LMFDB - Embedded newform 1100.2.cb.b.1049.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1100,2,Mod(49,1100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1100, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("1100.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.cb (of order $10$, degree $4$, not 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:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 56x^{12} - 141x^{10} + 551x^{8} - 1245x^{6} + 1400x^{4} + 125x^{2} + 625 $ x^16 - 11x^14 + 56x^12 - 141x^10 + 551x^8 - 1245x^6 + 1400x^4 + 125*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			1049.3
Root			$-0.456994 + 0.628998i$ of defining polynomial
Character	$\chi$	$=$	1100.1049
Dual form			1100.2.cb.b.949.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.151646 + 0.0492728i) q^{3} +(-1.93586 + 0.628998i) q^{7} +(-2.40648 - 1.74841i) q^{9} +(2.88699 + 1.63256i) q^{11} +(-0.384126 + 0.528704i) q^{13} +(2.52570 + 3.47632i) q^{17} +(0.919194 - 2.82899i) q^{19} -0.324558 q^{21} +6.11210i q^{23} +(-0.559952 - 0.770708i) q^{27} +(2.63577 + 8.11208i) q^{29} +(4.34733 + 3.15852i) q^{31} +(0.357361 + 0.389823i) q^{33} +(-3.28598 + 1.06768i) q^{37} +(-0.0843020 + 0.0612490i) q^{39} +(1.47374 - 4.53569i) q^{41} +10.1305i q^{43} +(6.94734 + 2.25733i) q^{47} +(-2.31122 + 1.67920i) q^{49} +(0.211724 + 0.651620i) q^{51} +(-6.53617 + 8.99626i) q^{53} +(0.278785 - 0.383714i) q^{57} +(-1.70562 - 5.24935i) q^{59} +(7.77155 - 5.64636i) q^{61} +(5.75835 + 1.87100i) q^{63} -5.60966i q^{67} +(-0.301160 + 0.926876i) q^{69} +(-0.0442449 + 0.0321458i) q^{71} +(-6.78819 + 2.20562i) q^{73} +(-6.61569 - 1.34450i) q^{77} +(2.37100 + 1.72263i) q^{79} +(2.71064 + 8.34250i) q^{81} +(-7.25807 - 9.98988i) q^{83} +1.36004i q^{87} -0.00487932 q^{89} +(0.411059 - 1.26511i) q^{91} +(0.503626 + 0.693182i) q^{93} +(-10.7307 + 14.7696i) q^{97} +(-4.09311 - 8.97639i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9} + 10 q^{11} + 14 q^{19} - 56 q^{21} + 2 q^{29} + 44 q^{31} - 54 q^{39} + 48 q^{41} + 54 q^{49} - 94 q^{51} + 18 q^{59} + 44 q^{61} - 22 q^{69} - 44 q^{71} + 50 q^{79} - 56 q^{81} - 16 q^{89}+ \cdots - 120 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 + 10 * q^11 + 14 * q^19 - 56 * q^21 + 2 * q^29 + 44 * q^31 - 54 * q^39 + 48 * q^41 + 54 * q^49 - 94 * q^51 + 18 * q^59 + 44 * q^61 - 22 * q^69 - 44 * q^71 + 50 * q^79 - 56 * q^81 - 16 * q^89 + 28 * q^91 - 120 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.151646	+	0.0492728i	0.0875530	+	0.0284477i	0.352466	−	0.935825i	$-0.385343\pi$
$3$	0.151646	+	0.0492728i	0.0875530	+	0.0284477i	−0.264913	+	0.964272i	$0.585343\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.93586	+	0.628998i	−0.731685	+	0.237739i	−0.651082	−	0.759007i	$-0.725685\pi$
$7$	−1.93586	+	0.628998i	−0.731685	+	0.237739i	−0.0806031	+	0.996746i	$0.525685\pi$
$8$		0			0
$9$	−2.40648	−	1.74841i	−0.802161	−	0.582804i
$10$		0			0
$11$	2.88699	+	1.63256i	0.870461	+	0.492237i
$11$	2.88699	+	1.63256i	0.870461	+	0.492237i
$12$		0			0
$13$	−0.384126	+	0.528704i	−0.106537	+	0.146636i	−0.858957	−	0.512048i	$-0.828887\pi$
$13$	−0.384126	+	0.528704i	−0.106537	+	0.146636i	0.752419	+	0.658685i	$0.228887\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.52570	+	3.47632i	0.612572	+	0.843132i	0.996786	−	0.0801115i	$-0.0255276\pi$
$17$	2.52570	+	3.47632i	0.612572	+	0.843132i	−0.384214	+	0.923244i	$0.625528\pi$
$18$		0			0
$19$	0.919194	−	2.82899i	0.210878	−	0.649015i	−0.788543	−	0.614980i	$-0.789164\pi$
$19$	0.919194	−	2.82899i	0.210878	−	0.649015i	0.999421	−	0.0340351i	$-0.0108358\pi$
$20$		0			0
$21$	−0.324558			−0.0708243
$22$		0			0
$23$			6.11210i			1.27446i	0.770673	+	0.637230i	$0.219920\pi$
$23$			6.11210i			1.27446i	−0.770673	+	0.637230i	$0.780080\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.559952	−	0.770708i	−0.107763	−	0.148323i
$28$		0			0
$29$	2.63577	+	8.11208i	0.489451	+	1.50638i	0.825429	+	0.564505i	$0.190933\pi$
$29$	2.63577	+	8.11208i	0.489451	+	1.50638i	−0.335978	+	0.941870i	$0.609067\pi$
$30$		0			0
$31$	4.34733	+	3.15852i	0.780803	+	0.567286i	0.905220	−	0.424944i	$-0.139706\pi$
$31$	4.34733	+	3.15852i	0.780803	+	0.567286i	−0.124417	+	0.992230i	$0.539706\pi$
$32$		0			0
$33$	0.357361	+	0.389823i	0.0622085	+	0.0678594i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.28598	+	1.06768i	−0.540212	+	0.175526i	−0.566399	−	0.824131i	$-0.691664\pi$
$37$	−3.28598	+	1.06768i	−0.540212	+	0.175526i	0.0261862	+	0.999657i	$0.491664\pi$
$38$		0			0
$39$	−0.0843020	+	0.0612490i	−0.0134991	+	0.00980769i
$40$		0			0
$41$	1.47374	−	4.53569i	0.230159	−	0.708356i	−0.767568	−	0.640968i	$-0.778533\pi$
$41$	1.47374	−	4.53569i	0.230159	−	0.708356i	0.997727	−	0.0673885i	$-0.0214667\pi$
$42$		0			0
$43$			10.1305i			1.54489i	0.635081	+	0.772446i	$0.280967\pi$
$43$			10.1305i			1.54489i	−0.635081	+	0.772446i	$0.719033\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.94734	+	2.25733i	1.01337	+	0.329265i	0.768197	−	0.640213i	$-0.221154\pi$
$47$	6.94734	+	2.25733i	1.01337	+	0.329265i	0.245177	+	0.969478i	$0.421154\pi$
$48$		0			0
$49$	−2.31122	+	1.67920i	−0.330174	+	0.239885i
$50$		0			0
$51$	0.211724	+	0.651620i	0.0296473	+	0.0912450i
$52$		0			0
$53$	−6.53617	+	8.99626i	−0.897812	+	1.23573i	0.0733491	+	0.997306i	$0.476631\pi$
$53$	−6.53617	+	8.99626i	−0.897812	+	1.23573i	−0.971161	+	0.238425i	$0.923369\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.278785	−	0.383714i	0.0369259	−	0.0508242i
$58$		0			0
$59$	−1.70562	−	5.24935i	−0.222052	−	0.683407i	−0.998577	−	0.0533204i	$-0.983020\pi$
$59$	−1.70562	−	5.24935i	−0.222052	−	0.683407i	0.776525	−	0.630086i	$-0.216980\pi$
$60$		0			0
$61$	7.77155	−	5.64636i	0.995045	−	0.722942i	0.0340247	−	0.999421i	$-0.489168\pi$
$61$	7.77155	−	5.64636i	0.995045	−	0.722942i	0.961020	+	0.276479i	$0.0891675\pi$
$62$		0			0
$63$	5.75835	+	1.87100i	0.725484	+	0.235724i
$64$		0			0
$65$		0			0
$66$		0			0
$67$		−	5.60966i		−	0.685329i	−0.939458	−	0.342664i	$-0.888671\pi$
$67$		−	5.60966i		−	0.685329i	0.939458	−	0.342664i	$-0.111329\pi$
$68$		0			0
$69$	−0.301160	+	0.926876i	−0.0362555	+	0.111583i
$70$		0			0
$71$	−0.0442449	+	0.0321458i	−0.00525091	+	0.00381501i	−0.590408	−	0.807105i	$-0.701033\pi$
$71$	−0.0442449	+	0.0321458i	−0.00525091	+	0.00381501i	0.585157	+	0.810920i	$0.301033\pi$
$72$		0			0
$73$	−6.78819	+	2.20562i	−0.794497	+	0.258148i	−0.678018	−	0.735045i	$-0.737161\pi$
