LMFDB - Embedded newform 770.2.m.e.197.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(43,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0, 2]))

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

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

chi := DirichletCharacter("770.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.m (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 32x^{14} + 404x^{12} + 2600x^{10} + 9170x^{8} + 17648x^{6} + 17180x^{4} + 6904x^{2} + 529 $ x^16 + 32x^14 + 404x^12 + 2600x^10 + 9170x^8 + 17648x^6 + 17180x^4 + 6904*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.8
Root			$-2.65904i$ of defining polynomial
Character	$\chi$	$=$	770.197
Dual form			770.2.m.e.43.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(2.22529 - 2.22529i) q^{3} -1.00000i q^{4} +(2.07027 + 0.844975i) q^{5} -3.14704i q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -6.90387i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(2.22529 - 2.22529i) q^{3} -1.00000i q^{4} +(2.07027 + 0.844975i) q^{5} -3.14704i q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -6.90387i q^{9} +(2.06139 - 0.866414i) q^{10} +(-2.91525 - 1.58156i) q^{11} +(-2.22529 - 2.22529i) q^{12} +(1.58156 + 1.58156i) q^{13} +1.00000i q^{14} +(6.48728 - 2.72664i) q^{15} -1.00000 q^{16} +(-2.76045 + 2.76045i) q^{17} +(-4.88177 - 4.88177i) q^{18} -4.12278 q^{19} +(0.844975 - 2.07027i) q^{20} +3.14704i q^{21} +(-3.17972 + 0.943055i) q^{22} +(1.38343 - 1.38343i) q^{23} -3.14704 q^{24} +(3.57203 + 3.49865i) q^{25} +2.23667 q^{26} +(-8.68726 - 8.68726i) q^{27} +(0.707107 + 0.707107i) q^{28} +9.22628 q^{29} +(2.65917 - 6.51522i) q^{30} +3.90387 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-10.0067 + 2.96783i) q^{33} +3.90387i q^{34} +(-2.06139 + 0.866414i) q^{35} -6.90387 q^{36} +(2.14054 + 2.14054i) q^{37} +(-2.91525 + 2.91525i) q^{38} +7.03889 q^{39} +(-0.866414 - 2.06139i) q^{40} -6.93512i q^{41} +(2.22529 + 2.22529i) q^{42} +(3.60160 + 3.60160i) q^{43} +(-1.58156 + 2.91525i) q^{44} +(5.83360 - 14.2929i) q^{45} -1.95646i q^{46} +(5.45059 + 5.45059i) q^{47} +(-2.22529 + 2.22529i) q^{48} -1.00000i q^{49} +(4.99973 - 0.0518870i) q^{50} +12.2856i q^{51} +(1.58156 - 1.58156i) q^{52} +(-3.66720 + 3.66720i) q^{53} -12.2856 q^{54} +(-4.69896 - 5.73758i) q^{55} +1.00000 q^{56} +(-9.17440 + 9.17440i) q^{57} +(6.52397 - 6.52397i) q^{58} +7.92746i q^{59} +(-2.72664 - 6.48728i) q^{60} +10.7554i q^{61} +(2.76045 - 2.76045i) q^{62} +(4.88177 + 4.88177i) q^{63} +1.00000i q^{64} +(1.93788 + 4.61065i) q^{65} +(-4.97725 + 9.17440i) q^{66} +(-3.07069 - 3.07069i) q^{67} +(2.76045 + 2.76045i) q^{68} -6.15707i q^{69} +(-0.844975 + 2.07027i) q^{70} -14.2077 q^{71} +(-4.88177 + 4.88177i) q^{72} +(-6.02736 - 6.02736i) q^{73} +3.02718 q^{74} +(15.7344 - 0.163291i) q^{75} +4.12278i q^{76} +(3.17972 - 0.943055i) q^{77} +(4.97725 - 4.97725i) q^{78} -11.7150 q^{79} +(-2.07027 - 0.844975i) q^{80} -17.9518 q^{81} +(-4.90387 - 4.90387i) q^{82} +(-6.05876 - 6.05876i) q^{83} +3.14704 q^{84} +(-8.04740 + 3.38237i) q^{85} +5.09344 q^{86} +(20.5312 - 20.5312i) q^{87} +(0.943055 + 3.17972i) q^{88} +3.23314i q^{89} +(-5.98161 - 14.2316i) q^{90} -2.23667 q^{91} +(-1.38343 - 1.38343i) q^{92} +(8.68726 - 8.68726i) q^{93} +7.70830 q^{94} +(-8.53526 - 3.48365i) q^{95} +3.14704i q^{96} +(3.90387 + 3.90387i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-10.9189 + 20.1265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 8 q^{5}+O(q^{10}) $ 16 * q - 8 * q^3 - 8 * q^5	$ 16 q - 8 q^{3} - 8 q^{5} - 8 q^{11} + 8 q^{12} + 24 q^{15} - 16 q^{16} + 16 q^{20} - 8 q^{22} + 32 q^{23} + 16 q^{25} + 16 q^{26} - 32 q^{27} - 24 q^{33} - 48 q^{36} - 48 q^{37} - 8 q^{38} - 8 q^{42} + 72 q^{45} + 8 q^{48} - 16 q^{53} - 48 q^{55} + 16 q^{56} + 32 q^{58} - 56 q^{60} - 32 q^{66} + 48 q^{67} - 16 q^{70} - 48 q^{71} + 112 q^{75} + 8 q^{77} + 32 q^{78} + 8 q^{80} - 80 q^{81} - 16 q^{82} + 32 q^{86} - 8 q^{88} - 16 q^{91} - 32 q^{92} + 32 q^{93}+O(q^{100}) $ 16 * q - 8 * q^3 - 8 * q^5 - 8 * q^11 + 8 * q^12 + 24 * q^15 - 16 * q^16 + 16 * q^20 - 8 * q^22 + 32 * q^23 + 16 * q^25 + 16 * q^26 - 32 * q^27 - 24 * q^33 - 48 * q^36 - 48 * q^37 - 8 * q^38 - 8 * q^42 + 72 * q^45 + 8 * q^48 - 16 * q^53 - 48 * q^55 + 16 * q^56 + 32 * q^58 - 56 * q^60 - 32 * q^66 + 48 * q^67 - 16 * q^70 - 48 * q^71 + 112 * q^75 + 8 * q^77 + 32 * q^78 + 8 * q^80 - 80 * q^81 - 16 * q^82 + 32 * q^86 - 8 * q^88 - 16 * q^91 - 32 * q^92 + 32 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	2.22529	−	2.22529i	1.28477	−	1.28477i	0.346856	−	0.937918i	$-0.387249\pi$
$3$	2.22529	−	2.22529i	1.28477	−	1.28477i	0.937918	−	0.346856i	$-0.112751\pi$
$4$		−	1.00000i		−	0.500000i
$5$	2.07027	+	0.844975i	0.925853	+	0.377884i
$5$	2.07027	+	0.844975i	0.925853	+	0.377884i
$6$		−	3.14704i		−	1.28477i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	6.90387i		−	2.30129i
$10$	2.06139	−	0.866414i	0.651869	−	0.273984i
$11$	−2.91525	−	1.58156i	−0.878979	−	0.476860i
$11$	−2.91525	−	1.58156i	−0.878979	−	0.476860i
$12$	−2.22529	−	2.22529i	−0.642387	−	0.642387i
$13$	1.58156	+	1.58156i	0.438647	+	0.438647i	0.891557	−	0.452909i	$-0.149614\pi$
$13$	1.58156	+	1.58156i	0.438647	+	0.438647i	−0.452909	+	0.891557i	$0.649614\pi$
$14$			1.00000i			0.267261i
$15$	6.48728	−	2.72664i	1.67501	−	0.704016i
$16$	−1.00000			−0.250000
$17$	−2.76045	+	2.76045i	−0.669508	+	0.669508i	−0.957602	−	0.288094i	$-0.906978\pi$
$17$	−2.76045	+	2.76045i	−0.669508	+	0.669508i	0.288094	+	0.957602i	$0.406978\pi$
$18$	−4.88177	−	4.88177i	−1.15064	−	1.15064i
$19$	−4.12278			−0.945830			−0.472915	−	0.881108i	$-0.656798\pi$
$19$	−4.12278			−0.945830			−0.472915	+	0.881108i	$0.656798\pi$
$20$	0.844975	−	2.07027i	0.188942	−	0.462926i
$21$			3.14704i			0.686741i
$22$	−3.17972	+	0.943055i	−0.677920	+	0.201060i
$23$	1.38343	−	1.38343i	0.288465	−	0.288465i	−0.548008	−	0.836473i	$-0.684614\pi$
$23$	1.38343	−	1.38343i	0.288465	−	0.288465i	0.836473	+	0.548008i	$0.184614\pi$
$24$	−3.14704			−0.642387
$25$	3.57203	+	3.49865i	0.714407	+	0.699731i
$26$	2.23667			0.438647
$27$	−8.68726	−	8.68726i	−1.67186	−	1.67186i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$	9.22628			1.71328			0.856639	−	0.515916i	$-0.172548\pi$
$29$	9.22628			1.71328			0.856639	+	0.515916i	$0.172548\pi$
$30$	2.65917	−	6.51522i	0.485496	−	1.18951i
$31$	3.90387			0.701156			0.350578	−	0.936534i	$-0.385985\pi$
$31$	3.90387			0.701156			0.350578	+	0.936534i	$0.385985\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−10.0067	+	2.96783i	−1.74195	+	0.516633i
$34$			3.90387i			0.669508i
$35$	−2.06139	+	0.866414i	−0.348438	+	0.146451i
$36$	−6.90387			−1.15064
$37$	2.14054	+	2.14054i	0.351903	+	0.351903i	0.860817	−	0.508915i	$-0.169953\pi$
$37$	2.14054	+	2.14054i	0.351903	+	0.351903i	−0.508915	+	0.860817i	$0.669953\pi$
$38$	−2.91525	+	2.91525i	−0.472915	+	0.472915i
$39$	7.03889			1.12712
$40$	−0.866414	−	2.06139i	−0.136992	−	0.325934i
$41$		−	6.93512i		−	1.08308i	−0.840674	−	0.541542i	$-0.817841\pi$
$41$		−	6.93512i		−	1.08308i	0.840674	−	0.541542i	$-0.182159\pi$
$42$	2.22529	+	2.22529i	0.343370	+	0.343370i
$43$	3.60160	+	3.60160i	0.549240	+	0.549240i	0.926221	−	0.376981i	$-0.123038\pi$
$43$	3.60160	+	3.60160i	0.549240	+	0.549240i	−0.376981	+	0.926221i	$0.623038\pi$
$44$	−1.58156	+	2.91525i	−0.238430	+	0.439490i
$45$	5.83360	−	14.2929i	0.869622	−	2.13066i
$46$		−	1.95646i		−	0.288465i
$47$	5.45059	+	5.45059i	0.795050	+	0.795050i	0.982310	−	0.187260i	$-0.0599608\pi$
$47$	5.45059	+	5.45059i	0.795050	+	0.795050i	−0.187260	+	0.982310i	$0.559961\pi$
$48$	−2.22529	+	2.22529i	−0.321194	+	0.321194i
$49$		−	1.00000i		−	0.142857i
$50$	4.99973	−	0.0518870i	0.707069	−	0.00733793i
$51$			12.2856i			1.72033i
$52$	1.58156	−	1.58156i	0.219324	−	0.219324i
$53$	−3.66720	+	3.66720i	−0.503729	+	0.503729i	−0.912594	−	0.408866i	$-0.865924\pi$
$53$	−3.66720	+	3.66720i	−0.503729	+	0.503729i	0.408866	+	0.912594i	$0.365924\pi$
$54$	−12.2856			−1.67186
$55$	−4.69896	−	5.73758i	−0.633608	−	0.773654i
$56$	1.00000			0.133631
$57$	−9.17440	+	9.17440i	−1.21518	+	1.21518i
$58$	6.52397	−	6.52397i	0.856639	−	0.856639i
$59$			7.92746i			1.03207i	0.856568	+	0.516033i	$0.172592\pi$
$59$			7.92746i			1.03207i	−0.856568	+	0.516033i	$0.827408\pi$
$60$	−2.72664	−	6.48728i	−0.352008	−	0.837504i
$61$			10.7554i			1.37708i	0.725196	+	0.688542i	$0.241749\pi$
$61$			10.7554i			1.37708i	−0.725196	+	0.688542i	$0.758251\pi$
