LMFDB - Embedded newform 770.2.m.e.43.5

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			43.5
Root			$2.32893i$ of defining polynomial
Character	$\chi$	$=$	770.43
Dual form			770.2.m.e.197.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-2.14984 - 2.14984i) q^{3} +1.00000i q^{4} +(-1.71500 - 1.43484i) q^{5} -3.04034i q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +6.24365i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-2.14984 - 2.14984i) q^{3} +1.00000i q^{4} +(-1.71500 - 1.43484i) q^{5} -3.04034i q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +6.24365i q^{9} +(-0.198102 - 2.22728i) q^{10} +(0.280159 - 3.30477i) q^{11} +(2.14984 - 2.14984i) q^{12} +(-3.30477 + 3.30477i) q^{13} -1.00000i q^{14} +(0.602298 + 6.77167i) q^{15} -1.00000 q^{16} +(-2.29361 - 2.29361i) q^{17} +(-4.41493 + 4.41493i) q^{18} +0.396205 q^{19} +(1.43484 - 1.71500i) q^{20} +3.04034i q^{21} +(2.53493 - 2.13872i) q^{22} +(5.93428 + 5.93428i) q^{23} +3.04034 q^{24} +(0.882457 + 4.92151i) q^{25} -4.67365 q^{26} +(6.97334 - 6.97334i) q^{27} +(0.707107 - 0.707107i) q^{28} +4.95580 q^{29} +(-4.36240 + 5.21418i) q^{30} +3.24365 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.70704 + 6.50244i) q^{33} -3.24365i q^{34} +(0.198102 + 2.22728i) q^{35} -6.24365 q^{36} +(-5.43000 + 5.43000i) q^{37} +(0.280159 + 0.280159i) q^{38} +14.2095 q^{39} +(2.22728 - 0.198102i) q^{40} +6.00143i q^{41} +(-2.14984 + 2.14984i) q^{42} +(-7.83946 + 7.83946i) q^{43} +(3.30477 + 0.280159i) q^{44} +(8.95865 - 10.7079i) q^{45} +8.39234i q^{46} +(-3.29969 + 3.29969i) q^{47} +(2.14984 + 2.14984i) q^{48} +1.00000i q^{49} +(-2.85604 + 4.10403i) q^{50} +9.86179i q^{51} +(-3.30477 - 3.30477i) q^{52} +(-9.91730 - 9.91730i) q^{53} +9.86179 q^{54} +(-5.22230 + 5.26570i) q^{55} +1.00000 q^{56} +(-0.851778 - 0.851778i) q^{57} +(3.50428 + 3.50428i) q^{58} +12.4521i q^{59} +(-6.77167 + 0.602298i) q^{60} -7.90478i q^{61} +(2.29361 + 2.29361i) q^{62} +(4.41493 - 4.41493i) q^{63} -1.00000i q^{64} +(10.4095 - 0.925861i) q^{65} +(-10.0476 - 0.851778i) q^{66} +(8.03905 - 8.03905i) q^{67} +(2.29361 - 2.29361i) q^{68} -25.5156i q^{69} +(-1.43484 + 1.71500i) q^{70} +6.66397 q^{71} +(-4.41493 - 4.41493i) q^{72} +(-3.89212 + 3.89212i) q^{73} -7.67918 q^{74} +(8.68333 - 12.4776i) q^{75} +0.396205i q^{76} +(-2.53493 + 2.13872i) q^{77} +(10.0476 + 10.0476i) q^{78} -14.1181 q^{79} +(1.71500 + 1.43484i) q^{80} -11.2522 q^{81} +(-4.24365 + 4.24365i) q^{82} +(1.89651 - 1.89651i) q^{83} -3.04034 q^{84} +(0.642575 + 7.22450i) q^{85} -11.0867 q^{86} +(-10.6542 - 10.6542i) q^{87} +(2.13872 + 2.53493i) q^{88} +5.86857i q^{89} +(13.9063 - 1.23688i) q^{90} +4.67365 q^{91} +(-5.93428 + 5.93428i) q^{92} +(-6.97334 - 6.97334i) q^{93} -4.66646 q^{94} +(-0.679492 - 0.568491i) q^{95} +3.04034i q^{96} +(3.24365 - 3.24365i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(20.6338 + 1.74921i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	−2.14984	−	2.14984i	−1.24121	−	1.24121i	−0.959498	−	0.281714i	$-0.909097\pi$
$3$	−2.14984	−	2.14984i	−1.24121	−	1.24121i	−0.281714	−	0.959498i	$-0.590903\pi$
$4$			1.00000i			0.500000i
$5$	−1.71500	−	1.43484i	−0.766972	−	0.641681i
$5$	−1.71500	−	1.43484i	−0.766972	−	0.641681i
$6$		−	3.04034i		−	1.24121i
$7$	−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
$9$			6.24365i			2.08122i
$10$	−0.198102	−	2.22728i	−0.0626455	−	0.704326i
$11$	0.280159	−	3.30477i	0.0844711	−	0.996426i
$11$	0.280159	−	3.30477i	0.0844711	−	0.996426i
$12$	2.14984	−	2.14984i	0.620606	−	0.620606i
$13$	−3.30477	+	3.30477i	−0.916579	+	0.916579i	−0.996779	−	0.0802002i	$-0.974444\pi$
$13$	−3.30477	+	3.30477i	−0.916579	+	0.916579i	0.0802002	+	0.996779i	$0.474444\pi$
$14$		−	1.00000i		−	0.267261i
$15$	0.602298	+	6.77167i	0.155513	+	1.74844i
$16$	−1.00000			−0.250000
$17$	−2.29361	−	2.29361i	−0.556281	−	0.556281i	0.371965	−	0.928247i	$-0.378684\pi$
$17$	−2.29361	−	2.29361i	−0.556281	−	0.556281i	−0.928247	+	0.371965i	$0.878684\pi$
$18$	−4.41493	+	4.41493i	−1.04061	+	1.04061i
$19$	0.396205			0.0908956			0.0454478	−	0.998967i	$-0.485529\pi$
$19$	0.396205			0.0908956			0.0454478	+	0.998967i	$0.485529\pi$
$20$	1.43484	−	1.71500i	0.320840	−	0.383486i
$21$			3.04034i			0.663456i
$22$	2.53493	−	2.13872i	0.540449	−	0.455977i
$23$	5.93428	+	5.93428i	1.23738	+	1.23738i	0.961066	+	0.276317i	$0.0891141\pi$
$23$	5.93428	+	5.93428i	1.23738	+	1.23738i	0.276317	+	0.961066i	$0.410886\pi$
$24$	3.04034			0.620606
$25$	0.882457	+	4.92151i	0.176491	+	0.984302i
$26$	−4.67365			−0.916579
$27$	6.97334	−	6.97334i	1.34202	−	1.34202i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	4.95580			0.920270			0.460135	−	0.887849i	$-0.347801\pi$
$29$	4.95580			0.920270			0.460135	+	0.887849i	$0.347801\pi$
$30$	−4.36240	+	5.21418i	−0.796462	+	0.951975i
$31$	3.24365			0.582577			0.291288	−	0.956635i	$-0.405916\pi$
$31$	3.24365			0.582577			0.291288	+	0.956635i	$0.405916\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−7.70704	+	6.50244i	−1.34162	+	1.13193i
$34$		−	3.24365i		−	0.556281i
$35$	0.198102	+	2.22728i	0.0334854	+	0.376478i
$36$	−6.24365			−1.04061
$37$	−5.43000	+	5.43000i	−0.892687	+	0.892687i	−0.994775	−	0.102088i	$-0.967448\pi$
$37$	−5.43000	+	5.43000i	−0.892687	+	0.892687i	0.102088	+	0.994775i	$0.467448\pi$
$38$	0.280159	+	0.280159i	0.0454478	+	0.0454478i
$39$	14.2095			2.27534
$40$	2.22728	−	0.198102i	0.352163	−	0.0313227i
$41$			6.00143i			0.937265i	0.883393	+	0.468633i	$0.155253\pi$
$41$			6.00143i			0.937265i	−0.883393	+	0.468633i	$0.844747\pi$
$42$	−2.14984	+	2.14984i	−0.331728	+	0.331728i
$43$	−7.83946	+	7.83946i	−1.19551	+	1.19551i	−0.220009	+	0.975498i	$0.570609\pi$
$43$	−7.83946	+	7.83946i	−1.19551	+	1.19551i	−0.975498	+	0.220009i	$0.929391\pi$
$44$	3.30477	+	0.280159i	0.498213	+	0.0422356i
$45$	8.95865	−	10.7079i	1.33548	−	1.59623i
$46$			8.39234i			1.23738i
$47$	−3.29969	+	3.29969i	−0.481309	+	0.481309i	−0.905549	−	0.424241i	$-0.860541\pi$
$47$	−3.29969	+	3.29969i	−0.481309	+	0.481309i	0.424241	+	0.905549i	$0.360541\pi$
$48$	2.14984	+	2.14984i	0.310303	+	0.310303i
$49$			1.00000i			0.142857i
$50$	−2.85604	+	4.10403i	−0.403905	+	0.580397i
$51$			9.86179i			1.38093i
$52$	−3.30477	−	3.30477i	−0.458289	−	0.458289i
$53$	−9.91730	−	9.91730i	−1.36225	−	1.36225i	−0.871048	−	0.491198i	$-0.836559\pi$
$53$	−9.91730	−	9.91730i	−1.36225	−	1.36225i	−0.491198	−	0.871048i	$-0.663441\pi$
$54$	9.86179			1.34202
$55$	−5.22230	+	5.26570i	−0.704174	+	0.710027i
$56$	1.00000			0.133631
$57$	−0.851778	−	0.851778i	−0.112821	−	0.112821i
$58$	3.50428	+	3.50428i	0.460135	+	0.460135i
$59$			12.4521i			1.62112i	0.585654	+	0.810561i	$0.300838\pi$
$59$			12.4521i			1.62112i	−0.585654	+	0.810561i	$0.699162\pi$
$60$	−6.77167	+	0.602298i	−0.874219	+	0.0777563i
$61$		−	7.90478i		−	1.01210i	−0.862503	−	0.506052i	$-0.831104\pi$
$61$		−	7.90478i		−	1.01210i	0.862503	−	0.506052i	$-0.168896\pi$
$62$	2.29361	+	2.29361i	0.291288	+	0.291288i
$63$	4.41493	−	4.41493i	0.556229	−	0.556229i
$64$		−	1.00000i		−	0.125000i
$65$	10.4095	−	0.925861i	1.29114	−	0.114839i
$66$	−10.0476	−	0.851778i	−1.23678	−	0.104847i
$67$	8.03905	−	8.03905i	0.982127	−	0.982127i	−0.0177163	−	0.999843i	$-0.505640\pi$
$67$	8.03905	−	8.03905i	0.982127	−	0.982127i	0.999843	+	0.0177163i	$0.00563957\pi$
$68$	2.29361	−	2.29361i	0.278141	−	0.278141i
$69$		−	25.5156i		−	3.07171i
$70$	−1.43484	+	1.71500i	−0.171496	+	0.204982i
$71$	6.66397			0.790868			0.395434	−	0.918494i	$-0.370594\pi$
$71$	6.66397			0.790868			0.395434	+	0.918494i	$0.370594\pi$
$72$	−4.41493	−	4.41493i	−0.520304	−	0.520304i
$73$	−3.89212	+	3.89212i	−0.455538	+	0.455538i	−0.897187	−	0.441650i	$-0.854393\pi$
$73$	−3.89212	+	3.89212i	−0.455538	+	0.455538i	0.441650	+	0.897187i	$0.354393\pi$
$74$	−7.67918			−0.892687
$75$	8.68333	−	12.4776i	1.00266	−	1.44079i
$76$			0.396205i			0.0454478i
$77$	−2.53493	+	2.13872i	−0.288882	+	0.243730i
$78$	10.0476	+	10.0476i	1.13767	+	1.13767i
$79$	−14.1181			−1.58841			−0.794206	−	0.607648i	$-0.792113\pi$
$79$	−14.1181			−1.58841			−0.794206	+	0.607648i	$0.792113\pi$
$80$	1.71500	+	1.43484i	0.191743	+	0.160420i
$81$	−11.2522			−1.25025
