LMFDB - Embedded newform 429.2.j.a.122.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.j (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.13
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16086 - 1.16086i) q^{2} +(-1.66333 + 0.483035i) q^{3} +0.695179i q^{4} +(0.163665 + 0.163665i) q^{5} +(2.49163 + 1.37016i) q^{6} +(0.204315 + 0.204315i) q^{7} +(-1.51471 + 1.51471i) q^{8} +(2.53335 - 1.60690i) q^{9} +O(q^{10})$	\(q+(-1.16086 - 1.16086i) q^{2} +(-1.66333 + 0.483035i) q^{3} +0.695179i q^{4} +(0.163665 + 0.163665i) q^{5} +(2.49163 + 1.37016i) q^{6} +(0.204315 + 0.204315i) q^{7} +(-1.51471 + 1.51471i) q^{8} +(2.53335 - 1.60690i) q^{9} -0.379984i q^{10} +(0.707107 - 0.707107i) q^{11} +(-0.335796 - 1.15631i) q^{12} +(3.41950 + 1.14326i) q^{13} -0.474361i q^{14} +(-0.351286 - 0.193174i) q^{15} +4.90708 q^{16} -6.20069 q^{17} +(-4.80624 - 1.07548i) q^{18} +(3.98706 - 3.98706i) q^{19} +(-0.113777 + 0.113777i) q^{20} +(-0.438535 - 0.241152i) q^{21} -1.64170 q^{22} +2.08381 q^{23} +(1.78781 - 3.25113i) q^{24} -4.94643i q^{25} +(-2.64239 - 5.29671i) q^{26} +(-3.43762 + 3.89650i) q^{27} +(-0.142035 + 0.142035i) q^{28} -8.05272i q^{29} +(0.183546 + 0.632040i) q^{30} +(-2.94900 + 2.94900i) q^{31} +(-2.66700 - 2.66700i) q^{32} +(-0.834597 + 1.51771i) q^{33} +(7.19812 + 7.19812i) q^{34} +0.0668785i q^{35} +(1.11708 + 1.76114i) q^{36} +(-7.17056 - 7.17056i) q^{37} -9.25682 q^{38} +(-6.24000 - 0.249883i) q^{39} -0.495811 q^{40} +(-3.44137 - 3.44137i) q^{41} +(0.229133 + 0.789020i) q^{42} +4.63144i q^{43} +(0.491566 + 0.491566i) q^{44} +(0.677615 + 0.151629i) q^{45} +(-2.41901 - 2.41901i) q^{46} +(9.16030 - 9.16030i) q^{47} +(-8.16212 + 2.37029i) q^{48} -6.91651i q^{49} +(-5.74210 + 5.74210i) q^{50} +(10.3138 - 2.99515i) q^{51} +(-0.794770 + 2.37716i) q^{52} +0.449389i q^{53} +(8.51388 - 0.532695i) q^{54} +0.231458 q^{55} -0.618956 q^{56} +(-4.70592 + 8.55770i) q^{57} +(-9.34806 + 9.34806i) q^{58} +(-4.15663 + 4.15663i) q^{59} +(0.134290 - 0.244207i) q^{60} -1.36131 q^{61} +6.84673 q^{62} +(0.845915 + 0.189289i) q^{63} -3.62215i q^{64} +(0.372541 + 0.746765i) q^{65} +(2.73069 - 0.792999i) q^{66} +(10.6616 - 10.6616i) q^{67} -4.31059i q^{68} +(-3.46607 + 1.00655i) q^{69} +(0.0776364 - 0.0776364i) q^{70} +(8.60943 + 8.60943i) q^{71} +(-1.40331 + 6.27128i) q^{72} +(7.17521 + 7.17521i) q^{73} +16.6480i q^{74} +(2.38930 + 8.22756i) q^{75} +(2.77172 + 2.77172i) q^{76} +0.288945 q^{77} +(6.95367 + 7.53382i) q^{78} -10.0088 q^{79} +(0.803119 + 0.803119i) q^{80} +(3.83576 - 8.14168i) q^{81} +7.98989i q^{82} +(-2.68577 - 2.68577i) q^{83} +(0.167644 - 0.304860i) q^{84} +(-1.01484 - 1.01484i) q^{85} +(5.37644 - 5.37644i) q^{86} +(3.88975 + 13.3944i) q^{87} +2.14212i q^{88} +(12.2948 - 12.2948i) q^{89} +(-0.610595 - 0.962634i) q^{90} +(0.465069 + 0.932239i) q^{91} +1.44862i q^{92} +(3.48069 - 6.32963i) q^{93} -21.2676 q^{94} +1.30509 q^{95} +(5.72437 + 3.14786i) q^{96} +(3.09056 - 3.09056i) q^{97} +(-8.02908 + 8.02908i) q^{98} +(0.655104 - 2.92760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−1.16086	−	1.16086i	−0.820850	−	0.820850i	0.165380	−	0.986230i	$-0.447115\pi$
$2$	−1.16086	−	1.16086i	−0.820850	−	0.820850i	−0.986230	+	0.165380i	$0.947115\pi$
$3$	−1.66333	+	0.483035i	−0.960326	+	0.278881i
$3$	−1.66333	+	0.483035i	−0.960326	+	0.278881i
$4$			0.695179i			0.347590i
$5$	0.163665	+	0.163665i	0.0731934	+	0.0731934i	0.742756	−	0.669562i	$-0.233518\pi$
$5$	0.163665	+	0.163665i	0.0731934	+	0.0731934i	−0.669562	+	0.742756i	$0.733518\pi$
$6$	2.49163	+	1.37016i	1.01720	+	0.559364i
$7$	0.204315	+	0.204315i	0.0772238	+	0.0772238i	0.744664	−	0.667440i	$-0.232610\pi$
$7$	0.204315	+	0.204315i	0.0772238	+	0.0772238i	−0.667440	+	0.744664i	$0.732610\pi$
$8$	−1.51471	+	1.51471i	−0.535531	+	0.535531i
$9$	2.53335	−	1.60690i	0.844451	−	0.535632i
$10$		−	0.379984i		−	0.120162i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	−0.335796	−	1.15631i	−0.0969360	−	0.333799i
$13$	3.41950	+	1.14326i	0.948398	+	0.317083i
$13$	3.41950	+	1.14326i	0.948398	+	0.317083i
$14$		−	0.474361i		−	0.126778i
$15$	−0.351286	−	0.193174i	−0.0907017	−	0.0498773i
$16$	4.90708			1.22677
$17$	−6.20069			−1.50389			−0.751944	−	0.659227i	$-0.770884\pi$
$17$	−6.20069			−1.50389			−0.751944	+	0.659227i	$0.770884\pi$
$18$	−4.80624	−	1.07548i	−1.13284	−	0.253494i
$19$	3.98706	−	3.98706i	0.914694	−	0.914694i	−0.0819426	−	0.996637i	$-0.526112\pi$
$19$	3.98706	−	3.98706i	0.914694	−	0.914694i	0.996637	+	0.0819426i	$0.0261124\pi$
$20$	−0.113777	+	0.113777i	−0.0254413	+	0.0254413i
$21$	−0.438535	−	0.241152i	−0.0956962	−	0.0526238i
$22$	−1.64170			−0.350012
$23$	2.08381			0.434505			0.217252	−	0.976115i	$-0.430291\pi$
$23$	2.08381			0.434505			0.217252	+	0.976115i	$0.430291\pi$
$24$	1.78781	−	3.25113i	0.364935	−	0.663633i
$25$		−	4.94643i		−	0.989285i
$26$	−2.64239	−	5.29671i	−0.518215	−	1.03877i
$27$	−3.43762	+	3.89650i	−0.661571	+	0.749883i
$28$	−0.142035	+	0.142035i	−0.0268422	+	0.0268422i
$29$		−	8.05272i		−	1.49535i	−0.664064	−	0.747676i	$-0.731170\pi$
$29$		−	8.05272i		−	1.49535i	0.664064	−	0.747676i	$-0.268830\pi$
$30$	0.183546	+	0.632040i	0.0335107	+	0.115394i
$31$	−2.94900	+	2.94900i	−0.529655	+	0.529655i	−0.920470	−	0.390814i	$-0.872193\pi$
$31$	−2.94900	+	2.94900i	−0.529655	+	0.529655i	0.390814	+	0.920470i	$0.372193\pi$
$32$	−2.66700	−	2.66700i	−0.471464	−	0.471464i
$33$	−0.834597	+	1.51771i	−0.145285	+	0.264200i
$34$	7.19812	+	7.19812i	1.23447	+	1.23447i
$35$			0.0668785i			0.0113045i
$36$	1.11708	+	1.76114i	0.186180	+	0.293523i
$37$	−7.17056	−	7.17056i	−1.17883	−	1.17883i	−0.980042	−	0.198791i	$-0.936299\pi$
$37$	−7.17056	−	7.17056i	−1.17883	−	1.17883i	−0.198791	−	0.980042i	$-0.563701\pi$
$38$	−9.25682			−1.50165
$39$	−6.24000	−	0.249883i	−0.999199	−	0.0400133i
$40$	−0.495811			−0.0783946
$41$	−3.44137	−	3.44137i	−0.537452	−	0.537452i	0.385327	−	0.922780i	$-0.374088\pi$
$41$	−3.44137	−	3.44137i	−0.537452	−	0.537452i	−0.922780	+	0.385327i	$0.874088\pi$
$42$	0.229133	+	0.789020i	0.0353560	+	0.121748i
$43$			4.63144i			0.706287i	0.935569	+	0.353144i	$0.114887\pi$
$43$			4.63144i			0.706287i	−0.935569	+	0.353144i	$0.885113\pi$
$44$	0.491566	+	0.491566i	0.0741064	+	0.0741064i
$45$	0.677615	+	0.151629i	0.101013	+	0.0226035i
$46$	−2.41901	−	2.41901i	−0.356663	−	0.356663i
$47$	9.16030	−	9.16030i	1.33617	−	1.33617i	0.436428	−	0.899739i	$-0.356243\pi$
$47$	9.16030	−	9.16030i	1.33617	−	1.33617i	0.899739	−	0.436428i	$-0.143757\pi$
$48$	−8.16212	+	2.37029i	−1.17810	+	0.342123i
$49$		−	6.91651i		−	0.988073i
$50$	−5.74210	+	5.74210i	−0.812055	+	0.812055i
$51$	10.3138	−	2.99515i	1.44422	−	0.419405i
$52$	−0.794770	+	2.37716i	−0.110215	+	0.329653i
$53$			0.449389i			0.0617283i	0.999524	+	0.0308641i	$0.00982592\pi$
$53$			0.449389i			0.0617283i	−0.999524	+	0.0308641i	$0.990174\pi$
$54$	8.51388	−	0.532695i	1.15859	−	0.0724906i
$55$	0.231458			0.0312097
$56$	−0.618956			−0.0827114
$57$	−4.70592	+	8.55770i	−0.623314	+	1.13350i
$58$	−9.34806	+	9.34806i	−1.22746	+	1.22746i
$59$	−4.15663	+	4.15663i	−0.541148	+	0.541148i	−0.923865	−	0.382718i	$-0.874988\pi$
$59$	−4.15663	+	4.15663i	−0.541148	+	0.541148i	0.382718	+	0.923865i	$0.374988\pi$
$60$	0.134290	−	0.244207i	0.0173368	−	0.0315270i
$61$	−1.36131			−0.174297			−0.0871487	−	0.996195i	$-0.527776\pi$
$61$	−1.36131			−0.174297			−0.0871487	+	0.996195i	$0.527776\pi$
$62$	6.84673			0.869535
$63$	0.845915	+	0.189289i	0.106575	+	0.0238482i
$64$		−	3.62215i		−	0.452768i
$65$	0.372541	+	0.746765i	0.0462080	+	0.0926248i
$66$	2.73069	−	0.792999i	0.336125	−	0.0976114i
$67$	10.6616	−	10.6616i	1.30252	−	1.30252i	0.375837	−	0.926686i	$-0.377355\pi$
$67$	10.6616	−	10.6616i	1.30252	−	1.30252i	0.926686	−	0.375837i	$-0.122645\pi$
$68$		−	4.31059i		−	0.522736i
$69$	−3.46607	+	1.00655i	−0.417266	+	0.121175i
$70$	0.0776364	−	0.0776364i	0.00927932	−	0.00927932i
$71$	8.60943	+	8.60943i	1.02175	+	1.02175i	0.999758	+	0.0219931i	$0.00700118\pi$
$71$	8.60943	+	8.60943i	1.02175	+	1.02175i	0.0219931	+	0.999758i	$0.492999\pi$
$72$	−1.40331	+	6.27128i	−0.165382	+	0.739078i
$73$	7.17521	+	7.17521i	0.839795	+	0.839795i	0.988832	−	0.149037i	$-0.0476174\pi$
$73$	7.17521	+	7.17521i	0.839795	+	0.839795i	−0.149037	+	0.988832i	$0.547617\pi$
$74$			16.6480i			1.93529i
$75$	2.38930	+	8.22756i	0.275892	+	0.950036i
$76$	2.77172	+	2.77172i	0.317938	+	0.317938i
$77$	0.288945			0.0329283
