LMFDB - Embedded newform 350.2.q.c.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(11,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("350.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.q (of order $15$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	350.11
Dual form			350.2.q.c.191.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 + 0.406737i) q^{2} +(0.352973 + 0.392016i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.665386 - 2.13477i) q^{5} +(0.163009 + 0.501692i) q^{6} +(2.31380 + 1.28309i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.284499 - 2.70682i) q^{9} +O(q^{10})$	\(q+(0.913545 + 0.406737i) q^{2} +(0.352973 + 0.392016i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.665386 - 2.13477i) q^{5} +(0.163009 + 0.501692i) q^{6} +(2.31380 + 1.28309i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.284499 - 2.70682i) q^{9} +(0.260430 - 2.22085i) q^{10} +(-0.145550 - 1.38482i) q^{11} +(-0.0551398 + 0.524620i) q^{12} +(4.71406 + 3.42496i) q^{13} +(1.59188 + 2.11327i) q^{14} +(0.602003 - 1.01436i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(3.42155 + 0.727273i) q^{17} +(1.36087 - 2.35709i) q^{18} +(-4.28531 + 4.75932i) q^{19} +(1.14122 - 1.92292i) q^{20} +(0.313718 + 1.35994i) q^{21} +(0.430289 - 1.32429i) q^{22} +(-7.52222 - 3.34911i) q^{23} +(-0.263755 + 0.456837i) q^{24} +(-4.11452 + 2.84090i) q^{25} +(2.91345 + 5.04624i) q^{26} +(2.44183 - 1.77409i) q^{27} +(0.594715 + 2.57804i) q^{28} +(0.832518 - 2.56223i) q^{29} +(0.962534 - 0.681807i) q^{30} +(-0.803276 - 0.170742i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.491495 - 0.545861i) q^{33} +(2.82993 + 2.05607i) q^{34} +(1.19953 - 5.79320i) q^{35} +(2.20193 - 1.59979i) q^{36} +(0.320867 - 3.05285i) q^{37} +(-5.85062 + 2.60486i) q^{38} +(0.321294 + 3.05691i) q^{39} +(1.82468 - 1.29250i) q^{40} +(0.997736 + 0.724898i) q^{41} +(-0.266543 + 1.36997i) q^{42} -11.1564 q^{43} +(0.931727 - 1.03479i) q^{44} +(-5.96776 + 1.19374i) q^{45} +(-5.50968 - 6.11912i) q^{46} +(1.44280 - 0.306677i) q^{47} +(-0.426764 + 0.310062i) q^{48} +(3.70737 + 5.93763i) q^{49} +(-4.91430 + 0.921763i) q^{50} +(0.922612 + 1.59801i) q^{51} +(0.609077 + 5.79498i) q^{52} +(-2.46830 - 2.74133i) q^{53} +(2.95231 - 0.627534i) q^{54} +(-2.85942 + 1.23215i) q^{55} +(-0.505286 + 2.59705i) q^{56} -3.37833 q^{57} +(1.80269 - 2.00209i) q^{58} +(-5.09166 + 2.26695i) q^{59} +(1.15663 - 0.231364i) q^{60} +(-4.36526 - 1.94354i) q^{61} +(-0.664382 - 0.482702i) q^{62} +(4.13137 - 5.89802i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(4.17486 - 12.3424i) q^{65} +(0.671025 - 0.298760i) q^{66} +(7.42573 + 1.57839i) q^{67} +(1.74899 + 3.02935i) q^{68} +(-1.34224 - 4.13098i) q^{69} +(3.45213 - 4.80445i) q^{70} +(-2.11396 + 6.50611i) q^{71} +(2.66226 - 0.565880i) q^{72} +(-0.756316 - 7.19587i) q^{73} +(1.53483 - 2.65840i) q^{74} +(-2.56599 - 0.610199i) q^{75} -6.40430 q^{76} +(1.44007 - 3.39095i) q^{77} +(-0.949839 + 2.92331i) q^{78} +(6.22145 - 1.32241i) q^{79} +(2.19263 - 0.438596i) q^{80} +(-6.42940 - 1.36661i) q^{81} +(0.616635 + 1.06804i) q^{82} +(1.85104 + 5.69690i) q^{83} +(-0.800717 + 1.14312i) q^{84} +(-0.724088 - 7.78815i) q^{85} +(-10.1919 - 4.53770i) q^{86} +(1.29829 - 0.578036i) q^{87} +(1.27206 - 0.566358i) q^{88} +(-2.67526 - 1.19110i) q^{89} +(-5.93736 - 1.33677i) q^{90} +(6.51287 + 13.9732i) q^{91} +(-2.54447 - 7.83109i) q^{92} +(-0.216601 - 0.375164i) q^{93} +(1.44280 + 0.306677i) q^{94} +(13.0115 + 5.98139i) q^{95} +(-0.515982 + 0.109675i) q^{96} +(2.38458 - 7.33897i) q^{97} +(0.971797 + 6.93222i) q^{98} -3.78986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9}+O(q^{10}) $ 80 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 20 * q^8 + 4 * q^9	\( 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9} + 3 q^{10} + 10 q^{11} + 2 q^{12} - 12 q^{13} - 7 q^{14} + 22 q^{15} + 10 q^{16} - 8 q^{17} - 36 q^{18} + 8 q^{19} + 4 q^{20} + 17 q^{21} + 20 q^{22} + 5 q^{23} - 8 q^{24} + 32 q^{25} - 24 q^{26} + 32 q^{27} - 7 q^{28} + 12 q^{29} - 11 q^{30} - 9 q^{31} - 40 q^{32} + 33 q^{33} - 4 q^{34} - 22 q^{35} - 8 q^{36} - 14 q^{37} - 2 q^{38} - 2 q^{40} - 18 q^{41} - 19 q^{42} - 8 q^{43} - 10 q^{44} + 33 q^{45} - 10 q^{46} + 10 q^{47} - 4 q^{48} + 12 q^{49} + 36 q^{50} + 46 q^{51} + 6 q^{52} - 30 q^{53} + 14 q^{54} + 2 q^{55} - q^{56} - 52 q^{57} - 6 q^{58} + 40 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 100 q^{63} - 20 q^{64} - 25 q^{65} - 7 q^{66} + q^{67} + 12 q^{68} - 142 q^{69} + 25 q^{70} - 84 q^{71} + 14 q^{72} + 22 q^{73} + 6 q^{74} - 29 q^{75} + 24 q^{76} + 38 q^{77} - 30 q^{78} + 10 q^{79} + 3 q^{80} + 52 q^{81} - 6 q^{82} - 98 q^{83} + 2 q^{84} - 36 q^{85} - 26 q^{86} + 34 q^{87} + 10 q^{88} + 45 q^{89} + 24 q^{90} - 63 q^{91} + 20 q^{92} - 20 q^{93} + 10 q^{94} - 33 q^{95} + 2 q^{96} - 106 q^{97} - 55 q^{98} + 12 q^{99}+O(q^{100}) \) 80 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 20 * q^8 + 4 * q^9 + 3 * q^10 + 10 * q^11 + 2 * q^12 - 12 * q^13 - 7 * q^14 + 22 * q^15 + 10 * q^16 - 8 * q^17 - 36 * q^18 + 8 * q^19 + 4 * q^20 + 17 * q^21 + 20 * q^22 + 5 * q^23 - 8 * q^24 + 32 * q^25 - 24 * q^26 + 32 * q^27 - 7 * q^28 + 12 * q^29 - 11 * q^30 - 9 * q^31 - 40 * q^32 + 33 * q^33 - 4 * q^34 - 22 * q^35 - 8 * q^36 - 14 * q^37 - 2 * q^38 - 2 * q^40 - 18 * q^41 - 19 * q^42 - 8 * q^43 - 10 * q^44 + 33 * q^45 - 10 * q^46 + 10 * q^47 - 4 * q^48 + 12 * q^49 + 36 * q^50 + 46 * q^51 + 6 * q^52 - 30 * q^53 + 14 * q^54 + 2 * q^55 - q^56 - 52 * q^57 - 6 * q^58 + 40 * q^59 + 4 * q^60 + 16 * q^61 - 32 * q^62 - 100 * q^63 - 20 * q^64 - 25 * q^65 - 7 * q^66 + q^67 + 12 * q^68 - 142 * q^69 + 25 * q^70 - 84 * q^71 + 14 * q^72 + 22 * q^73 + 6 * q^74 - 29 * q^75 + 24 * q^76 + 38 * q^77 - 30 * q^78 + 10 * q^79 + 3 * q^80 + 52 * q^81 - 6 * q^82 - 98 * q^83 + 2 * q^84 - 36 * q^85 - 26 * q^86 + 34 * q^87 + 10 * q^88 + 45 * q^89 + 24 * q^90 - 63 * q^91 + 20 * q^92 - 20 * q^93 + 10 * q^94 - 33 * q^95 + 2 * q^96 - 106 * q^97 - 55 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$3$	0.352973	+	0.392016i	0.203789	+	0.226331i	0.836372	−	0.548162i	$-0.184672\pi$
$3$	0.352973	+	0.392016i	0.203789	+	0.226331i	−0.632583	+	0.774492i	$0.718005\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	−0.665386	−	2.13477i	−0.297570	−	0.954700i
$5$	−0.665386	−	2.13477i	−0.297570	−	0.954700i
$6$	0.163009	+	0.501692i	0.0665483	+	0.204815i
$7$	2.31380	+	1.28309i	0.874535	+	0.484962i
$7$	2.31380	+	1.28309i	0.874535	+	0.484962i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.284499	−	2.70682i	0.0948329	−	0.902274i
$10$	0.260430	−	2.22085i	0.0823553	−	0.702295i
$11$	−0.145550	−	1.38482i	−0.0438850	−	0.417538i	−0.994305	−	0.106570i	$-0.966013\pi$
$11$	−0.145550	−	1.38482i	−0.0438850	−	0.417538i	0.950420	−	0.310968i	$-0.100653\pi$
$12$	−0.0551398	+	0.524620i	−0.0159175	+	0.151445i
$13$	4.71406	+	3.42496i	1.30744	+	0.949914i	0.999999	−	0.00165152i	$-0.000525694\pi$
$13$	4.71406	+	3.42496i	1.30744	+	0.949914i	0.307446	+	0.951566i	$0.400526\pi$
$14$	1.59188	+	2.11327i	0.425449	+	0.564795i
$15$	0.602003	−	1.01436i	0.155436	−	0.261907i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	3.42155	+	0.727273i	0.829848	+	0.176390i	0.603203	−	0.797588i	$-0.293891\pi$
$17$	3.42155	+	0.727273i	0.829848	+	0.176390i	0.226645	+	0.973977i	$0.427224\pi$
$18$	1.36087	−	2.35709i	0.320759	−	0.555572i
$19$	−4.28531	+	4.75932i	−0.983118	+	1.09186i	0.0126464	+	0.999920i	$0.495974\pi$
$19$	−4.28531	+	4.75932i	−0.983118	+	1.09186i	−0.995764	+	0.0919430i	$0.970692\pi$
$20$	1.14122	−	1.92292i	0.255184	−	0.429978i
$21$	0.313718	+	1.35994i	0.0684589	+	0.296764i
$22$	0.430289	−	1.32429i	0.0917379	−	0.282340i
$23$	−7.52222	−	3.34911i	−1.56849	−	0.698337i	−0.575641	−	0.817703i	$-0.695247\pi$
$23$	−7.52222	−	3.34911i	−1.56849	−	0.698337i	−0.992850	+	0.119366i	$0.961914\pi$
$24$	−0.263755	+	0.456837i	−0.0538387	+	0.0932514i
$25$	−4.11452	+	2.84090i	−0.822905	+	0.568180i
$26$	2.91345	+	5.04624i	0.571374	+	0.989649i
$27$	2.44183	−	1.77409i	0.469931	−	0.341425i
$28$	0.594715	+	2.57804i	0.112391	+	0.487205i
$29$	0.832518	−	2.56223i	0.154595	−	0.475793i	−0.843525	−	0.537090i	$-0.819524\pi$
$29$	0.832518	−	2.56223i	0.154595	−	0.475793i	0.998120	+	0.0612966i	$0.0195235\pi$
$30$	0.962534	−	0.681807i	0.175734	−	0.124480i
$31$	−0.803276	−	0.170742i	−0.144273	−	0.0306661i	0.135209	−	0.990817i	$-0.456829\pi$
$31$	−0.803276	−	0.170742i	−0.144273	−	0.0306661i	−0.279482	+	0.960151i	$0.590163\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.491495	−	0.545861i	0.0855584	−	0.0950222i
$34$	2.82993	+	2.05607i	0.485329	+	0.352612i
$35$	1.19953	−	5.79320i	0.202758	−	0.979229i
$36$	2.20193	−	1.59979i	0.366988	−	0.266632i
$37$	0.320867	−	3.05285i	0.0527502	−	0.501885i	−0.935967	−	0.352089i	$-0.885472\pi$
$37$	0.320867	−	3.05285i	0.0527502	−	0.501885i	0.988717	−	0.149796i	$-0.0478617\pi$
$38$	−5.85062	+	2.60486i	−0.949095	+	0.422564i
$39$	0.321294	+	3.05691i	0.0514482	+	0.489497i
$40$	1.82468	−	1.29250i	0.288507	−	0.204362i
$41$	0.997736	+	0.724898i	0.155820	+	0.113210i	0.662963	−	0.748652i	$-0.269298\pi$
$41$	0.997736	+	0.724898i	0.155820	+	0.113210i	−0.507143	+	0.861862i	$0.669298\pi$
$42$	−0.266543	+	1.36997i	−0.0411285	+	0.211391i
$43$	−11.1564			−1.70133			−0.850665	−	0.525708i	$-0.823801\pi$
$43$	−11.1564			−1.70133			−0.850665	+	0.525708i	$0.823801\pi$
$44$	0.931727	−	1.03479i	0.140463	−	0.156000i
$45$	−5.96776	+	1.19374i	−0.889621	+	0.177953i
$46$	−5.50968	−	6.11912i	−0.812359	−	0.902216i
$47$	1.44280	−	0.306677i	0.210454	−	0.0447334i	−0.101478	−	0.994838i	$-0.532357\pi$
$47$	1.44280	−	0.306677i	0.210454	−	0.0447334i	0.311932	+	0.950104i	$0.399024\pi$
$48$	−0.426764	+	0.310062i	−0.0615981	+	0.0447537i
$49$	3.70737	+	5.93763i	0.529624	+	0.848233i
$50$	−4.91430	+	0.921763i	−0.694987	+	0.130357i
$51$	0.922612	+	1.59801i	0.129191	+	0.223766i
$52$	0.609077	+	5.79498i	0.0844637	+	0.803619i