$62$	2.76045	−	2.76045i	0.350578	−	0.350578i
$63$	4.88177	+	4.88177i	0.615046	+	0.615046i
$64$			1.00000i			0.125000i
$65$	1.93788	+	4.61065i	0.240365	+	0.571881i
$66$	−4.97725	+	9.17440i	−0.612657	+	1.12929i
$67$	−3.07069	−	3.07069i	−0.375144	−	0.375144i	0.494203	−	0.869347i	$-0.335460\pi$
$67$	−3.07069	−	3.07069i	−0.375144	−	0.375144i	−0.869347	+	0.494203i	$0.835460\pi$
$68$	2.76045	+	2.76045i	0.334754	+	0.334754i
$69$		−	6.15707i		−	0.741224i
$70$	−0.844975	+	2.07027i	−0.100994	+	0.247445i
$71$	−14.2077			−1.68614			−0.843072	−	0.537801i	$-0.819255\pi$
$71$	−14.2077			−1.68614			−0.843072	+	0.537801i	$0.819255\pi$
$72$	−4.88177	+	4.88177i	−0.575322	+	0.575322i
$73$	−6.02736	−	6.02736i	−0.705449	−	0.705449i	0.260126	−	0.965575i	$-0.416236\pi$
$73$	−6.02736	−	6.02736i	−0.705449	−	0.705449i	−0.965575	+	0.260126i	$0.916236\pi$
$74$	3.02718			0.351903
$75$	15.7344	−	0.163291i	1.81685	−	0.0188552i
$76$			4.12278i			0.472915i
$77$	3.17972	−	0.943055i	0.362363	−	0.107471i
$78$	4.97725	−	4.97725i	0.563562	−	0.563562i
$79$	−11.7150			−1.31804			−0.659021	−	0.752124i	$-0.729029\pi$
$79$	−11.7150			−1.31804			−0.659021	+	0.752124i	$0.729029\pi$
$80$	−2.07027	−	0.844975i	−0.231463	−	0.0944711i
$81$	−17.9518			−1.99465
$82$	−4.90387	−	4.90387i	−0.541542	−	0.541542i
$83$	−6.05876	−	6.05876i	−0.665035	−	0.665035i	0.291527	−	0.956562i	$-0.405837\pi$
$83$	−6.05876	−	6.05876i	−0.665035	−	0.665035i	−0.956562	+	0.291527i	$0.905837\pi$
$84$	3.14704			0.343370
$85$	−8.04740	+	3.38237i	−0.872863	+	0.366869i
$86$	5.09344			0.549240
$87$	20.5312	−	20.5312i	2.20118	−	2.20118i
$88$	0.943055	+	3.17972i	0.100530	+	0.338960i
$89$			3.23314i			0.342712i	0.985209	+	0.171356i	$0.0548149\pi$
$89$			3.23314i			0.342712i	−0.985209	+	0.171356i	$0.945185\pi$
$90$	−5.98161	−	14.2316i	−0.630517	−	1.50014i
$91$	−2.23667			−0.234467
$92$	−1.38343	−	1.38343i	−0.144232	−	0.144232i
$93$	8.68726	−	8.68726i	0.900827	−	0.900827i
$94$	7.70830			0.795050
$95$	−8.53526	−	3.48365i	−0.875700	−	0.357415i
$96$			3.14704i			0.321194i
$97$	3.90387	+	3.90387i	0.396378	+	0.396378i	0.876953	−	0.480575i	$-0.159572\pi$
$97$	3.90387	+	3.90387i	0.396378	+	0.396378i	−0.480575	+	0.876953i	$0.659572\pi$
$98$	−0.707107	−	0.707107i	−0.0714286	−	0.0714286i
$99$	−10.9189	+	20.1265i	−1.09739	+	2.02279i
$100$	3.49865	−	3.57203i	0.349865	−	0.357203i
$101$			12.5093i			1.24472i	0.782731	+	0.622360i	$0.213826\pi$
$101$			12.5093i			1.24472i	−0.782731	+	0.622360i	$0.786174\pi$
$102$	8.68726	+	8.68726i	0.860167	+	0.860167i
$103$	−8.83049	+	8.83049i	−0.870094	+	0.870094i	−0.992482	−	0.122388i	$-0.960945\pi$
$103$	−8.83049	+	8.83049i	−0.870094	+	0.870094i	0.122388	+	0.992482i	$0.460945\pi$
$104$		−	2.23667i		−	0.219324i
$105$	−2.65917	+	6.51522i	−0.259509	+	0.635821i
$106$			5.18620i			0.503729i
$107$	−0.422388	+	0.422388i	−0.0408338	+	0.0408338i	−0.727229	−	0.686395i	$-0.759192\pi$
$107$	−0.422388	+	0.422388i	−0.0408338	+	0.0408338i	0.686395	+	0.727229i	$0.259192\pi$
$108$	−8.68726	+	8.68726i	−0.835932	+	0.835932i
$109$	12.2856			1.17675			0.588375	−	0.808588i	$-0.299768\pi$
$109$	12.2856			1.17675			0.588375	+	0.808588i	$0.299768\pi$
$110$	−7.37975	−	0.734412i	−0.703631	−	0.0700234i
$111$	9.52666			0.904231
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	9.73436	−	9.73436i	0.915732	−	0.915732i	−0.0809839	−	0.996715i	$-0.525806\pi$
$113$	9.73436	−	9.73436i	0.915732	−	0.915732i	0.996715	+	0.0809839i	$0.0258062\pi$
$114$			12.9746i			1.21518i
$115$	4.03303	−	1.69511i	0.376082	−	0.158070i
$116$		−	9.22628i		−	0.856639i
$117$	10.9189	−	10.9189i	1.00945	−	1.00945i
$118$	5.60556	+	5.60556i	0.516033	+	0.516033i
$119$		−	3.90387i		−	0.357867i
$120$	−6.51522	−	2.65917i	−0.594756	−	0.242748i
$121$	5.99731	+	9.22130i	0.545210	+	0.838300i
$122$	7.60520	+	7.60520i	0.688542	+	0.688542i
$123$	−15.4327	−	15.4327i	−1.39152	−	1.39152i
$124$		−	3.90387i		−	0.350578i
$125$	4.43880	+	10.2614i	0.397018	+	0.917811i
$126$	6.90387			0.615046
$127$	13.4331	−	13.4331i	1.19200	−	1.19200i	0.215491	−	0.976506i	$-0.430865\pi$
$127$	13.4331	−	13.4331i	1.19200	−	1.19200i	0.976506	−	0.215491i	$-0.0691353\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	16.0293			1.41130
$130$	4.63051	+	1.88993i	0.406123	+	0.165758i
$131$		−	7.19093i		−	0.628274i	−0.949378	−	0.314137i	$-0.898285\pi$
$131$		−	7.19093i		−	0.628274i	0.949378	−	0.314137i	$-0.101715\pi$
$132$	2.96783	+	10.0067i	0.258317	+	0.870974i
$133$	2.91525	−	2.91525i	0.252784	−	0.252784i
$134$	−4.34261			−0.375144
$135$	−10.6444	−	25.3255i	−0.916128	−	2.17967i
$136$	3.90387			0.334754
$137$	5.37721	+	5.37721i	0.459406	+	0.459406i	0.898460	−	0.439054i	$-0.144686\pi$
$137$	5.37721	+	5.37721i	0.459406	+	0.459406i	−0.439054	+	0.898460i	$0.644686\pi$
$138$	−4.35371	−	4.35371i	−0.370612	−	0.370612i
$139$	−5.64575			−0.478867			−0.239433	−	0.970913i	$-0.576962\pi$
$139$	−5.64575			−0.478867			−0.239433	+	0.970913i	$0.576962\pi$
$140$	0.866414	+	2.06139i	0.0732253	+	0.174219i
$141$	24.2583			2.04292
$142$	−10.0464	+	10.0464i	−0.843072	+	0.843072i
$143$	−2.10930	−	7.11199i	−0.176389	−	0.594735i
$144$			6.90387i			0.575322i
$145$	19.1009	+	7.79598i	1.58624	+	0.647421i
$146$	−8.52397			−0.705449
$147$	−2.22529	−	2.22529i	−0.183539	−	0.183539i
$148$	2.14054	−	2.14054i	0.175951	−	0.175951i
$149$	−20.7387			−1.69898			−0.849492	−	0.527601i	$-0.823092\pi$
$149$	−20.7387			−1.69898			−0.849492	+	0.527601i	$0.823092\pi$
$150$	11.0104	−	11.2413i	0.898996	−	0.917851i
$151$		−	14.5718i		−	1.18584i	−0.805262	−	0.592919i	$-0.797976\pi$
$151$		−	14.5718i		−	1.18584i	0.805262	−	0.592919i	$-0.202024\pi$
$152$	2.91525	+	2.91525i	0.236458	+	0.236458i
$153$	19.0578	+	19.0578i	1.54073	+	1.54073i
$154$	1.58156	−	2.91525i	0.127446	−	0.234917i
$155$	8.08206	+	3.29867i	0.649167	+	0.264956i
$156$		−	7.03889i		−	0.563562i
$157$	−10.2960	−	10.2960i	−0.821709	−	0.821709i	0.164644	−	0.986353i	$-0.447352\pi$
$157$	−10.2960	−	10.2960i	−0.821709	−	0.821709i	−0.986353	+	0.164644i	$0.947352\pi$
$158$	−8.28377	+	8.28377i	−0.659021	+	0.659021i
$159$			16.3212i			1.29436i
$160$	−2.06139	+	0.866414i	−0.162967	+	0.0684960i
$161$			1.95646i			0.154191i
$162$	−12.6938	+	12.6938i	−0.997323	+	0.997323i
$163$	−12.6139	+	12.6139i	−0.987995	+	0.987995i	−0.999929	−	0.0119335i	$-0.996201\pi$
$163$	−12.6139	+	12.6139i	−0.987995	+	0.987995i	0.0119335	+	0.999929i	$0.496201\pi$
$164$	−6.93512			−0.541542
$165$	−23.2244	−	2.31122i	−1.80801	−	0.179929i
$166$	−8.56838			−0.665035
$167$	8.58525	−	8.58525i	0.664346	−	0.664346i	−0.292055	−	0.956402i	$-0.594339\pi$
$167$	8.58525	−	8.58525i	0.664346	−	0.664346i	0.956402	+	0.292055i	$0.0943391\pi$
$168$	2.22529	−	2.22529i	0.171685	−	0.171685i
$169$		−	7.99731i		−	0.615178i
$170$	−3.29867	+	8.08206i	−0.252997	+	0.619866i
$171$			28.4631i			2.17663i
$172$	3.60160	−	3.60160i	0.274620	−	0.274620i
$173$	−8.20306	−	8.20306i	−0.623667	−	0.623667i	0.322800	−	0.946467i	$-0.395376\pi$
$173$	−8.20306	−	8.20306i	−0.623667	−	0.623667i	−0.946467	+	0.322800i	$0.895376\pi$
$174$		−	29.0355i		−	2.20118i
$175$	−4.99973	+	0.0518870i	−0.377944	+	0.00392229i
$176$	2.91525	+	1.58156i	0.219745	+	0.119215i
$177$	17.6409	+	17.6409i	1.32597	+	1.32597i
$178$	2.28618	+	2.28618i	0.171356	+	0.171356i
$179$		−	12.2356i		−	0.914530i	−0.889331	−	0.457265i	$-0.848829\pi$
$179$		−	12.2356i		−	0.914530i	0.889331	−	0.457265i	$-0.151171\pi$
$180$	−14.2929	−	5.83360i	−1.06533	−	0.434811i
$181$	−7.66720			−0.569898			−0.284949	−	0.958543i	$-0.591977\pi$
$181$	−7.66720			−0.569898			−0.284949	+	0.958543i	$0.591977\pi$
$182$	−1.58156	+	1.58156i	−0.117233	+	0.117233i
$183$	23.9339	+	23.9339i	1.76924	+	1.76924i
$184$	−1.95646			−0.144232
$185$	2.62279	+	6.24020i	0.192831	+	0.458788i
$186$		−	12.2856i		−	0.900827i
$187$	12.4132	−	3.68156i	0.907745	−	0.269222i
$188$	5.45059	−	5.45059i	0.397525	−	0.397525i
$189$	12.2856			0.893649
$190$	−8.49865	+	3.57203i	−0.616557	+	0.259143i
$191$	−22.2077			−1.60689			−0.803446	−	0.595377i	$-0.797003\pi$
$191$	−22.2077			−1.60689			−0.803446	+	0.595377i	$0.797003\pi$
$192$	2.22529	+	2.22529i	0.160597	+	0.160597i
$193$	−5.22337	−	5.22337i	−0.375986	−	0.375986i	0.493666	−	0.869652i	$-0.335657\pi$
$193$	−5.22337	−	5.22337i	−0.375986	−	0.375986i	−0.869652	+	0.493666i	$0.835657\pi$
$194$	5.52091			0.396378
$195$	14.5724	+	5.94769i	1.04355	+	0.425923i
$196$	−1.00000			−0.0714286
$197$	17.6867	−	17.6867i	1.26012	−	1.26012i	0.309092	−	0.951032i	$-0.399975\pi$
