LMFDB - Embedded newform 430.2.j.a.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(49,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("430.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	430.49
Dual form			430.2.j.a.79.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.377570 - 0.217990i) q^{3} -1.00000 q^{4} +(2.13668 - 0.659257i) q^{5} +(-0.217990 + 0.377570i) q^{6} +(0.236341 - 0.136452i) q^{7} +1.00000i q^{8} +(-1.40496 - 2.43346i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.377570 - 0.217990i) q^{3} -1.00000 q^{4} +(2.13668 - 0.659257i) q^{5} +(-0.217990 + 0.377570i) q^{6} +(0.236341 - 0.136452i) q^{7} +1.00000i q^{8} +(-1.40496 - 2.43346i) q^{9} +(-0.659257 - 2.13668i) q^{10} +3.88264 q^{11} +(0.377570 + 0.217990i) q^{12} +(-0.559507 + 0.323031i) q^{13} +(-0.136452 - 0.236341i) q^{14} +(-0.950456 - 0.216858i) q^{15} +1.00000 q^{16} +(-1.73850 + 1.00373i) q^{17} +(-2.43346 + 1.40496i) q^{18} +(3.66757 - 6.35242i) q^{19} +(-2.13668 + 0.659257i) q^{20} -0.118980 q^{21} -3.88264i q^{22} +(-2.31413 - 1.33606i) q^{23} +(0.217990 - 0.377570i) q^{24} +(4.13076 - 2.81724i) q^{25} +(0.323031 + 0.559507i) q^{26} +2.53301i q^{27} +(-0.236341 + 0.136452i) q^{28} +(-1.52762 - 2.64591i) q^{29} +(-0.216858 + 0.950456i) q^{30} +(-0.240996 + 0.417418i) q^{31} -1.00000i q^{32} +(-1.46597 - 0.846377i) q^{33} +(1.00373 + 1.73850i) q^{34} +(0.415027 - 0.447362i) q^{35} +(1.40496 + 2.43346i) q^{36} +(-4.19721 - 2.42326i) q^{37} +(-6.35242 - 3.66757i) q^{38} +0.281671 q^{39} +(0.659257 + 2.13668i) q^{40} -2.71275 q^{41} +0.118980i q^{42} +(4.54136 + 4.73034i) q^{43} -3.88264 q^{44} +(-4.60622 - 4.27329i) q^{45} +(-1.33606 + 2.31413i) q^{46} -4.57802i q^{47} +(-0.377570 - 0.217990i) q^{48} +(-3.46276 + 5.99768i) q^{49} +(-2.81724 - 4.13076i) q^{50} +0.875209 q^{51} +(0.559507 - 0.323031i) q^{52} +(0.0419103 + 0.0241969i) q^{53} +2.53301 q^{54} +(8.29594 - 2.55966i) q^{55} +(0.136452 + 0.236341i) q^{56} +(-2.76953 + 1.59899i) q^{57} +(-2.64591 + 1.52762i) q^{58} +4.81150 q^{59} +(0.950456 + 0.216858i) q^{60} +(3.10578 + 5.37937i) q^{61} +(0.417418 + 0.240996i) q^{62} +(-0.664100 - 0.383418i) q^{63} -1.00000 q^{64} +(-0.982524 + 1.05907i) q^{65} +(-0.846377 + 1.46597i) q^{66} +(8.80656 + 5.08447i) q^{67} +(1.73850 - 1.00373i) q^{68} +(0.582497 + 1.00892i) q^{69} +(-0.447362 - 0.415027i) q^{70} +(5.77106 + 9.99577i) q^{71} +(2.43346 - 1.40496i) q^{72} +(-5.41208 + 3.12466i) q^{73} +(-2.42326 + 4.19721i) q^{74} +(-2.17378 + 0.163239i) q^{75} +(-3.66757 + 6.35242i) q^{76} +(0.917628 - 0.529793i) q^{77} -0.281671i q^{78} +(-1.35878 - 2.35347i) q^{79} +(2.13668 - 0.659257i) q^{80} +(-3.66271 + 6.34400i) q^{81} +2.71275i q^{82} +(9.28970 + 5.36341i) q^{83} +0.118980 q^{84} +(-3.05290 + 3.29076i) q^{85} +(4.73034 - 4.54136i) q^{86} +1.33202i q^{87} +3.88264i q^{88} +(-0.0807978 + 0.139946i) q^{89} +(-4.27329 + 4.60622i) q^{90} +(-0.0881563 + 0.152691i) q^{91} +(2.31413 + 1.33606i) q^{92} +(0.181986 - 0.105070i) q^{93} -4.57802 q^{94} +(3.64853 - 15.9909i) q^{95} +(-0.217990 + 0.377570i) q^{96} +13.1555i q^{97} +(5.99768 + 3.46276i) q^{98} +(-5.45496 - 9.44826i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	$ 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) $ 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.377570	−	0.217990i	−0.217990	−	0.125857i	0.387029	−	0.922067i	$-0.373501\pi$
$3$	−0.377570	−	0.217990i	−0.217990	−	0.125857i	−0.605019	+	0.796211i	$0.706835\pi$
$4$	−1.00000			−0.500000
$5$	2.13668	−	0.659257i	0.955550	−	0.294829i
$5$	2.13668	−	0.659257i	0.955550	−	0.294829i
$6$	−0.217990	+	0.377570i	−0.0889941	+	0.154142i
$7$	0.236341	−	0.136452i	0.0893285	−	0.0515739i	−0.454670	−	0.890660i	$-0.650243\pi$
$7$	0.236341	−	0.136452i	0.0893285	−	0.0515739i	0.543999	+	0.839086i	$0.316910\pi$
$8$			1.00000i			0.353553i
$9$	−1.40496	−	2.43346i	−0.468320	−	0.811154i
$10$	−0.659257	−	2.13668i	−0.208475	−	0.675676i
$11$	3.88264			1.17066			0.585330	−	0.810795i	$-0.300965\pi$
$11$	3.88264			1.17066			0.585330	+	0.810795i	$0.300965\pi$
$12$	0.377570	+	0.217990i	0.108995	+	0.0629283i
$13$	−0.559507	+	0.323031i	−0.155179	+	0.0895928i	−0.575579	−	0.817746i	$-0.695223\pi$
$13$	−0.559507	+	0.323031i	−0.155179	+	0.0895928i	0.420400	+	0.907339i	$0.361890\pi$
$14$	−0.136452	−	0.236341i	−0.0364682	−	0.0631648i
$15$	−0.950456	−	0.216858i	−0.245407	−	0.0559926i
$16$	1.00000			0.250000
$17$	−1.73850	+	1.00373i	−0.421649	+	0.243439i	−0.695783	−	0.718252i	$-0.744942\pi$
$17$	−1.73850	+	1.00373i	−0.421649	+	0.243439i	0.274134	+	0.961692i	$0.411609\pi$
$18$	−2.43346	+	1.40496i	−0.573573	+	0.331152i
$19$	3.66757	−	6.35242i	0.841399	−	1.45735i	−0.0473127	−	0.998880i	$-0.515066\pi$
$19$	3.66757	−	6.35242i	0.841399	−	1.45735i	0.888712	−	0.458466i	$-0.151601\pi$
$20$	−2.13668	+	0.659257i	−0.477775	+	0.147414i
$21$	−0.118980			−0.0259637
$22$		−	3.88264i		−	0.827782i
$23$	−2.31413	−	1.33606i	−0.482529	−	0.278589i	0.238941	−	0.971034i	$-0.423200\pi$
$23$	−2.31413	−	1.33606i	−0.482529	−	0.278589i	−0.721470	+	0.692446i	$0.756533\pi$
$24$	0.217990	−	0.377570i	0.0444971	−	0.0770712i
$25$	4.13076	−	2.81724i	0.826152	−	0.563447i
$26$	0.323031	+	0.559507i	0.0633517	+	0.109728i
$27$			2.53301i			0.487478i
$28$	−0.236341	+	0.136452i	−0.0446643	+	0.0257869i
$29$	−1.52762	−	2.64591i	−0.283672	−	0.491334i	0.688614	−	0.725128i	$-0.258219\pi$
$29$	−1.52762	−	2.64591i	−0.283672	−	0.491334i	−0.972286	+	0.233794i	$0.924886\pi$
$30$	−0.216858	+	0.950456i	−0.0395928	+	0.173529i
$31$	−0.240996	+	0.417418i	−0.0432842	+	0.0749704i	−0.886856	−	0.462046i	$-0.847115\pi$
$31$	−0.240996	+	0.417418i	−0.0432842	+	0.0749704i	0.843572	+	0.537017i	$0.180449\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.46597	−	0.846377i	−0.255192	−	0.147335i
$34$	1.00373	+	1.73850i	0.172138	+	0.298151i
$35$	0.415027	−	0.447362i	0.0701524	−	0.0756180i
$36$	1.40496	+	2.43346i	0.234160	+	0.405577i
$37$	−4.19721	−	2.42326i	−0.690018	−	0.398382i	0.113601	−	0.993526i	$-0.463761\pi$
$37$	−4.19721	−	2.42326i	−0.690018	−	0.398382i	−0.803619	+	0.595145i	$0.797095\pi$
$38$	−6.35242	−	3.66757i	−1.03050	−	0.594959i
$39$	0.281671			0.0451034
$40$	0.659257	+	2.13668i	0.104238	+	0.337838i
$41$	−2.71275			−0.423660			−0.211830	−	0.977307i	$-0.567942\pi$
$41$	−2.71275			−0.423660			−0.211830	+	0.977307i	$0.567942\pi$
$42$			0.118980i			0.0183591i
$43$	4.54136	+	4.73034i	0.692550	+	0.721370i
$43$	4.54136	+	4.73034i	0.692550	+	0.721370i
$44$	−3.88264			−0.585330
$45$	−4.60622	−	4.27329i	−0.686655	−	0.637024i
$46$	−1.33606	+	2.31413i	−0.196992	+	0.341200i
$47$		−	4.57802i		−	0.667773i	−0.942613	−	0.333887i	$-0.891640\pi$
$47$		−	4.57802i		−	0.667773i	0.942613	−	0.333887i	$-0.108360\pi$
$48$	−0.377570	−	0.217990i	−0.0544975	−	0.0314642i
$49$	−3.46276	+	5.99768i	−0.494680	+	0.856811i
$50$	−2.81724	−	4.13076i	−0.398417	−	0.584178i
$51$	0.875209			0.122554
$52$	0.559507	−	0.323031i	0.0775896	−	0.0447964i
$53$	0.0419103	+	0.0241969i	0.00575682	+	0.00332370i	0.502876	−	0.864359i	$-0.332275\pi$
$53$	0.0419103	+	0.0241969i	0.00575682	+	0.00332370i	−0.497119	+	0.867682i	$0.665609\pi$
$54$	2.53301			0.344699
$55$	8.29594	−	2.55966i	1.11862	−	0.345144i
$56$	0.136452	+	0.236341i	0.0182341	+	0.0315824i
$57$	−2.76953	+	1.59899i	−0.366833	+	0.211791i
$58$	−2.64591	+	1.52762i	−0.347425	+	0.200586i
$59$	4.81150			0.626404			0.313202	−	0.949686i	$-0.398598\pi$
$59$	4.81150			0.626404			0.313202	+	0.949686i	$0.398598\pi$
$60$	0.950456	+	0.216858i	0.122703	+	0.0279963i
$61$	3.10578	+	5.37937i	0.397654	+	0.688758i	0.993436	−	0.114389i	$-0.0364910\pi$
$61$	3.10578	+	5.37937i	0.397654	+	0.688758i	−0.595782	+	0.803146i	$0.703158\pi$
$62$	0.417418	+	0.240996i	0.0530121	+	0.0306066i
$63$	−0.664100	−	0.383418i	−0.0836687	−	0.0483062i
$64$	−1.00000			−0.125000
$65$	−0.982524	+	1.05907i	−0.121867	+	0.131362i
$66$	−0.846377	+	1.46597i	−0.104182	+	0.180448i
$67$	8.80656	+	5.08447i	1.07589	+	0.621167i	0.929786	−	0.368102i	$-0.119992\pi$
$67$	8.80656	+	5.08447i	1.07589	+	0.621167i	0.146107	+	0.989269i	$0.453326\pi$
$68$	1.73850	−	1.00373i	0.210825	−	0.121720i
$69$	0.582497	+	1.00892i	0.0701244	+	0.121459i
$70$	−0.447362	−	0.415027i	−0.0534700	−	0.0496053i
$71$	5.77106	+	9.99577i	0.684899	+	1.18628i	0.973469	+	0.228821i	$0.0734870\pi$
$71$	5.77106	+	9.99577i	0.684899	+	1.18628i	−0.288570	+	0.957459i	$0.593180\pi$
$72$	2.43346	−	1.40496i	0.286786	−	0.165576i
$73$	−5.41208	+	3.12466i	−0.633436	+	0.365714i	−0.782081	−	0.623176i	$-0.785842\pi$
$73$	−5.41208	+	3.12466i	−0.633436	+	0.365714i	0.148646	+	0.988890i	$0.452509\pi$
$74$	−2.42326	+	4.19721i	−0.281698	+	0.487916i
$75$	−2.17378	+	0.163239i	−0.251007	+	0.0188492i
$76$	−3.66757	+	6.35242i	−0.420700	+	0.728673i
$77$	0.917628	−	0.529793i	0.104573	−	0.0603755i
$78$		−	0.281671i		−	0.0318929i