$53$	−2.46830	−	2.74133i	−0.339047	−	0.376550i	0.549376	−	0.835575i	$-0.314865\pi$
$53$	−2.46830	−	2.74133i	−0.339047	−	0.376550i	−0.888423	+	0.459025i	$0.848199\pi$
$54$	2.95231	−	0.627534i	0.401759	−	0.0853965i
$55$	−2.85942	+	1.23215i	−0.385565	+	0.166144i
$56$	−0.505286	+	2.59705i	−0.0675216	+	0.347046i
$57$	−3.37833			−0.447471
$58$	1.80269	−	2.00209i	0.236705	−	0.262888i
$59$	−5.09166	+	2.26695i	−0.662878	+	0.295132i	−0.710463	−	0.703735i	$-0.751514\pi$
$59$	−5.09166	+	2.26695i	−0.662878	+	0.295132i	0.0475848	+	0.998867i	$0.484848\pi$
$60$	1.15663	−	0.231364i	0.149321	−	0.0298690i
$61$	−4.36526	−	1.94354i	−0.558915	−	0.248845i	0.107781	−	0.994175i	$-0.465625\pi$
$61$	−4.36526	−	1.94354i	−0.558915	−	0.248845i	−0.666696	+	0.745330i	$0.732292\pi$
$62$	−0.664382	−	0.482702i	−0.0843766	−	0.0613032i
$63$	4.13137	−	5.89802i	0.520503	−	0.743081i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	4.17486	−	12.3424i	0.517827	−	1.53088i
$66$	0.671025	−	0.298760i	0.0825975	−	0.0367748i
$67$	7.42573	+	1.57839i	0.907198	+	0.192831i	0.637803	−	0.770199i	$-0.279843\pi$
$67$	7.42573	+	1.57839i	0.907198	+	0.192831i	0.269394	+	0.963030i	$0.413177\pi$
$68$	1.74899	+	3.02935i	0.212097	+	0.367362i
$69$	−1.34224	−	4.13098i	−0.161586	−	0.497311i
$70$	3.45213	−	4.80445i	0.412609	−	0.574242i
$71$	−2.11396	+	6.50611i	−0.250881	+	0.772133i	0.743732	+	0.668478i	$0.233054\pi$
$71$	−2.11396	+	6.50611i	−0.250881	+	0.772133i	−0.994613	+	0.103655i	$0.966946\pi$
$72$	2.66226	−	0.565880i	0.313750	−	0.0666896i
$73$	−0.756316	−	7.19587i	−0.0885201	−	0.842213i	−0.945228	−	0.326411i	$-0.894161\pi$
$73$	−0.756316	−	7.19587i	−0.0885201	−	0.842213i	0.856708	−	0.515802i	$-0.172506\pi$
$74$	1.53483	−	2.65840i	0.178420	−	0.309033i
$75$	−2.56599	−	0.610199i	−0.296295	−	0.0704597i
$76$	−6.40430			−0.734623
$77$	1.44007	−	3.39095i	0.164111	−	0.386434i
$78$	−0.949839	+	2.92331i	−0.107548	+	0.330999i
$79$	6.22145	−	1.32241i	0.699968	−	0.148783i	0.155837	−	0.987783i	$-0.450193\pi$
$79$	6.22145	−	1.32241i	0.699968	−	0.148783i	0.544131	+	0.839000i	$0.316859\pi$
$80$	2.19263	−	0.438596i	0.245144	−	0.0490366i
$81$	−6.42940	−	1.36661i	−0.714377	−	0.151846i
$82$	0.616635	+	1.06804i	0.0680959	+	0.117946i
$83$	1.85104	+	5.69690i	0.203178	+	0.625316i	0.999783	+	0.0208171i	$0.00662678\pi$
$83$	1.85104	+	5.69690i	0.203178	+	0.625316i	−0.796606	+	0.604499i	$0.793373\pi$
$84$	−0.800717	+	1.14312i	−0.0873654	+	0.124724i
$85$	−0.724088	−	7.78815i	−0.0785384	−	0.844744i
$86$	−10.1919	−	4.53770i	−1.09902	−	0.489313i
$87$	1.29829	−	0.578036i	0.139191	−	0.0619720i
$88$	1.27206	−	0.566358i	0.135602	−	0.0603740i
$89$	−2.67526	−	1.19110i	−0.283577	−	0.126257i	0.260019	−	0.965603i	$-0.416271\pi$
$89$	−2.67526	−	1.19110i	−0.283577	−	0.126257i	−0.543596	+	0.839347i	$0.682938\pi$
$90$	−5.93736	−	1.33677i	−0.625852	−	0.140908i
$91$	6.51287	+	13.9732i	0.682734	+	1.46479i
$92$	−2.54447	−	7.83109i	−0.265280	−	0.816447i
$93$	−0.216601	−	0.375164i	−0.0224605	−	0.0389027i
$94$	1.44280	+	0.306677i	0.148813	+	0.0316313i
$95$	13.0115	+	5.98139i	1.33495	+	0.613677i
$96$	−0.515982	+	0.109675i	−0.0526622	+	0.0111937i
$97$	2.38458	−	7.33897i	0.242117	−	0.745159i	−0.753980	−	0.656897i	$-0.771869\pi$
$97$	2.38458	−	7.33897i	0.242117	−	0.745159i	0.996097	−	0.0882624i	$-0.0281314\pi$
$98$	0.971797	+	6.93222i	0.0981663	+	0.700260i
$99$	−3.78986			−0.380896
$100$	−4.86435	−	1.15675i	−0.486435	−	0.115675i
$101$	−8.37120	+	14.4993i	−0.832966	+	1.44274i	0.0627101	+	0.998032i	$0.480026\pi$
$101$	−8.37120	+	14.4993i	−0.832966	+	1.44274i	−0.895676	+	0.444707i	$0.853308\pi$
$102$	0.192878	+	1.83511i	0.0190978	+	0.181703i
$103$	−15.9048	+	3.38067i	−1.56715	+	0.333107i	−0.908021	−	0.418925i	$-0.862407\pi$
$103$	−15.9048	+	3.38067i	−1.56715	+	0.333107i	−0.659126	+	0.752033i	$0.729074\pi$
$104$	−1.80061	+	5.54171i	−0.176564	+	0.543409i
$105$	2.69443	−	1.57461i	0.262949	−	0.153666i
$106$	−1.13991	−	3.50828i	−0.110718	−	0.340754i
$107$	1.93071	+	3.34409i	0.186649	+	0.323285i	0.944131	−	0.329571i	$-0.106904\pi$
$107$	1.93071	+	3.34409i	0.186649	+	0.323285i	−0.757482	+	0.652856i	$0.773571\pi$
$108$	2.95231	+	0.627534i	0.284087	+	0.0603845i
$109$	−14.7364	+	6.56108i	−1.41149	+	0.628437i	−0.964013	−	0.265856i	$-0.914345\pi$
$109$	−14.7364	+	6.56108i	−1.41149	+	0.628437i	−0.447481	+	0.894294i	$0.647679\pi$
$110$	−3.11338	−	0.0374034i	−0.296849	−	0.00356628i
$111$	1.31002	−	0.951787i	0.124342	−	0.0903396i
$112$	−1.51792	+	2.16701i	−0.143430	+	0.204763i
$113$	−7.93459	−	5.76481i	−0.746423	−	0.542308i	0.148293	−	0.988943i	$-0.452622\pi$
$113$	−7.93459	−	5.76481i	−0.746423	−	0.542308i	−0.894716	+	0.446635i	$0.852622\pi$
$114$	−3.08626	−	1.37409i	−0.289055	−	0.128695i
$115$	−2.14441	+	18.2867i	−0.199967	+	1.70524i
$116$	2.46117	−	1.09578i	0.228514	−	0.101741i
$117$	10.6119	−	11.7857i	0.981072	−	1.08959i
$118$	−5.57352			−0.513084
$119$	6.98363	+	6.07292i	0.640189	+	0.556703i
$120$	1.15074	+	0.259084i	0.105048	+	0.0236510i
$121$	8.86309	−	1.88391i	0.805736	−	0.171264i
$122$	−3.19736	−	3.55102i	−0.289475	−	0.321495i
$123$	0.0680022	+	0.646998i	0.00613155	+	0.0583378i
$124$	−0.410611	−	0.711199i	−0.0368739	−	0.0638675i
$125$	8.80242	+	6.89328i	0.787313	+	0.616554i
$126$	6.17313	−	3.70773i	0.549946	−	0.330311i
$127$	4.73057	−	3.43696i	0.419770	−	0.304981i	−0.357775	−	0.933808i	$-0.616465\pi$
$127$	4.73057	−	3.43696i	0.419770	−	0.304981i	0.777545	+	0.628827i	$0.216465\pi$
$128$	−0.978148	+	0.207912i	−0.0864569	+	0.0183770i
$129$	−3.93790	−	4.37348i	−0.346713	−	0.385063i
$130$	8.83402	−	9.57725i	0.774794	−	0.839981i
$131$	3.83509	−	4.25930i	0.335074	−	0.372137i	−0.551937	−	0.833886i	$-0.686111\pi$
$131$	3.83509	−	4.25930i	0.335074	−	0.372137i	0.887011	+	0.461749i	$0.152778\pi$
$132$	0.734528			0.0639325
$133$	−16.0220	+	5.51369i	−1.38928	+	0.478098i
$134$	6.14176	+	4.46225i	0.530567	+	0.385479i
$135$	−5.41205	−	4.03230i	−0.465795	−	0.347045i
$136$	0.365639	+	3.47883i	0.0313533	+	0.298307i
$137$	17.3517	−	7.72547i	1.48245	−	0.660031i	0.503479	−	0.864007i	$-0.332053\pi$
$137$	17.3517	−	7.72547i	1.48245	−	0.660031i	0.978976	+	0.203976i	$0.0653865\pi$
$138$	0.454026	−	4.31977i	0.0386493	−	0.367723i
$139$	16.3122	−	11.8515i	1.38358	−	1.00523i	0.387050	−	0.922059i	$-0.373494\pi$
$139$	16.3122	−	11.8515i	1.38358	−	1.00523i	0.996535	−	0.0831743i	$-0.0265058\pi$
$140$	5.10783	−	2.98498i	0.431690	−	0.252277i
$141$	0.629491	+	0.457352i	0.0530127	+	0.0385160i
$142$	−4.57748	+	5.08380i	−0.384133	+	0.426623i
$143$	4.05682	−	7.02661i	0.339248	−	0.587595i
$144$	2.66226	+	0.565880i	0.221855	+	0.0471567i
$145$	−6.02372	−	0.0723677i	−0.500243	−	0.00600981i
$146$	2.23589	−	6.88138i	0.185044	−	0.569507i
$147$	−1.01905	+	3.54917i	−0.0840495	+	0.292731i
$148$	2.48341	−	1.80430i	0.204135	−	0.148313i
$149$	5.99602	+	10.3854i	0.491213	+	0.850806i	0.999949	−	0.0101168i	$-0.00322033\pi$
$149$	5.99602	+	10.3854i	0.491213	+	0.850806i	−0.508736	+	0.860923i	$0.669887\pi$
$150$	−2.09596	−	1.60113i	−0.171135	−	0.130732i
$151$	0.543307	−	0.941036i	0.0442137	−	0.0765804i	−0.843072	−	0.537801i	$-0.819255\pi$
$151$	0.543307	−	0.941036i	0.0442137	−	0.0765804i	0.887285	+	0.461221i	$0.152588\pi$
$152$	−5.85062	−	2.60486i	−0.474548	−	0.211282i
$153$	2.94202	−	9.05462i	0.237849	−	0.732023i
$154$	2.69479	−	2.51206i	0.217152	−	0.202427i
$155$	0.169994	+	1.82842i	0.0136542	+	0.146862i
$156$	−2.05674	+	2.28424i	−0.164671	+	0.182885i
$157$	−6.57294	+	11.3847i	−0.524578	+	0.908596i	0.475013	+	0.879979i	$0.342444\pi$
$157$	−6.57294	+	11.3847i	−0.524578	+	0.908596i	−0.999590	+	0.0286166i	$0.990890\pi$
$158$	6.22145	+	1.32241i	0.494952	+	0.105205i
$159$	0.203401	−	1.93523i	0.0161307	−	0.153474i
$160$	2.18146	+	0.491146i	0.172460	+	0.0388285i
$161$	−13.1077	−	17.4008i	−1.03303	−	1.37138i
$162$	−5.31770	−	3.86353i	−0.417798	−	0.303548i
$163$	−1.30909	+	12.4551i	−0.102536	+	0.975561i	0.815418	+	0.578873i	$0.196507\pi$
$163$	−1.30909	+	12.4551i	−0.102536	+	0.975561i	−0.917953	+	0.396688i	$0.870159\pi$
$164$	0.128912	+	1.22651i	0.0100663	+	0.0957746i
$165$	−1.49232	−	0.686023i	−0.116177	−	0.0534068i
$166$	−0.626134	+	5.95727i	−0.0485974	+	0.462373i
$167$	4.47823	+	13.7826i	0.346536	+	1.06653i	0.960757	+	0.277393i	$0.0894704\pi$
$167$	4.47823	+	13.7826i	0.346536	+	1.06653i	−0.614221	+	0.789134i	$0.710530\pi$
$168$	−1.19644	+	0.718610i	−0.0923073	+	0.0554419i
$169$	6.47475	+	19.9272i	0.498057	+	1.53286i
$170$	2.50624	−	7.40934i	0.192220	−	0.568271i
$171$	11.6635	+	12.9536i	0.891928	+	0.990587i
$172$	−7.46507	−	8.29080i	−0.569206	−	0.632168i
$173$	19.0703	+	8.49064i	1.44989	+	0.645531i	0.972445	−	0.233132i	$-0.0748976\pi$
$173$	19.0703	+	8.49064i	1.44989	+	0.645531i	0.477442	+	0.878663i	$0.341564\pi$
$174$	1.42116			0.107738
$175$	−13.1653	+	1.29398i	−0.995205	+	0.0978158i
$176$	1.39244			0.104959
$177$	−2.68590	−	1.19584i	−0.201885	−	0.0898848i
$178$	−1.95951	−	2.17625i	−0.146871	−	0.163117i
$179$	−8.18041	−	9.08526i	−0.611432	−	0.679064i	0.355330	−	0.934741i	$-0.384368\pi$
$179$	−8.18041	−	9.08526i	−0.611432	−	0.679064i	−0.966762	+	0.255676i	$0.917702\pi$
$180$	−4.88033	−	3.63614i	−0.363759	−	0.271022i
$181$	3.47217	+	10.6862i	0.258084	+	0.794302i	0.993206	+	0.116367i	$0.0371249\pi$
$181$	3.47217	+	10.6862i	0.258084	+	0.794302i	−0.735122	+	0.677935i	$0.762875\pi$
$182$	0.266370	+	15.4142i	0.0197447	+	1.14258i
$183$	−0.778920	−	2.39727i	−0.0575795	−	0.177211i
$184$	0.860697	−	8.18899i	0.0634514	−	0.603700i
$185$	−6.73064	+	1.34634i	−0.494846	+	0.0989851i
$186$	−0.0452820	−	0.430829i	−0.00332024	−	0.0315899i
$187$	0.509133	−	4.84407i	0.0372315	−	0.354234i
$188$	1.19333	+	0.867003i	0.0870323	+	0.0632327i
$189$	7.92624	−	0.971818i	0.576549	−	0.0706894i
$190$	9.45371	+	10.7565i	0.685844	+	0.780359i
$191$	−0.303617	+	2.88872i	−0.0219690	+	0.209021i	0.978031	+	0.208460i	$0.0668451\pi$
$191$	−0.303617	+	2.88872i	−0.0219690	+	0.209021i	−1.00000		0.000560697i	$0.999822\pi$