$82$	−4.24365	+	4.24365i	−0.468633	+	0.468633i
$83$	1.89651	−	1.89651i	0.208169	−	0.208169i	−0.595320	−	0.803489i	$-0.702975\pi$
$83$	1.89651	−	1.89651i	0.208169	−	0.208169i	0.803489	+	0.595320i	$0.202975\pi$
$84$	−3.04034			−0.331728
$85$	0.642575	+	7.22450i	0.0696970	+	0.783607i
$86$	−11.0867			−1.19551
$87$	−10.6542	−	10.6542i	−1.14225	−	1.14225i
$88$	2.13872	+	2.53493i	0.227989	+	0.270224i
$89$			5.86857i			0.622067i	0.950399	+	0.311033i	$0.100675\pi$
$89$			5.86857i			0.622067i	−0.950399	+	0.311033i	$0.899325\pi$
$90$	13.9063	−	1.23688i	1.46586	−	0.130379i
$91$	4.67365			0.489932
$92$	−5.93428	+	5.93428i	−0.618692	+	0.618692i
$93$	−6.97334	−	6.97334i	−0.723101	−	0.723101i
$94$	−4.66646			−0.481309
$95$	−0.679492	−	0.568491i	−0.0697144	−	0.0583260i
$96$			3.04034i			0.310303i
$97$	3.24365	−	3.24365i	0.329343	−	0.329343i	−0.522994	−	0.852337i	$-0.675185\pi$
$97$	3.24365	−	3.24365i	0.329343	−	0.329343i	0.852337	+	0.522994i	$0.175185\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	20.6338	+	1.74921i	2.07378	+	0.175803i
$100$	−4.92151	+	0.882457i	−0.492151	+	0.0882457i
$101$		−	2.98511i		−	0.297029i	−0.988910	−	0.148515i	$-0.952551\pi$
$101$		−	2.98511i		−	0.297029i	0.988910	−	0.148515i	$-0.0474492\pi$
$102$	−6.97334	+	6.97334i	−0.690463	+	0.690463i
$103$	−2.43968	−	2.43968i	−0.240389	−	0.240389i	0.576622	−	0.817011i	$-0.304371\pi$
$103$	−2.43968	−	2.43968i	−0.240389	−	0.240389i	−0.817011	+	0.576622i	$0.804371\pi$
$104$		−	4.67365i		−	0.458289i
$105$	4.36240	−	5.21418i	0.425727	−	0.508852i
$106$		−	14.0252i		−	1.36225i
$107$	−2.33929	−	2.33929i	−0.226147	−	0.226147i	0.584934	−	0.811081i	$-0.301120\pi$
$107$	−2.33929	−	2.33929i	−0.226147	−	0.226147i	−0.811081	+	0.584934i	$0.801120\pi$
$108$	6.97334	+	6.97334i	0.671010	+	0.671010i
$109$	−9.86179			−0.944588			−0.472294	−	0.881441i	$-0.656574\pi$
$109$	−9.86179			−0.944588			−0.472294	+	0.881441i	$0.656574\pi$
$110$	−7.41613	+	0.0306916i	−0.707101	+	0.00292633i
$111$	23.3473			2.21603
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	2.68333	+	2.68333i	0.252427	+	0.252427i	0.821965	−	0.569538i	$-0.192878\pi$
$113$	2.68333	+	2.68333i	0.252427	+	0.252427i	−0.569538	+	0.821965i	$0.692878\pi$
$114$		−	1.20460i		−	0.112821i
$115$	−1.66254	−	18.6921i	−0.155033	−	1.74304i
$116$			4.95580i			0.460135i
$117$	−20.6338	−	20.6338i	−1.90760	−	1.90760i
$118$	−8.80495	+	8.80495i	−0.810561	+	0.810561i
$119$			3.24365i			0.297345i
$120$	−5.21418	−	4.36240i	−0.475987	−	0.398231i
$121$	−10.8430	−	1.85172i	−0.985729	−	0.168338i
$122$	5.58952	−	5.58952i	0.506052	−	0.506052i
$123$	12.9021	−	12.9021i	1.16335	−	1.16335i
$124$			3.24365i			0.291288i
$125$	5.54818	−	9.70658i	0.496244	−	0.868183i
$126$	6.24365			0.556229
$127$	1.52521	+	1.52521i	0.135341	+	0.135341i	0.771532	−	0.636191i	$-0.219491\pi$
$127$	1.52521	+	1.52521i	0.135341	+	0.135341i	−0.636191	+	0.771532i	$0.719491\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	33.7072			2.96776
$130$	8.01532	+	6.70595i	0.702990	+	0.588151i
$131$			11.7099i			1.02310i	0.859254	+	0.511550i	$0.170928\pi$
$131$			11.7099i			1.02310i	−0.859254	+	0.511550i	$0.829072\pi$
$132$	−6.50244	−	7.70704i	−0.565965	−	0.670811i
$133$	−0.280159	−	0.280159i	−0.0242929	−	0.0242929i
$134$	11.3689			0.982127
$135$	−21.9649	+	1.95364i	−1.89044	+	0.168143i
$136$	3.24365			0.278141
$137$	−9.10365	+	9.10365i	−0.777778	+	0.777778i	−0.979453	−	0.201675i	$-0.935362\pi$
$137$	−9.10365	+	9.10365i	−0.777778	+	0.777778i	0.201675	+	0.979453i	$0.435362\pi$
$138$	18.0422	−	18.0422i	1.53586	−	1.53586i
$139$	−12.3301			−1.04583			−0.522914	−	0.852385i	$-0.675155\pi$
$139$	−12.3301			−1.04583			−0.522914	+	0.852385i	$0.675155\pi$
$140$	−2.22728	+	0.198102i	−0.188239	+	0.0167427i
$141$	14.1876			1.19481
$142$	4.71214	+	4.71214i	0.395434	+	0.395434i
$143$	9.99565	+	11.8474i	0.835878	+	0.990727i
$144$		−	6.24365i		−	0.520304i
$145$	−8.49921	−	7.11079i	−0.705821	−	0.590519i
$146$	−5.50428			−0.455538
$147$	2.14984	−	2.14984i	0.177316	−	0.177316i
$148$	−5.43000	−	5.43000i	−0.446343	−	0.446343i
$149$	−5.76190			−0.472033			−0.236017	−	0.971749i	$-0.575842\pi$
$149$	−5.76190			−0.472033			−0.236017	+	0.971749i	$0.575842\pi$
$150$	14.9631	−	2.68297i	1.22173	−	0.219063i
$151$		−	14.0115i		−	1.14024i	−0.821562	−	0.570120i	$-0.806897\pi$
$151$		−	14.0115i		−	1.14024i	0.821562	−	0.570120i	$-0.193103\pi$
$152$	−0.280159	+	0.280159i	−0.0227239	+	0.0227239i
$153$	14.3205	−	14.3205i	1.15774	−	1.15774i
$154$	−3.30477	−	0.280159i	−0.266306	−	0.0225759i
$155$	−5.56286	−	4.65412i	−0.446820	−	0.373828i
$156$			14.2095i			1.13767i
$157$	5.18890	−	5.18890i	0.414119	−	0.414119i	−0.469052	−	0.883171i	$-0.655404\pi$
$157$	5.18890	−	5.18890i	0.414119	−	0.414119i	0.883171	+	0.469052i	$0.155404\pi$
$158$	−9.98302	−	9.98302i	−0.794206	−	0.794206i
$159$			42.6413i			3.38167i
$160$	0.198102	+	2.22728i	0.0156614	+	0.176082i
$161$		−	8.39234i		−	0.661409i
$162$	−7.95652	−	7.95652i	−0.625123	−	0.625123i
$163$	8.77731	+	8.77731i	0.687492	+	0.687492i	0.961677	−	0.274185i	$-0.0884081\pi$
$163$	8.77731	+	8.77731i	0.687492	+	0.687492i	−0.274185	+	0.961677i	$0.588408\pi$
$164$	−6.00143			−0.468633
$165$	22.5476	−	0.0933128i	1.75532	−	0.00726439i
$166$	2.68207			0.208169
$167$	−7.12630	−	7.12630i	−0.551450	−	0.551450i	0.375410	−	0.926859i	$-0.377502\pi$
$167$	−7.12630	−	7.12630i	−0.551450	−	0.551450i	−0.926859	+	0.375410i	$0.877502\pi$
$168$	−2.14984	−	2.14984i	−0.165864	−	0.165864i
$169$		−	8.84302i		−	0.680232i
$170$	−4.65412	+	5.56286i	−0.356955	+	0.426652i
$171$			2.47376i			0.189173i
$172$	−7.83946	−	7.83946i	−0.597753	−	0.597753i
$173$	−11.6695	+	11.6695i	−0.887216	+	0.887216i	−0.994255	−	0.107039i	$-0.965863\pi$
$173$	−11.6695	+	11.6695i	−0.887216	+	0.887216i	0.107039	+	0.994255i	$0.465863\pi$
$174$		−	15.0673i		−	1.14225i
$175$	2.85604	−	4.10403i	0.215897	−	0.310235i
$176$	−0.280159	+	3.30477i	−0.0211178	+	0.249106i
$177$	26.7700	−	26.7700i	2.01216	−	2.01216i
$178$	−4.14970	+	4.14970i	−0.311033	+	0.311033i
$179$			7.23523i			0.540787i	0.962750	+	0.270393i	$0.0871537\pi$
$179$			7.23523i			0.540787i	−0.962750	+	0.270393i	$0.912846\pi$
$180$	10.7079	+	8.95865i	0.798117	+	0.667738i
$181$	−13.9173			−1.03446			−0.517232	−	0.855845i	$-0.673038\pi$
$181$	−13.9173			−1.03446			−0.517232	+	0.855845i	$0.673038\pi$
$182$	3.30477	+	3.30477i	0.244966	+	0.244966i
$183$	−16.9940	+	16.9940i	−1.25624	+	1.25624i
$184$	−8.39234			−0.618692
$185$	17.1037	−	1.52126i	1.25749	−	0.111846i
$186$		−	9.86179i		−	0.723101i
$187$	−8.22242	+	6.93727i	−0.601283	+	0.507303i
$188$	−3.29969	−	3.29969i	−0.240654	−	0.240654i
$189$	−9.86179			−0.717340
$190$	−0.0784891	−	0.882457i	−0.00569420	−	0.0640202i
$191$	−1.33603			−0.0966716			−0.0483358	−	0.998831i	$-0.515392\pi$
$191$	−1.33603			−0.0966716			−0.0483358	+	0.998831i	$0.515392\pi$
$192$	−2.14984	+	2.14984i	−0.155152	+	0.155152i
$193$	−9.99085	+	9.99085i	−0.719157	+	0.719157i	−0.968433	−	0.249275i	$-0.919808\pi$
$193$	−9.99085	+	9.99085i	−0.719157	+	0.719157i	0.249275	+	0.968433i	$0.419808\pi$
$194$	4.58721			0.329343
$195$	−24.3693	−	20.3884i	−1.74512	−	1.46004i
$196$	−1.00000			−0.0714286
$197$	−9.91342	−	9.91342i	−0.706302	−	0.706302i	0.259454	−	0.965756i	$-0.416458\pi$
$197$	−9.91342	−	9.91342i	−0.706302	−	0.706302i	−0.965756	+	0.259454i	$0.916458\pi$
$198$	13.3534	+	15.8272i	0.948988	+	1.12479i
$199$			8.36429i			0.592929i	0.955044	+	0.296464i	$0.0958076\pi$
$199$			8.36429i			0.592929i	−0.955044	+	0.296464i	$0.904192\pi$
$200$	−4.10403	−	2.85604i	−0.290198	−	0.201953i
$201$	−34.5654			−2.43806
$202$	2.11079	−	2.11079i	0.148515	−	0.148515i
$203$	−3.50428	−	3.50428i	−0.245952	−	0.245952i
$204$	−9.86179			−0.690463
$205$	8.61110	−	10.2925i	0.601425	−	0.718856i
$206$		−	3.45023i		−	0.240389i
$207$	−37.0516	+	37.0516i	−2.57526	+	2.57526i
$208$	3.30477	−	3.30477i	0.229145	−	0.229145i
$209$	0.111000	−	1.30937i	0.00767805	−	0.0905707i
$210$	6.77167	−	0.602298i	0.467289	−	0.0415625i
$211$		−	21.1203i		−	1.45398i	−0.686649	−	0.726990i	$-0.740919\pi$
$211$		−	21.1203i		−	1.45398i	0.686649	−	0.726990i	$-0.259081\pi$
$212$	9.91730	−	9.91730i	0.681123	−	0.681123i
