LMFDB - Embedded newform 665.2.i.h.596.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [665,2,Mod(106,665)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(665, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("665.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 665 = 5 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	665.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.31005173442$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 20 x^{18} - 43 x^{17} + 207 x^{16} - 401 x^{15} + 1351 x^{14} - 2135 x^{13} + \cdots + 1024 $ x^20 - 3x^19 + 20x^18 - 43x^17 + 207x^16 - 401x^15 + 1351x^14 - 2135x^13 + 5714x^12 - 7983x^11 + 16723x^10 - 18718x^9 + 30867x^8 - 28726x^7 + 37857x^6 - 24848x^5 + 21360x^4 - 7488x^3 + 5888x^2 - 1536*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			596.6
Root			$0.449475 + 0.778513i$ of defining polynomial
Character	$\chi$	$=$	665.596
Dual form			665.2.i.h.106.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.449475 + 0.778513i) q^{2} +(-1.28912 - 2.23283i) q^{3} +(0.595945 - 1.03221i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.15886 - 2.00720i) q^{6} -1.00000 q^{7} +2.86935 q^{8} +(-1.82367 + 3.15869i) q^{9} +O(q^{10})$	\(q+(0.449475 + 0.778513i) q^{2} +(-1.28912 - 2.23283i) q^{3} +(0.595945 - 1.03221i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.15886 - 2.00720i) q^{6} -1.00000 q^{7} +2.86935 q^{8} +(-1.82367 + 3.15869i) q^{9} +(-0.449475 + 0.778513i) q^{10} +5.14308 q^{11} -3.07298 q^{12} +(1.92508 - 3.33434i) q^{13} +(-0.449475 - 0.778513i) q^{14} +(1.28912 - 2.23283i) q^{15} +(0.0978087 + 0.169410i) q^{16} +(0.102596 + 0.177702i) q^{17} -3.27878 q^{18} +(-1.99594 - 3.87508i) q^{19} +1.19189 q^{20} +(1.28912 + 2.23283i) q^{21} +(2.31168 + 4.00395i) q^{22} +(-3.70395 + 6.41543i) q^{23} +(-3.69894 - 6.40675i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.46110 q^{26} +1.66901 q^{27} +(-0.595945 + 1.03221i) q^{28} +(4.74144 - 8.21241i) q^{29} +2.31771 q^{30} -0.731444 q^{31} +(2.78142 - 4.81756i) q^{32} +(-6.63006 - 11.4836i) q^{33} +(-0.0922287 + 0.159745i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(2.17362 + 3.76482i) q^{36} -7.77996 q^{37} +(2.11967 - 3.29562i) q^{38} -9.92666 q^{39} +(1.43467 + 2.48493i) q^{40} +(-3.43044 - 5.94170i) q^{41} +(-1.15886 + 2.00720i) q^{42} +(0.336385 + 0.582635i) q^{43} +(3.06499 - 5.30872i) q^{44} -3.64734 q^{45} -6.65932 q^{46} +(-2.30829 + 3.99807i) q^{47} +(0.252175 - 0.436779i) q^{48} +1.00000 q^{49} -0.898949 q^{50} +(0.264518 - 0.458158i) q^{51} +(-2.29449 - 3.97417i) q^{52} +(4.60152 - 7.97007i) q^{53} +(0.750179 + 1.29935i) q^{54} +(2.57154 + 4.45404i) q^{55} -2.86935 q^{56} +(-6.07935 + 9.45204i) q^{57} +8.52462 q^{58} +(5.55254 + 9.61728i) q^{59} +(-1.53649 - 2.66128i) q^{60} +(2.72714 - 4.72355i) q^{61} +(-0.328766 - 0.569439i) q^{62} +(1.82367 - 3.15869i) q^{63} +5.39195 q^{64} +3.85016 q^{65} +(5.96009 - 10.3232i) q^{66} +(-0.123859 + 0.214529i) q^{67} +0.244567 q^{68} +19.0994 q^{69} +(0.449475 - 0.778513i) q^{70} +(6.25825 + 10.8396i) q^{71} +(-5.23275 + 9.06339i) q^{72} +(-3.74890 - 6.49328i) q^{73} +(-3.49689 - 6.05680i) q^{74} +2.57824 q^{75} +(-5.18935 - 0.249106i) q^{76} -5.14308 q^{77} +(-4.46178 - 7.72804i) q^{78} +(7.21180 + 12.4912i) q^{79} +(-0.0978087 + 0.169410i) q^{80} +(3.31946 + 5.74947i) q^{81} +(3.08380 - 5.34129i) q^{82} -0.829940 q^{83} +3.07298 q^{84} +(-0.102596 + 0.177702i) q^{85} +(-0.302393 + 0.523760i) q^{86} -24.4492 q^{87} +14.7573 q^{88} +(-5.22941 + 9.05760i) q^{89} +(-1.63939 - 2.83950i) q^{90} +(-1.92508 + 3.33434i) q^{91} +(4.41470 + 7.64648i) q^{92} +(0.942921 + 1.63319i) q^{93} -4.15006 q^{94} +(2.35794 - 3.66608i) q^{95} -14.3424 q^{96} +(3.95529 + 6.85077i) q^{97} +(0.449475 + 0.778513i) q^{98} +(-9.37929 + 16.2454i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} + q^{15} - 5 q^{16} + 8 q^{17} - 76 q^{18} + 17 q^{19} - 22 q^{20} + q^{21} - 4 q^{22} + 3 q^{23} - 6 q^{24} - 10 q^{25} + 18 q^{26} + 20 q^{27} + 11 q^{28} + q^{29} - 12 q^{30} + 10 q^{31} + 18 q^{32} + q^{33} - 26 q^{34} - 10 q^{35} - 19 q^{36} - 66 q^{37} + 19 q^{38} + 34 q^{39} - 29 q^{41} + 6 q^{42} + q^{43} - 28 q^{44} - 18 q^{45} + 6 q^{46} - 7 q^{47} + 15 q^{48} + 20 q^{49} - 6 q^{50} + 16 q^{51} - 6 q^{52} + 40 q^{53} + 35 q^{54} + q^{55} + 24 q^{57} - 18 q^{58} - 9 q^{59} - 2 q^{60} + 10 q^{61} - 8 q^{62} + 9 q^{63} + 44 q^{64} + 12 q^{65} - 19 q^{66} + 22 q^{67} - 42 q^{68} + 60 q^{69} + 3 q^{70} - 8 q^{71} + 18 q^{72} + 14 q^{73} - 24 q^{74} + 2 q^{75} - 49 q^{76} - 2 q^{77} + 23 q^{78} + 9 q^{79} + 5 q^{80} - 42 q^{81} - 5 q^{82} - 54 q^{83} + 4 q^{84} - 8 q^{85} + 37 q^{86} + 18 q^{87} - 28 q^{88} - 25 q^{89} - 38 q^{90} - 6 q^{91} + 68 q^{92} + 11 q^{93} - 118 q^{94} + 10 q^{95} + 102 q^{96} + 29 q^{97} + 3 q^{98} + 34 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 + q^15 - 5 * q^16 + 8 * q^17 - 76 * q^18 + 17 * q^19 - 22 * q^20 + q^21 - 4 * q^22 + 3 * q^23 - 6 * q^24 - 10 * q^25 + 18 * q^26 + 20 * q^27 + 11 * q^28 + q^29 - 12 * q^30 + 10 * q^31 + 18 * q^32 + q^33 - 26 * q^34 - 10 * q^35 - 19 * q^36 - 66 * q^37 + 19 * q^38 + 34 * q^39 - 29 * q^41 + 6 * q^42 + q^43 - 28 * q^44 - 18 * q^45 + 6 * q^46 - 7 * q^47 + 15 * q^48 + 20 * q^49 - 6 * q^50 + 16 * q^51 - 6 * q^52 + 40 * q^53 + 35 * q^54 + q^55 + 24 * q^57 - 18 * q^58 - 9 * q^59 - 2 * q^60 + 10 * q^61 - 8 * q^62 + 9 * q^63 + 44 * q^64 + 12 * q^65 - 19 * q^66 + 22 * q^67 - 42 * q^68 + 60 * q^69 + 3 * q^70 - 8 * q^71 + 18 * q^72 + 14 * q^73 - 24 * q^74 + 2 * q^75 - 49 * q^76 - 2 * q^77 + 23 * q^78 + 9 * q^79 + 5 * q^80 - 42 * q^81 - 5 * q^82 - 54 * q^83 + 4 * q^84 - 8 * q^85 + 37 * q^86 + 18 * q^87 - 28 * q^88 - 25 * q^89 - 38 * q^90 - 6 * q^91 + 68 * q^92 + 11 * q^93 - 118 * q^94 + 10 * q^95 + 102 * q^96 + 29 * q^97 + 3 * q^98 + 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/665\mathbb{Z}\right)^\times$.

$n$	$211$	$267$	$381$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.449475	+	0.778513i	0.317827	+	0.550492i	0.980034	−	0.198829i	$-0.0637137\pi$
$2$	0.449475	+	0.778513i	0.317827	+	0.550492i	−0.662208	+	0.749320i	$0.730380\pi$
$3$	−1.28912	−	2.23283i	−0.744275	−	1.28912i	−0.950533	−	0.310625i	$-0.899462\pi$
$3$	−1.28912	−	2.23283i	−0.744275	−	1.28912i	0.206258	−	0.978498i	$-0.433872\pi$
$4$	0.595945	−	1.03221i	0.297973	−	0.516104i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.15886	−	2.00720i	0.473101	−	0.819435i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.86935			1.01447
$9$	−1.82367	+	3.15869i	−0.607891	+	1.05290i
$10$	−0.449475	+	0.778513i	−0.142136	+	0.246187i
$11$	5.14308			1.55070			0.775348	−	0.631534i	$-0.217574\pi$
$11$	5.14308			1.55070			0.775348	+	0.631534i	$0.217574\pi$
$12$	−3.07298			−0.887094
$13$	1.92508	−	3.33434i	0.533922	−	0.924779i	−0.465293	−	0.885157i	$-0.654051\pi$
$13$	1.92508	−	3.33434i	0.533922	−	0.924779i	0.999215	−	0.0396228i	$-0.0126156\pi$
$14$	−0.449475	−	0.778513i	−0.120127	−	0.208066i
$15$	1.28912	−	2.23283i	0.332850	−	0.576513i
$16$	0.0978087	+	0.169410i	0.0244522	+	0.0423524i
$17$	0.102596	+	0.177702i	0.0248832	+	0.0430990i	0.878199	−	0.478296i	$-0.158745\pi$
$17$	0.102596	+	0.177702i	0.0248832	+	0.0430990i	−0.853316	+	0.521395i	$0.825412\pi$
$18$	−3.27878			−0.772815
$19$	−1.99594	−	3.87508i	−0.457901	−	0.889003i
$19$	−1.99594	−	3.87508i	−0.457901	−	0.889003i
$20$	1.19189			0.266515
$21$	1.28912	+	2.23283i	0.281310	+	0.487242i
$22$	2.31168	+	4.00395i	0.492853	+	0.853646i
$23$	−3.70395	+	6.41543i	−0.772327	+	1.33771i	0.163958	+	0.986467i	$0.447574\pi$
$23$	−3.70395	+	6.41543i	−0.772327	+	1.33771i	−0.936285	+	0.351242i	$0.885760\pi$
$24$	−3.69894	−	6.40675i	−0.755043	−	1.30777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.46110			0.678778
$27$	1.66901			0.321202
$28$	−0.595945	+	1.03221i	−0.112623	+	0.195069i
$29$	4.74144	−	8.21241i	0.880462	−	1.52501i	0.0296348	−	0.999561i	$-0.490566\pi$
$29$	4.74144	−	8.21241i	0.880462	−	1.52501i	0.850828	−	0.525445i	$-0.176101\pi$
$30$	2.31771			0.423154
$31$	−0.731444			−0.131371			−0.0656856	−	0.997840i	$-0.520923\pi$
$31$	−0.731444			−0.131371			−0.0656856	+	0.997840i	$0.520923\pi$
$32$	2.78142	−	4.81756i	0.491691	−	0.851633i
$33$	−6.63006	−	11.4836i	−1.15414	−	1.99904i
$34$	−0.0922287	+	0.159745i	−0.0158171	+	0.0273960i
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	2.17362	+	3.76482i	0.362270	+	0.627469i
$37$	−7.77996			−1.27902			−0.639509	−	0.768784i	$-0.720862\pi$
$37$	−7.77996			−1.27902			−0.639509	+	0.768784i	$0.720862\pi$
$38$	2.11967	−	3.29562i	0.343856	−	0.534619i
$39$	−9.92666			−1.58954
$40$	1.43467	+	2.48493i	0.226842	+	0.392902i
$41$	−3.43044	−	5.94170i	−0.535745	−	0.927938i	−0.999127	−	0.0417794i	$-0.986697\pi$
$41$	−3.43044	−	5.94170i	−0.535745	−	0.927938i	0.463381	−	0.886159i	$-0.346636\pi$
$42$	−1.15886	+	2.00720i	−0.178815	+	0.309717i
$43$	0.336385	+	0.582635i	0.0512982	+	0.0888510i	0.890534	−	0.454916i	$-0.150331\pi$
