LMFDB - Embedded newform 770.2.m.f.43.6

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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.6
Character	$\chi$	$=$	770.43
Dual form			770.2.m.f.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.436316 + 0.436316i) q^{3} +1.00000i q^{4} +(0.925572 - 2.03551i) q^{5} -0.617044i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.61926i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.436316 + 0.436316i) q^{3} +1.00000i q^{4} +(0.925572 - 2.03551i) q^{5} -0.617044i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.61926i q^{9} +(-2.09380 + 0.784847i) q^{10} +(-0.0914983 - 3.31536i) q^{11} +(-0.436316 + 0.436316i) q^{12} +(-2.24499 + 2.24499i) q^{13} +1.00000i q^{14} +(1.29197 - 0.484285i) q^{15} -1.00000 q^{16} +(-0.882457 - 0.882457i) q^{17} +(-1.85209 + 1.85209i) q^{18} -5.11418 q^{19} +(2.03551 + 0.925572i) q^{20} -0.617044i q^{21} +(-2.27962 + 2.40901i) q^{22} +(4.55205 + 4.55205i) q^{23} +0.617044 q^{24} +(-3.28663 - 3.76803i) q^{25} +3.17489 q^{26} +(2.45177 - 2.45177i) q^{27} +(0.707107 - 0.707107i) q^{28} -3.89734 q^{29} +(-1.25600 - 0.571118i) q^{30} -6.56008 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.40662 - 1.48647i) q^{33} +1.24798i q^{34} +(-2.09380 + 0.784847i) q^{35} +2.61926 q^{36} +(1.13731 - 1.13731i) q^{37} +(3.61627 + 3.61627i) q^{38} -1.95905 q^{39} +(-0.784847 - 2.09380i) q^{40} +2.41131i q^{41} +(-0.436316 + 0.436316i) q^{42} +(6.96143 - 6.96143i) q^{43} +(3.31536 - 0.0914983i) q^{44} +(-5.33153 - 2.42431i) q^{45} -6.43757i q^{46} +(6.01305 - 6.01305i) q^{47} +(-0.436316 - 0.436316i) q^{48} +1.00000i q^{49} +(-0.340400 + 4.98840i) q^{50} -0.770060i q^{51} +(-2.24499 - 2.24499i) q^{52} +(-8.55813 - 8.55813i) q^{53} -3.46733 q^{54} +(-6.83315 - 2.88236i) q^{55} -1.00000 q^{56} +(-2.23140 - 2.23140i) q^{57} +(2.75584 + 2.75584i) q^{58} +8.83463i q^{59} +(0.484285 + 1.29197i) q^{60} -6.74866i q^{61} +(4.63868 + 4.63868i) q^{62} +(-1.85209 + 1.85209i) q^{63} -1.00000i q^{64} +(2.49181 + 6.64761i) q^{65} +(-2.04572 + 0.0564584i) q^{66} +(1.48033 - 1.48033i) q^{67} +(0.882457 - 0.882457i) q^{68} +3.97226i q^{69} +(2.03551 + 0.925572i) q^{70} -3.65820 q^{71} +(-1.85209 - 1.85209i) q^{72} +(2.44181 - 2.44181i) q^{73} -1.60841 q^{74} +(0.210041 - 3.07806i) q^{75} -5.11418i q^{76} +(-2.27962 + 2.40901i) q^{77} +(1.38526 + 1.38526i) q^{78} +8.00894 q^{79} +(-0.925572 + 2.03551i) q^{80} -5.71828 q^{81} +(1.70506 - 1.70506i) q^{82} +(3.86105 - 3.86105i) q^{83} +0.617044 q^{84} +(-2.61303 + 0.979476i) q^{85} -9.84495 q^{86} +(-1.70047 - 1.70047i) q^{87} +(-2.40901 - 2.27962i) q^{88} -5.55251i q^{89} +(2.05572 + 5.48421i) q^{90} +3.17489 q^{91} +(-4.55205 + 4.55205i) q^{92} +(-2.86227 - 2.86227i) q^{93} -8.50374 q^{94} +(-4.73354 + 10.4100i) q^{95} +0.617044i q^{96} +(-2.55385 + 2.55385i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-8.68379 + 0.239658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{3}+O(q^{10}) $ 36 * q - 4 * q^3	$ 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) $ 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

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
$3$	0.436316	+	0.436316i	0.251907	+	0.251907i	0.821752	−	0.569845i	$-0.192997\pi$
$3$	0.436316	+	0.436316i	0.251907	+	0.251907i	−0.569845	+	0.821752i	$0.692997\pi$
$4$			1.00000i			0.500000i
$5$	0.925572	−	2.03551i	0.413928	−	0.910309i
$5$	0.925572	−	2.03551i	0.413928	−	0.910309i
$6$		−	0.617044i		−	0.251907i
$7$	−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
$9$		−	2.61926i		−	0.873086i
$10$	−2.09380	+	0.784847i	−0.662119	+	0.248190i
$11$	−0.0914983	−	3.31536i	−0.0275878	−	0.999619i
$11$	−0.0914983	−	3.31536i	−0.0275878	−	0.999619i
$12$	−0.436316	+	0.436316i	−0.125953	+	0.125953i
$13$	−2.24499	+	2.24499i	−0.622648	+	0.622648i	−0.946208	−	0.323560i	$-0.895120\pi$
$13$	−2.24499	+	2.24499i	−0.622648	+	0.622648i	0.323560	+	0.946208i	$0.395120\pi$
$14$			1.00000i			0.267261i
$15$	1.29197	−	0.484285i	0.333585	−	0.125042i
$16$	−1.00000			−0.250000
$17$	−0.882457	−	0.882457i	−0.214027	−	0.214027i	0.591948	−	0.805976i	$-0.298359\pi$
$17$	−0.882457	−	0.882457i	−0.214027	−	0.214027i	−0.805976	+	0.591948i	$0.798359\pi$
$18$	−1.85209	+	1.85209i	−0.436543	+	0.436543i
$19$	−5.11418			−1.17327			−0.586636	−	0.809851i	$-0.699548\pi$
$19$	−5.11418			−1.17327			−0.586636	+	0.809851i	$0.699548\pi$
$20$	2.03551	+	0.925572i	0.455155	+	0.206964i
$21$		−	0.617044i		−	0.134650i
$22$	−2.27962	+	2.40901i	−0.486016	+	0.513604i
$23$	4.55205	+	4.55205i	0.949168	+	0.949168i	0.998769	−	0.0496010i	$-0.0157950\pi$
$23$	4.55205	+	4.55205i	0.949168	+	0.949168i	−0.0496010	+	0.998769i	$0.515795\pi$
$24$	0.617044			0.125953
$25$	−3.28663	−	3.76803i	−0.657326	−	0.753606i
$26$	3.17489			0.622648
$27$	2.45177	−	2.45177i	0.471843	−	0.471843i
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$	−3.89734			−0.723718			−0.361859	−	0.932233i	$-0.617858\pi$
$29$	−3.89734			−0.723718			−0.361859	+	0.932233i	$0.617858\pi$
$30$	−1.25600	−	0.571118i	−0.229313	−	0.104271i
$31$	−6.56008			−1.17823			−0.589113	−	0.808051i	$-0.700523\pi$
$31$	−6.56008			−1.17823			−0.589113	+	0.808051i	$0.700523\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.40662	−	1.48647i	0.244862	−	0.258761i
$34$			1.24798i			0.214027i
$35$	−2.09380	+	0.784847i	−0.353917	+	0.132663i
$36$	2.61926			0.436543
$37$	1.13731	−	1.13731i	0.186973	−	0.186973i	−0.607413	−	0.794386i	$-0.707793\pi$
$37$	1.13731	−	1.13731i	0.186973	−	0.186973i	0.794386	+	0.607413i	$0.207793\pi$
$38$	3.61627	+	3.61627i	0.586636	+	0.586636i
$39$	−1.95905			−0.313699
$40$	−0.784847	−	2.09380i	−0.124095	−	0.331059i
$41$			2.41131i			0.376584i	0.982113	+	0.188292i	$0.0602951\pi$
$41$			2.41131i			0.376584i	−0.982113	+	0.188292i	$0.939705\pi$
$42$	−0.436316	+	0.436316i	−0.0673250	+	0.0673250i
$43$	6.96143	−	6.96143i	1.06161	−	1.06161i	0.0636352	−	0.997973i	$-0.479731\pi$
$43$	6.96143	−	6.96143i	1.06161	−	1.06161i	0.997973	−	0.0636352i	$-0.0202694\pi$
$44$	3.31536	−	0.0914983i	0.499810	−	0.0137939i
$45$	−5.33153	−	2.42431i	−0.794778	−	0.361395i
$46$		−	6.43757i		−	0.949168i
$47$	6.01305	−	6.01305i	0.877094	−	0.877094i	−0.116139	−	0.993233i	$-0.537052\pi$
$47$	6.01305	−	6.01305i	0.877094	−	0.877094i	0.993233	+	0.116139i	$0.0370519\pi$
$48$	−0.436316	−	0.436316i	−0.0629767	−	0.0629767i
$49$			1.00000i			0.142857i
$50$	−0.340400	+	4.98840i	−0.0481398	+	0.705466i
$51$		−	0.770060i		−	0.107830i
$52$	−2.24499	−	2.24499i	−0.311324	−	0.311324i
$53$	−8.55813	−	8.55813i	−1.17555	−	1.17555i	−0.980866	−	0.194683i	$-0.937632\pi$
$53$	−8.55813	−	8.55813i	−1.17555	−	1.17555i	−0.194683	−	0.980866i	$-0.562368\pi$
$54$	−3.46733			−0.471843
$55$	−6.83315	−	2.88236i	−0.921382	−	0.388658i
$56$	−1.00000			−0.133631
$57$	−2.23140	−	2.23140i	−0.295556	−	0.295556i
$58$	2.75584	+	2.75584i	0.361859	+	0.361859i
$59$			8.83463i			1.15017i	0.818093	+	0.575085i	$0.195031\pi$
$59$			8.83463i			1.15017i	−0.818093	+	0.575085i	$0.804969\pi$
$60$	0.484285	+	1.29197i	0.0625209	+	0.166792i
$61$		−	6.74866i		−	0.864078i	−0.901855	−	0.432039i	$-0.857794\pi$
$61$		−	6.74866i		−	0.864078i	0.901855	−	0.432039i	$-0.142206\pi$
$62$	4.63868	+	4.63868i	0.589113	+	0.589113i
$63$	−1.85209	+	1.85209i	−0.233342	+	0.233342i
$64$		−	1.00000i		−	0.125000i
$65$	2.49181	+	6.64761i	0.309071	+	0.824534i
$66$	−2.04572	+	0.0564584i	−0.251811	+	0.00694955i
$67$	1.48033	−	1.48033i	0.180851	−	0.180851i	−0.610876	−	0.791727i	$-0.709182\pi$
$67$	1.48033	−	1.48033i	0.180851	−	0.180851i	0.791727	+	0.610876i	$0.209182\pi$
$68$	0.882457	−	0.882457i	0.107014	−	0.107014i
$69$			3.97226i			0.478204i
$70$	2.03551	+	0.925572i	0.243290	+	0.110627i
$71$	−3.65820			−0.434149			−0.217075	−	0.976155i	$-0.569651\pi$
$71$	−3.65820			−0.434149			−0.217075	+	0.976155i	$0.569651\pi$
$72$	−1.85209	−	1.85209i	−0.218271	−	0.218271i
$73$	2.44181	−	2.44181i	0.285792	−	0.285792i	−0.549622	−	0.835414i	$-0.685228\pi$
$73$	2.44181	−	2.44181i	0.285792	−	0.285792i	0.835414	+	0.549622i	$0.185228\pi$
$74$	−1.60841			−0.186973
$75$	0.210041	−	3.07806i	0.0242535	−	0.355424i
$76$		−	5.11418i		−	0.586636i
$77$	−2.27962	+	2.40901i	−0.259786	+	0.274533i
$78$	1.38526	+	1.38526i	0.156849	+	0.156849i
$79$	8.00894			0.901076			0.450538	−	0.892757i	$-0.351232\pi$
$79$	8.00894			0.901076			0.450538	+	0.892757i	$0.351232\pi$