$213$	−14.3265	−	14.3265i	−0.981635	−	0.981635i
$214$		−	3.30825i		−	0.226147i
$215$	24.6931	−	2.19630i	1.68405	−	0.149786i
$216$			9.86179i			0.671010i
$217$	−2.29361	−	2.29361i	−0.155700	−	0.155700i
$218$	−6.97334	−	6.97334i	−0.472294	−	0.472294i
$219$	16.7349			1.13084
$220$	−5.26570	−	5.22230i	−0.355014	−	0.352087i
$221$	15.1597			1.01975
$222$	16.5090	+	16.5090i	1.10801	+	1.10801i
$223$	7.59095	+	7.59095i	0.508328	+	0.508328i	0.914013	−	0.405685i	$-0.132967\pi$
$223$	7.59095	+	7.59095i	0.508328	+	0.508328i	−0.405685	+	0.914013i	$0.632967\pi$
$224$			1.00000i			0.0668153i
$225$	−30.7282	+	5.50975i	−2.04855	+	0.367317i
$226$			3.79480i			0.252427i
$227$	18.3263	+	18.3263i	1.21636	+	1.21636i	0.968898	+	0.247462i	$0.0795964\pi$
$227$	18.3263	+	18.3263i	1.21636	+	1.21636i	0.247462	+	0.968898i	$0.420404\pi$
$228$	0.851778	−	0.851778i	0.0564104	−	0.0564104i
$229$			2.02681i			0.133935i	0.997755	+	0.0669676i	$0.0213324\pi$
$229$			2.02681i			0.133935i	−0.997755	+	0.0669676i	$0.978668\pi$
$230$	12.0417	−	14.3929i	0.794005	−	0.949038i
$231$	10.0476	+	0.851778i	0.661085	+	0.0560429i
$232$	−3.50428	+	3.50428i	−0.230067	+	0.230067i
$233$	−5.66641	+	5.66641i	−0.371219	+	0.371219i	−0.867921	−	0.496702i	$-0.834544\pi$
$233$	−5.66641	+	5.66641i	−0.371219	+	0.371219i	0.496702	+	0.867921i	$0.334544\pi$
$234$		−	29.1806i		−	1.90760i
$235$	10.3935	−	0.924437i	0.677997	−	0.0603036i
$236$	−12.4521			−0.810561
$237$	30.3517	+	30.3517i	1.97156	+	1.97156i
$238$	−2.29361	+	2.29361i	−0.148672	+	0.148672i
$239$	0.0913582			0.00590947			0.00295474	−	0.999996i	$-0.499059\pi$
$239$	0.0913582			0.00590947			0.00295474	+	0.999996i	$0.499059\pi$
$240$	−0.602298	−	6.77167i	−0.0388782	−	0.437109i
$241$			24.6673i			1.58896i	0.607291	+	0.794479i	$0.292256\pi$
$241$			24.6673i			1.58896i	−0.607291	+	0.794479i	$0.707744\pi$
$242$	−6.35781	−	8.97654i	−0.408695	−	0.577034i
$243$	3.27048	+	3.27048i	0.209801	+	0.209801i
$244$	7.90478			0.506052
$245$	1.43484	−	1.71500i	0.0916687	−	0.109567i
$246$	18.2464			1.16335
$247$	−1.30937	+	1.30937i	−0.0833130	+	0.0833130i
$248$	−2.29361	+	2.29361i	−0.145644	+	0.145644i
$249$	−8.15440			−0.516764
$250$	10.7867	−	2.94044i	0.682214	−	0.185970i
$251$	4.52253			0.285459			0.142730	−	0.989762i	$-0.454412\pi$
$251$	4.52253			0.285459			0.142730	+	0.989762i	$0.454412\pi$
$252$	4.41493	+	4.41493i	0.278114	+	0.278114i
$253$	21.2740	−	17.9489i	1.33748	−	1.12844i
$254$			2.15698i			0.135341i
$255$	14.1501	−	16.9130i	0.886114	−	1.05913i
$256$	1.00000			0.0625000
$257$	4.19603	−	4.19603i	0.261741	−	0.261741i	−0.564020	−	0.825761i	$-0.690746\pi$
$257$	4.19603	−	4.19603i	0.261741	−	0.261741i	0.825761	+	0.564020i	$0.190746\pi$
$258$	23.8346	+	23.8346i	1.48388	+	1.48388i
$259$	7.67918			0.477161
$260$	0.925861	+	10.4095i	0.0574195	+	0.645570i
$261$			30.9423i			1.91528i
$262$	−8.28016	+	8.28016i	−0.511550	+	0.511550i
$263$	0.0552305	−	0.0552305i	0.00340566	−	0.00340566i	−0.705402	−	0.708808i	$-0.749233\pi$
$263$	0.0552305	−	0.0552305i	0.00340566	−	0.00340566i	0.708808	+	0.705402i	$0.249233\pi$
$264$	0.851778	−	10.0476i	0.0524233	−	0.618388i
$265$	2.77842	+	31.2379i	0.170677	+	1.91893i
$266$		−	0.396205i		−	0.0242929i
$267$	12.6165	−	12.6165i	0.772117	−	0.772117i
$268$	8.03905	+	8.03905i	0.491063	+	0.491063i
$269$			12.1268i			0.739387i	0.929154	+	0.369693i	$0.120537\pi$
$269$			12.1268i			0.739387i	−0.929154	+	0.369693i	$0.879463\pi$
$270$	−16.9130	−	14.1501i	−1.02929	−	0.861148i
$271$			29.5438i			1.79466i	0.441361	+	0.897330i	$0.354496\pi$
$271$			29.5438i			1.79466i	−0.441361	+	0.897330i	$0.645504\pi$
$272$	2.29361	+	2.29361i	0.139070	+	0.139070i
$273$	−10.0476	−	10.0476i	−0.608109	−	0.608109i
$274$	−12.8745			−0.777778
$275$	16.5117	−	1.53751i	0.995693	−	0.0927155i
$276$	25.5156			1.53586
$277$	13.8272	+	13.8272i	0.830796	+	0.830796i	0.987626	−	0.156830i	$-0.0501274\pi$
$277$	13.8272	+	13.8272i	0.830796	+	0.830796i	−0.156830	+	0.987626i	$0.550127\pi$
$278$	−8.71872	−	8.71872i	−0.522914	−	0.522914i
$279$			20.2522i			1.21247i
$280$	−1.71500	−	1.43484i	−0.102491	−	0.0857482i
$281$			9.82025i			0.585827i	0.956139	+	0.292913i	$0.0946248\pi$
$281$			9.82025i			0.585827i	−0.956139	+	0.292913i	$0.905375\pi$
$282$	10.0322	+	10.0322i	0.597406	+	0.597406i
$283$	16.4625	−	16.4625i	0.978592	−	0.978592i	−0.0211836	−	0.999776i	$-0.506743\pi$
$283$	16.4625	−	16.4625i	0.978592	−	0.978592i	0.999776	+	0.0211836i	$0.00674345\pi$
$284$			6.66397i			0.395434i
$285$	0.238633	+	2.68297i	0.0141354	+	0.158925i
$286$	−1.30937	+	15.4453i	−0.0774244	+	0.913303i
$287$	4.24365	−	4.24365i	0.250495	−	0.250495i
$288$	4.41493	−	4.41493i	0.260152	−	0.260152i
$289$		−	6.47874i		−	0.381102i
$290$	−0.981756	−	11.0379i	−0.0576507	−	0.648170i
$291$	−13.9467			−0.817569
$292$	−3.89212	−	3.89212i	−0.227769	−	0.227769i
$293$	−0.805207	+	0.805207i	−0.0470407	+	0.0470407i	−0.730236	−	0.683195i	$-0.760590\pi$
$293$	−0.805207	+	0.805207i	−0.0470407	+	0.0470407i	0.683195	+	0.730236i	$0.260590\pi$
$294$	3.04034			0.177316
$295$	17.8668	−	21.3553i	1.04024	−	1.24335i
$296$		−	7.67918i		−	0.446343i
$297$	−21.0916	−	24.9989i	−1.22386	−	1.45058i
$298$	−4.07428	−	4.07428i	−0.236017	−	0.236017i
$299$	−39.2229			−2.26832
$300$	12.4776	+	8.68333i	0.720396	+	0.501332i
$301$	11.0867			0.639025
$302$	9.90762	−	9.90762i	0.570120	−	0.570120i
$303$	−6.41751	+	6.41751i	−0.368676	+	0.368676i
$304$	−0.396205			−0.0227239
$305$	−11.3421	+	13.5567i	−0.649447	+	0.776255i
$306$	20.2522			1.15774
$307$	−20.5089	−	20.5089i	−1.17051	−	1.17051i	−0.982089	−	0.188416i	$-0.939665\pi$
$307$	−20.5089	−	20.5089i	−1.17051	−	1.17051i	−0.188416	−	0.982089i	$-0.560335\pi$
$308$	−2.13872	−	2.53493i	−0.121865	−	0.144441i
$309$			10.4899i			0.596748i
$310$	−0.642575	−	7.22450i	−0.0364958	−	0.410324i
$311$	3.03411			0.172049			0.0860243	−	0.996293i	$-0.472584\pi$
$311$	3.03411			0.172049			0.0860243	+	0.996293i	$0.472584\pi$
$312$	−10.0476	+	10.0476i	−0.568834	+	0.568834i
$313$	−10.7870	−	10.7870i	−0.609716	−	0.609716i	0.333155	−	0.942872i	$-0.391887\pi$
$313$	−10.7870	−	10.7870i	−0.609716	−	0.609716i	−0.942872	+	0.333155i	$0.891887\pi$
$314$	7.33821			0.414119
$315$	−13.9063	+	1.23688i	−0.783533	+	0.0696904i
$316$		−	14.1181i		−	0.794206i
$317$	1.99158	−	1.99158i	0.111858	−	0.111858i	−0.648962	−	0.760821i	$-0.724797\pi$
$317$	1.99158	−	1.99158i	0.111858	−	0.111858i	0.760821	+	0.648962i	$0.224797\pi$
$318$	−30.1519	+	30.1519i	−1.69084	+	1.69084i
$319$	1.38841	−	16.3778i	0.0777362	−	0.916980i
$320$	−1.43484	+	1.71500i	−0.0802101	+	0.0958715i
$321$			10.0582i			0.561394i
$322$	5.93428	−	5.93428i	0.330705	−	0.330705i
$323$	−0.908738	−	0.908738i	−0.0505635	−	0.0505635i
$324$		−	11.2522i		−	0.625123i
$325$	−19.1808	−	13.3481i	−1.06396	−	0.740422i
$326$			12.4130i			0.687492i
$327$	21.2013	+	21.2013i	1.17243	+	1.17243i
$328$	−4.24365	−	4.24365i	−0.234316	−	0.234316i
$329$	4.66646			0.257270
$330$	16.0095	+	15.8775i	0.881294	+	0.874030i
$331$	18.2292			1.00197			0.500985	−	0.865456i	$-0.332971\pi$
$331$	18.2292			1.00197			0.500985	+	0.865456i	$0.332971\pi$
$332$	1.89651	+	1.89651i	0.104085	+	0.104085i
$333$	−33.9030	−	33.9030i	−1.85787	−	1.85787i
$334$		−	10.0781i		−	0.551450i
$335$	−25.3218	+	2.25221i	−1.38348	+	0.123052i
$336$		−	3.04034i		−	0.165864i
$337$	−12.3955	−	12.3955i	−0.675224	−	0.675224i	0.283692	−	0.958916i	$-0.408441\pi$
$337$	−12.3955	−	12.3955i	−0.675224	−	0.675224i	−0.958916	+	0.283692i	$0.908441\pi$
$338$	6.25296	−	6.25296i	0.340116	−	0.340116i
$339$		−	11.5375i		−	0.626630i
$340$	−7.22450	+	0.642575i	−0.391804	+	0.0348485i
$341$	0.908738	−	10.7195i	0.0492109	−	0.580495i
$342$	−1.74921	+	1.74921i	−0.0945867	+	0.0945867i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		−	11.0867i		−	0.597753i
$345$	−36.6108	+	43.7592i	−1.97106	+	2.35592i
$346$	−16.5032			−0.887216
$347$	12.2112	+	12.2112i	0.655530	+	0.655530i	0.954319	−	0.298789i	$-0.0965828\pi$
$347$	12.2112	+	12.2112i	0.655530	+	0.655530i	−0.298789	+	0.954319i	$0.596583\pi$
$348$	10.6542	−	10.6542i	0.571125	−	0.571125i
$349$	−28.1572			−1.50722			−0.753611	−	0.657321i	$-0.771690\pi$
