LMFDB - Embedded newform 650.2.bd.b.47.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(47,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17, 5]))

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

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

chi := DirichletCharacter("650.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.bd (of order $20$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.1
Character	$\chi$	$=$	650.47
Dual form			650.2.bd.b.83.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.951057 - 0.309017i) q^{2} +(-3.19611 + 0.506214i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.82170 - 1.29670i) q^{5} +(3.19611 + 0.506214i) q^{6} -0.716524 q^{7} +(-0.587785 - 0.809017i) q^{8} +(7.10571 - 2.30878i) q^{9} +(1.33184 + 1.79617i) q^{10} +(-2.16729 - 4.25354i) q^{11} +(-2.88325 - 1.46909i) q^{12} +(1.98692 + 3.00868i) q^{13} +(0.681455 + 0.221418i) q^{14} +(6.47875 + 3.22222i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.06204 - 6.70543i) q^{17} -7.47138 q^{18} +(0.897858 - 5.66885i) q^{19} +(-0.711605 - 2.11982i) q^{20} +(2.29009 - 0.362715i) q^{21} +(0.746796 + 4.71509i) q^{22} +(-4.39608 + 2.23991i) q^{23} +(2.28816 + 2.28816i) q^{24} +(1.63716 + 4.72437i) q^{25} +(-0.959942 - 3.47542i) q^{26} +(-12.8921 + 6.56887i) q^{27} +(-0.579680 - 0.421162i) q^{28} +(-0.358315 + 0.493179i) q^{29} +(-5.16594 - 5.06655i) q^{30} +(2.84986 + 0.451374i) q^{31} -1.00000i q^{32} +(9.08010 + 12.4977i) q^{33} +(-3.08215 + 6.04905i) q^{34} +(1.30529 + 0.929113i) q^{35} +(7.10571 + 2.30878i) q^{36} +(1.73847 + 5.35046i) q^{37} +(-2.60569 + 5.11395i) q^{38} +(-7.87346 - 8.61026i) q^{39} +(0.0217176 + 2.23596i) q^{40} +(-2.77218 + 5.44071i) q^{41} +(-2.29009 - 0.362715i) q^{42} +(-8.48333 - 8.48333i) q^{43} +(0.746796 - 4.71509i) q^{44} +(-15.9382 - 5.00804i) q^{45} +(4.87309 - 0.771821i) q^{46} +(0.671601 + 0.487947i) q^{47} +(-1.46909 - 2.88325i) q^{48} -6.48659 q^{49} +(-0.0971196 - 4.99906i) q^{50} +21.9689i q^{51} +(-0.161003 + 3.60195i) q^{52} +(-7.39192 + 1.17077i) q^{53} +(14.2910 - 2.26348i) q^{54} +(-1.56741 + 10.5590i) q^{55} +(0.421162 + 0.579680i) q^{56} +18.5728i q^{57} +(0.493179 - 0.358315i) q^{58} +(0.366676 - 0.719642i) q^{59} +(3.34745 + 6.41494i) q^{60} +(-1.30445 + 4.01467i) q^{61} +(-2.57090 - 1.30994i) q^{62} +(-5.09141 + 1.65430i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.281771 - 8.05733i) q^{65} +(-4.77369 - 14.6919i) q^{66} +(-1.33679 - 1.83994i) q^{67} +(4.80056 - 4.80056i) q^{68} +(12.9165 - 9.38437i) q^{69} +(-0.954292 - 1.28700i) q^{70} +(2.50553 + 15.8193i) q^{71} +(-6.04448 - 4.39157i) q^{72} +(5.45163 + 1.77134i) q^{73} -5.62580i q^{74} +(-7.62409 - 14.2709i) q^{75} +(4.05845 - 4.05845i) q^{76} +(1.55291 + 3.04776i) q^{77} +(4.82739 + 10.6219i) q^{78} +(-7.75298 + 10.6711i) q^{79} +(0.670296 - 2.13324i) q^{80} +(19.7460 - 14.3463i) q^{81} +(4.31777 - 4.31777i) q^{82} +(5.05056 - 3.66944i) q^{83} +(2.06592 + 1.05264i) q^{84} +(-10.6296 + 10.8381i) q^{85} +(5.44663 + 10.6896i) q^{86} +(0.895562 - 1.75764i) q^{87} +(-2.16729 + 4.25354i) q^{88} +(13.9811 - 7.12373i) q^{89} +(13.6106 + 9.68811i) q^{90} +(-1.42368 - 2.15579i) q^{91} +(-4.87309 - 0.771821i) q^{92} -9.33697 q^{93} +(-0.487947 - 0.671601i) q^{94} +(-8.98640 + 9.16268i) q^{95} +(0.506214 + 3.19611i) q^{96} +(5.13215 - 7.06380i) q^{97} +(6.16912 + 2.00447i) q^{98} +(-25.2206 - 25.2206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} - 2 q^{5} - 20 q^{9} + 12 q^{13} - 26 q^{15} - 36 q^{16} + 6 q^{17} - 152 q^{18} - 20 q^{19} - 8 q^{20} - 6 q^{21} - 12 q^{23} - 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} - 12 q^{30}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 - 2 * q^5 - 20 * q^9 + 12 * q^13 - 26 * q^15 - 36 * q^16 + 6 * q^17 - 152 * q^18 - 20 * q^19 - 8 * q^20 - 6 * q^21 - 12 * q^23 - 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 - 12 * q^30 - 6 * q^31 + 30 * q^33 + 24 * q^34 + 40 * q^35 - 20 * q^36 - 6 * q^37 + 60 * q^39 - 8 * q^41 + 6 * q^42 + 12 * q^43 - 30 * q^45 - 12 * q^46 - 18 * q^47 + 160 * q^49 - 12 * q^52 + 20 * q^53 + 6 * q^54 - 32 * q^55 - 24 * q^58 + 16 * q^59 + 6 * q^60 + 12 * q^61 - 6 * q^62 - 40 * q^63 + 36 * q^64 - 54 * q^65 - 16 * q^66 - 6 * q^68 - 26 * q^69 + 2 * q^70 + 12 * q^71 - 48 * q^72 + 40 * q^73 - 32 * q^75 + 56 * q^77 + 16 * q^78 - 20 * q^79 - 2 * q^80 + 124 * q^81 + 22 * q^82 + 74 * q^83 - 24 * q^84 - 60 * q^85 + 12 * q^86 + 8 * q^87 - 58 * q^89 + 14 * q^90 - 16 * q^91 + 12 * q^92 - 16 * q^93 + 50 * q^94 + 46 * q^95 - 40 * q^98 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−3.19611	+	0.506214i	−1.84528	+	0.292263i	−0.978471	−	0.206384i	$-0.933830\pi$
$3$	−3.19611	+	0.506214i	−1.84528	+	0.292263i	−0.866805	+	0.498647i	$0.833830\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−1.82170	−	1.29670i	−0.814688	−	0.579900i
$5$	−1.82170	−	1.29670i	−0.814688	−	0.579900i
$6$	3.19611	+	0.506214i	1.30481	+	0.206661i
$7$	−0.716524			−0.270821			−0.135410	−	0.990790i	$-0.543235\pi$
$7$	−0.716524			−0.270821			−0.135410	+	0.990790i	$0.543235\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	7.10571	−	2.30878i	2.36857	−	0.769595i
$10$	1.33184	+	1.79617i	0.421163	+	0.567998i
$11$	−2.16729	−	4.25354i	−0.653462	−	1.28249i	−0.945356	−	0.326040i	$-0.894285\pi$
$11$	−2.16729	−	4.25354i	−0.653462	−	1.28249i	0.291894	−	0.956451i	$-0.405715\pi$
$12$	−2.88325	−	1.46909i	−0.832324	−	0.424090i
$13$	1.98692	+	3.00868i	0.551073	+	0.834457i
$13$	1.98692	+	3.00868i	0.551073	+	0.834457i
$14$	0.681455	+	0.221418i	0.182126	+	0.0591765i
$15$	6.47875	+	3.22222i	1.67281	+	0.831973i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.06204	−	6.70543i	0.257581	−	1.62630i	−0.431844	−	0.901948i	$-0.642137\pi$
$17$	1.06204	−	6.70543i	0.257581	−	1.62630i	0.689426	−	0.724357i	$-0.257863\pi$
$18$	−7.47138			−1.76102
$19$	0.897858	−	5.66885i	0.205983	−	1.30052i	−0.640438	−	0.768010i	$-0.721247\pi$
$19$	0.897858	−	5.66885i	0.205983	−	1.30052i	0.846421	−	0.532514i	$-0.178753\pi$
$20$	−0.711605	−	2.11982i	−0.159120	−	0.474005i
$21$	2.29009	−	0.362715i	0.499739	−	0.0791508i
$22$	0.746796	+	4.71509i	0.159218	+	1.00526i
$23$	−4.39608	+	2.23991i	−0.916645	+	0.467054i	−0.847646	−	0.530563i	$-0.821981\pi$
$23$	−4.39608	+	2.23991i	−0.916645	+	0.467054i	−0.0689995	+	0.997617i	$0.521981\pi$
$24$	2.28816	+	2.28816i	0.467069	+	0.467069i
$25$	1.63716	+	4.72437i	0.327432	+	0.944875i
$26$	−0.959942	−	3.47542i	−0.188260	−	0.681585i
$27$	−12.8921	+	6.56887i	−2.48109	+	1.26418i
$28$	−0.579680	−	0.421162i	−0.109549	−	0.0795922i
$29$	−0.358315	+	0.493179i	−0.0665375	+	0.0915810i	−0.840989	−	0.541052i	$-0.818026\pi$
$29$	−0.358315	+	0.493179i	−0.0665375	+	0.0915810i	0.774451	+	0.632633i	$0.218026\pi$
$30$	−5.16594	−	5.06655i	−0.943168	−	0.925022i
$31$	2.84986	+	0.451374i	0.511850	+	0.0810691i	0.407017	−	0.913421i	$-0.366569\pi$
$31$	2.84986	+	0.451374i	0.511850	+	0.0810691i	0.104833	+	0.994490i	$0.466569\pi$
$32$		−	1.00000i		−	0.176777i
$33$	9.08010	+	12.4977i	1.58064	+	2.17557i
$34$	−3.08215	+	6.04905i	−0.528584	+	1.03740i
$35$	1.30529	+	0.929113i	0.220634	+	0.157049i
$36$	7.10571	+	2.30878i	1.18428	+	0.384797i
$37$	1.73847	+	5.35046i	0.285803	+	0.879610i	0.986157	+	0.165815i	$0.0530253\pi$
$37$	1.73847	+	5.35046i	0.285803	+	0.879610i	−0.700354	+	0.713795i	$0.746975\pi$
$38$	−2.60569	+	5.11395i	−0.422698	+	0.829592i
$39$	−7.87346	−	8.61026i	−1.26076	−	1.37875i
$40$	0.0217176	+	2.23596i	0.00343386	+	0.353537i
$41$	−2.77218	+	5.44071i	−0.432942	+	0.849697i	0.566725	+	0.823907i	$0.308210\pi$
$41$	−2.77218	+	5.44071i	−0.432942	+	0.849697i	−0.999667	+	0.0257898i	$0.991790\pi$
$42$	−2.29009	−	0.362715i	−0.353369	−	0.0559681i
$43$	−8.48333	−	8.48333i	−1.29370	−	1.29370i	−0.932484	−	0.361211i	$-0.882363\pi$
$43$	−8.48333	−	8.48333i	−1.29370	−	1.29370i	−0.361211	−	0.932484i	$-0.617637\pi$
$44$	0.746796	−	4.71509i	0.112584	−	0.710826i
$45$	−15.9382	−	5.00804i	−2.37593	−	0.746554i
$46$	4.87309	−	0.771821i	0.718498	−	0.113799i
$47$	0.671601	+	0.487947i	0.0979631	+	0.0711744i	0.635689	−	0.771946i	$-0.280716\pi$
$47$	0.671601	+	0.487947i	0.0979631	+	0.0711744i	−0.537725	+	0.843120i	$0.680716\pi$
$48$	−1.46909	−	2.88325i	−0.212045	−	0.416162i
$49$	−6.48659			−0.926656
$50$	−0.0971196	−	4.99906i	−0.0137348	−	0.706973i
$51$			21.9689i			3.07626i
$52$	−0.161003	+	3.60195i	−0.0223271	+	0.499501i
$53$	−7.39192	+	1.17077i	−1.01536	+	0.160817i	−0.641866	−	0.766816i	$-0.721840\pi$
$53$	−7.39192	+	1.17077i	−1.01536	+	0.160817i	−0.373492	+	0.927633i	$0.621840\pi$
$54$	14.2910	−	2.26348i	1.94477	−	0.308021i
$55$	−1.56741	+	10.5590i	−0.211349	+	1.42377i
$56$	0.421162	+	0.579680i	0.0562802	+	0.0774630i
$57$			18.5728i			2.46003i
$58$	0.493179	−	0.358315i	0.0647575	−	0.0470491i
$59$	0.366676	−	0.719642i	0.0477372	−	0.0936894i	−0.865906	−	0.500207i	$-0.833257\pi$
$59$	0.366676	−	0.719642i	0.0477372	−	0.0936894i	0.913643	+	0.406518i	$0.133257\pi$
$60$	3.34745	+	6.41494i	0.432154	+	0.828166i
$61$	−1.30445	+	4.01467i	−0.167017	+	0.514026i	−0.999179	−	0.0405066i	$-0.987103\pi$
$61$	−1.30445	+	4.01467i	−0.167017	+	0.514026i	0.832162	+	0.554532i	$0.187103\pi$
$62$	−2.57090	−	1.30994i	−0.326504	−	0.166362i
$63$	−5.09141	+	1.65430i	−0.641457	+	0.208422i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	0.281771	−	8.05733i	0.0349494	−	0.999389i
$66$	−4.77369	−	14.6919i	−0.587601	−	1.80845i
