LMFDB - Embedded newform 150.2.l.a.137.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			137.3
Character	$\chi$	$=$	150.137
Dual form			150.2.l.a.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 + 0.156434i) q^{2} +(0.487767 + 1.66195i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.22772 + 0.193062i) q^{5} +(-0.741748 - 1.56519i) q^{6} +(-0.104631 - 0.104631i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-2.52417 + 1.62129i) q^{9} +O(q^{10})$	\(q+(-0.987688 + 0.156434i) q^{2} +(0.487767 + 1.66195i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.22772 + 0.193062i) q^{5} +(-0.741748 - 1.56519i) q^{6} +(-0.104631 - 0.104631i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-2.52417 + 1.62129i) q^{9} +(-2.23049 + 0.157807i) q^{10} +(1.81255 - 2.49477i) q^{11} +(0.977465 + 1.42988i) q^{12} +(-0.711182 + 4.49023i) q^{13} +(0.119711 + 0.0869753i) q^{14} +(0.765748 + 3.79653i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.68388 + 3.30481i) q^{17} +(2.23946 - 1.99620i) q^{18} +(-3.32698 - 1.08100i) q^{19} +(2.17835 - 0.504790i) q^{20} +(0.122857 - 0.224928i) q^{21} +(-1.39997 + 2.74760i) q^{22} +(-0.773401 - 4.88306i) q^{23} +(-1.18911 - 1.25937i) q^{24} +(4.92545 + 0.860175i) q^{25} -4.54620i q^{26} +(-3.92571 - 3.40423i) q^{27} +(-0.131843 - 0.0671775i) q^{28} +(-0.509399 - 1.56777i) q^{29} +(-1.35023 - 3.63000i) q^{30} +(2.45755 - 7.56355i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.03028 + 1.79551i) q^{33} +(-2.18014 - 3.00070i) q^{34} +(-0.212889 - 0.253290i) q^{35} +(-1.89962 + 2.32195i) q^{36} +(-8.30199 - 1.31491i) q^{37} +(3.45513 + 0.547238i) q^{38} +(-7.80943 + 1.00823i) q^{39} +(-2.07256 + 0.839343i) q^{40} +(-1.27149 - 1.75005i) q^{41} +(-0.0861576 + 0.241378i) q^{42} +(2.77052 - 2.77052i) q^{43} +(0.952916 - 2.93277i) q^{44} +(-5.93614 + 3.12446i) q^{45} +(1.52776 + 4.70196i) q^{46} +(4.77725 + 2.43413i) q^{47} +(1.37148 + 1.05784i) q^{48} -6.97810i q^{49} +(-4.99937 - 0.0790741i) q^{50} +(-4.67109 + 4.41051i) q^{51} +(0.711182 + 4.49023i) q^{52} +(5.24200 - 10.2880i) q^{53} +(4.40992 + 2.74820i) q^{54} +(4.51950 - 5.20770i) q^{55} +(0.140729 + 0.0457256i) q^{56} +(0.173781 - 6.05656i) q^{57} +(0.748381 + 1.46878i) q^{58} +(-10.4207 + 7.57107i) q^{59} +(1.90146 + 3.37408i) q^{60} +(11.8153 + 8.58430i) q^{61} +(-1.24409 + 7.85487i) q^{62} +(0.433745 + 0.0944693i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-2.45120 + 9.86565i) q^{65} +(-5.24923 - 0.986496i) q^{66} +(3.23605 - 1.64885i) q^{67} +(2.62271 + 2.62271i) q^{68} +(7.73817 - 3.66715i) q^{69} +(0.249891 + 0.216868i) q^{70} +(-4.79465 + 1.55788i) q^{71} +(1.51300 - 2.59053i) q^{72} +(-10.6274 + 1.68322i) q^{73} +8.40547 q^{74} +(0.972905 + 8.60543i) q^{75} -3.49819 q^{76} +(-0.450681 + 0.0713809i) q^{77} +(7.55556 - 2.21748i) q^{78} +(8.57556 - 2.78637i) q^{79} +(1.91574 - 1.15323i) q^{80} +(3.74283 - 8.18481i) q^{81} +(1.52960 + 1.52960i) q^{82} +(-9.01058 + 4.59112i) q^{83} +(0.0473370 - 0.251884i) q^{84} +(3.11318 + 7.68727i) q^{85} +(-2.30301 + 3.16982i) q^{86} +(2.35709 - 1.61130i) q^{87} +(-0.482397 + 3.04574i) q^{88} +(6.13326 + 4.45607i) q^{89} +(5.37428 - 4.01461i) q^{90} +(0.544231 - 0.395407i) q^{91} +(-2.24450 - 4.40507i) q^{92} +(13.7690 + 0.395073i) q^{93} +(-5.09921 - 1.65683i) q^{94} +(-7.20287 - 3.05048i) q^{95} +(-1.52008 - 0.830274i) q^{96} +(-4.20877 + 8.26018i) q^{97} +(1.09162 + 6.89219i) q^{98} +(-0.530447 + 9.23588i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$2$	−0.987688	+	0.156434i	−0.698401	+	0.110616i
$3$	0.487767	+	1.66195i	0.281612	+	0.959528i
$3$	0.487767	+	1.66195i	0.281612	+	0.959528i
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	2.22772	+	0.193062i	0.996266	+	0.0863399i
$5$	2.22772	+	0.193062i	0.996266	+	0.0863399i
$6$	−0.741748	−	1.56519i	−0.302817	−	0.638985i
$7$	−0.104631	−	0.104631i	−0.0395470	−	0.0395470i	0.687057	−	0.726604i	$-0.258902\pi$
$7$	−0.104631	−	0.104631i	−0.0395470	−	0.0395470i	−0.726604	+	0.687057i	$0.758902\pi$
$8$	−0.891007	+	0.453990i	−0.315018	+	0.160510i
$9$	−2.52417	+	1.62129i	−0.841389	+	0.540430i
$10$	−2.23049	+	0.157807i	−0.705344	+	0.0499029i
$11$	1.81255	−	2.49477i	0.546506	−	0.752200i	−0.443027	−	0.896508i	$-0.646096\pi$
$11$	1.81255	−	2.49477i	0.546506	−	0.752200i	0.989533	+	0.144308i	$0.0460955\pi$
$12$	0.977465	+	1.42988i	0.282170	+	0.412771i
$13$	−0.711182	+	4.49023i	−0.197246	+	1.24536i	0.668055	+	0.744112i	$0.267127\pi$
$13$	−0.711182	+	4.49023i	−0.197246	+	1.24536i	−0.865301	+	0.501252i	$0.832873\pi$
$14$	0.119711	+	0.0869753i	0.0319942	+	0.0232451i
$15$	0.765748	+	3.79653i	0.197715	+	0.980260i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	1.68388	+	3.30481i	0.408402	+	0.801533i	0.999989	−	0.00470771i	$-0.00149852\pi$
$17$	1.68388	+	3.30481i	0.408402	+	0.801533i	−0.591587	+	0.806241i	$0.701499\pi$
$18$	2.23946	−	1.99620i	0.527847	−	0.470508i
$19$	−3.32698	−	1.08100i	−0.763262	−	0.247999i	−0.0985837	−	0.995129i	$-0.531431\pi$
$19$	−3.32698	−	1.08100i	−0.763262	−	0.247999i	−0.664678	+	0.747130i	$0.731431\pi$
$20$	2.17835	−	0.504790i	0.487093	−	0.112874i
$21$	0.122857	−	0.224928i	0.0268095	−	0.0490834i
$22$	−1.39997	+	2.74760i	−0.298475	+	0.585790i
$23$	−0.773401	−	4.88306i	−0.161265	−	1.01819i	−0.927008	−	0.375042i	$-0.877628\pi$
$23$	−0.773401	−	4.88306i	−0.161265	−	1.01819i	0.765743	−	0.643147i	$-0.222372\pi$
$24$	−1.18911	−	1.25937i	−0.242727	−	0.257067i
$25$	4.92545	+	0.860175i	0.985091	+	0.172035i
$26$		−	4.54620i		−	0.891583i
$27$	−3.92571	−	3.40423i	−0.755504	−	0.655145i
$28$	−0.131843	−	0.0671775i	−0.0249161	−	0.0126954i
$29$	−0.509399	−	1.56777i	−0.0945931	−	0.291128i	0.892554	−	0.450940i	$-0.148911\pi$
$29$	−0.509399	−	1.56777i	−0.0945931	−	0.291128i	−0.987147	+	0.159812i	$0.948911\pi$
$30$	−1.35023	−	3.63000i	−0.246517	−	0.662744i
$31$	2.45755	−	7.56355i	0.441388	−	1.35845i	−0.445008	−	0.895527i	$-0.646799\pi$
$31$	2.45755	−	7.56355i	0.441388	−	1.35845i	0.886396	−	0.462927i	$-0.153201\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	5.03028	+	1.79551i	0.875660	+	0.312559i
$34$	−2.18014	−	3.00070i	−0.373890	−	0.514616i
$35$	−0.212889	−	0.253290i	−0.0359848	−	0.0428138i
$36$	−1.89962	+	2.32195i	−0.316603	+	0.386992i
$37$	−8.30199	−	1.31491i	−1.36484	−	0.216169i	−0.569329	−	0.822110i	$-0.692797\pi$
$37$	−8.30199	−	1.31491i	−1.36484	−	0.216169i	−0.795510	+	0.605941i	$0.792797\pi$
$38$	3.45513	+	0.547238i	0.560495	+	0.0887737i
$39$	−7.80943	+	1.00823i	−1.25051	+	0.161447i
$40$	−2.07256	+	0.839343i	−0.327700	+	0.132712i
$41$	−1.27149	−	1.75005i	−0.198573	−	0.273312i	0.698105	−	0.715995i	$-0.254027\pi$
$41$	−1.27149	−	1.75005i	−0.198573	−	0.273312i	−0.896678	+	0.442683i	$0.854027\pi$
$42$	−0.0861576	+	0.241378i	−0.0132944	+	0.0372454i
$43$	2.77052	−	2.77052i	0.422501	−	0.422501i	−0.463563	−	0.886064i	$-0.653429\pi$
$43$	2.77052	−	2.77052i	0.422501	−	0.422501i	0.886064	+	0.463563i	$0.153429\pi$
$44$	0.952916	−	2.93277i	0.143657	−	0.442132i
$45$	−5.93614	+	3.12446i	−0.884908	+	0.465767i
$46$	1.52776	+	4.70196i	0.225256	+	0.693266i
$47$	4.77725	+	2.43413i	0.696833	+	0.355054i	0.766258	−	0.642533i	$-0.222116\pi$
$47$	4.77725	+	2.43413i	0.696833	+	0.355054i	−0.0694250	+	0.997587i	$0.522116\pi$
$48$	1.37148	+	1.05784i	0.197956	+	0.152687i
$49$		−	6.97810i		−	0.996872i
$50$	−4.99937	−	0.0790741i	−0.707018	−	0.0111828i
$51$	−4.67109	+	4.41051i	−0.654083	+	0.617595i
$52$	0.711182	+	4.49023i	0.0986232	+	0.622682i
$53$	5.24200	−	10.2880i	0.720045	−	1.41317i	−0.182778	−	0.983154i	$-0.558509\pi$
$53$	5.24200	−	10.2880i	0.720045	−	1.41317i	0.902823	−	0.430013i	$-0.141491\pi$
$54$	4.40992	+	2.74820i	0.600114	+	0.373983i
$55$	4.51950	−	5.20770i	0.609410	−	0.702206i
$56$	0.140729	+	0.0457256i	0.0188057	+	0.00611035i
$57$	0.173781	−	6.05656i	0.0230178	−	0.802211i
$58$	0.748381	+	1.46878i	0.0982673	+	0.192860i
$59$	−10.4207	+	7.57107i	−1.35666	+	0.985670i	−0.358009	+	0.933718i	$0.616544\pi$
$59$	−10.4207	+	7.57107i	−1.35666	+	0.985670i	−0.998650	+	0.0519515i	$0.983456\pi$
$60$	1.90146	+	3.37408i	0.245478	+	0.435592i
$61$	11.8153	+	8.58430i	1.51279	+	1.09911i	0.964920	+	0.262544i	$0.0845614\pi$
$61$	11.8153	+	8.58430i	1.51279	+	1.09911i	0.547871	+	0.836563i	$0.315439\pi$
$62$	−1.24409	+	7.85487i	−0.158000	+	0.997570i
$63$	0.433745	+	0.0944693i	0.0546468	+	0.0119020i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−2.45120	+	9.86565i	−0.304034	+	1.22368i
$66$	−5.24923	−	0.986496i	−0.646136	−	0.121429i
$67$	3.23605	−	1.64885i	0.395346	−	0.201439i	−0.245004	−	0.969522i	$-0.578789\pi$
$67$	3.23605	−	1.64885i	0.395346	−	0.201439i	0.640350	+	0.768083i	$0.278789\pi$
$68$	2.62271	+	2.62271i	0.318050	+	0.318050i
$69$	7.73817	−	3.66715i	0.931567	−	0.441473i
$70$	0.249891	+	0.216868i	0.0298677	+	0.0259207i
$71$	−4.79465	+	1.55788i	−0.569020	+	0.184886i	−0.579376	−	0.815061i	$-0.696704\pi$
$71$	−4.79465	+	1.55788i	−0.569020	+	0.184886i	0.0103558	+	0.999946i	$0.496704\pi$
$72$	1.51300	−	2.59053i	0.178309	−	0.305297i
$73$	−10.6274	+	1.68322i	−1.24385	+	0.197006i	−0.743451	−	0.668791i	$-0.766812\pi$
$73$	−10.6274	+	1.68322i	−1.24385	+	0.197006i	−0.500396	+	0.865797i	$0.666812\pi$
$74$	8.40547			0.977116
$75$	0.972905	+	8.60543i	0.112341	+	0.993670i
$76$	−3.49819			−0.401270
$77$	−0.450681	+	0.0713809i	−0.0513599	+	0.00813461i
$78$	7.55556	−	2.21748i	0.855499	−	0.251081i
$79$	8.57556	−	2.78637i	0.964826	−	0.313491i	0.216100	−	0.976371i	$-0.430666\pi$