$349$	−28.1572			−1.50722			−0.753611	+	0.657321i	$0.771690\pi$
$350$	4.92151	−	0.882457i	0.263066	−	0.0471693i
$351$			46.0906i			2.46013i
$352$	−2.53493	+	2.13872i	−0.135112	+	0.113994i
$353$	−7.08667	−	7.08667i	−0.377185	−	0.377185i	0.492900	−	0.870086i	$-0.335937\pi$
$353$	−7.08667	−	7.08667i	−0.377185	−	0.377185i	−0.870086	+	0.492900i	$0.835937\pi$
$354$	37.8585			2.01216
$355$	−11.4287	−	9.56175i	−0.606573	−	0.507485i
$356$	−5.86857			−0.311033
$357$	6.97334	−	6.97334i	0.369068	−	0.369068i
$358$	−5.11608	+	5.11608i	−0.270393	+	0.270393i
$359$	2.73707			0.144457			0.0722285	−	0.997388i	$-0.476989\pi$
$359$	2.73707			0.144457			0.0722285	+	0.997388i	$0.476989\pi$
$360$	1.23688	+	13.9063i	0.0651894	+	0.732928i
$361$	−18.8430			−0.991738
$362$	−9.84102	−	9.84102i	−0.517232	−	0.517232i
$363$	19.3299	+	27.2917i	1.01456	+	1.43244i
$364$			4.67365i			0.244966i
$365$	12.2596	−	1.09041i	0.641694	−	0.0570747i
$366$	−24.0332			−1.25624
$367$	−0.607936	+	0.607936i	−0.0317340	+	0.0317340i	−0.722796	−	0.691062i	$-0.757143\pi$
$367$	−0.607936	+	0.607936i	−0.0317340	+	0.0317340i	0.691062	+	0.722796i	$0.257143\pi$
$368$	−5.93428	−	5.93428i	−0.309346	−	0.309346i
$369$	−37.4708			−1.95065
$370$	13.1698	+	11.0184i	0.684666	+	0.572820i
$371$			14.0252i			0.728151i
$372$	6.97334	−	6.97334i	0.361551	−	0.361551i
$373$	0.912961	−	0.912961i	0.0472713	−	0.0472713i	−0.683076	−	0.730347i	$-0.739358\pi$
$373$	0.912961	−	0.912961i	0.0472713	−	0.0472713i	0.730347	+	0.683076i	$0.239358\pi$
$374$	−10.7195	−	0.908738i	−0.554293	−	0.0469897i
$375$	−32.7953	+	8.93992i	−1.69354	+	0.461656i
$376$		−	4.66646i		−	0.240654i
$377$	−16.3778	+	16.3778i	−0.843499	+	0.843499i
$378$	−6.97334	−	6.97334i	−0.358670	−	0.358670i
$379$			4.09747i			0.210473i	0.994447	+	0.105236i	$0.0335599\pi$
$379$			4.09747i			0.210473i	−0.994447	+	0.105236i	$0.966440\pi$
$380$	0.568491	−	0.679492i	0.0291630	−	0.0348572i
$381$		−	6.55794i		−	0.335973i
$382$	−0.944714	−	0.944714i	−0.0483358	−	0.0483358i
$383$	−16.3864	−	16.3864i	−0.837304	−	0.837304i	0.151200	−	0.988503i	$-0.451686\pi$
$383$	−16.3864	−	16.3864i	−0.837304	−	0.837304i	−0.988503	+	0.151200i	$0.951686\pi$
$384$	−3.04034			−0.155152
$385$	7.41613	−	0.0306916i	0.377961	−	0.00156419i
$386$	−14.1292			−0.719157
$387$	−48.9468	−	48.9468i	−2.48811	−	2.48811i
$388$	3.24365	+	3.24365i	0.164671	+	0.164671i
$389$			25.7371i			1.30492i	0.757821	+	0.652462i	$0.226264\pi$
$389$			25.7371i			1.30492i	−0.757821	+	0.652462i	$0.773736\pi$
$390$	−2.81493	−	31.6484i	−0.142540	−	1.60258i
$391$		−	27.2218i		−	1.37667i
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	25.1745	−	25.1745i	1.26988	−	1.26988i
$394$		−	14.0197i		−	0.706302i
$395$	24.2126	+	20.2573i	1.21827	+	1.01925i
$396$	−1.74921	+	20.6338i	−0.0879014	+	1.03689i
$397$	−7.97079	+	7.97079i	−0.400043	+	0.400043i	−0.878248	−	0.478205i	$-0.841287\pi$
$397$	−7.97079	+	7.97079i	−0.400043	+	0.400043i	0.478205	+	0.878248i	$0.341287\pi$
$398$	−5.91444	+	5.91444i	−0.296464	+	0.296464i
$399$			1.20460i			0.0603052i
$400$	−0.882457	−	4.92151i	−0.0441229	−	0.246076i
$401$	26.0503			1.30089			0.650446	−	0.759553i	$-0.274582\pi$
$401$	26.0503			1.30089			0.650446	+	0.759553i	$0.274582\pi$
$402$	−24.4414	−	24.4414i	−1.21903	−	1.21903i
$403$	−10.7195	+	10.7195i	−0.533977	+	0.533977i
$404$	2.98511			0.148515
$405$	19.2976	+	16.1451i	0.958903	+	0.802259i
$406$		−	4.95580i		−	0.245952i
$407$	16.4236	+	19.4662i	0.814090	+	0.964903i
$408$	−6.97334	−	6.97334i	−0.345232	−	0.345232i
$409$	−8.50930			−0.420758			−0.210379	−	0.977620i	$-0.567470\pi$
$409$	−8.50930			−0.420758			−0.210379	+	0.977620i	$0.567470\pi$
$410$	13.3668	−	1.18890i	0.660141	−	0.0587154i
$411$	39.1429			1.93077
$412$	2.43968	−	2.43968i	0.120195	−	0.120195i
$413$	8.80495	−	8.80495i	0.433263	−	0.433263i
$414$	−52.3989			−2.57526
$415$	−5.97371	+	0.531324i	−0.293238	+	0.0260817i
$416$	4.67365			0.229145
$417$	26.5079	+	26.5079i	1.29810	+	1.29810i
$418$	1.00435	−	0.847372i	0.0491244	−	0.0414463i
$419$			3.69905i			0.180711i	0.995910	+	0.0903553i	$0.0288003\pi$
$419$			3.69905i			0.180711i	−0.995910	+	0.0903553i	$0.971200\pi$
$420$	5.21418	+	4.36240i	0.254426	+	0.212863i
$421$	−13.8295			−0.674009			−0.337005	−	0.941503i	$-0.609414\pi$
$421$	−13.8295			−0.674009			−0.337005	+	0.941503i	$0.609414\pi$
$422$	14.9343	−	14.9343i	0.726990	−	0.726990i
$423$	−20.6021	−	20.6021i	−1.00171	−	1.00171i
$424$	14.0252			0.681123
$425$	9.26400	−	13.3120i	0.449370	−	0.645728i
$426$		−	20.2607i		−	0.981635i
$427$	−5.58952	+	5.58952i	−0.270496	+	0.270496i
$428$	2.33929	−	2.33929i	0.113074	−	0.113074i
$429$	3.98091	−	46.9591i	0.192200	−	2.26721i
$430$	19.0137	+	15.9076i	0.916920	+	0.767134i
$431$		−	34.4635i		−	1.66005i	−0.557727	−	0.830024i	$-0.688327\pi$
$431$		−	34.4635i		−	1.66005i	0.557727	−	0.830024i	$-0.311673\pi$
$432$	−6.97334	+	6.97334i	−0.335505	+	0.335505i
$433$	6.51285	+	6.51285i	0.312987	+	0.312987i	0.846066	−	0.533078i	$-0.178965\pi$
$433$	6.51285	+	6.51285i	0.312987	+	0.312987i	−0.533078	+	0.846066i	$0.678965\pi$
$434$		−	3.24365i		−	0.155700i
$435$	2.98487	+	33.5591i	0.143114	+	1.60903i
$436$		−	9.86179i		−	0.472294i
$437$	2.35119	+	2.35119i	0.112473	+	0.112473i
$438$	11.8333	+	11.8333i	0.565419	+	0.565419i
$439$	25.6850			1.22588			0.612940	−	0.790129i	$-0.289987\pi$
$439$	25.6850			1.22588			0.612940	+	0.790129i	$0.289987\pi$
$440$	−0.0306916	−	7.41613i	−0.00146316	−	0.353550i
$441$	−6.24365			−0.297317
$442$	10.7195	+	10.7195i	0.509876	+	0.509876i
$443$	22.1440	+	22.1440i	1.05209	+	1.05209i	0.998566	+	0.0535252i	$0.0170458\pi$
$443$	22.1440	+	22.1440i	1.05209	+	1.05209i	0.0535252	+	0.998566i	$0.482954\pi$
$444$			23.3473i			1.10801i
$445$	8.42047	−	10.0646i	0.399168	−	0.477108i
$446$			10.7352i			0.508328i
$447$	12.3872	+	12.3872i	0.585894	+	0.585894i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$		−	8.11207i		−	0.382832i	−0.981509	−	0.191416i	$-0.938692\pi$
$449$		−	8.11207i		−	0.382832i	0.981509	−	0.191416i	$-0.0613080\pi$
$450$	−25.6241	−	17.8321i	−1.20793	−	0.840615i
$451$	19.8333	+	1.68135i	0.933916	+	0.0791719i
$452$	−2.68333	+	2.68333i	−0.126213	+	0.126213i
$453$	−30.1225	+	30.1225i	−1.41528	+	1.41528i
$454$			25.9173i			1.21636i
$455$	−8.01532	−	6.70595i	−0.375764	−	0.314380i
$456$	1.20460			0.0564104
$457$	3.42443	+	3.42443i	0.160188	+	0.160188i	0.782650	−	0.622462i	$-0.213867\pi$
$457$	3.42443	+	3.42443i	0.160188	+	0.160188i	−0.622462	+	0.782650i	$0.713867\pi$
$458$	−1.43317	+	1.43317i	−0.0669676	+	0.0669676i
$459$	−31.9882			−1.49308
$460$	18.6921	−	1.66254i	0.871522	−	0.0775165i
$461$			12.1649i			0.566578i	0.959035	+	0.283289i	$0.0914256\pi$
$461$			12.1649i			0.566578i	−0.959035	+	0.283289i	$0.908574\pi$
$462$	6.50244	+	7.70704i	0.302521	+	0.358564i
$463$	−10.6249	−	10.6249i	−0.493782	−	0.493782i	0.415714	−	0.909496i	$-0.363532\pi$
$463$	−10.6249	−	10.6249i	−0.493782	−	0.493782i	−0.909496	+	0.415714i	$0.863532\pi$
$464$	−4.95580			−0.230067
$465$	1.95364	+	21.9649i	0.0905981	+	1.01860i
$466$	−8.01351			−0.371219
$467$	3.74065	−	3.74065i	0.173097	−	0.173097i	−0.615242	−	0.788338i	$-0.710942\pi$
$467$	3.74065	−	3.74065i	0.173097	−	0.173097i	0.788338	+	0.615242i	$0.210942\pi$
$468$	20.6338	−	20.6338i	0.953799	−	0.953799i
$469$	−11.3689			−0.524969
$470$	8.00298	+	6.69563i	0.369150	+	0.308847i
$471$	−22.3106			−1.02802
$472$	−8.80495	−	8.80495i	−0.405280	−	0.405280i
$473$	23.7113	+	28.1039i	1.09025	+	1.29222i
$474$			42.9238i			1.97156i
$475$	0.349634	+	1.94993i	0.0160423	+	0.0894687i
$476$	−3.24365			−0.148672
$477$	61.9202	−	61.9202i	2.83513	−	2.83513i
$478$	0.0646000	+	0.0646000i	0.00295474	+	0.00295474i
$479$	−24.1281			−1.10244			−0.551220	−	0.834360i	$-0.685837\pi$
$479$	−24.1281			−1.10244			−0.551220	+	0.834360i	$0.685837\pi$
$480$	4.36240	−	5.21418i	0.199116	−	0.237994i
$481$		−	35.8898i		−	1.63644i
$482$	−17.4424	+	17.4424i	−0.794479	+	0.794479i
$483$	−18.0422	+	18.0422i	−0.820950	+	0.820950i
$484$	1.85172	−	10.8430i	0.0841692	−	0.492865i
$485$	−10.2170	+	0.908738i	−0.463930	+	0.0412637i
$486$			4.62516i			0.209801i
$487$	−12.1610	+	12.1610i	−0.551065	+	0.551065i	−0.926748	−	0.375683i	$-0.877408\pi$
