LMFDB - Embedded newform 630.2.bk.c.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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([1, 0, 1]))

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

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

chi := DirichletCharacter("630.101");

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.bk (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.c.131.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.69553 - 0.353784i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.353784 + 1.69553i) q^{6} +(-1.70202 - 2.02561i) q^{7} +1.00000i q^{8} +(2.74967 + 1.19970i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.69553 - 0.353784i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.353784 + 1.69553i) q^{6} +(-1.70202 - 2.02561i) q^{7} +1.00000i q^{8} +(2.74967 + 1.19970i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-4.48534 + 2.58961i) q^{11} +(1.69553 + 0.353784i) q^{12} +(-0.604908 + 0.349244i) q^{13} +(-2.02561 + 1.70202i) q^{14} +(-1.15415 + 1.29148i) q^{15} +1.00000 q^{16} +(1.77552 - 3.07528i) q^{17} +(1.19970 - 2.74967i) q^{18} +(-4.54260 + 2.62267i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.16921 + 4.03665i) q^{21} +(2.58961 + 4.48534i) q^{22} +(4.98463 + 2.87788i) q^{23} +(0.353784 - 1.69553i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.349244 + 0.604908i) q^{26} +(-4.23773 - 3.00693i) q^{27} +(1.70202 + 2.02561i) q^{28} +(-4.60677 - 2.65972i) q^{29} +(1.29148 + 1.15415i) q^{30} +5.55614i q^{31} -1.00000i q^{32} +(8.52121 - 2.80394i) q^{33} +(-3.07528 - 1.77552i) q^{34} +(-2.60525 + 0.461188i) q^{35} +(-2.74967 - 1.19970i) q^{36} +(5.06492 + 8.77270i) q^{37} +(2.62267 + 4.54260i) q^{38} +(1.14920 - 0.378148i) q^{39} +(0.866025 + 0.500000i) q^{40} +(3.18922 + 5.52390i) q^{41} +(4.03665 - 2.16921i) q^{42} +(-5.94790 + 10.3021i) q^{43} +(4.48534 - 2.58961i) q^{44} +(2.41381 - 1.78144i) q^{45} +(2.87788 - 4.98463i) q^{46} +8.16214 q^{47} +(-1.69553 - 0.353784i) q^{48} +(-1.20623 + 6.89529i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-4.09843 + 4.58610i) q^{51} +(0.604908 - 0.349244i) q^{52} +(-8.82550 - 5.09540i) q^{53} +(-3.00693 + 4.23773i) q^{54} +5.17923i q^{55} +(2.02561 - 1.70202i) q^{56} +(8.63000 - 2.83973i) q^{57} +(-2.65972 + 4.60677i) q^{58} -1.35947 q^{59} +(1.15415 - 1.29148i) q^{60} -6.10031i q^{61} +5.55614 q^{62} +(-2.24987 - 7.61171i) q^{63} -1.00000 q^{64} +0.698487i q^{65} +(-2.80394 - 8.52121i) q^{66} -4.42092 q^{67} +(-1.77552 + 3.07528i) q^{68} +(-7.43347 - 6.64303i) q^{69} +(0.461188 + 2.60525i) q^{70} +4.76008i q^{71} +(-1.19970 + 2.74967i) q^{72} +(-3.19635 - 1.84541i) q^{73} +(8.77270 - 5.06492i) q^{74} +(0.541382 + 1.64527i) q^{75} +(4.54260 - 2.62267i) q^{76} +(12.8797 + 4.67799i) q^{77} +(-0.378148 - 1.14920i) q^{78} -11.6278 q^{79} +(0.500000 - 0.866025i) q^{80} +(6.12142 + 6.59760i) q^{81} +(5.52390 - 3.18922i) q^{82} +(7.80303 - 13.5153i) q^{83} +(-2.16921 - 4.03665i) q^{84} +(-1.77552 - 3.07528i) q^{85} +(10.3021 + 5.94790i) q^{86} +(6.86998 + 6.13945i) q^{87} +(-2.58961 - 4.48534i) q^{88} +(-2.57504 - 4.46009i) q^{89} +(-1.78144 - 2.41381i) q^{90} +(1.73700 + 0.630889i) q^{91} +(-4.98463 - 2.87788i) q^{92} +(1.96567 - 9.42062i) q^{93} -8.16214i q^{94} +5.24535i q^{95} +(-0.353784 + 1.69553i) q^{96} +(-15.5913 - 9.00162i) q^{97} +(6.89529 + 1.20623i) q^{98} +(-15.4400 + 1.73951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.69553	−	0.353784i	−0.978917	−	0.204257i
$3$	−1.69553	−	0.353784i	−0.978917	−	0.204257i
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.353784	+	1.69553i	−0.144432	+	0.692199i
$7$	−1.70202	−	2.02561i	−0.643304	−	0.765610i
$7$	−1.70202	−	2.02561i	−0.643304	−	0.765610i
$8$			1.00000i			0.353553i
$9$	2.74967	+	1.19970i	0.916558	+	0.399902i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	−4.48534	+	2.58961i	−1.35238	+	0.780798i	−0.988583	−	0.150680i	$-0.951854\pi$
$11$	−4.48534	+	2.58961i	−1.35238	+	0.780798i	−0.363799	+	0.931478i	$0.618520\pi$
$12$	1.69553	+	0.353784i	0.489459	+	0.102129i
$13$	−0.604908	+	0.349244i	−0.167771	+	0.0968627i	−0.581534	−	0.813522i	$-0.697547\pi$
$13$	−0.604908	+	0.349244i	−0.167771	+	0.0968627i	0.413763	+	0.910385i	$0.364214\pi$
$14$	−2.02561	+	1.70202i	−0.541368	+	0.454885i
$15$	−1.15415	+	1.29148i	−0.298001	+	0.333460i
$16$	1.00000			0.250000
$17$	1.77552	−	3.07528i	0.430626	−	0.745866i	−0.566302	−	0.824198i	$-0.691626\pi$
$17$	1.77552	−	3.07528i	0.430626	−	0.745866i	0.996927	+	0.0783325i	$0.0249596\pi$
$18$	1.19970	−	2.74967i	0.282773	−	0.648104i
$19$	−4.54260	+	2.62267i	−1.04214	+	0.601682i	−0.920440	−	0.390884i	$-0.872169\pi$
$19$	−4.54260	+	2.62267i	−1.04214	+	0.601682i	−0.121705	+	0.992566i	$0.538836\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	2.16921	+	4.03665i	0.473360	+	0.880869i
$22$	2.58961	+	4.48534i	0.552107	+	0.956278i
$23$	4.98463	+	2.87788i	1.03937	+	0.600079i	0.919654	−	0.392729i	$-0.128469\pi$
$23$	4.98463	+	2.87788i	1.03937	+	0.600079i	0.119714	+	0.992808i	$0.461802\pi$
$24$	0.353784	−	1.69553i	0.0722158	−	0.346100i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.349244	+	0.604908i	0.0684923	+	0.118632i
$27$	−4.23773	−	3.00693i	−0.815552	−	0.578684i
$28$	1.70202	+	2.02561i	0.321652	+	0.382805i
$29$	−4.60677	−	2.65972i	−0.855456	−	0.493898i	0.00703191	−	0.999975i	$-0.497762\pi$
$29$	−4.60677	−	2.65972i	−0.855456	−	0.493898i	−0.862488	+	0.506077i	$0.831095\pi$
$30$	1.29148	+	1.15415i	0.235792	+	0.210719i
$31$			5.55614i			0.997912i	0.866627	+	0.498956i	$0.166283\pi$
$31$			5.55614i			0.997912i	−0.866627	+	0.498956i	$0.833717\pi$
$32$		−	1.00000i		−	0.176777i
$33$	8.52121	−	2.80394i	1.48335	−	0.488103i
$34$	−3.07528	−	1.77552i	−0.527407	−	0.304498i
$35$	−2.60525	+	0.461188i	−0.440367	+	0.0779550i
$36$	−2.74967	−	1.19970i	−0.458279	−	0.199951i
$37$	5.06492	+	8.77270i	0.832668	+	1.44222i	0.895915	+	0.444225i	$0.146521\pi$
$37$	5.06492	+	8.77270i	0.832668	+	1.44222i	−0.0632476	+	0.997998i	$0.520146\pi$
$38$	2.62267	+	4.54260i	0.425454	+	0.736907i
$39$	1.14920	−	0.378148i	0.184019	−	0.0605522i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	3.18922	+	5.52390i	0.498073	+	0.862688i	0.999998	−	0.00222350i	$-0.000707761\pi$
$41$	3.18922	+	5.52390i	0.498073	+	0.862688i	−0.501924	+	0.864912i	$0.667374\pi$
$42$	4.03665	−	2.16921i	0.622868	−	0.334716i
$43$	−5.94790	+	10.3021i	−0.907046	+	1.57105i	−0.0888985	+	0.996041i	$0.528335\pi$
$43$	−5.94790	+	10.3021i	−0.907046	+	1.57105i	−0.818147	+	0.575009i	$0.804999\pi$
$44$	4.48534	−	2.58961i	0.676191	−	0.390399i
$45$	2.41381	−	1.78144i	0.359830	−	0.265561i
$46$	2.87788	−	4.98463i	0.424320	−	0.734944i
$47$	8.16214			1.19057			0.595285	−	0.803515i	$-0.297039\pi$
$47$	8.16214			1.19057			0.595285	+	0.803515i	$0.297039\pi$
$48$	−1.69553	−	0.353784i	−0.244729	−	0.0510643i
$49$	−1.20623	+	6.89529i	−0.172319	+	0.985041i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	−4.09843	+	4.58610i	−0.573895	+	0.642182i
$52$	0.604908	−	0.349244i	0.0838856	−	0.0484314i
$53$	−8.82550	−	5.09540i	−1.21228	−	0.699908i	−0.249021	−	0.968498i	$-0.580109\pi$
$53$	−8.82550	−	5.09540i	−1.21228	−	0.699908i	−0.963254	+	0.268591i	$0.913442\pi$
$54$	−3.00693	+	4.23773i	−0.409191	+	0.576682i
$55$			5.17923i			0.698367i
$56$	2.02561	−	1.70202i	0.270684	−	0.227442i
$57$	8.63000	−	2.83973i	1.14307	−	0.376132i
$58$	−2.65972	+	4.60677i	−0.349239	+	0.604899i
$59$	−1.35947			−0.176988			−0.0884939	−	0.996077i	$-0.528205\pi$
$59$	−1.35947			−0.176988			−0.0884939	+	0.996077i	$0.528205\pi$
$60$	1.15415	−	1.29148i	0.149000	−	0.166730i
$61$		−	6.10031i		−	0.781065i	−0.920589	−	0.390532i	$-0.872291\pi$
$61$		−	6.10031i		−	0.781065i	0.920589	−	0.390532i	$-0.127709\pi$
$62$	5.55614			0.705630
$63$	−2.24987	−	7.61171i	−0.283457	−	0.958985i
$64$	−1.00000			−0.125000
$65$			0.698487i			0.0866367i
$66$	−2.80394	−	8.52121i	−0.345141	−	1.04889i
$67$	−4.42092			−0.540102			−0.270051	−	0.962846i	$-0.587041\pi$
$67$	−4.42092			−0.540102			−0.270051	+	0.962846i	$0.587041\pi$
$68$	−1.77552	+	3.07528i	−0.215313	+	0.372933i
$69$	−7.43347	−	6.64303i	−0.894885	−	0.799726i
$70$	0.461188	+	2.60525i	0.0551225	+	0.311386i
$71$			4.76008i			0.564917i	0.959279	+	0.282459i	$0.0911500\pi$
$71$			4.76008i			0.564917i	−0.959279	+	0.282459i	$0.908850\pi$
$72$	−1.19970	+	2.74967i	−0.141387	+	0.324052i
$73$	−3.19635	−	1.84541i	−0.374104	−	0.215989i	0.301146	−	0.953578i	$-0.402631\pi$
$73$	−3.19635	−	1.84541i	−0.374104	−	0.215989i	−0.675250	+	0.737589i	$0.735964\pi$
$74$	8.77270	−	5.06492i	1.01981	−	0.588785i
$75$	0.541382	+	1.64527i	0.0625134	+	0.189979i
$76$	4.54260	−	2.62267i	0.521072	−	0.300841i
$77$	12.8797	+	4.67799i	1.46778	+	0.533107i
$78$	−0.378148	−	1.14920i	−0.0428168	−	0.130121i
