LMFDB - Embedded newform 1148.2.ba.a.113.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.15
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.49455i q^{3} +(-0.331199 - 1.01933i) q^{5} +(-0.587785 - 0.809017i) q^{7} +0.766322 q^{9} +O(q^{10})$	\(q+1.49455i q^{3} +(-0.331199 - 1.01933i) q^{5} +(-0.587785 - 0.809017i) q^{7} +0.766322 q^{9} +(2.51743 + 0.817962i) q^{11} +(2.13014 - 2.93189i) q^{13} +(1.52343 - 0.494994i) q^{15} +(-4.41518 - 1.43458i) q^{17} +(-4.70970 - 6.48235i) q^{19} +(1.20912 - 0.878474i) q^{21} +(1.02450 + 0.744340i) q^{23} +(3.11575 - 2.26373i) q^{25} +5.62895i q^{27} +(5.56167 - 1.80710i) q^{29} +(-0.118298 + 0.364085i) q^{31} +(-1.22248 + 3.76242i) q^{33} +(-0.629979 + 0.867091i) q^{35} +(0.591352 + 1.82000i) q^{37} +(4.38186 + 3.18361i) q^{39} +(2.68889 - 5.81118i) q^{41} +(-1.78623 - 1.29777i) q^{43} +(-0.253805 - 0.781133i) q^{45} +(4.11743 - 5.66715i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.14405 - 6.59870i) q^{51} +(-0.335641 + 0.109056i) q^{53} -2.83699i q^{55} +(9.68819 - 7.03888i) q^{57} +(11.8101 + 8.58057i) q^{59} +(10.6461 - 7.73483i) q^{61} +(-0.450433 - 0.619967i) q^{63} +(-3.69406 - 1.20027i) q^{65} +(-4.13585 + 1.34382i) q^{67} +(-1.11245 + 1.53116i) q^{69} +(5.05236 + 1.64161i) q^{71} -3.35273 q^{73} +(3.38325 + 4.65664i) q^{75} +(-0.817962 - 2.51743i) q^{77} +10.3297i q^{79} -6.11379 q^{81} -1.94220 q^{83} +4.97564i q^{85} +(2.70080 + 8.31219i) q^{87} +(1.27320 + 1.75241i) q^{89} -3.62402 q^{91} +(-0.544142 - 0.176803i) q^{93} +(-5.04778 + 6.94768i) q^{95} +(4.24196 - 1.37830i) q^{97} +(1.92916 + 0.626822i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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			0
$2$		0			0
$3$			1.49455i			0.862879i	0.902142	+	0.431439i	$0.141994\pi$
$3$			1.49455i			0.862879i	−0.902142	+	0.431439i	$0.858006\pi$
$4$		0			0
$5$	−0.331199	−	1.01933i	−0.148117	−	0.455857i	0.849282	−	0.527940i	$-0.177035\pi$
$5$	−0.331199	−	1.01933i	−0.148117	−	0.455857i	−0.997399	+	0.0720829i	$0.977035\pi$
$6$		0			0
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$8$		0			0
$9$	0.766322			0.255441
$10$		0			0
$11$	2.51743	+	0.817962i	0.759033	+	0.246625i	0.662864	−	0.748740i	$-0.269341\pi$
$11$	2.51743	+	0.817962i	0.759033	+	0.246625i	0.0961695	+	0.995365i	$0.469341\pi$
$12$		0			0
$13$	2.13014	−	2.93189i	0.590796	−	0.813161i	−0.404031	−	0.914745i	$-0.632391\pi$
$13$	2.13014	−	2.93189i	0.590796	−	0.813161i	0.994827	+	0.101585i	$0.0323913\pi$
$14$		0			0
$15$	1.52343	−	0.494994i	0.393349	−	0.127807i
$16$		0			0
$17$	−4.41518	−	1.43458i	−1.07084	−	0.347936i	−0.280024	−	0.959993i	$-0.590342\pi$
$17$	−4.41518	−	1.43458i	−1.07084	−	0.347936i	−0.790814	+	0.612057i	$0.790342\pi$
$18$		0			0
$19$	−4.70970	−	6.48235i	−1.08048	−	1.48715i	−0.858992	−	0.511989i	$-0.828909\pi$
$19$	−4.70970	−	6.48235i	−1.08048	−	1.48715i	−0.221488	−	0.975163i	$-0.571091\pi$
$20$		0			0
$21$	1.20912	−	0.878474i	0.263851	−	0.191699i
$22$		0			0
$23$	1.02450	+	0.744340i	0.213622	+	0.155206i	0.689451	−	0.724332i	$-0.257852\pi$
$23$	1.02450	+	0.744340i	0.213622	+	0.155206i	−0.475829	+	0.879538i	$0.657852\pi$
$24$		0			0
$25$	3.11575	−	2.26373i	0.623150	−	0.452745i
$26$		0			0
$27$			5.62895i			1.08329i
$28$		0			0
$29$	5.56167	−	1.80710i	1.03278	−	0.335569i	0.256889	−	0.966441i	$-0.417303\pi$
$29$	5.56167	−	1.80710i	1.03278	−	0.335569i	0.775887	+	0.630872i	$0.217303\pi$
$30$		0			0
$31$	−0.118298	+	0.364085i	−0.0212470	+	0.0653915i	−0.961118	−	0.276139i	$-0.910945\pi$
$31$	−0.118298	+	0.364085i	−0.0212470	+	0.0653915i	0.939871	+	0.341530i	$0.110945\pi$
$32$		0			0
$33$	−1.22248	+	3.76242i	−0.212807	+	0.654953i
$34$		0			0
$35$	−0.629979	+	0.867091i	−0.106486	+	0.146565i
$36$		0			0
$37$	0.591352	+	1.82000i	0.0972177	+	0.299205i	0.987825	−	0.155567i	$-0.0497205\pi$
$37$	0.591352	+	1.82000i	0.0972177	+	0.299205i	−0.890608	+	0.454773i	$0.849721\pi$
$38$		0			0
$39$	4.38186	+	3.18361i	0.701659	+	0.509785i
$40$		0			0
$41$	2.68889	−	5.81118i	0.419934	−	0.907555i
$41$	2.68889	−	5.81118i	0.419934	−	0.907555i
$42$		0			0
$43$	−1.78623	−	1.29777i	−0.272397	−	0.197908i	0.443198	−	0.896424i	$-0.353844\pi$
$43$	−1.78623	−	1.29777i	−0.272397	−	0.197908i	−0.715594	+	0.698516i	$0.753844\pi$
$44$		0			0
$45$	−0.253805	−	0.781133i	−0.0378351	−	0.116444i
$46$		0			0
$47$	4.11743	−	5.66715i	0.600589	−	0.826639i	−0.395173	−	0.918607i	$-0.629315\pi$
$47$	4.11743	−	5.66715i	0.600589	−	0.826639i	0.995762	+	0.0919671i	$0.0293155\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	2.14405	−	6.59870i	0.300227	−	0.924003i
$52$		0			0
$53$	−0.335641	+	0.109056i	−0.0461039	+	0.0149801i	−0.331978	−	0.943287i	$-0.607716\pi$
$53$	−0.335641	+	0.109056i	−0.0461039	+	0.0149801i	0.285874	+	0.958267i	$0.407716\pi$
$54$		0			0
$55$		−	2.83699i		−	0.382540i
$56$		0			0
$57$	9.68819	−	7.03888i	1.28323	−	0.932323i
$58$		0			0
$59$	11.8101	+	8.58057i	1.53755	+	1.11709i	0.951849	+	0.306566i	$0.0991801\pi$
$59$	11.8101	+	8.58057i	1.53755	+	1.11709i	0.585699	+	0.810528i	$0.300820\pi$
$60$		0			0
$61$	10.6461	−	7.73483i	1.36309	−	0.990343i	0.364849	−	0.931067i	$-0.381121\pi$
$61$	10.6461	−	7.73483i	1.36309	−	0.990343i	0.998242	−	0.0592763i	$-0.0188793\pi$
$62$		0			0
$63$	−0.450433	−	0.619967i	−0.0567492	−	0.0781085i
$64$		0			0
$65$	−3.69406	−	1.20027i	−0.458192	−	0.148876i
$66$		0			0
$67$	−4.13585	+	1.34382i	−0.505275	+	0.164174i	−0.550552	−	0.834801i	$-0.685583\pi$
$67$	−4.13585	+	1.34382i	−0.505275	+	0.164174i	0.0452775	+	0.998974i	$0.485583\pi$
$68$		0			0
$69$	−1.11245	+	1.53116i	−0.133924	+	0.184330i
$70$		0			0
$71$	5.05236	+	1.64161i	0.599605	+	0.194824i	0.593064	−	0.805155i	$-0.297918\pi$
$71$	5.05236	+	1.64161i	0.599605	+	0.194824i	0.00654094	+	0.999979i	$0.497918\pi$
$72$		0			0
$73$	−3.35273			−0.392407			−0.196204	−	0.980563i	$-0.562861\pi$
$73$	−3.35273			−0.392407			−0.196204	+	0.980563i	$0.562861\pi$
$74$		0			0
$75$	3.38325	+	4.65664i	0.390664	+	0.537703i
$76$		0			0
$77$	−0.817962	−	2.51743i	−0.0932154	−	0.286888i
$78$		0			0
$79$			10.3297i			1.16218i	0.813838	+	0.581092i	$0.197374\pi$
$79$			10.3297i			1.16218i	−0.813838	+	0.581092i	$0.802626\pi$
$80$		0			0
$81$	−6.11379			−0.679309
$82$		0			0
$83$	−1.94220			−0.213185			−0.106592	−	0.994303i	$-0.533994\pi$
$83$	−1.94220			−0.213185			−0.106592	+	0.994303i	$0.533994\pi$
$84$		0			0
$85$			4.97564i			0.539684i
$86$		0			0
$87$	2.70080	+	8.31219i	0.289556	+	0.891161i