$80$	−0.925572	+	2.03551i	−0.103482	+	0.227577i
$81$	−5.71828			−0.635364
$82$	1.70506	−	1.70506i	0.188292	−	0.188292i
$83$	3.86105	−	3.86105i	0.423805	−	0.423805i	−0.462706	−	0.886512i	$-0.653122\pi$
$83$	3.86105	−	3.86105i	0.423805	−	0.423805i	0.886512	+	0.462706i	$0.153122\pi$
$84$	0.617044			0.0673250
$85$	−2.61303	+	0.979476i	−0.283423	+	0.106239i
$86$	−9.84495			−1.06161
$87$	−1.70047	−	1.70047i	−0.182310	−	0.182310i
$88$	−2.40901	−	2.27962i	−0.256802	−	0.243008i
$89$		−	5.55251i		−	0.588565i	−0.955719	−	0.294282i	$-0.904919\pi$
$89$		−	5.55251i		−	0.588565i	0.955719	−	0.294282i	$-0.0950806\pi$
$90$	2.05572	+	5.48421i	0.216692	+	0.578087i
$91$	3.17489			0.332819
$92$	−4.55205	+	4.55205i	−0.474584	+	0.474584i
$93$	−2.86227	−	2.86227i	−0.296803	−	0.296803i
$94$	−8.50374			−0.877094
$95$	−4.73354	+	10.4100i	−0.485651	+	1.06804i
$96$			0.617044i			0.0629767i
$97$	−2.55385	+	2.55385i	−0.259304	+	0.259304i	−0.824771	−	0.565467i	$-0.808696\pi$
$97$	−2.55385	+	2.55385i	−0.259304	+	0.259304i	0.565467	+	0.824771i	$0.308696\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$	−8.68379	+	0.239658i	−0.872753	+	0.0240865i
$100$	3.76803	−	3.28663i	0.376803	−	0.328663i
$101$		−	10.0811i		−	1.00310i	−0.865128	−	0.501551i	$-0.832763\pi$
$101$		−	10.0811i		−	1.00310i	0.865128	−	0.501551i	$-0.167237\pi$
$102$	−0.544515	+	0.544515i	−0.0539150	+	0.0539150i
$103$	−1.05376	−	1.05376i	−0.103830	−	0.103830i	0.653283	−	0.757114i	$-0.273391\pi$
$103$	−1.05376	−	1.05376i	−0.103830	−	0.103830i	−0.757114	+	0.653283i	$0.773391\pi$
$104$			3.17489i			0.311324i
$105$	−1.25600	−	0.571118i	−0.122573	−	0.0557355i
$106$			12.1030i			1.17555i
$107$	12.2918	+	12.2918i	1.18829	+	1.18829i	0.977540	+	0.210749i	$0.0675904\pi$
$107$	12.2918	+	12.2918i	1.18829	+	1.18829i	0.210749	+	0.977540i	$0.432410\pi$
$108$	2.45177	+	2.45177i	0.235922	+	0.235922i
$109$	−1.22726			−0.117551			−0.0587753	−	0.998271i	$-0.518720\pi$
$109$	−1.22726			−0.117551			−0.0587753	+	0.998271i	$0.518720\pi$
$110$	2.79363	+	6.86991i	0.266362	+	0.655020i
$111$	0.992457			0.0941998
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	2.33911	+	2.33911i	0.220045	+	0.220045i	0.808517	−	0.588472i	$-0.200270\pi$
$113$	2.33911	+	2.33911i	0.220045	+	0.220045i	−0.588472	+	0.808517i	$0.700270\pi$
$114$			3.15567i			0.295556i
$115$	13.4790	−	5.05251i	1.25692	−	0.471149i
$116$		−	3.89734i		−	0.361859i
$117$	5.88020	+	5.88020i	0.543625	+	0.543625i
$118$	6.24703	−	6.24703i	0.575085	−	0.575085i
$119$			1.24798i			0.114402i
$120$	0.571118	−	1.25600i	0.0521357	−	0.114657i
$121$	−10.9833	+	0.606700i	−0.998478	+	0.0551545i
$122$	−4.77203	+	4.77203i	−0.432039	+	0.432039i
$123$	−1.05209	+	1.05209i	−0.0948641	+	0.0948641i
$124$		−	6.56008i		−	0.589113i
$125$	−10.7119	+	3.20240i	−0.958101	+	0.286431i
$126$	2.61926			0.233342
$127$	5.98355	+	5.98355i	0.530954	+	0.530954i	0.920856	−	0.389902i	$-0.127491\pi$
$127$	5.98355	+	5.98355i	0.530954	+	0.530954i	−0.389902	+	0.920856i	$0.627491\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	6.07476			0.534853
$130$	2.93859	−	6.46254i	0.257732	−	0.566802i
$131$			4.77158i			0.416895i	0.978034	+	0.208447i	$0.0668410\pi$
$131$			4.77158i			0.416895i	−0.978034	+	0.208447i	$0.933159\pi$
$132$	1.48647	+	1.40662i	0.129380	+	0.122431i
$133$	3.61627	+	3.61627i	0.313570	+	0.313570i
$134$	−2.09350			−0.180851
$135$	−2.72132	−	7.25990i	−0.234214	−	0.624833i
$136$	−1.24798			−0.107014
$137$	9.10204	−	9.10204i	0.777640	−	0.777640i	−0.201789	−	0.979429i	$-0.564676\pi$
$137$	9.10204	−	9.10204i	0.777640	−	0.777640i	0.979429	+	0.201789i	$0.0646756\pi$
$138$	2.80881	−	2.80881i	0.239102	−	0.239102i
$139$	8.88225			0.753383			0.376691	−	0.926339i	$-0.377062\pi$
$139$	8.88225			0.753383			0.376691	+	0.926339i	$0.377062\pi$
$140$	−0.784847	−	2.09380i	−0.0663317	−	0.176959i
$141$	5.24718			0.441892
$142$	2.58674	+	2.58674i	0.217075	+	0.217075i
$143$	7.64837	+	7.23754i	0.639589	+	0.605234i
$144$			2.61926i			0.218271i
$145$	−3.60727	+	7.93309i	−0.299568	+	0.658808i
$146$	−3.45324			−0.285792
$147$	−0.436316	+	0.436316i	−0.0359867	+	0.0359867i
$148$	1.13731	+	1.13731i	0.0934867	+	0.0934867i
$149$	−1.47018			−0.120442			−0.0602208	−	0.998185i	$-0.519180\pi$
$149$	−1.47018			−0.120442			−0.0602208	+	0.998185i	$0.519180\pi$
$150$	−2.32504	+	2.02800i	−0.189839	+	0.165585i
$151$		−	2.74244i		−	0.223176i	−0.993755	−	0.111588i	$-0.964406\pi$
$151$		−	2.74244i		−	0.223176i	0.993755	−	0.111588i	$-0.0355938\pi$
$152$	−3.61627	+	3.61627i	−0.293318	+	0.293318i
$153$	−2.31138	+	2.31138i	−0.186864	+	0.186864i
$154$	3.31536	−	0.0914983i	0.267160	−	0.00737314i
$155$	−6.07183	+	13.3531i	−0.487701	+	1.07255i
$156$		−	1.95905i		−	0.156849i
$157$	4.17979	−	4.17979i	0.333584	−	0.333584i	−0.520362	−	0.853946i	$-0.674203\pi$
$157$	4.17979	−	4.17979i	0.333584	−	0.333584i	0.853946	+	0.520362i	$0.174203\pi$
$158$	−5.66318	−	5.66318i	−0.450538	−	0.450538i
$159$		−	7.46809i		−	0.592258i
$160$	2.09380	−	0.784847i	0.165530	−	0.0620476i
$161$		−	6.43757i		−	0.507352i
$162$	4.04343	+	4.04343i	0.317682	+	0.317682i
$163$	−3.92332	−	3.92332i	−0.307298	−	0.307298i	0.536562	−	0.843861i	$-0.319723\pi$
$163$	−3.92332	−	3.92332i	−0.307298	−	0.307298i	−0.843861	+	0.536562i	$0.819723\pi$
$164$	−2.41131			−0.188292
$165$	−1.72379	−	4.23903i	−0.134197	−	0.330008i
$166$	−5.46035			−0.423805
$167$	10.2854	+	10.2854i	0.795910	+	0.795910i	0.982448	−	0.186538i	$-0.0597267\pi$
$167$	10.2854	+	10.2854i	0.795910	+	0.795910i	−0.186538	+	0.982448i	$0.559727\pi$
$168$	−0.436316	−	0.436316i	−0.0336625	−	0.0336625i
$169$			2.92005i			0.224619i
$170$	2.54029	+	1.15510i	0.194831	+	0.0885920i
$171$			13.3953i			1.02437i
$172$	6.96143	+	6.96143i	0.530804	+	0.530804i
$173$	−6.51265	+	6.51265i	−0.495147	+	0.495147i	−0.909923	−	0.414776i	$-0.863860\pi$
$173$	−6.51265	+	6.51265i	−0.495147	+	0.495147i	0.414776	+	0.909923i	$0.363860\pi$
$174$			2.40483i			0.182310i
$175$	−0.340400	+	4.98840i	−0.0257318	+	0.377088i
$176$	0.0914983	+	3.31536i	0.00689694	+	0.249905i
$177$	−3.85469	+	3.85469i	−0.289736	+	0.289736i
$178$	−3.92622	+	3.92622i	−0.294282	+	0.294282i
$179$		−	25.6582i		−	1.91778i	−0.283772	−	0.958892i	$-0.591586\pi$
$179$		−	25.6582i		−	1.91778i	0.283772	−	0.958892i	$-0.408414\pi$
$180$	2.42431	−	5.33153i	0.180698	−	0.397389i
$181$	15.5220			1.15374			0.576870	−	0.816836i	$-0.304274\pi$
$181$	15.5220			1.15374			0.576870	+	0.816836i	$0.304274\pi$
$182$	−2.24499	−	2.24499i	−0.166410	−	0.166410i
$183$	2.94455	−	2.94455i	0.217667	−	0.217667i
$184$	6.43757			0.474584
$185$	−1.26235	−	3.36769i	−0.0928100	−	0.247597i
$186$			4.04786i			0.296803i
$187$	−2.84492	+	3.00641i	−0.208041	+	0.219850i
$188$	6.01305	+	6.01305i	0.438547	+	0.438547i
$189$	−3.46733			−0.252211
$190$	10.7081	−	4.01385i	0.776846	−	0.291195i
$191$	17.4965			1.26600			0.633001	−	0.774151i	$-0.281823\pi$
$191$	17.4965			1.26600			0.633001	+	0.774151i	$0.281823\pi$
$192$	0.436316	−	0.436316i	0.0314884	−	0.0314884i
$193$	15.9302	−	15.9302i	1.14668	−	1.14668i	0.159478	−	0.987202i	$-0.449019\pi$
$193$	15.9302	−	15.9302i	1.14668	−	1.14668i	0.987202	−	0.159478i	$-0.0509810\pi$
$194$	3.61169			0.259304
$195$	−1.81324	+	3.98767i	−0.129849	+	0.285563i
$196$	−1.00000			−0.0714286
$197$	17.9138	+	17.9138i	1.27631	+	1.27631i	0.942719	+	0.333588i	$0.108259\pi$
$197$	17.9138	+	17.9138i	1.27631	+	1.27631i	0.333588	+	0.942719i	$0.391741\pi$
$198$	6.30983	+	5.97090i	0.448420	+	0.424333i
$199$			18.9637i			1.34430i	0.740413	+	0.672152i	$0.234630\pi$
$199$			18.9637i			1.34430i	−0.740413	+	0.672152i	$0.765370\pi$
$200$	−4.98840	−	0.340400i	−0.352733	−	0.0240699i
$201$	1.29178			0.0911153
$202$	−7.12838	+	7.12838i	−0.501551	+	0.501551i
$203$	2.75584	+	2.75584i	0.193422	+	0.193422i
$204$	0.770060			0.0539150
$205$	4.90826	+	2.23184i	0.342808	+	0.155879i
$206$			1.49025i			0.103830i
$207$	11.9230	−	11.9230i	0.828705	−	0.828705i
$208$	2.24499	−	2.24499i	0.155662	−	0.155662i
$209$	0.467938	+	16.9553i	0.0323680	+	1.17283i
$210$	0.484285	+	1.29197i	0.0334188	+	0.0891543i
$211$		−	28.6962i		−	1.97553i	−0.155961	−	0.987763i	$-0.549847\pi$
$211$		−	28.6962i		−	1.97553i	0.155961	−	0.987763i	$-0.450153\pi$
$212$	8.55813	−	8.55813i	0.587775	−	0.587775i
$213$	−1.59613	−	1.59613i	−0.109365	−	0.109365i
$214$		−	17.3832i		−	1.18829i
$215$	−7.72678	−	20.6134i	−0.526962	−	1.40582i