$79$	−1.35878	−	2.35347i	−0.152875	−	0.264786i	0.779409	−	0.626516i	$-0.215520\pi$
$79$	−1.35878	−	2.35347i	−0.152875	−	0.264786i	−0.932283	+	0.361730i	$0.882186\pi$
$80$	2.13668	−	0.659257i	0.238888	−	0.0737072i
$81$	−3.66271	+	6.34400i	−0.406968	+	0.704889i
$82$			2.71275i			0.299573i
$83$	9.28970	+	5.36341i	1.01968	+	0.588711i	0.914010	−	0.405691i	$-0.132969\pi$
$83$	9.28970	+	5.36341i	1.01968	+	0.588711i	0.105667	+	0.994402i	$0.466302\pi$
$84$	0.118980			0.0129818
$85$	−3.05290	+	3.29076i	−0.331134	+	0.356933i
$86$	4.73034	−	4.54136i	0.510085	−	0.489707i
$87$			1.33202i			0.142808i
$88$			3.88264i			0.413891i
$89$	−0.0807978	+	0.139946i	−0.00856455	+	0.0148342i	−0.870276	−	0.492565i	$-0.836060\pi$
$89$	−0.0807978	+	0.139946i	−0.00856455	+	0.0148342i	0.861711	+	0.507399i	$0.169393\pi$
$90$	−4.27329	+	4.60622i	−0.450444	+	0.485538i
$91$	−0.0881563	+	0.152691i	−0.00924129	+	0.0160064i
$92$	2.31413	+	1.33606i	0.241265	+	0.139294i
$93$	0.181986	−	0.105070i	0.0188711	−	0.0108952i
$94$	−4.57802			−0.472187
$95$	3.64853	−	15.9909i	0.374332	−	1.64064i
$96$	−0.217990	+	0.377570i	−0.0222485	+	0.0385356i
$97$			13.1555i			1.33574i	0.744280	+	0.667868i	$0.232793\pi$
$97$			13.1555i			1.33574i	−0.744280	+	0.667868i	$0.767207\pi$
$98$	5.99768	+	3.46276i	0.605857	+	0.349792i
$99$	−5.45496	−	9.44826i	−0.548244	−	0.949586i
$100$	−4.13076	+	2.81724i	−0.413076	+	0.281724i
$101$	8.12302	+	14.0695i	0.808271	+	1.39997i	0.914061	+	0.405578i	$0.132930\pi$
$101$	8.12302	+	14.0695i	0.808271	+	1.39997i	−0.105790	+	0.994389i	$0.533737\pi$
$102$		−	0.875209i		−	0.0866586i
$103$	1.41398	−	0.816364i	0.139324	−	0.0804387i	−0.428718	−	0.903438i	$-0.641035\pi$
$103$	1.41398	−	0.816364i	0.139324	−	0.0804387i	0.568042	+	0.823000i	$0.307701\pi$
$104$	−0.323031	−	0.559507i	−0.0316758	−	0.0548642i
$105$	−0.254222	+	0.0784387i	−0.0248096	+	0.00765483i
$106$	0.0241969	−	0.0419103i	0.00235021	−	0.00407069i
$107$		−	12.1237i		−	1.17204i	−0.810297	−	0.586019i	$-0.800694\pi$
$107$		−	12.1237i		−	1.17204i	0.810297	−	0.586019i	$-0.199306\pi$
$108$		−	2.53301i		−	0.243739i
$109$	2.29092	−	3.96798i	0.219430	−	0.380064i	−0.735204	−	0.677846i	$-0.762914\pi$
$109$	2.29092	−	3.96798i	0.219430	−	0.380064i	0.954634	+	0.297782i	$0.0962469\pi$
$110$	−2.55966	−	8.29594i	−0.244054	−	0.790987i
$111$	1.05649	+	1.82990i	0.100278	+	0.173687i
$112$	0.236341	−	0.136452i	0.0223321	−	0.0128935i
$113$		−	1.03908i		−	0.0977483i	−0.998805	−	0.0488741i	$-0.984437\pi$
$113$		−	1.03908i		−	0.0977483i	0.998805	−	0.0488741i	$-0.0155633\pi$
$114$	1.59899	+	2.76953i	0.149759	+	0.259390i
$115$	−5.82535	−	1.32913i	−0.543217	−	0.123942i
$116$	1.52762	+	2.64591i	0.141836	+	0.245667i
$117$	1.57217	+	0.907693i	0.145347	+	0.0839162i
$118$		−	4.81150i		−	0.442935i
$119$	−0.273920	+	0.474443i	−0.0251102	+	0.0434921i
$120$	0.216858	−	0.950456i	0.0197964	−	0.0867644i
$121$	4.07490			0.370445
$122$	5.37937	−	3.10578i	0.487025	−	0.281184i
$123$	1.02425	+	0.591352i	0.0923537	+	0.0533204i
$124$	0.240996	−	0.417418i	0.0216421	−	0.0374852i
$125$	6.96881	−	8.74275i	0.623309	−	0.781975i
$126$	−0.383418	+	0.664100i	−0.0341576	+	0.0591627i
$127$			17.2962i			1.53479i	0.641175	+	0.767395i	$0.278447\pi$
$127$			17.2962i			1.53479i	−0.641175	+	0.767395i	$0.721553\pi$
$128$			1.00000i			0.0883883i
$129$	−0.683513	−	2.77600i	−0.0601800	−	0.244414i
$130$	1.05907	+	0.982524i	0.0928868	+	0.0861730i
$131$	−4.30253			−0.375914			−0.187957	−	0.982177i	$-0.560187\pi$
$131$	−4.30253			−0.375914			−0.187957	+	0.982177i	$0.560187\pi$
$132$	1.46597	+	0.846377i	0.127596	+	0.0736677i
$133$		−	2.00179i		−	0.173577i
$134$	5.08447	−	8.80656i	0.439231	−	0.760771i
$135$	1.66991	+	5.41222i	0.143723	+	0.465810i
$136$	−1.00373	−	1.73850i	−0.0860688	−	0.149075i
$137$		−	15.2222i		−	1.30052i	−0.759713	−	0.650259i	$-0.774661\pi$
$137$		−	15.2222i		−	1.30052i	0.759713	−	0.650259i	$-0.225339\pi$
$138$	1.00892	−	0.582497i	0.0858846	−	0.0495855i
$139$	−6.11869	+	10.5979i	−0.518980	+	0.898900i	0.480777	+	0.876843i	$0.340355\pi$
$139$	−6.11869	+	10.5979i	−0.518980	+	0.898900i	−0.999757	+	0.0220568i	$0.992979\pi$
$140$	−0.415027	+	0.447362i	−0.0350762	+	0.0378090i
$141$	−0.997964	+	1.72852i	−0.0840437	+	0.145568i
$142$	9.99577	−	5.77106i	0.838826	−	0.484297i
$143$	−2.17236	+	1.25421i	−0.181662	+	0.104883i
$144$	−1.40496	−	2.43346i	−0.117080	−	0.202789i
$145$	−5.00836	−	4.64636i	−0.415922	−	0.385860i
$146$	3.12466	+	5.41208i	0.258599	+	0.447907i
$147$	2.61487	−	1.50970i	0.215671	−	0.124518i
$148$	4.19721	+	2.42326i	0.345009	+	0.199191i
$149$	−8.02312	+	13.8965i	−0.657280	+	1.13844i	0.324037	+	0.946044i	$0.394960\pi$
$149$	−8.02312	+	13.8965i	−0.657280	+	1.13844i	−0.981317	+	0.192398i	$0.938374\pi$
$150$	0.163239	+	2.17378i	0.0133284	+	0.177488i
$151$	11.1579			0.908018			0.454009	−	0.890997i	$-0.349993\pi$
$151$	11.1579			0.908018			0.454009	+	0.890997i	$0.349993\pi$
$152$	6.35242	+	3.66757i	0.515250	+	0.297480i
$153$	4.88506	+	2.82039i	0.394934	+	0.228015i
$154$	−0.529793	−	0.917628i	−0.0426919	−	0.0739445i
$155$	−0.239745	+	1.05076i	−0.0192568	+	0.0843994i
$156$	−0.281671			−0.0225517
$157$	−12.2319	+	7.06210i	−0.976213	+	0.563617i	−0.901125	−	0.433560i	$-0.857257\pi$
$157$	−12.2319	+	7.06210i	−0.976213	+	0.563617i	−0.0750881	+	0.997177i	$0.523924\pi$
$158$	−2.35347	+	1.35878i	−0.187232	+	0.108099i
$159$	−0.0105494	−	0.0182721i	−0.000836620	−	0.00144907i
$160$	−0.659257	−	2.13668i	−0.0521188	−	0.168919i
$161$	−0.729232			−0.0574715
$162$	6.34400	+	3.66271i	0.498432	+	0.287770i
$163$	−7.01941	+	4.05266i	−0.549803	+	0.317429i	−0.749043	−	0.662522i	$-0.769486\pi$
$163$	−7.01941	+	4.05266i	−0.549803	+	0.317429i	0.199240	+	0.979951i	$0.436153\pi$
$164$	2.71275			0.211830
$165$	−3.69028	−	0.841983i	−0.287288	−	0.0655483i
$166$	5.36341	−	9.28970i	0.416281	−	0.721021i
$167$	−12.8712	−	7.43118i	−0.996002	−	0.575042i	−0.0889393	−	0.996037i	$-0.528348\pi$
$167$	−12.8712	−	7.43118i	−0.996002	−	0.575042i	−0.907063	+	0.420995i	$0.861681\pi$
$168$		−	0.118980i		−	0.00917954i
$169$	−6.29130	+	10.8969i	−0.483946	+	0.838220i
$170$	3.29076	+	3.05290i	0.252389	+	0.234147i
$171$	−20.6112			−1.57618
$172$	−4.54136	−	4.73034i	−0.346275	−	0.360685i
$173$		−	23.6777i		−	1.80018i	−0.435703	−	0.900090i	$-0.643500\pi$
$173$		−	23.6777i		−	1.80018i	0.435703	−	0.900090i	$-0.356500\pi$
$174$	1.33202			0.100980
$175$	0.591852	−	1.22948i	0.0447398	−	0.0929398i
$176$	3.88264			0.292665
$177$	−1.81668	−	1.04886i	−0.136550	−	0.0788372i
$178$	0.139946	+	0.0807978i	0.0104894	+	0.00605605i
$179$	−0.675645	−	1.17025i	−0.0505001	−	0.0874687i	0.839670	−	0.543096i	$-0.182748\pi$
$179$	−0.675645	−	1.17025i	−0.0505001	−	0.0874687i	−0.890170	+	0.455628i	$0.849415\pi$
$180$	4.60622	+	4.27329i	0.343328	+	0.318512i
$181$	−2.86323	−	4.95925i	−0.212822	−	0.368618i	0.739775	−	0.672855i	$-0.234932\pi$
$181$	−2.86323	−	4.95925i	−0.212822	−	0.368618i	−0.952597	+	0.304236i	$0.901599\pi$
$182$	0.152691	+	0.0881563i	0.0113182	+	0.00653458i
$183$		−	2.70812i		−	0.200190i
$184$	1.33606	−	2.31413i	0.0984959	−	0.170600i
$185$	−10.5656	−	2.41068i	−0.776801	−	0.177237i
$186$	−0.105070	−	0.181986i	−0.00770408	−	0.0133439i
$187$	−6.74998	+	3.89711i	−0.493608	+	0.284985i
$188$			4.57802i			0.333887i
$189$	0.345633	+	0.598655i	0.0251411	+	0.0435457i
$190$	−15.9909	−	3.64853i	−1.16010	−	0.264692i
$191$	1.04898	−	1.81689i	0.0759017	−	0.131466i	−0.825576	−	0.564290i	$-0.809150\pi$
$191$	1.04898	−	1.81689i	0.0759017	−	0.131466i	0.901478	+	0.432825i	$0.142483\pi$
$192$	0.377570	+	0.217990i	0.0272488	+	0.0157321i
$193$		−	1.77027i		−	0.127426i	−0.997968	−	0.0637132i	$-0.979706\pi$
$193$		−	1.77027i		−	0.127426i	0.997968	−	0.0637132i	$-0.0202943\pi$
$194$	13.1555			0.944508
$195$	0.601839	−	0.185693i	0.0430986	−	0.0132978i
$196$	3.46276	−	5.99768i	0.247340	−	0.428406i
$197$	−20.6151	+	11.9022i	−1.46877	+	0.847994i	−0.999387	−	0.0350024i	$-0.988856\pi$
$197$	−20.6151	+	11.9022i	−1.46877	+	0.847994i	−0.469381	+	0.882996i	$0.655523\pi$
$198$	−9.44826	+	5.45496i	−0.671459	+	0.387667i
$199$	4.95598			0.351320			0.175660	−	0.984451i	$-0.443794\pi$
$199$	4.95598			0.351320			0.175660	+	0.984451i	$0.443794\pi$
$200$	2.81724	+	4.13076i	0.199209	+	0.292089i
$201$	−2.21673	−	3.83949i	−0.156356	−	0.270817i
$202$	14.0695	−	8.12302i	0.989926	−	0.571534i
$203$	−0.722078	−	0.416892i	−0.0506800	−	0.0292601i
$204$	−0.875209			−0.0612769
$205$	−5.79626	+	1.78840i	−0.404828	+	0.124907i
$206$	−0.816364	−	1.41398i	−0.0568788	−	0.0985169i
$207$			7.50847i			0.521874i
$208$	−0.559507	+	0.323031i	−0.0387948	+	0.0223982i
$209$	14.2399	−	24.6642i	0.984993	−	1.70606i
$210$	0.0784387	+	0.254222i	0.00541278	+	0.0175430i
$211$	15.6556			1.07777			0.538886	−	0.842378i	$-0.318845\pi$
$211$	15.6556			1.07777			0.538886	+	0.842378i	$0.318845\pi$
$212$	−0.0419103	−	0.0241969i	−0.00287841	−	0.00166185i
$213$		−	5.03214i		−	0.344796i
