LMFDB - Embedded newform 1110.2.o.a.253.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.18
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.64803 + 1.51129i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.64803 + 1.51129i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(1.64803 - 1.51129i) q^{10} +0.350472i q^{11} +(0.707107 - 0.707107i) q^{12} +3.27075 q^{13} +(-2.75974 + 2.75974i) q^{14} +(-0.0966903 + 2.23398i) q^{15} +1.00000 q^{16} +7.07368i q^{17} +1.00000i q^{18} +(2.01227 + 2.01227i) q^{19} +(-1.64803 + 1.51129i) q^{20} -3.90286i q^{21} -0.350472i q^{22} -1.24836 q^{23} +(-0.707107 + 0.707107i) q^{24} +(0.432008 - 4.98130i) q^{25} -3.27075 q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.75974 - 2.75974i) q^{28} +(6.14644 - 6.14644i) q^{29} +(0.0966903 - 2.23398i) q^{30} +(-2.76854 - 2.76854i) q^{31} -1.00000 q^{32} +(0.247821 + 0.247821i) q^{33} -7.07368i q^{34} +(-0.377368 + 8.71889i) q^{35} -1.00000i q^{36} +(-3.58895 + 4.91116i) q^{37} +(-2.01227 - 2.01227i) q^{38} +(2.31277 - 2.31277i) q^{39} +(1.64803 - 1.51129i) q^{40} -5.57830i q^{41} +3.90286i q^{42} +3.23195 q^{43} +0.350472i q^{44} +(1.51129 + 1.64803i) q^{45} +1.24836 q^{46} +(5.76291 - 5.76291i) q^{47} +(0.707107 - 0.707107i) q^{48} -8.23228i q^{49} +(-0.432008 + 4.98130i) q^{50} +(5.00185 + 5.00185i) q^{51} +3.27075 q^{52} +(-3.45760 - 3.45760i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-0.529665 - 0.577588i) q^{55} +(-2.75974 + 2.75974i) q^{56} +2.84578 q^{57} +(-6.14644 + 6.14644i) q^{58} +(10.6205 + 10.6205i) q^{59} +(-0.0966903 + 2.23398i) q^{60} +(1.30384 + 1.30384i) q^{61} +(2.76854 + 2.76854i) q^{62} +(-2.75974 - 2.75974i) q^{63} +1.00000 q^{64} +(-5.39030 + 4.94305i) q^{65} +(-0.247821 - 0.247821i) q^{66} +(10.6169 + 10.6169i) q^{67} +7.07368i q^{68} +(-0.882722 + 0.882722i) q^{69} +(0.377368 - 8.71889i) q^{70} +15.8980 q^{71} +1.00000i q^{72} +(0.998067 - 0.998067i) q^{73} +(3.58895 - 4.91116i) q^{74} +(-3.21684 - 3.82779i) q^{75} +(2.01227 + 2.01227i) q^{76} +(0.967210 + 0.967210i) q^{77} +(-2.31277 + 2.31277i) q^{78} +(2.47200 + 2.47200i) q^{79} +(-1.64803 + 1.51129i) q^{80} -1.00000 q^{81} +5.57830i q^{82} +(-10.6094 - 10.6094i) q^{83} -3.90286i q^{84} +(-10.6904 - 11.6576i) q^{85} -3.23195 q^{86} -8.69238i q^{87} -0.350472i q^{88} +(3.03601 - 3.03601i) q^{89} +(-1.51129 - 1.64803i) q^{90} +(9.02641 - 9.02641i) q^{91} -1.24836 q^{92} -3.91530 q^{93} +(-5.76291 + 5.76291i) q^{94} +(-6.35741 - 0.275159i) q^{95} +(-0.707107 + 0.707107i) q^{96} -7.94277i q^{97} +8.23228i q^{98} +0.350472 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	−1.64803	+	1.51129i	−0.737022	+	0.675869i
$5$	−1.64803	+	1.51129i	−0.737022	+	0.675869i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	2.75974	−	2.75974i	1.04308	−	1.04308i	0.0440528	−	0.999029i	$-0.485973\pi$
$7$	2.75974	−	2.75974i	1.04308	−	1.04308i	0.999029	−	0.0440528i	$-0.0140270\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	1.64803	−	1.51129i	0.521153	−	0.477912i
$11$			0.350472i			0.105671i	0.998603	+	0.0528356i	$0.0168259\pi$
$11$			0.350472i			0.105671i	−0.998603	+	0.0528356i	$0.983174\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	3.27075			0.907143			0.453572	−	0.891220i	$-0.350150\pi$
$13$	3.27075			0.907143			0.453572	+	0.891220i	$0.350150\pi$
$14$	−2.75974	+	2.75974i	−0.737570	+	0.737570i
$15$	−0.0966903	+	2.23398i	−0.0249653	+	0.576810i
$16$	1.00000			0.250000
$17$			7.07368i			1.71562i	0.513967	+	0.857810i	$0.328176\pi$
$17$			7.07368i			1.71562i	−0.513967	+	0.857810i	$0.671824\pi$
$18$			1.00000i			0.235702i
$19$	2.01227	+	2.01227i	0.461647	+	0.461647i	0.899195	−	0.437548i	$-0.144153\pi$
$19$	2.01227	+	2.01227i	0.461647	+	0.461647i	−0.437548	+	0.899195i	$0.644153\pi$
$20$	−1.64803	+	1.51129i	−0.368511	+	0.337935i
$21$		−	3.90286i		−	0.851673i
$22$		−	0.350472i		−	0.0747209i
$23$	−1.24836			−0.260301			−0.130150	−	0.991494i	$-0.541546\pi$
$23$	−1.24836			−0.260301			−0.130150	+	0.991494i	$0.541546\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	0.432008	−	4.98130i	0.0864015	−	0.996260i
$26$	−3.27075			−0.641447
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	2.75974	−	2.75974i	0.521541	−	0.521541i
$29$	6.14644	−	6.14644i	1.14137	−	1.14137i	0.153165	−	0.988201i	$-0.451053\pi$
$29$	6.14644	−	6.14644i	1.14137	−	1.14137i	0.988201	−	0.153165i	$-0.0489467\pi$
$30$	0.0966903	−	2.23398i	0.0176532	−	0.407866i
$31$	−2.76854	−	2.76854i	−0.497244	−	0.497244i	0.413335	−	0.910579i	$-0.364364\pi$
$31$	−2.76854	−	2.76854i	−0.497244	−	0.497244i	−0.910579	+	0.413335i	$0.864364\pi$
$32$	−1.00000			−0.176777
$33$	0.247821	+	0.247821i	0.0431401	+	0.0431401i
$34$		−	7.07368i		−	1.21313i
$35$	−0.377368	+	8.71889i	−0.0637869	+	1.47376i
$36$		−	1.00000i		−	0.166667i
$37$	−3.58895	+	4.91116i	−0.590019	+	0.807389i
$37$	−3.58895	+	4.91116i	−0.590019	+	0.807389i
$38$	−2.01227	−	2.01227i	−0.326433	−	0.326433i
$39$	2.31277	−	2.31277i	0.370340	−	0.370340i
$40$	1.64803	−	1.51129i	0.260576	−	0.238956i
$41$		−	5.57830i		−	0.871185i	−0.900144	−	0.435592i	$-0.856539\pi$
$41$		−	5.57830i		−	0.871185i	0.900144	−	0.435592i	$-0.143461\pi$
$42$			3.90286i			0.602224i
$43$	3.23195			0.492868			0.246434	−	0.969160i	$-0.420741\pi$
$43$	3.23195			0.492868			0.246434	+	0.969160i	$0.420741\pi$
$44$			0.350472i			0.0528356i
$45$	1.51129	+	1.64803i	0.225290	+	0.245674i
$46$	1.24836			0.184060
$47$	5.76291	−	5.76291i	0.840606	−	0.840606i	−0.148331	−	0.988938i	$-0.547390\pi$
$47$	5.76291	−	5.76291i	0.840606	−	0.840606i	0.988938	+	0.148331i	$0.0473902\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		−	8.23228i		−	1.17604i
$50$	−0.432008	+	4.98130i	−0.0610951	+	0.704462i
$51$	5.00185	+	5.00185i	0.700399	+	0.700399i
$52$	3.27075			0.453572
$53$	−3.45760	−	3.45760i	−0.474938	−	0.474938i	0.428571	−	0.903508i	$-0.359017\pi$
$53$	−3.45760	−	3.45760i	−0.474938	−	0.474938i	−0.903508	+	0.428571i	$0.859017\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	−0.529665	−	0.577588i	−0.0714200	−	0.0778820i
$56$	−2.75974	+	2.75974i	−0.368785	+	0.368785i
$57$	2.84578			0.376933
$58$	−6.14644	+	6.14644i	−0.807068	+	0.807068i
$59$	10.6205	+	10.6205i	1.38267	+	1.38267i	0.839841	+	0.542832i	$0.182648\pi$
$59$	10.6205	+	10.6205i	1.38267	+	1.38267i	0.542832	+	0.839841i	$0.317352\pi$
$60$	−0.0966903	+	2.23398i	−0.0124827	+	0.288405i
$61$	1.30384	+	1.30384i	0.166940	+	0.166940i	0.785633	−	0.618693i	$-0.212338\pi$
$61$	1.30384	+	1.30384i	0.166940	+	0.166940i	−0.618693	+	0.785633i	$0.712338\pi$
$62$	2.76854	+	2.76854i	0.351605	+	0.351605i
$63$	−2.75974	−	2.75974i	−0.347694	−	0.347694i
$64$	1.00000			0.125000
$65$	−5.39030	+	4.94305i	−0.668584	+	0.613110i
$66$	−0.247821	−	0.247821i	−0.0305047	−	0.0305047i
$67$	10.6169	+	10.6169i	1.29707	+	1.29707i	0.930322	+	0.366744i	$0.119527\pi$
$67$	10.6169	+	10.6169i	1.29707	+	1.29707i	0.366744	+	0.930322i	$0.380473\pi$
$68$			7.07368i			0.857810i
$69$	−0.882722	+	0.882722i	−0.106267	+	0.106267i
$70$	0.377368	−	8.71889i	0.0451041	−	1.04211i
$71$	15.8980			1.88675			0.943373	−	0.331733i	$-0.107633\pi$
$71$	15.8980			1.88675			0.943373	+	0.331733i	$0.107633\pi$
$72$			1.00000i			0.117851i
$73$	0.998067	−	0.998067i	0.116815	−	0.116815i	−0.646283	−	0.763098i	$-0.723677\pi$
$73$	0.998067	−	0.998067i	0.116815	−	0.116815i	0.763098	+	0.646283i	$0.223677\pi$
$74$	3.58895	−	4.91116i	0.417207	−	0.570910i
$75$	−3.21684	−	3.82779i	−0.371448	−	0.441995i
$76$	2.01227	+	2.01227i	0.230823	+	0.230823i
$77$	0.967210	+	0.967210i	0.110224	+	0.110224i
$78$	−2.31277	+	2.31277i	−0.261870	+	0.261870i
$79$	2.47200	+	2.47200i	0.278122	+	0.278122i	0.832359	−	0.554237i	$-0.186990\pi$
$79$	2.47200	+	2.47200i	0.278122	+	0.278122i	−0.554237	+	0.832359i	$0.686990\pi$
$80$	−1.64803	+	1.51129i	−0.184255	+	0.168967i
$81$	−1.00000			−0.111111
$82$			5.57830i			0.616020i
$83$	−10.6094	−	10.6094i	−1.16454	−	1.16454i	−0.983471	−	0.181065i	$-0.942046\pi$
$83$	−10.6094	−	10.6094i	−1.16454	−	1.16454i	−0.181065	−	0.983471i	$-0.557954\pi$
$84$		−	3.90286i		−	0.425836i