$197$	17.6867	−	17.6867i	1.26012	−	1.26012i	0.951032	−	0.309092i	$-0.100025\pi$
$198$	6.51073	+	21.9524i	0.462697	+	1.56009i
$199$			3.75711i			0.266335i	0.991094	+	0.133167i	$0.0425147\pi$
$199$			3.75711i			0.266335i	−0.991094	+	0.133167i	$0.957485\pi$
$200$	−0.0518870	−	4.99973i	−0.00366897	−	0.353534i
$201$	−13.6664			−0.963951
$202$	8.84539	+	8.84539i	0.622360	+	0.622360i
$203$	−6.52397	+	6.52397i	−0.457893	+	0.457893i
$204$	12.2856			0.860167
$205$	5.86000	−	14.3576i	0.409280	−	1.00278i
$206$			12.4882i			0.870094i
$207$	−9.55101	−	9.55101i	−0.663841	−	0.663841i
$208$	−1.58156	−	1.58156i	−0.109662	−	0.109662i
$209$	12.0189	+	6.52044i	0.831365	+	0.451028i
$210$	2.72664	+	6.48728i	0.188156	+	0.447665i
$211$			14.6844i			1.01091i	0.862852	+	0.505457i	$0.168676\pi$
$211$			14.6844i			1.01091i	−0.862852	+	0.505457i	$0.831324\pi$
$212$	3.66720	+	3.66720i	0.251864	+	0.251864i
$213$	−31.6163	+	31.6163i	−2.16631	+	2.16631i
$214$			0.597347i			0.0408338i
$215$	4.41303	+	10.4996i	0.300966	+	0.716064i
$216$			12.2856i			0.835932i
$217$	−2.76045	+	2.76045i	−0.187392	+	0.187392i
$218$	8.68726	−	8.68726i	0.588375	−	0.588375i
$219$	−26.8253			−1.81268
$220$	−5.73758	+	4.69896i	−0.386827	+	0.316804i
$221$	−8.73167			−0.587356
$222$	6.73637	−	6.73637i	0.452115	−	0.452115i
$223$	−5.56947	+	5.56947i	−0.372959	+	0.372959i	−0.868554	−	0.495595i	$-0.834950\pi$
$223$	−5.56947	+	5.56947i	−0.372959	+	0.372959i	0.495595	+	0.868554i	$0.334950\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	24.1542	−	24.6609i	1.61028	−	1.64406i
$226$		−	13.7665i		−	0.915732i
$227$	13.9068	−	13.9068i	0.923027	−	0.923027i	−0.0742149	−	0.997242i	$-0.523645\pi$
$227$	13.9068	−	13.9068i	0.923027	−	0.923027i	0.997242	+	0.0742149i	$0.0236451\pi$
$228$	9.17440	+	9.17440i	0.607589	+	0.607589i
$229$		−	28.0669i		−	1.85471i	−0.374179	−	0.927357i	$-0.622075\pi$
$229$		−	28.0669i		−	1.85471i	0.374179	−	0.927357i	$-0.377925\pi$
$230$	1.65316	−	4.05041i	0.109006	−	0.267076i
$231$	4.97725	−	9.17440i	0.327479	−	0.603631i
$232$	−6.52397	−	6.52397i	−0.428319	−	0.428319i
$233$	7.66140	+	7.66140i	0.501915	+	0.501915i	0.912033	−	0.410118i	$-0.134512\pi$
$233$	7.66140	+	7.66140i	0.501915	+	0.501915i	−0.410118	+	0.912033i	$0.634512\pi$
$234$		−	15.4417i		−	1.00945i
$235$	6.67858	+	15.8898i	0.435662	+	1.03654i
$236$	7.92746			0.516033
$237$	−26.0694	+	26.0694i	−1.69339	+	1.69339i
$238$	−2.76045	−	2.76045i	−0.178934	−	0.178934i
$239$	−4.67613			−0.302474			−0.151237	−	0.988498i	$-0.548326\pi$
$239$	−4.67613			−0.302474			−0.151237	+	0.988498i	$0.548326\pi$
$240$	−6.48728	+	2.72664i	−0.418752	+	0.176004i
$241$			23.8981i			1.53941i	0.638400	+	0.769705i	$0.279597\pi$
$241$			23.8981i			1.53941i	−0.638400	+	0.769705i	$0.720403\pi$
$242$	10.7612	+	2.27970i	0.691755	+	0.146545i
$243$	−13.8863	+	13.8863i	−0.890805	+	0.890805i
$244$	10.7554			0.688542
$245$	0.844975	−	2.07027i	0.0539835	−	0.132265i
$246$	−21.8251			−1.39152
$247$	−6.52044	−	6.52044i	−0.414886	−	0.414886i
$248$	−2.76045	−	2.76045i	−0.175289	−	0.175289i
$249$	−26.9650			−1.70884
$250$	10.3946	+	4.11723i	0.657414	+	0.260396i
$251$	27.5429			1.73849			0.869247	−	0.494378i	$-0.164604\pi$
$251$	27.5429			1.73849			0.869247	+	0.494378i	$0.164604\pi$
$252$	4.88177	−	4.88177i	0.307523	−	0.307523i
$253$	−6.22101	+	1.84505i	−0.391112	+	0.115997i
$254$		−	18.9973i		−	1.19200i
$255$	−10.3811	+	25.4346i	−0.650087	+	1.59278i
$256$	1.00000			0.0625000
$257$	9.92662	+	9.92662i	0.619206	+	0.619206i	0.945328	−	0.326122i	$-0.105742\pi$
$257$	9.92662	+	9.92662i	0.619206	+	0.619206i	−0.326122	+	0.945328i	$0.605742\pi$
$258$	11.3344	−	11.3344i	0.705649	−	0.705649i
$259$	−3.02718			−0.188100
$260$	4.61065	−	1.93788i	0.285940	−	0.120182i
$261$		−	63.6971i		−	3.94275i
$262$	−5.08475	−	5.08475i	−0.314137	−	0.314137i
$263$	−15.6563	−	15.6563i	−0.965410	−	0.965410i	0.0340116	−	0.999421i	$-0.489172\pi$
$263$	−15.6563	−	15.6563i	−0.965410	−	0.965410i	−0.999421	+	0.0340116i	$0.989172\pi$
$264$	9.17440	+	4.97725i	0.564645	+	0.306328i
$265$	−10.6908	+	4.49340i	−0.656730	+	0.276027i
$266$		−	4.12278i		−	0.252784i
$267$	7.19469	+	7.19469i	0.440308	+	0.440308i
$268$	−3.07069	+	3.07069i	−0.187572	+	0.187572i
$269$			7.24103i			0.441493i	0.975331	+	0.220747i	$0.0708494\pi$
$269$			7.24103i			0.441493i	−0.975331	+	0.220747i	$0.929151\pi$
$270$	−25.4346	−	10.3811i	−1.54790	−	0.631771i
$271$			1.44258i			0.0876306i	0.999040	+	0.0438153i	$0.0139513\pi$
$271$			1.44258i			0.0876306i	−0.999040	+	0.0438153i	$0.986049\pi$
$272$	2.76045	−	2.76045i	0.167377	−	0.167377i
$273$	−4.97725	+	4.97725i	−0.301237	+	0.301237i
$274$	7.60452			0.459406
$275$	−4.88001	−	15.8488i	−0.294275	−	0.955721i
$276$	−6.15707			−0.370612
$277$	−16.4245	+	16.4245i	−0.986853	+	0.986853i	−0.999915	−	0.0130618i	$-0.995842\pi$
$277$	−16.4245	+	16.4245i	−0.986853	+	0.986853i	0.0130618	+	0.999915i	$0.495842\pi$
$278$	−3.99215	+	3.99215i	−0.239433	+	0.239433i
$279$		−	26.9518i		−	1.61356i
$280$	2.07027	+	0.844975i	0.123722	+	0.0504969i
$281$		−	23.1287i		−	1.37974i	−0.723932	−	0.689871i	$-0.757667\pi$
$281$		−	23.1287i		−	1.37974i	0.723932	−	0.689871i	$-0.242333\pi$
$282$	17.1532	−	17.1532i	1.02146	−	1.02146i
$283$	−3.86756	−	3.86756i	−0.229903	−	0.229903i	0.582749	−	0.812652i	$-0.301977\pi$
$283$	−3.86756	−	3.86756i	−0.229903	−	0.229903i	−0.812652	+	0.582749i	$0.801977\pi$
$284$			14.2077i			0.843072i
$285$	−26.7456	+	11.2413i	−1.58427	+	0.665879i
$286$	−6.52044	−	3.53744i	−0.385562	−	0.209173i
$287$	4.90387	+	4.90387i	0.289466	+	0.289466i
$288$	4.88177	+	4.88177i	0.287661	+	0.287661i
$289$			1.75980i			0.103518i
$290$	19.0190	−	7.99378i	1.11683	−	0.469411i
$291$	17.3745			1.01851
$292$	−6.02736	+	6.02736i	−0.352724	+	0.352724i
$293$	1.42953	+	1.42953i	0.0835139	+	0.0835139i	0.747630	−	0.664116i	$-0.231192\pi$
$293$	1.42953	+	1.42953i	0.0835139	+	0.0835139i	−0.664116	+	0.747630i	$0.731192\pi$
$294$	−3.14704			−0.183539
$295$	−6.69850	+	16.4120i	−0.390002	+	0.955542i
$296$		−	3.02718i		−	0.175951i
$297$	11.5860	+	39.0649i	0.672290	+	2.26678i
$298$	−14.6645	+	14.6645i	−0.849492	+	0.849492i
$299$	4.37596			0.253068
$300$	−0.163291	−	15.7344i	−0.00942759	−	0.908424i
$301$	−5.09344			−0.293581
$302$	−10.3038	−	10.3038i	−0.592919	−	0.592919i
$303$	27.8368	+	27.8368i	1.59918	+	1.59918i
$304$	4.12278			0.236458
$305$	−9.08802	+	22.2665i	−0.520379	+	1.27498i
$306$	26.9518			1.54073
$307$	−4.64835	+	4.64835i	−0.265295	+	0.265295i	−0.827201	−	0.561906i	$-0.810068\pi$
$307$	−4.64835	+	4.64835i	−0.265295	+	0.265295i	0.561906	+	0.827201i	$0.310068\pi$
$308$	−0.943055	−	3.17972i	−0.0537355	−	0.181182i
$309$			39.3009i			2.23575i
$310$	8.04740	−	3.38237i	0.457061	−	0.192106i
$311$	16.8121			0.953327			0.476663	−	0.879086i	$-0.341846\pi$
$311$	16.8121			0.953327			0.476663	+	0.879086i	$0.341846\pi$
$312$	−4.97725	−	4.97725i	−0.281781	−	0.281781i
$313$	−3.35715	+	3.35715i	−0.189757	+	0.189757i	−0.795591	−	0.605834i	$-0.792840\pi$
$313$	−3.35715	+	3.35715i	−0.189757	+	0.189757i	0.605834	+	0.795591i	$0.292840\pi$
$314$	−14.5607			−0.821709
$315$	5.98161	+	14.2316i	0.337025	+	0.801858i
$316$			11.7150i			0.659021i
$317$	6.33171	+	6.33171i	0.355624	+	0.355624i	0.862197	−	0.506573i	$-0.169088\pi$
$317$	6.33171	+	6.33171i	0.355624	+	0.355624i	−0.506573	+	0.862197i	$0.669088\pi$
$318$	11.5408	+	11.5408i	0.647178	+	0.647178i
$319$	−26.8969	−	14.5920i	−1.50594	−	0.816993i
$320$	−0.844975	+	2.07027i	−0.0472356	+	0.115732i
$321$			1.87988i			0.104924i
$322$	1.38343	+	1.38343i	0.0770955	+	0.0770955i
$323$	11.3807	−	11.3807i	0.633241	−	0.633241i
$324$			17.9518i			0.997323i
$325$	0.116054	+	11.1827i	0.00643752	+	0.620307i
$326$			17.8387i			0.987995i
$327$	27.3392	−	27.3392i	1.51186	−	1.51186i
$328$	−4.90387	+	4.90387i	−0.270771	+	0.270771i
$329$	−7.70830			−0.424972
$330$	−18.0564	+	14.7878i	−0.993971	+	0.814043i
$331$	−33.9210			−1.86447			−0.932233	−	0.361859i	$-0.882142\pi$
$331$	−33.9210			−1.86447			−0.932233	+	0.361859i	$0.882142\pi$
$332$	−6.05876	+	6.05876i	−0.332518	+	0.332518i
$333$	14.7780	−	14.7780i	0.809830	−	0.809830i
$334$		−	12.1414i		−	0.664346i
$335$	−3.76250	−	8.95181i	−0.205567	−	0.489089i
$336$		−	3.14704i		−	0.171685i
$337$	−20.0027	+	20.0027i	−1.08962	+	1.08962i	−0.0940508	+	0.995567i	$0.529982\pi$
$337$	−20.0027	+	20.0027i	−1.08962	+	1.08962i	−0.995567	+	0.0940508i	$0.970018\pi$
$338$	−5.65495	−	5.65495i	−0.307589	−	0.307589i
$339$		−	43.3236i		−	2.35302i
