LMFDB - Embedded newform 46.3.b.a.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,3,Mod(45,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("46.45");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	46.b (of order $2$, degree $1$, 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:	$1.25340921606$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.0.613376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 58x^{2} + 599 $ x^4 + 58*x^2 + 599
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			45.1
Root			$6.67505i$ of defining polynomial
Character	$\chi$	$=$	46.45
Dual form			46.3.b.a.45.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} -2.41421 q^{3} +2.00000 q^{4} -9.43995i q^{5} +3.41421 q^{6} -3.91016i q^{7} -2.82843 q^{8} -3.17157 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} -2.41421 q^{3} +2.00000 q^{4} -9.43995i q^{5} +3.41421 q^{6} -3.91016i q^{7} -2.82843 q^{8} -3.17157 q^{9} +13.3501i q^{10} +3.91016i q^{11} -4.82843 q^{12} +10.3137 q^{13} +5.52980i q^{14} +22.7901i q^{15} +4.00000 q^{16} -17.2603i q^{17} +4.48528 q^{18} +26.7002i q^{19} -18.8799i q^{20} +9.43995i q^{21} -5.52980i q^{22} +(3.10051 - 22.7901i) q^{23} +6.82843 q^{24} -64.1127 q^{25} -14.5858 q^{26} +29.3848 q^{27} -7.82031i q^{28} +35.1421 q^{29} -32.2300i q^{30} +33.2426 q^{31} -5.65685 q^{32} -9.43995i q^{33} +24.4097i q^{34} -36.9117 q^{35} -6.34315 q^{36} -39.3794i q^{37} -37.7598i q^{38} -24.8995 q^{39} +26.7002i q^{40} +13.4853 q^{41} -13.3501i q^{42} +29.9395i q^{43} +7.82031i q^{44} +29.9395i q^{45} +(-4.38478 + 32.2300i) q^{46} -31.0416 q^{47} -9.65685 q^{48} +33.7107 q^{49} +90.6690 q^{50} +41.6700i q^{51} +20.6274 q^{52} +61.2207i q^{53} -41.5563 q^{54} +36.9117 q^{55} +11.0596i q^{56} -64.4600i q^{57} -49.6985 q^{58} -26.2010 q^{59} +45.5801i q^{60} -15.6406i q^{61} -47.0122 q^{62} +12.4013i q^{63} +8.00000 q^{64} -97.3609i q^{65} +13.3501i q^{66} -68.3702i q^{67} -34.5205i q^{68} +(-7.48528 + 55.0201i) q^{69} +52.2010 q^{70} -111.267 q^{71} +8.97056 q^{72} +47.8528 q^{73} +55.6910i q^{74} +154.782 q^{75} +53.4004i q^{76} +15.2893 q^{77} +35.2132 q^{78} -117.860i q^{79} -37.7598i q^{80} -42.3970 q^{81} -19.0711 q^{82} +74.8487i q^{83} +18.8799i q^{84} -162.936 q^{85} -42.3408i q^{86} -84.8406 q^{87} -11.0596i q^{88} +39.1016i q^{89} -42.3408i q^{90} -40.3282i q^{91} +(6.20101 - 45.5801i) q^{92} -80.2548 q^{93} +43.8995 q^{94} +252.049 q^{95} +13.6569 q^{96} -66.0797i q^{97} -47.6741 q^{98} -12.4013i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 8 q^{4} + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 8 * q^4 + 8 * q^6 - 24 * q^9	$ 4 q - 4 q^{3} + 8 q^{4} + 8 q^{6} - 24 q^{9} - 8 q^{12} - 4 q^{13} + 16 q^{16} - 16 q^{18} + 52 q^{23} + 16 q^{24} - 132 q^{25} - 64 q^{26} + 44 q^{27} + 84 q^{29} + 116 q^{31} + 56 q^{35} - 48 q^{36} - 60 q^{39} + 20 q^{41} + 56 q^{46} - 28 q^{47} - 16 q^{48} - 148 q^{49} + 176 q^{50} - 8 q^{52} - 104 q^{54} - 56 q^{55} - 80 q^{58} - 184 q^{59} - 24 q^{62} + 32 q^{64} + 4 q^{69} + 288 q^{70} - 100 q^{71} - 32 q^{72} - 148 q^{73} + 308 q^{75} + 344 q^{77} + 56 q^{78} + 68 q^{81} - 48 q^{82} - 120 q^{85} - 164 q^{87} + 104 q^{92} - 140 q^{93} + 136 q^{94} + 352 q^{95} + 32 q^{96} - 400 q^{98}+O(q^{100}) $ 4 * q - 4 * q^3 + 8 * q^4 + 8 * q^6 - 24 * q^9 - 8 * q^12 - 4 * q^13 + 16 * q^16 - 16 * q^18 + 52 * q^23 + 16 * q^24 - 132 * q^25 - 64 * q^26 + 44 * q^27 + 84 * q^29 + 116 * q^31 + 56 * q^35 - 48 * q^36 - 60 * q^39 + 20 * q^41 + 56 * q^46 - 28 * q^47 - 16 * q^48 - 148 * q^49 + 176 * q^50 - 8 * q^52 - 104 * q^54 - 56 * q^55 - 80 * q^58 - 184 * q^59 - 24 * q^62 + 32 * q^64 + 4 * q^69 + 288 * q^70 - 100 * q^71 - 32 * q^72 - 148 * q^73 + 308 * q^75 + 344 * q^77 + 56 * q^78 + 68 * q^81 - 48 * q^82 - 120 * q^85 - 164 * q^87 + 104 * q^92 - 140 * q^93 + 136 * q^94 + 352 * q^95 + 32 * q^96 - 400 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−2.41421			−0.804738			−0.402369	−	0.915478i	$-0.631813\pi$
$3$	−2.41421			−0.804738			−0.402369	+	0.915478i	$0.631813\pi$
$4$	2.00000			0.500000
$5$		−	9.43995i		−	1.88799i	−0.329959	−	0.943995i	$-0.607035\pi$
$5$		−	9.43995i		−	1.88799i	0.329959	−	0.943995i	$-0.392965\pi$
$6$	3.41421			0.569036
$7$		−	3.91016i		−	0.558594i	−0.960205	−	0.279297i	$-0.909899\pi$
$7$		−	3.91016i		−	0.558594i	0.960205	−	0.279297i	$-0.0901014\pi$
$8$	−2.82843			−0.353553
$9$	−3.17157			−0.352397
$10$			13.3501i			1.33501i
$11$			3.91016i			0.355469i	0.984078	+	0.177734i	$0.0568768\pi$
$11$			3.91016i			0.355469i	−0.984078	+	0.177734i	$0.943123\pi$
$12$	−4.82843			−0.402369
$13$	10.3137			0.793362			0.396681	−	0.917956i	$-0.370162\pi$
$13$	10.3137			0.793362			0.396681	+	0.917956i	$0.370162\pi$
$14$			5.52980i			0.394985i
$15$			22.7901i			1.51934i
$16$	4.00000			0.250000
$17$		−	17.2603i		−	1.01531i	−0.861561	−	0.507655i	$-0.830513\pi$
$17$		−	17.2603i		−	1.01531i	0.861561	−	0.507655i	$-0.169487\pi$
$18$	4.48528			0.249182
$19$			26.7002i			1.40527i	0.711548	+	0.702637i	$0.247994\pi$
$19$			26.7002i			1.40527i	−0.711548	+	0.702637i	$0.752006\pi$
$20$		−	18.8799i		−	0.943995i
$21$			9.43995i			0.449522i
$22$		−	5.52980i		−	0.251354i
$23$	3.10051	−	22.7901i	0.134805	−	0.990872i
$23$	3.10051	−	22.7901i	0.134805	−	0.990872i
$24$	6.82843			0.284518
$25$	−64.1127			−2.56451
$26$	−14.5858			−0.560992
$27$	29.3848			1.08833
$28$		−	7.82031i		−	0.279297i
$29$	35.1421			1.21180			0.605899	−	0.795542i	$-0.292814\pi$
$29$	35.1421			1.21180			0.605899	+	0.795542i	$0.292814\pi$
$30$		−	32.2300i		−	1.07433i
$31$	33.2426			1.07234			0.536172	−	0.844109i	$-0.319870\pi$
$31$	33.2426			1.07234			0.536172	+	0.844109i	$0.319870\pi$
$32$	−5.65685			−0.176777
$33$		−	9.43995i		−	0.286059i
$34$			24.4097i			0.717932i
$35$	−36.9117			−1.05462
$36$	−6.34315			−0.176198
$37$		−	39.3794i		−	1.06431i	−0.846647	−	0.532155i	$-0.821382\pi$
$37$		−	39.3794i		−	1.06431i	0.846647	−	0.532155i	$-0.178618\pi$
$38$		−	37.7598i		−	0.993679i
$39$	−24.8995			−0.638449
$40$			26.7002i			0.667505i
$41$	13.4853			0.328909			0.164455	−	0.986385i	$-0.447414\pi$
$41$	13.4853			0.328909			0.164455	+	0.986385i	$0.447414\pi$
$42$		−	13.3501i		−	0.317860i
$43$			29.9395i			0.696267i	0.937445	+	0.348134i	$0.113184\pi$
$43$			29.9395i			0.696267i	−0.937445	+	0.348134i	$0.886816\pi$
$44$			7.82031i			0.177734i
$45$			29.9395i			0.665322i
$46$	−4.38478	+	32.2300i	−0.0953212	+	0.700652i
$47$	−31.0416			−0.660460			−0.330230	−	0.943900i	$-0.607126\pi$
$47$	−31.0416			−0.660460			−0.330230	+	0.943900i	$0.607126\pi$
$48$	−9.65685			−0.201184
$49$	33.7107			0.687973
$50$	90.6690			1.81338
$51$			41.6700i			0.817058i
$52$	20.6274			0.396681
$53$			61.2207i			1.15511i	0.816352	+	0.577554i	$0.195993\pi$
$53$			61.2207i			1.15511i	−0.816352	+	0.577554i	$0.804007\pi$
$54$	−41.5563			−0.769562