$487$	−12.1610	+	12.1610i	−0.551065	+	0.551065i	0.375683	+	0.926748i	$0.377408\pi$
$488$	5.58952	+	5.58952i	0.253026	+	0.253026i
$489$		−	37.7397i		−	1.70665i
$490$	2.22728	−	0.198102i	0.100618	−	0.00894935i
$491$		−	5.15042i		−	0.232435i	−0.993224	−	0.116218i	$-0.962923\pi$
$491$		−	5.15042i		−	0.232435i	0.993224	−	0.116218i	$-0.0370770\pi$
$492$	12.9021	+	12.9021i	0.581673	+	0.581673i
$493$	−11.3667	−	11.3667i	−0.511929	−	0.511929i
$494$	−1.85172			−0.0833130
$495$	−32.8772	−	32.6062i	−1.47772	−	1.46554i
$496$	−3.24365			−0.145644
$497$	−4.71214	−	4.71214i	−0.211368	−	0.211368i
$498$	−5.76603	−	5.76603i	−0.258382	−	0.258382i
$499$		−	28.5435i		−	1.27778i	−0.769297	−	0.638891i	$-0.779394\pi$
$499$		−	28.5435i		−	1.27778i	0.769297	−	0.638891i	$-0.220606\pi$
$500$	9.70658	+	5.54818i	0.434092	+	0.248122i
$501$			30.6408i			1.36893i
$502$	3.19791	+	3.19791i	0.142730	+	0.142730i
$503$	−0.756282	+	0.756282i	−0.0337209	+	0.0337209i	−0.723766	−	0.690045i	$-0.757591\pi$
$503$	−0.756282	+	0.756282i	−0.0337209	+	0.0337209i	0.690045	+	0.723766i	$0.257591\pi$
$504$			6.24365i			0.278114i
$505$	−4.28316	+	5.11946i	−0.190598	+	0.227813i
$506$	27.7348	+	2.35119i	1.23296	+	0.104523i
$507$	−19.0111	+	19.0111i	−0.844313	+	0.844313i
$508$	−1.52521	+	1.52521i	−0.0676704	+	0.0676704i
$509$			15.1157i			0.669992i	0.942220	+	0.334996i	$0.108735\pi$
$509$			15.1157i			0.669992i	−0.942220	+	0.334996i	$0.891265\pi$
$510$	21.9649	−	1.95364i	0.972623	−	0.0865088i
$511$	5.50428			0.243495
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	2.76287	−	2.76287i	0.121984	−	0.121984i
$514$	5.93409			0.261741
$515$	0.683499	+	7.68461i	0.0301186	+	0.338625i
$516$			33.7072i			1.48388i
$517$	9.98027	+	11.8291i	0.438932	+	0.520245i
$518$	5.43000	+	5.43000i	0.238581	+	0.238581i
$519$	50.1752			2.20245
$520$	−6.70595	+	8.01532i	−0.294075	+	0.351495i
$521$	31.0844			1.36183			0.680917	−	0.732361i	$-0.261581\pi$
$521$	31.0844			1.36183			0.680917	+	0.732361i	$0.261581\pi$
$522$	−21.8795	+	21.8795i	−0.957640	+	0.957640i
$523$	−11.5361	+	11.5361i	−0.504437	+	0.504437i	−0.912813	−	0.408377i	$-0.866095\pi$
$523$	−11.5361	+	11.5361i	−0.504437	+	0.504437i	0.408377	+	0.912813i	$0.366095\pi$
$524$	−11.7099			−0.511550
$525$	−14.9631	+	2.68297i	−0.653041	+	0.117094i
$526$	0.0781078			0.00340566
$527$	−7.43966	−	7.43966i	−0.324077	−	0.324077i
$528$	7.70704	−	6.50244i	0.335406	−	0.282982i
$529$			47.4315i			2.06224i
$530$	−20.1239	+	24.0532i	−0.874127	+	1.04480i
$531$	−77.7464			−3.37391
$532$	0.280159	−	0.280159i	0.0121464	−	0.0121464i
$533$	−19.8333	−	19.8333i	−0.859077	−	0.859077i
$534$	17.8424			0.772117
$535$	0.655372	+	7.36838i	0.0283342	+	0.318563i
$536$			11.3689i			0.491063i
$537$	15.5546	−	15.5546i	0.671231	−	0.671231i
$538$	−8.57497	+	8.57497i	−0.369693	+	0.369693i
$539$	3.30477	+	0.280159i	0.142347	+	0.0120673i
$540$	−1.95364	−	21.9649i	−0.0840714	−	0.945220i
$541$		−	35.3282i		−	1.51888i	−0.650579	−	0.759438i	$-0.725474\pi$
$541$		−	35.3282i		−	1.51888i	0.650579	−	0.759438i	$-0.274526\pi$
$542$	−20.8906	+	20.8906i	−0.897330	+	0.897330i
$543$	29.9200	+	29.9200i	1.28399	+	1.28399i
$544$			3.24365i			0.139070i
$545$	16.9130	+	14.1501i	0.724472	+	0.606124i
$546$		−	14.2095i		−	0.608109i
$547$	15.7186	+	15.7186i	0.672081	+	0.672081i	0.958195	−	0.286115i	$-0.0923638\pi$
$547$	15.7186	+	15.7186i	0.672081	+	0.672081i	−0.286115	+	0.958195i	$0.592364\pi$
$548$	−9.10365	−	9.10365i	−0.388889	−	0.388889i
$549$	49.3547			2.10641
$550$	12.7627	+	10.5883i	0.544204	+	0.451489i
$551$	1.96351			0.0836484
$552$	18.0422	+	18.0422i	0.767928	+	0.767928i
$553$	9.98302	+	9.98302i	0.424521	+	0.424521i
$554$			19.5546i			0.830796i
$555$	−40.0406	−	33.4997i	−1.69963	−	1.42198i
$556$		−	12.3301i		−	0.522914i
$557$	−9.98234	−	9.98234i	−0.422965	−	0.422965i	0.463258	−	0.886223i	$-0.346680\pi$
$557$	−9.98234	−	9.98234i	−0.422965	−	0.422965i	−0.886223	+	0.463258i	$0.846680\pi$
$558$	−14.3205	+	14.3205i	−0.606234	+	0.606234i
$559$		−	51.8152i		−	2.19155i
$560$	−0.198102	−	2.22728i	−0.00837135	−	0.0941196i
$561$	32.5910	+	2.76287i	1.37599	+	0.116648i
$562$	−6.94396	+	6.94396i	−0.292913	+	0.292913i
$563$	14.4920	−	14.4920i	0.610764	−	0.610764i	−0.332381	−	0.943145i	$-0.607852\pi$
$563$	14.4920	−	14.4920i	0.610764	−	0.610764i	0.943145	+	0.332381i	$0.107852\pi$
$564$			14.1876i			0.597406i
$565$	−0.751760	−	8.45207i	−0.0316268	−	0.355581i
$566$	23.2814			0.978592
$567$	7.95652	+	7.95652i	0.334142	+	0.334142i
$568$	−4.71214	+	4.71214i	−0.197717	+	0.197717i
$569$	22.6568			0.949824			0.474912	−	0.880033i	$-0.342480\pi$
$569$	22.6568			0.949824			0.474912	+	0.880033i	$0.342480\pi$
$570$	−1.72840	+	2.06588i	−0.0723949	+	0.0865303i
$571$		−	18.4539i		−	0.772272i	−0.922442	−	0.386136i	$-0.873810\pi$
$571$		−	18.4539i		−	0.772272i	0.922442	−	0.386136i	$-0.126190\pi$
$572$	−11.8474	+	9.99565i	−0.495364	+	0.417939i
$573$	2.87225	+	2.87225i	0.119990	+	0.119990i
$574$	6.00143			0.250495
$575$	−23.9689	+	34.4424i	−0.999572	+	1.43635i
$576$	6.24365			0.260152
$577$	−12.6833	+	12.6833i	−0.528014	+	0.528014i	−0.919980	−	0.391966i	$-0.871795\pi$
$577$	−12.6833	+	12.6833i	−0.528014	+	0.528014i	0.391966	+	0.919980i	$0.371795\pi$
$578$	4.58116	−	4.58116i	0.190551	−	0.190551i
$579$	42.9575			1.78525
$580$	7.11079	−	8.49921i	0.295260	−	0.352910i
$581$	−2.68207			−0.111271
$582$	−9.86179	−	9.86179i	−0.408784	−	0.408784i
$583$	−35.5528	+	29.9960i	−1.47245	+	1.24231i
$584$		−	5.50428i		−	0.227769i
$585$	5.78075	+	64.9933i	0.239005	+	2.68714i
$586$	−1.13873			−0.0470407
$587$	18.6007	−	18.6007i	0.767731	−	0.767731i	−0.209975	−	0.977707i	$-0.567338\pi$
$587$	18.6007	−	18.6007i	0.767731	−	0.767731i	0.977707	+	0.209975i	$0.0673384\pi$
$588$	2.14984	+	2.14984i	0.0886580	+	0.0886580i
$589$	1.28515			0.0529537
$590$	27.7342	−	2.46679i	1.14180	−	0.101556i
$591$			42.6246i			1.75334i
$592$	5.43000	−	5.43000i	0.223172	−	0.223172i
$593$	33.5426	−	33.5426i	1.37743	−	1.37743i	0.528486	−	0.848942i	$-0.322760\pi$
$593$	33.5426	−	33.5426i	1.37743	−	1.37743i	0.848942	−	0.528486i	$-0.177240\pi$
$594$	2.76287	−	32.5910i	0.113362	−	1.33722i
$595$	4.65412	−	5.56286i	0.190801	−	0.228055i
$596$		−	5.76190i		−	0.236017i
$597$	17.9819	−	17.9819i	0.735950	−	0.735950i
$598$	−27.7348	−	27.7348i	−1.13416	−	1.13416i
$599$		−	17.9354i		−	0.732821i	−0.930453	−	0.366410i	$-0.880587\pi$
$599$		−	17.9354i		−	0.732821i	0.930453	−	0.366410i	$-0.119413\pi$
$600$	2.68297	+	14.9631i	0.109532	+	0.610864i
$601$		−	9.42764i		−	0.384562i	−0.981340	−	0.192281i	$-0.938412\pi$
$601$		−	9.42764i		−	0.384562i	0.981340	−	0.192281i	$-0.0615884\pi$
$602$	7.83946	+	7.83946i	0.319513	+	0.319513i
$603$	50.1930	+	50.1930i	2.04402	+	2.04402i
$604$	14.0115			0.570120
$605$	15.9389	+	18.7337i	0.648007	+	0.761634i
$606$	−9.07573			−0.368676
$607$	0.368589	+	0.368589i	0.0149606	+	0.0149606i	0.714548	−	0.699587i	$-0.246633\pi$
$607$	0.368589	+	0.368589i	0.0149606	+	0.0149606i	−0.699587	+	0.714548i	$0.746633\pi$
$608$	−0.280159	−	0.280159i	−0.0113619	−	0.0113619i
$609$			15.0673i			0.610558i
$610$	−17.6061	+	1.56596i	−0.712851	+	0.0634037i
$611$		−	21.8094i		−	0.882314i
$612$	14.3205	+	14.3205i	0.578871	+	0.578871i
$613$	6.75253	−	6.75253i	0.272732	−	0.272732i	−0.557467	−	0.830199i	$-0.688227\pi$
$613$	6.75253	−	6.75253i	0.272732	−	0.272732i	0.830199	+	0.557467i	$0.188227\pi$
$614$		−	29.0040i		−	1.17051i
$615$	−40.6397	+	3.61465i	−1.63875	+	0.145757i
$616$	0.280159	−	3.30477i	0.0112879	−	0.133153i
$617$	6.80159	−	6.80159i	0.273822	−	0.273822i	−0.556815	−	0.830637i	$-0.687977\pi$
$617$	6.80159	−	6.80159i	0.273822	−	0.273822i	0.830637	+	0.556815i	$0.187977\pi$
$618$	−7.41746	+	7.41746i	−0.298374	+	0.298374i
$619$		−	13.1025i		−	0.526635i	−0.964709	−	0.263318i	$-0.915183\pi$
$619$		−	13.1025i		−	0.526635i	0.964709	−	0.263318i	$-0.0848168\pi$
$620$	4.65412	−	5.56286i	0.186914	−	0.223410i
$621$	82.7635			3.32119
$622$	2.14544	+	2.14544i	0.0860243	+	0.0860243i
$623$	4.14970	−	4.14970i	0.166254	−	0.166254i
$624$	−14.2095			−0.568834
$625$	−23.4425	+	8.68604i	−0.937702	+	0.347442i
$626$		−	15.2551i		−	0.609716i
$627$	−3.05356	+	2.57630i	−0.121948	+	0.102887i
