LMFDB - Embedded newform 552.2.x.a.35.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(35,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 11, 20]))

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

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

chi := DirichletCharacter("552.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.x (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$920$
Relative dimension:	$92$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.16
Character	$\chi$	$=$	552.35
Dual form			552.2.x.a.347.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27084 - 0.620447i) q^{2} +(-1.72827 + 0.114318i) q^{3} +(1.23009 + 1.57698i) q^{4} +(4.02671 - 1.18235i) q^{5} +(2.26730 + 0.927022i) q^{6} +(1.49077 - 1.29176i) q^{7} +(-0.584820 - 2.76731i) q^{8} +(2.97386 - 0.395146i) q^{9} +O(q^{10})$	\(q+(-1.27084 - 0.620447i) q^{2} +(-1.72827 + 0.114318i) q^{3} +(1.23009 + 1.57698i) q^{4} +(4.02671 - 1.18235i) q^{5} +(2.26730 + 0.927022i) q^{6} +(1.49077 - 1.29176i) q^{7} +(-0.584820 - 2.76731i) q^{8} +(2.97386 - 0.395146i) q^{9} +(-5.85090 - 0.995778i) q^{10} +(1.36608 - 2.12566i) q^{11} +(-2.30621 - 2.58484i) q^{12} +(1.56954 + 1.36001i) q^{13} +(-2.69601 + 0.716684i) q^{14} +(-6.82409 + 2.50375i) q^{15} +(-0.973751 + 3.87967i) q^{16} +(-1.64691 + 0.752119i) q^{17} +(-4.02448 - 1.34296i) q^{18} +(-0.592234 + 1.29681i) q^{19} +(6.81776 + 4.89565i) q^{20} +(-2.42879 + 2.40294i) q^{21} +(-3.05493 + 1.85380i) q^{22} +(1.06168 + 4.67684i) q^{23} +(1.32708 + 4.71581i) q^{24} +(10.6102 - 6.81873i) q^{25} +(-1.15082 - 2.70218i) q^{26} +(-5.09448 + 1.02289i) q^{27} +(3.87088 + 0.761939i) q^{28} +(-1.04636 - 2.29120i) q^{29} +(10.2258 + 1.05211i) q^{30} +(-3.65768 + 0.525895i) q^{31} +(3.64461 - 4.32629i) q^{32} +(-2.11796 + 3.82989i) q^{33} +(2.55962 + 0.0659945i) q^{34} +(4.47560 - 6.96416i) q^{35} +(4.28126 + 4.20367i) q^{36} +(1.36417 - 4.64592i) q^{37} +(1.55724 - 1.28060i) q^{38} +(-2.86806 - 2.17105i) q^{39} +(-5.62682 - 10.4517i) q^{40} +(2.21175 + 7.53253i) q^{41} +(4.57752 - 1.54683i) q^{42} +(1.64242 - 11.4233i) q^{43} +(5.03253 - 0.460473i) q^{44} +(11.5077 - 5.10728i) q^{45} +(1.55250 - 6.60225i) q^{46} -11.2774 q^{47} +(1.23939 - 6.81644i) q^{48} +(-0.442448 + 3.07730i) q^{49} +(-17.7145 + 2.08251i) q^{50} +(2.76033 - 1.48814i) q^{51} +(-0.214041 + 4.14807i) q^{52} +(-2.82963 - 3.26557i) q^{53} +(7.10894 + 1.86092i) q^{54} +(2.98753 - 10.1746i) q^{55} +(-4.44654 - 3.36998i) q^{56} +(0.875294 - 2.30895i) q^{57} +(-0.0918124 + 3.56097i) q^{58} +(7.54095 + 6.53427i) q^{59} +(-12.3426 - 7.68164i) q^{60} +(6.86099 - 0.986461i) q^{61} +(4.97463 + 1.60107i) q^{62} +(3.92292 - 4.43060i) q^{63} +(-7.31597 + 3.23676i) q^{64} +(7.92807 + 3.62063i) q^{65} +(5.06784 - 3.55312i) q^{66} +(7.81614 - 5.02313i) q^{67} +(-3.21193 - 1.67198i) q^{68} +(-2.36952 - 7.96149i) q^{69} +(-10.0087 + 6.07350i) q^{70} +(0.000818609 - 0.000526088i) q^{71} +(-2.83267 - 7.99850i) q^{72} +(3.01810 - 6.60872i) q^{73} +(-4.61619 + 5.05785i) q^{74} +(-17.5577 + 12.9976i) q^{75} +(-2.77355 + 0.661254i) q^{76} +(-0.709335 - 4.93353i) q^{77} +(2.29784 + 4.53854i) q^{78} +(5.34299 + 4.62973i) q^{79} +(0.666106 + 16.7736i) q^{80} +(8.68772 - 2.35022i) q^{81} +(1.86274 - 10.9450i) q^{82} +(0.583530 - 1.98732i) q^{83} +(-6.77704 - 0.874328i) q^{84} +(-5.74236 + 4.97579i) q^{85} +(-9.17478 + 13.4981i) q^{86} +(2.07032 + 3.84021i) q^{87} +(-6.68127 - 2.53723i) q^{88} +(4.84169 + 0.696130i) q^{89} +(-17.7933 - 0.649346i) q^{90} +4.09664 q^{91} +(-6.06934 + 7.42719i) q^{92} +(6.26136 - 1.32703i) q^{93} +(14.3318 + 6.99703i) q^{94} +(-0.851470 + 5.92211i) q^{95} +(-5.80432 + 7.89366i) q^{96} +(-17.4775 + 5.13187i) q^{97} +(2.47158 - 3.63625i) q^{98} +(3.22259 - 6.86122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	$ 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) $ 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.27084	−	0.620447i	−0.898623	−	0.438722i
$2$	−1.27084	−	0.620447i	−0.898623	−	0.438722i
$3$	−1.72827	+	0.114318i	−0.997820	+	0.0660016i
$3$	−1.72827	+	0.114318i	−0.997820	+	0.0660016i
$4$	1.23009	+	1.57698i	0.615046	+	0.788492i
$5$	4.02671	−	1.18235i	1.80080	−	0.528762i	0.803055	−	0.595906i	$-0.203207\pi$
$5$	4.02671	−	1.18235i	1.80080	−	0.528762i	0.997743	+	0.0671436i	$0.0213886\pi$
$6$	2.26730	+	0.927022i	0.925620	+	0.378455i
$7$	1.49077	−	1.29176i	0.563460	−	0.488241i	−0.325928	−	0.945395i	$-0.605677\pi$
$7$	1.49077	−	1.29176i	0.563460	−	0.488241i	0.889387	+	0.457154i	$0.151131\pi$
$8$	−0.584820	−	2.76731i	−0.206765	−	0.978391i
$9$	2.97386	−	0.395146i	0.991288	−	0.131715i
$10$	−5.85090	−	0.995778i	−1.85022	−	0.314892i
$11$	1.36608	−	2.12566i	0.411888	−	0.640911i	−0.571883	−	0.820335i	$-0.693787\pi$
$11$	1.36608	−	2.12566i	0.411888	−	0.640911i	0.983772	+	0.179424i	$0.0574234\pi$
$12$	−2.30621	−	2.58484i	−0.665746	−	0.746178i
$13$	1.56954	+	1.36001i	0.435311	+	0.377199i	0.844770	−	0.535129i	$-0.179737\pi$
$13$	1.56954	+	1.36001i	0.435311	+	0.377199i	−0.409459	+	0.912328i	$0.634283\pi$
$14$	−2.69601	+	0.716684i	−0.720540	+	0.191542i
$15$	−6.82409	+	2.50375i	−1.76197	+	0.646464i
$16$	−0.973751	+	3.87967i	−0.243438	+	0.969917i
$17$	−1.64691	+	0.752119i	−0.399435	+	0.182416i	−0.604996	−	0.796229i	$-0.706825\pi$
$17$	−1.64691	+	0.752119i	−0.399435	+	0.182416i	0.205561	+	0.978644i	$0.434098\pi$
$18$	−4.02448	−	1.34296i	−0.948580	−	0.316538i
$19$	−0.592234	+	1.29681i	−0.135868	+	0.297509i	−0.965320	−	0.261068i	$-0.915925\pi$
$19$	−0.592234	+	1.29681i	−0.135868	+	0.297509i	0.829453	+	0.558577i	$0.188653\pi$
$20$	6.81776	+	4.89565i	1.52450	+	1.09470i
$21$	−2.42879	+	2.40294i	−0.530006	+	0.524365i
$22$	−3.05493	+	1.85380i	−0.651314	+	0.395232i
$23$	1.06168	+	4.67684i	0.221375	+	0.975189i
$23$	1.06168	+	4.67684i	0.221375	+	0.975189i
$24$	1.32708	+	4.71581i	0.270890	+	0.962610i
$25$	10.6102	−	6.81873i	2.12203	−	1.36375i
$26$	−1.15082	−	2.70218i	−0.225695	−	0.529940i
$27$	−5.09448	+	1.02289i	−0.980433	+	0.196855i
$28$	3.87088	+	0.761939i	0.731527	+	0.143993i
$29$	−1.04636	−	2.29120i	−0.194304	−	0.425466i	0.787255	−	0.616628i	$-0.211502\pi$
$29$	−1.04636	−	2.29120i	−0.194304	−	0.425466i	−0.981558	+	0.191162i	$0.938774\pi$
$30$	10.2258	+	1.05211i	1.86697	+	0.192089i
$31$	−3.65768	+	0.525895i	−0.656939	+	0.0944536i	−0.462720	−	0.886505i	$-0.653126\pi$
$31$	−3.65768	+	0.525895i	−0.656939	+	0.0944536i	−0.194219	+	0.980958i	$0.562217\pi$
$32$	3.64461	−	4.32629i	0.644283	−	0.764788i
$33$	−2.11796	+	3.82989i	−0.368689	+	0.666699i
$34$	2.55962	+	0.0659945i	0.438971	+	0.0113180i
$35$	4.47560	−	6.96416i	0.756514	−	1.17716i
$36$	4.28126	+	4.20367i	0.713543	+	0.700611i
$37$	1.36417	−	4.64592i	0.224267	−	0.763784i	−0.768085	−	0.640348i	$-0.778790\pi$
$37$	1.36417	−	4.64592i	0.224267	−	0.763784i	0.992352	−	0.123437i	$-0.0393916\pi$
$38$	1.55724	−	1.28060i	0.252618	−	0.207740i
$39$	−2.86806	−	2.17105i	−0.459258	−	0.347645i
$40$	−5.62682	−	10.4517i	−0.889678	−	1.65255i
$41$	2.21175	+	7.53253i	0.345417	+	1.17638i	0.930770	+	0.365605i	$0.119138\pi$
$41$	2.21175	+	7.53253i	0.345417	+	1.17638i	−0.585353	+	0.810779i	$0.699044\pi$
$42$	4.57752	−	1.54683i	0.706326	−	0.238681i
$43$	1.64242	−	11.4233i	0.250466	−	1.74203i	−0.344958	−	0.938618i	$-0.612107\pi$
$43$	1.64242	−	11.4233i	0.250466	−	1.74203i	0.595424	−	0.803412i	$-0.296984\pi$
$44$	5.03253	−	0.460473i	0.758683	−	0.0694189i
$45$	11.5077	−	5.10728i	1.71546	−	0.761348i
$46$	1.55250	−	6.60225i	0.228904	−	0.973449i
$47$	−11.2774			−1.64498			−0.822489	−	0.568781i	$-0.807415\pi$
$47$	−11.2774			−1.64498			−0.822489	+	0.568781i	$0.807415\pi$
$48$	1.23939	−	6.81644i	0.178891	−	0.983869i
$49$	−0.442448	+	3.07730i	−0.0632069	+	0.439614i
$50$	−17.7145	+	2.08251i	−2.50521	+	0.294511i
$51$	2.76033	−	1.48814i	0.386524	−	0.208381i
$52$	−0.214041	+	4.14807i	−0.0296822	+	0.575234i
$53$	−2.82963	−	3.26557i	−0.388680	−	0.448561i	0.527363	−	0.849640i	$-0.323181\pi$
$53$	−2.82963	−	3.26557i	−0.388680	−	0.448561i	−0.916043	+	0.401079i	$0.868635\pi$
$54$	7.10894	+	1.86092i	0.967404	+	0.253240i
$55$	2.98753	−	10.1746i	0.402838	−	1.37194i
$56$	−4.44654	−	3.36998i	−0.594194	−	0.450332i
$57$	0.875294	−	2.30895i	0.115935	−	0.305828i
$58$	−0.0918124	+	3.56097i	−0.0120556	+	0.467579i
$59$	7.54095	+	6.53427i	0.981748	+	0.850690i	0.988794	−	0.149286i	$-0.0476974\pi$
$59$	7.54095	+	6.53427i	0.981748	+	0.850690i	−0.00704605	+	0.999975i	$0.502243\pi$
$60$	−12.3426	−	7.68164i	−1.59343	−	0.991695i
$61$	6.86099	−	0.986461i	0.878459	−	0.126303i	0.311694	−	0.950183i	$-0.399104\pi$
$61$	6.86099	−	0.986461i	0.878459	−	0.126303i	0.566765	+	0.823879i	$0.308195\pi$
$62$	4.97463	+	1.60107i	0.631779	+	0.203336i
$63$	3.92292	−	4.43060i	0.494242	−	0.558203i
$64$	−7.31597	+	3.23676i	−0.914496	+	0.404594i
$65$	7.92807	+	3.62063i	0.983356	+	0.449084i
$66$	5.06784	−	3.55312i	0.623808	−	0.437358i
$67$	7.81614	−	5.02313i	0.954894	−	0.613673i	0.0323132	−	0.999478i	$-0.489713\pi$
$67$	7.81614	−	5.02313i	0.954894	−	0.613673i	0.922580	+	0.385805i	$0.126076\pi$
$68$	−3.21193	−	1.67198i	−0.389504	−	0.202757i
$69$	−2.36952	−	7.96149i	−0.285257	−	0.958451i
$70$	−10.0087	+	6.07350i	−1.19627	+	0.725922i
$71$	0.000818609	0	0.000526088i	9.71511e−5	0	6.24352e-5i	−0.540592	−	0.841285i	$-0.681800\pi$
$71$	0.000818609	0	0.000526088i	9.71511e−5	0	6.24352e-5i	0.540689	+	0.841222i	$0.318163\pi$
$72$	−2.83267	−	7.99850i	−0.333833	−	0.942632i
$73$	3.01810	−	6.60872i	0.353242	−	0.773492i	−0.646700	−	0.762744i	$-0.723851\pi$
$73$	3.01810	−	6.60872i	0.353242	−	0.773492i	0.999942	−	0.0107479i	$-0.00342123\pi$