$340$	3.38237	+	8.04740i	0.183435	+	0.436431i
$341$	−11.3807	−	6.17422i	−0.616301	−	0.334353i
$342$	20.1265	+	20.1265i	1.08831	+	1.08831i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$		−	5.09344i		−	0.274620i
$345$	5.20257	−	12.7468i	0.280097	−	0.686265i
$346$	−11.6009			−0.623667
$347$	18.1500	−	18.1500i	0.974345	−	0.974345i	−0.0253338	−	0.999679i	$-0.508065\pi$
$347$	18.1500	−	18.1500i	0.974345	−	0.974345i	0.999679	+	0.0253338i	$0.00806486\pi$
$348$	−20.5312	−	20.5312i	−1.10059	−	1.10059i
$349$	10.6850			0.571952			0.285976	−	0.958237i	$-0.407682\pi$
$349$	10.6850			0.571952			0.285976	+	0.958237i	$0.407682\pi$
$350$	−3.49865	+	3.57203i	−0.187011	+	0.190933i
$351$		−	27.4789i		−	1.46672i
$352$	3.17972	−	0.943055i	0.169480	−	0.0502650i
$353$	9.09344	−	9.09344i	0.483995	−	0.483995i	−0.422410	−	0.906405i	$-0.638816\pi$
$353$	9.09344	−	9.09344i	0.483995	−	0.483995i	0.906405	+	0.422410i	$0.138816\pi$
$354$	24.9480			1.32597
$355$	−29.4138	−	12.0052i	−1.56112	−	0.637168i
$356$	3.23314			0.171356
$357$	−8.68726	−	8.68726i	−0.459778	−	0.459778i
$358$	−8.65186	−	8.65186i	−0.457265	−	0.457265i
$359$	7.50456			0.396075			0.198038	−	0.980194i	$-0.436543\pi$
$359$	7.50456			0.396075			0.198038	+	0.980194i	$0.436543\pi$
$360$	−14.2316	+	5.98161i	−0.750069	+	0.315258i
$361$	−2.00269			−0.105405
$362$	−5.42153	+	5.42153i	−0.284949	+	0.284949i
$363$	33.8659	+	7.17432i	1.77750	+	0.376554i
$364$			2.23667i			0.117233i
$365$	−7.38528	−	17.5712i	−0.386563	−	0.919720i
$366$	33.8476			1.76924
$367$	10.8532	+	10.8532i	0.566535	+	0.566535i	0.931156	−	0.364621i	$-0.118802\pi$
$367$	10.8532	+	10.8532i	0.566535	+	0.566535i	−0.364621	+	0.931156i	$0.618802\pi$
$368$	−1.38343	+	1.38343i	−0.0721162	+	0.0721162i
$369$	−47.8792			−2.49249
$370$	6.26708	+	2.55789i	0.325810	+	0.132978i
$371$		−	5.18620i		−	0.269254i
$372$	−8.68726	−	8.68726i	−0.450413	−	0.450413i
$373$	−9.54490	−	9.54490i	−0.494216	−	0.494216i	0.415416	−	0.909632i	$-0.363636\pi$
$373$	−9.54490	−	9.54490i	−0.494216	−	0.494216i	−0.909632	+	0.415416i	$0.863636\pi$
$374$	6.17422	−	11.3807i	0.319261	−	0.588484i
$375$	32.7123	+	12.9571i	1.68926	+	0.669101i
$376$		−	7.70830i		−	0.397525i
$377$	14.5920	+	14.5920i	0.751524	+	0.751524i
$378$	8.68726	−	8.68726i	0.446824	−	0.446824i
$379$		−	9.80068i		−	0.503427i	−0.967802	−	0.251714i	$-0.919006\pi$
$379$		−	9.80068i		−	0.503427i	0.967802	−	0.251714i	$-0.0809941\pi$
$380$	−3.48365	+	8.53526i	−0.178707	+	0.437850i
$381$		−	59.7853i		−	3.06289i
$382$	−15.7032	+	15.7032i	−0.803446	+	0.803446i
$383$	8.54403	−	8.54403i	0.436579	−	0.436579i	−0.454280	−	0.890859i	$-0.650103\pi$
$383$	8.54403	−	8.54403i	0.436579	−	0.436579i	0.890859	+	0.454280i	$0.150103\pi$
$384$	3.14704			0.160597
$385$	7.37975	+	0.734412i	0.376107	+	0.0374291i
$386$	−7.38696			−0.375986
$387$	24.8650	−	24.8650i	1.26396	−	1.26396i
$388$	3.90387	−	3.90387i	0.198189	−	0.198189i
$389$		−	7.53371i		−	0.381974i	−0.981593	−	0.190987i	$-0.938831\pi$
$389$		−	7.53371i		−	0.381974i	0.981593	−	0.190987i	$-0.0611689\pi$
$390$	14.5099	−	6.09859i	0.734737	−	0.308814i
$391$			7.63778i			0.386259i
$392$	−0.707107	+	0.707107i	−0.0357143	+	0.0357143i
$393$	−16.0019	−	16.0019i	−0.807191	−	0.807191i
$394$		−	25.0127i		−	1.26012i
$395$	−24.2533	−	9.89890i	−1.22031	−	0.498068i
$396$	20.1265	+	10.9189i	1.01139	+	0.548696i
$397$	0.435686	+	0.435686i	0.0218665	+	0.0218665i	0.717955	−	0.696089i	$-0.245078\pi$
$397$	0.435686	+	0.435686i	0.0218665	+	0.0218665i	−0.696089	+	0.717955i	$0.745078\pi$
$398$	2.65668	+	2.65668i	0.133167	+	0.133167i
$399$		−	12.9746i		−	0.649540i
$400$	−3.57203	−	3.49865i	−0.178602	−	0.174933i
$401$	−19.7517			−0.986354			−0.493177	−	0.869929i	$-0.664165\pi$
$401$	−19.7517			−0.986354			−0.493177	+	0.869929i	$0.664165\pi$
$402$	−9.66358	+	9.66358i	−0.481976	+	0.481976i
$403$	6.17422	+	6.17422i	0.307560	+	0.307560i
$404$	12.5093			0.622360
$405$	−37.1651	−	15.1688i	−1.84675	−	0.753745i
$406$			9.22628i			0.457893i
$407$	−2.85480	−	9.62560i	−0.141507	−	0.477123i
$408$	8.68726	−	8.68726i	0.430083	−	0.430083i
$409$	−10.9124			−0.539583			−0.269792	−	0.962919i	$-0.586955\pi$
$409$	−10.9124			−0.539583			−0.269792	+	0.962919i	$0.586955\pi$
$410$	−6.00868	−	14.2960i	−0.296748	−	0.706028i
$411$	23.9317			1.18047
$412$	8.83049	+	8.83049i	0.435047	+	0.435047i
$413$	−5.60556	−	5.60556i	−0.275831	−	0.275831i
$414$	−13.5072			−0.663841
$415$	−7.42376	−	17.6628i	−0.364418	−	0.867031i
$416$	−2.23667			−0.109662
$417$	−12.5635	+	12.5635i	−0.615236	+	0.615236i
$418$	13.1093	−	3.88801i	0.641197	−	0.190169i
$419$			5.85215i			0.285896i	0.989730	+	0.142948i	$0.0456582\pi$
$419$			5.85215i			0.285896i	−0.989730	+	0.142948i	$0.954342\pi$
$420$	6.51522	+	2.65917i	0.317910	+	0.129754i
$421$	−15.8375			−0.771875			−0.385937	−	0.922525i	$-0.626122\pi$
$421$	−15.8375			−0.771875			−0.385937	+	0.922525i	$0.626122\pi$
$422$	10.3834	+	10.3834i	0.505457	+	0.505457i
$423$	37.6302	−	37.6302i	1.82964	−	1.82964i
$424$	5.18620			0.251864
$425$	−19.5183	+	0.202560i	−0.946776	+	0.00982561i
$426$			44.7122i			2.16631i
$427$	−7.60520	−	7.60520i	−0.368041	−	0.368041i
$428$	0.422388	+	0.422388i	0.0204169	+	0.0204169i
$429$	−20.5201	−	11.1325i	−0.990720	−	0.537480i
$430$	10.5448	+	4.30383i	0.508515	+	0.207549i
$431$		−	3.19648i		−	0.153969i	−0.997032	−	0.0769846i	$-0.975471\pi$
$431$		−	3.19648i		−	0.153969i	0.997032	−	0.0769846i	$-0.0245292\pi$
$432$	8.68726	+	8.68726i	0.417966	+	0.417966i
$433$	15.5719	−	15.5719i	0.748338	−	0.748338i	−0.225829	−	0.974167i	$-0.572509\pi$
$433$	15.5719	−	15.5719i	0.748338	−	0.748338i	0.974167	+	0.225829i	$0.0725091\pi$
$434$			3.90387i			0.187392i
$435$	59.8535	−	25.1568i	2.86975	−	1.20617i
$436$		−	12.2856i		−	0.588375i
$437$	−5.70357	+	5.70357i	−0.272839	+	0.272839i
$438$	−18.9683	+	18.9683i	−0.906342	+	0.906342i
$439$	28.9831			1.38329			0.691644	−	0.722238i	$-0.256887\pi$
$439$	28.9831			1.38329			0.691644	+	0.722238i	$0.256887\pi$
$440$	−0.734412	+	7.37975i	−0.0350117	+	0.351816i
$441$	−6.90387			−0.328756
$442$	−6.17422	+	6.17422i	−0.293678	+	0.293678i
$443$	14.8548	−	14.8548i	0.705775	−	0.705775i	−0.259869	−	0.965644i	$-0.583679\pi$
$443$	14.8548	−	14.8548i	0.705775	−	0.705775i	0.965644	+	0.259869i	$0.0836794\pi$
$444$		−	9.52666i		−	0.452115i
$445$	−2.73193	+	6.69348i	−0.129506	+	0.317301i
$446$			7.87642i			0.372959i
$447$	−46.1498	+	46.1498i	−2.18281	+	2.18281i
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$		−	10.7089i		−	0.505385i	−0.967547	−	0.252693i	$-0.918684\pi$
$449$		−	10.7089i		−	0.505385i	0.967547	−	0.252693i	$-0.0813161\pi$
$450$	−0.358221	−	34.5175i	−0.0168867	−	1.62717i
$451$	−10.9683	+	20.2176i	−0.516479	+	0.952008i
$452$	−9.73436	−	9.73436i	−0.457866	−	0.457866i
$453$	−32.4266	−	32.4266i	−1.52353	−	1.52353i
$454$		−	19.6672i		−	0.923027i
$455$	−4.63051	−	1.88993i	−0.217082	−	0.0886013i
$456$	12.9746			0.607589
$457$	−15.8229	+	15.8229i	−0.740164	+	0.740164i	−0.972609	−	0.232446i	$-0.925327\pi$
$457$	−15.8229	+	15.8229i	−0.740164	+	0.740164i	0.232446	+	0.972609i	$0.425327\pi$
$458$	−19.8463	−	19.8463i	−0.927357	−	0.927357i
$459$	47.9615			2.23865
$460$	−1.69511	−	4.03303i	−0.0790348	−	0.188041i
$461$			22.8434i			1.06392i	0.846768	+	0.531962i	$0.178545\pi$
$461$			22.8434i			1.06392i	−0.846768	+	0.531962i	$0.821455\pi$
$462$	−2.96783	−	10.0067i	−0.138076	−	0.465555i
$463$	−0.862988	+	0.862988i	−0.0401064	+	0.0401064i	−0.726876	−	0.686769i	$-0.759028\pi$
$463$	−0.862988	+	0.862988i	−0.0401064	+	0.0401064i	0.686769	+	0.726876i	$0.259028\pi$
$464$	−9.22628			−0.428319
$465$	25.3255	−	10.6444i	1.17444	−	0.493624i
$466$	10.8349			0.501915
$467$	−24.1744	−	24.1744i	−1.11866	−	1.11866i	−0.991939	−	0.126720i	$-0.959555\pi$
$467$	−24.1744	−	24.1744i	−1.11866	−	1.11866i	−0.126720	−	0.991939i	$-0.540445\pi$
$468$	−10.9189	−	10.9189i	−0.504727	−	0.504727i
$469$	4.34261			0.200523
$470$	15.9583	+	6.51332i	0.736099	+	0.300437i
$471$	−45.8232			−2.11142
$472$	5.60556	−	5.60556i	0.258017	−	0.258017i
$473$	−4.80339	−	16.1957i	−0.220860	−	0.744680i
$474$			36.8677i			1.69339i
$475$	−14.7267	−	14.4242i	−0.675708	−	0.661827i
$476$	−3.90387			−0.178934
$477$	25.3179	+	25.3179i	1.15923	+	1.15923i
$478$	−3.30652	+	3.30652i	−0.151237	+	0.151237i
$479$	9.69812			0.443118			0.221559	−	0.975147i	$-0.428885\pi$
$479$	9.69812			0.443118			0.221559	+	0.975147i	$0.428885\pi$
$480$	−2.65917	+	6.51522i	−0.121374	+	0.297378i