$628$	5.18890	+	5.18890i	0.207060	+	0.207060i
$629$	24.9086			0.993170
$630$	−10.7079	−	8.95865i	−0.426612	−	0.356921i
$631$	−48.4453			−1.92857			−0.964287	−	0.264858i	$-0.914675\pi$
$631$	−48.4453			−1.92857			−0.964287	+	0.264858i	$0.914675\pi$
$632$	9.98302	−	9.98302i	0.397103	−	0.397103i
$633$	−45.4053	+	45.4053i	−1.80470	+	1.80470i
$634$	2.81652			0.111858
$635$	−0.427302	−	4.80418i	−0.0169570	−	0.190648i
$636$	−42.6413			−1.69084
$637$	−3.30477	−	3.30477i	−0.130940	−	0.130940i
$638$	12.5626	−	10.5991i	0.497358	−	0.419622i
$639$			41.6075i			1.64597i
$640$	−2.22728	+	0.198102i	−0.0880408	+	0.00783068i
$641$	18.5376			0.732192			0.366096	−	0.930577i	$-0.380694\pi$
$641$	18.5376			0.732192			0.366096	+	0.930577i	$0.380694\pi$
$642$	−7.11222	+	7.11222i	−0.280697	+	0.280697i
$643$	24.1330	+	24.1330i	0.951713	+	0.951713i	0.998887	−	0.0471738i	$-0.0150215\pi$
$643$	24.1330	+	24.1330i	0.951713	+	0.951713i	−0.0471738	+	0.998887i	$0.515021\pi$
$644$	8.39234			0.330705
$645$	−57.8079	−	48.3645i	−2.27618	−	1.90435i
$646$		−	1.28515i		−	0.0505635i
$647$	−26.8627	+	26.8627i	−1.05608	+	1.05608i	−0.0577513	+	0.998331i	$0.518393\pi$
$647$	−26.8627	+	26.8627i	−1.05608	+	1.05608i	−0.998331	+	0.0577513i	$0.981607\pi$
$648$	7.95652	−	7.95652i	0.312561	−	0.312561i
$649$	41.1513	+	3.48856i	1.61533	+	0.136938i
$650$	−4.12430	−	23.0014i	−0.161768	−	0.902190i
$651$			9.86179i			0.386514i
$652$	−8.77731	+	8.77731i	−0.343746	+	0.343746i
$653$	−9.03668	−	9.03668i	−0.353632	−	0.353632i	0.507827	−	0.861459i	$-0.330449\pi$
$653$	−9.03668	−	9.03668i	−0.353632	−	0.353632i	−0.861459	+	0.507827i	$0.830449\pi$
$654$			29.9832i			1.17243i
$655$	16.8019	−	20.0825i	0.656504	−	0.784689i
$656$		−	6.00143i		−	0.234316i
$657$	−24.3010	−	24.3010i	−0.948072	−	0.948072i
$658$	3.29969	+	3.29969i	0.128635	+	0.128635i
$659$	−13.8288			−0.538693			−0.269346	−	0.963043i	$-0.586808\pi$
$659$	−13.8288			−0.538693			−0.269346	+	0.963043i	$0.586808\pi$
$660$	0.0933128	+	22.5476i	0.00363220	+	0.877662i
$661$	15.8833			0.617790			0.308895	−	0.951096i	$-0.400041\pi$
$661$	15.8833			0.617790			0.308895	+	0.951096i	$0.400041\pi$
$662$	12.8900	+	12.8900i	0.500985	+	0.500985i
$663$	−32.5910	−	32.5910i	−1.26573	−	1.26573i
$664$			2.68207i			0.104085i
$665$	0.0784891	+	0.882457i	0.00304368	+	0.0342202i
$666$		−	47.9461i		−	1.85787i
$667$	29.4091	+	29.4091i	1.13873	+	1.13873i
$668$	7.12630	−	7.12630i	0.275725	−	0.275725i
$669$		−	32.6387i		−	1.26189i
$670$	−19.4977	−	16.3126i	−0.753263	−	0.630212i
$671$	−26.1235	−	2.21460i	−1.00849	−	0.0854935i
$672$	2.14984	−	2.14984i	0.0829320	−	0.0829320i
$673$	−28.4404	+	28.4404i	−1.09630	+	1.09630i	−0.101457	+	0.994840i	$0.532351\pi$
$673$	−28.4404	+	28.4404i	−1.09630	+	1.09630i	−0.994840	+	0.101457i	$0.967649\pi$
$674$		−	17.5298i		−	0.675224i
$675$	40.4730	+	28.1657i	1.55781	+	1.08410i
$676$	8.84302			0.340116
$677$	7.22013	+	7.22013i	0.277492	+	0.277492i	0.832107	−	0.554615i	$-0.187134\pi$
$677$	7.22013	+	7.22013i	0.277492	+	0.277492i	−0.554615	+	0.832107i	$0.687134\pi$
$678$	8.15823	−	8.15823i	0.313315	−	0.313315i
$679$	−4.58721			−0.176041
$680$	−5.56286	−	4.65412i	−0.213326	−	0.178478i
$681$		−	78.7973i		−	3.01952i
$682$	8.22242	−	6.93727i	0.314853	−	0.265642i
$683$	0.553161	+	0.553161i	0.0211661	+	0.0211661i	0.717611	−	0.696445i	$-0.245236\pi$
$683$	0.553161	+	0.553161i	0.0211661	+	0.0211661i	−0.696445	+	0.717611i	$0.745236\pi$
$684$	−2.47376			−0.0945867
$685$	28.6751	−	2.55047i	1.09562	−	0.0974485i
$686$	1.00000			0.0381802
$687$	4.35732	−	4.35732i	0.166242	−	0.166242i
$688$	7.83946	−	7.83946i	0.298877	−	0.298877i
$689$	65.5488			2.49721
$690$	−56.8302	+	5.05469i	−2.16349	+	0.192429i
$691$	−37.0102			−1.40793			−0.703966	−	0.710233i	$-0.748589\pi$
$691$	−37.0102			−1.40793			−0.703966	+	0.710233i	$0.748589\pi$
$692$	−11.6695	−	11.6695i	−0.443608	−	0.443608i
$693$	−13.3534	−	15.8272i	−0.507255	−	0.601226i
$694$			17.2692i			0.655530i
$695$	21.1462	+	17.6918i	0.802121	+	0.671088i
$696$	15.0673			0.571125
$697$	13.7649	−	13.7649i	0.521383	−	0.521383i
$698$	−19.9102	−	19.9102i	−0.753611	−	0.753611i
$699$	24.3638			0.921522
$700$	4.10403	+	2.85604i	0.155118	+	0.107948i
$701$		−	17.0518i		−	0.644038i	−0.946733	−	0.322019i	$-0.895639\pi$
$701$		−	17.0518i		−	0.644038i	0.946733	−	0.322019i	$-0.104361\pi$
$702$	−32.5910	+	32.5910i	−1.23007	+	1.23007i
$703$	−2.15139	+	2.15139i	−0.0811413	+	0.0811413i
$704$	−3.30477	−	0.280159i	−0.124553	−	0.0105589i
$705$	−24.3318	−	20.3570i	−0.916388	−	0.766688i
$706$		−	10.0221i		−	0.377185i
$707$	−2.11079	+	2.11079i	−0.0793844	+	0.0793844i
$708$	26.7700	+	26.7700i	1.00608	+	1.00608i
$709$			49.0505i			1.84213i	0.389410	+	0.921065i	$0.372679\pi$
$709$			49.0505i			1.84213i	−0.389410	+	0.921065i	$0.627321\pi$
$710$	−1.32015	−	14.8425i	−0.0495443	−	0.557029i
$711$		−	88.1486i		−	3.30583i
$712$	−4.14970	−	4.14970i	−0.155517	−	0.155517i
$713$	19.2487	+	19.2487i	0.720871	+	0.720871i
$714$	9.86179			0.369068
$715$	−0.143442	−	34.6604i	−0.00536442	−	1.29623i
$716$	−7.23523			−0.270393
$717$	−0.196406	−	0.196406i	−0.00733491	−	0.00733491i
$718$	1.93540	+	1.93540i	0.0722285	+	0.0722285i
$719$		−	30.3303i		−	1.13113i	−0.824704	−	0.565565i	$-0.808658\pi$
$719$		−	30.3303i		−	1.13113i	0.824704	−	0.565565i	$-0.191342\pi$
$720$	−8.95865	+	10.7079i	−0.333869	+	0.399059i
$721$			3.45023i			0.128493i
$722$	−13.3240	−	13.3240i	−0.495869	−	0.495869i
$723$	53.0308	−	53.0308i	1.97224	−	1.97224i
$724$		−	13.9173i		−	0.517232i
$725$	4.37328	+	24.3900i	0.162420	+	0.905823i
$726$	−5.62986	+	32.9664i	−0.208944	+	1.22350i
$727$	−17.5774	+	17.5774i	−0.651911	+	0.651911i	−0.953453	−	0.301542i	$-0.902499\pi$
$727$	−17.5774	+	17.5774i	−0.651911	+	0.651911i	0.301542	+	0.953453i	$0.402499\pi$
$728$	−3.30477	+	3.30477i	−0.122483	+	0.122483i
$729$			19.6946i			0.729430i
$730$	9.43985	+	7.89777i	0.349384	+	0.292310i
$731$	35.9613			1.33008
$732$	−16.9940	−	16.9940i	−0.628118	−	0.628118i
$733$	−13.4698	+	13.4698i	−0.497519	+	0.497519i	−0.910665	−	0.413146i	$-0.864430\pi$
$733$	−13.4698	+	13.4698i	−0.497519	+	0.497519i	0.413146	+	0.910665i	$0.364430\pi$
$734$	−0.859751			−0.0317340
$735$	−6.77167	+	0.602298i	−0.249777	+	0.0222161i
$736$		−	8.39234i		−	0.309346i
$737$	−24.3150	−	28.8194i	−0.895655	−	1.06158i
$738$	−26.4959	−	26.4959i	−0.975326	−	0.975326i
$739$	−40.8681			−1.50336			−0.751678	−	0.659530i	$-0.770755\pi$
$739$	−40.8681			−1.50336			−0.751678	+	0.659530i	$0.770755\pi$
$740$	1.52126	+	17.1037i	0.0559228	+	0.628743i
$741$	5.62986			0.206818
$742$	−9.91730	+	9.91730i	−0.364076	+	0.364076i
$743$	25.1350	−	25.1350i	0.922112	−	0.922112i	−0.0750665	−	0.997179i	$-0.523917\pi$
$743$	25.1350	−	25.1350i	0.922112	−	0.922112i	0.997179	+	0.0750665i	$0.0239169\pi$
$744$	9.86179			0.361551
$745$	9.88167	+	8.26742i	0.362036	+	0.302895i
$746$	1.29112			0.0472713
$747$	11.8411	+	11.8411i	0.433245	+	0.433245i
$748$	−6.93727	−	8.22242i	−0.253652	−	0.300641i
$749$			3.30825i			0.120881i
$750$	−29.5113	−	16.8683i	−1.07760	−	0.615944i
$751$	14.9041			0.543860			0.271930	−	0.962317i	$-0.412338\pi$
$751$	14.9041			0.543860			0.271930	+	0.962317i	$0.412338\pi$
$752$	3.29969	−	3.29969i	0.120327	−	0.120327i
$753$	−9.72272	−	9.72272i	−0.354316	−	0.354316i
$754$	−23.1617			−0.843499
$755$	−20.1043	+	24.0297i	−0.731670	+	0.874531i
$756$		−	9.86179i		−	0.358670i
$757$	−33.1370	+	33.1370i	−1.20438	+	1.20438i	−0.231565	+	0.972819i	$0.574385\pi$
$757$	−33.1370	+	33.1370i	−1.20438	+	1.20438i	−0.972819	+	0.231565i	$0.925615\pi$
$758$	−2.89735	+	2.89735i	−0.105236	+	0.105236i
$759$	−84.3231	−	7.14841i	−3.06073	−	0.259471i
$760$	0.882457	−	0.0784891i	0.0320101	−	0.00284710i
$761$		−	35.8947i		−	1.30118i	−0.759428	−	0.650592i	$-0.774521\pi$
$761$		−	35.8947i		−	1.30118i	0.759428	−	0.650592i	$-0.225479\pi$
$762$	4.63716	−	4.63716i	0.167987	−	0.167987i
$763$	6.97334	+	6.97334i	0.252452	+	0.252452i
$764$		−	1.33603i		−	0.0483358i
$765$	−45.1073	+	4.01201i	−1.63086	+	0.145055i
$766$		−	23.1738i		−	0.837304i
$767$	−41.1513	−	41.1513i	−1.48589	−	1.48589i
$768$	−2.14984	−	2.14984i	−0.0775758	−	0.0775758i
