LMFDB - Embedded newform 195.2.t.a.73.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(73,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("195.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.t (of order $4$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.13
Character	$\chi$	$=$	195.73
Dual form			195.2.t.a.187.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.21780 q^{2} +(0.707107 + 0.707107i) q^{3} +2.91862 q^{4} +(-1.56243 + 1.59963i) q^{5} +(1.56822 + 1.56822i) q^{6} -4.11325i q^{7} +2.03732 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+2.21780 q^{2} +(0.707107 + 0.707107i) q^{3} +2.91862 q^{4} +(-1.56243 + 1.59963i) q^{5} +(1.56822 + 1.56822i) q^{6} -4.11325i q^{7} +2.03732 q^{8} +1.00000i q^{9} +(-3.46515 + 3.54765i) q^{10} +(-2.59303 + 2.59303i) q^{11} +(2.06378 + 2.06378i) q^{12} +(1.47066 - 3.29198i) q^{13} -9.12235i q^{14} +(-2.23591 + 0.0263025i) q^{15} -1.31889 q^{16} +(1.98080 + 1.98080i) q^{17} +2.21780i q^{18} +(-2.76089 + 2.76089i) q^{19} +(-4.56015 + 4.66871i) q^{20} +(2.90851 - 2.90851i) q^{21} +(-5.75081 + 5.75081i) q^{22} +(1.53954 - 1.53954i) q^{23} +(1.44060 + 1.44060i) q^{24} +(-0.117620 - 4.99862i) q^{25} +(3.26162 - 7.30095i) q^{26} +(-0.707107 + 0.707107i) q^{27} -12.0050i q^{28} -8.40712i q^{29} +(-4.95880 + 0.0583336i) q^{30} +(2.11332 + 2.11332i) q^{31} -6.99966 q^{32} -3.66710 q^{33} +(4.39301 + 4.39301i) q^{34} +(6.57967 + 6.42667i) q^{35} +2.91862i q^{36} +7.83564i q^{37} +(-6.12310 + 6.12310i) q^{38} +(3.36770 - 1.28787i) q^{39} +(-3.18317 + 3.25895i) q^{40} +(1.65250 + 1.65250i) q^{41} +(6.45048 - 6.45048i) q^{42} +(1.27192 - 1.27192i) q^{43} +(-7.56807 + 7.56807i) q^{44} +(-1.59963 - 1.56243i) q^{45} +(3.41439 - 3.41439i) q^{46} +6.35092i q^{47} +(-0.932593 - 0.932593i) q^{48} -9.91882 q^{49} +(-0.260858 - 11.0859i) q^{50} +2.80127i q^{51} +(4.29230 - 9.60806i) q^{52} +(5.31987 + 5.31987i) q^{53} +(-1.56822 + 1.56822i) q^{54} +(-0.0964538 - 8.19931i) q^{55} -8.38000i q^{56} -3.90449 q^{57} -18.6453i q^{58} +(6.51015 + 6.51015i) q^{59} +(-6.52579 + 0.0767671i) q^{60} +7.84876 q^{61} +(4.68691 + 4.68691i) q^{62} +4.11325 q^{63} -12.8861 q^{64} +(2.96815 + 7.49601i) q^{65} -8.13287 q^{66} -12.3496 q^{67} +(5.78120 + 5.78120i) q^{68} +2.17724 q^{69} +(14.5924 + 14.2530i) q^{70} +(-7.75627 - 7.75627i) q^{71} +2.03732i q^{72} +5.27944 q^{73} +17.3779i q^{74} +(3.45139 - 3.61773i) q^{75} +(-8.05801 + 8.05801i) q^{76} +(10.6658 + 10.6658i) q^{77} +(7.46887 - 2.85624i) q^{78} -8.45538i q^{79} +(2.06067 - 2.10973i) q^{80} -1.00000 q^{81} +(3.66491 + 3.66491i) q^{82} +4.49388i q^{83} +(8.48883 - 8.48883i) q^{84} +(-6.26340 + 0.0736805i) q^{85} +(2.82085 - 2.82085i) q^{86} +(5.94473 - 5.94473i) q^{87} +(-5.28283 + 5.28283i) q^{88} +(-8.91884 - 8.91884i) q^{89} +(-3.54765 - 3.46515i) q^{90} +(-13.5408 - 6.04919i) q^{91} +(4.49334 - 4.49334i) q^{92} +2.98868i q^{93} +14.0850i q^{94} +(-0.102698 - 8.73011i) q^{95} +(-4.94951 - 4.94951i) q^{96} +17.6029 q^{97} -21.9979 q^{98} +(-2.59303 - 2.59303i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} + 28 q^{4} - 4 q^{5} - 12 q^{8}+O(q^{10}) $ 28 * q - 4 * q^2 + 28 * q^4 - 4 * q^5 - 12 * q^8	$ 28 q - 4 q^{2} + 28 q^{4} - 4 q^{5} - 12 q^{8} - 8 q^{11} - 8 q^{12} - 4 q^{15} + 28 q^{16} + 28 q^{17} + 12 q^{20} + 8 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{25} - 16 q^{31} - 68 q^{32} - 8 q^{33} - 28 q^{34} - 8 q^{39} - 48 q^{40} + 4 q^{41} - 40 q^{44} - 8 q^{45} - 16 q^{46} - 16 q^{48} + 28 q^{49} + 4 q^{50} + 48 q^{52} + 20 q^{53} - 8 q^{55} - 32 q^{59} - 60 q^{60} + 8 q^{61} - 72 q^{62} + 28 q^{64} + 64 q^{65} + 16 q^{66} + 32 q^{67} + 60 q^{68} - 8 q^{69} - 16 q^{70} + 40 q^{71} + 56 q^{73} + 16 q^{75} - 40 q^{76} + 48 q^{77} + 40 q^{78} - 12 q^{80} - 28 q^{81} - 4 q^{82} + 32 q^{84} + 44 q^{85} + 16 q^{86} - 24 q^{87} - 72 q^{88} + 36 q^{89} + 12 q^{90} - 56 q^{91} - 32 q^{92} - 56 q^{95} + 48 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) $ 28 * q - 4 * q^2 + 28 * q^4 - 4 * q^5 - 12 * q^8 - 8 * q^11 - 8 * q^12 - 4 * q^15 + 28 * q^16 + 28 * q^17 + 12 * q^20 + 8 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^25 - 16 * q^31 - 68 * q^32 - 8 * q^33 - 28 * q^34 - 8 * q^39 - 48 * q^40 + 4 * q^41 - 40 * q^44 - 8 * q^45 - 16 * q^46 - 16 * q^48 + 28 * q^49 + 4 * q^50 + 48 * q^52 + 20 * q^53 - 8 * q^55 - 32 * q^59 - 60 * q^60 + 8 * q^61 - 72 * q^62 + 28 * q^64 + 64 * q^65 + 16 * q^66 + 32 * q^67 + 60 * q^68 - 8 * q^69 - 16 * q^70 + 40 * q^71 + 56 * q^73 + 16 * q^75 - 40 * q^76 + 48 * q^77 + 40 * q^78 - 12 * q^80 - 28 * q^81 - 4 * q^82 + 32 * q^84 + 44 * q^85 + 16 * q^86 - 24 * q^87 - 72 * q^88 + 36 * q^89 + 12 * q^90 - 56 * q^91 - 32 * q^92 - 56 * q^95 + 48 * q^97 - 12 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	2.21780			1.56822			0.784110	−	0.620622i	$-0.213120\pi$
$2$	2.21780			1.56822			0.784110	+	0.620622i	$0.213120\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	2.91862			1.45931
$5$	−1.56243	+	1.59963i	−0.698740	+	0.715375i
$5$	−1.56243	+	1.59963i	−0.698740	+	0.715375i
$6$	1.56822	+	1.56822i	0.640223	+	0.640223i
$7$		−	4.11325i		−	1.55466i	−0.629092	−	0.777331i	$-0.716573\pi$
$7$		−	4.11325i		−	1.55466i	0.629092	−	0.777331i	$-0.283427\pi$
$8$	2.03732			0.720301
$9$			1.00000i			0.333333i
$10$	−3.46515	+	3.54765i	−1.09578	+	1.12187i
$11$	−2.59303	+	2.59303i	−0.781827	+	0.781827i	−0.980139	−	0.198312i	$-0.936454\pi$
$11$	−2.59303	+	2.59303i	−0.781827	+	0.781827i	0.198312	+	0.980139i	$0.436454\pi$
$12$	2.06378	+	2.06378i	0.595761	+	0.595761i
$13$	1.47066	−	3.29198i	0.407887	−	0.913032i
$13$	1.47066	−	3.29198i	0.407887	−	0.913032i
$14$		−	9.12235i		−	2.43805i
$15$	−2.23591	+	0.0263025i	−0.577310	+	0.00679128i
$16$	−1.31889			−0.329721
$17$	1.98080	+	1.98080i	0.480414	+	0.480414i	0.905264	−	0.424850i	$-0.139673\pi$
$17$	1.98080	+	1.98080i	0.480414	+	0.480414i	−0.424850	+	0.905264i	$0.639673\pi$
$18$			2.21780i			0.522740i
$19$	−2.76089	+	2.76089i	−0.633393	+	0.633393i	−0.948917	−	0.315525i	$-0.897819\pi$
$19$	−2.76089	+	2.76089i	−0.633393	+	0.633393i	0.315525	+	0.948917i	$0.397819\pi$
$20$	−4.56015	+	4.66871i	−1.01968	+	1.04396i
$21$	2.90851	−	2.90851i	0.634688	−	0.634688i
$22$	−5.75081	+	5.75081i	−1.22608	+	1.22608i
$23$	1.53954	−	1.53954i	0.321017	−	0.321017i	−0.528140	−	0.849157i	$-0.677110\pi$
$23$	1.53954	−	1.53954i	0.321017	−	0.321017i	0.849157	+	0.528140i	$0.177110\pi$
$24$	1.44060	+	1.44060i	0.294062	+	0.294062i
$25$	−0.117620	−	4.99862i	−0.0235241	−	0.999723i
$26$	3.26162	−	7.30095i	0.639657	−	1.43183i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		−	12.0050i		−	2.26874i
$29$		−	8.40712i		−	1.56116i	−0.625054	−	0.780582i	$-0.714923\pi$
$29$		−	8.40712i		−	1.56116i	0.625054	−	0.780582i	$-0.285077\pi$
$30$	−4.95880	+	0.0583336i	−0.905349	+	0.0106502i
$31$	2.11332	+	2.11332i	0.379563	+	0.379563i	0.870944	−	0.491381i	$-0.163508\pi$
$31$	2.11332	+	2.11332i	0.379563	+	0.379563i	−0.491381	+	0.870944i	$0.663508\pi$
$32$	−6.99966			−1.23738
$33$	−3.66710			−0.638359
$34$	4.39301	+	4.39301i	0.753395	+	0.753395i
$35$	6.57967	+	6.42667i	1.11217	+	1.08631i
$36$			2.91862i			0.486437i
$37$			7.83564i			1.28817i	0.764953	+	0.644086i	$0.222762\pi$
$37$			7.83564i			1.28817i	−0.764953	+	0.644086i	$0.777238\pi$
$38$	−6.12310	+	6.12310i	−0.993299	+	0.993299i
$39$	3.36770	−	1.28787i	0.539263	−	0.206225i
$40$	−3.18317	+	3.25895i	−0.503304	+	0.515286i
$41$	1.65250	+	1.65250i	0.258077	+	0.258077i	0.824272	−	0.566195i	$-0.191585\pi$
$41$	1.65250	+	1.65250i	0.258077	+	0.258077i	−0.566195	+	0.824272i	$0.691585\pi$
$42$	6.45048	−	6.45048i	0.995330	−	0.995330i
$43$	1.27192	−	1.27192i	0.193965	−	0.193965i	−0.603442	−	0.797407i	$-0.706204\pi$
$43$	1.27192	−	1.27192i	0.193965	−	0.193965i	0.797407	+	0.603442i	$0.206204\pi$
$44$	−7.56807	+	7.56807i	−1.14093	+	1.14093i
$45$	−1.59963	−	1.56243i	−0.238458	−	0.232913i
$46$	3.41439	−	3.41439i	0.503425	−	0.503425i
$47$			6.35092i			0.926376i	0.886260	+	0.463188i	$0.153295\pi$
$47$			6.35092i			0.926376i	−0.886260	+	0.463188i	$0.846705\pi$
$48$	−0.932593	−	0.932593i	−0.134608	−	0.134608i
$49$	−9.91882			−1.41697
$50$	−0.260858	−	11.0859i	−0.0368909	−	1.56779i
$51$			2.80127i			0.392257i
$52$	4.29230	−	9.60806i	0.595235	−	1.33240i
$53$	5.31987	+	5.31987i	0.730740	+	0.730740i	0.970766	−	0.240027i	$-0.0771562\pi$
$53$	5.31987	+	5.31987i	0.730740	+	0.730740i	−0.240027	+	0.970766i	$0.577156\pi$
$54$	−1.56822	+	1.56822i	−0.213408	+	0.213408i
$55$	−0.0964538	−	8.19931i	−0.0130058	−	1.10559i
$56$		−	8.38000i		−	1.11983i
$57$	−3.90449			−0.517163
$58$		−	18.6453i		−	2.44825i