$78$	6.95367	+	7.53382i	0.787348	+	0.853038i
$79$	−10.0088			−1.12608			−0.563039	−	0.826430i	$-0.690368\pi$
$79$	−10.0088			−1.12608			−0.563039	+	0.826430i	$0.690368\pi$
$80$	0.803119	+	0.803119i	0.0897915	+	0.0897915i
$81$	3.83576	−	8.14168i	0.426196	−	0.904631i
$82$			7.98989i			0.882336i
$83$	−2.68577	−	2.68577i	−0.294801	−	0.294801i	0.544172	−	0.838974i	$-0.316844\pi$
$83$	−2.68577	−	2.68577i	−0.294801	−	0.294801i	−0.838974	+	0.544172i	$0.816844\pi$
$84$	0.167644	−	0.304860i	0.0182915	−	0.0332630i
$85$	−1.01484	−	1.01484i	−0.110075	−	0.110075i
$86$	5.37644	−	5.37644i	0.579756	−	0.579756i
$87$	3.88975	+	13.3944i	0.417025	+	1.43603i
$88$			2.14212i			0.228351i
$89$	12.2948	−	12.2948i	1.30324	−	1.30324i	0.377048	−	0.926194i	$-0.376939\pi$
$89$	12.2948	−	12.2948i	1.30324	−	1.30324i	0.926194	−	0.377048i	$-0.123061\pi$
$90$	−0.610595	−	0.962634i	−0.0643624	−	0.101471i
$91$	0.465069	+	0.932239i	0.0487525	+	0.0977252i
$92$			1.44862i			0.151029i
$93$	3.48069	−	6.32963i	0.360931	−	0.656352i
$94$	−21.2676			−2.19359
$95$	1.30509			0.133899
$96$	5.72437	+	3.14786i	0.584241	+	0.321277i
$97$	3.09056	−	3.09056i	0.313799	−	0.313799i	−0.532580	−	0.846379i	$-0.678778\pi$
$97$	3.09056	−	3.09056i	0.313799	−	0.313799i	0.846379	+	0.532580i	$0.178778\pi$
$98$	−8.02908	+	8.02908i	−0.811060	+	0.811060i
$99$	0.655104	−	2.92760i	0.0658404	−	0.294235i
$100$	3.43865			0.343865
$101$	9.48159			0.943453			0.471727	−	0.881745i	$-0.343631\pi$
$101$	9.48159			0.943453			0.471727	+	0.881745i	$0.343631\pi$
$102$	−15.4498	−	8.49592i	−1.52976	−	0.841222i
$103$			14.4713i			1.42590i	0.701215	+	0.712950i	$0.252641\pi$
$103$			14.4713i			1.42590i	−0.701215	+	0.712950i	$0.747359\pi$
$104$	−6.91125	+	3.44784i	−0.677704	+	0.338089i
$105$	−0.0323047	−	0.111241i	−0.00315261	−	0.0108560i
$106$	0.521676	−	0.521676i	0.0506697	−	0.0506697i
$107$			8.22258i			0.794906i	0.917622	+	0.397453i	$0.130106\pi$
$107$			8.22258i			0.794906i	−0.917622	+	0.397453i	$0.869894\pi$
$108$	−2.70877	−	2.38976i	−0.260651	−	0.229955i
$109$	4.05233	−	4.05233i	0.388143	−	0.388143i	−0.485882	−	0.874025i	$-0.661501\pi$
$109$	4.05233	−	4.05233i	0.388143	−	0.388143i	0.874025	+	0.485882i	$0.161501\pi$
$110$	−0.268689	−	0.268689i	−0.0256185	−	0.0256185i
$111$	15.3907	+	8.46340i	1.46082	+	0.803310i
$112$	1.00259	+	1.00259i	0.0947359	+	0.0947359i
$113$		−	11.4386i		−	1.07606i	−0.842927	−	0.538028i	$-0.819169\pi$
$113$		−	11.4386i		−	1.07606i	0.842927	−	0.538028i	$-0.180831\pi$
$114$	15.3972	−	4.47137i	1.44208	−	0.418782i
$115$	0.341048	+	0.341048i	0.0318029	+	0.0318029i
$116$	5.59808			0.519769
$117$	10.4999	−	2.59850i	0.970716	−	0.240231i
$118$	9.65052			0.888402
$119$	−1.26689	−	1.26689i	−0.116136	−	0.116136i
$120$	0.824699	−	0.239494i	0.0752844	−	0.0218627i
$121$		−	1.00000i		−	0.0909091i
$122$	1.58028	+	1.58028i	0.143072	+	0.143072i
$123$	7.38646	+	4.06185i	0.666014	+	0.366244i
$124$	−2.05008	−	2.05008i	−0.184103	−	0.184103i
$125$	1.62789	−	1.62789i	0.145602	−	0.145602i
$126$	−0.762249	−	1.20172i	−0.0679065	−	0.107058i
$127$			4.14046i			0.367407i	0.982982	+	0.183703i	$0.0588086\pi$
$127$			4.14046i			0.367407i	−0.982982	+	0.183703i	$0.941191\pi$
$128$	−9.53880	+	9.53880i	−0.843119	+	0.843119i
$129$	−2.23715	−	7.70362i	−0.196970	−	0.678266i
$130$	0.434420	−	1.29935i	0.0381012	−	0.113961i
$131$		−	4.06200i		−	0.354898i	−0.984130	−	0.177449i	$-0.943215\pi$
$131$		−	4.06200i		−	0.354898i	0.984130	−	0.177449i	$-0.0567845\pi$
$132$	−1.05508	−	0.580194i	−0.0918331	−	0.0504994i
$133$	1.62923			0.141272
$134$	−24.7532			−2.13835
$135$	−1.20034	+	0.0751029i	−0.103309	+	0.00646383i
$136$	9.39225	−	9.39225i	0.805379	−	0.805379i
$137$	1.13960	−	1.13960i	0.0973629	−	0.0973629i	−0.656748	−	0.754110i	$-0.728068\pi$
$137$	1.13960	−	1.13960i	0.0973629	−	0.0973629i	0.754110	+	0.656748i	$0.228068\pi$
$138$	5.19208	+	2.85515i	0.441979	+	0.243046i
$139$	−17.6863			−1.50013			−0.750067	−	0.661362i	$-0.769979\pi$
$139$	−17.6863			−1.50013			−0.750067	+	0.661362i	$0.769979\pi$
$140$	−0.0464926			−0.00392934
$141$	−10.8119	+	19.6614i	−0.910525	+	1.65579i
$142$		−	19.9886i		−	1.67741i
$143$	3.22636	−	1.60954i	0.269801	−	0.134597i
$144$	12.4314	−	7.88518i	1.03595	−	0.657098i
$145$	1.31795	−	1.31795i	0.109450	−	0.109450i
$146$		−	16.6588i		−	1.37869i
$147$	3.34092	+	11.5045i	0.275554	+	0.948872i
$148$	4.98483	−	4.98483i	0.409750	−	0.409750i
$149$	2.68878	+	2.68878i	0.220274	+	0.220274i	0.808614	−	0.588340i	$-0.200218\pi$
$149$	2.68878	+	2.68878i	0.220274	+	0.220274i	−0.588340	+	0.808614i	$0.700218\pi$
$150$	6.77738	−	12.3247i	0.553371	−	1.00630i
$151$	1.18431	+	1.18431i	0.0963781	+	0.0963781i	0.753652	−	0.657274i	$-0.228290\pi$
$151$	1.18431	+	1.18431i	0.0963781	+	0.0963781i	−0.657274	+	0.753652i	$0.728290\pi$
$152$			12.0785i			0.979695i
$153$	−15.7085	+	9.96387i	−1.26996	+	0.805531i
$154$	−0.335424	−	0.335424i	−0.0270292	−	0.0270292i
$155$	−0.965297			−0.0775345
$156$	0.173713	−	4.33792i	0.0139082	−	0.347311i
$157$	−12.2812			−0.980146			−0.490073	−	0.871681i	$-0.663030\pi$
$157$	−12.2812			−0.980146			−0.490073	+	0.871681i	$0.663030\pi$
$158$	11.6188	+	11.6188i	0.924342	+	0.924342i
$159$	−0.217071	−	0.747483i	−0.0172148	−	0.0592792i
$160$		−	0.872992i		−	0.0690161i
$161$	0.425754	+	0.425754i	0.0335541	+	0.0335541i
$162$	−13.9041	+	4.99855i	−1.09241	+	0.392723i
$163$	0.197427	+	0.197427i	0.0154636	+	0.0154636i	0.714796	−	0.699333i	$-0.246519\pi$
$163$	0.197427	+	0.197427i	0.0154636	+	0.0154636i	−0.699333	+	0.714796i	$0.746519\pi$
$164$	2.39237	−	2.39237i	0.186813	−	0.186813i
$165$	−0.384991	+	0.111802i	−0.0299715	+	0.00870379i
$166$			6.23559i			0.483975i
$167$	−3.44251	+	3.44251i	−0.266390	+	0.266390i	−0.827644	−	0.561254i	$-0.810319\pi$
$167$	−3.44251	+	3.44251i	−0.266390	+	0.266390i	0.561254	+	0.827644i	$0.310319\pi$
$168$	1.02953	−	0.298977i	0.0794299	−	0.0230666i
$169$	10.3859	+	7.81874i	0.798917	+	0.601442i
$170$			2.35616i			0.180710i
$171$	3.69384	−	16.5074i	0.282475	−	1.26235i
$172$	−3.21968			−0.245498
$173$	−18.6683			−1.41933			−0.709663	−	0.704541i	$-0.751153\pi$
$173$	−18.6683			−1.41933			−0.709663	+	0.704541i	$0.751153\pi$
$174$	11.0335	−	20.0644i	0.836447	−	1.52108i
$175$	1.01063	−	1.01063i	0.0763963	−	0.0763963i
$176$	3.46983	−	3.46983i	0.261548	−	0.261548i
$177$	4.90607	−	8.92167i	0.368762	−	0.670593i
$178$	−28.5449			−2.13953
$179$	−0.282481			−0.0211136			−0.0105568	−	0.999944i	$-0.503360\pi$
$179$	−0.282481			−0.0211136			−0.0105568	+	0.999944i	$0.503360\pi$
$180$	−0.105409	+	0.471064i	−0.00785674	+	0.0351111i
$181$			15.9660i			1.18674i	0.804930	+	0.593370i	$0.202203\pi$
$181$			15.9660i			1.18674i	−0.804930	+	0.593370i	$0.797797\pi$
$182$	0.542317	−	1.62208i	0.0401992	−	0.120236i
$183$	2.26431	−	0.657559i	0.167382	−	0.0486081i
$184$	−3.15637	+	3.15637i	−0.232691	+	0.232691i
$185$		−	2.34714i		−	0.172565i
$186$	−11.3884	+	3.30721i	−0.835037	+	0.242496i
$187$	−4.38455	+	4.38455i	−0.320630	+	0.320630i
$188$	6.36805	+	6.36805i	0.464438	+	0.464438i
$189$	−1.49847	+	0.0937562i	−0.108998	+	0.00681976i
$190$	−1.51502	−	1.51502i	−0.109911	−	0.109911i
$191$		−	14.5956i		−	1.05610i	−0.849213	−	0.528051i	$-0.822923\pi$
$191$		−	14.5956i		−	1.05610i	0.849213	−	0.528051i	$-0.177077\pi$
$192$	1.74962	+	6.02484i	0.126268	+	0.434805i
$193$	−14.3858	−	14.3858i	−1.03551	−	1.03551i	−0.999346	−	0.0361692i	$-0.988484\pi$
$193$	−14.3858	−	14.3858i	−1.03551	−	1.03551i	−0.0361692	−	0.999346i	$-0.511516\pi$
$194$	−7.17541			−0.515164
$195$	−0.980374	−	1.06217i	−0.0702060	−	0.0760634i
$196$	4.80822			0.343444
$197$	10.5876	+	10.5876i	0.754338	+	0.754338i	0.975286	−	0.220948i	$-0.0709150\pi$
$197$	10.5876	+	10.5876i	0.754338	+	0.754338i	−0.220948	+	0.975286i	$0.570915\pi$
$198$	−4.15901	+	2.63804i	−0.295568	+	0.187478i
$199$		−	4.35663i		−	0.308833i	−0.988006	−	0.154417i	$-0.950650\pi$
$199$		−	4.35663i		−	0.308833i	0.988006	−	0.154417i	$-0.0493498\pi$
$200$	7.49241	+	7.49241i	0.529793	+	0.529793i
$201$	−12.5839	+	22.8837i	−0.887598	+	1.61409i
$202$	−11.0068	−	11.0068i	−0.774434	−	0.774434i
$203$	1.64529	−	1.64529i	0.115477	−	0.115477i
$204$	2.08217	+	7.16995i	0.145781	+	0.501997i
$205$		−	1.12647i		−	0.0786759i
$206$	16.7991	−	16.7991i	1.17045	−	1.17045i
$207$	5.27903	−	3.34847i	0.366918	−	0.232735i
$208$	16.7798	+	5.61007i	1.16347	+	0.388988i
$209$		−	5.63856i		−	0.390027i
$210$	−0.0916341	+	0.166636i	−0.00632335	+	0.0114990i