$43$	0.336385	+	0.582635i	0.0512982	+	0.0888510i	−0.839236	+	0.543767i	$0.816997\pi$
$44$	3.06499	−	5.30872i	0.462065	−	0.800320i
$45$	−3.64734			−0.543714
$46$	−6.65932			−0.981864
$47$	−2.30829	+	3.99807i	−0.336698	+	0.583178i	−0.983810	−	0.179217i	$-0.942644\pi$
$47$	−2.30829	+	3.99807i	−0.336698	+	0.583178i	0.647111	+	0.762395i	$0.275977\pi$
$48$	0.252175	−	0.436779i	0.0363983	−	0.0630437i
$49$	1.00000			0.142857
$50$	−0.898949			−0.127131
$51$	0.264518	−	0.458158i	0.0370399	−	0.0641550i
$52$	−2.29449	−	3.97417i	−0.318188	−	0.551118i
$53$	4.60152	−	7.97007i	0.632068	−	1.09477i	−0.355061	−	0.934843i	$-0.615540\pi$
$53$	4.60152	−	7.97007i	0.632068	−	1.09477i	0.987128	−	0.159930i	$-0.0511269\pi$
$54$	0.750179	+	1.29935i	0.102086	+	0.176819i
$55$	2.57154	+	4.45404i	0.346746	+	0.600582i
$56$	−2.86935			−0.383433
$57$	−6.07935	+	9.45204i	−0.805230	+	1.25195i
$58$	8.52462			1.11934
$59$	5.55254	+	9.61728i	0.722879	+	1.25206i	0.959841	+	0.280545i	$0.0905151\pi$
$59$	5.55254	+	9.61728i	0.722879	+	1.25206i	−0.236962	+	0.971519i	$0.576152\pi$
$60$	−1.53649	−	2.66128i	−0.198360	−	0.343570i
$61$	2.72714	−	4.72355i	0.349175	−	0.604789i	−0.636928	−	0.770923i	$-0.719795\pi$
$61$	2.72714	−	4.72355i	0.349175	−	0.604789i	0.986103	+	0.166135i	$0.0531286\pi$
$62$	−0.328766	−	0.569439i	−0.0417533	−	0.0723188i
$63$	1.82367	−	3.15869i	0.229761	−	0.397958i
$64$	5.39195			0.673994
$65$	3.85016			0.477554
$66$	5.96009	−	10.3232i	0.733636	−	1.27069i
$67$	−0.123859	+	0.214529i	−0.0151317	+	0.0262089i	−0.873492	−	0.486838i	$-0.838150\pi$
$67$	−0.123859	+	0.214529i	−0.0151317	+	0.0262089i	0.858360	+	0.513047i	$0.171483\pi$
$68$	0.244567			0.0296581
$69$	19.0994			2.29929
$70$	0.449475	−	0.778513i	0.0537225	−	0.0930501i
$71$	6.25825	+	10.8396i	0.742717	+	1.28642i	0.951254	+	0.308410i	$0.0997968\pi$
$71$	6.25825	+	10.8396i	0.742717	+	1.28642i	−0.208536	+	0.978015i	$0.566870\pi$
$72$	−5.23275	+	9.06339i	−0.616685	+	1.06813i
$73$	−3.74890	−	6.49328i	−0.438775	−	0.759981i	0.558820	−	0.829289i	$-0.311254\pi$
$73$	−3.74890	−	6.49328i	−0.438775	−	0.759981i	−0.997595	+	0.0693077i	$0.977921\pi$
$74$	−3.49689	−	6.05680i	−0.406506	−	0.704089i
$75$	2.57824			0.297710
$76$	−5.18935	−	0.249106i	−0.595260	−	0.0285744i
$77$	−5.14308			−0.586108
$78$	−4.46178	−	7.72804i	−0.505198	−	0.875028i
$79$	7.21180	+	12.4912i	0.811391	+	1.40537i	0.911890	+	0.410434i	$0.134623\pi$
$79$	7.21180	+	12.4912i	0.811391	+	1.40537i	−0.100499	+	0.994937i	$0.532044\pi$
$80$	−0.0978087	+	0.169410i	−0.0109353	+	0.0189406i
$81$	3.31946	+	5.74947i	0.368828	+	0.638830i
$82$	3.08380	−	5.34129i	0.340548	−	0.589847i
$83$	−0.829940			−0.0910978			−0.0455489	−	0.998962i	$-0.514504\pi$
$83$	−0.829940			−0.0910978			−0.0455489	+	0.998962i	$0.514504\pi$
$84$	3.07298			0.335290
$85$	−0.102596	+	0.177702i	−0.0111281	+	0.0192745i
$86$	−0.302393	+	0.523760i	−0.0326078	+	0.0564784i
$87$	−24.4492			−2.62122
$88$	14.7573			1.57313
$89$	−5.22941	+	9.05760i	−0.554316	+	0.960104i	0.443640	+	0.896205i	$0.353687\pi$
$89$	−5.22941	+	9.05760i	−0.554316	+	0.960104i	−0.997956	+	0.0638989i	$0.979646\pi$
$90$	−1.63939	−	2.83950i	−0.172807	−	0.299310i
$91$	−1.92508	+	3.33434i	−0.201803	+	0.349534i
$92$	4.41470	+	7.64648i	0.460264	+	0.797201i
$93$	0.942921	+	1.63319i	0.0977763	+	0.169354i
$94$	−4.15006			−0.428046
$95$	2.35794	−	3.66608i	0.241920	−	0.376131i
$96$	−14.3424			−1.46381
$97$	3.95529	+	6.85077i	0.401599	+	0.695590i	0.993919	−	0.110113i	$-0.0351212\pi$
$97$	3.95529	+	6.85077i	0.401599	+	0.695590i	−0.592320	+	0.805703i	$0.701788\pi$
$98$	0.449475	+	0.778513i	0.0454038	+	0.0786417i
$99$	−9.37929	+	16.2454i	−0.942654	+	1.63272i
$100$	0.595945	+	1.03221i	0.0595945	+	0.103221i
$101$	2.20047	−	3.81132i	0.218955	−	0.379241i	−0.735534	−	0.677488i	$-0.763069\pi$
$101$	2.20047	−	3.81132i	0.218955	−	0.379241i	0.954489	+	0.298247i	$0.0964020\pi$
$102$	0.475576			0.0470891
$103$	9.01446			0.888222			0.444111	−	0.895972i	$-0.353520\pi$
$103$	9.01446			0.888222			0.444111	+	0.895972i	$0.353520\pi$
$104$	5.52373	−	9.56738i	0.541646	−	0.938159i
$105$	−1.28912	+	2.23283i	−0.125805	+	0.217901i
$106$	8.27307			0.803552
$107$	16.6085			1.60560			0.802801	−	0.596247i	$-0.203342\pi$
$107$	16.6085			1.60560			0.802801	+	0.596247i	$0.203342\pi$
$108$	0.994640	−	1.72277i	0.0957092	−	0.165773i
$109$	−3.50267	−	6.06681i	−0.335495	−	0.581095i	0.648085	−	0.761568i	$-0.275570\pi$
$109$	−3.50267	−	6.06681i	−0.335495	−	0.581095i	−0.983580	+	0.180474i	$0.942237\pi$
$110$	−2.31168	+	4.00395i	−0.220410	+	0.381762i
$111$	10.0293	+	17.3713i	0.951941	+	1.64881i
$112$	−0.0978087	−	0.169410i	−0.00924205	−	0.0160077i
$113$	−14.5253			−1.36642			−0.683211	−	0.730221i	$-0.739417\pi$
$113$	−14.5253			−1.36642			−0.683211	+	0.730221i	$0.739417\pi$
$114$	−10.0910	−	0.484404i	−0.945113	−	0.0453685i
$115$	−7.40790			−0.690790
$116$	−5.65127	−	9.78829i	−0.524707	−	0.908820i
$117$	7.02144	+	12.1615i	0.649132	+	1.12433i
$118$	−4.99145	+	8.64545i	−0.459501	+	0.795878i
$119$	−0.102596	−	0.177702i	−0.00940497	−	0.0162899i
$120$	3.69894	−	6.40675i	0.337665	−	0.584854i
$121$	15.4513			1.40466
$122$	4.90313			0.443908
$123$	−8.84453	+	15.3192i	−0.797484	+	1.38128i
$124$	−0.435901	+	0.755002i	−0.0391450	+	0.0678012i
$125$	−1.00000			−0.0894427
$126$	3.27878			0.292097
$127$	−8.13022	+	14.0820i	−0.721440	+	1.24957i	0.238982	+	0.971024i	$0.423186\pi$
$127$	−8.13022	+	14.0820i	−0.721440	+	1.24957i	−0.960423	+	0.278547i	$0.910147\pi$
$128$	−3.13930	−	5.43743i	−0.277478	−	0.480605i
$129$	0.867282	−	1.50218i	0.0763599	−	0.132259i
$130$	1.73055	+	2.99740i	0.151779	+	0.262890i
$131$	−3.26070	−	5.64770i	−0.284889	−	0.493442i	0.687693	−	0.726001i	$-0.258623\pi$
$131$	−3.26070	−	5.64770i	−0.284889	−	0.493442i	−0.972582	+	0.232559i	$0.925290\pi$
$132$	−15.8046			−1.37561
$133$	1.99594	+	3.87508i	0.173070	+	0.336012i
$134$	−0.222685			−0.0192371
$135$	0.834506	+	1.44541i	0.0718228	+	0.124401i
$136$	0.294384	+	0.509888i	0.0252432	+	0.0437225i
$137$	−4.10205	+	7.10497i	−0.350462	+	0.607018i	−0.986330	−	0.164779i	$-0.947309\pi$
$137$	−4.10205	+	7.10497i	−0.350462	+	0.607018i	0.635868	+	0.771798i	$0.280642\pi$
$138$	8.58468	+	14.8691i	0.730777	+	1.26574i
$139$	1.36229	−	2.35956i	0.115548	−	0.200135i	−0.802451	−	0.596719i	$-0.796471\pi$
$139$	1.36229	−	2.35956i	0.115548	−	0.200135i	0.917999	+	0.396583i	$0.129804\pi$
$140$	−1.19189			−0.100733
$141$	11.9027			1.00238
$142$	−5.62585	+	9.74425i	−0.472111	+	0.817720i
$143$	9.90085	−	17.1488i	0.827951	−	1.43405i
$144$	−0.713484			−0.0594570
$145$	9.48287			0.787510
$146$	3.37007	−	5.83713i	0.278909	−	0.483085i
$147$	−1.28912	−	2.23283i	−0.106325	−	0.184160i
$148$	−4.63643	+	8.03053i	−0.381112	+	0.660106i
$149$	0.677102	+	1.17277i	0.0554703	+	0.0960775i	0.892427	−	0.451191i	$-0.149001\pi$
$149$	0.677102	+	1.17277i	0.0554703	+	0.0960775i	−0.836957	+	0.547269i	$0.815668\pi$
$150$	1.15886	+	2.00720i	0.0946202	+	0.163887i
$151$	6.67310			0.543050			0.271525	−	0.962431i	$-0.412472\pi$
$151$	6.67310			0.543050			0.271525	+	0.962431i	$0.412472\pi$
$152$	−5.72705	−	11.1189i	−0.464525	−	0.901865i
$153$	−0.748407			−0.0605051
$154$	−2.31168	−	4.00395i	−0.186281	−	0.322648i
$155$	−0.365722	−	0.633449i	−0.0293755	−	0.0508799i
$156$	−5.91575	+	10.2464i	−0.473639	+	0.820366i
$157$	8.79509	+	15.2335i	0.701924	+	1.21577i	0.967790	+	0.251759i	$0.0810089\pi$
$157$	8.79509	+	15.2335i	0.701924	+	1.21577i	−0.265866	+	0.964010i	$0.585658\pi$
$158$	−6.48305	+	11.2290i	−0.515763	+	0.893328i
$159$	−23.7277			−1.88173
$160$	5.56284			0.439781
$161$	3.70395	−	6.41543i	0.291912	−	0.505606i
$162$	−2.98402	+	5.16848i	−0.234447	+	0.406074i
$163$	−3.27946			−0.256867			−0.128434	−	0.991718i	$-0.540995\pi$
$163$	−3.27946			−0.256867			−0.128434	+	0.991718i	$0.540995\pi$
$164$	−8.17743			−0.638550
$165$	6.63006	−	11.4836i	0.516149	−	0.893997i
$166$	−0.373037	−	0.646119i	−0.0289533	−	0.0501486i
$167$	7.09155	−	12.2829i	0.548761	−	0.950481i	−0.449599	−	0.893230i	$-0.648433\pi$
$167$	7.09155	−	12.2829i	0.548761	−	0.950481i	0.998360	−	0.0572507i	$-0.0182334\pi$
$168$	3.69894	+	6.40675i	0.285379	+	0.494292i
$169$	−0.911881	−	1.57942i	−0.0701447	−	0.121494i
$170$	−0.184457			−0.0141472
$171$	15.8801	+	0.762298i	1.21438	+	0.0582944i
$172$	0.801867			0.0611418
$173$	1.07042	+	1.85402i	0.0813823	+	0.140958i	0.903844	−	0.427862i	$-0.140733\pi$
$173$	1.07042	+	1.85402i	0.0813823	+	0.140958i	−0.822462	+	0.568821i	$0.807400\pi$
$174$	−10.9893	−	19.0340i	−0.833095	−	1.44296i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	0.503038	+	0.871287i	0.0379179	+	0.0656757i
$177$	14.3158	−	24.7957i	1.07604	−	1.86376i
$178$	−9.40195			−0.704706
$179$	9.12996			0.682405			0.341202	−	0.939990i	$-0.389166\pi$
$179$	9.12996			0.682405			0.341202	+	0.939990i	$0.389166\pi$
$180$	−2.17362	+	3.76482i	−0.162012	+	0.280613i
$181$	0.815824	−	1.41305i	0.0606398	−	0.105031i	−0.834112	−	0.551595i	$-0.814019\pi$
$181$	0.815824	−	1.41305i	0.0606398	−	0.105031i	0.894752	+	0.446564i	$0.147353\pi$