$79$	8.57556	−	2.78637i	0.964826	−	0.313491i	0.748725	+	0.662880i	$0.230666\pi$
$80$	1.91574	−	1.15323i	0.214186	−	0.128935i
$81$	3.74283	−	8.18481i	0.415871	−	0.909424i
$82$	1.52960	+	1.52960i	0.168916	+	0.168916i
$83$	−9.01058	+	4.59112i	−0.989039	+	0.503941i	−0.872168	−	0.489206i	$-0.837286\pi$
$83$	−9.01058	+	4.59112i	−0.989039	+	0.503941i	−0.116871	+	0.993147i	$0.537286\pi$
$84$	0.0473370	−	0.251884i	0.00516489	−	0.0274828i
$85$	3.11318	+	7.68727i	0.337672	+	0.833801i
$86$	−2.30301	+	3.16982i	−0.248340	+	0.341810i
$87$	2.35709	−	1.61130i	0.252707	−	0.172750i
$88$	−0.482397	+	3.04574i	−0.0514237	+	0.324676i
$89$	6.13326	+	4.45607i	0.650124	+	0.472343i	0.863314	−	0.504668i	$-0.168385\pi$
$89$	6.13326	+	4.45607i	0.650124	+	0.472343i	−0.213189	+	0.977011i	$0.568385\pi$
$90$	5.37428	−	4.01461i	0.566499	−	0.423177i
$91$	0.544231	−	0.395407i	0.0570509	−	0.0414499i
$92$	−2.24450	−	4.40507i	−0.234005	−	0.459261i
$93$	13.7690	+	0.395073i	1.42778	+	0.0409672i
$94$	−5.09921	−	1.65683i	−0.525944	−	0.170889i
$95$	−7.20287	−	3.05048i	−0.738999	−	0.312973i
$96$	−1.52008	−	0.830274i	−0.155143	−	0.0847395i
$97$	−4.20877	+	8.26018i	−0.427336	+	0.838694i	0.572487	+	0.819913i	$0.305979\pi$
$97$	−4.20877	+	8.26018i	−0.427336	+	0.838694i	−0.999824	+	0.0187810i	$0.994021\pi$
$98$	1.09162	+	6.89219i	0.110270	+	0.696217i
$99$	−0.530447	+	9.23588i	−0.0533120	+	0.928241i
$100$	4.95019	−	0.703974i	0.495019	−	0.0703974i
$101$			4.19074i			0.416994i	0.978023	+	0.208497i	$0.0668571\pi$
$101$			4.19074i			0.416994i	−0.978023	+	0.208497i	$0.933143\pi$
$102$	3.92362	−	5.08693i	0.388496	−	0.503681i
$103$	−15.5940	−	7.94553i	−1.53652	−	0.782896i	−0.538312	−	0.842745i	$-0.680938\pi$
$103$	−15.5940	−	7.94553i	−1.53652	−	0.782896i	−0.998207	+	0.0598493i	$0.980938\pi$
$104$	−1.40485	−	4.32369i	−0.137757	−	0.423973i
$105$	0.317115	−	0.477358i	0.0309473	−	0.0465853i
$106$	−3.56807	+	10.9814i	−0.346561	+	1.06661i
$107$	0.457779	−	0.457779i	0.0442552	−	0.0442552i	−0.684633	−	0.728888i	$-0.740037\pi$
$107$	0.457779	−	0.457779i	0.0442552	−	0.0442552i	0.728888	+	0.684633i	$0.240037\pi$
$108$	−4.78554	−	2.02450i	−0.460489	−	0.194808i
$109$	−0.0442666	−	0.0609277i	−0.00423997	−	0.00583582i	0.806892	−	0.590699i	$-0.201148\pi$
$109$	−0.0442666	−	0.0609277i	−0.00423997	−	0.00583582i	−0.811132	+	0.584864i	$0.801148\pi$
$110$	−3.64920	+	5.85059i	−0.347937	+	0.557832i
$111$	−1.86413	−	14.4389i	−0.176935	−	1.37048i
$112$	−0.146149	−	0.0231478i	−0.0138098	−	0.00218726i
$113$	−16.9061	−	2.67766i	−1.59039	−	0.251893i	−0.702408	−	0.711774i	$-0.747892\pi$
$113$	−16.9061	−	2.67766i	−1.59039	−	0.251893i	−0.887980	+	0.459881i	$0.847892\pi$
$114$	0.775813	+	6.00918i	0.0726615	+	0.562811i
$115$	−0.780186	−	11.0274i	−0.0727527	−	1.02831i
$116$	−0.968935	−	1.33363i	−0.0899634	−	0.123824i
$117$	−5.48482	−	12.4871i	−0.507072	−	1.15443i
$118$	9.10802	−	9.10802i	0.838461	−	0.838461i
$119$	0.169600	−	0.521974i	0.0155472	−	0.0478493i
$120$	−2.40587	−	3.03509i	−0.219625	−	0.277065i
$121$	0.460680	+	1.41783i	0.0418800	+	0.128893i
$122$	−13.0127	−	6.63030i	−1.17811	−	0.600279i
$123$	2.28831	−	2.96676i	0.206330	−	0.267504i
$124$		−	7.95279i		−	0.714181i
$125$	10.8065	+	2.86715i	0.966559	+	0.256445i
$126$	−0.443183	−	0.0254535i	−0.0394819	−	0.00226758i
$127$	1.39490	+	8.80705i	0.123777	+	0.781499i	0.968996	+	0.247078i	$0.0794704\pi$
$127$	1.39490	+	8.80705i	0.123777	+	0.781499i	−0.845218	+	0.534421i	$0.820530\pi$
$128$	−0.453990	+	0.891007i	−0.0401275	+	0.0787546i
$129$	5.95584	+	3.25310i	0.524383	+	0.286420i
$130$	0.877698	−	10.1276i	0.0769792	−	0.888253i
$131$	1.60573	+	0.521733i	0.140293	+	0.0455840i	0.378322	−	0.925674i	$-0.376501\pi$
$131$	1.60573	+	0.521733i	0.140293	+	0.0455840i	−0.238029	+	0.971258i	$0.576501\pi$
$132$	5.33893	+	0.153190i	0.464694	+	0.0133335i
$133$	0.235000	+	0.461214i	0.0203771	+	0.0399923i
$134$	−2.93827	+	2.13478i	−0.253828	+	0.184417i
$135$	−8.08815	−	8.34157i	−0.696117	−	0.717928i
$136$	−3.00070	−	2.18014i	−0.257308	−	0.186945i
$137$	2.28802	−	14.4460i	0.195479	−	1.23420i	−0.673438	−	0.739244i	$-0.735183\pi$
$137$	2.28802	−	14.4460i	0.195479	−	1.23420i	0.868916	−	0.494959i	$-0.164817\pi$
$138$	−7.06923	+	4.83252i	−0.601773	+	0.411371i
$139$	−10.4809	+	14.4257i	−0.888977	+	1.22357i	0.0848764	+	0.996391i	$0.472950\pi$
$139$	−10.4809	+	14.4257i	−0.888977	+	1.22357i	−0.973853	+	0.227180i	$0.927050\pi$
$140$	−0.280740	−	0.175107i	−0.0237269	−	0.0147992i
$141$	−1.71522	+	9.12684i	−0.144448	+	0.768619i
$142$	4.49191	−	2.28874i	0.376953	−	0.192067i
$143$	9.91301	+	9.91301i	0.828967	+	0.828967i
$144$	−1.08912	+	2.79532i	−0.0907603	+	0.232943i
$145$	−0.832121	−	3.59090i	−0.0691039	−	0.298208i
$146$	10.2333	−	3.32499i	0.846912	−	0.275178i
$147$	11.5973	−	3.40369i	0.956527	−	0.280732i
$148$	−8.30199	+	1.31491i	−0.682419	+	0.108085i
$149$	15.4486			1.26560			0.632800	−	0.774316i	$-0.281906\pi$
$149$	15.4486			1.26560			0.632800	+	0.774316i	$0.281906\pi$
$150$	−2.30711	−	8.34729i	−0.188375	−	0.681553i
$151$	−7.09145			−0.577094			−0.288547	−	0.957466i	$-0.593172\pi$
$151$	−7.09145			−0.577094			−0.288547	+	0.957466i	$0.593172\pi$
$152$	3.45513	−	0.547238i	0.280248	−	0.0443869i
$153$	−9.60845	−	5.61182i	−0.776797	−	0.453689i
$154$	0.433966	−	0.141004i	0.0349700	−	0.0113624i
$155$	6.93495	−	16.3750i	0.557029	−	1.31527i
$156$	−7.11565	+	3.37213i	−0.569708	+	0.269987i
$157$	5.10830	+	5.10830i	0.407687	+	0.407687i	0.880931	−	0.473244i	$-0.156917\pi$
$157$	5.10830	+	5.10830i	0.407687	+	0.407687i	−0.473244	+	0.880931i	$0.656917\pi$
$158$	−8.03409	+	4.09358i	−0.639158	+	0.325667i
$159$	19.6551	+	3.69380i	1.55875	+	0.292938i
$160$	−1.71175	+	1.43872i	−0.135326	+	0.113741i
$161$	−0.430000	+	0.591844i	−0.0338887	+	0.0466439i
$162$	−2.41637	+	8.66955i	−0.189848	+	0.681145i
$163$	−0.335098	+	2.11572i	−0.0262469	+	0.165716i	−0.997330	−	0.0730249i	$-0.976735\pi$
$163$	−0.335098	+	2.11572i	−0.0262469	+	0.165716i	0.971083	+	0.238741i	$0.0767347\pi$
$164$	−1.75005	−	1.27149i	−0.136656	−	0.0992863i
$165$	10.8594	+	4.97105i	0.845404	+	0.386996i
$166$	8.18143	−	5.94416i	0.635002	−	0.461356i
$167$	1.90498	+	3.73873i	0.147412	+	0.289312i	0.952891	−	0.303312i	$-0.0980923\pi$
$167$	1.90498	+	3.73873i	0.147412	+	0.289312i	−0.805480	+	0.592623i	$0.798092\pi$
$168$	−0.00735081	+	0.256188i	−0.000567128	+	0.0197654i
$169$	−7.29261	−	2.36951i	−0.560970	−	0.182270i
$170$	−4.27741	−	7.10562i	−0.328062	−	0.544976i
$171$	10.1505	−	2.66537i	0.776226	−	0.203826i
$172$	1.77878	−	3.49106i	0.135631	−	0.266191i
$173$	−0.0170042	−	0.107360i	−0.00129280	−	0.00816244i	0.987034	−	0.160514i	$-0.0513153\pi$
$173$	−0.0170042	−	0.107360i	−0.00129280	−	0.00816244i	−0.988326	+	0.152352i	$0.951315\pi$
$174$	−2.07601	+	1.96020i	−0.157382	+	0.148602i
$175$	−0.425356	−	0.605359i	−0.0321539	−	0.0457608i
$176$		−	3.08370i		−	0.232443i
$177$	−17.6656	−	13.6258i	−1.32783	−	1.02417i
$178$	−6.75483	−	3.44176i	−0.506296	−	0.257971i
$179$	−0.495650	−	1.52545i	−0.0370466	−	0.114018i	0.930823	−	0.365470i	$-0.119092\pi$
$179$	−0.495650	−	1.52545i	−0.0370466	−	0.114018i	−0.967870	+	0.251452i	$0.919092\pi$
$180$	−4.68009	+	4.80590i	−0.348834	+	0.358211i
$181$	−3.90297	+	12.0121i	−0.290105	+	0.892852i	0.694717	+	0.719284i	$0.255530\pi$
$181$	−3.90297	+	12.0121i	−0.290105	+	0.892852i	−0.984822	+	0.173568i	$0.944470\pi$
$182$	−0.475675	+	0.475675i	−0.0352594	+	0.0352594i
$183$	−8.50359	+	23.8236i	−0.628603	+	1.76109i
$184$	2.90597	+	3.99972i	0.214231	+	0.294864i
$185$	−18.2406	−	4.53204i	−1.34108	−	0.333202i
$186$	−13.6612	+	1.76373i	−1.00169	+	0.129323i
$187$	11.2968	+	1.78924i	0.826107	+	0.130843i
$188$	5.29562	+	0.838744i	0.386223	+	0.0611717i
$189$	0.0545633	+	0.766943i	0.00396889	+	0.0557869i
$190$	7.59139	+	1.88615i	0.550738	+	0.136835i
$191$	12.2687	+	16.8865i	0.887734	+	1.22186i	0.974218	+	0.225608i	$0.0724369\pi$
$191$	12.2687	+	16.8865i	0.887734	+	1.22186i	−0.0864840	+	0.996253i	$0.527563\pi$
$192$	1.63125	+	0.582259i	0.117725	+	0.0420209i
$193$	−4.75446	+	4.75446i	−0.342233	+	0.342233i	−0.857206	−	0.514973i	$-0.827802\pi$
$193$	−4.75446	+	4.75446i	−0.342233	+	0.342233i	0.514973	+	0.857206i	$0.327802\pi$
$194$	2.86478	−	8.81688i	0.205679	−	0.633015i
$195$	−17.5919	+	0.738358i	−1.25978	+	0.0528749i
$196$	−2.15635	−	6.63657i	−0.154025	−	0.474041i
$197$	3.85665	+	1.96506i	0.274775	+	0.140005i	0.585948	−	0.810348i	$-0.300722\pi$
$197$	3.85665	+	1.96506i	0.274775	+	0.140005i	−0.311174	+	0.950353i	$0.600722\pi$
$198$	−0.920894	−	9.20515i	−0.0654451	−	0.654182i
$199$		−	0.610848i		−	0.0433019i	−0.999766	−	0.0216509i	$-0.993108\pi$
$199$		−	0.610848i		−	0.0433019i	0.999766	−	0.0216509i	$-0.00689224\pi$
$200$	−4.77912	+	1.46969i	−0.337935	+	0.103923i
$201$	4.31874	+	4.57390i	0.304621	+	0.322618i
$202$	−0.655576	−	4.13914i	−0.0461261	−	0.291229i
$203$	−0.110739	+	0.217337i	−0.00777235	+	0.0152541i
$204$	−3.07954	+	5.63809i	−0.215611	+	0.394745i
$205$	−2.49464	−	4.14409i	−0.174233	−	0.289436i
$206$	16.6449	+	5.40827i	1.15971	+	0.376812i
$207$	9.86905	+	11.0718i	0.685947	+	0.769540i
$208$	2.06393	+	4.05069i	0.143108	+	0.280865i
$209$	−8.72718	+	6.34067i	−0.603671	+	0.438593i
$210$	−0.238536	+	0.521088i	−0.0164605	+	0.0359585i
$211$	3.67523	+	2.67021i	0.253013	+	0.183825i	0.707061	−	0.707152i	$-0.250020\pi$
$211$	3.67523	+	2.67021i	0.253013	+	0.183825i	−0.454048	+	0.890977i	$0.650020\pi$
$212$	1.80627	−	11.4044i	0.124055	−	0.783254i
