LMFDB - Embedded newform 630.2.j.l.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 0]))

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			421.1
Root			$2.06288i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.l.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.70236 + 0.319344i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.574618 - 1.63396i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.79604 - 1.08728i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.70236 + 0.319344i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.574618 - 1.63396i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.79604 - 1.08728i) q^{9} -1.00000 q^{10} +(-1.83010 + 3.16982i) q^{11} +(1.12774 + 1.31461i) q^{12} +(-1.78651 - 3.09432i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-1.12774 - 1.31461i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.46677 q^{17} +(-0.456412 + 2.96508i) q^{18} +5.59208 q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.574618 + 1.63396i) q^{21} +(-1.83010 - 3.16982i) q^{22} +(1.33010 + 2.30379i) q^{23} +(-1.70236 + 0.319344i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.57301 q^{26} +(-4.41264 + 2.74383i) q^{27} -1.00000 q^{28} +(0.223855 - 0.387729i) q^{29} +(1.70236 - 0.319344i) q^{30} +(4.59208 + 7.95371i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.10321 - 5.98059i) q^{33} +(-2.23339 + 3.86834i) q^{34} +1.00000 q^{35} +(-2.33963 - 1.87780i) q^{36} -10.1651 q^{37} +(-2.79604 + 4.84288i) q^{38} +(4.02943 + 4.69713i) q^{39} +(0.500000 + 0.866025i) q^{40} +(2.28651 + 3.96035i) q^{41} +(-1.12774 - 1.31461i) q^{42} +(-3.61660 + 6.26414i) q^{43} +3.66019 q^{44} +(2.33963 + 1.87780i) q^{45} -2.66019 q^{46} +(-6.13567 + 10.6273i) q^{47} +(0.574618 - 1.63396i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-7.60404 + 1.42644i) q^{51} +(-1.78651 + 3.09432i) q^{52} +4.98094 q^{53} +(-0.169904 - 5.19337i) q^{54} -3.66019 q^{55} +(0.500000 - 0.866025i) q^{56} +(-9.51971 + 1.78580i) q^{57} +(0.223855 + 0.387729i) q^{58} +(6.45623 + 11.1825i) q^{59} +(-0.574618 + 1.63396i) q^{60} +(-0.596708 + 1.03353i) q^{61} -9.18416 q^{62} +(0.456412 - 2.96508i) q^{63} +1.00000 q^{64} +(1.78651 - 3.09432i) q^{65} +(4.12774 + 4.81173i) q^{66} +(-4.88322 - 8.45798i) q^{67} +(-2.23339 - 3.86834i) q^{68} +(-3.00000 - 3.49712i) q^{69} +(-0.500000 + 0.866025i) q^{70} +3.89376 q^{71} +(2.79604 - 1.08728i) q^{72} +6.14603 q^{73} +(5.08255 - 8.80323i) q^{74} +(0.574618 - 1.63396i) q^{75} +(-2.79604 - 4.84288i) q^{76} +(1.83010 + 3.16982i) q^{77} +(-6.08255 + 1.14102i) q^{78} +(1.11660 - 1.93401i) q^{79} -1.00000 q^{80} +(6.63567 - 6.08013i) q^{81} -4.57301 q^{82} +(5.68962 - 9.85471i) q^{83} +(1.70236 - 0.319344i) q^{84} +(2.23339 + 3.86834i) q^{85} +(-3.61660 - 6.26414i) q^{86} +(-0.257263 + 0.731540i) q^{87} +(-1.83010 + 3.16982i) q^{88} +13.3585 q^{89} +(-2.79604 + 1.08728i) q^{90} -3.57301 q^{91} +(1.33010 - 2.30379i) q^{92} +(-10.3573 - 12.0736i) q^{93} +(-6.13567 - 10.6273i) q^{94} +(2.79604 + 4.84288i) q^{95} +(1.12774 + 1.31461i) q^{96} +(4.26643 - 7.38968i) q^{97} +1.00000 q^{98} +(-1.67055 + 10.8528i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9} - 8 q^{10} + 2 q^{11} + 3 q^{12} + 3 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{22} - 6 q^{23} - 3 q^{24} - 4 q^{25} - 6 q^{26} + 18 q^{27} - 8 q^{28} - 12 q^{29} + 3 q^{30} - 2 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 8 q^{35} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 4 q^{40} + q^{41} - 3 q^{42} + 5 q^{43} - 4 q^{44} + 12 q^{46} - 11 q^{47} - 4 q^{49} - 4 q^{50} - 21 q^{51} + 3 q^{52} + 44 q^{53} - 18 q^{54} + 4 q^{55} + 4 q^{56} + 9 q^{57} - 12 q^{58} - q^{59} - 4 q^{61} + 4 q^{62} + 3 q^{63} + 8 q^{64} - 3 q^{65} + 27 q^{66} - 21 q^{67} - 2 q^{68} - 24 q^{69} - 4 q^{70} + 34 q^{71} + 3 q^{72} - 20 q^{73} + 4 q^{74} - 3 q^{76} - 2 q^{77} - 12 q^{78} - 25 q^{79} - 8 q^{80} + 15 q^{81} - 2 q^{82} - 23 q^{83} + 3 q^{84} + 2 q^{85} + 5 q^{86} - 72 q^{87} + 2 q^{88} + 32 q^{89} - 3 q^{90} + 6 q^{91} - 6 q^{92} + 6 q^{93} - 11 q^{94} + 3 q^{95} + 3 q^{96} - 2 q^{97} + 8 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9 - 8 * q^10 + 2 * q^11 + 3 * q^12 + 3 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^22 - 6 * q^23 - 3 * q^24 - 4 * q^25 - 6 * q^26 + 18 * q^27 - 8 * q^28 - 12 * q^29 + 3 * q^30 - 2 * q^31 - 4 * q^32 + 6 * q^33 - 2 * q^34 + 8 * q^35 - 8 * q^37 - 3 * q^38 - 3 * q^39 + 4 * q^40 + q^41 - 3 * q^42 + 5 * q^43 - 4 * q^44 + 12 * q^46 - 11 * q^47 - 4 * q^49 - 4 * q^50 - 21 * q^51 + 3 * q^52 + 44 * q^53 - 18 * q^54 + 4 * q^55 + 4 * q^56 + 9 * q^57 - 12 * q^58 - q^59 - 4 * q^61 + 4 * q^62 + 3 * q^63 + 8 * q^64 - 3 * q^65 + 27 * q^66 - 21 * q^67 - 2 * q^68 - 24 * q^69 - 4 * q^70 + 34 * q^71 + 3 * q^72 - 20 * q^73 + 4 * q^74 - 3 * q^76 - 2 * q^77 - 12 * q^78 - 25 * q^79 - 8 * q^80 + 15 * q^81 - 2 * q^82 - 23 * q^83 + 3 * q^84 + 2 * q^85 + 5 * q^86 - 72 * q^87 + 2 * q^88 + 32 * q^89 - 3 * q^90 + 6 * q^91 - 6 * q^92 + 6 * q^93 - 11 * q^94 + 3 * q^95 + 3 * q^96 - 2 * q^97 + 8 * q^98 + 51 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.70236	+	0.319344i	−0.982856	+	0.184373i
$3$	−1.70236	+	0.319344i	−0.982856	+	0.184373i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.574618	−	1.63396i	0.234587	−	0.667060i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	2.79604	−	1.08728i	0.932013	−	0.362425i
$10$	−1.00000			−0.316228
$11$	−1.83010	+	3.16982i	−0.551795	+	0.955736i	0.446351	+	0.894858i	$0.352723\pi$
$11$	−1.83010	+	3.16982i	−0.551795	+	0.955736i	−0.998145	+	0.0608781i	$0.980610\pi$
$12$	1.12774	+	1.31461i	0.325550	+	0.379496i
$13$	−1.78651	−	3.09432i	−0.495488	−	0.858210i	0.504499	−	0.863413i	$-0.331677\pi$
$13$	−1.78651	−	3.09432i	−0.495488	−	0.858210i	−0.999986	+	0.00520227i	$0.998344\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	−1.12774	−	1.31461i	−0.291181	−	0.339431i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.46677			1.08335			0.541676	−	0.840587i	$-0.317790\pi$
$17$	4.46677			1.08335			0.541676	+	0.840587i	$0.317790\pi$
$18$	−0.456412	+	2.96508i	−0.107577	+	0.698876i
$19$	5.59208			1.28291			0.641455	−	0.767160i	$-0.278331\pi$
$19$	5.59208			1.28291			0.641455	+	0.767160i	$0.278331\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−0.574618	+	1.63396i	−0.125392	+	0.356559i
$22$	−1.83010	−	3.16982i	−0.390178	−	0.675808i
$23$	1.33010	+	2.30379i	0.277344	+	0.480374i	0.970724	−	0.240198i	$-0.0772125\pi$
$23$	1.33010	+	2.30379i	0.277344	+	0.480374i	−0.693380	+	0.720572i	$0.743879\pi$
$24$	−1.70236	+	0.319344i	−0.347492	+	0.0651858i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.57301			0.700726
$27$	−4.41264	+	2.74383i	−0.849213	+	0.528050i
$28$	−1.00000			−0.188982
$29$	0.223855	−	0.387729i	0.0415689	−	0.0719995i	−0.844492	−	0.535568i	$-0.820098\pi$
$29$	0.223855	−	0.387729i	0.0415689	−	0.0719995i	0.886061	+	0.463568i	$0.153431\pi$
$30$	1.70236	−	0.319344i	0.310806	−	0.0583040i
$31$	4.59208	+	7.95371i	0.824761	+	1.42853i	0.902101	+	0.431524i	$0.142024\pi$
$31$	4.59208	+	7.95371i	0.824761	+	1.42853i	−0.0773400	+	0.997005i	$0.524643\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	2.10321	−	5.98059i	0.366122	−	1.04109i
$34$	−2.23339	+	3.86834i	−0.383023	+	0.663415i
$35$	1.00000			0.169031
$36$	−2.33963	−	1.87780i	−0.389938	−	0.312967i
$37$	−10.1651			−1.67113			−0.835565	−	0.549391i	$-0.814860\pi$
$37$	−10.1651			−1.67113			−0.835565	+	0.549391i	$0.814860\pi$
$38$	−2.79604	+	4.84288i	−0.453577	+	0.785619i
$39$	4.02943	+	4.69713i	0.645225	+	0.752143i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	2.28651	+	3.96035i	0.357092	+	0.618502i	0.987474	−	0.157783i	$-0.0504348\pi$
$41$	2.28651	+	3.96035i	0.357092	+	0.618502i	−0.630381	+	0.776286i	$0.717101\pi$
$42$	−1.12774	−	1.31461i	−0.174014	−	0.202849i
$43$	−3.61660	+	6.26414i	−0.551527	+	0.955272i	0.446638	+	0.894715i	$0.352621\pi$
$43$	−3.61660	+	6.26414i	−0.551527	+	0.955272i	−0.998165	+	0.0605576i	$0.980712\pi$
$44$	3.66019			0.551795
$45$	2.33963	+	1.87780i	0.348771	+	0.279926i
$46$	−2.66019			−0.392224
$47$	−6.13567	+	10.6273i	−0.894979	+	1.55015i	−0.0611481	+	0.998129i	$0.519476\pi$
$47$	−6.13567	+	10.6273i	−0.894979	+	1.55015i	−0.833831	+	0.552020i	$0.813857\pi$
$48$	0.574618	−	1.63396i	0.0829390	−	0.235841i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−7.60404	+	1.42644i	−1.06478	+	0.199741i
$52$	−1.78651	+	3.09432i	−0.247744	+	0.429105i
$53$	4.98094			0.684184			0.342092	−	0.939666i	$-0.388865\pi$
$53$	4.98094			0.684184			0.342092	+	0.939666i	$0.388865\pi$
$54$	−0.169904	−	5.19337i	−0.0231211	−	0.706729i
$55$	−3.66019			−0.493540
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	−9.51971	+	1.78580i	−1.26092	+	0.236535i
$58$	0.223855	+	0.387729i	0.0293937	+	0.0509113i
$59$	6.45623	+	11.1825i	0.840530	+	1.45584i	0.889448	+	0.457037i	$0.151089\pi$
$59$	6.45623	+	11.1825i	0.840530	+	1.45584i	−0.0489181	+	0.998803i	$0.515577\pi$
$60$	−0.574618	+	1.63396i	−0.0741829	+	0.210943i
