LMFDB - Embedded newform 912.3.be.j.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(145,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.be (of order $6$, degree $2$, 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:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 154 x^{18} - 24 x^{17} + 16374 x^{16} - 4328 x^{15} + 911836 x^{14} - 590088 x^{13} + \cdots + 338560000 $ x^20 + 154x^18 - 24x^17 + 16374x^16 - 4328x^15 + 911836x^14 - 590088x^13 + 36808708x^12 - 29040960x^11 + 727387008x^10 - 1003792064x^9 + 10261479936x^8 - 7069668864x^7 + 36940887936x^6 + 52280031232x^5 + 60574204416x^4 + 32700144640x^3 + 13448832000x^2 + 2490624000x + 338560000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$4.40690 - 7.63297i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.j.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(-4.40690 - 7.63297i) q^{5} -3.21766 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(-4.40690 - 7.63297i) q^{5} -3.21766 q^{7} +(1.50000 - 2.59808i) q^{9} -4.38505 q^{11} +(-2.79075 - 1.61124i) q^{13} +(-13.2207 - 7.63297i) q^{15} +(-2.20532 - 3.81972i) q^{17} +(17.9284 - 6.29067i) q^{19} +(-4.82648 + 2.78657i) q^{21} +(-2.03748 + 3.52902i) q^{23} +(-26.3415 + 45.6248i) q^{25} -5.19615i q^{27} +(-31.5633 - 18.2231i) q^{29} -31.7856i q^{31} +(-6.57758 + 3.79757i) q^{33} +(14.1799 + 24.5603i) q^{35} +44.8822i q^{37} -5.58151 q^{39} +(-40.6444 + 23.4660i) q^{41} +(29.3011 + 50.7510i) q^{43} -26.4414 q^{45} +(0.191229 - 0.331218i) q^{47} -38.6467 q^{49} +(-6.61595 - 3.81972i) q^{51} +(-6.55327 - 3.78353i) q^{53} +(19.3245 + 33.4710i) q^{55} +(21.4447 - 24.9625i) q^{57} +(-18.3235 + 10.5791i) q^{59} +(-17.1268 + 29.6644i) q^{61} +(-4.82648 + 8.35972i) q^{63} +28.4023i q^{65} +(97.9226 + 56.5356i) q^{67} +7.05804i q^{69} +(-48.9334 + 28.2517i) q^{71} +(32.6789 + 56.6015i) q^{73} +91.2495i q^{75} +14.1096 q^{77} +(-65.2985 + 37.7001i) q^{79} +(-4.50000 - 7.79423i) q^{81} +29.8871 q^{83} +(-19.4372 + 33.6662i) q^{85} -63.1265 q^{87} +(23.3536 + 13.4832i) q^{89} +(8.97969 + 5.18443i) q^{91} +(-27.5271 - 47.6783i) q^{93} +(-127.025 - 109.125i) q^{95} +(-115.337 + 66.5899i) q^{97} +(-6.57758 + 11.3927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	$ 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) $ 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	−4.40690	−	7.63297i	−0.881379	−	1.52659i	−0.849808	−	0.527092i	$-0.823282\pi$
$5$	−4.40690	−	7.63297i	−0.881379	−	1.52659i	−0.0315712	−	0.999502i	$-0.510051\pi$
$6$		0			0
$7$	−3.21766			−0.459665			−0.229833	−	0.973230i	$-0.573818\pi$
$7$	−3.21766			−0.459665			−0.229833	+	0.973230i	$0.573818\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	−4.38505			−0.398641			−0.199321	−	0.979934i	$-0.563873\pi$
$11$	−4.38505			−0.398641			−0.199321	+	0.979934i	$0.563873\pi$
$12$		0			0
$13$	−2.79075	−	1.61124i	−0.214673	−	0.123942i	0.388808	−	0.921319i	$-0.372887\pi$
$13$	−2.79075	−	1.61124i	−0.214673	−	0.123942i	−0.603481	+	0.797377i	$0.706220\pi$
$14$		0			0
$15$	−13.2207	−	7.63297i	−0.881379	−	0.508865i
$16$		0			0
$17$	−2.20532	−	3.81972i	−0.129725	−	0.224690i	0.793845	−	0.608120i	$-0.208076\pi$