$481$			6.77080i			0.308722i
$482$	16.8985	+	16.8985i	0.769705	+	0.769705i
$483$	4.35371	+	4.35371i	0.198101	+	0.198101i
$484$	9.22130	−	5.99731i	0.419150	−	0.272605i
$485$	4.78339	+	11.3807i	0.217203	+	0.516773i
$486$			19.6382i			0.890805i
$487$	−6.57107	−	6.57107i	−0.297764	−	0.297764i	0.542374	−	0.840137i	$-0.317526\pi$
$487$	−6.57107	−	6.57107i	−0.297764	−	0.297764i	−0.840137	+	0.542374i	$0.817526\pi$
$488$	7.60520	−	7.60520i	0.344271	−	0.344271i
$489$			56.1392i			2.53870i
$490$	−0.866414	−	2.06139i	−0.0391406	−	0.0931241i
$491$		−	6.25193i		−	0.282146i	−0.989999	−	0.141073i	$-0.954945\pi$
$491$		−	6.25193i		−	0.282146i	0.989999	−	0.141073i	$-0.0450552\pi$
$492$	−15.4327	+	15.4327i	−0.695759	+	0.695759i
$493$	−25.4687	+	25.4687i	−1.14705	+	1.14705i
$494$	−9.22130			−0.414886
$495$	−39.6115	+	32.4410i	−1.78040	+	1.45811i
$496$	−3.90387			−0.175289
$497$	10.0464	−	10.0464i	0.450641	−	0.450641i
$498$	−19.0672	+	19.0672i	−0.854420	+	0.854420i
$499$			30.8329i			1.38027i	0.723680	+	0.690136i	$0.242449\pi$
$499$			30.8329i			1.38027i	−0.723680	+	0.690136i	$0.757551\pi$
$500$	10.2614	−	4.43880i	0.458905	−	0.198509i
$501$		−	38.2094i		−	1.70707i
$502$	19.4758	−	19.4758i	0.869247	−	0.869247i
$503$	19.2257	+	19.2257i	0.857234	+	0.857234i	0.991011	−	0.133778i	$-0.0427108\pi$
$503$	19.2257	+	19.2257i	0.857234	+	0.857234i	−0.133778	+	0.991011i	$0.542711\pi$
$504$		−	6.90387i		−	0.307523i
$505$	−10.5700	+	25.8976i	−0.470360	+	1.15243i
$506$	−3.09427	+	5.70357i	−0.137557	+	0.253555i
$507$	−17.7964	−	17.7964i	−0.790364	−	0.790364i
$508$	−13.4331	−	13.4331i	−0.595999	−	0.595999i
$509$		−	40.8197i		−	1.80930i	−0.426156	−	0.904650i	$-0.640133\pi$
$509$		−	40.8197i		−	1.80930i	0.426156	−	0.904650i	$-0.359867\pi$
$510$	10.6444	+	25.3255i	0.471344	+	1.12143i
$511$	8.52397			0.377078
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	35.8156	+	35.8156i	1.58130	+	1.58130i
$514$	14.0384			0.619206
$515$	−25.7430	+	10.8199i	−1.13437	+	0.476784i
$516$		−	16.0293i		−	0.705649i
$517$	−7.26934	−	24.5103i	−0.319705	−	1.07796i
$518$	−2.14054	+	2.14054i	−0.0940499	+	0.0940499i
$519$	−36.5084			−1.60254
$520$	1.88993	−	4.63051i	0.0828790	−	0.203061i
$521$	−0.939626			−0.0411657			−0.0205829	−	0.999788i	$-0.506552\pi$
$521$	−0.939626			−0.0411657			−0.0205829	+	0.999788i	$0.506552\pi$
$522$	−45.0406	−	45.0406i	−1.97137	−	1.97137i
$523$	−4.96198	−	4.96198i	−0.216972	−	0.216972i	0.590249	−	0.807221i	$-0.299030\pi$
$523$	−4.96198	−	4.96198i	−0.216972	−	0.216972i	−0.807221	+	0.590249i	$0.799030\pi$
$524$	−7.19093			−0.314137
$525$	−11.0104	+	11.2413i	−0.480534	+	0.490612i
$526$	−22.1414			−0.965410
$527$	−10.7764	+	10.7764i	−0.469429	+	0.469429i
$528$	10.0067	−	2.96783i	0.435487	−	0.129158i
$529$			19.1723i			0.833576i
$530$	−4.38221	+	10.7368i	−0.190351	+	0.466379i
$531$	54.7301			2.37508
$532$	−2.91525	−	2.91525i	−0.126392	−	0.126392i
$533$	10.9683	−	10.9683i	0.475091	−	0.475091i
$534$	10.1748			0.440308
$535$	−1.23137	+	0.517550i	−0.0532366	+	0.0223756i
$536$			4.34261i			0.187572i
$537$	−27.2278	−	27.2278i	−1.17496	−	1.17496i
$538$	5.12018	+	5.12018i	0.220747	+	0.220747i
$539$	−1.58156	+	2.91525i	−0.0681228	+	0.125568i
$540$	−25.3255	+	10.6444i	−1.08984	+	0.458064i
$541$			10.5183i			0.452218i	0.974102	+	0.226109i	$0.0726006\pi$
$541$			10.5183i			0.452218i	−0.974102	+	0.226109i	$0.927399\pi$
$542$	1.02006	+	1.02006i	0.0438153	+	0.0438153i
$543$	−17.0618	+	17.0618i	−0.732191	+	0.732191i
$544$		−	3.90387i		−	0.167377i
$545$	25.4346	+	10.3811i	1.08950	+	0.444676i
$546$			7.03889i			0.301237i
$547$	−6.47829	+	6.47829i	−0.276992	+	0.276992i	−0.831907	−	0.554915i	$-0.812751\pi$
$547$	−6.47829	+	6.47829i	−0.276992	+	0.276992i	0.554915	+	0.831907i	$0.312751\pi$
$548$	5.37721	−	5.37721i	0.229703	−	0.229703i
$549$	74.2537			3.16907
$550$	−14.6575	−	7.75613i	−0.624998	−	0.330723i
$551$	−38.0379			−1.62047
$552$	−4.35371	+	4.35371i	−0.185306	+	0.185306i
$553$	8.28377	−	8.28377i	0.352262	−	0.352262i
$554$			23.2278i			0.986853i
$555$	19.7228	+	8.04979i	0.837184	+	0.341695i
$556$			5.64575i			0.239433i
$557$	13.5850	−	13.5850i	0.575614	−	0.575614i	−0.358078	−	0.933692i	$-0.616568\pi$
$557$	13.5850	−	13.5850i	0.575614	−	0.575614i	0.933692	+	0.358078i	$0.116568\pi$
$558$	−19.0578	−	19.0578i	−0.806781	−	0.806781i
$559$			11.3923i			0.481845i
$560$	2.06139	−	0.866414i	0.0871096	−	0.0366127i
$561$	19.4305	−	35.8156i	0.820358	−	1.51214i
$562$	−16.3545	−	16.3545i	−0.689871	−	0.689871i
$563$	14.0945	+	14.0945i	0.594011	+	0.594011i	0.938712	−	0.344702i	$-0.112020\pi$
$563$	14.0945	+	14.0945i	0.594011	+	0.594011i	−0.344702	+	0.938712i	$0.612020\pi$
$564$		−	24.2583i		−	1.02146i
$565$	28.3780	−	11.9275i	1.19387	−	0.501792i
$566$	−5.46955			−0.229903
$567$	12.6938	−	12.6938i	0.533091	−	0.533091i
$568$	10.0464	+	10.0464i	0.421536	+	0.421536i
$569$	−21.3400			−0.894619			−0.447309	−	0.894379i	$-0.647618\pi$
$569$	−21.3400			−0.894619			−0.447309	+	0.894379i	$0.647618\pi$
$570$	−10.9632	+	26.8608i	−0.459197	+	1.12508i
$571$			37.1655i			1.55533i	0.628680	+	0.777664i	$0.283596\pi$
$571$			37.1655i			1.55533i	−0.628680	+	0.777664i	$0.716404\pi$
$572$	−7.11199	+	2.10930i	−0.297367	+	0.0881943i
$573$	−49.4187	+	49.4187i	−2.06449	+	2.06449i
$574$	6.93512			0.289466
$575$	9.78179	−	0.101515i	0.407929	−	0.00423347i
$576$	6.90387			0.287661
$577$	−19.7344	−	19.7344i	−0.821552	−	0.821552i	0.164778	−	0.986331i	$-0.447309\pi$
$577$	−19.7344	−	19.7344i	−0.821552	−	0.821552i	−0.986331	+	0.164778i	$0.947309\pi$
$578$	1.24437	+	1.24437i	0.0517589	+	0.0517589i
$579$	−23.2471			−0.966115
$580$	7.79598	−	19.1009i	0.323711	−	0.793122i
$581$	8.56838			0.355476
$582$	12.2856	−	12.2856i	0.509256	−	0.509256i
$583$	16.4907	−	4.89087i	0.682975	−	0.202559i
$584$			8.52397i			0.352724i
$585$	31.8313	−	13.3789i	1.31606	−	0.553149i
$586$	2.02166			0.0835139
$587$	−24.4555	−	24.4555i	−1.00939	−	1.00939i	−0.999956	−	0.00943040i	$-0.996998\pi$
$587$	−24.4555	−	24.4555i	−1.00939	−	1.00939i	−0.00943040	−	0.999956i	$-0.503002\pi$
$588$	−2.22529	+	2.22529i	−0.0917696	+	0.0917696i
$589$	−16.0948			−0.663174
$590$	6.86846	+	16.3416i	0.282770	+	0.672772i
$591$		−	78.7161i		−	3.23795i
$592$	−2.14054	−	2.14054i	−0.0879756	−	0.0879756i
$593$	30.8716	+	30.8716i	1.26775	+	1.26775i	0.947250	+	0.320495i	$0.103849\pi$
$593$	30.8716	+	30.8716i	1.26775	+	1.26775i	0.320495	+	0.947250i	$0.396151\pi$
$594$	35.8156	+	19.4305i	1.46953	+	0.797244i
$595$	3.29867	−	8.08206i	0.135232	−	0.331332i
$596$			20.7387i			0.849492i
$597$	8.36068	+	8.36068i	0.342180	+	0.342180i
$598$	3.09427	−	3.09427i	0.126534	−	0.126534i
$599$			21.3065i			0.870561i	0.900295	+	0.435280i	$0.143351\pi$
$599$			21.3065i			0.870561i	−0.900295	+	0.435280i	$0.856649\pi$
$600$	−11.2413	−	11.0104i	−0.458926	−	0.449498i
$601$			16.9962i			0.693290i	0.937996	+	0.346645i	$0.112679\pi$
$601$			16.9962i			0.693290i	−0.937996	+	0.346645i	$0.887321\pi$
$602$	−3.60160	+	3.60160i	−0.146790	+	0.146790i
$603$	−21.1996	+	21.1996i	−0.863315	+	0.863315i
$604$	−14.5718			−0.592919
$605$	4.62428	+	24.1581i	0.188004	+	0.982168i
$606$	39.3672			1.59918
$607$	3.70538	−	3.70538i	0.150397	−	0.150397i	−0.627899	−	0.778295i	$-0.716085\pi$
$607$	3.70538	−	3.70538i	0.150397	−	0.150397i	0.778295	+	0.627899i	$0.216085\pi$
$608$	2.91525	−	2.91525i	0.118229	−	0.118229i
$609$			29.0355i			1.17658i
$610$	9.31860	+	22.1710i	0.377299	+	0.897678i
$611$			17.2409i			0.697493i
$612$	19.0578	−	19.0578i	0.770366	−	0.770366i
$613$	−13.2403	−	13.2403i	−0.534771	−	0.534771i	0.387218	−	0.921988i	$-0.373436\pi$
$613$	−13.2403	−	13.2403i	−0.534771	−	0.534771i	−0.921988	+	0.387218i	$0.873436\pi$
$614$			6.57376i			0.265295i
$615$	−18.9096	−	44.9900i	−0.762508	−	1.81417i
$616$	−2.91525	−	1.58156i	−0.117459	−	0.0637230i
$617$	−25.1525	−	25.1525i	−1.01260	−	1.01260i	−0.999920	−	0.0126799i	$-0.995964\pi$
$617$	−25.1525	−	25.1525i	−1.01260	−	1.01260i	−0.0126799	−	0.999920i	$-0.504036\pi$
$618$	27.7899	+	27.7899i	1.11787	+	1.11787i
$619$		−	9.30030i		−	0.373811i	−0.982378	−	0.186905i	$-0.940154\pi$
$619$		−	9.30030i		−	0.373811i	0.982378	−	0.186905i	$-0.0598458\pi$
$620$	3.29867	−	8.08206i	0.132478	−	0.324583i
$621$	−24.0364			−0.964548
$622$	11.8880	−	11.8880i	0.476663	−	0.476663i
$623$	−2.28618	−	2.28618i	−0.0915938	−	0.0915938i
$624$	−7.03889			−0.281781
$625$	0.518842	+	24.9946i	0.0207537	+	0.999785i
$626$			4.74773i			0.189757i
$627$	41.2555	−	12.2357i	1.64759	−	0.488647i