$85$	−10.6904	−	11.6576i	−1.15954	−	1.26445i
$86$	−3.23195			−0.348510
$87$		−	8.69238i		−	0.931921i
$88$		−	0.350472i		−	0.0373604i
$89$	3.03601	−	3.03601i	0.321816	−	0.321816i	−0.527647	−	0.849464i	$-0.676926\pi$
$89$	3.03601	−	3.03601i	0.321816	−	0.321816i	0.849464	+	0.527647i	$0.176926\pi$
$90$	−1.51129	−	1.64803i	−0.159304	−	0.173718i
$91$	9.02641	−	9.02641i	0.946225	−	0.946225i
$92$	−1.24836			−0.130150
$93$	−3.91530			−0.405998
$94$	−5.76291	+	5.76291i	−0.594398	+	0.594398i
$95$	−6.35741	−	0.275159i	−0.652256	−	0.0282308i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$		−	7.94277i		−	0.806466i	−0.915097	−	0.403233i	$-0.867886\pi$
$97$		−	7.94277i		−	0.806466i	0.915097	−	0.403233i	$-0.132114\pi$
$98$			8.23228i			0.831586i
$99$	0.350472			0.0352238
$100$	0.432008	−	4.98130i	0.0432008	−	0.498130i
$101$		−	0.514124i		−	0.0511573i	−0.999673	−	0.0255786i	$-0.991857\pi$
$101$		−	0.514124i		−	0.0511573i	0.999673	−	0.0255786i	$-0.00814282\pi$
$102$	−5.00185	−	5.00185i	−0.495257	−	0.495257i
$103$		−	9.07861i		−	0.894542i	−0.894398	−	0.447271i	$-0.852396\pi$
$103$		−	9.07861i		−	0.894542i	0.894398	−	0.447271i	$-0.147604\pi$
$104$	−3.27075			−0.320724
$105$	5.89834	+	6.43202i	0.575620	+	0.627701i
$106$	3.45760	+	3.45760i	0.335832	+	0.335832i
$107$	1.33354	−	1.33354i	0.128919	−	0.128919i	−0.639703	−	0.768622i	$-0.720943\pi$
$107$	1.33354	−	1.33354i	0.128919	−	0.128919i	0.768622	+	0.639703i	$0.220943\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−2.30925	−	2.30925i	−0.221186	−	0.221186i	0.587812	−	0.808998i	$-0.299990\pi$
$109$	−2.30925	−	2.30925i	−0.221186	−	0.221186i	−0.808998	+	0.587812i	$0.799990\pi$
$110$	0.529665	+	0.577588i	0.0505015	+	0.0550709i
$111$	0.934944	+	6.01048i	0.0887410	+	0.570490i
$112$	2.75974	−	2.75974i	0.260770	−	0.260770i
$113$		−	7.85255i		−	0.738705i	−0.929289	−	0.369353i	$-0.879579\pi$
$113$		−	7.85255i		−	0.738705i	0.929289	−	0.369353i	$-0.120421\pi$
$114$	−2.84578			−0.266532
$115$	2.05733	−	1.88663i	0.191847	−	0.175929i
$116$	6.14644	−	6.14644i	0.570683	−	0.570683i
$117$		−	3.27075i		−	0.302381i
$118$	−10.6205	−	10.6205i	−0.977698	−	0.977698i
$119$	19.5215	+	19.5215i	1.78953	+	1.78953i
$120$	0.0966903	−	2.23398i	0.00882658	−	0.203933i
$121$	10.8772			0.988834
$122$	−1.30384	−	1.30384i	−0.118044	−	0.118044i
$123$	−3.94446	−	3.94446i	−0.355660	−	0.355660i
$124$	−2.76854	−	2.76854i	−0.248622	−	0.248622i
$125$	6.81623	+	8.86223i	0.609662	+	0.792662i
$126$	2.75974	+	2.75974i	0.245857	+	0.245857i
$127$	−14.6420	+	14.6420i	−1.29927	+	1.29927i	−0.370388	+	0.928877i	$0.620775\pi$
$127$	−14.6420	+	14.6420i	−1.29927	+	1.29927i	−0.928877	+	0.370388i	$0.879225\pi$
$128$	−1.00000			−0.0883883
$129$	2.28533	−	2.28533i	0.201212	−	0.201212i
$130$	5.39030	−	4.94305i	0.472760	−	0.433534i
$131$	−3.62929	−	3.62929i	−0.317093	−	0.317093i	0.530557	−	0.847649i	$-0.321983\pi$
$131$	−3.62929	−	3.62929i	−0.317093	−	0.317093i	−0.847649	+	0.530557i	$0.821983\pi$
$132$	0.247821	+	0.247821i	0.0215701	+	0.0215701i
$133$	11.1067			0.963070
$134$	−10.6169	−	10.6169i	−0.917164	−	0.917164i
$135$	2.23398	+	0.0966903i	0.192270	+	0.00832178i
$136$		−	7.07368i		−	0.606563i
$137$	−12.5315	+	12.5315i	−1.07064	+	1.07064i	−0.0733326	+	0.997308i	$0.523363\pi$
$137$	−12.5315	+	12.5315i	−1.07064	+	1.07064i	−0.997308	+	0.0733326i	$0.976637\pi$
$138$	0.882722	−	0.882722i	0.0751423	−	0.0751423i
$139$	3.66631			0.310972			0.155486	−	0.987838i	$-0.450306\pi$
$139$	3.66631			0.310972			0.155486	+	0.987838i	$0.450306\pi$
$140$	−0.377368	+	8.71889i	−0.0318934	+	0.736880i
$141$		−	8.14998i		−	0.686352i
$142$	−15.8980			−1.33413
$143$			1.14631i			0.0958590i
$144$		−	1.00000i		−	0.0833333i
$145$	−0.840469	+	19.4186i	−0.0697972	+	1.61263i
$146$	−0.998067	+	0.998067i	−0.0826007	+	0.0826007i
$147$	−5.82110	−	5.82110i	−0.480116	−	0.480116i
$148$	−3.58895	+	4.91116i	−0.295010	+	0.403695i
$149$		−	16.9433i		−	1.38805i	−0.719951	−	0.694025i	$-0.755836\pi$
$149$		−	16.9433i		−	1.38805i	0.719951	−	0.694025i	$-0.244164\pi$
$150$	3.21684	+	3.82779i	0.262654	+	0.312538i
$151$			10.7953i			0.878510i	0.898362	+	0.439255i	$0.144758\pi$
$151$			10.7953i			0.878510i	−0.898362	+	0.439255i	$0.855242\pi$
$152$	−2.01227	−	2.01227i	−0.163217	−	0.163217i
$153$	7.07368			0.571873
$154$	−0.967210	−	0.967210i	−0.0779400	−	0.0779400i
$155$	8.74670	+	0.378572i	0.702552	+	0.0304076i
$156$	2.31277	−	2.31277i	0.185170	−	0.185170i
$157$	6.59408	−	6.59408i	0.526265	−	0.526265i	−0.393192	−	0.919457i	$-0.628629\pi$
$157$	6.59408	−	6.59408i	0.526265	−	0.526265i	0.919457	+	0.393192i	$0.128629\pi$
$158$	−2.47200	−	2.47200i	−0.196662	−	0.196662i
$159$	−4.88978			−0.387785
$160$	1.64803	−	1.51129i	0.130288	−	0.119478i
$161$	−3.44514	+	3.44514i	−0.271515	+	0.271515i
$162$	1.00000			0.0785674
$163$		−	7.00131i		−	0.548385i	−0.961675	−	0.274193i	$-0.911589\pi$
$163$		−	7.00131i		−	0.548385i	0.961675	−	0.274193i	$-0.0884106\pi$
$164$		−	5.57830i		−	0.435592i
$165$	−0.782946	−	0.0338872i	−0.0609523	−	0.00263812i
$166$	10.6094	+	10.6094i	0.823451	+	0.823451i
$167$			14.7018i			1.13766i	0.822455	+	0.568830i	$0.192604\pi$
$167$			14.7018i			1.13766i	−0.822455	+	0.568830i	$0.807396\pi$
$168$			3.90286i			0.301112i
$169$	−2.30219			−0.177091
$170$	10.6904	+	11.6576i	0.819915	+	0.894101i
$171$	2.01227	−	2.01227i	0.153882	−	0.153882i
$172$	3.23195			0.246434
$173$	3.00005	−	3.00005i	0.228090	−	0.228090i	−0.583805	−	0.811894i	$-0.698437\pi$
$173$	3.00005	−	3.00005i	0.228090	−	0.228090i	0.811894	+	0.583805i	$0.198437\pi$
$174$			8.69238i			0.658968i
$175$	−12.5548	−	14.9393i	−0.949057	−	1.12931i
$176$			0.350472i			0.0264178i
$177$	15.0197			1.12895
$178$	−3.03601	+	3.03601i	−0.227559	+	0.227559i
$179$	−9.62402	+	9.62402i	−0.719333	+	0.719333i	−0.968469	−	0.249136i	$-0.919853\pi$
$179$	−9.62402	+	9.62402i	−0.719333	+	0.719333i	0.249136	+	0.968469i	$0.419853\pi$
$180$	1.51129	+	1.64803i	0.112645	+	0.122837i
$181$	14.0878			1.04713			0.523567	−	0.851984i	$-0.324601\pi$
$181$	14.0878			1.04713			0.523567	+	0.851984i	$0.324601\pi$
$182$	−9.02641	+	9.02641i	−0.669082	+	0.669082i
$183$	1.84391			0.136306
$184$	1.24836			0.0920302
$185$	−1.50749	−	13.5177i	−0.110833	−	0.993839i
$186$	3.91530			0.287084
$187$	−2.47913			−0.181292
$188$	5.76291	−	5.76291i	0.420303	−	0.420303i
$189$	−3.90286			−0.283891
$190$	6.35741	+	0.275159i	0.461215	+	0.0199622i
$191$	2.11691	−	2.11691i	0.153174	−	0.153174i	−0.626360	−	0.779534i	$-0.715456\pi$
$191$	2.11691	−	2.11691i	0.153174	−	0.153174i	0.779534	+	0.626360i	$0.215456\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−20.7874			−1.49631			−0.748154	−	0.663525i	$-0.769060\pi$
$193$	−20.7874			−1.49631			−0.748154	+	0.663525i	$0.769060\pi$
$194$			7.94277i			0.570257i
$195$	−0.316250	+	7.30678i	−0.0226471	+	0.523249i
$196$		−	8.23228i		−	0.588020i
$197$	−11.8547	+	11.8547i	−0.844614	+	0.844614i	−0.989455	−	0.144841i	$-0.953733\pi$
$197$	−11.8547	+	11.8547i	−0.844614	+	0.844614i	0.144841	+	0.989455i	$0.453733\pi$
$198$	−0.350472			−0.0249070
$199$	−6.76638	+	6.76638i	−0.479656	+	0.479656i	−0.905022	−	0.425366i	$-0.860146\pi$
$199$	−6.76638	+	6.76638i	−0.479656	+	0.479656i	0.425366	+	0.905022i	$0.360146\pi$
$200$	−0.432008	+	4.98130i	−0.0305476	+	0.352231i
$201$	15.0146			1.05905
$202$			0.514124i			0.0361737i
$203$		−	33.9251i		−	2.38108i
$204$	5.00185	+	5.00185i	0.350200	+	0.350200i
$205$	8.43043	+	9.19321i	0.588807	+	0.642082i
$206$			9.07861i			0.632537i
$207$			1.24836i			0.0867669i
$208$	3.27075			0.226786
$209$	−0.705244	+	0.705244i	−0.0487828	+	0.0487828i
$210$	−5.89834	−	6.43202i	−0.407024	−	0.443852i
$211$	−9.92928			−0.683560			−0.341780	−	0.939780i	$-0.611030\pi$
$211$	−9.92928			−0.683560			−0.341780	+	0.939780i	$0.611030\pi$
$212$	−3.45760	−	3.45760i	−0.237469	−	0.237469i
$213$	11.2416	−	11.2416i	0.770261	−	0.770261i
$214$	−1.33354	+	1.33354i	−0.0911592	+	0.0911592i
$215$	−5.32635	+	4.88441i	−0.363254	+	0.333114i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−15.2809			−1.03733
$218$	2.30925	+	2.30925i	0.156402	+	0.156402i