$73$	−6.78819	+	2.20562i	−0.794497	+	0.258148i	−0.116479	+	0.993193i	$0.537161\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.61569	−	1.34450i	−0.753927	−	0.153220i
$78$		0			0
$79$	2.37100	+	1.72263i	0.266759	+	0.193811i	0.713121	−	0.701041i	$-0.247281\pi$
$79$	2.37100	+	1.72263i	0.266759	+	0.193811i	−0.446363	+	0.894852i	$0.647281\pi$
$80$		0			0
$81$	2.71064	+	8.34250i	0.301183	+	0.926945i
$82$		0			0
$83$	−7.25807	−	9.98988i	−0.796677	−	1.09653i	−0.993244	−	0.116041i	$-0.962980\pi$
$83$	−7.25807	−	9.98988i	−0.796677	−	1.09653i	0.196568	−	0.980490i	$-0.437020\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			1.36004i			0.145811i
$88$		0			0
$89$	−0.00487932			−0.000517207			−0.000258603	−	1.00000i	$-0.500082\pi$
$89$	−0.00487932			−0.000517207			−0.000258603		1.00000i	$0.500082\pi$
$90$		0			0
$91$	0.411059	−	1.26511i	0.0430907	−	0.132620i
$92$		0			0
$93$	0.503626	+	0.693182i	0.0522236	+	0.0718797i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.7307	+	14.7696i	−1.08954	+	1.49962i	−0.240973	+	0.970532i	$0.577467\pi$
$97$	−10.7307	+	14.7696i	−1.08954	+	1.49962i	−0.848566	+	0.529090i	$0.822533\pi$
$98$		0			0
$99$	−4.09311	−	8.97639i	−0.411373	−	0.902161i
$100$		0			0
$101$	−2.14782	−	1.56048i	−0.213716	−	0.155274i	0.475777	−	0.879566i	$-0.342167\pi$
$101$	−2.14782	−	1.56048i	−0.213716	−	0.155274i	−0.689493	+	0.724292i	$0.742167\pi$
$102$		0			0
$103$	15.6546	−	5.08650i	1.54250	−	0.501188i	0.590433	−	0.807086i	$-0.298957\pi$
$103$	15.6546	−	5.08650i	1.54250	−	0.501188i	0.952064	+	0.305898i	$0.0989568\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.6988	+	3.80116i	1.13096	+	0.367472i	0.813942	−	0.580946i	$-0.197317\pi$
$107$	11.6988	+	3.80116i	1.13096	+	0.367472i	0.317021	+	0.948419i	$0.397317\pi$
$108$		0			0
$109$	8.73635			0.836790			0.418395	−	0.908265i	$-0.362593\pi$
$109$	8.73635			0.836790			0.418395	+	0.908265i	$0.362593\pi$
$110$		0			0
$111$	−0.550915			−0.0522905
$112$		0			0
$113$	1.57099	+	0.510445i	0.147786	+	0.0480186i	0.381976	−	0.924172i	$-0.375244\pi$
$113$	1.57099	+	0.510445i	0.147786	+	0.0480186i	−0.234190	+	0.972191i	$0.575244\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.84878	−	0.600707i	0.170920	−	0.0555353i
$118$		0			0
$119$	−7.07599	−	5.14101i	−0.648655	−	0.471275i
$120$		0			0
$121$	5.66947	+	9.42641i	0.515406	+	0.856946i
$122$		0			0
$123$	0.446973	−	0.615205i	0.0403022	−	0.0554712i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.61841	+	2.22754i	0.143610	+	0.197663i	0.874763	−	0.484552i	$-0.161017\pi$
$127$	1.61841	+	2.22754i	0.143610	+	0.197663i	−0.731152	+	0.682214i	$0.761017\pi$
$128$		0			0
$129$	−0.499160	+	1.53626i	−0.0439486	+	0.135260i
$130$		0			0
$131$	−2.85760			−0.249670			−0.124835	−	0.992178i	$-0.539840\pi$
$131$	−2.85760			−0.249670			−0.124835	+	0.992178i	$0.539840\pi$
$132$		0			0
$133$			6.05469i			0.525008i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.91464	−	8.14080i	−0.505322	−	0.695516i	0.477800	−	0.878469i	$-0.341434\pi$
$137$	−5.91464	−	8.14080i	−0.505322	−	0.695516i	−0.983122	+	0.182953i	$0.941434\pi$
$138$		0			0
$139$	−0.118702	−	0.365326i	−0.0100682	−	0.0309866i	0.945896	−	0.324469i	$-0.105186\pi$
$139$	−0.118702	−	0.365326i	−0.0100682	−	0.0309866i	−0.955964	+	0.293483i	$0.905186\pi$
$140$		0			0
$141$	0.942313	+	0.684631i	0.0793571	+	0.0576563i
$142$		0			0
$143$	−1.97211	+	0.899255i	−0.164916	+	0.0751995i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.433226	+	0.140764i	−0.0357319	+	0.0116100i
$148$		0			0
$149$	−6.72161	+	4.88353i	−0.550656	+	0.400075i	−0.828027	−	0.560688i	$-0.810537\pi$
$149$	−6.72161	+	4.88353i	−0.550656	+	0.400075i	0.277372	+	0.960763i	$0.410537\pi$
$150$		0			0
$151$	1.65310	−	5.08772i	0.134527	−	0.414033i	−0.860989	−	0.508624i	$-0.830154\pi$
$151$	1.65310	−	5.08772i	0.134527	−	0.414033i	0.995516	+	0.0945910i	$0.0301543\pi$
$152$		0			0
$153$		−	12.7817i		−	1.03334i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.14768	−	2.32242i	−0.570447	−	0.185349i	0.00956968	−	0.999954i	$-0.496954\pi$
$157$	−7.14768	−	2.32242i	−0.570447	−	0.185349i	−0.580016	+	0.814605i	$0.696954\pi$
$158$		0			0
$159$	−1.43446	+	1.04219i	−0.113760	+	0.0826513i
$160$		0			0
$161$	−3.84450	−	11.8321i	−0.302989	−	0.932504i
$162$		0			0
$163$	1.78725	−	2.45994i	0.139988	−	0.192678i	−0.733266	−	0.679942i	$-0.762005\pi$
$163$	1.78725	−	2.45994i	0.139988	−	0.192678i	0.873255	+	0.487264i	$0.162005\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.10379	−	11.1539i	0.627090	−	0.863115i	−0.370755	−	0.928731i	$-0.620901\pi$
$167$	8.10379	−	11.1539i	0.627090	−	0.863115i	0.997845	+	0.0656157i	$0.0209011\pi$
$168$		0			0
$169$	3.88525	+	11.9576i	0.298865	+	0.919812i
$170$		0			0
$171$	−7.15826	+	5.20078i	−0.547406	+	0.397714i
$172$		0			0
$173$	13.1240	+	4.26425i	0.997801	+	0.324205i	0.761986	−	0.647593i	$-0.224224\pi$
$173$	13.1240	+	4.26425i	0.997801	+	0.324205i	0.235814	+	0.971798i	$0.424224\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	0.880084i		−	0.0661512i
$178$		0			0
$179$	−1.54508	+	4.75528i	−0.115485	+	0.355427i	−0.992048	−	0.125861i	$-0.959831\pi$
$179$	−1.54508	+	4.75528i	−0.115485	+	0.355427i	0.876563	+	0.481287i	$0.159831\pi$
$180$		0			0
$181$	−18.1760	+	13.2056i	−1.35101	+	0.981567i	−0.352051	+	0.935981i	$0.614516\pi$
$181$	−18.1760	+	13.2056i	−1.35101	+	0.981567i	−0.998960	+	0.0455868i	$0.985484\pi$
$182$		0			0
$183$	1.45674	−	0.473323i	0.107685	−	0.0349890i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.61635	+	14.1595i	0.118199	+	1.03544i
$188$		0			0
$189$	1.56876	+	1.13977i	0.114111	+	0.0829062i
$190$		0			0
$191$	−2.22754	−	6.85567i	−0.161179	−	0.496059i	0.837555	−	0.546353i	$-0.183984\pi$
$191$	−2.22754	−	6.85567i	−0.161179	−	0.496059i	−0.998734	+	0.0502937i	$0.983984\pi$
$192$		0			0
$193$	−12.4352	−	17.1155i	−0.895102	−	1.23200i	−0.972004	−	0.234964i	$-0.924503\pi$
$193$	−12.4352	−	17.1155i	−0.895102	−	1.23200i	0.0769019	−	0.997039i	$-0.475497\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	20.5970i		−	1.46748i	−0.679432	−	0.733738i	$-0.737774\pi$
$197$		−	20.5970i		−	1.46748i	0.679432	−	0.733738i	$-0.262226\pi$
$198$		0			0
$199$	11.3763			0.806445			0.403223	−	0.915102i	$-0.367890\pi$
$199$	11.3763			0.806445			0.403223	+	0.915102i	$0.367890\pi$
$200$		0			0
$201$	0.276404	−	0.850683i	0.0194960	−	0.0600026i
$202$		0			0