$74$	−4.61619	+	5.05785i	−0.536621	+	0.587963i
$75$	−17.5577	+	12.9976i	−2.02739	+	1.50083i
$76$	−2.77355	+	0.661254i	−0.318148	+	0.0758510i
$77$	−0.709335	−	4.93353i	−0.0808362	−	0.562228i
$78$	2.29784	+	4.53854i	0.260180	+	0.513889i
$79$	5.34299	+	4.62973i	0.601133	+	0.520885i	0.901410	−	0.432967i	$-0.142533\pi$
$79$	5.34299	+	4.62973i	0.601133	+	0.520885i	−0.300276	+	0.953852i	$0.597079\pi$
$80$	0.666106	+	16.7736i	0.0744729	+	1.87534i
$81$	8.68772	−	2.35022i	0.965302	−	0.261135i
$82$	1.86274	−	10.9450i	0.205706	−	1.20867i
$83$	0.583530	−	1.98732i	0.0640508	−	0.218137i	−0.921248	−	0.388975i	$-0.872829\pi$
$83$	0.583530	−	1.98732i	0.0640508	−	0.218137i	0.985299	+	0.170838i	$0.0546475\pi$
$84$	−6.77704	−	0.874328i	−0.739436	−	0.0953970i
$85$	−5.74236	+	4.97579i	−0.622847	+	0.539700i
$86$	−9.17478	+	13.4981i	−0.989342	+	1.45554i
$87$	2.07032	+	3.84021i	0.221961	+	0.411714i
$88$	−6.68127	−	2.53723i	−0.712225	−	0.270470i
$89$	4.84169	+	0.696130i	0.513218	+	0.0737896i	0.394058	−	0.919086i	$-0.371071\pi$
$89$	4.84169	+	0.696130i	0.513218	+	0.0737896i	0.119160	+	0.992875i	$0.461980\pi$
$90$	−17.7933	−	0.649346i	−1.87557	−	0.0684471i
$91$	4.09664			0.429444
$92$	−6.06934	+	7.42719i	−0.632772	+	0.774338i
$93$	6.26136	−	1.32703i	0.649272	−	0.137607i
$94$	14.3318	+	6.99703i	1.47821	+	0.721688i
$95$	−0.851470	+	5.92211i	−0.0873590	+	0.607595i
$96$	−5.80432	+	7.89366i	−0.592401	+	0.805644i
$97$	−17.4775	+	5.13187i	−1.77458	+	0.521062i	−0.994511	−	0.104636i	$-0.966632\pi$
$97$	−17.4775	+	5.13187i	−1.77458	+	0.521062i	−0.780065	+	0.625698i	$0.784814\pi$
$98$	2.47158	−	3.63625i	0.249668	−	0.367317i
$99$	3.22259	−	6.86122i	0.323882	−	0.689579i
$100$	23.8045	+	8.34437i	2.38045	+	0.834437i
$101$	2.46746	+	0.724513i	0.245522	+	0.0720917i	0.402178	−	0.915561i	$-0.368253\pi$
$101$	2.46746	+	0.724513i	0.245522	+	0.0720917i	−0.156656	+	0.987653i	$0.550071\pi$
$102$	−4.43127	+	0.178554i	−0.438761	+	0.0176795i
$103$	−6.62213	+	10.3042i	−0.652498	+	1.01531i	0.344568	+	0.938761i	$0.388025\pi$
$103$	−6.62213	+	10.3042i	−0.652498	+	1.01531i	−0.997066	+	0.0765455i	$0.975611\pi$
$104$	2.84567	−	5.13875i	0.279041	−	0.503896i
$105$	−6.93893	+	12.5476i	−0.677170	+	1.22452i
$106$	1.56991	+	5.90567i	0.152483	+	0.573609i
$107$	−8.29893	+	1.19321i	−0.802287	+	0.115352i	−0.531248	−	0.847217i	$-0.678277\pi$
$107$	−8.29893	+	1.19321i	−0.802287	+	0.115352i	−0.271040	+	0.962568i	$0.587368\pi$
$108$	−7.87975	−	6.77566i	−0.758229	−	0.651988i
$109$	−17.4188	+	7.95491i	−1.66842	+	0.761942i	−0.668588	+	0.743633i	$0.733101\pi$
$109$	−17.4188	+	7.95491i	−1.66842	+	0.761942i	−0.999832	+	0.0183092i	$0.994172\pi$
$110$	−10.1095	+	11.0767i	−0.963901	+	1.05612i
$111$	−1.82654	+	8.18537i	−0.173367	+	0.776921i
$112$	3.55997	+	7.04156i	0.336385	+	0.665365i
$113$	−7.91796	−	12.3206i	−0.744859	−	1.15902i	−0.982244	−	0.187607i	$-0.939927\pi$
$113$	−7.91796	−	12.3206i	−0.744859	−	1.15902i	0.237386	−	0.971416i	$-0.423710\pi$
$114$	−2.54494	+	2.39124i	−0.238356	+	0.223960i
$115$	9.80472	+	17.5770i	0.914295	+	1.63906i
$116$	2.32607	−	4.46848i	0.215971	−	0.414888i
$117$	5.20499	+	3.42429i	0.481201	+	0.316576i
$118$	−5.52921	−	12.9828i	−0.509005	−	1.19516i
$119$	−1.48361	+	3.24866i	−0.136003	+	0.297804i
$120$	10.9195	+	17.4201i	0.996809	+	1.59023i
$121$	1.91730	+	4.19831i	0.174300	+	0.381665i
$122$	−9.33129	−	3.00324i	−0.844816	−	0.271901i
$123$	−4.68362	−	12.7654i	−0.422307	−	1.15102i
$124$	−5.32861	−	5.12120i	−0.478523	−	0.459897i
$125$	20.9206	−	24.1436i	1.87119	−	2.15947i
$126$	−7.73438	+	3.19664i	−0.689033	+	0.284779i
$127$	7.66965	−	11.9342i	0.680572	−	1.05899i	−0.313428	−	0.949612i	$-0.601478\pi$
$127$	7.66965	−	11.9342i	0.680572	−	1.05899i	0.994000	−	0.109379i	$-0.0348861\pi$
$128$	11.3057	+	0.425759i	0.999292	+	0.0376321i
$129$	−1.53266	+	19.9303i	−0.134943	+	1.75476i
$130$	−7.82893	−	9.52020i	−0.686643	−	0.834977i
$131$	11.6902	−	10.1296i	1.02138	−	0.885027i	0.0279618	−	0.999609i	$-0.491098\pi$
$131$	11.6902	−	10.1296i	1.02138	−	0.885027i	0.993414	+	0.114582i	$0.0365529\pi$
$132$	−8.64496	+	1.37113i	−0.752447	+	0.119342i
$133$	0.792286	+	2.69828i	0.0686999	+	0.233970i
$134$	−13.0497	+	1.53411i	−1.12732	+	0.132527i
$135$	−19.3046	+	10.1423i	−1.66147	+	0.872911i
$136$	3.04449	+	4.11765i	0.261063	+	0.353086i
$137$			16.2192i			1.38570i	0.721080	+	0.692852i	$0.243646\pi$
$137$			16.2192i			1.38570i	−0.721080	+	0.692852i	$0.756354\pi$
$138$	−1.92839	+	11.5880i	−0.164156	+	0.986434i
$139$	6.24386			0.529597			0.264799	−	0.964304i	$-0.414694\pi$
$139$	6.24386			0.529597			0.264799	+	0.964304i	$0.414694\pi$
$140$	16.4878	−	1.50862i	1.39347	−	0.127501i
$141$	19.4904	−	1.28921i	1.64139	−	0.108571i
$142$	−0.00136673		0.000160673i	−0.000114694		1.34834e-5i
$143$	5.03503	−	1.47842i	0.421051	−	0.123632i
$144$	−1.36277	+	11.9224i	−0.113564	+	0.993531i
$145$	−6.92237	−	7.98885i	−0.574872	−	0.663438i
$146$	−7.93590	+	6.52608i	−0.656780	+	0.540103i
$147$	0.412882	−	5.36899i	0.0340539	−	0.442827i
$148$	9.00458	−	3.56364i	0.740172	−	0.292929i
$149$	−3.63199	−	2.33414i	−0.297544	−	0.191220i	0.383347	−	0.923604i	$-0.374771\pi$
$149$	−3.63199	−	2.33414i	−0.297544	−	0.191220i	−0.680892	+	0.732384i	$0.738408\pi$
$150$	30.3775	−	5.62424i	2.48031	−	0.459217i
$151$	0.954879	+	0.827407i	0.0777070	+	0.0673335i	0.692848	−	0.721083i	$-0.256356\pi$
$151$	0.954879	+	0.827407i	0.0777070	+	0.0673335i	−0.615141	+	0.788417i	$0.710901\pi$
$152$	3.93503	+	0.880491i	0.319173	+	0.0714173i
$153$	−4.60049	+	2.88747i	−0.371928	+	0.233438i
$154$	−2.15954	+	6.70985i	−0.174021	+	0.540695i
$155$	−14.1066	+	6.44228i	−1.13307	+	0.517456i
$156$	−0.104277	−	7.19347i	−0.00834887	−	0.575939i
$157$	−8.45704	−	3.86220i	−0.674946	−	0.308237i	0.0482954	−	0.998833i	$-0.484621\pi$
$157$	−8.45704	−	3.86220i	−0.674946	−	0.308237i	−0.723241	+	0.690596i	$0.757348\pi$
$158$	−3.91761	−	9.19871i	−0.311668	−	0.731810i
$159$	5.26369	+	5.32032i	0.417438	+	0.421929i
$160$	9.56060	−	21.7299i	0.755832	−	1.71790i
$161$	7.62409	+	5.60068i	0.600863	+	0.441395i
$162$	−12.4989	−	2.40351i	−0.982008	−	0.188837i
$163$	−5.35575	+	3.44193i	−0.419494	+	0.269593i	−0.733314	−	0.679890i	$-0.762028\pi$
$163$	−5.35575	+	3.44193i	−0.419494	+	0.269593i	0.313820	+	0.949483i	$0.398391\pi$
$164$	−9.15802	+	12.7536i	−0.715121	+	0.995889i
$165$	−4.00013	+	17.9260i	−0.311410	+	1.39554i
$166$	−1.97460	+	2.16353i	−0.153259	+	0.167922i
$167$	6.89347	+	15.0946i	0.533433	+	1.16805i	0.964099	+	0.265543i	$0.0855513\pi$
$167$	6.89347	+	15.0946i	0.533433	+	1.16805i	−0.430666	+	0.902511i	$0.641721\pi$
$168$	8.07009	+	5.31593i	0.622621	+	0.410133i
$169$	−1.23628	−	8.59851i	−0.0950983	−	0.661424i
$170$	10.3849	−	2.76062i	0.796482	−	0.211730i
$171$	−1.24879	+	4.09056i	−0.0954976	+	0.312813i
$172$	20.0346	−	11.4616i	1.52762	−	0.873937i
$173$	−10.2971	−	6.61754i	−0.782873	−	0.503122i	0.0871128	−	0.996198i	$-0.472236\pi$
$173$	−10.2971	−	6.61754i	−0.782873	−	0.503122i	−0.869986	+	0.493076i	$0.835872\pi$
$174$	−0.248406	−	6.16483i	−0.0188316	−	0.467355i
$175$	7.00915	−	23.8710i	0.529842	−	1.80448i
$176$	6.91663	+	7.36980i	0.521361	+	0.555519i
$177$	−13.7798	−	10.4309i	−1.03575	−	0.784038i
$178$	−5.72112	−	3.88868i	−0.428816	−	0.291469i
$179$	3.29569	+	11.2241i	0.246332	+	0.838928i	0.986112	+	0.166080i	$0.0531110\pi$
$179$	3.29569	+	11.2241i	0.246332	+	0.838928i	−0.739781	+	0.672848i	$0.765071\pi$
$180$	22.2096	+	11.8650i	1.65540	+	0.884364i
$181$	−20.9517	−	3.01239i	−1.55732	−	0.223909i	−0.690800	−	0.723046i	$-0.742742\pi$
$181$	−20.9517	−	3.01239i	−1.55732	−	0.223909i	−0.866524	+	0.499136i	$0.833651\pi$
$182$	−5.20619	−	2.54174i	−0.385908	−	0.188407i
$183$	−11.7449	+	2.48921i	−0.868208	+	0.184008i
$184$	12.3214	−	5.67310i	0.908343	−	0.418227i
$185$		−	20.3207i		−	1.49401i
$186$	−8.78056	−	2.19839i	−0.643822	−	0.161194i
$187$	−0.651061	+	4.52823i	−0.0476103	+	0.331137i
$188$	−13.8722	−	17.7843i	−1.01174	−	1.29705i
$189$	−6.27339	+	8.10575i	−0.456322	+	0.589607i
$190$	4.75644	−	6.99778i	0.345068	−	0.507673i
$191$	1.25120	+	1.44397i	0.0905340	+	0.104482i	0.799209	−	0.601053i	$-0.205252\pi$
$191$	1.25120	+	1.44397i	0.0905340	+	0.104482i	−0.708675	+	0.705535i	$0.750707\pi$
$192$	12.2740	−	6.43035i	0.885798	−	0.464070i
$193$	−1.89028	−	0.555037i	−0.136065	−	0.0399524i	0.212991	−	0.977054i	$-0.431680\pi$
$193$	−1.89028	−	0.555037i	−0.136065	−	0.0399524i	−0.349056	+	0.937102i	$0.613498\pi$
$194$	25.3953	+	4.32208i	1.82328	+	0.310307i
$195$	−14.1158	−	5.35112i	−1.01085	−	0.383201i
$196$	−5.39710	+	3.08762i	−0.385507	+	0.220544i
$197$	−4.68947	+	5.41193i	−0.334111	+	0.385584i	−0.897801	−	0.440402i	$-0.854836\pi$
$197$	−4.68947	+	5.41193i	−0.334111	+	0.385584i	0.563690	+	0.825986i	$0.309381\pi$
$198$	−8.35243	+	6.72010i	−0.593581	+	0.477577i
$199$	−9.97751	+	1.43455i	−0.707287	+	0.101693i	−0.486565	−	0.873644i	$-0.661750\pi$
$199$	−9.97751	+	1.43455i	−0.707287	+	0.101693i	−0.220722	+	0.975337i	$0.570841\pi$
$200$	−25.0745	−	25.3738i	−1.77304	−	1.79420i
$201$	−12.9342	+	9.57487i	−0.912308	+	0.675359i
$202$	−2.68624	−	2.45167i	−0.189003	−	0.172499i
$203$	−4.51957	−	2.06402i	−0.317212	−	0.144866i
$204$	5.74223	+	2.52245i	0.402037	+	0.176607i
$205$	17.8121	+	27.7162i	1.24405	+	1.93579i
$206$	14.8089	−	8.98640i	1.03179	−	0.626112i
$207$	5.00532	+	13.4888i	0.347894	+	0.937534i
$208$	−6.80473	+	4.76497i	−0.471823	+	0.330391i
$209$	1.94754	+	3.03044i	0.134714	+	0.209620i
$210$	16.6034	−	11.6408i	1.14575	−	0.803295i
$211$	−0.0675975	+	0.148018i	−0.00465360	+	0.0101900i	−0.911945	−	0.410314i	$-0.865419\pi$