$214$	−12.1237			−0.828756
$215$	12.8219	+	7.11327i	0.874447	+	0.485121i
$216$	−2.53301			−0.172350
$217$			0.131537i			0.00892933i
$218$	−3.96798	−	2.29092i	−0.268746	−	0.155160i
$219$	2.72458			0.184110
$220$	−8.29594	+	2.55966i	−0.559312	+	0.172572i
$221$	0.648470	−	1.12318i	0.0436208	−	0.0755534i
$222$	1.82990	−	1.05649i	0.122815	−	0.0709073i
$223$		−	2.56042i		−	0.171458i	−0.996318	−	0.0857291i	$-0.972678\pi$
$223$		−	2.56042i		−	0.171458i	0.996318	−	0.0857291i	$-0.0273220\pi$
$224$	−0.136452	−	0.236341i	−0.00911706	−	0.0157912i
$225$	−12.6592	−	6.09395i	−0.843946	−	0.406263i
$226$	−1.03908			−0.0691185
$227$	−21.8083	−	12.5910i	−1.44746	−	0.835694i	−0.449135	−	0.893464i	$-0.648268\pi$
$227$	−21.8083	−	12.5910i	−1.44746	−	0.835694i	−0.998330	+	0.0577702i	$0.981601\pi$
$228$	2.76953	−	1.59899i	0.183417	−	0.105896i
$229$	1.73608	+	3.00697i	0.114723	+	0.198706i	0.917669	−	0.397346i	$-0.130069\pi$
$229$	1.73608	+	3.00697i	0.114723	+	0.198706i	−0.802946	+	0.596052i	$0.796735\pi$
$230$	−1.32913	+	5.82535i	−0.0876401	+	0.384112i
$231$	−0.461958			−0.0303946
$232$	2.64591	−	1.52762i	0.173713	−	0.100293i
$233$	23.8867	−	13.7910i	1.56487	−	0.903477i	0.568115	−	0.822949i	$-0.307673\pi$
$233$	23.8867	−	13.7910i	1.56487	−	0.903477i	0.996752	−	0.0805274i	$-0.0256604\pi$
$234$	0.907693	−	1.57217i	0.0593377	−	0.102776i
$235$	−3.01809	−	9.78174i	−0.196879	−	0.638091i
$236$	−4.81150			−0.313202
$237$			1.18480i			0.0769611i
$238$	0.474443	+	0.273920i	0.0307536	+	0.0177556i
$239$	6.71189	−	11.6253i	0.434156	−	0.751981i	−0.563070	−	0.826409i	$-0.690380\pi$
$239$	6.71189	−	11.6253i	0.434156	−	0.751981i	0.997226	+	0.0744284i	$0.0237132\pi$
$240$	−0.950456	−	0.216858i	−0.0613517	−	0.0139982i
$241$	5.21343	+	9.02993i	0.335827	+	0.581669i	0.983643	−	0.180127i	$-0.0576510\pi$
$241$	5.21343	+	9.02993i	0.335827	+	0.581669i	−0.647816	+	0.761796i	$0.724318\pi$
$242$		−	4.07490i		−	0.261944i
$243$	9.34681	−	5.39639i	0.599598	−	0.346178i
$244$	−3.10578	−	5.37937i	−0.198827	−	0.344379i
$245$	−3.44478	+	15.0979i	−0.220079	+	0.964572i
$246$	0.591352	−	1.02425i	0.0377032	−	0.0653039i
$247$			4.73897i			0.301533i
$248$	−0.417418	−	0.240996i	−0.0265061	−	0.0153033i
$249$	−2.33834	−	4.05013i	−0.148186	−	0.256666i
$250$	−8.74275	−	6.96881i	−0.552940	−	0.440746i
$251$	3.08514	+	5.34363i	0.194733	+	0.337287i	0.946813	−	0.321785i	$-0.104283\pi$
$251$	3.08514	+	5.34363i	0.194733	+	0.337287i	−0.752080	+	0.659072i	$0.770949\pi$
$252$	0.664100	+	0.383418i	0.0418344	+	0.0241531i
$253$	−8.98494	−	5.18745i	−0.564878	−	0.326132i
$254$	17.2962			1.08526
$255$	1.87004	−	0.576988i	0.117106	−	0.0361324i
$256$	1.00000			0.0625000
$257$		−	0.713069i		−	0.0444800i	−0.999753	−	0.0222400i	$-0.992920\pi$
$257$		−	0.713069i		−	0.0444800i	0.999753	−	0.0222400i	$-0.00707980\pi$
$258$	−2.77600	+	0.683513i	−0.172826	+	0.0425537i
$259$	−1.32263			−0.0821843
$260$	0.982524	−	1.05907i	0.0609335	−	0.0656809i
$261$	−4.29249	+	7.43481i	−0.265698	+	0.460203i
$262$			4.30253i			0.265811i
$263$	1.61737	+	0.933791i	0.0997316	+	0.0575800i	0.549036	−	0.835799i	$-0.314995\pi$
$263$	1.61737	+	0.933791i	0.0997316	+	0.0575800i	−0.449305	+	0.893379i	$0.648328\pi$
$264$	0.846377	−	1.46597i	0.0520909	−	0.0902241i
$265$	0.105501	+	0.0240713i	0.00648085	+	0.00147869i
$266$	−2.00179			−0.122737
$267$	0.0610136	−	0.0352262i	0.00373397	−	0.00215581i
$268$	−8.80656	−	5.08447i	−0.537946	−	0.310584i
$269$	7.98593			0.486911			0.243455	−	0.969912i	$-0.421719\pi$
$269$	7.98593			0.486911			0.243455	+	0.969912i	$0.421719\pi$
$270$	5.41222	−	1.66991i	0.329377	−	0.101627i
$271$	−12.9016	−	22.3462i	−0.783716	−	1.35744i	−0.929763	−	0.368158i	$-0.879988\pi$
$271$	−12.9016	−	22.3462i	−0.783716	−	1.35744i	0.146047	−	0.989278i	$-0.453345\pi$
$272$	−1.73850	+	1.00373i	−0.105412	+	0.0608598i
$273$	0.0665704	−	0.0384344i	0.00402902	−	0.00232616i
$274$	−15.2222			−0.919605
$275$	16.0383	−	10.9383i	0.967143	−	0.659605i
$276$	−0.582497	−	1.00892i	−0.0350622	−	0.0607295i
$277$	−25.3868	−	14.6571i	−1.52535	−	0.880659i	−0.999548	−	0.0300494i	$-0.990434\pi$
$277$	−25.3868	−	14.6571i	−1.52535	−	0.880659i	−0.525798	−	0.850610i	$-0.676233\pi$
$278$	10.5979	+	6.11869i	0.635618	+	0.366974i
$279$	1.35436			0.0810835
$280$	0.447362	+	0.415027i	0.0267350	+	0.0248026i
$281$	2.98500	−	5.17017i	0.178070	−	0.308427i	−0.763149	−	0.646222i	$-0.776348\pi$
$281$	2.98500	−	5.17017i	0.178070	−	0.308427i	0.941219	+	0.337796i	$0.109681\pi$
$282$	1.72852	+	0.997964i	0.102932	+	0.0594279i
$283$	−18.5760	+	10.7249i	−1.10423	+	0.637527i	−0.937328	−	0.348447i	$-0.886709\pi$
$283$	−18.5760	+	10.7249i	−1.10423	+	0.637527i	−0.166900	+	0.985974i	$0.553376\pi$
$284$	−5.77106	−	9.99577i	−0.342449	−	0.593140i
$285$	−4.86344	+	5.24236i	−0.288086	+	0.310530i
$286$	1.25421	+	2.17236i	0.0741633	+	0.128455i
$287$	−0.641134	+	0.370159i	−0.0378449	+	0.0218498i
$288$	−2.43346	+	1.40496i	−0.143393	+	0.0827881i
$289$	−6.48507	+	11.2325i	−0.381475	+	0.660734i
$290$	−4.64636	+	5.00836i	−0.272844	+	0.294101i
$291$	2.86776	−	4.96711i	0.168111	−	0.291177i
$292$	5.41208	−	3.12466i	0.316718	−	0.182857i
$293$		−	23.8913i		−	1.39574i	−0.716223	−	0.697871i	$-0.754131\pi$
$293$		−	23.8913i		−	1.39574i	0.716223	−	0.697871i	$-0.245869\pi$
$294$	−1.50970	−	2.61487i	−0.0880473	−	0.152502i
$295$	10.2806	−	3.17202i	0.598561	−	0.184682i
$296$	2.42326	−	4.19721i	0.140849	−	0.243958i
$297$			9.83477i			0.570671i
$298$	13.8965	+	8.02312i	0.805000	+	0.464767i
$299$	1.72636			0.0998381
$300$	2.17378	−	0.163239i	0.125503	−	0.00942459i
$301$	1.71877	+	0.498298i	0.0990683	+	0.0287214i
$302$		−	11.1579i		−	0.642066i
$303$		−	7.08296i		−	0.406905i
$304$	3.66757	−	6.35242i	0.210350	−	0.364337i
$305$	10.1824	+	9.44646i	0.583044	+	0.540902i
$306$	2.82039	−	4.88506i	0.161231	−	0.279260i
$307$	9.29436	+	5.36610i	0.530457	+	0.306260i	0.741203	−	0.671281i	$-0.234256\pi$
$307$	9.29436	+	5.36610i	0.530457	+	0.306260i	−0.210745	+	0.977541i	$0.567589\pi$
$308$	−0.917628	+	0.529793i	−0.0522867	+	0.0301877i
$309$	−0.711837			−0.0404950
$310$	1.05076	+	0.239745i	0.0596794	+	0.0136166i
$311$	1.49946	−	2.59714i	0.0850266	−	0.147270i	−0.820376	−	0.571825i	$-0.806236\pi$
$311$	1.49946	−	2.59714i	0.0850266	−	0.147270i	0.905403	+	0.424554i	$0.139569\pi$
$312$			0.281671i			0.0159465i
$313$	26.4058	+	15.2454i	1.49254	+	0.861720i	0.999963	−	0.00854797i	$-0.00272094\pi$
$313$	26.4058	+	15.2454i	1.49254	+	0.861720i	0.492579	+	0.870268i	$0.336054\pi$
$314$	7.06210	+	12.2319i	0.398537	+	0.690287i
$315$	−1.67174	−	0.381428i	−0.0941917	−	0.0214910i
$316$	1.35878	+	2.35347i	0.0764373	+	0.132393i
$317$			10.3359i			0.580520i	0.956948	+	0.290260i	$0.0937418\pi$
$317$			10.3359i			0.580520i	−0.956948	+	0.290260i	$0.906258\pi$
$318$	−0.0182721	+	0.0105494i	−0.00102465	+	0.000591580i
$319$	−5.93120	−	10.2731i	−0.332083	−	0.575185i
$320$	−2.13668	+	0.659257i	−0.119444	+	0.0368536i
$321$	−2.64284	+	4.57753i	−0.147509	+	0.255493i
$322$			0.729232i			0.0406385i
$323$			14.7250i			0.819318i
$324$	3.66271	−	6.34400i	0.203484	−	0.352444i
$325$	−1.40113	+	2.91063i	−0.0777209	+	0.161453i
$326$	4.05266	+	7.01941i	0.224456	+	0.388769i
$327$	−1.72996	+	0.998794i	−0.0956671	+	0.0552335i
$328$		−	2.71275i		−	0.149786i
$329$	−0.624678	−	1.08197i	−0.0344396	−	0.0596512i
$330$	−0.841983	+	3.69028i	−0.0463497	+	0.203143i
$331$	4.24243	+	7.34810i	0.233185	+	0.403888i	0.958744	−	0.284272i	$-0.0917519\pi$
$331$	4.24243	+	7.34810i	0.233185	+	0.403888i	−0.725559	+	0.688160i	$0.758419\pi$
$332$	−9.28970	−	5.36341i	−0.509839	−	0.294355i
$333$			13.6184i			0.746281i
$334$	−7.43118	+	12.8712i	−0.406616	+	0.704280i
$335$	22.1687	+	5.05807i	1.21121	+	0.276352i
$336$	−0.118980			−0.00649091
$337$	17.9905	−	10.3868i	0.980005	−	0.565806i	0.0777337	−	0.996974i	$-0.475232\pi$
$337$	17.9905	−	10.3868i	0.980005	−	0.565806i	0.902272	+	0.431168i	$0.141898\pi$
$338$	10.8969	+	6.29130i	0.592711	+	0.342202i
$339$	−0.226509	+	0.392325i	−0.0123023	+	0.0213082i
$340$	3.05290	−	3.29076i	0.165567	−	0.178466i
$341$	−0.935702	+	1.62068i	−0.0506711	+	0.0877649i
$342$			20.6112i			1.11453i
$343$			3.80032i			0.205198i
$344$	−4.73034	+	4.54136i	−0.255043	+	0.244854i
$345$	1.90974	+	1.77171i	0.102817	+	0.0953856i
$346$	−23.6777			−1.27292
$347$	28.0470	+	16.1930i	1.50564	+	0.869284i	0.999979	+	0.00655467i	$0.00208643\pi$
$347$	28.0470	+	16.1930i	1.50564	+	0.869284i	0.505666	+	0.862729i	$0.331247\pi$
$348$		−	1.33202i		−	0.0714040i
$349$	−18.1847	+	31.4968i	−0.973403	+	1.68598i	−0.288295	+	0.957542i	$0.593088\pi$
$349$	−18.1847	+	31.4968i	−0.973403	+	1.68598i	−0.685108	+	0.728441i	$0.740245\pi$
$350$	−1.22948	−	0.591852i	−0.0657183	−	0.0316358i
$351$	−0.818242	−	1.41724i	−0.0436745	−	0.0756465i
$352$		−	3.88264i		−	0.206945i
$353$	−13.0119	+	7.51240i	−0.692552	+	0.399845i	−0.804567	−	0.593862i	$-0.797603\pi$