$61$	−0.596708	+	1.03353i	−0.0764007	+	0.132330i	−0.901695	−	0.432374i	$-0.857676\pi$
$61$	−0.596708	+	1.03353i	−0.0764007	+	0.132330i	0.825294	+	0.564704i	$0.191009\pi$
$62$	−9.18416			−1.16639
$63$	0.456412	−	2.96508i	0.0575025	−	0.373565i
$64$	1.00000			0.125000
$65$	1.78651	−	3.09432i	0.221589	−	0.383803i
$66$	4.12774	+	4.81173i	0.508089	+	0.592283i
$67$	−4.88322	−	8.45798i	−0.596580	−	1.03331i	−0.993322	−	0.115376i	$-0.963193\pi$
$67$	−4.88322	−	8.45798i	−0.596580	−	1.03331i	0.396742	−	0.917930i	$-0.370141\pi$
$68$	−2.23339	−	3.86834i	−0.270838	−	0.469105i
$69$	−3.00000	−	3.49712i	−0.361158	−	0.421004i
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$	3.89376			0.462104			0.231052	−	0.972941i	$-0.425783\pi$
$71$	3.89376			0.462104			0.231052	+	0.972941i	$0.425783\pi$
$72$	2.79604	−	1.08728i	0.329516	−	0.128137i
$73$	6.14603			0.719338			0.359669	−	0.933080i	$-0.382890\pi$
$73$	6.14603			0.719338			0.359669	+	0.933080i	$0.382890\pi$
$74$	5.08255	−	8.80323i	0.590834	−	1.02335i
$75$	0.574618	−	1.63396i	0.0663512	−	0.188673i
$76$	−2.79604	−	4.84288i	−0.320728	−	0.555517i
$77$	1.83010	+	3.16982i	0.208559	+	0.361234i
$78$	−6.08255	+	1.14102i	−0.688713	+	0.129195i
$79$	1.11660	−	1.93401i	0.125628	−	0.217593i	−0.796350	−	0.604835i	$-0.793239\pi$
$79$	1.11660	−	1.93401i	0.125628	−	0.217593i	0.921978	+	0.387242i	$0.126572\pi$
$80$	−1.00000			−0.111803
$81$	6.63567	−	6.08013i	0.737296	−	0.675570i
$82$	−4.57301			−0.505005
$83$	5.68962	−	9.85471i	0.624517	−	1.08169i	−0.364118	−	0.931353i	$-0.618629\pi$
$83$	5.68962	−	9.85471i	0.624517	−	1.08169i	0.988634	−	0.150341i	$-0.0480373\pi$
$84$	1.70236	−	0.319344i	0.185742	−	0.0348433i
$85$	2.23339	+	3.86834i	0.242245	+	0.419580i
$86$	−3.61660	−	6.26414i	−0.389988	−	0.675480i
$87$	−0.257263	+	0.731540i	−0.0275815	+	0.0784293i
$88$	−1.83010	+	3.16982i	−0.195089	+	0.337904i
$89$	13.3585			1.41600			0.708000	−	0.706213i	$-0.249598\pi$
$89$	13.3585			1.41600			0.708000	+	0.706213i	$0.249598\pi$
$90$	−2.79604	+	1.08728i	−0.294728	+	0.114609i
$91$	−3.57301			−0.374554
$92$	1.33010	−	2.30379i	0.138672	−	0.240187i
$93$	−10.3573	−	12.0736i	−1.07400	−	1.25197i
$94$	−6.13567	−	10.6273i	−0.632846	−	1.09612i
$95$	2.79604	+	4.84288i	0.286868	+	0.496869i
$96$	1.12774	+	1.31461i	0.115099	+	0.134172i
$97$	4.26643	−	7.38968i	0.433190	−	0.750308i	−0.563956	−	0.825805i	$-0.690721\pi$
$97$	4.26643	−	7.38968i	0.433190	−	0.750308i	0.997146	+	0.0754973i	$0.0240544\pi$
$98$	1.00000			0.101015
$99$	−1.67055	+	10.8528i	−0.167897	+	1.09074i
$100$	1.00000			0.100000
$101$	−6.64113	+	11.5028i	−0.660817	+	1.14457i	0.319584	+	0.947558i	$0.396457\pi$
$101$	−6.64113	+	11.5028i	−0.660817	+	1.14457i	−0.980401	+	0.197011i	$0.936877\pi$
$102$	2.56669	−	7.29851i	0.254140	−	0.722661i
$103$	7.15066	+	12.3853i	0.704575	+	1.22036i	0.966845	+	0.255366i	$0.0821958\pi$
$103$	7.15066	+	12.3853i	0.704575	+	1.22036i	−0.262269	+	0.964995i	$0.584471\pi$
$104$	−1.78651	−	3.09432i	−0.175181	−	0.303423i
$105$	−1.70236	+	0.319344i	−0.166133	+	0.0311648i
$106$	−2.49047	+	4.31362i	−0.241896	+	0.418976i
$107$	9.51582			0.919929			0.459965	−	0.887937i	$-0.347862\pi$
$107$	9.51582			0.919929			0.459965	+	0.887937i	$0.347862\pi$
$108$	4.58255	+	2.44955i	0.440956	+	0.235708i
$109$	0.465112			0.0445497			0.0222748	−	0.999752i	$-0.492909\pi$
$109$	0.465112			0.0445497			0.0222748	+	0.999752i	$0.492909\pi$
$110$	1.83010	−	3.16982i	0.174493	−	0.302230i
$111$	17.3046	−	3.24616i	1.64248	−	0.308112i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	−1.07320	−	1.85883i	−0.100958	−	0.174864i	0.811122	−	0.584877i	$-0.198857\pi$
$113$	−1.07320	−	1.85883i	−0.100958	−	0.174864i	−0.912080	+	0.410013i	$0.865524\pi$
$114$	3.21331	−	9.13721i	0.300954	−	0.855778i
$115$	−1.33010	+	2.30379i	−0.124032	+	0.214830i
$116$	−0.447711			−0.0415689
$117$	−8.35952	−	6.70942i	−0.772838	−	0.620286i
$118$	−12.9125			−1.18869
$119$	2.23339	−	3.86834i	0.204734	−	0.354610i
$120$	−1.12774	−	1.31461i	−0.102948	−	0.120007i
$121$	−1.19850	−	2.07586i	−0.108954	−	0.188715i
$122$	−0.596708	−	1.03353i	−0.0540234	−	0.0935714i
$123$	−5.15716	−	6.01174i	−0.465006	−	0.542060i
$124$	4.59208	−	7.95371i	0.412381	−	0.714264i
$125$	−1.00000			−0.0894427
$126$	2.33963	+	1.87780i	0.208431	+	0.167288i
$127$	−4.66019			−0.413525			−0.206763	−	0.978391i	$-0.566293\pi$
$127$	−4.66019			−0.413525			−0.206763	+	0.978391i	$0.566293\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.15633	−	11.8187i	0.365945	−	1.04058i
$130$	1.78651	+	3.09432i	0.156687	+	0.271390i
$131$	−7.83963	−	13.5786i	−0.684951	−	1.18637i	−0.973452	−	0.228891i	$-0.926490\pi$
$131$	−7.83963	−	13.5786i	−0.684951	−	1.18637i	0.288501	−	0.957480i	$-0.406843\pi$
$132$	−6.23095	+	1.16886i	−0.542335	+	0.101736i
$133$	2.79604	−	4.84288i	0.242447	−	0.419931i
$134$	9.76643			0.843691
$135$	−4.58255	−	2.44955i	−0.394403	−	0.210823i
$136$	4.46677			0.383023
$137$	−6.55312	+	11.3503i	−0.559871	+	0.969725i	0.437636	+	0.899152i	$0.355816\pi$
$137$	−6.55312	+	11.3503i	−0.559871	+	0.969725i	−0.997507	+	0.0705724i	$0.977517\pi$
$138$	4.52859	−	0.849516i	0.385500	−	0.0723156i
$139$	−8.51036	−	14.7404i	−0.721840	−	1.25026i	−0.960262	−	0.279101i	$-0.909964\pi$
$139$	−8.51036	−	14.7404i	−0.721840	−	1.25026i	0.238422	−	0.971162i	$-0.423370\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$	7.05133	−	20.0508i	0.593829	−	1.68858i
$142$	−1.94688	+	3.37209i	−0.163379	+	0.282980i
$143$	13.0779			1.09363
$144$	−0.456412	+	2.96508i	−0.0380343	+	0.247090i
$145$	0.447711			0.0371804
$146$	−3.07301	+	5.32262i	−0.254324	+	0.440503i
$147$	1.12774	+	1.31461i	0.0930143	+	0.108427i
$148$	5.08255	+	8.80323i	0.417783	+	0.723621i
$149$	−7.15473	−	12.3924i	−0.586138	−	1.01522i	−0.994732	−	0.102505i	$-0.967314\pi$
$149$	−7.15473	−	12.3924i	−0.586138	−	1.01522i	0.408594	−	0.912716i	$-0.366019\pi$
$150$	1.12774	+	1.31461i	0.0920795	+	0.107338i
$151$	−6.01036	+	10.4103i	−0.489116	+	0.847174i	−0.999922	−	0.0125221i	$-0.996014\pi$
$151$	−6.01036	+	10.4103i	−0.489116	+	0.847174i	0.510805	+	0.859696i	$0.329347\pi$
$152$	5.59208			0.453577
$153$	12.4893	−	4.85661i	1.00970	−	0.392634i
$154$	−3.66019			−0.294947
$155$	−4.59208	+	7.95371i	−0.368845	+	0.638858i
$156$	2.05312	−	5.83815i	0.164381	−	0.467426i
$157$	3.31973	+	5.74995i	0.264944	+	0.458896i	0.967549	−	0.252684i	$-0.0813133\pi$
$157$	3.31973	+	5.74995i	0.264944	+	0.458896i	−0.702605	+	0.711580i	$0.747980\pi$
$158$	1.11660	+	1.93401i	0.0888321	+	0.153862i
$159$	−8.47933	+	1.59063i	−0.672455	+	0.126145i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	2.66019			0.209652
$162$	1.94771	+	8.78672i	0.153027	+	0.690350i
$163$	7.46677			0.584843			0.292421	−	0.956290i	$-0.405539\pi$
$163$	7.46677			0.584843			0.292421	+	0.956290i	$0.405539\pi$
$164$	2.28651	−	3.96035i	0.178546	−	0.309251i
$165$	6.23095	−	1.16886i	0.485079	−	0.0909956i
$166$	5.68962	+	9.85471i	0.441600	+	0.764874i
$167$	−1.98501	−	3.43813i	−0.153604	−	0.266051i	0.778946	−	0.627092i	$-0.215755\pi$
$167$	−1.98501	−	3.43813i	−0.153604	−	0.266051i	−0.932550	+	0.361041i	$0.882421\pi$
$168$	−0.574618	+	1.63396i	−0.0443328	+	0.126062i
$169$	0.116784	−	0.202277i	0.00898342	−	0.0155597i
$170$	−4.46677			−0.342586
$171$	15.6357	−	6.08013i	1.19569	−	0.464959i
$172$	7.23321			0.551527
$173$	4.59208	−	7.95371i	0.349129	−	0.604710i	−0.636966	−	0.770892i	$-0.719811\pi$
$173$	4.59208	−	7.95371i	0.349129	−	0.604710i	0.986095	+	0.166183i	$0.0531441\pi$
$174$	−0.504901	−	0.588566i	−0.0382764	−	0.0446191i
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	−1.83010	−	3.16982i	−0.137949	−	0.238934i
$177$	−14.5619	−	16.9749i	−1.09454	−	1.27591i
$178$	−6.67925	+	11.5688i	−0.500631	+	0.867119i
$179$	2.34147			0.175010			0.0875049	−	0.996164i	$-0.472111\pi$
$179$	2.34147			0.175010			0.0875049	+	0.996164i	$0.472111\pi$
$180$	0.456412	−	2.96508i	0.0340189	−	0.221004i
$181$	18.6789			1.38839			0.694196	−	0.719786i	$-0.255760\pi$
$181$	18.6789			1.38839			0.694196	+	0.719786i	$0.255760\pi$
$182$	1.78651	−	3.09432i	0.132425	−	0.229366i
$183$	0.685759	−	1.94999i	0.0506928	−	0.144147i
$184$	1.33010	+	2.30379i	0.0980559	+	0.169838i
$185$	−5.08255	−	8.80323i	−0.373676	−	0.647226i
$186$	15.6347	−	2.93290i	1.14639	−	0.215051i
$187$	−8.17462	+	14.1589i	−0.597788	+	1.03540i
$188$	12.2713			0.894979
$189$	0.169904	+	5.19337i	0.0123587	+	0.377762i
$190$	−5.59208			−0.405692
$191$	−9.37960	+	16.2459i	−0.678684	+	1.17551i	0.296694	+	0.954973i	$0.404116\pi$
$191$	−9.37960	+	16.2459i	−0.678684	+	1.17551i	−0.975377	+	0.220542i	$0.929217\pi$
$192$	−1.70236	+	0.319344i	−0.122857	+	0.0230467i
$193$	−4.01989	−	6.96266i	−0.289358	−	0.501183i	0.684298	−	0.729202i	$-0.260109\pi$
$193$	−4.01989	−	6.96266i	−0.289358	−	0.501183i	−0.973657	+	0.228019i	$0.926775\pi$
$194$	4.26643	+	7.38968i	0.306312	+	0.530548i
$195$	−2.05312	+	5.83815i	−0.147027	+	0.418079i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	7.15529			0.509793			0.254897	−	0.966968i	$-0.417959\pi$
$197$	7.15529			0.509793			0.254897	+	0.966968i	$0.417959\pi$
$198$	−8.56348	−	6.87312i	−0.608580	−	0.488451i