$211$	−0.0675975	+	0.148018i	−0.00465360	+	0.0101900i	0.907291	+	0.420503i	$0.138147\pi$
$212$	1.66904	−	8.47923i	0.114630	−	0.582356i
$213$	−0.00135464	+	0.00100281i	−9.28184e−5	+	6.87112e-5i
$214$	11.2870	+	3.63266i	0.771561	+	0.248324i
$215$	−6.89273	−	47.9400i	−0.470080	−	3.26948i
$216$	5.81000	+	13.4998i	0.395320	+	0.918543i
$217$	−4.77344	+	5.50885i	−0.324042	+	0.373965i
$218$	27.0722	+	0.698001i	1.83356	+	0.0472746i
$219$	−4.46061	+	11.7667i	−0.301420	+	0.795120i
$220$	19.7201	−	7.80439i	1.32953	−	0.526172i
$221$	−3.60778	−	1.05934i	−0.242685	−	0.0712589i
$222$	7.39983	−	9.26906i	0.496644	−	0.622099i
$223$	3.27289	−	2.83597i	0.219169	−	0.189911i	−0.538355	−	0.842718i	$-0.680954\pi$
$223$	3.27289	−	2.83597i	0.219169	−	0.189911i	0.757524	+	0.652807i	$0.226409\pi$
$224$	−0.155250	−	11.1575i	−0.0103731	−	0.745492i
$225$	28.8587	−	24.4705i	1.92392	−	1.63137i
$226$	2.41822	+	20.5702i	0.160858	+	1.36831i
$227$	3.88386	+	0.558414i	0.257781	+	0.0370632i	0.269993	−	0.962862i	$-0.412978\pi$
$227$	3.88386	+	0.558414i	0.257781	+	0.0370632i	−0.0122128	+	0.999925i	$0.503888\pi$
$228$	4.71786	−	1.45989i	0.312448	−	0.0966839i
$229$			1.49676i			0.0989088i	0.998776	+	0.0494544i	$0.0157482\pi$
$229$			1.49676i			0.0989088i	−0.998776	+	0.0494544i	$0.984252\pi$
$230$	−1.55468	−	28.4209i	−0.102513	−	1.87402i
$231$	1.78992	+	8.44540i	0.117768	+	0.555667i
$232$	−5.72853	+	4.23554i	−0.376097	+	0.278077i
$233$	28.6247	+	4.11561i	1.87527	+	0.269623i	0.983234	−	0.182347i	$-0.0583695\pi$
$233$	28.6247	+	4.11561i	1.87527	+	0.269623i	0.892033	+	0.451970i	$0.149279\pi$
$234$	−4.49014	−	7.58116i	−0.293530	−	0.495596i
$235$	−45.4108	+	13.3338i	−2.96227	+	0.869802i
$236$	−1.02838	+	19.9297i	−0.0669416	+	1.29731i
$237$	−9.76341	−	7.39064i	−0.634202	−	0.480074i
$238$	3.90106	−	3.20804i	0.252868	−	0.207946i
$239$	−7.47555	−	2.19502i	−0.483553	−	0.141984i	0.0308648	−	0.999524i	$-0.490174\pi$
$239$	−7.47555	−	2.19502i	−0.483553	−	0.141984i	−0.514418	+	0.857539i	$0.671992\pi$
$240$	−3.06874	−	28.9132i	−0.198086	−	1.86634i
$241$	−5.78733	−	3.71929i	−0.372794	−	0.239580i	0.340806	−	0.940134i	$-0.389300\pi$
$241$	−5.78733	−	3.71929i	−0.372794	−	0.239580i	−0.713600	+	0.700553i	$0.752937\pi$
$242$	0.168233	−	6.52498i	0.0108144	−	0.419442i
$243$	−14.7461	+	5.05499i	−0.945962	+	0.324277i
$244$	9.99527	+	9.60622i	0.639882	+	0.614975i
$245$	1.85682	+	12.9145i	0.118628	+	0.825077i
$246$	−1.96813	+	19.1288i	−0.125483	+	1.21961i
$247$	−2.69321	+	1.22995i	−0.171365	+	0.0782597i
$248$	3.59440	+	9.81437i	0.228245	+	0.623213i
$249$	−0.781314	+	3.50134i	−0.0495137	+	0.221889i
$250$	−41.5666	+	17.7027i	−2.62891	+	1.11962i
$251$	−9.35608	−	14.5583i	−0.590551	−	0.918915i	−0.999978	−	0.00657205i	$-0.997908\pi$
$251$	−9.35608	−	14.5583i	−0.590551	−	0.918915i	0.409428	−	0.912342i	$-0.365728\pi$
$252$	11.8125	+	0.736341i	0.744120	+	0.0463851i
$253$	11.3917	+	4.13217i	0.716191	+	0.259787i
$254$	−17.1515	+	10.4079i	−1.07618	+	0.653051i
$255$	9.35555	−	9.25598i	0.585868	−	0.579632i
$256$	−14.1036	−	7.55566i	−0.881476	−	0.472229i
$257$	−6.98516	−	3.19002i	−0.435723	−	0.198988i	0.185463	−	0.982651i	$-0.440621\pi$
$257$	−6.98516	−	3.19002i	−0.435723	−	0.198988i	−0.621186	+	0.783663i	$0.713349\pi$
$258$	14.3134	−	24.3773i	0.891116	−	1.51767i
$259$	−3.96777	−	8.68819i	−0.246545	−	0.539858i
$260$	4.04258	+	16.9561i	0.250710	+	1.05157i
$261$	−4.01708	−	6.40026i	−0.248651	−	0.396166i
$262$	−21.1413	+	5.62001i	−1.30611	+	0.347205i
$263$	−14.6721	+	16.9325i	−0.904720	+	1.04410i	0.0941009	+	0.995563i	$0.470002\pi$
$263$	−14.6721	+	16.9325i	−0.904720	+	1.04410i	−0.998821	+	0.0485403i	$0.984543\pi$
$264$	11.8371	+	3.62124i	0.728524	+	0.222872i
$265$	−15.2551	−	9.80388i	−0.937116	−	0.602248i
$266$	0.667266	−	3.92066i	0.0409127	−	0.240391i
$267$	−8.44734	−	0.649610i	−0.516969	−	0.0397555i
$268$	17.5360	+	6.14701i	1.07118	+	0.375489i
$269$	19.7272	+	22.7665i	1.20279	+	1.38810i	0.900487	+	0.434884i	$0.143211\pi$
$269$	19.7272	+	22.7665i	1.20279	+	1.38810i	0.302305	+	0.953211i	$0.402244\pi$
$270$	30.8259	−	0.911842i	1.87600	−	0.0554929i
$271$	0.726041	+	2.47267i	0.0441039	+	0.150204i	0.978601	−	0.205766i	$-0.0659687\pi$
$271$	0.726041	+	2.47267i	0.0441039	+	0.150204i	−0.934497	+	0.355970i	$0.884150\pi$
$272$	−1.31429	−	7.12184i	−0.0796906	−	0.431825i
$273$	−7.08011	+	0.468319i	−0.428508	+	0.0283440i
$274$	10.0632	−	20.6121i	0.607939	−	1.24522i
$275$		−	31.8685i		−	1.92174i
$276$	9.64042	−	13.5301i	0.580285	−	0.814414i
$277$			12.3022i			0.739166i	0.929198	+	0.369583i	$0.120499\pi$
$277$			12.3022i			0.739166i	−0.929198	+	0.369583i	$0.879501\pi$
$278$	−7.93498	−	3.87398i	−0.475908	−	0.232346i
$279$	−10.6696	+	3.00926i	−0.638774	+	0.180160i
$280$	−21.8894	−	8.31256i	−1.30814	−	0.496771i
$281$	−8.52837	−	29.0450i	−0.508760	−	1.73268i	−0.666793	−	0.745243i	$-0.732333\pi$
$281$	−8.52837	−	29.0450i	−0.508760	−	1.73268i	0.158033	−	0.987434i	$-0.449485\pi$
$282$	−25.5692	−	10.4544i	−1.52262	−	0.622550i
$283$	6.56250	+	7.57352i	0.390100	+	0.450199i	0.916498	−	0.400039i	$-0.131003\pi$
$283$	6.56250	+	7.57352i	0.390100	+	0.450199i	−0.526398	+	0.850238i	$0.676458\pi$
$284$	0.00183660		0.000643796i	0.000108982		3.82023e-5i
$285$	0.794571	−	10.3324i	0.0470663	−	0.612036i
$286$	−7.31602	−	1.24513i	−0.432606	−	0.0736261i
$287$	13.0275	+	8.37225i	0.768987	+	0.494198i
$288$	9.12906	−	14.3060i	0.537935	−	0.842986i
$289$	−8.98600	+	10.3704i	−0.528588	+	0.610023i
$290$	3.84061	+	14.4475i	0.225528	+	0.848389i
$291$	29.6193	−	10.8673i	1.73632	−	0.637051i
$292$	14.1344	−	3.36983i	0.827152	−	0.197205i
$293$	7.44325	+	16.2984i	0.434839	+	0.952166i	0.992517	+	0.122108i	$0.0389654\pi$
$293$	7.44325	+	16.2984i	0.434839	+	0.952166i	−0.557677	+	0.830058i	$0.688307\pi$
$294$	−3.85588	+	6.56698i	−0.224880	+	0.382994i
$295$	38.0910	+	17.3956i	2.21774	+	1.01281i
$296$	−13.6545	−	1.05803i	−0.793650	−	0.0614970i
$297$	−4.78515	+	12.2265i	−0.277663	+	0.709452i
$298$	3.16748	+	5.21978i	0.183487	+	0.302374i
$299$	−4.69421	+	8.78437i	−0.271473	+	0.508013i
$300$	−42.0946	−	11.7001i	−2.43033	−	0.675504i
$301$	−12.3077	−	19.1511i	−0.709402	−	1.10385i
$302$	−0.700140	−	1.64396i	−0.0402886	−	0.0945991i
$303$	−4.34728	−	0.970081i	−0.249745	−	0.0557297i
$304$	−4.45451	−	3.56044i	−0.255484	−	0.204205i
$305$	26.4608	−	12.0843i	1.51514	−	0.691943i
$306$	7.63803	−	0.815164i	0.436637	−	0.0465998i
$307$	0.322769	+	2.24491i	0.0184214	+	0.128124i	0.996957	−	0.0779547i	$-0.0248390\pi$
$307$	0.322769	+	2.24491i	0.0184214	+	0.128124i	−0.978536	+	0.206078i	$0.933930\pi$
$308$	6.90755	−	7.18730i	0.393594	−	0.409534i
$309$	10.2669	−	18.5656i	0.584064	−	1.05616i
$310$	21.9244	+	0.565276i	1.24522	+	0.0321055i
$311$	1.84100	+	1.18314i	0.104394	+	0.0670898i	0.591796	−	0.806088i	$-0.298419\pi$
$311$	1.84100	+	1.18314i	0.104394	+	0.0670898i	−0.487402	+	0.873178i	$0.662055\pi$
$312$	−4.33065	+	9.20648i	−0.245175	+	0.521214i
$313$	4.79006	+	1.40649i	0.270750	+	0.0794995i	0.414290	−	0.910145i	$-0.364030\pi$
$313$	4.79006	+	1.40649i	0.270750	+	0.0794995i	−0.143539	+	0.989645i	$0.545848\pi$
$314$	8.35130	+	10.1554i	0.471291	+	0.573103i
$315$	10.5579	−	22.4790i	0.594873	−	1.26655i
$316$	−0.728636	+	14.1208i	−0.0409890	+	0.794357i
$317$	−18.5889	+	5.45819i	−1.04406	+	0.306563i	−0.758414	−	0.651774i	$-0.774025\pi$
$317$	−18.5889	+	5.45819i	−1.04406	+	0.306563i	−0.285643	+	0.958336i	$0.592207\pi$
$318$	−3.38836	−	10.0271i	−0.190010	−	0.562294i
$319$	−6.29973	−	0.905764i	−0.352717	−	0.0507131i
$320$	−25.6323	+	21.6835i	−1.43289	+	1.21214i
$321$	14.2064	−	3.01090i	0.792925	−	0.168052i
$322$	−6.21411	−	11.8479i	−0.346299	−	0.660259i
$323$		−	2.58116i		−	0.143620i
$324$	14.3929	+	10.8094i	0.799608	+	0.600522i
$325$	25.9266	+	3.72768i	1.43815	+	0.206774i
$326$	8.94186	−	1.05120i	0.495244	−	0.0582206i
$327$	29.1951	−	15.7395i	1.61449	−	0.870399i
$328$	19.5513	−	10.5258i	1.07954	−	0.581189i
$329$	−16.8121	+	14.5677i	−0.926878	+	0.803145i
$330$	16.2057	−	20.2993i	0.892094	−	1.11744i
$331$	25.7788	+	7.56934i	1.41693	+	0.416049i	0.898464	−	0.439048i	$-0.144684\pi$
$331$	25.7788	+	7.56934i	1.41693	+	0.416049i	0.518468	+	0.855097i	$0.326502\pi$
$332$	3.85177	−	1.52437i	0.211393	−	0.0836607i
$333$	2.22102	−	14.3554i	0.121711	−	0.786669i
$334$	0.604866	−	23.4599i	0.0330968	−	1.28367i
$335$	25.5342	−	29.4681i	1.39508	−	1.61001i
$336$	−6.95758	−	11.7628i	−0.379567	−	0.641712i
$337$	1.66443	+	11.5763i	0.0906671	+	0.630604i	0.983593	+	0.180400i	$0.0577394\pi$
$337$	1.66443	+	11.5763i	0.0906671	+	0.630604i	−0.892926	+	0.450203i	$0.851352\pi$
$338$	−3.76380	+	11.6944i	−0.204724	+	0.636092i
$339$	15.0929	+	20.3882i	0.819732	+	1.10733i
$340$	−14.9104	−	2.93494i	−0.808628	−	0.159169i
$341$	−3.87881	+	8.49340i	−0.210049	+	0.459944i
$342$	4.12500	−	4.42365i	0.223054	−	0.239204i
$343$	10.7807	+	16.7752i	0.582105	+	0.905773i
$344$	−32.5722	+	2.13548i	−1.75617	+	0.115138i
$345$	−18.9546	−	29.2570i	−1.02048	−	1.57514i
$346$	8.98017	+	14.7987i	0.482777	+	0.795581i
$347$	12.2476	+	19.0576i	0.657485	+	1.02307i	0.996606	+	0.0823232i	$0.0262340\pi$
$347$	12.2476	+	19.0576i	0.657485	+	1.02307i	−0.339121	+	0.940743i	$0.610130\pi$
$348$	−3.50927	+	7.98867i	−0.188116	+	0.428238i
$349$	−23.1078	−	10.5530i	−1.23693	−	0.564889i	−0.313845	−	0.949474i	$-0.601617\pi$
$349$	−23.1078	−	10.5530i	−1.23693	−	0.564889i	−0.923089	+	0.384585i	$0.874344\pi$
$350$	−23.7182	+	25.9875i	−1.26779	+	1.38909i
$351$	−9.38710	−	5.32309i	−0.501047	−	0.284125i
$352$	−4.21740	−	13.6573i	−0.224788	−	0.727935i