$353$	−13.0119	+	7.51240i	−0.692552	+	0.399845i	0.112016	+	0.993706i	$0.464269\pi$
$354$	−1.04886	+	1.81668i	−0.0557463	+	0.0965554i
$355$	18.9207	+	17.5531i	1.00420	+	0.931622i
$356$	0.0807978	−	0.139946i	0.00428227	−	0.00741711i
$357$	0.206848	−	0.119424i	0.0109476	−	0.00632057i
$358$	−1.17025	+	0.675645i	−0.0618497	+	0.0357090i
$359$	−2.64915	−	4.58847i	−0.139817	−	0.242170i	0.787610	−	0.616174i	$-0.211318\pi$
$359$	−2.64915	−	4.58847i	−0.139817	−	0.242170i	−0.927427	+	0.374004i	$0.877985\pi$
$360$	4.27329	−	4.60622i	0.225222	−	0.242769i
$361$	−17.4022	−	30.1415i	−0.915905	−	1.58639i
$362$	−4.95925	+	2.86323i	−0.260653	+	0.150488i
$363$	−1.53856	−	0.888288i	−0.0807534	−	0.0466230i
$364$	0.0881563	−	0.152691i	0.00462065	−	0.00800319i
$365$	−9.50389	+	10.2443i	−0.497456	+	0.536213i
$366$	−2.70812			−0.141556
$367$	22.0432	+	12.7267i	1.15065	+	0.664326i	0.949045	−	0.315141i	$-0.102052\pi$
$367$	22.0432	+	12.7267i	1.15065	+	0.664326i	0.201602	+	0.979467i	$0.435385\pi$
$368$	−2.31413	−	1.33606i	−0.120632	−	0.0696471i
$369$	3.81130	+	6.60137i	0.198409	+	0.343654i
$370$	−2.41068	+	10.5656i	−0.125325	+	0.549281i
$371$	0.0132068			0.000685665
$372$	−0.181986	+	0.105070i	−0.00943553	+	0.00544761i
$373$	30.9154	−	17.8490i	1.60074	−	0.924188i	0.609402	−	0.792862i	$-0.291410\pi$
$373$	30.9154	−	17.8490i	1.60074	−	0.924188i	0.991339	−	0.131327i	$-0.0419236\pi$
$374$	3.89711	+	6.74998i	0.201515	+	0.349033i
$375$	−4.53705	+	1.78187i	−0.234292	+	0.0920153i
$376$	4.57802			0.236093
$377$	1.70943	+	0.986938i	0.0880399	+	0.0508299i
$378$	0.598655	−	0.345633i	0.0307915	−	0.0177775i
$379$	−26.1992			−1.34576			−0.672880	−	0.739752i	$-0.734943\pi$
$379$	−26.1992			−1.34576			−0.672880	+	0.739752i	$0.734943\pi$
$380$	−3.64853	+	15.9909i	−0.187166	+	0.820318i
$381$	3.77040	−	6.53053i	0.193164	−	0.334569i
$382$	−1.81689	−	1.04898i	−0.0929602	−	0.0536706i
$383$			1.66502i			0.0850787i	0.999095	+	0.0425394i	$0.0135448\pi$
$383$			1.66502i			0.0850787i	−0.999095	+	0.0425394i	$0.986455\pi$
$384$	0.217990	−	0.377570i	0.0111243	−	0.0192678i
$385$	1.61140	−	1.73695i	0.0821247	−	0.0885230i
$386$	−1.77027			−0.0901041
$387$	5.13067	−	17.6972i	0.260807	−	0.899597i
$388$		−	13.1555i		−	0.667868i
$389$	−22.8797			−1.16005			−0.580024	−	0.814599i	$-0.696957\pi$
$389$	−22.8797			−1.16005			−0.580024	+	0.814599i	$0.696957\pi$
$390$	−0.185693	−	0.601839i	−0.00940295	−	0.0304753i
$391$	5.36416			0.271277
$392$	−5.99768	−	3.46276i	−0.302929	−	0.174896i
$393$	1.62451	+	0.937909i	0.0819455	+	0.0473113i
$394$	11.9022	+	20.6151i	0.599622	+	1.03858i
$395$	−4.45481	−	4.13282i	−0.224146	−	0.207945i
$396$	5.45496	+	9.44826i	0.274122	+	0.474793i
$397$	−6.11251	−	3.52906i	−0.306778	−	0.177118i	0.338706	−	0.940892i	$-0.390011\pi$
$397$	−6.11251	−	3.52906i	−0.306778	−	0.177118i	−0.645484	+	0.763774i	$0.723344\pi$
$398$		−	4.95598i		−	0.248421i
$399$	−0.436369	+	0.755814i	−0.0218458	+	0.0378380i
$400$	4.13076	−	2.81724i	0.206538	−	0.140862i
$401$	−17.3819	−	30.1063i	−0.868011	−	1.50344i	−0.864026	−	0.503446i	$-0.832065\pi$
$401$	−17.3819	−	30.1063i	−0.868011	−	1.50344i	−0.00398424	−	0.999992i	$-0.501268\pi$
$402$	−3.83949	+	2.21673i	−0.191496	+	0.110560i
$403$		−	0.311397i		−	0.0155118i
$404$	−8.12302	−	14.0695i	−0.404135	−	0.699983i
$405$	−3.64370	+	15.9697i	−0.181057	+	0.793542i
$406$	−0.416892	+	0.722078i	−0.0206900	+	0.0358361i
$407$	−16.2963	−	9.40866i	−0.807776	−	0.466370i
$408$			0.875209i			0.0433293i
$409$	20.2355			1.00058			0.500291	−	0.865857i	$-0.333226\pi$
$409$	20.2355			1.00058			0.500291	+	0.865857i	$0.333226\pi$
$410$	1.78840	+	5.79626i	0.0883227	+	0.286257i
$411$	−3.31828	+	5.74743i	−0.163679	+	0.283500i
$412$	−1.41398	+	0.816364i	−0.0696620	+	0.0402194i
$413$	1.13716	−	0.656537i	0.0559558	−	0.0323061i
$414$	7.50847			0.369021
$415$	23.3849	+	5.33557i	1.14792	+	0.261913i
$416$	0.323031	+	0.559507i	0.0158379	+	0.0274321i
$417$	4.62046	−	2.66763i	0.226265	−	0.130634i
$418$	−24.6642	−	14.2399i	−1.20636	−	0.696495i
$419$	35.0160			1.71064			0.855321	−	0.518098i	$-0.173360\pi$
$419$	35.0160			1.71064			0.855321	+	0.518098i	$0.173360\pi$
$420$	0.254222	−	0.0784387i	0.0124048	−	0.00382742i
$421$	−8.72026	−	15.1039i	−0.425000	−	0.736121i	0.571421	−	0.820657i	$-0.306392\pi$
$421$	−8.72026	−	15.1039i	−0.425000	−	0.736121i	−0.996420	+	0.0845364i	$0.973059\pi$
$422$		−	15.6556i		−	0.762101i
$423$	−11.1404	+	6.43194i	−0.541667	+	0.312732i
$424$	−0.0241969	+	0.0419103i	−0.00117511	+	0.00203534i
$425$	−4.35361	+	9.04392i	−0.211181	+	0.438695i
$426$	−5.03214			−0.243808
$427$	1.46805	+	0.847577i	0.0710438	+	0.0410171i
$428$			12.1237i			0.586019i
$429$	1.09363			0.0528008
$430$	7.11327	−	12.8219i	0.343032	−	0.618327i
$431$	−25.4038			−1.22366			−0.611828	−	0.790991i	$-0.709566\pi$
$431$	−25.4038			−1.22366			−0.611828	+	0.790991i	$0.709566\pi$
$432$			2.53301i			0.121870i
$433$	21.1819	+	12.2294i	1.01794	+	0.587705i	0.913505	−	0.406827i	$-0.133365\pi$
$433$	21.1819	+	12.2294i	1.01794	+	0.587705i	0.104430	+	0.994532i	$0.466698\pi$
$434$	0.131537			0.00631399
$435$	0.878146	+	2.84610i	0.0421039	+	0.136460i
$436$	−2.29092	+	3.96798i	−0.109715	+	0.190032i
$437$	−16.9745	+	9.80022i	−0.812000	+	0.468808i
$438$		−	2.72458i		−	0.130186i
$439$	15.1442	+	26.2305i	0.722794	+	1.25192i	0.959876	+	0.280426i	$0.0904757\pi$
$439$	15.1442	+	26.2305i	0.722794	+	1.25192i	−0.237082	+	0.971490i	$0.576191\pi$
$440$	2.55966	+	8.29594i	0.122027	+	0.395493i
$441$	19.4602			0.926675
$442$	−1.12318	−	0.648470i	−0.0534243	−	0.0308446i
$443$	−23.5873	+	13.6182i	−1.12067	+	0.647018i	−0.941572	−	0.336813i	$-0.890651\pi$
$443$	−23.5873	+	13.6182i	−1.12067	+	0.647018i	−0.179097	+	0.983831i	$0.557318\pi$
$444$	−1.05649	−	1.82990i	−0.0501390	−	0.0868433i
$445$	−0.0803783	+	0.352285i	−0.00381030	+	0.0166999i
$446$	−2.56042			−0.121239
$447$	6.05858	−	3.49792i	0.286561	−	0.165446i
$448$	−0.236341	+	0.136452i	−0.0111661	+	0.00644673i
$449$	6.56413	−	11.3694i	0.309780	−	0.536555i	−0.668534	−	0.743682i	$-0.733078\pi$
$449$	6.56413	−	11.3694i	0.309780	−	0.536555i	0.978314	+	0.207127i	$0.0664112\pi$
$450$	−6.09395	+	12.6592i	−0.287271	+	0.596760i
$451$	−10.5326			−0.495962
$452$			1.03908i			0.0488741i
$453$	−4.21289	−	2.43231i	−0.197939	−	0.114280i
$454$	−12.5910	+	21.8083i	−0.590925	+	1.02351i
$455$	−0.0876986	+	0.384369i	−0.00411138	+	0.0180195i
$456$	−1.59899	−	2.76953i	−0.0748796	−	0.129695i
$457$		−	6.24910i		−	0.292320i	−0.989261	−	0.146160i	$-0.953309\pi$
$457$		−	6.24910i		−	0.292320i	0.989261	−	0.146160i	$-0.0466915\pi$
$458$	3.00697	−	1.73608i	0.140507	−	0.0811215i
$459$	−2.54245	−	4.40365i	−0.118671	−	0.205545i
$460$	5.82535	+	1.32913i	0.271608	+	0.0619709i
$461$	−9.20863	+	15.9498i	−0.428889	+	0.742857i	−0.996775	−	0.0802500i	$-0.974428\pi$
$461$	−9.20863	+	15.9498i	−0.428889	+	0.742857i	0.567886	+	0.823107i	$0.307761\pi$
$462$			0.461958i			0.0214922i
$463$	−2.62966	−	1.51823i	−0.122211	−	0.0705583i	0.437649	−	0.899146i	$-0.355811\pi$
$463$	−2.62966	−	1.51823i	−0.122211	−	0.0705583i	−0.559859	+	0.828588i	$0.689145\pi$
$464$	−1.52762	−	2.64591i	−0.0709179	−	0.122833i
$465$	0.319577	−	0.344475i	0.0148200	−	0.0159746i
$466$	−13.7910	−	23.8867i	−0.638854	−	1.10653i
$467$	21.2984	+	12.2966i	0.985572	+	0.569020i	0.903948	−	0.427643i	$-0.140656\pi$
$467$	21.2984	+	12.2966i	0.985572	+	0.569020i	0.0816243	+	0.996663i	$0.473989\pi$
$468$	−1.57217	−	0.907693i	−0.0726736	−	0.0419581i
$469$	2.77514			0.128144
$470$	−9.78174	+	3.01809i	−0.451198	+	0.139214i
$471$	6.15787			0.283740
$472$			4.81150i			0.221467i
$473$	17.6325	+	18.3662i	0.810741	+	0.844479i
$474$	1.18480			0.0544197
$475$	−2.74641	−	36.5728i	−0.126014	−	1.67807i
$476$	0.273920	−	0.474443i	0.0125551	−	0.0217461i
$477$		−	0.135983i		−	0.00622623i
$478$	−11.6253	−	6.71189i	−0.531731	−	0.306995i
$479$	−0.277788	+	0.481144i	−0.0126925	+	0.0219840i	−0.872302	−	0.488968i	$-0.837374\pi$
$479$	−0.277788	+	0.481144i	−0.0126925	+	0.0219840i	0.859609	+	0.510952i	$0.170707\pi$
$480$	−0.216858	+	0.950456i	−0.00989819	+	0.0433822i
$481$	3.13116			0.142769
$482$	9.02993	−	5.21343i	0.411302	−	0.237465i
$483$	0.275336	+	0.158965i	0.0125282	+	0.00723318i
$484$	−4.07490			−0.185223
$485$	8.67284	+	28.1090i	0.393813	+	1.27636i
$486$	−5.39639	−	9.34681i	−0.244785	−	0.423980i
$487$	−3.17777	+	1.83469i	−0.143999	+	0.0831377i	−0.570268	−	0.821458i	$-0.693161\pi$
$487$	−3.17777	+	1.83469i	−0.143999	+	0.0831377i	0.426270	+	0.904596i	$0.359827\pi$
$488$	−5.37937	+	3.10578i	−0.243513	+	0.140592i
$489$	3.53376			0.159802
$490$	15.0979	+	3.44478i	0.682056	+	0.155620i
$491$	−10.1685	−	17.6123i	−0.458896	−	0.794831i	0.540007	−	0.841660i	$-0.318422\pi$
$491$	−10.1685	−	17.6123i	−0.458896	−	0.794831i	−0.998903	+	0.0468297i	$0.985088\pi$
$492$	−1.02425	−	0.591352i	−0.0461768	−	0.0266602i
$493$	5.31154	+	3.06662i	0.239220	+	0.138114i