$67$	−1.33679	−	1.83994i	−0.163315	−	0.224784i	0.719514	−	0.694478i	$-0.244365\pi$
$67$	−1.33679	−	1.83994i	−0.163315	−	0.224784i	−0.882830	+	0.469693i	$0.844365\pi$
$68$	4.80056	−	4.80056i	0.582153	−	0.582153i
$69$	12.9165	−	9.38437i	1.55496	−	1.12975i
$70$	−0.954292	−	1.28700i	−0.114060	−	0.153825i
$71$	2.50553	+	15.8193i	0.297351	+	1.87740i	0.455871	+	0.890046i	$0.349328\pi$
$71$	2.50553	+	15.8193i	0.297351	+	1.87740i	−0.158520	+	0.987356i	$0.550672\pi$
$72$	−6.04448	−	4.39157i	−0.712348	−	0.517551i
$73$	5.45163	+	1.77134i	0.638065	+	0.207320i	0.610144	−	0.792290i	$-0.291111\pi$
$73$	5.45163	+	1.77134i	0.638065	+	0.207320i	0.0279206	+	0.999610i	$0.491111\pi$
$74$		−	5.62580i		−	0.653986i
$75$	−7.62409	−	14.2709i	−0.880354	−	1.64786i
$76$	4.05845	−	4.05845i	0.465536	−	0.465536i
$77$	1.55291	+	3.04776i	0.176971	+	0.347325i
$78$	4.82739	+	10.6219i	0.546594	+	1.20269i
$79$	−7.75298	+	10.6711i	−0.872279	+	1.20059i	0.106221	+	0.994343i	$0.466125\pi$
$79$	−7.75298	+	10.6711i	−0.872279	+	1.20059i	−0.978500	+	0.206246i	$0.933875\pi$
$80$	0.670296	−	2.13324i	0.0749413	−	0.238503i
$81$	19.7460	−	14.3463i	2.19400	−	1.59404i
$82$	4.31777	−	4.31777i	0.476818	−	0.476818i
$83$	5.05056	−	3.66944i	0.554370	−	0.402774i	−0.275024	−	0.961437i	$-0.588686\pi$
$83$	5.05056	−	3.66944i	0.554370	−	0.402774i	0.829394	+	0.558664i	$0.188686\pi$
$84$	2.06592	+	1.05264i	0.225410	+	0.114852i
$85$	−10.6296	+	10.8381i	−1.15294	+	1.17556i
$86$	5.44663	+	10.6896i	0.587325	+	1.15269i
$87$	0.895562	−	1.75764i	0.0960143	−	0.188439i
$88$	−2.16729	+	4.25354i	−0.231034	+	0.453429i
$89$	13.9811	−	7.12373i	1.48199	−	0.755114i	0.488890	−	0.872346i	$-0.337402\pi$
$89$	13.9811	−	7.12373i	1.48199	−	0.755114i	0.993105	+	0.117232i	$0.0374021\pi$
$90$	13.6106	+	9.68811i	1.43468	+	1.02122i
$91$	−1.42368	−	2.15579i	−0.149242	−	0.225988i
$92$	−4.87309	−	0.771821i	−0.508055	−	0.0804679i
$93$	−9.33697			−0.968198
$94$	−0.487947	−	0.671601i	−0.0503279	−	0.0692704i
$95$	−8.98640	+	9.16268i	−0.921985	+	0.940071i
$96$	0.506214	+	3.19611i	0.0516653	+	0.326202i
$97$	5.13215	−	7.06380i	0.521091	−	0.717221i	−0.464649	−	0.885495i	$-0.653819\pi$
$97$	5.13215	−	7.06380i	0.521091	−	0.717221i	0.985740	+	0.168274i	$0.0538194\pi$
$98$	6.16912	+	2.00447i	0.623175	+	0.202482i
$99$	−25.2206	−	25.2206i	−2.53477	−	2.53477i
$100$	−1.45243	+	4.78440i	−0.145243	+	0.478440i
$101$		−	2.92149i		−	0.290699i	−0.989380	−	0.145350i	$-0.953569\pi$
$101$		−	2.92149i		−	0.290699i	0.989380	−	0.145350i	$-0.0464307\pi$
$102$	6.78877	−	20.8937i	0.672188	−	2.06878i
$103$	−0.0707648	−	0.446791i	−0.00697266	−	0.0440237i	0.983957	−	0.178407i	$-0.0570945\pi$
$103$	−0.0707648	−	0.446791i	−0.00697266	−	0.0440237i	−0.990929	+	0.134384i	$0.957095\pi$
$104$	1.26619	−	3.37591i	0.124160	−	0.331035i
$105$	−4.64218	−	2.30879i	−0.453030	−	0.225315i
$106$	7.39192	+	1.17077i	0.717967	+	0.113715i
$107$	−0.255579	−	0.255579i	−0.0247078	−	0.0247078i	0.694645	−	0.719353i	$-0.255561\pi$
$107$	−0.255579	−	0.255579i	−0.0247078	−	0.0247078i	−0.719353	+	0.694645i	$0.755561\pi$
$108$	−14.2910	−	2.26348i	−1.37516	−	0.217803i
$109$	−11.4189	−	5.81823i	−1.09373	−	0.557285i	−0.188445	−	0.982084i	$-0.560345\pi$
$109$	−11.4189	−	5.81823i	−1.09373	−	0.557285i	−0.905288	+	0.424799i	$0.860345\pi$
$110$	4.75360	−	9.55783i	0.453238	−	0.911303i
$111$	−8.26482	−	16.2206i	−0.784462	−	1.53959i
$112$	−0.221418	−	0.681455i	−0.0209220	−	0.0643914i
$113$	1.55507	+	0.792348i	0.146289	+	0.0745378i	0.525603	−	0.850730i	$-0.323840\pi$
$113$	1.55507	+	0.792348i	0.146289	+	0.0745378i	−0.379314	+	0.925268i	$0.623840\pi$
$114$	5.73931	−	17.6638i	0.537536	−	1.65436i
$115$	10.9128	+	1.61993i	1.01762	+	0.151059i
$116$	−0.579766	+	0.188378i	−0.0538300	+	0.0174904i
$117$	21.0649	+	16.7914i	1.94745	+	1.55237i
$118$	−0.571111	+	0.571111i	−0.0525751	+	0.0525751i
$119$	−0.760973	+	4.80460i	−0.0697583	+	0.440437i
$120$	−1.20129	−	7.13539i	−0.109662	−	0.651369i
$121$	−6.92984	+	9.53811i	−0.629986	+	0.867101i
$122$	2.48120	−	3.41508i	0.224637	−	0.309187i
$123$	6.10604	−	18.7924i	0.550563	−	1.69446i
$124$	2.04028	+	2.04028i	0.183222	+	0.183222i
$125$	3.14367	−	10.7293i	0.281178	−	0.959656i
$126$	5.35342			0.476921
$127$	4.42524	+	8.68503i	0.392677	+	0.770672i	0.999712	−	0.0240034i	$-0.00764126\pi$
$127$	4.42524	+	8.68503i	0.392677	+	0.770672i	−0.607035	+	0.794675i	$0.707641\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	31.4080	+	22.8193i	2.76532	+	2.00913i
$130$	−2.75783	+	7.57591i	−0.241878	+	0.664451i
$131$	−11.4820	+	8.34218i	−1.00319	+	0.728860i	−0.962770	−	0.270323i	$-0.912870\pi$
$131$	−11.4820	+	8.34218i	−1.00319	+	0.728860i	−0.0404199	+	0.999183i	$0.512870\pi$
$132$			15.4480i			1.34457i
$133$	−0.643337	+	4.06187i	−0.0557844	+	0.352209i
$134$	0.702794	+	2.16298i	0.0607122	+	0.186853i
$135$	32.0034	+	4.75069i	2.75441	+	0.408874i
$136$	−6.04905	+	3.08215i	−0.518702	+	0.264292i
$137$	−3.11551	−	9.58855i	−0.266176	−	0.819205i	−0.991420	−	0.130714i	$-0.958273\pi$
$137$	−3.11551	−	9.58855i	−0.266176	−	0.819205i	0.725244	−	0.688492i	$-0.241727\pi$
$138$	−15.1842	+	4.93365i	−1.29257	+	0.419981i
$139$	−4.09765	−	1.33141i	−0.347558	−	0.112928i	0.130036	−	0.991509i	$-0.458491\pi$
$139$	−4.09765	−	1.33141i	−0.347558	−	0.112928i	−0.477593	+	0.878581i	$0.658491\pi$
$140$	0.509882	+	1.51890i	0.0430929	+	0.128370i
$141$	−2.39352	−	1.21956i	−0.201571	−	0.102705i
$142$	2.50553	−	15.8193i	0.210259	−	1.32752i
$143$	8.49131	−	14.9721i	0.710079	−	1.25203i
$144$	4.39157	+	6.04448i	0.365964	+	0.503706i
$145$	1.29224	−	0.433796i	0.107315	−	0.0360248i
$146$	−4.63743	−	3.36929i	−0.383797	−	0.278845i
$147$	20.7319	−	3.28361i	1.70994	−	0.270827i
$148$	−1.73847	+	5.35046i	−0.142901	+	0.439805i
$149$	−9.55512	+	9.55512i	−0.782786	+	0.782786i	−0.980300	−	0.197514i	$-0.936713\pi$
$149$	−9.55512	+	9.55512i	−0.782786	+	0.782786i	0.197514	+	0.980300i	$0.436713\pi$
$150$	2.84100	+	15.9284i	0.231967	+	1.30055i
$151$	−3.58435	+	3.58435i	−0.291690	+	0.291690i	−0.837748	−	0.546058i	$-0.816128\pi$
$151$	−3.58435	+	3.58435i	−0.291690	+	0.291690i	0.546058	+	0.837748i	$0.316128\pi$
$152$	−5.11395	+	2.60569i	−0.414796	+	0.211349i
$153$	−7.93487	−	50.0988i	−0.641497	−	4.05025i
$154$	−0.535097	−	3.37847i	−0.0431194	−	0.272245i
$155$	−4.60629	−	4.51767i	−0.369986	−	0.362868i
$156$	−1.30878	−	11.5938i	−0.104786	−	0.928243i
$157$	8.96835	+	8.96835i	0.715752	+	0.715752i	0.967732	−	0.251980i	$-0.0810818\pi$
$157$	8.96835	+	8.96835i	0.715752	+	0.715752i	−0.251980	+	0.967732i	$0.581082\pi$
$158$	10.6711	−	7.75298i	0.848944	−	0.616794i
$159$	23.0327	−	7.48379i	1.82662	−	0.593503i
$160$	−1.29670	+	1.82170i	−0.102513	+	0.144018i
$161$	3.14989	−	1.60495i	0.248246	−	0.126488i
$162$	−23.2129	+	7.54231i	−1.82377	+	0.592580i
$163$	11.1573	−	3.62522i	0.873905	−	0.283949i	0.162481	−	0.986712i	$-0.448051\pi$
$163$	11.1573	−	3.62522i	0.873905	−	0.283949i	0.711424	+	0.702763i	$0.248051\pi$
$164$	−5.44071	+	2.77218i	−0.424848	+	0.216471i
$165$	−0.335494	−	34.5411i	−0.0261181	−	2.68902i
$166$	−5.93728	+	1.92914i	−0.460823	+	0.149730i
$167$	−3.50650	+	2.54762i	−0.271341	+	0.197141i	−0.715132	−	0.698990i	$-0.753633\pi$
$167$	−3.50650	+	2.54762i	−0.271341	+	0.197141i	0.443791	+	0.896130i	$0.353633\pi$
$168$	−1.63952	−	1.63952i	−0.126492	−	0.126492i
$169$	−5.10428	+	11.9560i	−0.392637	+	0.919693i
$170$	13.4585	−	7.02293i	1.03222	−	0.538635i
$171$	−6.70824	−	42.3542i	−0.512992	−	3.23890i
$172$	−1.87678	−	11.8495i	−0.143103	−	0.903518i
$173$	−14.0838	+	7.17606i	−1.07077	+	0.545585i	−0.898279	−	0.439425i	$-0.855182\pi$
$173$	−14.0838	+	7.17606i	−1.07077	+	0.545585i	−0.172493	+	0.985011i	$0.555182\pi$
$174$	−1.39487	+	1.39487i	−0.105745	+	0.105745i
$175$	−1.17306	−	3.38513i	−0.0886753	−	0.255891i
$176$	3.37563	−	3.37563i	0.254448	−	0.254448i
$177$	−0.807644	+	2.48567i	−0.0607063	+	0.186835i
$178$	−15.4982	+	2.45467i	−1.16164	+	0.183985i
$179$	5.55028	+	4.03252i	0.414848	+	0.301405i	0.775561	−	0.631272i	$-0.217467\pi$
$179$	5.55028	+	4.03252i	0.414848	+	0.301405i	−0.360714	+	0.932677i	$0.617467\pi$
$180$	−9.95066	−	13.4199i	−0.741678	−	1.00026i
$181$	2.85876	+	3.93475i	0.212490	+	0.292467i	0.901936	−	0.431870i	$-0.142146\pi$
$181$	2.85876	+	3.93475i	0.212490	+	0.292467i	−0.689446	+	0.724337i	$0.742146\pi$
$182$	0.687821	+	2.49022i	0.0509847	+	0.184587i
$183$	2.13687	−	13.4917i	0.157962	−	0.997332i
$184$	4.39608	+	2.23991i	0.324083	+	0.165129i
$185$	3.77095	−	12.0012i	0.277246	−	0.882344i
$186$	8.87998	+	2.88528i	0.651112	+	0.211559i
$187$	−30.8235	+	10.0152i	−2.25404	+	0.732382i
$188$	0.256529	+	0.789515i	0.0187093	+	0.0575813i
$189$	9.23752	−	4.70675i	0.671931	−	0.342366i
$190$	11.3780	−	5.93728i	0.825447	−	0.430735i
$191$	0.727524	+	2.23909i	0.0526418	+	0.162015i	0.973921	−	0.226887i	$-0.0728547\pi$
$191$	0.727524	+	2.23909i	0.0526418	+	0.162015i	−0.921279	+	0.388901i	$0.872855\pi$
$192$	0.506214	−	3.19611i	0.0365329	−	0.230660i
$193$			1.86029i			0.133907i	0.997756	+	0.0669534i	$0.0213279\pi$
$193$			1.86029i			0.133907i	−0.997756	+	0.0669534i	$0.978672\pi$
$194$	−7.06380	+	5.13215i	−0.507152	+	0.368467i
$195$	3.17817	+	25.8948i	0.227593	+	1.85436i
$196$	−5.24776	−	3.81272i	−0.374840	−	0.272337i
$197$	−10.4379	+	14.3666i	−0.743672	+	1.02358i	0.254727	+	0.967013i	$0.418014\pi$
$197$	−10.4379	+	14.3666i	−0.743672	+	1.02358i	−0.998399	+	0.0565639i	$0.981986\pi$
$198$	16.1926	+	31.7798i	1.15076	+	2.25850i
$199$	1.75969			0.124741			0.0623705	−	0.998053i	$-0.480134\pi$
