+	0.986643i	$0.447915\pi$
$812$	−3.81886	−	4.78870i	−0.134016	−	0.168051i
$813$	1.47195	+	6.44904i	0.0516236	+	0.226178i
$814$	−26.3873	+	33.0887i	−0.924875	+	1.15976i
$815$	−55.0997	−	12.5761i	−1.93006	−	0.440523i
$816$	−7.95742	−	3.83209i	−0.278565	−	0.134150i
$817$	−36.4892	−	17.5723i	−1.27659	−	0.614776i
$818$	54.4635	+	43.4332i	1.90427	+	1.51861i
$819$	−3.42543	+	7.11297i	−0.119694	+	0.248547i
$820$	−15.2409	−	12.1542i	−0.532237	−	0.424445i
$821$	−38.6353			−1.34838			−0.674191	−	0.738557i	$-0.735508\pi$
$821$	−38.6353			−1.34838			−0.674191	+	0.738557i	$0.735508\pi$
$822$	22.4269	−	10.8002i	0.782229	−	0.376701i
$823$	6.47637	+	1.47819i	0.225752	+	0.0515264i	0.333901	−	0.942608i	$-0.391635\pi$
$823$	6.47637	+	1.47819i	0.225752	+	0.0515264i	−0.108148	+	0.994135i	$0.534492\pi$
$824$	1.96077			0.0683067
$825$	0.352643	+	1.54503i	0.0122774	+	0.0537910i
$826$	0.276447	−	0.574047i	0.00961881	−	0.0199737i
$827$	−2.30380	−	10.0936i	−0.0801109	−	0.350989i	0.918947	−	0.394381i	$-0.129041\pi$
$827$	−2.30380	−	10.0936i	−0.0801109	−	0.350989i	−0.999058	+	0.0433917i	$0.986184\pi$
$828$	−32.8669	−	15.8279i	−1.14220	−	0.550056i
$829$	21.3083	−	26.7197i	0.740067	−	0.928015i	−0.259218	−	0.965819i	$-0.583465\pi$
$829$	21.3083	−	26.7197i	0.740067	−	0.928015i	0.999285	+	0.0378042i	$0.0120363\pi$
$830$	30.7047	−	14.7866i	1.06578	−	0.513250i
$831$	1.67725	+	0.807722i	0.0581832	+	0.0280196i
$832$	31.4061	−	7.16824i	1.08881	−	0.248514i
$833$	−14.8517	+	3.38980i	−0.514580	+	0.117450i
$834$	−17.5450	+	13.9917i	−0.607535	+	0.484493i
$835$	1.03564	+	4.53743i	0.0358398	+	0.157024i
$836$	35.0073	−	7.99019i	1.21075	−	0.276346i
$837$	−26.3632	+	33.0584i	−0.911247	+	1.14267i
$838$	19.0199	+	4.34117i	0.657032	+	0.149963i
$839$	−2.42208	+	10.6118i	−0.0836193	+	0.366360i	−0.999374	−	0.0353777i	$-0.988737\pi$
$839$	−2.42208	+	10.6118i	−0.0836193	+	0.366360i	0.915755	+	0.401738i	$0.131594\pi$
$840$	0.235062	+	0.488111i	0.00811041	+	0.0168414i
$841$	−3.03870	−	3.81040i	−0.104783	−	0.131393i
$842$	18.8319	−	23.6145i	0.648990	−	0.813808i
$843$	10.3177	−	4.96873i	0.355359	−	0.171132i
$844$	29.4306	−	23.4701i	1.01304	−	0.807874i
$845$	−12.9512	−	26.8935i	−0.445535	−	0.925164i
$846$	4.72252	−	3.76608i	0.162364	−	0.129481i
$847$	−3.09299	−	1.48951i	−0.106276	−	0.0511800i
$848$	39.4843	−	19.0147i	1.35590	−	0.652966i
$849$	−11.7557	−	5.66125i	−0.403455	−	0.194294i
$850$	1.29822	+	1.62791i	0.0445285	+	0.0558369i
$851$	−10.8922	+	47.7220i	−0.373381	+	1.63589i
$852$	−5.73609	+	2.76236i	−0.196515	+	0.0946368i
$853$	18.1019	+	22.6990i	0.619796	+	0.777199i	0.988316	−	0.152421i	$-0.0487069\pi$
$853$	18.1019	+	22.6990i	0.619796	+	0.777199i	−0.368520	+	0.929620i	$0.620135\pi$