$494$	4.73897			0.213216
$495$	−17.8843	−	16.5916i	−0.803840	−	0.745739i
$496$	−0.240996	+	0.417418i	−0.0108211	+	0.0187426i
$497$	2.72788	+	1.57494i	0.122362	+	0.0706458i
$498$	−4.05013	+	2.33834i	−0.181491	+	0.104784i
$499$	20.3994	+	35.3327i	0.913201	+	1.58171i	0.809515	+	0.587100i	$0.199730\pi$
$499$	20.3994	+	35.3327i	0.913201	+	1.58171i	0.103686	+	0.994610i	$0.466936\pi$
$500$	−6.96881	+	8.74275i	−0.311655	+	0.390988i
$501$	3.23985	+	5.61158i	0.144746	+	0.250707i
$502$	5.34363	−	3.08514i	0.238498	−	0.137697i
$503$	−32.1125	+	18.5402i	−1.43183	+	0.826665i	−0.997260	−	0.0739749i	$-0.976432\pi$
$503$	−32.1125	+	18.5402i	−1.43183	+	0.826665i	−0.434566	+	0.900640i	$0.643098\pi$
$504$	0.383418	−	0.664100i	0.0170788	−	0.0295814i
$505$	26.6317	+	24.7068i	1.18509	+	1.09944i
$506$	−5.18745	+	8.98494i	−0.230610	+	0.399429i
$507$	4.75081	−	2.74288i	0.210991	−	0.121816i
$508$		−	17.2962i		−	0.767395i
$509$	6.02012	+	10.4272i	0.266837	+	0.462176i	0.968043	−	0.250783i	$-0.0806881\pi$
$509$	6.02012	+	10.4272i	0.266837	+	0.462176i	−0.701206	+	0.712959i	$0.747355\pi$
$510$	−0.576988	−	1.87004i	−0.0255494	−	0.0828066i
$511$	−0.852731	+	1.47697i	−0.0377226	+	0.0653374i
$512$		−	1.00000i		−	0.0441942i
$513$	16.0908	+	9.29001i	0.710425	+	0.410164i
$514$	−0.713069			−0.0314521
$515$	2.48303	−	2.67648i	0.109415	−	0.117940i
$516$	0.683513	+	2.77600i	0.0300900	+	0.122207i
$517$		−	17.7748i		−	0.781735i
$518$			1.32263i			0.0581131i
$519$	−5.16150	+	8.93998i	−0.226565	+	0.392422i
$520$	−1.05907	−	0.982524i	−0.0464434	−	0.0430865i
$521$	10.0503	−	17.4076i	0.440312	−	0.762643i	−0.557400	−	0.830244i	$-0.688201\pi$
$521$	10.0503	−	17.4076i	0.440312	−	0.762643i	0.997712	+	0.0676010i	$0.0215345\pi$
$522$	7.43481	+	4.29249i	0.325413	+	0.187877i
$523$	−24.4409	+	14.1110i	−1.06873	+	0.617030i	−0.927833	−	0.372995i	$-0.878331\pi$
$523$	−24.4409	+	14.1110i	−1.06873	+	0.617030i	−0.140893	+	0.990025i	$0.544997\pi$
$524$	4.30253			0.187957
$525$	−0.491480	+	0.335196i	−0.0214499	+	0.0146291i
$526$	0.933791	−	1.61737i	0.0407152	−	0.0705209i
$527$		−	0.967576i		−	0.0421483i
$528$	−1.46597	−	0.846377i	−0.0637981	−	0.0368338i
$529$	−7.92987	−	13.7349i	−0.344777	−	0.597171i
$530$	0.0240713	−	0.105501i	0.00104559	−	0.00458266i
$531$	−6.75997	−	11.7086i	−0.293358	−	0.508111i
$532$			2.00179i			0.0867884i
$533$	1.51780	−	0.876303i	0.0657432	−	0.0379569i
$534$	−0.0352262	−	0.0610136i	−0.00152439	−	0.00264032i
$535$	−7.99260	−	25.9043i	−0.345550	−	1.11994i
$536$	−5.08447	+	8.80656i	−0.219616	+	0.380386i
$537$			0.589136i			0.0254231i
$538$		−	7.98593i		−	0.344298i
$539$	−13.4447	+	23.2868i	−0.579103	+	1.00303i
$540$	−1.66991	−	5.41222i	−0.0718613	−	0.232905i
$541$	−14.1846	−	24.5684i	−0.609842	−	1.05628i	−0.991266	−	0.131878i	$-0.957899\pi$
$541$	−14.1846	−	24.5684i	−0.609842	−	1.05628i	0.381424	−	0.924400i	$-0.375434\pi$
$542$	−22.3462	+	12.9016i	−0.959852	+	0.554171i
$543$			2.49662i			0.107140i
$544$	1.00373	+	1.73850i	0.0430344	+	0.0745377i
$545$	2.27902	−	9.98859i	0.0976226	−	0.427864i
$546$	−0.0384344	−	0.0665704i	−0.00164484	−	0.00284895i
$547$	1.89925	+	1.09654i	0.0812063	+	0.0468845i	0.540053	−	0.841631i	$-0.318404\pi$
$547$	1.89925	+	1.09654i	0.0812063	+	0.0468845i	−0.458847	+	0.888515i	$0.651737\pi$
$548$			15.2222i			0.650259i
$549$	8.72700	−	15.1156i	0.372459	−	0.645118i
$550$	−10.9383	−	16.0383i	−0.466411	−	0.683874i
$551$	−22.4106			−0.954725
$552$	−1.00892	+	0.582497i	−0.0429423	+	0.0247927i
$553$	−0.642270	−	0.370815i	−0.0273121	−	0.0157687i
$554$	−14.6571	+	25.3868i	−0.622720	+	1.07858i
$555$	3.46376	+	3.21340i	0.147028	+	0.136401i
$556$	6.11869	−	10.5979i	0.259490	−	0.449450i
$557$			9.65713i			0.409186i	0.978847	+	0.204593i	$0.0655870\pi$
$557$			9.65713i			0.409186i	−0.978847	+	0.204593i	$0.934413\pi$
$558$		−	1.35436i		−	0.0573347i
$559$	−4.06897	−	1.17965i	−0.172099	−	0.0498941i
$560$	0.415027	−	0.447362i	0.0175381	−	0.0189045i
$561$	3.39812			0.143469
$562$	−5.17017	−	2.98500i	−0.218091	−	0.125915i
$563$		−	21.4161i		−	0.902581i	−0.892377	−	0.451291i	$-0.850964\pi$
$563$		−	21.4161i		−	0.902581i	0.892377	−	0.451291i	$-0.149036\pi$
$564$	0.997964	−	1.72852i	0.0420218	−	0.0727840i
$565$	−0.685020	−	2.22017i	−0.0288190	−	0.0934034i
$566$	10.7249	+	18.5760i	0.450799	+	0.780807i
$567$			1.99913i			0.0839556i
$568$	−9.99577	+	5.77106i	−0.419413	+	0.242148i
$569$	15.9189	−	27.5723i	0.667353	−	1.15589i	−0.311289	−	0.950315i	$-0.600761\pi$
$569$	15.9189	−	27.5723i	0.667353	−	1.15589i	0.978642	−	0.205574i	$-0.0659061\pi$
$570$	5.24236	+	4.86344i	0.219578	+	0.203707i
$571$	12.6945	−	21.9876i	0.531249	−	0.920151i	−0.468085	−	0.883683i	$-0.655056\pi$
$571$	12.6945	−	21.9876i	0.531249	−	0.920151i	0.999335	−	0.0364678i	$-0.0116106\pi$
$572$	2.17236	−	1.25421i	0.0908311	−	0.0524414i
$573$	−0.792128	+	0.457335i	−0.0330916	+	0.0191055i
$574$	0.370159	+	0.641134i	0.0154501	+	0.0267604i
$575$	−13.3231	+	1.00049i	−0.555613	+	0.0417234i
$576$	1.40496	+	2.43346i	0.0585400	+	0.101394i
$577$	8.73558	−	5.04349i	0.363667	−	0.209963i	−0.307021	−	0.951703i	$-0.599332\pi$
$577$	8.73558	−	5.04349i	0.363667	−	0.209963i	0.670688	+	0.741739i	$0.265999\pi$
$578$	11.2325	+	6.48507i	0.467209	+	0.269743i
$579$	−0.385900	+	0.668399i	−0.0160375	+	0.0277777i
$580$	5.00836	+	4.64636i	0.207961	+	0.192930i
$581$	2.92738			0.121448
$582$	−4.96711	−	2.86776i	−0.205893	−	0.118873i
$583$	0.162723	+	0.0939479i	0.00673928	+	0.00389093i
$584$	−3.12466	−	5.41208i	−0.129299	−	0.223953i
$585$	3.95762	+	0.902980i	0.163627	+	0.0373336i
$586$	−23.8913			−0.986939
$587$	−8.25030	+	4.76331i	−0.340526	+	0.196603i	−0.660505	−	0.750822i	$-0.729658\pi$
$587$	−8.25030	+	4.76331i	−0.340526	+	0.196603i	0.319979	+	0.947425i	$0.396324\pi$
$588$	−2.61487	+	1.50970i	−0.107835	+	0.0622588i
$589$	1.76774	+	3.06182i	0.0728386	+	0.126160i
$590$	−3.17202	−	10.2806i	−0.130590	−	0.423246i
$591$	10.3782			0.426903
$592$	−4.19721	−	2.42326i	−0.172504	−	0.0995955i
$593$	−4.18280	+	2.41494i	−0.171767	+	0.0991696i	−0.583419	−	0.812172i	$-0.698285\pi$
$593$	−4.18280	+	2.41494i	−0.171767	+	0.0991696i	0.411652	+	0.911341i	$0.364952\pi$
$594$	9.83477			0.403526
$595$	−0.272498	+	1.19431i	−0.0111713	+	0.0489621i
$596$	8.02312	−	13.8965i	0.328640	−	0.569221i
$597$	−1.87123	−	1.08036i	−0.0765844	−	0.0442160i
$598$		−	1.72636i		−	0.0705962i
$599$	3.46579	−	6.00293i	0.141608	−	0.245273i	−0.786494	−	0.617598i	$-0.788106\pi$
$599$	3.46579	−	6.00293i	0.141608	−	0.245273i	0.928102	+	0.372325i	$0.121439\pi$
$600$	−0.163239	−	2.17378i	−0.00666419	−	0.0887442i
$601$	38.5023			1.57054			0.785271	−	0.619152i	$-0.212523\pi$
$601$	38.5023			1.57054			0.785271	+	0.619152i	$0.212523\pi$
$602$	0.498298	−	1.71877i	0.0203091	−	0.0700519i
$603$		−	28.5739i		−	1.16362i
$604$	−11.1579			−0.454009
$605$	8.70673	−	2.68641i	0.353979	−	0.109218i
$606$	−7.08296			−0.287725
$607$	−7.25720	−	4.18995i	−0.294561	−	0.170065i	0.345436	−	0.938442i	$-0.387731\pi$
$607$	−7.25720	−	4.18995i	−0.294561	−	0.170065i	−0.639997	+	0.768378i	$0.721064\pi$
$608$	−6.35242	−	3.66757i	−0.257625	−	0.148740i
$609$	0.181757	+	0.314812i	0.00736515	+	0.0127568i
$610$	9.44646	−	10.1824i	0.382476	−	0.412274i
$611$	1.47884	+	2.56143i	0.0598277	+	0.103625i
$612$	−4.88506	−	2.82039i	−0.197467	−	0.114007i
$613$		−	9.49456i		−	0.383482i	−0.981446	−	0.191741i	$-0.938587\pi$
$613$		−	9.49456i		−	0.383482i	0.981446	−	0.191741i	$-0.0614133\pi$
$614$	5.36610	−	9.29436i	0.216558	−	0.375090i
$615$	2.57835	+	0.588282i	0.103969	+	0.0237218i
$616$	0.529793	+	0.917628i	0.0213459	+	0.0369723i
$617$	8.46440	−	4.88692i	0.340764	−	0.196740i	−0.319846	−	0.947470i	$-0.603631\pi$
$617$	8.46440	−	4.88692i	0.340764	−	0.196740i	0.660610	+	0.750729i	$0.270298\pi$
$618$			0.711837i			0.0286343i
$619$	−1.27842	−	2.21429i	−0.0513842	−	0.0890000i	0.839189	−	0.543839i	$-0.183030\pi$
$619$	−1.27842	−	2.21429i	−0.0513842	−	0.0890000i	−0.890573	+	0.454839i	$0.849697\pi$
$620$	0.239745	−	1.05076i	0.00962839	−	0.0421997i
$621$	3.38426	−	5.86172i	0.135806	−	0.235223i
$622$	−2.59714	−	1.49946i	−0.104136	−	0.0601229i
$623$			0.0440999i			0.00176683i
$624$	0.281671			0.0112759
$625$	9.12636	−	23.2747i	0.365055	−	0.930986i
$626$	15.2454	−	26.4058i	0.609328	−	1.05539i
$627$	−10.7531	+	6.20830i	−0.429437	+	0.247936i
$628$	12.2319	−	7.06210i	0.488106	−	0.281808i
$629$	9.72916			0.387927
$630$	−0.381428	+	1.67174i	−0.0151964	+	0.0666036i
$631$	0.737797	+	1.27790i	0.0293712	+	0.0508725i	0.880337	−	0.474348i	$-0.157316\pi$
$631$	0.737797	+	1.27790i	0.0293712	+	0.0508725i	−0.850966	+	0.525221i	$0.823983\pi$
$632$	2.35347	−	1.35878i	0.0936162	−	0.0540493i
$633$	−5.91107	−	3.41276i	−0.234944	−	0.135645i
$634$	10.3359			0.410490
$635$	11.4026	+	36.9564i	0.452500	+	1.46657i
$636$	0.0105494	+	0.0182721i	0.000418310	+	0.000724534i
$637$		−	4.47432i		−	0.177279i