$353$	25.6711	−	3.69095i	1.36634	−	0.196449i	0.580185	−	0.814485i	$-0.302980\pi$
$353$	25.6711	−	3.69095i	1.36634	−	0.196449i	0.786150	+	0.618035i	$0.212071\pi$
$354$	11.0402	+	21.8057i	0.586778	+	1.15896i
$355$	0.00267428	−	0.00308628i	0.000141936	−	0.000163803i
$356$	4.85793	+	8.49156i	0.257470	+	0.450052i
$357$	2.19271	−	5.78418i	0.116050	−	0.306131i
$358$	2.77564	−	16.3089i	0.146697	−	0.861951i
$359$	−16.2534	−	4.77244i	−0.857823	−	0.251880i	−0.176895	−	0.984230i	$-0.556605\pi$
$359$	−16.2534	−	4.77244i	−0.857823	−	0.251880i	−0.680928	+	0.732350i	$0.738423\pi$
$360$	−20.8633	−	28.8584i	−1.09959	−	1.52097i
$361$	11.1114	+	12.8232i	0.584809	+	0.674906i
$362$	24.7573	+	16.8277i	1.30121	+	0.884443i
$363$	−3.79357	−	7.03665i	−0.199111	−	0.369328i
$364$	5.03924	+	6.46032i	0.264128	+	0.338613i
$365$	4.33920	−	30.1798i	0.227124	−	1.57968i
$366$	16.4704	+	4.12369i	0.860919	+	0.215548i
$367$		−	13.1566i		−	0.686770i	−0.939195	−	0.343385i	$-0.888426\pi$
$367$		−	13.1566i		−	0.686770i	0.939195	−	0.343385i	$-0.111574\pi$
$368$	−19.1784	−	0.435119i	−0.999743	−	0.0226821i
$369$	9.55389	+	21.5268i	0.497356	+	1.12064i
$370$	−12.6079	+	25.8244i	−0.655453	+	1.34255i
$371$	−8.43669	−	1.21301i	−0.438011	−	0.0629765i
$372$	9.79474	+	8.24168i	0.507834	+	0.427311i
$373$	−1.56790	−	5.33978i	−0.0811829	−	0.276484i	0.908891	−	0.417035i	$-0.136931\pi$
$373$	−1.56790	−	5.33978i	−0.0811829	−	0.276484i	−0.990073	+	0.140551i	$0.955113\pi$
$374$	3.63692	−	5.35073i	0.188061	−	0.276679i
$375$	−33.3964	+	44.1184i	−1.72458	+	2.27826i
$376$	6.59525	+	31.2080i	0.340124	+	1.60943i
$377$	1.47377	−	5.01919i	0.0759028	−	0.258501i
$378$	13.0017	−	6.40884i	0.668735	−	0.329635i
$379$	0.363711	+	0.233743i	0.0186826	+	0.0120066i	0.549949	−	0.835198i	$-0.314647\pi$
$379$	0.363711	+	0.233743i	0.0186826	+	0.0120066i	−0.531266	+	0.847205i	$0.678284\pi$
$380$	−10.3864	+	5.94198i	−0.532814	+	0.304817i
$381$	−11.8910	+	21.5024i	−0.609193	+	1.10160i
$382$	−0.694181	−	2.61136i	−0.0355174	−	0.133609i
$383$	2.13915	+	14.8781i	0.109305	+	0.760236i	0.968577	+	0.248715i	$0.0800084\pi$
$383$	2.13915	+	14.8781i	0.109305	+	0.760236i	−0.859271	+	0.511520i	$0.829082\pi$
$384$	−19.5880	+	0.556617i	−0.999597	+	0.0284047i
$385$	−8.68943	−	19.0272i	−0.442854	−	0.969716i
$386$	2.05788	+	1.87818i	0.104743	+	0.0955971i
$387$	0.370469	−	34.6202i	0.0188320	−	1.75984i
$388$	−29.5918	−	21.2491i	−1.50230	−	1.07876i
$389$	−14.0434	+	9.02515i	−0.712029	+	0.457593i	−0.845856	−	0.533411i	$-0.820910\pi$
$389$	−14.0434	+	9.02515i	−0.712029	+	0.457593i	0.133827	+	0.991005i	$0.457273\pi$
$390$	14.6189	+	15.5585i	0.740255	+	0.787837i
$391$	−5.26603	−	6.90383i	−0.266315	−	0.349142i
$392$	8.77458	−	0.575276i	0.443183	−	0.0290558i
$393$	−19.0458	+	18.8431i	−0.960735	+	0.950510i
$394$	9.31740	−	3.96816i	0.469404	−	0.199913i
$395$	26.9886	+	12.3253i	1.35794	+	0.620152i
$396$	14.7841	−	3.35797i	0.742929	−	0.168744i
$397$	−6.47879	+	2.95876i	−0.325161	+	0.148496i	−0.571306	−	0.820737i	$-0.693563\pi$
$397$	−6.47879	+	2.95876i	−0.325161	+	0.148496i	0.246145	+	0.969233i	$0.420836\pi$
$398$	13.5699	+	4.36743i	0.680199	+	0.218919i
$399$	−1.67775	−	4.57279i	−0.0839925	−	0.228926i
$400$	16.1228	+	47.8036i	0.806138	+	2.39018i
$401$	−10.2609	−	8.89114i	−0.512406	−	0.444002i	0.359880	−	0.932999i	$-0.382818\pi$
$401$	−10.2609	−	8.89114i	−0.512406	−	0.444002i	−0.872286	+	0.488996i	$0.837363\pi$
$402$	22.3781	−	4.14319i	1.11612	−	0.206643i
$403$	−6.45609	−	4.14907i	−0.321601	−	0.206680i
$404$	1.89266	+	4.78236i	0.0941634	+	0.237932i
$405$	32.2041	−	19.7355i	1.60024	−	0.980667i
$406$	4.46306	+	5.42721i	0.221498	+	0.269348i
$407$	−8.01209	−	9.24645i	−0.397145	−	0.458329i
$408$	−5.73244	−	6.76839i	−0.283798	−	0.335085i
$409$	17.6367	−	5.17860i	0.872078	−	0.256065i	0.185079	−	0.982724i	$-0.440746\pi$
$409$	17.6367	−	5.17860i	0.872078	−	0.256065i	0.686999	+	0.726658i	$0.258928\pi$
$410$	−5.44001	−	46.2745i	−0.268663	−	2.28534i
$411$	−1.85415	−	28.0313i	−0.0914586	−	1.38268i
$412$	−24.3954	+	2.23216i	−1.20188	+	0.109971i
$413$	19.6826			0.968516
$414$	2.00808	−	20.2477i	0.0986917	−	0.995118i
$415$		−	8.69230i		−	0.426688i
$416$	11.6042	−	1.83356i	0.568941	−	0.0898976i
$417$	−10.7911	+	0.713786i	−0.528443	+	0.0349542i
$418$	−0.594800	−	5.05956i	−0.0290926	−	0.247471i
$419$	5.29195	+	18.0227i	0.258529	+	0.880467i	0.981802	+	0.189906i	$0.0608183\pi$
$419$	5.29195	+	18.0227i	0.258529	+	0.880467i	−0.723274	+	0.690561i	$0.757364\pi$
$420$	−28.3229	+	4.49215i	−1.38202	+	0.219195i
$421$	−17.6049	+	15.2547i	−0.858010	+	0.743470i	−0.968130	−	0.250448i	$-0.919422\pi$
$421$	−17.6049	+	15.2547i	−0.858010	+	0.743470i	0.110120	+	0.993918i	$0.464877\pi$
$422$	0.177743	−	0.146167i	0.00865240	−	0.00711530i
$423$	−33.5374	+	4.45622i	−1.63065	+	0.216669i
$424$	−7.38201	+	9.74023i	−0.358502	+	0.473028i
$425$	−12.3455	+	19.2099i	−0.598844	+	0.931819i
$426$	0.00234372		0.000433929i	0.000113554		2.10239e-5i
$427$	8.95391	−	10.3334i	0.433310	−	0.500066i
$428$	−12.0901	−	11.6195i	−0.584397	−	0.561650i
$429$	−8.53291	+	3.13071i	−0.411973	+	0.151152i
$430$	−20.9846	+	65.2008i	−1.01197	+	3.14426i
$431$	−13.9510	−	30.5483i	−0.671994	−	1.47146i	−0.870909	−	0.491444i	$-0.836469\pi$
$431$	−13.9510	−	30.5483i	−0.671994	−	1.47146i	0.198915	−	0.980017i	$-0.436258\pi$
$432$	0.992294	−	20.7609i	0.0477418	−	0.998860i
$433$	−13.0772	+	28.6351i	−0.628452	+	1.37612i	0.280758	+	0.959779i	$0.409414\pi$
$433$	−13.0772	+	28.6351i	−0.628452	+	1.37612i	−0.909210	+	0.416339i	$0.863313\pi$
$434$	9.48425	−	4.03922i	0.455259	−	0.193889i
$435$	12.8770	+	13.0156i	0.617406	+	0.624049i
$436$	−33.9715	−	17.6839i	−1.62694	−	0.846906i
$437$	−6.69374	−	1.39299i	−0.320205	−	0.0666356i
$438$	12.9694	−	12.1861i	0.619700	−	0.582273i
$439$	20.4047	+	31.7503i	0.973861	+	1.51536i	0.852486	+	0.522751i	$0.175094\pi$
$439$	20.4047	+	31.7503i	0.973861	+	1.51536i	0.121376	+	0.992607i	$0.461269\pi$
$440$	−29.9034	−	2.31710i	−1.42559	−	0.110463i
$441$	−0.0998001	+	9.32629i	−0.00475239	+	0.444109i
$442$	3.92766	+	3.58469i	0.186820	+	0.170506i
$443$	−6.15767	+	2.81211i	−0.292560	+	0.133607i	−0.556288	−	0.830989i	$-0.687775\pi$
$443$	−6.15767	+	2.81211i	−0.292560	+	0.133607i	0.263729	+	0.964597i	$0.415048\pi$
$444$	−15.1550	+	7.18833i	−0.719224	+	0.341143i
$445$	20.3191	−	2.92145i	0.963219	−	0.138490i
$446$	−5.91891	+	1.57343i	−0.280268	+	0.0745040i
$447$	6.54391	+	3.61883i	0.309516	+	0.171165i
$448$	−6.72534	+	14.2758i	−0.317742	+	0.674467i
$449$	−11.6525	+	18.1316i	−0.549914	+	0.855683i	−0.999291	−	0.0376596i	$-0.988010\pi$
$449$	−11.6525	+	18.1316i	−0.549914	+	0.855683i	0.449377	+	0.893342i	$0.351646\pi$
$450$	−51.8576	+	13.1929i	−2.44459	+	0.621920i
$451$	19.0330	+	5.58860i	0.896231	+	0.263157i
$452$	9.68954	−	27.6419i	0.455757	−	1.30017i
$453$	−1.74488	−	1.32083i	−0.0819816	−	0.0620579i
$454$	−4.58931	−	3.11938i	−0.215387	−	0.146400i
$455$	16.4959	−	4.84365i	0.773342	−	0.227074i
$456$	−6.90146	−	1.07189i	−0.323190	−	0.0501956i
$457$	1.78880	−	12.4414i	0.0836765	−	0.581983i	−0.904243	−	0.427017i	$-0.859564\pi$
$457$	1.78880	−	12.4414i	0.0836765	−	0.581983i	0.987920	−	0.154965i	$-0.0495266\pi$
$458$	0.928661	−	1.90215i	0.0433935	−	0.0888817i
$459$	7.62082	−	5.51626i	0.355709	−	0.257477i
$460$	−15.6579	+	37.0832i	−0.730054	+	1.72901i
$461$	−1.13754			−0.0529805			−0.0264902	−	0.999649i	$-0.508433\pi$
$461$	−1.13754			−0.0529805			−0.0264902	+	0.999649i	$0.508433\pi$
$462$	2.96522	−	11.8433i	0.137954	−	0.551002i
$463$	26.0654	+	3.74764i	1.21136	+	0.174168i	0.718242	−	0.695793i	$-0.244947\pi$
$463$	26.0654	+	3.74764i	1.21136	+	0.174168i	0.493120	+	0.869961i	$0.335856\pi$
$464$	9.90800	−	1.82846i	0.459967	−	0.0848840i
$465$	23.6436	−	12.7467i	1.09645	−	0.591112i
$466$	−33.8240	−	22.9904i	−1.56687	−	1.06501i
$467$	−18.2007	+	15.7710i	−0.842229	+	0.729795i	−0.964890	−	0.262653i	$-0.915402\pi$
$467$	−18.2007	+	15.7710i	−0.842229	+	0.729795i	0.122662	+	0.992449i	$0.460857\pi$
$468$	1.00256	+	12.4204i	0.0463435	+	0.574132i
$469$	5.16341	−	17.5850i	0.238424	−	0.811998i
$470$	65.9830	+	11.2298i	3.04357	+	0.517991i
$471$	15.0576	+	5.70815i	0.693818	+	0.263018i
$472$	13.6722	−	24.6895i	0.629315	−	1.13643i
$473$	−22.0383	−	19.0963i	−1.01332	−	0.878048i
$474$	7.82228	+	15.4500i	0.359289	+	0.709643i
$475$	2.55892	+	17.7977i	0.117411	+	0.816612i
$476$	−6.94806	+	1.65652i	−0.318464	+	0.0759262i
$477$	−9.70532	−	8.59324i	−0.444376	−	0.393457i
$478$	8.13837	+	7.42771i	0.372241	+	0.339736i
$479$	−10.0156	+	21.9310i	−0.457623	+	1.00206i	0.530400	+	0.847748i	$0.322042\pi$
$479$	−10.0156	+	21.9310i	−0.457623	+	1.00206i	−0.988023	+	0.154307i	$0.950685\pi$
$480$	−14.0392	+	38.6482i	−0.640800	+	1.76404i
$481$	8.45961	−	5.43666i	0.385725	−	0.247890i
$482$	5.04717	+	8.31736i	0.229892	+	0.378846i
$483$	−13.8168	−	8.80793i	−0.628685	−	0.400775i
$484$	−4.26220	+	8.18786i	−0.193737	+	0.372175i
$485$	−64.3093	+	41.3291i	−2.92013	+	1.87666i
$486$	21.8763	+	2.72506i	0.992331	+	0.123611i
$487$	−31.5574	−	14.4118i	−1.43000	−	0.653060i	−0.458198	−	0.888850i	$-0.651505\pi$
$487$	−31.5574	−	14.4118i	−1.43000	−	0.653060i	−0.971804	+	0.235791i	$0.924232\pi$
$488$	−6.74228	−	18.4095i	−0.305209	−	0.833361i
$489$	8.86272	−	6.56086i	0.400786	−	0.296692i
$490$	5.65303	−	17.5644i	0.255378	−	0.793478i
$491$	25.3013	−	3.63778i	1.14183	−	0.164171i	0.454660	−	0.890665i	$-0.349761\pi$
$491$	25.3013	−	3.63778i	1.14183	−	0.164171i	0.687172	+	0.726495i	$0.258852\pi$
$492$	14.3696	−	23.0886i	0.647832	−	1.04092i
$493$	3.44652	+	2.98642i	0.155223	+	0.134502i