$192$	−0.515982	−	0.109675i	−0.0372378	−	0.00791514i
$193$	9.41478	−	16.3069i	0.677691	−	1.17379i	−0.297984	−	0.954571i	$-0.596314\pi$
$193$	9.41478	−	16.3069i	0.677691	−	1.17379i	0.975675	−	0.219224i	$-0.0703525\pi$
$194$	5.16345	−	5.73459i	0.370714	−	0.411719i
$195$	6.31202	−	2.71991i	0.452013	−	0.194777i
$196$	−1.93181	+	6.72816i	−0.137986	+	0.480583i
$197$	6.23701	−	19.1955i	0.444368	−	1.36763i	−0.438807	−	0.898581i	$-0.644599\pi$
$197$	6.23701	−	19.1955i	0.444368	−	1.36763i	0.883175	−	0.469044i	$-0.155401\pi$
$198$	−3.46221	−	1.54148i	−0.246049	−	0.109548i
$199$	−2.62204	+	4.54150i	−0.185871	+	0.321939i	−0.943870	−	0.330318i	$-0.892844\pi$
$199$	−2.62204	+	4.54150i	−0.185871	+	0.321939i	0.757998	+	0.652256i	$0.226177\pi$
$200$	−3.97331	−	3.03526i	−0.280956	−	0.214625i
$201$	2.00233	+	3.46814i	0.141233	+	0.244623i
$202$	−13.5449	+	9.84094i	−0.953015	+	0.692406i
$203$	5.21384	−	4.86029i	0.365940	−	0.341126i
$204$	−0.570205	+	1.75491i	−0.0399224	+	0.122868i
$205$	0.883613	−	2.61228i	0.0617142	−	0.182449i
$206$	−15.9048	−	3.38067i	−1.10814	−	0.235542i
$207$	−11.2055	+	19.4085i	−0.778836	+	1.34898i
$208$	−3.89895	+	4.33023i	−0.270344	+	0.300247i
$209$	7.21451	+	5.24165i	0.499038	+	0.362573i
$210$	3.10193	−	0.342551i	0.214054	−	0.0236382i
$211$	−0.983400	+	0.714482i	−0.0677001	+	0.0491870i	−0.621121	−	0.783715i	$-0.713322\pi$
$211$	−0.983400	+	0.714482i	−0.0677001	+	0.0491870i	0.553420	+	0.832902i	$0.313322\pi$
$212$	0.385587	−	3.66861i	0.0264822	−	0.251961i
$213$	−3.29667	+	1.46777i	−0.225884	+	0.100570i
$214$	0.403628	+	3.84027i	0.0275915	+	0.262515i
$215$	7.42329	+	23.8163i	0.506264	+	1.62426i
$216$	2.44183	+	1.77409i	0.166146	+	0.120712i
$217$	−1.63955	−	1.42574i	−0.111300	−	0.0967853i
$218$	−16.1310			−1.09253
$219$	2.55394	−	2.83644i	0.172579	−	0.191669i
$220$	−2.82900	−	1.30049i	−0.190731	−	0.0876793i
$221$	13.6385	+	15.1471i	0.917425	+	1.01890i
$222$	1.58389	−	0.336666i	0.106304	−	0.0225956i
$223$	23.3454	−	16.9615i	1.56333	−	1.13582i	0.630112	−	0.776504i	$-0.283009\pi$
$223$	23.3454	−	16.9615i	1.56333	−	1.13582i	0.933215	−	0.359319i	$-0.116991\pi$
$224$	−2.26809	+	1.36227i	−0.151543	+	0.0910203i
$225$	6.51923	+	11.9455i	0.434616	+	0.796368i
$226$	−4.90384	−	8.49371i	−0.326199	−	0.564993i
$227$	−1.69888	−	16.1638i	−0.112759	−	1.07283i	−0.893836	−	0.448393i	$-0.851996\pi$
$227$	−1.69888	−	16.1638i	−0.112759	−	1.07283i	0.781078	−	0.624434i	$-0.214670\pi$
$228$	−2.26054	−	2.51059i	−0.149708	−	0.166268i
$229$	−1.05491	+	0.224228i	−0.0697105	+	0.0148174i	−0.242635	−	0.970118i	$-0.578012\pi$
$229$	−1.05491	+	0.224228i	−0.0697105	+	0.0148174i	0.172924	+	0.984935i	$0.444678\pi$
$230$	−9.39688	+	15.8335i	−0.619612	+	1.04403i
$231$	1.83761	−	0.632382i	0.120906	−	0.0416077i
$232$	2.69408			0.176875
$233$	17.8610	−	19.8367i	1.17011	−	1.29954i	0.224417	−	0.974493i	$-0.427952\pi$
$233$	17.8610	−	19.8367i	1.17011	−	1.29954i	0.945697	−	0.325050i	$-0.105381\pi$
$234$	14.4882	−	6.45054i	0.947120	−	0.421685i
$235$	−1.61470	−	2.87599i	−0.105332	−	0.187609i
$236$	−5.09166	−	2.26695i	−0.331439	−	0.147566i
$237$	2.71441	+	1.97213i	0.176320	+	0.128104i
$238$	3.90979	+	8.38839i	0.253434	+	0.543738i
$239$	−5.52160	+	4.01168i	−0.357163	+	0.259494i	−0.751868	−	0.659314i	$-0.770847\pi$
$239$	−5.52160	+	4.01168i	−0.357163	+	0.259494i	0.394705	+	0.918808i	$0.370847\pi$
$240$	0.945877	+	0.704734i	0.0610561	+	0.0454904i
$241$	15.8414	−	7.05305i	1.02043	−	0.454327i	0.172828	−	0.984952i	$-0.444709\pi$
$241$	15.8414	−	7.05305i	1.02043	−	0.454327i	0.847607	+	0.530625i	$0.178043\pi$
$242$	8.86309	+	1.88391i	0.569741	+	0.121102i
$243$	−6.26108	−	10.8445i	−0.401648	−	0.695675i
$244$	−1.47660	−	4.54450i	−0.0945296	−	0.290932i
$245$	10.2087	−	11.8652i	0.652208	−	0.758040i
$246$	−0.201035	+	0.618721i	−0.0128175	+	0.0394482i
$247$	−36.5017	+	7.75868i	−2.32255	+	0.493673i
$248$	−0.0858410	−	0.816723i	−0.00545091	−	0.0518620i
$249$	−1.57991	+	2.73649i	−0.100123	+	0.173418i
$250$	5.23766	+	9.87760i	0.331259	+	0.624714i
$251$	−5.96477			−0.376493			−0.188247	−	0.982122i	$-0.560280\pi$
$251$	−5.96477			−0.376493			−0.188247	+	0.982122i	$0.560280\pi$
$252$	7.14751	−	0.876340i	0.450251	−	0.0552042i
$253$	−3.54304	+	10.9044i	−0.222749	+	0.685551i
$254$	5.71953	−	1.21572i	0.358875	−	0.0762813i
$255$	2.79750	−	3.03286i	0.175186	−	0.189925i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−9.43895	−	16.3487i	−0.588786	−	1.01981i	−0.994392	−	0.105759i	$-0.966273\pi$
$257$	−9.43895	−	16.3487i	−0.588786	−	1.01981i	0.405606	−	0.914048i	$-0.367060\pi$
$258$	−1.81859	−	5.59706i	−0.113221	−	0.348458i
$259$	4.65949	−	6.65198i	0.289527	−	0.413334i
$260$	11.9657	−	5.15614i	0.742081	−	0.319770i
$261$	−6.69864	−	2.98243i	−0.414636	−	0.184608i
$262$	5.23595	−	2.33119i	0.323478	−	0.144022i
$263$	0.580854	−	0.258613i	0.0358170	−	0.0159467i	−0.388750	−	0.921343i	$-0.627093\pi$
$263$	0.580854	−	0.258613i	0.0358170	−	0.0159467i	0.424567	+	0.905397i	$0.360426\pi$
$264$	0.671025	+	0.298760i	0.0412987	+	0.0183874i
$265$	−4.20974	+	7.09331i	−0.258602	+	0.435739i
$266$	−16.8794	−	1.47972i	−1.03495	−	0.0907276i
$267$	−0.477363	−	1.46917i	−0.0292141	−	0.0899119i
$268$	3.79581	+	6.57454i	0.231866	+	0.401604i
$269$	−20.6941	−	4.39868i	−1.26174	−	0.268192i	−0.471984	−	0.881607i	$-0.656462\pi$
$269$	−20.6941	−	4.39868i	−1.26174	−	0.268192i	−0.789761	+	0.613415i	$0.789795\pi$
$270$	−3.30407	−	5.88497i	−0.201079	−	0.358148i
$271$	18.3726	−	3.90522i	1.11606	−	0.237225i	0.387271	−	0.921966i	$-0.373418\pi$
$271$	18.3726	−	3.90522i	1.11606	−	0.237225i	0.728787	+	0.684741i	$0.240085\pi$
$272$	−1.08094	+	3.32678i	−0.0655415	+	0.201716i
$273$	−3.17887	+	7.48533i	−0.192394	+	0.453033i
$274$	18.9938			1.14746
$275$	4.53299	+	5.28437i	0.273350	+	0.318659i
$276$	2.17178	−	3.76164i	0.130726	−	0.226424i
$277$	2.97904	+	28.3437i	0.178993	+	1.70301i	0.603322	+	0.797498i	$0.293844\pi$
$277$	2.97904	+	28.3437i	0.178993	+	1.70301i	−0.424328	+	0.905508i	$0.639490\pi$
$278$	19.7224	−	4.19213i	1.18287	−	0.251427i
$279$	−0.690698	+	2.12575i	−0.0413510	+	0.127265i
$280$	5.88033	−	0.649373i	0.351417	−	0.0388074i
$281$	−6.94868	−	21.3858i	−0.414523	−	1.27577i	−0.912677	−	0.408683i	$-0.865988\pi$
$281$	−6.94868	−	21.3858i	−0.414523	−	1.27577i	0.498153	−	0.867089i	$-0.334012\pi$
$282$	0.389047	+	0.673849i	0.0231674	+	0.0401271i
$283$	9.31657	+	1.98030i	0.553812	+	0.117716i	0.476313	−	0.879276i	$-0.341973\pi$
$283$	9.31657	+	1.98030i	0.553812	+	0.117716i	0.0774996	+	0.996992i	$0.475306\pi$
$284$	−6.24950	+	2.78246i	−0.370840	+	0.165108i
$285$	2.24789	+	7.21197i	0.133154	+	0.427200i
$286$	6.56407	−	4.76907i	0.388141	−	0.282001i
$287$	1.37846	+	2.95745i	0.0813677	+	0.174573i
$288$	2.20193	+	1.59979i	0.129750	+	0.0942688i
$289$	−4.35220	−	1.93772i	−0.256012	−	0.113984i
$290$	−5.47351	−	2.51618i	−0.321415	−	0.147755i
$291$	3.71869	−	1.65567i	0.217993	−	0.0970568i
$292$	4.84150	−	5.37703i	0.283327	−	0.314667i
$293$	1.56537			0.0914500			0.0457250	−	0.998954i	$-0.485440\pi$
$293$	1.56537			0.0914500			0.0457250	+	0.998954i	$0.485440\pi$
$294$	−2.37452	+	2.82784i	−0.138485	+	0.164923i
$295$	8.22735	+	9.36115i	0.479015	+	0.545027i
$296$	3.00258	−	0.638218i	0.174522	−	0.0370957i
$297$	−2.81221	−	3.12327i	−0.163181	−	0.181231i
$298$	1.25351	+	11.9263i	0.0726138	+	0.690875i
$299$	−23.9896	−	41.5512i	−1.38735	−	2.40297i
$300$	−1.26352	−	2.31521i	−0.0729493	−	0.133669i
$301$	−25.8136	−	14.3146i	−1.48787	−	0.825081i
$302$	0.879090	−	0.638696i	0.0505859	−	0.0367528i
$303$	−8.63879	+	1.83623i	−0.496285	+	0.105489i
$304$	−4.28531	−	4.75932i	−0.245779	−	0.272966i
$305$	−1.24443	+	10.6121i	−0.0712561	+	0.607645i
$306$	6.37052	−	7.07518i	0.364178	−	0.404461i
$307$	−13.4495			−0.767604			−0.383802	−	0.923415i	$-0.625386\pi$
$307$	−13.4495			−0.767604			−0.383802	+	0.923415i	$0.625386\pi$
$308$	3.48356	−	1.19881i	0.198494	−	0.0683084i
$309$	−6.93924	−	5.04165i	−0.394760	−	0.286810i
$310$	−0.588389	+	1.73949i	−0.0334182	+	0.0987964i
$311$	1.74983	+	16.6485i	0.0992236	+	0.944050i	0.924978	+	0.380020i	$0.124083\pi$
$311$	1.74983	+	16.6485i	0.0992236	+	0.944050i	−0.825755	+	0.564030i	$0.809250\pi$
$312$	−2.80801	+	1.25020i	−0.158972	+	0.0707789i
$313$	0.186769	−	1.77699i	0.0105568	−	0.100441i	−0.987975	−	0.154616i	$-0.950586\pi$
$313$	0.186769	−	1.77699i	0.0105568	−	0.100441i	0.998531	+	0.0541745i	$0.0172527\pi$
$314$	−10.6352	+	7.72696i	−0.600182	+	0.436057i
$315$	−15.3399	−	4.89508i	−0.864305	−	0.275806i
$316$	5.14570	+	3.73857i	0.289469	+	0.210311i
$317$	−0.00954748	+	0.0106035i	−0.000536240	+	0.000595555i	−0.743413	−	0.668833i	$-0.766794\pi$
$317$	−0.00954748	+	0.0106035i	−0.000536240	+	0.000595555i	0.742877	+	0.669428i	$0.233461\pi$
$318$	0.972944	−	1.68519i	0.0545600	−	0.0945007i
$319$	−3.66939	−	0.779952i	−0.205446	−	0.0436689i
$320$	1.79310	+	1.33596i	0.100237	+	0.0746827i
$321$	−0.629448	+	1.93724i	−0.0351324	+	0.108126i
$322$	−4.89694	−	21.2279i	−0.272896	−	1.18298i
$323$	−18.1237	+	13.1677i	−1.00843	+	0.732668i
$324$	−3.28652	−	5.69241i	−0.182584	−	0.316245i
$325$	−29.1261	−	0.699930i	−1.61562	−	0.0388251i
$326$	−6.26187	+	10.8459i	−0.346813	+	0.600698i
$327$	−7.77361	−	3.46103i	−0.429881	−	0.191396i
$328$	−0.381101	+	1.17291i	−0.0210428	+	0.0647631i
$329$	3.73185	+	1.14165i	0.205743	+	0.0629413i
$330$	−1.08427	−	1.23370i	−0.0596874	−	0.0679128i
$331$	1.08446	−	1.20441i	0.0596072	−	0.0662005i	−0.712604	−	0.701567i	$-0.752484\pi$
$331$	1.08446	−	1.20441i	0.0596072	−	0.0662005i	0.772211	+	0.635366i	$0.219151\pi$
$332$	−2.99504	+	5.18756i	−0.164374	+	0.284704i
$333$	−8.17223	−	1.73706i	−0.447835	−	0.0951903i
$334$	−1.51481	+	14.4125i	−0.0828868	+	0.788615i
$335$	−1.57148	−	16.9025i	−0.0858590	−	0.923482i
$336$	−1.38529	+	0.169847i	−0.0755736	+	0.00926590i
$337$	−0.971591	−	0.705902i	−0.0529259	−	0.0384529i	0.561008	−	0.827811i	$-0.310414\pi$
$337$	−0.971591	−	0.705902i	−0.0529259	−	0.0384529i	−0.613934	+	0.789358i	$0.710414\pi$