$213$	−4.92778	−	7.20859i	−0.337646	−	0.493925i
$214$	−0.380531	+	0.523756i	−0.0260125	+	0.0358032i
$215$	6.70682	−	5.63706i	0.457401	−	0.384444i
$216$	5.04332	+	1.25096i	0.343155	+	0.0851168i
$217$	−1.04852	+	0.534249i	−0.0711783	+	0.0362672i
$218$	0.0532528	+	0.0532528i	0.00360673	+	0.00360673i
$219$	−7.98114	−	16.8413i	−0.539316	−	1.13803i
$220$	2.68903	−	6.34942i	0.181295	−	0.428078i
$221$	−16.0369	+	5.21070i	−1.07876	+	0.350509i
$222$	4.09991	+	13.9695i	0.275168	+	0.937571i
$223$	19.2711	−	3.05224i	1.29049	−	0.204393i	0.526805	−	0.849986i	$-0.323390\pi$
$223$	19.2711	−	3.05224i	1.29049	−	0.204393i	0.763681	+	0.645593i	$0.223390\pi$
$224$	0.147971			0.00988675
$225$	−13.8273	+	5.81437i	−0.921817	+	0.387624i
$226$	17.1168			1.13859
$227$	11.9356	−	1.89042i	0.792194	−	0.125471i	0.252793	−	0.967520i	$-0.418651\pi$
$227$	11.9356	−	1.89042i	0.792194	−	0.125471i	0.539401	+	0.842049i	$0.318651\pi$
$228$	−1.70630	−	5.81383i	−0.113003	−	0.385030i
$229$	5.88719	−	1.91287i	0.389037	−	0.126406i	−0.107966	−	0.994155i	$-0.534434\pi$
$229$	5.88719	−	1.91287i	0.389037	−	0.126406i	0.497003	+	0.867749i	$0.334434\pi$
$230$	2.49565	+	10.7696i	0.164558	+	0.710125i
$231$	−0.338459	−	0.714193i	−0.0222690	−	0.0469905i
$232$	1.16563	+	1.16563i	0.0765274	+	0.0765274i
$233$	6.74965	−	3.43912i	0.442184	−	0.225304i	−0.218700	−	0.975792i	$-0.570182\pi$
$233$	6.74965	−	3.43912i	0.442184	−	0.225304i	0.660884	+	0.750488i	$0.270182\pi$
$234$	7.37071	+	11.4754i	0.481838	+	0.750168i
$235$	10.1724	+	6.34486i	0.663575	+	0.413893i
$236$	−7.57107	+	10.4207i	−0.492835	+	0.678329i
$237$	8.81368	+	12.8931i	0.572510	+	0.837494i
$238$	−0.0858568	+	0.542079i	−0.00556527	+	0.0351377i
$239$	−13.6576	−	9.92281i	−0.883435	−	0.641853i	0.0507228	−	0.998713i	$-0.483848\pi$
$239$	−13.6576	−	9.92281i	−0.883435	−	0.641853i	−0.934158	+	0.356859i	$0.883848\pi$
$240$	2.85105	+	2.62136i	0.184034	+	0.169208i
$241$	−7.96740	+	5.78866i	−0.513225	+	0.372880i	−0.814046	−	0.580801i	$-0.802740\pi$
$241$	−7.96740	+	5.78866i	−0.513225	+	0.372880i	0.300820	+	0.953681i	$0.402740\pi$
$242$	−0.676805	−	1.32830i	−0.0435066	−	0.0853866i
$243$	15.4284	+	2.22813i	0.989732	+	0.142934i
$244$	13.8897	+	4.51303i	0.889196	+	0.288917i
$245$	1.34721	−	15.5452i	0.0860699	−	0.993149i
$246$	−1.79603	+	3.28821i	−0.114511	+	0.209648i
$247$	7.22003	−	14.1701i	0.459399	−	0.901622i
$248$	1.24409	+	7.85487i	0.0789998	+	0.498785i
$249$	−12.0253	−	12.7357i	−0.762071	−	0.807095i
$250$	−11.1219	−	1.14134i	−0.703413	−	0.0721849i
$251$		−	0.308302i		−	0.0194599i	−0.999953	−	0.00972993i	$-0.996903\pi$
$251$		−	0.308302i		−	0.0194599i	0.999953	−	0.00972993i	$-0.00309718\pi$
$252$	0.441709	−	0.0441891i	0.0278250	−	0.00278365i
$253$	−13.5839	−	6.92136i	−0.854014	−	0.435142i
$254$	−2.75545	−	8.48041i	−0.172892	−	0.532108i
$255$	−11.2574	+	8.92356i	−0.704963	+	0.558815i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−5.10907	+	5.10907i	−0.318695	+	0.318695i	−0.848266	−	0.529571i	$-0.822353\pi$
$257$	−5.10907	+	5.10907i	−0.318695	+	0.318695i	0.529571	+	0.848266i	$0.322353\pi$
$258$	−6.39141	−	2.28135i	−0.397912	−	0.142031i
$259$	0.731069	+	1.00623i	0.0454264	+	0.0625241i
$260$	0.717421	+	10.1403i	0.0444926	+	0.628872i
$261$	3.82762	+	3.13143i	0.236924	+	0.193831i
$262$	−1.66758	−	0.264118i	−0.103023	−	0.0163173i
$263$	5.16055	+	0.817350i	0.318213	+	0.0504000i	0.313498	−	0.949589i	$-0.398499\pi$
$263$	5.16055	+	0.817350i	0.318213	+	0.0504000i	0.00471508	+	0.999989i	$0.498499\pi$
$264$	−5.29716	+	0.683889i	−0.326018	+	0.0420904i
$265$	13.6639	−	21.9068i	0.839369	−	1.34572i
$266$	−0.304257	−	0.418773i	−0.0186552	−	0.0256766i
$267$	−4.41418	+	12.3667i	−0.270143	+	0.756830i
$268$	2.56814	−	2.56814i	0.156874	−	0.156874i
$269$	0.702217	−	2.16120i	0.0428149	−	0.131771i	−0.927364	−	0.374160i	$-0.877931\pi$
$269$	0.702217	−	2.16120i	0.0428149	−	0.131771i	0.970179	+	0.242389i	$0.0779311\pi$
$270$	9.29348	+	6.97361i	0.565583	+	0.424400i
$271$	−5.82840	−	17.9380i	−0.354050	−	1.08965i	−0.956558	−	0.291541i	$-0.905832\pi$
$271$	−5.82840	−	17.9380i	−0.354050	−	1.08965i	0.602508	−	0.798113i	$-0.294168\pi$
$272$	3.30481	+	1.68388i	0.200383	+	0.102100i
$273$	0.922605	+	0.711619i	0.0558386	+	0.0430691i
$274$			14.6260i			0.883592i
$275$	11.0736	−	10.7287i	0.667762	−	0.646968i
$276$	6.22623	−	5.87890i	0.374775	−	0.353868i
$277$	2.59202	+	16.3654i	0.155739	+	0.983299i	0.934496	+	0.355973i	$0.115851\pi$
$277$	2.59202	+	16.3654i	0.155739	+	0.983299i	−0.778757	+	0.627326i	$0.784149\pi$
$278$	8.09517	−	15.8877i	0.485516	−	0.952878i
$279$	6.05945	+	23.0761i	0.362770	+	1.38153i
$280$	0.304677	+	0.129033i	0.0182079	+	0.00771121i
$281$	−23.8171	−	7.73865i	−1.42081	−	0.461649i	−0.504951	−	0.863148i	$-0.668489\pi$
$281$	−23.8171	−	7.73865i	−1.42081	−	0.461649i	−0.915859	+	0.401499i	$0.868489\pi$
$282$	0.266351	−	9.28279i	0.0158610	−	0.552782i
$283$	12.1655	+	23.8762i	0.723165	+	1.41929i	0.900374	+	0.435117i	$0.143293\pi$
$283$	12.1655	+	23.8762i	0.723165	+	1.41929i	−0.177209	+	0.984173i	$0.556707\pi$
$284$	−4.07857	+	2.96325i	−0.242019	+	0.175837i
$285$	1.55643	−	13.4588i	0.0921947	−	0.797228i
$286$	−11.3417	−	8.24023i	−0.670649	−	0.487255i
$287$	−0.0500729	+	0.316148i	−0.00295571	+	0.0186616i
$288$	0.638430	−	2.93128i	0.0376198	−	0.172727i
$289$	1.90607	−	2.62348i	0.112122	−	0.154322i
$290$	1.38362	+	3.41651i	0.0812488	+	0.200625i
$291$	−15.7809	−	2.96573i	−0.925094	−	0.173854i
$292$	−9.58715	+	4.88489i	−0.561045	+	0.285867i
$293$	1.78525	+	1.78525i	0.104296	+	0.104296i	0.757329	−	0.653033i	$-0.226504\pi$
$293$	1.78525	+	1.78525i	0.104296	+	0.104296i	−0.653033	+	0.757329i	$0.726504\pi$
$294$	−10.9220	+	5.17600i	−0.636986	+	0.301870i
$295$	−24.6760	+	14.8544i	−1.43669	+	0.864855i
$296$	7.99408	−	2.59743i	0.464646	−	0.150973i
$297$	−15.6083	+	3.62338i	−0.905687	+	0.210250i
$298$	−15.2584	+	2.41669i	−0.883896	+	0.139995i
$299$	22.4761			1.29983
$300$	3.58451	+	7.88361i	0.206952	+	0.455160i
$301$	−0.579767			−0.0334172
$302$	7.00414	−	1.10935i	0.403043	−	0.0638357i
$303$	−6.96480	+	2.04410i	−0.400117	+	0.117431i
$304$	−3.32698	+	1.08100i	−0.190815	+	0.0619997i
$305$	24.6638	+	21.4045i	1.41224	+	1.22562i
$306$	10.3680	+	4.03963i	0.592701	+	0.230931i
$307$	−18.1356	−	18.1356i	−1.03505	−	1.03505i	−0.999363	−	0.0356889i	$-0.988637\pi$
$307$	−18.1356	−	18.1356i	−1.03505	−	1.03505i	−0.0356889	−	0.999363i	$-0.511363\pi$
$308$	−0.406565	+	0.207155i	−0.0231662	+	0.0118038i
$309$	5.59885	−	29.7920i	0.318508	−	1.69481i
$310$	−4.28796	+	17.2583i	−0.243540	+	0.980203i
$311$	6.19053	−	8.52054i	0.351033	−	0.483155i	−0.596590	−	0.802546i	$-0.703478\pi$
$311$	6.19053	−	8.52054i	0.351033	−	0.483155i	0.947623	+	0.319391i	$0.103478\pi$
$312$	6.50052	−	4.44375i	0.368020	−	0.251578i
$313$	2.76954	−	17.4862i	0.156543	−	0.988377i	−0.776893	−	0.629633i	$-0.783205\pi$
$313$	2.76954	−	17.4862i	0.156543	−	0.988377i	0.933436	−	0.358744i	$-0.116795\pi$
$314$	−5.84453	−	4.24630i	−0.329826	−	0.239632i
$315$	0.948024	+	0.294191i	0.0534151	+	0.0165758i
$316$	7.29480	−	5.29999i	0.410365	−	0.298147i
$317$	2.31211	+	4.53776i	0.129861	+	0.254866i	0.946777	−	0.321890i	$-0.104318\pi$
$317$	2.31211	+	4.53776i	0.129861	+	0.254866i	−0.816916	+	0.576756i	$0.804318\pi$
$318$	−19.9909	−	0.573599i	−1.12103	−	0.0321659i
$319$	−4.83453	−	1.57084i	−0.270682	−	0.0879499i
$320$	1.46561	−	1.68878i	0.0819301	−	0.0944058i
$321$	0.984096	+	0.537517i	0.0549269	+	0.0300013i
$322$	0.332121	−	0.651824i	0.0185084	−	0.0363248i
$323$	−2.02974	−	12.8153i	−0.112938	−	0.713063i
$324$	1.03040	−	8.94082i	0.0572445	−	0.496712i
$325$	−7.36527	+	21.5047i	−0.408552	+	1.19286i
$326$		−	2.14210i		−	0.118640i
$327$	0.0796671	−	0.103287i	0.00440560	−	0.00571181i
$328$	1.92741	+	0.982063i	0.106423	+	0.0542254i
$329$	−0.245164	−	0.754537i	−0.0135163	−	0.0415990i
$330$	−11.5034	−	3.21106i	−0.633239	−	0.176763i
$331$	−4.54014	+	13.9731i	−0.249548	+	0.768031i	0.745307	+	0.666722i	$0.232303\pi$
$331$	−4.54014	+	13.9731i	−0.249548	+	0.768031i	−0.994855	+	0.101309i	$0.967697\pi$
$332$	−7.15083	+	7.15083i	−0.392453	+	0.392453i
$333$	23.0874	−	10.1409i	1.26518	−	0.555717i
$334$	−2.46639	−	3.39470i	−0.134955	−	0.185750i
$335$	7.52733	−	3.04841i	0.411262	−	0.166553i
$336$	−0.0328164	−	0.254184i	−0.00179028	−	0.0138669i
$337$	−24.4578	−	3.87373i	−1.33230	−	0.211015i	−0.550651	−	0.834735i	$-0.685621\pi$
$337$	−24.4578	−	3.87373i	−1.33230	−	0.211015i	−0.781648	+	0.623720i	$0.785621\pi$
$338$	7.57350	+	1.19952i	0.411944	+	0.0652455i
$339$	−3.79608	−	29.4031i	−0.206175	−	1.59696i
$340$	5.33631	+	6.34900i	0.289402	+	0.344323i
$341$	−14.4149	−	19.8403i	−0.780608	−	1.07441i
$342$	−9.60854	+	4.22044i	−0.519571	+	0.228215i
$343$	−1.46255	+	1.46255i	−0.0789703	+	0.0789703i
$344$	−1.21076	+	3.72634i	−0.0652799	+	0.200911i
$345$	17.9465	−	6.67543i	0.966205	−	0.359393i
$346$	0.0335897	+	0.103378i	0.00180579	+	0.00555765i
$347$	−28.4710	−	14.5067i	−1.52840	−	0.778760i	−0.530769	−	0.847516i	$-0.678097\pi$
$347$	−28.4710	−	14.5067i	−1.52840	−	0.778760i	−0.997633	+	0.0687565i	$0.978097\pi$
$348$	1.74381	−	2.26082i	0.0934778	−	0.121193i
$349$		−	27.0969i		−	1.45047i	−0.688504	−	0.725233i	$-0.741732\pi$
$349$		−	27.0969i		−	1.45047i	0.688504	−	0.725233i	$-0.258268\pi$
$350$	0.514818	+	0.531366i	0.0275182	+	0.0284027i
$351$	18.0777	−	15.2063i	0.964914	−	0.811652i
$352$	0.482397	+	3.04574i	0.0257118	+	0.162338i