$203$	−10.2050	−	14.0459i	−0.716248	−	0.985831i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	10.6865	−	14.7087i	0.742761	−	1.02232i
$208$		0			0
$209$	7.27222	−	6.66663i	0.503030	−	0.461141i
$210$		0			0
$211$	−22.7568	−	16.5338i	−1.56665	−	1.13823i	−0.930282	−	0.366846i	$-0.880437\pi$
$211$	−22.7568	−	16.5338i	−1.56665	−	1.13823i	−0.636364	−	0.771389i	$-0.719563\pi$
$212$		0			0
$213$	−0.00829349	+	0.00269472i	−0.000568261	+	0.000184639i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−10.4025	−	3.37998i	−0.706168	−	0.229448i
$218$		0			0
$219$	−1.13808			−0.0769043
$220$		0			0
$221$	−2.80813			−0.188895
$222$		0			0
$223$	−18.6561	−	6.06173i	−1.24930	−	0.405923i	−0.391633	−	0.920122i	$-0.628090\pi$
$223$	−18.6561	−	6.06173i	−1.24930	−	0.405923i	−0.857671	+	0.514198i	$0.828090\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.3306	−	4.98120i	1.01753	−	0.330614i	0.247678	−	0.968842i	$-0.420332\pi$
$227$	15.3306	−	4.98120i	1.01753	−	0.330614i	0.769847	+	0.638228i	$0.220332\pi$
$228$		0			0
$229$	3.13012	+	2.27416i	0.206844	+	0.150281i	0.686385	−	0.727239i	$-0.259197\pi$
$229$	3.13012	+	2.27416i	0.206844	+	0.150281i	−0.479541	+	0.877520i	$0.659197\pi$
$230$		0			0
$231$	−0.936997	−	0.529862i	−0.0616498	−	0.0348623i
$232$		0			0
$233$	16.7141	−	23.0050i	1.09498	−	1.50711i	0.253095	−	0.967441i	$-0.418551\pi$
$233$	16.7141	−	23.0050i	1.09498	−	1.50711i	0.841881	−	0.539664i	$-0.181449\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.274674	+	0.378057i	0.0178420	+	0.0245574i
$238$		0			0
$239$	0.517313	−	1.59212i	0.0334622	−	0.102986i	−0.932930	−	0.360057i	$-0.882757\pi$
$239$	0.517313	−	1.59212i	0.0334622	−	0.102986i	0.966393	+	0.257071i	$0.0827573\pi$
$240$		0			0
$241$	−21.4676			−1.38285			−0.691425	−	0.722448i	$-0.743017\pi$
$241$	−21.4676			−1.38285			−0.691425	+	0.722448i	$0.743017\pi$
$242$		0			0
$243$			4.25661i			0.273062i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.14261	+	1.57267i	0.0727026	+	0.100067i
$248$		0			0
$249$	−0.608429	−	1.87255i	−0.0385576	−	0.118668i
$250$		0			0
$251$	14.4964	+	10.5322i	0.915003	+	0.664789i	0.942275	−	0.334839i	$-0.108682\pi$
$251$	14.4964	+	10.5322i	0.915003	+	0.664789i	−0.0272722	+	0.999628i	$0.508682\pi$
$252$		0			0
$253$	−9.97839	+	17.6456i	−0.627336	+	1.10937i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.91807	−	0.948139i	0.182024	−	0.0591433i	−0.216587	−	0.976263i	$-0.569492\pi$
$257$	2.91807	−	0.948139i	0.182024	−	0.0591433i	0.398611	+	0.917120i	$0.369492\pi$
$258$		0			0
$259$	5.68962	−	4.13375i	0.353536	−	0.256859i
$260$		0			0
$261$	7.84031	−	24.1300i	0.485303	−	1.49361i
$262$		0			0
$263$		−	20.4278i		−	1.25963i	−0.776744	−	0.629816i	$-0.783130\pi$
$263$		−	20.4278i		−	1.25963i	0.776744	−	0.629816i	$-0.216870\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.000739930	0	0.000240418i	−4.52830e−5	0	1.47133e-5i
$268$		0			0
$269$	6.56147	−	4.76718i	0.400060	−	0.290660i	−0.369506	−	0.929228i	$-0.620473\pi$
$269$	6.56147	−	4.76718i	0.400060	−	0.290660i	0.769565	+	0.638568i	$0.220473\pi$
$270$		0			0
$271$	3.17624	+	9.77547i	0.192943	+	0.593818i	0.999994	+	0.00333647i	$0.00106203\pi$
$271$	3.17624	+	9.77547i	0.192943	+	0.593818i	−0.807051	+	0.590481i	$0.798938\pi$
$272$		0			0
$273$	0.124671	−	0.171595i	0.00754544	−	0.0103854i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.81209	+	13.5052i	−0.589551	+	0.811447i	−0.994702	−	0.102802i	$-0.967219\pi$
$277$	−9.81209	+	13.5052i	−0.589551	+	0.811447i	0.405151	+	0.914250i	$0.367219\pi$
$278$		0			0
$279$	−4.93937	−	15.2018i	−0.295713	−	0.910110i
$280$		0			0
$281$	−16.6701	+	12.1115i	−0.994455	+	0.722514i	−0.960892	−	0.276923i	$-0.910685\pi$
$281$	−16.6701	+	12.1115i	−0.994455	+	0.722514i	−0.0335629	+	0.999437i	$0.510685\pi$
$282$		0			0
$283$	27.9991	+	9.09747i	1.66437	+	0.540788i	0.981782	−	0.190011i	$-0.0608523\pi$
$283$	27.9991	+	9.09747i	1.66437	+	0.540788i	0.682593	+	0.730799i	$0.260852\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			9.70743i			0.573011i
$288$		0			0
$289$	−0.452393	+	1.39232i	−0.0266113	+	0.0819012i
$290$		0			0
$291$	−2.35501	+	1.71102i	−0.138053	+	0.100301i
$292$		0			0
$293$	6.93732	−	2.25407i	0.405283	−	0.131684i	−0.0992797	−	0.995060i	$-0.531654\pi$
$293$	6.93732	−	2.25407i	0.405283	−	0.131684i	0.504562	+	0.863375i	$0.331654\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.358348	−	3.13919i	−0.0207935	−	0.182154i
$298$		0			0
$299$	−3.23149	−	2.34782i	−0.186882	−	0.135778i
$300$		0			0
$301$	−6.37208	−	19.6113i	−0.367281	−	1.13037i
$302$		0			0
$303$	−0.248819	−	0.342470i	−0.0142943	−	0.0196744i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			2.71978i			0.155226i	0.996984	+	0.0776130i	$0.0247299\pi$
$307$			2.71978i			0.155226i	−0.996984	+	0.0776130i	$0.975270\pi$
$308$		0			0
$309$	2.62459			0.149308
$310$		0			0
$311$	−4.70857	+	14.4915i	−0.266999	+	0.821738i	0.724227	+	0.689561i	$0.242197\pi$
$311$	−4.70857	+	14.4915i	−0.266999	+	0.821738i	−0.991226	+	0.132177i	$0.957803\pi$
$312$		0			0
$313$	−17.0233	−	23.4305i	−0.962213	−	1.32437i	−0.945884	−	0.324506i	$-0.894802\pi$
$313$	−17.0233	−	23.4305i	−0.962213	−	1.32437i	−0.0163292	−	0.999867i	$-0.505198\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.57667	+	4.92286i	−0.200886	+	0.276496i	−0.897560	−	0.440892i	$-0.854662\pi$
$317$	−3.57667	+	4.92286i	−0.200886	+	0.276496i	0.696674	+	0.717387i	$0.254662\pi$
$318$		0			0
$319$	−5.63403	+	27.7226i	−0.315445	+	1.55217i
$320$		0			0
$321$	1.58678	+	1.15286i	0.0885654	+	0.0643465i
$322$		0			0
$323$	12.1561	−	3.94975i	0.676383	−	0.219770i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	1.32483	+	0.430465i	0.0732635	+	0.0238047i
$328$		0			0
$329$	−14.8689			−0.819750
$330$		0			0
$331$	18.0542			0.992349			0.496175	−	0.868223i	$-0.334738\pi$
$331$	18.0542			0.992349			0.496175	+	0.868223i	$0.334738\pi$
$332$		0			0
$333$	9.77441	+	3.17590i	0.535634	+	0.174038i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−9.95528	+	3.23467i	−0.542299	+	0.176204i	−0.567341	−	0.823483i	$-0.692028\pi$
$337$	−9.95528	+	3.23467i	−0.542299	+	0.176204i	0.0250425	+	0.999686i	$0.492028\pi$
$338$		0			0
$339$	0.213083	+	0.154814i	0.0115731	+	0.00840834i
$340$		0			0
$341$	7.39422	+	16.2159i	0.400420	+	0.878141i
$342$		0			0
$343$	11.7929	−	16.2316i	0.636759	−	0.876424i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.1918	−	23.6624i	−0.922902	−	1.27027i	−0.962565	−	0.271052i	$-0.912628\pi$