$338$	−2.19016	+	20.8379i	−0.119129	+	1.13343i
$339$	−0.540794	−	5.14531i	−0.0293719	−	0.279455i
$340$	5.30322	−	5.74939i	0.287607	−	0.311805i
$341$	−0.119529	+	1.13724i	−0.00647285	+	0.0615851i
$342$	5.38641	+	16.5777i	0.291264	+	0.896418i
$343$	0.959610	+	18.4954i	0.0518141	+	0.998657i
$344$	−3.44751	−	10.6103i	−0.185877	−	0.572071i
$345$	−7.92560	+	5.61406i	−0.426700	+	0.302251i
$346$	13.9681	+	15.5132i	0.750931	+	0.833993i
$347$	−10.7613	−	11.9517i	−0.577699	−	0.641599i	0.381488	−	0.924374i	$-0.375412\pi$
$347$	−10.7613	−	11.9517i	−0.577699	−	0.641599i	−0.959186	+	0.282774i	$0.908745\pi$
$348$	1.29829	+	0.578036i	0.0695957	+	0.0309860i
$349$	−26.1328			−1.39886			−0.699429	−	0.714702i	$-0.746562\pi$
$349$	−26.1328			−1.39886			−0.699429	+	0.714702i	$0.746562\pi$
$350$	−12.5534	−	4.17271i	−0.671009	−	0.223041i
$351$	17.5871			0.938733
$352$	1.27206	+	0.566358i	0.0678011	+	0.0301870i
$353$	−0.738420	−	0.820098i	−0.0393021	−	0.0436494i	0.723173	−	0.690667i	$-0.242683\pi$
$353$	−0.738420	−	0.820098i	−0.0393021	−	0.0436494i	−0.762475	+	0.647017i	$0.776016\pi$
$354$	−1.96730	−	2.18491i	−0.104561	−	0.116127i
$355$	15.2957	+	0.183759i	0.811810	+	0.00975292i
$356$	−0.904937	−	2.78511i	−0.0479616	−	0.147610i
$357$	0.0843524	+	4.88127i	0.00446440	+	0.258344i
$358$	−3.77786	−	11.6271i	−0.199666	−	0.614510i
$359$	1.77325	−	16.8714i	0.0935886	−	0.890436i	−0.842506	−	0.538687i	$-0.818920\pi$
$359$	1.77325	−	16.8714i	0.0935886	−	0.890436i	0.936094	−	0.351749i	$-0.114413\pi$
$360$	−2.97946	−	5.30679i	−0.157031	−	0.279692i
$361$	−2.30120	−	21.8944i	−0.121116	−	1.15234i
$362$	−1.17450	+	11.1746i	−0.0617304	+	0.587325i
$363$	3.86695	+	2.80951i	0.202962	+	0.147461i
$364$	−6.02619	+	14.1899i	−0.315858	+	0.743754i
$365$	−14.8583	+	6.40260i	−0.777720	+	0.335127i
$366$	0.263479	−	2.50683i	0.0137722	−	0.131034i
$367$	16.0316	+	3.40762i	0.836843	+	0.177876i	0.606350	−	0.795198i	$-0.292633\pi$
$367$	16.0316	+	3.40762i	0.836843	+	0.177876i	0.230492	+	0.973074i	$0.425966\pi$
$368$	4.11705	−	7.13093i	0.214616	−	0.371726i
$369$	2.24602	−	2.49446i	0.116923	−	0.129857i
$370$	−6.69635	−	1.50765i	−0.348127	−	0.0783791i
$371$	−2.19380	−	9.50994i	−0.113896	−	0.493732i
$372$	0.133867	−	0.412000i	0.00694068	−	0.0213612i
$373$	25.9957	+	11.5740i	1.34601	+	0.599281i	0.948050	−	0.318122i	$-0.103052\pi$
$373$	25.9957	+	11.5740i	1.34601	+	0.599281i	0.397958	+	0.917404i	$0.369719\pi$
$374$	2.43538	−	4.21820i	0.125930	−	0.218118i
$375$	0.404739	+	5.88383i	0.0209006	+	0.303840i
$376$	0.737516	+	1.27742i	0.0380345	+	0.0658777i
$377$	12.7001	−	9.22714i	0.654087	−	0.475222i
$378$	7.63625	+	2.33609i	0.392767	+	0.120156i
$379$	−10.8635	+	33.4345i	−0.558022	+	1.71741i	0.129804	+	0.991540i	$0.458565\pi$
$379$	−10.8635	+	33.4345i	−0.558022	+	1.71741i	−0.687826	+	0.725875i	$0.741435\pi$
$380$	4.26133	+	13.6717i	0.218602	+	0.701345i
$381$	3.01711	+	0.641306i	0.154571	+	0.0328551i
$382$	−1.45232	+	2.51549i	−0.0743071	+	0.128704i
$383$	8.40269	−	9.33213i	0.429357	−	0.476850i	−0.489181	−	0.872183i	$-0.662704\pi$
$383$	8.40269	−	9.33213i	0.429357	−	0.476850i	0.918538	+	0.395333i	$0.129371\pi$
$384$	−0.426764	−	0.310062i	−0.0217782	−	0.0158228i
$385$	−8.19711	−	0.817933i	−0.417763	−	0.0416857i
$386$	15.2334	−	11.0677i	0.775361	−	0.563333i
$387$	−3.17397	+	30.1983i	−0.161342	+	1.53507i
$388$	7.04951	−	3.13864i	0.357885	−	0.159340i
$389$	−2.31543	−	22.0298i	−0.117397	−	1.11696i	−0.881605	−	0.471988i	$-0.843537\pi$
$389$	−2.31543	−	22.0298i	−0.117397	−	1.11696i	0.764208	−	0.644970i	$-0.223130\pi$
$390$	6.87261	+	0.0825660i	0.348008	+	0.00418089i
$391$	−23.3019	−	16.9298i	−1.17843	−	0.856179i
$392$	−4.50138	+	5.36074i	−0.227354	+	0.270758i
$393$	3.02340			0.152510
$394$	13.5053	−	14.9992i	0.680388	−	0.755647i
$395$	−6.96271	−	12.4015i	−0.350332	−	0.623986i
$396$	−2.53591	−	2.81642i	−0.127434	−	0.141530i
$397$	−37.1893	+	7.90483i	−1.86648	+	0.396732i	−0.995514	−	0.0946164i	$-0.969838\pi$
$397$	−37.1893	+	7.90483i	−1.86648	+	0.396732i	−0.870963	+	0.491348i	$0.836504\pi$
$398$	−4.24255	+	3.08239i	−0.212660	+	0.154506i
$399$	−7.81679	−	4.33470i	−0.391329	−	0.217006i
$400$	−2.39525	−	4.38894i	−0.119763	−	0.219447i
$401$	6.15978	+	10.6691i	0.307605	+	0.532787i	0.977838	−	0.209363i	$-0.0671392\pi$
$401$	6.15978	+	10.6691i	0.307605	+	0.532787i	−0.670233	+	0.742151i	$0.733806\pi$
$402$	0.418601	+	3.98272i	0.0208779	+	0.198640i
$403$	−3.20191	−	3.55608i	−0.159498	−	0.177141i
$404$	−16.3765	+	3.48094i	−0.814764	+	0.173183i
$405$	1.36063	+	14.6346i	0.0676101	+	0.727201i
$406$	6.73994	−	2.31944i	0.334498	−	0.115112i
$407$	−4.27433			−0.211871
$408$	−1.23470	+	1.37127i	−0.0611265	+	0.0678879i
$409$	8.81572	−	3.92501i	0.435909	−	0.194079i	−0.177036	−	0.984204i	$-0.556651\pi$
$409$	8.81572	−	3.92501i	0.435909	−	0.194079i	0.612946	+	0.790125i	$0.289984\pi$
$410$	1.86973	−	2.02704i	0.0923394	−	0.100108i
$411$	9.15319	+	4.07526i	0.451493	+	0.201018i
$412$	−13.1547	−	9.55746i	−0.648086	−	0.470862i
$413$	−14.6898	−	1.28777i	−0.722838	−	0.0633670i
$414$	−18.1309	+	13.1729i	−0.891084	+	0.647411i
$415$	10.9300	−	7.74219i	0.536530	−	0.380049i
$416$	−5.32313	+	2.37001i	−0.260988	+	0.116199i
$417$	10.4038	+	2.21139i	0.509474	+	0.108292i
$418$	4.45882	+	7.72289i	0.218088	+	0.377739i
$419$	−5.32381	−	16.3850i	−0.260085	−	0.800459i	−0.992785	−	0.119908i	$-0.961740\pi$
$419$	−5.32381	−	16.3850i	−0.260085	−	0.800459i	0.732700	−	0.680552i	$-0.238260\pi$
$420$	2.97308	+	0.948734i	0.145072	+	0.0462935i
$421$	8.99101	−	27.6715i	0.438195	−	1.34863i	−0.451581	−	0.892230i	$-0.649140\pi$
$421$	8.99101	−	27.6715i	0.438195	−	1.34863i	0.889777	−	0.456396i	$-0.150860\pi$
$422$	−1.18899	+	0.252727i	−0.0578790	+	0.0123026i
$423$	−0.419645	−	3.99265i	−0.0204038	−	0.194129i
$424$	1.84441	−	3.19461i	0.0895725	−	0.155144i
$425$	−16.1441	+	6.72789i	−0.783106	+	0.326351i
$426$	−3.60866			−0.174840
$427$	−7.60662	−	10.0980i	−0.368110	−	0.488676i
$428$	−1.19324	+	3.67243i	−0.0576776	+	0.177514i
$429$	4.18649	−	0.889866i	0.202126	−	0.0429631i
$430$	−2.90546	+	24.7766i	−0.140114	+	1.19484i
$431$	−33.0172	−	7.01802i	−1.59038	−	0.338046i	−0.674118	−	0.738624i	$-0.735476\pi$
$431$	−33.0172	−	7.01802i	−1.59038	−	0.338046i	−0.916263	+	0.400578i	$0.868809\pi$
$432$	1.50914	+	2.61390i	0.0726083	+	0.125761i
$433$	3.17077	+	9.75863i	0.152378	+	0.468970i	0.997886	−	0.0649926i	$-0.0207024\pi$
$433$	3.17077	+	9.75863i	0.152378	+	0.468970i	−0.845508	+	0.533962i	$0.820702\pi$
$434$	−0.917900	−	1.96934i	−0.0440606	−	0.0945313i
$435$	−2.09784	−	2.38694i	−0.100584	−	0.114445i
$436$	−14.7364	−	6.56108i	−0.705747	−	0.314219i
$437$	48.1745	−	21.4487i	2.30450	−	1.02603i
$438$	3.48682	−	1.55243i	0.166607	−	0.0741781i
$439$	3.03164	+	1.34977i	0.144692	+	0.0644211i	0.477805	−	0.878466i	$-0.341432\pi$
$439$	3.03164	+	1.34977i	0.144692	+	0.0644211i	−0.333113	+	0.942887i	$0.608099\pi$
$440$	−2.05546	−	2.33872i	−0.0979902	−	0.111494i
$441$	17.1269	−	8.34594i	0.815564	−	0.397426i
$442$	6.29851	+	19.3848i	0.299590	+	0.922042i
$443$	13.3273	+	23.0836i	0.633199	+	1.09673i	0.986894	+	0.161372i	$0.0515918\pi$
$443$	13.3273	+	23.0836i	0.633199	+	1.09673i	−0.353695	+	0.935361i	$0.615075\pi$
$444$	1.58389	+	0.336666i	0.0751682	+	0.0159775i
$445$	−0.762654	+	6.50362i	−0.0361533	+	0.308301i
$446$	28.2260	−	5.99962i	1.33654	−	0.284090i
$447$	−1.95482	+	6.01630i	−0.0924596	+	0.284561i
$448$	−2.62609	+	0.321979i	−0.124071	+	0.0152121i
$449$	14.9933			0.707575			0.353788	−	0.935326i	$-0.384894\pi$
$449$	14.9933			0.707575			0.353788	+	0.935326i	$0.384894\pi$
$450$	1.09694	+	13.5644i	0.0517101	+	0.639431i
$451$	0.858630	−	1.48719i	0.0404313	−	0.0700291i
$452$	−1.02518	−	9.75396i	−0.0482205	−	0.458788i
$453$	0.560674	−	0.119175i	0.0263428	−	0.00559933i
$454$	5.02239	−	15.4573i	0.235713	−	0.725449i
$455$	25.4962	−	23.2011i	1.19528	−	1.08768i
$456$	−1.04396	−	3.21298i	−0.0488880	−	0.150462i
$457$	11.3130	+	19.5946i	0.529198	+	0.916598i	0.999420	+	0.0340497i	$0.0108405\pi$
$457$	11.3130	+	19.5946i	0.529198	+	0.916598i	−0.470222	+	0.882548i	$0.655826\pi$
$458$	−1.05491	−	0.224228i	−0.0492928	−	0.0104775i
$459$	9.64510	−	4.29427i	0.450195	−	0.200440i
$460$	−15.0245	+	10.6426i	−0.700523	+	0.496213i
$461$	−7.72888	+	5.61536i	−0.359970	+	0.261533i	−0.753040	−	0.657975i	$-0.771413\pi$
$461$	−7.72888	+	5.61536i	−0.359970	+	0.261533i	0.393070	+	0.919509i	$0.371413\pi$
$462$	1.93595	+	0.169714i	0.0900688	+	0.00789580i
$463$	−7.70194	−	5.59579i	−0.357939	−	0.260058i	0.394253	−	0.919002i	$-0.371003\pi$
$463$	−7.70194	−	5.59579i	−0.357939	−	0.260058i	−0.752192	+	0.658944i	$0.771003\pi$
$464$	2.46117	+	1.09578i	0.114257	+	0.0508704i
$465$	−0.656768	+	0.712024i	−0.0304569	+	0.0330193i
$466$	24.3852	−	10.8570i	1.12962	−	0.502939i
$467$	−3.14758	+	3.49574i	−0.145652	+	0.161763i	−0.811556	−	0.584274i	$-0.801379\pi$
$467$	−3.14758	+	3.49574i	−0.145652	+	0.161763i	0.665904	+	0.746037i	$0.268046\pi$
$468$	15.8593			0.733094
$469$	15.1565	+	13.1800i	0.699861	+	0.608594i
$470$	−0.305334	−	3.28411i	−0.0140840	−	0.151485i
$471$	−6.78305	+	1.44178i	−0.312546	+	0.0664338i
$472$	−3.72941	−	4.14193i	−0.171660	−	0.190648i
$473$	1.62381	+	15.4495i	0.0746629	+	0.710370i
$474$	1.67760	+	2.90568i	0.0770546	+	0.133462i
$475$	4.11126	−	31.7565i	0.188638	−	1.45709i
$476$	0.159907	+	9.25343i	0.00732932	+	0.424130i
$477$	−8.12252	+	5.90135i	−0.371905	+	0.270204i
$478$	−6.67593	+	1.41901i	−0.305350	+	0.0649042i
$479$	−19.1285	−	21.2444i	−0.874004	−	0.970680i	0.125767	−	0.992060i	$-0.459861\pi$
$479$	−19.1285	−	21.2444i	−0.874004	−	0.970680i	−0.999771	+	0.0213800i	$0.993194\pi$
$480$	0.577460	+	1.02853i	0.0263573	+	0.0469457i
$481$	11.9685	−	13.2923i	0.545715	−	0.606078i
$482$	17.3406			0.789842
$483$	2.19474	−	11.2805i	0.0998641	−	0.513279i
$484$	7.33058	+	5.32598i	0.333208	+	0.242090i
$485$	−17.2537	−	0.207282i	−0.783450	−	0.00941221i
$486$	−1.30892	−	12.4536i	−0.0593739	−	0.564905i