$854$	0.951747	−	1.97632i	0.0325681	−	0.0676284i
$855$	−25.5254	+	5.82601i	−0.872951	+	0.199245i
$856$			4.00350i			0.136837i
$857$		−	5.61428i		−	0.191780i	−0.995392	−	0.0958901i	$-0.969430\pi$
$857$		−	5.61428i		−	0.191780i	0.995392	−	0.0958901i	$-0.0305697\pi$
$858$	−21.3986	+	26.8330i	−0.730535	+	0.916062i
$859$	−10.2661	−	8.18691i	−0.350273	−	0.279334i	0.432508	−	0.901630i	$-0.357629\pi$
$859$	−10.2661	−	8.18691i	−0.350273	−	0.279334i	−0.782782	+	0.622296i	$0.786200\pi$
$860$	14.8296	−	30.7940i	0.505686	−	1.05007i
$861$	2.71127	−	0.618829i	0.0923997	−	0.0210896i
$862$	5.56651	+	1.27052i	0.189596	+	0.0432740i
$863$	−8.52811	+	6.80094i	−0.290300	+	0.231507i	−0.757801	−	0.652486i	$-0.773726\pi$
$863$	−8.52811	+	6.80094i	−0.290300	+	0.231507i	0.467500	+	0.883993i	$0.345155\pi$
$864$	21.9242	+	27.4921i	0.745877	+	0.935301i
$865$			44.7222i			1.52060i
$866$	−60.7380	−	13.8631i	−2.06396	−	0.471086i
$867$	−7.83124	+	6.24521i	−0.265963	+	0.212098i
$868$	−9.05376	+	7.22013i	−0.307305	+	0.245067i
$869$	5.40754	+	23.6920i	0.183438	+	0.803696i
$870$	8.42377	+	17.4921i	0.285593	+	0.593039i
$871$	58.3105			1.97578
$872$			0.638297i			0.0216155i
$873$	3.36443	+	14.7405i	0.113869	+	0.498891i
$874$	68.5086	−	54.6337i	2.31734	−	1.84801i
$875$			7.34400i			0.248272i
$876$	3.39224	−	14.8624i	0.114613	−	0.502153i
$877$	−14.5789	−	30.2734i	−0.492294	−	1.02226i	−0.988098	−	0.153825i	$-0.950841\pi$
$877$	−14.5789	−	30.2734i	−0.492294	−	1.02226i	0.495804	−	0.868434i	$-0.334873\pi$
$878$	−5.88524	+	25.7849i	−0.198617	+	0.870199i
$879$	−5.22066	+	1.19158i	−0.176089	+	0.0401911i
$880$	−9.04809	−	39.6423i	−0.305011	−	1.33634i
$881$	−6.96376			−0.234615			−0.117307	−	0.993096i	$-0.537426\pi$
$881$	−6.96376			−0.234615			−0.117307	+	0.993096i	$0.537426\pi$
$882$	27.8545	+	6.35761i	0.937910	+	0.214072i
$883$	−23.7359	−	18.9287i	−0.798775	−	0.637002i	0.136613	−	0.990624i	$-0.456378\pi$
$883$	−23.7359	−	18.9287i	−0.798775	−	0.637002i	−0.935388	+	0.353623i	$0.884950\pi$
$884$	−4.75571	+	20.8361i	−0.159952	+	0.700795i
$885$	−0.596802	+	0.748366i	−0.0200613	+	0.0251561i
$886$	17.2017	+	35.7197i	0.577903	+	1.20003i
$887$	3.30582	+	6.86461i	0.110999	+	0.230491i	0.949067	−	0.315074i	$-0.102029\pi$
$887$	3.30582	+	6.86461i	0.110999	+	0.230491i	−0.838068	+	0.545565i	$0.816315\pi$
$888$	1.13520	−	1.42350i	0.0380949	−	0.0477695i
$889$	−1.22587	+	5.37090i	−0.0411145	+	0.180134i
$890$	−15.7538	−	12.5633i	−0.528070	−	0.421122i
$891$	10.8663	+	2.48016i	0.364034	+	0.0830885i
$892$	−23.9487			−0.801861
$893$	1.53020	+	6.70426i	0.0512063	+	0.224350i
$894$	17.4189	−	3.97574i	0.582574	−	0.132969i
$895$	−3.07806	+	13.4858i	−0.102888	+	0.450782i