$79$	−11.6278			−1.30823			−0.654115	−	0.756395i	$-0.726959\pi$
$79$	−11.6278			−1.30823			−0.654115	+	0.756395i	$0.726959\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	6.12142	+	6.59760i	0.680157	+	0.733066i
$82$	5.52390	−	3.18922i	0.610013	−	0.352191i
$83$	7.80303	−	13.5153i	0.856494	−	1.48349i	−0.0187577	−	0.999824i	$-0.505971\pi$
$83$	7.80303	−	13.5153i	0.856494	−	1.48349i	0.875252	−	0.483667i	$-0.160696\pi$
$84$	−2.16921	−	4.03665i	−0.236680	−	0.440434i
$85$	−1.77552	−	3.07528i	−0.192582	−	0.333561i
$86$	10.3021	+	5.94790i	1.11090	+	0.641378i
$87$	6.86998	+	6.13945i	0.736539	+	0.658218i
$88$	−2.58961	−	4.48534i	−0.276054	−	0.478139i
$89$	−2.57504	−	4.46009i	−0.272953	−	0.472769i	0.696663	−	0.717398i	$-0.254667\pi$
$89$	−2.57504	−	4.46009i	−0.272953	−	0.472769i	−0.969617	+	0.244629i	$0.921334\pi$
$90$	−1.78144	−	2.41381i	−0.187780	−	0.254438i
$91$	1.73700	+	0.630889i	0.182087	+	0.0661351i
$92$	−4.98463	−	2.87788i	−0.519684	−	0.300040i
$93$	1.96567	−	9.42062i	0.203831	−	0.976873i
$94$		−	8.16214i		−	0.841860i
$95$			5.24535i			0.538161i
$96$	−0.353784	+	1.69553i	−0.0361079	+	0.173050i
$97$	−15.5913	−	9.00162i	−1.58305	−	0.913976i	−0.994411	−	0.105583i	$-0.966329\pi$
$97$	−15.5913	−	9.00162i	−1.58305	−	0.913976i	−0.588642	−	0.808393i	$-0.700337\pi$
$98$	6.89529	+	1.20623i	0.696529	+	0.121848i
$99$	−15.4400	+	1.73951i	−1.55178	+	0.174827i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−1.44322	−	2.49974i	−0.143606	−	0.248733i	0.785246	−	0.619184i	$-0.212537\pi$
$101$	−1.44322	−	2.49974i	−0.143606	−	0.248733i	−0.928852	+	0.370451i	$0.879203\pi$
$102$	4.58610	+	4.09843i	0.454092	+	0.405805i
$103$	−10.9075	−	6.29744i	−1.07475	−	0.620506i	−0.145273	−	0.989392i	$-0.546406\pi$
$103$	−10.9075	−	6.29744i	−1.07475	−	0.620506i	−0.929475	+	0.368886i	$0.879739\pi$
$104$	−0.349244	−	0.604908i	−0.0342462	−	0.0593161i
$105$	4.58044	+	0.139733i	0.447006	+	0.0136365i
$106$	−5.09540	+	8.82550i	−0.494909	+	0.857208i
$107$	5.42968	−	3.13483i	0.524907	−	0.303055i	−0.214033	−	0.976826i	$-0.568660\pi$
$107$	5.42968	−	3.13483i	0.524907	−	0.303055i	0.738940	+	0.673771i	$0.235327\pi$
$108$	4.23773	+	3.00693i	0.407776	+	0.289342i
$109$	−7.56565	+	13.1041i	−0.724657	+	1.25514i	0.234457	+	0.972126i	$0.424669\pi$
$109$	−7.56565	+	13.1041i	−0.724657	+	1.25514i	−0.959115	+	0.283017i	$0.908665\pi$
$110$	5.17923			0.493820
$111$	−5.48411	−	16.6663i	−0.520529	−	1.58190i
$112$	−1.70202	−	2.02561i	−0.160826	−	0.191403i
$113$	−13.4182	+	7.74702i	−1.26228	+	0.728778i	−0.973515	−	0.228622i	$-0.926578\pi$
$113$	−13.4182	+	7.74702i	−1.26228	+	0.728778i	−0.288765	+	0.957400i	$0.593245\pi$
$114$	−2.83973	−	8.63000i	−0.265965	−	0.808273i
$115$	4.98463	−	2.87788i	0.464820	−	0.268364i
$116$	4.60677	+	2.65972i	0.427728	+	0.246949i
$117$	−2.08229	+	0.234595i	−0.192508	+	0.0216884i
$118$			1.35947i			0.125149i
$119$	−9.25131	+	1.63769i	−0.848066	+	0.150127i
$120$	−1.29148	−	1.15415i	−0.117896	−	0.105359i
$121$	7.91219	−	13.7043i	0.719290	−	1.24585i
$122$	−6.10031			−0.552296
$123$	−3.45317	−	10.4943i	−0.311362	−	0.946235i
$124$		−	5.55614i		−	0.498956i
$125$	−1.00000			−0.0894427
$126$	−7.61171	+	2.24987i	−0.678105	+	0.200434i
$127$	4.77969			0.424129			0.212065	−	0.977256i	$-0.431981\pi$
$127$	4.77969			0.424129			0.212065	+	0.977256i	$0.431981\pi$
$128$			1.00000i			0.0883883i
$129$	13.7296	−	15.3632i	1.20882	−	1.35266i
$130$	0.698487			0.0612614
$131$	0.00771873	−	0.0133692i	0.000674389	−	0.00116808i	−0.865688	−	0.500584i	$-0.833119\pi$
$131$	0.00771873	−	0.0133692i	0.000674389	−	0.00116808i	0.866362	+	0.499416i	$0.166452\pi$
$132$	−8.52121	+	2.80394i	−0.741677	+	0.244051i
$133$	13.0441	+	4.73771i	1.13107	+	0.410812i
$134$			4.42092i			0.381910i
$135$	−4.72294	+	2.16652i	−0.406486	+	0.186464i
$136$	3.07528	+	1.77552i	0.263703	+	0.152249i
$137$	−7.47025	+	4.31295i	−0.638226	+	0.368480i	−0.783931	−	0.620848i	$-0.786788\pi$
$137$	−7.47025	+	4.31295i	−0.638226	+	0.368480i	0.145705	+	0.989328i	$0.453455\pi$
$138$	−6.64303	+	7.43347i	−0.565492	+	0.632779i
$139$	0.719473	−	0.415388i	0.0610249	−	0.0352327i	−0.469177	−	0.883104i	$-0.655449\pi$
$139$	0.719473	−	0.415388i	0.0610249	−	0.0352327i	0.530202	+	0.847871i	$0.322116\pi$
$140$	2.60525	−	0.461188i	0.220183	−	0.0389775i
$141$	−13.8392	−	2.88763i	−1.16547	−	0.243182i
$142$	4.76008			0.399457
$143$	1.80881	−	3.13295i	0.151260	−	0.261991i
$144$	2.74967	+	1.19970i	0.229140	+	0.0999754i
$145$	−4.60677	+	2.65972i	−0.382572	+	0.220878i
$146$	−1.84541	+	3.19635i	−0.152727	+	0.264532i
$147$	4.48465	−	11.2645i	0.369887	−	0.929077i
$148$	−5.06492	−	8.77270i	−0.416334	−	0.721111i
$149$	2.29258	+	1.32362i	0.187816	+	0.108435i	0.590960	−	0.806701i	$-0.298749\pi$
$149$	2.29258	+	1.32362i	0.187816	+	0.108435i	−0.403144	+	0.915137i	$0.632083\pi$
$150$	1.64527	−	0.541382i	0.134336	−	0.0442036i
$151$	2.15339	+	3.72979i	0.175241	+	0.303526i	0.940245	−	0.340500i	$-0.110596\pi$
$151$	2.15339	+	3.72979i	0.175241	+	0.303526i	−0.765004	+	0.644026i	$0.777263\pi$
$152$	−2.62267	−	4.54260i	−0.212727	−	0.368454i
$153$	8.57152	−	6.32593i	0.692966	−	0.511421i
$154$	4.67799	−	12.8797i	0.376963	−	1.03788i
$155$	4.81176	+	2.77807i	0.386490	+	0.223140i
$156$	−1.14920	+	0.378148i	−0.0920095	+	0.0302761i
$157$			16.7765i			1.33891i	0.742854	+	0.669454i	$0.233472\pi$
$157$			16.7765i			1.33891i	−0.742854	+	0.669454i	$0.766528\pi$
$158$			11.6278i			0.925058i
$159$	13.1613	+	11.7618i	1.04376	+	0.932767i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−2.65449	−	14.9952i	−0.209203	−	1.18178i
$162$	6.59760	−	6.12142i	0.518356	−	0.480944i
$163$	−7.87086	−	13.6327i	−0.616493	−	1.06780i	−0.990121	−	0.140218i	$-0.955220\pi$
$163$	−7.87086	−	13.6327i	−0.616493	−	1.06780i	0.373628	−	0.927579i	$-0.378114\pi$
$164$	−3.18922	−	5.52390i	−0.249037	−	0.431344i
$165$	1.83233	−	8.78156i	0.142646	−	0.683643i
$166$	−13.5153	−	7.80303i	−1.04899	−	0.605633i
$167$	−8.01543	−	13.8831i	−0.620253	−	1.07431i	−0.989438	−	0.144954i	$-0.953697\pi$
$167$	−8.01543	−	13.8831i	−0.620253	−	1.07431i	0.369185	−	0.929356i	$-0.379637\pi$
$168$	−4.03665	+	2.16921i	−0.311434	+	0.167358i
$169$	−6.25606	+	10.8358i	−0.481235	+	0.833524i
$170$	−3.07528	+	1.77552i	−0.235863	+	0.136176i
$171$	−15.6371	+	1.76171i	−1.19580	+	0.134722i
$172$	5.94790	−	10.3021i	0.453523	−	0.785525i
$173$	9.09408			0.691410			0.345705	−	0.938343i	$-0.387640\pi$
$173$	9.09408			0.691410			0.345705	+	0.938343i	$0.387640\pi$
$174$	6.13945	−	6.86998i	0.465430	−	0.520811i
$175$	−0.903222	+	2.48680i	−0.0682772	+	0.187985i
$176$	−4.48534	+	2.58961i	−0.338095	+	0.195199i
$177$	2.30503	+	0.480958i	0.173256	+	0.0361510i
$178$	−4.46009	+	2.57504i	−0.334298	+	0.193007i
$179$	−11.0133	−	6.35855i	−0.823175	−	0.475261i	0.0283349	−	0.999598i	$-0.490980\pi$
$179$	−11.0133	−	6.35855i	−0.823175	−	0.475261i	−0.851510	+	0.524338i	$0.824313\pi$
$180$	−2.41381	+	1.78144i	−0.179915	+	0.132780i
$181$			17.3337i			1.28840i	0.764856	+	0.644201i	$0.222810\pi$
$181$			17.3337i			1.28840i	−0.764856	+	0.644201i	$0.777190\pi$
$182$	0.630889	−	1.73700i	0.0467646	−	0.128755i
$183$	−2.15819	+	10.3433i	−0.159538	+	0.764598i
$184$	−2.87788	+	4.98463i	−0.212160	+	0.367472i
$185$	10.1298			0.744761
$186$	−9.42062	−	1.96567i	−0.690754	−	0.144130i
$187$			18.3916i			1.34493i
$188$	−8.16214			−0.595285
$189$	1.12184	+	13.7019i	0.0816015	+	0.996665i
$190$	5.24535			0.380537
$191$			6.45755i			0.467252i	0.972327	+	0.233626i	$0.0750591\pi$
$191$			6.45755i			0.467252i	−0.972327	+	0.233626i	$0.924941\pi$
$192$	1.69553	+	0.353784i	0.122365	+	0.0255321i
$193$	8.46355			0.609220			0.304610	−	0.952477i	$-0.401474\pi$
$193$	8.46355			0.609220			0.304610	+	0.952477i	$0.401474\pi$
$194$	−9.00162	+	15.5913i	−0.646279	+	1.11939i
$195$	0.247113	−	1.18431i	0.0176962	−	0.0848101i
$196$	1.20623	−	6.89529i	0.0861594	−	0.492521i
$197$		−	0.916820i		−	0.0653207i	−0.999467	−	0.0326603i	$-0.989602\pi$
$197$		−	0.916820i		−	0.0653207i	0.999467	−	0.0326603i	$-0.0103980\pi$
$198$	1.73951	+	15.4400i	0.123621	+	1.09727i
$199$	−5.18024	−	2.99081i	−0.367217	−	0.212013i	0.305025	−	0.952344i	$-0.401335\pi$
$199$	−5.18024	−	2.99081i	−0.367217	−	0.212013i	−0.672242	+	0.740331i	$0.734669\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	7.49583	+	1.56405i	0.528715	+	0.110320i
$202$	−2.49974	+	1.44322i	−0.175881	+	0.101545i
$203$	2.45326	+	13.8585i	0.172185	+	0.972673i
$204$	4.09843	−	4.58610i	0.286948	−	0.321091i
$205$	6.37845			0.445490
$206$	−6.29744	+	10.9075i	−0.438764	+	0.759961i
$207$	10.2535	+	13.8933i	0.712668	+	0.965653i
$208$	−0.604908	+	0.349244i	−0.0419428	+	0.0242157i
$209$	13.5834	−	23.5272i	0.939585	−	1.62741i
$210$	0.139733	−	4.58044i	0.00964248	−	0.316081i
$211$	−3.99645	−	6.92206i	−0.275127	−	0.476534i	0.695040	−	0.718971i	$-0.255387\pi$