$211$	−28.5504			−1.96549			−0.982746	−	0.184960i	$-0.940784\pi$
$211$	−28.5504			−1.96549			−0.982746	+	0.184960i	$0.940784\pi$
$212$	−0.312406			−0.0214561
$213$	−18.4790	−	10.1617i	−1.26616	−	0.696268i
$214$	9.54524	−	9.54524i	0.652499	−	0.652499i
$215$	−0.758006	+	0.758006i	−0.0516955	+	0.0516955i
$216$	−0.695072	−	11.1091i	−0.0472936	−	0.755877i
$217$	−1.20505			−0.0818039
$218$	−9.40836			−0.637214
$219$	−15.4006	−	8.46888i	−1.04068	−	0.572274i
$220$			0.160905i			0.0108482i
$221$	−21.2032	−	7.08899i	−1.42628	−	0.476857i
$222$	−8.04157	−	27.6912i	−0.539715	−	1.85851i
$223$	3.46976	−	3.46976i	0.232352	−	0.232352i	−0.581322	−	0.813674i	$-0.697464\pi$
$223$	3.46976	−	3.46976i	0.232352	−	0.232352i	0.813674	+	0.581322i	$0.197464\pi$
$224$		−	1.08982i		−	0.0728165i
$225$	−7.94840	−	12.5311i	−0.529893	−	0.835403i
$226$	−13.2786	+	13.2786i	−0.883280	+	0.883280i
$227$	2.06683	+	2.06683i	0.137180	+	0.137180i	0.772362	−	0.635182i	$-0.219075\pi$
$227$	2.06683	+	2.06683i	0.137180	+	0.137180i	−0.635182	+	0.772362i	$0.719075\pi$
$228$	−5.94914	−	3.27146i	−0.393991	−	0.216658i
$229$	−0.445856	−	0.445856i	−0.0294630	−	0.0294630i	0.692222	−	0.721685i	$-0.256632\pi$
$229$	−0.445856	−	0.445856i	−0.0294630	−	0.0294630i	−0.721685	+	0.692222i	$0.756632\pi$
$230$		−	0.791815i		−	0.0522107i
$231$	−0.480611	+	0.139571i	−0.0316219	+	0.00918307i
$232$	12.1975	+	12.1975i	0.800807	+	0.800807i
$233$	0.486506			0.0318720			0.0159360	−	0.999873i	$-0.494927\pi$
$233$	0.486506			0.0318720			0.0159360	+	0.999873i	$0.494927\pi$
$234$	−15.2054	−	9.17239i	−0.994006	−	0.599618i
$235$	2.99845			0.195597
$236$	−2.88961	−	2.88961i	−0.188097	−	0.188097i
$237$	16.6480	−	4.83460i	1.08140	−	0.314041i
$238$			2.94136i			0.190660i
$239$	15.4233	+	15.4233i	0.997649	+	0.997649i	0.999997	−	0.00234862i	$-0.000747590\pi$
$239$	15.4233	+	15.4233i	0.997649	+	0.997649i	−0.00234862	+	0.999997i	$0.500748\pi$
$240$	−1.72379	−	0.947920i	−0.111270	−	0.0611880i
$241$	16.9215	+	16.9215i	1.09001	+	1.09001i	0.995526	+	0.0944843i	$0.0301202\pi$
$241$	16.9215	+	16.9215i	1.09001	+	1.09001i	0.0944843	+	0.995526i	$0.469880\pi$
$242$	−1.16086	+	1.16086i	−0.0746227	+	0.0746227i
$243$	−2.44744	+	15.3951i	−0.157003	+	0.987598i
$244$		−	0.946352i		−	0.0605840i
$245$	1.13199	−	1.13199i	0.0723204	−	0.0723204i
$246$	−3.85940	−	13.2898i	−0.246066	−	0.847330i
$247$	18.1920	−	9.07550i	1.15753	−	0.577460i
$248$		−	8.93375i		−	0.567294i
$249$	5.76465	+	3.17001i	0.365320	+	0.200891i
$250$	−3.77948			−0.239036
$251$	22.7980			1.43900			0.719498	−	0.694494i	$-0.244372\pi$
$251$	22.7980			1.43900			0.719498	+	0.694494i	$0.244372\pi$
$252$	−0.131590	+	0.588062i	−0.00828937	+	0.0370445i
$253$	1.47348	−	1.47348i	0.0926367	−	0.0926367i
$254$	4.80649	−	4.80649i	0.301586	−	0.301586i
$255$	2.17822	+	1.19781i	0.136405	+	0.0750098i
$256$	14.9021			0.931380
$257$	−15.2829			−0.953324			−0.476662	−	0.879087i	$-0.658153\pi$
$257$	−15.2829			−0.953324			−0.476662	+	0.879087i	$0.658153\pi$
$258$	−6.34580	+	11.5398i	−0.395072	+	0.718437i
$259$		−	2.93010i		−	0.182068i
$260$	−0.519136	+	0.258983i	−0.0321954	+	0.0160614i
$261$	−12.9399	−	20.4004i	−0.800959	−	1.26275i
$262$	−4.71540	+	4.71540i	−0.291318	+	0.291318i
$263$		−	14.6908i		−	0.905872i	−0.891543	−	0.452936i	$-0.850377\pi$
$263$		−	14.6908i		−	0.905872i	0.891543	−	0.452936i	$-0.149623\pi$
$264$	−1.03472	−	3.56307i	−0.0636827	−	0.219292i
$265$	−0.0735493	+	0.0735493i	−0.00451810	+	0.00451810i
$266$	−1.89131	−	1.89131i	−0.115963	−	0.115963i
$267$	−14.5115	+	26.3891i	−0.888088	+	1.61499i
$268$	7.41173	+	7.41173i	0.452744	+	0.452744i
$269$			12.5212i			0.763430i	0.924280	+	0.381715i	$0.124666\pi$
$269$			12.5212i			0.763430i	−0.924280	+	0.381715i	$0.875334\pi$
$270$	1.48061	+	1.30624i	0.0901070	+	0.0794954i
$271$	6.04682	+	6.04682i	0.367318	+	0.367318i	0.866498	−	0.499180i	$-0.166365\pi$
$271$	6.04682	+	6.04682i	0.367318	+	0.367318i	−0.499180	+	0.866498i	$0.666365\pi$
$272$	−30.4273			−1.84493
$273$	−1.22387	−	1.32598i	−0.0740719	−	0.0802519i
$274$	−2.64583			−0.159841
$275$	−3.49765	−	3.49765i	−0.210916	−	0.210916i
$276$	−0.699736	−	2.40954i	−0.0421191	−	0.145037i
$277$		−	15.0538i		−	0.904494i	−0.891893	−	0.452247i	$-0.850622\pi$
$277$		−	15.0538i		−	0.904494i	0.891893	−	0.452247i	$-0.149378\pi$
$278$	20.5313	+	20.5313i	1.23138	+	1.23138i
$279$	−2.73212	+	12.2096i	−0.163568	+	0.730969i
$280$	−0.101302	−	0.101302i	−0.00605393	−	0.00605393i
$281$	2.43286	−	2.43286i	0.145132	−	0.145132i	−0.630807	−	0.775939i	$-0.717276\pi$
$281$	2.43286	−	2.43286i	0.145132	−	0.145132i	0.775939	+	0.630807i	$0.217276\pi$
$282$	35.3751	−	10.2730i	2.10656	−	0.611748i
$283$		−	1.92828i		−	0.114624i	−0.998356	−	0.0573121i	$-0.981747\pi$
$283$		−	1.92828i		−	0.114624i	0.998356	−	0.0573121i	$-0.0182530\pi$
$284$	−5.98510	+	5.98510i	−0.355150	+	0.355150i
$285$	−2.17079	+	0.630403i	−0.128587	+	0.0373419i
$286$	−5.61379	−	1.87689i	−0.331950	−	0.110983i
$287$		−	1.40625i		−	0.0830082i
$288$	−11.0421	−	2.47086i	−0.650660	−	0.145597i
$289$	21.4486			1.26168
$290$	−3.05990			−0.179684
$291$	−3.64778	+	6.63349i	−0.213837	+	0.388862i
$292$	−4.98806	+	4.98806i	−0.291904	+	0.291904i
$293$	−18.4446	+	18.4446i	−1.07755	+	1.07755i	−0.0808171	+	0.996729i	$0.525753\pi$
$293$	−18.4446	+	18.4446i	−1.07755	+	1.07755i	−0.996729	+	0.0808171i	$0.974247\pi$
$294$	9.47671	−	17.2334i	0.552693	−	1.00507i
$295$	−1.36059			−0.0792168
$296$	21.7226			1.26260
$297$	0.324478	+	5.18601i	0.0188281	+	0.300923i
$298$		−	6.24259i		−	0.361623i
$299$	7.12559	+	2.38234i	0.412083	+	0.137774i
$300$	−5.71963	+	1.66099i	−0.330223	+	0.0958974i
$301$	−0.946271	+	0.946271i	−0.0545422	+	0.0545422i
$302$		−	2.74964i		−	0.158224i
$303$	−15.7710	+	4.57994i	−0.906023	+	0.263111i
$304$	19.5648	−	19.5648i	1.12212	−	1.12212i
$305$	−0.222799	−	0.222799i	−0.0127574	−	0.0127574i
$306$	29.8020	+	6.66874i	1.70367	+	0.381227i
$307$	1.54827	+	1.54827i	0.0883644	+	0.0883644i	0.749907	−	0.661543i	$-0.230098\pi$
$307$	1.54827	+	1.54827i	0.0883644	+	0.0883644i	−0.661543	+	0.749907i	$0.730098\pi$
$308$			0.200868i			0.0114455i
$309$	−6.99015	−	24.0706i	−0.397656	−	1.36933i
$310$	1.12057	+	1.12057i	0.0636442	+	0.0636442i
$311$	16.3060			0.924626			0.462313	−	0.886717i	$-0.347020\pi$
$311$	16.3060			0.924626			0.462313	+	0.886717i	$0.347020\pi$
$312$	9.83029	−	9.07329i	0.556531	−	0.513674i
$313$	6.24591			0.353040			0.176520	−	0.984297i	$-0.443516\pi$
$313$	6.24591			0.353040			0.176520	+	0.984297i	$0.443516\pi$
$314$	14.2567	+	14.2567i	0.804553	+	0.804553i
$315$	0.107467	+	0.169427i	0.00605507	+	0.00954613i
$316$		−	6.95791i		−	0.391413i
$317$	−4.35590	−	4.35590i	−0.244651	−	0.244651i	0.574120	−	0.818771i	$-0.305344\pi$
$317$	−4.35590	−	4.35590i	−0.244651	−	0.244651i	−0.818771	+	0.574120i	$0.805344\pi$
$318$	−0.615733	+	1.11971i	−0.0345286	+	0.0627902i
$319$	−5.69413	−	5.69413i	−0.318810	−	0.318810i
$320$	0.592820	−	0.592820i	0.0331396	−	0.0331396i
$321$	−3.97179	−	13.6769i	−0.221684	−	0.763369i
$322$		−	0.988478i		−	0.0550857i
$323$	−24.7225	+	24.7225i	−1.37560	+	1.37560i
$324$	5.65993	+	2.66654i	0.314440	+	0.148141i
$325$	5.65505	−	16.9143i	0.313686	−	0.938236i
$326$		−	0.458368i		−	0.0253867i
$327$	−4.78296	+	8.69779i	−0.264498	+	0.480989i
$328$	10.4254			0.575645
$329$	3.74317			0.206368
$330$	0.576706	+	0.317133i	0.0317466	+	0.0174576i
$331$	12.0969	−	12.0969i	0.664905	−	0.664905i	−0.291627	−	0.956532i	$-0.594197\pi$
$331$	12.0969	−	12.0969i	0.664905	−	0.664905i	0.956532	+	0.291627i	$0.0941967\pi$
$332$	1.86709	−	1.86709i	0.102470	−	0.102470i
$333$	−29.6879	−	6.64321i	−1.62689	−	0.364046i
$334$	7.99253			0.437332
$335$	3.48987			0.190672
$336$	−2.15193	−	1.18336i	−0.117397	−	0.0645573i
$337$			8.28746i			0.451447i	0.974191	+	0.225723i	$0.0724745\pi$
$337$			8.28746i			0.451447i	−0.974191	+	0.225723i	$0.927525\pi$
$338$	−2.98013	−	21.1330i	−0.162098	−	1.14948i
$339$	5.52526	+	19.0263i	0.300091	+	1.03336i
$340$	0.705494	−	0.705494i	0.0382608	−	0.0382608i
$341$			4.17051i			0.225846i
$342$	−23.4508	+	14.8748i	−1.26807	+	0.804334i
$343$	2.84335	−	2.84335i	0.153526	−	0.153526i
$344$	−7.01529	−	7.01529i	−0.378239	−	0.378239i
$345$	−0.732014	−	0.402538i	−0.0394103	−	0.0216719i
$346$	21.6713	+	21.6713i	1.16505	+	1.16505i
$347$		−	3.05835i		−	0.164181i	−0.996625	−	0.0820904i	$-0.973840\pi$
$347$		−	3.05835i		−	0.164181i	0.996625	−	0.0820904i	$-0.0261596\pi$
$348$	−9.31148	+	2.70407i	−0.499148	+	0.144953i