$896$	−0.923108	−	1.91685i	−0.0308389	−	0.0640376i
$897$	−8.83297	+	38.6998i	−0.294924	+	1.29215i
$898$			46.7238i			1.55919i
$899$	35.6628	−	28.4401i	1.18942	−	0.948531i
$900$	−0.411854	−	1.80445i	−0.0137285	−	0.0601483i
$901$			23.4974i			0.782812i
$902$	−36.0750			−1.20117
$903$	2.11559	+	4.39306i	0.0704024	+	0.146192i
$904$	−1.11184	−	4.87127i	−0.0369791	−	0.162016i
$905$	38.0996	−	30.3834i	1.26647	−	1.00998i
$906$	−10.5950	+	8.44924i	−0.351996	+	0.280707i
$907$	43.9247	+	10.0255i	1.45849	+	0.332892i	0.876934	−	0.480611i	$-0.159585\pi$
$907$	43.9247	+	10.0255i	1.45849	+	0.332892i	0.581561	+	0.813503i	$0.302442\pi$
$908$			10.9608i			0.363747i
$909$	−0.0685317	−	0.0859360i	−0.00227305	−	0.00285032i
$910$	12.5124	−	9.97829i	0.414781	−	0.330777i
$911$	38.0628	+	8.68758i	1.26108	+	0.287832i	0.800255	−	0.599660i	$-0.204698\pi$
$911$	38.0628	+	8.68758i	1.26108	+	0.287832i	0.460822	+	0.887493i	$0.347555\pi$
$912$	−18.3854	+	4.19634i	−0.608800	+	0.138955i
$913$	12.9691	−	26.9307i	0.429216	−	0.891275i
$914$	−10.3922	−	8.28753i	−0.343745	−	0.274127i
$915$	−2.05466	+	2.57647i	−0.0679251	+	0.0851753i
$916$			12.1996i			0.403086i
$917$		−	12.9662i		−	0.428181i
$918$	−20.2195	+	4.61496i	−0.667342	+	0.152316i
$919$	16.3373	−	33.9247i	0.538917	−	1.11907i	−0.436703	−	0.899606i	$-0.643854\pi$
$919$	16.3373	−	33.9247i	0.538917	−	1.11907i	0.975620	−	0.219467i	$-0.0704319\pi$
$920$	−5.06787	−	6.35491i	−0.167083	−	0.209515i
$921$	10.2349	−	4.92887i	0.337251	−	0.162412i
$922$	−9.86001	+	43.1995i	−0.324722	+	1.42270i
$923$	−12.8889	−	16.1622i	−0.424243	−	0.531984i
$924$	−3.89493	−	1.87570i	−0.128134	−	0.0617060i
$925$	−2.23759	+	1.07756i	−0.0735714	+	0.0354301i
$926$	−11.8901	−	5.72596i	−0.390732	−	0.188167i
$927$	8.91939	−	7.11297i	0.292951	−	0.233621i
$928$	−16.4589	−	34.1773i	−0.540290	−	1.12192i
$929$	−13.7033	+	10.9280i	−0.449592	+	0.358537i	−0.821958	−	0.569549i	$-0.807118\pi$
$929$	−13.7033	+	10.9280i	−0.449592	+	0.358537i	0.372366	+	0.928086i	$0.378547\pi$
$930$	33.0715	−	15.9264i	1.08446	−	0.522247i
$931$	−20.2801	+	25.4304i	−0.664653	+	0.833449i
$932$	−4.65279	−	5.83442i	−0.152407	−	0.191113i
$933$	3.91425	+	8.12802i	0.128147	+	0.266099i
$934$	8.88822	−	38.9419i	0.290832	−	1.27422i
$935$	21.2551	+	4.85134i	0.695116	+	0.158656i
$936$	−2.74698	+	3.44460i	−0.0897878	+	0.112590i
$937$	−4.70158	+	1.07310i	−0.153594	+	0.0350568i	−0.298626	−	0.954370i	$-0.596528\pi$
$937$	−4.70158	+	1.07310i	−0.153594	+	0.0350568i	0.145033	+	0.989427i	$0.453671\pi$
$938$	3.44839	+	15.1084i	0.112594	+	0.493307i
$939$	−19.5271	+	15.5724i	−0.637244	+	0.508185i
$940$	−5.65787	+	1.29137i	−0.184540	+	0.0421199i