$55$	36.9117			0.671122
$56$			11.0596i			0.197493i
$57$		−	64.4600i		−	1.13088i
$58$	−49.6985			−0.856870
$59$	−26.2010			−0.444085			−0.222042	−	0.975037i	$-0.571272\pi$
$59$	−26.2010			−0.444085			−0.222042	+	0.975037i	$0.571272\pi$
$60$			45.5801i			0.759669i
$61$		−	15.6406i		−	0.256404i	−0.991748	−	0.128202i	$-0.959079\pi$
$61$		−	15.6406i		−	0.256404i	0.991748	−	0.128202i	$-0.0409205\pi$
$62$	−47.0122			−0.758261
$63$			12.4013i			0.196847i
$64$	8.00000			0.125000
$65$		−	97.3609i		−	1.49786i
$66$			13.3501i			0.202274i
$67$		−	68.3702i		−	1.02045i	−0.860041	−	0.510225i	$-0.829562\pi$
$67$		−	68.3702i		−	1.02045i	0.860041	−	0.510225i	$-0.170438\pi$
$68$		−	34.5205i		−	0.507655i
$69$	−7.48528	+	55.0201i	−0.108482	+	0.797392i
$70$	52.2010			0.745729
$71$	−111.267			−1.56714			−0.783571	−	0.621303i	$-0.786604\pi$
$71$	−111.267			−1.56714			−0.783571	+	0.621303i	$0.786604\pi$
$72$	8.97056			0.124591
$73$	47.8528			0.655518			0.327759	−	0.944761i	$-0.393707\pi$
$73$	47.8528			0.655518			0.327759	+	0.944761i	$0.393707\pi$
$74$			55.6910i			0.752580i
$75$	154.782			2.06376
$76$			53.4004i			0.702637i
$77$	15.2893			0.198563
$78$	35.2132			0.451451
$79$		−	117.860i		−	1.49190i	−0.665999	−	0.745952i	$-0.731995\pi$
$79$		−	117.860i		−	1.49190i	0.665999	−	0.745952i	$-0.268005\pi$
$80$		−	37.7598i		−	0.471998i
$81$	−42.3970			−0.523419
$82$	−19.0711			−0.232574
$83$			74.8487i			0.901792i	0.892576	+	0.450896i	$0.148895\pi$
$83$			74.8487i			0.901792i	−0.892576	+	0.450896i	$0.851105\pi$
$84$			18.8799i			0.224761i
$85$	−162.936			−1.91689
$86$		−	42.3408i		−	0.492335i
$87$	−84.8406			−0.975180
$88$		−	11.0596i		−	0.125677i
$89$			39.1016i			0.439343i	0.975574	+	0.219672i	$0.0704986\pi$
$89$			39.1016i			0.439343i	−0.975574	+	0.219672i	$0.929501\pi$
$90$		−	42.3408i		−	0.470454i
$91$		−	40.3282i		−	0.443167i
$92$	6.20101	−	45.5801i	0.0674023	−	0.495436i
$93$	−80.2548			−0.862955
$94$	43.8995			0.467016
$95$	252.049			2.65314
$96$	13.6569			0.142259
$97$		−	66.0797i		−	0.681234i	−0.940202	−	0.340617i	$-0.889364\pi$
$97$		−	66.0797i		−	0.681234i	0.940202	−	0.340617i	$-0.110636\pi$
$98$	−47.6741			−0.486470
$99$		−	12.4013i		−	0.125266i
$100$	−128.225			−1.28225
$101$	101.338			1.00335			0.501674	−	0.865057i	$-0.332718\pi$
$101$	101.338			1.00335			0.501674	+	0.865057i	$0.332718\pi$
$102$		−	58.9302i		−	0.577747i
$103$			101.549i			0.985912i	0.870054	+	0.492956i	$0.164084\pi$
$103$			101.549i			0.985912i	−0.870054	+	0.492956i	$0.835916\pi$
$104$	−29.1716			−0.280496
$105$	89.1127			0.848692
$106$		−	86.5792i		−	0.816785i
$107$		−	75.5196i		−	0.705791i	−0.935663	−	0.352895i	$-0.885197\pi$
$107$		−	75.5196i		−	0.705791i	0.935663	−	0.352895i	$-0.114803\pi$
$108$	58.7696			0.544163
$109$			138.638i			1.27191i	0.771727	+	0.635954i	$0.219393\pi$
$109$			138.638i			1.27191i	−0.771727	+	0.635954i	$0.780607\pi$
$110$	−52.2010			−0.474555
$111$			95.0704i			0.856490i
$112$		−	15.6406i		−	0.139648i
$113$			180.701i			1.59912i	0.600585	+	0.799561i	$0.294935\pi$
$113$			180.701i			1.59912i	−0.600585	+	0.799561i	$0.705065\pi$
$114$			91.1602i			0.799651i
$115$	−215.137	−	29.2686i	−1.87076	−	0.254510i
$116$	70.2843			0.605899
$117$	−32.7107			−0.279578
$118$	37.0538			0.314015
$119$	−67.4903			−0.567146
$120$		−	64.4600i		−	0.537167i
$121$	105.711			0.873642
$122$			22.1192i			0.181305i
$123$	−32.5563			−0.264686
$124$	66.4853			0.536172
$125$			369.222i			2.95378i
$126$		−	17.5382i		−	0.139192i
$127$	36.3898			0.286534			0.143267	−	0.989684i	$-0.454239\pi$
$127$	36.3898			0.286534			0.143267	+	0.989684i	$0.454239\pi$
$128$	−11.3137			−0.0883883
$129$		−	72.2803i		−	0.560313i
$130$			137.689i			1.05915i
$131$	−65.3848			−0.499120			−0.249560	−	0.968359i	$-0.580286\pi$
$131$	−65.3848			−0.499120			−0.249560	+	0.968359i	$0.580286\pi$
$132$		−	18.8799i		−	0.143030i
$133$	104.402			0.784978
$134$			96.6900i			0.721567i
$135$		−	277.391i		−	2.05475i
$136$			48.8194i			0.358966i
$137$		−	65.8018i		−	0.480305i	−0.970735	−	0.240152i	$-0.922803\pi$
$137$		−	65.8018i		−	0.480305i	0.970735	−	0.240152i	$-0.0771974\pi$
$138$	10.5858	−	77.8101i	0.0767086	−	0.563842i
$139$	29.4092			0.211577			0.105788	−	0.994389i	$-0.466263\pi$
$139$	29.4092			0.211577			0.105788	+	0.994389i	$0.466263\pi$
$140$	−73.8234			−0.527310
$141$	74.9411			0.531497
$142$	157.355			1.10814
$143$			40.3282i			0.282015i
$144$	−12.6863			−0.0880992
$145$		−	331.740i		−	2.28786i
$146$	−67.6741			−0.463521
$147$	−81.3848			−0.553638
$148$		−	78.7589i		−	0.532155i
$149$		−	3.23928i		−	0.0217401i	−0.999941	−	0.0108701i	$-0.996540\pi$
$149$		−	3.23928i		−	0.0217401i	0.999941	−	0.0108701i	$-0.00346012\pi$
$150$	−218.894			−1.45930
$151$	−2.41421			−0.0159882			−0.00799408	−	0.999968i	$-0.502545\pi$
$151$	−2.41421			−0.0159882			−0.00799408	+	0.999968i	$0.502545\pi$
$152$		−	75.5196i		−	0.496840i
$153$			54.7422i			0.357792i
$154$	−21.6224			−0.140405
$155$		−	313.809i		−	2.02457i
$156$	−49.7990			−0.319224
$157$			73.6221i			0.468931i	0.972124	+	0.234465i	$0.0753339\pi$
$157$			73.6221i			0.468931i	−0.972124	+	0.234465i	$0.924666\pi$
$158$			166.680i			1.05494i
$159$		−	147.800i		−	0.929559i
$160$			53.4004i			0.333753i
$161$	−89.1127	−	12.1235i	−0.553495	−	0.0753010i
$162$	59.9584			0.370113
$163$	125.586			0.770465			0.385232	−	0.922820i	$-0.374121\pi$
$163$	125.586			0.770465			0.385232	+	0.922820i	$0.374121\pi$
$164$	26.9706			0.164455
$165$	−89.1127			−0.540077
$166$		−	105.852i		−	0.637663i
$167$	−92.8284			−0.555859			−0.277929	−	0.960601i	$-0.589648\pi$
$167$	−92.8284			−0.555859			−0.277929	+	0.960601i	$0.589648\pi$
$168$		−	26.7002i		−	0.158930i
$169$	−62.6274			−0.370576
$170$	230.426			1.35545
$171$		−	84.6817i		−	0.495215i
$172$			59.8790i			0.348134i
$173$	−6.71068			−0.0387900			−0.0193950	−	0.999812i	$-0.506174\pi$
$173$	−6.71068			−0.0387900			−0.0193950	+	0.999812i	$0.506174\pi$
$174$	119.983			0.689556
$175$			250.691i			1.43252i
$176$			15.6406i			0.0888672i
$177$	63.2548			0.357372
$178$		−	55.2980i		−	0.310663i
$179$	278.262			1.55454			0.777268	−	0.629170i	$-0.216605\pi$
$179$	278.262			1.55454			0.777268	+	0.629170i	$0.216605\pi$
$180$			59.8790i			0.332661i
$181$			53.6783i			0.296565i	0.988945	+	0.148283i	$0.0473745\pi$
$181$			53.6783i			0.296565i	−0.988945	+	0.148283i	$0.952625\pi$
$182$			57.0327i			0.313367i
$183$			37.7598i			0.206338i
$184$	−8.76955	+	64.4600i	−0.0476606	+	0.350326i
$185$	−371.740			−2.00941
$186$	113.497			0.610201
$187$	67.4903			0.360911
$188$	−62.0833			−0.330230
$189$		−	114.899i		−	0.607932i
$190$	−356.451			−1.87606
$191$			168.692i			0.883207i	0.897210	+	0.441603i	$0.145590\pi$
$191$			168.692i			0.883207i	−0.897210	+	0.441603i	$0.854410\pi$
$192$	−19.3137			−0.100592
$193$	−95.3188			−0.493880			−0.246940	−	0.969031i	$-0.579425\pi$