$487$	15.1104	−	6.72759i	0.684718	−	0.304856i	−0.0347354	−	0.999397i	$-0.511059\pi$
$487$	15.1104	−	6.72759i	0.684718	−	0.304856i	0.719454	+	0.694540i	$0.244392\pi$
$488$	0.499476	−	4.75220i	0.0226102	−	0.215122i
$489$	−5.34469	+	3.88314i	−0.241695	+	0.175602i
$490$	14.1521	−	6.68717i	0.639326	−	0.302095i
$491$	24.6939	+	17.9412i	1.11442	+	0.809673i	0.983354	−	0.181700i	$-0.0581601\pi$
$491$	24.6939	+	17.9412i	1.11442	+	0.809673i	0.131066	+	0.991374i	$0.458160\pi$
$492$	−0.435311	+	0.483462i	−0.0196253	+	0.0217961i
$493$	4.71194	−	8.16131i	0.212215	−	0.367567i
$494$	−36.5017	−	7.75868i	−1.64229	−	0.349079i
$495$	2.52172	+	8.09050i	0.113343	+	0.363641i
$496$	0.253771	−	0.781028i	0.0113947	−	0.0350692i
$497$	−13.2392	+	12.3415i	−0.593860	+	0.553590i
$498$	−2.55635	+	1.85730i	−0.114553	+	0.0832276i
$499$	8.41633	+	14.5775i	0.376767	+	0.652579i	0.990590	−	0.136865i	$-0.0437025\pi$
$499$	8.41633	+	14.5775i	0.376767	+	0.652579i	−0.613823	+	0.789444i	$0.710369\pi$
$500$	0.767264	+	11.1540i	0.0343131	+	0.498821i
$501$	−3.82230	+	6.62041i	−0.170768	+	0.295778i
$502$	−5.44909	−	2.42609i	−0.243205	−	0.108282i
$503$	−8.56517	+	26.3609i	−0.381902	+	1.17537i	0.556801	+	0.830646i	$0.312029\pi$
$503$	−8.56517	+	26.3609i	−0.381902	+	1.17537i	−0.938703	+	0.344728i	$0.887971\pi$
$504$	6.88601	+	2.10658i	0.306727	+	0.0938344i
$505$	36.5229	+	8.22296i	1.62525	+	0.365917i
$506$	−7.67193	+	8.52054i	−0.341059	+	0.378784i
$507$	−5.52638	+	9.57198i	−0.245435	+	0.425106i
$508$	5.71953	+	1.21572i	0.253763	+	0.0539390i
$509$	−1.25769	+	11.9661i	−0.0557460	+	0.530388i	0.930639	+	0.365938i	$0.119252\pi$
$509$	−1.25769	+	11.9661i	−0.0557460	+	0.530388i	−0.986385	+	0.164450i	$0.947415\pi$
$510$	3.78922	−	1.63281i	0.167789	−	0.0723021i
$511$	7.48297	−	17.6202i	0.331027	−	0.779474i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−2.02052	+	19.2240i	−0.0892084	+	0.848761i
$514$	−1.97328	−	18.7745i	−0.0870376	−	0.828107i
$515$	17.7998	+	31.7037i	0.784353	+	1.39703i
$516$	0.615160	−	5.85286i	0.0270809	−	0.257658i
$517$	−0.634691	−	1.95338i	−0.0279137	−	0.0859094i
$518$	6.96226	−	4.18170i	0.305904	−	0.183733i
$519$	3.40283	+	10.4728i	0.149368	+	0.459706i
$520$	13.0284	+	0.156520i	0.571333	+	0.00686387i
$521$	7.11527	+	7.90231i	0.311726	+	0.346206i	0.878566	−	0.477621i	$-0.158501\pi$
$521$	7.11527	+	7.90231i	0.311726	+	0.346206i	−0.566840	+	0.823828i	$0.691834\pi$
$522$	−4.90645	−	5.44917i	−0.214750	−	0.238504i
$523$	−32.4473	−	14.4465i	−1.41882	−	0.631699i	−0.453141	−	0.891439i	$-0.649697\pi$
$523$	−32.4473	−	14.4465i	−1.41882	−	0.631699i	−0.965679	+	0.259740i	$0.916363\pi$
$524$	5.73146			0.250380
$525$	−5.15426	−	4.70428i	−0.224950	−	0.205312i
$526$	0.635823			0.0277232
$527$	−2.62427	−	1.16840i	−0.114315	−	0.0508964i
$528$	0.491495	+	0.545861i	0.0213896	+	0.0237555i
$529$	29.9772	+	33.2931i	1.30336	+	1.44753i
$530$	−6.73090	+	4.76780i	−0.292372	+	0.207100i
$531$	4.68767	+	14.4272i	0.203428	+	0.626086i
$532$	−14.8183	−	8.21728i	−0.642454	−	0.356264i
$533$	2.22064	+	6.83442i	0.0961865	+	0.296032i
$534$	0.161473	−	1.53632i	0.00698764	−	0.0664829i
$535$	5.85420	−	6.34674i	0.253099	−	0.274393i
$536$	0.793541	+	7.55004i	0.0342758	+	0.326112i
$537$	0.674108	−	6.41370i	0.0290899	−	0.276772i
$538$	−17.1159	−	12.4355i	−0.737921	−	0.536131i
$539$	7.68292	−	5.99825i	0.330927	−	0.258363i
$540$	−0.624786	−	6.72008i	−0.0268865	−	0.289186i
$541$	3.47242	−	33.0379i	0.149291	−	1.42041i	−0.621546	−	0.783378i	$-0.713495\pi$
$541$	3.47242	−	33.0379i	0.149291	−	1.42041i	0.770837	−	0.637033i	$-0.219838\pi$
$542$	18.3726	+	3.90522i	0.789172	+	0.167744i
$543$	−2.96360	+	5.13310i	−0.127180	+	0.220283i
$544$	−2.34061	+	2.59951i	−0.100353	+	0.111453i
$545$	23.8118	+	27.0933i	1.01999	+	1.16055i
$546$	−5.94860	+	5.54522i	−0.254577	+	0.237314i
$547$	11.1088	−	34.1894i	0.474978	−	1.46183i	−0.371009	−	0.928629i	$-0.620988\pi$
$547$	11.1088	−	34.1894i	0.474978	−	1.46183i	0.845987	−	0.533204i	$-0.179012\pi$
$548$	17.3517	+	7.72547i	0.741227	+	0.330016i
$549$	−6.50273	+	11.2631i	−0.277530	+	0.480696i
$550$	1.99175	+	6.67124i	0.0849285	+	0.284463i
$551$	8.62686	+	14.9422i	0.367516	+	0.636557i
$552$	3.51402	−	2.55308i	0.149567	−	0.108666i
$553$	16.0920	+	4.92288i	0.684301	+	0.209342i
$554$	−8.80692	+	27.1049i	−0.374170	+	1.15158i
$555$	−2.90352	−	2.16330i	−0.123248	−	0.0918268i
$556$	19.7224	+	4.19213i	0.836416	+	0.177786i
$557$	−9.79798	+	16.9706i	−0.415154	+	0.719067i	−0.995445	−	0.0953422i	$-0.969605\pi$
$557$	−9.79798	+	16.9706i	−0.415154	+	0.719067i	0.580291	+	0.814409i	$0.302939\pi$
$558$	−1.49560	+	1.66104i	−0.0633140	+	0.0703173i
$559$	−52.5918	−	38.2102i	−2.22440	−	1.61612i
$560$	5.63608	+	1.79852i	0.238168	+	0.0760011i
$561$	2.07867	−	1.51024i	0.0877613	−	0.0637623i
$562$	2.35047	−	22.3632i	0.0991485	−	0.943335i
$563$	39.9905	−	17.8049i	1.68540	−	0.750388i	0.685651	−	0.727930i	$-0.259518\pi$
$563$	39.9905	−	17.8049i	1.68540	−	0.750388i	0.999748	−	0.0224577i	$-0.00714912\pi$
$564$	0.0813330	+	0.773832i	0.00342474	+	0.0325842i
$565$	−7.02701	+	20.7744i	−0.295629	+	0.873985i
$566$	7.70565	+	5.59848i	0.323893	+	0.235322i
$567$	−13.1229	−	11.4116i	−0.551109	−	0.479240i
$568$	−6.84093			−0.287039
$569$	−15.9583	+	17.7235i	−0.669008	+	0.743009i	−0.978126	−	0.208015i	$-0.933300\pi$
$569$	−15.9583	+	17.7235i	−0.669008	+	0.743009i	0.309118	+	0.951024i	$0.399966\pi$
$570$	−0.879820	+	7.50276i	−0.0368516	+	0.314256i
$571$	3.45371	+	3.83574i	0.144533	+	0.160521i	0.811065	−	0.584956i	$-0.198888\pi$
$571$	3.45371	+	3.83574i	0.144533	+	0.160521i	−0.666531	+	0.745477i	$0.732222\pi$
$572$	7.93633	−	1.68692i	0.331835	−	0.0705336i
$573$	−1.23960	+	0.900619i	−0.0517848	+	0.0376239i
$574$	0.0563776	+	3.26244i	0.00235316	+	0.136172i
$575$	40.4648	−	7.58988i	1.68750	−	0.316520i
$576$	1.36087	+	2.35709i	0.0567028	+	0.0982121i
$577$	−2.03736	−	19.3842i	−0.0848165	−	0.806975i	−0.951403	−	0.307948i	$-0.900358\pi$
$577$	−2.03736	−	19.3842i	−0.0848165	−	0.806975i	0.866587	−	0.499027i	$-0.166309\pi$
$578$	−3.18779	−	3.54040i	−0.132595	−	0.147261i
$579$	9.71572	−	2.06514i	0.403772	−	0.0858243i
$580$	−3.97688	−	4.52492i	−0.165131	−	0.187887i
$581$	−3.02670	+	15.5566i	−0.125569	+	0.645395i
$582$	4.07061			0.168732
$583$	−3.43697	+	3.81715i	−0.142345	+	0.158090i
$584$	6.60996	−	2.94295i	0.273522	−	0.121780i
$585$	−32.2209	−	14.8120i	−1.33217	−	0.612400i
$586$	1.43004	+	0.636694i	0.0590743	+	0.0263016i
$587$	1.11681	+	0.811409i	0.0460956	+	0.0334904i	0.610594	−	0.791943i	$-0.290931\pi$
$587$	1.11681	+	0.811409i	0.0460956	+	0.0334904i	−0.564499	+	0.825434i	$0.690931\pi$
$588$	−3.31942	+	1.61756i	−0.136891	+	0.0667070i
$589$	4.25490	−	3.09137i	0.175320	−	0.127378i
$590$	3.70854	+	11.8982i	0.152678	+	0.489841i
$591$	9.72645	−	4.33050i	0.400093	−	0.178133i
$592$	3.00258	+	0.638218i	0.123405	+	0.0262306i
$593$	17.0599	+	29.5485i	0.700564	+	1.21341i	0.968269	+	0.249912i	$0.0804017\pi$
$593$	17.0599	+	29.5485i	0.700564	+	1.21341i	−0.267704	+	0.963501i	$0.586265\pi$
$594$	−1.29873	−	3.99708i	−0.0532875	−	0.164002i
$595$	8.31749	−	18.9493i	0.340984	−	0.776846i
$596$	−3.70574	+	11.4051i	−0.151793	+	0.467171i
$597$	−2.70585	+	0.575146i	−0.110743	+	0.0235392i
$598$	−5.01519	−	47.7164i	−0.205086	−	1.95127i
$599$	3.61310	−	6.25808i	0.147627	−	0.255698i	−0.782723	−	0.622371i	$-0.786170\pi$
$599$	3.61310	−	6.25808i	0.147627	−	0.255698i	0.930350	+	0.366672i	$0.119503\pi$
$600$	−0.212602	−	2.62897i	−0.00867943	−	0.107327i
$601$	−11.7522			−0.479381			−0.239690	−	0.970849i	$-0.577046\pi$
$601$	−11.7522			−0.479381			−0.239690	+	0.970849i	$0.577046\pi$
$602$	−17.7597	−	23.5764i	−0.723830	−	0.960903i
$603$	6.38503	−	19.6511i	0.260019	−	0.800255i
$604$	1.06287	−	0.225920i	0.0432476	−	0.00919255i
$605$	−9.91910	−	17.6672i	−0.403269	−	0.718273i
$606$	−8.63879	−	1.83623i	−0.350927	−	0.0745918i
$607$	16.4030	+	28.4108i	0.665777	+	1.15316i	0.979074	+	0.203504i	$0.0652331\pi$
$607$	16.4030	+	28.4108i	0.665777	+	1.15316i	−0.313297	+	0.949655i	$0.601434\pi$
$608$	−1.97904	−	6.09085i	−0.0802605	−	0.247017i
$609$	3.74566	+	0.328360i	0.151782	+	0.0133058i
$610$	−5.45316	+	9.18844i	−0.220792	+	0.372029i
$611$	7.85180	+	3.49585i	0.317650	+	0.141427i
$612$	8.69749	−	3.87237i	0.351575	−	0.156531i
$613$	4.76273	−	2.12050i	0.192365	−	0.0856463i	−0.308294	−	0.951291i	$-0.599758\pi$
$613$	4.76273	−	2.12050i	0.192365	−	0.0856463i	0.500658	+	0.865645i	$0.333091\pi$
$614$	−12.2867	−	5.47041i	−0.495852	−	0.220768i
$615$	1.33595	−	0.575673i	0.0538706	−	0.0232134i
$616$	3.66999	+	0.321727i	0.147868	+	0.0129627i
$617$	−11.7764	−	36.2441i	−0.474101	−	1.45913i	−0.847166	−	0.531329i	$-0.821693\pi$
$617$	−11.7764	−	36.2441i	−0.474101	−	1.45913i	0.373064	−	0.927805i	$-0.378307\pi$
$618$	−4.28869	−	7.42822i	−0.172516	−	0.298807i
$619$	43.8517	+	9.32097i	1.76255	+	0.374641i	0.971487	−	0.237094i	$-0.0761948\pi$
$619$	43.8517	+	9.32097i	1.76255	+	0.374641i	0.791063	+	0.611735i	$0.209528\pi$
$620$	−1.24503	+	1.34978i	−0.0500018	+	0.0542086i
$621$	−24.3096	+	5.16717i	−0.975512	+	0.207351i
$622$	−5.17301	+	15.9209i	−0.207419	+	0.638369i
$623$	−4.66173	−	6.18857i	−0.186768	−	0.247940i
$624$	−3.07374			−0.123048
$625$	8.85859	−	23.3779i	0.354344	−	0.935115i
$626$	0.893387	−	1.54739i	0.0357069	−	0.0618462i
$627$	0.491716	+	4.67837i	0.0196373	+	0.186836i
$628$	−12.8586	+	2.73318i	−0.513115	+	0.109066i
$629$	3.31811	−	10.2121i	0.132302	−	0.407183i
$630$	−12.0227	−	10.7112i	−0.478995	−	0.426743i
$631$	−3.15651	−	9.71473i	−0.125659	−	0.386737i	0.868362	−	0.495931i	$-0.165173\pi$
$631$	−3.15651	−	9.71473i	−0.125659	−	0.386737i	−0.994020	+	0.109194i	$0.965173\pi$
$632$	3.18022	+	5.50830i	0.126502	+	0.219109i
$633$	−0.627202	−	0.133316i	−0.0249290	−	0.00529883i
$634$	−0.0130349	+	0.00580351i	−0.000517682	+	0.000230487i
$635$	−10.4848	−	7.81180i	−0.416076	−	0.310002i
$636$	1.57426	−	1.14376i	0.0624233	−	0.0453532i