$182$	−3.46110			−0.256554
$183$	−14.0625			−1.03953
$184$	−10.6279	+	18.4081i	−0.783500	+	1.35706i
$185$	−3.88998	−	6.73764i	−0.285997	−	0.495361i
$186$	−0.847638	+	1.46815i	−0.0621518	+	0.107650i
$187$	0.527660	+	0.913934i	0.0385863	+	0.0668334i
$188$	2.75122	+	4.76526i	0.200654	+	0.347542i
$189$	−1.66901			−0.121403
$190$	3.91392	+	0.187881i	0.283946	+	0.0136303i
$191$	−10.3641			−0.749923			−0.374961	−	0.927040i	$-0.622344\pi$
$191$	−10.3641			−0.749923			−0.374961	+	0.927040i	$0.622344\pi$
$192$	−6.95088	−	12.0393i	−0.501637	−	0.868860i
$193$	8.57538	+	14.8530i	0.617269	+	1.06914i	0.989982	+	0.141195i	$0.0450944\pi$
$193$	8.57538	+	14.8530i	0.617269	+	1.06914i	−0.372712	+	0.927947i	$0.621572\pi$
$194$	−3.55561	+	6.15849i	−0.255278	+	0.442154i
$195$	−4.96333	−	8.59674i	−0.355432	−	0.615626i
$196$	0.595945	−	1.03221i	0.0425675	−	0.0737291i
$197$	−16.3639			−1.16588			−0.582938	−	0.812516i	$-0.698097\pi$
$197$	−16.3639			−1.16588			−0.582938	+	0.812516i	$0.698097\pi$
$198$	−16.8630			−1.19840
$199$	−12.2693	+	21.2511i	−0.869748	+	1.50645i	−0.00749318	+	0.999972i	$0.502385\pi$
$199$	−12.2693	+	21.2511i	−0.869748	+	1.50645i	−0.862255	+	0.506475i	$0.830948\pi$
$200$	−1.43467	+	2.48493i	−0.101447	+	0.175711i
$201$	0.638675			0.0450487
$202$	3.95622			0.278359
$203$	−4.74144	+	8.21241i	−0.332784	+	0.576398i
$204$	−0.315276	−	0.546074i	−0.0220737	−	0.0382329i
$205$	3.43044	−	5.94170i	0.239593	−	0.414987i
$206$	4.05177	+	7.01788i	0.282300	+	0.488959i
$207$	−13.5096	−	23.3993i	−0.938980	−	1.62636i
$208$	0.753159			0.0522222
$209$	−10.2653	−	19.9298i	−0.710065	−	1.37857i
$210$	−2.31771			−0.159937
$211$	−7.47436	−	12.9460i	−0.514556	−	0.891238i	−0.999857	−	0.0168906i	$-0.994623\pi$
$211$	−7.47436	−	12.9460i	−0.514556	−	0.891238i	0.485301	−	0.874347i	$-0.338710\pi$
$212$	−5.48451	−	9.49945i	−0.376678	−	0.652425i
$213$	16.1353	−	27.9471i	1.10557	−	1.91491i
$214$	7.46509	+	12.9299i	0.510303	+	0.883870i
$215$	−0.336385	+	0.582635i	−0.0229412	+	0.0397354i
$216$	4.78898			0.325849
$217$	0.731444			0.0496537
$218$	3.14873	−	5.45375i	0.213259	−	0.369375i
$219$	−9.66558	+	16.7413i	−0.653139	+	1.13127i
$220$	6.12999			0.413284
$221$	0.790024			0.0531427
$222$	−9.01585	+	15.6159i	−0.605104	+	1.04807i
$223$	−6.34789	−	10.9949i	−0.425086	−	0.736271i	0.571342	−	0.820712i	$-0.306423\pi$
$223$	−6.34789	−	10.9949i	−0.425086	−	0.736271i	−0.996428	+	0.0844408i	$0.973090\pi$
$224$	−2.78142	+	4.81756i	−0.185842	+	0.321887i
$225$	−1.82367	−	3.15869i	−0.121578	−	0.210580i
$226$	−6.52874	−	11.3081i	−0.434285	−	0.752204i
$227$	−25.2895			−1.67852			−0.839260	−	0.543730i	$-0.817012\pi$
$227$	−25.2895			−1.67852			−0.839260	+	0.543730i	$0.817012\pi$
$228$	6.13350	+	11.9080i	0.406201	+	0.788630i
$229$	8.11685			0.536376			0.268188	−	0.963367i	$-0.413575\pi$
$229$	8.11685			0.536376			0.268188	+	0.963367i	$0.413575\pi$
$230$	−3.32966	−	5.76714i	−0.219551	−	0.380274i
$231$	6.63006	+	11.4836i	0.436226	+	0.755565i
$232$	13.6048	−	23.5642i	0.893201	−	1.54707i
$233$	4.93601	+	8.54942i	0.323369	+	0.560091i	0.981181	−	0.193091i	$-0.0618513\pi$
$233$	4.93601	+	8.54942i	0.323369	+	0.560091i	−0.657812	+	0.753182i	$0.728518\pi$
$234$	−6.31192	+	10.9326i	−0.412623	+	0.714684i
$235$	−4.61657			−0.301152
$236$	13.2360			0.861593
$237$	18.5938	−	32.2054i	1.20780	−	2.09197i
$238$	0.0922287	−	0.159745i	0.00597830	−	0.0103547i
$239$	7.62331			0.493111			0.246556	−	0.969129i	$-0.420701\pi$
$239$	7.62331			0.493111			0.246556	+	0.969129i	$0.420701\pi$
$240$	0.504349			0.0325556
$241$	2.30054	−	3.98465i	0.148191	−	0.256674i	−0.782368	−	0.622816i	$-0.785988\pi$
$241$	2.30054	−	3.98465i	0.148191	−	0.256674i	0.930559	+	0.366142i	$0.119322\pi$
$242$	6.94495	+	12.0290i	0.446438	+	0.773254i
$243$	11.0619	−	19.1598i	0.709620	−	1.22910i
$244$	−3.25045	−	5.62995i	−0.208089	−	0.360421i
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	−15.9016			−1.01385
$247$	−16.7632	−	0.804687i	−1.06662	−	0.0512010i
$248$	−2.09877			−0.133272
$249$	1.06989	+	1.85311i	0.0678018	+	0.117436i
$250$	−0.449475	−	0.778513i	−0.0284273	−	0.0492375i
$251$	−7.68789	+	13.3158i	−0.485255	+	0.840487i	−0.999856	−	0.0169429i	$-0.994607\pi$
$251$	−7.68789	+	13.3158i	−0.485255	+	0.840487i	0.514601	+	0.857430i	$0.327940\pi$
$252$	−2.17362	−	3.76482i	−0.136925	−	0.237161i
$253$	−19.0497	+	32.9950i	−1.19764	+	2.07438i
$254$	−14.6173			−0.917171
$255$	0.529036			0.0331295
$256$	8.21402	−	14.2271i	0.513376	−	0.889194i
$257$	10.2816	−	17.8083i	0.641350	−	1.11085i	−0.343782	−	0.939050i	$-0.611708\pi$
$257$	10.2816	−	17.8083i	0.641350	−	1.11085i	0.985132	−	0.171801i	$-0.0549587\pi$
$258$	1.55928			0.0970768
$259$	7.77996			0.483423
$260$	2.29449	−	3.97417i	0.142298	−	0.246467i
$261$	17.2936	+	29.9535i	1.07045	+	1.85407i
$262$	2.93121	−	5.07700i	0.181091	−	0.313658i
$263$	−2.42801	−	4.20544i	−0.149718	−	0.259319i	0.781405	−	0.624024i	$-0.214503\pi$
$263$	−2.42801	−	4.20544i	−0.149718	−	0.259319i	−0.931123	+	0.364705i	$0.881170\pi$
$264$	−19.0239	−	32.9504i	−1.17084	−	2.02796i
$265$	9.20305			0.565339
$266$	−2.11967	+	3.29562i	−0.129965	+	0.202067i
$267$	26.9654			1.65026
$268$	0.147626	+	0.255695i	0.00901768	+	0.0156191i
$269$	16.2922	+	28.2190i	0.993356	+	1.72054i	0.596344	+	0.802729i	$0.296619\pi$
$269$	16.2922	+	28.2190i	0.993356	+	1.72054i	0.397011	+	0.917814i	$0.370047\pi$
$270$	−0.750179	+	1.29935i	−0.0456544	+	0.0790758i
$271$	10.0666	+	17.4358i	0.611499	+	1.05915i	0.990988	+	0.133952i	$0.0427666\pi$
$271$	10.0666	+	17.4358i	0.611499	+	1.05915i	−0.379489	+	0.925196i	$0.623900\pi$
$272$	−0.0200696	+	0.0347615i	−0.00121690	+	0.00210773i
$273$	9.92666			0.600789
$274$	−7.37508			−0.445545
$275$	−2.57154	+	4.45404i	−0.155070	+	0.268589i
$276$	11.3822	−	19.7145i	0.685126	−	1.18667i
$277$	6.21635			0.373504			0.186752	−	0.982407i	$-0.440204\pi$
$277$	6.21635			0.373504			0.186752	+	0.982407i	$0.440204\pi$
$278$	2.44926			0.146897
$279$	1.33391	−	2.31041i	0.0798594	−	0.138320i
$280$	−1.43467	−	2.48493i	−0.0857382	−	0.148503i
$281$	0.421421	−	0.729923i	0.0251399	−	0.0435436i	−0.853182	−	0.521614i	$-0.825330\pi$
$281$	0.421421	−	0.729923i	0.0251399	−	0.0435436i	0.878322	+	0.478070i	$0.158664\pi$
$282$	5.34994	+	9.26637i	0.318584	+	0.551804i
$283$	5.11722	+	8.86329i	0.304187	+	0.526868i	0.977080	−	0.212872i	$-0.0682818\pi$
$283$	5.11722	+	8.86329i	0.304187	+	0.526868i	−0.672893	+	0.739740i	$0.734948\pi$
$284$	14.9183			0.885238
$285$	−11.2254	−	0.538855i	−0.664934	−	0.0319190i
$286$	17.8007			1.05258
$287$	3.43044	+	5.94170i	0.202493	+	0.350728i
$288$	10.1448	+	17.5713i	0.597788	+	1.03540i
$289$	8.47895	−	14.6860i	0.498762	−	0.863881i
$290$	4.26231	+	7.38254i	0.250291	+	0.433518i
$291$	10.1977	−	17.6629i	0.597800	−	1.03542i
$292$	−8.93655			−0.522972
$293$	21.2496			1.24142			0.620708	−	0.784042i	$-0.286845\pi$
$293$	21.2496			1.24142			0.620708	+	0.784042i	$0.286845\pi$
$294$	1.15886	−	2.00720i	0.0675858	−	0.117062i
$295$	−5.55254	+	9.61728i	−0.323281	+	0.559940i
$296$	−22.3234			−1.29752
$297$	8.58386			0.498086
$298$	−0.608680	+	1.05427i	−0.0352599	+	0.0610719i
$299$	14.2608	+	24.7004i	0.824724	+	1.42846i
$300$	1.53649	−	2.66128i	0.0887094	−	0.153649i
$301$	−0.336385	−	0.582635i	−0.0193889	−	0.0335825i
$302$	2.99939	+	5.19510i	0.172596	+	0.298944i
$303$	−11.3467			−0.651850
$304$	0.461254	−	0.717148i	0.0264548	−	0.0411312i
$305$	5.45429			0.312311
$306$	−0.336390	−	0.582644i	−0.0192301	−	0.0333076i
$307$	3.84010	+	6.65124i	0.219166	+	0.379607i	0.954553	−	0.298041i	$-0.0963331\pi$
$307$	3.84010	+	6.65124i	0.219166	+	0.379607i	−0.735387	+	0.677647i	$0.763000\pi$
$308$	−3.06499	+	5.30872i	−0.174644	+	0.302493i
$309$	−11.6207	−	20.1277i	−0.661081	−	1.14503i
$310$	0.328766	−	0.569439i	0.0186726	−	0.0323419i
$311$	−27.9685			−1.58595			−0.792973	−	0.609257i	$-0.791468\pi$
$311$	−27.9685			−1.58595			−0.792973	+	0.609257i	$0.791468\pi$
$312$	−28.4830			−1.61253
$313$	−14.2525	+	24.6860i	−0.805597	+	1.39534i	0.110290	+	0.993899i	$0.464822\pi$
$313$	−14.2525	+	24.6860i	−0.805597	+	1.39534i	−0.915887	+	0.401436i	$0.868511\pi$
$314$	−7.90634	+	13.6942i	−0.446180	+	0.772807i
$315$	3.64734			0.205505
$316$	17.1914			0.967089
$317$	13.9749	−	24.2053i	0.784909	−	1.35950i	−0.144144	−	0.989557i	$-0.546043\pi$
$317$	13.9749	−	24.2053i	0.784909	−	1.35950i	0.929053	−	0.369946i	$-0.120624\pi$
$318$	−10.6650	−	18.4723i	−0.598064	−	1.03588i
$319$	24.3856	−	42.2371i	1.36533	−	2.36482i
$320$	2.69597	+	4.66957i	0.150710	+	0.261037i
$321$	−21.4104	−	37.0838i	−1.19501	−	2.06982i
$322$	6.65932			0.371110
$323$	0.483831	−	0.752250i	0.0269211	−	0.0418563i
$324$	7.91285			0.439603
$325$	1.92508	+	3.33434i	0.106784	+	0.184956i
$326$	−1.47404	−	2.55310i	−0.0816393	−	0.141403i
$327$	−9.03075	+	15.6417i	−0.499401	+	0.864989i
$328$	−9.84314	−	17.0488i	−0.543496	−	0.941363i
$329$	2.30829	−	3.99807i	0.127260	−	0.220421i
$330$	11.9202			0.656184
$331$	11.6884			0.642455			0.321228	−	0.947002i	$-0.395905\pi$
$331$	11.6884			0.642455			0.321228	+	0.947002i	$0.395905\pi$