$88$		0			0
$89$	1.27320	+	1.75241i	0.134959	+	0.185755i	0.871147	−	0.491022i	$-0.163376\pi$
$89$	1.27320	+	1.75241i	0.134959	+	0.185755i	−0.736189	+	0.676776i	$0.763376\pi$
$90$		0			0
$91$	−3.62402			−0.379900
$92$		0			0
$93$	−0.544142	−	0.176803i	−0.0564249	−	0.0183336i
$94$		0			0
$95$	−5.04778	+	6.94768i	−0.517891	+	0.712816i
$96$		0			0
$97$	4.24196	−	1.37830i	0.430706	−	0.139945i	−0.0856377	−	0.996326i	$-0.527293\pi$
$97$	4.24196	−	1.37830i	0.430706	−	0.139945i	0.516344	+	0.856382i	$0.327293\pi$
$98$		0			0
$99$	1.92916	+	0.626822i	0.193888	+	0.0629980i
$100$		0			0
$101$	−2.16400	−	2.97849i	−0.215326	−	0.296371i	0.687667	−	0.726026i	$-0.258635\pi$
$101$	−2.16400	−	2.97849i	−0.215326	−	0.296371i	−0.902993	+	0.429655i	$0.858635\pi$
$102$		0			0
$103$	−3.73549	+	2.71399i	−0.368069	+	0.267418i	−0.756410	−	0.654098i	$-0.773048\pi$
$103$	−3.73549	+	2.71399i	−0.368069	+	0.267418i	0.388341	+	0.921516i	$0.373048\pi$
$104$		0			0
$105$	−1.29591	−	0.941535i	−0.126468	−	0.0918844i
$106$		0			0
$107$	−1.10062	+	0.799649i	−0.106401	+	0.0773050i	−0.639714	−	0.768613i	$-0.720947\pi$
$107$	−1.10062	+	0.799649i	−0.106401	+	0.0773050i	0.533312	+	0.845918i	$0.320947\pi$
$108$		0			0
$109$			10.0640i			0.963956i	0.876183	+	0.481978i	$0.160081\pi$
$109$			10.0640i			0.963956i	−0.876183	+	0.481978i	$0.839919\pi$
$110$		0			0
$111$	−2.72007	+	0.883805i	−0.258178	+	0.0838871i
$112$		0			0
$113$	0.254840	−	0.784317i	0.0239733	−	0.0737823i	−0.938354	−	0.345676i	$-0.887650\pi$
$113$	0.254840	−	0.784317i	0.0239733	−	0.0737823i	0.962327	+	0.271893i	$0.0876498\pi$
$114$		0			0
$115$	0.419413	−	1.29082i	0.0391105	−	0.120370i
$116$		0			0
$117$	1.63238	−	2.24677i	0.150913	−	0.207714i
$118$		0			0
$119$	1.43458	+	4.41518i	0.131508	+	0.404739i
$120$		0			0
$121$	−3.23081	−	2.34732i	−0.293710	−	0.213392i
$122$		0			0
$123$	8.68510	+	4.01868i	0.783109	+	0.362352i
$124$		0			0
$125$	−7.67487	−	5.57612i	−0.686461	−	0.498743i
$126$		0			0
$127$	4.02156	+	12.3771i	0.356856	+	1.09829i	0.954926	+	0.296845i	$0.0959345\pi$
$127$	4.02156	+	12.3771i	0.356856	+	1.09829i	−0.598070	+	0.801444i	$0.704066\pi$
$128$		0			0
$129$	1.93958	−	2.66960i	0.170770	−	0.235045i
$130$		0			0
$131$	4.55842	−	14.0294i	0.398271	−	1.22575i	−0.528114	−	0.849174i	$-0.677101\pi$
$131$	4.55842	−	14.0294i	0.398271	−	1.22575i	0.926385	−	0.376578i	$-0.122899\pi$
$132$		0			0
$133$	−2.47604	+	7.62046i	−0.214700	+	0.660777i
$134$		0			0
$135$	5.73775	−	1.86431i	0.493827	−	0.160454i
$136$		0			0
$137$		−	17.2129i		−	1.47060i	−0.677743	−	0.735298i	$-0.737042\pi$
$137$		−	17.2129i		−	1.47060i	0.677743	−	0.735298i	$-0.262958\pi$
$138$		0			0
$139$	6.36351	−	4.62336i	0.539746	−	0.392148i	−0.284245	−	0.958752i	$-0.591743\pi$
$139$	6.36351	−	4.62336i	0.539746	−	0.392148i	0.823991	+	0.566603i	$0.191743\pi$
$140$		0			0
$141$	8.46984	+	6.15370i	0.713289	+	0.518235i
$142$		0			0
$143$	7.76066	−	5.63845i	0.648979	−	0.471511i
$144$		0			0
$145$	−3.68404	−	5.07065i	−0.305943	−	0.421095i
$146$		0			0
$147$	−1.42140	−	0.461841i	−0.117235	−	0.0380920i
$148$		0			0
$149$	−8.05944	+	2.61867i	−0.660255	+	0.214530i	−0.619930	−	0.784657i	$-0.712839\pi$
$149$	−8.05944	+	2.61867i	−0.660255	+	0.214530i	−0.0403246	+	0.999187i	$0.512839\pi$
$150$		0			0
$151$	3.14927	−	4.33459i	0.256284	−	0.352744i	−0.661416	−	0.750019i	$-0.730044\pi$
$151$	3.14927	−	4.33459i	0.256284	−	0.352744i	0.917700	+	0.397275i	$0.130044\pi$
$152$		0			0
$153$	−3.38345	−	1.09935i	−0.273536	−	0.0888771i
$154$		0			0
$155$	0.410302			0.0329562
$156$		0			0
$157$	5.33909	+	7.34863i	0.426106	+	0.586485i	0.967054	−	0.254571i	$-0.0819344\pi$
$157$	5.33909	+	7.34863i	0.426106	+	0.586485i	−0.540948	+	0.841056i	$0.681934\pi$
$158$		0			0
$159$	−0.162990	−	0.501632i	−0.0129260	−	0.0397820i
$160$		0			0
$161$		−	1.26635i		−	0.0998021i
$162$		0			0
$163$	−24.5690			−1.92439			−0.962197	−	0.272355i	$-0.912197\pi$
$163$	−24.5690			−1.92439			−0.962197	+	0.272355i	$0.912197\pi$
$164$		0			0
$165$	4.24002			0.330085
$166$		0			0
$167$		−	9.31857i		−	0.721093i	−0.932741	−	0.360546i	$-0.882590\pi$
$167$		−	9.31857i		−	0.721093i	0.932741	−	0.360546i	$-0.117410\pi$
$168$		0			0
$169$	−0.0412563	−	0.126974i	−0.00317356	−	0.00976721i
$170$		0			0
$171$	−3.60915	−	4.96756i	−0.275998	−	0.379879i
$172$		0			0
$173$	−7.25967			−0.551942			−0.275971	−	0.961166i	$-0.588999\pi$
$173$	−7.25967			−0.551942			−0.275971	+	0.961166i	$0.588999\pi$
$174$		0			0
$175$	−3.66278	−	1.19011i	−0.276880	−	0.0899639i
$176$		0			0
$177$	−12.8241	+	17.6508i	−0.963917	+	1.32672i
$178$		0			0
$179$	−15.2904	+	4.96816i	−1.14286	+	0.371338i	−0.818449	−	0.574579i	$-0.805166\pi$
$179$	−15.2904	+	4.96816i	−1.14286	+	0.371338i	−0.324411	+	0.945916i	$0.605166\pi$
$180$		0			0
$181$	−22.6258	−	7.35156i	−1.68176	−	0.546438i	−0.696510	−	0.717547i	$-0.745265\pi$
$181$	−22.6258	−	7.35156i	−1.68176	−	0.546438i	−0.985252	+	0.171110i	$0.945265\pi$
$182$		0			0
$183$	11.5601	+	15.9111i	0.854546	+	1.17618i
$184$		0			0
$185$	1.65932	−	1.20556i	0.121995	−	0.0886348i
$186$		0			0
$187$	−9.94146	−	7.22290i	−0.726992	−	0.528190i
$188$		0			0
$189$	4.55392	−	3.30862i	0.331249	−	0.240666i
$190$		0			0
$191$			1.43742i			0.104008i	0.998647	+	0.0520039i	$0.0165608\pi$
$191$			1.43742i			0.104008i	−0.998647	+	0.0520039i	$0.983439\pi$
$192$		0			0
$193$	14.3423	−	4.66009i	1.03238	−	0.335440i	0.256649	−	0.966505i	$-0.417382\pi$
$193$	14.3423	−	4.66009i	1.03238	−	0.335440i	0.775730	+	0.631064i	$0.217382\pi$
$194$		0			0
$195$	1.79387	−	5.52096i	0.128461	−	0.395364i
$196$		0			0
$197$	1.23566	−	3.80297i	0.0880371	−	0.270950i	−0.897339	−	0.441341i	$-0.854503\pi$
$197$	1.23566	−	3.80297i	0.0880371	−	0.270950i	0.985377	+	0.170391i	$0.0545029\pi$
$198$		0			0
$199$	−15.1894	+	20.9064i	−1.07675	+	1.48202i	−0.213697	+	0.976900i	$0.568551\pi$
$199$	−15.1894	+	20.9064i	−1.07675	+	1.48202i	−0.863051	+	0.505117i	$0.831449\pi$
$200$		0			0
$201$	−2.00841	−	6.18124i	−0.141662	−	0.435991i
$202$		0			0
$203$	−4.73104	−	3.43730i	−0.332054	−	0.241251i
$204$		0			0
$205$	−6.81406	−	0.816197i	−0.475914	−	0.0570057i
$206$		0			0
$207$	0.785093	+	0.570404i	0.0545678	+	0.0396458i
$208$		0			0
$209$	−6.55402	−	20.1712i	−0.453351	−	1.39527i
$210$		0			0
$211$	7.18518	−	9.88955i	0.494648	−	0.680825i	−0.486589	−	0.873631i	$-0.661759\pi$
$211$	7.18518	−	9.88955i	0.494648	−	0.680825i	0.981237	+	0.192807i	$0.0617590\pi$
$212$		0			0