$628$	−10.2960	+	10.2960i	−0.410854	+	0.410854i
$629$	−11.8177			−0.471203
$630$	14.2929	+	5.83360i	0.569442	+	0.232416i
$631$	16.2478			0.646815			0.323408	−	0.946260i	$-0.395171\pi$
$631$	16.2478			0.646815			0.323408	+	0.946260i	$0.395171\pi$
$632$	8.28377	+	8.28377i	0.329511	+	0.329511i
$633$	32.6771	+	32.6771i	1.29880	+	1.29880i
$634$	8.95439			0.355624
$635$	39.1609	−	16.4595i	1.55405	−	0.653177i
$636$	16.3212			0.647178
$637$	1.58156	−	1.58156i	0.0626639	−	0.0626639i
$638$	−29.3370	+	8.70089i	−1.16146	+	0.344472i
$639$			98.0881i			3.88031i
$640$	0.866414	+	2.06139i	0.0342480	+	0.0814836i
$641$	−25.9440			−1.02473			−0.512363	−	0.858769i	$-0.671230\pi$
$641$	−25.9440			−1.02473			−0.512363	+	0.858769i	$0.671230\pi$
$642$	1.32927	+	1.32927i	0.0524622	+	0.0524622i
$643$	28.4381	−	28.4381i	1.12149	−	1.12149i	0.129972	−	0.991518i	$-0.458511\pi$
$643$	28.4381	−	28.4381i	1.12149	−	1.12149i	0.991518	−	0.129972i	$-0.0414889\pi$
$644$	1.95646			0.0770955
$645$	33.1849	+	13.5443i	1.30665	+	0.533308i
$646$		−	16.0948i		−	0.633241i
$647$	29.0101	+	29.0101i	1.14050	+	1.14050i	0.988358	+	0.152145i	$0.0486180\pi$
$647$	29.0101	+	29.0101i	1.14050	+	1.14050i	0.152145	+	0.988358i	$0.451382\pi$
$648$	12.6938	+	12.6938i	0.498661	+	0.498661i
$649$	12.5378	−	23.1105i	0.492151	−	0.907166i
$650$	7.98946	+	7.82533i	0.313372	+	0.306935i
$651$			12.2856i			0.481512i
$652$	12.6139	+	12.6139i	0.493998	+	0.493998i
$653$	28.2965	−	28.2965i	1.10733	−	1.10733i	0.113828	−	0.993500i	$-0.463689\pi$
$653$	28.2965	−	28.2965i	1.10733	−	1.10733i	0.993500	−	0.113828i	$-0.0363112\pi$
$654$		−	38.6634i		−	1.51186i
$655$	6.07616	−	14.8872i	0.237415	−	0.581690i
$656$			6.93512i			0.270771i
$657$	−41.6121	+	41.6121i	−1.62344	+	1.62344i
$658$	−5.45059	+	5.45059i	−0.212486	+	0.212486i
$659$	5.21956			0.203325			0.101663	−	0.994819i	$-0.467584\pi$
$659$	5.21956			0.203325			0.101663	+	0.994819i	$0.467584\pi$
$660$	−2.31122	+	23.2244i	−0.0899643	+	0.904007i
$661$	6.23474			0.242503			0.121252	−	0.992622i	$-0.461309\pi$
$661$	6.23474			0.242503			0.121252	+	0.992622i	$0.461309\pi$
$662$	−23.9858	+	23.9858i	−0.932233	+	0.932233i
$663$	−19.4305	+	19.4305i	−0.754619	+	0.754619i
$664$			8.56838i			0.332518i
$665$	8.49865	−	3.57203i	0.329564	−	0.138518i
$666$		−	20.8993i		−	0.809830i
$667$	12.7639	−	12.7639i	0.494220	−	0.494220i
$668$	−8.58525	−	8.58525i	−0.332173	−	0.332173i
$669$			24.7874i			0.958337i
$670$	−8.99037	−	3.66940i	−0.347328	−	0.141761i
$671$	17.0103	−	31.3545i	0.656676	−	1.21043i
$672$	−2.22529	−	2.22529i	−0.0858426	−	0.0858426i
$673$	5.36642	+	5.36642i	0.206860	+	0.206860i	0.802932	−	0.596071i	$-0.203272\pi$
$673$	5.36642	+	5.36642i	0.206860	+	0.206860i	−0.596071	+	0.802932i	$0.703272\pi$
$674$			28.2881i			1.08962i
$675$	−0.637465	−	61.4249i	−0.0245360	−	2.36424i
$676$	−7.99731			−0.307589
$677$	10.8856	−	10.8856i	0.418366	−	0.418366i	−0.466274	−	0.884640i	$-0.654404\pi$
$677$	10.8856	−	10.8856i	0.418366	−	0.418366i	0.884640	+	0.466274i	$0.154404\pi$
$678$	−30.6344	−	30.6344i	−1.17651	−	1.17651i
$679$	−5.52091			−0.211873
$680$	8.08206	+	3.29867i	0.309933	+	0.126498i
$681$		−	61.8935i		−	2.37176i
$682$	−12.4132	+	3.68156i	−0.475327	+	0.140974i
$683$	16.8040	−	16.8040i	0.642985	−	0.642985i	−0.308303	−	0.951288i	$-0.599761\pi$
$683$	16.8040	−	16.8040i	0.642985	−	0.642985i	0.951288	+	0.308303i	$0.0997610\pi$
$684$	28.4631			1.08831
$685$	6.58866	+	15.6759i	0.251740	+	0.598945i
$686$	1.00000			0.0381802
$687$	−62.4571	−	62.4571i	−2.38289	−	2.38289i
$688$	−3.60160	−	3.60160i	−0.137310	−	0.137310i
$689$	−11.5998			−0.441918
$690$	−5.33457	−	12.6921i	−0.203084	−	0.483181i
$691$	5.60413			0.213191			0.106596	−	0.994302i	$-0.466005\pi$
$691$	5.60413			0.213191			0.106596	+	0.994302i	$0.466005\pi$
$692$	−8.20306	+	8.20306i	−0.311833	+	0.311833i
$693$	−6.51073	−	21.9524i	−0.247322	−	0.833903i
$694$		−	25.6680i		−	0.974345i
$695$	−11.6882	−	4.77052i	−0.443360	−	0.180956i
$696$	−29.0355			−1.10059
$697$	19.1441	+	19.1441i	0.725133	+	0.725133i
$698$	7.55540	−	7.55540i	0.285976	−	0.285976i
$699$	34.0977			1.28969
$700$	0.0518870	+	4.99973i	0.00196114	+	0.188972i
$701$			44.3044i			1.67335i	0.547697	+	0.836676i	$0.315505\pi$
$701$			44.3044i			1.67335i	−0.547697	+	0.836676i	$0.684495\pi$
$702$	−19.4305	−	19.4305i	−0.733358	−	0.733358i
$703$	−8.82497	−	8.82497i	−0.332840	−	0.332840i
$704$	1.58156	−	2.91525i	0.0596075	−	0.109872i
$705$	50.2213	+	20.4977i	1.89144	+	0.771988i
$706$		−	12.8601i		−	0.483995i
$707$	−8.84539	−	8.84539i	−0.332665	−	0.332665i
$708$	17.6409	−	17.6409i	0.662986	−	0.662986i
$709$		−	13.6279i		−	0.511807i	−0.966702	−	0.255904i	$-0.917627\pi$
$709$		−	13.6279i		−	0.511807i	0.966702	−	0.255904i	$-0.0823730\pi$
$710$	−29.2876	+	12.3097i	−1.09914	+	0.461977i
$711$			80.8790i			3.03320i
$712$	2.28618	−	2.28618i	0.0856781	−	0.0856781i
$713$	5.40072	−	5.40072i	0.202259	−	0.202259i
$714$	−12.2856			−0.459778
$715$	1.64264	−	16.5061i	0.0614311	−	0.617291i
$716$	−12.2356			−0.457265
$717$	−10.4058	+	10.4058i	−0.388610	+	0.388610i
$718$	5.30652	−	5.30652i	0.198038	−	0.198038i
$719$			14.8104i			0.552336i	0.961109	+	0.276168i	$0.0890646\pi$
$719$			14.8104i			0.552336i	−0.961109	+	0.276168i	$0.910935\pi$
$720$	−5.83360	+	14.2929i	−0.217405	+	0.532664i
$721$		−	12.4882i		−	0.465085i
$722$	−1.41612	+	1.41612i	−0.0527024	+	0.0527024i
$723$	53.1802	+	53.1802i	1.97779	+	1.97779i
$724$			7.66720i			0.284949i
$725$	32.9566	+	32.2796i	1.22398	+	1.19883i
$726$	29.0198	−	18.8738i	1.07703	−	0.700472i
$727$	−23.2654	−	23.2654i	−0.862865	−	0.862865i	0.128805	−	0.991670i	$-0.458886\pi$
$727$	−23.2654	−	23.2654i	−0.862865	−	0.862865i	−0.991670	+	0.128805i	$0.958886\pi$
$728$	1.58156	+	1.58156i	0.0586167	+	0.0586167i
$729$			7.94668i			0.294321i
$730$	−17.6469	−	7.20254i	−0.653142	−	0.266578i
$731$	−19.8841			−0.735441
$732$	23.9339	−	23.9339i	0.884621	−	0.884621i
$733$	24.5188	+	24.5188i	0.905623	+	0.905623i	0.995915	−	0.0902927i	$-0.0287803\pi$
$733$	24.5188	+	24.5188i	0.905623	+	0.905623i	−0.0902927	+	0.995915i	$0.528780\pi$
$734$	15.3488			0.566535
$735$	−2.72664	−	6.48728i	−0.100574	−	0.239287i
$736$			1.95646i			0.0721162i
$737$	4.09532	+	13.8083i	0.150853	+	0.508635i
$738$	−33.8557	+	33.8557i	−1.24624	+	1.24624i
$739$	−7.21925			−0.265565			−0.132782	−	0.991145i	$-0.542391\pi$
$739$	−7.21925			−0.265565			−0.132782	+	0.991145i	$0.542391\pi$
$740$	6.24020	−	2.62279i	0.229394	−	0.0964157i
$741$	−29.0198			−1.06607
$742$	−3.66720	−	3.66720i	−0.134627	−	0.134627i
$743$	−2.04782	−	2.04782i	−0.0751271	−	0.0751271i	0.668545	−	0.743672i	$-0.266918\pi$
$743$	−2.04782	−	2.04782i	−0.0751271	−	0.0751271i	−0.743672	+	0.668545i	$0.766918\pi$
$744$	−12.2856			−0.450413
$745$	−42.9348	−	17.5237i	−1.57301	−	0.642020i
$746$	−13.4985			−0.494216
$747$	−41.8289	+	41.8289i	−1.53044	+	1.53044i
$748$	−3.68156	−	12.4132i	−0.134611	−	0.453873i
$749$		−	0.597347i		−	0.0218266i
$750$	32.2932	−	13.9691i	1.17918	−	0.510078i
$751$	−25.8549			−0.943459			−0.471730	−	0.881743i	$-0.656370\pi$
$751$	−25.8549			−0.943459			−0.471730	+	0.881743i	$0.656370\pi$
$752$	−5.45059	−	5.45059i	−0.198763	−	0.198763i
$753$	61.2911	−	61.2911i	2.23357	−	2.23357i
$754$	20.6362			0.751524
$755$	12.3128	−	30.1676i	0.448110	−	1.09791i
$756$		−	12.2856i		−	0.446824i
$757$	28.8452	+	28.8452i	1.04840	+	1.04840i	0.998768	+	0.0496275i	$0.0158034\pi$
$757$	28.8452	+	28.8452i	1.04840	+	1.04840i	0.0496275	+	0.998768i	$0.484197\pi$
$758$	−6.93013	−	6.93013i	−0.251714	−	0.251714i
$759$	−9.73781	+	17.9494i	−0.353460	+	0.651521i
$760$	3.57203	+	8.49865i	0.129571	+	0.308279i
$761$			35.8344i			1.29900i	0.760363	+	0.649498i	$0.225021\pi$
$761$			35.8344i			1.29900i	−0.760363	+	0.649498i	$0.774979\pi$
$762$	−42.2746	−	42.2746i	−1.53145	−	1.53145i
$763$	−8.68726	+	8.68726i	−0.314500	+	0.314500i
$764$			22.2077i			0.803446i
$765$	23.3514	+	55.5582i	0.844272	+	2.00871i
$766$		−	12.0831i		−	0.436579i
$767$	−12.5378	+	12.5378i	−0.452713	+	0.452713i
$768$	2.22529	−	2.22529i	0.0802984	−	0.0802984i
$769$	11.9050			0.429305			0.214652	−	0.976691i	$-0.431138\pi$
$769$	11.9050			0.429305			0.214652	+	0.976691i	$0.431138\pi$
$770$	5.73758	−	4.69896i	0.206768	−	0.169339i
$771$	44.1793			1.59108
$772$	−5.22337	+	5.22337i	−0.187993	+	0.187993i
$773$	−23.2034	+	23.2034i	−0.834567	+	0.834567i	−0.988138	−	0.153570i	$-0.950923\pi$
$773$	−23.2034	+	23.2034i	−0.834567	+	0.834567i	0.153570	+	0.988138i	$0.450923\pi$