$637$	−2.85942	+	40.6879i	−0.113294	+	1.61211i
$638$	−3.03492	−	2.20500i	−0.120153	−	0.0872966i
$639$	17.0095	+	7.57311i	0.672884	+	0.299587i
$640$	1.09469	+	1.94978i	0.0432714	+	0.0770719i
$641$	−7.83501	+	3.48837i	−0.309464	+	0.137782i	−0.555592	−	0.831455i	$-0.687508\pi$
$641$	−7.83501	+	3.48837i	−0.309464	+	0.137782i	0.246128	+	0.969237i	$0.420842\pi$
$642$	−1.36298	+	1.51374i	−0.0537924	+	0.0597425i
$643$	7.88170			0.310824			0.155412	−	0.987850i	$-0.450329\pi$
$643$	7.88170			0.310824			0.155412	+	0.987850i	$0.450329\pi$
$644$	4.16057	−	21.3844i	0.163949	−	0.842663i
$645$	−6.71617	+	11.3166i	−0.264449	+	0.445590i
$646$	−21.9126	+	4.65767i	−0.862140	+	0.183254i
$647$	9.68457	+	10.7558i	0.380740	+	0.422854i	0.902804	−	0.430052i	$-0.141505\pi$
$647$	9.68457	+	10.7558i	0.380740	+	0.422854i	−0.522065	+	0.852906i	$0.674838\pi$
$648$	−0.687069	−	6.53703i	−0.0269906	−	0.256799i
$649$	3.88041	+	6.72106i	0.152319	+	0.263825i
$650$	−26.3233	−	12.4861i	−1.03248	−	0.489744i
$651$	−0.0198034	−	1.14597i	−0.000776156	−	0.0449143i
$652$	−10.1319	+	7.36127i	−0.396797	+	0.288290i
$653$	47.8772	−	10.1766i	1.87358	−	0.398242i	0.876971	−	0.480542i	$-0.159560\pi$
$653$	47.8772	−	10.1766i	1.87358	−	0.398242i	0.996608	+	0.0823009i	$0.0262269\pi$
$654$	−5.69381	−	6.32362i	−0.222646	−	0.247273i
$655$	−11.6445	−	5.35298i	−0.454987	−	0.209158i
$656$	−0.825218	+	0.916498i	−0.0322194	+	0.0357832i
$657$	−19.6931			−0.768302
$658$	2.94486	+	2.56083i	0.114803	+	0.0998315i
$659$	−2.98994	−	2.17232i	−0.116472	−	0.0846215i	0.528025	−	0.849229i	$-0.322933\pi$
$659$	−2.98994	−	2.17232i	−0.116472	−	0.0846215i	−0.644496	+	0.764608i	$0.722933\pi$
$660$	−0.488745	−	1.56805i	−0.0190244	−	0.0610363i
$661$	0.306056	+	2.91193i	0.0119042	+	0.113261i	0.998860	−	0.0477284i	$-0.0151982\pi$
$661$	0.306056	+	2.91193i	0.0119042	+	0.113261i	−0.986956	+	0.160989i	$0.948532\pi$
$662$	1.48058	−	0.659196i	0.0575444	−	0.0256204i
$663$	−1.12388	+	10.6930i	−0.0436480	+	0.415283i
$664$	−4.84608	+	3.52088i	−0.188064	+	0.136637i
$665$	22.4313	+	30.5346i	0.869849	+	1.18408i
$666$	−6.75918	−	4.91083i	−0.261913	−	0.190291i
$667$	−14.8435	+	16.4854i	−0.574745	+	0.638318i
$668$	−7.24593	+	12.5503i	−0.280353	+	0.485586i
$669$	14.8895	+	3.16486i	0.575661	+	0.122360i
$670$	5.43925	−	16.0804i	0.210137	−	0.621239i
$671$	−2.05608	+	6.32797i	−0.0793742	+	0.244289i
$672$	−1.33460	−	0.408284i	−0.0514835	−	0.0157499i
$673$	−20.4906	+	14.8873i	−0.789855	+	0.573863i	−0.907920	−	0.419142i	$-0.862331\pi$
$673$	−20.4906	+	14.8873i	−0.789855	+	0.573863i	0.118065	+	0.993006i	$0.462331\pi$
$674$	−0.600476	−	1.04006i	−0.0231295	−	0.0400614i
$675$	−5.00695	+	14.2366i	−0.192718	+	0.547965i
$676$	−10.4764	+	18.1456i	−0.402937	+	0.697907i
$677$	27.8523	+	12.4006i	1.07045	+	0.476595i	0.864844	−	0.502040i	$-0.167417\pi$
$677$	27.8523	+	12.4006i	1.07045	+	0.476595i	0.205606	+	0.978635i	$0.434084\pi$
$678$	1.59875	−	4.92043i	0.0613995	−	0.188968i
$679$	14.9340	−	13.9213i	0.573114	−	0.534251i
$680$	7.18322	−	3.09532i	0.275464	−	0.118700i
$681$	5.73680	−	6.37136i	0.219835	−	0.244151i
$682$	−0.571753	+	0.990305i	−0.0218935	+	0.0379207i
$683$	−36.1494	−	7.68380i	−1.38322	−	0.294012i	−0.544585	−	0.838706i	$-0.683313\pi$
$683$	−36.1494	−	7.68380i	−1.38322	−	0.294012i	−0.838635	+	0.544693i	$0.816646\pi$
$684$	−1.82201	+	17.3353i	−0.0696664	+	0.662832i
$685$	−28.0377	−	31.9015i	−1.07127	−	1.21889i
$686$	−6.64610	+	17.2867i	−0.253749	+	0.660009i
$687$	−0.460256	−	0.334396i	−0.0175599	−	0.0127580i
$688$	1.16616	−	11.0953i	0.0444594	−	0.423003i
$689$	−2.24677	−	21.3766i	−0.0855953	−	0.814384i
$690$	−9.52384	+	1.90507i	−0.362566	+	0.0725248i
$691$	−0.789268	+	7.50938i	−0.0300252	+	0.285670i	0.969199	+	0.246280i	$0.0792083\pi$
$691$	−0.789268	+	7.50938i	−0.0300252	+	0.285670i	−0.999224	+	0.0393904i	$0.987458\pi$
$692$	6.45074	+	19.8533i	0.245220	+	0.754710i
$693$	−8.76900	−	4.86273i	−0.333107	−	0.184720i
$694$	−4.96979	−	15.2954i	−0.188650	−	0.580606i
$695$	−36.1543	−	26.9371i	−1.37141	−	1.02178i
$696$	0.950939	+	1.05612i	0.0360452	+	0.0400323i
$697$	2.88660	+	3.20590i	0.109338	+	0.121432i
$698$	−23.8735	−	10.6292i	−0.903626	−	0.402320i
$699$	14.0808			0.532583
$700$	−9.77093	−	8.91790i	−0.369307	−	0.337065i
$701$	−4.79681			−0.181173			−0.0905865	−	0.995889i	$-0.528874\pi$
$701$	−4.79681			−0.181173			−0.0905865	+	0.995889i	$0.528874\pi$
$702$	16.0667	+	7.15334i	0.606397	+	0.269985i
$703$	13.1545	+	14.6095i	0.496130	+	0.551008i
$704$	0.931727	+	1.03479i	0.0351158	+	0.0390000i
$705$	0.557489	−	1.64814i	0.0209963	−	0.0620725i
$706$	−0.341016	−	1.04954i	−0.0128343	−	0.0394999i
$707$	−37.9733	+	22.8076i	−1.42813	+	0.857769i
$708$	−0.908536	−	2.79619i	−0.0341449	−	0.105087i
$709$	−2.73055	+	25.9795i	−0.102548	+	0.975680i	0.815378	+	0.578929i	$0.196529\pi$
$709$	−2.73055	+	25.9795i	−0.102548	+	0.975680i	−0.917926	+	0.396751i	$0.870138\pi$
$710$	13.8986	+	6.38919i	0.521604	+	0.239782i
$711$	−1.80954	−	17.2166i	−0.0678629	−	0.645673i
$712$	0.306105	−	2.91239i	0.0114718	−	0.109147i
$713$	5.47059	+	3.97461i	0.204875	+	0.148850i
$714$	−1.90833	+	4.49357i	−0.0714176	+	0.168168i
$715$	−17.6996	−	3.98498i	−0.661927	−	0.149030i
$716$	1.27791	−	12.1585i	0.0477576	−	0.454383i
$717$	−3.52162	−	0.748544i	−0.131517	−	0.0279549i
$718$	8.48215	−	14.6915i	0.316551	−	0.548282i
$719$	−18.8039	+	20.8839i	−0.701268	+	0.778837i	−0.983577	−	0.180487i	$-0.942233\pi$
$719$	−18.8039	+	20.8839i	−0.701268	+	0.778837i	0.282310	+	0.959323i	$0.408899\pi$
$720$	−0.563402	−	6.05985i	−0.0209968	−	0.225837i
$721$	−41.1383	−	12.5851i	−1.53207	−	0.468692i
$722$	6.80302	−	20.9375i	0.253182	−	0.779214i
$723$	8.35650	+	3.72055i	0.310781	+	0.138369i
$724$	−5.61809	+	9.73082i	−0.208795	+	0.361643i
$725$	3.85361	+	12.9074i	0.143120	+	0.479370i
$726$	2.38991	+	4.13944i	0.0886978	+	0.153629i
$727$	25.0590	−	18.2064i	0.929385	−	0.675238i	−0.0164569	−	0.999865i	$-0.505239\pi$
$727$	25.0590	−	18.2064i	0.929385	−	0.675238i	0.945842	+	0.324627i	$0.105239\pi$
$728$	−11.2768	+	10.5121i	−0.417945	+	0.389603i
$729$	−4.05231	+	12.4717i	−0.150085	+	0.461916i
$730$	−16.1779	−	0.194358i	−0.598772	−	0.00719351i
$731$	−38.1721	−	8.11372i	−1.41185	−	0.300097i
$732$	1.26032	−	2.18294i	0.0465828	−	0.0806837i
$733$	−3.47999	+	3.86492i	−0.128536	+	0.142754i	−0.803977	−	0.594660i	$-0.797287\pi$
$733$	−3.47999	+	3.86492i	−0.128536	+	0.142754i	0.675441	+	0.737414i	$0.263953\pi$
$734$	13.2596	+	9.63365i	0.489420	+	0.355585i
$735$	8.25474	−	0.186135i	0.304481	−	0.00686568i
$736$	6.66152	−	4.83988i	0.245547	−	0.178400i
$737$	1.10496	−	10.5130i	0.0407018	−	0.387252i
$738$	3.06643	−	1.36526i	0.112877	−	0.0502561i
$739$	0.290015	+	2.75931i	0.0106684	+	0.101503i	0.998560	−	0.0536408i	$-0.0170826\pi$
$739$	0.290015	+	2.75931i	0.0106684	+	0.101503i	−0.987892	+	0.155144i	$0.950416\pi$
$740$	−5.50420	−	4.10096i	−0.202338	−	0.150754i
$741$	−15.9256	−	11.5707i	−0.585043	−	0.425059i
$742$	1.86391	−	9.58006i	0.0684262	−	0.351695i
$743$	−44.5865			−1.63572			−0.817860	−	0.575417i	$-0.804840\pi$
$743$	−44.5865			−1.63572			−0.817860	+	0.575417i	$0.804840\pi$
$744$	0.289869	−	0.321932i	0.0106271	−	0.0118026i
$745$	18.1808	−	19.7105i	0.666094	−	0.722135i
$746$	19.0407	+	21.1468i	0.697129	+	0.774240i
$747$	15.9471	−	3.38967i	0.583475	−	0.124021i
$748$	3.94052	−	2.86296i	0.144080	−	0.104680i
$749$	0.176521	+	10.2148i	0.00644993	+	0.373242i
$750$	−2.02342	+	5.53977i	−0.0738850	+	0.202284i
$751$	12.5535	+	21.7434i	0.458085	+	0.793427i	0.998860	−	0.0477406i	$-0.0152021\pi$
$751$	12.5535	+	21.7434i	0.458085	+	0.793427i	−0.540774	+	0.841168i	$0.681869\pi$
$752$	0.154183	+	1.46695i	0.00562247	+	0.0534943i
$753$	−2.10540	−	2.33829i	−0.0767252	−	0.0852119i
$754$	15.3551	−	3.26383i	0.559200	−	0.118862i
$755$	−2.37041	−	0.533686i	−0.0862680	−	0.0194228i
$756$	6.02589	+	5.24007i	0.219160	+	0.190580i
$757$	−28.9145			−1.05092			−0.525459	−	0.850819i	$-0.676106\pi$
$757$	−28.9145			−1.05092			−0.525459	+	0.850819i	$0.676106\pi$
$758$	−23.5234	+	26.1253i	−0.854407	+	0.948915i
$759$	−5.52528	+	2.46001i	−0.200555	+	0.0892929i
$760$	−1.66787	+	14.2230i	−0.0605001	+	0.515922i
$761$	11.0569	+	4.92284i	0.400812	+	0.178453i	0.597235	−	0.802066i	$-0.296266\pi$
$761$	11.0569	+	4.92284i	0.400812	+	0.178453i	−0.196423	+	0.980519i	$0.562933\pi$
$762$	2.49542	+	1.81303i	0.0903996	+	0.0656792i
$763$	−42.5156	−	3.72710i	−1.53917	−	0.134930i
$764$	−2.34990	+	1.70730i	−0.0850164	+	0.0617680i
$765$	−21.2872	−	0.255739i	−0.769639	−	0.00924628i
$766$	11.4720	−	5.10765i	0.414499	−	0.184547i
$767$	−31.7666	−	6.75220i	−1.14703	−	0.243808i
$768$	−0.263755	−	0.456837i	−0.00951744	−	0.0164847i
$769$	7.39377	+	22.7557i	0.266626	+	0.820591i	0.991314	+	0.131514i	$0.0419838\pi$
$769$	7.39377	+	22.7557i	0.266626	+	0.820591i	−0.724688	+	0.689077i	$0.758016\pi$
$770$	−7.15575	−	4.08128i	−0.257875	−	0.147079i
$771$	3.07728	−	9.47089i	0.110825	−	0.341086i
$772$	18.4181	−	3.91489i	0.662881	−	0.140900i
$773$	2.15693	+	20.5218i	0.0775792	+	0.738117i	0.962299	+	0.271994i	$0.0876830\pi$
$773$	2.15693	+	20.5218i	0.0775792	+	0.738117i	−0.884720	+	0.466123i	$0.845650\pi$
$774$	−15.1823	+	26.2966i	−0.545718	+	0.945211i
$775$	3.79016	−	1.57951i	0.136146	−	0.0567375i
$776$	7.71665			0.277012
$777$	4.25236	−	0.521372i	0.152553	−	0.0187041i
$778$	6.84509	−	21.0670i	0.245409	−	0.755290i
$779$	−7.72563	+	1.64213i	−0.276799	+	0.0588355i
$780$	6.24486	+	2.87077i	0.223602	+	0.102790i
$781$	9.31746	+	1.98049i	0.333405	+	0.0708674i
$782$	−14.4014	−	24.9439i	−0.514992	−	0.891993i
$783$	−2.51276	−	7.73349i	−0.0897988	−	0.276372i
$784$	−6.29263	+	3.06641i	−0.224737	+	0.109514i
$785$	28.6772	+	6.45655i	1.02353	+	0.230444i
$786$	2.76201	+	1.22973i	0.0985178	+	0.0438629i
$787$	5.91025	−	2.63141i	0.210678	−	0.0937997i	−0.298685	−	0.954352i	$-0.596548\pi$
$787$	5.91025	−	2.63141i	0.210678	−	0.0937997i	0.509362	+	0.860552i	$0.329881\pi$
$788$	18.4384	−	8.20932i	0.656842	−	0.292445i