$216$		−	3.46733i		−	0.235922i
$217$	4.63868	+	4.63868i	0.314894	+	0.314894i
$218$	0.867807	+	0.867807i	0.0587753	+	0.0587753i
$219$	2.13080			0.143986
$220$	2.88236	−	6.83315i	0.194329	−	0.460691i
$221$	3.96221			0.266527
$222$	−0.701773	−	0.701773i	−0.0470999	−	0.0470999i
$223$	6.40852	+	6.40852i	0.429147	+	0.429147i	0.888338	−	0.459191i	$-0.151861\pi$
$223$	6.40852	+	6.40852i	0.429147	+	0.429147i	−0.459191	+	0.888338i	$0.651861\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−9.86944	+	8.60853i	−0.657963	+	0.573902i
$226$		−	3.30800i		−	0.220045i
$227$	3.48983	+	3.48983i	0.231628	+	0.231628i	0.813372	−	0.581744i	$-0.197629\pi$
$227$	3.48983	+	3.48983i	0.231628	+	0.231628i	−0.581744	+	0.813372i	$0.697629\pi$
$228$	2.23140	−	2.23140i	0.147778	−	0.147778i
$229$			7.10111i			0.469254i	0.972085	+	0.234627i	$0.0753869\pi$
$229$			7.10111i			0.469254i	−0.972085	+	0.234627i	$0.924613\pi$
$230$	−13.1038	−	5.95844i	−0.864037	−	0.392888i
$231$	−2.04572	+	0.0564584i	−0.134599	+	0.00371469i
$232$	−2.75584	+	2.75584i	−0.180930	+	0.180930i
$233$	−5.34796	+	5.34796i	−0.350356	+	0.350356i	−0.860242	−	0.509886i	$-0.829688\pi$
$233$	−5.34796	+	5.34796i	−0.350356	+	0.350356i	0.509886	+	0.860242i	$0.329688\pi$
$234$		−	8.31587i		−	0.543625i
$235$	−6.67414	−	17.8052i	−0.435373	−	1.16148i
$236$	−8.83463			−0.575085
$237$	3.49443	+	3.49443i	0.226987	+	0.226987i
$238$	0.882457	−	0.882457i	0.0572012	−	0.0572012i
$239$	11.4855			0.742937			0.371468	−	0.928446i	$-0.378854\pi$
$239$	11.4855			0.742937			0.371468	+	0.928446i	$0.378854\pi$
$240$	−1.29197	+	0.484285i	−0.0833962	+	0.0312605i
$241$		−	4.55965i		−	0.293713i	−0.989158	−	0.146857i	$-0.953084\pi$
$241$		−	4.55965i		−	0.293713i	0.989158	−	0.146857i	$-0.0469156\pi$
$242$	8.19534	+	7.33733i	0.526816	+	0.471662i
$243$	−9.85029	−	9.85029i	−0.631896	−	0.631896i
$244$	6.74866			0.432039
$245$	2.03551	+	0.925572i	0.130044	+	0.0591326i
$246$	1.48789			0.0948641
$247$	11.4813	−	11.4813i	0.730536	−	0.730536i
$248$	−4.63868	+	4.63868i	−0.294556	+	0.294556i
$249$	3.36927			0.213519
$250$	9.83889	+	5.31001i	0.622266	+	0.335835i
$251$	14.7018			0.927970			0.463985	−	0.885843i	$-0.346419\pi$
$251$	14.7018			0.927970			0.463985	+	0.885843i	$0.346419\pi$
$252$	−1.85209	−	1.85209i	−0.116671	−	0.116671i
$253$	14.6752	−	15.5082i	0.922621	−	0.974992i
$254$		−	8.46201i		−	0.530954i
$255$	−1.56747	−	0.712746i	−0.0981586	−	0.0446339i
$256$	1.00000			0.0625000
$257$	−17.8735	+	17.8735i	−1.11492	+	1.11492i	−0.122440	+	0.992476i	$0.539072\pi$
$257$	−17.8735	+	17.8735i	−1.11492	+	1.11492i	−0.992476	+	0.122440i	$0.960928\pi$
$258$	−4.29551	−	4.29551i	−0.267427	−	0.267427i
$259$	−1.60841			−0.0999415
$260$	−6.64761	+	2.49181i	−0.412267	+	0.154535i
$261$			10.2081i			0.631868i
$262$	3.37402	−	3.37402i	0.208447	−	0.208447i
$263$	−7.34425	+	7.34425i	−0.452866	+	0.452866i	−0.896305	−	0.443439i	$-0.853758\pi$
$263$	−7.34425	+	7.34425i	−0.452866	+	0.452866i	0.443439	+	0.896305i	$0.353758\pi$
$264$	−0.0564584	−	2.04572i	−0.00347478	−	0.125906i
$265$	−25.3414	+	9.49902i	−1.55671	+	0.583520i
$266$		−	5.11418i		−	0.313570i
$267$	2.42265	−	2.42265i	0.148264	−	0.148264i
$268$	1.48033	+	1.48033i	0.0904255	+	0.0904255i
$269$			32.5944i			1.98732i	0.112439	+	0.993659i	$0.464134\pi$
$269$			32.5944i			1.98732i	−0.112439	+	0.993659i	$0.535866\pi$
$270$	−3.20926	+	7.05779i	−0.195309	+	0.429523i
$271$		−	11.0571i		−	0.671670i	−0.941921	−	0.335835i	$-0.890982\pi$
$271$		−	11.0571i		−	0.671670i	0.941921	−	0.335835i	$-0.109018\pi$
$272$	0.882457	+	0.882457i	0.0535068	+	0.0535068i
$273$	1.38526	+	1.38526i	0.0838395	+	0.0838395i
$274$	−12.8722			−0.777640
$275$	−12.1917	+	11.2411i	−0.735185	+	0.677867i
$276$	−3.97226			−0.239102
$277$	5.90203	+	5.90203i	0.354619	+	0.354619i	0.861825	−	0.507206i	$-0.169322\pi$
$277$	5.90203	+	5.90203i	0.354619	+	0.354619i	−0.507206	+	0.861825i	$0.669322\pi$
$278$	−6.28070	−	6.28070i	−0.376691	−	0.376691i
$279$			17.1825i			1.02869i
$280$	−0.925572	+	2.03551i	−0.0553135	+	0.121645i
$281$		−	17.0150i		−	1.01503i	−0.861643	−	0.507515i	$-0.830564\pi$
$281$		−	17.0150i		−	1.01503i	0.861643	−	0.507515i	$-0.169436\pi$
$282$	−3.71032	−	3.71032i	−0.220946	−	0.220946i
$283$	−0.223986	+	0.223986i	−0.0133146	+	0.0133146i	−0.713733	−	0.700418i	$-0.752997\pi$
$283$	−0.223986	+	0.223986i	−0.0133146	+	0.0133146i	0.700418	+	0.713733i	$0.252997\pi$
$284$		−	3.65820i		−	0.217075i
$285$	−6.60735	+	2.47672i	−0.391386	+	0.146708i
$286$	−0.290497	−	10.5259i	−0.0171775	−	0.622411i
$287$	1.70506	−	1.70506i	0.100646	−	0.100646i
$288$	1.85209	−	1.85209i	0.109136	−	0.109136i
$289$		−	15.4425i		−	0.908385i
$290$	8.16027	−	3.05882i	0.479188	−	0.179620i
$291$	−2.22857			−0.130641
$292$	2.44181	+	2.44181i	0.142896	+	0.142896i
$293$	−15.6316	+	15.6316i	−0.913206	+	0.913206i	−0.996523	−	0.0833175i	$-0.973448\pi$
$293$	−15.6316	+	15.6316i	−0.913206	+	0.913206i	0.0833175	+	0.996523i	$0.473448\pi$
$294$	0.617044			0.0359867
$295$	17.9830	+	8.17709i	1.04701	+	0.476088i
$296$		−	1.60841i		−	0.0934867i
$297$	−8.35284	−	7.90417i	−0.484681	−	0.458647i
$298$	1.03957	+	1.03957i	0.0602208	+	0.0602208i
$299$	−20.4386			−1.18200
$300$	3.07806	+	0.210041i	0.177712	+	0.0121267i
$301$	−9.84495			−0.567454
$302$	−1.93920	+	1.93920i	−0.111588	+	0.111588i
$303$	4.39852	−	4.39852i	0.252689	−	0.252689i
$304$	5.11418			0.293318
$305$	−13.7370	−	6.24638i	−0.786578	−	0.357666i
$306$	3.26879			0.186864
$307$	2.12324	+	2.12324i	0.121180	+	0.121180i	0.765096	−	0.643916i	$-0.222692\pi$
$307$	2.12324	+	2.12324i	0.121180	+	0.121180i	−0.643916	+	0.765096i	$0.722692\pi$
$308$	−2.40901	−	2.27962i	−0.137266	−	0.129893i
$309$		−	0.919547i		−	0.0523112i
$310$	13.7355	−	5.14866i	0.780125	−	0.292424i
$311$	19.5805			1.11031			0.555155	−	0.831747i	$-0.312659\pi$
$311$	19.5805			1.11031			0.555155	+	0.831747i	$0.312659\pi$
$312$	−1.38526	+	1.38526i	−0.0784247	+	0.0784247i
$313$	−19.6853	−	19.6853i	−1.11268	−	1.11268i	−0.992787	−	0.119889i	$-0.961746\pi$
$313$	−19.6853	−	19.6853i	−1.11268	−	1.11268i	−0.119889	−	0.992787i	$-0.538254\pi$
$314$	−5.91111			−0.333584
$315$	2.05572	+	5.48421i	0.115827	+	0.309000i
$316$			8.00894i			0.450538i
$317$	−6.71828	+	6.71828i	−0.377336	+	0.377336i	−0.870140	−	0.492804i	$-0.835972\pi$
$317$	−6.71828	+	6.71828i	−0.377336	+	0.377336i	0.492804	+	0.870140i	$0.335972\pi$
$318$	−5.28074	+	5.28074i	−0.296129	+	0.296129i
$319$	0.356600	+	12.9211i	0.0199658	+	0.723443i
$320$	−2.03551	−	0.925572i	−0.113789	−	0.0517411i
$321$			10.7262i			0.598677i
$322$	−4.55205	+	4.55205i	−0.253676	+	0.253676i
$323$	4.51304	+	4.51304i	0.251112	+	0.251112i
$324$		−	5.71828i		−	0.317682i
$325$	15.8376	+	1.08073i	0.878514	+	0.0599483i
$326$			5.54841i			0.307298i
$327$	−0.535475	−	0.535475i	−0.0296118	−	0.0296118i
$328$	1.70506	+	1.70506i	0.0941460	+	0.0941460i
$329$	−8.50374			−0.468826
$330$	−1.77854	+	4.21635i	−0.0979055	+	0.232103i
$331$	−32.5378			−1.78844			−0.894220	−	0.447628i	$-0.852269\pi$
$331$	−32.5378			−1.78844			−0.894220	+	0.447628i	$0.852269\pi$
$332$	3.86105	+	3.86105i	0.211903	+	0.211903i
$333$	−2.97892	−	2.97892i	−0.163244	−	0.163244i
$334$		−	14.5458i		−	0.795910i
$335$	−1.64308	−	4.38338i	−0.0897710	−	0.239490i
$336$			0.617044i			0.0336625i
$337$	−1.46609	−	1.46609i	−0.0798631	−	0.0798631i	0.666047	−	0.745910i	$-0.267985\pi$
$337$	−1.46609	−	1.46609i	−0.0798631	−	0.0798631i	−0.745910	+	0.666047i	$0.767985\pi$
$338$	2.06478	−	2.06478i	0.112309	−	0.112309i
$339$			2.04118i			0.110862i
$340$	−0.979476	−	2.61303i	−0.0531195	−	0.141712i
$341$	0.600236	+	21.7491i	0.0325046	+	1.17778i
$342$	9.47194	−	9.47194i	0.512184	−	0.512184i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		−	9.84495i		−	0.530804i
$345$	8.08559	+	3.67662i	0.435314	+	0.197942i
$346$	9.21027			0.495147
$347$	−5.86827	−	5.86827i	−0.315025	−	0.315025i	0.531828	−	0.846853i	$-0.321505\pi$
$347$	−5.86827	−	5.86827i	−0.315025	−	0.315025i	−0.846853	+	0.531828i	$0.821505\pi$
$348$	1.70047	−	1.70047i	0.0911549	−	0.0911549i
$349$	−33.6267			−1.80000			−0.899999	−	0.435893i	$-0.856433\pi$
$349$	−33.6267			−1.80000			−0.899999	+	0.435893i	$0.856433\pi$
$350$	3.76803	−	3.28663i	0.201410	−	0.175678i
$351$			11.0084i			0.587585i
$352$	2.27962	−	2.40901i	0.121504	−	0.128401i
$353$	−2.81364	−	2.81364i	−0.149755	−	0.149755i	0.628254	−	0.778008i	$-0.283770\pi$