$219$		−	1.41148i		−	0.0953790i
$220$	−0.529665	−	0.577588i	−0.0357100	−	0.0389410i
$221$			23.1363i			1.55631i
$222$	−0.934944	−	6.01048i	−0.0627494	−	0.403397i
$223$	−6.49659	−	6.49659i	−0.435044	−	0.435044i	0.455296	−	0.890340i	$-0.349533\pi$
$223$	−6.49659	−	6.49659i	−0.435044	−	0.435044i	−0.890340	+	0.455296i	$0.849533\pi$
$224$	−2.75974	+	2.75974i	−0.184393	+	0.184393i
$225$	−4.98130	−	0.432008i	−0.332087	−	0.0288005i
$226$			7.85255i			0.522344i
$227$			16.6142i			1.10273i	0.834265	+	0.551363i	$0.185892\pi$
$227$			16.6142i			1.10273i	−0.834265	+	0.551363i	$0.814108\pi$
$228$	2.84578			0.188466
$229$		−	2.86631i		−	0.189411i	−0.995505	−	0.0947056i	$-0.969809\pi$
$229$		−	2.86631i		−	0.189411i	0.995505	−	0.0947056i	$-0.0301910\pi$
$230$	−2.05733	+	1.88663i	−0.135656	+	0.124401i
$231$	1.36784			0.0899974
$232$	−6.14644	+	6.14644i	−0.403534	+	0.403534i
$233$	−8.37425	+	8.37425i	−0.548615	+	0.548615i	−0.926040	−	0.377425i	$-0.876810\pi$
$233$	−8.37425	+	8.37425i	−0.548615	+	0.548615i	0.377425	+	0.926040i	$0.376810\pi$
$234$			3.27075i			0.213816i
$235$	−0.788024	+	18.2069i	−0.0514050	+	1.18769i
$236$	10.6205	+	10.6205i	0.691337	+	0.691337i
$237$	3.49594			0.227085
$238$	−19.5215	−	19.5215i	−1.26539	−	1.26539i
$239$	−16.9584	−	16.9584i	−1.09695	−	1.09695i	−0.994765	−	0.102185i	$-0.967417\pi$
$239$	−16.9584	−	16.9584i	−1.09695	−	1.09695i	−0.102185	−	0.994765i	$-0.532583\pi$
$240$	−0.0966903	+	2.23398i	−0.00624133	+	0.144203i
$241$	9.32818	−	9.32818i	0.600881	−	0.600881i	−0.339665	−	0.940546i	$-0.610314\pi$
$241$	9.32818	−	9.32818i	0.600881	−	0.600881i	0.940546	+	0.339665i	$0.110314\pi$
$242$	−10.8772			−0.699211
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	1.30384	+	1.30384i	0.0834698	+	0.0834698i
$245$	12.4414	+	13.5670i	0.794849	+	0.866767i
$246$	3.94446	+	3.94446i	0.251489	+	0.251489i
$247$	6.58164	+	6.58164i	0.418780	+	0.418780i
$248$	2.76854	+	2.76854i	0.175802	+	0.175802i
$249$	−15.0040			−0.950840
$250$	−6.81623	−	8.86223i	−0.431096	−	0.560496i
$251$	−21.5270	−	21.5270i	−1.35877	−	1.35877i	−0.875437	−	0.483333i	$-0.839426\pi$
$251$	−21.5270	−	21.5270i	−1.35877	−	1.35877i	−0.483333	−	0.875437i	$-0.660574\pi$
$252$	−2.75974	−	2.75974i	−0.173847	−	0.173847i
$253$		−	0.437515i		−	0.0275063i
$254$	14.6420	−	14.6420i	0.918719	−	0.918719i
$255$	−15.8024	−	0.683957i	−0.989587	−	0.0428310i
$256$	1.00000			0.0625000
$257$			0.409575i			0.0255486i	0.999918	+	0.0127743i	$0.00406630\pi$
$257$			0.409575i			0.0255486i	−0.999918	+	0.0127743i	$0.995934\pi$
$258$	−2.28533	+	2.28533i	−0.142279	+	0.142279i
$259$	3.64895	+	23.4580i	0.226735	+	1.45761i
$260$	−5.39030	+	4.94305i	−0.334292	+	0.306555i
$261$	−6.14644	−	6.14644i	−0.380455	−	0.380455i
$262$	3.62929	+	3.62929i	0.224218	+	0.224218i
$263$	−10.0366	+	10.0366i	−0.618882	+	0.618882i	−0.945245	−	0.326362i	$-0.894177\pi$
$263$	−10.0366	+	10.0366i	−0.618882	+	0.618882i	0.326362	+	0.945245i	$0.394177\pi$
$264$	−0.247821	−	0.247821i	−0.0152523	−	0.0152523i
$265$	10.9237	+	0.472795i	0.671035	+	0.0290435i
$266$	−11.1067			−0.680994
$267$		−	4.29357i		−	0.262762i
$268$	10.6169	+	10.6169i	0.648533	+	0.648533i
$269$			19.9758i			1.21794i	0.793192	+	0.608972i	$0.208418\pi$
$269$			19.9758i			1.21794i	−0.793192	+	0.608972i	$0.791582\pi$
$270$	−2.23398	−	0.0966903i	−0.135955	−	0.00588438i
$271$	11.0572			0.671678			0.335839	−	0.941919i	$-0.390980\pi$
$271$	11.0572			0.671678			0.335839	+	0.941919i	$0.390980\pi$
$272$			7.07368i			0.428905i
$273$		−	12.7653i		−	0.772589i
$274$	12.5315	−	12.5315i	0.757057	−	0.757057i
$275$	1.74581	+	0.151407i	0.105276	+	0.00913016i
$276$	−0.882722	+	0.882722i	−0.0531336	+	0.0531336i
$277$	24.4538			1.46929			0.734644	−	0.678453i	$-0.237349\pi$
$277$	24.4538			1.46929			0.734644	+	0.678453i	$0.237349\pi$
$278$	−3.66631			−0.219890
$279$	−2.76854	+	2.76854i	−0.165748	+	0.165748i
$280$	0.377368	−	8.71889i	0.0225521	−	0.521053i
$281$	−7.23968	+	7.23968i	−0.431883	+	0.431883i	−0.889269	−	0.457385i	$-0.848786\pi$
$281$	−7.23968	+	7.23968i	−0.431883	+	0.431883i	0.457385	+	0.889269i	$0.348786\pi$
$282$			8.14998i			0.485324i
$283$			30.2054i			1.79552i	0.440483	+	0.897761i	$0.354807\pi$
$283$			30.2054i			1.79552i	−0.440483	+	0.897761i	$0.645193\pi$
$284$	15.8980			0.943373
$285$	−4.68993	+	4.30080i	−0.277808	+	0.254757i
$286$		−	1.14631i		−	0.0677825i
$287$	−15.3946	−	15.3946i	−0.908717	−	0.908717i
$288$			1.00000i			0.0589256i
$289$	−33.0370			−1.94335
$290$	0.840469	−	19.4186i	0.0493540	−	1.14030i
$291$	−5.61638	−	5.61638i	−0.329238	−	0.329238i
$292$	0.998067	−	0.998067i	0.0584075	−	0.0584075i
$293$	−0.618270	−	0.618270i	−0.0361197	−	0.0361197i	0.688816	−	0.724936i	$-0.258131\pi$
$293$	−0.618270	−	0.618270i	−0.0361197	−	0.0361197i	−0.724936	+	0.688816i	$0.758131\pi$
$294$	5.82110	+	5.82110i	0.339494	+	0.339494i
$295$	−33.5536	−	1.45226i	−1.95357	−	0.0845537i
$296$	3.58895	−	4.91116i	0.208603	−	0.285455i
$297$	0.247821	−	0.247821i	0.0143800	−	0.0143800i
$298$			16.9433i			0.981499i
$299$	−4.08307			−0.236130
$300$	−3.21684	−	3.82779i	−0.185724	−	0.220997i
$301$	8.91933	−	8.91933i	0.514101	−	0.514101i
$302$		−	10.7953i		−	0.621201i
$303$	−0.363541	−	0.363541i	−0.0208849	−	0.0208849i
$304$	2.01227	+	2.01227i	0.115412	+	0.115412i
$305$	−4.11925	−	0.178288i	−0.235867	−	0.0102087i
$306$	−7.07368			−0.404376
$307$	−8.55841	−	8.55841i	−0.488454	−	0.488454i	0.419364	−	0.907818i	$-0.362253\pi$
$307$	−8.55841	−	8.55841i	−0.488454	−	0.488454i	−0.907818	+	0.419364i	$0.862253\pi$
$308$	0.967210	+	0.967210i	0.0551119	+	0.0551119i
$309$	−6.41955	−	6.41955i	−0.365195	−	0.365195i
$310$	−8.74670	−	0.378572i	−0.496779	−	0.0215014i
$311$	7.07966	+	7.07966i	0.401451	+	0.401451i	0.878744	−	0.477293i	$-0.158382\pi$
$311$	7.07966	+	7.07966i	0.401451	+	0.401451i	−0.477293	+	0.878744i	$0.658382\pi$
$312$	−2.31277	+	2.31277i	−0.130935	+	0.130935i
$313$	−21.8518			−1.23514			−0.617568	−	0.786518i	$-0.711882\pi$
$313$	−21.8518			−1.23514			−0.617568	+	0.786518i	$0.711882\pi$
$314$	−6.59408	+	6.59408i	−0.372126	+	0.372126i
$315$	8.71889	+	0.377368i	0.491254	+	0.0212623i
$316$	2.47200	+	2.47200i	0.139061	+	0.139061i
$317$	−19.1074	−	19.1074i	−1.07318	−	1.07318i	−0.997102	−	0.0760779i	$-0.975760\pi$
$317$	−19.1074	−	19.1074i	−1.07318	−	1.07318i	−0.0760779	−	0.997102i	$-0.524240\pi$
$318$	4.88978			0.274205
$319$	2.15416	+	2.15416i	0.120610	+	0.120610i
$320$	−1.64803	+	1.51129i	−0.0921277	+	0.0844837i
$321$		−	1.88592i		−	0.105262i
$322$	3.44514	−	3.44514i	0.191990	−	0.191990i
$323$	−14.2342	+	14.2342i	−0.792010	+	0.792010i
$324$	−1.00000			−0.0555556
$325$	1.41299	−	16.2926i	0.0783786	−	0.903751i
$326$			7.00131i			0.387767i
$327$	−3.26578			−0.180598
$328$			5.57830i			0.308010i
$329$		−	31.8082i		−	1.75364i
$330$	0.782946	+	0.0338872i	0.0430998	+	0.00186543i
$331$	2.84439	−	2.84439i	0.156342	−	0.156342i	−0.624602	−	0.780943i	$-0.714739\pi$
$331$	2.84439	−	2.84439i	0.156342	−	0.156342i	0.780943	+	0.624602i	$0.214739\pi$
$332$	−10.6094	−	10.6094i	−0.582268	−	0.582268i
$333$	4.91116	+	3.58895i	0.269130	+	0.196673i
$334$		−	14.7018i		−	0.804447i
$335$	−33.5423	−	1.45177i	−1.83261	−	0.0793186i
$336$		−	3.90286i		−	0.212918i
$337$	12.4436	+	12.4436i	0.677844	+	0.677844i	0.959512	−	0.281668i	$-0.0908876\pi$
$337$	12.4436	+	12.4436i	0.677844	+	0.677844i	−0.281668	+	0.959512i	$0.590888\pi$
$338$	2.30219			0.125222
$339$	−5.55259	−	5.55259i	−0.301575	−	0.301575i
$340$	−10.6904	−	11.6576i	−0.579768	−	0.632225i
$341$	0.970295	−	0.970295i	0.0525444	−	0.0525444i
$342$	−2.01227	+	2.01227i	−0.108811	+	0.108811i
$343$	−3.40077	−	3.40077i	−0.183624	−	0.183624i
$344$	−3.23195			−0.174255
$345$	0.120704	−	2.78880i	0.00649849	−	0.150144i
$346$	−3.00005	+	3.00005i	−0.161284	+	0.161284i
$347$	−13.9100			−0.746727			−0.373363	−	0.927685i	$-0.621796\pi$
$347$	−13.9100			−0.746727			−0.373363	+	0.927685i	$0.621796\pi$
$348$		−	8.69238i		−	0.465961i
$349$		−	0.414422i		−	0.0221835i	−0.999938	−	0.0110918i	$-0.996469\pi$
$349$		−	0.414422i		−	0.0221835i	0.999938	−	0.0110918i	$-0.00353069\pi$