$349$	1.67681	+	1.67681i	0.0897578	+	0.0897578i	0.750560	−	0.660802i	$-0.229784\pi$
$349$	1.67681	+	1.67681i	0.0897578	+	0.0897578i	−0.660802	+	0.750560i	$0.729784\pi$
$350$	−2.34639			−0.125420
$351$	−16.2097	+	9.39399i	−0.865207	+	0.501414i
$352$	−3.77171			−0.201033
$353$	13.7952	+	13.7952i	0.734245	+	0.734245i	0.971458	−	0.237213i	$-0.0762339\pi$
$353$	13.7952	+	13.7952i	0.734245	+	0.734245i	−0.237213	+	0.971458i	$0.576234\pi$
$354$	−16.0520	+	4.66154i	−0.853155	+	0.247758i
$355$			2.81813i			0.149571i
$356$	8.54706	+	8.54706i	0.452993	+	0.452993i
$357$	2.71922	+	1.49531i	0.143916	+	0.0791403i
$358$	0.327920	+	0.327920i	0.0173311	+	0.0173311i
$359$	2.48807	−	2.48807i	0.131315	−	0.131315i	−0.638394	−	0.769710i	$-0.720401\pi$
$359$	2.48807	−	2.48807i	0.131315	−	0.131315i	0.769710	+	0.638394i	$0.220401\pi$
$360$	−1.25607	+	0.796717i	−0.0662004	+	0.0419907i
$361$		−	12.7933i		−	0.673332i
$362$	18.5342	−	18.5342i	0.974136	−	0.974136i
$363$	0.483035	+	1.66333i	0.0253528	+	0.0873023i
$364$	−0.648073	+	0.323307i	−0.0339683	+	0.0169459i
$365$			2.34867i			0.122935i
$366$	−3.39187	−	1.86520i	−0.177296	−	0.0974957i
$367$	27.4576			1.43328			0.716638	−	0.697445i	$-0.245680\pi$
$367$	27.4576			1.43328			0.716638	+	0.697445i	$0.245680\pi$
$368$	10.2254			0.533038
$369$	−14.2482	−	3.18829i	−0.741729	−	0.165975i
$370$	−2.72470	+	2.72470i	−0.141650	+	0.141650i
$371$	−0.0918168	+	0.0918168i	−0.00476689	+	0.00476689i
$372$	4.40023	+	2.41971i	0.228141	+	0.125456i
$373$	−7.16523			−0.371001			−0.185501	−	0.982644i	$-0.559391\pi$
$373$	−7.16523			−0.371001			−0.185501	+	0.982644i	$0.559391\pi$
$374$	10.1797			0.526378
$375$	−1.92139	+	3.49404i	−0.0992201	+	0.180432i
$376$			27.7504i			1.43112i
$377$	9.20634	−	27.5362i	0.474151	−	1.41819i
$378$	1.84835	+	1.63067i	0.0950688	+	0.0838728i
$379$	−11.7132	+	11.7132i	−0.601665	+	0.601665i	−0.940754	−	0.339089i	$-0.889881\pi$
$379$	−11.7132	+	11.7132i	−0.601665	+	0.601665i	0.339089	+	0.940754i	$0.389881\pi$
$380$			0.907270i			0.0465419i
$381$	−1.99999	−	6.88697i	−0.102463	−	0.352830i
$382$	−16.9434	+	16.9434i	−0.866902	+	0.866902i
$383$	16.2587	+	16.2587i	0.830779	+	0.830779i	0.987623	−	0.156845i	$-0.0501322\pi$
$383$	16.2587	+	16.2587i	0.830779	+	0.830779i	−0.156845	+	0.987623i	$0.550132\pi$
$384$	11.2586	−	20.4738i	0.574540	−	1.04480i
$385$	0.0472902	+	0.0472902i	0.00241013	+	0.00241013i
$386$			33.3998i			1.70000i
$387$	7.44224	+	11.7331i	0.378310	+	0.596425i
$388$	2.14850	+	2.14850i	0.109073	+	0.109073i
$389$	−10.8337			−0.549290			−0.274645	−	0.961546i	$-0.588560\pi$
$389$	−10.8337			−0.549290			−0.274645	+	0.961546i	$0.588560\pi$
$390$	−0.0949515	+	2.37110i	−0.00480806	+	0.120065i
$391$	−12.9211			−0.653446
$392$	10.4765	+	10.4765i	0.529144	+	0.529144i
$393$	1.96209	+	6.75646i	0.0989743	+	0.340818i
$394$		−	24.5815i		−	1.23840i
$395$	−1.63809	−	1.63809i	−0.0824214	−	0.0824214i
$396$	2.03521	+	0.455415i	0.102273	+	0.0228855i
$397$	−1.84234	−	1.84234i	−0.0924643	−	0.0924643i	0.659362	−	0.751826i	$-0.270827\pi$
$397$	−1.84234	−	1.84234i	−0.0924643	−	0.0924643i	−0.751826	+	0.659362i	$0.770827\pi$
$398$	−5.05742	+	5.05742i	−0.253506	+	0.253506i
$399$	−2.70995	+	0.786976i	−0.135667	+	0.0393981i
$400$		−	24.2725i		−	1.21363i
$401$	13.3204	−	13.3204i	0.665191	−	0.665191i	−0.291408	−	0.956599i	$-0.594124\pi$
$401$	13.3204	−	13.3204i	0.665191	−	0.665191i	0.956599	+	0.291408i	$0.0941237\pi$
$402$	41.1728	−	11.9567i	2.05351	−	0.596345i
$403$	−13.4555	+	6.71262i	−0.670269	+	0.334379i
$404$			6.59140i			0.327935i
$405$	1.96029	−	0.704729i	0.0974077	−	0.0350183i
$406$	−3.81989			−0.189578
$407$	−10.1407			−0.502656
$408$	−11.0857	+	20.1592i	−0.548822	+	0.998031i
$409$	3.04122	−	3.04122i	0.150378	−	0.150378i	−0.627909	−	0.778287i	$-0.716089\pi$
$409$	3.04122	−	3.04122i	0.150378	−	0.150378i	0.778287	+	0.627909i	$0.216089\pi$
$410$	−1.30767	+	1.30767i	−0.0645811	+	0.0645811i
$411$	−1.34507	+	2.44601i	−0.0663475	+	0.120653i
$412$	−10.0602			−0.495628
$413$	−1.69852			−0.0835789
$414$	−10.0153	−	2.24111i	−0.492225	−	0.110144i
$415$		−	0.879134i		−	0.0431550i
$416$	−6.07073	−	12.1689i	−0.297642	−	0.596629i
$417$	29.4182	−	8.54311i	1.44062	−	0.418358i
$418$	−6.54556	+	6.54556i	−0.320154	+	0.320154i
$419$			15.3377i			0.749294i	0.927168	+	0.374647i	$0.122236\pi$
$419$			15.3377i			0.749294i	−0.927168	+	0.374647i	$0.877764\pi$
$420$	0.0773326	−	0.0224575i	0.00377344	−	0.00109582i
$421$	−14.0602	+	14.0602i	−0.685251	+	0.685251i	−0.961179	−	0.275927i	$-0.911015\pi$
$421$	−14.0602	+	14.0602i	−0.685251	+	0.685251i	0.275927	+	0.961179i	$0.411015\pi$
$422$	33.1430	+	33.1430i	1.61337	+	1.61337i
$423$	8.48662	−	37.9259i	0.412634	−	1.84402i
$424$	−0.680694	−	0.680694i	−0.0330574	−	0.0330574i
$425$			30.6713i			1.48777i
$426$	9.65522	+	33.2478i	0.467797	+	1.61086i
$427$	−0.278135	−	0.278135i	−0.0134599	−	0.0134599i
$428$	−5.71617			−0.276301
$429$	−4.58904	+	4.23565i	−0.221561	+	0.204499i
$430$	1.75987			0.0848686
$431$	2.98446	+	2.98446i	0.143756	+	0.143756i	0.775322	−	0.631566i	$-0.217587\pi$
$431$	2.98446	+	2.98446i	0.143756	+	0.143756i	−0.631566	+	0.775322i	$0.717587\pi$
$432$	−16.8687	+	19.1205i	−0.811596	+	0.919934i
$433$			14.5556i			0.699498i	0.936843	+	0.349749i	$0.113733\pi$
$433$			14.5556i			0.699498i	−0.936843	+	0.349749i	$0.886267\pi$
$434$	1.39889	+	1.39889i	0.0671488	+	0.0671488i
$435$	−1.55557	+	2.82881i	−0.0745841	+	0.135631i
$436$	2.81710	+	2.81710i	0.134914	+	0.134914i
$437$	8.30828	−	8.30828i	0.397439	−	0.397439i
$438$	8.04678	+	27.7091i	0.384490	+	1.32399i
$439$			13.0859i			0.624554i	0.949991	+	0.312277i	$0.101092\pi$
$439$			13.0859i			0.624554i	−0.949991	+	0.312277i	$0.898908\pi$
$440$	−0.350591	+	0.350591i	−0.0167138	+	0.0167138i
$441$	−11.1141	−	17.5220i	−0.529244	−	0.834380i
$442$	16.3846	+	32.8432i	0.779337	+	1.56219i
$443$			30.5892i			1.45334i	0.686988	+	0.726669i	$0.258932\pi$
$443$			30.5892i			1.45334i	−0.686988	+	0.726669i	$0.741068\pi$
$444$	−5.88358	+	10.6993i	−0.279222	+	0.507765i
$445$	4.02445			0.190777
$446$	−8.05579			−0.381453
$447$	−5.77112	−	3.17357i	−0.272965	−	0.150104i
$448$	0.740058	−	0.740058i	0.0349645	−	0.0349645i
$449$	8.36190	−	8.36190i	0.394623	−	0.394623i	−0.481709	−	0.876331i	$-0.659984\pi$
$449$	8.36190	−	8.36190i	0.394623	−	0.394623i	0.876331	+	0.481709i	$0.159984\pi$
$450$	−5.31980	+	23.7737i	−0.250778	+	1.12070i
$451$	−4.86684			−0.229170
$452$	7.95190			0.374026
$453$	−2.54197	−	1.39784i	−0.119432	−	0.0656764i
$454$		−	4.79859i		−	0.225209i
$455$	−0.0764594	+	0.228691i	−0.00358447	+	0.0107212i
$456$	−5.83433	−	20.0905i	−0.273218	−	0.940826i
$457$	−23.2124	+	23.2124i	−1.08583	+	1.08583i	−0.0898786	+	0.995953i	$0.528648\pi$
$457$	−23.2124	+	23.2124i	−1.08583	+	1.08583i	−0.995953	+	0.0898786i	$0.971352\pi$
$458$			1.03515i			0.0483694i
$459$	21.3156	−	24.1610i	0.994929	−	1.12774i
$460$	−0.237089	+	0.237089i	−0.0110543	+	0.0110543i
$461$	22.1872	+	22.1872i	1.03336	+	1.03336i	0.999424	+	0.0339367i	$0.0108045\pi$
$461$	22.1872	+	22.1872i	1.03336	+	1.03336i	0.0339367	+	0.999424i	$0.489196\pi$
$462$	0.719943	+	0.395900i	0.0334948	+	0.0184189i
$463$	−10.5780	−	10.5780i	−0.491603	−	0.491603i	0.417208	−	0.908811i	$-0.363009\pi$
$463$	−10.5780	−	10.5780i	−0.491603	−	0.491603i	−0.908811	+	0.417208i	$0.863009\pi$
$464$		−	39.5154i		−	1.83445i
$465$	1.60561	−	0.466272i	0.0744584	−	0.0216229i
$466$	−0.564764	−	0.564764i	−0.0261622	−	0.0261622i
$467$	−30.4896			−1.41089			−0.705446	−	0.708764i	$-0.749253\pi$
$467$	−30.4896			−1.41089			−0.705446	+	0.708764i	$0.749253\pi$
$468$	1.80642	+	7.29931i	0.0835020	+	0.337411i
$469$	4.35665			0.201171
$470$	−3.48077	−	3.48077i	−0.160556	−	0.160556i
$471$	20.4277	−	5.93225i	0.941260	−	0.273344i
$472$		−	12.5922i		−	0.579603i
$473$	3.27492	+	3.27492i	0.150581	+	0.150581i
$474$	−24.9382	−	13.7136i	−1.14545	−	0.629888i
$475$	−19.7217	−	19.7217i	−0.904894	−	0.904894i
$476$	0.880718	−	0.880718i	0.0403676	−	0.0403676i
$477$	0.722121	+	1.13846i	0.0330637	+	0.0521265i
$478$		−	35.8084i		−	1.63784i
$479$	9.24556	−	9.24556i	0.422440	−	0.422440i	−0.463603	−	0.886043i	$-0.653444\pi$
$479$	9.24556	−	9.24556i	0.422440	−	0.422440i	0.886043	+	0.463603i	$0.153444\pi$
$480$	0.421686	+	1.45208i	0.0192472	+	0.0662779i
$481$	−16.3219	−	32.7175i	−0.744215	−	1.49179i
$482$		−	39.2869i		−	1.78947i
$483$	−0.913824	−	0.502516i	−0.0415804	−	0.0228653i