$59$	6.51015	+	6.51015i	0.847550	+	0.847550i	0.989827	−	0.142277i	$-0.0454423\pi$
$59$	6.51015	+	6.51015i	0.847550	+	0.847550i	−0.142277	+	0.989827i	$0.545442\pi$
$60$	−6.52579	+	0.0767671i	−0.842476	+	0.00991059i
$61$	7.84876			1.00493			0.502465	−	0.864597i	$-0.332426\pi$
$61$	7.84876			1.00493			0.502465	+	0.864597i	$0.332426\pi$
$62$	4.68691	+	4.68691i	0.595238	+	0.595238i
$63$	4.11325			0.518221
$64$	−12.8861			−1.61076
$65$	2.96815	+	7.49601i	0.368154	+	0.929765i
$66$	−8.13287			−1.00109
$67$	−12.3496			−1.50874			−0.754372	−	0.656447i	$-0.772058\pi$
$67$	−12.3496			−1.50874			−0.754372	+	0.656447i	$0.772058\pi$
$68$	5.78120	+	5.78120i	0.701074	+	0.701074i
$69$	2.17724			0.262109
$70$	14.5924	+	14.2530i	1.74412	+	1.70356i
$71$	−7.75627	−	7.75627i	−0.920500	−	0.920500i	0.0765650	−	0.997065i	$-0.475605\pi$
$71$	−7.75627	−	7.75627i	−0.920500	−	0.920500i	−0.997065	+	0.0765650i	$0.975605\pi$
$72$			2.03732i			0.240100i
$73$	5.27944			0.617912			0.308956	−	0.951076i	$-0.400020\pi$
$73$	5.27944			0.617912			0.308956	+	0.951076i	$0.400020\pi$
$74$			17.3779i			2.02014i
$75$	3.45139	−	3.61773i	0.398532	−	0.417739i
$76$	−8.05801	+	8.05801i	−0.924317	+	0.924317i
$77$	10.6658	+	10.6658i	1.21548	+	1.21548i
$78$	7.46887	−	2.85624i	0.845683	−	0.323405i
$79$		−	8.45538i		−	0.951305i	−0.879633	−	0.475653i	$-0.842212\pi$
$79$		−	8.45538i		−	0.951305i	0.879633	−	0.475653i	$-0.157788\pi$
$80$	2.06067	−	2.10973i	0.230390	−	0.235874i
$81$	−1.00000			−0.111111
$82$	3.66491	+	3.66491i	0.404722	+	0.404722i
$83$			4.49388i			0.493267i	0.969109	+	0.246634i	$0.0793244\pi$
$83$			4.49388i			0.493267i	−0.969109	+	0.246634i	$0.920676\pi$
$84$	8.48883	−	8.48883i	0.926208	−	0.926208i
$85$	−6.26340	+	0.0736805i	−0.679361	+	0.00799177i
$86$	2.82085	−	2.82085i	0.304180	−	0.304180i
$87$	5.94473	−	5.94473i	0.637342	−	0.637342i
$88$	−5.28283	+	5.28283i	−0.563151	+	0.563151i
$89$	−8.91884	−	8.91884i	−0.945395	−	0.945395i	0.0531890	−	0.998584i	$-0.483061\pi$
$89$	−8.91884	−	8.91884i	−0.945395	−	0.945395i	−0.998584	+	0.0531890i	$0.983061\pi$
$90$	−3.54765	−	3.46515i	−0.373955	−	0.365259i
$91$	−13.5408	−	6.04919i	−1.41946	−	0.634127i
$92$	4.49334	−	4.49334i	0.468464	−	0.468464i
$93$			2.98868i			0.309912i
$94$			14.0850i			1.45276i
$95$	−0.102698	−	8.73011i	−0.0105366	−	0.895691i
$96$	−4.94951	−	4.94951i	−0.505157	−	0.505157i
$97$	17.6029			1.78730			0.893650	−	0.448765i	$-0.148136\pi$
$97$	17.6029			1.78730			0.893650	+	0.448765i	$0.148136\pi$
$98$	−21.9979			−2.22213
$99$	−2.59303	−	2.59303i	−0.260609	−	0.260609i
$100$	−0.343289	−	14.5891i	−0.0343289	−	1.45891i
$101$			4.66632i			0.464316i	0.972678	+	0.232158i	$0.0745787\pi$
$101$			4.66632i			0.464316i	−0.972678	+	0.232158i	$0.925421\pi$
$102$			6.21265i			0.615144i
$103$	−2.08089	+	2.08089i	−0.205036	+	0.205036i	−0.802154	−	0.597118i	$-0.796313\pi$
$103$	−2.08089	+	2.08089i	−0.205036	+	0.205036i	0.597118	+	0.802154i	$0.296313\pi$
$104$	2.99620	−	6.70683i	0.293802	−	0.657658i
$105$	0.108189	+	9.19687i	0.0105581	+	0.897522i
$106$	11.7984	+	11.7984i	1.14596	+	1.14596i
$107$	1.71214	−	1.71214i	0.165519	−	0.165519i	−0.619488	−	0.785006i	$-0.712660\pi$
$107$	1.71214	−	1.71214i	0.165519	−	0.165519i	0.785006	+	0.619488i	$0.212660\pi$
$108$	−2.06378	+	2.06378i	−0.198587	+	0.198587i
$109$	4.77725	−	4.77725i	0.457578	−	0.457578i	−0.440282	−	0.897860i	$-0.645121\pi$
$109$	4.77725	−	4.77725i	0.457578	−	0.457578i	0.897860	+	0.440282i	$0.145121\pi$
$110$	−0.213915	−	18.1844i	−0.0203960	−	1.73381i
$111$	−5.54064	+	5.54064i	−0.525894	+	0.525894i
$112$			5.42490i			0.512605i
$113$	−1.95021	−	1.95021i	−0.183460	−	0.183460i	0.609402	−	0.792862i	$-0.291410\pi$
$113$	−1.95021	−	1.95021i	−0.183460	−	0.183460i	−0.792862	+	0.609402i	$0.791410\pi$
$114$	−8.65938			−0.811025
$115$	0.0572669	+	4.86812i	0.00534017	+	0.453955i
$116$		−	24.5372i		−	2.27822i
$117$	3.29198	+	1.47066i	0.304344	+	0.135962i
$118$	14.4382	+	14.4382i	1.32914	+	1.32914i
$119$	8.14752	−	8.14752i	0.746882	−	0.746882i
$120$	−4.55527	+	0.0535866i	−0.415837	+	0.00489177i
$121$		−	2.44759i		−	0.222508i
$122$	17.4070			1.57595
$123$			2.33699i			0.210719i
$124$	6.16798	+	6.16798i	0.553901	+	0.553901i
$125$	8.17970	+	7.62184i	0.731615	+	0.681718i
$126$	9.12235			0.812684
$127$	−4.33250	−	4.33250i	−0.384447	−	0.384447i	0.488254	−	0.872701i	$-0.337634\pi$
$127$	−4.33250	−	4.33250i	−0.384447	−	0.384447i	−0.872701	+	0.488254i	$0.837634\pi$
$128$	−14.5793			−1.28864
$129$	1.79876			0.158372
$130$	6.58275	+	16.6246i	0.577345	+	1.45808i
$131$	−11.7646			−1.02788			−0.513939	−	0.857827i	$-0.671814\pi$
$131$	−11.7646			−1.02788			−0.513939	+	0.857827i	$0.671814\pi$
$132$	−10.7029			−0.931565
$133$	11.3562	+	11.3562i	0.984712	+	0.984712i
$134$	−27.3889			−2.36604
$135$	−0.0263025	−	2.23591i	−0.00226376	−	0.192437i
$136$	4.03552	+	4.03552i	0.346043	+	0.346043i
$137$		−	12.3668i		−	1.05657i	−0.849067	−	0.528286i	$-0.822835\pi$
$137$		−	12.3668i		−	1.05657i	0.849067	−	0.528286i	$-0.177165\pi$
$138$	4.82868			0.411045
$139$		−	15.1730i		−	1.28695i	−0.765466	−	0.643477i	$-0.777491\pi$
$139$		−	15.1730i		−	1.28695i	0.765466	−	0.643477i	$-0.222509\pi$
$140$	19.2036	+	18.7570i	1.62300	+	1.58526i
$141$	−4.49078	+	4.49078i	−0.378192	+	0.378192i
$142$	−17.2018	−	17.2018i	−1.44355	−	1.44355i
$143$	4.72275	+	12.3497i	0.394936	+	1.03273i
$144$		−	1.31889i		−	0.109907i
$145$	13.4483	+	13.1355i	1.11682	+	1.09085i
$146$	11.7087			0.969022
$147$	−7.01366	−	7.01366i	−0.578477	−	0.578477i
$148$			22.8693i			1.87984i
$149$	−6.53739	+	6.53739i	−0.535564	+	0.535564i	−0.922223	−	0.386659i	$-0.873629\pi$
$149$	−6.53739	+	6.53739i	−0.535564	+	0.535564i	0.386659	+	0.922223i	$0.373629\pi$
$150$	7.65447	−	8.02338i	0.624985	−	0.655106i
$151$	2.56165	−	2.56165i	0.208464	−	0.208464i	−0.595150	−	0.803614i	$-0.702907\pi$
$151$	2.56165	−	2.56165i	0.208464	−	0.208464i	0.803614	+	0.595150i	$0.202907\pi$
$152$	−5.62483	+	5.62483i	−0.456234	+	0.456234i
$153$	−1.98080	+	1.98080i	−0.160138	+	0.160138i
$154$	23.6545	+	23.6545i	1.90613	+	1.90613i
$155$	−6.68243	+	0.0786099i	−0.536746	+	0.00631410i
$156$	9.82904	−	3.75881i	0.786953	−	0.300946i
$157$	−2.92797	+	2.92797i	−0.233678	+	0.233678i	−0.814226	−	0.580548i	$-0.802838\pi$
$157$	−2.92797	+	2.92797i	−0.233678	+	0.233678i	0.580548	+	0.814226i	$0.302838\pi$
$158$		−	18.7523i		−	1.49185i
$159$			7.52343i			0.596646i
$160$	10.9365	−	11.1969i	0.864605	−	0.885189i
$161$	−6.33252	−	6.33252i	−0.499073	−	0.499073i
$162$	−2.21780			−0.174247
$163$	8.49438			0.665331			0.332666	−	0.943045i	$-0.392052\pi$
$163$	8.49438			0.665331			0.332666	+	0.943045i	$0.392052\pi$
$164$	4.82302	+	4.82302i	0.376615	+	0.376615i
$165$	5.72958	−	5.86599i	0.446047	−	0.456667i
$166$			9.96651i			0.773551i
$167$		−	13.2559i		−	1.02577i	−0.858457	−	0.512886i	$-0.828576\pi$
$167$		−	13.2559i		−	1.02577i	0.858457	−	0.512886i	$-0.171424\pi$
$168$	5.92556	−	5.92556i	0.457167	−	0.457167i
$169$	−8.67432	−	9.68277i	−0.667256	−	0.744829i
$170$	−13.8910	+	0.163408i	−1.06539	+	0.0125329i
$171$	−2.76089	−	2.76089i	−0.211131	−	0.211131i
$172$	3.71224	−	3.71224i	0.283056	−	0.283056i
$173$	7.94523	−	7.94523i	0.604065	−	0.604065i	−0.337324	−	0.941389i	$-0.609522\pi$
$173$	7.94523	−	7.94523i	0.604065	−	0.604065i	0.941389	+	0.337324i	$0.109522\pi$
$174$	13.1842	−	13.1842i	0.999493	−	0.999493i
$175$	−20.5606	+	0.483802i	−1.55423	+	0.0365720i
$176$	3.41991	−	3.41991i	0.257785	−	0.257785i
$177$			9.20675i			0.692022i
$178$	−19.7802	−	19.7802i	−1.48259	−	1.48259i
$179$	−1.37631			−0.102870			−0.0514350	−	0.998676i	$-0.516379\pi$
$179$	−1.37631			−0.102870			−0.0514350	+	0.998676i	$0.516379\pi$
$180$	−4.66871	−	4.56015i	−0.347985	−	0.339893i
$181$			23.4687i			1.74442i	0.489136	+	0.872208i	$0.337312\pi$
$181$			23.4687i			1.74442i	−0.489136	+	0.872208i	$0.662688\pi$
$182$	−30.0306	−	13.4159i	−2.22602	−	0.994450i
$183$	5.54991	+	5.54991i	0.410261	+	0.410261i
$184$	3.13654	−	3.13654i	0.231229	−	0.231229i
$185$	−12.5341	−	12.2427i	−0.921527	−	0.900098i
$186$			6.62829i			0.486010i
$187$	−10.2725			−0.751202
$188$			18.5359i			1.35187i
$189$	2.90851	+	2.90851i	0.211563	+	0.211563i
$190$	−0.227763	−	19.3616i	−0.0165237	−	1.40464i
$191$	−2.92479			−0.211630			−0.105815	−	0.994386i	$-0.533745\pi$
$191$	−2.92479			−0.211630			−0.105815	+	0.994386i	$0.533745\pi$
$192$	−9.11181	−	9.11181i	−0.657589	−	0.657589i
$193$	−20.6977			−1.48985			−0.744927	−	0.667146i	$-0.767516\pi$
$193$	−20.6977			−1.48985			−0.744927	+	0.667146i	$0.767516\pi$
$194$	39.0396			2.80288
$195$	−3.20168	+	7.39927i	−0.229277	+	0.529873i
$196$	−28.9493			−2.06781
$197$	−6.16201			−0.439025			−0.219513	−	0.975610i	$-0.570447\pi$