$193$	−95.3188			−0.493880			−0.246940	+	0.969031i	$0.579425\pi$
$194$			93.4508i			0.481705i
$195$			235.050i			1.20538i
$196$	67.4214			0.343987
$197$	249.083			1.26438			0.632191	−	0.774813i	$-0.282156\pi$
$197$	249.083			1.26438			0.632191	+	0.774813i	$0.282156\pi$
$198$			17.5382i			0.0885765i
$199$			76.1905i			0.382867i	0.981506	+	0.191433i	$0.0613136\pi$
$199$			76.1905i			0.382867i	−0.981506	+	0.191433i	$0.938686\pi$
$200$	181.338			0.906690
$201$			165.060i			0.821195i
$202$	−143.314			−0.709474
$203$		−	137.411i		−	0.676903i
$204$			83.3399i			0.408529i
$205$		−	127.300i		−	0.620978i
$206$		−	143.612i		−	0.697145i
$207$	−9.83348	+	72.2803i	−0.0475047	+	0.349180i
$208$	41.2548			0.198341
$209$	−104.402			−0.499531
$210$	−126.024			−0.600116
$211$	−71.1716			−0.337306			−0.168653	−	0.985675i	$-0.553942\pi$
$211$	−71.1716			−0.337306			−0.168653	+	0.985675i	$0.553942\pi$
$212$			122.441i			0.577554i
$213$	268.622			1.26114
$214$			106.801i			0.499069i
$215$	282.627			1.31455
$216$	−83.1127			−0.384781
$217$		−	129.984i		−	0.599004i
$218$		−	196.064i		−	0.899374i
$219$	−115.527			−0.527520
$220$	73.8234			0.335561
$221$		−	178.017i		−	0.805508i
$222$		−	134.450i		−	0.605630i
$223$	−84.0833			−0.377055			−0.188527	−	0.982068i	$-0.560371\pi$
$223$	−84.0833			−0.377055			−0.188527	+	0.982068i	$0.560371\pi$
$224$			22.1192i			0.0987464i
$225$	203.338			0.903725
$226$		−	255.550i		−	1.13075i
$227$			263.092i			1.15900i	0.814974	+	0.579498i	$0.196751\pi$
$227$			263.092i			1.15900i	−0.814974	+	0.579498i	$0.803249\pi$
$228$		−	128.920i		−	0.565439i
$229$			141.321i			0.617124i	0.951204	+	0.308562i	$0.0998477\pi$
$229$			141.321i			0.617124i	−0.951204	+	0.308562i	$0.900152\pi$
$230$	304.250	+	41.3921i	1.32283	+	0.179966i
$231$	−36.9117			−0.159791
$232$	−99.3970			−0.428435
$233$	−353.784			−1.51839			−0.759193	−	0.650866i	$-0.774406\pi$
$233$	−353.784			−1.51839			−0.759193	+	0.650866i	$0.774406\pi$
$234$	46.2599			0.197692
$235$			293.032i			1.24694i
$236$	−52.4020			−0.222042
$237$			284.540i			1.20059i
$238$	95.4457			0.401033
$239$	−272.286			−1.13927			−0.569637	−	0.821897i	$-0.692916\pi$
$239$	−272.286			−1.13927			−0.569637	+	0.821897i	$0.692916\pi$
$240$			91.1602i			0.379834i
$241$		−	443.678i		−	1.84099i	−0.390758	−	0.920493i	$-0.627787\pi$
$241$		−	443.678i		−	1.84099i	0.390758	−	0.920493i	$-0.372213\pi$
$242$	−149.497			−0.617758
$243$	−162.108			−0.667110
$244$		−	31.2812i		−	0.128202i
$245$		−	318.227i		−	1.29889i
$246$	46.0416			0.187161
$247$			275.378i			1.11489i
$248$	−94.0244			−0.379131
$249$		−	180.701i		−	0.725706i
$250$		−	522.159i		−	2.08864i
$251$			194.607i			0.775326i	0.921801	+	0.387663i	$0.126718\pi$
$251$			194.607i			0.775326i	−0.921801	+	0.387663i	$0.873282\pi$
$252$			24.8027i			0.0984234i
$253$	89.1127	+	12.1235i	0.352224	+	0.0479188i
$254$	−51.4630			−0.202610
$255$	393.362			1.54260
$256$	16.0000			0.0625000
$257$	−22.1371			−0.0861365			−0.0430683	−	0.999072i	$-0.513713\pi$
$257$	−22.1371			−0.0861365			−0.0430683	+	0.999072i	$0.513713\pi$
$258$			102.220i			0.396201i
$259$	−153.980			−0.594517
$260$		−	194.722i		−	0.748930i
$261$	−111.456			−0.427034
$262$	92.4680			0.352931
$263$		−	425.076i		−	1.61626i	−0.589006	−	0.808129i	$-0.700481\pi$
$263$		−	425.076i		−	1.61626i	0.589006	−	0.808129i	$-0.299519\pi$
$264$			26.7002i			0.101137i
$265$	577.921			2.18083
$266$	−147.647			−0.555063
$267$		−	94.3995i		−	0.353556i
$268$		−	136.740i		−	0.510225i
$269$	411.215			1.52868			0.764341	−	0.644813i	$-0.223065\pi$
$269$	411.215			1.52868			0.764341	+	0.644813i	$0.223065\pi$
$270$			392.290i			1.45293i
$271$	−98.8183			−0.364643			−0.182322	−	0.983239i	$-0.558361\pi$
$271$	−98.8183			−0.364643			−0.182322	+	0.983239i	$0.558361\pi$
$272$		−	69.0411i		−	0.253827i
$273$			97.3609i			0.356633i
$274$			93.0578i			0.339627i
$275$		−	250.691i		−	0.911602i
$276$	−14.9706	+	110.040i	−0.0542412	+	0.398696i
$277$	−207.319			−0.748443			−0.374222	−	0.927339i	$-0.622090\pi$
$277$	−207.319			−0.748443			−0.374222	+	0.927339i	$0.622090\pi$
$278$	−41.5908			−0.149607
$279$	−105.431			−0.377891
$280$	104.402			0.372864
$281$			31.0034i			0.110332i	0.998477	+	0.0551661i	$0.0175688\pi$
$281$			31.0034i			0.110332i	−0.998477	+	0.0551661i	$0.982431\pi$
$282$	−105.983			−0.375825
$283$			225.888i			0.798191i	0.916909	+	0.399095i	$0.130676\pi$
$283$			225.888i			0.798191i	−0.916909	+	0.399095i	$0.869324\pi$
$284$	−222.534			−0.783571
$285$	−608.500			−2.13509
$286$		−	57.0327i		−	0.199415i
$287$		−	52.7296i		−	0.183727i
$288$	17.9411			0.0622956
$289$	−8.91674			−0.0308538
$290$			469.151i			1.61776i
$291$			159.530i			0.548215i
$292$	95.7056			0.327759
$293$		−	162.099i		−	0.553238i	−0.960980	−	0.276619i	$-0.910786\pi$
$293$		−	162.099i		−	0.553238i	0.960980	−	0.276619i	$-0.0892140\pi$
$294$	115.095			0.391481
$295$			247.336i			0.838428i
$296$			111.382i			0.376290i
$297$			114.899i			0.386866i
$298$			4.58103i			0.0153726i
$299$	31.9777	−	235.050i	0.106949	−	0.786121i
$300$	309.563			1.03188
$301$	117.068			0.388931
$302$	3.41421			0.0113053
$303$	−244.652			−0.807432
$304$			106.801i			0.351319i
$305$	−147.647			−0.484088
$306$		−	77.4171i		−	0.252997i
$307$	342.299			1.11498			0.557490	−	0.830184i	$-0.311765\pi$
$307$	342.299			1.11498			0.557490	+	0.830184i	$0.311765\pi$
$308$	30.5786			0.0992813
$309$		−	245.161i		−	0.793401i
$310$			443.793i			1.43159i
$311$	464.654			1.49406			0.747032	−	0.664788i	$-0.231478\pi$
$311$	464.654			1.49406			0.747032	+	0.664788i	$0.231478\pi$
$312$	70.4264			0.225726
$313$		−	95.1855i		−	0.304107i	−0.988372	−	0.152054i	$-0.951411\pi$
$313$		−	95.1855i		−	0.304107i	0.988372	−	0.152054i	$-0.0485886\pi$
$314$		−	104.117i		−	0.331584i
$315$	117.068			0.371645
$316$		−	235.721i		−	0.745952i
$317$	−210.142			−0.662909			−0.331454	−	0.943471i	$-0.607539\pi$
$317$	−210.142			−0.662909			−0.331454	+	0.943471i	$0.607539\pi$
$318$			209.021i			0.657298i
$319$			137.411i			0.430756i
$320$		−	75.5196i		−	0.235999i
$321$			182.320i			0.567977i
$322$	126.024	+	17.1452i	0.391380	+	0.0532458i
$323$	460.853			1.42679
$324$	−84.7939			−0.261710
$325$	−661.240			−2.03458
$326$	−177.605			−0.544801
$327$		−	334.701i		−	1.02355i
$328$	−38.1421			−0.116287
$329$			121.378i			0.368929i
$330$	126.024			0.381892
$331$	66.2822			0.200248			0.100124	−	0.994975i	$-0.468076\pi$
$331$	66.2822			0.200248			0.100124	+	0.994975i	$0.468076\pi$
$332$			149.697i			0.450896i
$333$			124.895i			0.375059i
$334$	131.279			0.393052
$335$	−645.411			−1.92660
$336$			37.7598i			0.112380i
$337$			453.348i			1.34525i	0.739985	+	0.672623i	$0.234832\pi$
$337$			453.348i			1.34525i	−0.739985	+	0.672623i	$0.765168\pi$
$338$	88.5685			0.262037
$339$		−	436.250i		−	1.28687i
$340$	−325.872			−0.958447