$199$	6.87267			0.487191			0.243595	−	0.969877i	$-0.421673\pi$
$199$	6.87267			0.487191			0.243595	+	0.969877i	$0.421673\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	11.0140	+	12.8391i	0.776866	+	0.905598i
$202$	−6.64113	−	11.5028i	−0.467268	−	0.809332i
$203$	−0.223855	−	0.387729i	−0.0157116	−	0.0272132i
$204$	5.03735	+	5.87208i	0.352685	+	0.411128i
$205$	−2.28651	+	3.96035i	−0.159697	+	0.276603i
$206$	−14.3013			−0.996420
$207$	6.22386	+	4.99532i	0.432588	+	0.347198i
$208$	3.57301			0.247744
$209$	−10.2340	+	17.7259i	−0.707903	+	1.22612i
$210$	0.574618	−	1.63396i	0.0396524	−	0.112754i
$211$	−12.3879	−	21.4565i	−0.852821	−	1.47713i	−0.878652	−	0.477462i	$-0.841557\pi$
$211$	−12.3879	−	21.4565i	−0.852821	−	1.47713i	0.0258316	−	0.999666i	$-0.491777\pi$
$212$	−2.49047	−	4.31362i	−0.171046	−	0.296260i
$213$	−6.62857	+	1.24345i	−0.454182	+	0.0851997i
$214$	−4.75791	+	8.24095i	−0.325244	+	0.563339i
$215$	−7.23321			−0.493301
$216$	−4.41264	+	2.74383i	−0.300242	+	0.186694i
$217$	9.18416			0.623461
$218$	−0.232556	+	0.402799i	−0.0157507	+	0.0272810i
$219$	−10.4627	+	1.96270i	−0.707006	+	0.132627i
$220$	1.83010	+	3.16982i	0.123385	+	0.213709i
$221$	−7.97992	−	13.8216i	−0.536788	−	0.929744i
$222$	−5.84105	+	16.6093i	−0.392026	+	1.11474i
$223$	14.8784	−	25.7702i	0.996332	−	1.72570i	0.424054	−	0.905637i	$-0.360607\pi$
$223$	14.8784	−	25.7702i	0.996332	−	1.72570i	0.572278	−	0.820060i	$-0.306060\pi$
$224$	−1.00000			−0.0668153
$225$	−0.456412	+	2.96508i	−0.0304274	+	0.197672i
$226$	2.14639			0.142776
$227$	−7.32991	+	12.6958i	−0.486503	+	0.842649i	−0.999880	−	0.0155150i	$-0.995061\pi$
$227$	−7.32991	+	12.6958i	−0.486503	+	0.842649i	0.513376	+	0.858164i	$0.328395\pi$
$228$	6.30640	+	7.35141i	0.417652	+	0.486859i
$229$	9.74274	+	16.8749i	0.643818	+	1.11513i	0.984573	+	0.174974i	$0.0559840\pi$
$229$	9.74274	+	16.8749i	0.643818	+	1.11513i	−0.340755	+	0.940152i	$0.610683\pi$
$230$	−1.33010	−	2.30379i	−0.0877039	−	0.151908i
$231$	−4.12774	−	4.81173i	−0.271585	−	0.316589i
$232$	0.223855	−	0.387729i	0.0146968	−	0.0254557i
$233$	−11.7572			−0.770238			−0.385119	−	0.922867i	$-0.625840\pi$
$233$	−11.7572			−0.770238			−0.385119	+	0.922867i	$0.625840\pi$
$234$	9.99029	−	3.88485i	0.653085	−	0.253961i
$235$	−12.2713			−0.800493
$236$	6.45623	−	11.1825i	0.420265	−	0.727920i
$237$	−1.28324	+	3.64896i	−0.0833555	+	0.237025i
$238$	2.23339	+	3.86834i	0.144769	+	0.250747i
$239$	2.03813	+	3.53014i	0.131835	+	0.228346i	0.924384	−	0.381463i	$-0.124580\pi$
$239$	2.03813	+	3.53014i	0.131835	+	0.228346i	−0.792549	+	0.609809i	$0.791246\pi$
$240$	1.70236	−	0.319344i	0.109887	−	0.0206136i
$241$	11.5057	−	19.9285i	0.741149	−	1.28371i	−0.210823	−	0.977524i	$-0.567614\pi$
$241$	11.5057	−	19.9285i	0.741149	−	1.28371i	0.951972	−	0.306184i	$-0.0990523\pi$
$242$	2.39700			0.154085
$243$	−9.35462	+	12.4696i	−0.600099	+	0.799926i
$244$	1.19342			0.0764007
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	7.78490	−	1.46036i	0.496347	−	0.0931095i
$247$	−9.99029	−	17.3037i	−0.635667	−	1.10101i
$248$	4.59208	+	7.95371i	0.291597	+	0.505061i
$249$	−6.53872	+	18.5932i	−0.414374	+	1.17829i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−22.5155			−1.42116			−0.710582	−	0.703615i	$-0.751568\pi$
$251$	−22.5155			−1.42116			−0.710582	+	0.703615i	$0.751568\pi$
$252$	−2.79604	+	1.08728i	−0.176134	+	0.0684919i
$253$	−9.73681			−0.612148
$254$	2.33010	−	4.03584i	0.146203	−	0.253231i
$255$	−5.03735	−	5.87208i	−0.315451	−	0.367724i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.32565	+	4.02814i	0.145070	+	0.251268i	0.929399	−	0.369077i	$-0.120326\pi$
$257$	2.32565	+	4.02814i	0.145070	+	0.251268i	−0.784329	+	0.620345i	$0.786993\pi$
$258$	8.15716	+	9.50886i	0.507843	+	0.591996i
$259$	−5.08255	+	8.80323i	−0.315814	+	0.547006i
$260$	−3.57301			−0.221589
$261$	0.204340	−	1.32750i	0.0126484	−	0.0821700i
$262$	15.6793			0.968668
$263$	−6.24292	+	10.8131i	−0.384955	+	0.666761i	−0.991763	−	0.128087i	$-0.959116\pi$
$263$	−6.24292	+	10.8131i	−0.384955	+	0.666761i	0.606808	+	0.794848i	$0.292450\pi$
$264$	2.10321	−	5.98059i	0.129444	−	0.368080i
$265$	2.49047	+	4.31362i	0.152988	+	0.264983i
$266$	2.79604	+	4.84288i	0.171436	+	0.296936i
$267$	−22.7410	+	4.26596i	−1.39172	+	0.261072i
$268$	−4.88322	+	8.45798i	−0.298290	+	0.516653i
$269$	−10.3394			−0.630407			−0.315204	−	0.949024i	$-0.602073\pi$
$269$	−10.3394			−0.630407			−0.315204	+	0.949024i	$0.602073\pi$
$270$	4.41264	−	2.74383i	0.268545	−	0.166984i
$271$	−6.94892			−0.422117			−0.211059	−	0.977473i	$-0.567691\pi$
$271$	−6.94892			−0.422117			−0.211059	+	0.977473i	$0.567691\pi$
$272$	−2.23339	+	3.86834i	−0.135419	+	0.234553i
$273$	6.08255	−	1.14102i	0.368132	−	0.0690577i
$274$	−6.55312	−	11.3503i	−0.395888	−	0.685699i
$275$	−1.83010	−	3.16982i	−0.110359	−	0.191147i
$276$	−1.52859	+	4.34664i	−0.0920106	+	0.261637i
$277$	6.64113	−	11.5028i	0.399027	−	0.691135i	−0.594579	−	0.804037i	$-0.702681\pi$
$277$	6.64113	−	11.5028i	0.399027	−	0.691135i	0.993606	+	0.112902i	$0.0360147\pi$
$278$	17.0207			1.02084
$279$	21.4875	+	17.2460i	1.28642	+	1.03249i
$280$	1.00000			0.0597614
$281$	9.65455	−	16.7222i	0.575942	−	0.997561i	−0.419997	−	0.907526i	$-0.637969\pi$
$281$	9.65455	−	16.7222i	0.575942	−	0.997561i	0.995939	−	0.0900352i	$-0.0286979\pi$
$282$	13.8389	+	16.1320i	0.824092	+	0.960649i
$283$	7.13567	+	12.3593i	0.424171	+	0.734686i	0.996343	−	0.0854478i	$-0.0272321\pi$
$283$	7.13567	+	12.3593i	0.424171	+	0.734686i	−0.572171	+	0.820134i	$0.693899\pi$
$284$	−1.94688	−	3.37209i	−0.115526	−	0.200097i
$285$	−6.30640	−	7.35141i	−0.373559	−	0.435460i
$286$	−6.53896	+	11.3258i	−0.386657	+	0.669709i
$287$	4.57301			0.269936
$288$	−2.33963	−	1.87780i	−0.137864	−	0.110651i
$289$	2.95207			0.173651
$290$	−0.223855	+	0.387729i	−0.0131452	+	0.0227682i
$291$	−4.90314	+	13.9423i	−0.287427	+	0.817314i
$292$	−3.07301	−	5.32262i	−0.179835	−	0.311483i
$293$	−4.56164	−	7.90099i	−0.266494	−	0.461581i	0.701460	−	0.712709i	$-0.252532\pi$
$293$	−4.56164	−	7.90099i	−0.266494	−	0.461581i	−0.967954	+	0.251128i	$0.919199\pi$
$294$	−1.70236	+	0.319344i	−0.0992835	+	0.0186245i
$295$	−6.45623	+	11.1825i	−0.375896	+	0.651071i
$296$	−10.1651			−0.590834
$297$	−0.621883	−	19.0087i	−0.0360853	−	1.10300i
$298$	14.3095			0.828925
$299$	4.75245	−	8.23149i	0.274841	−	0.476039i
$300$	−1.70236	+	0.319344i	−0.0982856	+	0.0184373i
$301$	3.61660	+	6.26414i	0.208458	+	0.361059i
$302$	−6.01036	−	10.4103i	−0.345858	−	0.599043i
$303$	7.63223	−	21.7026i	0.438460	−	1.24678i
$304$	−2.79604	+	4.84288i	−0.160364	+	0.277758i
$305$	−1.19342			−0.0683349
$306$	−2.03869	+	13.2443i	−0.116544	+	0.757128i
$307$	−13.4892			−0.769867			−0.384934	−	0.922944i	$-0.625776\pi$
$307$	−13.4892			−0.769867			−0.384934	+	0.922944i	$0.625776\pi$
$308$	1.83010	−	3.16982i	0.104279	−	0.180617i
$309$	−16.1281	−	18.8007i	−0.917498	−	1.06953i
$310$	−4.59208	−	7.95371i	−0.260812	−	0.451740i
$311$	−4.87267	−	8.43971i	−0.276304	−	0.478572i	0.694159	−	0.719821i	$-0.255776\pi$
$311$	−4.87267	−	8.43971i	−0.276304	−	0.478572i	−0.970463	+	0.241249i	$0.922443\pi$
$312$	4.02943	+	4.69713i	0.228121	+	0.265923i
$313$	2.58356	−	4.47485i	0.146031	−	0.252934i	−0.783726	−	0.621107i	$-0.786683\pi$
$313$	2.58356	−	4.47485i	0.146031	−	0.252934i	0.929757	+	0.368173i	$0.120017\pi$
$314$	−6.63947			−0.374687
$315$	2.79604	−	1.08728i	0.157539	−	0.0612610i
$316$	−2.23321			−0.125628
$317$	3.04442	−	5.27309i	0.170992	−	0.296166i	−0.767775	−	0.640719i	$-0.778636\pi$
$317$	3.04442	−	5.27309i	0.170992	−	0.296166i	0.938767	+	0.344553i	$0.111970\pi$
$318$	2.86214	−	8.13863i	0.160501	−	0.456392i
$319$	0.819354	+	1.41916i	0.0458750	+	0.0794578i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−16.1993	+	3.03882i	−0.904158	+	0.169610i
$322$	−1.33010	+	2.30379i	−0.0741233	+	0.128385i
$323$	24.9785			1.38984
$324$	−8.58338	−	2.70659i	−0.476854	−	0.150366i
$325$	3.57301			0.198195
$326$	−3.73339	+	6.46642i	−0.206773	+	0.358142i
$327$	−0.791787	+	0.148531i	−0.0437859	+	0.00821377i
$328$	2.28651	+	3.96035i	0.126251	+	0.218674i
$329$	6.13567	+	10.6273i	0.338270	+	0.585901i
$330$	−2.10321	+	5.98059i	−0.115778	+	0.329221i
$331$	−15.7277	+	27.2413i	−0.864475	+	1.49731i	0.00309258	+	0.999995i	$0.499016\pi$
$331$	−15.7277	+	27.2413i	−0.864475	+	1.49731i	−0.867568	+	0.497319i	$0.834318\pi$
$332$	−11.3792			−0.624517
$333$	−28.4220	+	11.0523i	−1.55752	+	0.605660i
$334$	3.97001			0.217229
$335$	4.88322	−	8.45798i	0.266799	−	0.462109i
$336$	−1.12774	−	1.31461i	−0.0615232	−	0.0717180i
$337$	11.6991	+	20.2635i	0.637293	+	1.10382i	0.986024	+	0.166601i	$0.0532793\pi$
$337$	11.6991	+	20.2635i	0.637293	+	1.10382i	−0.348731	+	0.937223i	$0.613387\pi$
$338$	0.116784	+	0.202277i	0.00635223	+	0.0110024i
$339$	2.42057	+	2.82167i	0.131467	+	0.153252i
$340$	2.23339	−	3.86834i	0.121122	−	0.209790i
$341$	−33.6158			−1.82040
$342$	−2.55229	+	16.5809i	−0.138012	+	0.896595i
$343$	−1.00000			−0.0539949
$344$	−3.61660	+	6.26414i	−0.194994	+	0.337740i
$345$	1.52859	−	4.34664i	0.0822968	−	0.234015i
$346$	4.59208	+	7.95371i	0.246872	+	0.427594i