$353$	−2.81680	+	5.52827i	−0.149923	+	0.294240i	−0.953738	−	0.300639i	$-0.902800\pi$
$353$	−2.81680	+	5.52827i	−0.149923	+	0.294240i	0.803815	+	0.594879i	$0.202800\pi$
$354$	19.5797	+	10.6945i	1.04065	+	0.568406i
$355$	−10.9819	+	2.54484i	−0.582858	+	0.135066i
$356$	7.21008	+	2.34270i	0.382133	+	0.124163i
$357$	0.950221	+	0.0272647i	0.0502910	+	0.00144300i
$358$	0.728181	+	1.42914i	0.0384855	+	0.0755321i
$359$	−27.6886	+	20.1169i	−1.46135	+	1.06173i	−0.478338	+	0.878176i	$0.658761\pi$
$359$	−27.6886	+	20.1169i	−1.46135	+	1.06173i	−0.983009	+	0.183555i	$0.941239\pi$
$360$	3.87067	−	5.47886i	0.204002	−	0.288761i
$361$	−5.47109	−	3.97498i	−0.287952	−	0.209209i
$362$	1.97581	−	12.4748i	0.103846	−	0.655659i
$363$	−2.13165	+	1.45720i	−0.111883	+	0.0764829i
$364$	0.395407	−	0.544231i	0.0207250	−	0.0285255i
$365$	−23.9999	+	1.69799i	−1.25621	+	0.0888767i
$366$	4.67207	−	24.8605i	0.244213	−	1.29948i
$367$	10.8271	−	5.51668i	0.565170	−	0.287968i	−0.147968	−	0.988992i	$-0.547273\pi$
$367$	10.8271	−	5.51668i	0.565170	−	0.287968i	0.713138	+	0.701024i	$0.247273\pi$
$368$	−3.49589	−	3.49589i	−0.182236	−	0.182236i
$369$	6.04678	+	2.35597i	0.314783	+	0.122647i
$370$	18.7250	+	1.62278i	0.973467	+	0.0843641i
$371$	−1.62493	+	0.527971i	−0.0843621	+	0.0274109i
$372$	13.2171	−	3.87911i	0.685277	−	0.201122i
$373$	25.3102	−	4.00874i	1.31051	−	0.207565i	0.538205	−	0.842814i	$-0.319103\pi$
$373$	25.3102	−	4.00874i	1.31051	−	0.207565i	0.772307	+	0.635249i	$0.219103\pi$
$374$	−11.4377			−0.591427
$375$	0.505976	+	19.3583i	0.0261285	+	0.999659i
$376$	−5.36163			−0.276505
$377$	7.40192	−	1.17235i	0.381218	−	0.0603790i
$378$	−0.173868	−	0.748965i	−0.00894279	−	0.0385226i
$379$	−6.14399	+	1.99630i	−0.315596	+	0.102543i	−0.462532	−	0.886603i	$-0.653059\pi$
$379$	−6.14399	+	1.99630i	−0.315596	+	0.102543i	0.146936	+	0.989146i	$0.453059\pi$
$380$	−7.79299	−	0.675368i	−0.399772	−	0.0346457i
$381$	−13.9565	+	6.61404i	−0.715013	+	0.338848i
$382$	−14.7593	−	14.7593i	−0.755152	−	0.755152i
$383$	0.244359	−	0.124507i	0.0124861	−	0.00636200i	−0.447736	−	0.894166i	$-0.647770\pi$
$383$	0.244359	−	0.124507i	0.0124861	−	0.00636200i	0.460222	+	0.887804i	$0.347770\pi$
$384$	−1.70225	−	0.319907i	−0.0868677	−	0.0163252i
$385$	−1.01777	+	0.0720071i	−0.0518705	+	0.00366982i
$386$	3.95216	−	5.43968i	0.201160	−	0.276873i
$387$	−2.50144	+	11.4851i	−0.127155	+	0.583819i
$388$	−1.45024	+	9.15648i	−0.0736250	+	0.464850i
$389$	22.1354	+	16.0823i	1.12231	+	0.815407i	0.984558	−	0.175059i	$-0.0560117\pi$
$389$	22.1354	+	16.0823i	1.12231	+	0.815407i	0.137754	+	0.990467i	$0.456012\pi$
$390$	17.2598	−	3.48124i	0.873982	−	0.176279i
$391$	14.8353	−	10.7784i	0.750251	−	0.545089i
$392$	3.16799	+	6.21754i	0.160008	+	0.314033i
$393$	−0.0838734	+	2.92313i	−0.00423085	+	0.147452i
$394$	−4.11657	−	1.33755i	−0.207390	−	0.0673850i
$395$	19.6419	−	4.55163i	0.988289	−	0.229017i
$396$	2.34956	+	8.94776i	0.118070	+	0.449642i
$397$	0.538470	−	1.05681i	0.0270250	−	0.0530396i	−0.877099	−	0.480309i	$-0.840524\pi$
$397$	0.538470	−	1.05681i	0.0270250	−	0.0530396i	0.904124	+	0.427270i	$0.140524\pi$
$398$	0.0955577	+	0.603327i	0.00478987	+	0.0302421i
$399$	−0.651890	+	0.615524i	−0.0326353	+	0.0308147i
$400$	4.49037	−	2.19921i	0.224519	−	0.109961i
$401$			4.37934i			0.218694i	0.994004	+	0.109347i	$0.0348759\pi$
$401$			4.37934i			0.218694i	−0.994004	+	0.109347i	$0.965124\pi$
$402$	−4.98109	−	3.84199i	−0.248434	−	0.191621i
$403$	32.2143	+	16.4140i	1.60471	+	0.817639i
$404$	1.29501	+	3.98563i	0.0644291	+	0.198292i
$405$	9.91816	−	17.5109i	0.492837	−	0.870122i
$406$	0.0753765	−	0.231985i	0.00374087	−	0.0115132i
$407$	−18.3282	+	18.3282i	−0.908494	+	0.908494i
$408$	2.15964	−	6.05042i	0.106918	−	0.299540i
$409$	19.0597	+	26.2334i	0.942440	+	1.29716i	0.954805	+	0.297234i	$0.0960641\pi$
$409$	19.0597	+	26.2334i	0.942440	+	1.29716i	−0.0123647	+	0.999924i	$0.503936\pi$
$410$	3.11221	+	3.70282i	0.153701	+	0.182869i
$411$	25.1245	−	3.24369i	1.23930	−	0.160000i
$412$	−17.2861	−	2.73784i	−0.851623	−	0.134884i
$413$	1.88250	+	0.298159i	0.0926320	+	0.0146715i
$414$	−11.4796	−	9.39158i	−0.564189	−	0.461571i
$415$	−20.9594	+	8.48812i	−1.02886	+	0.416665i
$416$	−2.67219	−	3.67795i	−0.131015	−	0.180326i
$417$	−29.0870	−	10.3823i	−1.42440	−	0.508425i
$418$	7.62783	−	7.62783i	0.373089	−	0.373089i
$419$	−9.10066	+	28.0089i	−0.444596	+	1.36833i	0.438330	+	0.898814i	$0.355570\pi$
$419$	−9.10066	+	28.0089i	−0.444596	+	1.36833i	−0.882926	+	0.469512i	$0.844430\pi$
$420$	0.154083	−	0.551988i	0.00751847	−	0.0269343i
$421$	1.83346	+	5.64281i	0.0893574	+	0.275014i	0.985742	−	0.168263i	$-0.0538158\pi$
$421$	1.83346	+	5.64281i	0.0893574	+	0.275014i	−0.896385	+	0.443277i	$0.853816\pi$
$422$	−4.04770	−	2.06240i	−0.197039	−	0.100396i
$423$	−16.0050	+	1.60116i	−0.778190	+	0.0778509i
$424$			11.5465i			0.560748i
$425$	5.45118	+	17.7261i	0.264421	+	0.859842i
$426$	5.99479	+	6.34897i	0.290448	+	0.307608i
$427$	−0.338062	−	2.13444i	−0.0163600	−	0.103293i
$428$	0.293912	−	0.576835i	0.0142068	−	0.0278824i
$429$	−11.6397	+	21.3102i	−0.561970	+	1.02887i
$430$	−5.74242	+	6.61683i	−0.276924	+	0.319092i
$431$	−16.7496	−	5.44228i	−0.806801	−	0.262146i	−0.123559	−	0.992337i	$-0.539431\pi$
$431$	−16.7496	−	5.44228i	−0.806801	−	0.262146i	−0.683242	+	0.730192i	$0.739431\pi$
$432$	−5.17692	−	0.446605i	−0.249075	−	0.0214873i
$433$	−4.11844	−	8.08290i	−0.197920	−	0.388439i	0.770621	−	0.637293i	$-0.219946\pi$
$433$	−4.11844	−	8.08290i	−0.197920	−	0.388439i	−0.968541	+	0.248854i	$0.919946\pi$
$434$	0.952038	−	0.691696i	0.0456993	−	0.0332025i
$435$	5.56201	−	3.13447i	0.266678	−	0.150286i
$436$	−0.0609277	−	0.0442666i	−0.00291791	−	0.00211998i
$437$	−2.70551	+	17.0819i	−0.129422	+	0.817138i
$438$	10.5174	+	15.3854i	0.502542	+	0.735142i
$439$	16.9822	−	23.3740i	0.810517	−	1.11558i	−0.180726	−	0.983533i	$-0.557845\pi$
$439$	16.9822	−	23.3740i	0.810517	−	1.11558i	0.991243	−	0.132048i	$-0.0421553\pi$
$440$	−1.66266	+	6.69191i	−0.0792642	+	0.319024i
$441$	11.3135	+	17.6139i	0.538740	+	0.838757i
$442$	15.0243	−	7.65526i	0.714633	−	0.364124i
$443$	12.4501	+	12.4501i	0.591523	+	0.591523i	0.938043	−	0.346520i	$-0.112637\pi$
$443$	12.4501	+	12.4501i	0.591523	+	0.591523i	−0.346520	+	0.938043i	$0.612637\pi$
$444$	−6.23474	−	13.1561i	−0.295888	−	0.624362i
$445$	12.8029	+	11.1110i	0.606915	+	0.526711i
$446$	−18.5563	+	6.02932i	−0.878668	+	0.285497i
$447$	7.53532	+	25.6748i	0.356408	+	1.21438i
$448$	−0.146149	+	0.0231478i	−0.00690491	+	0.00109363i
$449$	−12.8503			−0.606444			−0.303222	−	0.952920i	$-0.598062\pi$
$449$	−12.8503			−0.606444			−0.303222	+	0.952920i	$0.598062\pi$
$450$	12.7475	−	7.90584i	0.600921	−	0.372685i
$451$	−6.67060			−0.314106
$452$	−16.9061	+	2.67766i	−0.795194	+	0.125946i
$453$	−3.45897	−	11.7856i	−0.162517	−	0.553738i
$454$	−11.4929	+	3.73428i	−0.539390	+	0.175259i
$455$	1.28873	−	0.775785i	0.0604166	−	0.0363694i
$456$	2.59478	+	5.47533i	0.121512	+	0.256406i
$457$	10.9813	+	10.9813i	0.513683	+	0.513683i	0.915653	−	0.401970i	$-0.131674\pi$
$457$	10.9813	+	10.9813i	0.513683	+	0.513683i	−0.401970	+	0.915653i	$0.631674\pi$
$458$	−5.51547	+	2.81027i	−0.257721	+	0.131316i
$459$	4.63989	−	18.7060i	0.216571	−	0.873123i
$460$	−4.14965	−	10.2466i	−0.193479	−	0.477750i
$461$	6.59561	−	9.07808i	0.307188	−	0.422808i	−0.627314	−	0.778767i	$-0.715846\pi$
$461$	6.59561	−	9.07808i	0.307188	−	0.422808i	0.934502	+	0.355958i	$0.115846\pi$
$462$	0.446017	+	0.652454i	0.0207506	+	0.0303549i
$463$	0.201904	−	1.27477i	0.00938330	−	0.0592438i	−0.982552	−	0.185986i	$-0.940452\pi$
$463$	0.201904	−	1.27477i	0.00938330	−	0.0592438i	0.991936	+	0.126742i	$0.0404521\pi$
$464$	−1.33363	−	0.968935i	−0.0619120	−	0.0449817i
$465$	30.5971	+	3.53837i	1.41891	+	0.164088i
$466$	−6.12855	+	4.45265i	−0.283900	+	0.206265i
$467$	16.6117	+	32.6024i	0.768700	+	1.50866i	0.858565	+	0.512705i	$0.171356\pi$
$467$	16.6117	+	32.6024i	0.768700	+	1.50866i	−0.0898651	+	0.995954i	$0.528644\pi$
$468$	−9.07510	−	10.1810i	−0.419497	−	0.470619i
$469$	−0.511114	−	0.166071i	−0.0236010	−	0.00766845i
$470$	−11.0397	−	4.67542i	−0.509225	−	0.215661i
$471$	−5.99809	+	10.9814i	−0.276377	+	0.505997i
$472$	5.84771	−	11.4768i	0.269162	−	0.528261i
$473$	−1.89008	−	11.9335i	−0.0869062	−	0.548704i
$474$	−10.7221	−	11.3556i	−0.492482	−	0.521578i
$475$	−15.4570	−	8.18621i	−0.709218	−	0.375609i
$476$		−	0.548836i		−	0.0251559i
$477$	3.44816	+	34.4675i	0.157881	+	1.57816i
$478$	15.0417	+	7.66413i	0.687991	+	0.350549i
$479$	−8.59259	−	26.4453i	−0.392605	−	1.20832i	−0.930811	−	0.365502i	$-0.880897\pi$
$479$	−8.59259	−	26.4453i	−0.392605	−	1.20832i	0.538205	−	0.842814i	$-0.319103\pi$
$480$	−3.22602	−	2.14309i	−0.147247	−	0.0978180i
$481$	11.8084	−	36.3427i	0.538419	−	1.65708i
$482$	6.96376	−	6.96376i	0.317191	−	0.317191i
$483$	−1.19336	−	0.425957i	−0.0542996	−	0.0193817i
$484$	0.876264	+	1.20607i	0.0398302	+	0.0548216i
$485$	−10.9707	+	17.5888i	−0.498153	+	0.798666i
$486$	−15.5870	+	0.212837i	−0.707041	+	0.00965449i
$487$	9.45297	+	1.49720i	0.428355	+	0.0678448i	0.366890	−	0.930264i	$-0.380423\pi$
$487$	9.45297	+	1.49720i	0.428355	+	0.0678448i	0.0614653	+	0.998109i	$0.480423\pi$
$488$	−14.4247	−	2.28464i	−0.652974	−	0.103421i
$489$	−3.67968	+	0.475064i	−0.166401	+	0.0214831i
$490$	1.10119	+	15.5646i	0.0497468	+	0.703137i
$491$	6.14271	+	8.45471i	0.277216	+	0.381556i	0.924809	−	0.380431i	$-0.124224\pi$
$491$	6.14271	+	8.45471i	0.277216	+	0.381556i	−0.647593	+	0.761986i	$0.724224\pi$