$941$	−30.3466	+	6.92641i	−0.989271	+	0.225795i	−0.686390	−	0.727234i	$-0.740806\pi$
$941$	−30.3466	+	6.92641i	−0.989271	+	0.225795i	−0.302881	+	0.953028i	$0.597948\pi$
$942$	−15.5465	−	7.48681i	−0.506533	−	0.243934i
$943$	−37.5921	+	18.1034i	−1.22417	+	0.589528i
$944$	1.28269	−	1.60844i	0.0417481	−	0.0523504i
$945$	6.63169	+	3.19365i	0.215729	+	0.103890i
$946$	−14.0746	−	61.6647i	−0.457604	−	2.00489i
$947$	−21.0323	+	43.6740i	−0.683457	+	1.41921i	0.213431	+	0.976958i	$0.431536\pi$
$947$	−21.0323	+	43.6740i	−0.683457	+	1.41921i	−0.896889	+	0.442256i	$0.854178\pi$
$948$	2.11649	+	9.27295i	0.0687404	+	0.301171i
$949$	49.4989			1.60680
$950$	4.33439	+	0.989296i	0.140626	+	0.0320970i
$951$	16.3491	−	7.87332i	0.530157	−	0.255310i
$952$	0.624318			0.0202343
$953$	−34.1199	−	27.2097i	−1.10525	−	0.881409i	−0.111583	−	0.993755i	$-0.535592\pi$
$953$	−34.1199	−	27.2097i	−1.10525	−	0.881409i	−0.993669	+	0.112346i	$0.964163\pi$
$954$	19.1211	−	39.7054i	0.619068	−	1.28551i
$955$	6.76079	+	5.39155i	0.218774	+	0.174466i
$956$	−35.3168	−	17.0077i	−1.14223	−	0.550067i
$957$	15.3421	+	7.38838i	0.495940	+	0.238832i
$958$	−46.1341	−	10.5298i	−1.49053	−	0.340203i
$959$	−6.34750	+	7.95952i	−0.204972	+	0.257026i
$960$	−2.86204	−	12.5394i	−0.0923718	−	0.404707i
$961$	−34.4421	−	43.1890i	−1.11104	−	1.39320i
$962$	−48.4587	−	23.3365i	−1.56237	−	0.752398i
$963$	14.5233	+	18.2116i	0.468006	+	0.586860i
$964$	−30.8739	−	24.6211i	−0.994381	−	0.792992i
$965$			46.4712i			1.49596i
$966$	−10.5496			−0.339427
$967$	−13.6308	−	28.3046i	−0.438337	−	0.910215i	−0.996743	−	0.0806475i	$-0.974301\pi$
$967$	−13.6308	−	28.3046i	−0.438337	−	0.910215i	0.558406	−	0.829568i	$-0.311413\pi$
$968$	−1.49784	−	1.19449i	−0.0481425	−	0.0383924i
$969$	2.24996	−	9.85773i	0.0722792	−	0.316676i
$970$	6.82019	−	29.8812i	0.218983	−	0.959428i
$971$			34.2192i			1.09814i	0.835775	+	0.549072i	$0.185019\pi$
$971$			34.2192i			1.09814i	−0.835775	+	0.549072i	$0.814981\pi$
$972$	28.2494	+	6.44775i	0.906101	+	0.206812i
$973$	3.98225	−	8.26922i	0.127665	−	0.265099i
$974$	8.81568	−	18.3059i	0.282472	−	0.586560i
$975$	−1.81455	+	0.873842i	−0.0581122	+	0.0279853i
$976$	4.41603	−	5.53753i	0.141354	−	0.177252i
$977$	−60.0091	+	13.6967i	−1.91986	+	0.438196i	−0.921050	+	0.389445i	$0.872667\pi$
$977$	−60.0091	+	13.6967i	−1.91986	+	0.438196i	−0.998811	+	0.0487506i	$0.984476\pi$
$978$	−36.8817	+	17.7613i	−1.17935	+	0.567943i
$979$	−17.6732			−0.564839
$980$	−21.4613	−	17.1148i	−0.685556	−	0.546713i
$981$	2.31551	+	2.90356i	0.0739286	+	0.0927035i
$982$	−20.1179	−	41.7752i	−0.641987	−	1.33310i
$983$	−12.9000	+	26.7871i	−0.411446	+	0.854377i	0.587533	+	0.809200i	$0.300099\pi$