$341$			129.984i			0.381185i
$342$			119.758i			0.350170i
$343$		−	323.412i		−	0.942891i
$344$		−	84.6817i		−	0.246168i
$345$	519.387	+	70.6607i	1.50547	+	0.204814i
$346$	9.49033			0.0274287
$347$	−291.750			−0.840779			−0.420389	−	0.907344i	$-0.638107\pi$
$347$	−291.750			−0.840779			−0.420389	+	0.907344i	$0.638107\pi$
$348$	−169.681			−0.487590
$349$	150.951			0.432525			0.216263	−	0.976335i	$-0.430613\pi$
$349$	150.951			0.432525			0.216263	+	0.976335i	$0.430613\pi$
$350$		−	354.530i		−	1.01294i
$351$	303.066			0.863436
$352$		−	22.1192i		−	0.0628386i
$353$	377.059			1.06816			0.534078	−	0.845435i	$-0.320659\pi$
$353$	377.059			1.06816			0.534078	+	0.845435i	$0.320659\pi$
$354$	−89.4558			−0.252700
$355$			1050.36i			2.95875i
$356$			78.2031i			0.219672i
$357$	162.936			0.456404
$358$	−393.522			−1.09922
$359$		−	352.240i		−	0.981169i	−0.871394	−	0.490584i	$-0.836783\pi$
$359$		−	352.240i		−	0.981169i	0.871394	−	0.490584i	$-0.163217\pi$
$360$		−	84.6817i		−	0.235227i
$361$	−351.902			−0.974797
$362$		−	75.9126i		−	0.209703i
$363$	−255.208			−0.703053
$364$		−	80.6564i		−	0.221584i
$365$		−	451.728i		−	1.23761i
$366$		−	53.4004i		−	0.145903i
$367$			320.843i			0.874232i	0.899405	+	0.437116i	$0.144000\pi$
$367$			320.843i			0.874232i	−0.899405	+	0.437116i	$0.856000\pi$
$368$	12.4020	−	91.1602i	0.0337011	−	0.247718i
$369$	−42.7696			−0.115907
$370$	525.720			1.42086
$371$	239.383			0.645236
$372$	−160.510			−0.431478
$373$		−	156.128i		−	0.418575i	−0.977854	−	0.209287i	$-0.932886\pi$
$373$		−	156.128i		−	0.418575i	0.977854	−	0.209287i	$-0.0671144\pi$
$374$	−95.4457			−0.255203
$375$		−	891.381i		−	2.37702i
$376$	87.7990			0.233508
$377$	362.446			0.961395
$378$			162.492i			0.429873i
$379$		−	451.220i		−	1.19055i	−0.803520	−	0.595277i	$-0.797042\pi$
$379$		−	451.220i		−	1.19055i	0.803520	−	0.595277i	$-0.202958\pi$
$380$	504.098			1.32657
$381$	−87.8528			−0.230585
$382$		−	238.567i		−	0.624521i
$383$			423.178i			1.10490i	0.833545	+	0.552452i	$0.186308\pi$
$383$			423.178i			1.10490i	−0.833545	+	0.552452i	$0.813692\pi$
$384$	27.3137			0.0711294
$385$		−	144.330i		−	0.374884i
$386$	134.801			0.349226
$387$		−	94.9553i		−	0.245363i
$388$		−	132.159i		−	0.340617i
$389$		−	11.0596i		−	0.0284308i	−0.999899	−	0.0142154i	$-0.995475\pi$
$389$		−	11.0596i		−	0.0284308i	0.999899	−	0.0142154i	$-0.00452506\pi$
$390$		−	332.411i		−	0.852336i
$391$	−393.362	−	53.5155i	−1.00604	−	0.136868i
$392$	−95.3482			−0.243235
$393$	157.853			0.401661
$394$	−352.257			−0.894053
$395$	−1112.60			−2.81670
$396$		−	24.8027i		−	0.0626331i
$397$	−332.578			−0.837727			−0.418864	−	0.908049i	$-0.637571\pi$
$397$	−332.578			−0.837727			−0.418864	+	0.908049i	$0.637571\pi$
$398$		−	107.750i		−	0.270728i
$399$	−252.049			−0.631701
$400$	−256.451			−0.641127
$401$		−	51.7808i		−	0.129129i	−0.997914	−	0.0645646i	$-0.979434\pi$
$401$		−	51.7808i		−	0.129129i	0.997914	−	0.0645646i	$-0.0205658\pi$
$402$		−	233.430i		−	0.580673i
$403$	342.855			0.850757
$404$	202.676			0.501674
$405$			400.225i			0.988211i
$406$			194.329i			0.478642i
$407$	153.980			0.378329
$408$		−	117.860i		−	0.288874i
$409$	256.088			0.626133			0.313066	−	0.949731i	$-0.398644\pi$
$409$	256.088			0.626133			0.313066	+	0.949731i	$0.398644\pi$
$410$			180.030i			0.439097i
$411$			158.860i			0.386520i
$412$			203.098i			0.492956i
$413$			102.450i			0.248063i
$414$	13.9066	−	102.220i	0.0335909	−	0.246908i
$415$	706.569			1.70257
$416$	−58.3431			−0.140248
$417$	−71.0000			−0.170264
$418$	147.647			0.353222
$419$		−	241.644i		−	0.576715i	−0.957523	−	0.288358i	$-0.906891\pi$
$419$		−	241.644i		−	0.576715i	0.957523	−	0.288358i	$-0.0931092\pi$
$420$	178.225			0.424346
$421$		−	312.860i		−	0.743136i	−0.928406	−	0.371568i	$-0.878820\pi$
$421$		−	312.860i		−	0.743136i	0.928406	−	0.371568i	$-0.121180\pi$
$422$	100.652			0.238511
$423$	98.4508			0.232744
$424$		−	173.158i		−	0.408392i
$425$			1106.60i			2.60377i
$426$	−379.889			−0.891759
$427$	−61.1573			−0.143225
$428$		−	151.039i		−	0.352895i
$429$		−	97.3609i		−	0.226949i
$430$	−399.696			−0.929524
$431$			672.412i			1.56012i	0.625704	+	0.780060i	$0.284812\pi$
$431$			672.412i			1.56012i	−0.625704	+	0.780060i	$0.715188\pi$
$432$	117.539			0.272081
$433$			395.414i			0.913197i	0.889673	+	0.456598i	$0.150932\pi$
$433$			395.414i			0.913197i	−0.889673	+	0.456598i	$0.849068\pi$
$434$			183.825i			0.423560i
$435$			800.891i			1.84113i
$436$			277.276i			0.635954i
$437$	608.500	+	82.7842i	1.39245	+	0.189437i
$438$	163.380			0.373013
$439$	836.997			1.90660			0.953300	−	0.302026i	$-0.0976630\pi$
$439$	836.997			1.90660			0.953300	+	0.302026i	$0.0976630\pi$
$440$	−104.402			−0.237277
$441$	−106.916			−0.242440
$442$			251.755i			0.569580i
$443$	−227.905			−0.514457			−0.257229	−	0.966351i	$-0.582809\pi$
$443$	−227.905			−0.514457			−0.257229	+	0.966351i	$0.582809\pi$
$444$			190.141i			0.428245i
$445$	369.117			0.829476
$446$	118.912			0.266618
$447$			7.82031i			0.0174951i
$448$		−	31.2812i		−	0.0698242i
$449$	−439.019			−0.977771			−0.488886	−	0.872348i	$-0.662596\pi$
$449$	−439.019			−0.977771			−0.488886	+	0.872348i	$0.662596\pi$
$450$	−287.563			−0.639030
$451$			52.7296i			0.116917i
$452$			361.402i			0.799561i
$453$	5.82843			0.0128663
$454$		−	372.068i		−	0.819534i
$455$	−380.696			−0.836695
$456$			182.320i			0.399826i
$457$			40.1654i			0.0878893i	0.999034	+	0.0439447i	$0.0139925\pi$
$457$			40.1654i			0.0878893i	−0.999034	+	0.0439447i	$0.986007\pi$
$458$		−	199.859i		−	0.436373i
$459$		−	507.189i		−	1.10499i
$460$	−430.274	−	58.5372i	−0.935379	−	0.127255i
$461$	65.6762			0.142465			0.0712323	−	0.997460i	$-0.477307\pi$
$461$	65.6762			0.142465			0.0712323	+	0.997460i	$0.477307\pi$
$462$	52.2010			0.112989
$463$	−673.436			−1.45450			−0.727252	−	0.686370i	$-0.759203\pi$
$463$	−673.436			−1.45450			−0.727252	+	0.686370i	$0.759203\pi$
$464$	140.569			0.302949
$465$			757.602i			1.62925i
$466$	500.326			1.07366
$467$			310.685i			0.665278i	0.943054	+	0.332639i	$0.107939\pi$
$467$			310.685i			0.665278i	−0.943054	+	0.332639i	$0.892061\pi$
$468$	−65.4214			−0.139789
$469$	−267.338			−0.570017
$470$		−	414.409i		−	0.881722i
$471$		−	177.739i		−	0.377366i
$472$	74.1076			0.157008
$473$	−117.068			−0.247501
$474$		−	402.401i		−	0.848947i
$475$		−	1711.82i		−	3.60384i
$476$	−134.981			−0.283573
$477$		−	194.166i		−	0.407057i
$478$	385.071			0.805588
$479$		−	230.469i		−	0.481146i	−0.970631	−	0.240573i	$-0.922665\pi$
$479$		−	230.469i		−	0.481146i	0.970631	−	0.240573i	$-0.0773354\pi$
$480$		−	128.920i		−	0.268583i
$481$		−	406.148i		−	0.844383i
$482$			627.455i			1.30177i
$483$	215.137	+	29.2686i	0.445418	+	0.0605976i
$484$	211.421			0.436821
$485$	−623.789			−1.28616
$486$	229.255			0.471718
$487$	372.360			0.764599			0.382299	−	0.924039i	$-0.375132\pi$