$638$	−10.2731	+	5.93120i	−0.406717	+	0.234818i
$639$	16.2162	−	28.0873i	0.641504	−	1.11112i
$640$	0.659257	+	2.13668i	0.0260594	+	0.0844595i
$641$	−1.05696			−0.0417475			−0.0208738	−	0.999782i	$-0.506645\pi$
$641$	−1.05696			−0.0417475			−0.0208738	+	0.999782i	$0.506645\pi$
$642$	4.57753	+	2.64284i	0.180661	+	0.104304i
$643$			1.48883i			0.0587138i	0.999569	+	0.0293569i	$0.00934594\pi$
$643$			1.48883i			0.0587138i	−0.999569	+	0.0293569i	$0.990654\pi$
$644$	0.729232			0.0287358
$645$	−3.29055	−	5.48081i	−0.129565	−	0.215807i
$646$	14.7250			0.579345
$647$		−	35.0629i		−	1.37847i	−0.724539	−	0.689233i	$-0.757947\pi$
$647$		−	35.0629i		−	1.37847i	0.724539	−	0.689233i	$-0.242053\pi$
$648$	−6.34400	−	3.66271i	−0.249216	−	0.143885i
$649$	18.6813			0.733307
$650$	2.91063	+	1.40113i	0.114164	+	0.0549570i
$651$	0.0286738	−	0.0496645i	0.00112382	−	0.00194651i
$652$	7.01941	−	4.05266i	0.274901	−	0.158714i
$653$		−	28.9341i		−	1.13228i	−0.824309	−	0.566140i	$-0.808436\pi$
$653$		−	28.9341i		−	1.13228i	0.824309	−	0.566140i	$-0.191564\pi$
$654$	0.998794	+	1.72996i	0.0390559	+	0.0676469i
$655$	−9.19311	+	2.83647i	−0.359204	+	0.110830i
$656$	−2.71275			−0.105915
$657$	15.2075	+	8.78006i	0.593301	+	0.342543i
$658$	−1.08197	+	0.624678i	−0.0421798	+	0.0243525i
$659$	−18.8902	−	32.7188i	−0.735858	−	1.27454i	−0.954346	−	0.298703i	$-0.903446\pi$
$659$	−18.8902	−	32.7188i	−0.735858	−	1.27454i	0.218488	−	0.975840i	$-0.429887\pi$
$660$	3.69028	+	0.841983i	0.143644	+	0.0327742i
$661$	−46.3558			−1.80303			−0.901515	−	0.432747i	$-0.857544\pi$
$661$	−46.3558			−1.80303			−0.901515	+	0.432747i	$0.857544\pi$
$662$	7.34810	−	4.24243i	0.285592	−	0.164887i
$663$	−0.489685	+	0.282720i	−0.0190178	+	0.0109799i
$664$	−5.36341	+	9.28970i	−0.208141	+	0.360510i
$665$	−1.31969	−	4.27716i	−0.0511754	−	0.165861i
$666$	13.6184			0.527700
$667$			8.16398i			0.316111i
$668$	12.8712	+	7.43118i	0.498001	+	0.287521i
$669$	−0.558146	+	0.966737i	−0.0215792	+	0.0373762i
$670$	5.05807	−	22.1687i	0.195410	−	0.856453i
$671$	12.0586	+	20.8862i	0.465518	+	0.806301i
$672$			0.118980i			0.00458977i
$673$	−28.5490	+	16.4828i	−1.10048	+	0.635365i	−0.936348	−	0.351073i	$-0.885817\pi$
$673$	−28.5490	+	16.4828i	−1.10048	+	0.635365i	−0.164136	+	0.986438i	$0.552484\pi$
$674$	−10.3868	−	17.9905i	−0.400086	−	0.692969i
$675$	7.13609	+	10.4633i	0.274668	+	0.402731i
$676$	6.29130	−	10.8969i	0.241973	−	0.419110i
$677$		−	6.62909i		−	0.254777i	−0.991853	−	0.127388i	$-0.959341\pi$
$677$		−	6.62909i		−	0.254777i	0.991853	−	0.127388i	$-0.0406594\pi$
$678$	0.392325	+	0.226509i	0.0150671	+	0.00869902i
$679$	1.79509	+	3.10918i	0.0688891	+	0.119319i
$680$	−3.29076	−	3.05290i	−0.126195	−	0.117074i
$681$	5.48943	+	9.50797i	0.210355	+	0.364346i
$682$	1.62068	+	0.935702i	0.0620592	+	0.0358299i
$683$	−31.7037	−	18.3042i	−1.21311	−	0.700389i	−0.249674	−	0.968330i	$-0.580324\pi$
$683$	−31.7037	−	18.3042i	−1.21311	−	0.700389i	−0.963435	+	0.267941i	$0.913657\pi$
$684$	20.6112			0.788088
$685$	−10.0353	−	32.5248i	−0.383430	−	1.24271i
$686$	3.80032			0.145097
$687$		−	1.51379i		−	0.0577547i
$688$	4.54136	+	4.73034i	0.173138	+	0.180342i
$689$	−0.0312655			−0.00119112
$690$	1.77171	−	1.90974i	0.0674478	−	0.0727026i
$691$	15.2759	−	26.4586i	0.581123	−	1.00653i	−0.414224	−	0.910175i	$-0.635947\pi$
$691$	15.2759	−	26.4586i	0.581123	−	1.00653i	0.995347	−	0.0963591i	$-0.0307197\pi$
$692$			23.6777i			0.900090i
$693$	−2.57846	−	1.48868i	−0.0979476	−	0.0565501i
$694$	16.1930	−	28.0470i	0.614677	−	1.06465i
$695$	−6.08692	+	26.6780i	−0.230890	+	1.01195i
$696$	−1.33202			−0.0504902
$697$	4.71612	−	2.72285i	0.178636	−	0.103135i
$698$	31.4968	+	18.1847i	1.19217	+	0.688300i
$699$	−12.0252			−0.454834
$700$	−0.591852	+	1.22948i	−0.0223699	+	0.0464699i
$701$	−12.5858	−	21.7992i	−0.475358	−	0.823344i	0.524244	−	0.851568i	$-0.324348\pi$
$701$	−12.5858	−	21.7992i	−0.475358	−	0.823344i	−0.999602	+	0.0282242i	$0.991015\pi$
$702$	−1.41724	+	0.818242i	−0.0534902	+	0.0308826i
$703$	−30.7872	+	17.7750i	−1.16116	+	0.670396i
$704$	−3.88264			−0.146333
$705$	−0.992783	+	4.35121i	−0.0373904	+	0.163876i
$706$	7.51240	+	13.0119i	0.282733	+	0.489708i
$707$	3.83961	+	2.21680i	0.144403	+	0.0833713i
$708$	1.81668	+	1.04886i	0.0682750	+	0.0394186i
$709$	−32.8662			−1.23432			−0.617158	−	0.786839i	$-0.711716\pi$
$709$	−32.8662			−1.23432			−0.617158	+	0.786839i	$0.711716\pi$
$710$	17.5531	−	18.9207i	0.658756	−	0.710080i
$711$	−3.81806	+	6.61308i	−0.143188	+	0.248010i
$712$	−0.139946	−	0.0807978i	−0.00524469	−	0.00302802i
$713$	1.11539	−	0.643973i	0.0417718	−	0.0241170i
$714$	−0.119424	−	0.206848i	−0.00446932	−	0.00774109i
$715$	−3.81479	+	4.11200i	−0.142665	+	0.153780i
$716$	0.675645	+	1.17025i	0.0252500	+	0.0437344i
$717$	−5.06842	+	2.92625i	−0.189284	+	0.109283i
$718$	−4.58847	+	2.64915i	−0.171240	+	0.0988655i
$719$	−7.24961	+	12.5567i	−0.270365	+	0.468286i	−0.968955	−	0.247236i	$-0.920478\pi$
$719$	−7.24961	+	12.5567i	−0.270365	+	0.468286i	0.698590	+	0.715522i	$0.253811\pi$
$720$	−4.60622	−	4.27329i	−0.171664	−	0.159256i
$721$	0.222788	−	0.385881i	0.00829707	−	0.0143709i
$722$	−30.1415	+	17.4022i	−1.12175	+	0.647643i
$723$		−	4.54591i		−	0.169064i
$724$	2.86323	+	4.95925i	0.106411	+	0.184309i
$725$	−13.7644	−	6.62597i	−0.511197	−	0.246082i
$726$	−0.888288	+	1.53856i	−0.0329675	+	0.0571013i
$727$			6.06731i			0.225024i	0.993650	+	0.112512i	$0.0358897\pi$
$727$			6.06731i			0.225024i	−0.993650	+	0.112512i	$0.964110\pi$
$728$	−0.152691	−	0.0881563i	−0.00565911	−	0.00326729i
$729$	17.2708			0.639660
$730$	10.2443	+	9.50389i	0.379160	+	0.351755i
$731$	−12.6431	−	3.66543i	−0.467623	−	0.135571i
$732$			2.70812i			0.100095i
$733$		−	14.9815i		−	0.553355i	−0.960963	−	0.276677i	$-0.910767\pi$
$733$		−	14.9815i		−	0.553355i	0.960963	−	0.276677i	$-0.0892333\pi$
$734$	12.7267	−	22.0432i	0.469750	−	0.813630i
$735$	4.59185	−	4.94960i	0.169373	−	0.182569i
$736$	−1.33606	+	2.31413i	−0.0492480	+	0.0853000i
$737$	34.1927	+	19.7412i	1.25950	+	0.727176i
$738$	6.60137	−	3.81130i	0.243000	−	0.140296i
$739$	−19.8487			−0.730146			−0.365073	−	0.930979i	$-0.618956\pi$
$739$	−19.8487			−0.730146			−0.365073	+	0.930979i	$0.618956\pi$
$740$	10.5656	+	2.41068i	0.388400	+	0.0886184i
$741$	1.03305	−	1.78929i	0.0379500	−	0.0657313i
$742$		−	0.0132068i		−	0.000484838i
$743$	−10.0255	−	5.78824i	−0.367801	−	0.212350i	0.304696	−	0.952450i	$-0.401445\pi$
$743$	−10.0255	−	5.78824i	−0.367801	−	0.212350i	−0.672497	+	0.740100i	$0.734778\pi$
$744$	0.105070	+	0.181986i	0.00385204	+	0.00667193i
$745$	−7.98147	+	34.9815i	−0.292418	+	1.28162i
$746$	−17.8490	−	30.9154i	−0.653500	−	1.13189i
$747$		−	30.1415i		−	1.10282i
$748$	6.74998	−	3.89711i	0.246804	−	0.142492i
$749$	−1.65429	−	2.86532i	−0.0604465	−	0.104696i
$750$	1.78187	+	4.53705i	0.0650646	+	0.165670i
$751$	−1.70504	+	2.95322i	−0.0622180	+	0.107765i	−0.895457	−	0.445149i	$-0.853151\pi$
$751$	−1.70504	+	2.95322i	−0.0622180	+	0.107765i	0.833239	+	0.552914i	$0.186484\pi$
$752$		−	4.57802i		−	0.166943i
$753$		−	2.69012i		−	0.0980335i
$754$	0.986938	−	1.70943i	0.0359422	−	0.0622536i
$755$	23.8408	−	7.35593i	0.867657	−	0.267710i
$756$	−0.345633	−	0.598655i	−0.0125706	−	0.0217729i
$757$	−41.2558	+	23.8191i	−1.49947	+	0.865719i	−1.00000		0.000612579i	$-0.999805\pi$
$757$	−41.2558	+	23.8191i	−1.49947	+	0.865719i	−0.499469	+	0.866332i	$0.666472\pi$
$758$			26.1992i			0.951596i
$759$	2.26163	+	3.91725i	0.0820919	+	0.142187i
$760$	15.9909	+	3.64853i	0.580052	+	0.132346i
$761$	8.74476	+	15.1464i	0.316997	+	0.549056i	0.979860	−	0.199685i	$-0.0639920\pi$
$761$	8.74476	+	15.1464i	0.316997	+	0.549056i	−0.662863	+	0.748741i	$0.730659\pi$
$762$	−6.53053	−	3.77040i	−0.236576	−	0.136587i
$763$		−	1.25040i		−	0.0452674i
$764$	−1.04898	+	1.81689i	−0.0379508	+	0.0657328i
$765$	12.2971	+	2.80575i	0.444604	+	0.101442i
$766$	1.66502			0.0601597
$767$	−2.69207	+	1.55427i	−0.0972050	+	0.0561213i
$768$	−0.377570	−	0.217990i	−0.0136244	−	0.00786604i
$769$	2.47381	−	4.28476i	0.0892078	−	0.154512i	−0.817969	−	0.575263i	$-0.804900\pi$
$769$	2.47381	−	4.28476i	0.0892078	−	0.154512i	0.907177	+	0.420750i	$0.138233\pi$
$770$	−1.73695	−	1.61140i	−0.0625952	−	0.0580709i
$771$	−0.155442	+	0.269233i	−0.00559811	+	0.00969620i
$772$			1.77027i			0.0637132i
$773$			32.1714i			1.15713i	0.815638	+	0.578563i	$0.196386\pi$
$773$			32.1714i			1.15713i	−0.815638	+	0.578563i	$0.803614\pi$
$774$	−17.6972	−	5.13067i	−0.636111	−	0.184418i
$775$	0.180466	+	2.40320i	0.00648255	+	0.0863253i
$776$	−13.1555			−0.472254
$777$	0.499386	+	0.288321i	0.0179154	+	0.0103434i
$778$			22.8797i			0.820278i
$779$	−9.94920	+	17.2325i	−0.356467	+	0.617419i
$780$	−0.601839	+	0.185693i	−0.0215493	+	0.00664889i
$781$	22.4070	+	38.8100i	0.801784	+	1.38873i
$782$		−	5.36416i		−	0.191822i
$783$	6.70213	−	3.86948i	0.239515	−	0.138284i