$199$	1.75969			0.124741			0.0623705	+	0.998053i	$0.480134\pi$
$200$	2.85980	−	4.10141i	0.202218	−	0.290013i
$201$	5.20395	+	5.20395i	0.367058	+	0.367058i
$202$	−0.902790	+	2.77850i	−0.0635201	+	0.195495i
$203$	0.256741	−	0.353374i	0.0180197	−	0.0248020i
$204$	−12.9130	+	17.7732i	−0.904091	+	1.24437i
$205$	12.1050	−	6.31665i	0.845452	−	0.441174i
$206$	−0.0707648	+	0.446791i	−0.00493042	+	0.0311294i
$207$	−26.0658	+	26.0658i	−1.81170	+	1.81170i
$208$	−2.24743	+	2.81941i	−0.155831	+	0.195491i
$209$	−26.0586	+	8.46696i	−1.80251	+	0.585672i
$210$	3.70152	+	3.63031i	0.255429	+	0.250515i
$211$	−7.83176	+	24.1037i	−0.539160	+	1.65937i	0.195323	+	0.980739i	$0.437424\pi$
$211$	−7.83176	+	24.1037i	−0.539160	+	1.65937i	−0.734484	+	0.678626i	$0.762576\pi$
$212$	−6.66835	−	3.39769i	−0.457984	−	0.233354i
$213$	−16.0159	−	49.2918i	−1.09739	−	3.37742i
$214$	0.164092	+	0.322048i	0.0112171	+	0.0220148i
$215$	4.45376	+	26.4543i	0.303744	+	1.80417i
$216$	12.8921	+	6.56887i	0.877199	+	0.446955i
$217$	−2.04199	−	0.323420i	−0.138620	−	0.0219552i
$218$	9.06210	+	9.06210i	0.613763	+	0.613763i
$219$	−18.3207	−	2.90171i	−1.23800	−	0.196080i
$220$	−7.47447	+	7.62109i	−0.503929	+	0.513814i
$221$	22.2846	−	10.1278i	1.49903	−	0.681272i
$222$	2.84786	+	17.9807i	0.191136	+	1.20679i
$223$	−2.82343	+	8.68962i	−0.189071	+	0.581900i	−0.999995	−	0.00325165i	$-0.998965\pi$
$223$	−2.82343	+	8.68962i	−0.189071	+	0.581900i	0.810924	+	0.585152i	$0.198965\pi$
$224$			0.716524i			0.0478748i
$225$	22.5407	+	29.7902i	1.50272	+	1.98601i
$226$	−1.23411	−	1.23411i	−0.0820919	−	0.0820919i
$227$	1.91628	+	0.622638i	0.127188	+	0.0413259i	0.371919	−	0.928265i	$-0.378700\pi$
$227$	1.91628	+	0.622638i	0.127188	+	0.0413259i	−0.244731	+	0.969591i	$0.578700\pi$
$228$	−10.9168	+	15.0257i	−0.722984	+	0.995102i
$229$	−1.76675	−	11.1548i	−0.116750	−	0.737133i	−0.974720	−	0.223432i	$-0.928274\pi$
$229$	−1.76675	−	11.1548i	−0.116750	−	0.737133i	0.857969	−	0.513701i	$-0.171726\pi$
$230$	−9.87811	−	4.91289i	−0.651343	−	0.323946i
$231$	−6.50611	−	8.95489i	−0.428070	−	0.589188i
$232$	0.609602			0.0400224
$233$	5.62467	+	0.890860i	0.368484	+	0.0583622i	0.337931	−	0.941171i	$-0.390273\pi$
$233$	5.62467	+	0.890860i	0.368484	+	0.0583622i	0.0305534	+	0.999533i	$0.490273\pi$
$234$	−14.8451	−	22.4790i	−0.970452	−	1.46950i
$235$	−0.590735	−	1.75975i	−0.0385353	−	0.114794i
$236$	0.719642	−	0.366676i	0.0468447	−	0.0238686i
$237$	19.3776	−	38.0306i	1.25871	−	2.47035i
$238$	2.20843	−	4.33429i	0.143151	−	0.280950i
$239$	−3.04828	−	5.98259i	−0.197177	−	0.386982i	0.771155	−	0.636647i	$-0.219679\pi$
$239$	−3.04828	−	5.98259i	−0.197177	−	0.386982i	−0.968332	+	0.249666i	$0.919679\pi$
$240$	−1.06246	+	7.15738i	−0.0685818	+	0.462007i
$241$	12.2309	+	6.23197i	0.787864	+	0.401437i	0.801141	−	0.598475i	$-0.204226\pi$
$241$	12.2309	+	6.23197i	0.787864	+	0.401437i	−0.0132775	+	0.999912i	$0.504226\pi$
$242$	9.53811	−	6.92984i	0.613133	−	0.445467i
$243$	−25.1544	+	25.1544i	−1.61366	+	1.61366i
$244$	−3.41508	+	2.48120i	−0.218628	+	0.158843i
$245$	11.8166	+	8.41114i	0.754935	+	0.537368i
$246$	−11.6144	+	15.9858i	−0.740505	+	1.01922i
$247$	18.8397	−	8.56220i	1.19874	−	0.544800i
$248$	−1.30994	−	2.57090i	−0.0831811	−	0.163252i
$249$	−14.2846	+	14.2846i	−0.905251	+	0.905251i
$250$	−6.30533	+	9.23270i	−0.398784	+	0.583927i
$251$			10.4978i			0.662617i	0.943522	+	0.331309i	$0.107490\pi$
$251$			10.4978i			0.662617i	−0.943522	+	0.331309i	$0.892510\pi$
$252$	−5.09141	−	1.65430i	−0.320729	−	0.104211i
$253$	19.0551	+	13.8444i	1.19799	+	0.870387i
$254$	−1.52483	−	9.62743i	−0.0956766	−	0.604079i
$255$	28.4870	−	40.0207i	1.78392	−	2.50619i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−6.25002	+	6.25002i	−0.389866	+	0.389866i	−0.874640	−	0.484774i	$-0.838902\pi$
$257$	−6.25002	+	6.25002i	−0.389866	+	0.389866i	0.484774	+	0.874640i	$0.338902\pi$
$258$	−22.8193	−	31.4080i	−1.42067	−	1.95538i
$259$	−1.24565	−	3.83373i	−0.0774012	−	0.238216i
$260$	4.96394	−	6.35290i	0.307850	−	0.393990i
$261$	−1.40744	+	4.33166i	−0.0871184	+	0.268123i
$262$	13.4979	−	4.38575i	0.833905	−	0.270952i
$263$	1.97569	+	1.00666i	0.121826	+	0.0620735i	0.513841	−	0.857885i	$-0.328222\pi$
$263$	1.97569	+	1.00666i	0.121826	+	0.0620735i	−0.392015	+	0.919959i	$0.628222\pi$
$264$	4.77369	−	14.6919i	0.293800	−	0.904224i
$265$	14.9840	+	7.45229i	0.920458	+	0.457791i
$266$	1.86704	−	3.66426i	0.114475	−	0.224670i
$267$	−41.0790	+	29.8457i	−2.51400	+	1.82653i
$268$		−	2.27429i		−	0.138924i
$269$	−4.56603	−	6.28460i	−0.278396	−	0.383179i	0.646806	−	0.762655i	$-0.276104\pi$
$269$	−4.56603	−	6.28460i	−0.278396	−	0.383179i	−0.925202	+	0.379476i	$0.876104\pi$
$270$	−28.9690	−	14.4078i	−1.76300	−	0.876829i
$271$	5.92687	−	0.938724i	0.360032	−	0.0570234i	0.0262017	−	0.999657i	$-0.491659\pi$
$271$	5.92687	−	0.938724i	0.360032	−	0.0570234i	0.333830	+	0.942633i	$0.391659\pi$
$272$	6.70543	−	1.06204i	0.406576	−	0.0643953i
$273$	5.64152	+	6.16946i	0.341440	+	0.373393i
$274$			10.0820i			0.609076i
$275$	16.5471	−	17.2028i	0.997829	−	1.03737i
$276$	15.9656			0.961019
$277$	−1.10425	−	2.16721i	−0.0663477	−	0.130215i	0.855451	−	0.517884i	$-0.173280\pi$
$277$	−1.10425	−	2.16721i	−0.0663477	−	0.130215i	−0.921798	+	0.387669i	$0.873280\pi$
$278$	3.48567	+	2.53248i	0.209056	+	0.151888i
$279$	21.2924	−	3.37239i	1.27474	−	0.201900i
$280$	−0.0155612	−	1.60212i	−0.000929959	−	0.0957450i
$281$	1.88520	−	11.9027i	0.112462	−	0.710055i	−0.865444	−	0.501006i	$-0.832963\pi$
$281$	1.88520	−	11.9027i	0.112462	−	0.710055i	0.977905	−	0.209049i	$-0.0670367\pi$
$282$	1.89951	+	1.89951i	0.113114	+	0.113114i
$283$	8.70903	+	1.37937i	0.517698	+	0.0819953i	0.409816	−	0.912168i	$-0.365593\pi$
$283$	8.70903	+	1.37937i	0.517698	+	0.0819953i	0.107882	+	0.994164i	$0.465593\pi$
$284$	−7.27132	+	14.2708i	−0.431473	+	0.846814i
$285$	24.0833	−	33.8340i	1.42657	−	2.00415i
$286$	−12.7024	+	11.6154i	−0.751106	+	0.686832i
$287$	1.98633	−	3.89840i	0.117250	−	0.230115i
$288$	−2.30878	−	7.10571i	−0.136046	−	0.418708i
$289$	−27.6669	−	8.98951i	−1.62746	−	0.528795i
$290$	−1.36305	+	0.0132391i	−0.0800410	+	0.000777428i
$291$	−12.8271	+	25.1747i	−0.751940	+	1.47577i
$292$	3.36929	+	4.63743i	0.197173	+	0.271385i
$293$			15.3174i			0.894854i	0.894320	+	0.447427i	$0.147660\pi$
$293$			15.3174i			0.894854i	−0.894320	+	0.447427i	$0.852340\pi$
$294$	−20.7319	−	3.28361i	−1.20911	−	0.191504i
$295$	−1.60113	+	0.835503i	−0.0932214	+	0.0486449i
$296$	3.30676	−	4.55137i	0.192202	−	0.264543i
$297$	55.8820	+	40.6006i	3.24260	+	2.35589i
$298$	12.0401	−	6.13476i	0.697467	−	0.355377i
$299$	−15.4738	−	8.77585i	−0.894875	−	0.507520i
$300$	2.22019	−	16.0267i	0.128183	−	0.925302i
$301$	6.07850	+	6.07850i	0.350359	+	0.350359i
$302$	4.51654	−	2.30129i	0.259898	−	0.132425i
$303$	1.47890	+	9.33741i	0.0849606	+	0.536420i
$304$	5.66885	−	0.897858i	0.325131	−	0.0514957i
$305$	7.58211	−	5.62204i	0.434150	−	0.321917i
$306$	−7.93487	+	50.0988i	−0.453607	+	2.86396i
$307$	−13.4594			−0.768167			−0.384083	−	0.923298i	$-0.625482\pi$
$307$	−13.4594			−0.768167			−0.384083	+	0.923298i	$0.625482\pi$
$308$	−0.535097	+	3.37847i	−0.0304900	+	0.192506i
$309$	0.452345	+	1.39217i	0.0257330	+	0.0791980i
$310$	2.98480	+	5.71998i	0.169526	+	0.324873i
$311$	−26.4454	−	8.59263i	−1.49958	−	0.487243i	−0.559685	−	0.828705i	$-0.689078\pi$
$311$	−26.4454	−	8.59263i	−1.49958	−	0.487243i	−0.939895	+	0.341462i	$0.889078\pi$
$312$	−2.33794	+	11.4307i	−0.132360	+	0.647139i
$313$	−15.6838	−	7.99131i	−0.886503	−	0.451696i	−0.0494240	−	0.998778i	$-0.515739\pi$
$313$	−15.6838	−	7.99131i	−0.886503	−	0.451696i	−0.837079	+	0.547082i	$0.815739\pi$
$314$	−5.75803	−	11.3008i	−0.324945	−	0.637740i
$315$	11.4201	+	3.58838i	0.643451	+	0.202182i
$316$	−12.5446	+	4.07598i	−0.705688	+	0.229292i
$317$	−1.49767	−	2.06137i	−0.0841178	−	0.115778i	0.764884	−	0.644168i	$-0.222796\pi$
$317$	−1.49767	−	2.06137i	−0.0841178	−	0.115778i	−0.849002	+	0.528389i	$0.822796\pi$
$318$	−24.2181			−1.35808
$319$	2.87433	+	0.455249i	0.160932	+	0.0254890i
$320$	1.79617	−	1.33184i	0.100409	−	0.0744519i
$321$	0.946237	+	0.687481i	0.0528138	+	0.0383715i
$322$	−3.49168	+	0.553028i	−0.194584	+	0.0308191i
$323$	−37.0585	−	12.0410i	−2.06199	−	0.669981i
$324$	24.4074			1.35597
$325$	−10.9612	+	14.3126i	−0.608019	+	0.793923i
$326$	−11.7314			−0.649745
$327$	39.4414	+	12.8153i	2.18111	+	0.708687i
$328$	6.03108	−	0.955229i	0.333010	−	0.0527437i
$329$	−0.481218	−	0.349626i	−0.0265304	−	0.0192755i
$330$	−10.3547	+	32.9542i	−0.570009	+	1.81407i
$331$	24.3897	+	3.86296i	1.34058	+	0.212327i	0.785187	−	0.619259i	$-0.212567\pi$
$331$	24.3897	+	3.86296i	1.34058	+	0.212327i	0.555395	+	0.831587i	$0.312567\pi$
$332$	6.24283			0.342620
$333$	24.7061	+	34.0050i	1.35389	+	1.86346i
$334$	4.12213	−	1.33936i	0.225553	−	0.0732867i
$335$	0.0493922	+	5.08523i	0.00269858	+	0.277836i
$336$	1.05264	+	2.06592i	0.0574262	+	0.112705i
$337$	−1.58430	−	0.807242i	−0.0863024	−	0.0439733i	0.410307	−	0.911948i	$-0.365422\pi$
$337$	−1.58430	−	0.807242i	−0.0863024	−	0.0439733i	−0.496609	+	0.867974i	$0.665422\pi$
$338$	8.54907	−	9.79354i	0.465008	−	0.532698i
$339$	−5.37128	−	1.74523i	−0.291728	−	0.0947881i
$340$	−14.9700	+	2.52030i	−0.811863	+	0.136682i
$341$	−4.25653	−	13.1003i	−0.230504	−	0.709419i
$342$	−6.70824	+	42.3542i	−0.362740	+	2.29025i
$343$	9.66346			0.521778
$344$	−1.87678	+	11.8495i	−0.101189	+	0.638884i