$347$	−17.1918	−	23.6624i	−0.922902	−	1.27027i	0.0396629	−	0.999213i	$-0.487372\pi$
$348$		0			0
$349$	−8.23527	+	25.3455i	−0.440824	+	1.35672i	0.446176	+	0.894945i	$0.352786\pi$
$349$	−8.23527	+	25.3455i	−0.440824	+	1.35672i	−0.886999	+	0.461770i	$0.847214\pi$
$350$		0			0
$351$	0.622569			0.0332303
$352$		0			0
$353$		−	0.908792i		−	0.0483701i	−0.999707	−	0.0241851i	$-0.992301\pi$
$353$		−	0.908792i		−	0.0483701i	0.999707	−	0.0241851i	$-0.00769909\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.819735	−	1.12827i	−0.0433850	−	0.0597143i
$358$		0			0
$359$	−10.3305	−	31.7939i	−0.545221	−	1.67802i	−0.720464	−	0.693493i	$-0.756071\pi$
$359$	−10.3305	−	31.7939i	−0.545221	−	1.67802i	0.175243	−	0.984525i	$-0.443929\pi$
$360$		0			0
$361$	8.21306	+	5.96714i	0.432266	+	0.314060i
$362$		0			0
$363$	0.395287	+	1.70883i	0.0207472	+	0.0896903i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.86120	−	2.87918i	0.462551	−	0.150292i	−0.0684653	−	0.997653i	$-0.521810\pi$
$367$	8.86120	−	2.87918i	0.462551	−	0.150292i	0.531016	+	0.847362i	$0.321810\pi$
$368$		0			0
$369$	−11.4768	+	8.33837i	−0.597457	+	0.434078i
$370$		0			0
$371$	6.99445	−	21.5267i	0.363134	−	1.11761i
$372$		0			0
$373$			0.730613i			0.0378297i	0.999821	+	0.0189148i	$0.00602114\pi$
$373$			0.730613i			0.0378297i	−0.999821	+	0.0189148i	$0.993979\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.30136	−	1.72252i	−0.273034	−	0.0887141i
$378$		0			0
$379$	24.5280	−	17.8206i	1.25992	−	0.915385i	0.261165	−	0.965294i	$-0.415893\pi$
$379$	24.5280	−	17.8206i	1.25992	−	0.915385i	0.998754	+	0.0499093i	$0.0158932\pi$
$380$		0			0
$381$	0.135668	+	0.417542i	0.00695046	+	0.0213913i
$382$		0			0
$383$	−15.2208	+	20.9497i	−0.777749	+	1.07048i	0.217778	+	0.975998i	$0.430119\pi$
$383$	−15.2208	+	20.9497i	−0.777749	+	1.07048i	−0.995527	+	0.0944808i	$0.969881\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	17.7123	−	24.3789i	0.900369	−	1.23925i
$388$		0			0
$389$	−1.72430	−	5.30686i	−0.0874256	−	0.269068i	0.897780	−	0.440444i	$-0.145179\pi$
$389$	−1.72430	−	5.30686i	−0.0874256	−	0.269068i	−0.985206	+	0.171375i	$0.945179\pi$
$390$		0			0
$391$	−21.2476	+	15.4373i	−1.07454	+	0.780698i
$392$		0			0
$393$	−0.433344	−	0.140802i	−0.0218593	−	0.00710252i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			31.4006i			1.57595i	0.615708	+	0.787974i	$0.288870\pi$
$397$			31.4006i			1.57595i	−0.615708	+	0.787974i	$0.711130\pi$
$398$		0			0
$399$	−0.298332	+	0.918171i	−0.0149353	+	0.0459660i
$400$		0			0
$401$	−15.0194	+	10.9122i	−0.750034	+	0.544932i	−0.895837	−	0.444382i	$-0.853423\pi$
$401$	−15.0194	+	10.9122i	−0.750034	+	0.544932i	0.145803	+	0.989314i	$0.453423\pi$
$402$		0			0
$403$	−3.33984	+	1.08518i	−0.166369	+	0.0540567i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.2297	−	2.28219i	−0.556634	−	0.113124i
$408$		0			0
$409$	5.05892	+	3.67552i	0.250147	+	0.181743i	0.705792	−	0.708419i	$-0.250591\pi$
$409$	5.05892	+	3.67552i	0.250147	+	0.181743i	−0.455645	+	0.890162i	$0.650591\pi$
$410$		0			0
$411$	−0.495812	−	1.52595i	−0.0244566	−	0.0752697i
$412$		0			0
$413$	6.60366	+	9.08915i	0.324945	+	0.447248i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	0.0612491i		−	0.00299938i
$418$		0			0
$419$	−25.4340			−1.24253			−0.621266	−	0.783599i	$-0.713382\pi$
$419$	−25.4340			−1.24253			−0.621266	+	0.783599i	$0.713382\pi$
$420$		0			0
$421$	6.09077	−	18.7455i	0.296846	−	0.913598i	−0.685749	−	0.727838i	$-0.740525\pi$
$421$	6.09077	−	18.7455i	0.296846	−	0.913598i	0.982595	−	0.185760i	$-0.0594747\pi$
$422$		0			0
$423$	−12.7719	−	17.5790i	−0.620992	−	0.854722i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−11.4931	+	15.8188i	−0.556188	+	0.765527i
$428$		0			0
$429$	−0.343372	+	0.0391970i	−0.0165782	+	0.00189245i
$430$		0			0
$431$	−13.1828	−	9.57788i	−0.634994	−	0.461350i	0.223133	−	0.974788i	$-0.428372\pi$
$431$	−13.1828	−	9.57788i	−0.634994	−	0.461350i	−0.858127	+	0.513438i	$0.828372\pi$
$432$		0			0
$433$	−22.5682	+	7.33287i	−1.08456	+	0.352395i	−0.796142	−	0.605110i	$-0.793129\pi$
$433$	−22.5682	+	7.33287i	−1.08456	+	0.352395i	−0.288418	+	0.957505i	$0.593129\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.2911	+	5.61821i	0.827144	+	0.268755i
$438$		0			0
$439$	14.3276			0.683818			0.341909	−	0.939733i	$-0.388927\pi$
$439$	14.3276			0.683818			0.341909	+	0.939733i	$0.388927\pi$
$440$		0			0
$441$	8.49783			0.404658
$442$		0			0
$443$	7.15093	+	2.32348i	0.339751	+	0.110392i	0.473923	−	0.880566i	$-0.342838\pi$
$443$	7.15093	+	2.32348i	0.339751	+	0.110392i	−0.134172	+	0.990958i	$0.542838\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.25993	+	0.409377i	−0.0595927	+	0.0193629i
$448$		0			0
$449$	21.8022	+	15.8402i	1.02891	+	0.747546i	0.968090	−	0.250603i	$-0.0806290\pi$
$449$	21.8022	+	15.8402i	1.02891	+	0.747546i	0.0608183	+	0.998149i	$0.480629\pi$
$450$		0			0
$451$	11.6595	−	10.6885i	0.549023	−	0.503304i
$452$		0			0
$453$	0.501373	−	0.690081i	0.0235566	−	0.0324228i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.96323	−	9.58406i	−0.325726	−	0.448323i	0.614479	−	0.788933i	$-0.289366\pi$
$457$	−6.96323	−	9.58406i	−0.325726	−	0.448323i	−0.940205	+	0.340610i	$0.889366\pi$
$458$		0			0
$459$	1.26496	−	3.89315i	0.0590433	−	0.181717i
$460$		0			0
$461$	40.9558			1.90750			0.953751	−	0.300599i	$-0.0971866\pi$
$461$	40.9558			1.90750			0.953751	+	0.300599i	$0.0971866\pi$
$462$		0			0
$463$			37.2115i			1.72937i	0.502317	+	0.864684i	$0.332481\pi$
$463$			37.2115i			1.72937i	−0.502317	+	0.864684i	$0.667519\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.89926	+	9.49602i	0.319260	+	0.439424i	0.938241	−	0.345982i	$-0.112454\pi$
$467$	6.89926	+	9.49602i	0.319260	+	0.439424i	−0.618981	+	0.785406i	$0.712454\pi$
$468$		0			0
$469$	3.52846	+	10.8595i	0.162929	+	0.501445i
$470$		0			0
$471$	−0.969486	−	0.704373i	−0.0446715	−	0.0324558i
$472$		0			0
$473$	−16.5387	+	29.2468i	−0.760452	+	1.34477i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	31.4583	−	10.2214i	1.44038	−	0.468007i
$478$		0			0
$479$	20.7572	−	15.0810i	0.948421	−	0.689068i	−0.00201220	−	0.999998i	$-0.500641\pi$
$479$	20.7572	−	15.0810i	0.948421	−	0.689068i	0.950433	+	0.310930i	$0.100641\pi$
$480$		0			0
$481$	0.697744	−	2.14744i	0.0318144	−	0.0979147i
$482$		0			0
$483$		−	1.98373i		−	0.0902628i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−7.90636	−	2.56893i	−0.358272	−	0.116409i	0.124350	−	0.992238i	$-0.460315\pi$