$350$	12.5548	+	14.9393i	0.671085	+	0.798539i
$351$	−2.31277	−	2.31277i	−0.123447	−	0.123447i
$352$		−	0.350472i		−	0.0186802i
$353$			29.7855i			1.58532i	0.609661	+	0.792662i	$0.291305\pi$
$353$			29.7855i			1.58532i	−0.609661	+	0.792662i	$0.708695\pi$
$354$	−15.0197			−0.798287
$355$	−26.2004	+	24.0265i	−1.39057	+	1.27519i
$356$	3.03601	−	3.03601i	0.160908	−	0.160908i
$357$	27.6076			1.46115
$358$	9.62402	−	9.62402i	0.508645	−	0.508645i
$359$		−	8.57788i		−	0.452723i	−0.974043	−	0.226362i	$-0.927317\pi$
$359$		−	8.57788i		−	0.452723i	0.974043	−	0.226362i	$-0.0726831\pi$
$360$	−1.51129	−	1.64803i	−0.0796520	−	0.0868588i
$361$		−	10.9015i		−	0.573765i
$362$	−14.0878			−0.740436
$363$	7.69132	−	7.69132i	0.403690	−	0.403690i
$364$	9.02641	−	9.02641i	0.473112	−	0.473112i
$365$	−0.136476	+	3.15321i	−0.00714350	+	0.165047i
$366$	−1.84391			−0.0963826
$367$	−9.30759	+	9.30759i	−0.485852	+	0.485852i	−0.906995	−	0.421142i	$-0.861629\pi$
$367$	−9.30759	+	9.30759i	−0.485852	+	0.485852i	0.421142	+	0.906995i	$0.361629\pi$
$368$	−1.24836			−0.0650752
$369$	−5.57830			−0.290395
$370$	1.50749	+	13.5177i	0.0783706	+	0.702750i
$371$	−19.0841			−0.990798
$372$	−3.91530			−0.202999
$373$	−18.3349	+	18.3349i	−0.949345	+	0.949345i	−0.998777	−	0.0494321i	$-0.984259\pi$
$373$	−18.3349	+	18.3349i	−0.949345	+	0.949345i	0.0494321	+	0.998777i	$0.484259\pi$
$374$	2.47913			0.128193
$375$	11.0863	+	1.44674i	0.572496	+	0.0747093i
$376$	−5.76291	+	5.76291i	−0.297199	+	0.297199i
$377$	20.1035	−	20.1035i	1.03538	−	1.03538i
$378$	3.90286			0.200741
$379$			0.736373i			0.0378249i	0.999821	+	0.0189125i	$0.00602038\pi$
$379$			0.736373i			0.0378249i	−0.999821	+	0.0189125i	$0.993980\pi$
$380$	−6.35741	−	0.275159i	−0.326128	−	0.0141154i
$381$			20.7069i			1.06085i
$382$	−2.11691	+	2.11691i	−0.108311	+	0.108311i
$383$	2.85854			0.146065			0.0730323	−	0.997330i	$-0.476732\pi$
$383$	2.85854			0.146065			0.0730323	+	0.997330i	$0.476732\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−3.05573	−	0.132257i	−0.155734	−	0.00674044i
$386$	20.7874			1.05805
$387$		−	3.23195i		−	0.164289i
$388$		−	7.94277i		−	0.403233i
$389$	14.3095	+	14.3095i	0.725519	+	0.725519i	0.969724	−	0.244205i	$-0.0785269\pi$
$389$	14.3095	+	14.3095i	0.725519	+	0.725519i	−0.244205	+	0.969724i	$0.578527\pi$
$390$	0.316250	−	7.30678i	0.0160139	−	0.369993i
$391$		−	8.83049i		−	0.446577i
$392$			8.23228i			0.415793i
$393$	−5.13259			−0.258905
$394$	11.8547	−	11.8547i	0.597233	−	0.597233i
$395$	−7.80984	−	0.338023i	−0.392956	−	0.0170078i
$396$	0.350472			0.0176119
$397$	−0.498839	−	0.498839i	−0.0250360	−	0.0250360i	0.694478	−	0.719514i	$-0.255635\pi$
$397$	−0.498839	−	0.498839i	−0.0250360	−	0.0250360i	−0.719514	+	0.694478i	$0.755635\pi$
$398$	6.76638	−	6.76638i	0.339168	−	0.339168i
$399$	7.85360	−	7.85360i	0.393172	−	0.393172i
$400$	0.432008	−	4.98130i	0.0216004	−	0.249065i
$401$	10.8582	+	10.8582i	0.542234	+	0.542234i	0.924183	−	0.381949i	$-0.124747\pi$
$401$	10.8582	+	10.8582i	0.542234	+	0.542234i	−0.381949	+	0.924183i	$0.624747\pi$
$402$	−15.0146			−0.748861
$403$	−9.05520	−	9.05520i	−0.451072	−	0.451072i
$404$		−	0.514124i		−	0.0255786i
$405$	1.64803	−	1.51129i	0.0818913	−	0.0750966i
$406$			33.9251i			1.68368i
$407$	−1.72122	−	1.25783i	−0.0853179	−	0.0623481i
$408$	−5.00185	−	5.00185i	−0.247628	−	0.247628i
$409$	7.92408	−	7.92408i	0.391820	−	0.391820i	−0.483515	−	0.875336i	$-0.660640\pi$
$409$	7.92408	−	7.92408i	0.391820	−	0.391820i	0.875336	+	0.483515i	$0.160640\pi$
$410$	−8.43043	−	9.19321i	−0.416349	−	0.454020i
$411$			17.7222i			0.874174i
$412$		−	9.07861i		−	0.447271i
$413$	58.6196			2.88448
$414$		−	1.24836i		−	0.0613535i
$415$	33.5186	+	1.45074i	1.64536	+	0.0712141i
$416$	−3.27075			−0.160362
$417$	2.59247	−	2.59247i	0.126954	−	0.126954i
$418$	0.705244	−	0.705244i	0.0344946	−	0.0344946i
$419$			13.1368i			0.641775i	0.947117	+	0.320887i	$0.103981\pi$
$419$			13.1368i			0.641775i	−0.947117	+	0.320887i	$0.896019\pi$
$420$	5.89834	+	6.43202i	0.287810	+	0.313851i
$421$	10.6585	+	10.6585i	0.519461	+	0.519461i	0.917408	−	0.397947i	$-0.130277\pi$
$421$	10.6585	+	10.6585i	0.519461	+	0.519461i	−0.397947	+	0.917408i	$0.630277\pi$
$422$	9.92928			0.483350
$423$	−5.76291	−	5.76291i	−0.280202	−	0.280202i
$424$	3.45760	+	3.45760i	0.167916	+	0.167916i
$425$	35.2362	+	3.05589i	1.70920	+	0.148232i
$426$	−11.2416	+	11.2416i	−0.544657	+	0.544657i
$427$	7.19651			0.348263
$428$	1.33354	−	1.33354i	0.0644593	−	0.0644593i
$429$	0.810561	+	0.810561i	0.0391343	+	0.0391343i
$430$	5.32635	−	4.88441i	0.256859	−	0.235547i
$431$	−13.6585	−	13.6585i	−0.657907	−	0.657907i	0.296978	−	0.954884i	$-0.404021\pi$
$431$	−13.6585	−	13.6585i	−0.657907	−	0.657907i	−0.954884	+	0.296978i	$0.904021\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−16.2196	−	16.2196i	−0.779466	−	0.779466i	0.200274	−	0.979740i	$-0.435817\pi$
$433$	−16.2196	−	16.2196i	−0.779466	−	0.779466i	−0.979740	+	0.200274i	$0.935817\pi$
$434$	15.2809			0.733505
$435$	13.1367	+	14.3253i	0.629857	+	0.686846i
$436$	−2.30925	−	2.30925i	−0.110593	−	0.110593i
$437$	−2.51203	−	2.51203i	−0.120167	−	0.120167i
$438$			1.41148i			0.0674431i
$439$	−4.52525	+	4.52525i	−0.215979	+	0.215979i	−0.806801	−	0.590823i	$-0.798803\pi$
$439$	−4.52525	+	4.52525i	−0.215979	+	0.215979i	0.590823	+	0.806801i	$0.298803\pi$
$440$	0.529665	+	0.577588i	0.0252508	+	0.0275354i
$441$	−8.23228			−0.392013
$442$		−	23.1363i		−	1.10048i
$443$	17.5292	−	17.5292i	0.832839	−	0.832839i	−0.155066	−	0.987904i	$-0.549559\pi$
$443$	17.5292	−	17.5292i	0.832839	−	0.832839i	0.987904	+	0.155066i	$0.0495589\pi$
$444$	0.934944	+	6.01048i	0.0443705	+	0.285245i
$445$	−0.415146	+	9.59172i	−0.0196798	+	0.454691i
$446$	6.49659	+	6.49659i	0.307623	+	0.307623i
$447$	−11.9807	−	11.9807i	−0.566669	−	0.566669i
$448$	2.75974	−	2.75974i	0.130385	−	0.130385i
$449$	−24.1689	−	24.1689i	−1.14060	−	1.14060i	−0.988340	−	0.152263i	$-0.951344\pi$
$449$	−24.1689	−	24.1689i	−1.14060	−	1.14060i	−0.152263	−	0.988340i	$-0.548656\pi$
$450$	4.98130	+	0.432008i	0.234821	+	0.0203650i
$451$	1.95504			0.0920592
$452$		−	7.85255i		−	0.369353i
$453$	7.63344	+	7.63344i	0.358650	+	0.358650i
$454$		−	16.6142i		−	0.779745i
$455$	−1.23428	+	28.5173i	−0.0578638	+	1.33691i
$456$	−2.84578			−0.133266
$457$			15.3091i			0.716131i	0.933697	+	0.358065i	$0.116564\pi$
$457$			15.3091i			0.716131i	−0.933697	+	0.358065i	$0.883436\pi$
$458$			2.86631i			0.133934i
$459$	5.00185	−	5.00185i	0.233466	−	0.233466i
$460$	2.05733	−	1.88663i	0.0959236	−	0.0879646i
$461$	19.6061	−	19.6061i	0.913145	−	0.913145i	−0.0833730	−	0.996518i	$-0.526569\pi$
$461$	19.6061	−	19.6061i	0.913145	−	0.913145i	0.996518	+	0.0833730i	$0.0265693\pi$
$462$	−1.36784			−0.0636377
$463$	−25.4617			−1.18331			−0.591653	−	0.806192i	$-0.701525\pi$
$463$	−25.4617			−1.18331			−0.591653	+	0.806192i	$0.701525\pi$
$464$	6.14644	−	6.14644i	0.285341	−	0.285341i
$465$	6.45254	−	5.91716i	0.299229	−	0.274402i
$466$	8.37425	−	8.37425i	0.387930	−	0.387930i
$467$		−	18.9252i		−	0.875752i	−0.899035	−	0.437876i	$-0.855731\pi$
$467$		−	18.9252i		−	0.875752i	0.899035	−	0.437876i	$-0.144269\pi$
$468$		−	3.27075i		−	0.151191i
$469$	58.5999			2.70589
$470$	0.788024	−	18.2069i	0.0363488	−	0.839820i
$471$		−	9.32544i		−	0.429694i
$472$	−10.6205	−	10.6205i	−0.488849	−	0.488849i
$473$			1.13271i			0.0520820i
$474$	−3.49594			−0.160574
$475$	10.8930	−	9.15441i	0.499807	−	0.420033i
$476$	19.5215	+	19.5215i	0.894766	+	0.894766i
$477$	−3.45760	+	3.45760i	−0.158313	+	0.158313i
$478$	16.9584	+	16.9584i	0.775661	+	0.775661i
$479$	−3.00653	−	3.00653i	−0.137372	−	0.137372i	0.635077	−	0.772449i	$-0.280968\pi$
$479$	−3.00653	−	3.00653i	−0.137372	−	0.137372i	−0.772449	+	0.635077i	$0.780968\pi$
$480$	0.0966903	−	2.23398i	0.00441329	−	0.101967i
$481$	−11.7386	+	16.0632i	−0.535232	+	0.732418i
$482$	−9.32818	+	9.32818i	−0.424887	+	0.424887i
$483$			4.87216i			0.221691i
$484$	10.8772			0.494417
$485$	12.0038	+	13.0899i	0.545065	+	0.594383i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$			42.0200i			1.90411i	0.305929	+	0.952054i	$0.401033\pi$