$347$	7.56247	+	13.0986i	0.405975	+	0.703169i	0.994434	−	0.105358i	$-0.0335988\pi$
$347$	7.56247	+	13.0986i	0.405975	+	0.703169i	−0.588460	+	0.808527i	$0.700265\pi$
$348$	0.762164	−	0.142974i	0.0408563	−	0.00766420i
$349$	9.68555	−	16.7759i	0.518455	−	0.897991i	−0.481315	−	0.876548i	$-0.659841\pi$
$349$	9.68555	−	16.7759i	0.518455	−	0.897991i	0.999770	−	0.0214433i	$-0.00682613\pi$
$350$	−1.00000			−0.0534522
$351$	16.3735	+	8.75226i	0.873953	+	0.467161i
$352$	3.66019			0.195089
$353$	−14.7626	+	25.5696i	−0.785736	+	1.36093i	0.142823	+	0.989748i	$0.454382\pi$
$353$	−14.7626	+	25.5696i	−0.785736	+	1.36093i	−0.928559	+	0.371186i	$0.878951\pi$
$354$	21.9816	−	4.12352i	1.16831	−	0.219162i
$355$	1.94688	+	3.37209i	0.103330	+	0.178972i
$356$	−6.67925	−	11.5688i	−0.354000	−	0.613146i
$357$	−2.56669	+	7.29851i	−0.135844	+	0.386278i
$358$	−1.17074	+	2.02777i	−0.0618753	+	0.107171i
$359$	−15.6217			−0.824482			−0.412241	−	0.911075i	$-0.635254\pi$
$359$	−15.6217			−0.824482			−0.412241	+	0.911075i	$0.635254\pi$
$360$	2.33963	+	1.87780i	0.123309	+	0.0989689i
$361$	12.2713			0.645860
$362$	−9.33945	+	16.1764i	−0.490870	+	0.850212i
$363$	2.70319	+	3.15112i	0.141881	+	0.165391i
$364$	1.78651	+	3.09432i	0.0936384	+	0.162186i
$365$	3.07301	+	5.32262i	0.160849	+	0.278599i
$366$	1.34586	+	1.56888i	0.0703493	+	0.0820067i
$367$	12.6659	−	21.9380i	0.661156	−	1.14516i	−0.319156	−	0.947702i	$-0.603400\pi$
$367$	12.6659	−	21.9380i	0.661156	−	1.14516i	0.980312	−	0.197453i	$-0.0632671\pi$
$368$	−2.66019			−0.138672
$369$	10.6991	+	8.58722i	0.556975	+	0.447033i
$370$	10.1651			0.528458
$371$	2.49047	−	4.31362i	0.129299	−	0.223952i
$372$	−5.27739	+	15.0065i	−0.273620	+	0.778051i
$373$	8.00000	+	13.8564i	0.414224	+	0.717458i	0.995347	−	0.0963587i	$-0.0307196\pi$
$373$	8.00000	+	13.8564i	0.414224	+	0.717458i	−0.581122	+	0.813816i	$0.697386\pi$
$374$	−8.17462	−	14.1589i	−0.422700	−	0.732137i
$375$	1.70236	−	0.319344i	0.0879093	−	0.0164909i
$376$	−6.13567	+	10.6273i	−0.316423	+	0.548060i
$377$	−1.59968			−0.0823876
$378$	−4.58255	−	2.44955i	−0.235701	−	0.125991i
$379$	23.4571			1.20491			0.602456	−	0.798152i	$-0.294189\pi$
$379$	23.4571			1.20491			0.602456	+	0.798152i	$0.294189\pi$
$380$	2.79604	−	4.84288i	0.143434	−	0.248435i
$381$	7.93331	−	1.48820i	0.406436	−	0.0762430i
$382$	−9.37960	−	16.2459i	−0.479902	−	0.831215i
$383$	−5.99130	−	10.3772i	−0.306141	−	0.530252i	0.671374	−	0.741119i	$-0.265705\pi$
$383$	−5.99130	−	10.3772i	−0.306141	−	0.530252i	−0.977515	+	0.210867i	$0.932371\pi$
$384$	0.574618	−	1.63396i	0.0293234	−	0.0833825i
$385$	−1.83010	+	3.16982i	−0.0932703	+	0.161549i
$386$	8.03979			0.409214
$387$	−3.30132	+	21.4470i	−0.167815	+	1.09021i
$388$	−8.53286			−0.433190
$389$	−15.3008	+	26.5017i	−0.775779	+	1.34369i	0.158576	+	0.987347i	$0.449310\pi$
$389$	−15.3008	+	26.5017i	−0.775779	+	1.34369i	−0.934355	+	0.356342i	$0.884024\pi$
$390$	−4.02943	−	4.69713i	−0.204038	−	0.237848i
$391$	5.94124	+	10.2905i	0.300461	+	0.520414i
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$	17.6821	+	20.6121i	0.891944	+	1.03975i
$394$	−3.57765	+	6.19666i	−0.180239	+	0.312183i
$395$	2.23321			0.112365
$396$	10.2340	−	3.97963i	0.514280	−	0.199984i
$397$	−9.76477			−0.490080			−0.245040	−	0.969513i	$-0.578801\pi$
$397$	−9.76477			−0.490080			−0.245040	+	0.969513i	$0.578801\pi$
$398$	−3.43634	+	5.95191i	−0.172248	+	0.298342i
$399$	−3.21331	+	9.13721i	−0.160867	+	0.457433i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−17.1706	−	29.7403i	−0.857457	−	1.48516i	−0.874347	−	0.485301i	$-0.838710\pi$
$401$	−17.1706	−	29.7403i	−0.857457	−	1.48516i	0.0168907	−	0.999857i	$-0.494623\pi$
$402$	−16.6260	+	3.11885i	−0.829227	+	0.155554i
$403$	16.4076	−	28.4187i	0.817319	−	1.41564i
$404$	13.2823			0.660817
$405$	8.58338	+	2.70659i	0.426511	+	0.134492i
$406$	0.447711			0.0222195
$407$	18.6031	−	32.2215i	0.922121	−	1.59716i
$408$	−7.60404	+	1.42644i	−0.376456	+	0.0706192i
$409$	−8.68517	−	15.0432i	−0.429454	−	0.743836i	0.567371	−	0.823462i	$-0.307961\pi$
$409$	−8.68517	−	15.0432i	−0.429454	−	0.743836i	−0.996825	+	0.0796264i	$0.974627\pi$
$410$	−2.28651	−	3.96035i	−0.112923	−	0.195588i
$411$	7.53109	−	21.4150i	0.371481	−	1.05633i
$412$	7.15066	−	12.3853i	0.352288	−	0.610180i
$413$	12.9125			0.635381
$414$	−7.43800	+	2.89236i	−0.365558	+	0.142152i
$415$	11.3792			0.558585
$416$	−1.78651	+	3.09432i	−0.0875907	+	0.151712i
$417$	19.1949	+	22.3757i	0.939980	+	1.09574i
$418$	−10.2340	−	17.7259i	−0.500563	−	0.867001i
$419$	11.6653	+	20.2048i	0.569886	+	0.987071i	0.996577	+	0.0826738i	$0.0263459\pi$
$419$	11.6653	+	20.2048i	0.569886	+	0.987071i	−0.426691	+	0.904398i	$0.640321\pi$
$420$	1.12774	+	1.31461i	0.0550280	+	0.0641465i
$421$	−5.66120	+	9.80549i	−0.275910	+	0.477890i	−0.970364	−	0.241646i	$-0.922313\pi$
$421$	−5.66120	+	9.80549i	−0.275910	+	0.477890i	0.694454	+	0.719537i	$0.255646\pi$
$422$	24.7759			1.20607
$423$	−5.60078	+	36.3855i	−0.272319	+	1.76912i
$424$	4.98094			0.241896
$425$	−2.23339	+	3.86834i	−0.108335	+	0.187642i
$426$	2.23743	−	6.36223i	0.108404	−	0.308251i
$427$	0.596708	+	1.03353i	0.0288767	+	0.0500160i
$428$	−4.75791	−	8.24095i	−0.229982	−	0.398341i
$429$	−22.2633	+	4.17635i	−1.07488	+	0.201636i
$430$	3.61660	−	6.26414i	0.174408	−	0.302084i
$431$	7.97927			0.384348			0.192174	−	0.981361i	$-0.438446\pi$
$431$	7.97927			0.384348			0.192174	+	0.981361i	$0.438446\pi$
$432$	−0.169904	−	5.19337i	−0.00817453	−	0.249866i
$433$	−23.7799			−1.14279			−0.571395	−	0.820675i	$-0.693598\pi$
$433$	−23.7799			−1.14279			−0.571395	+	0.820675i	$0.693598\pi$
$434$	−4.59208	+	7.95371i	−0.220427	+	0.381790i
$435$	−0.762164	+	0.142974i	−0.0365430	+	0.00685507i
$436$	−0.232556	−	0.402799i	−0.0111374	−	0.0192906i
$437$	7.43800	+	12.8830i	0.355808	+	0.616277i
$438$	3.53162	−	10.0423i	0.168747	−	0.479842i
$439$	12.9412	−	22.4149i	0.617652	−	1.06980i	−0.372262	−	0.928128i	$-0.621418\pi$
$439$	12.9412	−	22.4149i	0.617652	−	1.06980i	0.989913	−	0.141676i	$-0.0452491\pi$
$440$	−3.66019			−0.174493
$441$	−2.33963	−	1.87780i	−0.111411	−	0.0894192i
$442$	15.9598			0.759133
$443$	4.95807	−	8.58764i	0.235565	−	0.408011i	−0.723872	−	0.689935i	$-0.757639\pi$
$443$	4.95807	−	8.58764i	0.235565	−	0.408011i	0.959437	+	0.281924i	$0.0909726\pi$
$444$	−11.4636	−	13.3632i	−0.544037	−	0.634187i
$445$	6.67925	+	11.5688i	0.316627	+	0.548414i
$446$	14.8784	+	25.7702i	0.704513	+	1.22025i
$447$	16.1373	+	18.8114i	0.763269	+	0.889748i
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−4.19544			−0.197995			−0.0989976	−	0.995088i	$-0.531564\pi$
$449$	−4.19544			−0.197995			−0.0989976	+	0.995088i	$0.531564\pi$
$450$	−2.33963	−	1.87780i	−0.110291	−	0.0885205i
$451$	−16.7381			−0.788167
$452$	−1.07320	+	1.85883i	−0.0504789	+	0.0874320i
$453$	6.90733	−	19.6413i	0.324535	−	0.922831i
$454$	−7.32991	−	12.6958i	−0.344010	−	0.595843i
$455$	−1.78651	−	3.09432i	−0.0837527	−	0.145064i
$456$	−9.51971	+	1.78580i	−0.445801	+	0.0836276i
$457$	6.43087	−	11.1386i	0.300824	−	0.521042i	−0.675499	−	0.737361i	$-0.736072\pi$
$457$	6.43087	−	11.1386i	0.300824	−	0.521042i	0.976323	+	0.216319i	$0.0694051\pi$
$458$	−19.4855			−0.910496
$459$	−19.7103	+	12.2561i	−0.919997	+	0.572064i
$460$	2.66019			0.124032
$461$	−7.49213	+	12.9768i	−0.348943	+	0.604388i	−0.986062	−	0.166378i	$-0.946793\pi$
$461$	−7.49213	+	12.9768i	−0.348943	+	0.604388i	0.637119	+	0.770766i	$0.280126\pi$
$462$	6.23095	−	1.16886i	0.289890	−	0.0543803i
$463$	1.72830	+	2.99351i	0.0803211	+	0.139120i	0.903388	−	0.428824i	$-0.141072\pi$
$463$	1.72830	+	2.99351i	0.0803211	+	0.139120i	−0.823067	+	0.567945i	$0.807739\pi$
$464$	0.223855	+	0.387729i	0.0103922	+	0.0179999i
$465$	5.27739	−	15.0065i	0.244733	−	0.695910i
$466$	5.87858	−	10.1820i	0.272320	−	0.471672i
$467$	14.1586			0.655183			0.327591	−	0.944820i	$-0.393763\pi$
$467$	14.1586			0.655183			0.327591	+	0.944820i	$0.393763\pi$
$468$	−1.63077	+	10.5943i	−0.0753821	+	0.489720i
$469$	−9.76643			−0.450972
$470$	6.13567	−	10.6273i	0.283017	−	0.490200i
$471$	−7.48758	−	8.72832i	−0.345010	−	0.402180i
$472$	6.45623	+	11.1825i	0.297172	+	0.514717i
$473$	−13.2375	−	22.9279i	−0.608659	−	1.05423i
$474$	−2.51847	−	2.93580i	−0.115677	−	0.134846i
$475$	−2.79604	+	4.84288i	−0.128291	+	0.222207i
$476$	−4.46677			−0.204734
$477$	13.9269	−	5.41565i	0.637669	−	0.247965i
$478$	−4.07625			−0.186443
$479$	17.8346	−	30.8905i	0.814885	−	1.41142i	−0.0945251	−	0.995522i	$-0.530133\pi$
$479$	17.8346	−	30.8905i	0.814885	−	1.41142i	0.909410	−	0.415900i	$-0.136533\pi$
$480$	−0.574618	+	1.63396i	−0.0262276	+	0.0745796i
$481$	18.1600	+	31.4541i	0.828025	+	1.43418i
$482$	11.5057	+	19.9285i	0.524072	+	0.907719i
$483$	−4.52859	+	0.849516i	−0.206058	+	0.0386543i
$484$	−1.19850	+	2.07586i	−0.0544772	+	0.0943574i
$485$	8.53286			0.387457
$486$	−6.12169	−	14.3361i	−0.277685	−	0.650301i
$487$	−21.8290			−0.989165			−0.494583	−	0.869131i	$-0.664679\pi$
$487$	−21.8290			−0.989165			−0.494583	+	0.869131i	$0.664679\pi$
$488$	−0.596708	+	1.03353i	−0.0270117	+	0.0467857i
$489$	−12.7111	+	2.38447i	−0.574817	+	0.107829i