$484$	0.695179			0.0315991
$485$	1.01164			0.0459360
$486$	20.7127	−	15.0304i	0.939546	−	0.681794i
$487$	14.7518	−	14.7518i	0.668468	−	0.668468i	−0.288893	−	0.957361i	$-0.593287\pi$
$487$	14.7518	−	14.7518i	0.668468	−	0.668468i	0.957361	+	0.288893i	$0.0932872\pi$
$488$	2.06198	−	2.06198i	0.0933417	−	0.0933417i
$489$	−0.423750	−	0.233022i	−0.0191626	−	0.0105376i
$490$	−2.62816			−0.118728
$491$	−29.1667			−1.31628			−0.658138	−	0.752898i	$-0.728655\pi$
$491$	−29.1667			−1.31628			−0.658138	+	0.752898i	$0.728655\pi$
$492$	−2.82371	+	5.13491i	−0.127303	+	0.231500i
$493$			49.9324i			2.24884i
$494$	−31.6537	−	10.5829i	−1.42417	−	0.476149i
$495$	0.586364	−	0.371929i	0.0263551	−	0.0167170i
$496$	−14.4710	+	14.4710i	−0.649766	+	0.649766i
$497$			3.51807i			0.157807i
$498$	−3.01201	−	10.3719i	−0.134971	−	0.464774i
$499$	−6.17284	+	6.17284i	−0.276334	+	0.276334i	−0.831644	−	0.555310i	$-0.812600\pi$
$499$	−6.17284	+	6.17284i	−0.276334	+	0.276334i	0.555310	+	0.831644i	$0.312600\pi$
$500$	1.13167	+	1.13167i	0.0506099	+	0.0506099i
$501$	4.06319	−	7.38890i	0.181530	−	0.330112i
$502$	−26.4652	−	26.4652i	−1.18120	−	1.18120i
$503$		−	25.5179i		−	1.13778i	−0.822412	−	0.568892i	$-0.807372\pi$
$503$		−	25.5179i		−	1.13778i	0.822412	−	0.568892i	$-0.192628\pi$
$504$	−1.56803	+	0.994598i	−0.0698458	+	0.0443029i
$505$	1.55181	+	1.55181i	0.0690545	+	0.0690545i
$506$	−3.42099			−0.152082
$507$	−21.0520	−	7.98841i	−0.934951	−	0.354778i
$508$	−2.87836			−0.127707
$509$	−11.8530	−	11.8530i	−0.525374	−	0.525374i	0.393815	−	0.919190i	$-0.371155\pi$
$509$	−11.8530	−	11.8530i	−0.525374	−	0.525374i	−0.919190	+	0.393815i	$0.871155\pi$
$510$	−1.13811	−	3.91909i	−0.0503964	−	0.173540i
$511$			2.93200i			0.129704i
$512$	1.77841	+	1.77841i	0.0785955	+	0.0785955i
$513$	1.82959	+	29.2416i	0.0807782	+	1.29105i
$514$	17.7413	+	17.7413i	0.782536	+	0.782536i
$515$	−2.36845	+	2.36845i	−0.104366	+	0.104366i
$516$	5.35540	−	1.55522i	0.235758	−	0.0684647i
$517$		−	12.9546i		−	0.569744i
$518$	−3.40143	+	3.40143i	−0.149450	+	0.149450i
$519$	31.0516	−	9.01746i	1.36302	−	0.395822i
$520$	−1.69542	−	0.566841i	−0.0743493	−	0.0248576i
$521$			11.9397i			0.523090i	0.965191	+	0.261545i	$0.0842319\pi$
$521$			11.9397i			0.523090i	−0.965191	+	0.261545i	$0.915768\pi$
$522$	−8.66057	+	38.7033i	−0.379063	+	1.69400i
$523$	14.7603			0.645424			0.322712	−	0.946497i	$-0.395405\pi$
$523$	14.7603			0.645424			0.322712	+	0.946497i	$0.395405\pi$
$524$	2.82382			0.123359
$525$	−1.19284	+	2.16918i	−0.0520599	+	0.0946708i
$526$	−17.0539	+	17.0539i	−0.743585	+	0.743585i
$527$	18.2858	−	18.2858i	0.796542	−	0.796542i
$528$	−4.09544	+	7.44754i	−0.178231	+	0.324113i
$529$	−18.6577			−0.811206
$530$	0.170761			0.00741736
$531$	−3.85094	+	17.2095i	−0.167117	+	0.746829i
$532$			1.13261i			0.0491048i
$533$	−7.83339	−	15.7022i	−0.339302	−	0.680136i
$534$	47.4797	−	13.7882i	2.05465	−	0.596674i
$535$	−1.34575	+	1.34575i	−0.0581819	+	0.0581819i
$536$			32.2985i			1.39508i
$537$	0.469859	−	0.136448i	0.0202759	−	0.00588817i
$538$	14.5353	−	14.5353i	0.626661	−	0.626661i
$539$	−4.89071	−	4.89071i	−0.210658	−	0.210658i
$540$	−0.0522100	−	0.834453i	−0.00224676	−	0.0359091i
$541$	−17.8726	−	17.8726i	−0.768404	−	0.768404i	0.209422	−	0.977825i	$-0.432842\pi$
$541$	−17.8726	−	17.8726i	−0.768404	−	0.768404i	−0.977825	+	0.209422i	$0.932842\pi$
$542$		−	14.0390i		−	0.603027i
$543$	−7.71212	−	26.5567i	−0.330959	−	1.13966i
$544$	16.5373	+	16.5373i	0.709029	+	0.709029i
$545$	1.32645			0.0568190
$546$	−0.118535	+	2.96001i	−0.00507281	+	0.126677i
$547$	23.5162			1.00548			0.502740	−	0.864438i	$-0.332325\pi$
$547$	23.5162			1.00548			0.502740	+	0.864438i	$0.332325\pi$
$548$	0.792229	+	0.792229i	0.0338423	+	0.0338423i
$549$	−3.44867	+	2.18748i	−0.147186	+	0.0933593i
$550$			8.12055i			0.346261i
$551$	−32.1067	−	32.1067i	−1.36779	−	1.36779i
$552$	3.72546	−	6.77473i	0.158566	−	0.288352i
$553$	−2.04495	−	2.04495i	−0.0869600	−	0.0869600i
$554$	−17.4753	+	17.4753i	−0.742454	+	0.742454i
$555$	1.13375	+	3.90408i	0.0481251	+	0.165719i
$556$		−	12.2952i		−	0.521431i
$557$	−15.7555	+	15.7555i	−0.667582	+	0.667582i	−0.957156	−	0.289574i	$-0.906486\pi$
$557$	−15.7555	+	15.7555i	−0.667582	+	0.667582i	0.289574	+	0.957156i	$0.406486\pi$
$558$	17.3452	−	11.0020i	0.734280	−	0.465751i
$559$	−5.29493	+	15.8372i	−0.223952	+	0.669841i
$560$			0.328178i			0.0138681i
$561$	5.17507	−	9.41086i	0.218492	−	0.397327i
$562$	−5.64840			−0.238263
$563$	−16.3659			−0.689743			−0.344871	−	0.938650i	$-0.612077\pi$
$563$	−16.3659			−0.689743			−0.344871	+	0.938650i	$0.612077\pi$
$564$	−13.6682	−	7.51620i	−0.575534	−	0.316489i
$565$	1.87211	−	1.87211i	0.0787601	−	0.0787601i
$566$	−2.23846	+	2.23846i	−0.0940893	+	0.0940893i
$567$	2.44717	−	0.879762i	0.102771	−	0.0369465i
$568$	−26.0816			−1.09436
$569$	5.59157			0.234411			0.117205	−	0.993108i	$-0.462606\pi$
$569$	5.59157			0.234411			0.117205	+	0.993108i	$0.462606\pi$
$570$	3.25179	+	1.78817i	0.136203	+	0.0748984i
$571$			30.7616i			1.28733i	0.765307	+	0.643666i	$0.222587\pi$
$571$			30.7616i			1.28733i	−0.765307	+	0.643666i	$0.777413\pi$
$572$	1.11892	+	2.24290i	0.0467845	+	0.0937802i
$573$	7.05020	+	24.2774i	0.294526	+	1.01420i
$574$	−1.63245	+	1.63245i	−0.0681373	+	0.0681373i
$575$		−	10.3074i		−	0.429849i
$576$	−5.82042	−	9.17618i	−0.242517	−	0.382341i
$577$	19.0918	−	19.0918i	0.794801	−	0.794801i	−0.187469	−	0.982270i	$-0.560028\pi$
$577$	19.0918	−	19.0918i	0.794801	−	0.794801i	0.982270	+	0.187469i	$0.0600285\pi$
$578$	−24.8987	−	24.8987i	−1.03565	−	1.03565i
$579$	30.8773	+	16.9796i	1.28322	+	0.705647i
$580$	0.916212	+	0.916212i	0.0380436	+	0.0380436i
$581$		−	1.09748i		−	0.0455313i
$582$	11.9351	−	3.46597i	0.494725	−	0.143669i
$583$	0.317766	+	0.317766i	0.0131605	+	0.0131605i
$584$	−21.7367			−0.899472
$585$	2.14375	+	1.29318i	0.0886333	+	0.0534666i
$586$	42.8231			1.76901
$587$	−26.2774	−	26.2774i	−1.08458	−	1.08458i	−0.996075	−	0.0885077i	$-0.971790\pi$
$587$	−26.2774	−	26.2774i	−1.08458	−	1.08458i	−0.0885077	−	0.996075i	$-0.528210\pi$
$588$	−7.99766	+	2.32254i	−0.329818	+	0.0957798i
$589$			23.5157i			0.968946i
$590$	1.57945	+	1.57945i	0.0650251	+	0.0650251i
$591$	−22.7250	−	12.4966i	−0.934780	−	0.514040i
$592$	−35.1865	−	35.1865i	−1.44616	−	1.44616i
$593$	19.7952	−	19.7952i	0.812891	−	0.812891i	−0.172176	−	0.985066i	$-0.555080\pi$
$593$	19.7952	−	19.7952i	0.812891	−	0.812891i	0.985066	+	0.172176i	$0.0550797\pi$
$594$	5.64355	−	6.39689i	0.231558	−	0.262468i
$595$		−	0.414693i		−	0.0170008i
$596$	−1.86919	+	1.86919i	−0.0765649	+	0.0765649i
$597$	2.10440	+	7.24652i	0.0861276	+	0.296580i
$598$	−5.50624	−	11.0373i	−0.225167	−	0.451350i
$599$			14.1530i			0.578275i	0.957288	+	0.289137i	$0.0933685\pi$
$599$			14.1530i			0.578275i	−0.957288	+	0.289137i	$0.906632\pi$
$600$	−16.0815	−	8.84327i	−0.656523	−	0.361025i
$601$	22.4793			0.916950			0.458475	−	0.888707i	$-0.348396\pi$
$601$	22.4793			0.916950			0.458475	+	0.888707i	$0.348396\pi$
$602$	2.19697			0.0895419
$603$	9.87752	−	44.1417i	0.402244	−	1.79759i
$604$	−0.823311	+	0.823311i	−0.0335000	+	0.0335000i
$605$	0.163665	−	0.163665i	0.00665394	−	0.00665394i
$606$	23.6246	+	12.9913i	0.959683	+	0.527734i
$607$	31.8360			1.29218			0.646091	−	0.763261i	$-0.276403\pi$
$607$	31.8360			1.29218			0.646091	+	0.763261i	$0.276403\pi$
$608$	−21.2670			−0.862491
$609$	−1.94193	+	3.53140i	−0.0786911	+	0.143099i
$610$			0.517275i			0.0209438i
$611$	41.7962	−	20.8510i	1.69089	−	0.843542i
$612$	−6.92668	−	10.9203i	−0.279994	−	0.441425i
$613$	9.97781	−	9.97781i	0.403000	−	0.403000i	−0.476289	−	0.879289i	$-0.658018\pi$
$613$	9.97781	−	9.97781i	0.403000	−	0.403000i	0.879289	+	0.476289i	$0.158018\pi$
$614$		−	3.59464i		−	0.145068i
$615$	0.544123	+	1.87369i	0.0219412	+	0.0755545i
$616$	−0.437668	+	0.437668i	−0.0176341	+	0.0176341i
$617$	−6.31884	−	6.31884i	−0.254387	−	0.254387i	0.568380	−	0.822767i	$-0.307571\pi$
$617$	−6.31884	−	6.31884i	−0.254387	−	0.254387i	−0.822767	+	0.568380i	$0.807571\pi$
$618$	−19.8280	+	36.0571i	−0.797598	+	1.45043i
$619$	−0.282122	−	0.282122i	−0.0113394	−	0.0113394i	0.701414	−	0.712754i	$-0.252552\pi$
$619$	−0.282122	−	0.282122i	−0.0113394	−	0.0113394i	−0.712754	+	0.701414i	$0.752552\pi$
$620$		−	0.671054i		−	0.0269502i
$621$	−7.16336	+	8.11958i	−0.287456	+	0.325827i
$622$	−18.9289	−	18.9289i	−0.758980	−	0.758980i
$623$	5.02400			0.201282
$624$	−30.6202	−	1.22620i	−1.22579	−	0.0490871i