$197$	−6.16201			−0.439025			−0.219513	+	0.975610i	$0.570447\pi$
$198$	−5.75081	−	5.75081i	−0.408692	−	0.408692i
$199$	−23.2876			−1.65081			−0.825407	−	0.564538i	$-0.809054\pi$
$199$	−23.2876			−1.65081			−0.825407	+	0.564538i	$0.809054\pi$
$200$	−0.239630	−	10.1838i	−0.0169444	−	0.720102i
$201$	−8.73248	−	8.73248i	−0.615942	−	0.615942i
$202$			10.3489i			0.728150i
$203$	−34.5806			−2.42708
$204$			8.17586i			0.572424i
$205$	−5.22530	+	0.0614687i	−0.364951	+	0.00429316i
$206$	−4.61499	+	4.61499i	−0.321542	+	0.321542i
$207$	1.53954	+	1.53954i	0.107006	+	0.107006i
$208$	−1.93963	+	4.34175i	−0.134489	+	0.301046i
$209$		−	14.3182i		−	0.990407i
$210$	0.239941	+	20.3968i	0.0165575	+	1.40751i
$211$	11.6786			0.803990			0.401995	−	0.915642i	$-0.368317\pi$
$211$	11.6786			0.803990			0.401995	+	0.915642i	$0.368317\pi$
$212$	15.5267	+	15.5267i	1.06638	+	1.06638i
$213$		−	10.9690i		−	0.751585i
$214$	3.79718	−	3.79718i	0.259570	−	0.259570i
$215$	0.0473119	+	4.02187i	0.00322665	+	0.274289i
$216$	−1.44060	+	1.44060i	−0.0980206	+	0.0980206i
$217$	8.69260	−	8.69260i	0.590092	−	0.590092i
$218$	10.5950	−	10.5950i	0.717583	−	0.717583i
$219$	3.73313	+	3.73313i	0.252262	+	0.252262i
$220$	−0.281512	−	23.9307i	−0.0189796	−	1.61341i
$221$	9.43384	−	3.60768i	0.634588	−	0.242679i
$222$	−12.2880	+	12.2880i	−0.824717	+	0.824717i
$223$		−	16.7954i		−	1.12470i	−0.826898	−	0.562351i	$-0.809897\pi$
$223$		−	16.7954i		−	1.12470i	0.826898	−	0.562351i	$-0.190103\pi$
$224$			28.7913i			1.92370i
$225$	4.99862	−	0.117620i	0.333241	−	0.00784135i
$226$	−4.32517	−	4.32517i	−0.287706	−	0.287706i
$227$	−22.2305			−1.47549			−0.737746	−	0.675078i	$-0.764110\pi$
$227$	−22.2305			−1.47549			−0.737746	+	0.675078i	$0.764110\pi$
$228$	−11.3957			−0.754702
$229$	−1.99942	−	1.99942i	−0.132125	−	0.132125i	0.637951	−	0.770077i	$-0.279782\pi$
$229$	−1.99942	−	1.99942i	−0.132125	−	0.132125i	−0.770077	+	0.637951i	$0.779782\pi$
$230$	0.127006	+	10.7965i	0.00837456	+	0.711901i
$231$			15.0837i			0.992433i
$232$		−	17.1280i		−	1.12451i
$233$	7.60402	−	7.60402i	0.498156	−	0.498156i	−0.412708	−	0.910863i	$-0.635417\pi$
$233$	7.60402	−	7.60402i	0.498156	−	0.498156i	0.910863	+	0.412708i	$0.135417\pi$
$234$	7.30095	+	3.26162i	0.477278	+	0.213219i
$235$	−10.1591	−	9.92287i	−0.662707	−	0.647296i
$236$	19.0007	+	19.0007i	1.23684	+	1.23684i
$237$	5.97886	−	5.97886i	0.388369	−	0.388369i
$238$	18.0695	−	18.0695i	1.17127	−	1.17127i
$239$	−17.2164	+	17.2164i	−1.11363	+	1.11363i	−0.120979	+	0.992655i	$0.538603\pi$
$239$	−17.2164	+	17.2164i	−1.11363	+	1.11363i	−0.992655	+	0.120979i	$0.961397\pi$
$240$	2.94891	−	0.0346900i	0.190351	−	0.00223923i
$241$	10.2155	−	10.2155i	0.658040	−	0.658040i	−0.296876	−	0.954916i	$-0.595945\pi$
$241$	10.2155	−	10.2155i	0.658040	−	0.658040i	0.954916	+	0.296876i	$0.0959447\pi$
$242$		−	5.42825i		−	0.348941i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	22.9076			1.46651
$245$	15.4975	−	15.8664i	0.990097	−	1.01367i
$246$			5.18296i			0.330454i
$247$	5.02849	+	13.1492i	0.319955	+	0.836661i
$248$	4.30550	+	4.30550i	0.273400	+	0.273400i
$249$	−3.17765	+	3.17765i	−0.201376	+	0.201376i
$250$	18.1409	+	16.9037i	1.14733	+	1.06908i
$251$			18.7574i			1.18396i	0.805954	+	0.591978i	$0.201653\pi$
$251$			18.7574i			1.18396i	−0.805954	+	0.591978i	$0.798347\pi$
$252$	12.0050			0.756245
$253$			7.98415i			0.501959i
$254$	−9.60860	−	9.60860i	−0.602897	−	0.602897i
$255$	−4.48099	−	4.37679i	−0.280611	−	0.274085i
$256$	−6.56189			−0.410118
$257$	−1.40078	−	1.40078i	−0.0873784	−	0.0873784i	0.662067	−	0.749445i	$-0.269680\pi$
$257$	−1.40078	−	1.40078i	−0.0873784	−	0.0873784i	−0.749445	+	0.662067i	$0.769680\pi$
$258$	3.98928			0.248362
$259$	32.2300			2.00267
$260$	8.66291	+	21.8780i	0.537251	+	1.35682i
$261$	8.40712			0.520388
$262$	−26.0915			−1.61194
$263$	15.8782	+	15.8782i	0.979092	+	0.979092i	0.999786	−	0.0206938i	$-0.00658750\pi$
$263$	15.8782	+	15.8782i	0.979092	+	0.979092i	−0.0206938	+	0.999786i	$0.506587\pi$
$264$	−7.47105			−0.459811
$265$	−16.8217	+	0.197885i	−1.03335	+	0.0121560i
$266$	25.1859	+	25.1859i	1.54424	+	1.54424i
$267$		−	12.6131i		−	0.771912i
$268$	−36.0438			−2.20173
$269$			0.349269i			0.0212953i	0.999943	+	0.0106477i	$0.00338932\pi$
$269$			0.349269i			0.0212953i	−0.999943	+	0.0106477i	$0.996611\pi$
$270$	−0.0583336	−	4.95880i	−0.00355007	−	0.301783i
$271$	8.52139	−	8.52139i	0.517637	−	0.517637i	−0.399218	−	0.916856i	$-0.630719\pi$
$271$	8.52139	−	8.52139i	0.517637	−	0.517637i	0.916856	+	0.399218i	$0.130719\pi$
$272$	−2.61245	−	2.61245i	−0.158403	−	0.158403i
$273$	−5.29734	−	13.8522i	−0.320609	−	0.838372i
$274$		−	27.4272i		−	1.65694i
$275$	13.2665	+	12.6566i	0.800003	+	0.763219i
$276$	6.35455			0.382499
$277$	5.27671	+	5.27671i	0.317047	+	0.317047i	0.847632	−	0.530585i	$-0.178028\pi$
$277$	5.27671	+	5.27671i	0.317047	+	0.317047i	−0.530585	+	0.847632i	$0.678028\pi$
$278$		−	33.6505i		−	2.01823i
$279$	−2.11332	+	2.11332i	−0.126521	+	0.126521i
$280$	13.4049	+	13.0932i	0.801095	+	0.782467i
$281$	−5.98480	+	5.98480i	−0.357023	+	0.357023i	−0.862714	−	0.505691i	$-0.831237\pi$
$281$	−5.98480	+	5.98480i	−0.357023	+	0.357023i	0.505691	+	0.862714i	$0.331237\pi$
$282$	−9.95963	+	9.95963i	−0.593087	+	0.593087i
$283$	2.56174	−	2.56174i	0.152280	−	0.152280i	−0.626856	−	0.779135i	$-0.715658\pi$
$283$	2.56174	−	2.56174i	0.152280	−	0.152280i	0.779135	+	0.626856i	$0.215658\pi$
$284$	−22.6376	−	22.6376i	−1.34330	−	1.34330i
$285$	6.10050	−	6.24574i	0.361363	−	0.369966i
$286$	10.4741	+	27.3891i	0.619346	+	1.61955i
$287$	6.79714	−	6.79714i	0.401223	−	0.401223i
$288$		−	6.99966i		−	0.412459i
$289$		−	9.15288i		−	0.538404i
$290$	29.8255	+	29.1320i	1.75142	+	1.71069i
$291$	12.4471	+	12.4471i	0.729662	+	0.729662i
$292$	15.4087			0.901727
$293$	5.91537			0.345579			0.172790	−	0.984959i	$-0.444722\pi$
$293$	5.91537			0.345579			0.172790	+	0.984959i	$0.444722\pi$
$294$	−15.5549	−	15.5549i	−0.907179	−	0.907179i
$295$	−20.5855	+	0.242161i	−1.19853	+	0.0140991i
$296$			15.9637i			0.927872i
$297$		−	3.66710i		−	0.212786i
$298$	−14.4986	+	14.4986i	−0.839882	+	0.839882i
$299$	−2.80401	−	7.33229i	−0.162160	−	0.424037i
$300$	10.0733	−	10.5588i	0.581582	−	0.609611i
$301$	−5.23170	−	5.23170i	−0.301550	−	0.301550i
$302$	5.68122	−	5.68122i	0.326918	−	0.326918i
$303$	−3.29959	+	3.29959i	−0.189556	+	0.189556i
$304$	3.64130	−	3.64130i	0.208843	−	0.208843i
$305$	−12.2631	+	12.5551i	−0.702186	+	0.718903i
$306$	−4.39301	+	4.39301i	−0.251132	+	0.251132i
$307$			2.81730i			0.160792i	0.996763	+	0.0803960i	$0.0256185\pi$
$307$			2.81730i			0.160792i	−0.996763	+	0.0803960i	$0.974382\pi$
$308$	31.1294	+	31.1294i	1.77376	+	1.77376i
$309$	−2.94282			−0.167411
$310$	−14.8203	+	0.174341i	−0.841735	+	0.00990189i
$311$		−	9.18067i		−	0.520588i	−0.965529	−	0.260294i	$-0.916180\pi$
$311$		−	9.18067i		−	0.520588i	0.965529	−	0.260294i	$-0.0838195\pi$
$312$	6.86108	−	2.62381i	0.388432	−	0.148544i
$313$	16.4881	+	16.4881i	0.931960	+	0.931960i	0.997828	−	0.0658683i	$-0.0209817\pi$
$313$	16.4881	+	16.4881i	0.931960	+	0.931960i	−0.0658683	+	0.997828i	$0.520982\pi$
$314$	−6.49365	+	6.49365i	−0.366458	+	0.366458i
$315$	−6.42667	+	6.57967i	−0.362102	+	0.370722i
$316$		−	24.6781i		−	1.38825i
$317$	13.3835			0.751695			0.375847	−	0.926682i	$-0.377352\pi$
$317$	13.3835			0.751695			0.375847	+	0.926682i	$0.377352\pi$
$318$			16.6854i			0.935672i
$319$	21.7999	+	21.7999i	1.22056	+	1.22056i
$320$	20.1336	−	20.6129i	1.12550	−	1.15230i
$321$	2.42133			0.135145
$322$	−14.0442	−	14.0442i	−0.782655	−	0.782655i
$323$	−10.9376			−0.608582
$324$	−2.91862			−0.162146
$325$	−16.6283	−	6.96406i	−0.922375	−	0.386296i
$326$	18.8388			1.04339
$327$	6.75606			0.373611
$328$	3.36667	+	3.36667i	0.185893	+	0.185893i
$329$	26.1229			1.44020
$330$	12.7071	−	13.0096i	0.699500	−	0.716153i
$331$	−13.7828	−	13.7828i	−0.757572	−	0.757572i	0.218308	−	0.975880i	$-0.429946\pi$
$331$	−13.7828	−	13.7828i	−0.757572	−	0.757572i	−0.975880	+	0.218308i	$0.929946\pi$
$332$			13.1159i			0.719831i
$333$	−7.83564			−0.429391
$334$		−	29.3989i		−	1.60863i
$335$	19.2954	−	19.7548i	1.05422	−	1.07932i
$336$	−3.83599	+	3.83599i	−0.209270	+	0.209270i
$337$	24.8025	+	24.8025i	1.35108	+	1.35108i	0.884459	+	0.466618i	$0.154528\pi$
$337$	24.8025	+	24.8025i	1.35108	+	1.35108i	0.466618	+	0.884459i	$0.345472\pi$
$338$	−19.2379	−	21.4744i	−1.04640	−	1.16805i
$339$		−	2.75801i		−	0.149795i
$340$	−18.2805	+	0.215046i	−0.991400	+	0.0116625i
$341$	−10.9598			−0.593506
$342$	−6.12310	−	6.12310i	−0.331100	−	0.331100i
$343$			12.0058i			0.648254i
$344$	2.59130	−	2.59130i	0.139713	−	0.139713i
$345$	−3.40179	+	3.48278i	−0.183146	+	0.187506i