$487$	372.360			0.764599			0.382299	+	0.924039i	$0.375132\pi$
$488$			44.2384i			0.0906524i
$489$	−303.191			−0.620022
$490$			450.041i			0.918451i
$491$	258.026			0.525512			0.262756	−	0.964862i	$-0.415369\pi$
$491$	258.026			0.525512			0.262756	+	0.964862i	$0.415369\pi$
$492$	−65.1127			−0.132343
$493$		−	606.563i		−	1.23035i
$494$		−	389.444i		−	0.788347i
$495$	−117.068			−0.236501
$496$	132.971			0.268086
$497$			435.071i			0.875395i
$498$			255.550i			0.513152i
$499$	−372.747			−0.746988			−0.373494	−	0.927632i	$-0.621840\pi$
$499$	−372.747			−0.746988			−0.373494	+	0.927632i	$0.621840\pi$
$500$			738.444i			1.47689i
$501$	224.108			0.447321
$502$		−	275.215i		−	0.548238i
$503$		−	611.191i		−	1.21509i	−0.794284	−	0.607546i	$-0.792154\pi$
$503$		−	611.191i		−	1.21509i	0.794284	−	0.607546i	$-0.207846\pi$
$504$		−	35.0763i		−	0.0695958i
$505$		−	956.627i		−	1.89431i
$506$	−126.024	−	17.1452i	−0.249060	−	0.0338837i
$507$	151.196			0.298217
$508$	72.7797			0.143267
$509$	357.985			0.703310			0.351655	−	0.936130i	$-0.385619\pi$
$509$	357.985			0.703310			0.351655	+	0.936130i	$0.385619\pi$
$510$	−556.299			−1.09078
$511$		−	187.112i		−	0.366168i
$512$	−22.6274			−0.0441942
$513$			784.580i			1.52940i
$514$	31.3066			0.0609077
$515$	958.617			1.86139
$516$		−	144.561i		−	0.280156i
$517$		−	121.378i		−	0.234773i
$518$	217.760			0.420387
$519$	16.2010			0.0312158
$520$			275.378i			0.529574i
$521$			123.227i			0.236521i	0.992983	+	0.118261i	$0.0377318\pi$
$521$			123.227i			0.236521i	−0.992983	+	0.118261i	$0.962268\pi$
$522$	157.622			0.301959
$523$			246.110i			0.470573i	0.971926	+	0.235286i	$0.0756028\pi$
$523$			246.110i			0.470573i	−0.971926	+	0.235286i	$0.924397\pi$
$524$	−130.770			−0.249560
$525$		−	605.221i		−	1.15280i
$526$			601.148i			1.14287i
$527$		−	573.777i		−	1.08876i
$528$		−	37.7598i		−	0.0715148i
$529$	−509.774	−	141.321i	−0.963655	−	0.267148i
$530$	−817.304			−1.54208
$531$	83.0984			0.156494
$532$	208.804			0.392489
$533$	139.083			0.260944
$534$			133.501i			0.250002i
$535$	−712.902			−1.33253
$536$			193.380i			0.360784i
$537$	−671.784			−1.25099
$538$	−581.546			−1.08094
$539$			131.814i			0.244553i
$540$		−	554.782i		−	1.02737i
$541$	−425.922			−0.787286			−0.393643	−	0.919263i	$-0.628785\pi$
$541$	−425.922			−0.787286			−0.393643	+	0.919263i	$0.628785\pi$
$542$	139.750			0.257842
$543$		−	129.591i		−	0.238657i
$544$			97.6388i			0.179483i
$545$	1308.74			2.40135
$546$		−	137.689i		−	0.252178i
$547$	−715.070			−1.30726			−0.653629	−	0.756815i	$-0.726754\pi$
$547$	−715.070			−1.30726			−0.653629	+	0.756815i	$0.726754\pi$
$548$		−	131.604i		−	0.240152i
$549$			49.6054i			0.0903559i
$550$			354.530i			0.644600i
$551$			938.303i			1.70291i
$552$	21.1716	−	155.620i	0.0383543	−	0.281921i
$553$	−460.853			−0.833369
$554$	293.193			0.529229
$555$	897.460			1.61705
$556$	58.8183			0.105788
$557$			325.539i			0.584451i	0.956349	+	0.292226i	$0.0943958\pi$
$557$			325.539i			0.584451i	−0.956349	+	0.292226i	$0.905604\pi$
$558$	149.103			0.267209
$559$			308.787i			0.552392i
$560$	−147.647			−0.263655
$561$	−162.936			−0.290439
$562$		−	43.8454i		−	0.0780167i
$563$		−	636.780i		−	1.13105i	−0.824732	−	0.565524i	$-0.808674\pi$
$563$		−	636.780i		−	1.13105i	0.824732	−	0.565524i	$-0.191326\pi$
$564$	149.882			0.265749
$565$	1705.81			3.01913
$566$		−	319.454i		−	0.564406i
$567$			165.779i			0.292379i
$568$	314.711			0.554068
$569$			359.226i			0.631329i	0.948871	+	0.315665i	$0.102227\pi$
$569$			359.226i			0.631329i	−0.948871	+	0.315665i	$0.897773\pi$
$570$	860.548			1.50973
$571$		−	766.371i		−	1.34216i	−0.741387	−	0.671078i	$-0.765832\pi$
$571$		−	766.371i		−	1.34216i	0.741387	−	0.671078i	$-0.234168\pi$
$572$			80.6564i			0.141008i
$573$		−	407.260i		−	0.710750i
$574$			74.5709i			0.129914i
$575$	−198.782	+	1461.13i	−0.345707	+	2.54110i
$576$	−25.3726			−0.0440496
$577$	−966.661			−1.67532			−0.837661	−	0.546190i	$-0.816078\pi$
$577$	−966.661			−1.67532			−0.837661	+	0.546190i	$0.816078\pi$
$578$	12.6102			0.0218169
$579$	230.120			0.397444
$580$		−	663.480i		−	1.14393i
$581$	292.670			0.503735
$582$		−	225.610i		−	0.387646i
$583$	−239.383			−0.410605
$584$	−135.348			−0.231761
$585$			308.787i			0.527841i
$586$			229.242i			0.391199i
$587$	−855.933			−1.45815			−0.729074	−	0.684435i	$-0.760049\pi$
$587$	−855.933			−1.45815			−0.729074	+	0.684435i	$0.760049\pi$
$588$	−162.770			−0.276819
$589$			887.586i			1.50694i
$590$		−	349.786i		−	0.592858i
$591$	−601.340			−1.01750
$592$		−	157.518i		−	0.266077i
$593$	159.563			0.269078			0.134539	−	0.990908i	$-0.457045\pi$
$593$	159.563			0.269078			0.134539	+	0.990908i	$0.457045\pi$
$594$		−	162.492i		−	0.273555i
$595$			637.106i			1.07077i
$596$		−	6.47856i		−	0.0108701i
$597$		−	183.940i		−	0.308107i
$598$	−45.2233	+	332.411i	−0.0756243	+	0.555871i
$599$	−46.1320			−0.0770151			−0.0385075	−	0.999258i	$-0.512260\pi$
$599$	−46.1320			−0.0770151			−0.0385075	+	0.999258i	$0.512260\pi$
$600$	−437.789			−0.729648
$601$	−283.010			−0.470899			−0.235449	−	0.971887i	$-0.575656\pi$
$601$	−283.010			−0.470899			−0.235449	+	0.971887i	$0.575656\pi$
$602$	−165.559			−0.275015
$603$			216.841i			0.359604i
$604$	−4.82843			−0.00799408
$605$		−	997.904i		−	1.64943i
$606$	345.990			0.570940
$607$	690.250			1.13715			0.568575	−	0.822632i	$-0.307495\pi$
$607$	690.250			1.13715			0.568575	+	0.822632i	$0.307495\pi$
$608$		−	151.039i		−	0.248420i
$609$			331.740i			0.544729i
$610$	208.804			0.342302
$611$	−320.154			−0.523984
$612$			109.484i			0.178896i
$613$			247.058i			0.403032i	0.979485	+	0.201516i	$0.0645867\pi$
$613$			247.058i			0.403032i	−0.979485	+	0.201516i	$0.935413\pi$
$614$	−484.083			−0.788409
$615$			307.330i			0.499724i
$616$	−43.2447			−0.0702025
$617$			548.303i			0.888660i	0.895863	+	0.444330i	$0.146558\pi$
$617$			548.303i			0.888660i	−0.895863	+	0.444330i	$0.853442\pi$
$618$			346.710i			0.561019i
$619$			1090.68i			1.76201i	0.473108	+	0.881005i	$0.343132\pi$
$619$			1090.68i			1.76201i	−0.473108	+	0.881005i	$0.656868\pi$
$620$		−	627.618i		−	1.01229i
$621$	91.1076	−	669.681i	0.146711	−	1.07839i
$622$	−657.120			−1.05646
$623$	152.893			0.245414
$624$	−99.5980			−0.159612
$625$	1882.62			3.01219
$626$			134.613i			0.215036i
$627$	252.049			0.401992
$628$			147.244i			0.234465i
$629$	−679.700			−1.08060
$630$	−165.559			−0.262793
$631$		−	132.159i		−	0.209444i	−0.994502	−	0.104722i	$-0.966605\pi$
$631$		−	132.159i		−	0.209444i	0.994502	−	0.104722i	$-0.0333953\pi$
$632$			333.360i			0.527468i
$633$	171.823			0.271443
$634$	297.186			0.468747
$635$		−	343.518i		−	0.540974i
$636$		−	295.600i		−	0.464780i
$637$	347.682			0.545812
$638$		−	194.329i		−	0.304591i
$639$	352.891			0.552256
$640$			106.801i			0.166876i
$641$		−	349.786i		−	0.545688i	−0.962058	−	0.272844i	$-0.912036\pi$