$487$	−7.90636	−	2.56893i	−0.358272	−	0.116409i	−0.482622	+	0.875829i	$0.660315\pi$
$488$		0			0
$489$	0.392239	−	0.284978i	0.0177376	−	0.0128871i
$490$		0			0
$491$	7.45825	+	22.9541i	0.336586	+	1.03591i	0.965935	+	0.258783i	$0.0833215\pi$
$491$	7.45825	+	22.9541i	0.336586	+	1.03591i	−0.629349	+	0.777123i	$0.716678\pi$
$492$		0			0
$493$	−21.5430	+	29.6515i	−0.970250	+	1.33543i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.0654322	−	0.0900597i	0.00293504	−	0.00403973i
$498$		0			0
$499$	9.92681	+	30.5516i	0.444385	+	1.36768i	0.883157	+	0.469078i	$0.155414\pi$
$499$	9.92681	+	30.5516i	0.444385	+	1.36768i	−0.438772	+	0.898599i	$0.644586\pi$
$500$		0			0
$501$	1.77849	−	1.29215i	0.0794572	−	0.0577290i
$502$		0			0
$503$	36.2233	+	11.7697i	1.61512	+	0.524783i	0.970782	−	0.239962i	$-0.0771350\pi$
$503$	36.2233	+	11.7697i	1.61512	+	0.524783i	0.644333	+	0.764745i	$0.277135\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			2.00476i			0.0890343i
$508$		0			0
$509$	12.9730	−	39.9268i	0.575019	−	1.76973i	−0.0610967	−	0.998132i	$-0.519460\pi$
$509$	12.9730	−	39.9268i	0.575019	−	1.76973i	0.636115	−	0.771594i	$-0.280540\pi$
$510$		0			0
$511$	11.7536	−	8.53951i	0.519950	−	0.377766i
$512$		0			0
$513$	−2.69503	+	0.875668i	−0.118988	+	0.0386617i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	16.3717	+	17.8589i	0.720027	+	0.785432i
$518$		0			0
$519$	1.78010	+	1.29332i	0.0781376	+	0.0567703i
$520$		0			0
$521$	−8.98355	−	27.6485i	−0.393577	−	1.21130i	−0.930065	−	0.367396i	$-0.880249\pi$
$521$	−8.98355	−	27.6485i	−0.393577	−	1.21130i	0.536488	−	0.843908i	$-0.319751\pi$
$522$		0			0
$523$	7.38957	+	10.1709i	0.323123	+	0.444741i	0.939418	−	0.342775i	$-0.111367\pi$
$523$	7.38957	+	10.1709i	0.323123	+	0.444741i	−0.616294	+	0.787516i	$0.711367\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			23.0902i			1.00582i
$528$		0			0
$529$	−14.3577			−0.624250
$530$		0			0
$531$	−5.07348	+	15.6146i	−0.220170	+	0.677615i
$532$		0			0
$533$	1.83194	+	2.52145i	0.0793501	+	0.109216i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.468613	+	0.644990i	−0.0202221	+	0.0278334i
$538$		0			0
$539$	−9.41386	+	1.07462i	−0.405484	+	0.0462873i
$540$		0			0
$541$	16.1438	+	11.7292i	0.694076	+	0.504276i	0.877998	−	0.478665i	$-0.158879\pi$
$541$	16.1438	+	11.7292i	0.694076	+	0.504276i	−0.183921	+	0.982941i	$0.558879\pi$
$542$		0			0
$543$	−3.40700	+	1.10700i	−0.146208	+	0.0475060i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	24.6590	+	8.01221i	1.05434	+	0.342577i	0.784372	−	0.620291i	$-0.212985\pi$
$547$	24.6590	+	8.01221i	1.05434	+	0.342577i	0.269972	+	0.962868i	$0.412985\pi$
$548$		0			0
$549$	−28.5743			−1.21952
$550$		0			0
$551$	25.3718			1.08087
$552$		0			0
$553$	−5.67345	−	1.84342i	−0.241260	−	0.0783901i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.38143	+	2.39837i	−0.312761	+	0.101622i	−0.461192	−	0.887301i	$-0.652578\pi$
$557$	−7.38143	+	2.39837i	−0.312761	+	0.101622i	0.148430	+	0.988923i	$0.452578\pi$
$558$		0			0
$559$	−5.35605	−	3.89140i	−0.226537	−	0.164589i
$560$		0			0
$561$	−0.452565	+	2.22687i	−0.0191073	+	0.0940187i
$562$		0			0
$563$	−5.58253	+	7.68369i	−0.235275	+	0.323829i	−0.910287	−	0.413979i	$-0.864139\pi$
$563$	−5.58253	+	7.68369i	−0.235275	+	0.323829i	0.675011	+	0.737808i	$0.264139\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−10.4948	−	14.4449i	−0.440742	−	0.606629i
$568$		0			0
$569$	−3.69665	+	11.3771i	−0.154972	+	0.476954i	−0.998158	−	0.0606674i	$-0.980677\pi$
$569$	−3.69665	+	11.3771i	−0.154972	+	0.476954i	0.843186	+	0.537622i	$0.180677\pi$
$570$		0			0
$571$	−18.0419			−0.755028			−0.377514	−	0.926004i	$-0.623221\pi$
$571$	−18.0419			−0.755028			−0.377514	+	0.926004i	$0.623221\pi$
$572$		0			0
$573$		−	1.14939i		−	0.0480166i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−23.6493	−	32.5505i	−0.984533	−	1.35509i	−0.934351	−	0.356354i	$-0.884020\pi$
$577$	−23.6493	−	32.5505i	−0.984533	−	1.35509i	−0.0501822	−	0.998740i	$-0.515980\pi$
$578$		0			0
$579$	−1.04241	−	3.20822i	−0.0433212	−	0.133329i
$580$		0			0
$581$	20.3342	+	14.7737i	0.843605	+	0.612915i
$582$		0			0
$583$	−33.5569	+	15.3014i	−1.38978	+	0.633721i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−29.9577	+	9.73384i	−1.23649	+	0.401759i	−0.853060	−	0.521813i	$-0.825256\pi$
$587$	−29.9577	+	9.73384i	−1.23649	+	0.401759i	−0.383426	+	0.923572i	$0.625256\pi$
$588$		0			0
$589$	12.9314	−	9.39525i	0.532831	−	0.387124i
$590$		0			0
$591$	1.01487	−	3.12346i	0.0417463	−	0.128482i
$592$		0			0
$593$		−	15.9481i		−	0.654909i	−0.944867	−	0.327454i	$-0.893809\pi$
$593$		−	15.9481i		−	0.654909i	0.944867	−	0.327454i	$-0.106191\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.72517	+	0.560543i	0.0706067	+	0.0229415i
$598$		0			0
$599$	−35.3013	+	25.6479i	−1.44237	+	1.04794i	−0.454832	+	0.890577i	$0.650301\pi$
$599$	−35.3013	+	25.6479i	−1.44237	+	1.04794i	−0.987540	+	0.157367i	$0.949699\pi$
$600$		0			0
$601$	0.147257	+	0.453211i	0.00600675	+	0.0184869i	0.954015	−	0.299759i	$-0.0969063\pi$
$601$	0.147257	+	0.453211i	0.00600675	+	0.0184869i	−0.948008	+	0.318246i	$0.896906\pi$
$602$		0			0
$603$	−9.80799	+	13.4995i	−0.399412	+	0.549744i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−19.1994	+	26.4257i	−0.779280	+	1.07259i	0.216081	+	0.976375i	$0.430673\pi$
$607$	−19.1994	+	26.4257i	−0.779280	+	1.07259i	−0.995361	+	0.0962116i	$0.969327\pi$
$608$		0			0
$609$	−0.855461	−	2.63284i	−0.0346650	−	0.106688i
$610$		0			0
$611$	−3.86211	+	2.80599i	−0.156244	+	0.113518i
$612$		0			0
$613$	46.3965	+	15.0751i	1.87394	+	0.608879i	0.989960	+	0.141344i	$0.0451425\pi$
$613$	46.3965	+	15.0751i	1.87394	+	0.608879i	0.883975	+	0.467534i	$0.154858\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	7.77343i		−	0.312947i	−0.987682	−	0.156473i	$-0.949987\pi$
$617$		−	7.77343i		−	0.312947i	0.987682	−	0.156473i	$-0.0500125\pi$
$618$		0			0
$619$	−12.6221	+	38.8470i	−0.507327	+	1.56139i	0.289497	+	0.957179i	$0.406512\pi$
$619$	−12.6221	+	38.8470i	−0.507327	+	1.56139i	−0.796823	+	0.604212i	$0.793488\pi$
$620$		0			0
$621$	4.71064	−	3.42248i	0.189032	−	0.137340i
$622$		0			0
$623$	0.00944566	−	0.00306908i	0.000378432	−	0.000122960i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.43129	−	0.652647i	0.0571601	−	0.0260642i
$628$		0			0
$629$	−12.0110	−	8.72650i	−0.478910	−	0.347949i