$17$	−2.20532	−	3.81972i	−0.129725	−	0.224690i	−0.923570	+	0.383430i	$0.874743\pi$
$18$		0			0
$19$	17.9284	−	6.29067i	0.943600	−	0.331088i
$19$	17.9284	−	6.29067i	0.943600	−	0.331088i
$20$		0			0
$21$	−4.82648	+	2.78657i	−0.229833	+	0.132694i
$22$		0			0
$23$	−2.03748	+	3.52902i	−0.0885861	+	0.153436i	−0.906914	−	0.421316i	$-0.861568\pi$
$23$	−2.03748	+	3.52902i	−0.0885861	+	0.153436i	0.818328	+	0.574752i	$0.194902\pi$
$24$		0			0
$25$	−26.3415	+	45.6248i	−1.05366	+	1.82499i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	−31.5633	−	18.2231i	−1.08839	−	0.628381i	−0.155242	−	0.987877i	$-0.549616\pi$
$29$	−31.5633	−	18.2231i	−1.08839	−	0.628381i	−0.933147	+	0.359495i	$0.882949\pi$
$30$		0			0
$31$		−	31.7856i		−	1.02534i	−0.858586	−	0.512670i	$-0.828656\pi$
$31$		−	31.7856i		−	1.02534i	0.858586	−	0.512670i	$-0.171344\pi$
$32$		0			0
$33$	−6.57758	+	3.79757i	−0.199321	+	0.115078i
$34$		0			0
$35$	14.1799	+	24.5603i	0.405139	+	0.701722i
$36$		0			0
$37$			44.8822i			1.21303i	0.795071	+	0.606516i	$0.207433\pi$
$37$			44.8822i			1.21303i	−0.795071	+	0.606516i	$0.792567\pi$
$38$		0			0
$39$	−5.58151			−0.143116
$40$		0			0
$41$	−40.6444	+	23.4660i	−0.991326	+	0.572342i	−0.905670	−	0.423983i	$-0.860632\pi$
$41$	−40.6444	+	23.4660i	−0.991326	+	0.572342i	−0.0856555	+	0.996325i	$0.527298\pi$
$42$		0			0
$43$	29.3011	+	50.7510i	0.681421	+	1.18026i	0.974547	+	0.224182i	$0.0719711\pi$
$43$	29.3011	+	50.7510i	0.681421	+	1.18026i	−0.293126	+	0.956074i	$0.594696\pi$
$44$		0			0
$45$	−26.4414			−0.587586
$46$		0			0
$47$	0.191229	−	0.331218i	0.00406869	−	0.00704719i	−0.863984	−	0.503519i	$-0.832038\pi$
$47$	0.191229	−	0.331218i	0.00406869	−	0.00704719i	0.868053	+	0.496472i	$0.165372\pi$
$48$		0			0
$49$	−38.6467			−0.788708
$50$		0			0
$51$	−6.61595	−	3.81972i	−0.129725	−	0.0748965i
$52$		0			0
$53$	−6.55327	−	3.78353i	−0.123647	−	0.0713874i	0.436901	−	0.899510i	$-0.356076\pi$
$53$	−6.55327	−	3.78353i	−0.123647	−	0.0713874i	−0.560548	+	0.828122i	$0.689409\pi$
$54$		0			0
$55$	19.3245	+	33.4710i	0.351354	+	0.608563i
$56$		0			0
$57$	21.4447	−	24.9625i	0.376223	−	0.437938i
$58$		0			0
$59$	−18.3235	+	10.5791i	−0.310567	+	0.179306i	−0.647180	−	0.762337i	$-0.724052\pi$
$59$	−18.3235	+	10.5791i	−0.310567	+	0.179306i	0.336613	+	0.941643i	$0.390719\pi$
$60$		0			0
$61$	−17.1268	+	29.6644i	−0.280767	+	0.486302i	−0.971574	−	0.236737i	$-0.923922\pi$
$61$	−17.1268	+	29.6644i	−0.280767	+	0.486302i	0.690807	+	0.723039i	$0.257255\pi$
$62$		0			0
$63$	−4.82648	+	8.35972i	−0.0766109	+	0.132694i
$64$		0			0
$65$			28.4023i			0.436959i
$66$		0			0
$67$	97.9226	+	56.5356i	1.46153	+	0.843815i	0.999082	−	0.0428306i	$-0.0136376\pi$
$67$	97.9226	+	56.5356i	1.46153	+	0.843815i	0.462449	+	0.886646i	$0.346971\pi$
$68$		0			0
$69$			7.05804i			0.102290i
$70$		0			0
$71$	−48.9334	+	28.2517i	−0.689203	+	0.397912i	−0.803314	−	0.595556i	$-0.796932\pi$
$71$	−48.9334	+	28.2517i	−0.689203	+	0.397912i	0.114110	+	0.993468i	$0.463598\pi$
$72$		0			0
$73$	32.6789	+	56.6015i	0.447656	+	0.775363i	0.998233	−	0.0594212i	$-0.0189255\pi$
$73$	32.6789	+	56.6015i	0.447656	+	0.775363i	−0.550577	+	0.834785i	$0.685592\pi$
$74$		0			0
$75$			91.2495i			1.21666i
$76$		0			0
$77$	14.1096			0.183241
$78$		0			0