$213$	−2.45347	+	7.55101i	−0.168109	+	0.517387i
$214$		0			0
$215$	−0.731254	+	2.25057i	−0.0498711	+	0.153487i
$216$		0			0
$217$	0.364085	−	0.118298i	0.0247157	−	0.00803061i
$218$		0			0
$219$		−	5.01082i		−	0.338600i
$220$		0			0
$221$	−13.6110	+	9.88897i	−0.915575	+	0.665204i
$222$		0			0
$223$	9.94843	+	7.22796i	0.666196	+	0.484020i	0.868750	−	0.495251i	$-0.164924\pi$
$223$	9.94843	+	7.22796i	0.666196	+	0.484020i	−0.202554	+	0.979271i	$0.564924\pi$
$224$		0			0
$225$	2.38767	−	1.73474i	0.159178	−	0.115649i
$226$		0			0
$227$	4.20407	+	5.78640i	0.279034	+	0.384057i	0.925414	−	0.378959i	$-0.123718\pi$
$227$	4.20407	+	5.78640i	0.279034	+	0.384057i	−0.646380	+	0.763016i	$0.723718\pi$
$228$		0			0
$229$	−24.3949	−	7.92638i	−1.61206	−	0.523790i	−0.642009	−	0.766697i	$-0.721899\pi$
$229$	−24.3949	−	7.92638i	−1.61206	−	0.523790i	−0.970050	+	0.242907i	$0.921899\pi$
$230$		0			0
$231$	3.76242	−	1.22248i	0.247549	−	0.0804336i
$232$		0			0
$233$	11.3959	−	15.6851i	0.746570	−	1.02757i	−0.251644	−	0.967820i	$-0.580971\pi$
$233$	11.3959	−	15.6851i	0.746570	−	1.02757i	0.998214	−	0.0597454i	$-0.0190289\pi$
$234$		0			0
$235$	−7.14037	−	2.32005i	−0.465787	−	0.151343i
$236$		0			0
$237$	−15.4383			−1.00282
$238$		0			0
$239$	1.52483	+	2.09875i	0.0986331	+	0.135757i	0.855481	−	0.517834i	$-0.173262\pi$
$239$	1.52483	+	2.09875i	0.0986331	+	0.135757i	−0.756848	+	0.653591i	$0.773262\pi$
$240$		0			0
$241$	−2.30328	−	7.08875i	−0.148367	−	0.456627i	0.849062	−	0.528294i	$-0.177168\pi$
$241$	−2.30328	−	7.08875i	−0.148367	−	0.456627i	−0.997429	+	0.0716672i	$0.977168\pi$
$242$		0			0
$243$			7.74951i			0.497131i
$244$		0			0
$245$	1.07178			0.0684738
$246$		0			0
$247$	−29.0379			−1.84764
$248$		0			0
$249$		−	2.90272i		−	0.183952i
$250$		0			0
$251$	5.86948	+	18.0644i	0.370478	+	1.14021i	0.946479	+	0.322766i	$0.104613\pi$
$251$	5.86948	+	18.0644i	0.370478	+	1.14021i	−0.576001	+	0.817449i	$0.695387\pi$
$252$		0			0
$253$	1.97025	+	2.71182i	0.123869	+	0.170491i
$254$		0			0
$255$	−7.43634			−0.465682
$256$		0			0
$257$	−8.20644	−	2.66644i	−0.511904	−	0.166328i	0.0416640	−	0.999132i	$-0.486734\pi$
$257$	−8.20644	−	2.66644i	−0.511904	−	0.166328i	−0.553568	+	0.832804i	$0.686734\pi$
$258$		0			0
$259$	1.12482	−	1.54818i	0.0698929	−	0.0961993i
$260$		0			0
$261$	4.26203	−	1.38482i	0.263813	−	0.0857180i
$262$		0			0
$263$	27.7928	+	9.03043i	1.71378	+	0.556840i	0.990955	−	0.134193i	$-0.0428442\pi$
$263$	27.7928	+	9.03043i	1.71378	+	0.556840i	0.722823	+	0.691033i	$0.242844\pi$
$264$		0			0
$265$	0.222328	+	0.306009i	0.0136575	+	0.0187980i
$266$		0			0
$267$	−2.61906	+	1.90286i	−0.160284	+	0.116453i
$268$		0			0
$269$	10.9080	+	7.92512i	0.665072	+	0.483203i	0.868372	−	0.495913i	$-0.165167\pi$
$269$	10.9080	+	7.92512i	0.665072	+	0.483203i	−0.203300	+	0.979117i	$0.565167\pi$
$270$		0			0
$271$	5.80370	−	4.21663i	0.352550	−	0.256142i	−0.397388	−	0.917651i	$-0.630083\pi$
$271$	5.80370	−	4.21663i	0.352550	−	0.256142i	0.749938	+	0.661508i	$0.230083\pi$
$272$		0			0
$273$		−	5.41627i		−	0.327808i
$274$		0			0
$275$	9.69532	−	3.15020i	0.584650	−	0.189964i
$276$		0			0
$277$	−8.00344	+	24.6321i	−0.480880	+	1.48000i	0.356980	+	0.934112i	$0.383807\pi$
$277$	−8.00344	+	24.6321i	−0.480880	+	1.48000i	−0.837860	+	0.545885i	$0.816193\pi$
$278$		0			0
$279$	−0.0906545	+	0.279006i	−0.00542735	+	0.0167037i
$280$		0			0
$281$	−1.19229	+	1.64104i	−0.0711259	+	0.0978964i	−0.843098	−	0.537760i	$-0.819271\pi$
$281$	−1.19229	+	1.64104i	−0.0711259	+	0.0978964i	0.771972	+	0.635657i	$0.219271\pi$
$282$		0			0
$283$	−0.273225	−	0.840902i	−0.0162416	−	0.0499864i	0.942607	−	0.333903i	$-0.108366\pi$
$283$	−0.273225	−	0.840902i	−0.0162416	−	0.0499864i	−0.958849	+	0.283917i	$0.908366\pi$
$284$		0			0
$285$	−10.3836	−	7.54416i	−0.615074	−	0.446877i
$286$		0			0
$287$	−6.28184	+	1.24037i	−0.370805	+	0.0732168i
$288$		0			0
$289$	3.68249	+	2.67549i	0.216617	+	0.157382i
$290$		0			0
$291$	2.05993	+	6.33982i	0.120755	+	0.371647i
$292$		0			0
$293$	−17.0897	+	23.5219i	−0.998390	+	1.37417i	−0.0720823	+	0.997399i	$0.522964\pi$
$293$	−17.0897	+	23.5219i	−0.998390	+	1.37417i	−0.926308	+	0.376767i	$0.877036\pi$
$294$		0			0
$295$	4.83489	−	14.8803i	0.281498	−	0.866363i
$296$		0			0
$297$	−4.60427	+	14.1705i	−0.267167	+	0.822255i
$298$		0			0
$299$	4.36465	−	1.41816i	0.252414	−	0.0820143i
$300$		0			0
$301$			2.20790i			0.127261i
$302$		0			0
$303$	4.45150	−	3.23421i	0.255732	−	0.185800i
$304$		0			0
$305$	−11.4103	−	8.29006i	−0.653351	−	0.474688i
$306$		0			0
$307$	−21.9244	+	15.9290i	−1.25129	+	0.909119i	−0.998296	−	0.0583482i	$-0.981417\pi$
$307$	−21.9244	+	15.9290i	−1.25129	+	0.909119i	−0.252998	+	0.967467i	$0.581417\pi$
$308$		0			0
$309$	−4.05619	−	5.58287i	−0.230749	−	0.317599i
$310$		0			0
$311$	9.43566	+	3.06583i	0.535047	+	0.173847i	0.564063	−	0.825732i	$-0.309237\pi$
$311$	9.43566	+	3.06583i	0.535047	+	0.173847i	−0.0290161	+	0.999579i	$0.509237\pi$
$312$		0			0
$313$	−24.0323	+	7.80856i	−1.35839	+	0.441366i	−0.895504	−	0.445054i	$-0.853184\pi$
$313$	−24.0323	+	7.80856i	−1.35839	+	0.441366i	−0.462881	+	0.886420i	$0.653184\pi$
$314$		0			0
$315$	−0.482767	+	0.664471i	−0.0272008	+	0.0374387i
$316$		0			0
$317$	13.5051	+	4.38808i	0.758523	+	0.246459i	0.662644	−	0.748934i	$-0.269434\pi$
$317$	13.5051	+	4.38808i	0.758523	+	0.246459i	0.0958782	+	0.995393i	$0.469434\pi$
$318$		0			0
$319$	15.4792			0.866671
$320$		0			0
$321$	−1.19511	−	1.64493i	−0.0667048	−	0.0918113i
$322$		0			0
$323$	11.4947	+	35.3772i	0.639584	+	1.96844i
$324$		0			0
$325$		−	13.9571i		−	0.774201i
$326$		0			0
$327$	−15.0411			−0.831777
$328$		0			0
$329$	−7.00499			−0.386197
$330$		0			0
$331$		−	19.5106i		−	1.07240i	−0.844090	−	0.536201i	$-0.819859\pi$
$331$		−	19.5106i		−	1.07240i	0.844090	−	0.536201i	$-0.180141\pi$
$332$		0			0
$333$	0.453166	+	1.39470i	0.0248334	+	0.0764292i
$334$		0			0
$335$	2.73958	+	3.77071i	0.149679	+	0.206016i
$336$		0			0
$337$	−9.25542			−0.504175			−0.252088	−	0.967704i	$-0.581117\pi$
$337$	−9.25542			−0.504175			−0.252088	+	0.967704i	$0.581117\pi$
$338$		0			0
$339$	1.17220	+	0.380871i	0.0636652	+	0.0206861i
$340$		0			0
$341$	−0.595615	+	0.819793i	−0.0322543	+	0.0443943i
$342$		0			0
$343$	0.951057	−	0.309017i	0.0513522	−	0.0166853i
$344$		0			0
$345$	1.92920	+	0.626834i	0.103864	+	0.0337476i
$346$		0			0
$347$	−19.0582	−	26.2313i	−1.02310	−	1.40817i	−0.910010	−	0.414586i	$-0.863926\pi$