$211$	−3.99645	−	6.92206i	−0.275127	−	0.476534i	−0.970167	+	0.242437i	$0.922053\pi$
$212$	8.82550	+	5.09540i	0.606138	+	0.349954i
$213$	1.68404	−	8.07088i	0.115388	−	0.553007i
$214$	−3.13483	−	5.42968i	−0.214293	−	0.371166i
$215$	5.94790	+	10.3021i	0.405643	+	0.702595i
$216$	3.00693	−	4.23773i	0.204596	−	0.288341i
$217$	11.2546	−	9.45668i	0.764012	−	0.641961i
$218$	13.1041	+	7.56565i	0.887521	+	0.512410i
$219$	4.76664	+	4.25977i	0.322100	+	0.287849i
$220$		−	5.17923i		−	0.349183i
$221$			2.48035i			0.166846i
$222$	−16.6663	+	5.48411i	−1.11857	+	0.368069i
$223$	1.96805	+	1.13625i	0.131790	+	0.0760892i	0.564446	−	0.825470i	$-0.309090\pi$
$223$	1.96805	+	1.13625i	0.131790	+	0.0760892i	−0.432655	+	0.901559i	$0.642423\pi$
$224$	−2.02561	+	1.70202i	−0.135342	+	0.113721i
$225$	−0.335862	−	2.98114i	−0.0223908	−	0.198743i
$226$	7.74702	+	13.4182i	0.515324	+	0.892567i
$227$	5.32896	+	9.23003i	0.353696	+	0.612619i	0.986894	−	0.161371i	$-0.0515915\pi$
$227$	5.32896	+	9.23003i	0.353696	+	0.612619i	−0.633198	+	0.773990i	$0.718258\pi$
$228$	−8.63000	+	2.83973i	−0.571536	+	0.188066i
$229$	3.89544	+	2.24904i	0.257418	+	0.148620i	0.623156	−	0.782097i	$-0.285850\pi$
$229$	3.89544	+	2.24904i	0.257418	+	0.148620i	−0.365738	+	0.930718i	$0.619183\pi$
$230$	−2.87788	−	4.98463i	−0.189762	−	0.328677i
$231$	−20.1830	−	12.4883i	−1.32794	−	0.821672i
$232$	2.65972	−	4.60677i	0.174619	−	0.302449i
$233$	2.27726	−	1.31478i	0.149188	−	0.0861339i	−0.423548	−	0.905874i	$-0.639215\pi$
$233$	2.27726	−	1.31478i	0.149188	−	0.0861339i	0.572736	+	0.819740i	$0.305882\pi$
$234$	0.234595	+	2.08229i	0.0153360	+	0.136123i
$235$	4.08107	−	7.06862i	0.266220	−	0.461106i
$236$	1.35947			0.0884939
$237$	19.7153	+	4.11373i	1.28065	+	0.267215i
$238$	1.63769	+	9.25131i	0.106156	+	0.599673i
$239$	16.1358	−	9.31600i	1.04374	−	0.602602i	0.122848	−	0.992426i	$-0.460797\pi$
$239$	16.1358	−	9.31600i	1.04374	−	0.602602i	0.920890	+	0.389824i	$0.127464\pi$
$240$	−1.15415	+	1.29148i	−0.0745002	+	0.0833649i
$241$	18.2125	−	10.5150i	1.17317	−	0.677331i	0.218747	−	0.975782i	$-0.429803\pi$
$241$	18.2125	−	10.5150i	1.17317	−	0.677331i	0.954425	+	0.298451i	$0.0964699\pi$
$242$	−13.7043	−	7.91219i	−0.880947	−	0.508615i
$243$	−8.04495	−	13.3521i	−0.516084	−	0.856538i
$244$			6.10031i			0.390532i
$245$	5.36838	+	4.49227i	0.342973	+	0.287001i
$246$	−10.4943	+	3.45317i	−0.669089	+	0.220166i
$247$	1.83190	−	3.17295i	0.116561	−	0.201890i
$248$	−5.55614			−0.352815
$249$	−18.0118	+	20.1550i	−1.14145	+	1.27727i
$250$			1.00000i			0.0632456i
$251$	−22.9370			−1.44777			−0.723885	−	0.689920i	$-0.757646\pi$
$251$	−22.9370			−1.44777			−0.723885	+	0.689920i	$0.757646\pi$
$252$	2.24987	+	7.61171i	0.141729	+	0.479492i
$253$	−29.8104			−1.87416
$254$		−	4.77969i		−	0.299905i
$255$	1.92246	+	5.84240i	0.120389	+	0.365865i
$256$	1.00000			0.0625000
$257$	3.39912	−	5.88745i	0.212031	−	0.367249i	−0.740319	−	0.672256i	$-0.765325\pi$
$257$	3.39912	−	5.88745i	0.212031	−	0.367249i	0.952350	+	0.305007i	$0.0986588\pi$
$258$	−15.3632	−	13.7296i	−0.956473	−	0.854765i
$259$	9.14950	−	25.1909i	0.568522	−	1.56529i
$260$		−	0.698487i		−	0.0433183i
$261$	−9.47624	−	12.8401i	−0.586565	−	0.794784i
$262$	−0.0133692	−	0.00771873i	−0.000825954	−	0.000476865i
$263$	2.27245	−	1.31200i	0.140125	−	0.0809013i	−0.428299	−	0.903637i	$-0.640887\pi$
$263$	2.27245	−	1.31200i	0.140125	−	0.0809013i	0.568424	+	0.822736i	$0.307553\pi$
$264$	2.80394	+	8.52121i	0.172570	+	0.524444i
$265$	−8.82550	+	5.09540i	−0.542146	+	0.313008i
$266$	4.73771	−	13.0441i	0.290488	−	0.799788i
$267$	2.78815	+	8.47325i	0.170632	+	0.518554i
$268$	4.42092			0.270051
$269$	−7.92386	+	13.7245i	−0.483126	+	0.836799i	−0.999812	−	0.0193757i	$-0.993832\pi$
$269$	−7.92386	+	13.7245i	−0.483126	+	0.836799i	0.516686	+	0.856175i	$0.327165\pi$
$270$	2.16652	+	4.72294i	0.131850	+	0.287429i
$271$	5.00298	−	2.88847i	0.303910	−	0.175462i	−0.340288	−	0.940321i	$-0.610525\pi$
$271$	5.00298	−	2.88847i	0.303910	−	0.175462i	0.644198	+	0.764859i	$0.277191\pi$
$272$	1.77552	−	3.07528i	0.107656	−	0.186466i
$273$	−2.72195	−	1.68422i	−0.164740	−	0.101933i
$274$	4.31295	+	7.47025i	0.260555	+	0.451294i
$275$	4.48534	+	2.58961i	0.270476	+	0.156160i
$276$	7.43347	+	6.64303i	0.447442	+	0.399863i
$277$	0.335390	+	0.580912i	0.0201516	+	0.0349036i	0.875925	−	0.482447i	$-0.160252\pi$
$277$	0.335390	+	0.580912i	0.0201516	+	0.0349036i	−0.855774	+	0.517350i	$0.826918\pi$
$278$	−0.415388	−	0.719473i	−0.0249133	−	0.0431511i
$279$	−6.66573	+	15.2776i	−0.399067	+	0.914644i
$280$	−0.461188	−	2.60525i	−0.0275613	−	0.155693i
$281$	21.5027	+	12.4146i	1.28274	+	0.740591i	0.977349	−	0.211635i	$-0.0678789\pi$
$281$	21.5027	+	12.4146i	1.28274	+	0.740591i	0.305393	+	0.952226i	$0.401212\pi$
$282$	−2.88763	+	13.8392i	−0.171956	+	0.824111i
$283$		−	17.1374i		−	1.01871i	−0.860556	−	0.509355i	$-0.829884\pi$
$283$		−	17.1374i		−	1.01871i	0.860556	−	0.509355i	$-0.170116\pi$
$284$		−	4.76008i		−	0.282459i
$285$	1.85572	−	8.89366i	0.109923	−	0.526815i
$286$	−3.13295	−	1.80881i	−0.185255	−	0.106957i
$287$	5.76116	−	15.8619i	0.340070	−	0.936301i
$288$	1.19970	−	2.74967i	0.0706933	−	0.162026i
$289$	2.19509	+	3.80201i	0.129123	+	0.223647i
$290$	2.65972	+	4.60677i	0.156184	+	0.270519i
$291$	23.2509	+	20.7785i	1.36299	+	1.21806i
$292$	3.19635	+	1.84541i	0.187052	+	0.107995i
$293$	−8.02683	−	13.9029i	−0.468932	−	0.812215i	0.530437	−	0.847724i	$-0.322028\pi$
$293$	−8.02683	−	13.9029i	−0.468932	−	0.812215i	−0.999369	+	0.0355096i	$0.988695\pi$
$294$	−11.2645	−	4.48465i	−0.656956	−	0.261550i
$295$	−0.679735	+	1.17733i	−0.0395757	+	0.0685471i
$296$	−8.77270	+	5.06492i	−0.509903	+	0.294392i
$297$	26.7945	+	2.51303i	1.55477	+	0.145821i
$298$	1.32362	−	2.29258i	0.0766754	−	0.132806i
$299$	−4.02032			−0.232501
$300$	−0.541382	−	1.64527i	−0.0312567	−	0.0949896i
$301$	30.9915	−	5.48620i	1.78632	−	0.316219i
$302$	3.72979	−	2.15339i	0.214625	−	0.123914i
$303$	1.56267	+	4.74898i	0.0897730	+	0.272822i
$304$	−4.54260	+	2.62267i	−0.260536	+	0.150421i
$305$	−5.28303	−	3.05016i	−0.302505	−	0.174651i
$306$	−6.32593	−	8.57152i	−0.361629	−	0.490001i
$307$			14.9148i			0.851231i	0.904904	+	0.425615i	$0.139942\pi$
$307$			14.9148i			0.851231i	−0.904904	+	0.425615i	$0.860058\pi$
$308$	−12.8797	−	4.67799i	−0.733890	−	0.266553i
$309$	16.2661	+	14.5364i	0.925346	+	0.826949i
$310$	2.77807	−	4.81176i	0.157784	−	0.273289i
$311$	−11.6004			−0.657797			−0.328899	−	0.944365i	$-0.606677\pi$
$311$	−11.6004			−0.657797			−0.328899	+	0.944365i	$0.606677\pi$
$312$	0.378148	+	1.14920i	0.0214084	+	0.0650606i
$313$		−	6.62273i		−	0.374339i	−0.982328	−	0.187169i	$-0.940069\pi$
$313$		−	6.62273i		−	0.374339i	0.982328	−	0.187169i	$-0.0599313\pi$
$314$	16.7765			0.946751
$315$	−7.71687	−	1.85741i	−0.434796	−	0.104653i
$316$	11.6278			0.654115
$317$		−	34.3500i		−	1.92929i	−0.263554	−	0.964645i	$-0.584895\pi$
$317$		−	34.3500i		−	1.92929i	0.263554	−	0.964645i	$-0.415105\pi$
$318$	11.7618	−	13.1613i	0.659566	−	0.738047i
$319$	27.5506			1.54254
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−10.3153	+	3.39428i	−0.575742	+	0.189450i
$322$	−14.9952	+	2.65449i	−0.835648	+	0.147929i
$323$			18.6264i			1.03640i
$324$	−6.12142	−	6.59760i	−0.340079	−	0.366533i
$325$	0.604908	+	0.349244i	0.0335542	+	0.0193725i
$326$	−13.6327	+	7.87086i	−0.755047	+	0.435926i
$327$	17.4638	−	19.5418i	0.965752	−	1.08067i
$328$	−5.52390	+	3.18922i	−0.305006	+	0.176095i
$329$	−13.8921	−	16.5333i	−0.765899	−	0.911513i
$330$	−8.78156	−	1.83233i	−0.483409	−	0.100866i
$331$	14.9409			0.821225			0.410612	−	0.911810i	$-0.365315\pi$
$331$	14.9409			0.821225			0.410612	+	0.911810i	$0.365315\pi$
$332$	−7.80303	+	13.5153i	−0.428247	+	0.741746i
$333$	3.40223	+	30.1985i	0.186441	+	1.65487i
$334$	−13.8831	+	8.01543i	−0.759652	+	0.438585i
$335$	−2.21046	+	3.82863i	−0.120770	+	0.209181i
$336$	2.16921	+	4.03665i	0.118340	+	0.220217i
$337$	−4.19551	−	7.26684i	−0.228544	−	0.395850i	0.728833	−	0.684692i	$-0.240063\pi$
$337$	−4.19551	−	7.26684i	−0.228544	−	0.395850i	−0.957377	+	0.288842i	$0.906730\pi$
$338$	10.8358	+	6.25606i	0.589390	+	0.340285i
$339$	25.4918	−	8.38818i	1.38453	−	0.455584i
$340$	1.77552	+	3.07528i	0.0962908	+	0.166781i
$341$	−14.3883	−	24.9212i	−0.779167	−	1.34956i
$342$	1.76171	+	15.6371i	0.0952626	+	0.845558i
$343$	16.0202	−	9.29259i	0.865011	−	0.501752i
$344$	−10.3021	−	5.94790i	−0.555450	−	0.320689i
$345$	−9.46977	+	3.11606i	−0.509835	+	0.167763i
$346$		−	9.09408i		−	0.488901i
$347$			32.3178i			1.73491i	0.497514	+	0.867456i	$0.334246\pi$
$347$			32.3178i			1.73491i	−0.497514	+	0.867456i	$0.665754\pi$
$348$	−6.86998	−	6.13945i	−0.368269	−	0.329109i
$349$	10.2354	+	5.90940i	0.547888	+	0.316323i	0.748270	−	0.663395i	$-0.230885\pi$
$349$	10.2354	+	5.90940i	0.547888	+	0.316323i	−0.200382	+	0.979718i	$0.564218\pi$