$79$	−65.2985	+	37.7001i	−0.826563	+	0.477216i	−0.852674	−	0.522443i	$-0.825021\pi$
$79$	−65.2985	+	37.7001i	−0.826563	+	0.477216i	0.0261116	+	0.999659i	$0.491687\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	29.8871			0.360085			0.180043	−	0.983659i	$-0.442376\pi$
$83$	29.8871			0.360085			0.180043	+	0.983659i	$0.442376\pi$
$84$		0			0
$85$	−19.4372	+	33.6662i	−0.228673	+	0.396073i
$86$		0			0
$87$	−63.1265			−0.725592
$88$		0			0
$89$	23.3536	+	13.4832i	0.262400	+	0.151496i	0.625429	−	0.780281i	$-0.284924\pi$
$89$	23.3536	+	13.4832i	0.262400	+	0.151496i	−0.363029	+	0.931778i	$0.618257\pi$
$90$		0			0
$91$	8.97969	+	5.18443i	0.0986779	+	0.0569717i
$92$		0			0
$93$	−27.5271	−	47.6783i	−0.295990	−	0.512670i
$94$		0			0
$95$	−127.025	−	109.125i	−1.33711	−	1.14868i
$96$		0			0
$97$	−115.337	+	66.5899i	−1.18904	+	0.686494i	−0.958089	−	0.286471i	$-0.907518\pi$
$97$	−115.337	+	66.5899i	−1.18904	+	0.686494i	−0.230953	+	0.972965i	$0.574184\pi$
$98$		0			0
$99$	−6.57758	+	11.3927i	−0.0664402	+	0.115078i
$100$		0			0
$101$	−3.48309	+	6.03289i	−0.0344860	+	0.0597315i	−0.882753	−	0.469837i	$-0.844313\pi$
$101$	−3.48309	+	6.03289i	−0.0344860	+	0.0597315i	0.848267	+	0.529568i	$0.177646\pi$
$102$		0			0
$103$		−	139.013i		−	1.34964i	−0.737980	−	0.674822i	$-0.764220\pi$
$103$		−	139.013i		−	1.34964i	0.737980	−	0.674822i	$-0.235780\pi$
$104$		0			0
$105$	42.5396	+	24.5603i	0.405139	+	0.233907i
$106$		0			0
$107$		−	186.103i		−	1.73928i	−0.493688	−	0.869639i	$-0.664352\pi$
$107$		−	186.103i		−	1.73928i	0.493688	−	0.869639i	$-0.335648\pi$
$108$		0			0
$109$	119.933	−	69.2436i	1.10031	−	0.635262i	0.164005	−	0.986460i	$-0.447559\pi$
$109$	119.933	−	69.2436i	1.10031	−	0.635262i	0.936301	+	0.351197i	$0.114225\pi$
$110$		0			0
$111$	38.8691	+	67.3233i	0.350172	+	0.606516i
$112$		0			0
$113$		−	53.7208i		−	0.475405i	−0.971338	−	0.237703i	$-0.923606\pi$
$113$		−	53.7208i		−	0.475405i	0.971338	−	0.237703i	$-0.0763943\pi$
$114$		0			0
$115$	35.9159			0.312312
$116$		0			0
$117$	−8.37226	+	4.83373i	−0.0715578	+	0.0413139i
$118$		0			0
$119$	7.09595	+	12.2906i	0.0596299	+	0.103282i
$120$		0			0
$121$	−101.771			−0.841085
$122$		0			0
$123$	−40.6444	+	70.3981i	−0.330442	+	0.572342i
$124$		0			0
$125$	243.992			1.95193
$126$		0			0
$127$	−135.496	−	78.2288i	−1.06690	−	0.615974i	−0.139566	−	0.990213i	$-0.544571\pi$
$127$	−135.496	−	78.2288i	−1.06690	−	0.615974i	−0.927333	+	0.374238i	$0.877904\pi$
$128$		0			0
$129$	87.9033	+	50.7510i	0.681421	+	0.393419i
$130$		0			0
$131$	34.5893	+	59.9104i	0.264040	+	0.457331i	0.967312	−	0.253590i	$-0.0816115\pi$
$131$	34.5893	+	59.9104i	0.264040	+	0.457331i	−0.703272	+	0.710921i	$0.748278\pi$
$132$		0			0
$133$	−57.6874	+	20.2412i	−0.433740	+	0.152190i
$134$		0			0
$135$	−39.6621	+	22.8989i	−0.293793	+	0.169622i
$136$		0			0
$137$	129.654	−	224.568i	0.946381	−	1.63918i	0.193418	−	0.981117i	$-0.438043\pi$
$137$	129.654	−	224.568i	0.946381	−	1.63918i	0.752963	−	0.658063i	$-0.228624\pi$
$138$		0			0
$139$	−13.7467	+	23.8100i	−0.0988973	+	0.171295i	−0.911228	−	0.411901i	$-0.864865\pi$
$139$	−13.7467	+	23.8100i	−0.0988973	+	0.171295i	0.812331	+	0.583196i	$0.198198\pi$
$140$		0			0
$141$		−	0.662435i		−	0.00469812i
$142$		0			0