$347$	−19.0582	−	26.2313i	−1.02310	−	1.40817i	−0.113086	−	0.993585i	$-0.536074\pi$
$348$		0			0
$349$	−9.23809	+	6.71186i	−0.494504	+	0.359278i	−0.806914	−	0.590669i	$-0.798864\pi$
$349$	−9.23809	+	6.71186i	−0.494504	+	0.359278i	0.312410	+	0.949947i	$0.398864\pi$
$350$		0			0
$351$	16.5035	+	11.9905i	0.880891	+	0.640005i
$352$		0			0
$353$	25.8668	−	18.7933i	1.37675	−	1.00027i	0.379576	−	0.925161i	$-0.376070\pi$
$353$	25.8668	−	18.7933i	1.37675	−	1.00027i	0.997175	−	0.0751078i	$-0.0239301\pi$
$354$		0			0
$355$		−	5.69371i		−	0.302191i
$356$		0			0
$357$	−6.59870	+	2.14405i	−0.349240	+	0.113475i
$358$		0			0
$359$	6.53482	−	20.1121i	0.344895	−	1.06148i	−0.616745	−	0.787163i	$-0.711549\pi$
$359$	6.53482	−	20.1121i	0.344895	−	1.06148i	0.961640	−	0.274314i	$-0.0884508\pi$
$360$		0			0
$361$	−13.9682	+	42.9898i	−0.735169	+	2.26262i
$362$		0			0
$363$	3.50818	−	4.82860i	0.184132	−	0.253436i
$364$		0			0
$365$	1.11042	+	3.41753i	0.0581222	+	0.178882i
$366$		0			0
$367$	19.5162	+	14.1794i	1.01874	+	0.740157i	0.966024	−	0.258452i	$-0.0832125\pi$
$367$	19.5162	+	14.1794i	1.01874	+	0.740157i	0.0527151	+	0.998610i	$0.483212\pi$
$368$		0			0
$369$	2.06056	−	4.45324i	0.107268	−	0.231826i
$370$		0			0
$371$	0.285514	+	0.207438i	0.0148231	+	0.0107696i
$372$		0			0
$373$	−2.04184	−	6.28415i	−0.105723	−	0.325381i	0.884177	−	0.467153i	$-0.154720\pi$
$373$	−2.04184	−	6.28415i	−0.105723	−	0.325381i	−0.989899	+	0.141772i	$0.954720\pi$
$374$		0			0
$375$	8.33378	−	11.4705i	0.430355	−	0.592333i
$376$		0			0
$377$	6.54895	−	20.1556i	0.337288	−	1.03807i
$378$		0			0
$379$	−11.5492	+	35.5449i	−0.593245	+	1.82582i	−0.0299690	+	0.999551i	$0.509541\pi$
$379$	−11.5492	+	35.5449i	−0.593245	+	1.82582i	−0.563276	+	0.826269i	$0.690459\pi$
$380$		0			0
$381$	−18.4982	+	6.01042i	−0.947690	+	0.307923i
$382$		0			0
$383$			6.44871i			0.329514i	0.986334	+	0.164757i	$0.0526839\pi$
$383$			6.44871i			0.329514i	−0.986334	+	0.164757i	$0.947316\pi$
$384$		0			0
$385$	−2.29517	+	1.66754i	−0.116973	+	0.0849858i
$386$		0			0
$387$	−1.36882	−	0.994508i	−0.0695812	−	0.0505537i
$388$		0			0
$389$	−12.2445	+	8.89612i	−0.620819	+	0.451051i	−0.853207	−	0.521572i	$-0.825346\pi$
$389$	−12.2445	+	8.89612i	−0.620819	+	0.451051i	0.232389	+	0.972623i	$0.425346\pi$
$390$		0			0
$391$	−3.45552	−	4.75611i	−0.174753	−	0.240527i
$392$		0			0
$393$	20.9676	+	6.81278i	1.05768	+	0.343659i
$394$		0			0
$395$	10.5294	−	3.42119i	0.529789	−	0.172139i
$396$		0			0
$397$	6.47932	−	8.91801i	0.325188	−	0.447582i	−0.614855	−	0.788640i	$-0.710785\pi$
$397$	6.47932	−	8.91801i	0.325188	−	0.447582i	0.940042	+	0.341058i	$0.110785\pi$
$398$		0			0
$399$	−11.3891	−	3.70056i	−0.570171	−	0.185260i
$400$		0			0
$401$	−8.93915			−0.446400			−0.223200	−	0.974773i	$-0.571650\pi$
$401$	−8.93915			−0.446400			−0.223200	+	0.974773i	$0.571650\pi$
$402$		0			0
$403$	0.815464	+	1.12239i	0.0406212	+	0.0559103i
$404$		0			0
$405$	2.02488	+	6.23195i	0.100617	+	0.309668i
$406$		0			0
$407$			5.06541i			0.251083i
$408$		0			0
$409$	25.6774			1.26967			0.634834	−	0.772649i	$-0.281069\pi$
$409$	25.6774			1.26967			0.634834	+	0.772649i	$0.281069\pi$
$410$		0			0
$411$	25.7255			1.26895
$412$		0			0
$413$		−	14.5981i		−	0.718327i
$414$		0			0
$415$	0.643257	+	1.97974i	0.0315763	+	0.0971817i
$416$		0			0
$417$	6.90984	+	9.51058i	0.338376	+	0.465735i
$418$		0			0
$419$	25.5619			1.24878			0.624389	−	0.781113i	$-0.285348\pi$
$419$	25.5619			1.24878			0.624389	+	0.781113i	$0.285348\pi$
$420$		0			0
$421$	11.7297	+	3.81120i	0.571669	+	0.185747i	0.580565	−	0.814214i	$-0.302832\pi$
$421$	11.7297	+	3.81120i	0.571669	+	0.185747i	−0.00889582	+	0.999960i	$0.502832\pi$
$422$		0			0
$423$	3.15528	−	4.34286i	0.153415	−	0.211157i
$424$		0			0
$425$	−17.0041	+	5.52496i	−0.824819	+	0.268000i
$426$		0			0
$427$	−12.5152	−	4.06644i	−0.605654	−	0.196789i
$428$		0			0
$429$	8.42694	+	11.5987i	0.406857	+	0.559990i
$430$		0			0
$431$	5.35102	−	3.88774i	0.257750	−	0.187266i	−0.451405	−	0.892319i	$-0.649077\pi$
$431$	5.35102	−	3.88774i	0.257750	−	0.187266i	0.709154	+	0.705053i	$0.249077\pi$
$432$		0			0
$433$	−19.1414	−	13.9070i	−0.919877	−	0.668330i	0.0236163	−	0.999721i	$-0.492482\pi$
$433$	−19.1414	−	13.9070i	−0.919877	−	0.668330i	−0.943493	+	0.331391i	$0.892482\pi$
$434$		0			0
$435$	7.57834	−	5.50599i	0.363354	−	0.263992i
$436$		0			0
$437$		−	10.1468i		−	0.485385i
$438$		0			0
$439$	5.75343	−	1.86940i	0.274596	−	0.0892217i	−0.168482	−	0.985705i	$-0.553886\pi$
$439$	5.75343	−	1.86940i	0.274596	−	0.0892217i	0.443078	+	0.896483i	$0.353886\pi$
$440$		0			0
$441$	−0.236806	+	0.728815i	−0.0112765	+	0.0347055i
$442$		0			0
$443$	−2.20782	+	6.79497i	−0.104897	+	0.322839i	−0.989706	−	0.143114i	$-0.954288\pi$
$443$	−2.20782	+	6.79497i	−0.104897	+	0.322839i	0.884809	+	0.465953i	$0.154288\pi$
$444$		0			0
$445$	1.36459	−	1.87820i	0.0646880	−	0.0890353i
$446$		0			0
$447$	−3.91373	−	12.0452i	−0.185113	−	0.569720i
$448$		0			0
$449$	26.2350	+	19.0608i	1.23810	+	0.899536i	0.997471	−	0.0710801i	$-0.0226446\pi$
$449$	26.2350	+	19.0608i	1.23810	+	0.899536i	0.240634	+	0.970616i	$0.422645\pi$
$450$		0			0
$451$	11.5224	−	12.4298i	0.542569	−	0.585298i
$452$		0			0
$453$	6.47826	+	4.70673i	0.304375	+	0.221142i
$454$		0			0
$455$	1.20027	+	3.69406i	0.0562697	+	0.173180i
$456$		0			0
$457$	−7.74914	+	10.6658i	−0.362489	+	0.498924i	−0.950840	−	0.309682i	$-0.899777\pi$
$457$	−7.74914	+	10.6658i	−0.362489	+	0.498924i	0.588351	+	0.808606i	$0.299777\pi$
$458$		0			0
$459$	8.07518	−	24.8528i	0.376917	−	1.16003i
$460$		0			0
$461$	−8.90930	+	27.4200i	−0.414948	+	1.27708i	0.497350	+	0.867550i	$0.334306\pi$
$461$	−8.90930	+	27.4200i	−0.414948	+	1.27708i	−0.912298	+	0.409527i	$0.865694\pi$
$462$		0			0
$463$	−22.4730	+	7.30193i	−1.04441	+	0.339349i	−0.780472	−	0.625190i	$-0.785021\pi$
$463$	−22.4730	+	7.30193i	−1.04441	+	0.339349i	−0.263938	+	0.964540i	$0.585021\pi$
$464$		0			0
$465$			0.613216i			0.0284372i
$466$		0			0
$467$	−27.6492	+	20.0883i	−1.27945	+	0.929577i	−0.999536	−	0.0304473i	$-0.990307\pi$
$467$	−27.6492	+	20.0883i	−1.27945	+	0.929577i	−0.279917	+	0.960024i	$0.590307\pi$
$468$		0			0
$469$	3.51817	+	2.55610i	0.162454	+	0.118030i
$470$		0			0
$471$	−10.9829	+	7.97954i	−0.506065	+	0.367678i
$472$		0			0
$473$	−3.43517	−	4.72810i	−0.157949	−	0.217398i
$474$		0			0
$475$	−29.3485	−	9.53591i	−1.34660	−	0.437537i
$476$		0			0
$477$	−0.257209	+	0.0835723i	−0.0117768	+	0.00382651i
$478$		0			0