$641$		−	349.786i		−	0.545688i	0.962058	−	0.272844i	$-0.0879644\pi$
$642$		−	257.840i		−	0.401620i
$643$		−	147.129i		−	0.228817i	−0.993434	−	0.114408i	$-0.963503\pi$
$643$		−	147.129i		−	0.228817i	0.993434	−	0.114408i	$-0.0364972\pi$
$644$	−178.225	−	24.2469i	−0.276748	−	0.0376505i
$645$	−682.323			−1.05787
$646$	−651.744			−1.00889
$647$	966.252			1.49343			0.746717	−	0.665142i	$-0.231629\pi$
$647$	966.252			1.49343			0.746717	+	0.665142i	$0.231629\pi$
$648$	119.917			0.185057
$649$		−	102.450i		−	0.157858i
$650$	935.134			1.43867
$651$			313.809i			0.482041i
$652$	251.172			0.385232
$653$	−817.378			−1.25173			−0.625863	−	0.779933i	$-0.715253\pi$
$653$	−817.378			−1.25173			−0.625863	+	0.779933i	$0.715253\pi$
$654$			473.339i			0.723760i
$655$			617.229i			0.942335i
$656$	53.9411			0.0822273
$657$	−151.769			−0.231003
$658$		−	171.654i		−	0.260872i
$659$			1053.82i			1.59913i	0.600581	+	0.799564i	$0.294936\pi$
$659$			1053.82i			1.59913i	−0.600581	+	0.799564i	$0.705064\pi$
$660$	−178.225			−0.270038
$661$		−	1162.41i		−	1.75856i	−0.476305	−	0.879280i	$-0.658024\pi$
$661$		−	1162.41i		−	1.75856i	0.476305	−	0.879280i	$-0.341976\pi$
$662$	−93.7372			−0.141597
$663$			429.772i			0.648223i
$664$		−	211.704i		−	0.318832i
$665$		−	985.550i		−	1.48203i
$666$		−	176.628i		−	0.265207i
$667$	108.958	−	800.891i	0.163356	−	1.20074i
$668$	−185.657			−0.277929
$669$	202.995			0.303430
$670$	912.749			1.36231
$671$	61.1573			0.0911435
$672$		−	53.4004i		−	0.0794649i
$673$	−647.461			−0.962052			−0.481026	−	0.876706i	$-0.659736\pi$
$673$	−647.461			−0.962052			−0.481026	+	0.876706i	$0.659736\pi$
$674$		−	641.131i		−	0.951233i
$675$	−1883.94			−2.79102
$676$	−125.255			−0.185288
$677$		−	544.278i		−	0.803956i	−0.915649	−	0.401978i	$-0.868323\pi$
$677$		−	544.278i		−	0.803956i	0.915649	−	0.401978i	$-0.131677\pi$
$678$			616.951i			0.909958i
$679$	−258.382			−0.380533
$680$	460.853			0.677725
$681$		−	635.160i		−	0.932688i
$682$		−	183.825i		−	0.269538i
$683$	77.8314			0.113955			0.0569776	−	0.998375i	$-0.481854\pi$
$683$	77.8314			0.113955			0.0569776	+	0.998375i	$0.481854\pi$
$684$		−	169.363i		−	0.247607i
$685$	−621.166			−0.906811
$686$			457.373i			0.666725i
$687$		−	341.180i		−	0.496623i
$688$			119.758i			0.174067i
$689$			631.413i			0.916419i
$690$	−734.524	−	99.9293i	−1.06453	−	0.144825i
$691$	−223.769			−0.323833			−0.161917	−	0.986804i	$-0.551768\pi$
$691$	−223.769			−0.323833			−0.161917	+	0.986804i	$0.551768\pi$
$692$	−13.4214			−0.0193950
$693$	−48.4912			−0.0699729
$694$	412.597			0.594520
$695$		−	277.621i		−	0.399455i
$696$	239.966			0.344778
$697$		−	232.760i		−	0.333945i
$698$	−213.477			−0.305841
$699$	854.110			1.22190
$700$			501.381i			0.716259i
$701$		−	376.995i		−	0.537795i	−0.963169	−	0.268898i	$-0.913341\pi$
$701$		−	376.995i		−	0.537795i	0.963169	−	0.268898i	$-0.0866594\pi$
$702$	−428.600			−0.610541
$703$	1051.44			1.49565
$704$			31.2812i			0.0444336i
$705$		−	707.441i		−	1.00346i
$706$	−533.242			−0.755300
$707$		−	396.248i		−	0.560464i
$708$	126.510			0.178686
$709$			1182.12i			1.66731i	0.552287	+	0.833654i	$0.313755\pi$
$709$			1182.12i			1.66731i	−0.552287	+	0.833654i	$0.686245\pi$
$710$		−	1485.43i		−	2.09215i
$711$			373.803i			0.525743i
$712$		−	110.596i		−	0.155331i
$713$	103.069	−	757.602i	0.144557	−	1.06256i
$714$	−230.426			−0.322726
$715$	380.696			0.532443
$716$	556.524			0.777268
$717$	657.357			0.916817
$718$			498.142i			0.693791i
$719$	93.9941			0.130729			0.0653645	−	0.997861i	$-0.479179\pi$
$719$	93.9941			0.130729			0.0653645	+	0.997861i	$0.479179\pi$
$720$			119.758i			0.166331i
$721$	397.072			0.550724
$722$	497.664			0.689285
$723$			1071.13i			1.48151i
$724$			107.357i			0.148283i
$725$	−2253.06			−3.10767
$726$	360.919			0.497133
$727$		−	1303.61i		−	1.79314i	−0.442900	−	0.896571i	$-0.646050\pi$
$727$		−	1303.61i		−	1.79314i	0.442900	−	0.896571i	$-0.353950\pi$
$728$			114.065i			0.156683i
$729$	772.935			1.06027
$730$			638.840i			0.875124i
$731$	516.764			0.706927
$732$			75.5196i			0.103169i
$733$			635.946i			0.867594i	0.901011	+	0.433797i	$0.142826\pi$
$733$			635.946i			0.867594i	−0.901011	+	0.433797i	$0.857174\pi$
$734$		−	453.741i		−	0.618176i
$735$			768.268i			1.04526i
$736$	−17.5391	+	128.920i	−0.0238303	+	0.175163i
$737$	267.338			0.362738
$738$	60.4853			0.0819584
$739$	200.380			0.271150			0.135575	−	0.990767i	$-0.456712\pi$
$739$	200.380			0.271150			0.135575	+	0.990767i	$0.456712\pi$
$740$	−743.480			−1.00470
$741$		−	664.822i		−	0.897196i
$742$	−338.538			−0.456251
$743$		−	1210.79i		−	1.62959i	−0.579748	−	0.814796i	$-0.696849\pi$
$743$		−	1210.79i		−	1.62959i	0.579748	−	0.814796i	$-0.303151\pi$
$744$	226.995			0.305101
$745$	−30.5786			−0.0410452
$746$			220.799i			0.295977i
$747$		−	237.388i		−	0.317789i
$748$	134.981			0.180455
$749$	−295.294			−0.394250
$750$			1260.60i			1.68080i
$751$			983.883i			1.31010i	0.755587	+	0.655048i	$0.227352\pi$
$751$			983.883i			1.31010i	−0.755587	+	0.655048i	$0.772648\pi$
$752$	−124.167			−0.165115
$753$		−	469.822i		−	0.623934i
$754$	−512.576			−0.679809
$755$			22.7901i			0.0301855i
$756$		−	229.798i		−	0.303966i
$757$			1494.15i			1.97378i	0.161407	+	0.986888i	$0.448397\pi$
$757$			1494.15i			1.97378i	−0.161407	+	0.986888i	$0.551603\pi$
$758$			638.122i			0.841849i
$759$	−215.137	−	29.2686i	−0.283448	−	0.0385621i
$760$	−712.902			−0.938028
$761$	−779.132			−1.02383			−0.511913	−	0.859037i	$-0.671063\pi$
$761$	−779.132			−1.02383			−0.511913	+	0.859037i	$0.671063\pi$
$762$	124.243			0.163048
$763$	542.096			0.710479
$764$			337.385i			0.441603i
$765$	516.764			0.675508
$766$		−	598.464i		−	0.781285i
$767$	−270.230			−0.352320
$768$	−38.6274			−0.0502961
$769$			155.017i			0.201582i	0.994908	+	0.100791i	$0.0321374\pi$
$769$			155.017i			0.201582i	−0.994908	+	0.100791i	$0.967863\pi$
$770$			204.114i			0.265083i
$771$	53.4437			0.0693173
$772$	−190.638			−0.246940
$773$		−	97.8690i		−	0.126609i	−0.997994	−	0.0633047i	$-0.979836\pi$
$773$		−	97.8690i		−	0.126609i	0.997994	−	0.0633047i	$-0.0201640\pi$
$774$			134.287i			0.173498i
$775$	−2131.28			−2.75003
$776$			186.902i			0.240852i
$777$	371.740			0.478430
$778$			15.6406i			0.0201036i
$779$			360.060i			0.462208i
$780$			470.100i			0.602692i
$781$		−	435.071i		−	0.557070i
$782$	556.299	+	75.6824i	0.711379	+	0.0967806i
$783$	1032.64			1.31883
$784$	134.843			0.171993
$785$	694.989			0.885336
$786$	−223.238			−0.284017
$787$		−	728.726i		−	0.925954i	−0.886370	−	0.462977i	$-0.846781\pi$
$787$		−	728.726i		−	0.925954i	0.886370	−	0.462977i	$-0.153219\pi$
$788$	498.167			0.632191
$789$			1026.22i			1.30066i
$790$	1573.45			1.99171
$791$	706.569			0.893260
$792$			35.0763i			0.0442883i
$793$		−	161.313i		−	0.203421i
$794$	470.336			0.592363