$630$		0			0
$631$	2.54159	+	7.82221i	0.101179	+	0.311397i	0.988815	−	0.149149i	$-0.0476535\pi$
$631$	2.54159	+	7.82221i	0.101179	+	0.311397i	−0.887636	+	0.460546i	$0.847654\pi$
$632$		0			0
$633$	−2.63632	−	3.62859i	−0.104784	−	0.144223i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	1.86697i		−	0.0739721i
$638$		0			0
$639$	0.162679			0.00643547
$640$		0			0
$641$	−10.3204	+	31.7630i	−0.407632	+	1.25456i	0.511046	+	0.859553i	$0.329258\pi$
$641$	−10.3204	+	31.7630i	−0.407632	+	1.25456i	−0.918678	+	0.395008i	$0.870742\pi$
$642$		0			0
$643$	1.07023	+	1.47304i	0.0422057	+	0.0580912i	0.829598	−	0.558361i	$-0.188569\pi$
$643$	1.07023	+	1.47304i	0.0422057	+	0.0580912i	−0.787393	+	0.616452i	$0.788569\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.84479	−	10.7974i	0.308410	−	0.424491i	−0.626474	−	0.779442i	$-0.715503\pi$
$647$	7.84479	−	10.7974i	0.308410	−	0.424491i	0.934885	+	0.354952i	$0.115503\pi$
$648$		0			0
$649$	3.64579	−	17.9394i	0.143110	−	0.704181i
$650$		0			0
$651$	−1.41096	−	1.02512i	−0.0552998	−	0.0401777i
$652$		0			0
$653$	21.4893	−	6.98228i	0.840940	−	0.273238i	0.143293	−	0.989680i	$-0.454231\pi$
$653$	21.4893	−	6.98228i	0.840940	−	0.273238i	0.697646	+	0.716442i	$0.254231\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	20.1920	+	6.56077i	0.787764	+	0.255960i
$658$		0			0
$659$	16.9078			0.658636			0.329318	−	0.944219i	$-0.393181\pi$
$659$	16.9078			0.658636			0.329318	+	0.944219i	$0.393181\pi$
$660$		0			0
$661$	49.7772			1.93611			0.968055	−	0.250740i	$-0.0806738\pi$
$661$	49.7772			1.93611			0.968055	+	0.250740i	$0.0806738\pi$
$662$		0			0
$663$	−0.425843	−	0.138365i	−0.0165384	−	0.00537364i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−49.5818	+	16.1101i	−1.91982	+	0.623786i
$668$		0			0
$669$	−2.53045	−	1.83848i	−0.0978327	−	0.0710796i
$670$		0			0
$671$	31.6545	−	3.61346i	1.22201	−	0.139496i
$672$		0			0
$673$	15.2075	−	20.9313i	0.586206	−	0.806843i	−0.408153	−	0.912914i	$-0.633827\pi$
$673$	15.2075	−	20.9313i	0.586206	−	0.806843i	0.994359	+	0.106071i	$0.0338269\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.0060	+	23.4068i	0.653595	+	0.899597i	0.999248	−	0.0387658i	$-0.0123426\pi$
$677$	17.0060	+	23.4068i	0.653595	+	0.899597i	−0.345653	+	0.938362i	$0.612343\pi$
$678$		0			0
$679$	11.4831	−	35.3413i	0.440681	−	1.35628i
$680$		0			0
$681$	2.57026			0.0984926
$682$		0			0
$683$		−	11.9698i		−	0.458011i	−0.973425	−	0.229005i	$-0.926453\pi$
$683$		−	11.9698i		−	0.458011i	0.973425	−	0.229005i	$-0.0735473\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	0.362616	+	0.499098i	0.0138347	+	0.0190418i
$688$		0			0
$689$	−2.24565	−	6.91140i	−0.0855524	−	0.263303i
$690$		0			0
$691$	23.7872	+	17.2824i	0.904909	+	0.657455i	0.939722	−	0.341939i	$-0.111084\pi$
$691$	23.7872	+	17.2824i	0.904909	+	0.657455i	−0.0348130	+	0.999394i	$0.511084\pi$
$692$		0			0
$693$	13.5698	+	14.8025i	0.515474	+	0.562299i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	19.4897	−	6.33260i	0.738227	−	0.239864i
$698$		0			0
$699$	3.66815	−	2.66506i	0.138742	−	0.100802i
$700$		0			0
$701$	8.42772	−	25.9379i	0.318311	−	0.979659i	−0.656060	−	0.754709i	$-0.727778\pi$
$701$	8.42772	−	25.9379i	0.318311	−	0.979659i	0.974370	−	0.224950i	$-0.0722219\pi$
$702$		0			0
$703$			10.2774i			0.387620i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.13941	+	1.66990i	0.193287	+	0.0628029i
$708$		0			0
$709$	−6.16553	+	4.47952i	−0.231552	+	0.168232i	−0.697511	−	0.716574i	$-0.745709\pi$
$709$	−6.16553	+	4.47952i	−0.231552	+	0.168232i	0.465960	+	0.884806i	$0.345709\pi$
$710$		0			0
$711$	−2.69390	−	8.29098i	−0.101029	−	0.310936i
$712$		0			0
$713$	−19.3052	+	26.5713i	−0.722984	+	0.995102i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.156897	−	0.215950i	0.00585943	−	0.00806481i
$718$		0			0
$719$	6.58192	+	20.2571i	0.245464	+	0.755461i	0.995560	+	0.0941314i	$0.0300074\pi$
$719$	6.58192	+	20.2571i	0.245464	+	0.755461i	−0.750096	+	0.661329i	$0.769993\pi$
$720$		0			0
$721$	−27.1057	+	19.6935i	−1.00947	+	0.733423i
$722$		0			0
$723$	−3.25548	−	1.05777i	−0.121073	−	0.0393389i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			6.19488i			0.229755i	0.993380	+	0.114878i	$0.0366476\pi$
$727$			6.19488i			0.229755i	−0.993380	+	0.114878i	$0.963352\pi$
$728$		0			0
$729$	7.92220	−	24.3820i	0.293415	−	0.903037i
$730$		0			0
$731$	−35.2170	+	25.5866i	−1.30255	+	0.946356i
$732$		0			0
$733$	−9.70179	+	3.15230i	−0.358344	+	0.116433i	−0.482656	−	0.875810i	$-0.660328\pi$
$733$	−9.70179	+	3.15230i	−0.358344	+	0.116433i	0.124312	+	0.992243i	$0.460328\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.15813	−	16.1950i	0.337344	−	0.596552i
$738$		0			0
$739$	−3.50898	−	2.54942i	−0.129080	−	0.0937819i	0.521372	−	0.853329i	$-0.325420\pi$
$739$	−3.50898	−	2.54942i	−0.129080	−	0.0937819i	−0.650452	+	0.759548i	$0.725420\pi$
$740$		0			0
$741$	0.0957828	+	0.294789i	0.00351867	+	0.0108294i
$742$		0			0
$743$	−4.41812	−	6.08102i	−0.162085	−	0.223091i	0.720248	−	0.693717i	$-0.244028\pi$
$743$	−4.41812	−	6.08102i	−0.162085	−	0.223091i	−0.882333	+	0.470626i	$0.844028\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$			36.7306i			1.34390i
$748$		0			0
$749$	−25.0381			−0.914871
$750$		0			0
$751$	12.5726	−	38.6946i	0.458782	−	1.41199i	−0.407855	−	0.913047i	$-0.633723\pi$
$751$	12.5726	−	38.6946i	0.458782	−	1.41199i	0.866637	−	0.498939i	$-0.166277\pi$
$752$		0			0
$753$	1.67937	+	2.31145i	0.0611995	+	0.0842339i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−15.3986	+	21.1944i	−0.559672	+	0.770323i	−0.991285	−	0.131736i	$-0.957945\pi$
$757$	−15.3986	+	21.1944i	−0.559672	+	0.770323i	0.431613	+	0.902059i	$0.357945\pi$
$758$		0			0
$759$	−2.38263	+	2.18422i	−0.0864841	+	0.0792823i
$760$		0			0
$761$	−28.4182	−	20.6470i	−1.03016	−	0.748453i	−0.0618172	−	0.998087i	$-0.519690\pi$
$761$	−28.4182	−	20.6470i	−1.03016	−	0.748453i	−0.968340	+	0.249634i	$0.919690\pi$
$762$		0			0
$763$	−16.9123	+	5.49514i	−0.612267	+	0.198938i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.43052	+	1.11464i	0.123869	+	0.0402475i
$768$		0			0
$769$	29.6963			1.07088			0.535439	−	0.844574i	$-0.320146\pi$
$769$	29.6963			1.07088			0.535439	+	0.844574i	$0.320146\pi$
$770$		0			0
$771$	0.489232			0.0176193
$772$		0			0
$773$	14.7162	+	4.78158i	0.529305	+	0.171981i	0.561464	−	0.827501i	$-0.310238\pi$