$143$	12.2376	+	7.06538i	0.0855776	+	0.0494083i
$144$		0			0
$145$			321.229i			2.21537i
$146$		0			0
$147$	−57.9700	+	33.4690i	−0.394354	+	0.227680i
$148$		0			0
$149$	−98.3347	−	170.321i	−0.659965	−	1.14309i	−0.980624	−	0.195898i	$-0.937238\pi$
$149$	−98.3347	−	170.321i	−0.659965	−	1.14309i	0.320660	−	0.947195i	$-0.396095\pi$
$150$		0			0
$151$			44.3978i			0.294025i	0.989135	+	0.147013i	$0.0469658\pi$
$151$			44.3978i			0.294025i	−0.989135	+	0.147013i	$0.953034\pi$
$152$		0			0
$153$	−13.2319			−0.0864831
$154$		0			0
$155$	−242.618	+	140.076i	−1.56528	+	0.903714i
$156$		0			0
$157$	−143.645	−	248.800i	−0.914936	−	1.58472i	−0.806995	−	0.590559i	$-0.798907\pi$
$157$	−143.645	−	248.800i	−0.914936	−	1.58472i	−0.107941	−	0.994157i	$-0.534426\pi$
$158$		0			0
$159$	−13.1065			−0.0824310
$160$		0			0
$161$	6.55591	−	11.3552i	0.0407199	−	0.0705290i
$162$		0			0
$163$	−219.671			−1.34767			−0.673836	−	0.738881i	$-0.735355\pi$
$163$	−219.671			−1.34767			−0.673836	+	0.738881i	$0.735355\pi$
$164$		0			0
$165$	57.9734	+	33.4710i	0.351354	+	0.202854i
$166$		0			0
$167$	114.769	+	66.2622i	0.687242	+	0.396779i	0.802578	−	0.596547i	$-0.203461\pi$
$167$	114.769	+	66.2622i	0.687242	+	0.396779i	−0.115336	+	0.993327i	$0.536794\pi$
$168$		0			0
$169$	−79.3078	−	137.365i	−0.469277	−	0.812811i
$170$		0			0
$171$	10.5490	−	56.0154i	0.0616898	−	0.327575i
$172$		0			0
$173$	−93.9224	+	54.2262i	−0.542904	+	0.313446i	−0.746255	−	0.665660i	$-0.768150\pi$
$173$	−93.9224	+	54.2262i	−0.542904	+	0.313446i	0.203351	+	0.979106i	$0.434817\pi$
$174$		0			0
$175$	84.7578	−	146.805i	0.484330	−	0.838885i
$176$		0			0
$177$	−18.3235	+	31.7372i	−0.103522	+	0.179306i
$178$		0			0
$179$			268.827i			1.50183i	0.660401	+	0.750913i	$0.270386\pi$
$179$			268.827i			1.50183i	−0.660401	+	0.750913i	$0.729614\pi$
$180$		0			0
$181$	109.400	+	63.1620i	0.604419	+	0.348961i	0.770778	−	0.637104i	$-0.219868\pi$
$181$	109.400	+	63.1620i	0.604419	+	0.348961i	−0.166359	+	0.986065i	$0.553201\pi$
$182$		0			0
$183$			59.3288i			0.324201i
$184$		0			0
$185$	342.584	−	197.791i	1.85181	−	1.06914i
$186$		0			0
$187$	9.67043	+	16.7497i	0.0517135	+	0.0895705i
$188$		0			0
$189$			16.7194i			0.0884626i
$190$		0			0
$191$	−97.9560			−0.512859			−0.256429	−	0.966563i	$-0.582546\pi$
$191$	−97.9560			−0.512859			−0.256429	+	0.966563i	$0.582546\pi$
$192$		0			0
$193$	−174.212	+	100.581i	−0.902652	+	0.521147i	−0.878060	−	0.478551i	$-0.841162\pi$
$193$	−174.212	+	100.581i	−0.902652	+	0.521147i	−0.0245925	+	0.999698i	$0.507829\pi$
$194$		0			0
$195$	24.5971	+	42.6035i	0.126139	+	0.218479i
$196$		0			0
$197$	−168.844			−0.857075			−0.428538	−	0.903524i	$-0.640971\pi$
$197$	−168.844			−0.857075			−0.428538	+	0.903524i	$0.640971\pi$
$198$		0			0
$199$	−30.5485	+	52.9116i	−0.153510	+	0.265888i	−0.932516	−	0.361130i	$-0.882391\pi$
$199$	−30.5485	+	52.9116i	−0.153510	+	0.265888i	0.779005	+	0.627017i	$0.215724\pi$
$200$		0			0
$201$	195.845			0.974354
$202$		0			0
$203$	101.560	+	58.6355i	0.500294	+	0.288845i
$204$		0			0
$205$	358.231	+	206.825i	1.74747	+	1.00890i
$206$		0			0
$207$	6.11244	+	10.5871i	0.0295287	+	0.0511452i
$208$		0			0
$209$	−78.6170	+	27.5849i	−0.376158	+	0.131985i
$210$		0			0