$490$	0.500000	+	0.866025i	0.0225877	+	0.0391230i
$491$	−11.0874	−	19.2040i	−0.500369	−	0.866665i	−1.00000		0.000426678i	$-0.999864\pi$
$491$	−11.0874	−	19.2040i	−0.500369	−	0.866665i	0.499630	−	0.866239i	$-0.333469\pi$
$492$	−2.62774	+	7.47211i	−0.118468	+	0.336869i
$493$	0.999912	−	1.73190i	0.0450338	−	0.0780008i
$494$	19.9806			0.898968
$495$	−10.2340	+	3.97963i	−0.459986	+	0.178871i
$496$	−9.18416			−0.412381
$497$	1.94688	−	3.37209i	0.0873295	−	0.151259i
$498$	−12.8328	−	14.9593i	−0.575052	−	0.670341i
$499$	−2.97649	−	5.15543i	−0.133246	−	0.230789i	0.791680	−	0.610936i	$-0.209207\pi$
$499$	−2.97649	−	5.15543i	−0.133246	−	0.230789i	−0.924926	+	0.380147i	$0.875873\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	4.47714	+	5.21903i	0.200024	+	0.233169i
$502$	11.2577	−	19.4990i	0.502457	−	0.870281i
$503$	−41.4795			−1.84948			−0.924741	−	0.380598i	$-0.875718\pi$
$503$	−41.4795			−1.84948			−0.924741	+	0.380598i	$0.875718\pi$
$504$	0.456412	−	2.96508i	0.0203302	−	0.132075i
$505$	−13.2823			−0.591053
$506$	4.86840	−	8.43232i	0.216427	−	0.374862i
$507$	−0.134213	+	0.381641i	−0.00596061	+	0.0169493i
$508$	2.33010	+	4.03584i	0.103381	+	0.179062i
$509$	−0.596708	−	1.03353i	−0.0264486	−	0.0458104i	0.852498	−	0.522730i	$-0.175087\pi$
$509$	−0.596708	−	1.03353i	−0.0264486	−	0.0458104i	−0.878947	+	0.476920i	$0.841753\pi$
$510$	7.60404	−	1.42644i	0.336713	−	0.0631637i
$511$	3.07301	−	5.32262i	0.135942	−	0.235459i
$512$	1.00000			0.0441942
$513$	−24.6758	+	15.3437i	−1.08946	+	0.677441i
$514$	−4.65129			−0.205160
$515$	−7.15066	+	12.3853i	−0.315096	+	0.545762i
$516$	−12.3135	+	2.30988i	−0.542072	+	0.101687i
$517$	−22.4577	−	38.8979i	−0.987689	−	1.71073i
$518$	−5.08255	−	8.80323i	−0.223314	−	0.386792i
$519$	−5.27739	+	15.0065i	−0.231652	+	0.658713i
$520$	1.78651	−	3.09432i	0.0783435	−	0.135695i
$521$	−1.53452			−0.0672287			−0.0336144	−	0.999435i	$-0.510702\pi$
$521$	−1.53452			−0.0672287			−0.0336144	+	0.999435i	$0.510702\pi$
$522$	1.04748	+	0.840713i	0.0458468	+	0.0367970i
$523$	8.66833			0.379040			0.189520	−	0.981877i	$-0.439307\pi$
$523$	8.66833			0.379040			0.189520	+	0.981877i	$0.439307\pi$
$524$	−7.83963	+	13.5786i	−0.342476	+	0.593185i
$525$	−1.12774	−	1.31461i	−0.0492185	−	0.0573744i
$526$	−6.24292	−	10.8131i	−0.272204	−	0.471471i
$527$	20.5118	+	35.5274i	0.893507	+	1.54760i
$528$	4.12774	+	4.81173i	0.179637	+	0.209404i
$529$	7.96169	−	13.7901i	0.346161	−	0.599568i
$530$	−4.98094			−0.216358
$531$	30.2103	+	24.2471i	1.31102	+	1.05223i
$532$	−5.59208			−0.242447
$533$	8.16972	−	14.1504i	0.353870	−	0.612921i
$534$	7.67605	−	21.8272i	0.332175	−	0.944556i
$535$	4.75791	+	8.24095i	0.205702	+	0.356287i
$536$	−4.88322	−	8.45798i	−0.210923	−	0.365329i
$537$	−3.98602	+	0.747735i	−0.172009	+	0.0322671i
$538$	5.16972	−	8.95422i	0.222883	−	0.386044i
$539$	3.66019			0.157656
$540$	0.169904	+	5.19337i	0.00731152	+	0.223487i
$541$	30.0622			1.29247			0.646237	−	0.763137i	$-0.276342\pi$
$541$	30.0622			1.29247			0.646237	+	0.763137i	$0.276342\pi$
$542$	3.47446	−	6.01795i	0.149241	−	0.258493i
$543$	−31.7981	+	5.96499i	−1.36459	+	0.255982i
$544$	−2.23339	−	3.86834i	−0.0957557	−	0.165854i
$545$	0.232556	+	0.402799i	0.00996161	+	0.0172540i
$546$	−2.05312	+	5.83815i	−0.0878654	+	0.249850i
$547$	19.9070	−	34.4799i	0.851162	−	1.47426i	−0.0289988	−	0.999579i	$-0.509232\pi$
$547$	19.9070	−	34.4799i	0.851162	−	1.47426i	0.880161	−	0.474676i	$-0.157435\pi$
$548$	13.1062			0.559871
$549$	−0.544689	+	3.53857i	−0.0232468	+	0.151023i
$550$	3.66019			0.156071
$551$	1.25182	−	2.16821i	0.0533292	−	0.0923689i
$552$	−3.00000	−	3.49712i	−0.127688	−	0.148847i
$553$	−1.11660	−	1.93401i	−0.0474828	−	0.0822426i
$554$	6.64113	+	11.5028i	0.282154	+	0.488706i
$555$	11.4636	+	13.3632i	0.486601	+	0.567234i
$556$	−8.51036	+	14.7404i	−0.360920	+	0.625131i
$557$	18.9717			0.803856			0.401928	−	0.915671i	$-0.368340\pi$
$557$	18.9717			0.803856			0.401928	+	0.915671i	$0.368340\pi$
$558$	−25.6793	+	9.98570i	−1.08709	+	0.422729i
$559$	25.8443			1.09310
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	9.39458	−	26.7140i	0.396639	−	1.12786i
$562$	9.65455	+	16.7222i	0.407253	+	0.705382i
$563$	−5.79197	−	10.0320i	−0.244102	−	0.422798i	0.717776	−	0.696274i	$-0.245160\pi$
$563$	−5.79197	−	10.0320i	−0.244102	−	0.422798i	−0.961879	+	0.273476i	$0.911827\pi$
$564$	−20.8902	+	3.91878i	−0.879636	+	0.165010i
$565$	1.07320	−	1.85883i	0.0451497	−	0.0782016i
$566$	−14.2713			−0.599869
$567$	−1.94771	−	8.78672i	−0.0817962	−	0.369007i
$568$	3.89376			0.163379
$569$	2.53304	−	4.38736i	0.106191	−	0.183928i	−0.808033	−	0.589137i	$-0.799468\pi$
$569$	2.53304	−	4.38736i	0.106191	−	0.183928i	0.914224	+	0.405209i	$0.132801\pi$
$570$	9.51971	−	1.78580i	0.398737	−	0.0747988i
$571$	−22.6012	−	39.1465i	−0.945833	−	1.63823i	−0.754075	−	0.656788i	$-0.771915\pi$
$571$	−22.6012	−	39.1465i	−0.945833	−	1.63823i	−0.191757	−	0.981442i	$-0.561419\pi$
$572$	−6.53896	−	11.3258i	−0.273408	−	0.473556i
$573$	10.7794	−	30.6517i	0.450315	−	1.28049i
$574$	−2.28651	+	3.96035i	−0.0954370	+	0.165302i
$575$	−2.66019			−0.110938
$576$	2.79604	−	1.08728i	0.116502	−	0.0453031i
$577$	35.8246			1.49140			0.745698	−	0.666284i	$-0.232116\pi$
$577$	35.8246			1.49140			0.745698	+	0.666284i	$0.232116\pi$
$578$	−1.47604	+	2.55657i	−0.0613950	+	0.106339i
$579$	9.06678	+	10.5692i	0.376802	+	0.439241i
$580$	−0.223855	−	0.387729i	−0.00929509	−	0.0160996i
$581$	−5.68962	−	9.85471i	−0.236045	−	0.408842i
$582$	−9.62284	−	11.2174i	−0.398879	−	0.464976i
$583$	−9.11559	+	15.7887i	−0.377529	+	0.653900i
$584$	6.14603			0.254324
$585$	1.63077	−	10.5943i	0.0674238	−	0.438019i
$586$	9.12328			0.376879
$587$	1.85988	−	3.22142i	0.0767657	−	0.132962i	−0.825087	−	0.565006i	$-0.808874\pi$
$587$	1.85988	−	3.22142i	0.0767657	−	0.132962i	0.901853	+	0.432044i	$0.142207\pi$
$588$	0.574618	−	1.63396i	0.0236969	−	0.0673832i
$589$	25.6793	+	44.4778i	1.05810	+	1.83267i
$590$	−6.45623	−	11.1825i	−0.265799	−	0.460377i
$591$	−12.1809	+	2.28500i	−0.501054	+	0.0939923i
$592$	5.08255	−	8.80323i	0.208891	−	0.361810i
$593$	21.5845			0.886368			0.443184	−	0.896431i	$-0.353849\pi$
$593$	21.5845			0.886368			0.443184	+	0.896431i	$0.353849\pi$
$594$	16.7730	+	8.96580i	0.688204	+	0.367871i
$595$	4.46677			0.183120
$596$	−7.15473	+	12.3924i	−0.293069	+	0.507611i
$597$	−11.6997	+	2.19475i	−0.478838	+	0.0898250i
$598$	4.75245	+	8.23149i	0.194342	+	0.336610i
$599$	−8.32908	−	14.4264i	−0.340317	−	0.589447i	0.644174	−	0.764879i	$-0.277201\pi$
$599$	−8.32908	−	14.4264i	−0.340317	−	0.589447i	−0.984492	+	0.175432i	$0.943868\pi$
$600$	0.574618	−	1.63396i	0.0234587	−	0.0667060i
$601$	7.98685	−	13.8336i	0.325790	−	0.564286i	−0.655882	−	0.754864i	$-0.727703\pi$
$601$	7.98685	−	13.8336i	0.325790	−	0.564286i	0.981672	+	0.190578i	$0.0610363\pi$
$602$	−7.23321			−0.294803
$603$	−22.8498	−	18.3394i	−0.930516	−	0.746840i
$604$	12.0207			0.489116
$605$	1.19850	−	2.07586i	0.0487259	−	0.0843958i
$606$	14.9789	+	17.4610i	0.608477	+	0.709305i
$607$	1.78752	+	3.09608i	0.0725532	+	0.125666i	0.900020	−	0.435849i	$-0.143552\pi$
$607$	1.78752	+	3.09608i	0.0725532	+	0.125666i	−0.827466	+	0.561515i	$0.810219\pi$
$608$	−2.79604	−	4.84288i	−0.113394	−	0.196405i
$609$	0.504901	+	0.588566i	0.0204596	+	0.0238499i
$610$	0.596708	−	1.03353i	0.0241600	−	0.0418464i
$611$	43.8456			1.77380
$612$	−10.4506	−	8.38772i	−0.422440	−	0.339054i
$613$	−19.4388			−0.785126			−0.392563	−	0.919725i	$-0.628412\pi$
$613$	−19.4388			−0.785126			−0.392563	+	0.919725i	$0.628412\pi$
$614$	6.74458	−	11.6820i	0.272189	−	0.471445i
$615$	2.62774	−	7.47211i	0.105961	−	0.301304i
$616$	1.83010	+	3.16982i	0.0737367	+	0.127716i
$617$	−6.48667	−	11.2352i	−0.261143	−	0.452314i	0.705403	−	0.708807i	$-0.250766\pi$
$617$	−6.48667	−	11.2352i	−0.261143	−	0.452314i	−0.966546	+	0.256493i	$0.917433\pi$
$618$	24.3460	−	4.56704i	0.979338	−	0.183713i
$619$	17.7225	−	30.6962i	0.712327	−	1.23379i	−0.251655	−	0.967817i	$-0.580975\pi$
$619$	17.7225	−	30.6962i	0.712327	−	1.23379i	0.963982	−	0.265969i	$-0.0856918\pi$
$620$	9.18416			0.368845
$621$	−12.1904	−	6.51626i	−0.489186	−	0.261488i
$622$	9.74534			0.390753
$623$	6.67925	−	11.5688i	0.267599	−	0.463495i
$624$	−6.08255	+	1.14102i	−0.243497	+	0.0456774i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	2.58356	+	4.47485i	0.103260	+	0.178851i
$627$	11.7613	−	33.4439i	0.469702	−	1.33562i
$628$	3.31973	−	5.74995i	0.132472	−	0.229448i
$629$	−45.4052			−1.81042
$630$	−0.456412	+	2.96508i	−0.0181839	+	0.118132i
$631$	1.54505			0.0615076			0.0307538	−	0.999527i	$-0.490209\pi$
$631$	1.54505			0.0615076			0.0307538	+	0.999527i	$0.490209\pi$
$632$	1.11660	−	1.93401i	0.0444161	−	0.0769309i
$633$	27.9407	+	32.5707i	1.11054	+	1.29457i
$634$	3.04442	+	5.27309i	0.120909	+	0.209421i
$635$	−2.33010	−	4.03584i	−0.0924670	−	0.160158i
$636$	5.61719	+	6.54800i	0.222736	+	0.259645i
$637$	−1.78651	+	3.09432i	−0.0707840	+	0.122601i
$638$	−1.63871			−0.0648770
$639$	10.8871	−	4.23359i	0.430687	−	0.167478i
$640$	−1.00000			−0.0395285