$332$	−0.494599	+	0.856670i	−0.0271446	+	0.0470159i
$333$	14.1881	−	24.5745i	0.777503	−	1.34667i
$334$	12.7499			0.697643
$335$	−0.247717			−0.0135342
$336$	−0.252175	+	0.436779i	−0.0137573	+	0.0238283i
$337$	9.10428	+	15.7691i	0.495942	+	0.858996i	0.999989	−	0.00467963i	$-0.00148958\pi$
$337$	9.10428	+	15.7691i	0.495942	+	0.858996i	−0.504047	+	0.863676i	$0.668156\pi$
$338$	0.819735	−	1.41982i	0.0445877	−	0.0772281i
$339$	18.7248	+	32.4324i	1.01699	+	1.76149i
$340$	0.122283	+	0.211801i	0.00663174	+	0.0114865i
$341$	−3.76187			−0.203717
$342$	6.54425	+	12.7055i	0.353873	+	0.687035i
$343$	−1.00000			−0.0539949
$344$	0.965204	+	1.67178i	0.0520403	+	0.0901365i
$345$	9.54968	+	16.5405i	0.514138	+	0.890513i
$346$	−0.962251	+	1.66667i	−0.0517309	+	0.0896006i
$347$	−8.76355	−	15.1789i	−0.470452	−	0.814846i	0.528977	−	0.848636i	$-0.322576\pi$
$347$	−8.76355	−	15.1789i	−0.470452	−	0.814846i	−0.999429	+	0.0337896i	$0.989242\pi$
$348$	−14.5704	+	25.2366i	−0.781053	+	1.35282i
$349$	−14.0006			−0.749433			−0.374716	−	0.927139i	$-0.622260\pi$
$349$	−14.0006			−0.749433			−0.374716	+	0.927139i	$0.622260\pi$
$350$	0.898949			0.0480509
$351$	3.21299	−	5.56505i	0.171496	−	0.297041i
$352$	14.3051	−	24.7771i	0.762463	−	1.32062i
$353$	22.7707			1.21196			0.605981	−	0.795479i	$-0.292781\pi$
$353$	22.7707			1.21196			0.605981	+	0.795479i	$0.292781\pi$
$354$	25.7384			1.36798
$355$	−6.25825	+	10.8396i	−0.332153	+	0.575306i
$356$	6.23288	+	10.7957i	0.330342	+	0.572169i
$357$	−0.264518	+	0.458158i	−0.0139998	+	0.0242483i
$358$	4.10368	+	7.10779i	0.216886	+	0.375658i
$359$	11.2838	+	19.5442i	0.595539	+	1.03150i	0.993471	+	0.114088i	$0.0363947\pi$
$359$	11.2838	+	19.5442i	0.595539	+	1.03150i	−0.397932	+	0.917415i	$0.630272\pi$
$360$	−10.4655			−0.551580
$361$	−11.0324	+	15.4689i	−0.580654	+	0.814150i
$362$	1.46677			0.0770917
$363$	−19.9186	−	34.5000i	−1.04545	−	1.81078i
$364$	2.29449	+	3.97417i	0.120264	+	0.208303i
$365$	3.74890	−	6.49328i	0.196226	−	0.339874i
$366$	−6.32073	−	10.9478i	−0.330390	−	0.572252i
$367$	0.889012	−	1.53981i	0.0464060	−	0.0803776i	−0.841889	−	0.539650i	$-0.818557\pi$
$367$	0.889012	−	1.53981i	0.0464060	−	0.0803776i	0.888295	+	0.459273i	$0.151890\pi$
$368$	−1.44911			−0.0755402
$369$	25.0240			1.30270
$370$	3.49689	−	6.05680i	0.181795	−	0.314878i
$371$	−4.60152	+	7.97007i	−0.238899	+	0.413785i
$372$	2.24772			0.116539
$373$	−15.0180			−0.777601			−0.388801	−	0.921322i	$-0.627110\pi$
$373$	−15.0180			−0.777601			−0.388801	+	0.921322i	$0.627110\pi$
$374$	−0.474339	+	0.821580i	−0.0245275	+	0.0424829i
$375$	1.28912	+	2.23283i	0.0665700	+	0.115303i
$376$	−6.62327	+	11.4718i	−0.341569	+	0.591615i
$377$	−18.2553	−	31.6191i	−0.940196	−	1.62847i
$378$	−0.750179	−	1.29935i	−0.0385850	−	0.0668312i
$379$	−18.5149			−0.951046			−0.475523	−	0.879703i	$-0.657741\pi$
$379$	−18.5149			−0.951046			−0.475523	+	0.879703i	$0.657741\pi$
$380$	−2.37894	−	4.61866i	−0.122037	−	0.236933i
$381$	41.9234			2.14780
$382$	−4.65842	−	8.06862i	−0.238345	−	0.412826i
$383$	7.05968	+	12.2277i	0.360733	+	0.624807i	0.988082	−	0.153931i	$-0.0491934\pi$
$383$	7.05968	+	12.2277i	0.360733	+	0.624807i	−0.627349	+	0.778738i	$0.715860\pi$
$384$	−8.09388	+	14.0190i	−0.413039	+	0.715405i
$385$	−2.57154	−	4.45404i	−0.131058	−	0.226999i
$386$	−7.70883	+	13.3521i	−0.392369	+	0.679603i
$387$	−2.45382			−0.124735
$388$	9.42855			0.478662
$389$	−15.2000	+	26.3271i	−0.770668	+	1.33484i	0.166529	+	0.986037i	$0.446744\pi$
$389$	−15.2000	+	26.3271i	−0.770668	+	1.33484i	−0.937197	+	0.348800i	$0.886589\pi$
$390$	4.46178	−	7.72804i	0.225931	−	0.391324i
$391$	−1.52004			−0.0768719
$392$	2.86935			0.144924
$393$	−8.40689	+	14.5612i	−0.424071	+	0.734513i
$394$	−7.35514	−	12.7395i	−0.370547	−	0.641806i
$395$	−7.21180	+	12.4912i	−0.362865	+	0.628501i
$396$	11.1791	+	19.3627i	0.561770	+	0.973014i
$397$	10.3735	+	17.9674i	0.520630	+	0.901758i	0.999712	+	0.0239878i	$0.00763628\pi$
$397$	10.3735	+	17.9674i	0.520630	+	0.901758i	−0.479082	+	0.877770i	$0.659030\pi$
$398$	−22.0590			−1.10572
$399$	6.07935	−	9.45204i	0.304348	−	0.473194i
$400$	−0.195617			−0.00978087
$401$	−16.7915	−	29.0838i	−0.838530	−	1.45238i	−0.891124	−	0.453760i	$-0.850082\pi$
$401$	−16.7915	−	29.0838i	−0.838530	−	1.45238i	0.0525940	−	0.998616i	$-0.483251\pi$
$402$	0.287068	+	0.497217i	0.0143177	+	0.0247989i
$403$	−1.40809	+	2.43888i	−0.0701420	+	0.121489i
$404$	−2.62272	−	4.54268i	−0.130485	−	0.226007i
$405$	−3.31946	+	5.74947i	−0.164945	+	0.285693i
$406$	−8.52462			−0.423070
$407$	−40.0129			−1.98337
$408$	0.758994	−	1.31462i	0.0375758	−	0.0650832i
$409$	−5.01751	+	8.69058i	−0.248100	+	0.429721i	−0.962999	−	0.269507i	$-0.913139\pi$
$409$	−5.01751	+	8.69058i	−0.248100	+	0.429721i	0.714899	+	0.699228i	$0.246473\pi$
$410$	6.16759			0.304596
$411$	21.1522			1.04336
$412$	5.37213	−	9.30479i	0.264666	−	0.458414i
$413$	−5.55254	−	9.61728i	−0.273223	−	0.473236i
$414$	12.1444	−	21.0348i	0.596866	−	1.03380i
$415$	−0.414970	−	0.718749i	−0.0203701	−	0.0352820i
$416$	−10.7089	−	18.5484i	−0.525049	−	0.909411i
$417$	−7.02464			−0.343998
$418$	10.9016	−	16.9496i	0.533216	−	0.829033i
$419$	−10.0105			−0.489047			−0.244523	−	0.969643i	$-0.578632\pi$
$419$	−10.0105			−0.489047			−0.244523	+	0.969643i	$0.578632\pi$
$420$	1.53649	+	2.66128i	0.0749731	+	0.129857i
$421$	−18.7230	−	32.4293i	−0.912505	−	1.58051i	−0.810514	−	0.585720i	$-0.800812\pi$
$421$	−18.7230	−	32.4293i	−0.912505	−	1.58051i	−0.101991	−	0.994785i	$-0.532521\pi$
$422$	6.71907	−	11.6378i	0.327079	−	0.566518i
$423$	−8.41911	−	14.5823i	−0.409351	−	0.709017i
$424$	13.2034	−	22.8689i	0.641212	−	1.11061i
$425$	−0.205192			−0.00995328
$426$	29.0096			1.40552
$427$	−2.72714	+	4.72355i	−0.131976	+	0.228589i
$428$	9.89774	−	17.1434i	0.478425	−	0.828657i
$429$	−51.0536			−2.46489
$430$	−0.604785			−0.0291653
$431$	17.7805	−	30.7967i	0.856455	−	1.48342i	−0.0188341	−	0.999823i	$-0.505995\pi$
$431$	17.7805	−	30.7967i	0.856455	−	1.48342i	0.875289	−	0.483601i	$-0.160671\pi$
$432$	0.163244	+	0.282747i	0.00785407	+	0.0136037i
$433$	−8.73283	+	15.1257i	−0.419673	+	0.726895i	−0.995906	−	0.0903902i	$-0.971189\pi$
$433$	−8.73283	+	15.1257i	−0.419673	+	0.726895i	0.576233	+	0.817285i	$0.304522\pi$
$434$	0.328766	+	0.569439i	0.0157813	+	0.0273339i
$435$	−12.2246	−	21.1736i	−0.586124	−	1.01520i
$436$	−8.34960			−0.399873
$437$	32.2531	+	1.54826i	1.54288	+	0.0740632i
$438$	−17.3777			−0.830340
$439$	−7.12634	−	12.3432i	−0.340121	−	0.589108i	0.644334	−	0.764745i	$-0.277135\pi$
$439$	−7.12634	−	12.3432i	−0.340121	−	0.589108i	−0.984455	+	0.175637i	$0.943802\pi$
$440$	7.37864	+	12.7802i	0.351763	+	0.609271i
$441$	−1.82367	+	3.15869i	−0.0868415	+	0.150414i
$442$	0.355096	+	0.615044i	0.0168902	+	0.0292546i
$443$	4.19589	−	7.26750i	0.199353	−	0.345289i	−0.748966	−	0.662609i	$-0.769449\pi$
$443$	4.19589	−	7.26750i	0.199353	−	0.345289i	0.948319	+	0.317319i	$0.102783\pi$
$444$	23.9077			1.13461
$445$	−10.4588			−0.495796
$446$	5.70643	−	9.88383i	0.270207	−	0.468013i
$447$	1.74573	−	3.02370i	0.0825704	−	0.143016i
$448$	−5.39195			−0.254746
$449$	−17.4058			−0.821430			−0.410715	−	0.911764i	$-0.634721\pi$
$449$	−17.4058			−0.821430			−0.410715	+	0.911764i	$0.634721\pi$
$450$	1.63939	−	2.83950i	0.0772815	−	0.133856i
$451$	−17.6430	−	30.5587i	−0.830779	−	1.43895i
$452$	−8.65626	+	14.9931i	−0.407156	+	0.705215i
$453$	−8.60245	−	14.8999i	−0.404178	−	0.700057i
$454$	−11.3670	−	19.6882i	−0.533478	−	0.924012i
$455$	−3.85016			−0.180498
$456$	−17.4438	+	27.1212i	−0.816880	+	1.27007i
$457$	−8.32491			−0.389423			−0.194711	−	0.980861i	$-0.562377\pi$
$457$	−8.32491			−0.389423			−0.194711	+	0.980861i	$0.562377\pi$
$458$	3.64832	+	6.31907i	0.170475	+	0.295271i
$459$	0.171234	+	0.296586i	0.00799253	+	0.0138435i
$460$	−4.41470	+	7.64648i	−0.205836	+	0.356519i
$461$	10.3502	+	17.9270i	0.482056	+	0.834945i	0.999788	−	0.0205975i	$-0.00655684\pi$
$461$	10.3502	+	17.9270i	0.482056	+	0.834945i	−0.517732	+	0.855543i	$0.673224\pi$
$462$	−5.96009	+	10.3232i	−0.277288	+	0.480277i
$463$	38.7290			1.79989			0.899946	−	0.436002i	$-0.143606\pi$
$463$	38.7290			1.79989			0.899946	+	0.436002i	$0.143606\pi$
$464$	1.85501			0.0861168
$465$	−0.942921	+	1.63319i	−0.0437269	+	0.0757372i
$466$	−4.43722	+	7.68549i	−0.205550	+	0.356024i
$467$	−27.8673			−1.28954			−0.644772	−	0.764375i	$-0.723048\pi$
$467$	−27.8673			−1.28954			−0.644772	+	0.764375i	$0.723048\pi$
$468$	16.7376			0.773694
$469$	0.123859	−	0.214529i	0.00571925	−	0.00990604i
$470$	−2.07503	−	3.59406i	−0.0957141	−	0.165782i
$471$	22.6759	−	39.2758i	1.04485	−	1.80973i
$472$	15.9322	+	27.5953i	0.733338	+	1.27018i
$473$	1.73005	+	2.99654i	0.0795479	+	0.137781i
$474$	33.4298			1.53548
$475$	4.35389	+	0.209001i	0.199770	+	0.00958962i
$476$	−0.244567			−0.0112097
$477$	16.7833	+	29.0696i	0.768456	+	1.33101i
$478$	3.42649	+	5.93485i	0.156724	+	0.271454i
$479$	7.12617	−	12.3429i	0.325603	−	0.563961i	−0.656031	−	0.754734i	$-0.727766\pi$