$784$	−3.46276	+	5.99768i	−0.123670	+	0.214203i
$785$	−21.4799	+	23.1534i	−0.766650	+	0.826379i
$786$	0.937909	−	1.62451i	0.0334541	−	0.0579442i
$787$	35.1450	−	20.2910i	1.25278	−	0.723296i	0.281123	−	0.959672i	$-0.409293\pi$
$787$	35.1450	−	20.2910i	1.25278	−	0.723296i	0.971662	+	0.236376i	$0.0759598\pi$
$788$	20.6151	−	11.9022i	0.734384	−	0.423997i
$789$	−0.407115	−	0.705143i	−0.0144937	−	0.0251038i
$790$	−4.13282	+	4.45481i	−0.147039	+	0.158495i
$791$	−0.141784	−	0.245577i	−0.00504126	−	0.00873171i
$792$	9.44826	−	5.45496i	0.335729	−	0.193833i
$793$	−3.47541	−	2.00653i	−0.123415	−	0.0712539i
$794$	−3.52906	+	6.11251i	−0.125242	+	0.216925i
$795$	−0.0345866	−	0.0320867i	−0.00122666	−	0.00113800i
$796$	−4.95598			−0.175660
$797$	15.7644	+	9.10157i	0.558403	+	0.322394i	0.752504	−	0.658587i	$-0.228846\pi$
$797$	15.7644	+	9.10157i	0.558403	+	0.322394i	−0.194101	+	0.980982i	$0.562179\pi$
$798$	0.755814	+	0.436369i	0.0267555	+	0.0154473i
$799$	4.59508	+	7.95891i	0.162562	+	0.281566i
$800$	−2.81724	−	4.13076i	−0.0996043	−	0.146044i
$801$	0.454071			0.0160438
$802$	−30.1063	+	17.3819i	−1.06309	+	0.613776i
$803$	−21.0131	+	12.1319i	−0.741538	+	0.428127i
$804$	2.21673	+	3.83949i	0.0781780	+	0.135408i
$805$	−1.55813	+	0.480751i	−0.0549169	+	0.0169443i
$806$	−0.311397			−0.0109685
$807$	−3.01525	−	1.74085i	−0.106142	−	0.0612809i
$808$	−14.0695	+	8.12302i	−0.494963	+	0.285767i
$809$	−27.2476			−0.957976			−0.478988	−	0.877821i	$-0.658996\pi$
$809$	−27.2476			−0.957976			−0.478988	+	0.877821i	$0.658996\pi$
$810$	15.9697	+	3.64370i	0.561119	+	0.128026i
$811$	−22.8138	+	39.5146i	−0.801099	+	1.38754i	0.117794	+	0.993038i	$0.462418\pi$
$811$	−22.8138	+	39.5146i	−0.801099	+	1.38754i	−0.918893	+	0.394507i	$0.870915\pi$
$812$	0.722078	+	0.416892i	0.0253400	+	0.0146300i
$813$			11.2497i			0.394544i
$814$	−9.40866	+	16.2963i	−0.329773	+	0.571184i
$815$	−12.3265	+	13.2868i	−0.431777	+	0.465417i
$816$	0.875209			0.0306384
$817$	46.7049	−	11.4998i	1.63400	−	0.402326i
$818$		−	20.2355i		−	0.707519i
$819$	0.495425			0.0173115
$820$	5.79626	−	1.78840i	0.202414	−	0.0624536i
$821$	5.85337			0.204284			0.102142	−	0.994770i	$-0.467430\pi$
$821$	5.85337			0.204284			0.102142	+	0.994770i	$0.467430\pi$
$822$	5.74743	+	3.31828i	0.200465	+	0.115738i
$823$	19.2607	+	11.1202i	0.671386	+	0.387625i	0.796601	−	0.604505i	$-0.206629\pi$
$823$	19.2607	+	11.1202i	0.671386	+	0.387625i	−0.125216	+	0.992130i	$0.539962\pi$
$824$	0.816364	+	1.41398i	0.0284394	+	0.0492584i
$825$	−8.44001	+	0.633797i	−0.293843	+	0.0220660i
$826$	−0.656537	−	1.13716i	−0.0228439	−	0.0395667i
$827$	−42.9214	−	24.7807i	−1.49252	−	0.861709i	−0.492560	−	0.870279i	$-0.663939\pi$
$827$	−42.9214	−	24.7807i	−1.49252	−	0.861709i	−0.999963	+	0.00857018i	$0.997272\pi$
$828$		−	7.50847i		−	0.260937i
$829$	−14.5551	+	25.2101i	−0.505519	+	0.875584i	0.494461	+	0.869200i	$0.335365\pi$
$829$	−14.5551	+	25.2101i	−0.505519	+	0.875584i	−0.999980	+	0.00638401i	$0.997968\pi$
$830$	5.33557	−	23.3849i	0.185200	−	0.811703i
$831$	6.39020	+	11.0682i	0.221674	+	0.383950i
$832$	0.559507	−	0.323031i	0.0193974	−	0.0111991i
$833$		−	13.9027i		−	0.481698i
$834$	−2.66763	−	4.62046i	−0.0923723	−	0.159994i
$835$	−32.4006	−	7.39260i	−1.12127	−	0.255832i
$836$	−14.2399	+	24.6642i	−0.492496	+	0.853029i
$837$	−1.05732	−	0.610446i	−0.0365465	−	0.0211001i
$838$		−	35.0160i		−	1.20961i
$839$	−21.2381			−0.733222			−0.366611	−	0.930374i	$-0.619482\pi$
$839$	−21.2381			−0.733222			−0.366611	+	0.930374i	$0.619482\pi$
$840$	−0.0784387	−	0.254222i	−0.00270639	−	0.00877151i
$841$	9.83276	−	17.0308i	0.339061	−	0.587270i
$842$	−15.1039	+	8.72026i	−0.520516	+	0.300520i
$843$	−2.25409	+	1.30140i	−0.0776351	+	0.0448226i
$844$	−15.6556			−0.538886
$845$	−6.25864	+	27.4306i	−0.215304	+	0.943642i
$846$	6.43194	+	11.1404i	0.221135	+	0.383016i
$847$	0.963066	−	0.556026i	0.0330913	−	0.0191053i
$848$	0.0419103	+	0.0241969i	0.00143921	+	0.000830926i
$849$	9.35165			0.320948
$850$	9.04392	+	4.35361i	0.310204	+	0.149328i
$851$	6.47526	+	11.2155i	0.221969	+	0.384462i
$852$			5.03214i			0.172398i
$853$	38.1529	−	22.0276i	1.30633	−	0.754210i	0.324849	−	0.945766i	$-0.394687\pi$
$853$	38.1529	−	22.0276i	1.30633	−	0.754210i	0.981482	+	0.191556i	$0.0613533\pi$
$854$	0.847577	−	1.46805i	0.0290035	−	0.0502355i
$855$	−44.0394	+	13.5881i	−1.50612	+	0.464702i
$856$	12.1237			0.414378
$857$	22.5425	+	13.0149i	0.770038	+	0.444582i	0.832888	−	0.553441i	$-0.186686\pi$
$857$	22.5425	+	13.0149i	0.770038	+	0.444582i	−0.0628503	+	0.998023i	$0.520019\pi$
$858$		−	1.09363i		−	0.0373358i
$859$	32.8293			1.12012			0.560061	−	0.828452i	$-0.310778\pi$
$859$	32.8293			1.12012			0.560061	+	0.828452i	$0.310778\pi$
$860$	−12.8219	−	7.11327i	−0.437224	−	0.242561i
$861$	0.322764			0.0109998
$862$			25.4038i			0.865256i
$863$	17.4345	+	10.0658i	0.593477	+	0.342644i	0.766471	−	0.642279i	$-0.222011\pi$
$863$	17.4345	+	10.0658i	0.593477	+	0.342644i	−0.172994	+	0.984923i	$0.555344\pi$
$864$	2.53301			0.0861748
$865$	−15.6097	−	50.5915i	−0.530745	−	1.72016i
$866$	12.2294	−	21.1819i	0.415570	−	0.719789i
$867$	4.89714	−	2.82736i	0.166315	−	0.0960223i
$868$		−	0.131537i		−	0.00446467i
$869$	−5.27565	−	9.13769i	−0.178964	−	0.309975i
$870$	2.84610	−	0.878146i	0.0964919	−	0.0297719i
$871$	−6.56978			−0.222608
$872$	3.96798	+	2.29092i	0.134373	+	0.0775802i
$873$	32.0134	−	18.4829i	1.08349	−	0.625552i
$874$	9.80022	+	16.9745i	0.331498	+	0.574171i
$875$	0.454054	−	3.01718i	0.0153498	−	0.101999i
$876$	−2.72458			−0.0920551
$877$	16.7983	−	9.69851i	0.567239	−	0.327495i	−0.188807	−	0.982014i	$-0.560462\pi$
$877$	16.7983	−	9.69851i	0.567239	−	0.327495i	0.756046	+	0.654519i	$0.227129\pi$
$878$	26.2305	−	15.1442i	0.885238	−	0.511092i
$879$	−5.20806	+	9.02063i	−0.175664	+	0.304258i
$880$	8.29594	−	2.55966i	0.279656	−	0.0862861i
$881$	0.923567			0.0311158			0.0155579	−	0.999879i	$-0.495048\pi$
$881$	0.923567			0.0311158			0.0155579	+	0.999879i	$0.495048\pi$
$882$		−	19.4602i		−	0.655258i
$883$	−1.16244	−	0.671134i	−0.0391192	−	0.0225855i	0.480313	−	0.877097i	$-0.340523\pi$
$883$	−1.16244	−	0.671134i	−0.0391192	−	0.0225855i	−0.519432	+	0.854512i	$0.673856\pi$
$884$	−0.648470	+	1.12318i	−0.0218104	+	0.0377767i
$885$	−4.57312	−	1.04341i	−0.153724	−	0.0350740i
$886$	13.6182	+	23.5873i	0.457511	+	0.792432i
$887$		−	44.1867i		−	1.48364i	−0.670597	−	0.741822i	$-0.733962\pi$
$887$		−	44.1867i		−	1.48364i	0.670597	−	0.741822i	$-0.266038\pi$
$888$	−1.82990	+	1.05649i	−0.0614075	+	0.0354536i
$889$	2.36010	+	4.08780i	0.0791550	+	0.137101i
$890$	0.352285	+	0.0803783i	0.0118086	+	0.00269429i
$891$	−14.2210	+	24.6315i	−0.476421	+	0.825185i
$892$			2.56042i			0.0857291i
$893$	−29.0815	−	16.7902i	−0.973177	−	0.561864i
$894$	−3.49792	−	6.05858i	−0.116988	−	0.202629i
$895$	−2.21513	−	2.05502i	−0.0740436	−	0.0686919i
$896$	0.136452	+	0.236341i	0.00455853	+	0.00789560i
$897$	−0.651822	−	0.376330i	−0.0217637	−	0.0125653i
$898$	−11.3694	−	6.56413i	−0.379402	−	0.219048i
$899$	1.47260			0.0491140
$900$	12.6592	+	6.09395i	0.421973	+	0.203132i
$901$	−0.0971483			−0.00323648
$902$			10.5326i			0.350698i
$903$	−0.540332	−	0.562817i	−0.0179811	−	0.0187294i
$904$	1.03908			0.0345592
$905$	−9.38721	−	8.70871i	−0.312041	−	0.289487i
$906$	−2.43231	+	4.21289i	−0.0808083	+	0.139964i
$907$		−	32.1260i		−	1.06673i	−0.845886	−	0.533363i	$-0.820928\pi$
$907$		−	32.1260i		−	1.06673i	0.845886	−	0.533363i	$-0.179072\pi$
$908$	21.8083	+	12.5910i	0.723732	+	0.417847i
$909$	22.8251	−	39.5342i	0.757059	−	1.31127i
$910$	0.384369	+	0.0876986i	0.0127417	+	0.00290718i
$911$	−38.0279			−1.25992			−0.629960	−	0.776627i	$-0.716929\pi$
$911$	−38.0279			−1.25992			−0.629960	+	0.776627i	$0.716929\pi$
$912$	−2.76953	+	1.59899i	−0.0917084	+	0.0529479i
$913$	36.0686	+	20.8242i	1.19370	+	0.689180i
$914$	−6.24910			−0.206702
$915$	−1.78535	−	5.78637i	−0.0590217	−	0.191291i
$916$	−1.73608	−	3.00697i	−0.0573616	−	0.0993532i
$917$	−1.01686	+	0.587087i	−0.0335798	+	0.0193873i
$918$	−4.40365	+	2.54245i	−0.145342	+	0.0839133i
$919$	−41.3989			−1.36562			−0.682812	−	0.730594i	$-0.739243\pi$
$919$	−41.3989			−1.36562			−0.682812	+	0.730594i	$0.739243\pi$
$920$	1.32913	−	5.82535i	0.0438200	−	0.192056i
$921$	−2.33951	−	4.05216i	−0.0770896	−	0.133523i
$922$	15.9498	+	9.20863i	0.525279	+	0.303270i
$923$	−6.45790	−	3.72847i	−0.212564	−	0.122724i
$924$	0.461958			0.0151973
$925$	−24.1646	+	1.81462i	−0.794527	+	0.0596645i
$926$	−1.51823	+	2.62966i	−0.0498922	+	0.0864159i
$927$	−3.97318	−	2.29392i	−0.130496	−	0.0753421i
$928$	−2.64591	+	1.52762i	−0.0868564	+	0.0501465i
$929$	26.1966	+	45.3739i	0.859483	+	1.48867i	0.872423	+	0.488752i	$0.162548\pi$
$929$	26.1966	+	45.3739i	0.859483	+	1.48867i	−0.0129396	+	0.999916i	$0.504119\pi$
$930$	−0.344475	−	0.319577i	−0.0112958	−	0.0104793i
$931$	25.3999	+	43.9939i	0.832447	+	1.44184i