$211$	−79.5224	+	45.9123i	−0.376883	+	0.217594i	−0.676461	−	0.736478i	$-0.736487\pi$
$211$	−79.5224	+	45.9123i	−0.376883	+	0.217594i	0.299578	+	0.954072i	$0.403154\pi$
$212$		0			0
$213$	−48.9334	+	84.7552i	−0.229734	+	0.397912i
$214$		0			0
$215$	258.254	−	447.309i	1.20118	−	2.08051i
$216$		0			0
$217$			102.275i			0.471313i
$218$		0			0
$219$	98.0367	+	56.6015i	0.447656	+	0.258454i
$220$		0			0
$221$			14.2132i			0.0643132i
$222$		0			0
$223$	218.573	−	126.193i	0.980146	−	0.565887i	0.0778316	−	0.996967i	$-0.475200\pi$
$223$	218.573	−	126.193i	0.980146	−	0.565887i	0.902314	+	0.431079i	$0.141867\pi$
$224$		0			0
$225$	79.0244	+	136.874i	0.351220	+	0.608330i
$226$		0			0
$227$		−	13.0307i		−	0.0574039i	−0.999588	−	0.0287020i	$-0.990863\pi$
$227$		−	13.0307i		−	0.0574039i	0.999588	−	0.0287020i	$-0.00913737\pi$
$228$		0			0
$229$	−145.821			−0.636774			−0.318387	−	0.947961i	$-0.603141\pi$
$229$	−145.821			−0.636774			−0.318387	+	0.947961i	$0.603141\pi$
$230$		0			0
$231$	21.1644	−	12.2193i	0.0916207	−	0.0528972i
$232$		0			0
$233$	−139.011	−	240.775i	−0.596615	−	1.03337i	−0.993317	−	0.115420i	$-0.963179\pi$
$233$	−139.011	−	240.775i	−0.596615	−	1.03337i	0.396702	−	0.917948i	$-0.370155\pi$
$234$		0			0
$235$	−3.37090			−0.0143443
$236$		0			0
$237$	−65.2985	+	113.100i	−0.275521	+	0.477216i
$238$		0			0
$239$	29.3429			0.122774			0.0613868	−	0.998114i	$-0.480448\pi$
$239$	29.3429			0.122774			0.0613868	+	0.998114i	$0.480448\pi$
$240$		0			0
$241$	−279.250	−	161.225i	−1.15871	−	0.668983i	−0.207717	−	0.978189i	$-0.566603\pi$
$241$	−279.250	−	161.225i	−1.15871	−	0.668983i	−0.950995	+	0.309206i	$0.899937\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	170.312	+	294.989i	0.695151	+	1.20404i
$246$		0			0
$247$	−60.1696	−	11.3313i	−0.243601	−	0.0458757i
$248$		0			0
$249$	44.8306	−	25.8830i	0.180043	−	0.103948i
$250$		0			0
$251$	120.566	−	208.826i	0.480342	−	0.831976i	−0.519404	−	0.854529i	$-0.673846\pi$
$251$	120.566	−	208.826i	0.480342	−	0.831976i	0.999746	+	0.0225528i	$0.00717938\pi$
$252$		0			0
$253$	8.93446	−	15.4749i	0.0353141	−	0.0611657i
$254$		0			0
$255$			67.3325i			0.264049i
$256$		0			0
$257$	−46.8337	−	27.0394i	−0.182232	−	0.105212i	0.406109	−	0.913825i	$-0.366885\pi$
$257$	−46.8337	−	27.0394i	−0.182232	−	0.105212i	−0.588341	+	0.808613i	$0.700219\pi$
$258$		0			0
$259$		−	144.415i		−	0.557589i
$260$		0			0
$261$	−94.6898	+	54.6692i	−0.362796	+	0.209460i
$262$		0			0
$263$	−69.6306	−	120.604i	−0.264755	−	0.458569i	0.702744	−	0.711442i	$-0.251958\pi$
$263$	−69.6306	−	120.604i	−0.264755	−	0.458569i	−0.967499	+	0.252873i	$0.918624\pi$
$264$		0			0
$265$			66.6945i			0.251677i
$266$		0			0
$267$	46.7071			0.174933
$268$		0			0
$269$	367.620	−	212.245i	1.36662	−	0.789016i	0.376121	−	0.926571i	$-0.377258\pi$
$269$	367.620	−	212.245i	1.36662	−	0.789016i	0.990494	+	0.137555i	$0.0439243\pi$
$270$		0			0
$271$	−59.8521	−	103.667i	−0.220856	−	0.382534i	0.734212	−	0.678920i	$-0.237552\pi$
$271$	−59.8521	−	103.667i	−0.220856	−	0.382534i	−0.955068	+	0.296386i	$0.904219\pi$
$272$		0			0
$273$	17.9594			0.0657853
$274$		0			0
$275$	115.509	−	200.067i	0.420032	−	0.727516i
$276$		0			0
$277$	337.952			1.22004			0.610021	−	0.792385i	$-0.291161\pi$