$494$	4.18577	+	0.107921i	0.188327	+	0.00485562i
$495$	4.86406	−	31.4384i	0.218623	−	1.41305i
$496$	1.52137	−	14.7027i	0.0683116	−	0.660169i
$497$	0.000540780	−	0.00184173i	2.42573e−5	−	8.26128e-5i
$498$	3.16533	−	3.96490i	0.141842	−	0.177671i
$499$	−6.98201	−	8.05766i	−0.312557	−	0.360711i	0.577635	−	0.816295i	$-0.303976\pi$
$499$	−6.98201	−	8.05766i	−0.312557	−	0.360711i	−0.890192	+	0.455585i	$0.849430\pi$
$500$	63.8083	+	3.29252i	2.85359	+	0.147246i
$501$	−13.6394	−	25.2995i	−0.609363	−	1.13030i
$502$	2.85744	+	24.3063i	0.127534	+	1.08485i
$503$	2.74992	−	19.1261i	0.122613	−	0.852791i	−0.831965	−	0.554829i	$-0.812784\pi$
$503$	2.74992	−	19.1261i	0.122613	−	0.852791i	0.954578	−	0.297963i	$-0.0963071\pi$
$504$	−14.5550	−	8.26482i	−0.648333	−	0.368145i
$505$	10.7924			0.480254
$506$	−11.9133	−	12.3193i	−0.529611	−	0.547659i
$507$	3.11959	+	14.7192i	0.138546	+	0.653705i
$508$	28.2544	−	2.58526i	1.25359	−	0.114702i
$509$	2.01625	−	14.0234i	0.0893689	−	0.621574i	−0.895080	−	0.445905i	$-0.852882\pi$
$509$	2.01625	−	14.0234i	0.0893689	−	0.621574i	0.984449	−	0.175669i	$-0.0562090\pi$
$510$	−17.6323	+	5.95828i	−0.780771	+	0.263837i
$511$	−4.03759	−	13.7508i	−0.178613	−	0.608299i
$512$	13.2356	+	18.3526i	0.584937	+	0.811078i
$513$	1.69063	−	7.21237i	0.0746432	−	0.318434i
$514$	6.89782	+	8.38794i	0.304250	+	0.369976i
$515$	−14.4822	+	49.3218i	−0.638162	+	2.17338i
$516$	−33.3150	+	22.0991i	−1.46661	+	0.972857i
$517$	−15.4058	+	23.9719i	−0.677547	+	1.05428i
$518$	−0.348151	+	13.5031i	−0.0152969	+	0.593293i
$519$	18.5527	+	10.2598i	0.814373	+	0.450354i
$520$	5.38289	−	24.0568i	0.236055	−	1.05496i
$521$	−10.1744	+	1.46285i	−0.445747	+	0.0640888i	−0.361534	−	0.932359i	$-0.617747\pi$
$521$	−10.1744	+	1.46285i	−0.445747	+	0.0640888i	−0.0842135	+	0.996448i	$0.526838\pi$
$522$	1.13407	+	10.6261i	0.0496367	+	0.465093i
$523$	4.49114	+	9.83423i	0.196384	+	0.430021i	0.982048	−	0.188633i	$-0.0604056\pi$
$523$	4.49114	+	9.83423i	0.196384	+	0.430021i	−0.785664	+	0.618654i	$0.787678\pi$
$524$	30.3542	+	5.97488i	1.32603	+	0.261014i
$525$	−9.38485	+	42.0569i	−0.409589	+	1.83551i
$526$	29.1517	−	12.4153i	1.27107	−	0.541334i
$527$	5.62834	−	3.61712i	0.245174	−	0.157564i
$528$	−12.7963	−	11.9463i	−0.556889	−	0.519897i
$529$	−20.7457	+	9.93060i	−0.901986	+	0.431765i
$530$	13.3041	+	21.9242i	0.577894	+	0.952327i
$531$	25.0077	+	16.4522i	1.08524	+	0.713967i
$532$	−3.28056	+	4.56855i	−0.142230	+	0.198072i
$533$	−6.77290	+	14.8306i	−0.293367	+	0.642384i
$534$	10.3322	+	6.06668i	0.447118	+	0.262531i
$535$	−32.0066	+	14.6169i	−1.38376	+	0.631944i
$536$	−18.4716	−	18.6920i	−0.797851	−	0.807373i
$537$	−6.97897	−	19.0216i	−0.301165	−	0.820841i
$538$	−10.9449	−	41.1723i	−0.471867	−	1.77507i
$539$	5.93687	+	5.14433i	0.255719	+	0.221582i
$540$	−39.7406	−	17.9670i	−1.71016	−	0.773176i
$541$	6.92292	−	10.7723i	0.297640	−	0.463136i	−0.659935	−	0.751323i	$-0.729416\pi$
$541$	6.92292	−	10.7723i	0.297640	−	0.463136i	0.957574	+	0.288187i	$0.0930524\pi$
$542$	0.611474	−	3.59285i	0.0262651	−	0.154326i
$543$	36.5546	+	2.81109i	1.56871	+	0.120635i
$544$	−2.74847	+	9.86620i	−0.117840	+	0.423010i
$545$	−60.7350	+	52.6272i	−2.60160	+	2.25430i
$546$	9.28828	+	3.79767i	0.397502	+	0.162525i
$547$	−25.3231	+	7.43554i	−1.08274	+	0.317921i	−0.773973	−	0.633218i	$-0.781734\pi$
$547$	−25.3231	+	7.43554i	−1.08274	+	0.317921i	−0.308764	+	0.951139i	$0.599915\pi$
$548$	−25.5775	+	19.9512i	−1.09262	+	0.852271i
$549$	20.0138	−	5.64469i	0.854170	−	0.240909i
$550$	−19.7727	+	40.4999i	−0.843111	+	1.72692i
$551$	3.59095			0.152980
$552$	−20.6461	+	11.2132i	−0.878758	+	0.477267i
$553$	13.9457			0.593032
$554$	7.63284	−	15.6341i	0.324288	−	0.664231i
$555$	2.32302	+	35.1197i	0.0986067	+	1.49075i
$556$	7.68052	+	9.84646i	0.325727	+	0.417583i
$557$	15.9218	−	4.67505i	0.674627	−	0.198088i	0.0735646	−	0.997290i	$-0.476562\pi$
$557$	15.9218	−	4.67505i	0.674627	−	0.198088i	0.601062	+	0.799202i	$0.294744\pi$
$558$	15.4265	+	2.79564i	0.653057	+	0.118349i
$559$	18.1136	−	15.6955i	0.766123	−	0.663849i
$560$	22.6605	+	24.1452i	0.957581	+	1.02032i
$561$	0.607554	−	7.90045i	0.0256509	−	0.333557i
$562$	−7.18262	+	42.2030i	−0.302981	+	1.78023i
$563$	−6.33119	+	9.85153i	−0.266828	+	0.415193i	−0.948651	−	0.316325i	$-0.897551\pi$
$563$	−6.33119	+	9.85153i	−0.266828	+	0.415193i	0.681823	+	0.731517i	$0.261187\pi$
$564$	26.0081	+	29.1502i	1.09514	+	1.22745i
$565$	−46.4505	−	40.2496i	−1.95419	−	1.69331i
$566$	−3.64094	−	13.6965i	−0.153040	−	0.575705i
$567$	9.91550	−	14.7261i	0.416412	−	0.618439i
$568$	−0.00193459	−	0.00195768i	−8.11735e−5	−	8.21422e-5i
$569$	−13.4279	+	6.13233i	−0.562928	+	0.257081i	−0.676492	−	0.736450i	$-0.736501\pi$
$569$	−13.4279	+	6.13233i	−0.562928	+	0.257081i	0.113564	+	0.993531i	$0.463773\pi$
$570$	−7.42046	+	12.6378i	−0.310809	+	0.529341i
$571$	5.47552	−	11.9897i	0.229144	−	0.501754i	−0.759780	−	0.650180i	$-0.774693\pi$
$571$	5.47552	−	11.9897i	0.229144	−	0.501754i	0.988924	+	0.148426i	$0.0474207\pi$
$572$	8.52499	+	6.12157i	0.356448	+	0.255956i
$573$	−2.32750	−	2.35253i	−0.0972325	−	0.0982786i
$574$	−11.3614	−	18.7227i	−0.474214	−	0.781469i
$575$	43.1547	+	42.3827i	1.79967	+	1.76748i
$576$	−20.4777	+	12.5165i	−0.853238	+	0.521523i
$577$	−6.00613	+	3.85991i	−0.250039	+	0.160690i	−0.659657	−	0.751567i	$-0.729298\pi$
$577$	−6.00613	+	3.85991i	−0.250039	+	0.160690i	0.409618	+	0.912257i	$0.365662\pi$
$578$	17.8541	−	7.60382i	0.742632	−	0.316277i
$579$	3.33038	+	0.743162i	0.138406	+	0.0308848i
$580$	4.08312	−	20.7435i	0.169542	−	0.861326i
$581$	−1.69724	−	3.71643i	−0.0704133	−	0.154184i
$582$	−44.3841	−	4.56660i	−1.83978	−	0.189292i
$583$	−10.8070	+	1.55381i	−0.447580	+	0.0643523i
$584$	−20.0534	−	4.48710i	−0.829816	−	0.185677i
$585$	25.0077	+	7.63451i	1.03394	+	0.315648i
$586$	0.653106	−	25.3309i	0.0269796	−	1.04641i
$587$	4.25693	−	6.62392i	0.175702	−	0.273398i	−0.742222	−	0.670155i	$-0.766228\pi$
$587$	4.25693	−	6.62392i	0.175702	−	0.273398i	0.917924	+	0.396756i	$0.129864\pi$
$588$	8.97469	−	5.95324i	0.370110	−	0.245508i
$589$	1.48422	−	5.05478i	0.0611561	−	0.208278i
$590$	−37.6147	−	45.7405i	−1.54857	−	1.88311i
$591$	7.48600	−	9.88939i	0.307933	−	0.406795i
$592$	16.6963	+	9.81647i	0.686212	+	0.403455i
$593$	−9.44454	−	32.1652i	−0.387841	−	1.32086i	−0.889949	−	0.456060i	$-0.849260\pi$
$593$	−9.44454	−	32.1652i	−0.387841	−	1.32086i	0.502108	−	0.864805i	$-0.332558\pi$
$594$	13.6671	−	12.5690i	0.560766	−	0.515713i
$595$	−2.13303	+	14.8355i	−0.0874457	+	0.608198i
$596$	−0.786783	−	8.59879i	−0.0322279	−	0.352220i
$597$	17.0799	−	3.61990i	0.699033	−	0.148153i
$598$	11.4158	−	8.25105i	0.466829	−	0.337411i
$599$	20.2953			0.829243			0.414622	−	0.909994i	$-0.363914\pi$
$599$	20.2953			0.829243			0.414622	+	0.909994i	$0.363914\pi$
$600$	46.2364	+	40.9864i	1.88759	+	1.67326i
$601$	4.19994	−	29.2112i	0.171319	−	1.19155i	−0.704783	−	0.709423i	$-0.748956\pi$
$601$	4.19994	−	29.2112i	0.171319	−	1.19155i	0.876102	−	0.482126i	$-0.160135\pi$
$602$	3.75889	+	31.9743i	0.153201	+	1.30318i
$603$	21.2593	−	18.0266i	0.865744	−	0.734100i
$604$	−0.130219	+	2.52361i	−0.00529854	+	0.102684i
$605$	12.6843	+	14.6384i	0.515689	+	0.595137i
$606$	4.92283	+	3.93008i	0.199976	+	0.159648i
$607$	8.55999	−	29.1526i	0.347439	−	1.18327i	−0.581658	−	0.813434i	$-0.697596\pi$
$607$	8.55999	−	29.1526i	0.347439	−	1.18327i	0.929097	−	0.369836i	$-0.120586\pi$
$608$	3.45192	+	7.28855i	0.139994	+	0.295590i
$609$	8.04702	+	3.05052i	0.326082	+	0.123613i
$610$	−41.1252	−	1.06033i	−1.66511	−	0.0429315i
$611$	−17.7003	−	15.3374i	−0.716077	−	0.620484i
$612$	−10.2125	−	3.70305i	−0.412816	−	0.149687i
$613$	−15.8097	+	2.27309i	−0.638546	+	0.0918091i	−0.453981	−	0.891011i	$-0.649997\pi$
$613$	−15.8097	+	2.27309i	−0.638546	+	0.0918091i	−0.184565	+	0.982820i	$0.559088\pi$
$614$	0.982656	−	3.05319i	0.0396568	−	0.123217i
$615$	−33.9527	−	45.8650i	−1.36911	−	1.84946i
$616$	−13.2378	+	4.84818i	−0.533364	+	0.195339i
$617$	34.7517	+	15.8706i	1.39905	+	0.638926i	0.965069	−	0.261995i	$-0.0843804\pi$
$617$	34.7517	+	15.8706i	1.39905	+	0.638926i	0.433983	+	0.900921i	$0.357108\pi$
$618$	−24.5666	+	17.2239i	−0.988213	+	0.692847i
$619$	−0.990324	+	0.636443i	−0.0398045	+	0.0255808i	−0.560392	−	0.828228i	$-0.689349\pi$
$619$	−0.990324	+	0.636443i	−0.0398045	+	0.0255808i	0.520587	+	0.853808i	$0.325713\pi$
$620$	−27.5118	−	14.3213i	−1.10490	−	0.575158i
$621$	−10.1926	−	22.7401i	−0.409014	−	0.912528i
$622$	−1.60555	−	2.64583i	−0.0643768	−	0.106088i
$623$	8.11710	−	5.21654i	0.325205	−	0.208996i
$624$	11.2157	−	9.01307i	0.448988	−	0.360812i
$625$	29.4981	−	64.5919i	1.17993	−	2.58368i
$626$	−5.21478	−	4.75941i	−0.208424	−	0.190224i
$627$	−3.71232	−	5.01478i	−0.148256	−	0.200271i
$628$	−4.31231	−	18.0875i	−0.172080	−	0.721769i
$629$	1.24763	+	8.67743i	0.0497461	+	0.345992i
$630$	−27.3645	+	22.0166i	−1.09023	+	0.877164i
$631$	−25.8535	−	22.4022i	−1.02921	−	0.891816i	−0.0350135	−	0.999387i	$-0.511147\pi$
$631$	−25.8535	−	22.4022i	−1.02921	−	0.891816i	−0.994197	+	0.107571i	$0.965693\pi$
$632$	9.68718	−	17.4933i	0.385336	−	0.695844i
$633$	0.0999059	−	0.263543i	0.00397090	−	0.0104749i
$634$	27.0101	+	4.59691i	1.07271	+	0.182567i
$635$	16.7731	−	57.1238i	0.665618	−	2.26689i
$636$	−1.91523	+	14.8452i	−0.0759439	+	0.588652i
$637$	−4.87960	+	4.22819i	−0.193337	+	0.167527i
$638$	7.44400	+	5.05973i	0.294711	+	0.200317i
$639$	0.00222655	−	0.00188798i	8.80810e−5	−	7.46875e-5i
$640$	46.0281	−	11.6529i	1.81942	−	0.460620i
$641$	−3.23059	−	0.464489i	−0.127601	−	0.0183462i	0.0782185	−	0.996936i	$-0.475077\pi$