$479$	7.12617	−	12.3429i	0.325603	−	0.563961i	0.981634	+	0.190773i	$0.0610994\pi$
$480$	−7.17119	−	12.4209i	−0.327318	−	0.566932i
$481$	−14.9771	+	25.9410i	−0.682895	+	1.18281i
$482$	4.13614			0.188396
$483$	−19.0994			−0.869051
$484$	9.20810	−	15.9489i	0.418550	−	0.724950i
$485$	−3.95529	+	6.85077i	−0.179601	+	0.311077i
$486$	19.8882			0.902145
$487$	−4.89811			−0.221954			−0.110977	−	0.993823i	$-0.535398\pi$
$487$	−4.89811			−0.221954			−0.110977	+	0.993823i	$0.535398\pi$
$488$	7.82512	−	13.5535i	0.354227	−	0.613538i
$489$	4.22763	+	7.32247i	0.191180	+	0.331134i
$490$	−0.449475	+	0.778513i	−0.0203052	+	0.0351696i
$491$	−14.0040	−	24.2556i	−0.631991	−	1.09464i	−0.987144	−	0.159832i	$-0.948905\pi$
$491$	−14.0040	−	24.2556i	−0.631991	−	1.09464i	0.355153	−	0.934808i	$-0.384429\pi$
$492$	10.5417	+	18.2588i	0.475257	+	0.823169i
$493$	1.94581			0.0876349
$494$	−6.90816	−	13.4120i	−0.310813	−	0.603436i
$495$	−18.7586			−0.843135
$496$	−0.0715416	−	0.123914i	−0.00321231	−	0.00556389i
$497$	−6.25825	−	10.8396i	−0.280721	−	0.486223i
$498$	−0.961781	+	1.66585i	−0.0430984	+	0.0746487i
$499$	8.22239	+	14.2416i	0.368085	+	0.637541i	0.989266	−	0.146125i	$-0.0466803\pi$
$499$	8.22239	+	14.2416i	0.368085	+	0.637541i	−0.621181	+	0.783667i	$0.713347\pi$
$500$	−0.595945	+	1.03221i	−0.0266515	+	0.0461617i
$501$	−36.5675			−1.63372
$502$	−13.8220			−0.616908
$503$	−1.53064	+	2.65115i	−0.0682479	+	0.118209i	−0.898130	−	0.439730i	$-0.855074\pi$
$503$	−1.53064	+	2.65115i	−0.0682479	+	0.118209i	0.829882	+	0.557939i	$0.188408\pi$
$504$	5.23275	−	9.06339i	0.233085	−	0.403715i
$505$	4.40094			0.195839
$506$	−34.2494			−1.52257
$507$	−2.35105	+	4.07214i	−0.104414	+	0.180850i
$508$	9.69033	+	16.7841i	0.429939	+	0.744676i
$509$	−4.44259	+	7.69478i	−0.196914	+	0.341065i	−0.947526	−	0.319678i	$-0.896425\pi$
$509$	−4.44259	+	7.69478i	−0.196914	+	0.341065i	0.750612	+	0.660743i	$0.229759\pi$
$510$	0.237788	+	0.411861i	0.0105294	+	0.0182375i
$511$	3.74890	+	6.49328i	0.165842	+	0.287246i
$512$	2.21078			0.0977035
$513$	−3.33125	−	6.46755i	−0.147078	−	0.285549i
$514$	18.4853			0.815352
$515$	4.50723	+	7.80675i	0.198612	+	0.344007i
$516$	−1.03370	−	1.79043i	−0.0455063	−	0.0788192i
$517$	−11.8717	+	20.5624i	−0.522117	+	0.904333i
$518$	3.49689	+	6.05680i	0.153645	+	0.266120i
$519$	2.75980	−	4.78011i	0.121142	−	0.209824i
$520$	11.0475			0.484463
$521$	23.3072			1.02111			0.510554	−	0.859845i	$-0.329440\pi$
$521$	23.3072			1.02111			0.510554	+	0.859845i	$0.329440\pi$
$522$	−15.5461	+	26.9267i	−0.680435	+	1.17855i
$523$	7.22339	−	12.5113i	0.315857	−	0.547080i	−0.663762	−	0.747944i	$-0.731041\pi$
$523$	7.22339	−	12.5113i	0.315857	−	0.547080i	0.979619	+	0.200863i	$0.0643747\pi$
$524$	−7.77280			−0.339556
$525$	−2.57824			−0.112524
$526$	2.18266	−	3.78048i	0.0951686	−	0.164837i
$527$	−0.0750433	−	0.129979i	−0.00326894	−	0.00566197i
$528$	1.29695	−	2.24639i	0.0564427	−	0.0977616i
$529$	−15.9385	−	27.6062i	−0.692977	−	1.20027i
$530$	4.13654	+	7.16469i	0.179680	+	0.311214i
$531$	−40.5041			−1.75773
$532$	5.18935	+	0.249106i	0.224987	+	0.0108001i
$533$	−26.4156			−1.14418
$534$	12.1203	+	20.9929i	0.524495	+	0.908452i
$535$	8.30424	+	14.3834i	0.359023	+	0.621847i
$536$	−0.355393	+	0.615559i	−0.0153506	+	0.0265881i
$537$	−11.7696	−	20.3856i	−0.507897	−	0.879703i
$538$	−14.6459	+	25.3674i	−0.631430	+	1.09367i
$539$	5.14308			0.221528
$540$	1.98928			0.0856050
$541$	−3.50768	+	6.07549i	−0.150807	+	0.261206i	−0.931524	−	0.363679i	$-0.881521\pi$
$541$	−3.50768	+	6.07549i	−0.150807	+	0.261206i	0.780717	+	0.624884i	$0.214854\pi$
$542$	−9.04932	+	15.6739i	−0.388701	+	0.673251i
$543$	−4.20679			−0.180531
$544$	1.14145			0.0489394
$545$	3.50267	−	6.06681i	0.150038	−	0.259873i
$546$	4.46178	+	7.72804i	0.190947	+	0.330729i
$547$	5.91376	−	10.2429i	0.252854	−	0.437956i	−0.711456	−	0.702730i	$-0.751964\pi$
$547$	5.91376	−	10.2429i	0.252854	−	0.437956i	0.964310	+	0.264774i	$0.0852974\pi$
$548$	4.88920	+	8.46834i	0.208856	+	0.361750i
$549$	9.94683	+	17.2284i	0.424520	+	0.735291i
$550$	−4.62337			−0.197141
$551$	−41.2873	−	1.98193i	−1.75890	−	0.0844330i
$552$	54.8027			2.33256
$553$	−7.21180	−	12.4912i	−0.306677	−	0.531180i
$554$	2.79409	+	4.83951i	0.118710	+	0.205611i
$555$	−10.0293	+	17.3713i	−0.425721	+	0.737370i
$556$	−1.62370	−	2.81233i	−0.0688603	−	0.119270i
$557$	0.370894	−	0.642408i	0.0157153	−	0.0272197i	−0.858061	−	0.513548i	$-0.828331\pi$
$557$	0.370894	−	0.642408i	0.0157153	−	0.0272197i	0.873776	+	0.486328i	$0.161664\pi$
$558$	2.39824			0.101526
$559$	2.59027			0.109557
$560$	0.0978087	−	0.169410i	0.00413317	−	0.00715886i
$561$	1.36044	−	2.35634i	0.0574377	−	0.0994849i
$562$	0.757673			0.0319605
$563$	0.676831			0.0285250			0.0142625	−	0.999898i	$-0.495460\pi$
$563$	0.676831			0.0285250			0.0142625	+	0.999898i	$0.495460\pi$
$564$	7.09333	−	12.2860i	0.298683	−	0.517334i
$565$	−7.26263	−	12.5793i	−0.305541	−	0.529213i
$566$	−4.60012	+	7.96765i	−0.193358	+	0.334905i
$567$	−3.31946	−	5.74947i	−0.139404	−	0.241455i
$568$	17.9571	+	31.1026i	0.753463	+	1.30504i
$569$	−20.2579			−0.849254			−0.424627	−	0.905368i	$-0.639595\pi$
$569$	−20.2579			−0.849254			−0.424627	+	0.905368i	$0.639595\pi$
$570$	−4.62602	−	8.98131i	−0.193763	−	0.376186i
$571$	−33.4378			−1.39933			−0.699664	−	0.714472i	$-0.746667\pi$
$571$	−33.4378			−1.39933			−0.699664	+	0.714472i	$0.746667\pi$
$572$	−11.8007	−	20.4395i	−0.493413	−	0.854616i
$573$	13.3606	+	23.1413i	0.558149	+	0.966742i
$574$	−3.08380	+	5.34129i	−0.128715	+	0.222941i
$575$	−3.70395	−	6.41543i	−0.154465	−	0.267542i
$576$	−9.83315	+	17.0315i	−0.409715	+	0.709646i
$577$	−30.1620			−1.25566			−0.627831	−	0.778350i	$-0.716057\pi$
$577$	−30.1620			−1.25566			−0.627831	+	0.778350i	$0.716057\pi$
$578$	15.2443			0.634079
$579$	22.1094	−	38.2946i	0.918836	−	1.59147i
$580$	5.65127	−	9.78829i	0.234656	−	0.406437i
$581$	0.829940			0.0344317
$582$	18.3344			0.759987
$583$	23.6660	−	40.9907i	0.980145	−	1.69766i
$584$	−10.7569	−	18.6315i	−0.445123	−	0.770976i
$585$	−7.02144	+	12.1615i	−0.290301	+	0.502816i
$586$	9.55116	+	16.5431i	0.394555	+	0.683389i
$587$	18.1720	+	31.4749i	0.750041	+	1.29911i	0.947802	+	0.318858i	$0.103299\pi$
$587$	18.1720	+	31.4749i	0.750041	+	1.29911i	−0.197762	+	0.980250i	$0.563367\pi$
$588$	−3.07298			−0.126728
$589$	1.45992	+	2.83440i	0.0601550	+	0.116789i
$590$	−9.98291			−0.410990
$591$	21.0950	+	36.5376i	0.867733	+	1.50296i
$592$	−0.760947	−	1.31800i	−0.0312747	−	0.0541694i
$593$	12.1308	−	21.0112i	0.498152	−	0.862825i	−0.501846	−	0.864957i	$-0.667345\pi$
$593$	12.1308	−	21.0112i	0.498152	−	0.862825i	0.999998	+	0.00213255i	$0.000678814\pi$
$594$	3.85823	+	6.68265i	0.158305	+	0.274192i
$595$	0.102596	−	0.177702i	0.00420603	−	0.00728506i
$596$	1.61406			0.0661146
$597$	63.2665			2.58933
$598$	−12.8197	+	22.2044i	−0.524238	+	0.908007i
$599$	−1.79859	+	3.11525i	−0.0734884	+	0.127286i	−0.900428	−	0.435005i	$-0.856747\pi$
$599$	−1.79859	+	3.11525i	−0.0734884	+	0.127286i	0.826940	+	0.562291i	$0.190080\pi$
$600$	7.39788			0.302017
$601$	−23.7977			−0.970728			−0.485364	−	0.874312i	$-0.661313\pi$
$601$	−23.7977			−0.970728			−0.485364	+	0.874312i	$0.661313\pi$
$602$	0.302393	−	0.523760i	0.0123246	−	0.0213468i
$603$	−0.451755	−	0.782462i	−0.0183969	−	0.0318643i
$604$	3.97680	−	6.88803i	0.161814	−	0.280270i
$605$	7.72563	+	13.3812i	0.314092	+	0.544022i
$606$	−5.10005	−	8.83354i	−0.207175	−	0.358838i
$607$	29.2133			1.18573			0.592865	−	0.805302i	$-0.297997\pi$
$607$	29.2133			1.18573			0.592865	+	0.805302i	$0.297997\pi$
$608$	−24.2200	−	1.16264i	−0.982250	−	0.0471512i
$609$	24.4492			0.990730
$610$	2.45156	+	4.24623i	0.0992609	+	0.171925i
$611$	8.88728	+	15.3932i	0.359541	+	0.622743i
$612$	−0.446009	+	0.772511i	−0.0180289	+	0.0312269i
$613$	−4.20111	−	7.27653i	−0.169681	−	0.293896i	0.768627	−	0.639698i	$-0.220940\pi$
$613$	−4.20111	−	7.27653i	−0.169681	−	0.293896i	−0.938308	+	0.345801i	$0.887607\pi$
$614$	−3.45205	+	5.97913i	−0.139314	+	0.241298i
$615$	−17.6891			−0.713291
$616$	−14.7573			−0.594588
$617$	11.9907	−	20.7685i	0.482727	−	0.836107i	−0.517077	−	0.855939i	$-0.672980\pi$
$617$	11.9907	−	20.7685i	0.482727	−	0.836107i	0.999803	+	0.0198319i	$0.00631311\pi$
$618$	10.4465	−	18.0938i	0.420218	−	0.727839i
$619$	−31.7596			−1.27652			−0.638262	−	0.769819i	$-0.720347\pi$
$619$	−31.7596			−1.27652			−0.638262	+	0.769819i	$0.720347\pi$
$620$	−0.871801			−0.0350124
$621$	−6.18193	+	10.7074i	−0.248073	+	0.429674i
$622$	−12.5711	−	21.7738i	−0.504056	−	0.873050i
$623$	5.22941	−	9.05760i	0.209512	−	0.362885i
$624$	−0.970914	−	1.68167i	−0.0388677	−	0.0673207i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−25.6245			−1.02416
$627$	−31.2666	+	48.6126i	−1.24867	+	1.94140i
$628$	20.9656			0.836617
$629$	−0.798194	−	1.38251i	−0.0318261	−	0.0551244i
$630$	1.63939	+	2.83950i	0.0653148	+	0.113129i
$631$	15.1261	−	26.1992i	0.602162	−	1.04298i	−0.390331	−	0.920675i	$-0.627639\pi$
$631$	15.1261	−	26.1992i	0.602162	−	1.04298i	0.992493	−	0.122301i	$-0.0390272\pi$