$479$	3.62426	−	4.98836i	0.165597	−	0.227924i	−0.718152	−	0.695886i	$-0.755012\pi$
$479$	3.62426	−	4.98836i	0.165597	−	0.227924i	0.883748	+	0.467962i	$0.155012\pi$
$480$		0			0
$481$	6.59570	+	2.14307i	0.300738	+	0.0977157i
$482$		0			0
$483$	1.89262			0.0861171
$484$		0			0
$485$	−2.80987	−	3.86746i	−0.127590	−	0.175612i
$486$		0			0
$487$	−0.0479182	−	0.147477i	−0.00217138	−	0.00668282i	0.949965	−	0.312356i	$-0.101118\pi$
$487$	−0.0479182	−	0.147477i	−0.00217138	−	0.00668282i	−0.952136	+	0.305674i	$0.901118\pi$
$488$		0			0
$489$		−	36.7196i		−	1.66052i
$490$		0			0
$491$	11.0131			0.497012			0.248506	−	0.968630i	$-0.420060\pi$
$491$	11.0131			0.497012			0.248506	+	0.968630i	$0.420060\pi$
$492$		0			0
$493$	−27.1482			−1.22269
$494$		0			0
$495$		−	2.17405i		−	0.0977162i
$496$		0			0
$497$	−1.64161	−	5.05236i	−0.0736364	−	0.226630i
$498$		0			0
$499$	0.354823	+	0.488372i	0.0158841	+	0.0218625i	0.816885	−	0.576800i	$-0.195699\pi$
$499$	0.354823	+	0.488372i	0.0158841	+	0.0218625i	−0.801001	+	0.598663i	$0.795699\pi$
$500$		0			0
$501$	13.9271			0.622216
$502$		0			0
$503$	13.0882	+	4.25263i	0.583576	+	0.189615i	0.585902	−	0.810382i	$-0.300740\pi$
$503$	13.0882	+	4.25263i	0.583576	+	0.189615i	−0.00232615	+	0.999997i	$0.500740\pi$
$504$		0			0
$505$	−2.31934	+	3.19230i	−0.103209	+	0.142055i
$506$		0			0
$507$	0.189769	−	0.0616595i	0.00842792	−	0.00273840i
$508$		0			0
$509$	18.9828	+	6.16788i	0.841398	+	0.273387i	0.697839	−	0.716255i	$-0.254145\pi$
$509$	18.9828	+	6.16788i	0.841398	+	0.273387i	0.143559	+	0.989642i	$0.454145\pi$
$510$		0			0
$511$	1.97069	+	2.71242i	0.0871780	+	0.119990i
$512$		0			0
$513$	36.4888	−	26.5107i	1.61102	−	1.17048i
$514$		0			0
$515$	4.00364	+	2.90881i	0.176421	+	0.128178i
$516$		0			0
$517$	15.0008	−	10.8988i	0.659736	−	0.479327i
$518$		0			0
$519$		−	10.8499i		−	0.476259i
$520$		0			0
$521$	29.1020	−	9.45580i	1.27498	−	0.414266i	0.408170	−	0.912906i	$-0.366167\pi$
$521$	29.1020	−	9.45580i	1.27498	−	0.414266i	0.866809	+	0.498640i	$0.166167\pi$
$522$		0			0
$523$	−6.49194	+	19.9801i	−0.283873	+	0.873670i	0.702862	+	0.711327i	$0.251905\pi$
$523$	−6.49194	+	19.9801i	−0.283873	+	0.873670i	−0.986734	+	0.162344i	$0.948095\pi$
$524$		0			0
$525$	1.77868	−	5.47421i	0.0776279	−	0.238914i
$526$		0			0
$527$	1.04462	−	1.43779i	0.0455042	−	0.0626311i
$528$		0			0
$529$	−6.61184	−	20.3492i	−0.287471	−	0.884746i
$530$		0			0
$531$	9.05036	+	6.57547i	0.392752	+	0.285351i
$532$		0			0
$533$	−11.3100	−	20.2622i	−0.489892	−	0.877653i
$534$		0			0
$535$	1.17963	+	0.857051i	0.0509998	+	0.0370535i
$536$		0			0
$537$	−7.42516	−	22.8523i	−0.320419	−	0.986149i
$538$		0			0
$539$	−1.55586	+	2.14145i	−0.0670155	+	0.0922389i
$540$		0			0
$541$	9.28748	−	28.5839i	0.399300	−	1.22892i	−0.526262	−	0.850323i	$-0.676407\pi$
$541$	9.28748	−	28.5839i	0.399300	−	1.22892i	0.925562	−	0.378596i	$-0.123593\pi$
$542$		0			0
$543$	10.9873	−	33.8154i	0.471509	−	1.45116i
$544$		0			0
$545$	10.2585	−	3.33319i	0.439426	−	0.142778i
$546$		0			0
$547$			9.93488i			0.424785i	0.977184	+	0.212392i	$0.0681255\pi$
$547$			9.93488i			0.424785i	−0.977184	+	0.212392i	$0.931875\pi$
$548$		0			0
$549$	8.15832	−	5.92737i	0.348189	−	0.252974i
$550$		0			0
$551$	−37.9080	−	27.5418i	−1.61494	−	1.17332i
$552$		0			0
$553$	8.35691	−	6.07165i	0.355372	−	0.258193i
$554$		0			0
$555$	1.80177	+	2.47993i	0.0764810	+	0.105267i
$556$		0			0
$557$	38.0995	+	12.3793i	1.61433	+	0.524527i	0.970594	−	0.240722i	$-0.0773841\pi$
$557$	38.0995	+	12.3793i	1.61433	+	0.524527i	0.643735	+	0.765249i	$0.277384\pi$
$558$		0			0
$559$	−7.60984	+	2.47259i	−0.321862	+	0.104579i
$560$		0			0
$561$	10.7950	−	14.8580i	0.455764	−	0.627306i
$562$		0			0
$563$	−36.4224	−	11.8343i	−1.53502	−	0.498758i	−0.585023	−	0.811017i	$-0.698914\pi$
$563$	−36.4224	−	11.8343i	−1.53502	−	0.498758i	−0.949997	+	0.312259i	$0.898914\pi$
$564$		0			0
$565$	−0.883878			−0.0371850
$566$		0			0
$567$	3.59359	+	4.94616i	0.150917	+	0.207719i
$568$		0			0
$569$	13.6926	+	42.1416i	0.574025	+	1.76667i	0.639474	+	0.768813i	$0.279152\pi$
$569$	13.6926	+	42.1416i	0.574025	+	1.76667i	−0.0654484	+	0.997856i	$0.520848\pi$
$570$		0			0
$571$		−	26.7725i		−	1.12039i	−0.828360	−	0.560196i	$-0.810726\pi$
$571$		−	26.7725i		−	1.12039i	0.828360	−	0.560196i	$-0.189274\pi$
$572$		0			0
$573$	−2.14829			−0.0897462
$574$		0			0
$575$	4.87705			0.203387
$576$		0			0
$577$		−	15.8434i		−	0.659569i	−0.944056	−	0.329784i	$-0.893024\pi$
$577$		−	15.8434i		−	0.659569i	0.944056	−	0.329784i	$-0.106976\pi$
$578$		0			0
$579$	6.96473	+	21.4352i	0.289444	+	0.890818i
$580$		0			0
$581$	1.14160	+	1.57128i	0.0473615	+	0.0651875i
$582$		0			0
$583$	−0.934157			−0.0386888
$584$		0			0
$585$	−2.83084	−	0.919795i	−0.117041	−	0.0380289i
$586$		0			0
$587$	−3.19870	+	4.40263i	−0.132024	+	0.181716i	−0.869911	−	0.493209i	$-0.835824\pi$
$587$	−3.19870	+	4.40263i	−0.132024	+	0.181716i	0.737887	+	0.674925i	$0.235824\pi$
$588$		0			0
$589$	2.91727	−	0.947879i	0.120204	−	0.0390567i
$590$		0			0
$591$	5.68373	+	1.84675i	0.233797	+	0.0759653i
$592$		0			0
$593$	2.98305	+	4.10582i	0.122499	+	0.168606i	0.865862	−	0.500282i	$-0.166770\pi$
$593$	2.98305	+	4.10582i	0.122499	+	0.168606i	−0.743363	+	0.668888i	$0.766770\pi$
$594$		0			0
$595$	4.02538	−	2.92461i	0.165024	−	0.119897i
$596$		0			0
$597$	−31.2457	−	22.7013i	−1.27880	−	0.929103i
$598$		0			0
$599$	5.09991	−	3.70530i	0.208377	−	0.151395i	−0.478702	−	0.877977i	$-0.658893\pi$
$599$	5.09991	−	3.70530i	0.208377	−	0.151395i	0.687079	+	0.726583i	$0.258893\pi$
$600$		0			0
$601$		−	11.2134i		−	0.457405i	−0.973496	−	0.228703i	$-0.926552\pi$
$601$		−	11.2134i		−	0.457405i	0.973496	−	0.228703i	$-0.0734484\pi$
$602$		0			0
$603$	−3.16939	+	1.02980i	−0.129068	+	0.0419366i
$604$		0			0
$605$	−1.32264	+	4.07068i	−0.0537731	+	0.165497i
$606$		0			0
$607$	−8.16809	+	25.1388i	−0.331532	+	1.02035i	0.636873	+	0.770969i	$0.280228\pi$
$607$	−8.16809	+	25.1388i	−0.331532	+	1.02035i	−0.968405	+	0.249383i	$0.919772\pi$
$608$		0			0
$609$	5.13722	−	7.07077i	0.208171	−	0.286522i
$610$		0			0
$611$	−7.84477	−	24.1437i	−0.317365	−	0.976750i
$612$		0			0
$613$	18.0075	+	13.0832i	0.727318	+	0.528427i	0.888714	−	0.458463i	$-0.151600\pi$
$613$	18.0075	+	13.0832i	0.727318	+	0.528427i	−0.161396	+	0.986890i	$0.551600\pi$
$614$		0			0
$615$	1.21985	−	10.1839i	0.0491890	−	0.410656i
$616$		0			0
$617$	12.6834	+	9.21502i	0.510614	+	0.370983i	0.813056	−	0.582185i	$-0.197802\pi$