$345$	−35.6986	+	0.346736i	−1.92195	+	0.0186676i
$346$	15.6120	−	2.47270i	0.839307	−	0.132933i
$347$	2.90591	+	18.3472i	0.155997	+	0.984928i	0.934157	+	0.356862i	$0.116153\pi$
$347$	2.90591	+	18.3472i	0.155997	+	0.984928i	−0.778160	+	0.628066i	$0.783847\pi$
$348$	1.75764	−	0.895562i	0.0942193	−	0.0480071i
$349$	−1.95139	−	1.95139i	−0.104455	−	0.104455i	0.652948	−	0.757403i	$-0.273532\pi$
$349$	−1.95139	−	1.95139i	−0.104455	−	0.104455i	−0.757403	+	0.652948i	$0.773532\pi$
$350$	0.0695885	+	3.58194i	0.00371966	+	0.191463i
$351$	−45.3793	−	25.7365i	−2.42217	−	1.37371i
$352$	−4.25354	+	2.16729i	−0.226715	+	0.115517i
$353$	23.2830	+	16.9161i	1.23923	+	0.900352i	0.997547	−	0.0700038i	$-0.0223011\pi$
$353$	23.2830	+	16.9161i	1.23923	+	0.900352i	0.241681	+	0.970356i	$0.422301\pi$
$354$	1.53623	−	2.11444i	0.0816498	−	0.112381i
$355$	15.9485	−	32.0668i	0.846457	−	1.70193i
$356$	15.4982	+	2.45467i	0.821402	+	0.130097i
$357$		−	15.7412i		−	0.833115i
$358$	−4.03252	−	5.55028i	−0.213125	−	0.293342i
$359$	−6.11361	+	11.9986i	−0.322664	+	0.633264i	−0.994181	−	0.107725i	$-0.965643\pi$
$359$	−6.11361	+	11.9986i	−0.322664	+	0.633264i	0.671516	+	0.740990i	$0.265643\pi$
$360$	5.31668	+	15.8380i	0.280213	+	0.834734i
$361$	−13.2597	−	4.30833i	−0.697877	−	0.226754i
$362$	−1.50294	−	4.62557i	−0.0789927	−	0.243115i
$363$	17.3202	−	33.9929i	0.909076	−	1.78416i
$364$	0.115362	−	2.58089i	0.00604663	−	0.135275i
$365$	−7.63432	−	10.2960i	−0.399599	−	0.538915i
$366$	−6.20144	+	12.1710i	−0.324154	+	0.636189i
$367$	16.3731	+	2.59324i	0.854668	+	0.135366i	0.568369	−	0.822774i	$-0.307575\pi$
$367$	16.3731	+	2.59324i	0.854668	+	0.135366i	0.286300	+	0.958140i	$0.407575\pi$
$368$	−3.48875	−	3.48875i	−0.181863	−	0.181863i
$369$	−7.13688	+	45.0605i	−0.371531	+	2.34576i
$370$	−7.29496	+	10.2485i	−0.379247	+	0.532795i
$371$	5.29649	−	0.838881i	0.274980	−	0.0435525i
$372$	−7.55377	−	5.48813i	−0.391645	−	0.284546i
$373$	−1.80594	−	3.54435i	−0.0935078	−	0.183519i	0.839515	−	0.543336i	$-0.182839\pi$
$373$	−1.80594	−	3.54435i	−0.0935078	−	0.183519i	−0.933023	+	0.359817i	$0.882839\pi$
$374$	32.4098			1.67587
$375$	−4.61620	+	35.8833i	−0.238379	+	1.85301i
$376$		−	0.830145i		−	0.0428115i
$377$	−2.19576	−	0.0981478i	−0.113087	−	0.00505487i
$378$	−10.2399	+	1.62184i	−0.526682	+	0.0834183i
$379$	−25.3653	+	4.01747i	−1.30293	+	0.206363i	−0.769044	−	0.639195i	$-0.779267\pi$
$379$	−25.3653	+	4.01747i	−1.30293	+	0.206363i	−0.533882	+	0.845559i	$0.679267\pi$
$380$	−12.6558	+	2.13069i	−0.649231	+	0.109302i
$381$	−18.5401	−	25.5182i	−0.949836	−	1.30734i
$382$		−	2.35432i		−	0.120457i
$383$	−5.56965	+	4.04658i	−0.284596	+	0.206771i	−0.720919	−	0.693019i	$-0.756280\pi$
$383$	−5.56965	+	4.04658i	−0.284596	+	0.206771i	0.436324	+	0.899790i	$0.356280\pi$
$384$	−1.46909	+	2.88325i	−0.0749693	+	0.147135i
$385$	1.12309	−	7.56576i	0.0572377	−	0.385587i
$386$	0.574862	−	1.76924i	0.0292597	−	0.0900521i
$387$	−79.8662	−	40.6939i	−4.05983	−	2.06859i
$388$	8.30400	−	2.69813i	0.421572	−	0.136977i
$389$	9.82280	−	30.2315i	0.498036	−	1.53280i	−0.314136	−	0.949378i	$-0.601715\pi$
$389$	9.82280	−	30.2315i	0.498036	−	1.53280i	0.812172	−	0.583418i	$-0.198285\pi$
$390$	4.97931	−	25.6095i	0.252137	−	1.29679i
$391$	10.3508	+	31.8564i	0.523462	+	1.61105i
$392$	3.81272	+	5.24776i	0.192572	+	0.265052i
$393$	32.4749	−	32.4749i	1.63814	−	1.63814i
$394$	14.3666	−	10.4379i	0.723778	−	0.525856i
$395$	27.9607	−	9.38619i	1.40686	−	0.472270i
$396$	−5.57960	−	35.2282i	−0.280386	−	1.77029i
$397$	−24.6851	−	17.9347i	−1.23891	−	0.900119i	−0.241383	−	0.970430i	$-0.577601\pi$
$397$	−24.6851	−	17.9347i	−1.23891	−	0.900119i	−0.997525	+	0.0703108i	$0.977601\pi$
$398$	−1.67356	−	0.543774i	−0.0838882	−	0.0272569i
$399$		−	13.3078i		−	0.666226i
$400$	−3.98724	+	3.01694i	−0.199362	+	0.150847i
$401$	5.19962	−	5.19962i	0.259657	−	0.259657i	−0.565258	−	0.824914i	$-0.691223\pi$
$401$	5.19962	−	5.19962i	0.259657	−	0.259657i	0.824914	+	0.565258i	$0.191223\pi$
$402$	−3.34114	−	6.55736i	−0.166641	−	0.327051i
$403$	4.30441	+	9.47116i	0.214418	+	0.471792i
$404$	1.71721	−	2.36354i	0.0854344	−	0.117590i
$405$	−54.5741	+	0.530072i	−2.71181	+	0.0263395i
$406$	−0.353374	+	0.256741i	−0.0175377	+	0.0127419i
$407$	18.9906	−	18.9906i	0.941331	−	0.941331i
$408$	17.7732	−	12.9130i	0.879906	−	0.639289i
$409$	−2.03750	−	1.03816i	−0.100748	−	0.0513337i	0.402890	−	0.915248i	$-0.368006\pi$
$409$	−2.03750	−	1.03816i	−0.100748	−	0.0513337i	−0.503638	+	0.863915i	$0.668006\pi$
$410$	−13.4645	+	2.26684i	−0.664965	+	0.111951i
$411$	14.8114	+	29.0690i	0.730591	+	1.43387i
$412$	0.205367	−	0.403056i	0.0101177	−	0.0198572i
$413$	−0.262732	+	0.515641i	−0.0129282	+	0.0253730i
$414$	32.8448	−	16.7352i	1.61423	−	0.822493i
$415$	−13.9587	+	0.135579i	−0.685207	+	0.00665533i
$416$	3.00868	−	1.98692i	0.147513	−	0.0974169i
$417$	13.7705	+	2.18103i	0.674345	+	0.106806i
$418$	27.3997			1.34016
$419$	17.0428	+	23.4575i	0.832597	+	1.14597i	0.987434	+	0.158032i	$0.0505148\pi$
$419$	17.0428	+	23.4575i	0.832597	+	1.14597i	−0.154837	+	0.987940i	$0.549485\pi$
$420$	−2.39853	−	4.59646i	−0.117036	−	0.224284i
$421$	2.37603	+	15.0017i	0.115801	+	0.731136i	0.975445	+	0.220243i	$0.0706852\pi$
$421$	2.37603	+	15.0017i	0.115801	+	0.731136i	−0.859644	+	0.510893i	$0.829315\pi$
$422$	14.8969	−	20.5038i	0.725169	−	0.998110i
$423$	5.89877	+	1.91663i	0.286808	+	0.0931895i
$424$	5.29203	+	5.29203i	0.257004	+	0.257004i
$425$	33.4177	−	5.96040i	1.62099	−	0.289122i
$426$			51.8285i			2.51110i
$427$	0.934666	−	2.87661i	0.0452317	−	0.139209i
$428$	−0.0565422	−	0.356993i	−0.00273307	−	0.0172559i
$429$	−19.5601	+	52.1510i	−0.944368	+	2.51787i
$430$	3.93907	−	26.5359i	0.189959	−	1.27967i
$431$	−16.8926	−	2.67553i	−0.813688	−	0.128876i	−0.264298	−	0.964441i	$-0.585140\pi$
$431$	−16.8926	−	2.67553i	−0.813688	−	0.128876i	−0.549391	+	0.835566i	$0.685140\pi$
$432$	−10.2313	−	10.2313i	−0.492252	−	0.492252i
$433$	−37.0218	−	5.86367i	−1.77915	−	0.281790i	−0.821603	−	0.570060i	$-0.806920\pi$
$433$	−37.0218	−	5.86367i	−1.77915	−	0.281790i	−0.957549	+	0.288270i	$0.906920\pi$
$434$	1.84211	+	0.938601i	0.0884240	+	0.0450543i
$435$	−3.91057	+	2.04061i	−0.187497	+	0.0978400i
$436$	−5.81823	−	11.4189i	−0.278642	−	0.546867i
$437$	8.75068	+	26.9318i	0.418602	+	1.28832i
$438$	16.5273	+	8.42110i	0.789707	+	0.402376i
$439$	7.95495	−	24.4828i	0.379669	−	1.16850i	−0.560606	−	0.828083i	$-0.689432\pi$
$439$	7.95495	−	24.4828i	0.379669	−	1.16850i	0.940274	−	0.340418i	$-0.110568\pi$
$440$	9.46369	−	4.93835i	0.451164	−	0.235427i
$441$	−46.0918	+	14.9761i	−2.19485	+	0.713150i
$442$	−24.3236	+	2.74581i	−1.15696	+	0.130605i
$443$	−18.3260	+	18.3260i	−0.870693	+	0.870693i	−0.992548	−	0.121855i	$-0.961116\pi$
$443$	−18.3260	+	18.3260i	−0.870693	+	0.870693i	0.121855	+	0.992548i	$0.461116\pi$
$444$	2.84786	−	17.9807i	0.135154	−	0.853326i
$445$	−34.7066	−	5.15197i	−1.64525	−	0.244227i
$446$	5.37048	−	7.39183i	0.254300	−	0.350013i
$447$	25.7023	−	35.3762i	1.21568	−	1.67323i
$448$	0.221418	−	0.681455i	0.0104610	−	0.0321957i
$449$	−16.9161	−	16.9161i	−0.798319	−	0.798319i	0.184512	−	0.982830i	$-0.440930\pi$
$449$	−16.9161	−	16.9161i	−0.798319	−	0.798319i	−0.982830	+	0.184512i	$0.940930\pi$
$450$	−12.2319	−	35.2976i	−0.576615	−	1.66395i
$451$	29.1504			1.37264
$452$	0.792348	+	1.55507i	0.0372689	+	0.0731444i
$453$	9.64153	−	13.2704i	0.452999	−	0.623499i
$454$	−1.63009	−	1.18433i	−0.0765038	−	0.0555832i
$455$	−0.201895	+	5.77327i	−0.00946500	+	0.270655i
$456$	15.0257	−	10.9168i	0.703643	−	0.511227i
$457$		−	33.8855i		−	1.58510i	−0.609809	−	0.792549i	$-0.708754\pi$
$457$		−	33.8855i		−	1.58510i	0.609809	−	0.792549i	$-0.291246\pi$
$458$	−1.76675	+	11.1548i	−0.0825550	+	0.521232i
$459$	30.3552	+	93.4237i	1.41686	+	4.36064i
$460$	7.87647	+	7.72494i	0.367242	+	0.360177i
$461$	17.1644	−	8.74568i	0.799424	−	0.407327i	−0.00603259	−	0.999982i	$-0.501920\pi$
$461$	17.1644	−	8.74568i	0.799424	−	0.407327i	0.805456	+	0.592655i	$0.201920\pi$
$462$	3.42046	+	10.5271i	0.159134	+	0.489765i
$463$	−1.61363	+	0.524301i	−0.0749918	+	0.0243663i	−0.346273	−	0.938134i	$-0.612553\pi$
$463$	−1.61363	+	0.524301i	−0.0749918	+	0.0243663i	0.271281	+	0.962500i	$0.412553\pi$
$464$	−0.579766	−	0.188378i	−0.0269150	−	0.00874521i
$465$	17.0091	+	12.1072i	0.788779	+	0.561458i
$466$	−5.07409	−	2.58538i	−0.235052	−	0.119765i
$467$	2.46841	−	15.5850i	0.114225	−	0.721186i	−0.862399	−	0.506229i	$-0.831039\pi$
$467$	2.46841	−	15.5850i	0.114225	−	0.721186i	0.976624	−	0.214957i	$-0.0689610\pi$
$468$	7.17210	+	25.9662i	0.331530	+	1.20029i
$469$	0.957845	+	1.31836i	0.0442292	+	0.0608762i
$470$	0.0180288	+	1.85617i	0.000831605	+	0.0856189i
$471$	−33.2038	−	24.1239i	−1.52995	−	1.11157i
$472$	−0.797730	+	0.126348i	−0.0367185	+	0.00581564i
$473$	−17.6984	+	54.4700i	−0.813772	+	2.50453i
$474$	−30.1813	+	30.1813i	−1.38627	+	1.38627i
$475$	28.2517	−	5.03900i	1.29628	−	0.231205i
$476$	−3.43971	+	3.43971i	−0.157659	+	0.157659i
$477$	−49.8218	+	25.3855i	−2.28118	+	1.16232i
$478$	1.05037	+	6.63175i	0.0480426	+	0.303329i
$479$	−4.72569	−	29.8368i	−0.215922	−	1.36328i	−0.822731	−	0.568431i	$-0.807551\pi$
$479$	−4.72569	−	29.8368i	−0.215922	−	1.36328i	0.606809	−	0.794848i	$-0.292449\pi$
$480$	3.22222	−	6.47875i	0.147073	−	0.295713i
$481$	−12.6436	+	15.8614i	−0.576499	+	0.723219i
$482$	−9.70653	−	9.70653i	−0.442120	−	0.442120i
$483$	−9.25496	+	6.72412i	−0.421115	+	0.305958i
$484$	−11.2127	+	3.64323i	−0.509669	+	0.165602i