$277$	337.952			1.22004			0.610021	+	0.792385i	$0.291161\pi$
$278$		0			0
$279$	−82.5813	−	47.6783i	−0.295990	−	0.170890i
$280$		0			0
$281$	−3.13712	−	1.81122i	−0.0111641	−	0.00644561i	0.494408	−	0.869230i	$-0.335385\pi$
$281$	−3.13712	−	1.81122i	−0.0111641	−	0.00644561i	−0.505572	+	0.862785i	$0.668718\pi$
$282$		0			0
$283$	201.229	+	348.540i	0.711058	+	1.23159i	0.964460	+	0.264228i	$0.0851170\pi$
$283$	201.229	+	348.540i	0.711058	+	1.23159i	−0.253402	+	0.967361i	$0.581550\pi$
$284$		0			0
$285$	−285.042	−	53.6799i	−1.00015	−	0.188351i
$286$		0			0
$287$	130.780	−	75.5056i	0.455678	−	0.263086i
$288$		0			0
$289$	134.773	−	233.434i	0.466343	−	0.807730i
$290$		0			0
$291$	−115.337	+	199.770i	−0.396347	+	0.686494i
$292$		0			0
$293$		−	179.458i		−	0.612486i	−0.951953	−	0.306243i	$-0.900928\pi$
$293$		−	179.458i		−	0.612486i	0.951953	−	0.306243i	$-0.0990720\pi$
$294$		0			0
$295$	161.499	+	93.2416i	0.547455	+	0.316073i
$296$		0			0
$297$			22.7854i			0.0767185i
$298$		0			0
$299$	11.3722	−	6.56575i	0.0380342	−	0.0219590i
$300$		0			0
$301$	−94.2809	−	163.299i	−0.313226	−	0.542523i
$302$		0			0
$303$			12.0658i			0.0398210i
$304$		0			0
$305$	301.903			0.989847
$306$		0			0
$307$	−98.8255	+	57.0569i	−0.321907	+	0.185853i	−0.652242	−	0.758011i	$-0.726172\pi$
$307$	−98.8255	+	57.0569i	−0.321907	+	0.185853i	0.330335	+	0.943864i	$0.392838\pi$
$308$		0			0
$309$	−120.389	−	208.520i	−0.389609	−	0.674822i
$310$		0			0
$311$	449.922			1.44670			0.723348	−	0.690484i	$-0.242602\pi$
$311$	449.922			1.44670			0.723348	+	0.690484i	$0.242602\pi$
$312$		0			0
$313$	82.6821	−	143.210i	0.264160	−	0.457539i	−0.703183	−	0.711009i	$-0.748239\pi$
$313$	82.6821	−	143.210i	0.264160	−	0.457539i	0.967343	+	0.253470i	$0.0815719\pi$
$314$		0			0
$315$	85.0793			0.270093
$316$		0			0
$317$	−410.583	−	237.050i	−1.29521	−	0.747792i	−0.315640	−	0.948879i	$-0.602219\pi$
$317$	−410.583	−	237.050i	−1.29521	−	0.747792i	−0.979573	+	0.201087i	$0.935553\pi$
$318$		0			0
$319$	138.407	+	79.9091i	0.433876	+	0.250499i
$320$		0			0
$321$	−161.170	−	279.154i	−0.502086	−	0.869639i
$322$		0			0
$323$	−63.5664	−	54.6086i	−0.196800	−	0.169067i
$324$		0			0
$325$	147.025	−	84.8850i	0.452385	−	0.261185i
$326$		0			0
$327$	119.933	−	207.731i	0.366769	−	0.635262i
$328$		0			0
$329$	−0.615308	+	1.06574i	−0.00187024	+	0.00323935i
$330$		0			0
$331$		−	224.977i		−	0.679688i	−0.940482	−	0.339844i	$-0.889626\pi$
$331$		−	224.977i		−	0.679688i	0.940482	−	0.339844i	$-0.110374\pi$
$332$		0			0
$333$	116.607	+	67.3233i	0.350172	+	0.202172i
$334$		0			0
$335$		−	996.587i		−	2.97489i
$336$		0			0
$337$	−218.446	+	126.120i	−0.648207	+	0.374243i	−0.787769	−	0.615971i	$-0.788764\pi$
$337$	−218.446	+	126.120i	−0.648207	+	0.374243i	0.139562	+	0.990213i	$0.455431\pi$
$338$		0			0
$339$	−46.5236	−	80.5812i	−0.137238	−	0.237703i
$340$		0			0
$341$			139.381i			0.408743i
$342$		0			0
$343$	282.017			0.822207
$344$		0			0
$345$	53.8738	−	31.1040i	0.156156	−	0.0901567i
$346$		0			0
$347$	−193.182	−	334.602i	−0.556722	−	0.964270i	−0.997767	−	0.0667857i	$-0.978726\pi$
$347$	−193.182	−	334.602i	−0.556722	−	0.964270i	0.441046	−	0.897485i	$-0.354608\pi$
$348$		0			0