$632$	20.6932	+	35.8416i	0.823130	+	1.42570i
$633$	−19.2707	+	33.3779i	−0.765943	+	1.32665i
$634$	25.1255			0.997860
$635$	−16.2604			−0.645276
$636$	−14.1404	+	24.4919i	−0.560704	+	0.971167i
$637$	1.92508	−	3.33434i	0.0762745	−	0.132111i
$638$	43.8428			1.73575
$639$	−45.6520			−1.80596
$640$	3.13930	−	5.43743i	0.124092	−	0.214933i
$641$	10.9228	+	18.9188i	0.431424	+	0.747248i	0.996996	−	0.0774504i	$-0.0246779\pi$
$641$	10.9228	+	18.9188i	0.431424	+	0.747248i	−0.565572	+	0.824699i	$0.691345\pi$
$642$	19.2468	−	33.3365i	0.759611	−	1.31569i
$643$	−1.84990	−	3.20412i	−0.0729528	−	0.126358i	0.827241	−	0.561847i	$-0.189909\pi$
$643$	−1.84990	−	3.20412i	−0.0729528	−	0.126358i	−0.900194	+	0.435489i	$0.856576\pi$
$644$	−4.41470	−	7.64648i	−0.173964	−	0.301314i
$645$	1.73456			0.0682984
$646$	0.803106	+	0.0385517i	0.0315978	+	0.00151680i
$647$	−7.45842			−0.293221			−0.146610	−	0.989194i	$-0.546836\pi$
$647$	−7.45842			−0.293221			−0.146610	+	0.989194i	$0.546836\pi$
$648$	9.52467	+	16.4972i	0.374164	+	0.648072i
$649$	28.5572	+	49.4625i	1.12097	+	1.94157i
$650$	−1.73055	+	2.99740i	−0.0678778	+	0.117568i
$651$	−0.942921	−	1.63319i	−0.0369560	−	0.0640096i
$652$	−1.95438	+	3.38509i	−0.0765394	+	0.132570i
$653$	11.0195			0.431228			0.215614	−	0.976479i	$-0.430825\pi$
$653$	11.0195			0.431228			0.215614	+	0.976479i	$0.430825\pi$
$654$	−16.2364			−0.634892
$655$	3.26070	−	5.64770i	0.127406	−	0.220674i
$656$	0.671054	−	1.16230i	0.0262003	−	0.0453802i
$657$	27.3471			1.06691
$658$	4.15006			0.161786
$659$	−6.22758	+	10.7865i	−0.242592	+	0.420182i	−0.961452	−	0.274973i	$-0.911331\pi$
$659$	−6.22758	+	10.7865i	−0.242592	+	0.420182i	0.718860	+	0.695155i	$0.244664\pi$
$660$	−7.90230	−	13.6872i	−0.307597	−	0.532773i
$661$	−2.02257	+	3.50320i	−0.0786690	+	0.136259i	−0.902676	−	0.430321i	$-0.858400\pi$
$661$	−2.02257	+	3.50320i	−0.0786690	+	0.136259i	0.824007	+	0.566580i	$0.191734\pi$
$662$	5.25366	+	9.09961i	0.204189	+	0.353666i
$663$	−1.01844	−	1.76398i	−0.0395528	−	0.0685075i
$664$	−2.38139			−0.0924157
$665$	−2.35794	+	3.66608i	−0.0914371	+	0.142164i
$666$	25.5088			0.988444
$667$	35.1241	+	60.8367i	1.36001	+	2.35560i
$668$	−8.45235	−	14.6399i	−0.327031	−	0.566435i
$669$	−16.3664	+	28.3475i	−0.632762	+	1.09598i
$670$	−0.111343	−	0.192851i	−0.00430154	−	0.00745048i
$671$	14.0259	−	24.2936i	0.541464	−	0.937844i
$672$	14.3424			0.553269
$673$	−42.5842			−1.64150			−0.820750	−	0.571288i	$-0.806444\pi$
$673$	−42.5842			−1.64150			−0.820750	+	0.571288i	$0.806444\pi$
$674$	−8.18429	+	14.1756i	−0.315247	+	0.546024i
$675$	−0.834506	+	1.44541i	−0.0321202	+	0.0556337i
$676$	−2.17372			−0.0836048
$677$	5.25248			0.201869			0.100935	−	0.994893i	$-0.467817\pi$
$677$	5.25248			0.201869			0.100935	+	0.994893i	$0.467817\pi$
$678$	−16.8327	+	29.1551i	−0.646455	+	1.11969i
$679$	−3.95529	−	6.85077i	−0.151790	−	0.262908i
$680$	−0.294384	+	0.509888i	−0.0112891	+	0.0195533i
$681$	32.6012	+	56.4669i	1.24928	+	2.16382i
$682$	−1.69087	−	2.92867i	−0.0647467	−	0.112144i
$683$	−13.3623			−0.511293			−0.255647	−	0.966770i	$-0.582288\pi$
$683$	−13.3623			−0.511293			−0.255647	+	0.966770i	$0.582288\pi$
$684$	10.2505	−	15.9373i	0.391939	−	0.609377i
$685$	−8.20411			−0.313463
$686$	−0.449475	−	0.778513i	−0.0171610	−	0.0297238i
$687$	−10.4636	−	18.1235i	−0.399212	−	0.691455i
$688$	−0.0658027	+	0.113974i	−0.00250870	+	0.00434520i
$689$	−17.7166	−	30.6861i	−0.674949	−	1.16905i
$690$	−8.58468	+	14.8691i	−0.326813	+	0.566057i
$691$	0.0588850			0.00224009			0.00112005	−	0.999999i	$-0.499643\pi$
$691$	0.0588850			0.00224009			0.00112005	+	0.999999i	$0.499643\pi$
$692$	2.55164			0.0969988
$693$	9.37929	−	16.2454i	0.356290	−	0.617112i
$694$	7.87798	−	13.6451i	0.299044	−	0.517960i
$695$	2.72458			0.103349
$696$	−70.1531			−2.65915
$697$	0.703901	−	1.21919i	0.0266621	−	0.0461802i
$698$	−6.29290	−	10.8996i	−0.238190	−	0.412557i
$699$	12.7262	−	22.0425i	0.481351	−	0.833724i
$700$	−0.595945	−	1.03221i	−0.0225246	−	0.0390138i
$701$	−10.2350	−	17.7276i	−0.386572	−	0.669562i	0.605414	−	0.795911i	$-0.293008\pi$
$701$	−10.2350	−	17.7276i	−0.386572	−	0.669562i	−0.991986	+	0.126349i	$0.959674\pi$
$702$	5.77662			0.218025
$703$	15.5284	+	30.1479i	0.585663	+	1.13705i
$704$	27.7312			1.04516
$705$	5.95133	+	10.3080i	0.224140	+	0.388222i
$706$	10.2349	+	17.7273i	0.385194	+	0.667175i
$707$	−2.20047	+	3.81132i	−0.0827571	+	0.143340i
$708$	−17.0629	−	29.5538i	−0.641262	−	1.11070i
$709$	−4.43682	+	7.68480i	−0.166628	+	0.288609i	−0.937232	−	0.348705i	$-0.886621\pi$
$709$	−4.43682	+	7.68480i	−0.166628	+	0.288609i	0.770604	+	0.637314i	$0.219955\pi$
$710$	−11.2517			−0.422269
$711$	−52.6079			−1.97295
$712$	−15.0050	+	25.9894i	−0.562336	+	0.973994i
$713$	2.70923	−	4.69253i	0.101462	−	0.175736i
$714$	−0.475576			−0.0177980
$715$	19.8017			0.740541
$716$	5.44095	−	9.42401i	0.203338	−	0.352192i
$717$	−9.82738	−	17.0215i	−0.367010	−	0.635681i
$718$	−10.1436	+	17.5692i	−0.378556	+	0.655678i
$719$	19.7370	+	34.1854i	0.736064	+	1.27490i	0.954255	+	0.298994i	$0.0966511\pi$
$719$	19.7370	+	34.1854i	0.736064	+	1.27490i	−0.218191	+	0.975906i	$0.570016\pi$
$720$	−0.356742	−	0.617895i	−0.0132950	−	0.0230276i
$721$	−9.01446			−0.335716
$722$	−17.0015	−	1.63603i	−0.632730	−	0.0608866i
$723$	−11.8627			−0.441179
$724$	−0.972373	−	1.68420i	−0.0361380	−	0.0625928i
$725$	4.74144	+	8.21241i	0.176092	+	0.305001i
$726$	17.9058	−	31.0137i	0.664546	−	1.15103i
$727$	3.33774	+	5.78113i	0.123790	+	0.214410i	0.921259	−	0.388949i	$-0.127162\pi$
$727$	3.33774	+	5.78113i	0.123790	+	0.214410i	−0.797469	+	0.603359i	$0.793828\pi$
$728$	−5.52373	+	9.56738i	−0.204723	+	0.354591i
$729$	−37.1238			−1.37495
$730$	6.74014			0.249464
$731$	−0.0690235	+	0.119552i	−0.00255293	+	0.00442180i
$732$	−8.38047	+	14.5154i	−0.309751	+	0.536504i
$733$	36.8621			1.36153			0.680767	−	0.732500i	$-0.261647\pi$
$733$	36.8621			1.36153			0.680767	+	0.732500i	$0.261647\pi$
$734$	1.59835			0.0589963
$735$	1.28912	−	2.23283i	0.0475500	−	0.0823590i
$736$	20.6045	+	35.6880i	0.759492	+	1.31548i
$737$	−0.637014	+	1.10334i	−0.0234647	+	0.0406421i
$738$	11.2477	+	19.4815i	0.414032	+	0.717125i
$739$	−6.04188	−	10.4648i	−0.222254	−	0.384955i	0.733238	−	0.679972i	$-0.238008\pi$
$739$	−6.04188	−	10.4648i	−0.222254	−	0.384955i	−0.955492	+	0.295017i	$0.904675\pi$
$740$	−9.27286			−0.340877
$741$	19.8131	+	38.4666i	0.727851	+	1.41310i
$742$	−8.27307			−0.303714
$743$	23.5257	+	40.7476i	0.863073	+	1.49489i	0.868948	+	0.494903i	$0.164797\pi$
$743$	23.5257	+	40.7476i	0.863073	+	1.49489i	−0.00587526	+	0.999983i	$0.501870\pi$
$744$	2.70557	+	4.68618i	0.0991909	+	0.171804i
$745$	−0.677102	+	1.17277i	−0.0248071	+	0.0429671i
$746$	−6.75020	−	11.6917i	−0.247142	−	0.428063i
$747$	1.51354	−	2.62153i	0.0553775	−	0.0959166i
$748$	1.25783			0.0459906
$749$	−16.6085			−0.606860
$750$	−1.15886	+	2.00720i	−0.0423154	+	0.0732925i
$751$	−17.9734	+	31.1308i	−0.655858	+	1.13598i	0.325820	+	0.945432i	$0.394360\pi$
$751$	−17.9734	+	31.1308i	−0.655858	+	1.13598i	−0.981678	+	0.190547i	$0.938974\pi$
$752$	−0.903081			−0.0329320
$753$	39.6425			1.44465
$754$	16.4106	−	28.4240i	0.597638	−	1.03514i
$755$	3.33655	+	5.77908i	0.121430	+	0.210322i
$756$	−0.994640	+	1.72277i	−0.0361747	+	0.0626564i
$757$	2.42069	+	4.19276i	0.0879816	+	0.152389i	0.906658	−	0.421867i	$-0.138625\pi$
$757$	2.42069	+	4.19276i	0.0879816	+	0.152389i	−0.818676	+	0.574255i	$0.805292\pi$
$758$	−8.32197	−	14.4141i	−0.302268	−	0.523543i
$759$	98.2296			3.56551
$760$	6.76576	−	10.5192i	0.245420	−	0.381573i
$761$	−7.79923			−0.282722			−0.141361	−	0.989958i	$-0.545148\pi$
$761$	−7.79923			−0.282722			−0.141361	+	0.989958i	$0.545148\pi$
$762$	18.8435	+	32.6379i	0.682628	+	1.18235i
$763$	3.50267	+	6.06681i	0.126805	+	0.219633i
$764$	−6.17646	+	10.6979i	−0.223456	+	0.387038i
$765$	−0.374203	−	0.648139i	−0.0135293	−	0.0234335i
$766$	−6.34629	+	10.9921i	−0.229301	+	0.397161i
$767$	42.7564			1.54384
$768$	−42.3555			−1.52837
$769$	5.52927	−	9.57697i	0.199390	−	0.345354i	−0.748940	−	0.662637i	$-0.769437\pi$
$769$	5.52927	−	9.57697i	0.199390	−	0.345354i	0.948331	+	0.317283i	$0.102770\pi$
$770$	2.31168	−	4.00395i	0.0833073	−	0.144292i
$771$	−53.0171			−1.90936
$772$	20.4418			0.735717
$773$	26.3084	−	45.5676i	0.946249	−	1.63895i	0.193017	−	0.981195i	$-0.438173\pi$
$773$	26.3084	−	45.5676i	0.946249	−	1.63895i	0.753232	−	0.657756i	$-0.228494\pi$
$774$	−1.10293	−	1.91033i	−0.0396440	−	0.0686654i
$775$	0.365722	−	0.633449i	0.0131371	−	0.0227542i
$776$	11.3491	+	19.6572i	0.407409	+	0.705653i
$777$	−10.0293	−	17.3713i	−0.359800	−	0.623192i
$778$	−27.3280			−0.979756
$779$	−16.1776	+	25.1525i	−0.579622	+	0.901183i
$780$	−11.8315			−0.423635
$781$	32.1867	+	55.7489i	1.15173	+	1.99485i
$782$	−0.683221	−	1.18337i	−0.0244319	−	0.0423173i
$783$	7.91351	−	13.7066i	0.282806	−	0.489834i
$784$	0.0978087	+	0.169410i	0.00349317	+	0.00605034i
$785$	−8.79509	+	15.2335i	−0.313910	+	0.543708i
$786$	−15.1147			−0.539125