$485$	−18.5088	+	6.21327i	−0.840443	+	0.282130i
$486$	31.6964	−	16.1501i	1.43778	−	0.732585i
$487$	6.97247	−	2.26549i	0.315953	−	0.102659i	−0.146748	−	0.989174i	$-0.546881\pi$
$487$	6.97247	−	2.26549i	0.315953	−	0.102659i	0.462700	+	0.886515i	$0.346881\pi$
$488$	4.01467	−	1.30445i	0.181736	−	0.0590495i
$489$	−33.8247	+	17.2346i	−1.52961	+	0.779374i
$490$	−8.63908	−	11.6510i	−0.390274	−	0.526339i
$491$	8.86922	−	2.88178i	0.400262	−	0.130053i	−0.101967	−	0.994788i	$-0.532513\pi$
$491$	8.86922	−	2.88178i	0.400262	−	0.130053i	0.502229	+	0.864735i	$0.332513\pi$
$492$	15.9858	−	11.6144i	0.720696	−	0.523616i
$493$	2.92643	+	2.92643i	0.131800	+	0.131800i
$494$	−20.5635	+	2.32134i	−0.925196	+	0.104442i
$495$	13.2409	+	78.6478i	0.595132	+	3.53496i
$496$	0.451374	+	2.84986i	0.0202673	+	0.127963i
$497$	−1.79527	−	11.3349i	−0.0805288	−	0.508439i
$498$	17.9997	−	9.17129i	0.806584	−	0.410975i
$499$	28.7596	−	28.7596i	1.28746	−	1.28746i	0.351128	−	0.936327i	$-0.385798\pi$
$499$	28.7596	−	28.7596i	1.28746	−	1.28746i	0.936327	−	0.351128i	$-0.114202\pi$
$500$	8.84979	−	6.83237i	0.395775	−	0.305553i
$501$	9.91752	−	9.91752i	0.443082	−	0.443082i
$502$	3.24401	−	9.98403i	0.144787	−	0.445609i
$503$	1.43653	−	0.227524i	0.0640518	−	0.0101448i	−0.124326	−	0.992241i	$-0.539677\pi$
$503$	1.43653	−	0.227524i	0.0640518	−	0.0101448i	0.188378	+	0.982097i	$0.439677\pi$
$504$	4.33101	+	3.14666i	0.192919	+	0.140164i
$505$	−3.78829	+	5.32207i	−0.168576	+	0.236829i
$506$	−13.8444	−	19.0551i	−0.615457	−	0.847104i
$507$	10.2616	−	40.7966i	0.455732	−	1.81184i
$508$	−1.52483	+	9.62743i	−0.0676536	+	0.427148i
$509$	25.0992	+	12.7887i	1.11250	+	0.566849i	0.910903	−	0.412619i	$-0.135386\pi$
$509$	25.0992	+	12.7887i	1.11250	+	0.566849i	0.201599	+	0.979468i	$0.435386\pi$
$510$	−39.4598	+	29.2590i	−1.74731	+	1.29561i
$511$	−3.90622	−	1.26921i	−0.172801	−	0.0561465i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	25.6627	+	78.9816i	1.13303	+	3.48712i
$514$	7.87549	−	4.01276i	0.347373	−	0.176995i
$515$	−0.450441	+	0.905679i	−0.0198488	+	0.0399090i
$516$	11.9968	+	36.9224i	0.528130	+	1.62542i
$517$	0.619949	−	3.91421i	0.0272653	−	0.172147i
$518$			4.03102i			0.177113i
$519$	41.3808	−	30.0649i	1.81641	−	1.31970i
$520$	−6.68414	+	4.50802i	−0.293119	+	0.197690i
$521$	−22.9587	−	16.6805i	−1.00584	−	0.730784i	−0.0425059	−	0.999096i	$-0.513534\pi$
$521$	−22.9587	−	16.6805i	−1.00584	−	0.730784i	−0.963332	+	0.268312i	$0.913534\pi$
$522$	2.67711	−	3.68473i	0.117174	−	0.161276i
$523$	4.07485	+	7.99734i	0.178181	+	0.349699i	0.962772	−	0.270314i	$-0.0871274\pi$
$523$	4.07485	+	7.99734i	0.178181	+	0.349699i	−0.784592	+	0.620013i	$0.787127\pi$
$524$	−14.1926			−0.620005
$525$	5.46284	+	10.2254i	0.238418	+	0.446274i
$526$	−1.56791	−	1.56791i	−0.0683643	−	0.0683643i
$527$	6.05331	−	18.6302i	0.263686	−	0.811543i
$528$	−9.08010	+	12.4977i	−0.395161	+	0.543892i
$529$	0.789215	−	1.08626i	0.0343137	−	0.0472287i
$530$	−11.9477	−	11.7179i	−0.518975	−	0.508991i
$531$	0.943994	−	5.96015i	0.0409659	−	0.258648i
$532$	−2.90798	+	2.90798i	−0.126077	+	0.126077i
$533$	−21.8775	+	2.46967i	−0.947618	+	0.106973i
$534$	48.2913	−	15.6908i	2.08977	−	0.679007i
$535$	0.134179	+	0.796996i	0.00580108	+	0.0344571i
$536$	−0.702794	+	2.16298i	−0.0303561	+	0.0934265i
$537$	−19.7807	−	10.0787i	−0.853598	−	0.434930i
$538$	2.40050	+	7.38799i	0.103493	+	0.318519i
$539$	14.0583	+	27.5910i	0.605535	+	1.18843i
$540$	23.0989	+	22.6545i	0.994019	+	0.974895i
$541$	−26.8712	−	13.6916i	−1.15528	−	0.588647i	−0.231982	−	0.972720i	$-0.574521\pi$
$541$	−26.8712	−	13.6916i	−1.15528	−	0.588647i	−0.923303	+	0.384073i	$0.874521\pi$
$542$	−5.92687	−	0.938724i	−0.254581	−	0.0403217i
$543$	−11.1287	−	11.1287i	−0.477580	−	0.477580i
$544$	−6.70543	−	1.06204i	−0.287493	−	0.0455344i
$545$	13.2573	+	25.4059i	0.567881	+	1.08827i
$546$	−3.45894	−	7.61083i	−0.148029	−	0.325713i
$547$	−3.19832	−	20.1934i	−0.136750	−	0.863408i	−0.956722	−	0.291004i	$-0.906011\pi$
$547$	−3.19832	−	20.1934i	−0.136750	−	0.863408i	0.819972	−	0.572404i	$-0.193989\pi$
$548$	3.11551	−	9.58855i	0.133088	−	0.409603i
$549$			31.5388i			1.34604i
$550$	−21.0532	+	11.2475i	−0.897712	+	0.479595i
$551$	2.47404	+	2.47404i	0.105398	+	0.105398i
$552$	−15.1842	−	4.93365i	−0.646284	−	0.209990i
$553$	5.55520	−	7.64607i	0.236231	−	0.325144i
$554$	0.380497	+	2.40237i	0.0161658	+	0.102067i
$555$	−5.97722	+	40.2660i	−0.253719	+	1.70920i
$556$	−2.53248	−	3.48567i	−0.107401	−	0.147825i
$557$	−29.5687			−1.25287			−0.626433	−	0.779476i	$-0.715486\pi$
$557$	−29.5687			−1.25287			−0.626433	+	0.779476i	$0.715486\pi$
$558$	−21.2924	−	3.37239i	−0.901380	−	0.142765i
$559$	8.66789	−	42.3793i	0.366613	−	1.79245i
$560$	−0.480283	+	1.52852i	−0.0202957	+	0.0645916i
$561$	93.4457	−	47.6130i	3.94528	−	2.01022i
$562$	−5.47107	+	10.7376i	−0.230783	+	0.452937i
$563$	11.6864	−	22.9359i	0.492524	−	0.966632i	−0.502269	−	0.864712i	$-0.667501\pi$
$563$	11.6864	−	22.9359i	0.492524	−	0.966632i	0.994793	−	0.101921i	$-0.0324988\pi$
$564$	−1.21956	−	2.39352i	−0.0513527	−	0.100785i
$565$	−1.80543	−	3.45987i	−0.0759552	−	0.145558i
$566$	−7.85653	−	4.00310i	−0.330234	−	0.168263i
$567$	−14.1485	+	10.2795i	−0.594181	+	0.431698i
$568$	11.3253	−	11.3253i	0.475201	−	0.475201i
$569$	−35.2973	+	25.6450i	−1.47974	+	1.07509i	−0.502098	+	0.864811i	$0.667438\pi$
$569$	−35.2973	+	25.6450i	−1.47974	+	1.07509i	−0.977641	+	0.210282i	$0.932562\pi$
$570$	−33.3598	+	24.7359i	−1.39729	+	1.03607i
$571$	−1.63499	+	2.25037i	−0.0684222	+	0.0941751i	−0.841857	−	0.539701i	$-0.818537\pi$
$571$	−1.63499	+	2.25037i	−0.0684222	+	0.0941751i	0.773434	+	0.633876i	$0.218537\pi$
$572$	15.6700	−	7.12164i	0.655196	−	0.297771i
$573$	−3.45870	−	6.78809i	−0.144489	−	0.283577i
$574$	−3.09379	+	3.09379i	−0.129132	+	0.129132i
$575$	−17.7793	−	17.1016i	−0.741447	−	0.713187i
$576$			7.47138i			0.311308i
$577$	−7.99821	−	2.59877i	−0.332970	−	0.108188i	0.137761	−	0.990466i	$-0.456010\pi$
$577$	−7.99821	−	2.59877i	−0.332970	−	0.108188i	−0.470730	+	0.882277i	$0.656010\pi$
$578$	23.5348	+	17.0991i	0.978920	+	0.711227i
$579$	−0.941707	−	5.94570i	−0.0391360	−	0.247095i
$580$	1.30043	+	0.408614i	0.0539973	+	0.0169668i
$581$	−3.61884	+	2.62924i	−0.150135	+	0.109079i
$582$	19.9787	−	19.9787i	0.828145	−	0.828145i
$583$	21.0003	+	28.9045i	0.869744	+	1.19710i
$584$	−1.77134	−	5.45163i	−0.0732986	−	0.225590i
$585$	−16.6005	−	57.9036i	−0.686345	−	2.39402i
$586$	4.73335	−	14.5678i	0.195533	−	0.601788i
$587$	−4.89673	+	1.59104i	−0.202110	+	0.0656694i	−0.408322	−	0.912838i	$-0.633886\pi$
$587$	−4.89673	+	1.59104i	−0.202110	+	0.0656694i	0.206213	+	0.978507i	$0.433886\pi$
$588$	18.7025	+	9.52940i	0.771278	+	0.392986i
$589$	5.11754	−	15.7502i	0.210865	−	0.648975i
$590$	1.78095	−	0.299834i	0.0733205	−	0.0123440i
$591$	26.0882	−	51.2011i	1.07313	−	2.10613i
$592$	−4.55137	+	3.30676i	−0.187060	+	0.135907i
$593$			1.40629i			0.0577494i	0.999583	+	0.0288747i	$0.00919239\pi$
$593$			1.40629i			0.0577494i	−0.999583	+	0.0288747i	$0.990808\pi$
$594$	−40.6006	−	55.8820i	−1.66586	−	2.29286i
$595$	7.61636	−	7.76577i	0.312241	−	0.318365i
$596$	−13.3466	+	2.11389i	−0.546698	+	0.0865885i
$597$	−5.62416	+	0.890780i	−0.230182	+	0.0364572i
$598$	12.0046	+	13.1280i	0.490905	+	0.536844i
$599$		−	7.72588i		−	0.315671i	−0.987465	−	0.157836i	$-0.949548\pi$
$599$		−	7.72588i		−	0.315671i	0.987465	−	0.157836i	$-0.0504516\pi$
$600$	−7.06405	+	14.5562i	−0.288389	+	0.594256i
$601$	−7.79470			−0.317953			−0.158976	−	0.987282i	$-0.550819\pi$
$601$	−7.79470			−0.317953			−0.158976	+	0.987282i	$0.550819\pi$
$602$	−3.90264	−	7.65936i	−0.159060	−	0.312172i
$603$	−13.7469	−	9.98771i	−0.559817	−	0.406731i
$604$	−5.00663	+	0.792972i	−0.203717	+	0.0322656i
$605$	24.9921	−	8.38965i	1.01607	−	0.341088i
$606$	1.47890	−	9.33741i	0.0600762	−	0.379306i
$607$	−33.9691	−	33.9691i	−1.37876	−	1.37876i	−0.846715	−	0.532047i	$-0.821423\pi$
$607$	−33.9691	−	33.9691i	−1.37876	−	1.37876i	−0.532047	−	0.846715i	$-0.678577\pi$
$608$	−5.66885	−	0.897858i	−0.229902	−	0.0364130i
$609$	−0.641691	+	1.25939i	−0.0260026	+	0.0510331i
$610$	−8.94832	+	3.00388i	−0.362307	+	0.121624i
$611$	−0.133656	+	2.99014i	−0.00540713	+	0.120968i
$612$	23.0279	−	45.1948i	0.930848	−	1.82689i
$613$	7.26316	+	22.3537i	0.293356	+	0.902858i	0.983769	+	0.179442i	$0.0574291\pi$
$613$	7.26316	+	22.3537i	0.293356	+	0.902858i	−0.690412	+	0.723416i	$0.742571\pi$
$614$	12.8006	+	4.15917i	0.516591	+	0.167851i
$615$	−35.4914	+	26.3165i	−1.43115	+	1.06118i
$616$	1.55291	−	3.04776i	0.0625687	−	0.122798i
$617$	1.61889	+	2.22821i	0.0651739	+	0.0897042i	0.840360	−	0.542029i	$-0.182344\pi$
$617$	1.61889	+	2.22821i	0.0651739	+	0.0897042i	−0.775186	+	0.631733i	$0.782344\pi$
$618$		−	1.46382i		−	0.0588834i
$619$	16.2804	+	2.57856i	0.654364	+	0.103641i	0.474784	−	0.880102i	$-0.342526\pi$
$619$	16.2804	+	2.57856i	0.654364	+	0.103641i	0.179580	+	0.983743i	$0.442526\pi$
$620$	−1.07115	−	6.36238i	−0.0430183	−	0.255519i
$621$	41.9611	−	57.7545i	1.68384	−	2.31761i
$622$	22.4958	+	16.3441i	0.901999	+	0.655341i
$623$	−10.0178	+	5.10432i	−0.401354	+	0.204500i
$624$	5.75581	−	10.1488i	0.230417	−	0.406278i
$625$	−19.6394	+	15.4691i	−0.785577	+	0.618764i
$626$	12.4468	+	12.4468i	0.497473	+	0.497473i
$627$	79.0002	−	40.2526i	3.15496	−	1.60753i
$628$	1.98408	+	12.5270i	0.0791735	+	0.499882i
$629$	37.7234	−	5.97480i	1.50413	−	0.238231i
$630$	−9.75232	−	6.94176i	−0.388542	−	0.276566i