$617$	12.6834	+	9.21502i	0.510614	+	0.370983i	−0.302442	+	0.953168i	$0.597802\pi$
$618$		0			0
$619$	10.9348	+	33.6538i	0.439506	+	1.35266i	0.888397	+	0.459075i	$0.151819\pi$
$619$	10.9348	+	33.6538i	0.439506	+	1.35266i	−0.448891	+	0.893587i	$0.648181\pi$
$620$		0			0
$621$	−4.18985	+	5.76684i	−0.168133	+	0.231415i
$622$		0			0
$623$	0.669360	−	2.06008i	0.0268173	−	0.0825353i
$624$		0			0
$625$	2.80858	−	8.64391i	0.112343	−	0.345756i
$626$		0			0
$627$	30.1469	−	9.79531i	1.20395	−	0.391187i
$628$		0			0
$629$		−	8.88395i		−	0.354226i
$630$		0			0
$631$	25.8383	−	18.7726i	1.02861	−	0.747327i	0.0605778	−	0.998163i	$-0.480706\pi$
$631$	25.8383	−	18.7726i	1.02861	−	0.747327i	0.968029	+	0.250837i	$0.0807057\pi$
$632$		0			0
$633$	14.7804	+	10.7386i	0.587469	+	0.426821i
$634$		0			0
$635$	11.2844	−	8.19857i	0.447806	−	0.325350i
$636$		0			0
$637$	2.13014	+	2.93189i	0.0843994	+	0.116166i
$638$		0			0
$639$	3.87174	+	1.25800i	0.153164	+	0.0497659i
$640$		0			0
$641$	11.5720	−	3.75996i	0.457065	−	0.148509i	−0.0714305	−	0.997446i	$-0.522756\pi$
$641$	11.5720	−	3.75996i	0.457065	−	0.148509i	0.528495	+	0.848936i	$0.322756\pi$
$642$		0			0
$643$	−18.4099	+	25.3391i	−0.726017	+	0.999277i	0.273286	+	0.961933i	$0.411890\pi$
$643$	−18.4099	+	25.3391i	−0.726017	+	0.999277i	−0.999302	+	0.0373436i	$0.988110\pi$
$644$		0			0
$645$	−3.36359	−	1.09290i	−0.132441	−	0.0430327i
$646$		0			0
$647$	−39.1174			−1.53787			−0.768933	−	0.639330i	$-0.779212\pi$
$647$	−39.1174			−1.53787			−0.768933	+	0.639330i	$0.779212\pi$
$648$		0			0
$649$	22.7126	+	31.2612i	0.891547	+	1.22711i
$650$		0			0
$651$	0.176803	+	0.544142i	0.00692944	+	0.0213266i
$652$		0			0
$653$			0.201913i			0.00790149i	0.999992	+	0.00395074i	$0.00125756\pi$
$653$			0.201913i			0.00790149i	−0.999992	+	0.00395074i	$0.998742\pi$
$654$		0			0
$655$	−15.8103			−0.617758
$656$		0			0
$657$	−2.56927			−0.100237
$658$		0			0
$659$			7.55689i			0.294375i	0.989109	+	0.147187i	$0.0470220\pi$
$659$			7.55689i			0.294375i	−0.989109	+	0.147187i	$0.952978\pi$
$660$		0			0
$661$	2.23852	+	6.88947i	0.0870685	+	0.267969i	0.985106	−	0.171950i	$-0.0550069\pi$
$661$	2.23852	+	6.88947i	0.0870685	+	0.267969i	−0.898037	+	0.439920i	$0.855007\pi$
$662$		0			0
$663$	−14.7796	−	20.3423i	−0.573990	−	0.790030i
$664$		0			0
$665$	8.58780			0.333021
$666$		0			0
$667$	7.04300	+	2.28841i	0.272706	+	0.0886076i
$668$		0			0
$669$	−10.8025	+	14.8684i	−0.417650	+	0.574846i
$670$		0			0
$671$	33.1275	−	10.7638i	1.27887	−	0.415531i
$672$		0			0
$673$	16.7791	+	5.45187i	0.646787	+	0.210154i	0.613997	−	0.789308i	$-0.289561\pi$
$673$	16.7791	+	5.45187i	0.646787	+	0.210154i	0.0327903	+	0.999462i	$0.489561\pi$
$674$		0			0
$675$	12.7424	+	17.5384i	0.490455	+	0.675054i
$676$		0			0
$677$	−22.0606	+	16.0279i	−0.847856	+	0.616004i	−0.924554	−	0.381051i	$-0.875562\pi$
$677$	−22.0606	+	16.0279i	−0.847856	+	0.616004i	0.0766977	+	0.997054i	$0.475562\pi$
$678$		0			0
$679$	−3.60843	−	2.62168i	−0.138479	−	0.100611i
$680$		0			0
$681$	−8.64806	+	6.28319i	−0.331395	+	0.240772i
$682$		0			0
$683$		−	14.8951i		−	0.569946i	−0.958536	−	0.284973i	$-0.908015\pi$
$683$		−	14.8951i		−	0.569946i	0.958536	−	0.284973i	$-0.0919846\pi$
$684$		0			0
$685$	−17.5456	+	5.70090i	−0.670382	+	0.217820i
$686$		0			0
$687$	11.8464	−	36.4594i	0.451967	−	1.39101i
$688$		0			0
$689$	−0.395223	+	1.21637i	−0.0150568	+	0.0463400i
$690$		0			0
$691$	18.4323	−	25.3699i	0.701199	−	0.965117i	−0.298743	−	0.954334i	$-0.596567\pi$
$691$	18.4323	−	25.3699i	0.701199	−	0.965117i	0.999942	−	0.0107838i	$-0.00343264\pi$
$692$		0			0
$693$	−0.626822	−	1.92916i	−0.0238110	−	0.0732827i
$694$		0			0
$695$	−6.82031	−	4.95524i	−0.258709	−	0.187963i
$696$		0			0
$697$	−20.2085	+	21.8000i	−0.765453	+	0.825734i
$698$		0			0
$699$	23.4422	+	17.0317i	0.886664	+	0.644199i
$700$		0			0
$701$	15.8600	+	48.8120i	0.599024	+	1.84361i	0.533581	+	0.845749i	$0.320846\pi$
$701$	15.8600	+	48.8120i	0.599024	+	1.84361i	0.0654431	+	0.997856i	$0.479154\pi$
$702$		0			0
$703$	9.01275	−	12.4050i	0.339922	−	0.467863i
$704$		0			0
$705$	3.46743	−	10.6716i	0.130591	−	0.401917i
$706$		0			0
$707$	−1.13768	+	3.50143i	−0.0427870	+	0.131685i
$708$		0			0
$709$	4.69926	−	1.52688i	0.176484	−	0.0573432i	−0.219442	−	0.975626i	$-0.570424\pi$
$709$	4.69926	−	1.52688i	0.176484	−	0.0573432i	0.395926	+	0.918282i	$0.370424\pi$
$710$		0			0
$711$			7.91588i			0.296869i
$712$		0			0
$713$	−0.392199	+	0.284949i	−0.0146880	+	0.0106714i
$714$		0			0
$715$	−8.31775	−	6.04320i	−0.311066	−	0.226003i
$716$		0			0
$717$	−3.13669	+	2.27894i	−0.117142	+	0.0851084i
$718$		0			0
$719$	−12.7738	−	17.5816i	−0.476381	−	0.655682i	0.501423	−	0.865202i	$-0.332810\pi$
$719$	−12.7738	−	17.5816i	−0.476381	−	0.655682i	−0.977804	+	0.209520i	$0.932810\pi$
$720$		0			0
$721$	4.39133	+	1.42683i	0.163542	+	0.0531379i
$722$		0			0
$723$	10.5945	−	3.44236i	0.394013	−	0.128023i
$724$		0			0
$725$	13.2380	−	18.2206i	0.491647	−	0.676694i
$726$		0			0
$727$	−35.8157	−	11.6372i	−1.32833	−	0.431601i	−0.442983	−	0.896530i	$-0.646080\pi$
$727$	−35.8157	−	11.6372i	−1.32833	−	0.431601i	−0.885348	+	0.464929i	$0.846080\pi$
$728$		0			0
$729$	−29.9234			−1.10827
$730$		0			0
$731$	6.02475	+	8.29236i	0.222834	+	0.306704i
$732$		0			0
$733$	2.68677	+	8.26904i	0.0992383	+	0.305424i	0.988335	−	0.152295i	$-0.0486665\pi$
$733$	2.68677	+	8.26904i	0.0992383	+	0.305424i	−0.889097	+	0.457719i	$0.848666\pi$
$734$		0			0
$735$			1.60183i			0.0590845i
$736$		0			0
$737$	−11.5109			−0.424010
$738$		0			0
$739$	20.8067			0.765386			0.382693	−	0.923875i	$-0.374997\pi$
$739$	20.8067			0.765386			0.382693	+	0.923875i	$0.374997\pi$
$740$		0			0
$741$		−	43.3986i		−	1.59429i
$742$		0			0
$743$	8.59140	+	26.4416i	0.315188	+	0.970048i	0.975677	+	0.219213i	$0.0703489\pi$
$743$	8.59140	+	26.4416i	0.315188	+	0.970048i	−0.660489	+	0.750835i	$0.729651\pi$
$744$		0			0
$745$	5.33856	+	7.34790i	0.195590	+	0.269206i
$746$		0			0
$747$	−1.48835			−0.0544560
$748$		0			0
$749$	1.29386	+	0.420400i	0.0472766	+	0.0153611i
$750$		0			0
$751$	4.78137	−	6.58100i	0.174475	−	0.240144i	−0.712820	−	0.701347i	$-0.752582\pi$
$751$	4.78137	−	6.58100i	0.174475	−	0.240144i	0.887294	+	0.461203i	$0.152582\pi$
$752$		0			0
$753$	−26.9981	+	8.77223i	−0.983867	+	0.319678i
$754$		0			0
$755$	−5.46140	−	1.77452i	−0.198761	−	0.0645813i
$756$		0			0
$757$	17.2372	+	23.7250i	0.626497	+	0.862299i	0.997806	−	0.0662108i	$-0.0210910\pi$