$346$	17.6209	−	17.6209i	0.947306	−	0.947306i
$347$	2.24725	−	2.24725i	0.120639	−	0.120639i	−0.644210	−	0.764849i	$-0.722814\pi$
$347$	2.24725	−	2.24725i	0.120639	−	0.120639i	0.764849	+	0.644210i	$0.222814\pi$
$348$	17.3504	−	17.3504i	0.930081	−	0.930081i
$349$	19.2780	+	19.2780i	1.03193	+	1.03193i	0.999473	+	0.0324525i	$0.0103318\pi$
$349$	19.2780	+	19.2780i	1.03193	+	1.03193i	0.0324525	+	0.999473i	$0.489668\pi$
$350$	−45.5991	+	1.07297i	−2.43738	+	0.0573529i
$351$	1.28787	+	3.36770i	0.0687415	+	0.179754i
$352$	18.1503	−	18.1503i	0.967415	−	0.967415i
$353$			20.5850i			1.09563i	0.836600	+	0.547814i	$0.184540\pi$
$353$			20.5850i			1.09563i	−0.836600	+	0.547814i	$0.815460\pi$
$354$			20.4187i			1.08524i
$355$	24.5258	−	0.288513i	1.30169	−	0.0153127i
$356$	−26.0307	−	26.0307i	−1.37963	−	1.37963i
$357$	11.5223			0.609826
$358$	−3.05237			−0.161323
$359$	10.6029	+	10.6029i	0.559602	+	0.559602i	0.929194	−	0.369592i	$-0.120503\pi$
$359$	10.6029	+	10.6029i	0.559602	+	0.559602i	−0.369592	+	0.929194i	$0.620503\pi$
$360$	−3.25895	−	3.18317i	−0.171762	−	0.167768i
$361$			3.75492i			0.197627i
$362$			52.0488i			2.73563i
$363$	1.73071	−	1.73071i	0.0908385	−	0.0908385i
$364$	−39.5204	−	17.6553i	−2.07143	−	0.925389i
$365$	−8.24877	+	8.44515i	−0.431760	+	0.442039i
$366$	12.3086	+	12.3086i	0.643380	+	0.643380i
$367$	−1.02534	+	1.02534i	−0.0535221	+	0.0535221i	−0.733361	−	0.679839i	$-0.762050\pi$
$367$	−1.02534	+	1.02534i	−0.0535221	+	0.0535221i	0.679839	+	0.733361i	$0.262050\pi$
$368$	−2.03048	+	2.03048i	−0.105846	+	0.105846i
$369$	−1.65250	+	1.65250i	−0.0860257	+	0.0860257i
$370$	−27.7981	−	27.1517i	−1.44516	−	1.41155i
$371$	21.8819	−	21.8819i	1.13605	−	1.13605i
$372$			8.72284i			0.452258i
$373$	8.41567	+	8.41567i	0.435747	+	0.435747i	0.890578	−	0.454831i	$-0.150300\pi$
$373$	8.41567	+	8.41567i	0.435747	+	0.435747i	−0.454831	+	0.890578i	$0.650300\pi$
$374$	−22.7824			−1.17805
$375$	0.394465	+	11.1734i	0.0203701	+	0.576991i
$376$			12.9388i			0.667270i
$377$	−27.6761	−	12.3640i	−1.42539	−	0.636779i
$378$	6.45048	+	6.45048i	0.331777	+	0.331777i
$379$	−5.03557	+	5.03557i	−0.258660	+	0.258660i	−0.824509	−	0.565849i	$-0.808548\pi$
$379$	−5.03557	+	5.03557i	−0.258660	+	0.258660i	0.565849	+	0.824509i	$0.308548\pi$
$380$	−0.299737	−	25.4799i	−0.0153762	−	1.30709i
$381$		−	6.12708i		−	0.313900i
$382$	−6.48659			−0.331883
$383$		−	0.483559i		−	0.0247087i	−0.999924	−	0.0123543i	$-0.996067\pi$
$383$		−	0.483559i		−	0.0247087i	0.999924	−	0.0123543i	$-0.00393261\pi$
$384$	−10.3091	−	10.3091i	−0.526086	−	0.526086i
$385$	−33.7258	+	0.396739i	−1.71883	+	0.0202197i
$386$	−45.9033			−2.33642
$387$	1.27192	+	1.27192i	0.0646551	+	0.0646551i
$388$	51.3761			2.60823
$389$	17.5944			0.892070			0.446035	−	0.895015i	$-0.352836\pi$
$389$	17.5944			0.892070			0.446035	+	0.895015i	$0.352836\pi$
$390$	−7.10067	+	16.4101i	−0.359557	+	0.830957i
$391$	6.09905			0.308442
$392$	−20.2078			−1.02065
$393$	−8.31883	−	8.31883i	−0.419629	−	0.419629i
$394$	−13.6661			−0.688488
$395$	13.5255	+	13.2110i	0.680540	+	0.664715i
$396$	−7.56807	−	7.56807i	−0.380310	−	0.380310i
$397$			9.63810i			0.483722i	0.970311	+	0.241861i	$0.0777578\pi$
$397$			9.63810i			0.483722i	−0.970311	+	0.241861i	$0.922242\pi$
$398$	−51.6472			−2.58884
$399$			16.0602i			0.804014i
$400$	0.155128	+	6.59260i	0.00775638	+	0.329630i
$401$	−16.8784	+	16.8784i	−0.842865	+	0.842865i	−0.989231	−	0.146365i	$-0.953243\pi$
$401$	−16.8784	+	16.8784i	−0.842865	+	0.842865i	0.146365	+	0.989231i	$0.453243\pi$
$402$	−19.3669	−	19.3669i	−0.965932	−	0.965932i
$403$	10.0650	−	3.84904i	0.501372	−	0.191734i
$404$			13.6192i			0.677582i
$405$	1.56243	−	1.59963i	0.0776378	−	0.0794862i
$406$	−76.6927			−3.80620
$407$	−20.3180	−	20.3180i	−1.00713	−	1.00713i
$408$			5.70709i			0.282543i
$409$	−3.65546	+	3.65546i	−0.180751	+	0.180751i	−0.791683	−	0.610932i	$-0.790795\pi$
$409$	−3.65546	+	3.65546i	−0.180751	+	0.180751i	0.610932	+	0.791683i	$0.290795\pi$
$410$	−11.5887	+	0.136325i	−0.572323	+	0.00673261i
$411$	8.74468	−	8.74468i	0.431343	−	0.431343i
$412$	−6.07334	+	6.07334i	−0.299212	+	0.299212i
$413$	26.7779	−	26.7779i	1.31765	−	1.31765i
$414$	3.41439	+	3.41439i	0.167808	+	0.167808i
$415$	−7.18853	−	7.02137i	−0.352871	−	0.344666i
$416$	−10.2941	+	23.0428i	−0.504710	+	1.12976i
$417$	10.7289	−	10.7289i	0.525397	−	0.525397i
$418$		−	31.7548i		−	1.55318i
$419$		−	33.9420i		−	1.65818i	−0.559117	−	0.829089i	$-0.688860\pi$
$419$		−	33.9420i		−	1.65818i	0.559117	−	0.829089i	$-0.311140\pi$
$420$	0.315762	+	26.8422i	0.0154076	+	1.30976i
$421$	−19.7073	−	19.7073i	−0.960474	−	0.960474i	0.0387742	−	0.999248i	$-0.487655\pi$
$421$	−19.7073	−	19.7073i	−0.960474	−	0.960474i	−0.999248	+	0.0387742i	$0.987655\pi$
$422$	25.9008			1.26083
$423$	−6.35092			−0.308792
$424$	10.8383	+	10.8383i	0.526353	+	0.526353i
$425$	9.66827	−	10.1342i	0.468980	−	0.491583i
$426$		−	24.3271i		−	1.17865i
$427$		−	32.2839i		−	1.56233i
$428$	4.99709	−	4.99709i	0.241543	−	0.241543i
$429$	−5.39305	+	12.0720i	−0.260379	+	0.582843i
$430$	0.104928	+	8.91969i	0.00506009	+	0.430146i
$431$	10.7665	+	10.7665i	0.518606	+	0.518606i	0.917150	−	0.398543i	$-0.130484\pi$
$431$	10.7665	+	10.7665i	0.518606	+	0.518606i	−0.398543	+	0.917150i	$0.630484\pi$
$432$	0.932593	−	0.932593i	0.0448694	−	0.0448694i
$433$	−11.8525	+	11.8525i	−0.569594	+	0.569594i	−0.932015	−	0.362421i	$-0.881950\pi$
$433$	−11.8525	+	11.8525i	−0.569594	+	0.569594i	0.362421	+	0.932015i	$0.381950\pi$
$434$	19.2784	−	19.2784i	0.925394	−	0.925394i
$435$	0.221129	+	18.7976i	0.0106023	+	0.901276i
$436$	13.9430	−	13.9430i	0.667749	−	0.667749i
$437$			8.50103i			0.406659i
$438$	8.27933	+	8.27933i	0.395602	+	0.395602i
$439$	−2.02222			−0.0965152			−0.0482576	−	0.998835i	$-0.515367\pi$
$439$	−2.02222			−0.0965152			−0.0482576	+	0.998835i	$0.515367\pi$
$440$	−0.196507	−	16.7046i	−0.00936812	−	0.796361i
$441$		−	9.91882i		−	0.472325i
$442$	20.9223	−	8.00110i	0.995174	−	0.380573i
$443$	0.127396	+	0.127396i	0.00605277	+	0.00605277i	0.710127	−	0.704074i	$-0.248638\pi$
$443$	0.127396	+	0.127396i	0.00605277	+	0.00605277i	−0.704074	+	0.710127i	$0.748638\pi$
$444$	−16.1710	+	16.1710i	−0.767443	+	0.767443i
$445$	28.2019	−	0.331758i	1.33690	−	0.0157268i
$446$		−	37.2488i		−	1.76378i
$447$	−9.24527			−0.437286
$448$			53.0035i			2.50418i
$449$	−24.8640	−	24.8640i	−1.17341	−	1.17341i	−0.981392	−	0.192014i	$-0.938498\pi$
$449$	−24.8640	−	24.8640i	−1.17341	−	1.17341i	−0.192014	−	0.981392i	$-0.561502\pi$
$450$	11.0859	−	0.260858i	0.522595	−	0.0122970i
$451$	−8.56996			−0.403544
$452$	−5.69192	−	5.69192i	−0.267726	−	0.267726i
$453$	3.62272			0.170210
$454$	−49.3028			−2.31390
$455$	30.8329	−	12.2087i	1.44547	−	0.572354i
$456$	−7.95470			−0.372513
$457$	32.3018			1.51101			0.755507	−	0.655140i	$-0.227390\pi$
$457$	32.3018			1.51101			0.755507	+	0.655140i	$0.227390\pi$
$458$	−4.43430	−	4.43430i	−0.207201	−	0.207201i
$459$	−2.80127			−0.130752
$460$	0.167141	+	14.2082i	0.00779297	+	0.662462i
$461$	−14.5631	−	14.5631i	−0.678272	−	0.678272i	0.281337	−	0.959609i	$-0.409222\pi$
$461$	−14.5631	−	14.5631i	−0.678272	−	0.678272i	−0.959609	+	0.281337i	$0.909222\pi$
$462$			33.4525i			1.55635i
$463$	13.2720			0.616800			0.308400	−	0.951257i	$-0.400206\pi$
$463$	13.2720			0.616800			0.308400	+	0.951257i	$0.400206\pi$
$464$			11.0880i			0.514749i
$465$	−4.78078	−	4.66961i	−0.221703	−	0.216548i
$466$	16.8642	−	16.8642i	0.781217	−	0.781217i
$467$	21.6107	+	21.6107i	1.00002	+	1.00002i	1.00000		2.29542e-5i	$7.30656e-6\pi$
$467$	21.6107	+	21.6107i	1.00002	+	1.00002i	2.29542e−5		1.00000i	$0.499993\pi$
$468$	9.60806	+	4.29230i	0.444133	+	0.198412i
$469$			50.7970i			2.34559i
$470$	−22.5308	−	22.0069i	−1.03927	−	1.01510i
$471$	−4.14078			−0.190797
$472$	13.2633	+	13.2633i	0.610491	+	0.610491i
$473$			6.59622i			0.303295i
$474$	13.2599	−	13.2599i	0.609047	−	0.609047i
$475$	14.1254	+	13.4759i	0.648117	+	0.618317i
$476$	23.7795	−	23.7795i	1.08993	−	1.08993i
$477$	−5.31987	+	5.31987i	−0.243580	+	0.243580i
$478$	−38.1824	+	38.1824i	−1.74642	+	1.74642i
$479$	13.5992	+	13.5992i	0.621361	+	0.621361i	0.945879	−	0.324518i	$-0.105202\pi$
$479$	13.5992	+	13.5992i	0.621361	+	0.621361i	−0.324518	+	0.945879i	$0.605202\pi$
$480$	15.6506	−	0.184109i	0.714350	−	0.00840337i
$481$	25.7948	+	11.5236i	1.17614	+	0.525429i
$482$	22.6560	−	22.6560i	1.03195	−	1.03195i
$483$		−	8.95554i		−	0.407491i
$484$		−	7.14359i		−	0.324708i
$485$	−27.5032	+	28.1580i	−1.24886	+	1.27859i
$486$	−1.56822	−	1.56822i	−0.0711359	−	0.0711359i
$487$	16.1028			0.729687			0.364844	−	0.931069i	$-0.381122\pi$
$487$	16.1028			0.729687			0.364844	+	0.931069i	$0.381122\pi$