$492$	1.25953	−	3.52869i	0.0567840	−	0.159085i
$493$	4.32341	−	4.32341i	0.194716	−	0.194716i
$494$	−4.91445	+	15.1251i	−0.221111	+	0.680511i
$495$	−2.96478	+	20.4725i	−0.133257	+	0.920172i
$496$	−2.45755	−	7.56355i	−0.110347	−	0.339613i
$497$	0.664674	+	0.338668i	0.0298147	+	0.0151913i
$498$	13.8695	+	10.6978i	0.621509	+	0.479379i
$499$			15.0118i			0.672022i	0.941858	+	0.336011i	$0.109078\pi$
$499$			15.0118i			0.672022i	−0.941858	+	0.336011i	$0.890922\pi$
$500$	11.1635	−	0.612561i	0.499249	−	0.0273946i
$501$	−5.28441	+	4.98961i	−0.236090	+	0.222920i
$502$	0.0482291	+	0.304507i	0.00215257	+	0.0135908i
$503$	−5.04097	+	9.89345i	−0.224766	+	0.441127i	−0.975658	−	0.219297i	$-0.929624\pi$
$503$	−5.04097	+	9.89345i	−0.224766	+	0.441127i	0.750893	+	0.660424i	$0.229624\pi$
$504$	−0.429358	+	0.112744i	−0.0191251	+	0.00502200i
$505$	−0.809072	+	9.33578i	−0.0360032	+	0.415437i
$506$	14.4994	+	4.71115i	0.644578	+	0.209436i
$507$	0.380921	−	13.2757i	0.0169173	−	0.589596i
$508$	4.04816	+	7.94495i	0.179608	+	0.352500i
$509$	31.3045	−	22.7440i	1.38755	−	1.00811i	0.391416	−	0.920214i	$-0.371985\pi$
$509$	31.3045	−	22.7440i	1.38755	−	1.00811i	0.996130	−	0.0878971i	$-0.0280147\pi$
$510$	9.72281	−	10.5747i	0.430533	−	0.468257i
$511$	1.28808	+	0.935846i	0.0569814	+	0.0413994i
$512$	−0.156434	+	0.987688i	−0.00691349	+	0.0436501i
$513$	9.38079	+	15.5695i	0.414172	+	0.687411i
$514$	4.24694	−	5.84540i	0.187324	−	0.257830i
$515$	−33.2050	−	20.7110i	−1.46319	−	0.912635i
$516$	6.66961	+	1.25343i	0.293613	+	0.0551791i
$517$	14.7316	−	7.50612i	0.647895	−	0.330119i
$518$	−0.879477	−	0.879477i	−0.0386420	−	0.0386420i
$519$	0.170133	−	0.0806269i	0.00746802	−	0.00353913i
$520$	−2.29487	−	9.90319i	−0.100637	−	0.434283i
$521$	20.0378	−	6.51069i	0.877874	−	0.285239i	0.164800	−	0.986327i	$-0.447302\pi$
$521$	20.0378	−	6.51069i	0.877874	−	0.285239i	0.713074	+	0.701089i	$0.247302\pi$
$522$	−4.27036	−	2.49410i	−0.186909	−	0.109164i
$523$	11.4878	−	1.81949i	0.502326	−	0.0795606i	0.0998710	−	0.995000i	$-0.468157\pi$
$523$	11.4878	−	1.81949i	0.502326	−	0.0795606i	0.402455	+	0.915440i	$0.368157\pi$
$524$	1.68836			0.0737565
$525$	0.798603	−	1.00220i	0.0348539	−	0.0437394i
$526$	−5.22487			−0.227815
$527$	29.1343	−	4.61442i	1.26911	−	0.201007i
$528$	5.12496	−	1.50413i	0.223035	−	0.0654587i
$529$	−1.37184	+	0.445739i	−0.0596454	+	0.0193800i
$530$	−10.0687	+	23.7746i	−0.437358	+	1.03270i
$531$	14.0286	−	36.0056i	0.608791	−	1.56251i
$532$	0.366021	+	0.366021i	0.0158690	+	0.0158690i
$533$	8.76237	−	4.46465i	0.379541	−	0.193386i
$534$	2.42525	−	12.9050i	0.104951	−	0.558453i
$535$	1.10818	−	0.931423i	0.0479109	−	0.0402689i
$536$	−2.13478	+	2.93827i	−0.0922084	+	0.126914i
$537$	2.29347	−	1.56781i	0.0989704	−	0.0676560i
$538$	−0.355485	+	2.24445i	−0.0153261	+	0.0967649i
$539$	−17.4087	−	12.6482i	−0.749847	−	0.544796i
$540$	−10.2700	−	5.43393i	−0.441949	−	0.233839i
$541$	−13.9722	+	10.1514i	−0.600713	+	0.436443i	−0.846132	−	0.532974i	$-0.821074\pi$
$541$	−13.9722	+	10.1514i	−0.600713	+	0.436443i	0.245419	+	0.969417i	$0.421074\pi$
$542$	8.56276	+	16.8054i	0.367802	+	0.721852i
$543$	−21.8673	−	0.627438i	−0.938414	−	0.0269259i
$544$	−3.52754	−	1.14617i	−0.151242	−	0.0491415i
$545$	−0.0868506	−	0.144276i	−0.00372027	−	0.00618010i
$546$	−1.02257	−	0.558531i	−0.0437619	−	0.0239029i
$547$	2.54530	−	4.99544i	0.108829	−	0.213590i	−0.830169	−	0.557512i	$-0.811756\pi$
$547$	2.54530	−	4.99544i	0.108829	−	0.213590i	0.938998	+	0.343923i	$0.111756\pi$
$548$	−2.28802	−	14.4460i	−0.0977393	−	0.617101i
$549$	−43.7414	−	2.51221i	−1.86684	−	0.107219i
$550$	−9.25891	+	12.3289i	−0.394801	+	0.525708i
$551$			5.76660i			0.245666i
$552$	−5.22991	+	6.78051i	−0.222600	+	0.288598i
$553$	−1.18882	−	0.605732i	−0.0505536	−	0.0257583i
$554$	−5.12021	−	15.7584i	−0.217537	−	0.669510i
$555$	−1.36515	−	32.5256i	−0.0579474	−	1.38064i
$556$	−5.51012	+	16.9584i	−0.233681	+	0.719197i
$557$	0.714899	−	0.714899i	0.0302913	−	0.0302913i	−0.691799	−	0.722090i	$-0.743182\pi$
$557$	0.714899	−	0.714899i	0.0302913	−	0.0302913i	0.722090	+	0.691799i	$0.243182\pi$
$558$	−9.59474	−	21.8440i	−0.406178	−	0.924732i
$559$	10.4699	+	14.4106i	0.442830	+	0.609504i
$560$	−0.321111	−	0.0797827i	−0.0135694	−	0.00337143i
$561$	2.53659	+	19.6475i	0.107095	+	0.829520i
$562$	24.7345	+	3.91756i	1.04336	+	0.165252i
$563$	1.65657	+	0.262374i	0.0698159	+	0.0110578i	0.191245	−	0.981542i	$-0.438748\pi$
$563$	1.65657	+	0.262374i	0.0698159	+	0.0110578i	−0.121429	+	0.992600i	$0.538748\pi$
$564$	1.18908	+	9.21017i	0.0500692	+	0.387818i
$565$	−37.1450	−	9.22898i	−1.56270	−	0.388266i
$566$	−15.7508	−	21.6791i	−0.662055	−	0.911241i
$567$	−1.24801	+	0.464771i	−0.0524114	+	0.0195185i
$568$	3.56480	−	3.56480i	0.149576	−	0.149576i
$569$	3.81378	−	11.7376i	0.159882	−	0.492066i	−0.838741	−	0.544531i	$-0.816708\pi$
$569$	3.81378	−	11.7376i	0.159882	−	0.492066i	0.998623	+	0.0524648i	$0.0167077\pi$
$570$	0.568149	+	13.5365i	0.0237972	+	0.566983i
$571$	−1.99738	−	6.14731i	−0.0835879	−	0.257257i	0.900524	−	0.434806i	$-0.143183\pi$
$571$	−1.99738	−	6.14731i	−0.0835879	−	0.257257i	−0.984112	+	0.177549i	$0.943183\pi$
$572$	12.4911	+	6.36454i	0.522280	+	0.266115i
$573$	−22.0802	+	28.6267i	−0.922413	+	1.19590i
$574$		−	0.320088i		−	0.0133602i
$575$	0.390937	−	24.7166i	0.0163032	−	1.03075i
$576$	−0.172016	+	2.99506i	−0.00716735	+	0.124794i
$577$	−5.12648	−	32.3673i	−0.213418	−	1.34747i	−0.828935	−	0.559346i	$-0.811053\pi$
$577$	−5.12648	−	32.3673i	−0.213418	−	1.34747i	0.615516	−	0.788124i	$-0.288947\pi$
$578$	−1.47220	+	2.88935i	−0.0612354	+	0.120181i
$579$	−10.2207	−	5.58261i	−0.424760	−	0.232005i
$580$	−1.90104	−	3.15800i	−0.0789365	−	0.131129i
$581$	1.42317	+	0.462415i	0.0590429	+	0.0191842i
$582$	16.0506	+	0.460539i	0.665318	+	0.0190900i
$583$	−16.1648	−	31.7252i	−0.669477	−	1.31392i
$584$	8.70495	−	6.32451i	0.360213	−	0.261710i
$585$	−9.80784	−	28.8767i	−0.405504	−	1.19390i
$586$	−2.04255	−	1.48400i	−0.0843770	−	0.0613035i
$587$	4.09589	−	25.8604i	0.169056	−	1.06737i	−0.746559	−	0.665319i	$-0.768296\pi$
$587$	4.09589	−	25.8604i	0.169056	−	1.06737i	0.915615	−	0.402056i	$-0.131704\pi$
$588$	9.97786	−	6.82086i	0.411480	−	0.281287i
$589$	−16.3524	+	22.5072i	−0.673790	+	0.927392i
$590$	22.0485	−	18.5317i	0.907722	−	0.762937i
$591$	−1.38469	+	7.36805i	−0.0569585	+	0.303081i
$592$	−7.48933	+	3.81600i	−0.307810	+	0.156837i
$593$	−28.6751	−	28.6751i	−1.17754	−	1.17754i	−0.980368	−	0.197176i	$-0.936823\pi$
$593$	−28.6751	−	28.6751i	−1.17754	−	1.17754i	−0.197176	−	0.980368i	$-0.563177\pi$
$594$	14.8493	−	6.02045i	0.609276	−	0.247022i
$595$	0.478593	−	1.13007i	0.0196204	−	0.0463282i
$596$	14.6925	−	4.77388i	0.601828	−	0.195546i
$597$	1.01520	−	0.297951i	0.0415494	−	0.0121943i
$598$	−22.1994	+	3.51603i	−0.907799	+	0.143781i
$599$	23.8130			0.972971			0.486486	−	0.873689i	$-0.338279\pi$
$599$	23.8130			0.972971			0.486486	+	0.873689i	$0.338279\pi$
$600$	−4.77365	−	7.22581i	−0.194883	−	0.294992i
$601$	−24.9278			−1.01683			−0.508413	−	0.861113i	$-0.669768\pi$
$601$	−24.9278			−1.01683			−0.508413	+	0.861113i	$0.669768\pi$
$602$	0.572630	−	0.0906956i	0.0233386	−	0.00369648i
$603$	−5.49506	+	9.40854i	−0.223776	+	0.383145i
$604$	−6.74437	+	2.19138i	−0.274424	+	0.0891659i
$605$	0.752536	+	3.24746i	0.0305949	+	0.132028i
$606$	6.55929	−	3.10847i	0.266453	−	0.126273i
$607$	−12.2020	−	12.2020i	−0.495265	−	0.495265i	0.414695	−	0.909960i	$-0.363888\pi$
$607$	−12.2020	−	12.2020i	−0.495265	−	0.495265i	−0.909960	+	0.414695i	$0.863888\pi$
$608$	3.11691	−	1.58815i	0.126408	−	0.0644079i
$609$	−0.415219	−	0.0780327i	−0.0168255	−	0.00316205i
$610$	−27.7085	−	17.2827i	−1.12189	−	0.699755i
$611$	−14.3273	+	19.7198i	−0.579620	+	0.797778i
$612$	−10.8723	−	2.36798i	−0.439488	−	0.0957200i
$613$	−0.289494	+	1.82779i	−0.0116926	+	0.0738239i	−0.992845	−	0.119413i	$-0.961899\pi$
$613$	−0.289494	+	1.82779i	−0.0116926	+	0.0738239i	0.981152	+	0.193237i	$0.0618987\pi$
$614$	20.7493	+	15.0753i	0.837375	+	0.608388i
$615$	5.67048	−	6.16733i	0.228656	−	0.248691i
$616$	0.369154	−	0.268206i	0.0148736	−	0.0108063i
$617$	2.00017	+	3.92556i	0.0805239	+	0.158037i	0.927758	−	0.373183i	$-0.121734\pi$
$617$	2.00017	+	3.92556i	0.0805239	+	0.158037i	−0.847234	+	0.531220i	$0.821734\pi$
$618$	−0.869429	+	30.3011i	−0.0349736	+	1.21889i
$619$	−4.50152	−	1.46263i	−0.180931	−	0.0587882i	0.217150	−	0.976138i	$-0.430324\pi$
$619$	−4.50152	−	1.46263i	−0.180931	−	0.0587882i	−0.398082	+	0.917350i	$0.630324\pi$
$620$	1.53538	−	17.7166i	0.0616624	−	0.711514i
$621$	−13.5869	+	21.8023i	−0.545224	+	0.874897i
$622$	−4.78141	+	9.38405i	−0.191717	+	0.376266i
$623$	−0.175486	−	1.10798i	−0.00703072	−	0.0443902i
$624$	−5.72534	+	5.40595i	−0.229197	+	0.216411i
$625$	23.5202	+	8.47351i	0.940808	+	0.338940i
$626$			17.7041i			0.707599i
$627$	−14.7947	−	11.4114i	−0.590844	−	0.455727i
$628$	6.43684	+	3.27973i	0.256858	+	0.130876i
$629$	−9.63406	−	29.6506i	−0.384135	−	1.18225i
$630$	−0.982374	−	0.142265i	−0.0391387	−	0.00566798i
$631$	9.68700	−	29.8135i	0.385633	−	1.18686i	−0.550387	−	0.834910i	$-0.685520\pi$
$631$	9.68700	−	29.8135i	0.385633	−	1.18686i	0.936020	−	0.351947i	$-0.114480\pi$
$632$	−6.37589	+	6.37589i	−0.253619	+	0.253619i
$633$	−2.64511	+	7.41050i	−0.105134	+	0.294541i
$634$	−2.99350	−	4.12020i	−0.118887	−	0.163634i
$635$	1.40714	+	19.8889i	0.0558405	+	0.789268i
$636$	19.8345	−	2.56073i	0.786490	−	0.101540i