$487$			42.0200i			1.90411i	−0.305929	+	0.952054i	$0.598967\pi$
$488$	−1.30384	−	1.30384i	−0.0590221	−	0.0590221i
$489$	−4.95068	−	4.95068i	−0.223877	−	0.223877i
$490$	−12.4414	−	13.5670i	−0.562043	−	0.612897i
$491$	14.2813			0.644507			0.322254	−	0.946653i	$-0.395560\pi$
$491$	14.2813			0.644507			0.322254	+	0.946653i	$0.395560\pi$
$492$	−3.94446	−	3.94446i	−0.177830	−	0.177830i
$493$	43.4780	+	43.4780i	1.95815	+	1.95815i
$494$	−6.58164	−	6.58164i	−0.296122	−	0.296122i
$495$	−0.577588	+	0.529665i	−0.0259607	+	0.0238067i
$496$	−2.76854	−	2.76854i	−0.124311	−	0.124311i
$497$	43.8743	−	43.8743i	1.96803	−	1.96803i
$498$	15.0040			0.672345
$499$	4.58214	−	4.58214i	0.205125	−	0.205125i	−0.597067	−	0.802192i	$-0.703667\pi$
$499$	4.58214	−	4.58214i	0.205125	−	0.205125i	0.802192	+	0.597067i	$0.203667\pi$
$500$	6.81623	+	8.86223i	0.304831	+	0.396331i
$501$	10.3957	+	10.3957i	0.464447	+	0.464447i
$502$	21.5270	+	21.5270i	0.960795	+	0.960795i
$503$	4.41445			0.196831			0.0984153	−	0.995145i	$-0.468623\pi$
$503$	4.41445			0.196831			0.0984153	+	0.995145i	$0.468623\pi$
$504$	2.75974	+	2.75974i	0.122928	+	0.122928i
$505$	0.776991	+	0.847293i	0.0345756	+	0.0377040i
$506$			0.437515i			0.0194499i
$507$	−1.62789	+	1.62789i	−0.0722972	+	0.0722972i
$508$	−14.6420	+	14.6420i	−0.649633	+	0.649633i
$509$	23.7000			1.05048			0.525242	−	0.850953i	$-0.323975\pi$
$509$	23.7000			1.05048			0.525242	+	0.850953i	$0.323975\pi$
$510$	15.8024	+	0.683957i	0.699744	+	0.0302861i
$511$		−	5.50880i		−	0.243695i
$512$	−1.00000			−0.0441942
$513$		−	2.84578i		−	0.125644i
$514$		−	0.409575i		−	0.0180656i
$515$	13.7204	+	14.9618i	0.604594	+	0.659297i
$516$	2.28533	−	2.28533i	0.100606	−	0.100606i
$517$	2.01974	+	2.01974i	0.0888279	+	0.0888279i
$518$	−3.64895	−	23.4580i	−0.160326	−	1.03069i
$519$		−	4.24271i		−	0.186234i
$520$	5.39030	−	4.94305i	0.236380	−	0.216767i
$521$			22.6223i			0.991100i	0.868579	+	0.495550i	$0.165034\pi$
$521$			22.6223i			0.991100i	−0.868579	+	0.495550i	$0.834966\pi$
$522$	6.14644	+	6.14644i	0.269023	+	0.269023i
$523$	−38.2884			−1.67424			−0.837118	−	0.547023i	$-0.815761\pi$
$523$	−38.2884			−1.67424			−0.837118	+	0.547023i	$0.815761\pi$
$524$	−3.62929	−	3.62929i	−0.158546	−	0.158546i
$525$	−19.4413	−	1.68606i	−0.848488	−	0.0735858i
$526$	10.0366	−	10.0366i	0.437616	−	0.437616i
$527$	19.5838	−	19.5838i	0.853082	−	0.853082i
$528$	0.247821	+	0.247821i	0.0107850	+	0.0107850i
$529$	−21.4416			−0.932244
$530$	−10.9237	−	0.472795i	−0.474494	−	0.0205369i
$531$	10.6205	−	10.6205i	0.460891	−	0.460891i
$532$	11.1067			0.481535
$533$		−	18.2452i		−	0.790289i
$534$			4.29357i			0.185801i
$535$	−0.182350	+	4.21309i	−0.00788367	+	0.182148i
$536$	−10.6169	−	10.6169i	−0.458582	−	0.458582i
$537$			13.6104i			0.587333i
$538$		−	19.9758i		−	0.861217i
$539$	2.88518			0.124274
$540$	2.23398	+	0.0966903i	0.0961350	+	0.00416089i
$541$	8.89780	−	8.89780i	0.382546	−	0.382546i	−0.489472	−	0.872019i	$-0.662811\pi$
$541$	8.89780	−	8.89780i	0.382546	−	0.382546i	0.872019	+	0.489472i	$0.162811\pi$
$542$	−11.0572			−0.474948
$543$	9.96155	−	9.96155i	0.427491	−	0.427491i
$544$		−	7.07368i		−	0.303282i
$545$	7.29567	+	0.315769i	0.312512	+	0.0135260i
$546$			12.7653i			0.546303i
$547$	7.12339			0.304574			0.152287	−	0.988336i	$-0.451336\pi$
$547$	7.12339			0.304574			0.152287	+	0.988336i	$0.451336\pi$
$548$	−12.5315	+	12.5315i	−0.535320	+	0.535320i
$549$	1.30384	−	1.30384i	0.0556465	−	0.0556465i
$550$	−1.74581	−	0.151407i	−0.0744414	−	0.00645600i
$551$	24.7366			1.05382
$552$	0.882722	−	0.882722i	0.0375712	−	0.0375712i
$553$	13.6441			0.580208
$554$	−24.4538			−1.03894
$555$	−10.6244	−	8.49248i	−0.450980	−	0.360486i
$556$	3.66631			0.155486
$557$	45.3868			1.92310			0.961551	−	0.274626i	$-0.0885539\pi$
$557$	45.3868			1.92310			0.961551	+	0.274626i	$0.0885539\pi$
$558$	2.76854	−	2.76854i	0.117202	−	0.117202i
$559$	10.5709			0.447102
$560$	−0.377368	+	8.71889i	−0.0159467	+	0.368440i
$561$	−1.75301	+	1.75301i	−0.0740121	+	0.0740121i
$562$	7.23968	−	7.23968i	0.305388	−	0.305388i
$563$	5.35148			0.225538			0.112769	−	0.993621i	$-0.464028\pi$
$563$	5.35148			0.225538			0.112769	+	0.993621i	$0.464028\pi$
$564$		−	8.14998i		−	0.343176i
$565$	11.8675	+	12.9412i	0.499268	+	0.544442i
$566$		−	30.2054i		−	1.26963i
$567$	−2.75974	+	2.75974i	−0.115898	+	0.115898i
$568$	−15.8980			−0.667066
$569$	−13.2588	+	13.2588i	−0.555837	+	0.555837i	−0.928119	−	0.372283i	$-0.878575\pi$
$569$	−13.2588	+	13.2588i	−0.555837	+	0.555837i	0.372283	+	0.928119i	$0.378575\pi$
$570$	4.68993	−	4.30080i	0.196440	−	0.180141i
$571$	−39.9897			−1.67352			−0.836758	−	0.547574i	$-0.815552\pi$
$571$	−39.9897			−1.67352			−0.836758	+	0.547574i	$0.815552\pi$
$572$			1.14631i			0.0479295i
$573$		−	2.99376i		−	0.125066i
$574$	15.3946	+	15.3946i	0.642560	+	0.642560i
$575$	−0.539300	+	6.21845i	−0.0224904	+	0.259327i
$576$		−	1.00000i		−	0.0416667i
$577$		−	2.19671i		−	0.0914503i	−0.998954	−	0.0457251i	$-0.985440\pi$
$577$		−	2.19671i		−	0.0914503i	0.998954	−	0.0457251i	$-0.0145598\pi$
$578$	33.0370			1.37416
$579$	−14.6989	+	14.6989i	−0.610865	+	0.610865i
$580$	−0.840469	+	19.4186i	−0.0348986	+	0.806313i
$581$	−58.5584			−2.42941
$582$	5.61638	+	5.61638i	0.232807	+	0.232807i
$583$	1.21179	−	1.21179i	0.0501873	−	0.0501873i
$584$	−0.998067	+	0.998067i	−0.0413003	+	0.0413003i
$585$	4.94305	+	5.39030i	0.204370	+	0.222861i
$586$	0.618270	+	0.618270i	0.0255405	+	0.0255405i
$587$	40.3393			1.66498			0.832490	−	0.554041i	$-0.186915\pi$
$587$	40.3393			1.66498			0.832490	+	0.554041i	$0.186915\pi$
$588$	−5.82110	−	5.82110i	−0.240058	−	0.240058i
$589$		−	11.1421i		−	0.459102i
$590$	33.5536	+	1.45226i	1.38138	+	0.0597885i
$591$			16.7651i			0.689625i
$592$	−3.58895	+	4.91116i	−0.147505	+	0.201847i
$593$	−14.1348	−	14.1348i	−0.580448	−	0.580448i	0.354579	−	0.935026i	$-0.384624\pi$
$593$	−14.1348	−	14.1348i	−0.580448	−	0.580448i	−0.935026	+	0.354579i	$0.884624\pi$
$594$	−0.247821	+	0.247821i	−0.0101682	+	0.0101682i
$595$	−61.6747	−	2.66938i	−2.52841	−	0.109434i
$596$		−	16.9433i		−	0.694025i
$597$			9.56911i			0.391638i
$598$	4.08307			0.166969
$599$		−	23.9120i		−	0.977016i	−0.872559	−	0.488508i	$-0.837541\pi$
$599$		−	23.9120i		−	0.977016i	0.872559	−	0.488508i	$-0.162459\pi$
$600$	3.21684	+	3.82779i	0.131327	+	0.156269i
$601$	−24.5648			−1.00202			−0.501009	−	0.865442i	$-0.667038\pi$
$601$	−24.5648			−1.00202			−0.501009	+	0.865442i	$0.667038\pi$
$602$	−8.91933	+	8.91933i	−0.363525	+	0.363525i
$603$	10.6169	−	10.6169i	0.432355	−	0.432355i
$604$			10.7953i			0.439255i
$605$	−17.9259	+	16.4386i	−0.728792	+	0.668322i
$606$	0.363541	+	0.363541i	0.0147678	+	0.0147678i
$607$	−28.5020			−1.15686			−0.578430	−	0.815732i	$-0.696334\pi$
$607$	−28.5020			−1.15686			−0.578430	+	0.815732i	$0.696334\pi$
$608$	−2.01227	−	2.01227i	−0.0816084	−	0.0816084i
$609$	−23.9887	−	23.9887i	−0.972070	−	0.972070i
$610$	4.11925	+	0.178288i	0.166783	+	0.00721867i
$611$	18.8490	−	18.8490i	0.762550	−	0.762550i
$612$	7.07368			0.285937
$613$	20.5098	−	20.5098i	0.828384	−	0.828384i	−0.158909	−	0.987293i	$-0.550798\pi$
$613$	20.5098	−	20.5098i	0.828384	−	0.828384i	0.987293	+	0.158909i	$0.0507978\pi$
$614$	8.55841	+	8.55841i	0.345389	+	0.345389i
$615$	12.4618	+	0.539368i	0.502508	+	0.0217494i
$616$	−0.967210	−	0.967210i	−0.0389700	−	0.0389700i
$617$	14.5571	+	14.5571i	0.586047	+	0.586047i	0.936559	−	0.350511i	$-0.113992\pi$
$617$	14.5571	+	14.5571i	0.586047	+	0.586047i	−0.350511	+	0.936559i	$0.613992\pi$
$618$	6.41955	+	6.41955i	0.258232	+	0.258232i
$619$	22.6423			0.910070			0.455035	−	0.890474i	$-0.349627\pi$
$619$	22.6423			0.910070			0.455035	+	0.890474i	$0.349627\pi$
$620$	8.74670	+	0.378572i	0.351276	+	0.0152038i
$621$	0.882722	+	0.882722i	0.0354224	+	0.0354224i
$622$	−7.07966	−	7.07966i	−0.283869	−	0.283869i
$623$		−	16.7572i		−	0.671362i
$624$	2.31277	−	2.31277i	0.0925849	−	0.0925849i
$625$	−24.6267	−	4.30392i	−0.985070	−	0.172157i
$626$	21.8518			0.873372