$488$	15.9904			0.723853
$489$	6.00644	+	6.00644i	0.271620	+	0.271620i
$490$	34.3702	−	35.1885i	1.55269	−	1.58965i
$491$		−	20.7163i		−	0.934915i	−0.884016	−	0.467457i	$-0.845170\pi$
$491$		−	20.7163i		−	0.934915i	0.884016	−	0.467457i	$-0.154830\pi$
$492$			6.82079i			0.307505i
$493$	16.6528	−	16.6528i	0.750005	−	0.750005i
$494$	11.1522	+	29.1622i	0.501760	+	1.31207i
$495$	8.19931	−	0.0964538i	0.368531	−	0.00433528i
$496$	−2.78722	−	2.78722i	−0.125150	−	0.125150i
$497$	−31.9035	+	31.9035i	−1.43107	+	1.43107i
$498$	−7.04739	+	7.04739i	−0.315801	+	0.315801i
$499$	−4.09738	+	4.09738i	−0.183424	+	0.183424i	−0.792846	−	0.609422i	$-0.791401\pi$
$499$	−4.09738	+	4.09738i	−0.183424	+	0.183424i	0.609422	+	0.792846i	$0.291401\pi$
$500$	23.8735	+	22.2453i	1.06765	+	0.994840i
$501$	9.37333	−	9.37333i	0.418769	−	0.418769i
$502$			41.6001i			1.85670i
$503$	−23.4993	−	23.4993i	−1.04778	−	1.04778i	−0.998800	−	0.0489821i	$-0.984402\pi$
$503$	−23.4993	−	23.4993i	−1.04778	−	1.04778i	−0.0489821	−	0.998800i	$-0.515598\pi$
$504$	8.38000			0.373275
$505$	−7.46438	−	7.29080i	−0.332160	−	0.324436i
$506$			17.7072i			0.787182i
$507$	0.713080	−	12.9804i	0.0316690	−	0.576481i
$508$	−12.6449	−	12.6449i	−0.561028	−	0.561028i
$509$	−13.7959	+	13.7959i	−0.611492	+	0.611492i	−0.943335	−	0.331843i	$-0.892330\pi$
$509$	−13.7959	+	13.7959i	−0.611492	+	0.611492i	0.331843	+	0.943335i	$0.392330\pi$
$510$	−9.93793	−	9.70684i	−0.440059	−	0.429826i
$511$		−	21.7157i		−	0.960645i
$512$	14.6057			0.645488
$513$		−	3.90449i		−	0.172388i
$514$	−3.10665	−	3.10665i	−0.137029	−	0.137029i
$515$	−0.0774037	−	6.57990i	−0.00341081	−	0.289945i
$516$	5.24990			0.231114
$517$	−16.4681	−	16.4681i	−0.724266	−	0.724266i
$518$	71.4795			3.14063
$519$	11.2362			0.493217
$520$	6.04707	+	15.2718i	0.265181	+	0.669711i
$521$	−20.4402			−0.895503			−0.447752	−	0.894158i	$-0.647775\pi$
$521$	−20.4402			−0.895503			−0.447752	+	0.894158i	$0.647775\pi$
$522$	18.6453			0.816082
$523$	1.95338	+	1.95338i	0.0854154	+	0.0854154i	0.748524	−	0.663108i	$-0.230763\pi$
$523$	1.95338	+	1.95338i	0.0854154	+	0.0854154i	−0.663108	+	0.748524i	$0.730763\pi$
$524$	−34.3364			−1.49999
$525$	−14.8806	−	14.1964i	−0.649443	−	0.619582i
$526$	35.2146	+	35.2146i	1.53543	+	1.53543i
$527$			8.37211i			0.364695i
$528$	4.83648			0.210481
$529$			18.2596i			0.793896i
$530$	−37.3072	+	0.438869i	−1.62052	+	0.0190632i
$531$	−6.51015	+	6.51015i	−0.282517	+	0.282517i
$532$	33.1446	+	33.1446i	1.43700	+	1.43700i
$533$	7.87027	−	3.00974i	0.340899	−	0.130366i
$534$		−	27.9734i		−	1.21053i
$535$	0.0636871	+	5.41388i	0.00275343	+	0.234063i
$536$	−25.1601			−1.08675
$537$	−0.973196	−	0.973196i	−0.0419965	−	0.0419965i
$538$			0.774608i			0.0333957i
$539$	25.7198	−	25.7198i	1.10783	−	1.10783i
$540$	−0.0767671	−	6.52579i	−0.00330353	−	0.280825i
$541$	28.9135	−	28.9135i	1.24309	−	1.24309i	0.284374	−	0.958714i	$-0.408214\pi$
$541$	28.9135	−	28.9135i	1.24309	−	1.24309i	0.958714	−	0.284374i	$-0.0917856\pi$
$542$	18.8987	−	18.8987i	0.811769	−	0.811769i
$543$	−16.5949	+	16.5949i	−0.712155	+	0.712155i
$544$	−13.8649	−	13.8649i	−0.594453	−	0.594453i
$545$	0.177701	+	15.1060i	0.00761189	+	0.647068i
$546$	−11.7484	−	30.7213i	−0.502786	−	1.31475i
$547$	−21.7628	+	21.7628i	−0.930509	+	0.930509i	−0.997738	−	0.0672284i	$-0.978584\pi$
$547$	−21.7628	+	21.7628i	−0.930509	+	0.930509i	0.0672284	+	0.997738i	$0.478584\pi$
$548$		−	36.0942i		−	1.54187i
$549$			7.84876i			0.334977i
$550$	29.4225	+	28.0697i	1.25458	+	1.19690i
$551$	23.2112	+	23.2112i	0.988830	+	0.988830i
$552$	4.43574			0.188798
$553$	−34.7791			−1.47896
$554$	11.7027	+	11.7027i	0.497199	+	0.497199i
$555$	−0.206097	−	17.5198i	−0.00874834	−	0.743675i
$556$		−	44.2842i		−	1.87807i
$557$		−	37.6115i		−	1.59365i	−0.604210	−	0.796825i	$-0.706511\pi$
$557$		−	37.6115i		−	1.59365i	0.604210	−	0.796825i	$-0.293489\pi$
$558$	−4.68691	+	4.68691i	−0.198413	+	0.198413i
$559$	−2.31657	−	6.05768i	−0.0979805	−	0.256212i
$560$	−8.67783	−	8.47604i	−0.366705	−	0.358178i
$561$	−7.26378	−	7.26378i	−0.306677	−	0.306677i
$562$	−13.2731	+	13.2731i	−0.559890	+	0.559890i
$563$	−27.8463	+	27.8463i	−1.17358	+	1.17358i	−0.192234	+	0.981349i	$0.561573\pi$
$563$	−27.8463	+	27.8463i	−1.17358	+	1.17358i	−0.981349	+	0.192234i	$0.938427\pi$
$564$	−13.1069	+	13.1069i	−0.551899	+	0.551899i
$565$	6.16667	−	0.0725426i	0.259434	−	0.00305189i
$566$	5.68142	−	5.68142i	0.238808	−	0.238808i
$567$			4.11325i			0.172740i
$568$	−15.8020	−	15.8020i	−0.663037	−	0.663037i
$569$	−1.85521			−0.0777743			−0.0388872	−	0.999244i	$-0.512381\pi$
$569$	−1.85521			−0.0777743			−0.0388872	+	0.999244i	$0.512381\pi$
$570$	13.5297	−	13.8518i	0.566696	−	0.580187i
$571$			33.3973i			1.39763i	0.715302	+	0.698816i	$0.246289\pi$
$571$			33.3973i			1.39763i	−0.715302	+	0.698816i	$0.753711\pi$
$572$	13.7839	+	36.0440i	0.576335	+	1.50708i
$573$	−2.06814	−	2.06814i	−0.0863977	−	0.0863977i
$574$	15.0747	−	15.0747i	0.629205	−	0.629205i
$575$	−7.87666	−	7.51450i	−0.328480	−	0.313376i
$576$		−	12.8861i		−	0.536919i
$577$	−17.7281			−0.738030			−0.369015	−	0.929423i	$-0.620305\pi$
$577$	−17.7281			−0.738030			−0.369015	+	0.929423i	$0.620305\pi$
$578$		−	20.2992i		−	0.844336i
$579$	−14.6355	−	14.6355i	−0.608230	−	0.608230i
$580$	39.2504	+	38.3377i	1.62979	+	1.59189i
$581$	18.4844			0.766864
$582$	27.6051	+	27.6051i	1.14427	+	1.14427i
$583$	−27.5891			−1.14262
$584$	10.7559			0.445083
$585$	−7.49601	+	2.96815i	−0.309922	+	0.122718i
$586$	13.1191			0.541944
$587$	−33.3826			−1.37785			−0.688924	−	0.724834i	$-0.741917\pi$
$587$	−33.3826			−1.37785			−0.688924	+	0.724834i	$0.741917\pi$
$588$	−20.4702	−	20.4702i	−0.844179	−	0.844179i
$589$	−11.6693			−0.480825
$590$	−45.6544	+	0.537063i	−1.87956	+	0.0221105i
$591$	−4.35720	−	4.35720i	−0.179231	−	0.179231i
$592$		−	10.3343i		−	0.424738i
$593$	26.1087			1.07216			0.536078	−	0.844169i	$-0.319905\pi$
$593$	26.1087			1.07216			0.536078	+	0.844169i	$0.319905\pi$
$594$		−	8.13287i		−	0.333696i
$595$	0.303066	+	25.7629i	0.0124245	+	1.05618i
$596$	−19.0802	+	19.0802i	−0.781555	+	0.781555i
$597$	−16.4668	−	16.4668i	−0.673942	−	0.673942i
$598$	−6.21872	−	16.2615i	−0.254302	−	0.664984i
$599$			1.98183i			0.0809755i	0.999180	+	0.0404877i	$0.0128912\pi$
$599$			1.98183i			0.0809755i	−0.999180	+	0.0404877i	$0.987109\pi$
$600$	7.03158	−	7.37046i	0.287063	−	0.300898i
$601$	−7.83403			−0.319557			−0.159778	−	0.987153i	$-0.551078\pi$
$601$	−7.83403			−0.319557			−0.159778	+	0.987153i	$0.551078\pi$
$602$	−11.6029	−	11.6029i	−0.472897	−	0.472897i
$603$		−	12.3496i		−	0.502914i
$604$	7.47650	−	7.47650i	0.304214	−	0.304214i
$605$	3.91523	+	3.82419i	0.159177	+	0.155475i
$606$	−7.31781	+	7.31781i	−0.297266	+	0.297266i
$607$	15.2335	−	15.2335i	0.618309	−	0.618309i	−0.326788	−	0.945098i	$-0.605966\pi$
$607$	15.2335	−	15.2335i	0.618309	−	0.618309i	0.945098	+	0.326788i	$0.105966\pi$
$608$	19.3253	−	19.3253i	0.783745	−	0.783745i
$609$	−24.4522	−	24.4522i	−0.990852	−	0.990852i
$610$	−27.1972	+	27.8447i	−1.10118	+	1.12740i
$611$	20.9071	+	9.34003i	0.845811	+	0.377857i
$612$	−5.78120	+	5.78120i	−0.233691	+	0.233691i
$613$		−	34.9526i		−	1.41172i	−0.708349	−	0.705862i	$-0.750560\pi$
$613$		−	34.9526i		−	1.41172i	0.708349	−	0.705862i	$-0.249440\pi$
$614$			6.24821i			0.252157i
$615$	−3.73831	−	3.65138i	−0.150743	−	0.147238i
$616$	21.7296	+	21.7296i	0.875510	+	0.875510i
$617$	12.6145			0.507842			0.253921	−	0.967225i	$-0.418280\pi$
$617$	12.6145			0.507842			0.253921	+	0.967225i	$0.418280\pi$
$618$	−6.52658			−0.262538
$619$	21.5568	+	21.5568i	0.866442	+	0.866442i	0.992077	−	0.125635i	$-0.0400967\pi$
$619$	21.5568	+	21.5568i	0.866442	+	0.866442i	−0.125635	+	0.992077i	$0.540097\pi$
$620$	−19.5035	+	0.229433i	−0.783280	+	0.00921423i
$621$			2.17724i			0.0873697i
$622$		−	20.3609i		−	0.816396i
$623$	−36.6854	+	36.6854i	−1.46977	+	1.46977i
$624$	−4.44161	+	1.69855i	−0.177807	+	0.0679966i
$625$	−24.9723	+	1.17588i	−0.998893	+	0.0470351i
$626$	36.5672	+	36.5672i	1.46152	+	1.46152i
$627$	10.1245	−	10.1245i	0.404332	−	0.404332i
$628$	−8.54565	+	8.54565i	−0.341009	+	0.341009i
$629$	−15.5208	+	15.5208i	−0.618856	+	0.618856i
$630$	−14.2530	+	14.5924i	−0.567855	+	0.581374i
$631$	−25.2174	+	25.2174i	−1.00389	+	1.00389i	−0.00389463	+	0.999992i	$0.501240\pi$
$631$	−25.2174	+	25.2174i	−1.00389	+	1.00389i	−0.999992	+	0.00389463i	$0.998760\pi$
$632$		−	17.2263i		−	0.685226i
$633$	8.25804	+	8.25804i	0.328228	+	0.328228i
$634$	29.6820			1.17882
$635$	13.6996	−	0.161158i	0.543653	−	0.00639534i
$636$			21.9580i			0.870693i
$637$	−14.5872	+	32.6526i	−0.577966	+	1.29374i
$638$	48.3478	+	48.3478i	1.91411	+	1.91411i