$932$	−23.8867	+	13.7910i	−0.782434	+	0.451738i
$933$	−1.13230	+	0.653735i	−0.0370699	+	0.0214023i
$934$	12.2966	−	21.2984i	0.402358	−	0.696905i
$935$	−11.8533	+	12.7768i	−0.387645	+	0.417847i
$936$	−0.907693	+	1.57217i	−0.0296689	+	0.0513880i
$937$	−36.3204	+	20.9696i	−1.18653	+	0.685046i	−0.957517	−	0.288376i	$-0.906885\pi$
$937$	−36.3204	+	20.9696i	−1.18653	+	0.685046i	−0.229018	+	0.973422i	$0.573551\pi$
$938$		−	2.77514i		−	0.0906114i
$939$	−6.64668	−	11.5124i	−0.216906	−	0.375693i
$940$	3.01809	+	9.78174i	0.0984393	+	0.319045i
$941$	−29.0897	+	50.3849i	−0.948298	+	1.64250i	−0.199290	+	0.979941i	$0.563864\pi$
$941$	−29.0897	+	50.3849i	−0.948298	+	1.64250i	−0.749008	+	0.662561i	$0.769470\pi$
$942$		−	6.15787i		−	0.200634i
$943$	6.27765	+	3.62440i	0.204428	+	0.118027i
$944$	4.81150			0.156601
$945$	1.13317	+	1.05127i	0.0368621	+	0.0341978i
$946$	18.3662	−	17.6325i	0.597137	−	0.573281i
$947$		−	3.85152i		−	0.125158i	−0.998040	−	0.0625788i	$-0.980068\pi$
$947$		−	3.85152i		−	0.125158i	0.998040	−	0.0625788i	$-0.0199325\pi$
$948$		−	1.18480i		−	0.0384806i
$949$	2.01873	−	3.49654i	0.0655307	−	0.113503i
$950$	−36.5728	+	2.74641i	−1.18658	+	0.0891053i
$951$	2.25312	−	3.90251i	0.0730623	−	0.126548i
$952$	−0.474443	−	0.273920i	−0.0153768	−	0.00887780i
$953$	−10.7907	+	6.23001i	−0.349545	+	0.201810i	−0.664485	−	0.747302i	$-0.731349\pi$
$953$	−10.7907	+	6.23001i	−0.349545	+	0.201810i	0.314940	+	0.949112i	$0.398016\pi$
$954$	−0.135983			−0.00440261
$955$	1.04354	−	4.57365i	0.0337680	−	0.148000i
$956$	−6.71189	+	11.6253i	−0.217078	+	0.375990i
$957$			5.17177i			0.167180i
$958$	0.481144	+	0.277788i	0.0155450	+	0.00897494i
$959$	−2.07709	−	3.59762i	−0.0670727	−	0.116173i
$960$	0.950456	+	0.216858i	0.0306758	+	0.00699908i
$961$	15.3838	+	26.6456i	0.496253	+	0.859535i
$962$		−	3.13116i		−	0.100953i
$963$	−29.5025	+	17.0333i	−0.950704	+	0.548889i
$964$	−5.21343	−	9.02993i	−0.167913	−	0.290835i
$965$	−1.16706	−	3.78248i	−0.0375690	−	0.121762i
$966$	0.158965	−	0.275336i	0.00511463	−	0.00885879i
$967$			10.4595i			0.336354i	0.985757	+	0.168177i	$0.0537880\pi$
$967$			10.4595i			0.336354i	−0.985757	+	0.168177i	$0.946212\pi$
$968$			4.07490i			0.130972i
$969$	3.20989	−	5.55970i	0.103117	−	0.178603i
$970$	28.1090	−	8.67284i	0.902525	−	0.278468i
$971$	20.1368	+	34.8780i	0.646222	+	1.11929i	0.984018	+	0.178070i	$0.0569852\pi$
$971$	20.1368	+	34.8780i	0.646222	+	1.11929i	−0.337796	+	0.941219i	$0.609681\pi$
$972$	−9.34681	+	5.39639i	−0.299799	+	0.173089i
$973$			3.33962i			0.107063i
$974$	1.83469	+	3.17777i	0.0587872	+	0.101822i
$975$	1.16351	−	0.793533i	0.0372623	−	0.0254134i
$976$	3.10578	+	5.37937i	0.0994136	+	0.172189i
$977$	29.2910	+	16.9112i	0.937103	+	0.541036i	0.889051	−	0.457808i	$-0.151365\pi$
$977$	29.2910	+	16.9112i	0.937103	+	0.541036i	0.0480517	+	0.998845i	$0.484699\pi$
$978$		−	3.53376i		−	0.112997i
$979$	−0.313709	+	0.543359i	−0.0100262	+	0.0173658i
$980$	3.44478	−	15.0979i	0.110040	−	0.482286i
$981$	−12.8746			−0.411054
$982$	−17.6123	+	10.1685i	−0.562030	+	0.324488i
$983$	33.2997	+	19.2256i	1.06209	+	0.613201i	0.926011	−	0.377497i	$-0.123215\pi$
$983$	33.2997	+	19.2256i	1.06209	+	0.613201i	0.136084	+	0.990697i	$0.456548\pi$
$984$	−0.591352	+	1.02425i	−0.0188516	+	0.0326520i
$985$	−36.2013	+	39.0217i	−1.15347	+	1.24334i
$986$	3.06662	−	5.31154i	0.0976611	−	0.169154i
$987$			0.544695i			0.0173378i
$988$		−	4.73897i		−	0.150767i
$989$	−4.18926	−	17.0142i	−0.133211	−	0.541019i
$990$	−16.5916	+	17.8843i	−0.527317	+	0.568400i
$991$	34.9331			1.10969			0.554844	−	0.831955i	$-0.312778\pi$
$991$	34.9331			1.10969			0.554844	+	0.831955i	$0.312778\pi$
$992$	0.417418	+	0.240996i	0.0132530	+	0.00765164i
$993$		−	3.69923i		−	0.117392i
$994$	1.57494	−	2.72788i	0.0499541	−	0.0865230i
$995$	10.5893	−	3.26727i	0.335704	−	0.103579i
$996$	2.33834	+	4.05013i	0.0740932	+	0.128333i
$997$			16.0791i			0.509230i	0.967043	+	0.254615i	$0.0819487\pi$
$997$			16.0791i			0.509230i	−0.967043	+	0.254615i	$0.918051\pi$
$998$	35.3327	−	20.3994i	1.11844	−	0.645730i
$999$	6.13815	−	10.6316i	0.194202	−	0.336369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.j.a.49.5	✓	44
5.4	even	2	inner	430.2.j.a.49.18	yes	44
43.36	even	3	inner	430.2.j.a.79.7	yes	44
215.79	even	6	inner	430.2.j.a.79.16	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.j.a.49.5	✓	44	1.1	even	1	trivial
430.2.j.a.49.18	yes	44	5.4	even	2	inner
430.2.j.a.79.7	yes	44	43.36	even	3	inner
430.2.j.a.79.16	yes	44	215.79	even	6	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.377570 - 0.217990i) q^{3} -1.00000 q^{4} +(2.13668 - 0.659257i) q^{5} +(-0.217990 + 0.377570i) q^{6} +(0.236341 - 0.136452i) q^{7} +1.00000i q^{8} +(-1.40496 - 2.43346i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.377570 - 0.217990i) q^{3} -1.00000 q^{4} +(2.13668 - 0.659257i) q^{5} +(-0.217990 + 0.377570i) q^{6} +(0.236341 - 0.136452i) q^{7} +1.00000i q^{8} +(-1.40496 - 2.43346i) q^{9} +(-0.659257 - 2.13668i) q^{10} +3.88264 q^{11} +(0.377570 + 0.217990i) q^{12} +(-0.559507 + 0.323031i) q^{13} +(-0.136452 - 0.236341i) q^{14} +(-0.950456 - 0.216858i) q^{15} +1.00000 q^{16} +(-1.73850 + 1.00373i) q^{17} +(-2.43346 + 1.40496i) q^{18} +(3.66757 - 6.35242i) q^{19} +(-2.13668 + 0.659257i) q^{20} -0.118980 q^{21} -3.88264i q^{22} +(-2.31413 - 1.33606i) q^{23} +(0.217990 - 0.377570i) q^{24} +(4.13076 - 2.81724i) q^{25} +(0.323031 + 0.559507i) q^{26} +2.53301i q^{27} +(-0.236341 + 0.136452i) q^{28} +(-1.52762 - 2.64591i) q^{29} +(-0.216858 + 0.950456i) q^{30} +(-0.240996 + 0.417418i) q^{31} -1.00000i q^{32} +(-1.46597 - 0.846377i) q^{33} +(1.00373 + 1.73850i) q^{34} +(0.415027 - 0.447362i) q^{35} +(1.40496 + 2.43346i) q^{36} +(-4.19721 - 2.42326i) q^{37} +(-6.35242 - 3.66757i) q^{38} +0.281671 q^{39} +(0.659257 + 2.13668i) q^{40} -2.71275 q^{41} +0.118980i q^{42} +(4.54136 + 4.73034i) q^{43} -3.88264 q^{44} +(-4.60622 - 4.27329i) q^{45} +(-1.33606 + 2.31413i) q^{46} -4.57802i q^{47} +(-0.377570 - 0.217990i) q^{48} +(-3.46276 + 5.99768i) q^{49} +(-2.81724 - 4.13076i) q^{50} +0.875209 q^{51} +(0.559507 - 0.323031i) q^{52} +(0.0419103 + 0.0241969i) q^{53} +2.53301 q^{54} +(8.29594 - 2.55966i) q^{55} +(0.136452 + 0.236341i) q^{56} +(-2.76953 + 1.59899i) q^{57} +(-2.64591 + 1.52762i) q^{58} +4.81150 q^{59} +(0.950456 + 0.216858i) q^{60} +(3.10578 + 5.37937i) q^{61} +(0.417418 + 0.240996i) q^{62} +(-0.664100 - 0.383418i) q^{63} -1.00000 q^{64} +(-0.982524 + 1.05907i) q^{65} +(-0.846377 + 1.46597i) q^{66} +(8.80656 + 5.08447i) q^{67} +(1.73850 - 1.00373i) q^{68} +(0.582497 + 1.00892i) q^{69} +(-0.447362 - 0.415027i) q^{70} +(5.77106 + 9.99577i) q^{71} +(2.43346 - 1.40496i) q^{72} +(-5.41208 + 3.12466i) q^{73} +(-2.42326 + 4.19721i) q^{74} +(-2.17378 + 0.163239i) q^{75} +(-3.66757 + 6.35242i) q^{76} +(0.917628 - 0.529793i) q^{77} -0.281671i q^{78} +(-1.35878 - 2.35347i) q^{79} +(2.13668 - 0.659257i) q^{80} +(-3.66271 + 6.34400i) q^{81} +2.71275i q^{82} +(9.28970 + 5.36341i) q^{83} +0.118980 q^{84} +(-3.05290 + 3.29076i) q^{85} +(4.73034 - 4.54136i) q^{86} +1.33202i q^{87} +3.88264i q^{88} +(-0.0807978 + 0.139946i) q^{89} +(-4.27329 + 4.60622i) q^{90} +(-0.0881563 + 0.152691i) q^{91} +(2.31413 + 1.33606i) q^{92} +(0.181986 - 0.105070i) q^{93} -4.57802 q^{94} +(3.64853 - 15.9909i) q^{95} +(-0.217990 + 0.377570i) q^{96} +13.1555i q^{97} +(5.99768 + 3.46276i) q^{98} +(-5.45496 - 9.44826i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9}+O(q^{10}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9	\( 44 q - 44 q^{4} - 4 q^{5} + 2 q^{6} + 20 q^{9} + 8 q^{11} + 4 q^{14} - 4 q^{15} + 44 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} - 2 q^{24} + 12 q^{26} - 10 q^{29} - 20 q^{31} - 12 q^{34} + 12 q^{35} - 20 q^{36} + 120 q^{39} + 20 q^{41} - 8 q^{44} - 28 q^{45} + 42 q^{49} - 112 q^{51} - 68 q^{54} - 26 q^{55} - 4 q^{56} + 40 q^{59} + 4 q^{60} + 8 q^{61} - 44 q^{64} - 60 q^{65} - 12 q^{66} - 4 q^{69} + 48 q^{70} - 20 q^{71} - 12 q^{74} + 4 q^{75} + 4 q^{76} - 44 q^{79} - 4 q^{80} + 2 q^{81} + 24 q^{84} + 20 q^{85} + 14 q^{86} - 26 q^{89} + 68 q^{90} + 4 q^{94} - 34 q^{95} + 2 q^{96} + 72 q^{99}+O(q^{100}) \) 44 * q - 44 * q^4 - 4 * q^5 + 2 * q^6 + 20 * q^9 + 8 * q^11 + 4 * q^14 - 4 * q^15 + 44 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 - 2 * q^24 + 12 * q^26 - 10 * q^29 - 20 * q^31 - 12 * q^34 + 12 * q^35 - 20 * q^36 + 120 * q^39 + 20 * q^41 - 8 * q^44 - 28 * q^45 + 42 * q^49 - 112 * q^51 - 68 * q^54 - 26 * q^55 - 4 * q^56 + 40 * q^59 + 4 * q^60 + 8 * q^61 - 44 * q^64 - 60 * q^65 - 12 * q^66 - 4 * q^69 + 48 * q^70 - 20 * q^71 - 12 * q^74 + 4 * q^75 + 4 * q^76 - 44 * q^79 - 4 * q^80 + 2 * q^81 + 24 * q^84 + 20 * q^85 + 14 * q^86 - 26 * q^89 + 68 * q^90 + 4 * q^94 - 34 * q^95 + 2 * q^96 + 72 * q^99

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