$769$	−23.3132			−0.840696			−0.420348	−	0.907363i	$-0.638092\pi$
$769$	−23.3132			−0.840696			−0.420348	+	0.907363i	$0.638092\pi$
$770$	5.26570	+	5.22230i	0.189763	+	0.188199i
$771$	−18.0416			−0.649753
$772$	−9.99085	−	9.99085i	−0.359579	−	0.359579i
$773$	−9.24967	−	9.24967i	−0.332687	−	0.332687i	0.520919	−	0.853606i	$-0.325589\pi$
$773$	−9.24967	−	9.24967i	−0.332687	−	0.332687i	−0.853606	+	0.520919i	$0.825589\pi$
$774$		−	69.2213i		−	2.48811i
$775$	2.86238	+	15.9637i	0.102820	+	0.573432i
$776$			4.58721i			0.164671i
$777$	−16.5090	−	16.5090i	−0.592258	−	0.592258i
$778$	−18.1989	+	18.1989i	−0.652462	+	0.652462i
$779$			2.37779i			0.0851933i
$780$	20.3884	−	24.3693i	0.730020	−	0.872560i
$781$	1.86697	−	22.0229i	0.0668055	−	0.788041i
$782$	19.2487	−	19.2487i	0.688334	−	0.688334i
$783$	34.5585	−	34.5585i	1.23502	−	1.23502i
$784$		−	1.00000i		−	0.0357143i
$785$	−16.3442	+	1.45372i	−0.583350	+	0.0518854i
$786$	35.6021			1.26988
$787$	−38.5215	−	38.5215i	−1.37314	−	1.37314i	−0.855745	−	0.517398i	$-0.826901\pi$
$787$	−38.5215	−	38.5215i	−1.37314	−	1.37314i	−0.517398	−	0.855745i	$-0.673099\pi$
$788$	9.91342	−	9.91342i	0.353151	−	0.353151i
$789$	−0.237474			−0.00845430
$790$	2.79683	+	31.4449i	0.0995068	+	1.11876i
$791$		−	3.79480i		−	0.134928i
$792$	−15.8272	+	13.3534i	−0.562395	+	0.474494i
$793$	26.1235	+	26.1235i	0.927672	+	0.927672i
$794$	−11.2724			−0.400043
$795$	61.1835	−	73.1298i	2.16996	−	2.59365i
$796$	−8.36429			−0.296464
$797$	20.0195	−	20.0195i	0.709128	−	0.709128i	−0.257224	−	0.966352i	$-0.582808\pi$
$797$	20.0195	−	20.0195i	0.709128	−	0.709128i	0.966352	+	0.257224i	$0.0828078\pi$
$798$	−0.851778	+	0.851778i	−0.0301526	+	0.0301526i
$799$	15.1364			0.535486
$800$	2.85604	−	4.10403i	0.100976	−	0.145099i
$801$	−36.6413			−1.29466
$802$	18.4204	+	18.4204i	0.650446	+	0.650446i
$803$	11.7721	+	13.9530i	0.415430	+	0.492389i
$804$		−	34.5654i		−	1.21903i
$805$	−12.0417	+	14.3929i	−0.424414	+	0.507282i
$806$	−15.1597			−0.533977
$807$	26.0708	−	26.0708i	0.917736	−	0.917736i
$808$	2.11079	+	2.11079i	0.0742573	+	0.0742573i
$809$	−19.2982			−0.678488			−0.339244	−	0.940698i	$-0.610171\pi$
$809$	−19.2982			−0.678488			−0.339244	+	0.940698i	$0.610171\pi$
$810$	2.22909	+	25.0618i	0.0783222	+	0.880581i
$811$		−	37.9101i		−	1.33120i	−0.746307	−	0.665602i	$-0.768175\pi$
$811$		−	37.9101i		−	1.33120i	0.746307	−	0.665602i	$-0.231825\pi$
$812$	3.50428	−	3.50428i	0.122976	−	0.122976i
$813$	63.5146	−	63.5146i	2.22755	−	2.22755i
$814$	−2.15139	+	25.3779i	−0.0754063	+	0.889496i
$815$	−2.45904	−	27.6471i	−0.0861365	−	0.968437i
$816$		−	9.86179i		−	0.345232i
$817$	−3.10603	+	3.10603i	−0.108666	+	0.108666i
$818$	−6.01698	−	6.01698i	−0.210379	−	0.210379i
$819$			29.1806i			1.01965i
$820$	10.2925	+	8.61110i	0.359428	+	0.300713i
$821$			46.0769i			1.60809i	0.594566	+	0.804047i	$0.297324\pi$
$821$			46.0769i			1.60809i	−0.594566	+	0.804047i	$0.702676\pi$
$822$	27.6782	+	27.6782i	0.965387	+	0.965387i
$823$	−4.86619	−	4.86619i	−0.169625	−	0.169625i	0.617190	−	0.786814i	$-0.288271\pi$
$823$	−4.86619	−	4.86619i	−0.169625	−	0.169625i	−0.786814	+	0.617190i	$0.788271\pi$
$824$	3.45023			0.120195
$825$	−38.8030	−	32.1921i	−1.35095	−	1.12079i
$826$	12.4521			0.433263
$827$	14.7761	+	14.7761i	0.513814	+	0.513814i	0.915693	−	0.401879i	$-0.131643\pi$
$827$	14.7761	+	14.7761i	0.513814	+	0.513814i	−0.401879	+	0.915693i	$0.631643\pi$
$828$	−37.0516	−	37.0516i	−1.28763	−	1.28763i
$829$		−	18.8528i		−	0.654786i	−0.944888	−	0.327393i	$-0.893830\pi$
$829$		−	18.8528i		−	0.654786i	0.944888	−	0.327393i	$-0.106170\pi$
$830$	−4.59975	−	3.84835i	−0.159660	−	0.133578i
$831$		−	59.4526i		−	2.06239i
$832$	3.30477	+	3.30477i	0.114572	+	0.114572i
$833$	2.29361	−	2.29361i	0.0794688	−	0.0794688i
$834$			37.4878i			1.29810i
$835$	1.99650	+	22.4467i	0.0690916	+	0.776801i
$836$	1.30937	+	0.111000i	0.0452854	+	0.00383903i
$837$	22.6191	−	22.6191i	0.781829	−	0.781829i
$838$	−2.61563	+	2.61563i	−0.0903553	+	0.0903553i
$839$		−	47.8316i		−	1.65133i	−0.564160	−	0.825665i	$-0.690800\pi$
$839$		−	47.8316i		−	1.65133i	0.564160	−	0.825665i	$-0.309200\pi$
$840$	0.602298	+	6.77167i	0.0207813	+	0.233645i
$841$	−4.44002			−0.153104
$842$	−9.77894	−	9.77894i	−0.337005	−	0.337005i
$843$	21.1120	−	21.1120i	0.727136	−	0.727136i
$844$	21.1203			0.726990
$845$	−12.6883	+	15.1658i	−0.436492	+	0.521719i
$846$		−	29.1357i		−	1.00171i
$847$	6.35781	+	8.97654i	0.218457	+	0.308438i
$848$	9.91730	+	9.91730i	0.340562	+	0.340562i
$849$	−70.7834			−2.42928
$850$	15.9637	−	2.86238i	0.547549	−	0.0981789i
$851$	−64.4463			−2.20919
$852$	14.3265	−	14.3265i	0.490818	−	0.490818i
$853$	29.2794	−	29.2794i	1.00251	−	1.00251i	0.00251044	−	0.999997i	$-0.499201\pi$
$853$	29.2794	−	29.2794i	1.00251	−	1.00251i	0.999997	−	0.00251044i	$-0.000799098\pi$
$854$	−7.90478			−0.270496
$855$	3.54946	−	4.24251i	0.121389	−	0.145091i
$856$	3.30825			0.113074
$857$	6.57238	+	6.57238i	0.224508	+	0.224508i	0.810394	−	0.585886i	$-0.199253\pi$
$857$	6.57238	+	6.57238i	0.224508	+	0.224508i	−0.585886	+	0.810394i	$0.699253\pi$
$858$	36.0200	−	30.3901i	1.22970	−	1.03750i
$859$			16.3959i			0.559421i	0.960084	+	0.279710i	$0.0902384\pi$
$859$			16.3959i			0.559421i	−0.960084	+	0.279710i	$0.909762\pi$
$860$	2.19630	+	24.6931i	0.0748931	+	0.842027i
$861$	−18.2464			−0.621834
$862$	24.3694	−	24.3694i	0.830024	−	0.830024i
$863$	14.5603	+	14.5603i	0.495639	+	0.495639i	0.910077	−	0.414438i	$-0.136022\pi$
$863$	14.5603	+	14.5603i	0.495639	+	0.495639i	−0.414438	+	0.910077i	$0.636022\pi$
$864$	−9.86179			−0.335505
$865$	36.7571	−	3.26932i	1.24978	−	0.111160i
$866$			9.21055i			0.312987i
$867$	−13.9283	+	13.9283i	−0.473029	+	0.473029i
$868$	2.29361	−	2.29361i	0.0778501	−	0.0778501i
$869$	−3.95532	+	46.6571i	−0.134175	+	1.58274i
$870$	−21.6192	+	25.8405i	−0.732960	+	0.876073i
$871$			53.1345i			1.80039i
$872$	6.97334	−	6.97334i	0.236147	−	0.236147i
$873$	20.2522	+	20.2522i	0.685434	+	0.685434i
$874$			3.32509i			0.112473i
$875$	−10.7867	+	2.94044i	−0.364658	+	0.0994049i
$876$			16.7349i			0.565419i
$877$	19.8407	+	19.8407i	0.669974	+	0.669974i	0.957710	−	0.287736i	$-0.0929025\pi$
$877$	19.8407	+	19.8407i	0.669974	+	0.669974i	−0.287736	+	0.957710i	$0.592902\pi$
$878$	18.1621	+	18.1621i	0.612940	+	0.612940i
$879$	3.46214			0.116775
$880$	5.22230	−	5.26570i	0.176044	−	0.177507i
$881$	−6.16569			−0.207727			−0.103864	−	0.994592i	$-0.533121\pi$
$881$	−6.16569			−0.207727			−0.103864	+	0.994592i	$0.533121\pi$
$882$	−4.41493	−	4.41493i	−0.148658	−	0.148658i
$883$	13.6906	+	13.6906i	0.460727	+	0.460727i	0.898894	−	0.438167i	$-0.144372\pi$
$883$	13.6906	+	13.6906i	0.460727	+	0.460727i	−0.438167	+	0.898894i	$0.644372\pi$
$884$			15.1597i			0.509876i
$885$	−84.3213	+	7.49986i	−2.83443	+	0.252105i
$886$			31.3163i			1.05209i
$887$	−17.5547	−	17.5547i	−0.589428	−	0.589428i	0.348049	−	0.937476i	$-0.386844\pi$
$887$	−17.5547	−	17.5547i	−0.589428	−	0.589428i	−0.937476	+	0.348049i	$0.886844\pi$
$888$	−16.5090	+	16.5090i	−0.554007	+	0.554007i
$889$		−	2.15698i		−	0.0723427i
$890$	13.0709	−	1.16258i	0.438138	−	0.0389697i
$891$	−3.15241	+	37.1860i	−0.105610	+	1.24578i
$892$	−7.59095	+	7.59095i	−0.254164	+	0.254164i
$893$	−1.30735	+	1.30735i	−0.0437488	+	0.0437488i
$894$			17.5181i			0.585894i
$895$	10.3814	−	12.4084i	0.347012	−	0.414768i
$896$	−1.00000			−0.0334077
$897$	84.3231	+	84.3231i	2.81547	+	2.81547i
$898$	5.73610	−	5.73610i	0.191416	−	0.191416i
$899$	16.0749			0.536128
$900$	−5.50975	−	30.7282i	−0.183658	−	1.02427i
$901$			45.4928i			1.51558i
$902$	12.8354	+	15.2132i	0.427372	+	0.506544i
$903$	−23.8346	−	23.8346i	−0.793166	−	0.793166i
$904$	−3.79480			−0.126213
$905$	23.8682	+	19.9691i	0.793405	+	0.663796i
$906$	−42.5997			−1.41528
$907$	28.1124	−	28.1124i	0.933456	−	0.933456i	−0.0644643	−	0.997920i	$-0.520534\pi$
$907$	28.1124	−	28.1124i	0.933456	−	0.933456i	0.997920	+	0.0644643i	$0.0205339\pi$
$908$	−18.3263	+	18.3263i	−0.608180	+	0.608180i
$909$	18.6380			0.618182
$910$	−0.925861	−	10.4095i	−0.0306920	−	0.345072i
$911$	37.3644			1.23794			0.618969	−	0.785415i	$-0.287550\pi$
$911$	37.3644			1.23794			0.618969	+	0.785415i	$0.287550\pi$