$639$	7.75627	−	7.75627i	0.306833	−	0.306833i
$640$	22.7792	−	23.3215i	0.900427	−	0.921863i
$641$			15.3670i			0.606961i	0.952838	+	0.303481i	$0.0981487\pi$
$641$			15.3670i			0.606961i	−0.952838	+	0.303481i	$0.901851\pi$
$642$	5.37002			0.211938
$643$			5.80970i			0.229112i	0.993417	+	0.114556i	$0.0365445\pi$
$643$			5.80970i			0.229112i	−0.993417	+	0.114556i	$0.963455\pi$
$644$	−18.4822	−	18.4822i	−0.728302	−	0.728302i
$645$	−2.81044	+	2.87735i	−0.110661	+	0.113295i
$646$	−24.2573			−0.954389
$647$	21.0666	+	21.0666i	0.828212	+	0.828212i	0.987269	−	0.159057i	$-0.0508454\pi$
$647$	21.0666	+	21.0666i	0.828212	+	0.828212i	−0.159057	+	0.987269i	$0.550845\pi$
$648$	−2.03732			−0.0800335
$649$	−33.7620			−1.32528
$650$	−36.8783	−	15.4449i	−1.44649	−	0.605797i
$651$	12.2932			0.481808
$652$	24.7919			0.970926
$653$	−9.40721	−	9.40721i	−0.368132	−	0.368132i	0.498663	−	0.866796i	$-0.333824\pi$
$653$	−9.40721	−	9.40721i	−0.368132	−	0.368132i	−0.866796	+	0.498663i	$0.833824\pi$
$654$	14.9836			0.585904
$655$	18.3814	−	18.8190i	0.718220	−	0.735319i
$656$	−2.17946	−	2.17946i	−0.0850935	−	0.0850935i
$657$			5.27944i			0.205971i
$658$	57.9353			2.25855
$659$			2.27833i			0.0887510i	0.999015	+	0.0443755i	$0.0141298\pi$
$659$			2.27833i			0.0887510i	−0.999015	+	0.0443755i	$0.985870\pi$
$660$	16.7225	−	17.1206i	0.650922	−	0.666419i
$661$	22.0600	−	22.0600i	0.858036	−	0.858036i	−0.133071	−	0.991107i	$-0.542484\pi$
$661$	22.0600	−	22.0600i	0.858036	−	0.858036i	0.991107	+	0.133071i	$0.0424837\pi$
$662$	−30.5675	−	30.5675i	−1.18804	−	1.18804i
$663$	9.22174	+	4.11972i	0.358143	+	0.159996i
$664$			9.15547i			0.355301i
$665$	−35.9091	+	0.422423i	−1.39250	+	0.0163808i
$666$	−17.3779			−0.673379
$667$	−12.9431	−	12.9431i	−0.501160	−	0.501160i
$668$		−	38.6889i		−	1.49692i
$669$	11.8761	−	11.8761i	0.459158	−	0.459158i
$670$	42.7933	−	43.8121i	1.65325	−	1.69261i
$671$	−20.3521	+	20.3521i	−0.785682	+	0.785682i
$672$	−20.3586	+	20.3586i	−0.785348	+	0.785348i
$673$	24.7463	−	24.7463i	0.953900	−	0.953900i	−0.0450834	−	0.998983i	$-0.514355\pi$
$673$	24.7463	−	24.7463i	0.953900	−	0.953900i	0.998983	+	0.0450834i	$0.0143554\pi$
$674$	55.0069	+	55.0069i	2.11879	+	2.11879i
$675$	3.61773	+	3.45139i	0.139246	+	0.132844i
$676$	−25.3171	−	28.2604i	−0.973734	−	1.08694i
$677$	−11.5334	+	11.5334i	−0.443265	+	0.443265i	−0.893108	−	0.449843i	$-0.851480\pi$
$677$	−11.5334	+	11.5334i	−0.443265	+	0.443265i	0.449843	+	0.893108i	$0.351480\pi$
$678$		−	6.11671i		−	0.234911i
$679$		−	72.4049i		−	2.77865i
$680$	−12.7605	+	0.150111i	−0.489345	+	0.00575648i
$681$	−15.7194	−	15.7194i	−0.602367	−	0.602367i
$682$	−24.3066			−0.930747
$683$	33.8458			1.29507			0.647536	−	0.762035i	$-0.275800\pi$
$683$	33.8458			1.29507			0.647536	+	0.762035i	$0.275800\pi$
$684$	−8.05801	−	8.05801i	−0.308106	−	0.308106i
$685$	19.7824	+	19.3223i	0.755845	+	0.738269i
$686$			26.6265i			1.01660i
$687$		−	2.82760i		−	0.107880i
$688$	−1.67751	+	1.67751i	−0.0639545	+	0.0639545i
$689$	25.3366	−	9.68921i	0.965248	−	0.369129i
$690$	−7.54448	+	7.72409i	−0.287213	+	0.294051i
$691$	13.6461	+	13.6461i	0.519121	+	0.519121i	0.917305	−	0.398185i	$-0.130360\pi$
$691$	13.6461	+	13.6461i	0.519121	+	0.519121i	−0.398185	+	0.917305i	$0.630360\pi$
$692$	23.1891	−	23.1891i	0.881518	−	0.881518i
$693$	−10.6658	+	10.6658i	−0.405159	+	0.405159i
$694$	4.98395	−	4.98395i	0.189188	−	0.189188i
$695$	24.2711	+	23.7067i	0.920655	+	0.899246i
$696$	12.1113	−	12.1113i	0.459079	−	0.459079i
$697$			6.54654i			0.247968i
$698$	42.7546	+	42.7546i	1.61829	+	1.61829i
$699$	10.7537			0.406742
$700$	−60.0085	+	1.41203i	−2.26811	+	0.0533699i
$701$		−	36.0430i		−	1.36133i	−0.732597	−	0.680663i	$-0.761692\pi$
$701$		−	36.0430i		−	1.36133i	0.732597	−	0.680663i	$-0.238308\pi$
$702$	2.85624	+	7.46887i	0.107802	+	0.281894i
$703$	−21.6334	−	21.6334i	−0.815919	−	0.815919i
$704$	33.4139	−	33.4139i	1.25933	−	1.25933i
$705$	−0.167045	−	14.2001i	−0.00629128	−	0.534807i
$706$			45.6533i			1.71819i
$707$	19.1937			0.721855
$708$			26.8710i			1.00988i
$709$	−11.7237	−	11.7237i	−0.440292	−	0.440292i	0.451818	−	0.892110i	$-0.350776\pi$
$709$	−11.7237	−	11.7237i	−0.440292	−	0.440292i	−0.892110	+	0.451818i	$0.850776\pi$
$710$	54.3932	−	0.639863i	2.04134	−	0.0240136i
$711$	8.45538			0.317102
$712$	−18.1705	−	18.1705i	−0.680970	−	0.680970i
$713$	6.50708			0.243692
$714$	25.5542			0.956341
$715$	−27.1338	−	11.7409i	−1.01475	−	0.439083i
$716$	−4.01692			−0.150119
$717$	−24.3476			−0.909279
$718$	23.5152	+	23.5152i	0.877578	+	0.877578i
$719$	−15.7258			−0.586474			−0.293237	−	0.956040i	$-0.594733\pi$
$719$	−15.7258			−0.586474			−0.293237	+	0.956040i	$0.594733\pi$
$720$	2.10973	+	2.06067i	0.0786248	+	0.0767965i
$721$	8.55922	+	8.55922i	0.318762	+	0.318762i
$722$			8.32765i			0.309923i
$723$	14.4469			0.537288
$724$			68.4963i			2.54565i
$725$	−42.0240	+	0.988848i	−1.56073	+	0.0367249i
$726$	3.83835	−	3.83835i	0.142455	−	0.142455i
$727$	−29.7923	−	29.7923i	−1.10494	−	1.10494i	−0.993806	−	0.111131i	$-0.964553\pi$
$727$	−29.7923	−	29.7923i	−1.10494	−	1.10494i	−0.111131	−	0.993806i	$-0.535447\pi$
$728$	−27.5868	−	12.3241i	−1.02244	−	0.456763i
$729$		−	1.00000i		−	0.0370370i
$730$	−18.2941	+	18.7296i	−0.677095	+	0.693214i
$731$	5.03881			0.186367
$732$	16.1981	+	16.1981i	0.598699	+	0.598699i
$733$			21.4923i			0.793836i	0.917854	+	0.396918i	$0.129920\pi$
$733$			21.4923i			0.793836i	−0.917854	+	0.396918i	$0.870080\pi$
$734$	−2.27399	+	2.27399i	−0.0839344	+	0.0839344i
$735$	22.1776	−	0.260890i	0.818034	−	0.00962307i
$736$	−10.7763	+	10.7763i	−0.397219	+	0.397219i
$737$	32.0229	−	32.0229i	1.17958	−	1.17958i
$738$	−3.66491	+	3.66491i	−0.134907	+	0.134907i
$739$	−0.314385	−	0.314385i	−0.0115649	−	0.0115649i	0.701301	−	0.712866i	$-0.252603\pi$
$739$	−0.314385	−	0.314385i	−0.0115649	−	0.0115649i	−0.712866	+	0.701301i	$0.752603\pi$
$740$	−36.5824	−	35.7317i	−1.34479	−	1.31352i
$741$	−5.74218	+	12.8535i	−0.210944	+	0.472186i
$742$	48.5297	−	48.5297i	1.78158	−	1.78158i
$743$		−	22.1368i		−	0.812122i	−0.913846	−	0.406061i	$-0.866902\pi$
$743$		−	22.1368i		−	0.812122i	0.913846	−	0.406061i	$-0.133098\pi$
$744$			6.08890i			0.223230i
$745$	−0.243174	−	20.6716i	−0.00890920	−	0.757350i
$746$	18.6642	+	18.6642i	0.683347	+	0.683347i
$747$	−4.49388			−0.164422
$748$	−29.9816			−1.09624
$749$	−7.04245	−	7.04245i	−0.257326	−	0.257326i
$750$	0.874843	+	24.7803i	0.0319448	+	0.904848i
$751$			0.516848i			0.0188600i	0.999956	+	0.00943002i	$0.00300171\pi$
$751$			0.516848i			0.0188600i	−0.999956	+	0.00943002i	$0.996998\pi$
$752$		−	8.37613i		−	0.305446i
$753$	−13.2635	+	13.2635i	−0.483348	+	0.483348i
$754$	−61.3800	−	27.4209i	−2.23533	−	0.998609i
$755$	0.0952867	+	8.10010i	0.00346784	+	0.294793i
$756$	8.48883	+	8.48883i	0.308736	+	0.308736i
$757$	−24.0375	+	24.0375i	−0.873657	+	0.873657i	−0.992869	−	0.119212i	$-0.961963\pi$
$757$	−24.0375	+	24.0375i	−0.873657	+	0.873657i	0.119212	+	0.992869i	$0.461963\pi$
$758$	−11.1679	+	11.1679i	−0.405635	+	0.405635i
$759$	−5.64565	+	5.64565i	−0.204924	+	0.204924i
$760$	−0.209229	−	17.7860i	−0.00758952	−	0.645167i
$761$	−36.2711	+	36.2711i	−1.31483	+	1.31483i	−0.397015	+	0.917812i	$0.629954\pi$
$761$	−36.2711	+	36.2711i	−1.31483	+	1.31483i	−0.917812	+	0.397015i	$0.870046\pi$
$762$		−	13.5886i		−	0.492264i
$763$	−19.6500	−	19.6500i	−0.711379	−	0.711379i
$764$	−8.53636			−0.308835
$765$	−0.0736805	−	6.26340i	−0.00266392	−	0.226454i
$766$		−	1.07243i		−	0.0387486i
$767$	31.0055	−	11.8571i	1.11955	−	0.428136i
$768$	−4.63995	−	4.63995i	−0.167430	−	0.167430i
$769$	5.51342	−	5.51342i	0.198819	−	0.198819i	−0.600675	−	0.799494i	$-0.705101\pi$
$769$	5.51342	−	5.51342i	0.198819	−	0.198819i	0.799494	+	0.600675i	$0.205101\pi$
$770$	−74.7970	+	0.879886i	−2.69550	+	0.0317089i
$771$		−	1.98101i		−	0.0713442i
$772$	−60.4088			−2.17416
$773$		−	37.1946i		−	1.33780i	−0.743353	−	0.668899i	$-0.766766\pi$
$773$		−	37.1946i		−	1.33780i	0.743353	−	0.668899i	$-0.233234\pi$
$774$	2.82085	+	2.82085i	0.101393	+	0.101393i
$775$	10.3151	−	10.8122i	0.370529	−	0.388387i
$776$	35.8627			1.28739
$777$	22.7900	+	22.7900i	0.817587	+	0.817587i
$778$	39.0208			1.39896
$779$	−9.12476			−0.326928
$780$	−9.34449	+	21.5957i	−0.334587	+	0.773250i
$781$	40.2244			1.43934
$782$	13.5264			0.483705
$783$	5.94473	+	5.94473i	0.212447	+	0.212447i
$784$	13.0818			0.467207
$785$	−0.108913	−	9.25843i	−0.00388727	−	0.330447i
$786$	−18.4495	−	18.4495i	−0.658071	−	0.658071i
$787$			16.6120i			0.592154i	0.955164	+	0.296077i	$0.0956785\pi$
$787$			16.6120i			0.592154i	−0.955164	+	0.296077i	$0.904321\pi$
$788$	−17.9846			−0.640674
$789$			22.4552i			0.799425i