$787$	−27.5014			−0.980320			−0.490160	−	0.871633i	$-0.663062\pi$
$787$	−27.5014			−0.980320			−0.490160	+	0.871633i	$0.663062\pi$
$788$	−9.75196	+	16.8909i	−0.347399	+	0.601713i
$789$	−6.26001	+	10.8427i	−0.222862	+	0.386009i
$790$	−12.9661			−0.461313
$791$	14.5253			0.516459
$792$	−26.9124	+	46.6137i	−0.956292	+	1.65635i
$793$	−10.4999	−	18.1864i	−0.372864	−	0.645819i
$794$	−9.32523	+	16.1518i	−0.330940	+	0.573205i
$795$	−11.8639	−	20.5488i	−0.420767	−	0.728791i
$796$	14.6237	+	25.3289i	0.518322	+	0.897760i
$797$	6.17377			0.218686			0.109343	−	0.994004i	$-0.465125\pi$
$797$	6.17377			0.218686			0.109343	+	0.994004i	$0.465125\pi$
$798$	10.0910	+	0.484404i	0.357219	+	0.0171477i
$799$	−0.947285			−0.0335125
$800$	2.78142	+	4.81756i	0.0983381	+	0.170327i
$801$	−19.0735	−	33.0362i	−0.673927	−	1.16728i
$802$	15.0947	−	26.1449i	0.533014	−	0.923207i
$803$	−19.2809	−	33.3955i	−0.680408	−	1.17850i
$804$	0.380615	−	0.659245i	0.0134233	−	0.0232498i
$805$	7.40790			0.261094
$806$	−2.53160			−0.0891719
$807$	42.0054	−	72.7555i	1.47866	−	2.56111i
$808$	6.31391	−	10.9360i	0.222122	−	0.384727i
$809$	19.5098			0.685929			0.342965	−	0.939348i	$-0.388569\pi$
$809$	19.5098			0.685929			0.342965	+	0.939348i	$0.388569\pi$
$810$	−5.96804			−0.209696
$811$	−17.6289	+	30.5342i	−0.619035	+	1.07220i	0.370627	+	0.928782i	$0.379143\pi$
$811$	−17.6289	+	30.5342i	−0.619035	+	1.07220i	−0.989662	+	0.143418i	$0.954191\pi$
$812$	5.65127	+	9.78829i	0.198321	+	0.343502i
$813$	25.9540	−	44.9537i	0.910247	−	1.57659i
$814$	−17.9848	−	31.1506i	−0.630367	−	1.09183i
$815$	−1.63973	−	2.84010i	−0.0574373	−	0.0994843i
$816$	0.103489			0.00362282
$817$	1.58635	−	2.46642i	0.0554994	−	0.0862892i
$818$	−9.02097			−0.315411
$819$	−7.02144	−	12.1615i	−0.245349	−	0.424957i
$820$	−4.08871	−	7.08186i	−0.142784	−	0.247309i
$821$	24.7877	−	42.9336i	0.865098	−	1.49839i	−0.00185115	−	0.999998i	$-0.500589\pi$
$821$	24.7877	−	42.9336i	0.865098	−	1.49839i	0.866949	−	0.498396i	$-0.166077\pi$
$822$	9.50738	+	16.4673i	0.331608	+	0.574362i
$823$	4.12266	−	7.14065i	0.143707	−	0.248907i	−0.785183	−	0.619264i	$-0.787431\pi$
$823$	4.12266	−	7.14065i	0.143707	−	0.248907i	0.928890	+	0.370356i	$0.120764\pi$
$824$	25.8656			0.901072
$825$	13.2601			0.461658
$826$	4.99145	−	8.64545i	0.173675	−	0.300814i
$827$	−15.0609	+	26.0863i	−0.523720	+	0.907110i	0.475898	+	0.879500i	$0.342123\pi$
$827$	−15.0609	+	26.0863i	−0.523720	+	0.907110i	−0.999619	+	0.0276099i	$0.991210\pi$
$828$	−32.2039			−1.11916
$829$	−10.2027			−0.354356			−0.177178	−	0.984179i	$-0.556697\pi$
$829$	−10.2027			−0.354356			−0.177178	+	0.984179i	$0.556697\pi$
$830$	0.373037	−	0.646119i	0.0129483	−	0.0224271i
$831$	−8.01364	−	13.8800i	−0.277990	−	0.481493i
$832$	10.3799	−	17.9786i	0.359860	−	0.623296i
$833$	0.102596	+	0.177702i	0.00355474	+	0.00615700i
$834$	−3.15740	−	5.46877i	−0.109332	−	0.189368i
$835$	14.1831			0.490826
$836$	−26.6893	−	1.28117i	−0.923067	−	0.0443103i
$837$	−1.22079			−0.0421966
$838$	−4.49948	−	7.79334i	−0.155432	−	0.269216i
$839$	1.84232	+	3.19100i	0.0636041	+	0.110166i	0.896074	−	0.443905i	$-0.146407\pi$
$839$	1.84232	+	3.19100i	0.0636041	+	0.110166i	−0.832470	+	0.554070i	$0.813074\pi$
$840$	−3.69894	+	6.40675i	−0.127626	+	0.221054i
$841$	−30.4624	−	52.7625i	−1.05043	−	1.81940i
$842$	16.8311	−	29.1523i	0.580037	−	1.00465i
$843$	−2.17305			−0.0748440
$844$	−17.8172			−0.613295
$845$	0.911881	−	1.57942i	0.0313697	−	0.0543338i
$846$	7.56836	−	13.1088i	0.260205	−	0.450689i
$847$	−15.4513			−0.530912
$848$	1.80028			0.0618217
$849$	13.1935	−	22.8517i	0.452798	−	0.784269i
$850$	−0.0922287	−	0.159745i	−0.00316342	−	0.00547920i
$851$	28.8166	−	49.9118i	0.987819	−	1.71095i
$852$	−19.2315	−	33.3099i	−0.658860	−	1.14118i
$853$	−5.18112	−	8.97396i	−0.177398	−	0.307263i	0.763590	−	0.645701i	$-0.223435\pi$
$853$	−5.18112	−	8.97396i	−0.177398	−	0.307263i	−0.940989	+	0.338438i	$0.890101\pi$
$854$	−4.90313			−0.167782
$855$	7.27989	+	14.1337i	0.248967	+	0.483364i
$856$	47.6555			1.62883
$857$	−16.5120	−	28.5996i	−0.564038	−	0.976943i	−0.997138	−	0.0755969i	$-0.975914\pi$
$857$	−16.5120	−	28.5996i	−0.564038	−	0.976943i	0.433100	−	0.901346i	$-0.357420\pi$
$858$	−22.9473	−	39.7459i	−0.783408	−	1.35690i
$859$	11.6235	−	20.1326i	0.396590	−	0.686914i	−0.596713	−	0.802455i	$-0.703527\pi$
$859$	11.6235	−	20.1326i	0.396590	−	0.686914i	0.993303	+	0.115541i	$0.0368602\pi$
$860$	0.400934	+	0.694437i	0.0136717	+	0.0236801i
$861$	8.84453	−	15.3192i	0.301421	−	0.522076i
$862$	31.9675			1.08882
$863$	−12.0873			−0.411456			−0.205728	−	0.978609i	$-0.565956\pi$
$863$	−12.0873			−0.411456			−0.205728	+	0.978609i	$0.565956\pi$
$864$	4.64223	−	8.04057i	0.157932	−	0.273546i
$865$	−1.07042	+	1.85402i	−0.0363953	+	0.0630385i
$866$	−15.7007			−0.533533
$867$	−43.7216			−1.48486
$868$	0.435901	−	0.755002i	0.0147954	−	0.0256264i
$869$	37.0909	+	64.2433i	1.25822	+	2.17930i
$870$	10.9893	−	19.0340i	0.372571	−	0.645313i
$871$	0.476876	+	0.825973i	0.0161583	+	0.0279870i
$872$	−10.0504	−	17.4078i	−0.340349	−	0.589502i
$873$	−28.8526			−0.976513
$874$	13.2916	+	25.8054i	0.449596	+	0.872880i
$875$	1.00000			0.0338062
$876$	11.5203	+	19.9538i	0.389235	+	0.674175i
$877$	−11.1628	−	19.3345i	−0.376941	−	0.652881i	0.613674	−	0.789559i	$-0.289691\pi$
$877$	−11.1628	−	19.3345i	−0.376941	−	0.652881i	−0.990616	+	0.136678i	$0.956357\pi$
$878$	6.40621	−	11.0959i	0.216199	−	0.374468i
$879$	−27.3933	−	47.4467i	−0.923954	−	1.60034i
$880$	−0.503038	+	0.871287i	−0.0169574	+	0.0293711i
$881$	32.3319			1.08929			0.544644	−	0.838667i	$-0.316665\pi$
$881$	32.3319			1.08929			0.544644	+	0.838667i	$0.316665\pi$
$882$	−3.27878			−0.110402
$883$	5.72275	−	9.91209i	0.192586	−	0.333568i	−0.753521	−	0.657424i	$-0.771646\pi$
$883$	5.72275	−	9.91209i	0.192586	−	0.333568i	0.946106	+	0.323856i	$0.104979\pi$
$884$	0.470811	−	0.815468i	0.0158351	−	0.0274272i
$885$	28.6316			0.962441
$886$	7.54379			0.253439
$887$	−3.53178	+	6.11722i	−0.118586	+	0.205396i	−0.919207	−	0.393774i	$-0.871169\pi$
$887$	−3.53178	+	6.11722i	−0.118586	+	0.205396i	0.800622	+	0.599170i	$0.204503\pi$
$888$	28.7776	+	49.8443i	0.965713	+	1.67266i
$889$	8.13022	−	14.0820i	0.272679	−	0.472293i
$890$	−4.70097	−	8.14233i	−0.157577	−	0.272931i
$891$	17.0722	+	29.5700i	0.571941	+	0.990631i
$892$	−15.1320			−0.506656
$893$	20.1000	+	0.964867i	0.672622	+	0.0322881i
$894$	3.13865			0.104972
$895$	4.56498	+	7.90677i	0.152590	+	0.264294i
$896$	3.13930	+	5.43743i	0.104877	+	0.181652i
$897$	36.7678	−	63.6838i	1.22764	−	2.12634i
$898$	−7.82346	−	13.5506i	−0.261072	−	0.452190i
$899$	−3.46809	+	6.00692i	−0.115667	+	0.200342i
$900$	−4.34723			−0.144908
$901$	1.88839			0.0629115
$902$	15.8602	−	27.4707i	0.528087	−	0.914674i
$903$	−0.867282	+	1.50218i	−0.0288613	+	0.0499893i
$904$	−41.6780			−1.38619
$905$	1.63165			0.0542378
$906$	7.73316	−	13.3942i	0.256917	−	0.444994i
$907$	−23.6891	−	41.0307i	−0.786584	−	1.36240i	−0.928048	−	0.372460i	$-0.878514\pi$
$907$	−23.6891	−	41.0307i	−0.786584	−	1.36240i	0.141464	−	0.989943i	$-0.454819\pi$
$908$	−15.0711	+	26.1040i	−0.500153	+	0.866291i
$909$	8.02586	+	13.9012i	0.266201	+	0.461074i
$910$	−1.73055	−	2.99740i	−0.0573672	−	0.0993629i
$911$	−3.86212			−0.127958			−0.0639789	−	0.997951i	$-0.520379\pi$
$911$	−3.86212			−0.127958			−0.0639789	+	0.997951i	$0.520379\pi$
$912$	−2.19588	−	0.105409i	−0.0727128	−	0.00349045i
$913$	−4.26845			−0.141265
$914$	−3.74184	−	6.48105i	−0.123769	−	0.214374i
$915$	−7.03124	−	12.1785i	−0.232446	−	0.402608i
$916$	4.83719	−	8.37827i	0.159825	−	0.276826i
$917$	3.26070	+	5.64770i	0.107678	+	0.186504i
$918$	−0.153931	+	0.266616i	−0.00508047	+	0.00879964i
$919$	−40.1748			−1.32524			−0.662622	−	0.748954i	$-0.730556\pi$
$919$	−40.1748			−1.32524			−0.662622	+	0.748954i	$0.730556\pi$
$920$	−21.2558			−0.700784
$921$	9.90071	−	17.1485i	0.326240	−	0.565063i
$922$	−9.30429	+	16.1155i	−0.306420	+	0.530736i
$923$	48.1906			1.58621
$924$	15.8046			0.519933
$925$	3.88998	−	6.73764i	0.127902	−	0.221532i
$926$	17.4077	+	30.1511i	0.572053	+	0.990825i
$927$	−16.4394	+	28.4739i	−0.539942	+	0.935206i
$928$	−26.3759	−	45.6843i	−0.865830	−	1.49966i
$929$	−17.8846	−	30.9770i	−0.586774	−	1.01632i	−0.994652	−	0.103285i	$-0.967065\pi$
$929$	−17.8846	−	30.9770i	−0.586774	−	1.01632i	0.407878	−	0.913036i	$-0.366269\pi$
$930$	−1.69528			−0.0555903
$931$	−1.99594	−	3.87508i	−0.0654144	−	0.127000i
$932$	11.7664			0.385420
$933$	36.0548	+	62.4487i	1.18038	+	2.04448i
$934$	−12.5256	−	21.6950i	−0.409851	−	0.709883i
$935$	−0.527660	+	0.913934i	−0.0172563	+	0.0298888i
$936$	20.1469	+	34.8955i	0.658523	+	1.14060i
$937$	−2.42816	+	4.20569i	−0.0793245	+	0.137394i	−0.902959	−	0.429727i	$-0.858610\pi$
$937$	−2.42816	+	4.20569i	−0.0793245	+	0.137394i	0.823634	+	0.567121i	$0.191943\pi$
$938$	0.222685			0.00727092
$939$	73.4927			2.39834
$940$	−2.75122	+	4.76526i	−0.0897350	+	0.155426i
$941$	−22.8392	+	39.5587i	−0.744537	+	1.28958i	0.205874	+	0.978578i	$0.433996\pi$