$641$	7.62132	−	13.2005i	0.301024	−	0.521389i	−0.675344	−	0.737503i	$-0.736005\pi$
$641$	7.62132	−	13.2005i	0.301024	−	0.521389i	0.976368	+	0.216114i	$0.0693382\pi$
$642$	5.46797	−	15.5484i	0.215804	−	0.613648i
$643$	−8.32991	−	14.4278i	−0.328500	−	0.568978i	0.653715	−	0.756741i	$-0.273210\pi$
$643$	−8.32991	−	14.4278i	−0.328500	−	0.568978i	−0.982214	+	0.187763i	$0.939876\pi$
$644$	−1.33010	−	2.30379i	−0.0524131	−	0.0907822i
$645$	12.3135	−	2.30988i	0.484844	−	0.0909515i
$646$	−12.4893	+	21.6321i	−0.491384	+	0.851102i
$647$	−3.40995			−0.134059			−0.0670294	−	0.997751i	$-0.521352\pi$
$647$	−3.40995			−0.134059			−0.0670294	+	0.997751i	$0.521352\pi$
$648$	6.63567	−	6.08013i	0.260674	−	0.238850i
$649$	−47.2621			−1.85520
$650$	−1.78651	+	3.09432i	−0.0700726	+	0.121369i
$651$	−15.6347	+	2.93290i	−0.612773	+	0.114950i
$652$	−3.73339	−	6.46642i	−0.146211	−	0.253244i
$653$	14.8845	+	25.7807i	0.582475	+	1.00888i	0.995185	+	0.0980144i	$0.0312491\pi$
$653$	14.8845	+	25.7807i	0.582475	+	1.00888i	−0.412710	+	0.910863i	$0.635418\pi$
$654$	0.267262	−	0.759973i	0.0104508	−	0.0297173i
$655$	7.83963	−	13.5786i	0.306320	−	0.530561i
$656$	−4.57301			−0.178546
$657$	17.1845	−	6.68242i	0.670433	−	0.260706i
$658$	−12.2713			−0.478386
$659$	1.29132	−	2.23663i	0.0503027	−	0.0871268i	−0.839778	−	0.542930i	$-0.817315\pi$
$659$	1.29132	−	2.23663i	0.0503027	−	0.0871268i	0.890080	+	0.455804i	$0.150648\pi$
$660$	−4.12774	−	4.81173i	−0.160672	−	0.187296i
$661$	−4.75717	−	8.23966i	−0.185032	−	0.320486i	0.758555	−	0.651609i	$-0.225906\pi$
$661$	−4.75717	−	8.23966i	−0.185032	−	0.320486i	−0.943587	+	0.331123i	$0.892572\pi$
$662$	−15.7277	−	27.2413i	−0.611276	−	1.05876i
$663$	17.9985	+	20.9810i	0.699005	+	0.814835i
$664$	5.68962	−	9.85471i	0.220800	−	0.382437i
$665$	5.59208			0.216851
$666$	4.63947	−	30.1403i	0.179776	−	1.16791i
$667$	1.19100			0.0461156
$668$	−1.98501	+	3.43813i	−0.0768022	+	0.133025i
$669$	−17.0988	+	48.6213i	−0.661078	+	1.87981i
$670$	4.88322	+	8.45798i	0.188655	+	0.326760i
$671$	−2.18407	−	3.78291i	−0.0843150	−	0.146038i
$672$	1.70236	−	0.319344i	0.0656698	−	0.0123190i
$673$	6.93189	−	12.0064i	0.267205	−	0.462812i	−0.700934	−	0.713226i	$-0.747233\pi$
$673$	6.93189	−	12.0064i	0.267205	−	0.462812i	0.968139	+	0.250414i	$0.0805667\pi$
$674$	−23.3983			−0.901269
$675$	−0.169904	−	5.19337i	−0.00653963	−	0.199893i
$676$	−0.233569			−0.00898342
$677$	−19.1069	+	33.0941i	−0.734337	+	1.27191i	0.220676	+	0.975347i	$0.429174\pi$
$677$	−19.1069	+	33.0941i	−0.734337	+	1.27191i	−0.955013	+	0.296563i	$0.904160\pi$
$678$	−3.65393	+	0.685437i	−0.140328	+	0.0263241i
$679$	−4.26643	−	7.38968i	−0.163731	−	0.283590i
$680$	2.23339	+	3.86834i	0.0856465	+	0.148344i
$681$	8.42381	−	23.9535i	0.322801	−	0.917901i
$682$	16.8079	−	29.1121i	0.643607	−	1.11476i
$683$	33.0106			1.26311			0.631557	−	0.775329i	$-0.282416\pi$
$683$	33.0106			1.26311			0.631557	+	0.775329i	$0.282416\pi$
$684$	−13.0834	−	10.5008i	−0.500255	−	0.401509i
$685$	−13.1062			−0.500764
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−21.9745	−	25.6158i	−0.838380	−	0.977305i
$688$	−3.61660	−	6.26414i	−0.137882	−	0.238818i
$689$	−8.89848	−	15.4126i	−0.339005	−	0.587174i
$690$	3.00000	+	3.49712i	0.114208	+	0.133133i
$691$	−23.3411	+	40.4280i	−0.887938	+	1.53795i	−0.0456283	+	0.998958i	$0.514529\pi$
$691$	−23.3411	+	40.4280i	−0.887938	+	1.53795i	−0.842309	+	0.538995i	$0.818804\pi$
$692$	−9.18416			−0.349129
$693$	8.56348	+	6.87312i	0.325300	+	0.261088i
$694$	−15.1249			−0.574135
$695$	8.51036	−	14.7404i	0.322816	−	0.559134i
$696$	−0.257263	+	0.731540i	−0.00975153	+	0.0277290i
$697$	10.2133	+	17.6900i	0.386857	+	0.670056i
$698$	9.68555	+	16.7759i	0.366603	+	0.634976i
$699$	20.0149	−	3.75458i	0.757033	−	0.142011i
$700$	0.500000	−	0.866025i	0.0188982	−	0.0327327i
$701$	−18.8553			−0.712154			−0.356077	−	0.934457i	$-0.615886\pi$
$701$	−18.8553			−0.712154			−0.356077	+	0.934457i	$0.615886\pi$
$702$	−15.7664	+	9.80374i	−0.595066	+	0.370018i
$703$	−56.8440			−2.14391
$704$	−1.83010	+	3.16982i	−0.0689743	+	0.119467i
$705$	20.8902	−	3.91878i	0.786770	−	0.147590i
$706$	−14.7626	−	25.5696i	−0.555599	−	0.962326i
$707$	6.64113	+	11.5028i	0.249765	+	0.432606i
$708$	−7.41974	+	21.0984i	−0.278851	+	0.792926i
$709$	−1.90145	+	3.29340i	−0.0714104	+	0.123686i	−0.899520	−	0.436880i	$-0.856083\pi$
$709$	−1.90145	+	3.29340i	−0.0714104	+	0.123686i	0.828109	+	0.560567i	$0.189417\pi$
$710$	−3.89376			−0.146130
$711$	1.01926	−	6.62163i	0.0382253	−	0.248330i
$712$	13.3585			0.500631
$713$	−12.2158	+	21.1584i	−0.457485	+	0.792388i
$714$	−5.03735	−	5.87208i	−0.188518	−	0.219757i
$715$	6.53896	+	11.3258i	0.244543	+	0.423561i
$716$	−1.17074	−	2.02777i	−0.0437524	−	0.0757814i
$717$	−4.59695	−	5.35869i	−0.171676	−	0.200124i
$718$	7.81085	−	13.5288i	0.291498	−	0.504890i
$719$	−14.9530			−0.557652			−0.278826	−	0.960342i	$-0.589945\pi$
$719$	−14.9530			−0.557652			−0.278826	+	0.960342i	$0.589945\pi$
$720$	−2.79604	+	1.08728i	−0.104202	+	0.0405203i
$721$	14.3013			0.532609
$722$	−6.13567	+	10.6273i	−0.228346	+	0.395507i
$723$	−13.2228	+	37.5997i	−0.491762	+	1.39835i
$724$	−9.33945	−	16.1764i	−0.347098	−	0.601191i
$725$	0.223855	+	0.387729i	0.00831378	+	0.0143999i
$726$	−4.08055	+	0.765467i	−0.151443	+	0.0284092i
$727$	−16.1627	+	27.9946i	−0.599441	+	1.03826i	0.393463	+	0.919340i	$0.371277\pi$
$727$	−16.1627	+	27.9946i	−0.599441	+	1.03826i	−0.992904	+	0.118921i	$0.962056\pi$
$728$	−3.57301			−0.132425
$729$	11.9428	−	24.2151i	0.442326	−	0.896854i
$730$	−6.14603			−0.227475
$731$	−16.1545	+	27.9805i	−0.597498	+	1.03490i
$732$	−2.03162	+	0.381111i	−0.0750909	+	0.0140863i
$733$	9.96233	+	17.2553i	0.367967	+	0.637337i	0.989248	−	0.146251i	$-0.0467206\pi$
$733$	9.96233	+	17.2553i	0.367967	+	0.637337i	−0.621281	+	0.783588i	$0.713387\pi$
$734$	12.6659	+	21.9380i	0.467508	+	0.809747i
$735$	−0.574618	+	1.63396i	−0.0211951	+	0.0602694i
$736$	1.33010	−	2.30379i	0.0490280	−	0.0849189i
$737$	35.7470			1.31676
$738$	−12.7863	+	4.97212i	−0.470671	+	0.183026i
$739$	−50.3032			−1.85043			−0.925216	−	0.379441i	$-0.876116\pi$
$739$	−50.3032			−1.85043			−0.925216	+	0.379441i	$0.876116\pi$
$740$	−5.08255	+	8.80323i	−0.186838	+	0.323613i
$741$	22.5329	+	26.2667i	0.827765	+	0.964932i
$742$	2.49047	+	4.31362i	0.0914280	+	0.158358i
$743$	−9.23321	−	15.9924i	−0.338733	−	0.586704i	0.645461	−	0.763793i	$-0.276665\pi$
$743$	−9.23321	−	15.9924i	−0.338733	−	0.586704i	−0.984195	+	0.177089i	$0.943332\pi$
$744$	−10.3573	−	12.0736i	−0.379718	−	0.442640i
$745$	7.15473	−	12.3924i	0.262129	−	0.454021i
$746$	−16.0000			−0.585802
$747$	5.19361	−	33.7403i	0.190024	−	1.23449i
$748$	16.3492			0.597788
$749$	4.75791	−	8.24095i	0.173850	−	0.301118i
$750$	−0.574618	+	1.63396i	−0.0209821	+	0.0596637i
$751$	19.0348	+	32.9692i	0.694590	+	1.20306i	0.970319	+	0.241829i	$0.0777473\pi$
$751$	19.0348	+	32.9692i	0.694590	+	1.20306i	−0.275729	+	0.961235i	$0.588919\pi$
$752$	−6.13567	−	10.6273i	−0.223745	−	0.387537i
$753$	38.3294	−	7.19018i	1.39680	−	0.262025i
$754$	0.799839	−	1.38536i	0.0291284	−	0.0504519i
$755$	−12.0207			−0.437479
$756$	4.41264	−	2.74383i	0.160486	−	0.0997921i
$757$	−50.4531			−1.83375			−0.916875	−	0.399176i	$-0.869296\pi$
$757$	−50.4531			−1.83375			−0.916875	+	0.399176i	$0.869296\pi$
$758$	−11.7286	+	20.3145i	−0.426001	+	0.737855i
$759$	16.5755	−	3.10939i	0.601653	−	0.112864i
$760$	2.79604	+	4.84288i	0.101423	+	0.175670i
$761$	−10.4286	−	18.0629i	−0.378038	−	0.654781i	0.612739	−	0.790286i	$-0.290068\pi$
$761$	−10.4286	−	18.0629i	−0.378038	−	0.654781i	−0.990777	+	0.135504i	$0.956735\pi$
$762$	−2.67783	+	7.61455i	−0.0970076	+	0.275846i
$763$	0.232556	−	0.402799i	0.00841910	−	0.0145823i
$764$	18.7592			0.678684
$765$	10.4506	+	8.38772i	0.377842	+	0.303259i
$766$	11.9826			0.432949
$767$	23.0682	−	39.9553i	0.832944	−	1.44270i
$768$	1.12774	+	1.31461i	0.0406938	+	0.0474370i
$769$	11.5777	+	20.0532i	0.417504	+	0.723138i	0.995688	−	0.0927688i	$-0.0295717\pi$
$769$	11.5777	+	20.0532i	0.417504	+	0.723138i	−0.578184	+	0.815906i	$0.696238\pi$
$770$	−1.83010	−	3.16982i	−0.0659521	−	0.114232i
$771$	−5.24544	−	6.11465i	−0.188910	−	0.220214i
$772$	−4.01989	+	6.96266i	−0.144679	+	0.250592i
$773$	−47.8229			−1.72007			−0.860035	−	0.510235i	$-0.829558\pi$
$773$	−47.8229			−1.72007			−0.860035	+	0.510235i	$0.829558\pi$
$774$	−16.9230	−	13.5825i	−0.608285	−	0.488214i
$775$	−9.18416			−0.329905
$776$	4.26643	−	7.38968i	0.153156	−	0.265274i
$777$	5.84105	−	16.6093i	0.209546	−	0.595856i
$778$	−15.3008	−	26.5017i	−0.548559	−	0.950132i
$779$	12.7863	+	22.1466i	0.458118	+	0.793483i
$780$	6.08255	−	1.14102i	0.217790	−	0.0408551i
$781$	−7.12595	+	12.3425i	−0.254987	+	0.441650i
$782$	−11.8825			−0.424916
$783$	0.0760681	+	2.32513i	0.00271845	+	0.0830934i
$784$	1.00000			0.0357143
$785$	−3.31973	+	5.74995i	−0.118486	+	0.205224i
$786$	−26.6917	+	5.00708i	−0.952061	+	0.178596i
$787$	4.28169	+	7.41611i	0.152626	+	0.264356i	0.932192	−	0.361964i	$-0.117894\pi$
$787$	4.28169	+	7.41611i	0.152626	+	0.264356i	−0.779566	+	0.626320i	$0.784560\pi$