$349$	−103.483			−0.296512			−0.148256	−	0.988949i	$-0.547366\pi$
$349$	−103.483			−0.296512			−0.148256	+	0.988949i	$0.547366\pi$
$350$		0			0
$351$	−8.37226	+	14.5012i	−0.0238526	+	0.0413139i
$352$		0			0
$353$	−669.987			−1.89798			−0.948990	−	0.315307i	$-0.897892\pi$
$353$	−669.987			−1.89798			−0.948990	+	0.315307i	$0.897892\pi$
$354$		0			0
$355$	431.289	+	249.005i	1.21490	+	0.701422i
$356$		0			0
$357$	21.2879	+	12.2906i	0.0596299	+	0.0344273i
$358$		0			0
$359$	−131.674	−	228.067i	−0.366781	−	0.635284i	0.622279	−	0.782796i	$-0.286207\pi$
$359$	−131.674	−	228.067i	−0.366781	−	0.635284i	−0.989060	+	0.147512i	$0.952874\pi$
$360$		0			0
$361$	281.855	−	225.563i	0.780762	−	0.624829i
$362$		0			0
$363$	−152.657	+	88.1366i	−0.420543	+	0.242800i
$364$		0			0
$365$	288.025	−	498.874i	0.789110	−	1.36678i
$366$		0			0
$367$	143.319	−	248.237i	0.390516	−	0.676394i	−0.602002	−	0.798495i	$-0.705630\pi$
$367$	143.319	−	248.237i	0.390516	−	0.676394i	0.992518	+	0.122101i	$0.0389632\pi$
$368$		0			0
$369$			140.796i			0.381562i
$370$		0			0
$371$	21.0862	+	12.1741i	0.0568360	+	0.0328143i
$372$		0			0
$373$			108.762i			0.291586i	0.989315	+	0.145793i	$0.0465734\pi$
$373$			108.762i			0.291586i	−0.989315	+	0.145793i	$0.953427\pi$
$374$		0			0
$375$	365.988	−	211.303i	0.975967	−	0.563475i
$376$		0			0
$377$	58.7236	+	101.712i	0.155765	+	0.269794i
$378$		0			0
$379$			709.431i			1.87185i	0.352200	+	0.935925i	$0.385434\pi$
$379$			709.431i			1.87185i	−0.352200	+	0.935925i	$0.614566\pi$
$380$		0			0
$381$	−270.992			−0.711266
$382$		0			0
$383$	−375.294	+	216.676i	−0.979880	+	0.565734i	−0.902234	−	0.431247i	$-0.858074\pi$
$383$	−375.294	+	216.676i	−0.979880	+	0.565734i	−0.0776459	+	0.996981i	$0.524740\pi$
$384$		0			0
$385$	−62.1795	−	107.698i	−0.161505	−	0.279735i
$386$		0			0
$387$	175.807			0.454281
$388$		0			0
$389$	−374.731	+	649.053i	−0.963319	+	1.66852i	−0.249254	+	0.968438i	$0.580186\pi$
$389$	−374.731	+	649.053i	−0.963319	+	1.66852i	−0.714065	+	0.700080i	$0.753148\pi$
$390$		0			0
$391$	17.9732			0.0459672
$392$		0			0
$393$	103.768	+	59.9104i	0.264040	+	0.152444i
$394$		0			0
$395$	575.527	+	332.281i	1.45703	+	0.841217i
$396$		0			0
$397$	23.4179	+	40.5611i	0.0589873	+	0.102169i	0.894011	−	0.448045i	$-0.147880\pi$
$397$	23.4179	+	40.5611i	0.0589873	+	0.102169i	−0.835024	+	0.550214i	$0.814546\pi$
$398$		0			0
$399$	−69.0017	+	80.3206i	−0.172937	+	0.201305i
$400$		0			0
$401$	−248.277	+	143.343i	−0.619145	+	0.357464i	−0.776536	−	0.630073i	$-0.783025\pi$
$401$	−248.277	+	143.343i	−0.619145	+	0.357464i	0.157391	+	0.987536i	$0.449692\pi$
$402$		0			0
$403$	−51.2143	+	88.7057i	−0.127083	+	0.220113i
$404$		0			0
$405$	−39.6621	+	68.6967i	−0.0979310	+	0.169622i
$406$		0			0
$407$		−	196.811i		−	0.483564i
$408$		0			0
$409$	598.475	+	345.530i	1.46326	+	0.844816i	0.999161	−	0.0409644i	$-0.0130430\pi$
$409$	598.475	+	345.530i	1.46326	+	0.844816i	0.464104	+	0.885781i	$0.346376\pi$
$410$		0			0
$411$		−	449.135i		−	1.09279i
$412$		0			0
$413$	58.9586	−	34.0397i	0.142757	−	0.0824207i
$414$		0			0
$415$	−131.709	−	228.127i	−0.317372	−	0.549704i
$416$		0			0
$417$			47.6200i			0.114197i
$418$		0			0
$419$	353.366			0.843356			0.421678	−	0.906746i	$-0.361441\pi$