$912$	0.851778	+	0.851778i	0.0282052	+	0.0282052i
$913$	−5.73621	−	6.79886i	−0.189841	−	0.225009i
$914$			4.84288i			0.160188i
$915$	53.5286	−	4.76103i	1.76960	−	0.157395i
$916$	−2.02681			−0.0669676
$917$	8.28016	−	8.28016i	0.273435	−	0.273435i
$918$	−22.6191	−	22.6191i	−0.746540	−	0.746540i
$919$	24.3864			0.804433			0.402217	−	0.915544i	$-0.368240\pi$
$919$	24.3864			0.804433			0.402217	+	0.915544i	$0.368240\pi$
$920$	14.3929	+	12.0417i	0.474519	+	0.397003i
$921$			88.1819i			2.90569i
$922$	−8.60192	+	8.60192i	−0.283289	+	0.283289i
$923$	−22.0229	+	22.0229i	−0.724893	+	0.724893i
$924$	−0.851778	+	10.0476i	−0.0280214	+	0.330542i
$925$	−31.5156	−	21.9321i	−1.03623	−	0.721122i
$926$		−	15.0259i		−	0.493782i
$927$	15.2325	−	15.2325i	0.500302	−	0.500302i
$928$	−3.50428	−	3.50428i	−0.115034	−	0.115034i
$929$		−	27.2794i		−	0.895007i	−0.894282	−	0.447504i	$-0.852313\pi$
$929$		−	27.2794i		−	0.895007i	0.894282	−	0.447504i	$-0.147687\pi$
$930$	−14.1501	+	16.9130i	−0.464000	+	0.554598i
$931$			0.396205i			0.0129851i
$932$	−5.66641	−	5.66641i	−0.185609	−	0.185609i
$933$	−6.52286	−	6.52286i	−0.213549	−	0.213549i
$934$	5.29008			0.173097
$935$	24.0553	−	0.0995528i	0.786694	−	0.00325572i
$936$	29.1806			0.953799
$937$	−16.1087	−	16.1087i	−0.526248	−	0.526248i	0.393203	−	0.919452i	$-0.371367\pi$
$937$	−16.1087	−	16.1087i	−0.526248	−	0.526248i	−0.919452	+	0.393203i	$0.871367\pi$
$938$	−8.03905	−	8.03905i	−0.262484	−	0.262484i
$939$			46.3807i			1.51358i
$940$	0.924437	+	10.3935i	0.0301518	+	0.338998i
$941$		−	3.51397i		−	0.114552i	−0.998358	−	0.0572761i	$-0.981758\pi$
$941$		−	3.51397i		−	0.114552i	0.998358	−	0.0572761i	$-0.0182415\pi$
$942$	−15.7760	−	15.7760i	−0.514010	−	0.514010i
$943$	−35.6142	+	35.6142i	−1.15976	+	1.15976i
$944$		−	12.4521i		−	0.405280i
$945$	16.9130	+	14.1501i	0.550179	+	0.460303i
$946$	−3.10603	+	36.6389i	−0.100986	+	1.19123i
$947$	20.6556	−	20.6556i	0.671215	−	0.671215i	−0.286781	−	0.957996i	$-0.592585\pi$
$947$	20.6556	−	20.6556i	0.671215	−	0.671215i	0.957996	+	0.286781i	$0.0925852\pi$
$948$	−30.3517	+	30.3517i	−0.985779	+	0.985779i
$949$		−	25.7251i		−	0.835072i
$950$	−1.13158	+	1.62603i	−0.0367132	+	0.0527555i
$951$	−8.56318			−0.277680
$952$	−2.29361	−	2.29361i	−0.0743362	−	0.0743362i
$953$	−1.88351	+	1.88351i	−0.0610128	+	0.0610128i	−0.736955	−	0.675942i	$-0.763737\pi$
$953$	−1.88351	+	1.88351i	−0.0610128	+	0.0610128i	0.675942	+	0.736955i	$0.263737\pi$
$954$	87.5683			2.83513
$955$	2.29129	+	1.91699i	0.0741444	+	0.0620323i
$956$			0.0913582i			0.00295474i
$957$	−38.1946	+	32.2248i	−1.23465	+	1.04168i
$958$	−17.0611	−	17.0611i	−0.551220	−	0.551220i
$959$	12.8745			0.415740
$960$	6.77167	−	0.602298i	0.218555	−	0.0194391i
$961$	−20.4787			−0.660604
$962$	25.3779	−	25.3779i	0.818218	−	0.818218i
$963$	14.6057	−	14.6057i	0.470662	−	0.470662i
$964$	−24.6673			−0.794479
$965$	31.4696	−	2.79903i	1.01304	−	0.0901039i
$966$	−25.5156			−0.820950
$967$	6.65882	+	6.65882i	0.214133	+	0.214133i	0.806021	−	0.591887i	$-0.201617\pi$
$967$	6.65882	+	6.65882i	0.214133	+	0.214133i	−0.591887	+	0.806021i	$0.701617\pi$
$968$	8.97654	−	6.35781i	0.288517	−	0.204348i
$969$			3.90729i			0.125520i
$970$	−7.86708	−	6.58193i	−0.252597	−	0.211333i
$971$	−3.41873			−0.109712			−0.0548561	−	0.998494i	$-0.517470\pi$
$971$	−3.41873			−0.109712			−0.0548561	+	0.998494i	$0.517470\pi$
$972$	−3.27048	+	3.27048i	−0.104901	+	0.104901i
$973$	8.71872	+	8.71872i	0.279509	+	0.279509i
$974$	−17.1982			−0.551065
$975$	12.5393	+	69.9321i	0.401577	+	2.23962i
$976$			7.90478i			0.253026i
$977$	15.4705	−	15.4705i	0.494944	−	0.494944i	−0.414916	−	0.909860i	$-0.636189\pi$
$977$	15.4705	−	15.4705i	0.494944	−	0.494944i	0.909860	+	0.414916i	$0.136189\pi$
$978$	26.6860	−	26.6860i	0.853323	−	0.853323i
$979$	19.3943	+	1.64413i	0.619844	+	0.0525467i
$980$	1.71500	+	1.43484i	0.0547837	+	0.0458343i
$981$		−	61.5736i		−	1.96589i
$982$	3.64190	−	3.64190i	0.116218	−	0.116218i
$983$	5.78699	+	5.78699i	0.184576	+	0.184576i	0.793347	−	0.608770i	$-0.208337\pi$
$983$	5.78699	+	5.78699i	0.184576	+	0.184576i	−0.608770	+	0.793347i	$0.708337\pi$
$984$			18.2464i			0.581673i
$985$	2.77733	+	31.2257i	0.0884932	+	0.994934i
$986$		−	16.0749i		−	0.511929i
$987$	−10.0322	−	10.0322i	−0.319327	−	0.319327i
$988$	−1.30937	−	1.30937i	−0.0416565	−	0.0416565i
$989$	−93.0432			−2.95860
$990$	−0.191628	−	46.3037i	−0.00609032	−	1.47163i
$991$	30.8370			0.979570			0.489785	−	0.871843i	$-0.337075\pi$
$991$	30.8370			0.979570			0.489785	+	0.871843i	$0.337075\pi$
$992$	−2.29361	−	2.29361i	−0.0728221	−	0.0728221i
$993$	−39.1900	−	39.1900i	−1.24366	−	1.24366i
$994$		−	6.66397i		−	0.211368i
$995$	12.0014	−	14.3448i	0.380471	−	0.454759i
$996$		−	8.15440i		−	0.258382i
$997$	30.0148	+	30.0148i	0.950577	+	0.950577i	0.998835	−	0.0482580i	$-0.0153670\pi$
$997$	30.0148	+	30.0148i	0.950577	+	0.950577i	−0.0482580	+	0.998835i	$0.515367\pi$
$998$	20.1833	−	20.1833i	0.638891	−	0.638891i
$999$			75.7305i			2.39601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.e.43.5	yes	16
5.2	odd	4	inner	770.2.m.e.197.1	yes	16
11.10	odd	2	inner	770.2.m.e.43.1	✓	16
55.32	even	4	inner	770.2.m.e.197.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.e.43.1	✓	16	11.10	odd	2	inner
770.2.m.e.43.5	yes	16	1.1	even	1	trivial
770.2.m.e.197.1	yes	16	5.2	odd	4	inner
770.2.m.e.197.5	yes	16	55.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.14984 - 2.14984i) q^{3} +1.00000i q^{4} +(-1.71500 - 1.43484i) q^{5} -3.04034i q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +6.24365i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-2.14984 - 2.14984i) q^{3} +1.00000i q^{4} +(-1.71500 - 1.43484i) q^{5} -3.04034i q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +6.24365i q^{9} +(-0.198102 - 2.22728i) q^{10} +(0.280159 - 3.30477i) q^{11} +(2.14984 - 2.14984i) q^{12} +(-3.30477 + 3.30477i) q^{13} -1.00000i q^{14} +(0.602298 + 6.77167i) q^{15} -1.00000 q^{16} +(-2.29361 - 2.29361i) q^{17} +(-4.41493 + 4.41493i) q^{18} +0.396205 q^{19} +(1.43484 - 1.71500i) q^{20} +3.04034i q^{21} +(2.53493 - 2.13872i) q^{22} +(5.93428 + 5.93428i) q^{23} +3.04034 q^{24} +(0.882457 + 4.92151i) q^{25} -4.67365 q^{26} +(6.97334 - 6.97334i) q^{27} +(0.707107 - 0.707107i) q^{28} +4.95580 q^{29} +(-4.36240 + 5.21418i) q^{30} +3.24365 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.70704 + 6.50244i) q^{33} -3.24365i q^{34} +(0.198102 + 2.22728i) q^{35} -6.24365 q^{36} +(-5.43000 + 5.43000i) q^{37} +(0.280159 + 0.280159i) q^{38} +14.2095 q^{39} +(2.22728 - 0.198102i) q^{40} +6.00143i q^{41} +(-2.14984 + 2.14984i) q^{42} +(-7.83946 + 7.83946i) q^{43} +(3.30477 + 0.280159i) q^{44} +(8.95865 - 10.7079i) q^{45} +8.39234i q^{46} +(-3.29969 + 3.29969i) q^{47} +(2.14984 + 2.14984i) q^{48} +1.00000i q^{49} +(-2.85604 + 4.10403i) q^{50} +9.86179i q^{51} +(-3.30477 - 3.30477i) q^{52} +(-9.91730 - 9.91730i) q^{53} +9.86179 q^{54} +(-5.22230 + 5.26570i) q^{55} +1.00000 q^{56} +(-0.851778 - 0.851778i) q^{57} +(3.50428 + 3.50428i) q^{58} +12.4521i q^{59} +(-6.77167 + 0.602298i) q^{60} -7.90478i q^{61} +(2.29361 + 2.29361i) q^{62} +(4.41493 - 4.41493i) q^{63} -1.00000i q^{64} +(10.4095 - 0.925861i) q^{65} +(-10.0476 - 0.851778i) q^{66} +(8.03905 - 8.03905i) q^{67} +(2.29361 - 2.29361i) q^{68} -25.5156i q^{69} +(-1.43484 + 1.71500i) q^{70} +6.66397 q^{71} +(-4.41493 - 4.41493i) q^{72} +(-3.89212 + 3.89212i) q^{73} -7.67918 q^{74} +(8.68333 - 12.4776i) q^{75} +0.396205i q^{76} +(-2.53493 + 2.13872i) q^{77} +(10.0476 + 10.0476i) q^{78} -14.1181 q^{79} +(1.71500 + 1.43484i) q^{80} -11.2522 q^{81} +(-4.24365 + 4.24365i) q^{82} +(1.89651 - 1.89651i) q^{83} -3.04034 q^{84} +(0.642575 + 7.22450i) q^{85} -11.0867 q^{86} +(-10.6542 - 10.6542i) q^{87} +(2.13872 + 2.53493i) q^{88} +5.86857i q^{89} +(13.9063 - 1.23688i) q^{90} +4.67365 q^{91} +(-5.93428 + 5.93428i) q^{92} +(-6.97334 - 6.97334i) q^{93} -4.66646 q^{94} +(-0.679492 - 0.568491i) q^{95} +3.04034i q^{96} +(3.24365 - 3.24365i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(20.6338 + 1.74921i) 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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