$353$	−2.81364	−	2.81364i	−0.149755	−	0.149755i	−0.778008	+	0.628254i	$0.783770\pi$
$354$	5.45135			0.289736
$355$	−3.38593	+	7.44633i	−0.179707	+	0.395210i
$356$	5.55251			0.294282
$357$	−0.544515	+	0.544515i	−0.0288188	+	0.0288188i
$358$	−18.1431	+	18.1431i	−0.958892	+	0.958892i
$359$	−35.0052			−1.84750			−0.923752	−	0.382990i	$-0.874894\pi$
$359$	−35.0052			−1.84750			−0.923752	+	0.382990i	$0.874894\pi$
$360$	−5.48421	+	2.05572i	−0.289043	+	0.108346i
$361$	7.15480			0.376568
$362$	−10.9757	−	10.9757i	−0.576870	−	0.576870i
$363$	−5.05688	−	4.52745i	−0.265417	−	0.237630i
$364$			3.17489i			0.166410i
$365$	−2.71026	−	7.23040i	−0.141862	−	0.378457i
$366$	−4.16422			−0.217667
$367$	−12.2650	+	12.2650i	−0.640225	+	0.640225i	−0.950611	−	0.310385i	$-0.899542\pi$
$367$	−12.2650	+	12.2650i	−0.640225	+	0.640225i	0.310385	+	0.950611i	$0.399542\pi$
$368$	−4.55205	−	4.55205i	−0.237292	−	0.237292i
$369$	6.31585			0.328790
$370$	−1.48870	+	3.27393i	−0.0773936	+	0.170204i
$371$			12.1030i			0.628358i
$372$	2.86227	−	2.86227i	0.148402	−	0.148402i
$373$	21.1251	−	21.1251i	1.09381	−	1.09381i	0.0986975	−	0.995117i	$-0.468532\pi$
$373$	21.1251	−	21.1251i	1.09381	−	1.09381i	0.995117	−	0.0986975i	$-0.0314676\pi$
$374$	4.13752	−	0.114188i	0.213946	−	0.00590454i
$375$	−6.07102	−	3.27651i	−0.313506	−	0.169198i
$376$		−	8.50374i		−	0.438547i
$377$	8.74949	−	8.74949i	0.450622	−	0.450622i
$378$	2.45177	+	2.45177i	0.126105	+	0.126105i
$379$		−	4.70878i		−	0.241874i	−0.992660	−	0.120937i	$-0.961410\pi$
$379$		−	4.70878i		−	0.241874i	0.992660	−	0.120937i	$-0.0385898\pi$
$380$	−10.4100	−	4.73354i	−0.534020	−	0.242825i
$381$			5.22143i			0.267502i
$382$	−12.3719	−	12.3719i	−0.633001	−	0.633001i
$383$	9.81460	+	9.81460i	0.501503	+	0.501503i	0.911905	−	0.410402i	$-0.134612\pi$
$383$	9.81460	+	9.81460i	0.501503	+	0.501503i	−0.410402	+	0.911905i	$0.634612\pi$
$384$	−0.617044			−0.0314884
$385$	2.79363	+	6.86991i	0.142377	+	0.350123i
$386$	−22.5287			−1.14668
$387$	−18.2338	−	18.2338i	−0.926875	−	0.926875i
$388$	−2.55385	−	2.55385i	−0.129652	−	0.129652i
$389$			2.06500i			0.104700i	0.998629	+	0.0523499i	$0.0166711\pi$
$389$			2.06500i			0.104700i	−0.998629	+	0.0523499i	$0.983329\pi$
$390$	4.10186	−	1.53755i	0.207706	−	0.0778570i
$391$		−	8.03398i		−	0.406296i
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$	−2.08192	+	2.08192i	−0.105019	+	0.105019i
$394$		−	25.3340i		−	1.27631i
$395$	7.41285	−	16.3023i	0.372981	−	0.820258i
$396$	−0.239658	−	8.68379i	−0.0120432	−	0.436377i
$397$	−13.8886	+	13.8886i	−0.697048	+	0.697048i	−0.963773	−	0.266724i	$-0.914059\pi$
$397$	−13.8886	+	13.8886i	−0.697048	+	0.697048i	0.266724	+	0.963773i	$0.414059\pi$
$398$	13.4094	−	13.4094i	0.672152	−	0.672152i
$399$			3.15567i			0.157981i
$400$	3.28663	+	3.76803i	0.164332	+	0.188401i
$401$	3.92424			0.195967			0.0979835	−	0.995188i	$-0.468761\pi$
$401$	3.92424			0.195967			0.0979835	+	0.995188i	$0.468761\pi$
$402$	−0.913428	−	0.913428i	−0.0455576	−	0.0455576i
$403$	14.7273	−	14.7273i	0.733620	−	0.733620i
$404$	10.0811			0.501551
$405$	−5.29268	+	11.6396i	−0.262995	+	0.578378i
$406$		−	3.89734i		−	0.193422i
$407$	−3.87467	−	3.66655i	−0.192060	−	0.181744i
$408$	−0.544515	−	0.544515i	−0.0269575	−	0.0269575i
$409$	−18.7629			−0.927766			−0.463883	−	0.885896i	$-0.653544\pi$
$409$	−18.7629			−0.927766			−0.463883	+	0.885896i	$0.653544\pi$
$410$	−1.89251	−	5.04882i	−0.0934645	−	0.249343i
$411$	7.94273			0.391786
$412$	1.05376	−	1.05376i	0.0519152	−	0.0519152i
$413$	6.24703	−	6.24703i	0.307396	−	0.307396i
$414$	−16.8617			−0.828705
$415$	−4.28554	−	11.4329i	−0.210369	−	0.561219i
$416$	−3.17489			−0.155662
$417$	3.87547	+	3.87547i	0.189782	+	0.189782i
$418$	11.6584	−	12.3201i	0.570229	−	0.602597i
$419$			20.3396i			0.993657i	0.867849	+	0.496828i	$0.165502\pi$
$419$			20.3396i			0.993657i	−0.867849	+	0.496828i	$0.834498\pi$
$420$	0.571118	−	1.25600i	0.0278677	−	0.0612866i
$421$	13.8689			0.675928			0.337964	−	0.941159i	$-0.390262\pi$
$421$	13.8689			0.675928			0.337964	+	0.941159i	$0.390262\pi$
$422$	−20.2913	+	20.2913i	−0.987763	+	0.987763i
$423$	−15.7497	−	15.7497i	−0.765778	−	0.765778i
$424$	−12.1030			−0.587775
$425$	−0.424813	+	6.22544i	−0.0206065	+	0.301978i
$426$			2.25727i			0.109365i
$427$	−4.77203	+	4.77203i	−0.230935	+	0.230935i
$428$	−12.2918	+	12.2918i	−0.594145	+	0.594145i
$429$	0.179250	+	6.49496i	0.00865425	+	0.313579i
$430$	−9.11221	+	20.0395i	−0.439430	+	0.966392i
$431$		−	0.826197i		−	0.0397965i	−0.999802	−	0.0198983i	$-0.993666\pi$
$431$		−	0.826197i		−	0.0397965i	0.999802	−	0.0198983i	$-0.00633423\pi$
$432$	−2.45177	+	2.45177i	−0.117961	+	0.117961i
$433$	9.39830	+	9.39830i	0.451653	+	0.451653i	0.895903	−	0.444250i	$-0.146530\pi$
$433$	9.39830	+	9.39830i	0.451653	+	0.451653i	−0.444250	+	0.895903i	$0.646530\pi$
$434$		−	6.56008i		−	0.314894i
$435$	−5.03524	+	1.88742i	−0.241421	+	0.0904951i
$436$		−	1.22726i		−	0.0587753i
$437$	−23.2800	−	23.2800i	−1.11363	−	1.11363i
$438$	−1.50670	−	1.50670i	−0.0719930	−	0.0719930i
$439$	31.9995			1.52725			0.763627	−	0.645658i	$-0.223417\pi$
$439$	31.9995			1.52725			0.763627	+	0.645658i	$0.223417\pi$
$440$	−6.86991	+	2.79363i	−0.327510	+	0.133181i
$441$	2.61926			0.124727
$442$	−2.80171	−	2.80171i	−0.133264	−	0.133264i
$443$	17.0932	+	17.0932i	0.812125	+	0.812125i	0.984952	−	0.172827i	$-0.0552903\pi$
$443$	17.0932	+	17.0932i	0.812125	+	0.812125i	−0.172827	+	0.984952i	$0.555290\pi$
$444$			0.992457i			0.0470999i
$445$	−11.3022	−	5.13925i	−0.535776	−	0.243624i
$446$		−	9.06302i		−	0.429147i
$447$	−0.641461	−	0.641461i	−0.0303401	−	0.0303401i
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$		−	20.0439i		−	0.945929i	−0.881081	−	0.472965i	$-0.843184\pi$
$449$		−	20.0439i		−	0.945929i	0.881081	−	0.472965i	$-0.156816\pi$
$450$	13.0659	+	0.891594i	0.615932	+	0.0420301i
$451$	7.99438	−	0.220631i	0.376441	−	0.0103891i
$452$	−2.33911	+	2.33911i	−0.110023	+	0.110023i
$453$	1.19657	−	1.19657i	0.0562197	−	0.0562197i
$454$		−	4.93536i		−	0.231628i
$455$	2.93859	−	6.46254i	0.137763	−	0.302969i
$456$	−3.15567			−0.147778
$457$	−14.0176	−	14.0176i	−0.655717	−	0.655717i	0.298647	−	0.954364i	$-0.403465\pi$
$457$	−14.0176	−	14.0176i	−0.655717	−	0.655717i	−0.954364	+	0.298647i	$0.903465\pi$
$458$	5.02124	−	5.02124i	0.234627	−	0.234627i
$459$	−4.32716			−0.201975
$460$	5.05251	+	13.4790i	0.235574	+	0.628462i
$461$		−	40.9019i		−	1.90499i	−0.304552	−	0.952496i	$-0.598507\pi$
$461$		−	40.9019i		−	1.90499i	0.304552	−	0.952496i	$-0.401493\pi$
$462$	1.48647	+	1.40662i	0.0691567	+	0.0654420i
$463$	19.1135	+	19.1135i	0.888281	+	0.888281i	0.994358	−	0.106077i	$-0.0338289\pi$
$463$	19.1135	+	19.1135i	0.888281	+	0.888281i	−0.106077	+	0.994358i	$0.533829\pi$
$464$	3.89734			0.180930
$465$	−8.47542	+	3.17695i	−0.393038	+	0.147327i
$466$	7.56316			0.350356
$467$	29.9613	−	29.9613i	1.38644	−	1.38644i	0.553778	−	0.832664i	$-0.313185\pi$
$467$	29.9613	−	29.9613i	1.38644	−	1.38644i	0.832664	−	0.553778i	$-0.186815\pi$
$468$	−5.88020	+	5.88020i	−0.271813	+	0.271813i
$469$	−2.09350			−0.0966690
$470$	−7.87083	+	17.3095i	−0.363054	+	0.798427i
$471$	3.64742			0.168064
$472$	6.24703	+	6.24703i	0.287543	+	0.287543i
$473$	−23.7166	−	22.4427i	−1.09049	−	1.03192i
$474$		−	4.94187i		−	0.226987i
$475$	16.8084	+	19.2704i	0.771223	+	0.884185i
$476$	−1.24798			−0.0572012
$477$	−22.4159	+	22.4159i	−1.02636	+	1.02636i
$478$	−8.12149	−	8.12149i	−0.371468	−	0.371468i
$479$	13.6509			0.623723			0.311862	−	0.950127i	$-0.399047\pi$
$479$	13.6509			0.623723			0.311862	+	0.950127i	$0.399047\pi$
$480$	1.25600	+	0.571118i	0.0573283	+	0.0260679i
$481$			5.10652i			0.232837i
$482$	−3.22416	+	3.22416i	−0.146857	+	0.146857i
$483$	2.80881	−	2.80881i	0.127805	−	0.127805i
$484$	−0.606700	−	10.9833i	−0.0275773	−	0.499239i
$485$	2.83463	+	7.56218i	0.128714	+	0.343381i
$486$			13.9304i			0.631896i
$487$	12.2177	−	12.2177i	0.553637	−	0.553637i	−0.373852	−	0.927488i	$-0.621963\pi$
$487$	12.2177	−	12.2177i	0.553637	−	0.553637i	0.927488	+	0.373852i	$0.121963\pi$
$488$	−4.77203	−	4.77203i	−0.216019	−	0.216019i
$489$		−	3.42361i		−	0.154821i
$490$	−0.784847	−	2.09380i	−0.0354558	−	0.0945884i
$491$		−	26.2665i		−	1.18539i	−0.805427	−	0.592695i	$-0.798064\pi$
$491$		−	26.2665i		−	1.18539i	0.805427	−	0.592695i	$-0.201936\pi$
$492$	−1.05209	−	1.05209i	−0.0474321	−	0.0474321i