$790$	29.9967	+	29.2992i	1.06724	+	1.04242i
$791$	−8.02169	+	8.02169i	−0.285219	+	0.285219i
$792$	−5.28283	−	5.28283i	−0.187717	−	0.187717i
$793$	11.5428	−	25.8380i	0.409899	−	0.917534i
$794$			21.3753i			0.758582i
$795$	−12.0347	−	11.7548i	−0.426826	−	0.416901i
$796$	−67.9677			−2.40905
$797$	23.0821	+	23.0821i	0.817611	+	0.817611i	0.985761	−	0.168150i	$-0.0537793\pi$
$797$	23.0821	+	23.0821i	0.817611	+	0.817611i	−0.168150	+	0.985761i	$0.553779\pi$
$798$			35.6182i			1.26087i
$799$	−12.5799	+	12.5799i	−0.445044	+	0.445044i
$800$	0.823302	+	34.9886i	0.0291081	+	1.23703i
$801$	8.91884	−	8.91884i	0.315132	−	0.315132i
$802$	−37.4328	+	37.4328i	−1.32180	+	1.32180i
$803$	−13.6897	+	13.6897i	−0.483101	+	0.483101i
$804$	−25.4868	−	25.4868i	−0.898851	−	0.898851i
$805$	20.0238	−	0.235553i	0.705746	−	0.00830216i
$806$	22.3221	−	8.53639i	0.786262	−	0.300681i
$807$	−0.246971	+	0.246971i	−0.00869377	+	0.00869377i
$808$			9.50678i			0.334448i
$809$			10.9372i			0.384533i	0.981343	+	0.192267i	$0.0615838\pi$
$809$			10.9372i			0.384533i	−0.981343	+	0.192267i	$0.938416\pi$
$810$	3.46515	−	3.54765i	0.121753	−	0.124652i
$811$	17.0726	+	17.0726i	0.599501	+	0.599501i	0.940180	−	0.340679i	$-0.110657\pi$
$811$	17.0726	+	17.0726i	0.599501	+	0.599501i	−0.340679	+	0.940180i	$0.610657\pi$
$812$	−100.928			−3.54187
$813$	12.0511			0.422649
$814$	−45.0613	−	45.0613i	−1.57940	−	1.57940i
$815$	−13.2719	+	13.5879i	−0.464894	+	0.475962i
$816$		−	3.69456i		−	0.129335i
$817$			7.02325i			0.245712i
$818$	−8.10707	+	8.10707i	−0.283457	+	0.283457i
$819$	6.04919	−	13.5408i	0.211376	−	0.473152i
$820$	−15.2507	+	0.179404i	−0.532577	+	0.00626506i
$821$	−7.58466	−	7.58466i	−0.264706	−	0.264706i	0.562256	−	0.826963i	$-0.309933\pi$
$821$	−7.58466	−	7.58466i	−0.264706	−	0.264706i	−0.826963	+	0.562256i	$0.809933\pi$
$822$	19.3939	−	19.3939i	0.676441	−	0.676441i
$823$	20.2348	−	20.2348i	0.705341	−	0.705341i	−0.260211	−	0.965552i	$-0.583792\pi$
$823$	20.2348	−	20.2348i	0.705341	−	0.705341i	0.965552	+	0.260211i	$0.0837922\pi$
$824$	−4.23944	+	4.23944i	−0.147688	+	0.147688i
$825$	0.431325	+	18.3304i	0.0150168	+	0.638183i
$826$	59.3879	−	59.3879i	2.06637	−	2.06637i
$827$			0.322011i			0.0111974i	0.999984	+	0.00559871i	$0.00178213\pi$
$827$			0.322011i			0.0111974i	−0.999984	+	0.00559871i	$0.998218\pi$
$828$	4.49334	+	4.49334i	0.156155	+	0.156155i
$829$	2.29166			0.0795925			0.0397963	−	0.999208i	$-0.487329\pi$
$829$	2.29166			0.0795925			0.0397963	+	0.999208i	$0.487329\pi$
$830$	−15.9427	−	15.5720i	−0.553380	−	0.540511i
$831$			7.46240i			0.258868i
$832$	−18.9510	+	42.4207i	−0.657007	+	1.47067i
$833$	−19.6472	−	19.6472i	−0.680735	−	0.680735i
$834$	23.7945	−	23.7945i	0.823937	−	0.823937i
$835$	21.2045	+	20.7114i	0.733812	+	0.716748i
$836$		−	41.7893i		−	1.44531i
$837$	−2.98868			−0.103304
$838$		−	75.2766i		−	2.60039i
$839$	0.488256	+	0.488256i	0.0168565	+	0.0168565i	0.715485	−	0.698628i	$-0.246206\pi$
$839$	0.488256	+	0.488256i	0.0168565	+	0.0168565i	−0.698628	+	0.715485i	$0.746206\pi$
$840$	0.220415	+	18.7370i	0.00760505	+	0.646487i
$841$	−41.6797			−1.43723
$842$	−43.7067	−	43.7067i	−1.50623	−	1.50623i
$843$	−8.46378			−0.291508
$844$	34.0855			1.17327
$845$	29.0419	+	1.25297i	0.999071	+	0.0431034i
$846$	−14.0850			−0.484254
$847$	−10.0675			−0.345925
$848$	−7.01629	−	7.01629i	−0.240940	−	0.240940i
$849$	3.62285			0.124336
$850$	21.4423	−	22.4757i	0.735463	−	0.770909i
$851$	12.0633	+	12.0633i	0.413525	+	0.413525i
$852$		−	32.0144i		−	1.09680i
$853$	−2.53904			−0.0869352			−0.0434676	−	0.999055i	$-0.513841\pi$
$853$	−2.53904			−0.0869352			−0.0434676	+	0.999055i	$0.513841\pi$
$854$		−	71.5992i		−	2.45007i
$855$	8.73011	−	0.102698i	0.298564	−	0.00351220i
$856$	3.48817	−	3.48817i	0.119223	−	0.119223i
$857$	−3.15552	−	3.15552i	−0.107791	−	0.107791i	0.651155	−	0.758945i	$-0.274285\pi$
$857$	−3.15552	−	3.15552i	−0.107791	−	0.107791i	−0.758945	+	0.651155i	$0.774285\pi$
$858$	−11.9607	+	26.7733i	−0.408331	+	0.914025i
$859$			36.8208i			1.25631i	0.778088	+	0.628155i	$0.216190\pi$
$859$			36.8208i			1.25631i	−0.778088	+	0.628155i	$0.783810\pi$
$860$	0.138086	+	11.7383i	0.00470868	+	0.400274i
$861$	9.61261			0.327597
$862$	23.8780	+	23.8780i	0.813288	+	0.813288i
$863$		−	11.3029i		−	0.384754i	−0.981321	−	0.192377i	$-0.938380\pi$
$863$		−	11.3029i		−	0.384754i	0.981321	−	0.192377i	$-0.0616196\pi$
$864$	4.94951	−	4.94951i	0.168386	−	0.168386i
$865$	0.295542	+	25.1233i	0.0100487	+	0.854217i
$866$	−26.2864	+	26.2864i	−0.893248	+	0.893248i
$867$	6.47206	−	6.47206i	0.219803	−	0.219803i
$868$	25.3704	−	25.3704i	0.861129	−	0.861129i
$869$	21.9250	+	21.9250i	0.743756	+	0.743756i
$870$	0.490418	+	41.6893i	0.0166267	+	1.41340i
$871$	−18.1620	+	40.6547i	−0.615397	+	1.37753i
$872$	9.73279	−	9.73279i	0.329594	−	0.329594i
$873$			17.6029i			0.595767i
$874$			18.8536i			0.637731i
$875$	31.3505	−	33.6451i	1.05984	−	1.13741i
$876$	10.8956	+	10.8956i	0.368128	+	0.368128i
$877$	11.1316			0.375889			0.187944	−	0.982180i	$-0.439818\pi$
$877$	11.1316			0.375889			0.187944	+	0.982180i	$0.439818\pi$
$878$	−4.48487			−0.151357
$879$	4.18280	+	4.18280i	0.141082	+	0.141082i
$880$	0.127212	+	10.8139i	0.00428830	+	0.364538i
$881$		−	25.7462i		−	0.867410i	−0.901055	−	0.433705i	$-0.857206\pi$
$881$		−	25.7462i		−	0.867410i	0.901055	−	0.433705i	$-0.142794\pi$
$882$		−	21.9979i		−	0.740709i
$883$	3.65379	−	3.65379i	0.122960	−	0.122960i	−0.642949	−	0.765909i	$-0.722289\pi$
$883$	3.65379	−	3.65379i	0.122960	−	0.122960i	0.765909	+	0.642949i	$0.222289\pi$
$884$	27.5338	−	10.5295i	0.926062	−	0.354144i
$885$	−14.7274	−	14.3849i	−0.495055	−	0.483543i
$886$	0.282539	+	0.282539i	0.00949208	+	0.00949208i
$887$	−9.40170	+	9.40170i	−0.315678	+	0.315678i	−0.847105	−	0.531426i	$-0.821656\pi$
$887$	−9.40170	+	9.40170i	−0.315678	+	0.315678i	0.531426	+	0.847105i	$0.321656\pi$
$888$	−11.2880	+	11.2880i	−0.378802	+	0.378802i
$889$	−17.8206	+	17.8206i	−0.597685	+	0.597685i
$890$	62.5461	−	0.735771i	2.09655	−	0.0246631i
$891$	2.59303	−	2.59303i	0.0868697	−	0.0868697i
$892$		−	49.0194i		−	1.64129i
$893$	−17.5342	−	17.5342i	−0.586760	−	0.586760i
$894$	−20.5041			−0.685761
$895$	2.15038	−	2.20158i	0.0718794	−	0.0735907i
$896$			59.9684i			2.00340i
$897$	3.20198	−	7.16745i	0.106911	−	0.239314i
$898$	−55.1434	−	55.1434i	−1.84016	−	1.84016i
$899$	17.7669	−	17.7669i	0.592560	−	0.592560i
$900$	14.5891	−	0.343289i	0.486303	−	0.0114430i
$901$			21.0752i			0.702115i
$902$	−19.0064			−0.632845
$903$		−	7.39875i		−	0.246215i
$904$	−3.97320	−	3.97320i	−0.132147	−	0.132147i
$905$	−37.5412	−	36.6682i	−1.24791	−	1.21889i
$906$	8.03446			0.266927
$907$	−0.772139	−	0.772139i	−0.0256384	−	0.0256384i	0.694171	−	0.719810i	$-0.255771\pi$
$907$	−0.772139	−	0.772139i	−0.0256384	−	0.0256384i	−0.719810	+	0.694171i	$0.755771\pi$
$908$	−64.8825			−2.15320
$909$	−4.66632			−0.154772
$910$	68.3812	−	27.0765i	2.26681	−	0.897577i
$911$	−6.21262			−0.205833			−0.102917	−	0.994690i	$-0.532818\pi$
$911$	−6.21262			−0.205833			−0.102917	+	0.994690i	$0.532818\pi$
$912$	5.14958			0.170520
$913$	−11.6528	−	11.6528i	−0.385650	−	0.385650i
$914$	71.6388			2.36960
$915$	−17.5491	+	0.206442i	−0.580157	+	0.00682477i
$916$	−5.83555	−	5.83555i	−0.192812	−	0.192812i
$917$			48.3907i			1.59800i
$918$	−6.21265			−0.205048
$919$			29.9003i			0.986320i	0.869939	+	0.493160i	$0.164158\pi$
$919$			29.9003i			0.986320i	−0.869939	+	0.493160i	$0.835842\pi$
$920$	0.116671	+	9.91792i	0.00384653	+	0.326984i
$921$	−1.99213	+	1.99213i	−0.0656431	+	0.0656431i
$922$	−32.2980	−	32.2980i	−1.06368	−	1.06368i
$923$	−36.9403	+	14.1267i	−1.21591	+	0.464986i
$924$			44.0236i			1.44827i
$925$	39.1674	−	0.921631i	1.28782	−	0.0303030i
$926$	29.4345			0.967278
$927$	−2.08089	−	2.08089i	−0.0683454	−	0.0683454i
$928$			58.8470i			1.93175i
$929$	16.4364	−	16.4364i	0.539260	−	0.539260i	−0.384052	−	0.923312i	$-0.625472\pi$
$929$	16.4364	−	16.4364i	0.539260	−	0.539260i	0.923312	+	0.384052i	$0.125472\pi$
$930$	−10.6028	−	10.3562i	−0.347680	−	0.339595i
$931$	27.3848	−	27.3848i	0.897501	−	0.897501i
$932$	22.1933	−	22.1933i	0.726964	−	0.726964i
$933$	6.49171	−	6.49171i	0.212529	−	0.212529i
$934$	47.9281	+	47.9281i	1.56826	+	1.56826i
$935$	16.0501	−	16.4322i	0.524895	−	0.537391i
$936$	6.70683	+	2.99620i	0.219219	+	0.0979339i
$937$	15.7357	−	15.7357i	0.514064	−	0.514064i	−0.401705	−	0.915769i	$-0.631582\pi$
$937$	15.7357	−	15.7357i	0.514064	−	0.514064i	0.915769	+	0.401705i	$0.131582\pi$
$938$			112.657i			3.67839i
$939$			23.3176i			0.760942i
$940$	−29.6506	−	28.9611i	−0.967096	−	0.944607i
$941$	−6.42421	−	6.42421i	−0.209423	−	0.209423i	0.594599	−	0.804022i	$-0.297311\pi$