$350$	2.48680	+	0.903222i	0.132925	+	0.0482793i
$351$	3.61359	+	0.338915i	0.192879	+	0.0180899i
$352$	2.58961	+	4.48534i	0.138027	+	0.239070i
$353$	8.42649	+	14.5951i	0.448497	+	0.776819i	0.998288	−	0.0584825i	$-0.0186262\pi$
$353$	8.42649	+	14.5951i	0.448497	+	0.776819i	−0.549792	+	0.835302i	$0.685293\pi$
$354$	0.480958	−	2.30503i	0.0255626	−	0.122511i
$355$	4.12235	+	2.38004i	0.218792	+	0.126319i
$356$	2.57504	+	4.46009i	0.136477	+	0.236384i
$357$	16.2653	+	0.496196i	0.860851	+	0.0262615i
$358$	−6.35855	+	11.0133i	−0.336060	+	0.582073i
$359$	−15.3221	+	8.84623i	−0.808670	+	0.466886i	−0.846494	−	0.532399i	$-0.821291\pi$
$359$	−15.3221	+	8.84623i	−0.808670	+	0.466886i	0.0378237	+	0.999284i	$0.487957\pi$
$360$	1.78144	+	2.41381i	0.0938899	+	0.127219i
$361$	4.25683	−	7.37304i	0.224044	−	0.388055i
$362$	17.3337			0.911037
$363$	−18.2638	+	20.4369i	−0.958599	+	1.07266i
$364$	−1.73700	−	0.630889i	−0.0910435	−	0.0330676i
$365$	−3.19635	+	1.84541i	−0.167304	+	0.0965933i
$366$	10.3433	+	2.15819i	0.540652	+	0.112810i
$367$	−27.4610	+	15.8546i	−1.43345	+	0.827605i	−0.997382	−	0.0723069i	$-0.976964\pi$
$367$	−27.4610	+	15.8546i	−1.43345	+	0.827605i	−0.436072	+	0.899912i	$0.643631\pi$
$368$	4.98463	+	2.87788i	0.259842	+	0.150020i
$369$	2.14228	+	19.0150i	0.111523	+	0.989884i
$370$		−	10.1298i		−	0.526625i
$371$	4.69988	+	26.5496i	0.244006	+	1.37838i
$372$	−1.96567	+	9.42062i	−0.101915	+	0.488437i
$373$	−9.41361	+	16.3049i	−0.487419	+	0.844234i	−0.999895	−	0.0144674i	$-0.995395\pi$
$373$	−9.41361	+	16.3049i	−0.487419	+	0.844234i	0.512477	+	0.858701i	$0.328728\pi$
$374$	18.3916			0.951007
$375$	1.69553	+	0.353784i	0.0875570	+	0.0182693i
$376$			8.16214i			0.420930i
$377$	3.71556			0.191361
$378$	13.7019	−	1.12184i	0.704749	−	0.0577010i
$379$	−7.77895			−0.399578			−0.199789	−	0.979839i	$-0.564026\pi$
$379$	−7.77895			−0.399578			−0.199789	+	0.979839i	$0.564026\pi$
$380$		−	5.24535i		−	0.269081i
$381$	−8.10413	−	1.69098i	−0.415187	−	0.0866314i
$382$	6.45755			0.330397
$383$	−1.06464	+	1.84402i	−0.0544007	+	0.0942248i	−0.891943	−	0.452147i	$-0.850658\pi$
$383$	−1.06464	+	1.84402i	−0.0544007	+	0.0942248i	0.837543	+	0.546372i	$0.183992\pi$
$384$	0.353784	−	1.69553i	0.0180539	−	0.0865249i
$385$	10.4911	−	8.81517i	0.534677	−	0.449262i
$386$		−	8.46355i		−	0.430783i
$387$	−28.7142	+	21.1916i	−1.45963	+	1.07723i
$388$	15.5913	+	9.00162i	0.791527	+	0.456988i
$389$	−14.4219	+	8.32649i	−0.731220	+	0.422170i	−0.818868	−	0.573982i	$-0.805398\pi$
$389$	−14.4219	+	8.32649i	−0.731220	+	0.422170i	0.0876485	+	0.996151i	$0.472065\pi$
$390$	−1.18431	−	0.247113i	−0.0599698	−	0.0125131i
$391$	17.7006	−	10.2194i	0.895157	−	0.516819i
$392$	−6.89529	−	1.20623i	−0.348265	−	0.0609239i
$393$	−0.0178172	+	0.0199372i	−0.000898759	+	0.00100570i
$394$	−0.916820			−0.0461887
$395$	−5.81390	+	10.0700i	−0.292529	+	0.506675i
$396$	15.4400	−	1.73951i	0.775889	−	0.0874135i
$397$	−22.3718	+	12.9163i	−1.12281	+	0.648253i	−0.942116	−	0.335287i	$-0.891167\pi$
$397$	−22.3718	+	12.9163i	−1.12281	+	0.648253i	−0.180691	+	0.983540i	$0.557833\pi$
$398$	−2.99081	+	5.18024i	−0.149916	+	0.259662i
$399$	−20.4407	−	12.6478i	−1.02331	−	0.633180i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	6.98357	+	4.03197i	0.348743	+	0.201347i	0.664131	−	0.747616i	$-0.268802\pi$
$401$	6.98357	+	4.03197i	0.348743	+	0.201347i	−0.315389	+	0.948963i	$0.602135\pi$
$402$	1.56405	−	7.49583i	0.0780078	−	0.373858i
$403$	−1.94045	−	3.36095i	−0.0966605	−	0.167421i
$404$	1.44322	+	2.49974i	0.0718031	+	0.124367i
$405$	8.77439	−	2.00250i	0.436003	−	0.0995053i
$406$	13.8585	−	2.45326i	0.687784	−	0.121753i
$407$	−45.4358	−	26.2324i	−2.25217	−	1.30029i
$408$	−4.58610	−	4.09843i	−0.227046	−	0.202903i
$409$			22.4604i			1.11060i	0.831651	+	0.555298i	$0.187396\pi$
$409$			22.4604i			1.11060i	−0.831651	+	0.555298i	$0.812604\pi$
$410$		−	6.37845i		−	0.315009i
$411$	14.1919	−	4.66990i	0.700036	−	0.230349i
$412$	10.9075	+	6.29744i	0.537374	+	0.310253i
$413$	2.31385	+	2.75376i	0.113857	+	0.135504i
$414$	13.8933	−	10.2535i	0.682820	−	0.503933i
$415$	−7.80303	−	13.5153i	−0.383036	−	0.663438i
$416$	0.349244	+	0.604908i	0.0171231	+	0.0296580i
$417$	−1.36685	+	0.449766i	−0.0669348	+	0.0220252i
$418$	−23.5272	−	13.5834i	−1.15075	−	0.664387i
$419$	12.4020	+	21.4808i	0.605875	+	1.04941i	0.991913	+	0.126923i	$0.0405102\pi$
$419$	12.4020	+	21.4808i	0.605875	+	1.04941i	−0.386038	+	0.922483i	$0.626157\pi$
$420$	−4.58044	−	0.139733i	−0.223503	−	0.00681826i
$421$	15.4310	−	26.7272i	0.752059	−	1.30260i	−0.194765	−	0.980850i	$-0.562394\pi$
$421$	15.4310	−	26.7272i	0.752059	−	1.30260i	0.946823	−	0.321754i	$-0.104272\pi$
$422$	−6.92206	+	3.99645i	−0.336960	+	0.194544i
$423$	22.4432	+	9.79215i	1.09123	+	0.476111i
$424$	5.09540	−	8.82550i	0.247455	−	0.428604i
$425$	−3.55103			−0.172250
$426$	−8.07088	−	1.68404i	−0.391035	−	0.0815919i
$427$	−12.3569	+	10.3829i	−0.597991	+	0.502463i
$428$	−5.42968	+	3.13483i	−0.262454	+	0.151528i
$429$	−4.17529	+	4.67210i	−0.201585	+	0.225571i
$430$	10.3021	−	5.94790i	0.496809	−	0.286833i
$431$	−10.4525	−	6.03478i	−0.503482	−	0.290685i	0.226669	−	0.973972i	$-0.427217\pi$
$431$	−10.4525	−	6.03478i	−0.503482	−	0.290685i	−0.730150	+	0.683287i	$0.760550\pi$
$432$	−4.23773	−	3.00693i	−0.203888	−	0.144671i
$433$			2.36480i			0.113645i	0.998384	+	0.0568226i	$0.0180969\pi$
$433$			2.36480i			0.113645i	−0.998384	+	0.0568226i	$0.981903\pi$
$434$	−9.45668	−	11.2546i	−0.453935	−	0.540238i
$435$	8.75191	−	2.87985i	0.419622	−	0.138078i
$436$	7.56565	−	13.1041i	0.362329	−	0.627572i
$437$	−30.1910			−1.44423
$438$	4.25977	−	4.76664i	0.203540	−	0.227759i
$439$			3.37576i			0.161116i	0.996750	+	0.0805582i	$0.0256703\pi$
$439$			3.37576i			0.161116i	−0.996750	+	0.0805582i	$0.974330\pi$
$440$	−5.17923			−0.246910
$441$	−11.5891	+	17.5127i	−0.551860	+	0.833937i
$442$	2.48035			0.117978
$443$		−	25.8297i		−	1.22721i	−0.789615	−	0.613603i	$-0.789720\pi$
$443$		−	25.8297i		−	1.22721i	0.789615	−	0.613603i	$-0.210280\pi$
$444$	5.48411	+	16.6663i	0.260264	+	0.790948i
$445$	−5.15007			−0.244137
$446$	1.13625	−	1.96805i	0.0538032	−	0.0931899i
$447$	−3.41887	−	3.05532i	−0.161707	−	0.144512i
$448$	1.70202	+	2.02561i	0.0804131	+	0.0957013i
$449$			22.6610i			1.06944i	0.845030	+	0.534718i	$0.179582\pi$
$449$			22.6610i			1.06944i	−0.845030	+	0.534718i	$0.820418\pi$
$450$	−2.98114	+	0.335862i	−0.140532	+	0.0158327i
$451$	−28.6095	−	16.5177i	−1.34717	−	0.777789i
$452$	13.4182	−	7.74702i	0.631140	−	0.364389i
$453$	−2.33162	−	7.08582i	−0.109549	−	0.332921i
$454$	9.23003	−	5.32896i	0.433187	−	0.250101i
$455$	1.41487	−	1.18884i	0.0663299	−	0.0557338i
$456$	2.83973	+	8.63000i	0.132983	+	0.404137i
$457$	−0.350134			−0.0163786			−0.00818930	−	0.999966i	$-0.502607\pi$
$457$	−0.350134			−0.0163786			−0.00818930	+	0.999966i	$0.502607\pi$
$458$	2.24904	−	3.89544i	0.105091	−	0.182022i
$459$	−16.7713	+	7.69337i	−0.782818	+	0.359096i
$460$	−4.98463	+	2.87788i	−0.232410	+	0.134182i
$461$	14.6285	−	25.3374i	0.681319	−	1.18008i	−0.293260	−	0.956033i	$-0.594740\pi$
$461$	14.6285	−	25.3374i	0.681319	−	1.18008i	0.974579	−	0.224046i	$-0.0719265\pi$
$462$	−12.4883	+	20.1830i	−0.581010	+	0.938998i
$463$	11.8187	+	20.4706i	0.549262	+	0.951350i	0.998325	+	0.0578496i	$0.0184244\pi$
$463$	11.8187	+	20.4706i	0.549262	+	0.951350i	−0.449063	+	0.893500i	$0.648242\pi$
$464$	−4.60677	−	2.65972i	−0.213864	−	0.123474i
$465$	−7.17566	−	6.41263i	−0.332763	−	0.297379i
$466$	−1.31478	−	2.27726i	−0.0609059	−	0.105492i
$467$	1.38200	+	2.39369i	0.0639513	+	0.110767i	0.896228	−	0.443593i	$-0.146296\pi$
$467$	1.38200	+	2.39369i	0.0639513	+	0.110767i	−0.832277	+	0.554360i	$0.812963\pi$
$468$	2.08229	−	0.234595i	0.0962538	−	0.0108442i
$469$	7.52452	+	8.95509i	0.347450	+	0.413508i
$470$	−7.06862	−	4.08107i	−0.326051	−	0.188246i
$471$	5.93524	−	28.4451i	0.273481	−	1.31068i
$472$		−	1.35947i		−	0.0625746i
$473$		−	61.6110i		−	2.83288i
$474$	4.11373	−	19.7153i	0.188950	−	0.905556i
$475$	4.54260	+	2.62267i	0.208429	+	0.120336i
$476$	9.25131	−	1.63769i	0.424033	−	0.0750636i
$477$	−18.1543	−	24.5987i	−0.831227	−	1.12630i
$478$	−9.31600	−	16.1358i	−0.426104	−	0.738034i
$479$	−5.34975	−	9.26604i	−0.244436	−	0.423376i	0.717537	−	0.696521i	$-0.245270\pi$
$479$	−5.34975	−	9.26604i	−0.244436	−	0.423376i	−0.961973	+	0.273145i	$0.911936\pi$
$480$	1.29148	+	1.15415i	0.0589479	+	0.0526796i
$481$	−6.12762	−	3.53778i	−0.279395	−	0.161309i
$482$	−10.5150	−	18.2125i	−0.478945	−	0.829558i
$483$	−0.804269	+	26.3639i	−0.0365955	+	1.19960i
$484$	−7.91219	+	13.7043i	−0.359645	+	0.622924i
$485$	−15.5913	+	9.00162i	−0.707963	+	0.408743i
$486$	−13.3521	+	8.04495i	−0.605664	+	0.364926i
$487$	5.88059	−	10.1855i	0.266475	−	0.461548i	−0.701474	−	0.712695i	$-0.747474\pi$
$487$	5.88059	−	10.1855i	0.266475	−	0.461548i	0.967949	+	0.251147i	$0.0808077\pi$