$757$	17.2372	+	23.7250i	0.626497	+	0.862299i	−0.371309	+	0.928509i	$0.621091\pi$
$758$		0			0
$759$	−4.05295	+	2.94464i	−0.147113	+	0.106884i
$760$		0			0
$761$	−6.42303	−	4.66661i	−0.232835	−	0.169164i	0.465250	−	0.885179i	$-0.345964\pi$
$761$	−6.42303	−	4.66661i	−0.232835	−	0.169164i	−0.698085	+	0.716015i	$0.745964\pi$
$762$		0			0
$763$	8.14194	−	5.91547i	0.294758	−	0.214154i
$764$		0			0
$765$			3.81294i			0.137857i
$766$		0			0
$767$	50.3146	−	16.3482i	1.81675	−	0.590299i
$768$		0			0
$769$	6.37070	−	19.6070i	0.229733	−	0.707047i	−0.768043	−	0.640398i	$-0.778769\pi$
$769$	6.37070	−	19.6070i	0.229733	−	0.707047i	0.997777	−	0.0666486i	$-0.0212306\pi$
$770$		0			0
$771$	3.98512	−	12.2649i	0.143521	−	0.441711i
$772$		0			0
$773$	21.3090	−	29.3293i	0.766430	−	1.05490i	−0.230222	−	0.973138i	$-0.573945\pi$
$773$	21.3090	−	29.3293i	0.766430	−	1.05490i	0.996652	−	0.0817620i	$-0.0260547\pi$
$774$		0			0
$775$	0.455600	+	1.40219i	0.0163656	+	0.0503682i
$776$		0			0
$777$	2.31383	+	1.68110i	0.0830083	+	0.0603090i
$778$		0			0
$779$	−50.3340	+	9.93862i	−1.80340	+	0.356088i
$780$		0			0
$781$	11.3762	+	8.26528i	0.407072	+	0.295755i
$782$		0			0
$783$	10.1721	+	31.3064i	0.363520	+	1.11880i
$784$		0			0
$785$	5.72235	−	7.87614i	0.204240	−	0.281112i
$786$		0			0
$787$	7.50785	−	23.1068i	0.267626	−	0.823668i	−0.723451	−	0.690376i	$-0.757445\pi$
$787$	7.50785	−	23.1068i	0.267626	−	0.823668i	0.991077	−	0.133292i	$-0.0425548\pi$
$788$		0			0
$789$	−13.4964	+	41.5377i	−0.480486	+	1.47878i
$790$		0			0
$791$	−0.784317	+	0.254840i	−0.0278871	+	0.00906106i
$792$		0			0
$793$		−	47.6894i		−	1.69350i
$794$		0			0
$795$	−0.457345	+	0.332281i	−0.0162204	+	0.0117848i
$796$		0			0
$797$	−1.59441	−	1.15841i	−0.0564768	−	0.0410328i	0.559189	−	0.829040i	$-0.311113\pi$
$797$	−1.59441	−	1.15841i	−0.0564768	−	0.0410328i	−0.615665	+	0.788008i	$0.711113\pi$
$798$		0			0
$799$	−26.3092	+	19.1147i	−0.930751	+	0.676230i
$800$		0			0
$801$	0.975680	+	1.34291i	0.0344740	+	0.0474493i
$802$		0			0
$803$	−8.44026	−	2.74241i	−0.297850	−	0.0967774i
$804$		0			0
$805$	−1.29082	+	0.419413i	−0.0454955	+	0.0147824i
$806$		0			0
$807$	−11.8445	+	16.3025i	−0.416946	+	0.573877i
$808$		0			0
$809$	23.9945	+	7.79629i	0.843602	+	0.274103i	0.698764	−	0.715353i	$-0.253734\pi$
$809$	23.9945	+	7.79629i	0.843602	+	0.274103i	0.144838	+	0.989455i	$0.453734\pi$
$810$		0			0
$811$	−44.6349			−1.56734			−0.783672	−	0.621175i	$-0.786656\pi$
$811$	−44.6349			−1.56734			−0.783672	+	0.621175i	$0.786656\pi$
$812$		0			0
$813$	6.30197	+	8.67392i	0.221020	+	0.304208i
$814$		0			0
$815$	8.13724	+	25.0439i	0.285035	+	0.877248i
$816$		0			0
$817$			17.6910i			0.618931i
$818$		0			0
$819$	−2.77716			−0.0970420
$820$		0			0
$821$	43.2229			1.50849			0.754245	−	0.656594i	$-0.228003\pi$
$821$	43.2229			1.50849			0.754245	+	0.656594i	$0.228003\pi$
$822$		0			0
$823$			28.0341i			0.977206i	0.872506	+	0.488603i	$0.162493\pi$
$823$			28.0341i			0.977206i	−0.872506	+	0.488603i	$0.837507\pi$
$824$		0			0
$825$	4.70813	+	14.4901i	0.163916	+	0.504482i
$826$		0			0
$827$	−14.8553	−	20.4466i	−0.516570	−	0.710998i	0.468440	−	0.883496i	$-0.344816\pi$
$827$	−14.8553	−	20.4466i	−0.516570	−	0.710998i	−0.985010	+	0.172497i	$0.944816\pi$
$828$		0			0
$829$	22.6329			0.786075			0.393037	−	0.919523i	$-0.371424\pi$
$829$	22.6329			0.786075			0.393037	+	0.919523i	$0.371424\pi$
$830$		0			0
$831$	−36.8138	−	11.9615i	−1.27706	−	0.414941i
$832$		0			0
$833$	2.72873	−	3.75577i	0.0945449	−	0.130130i
$834$		0			0
$835$	−9.49867	+	3.08631i	−0.328715	+	0.106806i
$836$		0			0
$837$	−2.04942	−	0.665895i	−0.0708382	−	0.0230167i
$838$		0			0
$839$	15.9553	+	21.9605i	0.550837	+	0.758161i	0.990125	−	0.140184i	$-0.0447695\pi$
$839$	15.9553	+	21.9605i	0.550837	+	0.758161i	−0.439289	+	0.898346i	$0.644770\pi$
$840$		0			0
$841$	4.20509	−	3.05518i	0.145003	−	0.105351i
$842$		0			0
$843$	−2.45262	−	1.78193i	−0.0844727	−	0.0613730i
$844$		0			0
$845$	−0.115764	+	0.0841073i	−0.00398239	+	0.00289338i
$846$		0			0
$847$			3.99349i			0.137218i
$848$		0			0
$849$	1.25677	−	0.408349i	0.0431322	−	0.0140145i
$850$		0			0
$851$	−0.748857	+	2.30474i	−0.0256705	+	0.0790056i
$852$		0			0
$853$	−4.35222	+	13.3947i	−0.149017	+	0.458627i	−0.997506	−	0.0705863i	$-0.977513\pi$
$853$	−4.35222	+	13.3947i	−0.149017	+	0.458627i	0.848489	+	0.529214i	$0.177513\pi$
$854$		0			0
$855$	−3.86823	+	5.32416i	−0.132291	+	0.182082i
$856$		0			0
$857$	4.95152	+	15.2392i	0.169141	+	0.520562i	0.999318	−	0.0369385i	$-0.0117606\pi$
$857$	4.95152	+	15.2392i	0.169141	+	0.520562i	−0.830177	+	0.557500i	$0.811761\pi$
$858$		0			0
$859$	−6.04068	−	4.38881i	−0.206105	−	0.149744i	0.479944	−	0.877299i	$-0.340657\pi$
$859$	−6.04068	−	4.38881i	−0.206105	−	0.149744i	−0.686050	+	0.727555i	$0.740657\pi$
$860$		0			0
$861$	−1.85380	−	9.38852i	−0.0631772	−	0.319960i
$862$		0			0
$863$	35.4182	+	25.7328i	1.20565	+	0.875956i	0.994829	−	0.101569i	$-0.0323861\pi$
$863$	35.4182	+	25.7328i	1.20565	+	0.875956i	0.210821	+	0.977525i	$0.432386\pi$
$864$		0			0
$865$	2.40440	+	7.39998i	0.0817520	+	0.251607i
$866$		0			0
$867$	−3.99865	+	5.50367i	−0.135801	+	0.186914i
$868$		0			0
$869$	−8.44931	+	26.0043i	−0.286623	+	0.882136i
$870$		0			0
$871$	−4.87003	+	14.9884i	−0.165015	+	0.507863i
$872$		0			0
$873$	3.25071	−	1.05622i	0.110020	−	0.0357476i
$874$		0			0
$875$			9.48666i			0.320708i
$876$		0			0
$877$	−18.1688	+	13.2004i	−0.613517	+	0.445747i	−0.850651	−	0.525730i	$-0.823792\pi$
$877$	−18.1688	+	13.2004i	−0.613517	+	0.445747i	0.237134	+	0.971477i	$0.423792\pi$
$878$		0			0
$879$	−35.1547	−	25.5414i	−1.18574	−	0.861489i
$880$		0			0
$881$	44.8828	−	32.6093i	1.51214	−	1.09863i	0.546925	−	0.837182i	$-0.315798\pi$
$881$	44.8828	−	32.6093i	1.51214	−	1.09863i	0.965216	−	0.261453i	$-0.0842017\pi$
$882$		0			0
$883$	−17.9848	−	24.7539i	−0.605236	−	0.833036i	0.390939	−	0.920417i	$-0.372150\pi$
$883$	−17.9848	−	24.7539i	−0.605236	−	0.833036i	−0.996175	+	0.0873808i	$0.972150\pi$
$884$		0			0
$885$	22.2393	+	7.22599i	0.747566	+	0.242899i
$886$		0			0
$887$	3.11877	−	1.01335i	0.104718	−	0.0340250i	−0.256189	−	0.966627i	$-0.582467\pi$
$887$	3.11877	−	1.01335i	0.104718	−	0.0340250i	0.360907	+	0.932602i	$0.382467\pi$
$888$		0			0
$889$	7.64946	−	10.5286i	0.256555	−	0.353117i
$890$		0			0
$891$	−15.3910	−	5.00084i	−0.515618	−	0.167535i
$892$		0			0
$893$	−56.1283			−1.87826
$894$		0			0
$895$	10.1284	+	13.9405i	0.338554	+	0.465979i