$625$	−24.1993			−0.967971
$626$	−7.25061	−	7.25061i	−0.289793	−	0.289793i
$627$	2.72362	+	9.37880i	0.108771	+	0.374553i
$628$		−	8.53764i		−	0.340689i
$629$	44.4624	+	44.4624i	1.77283	+	1.77283i
$630$	0.0719268	−	0.321434i	0.00286563	−	0.0128062i
$631$	−10.8046	−	10.8046i	−0.430123	−	0.430123i	0.458547	−	0.888670i	$-0.348370\pi$
$631$	−10.8046	−	10.8046i	−0.430123	−	0.430123i	−0.888670	+	0.458547i	$0.848370\pi$
$632$	15.1604	−	15.1604i	0.603050	−	0.603050i
$633$	47.4889	−	13.7909i	1.88751	−	0.548137i
$634$			10.1131i			0.401644i
$635$	−0.677650	+	0.677650i	−0.0268917	+	0.0268917i
$636$	0.519635	−	0.150903i	0.0206049	−	0.00598369i
$637$	7.90736	−	23.6510i	0.313301	−	0.937086i
$638$			13.2201i			0.523391i
$639$	35.6452	+	7.97626i	1.41010	+	0.315536i
$640$	−3.12234			−0.123421
$641$	−30.4932			−1.20441			−0.602204	−	0.798343i	$-0.705710\pi$
$641$	−30.4932			−1.20441			−0.602204	+	0.798343i	$0.705710\pi$
$642$	−11.2662	+	20.4876i	−0.444642	+	0.808581i
$643$	18.2818	−	18.2818i	0.720962	−	0.720962i	−0.247839	−	0.968801i	$-0.579720\pi$
$643$	18.2818	−	18.2818i	0.720962	−	0.720962i	0.968801	+	0.247839i	$0.0797204\pi$
$644$	−0.295975	+	0.295975i	−0.0116631	+	0.0116631i
$645$	0.894672	−	1.62696i	0.0352277	−	0.0640614i
$646$	57.3987			2.25832
$647$	−12.3578			−0.485834			−0.242917	−	0.970047i	$-0.578104\pi$
$647$	−12.3578			−0.485834			−0.242917	+	0.970047i	$0.578104\pi$
$648$	6.52221	+	18.1424i	0.256217	+	0.712699i
$649$			5.87837i			0.230746i
$650$	−26.1998	+	13.0704i	−1.02764	+	0.512662i
$651$	2.00439	−	0.582080i	0.0785584	−	0.0228135i
$652$	−0.137247	+	0.137247i	−0.00537500	+	0.00537500i
$653$		−	47.5486i		−	1.86072i	−0.366647	−	0.930360i	$-0.619494\pi$
$653$		−	47.5486i		−	1.86072i	0.366647	−	0.930360i	$-0.380506\pi$
$654$	15.6492	−	4.54457i	0.611933	−	0.177707i
$655$	0.664808	−	0.664808i	0.0259762	−	0.0259762i
$656$	−16.8871	−	16.8871i	−0.659331	−	0.659331i
$657$	29.7072	+	6.64752i	1.15899	+	0.259344i
$658$	−4.34529	−	4.34529i	−0.169397	−	0.169397i
$659$			10.2132i			0.397848i	0.980015	+	0.198924i	$0.0637447\pi$
$659$			10.2132i			0.397848i	−0.980015	+	0.198924i	$0.936255\pi$
$660$	−0.0777226	−	0.267638i	−0.00302535	−	0.0104178i
$661$	−2.24351	−	2.24351i	−0.0872622	−	0.0872622i	0.662128	−	0.749391i	$-0.269653\pi$
$661$	−2.24351	−	2.24351i	−0.0872622	−	0.0872622i	−0.749391	+	0.662128i	$0.769653\pi$
$662$	−28.0855			−1.09157
$663$	38.6923	+	1.54945i	1.50268	+	0.0601755i
$664$	8.13632			0.315751
$665$	0.266649	+	0.266649i	0.0103402	+	0.0103402i
$666$	26.7516	+	42.1753i	1.03660	+	1.63426i
$667$		−	16.7803i		−	0.649737i
$668$	−2.39316	−	2.39316i	−0.0925943	−	0.0925943i
$669$	−4.09535	+	7.44738i	−0.158335	+	0.287932i
$670$	−4.05124	−	4.05124i	−0.156513	−	0.156513i
$671$	−0.962589	+	0.962589i	−0.0371603	+	0.0371603i
$672$	0.526420	+	1.81273i	0.0203071	+	0.0699275i
$673$			15.2857i			0.589219i	0.955618	+	0.294610i	$0.0951896\pi$
$673$			15.2857i			0.589219i	−0.955618	+	0.294610i	$0.904810\pi$
$674$	9.62055	−	9.62055i	0.370570	−	0.370570i
$675$	19.2738	+	17.0040i	0.741848	+	0.654483i
$676$	−5.43543	+	7.22008i	−0.209055	+	0.277695i
$677$			6.11459i			0.235003i	0.993073	+	0.117501i	$0.0374885\pi$
$677$			6.11459i			0.235003i	−0.993073	+	0.117501i	$0.962512\pi$
$678$	15.6727	−	28.5008i	0.601907	−	1.09457i
$679$	1.26290			0.0484655
$680$	3.07437			0.117897
$681$	−4.43618	−	2.43947i	−0.169995	−	0.0934808i
$682$	4.84137	−	4.84137i	0.185386	−	0.185386i
$683$	0.524708	−	0.524708i	0.0200774	−	0.0200774i	−0.696997	−	0.717074i	$-0.745481\pi$
$683$	0.524708	−	0.524708i	0.0200774	−	0.0200774i	0.717074	+	0.696997i	$0.245481\pi$
$684$	11.4756	+	2.56788i	0.438782	+	0.0981854i
$685$	0.373027			0.0142526
$686$	−6.60145			−0.252044
$687$	0.956970	+	0.526242i	0.0365107	+	0.0200774i
$688$			22.7269i			0.866453i
$689$	−0.513767	+	1.53668i	−0.0195730	+	0.0585430i
$690$	0.382475	+	1.31705i	0.0145606	+	0.0501393i
$691$	−11.9521	+	11.9521i	−0.454679	+	0.454679i	−0.896904	−	0.442225i	$-0.854189\pi$
$691$	−11.9521	+	11.9521i	−0.454679	+	0.454679i	0.442225	+	0.896904i	$0.354189\pi$
$692$		−	12.9778i		−	0.493343i
$693$	0.731999	−	0.464305i	0.0278064	−	0.0176375i
$694$	−3.55031	+	3.55031i	−0.134768	+	0.134768i
$695$	−2.89464	−	2.89464i	−0.109800	−	0.109800i
$696$	−26.1804	−	14.3967i	−0.992366	−	0.545706i
$697$	21.3389	+	21.3389i	0.808268	+	0.808268i
$698$		−	3.89308i		−	0.147355i
$699$	−0.809221	+	0.234999i	−0.0306075	+	0.00888849i
$700$	0.702568	+	0.702568i	0.0265546	+	0.0265546i
$701$	43.3892			1.63879			0.819394	−	0.573231i	$-0.194310\pi$
$701$	43.3892			1.63879			0.819394	+	0.573231i	$0.194310\pi$
$702$	29.7222	+	7.91201i	1.12179	+	0.298620i
$703$	−57.1789			−2.15654
$704$	−2.56124	−	2.56124i	−0.0965306	−	0.0965306i
$705$	−4.98742	+	1.44836i	−0.187837	+	0.0545482i
$706$		−	32.0285i		−	1.20541i
$707$	1.93723	+	1.93723i	0.0728570	+	0.0728570i
$708$	6.20216	+	3.41060i	0.233091	+	0.128178i
$709$	−11.9887	−	11.9887i	−0.450246	−	0.450246i	0.445190	−	0.895436i	$-0.353136\pi$
$709$	−11.9887	−	11.9887i	−0.450246	−	0.450246i	−0.895436	+	0.445190i	$0.853136\pi$
$710$	3.27145	−	3.27145i	0.122775	−	0.122775i
$711$	−25.3558	+	16.0831i	−0.950918	+	0.603164i
$712$			37.2460i			1.39585i
$713$	−6.14515	+	6.14515i	−0.230138	+	0.230138i
$714$	−1.42078	−	4.89247i	−0.0531715	−	0.183096i
$715$	0.791469	+	0.264616i	0.0295993	+	0.00989608i
$716$		−	0.196375i		−	0.00733887i
$717$	−33.1040	−	18.2041i	−1.23629	−	0.679843i
$718$	−5.77659			−0.215581
$719$	12.1502			0.453124			0.226562	−	0.973997i	$-0.427251\pi$
$719$	12.1502			0.453124			0.226562	+	0.973997i	$0.427251\pi$
$720$	3.32512	+	0.744056i	0.123920	+	0.0277293i
$721$	−2.95670	+	2.95670i	−0.110113	+	0.110113i
$722$	−14.8512	+	14.8512i	−0.552705	+	0.552705i
$723$	−36.3198	−	19.9724i	−1.35075	−	0.742783i
$724$	−11.0992			−0.412499
$725$	−39.8322			−1.47933
$726$	1.37016	−	2.49163i	0.0508513	−	0.0924730i
$727$			1.38534i			0.0513796i	0.999670	+	0.0256898i	$0.00817821\pi$
$727$			1.38534i			0.0513796i	−0.999670	+	0.0256898i	$0.991822\pi$
$728$	−2.11652	−	0.707627i	−0.0784433	−	0.0262264i
$729$	−3.36549	−	26.7894i	−0.124648	−	0.992201i
$730$	2.72647	−	2.72647i	0.100911	−	0.100911i
$731$		−	28.7181i		−	1.06218i
$732$	0.457121	+	1.57410i	0.0168957	+	0.0581803i
$733$	−2.93347	+	2.93347i	−0.108350	+	0.108350i	−0.759203	−	0.650853i	$-0.774411\pi$
$733$	−2.93347	+	2.93347i	−0.108350	+	0.108350i	0.650853	+	0.759203i	$0.274411\pi$
$734$	−31.8744	−	31.8744i	−1.17651	−	1.17651i
$735$	−1.33609	+	2.42967i	−0.0492824	+	0.0896199i
$736$	−5.55753	−	5.55753i	−0.204853	−	0.204853i
$737$		−	15.0778i		−	0.555398i
$738$	12.8389	+	20.2412i	0.472608	+	0.745090i
$739$	32.3576	+	32.3576i	1.19029	+	1.19029i	0.976985	+	0.213307i	$0.0684234\pi$
$739$	32.3576	+	32.3576i	1.19029	+	1.19029i	0.213307	+	0.976985i	$0.431577\pi$
$740$	1.63169			0.0599820
$741$	−25.8755	+	23.8829i	−0.950562	+	0.877362i
$742$	0.213172			0.00782580
$743$	−12.4922	−	12.4922i	−0.458295	−	0.458295i	0.439801	−	0.898095i	$-0.355049\pi$
$743$	−12.4922	−	12.4922i	−0.458295	−	0.458295i	−0.898095	+	0.439801i	$0.855049\pi$
$744$	4.31532	+	14.8598i	0.158207	+	0.544787i
$745$			0.880121i			0.0322451i
$746$	8.31781	+	8.31781i	0.304537	+	0.304537i
$747$	−11.1198	−	2.48825i	−0.406851	−	0.0910403i
$748$	−3.04805	−	3.04805i	−0.111448	−	0.111448i
$749$	−1.67999	+	1.67999i	−0.0613857	+	0.0613857i
$750$	6.28654	−	1.82562i	0.229552	−	0.0666624i
$751$			6.79402i			0.247917i	0.992287	+	0.123959i	$0.0395590\pi$
$751$			6.79402i			0.247917i	−0.992287	+	0.123959i	$0.960441\pi$
$752$	44.9504	−	44.9504i	1.63917	−	1.63917i
$753$	−37.9207	+	11.0122i	−1.38191	+	0.401308i
$754$	−42.6529	+	21.2784i	−1.55333	+	0.774914i
$755$			0.387662i			0.0141085i
$756$	−0.0651774	−	1.04171i	−0.00237048	−	0.0378865i
$757$	−17.1226			−0.622331			−0.311166	−	0.950356i	$-0.600719\pi$
$757$	−17.1226			−0.622331			−0.311166	+	0.950356i	$0.600719\pi$
$758$	27.1947			0.987754
$759$	−1.73914	+	3.16262i	−0.0631268	+	0.114796i
$760$	−1.97683	+	1.97683i	−0.0717071	+	0.0717071i
$761$	−15.2097	+	15.2097i	−0.551351	+	0.551351i	−0.926831	−	0.375480i	$-0.877478\pi$
$761$	−15.2097	+	15.2097i	−0.551351	+	0.551351i	0.375480	+	0.926831i	$0.377478\pi$
$762$	−5.67309	+	10.3165i	−0.205514	+	0.373727i
$763$	1.65590			0.0599477
$764$	10.1466			0.367090
$765$	−4.20168	−	0.940203i	−0.151912	−	0.0339931i
$766$		−	37.7480i		−	1.36389i
$767$	−18.9657	+	9.46149i	−0.684812	+	0.341634i