$941$	−6.42421	−	6.42421i	−0.209423	−	0.209423i	−0.804022	+	0.594599i	$0.797311\pi$
$942$	−9.18341			−0.299212
$943$	5.08819			0.165694
$944$	−8.58615	−	8.58615i	−0.279455	−	0.279455i
$945$	−9.19687	+	0.108189i	−0.299174	+	0.00351938i
$946$			14.6291i			0.475633i
$947$			12.4887i			0.405827i	0.979197	+	0.202914i	$0.0650411\pi$
$947$			12.4887i			0.405827i	−0.979197	+	0.202914i	$0.934959\pi$
$948$	17.4500	−	17.4500i	0.566751	−	0.566751i
$949$	7.76426	−	17.3799i	0.252039	−	0.564174i
$950$	31.3272	+	29.8868i	1.01639	+	0.969657i
$951$	9.46360	+	9.46360i	0.306878	+	0.306878i
$952$	16.5991	−	16.5991i	0.537980	−	0.537980i
$953$	−30.2555	+	30.2555i	−0.980072	+	0.980072i	−0.999805	−	0.0197332i	$-0.993718\pi$
$953$	−30.2555	+	30.2555i	−0.980072	+	0.980072i	0.0197332	+	0.999805i	$0.493718\pi$
$954$	−11.7984	+	11.7984i	−0.381987	+	0.381987i
$955$	4.56978	−	4.67858i	0.147875	−	0.151395i
$956$	−50.2481	+	50.2481i	−1.62514	+	1.62514i
$957$			30.8297i			0.996583i
$958$	30.1602	+	30.1602i	0.974431	+	0.974431i
$959$	−50.8679			−1.64261
$960$	28.8121	−	0.338936i	0.929906	−	0.0109391i
$961$		−	22.0678i		−	0.711864i
$962$	57.2077	+	25.5569i	1.84445	+	0.823988i
$963$	1.71214	+	1.71214i	0.0551729	+	0.0551729i
$964$	29.8153	−	29.8153i	0.960286	−	0.960286i
$965$	32.3387	−	33.1086i	1.04102	−	1.06580i
$966$		−	19.8616i		−	0.639035i
$967$	35.6086			1.14510			0.572548	−	0.819871i	$-0.305955\pi$
$967$	35.6086			1.14510			0.572548	+	0.819871i	$0.305955\pi$
$968$		−	4.98652i		−	0.160273i
$969$	−7.73402	−	7.73402i	−0.248452	−	0.248452i
$970$	−60.9966	+	62.4488i	−1.95848	+	2.00511i
$971$	−28.4165			−0.911929			−0.455964	−	0.889998i	$-0.650706\pi$
$971$	−28.4165			−0.911929			−0.455964	+	0.889998i	$0.650706\pi$
$972$	−2.06378	−	2.06378i	−0.0661957	−	0.0661957i
$973$	−62.4102			−2.00078
$974$	35.7127			1.14431
$975$	−6.83369	−	16.6823i	−0.218853	−	0.534263i
$976$	−10.3516			−0.331347
$977$	−42.8927			−1.37226			−0.686130	−	0.727479i	$-0.740692\pi$
$977$	−42.8927			−1.37226			−0.686130	+	0.727479i	$0.740692\pi$
$978$	13.3211	+	13.3211i	0.425960	+	0.425960i
$979$	46.2536			1.47827
$980$	45.2313	−	46.3081i	1.44486	−	1.47926i
$981$	4.77725	+	4.77725i	0.152526	+	0.152526i
$982$		−	45.9446i		−	1.46615i
$983$	39.1642			1.24914			0.624572	−	0.780967i	$-0.285273\pi$
$983$	39.1642			1.24914			0.624572	+	0.780967i	$0.285273\pi$
$984$			4.76119i			0.151781i
$985$	9.62772	−	9.85693i	0.306765	−	0.314068i
$986$	36.9326	−	36.9326i	1.17617	−	1.17617i
$987$	18.4717	+	18.4717i	0.587960	+	0.587960i
$988$	14.6763	+	38.3774i	0.466914	+	1.22095i
$989$		−	3.91633i		−	0.124532i
$990$	18.1844	−	0.213915i	0.577938	−	0.00679867i
$991$	7.60282			0.241512			0.120756	−	0.992682i	$-0.461468\pi$
$991$	7.60282			0.241512			0.120756	+	0.992682i	$0.461468\pi$
$992$	−14.7925	−	14.7925i	−0.469662	−	0.469662i
$993$		−	19.4918i		−	0.618555i
$994$	−70.7554	+	70.7554i	−2.24422	+	2.24422i
$995$	36.3853	−	37.2515i	1.15349	−	1.18095i
$996$	−9.27437	+	9.27437i	−0.293870	+	0.293870i
$997$	−1.06259	+	1.06259i	−0.0336527	+	0.0336527i	−0.723733	−	0.690080i	$-0.757575\pi$
$997$	−1.06259	+	1.06259i	−0.0336527	+	0.0336527i	0.690080	+	0.723733i	$0.257575\pi$
$998$	−9.08715	+	9.08715i	−0.287649	+	0.287649i
$999$	−5.54064	−	5.54064i	−0.175298	−	0.175298i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.t.a.73.13	yes	28
3.2	odd	2		585.2.w.g.73.2		28
5.2	odd	4		195.2.k.a.112.13	✓	28
5.3	odd	4		975.2.k.d.307.2		28
5.4	even	2		975.2.t.d.268.2		28
13.5	odd	4		195.2.k.a.148.2	yes	28
15.2	even	4		585.2.n.g.307.2		28
39.5	even	4		585.2.n.g.343.13		28
65.18	even	4		975.2.t.d.382.2		28
65.44	odd	4		975.2.k.d.343.13		28
65.57	even	4	inner	195.2.t.a.187.13	yes	28
195.122	odd	4		585.2.w.g.577.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.k.a.112.13	✓	28	5.2	odd	4
195.2.k.a.148.2	yes	28	13.5	odd	4
195.2.t.a.73.13	yes	28	1.1	even	1	trivial
195.2.t.a.187.13	yes	28	65.57	even	4	inner
585.2.n.g.307.2		28	15.2	even	4
585.2.n.g.343.13		28	39.5	even	4
585.2.w.g.73.2		28	3.2	odd	2
585.2.w.g.577.2		28	195.122	odd	4
975.2.k.d.307.2		28	5.3	odd	4
975.2.k.d.343.13		28	65.44	odd	4
975.2.t.d.268.2		28	5.4	even	2
975.2.t.d.382.2		28	65.18	even	4

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.21780 q^{2} +(0.707107 + 0.707107i) q^{3} +2.91862 q^{4} +(-1.56243 + 1.59963i) q^{5} +(1.56822 + 1.56822i) q^{6} -4.11325i q^{7} +2.03732 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+2.21780 q^{2} +(0.707107 + 0.707107i) q^{3} +2.91862 q^{4} +(-1.56243 + 1.59963i) q^{5} +(1.56822 + 1.56822i) q^{6} -4.11325i q^{7} +2.03732 q^{8} +1.00000i q^{9} +(-3.46515 + 3.54765i) q^{10} +(-2.59303 + 2.59303i) q^{11} +(2.06378 + 2.06378i) q^{12} +(1.47066 - 3.29198i) q^{13} -9.12235i q^{14} +(-2.23591 + 0.0263025i) q^{15} -1.31889 q^{16} +(1.98080 + 1.98080i) q^{17} +2.21780i q^{18} +(-2.76089 + 2.76089i) q^{19} +(-4.56015 + 4.66871i) q^{20} +(2.90851 - 2.90851i) q^{21} +(-5.75081 + 5.75081i) q^{22} +(1.53954 - 1.53954i) q^{23} +(1.44060 + 1.44060i) q^{24} +(-0.117620 - 4.99862i) q^{25} +(3.26162 - 7.30095i) q^{26} +(-0.707107 + 0.707107i) q^{27} -12.0050i q^{28} -8.40712i q^{29} +(-4.95880 + 0.0583336i) q^{30} +(2.11332 + 2.11332i) q^{31} -6.99966 q^{32} -3.66710 q^{33} +(4.39301 + 4.39301i) q^{34} +(6.57967 + 6.42667i) q^{35} +2.91862i q^{36} +7.83564i q^{37} +(-6.12310 + 6.12310i) q^{38} +(3.36770 - 1.28787i) q^{39} +(-3.18317 + 3.25895i) q^{40} +(1.65250 + 1.65250i) q^{41} +(6.45048 - 6.45048i) q^{42} +(1.27192 - 1.27192i) q^{43} +(-7.56807 + 7.56807i) q^{44} +(-1.59963 - 1.56243i) q^{45} +(3.41439 - 3.41439i) q^{46} +6.35092i q^{47} +(-0.932593 - 0.932593i) q^{48} -9.91882 q^{49} +(-0.260858 - 11.0859i) q^{50} +2.80127i q^{51} +(4.29230 - 9.60806i) q^{52} +(5.31987 + 5.31987i) q^{53} +(-1.56822 + 1.56822i) q^{54} +(-0.0964538 - 8.19931i) q^{55} -8.38000i q^{56} -3.90449 q^{57} -18.6453i q^{58} +(6.51015 + 6.51015i) q^{59} +(-6.52579 + 0.0767671i) q^{60} +7.84876 q^{61} +(4.68691 + 4.68691i) q^{62} +4.11325 q^{63} -12.8861 q^{64} +(2.96815 + 7.49601i) q^{65} -8.13287 q^{66} -12.3496 q^{67} +(5.78120 + 5.78120i) q^{68} +2.17724 q^{69} +(14.5924 + 14.2530i) q^{70} +(-7.75627 - 7.75627i) q^{71} +2.03732i q^{72} +5.27944 q^{73} +17.3779i q^{74} +(3.45139 - 3.61773i) q^{75} +(-8.05801 + 8.05801i) q^{76} +(10.6658 + 10.6658i) q^{77} +(7.46887 - 2.85624i) q^{78} -8.45538i q^{79} +(2.06067 - 2.10973i) q^{80} -1.00000 q^{81} +(3.66491 + 3.66491i) q^{82} +4.49388i q^{83} +(8.48883 - 8.48883i) q^{84} +(-6.26340 + 0.0736805i) q^{85} +(2.82085 - 2.82085i) q^{86} +(5.94473 - 5.94473i) q^{87} +(-5.28283 + 5.28283i) q^{88} +(-8.91884 - 8.91884i) q^{89} +(-3.54765 - 3.46515i) q^{90} +(-13.5408 - 6.04919i) q^{91} +(4.49334 - 4.49334i) q^{92} +2.98868i q^{93} +14.0850i q^{94} +(-0.102698 - 8.73011i) q^{95} +(-4.94951 - 4.94951i) q^{96} +17.6029 q^{97} -21.9979 q^{98} +(-2.59303 - 2.59303i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} + 28 q^{4} - 4 q^{5} - 12 q^{8}+O(q^{10}) \) 28 * q - 4 * q^2 + 28 * q^4 - 4 * q^5 - 12 * q^8	\( 28 q - 4 q^{2} + 28 q^{4} - 4 q^{5} - 12 q^{8} - 8 q^{11} - 8 q^{12} - 4 q^{15} + 28 q^{16} + 28 q^{17} + 12 q^{20} + 8 q^{21} - 32 q^{22} - 8 q^{23} + 4 q^{25} - 16 q^{31} - 68 q^{32} - 8 q^{33} - 28 q^{34} - 8 q^{39} - 48 q^{40} + 4 q^{41} - 40 q^{44} - 8 q^{45} - 16 q^{46} - 16 q^{48} + 28 q^{49} + 4 q^{50} + 48 q^{52} + 20 q^{53} - 8 q^{55} - 32 q^{59} - 60 q^{60} + 8 q^{61} - 72 q^{62} + 28 q^{64} + 64 q^{65} + 16 q^{66} + 32 q^{67} + 60 q^{68} - 8 q^{69} - 16 q^{70} + 40 q^{71} + 56 q^{73} + 16 q^{75} - 40 q^{76} + 48 q^{77} + 40 q^{78} - 12 q^{80} - 28 q^{81} - 4 q^{82} + 32 q^{84} + 44 q^{85} + 16 q^{86} - 24 q^{87} - 72 q^{88} + 36 q^{89} + 12 q^{90} - 56 q^{91} - 32 q^{92} - 56 q^{95} + 48 q^{97} - 12 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 + 28 * q^4 - 4 * q^5 - 12 * q^8 - 8 * q^11 - 8 * q^12 - 4 * q^15 + 28 * q^16 + 28 * q^17 + 12 * q^20 + 8 * q^21 - 32 * q^22 - 8 * q^23 + 4 * q^25 - 16 * q^31 - 68 * q^32 - 8 * q^33 - 28 * q^34 - 8 * q^39 - 48 * q^40 + 4 * q^41 - 40 * q^44 - 8 * q^45 - 16 * q^46 - 16 * q^48 + 28 * q^49 + 4 * q^50 + 48 * q^52 + 20 * q^53 - 8 * q^55 - 32 * q^59 - 60 * q^60 + 8 * q^61 - 72 * q^62 + 28 * q^64 + 64 * q^65 + 16 * q^66 + 32 * q^67 + 60 * q^68 - 8 * q^69 - 16 * q^70 + 40 * q^71 + 56 * q^73 + 16 * q^75 - 40 * q^76 + 48 * q^77 + 40 * q^78 - 12 * q^80 - 28 * q^81 - 4 * q^82 + 32 * q^84 + 44 * q^85 + 16 * q^86 - 24 * q^87 - 72 * q^88 + 36 * q^89 + 12 * q^90 - 56 * q^91 - 32 * q^92 - 56 * q^95 + 48 * q^97 - 12 * q^98 - 8 * q^99

Introduction

L-functions

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