$788$	−3.57765	−	6.19666i	−0.127448	−	0.220747i
$789$	7.17459	−	20.4013i	0.255422	−	0.726306i
$790$	−1.11660	+	1.93401i	−0.0397269	+	0.0688091i
$791$	−2.14639			−0.0763169
$792$	−1.67055	+	10.8528i	−0.0593605	+	0.385636i
$793$	4.26410			0.151422
$794$	4.88238	−	8.45654i	0.173269	−	0.300111i
$795$	−5.61719	−	6.54800i	−0.199221	−	0.232234i
$796$	−3.43634	−	5.95191i	−0.121798	−	0.210960i
$797$	20.2038	+	34.9940i	0.715655	+	1.23955i	0.962707	+	0.270548i	$0.0872048\pi$
$797$	20.2038	+	34.9940i	0.715655	+	1.23955i	−0.247052	+	0.969002i	$0.579462\pi$
$798$	−6.30640	−	7.35141i	−0.223244	−	0.260237i
$799$	−27.4066	+	47.4697i	−0.969577	+	1.67936i
$800$	1.00000			0.0353553
$801$	37.3509	−	14.5244i	1.31973	−	0.513193i
$802$	34.3411			1.21263
$803$	−11.2478	+	19.4818i	−0.396927	+	0.687498i
$804$	5.61197	−	15.9579i	0.197919	−	0.562793i
$805$	1.33010	+	2.30379i	0.0468797	+	0.0811980i
$806$	16.4076	+	28.4187i	0.577932	+	1.00101i
$807$	17.6014	−	3.30184i	0.619600	−	0.116230i
$808$	−6.64113	+	11.5028i	−0.233634	+	0.404666i
$809$	−28.9325			−1.01721			−0.508606	−	0.861000i	$-0.669839\pi$
$809$	−28.9325			−1.01721			−0.508606	+	0.861000i	$0.669839\pi$
$810$	−6.63567	+	6.08013i	−0.233154	+	0.213634i
$811$	2.27170			0.0797700			0.0398850	−	0.999204i	$-0.487301\pi$
$811$	2.27170			0.0797700			0.0398850	+	0.999204i	$0.487301\pi$
$812$	−0.223855	+	0.387729i	−0.00785579	+	0.0136066i
$813$	11.8296	−	2.21910i	0.414880	−	0.0778271i
$814$	18.6031	+	32.2215i	0.652038	+	1.12936i
$815$	3.73339	+	6.46642i	0.130775	+	0.226509i
$816$	2.56669	−	7.29851i	0.0898522	−	0.255499i
$817$	−20.2243	+	35.0296i	−0.707559	+	1.22553i
$818$	17.3703			0.607340
$819$	−9.99029	+	3.88485i	−0.349089	+	0.135748i
$820$	4.57301			0.159697
$821$	1.72932	−	2.99527i	0.0603536	−	0.104535i	−0.834270	−	0.551356i	$-0.814111\pi$
$821$	1.72932	−	2.99527i	0.0603536	−	0.104535i	0.894623	+	0.446821i	$0.147444\pi$
$822$	14.7804	+	17.2296i	0.515526	+	0.600952i
$823$	−7.64122	−	13.2350i	−0.266356	−	0.461342i	0.701562	−	0.712608i	$-0.252486\pi$
$823$	−7.64122	−	13.2350i	−0.266356	−	0.461342i	−0.967918	+	0.251266i	$0.919153\pi$
$824$	7.15066	+	12.3853i	0.249105	+	0.431463i
$825$	4.12774	+	4.81173i	0.143709	+	0.167523i
$826$	−6.45623	+	11.1825i	−0.224641	+	0.389090i
$827$	48.8246			1.69780			0.848898	−	0.528557i	$-0.177267\pi$
$827$	48.8246			1.69780			0.848898	+	0.528557i	$0.177267\pi$
$828$	1.21414	−	7.88767i	0.0421944	−	0.274116i
$829$	1.04793			0.0363961			0.0181980	−	0.999834i	$-0.494207\pi$
$829$	1.04793			0.0363961			0.0181980	+	0.999834i	$0.494207\pi$
$830$	−5.68962	+	9.85471i	−0.197489	+	0.342062i
$831$	−7.63223	+	21.7026i	−0.264759	+	0.752856i
$832$	−1.78651	−	3.09432i	−0.0619360	−	0.107276i
$833$	−2.23339	−	3.86834i	−0.0773823	−	0.134030i
$834$	−28.9754	+	5.43547i	−1.00333	+	0.188215i
$835$	1.98501	−	3.43813i	0.0686940	−	0.118981i
$836$	20.4681			0.707903
$837$	−42.0868	−	22.4970i	−1.45473	−	0.777610i
$838$	−23.3305			−0.805940
$839$	8.68897	−	15.0497i	0.299976	−	0.519575i	−0.676154	−	0.736761i	$-0.736354\pi$
$839$	8.68897	−	15.0497i	0.299976	−	0.519575i	0.976130	+	0.217186i	$0.0696878\pi$
$840$	−1.70236	+	0.319344i	−0.0587369	+	0.0110184i
$841$	14.3998	+	24.9411i	0.496544	+	0.860040i
$842$	−5.66120	−	9.80549i	−0.195098	−	0.337920i
$843$	−11.0954	+	31.5502i	−0.382145	+	1.08665i
$844$	−12.3879	+	21.4565i	−0.426410	+	0.738564i
$845$	0.233569			0.00803501
$846$	−28.7103	−	23.0431i	−0.987082	−	0.792240i
$847$	−2.39700			−0.0823619
$848$	−2.49047	+	4.31362i	−0.0855230	+	0.148130i
$849$	−16.0943	−	18.7613i	−0.552356	−	0.643885i
$850$	−2.23339	−	3.86834i	−0.0766045	−	0.132683i
$851$	−13.5205	−	23.4183i	−0.463478	−	0.802768i
$852$	4.39114	+	5.11879i	0.150438	+	0.175367i
$853$	7.78549	−	13.4849i	0.266570	−	0.461713i	−0.701404	−	0.712764i	$-0.747443\pi$
$853$	7.78549	−	13.4849i	0.266570	−	0.461713i	0.967974	+	0.251051i	$0.0807762\pi$
$854$	−1.19342			−0.0408379
$855$	13.0834	+	10.5008i	0.447442	+	0.359120i
$856$	9.51582			0.325244
$857$	17.6753	−	30.6145i	0.603776	−	1.04577i	−0.388468	−	0.921462i	$-0.626996\pi$
$857$	17.6753	−	30.6145i	0.603776	−	1.04577i	0.992244	−	0.124308i	$-0.0396711\pi$
$858$	7.51481	−	21.3687i	0.256551	−	0.729517i
$859$	−16.4940	−	28.5684i	−0.562768	−	0.974742i	−0.997254	−	0.0740637i	$-0.976403\pi$
$859$	−16.4940	−	28.5684i	−0.562768	−	0.974742i	0.434486	−	0.900679i	$-0.356930\pi$
$860$	3.61660	+	6.26414i	0.123325	+	0.213605i
$861$	−7.78490	+	1.46036i	−0.265309	+	0.0497691i
$862$	−3.98964	+	6.91025i	−0.135888	+	0.235364i
$863$	25.1656			0.856648			0.428324	−	0.903625i	$-0.359104\pi$
$863$	25.1656			0.856648			0.428324	+	0.903625i	$0.359104\pi$
$864$	4.58255	+	2.44955i	0.155901	+	0.0833352i
$865$	9.18416			0.312271
$866$	11.8900	−	20.5940i	0.404037	−	0.699813i
$867$	−5.02548	+	0.942726i	−0.170674	+	0.0320167i
$868$	−4.59208	−	7.95371i	−0.155865	−	0.269967i
$869$	4.08698	+	7.07886i	0.138641	+	0.240134i
$870$	0.257263	−	0.731540i	0.00872203	−	0.0248015i
$871$	−17.4478	+	30.2205i	−0.591196	+	1.02398i
$872$	0.465112			0.0157507
$873$	3.89450	−	25.3006i	0.131809	−	0.856296i
$874$	−14.8760			−0.503188
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$	6.93111	+	8.07965i	0.234181	+	0.272986i
$877$	−24.6535	−	42.7012i	−0.832491	−	1.44192i	−0.896057	−	0.443939i	$-0.853581\pi$
$877$	−24.6535	−	42.7012i	−0.832491	−	1.44192i	0.0635665	−	0.997978i	$-0.479753\pi$
$878$	12.9412	+	22.4149i	0.436746	+	0.756466i
$879$	10.2887	+	11.9936i	0.347028	+	0.404533i
$880$	1.83010	−	3.16982i	0.0616925	−	0.106855i
$881$	24.9811			0.841635			0.420818	−	0.907145i	$-0.361743\pi$
$881$	24.9811			0.841635			0.420818	+	0.907145i	$0.361743\pi$
$882$	2.79604	−	1.08728i	0.0941475	−	0.0366105i
$883$	−12.8743			−0.433256			−0.216628	−	0.976254i	$-0.569506\pi$
$883$	−12.8743			−0.433256			−0.216628	+	0.976254i	$0.569506\pi$
$884$	−7.97992	+	13.8216i	−0.268394	+	0.464872i
$885$	7.41974	−	21.0984i	0.249412	−	0.709215i
$886$	4.95807	+	8.58764i	0.166570	+	0.288507i
$887$	−4.65853	−	8.06881i	−0.156418	−	0.270924i	0.777156	−	0.629308i	$-0.216661\pi$
$887$	−4.65853	−	8.06881i	−0.156418	−	0.270924i	−0.933574	+	0.358383i	$0.883328\pi$
$888$	17.3046	−	3.24616i	0.580705	−	0.108934i
$889$	−2.33010	+	4.03584i	−0.0781489	+	0.135358i
$890$	−13.3585			−0.447778
$891$	7.12899	+	32.1611i	0.238830	+	1.07744i
$892$	−29.7568			−0.996332
$893$	−34.3111	+	59.4286i	−1.14818	+	1.98870i
$894$	−24.3598	+	4.56964i	−0.814714	+	0.152832i
$895$	1.17074	+	2.02777i	0.0391334	+	0.0677810i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	−5.46169	+	15.5306i	−0.182361	+	0.518551i
$898$	2.09772	−	3.63336i	0.0700019	−	0.121247i
$899$	4.11185			0.137138
$900$	2.79604	−	1.08728i	0.0932013	−	0.0362425i
$901$	22.2487			0.741212
$902$	8.36905	−	14.4956i	0.278659	−	0.482652i
$903$	−8.15716	−	9.50886i	−0.271453	−	0.316435i
$904$	−1.07320	−	1.85883i	−0.0356940	−	0.0618238i
$905$	9.33945	+	16.1764i	0.310454	+	0.537722i
$906$	13.5562	+	15.8026i	0.450376	+	0.525006i
$907$	3.98019	−	6.89390i	0.132160	−	0.228908i	−0.792349	−	0.610068i	$-0.791142\pi$
$907$	3.98019	−	6.89390i	0.132160	−	0.228908i	0.924509	+	0.381160i	$0.124475\pi$
$908$	14.6598			0.486503
$909$	−6.06218	+	39.3829i	−0.201070	+	1.30625i
$910$	3.57301			0.118444
$911$	−16.6067	+	28.7637i	−0.550205	+	0.952983i	0.448055	+	0.894006i	$0.352117\pi$
$911$	−16.6067	+	28.7637i	−0.550205	+	0.952983i	−0.998259	+	0.0589764i	$0.981216\pi$
$912$	3.21331	−	9.13721i	0.106403	−	0.302563i
$913$	20.8251	+	36.0701i	0.689210	+	1.19375i
$914$	6.43087	+	11.1386i	0.212714	+	0.368432i
$915$	2.03162	−	0.381111i	0.0671633	−	0.0125991i
$916$	9.74274	−	16.8749i	0.321909	−	0.557563i
$917$	−15.6793			−0.517775
$918$	−0.758925	−	23.1976i	−0.0250483	−	0.765636i
$919$	41.7394			1.37686			0.688428	−	0.725305i	$-0.258301\pi$
$919$	41.7394			1.37686			0.688428	+	0.725305i	$0.258301\pi$
$920$	−1.33010	+	2.30379i	−0.0438520	+	0.0759538i
$921$	22.9634	−	4.30768i	0.756669	−	0.141943i
$922$	−7.49213	−	12.9768i	−0.246740	−	0.427367i
$923$	−6.95623	−	12.0485i	−0.228967	−	0.396583i
$924$	−2.10321	+	5.98059i	−0.0691906	+	0.196747i
$925$	5.08255	−	8.80323i	0.167113	−	0.289448i
$926$	−3.45661			−0.113591
$927$	33.4598	+	26.8551i	1.09896	+	0.882036i
$928$	−0.447711			−0.0146968
$929$	12.0191	−	20.8176i	0.394333	−	0.683004i	−0.598683	−	0.800986i	$-0.704309\pi$
$929$	12.0191	−	20.8176i	0.394333	−	0.683004i	0.993016	+	0.117982i	$0.0376424\pi$
$930$	10.3573	+	12.0736i	0.339630	+	0.395909i
$931$	−2.79604	−	4.84288i	−0.0916365	−	0.158719i
$932$	5.87858	+	10.1820i	0.192559	+	0.333523i
$933$	10.9902	+	12.8113i	0.359803	+	0.419425i
$934$	−7.07931	+	12.2617i	−0.231642	+	0.401216i
$935$	−16.3492			−0.534678
$936$	−8.35952	−	6.70942i	−0.273240	−	0.219304i
$937$	24.0309			0.785055			0.392527	−	0.919740i	$-0.371601\pi$
$937$	24.0309			0.785055			0.392527	+	0.919740i	$0.371601\pi$
$938$	4.88322	−	8.45798i	0.159443	−	0.276163i
$939$	−2.96912	+	8.44284i	−0.0968936	+	0.275522i
$940$	6.13567	+	10.6273i	0.200123	+	0.346624i
$941$	18.6696	+	32.3367i	0.608613	+	1.05415i	0.991469	+	0.130340i	$0.0416069\pi$