$493$	3.43924	+	3.43924i	0.154895	+	0.154895i
$494$	−16.2370			−0.730536
$495$	−7.54965	+	17.8978i	−0.339331	+	0.804446i
$496$	6.56008			0.294556
$497$	2.58674	+	2.58674i	0.116031	+	0.116031i
$498$	−2.38244	−	2.38244i	−0.106759	−	0.106759i
$499$		−	22.8383i		−	1.02238i	−0.859467	−	0.511191i	$-0.829205\pi$
$499$		−	22.8383i		−	1.02238i	0.859467	−	0.511191i	$-0.170795\pi$
$500$	−3.20240	−	10.7119i	−0.143216	−	0.479050i
$501$			8.97538i			0.400990i
$502$	−10.3958	−	10.3958i	−0.463985	−	0.463985i
$503$	4.84635	−	4.84635i	0.216088	−	0.216088i	−0.590760	−	0.806848i	$-0.701172\pi$
$503$	4.84635	−	4.84635i	0.216088	−	0.216088i	0.806848	+	0.590760i	$0.201172\pi$
$504$			2.61926i			0.116671i
$505$	−20.5201	−	9.33075i	−0.913134	−	0.415213i
$506$	−21.3429	+	0.589027i	−0.948807	+	0.0261854i
$507$	−1.27406	+	1.27406i	−0.0565831	+	0.0565831i
$508$	−5.98355	+	5.98355i	−0.265477	+	0.265477i
$509$		−	40.5034i		−	1.79528i	−0.440730	−	0.897640i	$-0.645280\pi$
$509$		−	40.5034i		−	1.79528i	0.440730	−	0.897640i	$-0.354720\pi$
$510$	0.604379	+	1.61235i	0.0267624	+	0.0713963i
$511$	−3.45324			−0.152762
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−12.5388	+	12.5388i	−0.553601	+	0.553601i
$514$	25.2769			1.11492
$515$	−3.12028	+	1.16962i	−0.137496	+	0.0515394i
$516$			6.07476i			0.267427i
$517$	−20.4856	−	19.3853i	−0.900957	−	0.852563i
$518$	1.13731	+	1.13731i	0.0499707	+	0.0499707i
$519$	−5.68314			−0.249462
$520$	6.46254	+	2.93859i	0.283401	+	0.128866i
$521$	22.4904			0.985324			0.492662	−	0.870221i	$-0.336024\pi$
$521$	22.4904			0.985324			0.492662	+	0.870221i	$0.336024\pi$
$522$	7.21825	−	7.21825i	0.315934	−	0.315934i
$523$	−20.1476	+	20.1476i	−0.880992	+	0.880992i	−0.993635	−	0.112644i	$-0.964068\pi$
$523$	−20.1476	+	20.1476i	−0.880992	+	0.880992i	0.112644	+	0.993635i	$0.464068\pi$
$524$	−4.77158			−0.208447
$525$	−2.32504	+	2.02800i	−0.101473	+	0.0885090i
$526$	10.3863			0.452866
$527$	5.78899	+	5.78899i	0.252172	+	0.252172i
$528$	−1.40662	+	1.48647i	−0.0612154	+	0.0646902i
$529$			18.4423i			0.801840i
$530$	24.6359	+	11.2022i	1.07011	+	0.486593i
$531$	23.1402			1.00420
$532$	−3.61627	+	3.61627i	−0.156785	+	0.156785i
$533$	−5.41337	−	5.41337i	−0.234479	−	0.234479i
$534$	−3.42614			−0.148264
$535$	36.3970	−	13.6431i	1.57358	−	0.589844i
$536$		−	2.09350i		−	0.0904255i
$537$	11.1951	−	11.1951i	0.483103	−	0.483103i
$538$	23.0477	−	23.0477i	0.993659	−	0.993659i
$539$	3.31536	−	0.0914983i	0.142803	−	0.00394111i
$540$	7.25990	−	2.72132i	0.312416	−	0.117107i
$541$			1.16235i			0.0499735i	0.999688	+	0.0249867i	$0.00795435\pi$
$541$			1.16235i			0.0499735i	−0.999688	+	0.0249867i	$0.992046\pi$
$542$	−7.81853	+	7.81853i	−0.335835	+	0.335835i
$543$	6.77249	+	6.77249i	0.290635	+	0.290635i
$544$		−	1.24798i		−	0.0535068i
$545$	−1.13592	+	2.49811i	−0.0486575	+	0.107007i
$546$		−	1.95905i		−	0.0838395i
$547$	4.23579	+	4.23579i	0.181109	+	0.181109i	0.791839	−	0.610730i	$-0.209124\pi$
$547$	4.23579	+	4.23579i	0.181109	+	0.181109i	−0.610730	+	0.791839i	$0.709124\pi$
$548$	9.10204	+	9.10204i	0.388820	+	0.388820i
$549$	−17.6765			−0.754414
$550$	16.5695	+	0.672118i	0.706526	+	0.0286592i
$551$	19.9317			0.849119
$552$	2.80881	+	2.80881i	0.119551	+	0.119551i
$553$	−5.66318	−	5.66318i	−0.240823	−	0.240823i
$554$		−	8.34674i		−	0.354619i
$555$	0.918590	−	2.02016i	0.0389920	−	0.0857510i
$556$			8.88225i			0.376691i
$557$	22.8984	+	22.8984i	0.970234	+	0.970234i	0.999570	−	0.0293353i	$-0.00933905\pi$
$557$	22.8984	+	22.8984i	0.970234	+	0.970234i	−0.0293353	+	0.999570i	$0.509339\pi$
$558$	12.1499	−	12.1499i	0.514346	−	0.514346i
$559$			31.2567i			1.32202i
$560$	2.09380	−	0.784847i	0.0884794	−	0.0331658i
$561$	−2.55303	+	0.0704592i	−0.107789	+	0.00297479i
$562$	−12.0314	+	12.0314i	−0.507515	+	0.507515i
$563$	−20.6328	+	20.6328i	−0.869568	+	0.869568i	−0.992424	−	0.122857i	$-0.960794\pi$
$563$	−20.6328	+	20.6328i	−0.869568	+	0.869568i	0.122857	+	0.992424i	$0.460794\pi$
$564$			5.24718i			0.220946i
$565$	6.92631	−	2.59628i	0.291392	−	0.109226i
$566$	0.316764			0.0133146
$567$	4.04343	+	4.04343i	0.169808	+	0.169808i
$568$	−2.58674	+	2.58674i	−0.108537	+	0.108537i
$569$	6.92978			0.290512			0.145256	−	0.989394i	$-0.453599\pi$
$569$	6.92978			0.290512			0.145256	+	0.989394i	$0.453599\pi$
$570$	6.42341	+	2.92080i	0.269047	+	0.122339i
$571$			9.38778i			0.392866i	0.980517	+	0.196433i	$0.0629359\pi$
$571$			9.38778i			0.392866i	−0.980517	+	0.196433i	$0.937064\pi$
$572$	−7.23754	+	7.64837i	−0.302617	+	0.319794i
$573$	7.63400	+	7.63400i	0.318915	+	0.318915i
$574$	−2.41131			−0.100646
$575$	2.19135	−	32.1132i	0.0913855	−	1.33921i
$576$	−2.61926			−0.109136
$577$	−2.35193	+	2.35193i	−0.0979121	+	0.0979121i	−0.754366	−	0.656454i	$-0.772056\pi$
$577$	−2.35193	+	2.35193i	−0.0979121	+	0.0979121i	0.656454	+	0.754366i	$0.272056\pi$
$578$	−10.9195	+	10.9195i	−0.454192	+	0.454192i
$579$	13.9012			0.577713
$580$	−7.93309	−	3.60727i	−0.329404	−	0.149784i
$581$	−5.46035			−0.226533
$582$	1.57584	+	1.57584i	0.0653206	+	0.0653206i
$583$	−27.5902	+	29.1564i	−1.14267	+	1.20753i
$584$		−	3.45324i		−	0.142896i
$585$	17.4118	−	6.52668i	0.719889	−	0.269845i
$586$	22.1064			0.913206
$587$	24.7924	−	24.7924i	1.02329	−	1.02329i	0.0235692	−	0.999722i	$-0.492497\pi$
$587$	24.7924	−	24.7924i	1.02329	−	1.02329i	0.999722	−	0.0235692i	$-0.00750301\pi$
$588$	−0.436316	−	0.436316i	−0.0179934	−	0.0179934i
$589$	33.5494			1.38238
$590$	−6.93383	−	18.4980i	−0.285461	−	0.761550i
$591$			15.6322i			0.643021i
$592$	−1.13731	+	1.13731i	−0.0467434	+	0.0467434i
$593$	−25.6991	+	25.6991i	−1.05534	+	1.05534i	−0.0569596	+	0.998376i	$0.518141\pi$
$593$	−25.6991	+	25.6991i	−1.05534	+	1.05534i	−0.998376	+	0.0569596i	$0.981859\pi$
$594$	0.317254	+	11.4954i	0.0130171	+	0.471664i
$595$	2.54029	+	1.15510i	0.104142	+	0.0473544i
$596$		−	1.47018i		−	0.0602208i
$597$	−8.27418	+	8.27418i	−0.338640	+	0.338640i
$598$	14.4523	+	14.4523i	0.590998	+	0.590998i
$599$			40.0185i			1.63511i	0.575848	+	0.817557i	$0.304672\pi$
$599$			40.0185i			1.63511i	−0.575848	+	0.817557i	$0.695328\pi$
$600$	−2.02800	−	2.32504i	−0.0827926	−	0.0949193i
$601$			41.3242i			1.68565i	0.538188	+	0.842825i	$0.319109\pi$
$601$			41.3242i			1.68565i	−0.538188	+	0.842825i	$0.680891\pi$
$602$	6.96143	+	6.96143i	0.283727	+	0.283727i
$603$	−3.87736	−	3.87736i	−0.157898	−	0.157898i
$604$	2.74244			0.111588
$605$	−8.93085	+	22.9181i	−0.363091	+	0.931754i
$606$	−6.22045			−0.252689
$607$	−22.0937	−	22.0937i	−0.896756	−	0.896756i	0.0983922	−	0.995148i	$-0.468630\pi$
$607$	−22.0937	−	22.0937i	−0.896756	−	0.896756i	−0.995148	+	0.0983922i	$0.968630\pi$
$608$	−3.61627	−	3.61627i	−0.146659	−	0.146659i
$609$			2.40483i			0.0974486i
$610$	5.29667	+	14.1304i	0.214456	+	0.572122i
$611$			26.9985i			1.09224i
$612$	−2.31138	−	2.31138i	−0.0934321	−	0.0934321i
$613$	20.8933	−	20.8933i	0.843874	−	0.843874i	−0.145486	−	0.989360i	$-0.546475\pi$
$613$	20.8933	−	20.8933i	0.843874	−	0.843874i	0.989360	+	0.145486i	$0.0464747\pi$
$614$		−	3.00271i		−	0.121180i
$615$	1.16776	+	3.11534i	0.0470887	+	0.125623i
$616$	0.0914983	+	3.31536i	0.00368657	+	0.133580i
$617$	−20.4818	+	20.4818i	−0.824567	+	0.824567i	−0.986759	−	0.162192i	$-0.948143\pi$
$617$	−20.4818	+	20.4818i	−0.824567	+	0.824567i	0.162192	+	0.986759i	$0.448143\pi$
$618$	−0.650218	+	0.650218i	−0.0261556	+	0.0261556i
$619$		−	25.6865i		−	1.03243i	−0.856459	−	0.516215i	$-0.827341\pi$
$619$		−	25.6865i		−	1.03243i	0.856459	−	0.516215i	$-0.172659\pi$
$620$	−13.3531	−	6.07183i	−0.536275	−	0.243851i
$621$	22.3212			0.895717
$622$	−13.8455	−	13.8455i	−0.555155	−	0.555155i
$623$	−3.92622	+	3.92622i	−0.157300	+	0.157300i
$624$	1.95905			0.0784247
$625$	−3.39610	+	24.7683i	−0.135844	+	0.990730i
$626$			27.8391i			1.11268i
$627$	−7.19372	+	7.60205i	−0.287289	+	0.303597i
$628$	4.17979	+	4.17979i	0.166792	+	0.166792i
$629$	−2.00726			−0.0800348
$630$	2.42431	−	5.33153i	0.0965869	−	0.212413i
$631$	−8.46743			−0.337083			−0.168542	−	0.985695i	$-0.553906\pi$
$631$	−8.46743			−0.337083			−0.168542	+	0.985695i	$0.553906\pi$
$632$	5.66318	−	5.66318i	0.225269	−	0.225269i
$633$	12.5206	−	12.5206i	0.497649	−	0.497649i
$634$	9.50108			0.377336
$635$	17.7178	−	6.64139i	0.703109	−	0.263555i
$636$	7.46809			0.296129
$637$	−2.24499	−	2.24499i	−0.0889497	−	0.0889497i
$638$	8.88445	−	9.38875i	0.351739	−	0.371704i