$641$	−3.23059	−	0.464489i	−0.127601	−	0.0183462i	−0.205819	+	0.978590i	$0.565986\pi$
$642$	−19.9222	−	4.98794i	−0.786268	−	0.196858i
$643$	−5.79366			−0.228480			−0.114240	−	0.993453i	$-0.536443\pi$
$643$	−5.79366			−0.228480			−0.114240	+	0.993453i	$0.536443\pi$
$644$	0.546160	+	18.9124i	0.0215217	+	0.745253i
$645$	17.3929	+	82.0655i	0.684846	+	3.23133i
$646$	−1.60148	+	3.28026i	−0.0630092	+	0.129060i
$647$	−5.46129	+	37.9841i	−0.214706	+	1.49331i	0.542457	+	0.840083i	$0.317494\pi$
$647$	−5.46129	+	37.9841i	−0.214706	+	1.49331i	−0.757163	+	0.653226i	$0.773415\pi$
$648$	−11.5845	−	22.6671i	−0.455083	−	0.890449i
$649$	24.1912	−	7.10317i	0.949587	−	0.278824i
$650$	−30.6358	−	20.8234i	−1.20164	−	0.816759i
$651$	7.62006	−	10.0665i	0.298654	−	0.394537i
$652$	−12.0159	−	4.21203i	−0.470580	−	0.164956i
$653$	5.25203	+	1.54214i	0.205528	+	0.0603485i	0.382876	−	0.923800i	$-0.374934\pi$
$653$	5.25203	+	1.54214i	0.205528	+	0.0603485i	−0.177348	+	0.984148i	$0.556752\pi$
$654$	−46.8680	+	1.88850i	−1.83268	+	0.0738464i
$655$	35.0962	−	54.6108i	1.37132	−	2.13382i
$656$	−31.3774	+	1.24605i	−1.22508	+	0.0486499i
$657$	6.36401	−	20.8460i	0.248284	−	0.813281i
$658$	30.4040	−	8.08233i	1.18527	−	0.315082i
$659$	−28.9652	+	4.16457i	−1.12833	+	0.162229i	−0.681099	−	0.732192i	$-0.738498\pi$
$659$	−28.9652	+	4.16457i	−1.12833	+	0.162229i	−0.447227	+	0.894420i	$0.647588\pi$
$660$	−33.1895	+	15.7425i	−1.29190	+	0.612776i
$661$	13.6660	−	6.24103i	0.531544	−	0.242748i	−0.131516	−	0.991314i	$-0.541985\pi$
$661$	13.6660	−	6.24103i	0.531544	−	0.242748i	0.663060	+	0.748566i	$0.269257\pi$
$662$	−28.0645	−	25.6138i	−1.09076	−	0.995510i
$663$	6.35633	+	1.41839i	0.246859	+	0.0550859i
$664$	−5.84079	−	0.452581i	−0.226667	−	0.0175635i
$665$	6.38061	+	9.92842i	0.247429	+	0.385008i
$666$	−11.7293	+	16.8654i	−0.454502	+	0.653522i
$667$	9.60470	−	7.32617i	0.371895	−	0.283670i
$668$	−15.3243	+	29.4386i	−0.592916	+	1.13901i
$669$	−5.33225	+	5.27549i	−0.206157	+	0.203962i
$670$	−50.7334	+	21.6067i	−1.96000	+	0.834739i
$671$	7.27577	−	15.9317i	0.280878	−	0.615037i
$672$	1.54382	+	19.2655i	0.0595540	+	0.743182i
$673$	14.2894	+	31.2895i	0.550818	+	1.20612i	0.956399	+	0.292063i	$0.0943419\pi$
$673$	14.2894	+	31.2895i	0.550818	+	1.20612i	−0.405581	+	0.914059i	$0.632931\pi$
$674$	5.06728	−	15.7444i	0.195184	−	0.606452i
$675$	−47.0784	+	45.5908i	−1.81205	+	1.75479i
$676$	12.0390	−	12.5265i	0.463037	−	0.481790i
$677$	20.9780	−	24.2099i	0.806251	−	0.930463i	−0.192456	−	0.981306i	$-0.561645\pi$
$677$	20.9780	−	24.2099i	0.806251	−	0.930463i	0.998707	+	0.0508424i	$0.0161906\pi$
$678$	−6.53090	−	35.2745i	−0.250818	−	1.35471i
$679$	−19.4259	+	30.2273i	−0.745498	+	1.16002i
$680$	17.1278	+	12.9809i	0.656820	+	0.497796i
$681$	−6.77620	−	0.521098i	−0.259665	−	0.0199685i
$682$	10.1991	−	8.38720i	0.390542	−	0.321163i
$683$	11.6320	−	10.0792i	0.445086	−	0.385669i	−0.403282	−	0.915076i	$-0.632131\pi$
$683$	11.6320	−	10.0792i	0.445086	−	0.385669i	0.848368	+	0.529406i	$0.177585\pi$
$684$	−7.98687	+	3.06244i	−0.305386	+	0.117095i
$685$	19.1768	+	65.3101i	0.732707	+	2.49537i
$686$	−3.29255	−	28.0075i	−0.125710	−	1.06933i
$687$	−0.171107	−	2.58681i	−0.00652813	−	0.0986931i
$688$	42.7191	+	17.4954i	1.62865	+	0.667007i
$689$		−	8.97376i		−	0.341873i
$690$	5.93595	+	48.9414i	0.225978	+	1.86317i
$691$	−2.76499			−0.105185			−0.0525926	−	0.998616i	$-0.516748\pi$
$691$	−2.76499			−0.105185			−0.0525926	+	0.998616i	$0.516748\pi$
$692$	−2.23062	−	24.3785i	−0.0847953	−	0.926732i
$693$	−4.05893	−	14.3914i	−0.154186	−	0.546682i
$694$	−3.74054	−	31.8182i	−0.141989	−	1.20780i
$695$	25.1422	−	7.38241i	0.953698	−	0.280031i
$696$	9.41627	−	7.97504i	0.356923	−	0.302293i
$697$	−9.30792	−	10.7419i	−0.352563	−	0.406879i
$698$	22.8189	+	27.7484i	0.863708	+	1.05029i
$699$	−49.9418	−	3.84059i	−1.88897	−	0.145264i
$700$	46.2660	−	18.3102i	1.74869	−	0.692060i
$701$	−12.9044	−	8.29314i	−0.487392	−	0.313228i	0.273764	−	0.961797i	$-0.411731\pi$
$701$	−12.9044	−	8.29314i	−0.487392	−	0.313228i	−0.761156	+	0.648569i	$0.775368\pi$
$702$	8.62686	+	12.5890i	0.325600	+	0.475142i
$703$	5.21698	+	4.52054i	0.196762	+	0.170495i
$704$	−3.11395	+	19.9729i	−0.117361	+	0.752758i
$705$	76.9580	−	28.2357i	2.89840	−	1.06342i
$706$	−34.9140	−	11.2369i	−1.31401	−	0.422908i
$707$	4.61433	−	2.10729i	0.173540	−	0.0792529i
$708$	−0.501008	−	34.5615i	−0.0188290	−	1.29890i
$709$	−1.55115	−	0.708388i	−0.0582548	−	0.0266041i	0.386075	−	0.922468i	$-0.373831\pi$
$709$	−1.55115	−	0.708388i	−0.0582548	−	0.0266041i	−0.444329	+	0.895863i	$0.646558\pi$
$710$	−0.00531347	+	0.00226294i	−0.000199411	+	8.49265e-5i
$711$	17.7187	+	11.6569i	0.664505	+	0.437168i
$712$	−0.905114	−	13.8055i	−0.0339206	−	0.517385i
$713$	−6.34281	−	16.5481i	−0.237540	−	0.619730i
$714$	−6.37537	+	5.99033i	−0.238592	+	0.224182i
$715$	18.5266	−	11.9063i	0.692855	−	0.445271i
$716$	−13.6462	+	19.0039i	−0.509983	+	0.710209i
$717$	13.1707	+	2.93901i	0.491870	+	0.109759i
$718$	17.6945	+	16.1494i	0.660354	+	0.602691i
$719$	−2.22024	−	4.86166i	−0.0828011	−	0.181309i	0.863703	−	0.504001i	$-0.168139\pi$
$719$	−2.22024	−	4.86166i	−0.0828011	−	0.181309i	−0.946504	+	0.322692i	$0.895412\pi$
$720$	8.60892	+	49.6191i	0.320836	+	1.84920i
$721$	3.43853	+	23.9155i	0.128058	+	0.890660i
$722$	−6.16471	−	23.1903i	−0.229427	−	0.863054i
$723$	10.4273	+	5.76635i	0.387794	+	0.214453i
$724$	−21.0220	−	36.7459i	−0.781275	−	1.36565i
$725$	−26.7251	−	17.1752i	−0.992546	−	0.637870i
$726$	0.455170	+	11.2962i	0.0168929	+	0.419241i
$727$	5.56199	−	18.9424i	0.206283	−	0.702535i	−0.789740	−	0.613441i	$-0.789785\pi$
$727$	5.56199	−	18.9424i	0.206283	−	0.702535i	0.996023	−	0.0890938i	$-0.0283971\pi$
$728$	−2.39580	−	11.3366i	−0.0887941	−	0.420164i
$729$	24.9074	−	10.4221i	0.922497	−	0.386005i
$730$	−24.2394	+	35.6616i	−0.897142	+	1.31990i
$731$	5.88674	+	20.0484i	0.217729	+	0.741516i
$732$	−18.3727	−	15.4595i	−0.679076	−	0.571401i
$733$	−24.4059	−	3.50903i	−0.901451	−	0.129609i	−0.324021	−	0.946050i	$-0.605035\pi$
$733$	−24.4059	−	3.50903i	−0.901451	−	0.129609i	−0.577429	+	0.816441i	$0.695944\pi$
$734$	−8.16299	+	16.7200i	−0.301301	+	0.617147i
$735$	−4.68546	−	22.1075i	−0.172826	−	0.815448i
$736$	24.1028	+	12.4521i	0.888440	+	0.458992i
$737$		−	23.4765i		−	0.864766i
$738$	1.21470	−	33.2848i	0.0447136	−	1.22523i
$739$	5.28236	−	36.7396i	0.194315	−	1.35149i	−0.626111	−	0.779734i	$-0.715354\pi$
$739$	5.28236	−	36.7396i	0.194315	−	1.35149i	0.820425	−	0.571754i	$-0.193737\pi$
$740$	32.0454	−	24.9963i	1.17801	−	0.918882i
$741$	4.51400	−	2.43357i	0.165826	−	0.0893994i
$742$	9.96911	+	6.77607i	0.365977	+	0.248757i
$743$	5.48500	+	6.33002i	0.201225	+	0.232226i	0.847389	−	0.530973i	$-0.178173\pi$
$743$	5.48500	+	6.33002i	0.201225	+	0.232226i	−0.646164	+	0.763199i	$0.723628\pi$
$744$	−7.33407	−	16.5510i	−0.268880	−	0.606790i
$745$	−17.3847	−	5.10461i	−0.636927	−	0.187019i
$746$	−1.32049	+	7.75884i	−0.0483467	+	0.284071i
$747$	0.950057	−	6.14060i	0.0347608	−	0.224673i
$748$	−7.94181	+	4.54342i	−0.290381	+	0.166124i
$749$	−10.8305	+	12.4990i	−0.395737	+	0.456705i
$750$	69.8148	−	35.3469i	2.54928	−	1.29069i
$751$	1.40341	−	0.201780i	0.0512112	−	0.00736306i	−0.116662	−	0.993172i	$-0.537219\pi$
$751$	1.40341	−	0.201780i	0.0512112	−	0.00736306i	0.167873	+	0.985809i	$0.446310\pi$
$752$	10.9814	−	43.7525i	0.400450	−	1.59549i
$753$	17.8342	+	24.0912i	0.649913	+	0.877934i
$754$	−4.98707	+	5.46421i	−0.181618	+	0.198995i
$755$	4.82330	+	2.20273i	0.175538	+	0.0801655i
$756$	−20.4995	+	0.0777867i	−0.745559	+	0.00282907i
$757$	−7.29395	−	11.3496i	−0.265103	−	0.412509i	0.683026	−	0.730394i	$-0.260664\pi$
$757$	−7.29395	−	11.3496i	−0.265103	−	0.412509i	−0.948129	+	0.317886i	$0.897027\pi$
$758$	−0.317195	−	0.522715i	−0.0115211	−	0.0189859i
$759$	−20.1604	−	5.83924i	−0.731776	−	0.211951i
$760$	16.8862	−	1.10709i	0.612528	−	0.0401584i
$761$	−16.6745	−	25.9461i	−0.604452	−	0.940545i	−0.999758	−	0.0219957i	$-0.992998\pi$
$761$	−16.6745	−	25.9461i	−0.604452	−	0.940545i	0.395307	−	0.918549i	$-0.370638\pi$
$762$	28.4527	−	19.9485i	1.03073	−	0.722656i
$763$	−15.6917	+	34.3600i	−0.568077	+	1.24391i
$764$	−0.738015	+	3.74934i	−0.0267005	+	0.135646i
$765$	−15.1108	+	17.0664i	−0.546334	+	0.617036i
$766$	6.51255	−	20.2350i	0.235308	−	0.731120i
$767$	2.94912	+	20.5115i	0.106486	+	0.740629i
$768$	25.2387	+	11.4459i	0.910722	+	0.413020i
$769$	−20.1798	+	23.2887i	−0.727702	+	0.839812i	−0.992211	−	0.124571i	$-0.960245\pi$
$769$	−20.1798	+	23.2887i	−0.727702	+	0.839812i	0.264509	+	0.964383i	$0.414790\pi$
$770$	−0.762452	+	29.5719i	−0.0274769	+	1.06570i
$771$	12.4370	+	4.71469i	0.447906	+	0.169796i
$772$	−1.44994	−	3.66369i	−0.0521843	−	0.131859i
$773$	−15.9988	−	4.69767i	−0.575436	−	0.168963i	−0.0189504	−	0.999820i	$-0.506032\pi$
$773$	−15.9988	−	4.69767i	−0.575436	−	0.168963i	−0.556486	+	0.830857i	$0.687851\pi$
$774$	−21.9508	+	43.7670i	−0.789005	+	1.57317i
$775$	−35.2226	+	30.5206i	−1.26523	+	1.09633i
$776$	24.4227	+	45.3645i	0.876723	+	1.62849i
$777$	7.85060	+	14.5620i	0.281639	+	0.522409i
$778$	23.4466	−	2.75637i	0.840602	−	0.0988208i
$779$	−11.0782	−	1.59280i	−0.396916	−	0.0570679i
$780$	−8.92508	−	28.8427i	−0.319569	−	1.03273i
$781$		−	0.00245876i		−	8.79815e-5i
$782$	2.40885	+	12.0410i	0.0861402	+	0.430585i
$783$	7.67429	+	10.6022i	0.274257	+	0.378891i
$784$	−11.5080	−	4.71307i	−0.411002	−	0.168324i
$785$	−38.6205	−	5.55279i	−1.37842	−	0.198188i
$786$	35.8955	−	12.1297i	1.28035	−	0.432654i
$787$	27.5153	−	8.07921i	0.980813	−	0.287993i	0.248253	−	0.968695i	$-0.420143\pi$