$941$	18.6696	+	32.3367i	0.608613	+	1.05415i	−0.382857	+	0.923808i	$0.625060\pi$
$942$	11.3027	−	2.12027i	0.368263	−	0.0690822i
$943$	−6.08255	+	10.5353i	−0.198075	+	0.343076i
$944$	−12.9125			−0.420265
$945$	−4.41264	+	2.74383i	−0.143543	+	0.0892567i
$946$	26.4749			0.860774
$947$	26.1248	−	45.2495i	0.848943	−	1.47041i	−0.0332098	−	0.999448i	$-0.510573\pi$
$947$	26.1248	−	45.2495i	0.848943	−	1.47041i	0.882153	−	0.470964i	$-0.156094\pi$
$948$	3.80171	−	0.713161i	0.123474	−	0.0231624i
$949$	−10.9799	−	19.0178i	−0.356423	−	0.617343i
$950$	−2.79604	−	4.84288i	−0.0907155	−	0.157124i
$951$	−3.49876	+	9.94890i	−0.113455	+	0.322615i
$952$	2.23339	−	3.86834i	0.0723845	−	0.125374i
$953$	−9.95337			−0.322421			−0.161211	−	0.986920i	$-0.551540\pi$
$953$	−9.95337			−0.322421			−0.161211	+	0.986920i	$0.551540\pi$
$954$	−2.27336	+	14.7689i	−0.0736027	+	0.478160i
$955$	−18.7592			−0.607033
$956$	2.03813	−	3.53014i	0.0659177	−	0.114173i
$957$	−1.84803	−	2.15427i	−0.0597384	−	0.0696375i
$958$	17.8346	+	30.8905i	0.576211	+	0.998026i
$959$	6.55312	+	11.3503i	0.211611	+	0.366521i
$960$	−1.12774	−	1.31461i	−0.0363976	−	0.0424289i
$961$	−26.6744	+	46.2013i	−0.860463	+	1.49037i
$962$	−36.3200			−1.17100
$963$	26.6066	−	10.3463i	0.857386	−	0.333405i
$964$	−23.0115			−0.741149
$965$	4.01989	−	6.96266i	0.129405	−	0.224136i
$966$	1.52859	−	4.34664i	0.0491817	−	0.139851i
$967$	15.8362	+	27.4291i	0.509258	+	0.882061i	0.999943	+	0.0107235i	$0.00341346\pi$
$967$	15.8362	+	27.4291i	0.509258	+	0.882061i	−0.490684	+	0.871337i	$0.663253\pi$
$968$	−1.19850	−	2.07586i	−0.0385212	−	0.0667207i
$969$	−42.5224	+	7.97675i	−1.36602	+	0.256250i
$970$	−4.26643	+	7.38968i	−0.136987	+	0.237268i
$971$	25.8256			0.828784			0.414392	−	0.910098i	$-0.363994\pi$
$971$	25.8256			0.828784			0.414392	+	0.910098i	$0.363994\pi$
$972$	15.4763	+	1.86654i	0.496403	+	0.0598692i
$973$	−17.0207			−0.545659
$974$	10.9145	−	18.9044i	0.349723	−	0.605737i
$975$	−6.08255	+	1.14102i	−0.194797	+	0.0365419i
$976$	−0.596708	−	1.03353i	−0.0191002	−	0.0330825i
$977$	15.4863	+	26.8231i	0.495451	+	0.858146i	0.999986	−	0.00524503i	$-0.00166955\pi$
$977$	15.4863	+	26.8231i	0.495451	+	0.858146i	−0.504535	+	0.863391i	$0.668336\pi$
$978$	4.29055	−	12.2004i	0.137197	−	0.390125i
$979$	−24.4473	+	42.3440i	−0.781341	+	1.35332i
$980$	−1.00000			−0.0319438
$981$	1.30047	−	0.505705i	0.0415209	−	0.0161459i
$982$	22.1749			0.707629
$983$	22.8449	−	39.5685i	0.728639	−	1.26204i	−0.228819	−	0.973469i	$-0.573486\pi$
$983$	22.8449	−	39.5685i	0.728639	−	1.26204i	0.957458	−	0.288571i	$-0.0931803\pi$
$984$	−5.15716	−	6.01174i	−0.164404	−	0.191647i
$985$	3.57765	+	6.19666i	0.113993	+	0.197442i
$986$	0.999912	+	1.73190i	0.0318437	+	0.0551549i
$987$	−13.8389	−	16.1320i	−0.440496	−	0.513489i
$988$	−9.99029	+	17.3037i	−0.317833	+	0.550504i
$989$	−19.2417			−0.611851
$990$	1.67055	−	10.8528i	0.0530937	−	0.344923i
$991$	−38.4068			−1.22003			−0.610017	−	0.792389i	$-0.708837\pi$
$991$	−38.4068			−1.22003			−0.610017	+	0.792389i	$0.708837\pi$
$992$	4.59208	−	7.95371i	0.145799	−	0.252531i
$993$	18.0749	−	51.3969i	0.573590	−	1.63103i
$994$	1.94688	+	3.37209i	0.0617513	+	0.106956i
$995$	3.43634	+	5.95191i	0.108939	+	0.188688i
$996$	19.3715	−	3.63389i	0.613810	−	0.115144i
$997$	−28.4170	+	49.2197i	−0.899975	+	1.55880i	−0.0724518	+	0.997372i	$0.523082\pi$
$997$	−28.4170	+	49.2197i	−0.899975	+	1.55880i	−0.827523	+	0.561431i	$0.810251\pi$
$998$	5.95298			0.188438
$999$	44.8549	−	27.8913i	1.41915	−	0.882441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.l.421.1	yes	8
3.2	odd	2		1890.2.j.l.1261.4		8
9.2	odd	6		5670.2.a.bv.1.1		4
9.4	even	3	inner	630.2.j.l.211.1	✓	8
9.5	odd	6		1890.2.j.l.631.4		8
9.7	even	3		5670.2.a.bw.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.l.211.1	✓	8	9.4	even	3	inner
630.2.j.l.421.1	yes	8	1.1	even	1	trivial
1890.2.j.l.631.4		8	9.5	odd	6
1890.2.j.l.1261.4		8	3.2	odd	2
5670.2.a.bv.1.1		4	9.2	odd	6
5670.2.a.bw.1.4		4	9.7	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.70236 + 0.319344i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.574618 - 1.63396i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.79604 - 1.08728i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.70236 + 0.319344i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.574618 - 1.63396i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.79604 - 1.08728i) q^{9} -1.00000 q^{10} +(-1.83010 + 3.16982i) q^{11} +(1.12774 + 1.31461i) q^{12} +(-1.78651 - 3.09432i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-1.12774 - 1.31461i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.46677 q^{17} +(-0.456412 + 2.96508i) q^{18} +5.59208 q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.574618 + 1.63396i) q^{21} +(-1.83010 - 3.16982i) q^{22} +(1.33010 + 2.30379i) q^{23} +(-1.70236 + 0.319344i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.57301 q^{26} +(-4.41264 + 2.74383i) q^{27} -1.00000 q^{28} +(0.223855 - 0.387729i) q^{29} +(1.70236 - 0.319344i) q^{30} +(4.59208 + 7.95371i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.10321 - 5.98059i) q^{33} +(-2.23339 + 3.86834i) q^{34} +1.00000 q^{35} +(-2.33963 - 1.87780i) q^{36} -10.1651 q^{37} +(-2.79604 + 4.84288i) q^{38} +(4.02943 + 4.69713i) q^{39} +(0.500000 + 0.866025i) q^{40} +(2.28651 + 3.96035i) q^{41} +(-1.12774 - 1.31461i) q^{42} +(-3.61660 + 6.26414i) q^{43} +3.66019 q^{44} +(2.33963 + 1.87780i) q^{45} -2.66019 q^{46} +(-6.13567 + 10.6273i) q^{47} +(0.574618 - 1.63396i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-7.60404 + 1.42644i) q^{51} +(-1.78651 + 3.09432i) q^{52} +4.98094 q^{53} +(-0.169904 - 5.19337i) q^{54} -3.66019 q^{55} +(0.500000 - 0.866025i) q^{56} +(-9.51971 + 1.78580i) q^{57} +(0.223855 + 0.387729i) q^{58} +(6.45623 + 11.1825i) q^{59} +(-0.574618 + 1.63396i) q^{60} +(-0.596708 + 1.03353i) q^{61} -9.18416 q^{62} +(0.456412 - 2.96508i) q^{63} +1.00000 q^{64} +(1.78651 - 3.09432i) q^{65} +(4.12774 + 4.81173i) q^{66} +(-4.88322 - 8.45798i) q^{67} +(-2.23339 - 3.86834i) q^{68} +(-3.00000 - 3.49712i) q^{69} +(-0.500000 + 0.866025i) q^{70} +3.89376 q^{71} +(2.79604 - 1.08728i) q^{72} +6.14603 q^{73} +(5.08255 - 8.80323i) q^{74} +(0.574618 - 1.63396i) q^{75} +(-2.79604 - 4.84288i) q^{76} +(1.83010 + 3.16982i) q^{77} +(-6.08255 + 1.14102i) q^{78} +(1.11660 - 1.93401i) q^{79} -1.00000 q^{80} +(6.63567 - 6.08013i) q^{81} -4.57301 q^{82} +(5.68962 - 9.85471i) q^{83} +(1.70236 - 0.319344i) q^{84} +(2.23339 + 3.86834i) q^{85} +(-3.61660 - 6.26414i) q^{86} +(-0.257263 + 0.731540i) q^{87} +(-1.83010 + 3.16982i) q^{88} +13.3585 q^{89} +(-2.79604 + 1.08728i) q^{90} -3.57301 q^{91} +(1.33010 - 2.30379i) q^{92} +(-10.3573 - 12.0736i) q^{93} +(-6.13567 - 10.6273i) q^{94} +(2.79604 + 4.84288i) q^{95} +(1.12774 + 1.31461i) q^{96} +(4.26643 - 7.38968i) q^{97} +1.00000 q^{98} +(-1.67055 + 10.8528i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9	\( 8 q - 4 q^{2} - 3 q^{3} - 4 q^{4} + 4 q^{5} + 4 q^{7} + 8 q^{8} + 3 q^{9} - 8 q^{10} + 2 q^{11} + 3 q^{12} + 3 q^{13} + 4 q^{14} - 3 q^{15} - 4 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{22} - 6 q^{23} - 3 q^{24} - 4 q^{25} - 6 q^{26} + 18 q^{27} - 8 q^{28} - 12 q^{29} + 3 q^{30} - 2 q^{31} - 4 q^{32} + 6 q^{33} - 2 q^{34} + 8 q^{35} - 8 q^{37} - 3 q^{38} - 3 q^{39} + 4 q^{40} + q^{41} - 3 q^{42} + 5 q^{43} - 4 q^{44} + 12 q^{46} - 11 q^{47} - 4 q^{49} - 4 q^{50} - 21 q^{51} + 3 q^{52} + 44 q^{53} - 18 q^{54} + 4 q^{55} + 4 q^{56} + 9 q^{57} - 12 q^{58} - q^{59} - 4 q^{61} + 4 q^{62} + 3 q^{63} + 8 q^{64} - 3 q^{65} + 27 q^{66} - 21 q^{67} - 2 q^{68} - 24 q^{69} - 4 q^{70} + 34 q^{71} + 3 q^{72} - 20 q^{73} + 4 q^{74} - 3 q^{76} - 2 q^{77} - 12 q^{78} - 25 q^{79} - 8 q^{80} + 15 q^{81} - 2 q^{82} - 23 q^{83} + 3 q^{84} + 2 q^{85} + 5 q^{86} - 72 q^{87} + 2 q^{88} + 32 q^{89} - 3 q^{90} + 6 q^{91} - 6 q^{92} + 6 q^{93} - 11 q^{94} + 3 q^{95} + 3 q^{96} - 2 q^{97} + 8 q^{98} + 51 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 3 * q^3 - 4 * q^4 + 4 * q^5 + 4 * q^7 + 8 * q^8 + 3 * q^9 - 8 * q^10 + 2 * q^11 + 3 * q^12 + 3 * q^13 + 4 * q^14 - 3 * q^15 - 4 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^22 - 6 * q^23 - 3 * q^24 - 4 * q^25 - 6 * q^26 + 18 * q^27 - 8 * q^28 - 12 * q^29 + 3 * q^30 - 2 * q^31 - 4 * q^32 + 6 * q^33 - 2 * q^34 + 8 * q^35 - 8 * q^37 - 3 * q^38 - 3 * q^39 + 4 * q^40 + q^41 - 3 * q^42 + 5 * q^43 - 4 * q^44 + 12 * q^46 - 11 * q^47 - 4 * q^49 - 4 * q^50 - 21 * q^51 + 3 * q^52 + 44 * q^53 - 18 * q^54 + 4 * q^55 + 4 * q^56 + 9 * q^57 - 12 * q^58 - q^59 - 4 * q^61 + 4 * q^62 + 3 * q^63 + 8 * q^64 - 3 * q^65 + 27 * q^66 - 21 * q^67 - 2 * q^68 - 24 * q^69 - 4 * q^70 + 34 * q^71 + 3 * q^72 - 20 * q^73 + 4 * q^74 - 3 * q^76 - 2 * q^77 - 12 * q^78 - 25 * q^79 - 8 * q^80 + 15 * q^81 - 2 * q^82 - 23 * q^83 + 3 * q^84 + 2 * q^85 + 5 * q^86 - 72 * q^87 + 2 * q^88 + 32 * q^89 - 3 * q^90 + 6 * q^91 - 6 * q^92 + 6 * q^93 - 11 * q^94 + 3 * q^95 + 3 * q^96 - 2 * q^97 + 8 * q^98 + 51 * q^99

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