$639$			9.58178i			0.379049i
$640$	0.784847	+	2.09380i	0.0310238	+	0.0827649i
$641$	15.9178			0.628715			0.314357	−	0.949305i	$-0.398211\pi$
$641$	15.9178			0.628715			0.314357	+	0.949305i	$0.398211\pi$
$642$	7.58455	−	7.58455i	0.299338	−	0.299338i
$643$	−28.5595	−	28.5595i	−1.12628	−	1.12628i	−0.990778	−	0.135498i	$-0.956736\pi$
$643$	−28.5595	−	28.5595i	−1.12628	−	1.12628i	−0.135498	−	0.990778i	$-0.543264\pi$
$644$	6.43757			0.253676
$645$	5.62263	−	12.3653i	0.221391	−	0.486882i
$646$		−	6.38240i		−	0.251112i
$647$	21.3139	−	21.3139i	0.837934	−	0.837934i	−0.150653	−	0.988587i	$-0.548138\pi$
$647$	21.3139	−	21.3139i	0.837934	−	0.837934i	0.988587	+	0.150653i	$0.0481375\pi$
$648$	−4.04343	+	4.04343i	−0.158841	+	0.158841i
$649$	29.2900	−	0.808354i	1.14973	−	0.0317307i
$650$	−10.4347	−	11.9631i	−0.409283	−	0.469231i
$651$			4.04786i			0.158648i
$652$	3.92332	−	3.92332i	0.153649	−	0.153649i
$653$	−19.2406	−	19.2406i	−0.752943	−	0.752943i	0.222084	−	0.975027i	$-0.428714\pi$
$653$	−19.2406	−	19.2406i	−0.752943	−	0.752943i	−0.975027	+	0.222084i	$0.928714\pi$
$654$			0.757275i			0.0296118i
$655$	9.71262	+	4.41644i	0.379503	+	0.172565i
$656$		−	2.41131i		−	0.0941460i
$657$	−6.39572	−	6.39572i	−0.249521	−	0.249521i
$658$	6.01305	+	6.01305i	0.234413	+	0.234413i
$659$	42.1401			1.64155			0.820773	−	0.571254i	$-0.193543\pi$
$659$	42.1401			1.64155			0.820773	+	0.571254i	$0.193543\pi$
$660$	4.23903	−	1.72379i	0.165004	−	0.0670985i
$661$	−4.18504			−0.162779			−0.0813896	−	0.996682i	$-0.525936\pi$
$661$	−4.18504			−0.162779			−0.0813896	+	0.996682i	$0.525936\pi$
$662$	23.0077	+	23.0077i	0.894220	+	0.894220i
$663$	1.72878	+	1.72878i	0.0671401	+	0.0671401i
$664$		−	5.46035i		−	0.211903i
$665$	10.7081	−	4.01385i	0.415242	−	0.155650i
$666$			4.21283i			0.163244i
$667$	−17.7409	−	17.7409i	−0.686930	−	0.686930i
$668$	−10.2854	+	10.2854i	−0.397955	+	0.397955i
$669$			5.59228i			0.216210i
$670$	−1.93769	+	4.26135i	−0.0748594	+	0.164630i
$671$	−22.3743	+	0.617491i	−0.863749	+	0.0238380i
$672$	0.436316	−	0.436316i	0.0168312	−	0.0168312i
$673$	−0.435637	+	0.435637i	−0.0167926	+	0.0167926i	−0.715453	−	0.698661i	$-0.753780\pi$
$673$	−0.435637	+	0.435637i	−0.0167926	+	0.0167926i	0.698661	+	0.715453i	$0.253780\pi$
$674$			2.07337i			0.0798631i
$675$	−17.2964	−	1.18028i	−0.665739	−	0.0454289i
$676$	−2.92005			−0.112309
$677$	29.9161	+	29.9161i	1.14977	+	1.14977i	0.986598	+	0.163172i	$0.0521725\pi$
$677$	29.9161	+	29.9161i	1.14977	+	1.14977i	0.163172	+	0.986598i	$0.447828\pi$
$678$	1.44333	−	1.44333i	0.0554309	−	0.0554309i
$679$	3.61169			0.138604
$680$	−1.15510	+	2.54029i	−0.0442960	+	0.0974155i
$681$			3.04533i			0.116697i
$682$	14.9545	−	15.8033i	0.572636	−	0.605141i
$683$	−20.2251	−	20.2251i	−0.773891	−	0.773891i	0.204893	−	0.978784i	$-0.434315\pi$
$683$	−20.2251	−	20.2251i	−0.773891	−	0.773891i	−0.978784	+	0.204893i	$0.934315\pi$
$684$	−13.3953			−0.512184
$685$	−10.1027	−	26.9519i	−0.386006	−	1.02978i
$686$	−1.00000			−0.0381802
$687$	−3.09832	+	3.09832i	−0.118208	+	0.118208i
$688$	−6.96143	+	6.96143i	−0.265402	+	0.265402i
$689$	38.4258			1.46391
$690$	−3.11762	−	8.31714i	−0.118686	−	0.316628i
$691$	−41.9695			−1.59659			−0.798297	−	0.602264i	$-0.794266\pi$
$691$	−41.9695			−1.59659			−0.798297	+	0.602264i	$0.794266\pi$
$692$	−6.51265	−	6.51265i	−0.247574	−	0.247574i
$693$	6.30983	+	5.97090i	0.239691	+	0.226816i
$694$			8.29899i			0.315025i
$695$	8.22117	−	18.0799i	0.311847	−	0.685811i
$696$	−2.40483			−0.0911549
$697$	2.12788	−	2.12788i	0.0805992	−	0.0805992i
$698$	23.7777	+	23.7777i	0.899999	+	0.899999i
$699$	−4.66680			−0.176514
$700$	−4.98840	−	0.340400i	−0.188544	−	0.0128659i
$701$		−	6.81409i		−	0.257364i	−0.991686	−	0.128682i	$-0.958925\pi$
$701$		−	6.81409i		−	0.257364i	0.991686	−	0.128682i	$-0.0410747\pi$
$702$	7.78411	−	7.78411i	0.293792	−	0.293792i
$703$	−5.81643	+	5.81643i	−0.219371	+	0.219371i
$704$	−3.31536	+	0.0914983i	−0.124952	+	0.00344847i
$705$	4.85664	−	10.6807i	0.182912	−	0.402259i
$706$			3.97908i			0.149755i
$707$	−7.12838	+	7.12838i	−0.268090	+	0.268090i
$708$	−3.85469	−	3.85469i	−0.144868	−	0.144868i
$709$		−	29.2963i		−	1.10025i	−0.835084	−	0.550123i	$-0.814581\pi$
$709$		−	29.2963i		−	1.10025i	0.835084	−	0.550123i	$-0.185419\pi$
$710$	7.65956	−	2.87113i	0.287458	−	0.107752i
$711$		−	20.9775i		−	0.786717i
$712$	−3.92622	−	3.92622i	−0.147141	−	0.147141i
$713$	−29.8618	−	29.8618i	−1.11833	−	1.11833i
$714$	0.770060			0.0288188
$715$	21.8112	−	8.86949i	0.815694	−	0.331700i
$716$	25.6582			0.958892
$717$	5.01131	+	5.01131i	0.187151	+	0.187151i
$718$	24.7524	+	24.7524i	0.923752	+	0.923752i
$719$			40.8049i			1.52177i	0.648889	+	0.760883i	$0.275234\pi$
$719$			40.8049i			1.52177i	−0.648889	+	0.760883i	$0.724766\pi$
$720$	5.33153	+	2.42431i	0.198695	+	0.0903488i
$721$			1.49025i			0.0554997i
$722$	−5.05920	−	5.05920i	−0.188284	−	0.188284i
$723$	1.98945	−	1.98945i	0.0739884	−	0.0739884i
$724$			15.5220i			0.576870i
$725$	12.8091	+	14.6853i	0.475719	+	0.545398i
$726$	0.374360	+	6.77715i	0.0138938	+	0.251524i
$727$	13.2187	−	13.2187i	0.490256	−	0.490256i	−0.418131	−	0.908387i	$-0.637315\pi$
$727$	13.2187	−	13.2187i	0.490256	−	0.490256i	0.908387	+	0.418131i	$0.137315\pi$
$728$	2.24499	−	2.24499i	0.0832048	−	0.0832048i
$729$			8.55917i			0.317006i
$730$	−3.19622	+	7.02911i	−0.118297	+	0.260159i
$731$	−12.2863			−0.454426
$732$	2.94455	+	2.94455i	0.108834	+	0.108834i
$733$	−3.20750	+	3.20750i	−0.118472	+	0.118472i	−0.763857	−	0.645385i	$-0.776697\pi$
$733$	−3.20750	+	3.20750i	−0.118472	+	0.118472i	0.645385	+	0.763857i	$0.276697\pi$
$734$	17.3453			0.640225
$735$	0.484285	+	1.29197i	0.0178631	+	0.0476550i
$736$			6.43757i			0.237292i
$737$	−5.04328	−	4.77238i	−0.185771	−	0.175793i
$738$	−4.46598	−	4.46598i	−0.164395	−	0.164395i
$739$	−31.3122			−1.15184			−0.575918	−	0.817507i	$-0.695355\pi$
$739$	−31.3122			−1.15184			−0.575918	+	0.817507i	$0.695355\pi$
$740$	3.36769	−	1.26235i	0.123799	−	0.0464050i
$741$	10.0189			0.368054
$742$	8.55813	−	8.55813i	0.314179	−	0.314179i
$743$	11.7823	−	11.7823i	0.432250	−	0.432250i	−0.457143	−	0.889393i	$-0.651127\pi$
$743$	11.7823	−	11.7823i	0.432250	−	0.432250i	0.889393	+	0.457143i	$0.151127\pi$
$744$	−4.04786			−0.148402
$745$	−1.36076	+	2.99257i	−0.0498542	+	0.109639i
$746$	−29.8754			−1.09381
$747$	−10.1131	−	10.1131i	−0.370018	−	0.370018i
$748$	−3.00641	−	2.84492i	−0.109925	−	0.104021i
$749$		−	17.3832i		−	0.635167i
$750$	1.97602	+	6.60970i	0.0721541	+	0.241352i
$751$	−23.5720			−0.860156			−0.430078	−	0.902792i	$-0.641514\pi$
$751$	−23.5720			−0.860156			−0.430078	+	0.902792i	$0.641514\pi$
$752$	−6.01305	+	6.01305i	−0.219273	+	0.219273i
$753$	6.41463	+	6.41463i	0.233762	+	0.233762i
$754$	−12.3737			−0.450622
$755$	−5.58227	−	2.53832i	−0.203160	−	0.0923791i
$756$		−	3.46733i		−	0.126105i
$757$	23.1880	−	23.1880i	0.842781	−	0.842781i	−0.146439	−	0.989220i	$-0.546781\pi$
$757$	23.1880	−	23.1880i	0.842781	−	0.842781i	0.989220	+	0.146439i	$0.0467811\pi$
$758$	−3.32961	+	3.32961i	−0.120937	+	0.120937i
$759$	13.1695	−	0.363455i	0.478022	−	0.0131926i
$760$	4.01385	+	10.7081i	0.145598	+	0.388423i
$761$			18.1410i			0.657611i	0.944398	+	0.328806i	$0.106646\pi$
$761$			18.1410i			0.657611i	−0.944398	+	0.328806i	$0.893354\pi$
$762$	3.69211	−	3.69211i	0.133751	−	0.133751i
$763$	0.867807	+	0.867807i	0.0314167	+	0.0314167i
$764$			17.4965i			0.633001i
$765$	2.56550	+	6.84420i	0.0927558	+	0.247453i
$766$		−	13.8799i		−	0.501503i
$767$	−19.8337	−	19.8337i	−0.716152	−	0.716152i
$768$	0.436316	+	0.436316i	0.0157442	+	0.0157442i
$769$	33.9810			1.22538			0.612692	−	0.790322i	$-0.290087\pi$
$769$	33.9810			1.22538			0.612692	+	0.790322i	$0.290087\pi$
$770$	2.88236	−	6.83315i	0.103873	−	0.246250i
$771$	−15.5969			−0.561710
$772$	15.9302	+	15.9302i	0.573340	+	0.573340i
$773$	−5.45865	−	5.45865i	−0.196334	−	0.196334i	0.602092	−	0.798426i	$-0.294334\pi$
$773$	−5.45865	−	5.45865i	−0.196334	−	0.196334i	−0.798426	+	0.602092i	$0.794334\pi$
$774$			25.7865i			0.926875i
$775$	21.5606	+	24.7186i	0.774479	+	0.887918i
$776$			3.61169i			0.129652i
$777$	−0.701773	−	0.701773i	−0.0251760	−	0.0251760i
$778$	1.46018	−	1.46018i	0.0523499	−	0.0523499i
$779$		−	12.3319i		−	0.441835i
$780$	−3.98767	−	1.81324i	−0.142781	−	0.0649244i
$781$	0.334719	+	12.1283i	0.0119772	+	0.433984i
$782$	−5.68088	+	5.68088i	−0.203148	+	0.203148i