$637$	31.3333	+	4.96270i	1.24147	+	0.196629i
$638$	5.02075	+	0.795208i	0.198773	+	0.0314826i
$639$	9.57672	−	11.7059i	0.378849	−	0.463076i
$640$	−1.18338	+	1.89726i	−0.0467773	+	0.0749959i
$641$	17.3534	+	23.8849i	0.685419	+	0.943398i	0.999983	−	0.00583804i	$-0.00185832\pi$
$641$	17.3534	+	23.8849i	0.685419	+	0.943398i	−0.314564	+	0.949236i	$0.601858\pi$
$642$	−1.05607	−	0.376953i	−0.0416796	−	0.0148771i
$643$	−23.8141	+	23.8141i	−0.939135	+	0.939135i	−0.998251	−	0.0591164i	$-0.981172\pi$
$643$	−23.8141	+	23.8141i	−0.939135	+	0.939135i	0.0591164	+	0.998251i	$0.481172\pi$
$644$	−0.226064	+	0.695754i	−0.00890818	+	0.0274166i
$645$	12.6399	+	8.39684i	0.497695	+	0.330625i
$646$	4.00951	+	12.3400i	0.157752	+	0.485511i
$647$	−32.2362	−	16.4252i	−1.26734	−	0.645740i	−0.314509	−	0.949254i	$-0.601840\pi$
$647$	−32.2362	−	16.4252i	−1.26734	−	0.645740i	−0.952827	+	0.303514i	$0.901840\pi$
$648$	0.380938	+	8.99193i	0.0149647	+	0.353237i
$649$			39.7202i			1.55915i
$650$	3.91053	−	22.3921i	0.153383	−	0.878290i
$651$	−1.39933	−	1.48200i	−0.0548441	−	0.0580843i
$652$	0.335098	+	2.11572i	0.0131234	+	0.0828581i
$653$	−7.26139	+	14.2513i	−0.284160	+	0.557696i	−0.988329	−	0.152337i	$-0.951320\pi$
$653$	−7.26139	+	14.2513i	−0.284160	+	0.557696i	0.704168	+	0.710033i	$0.251320\pi$
$654$	−0.0625286	+	0.114478i	−0.00244506	+	0.00447646i
$655$	3.47639	+	1.47228i	0.135834	+	0.0575267i
$656$	−2.05731	−	0.668459i	−0.0803243	−	0.0260990i
$657$	24.0964	−	21.4789i	0.940091	−	0.837971i
$658$	0.360181	+	0.706895i	0.0140413	+	0.0275576i
$659$	−9.25834	+	6.72658i	−0.360654	+	0.262030i	−0.753325	−	0.657649i	$-0.771551\pi$
$659$	−9.25834	+	6.72658i	−0.360654	+	0.262030i	0.392671	+	0.919679i	$0.371551\pi$
$660$	11.8641	+	1.37201i	0.461808	+	0.0534053i
$661$	5.86553	+	4.26156i	0.228143	+	0.165755i	0.695984	−	0.718057i	$-0.254968\pi$
$661$	5.86553	+	4.26156i	0.228143	+	0.165755i	−0.467842	+	0.883812i	$0.654968\pi$
$662$	2.29836	−	14.5113i	0.0893285	−	0.563998i
$663$	−16.4822	−	24.1109i	−0.640115	−	0.936390i
$664$	5.94416	−	8.18143i	0.230678	−	0.317501i
$665$	0.434471	+	1.07282i	0.0168481	+	0.0416023i
$666$	−21.2168	+	13.6277i	−0.822135	+	0.528063i
$667$	−7.26155	+	3.69994i	−0.281168	+	0.143262i
$668$	2.96707	+	2.96707i	0.114800	+	0.114800i
$669$	14.4725	+	30.5388i	0.559538	+	1.18070i
$670$	−6.95778	+	4.18841i	−0.268803	+	0.161813i
$671$	42.8316	−	13.9168i	1.65350	−	0.537254i
$672$	0.0721755	+	0.245921i	0.00278423	+	0.00948661i
$673$	21.3991	−	3.38928i	0.824874	−	0.130647i	0.270294	−	0.962778i	$-0.412879\pi$
$673$	21.3991	−	3.38928i	0.824874	−	0.130647i	0.554580	+	0.832131i	$0.312879\pi$
$674$	24.7626			0.953821
$675$	−16.4077	−	20.1442i	−0.631532	−	0.775350i
$676$	−7.66790			−0.294919
$677$	1.71330	−	0.271360i	0.0658476	−	0.0104292i	−0.123424	−	0.992354i	$-0.539387\pi$
$677$	1.71330	−	0.271360i	0.0658476	−	0.0104292i	0.189271	+	0.981925i	$0.439387\pi$
$678$	8.34901	+	28.4473i	0.320642	+	1.09251i
$679$	1.30465	−	0.423905i	0.0500677	−	0.0162680i
$680$	−6.26381	−	5.43605i	−0.240206	−	0.208463i
$681$	8.96358	+	18.9143i	0.343485	+	0.724799i
$682$	17.3411	+	17.3411i	0.664025	+	0.664025i
$683$	11.0971	−	5.65426i	0.424619	−	0.216354i	−0.228604	−	0.973519i	$-0.573416\pi$
$683$	11.0971	−	5.65426i	0.424619	−	0.216354i	0.653224	+	0.757165i	$0.273416\pi$
$684$	8.83003	−	5.67159i	0.337624	−	0.216859i
$685$	7.88602	−	31.7398i	0.301310	−	1.21272i
$686$	1.21575	−	1.67334i	0.0464176	−	0.0638883i
$687$	6.05067	+	8.85120i	0.230847	+	0.337694i
$688$	0.612927	−	3.86987i	0.0233676	−	0.147537i
$689$	42.4675	+	30.8544i	1.61788	+	1.17546i
$690$	−16.6812	+	9.40069i	−0.635044	+	0.357878i
$691$	−30.9813	+	22.5093i	−1.17859	+	0.856293i	−0.992011	−	0.126148i	$-0.959738\pi$
$691$	−30.9813	+	22.5093i	−1.17859	+	0.856293i	−0.186574	+	0.982441i	$0.559738\pi$
$692$	−0.0493481	−	0.0968510i	−0.00187593	−	0.00368172i
$693$	1.02187	−	0.910863i	0.0388175	−	0.0346008i
$694$	30.3898	+	9.87425i	1.15358	+	0.374821i
$695$	−26.1335	+	30.1129i	−0.991300	+	1.14225i
$696$	−1.36867	+	2.50578i	−0.0518792	+	0.0949813i
$697$	3.64254	−	7.14889i	0.137971	−	0.270784i
$698$	4.23889	+	26.7633i	0.160445	+	1.01301i
$699$	9.00790	+	9.54010i	0.340710	+	0.360840i
$700$	−0.591604	−	0.444288i	−0.0223605	−	0.0167925i
$701$		−	22.4631i		−	0.848418i	−0.905564	−	0.424209i	$-0.860552\pi$
$701$		−	22.4631i		−	0.848418i	0.905564	−	0.424209i	$-0.139448\pi$
$702$	−15.4763	+	17.8471i	−0.584115	+	0.673594i
$703$	26.1991	+	13.3491i	0.988119	+	0.503472i
$704$	−0.952916	−	2.93277i	−0.0359144	−	0.110533i
$705$	−5.58307	+	20.0009i	−0.210271	+	0.753277i
$706$	1.91730	−	5.90085i	0.0721587	−	0.222082i
$707$	0.438483	−	0.438483i	0.0164909	−	0.0164909i
$708$	−21.0116	−	7.49989i	−0.789664	−	0.281863i
$709$	−23.3849	−	32.1865i	−0.878238	−	1.20879i	−0.976906	−	0.213670i	$-0.931458\pi$
$709$	−23.3849	−	32.1865i	−0.878238	−	1.20879i	0.0986680	−	0.995120i	$-0.468542\pi$
$710$	10.4486	−	4.23146i	0.392128	−	0.158804i
$711$	−17.1286	+	20.9367i	−0.642374	+	0.785188i
$712$	−7.48779	−	1.18595i	−0.280617	−	0.0444453i
$713$	−38.8339	−	6.15069i	−1.45434	−	0.230345i
$714$	−0.942787	+	0.121718i	−0.0352829	+	0.00455519i
$715$	20.1696	+	23.9972i	0.754299	+	0.897445i
$716$	−0.942782	−	1.29763i	−0.0352334	−	0.0484946i
$717$	9.82952	−	27.5383i	0.367090	−	1.02844i
$718$	24.2007	−	24.2007i	0.903162	−	0.903162i
$719$	−3.27225	+	10.0709i	−0.122034	+	0.375583i	−0.993349	−	0.115142i	$-0.963268\pi$
$719$	−3.27225	+	10.0709i	−0.122034	+	0.375583i	0.871315	+	0.490724i	$0.163268\pi$
$720$	−2.96593	+	6.01691i	−0.110534	+	0.224237i
$721$	0.800268	+	2.46297i	0.0298036	+	0.0917259i
$722$	6.02555	+	3.07017i	0.224248	+	0.114260i
$723$	−13.5067	−	10.4179i	−0.502320	−	0.387447i
$724$			12.6303i			0.469400i
$725$	−1.16047	−	8.16015i	−0.0430987	−	0.303060i
$726$	1.87745	−	1.77272i	0.0696788	−	0.0657918i
$727$	2.03732	+	12.8632i	0.0755602	+	0.477068i	0.996232	+	0.0867303i	$0.0276418\pi$
$727$	2.03732	+	12.8632i	0.0755602	+	0.477068i	−0.920672	+	0.390338i	$0.872358\pi$
$728$	−0.305402	+	0.599386i	−0.0113190	+	0.0222147i
$729$	3.82242	+	26.7281i	0.141571	+	0.989928i
$730$	23.4388	−	5.43149i	0.867508	−	0.201028i
$731$	13.8213	+	4.49080i	0.511198	+	0.166098i
$732$	−0.725511	+	25.2853i	−0.0268157	+	0.934571i
$733$	−19.6340	−	38.5339i	−0.725199	−	1.42328i	−0.898752	−	0.438458i	$-0.855525\pi$
$733$	−19.6340	−	38.5339i	−0.725199	−	1.42328i	0.173553	−	0.984824i	$-0.444475\pi$
$734$	−9.83080	+	7.14249i	−0.362861	+	0.263634i
$735$	26.4926	−	5.34347i	0.977193	−	0.197097i
$736$	3.99972	+	2.90597i	0.147432	+	0.107115i
$737$	1.75202	−	11.0618i	0.0645364	−	0.407467i
$738$	−6.34089	−	1.38104i	−0.233411	−	0.0508367i
$739$	−7.30628	+	10.0562i	−0.268766	+	0.369924i	−0.921973	−	0.387255i	$-0.873423\pi$
$739$	−7.30628	+	10.0562i	−0.268766	+	0.369924i	0.653207	+	0.757180i	$0.273423\pi$
$740$	−18.7483	+	1.32644i	−0.689203	+	0.0487609i
$741$	27.0717	+	5.08763i	0.994504	+	0.186899i
$742$	1.52233	−	0.775666i	0.0558865	−	0.0284756i
$743$	−5.87728	−	5.87728i	−0.215616	−	0.215616i	0.591032	−	0.806648i	$-0.298721\pi$
$743$	−5.87728	−	5.87728i	−0.215616	−	0.215616i	−0.806648	+	0.591032i	$0.798721\pi$
$744$	−12.4476	+	5.89897i	−0.456351	+	0.216267i
$745$	34.4151	+	2.98254i	1.26087	+	0.109272i
$746$	−24.3715	+	7.91878i	−0.892304	+	0.289927i
$747$	15.3007	−	26.1975i	0.559822	−	0.958517i
$748$	11.2968	−	1.78924i	0.413054	−	0.0654213i
$749$	−0.0957962			−0.00350032
$750$	−3.52805	−	19.0408i	−0.128826	−	0.695272i
$751$	−30.0007			−1.09474			−0.547371	−	0.836890i	$-0.684371\pi$
$751$	−30.0007			−1.09474			−0.547371	+	0.836890i	$0.684371\pi$
$752$	5.29562	−	0.838744i	0.193111	−	0.0305858i
$753$	0.512383	−	0.150380i	0.0186723	−	0.00548014i
$754$	−7.12739	+	2.31583i	−0.259564	+	0.0843376i
$755$	−15.7977	−	1.36909i	−0.574939	−	0.0498262i
$756$	0.288891	+	0.712545i	0.0105069	+	0.0259150i
$757$	0.751496	+	0.751496i	0.0273136	+	0.0273136i	0.720632	−	0.693318i	$-0.243852\pi$
$757$	0.751496	+	0.751496i	0.0273136	+	0.0273136i	−0.693318	+	0.720632i	$0.743852\pi$
$758$	5.75606	−	2.93286i	0.209069	−	0.106526i
$759$	4.87717	−	25.9518i	0.177030	−	0.941992i
$760$	7.80270	−	0.552039i	0.283034	−	0.0200246i
$761$	26.8487	−	36.9541i	0.973266	−	1.33959i	0.0328857	−	0.999459i	$-0.489530\pi$
$761$	26.8487	−	36.9541i	0.973266	−	1.33959i	0.940380	−	0.340126i	$-0.110470\pi$
$762$	12.7500	−	8.71589i	0.461884	−	0.315743i
$763$	−0.00174328	+	0.0110066i	−6.31110e−5	+	0.000398467i
$764$	16.8865	+	12.2687i	0.610931	+	0.443867i
$765$	−20.3215	−	14.3566i	−0.734725	−	0.519063i
$766$	−0.221873	+	0.161200i	−0.00801659	+	0.00582440i
$767$	−26.5848	−	52.1757i	−0.959922	−	1.88395i
$768$	1.73134	+	0.0496773i	0.0624743	+	0.00179258i
$769$	40.4186	+	13.1328i	1.45753	+	0.473580i	0.927315	−	0.374283i	$-0.122111\pi$
$769$	40.4186	+	13.1328i	1.45753	+	0.473580i	0.530216	+	0.847863i	$0.322111\pi$
$770$	0.993977	−	0.230335i	0.0358204	−	0.00830070i
$771$	−10.9831	−	5.99899i	−0.395545	−	0.216048i
$772$	−3.05255	+	5.99097i	−0.109864	+	0.215620i
$773$	7.18830	+	45.3851i	0.258545	+	1.63239i	0.685469	+	0.728102i	$0.259597\pi$
$773$	7.18830	+	45.3851i	0.258545	+	1.63239i	−0.426923	+	0.904288i	$0.640403\pi$
$774$	0.673979	−	11.7350i	0.0242257	−	0.421805i
$775$	18.6105	−	35.1400i	0.668509	−	1.26227i
$776$		−	9.27062i		−	0.332796i
$777$	−1.31571	+	1.70581i	−0.0472010	+	0.0611955i
$778$	−24.3788	−	12.4216i	−0.874021	−	0.445336i
$779$	2.33840	+	7.19686i	0.0837819	+	0.257854i