$488$	6.10031			0.276148
$489$	8.52227	+	25.8993i	0.385391	+	1.17121i
$490$	4.49227	−	5.36838i	0.202940	−	0.242519i
$491$	16.7933	−	9.69561i	0.757871	−	0.437557i	−0.0706601	−	0.997500i	$-0.522511\pi$
$491$	16.7933	−	9.69561i	0.757871	−	0.437557i	0.828531	+	0.559944i	$0.189177\pi$
$492$	3.45317	+	10.4943i	0.155681	+	0.473118i
$493$	−16.3588	+	9.44475i	−0.736763	+	0.425370i
$494$	−3.17295	−	1.83190i	−0.142758	−	0.0824212i
$495$	−6.21354	+	14.2412i	−0.279278	+	0.640094i
$496$			5.55614i			0.249478i
$497$	9.64209	−	8.10177i	0.432507	−	0.363414i
$498$	20.1550	+	18.0118i	0.903167	+	0.807127i
$499$	9.58126	−	16.5952i	0.428916	−	0.742904i	−0.567861	−	0.823124i	$-0.692229\pi$
$499$	9.58126	−	16.5952i	0.428916	−	0.742904i	0.996777	+	0.0802199i	$0.0255623\pi$
$500$	1.00000			0.0447214
$501$	8.67882	+	26.3751i	0.387741	+	1.17835i
$502$			22.9370i			1.02373i
$503$	13.5062			0.602214			0.301107	−	0.953590i	$-0.402644\pi$
$503$	13.5062			0.602214			0.301107	+	0.953590i	$0.402644\pi$
$504$	7.61171	−	2.24987i	0.339052	−	0.100217i
$505$	−2.88645			−0.128445
$506$			29.8104i			1.32523i
$507$	14.4409	−	16.1592i	0.641343	−	0.717655i
$508$	−4.77969			−0.212065
$509$	−3.92219	+	6.79342i	−0.173848	+	0.301113i	−0.939762	−	0.341830i	$-0.888953\pi$
$509$	−3.92219	+	6.79342i	−0.173848	+	0.301113i	0.765914	+	0.642943i	$0.222287\pi$
$510$	5.84240	−	1.92246i	0.258706	−	0.0851281i
$511$	1.70216	+	9.61550i	0.0752993	+	0.425365i
$512$		−	1.00000i		−	0.0441942i
$513$	27.1365	+	2.54511i	1.19811	+	0.112369i
$514$	−5.88745	−	3.39912i	−0.259684	−	0.149929i
$515$	−10.9075	+	6.29744i	−0.480642	+	0.277499i
$516$	−13.7296	+	15.3632i	−0.604410	+	0.676328i
$517$	−36.6100	+	21.1368i	−1.61010	+	0.929594i
$518$	−25.1909	−	9.14950i	−1.10683	−	0.402006i
$519$	−15.4193	−	3.21734i	−0.676833	−	0.141225i
$520$	−0.698487			−0.0306307
$521$	−12.9289	+	22.3935i	−0.566425	+	0.981077i	0.430490	+	0.902595i	$0.358341\pi$
$521$	−12.9289	+	22.3935i	−0.566425	+	0.981077i	−0.996916	+	0.0784821i	$0.974993\pi$
$522$	−12.8401	+	9.47624i	−0.561997	+	0.414764i
$523$	13.8469	−	7.99452i	0.605483	−	0.349576i	−0.165712	−	0.986174i	$-0.552992\pi$
$523$	13.8469	−	7.99452i	0.605483	−	0.349576i	0.771196	+	0.636598i	$0.219659\pi$
$524$	−0.00771873	+	0.0133692i	−0.000337194	+	0.000584038i
$525$	2.41123	−	3.89692i	0.105235	−	0.170075i
$526$	−1.31200	−	2.27245i	−0.0572058	−	0.0990834i
$527$	17.0867	+	9.86501i	0.744308	+	0.429727i
$528$	8.52121	−	2.80394i	0.370838	−	0.122026i
$529$	5.06439	+	8.77178i	0.220191	+	0.381382i
$530$	5.09540	+	8.82550i	0.221330	+	0.383355i
$531$	−3.73810	−	1.63096i	−0.162220	−	0.0707777i
$532$	−13.0441	−	4.73771i	−0.565535	−	0.205406i
$533$	−3.85837	−	2.22763i	−0.167125	−	0.0964895i
$534$	8.47325	−	2.78815i	0.366673	−	0.120655i
$535$		−	6.26966i		−	0.271061i
$536$		−	4.42092i		−	0.190955i
$537$	16.4239	+	14.6775i	0.708745	+	0.633380i
$538$	13.7245	+	7.92386i	0.591706	+	0.341622i
$539$	−12.4458	−	34.0514i	−0.536077	−	1.46670i
$540$	4.72294	−	2.16652i	0.203243	−	0.0932321i
$541$	5.01683	+	8.68940i	0.215690	+	0.373587i	0.953486	−	0.301438i	$-0.0974665\pi$
$541$	5.01683	+	8.68940i	0.215690	+	0.373587i	−0.737796	+	0.675024i	$0.764133\pi$
$542$	−2.88847	−	5.00298i	−0.124071	−	0.214897i
$543$	6.13237	−	29.3898i	0.263165	−	1.26124i
$544$	−3.07528	−	1.77552i	−0.131852	−	0.0761246i
$545$	7.56565	+	13.1041i	0.324077	+	0.561317i
$546$	−1.68422	+	2.72195i	−0.0720778	+	0.116489i
$547$	7.02968	−	12.1758i	0.300567	−	0.520598i	−0.675697	−	0.737179i	$-0.736157\pi$
$547$	7.02968	−	12.1758i	0.300567	−	0.520598i	0.976265	+	0.216581i	$0.0694906\pi$
$548$	7.47025	−	4.31295i	0.319113	−	0.184240i
$549$	7.31857	−	16.7739i	0.312349	−	0.715891i
$550$	2.58961	−	4.48534i	0.110421	−	0.191256i
$551$	27.9023			1.18868
$552$	6.64303	−	7.43347i	0.282746	−	0.316390i
$553$	19.7908	+	23.5535i	0.841590	+	1.00159i
$554$	0.580912	−	0.335390i	0.0246806	−	0.0142493i
$555$	−17.1755	−	3.58377i	−0.729059	−	0.152123i
$556$	−0.719473	+	0.415388i	−0.0305124	+	0.0176164i
$557$	12.1964	+	7.04161i	0.516779	+	0.298363i	0.735616	−	0.677399i	$-0.236893\pi$
$557$	12.1964	+	7.04161i	0.516779	+	0.298363i	−0.218837	+	0.975761i	$0.570226\pi$
$558$	15.2776	+	6.66573i	0.646751	+	0.282183i
$559$		−	8.30906i		−	0.351436i
$560$	−2.60525	+	0.461188i	−0.110092	+	0.0194888i
$561$	6.50665	−	31.1836i	0.274711	−	1.31657i
$562$	12.4146	−	21.5027i	0.523677	−	0.907035i
$563$	−21.8637			−0.921444			−0.460722	−	0.887544i	$-0.652410\pi$
$563$	−21.8637			−0.921444			−0.460722	+	0.887544i	$0.652410\pi$
$564$	13.8392	+	2.88763i	0.582735	+	0.121591i
$565$			15.4940i			0.651839i
$566$	−17.1374			−0.720337
$567$	2.94539	−	23.6289i	0.123695	−	0.992320i
$568$	−4.76008			−0.199728
$569$		−	8.97947i		−	0.376439i	−0.982127	−	0.188219i	$-0.939728\pi$
$569$		−	8.97947i		−	0.376439i	0.982127	−	0.188219i	$-0.0602716\pi$
$570$	−8.89366	−	1.85572i	−0.372515	−	0.0777275i
$571$	23.2561			0.973239			0.486619	−	0.873614i	$-0.338230\pi$
$571$	23.2561			0.973239			0.486619	+	0.873614i	$0.338230\pi$
$572$	−1.80881	+	3.13295i	−0.0756302	+	0.130995i
$573$	2.28457	−	10.9490i	0.0954395	−	0.457401i
$574$	−15.8619	−	5.76116i	−0.662065	−	0.240466i
$575$		−	5.75576i		−	0.240032i
$576$	−2.74967	−	1.19970i	−0.114570	−	0.0499877i
$577$	−29.4687	−	17.0138i	−1.22680	−	0.708292i	−0.260439	−	0.965490i	$-0.583867\pi$
$577$	−29.4687	−	17.0138i	−1.22680	−	0.708292i	−0.966359	+	0.257198i	$0.917201\pi$
$578$	3.80201	−	2.19509i	0.158143	−	0.0913037i
$579$	−14.3502	−	2.99427i	−0.596376	−	0.124437i
$580$	4.60677	−	2.65972i	0.191286	−	0.110439i
$581$	−40.6576	+	7.19734i	−1.68676	+	0.298596i
$582$	20.7785	−	23.2509i	0.861296	−	0.963781i
$583$	52.7805			2.18595
$584$	1.84541	−	3.19635i	0.0763637	−	0.132266i
$585$	−0.837979	+	1.92061i	−0.0346461	+	0.0794075i
$586$	−13.9029	+	8.02683i	−0.574323	+	0.331585i
$587$	14.1217	−	24.4595i	0.582864	−	1.00955i	−0.412274	−	0.911060i	$-0.635265\pi$
$587$	14.1217	−	24.4595i	0.582864	−	1.00955i	0.995138	−	0.0984899i	$-0.0314012\pi$
$588$	−4.48465	+	11.2645i	−0.184944	+	0.464538i
$589$	−14.5719	−	25.2393i	−0.600426	−	1.03997i
$590$	1.17733	+	0.679735i	0.0484701	+	0.0279842i
$591$	−0.324356	+	1.55450i	−0.0133422	+	0.0639435i
$592$	5.06492	+	8.77270i	0.208167	+	0.360556i
$593$	−9.93290	−	17.2043i	−0.407895	−	0.706495i	0.586758	−	0.809762i	$-0.300404\pi$
$593$	−9.93290	−	17.2043i	−0.407895	−	0.706495i	−0.994654	+	0.103267i	$0.967070\pi$
$594$	2.51303	−	26.7945i	0.103111	−	1.09939i
$595$	−3.20737	+	8.83071i	−0.131489	+	0.362024i
$596$	−2.29258	−	1.32362i	−0.0939078	−	0.0542177i
$597$	7.72517	+	6.90371i	0.316170	+	0.282550i
$598$			4.02032i			0.164403i
$599$		−	17.3582i		−	0.709235i	−0.935011	−	0.354617i	$-0.884611\pi$
$599$		−	17.3582i		−	0.709235i	0.935011	−	0.354617i	$-0.115389\pi$
$600$	−1.64527	+	0.541382i	−0.0671678	+	0.0221018i
$601$	−22.6903	−	13.1003i	−0.925558	−	0.534371i	−0.0401538	−	0.999194i	$-0.512785\pi$
$601$	−22.6903	−	13.1003i	−0.925558	−	0.534371i	−0.885404	+	0.464823i	$0.846118\pi$
$602$	−5.48620	−	30.9915i	−0.223601	−	1.26312i
$603$	−12.1561	−	5.30380i	−0.495035	−	0.215988i
$604$	−2.15339	−	3.72979i	−0.0876204	−	0.151763i
$605$	−7.91219	−	13.7043i	−0.321676	−	0.557160i
$606$	4.74898	−	1.56267i	0.192914	−	0.0634791i
$607$	8.07674	+	4.66311i	0.327825	+	0.189270i	0.654875	−	0.755737i	$-0.272721\pi$
$607$	8.07674	+	4.66311i	0.327825	+	0.189270i	−0.327050	+	0.945007i	$0.606055\pi$
$608$	2.62267	+	4.54260i	0.106363	+	0.184227i
$609$	0.743301	−	24.3654i	0.0301201	−	0.987336i
$610$	−3.05016	+	5.28303i	−0.123497	+	0.213903i
$611$	−4.93734	+	2.85057i	−0.199743	+	0.115322i
$612$	−8.57152	+	6.32593i	−0.346483	+	0.255711i
$613$	1.03769	−	1.79733i	0.0419119	−	0.0725936i	−0.844308	−	0.535857i	$-0.819988\pi$
$613$	1.03769	−	1.79733i	0.0419119	−	0.0725936i	0.886220	+	0.463264i	$0.153322\pi$
$614$	14.9148			0.601911
$615$	−10.8149	−	2.25659i	−0.436098	−	0.0909945i
$616$	−4.67799	+	12.8797i	−0.188482	+	0.518939i
$617$	−35.7034	+	20.6134i	−1.43737	+	0.829864i	−0.997666	−	0.0682807i	$-0.978249\pi$
$617$	−35.7034	+	20.6134i	−1.43737	+	0.829864i	−0.439700	+	0.898145i	$0.644915\pi$
$618$	14.5364	−	16.2661i	0.584741	−	0.654318i
$619$	6.25083	−	3.60892i	0.251242	−	0.145055i	−0.369091	−	0.929393i	$-0.620331\pi$
$619$	6.25083	−	3.60892i	0.251242	−	0.145055i	0.620333	+	0.784339i	$0.286998\pi$
$620$	−4.81176	−	2.77807i	−0.193245	−	0.111570i
$621$	−12.4700	−	27.1841i	−0.500402	−	1.09086i
$622$			11.6004i			0.465133i
$623$	−4.65166	+	12.8072i	−0.186365	+	0.513110i
$624$	1.14920	−	0.378148i	0.0460048	−	0.0151380i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.62273			−0.264698
$627$	−31.3547	+	35.0855i	−1.25219	+	1.40118i
$628$		−	16.7765i		−	0.669454i
$629$	35.9714			1.43427
$630$	−1.85741	+	7.71687i	−0.0740009	+	0.307447i