$896$		0			0
$897$	2.11951	+	6.52318i	0.0707684	+	0.217803i
$898$		0			0
$899$			2.23870i			0.0746647i
$900$		0			0
$901$	1.63837			0.0545819
$902$		0			0
$903$	−3.29981			−0.109811
$904$		0			0
$905$			25.4979i			0.847579i
$906$		0			0
$907$	5.13209	+	15.7949i	0.170408	+	0.524463i	0.999394	−	0.0348071i	$-0.0110817\pi$
$907$	5.13209	+	15.7949i	0.170408	+	0.524463i	−0.828986	+	0.559270i	$0.811082\pi$
$908$		0			0
$909$	−1.65832	−	2.28248i	−0.0550030	−	0.0757052i
$910$		0			0
$911$	−12.0319			−0.398634			−0.199317	−	0.979935i	$-0.563872\pi$
$911$	−12.0319			−0.398634			−0.199317	+	0.979935i	$0.563872\pi$
$912$		0			0
$913$	−4.88936	−	1.58865i	−0.161814	−	0.0525766i
$914$		0			0
$915$	12.3899	−	17.0532i	0.409598	−	0.563763i
$916$		0			0
$917$	−14.0294	+	4.55842i	−0.463291	+	0.150532i
$918$		0			0
$919$	1.63848	+	0.532375i	0.0540486	+	0.0175614i	0.335916	−	0.941892i	$-0.390954\pi$
$919$	1.63848	+	0.532375i	0.0540486	+	0.0175614i	−0.281868	+	0.959453i	$0.590954\pi$
$920$		0			0
$921$	−23.8067	−	32.7672i	−0.784459	−	1.07972i
$922$		0			0
$923$	15.5753	−	11.3161i	0.512667	−	0.372475i
$924$		0			0
$925$	5.96248	+	4.33199i	0.196045	+	0.142435i
$926$		0			0
$927$	−2.86259	+	2.07979i	−0.0940197	+	0.0683093i
$928$		0			0
$929$			22.3097i			0.731956i	0.930623	+	0.365978i	$0.119265\pi$
$929$			22.3097i			0.731956i	−0.930623	+	0.365978i	$0.880735\pi$
$930$		0			0
$931$	7.62046	−	2.47604i	0.249750	−	0.0811488i
$932$		0			0
$933$	−4.58204	+	14.1021i	−0.150009	+	0.461681i
$934$		0			0
$935$	−4.06989	+	12.5258i	−0.133100	+	0.409638i
$936$		0			0
$937$	−25.2243	+	34.7183i	−0.824043	+	1.13420i	0.164960	+	0.986300i	$0.447250\pi$
$937$	−25.2243	+	34.7183i	−0.824043	+	1.13420i	−0.989003	+	0.147897i	$0.952750\pi$
$938$		0			0
$939$	−11.6703	−	35.9174i	−0.380845	−	1.17212i
$940$		0			0
$941$	−19.5382	−	14.1954i	−0.636928	−	0.462755i	0.221865	−	0.975077i	$-0.428785\pi$
$941$	−19.5382	−	14.1954i	−0.636928	−	0.462755i	−0.858793	+	0.512322i	$0.828785\pi$
$942$		0			0
$943$	7.08025	−	3.95209i	0.230565	−	0.128698i
$944$		0			0
$945$	−4.88082	−	3.54612i	−0.158773	−	0.115355i
$946$		0			0
$947$	−7.33318	−	22.5692i	−0.238296	−	0.733400i	−0.996667	−	0.0815769i	$-0.974004\pi$
$947$	−7.33318	−	22.5692i	−0.238296	−	0.733400i	0.758371	−	0.651823i	$-0.225996\pi$
$948$		0			0
$949$	−7.14180	+	9.82984i	−0.231833	+	0.319090i
$950$		0			0
$951$	−6.55820	+	20.1841i	−0.212664	+	0.654513i
$952$		0			0
$953$	10.9012	−	33.5504i	0.353124	−	1.08681i	−0.603965	−	0.797011i	$-0.706413\pi$
$953$	10.9012	−	33.5504i	0.353124	−	1.08681i	0.957089	−	0.289794i	$-0.0935869\pi$
$954$		0			0
$955$	1.46520	−	0.476072i	0.0474127	−	0.0154053i
$956$		0			0
$957$			23.1345i			0.747832i
$958$		0			0
$959$	−13.9255	+	10.1175i	−0.449679	+	0.326711i
$960$		0			0
$961$	24.9610	+	18.1352i	0.805192	+	0.585007i
$962$		0			0
$963$	−0.843431	+	0.612788i	−0.0271792	+	0.0197468i
$964$		0			0
$965$	−9.50030	−	13.0760i	−0.305826	−	0.420933i
$966$		0			0
$967$	−25.7688	−	8.37278i	−0.828668	−	0.269250i	−0.136184	−	0.990684i	$-0.543484\pi$
$967$	−25.7688	−	8.37278i	−0.828668	−	0.269250i	−0.692484	+	0.721433i	$0.743484\pi$
$968$		0			0
$969$	−52.8729	+	17.1794i	−1.69852	+	0.551883i
$970$		0			0
$971$	27.7126	−	38.1431i	0.889340	−	1.22407i	−0.0844055	−	0.996431i	$-0.526899\pi$
$971$	27.7126	−	38.1431i	0.889340	−	1.22407i	0.973745	−	0.227640i	$-0.0731009\pi$
$972$		0			0
$973$	−7.48075	−	2.43064i	−0.239822	−	0.0779229i
$974$		0			0
$975$	20.8596			0.668041
$976$		0			0
$977$	3.55771	+	4.89676i	0.113821	+	0.156661i	0.862127	−	0.506693i	$-0.169132\pi$
$977$	3.55771	+	4.89676i	0.113821	+	0.156661i	−0.748305	+	0.663354i	$0.769132\pi$
$978$		0			0
$979$	1.77178	+	5.45299i	0.0566264	+	0.174278i
$980$		0			0
$981$			7.71226i			0.246233i
$982$		0			0
$983$	−40.5540			−1.29347			−0.646736	−	0.762714i	$-0.723866\pi$
$983$	−40.5540			−1.29347			−0.646736	+	0.762714i	$0.723866\pi$
$984$		0			0
$985$	−4.28572			−0.136554
$986$		0			0
$987$		−	10.4693i		−	0.333242i
$988$		0			0
$989$	−0.863999	−	2.65912i	−0.0274736	−	0.0845550i
$990$		0			0
$991$	−33.0855	−	45.5383i	−1.05100	−	1.44657i	−0.887942	−	0.459956i	$-0.847865\pi$
$991$	−33.0855	−	45.5383i	−1.05100	−	1.44657i	−0.163055	−	0.986617i	$-0.552135\pi$
$992$		0			0
$993$	29.1596			0.925352
$994$		0			0
$995$	26.3412	+	8.55878i	0.835072	+	0.271331i
$996$		0			0
$997$	−0.204638	+	0.281660i	−0.00648095	+	0.00892027i	−0.812245	−	0.583316i	$-0.801755\pi$
$997$	−0.204638	+	0.281660i	−0.00648095	+	0.00892027i	0.805764	+	0.592236i	$0.201755\pi$
$998$		0			0
$999$	−10.2447	+	3.32870i	−0.324127	+	0.105315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.15	✓	80
41.4	even	10	inner	1148.2.ba.a.701.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.15	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.6	yes	80	41.4	even	10	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.49455i q^{3} +(-0.331199 - 1.01933i) q^{5} +(-0.587785 - 0.809017i) q^{7} +0.766322 q^{9} +O(q^{10})\)	\(q+1.49455i q^{3} +(-0.331199 - 1.01933i) q^{5} +(-0.587785 - 0.809017i) q^{7} +0.766322 q^{9} +(2.51743 + 0.817962i) q^{11} +(2.13014 - 2.93189i) q^{13} +(1.52343 - 0.494994i) q^{15} +(-4.41518 - 1.43458i) q^{17} +(-4.70970 - 6.48235i) q^{19} +(1.20912 - 0.878474i) q^{21} +(1.02450 + 0.744340i) q^{23} +(3.11575 - 2.26373i) q^{25} +5.62895i q^{27} +(5.56167 - 1.80710i) q^{29} +(-0.118298 + 0.364085i) q^{31} +(-1.22248 + 3.76242i) q^{33} +(-0.629979 + 0.867091i) q^{35} +(0.591352 + 1.82000i) q^{37} +(4.38186 + 3.18361i) q^{39} +(2.68889 - 5.81118i) q^{41} +(-1.78623 - 1.29777i) q^{43} +(-0.253805 - 0.781133i) q^{45} +(4.11743 - 5.66715i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(2.14405 - 6.59870i) q^{51} +(-0.335641 + 0.109056i) q^{53} -2.83699i q^{55} +(9.68819 - 7.03888i) q^{57} +(11.8101 + 8.58057i) q^{59} +(10.6461 - 7.73483i) q^{61} +(-0.450433 - 0.619967i) q^{63} +(-3.69406 - 1.20027i) q^{65} +(-4.13585 + 1.34382i) q^{67} +(-1.11245 + 1.53116i) q^{69} +(5.05236 + 1.64161i) q^{71} -3.35273 q^{73} +(3.38325 + 4.65664i) q^{75} +(-0.817962 - 2.51743i) q^{77} +10.3297i q^{79} -6.11379 q^{81} -1.94220 q^{83} +4.97564i q^{85} +(2.70080 + 8.31219i) q^{87} +(1.27320 + 1.75241i) q^{89} -3.62402 q^{91} +(-0.544142 - 0.176803i) q^{93} +(-5.04778 + 6.94768i) q^{95} +(4.24196 - 1.37830i) q^{97} +(1.92916 + 0.626822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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