$780$	−16.5027	+	6.13840i	−0.590891	+	0.219790i
$781$	−4.80402	+	14.7853i	−0.171901	+	0.529058i
$782$	−12.9665	+	12.9665i	−0.463681	+	0.463681i
$783$	−3.33730	+	7.88873i	−0.119265	+	0.281920i
$784$	−4.10163	−	5.64541i	−0.146487	−	0.201622i
$785$	10.3936	+	12.3661i	0.370965	+	0.441364i
$786$	−0.374437	−	2.90026i	−0.0133557	−	0.103449i
$787$	−21.3780	−	3.38594i	−0.762043	−	0.120696i	−0.236696	−	0.971584i	$-0.576064\pi$
$787$	−21.3780	−	3.38594i	−0.762043	−	0.120696i	−0.525347	+	0.850888i	$0.676064\pi$
$788$	4.27513	+	0.677114i	0.152295	+	0.0241212i
$789$	1.15875	+	8.97526i	0.0412525	+	0.319528i
$790$	−18.6880	+	7.56825i	−0.664889	+	0.269266i
$791$	1.48874	+	2.04907i	0.0529335	+	0.0728567i
$792$	−3.72037	−	8.47005i	−0.132198	−	0.300970i
$793$	−46.9482	+	46.9482i	−1.66718	+	1.66718i
$794$	−0.366520	+	1.12803i	−0.0130073	+	0.0400323i
$795$	43.0728	+	12.0234i	1.52763	+	0.426426i
$796$	−0.188762	−	0.580951i	−0.00669050	−	0.0205913i
$797$	19.8941	+	10.1366i	0.704685	+	0.359055i	0.769328	−	0.638853i	$-0.220591\pi$
$797$	19.8941	+	10.1366i	0.704685	+	0.359055i	−0.0646433	+	0.997908i	$0.520591\pi$
$798$	0.547575	−	0.709924i	0.0193839	−	0.0251310i
$799$			19.8867i			0.703539i
$800$	−4.09106	+	2.87459i	−0.144641	+	0.101632i
$801$	−22.7060	−	1.30408i	−0.802276	−	0.0460773i
$802$	−0.685079	−	4.32542i	−0.0241910	−	0.152736i
$803$	−15.0636	+	29.5639i	−0.531581	+	1.04329i
$804$	5.52078	+	3.01547i	0.194703	+	0.106348i
$805$	−1.07218	+	1.23545i	−0.0377894	+	0.0435437i
$806$	−34.3854	−	11.1725i	−1.21117	−	0.393534i
$807$	3.93433	+	0.112888i	0.138495	+	0.00397384i
$808$	−1.90255	−	3.73397i	−0.0669316	−	0.131361i
$809$	−10.1700	+	7.38891i	−0.357557	+	0.259780i	−0.752032	−	0.659126i	$-0.770926\pi$
$809$	−10.1700	+	7.38891i	−0.357557	+	0.259780i	0.394476	+	0.918906i	$0.370926\pi$
$810$	−7.05675	+	18.8468i	−0.247949	+	0.662209i
$811$	20.5014	+	14.8951i	0.719902	+	0.523039i	0.886353	−	0.463010i	$-0.153231\pi$
$811$	20.5014	+	14.8951i	0.719902	+	0.523039i	−0.166451	+	0.986050i	$0.553231\pi$
$812$	−0.0381580	+	0.240920i	−0.00133908	+	0.00845465i
$813$	26.9691	−	18.4361i	0.945849	−	0.646581i
$814$	15.2354	−	20.9697i	0.533999	−	0.734987i
$815$	−1.15497	+	4.64854i	−0.0404568	+	0.162831i
$816$	−1.18656	+	6.31377i	−0.0415378	+	0.221026i
$817$	−12.2124	+	6.22253i	−0.427258	+	0.217699i
$818$	−22.9288	−	22.9288i	−0.801687	−	0.801687i
$819$	−0.732660	+	1.88043i	−0.0256012	+	0.0657075i
$820$	−3.65314	−	3.17038i	−0.127573	−	0.110714i
$821$	−23.8661	+	7.75457i	−0.832933	+	0.270636i	−0.694280	−	0.719705i	$-0.744277\pi$
$821$	−23.8661	+	7.75457i	−0.832933	+	0.270636i	−0.138653	+	0.990341i	$0.544277\pi$
$822$	−24.3078	+	7.13410i	−0.847831	+	0.248830i
$823$	−42.8332	+	6.78412i	−1.49307	+	0.236479i	−0.848962	−	0.528454i	$-0.822772\pi$
$823$	−42.8332	+	6.78412i	−1.49307	+	0.236479i	−0.644110	+	0.764933i	$0.722772\pi$
$824$	17.5015			0.609695
$825$	23.2320	+	13.1706i	0.808834	+	0.458543i
$826$	−1.90597			−0.0663172
$827$	2.20597	−	0.349392i	0.0767091	−	0.0121495i	−0.117962	−	0.993018i	$-0.537636\pi$
$827$	2.20597	−	0.349392i	0.0767091	−	0.0121495i	0.194671	+	0.980869i	$0.437636\pi$
$828$	12.8074	+	7.48016i	0.445088	+	0.259953i
$829$	−8.12669	+	2.64052i	−0.282251	+	0.0917091i	−0.446722	−	0.894673i	$-0.647409\pi$
$829$	−8.12669	+	2.64052i	−0.282251	+	0.0917091i	0.164470	+	0.986382i	$0.447409\pi$
$830$	19.3735	−	11.6624i	0.672464	−	0.404807i
$831$	−25.9341	+	12.2903i	−0.899645	+	0.426345i
$832$	3.21465	+	3.21465i	0.111448	+	0.111448i
$833$	23.0613	−	11.7503i	0.799026	−	0.407124i
$834$	30.3531	+	5.70430i	1.05104	+	0.197524i
$835$	3.52195	+	8.69662i	0.121882	+	0.300959i
$836$	−6.34067	+	8.72718i	−0.219296	+	0.301836i
$837$	−35.3957	+	21.3263i	−1.22345	+	0.737143i
$838$	4.60705	−	29.0878i	0.159148	−	1.00482i
$839$	−0.581684	−	0.422618i	−0.0200819	−	0.0145904i	0.577699	−	0.816250i	$-0.303951\pi$
$839$	−0.581684	−	0.422618i	−0.0200819	−	0.0145904i	−0.597781	+	0.801659i	$0.703951\pi$
$840$	−0.0658358	+	0.569296i	−0.00227155	+	0.0196426i
$841$	21.2631	−	15.4485i	0.733210	−	0.532708i
$842$	−2.69362	−	5.28652i	−0.0928282	−	0.182186i
$843$	1.24406	−	43.3576i	0.0428477	−	1.49331i
$844$	4.32049	+	1.40381i	0.148718	+	0.0483213i
$845$	−15.7884	−	6.68653i	−0.543138	−	0.230024i
$846$	15.5575	−	4.08518i	0.534877	−	0.140451i
$847$	0.100148	−	0.196551i	0.00344111	−	0.00675357i
$848$	−1.80627	−	11.4044i	−0.0620276	−	0.391627i
$849$	−33.7471	+	31.8645i	−1.15820	+	1.09359i
$850$	−8.15704	−	16.6551i	−0.279784	−	0.571266i
$851$			41.5561i			1.42452i
$852$	−6.91418	−	5.33301i	−0.236876	−	0.182706i
$853$	35.5102	+	18.0934i	1.21585	+	0.619505i	0.939828	−	0.341647i	$-0.110985\pi$
$853$	35.5102	+	18.0934i	1.21585	+	0.619505i	0.276019	+	0.961152i	$0.410985\pi$
$854$	0.667799	+	2.05527i	0.0228516	+	0.0703300i
$855$	23.1270	−	3.97803i	0.790926	−	0.136046i
$856$	−0.200057	+	0.615712i	−0.00683780	+	0.0210446i
$857$	24.3570	−	24.3570i	0.832018	−	0.832018i	−0.155774	−	0.987793i	$-0.549787\pi$
$857$	24.3570	−	24.3570i	0.832018	−	0.832018i	0.987793	+	0.155774i	$0.0497872\pi$
$858$	8.16275	−	22.8687i	0.278672	−	0.780723i
$859$	12.1583	+	16.7344i	0.414835	+	0.570971i	0.964389	−	0.264487i	$-0.0852025\pi$
$859$	12.1583	+	16.7344i	0.414835	+	0.570971i	−0.549555	+	0.835458i	$0.685203\pi$
$860$	4.63662	−	7.43368i	0.158107	−	0.253486i
$861$	−0.549846	+	0.0709877i	−0.0187387	+	0.00241925i
$862$	17.3948	+	2.75506i	0.592468	+	0.0938378i
$863$	57.0595	+	9.03734i	1.94233	+	0.307634i	0.999659	−	0.0260968i	$-0.00830780\pi$
$863$	57.0595	+	9.03734i	1.94233	+	0.307634i	0.942668	+	0.333731i	$0.108308\pi$
$864$	5.18305	−	0.368742i	0.176331	−	0.0125449i
$865$	−0.0171534	−	0.242451i	−0.000583232	−	0.00824358i
$866$	5.33218	+	7.33912i	0.181195	+	0.249393i
$867$	5.28981	+	1.88815i	0.179651	+	0.0641248i
$868$	−0.832112	+	0.832112i	−0.0282437	+	0.0282437i
$869$	8.59232	−	26.4445i	0.291475	−	0.897067i
$870$	−5.00320	+	3.96597i	−0.169624	+	0.134459i
$871$	5.10228	+	15.7032i	0.172884	+	0.532083i
$872$	0.0671024	+	0.0341904i	0.00227237	+	0.00115783i
$873$	−2.76851	−	27.6737i	−0.0936999	−	0.936614i
$874$		−	17.2948i		−	0.585006i
$875$	−0.830702	−	1.43069i	−0.0280828	−	0.0483661i
$876$	−12.7948	−	13.5507i	−0.432295	−	0.457835i
$877$	−6.20286	−	39.1633i	−0.209456	−	1.32245i	−0.838423	−	0.545020i	$-0.816522\pi$
$877$	−6.20286	−	39.1633i	−0.209456	−	1.32245i	0.628967	−	0.777432i	$-0.283478\pi$
$878$	−13.1166	+	25.7429i	−0.442665	+	0.868779i
$879$	−2.09622	+	3.83779i	−0.0707037	+	0.129446i
$880$	0.595345	−	6.86962i	0.0200691	−	0.231575i
$881$	17.2013	+	5.58904i	0.579526	+	0.188299i	0.584088	−	0.811690i	$-0.301452\pi$
$881$	17.2013	+	5.58904i	0.579526	+	0.188299i	−0.00456226	+	0.999990i	$0.501452\pi$
$882$	−13.9297	−	15.6272i	−0.469036	−	0.526196i
$883$	−22.3549	−	43.8739i	−0.752301	−	1.47647i	−0.875048	−	0.484037i	$-0.839170\pi$
$883$	−22.3549	−	43.8739i	−0.752301	−	1.47647i	0.122746	−	0.992438i	$-0.460830\pi$
$884$	−13.6418	+	9.91133i	−0.458823	+	0.333354i
$885$	−36.7234	−	33.7649i	−1.23444	−	1.13500i
$886$	−14.2445	−	10.3492i	−0.478552	−	0.347689i
$887$	1.57316	−	9.93256i	0.0528216	−	0.333503i	−0.947099	−	0.320940i	$-0.896001\pi$
$887$	1.57316	−	9.93256i	0.0528216	−	0.333503i	0.999921	−	0.0125625i	$-0.00399886\pi$
$888$	8.21606	+	12.0188i	0.275713	+	0.403326i
$889$	0.775544	−	1.06745i	0.0260109	−	0.0358010i
$890$	−14.3834	−	8.97137i	−0.482132	−	0.300721i
$891$	−13.6351	−	24.1729i	−0.456793	−	0.809823i
$892$	17.3847	−	8.85794i	0.582082	−	0.296586i
$893$	−13.2625	−	13.2625i	−0.443813	−	0.443813i
$894$	−11.4590	−	24.1800i	−0.383246	−	0.808699i
$895$	−0.809661	−	3.49397i	−0.0270640	−	0.116791i
$896$	0.140729	−	0.0457256i	0.00470143	−	0.00152759i
$897$	10.9631	+	37.3542i	0.366047	+	1.24722i
$898$	12.6921	−	2.01023i	0.423541	−	0.0670823i
$899$	−13.1098			−0.437236
$900$	−11.3538	+	9.80265i	−0.378459	+	0.326755i
$901$	42.8268			1.42677
$902$	6.58847	−	1.04351i	0.219372	−	0.0347451i
$903$	−0.282791	−	0.963546i	−0.00941071	−	0.0320648i
$904$	16.2790	−	5.28938i	0.541433	−	0.175922i
$905$	−11.0138	+	26.0060i	−0.366111	+	0.864470i
$906$	5.26007	+	11.0994i	0.174754	+	0.368754i
$907$	22.2868	+	22.2868i	0.740021	+	0.740021i	0.972582	−	0.232561i	$-0.0747104\pi$
$907$	22.2868	+	22.2868i	0.740021	+	0.740021i	−0.232561	+	0.972582i	$0.574710\pi$
$908$	10.7673	−	5.48620i	0.357324	−	0.182066i
$909$	−6.79440	−	10.5781i	−0.225356	−	0.350854i
$910$	−1.15151	+	0.967836i	−0.0381720	+	0.0320834i
$911$	−3.12524	+	4.30152i	−0.103544	+	0.142516i	−0.857645	−	0.514243i	$-0.828073\pi$
$911$	−3.12524	+	4.30152i	−0.103544	+	0.142516i	0.754101	+	0.656759i	$0.228073\pi$
$912$	−3.41936	−	5.00200i	−0.113226	−	0.165633i
$913$	−4.87839	+	30.8009i	−0.161451	+	1.01936i
$914$	−12.5639	−	9.12823i	−0.415578	−	0.301935i
$915$	−23.5430	+	51.4304i	−0.778308	+	1.70024i
$916$	5.00795	−	3.63849i	0.165467	−	0.120219i
$917$	−0.113420	−	0.222600i	−0.00374546	−	0.00735089i
$918$	−1.65649	+	19.2016i	−0.0546723	+	0.633746i
$919$	−21.4823	−	6.98001i	−0.708635	−	0.230249i	−0.0675461	−	0.997716i	$-0.521517\pi$
$919$	−21.4823	−	6.98001i	−0.708635	−	0.230249i	−0.641089	+	0.767467i	$0.721517\pi$
$920$	5.70148	+	9.47129i	0.187972	+	0.312259i
$921$	21.2945	−	38.9864i	0.701678	−	1.28464i
$922$	−5.09428	+	9.99809i	−0.167771	+	0.329270i
$923$	−3.58534	−	22.6370i	−0.118013	−	0.745105i
$924$	−0.542592	−	0.574649i	−0.0178500	−	0.0189045i
$925$	−39.7600	−	13.6177i	−1.30730	−	0.447746i