$627$			0.997366i			0.0398310i
$628$	6.59408	−	6.59408i	0.263132	−	0.263132i
$629$	−34.7400	−	25.3871i	−1.38517	−	1.01225i
$630$	−8.71889	−	0.377368i	−0.347369	−	0.0150347i
$631$	23.0961	+	23.0961i	0.919443	+	0.919443i	0.996989	−	0.0775462i	$-0.0247085\pi$
$631$	23.0961	+	23.0961i	0.919443	+	0.919443i	−0.0775462	+	0.996989i	$0.524709\pi$
$632$	−2.47200	−	2.47200i	−0.0983309	−	0.0983309i
$633$	−7.02106	+	7.02106i	−0.279062	+	0.279062i
$634$	19.1074	+	19.1074i	0.758853	+	0.758853i
$635$	2.00215	−	46.2587i	0.0794531	−	1.83572i
$636$	−4.88978			−0.193893
$637$		−	26.9257i		−	1.06684i
$638$	−2.15416	−	2.15416i	−0.0852839	−	0.0852839i
$639$		−	15.8980i		−	0.628916i
$640$	1.64803	−	1.51129i	0.0651441	−	0.0597390i
$641$	−42.5772			−1.68170			−0.840849	−	0.541269i	$-0.817944\pi$
$641$	−42.5772			−1.68170			−0.840849	+	0.541269i	$0.817944\pi$
$642$			1.88592i			0.0744312i
$643$			19.1904i			0.756794i	0.925643	+	0.378397i	$0.123525\pi$
$643$			19.1904i			0.756794i	−0.925643	+	0.378397i	$0.876475\pi$
$644$	−3.44514	+	3.44514i	−0.135757	+	0.135757i
$645$	−0.312498	+	7.22010i	−0.0123046	+	0.284291i
$646$	14.2342	−	14.2342i	0.560036	−	0.560036i
$647$	−28.2302			−1.10984			−0.554921	−	0.831903i	$-0.687251\pi$
$647$	−28.2302			−1.10984			−0.554921	+	0.831903i	$0.687251\pi$
$648$	1.00000			0.0392837
$649$	−3.72219	+	3.72219i	−0.146109	+	0.146109i
$650$	−1.41299	+	16.2926i	−0.0554220	+	0.639048i
$651$	−10.8052	+	10.8052i	−0.423489	+	0.423489i
$652$		−	7.00131i		−	0.274193i
$653$			5.24225i			0.205145i	0.994726	+	0.102573i	$0.0327074\pi$
$653$			5.24225i			0.205145i	−0.994726	+	0.102573i	$0.967293\pi$
$654$	3.26578			0.127702
$655$	11.4661	+	0.496272i	0.448017	+	0.0193910i
$656$		−	5.57830i		−	0.217796i
$657$	−0.998067	−	0.998067i	−0.0389383	−	0.0389383i
$658$			31.8082i			1.24001i
$659$	30.0925			1.17224			0.586119	−	0.810225i	$-0.300655\pi$
$659$	30.0925			1.17224			0.586119	+	0.810225i	$0.300655\pi$
$660$	−0.782946	−	0.0338872i	−0.0304761	−	0.00131906i
$661$	−32.5054	−	32.5054i	−1.26432	−	1.26432i	−0.948981	−	0.315335i	$-0.897883\pi$
$661$	−32.5054	−	32.5054i	−1.26432	−	1.26432i	−0.315335	−	0.948981i	$-0.602117\pi$
$662$	−2.84439	+	2.84439i	−0.110550	+	0.110550i
$663$	16.3598	+	16.3598i	0.635362	+	0.635362i
$664$	10.6094	+	10.6094i	0.411726	+	0.411726i
$665$	−18.3041	+	16.7854i	−0.709804	+	0.650910i
$666$	−4.91116	−	3.58895i	−0.190303	−	0.139069i
$667$	−7.67296	+	7.67296i	−0.297098	+	0.297098i
$668$			14.7018i			0.568830i
$669$	−9.18757			−0.355212
$670$	33.5423	+	1.45177i	1.29585	+	0.0560867i
$671$	−0.456959	+	0.456959i	−0.0176407	+	0.0176407i
$672$			3.90286i			0.150556i
$673$	−9.11977	−	9.11977i	−0.351541	−	0.351541i	0.509141	−	0.860683i	$-0.329963\pi$
$673$	−9.11977	−	9.11977i	−0.351541	−	0.351541i	−0.860683	+	0.509141i	$0.829963\pi$
$674$	−12.4436	−	12.4436i	−0.479308	−	0.479308i
$675$	−3.82779	+	3.21684i	−0.147332	+	0.123816i
$676$	−2.30219			−0.0885456
$677$	−19.8062	−	19.8062i	−0.761213	−	0.761213i	0.215329	−	0.976542i	$-0.430918\pi$
$677$	−19.8062	−	19.8062i	−0.761213	−	0.761213i	−0.976542	+	0.215329i	$0.930918\pi$
$678$	5.55259	+	5.55259i	0.213246	+	0.213246i
$679$	−21.9199	−	21.9199i	−0.841210	−	0.841210i
$680$	10.6904	+	11.6576i	0.409958	+	0.447050i
$681$	11.7480	+	11.7480i	0.450186	+	0.450186i
$682$	−0.970295	+	0.970295i	−0.0371545	+	0.0371545i
$683$	−9.00362			−0.344514			−0.172257	−	0.985052i	$-0.555106\pi$
$683$	−9.00362			−0.344514			−0.172257	+	0.985052i	$0.555106\pi$
$684$	2.01227	−	2.01227i	0.0769411	−	0.0769411i
$685$	1.71357	−	39.5911i	0.0654721	−	1.51270i
$686$	3.40077	+	3.40077i	0.129842	+	0.129842i
$687$	−2.02679	−	2.02679i	−0.0773268	−	0.0773268i
$688$	3.23195			0.123217
$689$	−11.3089	−	11.3089i	−0.430837	−	0.430837i
$690$	−0.120704	+	2.78880i	−0.00459513	+	0.106168i
$691$		−	8.79710i		−	0.334657i	−0.985901	−	0.167329i	$-0.946486\pi$
$691$		−	8.79710i		−	0.334657i	0.985901	−	0.167329i	$-0.0535141\pi$
$692$	3.00005	−	3.00005i	0.114045	−	0.114045i
$693$	0.967210	−	0.967210i	0.0367413	−	0.0367413i
$694$	13.9100			0.528016
$695$	−6.04219	+	5.54085i	−0.229193	+	0.210176i
$696$			8.69238i			0.329484i
$697$	39.4592			1.49462
$698$			0.414422i			0.0156861i
$699$			11.8430i			0.447943i
$700$	−12.5548	−	14.9393i	−0.474529	−	0.564653i
$701$	6.74494	−	6.74494i	0.254753	−	0.254753i	−0.568163	−	0.822916i	$-0.692346\pi$
$701$	6.74494	−	6.74494i	0.254753	−	0.254753i	0.822916	+	0.568163i	$0.192346\pi$
$702$	2.31277	+	2.31277i	0.0872899	+	0.0872899i
$703$	−17.1045	+	2.66065i	−0.645109	+	0.100348i
$704$			0.350472i			0.0132089i
$705$	12.3170	+	13.4314i	0.463884	+	0.505856i
$706$		−	29.7855i		−	1.12099i
$707$	−1.41885	−	1.41885i	−0.0533612	−	0.0533612i
$708$	15.0197			0.564474
$709$	27.6225	+	27.6225i	1.03739	+	1.03739i	0.999273	+	0.0381132i	$0.0121347\pi$
$709$	27.6225	+	27.6225i	1.03739	+	1.03739i	0.0381132	+	0.999273i	$0.487865\pi$
$710$	26.2004	−	24.0265i	0.983284	−	0.901698i
$711$	2.47200	−	2.47200i	0.0927072	−	0.0927072i
$712$	−3.03601	+	3.03601i	−0.113779	+	0.113779i
$713$	3.45613	+	3.45613i	0.129433	+	0.129433i
$714$	−27.6076			−1.03319
$715$	−1.73240	−	1.88915i	−0.0647881	−	0.0706501i
$716$	−9.62402	+	9.62402i	−0.359666	+	0.359666i
$717$	−23.9829			−0.895656
$718$			8.57788i			0.320124i
$719$			11.0173i			0.410878i	0.978670	+	0.205439i	$0.0658622\pi$
$719$			11.0173i			0.410878i	−0.978670	+	0.205439i	$0.934138\pi$
$720$	1.51129	+	1.64803i	0.0563224	+	0.0614185i
$721$	−25.0546	−	25.0546i	−0.933081	−	0.933081i
$722$			10.9015i			0.405713i
$723$		−	13.1920i		−	0.490617i
$724$	14.0878			0.523567
$725$	−27.9620	−	33.2726i	−1.03848	−	1.23571i
$726$	−7.69132	+	7.69132i	−0.285452	+	0.285452i
$727$	8.80697			0.326632			0.163316	−	0.986574i	$-0.447781\pi$
$727$	8.80697			0.326632			0.163316	+	0.986574i	$0.447781\pi$
$728$	−9.02641	+	9.02641i	−0.334541	+	0.334541i
$729$			1.00000i			0.0370370i
$730$	0.136476	−	3.15321i	0.00505122	−	0.116706i
$731$			22.8618i			0.845574i
$732$	1.84391			0.0681528
$733$	11.9215	−	11.9215i	0.440331	−	0.440331i	−0.451792	−	0.892123i	$-0.649215\pi$
$733$	11.9215	−	11.9215i	0.440331	−	0.440331i	0.892123	+	0.451792i	$0.149215\pi$
$734$	9.30759	−	9.30759i	0.343549	−	0.343549i
$735$	18.3907	+	0.795982i	0.678352	+	0.0293602i
$736$	1.24836			0.0460151
$737$	−3.72094	+	3.72094i	−0.137063	+	0.137063i
$738$	5.57830			0.205340
$739$	−1.03649			−0.0381277			−0.0190639	−	0.999818i	$-0.506069\pi$
$739$	−1.03649			−0.0381277			−0.0190639	+	0.999818i	$0.506069\pi$
$740$	−1.50749	−	13.5177i	−0.0554164	−	0.496920i
$741$	9.30784			0.341932
$742$	19.0841			0.700600
$743$	16.2854	−	16.2854i	0.597453	−	0.597453i	−0.342181	−	0.939634i	$-0.611166\pi$
$743$	16.2854	−	16.2854i	0.597453	−	0.597453i	0.939634	+	0.342181i	$0.111166\pi$
$744$	3.91530			0.143542
$745$	25.6062	+	27.9231i	0.938140	+	1.02302i
$746$	18.3349	−	18.3349i	0.671289	−	0.671289i
$747$	−10.6094	+	10.6094i	−0.388179	+	0.388179i
$748$	−2.47913			−0.0906459
$749$		−	7.36046i		−	0.268945i
$750$	−11.0863	−	1.44674i	−0.404816	−	0.0528274i
$751$			44.5447i			1.62546i	0.582641	+	0.812729i	$0.302019\pi$
$751$			44.5447i			1.62546i	−0.582641	+	0.812729i	$0.697981\pi$
$752$	5.76291	−	5.76291i	0.210152	−	0.210152i
$753$	−30.4437			−1.10943
$754$	−20.1035	+	20.1035i	−0.732126	+	0.732126i
$755$	−16.3148	−	17.7910i	−0.593758	−	0.647481i
$756$	−3.90286			−0.141945
$757$			6.50328i			0.236366i	0.992992	+	0.118183i	$0.0377069\pi$
$757$			6.50328i			0.236366i	−0.992992	+	0.118183i	$0.962293\pi$
$758$		−	0.736373i		−	0.0267463i
$759$	−0.309369	−	0.309369i	−0.0112294	−	0.0112294i
$760$	6.35741	+	0.275159i	0.230607	+	0.00998108i
$761$			30.3235i			1.09923i	0.835419	+	0.549613i	$0.185225\pi$
$761$			30.3235i			1.09923i	−0.835419	+	0.549613i	$0.814775\pi$
$762$		−	20.7069i		−	0.750131i
$763$	−12.7459			−0.461431
$764$	2.11691	−	2.11691i	0.0765871	−	0.0765871i
$765$	−11.6576	+	10.6904i	−0.421483	+	0.386512i
$766$	−2.85854			−0.103283
$767$	34.7371	+	34.7371i	1.25428	+	1.25428i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−20.4408	+	20.4408i	−0.737113	+	0.737113i	−0.972018	−	0.234906i	$-0.924522\pi$