$941$	−22.8392	+	39.5587i	−0.744537	+	1.28958i	−0.950411	+	0.310997i	$0.899337\pi$
$942$	40.7689			1.32832
$943$	50.8248			1.65508
$944$	−1.08617	+	1.88131i	−0.0353519	+	0.0612313i
$945$	−0.834506	−	1.44541i	−0.0271465	−	0.0470191i
$946$	−1.55523	+	2.69374i	−0.0505649	+	0.0875809i
$947$	19.0004	+	32.9097i	0.617430	+	1.06942i	0.989953	+	0.141397i	$0.0451595\pi$
$947$	19.0004	+	32.9097i	0.617430	+	1.06942i	−0.372523	+	0.928023i	$0.621507\pi$
$948$	−22.1618	−	38.3853i	−0.719781	−	1.24670i
$949$	−28.8678			−0.937087
$950$	1.79425	+	3.48350i	0.0582132	+	0.113020i
$951$	−72.0615			−2.33675
$952$	−0.294384	−	0.509888i	−0.00954104	−	0.0165256i
$953$	−12.1436	−	21.0333i	−0.393369	−	0.681335i	0.599522	−	0.800358i	$-0.295357\pi$
$953$	−12.1436	−	21.0333i	−0.393369	−	0.681335i	−0.992892	+	0.119023i	$0.962024\pi$
$954$	−15.0874	+	26.1321i	−0.488472	+	0.846058i
$955$	−5.18207	−	8.97561i	−0.167688	−	0.290444i
$956$	4.54308	−	7.86884i	0.146934	−	0.254496i
$957$	−125.744			−4.06472
$958$	12.8121			0.413941
$959$	4.10205	−	7.10497i	0.132462	−	0.229431i
$960$	6.95088	−	12.0393i	0.224339	−	0.388566i
$961$	−30.4650			−0.982742
$962$	−26.9272			−0.868169
$963$	−30.2884	+	52.4611i	−0.976030	+	1.69053i
$964$	−2.74199	−	4.74927i	−0.0883136	−	0.152964i
$965$	−8.57538	+	14.8530i	−0.276051	+	0.478135i
$966$	−8.58468	−	14.8691i	−0.276208	−	0.478406i
$967$	−15.7622	−	27.3010i	−0.506879	−	0.877941i	−0.999968	−	0.00796189i	$-0.997466\pi$
$967$	−15.7622	−	27.3010i	−0.506879	−	0.877941i	0.493089	−	0.869979i	$-0.335868\pi$
$968$	44.3350			1.42498
$969$	−2.30336	−	0.110569i	−0.0739946	−	0.00355198i
$970$	−7.11121			−0.228327
$971$	−27.3519	−	47.3749i	−0.877765	−	1.52033i	−0.853787	−	0.520622i	$-0.825700\pi$
$971$	−27.3519	−	47.3749i	−0.877765	−	1.52033i	−0.0239782	−	0.999712i	$-0.507633\pi$
$972$	−13.1846	−	22.8363i	−0.422895	−	0.732475i
$973$	−1.36229	+	2.35956i	−0.0436731	+	0.0756440i
$974$	−2.20158	−	3.81324i	−0.0705430	−	0.122184i
$975$	4.96333	−	8.59674i	0.158954	−	0.275316i
$976$	1.06695			0.0341523
$977$	27.3235			0.874158			0.437079	−	0.899423i	$-0.356013\pi$
$977$	27.3235			0.874158			0.437079	+	0.899423i	$0.356013\pi$
$978$	−3.80042	+	6.58253i	−0.121524	+	0.210486i
$979$	−26.8953	+	46.5840i	−0.859576	+	1.48883i
$980$	1.19189			0.0380735
$981$	25.5509			0.815778
$982$	12.5889	−	21.8046i	0.401727	−	0.695812i
$983$	−13.0570	−	22.6153i	−0.416453	−	0.721318i	0.579127	−	0.815237i	$-0.303394\pi$
$983$	−13.0570	−	22.6153i	−0.416453	−	0.721318i	−0.995580	+	0.0939199i	$0.970060\pi$
$984$	−25.3780	+	43.9560i	−0.809022	+	1.40127i
$985$	−8.18193	−	14.1715i	−0.260698	−	0.451542i
$986$	0.874593	+	1.51484i	0.0278527	+	0.0482423i
$987$	−11.9027			−0.378866
$988$	−10.8205	+	16.8235i	−0.344247	+	0.535227i
$989$	−4.98381			−0.158476
$990$	−8.43151	−	14.6038i	−0.267971	−	0.464139i
$991$	−6.51798	−	11.2895i	−0.207051	−	0.358622i	0.743734	−	0.668476i	$-0.233053\pi$
$991$	−6.51798	−	11.2895i	−0.207051	−	0.358622i	−0.950784	+	0.309854i	$0.899720\pi$
$992$	−2.03445	+	3.52378i	−0.0645940	+	0.111880i
$993$	−15.0678	−	26.0983i	−0.478163	−	0.828203i
$994$	5.62585	−	9.74425i	0.178441	−	0.309069i
$995$	−24.5386			−0.777926
$996$	2.55039			0.0808123
$997$	−18.4439	+	31.9458i	−0.584125	+	1.01173i	0.410859	+	0.911699i	$0.365229\pi$
$997$	−18.4439	+	31.9458i	−0.584125	+	1.01173i	−0.994984	+	0.100035i	$0.968105\pi$
$998$	−7.39151	+	12.8025i	−0.233974	+	0.405255i
$999$	−12.9848			−0.410822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	665.2.i.h.596.6	yes	20
19.11	even	3	inner	665.2.i.h.106.6	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
665.2.i.h.106.6	✓	20	19.11	even	3	inner
665.2.i.h.596.6	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 665 = 5 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	665.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.449475 + 0.778513i) q^{2} +(-1.28912 - 2.23283i) q^{3} +(0.595945 - 1.03221i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.15886 - 2.00720i) q^{6} -1.00000 q^{7} +2.86935 q^{8} +(-1.82367 + 3.15869i) q^{9} +O(q^{10})\)	\(q+(0.449475 + 0.778513i) q^{2} +(-1.28912 - 2.23283i) q^{3} +(0.595945 - 1.03221i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.15886 - 2.00720i) q^{6} -1.00000 q^{7} +2.86935 q^{8} +(-1.82367 + 3.15869i) q^{9} +(-0.449475 + 0.778513i) q^{10} +5.14308 q^{11} -3.07298 q^{12} +(1.92508 - 3.33434i) q^{13} +(-0.449475 - 0.778513i) q^{14} +(1.28912 - 2.23283i) q^{15} +(0.0978087 + 0.169410i) q^{16} +(0.102596 + 0.177702i) q^{17} -3.27878 q^{18} +(-1.99594 - 3.87508i) q^{19} +1.19189 q^{20} +(1.28912 + 2.23283i) q^{21} +(2.31168 + 4.00395i) q^{22} +(-3.70395 + 6.41543i) q^{23} +(-3.69894 - 6.40675i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.46110 q^{26} +1.66901 q^{27} +(-0.595945 + 1.03221i) q^{28} +(4.74144 - 8.21241i) q^{29} +2.31771 q^{30} -0.731444 q^{31} +(2.78142 - 4.81756i) q^{32} +(-6.63006 - 11.4836i) q^{33} +(-0.0922287 + 0.159745i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(2.17362 + 3.76482i) q^{36} -7.77996 q^{37} +(2.11967 - 3.29562i) q^{38} -9.92666 q^{39} +(1.43467 + 2.48493i) q^{40} +(-3.43044 - 5.94170i) q^{41} +(-1.15886 + 2.00720i) q^{42} +(0.336385 + 0.582635i) q^{43} +(3.06499 - 5.30872i) q^{44} -3.64734 q^{45} -6.65932 q^{46} +(-2.30829 + 3.99807i) q^{47} +(0.252175 - 0.436779i) q^{48} +1.00000 q^{49} -0.898949 q^{50} +(0.264518 - 0.458158i) q^{51} +(-2.29449 - 3.97417i) q^{52} +(4.60152 - 7.97007i) q^{53} +(0.750179 + 1.29935i) q^{54} +(2.57154 + 4.45404i) q^{55} -2.86935 q^{56} +(-6.07935 + 9.45204i) q^{57} +8.52462 q^{58} +(5.55254 + 9.61728i) q^{59} +(-1.53649 - 2.66128i) q^{60} +(2.72714 - 4.72355i) q^{61} +(-0.328766 - 0.569439i) q^{62} +(1.82367 - 3.15869i) q^{63} +5.39195 q^{64} +3.85016 q^{65} +(5.96009 - 10.3232i) q^{66} +(-0.123859 + 0.214529i) q^{67} +0.244567 q^{68} +19.0994 q^{69} +(0.449475 - 0.778513i) q^{70} +(6.25825 + 10.8396i) q^{71} +(-5.23275 + 9.06339i) q^{72} +(-3.74890 - 6.49328i) q^{73} +(-3.49689 - 6.05680i) q^{74} +2.57824 q^{75} +(-5.18935 - 0.249106i) q^{76} -5.14308 q^{77} +(-4.46178 - 7.72804i) q^{78} +(7.21180 + 12.4912i) q^{79} +(-0.0978087 + 0.169410i) q^{80} +(3.31946 + 5.74947i) q^{81} +(3.08380 - 5.34129i) q^{82} -0.829940 q^{83} +3.07298 q^{84} +(-0.102596 + 0.177702i) q^{85} +(-0.302393 + 0.523760i) q^{86} -24.4492 q^{87} +14.7573 q^{88} +(-5.22941 + 9.05760i) q^{89} +(-1.63939 - 2.83950i) q^{90} +(-1.92508 + 3.33434i) q^{91} +(4.41470 + 7.64648i) q^{92} +(0.942921 + 1.63319i) q^{93} -4.15006 q^{94} +(2.35794 - 3.66608i) q^{95} -14.3424 q^{96} +(3.95529 + 6.85077i) q^{97} +(0.449475 + 0.778513i) q^{98} +(-9.37929 + 16.2454i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9	\( 20 q + 3 q^{2} - q^{3} - 11 q^{4} + 10 q^{5} - 6 q^{6} - 20 q^{7} - 9 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} + 6 q^{13} - 3 q^{14} + q^{15} - 5 q^{16} + 8 q^{17} - 76 q^{18} + 17 q^{19} - 22 q^{20} + q^{21} - 4 q^{22} + 3 q^{23} - 6 q^{24} - 10 q^{25} + 18 q^{26} + 20 q^{27} + 11 q^{28} + q^{29} - 12 q^{30} + 10 q^{31} + 18 q^{32} + q^{33} - 26 q^{34} - 10 q^{35} - 19 q^{36} - 66 q^{37} + 19 q^{38} + 34 q^{39} - 29 q^{41} + 6 q^{42} + q^{43} - 28 q^{44} - 18 q^{45} + 6 q^{46} - 7 q^{47} + 15 q^{48} + 20 q^{49} - 6 q^{50} + 16 q^{51} - 6 q^{52} + 40 q^{53} + 35 q^{54} + q^{55} + 24 q^{57} - 18 q^{58} - 9 q^{59} - 2 q^{60} + 10 q^{61} - 8 q^{62} + 9 q^{63} + 44 q^{64} + 12 q^{65} - 19 q^{66} + 22 q^{67} - 42 q^{68} + 60 q^{69} + 3 q^{70} - 8 q^{71} + 18 q^{72} + 14 q^{73} - 24 q^{74} + 2 q^{75} - 49 q^{76} - 2 q^{77} + 23 q^{78} + 9 q^{79} + 5 q^{80} - 42 q^{81} - 5 q^{82} - 54 q^{83} + 4 q^{84} - 8 q^{85} + 37 q^{86} + 18 q^{87} - 28 q^{88} - 25 q^{89} - 38 q^{90} - 6 q^{91} + 68 q^{92} + 11 q^{93} - 118 q^{94} + 10 q^{95} + 102 q^{96} + 29 q^{97} + 3 q^{98} + 34 q^{99}+O(q^{100}) \) 20 * q + 3 * q^2 - q^3 - 11 * q^4 + 10 * q^5 - 6 * q^6 - 20 * q^7 - 9 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 + 6 * q^13 - 3 * q^14 + q^15 - 5 * q^16 + 8 * q^17 - 76 * q^18 + 17 * q^19 - 22 * q^20 + q^21 - 4 * q^22 + 3 * q^23 - 6 * q^24 - 10 * q^25 + 18 * q^26 + 20 * q^27 + 11 * q^28 + q^29 - 12 * q^30 + 10 * q^31 + 18 * q^32 + q^33 - 26 * q^34 - 10 * q^35 - 19 * q^36 - 66 * q^37 + 19 * q^38 + 34 * q^39 - 29 * q^41 + 6 * q^42 + q^43 - 28 * q^44 - 18 * q^45 + 6 * q^46 - 7 * q^47 + 15 * q^48 + 20 * q^49 - 6 * q^50 + 16 * q^51 - 6 * q^52 + 40 * q^53 + 35 * q^54 + q^55 + 24 * q^57 - 18 * q^58 - 9 * q^59 - 2 * q^60 + 10 * q^61 - 8 * q^62 + 9 * q^63 + 44 * q^64 + 12 * q^65 - 19 * q^66 + 22 * q^67 - 42 * q^68 + 60 * q^69 + 3 * q^70 - 8 * q^71 + 18 * q^72 + 14 * q^73 - 24 * q^74 + 2 * q^75 - 49 * q^76 - 2 * q^77 + 23 * q^78 + 9 * q^79 + 5 * q^80 - 42 * q^81 - 5 * q^82 - 54 * q^83 + 4 * q^84 - 8 * q^85 + 37 * q^86 + 18 * q^87 - 28 * q^88 - 25 * q^89 - 38 * q^90 - 6 * q^91 + 68 * q^92 + 11 * q^93 - 118 * q^94 + 10 * q^95 + 102 * q^96 + 29 * q^97 + 3 * q^98 + 34 * q^99

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