$773$	14.7162	+	4.78158i	0.529305	+	0.171981i	−0.0321592	+	0.999483i	$0.510238\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.06649	−	0.346524i	0.0382602	−	0.0124315i
$778$		0			0
$779$	−11.4768	−	8.33837i	−0.411198	−	0.298753i
$780$		0			0
$781$	−0.180215	+	0.0205721i	−0.00644860	+	0.000736128i
$782$		0			0
$783$	4.77614	−	6.57379i	0.170685	−	0.234928i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−13.6720	−	18.8179i	−0.487353	−	0.670784i	0.492544	−	0.870288i	$-0.336067\pi$
$787$	−13.6720	−	18.8179i	−0.487353	−	0.670784i	−0.979897	+	0.199503i	$0.936067\pi$
$788$		0			0
$789$	1.00654	−	3.09780i	0.0358336	−	0.110285i
$790$		0			0
$791$	−3.36228			−0.119549
$792$		0			0
$793$			6.27776i			0.222930i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.08758	+	1.49693i	0.0385242	+	0.0530240i	0.827845	−	0.560958i	$-0.189567\pi$
$797$	1.08758	+	1.49693i	0.0385242	+	0.0530240i	−0.789320	+	0.613982i	$0.789567\pi$
$798$		0			0
$799$	9.69968	+	29.8525i	0.343150	+	1.05611i
$800$		0			0
$801$	0.0117420	+	0.00853106i	0.000414883	+	0.000301430i
$802$		0			0
$803$	−23.1983	−	4.71455i	−0.818649	−	0.166373i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.22991	−	0.399623i	0.0432950	−	0.0140674i
$808$		0			0
$809$	27.4388	−	19.9354i	0.964696	−	0.700893i	0.0104597	−	0.999945i	$-0.496671\pi$
$809$	27.4388	−	19.9354i	0.964696	−	0.700893i	0.954237	+	0.299052i	$0.0966705\pi$
$810$		0			0
$811$	17.3581	−	53.4228i	0.609526	−	1.87593i	0.147503	−	0.989062i	$-0.452876\pi$
$811$	17.3581	−	53.4228i	0.609526	−	1.87593i	0.462024	−	0.886868i	$-0.347124\pi$
$812$		0			0
$813$			1.63892i			0.0574793i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	28.6592	+	9.31193i	1.00266	+	0.325783i
$818$		0			0
$819$	−3.20114	+	2.32576i	−0.111857	+	0.0812688i
$820$		0			0
$821$	3.61846	+	11.1365i	0.126285	+	0.388666i	0.994133	−	0.108164i	$-0.0344972\pi$
$821$	3.61846	+	11.1365i	0.126285	+	0.388666i	−0.867848	+	0.496830i	$0.834497\pi$
$822$		0			0
$823$	−8.50793	+	11.7102i	−0.296568	+	0.408191i	−0.931134	−	0.364678i	$-0.881179\pi$
$823$	−8.50793	+	11.7102i	−0.296568	+	0.408191i	0.634566	+	0.772869i	$0.281179\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.3693	−	37.6707i	0.951725	−	1.30994i	0.000968458	−	1.00000i	$-0.499692\pi$
$827$	27.3693	−	37.6707i	0.951725	−	1.30994i	0.950757	−	0.309938i	$-0.100308\pi$
$828$		0			0
$829$	−2.05309	−	6.31876i	−0.0713068	−	0.219460i	0.909052	−	0.416683i	$-0.136808\pi$
$829$	−2.05309	−	6.31876i	−0.0713068	−	0.219460i	−0.980359	+	0.197223i	$0.936808\pi$
$830$		0			0
$831$	−2.15340	+	1.56454i	−0.0747008	+	0.0542733i
$832$		0			0
$833$	−11.6749	−	3.79339i	−0.404510	−	0.131433i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	5.11914i		−	0.176943i
$838$		0			0
$839$	−0.276899	+	0.852208i	−0.00955962	+	0.0294215i	−0.955723	−	0.294269i	$-0.904924\pi$
$839$	−0.276899	+	0.852208i	−0.00955962	+	0.0294215i	0.946163	+	0.323691i	$0.104924\pi$
$840$		0			0
$841$	−35.3970	+	25.7174i	−1.22059	+	0.886808i
$842$		0			0
$843$	−3.12473	+	1.01529i	−0.107621	+	0.0349683i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−16.9045	−	14.6821i	−0.580844	−	0.504483i
$848$		0			0
$849$	3.79770	+	2.75919i	0.130337	+	0.0946952i
$850$		0			0
$851$	−6.52577	−	20.0843i	−0.223700	−	0.688479i
$852$		0			0
$853$	−18.3274	−	25.2255i	−0.627519	−	0.863706i	0.370354	−	0.928891i	$-0.379236\pi$
$853$	−18.3274	−	25.2255i	−0.627519	−	0.863706i	−0.997873	+	0.0651850i	$0.979236\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	45.0004i		−	1.53718i	−0.639740	−	0.768592i	$-0.720958\pi$
$857$		−	45.0004i		−	1.53718i	0.639740	−	0.768592i	$-0.279042\pi$
$858$		0			0
$859$	31.3959			1.07122			0.535608	−	0.844467i	$-0.320083\pi$
$859$	31.3959			1.07122			0.535608	+	0.844467i	$0.320083\pi$
$860$		0			0
$861$	−0.478312	+	1.47209i	−0.0163008	+	0.0501688i
$862$		0			0
$863$	−25.6652	−	35.3252i	−0.873654	−	1.20248i	−0.978138	−	0.207956i	$-0.933319\pi$
$863$	−25.6652	−	35.3252i	−0.873654	−	1.20248i	0.104484	−	0.994527i	$-0.466681\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−0.137207	+	0.188850i	−0.00465980	+	0.00641367i
$868$		0			0
$869$	4.03276	+	8.84405i	0.136802	+	0.300014i
$870$		0			0
$871$	2.96585	+	2.15482i	0.100494	+	0.0730131i
$872$		0			0
$873$	51.6465	−	16.7810i	1.74797	−	0.567950i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−24.7944	−	8.05620i	−0.837248	−	0.272038i	−0.141153	−	0.989988i	$-0.545081\pi$
$877$	−24.7944	−	8.05620i	−0.837248	−	0.272038i	−0.696095	+	0.717949i	$0.745081\pi$
$878$		0			0
$879$	1.16308			0.0392298
$880$		0			0
$881$	−25.3513			−0.854106			−0.427053	−	0.904227i	$-0.640448\pi$
$881$	−25.3513			−0.854106			−0.427053	+	0.904227i	$0.640448\pi$
$882$		0			0
$883$	3.32728	+	1.08110i	0.111972	+	0.0363819i	0.364467	−	0.931216i	$-0.381251\pi$
$883$	3.32728	+	1.08110i	0.111972	+	0.0363819i	−0.252495	+	0.967598i	$0.581251\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	35.1849	−	11.4323i	1.18139	−	0.383858i	0.348510	−	0.937305i	$-0.386688\pi$
$887$	35.1849	−	11.4323i	1.18139	−	0.383858i	0.832885	+	0.553447i	$0.186688\pi$
$888$		0			0
$889$	−4.53412	−	3.29423i	−0.152070	−	0.110485i
$890$		0			0
$891$	−5.79406	+	28.5101i	−0.194108	+	0.955123i
$892$		0			0
$893$	12.7719	−	17.5790i	0.427396	−	0.588260i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.374360	−	0.515262i	−0.0124995	−	0.0172041i
$898$		0			0
$899$	−14.1636	+	43.5910i	−0.472382	+	1.45384i
$900$		0			0
$901$	−47.7823			−1.59186
$902$		0			0
$903$		−	3.28794i		−	0.109416i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.96077	+	2.69877i	0.0651063	+	0.0896111i	0.840328	−	0.542078i	$-0.182362\pi$
$907$	1.96077	+	2.69877i	0.0651063	+	0.0896111i	−0.775222	+	0.631689i	$0.782362\pi$
$908$		0			0
$909$	2.44032	+	7.51054i	0.0809404	+	0.249109i
$910$		0			0
$911$	−22.5772	−	16.4033i	−0.748017	−	0.543466i	0.147194	−	0.989108i	$-0.452976\pi$
$911$	−22.5772	−	16.4033i	−0.748017	−	0.543466i	−0.895212	+	0.445641i	$0.852976\pi$
$912$		0			0
$913$	−4.64489	−	40.6900i	−0.153723	−	1.34664i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.53190	−	1.79742i	0.182679	−	0.0593562i
$918$		0			0
$919$	−39.9573	+	29.0307i	−1.31807	+	0.957635i	−0.318117	+	0.948051i	$0.603051\pi$
$919$	−39.9573	+	29.0307i	−1.31807	+	0.957635i	−0.999954	+	0.00958329i	$0.996949\pi$
$920$		0			0
$921$	−0.134011	+	0.412444i	−0.00441582	+	0.0135905i
$922$		0			0