$769$	−20.4408	+	20.4408i	−0.737113	+	0.737113i	0.234906	+	0.972018i	$0.424522\pi$
$770$	3.05573	+	0.132257i	0.110121	+	0.00476621i
$771$	0.289614	+	0.289614i	0.0104302	+	0.0104302i
$772$	−20.7874			−0.748154
$773$	−12.8496	−	12.8496i	−0.462167	−	0.462167i	0.437198	−	0.899365i	$-0.355971\pi$
$773$	−12.8496	−	12.8496i	−0.462167	−	0.462167i	−0.899365	+	0.437198i	$0.855971\pi$
$774$			3.23195i			0.116170i
$775$	−14.9870	+	12.5949i	−0.538347	+	0.452422i
$776$			7.94277i			0.285129i
$777$	19.1675	+	14.0071i	0.687632	+	0.502503i
$778$	−14.3095	−	14.3095i	−0.513019	−	0.513019i
$779$	11.2251	−	11.2251i	0.402179	−	0.402179i
$780$	−0.316250	+	7.30678i	−0.0113236	+	0.261625i
$781$			5.57181i			0.199375i
$782$			8.83049i			0.315778i
$783$	−8.69238			−0.310640
$784$		−	8.23228i		−	0.294010i
$785$	−0.901679	+	20.8328i	−0.0321823	+	0.743555i
$786$	5.13259			0.183074
$787$	−20.2540	+	20.2540i	−0.721978	+	0.721978i	−0.969008	−	0.247030i	$-0.920545\pi$
$787$	−20.2540	+	20.2540i	−0.721978	+	0.721978i	0.247030	+	0.969008i	$0.420545\pi$
$788$	−11.8547	+	11.8547i	−0.422307	+	0.422307i
$789$			14.1939i			0.505315i
$790$	7.80984	+	0.338023i	0.277862	+	0.0120263i
$791$	−21.6709	−	21.6709i	−0.770530	−	0.770530i
$792$	−0.350472			−0.0124535
$793$	4.26454	+	4.26454i	0.151438	+	0.151438i
$794$	0.498839	+	0.498839i	0.0177031	+	0.0177031i
$795$	8.05851	−	7.38988i	0.285806	−	0.262092i
$796$	−6.76638	+	6.76638i	−0.239828	+	0.239828i
$797$	−33.9189			−1.20147			−0.600734	−	0.799449i	$-0.705125\pi$
$797$	−33.9189			−1.20147			−0.600734	+	0.799449i	$0.705125\pi$
$798$	−7.85360	+	7.85360i	−0.278014	+	0.278014i
$799$	40.7650	+	40.7650i	1.44216	+	1.44216i
$800$	−0.432008	+	4.98130i	−0.0152738	+	0.176116i
$801$	−3.03601	−	3.03601i	−0.107272	−	0.107272i
$802$	−10.8582	−	10.8582i	−0.383417	−	0.383417i
$803$	0.349795	+	0.349795i	0.0123440	+	0.0123440i
$804$	15.0146			0.529525
$805$	0.471091	−	10.8843i	0.0166038	−	0.383621i
$806$	9.05520	+	9.05520i	0.318956	+	0.318956i
$807$	14.1250	+	14.1250i	0.497224	+	0.497224i
$808$			0.514124i			0.0180868i
$809$	11.7103	−	11.7103i	0.411713	−	0.411713i	−0.470622	−	0.882335i	$-0.655970\pi$
$809$	11.7103	−	11.7103i	0.411713	−	0.411713i	0.882335	+	0.470622i	$0.155970\pi$
$810$	−1.64803	+	1.51129i	−0.0579059	+	0.0531013i
$811$	12.1269			0.425834			0.212917	−	0.977070i	$-0.431704\pi$
$811$	12.1269			0.425834			0.212917	+	0.977070i	$0.431704\pi$
$812$		−	33.9251i		−	1.19054i
$813$	7.81863	−	7.81863i	0.274211	−	0.274211i
$814$	1.72122	+	1.25783i	0.0603288	+	0.0440867i
$815$	10.5810	+	11.5384i	0.370637	+	0.404172i
$816$	5.00185	+	5.00185i	0.175100	+	0.175100i
$817$	6.50356	+	6.50356i	0.227531	+	0.227531i
$818$	−7.92408	+	7.92408i	−0.277059	+	0.277059i
$819$	−9.02641	−	9.02641i	−0.315408	−	0.315408i
$820$	8.43043	+	9.19321i	0.294403	+	0.321041i
$821$	29.1034			1.01571			0.507857	−	0.861441i	$-0.330438\pi$
$821$	29.1034			1.01571			0.507857	+	0.861441i	$0.330438\pi$
$822$		−	17.7222i		−	0.618134i
$823$	−17.5087	−	17.5087i	−0.610316	−	0.610316i	0.332712	−	0.943028i	$-0.392036\pi$
$823$	−17.5087	−	17.5087i	−0.610316	−	0.610316i	−0.943028	+	0.332712i	$0.892036\pi$
$824$			9.07861i			0.316268i
$825$	1.34153	−	1.12741i	0.0467062	−	0.0392514i
$826$	−58.6196			−2.03964
$827$			14.9493i			0.519837i	0.965631	+	0.259918i	$0.0836956\pi$
$827$			14.9493i			0.519837i	−0.965631	+	0.259918i	$0.916304\pi$
$828$			1.24836i			0.0433834i
$829$	8.25148	−	8.25148i	0.286586	−	0.286586i	−0.549143	−	0.835729i	$-0.685046\pi$
$829$	8.25148	−	8.25148i	0.286586	−	0.286586i	0.835729	+	0.549143i	$0.185046\pi$
$830$	−33.5186	−	1.45074i	−1.16345	−	0.0503560i
$831$	17.2915	−	17.2915i	0.599834	−	0.599834i
$832$	3.27075			0.113393
$833$	58.2326			2.01764
$834$	−2.59247	+	2.59247i	−0.0897699	+	0.0897699i
$835$	−22.2187	−	24.2290i	−0.768909	−	0.838479i
$836$	−0.705244	+	0.705244i	−0.0243914	+	0.0243914i
$837$			3.91530i			0.135333i
$838$		−	13.1368i		−	0.453803i
$839$	12.0705			0.416720			0.208360	−	0.978052i	$-0.433187\pi$
$839$	12.0705			0.416720			0.208360	+	0.978052i	$0.433187\pi$
$840$	−5.89834	−	6.43202i	−0.203512	−	0.221926i
$841$		−	46.5575i		−	1.60543i
$842$	−10.6585	−	10.6585i	−0.367315	−	0.367315i
$843$			10.2385i			0.352631i
$844$	−9.92928			−0.341780
$845$	3.79407	−	3.47927i	0.130520	−	0.119691i
$846$	5.76291	+	5.76291i	0.198133	+	0.198133i
$847$	30.0181	−	30.0181i	1.03143	−	1.03143i
$848$	−3.45760	−	3.45760i	−0.118734	−	0.118734i
$849$	21.3584	+	21.3584i	0.733019	+	0.733019i
$850$	−35.2362	−	3.05589i	−1.20859	−	0.104816i
$851$	4.48029	−	6.13088i	0.153582	−	0.210164i
$852$	11.2416	−	11.2416i	0.385131	−	0.385131i
$853$		−	55.2308i		−	1.89107i	−0.325527	−	0.945533i	$-0.605542\pi$
$853$		−	55.2308i		−	1.89107i	0.325527	−	0.945533i	$-0.394458\pi$
$854$	−7.19651			−0.246259
$855$	−0.275159	+	6.35741i	−0.00941025	+	0.217419i
$856$	−1.33354	+	1.33354i	−0.0455796	+	0.0455796i
$857$		−	42.6736i		−	1.45770i	−0.684672	−	0.728851i	$-0.740054\pi$
$857$		−	42.6736i		−	1.45770i	0.684672	−	0.728851i	$-0.259946\pi$
$858$	−0.810561	−	0.810561i	−0.0276721	−	0.0276721i
$859$	−37.8772	−	37.8772i	−1.29235	−	1.29235i	−0.933327	−	0.359028i	$-0.883108\pi$
$859$	−37.8772	−	37.8772i	−1.29235	−	1.29235i	−0.359028	−	0.933327i	$-0.616892\pi$
$860$	−5.32635	+	4.88441i	−0.181627	+	0.166557i
$861$	−21.7713			−0.741964
$862$	13.6585	+	13.6585i	0.465210	+	0.465210i
$863$	27.1162	+	27.1162i	0.923047	+	0.923047i	0.997244	−	0.0741970i	$-0.0236394\pi$
$863$	27.1162	+	27.1162i	0.923047	+	0.923047i	−0.0741970	+	0.997244i	$0.523639\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	−0.410229	+	9.47812i	−0.0139482	+	0.322266i
$866$	16.2196	+	16.2196i	0.551166	+	0.551166i
$867$	−23.3607	+	23.3607i	−0.793371	+	0.793371i
$868$	−15.2809			−0.518666
$869$	−0.866367	+	0.866367i	−0.0293895	+	0.0293895i
$870$	−13.1367	−	14.3253i	−0.445376	−	0.485674i
$871$	34.7254	+	34.7254i	1.17662	+	1.17662i
$872$	2.30925	+	2.30925i	0.0782011	+	0.0782011i
$873$	−7.94277			−0.268822
$874$	2.51203	+	2.51203i	0.0849708	+	0.0849708i
$875$	43.2684	+	5.64641i	1.46274	+	0.190884i
$876$		−	1.41148i		−	0.0476895i
$877$	3.65778	−	3.65778i	0.123514	−	0.123514i	−0.642648	−	0.766162i	$-0.722164\pi$
$877$	3.65778	−	3.65778i	0.123514	−	0.123514i	0.766162	+	0.642648i	$0.222164\pi$
$878$	4.52525	−	4.52525i	0.152720	−	0.152720i
$879$	−0.874366			−0.0294916
$880$	−0.529665	−	0.577588i	−0.0178550	−	0.0194705i
$881$		−	35.1647i		−	1.18473i	−0.805670	−	0.592364i	$-0.798195\pi$
$881$		−	35.1647i		−	1.18473i	0.805670	−	0.592364i	$-0.201805\pi$
$882$	8.23228			0.277195
$883$			28.4200i			0.956410i	0.878248	+	0.478205i	$0.158712\pi$
$883$			28.4200i			0.956410i	−0.878248	+	0.478205i	$0.841288\pi$
$884$			23.1363i			0.778157i
$885$	−24.7529	+	22.6991i	−0.832059	+	0.763021i
$886$	−17.5292	+	17.5292i	−0.588906	+	0.588906i
$887$	−30.2121	−	30.2121i	−1.01442	−	1.01442i	−0.999894	−	0.0145284i	$-0.995375\pi$
$887$	−30.2121	−	30.2121i	−1.01442	−	1.01442i	−0.0145284	−	0.999894i	$-0.504625\pi$
$888$	−0.934944	−	6.01048i	−0.0313747	−	0.201699i
$889$			80.8160i			2.71048i
$890$	0.415146	−	9.59172i	0.0139157	−	0.321515i
$891$		−	0.350472i		−	0.0117413i
$892$	−6.49659	−	6.49659i	−0.217522	−	0.217522i
$893$	23.1931			0.776126
$894$	11.9807	+	11.9807i	0.400695	+	0.400695i
$895$	1.31599	−	30.4053i	0.0439889	−	1.01634i
$896$	−2.75974	+	2.75974i	−0.0921963	+	0.0921963i
$897$	−2.88717	+	2.88717i	−0.0963997	+	0.0963997i
$898$	24.1689	+	24.1689i	0.806528	+	0.806528i
$899$	−34.0333			−1.13508
$900$	−4.98130	−	0.432008i	−0.166043	−	0.0144003i
$901$	24.4580	−	24.4580i	0.814813	−	0.814813i
$902$	−1.95504			−0.0650957
$903$		−	12.6138i		−	0.419762i
$904$			7.85255i			0.261172i
$905$	−23.2171	+	21.2907i	−0.771761	+	0.707726i
$906$	−7.63344	−	7.63344i	−0.253604	−	0.253604i
$907$			13.2909i			0.441317i	0.975351	+	0.220658i	$0.0708206\pi$
$907$			13.2909i			0.441317i	−0.975351	+	0.220658i	$0.929179\pi$
$908$			16.6142i			0.551363i
$909$	−0.514124			−0.0170524
$910$	1.23428	−	28.5173i	0.0409159	−	0.945340i