$631$	4.76515	−	30.0860i	0.189698	−	1.19770i	−0.690584	−	0.723252i	$-0.742646\pi$
$631$	4.76515	−	30.0860i	0.189698	−	1.19770i	0.880282	−	0.474452i	$-0.157354\pi$
$632$	13.1902			0.524677
$633$	12.8295	−	81.0026i	0.509929	−	3.21956i
$634$	0.787374	+	2.42329i	0.0312706	+	0.0962411i
$635$	3.20039	−	21.5597i	0.127004	−	0.855570i
$636$	23.0327	+	7.48379i	0.913308	+	0.296752i
$637$	−12.8884	−	19.5161i	−0.510655	−	0.773255i
$638$	−2.59297	−	1.32118i	−0.102657	−	0.0523062i
$639$	54.3268	+	106.622i	2.14914	+	4.21792i
$640$	−2.11982	+	0.711605i	−0.0837931	+	0.0281287i
$641$	19.7455	−	6.41571i	0.779901	−	0.253405i	0.108103	−	0.994140i	$-0.465522\pi$
$641$	19.7455	−	6.41571i	0.779901	−	0.253405i	0.671798	+	0.740735i	$0.265522\pi$
$642$	−0.687481	−	0.946237i	−0.0271327	−	0.0373450i
$643$	21.9259			0.864673			0.432336	−	0.901712i	$-0.357689\pi$
$643$	21.9259			0.864673			0.432336	+	0.901712i	$0.357689\pi$
$644$	3.49168	+	0.553028i	0.137592	+	0.0217924i
$645$	−27.6263	−	82.2965i	−1.08778	−	3.24042i
$646$	31.5239	+	22.9034i	1.24029	+	0.901123i
$647$	−19.5846	+	3.10189i	−0.769949	+	0.121948i	−0.529037	−	0.848599i	$-0.677447\pi$
$647$	−19.5846	+	3.10189i	−0.769949	+	0.121948i	−0.240912	+	0.970547i	$0.577447\pi$
$648$	−23.2129	−	7.54231i	−0.911887	−	0.296290i
$649$	−3.85572			−0.151350
$650$	14.8476	−	10.2249i	0.582370	−	0.401055i
$651$	6.69016			0.262208
$652$	11.1573	+	3.62522i	0.436952	+	0.141974i
$653$	44.6722	−	7.07539i	1.74816	−	0.276881i	0.801238	−	0.598346i	$-0.204175\pi$
$653$	44.6722	−	7.07539i	1.74816	−	0.276881i	0.946922	+	0.321465i	$0.104175\pi$
$654$	−33.5508	−	24.3761i	−1.31194	−	0.953182i
$655$	31.7341	−	0.308229i	1.23995	−	0.0120435i
$656$	−6.03108	−	0.955229i	−0.235474	−	0.0372954i
$657$	42.8273			1.67085
$658$	0.349626	+	0.481218i	0.0136298	+	0.0187598i
$659$	27.0358	−	8.78446i	1.05316	−	0.342194i	0.269255	−	0.963069i	$-0.413223\pi$
$659$	27.0358	−	8.78446i	1.05316	−	0.342194i	0.783910	+	0.620875i	$0.213223\pi$
$660$	20.0313	−	28.1416i	0.779719	−	1.09541i
$661$	−12.7360	−	24.9957i	−0.495372	−	0.972222i	−0.994405	−	0.105639i	$-0.966311\pi$
$661$	−12.7360	−	24.9957i	−0.495372	−	0.972222i	0.499033	−	0.866583i	$-0.333689\pi$
$662$	−22.0023	−	11.2107i	−0.855144	−	0.435718i
$663$	−66.0974	+	43.6505i	−2.56701	+	1.69525i
$664$	−5.93728	−	1.92914i	−0.230411	−	0.0748652i
$665$	6.43897	−	6.56528i	0.249693	−	0.254591i
$666$	−12.9888	−	39.9753i	−0.503305	−	1.54901i
$667$	0.470504	−	2.97065i	0.0182180	−	0.115024i
$668$	−4.33427			−0.167698
$669$	4.62518	−	29.2023i	0.178820	−	1.12902i
$670$	1.52445	−	4.85160i	0.0588945	−	0.187434i
$671$	19.9037	−	3.15243i	0.768373	−	0.121698i
$672$	−0.362715	−	2.29009i	−0.0139920	−	0.0883421i
$673$	33.3964	−	17.0163i	1.28734	−	0.655931i	0.329748	−	0.944069i	$-0.393036\pi$
$673$	33.3964	−	17.0163i	1.28734	−	0.655931i	0.957589	+	0.288138i	$0.0930363\pi$
$674$	1.25731	+	1.25731i	0.0484297	+	0.0484297i
$675$	−52.1403	−	50.1530i	−2.00688	−	1.93039i
$676$	−11.1570	+	6.67240i	−0.429116	+	0.256631i
$677$	−26.7235	+	13.6163i	−1.02707	+	0.523316i	−0.884535	−	0.466474i	$-0.845524\pi$
$677$	−26.7235	+	13.6163i	−1.02707	+	0.523316i	−0.142531	+	0.989790i	$0.545524\pi$
$678$	4.56908	+	3.31963i	0.175475	+	0.127490i
$679$	−3.67731	+	5.06138i	−0.141122	+	0.194238i
$680$	15.0161	+	2.22905i	0.575843	+	0.0854800i
$681$	−6.43984	−	1.01997i	−0.246775	−	0.0390854i
$682$			13.7744i			0.527450i
$683$	1.11076	+	1.52884i	0.0425022	+	0.0584993i	0.829739	−	0.558151i	$-0.188489\pi$
$683$	1.11076	+	1.52884i	0.0425022	+	0.0584993i	−0.787237	+	0.616651i	$0.788489\pi$
$684$	19.4681	−	38.2083i	0.744381	−	1.46093i
$685$	−6.75792	+	21.5073i	−0.258207	+	0.821752i
$686$	−9.19050	−	2.98617i	−0.350895	−	0.114013i
$687$	11.2935	+	34.7578i	0.430873	+	1.32609i
$688$	5.44663	−	10.6896i	0.207651	−	0.407538i
$689$	−18.2096	−	19.9137i	−0.693731	−	0.758651i
$690$	34.0585	+	10.7017i	1.29659	+	0.407407i
$691$	0.492457	−	0.966502i	0.0187340	−	0.0367675i	−0.881450	−	0.472278i	$-0.843432\pi$
$691$	0.492457	−	0.966502i	0.0187340	−	0.0367675i	0.900184	+	0.435510i	$0.143432\pi$
$692$	−15.6120	−	2.47270i	−0.593480	−	0.0939980i
$693$	18.0712	+	18.0712i	0.686467	+	0.686467i
$694$	2.90591	−	18.3472i	0.110307	−	0.696449i
$695$	5.73824	+	7.73882i	0.217664	+	0.293550i
$696$	−1.94836	+	0.308590i	−0.0738523	+	0.0116971i
$697$	33.5381	+	24.3669i	1.27035	+	0.922962i
$698$	1.25287	+	2.45889i	0.0474218	+	0.0930705i
$699$	−18.4280			−0.697012
$700$	1.04070	−	3.42813i	0.0393347	−	0.129571i
$701$			37.1633i			1.40364i	0.712356	+	0.701818i	$0.247628\pi$
$701$			37.1633i			1.40364i	−0.712356	+	0.701818i	$0.752372\pi$
$702$	35.2053	+	38.4998i	1.32874	+	1.45308i
$703$	31.8919	−	5.05117i	1.20282	−	0.190509i
$704$	4.71509	−	0.746796i	0.177707	−	0.0281460i
$705$	2.77887	+	5.32533i	0.104658	+	0.200564i
$706$	−16.9161	−	23.2830i	−0.636645	−	0.876267i
$707$			2.09332i			0.0787273i
$708$	−2.11444	+	1.53623i	−0.0794655	+	0.0577351i
$709$	−13.6363	+	26.7627i	−0.512120	+	1.00509i	0.479698	+	0.877434i	$0.340746\pi$
$709$	−13.6363	+	26.7627i	−0.512120	+	1.00509i	−0.991818	+	0.127659i	$0.959254\pi$
$710$	−25.0771	+	25.5690i	−0.941126	+	0.959588i
$711$	−30.4532	+	93.7255i	−1.14209	+	3.51498i
$712$	−13.9811	−	7.12373i	−0.523964	−	0.266973i
$713$	−13.5392	+	4.39917i	−0.507049	+	0.164750i
$714$	−4.86431	+	14.9708i	−0.182042	+	0.560269i
$715$	−34.8829	+	16.2640i	−1.30455	+	0.608240i
$716$	2.12002	+	6.52475i	0.0792289	+	0.243841i
$717$	12.7711	+	17.5779i	0.476946	+	0.656460i
$718$	9.52218	−	9.52218i	0.355365	−	0.355365i
$719$	19.7689	−	14.3630i	0.737257	−	0.535649i	−0.154594	−	0.987978i	$-0.549407\pi$
$719$	19.7689	−	14.3630i	0.737257	−	0.535649i	0.891851	+	0.452330i	$0.149407\pi$
$720$	−0.162261	−	16.7057i	−0.00604710	−	0.622586i
$721$	0.0507047	+	0.320137i	0.00188834	+	0.0119225i
$722$	11.2793	+	8.19492i	0.419774	+	0.304983i
$723$	−42.2462	−	13.7266i	−1.57115	−	0.510498i
$724$			4.86361i			0.180755i
$725$	−2.91658	−	0.885403i	−0.108319	−	0.0328831i
$726$	−26.9769	+	26.9769i	−1.00121	+	1.00121i
$727$	12.5685	+	24.6671i	0.466140	+	0.914851i	0.997697	+	0.0678285i	$0.0216071\pi$
$727$	12.5685	+	24.6671i	0.466140	+	0.914851i	−0.531557	+	0.847022i	$0.678393\pi$
$728$	−0.907254	+	2.41892i	−0.0336251	+	0.0896511i
$729$	24.6238	−	33.8918i	0.911994	−	1.25525i
$730$	4.07905	+	12.1512i	0.150972	+	0.449735i
$731$	−65.8939	+	47.8747i	−2.43717	+	1.77071i
$732$	9.65896	−	9.65896i	0.357006	−	0.357006i
$733$	10.7963	−	7.84395i	0.398770	−	0.289723i	−0.370270	−	0.928924i	$-0.620735\pi$
$733$	10.7963	−	7.84395i	0.398770	−	0.289723i	0.769040	+	0.639201i	$0.220735\pi$
$734$	−14.7704	−	7.52588i	−0.545185	−	0.277785i
$735$	−42.0250	−	20.9012i	−1.55012	−	0.770953i
$736$	2.23991	+	4.39608i	0.0825643	+	0.162042i
$737$	−4.92904	+	9.67379i	−0.181564	+	0.356339i
$738$	20.7120	−	40.6497i	0.762421	−	1.49633i
$739$	−32.7789	+	16.7017i	−1.20579	+	0.614380i	−0.937172	−	0.348867i	$-0.886567\pi$
$739$	−32.7789	+	16.7017i	−1.20579	+	0.614380i	−0.268617	+	0.963247i	$0.586567\pi$
$740$	10.1049	−	7.49265i	0.371463	−	0.275435i
$741$	−55.8796	+	36.9027i	−2.05279	+	1.35565i
$742$	−5.29649	−	0.838881i	−0.194440	−	0.0307963i
$743$	−10.8987			−0.399835			−0.199918	−	0.979813i	$-0.564067\pi$
$743$	−10.8987			−0.399835			−0.199918	+	0.979813i	$0.564067\pi$
$744$	5.48813	+	7.55377i	0.201205	+	0.276934i
$745$	29.7966	−	5.01645i	1.09166	−	0.183788i
$746$	0.622283	+	3.92894i	0.0227834	+	0.143849i
$747$	27.4158	−	37.7346i	1.00309	−	1.38064i
$748$	−30.8235	−	10.0152i	−1.12702	−	0.366191i
$749$	0.183128	+	0.183128i	0.00669137	+	0.00669137i
$750$	15.4788	−	32.7006i	0.565207	−	1.19406i
$751$			45.1075i			1.64600i	0.568045	+	0.822998i	$0.307700\pi$
$751$			45.1075i			1.64600i	−0.568045	+	0.822998i	$0.692300\pi$
$752$	−0.256529	+	0.789515i	−0.00935465	+	0.0287906i
$753$	−5.31415	−	33.5522i	−0.193658	−	1.22271i
$754$	2.05796	+	0.771871i	0.0749466	+	0.0281099i
$755$	11.1774	−	1.88179i	0.406787	−	0.0684852i
$756$	10.2399	+	1.62184i	0.372421	+	0.0589856i
$757$	21.0142	+	21.0142i	0.763775	+	0.763775i	0.977003	−	0.213227i	$-0.0683974\pi$
$757$	21.0142	+	21.0142i	0.763775	+	0.763775i	−0.213227	+	0.977003i	$0.568397\pi$
$758$	25.3653	+	4.01747i	0.921308	+	0.145921i
$759$	−67.9105	−	34.6021i	−2.46500	−	1.25598i
$760$	12.6948	+	1.88446i	0.460490	+	0.0683567i
$761$	12.9651	+	25.4455i	0.469985	+	0.922397i	0.997350	+	0.0727580i	$0.0231801\pi$
$761$	12.9651	+	25.4455i	0.469985	+	0.922397i	−0.527365	+	0.849639i	$0.676820\pi$
$762$	9.74709	+	29.9984i	0.353100	+	1.08673i
$763$	8.18192	+	4.16890i	0.296205	+	0.150924i
$764$	−0.727524	+	2.23909i	−0.0263209	+	0.0810073i
$765$	−50.5080	+	101.554i	−1.82612	+	3.67169i
$766$	6.54751	−	2.12742i	0.236571	−	0.0768667i
$767$	2.89373	−	0.326663i	0.104486	−	0.0117951i
$768$	2.28816	−	2.28816i	0.0825670	−	0.0825670i
$769$	−8.42077	+	53.1666i	−0.303661	+	1.91724i	0.0860307	+	0.996292i	$0.472582\pi$
$769$	−8.42077	+	53.1666i	−0.303661	+	1.91724i	−0.389691	+	0.920946i	$0.627418\pi$
$770$	−3.40607	+	6.84841i	−0.122746	+	0.246800i
$771$	16.8119	−	23.1396i	0.605467	−	0.833353i
$772$	−1.09345	+	1.50501i	−0.0393542	+	0.0541664i
$773$	8.66050	−	26.6543i	0.311497	−	0.958688i	−0.665676	−	0.746241i	$-0.731857\pi$
$773$	8.66050	−	26.6543i	0.311497	−	0.958688i	0.977173	−	0.212447i	$-0.0681433\pi$
$774$	63.3822	+	63.3822i	2.27823	+	2.27823i
$775$	2.53322	+	14.2028i	0.0909959	+	0.510179i
$776$	−8.73134			−0.313437