$631$	−2.44585			−0.0973679			−0.0486840	−	0.998814i	$-0.515503\pi$
$631$	−2.44585			−0.0973679			−0.0486840	+	0.998814i	$0.515503\pi$
$632$		−	11.6278i		−	0.462529i
$633$	4.32721	+	13.1505i	0.171991	+	0.522684i
$634$	−34.3500			−1.36421
$635$	2.38985	−	4.13933i	0.0948382	−	0.164264i
$636$	−13.1613	−	11.7618i	−0.521878	−	0.466384i
$637$	−1.67848	−	4.59228i	−0.0665037	−	0.181953i
$638$		−	27.5506i		−	1.09074i
$639$	−5.71069	+	13.0887i	−0.225911	+	0.517780i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	−16.3280	+	9.42700i	−0.644919	+	0.372344i	−0.786507	−	0.617581i	$-0.788113\pi$
$641$	−16.3280	+	9.42700i	−0.644919	+	0.372344i	0.141588	+	0.989926i	$0.454779\pi$
$642$	3.39428	+	10.3153i	0.133961	+	0.407111i
$643$	−2.65502	+	1.53288i	−0.104704	+	0.0604508i	−0.551438	−	0.834216i	$-0.685920\pi$
$643$	−2.65502	+	1.53288i	−0.104704	+	0.0604508i	0.446734	+	0.894667i	$0.352587\pi$
$644$	2.65449	+	14.9952i	0.104602	+	0.590892i
$645$	−6.44016	−	19.5718i	−0.253581	−	0.770638i
$646$	18.6264			0.732845
$647$	8.51910	−	14.7555i	0.334920	−	0.580099i	−0.648549	−	0.761173i	$-0.724624\pi$
$647$	8.51910	−	14.7555i	0.334920	−	0.580099i	0.983470	+	0.181074i	$0.0579572\pi$
$648$	−6.59760	+	6.12142i	−0.259178	+	0.240472i
$649$	6.09768	−	3.52050i	0.239355	−	0.138192i
$650$	0.349244	−	0.604908i	0.0136985	−	0.0237264i
$651$	−22.4282	+	12.0524i	−0.879030	+	0.472372i
$652$	7.87086	+	13.6327i	0.308247	+	0.533899i
$653$	21.4526	+	12.3857i	0.839507	+	0.484689i	0.857096	−	0.515156i	$-0.172266\pi$
$653$	21.4526	+	12.3857i	0.839507	+	0.484689i	−0.0175898	+	0.999845i	$0.505599\pi$
$654$	−19.5418	−	17.4638i	−0.764146	−	0.682890i
$655$	−0.00771873	−	0.0133692i	−0.000301596	−	0.000522379i
$656$	3.18922	+	5.52390i	0.124518	+	0.215672i
$657$	−6.57496	−	8.90895i	−0.256514	−	0.347571i
$658$	−16.5333	+	13.8921i	−0.644537	+	0.541572i
$659$	16.5930	+	9.57998i	0.646372	+	0.373183i	0.787065	−	0.616870i	$-0.211600\pi$
$659$	16.5930	+	9.57998i	0.646372	+	0.373183i	−0.140693	+	0.990053i	$0.544933\pi$
$660$	−1.83233	+	8.78156i	−0.0713232	+	0.341822i
$661$		−	32.1531i		−	1.25061i	−0.780380	−	0.625305i	$-0.784975\pi$
$661$		−	32.1531i		−	1.25061i	0.780380	−	0.625305i	$-0.215025\pi$
$662$		−	14.9409i		−	0.580693i
$663$	0.877507	−	4.20552i	0.0340796	−	0.163329i
$664$	13.5153	+	7.80303i	0.524493	+	0.302816i
$665$	10.6251	−	8.92770i	0.412022	−	0.346201i
$666$	30.1985	−	3.40223i	1.17017	−	0.131834i
$667$	−15.3087	−	26.5155i	−0.592756	−	1.02668i
$668$	8.01543	+	13.8831i	0.310126	+	0.537155i
$669$	−2.93491	−	2.62282i	−0.113470	−	0.101404i
$670$	3.82863	+	2.21046i	0.147913	+	0.0853976i
$671$	15.7974	+	27.3620i	0.609854	+	1.05630i
$672$	4.03665	−	2.16921i	0.155717	−	0.0836791i
$673$	16.0669	−	27.8287i	0.619335	−	1.07272i	−0.370273	−	0.928923i	$-0.620736\pi$
$673$	16.0669	−	27.8287i	0.619335	−	1.07272i	0.989607	−	0.143796i	$-0.0459309\pi$
$674$	−7.26684	+	4.19551i	−0.279908	+	0.161605i
$675$	−0.485213	+	5.17345i	−0.0186759	+	0.199126i
$676$	6.25606	−	10.8358i	0.240618	−	0.416762i
$677$	−9.87449			−0.379507			−0.189754	−	0.981832i	$-0.560769\pi$
$677$	−9.87449			−0.379507			−0.189754	+	0.981832i	$0.560769\pi$
$678$	−8.38818	−	25.4918i	−0.322146	−	0.979008i
$679$	8.30288	+	46.9029i	0.318635	+	1.79997i
$680$	3.07528	−	1.77552i	0.117932	−	0.0680879i
$681$	−5.77000	−	17.5351i	−0.221107	−	0.671948i
$682$	−24.9212	+	14.3883i	−0.954281	+	0.550955i
$683$	−27.9263	−	16.1232i	−1.06857	−	0.616939i	−0.140779	−	0.990041i	$-0.544961\pi$
$683$	−27.9263	−	16.1232i	−1.06857	−	0.616939i	−0.927790	+	0.373102i	$0.878294\pi$
$684$	15.6371	−	1.76171i	0.597900	−	0.0673608i
$685$			8.62590i			0.329579i
$686$	−9.29259	−	16.0202i	−0.354793	−	0.611655i
$687$	−5.80919	−	5.19146i	−0.221634	−	0.198067i
$688$	−5.94790	+	10.3021i	−0.226761	+	0.392762i
$689$	7.11815			0.271180
$690$	3.11606	+	9.46977i	0.118626	+	0.360508i
$691$			6.77328i			0.257668i	0.991666	+	0.128834i	$0.0411234\pi$
$691$			6.77328i			0.257668i	−0.991666	+	0.128834i	$0.958877\pi$
$692$	−9.09408			−0.345705
$693$	29.8028	+	28.3148i	1.13212	+	1.07559i
$694$	32.3178			1.22677
$695$		−	0.830775i		−	0.0315131i
$696$	−6.13945	+	6.86998i	−0.232715	+	0.260406i
$697$	22.6501			0.857933
$698$	5.90940	−	10.2354i	0.223674	−	0.387415i
$699$	−4.32632	+	1.42359i	−0.163636	+	0.0538452i
$700$	0.903222	−	2.48680i	0.0341386	−	0.0939923i
$701$			7.49030i			0.282905i	0.989945	+	0.141452i	$0.0451772\pi$
$701$			7.49030i			0.282905i	−0.989945	+	0.141452i	$0.954823\pi$
$702$	0.338915	−	3.61359i	0.0127915	−	0.136386i
$703$	−46.0158	−	26.5673i	−1.73552	−	1.00200i
$704$	4.48534	−	2.58961i	0.169048	−	0.0975997i
$705$	−9.42035	+	10.5413i	−0.354791	+	0.397007i
$706$	14.5951	−	8.42649i	0.549294	−	0.317135i
$707$	−2.60710	+	7.17803i	−0.0980502	+	0.269958i
$708$	−2.30503	−	0.480958i	−0.0866282	−	0.0180755i
$709$	−40.0999			−1.50598			−0.752992	−	0.658029i	$-0.771390\pi$
$709$	−40.0999			−1.50598			−0.752992	+	0.658029i	$0.771390\pi$
$710$	2.38004	−	4.12235i	0.0893213	−	0.154709i
$711$	−31.9727	−	13.9499i	−1.19907	−	0.523163i
$712$	4.46009	−	2.57504i	0.167149	−	0.0965035i
$713$	−15.9899	+	27.6953i	−0.598827	+	1.03720i
$714$	0.496196	−	16.2653i	0.0185697	−	0.608714i
$715$	−1.80881	−	3.13295i	−0.0676457	−	0.117166i
$716$	11.0133	+	6.35855i	0.411588	+	0.237630i
$717$	−30.6546	+	10.0870i	−1.14482	+	0.376707i
$718$	8.84623	+	15.3221i	0.330138	+	0.571816i
$719$	−3.69335	−	6.39706i	−0.137739	−	0.238570i	0.788902	−	0.614519i	$-0.210650\pi$
$719$	−3.69335	−	6.39706i	−0.137739	−	0.238570i	−0.926640	+	0.375949i	$0.877317\pi$
$720$	2.41381	−	1.78144i	0.0899575	−	0.0663902i
$721$	5.80862	+	32.8128i	0.216324	+	1.22201i
$722$	−7.37304	−	4.25683i	−0.274396	−	0.158423i
$723$	−34.6000	+	11.3853i	−1.28679	+	0.423422i
$724$		−	17.3337i		−	0.644201i
$725$			5.31944i			0.197559i
$726$	20.4369	+	18.2638i	0.758486	+	0.677832i
$727$	−38.2486	−	22.0829i	−1.41856	−	0.819008i	−0.422391	−	0.906414i	$-0.638809\pi$
$727$	−38.2486	−	22.0829i	−1.41856	−	0.819008i	−0.996173	+	0.0874056i	$0.972142\pi$
$728$	−0.630889	+	1.73700i	−0.0233823	+	0.0643775i
$729$	8.91673	+	25.4851i	0.330249	+	0.943894i
$730$	1.84541	+	3.19635i	0.0683017	+	0.118302i
$731$	21.1212	+	36.5829i	0.781195	+	1.35307i
$732$	2.15819	−	10.3433i	0.0797690	−	0.382299i
$733$	7.07598	+	4.08532i	0.261357	+	0.150895i	0.624954	−	0.780662i	$-0.285118\pi$
$733$	7.07598	+	4.08532i	0.261357	+	0.150895i	−0.363596	+	0.931557i	$0.618451\pi$
$734$	15.8546	+	27.4610i	0.585205	+	1.01361i
$735$	−7.51298	−	9.51605i	−0.277120	−	0.351005i
$736$	2.87788	−	4.98463i	0.106080	−	0.183736i
$737$	19.8294	−	11.4485i	0.730424	−	0.421710i
$738$	19.0150	−	2.14228i	0.699954	−	0.0788584i
$739$	19.0097	−	32.9258i	0.699283	−	1.21119i	−0.269432	−	0.963019i	$-0.586836\pi$
$739$	19.0097	−	32.9258i	0.699283	−	1.21119i	0.968715	−	0.248175i	$-0.0798307\pi$
$740$	−10.1298			−0.372380
$741$	−4.22859	+	4.73175i	−0.155341	+	0.173825i
$742$	26.5496	−	4.69988i	0.974665	−	0.172538i
$743$	13.7119	−	7.91654i	0.503039	−	0.290430i	−0.226929	−	0.973911i	$-0.572868\pi$
$743$	13.7119	−	7.91654i	0.503039	−	0.290430i	0.729968	+	0.683482i	$0.239535\pi$
$744$	9.42062	+	1.96567i	0.345377	+	0.0720650i
$745$	2.29258	−	1.32362i	0.0839936	−	0.0484938i
$746$	16.3049	+	9.41361i	0.596963	+	0.344657i
$747$	37.6701	−	27.8012i	1.37828	−	1.01719i
$748$		−	18.3916i		−	0.672463i
$749$	−15.5914	−	5.66290i	−0.569698	−	0.206918i
$750$	0.353784	−	1.69553i	0.0129184	−	0.0619122i
$751$	−14.2851	+	24.7425i	−0.521271	+	0.902868i	0.478423	+	0.878130i	$0.341209\pi$
$751$	−14.2851	+	24.7425i	−0.521271	+	0.902868i	−0.999694	+	0.0247387i	$0.992125\pi$
$752$	8.16214			0.297642
$753$	38.8905	+	8.11474i	1.41725	+	0.295717i
$754$		−	3.71556i		−	0.135313i
$755$	4.30679			0.156740
$756$	−1.12184	−	13.7019i	−0.0408008	−	0.498333i
$757$	40.7589			1.48141			0.740703	−	0.671832i	$-0.234492\pi$
$757$	40.7589			1.48141			0.740703	+	0.671832i	$0.234492\pi$
$758$			7.77895i			0.282544i
$759$	50.5445	+	10.5464i	1.83465	+	0.382811i
$760$	−5.24535			−0.190269
$761$	15.3184	−	26.5323i	0.555292	−	0.961794i	−0.442589	−	0.896725i	$-0.645940\pi$
$761$	15.3184	−	26.5323i	0.555292	−	0.961794i	0.997881	−	0.0650689i	$-0.0207267\pi$
$762$	−1.69098	+	8.10413i	−0.0612576	+	0.293582i
$763$	39.4207	−	6.97837i	1.42713	−	0.252634i
$764$		−	6.45755i		−	0.233626i
$765$	−1.19266	−	10.5861i	−0.0431206	−	0.382742i
$766$	1.84402	+	1.06464i	0.0666270	+	0.0384671i
$767$	0.822353	−	0.474786i	0.0296935	−	0.0171435i
$768$	−1.69553	−	0.353784i	−0.0611823	−	0.0127661i
$769$	12.2591	−	7.07780i	0.442075	−	0.255232i	−0.262403	−	0.964958i	$-0.584515\pi$
$769$	12.2591	−	7.07780i	0.442075	−	0.255232i	0.704477	+	0.709727i	$0.251182\pi$
$770$	−8.81517	−	10.4911i	−0.317677	−	0.378074i
$771$	−7.84621	+	8.77982i	−0.282574	+	0.316198i
$772$	−8.46355			−0.304610