$911$	−31.5562	+	31.5562i	−1.04550	+	1.04550i	−0.0465896	+	0.998914i	$0.514835\pi$
$911$	−31.5562	+	31.5562i	−1.04550	+	1.04550i	−0.998914	+	0.0465896i	$0.985165\pi$
$912$	2.84578			0.0942332
$913$	3.71831	−	3.71831i	0.123058	−	0.123058i
$914$		−	15.3091i		−	0.506381i
$915$	−3.03882	+	2.78668i	−0.100460	+	0.0921248i
$916$		−	2.86631i		−	0.0947056i
$917$	−20.0318			−0.661507
$918$	−5.00185	+	5.00185i	−0.165086	+	0.165086i
$919$	1.91721	−	1.91721i	0.0632431	−	0.0632431i	−0.674778	−	0.738021i	$-0.735761\pi$
$919$	1.91721	−	1.91721i	0.0632431	−	0.0632431i	0.738021	+	0.674778i	$0.235761\pi$
$920$	−2.05733	+	1.88663i	−0.0678282	+	0.0622004i
$921$	−12.1034			−0.398821
$922$	−19.6061	+	19.6061i	−0.645691	+	0.645691i
$923$	51.9984			1.71155
$924$	1.36784			0.0449987
$925$	22.9135	+	19.9993i	0.753391	+	0.657572i
$926$	25.4617			0.836724
$927$	−9.07861			−0.298181
$928$	−6.14644	+	6.14644i	−0.201767	+	0.201767i
$929$	−53.6670			−1.76076			−0.880378	−	0.474273i	$-0.842711\pi$
$929$	−53.6670			−1.76076			−0.880378	+	0.474273i	$0.842711\pi$
$930$	−6.45254	+	5.91716i	−0.211587	+	0.194031i
$931$	16.5656	−	16.5656i	0.542915	−	0.542915i
$932$	−8.37425	+	8.37425i	−0.274308	+	0.274308i
$933$	10.0122			0.327783
$934$			18.9252i			0.619250i
$935$	4.08568	−	3.74668i	0.133616	−	0.122530i
$936$			3.27075i			0.106908i
$937$	18.7194	−	18.7194i	0.611538	−	0.611538i	−0.331809	−	0.943347i	$-0.607659\pi$
$937$	18.7194	−	18.7194i	0.611538	−	0.611538i	0.943347	+	0.331809i	$0.107659\pi$
$938$	−58.5999			−1.91335
$939$	−15.4515	+	15.4515i	−0.504242	+	0.504242i
$940$	−0.788024	+	18.2069i	−0.0257025	+	0.593843i
$941$	12.7400			0.415313			0.207657	−	0.978202i	$-0.433416\pi$
$941$	12.7400			0.415313			0.207657	+	0.978202i	$0.433416\pi$
$942$			9.32544i			0.303839i
$943$			6.96372i			0.226770i
$944$	10.6205	+	10.6205i	0.345668	+	0.345668i
$945$	6.43202	−	5.89834i	0.209234	−	0.191873i
$946$		−	1.13271i		−	0.0368275i
$947$			13.4498i			0.437059i	0.975830	+	0.218529i	$0.0701260\pi$
$947$			13.4498i			0.437059i	−0.975830	+	0.218529i	$0.929874\pi$
$948$	3.49594			0.113543
$949$	3.26443	−	3.26443i	0.105968	−	0.105968i
$950$	−10.8930	+	9.15441i	−0.353417	+	0.297008i
$951$	−27.0220			−0.876248
$952$	−19.5215	−	19.5215i	−0.632695	−	0.632695i
$953$	−0.709621	+	0.709621i	−0.0229869	+	0.0229869i	−0.718507	−	0.695520i	$-0.755174\pi$
$953$	−0.709621	+	0.709621i	−0.0229869	+	0.0229869i	0.695520	+	0.718507i	$0.255174\pi$
$954$	3.45760	−	3.45760i	0.111944	−	0.111944i
$955$	−0.289468	+	6.68799i	−0.00936696	+	0.216418i
$956$	−16.9584	−	16.9584i	−0.548475	−	0.548475i
$957$	3.04644			0.0984773
$958$	3.00653	+	3.00653i	0.0971366	+	0.0971366i
$959$			69.1674i			2.23353i
$960$	−0.0966903	+	2.23398i	−0.00312067	+	0.0721013i
$961$		−	15.6704i		−	0.505496i
$962$	11.7386	−	16.0632i	0.378466	−	0.517898i
$963$	−1.33354	−	1.33354i	−0.0429729	−	0.0429729i
$964$	9.32818	−	9.32818i	0.300441	−	0.300441i
$965$	34.2582	−	31.4158i	1.10281	−	1.01131i
$966$		−	4.87216i		−	0.156759i
$967$			4.89161i			0.157304i	0.996902	+	0.0786519i	$0.0250615\pi$
$967$			4.89161i			0.157304i	−0.996902	+	0.0786519i	$0.974938\pi$
$968$	−10.8772			−0.349605
$969$			20.1302i			0.646674i
$970$	−12.0038	−	13.0899i	−0.385419	−	0.420292i
$971$	−50.8953			−1.63331			−0.816654	−	0.577128i	$-0.804173\pi$
$971$	−50.8953			−1.63331			−0.816654	+	0.577128i	$0.804173\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	10.1180	−	10.1180i	0.324369	−	0.324369i
$974$		−	42.0200i		−	1.34641i
$975$	−10.5215	−	12.5197i	−0.336957	−	0.400953i
$976$	1.30384	+	1.30384i	0.0417349	+	0.0417349i
$977$	−56.6245			−1.81158			−0.905790	−	0.423727i	$-0.860721\pi$
$977$	−56.6245			−1.81158			−0.905790	+	0.423727i	$0.860721\pi$
$978$	4.95068	+	4.95068i	0.158305	+	0.158305i
$979$	1.06404	+	1.06404i	0.0340067	+	0.0340067i
$980$	12.4414	+	13.5670i	0.397425	+	0.433383i
$981$	−2.30925	+	2.30925i	−0.0737287	+	0.0737287i
$982$	−14.2813			−0.455735
$983$	38.4422	−	38.4422i	1.22612	−	1.22612i	0.260694	−	0.965422i	$-0.416049\pi$
$983$	38.4422	−	38.4422i	1.22612	−	1.22612i	0.965422	−	0.260694i	$-0.0839512\pi$
$984$	3.94446	+	3.94446i	0.125745	+	0.125745i
$985$	1.62102	−	37.4529i	0.0516501	−	1.19335i
$986$	−43.4780	−	43.4780i	−1.38462	−	1.38462i
$987$	−22.4918	−	22.4918i	−0.715922	−	0.715922i
$988$	6.58164	+	6.58164i	0.209390	+	0.209390i
$989$	−4.03463			−0.128294
$990$	0.577588	−	0.529665i	0.0183570	−	0.0168338i
$991$	−32.4216	−	32.4216i	−1.02991	−	1.02991i	−0.999539	−	0.0303674i	$-0.990332\pi$
$991$	−32.4216	−	32.4216i	−1.02991	−	1.02991i	−0.0303674	−	0.999539i	$-0.509668\pi$
$992$	2.76854	+	2.76854i	0.0879012	+	0.0879012i
$993$		−	4.02257i		−	0.127652i
$994$	−43.8743	+	43.8743i	−1.39161	+	1.39161i
$995$	0.925240	−	21.3772i	0.0293321	−	0.677702i
$996$	−15.0040			−0.475420
$997$			6.92720i			0.219387i	0.993965	+	0.109693i	$0.0349869\pi$
$997$			6.92720i			0.219387i	−0.993965	+	0.109693i	$0.965013\pi$
$998$	−4.58214	+	4.58214i	−0.145045	+	0.145045i
$999$	6.01048	−	0.934944i	0.190163	−	0.0295803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.253.18	yes	36
5.2	odd	4		1110.2.l.a.697.1	yes	36
37.6	odd	4		1110.2.l.a.43.1	✓	36
185.117	even	4	inner	1110.2.o.a.487.18	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.1	✓	36	37.6	odd	4
1110.2.l.a.697.1	yes	36	5.2	odd	4
1110.2.o.a.253.18	yes	36	1.1	even	1	trivial
1110.2.o.a.487.18	yes	36	185.117	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.64803 + 1.51129i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.64803 + 1.51129i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.75974 - 2.75974i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(1.64803 - 1.51129i) q^{10} +0.350472i q^{11} +(0.707107 - 0.707107i) q^{12} +3.27075 q^{13} +(-2.75974 + 2.75974i) q^{14} +(-0.0966903 + 2.23398i) q^{15} +1.00000 q^{16} +7.07368i q^{17} +1.00000i q^{18} +(2.01227 + 2.01227i) q^{19} +(-1.64803 + 1.51129i) q^{20} -3.90286i q^{21} -0.350472i q^{22} -1.24836 q^{23} +(-0.707107 + 0.707107i) q^{24} +(0.432008 - 4.98130i) q^{25} -3.27075 q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.75974 - 2.75974i) q^{28} +(6.14644 - 6.14644i) q^{29} +(0.0966903 - 2.23398i) q^{30} +(-2.76854 - 2.76854i) q^{31} -1.00000 q^{32} +(0.247821 + 0.247821i) q^{33} -7.07368i q^{34} +(-0.377368 + 8.71889i) q^{35} -1.00000i q^{36} +(-3.58895 + 4.91116i) q^{37} +(-2.01227 - 2.01227i) q^{38} +(2.31277 - 2.31277i) q^{39} +(1.64803 - 1.51129i) q^{40} -5.57830i q^{41} +3.90286i q^{42} +3.23195 q^{43} +0.350472i q^{44} +(1.51129 + 1.64803i) q^{45} +1.24836 q^{46} +(5.76291 - 5.76291i) q^{47} +(0.707107 - 0.707107i) q^{48} -8.23228i q^{49} +(-0.432008 + 4.98130i) q^{50} +(5.00185 + 5.00185i) q^{51} +3.27075 q^{52} +(-3.45760 - 3.45760i) q^{53} +(0.707107 + 0.707107i) q^{54} +(-0.529665 - 0.577588i) q^{55} +(-2.75974 + 2.75974i) q^{56} +2.84578 q^{57} +(-6.14644 + 6.14644i) q^{58} +(10.6205 + 10.6205i) q^{59} +(-0.0966903 + 2.23398i) q^{60} +(1.30384 + 1.30384i) q^{61} +(2.76854 + 2.76854i) q^{62} +(-2.75974 - 2.75974i) q^{63} +1.00000 q^{64} +(-5.39030 + 4.94305i) q^{65} +(-0.247821 - 0.247821i) q^{66} +(10.6169 + 10.6169i) q^{67} +7.07368i q^{68} +(-0.882722 + 0.882722i) q^{69} +(0.377368 - 8.71889i) q^{70} +15.8980 q^{71} +1.00000i q^{72} +(0.998067 - 0.998067i) q^{73} +(3.58895 - 4.91116i) q^{74} +(-3.21684 - 3.82779i) q^{75} +(2.01227 + 2.01227i) q^{76} +(0.967210 + 0.967210i) q^{77} +(-2.31277 + 2.31277i) q^{78} +(2.47200 + 2.47200i) q^{79} +(-1.64803 + 1.51129i) q^{80} -1.00000 q^{81} +5.57830i q^{82} +(-10.6094 - 10.6094i) q^{83} -3.90286i q^{84} +(-10.6904 - 11.6576i) q^{85} -3.23195 q^{86} -8.69238i q^{87} -0.350472i q^{88} +(3.03601 - 3.03601i) q^{89} +(-1.51129 - 1.64803i) q^{90} +(9.02641 - 9.02641i) q^{91} -1.24836 q^{92} -3.91530 q^{93} +(-5.76291 + 5.76291i) q^{94} +(-6.35741 - 0.275159i) q^{95} +(-0.707107 + 0.707107i) q^{96} -7.94277i q^{97} +8.23228i q^{98} +0.350472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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