$923$		−	0.0357405i		−	0.00117641i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−46.5659	−	15.1302i	−1.52943	−	0.496940i
$928$		0			0
$929$	16.9604	−	12.3224i	0.556451	−	0.404286i	−0.273707	−	0.961813i	$-0.588250\pi$
$929$	16.9604	−	12.3224i	0.556451	−	0.404286i	0.830159	+	0.557527i	$0.188250\pi$
$930$		0			0
$931$	2.62597	+	8.08191i	0.0860628	+	0.264874i
$932$		0			0
$933$	−1.42807	+	1.96558i	−0.0467531	+	0.0643501i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.31452	−	4.56205i	0.108281	−	0.149036i	−0.751437	−	0.659804i	$-0.770639\pi$
$937$	3.31452	−	4.56205i	0.108281	−	0.149036i	0.859718	+	0.510769i	$0.170639\pi$
$938$		0			0
$939$	−1.42703	−	4.39194i	−0.0465693	−	0.143325i
$940$		0			0
$941$	8.84980	−	6.42976i	0.288495	−	0.209604i	−0.434119	−	0.900856i	$-0.642940\pi$
$941$	8.84980	−	6.42976i	0.288495	−	0.209604i	0.722614	+	0.691251i	$0.242940\pi$
$942$		0			0
$943$	27.7226	+	9.00762i	0.902772	+	0.293328i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	20.5884i		−	0.669032i	−0.942390	−	0.334516i	$-0.891427\pi$
$947$		−	20.5884i		−	0.669032i	0.942390	−	0.334516i	$-0.108573\pi$
$948$		0			0
$949$	1.44140	−	4.43618i	0.0467899	−	0.144004i
$950$		0			0
$951$	−0.784952	+	0.570301i	−0.0254538	+	0.0184933i
$952$		0			0
$953$	−1.40029	+	0.454983i	−0.0453600	+	0.0147384i	−0.331609	−	0.943417i	$-0.607592\pi$
$953$	−1.40029	+	0.454983i	−0.0453600	+	0.0147384i	0.286249	+	0.958155i	$0.407592\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−2.22035	+	3.92642i	−0.0717737	+	0.126923i
$958$		0			0
$959$	16.5704	+	12.0391i	0.535087	+	0.388764i
$960$		0			0
$961$	−0.656515	−	2.02055i	−0.0211779	−	0.0651789i
$962$		0			0
$963$	−21.5069	−	29.6017i	−0.693050	−	0.953901i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			5.72960i			0.184252i	0.995747	+	0.0921258i	$0.0293662\pi$
$967$			5.72960i			0.184252i	−0.995747	+	0.0921258i	$0.970634\pi$
$968$		0			0
$969$	2.03804			0.0654713
$970$		0			0
$971$	4.37523	−	13.4656i	0.140408	−	0.432131i	−0.855984	−	0.517002i	$-0.827048\pi$
$971$	4.37523	−	13.4656i	0.140408	−	0.432131i	0.996392	+	0.0848714i	$0.0270479\pi$
$972$		0			0
$973$	0.459579	+	0.632556i	0.0147334	+	0.0202788i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.270689	−	0.372572i	0.00866012	−	0.0119196i	−0.804665	−	0.593729i	$-0.797655\pi$
$977$	0.270689	−	0.372572i	0.00866012	−	0.0119196i	0.813325	+	0.581809i	$0.197655\pi$
$978$		0			0
$979$	−0.0140866	−	0.00796580i	−0.000450208	−	0.000254588i
$980$		0			0
$981$	−21.0239	−	15.2747i	−0.671240	−	0.487685i
$982$		0			0
$983$	12.5134	−	4.06585i	0.399115	−	0.129680i	−0.102580	−	0.994725i	$-0.532710\pi$
$983$	12.5134	−	4.06585i	0.399115	−	0.129680i	0.501696	+	0.865044i	$0.332710\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.25481	−	0.732634i	−0.0717715	−	0.0233200i
$988$		0			0
$989$	−61.9188			−1.96890
$990$		0			0
$991$	−37.4029			−1.18814			−0.594072	−	0.804412i	$-0.702480\pi$
$991$	−37.4029			−1.18814			−0.594072	+	0.804412i	$0.702480\pi$
$992$		0			0
$993$	2.73785	+	0.889582i	0.0868831	+	0.0282300i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	7.73384	−	2.51288i	0.244933	−	0.0795836i	−0.183978	−	0.982930i	$-0.558897\pi$
$997$	7.73384	−	2.51288i	0.244933	−	0.0795836i	0.428911	+	0.903347i	$0.358897\pi$
$998$		0			0
$999$	2.66286	+	1.93468i	0.0842493	+	0.0612107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.cb.b.1049.3		16
5.2	odd	4		1100.2.n.b.301.2		8
5.3	odd	4		220.2.m.b.81.1	✓	8
5.4	even	2	inner	1100.2.cb.b.1049.2		16
11.3	even	5	inner	1100.2.cb.b.949.2		16
15.8	even	4		1980.2.z.d.1621.2		8
20.3	even	4		880.2.bo.c.81.2		8
55.3	odd	20		220.2.m.b.201.1	yes	8
55.14	even	10	inner	1100.2.cb.b.949.3		16
55.28	even	20		2420.2.a.l.1.2		4
55.38	odd	20		2420.2.a.k.1.2		4
55.47	odd	20		1100.2.n.b.201.2		8
165.113	even	20		1980.2.z.d.1081.2		8
220.3	even	20		880.2.bo.c.641.2		8
220.83	odd	20		9680.2.a.co.1.3		4
220.203	even	20		9680.2.a.cp.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.b.81.1	✓	8	5.3	odd	4
220.2.m.b.201.1	yes	8	55.3	odd	20
880.2.bo.c.81.2		8	20.3	even	4
880.2.bo.c.641.2		8	220.3	even	20
1100.2.n.b.201.2		8	55.47	odd	20
1100.2.n.b.301.2		8	5.2	odd	4
1100.2.cb.b.949.2		16	11.3	even	5	inner
1100.2.cb.b.949.3		16	55.14	even	10	inner
1100.2.cb.b.1049.2		16	5.4	even	2	inner
1100.2.cb.b.1049.3		16	1.1	even	1	trivial
1980.2.z.d.1081.2		8	165.113	even	20
1980.2.z.d.1621.2		8	15.8	even	4
2420.2.a.k.1.2		4	55.38	odd	20
2420.2.a.l.1.2		4	55.28	even	20
9680.2.a.co.1.3		4	220.83	odd	20
9680.2.a.cp.1.3		4	220.203	even	20

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:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.cb (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.151646 + 0.0492728i) q^{3} +(-1.93586 + 0.628998i) q^{7} +(-2.40648 - 1.74841i) q^{9} +(2.88699 + 1.63256i) q^{11} +(-0.384126 + 0.528704i) q^{13} +(2.52570 + 3.47632i) q^{17} +(0.919194 - 2.82899i) q^{19} -0.324558 q^{21} +6.11210i q^{23} +(-0.559952 - 0.770708i) q^{27} +(2.63577 + 8.11208i) q^{29} +(4.34733 + 3.15852i) q^{31} +(0.357361 + 0.389823i) q^{33} +(-3.28598 + 1.06768i) q^{37} +(-0.0843020 + 0.0612490i) q^{39} +(1.47374 - 4.53569i) q^{41} +10.1305i q^{43} +(6.94734 + 2.25733i) q^{47} +(-2.31122 + 1.67920i) q^{49} +(0.211724 + 0.651620i) q^{51} +(-6.53617 + 8.99626i) q^{53} +(0.278785 - 0.383714i) q^{57} +(-1.70562 - 5.24935i) q^{59} +(7.77155 - 5.64636i) q^{61} +(5.75835 + 1.87100i) q^{63} -5.60966i q^{67} +(-0.301160 + 0.926876i) q^{69} +(-0.0442449 + 0.0321458i) q^{71} +(-6.78819 + 2.20562i) q^{73} +(-6.61569 - 1.34450i) q^{77} +(2.37100 + 1.72263i) q^{79} +(2.71064 + 8.34250i) q^{81} +(-7.25807 - 9.98988i) q^{83} +1.36004i q^{87} -0.00487932 q^{89} +(0.411059 - 1.26511i) q^{91} +(0.503626 + 0.693182i) q^{93} +(-10.7307 + 14.7696i) q^{97} +(-4.09311 - 8.97639i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9} + 10 q^{11} + 14 q^{19} - 56 q^{21} + 2 q^{29} + 44 q^{31} - 54 q^{39} + 48 q^{41} + 54 q^{49} - 94 q^{51} + 18 q^{59} + 44 q^{61} - 22 q^{69} - 44 q^{71} + 50 q^{79} - 56 q^{81} - 16 q^{89}+ \cdots - 120 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 + 10 * q^11 + 14 * q^19 - 56 * q^21 + 2 * q^29 + 44 * q^31 - 54 * q^39 + 48 * q^41 + 54 * q^49 - 94 * q^51 + 18 * q^59 + 44 * q^61 - 22 * q^69 - 44 * q^71 + 50 * q^79 - 56 * q^81 - 16 * q^89 + 28 * q^91 - 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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