$783$	−9.55539	+	9.55539i	−0.341482	+	0.341482i
$784$		−	1.00000i		−	0.0357143i
$785$	−4.63932	−	12.3767i	−0.165584	−	0.441744i
$786$	2.94427			0.105019
$787$	9.88423	+	9.88423i	0.352335	+	0.352335i	0.860978	−	0.508643i	$-0.169853\pi$
$787$	9.88423	+	9.88423i	0.352335	+	0.352335i	−0.508643	+	0.860978i	$0.669853\pi$
$788$	−17.9138	+	17.9138i	−0.638153	+	0.638153i
$789$	−6.40882			−0.228160
$790$	−16.7692	+	6.28579i	−0.596620	+	0.223639i
$791$		−	3.30800i		−	0.117619i
$792$	−5.97090	+	6.30983i	−0.212167	+	0.224210i
$793$	15.1507	+	15.1507i	0.538016	+	0.538016i
$794$	19.6414			0.697048
$795$	−15.2014	−	6.91226i	−0.539138	−	0.245153i
$796$	−18.9637			−0.672152
$797$	34.3515	−	34.3515i	1.21679	−	1.21679i	0.248045	−	0.968749i	$-0.420212\pi$
$797$	34.3515	−	34.3515i	1.21679	−	1.21679i	0.968749	−	0.248045i	$-0.0797879\pi$
$798$	2.23140	−	2.23140i	0.0789905	−	0.0789905i
$799$	−10.6125			−0.375444
$800$	0.340400	−	4.98840i	0.0120349	−	0.176367i
$801$	−14.5434			−0.513867
$802$	−2.77485	−	2.77485i	−0.0979835	−	0.0979835i
$803$	−8.31890	−	7.87206i	−0.293568	−	0.277799i
$804$			1.29178i			0.0455576i
$805$	−13.1038	−	5.95844i	−0.461847	−	0.210007i
$806$	−20.8276			−0.733620
$807$	−14.2215	+	14.2215i	−0.500619	+	0.500619i
$808$	−7.12838	−	7.12838i	−0.250776	−	0.250776i
$809$	42.5931			1.49749			0.748747	−	0.662856i	$-0.230656\pi$
$809$	42.5931			1.49749			0.748747	+	0.662856i	$0.230656\pi$
$810$	11.9730	−	4.48798i	0.420687	−	0.157691i
$811$			18.1005i			0.635596i	0.948158	+	0.317798i	$0.102943\pi$
$811$			18.1005i			0.635596i	−0.948158	+	0.317798i	$0.897057\pi$
$812$	−2.75584	+	2.75584i	−0.0967109	+	0.0967109i
$813$	4.82438	−	4.82438i	0.169198	−	0.169198i
$814$	0.147166	+	5.33245i	0.00515818	+	0.186902i
$815$	−11.6173	+	4.35466i	−0.406936	+	0.152537i
$816$			0.770060i			0.0269575i
$817$	−35.6020	+	35.6020i	−1.24556	+	1.24556i
$818$	13.2674	+	13.2674i	0.463883	+	0.463883i
$819$		−	8.31587i		−	0.290580i
$820$	−2.23184	+	4.90826i	−0.0779394	+	0.171404i
$821$		−	26.1527i		−	0.912734i	−0.889792	−	0.456367i	$-0.849150\pi$
$821$		−	26.1527i		−	0.912734i	0.889792	−	0.456367i	$-0.150850\pi$
$822$	−5.61636	−	5.61636i	−0.195893	−	0.195893i
$823$	29.0183	+	29.0183i	1.01151	+	1.01151i	0.999933	+	0.0115818i	$0.00368670\pi$
$823$	29.0183	+	29.0183i	1.01151	+	1.01151i	0.0115818	+	0.999933i	$0.496313\pi$
$824$	−1.49025			−0.0519152
$825$	−10.2241	−	0.414726i	−0.355958	−	0.0144389i
$826$	−8.83463			−0.307396
$827$	4.75890	+	4.75890i	0.165483	+	0.165483i	0.784991	−	0.619508i	$-0.212668\pi$
$827$	4.75890	+	4.75890i	0.165483	+	0.165483i	−0.619508	+	0.784991i	$0.712668\pi$
$828$	11.9230	+	11.9230i	0.414353	+	0.414353i
$829$		−	38.1225i		−	1.32405i	−0.749482	−	0.662025i	$-0.769697\pi$
$829$		−	38.1225i		−	1.32405i	0.749482	−	0.662025i	$-0.230303\pi$
$830$	−5.05395	+	11.1146i	−0.175425	+	0.385794i
$831$			5.15030i			0.178662i
$832$	2.24499	+	2.24499i	0.0778310	+	0.0778310i
$833$	0.882457	−	0.882457i	0.0305753	−	0.0305753i
$834$		−	5.48074i		−	0.189782i
$835$	30.4560	−	11.4162i	1.05397	−	0.395074i
$836$	−16.9553	+	0.467938i	−0.586413	+	0.0161840i
$837$	−16.0838	+	16.0838i	−0.555938	+	0.555938i
$838$	14.3823	−	14.3823i	0.496828	−	0.496828i
$839$			40.6702i			1.40409i	0.712132	+	0.702046i	$0.247730\pi$
$839$			40.6702i			1.40409i	−0.712132	+	0.702046i	$0.752270\pi$
$840$	−1.29197	+	0.484285i	−0.0445771	+	0.0167094i
$841$	−13.8107			−0.476232
$842$	−9.80678	−	9.80678i	−0.337964	−	0.337964i
$843$	7.42392	−	7.42392i	0.255693	−	0.255693i
$844$	28.6962			0.987763
$845$	5.94379	+	2.70271i	0.204473	+	0.0929762i
$846$			22.2735i			0.765778i
$847$	8.19534	+	7.33733i	0.281595	+	0.252114i
$848$	8.55813	+	8.55813i	0.293887	+	0.293887i
$849$	−0.195457			−0.00670808
$850$	4.70244	−	4.10166i	0.161292	−	0.140686i
$851$	10.3542			0.354938
$852$	1.59613	−	1.59613i	0.0546826	−	0.0546826i
$853$	−23.7340	+	23.7340i	−0.812636	+	0.812636i	−0.985028	−	0.172392i	$-0.944850\pi$
$853$	−23.7340	+	23.7340i	−0.812636	+	0.812636i	0.172392	+	0.985028i	$0.444850\pi$
$854$	6.74866			0.230935
$855$	27.2664	+	12.3984i	0.932491	+	0.424015i
$856$	17.3832			0.594145
$857$	−38.0719	−	38.0719i	−1.30051	−	1.30051i	−0.928045	−	0.372467i	$-0.878512\pi$
$857$	−38.0719	−	38.0719i	−1.30051	−	1.30051i	−0.372467	−	0.928045i	$-0.621488\pi$
$858$	4.46588	−	4.71938i	0.152463	−	0.161117i
$859$		−	19.1421i		−	0.653120i	−0.945176	−	0.326560i	$-0.894111\pi$
$859$		−	19.1421i		−	0.653120i	0.945176	−	0.326560i	$-0.105889\pi$
$860$	20.6134	−	7.72678i	0.702911	−	0.263481i
$861$	1.48789			0.0507070
$862$	−0.584210	+	0.584210i	−0.0198983	+	0.0198983i
$863$	24.8072	+	24.8072i	0.844446	+	0.844446i	0.989433	−	0.144988i	$-0.0463143\pi$
$863$	24.8072	+	24.8072i	0.844446	+	0.844446i	−0.144988	+	0.989433i	$0.546314\pi$
$864$	3.46733			0.117961
$865$	7.22866	+	19.2845i	0.245782	+	0.655693i
$866$		−	13.2912i		−	0.451653i
$867$	6.73782	−	6.73782i	0.228828	−	0.228828i
$868$	−4.63868	+	4.63868i	−0.157447	+	0.157447i
$869$	−0.732804	−	26.5525i	−0.0248587	−	0.900733i
$870$	4.89507	+	2.22584i	0.165958	+	0.0754632i
$871$			6.64665i			0.225213i
$872$	−0.867807	+	0.867807i	−0.0293876	+	0.0293876i
$873$	6.68920	+	6.68920i	0.226395	+	0.226395i
$874$			32.9229i			1.11363i
$875$	9.83889	+	5.31001i	0.332615	+	0.179511i
$876$			2.13080i			0.0719930i
$877$	−26.3717	−	26.3717i	−0.890509	−	0.890509i	0.104061	−	0.994571i	$-0.466816\pi$
$877$	−26.3717	−	26.3717i	−0.890509	−	0.890509i	−0.994571	+	0.104061i	$0.966816\pi$
$878$	−22.6271	−	22.6271i	−0.763627	−	0.763627i
$879$	−13.6406			−0.460086
$880$	6.83315	+	2.88236i	0.230346	+	0.0971644i
$881$	39.6112			1.33454			0.667268	−	0.744818i	$-0.267463\pi$
$881$	39.6112			1.33454			0.667268	+	0.744818i	$0.267463\pi$
$882$	−1.85209	−	1.85209i	−0.0623633	−	0.0623633i
$883$	−11.0649	−	11.0649i	−0.372363	−	0.372363i	0.495974	−	0.868337i	$-0.334811\pi$
$883$	−11.0649	−	11.0649i	−0.372363	−	0.372363i	−0.868337	+	0.495974i	$0.834811\pi$
$884$			3.96221i			0.133264i
$885$	4.27848	+	11.4141i	0.143819	+	0.383680i
$886$		−	24.1735i		−	0.812125i
$887$	7.84481	+	7.84481i	0.263403	+	0.263403i	0.826435	−	0.563032i	$-0.190365\pi$
$887$	7.84481	+	7.84481i	0.263403	+	0.263403i	−0.563032	+	0.826435i	$0.690365\pi$
$888$	0.701773	−	0.701773i	0.0235500	−	0.0235500i
$889$		−	8.46201i		−	0.283807i
$890$	4.35787	+	11.6259i	0.146076	+	0.389700i
$891$	0.523213	+	18.9582i	0.0175283	+	0.635123i
$892$	−6.40852	+	6.40852i	−0.214573	+	0.214573i
$893$	−30.7518	+	30.7518i	−1.02907	+	1.02907i
$894$			0.907163i			0.0303401i
$895$	−52.2276	−	23.7485i	−1.74578	−	0.793825i
$896$	1.00000			0.0334077
$897$	−8.91769	−	8.91769i	−0.297753	−	0.297753i
$898$	−14.1732	+	14.1732i	−0.472965	+	0.472965i
$899$	25.5669			0.852704
$900$	−8.60853	−	9.86944i	−0.286951	−	0.328981i
$901$			15.1044i			0.503199i
$902$	−5.80889	−	5.49687i	−0.193415	−	0.183026i
$903$	−4.29551	−	4.29551i	−0.142946	−	0.142946i
$904$	3.30800			0.110023
$905$	14.3667	−	31.5952i	0.477566	−	1.05026i
$906$	−1.69220			−0.0562197
$907$	0.401198	−	0.401198i	0.0133216	−	0.0133216i	−0.700415	−	0.713736i	$-0.747002\pi$
$907$	0.401198	−	0.401198i	0.0133216	−	0.0133216i	0.713736	+	0.700415i	$0.247002\pi$
$908$	−3.48983	+	3.48983i	−0.115814	+	0.115814i
$909$	−26.4049			−0.875795
$910$	−6.64761	+	2.49181i	−0.220366	+	0.0826026i
$911$	−42.7107			−1.41507			−0.707535	−	0.706678i	$-0.750193\pi$
$911$	−42.7107			−1.41507			−0.707535	+	0.706678i	$0.750193\pi$
$912$	2.23140	+	2.23140i	0.0738889	+	0.0738889i
$913$	−13.1541	−	12.4475i	−0.435336	−	0.411952i
$914$			19.8239i			0.655717i
$915$	−3.26828	−	8.71906i	−0.108046	−	0.288243i
$916$	−7.10111			−0.234627
$917$	3.37402	−	3.37402i	0.111420	−	0.111420i
$918$	3.05977	+	3.05977i	0.100987	+	0.100987i
$919$	−31.3141			−1.03296			−0.516478	−	0.856300i	$-0.672757\pi$
$919$	−31.3141			−1.03296			−0.516478	+	0.856300i	$0.672757\pi$
$920$	5.95844	−	13.1038i	0.196444	−	0.432018i
$921$			1.85281i			0.0610520i
$922$	−28.9220	+	28.9220i	−0.952496	+	0.952496i
$923$	8.21263	−	8.21263i	0.270322	−	0.270322i
$924$	−0.0564584	−	2.04572i	−0.00185735	−	0.0672994i
$925$	−8.02337	−	0.547501i	−0.263807	−	0.0180017i
$926$		−	27.0306i		−	0.888281i
$927$	−2.76008	+	2.76008i	−0.0906529	+	0.0906529i
$928$	−2.75584	−	2.75584i	−0.0904648	−	0.0904648i
$929$		−	2.44867i		−	0.0803382i	−0.999193	−	0.0401691i	$-0.987210\pi$