$774$		−	35.1644i		−	1.26396i
$775$	13.9448	+	13.6583i	0.500910	+	0.490620i
$776$		−	5.52091i		−	0.198189i
$777$	−6.73637	+	6.73637i	−0.241666	+	0.241666i
$778$	−5.32714	−	5.32714i	−0.190987	−	0.190987i
$779$			28.5920i			1.02441i
$780$	5.94769	−	14.5724i	0.212962	−	0.521776i
$781$	41.4189	+	22.4704i	1.48209	+	0.804054i
$782$	5.40072	+	5.40072i	0.193130	+	0.193130i
$783$	−80.1511	−	80.1511i	−2.86437	−	2.86437i
$784$			1.00000i			0.0357143i
$785$	−12.6156	−	30.0153i	−0.450270	−	1.07129i
$786$	−22.6302			−0.807191
$787$	−29.5830	+	29.5830i	−1.05452	+	1.05452i	−0.0560954	+	0.998425i	$0.517865\pi$
$787$	−29.5830	+	29.5830i	−1.05452	+	1.05452i	−0.998425	+	0.0560954i	$0.982135\pi$
$788$	−17.6867	−	17.6867i	−0.630062	−	0.630062i
$789$	−69.6798			−2.48067
$790$	−24.1492	+	10.1501i	−0.859191	+	0.361123i
$791$			13.7665i			0.489479i
$792$	21.9524	−	6.51073i	0.780045	−	0.231349i
$793$	−17.0103	+	17.0103i	−0.604054	+	0.604054i
$794$	0.616153			0.0218665
$795$	−13.7910	+	33.7893i	−0.489117	+	1.19838i
$796$	3.75711			0.133167
$797$	14.4647	+	14.4647i	0.512364	+	0.512364i	0.915250	−	0.402886i	$-0.131993\pi$
$797$	14.4647	+	14.4647i	0.512364	+	0.512364i	−0.402886	+	0.915250i	$0.631993\pi$
$798$	−9.17440	−	9.17440i	−0.324770	−	0.324770i
$799$	−30.0922			−1.06458
$800$	−4.99973	+	0.0518870i	−0.176767	+	0.00183448i
$801$	22.3212			0.788681
$802$	−13.9666	+	13.9666i	−0.493177	+	0.493177i
$803$	8.03857	+	27.1039i	0.283675	+	0.956475i
$804$			13.6664i			0.481976i
$805$	−1.65316	+	4.05041i	−0.0582664	+	0.142758i
$806$	8.73167			0.307560
$807$	16.1134	+	16.1134i	0.567219	+	0.567219i
$808$	8.84539	−	8.84539i	0.311180	−	0.311180i
$809$	23.8253			0.837652			0.418826	−	0.908066i	$-0.362442\pi$
$809$	23.8253			0.837652			0.418826	+	0.908066i	$0.362442\pi$
$810$	−37.0057	+	15.5537i	−1.30025	+	0.546501i
$811$			19.5470i			0.686388i	0.939265	+	0.343194i	$0.111509\pi$
$811$			19.5470i			0.686388i	−0.939265	+	0.343194i	$0.888491\pi$
$812$	6.52397	+	6.52397i	0.228946	+	0.228946i
$813$	3.21017	+	3.21017i	0.112585	+	0.112585i
$814$	−8.82497	−	4.78768i	−0.309315	−	0.167808i
$815$	−36.7725	+	15.4557i	−1.28809	+	0.541390i
$816$		−	12.2856i		−	0.430083i
$817$	−14.8486	−	14.8486i	−0.519487	−	0.519487i
$818$	−7.71623	+	7.71623i	−0.269792	+	0.269792i
$819$			15.4417i			0.539576i
$820$	−14.3576	−	5.86000i	−0.501388	−	0.204640i
$821$		−	7.72090i		−	0.269461i	−0.990882	−	0.134731i	$-0.956983\pi$
$821$		−	7.72090i		−	0.269461i	0.990882	−	0.134731i	$-0.0430169\pi$
$822$	16.9223	−	16.9223i	0.590233	−	0.590233i
$823$	30.4590	−	30.4590i	1.06173	−	1.06173i	0.0637683	−	0.997965i	$-0.479688\pi$
$823$	30.4590	−	30.4590i	1.06173	−	1.06173i	0.997965	−	0.0637683i	$-0.0203119\pi$
$824$	12.4882			0.435047
$825$	−46.1278	−	24.4089i	−1.60596	−	0.849808i
$826$	−7.92746			−0.275831
$827$	32.3550	−	32.3550i	1.12509	−	1.12509i	0.134129	−	0.990964i	$-0.457176\pi$
$827$	32.3550	−	32.3550i	1.12509	−	1.12509i	0.990964	−	0.134129i	$-0.0428237\pi$
$828$	−9.55101	+	9.55101i	−0.331921	+	0.331921i
$829$			26.3534i			0.915290i	0.889135	+	0.457645i	$0.151307\pi$
$829$			26.3534i			0.915290i	−0.889135	+	0.457645i	$0.848693\pi$
$830$	−17.7389	−	7.24007i	−0.615724	−	0.251306i
$831$			73.0987i			2.53577i
$832$	−1.58156	+	1.58156i	−0.0548309	+	0.0548309i
$833$	2.76045	+	2.76045i	0.0956440	+	0.0956440i
$834$			17.7674i			0.615236i
$835$	25.0281	−	10.5195i	0.866133	−	0.364041i
$836$	6.52044	−	12.0189i	0.225514	−	0.415683i
$837$	−33.9139	−	33.9139i	−1.17224	−	1.17224i
$838$	4.13809	+	4.13809i	0.142948	+	0.142948i
$839$		−	41.7918i		−	1.44281i	−0.692511	−	0.721407i	$-0.743496\pi$
$839$		−	41.7918i		−	1.44281i	0.692511	−	0.721407i	$-0.256504\pi$
$840$	6.48728	−	2.72664i	0.223832	−	0.0940780i
$841$	56.1243			1.93532
$842$	−11.1988	+	11.1988i	−0.385937	+	0.385937i
$843$	−51.4682	−	51.4682i	−1.77266	−	1.77266i
$844$	14.6844			0.505457
$845$	6.75753	−	16.5566i	0.232466	−	0.569564i
$846$		−	53.2171i		−	1.82964i
$847$	−10.7612	−	2.27970i	−0.369758	−	0.0783316i
$848$	3.66720	−	3.66720i	0.125932	−	0.125932i
$849$	−17.2129			−0.590746
$850$	−13.6583	+	13.9448i	−0.468475	+	0.478301i
$851$	5.92257			0.203023
$852$	31.6163	+	31.6163i	1.08316	+	1.08316i
$853$	−3.00806	−	3.00806i	−0.102994	−	0.102994i	0.653732	−	0.756726i	$-0.273202\pi$
$853$	−3.00806	−	3.00806i	−0.102994	−	0.102994i	−0.756726	+	0.653732i	$0.773202\pi$
$854$	−10.7554			−0.368041
$855$	−24.0506	+	58.9264i	−0.822515	+	2.01524i
$856$	0.597347			0.0204169
$857$	17.9833	−	17.9833i	0.614297	−	0.614297i	−0.329766	−	0.944063i	$-0.606970\pi$
$857$	17.9833	−	17.9833i	0.614297	−	0.614297i	0.944063	+	0.329766i	$0.106970\pi$
$858$	−22.3817	+	6.63806i	−0.764100	+	0.226620i
$859$			4.95264i			0.168982i	0.996424	+	0.0844909i	$0.0269264\pi$
$859$			4.95264i			0.168982i	−0.996424	+	0.0844909i	$0.973074\pi$
$860$	10.4996	−	4.41303i	0.358032	−	0.150483i
$861$	21.8251			0.743798
$862$	−2.26026	−	2.26026i	−0.0769846	−	0.0769846i
$863$	8.16951	−	8.16951i	0.278093	−	0.278093i	−0.554254	−	0.832347i	$-0.686996\pi$
$863$	8.16951	−	8.16951i	0.278093	−	0.278093i	0.832347	+	0.554254i	$0.186996\pi$
$864$	12.2856			0.417966
$865$	−10.0512	−	23.9139i	−0.341750	−	0.813098i
$866$		−	22.0220i		−	0.748338i
$867$	3.91608	+	3.91608i	0.132997	+	0.132997i
$868$	2.76045	+	2.76045i	0.0936959	+	0.0936959i
$869$	34.1522	+	18.5281i	1.15853	+	0.628521i
$870$	24.5343	−	60.1113i	0.831790	−	2.03796i
$871$		−	9.71298i		−	0.329112i
$872$	−8.68726	−	8.68726i	−0.294188	−	0.294188i
$873$	26.9518	−	26.9518i	0.912180	−	0.912180i
$874$			8.06607i			0.272839i
$875$	−10.3946	−	4.11723i	−0.351403	−	0.139188i
$876$			26.8253i			0.906342i
$877$	−0.936314	+	0.936314i	−0.0316171	+	0.0316171i	−0.722739	−	0.691122i	$-0.757117\pi$
$877$	−0.936314	+	0.936314i	−0.0316171	+	0.0316171i	0.691122	+	0.722739i	$0.257117\pi$
$878$	20.4942	−	20.4942i	0.691644	−	0.691644i
$879$	6.36224			0.214593
$880$	4.69896	+	5.73758i	0.158402	+	0.193414i
$881$	−39.4249			−1.32826			−0.664129	−	0.747618i	$-0.731197\pi$
$881$	−39.4249			−1.32826			−0.664129	+	0.747618i	$0.731197\pi$
$882$	−4.88177	+	4.88177i	−0.164378	+	0.164378i
$883$	8.47956	−	8.47956i	0.285360	−	0.285360i	−0.549882	−	0.835242i	$-0.685327\pi$
$883$	8.47956	−	8.47956i	0.285360	−	0.285360i	0.835242	+	0.549882i	$0.185327\pi$
$884$			8.73167i			0.293678i
$885$	21.6153	+	51.4276i	0.726591	+	1.72872i
$886$		−	21.0079i		−	0.705775i
$887$	−4.44520	+	4.44520i	−0.149255	+	0.149255i	−0.777785	−	0.628530i	$-0.783657\pi$
$887$	−4.44520	+	4.44520i	−0.149255	+	0.149255i	0.628530	+	0.777785i	$0.283657\pi$
$888$	−6.73637	−	6.73637i	−0.226058	−	0.226058i
$889$			18.9973i			0.637149i
$890$	2.80124	+	6.66477i	0.0938978	+	0.223403i
$891$	52.3339	+	28.3919i	1.75325	+	0.951166i
$892$	5.56947	+	5.56947i	0.186480	+	0.186480i
$893$	−22.4716	−	22.4716i	−0.751983	−	0.751983i
$894$			65.2657i			2.18281i
$895$	10.3388	−	25.3309i	0.345587	−	0.846720i
$896$	−1.00000			−0.0334077
$897$	9.73781	−	9.73781i	0.325136	−	0.325136i
$898$	−7.57235	−	7.57235i	−0.252693	−	0.252693i
$899$	36.0182			1.20127
$900$	−24.6609	−	24.1542i	−0.822028	−	0.805142i
$901$		−	20.2463i		−	0.674501i
$902$	6.54020	+	22.0518i	0.217765	+	0.734244i
$903$	−11.3344	+	11.3344i	−0.377185	+	0.377185i
$904$	−13.7665			−0.457866
$905$	−15.8732	−	6.47859i	−0.527642	−	0.215356i
$906$	−45.8581			−1.52353
$907$	30.0504	+	30.0504i	0.997806	+	0.997806i	0.999998	−	0.00219146i	$-0.000697565\pi$
$907$	30.0504	+	30.0504i	0.997806	+	0.997806i	−0.00219146	+	0.999998i	$0.500698\pi$
$908$	−13.9068	−	13.9068i	−0.461514	−	0.461514i
$909$	86.3624			2.86446
$910$	−4.61065	+	1.93788i	−0.152841	+	0.0642402i
$911$	35.6225			1.18023			0.590114	−	0.807320i	$-0.299083\pi$
$911$	35.6225			1.18023			0.590114	+	0.807320i	$0.299083\pi$
$912$	9.17440	−	9.17440i	0.303795	−	0.303795i
$913$	8.08045	+	27.2451i	0.267424	+	0.901680i
$914$			22.3770i			0.740164i
$915$	29.3260	+	69.7731i	0.969489	+	2.30663i
$916$	−28.0669			−0.927357
$917$	5.08475	+	5.08475i	0.167913	+	0.167913i
$918$	33.9139	−	33.9139i	1.11933	−	1.11933i
$919$	39.9989			1.31944			0.659721	−	0.751510i	$-0.270674\pi$
$919$	39.9989			1.31944			0.659721	+	0.751510i	$0.270674\pi$
$920$	−4.05041	−	1.65316i	−0.133538	−	0.0545032i
$921$			20.6879i			0.681689i
$922$	16.1527	+	16.1527i	0.531962	+	0.531962i
$923$	−22.4704	−	22.4704i	−0.739622	−	0.739622i
$924$	−9.17440	−	4.97725i	−0.301815	−	0.163739i
$925$	0.157071	+	15.1351i	0.00516447	+	0.497639i
$926$			1.22045i			0.0401064i