$795$	−1395.22			−1.75500
$796$			152.381i			0.191433i
$797$			279.729i			0.350978i	0.984481	+	0.175489i	$0.0561506\pi$
$797$			279.729i			0.350978i	−0.984481	+	0.175489i	$0.943849\pi$
$798$	356.451			0.446680
$799$			535.787i			0.670572i
$800$	362.676			0.453345
$801$		−	124.013i		−	0.154823i
$802$			73.2291i			0.0913081i
$803$			187.112i			0.233016i
$804$			330.120i			0.410598i
$805$	−114.445	+	841.220i	−0.142168	+	1.04499i
$806$	−484.870			−0.601576
$807$	−992.762			−1.23019
$808$	−286.627			−0.354737
$809$	1156.82			1.42994			0.714968	−	0.699157i	$-0.246441\pi$
$809$	1156.82			1.42994			0.714968	+	0.699157i	$0.246441\pi$
$810$		−	566.004i		−	0.698771i
$811$	1178.54			1.45319			0.726594	−	0.687067i	$-0.241102\pi$
$811$	1178.54			1.45319			0.726594	+	0.687067i	$0.241102\pi$
$812$		−	274.822i		−	0.338451i
$813$	238.569			0.293442
$814$	−217.760			−0.267519
$815$		−	1185.52i		−	1.45463i
$816$			166.680i			0.204265i
$817$	−799.391			−0.978447
$818$	−362.164			−0.442743
$819$			127.904i			0.156171i
$820$		−	254.601i		−	0.310489i
$821$	−732.347			−0.892019			−0.446009	−	0.895028i	$-0.647155\pi$
$821$	−732.347			−0.892019			−0.446009	+	0.895028i	$0.647155\pi$
$822$		−	224.661i		−	0.273311i
$823$	−882.012			−1.07170			−0.535852	−	0.844312i	$-0.680009\pi$
$823$	−882.012			−1.07170			−0.535852	+	0.844312i	$0.680009\pi$
$824$		−	287.224i		−	0.348573i
$825$			605.221i			0.733601i
$826$		−	144.886i		−	0.175407i
$827$		−	1039.74i		−	1.25724i	−0.777713	−	0.628619i	$-0.783620\pi$
$827$		−	1039.74i		−	1.25724i	0.777713	−	0.628619i	$-0.216380\pi$
$828$	−19.6670	+	144.561i	−0.0237524	+	0.174590i
$829$	413.505			0.498799			0.249400	−	0.968401i	$-0.419767\pi$
$829$	413.505			0.498799			0.249400	+	0.968401i	$0.419767\pi$
$830$	−999.239			−1.20390
$831$	500.512			0.602301
$832$	82.5097			0.0991703
$833$		−	581.855i		−	0.698506i
$834$	100.409			0.120395
$835$			876.296i			1.04946i
$836$	−208.804			−0.249766
$837$	976.828			1.16706
$838$			341.736i			0.407799i
$839$		−	254.486i		−	0.303320i	−0.988433	−	0.151660i	$-0.951538\pi$
$839$		−	254.486i		−	0.303320i	0.988433	−	0.151660i	$-0.0484619\pi$
$840$	−252.049			−0.300058
$841$	393.970			0.468454
$842$			442.451i			0.525476i
$843$		−	74.8487i		−	0.0887885i
$844$	−142.343			−0.168653
$845$			591.200i			0.699645i
$846$	−139.230			−0.164575
$847$		−	413.345i		−	0.488011i
$848$			244.883i			0.288777i
$849$		−	545.342i		−	0.642334i
$850$		−	1564.97i		−	1.84114i
$851$	−897.460	−	122.096i	−1.05459	−	0.143474i
$852$	537.245			0.630569
$853$	744.132			0.872370			0.436185	−	0.899857i	$-0.356329\pi$
$853$	744.132			0.872370			0.436185	+	0.899857i	$0.356329\pi$
$854$	86.4895			0.101276
$855$	−799.391			−0.934960
$856$			213.602i			0.249535i
$857$	−578.921			−0.675520			−0.337760	−	0.941232i	$-0.609669\pi$
$857$	−578.921			−0.675520			−0.337760	+	0.941232i	$0.609669\pi$
$858$			137.689i			0.160477i
$859$	−1395.20			−1.62421			−0.812106	−	0.583510i	$-0.801679\pi$
$859$	−1395.20			−1.62421			−0.812106	+	0.583510i	$0.801679\pi$
$860$	565.255			0.657273
$861$			127.300i			0.147852i
$862$		−	950.934i		−	1.10317i
$863$	565.704			0.655508			0.327754	−	0.944763i	$-0.393708\pi$
$863$	565.704			0.655508			0.327754	+	0.944763i	$0.393708\pi$
$864$	−166.225			−0.192391
$865$			63.3485i			0.0732352i
$866$		−	559.200i		−	0.645728i
$867$	21.5269			0.0248292
$868$		−	259.968i		−	0.299502i
$869$	460.853			0.530325
$870$		−	1132.63i		−	1.30188i
$871$		−	705.150i		−	0.809587i
$872$		−	392.127i		−	0.449687i
$873$			209.576i			0.240065i
$874$	−860.548	−	117.074i	−0.984609	−	0.133952i
$875$	1443.72			1.64996
$876$	−231.054			−0.263760
$877$	−468.112			−0.533765			−0.266882	−	0.963729i	$-0.585994\pi$
$877$	−468.112			−0.533765			−0.266882	+	0.963729i	$0.585994\pi$
$878$	−1183.69			−1.34817
$879$			391.341i			0.445212i
$880$	147.647			0.167780
$881$			1317.52i			1.49548i	0.663990	+	0.747741i	$0.268862\pi$
$881$			1317.52i			1.49548i	−0.663990	+	0.747741i	$0.731138\pi$
$882$	151.202			0.171431
$883$	−257.377			−0.291480			−0.145740	−	0.989323i	$-0.546556\pi$
$883$	−257.377			−0.291480			−0.145740	+	0.989323i	$0.546556\pi$
$884$		−	356.035i		−	0.402754i
$885$		−	597.123i		−	0.674715i
$886$	322.306			0.363776
$887$	331.722			0.373982			0.186991	−	0.982362i	$-0.440126\pi$
$887$	331.722			0.373982			0.186991	+	0.982362i	$0.440126\pi$
$888$		−	268.900i		−	0.302815i
$889$		−	142.290i		−	0.160056i
$890$	−522.010			−0.586528
$891$		−	165.779i		−	0.186059i
$892$	−168.167			−0.188527
$893$		−	828.818i		−	0.928128i
$894$		−	11.0596i		−	0.0123709i
$895$		−	2626.78i		−	2.93495i
$896$			44.2384i			0.0493732i
$897$	−77.2010	+	567.461i	−0.0860658	+	0.632621i
$898$	620.867			0.691389
$899$	1168.22			1.29946
$900$	406.676			0.451862
$901$	1056.69			1.17279
$902$		−	74.5709i		−	0.0826728i
$903$	−282.627			−0.312987
$904$		−	511.099i		−	0.565375i
$905$	506.721			0.559912
$906$	−8.24264			−0.00909784
$907$		−	436.596i		−	0.481362i	−0.970604	−	0.240681i	$-0.922629\pi$
$907$		−	436.596i		−	0.481362i	0.970604	−	0.240681i	$-0.0773708\pi$
$908$			526.184i			0.579498i
$909$	−321.401			−0.353577
$910$	538.386			0.591633
$911$			1530.29i			1.67979i	0.542749	+	0.839895i	$0.317383\pi$
$911$			1530.29i			1.67979i	−0.542749	+	0.839895i	$0.682617\pi$
$912$		−	257.840i		−	0.282719i
$913$	−292.670			−0.320559
$914$		−	56.8025i		−	0.0621472i
$915$	356.451			0.389564
$916$			282.643i			0.308562i
$917$			255.665i			0.278806i
$918$			717.274i			0.781344i
$919$			676.783i			0.736434i	0.929740	+	0.368217i	$0.120032\pi$
$919$			676.783i			0.736434i	−0.929740	+	0.368217i	$0.879968\pi$
$920$	608.500	+	82.7842i	0.661413	+	0.0899828i
$921$	−826.382			−0.897266
$922$	−92.8802			−0.100738
$923$	−1147.58			−1.24331
$924$	−73.8234			−0.0798954
$925$			2524.72i			2.72943i
$926$	952.382			1.02849
$927$		−	322.070i		−	0.347432i
$928$	−198.794			−0.214218
$929$	−686.535			−0.739004			−0.369502	−	0.929230i	$-0.620472\pi$
$929$	−686.535			−0.739004			−0.369502	+	0.929230i	$0.620472\pi$
$930$		−	1071.41i		−	1.15205i
$931$			900.082i			0.966791i
$932$	−707.568			−0.759193
$933$	−1121.77			−1.20233
$934$		−	439.375i		−	0.470422i
$935$		−	637.106i		−	0.681396i
$936$	92.5198			0.0988459
$937$			774.354i			0.826418i	0.910636	+	0.413209i	$0.135592\pi$
$937$			774.354i			0.826418i	−0.910636	+	0.413209i	$0.864408\pi$
$938$	378.073			0.403063
$939$			229.798i			0.244726i
$940$			586.063i			0.623471i
$941$			774.814i			0.823395i	0.911321	+	0.411697i	$0.135064\pi$
$941$			774.814i			0.823395i	−0.911321	+	0.411697i	$0.864936\pi$
$942$			251.362i			0.266838i
$943$	41.8112	−	307.330i	0.0443385	−	0.325907i
$944$	−104.804			−0.111021
$945$	−1084.64			−1.14777
$946$	165.559			0.175010
$947$	−1090.69			−1.15173			−0.575865	−	0.817545i	$-0.695335\pi$
$947$	−1090.69			−1.15173			−0.575865	+	0.817545i	$0.695335\pi$