$789$	0.306406	+	0.136421i	0.0109083	+	0.00485671i
$790$	−1.31662	−	14.1613i	−0.0468432	−	0.503837i
$791$	−10.9623	−	23.5194i	−0.389774	−	0.836254i
$792$	−1.17113	−	3.60437i	−0.0416144	−	0.128076i
$793$	−13.9215	−	24.1128i	−0.494369	−	0.856272i
$794$	−37.1893	−	7.90483i	−1.31980	−	0.280532i
$795$	−4.26662	+	0.853460i	−0.151321	+	0.0302691i
$796$	−5.12948	+	1.09030i	−0.181810	+	0.0386448i
$797$	−6.28044	+	19.3292i	−0.222465	+	0.684675i	0.776075	+	0.630641i	$0.217208\pi$
$797$	−6.28044	+	19.3292i	−0.222465	+	0.684675i	−0.998539	+	0.0540343i	$0.982792\pi$
$798$	−5.37791	−	7.13932i	−0.190376	−	0.252729i
$799$	5.15965			0.182535
$800$	−0.403029	−	4.98373i	−0.0142492	−	0.176201i
$801$	−3.98521	+	6.90259i	−0.140811	+	0.243891i
$802$	1.28775	+	12.2521i	0.0454719	+	0.432636i
$803$	−9.85488	+	2.09472i	−0.347771	+	0.0739210i
$804$	−1.23751	+	3.80866i	−0.0436435	+	0.134321i
$805$	−28.4252	+	39.5603i	−1.00186	+	1.39432i
$806$	−1.47870	−	4.55097i	−0.0520850	−	0.160301i
$807$	−5.58012	−	9.66505i	−0.196430	−	0.340226i
$808$	−16.3765	−	3.48094i	−0.576125	−	0.122459i
$809$	3.95693	−	1.76174i	0.139118	−	0.0619394i	−0.335997	−	0.941863i	$-0.609073\pi$
$809$	3.95693	−	1.76174i	0.139118	−	0.0619394i	0.475115	+	0.879924i	$0.342406\pi$
$810$	−4.70945	+	13.9228i	−0.165473	+	0.489198i
$811$	6.63044	−	4.81730i	0.232826	−	0.169158i	−0.465255	−	0.885177i	$-0.654037\pi$
$811$	6.63044	−	4.81730i	0.232826	−	0.169158i	0.698081	+	0.716018i	$0.254037\pi$
$812$	7.10064	+	0.622472i	0.249184	+	0.0218445i
$813$	8.01595	+	5.82393i	0.281132	+	0.204254i
$814$	−3.90480	−	1.73853i	−0.136863	−	0.0609354i
$815$	27.4599	−	5.49287i	0.961880	−	0.192407i
$816$	−1.68570	+	0.750520i	−0.0590111	+	0.0262735i
$817$	47.8085	−	53.0967i	1.67261	−	1.85762i
$818$	9.65001			0.337405
$819$	39.6760	−	13.6538i	1.38639	−	0.477103i
$820$	2.53255	−	1.09130i	0.0884406	−	0.0381099i
$821$	−44.9899	+	9.56291i	−1.57016	+	0.333748i	−0.909098	−	0.416583i	$-0.863227\pi$
$821$	−44.9899	+	9.56291i	−1.57016	+	0.333748i	−0.661062	+	0.750331i	$0.729894\pi$
$822$	6.70429	+	7.44587i	0.233839	+	0.259705i
$823$	−3.72886	−	35.4777i	−0.129980	−	1.23668i	−0.843920	−	0.536469i	$-0.819758\pi$
$823$	−3.72886	−	35.4777i	−0.129980	−	1.23668i	0.713940	−	0.700207i	$-0.246909\pi$
$824$	−8.13006	−	14.0817i	−0.283224	−	0.490559i
$825$	−0.471533	+	3.64225i	−0.0164167	+	0.126807i
$826$	−12.8960	−	7.15132i	−0.448710	−	0.248826i
$827$	−15.2766	+	11.0991i	−0.531221	+	0.385955i	−0.820814	−	0.571195i	$-0.806480\pi$
$827$	−15.2766	+	11.0991i	−0.531221	+	0.385955i	0.289593	+	0.957150i	$0.406480\pi$
$828$	−21.9213	+	4.65951i	−0.761817	+	0.161929i
$829$	−18.4356	−	20.4748i	−0.640296	−	0.711120i	0.332417	−	0.943132i	$-0.392136\pi$
$829$	−18.4356	−	20.4748i	−0.640296	−	0.711120i	−0.972713	+	0.232012i	$0.925469\pi$
$830$	13.1340	−	2.62723i	0.455889	−	0.0911924i
$831$	−10.0597	+	11.1724i	−0.348966	+	0.387566i
$832$	−5.82690			−0.202011
$833$	8.36666	+	23.0122i	0.289888	+	0.797324i
$834$	8.60486	+	6.25180i	0.297962	+	0.216482i
$835$	26.4429	−	18.7307i	0.915095	−	0.648204i
$836$	0.932146	+	8.86878i	0.0322390	+	0.306733i
$837$	−2.26438	+	1.00817i	−0.0782683	+	0.0348473i
$838$	1.80084	−	17.1338i	0.0622089	−	0.591878i
$839$	6.10738	−	4.43727i	0.210850	−	0.153192i	−0.477348	−	0.878714i	$-0.658402\pi$
$839$	6.10738	−	4.43727i	0.210850	−	0.153192i	0.688198	+	0.725523i	$0.258402\pi$
$840$	2.33016	+	2.07597i	0.0803983	+	0.0716279i
$841$	17.5896	+	12.7796i	0.606537	+	0.440675i
$842$	19.4687	−	21.6222i	0.670936	−	0.745150i
$843$	5.93090	−	10.2726i	0.204271	−	0.353808i
$844$	−1.18899	−	0.252727i	−0.0409266	−	0.00869922i
$845$	38.2319	−	27.0814i	1.31522	−	0.931629i
$846$	1.24059	−	3.81816i	0.0426525	−	0.131271i
$847$	22.9247	+	7.01314i	0.787701	+	0.240974i
$848$	2.98432	−	2.16823i	0.102482	−	0.0744575i
$849$	2.51219	+	4.35124i	0.0862180	+	0.149334i
$850$	−17.4849	−	0.420180i	−0.599727	−	0.0144121i
$851$	−12.6379	+	21.8896i	−0.433223	+	0.750364i
$852$	−3.29667	−	1.46777i	−0.112942	−	0.0502851i
$853$	0.714486	−	2.19896i	0.0244635	−	0.0752910i	−0.938079	−	0.346420i	$-0.887397\pi$
$853$	0.714486	−	2.19896i	0.0244635	−	0.0752910i	0.962543	+	0.271129i	$0.0873971\pi$
$854$	−2.84177	−	12.3189i	−0.0972435	−	0.421543i
$855$	19.8923	−	33.5180i	0.680302	−	1.14629i
$856$	−2.58379	+	2.86959i	−0.0883123	+	0.0980807i
$857$	2.59824	−	4.50028i	0.0887540	−	0.153726i	−0.818231	−	0.574890i	$-0.805045\pi$
$857$	2.59824	−	4.50028i	0.0887540	−	0.153726i	0.906985	+	0.421164i	$0.138378\pi$
$858$	4.18649	+	0.889866i	0.142924	+	0.0303795i
$859$	−0.749257	+	7.12871i	−0.0255643	+	0.243228i	0.974276	+	0.225358i	$0.0723552\pi$
$859$	−0.749257	+	7.12871i	−0.0255643	+	0.243228i	−0.999840	+	0.0178702i	$0.994311\pi$
$860$	−12.7318	+	21.4528i	−0.434152	+	0.731535i
$861$	−0.672812	+	1.58428i	−0.0229294	+	0.0539921i
$862$	−27.3082	−	19.8406i	−0.930121	−	0.675772i
$863$	3.68687	−	35.0782i	0.125503	−	1.19408i	−0.732622	−	0.680636i	$-0.761704\pi$
$863$	3.68687	−	35.0782i	0.125503	−	1.19408i	0.858125	−	0.513441i	$-0.171630\pi$
$864$	0.315495	+	3.00174i	0.0107334	+	0.102121i
$865$	5.43649	−	46.3603i	0.184846	−	1.57630i
$866$	−1.07255	+	10.2046i	−0.0364467	+	0.346767i
$867$	−0.776589	−	2.39010i	−0.0263744	−	0.0811719i
$868$	−0.0375413	−	2.17242i	−0.00127423	−	0.0737369i
$869$	−2.73683	−	8.42309i	−0.0928405	−	0.285734i
$870$	−0.945617	−	3.03385i	−0.0320594	−	0.102857i
$871$	29.5994	+	32.8735i	1.00294	+	1.11388i
$872$	−10.7938	−	11.9877i	−0.365523	−	0.405954i
$873$	−19.1869	−	8.54255i	−0.649378	−	0.289122i
$874$	52.7336			1.78374
$875$	11.5224	+	27.2440i	0.389527	+	0.921015i
$876$	3.81680			0.128958
$877$	−1.40495	−	0.625526i	−0.0474419	−	0.0211225i	0.382879	−	0.923799i	$-0.374933\pi$
$877$	−1.40495	−	0.625526i	−0.0474419	−	0.0211225i	−0.430320	+	0.902676i	$0.641599\pi$
$878$	2.22054	+	2.46616i	0.0749395	+	0.0832288i
$879$	0.552534	+	0.613651i	0.0186365	+	0.0206979i
$880$	−0.926513	−	2.97256i	−0.0312328	−	0.100205i
$881$	10.3149	+	31.7461i	0.347519	+	1.06955i	0.960221	+	0.279240i	$0.0900824\pi$
$881$	10.3149	+	31.7461i	0.347519	+	1.06955i	−0.612703	+	0.790314i	$0.709918\pi$
$882$	19.0408	−	0.658276i	0.641136	−	0.0221653i
$883$	8.48628	+	26.1181i	0.285586	+	0.878943i	0.986222	+	0.165425i	$0.0528996\pi$
$883$	8.48628	+	26.1181i	0.285586	+	0.878943i	−0.700636	+	0.713519i	$0.747100\pi$
$884$	−2.13054	+	20.2708i	−0.0716579	+	0.681779i
$885$	−0.765687	+	6.52949i	−0.0257383	+	0.219486i
$886$	2.78616	+	26.5086i	0.0936030	+	0.890573i
$887$	−2.26316	+	21.5325i	−0.0759895	+	0.722992i	0.888501	+	0.458874i	$0.151747\pi$
$887$	−2.26316	+	21.5325i	−0.0759895	+	0.722992i	−0.964491	+	0.264117i	$0.914919\pi$
$888$	1.31002	+	0.951787i	0.0439615	+	0.0319399i
$889$	15.3555	−	1.88271i	0.515008	−	0.0631440i
$890$	−3.34198	+	5.63115i	−0.112023	+	0.188757i
$891$	−0.956706	+	9.10245i	−0.0320508	+	0.304943i
$892$	28.2260	+	5.99962i	0.945076	+	0.200882i
$893$	−4.72327	+	8.18095i	−0.158058	+	0.273765i
$894$	−4.23286	+	4.70107i	−0.141568	+	0.157227i
$895$	−13.9519	+	23.5085i	−0.466359	+	0.785804i
$896$	−2.53001	−	0.773984i	−0.0845217	−	0.0258570i
$897$	7.82107	−	24.0708i	0.261138	−	0.803700i
$898$	13.6970	+	6.09831i	0.457075	+	0.203503i
$899$	−1.10622	+	1.91603i	−0.0368945	+	0.0639031i
$900$	−4.51503	+	12.8378i	−0.150501	+	0.427928i
$901$	−6.45172	−	11.1747i	−0.214938	−	0.372284i
$902$	1.38929	−	1.00938i	0.0462584	−	0.0336087i
$903$	−3.49996	−	15.1720i	−0.116471	−	0.504894i
$904$	3.03074	−	9.32766i	0.100801	−	0.310234i
$905$	20.5024	−	14.5228i	0.681522	−	0.482754i
$906$	0.560674	+	0.119175i	0.0186272	+	0.00395932i
$907$	17.2100	−	29.8086i	0.571449	−	0.989779i	−0.424968	−	0.905208i	$-0.639715\pi$
$907$	17.2100	−	29.8086i	0.571449	−	0.989779i	0.996417	−	0.0845707i	$-0.0269519\pi$
$908$	10.8753	−	12.0782i	0.360908	−	0.400829i
$909$	36.8656	+	26.7844i	1.22275	+	0.888383i
$910$	32.7286	−	10.8250i	1.08494	−	0.358847i
$911$	5.98439	−	4.34792i	0.198272	−	0.144053i	−0.484220	−	0.874946i	$-0.660896\pi$
$911$	5.98439	−	4.34792i	0.198272	−	0.144053i	0.682491	+	0.730894i	$0.260896\pi$
$912$	0.353132	−	3.35982i	0.0116934	−	0.111255i
$913$	7.61975	−	3.39253i	0.252177	−	0.112276i
$914$	2.36505	+	22.5020i	0.0782290	+	0.744299i
$915$	−4.59935	+	3.25793i	−0.152050	+	0.107704i
$916$	−0.872508	−	0.633914i	−0.0288285	−	0.0209451i
$917$	14.3387	−	4.93442i	0.473506	−	0.162949i
$918$	10.5579			0.348462
$919$	26.2108	−	29.1101i	0.864615	−	0.960252i	−0.134916	−	0.990857i	$-0.543077\pi$
$919$	26.2108	−	29.1101i	0.864615	−	0.960252i	0.999532	+	0.0306046i	$0.00974328\pi$
$920$	−18.0543	+	3.61144i	−0.595234	+	0.119066i
$921$	−4.74731	−	5.27243i	−0.156429	−	0.173732i
$922$	−9.34466	+	1.98627i	−0.307750	+	0.0654143i
$923$	−32.2485	+	23.4299i	−1.06147	+	0.771206i
$924$	1.69955	+	0.942465i	0.0559112	+	0.0310048i
$925$	7.35261	+	13.4726i	0.241752	+	0.442975i
$926$	−4.76006	−	8.24466i	−0.156425	−	0.270936i
$927$	4.62598	+	44.0133i	0.151937	+	1.44559i
$928$	1.80269	+	2.00209i	0.0591763	+	0.0657220i
$929$	29.3504	−	6.23861i	0.962954	−	0.204682i	0.300498	−	0.953783i	$-0.402847\pi$
$929$	29.3504	−	6.23861i	0.962954	−	0.204682i	0.662457	+	0.749100i	$0.269514\pi$
$930$	−0.889593	+	0.383335i	−0.0291709	+	0.0125700i
$931$	−44.1463	−	7.80004i	−1.44684	−	0.255636i
$932$	26.6929			0.874354
$933$	−5.90884	+	6.56243i	−0.193447	+	0.214844i
$934$	−4.29730	+	1.91328i	−0.140612	+	0.0626044i
$935$	−10.6798	+	2.13630i	−0.349266	+	0.0698644i
$936$	14.4882	+	6.45054i	0.473560	+	0.210843i
$937$	−34.9527	−	25.3946i	−1.14186	−	0.829606i	−0.154479	−	0.987996i	$-0.549370\pi$
$937$	−34.9527	−	25.3946i	−1.14186	−	0.829606i	−0.987377	+	0.158390i	$0.949370\pi$
$938$	8.48535	+	18.2052i	0.277057	+	0.594420i
$939$	0.762532	−	0.554012i	0.0248843	−	0.0180795i
$940$	1.05683	−	3.12437i	0.0344701	−	0.101906i
$941$	−45.3710	+	20.2005i	−1.47905	+	0.658516i	−0.978322	−	0.207088i	$-0.933601\pi$
$941$	−45.3710	+	20.2005i	−1.47905	+	0.658516i	−0.500729	+	0.865604i	$0.666935\pi$