$787$	27.5153	−	8.07921i	0.980813	−	0.287993i	0.732560	+	0.680702i	$0.238325\pi$
$788$	−14.3030	−	0.738037i	−0.509523	−	0.0262915i
$789$	23.4217	−	30.9413i	0.833835	−	1.10154i
$790$	−26.6511	−	32.4085i	−0.948205	−	1.15304i
$791$	−27.7192	−	8.13908i	−0.985580	−	0.289392i
$792$	−20.8717	−	4.90530i	−0.741645	−	0.174302i
$793$	12.1102	+	7.78273i	0.430045	+	0.276373i
$794$	10.0693	+	0.259616i	0.357346	+	0.00921343i
$795$	27.4858	+	15.1999i	0.974822	+	0.539083i
$796$	−14.5355	−	13.9697i	−0.515197	−	0.495144i
$797$	2.09840	+	14.5947i	0.0743291	+	0.516971i	0.992639	+	0.121109i	$0.0386450\pi$
$797$	2.09840	+	14.5947i	0.0743291	+	0.516971i	−0.918310	+	0.395862i	$0.870446\pi$
$798$	−0.705016	+	6.85226i	−0.0249573	+	0.242568i
$799$	18.5729	−	8.48195i	0.657061	−	0.300070i
$800$	9.17008	−	70.7542i	0.324211	−	2.50154i
$801$	14.6736	+	0.157021i	0.518466	+	0.00554807i
$802$	7.52356	+	17.6656i	0.265666	+	0.623795i
$803$	−9.92493	−	15.4435i	−0.350243	−	0.544989i
$804$	−31.0097	−	8.61905i	−1.09363	−	0.303970i
$805$	37.3219	+	13.5379i	1.31543	+	0.477150i
$806$	5.63040	+	9.27849i	0.198322	+	0.326821i
$807$	−36.6967	−	37.0915i	−1.29179	−	1.30568i
$808$	0.561925	−	7.25194i	0.0197685	−	0.255122i
$809$	48.3692	+	22.0895i	1.70057	+	0.776625i	0.997877	+	0.0651334i	$0.0207473\pi$
$809$	48.3692	+	22.0895i	1.70057	+	0.776625i	0.702695	+	0.711491i	$0.251980\pi$
$810$	−53.1713	+	5.09986i	−1.86825	+	0.179191i
$811$	−11.5095	−	25.2023i	−0.404153	−	0.884971i	−0.996832	−	0.0795326i	$-0.974657\pi$
$811$	−11.5095	−	25.2023i	−0.404153	−	0.884971i	0.592680	−	0.805438i	$-0.298070\pi$
$812$	−2.30456	−	9.66623i	−0.0808743	−	0.339218i
$813$	−1.53747	−	4.19045i	−0.0539214	−	0.146965i
$814$	4.44519	+	16.7219i	0.155804	+	0.586101i
$815$	−17.4965	+	20.1920i	−0.612874	+	0.707295i
$816$	3.08561	+	12.1583i	0.108018	+	0.425624i
$817$	13.8411	+	8.89514i	0.484239	+	0.311202i
$818$	−25.6265	−	4.36143i	−0.896011	−	0.152494i
$819$	12.1828	−	1.61877i	0.425703	−	0.0565643i
$820$	−21.7975	+	62.1830i	−0.761201	+	2.17152i
$821$	31.7091	+	36.5942i	1.10666	+	1.27715i	0.957531	+	0.288330i	$0.0930999\pi$
$821$	31.7091	+	36.5942i	1.10666	+	1.27715i	0.149124	+	0.988819i	$0.452355\pi$
$822$	−15.0356	+	36.7738i	−0.524427	+	1.28263i
$823$	3.34312	+	11.3856i	0.116534	+	0.396878i	0.997015	−	0.0772023i	$-0.0245987\pi$
$823$	3.34312	+	11.3856i	0.116534	+	0.396878i	−0.880482	+	0.474081i	$0.842781\pi$
$824$	32.3877	+	12.2993i	1.12828	+	0.428468i
$825$	3.64315	+	55.0775i	0.126838	+	1.91755i
$826$	−25.0135	−	12.2120i	−0.870331	−	0.424910i
$827$		−	10.9723i		−	0.381543i	−0.981635	−	0.190771i	$-0.938901\pi$
$827$		−	10.9723i		−	0.381543i	0.981635	−	0.190771i	$-0.0610989\pi$
$828$	−15.1146	+	24.4857i	−0.525267	+	0.850937i
$829$		−	14.6787i		−	0.509811i	−0.966966	−	0.254906i	$-0.917956\pi$
$829$		−	14.6787i		−	0.509811i	0.966966	−	0.254906i	$-0.0820444\pi$
$830$	−5.39311	+	11.0466i	−0.187198	+	0.383432i
$831$	−1.40636	−	21.2615i	−0.0487861	−	0.737554i
$832$	−15.8847	−	4.86959i	−0.550703	−	0.168823i
$833$	−1.58582	−	5.40081i	−0.0549454	−	0.187127i
$834$	14.1567	+	5.78820i	0.490206	+	0.200429i
$835$	45.6050	+	52.6310i	1.57823	+	1.82137i
$836$	−2.38329	+	6.79896i	−0.0824278	+	0.235147i
$837$	18.0960	−	6.42055i	0.625491	−	0.221927i
$838$	4.45690	−	26.1874i	0.153961	−	0.904630i
$839$	10.4997	+	6.74777i	0.362491	+	0.232959i	0.709190	−	0.705018i	$-0.249061\pi$
$839$	10.4997	+	6.74777i	0.362491	+	0.232959i	−0.346699	+	0.937977i	$0.612697\pi$
$840$	38.7811	+	11.8640i	1.33808	+	0.409348i
$841$	14.8362	−	17.1219i	0.511593	−	0.590410i
$842$	31.8378	−	8.46348i	1.09720	−	0.291671i
$843$	18.0597	+	49.2227i	0.622010	+	1.69532i
$844$	−0.316573	+	0.0754754i	−0.0108969	+	0.00259797i
$845$	−15.1446	−	33.1619i	−0.520988	−	1.14081i
$846$	45.3857	+	15.1450i	1.56039	+	0.520697i
$847$	8.28149	+	3.78203i	0.284555	+	0.129952i
$848$	15.4247	−	7.79818i	0.529686	−	0.267791i
$849$	−12.2076	−	12.3389i	−0.418963	−	0.423470i
$850$	27.6079	−	16.7531i	0.946944	−	0.574628i
$851$	23.1765	+	1.44751i	0.794481	+	0.0496200i
$852$	−0.00324774		0.000902701i	−0.000111266		3.09260e-5i
$853$	18.5493	+	28.8633i	0.635117	+	0.988262i	0.998398	+	0.0565819i	$0.0180202\pi$
$853$	18.5493	+	28.8633i	0.635117	+	0.988262i	−0.363281	+	0.931680i	$0.618343\pi$
$854$	−17.7903	+	7.57667i	−0.608772	+	0.259268i
$855$	−0.192060	+	17.9480i	−0.00656833	+	0.613808i
$856$	8.15535	+	22.2679i	0.278744	+	0.761100i
$857$	15.4459	−	7.05391i	0.527622	−	0.240957i	−0.133750	−	0.991015i	$-0.542702\pi$
$857$	15.4459	−	7.05391i	0.527622	−	0.240957i	0.661372	+	0.750058i	$0.269975\pi$
$858$	12.7864	+	1.31557i	0.436522	+	0.0449129i
$859$	0.973543	+	6.77114i	0.0332169	+	0.231028i	0.999666	−	0.0258282i	$-0.00822229\pi$
$859$	0.973543	+	6.77114i	0.0332169	+	0.231028i	−0.966450	+	0.256857i	$0.917313\pi$
$860$	67.1219	−	69.8403i	2.28884	−	2.38153i
$861$	−23.4721	−	12.9803i	−0.799928	−	0.442366i
$862$	−1.22412	+	47.4780i	−0.0416938	+	1.61711i
$863$	−39.3880	−	25.3131i	−1.34078	−	0.861669i	−0.343781	−	0.939050i	$-0.611708\pi$
$863$	−39.3880	−	25.3131i	−1.34078	−	0.861669i	−0.997002	+	0.0773808i	$0.975344\pi$
$864$	−14.1421	+	25.7682i	−0.481124	+	0.876653i
$865$	−49.2876	−	14.4721i	−1.67583	−	0.492068i
$866$	34.3857	−	28.2771i	1.16847	−	0.960895i
$867$	14.3447	−	18.9501i	0.487173	−	0.643581i
$868$	−14.5591	−	0.751254i	−0.494169	−	0.0254992i
$869$	17.1402	−	5.03281i	0.581441	−	0.170726i
$870$	−8.28924	−	24.5303i	−0.281031	−	0.831654i
$871$	19.0992	+	2.74605i	0.647153	+	0.0930465i
$872$	32.2006	+	43.5510i	1.09045	+	1.47482i
$873$	−49.9480	+	22.1677i	−1.69048	+	0.750261i
$874$	7.64243	+	5.92338i	0.258509	+	0.200361i
$875$		−	63.0171i		−	2.13037i
$876$	−24.0428	+	7.43981i	−0.812333	+	0.251368i
$877$	−14.6095	−	2.10053i	−0.493328	−	0.0709298i	−0.108839	−	0.994059i	$-0.534713\pi$
$877$	−14.6095	−	2.10053i	−0.493328	−	0.0709298i	−0.384489	+	0.923130i	$0.625622\pi$
$878$	−6.23179	−	53.0097i	−0.210313	−	1.78899i
$879$	−14.7272	−	27.3173i	−0.496736	−	0.921389i
$880$	36.5649	+	21.4981i	1.23260	+	0.724702i
$881$	14.4267	−	12.5008i	0.486046	−	0.421162i	−0.377056	−	0.926190i	$-0.623064\pi$
$881$	14.4267	−	12.5008i	0.486046	−	0.421162i	0.863102	+	0.505029i	$0.168518\pi$
$882$	5.91330	−	11.7903i	0.199111	−	0.397002i
$883$	−29.4865	−	8.65801i	−0.992299	−	0.291365i	−0.255007	−	0.966939i	$-0.582078\pi$
$883$	−29.4865	−	8.65801i	−0.992299	−	0.291365i	−0.737292	+	0.675574i	$0.763896\pi$
$884$	−2.76734	−	6.99249i	−0.0930756	−	0.235183i
$885$	−67.8203	−	25.7098i	−2.27975	−	0.864226i
$886$	9.57020	+	0.246748i	0.321517	+	0.00828966i
$887$	−25.5492	+	29.4853i	−0.857858	+	0.990021i	0.142142	+	0.989846i	$0.454601\pi$
$887$	−25.5492	+	29.4853i	−0.857858	+	0.990021i	−1.00000		0.000174645i	$0.999944\pi$
$888$	23.7196	+	0.267620i	0.795979	+	0.00898073i
$889$	−3.98246	−	27.6986i	−0.133567	−	0.928981i
$890$	−27.6350	−	8.89423i	−0.926329	−	0.298135i
$891$	6.87235	−	21.6777i	0.230232	−	0.726231i
$892$	8.49824	+	1.67278i	0.284542	+	0.0560089i
$893$	6.67886	−	14.6247i	0.223500	−	0.489396i
$894$	−6.07100	−	8.65911i	−0.203045	−	0.289604i
$895$	26.5416	+	41.2995i	0.887187	+	1.38049i
$896$	17.4042	−	13.9696i	0.581434	−	0.466691i
$897$	7.10867	−	15.7184i	0.237352	−	0.524823i
$898$	26.0582	−	15.8127i	0.869572	−	0.527677i
$899$	5.03218	+	7.83022i	0.167832	+	0.261152i
$900$	74.0885	+	15.4088i	2.46962	+	0.513625i
$901$	7.11625	+	3.24988i	0.237077	+	0.108269i
$902$	−20.7206	−	18.9112i	−0.689920	−	0.629675i
$903$	23.4603	+	31.6914i	0.780711	+	1.05462i
$904$	−29.4642	+	29.1167i	−0.979966	+	0.968408i
$905$	−87.9278	+	12.6421i	−2.92282	+	0.420238i
$906$	1.39797	+	2.76117i	0.0464444	+	0.0917338i
$907$	33.9624	−	39.1948i	1.12770	−	1.30144i	0.179508	−	0.983757i	$-0.442549\pi$
$907$	33.9624	−	39.1948i	1.12770	−	1.30144i	0.948197	−	0.317684i	$-0.102905\pi$
$908$	3.89689	+	6.81167i	0.129323	+	0.226053i
$909$	7.62419	+	1.17959i	0.252878	+	0.0391246i
$910$	−23.9690	−	4.07934i	−0.794565	−	0.135229i
$911$	−28.1213	−	8.25716i	−0.931700	−	0.273572i	−0.219552	−	0.975601i	$-0.570459\pi$
$911$	−28.1213	−	8.25716i	−0.931700	−	0.273572i	−0.712148	+	0.702029i	$0.752278\pi$
$912$	8.10563	+	5.64419i	0.268404	+	0.186898i
$913$	−3.42722	−	3.95523i	−0.113425	−	0.130899i
$914$	−9.99250	+	14.7012i	−0.330522	+	0.486272i
$915$	−44.3501	+	23.9099i	−1.46617	+	0.790436i
$916$	−2.36037	+	1.84115i	−0.0779887	+	0.0608334i
$917$	4.34237	−	30.2019i	0.143398	−	0.997354i
$918$	−13.1074	+	2.28199i	−0.432609	+	0.0753169i
$919$			15.7181i			0.518492i	0.965811	+	0.259246i	$0.0834740\pi$
$919$			15.7181i			0.518492i	−0.965811	+	0.259246i	$0.916526\pi$
$920$	42.9069	−	37.4120i	1.41460	−	1.23344i
$921$	−0.814466	−	3.84291i	−0.0268376	−	0.126628i
$922$	1.44564	+	0.705783i	0.0476095	+	0.0232437i
$923$	0.00200032		0.000287603i	6.58414e−5		9.46657e-6i
$924$	−11.1165	+	13.2113i	−0.365706	+	0.434619i
$925$	−17.2053	−	58.5958i	−0.565706	−	1.92662i
$926$	−30.7999	−	20.9349i	−1.01215	−	0.687962i
$927$	−15.6216	+	33.2601i	−0.513082	+	1.09241i
$928$	−13.7260	−	3.82370i	−0.450577	−	0.125519i
$929$	−5.81936	+	19.8189i	−0.190927	+	0.650237i	0.807268	+	0.590185i	$0.200945\pi$
$929$	−5.81936	+	19.8189i	−0.190927	+	0.650237i	−0.998195	+	0.0600528i	$0.980873\pi$
$930$	−37.9560	+	1.52940i	−1.24463	+	0.0501511i
$931$	−3.72864	−	2.39625i	−0.122201	−	0.0785340i
$932$	28.7208	+	50.2033i	0.940780	+	1.64446i
$933$	−3.31701	−	1.83433i	−0.108594	−	0.0600534i
$934$	32.9154	−	8.74992i	1.07702	−	0.286306i
$935$	2.73231	+	19.0036i	0.0893561	+	0.621485i
$936$	6.43208	−	16.4064i	0.210239	−	0.536260i