$948$			569.081i			0.600296i
$949$	493.540			0.520063
$950$			2420.88i			2.54830i
$951$	507.328			0.533468
$952$	190.891			0.200516
$953$			60.7603i			0.0637569i	0.999492	+	0.0318785i	$0.0101489\pi$
$953$			60.7603i			0.0637569i	−0.999492	+	0.0318785i	$0.989851\pi$
$954$			274.592i			0.287833i
$955$	1592.45			1.66749
$956$	−544.573			−0.569637
$957$		−	331.740i		−	0.346646i
$958$			325.932i			0.340222i
$959$	−257.295			−0.268295
$960$			182.320i			0.189917i
$961$	144.073			0.149920
$962$			574.380i			0.597069i
$963$			239.516i			0.248719i
$964$		−	887.356i		−	0.920493i
$965$			899.805i			0.932440i
$966$	−304.250	−	41.3921i	−0.314958	−	0.0428489i
$967$	1715.83			1.77438			0.887192	−	0.461400i	$-0.152653\pi$
$967$	1715.83			1.77438			0.887192	+	0.461400i	$0.152653\pi$
$968$	−298.995			−0.308879
$969$	−1112.60			−1.14819
$970$	882.171			0.909454
$971$			1071.57i			1.10358i	0.833984	+	0.551789i	$0.186054\pi$
$971$			1071.57i			1.10358i	−0.833984	+	0.551789i	$0.813946\pi$
$972$	−324.215			−0.333555
$973$		−	114.994i		−	0.118185i
$974$	−526.596			−0.540653
$975$	1596.37			1.63731
$976$		−	62.5625i		−	0.0641009i
$977$		−	456.079i		−	0.466816i	−0.972379	−	0.233408i	$-0.925012\pi$
$977$		−	456.079i		−	0.466816i	0.972379	−	0.233408i	$-0.0749877\pi$
$978$	428.777			0.438422
$979$	−152.893			−0.156173
$980$		−	636.454i		−	0.649443i
$981$		−	439.700i		−	0.448216i
$982$	−364.905			−0.371593
$983$			216.055i			0.219791i	0.993943	+	0.109896i	$0.0350517\pi$
$983$			216.055i			0.219791i	−0.993943	+	0.109896i	$0.964948\pi$
$984$	92.0833			0.0935805
$985$		−	2351.33i		−	2.38714i
$986$			857.809i			0.869989i
$987$		−	293.032i		−	0.296891i
$988$			550.757i			0.557446i
$989$	682.323	+	92.8276i	0.689912	+	0.0938600i
$990$	165.559			0.167232
$991$	−520.142			−0.524866			−0.262433	−	0.964950i	$-0.584525\pi$
$991$	−520.142			−0.524866			−0.262433	+	0.964950i	$0.584525\pi$
$992$	−188.049			−0.189565
$993$	−160.019			−0.161147
$994$		−	615.284i		−	0.618998i
$995$	719.235			0.722849
$996$		−	361.402i		−	0.362853i
$997$	466.877			0.468282			0.234141	−	0.972203i	$-0.424772\pi$
$997$	466.877			0.468282			0.234141	+	0.972203i	$0.424772\pi$
$998$	527.144			0.528201
$999$		−	1157.16i		−	1.15831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.3.b.a.45.1	✓	4
3.2	odd	2		414.3.b.a.91.4		4
4.3	odd	2		368.3.f.c.321.3		4
5.2	odd	4		1150.3.c.a.1149.4		8
5.3	odd	4		1150.3.c.a.1149.5		8
5.4	even	2		1150.3.d.a.551.4		4
8.3	odd	2		1472.3.f.c.321.2		4
8.5	even	2		1472.3.f.f.321.4		4
23.22	odd	2	inner	46.3.b.a.45.2	yes	4
69.68	even	2		414.3.b.a.91.3		4
92.91	even	2		368.3.f.c.321.4		4
115.22	even	4		1150.3.c.a.1149.3		8
115.68	even	4		1150.3.c.a.1149.6		8
115.114	odd	2		1150.3.d.a.551.3		4
184.45	odd	2		1472.3.f.f.321.3		4
184.91	even	2		1472.3.f.c.321.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.3.b.a.45.1	✓	4	1.1	even	1	trivial
46.3.b.a.45.2	yes	4	23.22	odd	2	inner
368.3.f.c.321.3		4	4.3	odd	2
368.3.f.c.321.4		4	92.91	even	2
414.3.b.a.91.3		4	69.68	even	2
414.3.b.a.91.4		4	3.2	odd	2
1150.3.c.a.1149.3		8	115.22	even	4
1150.3.c.a.1149.4		8	5.2	odd	4
1150.3.c.a.1149.5		8	5.3	odd	4
1150.3.c.a.1149.6		8	115.68	even	4
1150.3.d.a.551.3		4	115.114	odd	2
1150.3.d.a.551.4		4	5.4	even	2
1472.3.f.c.321.1		4	184.91	even	2
1472.3.f.c.321.2		4	8.3	odd	2
1472.3.f.f.321.3		4	184.45	odd	2
1472.3.f.f.321.4		4	8.5	even	2

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:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	46.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -2.41421 q^{3} +2.00000 q^{4} -9.43995i q^{5} +3.41421 q^{6} -3.91016i q^{7} -2.82843 q^{8} -3.17157 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} -2.41421 q^{3} +2.00000 q^{4} -9.43995i q^{5} +3.41421 q^{6} -3.91016i q^{7} -2.82843 q^{8} -3.17157 q^{9} +13.3501i q^{10} +3.91016i q^{11} -4.82843 q^{12} +10.3137 q^{13} +5.52980i q^{14} +22.7901i q^{15} +4.00000 q^{16} -17.2603i q^{17} +4.48528 q^{18} +26.7002i q^{19} -18.8799i q^{20} +9.43995i q^{21} -5.52980i q^{22} +(3.10051 - 22.7901i) q^{23} +6.82843 q^{24} -64.1127 q^{25} -14.5858 q^{26} +29.3848 q^{27} -7.82031i q^{28} +35.1421 q^{29} -32.2300i q^{30} +33.2426 q^{31} -5.65685 q^{32} -9.43995i q^{33} +24.4097i q^{34} -36.9117 q^{35} -6.34315 q^{36} -39.3794i q^{37} -37.7598i q^{38} -24.8995 q^{39} +26.7002i q^{40} +13.4853 q^{41} -13.3501i q^{42} +29.9395i q^{43} +7.82031i q^{44} +29.9395i q^{45} +(-4.38478 + 32.2300i) q^{46} -31.0416 q^{47} -9.65685 q^{48} +33.7107 q^{49} +90.6690 q^{50} +41.6700i q^{51} +20.6274 q^{52} +61.2207i q^{53} -41.5563 q^{54} +36.9117 q^{55} +11.0596i q^{56} -64.4600i q^{57} -49.6985 q^{58} -26.2010 q^{59} +45.5801i q^{60} -15.6406i q^{61} -47.0122 q^{62} +12.4013i q^{63} +8.00000 q^{64} -97.3609i q^{65} +13.3501i q^{66} -68.3702i q^{67} -34.5205i q^{68} +(-7.48528 + 55.0201i) q^{69} +52.2010 q^{70} -111.267 q^{71} +8.97056 q^{72} +47.8528 q^{73} +55.6910i q^{74} +154.782 q^{75} +53.4004i q^{76} +15.2893 q^{77} +35.2132 q^{78} -117.860i q^{79} -37.7598i q^{80} -42.3970 q^{81} -19.0711 q^{82} +74.8487i q^{83} +18.8799i q^{84} -162.936 q^{85} -42.3408i q^{86} -84.8406 q^{87} -11.0596i q^{88} +39.1016i q^{89} -42.3408i q^{90} -40.3282i q^{91} +(6.20101 - 45.5801i) q^{92} -80.2548 q^{93} +43.8995 q^{94} +252.049 q^{95} +13.6569 q^{96} -66.0797i q^{97} -47.6741 q^{98} -12.4013i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 8 q^{4} + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 8 * q^4 + 8 * q^6 - 24 * q^9	\( 4 q - 4 q^{3} + 8 q^{4} + 8 q^{6} - 24 q^{9} - 8 q^{12} - 4 q^{13} + 16 q^{16} - 16 q^{18} + 52 q^{23} + 16 q^{24} - 132 q^{25} - 64 q^{26} + 44 q^{27} + 84 q^{29} + 116 q^{31} + 56 q^{35} - 48 q^{36} - 60 q^{39} + 20 q^{41} + 56 q^{46} - 28 q^{47} - 16 q^{48} - 148 q^{49} + 176 q^{50} - 8 q^{52} - 104 q^{54} - 56 q^{55} - 80 q^{58} - 184 q^{59} - 24 q^{62} + 32 q^{64} + 4 q^{69} + 288 q^{70} - 100 q^{71} - 32 q^{72} - 148 q^{73} + 308 q^{75} + 344 q^{77} + 56 q^{78} + 68 q^{81} - 48 q^{82} - 120 q^{85} - 164 q^{87} + 104 q^{92} - 140 q^{93} + 136 q^{94} + 352 q^{95} + 32 q^{96} - 400 q^{98}+O(q^{100}) \) 4 * q - 4 * q^3 + 8 * q^4 + 8 * q^6 - 24 * q^9 - 8 * q^12 - 4 * q^13 + 16 * q^16 - 16 * q^18 + 52 * q^23 + 16 * q^24 - 132 * q^25 - 64 * q^26 + 44 * q^27 + 84 * q^29 + 116 * q^31 + 56 * q^35 - 48 * q^36 - 60 * q^39 + 20 * q^41 + 56 * q^46 - 28 * q^47 - 16 * q^48 - 148 * q^49 + 176 * q^50 - 8 * q^52 - 104 * q^54 - 56 * q^55 - 80 * q^58 - 184 * q^59 - 24 * q^62 + 32 * q^64 + 4 * q^69 + 288 * q^70 - 100 * q^71 - 32 * q^72 - 148 * q^73 + 308 * q^75 + 344 * q^77 + 56 * q^78 + 68 * q^81 - 48 * q^82 - 120 * q^85 - 164 * q^87 + 104 * q^92 - 140 * q^93 + 136 * q^94 + 352 * q^95 + 32 * q^96 - 400 * q^98

Introduction

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