$942$	−6.78305	−	1.44178i	−0.221004	−	0.0469758i
$943$	−5.07743	−	8.79436i	−0.165344	−	0.286384i
$944$	−1.72231	−	5.30073i	−0.0560565	−	0.172524i
$945$	−7.34862	−	16.2741i	−0.239051	−	0.529396i
$946$	−4.80046	+	14.7743i	−0.156077	+	0.480354i
$947$	−34.8371	+	7.40485i	−1.13205	+	0.240625i	−0.735591	−	0.677426i	$-0.763095\pi$
$947$	−34.8371	+	7.40485i	−1.13205	+	0.240625i	−0.396462	+	0.918051i	$0.629762\pi$
$948$	0.350713	+	3.33681i	0.0113906	+	0.108375i
$949$	21.0803	−	36.5121i	0.684295	−	1.18523i
$950$	16.6723	−	27.3388i	0.540922	−	0.886987i
$951$	−0.00752676			−0.000244072
$952$	−3.61763	+	8.51847i	−0.117248	+	0.276085i
$953$	−3.75581	+	11.5592i	−0.121663	+	0.374439i	−0.993278	−	0.115751i	$-0.963073\pi$
$953$	−3.75581	+	11.5592i	−0.121663	+	0.374439i	0.871616	+	0.490190i	$0.163073\pi$
$954$	−9.82059	+	2.08743i	−0.317953	+	0.0675830i
$955$	6.36880	−	1.27396i	0.206089	−	0.0412245i
$956$	−6.67593	−	1.41901i	−0.215915	−	0.0458942i
$957$	−0.989440	−	1.71376i	−0.0319841	−	0.0553980i
$958$	−8.83390	−	27.1880i	−0.285410	−	0.878403i
$959$	50.0609	+	4.38854i	1.61655	+	0.141713i
$960$	0.109195	+	1.17448i	0.00352426	+	0.0379063i
$961$	−27.7038	−	12.3345i	−0.893671	−	0.397888i
$962$	16.3402	−	7.27514i	0.526830	−	0.234560i
$963$	9.60114	−	4.27470i	0.309392	−	0.137750i
$964$	15.8414	+	7.05305i	0.510217	+	0.227163i
$965$	−41.0760	−	9.24806i	−1.32228	−	0.297706i
$966$	6.59318	−	9.41254i	0.212132	−	0.302844i
$967$	2.11743	+	6.51679i	0.0680920	+	0.209566i	0.979313	−	0.202353i	$-0.0648588\pi$
$967$	2.11743	+	6.51679i	0.0680920	+	0.209566i	−0.911221	+	0.411919i	$0.864859\pi$
$968$	4.53055	+	7.84714i	0.145617	+	0.252217i
$969$	−11.5591	−	2.45697i	−0.371332	−	0.0789292i
$970$	−15.6777	−	7.20708i	−0.503382	−	0.231405i
$971$	−37.9189	+	8.05992i	−1.21688	+	0.258655i	−0.771232	−	0.636555i	$-0.780359\pi$
$971$	−37.9189	+	8.05992i	−1.21688	+	0.258655i	−0.445645	+	0.895210i	$0.647026\pi$
$972$	3.86956	−	11.9093i	0.124116	−	0.381990i
$973$	52.9498	−	6.49206i	1.69749	−	0.208126i
$974$	16.5404			0.529989
$975$	−10.0063	−	11.6649i	−0.320459	−	0.373577i
$976$	2.38919	−	4.13819i	0.0764760	−	0.132460i
$977$	0.237039	+	2.25527i	0.00758355	+	0.0721526i	0.997659	−	0.0683833i	$-0.0217841\pi$
$977$	0.237039	+	2.25527i	0.00758355	+	0.0721526i	−0.990076	+	0.140536i	$0.955117\pi$
$978$	−6.46203	+	1.37355i	−0.206633	+	0.0439212i
$979$	−1.26007	+	3.87811i	−0.0402722	+	0.123945i
$980$	15.6485	−	0.352855i	0.499873	−	0.0112715i
$981$	13.5672	+	41.7555i	0.433167	+	1.33315i
$982$	15.2617	+	26.4340i	0.487019	+	0.843542i
$983$	−30.3159	−	6.44384i	−0.966927	−	0.205527i	−0.302723	−	0.953078i	$-0.597896\pi$
$983$	−30.3159	−	6.44384i	−0.966927	−	0.205527i	−0.664203	+	0.747552i	$0.731229\pi$
$984$	−0.594318	+	0.264607i	−0.0189462	+	0.00843537i
$985$	−45.1281	−	0.542160i	−1.43790	−	0.0172747i
$986$	7.62407	−	5.53921i	0.242800	−	0.176405i
$987$	0.869695	+	1.86592i	0.0276827	+	0.0593928i
$988$	−30.1902	−	21.9345i	−0.960479	−	0.697829i
$989$	83.9207	+	37.3639i	2.66852	+	1.18810i
$990$	−0.986996	+	8.41672i	−0.0313688	+	0.267501i
$991$	16.9308	−	7.53809i	0.537825	−	0.239455i	−0.119803	−	0.992798i	$-0.538226\pi$
$991$	16.9308	−	7.53809i	0.537825	−	0.239455i	0.657628	+	0.753342i	$0.271560\pi$
$992$	0.549505	−	0.610287i	0.0174468	−	0.0193766i
$993$	0.854933			0.0271305
$994$	−17.1143	+	5.88961i	−0.542834	+	0.186807i
$995$	11.4398	+	2.57561i	0.362665	+	0.0816522i
$996$	−3.09078	+	0.656965i	−0.0979350	+	0.0208167i
$997$	2.61221	+	2.90116i	0.0827296	+	0.0918805i	0.783088	−	0.621911i	$-0.213643\pi$
$997$	2.61221	+	2.90116i	0.0827296	+	0.0918805i	−0.700359	+	0.713791i	$0.746977\pi$
$998$	1.75949	+	16.7404i	0.0556957	+	0.529910i
$999$	−4.63253	−	8.02378i	−0.146567	−	0.253861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.q.c.11.6	✓	80
7.2	even	3	inner	350.2.q.c.261.5	yes	80
25.16	even	5	inner	350.2.q.c.291.5	yes	80
175.16	even	15	inner	350.2.q.c.191.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.q.c.11.6	✓	80	1.1	even	1	trivial
350.2.q.c.191.6	yes	80	175.16	even	15	inner
350.2.q.c.261.5	yes	80	7.2	even	3	inner
350.2.q.c.291.5	yes	80	25.16	even	5	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 + 0.406737i) q^{2} +(0.352973 + 0.392016i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.665386 - 2.13477i) q^{5} +(0.163009 + 0.501692i) q^{6} +(2.31380 + 1.28309i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.284499 - 2.70682i) q^{9} +O(q^{10})\)	\(q+(0.913545 + 0.406737i) q^{2} +(0.352973 + 0.392016i) q^{3} +(0.669131 + 0.743145i) q^{4} +(-0.665386 - 2.13477i) q^{5} +(0.163009 + 0.501692i) q^{6} +(2.31380 + 1.28309i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.284499 - 2.70682i) q^{9} +(0.260430 - 2.22085i) q^{10} +(-0.145550 - 1.38482i) q^{11} +(-0.0551398 + 0.524620i) q^{12} +(4.71406 + 3.42496i) q^{13} +(1.59188 + 2.11327i) q^{14} +(0.602003 - 1.01436i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(3.42155 + 0.727273i) q^{17} +(1.36087 - 2.35709i) q^{18} +(-4.28531 + 4.75932i) q^{19} +(1.14122 - 1.92292i) q^{20} +(0.313718 + 1.35994i) q^{21} +(0.430289 - 1.32429i) q^{22} +(-7.52222 - 3.34911i) q^{23} +(-0.263755 + 0.456837i) q^{24} +(-4.11452 + 2.84090i) q^{25} +(2.91345 + 5.04624i) q^{26} +(2.44183 - 1.77409i) q^{27} +(0.594715 + 2.57804i) q^{28} +(0.832518 - 2.56223i) q^{29} +(0.962534 - 0.681807i) q^{30} +(-0.803276 - 0.170742i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.491495 - 0.545861i) q^{33} +(2.82993 + 2.05607i) q^{34} +(1.19953 - 5.79320i) q^{35} +(2.20193 - 1.59979i) q^{36} +(0.320867 - 3.05285i) q^{37} +(-5.85062 + 2.60486i) q^{38} +(0.321294 + 3.05691i) q^{39} +(1.82468 - 1.29250i) q^{40} +(0.997736 + 0.724898i) q^{41} +(-0.266543 + 1.36997i) q^{42} -11.1564 q^{43} +(0.931727 - 1.03479i) q^{44} +(-5.96776 + 1.19374i) q^{45} +(-5.50968 - 6.11912i) q^{46} +(1.44280 - 0.306677i) q^{47} +(-0.426764 + 0.310062i) q^{48} +(3.70737 + 5.93763i) q^{49} +(-4.91430 + 0.921763i) q^{50} +(0.922612 + 1.59801i) q^{51} +(0.609077 + 5.79498i) q^{52} +(-2.46830 - 2.74133i) q^{53} +(2.95231 - 0.627534i) q^{54} +(-2.85942 + 1.23215i) q^{55} +(-0.505286 + 2.59705i) q^{56} -3.37833 q^{57} +(1.80269 - 2.00209i) q^{58} +(-5.09166 + 2.26695i) q^{59} +(1.15663 - 0.231364i) q^{60} +(-4.36526 - 1.94354i) q^{61} +(-0.664382 - 0.482702i) q^{62} +(4.13137 - 5.89802i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(4.17486 - 12.3424i) q^{65} +(0.671025 - 0.298760i) q^{66} +(7.42573 + 1.57839i) q^{67} +(1.74899 + 3.02935i) q^{68} +(-1.34224 - 4.13098i) q^{69} +(3.45213 - 4.80445i) q^{70} +(-2.11396 + 6.50611i) q^{71} +(2.66226 - 0.565880i) q^{72} +(-0.756316 - 7.19587i) q^{73} +(1.53483 - 2.65840i) q^{74} +(-2.56599 - 0.610199i) q^{75} -6.40430 q^{76} +(1.44007 - 3.39095i) q^{77} +(-0.949839 + 2.92331i) q^{78} +(6.22145 - 1.32241i) q^{79} +(2.19263 - 0.438596i) q^{80} +(-6.42940 - 1.36661i) q^{81} +(0.616635 + 1.06804i) q^{82} +(1.85104 + 5.69690i) q^{83} +(-0.800717 + 1.14312i) q^{84} +(-0.724088 - 7.78815i) q^{85} +(-10.1919 - 4.53770i) q^{86} +(1.29829 - 0.578036i) q^{87} +(1.27206 - 0.566358i) q^{88} +(-2.67526 - 1.19110i) q^{89} +(-5.93736 - 1.33677i) q^{90} +(6.51287 + 13.9732i) q^{91} +(-2.54447 - 7.83109i) q^{92} +(-0.216601 - 0.375164i) q^{93} +(1.44280 + 0.306677i) q^{94} +(13.0115 + 5.98139i) q^{95} +(-0.515982 + 0.109675i) q^{96} +(2.38458 - 7.33897i) q^{97} +(0.971797 + 6.93222i) q^{98} -3.78986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9}+O(q^{10}) \) 80 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 20 * q^8 + 4 * q^9	\( 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9} + 3 q^{10} + 10 q^{11} + 2 q^{12} - 12 q^{13} - 7 q^{14} + 22 q^{15} + 10 q^{16} - 8 q^{17} - 36 q^{18} + 8 q^{19} + 4 q^{20} + 17 q^{21} + 20 q^{22} + 5 q^{23} - 8 q^{24} + 32 q^{25} - 24 q^{26} + 32 q^{27} - 7 q^{28} + 12 q^{29} - 11 q^{30} - 9 q^{31} - 40 q^{32} + 33 q^{33} - 4 q^{34} - 22 q^{35} - 8 q^{36} - 14 q^{37} - 2 q^{38} - 2 q^{40} - 18 q^{41} - 19 q^{42} - 8 q^{43} - 10 q^{44} + 33 q^{45} - 10 q^{46} + 10 q^{47} - 4 q^{48} + 12 q^{49} + 36 q^{50} + 46 q^{51} + 6 q^{52} - 30 q^{53} + 14 q^{54} + 2 q^{55} - q^{56} - 52 q^{57} - 6 q^{58} + 40 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 100 q^{63} - 20 q^{64} - 25 q^{65} - 7 q^{66} + q^{67} + 12 q^{68} - 142 q^{69} + 25 q^{70} - 84 q^{71} + 14 q^{72} + 22 q^{73} + 6 q^{74} - 29 q^{75} + 24 q^{76} + 38 q^{77} - 30 q^{78} + 10 q^{79} + 3 q^{80} + 52 q^{81} - 6 q^{82} - 98 q^{83} + 2 q^{84} - 36 q^{85} - 26 q^{86} + 34 q^{87} + 10 q^{88} + 45 q^{89} + 24 q^{90} - 63 q^{91} + 20 q^{92} - 20 q^{93} + 10 q^{94} - 33 q^{95} + 2 q^{96} - 106 q^{97} - 55 q^{98} + 12 q^{99}+O(q^{100}) \) 80 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 20 * q^8 + 4 * q^9 + 3 * q^10 + 10 * q^11 + 2 * q^12 - 12 * q^13 - 7 * q^14 + 22 * q^15 + 10 * q^16 - 8 * q^17 - 36 * q^18 + 8 * q^19 + 4 * q^20 + 17 * q^21 + 20 * q^22 + 5 * q^23 - 8 * q^24 + 32 * q^25 - 24 * q^26 + 32 * q^27 - 7 * q^28 + 12 * q^29 - 11 * q^30 - 9 * q^31 - 40 * q^32 + 33 * q^33 - 4 * q^34 - 22 * q^35 - 8 * q^36 - 14 * q^37 - 2 * q^38 - 2 * q^40 - 18 * q^41 - 19 * q^42 - 8 * q^43 - 10 * q^44 + 33 * q^45 - 10 * q^46 + 10 * q^47 - 4 * q^48 + 12 * q^49 + 36 * q^50 + 46 * q^51 + 6 * q^52 - 30 * q^53 + 14 * q^54 + 2 * q^55 - q^56 - 52 * q^57 - 6 * q^58 + 40 * q^59 + 4 * q^60 + 16 * q^61 - 32 * q^62 - 100 * q^63 - 20 * q^64 - 25 * q^65 - 7 * q^66 + q^67 + 12 * q^68 - 142 * q^69 + 25 * q^70 - 84 * q^71 + 14 * q^72 + 22 * q^73 + 6 * q^74 - 29 * q^75 + 24 * q^76 + 38 * q^77 - 30 * q^78 + 10 * q^79 + 3 * q^80 + 52 * q^81 - 6 * q^82 - 98 * q^83 + 2 * q^84 - 36 * q^85 - 26 * q^86 + 34 * q^87 + 10 * q^88 + 45 * q^89 + 24 * q^90 - 63 * q^91 + 20 * q^92 - 20 * q^93 + 10 * q^94 - 33 * q^95 + 2 * q^96 - 106 * q^97 - 55 * q^98 + 12 * q^99

Introduction

L-functions

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