$773$	−19.4256	+	33.6461i	−0.698691	+	1.21017i	0.270230	+	0.962796i	$0.412900\pi$
$773$	−19.4256	+	33.6461i	−0.698691	+	1.21017i	−0.968921	+	0.247372i	$0.920433\pi$
$774$	21.1916	+	28.7142i	0.761716	+	1.03211i
$775$	4.81176	−	2.77807i	0.172843	−	0.0997912i
$776$	9.00162	−	15.5913i	0.323139	−	0.559694i
$777$	−24.4254	+	39.4751i	−0.876257	+	1.41616i
$778$	8.32649	+	14.4219i	0.298519	+	0.517050i
$779$	−28.9748	−	16.7286i	−1.03813	−	0.599364i
$780$	−0.247113	+	1.18431i	−0.00884808	+	0.0424051i
$781$	−12.3268	−	21.3506i	−0.441086	−	0.763984i
$782$	−10.2194	−	17.7006i	−0.365446	−	0.632972i
$783$	11.5247	+	25.1234i	0.411858	+	0.897838i
$784$	−1.20623	+	6.89529i	−0.0430797	+	0.246260i
$785$	14.5288	+	8.38823i	0.518557	+	0.299389i
$786$	0.0199372	+	0.0178172i	0.000711138	+	0.000635518i
$787$		−	38.7497i		−	1.38128i	−0.723199	−	0.690639i	$-0.757329\pi$
$787$		−	38.7497i		−	1.38128i	0.723199	−	0.690639i	$-0.242671\pi$
$788$			0.916820i			0.0326603i
$789$	−4.31718	+	1.42058i	−0.153696	+	0.0505741i
$790$	10.0700	+	5.81390i	0.358274	+	0.206849i
$791$	38.5306	+	13.9946i	1.36999	+	0.497589i
$792$	−1.73951	−	15.4400i	−0.0618107	−	0.548637i
$793$	2.13050	+	3.69013i	0.0756561	+	0.131040i
$794$	12.9163	+	22.3718i	0.458384	+	0.793944i
$795$	16.7666	−	5.51712i	0.594650	−	0.195672i
$796$	5.18024	+	2.99081i	0.183609	+	0.106006i
$797$	−11.8594	−	20.5410i	−0.420080	−	0.727600i	0.575867	−	0.817544i	$-0.304665\pi$
$797$	−11.8594	−	20.5410i	−0.420080	−	0.727600i	−0.995947	+	0.0899433i	$0.971331\pi$
$798$	−12.6478	+	20.4407i	−0.447726	+	0.723592i
$799$	14.4920	−	25.1009i	0.512690	−	0.888005i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−1.72971	−	15.3531i	−0.0611165	−	0.542475i
$802$	4.03197	−	6.98357i	0.142374	−	0.246598i
$803$	19.1156			0.674575
$804$	−7.49583	−	1.56405i	−0.264357	−	0.0551598i
$805$	−14.3134	−	5.19873i	−0.504483	−	0.183231i
$806$	−3.36095	+	1.94045i	−0.118384	+	0.0683493i
$807$	18.2907	−	20.4671i	0.643863	−	0.720475i
$808$	2.49974	−	1.44322i	0.0879405	−	0.0507724i
$809$	16.5030	+	9.52799i	0.580213	+	0.334986i	0.761218	−	0.648496i	$-0.224602\pi$
$809$	16.5030	+	9.52799i	0.580213	+	0.334986i	−0.181005	+	0.983482i	$0.557935\pi$
$810$	−2.00250	−	8.77439i	−0.0703608	−	0.308301i
$811$			40.2764i			1.41430i	0.707065	+	0.707149i	$0.250019\pi$
$811$			40.2764i			1.41430i	−0.707065	+	0.707149i	$0.749981\pi$
$812$	−2.45326	−	13.8585i	−0.0860927	−	0.486336i
$813$	−9.50463	+	3.12753i	−0.333342	+	0.109687i
$814$	−26.2324	+	45.4358i	−0.919444	+	1.59252i
$815$	−15.7417			−0.551408
$816$	−4.09843	+	4.58610i	−0.143474	+	0.160546i
$817$		−	62.3976i		−	2.18301i
$818$	22.4604			0.785310
$819$	4.01930	+	3.81863i	0.140446	+	0.133434i
$820$	−6.37845			−0.222745
$821$		−	0.403580i		−	0.0140850i	−0.999975	−	0.00704252i	$-0.997758\pi$
$821$		−	0.403580i		−	0.0140850i	0.999975	−	0.00704252i	$-0.00224172\pi$
$822$	−4.66990	−	14.1919i	−0.162882	−	0.495000i
$823$	−45.6412			−1.59095			−0.795476	−	0.605985i	$-0.792779\pi$
$823$	−45.6412			−1.59095			−0.795476	+	0.605985i	$0.792779\pi$
$824$	6.29744	−	10.9075i	0.219382	−	0.379981i
$825$	−6.68889	−	5.97762i	−0.232877	−	0.208114i
$826$	2.75376	−	2.31385i	0.0958156	−	0.0805091i
$827$			45.1188i			1.56894i	0.620169	+	0.784468i	$0.287064\pi$
$827$			45.1188i			1.56894i	−0.620169	+	0.784468i	$0.712936\pi$
$828$	−10.2535	−	13.8933i	−0.356334	−	0.482826i
$829$	17.5137	+	10.1115i	0.608276	+	0.351188i	0.772291	−	0.635270i	$-0.219111\pi$
$829$	17.5137	+	10.1115i	0.608276	+	0.351188i	−0.164014	+	0.986458i	$0.552444\pi$
$830$	−13.5153	+	7.80303i	−0.469121	+	0.270847i
$831$	−0.363148	−	1.10361i	−0.0125975	−	0.0382839i
$832$	0.604908	−	0.349244i	0.0209714	−	0.0121078i
$833$	19.0633	+	15.9522i	0.660504	+	0.552711i
$834$	0.449766	+	1.36685i	0.0155741	+	0.0473301i
$835$	−16.0309			−0.554771
$836$	−13.5834	+	23.5272i	−0.469792	+	0.813704i
$837$	16.7069	−	23.5454i	0.577476	−	0.813849i
$838$	21.4808	−	12.4020i	0.742042	−	0.428418i
$839$	−20.6859	+	35.8291i	−0.714157	+	1.23696i	0.249127	+	0.968471i	$0.419856\pi$
$839$	−20.6859	+	35.8291i	−0.714157	+	1.23696i	−0.963284	+	0.268485i	$0.913477\pi$
$840$	−0.139733	+	4.58044i	−0.00482124	+	0.158040i
$841$	−0.351766	−	0.609277i	−0.0121299	−	0.0210095i
$842$	−26.7272	−	15.4310i	−0.921080	−	0.531786i
$843$	−32.0664	−	28.6566i	−1.10443	−	0.986987i
$844$	3.99645	+	6.92206i	0.137564	+	0.238267i
$845$	6.25606	+	10.8358i	0.215215	+	0.372763i
$846$	9.79215	−	22.4432i	0.336661	−	0.771614i
$847$	−41.2264	+	7.29802i	−1.41656	+	0.250763i
$848$	−8.82550	−	5.09540i	−0.303069	−	0.174977i
$849$	−6.06292	+	29.0570i	−0.208079	+	0.997233i
$850$			3.55103i			0.121799i
$851$			58.3049i			1.99867i
$852$	−1.68404	+	8.07088i	−0.0576942	+	0.276504i
$853$	−13.6296	−	7.86904i	−0.466668	−	0.269431i	0.248176	−	0.968715i	$-0.420169\pi$
$853$	−13.6296	−	7.86904i	−0.466668	−	0.269431i	−0.714844	+	0.699284i	$0.753502\pi$
$854$	10.3829	+	12.3569i	0.355295	+	0.422844i
$855$	−6.29287	+	14.4230i	−0.215212	+	0.493256i
$856$	3.13483	+	5.42968i	0.107146	+	0.185583i
$857$	18.7675	+	32.5063i	0.641086	+	1.11039i	0.985191	+	0.171463i	$0.0548493\pi$
$857$	18.7675	+	32.5063i	0.641086	+	1.11039i	−0.344104	+	0.938931i	$0.611817\pi$
$858$	4.67210	+	4.17529i	0.159503	+	0.142542i
$859$	16.6176	+	9.59419i	0.566986	+	0.327350i	0.755945	−	0.654635i	$-0.227178\pi$
$859$	16.6176	+	9.59419i	0.566986	+	0.327350i	−0.188958	+	0.981985i	$0.560511\pi$
$860$	−5.94790	−	10.3021i	−0.202822	−	0.351297i
$861$	−15.3799	+	24.8563i	−0.524147	+	0.847100i
$862$	−6.03478	+	10.4525i	−0.205545	+	0.356015i
$863$	35.4082	−	20.4430i	1.20531	−	0.695886i	0.243579	−	0.969881i	$-0.421678\pi$
$863$	35.4082	−	20.4430i	1.20531	−	0.695886i	0.961731	+	0.273995i	$0.0883450\pi$
$864$	−3.00693	+	4.23773i	−0.102298	+	0.144171i
$865$	4.54704	−	7.87570i	0.154604	−	0.267782i
$866$	2.36480			0.0803592
$867$	−2.37676	−	7.22302i	−0.0807191	−	0.245307i
$868$	−11.2546	+	9.45668i	−0.382006	+	0.320981i
$869$	52.1547	−	30.1115i	1.76923	−	1.02146i
$870$	−2.87985	−	8.75191i	−0.0976360	−	0.296717i
$871$	2.67425	−	1.54398i	0.0906135	−	0.0523157i
$872$	−13.1041	−	7.56565i	−0.443760	−	0.256205i
$873$	−32.0716	−	43.4564i	−1.08546	−	1.47078i
$874$			30.1910i			1.02122i
$875$	1.70202	+	2.02561i	0.0575389	+	0.0684783i
$876$	−4.76664	−	4.25977i	−0.161050	−	0.143924i
$877$	−23.2755	+	40.3144i	−0.785959	+	1.36132i	0.142466	+	0.989800i	$0.454497\pi$
$877$	−23.2755	+	40.3144i	−0.785959	+	1.36132i	−0.928425	+	0.371521i	$0.878836\pi$
$878$	3.37576			0.113927
$879$	8.69116	+	26.4126i	0.293145	+	0.890874i
$880$			5.17923i			0.174592i
$881$	45.4522			1.53132			0.765661	−	0.643244i	$-0.222412\pi$
$881$	45.4522			1.53132			0.765661	+	0.643244i	$0.222412\pi$
$882$	17.5127	+	11.5891i	0.589682	+	0.390224i
$883$	37.4352			1.25979			0.629897	−	0.776679i	$-0.283097\pi$
$883$	37.4352			1.25979			0.629897	+	0.776679i	$0.283097\pi$
$884$		−	2.48035i		−	0.0834232i
$885$	1.56904	−	1.75573i	0.0527425	−	0.0590183i
$886$	−25.8297			−0.867765
$887$	−23.9255	+	41.4402i	−0.803340	+	1.39143i	0.114066	+	0.993473i	$0.463612\pi$
$887$	−23.9255	+	41.4402i	−0.803340	+	1.39143i	−0.917406	+	0.397953i	$0.869721\pi$
$888$	16.6663	−	5.48411i	0.559284	−	0.184035i
$889$	−8.13515	−	9.68182i	−0.272844	−	0.324718i
$890$			5.15007i			0.172631i
$891$	−44.5419	−	13.7404i	−1.49221	−	0.460320i
$892$	−1.96805	−	1.13625i	−0.0658952	−	0.0380446i
$893$	−37.0773	+	21.4066i	−1.24075	+	0.716345i
$894$	−3.05532	+	3.41887i	−0.102185	+	0.114344i
$895$	−11.0133	+	6.35855i	−0.368135	+	0.212543i
$896$	2.02561	−	1.70202i	0.0676710	−	0.0568606i
$897$	6.81660	+	1.42233i	0.227600	+	0.0474901i
$898$	22.6610			0.756206
$899$	14.7778	−	25.5959i	0.492867	−	0.853670i
$900$	0.335862	+	2.98114i	0.0111954	+	0.0993713i
$901$	−31.3396	+	18.0939i	−1.04407	+	0.602796i
$902$	−16.5177	+	28.6095i	−0.549980	+	0.952593i
$903$	−54.4880	−	1.66223i	−1.81325	−	0.0553156i
$904$	−7.74702	−	13.4182i	−0.257662	−	0.446284i
$905$	15.0114	+	8.66683i	0.498996	+	0.288095i
$906$	−7.08582	+	2.33162i	−0.235411	+	0.0774628i
$907$	−15.9504	−	27.6270i	−0.529626	−	0.917339i	−0.999403	−	0.0345536i	$-0.988999\pi$
$907$	−15.9504	−	27.6270i	−0.529626	−	0.917339i	0.469777	−	0.882785i	$-0.344334\pi$
$908$	−5.32896	−	9.23003i	−0.176848	−	0.306309i
$909$	−0.969449	−	8.60491i	−0.0321546	−	0.285407i
$910$	−1.18884	−	1.41487i	−0.0394097	−	0.0469024i
$911$	46.8523	+	27.0502i	1.55229	+	0.896213i	0.997955	+	0.0639167i	$0.0203592\pi$
$911$	46.8523	+	27.0502i	1.55229	+	0.896213i	0.554331	+	0.832296i	$0.312974\pi$
$912$	8.63000	−	2.83973i	0.285768	−	0.0940330i
$913$			80.8274i			2.67499i
$914$			0.350134i			0.0115814i
$915$	7.87846	+	7.04069i	0.260454	+	0.232758i
$916$	−3.89544	−	2.24904i	−0.128709	−	0.0743102i
$917$	−0.0402184	+	0.00711958i	−0.00132813	+	0.000235109i
$918$	7.69337	+	16.7713i	0.253919	+	0.553536i