$937$	17.7937	+	38.9627i	0.581294	+	1.27286i	0.940562	+	0.339622i	$0.110299\pi$
$937$	17.7937	+	38.9627i	0.581294	+	1.27286i	−0.359268	+	0.933234i	$0.616974\pi$
$938$	−17.4724	+	19.1441i	−0.570495	+	0.625078i
$939$	−8.43933	−	1.88321i	−0.275407	−	0.0614562i
$940$	−76.8866	−	55.2102i	−2.50776	−	1.80076i
$941$	9.88064	−	6.34990i	0.322100	−	0.207001i	−0.369592	−	0.929194i	$-0.620502\pi$
$941$	9.88064	−	6.34990i	0.322100	−	0.207001i	0.691691	+	0.722194i	$0.256866\pi$
$942$	−15.5943	−	16.5966i	−0.508089	−	0.540747i
$943$	−32.8803	+	18.3411i	−1.07073	+	0.597270i
$944$	−32.6938	+	22.8936i	−1.06409	+	0.745124i
$945$	−15.6773	+	40.0568i	−0.509982	+	1.30305i
$946$	16.1590	+	37.9420i	0.525375	+	1.23360i
$947$	−7.59368	−	3.46792i	−0.246761	−	0.112692i	0.288195	−	0.957572i	$-0.406945\pi$
$947$	−7.59368	−	3.46792i	−0.246761	−	0.112692i	−0.534957	+	0.844880i	$0.679672\pi$
$948$	−0.354979	−	24.4879i	−0.0115292	−	0.795330i
$949$	13.7250	−	6.26798i	0.445531	−	0.203467i
$950$	7.79051	−	24.2057i	0.252758	−	0.785337i
$951$	31.5027	−	11.5583i	1.02155	−	0.374803i
$952$	9.85768	+	2.20573i	0.319489	+	0.0714881i
$953$	−19.6906	−	17.0620i	−0.637842	−	0.552693i	0.274775	−	0.961509i	$-0.411397\pi$
$953$	−19.6906	−	17.0620i	−0.637842	−	0.552693i	−0.912617	+	0.408815i	$0.865942\pi$
$954$	7.00230	+	16.9423i	0.226708	+	0.548527i
$955$	6.74550	+	4.33507i	0.218279	+	0.140280i
$956$	−5.73410	−	14.4889i	−0.185454	−	0.468604i
$957$	10.9912	+	0.845236i	0.355295	+	0.0273226i
$958$	26.3353	−	21.6568i	0.850855	−	0.699700i
$959$	20.9514	+	24.1792i	0.676557	+	0.780788i
$960$	41.8208	−	40.4052i	1.34976	−	1.30407i
$961$	−16.6422	+	4.88660i	−0.536846	+	0.157632i
$962$	−14.1240	+	1.66041i	−0.455376	+	0.0535338i
$963$	−24.2084	+	6.82771i	−0.780104	+	0.220020i
$964$	−1.25368	−	13.7016i	−0.0403785	−	0.441298i
$965$	−8.26786			−0.266152
$966$	12.0941	+	19.7661i	0.389122	+	0.635963i
$967$			27.5860i			0.887105i	0.896248	+	0.443553i	$0.146282\pi$
$967$			27.5860i			0.887105i	−0.896248	+	0.443553i	$0.853718\pi$
$968$	10.4967	−	7.76103i	0.337378	−	0.249449i
$969$	0.295074	+	4.46096i	0.00947913	+	0.143307i
$970$	107.370	−	12.6223i	3.44743	−	0.405278i
$971$	5.04746	+	17.1901i	0.161981	+	0.551656i	0.999982	+	0.00598763i	$0.00190593\pi$
$971$	5.04746	+	17.1901i	0.161981	+	0.551656i	−0.838001	+	0.545668i	$0.816276\pi$
$972$	−26.1107	−	17.0362i	−0.837500	−	0.546438i
$973$	9.30818	−	8.06559i	0.298407	−	0.258571i
$974$	31.1628	+	37.8948i	0.998520	+	1.21423i
$975$	−45.2344	−	3.47857i	−1.44866	−	0.111404i
$976$	−2.85375	+	27.5789i	−0.0913464	+	0.882779i
$977$	−4.05269	+	6.30611i	−0.129657	+	0.201750i	−0.900012	−	0.435865i	$-0.856443\pi$
$977$	−4.05269	+	6.30611i	−0.129657	+	0.201750i	0.770355	+	0.637615i	$0.220079\pi$
$978$	−15.3338	+	2.83898i	−0.490321	+	0.0907805i
$979$	8.09386	−	9.34082i	0.258681	−	0.298534i
$980$	−18.0819	+	18.8142i	−0.577605	+	0.600997i
$981$	−48.6578	+	30.5398i	−1.55353	+	0.975060i
$982$	−34.4111	−	11.0751i	−1.09810	−	0.353419i
$983$	−7.11871	−	15.5878i	−0.227051	−	0.497173i	0.761480	−	0.648188i	$-0.224473\pi$
$983$	−7.11871	−	15.5878i	−0.227051	−	0.497173i	−0.988531	+	0.151015i	$0.951746\pi$
$984$	−32.5868	+	20.4265i	−1.03883	+	0.651173i
$985$	−12.4843	+	27.3368i	−0.397783	+	0.871024i
$986$	−2.52707	−	5.93366i	−0.0804783	−	0.188966i
$987$	27.3905	−	27.0989i	0.871849	−	0.862569i
$988$	−5.25250	−	2.73420i	−0.167104	−	0.0869865i
$989$	55.1685	−	4.44651i	1.75425	−	0.141391i
$990$	−25.6873	+	36.9354i	−0.816396	+	1.17388i
$991$	16.7315	+	26.0347i	0.531494	+	0.827020i	0.998356	−	0.0573095i	$-0.0182522\pi$
$991$	16.7315	+	26.0347i	0.531494	+	0.827020i	−0.466863	+	0.884330i	$0.654616\pi$
$992$	−11.0557	+	17.7409i	−0.351017	+	0.563273i
$993$	−45.4182	−	10.1349i	−1.44130	−	0.321622i
$994$	−0.00182994	+	0.00200502i	−5.80422e−5	+	6.35955e-5i
$995$	−38.4804	+	17.5734i	−1.21991	+	0.557114i
$996$	−6.48265	+	3.07486i	−0.205411	+	0.0974305i
$997$	23.0054	−	3.30767i	0.728588	−	0.104755i	0.231968	−	0.972723i	$-0.425483\pi$
$997$	23.0054	−	3.30767i	0.728588	−	0.104755i	0.496620	+	0.867968i	$0.334574\pi$
$998$	3.87369	+	14.5720i	0.122620	+	0.461269i
$999$	−2.19746	+	25.0639i	−0.0695246	+	0.792987i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.x.a.35.16	✓	920
3.2	odd	2	inner	552.2.x.a.35.77	yes	920
8.3	odd	2	inner	552.2.x.a.35.43	yes	920
23.2	even	11	inner	552.2.x.a.347.50	yes	920
24.11	even	2	inner	552.2.x.a.35.50	yes	920
69.2	odd	22	inner	552.2.x.a.347.43	yes	920
184.163	odd	22	inner	552.2.x.a.347.77	yes	920
552.347	even	22	inner	552.2.x.a.347.16	yes	920

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.x.a.35.16	✓	920	1.1	even	1	trivial
552.2.x.a.35.43	yes	920	8.3	odd	2	inner
552.2.x.a.35.50	yes	920	24.11	even	2	inner
552.2.x.a.35.77	yes	920	3.2	odd	2	inner
552.2.x.a.347.16	yes	920	552.347	even	22	inner
552.2.x.a.347.43	yes	920	69.2	odd	22	inner
552.2.x.a.347.50	yes	920	23.2	even	11	inner
552.2.x.a.347.77	yes	920	184.163	odd	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.x (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27084 - 0.620447i) q^{2} +(-1.72827 + 0.114318i) q^{3} +(1.23009 + 1.57698i) q^{4} +(4.02671 - 1.18235i) q^{5} +(2.26730 + 0.927022i) q^{6} +(1.49077 - 1.29176i) q^{7} +(-0.584820 - 2.76731i) q^{8} +(2.97386 - 0.395146i) q^{9} +O(q^{10})\)	\(q+(-1.27084 - 0.620447i) q^{2} +(-1.72827 + 0.114318i) q^{3} +(1.23009 + 1.57698i) q^{4} +(4.02671 - 1.18235i) q^{5} +(2.26730 + 0.927022i) q^{6} +(1.49077 - 1.29176i) q^{7} +(-0.584820 - 2.76731i) q^{8} +(2.97386 - 0.395146i) q^{9} +(-5.85090 - 0.995778i) q^{10} +(1.36608 - 2.12566i) q^{11} +(-2.30621 - 2.58484i) q^{12} +(1.56954 + 1.36001i) q^{13} +(-2.69601 + 0.716684i) q^{14} +(-6.82409 + 2.50375i) q^{15} +(-0.973751 + 3.87967i) q^{16} +(-1.64691 + 0.752119i) q^{17} +(-4.02448 - 1.34296i) q^{18} +(-0.592234 + 1.29681i) q^{19} +(6.81776 + 4.89565i) q^{20} +(-2.42879 + 2.40294i) q^{21} +(-3.05493 + 1.85380i) q^{22} +(1.06168 + 4.67684i) q^{23} +(1.32708 + 4.71581i) q^{24} +(10.6102 - 6.81873i) q^{25} +(-1.15082 - 2.70218i) q^{26} +(-5.09448 + 1.02289i) q^{27} +(3.87088 + 0.761939i) q^{28} +(-1.04636 - 2.29120i) q^{29} +(10.2258 + 1.05211i) q^{30} +(-3.65768 + 0.525895i) q^{31} +(3.64461 - 4.32629i) q^{32} +(-2.11796 + 3.82989i) q^{33} +(2.55962 + 0.0659945i) q^{34} +(4.47560 - 6.96416i) q^{35} +(4.28126 + 4.20367i) q^{36} +(1.36417 - 4.64592i) q^{37} +(1.55724 - 1.28060i) q^{38} +(-2.86806 - 2.17105i) q^{39} +(-5.62682 - 10.4517i) q^{40} +(2.21175 + 7.53253i) q^{41} +(4.57752 - 1.54683i) q^{42} +(1.64242 - 11.4233i) q^{43} +(5.03253 - 0.460473i) q^{44} +(11.5077 - 5.10728i) q^{45} +(1.55250 - 6.60225i) q^{46} -11.2774 q^{47} +(1.23939 - 6.81644i) q^{48} +(-0.442448 + 3.07730i) q^{49} +(-17.7145 + 2.08251i) q^{50} +(2.76033 - 1.48814i) q^{51} +(-0.214041 + 4.14807i) q^{52} +(-2.82963 - 3.26557i) q^{53} +(7.10894 + 1.86092i) q^{54} +(2.98753 - 10.1746i) q^{55} +(-4.44654 - 3.36998i) q^{56} +(0.875294 - 2.30895i) q^{57} +(-0.0918124 + 3.56097i) q^{58} +(7.54095 + 6.53427i) q^{59} +(-12.3426 - 7.68164i) q^{60} +(6.86099 - 0.986461i) q^{61} +(4.97463 + 1.60107i) q^{62} +(3.92292 - 4.43060i) q^{63} +(-7.31597 + 3.23676i) q^{64} +(7.92807 + 3.62063i) q^{65} +(5.06784 - 3.55312i) q^{66} +(7.81614 - 5.02313i) q^{67} +(-3.21193 - 1.67198i) q^{68} +(-2.36952 - 7.96149i) q^{69} +(-10.0087 + 6.07350i) q^{70} +(0.000818609 - 0.000526088i) q^{71} +(-2.83267 - 7.99850i) q^{72} +(3.01810 - 6.60872i) q^{73} +(-4.61619 + 5.05785i) q^{74} +(-17.5577 + 12.9976i) q^{75} +(-2.77355 + 0.661254i) q^{76} +(-0.709335 - 4.93353i) q^{77} +(2.29784 + 4.53854i) q^{78} +(5.34299 + 4.62973i) q^{79} +(0.666106 + 16.7736i) q^{80} +(8.68772 - 2.35022i) q^{81} +(1.86274 - 10.9450i) q^{82} +(0.583530 - 1.98732i) q^{83} +(-6.77704 - 0.874328i) q^{84} +(-5.74236 + 4.97579i) q^{85} +(-9.17478 + 13.4981i) q^{86} +(2.07032 + 3.84021i) q^{87} +(-6.68127 - 2.53723i) q^{88} +(4.84169 + 0.696130i) q^{89} +(-17.7933 - 0.649346i) q^{90} +4.09664 q^{91} +(-6.06934 + 7.42719i) q^{92} +(6.26136 - 1.32703i) q^{93} +(14.3318 + 6.99703i) q^{94} +(-0.851470 + 5.92211i) q^{95} +(-5.80432 + 7.89366i) q^{96} +(-17.4775 + 5.13187i) q^{97} +(2.47158 - 3.63625i) q^{98} +(3.22259 - 6.86122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9}+O(q^{10}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9	\( 920 q - 18 q^{3} - 14 q^{4} - 16 q^{6} - 18 q^{9} - 14 q^{10} - 6 q^{12} - 30 q^{16} - 16 q^{18} - 52 q^{19} - 32 q^{22} - 26 q^{24} - 112 q^{25} - 30 q^{27} - 34 q^{28} + 11 q^{30} - 30 q^{33} - 88 q^{34} - 18 q^{36} + 124 q^{40} - 3 q^{42} - 36 q^{43} - 110 q^{46} + 32 q^{49} - 30 q^{51} + 90 q^{52} - 39 q^{54} - 6 q^{57} - 68 q^{58} + 13 q^{60} + 28 q^{64} - 46 q^{66} - 100 q^{67} - 92 q^{70} + 29 q^{72} - 36 q^{73} + 14 q^{75} - 50 q^{76} - 86 q^{78} - 2 q^{81} - 12 q^{82} - 151 q^{84} - 42 q^{88} - 196 q^{90} - 136 q^{91} - 68 q^{94} - 175 q^{96} - 36 q^{97} - 54 q^{99}+O(q^{100}) \) 920 * q - 18 * q^3 - 14 * q^4 - 16 * q^6 - 18 * q^9 - 14 * q^10 - 6 * q^12 - 30 * q^16 - 16 * q^18 - 52 * q^19 - 32 * q^22 - 26 * q^24 - 112 * q^25 - 30 * q^27 - 34 * q^28 + 11 * q^30 - 30 * q^33 - 88 * q^34 - 18 * q^36 + 124 * q^40 - 3 * q^42 - 36 * q^43 - 110 * q^46 + 32 * q^49 - 30 * q^51 + 90 * q^52 - 39 * q^54 - 6 * q^57 - 68 * q^58 + 13 * q^60 + 28 * q^64 - 46 * q^66 - 100 * q^67 - 92 * q^70 + 29 * q^72 - 36 * q^73 + 14 * q^75 - 50 * q^76 - 86 * q^78 - 2 * q^81 - 12 * q^82 - 151 * q^84 - 42 * q^88 - 196 * q^90 - 136 * q^91 - 68 * q^94 - 175 * q^96 - 36 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more