$768$	−24.7871	+	7.19823i	−0.894429	+	0.259744i
$769$	6.02723	−	6.02723i	0.217347	−	0.217347i	−0.590032	−	0.807380i	$-0.700885\pi$
$769$	6.02723	−	6.02723i	0.217347	−	0.217347i	0.807380	+	0.590032i	$0.200885\pi$
$770$		−	0.109794i		−	0.00395672i
$771$	25.4206	−	7.38220i	0.915501	−	0.265863i
$772$	10.0007	−	10.0007i	0.359934	−	0.359934i
$773$	28.5781	+	28.5781i	1.02788	+	1.02788i	0.999600	+	0.0282823i	$0.00900375\pi$
$773$	28.5781	+	28.5781i	1.02788	+	1.02788i	0.0282823	+	0.999600i	$0.490996\pi$
$774$	4.98104	−	22.2598i	0.179040	−	0.800112i
$775$	14.5870	+	14.5870i	0.523980	+	0.523980i
$776$			9.36262i			0.336098i
$777$	1.41534	+	4.87374i	0.0507752	+	0.174844i
$778$	12.5764	+	12.5764i	0.450884	+	0.450884i
$779$	−27.4419			−0.983210
$780$	0.738397	−	0.681536i	0.0264389	−	0.0244029i
$781$	12.1756			0.435676
$782$	14.9995	+	14.9995i	0.536382	+	0.536382i
$783$	31.3774	+	27.6822i	1.12134	+	0.989281i
$784$		−	33.9399i		−	1.21214i
$785$	−2.01001	−	2.01001i	−0.0717402	−	0.0717402i
$786$	5.56558	−	10.1210i	0.198518	−	0.361004i
$787$	−5.03551	−	5.03551i	−0.179496	−	0.179496i	0.611640	−	0.791136i	$-0.290510\pi$
$787$	−5.03551	−	5.03551i	−0.179496	−	0.179496i	−0.791136	+	0.611640i	$0.790510\pi$
$788$	−7.36031	+	7.36031i	−0.262200	+	0.262200i
$789$	7.09617	+	24.4357i	0.252630	+	0.869933i
$790$			3.80319i			0.135311i
$791$	2.33708	−	2.33708i	0.0830971	−	0.0830971i
$792$	3.44217	+	5.42676i	0.122312	+	0.192831i
$793$	−4.65498	−	1.55633i	−0.165303	−	0.0552667i
$794$			4.27738i			0.151799i
$795$	0.0868101	−	0.157864i	0.00307884	−	0.00559886i
$796$	3.02864			0.107347
$797$	35.7990			1.26807			0.634033	−	0.773306i	$-0.281398\pi$
$797$	35.7990			1.26807			0.634033	+	0.773306i	$0.281398\pi$
$798$	4.05944	+	2.23230i	0.143703	+	0.0790227i
$799$	−56.8002	+	56.8002i	−2.00945	+	2.00945i
$800$	−13.1921	+	13.1921i	−0.466413	+	0.466413i
$801$	11.3906	−	50.9034i	0.402466	−	1.79858i
$802$	−30.9262			−1.09204
$803$	10.1473			0.358090
$804$	−15.9083	−	8.74805i	−0.561043	−	0.308520i
$805$			0.139362i			0.00491187i
$806$	23.4124	+	7.82758i	0.824665	+	0.275715i
$807$	−6.04817	−	20.8269i	−0.212906	−	0.733141i
$808$	−14.3619	+	14.3619i	−0.505249	+	0.505249i
$809$		−	15.1087i		−	0.531195i	−0.964084	−	0.265597i	$-0.914431\pi$
$809$		−	15.1087i		−	0.531195i	0.964084	−	0.265597i	$-0.0855692\pi$
$810$	−3.09371	−	1.45753i	−0.108702	−	0.0512124i
$811$	10.9992	−	10.9992i	0.386236	−	0.386236i	−0.487107	−	0.873342i	$-0.661948\pi$
$811$	10.9992	−	10.9992i	0.386236	−	0.386236i	0.873342	+	0.487107i	$0.161948\pi$
$812$	1.14377	+	1.14377i	0.0401385	+	0.0401385i
$813$	−12.9787	−	7.13705i	−0.455183	−	0.250307i
$814$	11.7719	+	11.7719i	0.412605	+	0.412605i
$815$			0.0646238i			0.00226367i
$816$	50.6108	−	14.6975i	1.77173	−	0.514514i
$817$	18.4658	+	18.4658i	0.646037	+	0.646037i
$818$	−7.06084			−0.246876
$819$	2.67620	+	1.61437i	0.0935139	+	0.0564107i
$820$	0.783097			0.0273469
$821$	−23.7338	−	23.7338i	−0.828316	−	0.828316i	0.158968	−	0.987284i	$-0.449183\pi$
$821$	−23.7338	−	23.7338i	−0.828316	−	0.828316i	−0.987284	+	0.158968i	$0.949183\pi$
$822$	4.40090	−	1.27803i	0.153499	−	0.0445765i
$823$			31.5937i			1.10129i	0.834741	+	0.550643i	$0.185618\pi$
$823$			31.5937i			1.10129i	−0.834741	+	0.550643i	$0.814382\pi$
$824$	−21.9198	−	21.9198i	−0.763614	−	0.763614i
$825$	7.50725	+	4.12827i	0.261369	+	0.143728i
$826$	1.97174	+	1.97174i	0.0686057	+	0.0686057i
$827$	−36.3112	+	36.3112i	−1.26266	+	1.26266i	−0.312866	+	0.949797i	$0.601289\pi$
$827$	−36.3112	+	36.3112i	−1.26266	+	1.26266i	−0.949797	+	0.312866i	$0.898711\pi$
$828$	2.32779	+	3.66987i	0.0808962	+	0.127537i
$829$			6.17523i			0.214474i	0.994233	+	0.107237i	$0.0342004\pi$
$829$			6.17523i			0.214474i	−0.994233	+	0.107237i	$0.965800\pi$
$830$	−1.02055	+	1.02055i	−0.0354238	+	0.0354238i
$831$	7.27151	+	25.0395i	0.252246	+	0.868609i
$832$	4.14105	−	12.3859i	0.143565	−	0.429405i
$833$			42.8871i			1.48595i
$834$	−44.0677	−	24.2330i	−1.52594	−	0.839121i
$835$	−1.12684			−0.0389959
$836$	3.91981			0.135569
$837$	−1.35324	−	21.6283i	−0.0467747	−	0.747584i
$838$	17.8048	−	17.8048i	0.615058	−	0.615058i
$839$	−34.6775	+	34.6775i	−1.19720	+	1.19720i	−0.222198	+	0.975002i	$0.571323\pi$
$839$	−34.6775	+	34.6775i	−1.19720	+	1.19720i	−0.975002	+	0.222198i	$0.928677\pi$
$840$	0.217430	+	0.119566i	0.00750206	+	0.00412542i
$841$	−35.8463			−1.23608
$842$	32.6437			1.12498
$843$	−2.87150	+	5.22181i	−0.0988996	+	0.179849i
$844$		−	19.8477i		−	0.683185i
$845$	0.420158	+	2.97947i	0.0144539	+	0.102497i
$846$	−53.8784	+	34.1748i	−1.85238	+	1.17496i
$847$	0.204315	−	0.204315i	0.00702034	−	0.00702034i
$848$			2.20519i			0.0757265i
$849$	0.931426	+	3.20737i	0.0319665	+	0.110077i
$850$	35.6050	−	35.6050i	1.22124	−	1.22124i
$851$	−14.9421	−	14.9421i	−0.512208	−	0.512208i
$852$	7.06420	−	12.8462i	0.242015	−	0.440104i
$853$	−8.64307	−	8.64307i	−0.295933	−	0.295933i	0.543485	−	0.839419i	$-0.317104\pi$
$853$	−8.64307	−	8.64307i	−0.295933	−	0.295933i	−0.839419	+	0.543485i	$0.817104\pi$
$854$			0.645750i			0.0220971i
$855$	3.30625	−	2.09714i	0.113071	−	0.0717207i
$856$	−12.4548	−	12.4548i	−0.425697	−	0.425697i
$857$	−6.55512			−0.223918			−0.111959	−	0.993713i	$-0.535713\pi$
$857$	−6.55512			−0.223918			−0.111959	+	0.993713i	$0.535713\pi$
$858$	10.2442	+	0.410233i	0.349731	+	0.0140051i
$859$	28.3167			0.966154			0.483077	−	0.875578i	$-0.339519\pi$
$859$	28.3167			0.966154			0.483077	+	0.875578i	$0.339519\pi$
$860$	−0.526950	−	0.526950i	−0.0179688	−	0.0179688i
$861$	0.679267	+	2.33906i	0.0231494	+	0.0797149i
$862$		−	6.92906i		−	0.236005i
$863$	−17.1872	−	17.1872i	−0.585059	−	0.585059i	0.351230	−	0.936289i	$-0.385764\pi$
$863$	−17.1872	−	17.1872i	−0.585059	−	0.585059i	−0.936289	+	0.351230i	$0.885764\pi$
$864$	19.5601	−	1.22384i	0.665450	−	0.0416358i
$865$	−3.05536	−	3.05536i	−0.103885	−	0.103885i
$866$	16.8970	−	16.8970i	0.574183	−	0.574183i
$867$	−35.6761	+	10.3604i	−1.21162	+	0.351858i
$868$		−	0.837724i		−	0.0284342i
$869$	−7.07729	+	7.07729i	−0.240081	+	0.240081i
$870$	5.08964	−	1.47804i	0.172555	−	0.0501103i
$871$	48.6463	−	24.2684i	1.64832	−	0.822302i
$872$			12.2762i			0.415725i
$873$	2.86327	−	12.7957i	0.0969071	−	0.433069i
$874$	−19.2895			−0.652476
$875$	0.665202			0.0224879
$876$	5.88739	−	10.7062i	0.198917	−	0.361729i
$877$	7.81744	−	7.81744i	0.263976	−	0.263976i	−0.562691	−	0.826667i	$-0.690234\pi$
$877$	7.81744	−	7.81744i	0.263976	−	0.263976i	0.826667	+	0.562691i	$0.190234\pi$
$878$	15.1908	−	15.1908i	0.512665	−	0.512665i
$879$	21.7701	−	39.5889i	0.734289	−	1.33530i
$880$	1.13578			0.0382872
$881$	−9.69056			−0.326483			−0.163242	−	0.986586i	$-0.552195\pi$
$881$	−9.69056			−0.326483			−0.163242	+	0.986586i	$0.552195\pi$
$882$	−7.43860	+	33.2424i	−0.250471	+	1.11933i
$883$			13.0101i			0.437824i	0.975745	+	0.218912i	$0.0702508\pi$
$883$			13.0101i			0.437824i	−0.975745	+	0.218912i	$0.929749\pi$
$884$	4.92812	−	14.7401i	0.165751	−	0.495762i
$885$	2.26312	−	0.657215i	0.0760739	−	0.0220920i
$886$	35.5097	−	35.5097i	1.19297	−	1.19297i
$887$		−	37.6724i		−	1.26492i	−0.774595	−	0.632458i	$-0.782046\pi$
$887$		−	37.6724i		−	1.26492i	0.774595	−	0.632458i	$-0.217954\pi$
$888$	−36.1320	+	10.4928i	−1.21251	+	0.352115i
$889$	−0.845958	+	0.845958i	−0.0283725	+	0.0283725i
$890$	−4.67181	−	4.67181i	−0.156600	−	0.156600i
$891$	−3.04474	−	8.46933i	−0.102003	−	0.283733i
$892$	2.41210	+	2.41210i	0.0807632	+	0.0807632i
$893$		−	73.0453i		−	2.44437i
$894$	3.01539	+	10.3835i	0.100850	+	0.347276i
$895$	−0.0462323	−	0.0462323i	−0.00154538	−	0.00154538i
$896$	−3.89784			−0.130218
$897$	−13.0030	−	0.520709i	−0.434157	−	0.0173860i
$898$	−19.4139			−0.647852
$899$	23.7474	+	23.7474i	0.792021	+	0.792021i
$900$	8.71133	−	5.52556i	0.290378	−	0.184185i
$901$		−	2.78652i		−	0.0928324i
$902$	5.64971	+	5.64971i	0.188115	+	0.188115i
$903$	1.11688	−	2.03105i	0.0371675	−	0.0675890i
$904$	17.3262	+	17.3262i	0.576261	+	0.576261i
$905$	−2.61307	+	2.61307i	−0.0868615	+	0.0868615i
$906$	1.32817	+	4.57357i	0.0441256	+	0.151947i
$907$			19.4464i			0.645708i	0.946449	+	0.322854i	$0.104642\pi$
$907$			19.4464i			0.645708i	−0.946449	+	0.322854i	$0.895358\pi$
$908$	−1.43682	+	1.43682i	−0.0476824	+	0.0476824i
$909$	24.0202	−	15.2359i	0.796700	−	0.505344i
$910$	0.354236	−	0.176719i	0.0117428	−	0.00585818i
$911$			7.96035i			0.263738i	0.991267	+	0.131869i	$0.0420979\pi$