$777$	5.92194	+	11.6225i	0.212448	+	0.416953i
$778$	−18.6841	+	25.7164i	−0.669856	+	0.921978i
$779$	28.3536	+	20.6001i	1.01587	+	0.738074i
$780$	−12.6494	+	22.8174i	−0.452920	+	0.816994i
$781$	61.8577	−	44.9423i	2.21344	−	1.60816i
$782$		−	33.4958i		−	1.19781i
$783$	1.37982	−	8.71186i	0.0493108	−	0.311336i
$784$	−2.00447	−	6.16912i	−0.0715881	−	0.220326i
$785$	−4.70839	−	27.9668i	−0.168050	−	0.998179i
$786$	−40.9208	+	20.8502i	−1.45960	+	0.743701i
$787$	−0.0148652	−	0.0457504i	−0.000529887	−	0.00163082i	0.950791	−	0.309832i	$-0.100273\pi$
$787$	−0.0148652	−	0.0457504i	−0.000529887	−	0.00163082i	−0.951321	+	0.308201i	$0.900273\pi$
$788$	−16.8889	+	5.48755i	−0.601643	+	0.195486i
$789$	−6.82410	−	2.21729i	−0.242945	−	0.0789375i
$790$	−29.4927	+	0.286459i	−1.04930	+	0.0101918i
$791$	−1.11425	−	0.567736i	−0.0396180	−	0.0201864i
$792$	−5.57960	+	35.2282i	−0.198263	+	1.25178i
$793$	−14.6707	+	4.05218i	−0.520971	+	0.143897i
$794$	17.9347	+	24.6851i	0.636480	+	0.876040i
$795$	−51.6629	−	16.2333i	−1.83229	−	0.575735i
$796$	1.42362	+	1.03432i	0.0504588	+	0.0366605i
$797$	−32.7263	+	5.18334i	−1.15923	+	0.183603i	−0.706279	−	0.707934i	$-0.749627\pi$
$797$	−32.7263	+	5.18334i	−1.15923	+	0.183603i	−0.452947	+	0.891537i	$0.649627\pi$
$798$	−4.11235	+	12.6565i	−0.145576	+	0.448036i
$799$	3.98516	−	3.98516i	0.140985	−	0.140985i
$800$	4.72437	−	1.63716i	0.167032	−	0.0578823i
$801$	82.8985	−	82.8985i	2.92907	−	2.92907i
$802$	−6.55190	+	3.33836i	−0.231356	+	0.117882i
$803$	−4.28077	−	27.0277i	−0.151065	−	0.953788i
$804$	1.15128	+	7.26889i	0.0406025	+	0.256354i
$805$	−7.81928	−	1.16072i	−0.275594	−	0.0409100i
$806$	−1.16699	−	10.3377i	−0.0411055	−	0.364132i
$807$	17.7749	+	17.7749i	0.625706	+	0.625706i
$808$	−2.36354	+	1.71721i	−0.0831489	+	0.0604112i
$809$	−37.3602	+	12.1391i	−1.31351	+	0.426787i	−0.880263	−	0.474487i	$-0.842634\pi$
$809$	−37.3602	+	12.1391i	−1.31351	+	0.426787i	−0.433251	+	0.901273i	$0.642634\pi$
$810$	52.0669	+	16.3602i	1.82944	+	0.574839i
$811$	1.05867	−	0.539419i	0.0371749	−	0.0189416i	−0.435304	−	0.900283i	$-0.643359\pi$
$811$	1.05867	−	0.539419i	0.0371749	−	0.0189416i	0.472479	+	0.881342i	$0.343359\pi$
$812$	0.415416	−	0.134977i	0.0145783	−	0.00473676i
$813$	−18.4678	+	6.00054i	−0.647692	+	0.210448i
$814$	−23.9296	+	12.1927i	−0.838732	+	0.427355i
$815$	−25.0260	−	7.86354i	−0.876621	−	0.275448i
$816$	−20.8937	+	6.78877i	−0.731425	+	0.237654i
$817$	−55.7075	+	40.4739i	−1.94896	+	1.41600i
$818$	1.61697	+	1.61697i	0.0565361	+	0.0565361i
$819$	−15.0935	−	12.0314i	−0.527409	−	0.420413i
$820$	13.5060	+	2.00487i	0.471650	+	0.0700133i
$821$	−4.51626	−	28.5146i	−0.157619	−	0.995165i	−0.932003	−	0.362450i	$-0.881940\pi$
$821$	−4.51626	−	28.5146i	−0.157619	−	0.995165i	0.774385	−	0.632715i	$-0.218060\pi$
$822$	−5.10365	−	32.2232i	−0.178010	−	1.12391i
$823$	34.7672	−	17.7148i	1.21191	−	0.617499i	0.273117	−	0.961981i	$-0.411945\pi$
$823$	34.7672	−	17.7148i	1.21191	−	0.617499i	0.938793	+	0.344482i	$0.111945\pi$
$824$	−0.319867	+	0.319867i	−0.0111431	+	0.0111431i
$825$	−44.1782	+	63.3585i	−1.53809	+	2.20586i
$826$	0.409215	−	0.409215i	0.0142384	−	0.0142384i
$827$	−3.36345	+	10.3516i	−0.116959	+	0.359962i	−0.992351	−	0.123452i	$-0.960603\pi$
$827$	−3.36345	+	10.3516i	−0.116959	+	0.359962i	0.875392	+	0.483414i	$0.160603\pi$
$828$	−36.4087	+	5.76657i	−1.26529	+	0.200402i
$829$	7.40113	+	5.37723i	0.257052	+	0.186759i	0.708846	−	0.705363i	$-0.249216\pi$
$829$	7.40113	+	5.37723i	0.257052	+	0.186759i	−0.451795	+	0.892122i	$0.649216\pi$
$830$	13.3174	+	4.18454i	0.462255	+	0.145248i
$831$	4.62637	+	6.36765i	0.160487	+	0.220891i
$832$	−3.47542	+	0.959942i	−0.120488	+	0.0332800i
$833$	−6.88899	+	43.4954i	−0.238689	+	1.50703i
$834$	−12.4226	−	6.32961i	−0.430158	−	0.219176i
$835$	9.69126	−	0.0941300i	0.335380	−	0.00325750i
$836$	−26.0586	−	8.46696i	−0.901256	−	0.292836i
$837$	−39.7058	+	12.9012i	−1.37243	+	0.445931i
$838$	−8.95995	−	27.5759i	−0.309516	−	0.952594i
$839$	−20.8007	+	10.5985i	−0.718120	+	0.365900i	−0.774556	−	0.632506i	$-0.782026\pi$
$839$	−20.8007	+	10.5985i	−0.718120	+	0.365900i	0.0564356	+	0.998406i	$0.482026\pi$
$840$	0.860752	+	5.11268i	0.0296988	+	0.176404i
$841$	8.84666	+	27.2272i	0.305057	+	0.938869i
$842$	2.37603	−	15.0017i	0.0818834	−	0.516992i
$843$			38.9966i			1.34312i
$844$	−20.5038	+	14.8969i	−0.705770	+	0.512772i
$845$	24.8018	−	15.1615i	0.853207	−	0.521573i
$846$	−5.01779	−	3.64564i	−0.172515	−	0.125340i
$847$	4.96540	−	6.83428i	0.170613	−	0.234829i
$848$	−3.39769	−	6.66835i	−0.116677	−	0.228992i
$849$	−28.5333			−0.979260
$850$	−33.6240	−	4.65795i	−1.15329	−	0.159766i
$851$	−19.6270	−	19.6270i	−0.672805	−	0.672805i
$852$	16.0159	−	49.2918i	0.548695	−	1.68871i
$853$	−16.6717	+	22.9466i	−0.570827	+	0.785676i	−0.992652	−	0.121001i	$-0.961390\pi$
$853$	−16.6717	+	22.9466i	−0.570827	+	0.785676i	0.421825	+	0.906677i	$0.361390\pi$
$854$	−1.77784	+	2.44699i	−0.0608364	+	0.0837342i
$855$	−42.7001	+	85.8550i	−1.46031	+	2.93618i
$856$	−0.0565422	+	0.356993i	−0.00193257	+	0.0122018i
$857$	−1.40695	+	1.40695i	−0.0480606	+	0.0480606i	−0.730729	−	0.682668i	$-0.760820\pi$
$857$	−1.40695	+	1.40695i	−0.0480606	+	0.0480606i	0.682668	+	0.730729i	$0.260820\pi$
$858$	34.7183	−	43.5542i	1.18526	−	1.48691i
$859$	31.5687	−	10.2573i	1.07711	−	0.349974i	0.283857	−	0.958867i	$-0.408386\pi$
$859$	31.5687	−	10.2573i	1.07711	−	0.349974i	0.793253	+	0.608893i	$0.208386\pi$
$860$	−11.9463	+	24.0199i	−0.407366	+	0.819071i
$861$	−4.37512	+	13.4652i	−0.149104	+	0.458894i
$862$	15.2390	+	7.76468i	0.519044	+	0.264466i
$863$	−6.42242	−	19.7662i	−0.218622	−	0.672848i	−0.998877	−	0.0473867i	$-0.984911\pi$
$863$	−6.42242	−	19.7662i	−0.218622	−	0.672848i	0.780255	−	0.625462i	$-0.215089\pi$
$864$	6.56887	+	12.8921i	0.223478	+	0.438600i
$865$	34.9616	+	5.18981i	1.18873	+	0.176459i
$866$	33.3978	+	17.0170i	1.13490	+	0.578262i
$867$	92.9770	+	14.7261i	3.15767	+	0.500125i
$868$	−1.46191	−	1.46191i	−0.0496203	−	0.0496203i
$869$	62.1928	+	9.85037i	2.10975	+	0.334151i
$870$	4.34975	−	0.732308i	0.147470	−	0.0248276i
$871$	2.87968	−	7.67780i	0.0975742	−	0.260152i
$872$	2.00482	+	12.6580i	0.0678919	+	0.428653i
$873$	20.1588	−	62.0424i	0.682272	−	2.09982i
$874$		−	28.3178i		−	0.957864i
$875$	−2.25251	+	7.68778i	−0.0761488	+	0.259894i
$876$	−13.1162	−	13.1162i	−0.443154	−	0.443154i
$877$	−10.2253	−	3.32241i	−0.345285	−	0.112190i	0.131240	−	0.991351i	$-0.458104\pi$
$877$	−10.2253	−	3.32241i	−0.345285	−	0.112190i	−0.476526	+	0.879161i	$0.658104\pi$
$878$	−15.1312	+	20.8263i	−0.510653	+	0.702854i
$879$	−7.75391	−	48.9563i	−0.261533	−	1.65125i
$880$	−10.5265	+	1.77221i	−0.354850	+	0.0597412i
$881$	7.81721	+	10.7595i	0.263369	+	0.362496i	0.920137	−	0.391597i	$-0.128077\pi$
$881$	7.81721	+	10.7595i	0.263369	+	0.362496i	−0.656768	+	0.754092i	$0.728077\pi$
$882$	48.4638			1.63186
$883$	5.46223	+	0.865132i	0.183819	+	0.0291140i	0.247665	−	0.968846i	$-0.420337\pi$
$883$	5.46223	+	0.865132i	0.183819	+	0.0291140i	−0.0638464	+	0.997960i	$0.520337\pi$
$884$	23.9817	+	4.90500i	0.806590	+	0.164973i
$885$	4.69445	−	3.48088i	0.157802	−	0.117008i
$886$	23.0921	−	11.7660i	0.775793	−	0.395286i
$887$	−23.3113	+	45.7510i	−0.782717	+	1.53617i	0.0602374	+	0.998184i	$0.480814\pi$
$887$	−23.3113	+	45.7510i	−0.782717	+	1.53617i	−0.842955	+	0.537985i	$0.819186\pi$
$888$	−8.26482	+	16.2206i	−0.277349	+	0.544328i
$889$	−3.17079	−	6.22303i	−0.106345	−	0.208714i
$890$	31.4159	+	15.6248i	1.05306	+	0.523743i
$891$	−103.818	−	52.8979i	−3.47804	−	1.77215i
$892$	−7.39183	+	5.37048i	−0.247497	+	0.179817i
$893$	3.36910	−	3.36910i	0.112743	−	0.112743i
$894$	−35.3762	+	25.7023i	−1.18316	+	0.859613i
$895$	−4.88199	−	14.5431i	−0.163187	−	0.486121i
$896$	−0.421162	+	0.579680i	−0.0140700	+	0.0193657i
$897$	53.8986	+	20.2155i	1.79962	+	0.674976i
$898$	10.8608	+	21.3155i	0.362429	+	0.711307i
$899$	−1.24376	+	1.24376i	−0.0414816	+	0.0414816i
$900$	0.725618	+	37.3499i	0.0241873	+	1.24500i
$901$			50.8094i			1.69271i
$902$	−27.7237	−	9.00797i	−0.923098	−	0.299933i
$903$	−22.5046	−	16.3506i	−0.748906	−	0.544112i
$904$	−0.273025	−	1.72381i	−0.00908066	−	0.0573330i
$905$	−0.105626	−	10.8749i	−0.00351113	−	0.361493i
$906$	−13.2704	+	9.64153i	−0.440880	+	0.320318i
$907$	1.87366	−	1.87366i	0.0622140	−	0.0622140i	−0.675315	−	0.737529i	$-0.735992\pi$
$907$	1.87366	−	1.87366i	0.0622140	−	0.0622140i	0.737529	+	0.675315i	$0.235992\pi$
$908$	1.18433	+	1.63009i	0.0393033	+	0.0540963i
$909$	−6.74509	−	20.7593i	−0.223721	−	0.688541i
$910$	1.97605	−	5.42832i	0.0655055	−	0.179947i
$911$	−7.16652	+	22.0563i	−0.237437	+	0.730757i	0.759351	+	0.650681i	$0.225516\pi$
$911$	−7.16652	+	22.0563i	−0.237437	+	0.730757i	−0.996789	+	0.0800764i	$0.974484\pi$
$912$	−17.6638	+	5.73931i	−0.584906	+	0.190048i
$913$	−26.5541	−	13.5300i	−0.878814	−	0.447778i
$914$	−10.4712	+	32.2270i	−0.346356	+	1.06598i
$915$	−21.3873	+	21.8069i	−0.707043	+	0.720912i
$916$	5.12732	−	10.0629i	0.169411	−	0.332489i
$917$	8.22715	−	5.97737i	0.271684	−	0.197390i
$918$		−	98.2315i		−	3.24212i
$919$	−34.0948	−	46.9275i	−1.12468	−	1.54799i	−0.797792	−	0.602932i	$-0.793999\pi$
$919$	−34.0948	−	46.9275i	−1.12468	−	1.54799i	−0.326891	−	0.945062i	$-0.606001\pi$
$920$	−5.10383	−	9.78082i	−0.168268	−	0.322464i
$921$	43.0176	−	6.81333i	1.41748	−	0.224507i
$922$	−19.0268	+	3.01355i	−0.626615	+	0.0992461i
$923$	−42.6168	+	38.9700i	−1.40275	+	1.28271i
$924$		−	11.0688i		−	0.364138i