$929$		−	2.44867i		−	0.0803382i	0.999193	−	0.0401691i	$-0.0127897\pi$
$930$	8.23947	+	3.74658i	0.270183	+	0.122855i
$931$		−	5.11418i		−	0.167610i
$932$	−5.34796	−	5.34796i	−0.175178	−	0.175178i
$933$	8.54330	+	8.54330i	0.279695	+	0.279695i
$934$	−42.3716			−1.38644
$935$	3.48641	+	8.57353i	0.114018	+	0.280384i
$936$	8.31587			0.271813
$937$	26.7499	+	26.7499i	0.873882	+	0.873882i	0.992893	−	0.119011i	$-0.0379723\pi$
$937$	26.7499	+	26.7499i	0.873882	+	0.873882i	−0.119011	+	0.992893i	$0.537972\pi$
$938$	1.48033	+	1.48033i	0.0483345	+	0.0483345i
$939$		−	17.1780i		−	0.560582i
$940$	17.8052	−	6.67414i	0.580740	−	0.217686i
$941$			46.4769i			1.51510i	0.652776	+	0.757551i	$0.273604\pi$
$941$			46.4769i			1.51510i	−0.652776	+	0.757551i	$0.726396\pi$
$942$	−2.57911	−	2.57911i	−0.0840320	−	0.0840320i
$943$	−10.9764	+	10.9764i	−0.357441	+	0.357441i
$944$		−	8.83463i		−	0.287543i
$945$	−3.20926	+	7.05779i	−0.104397	+	0.229590i
$946$	0.900796	+	32.6396i	0.0292874	+	1.06120i
$947$	29.2953	−	29.2953i	0.951971	−	0.951971i	−0.0469277	−	0.998898i	$-0.514943\pi$
$947$	29.2953	−	29.2953i	0.951971	−	0.951971i	0.998898	+	0.0469277i	$0.0149430\pi$
$948$	−3.49443	+	3.49443i	−0.113494	+	0.113494i
$949$			10.9637i			0.355896i
$950$	1.74086	−	25.5116i	0.0564811	−	0.827704i
$951$	−5.86258			−0.190107
$952$	0.882457	+	0.882457i	0.0286006	+	0.0286006i
$953$	−24.5759	+	24.5759i	−0.796090	+	0.796090i	−0.982477	−	0.186386i	$-0.940322\pi$
$953$	−24.5759	+	24.5759i	−0.796090	+	0.796090i	0.186386	+	0.982477i	$0.440322\pi$
$954$	31.7009			1.02636
$955$	16.1943	−	35.6144i	0.524035	−	1.15245i
$956$			11.4855i			0.371468i
$957$	−5.48209	+	5.79327i	−0.177211	+	0.187270i
$958$	−9.65261	−	9.65261i	−0.311862	−	0.311862i
$959$	−12.8722			−0.415666
$960$	−0.484285	−	1.29197i	−0.0156302	−	0.0416981i
$961$	12.0347			0.388216
$962$	3.61085	−	3.61085i	0.116419	−	0.116419i
$963$	32.1953	−	32.1953i	1.03748	−	1.03748i
$964$	4.55965			0.146857
$965$	−17.6816	−	47.1706i	−0.569190	−	1.51848i
$966$	−3.97226			−0.127805
$967$	−17.7484	−	17.7484i	−0.570751	−	0.570751i	0.361587	−	0.932338i	$-0.382235\pi$
$967$	−17.7484	−	17.7484i	−0.570751	−	0.570751i	−0.932338	+	0.361587i	$0.882235\pi$
$968$	−7.33733	+	8.19534i	−0.235831	+	0.263408i
$969$			3.93822i			0.126514i
$970$	3.34288	−	7.35165i	0.107334	−	0.236047i
$971$	−30.4035			−0.975694			−0.487847	−	0.872929i	$-0.662218\pi$
$971$	−30.4035			−0.975694			−0.487847	+	0.872929i	$0.662218\pi$
$972$	9.85029	−	9.85029i	0.315948	−	0.315948i
$973$	−6.28070	−	6.28070i	−0.201350	−	0.201350i
$974$	−17.2784			−0.553637
$975$	6.43867	+	7.38175i	0.206203	+	0.236405i
$976$			6.74866i			0.216019i
$977$	7.69315	−	7.69315i	0.246126	−	0.246126i	−0.573253	−	0.819378i	$-0.694319\pi$
$977$	7.69315	−	7.69315i	0.246126	−	0.246126i	0.819378	+	0.573253i	$0.194319\pi$
$978$	−2.42086	+	2.42086i	−0.0774106	+	0.0774106i
$979$	−18.4086	+	0.508045i	−0.588340	+	0.0162372i
$980$	−0.925572	+	2.03551i	−0.0295663	+	0.0650221i
$981$			3.21452i			0.102632i
$982$	−18.5732	+	18.5732i	−0.592695	+	0.592695i
$983$	−19.1109	−	19.1109i	−0.609545	−	0.609545i	0.333282	−	0.942827i	$-0.391844\pi$
$983$	−19.1109	−	19.1109i	−0.609545	−	0.609545i	−0.942827	+	0.333282i	$0.891844\pi$
$984$			1.48789i			0.0474321i
$985$	53.0444	−	19.8833i	1.69013	−	0.633534i
$986$		−	4.86382i		−	0.154895i
$987$	−3.71032	−	3.71032i	−0.118101	−	0.118101i
$988$	11.4813	+	11.4813i	0.365268	+	0.365268i
$989$	63.3776			2.01529
$990$	17.9941	−	7.31724i	0.571889	−	0.232557i
$991$	2.15323			0.0683997			0.0341999	−	0.999415i	$-0.489112\pi$
$991$	2.15323			0.0683997			0.0341999	+	0.999415i	$0.489112\pi$
$992$	−4.63868	−	4.63868i	−0.147278	−	0.147278i
$993$	−14.1968	−	14.1968i	−0.450520	−	0.450520i
$994$		−	3.65820i		−	0.116031i
$995$	38.6010	+	17.5523i	1.22373	+	0.556446i
$996$			3.36927i			0.106759i
$997$	−28.1769	−	28.1769i	−0.892370	−	0.892370i	0.102376	−	0.994746i	$-0.467356\pi$
$997$	−28.1769	−	28.1769i	−0.892370	−	0.892370i	−0.994746	+	0.102376i	$0.967356\pi$
$998$	−16.1491	+	16.1491i	−0.511191	+	0.511191i
$999$		−	5.57687i		−	0.176444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.m.f.43.6	✓	36
5.2	odd	4	inner	770.2.m.f.197.15	yes	36
11.10	odd	2	inner	770.2.m.f.43.15	yes	36
55.32	even	4	inner	770.2.m.f.197.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.m.f.43.6	✓	36	1.1	even	1	trivial
770.2.m.f.43.15	yes	36	11.10	odd	2	inner
770.2.m.f.197.6	yes	36	55.32	even	4	inner
770.2.m.f.197.15	yes	36	5.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.436316 + 0.436316i) q^{3} +1.00000i q^{4} +(0.925572 - 2.03551i) q^{5} -0.617044i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.61926i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.436316 + 0.436316i) q^{3} +1.00000i q^{4} +(0.925572 - 2.03551i) q^{5} -0.617044i q^{6} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} -2.61926i q^{9} +(-2.09380 + 0.784847i) q^{10} +(-0.0914983 - 3.31536i) q^{11} +(-0.436316 + 0.436316i) q^{12} +(-2.24499 + 2.24499i) q^{13} +1.00000i q^{14} +(1.29197 - 0.484285i) q^{15} -1.00000 q^{16} +(-0.882457 - 0.882457i) q^{17} +(-1.85209 + 1.85209i) q^{18} -5.11418 q^{19} +(2.03551 + 0.925572i) q^{20} -0.617044i q^{21} +(-2.27962 + 2.40901i) q^{22} +(4.55205 + 4.55205i) q^{23} +0.617044 q^{24} +(-3.28663 - 3.76803i) q^{25} +3.17489 q^{26} +(2.45177 - 2.45177i) q^{27} +(0.707107 - 0.707107i) q^{28} -3.89734 q^{29} +(-1.25600 - 0.571118i) q^{30} -6.56008 q^{31} +(0.707107 + 0.707107i) q^{32} +(1.40662 - 1.48647i) q^{33} +1.24798i q^{34} +(-2.09380 + 0.784847i) q^{35} +2.61926 q^{36} +(1.13731 - 1.13731i) q^{37} +(3.61627 + 3.61627i) q^{38} -1.95905 q^{39} +(-0.784847 - 2.09380i) q^{40} +2.41131i q^{41} +(-0.436316 + 0.436316i) q^{42} +(6.96143 - 6.96143i) q^{43} +(3.31536 - 0.0914983i) q^{44} +(-5.33153 - 2.42431i) q^{45} -6.43757i q^{46} +(6.01305 - 6.01305i) q^{47} +(-0.436316 - 0.436316i) q^{48} +1.00000i q^{49} +(-0.340400 + 4.98840i) q^{50} -0.770060i q^{51} +(-2.24499 - 2.24499i) q^{52} +(-8.55813 - 8.55813i) q^{53} -3.46733 q^{54} +(-6.83315 - 2.88236i) q^{55} -1.00000 q^{56} +(-2.23140 - 2.23140i) q^{57} +(2.75584 + 2.75584i) q^{58} +8.83463i q^{59} +(0.484285 + 1.29197i) q^{60} -6.74866i q^{61} +(4.63868 + 4.63868i) q^{62} +(-1.85209 + 1.85209i) q^{63} -1.00000i q^{64} +(2.49181 + 6.64761i) q^{65} +(-2.04572 + 0.0564584i) q^{66} +(1.48033 - 1.48033i) q^{67} +(0.882457 - 0.882457i) q^{68} +3.97226i q^{69} +(2.03551 + 0.925572i) q^{70} -3.65820 q^{71} +(-1.85209 - 1.85209i) q^{72} +(2.44181 - 2.44181i) q^{73} -1.60841 q^{74} +(0.210041 - 3.07806i) q^{75} -5.11418i q^{76} +(-2.27962 + 2.40901i) q^{77} +(1.38526 + 1.38526i) q^{78} +8.00894 q^{79} +(-0.925572 + 2.03551i) q^{80} -5.71828 q^{81} +(1.70506 - 1.70506i) q^{82} +(3.86105 - 3.86105i) q^{83} +0.617044 q^{84} +(-2.61303 + 0.979476i) q^{85} -9.84495 q^{86} +(-1.70047 - 1.70047i) q^{87} +(-2.40901 - 2.27962i) q^{88} -5.55251i q^{89} +(2.05572 + 5.48421i) q^{90} +3.17489 q^{91} +(-4.55205 + 4.55205i) q^{92} +(-2.86227 - 2.86227i) q^{93} -8.50374 q^{94} +(-4.73354 + 10.4100i) q^{95} +0.617044i q^{96} +(-2.55385 + 2.55385i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-8.68379 + 0.239658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{3}+O(q^{10}) \) 36 * q - 4 * q^3	\( 36 q - 4 q^{3} + 12 q^{11} + 4 q^{12} - 4 q^{15} - 36 q^{16} - 12 q^{20} - 12 q^{22} + 4 q^{23} + 12 q^{25} + 24 q^{26} + 56 q^{27} + 8 q^{31} - 44 q^{33} - 44 q^{36} - 28 q^{37} + 16 q^{38} + 4 q^{42} - 44 q^{45} + 12 q^{47} + 4 q^{48} + 28 q^{53} + 40 q^{55} - 36 q^{56} - 24 q^{58} + 12 q^{60} + 24 q^{66} + 12 q^{67} - 12 q^{70} - 112 q^{71} - 52 q^{75} - 12 q^{77} + 48 q^{78} + 4 q^{81} + 40 q^{82} + 32 q^{86} - 12 q^{88} + 24 q^{91} - 4 q^{92} - 80 q^{93} + 100 q^{97}+O(q^{100}) \) 36 * q - 4 * q^3 + 12 * q^11 + 4 * q^12 - 4 * q^15 - 36 * q^16 - 12 * q^20 - 12 * q^22 + 4 * q^23 + 12 * q^25 + 24 * q^26 + 56 * q^27 + 8 * q^31 - 44 * q^33 - 44 * q^36 - 28 * q^37 + 16 * q^38 + 4 * q^42 - 44 * q^45 + 12 * q^47 + 4 * q^48 + 28 * q^53 + 40 * q^55 - 36 * q^56 - 24 * q^58 + 12 * q^60 + 24 * q^66 + 12 * q^67 - 12 * q^70 - 112 * q^71 - 52 * q^75 - 12 * q^77 + 48 * q^78 + 4 * q^81 + 40 * q^82 + 32 * q^86 - 12 * q^88 + 24 * q^91 - 4 * q^92 - 80 * q^93 + 100 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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