$926$			1.29066i			0.0424139i
$927$	52.2438	−	5.22653i	1.71591	−	0.171662i
$928$	1.46878	+	0.748381i	0.0482151	+	0.0245668i
$929$	−14.5401	−	44.7499i	−0.477046	−	1.46820i	−0.843178	−	0.537634i	$-0.819318\pi$
$929$	−14.5401	−	44.7499i	−0.477046	−	1.46820i	0.366132	−	0.930563i	$-0.380682\pi$
$930$	−30.7739	+	1.29163i	−1.00912	+	0.0423542i
$931$	−7.54334	+	23.2160i	−0.247223	+	0.760874i
$932$	5.35655	−	5.35655i	0.175460	−	0.175460i
$933$	17.1803	+	6.13233i	0.562456	+	0.200763i
$934$	−21.5074	−	29.6023i	−0.703743	−	0.968618i
$935$	24.8208	+	6.16692i	0.811725	+	0.201680i
$936$	10.5560	+	8.63604i	0.345035	+	0.282278i
$937$	−33.0266	−	5.23090i	−1.07893	−	0.170886i	−0.408427	−	0.912791i	$-0.633923\pi$
$937$	−33.0266	−	5.23090i	−1.07893	−	0.170886i	−0.670505	+	0.741905i	$0.733923\pi$
$938$	0.530801	+	0.0840705i	0.0173313	+	0.00274500i
$939$	30.4121	−	3.92634i	0.992460	−	0.128131i
$940$	11.6352	+	2.89087i	0.379499	+	0.0942897i
$941$	3.42075	+	4.70826i	0.111513	+	0.153485i	0.861126	−	0.508392i	$-0.169760\pi$
$941$	3.42075	+	4.70826i	0.111513	+	0.153485i	−0.749612	+	0.661877i	$0.769760\pi$
$942$	4.20637	−	11.7845i	0.137051	−	0.383960i
$943$	−7.56223	+	7.56223i	−0.246260	+	0.246260i
$944$	−3.98035	+	12.2503i	−0.129549	+	0.398712i
$945$	−0.0265159	+	1.71907i	−0.000862561	+	0.0559212i
$946$	3.73363	+	11.4909i	0.121391	+	0.373602i
$947$	−15.0412	−	7.66387i	−0.488773	−	0.249042i	0.192193	−	0.981357i	$-0.438440\pi$
$947$	−15.0412	−	7.66387i	−0.488773	−	0.249042i	−0.680966	+	0.732315i	$0.738440\pi$
$948$	12.3665	+	9.53845i	0.401645	+	0.309795i
$949$		−	48.9166i		−	1.58790i
$950$	16.5473	+	5.66741i	0.536867	+	0.183875i
$951$	−6.41377	+	6.05598i	−0.207981	+	0.196379i
$952$	0.0858568	+	0.542079i	0.00278264	+	0.0175689i
$953$	−8.09351	+	15.8844i	−0.262175	+	0.514547i	−0.984142	−	0.177380i	$-0.943238\pi$
$953$	−8.09351	+	15.8844i	−0.262175	+	0.514547i	0.721968	+	0.691927i	$0.243238\pi$
$954$	−8.79761	−	33.5037i	−0.284833	−	1.08472i
$955$	24.0711	+	39.9869i	0.778924	+	1.29395i
$956$	−16.0554	−	5.21673i	−0.519270	−	0.168721i
$957$	0.252526	−	8.80096i	0.00816301	−	0.284495i
$958$	12.6238	+	24.7755i	0.407855	+	0.800460i
$959$	−1.75090	+	1.27210i	−0.0565396	+	0.0410784i
$960$	3.52155	+	1.61204i	0.113658	+	0.0520284i
$961$	−26.0882	−	18.9542i	−0.841556	−	0.611426i
$962$	−5.97782	+	37.7425i	−0.192733	+	1.21687i
$963$	−0.413318	+	1.89770i	−0.0133190	+	0.0611527i
$964$	−5.78866	+	7.96740i	−0.186440	+	0.256613i
$965$	−11.5095	+	9.67368i	−0.370504	+	0.311407i
$966$	1.24530	+	0.234031i	0.0400668	+	0.00752982i
$967$	−35.9477	+	18.3163i	−1.15600	+	0.589011i	−0.923505	−	0.383586i	$-0.874689\pi$
$967$	−35.9477	+	18.3163i	−1.15600	+	0.589011i	−0.232495	+	0.972598i	$0.574689\pi$
$968$	−1.05415	−	1.05415i	−0.0338816	−	0.0338816i
$969$	20.3084	−	9.62422i	0.652399	−	0.309175i
$970$	8.08412	−	19.0884i	0.259566	−	0.612893i
$971$	−25.6210	+	8.32477i	−0.822217	+	0.267155i	−0.689764	−	0.724035i	$-0.742286\pi$
$971$	−25.6210	+	8.32477i	−0.822217	+	0.267155i	−0.132454	+	0.991189i	$0.542286\pi$
$972$	15.3618	−	2.64856i	0.492730	−	0.0849526i
$973$	2.60601	−	0.412752i	0.0835449	−	0.0132322i
$974$	−9.57080			−0.306668
$975$	−39.3322	−	1.75147i	−1.25964	−	0.0560918i
$976$	14.6045			0.467478
$977$	−11.3526	+	1.79808i	−0.363202	+	0.0575256i	−0.335369	−	0.942087i	$-0.608861\pi$
$977$	−11.3526	+	1.79808i	−0.363202	+	0.0575256i	−0.0278335	+	0.999613i	$0.508861\pi$
$978$	3.56006	−	1.04484i	0.113838	−	0.0334104i
$979$	22.2337	−	7.22418i	0.710593	−	0.230886i
$980$	−3.52248	−	15.2007i	−0.112521	−	0.485569i
$981$	0.210518	+	0.0820227i	0.00672131	+	0.00261878i
$982$	−7.38969	−	7.38969i	−0.235814	−	0.235814i
$983$	28.5844	−	14.5645i	0.911702	−	0.464535i	0.0657754	−	0.997834i	$-0.479048\pi$
$983$	28.5844	−	14.5645i	0.911702	−	0.464535i	0.845927	+	0.533299i	$0.179048\pi$
$984$	−0.692016	+	3.68228i	−0.0220607	+	0.117387i
$985$	8.21215	+	5.12217i	0.261661	+	0.163206i
$986$	−3.59385	+	4.94651i	−0.114451	+	0.157529i
$987$	1.13442	−	0.775489i	0.0361090	−	0.0246841i
$988$	2.48785	−	15.7077i	0.0791491	−	0.499728i
$989$	−15.6713	−	11.3859i	−0.498320	−	0.362051i
$990$	−0.274327	−	20.6843i	−0.00871868	−	0.657389i
$991$	12.7382	−	9.25484i	0.404642	−	0.293990i	−0.366787	−	0.930305i	$-0.619542\pi$
$991$	12.7382	−	9.25484i	0.404642	−	0.293990i	0.771429	+	0.636315i	$0.219542\pi$
$992$	3.61049	+	7.08598i	0.114633	+	0.224980i
$993$	−25.4371	−	0.729868i	−0.807223	−	0.0231617i
$994$	−0.709470	−	0.230521i	−0.0225030	−	0.00731167i
$995$	0.117931	−	1.36080i	0.00373868	−	0.0431402i
$996$	−15.3723	−	8.39640i	−0.487089	−	0.266050i
$997$	−4.15513	+	8.15491i	−0.131594	+	0.258269i	−0.947396	−	0.320063i	$-0.896296\pi$
$997$	−4.15513	+	8.15491i	−0.131594	+	0.258269i	0.815802	+	0.578331i	$0.196296\pi$
$998$	−2.34837	−	14.8270i	−0.0743363	−	0.469341i
$999$	28.1150	+	33.4238i	0.889518	+	1.05748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.137.3	yes	80
3.2	odd	2	inner	150.2.l.a.137.10	yes	80
5.2	odd	4		750.2.l.a.293.5		80
5.3	odd	4		750.2.l.c.293.6		80
5.4	even	2		750.2.l.b.707.8		80
15.2	even	4		750.2.l.a.293.8		80
15.8	even	4		750.2.l.c.293.3		80
15.14	odd	2		750.2.l.b.707.1		80
25.2	odd	20		750.2.l.b.593.1		80
25.11	even	5		750.2.l.c.407.3		80
25.14	even	10		750.2.l.a.407.8		80
25.23	odd	20	inner	150.2.l.a.23.10	yes	80
75.2	even	20		750.2.l.b.593.8		80
75.11	odd	10		750.2.l.c.407.6		80
75.14	odd	10		750.2.l.a.407.5		80
75.23	even	20	inner	150.2.l.a.23.3	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.23.3	✓	80	75.23	even	20	inner
150.2.l.a.23.10	yes	80	25.23	odd	20	inner
150.2.l.a.137.3	yes	80	1.1	even	1	trivial
150.2.l.a.137.10	yes	80	3.2	odd	2	inner
750.2.l.a.293.5		80	5.2	odd	4
750.2.l.a.293.8		80	15.2	even	4
750.2.l.a.407.5		80	75.14	odd	10
750.2.l.a.407.8		80	25.14	even	10
750.2.l.b.593.1		80	25.2	odd	20
750.2.l.b.593.8		80	75.2	even	20
750.2.l.b.707.1		80	15.14	odd	2
750.2.l.b.707.8		80	5.4	even	2
750.2.l.c.293.3		80	15.8	even	4
750.2.l.c.293.6		80	5.3	odd	4
750.2.l.c.407.3		80	25.11	even	5
750.2.l.c.407.6		80	75.11	odd	10

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.487767 + 1.66195i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.22772 + 0.193062i) q^{5} +(-0.741748 - 1.56519i) q^{6} +(-0.104631 - 0.104631i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-2.52417 + 1.62129i) q^{9} +O(q^{10})\)	\(q+(-0.987688 + 0.156434i) q^{2} +(0.487767 + 1.66195i) q^{3} +(0.951057 - 0.309017i) q^{4} +(2.22772 + 0.193062i) q^{5} +(-0.741748 - 1.56519i) q^{6} +(-0.104631 - 0.104631i) q^{7} +(-0.891007 + 0.453990i) q^{8} +(-2.52417 + 1.62129i) q^{9} +(-2.23049 + 0.157807i) q^{10} +(1.81255 - 2.49477i) q^{11} +(0.977465 + 1.42988i) q^{12} +(-0.711182 + 4.49023i) q^{13} +(0.119711 + 0.0869753i) q^{14} +(0.765748 + 3.79653i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.68388 + 3.30481i) q^{17} +(2.23946 - 1.99620i) q^{18} +(-3.32698 - 1.08100i) q^{19} +(2.17835 - 0.504790i) q^{20} +(0.122857 - 0.224928i) q^{21} +(-1.39997 + 2.74760i) q^{22} +(-0.773401 - 4.88306i) q^{23} +(-1.18911 - 1.25937i) q^{24} +(4.92545 + 0.860175i) q^{25} -4.54620i q^{26} +(-3.92571 - 3.40423i) q^{27} +(-0.131843 - 0.0671775i) q^{28} +(-0.509399 - 1.56777i) q^{29} +(-1.35023 - 3.63000i) q^{30} +(2.45755 - 7.56355i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.03028 + 1.79551i) q^{33} +(-2.18014 - 3.00070i) q^{34} +(-0.212889 - 0.253290i) q^{35} +(-1.89962 + 2.32195i) q^{36} +(-8.30199 - 1.31491i) q^{37} +(3.45513 + 0.547238i) q^{38} +(-7.80943 + 1.00823i) q^{39} +(-2.07256 + 0.839343i) q^{40} +(-1.27149 - 1.75005i) q^{41} +(-0.0861576 + 0.241378i) q^{42} +(2.77052 - 2.77052i) q^{43} +(0.952916 - 2.93277i) q^{44} +(-5.93614 + 3.12446i) q^{45} +(1.52776 + 4.70196i) q^{46} +(4.77725 + 2.43413i) q^{47} +(1.37148 + 1.05784i) q^{48} -6.97810i q^{49} +(-4.99937 - 0.0790741i) q^{50} +(-4.67109 + 4.41051i) q^{51} +(0.711182 + 4.49023i) q^{52} +(5.24200 - 10.2880i) q^{53} +(4.40992 + 2.74820i) q^{54} +(4.51950 - 5.20770i) q^{55} +(0.140729 + 0.0457256i) q^{56} +(0.173781 - 6.05656i) q^{57} +(0.748381 + 1.46878i) q^{58} +(-10.4207 + 7.57107i) q^{59} +(1.90146 + 3.37408i) q^{60} +(11.8153 + 8.58430i) q^{61} +(-1.24409 + 7.85487i) q^{62} +(0.433745 + 0.0944693i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-2.45120 + 9.86565i) q^{65} +(-5.24923 - 0.986496i) q^{66} +(3.23605 - 1.64885i) q^{67} +(2.62271 + 2.62271i) q^{68} +(7.73817 - 3.66715i) q^{69} +(0.249891 + 0.216868i) q^{70} +(-4.79465 + 1.55788i) q^{71} +(1.51300 - 2.59053i) q^{72} +(-10.6274 + 1.68322i) q^{73} +8.40547 q^{74} +(0.972905 + 8.60543i) q^{75} -3.49819 q^{76} +(-0.450681 + 0.0713809i) q^{77} +(7.55556 - 2.21748i) q^{78} +(8.57556 - 2.78637i) q^{79} +(1.91574 - 1.15323i) q^{80} +(3.74283 - 8.18481i) q^{81} +(1.52960 + 1.52960i) q^{82} +(-9.01058 + 4.59112i) q^{83} +(0.0473370 - 0.251884i) q^{84} +(3.11318 + 7.68727i) q^{85} +(-2.30301 + 3.16982i) q^{86} +(2.35709 - 1.61130i) q^{87} +(-0.482397 + 3.04574i) q^{88} +(6.13326 + 4.45607i) q^{89} +(5.37428 - 4.01461i) q^{90} +(0.544231 - 0.395407i) q^{91} +(-2.24450 - 4.40507i) q^{92} +(13.7690 + 0.395073i) q^{93} +(-5.09921 - 1.65683i) q^{94} +(-7.20287 - 3.05048i) q^{95} +(-1.52008 - 0.830274i) q^{96} +(-4.20877 + 8.26018i) q^{97} +(1.09162 + 6.89219i) q^{98} +(-0.530447 + 9.23588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

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