$925$	−22.4314	+	16.9727i	−0.737540	+	0.558060i
$926$	1.69667			0.0557561
$927$	−1.53438	−	3.01139i	−0.0503956	−	0.0989070i
$928$	0.493179	+	0.358315i	0.0161894	+	0.0117623i
$929$	−37.3318	+	5.91278i	−1.22482	+	0.193992i	−0.735142	−	0.677913i	$-0.762885\pi$
$929$	−37.3318	+	5.91278i	−1.22482	+	0.193992i	−0.489675	+	0.871905i	$0.662885\pi$
$930$	−12.4353	−	16.7707i	−0.407770	−	0.549934i
$931$	−5.82404	+	36.7715i	−0.190875	+	1.20514i
$932$	4.02682	+	4.02682i	0.131903	+	0.131903i
$933$	88.8721	+	14.0760i	2.90954	+	0.460826i
$934$	−7.16362	+	14.0594i	−0.234401	+	0.460037i
$935$	69.1378	+	21.7241i	2.26105	+	0.710456i
$936$	1.20292	−	26.9116i	0.0393185	−	0.879633i
$937$	24.0353	−	47.1718i	0.785198	−	1.54104i	−0.0548315	−	0.998496i	$-0.517462\pi$
$937$	24.0353	−	47.1718i	0.785198	−	1.54104i	0.840029	−	0.542541i	$-0.182538\pi$
$938$	−0.503569	−	1.54983i	−0.0164421	−	0.0506036i
$939$	54.1726	+	17.6018i	1.76786	+	0.574411i
$940$	0.556443	−	1.77090i	0.0181492	−	0.0577603i
$941$	−16.9111	+	33.1898i	−0.551285	+	1.08196i	0.432337	+	0.901712i	$0.357689\pi$
$941$	−16.9111	+	33.1898i	−0.551285	+	1.08196i	−0.983622	+	0.180245i	$0.942311\pi$
$942$	24.1239	+	33.2038i	0.786000	+	1.08184i
$943$		−	30.1272i		−	0.981078i
$944$	0.797730	+	0.126348i	0.0259639	+	0.00411228i
$945$	−22.9312	−	3.40398i	−0.745952	−	0.110731i
$946$	33.6643	−	46.3349i	1.09452	−	1.50648i
$947$	−6.15120	−	4.46911i	−0.199887	−	0.145226i	0.483339	−	0.875433i	$-0.339424\pi$
$947$	−6.15120	−	4.46911i	−0.199887	−	0.145226i	−0.683226	+	0.730207i	$0.739424\pi$
$948$	38.0306	−	19.3776i	1.23518	−	0.629354i
$949$	5.50256	+	19.9217i	0.178621	+	0.646686i
$950$	−28.4261	−	3.93789i	−0.922265	−	0.127762i
$951$	5.83023	+	5.83023i	0.189058	+	0.189058i
$952$	4.33429	−	2.20843i	0.140475	−	0.0715757i
$953$	−0.828576	−	5.23143i	−0.0268402	−	0.169462i	0.970627	−	0.240589i	$-0.0773406\pi$
$953$	−0.828576	−	5.23143i	−0.0268402	−	0.169462i	−0.997467	+	0.0711265i	$0.977341\pi$
$954$	55.2279	−	8.74724i	1.78807	−	0.283202i
$955$	1.57809	−	5.02232i	0.0510657	−	0.162518i
$956$	1.05037	−	6.63175i	0.0339713	−	0.214486i
$957$	−9.41713			−0.304413
$958$	−4.72569	+	29.8368i	−0.152680	+	0.963983i
$959$	2.23234	+	6.87042i	0.0720859	+	0.221858i
$960$	−5.06655	+	5.16594i	−0.163522	+	0.166730i
$961$	−21.5648	−	7.00682i	−0.695638	−	0.226027i
$962$	16.9262	−	11.1780i	0.545724	−	0.360394i
$963$	−2.40615	−	1.22599i	−0.0775370	−	0.0395071i
$964$	6.23197	+	12.2309i	0.200718	+	0.393932i
$965$	2.41223	−	3.38889i	0.0776525	−	0.109092i
$966$	10.8799	−	3.53508i	0.350054	−	0.113739i
$967$	−1.07725	−	1.48271i	−0.0346420	−	0.0476807i	0.791345	−	0.611370i	$-0.209381\pi$
$967$	−1.07725	−	1.48271i	−0.0346420	−	0.0476807i	−0.825987	+	0.563690i	$0.809381\pi$
$968$	11.7898			0.378937
$969$	124.539	+	19.7250i	4.00075	+	0.633657i
$970$	19.5230	−	0.189624i	0.626844	−	0.00608846i
$971$	−29.6545	−	21.5453i	−0.951659	−	0.691421i	−0.000460544	−	1.00000i	$-0.500147\pi$
$971$	−29.6545	−	21.5453i	−0.951659	−	0.691421i	−0.951199	+	0.308579i	$0.900147\pi$
$972$	−35.1358	+	5.56496i	−1.12698	+	0.178496i
$973$	2.93606	+	0.953984i	0.0941258	+	0.0305833i
$974$	−7.33128			−0.234910
$975$	27.7880	−	51.2935i	0.889928	−	1.64271i
$976$	−4.22127			−0.135120
$977$	−47.2187	−	15.3423i	−1.51066	−	0.490843i	−0.567553	−	0.823337i	$-0.692110\pi$
$977$	−47.2187	−	15.3423i	−1.51066	−	0.490843i	−0.943105	+	0.332494i	$0.892110\pi$
$978$	37.4950	−	5.93863i	1.19896	−	0.189896i
$979$	−60.6022	−	44.0300i	−1.93685	−	1.40721i
$980$	4.61589	+	13.7504i	0.147449	+	0.439240i
$981$	−94.5725	−	14.9788i	−3.01947	−	0.478237i
$982$	−9.32565			−0.297593
$983$	8.43754	+	11.6133i	0.269116	+	0.370406i	0.922091	−	0.386973i	$-0.126479\pi$
$983$	8.43754	+	11.6133i	0.269116	+	0.370406i	−0.652975	+	0.757379i	$0.726479\pi$
$984$	−18.7924	+	6.10604i	−0.599081	+	0.194653i
$985$	37.6439	−	12.6367i	1.19943	−	0.402640i
$986$	−1.87888	−	3.68752i	−0.0598359	−	0.117434i
$987$	1.71501	+	0.873843i	0.0545895	+	0.0278147i
$988$	20.2744	+	4.14675i	0.645014	+	0.131926i
$989$	56.2953	+	18.2914i	1.79008	+	0.581634i
$990$	11.7107	−	78.8902i	0.372191	−	2.50729i
$991$	−9.26236	−	28.5066i	−0.294229	−	0.905542i	−0.983479	−	0.181020i	$-0.942060\pi$
$991$	−9.26236	−	28.5066i	−0.294229	−	0.905542i	0.689251	−	0.724523i	$-0.257940\pi$
$992$	0.451374	−	2.84986i	0.0143311	−	0.0904832i
$993$	−79.9079			−2.53580
$994$	−1.79527	+	11.3349i	−0.0569425	+	0.359521i
$995$	−3.20562	−	2.28178i	−0.101625	−	0.0723373i
$996$	−19.9528	+	3.16021i	−0.632228	+	0.100135i
$997$	−5.57986	−	35.2298i	−0.176716	−	1.11574i	−0.903410	−	0.428778i	$-0.858944\pi$
$997$	−5.57986	−	35.2298i	−0.176716	−	1.11574i	0.726694	−	0.686961i	$-0.241056\pi$
$998$	−36.2392	+	18.4648i	−1.14713	+	0.584493i
$999$	−57.5591	−	57.5591i	−1.82109	−	1.82109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.bd.b.47.1	yes	144
13.5	odd	4		650.2.ba.b.447.1	yes	144
25.8	odd	20		650.2.ba.b.333.1	✓	144
325.83	even	20	inner	650.2.bd.b.83.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.ba.b.333.1	✓	144	25.8	odd	20
650.2.ba.b.447.1	yes	144	13.5	odd	4
650.2.bd.b.47.1	yes	144	1.1	even	1	trivial
650.2.bd.b.83.1	yes	144	325.83	even	20	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.bd (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-3.19611 + 0.506214i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-1.82170 - 1.29670i) q^{5} +(3.19611 + 0.506214i) q^{6} -0.716524 q^{7} +(-0.587785 - 0.809017i) q^{8} +(7.10571 - 2.30878i) q^{9} +(1.33184 + 1.79617i) q^{10} +(-2.16729 - 4.25354i) q^{11} +(-2.88325 - 1.46909i) q^{12} +(1.98692 + 3.00868i) q^{13} +(0.681455 + 0.221418i) q^{14} +(6.47875 + 3.22222i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.06204 - 6.70543i) q^{17} -7.47138 q^{18} +(0.897858 - 5.66885i) q^{19} +(-0.711605 - 2.11982i) q^{20} +(2.29009 - 0.362715i) q^{21} +(0.746796 + 4.71509i) q^{22} +(-4.39608 + 2.23991i) q^{23} +(2.28816 + 2.28816i) q^{24} +(1.63716 + 4.72437i) q^{25} +(-0.959942 - 3.47542i) q^{26} +(-12.8921 + 6.56887i) q^{27} +(-0.579680 - 0.421162i) q^{28} +(-0.358315 + 0.493179i) q^{29} +(-5.16594 - 5.06655i) q^{30} +(2.84986 + 0.451374i) q^{31} -1.00000i q^{32} +(9.08010 + 12.4977i) q^{33} +(-3.08215 + 6.04905i) q^{34} +(1.30529 + 0.929113i) q^{35} +(7.10571 + 2.30878i) q^{36} +(1.73847 + 5.35046i) q^{37} +(-2.60569 + 5.11395i) q^{38} +(-7.87346 - 8.61026i) q^{39} +(0.0217176 + 2.23596i) q^{40} +(-2.77218 + 5.44071i) q^{41} +(-2.29009 - 0.362715i) q^{42} +(-8.48333 - 8.48333i) q^{43} +(0.746796 - 4.71509i) q^{44} +(-15.9382 - 5.00804i) q^{45} +(4.87309 - 0.771821i) q^{46} +(0.671601 + 0.487947i) q^{47} +(-1.46909 - 2.88325i) q^{48} -6.48659 q^{49} +(-0.0971196 - 4.99906i) q^{50} +21.9689i q^{51} +(-0.161003 + 3.60195i) q^{52} +(-7.39192 + 1.17077i) q^{53} +(14.2910 - 2.26348i) q^{54} +(-1.56741 + 10.5590i) q^{55} +(0.421162 + 0.579680i) q^{56} +18.5728i q^{57} +(0.493179 - 0.358315i) q^{58} +(0.366676 - 0.719642i) q^{59} +(3.34745 + 6.41494i) q^{60} +(-1.30445 + 4.01467i) q^{61} +(-2.57090 - 1.30994i) q^{62} +(-5.09141 + 1.65430i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.281771 - 8.05733i) q^{65} +(-4.77369 - 14.6919i) q^{66} +(-1.33679 - 1.83994i) q^{67} +(4.80056 - 4.80056i) q^{68} +(12.9165 - 9.38437i) q^{69} +(-0.954292 - 1.28700i) q^{70} +(2.50553 + 15.8193i) q^{71} +(-6.04448 - 4.39157i) q^{72} +(5.45163 + 1.77134i) q^{73} -5.62580i q^{74} +(-7.62409 - 14.2709i) q^{75} +(4.05845 - 4.05845i) q^{76} +(1.55291 + 3.04776i) q^{77} +(4.82739 + 10.6219i) q^{78} +(-7.75298 + 10.6711i) q^{79} +(0.670296 - 2.13324i) q^{80} +(19.7460 - 14.3463i) q^{81} +(4.31777 - 4.31777i) q^{82} +(5.05056 - 3.66944i) q^{83} +(2.06592 + 1.05264i) q^{84} +(-10.6296 + 10.8381i) q^{85} +(5.44663 + 10.6896i) q^{86} +(0.895562 - 1.75764i) q^{87} +(-2.16729 + 4.25354i) q^{88} +(13.9811 - 7.12373i) q^{89} +(13.6106 + 9.68811i) q^{90} +(-1.42368 - 2.15579i) q^{91} +(-4.87309 - 0.771821i) q^{92} -9.33697 q^{93} +(-0.487947 - 0.671601i) q^{94} +(-8.98640 + 9.16268i) q^{95} +(0.506214 + 3.19611i) q^{96} +(5.13215 - 7.06380i) q^{97} +(6.16912 + 2.00447i) q^{98} +(-25.2206 - 25.2206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} - 2 q^{5} - 20 q^{9} + 12 q^{13} - 26 q^{15} - 36 q^{16} + 6 q^{17} - 152 q^{18} - 20 q^{19} - 8 q^{20} - 6 q^{21} - 12 q^{23} - 2 q^{25} + 14 q^{26} - 24 q^{27} + 20 q^{29} - 12 q^{30}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 - 2 * q^5 - 20 * q^9 + 12 * q^13 - 26 * q^15 - 36 * q^16 + 6 * q^17 - 152 * q^18 - 20 * q^19 - 8 * q^20 - 6 * q^21 - 12 * q^23 - 2 * q^25 + 14 * q^26 - 24 * q^27 + 20 * q^29 - 12 * q^30 - 6 * q^31 + 30 * q^33 + 24 * q^34 + 40 * q^35 - 20 * q^36 - 6 * q^37 + 60 * q^39 - 8 * q^41 + 6 * q^42 + 12 * q^43 - 30 * q^45 - 12 * q^46 - 18 * q^47 + 160 * q^49 - 12 * q^52 + 20 * q^53 + 6 * q^54 - 32 * q^55 - 24 * q^58 + 16 * q^59 + 6 * q^60 + 12 * q^61 - 6 * q^62 - 40 * q^63 + 36 * q^64 - 54 * q^65 - 16 * q^66 - 6 * q^68 - 26 * q^69 + 2 * q^70 + 12 * q^71 - 48 * q^72 + 40 * q^73 - 32 * q^75 + 56 * q^77 + 16 * q^78 - 20 * q^79 - 2 * q^80 + 124 * q^81 + 22 * q^82 + 74 * q^83 - 24 * q^84 - 60 * q^85 + 12 * q^86 + 8 * q^87 - 58 * q^89 + 14 * q^90 - 16 * q^91 + 12 * q^92 - 16 * q^93 + 50 * q^94 + 46 * q^95 - 40 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

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Representations

Groups

Database

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