$983$	−12.9000	+	26.7871i	−0.411446	+	0.854377i	−0.998979	+	0.0451768i	$0.985615\pi$
$984$	1.55197			0.0494751
$985$	−26.1277	−	19.8090i	−0.832497	−	0.631169i
$986$	22.3733			0.712511
$987$	0.359216	−	0.745919i	0.0114340	−	0.0237429i
$988$	19.7995	+	41.1142i	0.629907	+	1.30802i
$989$	−45.6115	−	57.1950i	−1.45036	−	1.81869i
$990$	−31.9686	−	25.4941i	−1.01603	−	0.810256i
$991$	26.0000			0.825917			0.412959	−	0.910750i	$-0.364495\pi$
$991$	26.0000			0.825917			0.412959	+	0.910750i	$0.364495\pi$
$992$	−64.6173	+	31.1180i	−2.05160	+	0.987999i
$993$	7.60842	−	1.73657i	0.241446	−	0.0551085i
$994$	3.42543	−	4.29535i	0.108648	−	0.136240i
$995$	42.9447	−	20.6811i	1.36144	−	0.655634i
$996$	5.07606	−	10.5406i	0.160841	−	0.333990i
$997$	14.0873	−	29.2526i	0.446150	−	0.926440i	−0.549694	−	0.835366i	$-0.685256\pi$
$997$	14.0873	−	29.2526i	0.446150	−	0.926440i	0.995844	−	0.0910738i	$-0.0290299\pi$
$998$	−73.3884	−	16.7504i	−2.32307	−	0.530225i
$999$		−	24.7371i		−	0.782648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.e.a.93.1	✓	6
197.161	even	14	inner	197.2.e.a.161.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.e.a.93.1	✓	6	1.1	even	1	trivial
197.2.e.a.161.1	yes	6	197.161	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.846011 - 1.75676i) q^{2} +(-0.376510 - 0.781831i) q^{3} +(-1.12349 - 1.40881i) q^{4} +(-1.82640 - 1.45650i) q^{5} -1.69202 q^{6} +(0.623490 - 0.300257i) q^{7} +(0.376510 - 0.0859360i) q^{8} +(1.40097 - 1.75676i) q^{9} +(-4.10388 + 1.97632i) q^{10} +(-1.73341 + 3.59945i) q^{11} +(-0.678448 + 1.40881i) q^{12} +(-4.94989 - 1.12978i) q^{13} -1.34934i q^{14} +(-0.451083 + 1.97632i) q^{15} +(0.969501 - 4.24766i) q^{16} +(1.82640 + 1.45650i) q^{17} +(-1.90097 - 3.94740i) q^{18} +4.98792 q^{19} +4.20941i q^{20} +(-0.469501 - 0.374414i) q^{21} +(4.85690 + 6.09035i) q^{22} +(8.11745 + 3.90916i) q^{23} +(-0.208947 - 0.262012i) q^{24} +(0.101720 + 0.445662i) q^{25} +(-6.17241 + 7.73995i) q^{26} +(-4.43900 - 1.01317i) q^{27} +(-1.12349 - 0.541044i) q^{28} +(4.42543 + 2.13117i) q^{29} +(3.09030 + 2.46443i) q^{30} +(4.02930 - 8.36693i) q^{31} +(-6.03803 - 4.81517i) q^{32} +3.46681 q^{33} +(4.10388 - 1.97632i) q^{34} +(-1.57606 - 0.359726i) q^{35} -4.04892 q^{36} +(1.20895 + 5.29674i) q^{37} +(4.21983 - 8.76257i) q^{38} +(0.980386 + 4.29535i) q^{39} +(-0.812823 - 0.391435i) q^{40} +(-2.88740 + 3.62068i) q^{41} +(-1.05496 + 0.508041i) q^{42} +(-7.31551 - 3.52296i) q^{43} +(7.01842 - 1.60191i) q^{44} +(-5.11745 + 1.16802i) q^{45} +(13.7349 - 10.9532i) q^{46} +(0.306782 + 1.34410i) q^{47} +(-3.68598 + 0.841301i) q^{48} +(-4.06584 + 5.09841i) q^{49} +(0.868977 + 0.198338i) q^{50} +(0.451083 - 1.97632i) q^{51} +(3.96950 + 8.24275i) q^{52} +(6.27144 + 7.86413i) q^{53} +(-5.53534 + 6.94110i) q^{54} +(8.40850 - 4.04932i) q^{55} +(0.208947 - 0.166630i) q^{56} +(-1.87800 - 3.89971i) q^{57} +(7.48792 - 5.97142i) q^{58} +(0.425428 + 0.204875i) q^{59} +(3.29105 - 1.58489i) q^{60} +(1.46466 + 0.705341i) q^{61} +(-11.2899 - 14.1570i) q^{62} +(0.346011 - 1.51597i) q^{63} +(-5.71648 + 2.75291i) q^{64} +(7.39493 + 9.27295i) q^{65} +(2.93296 - 6.09035i) q^{66} +(-11.1969 + 2.55561i) q^{67} -4.20941i q^{68} -7.81831i q^{69} +(-1.96532 + 2.46443i) q^{70} +(3.18329 + 2.53859i) q^{71} +(0.376510 - 0.781831i) q^{72} +(-9.50484 + 2.16942i) q^{73} +(10.3279 + 2.35727i) q^{74} +(0.310134 - 0.247324i) q^{75} +(-5.60388 - 7.02704i) q^{76} +2.76469i q^{77} +(8.37531 + 1.91161i) q^{78} +(4.75571 - 3.79255i) q^{79} +(-7.95742 + 6.34583i) q^{80} +(-0.620801 - 2.71991i) q^{81} +(3.91789 + 8.13559i) q^{82} -7.48188 q^{83} +1.08209i q^{84} +(-1.21432 - 5.32030i) q^{85} +(-12.3780 + 9.87113i) q^{86} -4.26235i q^{87} +(-0.343322 + 1.50419i) q^{88} +(1.91939 + 3.98565i) q^{89} +(-2.27748 + 9.97829i) q^{90} +(-3.42543 + 0.781831i) q^{91} +(-3.61260 - 15.8279i) q^{92} -8.05861 q^{93} +(2.62080 + 0.598181i) q^{94} +(-9.10992 - 7.26492i) q^{95} +(-1.49127 + 6.53368i) q^{96} +(-4.19537 + 5.26083i) q^{97} +(5.51693 + 11.4560i) q^{98} +(3.89493 + 8.08790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 7 q^{3} - 2 q^{4} + 7 q^{5} - q^{7} + 7 q^{8} + 4 q^{9} - 7 q^{10} - 7 q^{11} - 7 q^{13} - 21 q^{15} - 4 q^{16} - 7 q^{17} - 7 q^{18} - 8 q^{19} + 7 q^{21} + 21 q^{22} + 25 q^{23} - 7 q^{24} + 2 q^{25}+ \cdots + 49 q^{98}+O(q^{100}) \) 6 * q - 7 * q^3 - 2 * q^4 + 7 * q^5 - q^7 + 7 * q^8 + 4 * q^9 - 7 * q^10 - 7 * q^11 - 7 * q^13 - 21 * q^15 - 4 * q^16 - 7 * q^17 - 7 * q^18 - 8 * q^19 + 7 * q^21 + 21 * q^22 + 25 * q^23 - 7 * q^24 + 2 * q^25 - 14 * q^26 - 7 * q^27 - 2 * q^28 + 13 * q^29 + 7 * q^30 - 7 * q^31 - 21 * q^32 + 14 * q^33 + 7 * q^34 + 21 * q^35 - 6 * q^36 + 13 * q^37 + 28 * q^38 - 7 * q^39 + 7 * q^40 - 19 * q^41 - 7 * q^42 - 29 * q^43 + 14 * q^44 - 7 * q^45 + 35 * q^46 - 29 * q^47 + 7 * q^48 - 22 * q^49 + 35 * q^50 + 21 * q^51 + 14 * q^52 + 19 * q^53 - 21 * q^54 + 21 * q^55 + 7 * q^56 + 28 * q^57 + 7 * q^58 - 11 * q^59 + 14 * q^60 + 21 * q^61 - 21 * q^62 - 3 * q^63 - 15 * q^64 + 21 * q^65 - 21 * q^66 - 35 * q^67 - 49 * q^70 - 7 * q^71 + 7 * q^72 - 35 * q^73 - 7 * q^75 - 16 * q^76 + 14 * q^78 + 35 * q^79 - 2 * q^81 + 35 * q^82 + 12 * q^83 - 7 * q^85 - 35 * q^86 - 21 * q^89 - 14 * q^90 - 7 * q^91 - 20 * q^92 + 14 * q^93 + 14 * q^94 - 56 * q^95 + 7 * q^96 - 37 * q^97 + 49 * q^98

Introduction

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