$919$	−0.0315932	−	0.0547210i	−0.00104216	−	0.00180508i	0.865504	−	0.500902i	$-0.166998\pi$
$919$	−0.0315932	−	0.0547210i	−0.00104216	−	0.00180508i	−0.866546	+	0.499097i	$0.833665\pi$
$920$	2.87788	+	4.98463i	0.0948809	+	0.164339i
$921$	5.27660	−	25.2885i	0.173870	−	0.833285i
$922$	−25.3374	−	14.6285i	−0.834442	−	0.481765i
$923$	−1.66243	−	2.87941i	−0.0547194	−	0.0947769i
$924$	20.1830	+	12.4883i	0.663972	+	0.410836i
$925$	5.06492	−	8.77270i	0.166534	−	0.288445i
$926$	20.4706	−	11.8187i	0.672706	−	0.388387i
$927$	−22.4370	−	30.4017i	−0.736927	−	0.998523i
$928$	−2.65972	+	4.60677i	−0.0873096	+	0.151225i
$929$	32.5066			1.06651			0.533254	−	0.845955i	$-0.320969\pi$
$929$	32.5066			1.06651			0.533254	+	0.845955i	$0.320969\pi$
$930$	−6.41263	+	7.17566i	−0.210279	+	0.235299i
$931$	−12.6047	−	34.4861i	−0.413101	−	1.13024i
$932$	−2.27726	+	1.31478i	−0.0745941	+	0.0430669i
$933$	19.6688	+	4.10402i	0.643929	+	0.134360i
$934$	2.39369	−	1.38200i	0.0783240	−	0.0452204i
$935$	15.9276	+	9.19580i	0.520888	+	0.300735i
$936$	−0.234595	−	2.08229i	−0.00766799	−	0.0680617i
$937$			57.3482i			1.87348i	0.350023	+	0.936741i	$0.386174\pi$
$937$			57.3482i			1.87348i	−0.350023	+	0.936741i	$0.613826\pi$
$938$	8.95509	−	7.52452i	0.292394	−	0.245684i
$939$	−2.34301	+	11.2291i	−0.0764614	+	0.366447i
$940$	−4.08107	+	7.06862i	−0.133110	+	0.230553i
$941$	−20.0112			−0.652345			−0.326172	−	0.945310i	$-0.605759\pi$
$941$	−20.0112			−0.652345			−0.326172	+	0.945310i	$0.605759\pi$
$942$	−28.4451	−	5.93524i	−0.926791	−	0.193381i
$943$			36.7128i			1.19553i
$944$	−1.35947			−0.0442470
$945$	12.4271	+	5.87940i	0.404253	+	0.191257i
$946$	−61.6110			−2.00315
$947$			43.6167i			1.41735i	0.705534	+	0.708676i	$0.250707\pi$
$947$			43.6167i			1.41735i	−0.705534	+	0.708676i	$0.749293\pi$
$948$	−19.7153	−	4.11373i	−0.640324	−	0.133608i
$949$	2.57799			0.0836852
$950$	2.62267	−	4.54260i	0.0850907	−	0.147381i
$951$	−12.1525	+	58.2416i	−0.394071	+	1.88861i
$952$	−1.63769	−	9.25131i	−0.0530780	−	0.299837i
$953$		−	21.8792i		−	0.708736i	−0.935106	−	0.354368i	$-0.884696\pi$
$953$		−	21.8792i		−	0.708736i	0.935106	−	0.354368i	$-0.115304\pi$
$954$	−24.5987	+	18.1543i	−0.796412	+	0.587766i
$955$	5.59240	+	3.22877i	0.180966	+	0.104481i
$956$	−16.1358	+	9.31600i	−0.521869	+	0.301301i
$957$	−46.7130	−	9.74695i	−1.51002	−	0.315074i
$958$	−9.26604	+	5.34975i	−0.299372	+	0.172843i
$959$	21.4509	+	7.79110i	0.692686	+	0.251588i
$960$	1.15415	−	1.29148i	0.0372501	−	0.0416825i
$961$	0.129322			0.00417167
$962$	−3.53778	+	6.12762i	−0.114063	+	0.197562i
$963$	18.6907	−	2.10574i	0.602301	−	0.0678566i
$964$	−18.2125	+	10.5150i	−0.586586	+	0.338665i
$965$	4.23178	−	7.32965i	0.136226	−	0.235950i
$966$	26.3639	+	0.804269i	0.848246	+	0.0258769i
$967$	−6.63288	−	11.4885i	−0.213299	−	0.369445i	0.739446	−	0.673216i	$-0.235088\pi$
$967$	−6.63288	−	11.4885i	−0.213299	−	0.369445i	−0.952745	+	0.303771i	$0.901754\pi$
$968$	13.7043	+	7.91219i	0.440474	+	0.254308i
$969$	6.58971	−	31.5817i	0.211692	−	1.01455i
$970$	9.00162	+	15.5913i	0.289025	+	0.500605i
$971$	8.25536	+	14.2987i	0.264927	+	0.458867i	0.967544	−	0.252701i	$-0.0813188\pi$
$971$	8.25536	+	14.2987i	0.264927	+	0.458867i	−0.702618	+	0.711568i	$0.747985\pi$
$972$	8.04495	+	13.3521i	0.258042	+	0.428269i
$973$	−2.06597	−	0.750375i	−0.0662321	−	0.0240559i
$974$	−10.1855	−	5.88059i	−0.326364	−	0.188426i
$975$	−0.902085	−	0.806161i	−0.0288898	−	0.0258178i
$976$		−	6.10031i		−	0.195266i
$977$		−	34.8677i		−	1.11552i	−0.830004	−	0.557758i	$-0.811662\pi$
$977$		−	34.8677i		−	1.11552i	0.830004	−	0.557758i	$-0.188338\pi$
$978$	25.8993	−	8.52227i	0.828169	−	0.272512i
$979$	23.0998	+	13.3367i	0.738274	+	0.426243i
$980$	−5.36838	−	4.49227i	−0.171487	−	0.143500i
$981$	−36.5241	+	26.9554i	−1.16612	+	0.860620i
$982$	−9.69561	−	16.7933i	−0.309399	−	0.535895i
$983$	−12.8116	−	22.1904i	−0.408628	−	0.707764i	0.586108	−	0.810233i	$-0.300659\pi$
$983$	−12.8116	−	22.1904i	−0.408628	−	0.707764i	−0.994736	+	0.102468i	$0.967326\pi$
$984$	10.4943	−	3.45317i	0.334545	−	0.110083i
$985$	−0.793989	−	0.458410i	−0.0252986	−	0.0146061i
$986$	9.44475	+	16.3588i	0.300782	+	0.520970i
$987$	17.7054	+	32.9477i	0.563569	+	1.04874i
$988$	−1.83190	+	3.17295i	−0.0582806	+	0.100945i
$989$	−59.2962	+	34.2347i	−1.88551	+	1.08860i
$990$	14.2412	+	6.21354i	0.452615	+	0.197479i
$991$	18.6962	−	32.3828i	0.593904	−	1.02867i	−0.399796	−	0.916604i	$-0.630919\pi$
$991$	18.6962	−	32.3828i	0.593904	−	1.02867i	0.993701	−	0.112068i	$-0.0357475\pi$
$992$	5.55614			0.176408
$993$	−25.3328	−	5.28584i	−0.803911	−	0.167741i
$994$	−8.10177	−	9.64209i	−0.256972	−	0.305828i
$995$	−5.18024	+	2.99081i	−0.164225	+	0.0948151i
$996$	18.0118	−	20.1550i	0.570725	−	0.638635i
$997$	−46.1607	+	26.6509i	−1.46192	+	0.844042i	−0.999100	−	0.0424085i	$-0.986497\pi$
$997$	−46.1607	+	26.6509i	−1.46192	+	0.844042i	−0.462823	+	0.886451i	$0.653164\pi$
$998$	−16.5952	−	9.58126i	−0.525313	−	0.303289i
$999$	4.91513	−	52.4062i	0.155508	−	1.65806i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.c.101.1	yes	32
3.2	odd	2		1890.2.bk.c.521.2		32
7.5	odd	6		630.2.t.c.551.3	yes	32
9.4	even	3		1890.2.t.c.1151.10		32
9.5	odd	6		630.2.t.c.311.3	✓	32
21.5	even	6		1890.2.t.c.1601.10		32
63.5	even	6	inner	630.2.bk.c.131.9	yes	32
63.40	odd	6		1890.2.bk.c.341.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.3	✓	32	9.5	odd	6
630.2.t.c.551.3	yes	32	7.5	odd	6
630.2.bk.c.101.1	yes	32	1.1	even	1	trivial
630.2.bk.c.131.9	yes	32	63.5	even	6	inner
1890.2.t.c.1151.10		32	9.4	even	3
1890.2.t.c.1601.10		32	21.5	even	6
1890.2.bk.c.341.2		32	63.40	odd	6
1890.2.bk.c.521.2		32	3.2	odd	2

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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.69553 - 0.353784i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.353784 + 1.69553i) q^{6} +(-1.70202 - 2.02561i) q^{7} +1.00000i q^{8} +(2.74967 + 1.19970i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.69553 - 0.353784i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.353784 + 1.69553i) q^{6} +(-1.70202 - 2.02561i) q^{7} +1.00000i q^{8} +(2.74967 + 1.19970i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(-4.48534 + 2.58961i) q^{11} +(1.69553 + 0.353784i) q^{12} +(-0.604908 + 0.349244i) q^{13} +(-2.02561 + 1.70202i) q^{14} +(-1.15415 + 1.29148i) q^{15} +1.00000 q^{16} +(1.77552 - 3.07528i) q^{17} +(1.19970 - 2.74967i) q^{18} +(-4.54260 + 2.62267i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(2.16921 + 4.03665i) q^{21} +(2.58961 + 4.48534i) q^{22} +(4.98463 + 2.87788i) q^{23} +(0.353784 - 1.69553i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(0.349244 + 0.604908i) q^{26} +(-4.23773 - 3.00693i) q^{27} +(1.70202 + 2.02561i) q^{28} +(-4.60677 - 2.65972i) q^{29} +(1.29148 + 1.15415i) q^{30} +5.55614i q^{31} -1.00000i q^{32} +(8.52121 - 2.80394i) q^{33} +(-3.07528 - 1.77552i) q^{34} +(-2.60525 + 0.461188i) q^{35} +(-2.74967 - 1.19970i) q^{36} +(5.06492 + 8.77270i) q^{37} +(2.62267 + 4.54260i) q^{38} +(1.14920 - 0.378148i) q^{39} +(0.866025 + 0.500000i) q^{40} +(3.18922 + 5.52390i) q^{41} +(4.03665 - 2.16921i) q^{42} +(-5.94790 + 10.3021i) q^{43} +(4.48534 - 2.58961i) q^{44} +(2.41381 - 1.78144i) q^{45} +(2.87788 - 4.98463i) q^{46} +8.16214 q^{47} +(-1.69553 - 0.353784i) q^{48} +(-1.20623 + 6.89529i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-4.09843 + 4.58610i) q^{51} +(0.604908 - 0.349244i) q^{52} +(-8.82550 - 5.09540i) q^{53} +(-3.00693 + 4.23773i) q^{54} +5.17923i q^{55} +(2.02561 - 1.70202i) q^{56} +(8.63000 - 2.83973i) q^{57} +(-2.65972 + 4.60677i) q^{58} -1.35947 q^{59} +(1.15415 - 1.29148i) q^{60} -6.10031i q^{61} +5.55614 q^{62} +(-2.24987 - 7.61171i) q^{63} -1.00000 q^{64} +0.698487i q^{65} +(-2.80394 - 8.52121i) q^{66} -4.42092 q^{67} +(-1.77552 + 3.07528i) q^{68} +(-7.43347 - 6.64303i) q^{69} +(0.461188 + 2.60525i) q^{70} +4.76008i q^{71} +(-1.19970 + 2.74967i) q^{72} +(-3.19635 - 1.84541i) q^{73} +(8.77270 - 5.06492i) q^{74} +(0.541382 + 1.64527i) q^{75} +(4.54260 - 2.62267i) q^{76} +(12.8797 + 4.67799i) q^{77} +(-0.378148 - 1.14920i) q^{78} -11.6278 q^{79} +(0.500000 - 0.866025i) q^{80} +(6.12142 + 6.59760i) q^{81} +(5.52390 - 3.18922i) q^{82} +(7.80303 - 13.5153i) q^{83} +(-2.16921 - 4.03665i) q^{84} +(-1.77552 - 3.07528i) q^{85} +(10.3021 + 5.94790i) q^{86} +(6.86998 + 6.13945i) q^{87} +(-2.58961 - 4.48534i) q^{88} +(-2.57504 - 4.46009i) q^{89} +(-1.78144 - 2.41381i) q^{90} +(1.73700 + 0.630889i) q^{91} +(-4.98463 - 2.87788i) q^{92} +(1.96567 - 9.42062i) q^{93} -8.16214i q^{94} +5.24535i q^{95} +(-0.353784 + 1.69553i) q^{96} +(-15.5913 - 9.00162i) q^{97} +(6.89529 + 1.20623i) q^{98} +(-15.4400 + 1.73951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

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