$927$	60.9646	+	60.9646i	2.00234	+	2.00234i
$928$	−6.52397	+	6.52397i	−0.214160	+	0.214160i
$929$			6.66174i			0.218565i	0.994011	+	0.109282i	$0.0348553\pi$
$929$			6.66174i			0.218565i	−0.994011	+	0.109282i	$0.965145\pi$
$930$	10.3811	−	25.4346i	0.340408	−	0.834033i
$931$			4.12278i			0.135119i
$932$	7.66140	−	7.66140i	0.250957	−	0.250957i
$933$	37.4119	−	37.4119i	1.22481	−	1.22481i
$934$	−34.1878			−1.11866
$935$	28.8096	+	2.86705i	0.942173	+	0.0937625i
$936$	−15.4417			−0.504727
$937$	22.2171	−	22.2171i	0.725802	−	0.725802i	−0.243979	−	0.969781i	$-0.578453\pi$
$937$	22.2171	−	22.2171i	0.725802	−	0.725802i	0.969781	+	0.243979i	$0.0784527\pi$
$938$	3.07069	−	3.07069i	0.100261	−	0.100261i
$939$			14.9413i			0.487591i
$940$	15.8898	−	6.67858i	0.518268	−	0.217831i
$941$			15.6402i			0.509857i	0.966960	+	0.254928i	$0.0820519\pi$
$941$			15.6402i			0.509857i	−0.966960	+	0.254928i	$0.917948\pi$
$942$	−32.4019	+	32.4019i	−1.05571	+	1.05571i
$943$	−9.59424	−	9.59424i	−0.312431	−	0.312431i
$944$		−	7.92746i		−	0.258017i
$945$	25.4346	+	10.3811i	0.827387	+	0.337696i
$946$	−14.8486	−	8.05560i	−0.482770	−	0.261910i
$947$	4.12401	+	4.12401i	0.134012	+	0.134012i	0.770931	−	0.636919i	$-0.219791\pi$
$947$	4.12401	+	4.12401i	0.134012	+	0.134012i	−0.636919	+	0.770931i	$0.719791\pi$
$948$	26.0694	+	26.0694i	0.846694	+	0.846694i
$949$		−	19.0653i		−	0.618886i
$950$	−20.6128	+	0.213919i	−0.668767	+	0.00694044i
$951$	28.1798			0.913793
$952$	−2.76045	+	2.76045i	−0.0894668	+	0.0894668i
$953$	27.5538	+	27.5538i	0.892556	+	0.892556i	0.994763	−	0.102207i	$-0.0325905\pi$
$953$	27.5538	+	27.5538i	0.892556	+	0.892556i	−0.102207	+	0.994763i	$0.532591\pi$
$954$	35.8049			1.15923
$955$	−45.9759	−	18.7650i	−1.48775	−	0.607220i
$956$			4.67613i			0.151237i
$957$	−92.3249	+	27.3821i	−2.98444	+	0.885136i
$958$	6.85760	−	6.85760i	0.221559	−	0.221559i
$959$	−7.60452			−0.245563
$960$	2.72664	+	6.48728i	0.0880019	+	0.209376i
$961$	−15.7598			−0.508381
$962$	4.78768	+	4.78768i	0.154361	+	0.154361i
$963$	2.91611	+	2.91611i	0.0939704	+	0.0939704i
$964$	23.8981			0.769705
$965$	−6.40016	−	15.2274i	−0.206028	−	0.490187i
$966$	6.15707			0.198101
$967$	−15.7565	+	15.7565i	−0.506694	+	0.506694i	−0.913510	−	0.406816i	$-0.866639\pi$
$967$	−15.7565	+	15.7565i	−0.506694	+	0.506694i	0.406816	+	0.913510i	$0.366639\pi$
$968$	2.27970	−	10.7612i	0.0732725	−	0.345877i
$969$		−	50.6510i		−	1.62714i
$970$	11.4298	+	4.66503i	0.366988	+	0.149785i
$971$	−30.5405			−0.980091			−0.490046	−	0.871697i	$-0.663020\pi$
$971$	−30.5405			−0.980091			−0.490046	+	0.871697i	$0.663020\pi$
$972$	13.8863	+	13.8863i	0.445402	+	0.445402i
$973$	3.99215	−	3.99215i	0.127982	−	0.127982i
$974$	−9.29289			−0.297764
$975$	25.1432	+	24.6266i	0.805226	+	0.788684i
$976$		−	10.7554i		−	0.344271i
$977$	25.4712	+	25.4712i	0.814894	+	0.814894i	0.985363	−	0.170469i	$-0.0545282\pi$
$977$	25.4712	+	25.4712i	0.814894	+	0.814894i	−0.170469	+	0.985363i	$0.554528\pi$
$978$	39.6964	+	39.6964i	1.26935	+	1.26935i
$979$	5.11342	−	9.42540i	0.163426	−	0.301237i
$980$	−2.07027	−	0.844975i	−0.0661323	−	0.0269917i
$981$		−	84.8184i		−	2.70804i
$982$	−4.42078	−	4.42078i	−0.141073	−	0.141073i
$983$	−1.64285	+	1.64285i	−0.0523988	+	0.0523988i	−0.732821	−	0.680422i	$-0.761797\pi$
$983$	−1.64285	+	1.64285i	−0.0523988	+	0.0523988i	0.680422	+	0.732821i	$0.261797\pi$
$984$			21.8251i			0.695759i
$985$	51.5610	−	21.6714i	1.64287	−	0.690508i
$986$			36.0182i			1.14705i
$987$	−17.1532	+	17.1532i	−0.545993	+	0.545993i
$988$	−6.52044	+	6.52044i	−0.207443	+	0.207443i
$989$	9.96513			0.316873
$990$	−5.07028	+	50.9488i	−0.161144	+	1.61926i
$991$	−43.1539			−1.37083			−0.685414	−	0.728154i	$-0.740379\pi$
$991$	−43.1539			−1.37083			−0.685414	+	0.728154i	$0.740379\pi$
$992$	−2.76045	+	2.76045i	−0.0876445	+	0.0876445i
$993$	−75.4842	+	75.4842i	−2.39542	+	2.39542i
$994$		−	14.2077i		−	0.450641i
$995$	−3.17467	+	7.77823i	−0.100644	+	0.246587i
$996$			26.9650i			0.854420i
$997$	40.5419	−	40.5419i	1.28398	−	1.28398i	0.345591	−	0.938385i	$-0.387678\pi$
$997$	40.5419	−	40.5419i	1.28398	−	1.28398i	0.938385	−	0.345591i	$-0.112322\pi$
$998$	21.8022	+	21.8022i	0.690136	+	0.690136i
$999$		−	37.1908i		−	1.17667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.e.197.8	yes	16
5.3	odd	4	inner	770.2.m.e.43.4	✓	16
11.10	odd	2	inner	770.2.m.e.197.4	yes	16
55.43	even	4	inner	770.2.m.e.43.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.e.43.4	✓	16	5.3	odd	4	inner
770.2.m.e.43.8	yes	16	55.43	even	4	inner
770.2.m.e.197.4	yes	16	11.10	odd	2	inner
770.2.m.e.197.8	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(2.22529 - 2.22529i) q^{3} -1.00000i q^{4} +(2.07027 + 0.844975i) q^{5} -3.14704i q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -6.90387i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(2.22529 - 2.22529i) q^{3} -1.00000i q^{4} +(2.07027 + 0.844975i) q^{5} -3.14704i q^{6} +(-0.707107 + 0.707107i) q^{7} +(-0.707107 - 0.707107i) q^{8} -6.90387i q^{9} +(2.06139 - 0.866414i) q^{10} +(-2.91525 - 1.58156i) q^{11} +(-2.22529 - 2.22529i) q^{12} +(1.58156 + 1.58156i) q^{13} +1.00000i q^{14} +(6.48728 - 2.72664i) q^{15} -1.00000 q^{16} +(-2.76045 + 2.76045i) q^{17} +(-4.88177 - 4.88177i) q^{18} -4.12278 q^{19} +(0.844975 - 2.07027i) q^{20} +3.14704i q^{21} +(-3.17972 + 0.943055i) q^{22} +(1.38343 - 1.38343i) q^{23} -3.14704 q^{24} +(3.57203 + 3.49865i) q^{25} +2.23667 q^{26} +(-8.68726 - 8.68726i) q^{27} +(0.707107 + 0.707107i) q^{28} +9.22628 q^{29} +(2.65917 - 6.51522i) q^{30} +3.90387 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-10.0067 + 2.96783i) q^{33} +3.90387i q^{34} +(-2.06139 + 0.866414i) q^{35} -6.90387 q^{36} +(2.14054 + 2.14054i) q^{37} +(-2.91525 + 2.91525i) q^{38} +7.03889 q^{39} +(-0.866414 - 2.06139i) q^{40} -6.93512i q^{41} +(2.22529 + 2.22529i) q^{42} +(3.60160 + 3.60160i) q^{43} +(-1.58156 + 2.91525i) q^{44} +(5.83360 - 14.2929i) q^{45} -1.95646i q^{46} +(5.45059 + 5.45059i) q^{47} +(-2.22529 + 2.22529i) q^{48} -1.00000i q^{49} +(4.99973 - 0.0518870i) q^{50} +12.2856i q^{51} +(1.58156 - 1.58156i) q^{52} +(-3.66720 + 3.66720i) q^{53} -12.2856 q^{54} +(-4.69896 - 5.73758i) q^{55} +1.00000 q^{56} +(-9.17440 + 9.17440i) q^{57} +(6.52397 - 6.52397i) q^{58} +7.92746i q^{59} +(-2.72664 - 6.48728i) q^{60} +10.7554i q^{61} +(2.76045 - 2.76045i) q^{62} +(4.88177 + 4.88177i) q^{63} +1.00000i q^{64} +(1.93788 + 4.61065i) q^{65} +(-4.97725 + 9.17440i) q^{66} +(-3.07069 - 3.07069i) q^{67} +(2.76045 + 2.76045i) q^{68} -6.15707i q^{69} +(-0.844975 + 2.07027i) q^{70} -14.2077 q^{71} +(-4.88177 + 4.88177i) q^{72} +(-6.02736 - 6.02736i) q^{73} +3.02718 q^{74} +(15.7344 - 0.163291i) q^{75} +4.12278i q^{76} +(3.17972 - 0.943055i) q^{77} +(4.97725 - 4.97725i) q^{78} -11.7150 q^{79} +(-2.07027 - 0.844975i) q^{80} -17.9518 q^{81} +(-4.90387 - 4.90387i) q^{82} +(-6.05876 - 6.05876i) q^{83} +3.14704 q^{84} +(-8.04740 + 3.38237i) q^{85} +5.09344 q^{86} +(20.5312 - 20.5312i) q^{87} +(0.943055 + 3.17972i) q^{88} +3.23314i q^{89} +(-5.98161 - 14.2316i) q^{90} -2.23667 q^{91} +(-1.38343 - 1.38343i) q^{92} +(8.68726 - 8.68726i) q^{93} +7.70830 q^{94} +(-8.53526 - 3.48365i) q^{95} +3.14704i q^{96} +(3.90387 + 3.90387i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-10.9189 + 20.1265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 8 q^{5}+O(q^{10}) \) 16 * q - 8 * q^3 - 8 * q^5	\( 16 q - 8 q^{3} - 8 q^{5} - 8 q^{11} + 8 q^{12} + 24 q^{15} - 16 q^{16} + 16 q^{20} - 8 q^{22} + 32 q^{23} + 16 q^{25} + 16 q^{26} - 32 q^{27} - 24 q^{33} - 48 q^{36} - 48 q^{37} - 8 q^{38} - 8 q^{42} + 72 q^{45} + 8 q^{48} - 16 q^{53} - 48 q^{55} + 16 q^{56} + 32 q^{58} - 56 q^{60} - 32 q^{66} + 48 q^{67} - 16 q^{70} - 48 q^{71} + 112 q^{75} + 8 q^{77} + 32 q^{78} + 8 q^{80} - 80 q^{81} - 16 q^{82} + 32 q^{86} - 8 q^{88} - 16 q^{91} - 32 q^{92} + 32 q^{93}+O(q^{100}) \) 16 * q - 8 * q^3 - 8 * q^5 - 8 * q^11 + 8 * q^12 + 24 * q^15 - 16 * q^16 + 16 * q^20 - 8 * q^22 + 32 * q^23 + 16 * q^25 + 16 * q^26 - 32 * q^27 - 24 * q^33 - 48 * q^36 - 48 * q^37 - 8 * q^38 - 8 * q^42 + 72 * q^45 + 8 * q^48 - 16 * q^53 - 48 * q^55 + 16 * q^56 + 32 * q^58 - 56 * q^60 - 32 * q^66 + 48 * q^67 - 16 * q^70 - 48 * q^71 + 112 * q^75 + 8 * q^77 + 32 * q^78 + 8 * q^80 - 80 * q^81 - 16 * q^82 + 32 * q^86 - 8 * q^88 - 16 * q^91 - 32 * q^92 + 32 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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