$911$			7.96035i			0.263738i	−0.991267	+	0.131869i	$0.957902\pi$
$912$	−23.0923	+	41.9934i	−0.764664	+	1.39054i
$913$	−3.79825			−0.125704
$914$	53.8926			1.78261
$915$	0.478208	+	0.262969i	0.0158091	+	0.00869348i
$916$	0.309950	−	0.309950i	0.0102410	−	0.0102410i
$917$	0.829926	−	0.829926i	0.0274066	−	0.0274066i
$918$	−52.7919	+	3.30308i	−1.74239	+	0.109018i
$919$	27.3089			0.900836			0.450418	−	0.892818i	$-0.351275\pi$
$919$	27.3089			0.900836			0.450418	+	0.892818i	$0.351275\pi$
$920$	−1.03318			−0.0340628
$921$	−3.32316	−	1.82742i	−0.109502	−	0.0602155i
$922$		−	51.5123i		−	1.69647i
$923$	19.5971	+	39.2827i	0.645047	+	1.29301i
$924$	−0.0970266	−	0.334111i	−0.00319194	−	0.0109915i
$925$	−35.4687	+	35.4687i	−1.16620	+	1.16620i
$926$			24.5592i			0.807065i
$927$	23.2539	+	36.6609i	0.763758	+	1.20410i
$928$	−21.4766	+	21.4766i	−0.705005	+	0.705005i
$929$	28.8408	+	28.8408i	0.946235	+	0.946235i	0.998627	−	0.0523914i	$-0.0166844\pi$
$929$	28.8408	+	28.8408i	0.946235	+	0.946235i	−0.0523914	+	0.998627i	$0.516684\pi$
$930$	−2.40516	−	1.32261i	−0.0788683	−	0.0433700i
$931$	−27.5765	−	27.5765i	−0.903785	−	0.903785i
$932$			0.338209i			0.0110784i
$933$	−27.1222	+	7.87636i	−0.887943	+	0.257860i
$934$	35.3941	+	35.3941i	1.15813	+	1.15813i
$935$	−1.43520			−0.0469360
$936$	−11.9683	+	19.8403i	−0.391197	+	0.648500i
$937$	−38.0247			−1.24221			−0.621106	−	0.783727i	$-0.713316\pi$
$937$	−38.0247			−1.24221			−0.621106	+	0.783727i	$0.713316\pi$
$938$	−5.05745	−	5.05745i	−0.165132	−	0.165132i
$939$	−10.3890	+	3.01699i	−0.339033	+	0.0984559i
$940$			2.08446i			0.0679875i
$941$	24.3530	+	24.3530i	0.793884	+	0.793884i	0.982123	−	0.188239i	$-0.0602779\pi$
$941$	24.3530	+	24.3530i	0.793884	+	0.793884i	−0.188239	+	0.982123i	$0.560278\pi$
$942$	−30.6002	−	16.8272i	−0.997007	−	0.548259i
$943$	−7.17118	−	7.17118i	−0.233526	−	0.233526i
$944$	−20.3969	+	20.3969i	−0.663864	+	0.663864i
$945$	−0.260592	−	0.229903i	−0.00847707	−	0.00747875i
$946$		−	7.60343i		−	0.247209i
$947$	19.3475	−	19.3475i	0.628709	−	0.628709i	−0.319034	−	0.947743i	$-0.603358\pi$
$947$	19.3475	−	19.3475i	0.628709	−	0.628709i	0.947743	+	0.319034i	$0.103358\pi$
$948$	3.36092	+	11.5733i	0.109158	+	0.375884i
$949$	16.3325	+	32.7387i	0.530175	+	1.06274i
$950$			45.7882i			1.48556i
$951$	9.34936	+	5.14125i	0.303174	+	0.166717i
$952$	3.83795			0.124389
$953$	39.6570			1.28462			0.642308	−	0.766446i	$-0.277977\pi$
$953$	39.6570			1.28462			0.642308	+	0.766446i	$0.277977\pi$
$954$	0.483310	−	2.15987i	0.0156477	−	0.0699284i
$955$	2.38880	−	2.38880i	0.0772997	−	0.0772997i
$956$	−10.7219	+	10.7219i	−0.346772	+	0.346772i
$957$	12.2217	+	6.72077i	0.395072	+	0.217252i
$958$	−21.4655			−0.693520
$959$	0.465676			0.0150375
$960$	−0.699704	+	1.27241i	−0.0225828	+	0.0410668i
$961$			13.6068i			0.438931i
$962$	−19.0330	+	56.9278i	−0.613647	+	1.83542i
$963$	13.2128	+	20.8307i	0.425778	+	0.671260i
$964$	−11.7635	+	11.7635i	−0.378876	+	0.378876i
$965$		−	4.70892i		−	0.151586i
$966$	0.477470	+	1.64417i	0.0153623	+	0.0529003i
$967$	18.4345	−	18.4345i	0.592814	−	0.592814i	−0.345577	−	0.938390i	$-0.612317\pi$
$967$	18.4345	−	18.4345i	0.592814	−	0.592814i	0.938390	+	0.345577i	$0.112317\pi$
$968$	1.51471	+	1.51471i	0.0486846	+	0.0486846i
$969$	29.1799	−	53.0637i	0.937395	−	1.70465i
$970$	−1.17436	−	1.17436i	−0.0377066	−	0.0377066i
$971$		−	53.7610i		−	1.72527i	−0.505826	−	0.862636i	$-0.668812\pi$
$971$		−	53.7610i		−	1.72527i	0.505826	−	0.862636i	$-0.331188\pi$
$972$	−10.7024	−	1.70141i	−0.343279	−	0.0545726i
$973$	−3.61358	−	3.61358i	−0.115846	−	0.115846i
$974$	−34.2495			−1.09742
$975$	−1.23603	+	30.8657i	−0.0395846	+	0.988493i
$976$	−6.68004			−0.213823
$977$	38.9280	+	38.9280i	1.24542	+	1.24542i	0.957722	+	0.287694i	$0.0928887\pi$
$977$	38.9280	+	38.9280i	1.24542	+	1.24542i	0.287694	+	0.957722i	$0.407111\pi$
$978$	0.221408	+	0.762419i	0.00707985	+	0.0243795i
$979$		−	17.3874i		−	0.555704i
$980$	0.786938	+	0.786938i	0.0251378	+	0.0251378i
$981$	3.75431	−	16.7777i	0.119866	−	0.535670i
$982$	33.8584	+	33.8584i	1.08046	+	1.08046i
$983$	4.66297	−	4.66297i	0.148726	−	0.148726i	−0.628823	−	0.777549i	$-0.716463\pi$
$983$	4.66297	−	4.66297i	0.148726	−	0.148726i	0.777549	+	0.628823i	$0.216463\pi$
$984$	−17.3409	+	5.03582i	−0.552807	+	0.160536i
$985$			3.46566i			0.110425i
$986$	57.9644	−	57.9644i	1.84596	−	1.84596i
$987$	−6.22614	+	1.80808i	−0.198180	+	0.0575519i
$988$	6.30910	+	12.6467i	0.200719	+	0.402345i
$989$			9.65104i			0.306885i
$990$	−1.11244	−	0.248929i	−0.0353557	−	0.00791149i
$991$	10.9857			0.348971			0.174486	−	0.984660i	$-0.444174\pi$
$991$	10.9857			0.348971			0.174486	+	0.984660i	$0.444174\pi$
$992$	15.7300			0.499427
$993$	−14.2779	+	25.9644i	−0.453096	+	0.823954i
$994$	4.08398	−	4.08398i	0.129536	−	0.129536i
$995$	0.713029	−	0.713029i	0.0226045	−	0.0226045i
$996$	−2.20372	+	4.00746i	−0.0698276	+	0.126981i
$997$	55.4992			1.75768			0.878838	−	0.477120i	$-0.158319\pi$
$997$	55.4992			1.75768			0.878838	+	0.477120i	$0.158319\pi$
$998$	14.3316			0.453658
$999$	52.5898	−	3.29043i	1.66387	−	0.104105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.13	✓	96
3.2	odd	2	inner	429.2.j.a.122.36	yes	96
13.8	odd	4	inner	429.2.j.a.320.36	yes	96
39.8	even	4	inner	429.2.j.a.320.13	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.13	✓	96	1.1	even	1	trivial
429.2.j.a.122.36	yes	96	3.2	odd	2	inner
429.2.j.a.320.13	yes	96	39.8	even	4	inner
429.2.j.a.320.36	yes	96	13.8	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16086 - 1.16086i) q^{2} +(-1.66333 + 0.483035i) q^{3} +0.695179i q^{4} +(0.163665 + 0.163665i) q^{5} +(2.49163 + 1.37016i) q^{6} +(0.204315 + 0.204315i) q^{7} +(-1.51471 + 1.51471i) q^{8} +(2.53335 - 1.60690i) q^{9} +O(q^{10})\)	\(q+(-1.16086 - 1.16086i) q^{2} +(-1.66333 + 0.483035i) q^{3} +0.695179i q^{4} +(0.163665 + 0.163665i) q^{5} +(2.49163 + 1.37016i) q^{6} +(0.204315 + 0.204315i) q^{7} +(-1.51471 + 1.51471i) q^{8} +(2.53335 - 1.60690i) q^{9} -0.379984i q^{10} +(0.707107 - 0.707107i) q^{11} +(-0.335796 - 1.15631i) q^{12} +(3.41950 + 1.14326i) q^{13} -0.474361i q^{14} +(-0.351286 - 0.193174i) q^{15} +4.90708 q^{16} -6.20069 q^{17} +(-4.80624 - 1.07548i) q^{18} +(3.98706 - 3.98706i) q^{19} +(-0.113777 + 0.113777i) q^{20} +(-0.438535 - 0.241152i) q^{21} -1.64170 q^{22} +2.08381 q^{23} +(1.78781 - 3.25113i) q^{24} -4.94643i q^{25} +(-2.64239 - 5.29671i) q^{26} +(-3.43762 + 3.89650i) q^{27} +(-0.142035 + 0.142035i) q^{28} -8.05272i q^{29} +(0.183546 + 0.632040i) q^{30} +(-2.94900 + 2.94900i) q^{31} +(-2.66700 - 2.66700i) q^{32} +(-0.834597 + 1.51771i) q^{33} +(7.19812 + 7.19812i) q^{34} +0.0668785i q^{35} +(1.11708 + 1.76114i) q^{36} +(-7.17056 - 7.17056i) q^{37} -9.25682 q^{38} +(-6.24000 - 0.249883i) q^{39} -0.495811 q^{40} +(-3.44137 - 3.44137i) q^{41} +(0.229133 + 0.789020i) q^{42} +4.63144i q^{43} +(0.491566 + 0.491566i) q^{44} +(0.677615 + 0.151629i) q^{45} +(-2.41901 - 2.41901i) q^{46} +(9.16030 - 9.16030i) q^{47} +(-8.16212 + 2.37029i) q^{48} -6.91651i q^{49} +(-5.74210 + 5.74210i) q^{50} +(10.3138 - 2.99515i) q^{51} +(-0.794770 + 2.37716i) q^{52} +0.449389i q^{53} +(8.51388 - 0.532695i) q^{54} +0.231458 q^{55} -0.618956 q^{56} +(-4.70592 + 8.55770i) q^{57} +(-9.34806 + 9.34806i) q^{58} +(-4.15663 + 4.15663i) q^{59} +(0.134290 - 0.244207i) q^{60} -1.36131 q^{61} +6.84673 q^{62} +(0.845915 + 0.189289i) q^{63} -3.62215i q^{64} +(0.372541 + 0.746765i) q^{65} +(2.73069 - 0.792999i) q^{66} +(10.6616 - 10.6616i) q^{67} -4.31059i q^{68} +(-3.46607 + 1.00655i) q^{69} +(0.0776364 - 0.0776364i) q^{70} +(8.60943 + 8.60943i) q^{71} +(-1.40331 + 6.27128i) q^{72} +(7.17521 + 7.17521i) q^{73} +16.6480i q^{74} +(2.38930 + 8.22756i) q^{75} +(2.77172 + 2.77172i) q^{76} +0.288945 q^{77} +(6.95367 + 7.53382i) q^{78} -10.0088 q^{79} +(0.803119 + 0.803119i) q^{80} +(3.83576 - 8.14168i) q^{81} +7.98989i q^{82} +(-2.68577 - 2.68577i) q^{83} +(0.167644 - 0.304860i) q^{84} +(-1.01484 - 1.01484i) q^{85} +(5.37644 - 5.37644i) q^{86} +(3.88975 + 13.3944i) q^{87} +2.14212i q^{88} +(12.2948 - 12.2948i) q^{89} +(-0.610595 - 0.962634i) q^{90} +(0.465069 + 0.932239i) q^{91} +1.44862i q^{92} +(3.48069 - 6.32963i) q^{93} -21.2676 q^{94} +1.30509 q^{95} +(5.72437 + 3.14786i) q^{96} +(3.09056 - 3.09056i) q^{97} +(-8.02908 + 8.02908i) q^{98} +(0.655104 - 2.92760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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