$419$	353.366			0.843356			0.421678	+	0.906746i	$0.361441\pi$
$420$		0			0
$421$	−44.8284	+	25.8817i	−0.106481	+	0.0614768i	−0.552295	−	0.833649i	$-0.686248\pi$
$421$	−44.8284	+	25.8817i	−0.106481	+	0.0614768i	0.445814	+	0.895126i	$0.352914\pi$
$422$		0			0
$423$	−0.573686	−	0.993653i	−0.00135623	−	0.00234906i
$424$		0			0
$425$	232.365			0.546742
$426$		0			0
$427$	55.1080	−	95.4499i	0.129059	−	0.223536i
$428$		0			0
$429$	24.4752			0.0570518
$430$		0			0
$431$	−15.6103	−	9.01260i	−0.0362188	−	0.0209109i	0.481781	−	0.876291i	$-0.339990\pi$
$431$	−15.6103	−	9.01260i	−0.0362188	−	0.0209109i	−0.518000	+	0.855381i	$0.673323\pi$
$432$		0			0
$433$	679.340	+	392.217i	1.56891	+	0.905813i	0.996296	+	0.0859905i	$0.0274055\pi$
$433$	679.340	+	392.217i	1.56891	+	0.905813i	0.572618	+	0.819822i	$0.305928\pi$
$434$		0			0
$435$	278.192	+	481.843i	0.639522	+	1.10768i
$436$		0			0
$437$	−14.3289	+	76.0868i	−0.0327892	+	0.174112i
$438$		0			0
$439$	−672.263	+	388.131i	−1.53135	+	0.884125i	−0.532050	+	0.846713i	$0.678578\pi$
$439$	−672.263	+	388.131i	−1.53135	+	0.884125i	−0.999300	+	0.0374124i	$0.988088\pi$
$440$		0			0
$441$	−57.9700	+	100.407i	−0.131451	+	0.227680i
$442$		0			0
$443$	123.539	−	213.975i	0.278868	−	0.483013i	−0.692236	−	0.721671i	$-0.743374\pi$
$443$	123.539	−	213.975i	0.278868	−	0.483013i	0.971104	+	0.238658i	$0.0767075\pi$
$444$		0			0
$445$		−	237.676i		−	0.534103i
$446$		0			0
$447$	−295.004	−	170.321i	−0.659965	−	0.381031i
$448$		0			0
$449$		−	860.508i		−	1.91650i	−0.285934	−	0.958249i	$-0.592304\pi$
$449$		−	860.508i		−	1.91650i	0.285934	−	0.958249i	$-0.407696\pi$
$450$		0			0
$451$	178.228	−	102.900i	0.395183	−	0.228159i
$452$		0			0
$453$	38.4497	+	66.5968i	0.0848778	+	0.147013i
$454$		0			0
$455$		−	91.3889i		−	0.200855i
$456$		0			0
$457$	254.292			0.556437			0.278219	−	0.960518i	$-0.410256\pi$
$457$	254.292			0.556437			0.278219	+	0.960518i	$0.410256\pi$
$458$		0			0
$459$	−19.8479	+	11.4592i	−0.0432415	+	0.0249655i
$460$		0			0
$461$	−48.9928	−	84.8579i	−0.106275	−	0.184074i	0.807983	−	0.589205i	$-0.200559\pi$
$461$	−48.9928	−	84.8579i	−0.106275	−	0.184074i	−0.914258	+	0.405132i	$0.867226\pi$
$462$		0			0
$463$	−573.063			−1.23772			−0.618859	−	0.785502i	$-0.712405\pi$
$463$	−573.063			−1.23772			−0.618859	+	0.785502i	$0.712405\pi$
$464$		0			0
$465$	−242.618	+	420.227i	−0.521760	+	0.903714i
$466$		0			0
$467$	571.355			1.22346			0.611729	−	0.791067i	$-0.290474\pi$
$467$	571.355			1.22346			0.611729	+	0.791067i	$0.290474\pi$
$468$		0			0
$469$	−315.081	−	181.912i	−0.671815	−	0.387872i
$470$		0			0
$471$	−430.935	−	248.800i	−0.914936	−	0.528239i
$472$		0			0
$473$	−128.487	−	222.546i	−0.271642	−	0.470498i
$474$		0			0
$475$	−185.250	+	983.685i	−0.390000	+	2.07091i
$476$		0			0
$477$	−19.6598	+	11.3506i	−0.0412155	+	0.0237958i
$478$		0			0
$479$	−435.243	+	753.863i	−0.908649	+	1.57383i	−0.0927070	+	0.995693i	$0.529552\pi$
$479$	−435.243	+	753.863i	−0.908649	+	1.57383i	−0.815942	+	0.578133i	$0.803781\pi$
$480$		0			0
$481$	72.3161	−	125.255i	0.150345	−	0.260406i
$482$		0			0
$483$		−	22.7103i		−	0.0470193i
$484$		0			0
$485$	1016.56	+	586.909i	2.09599	+	1.21012i
$486$		0			0
$487$			279.996i			0.574941i	0.957789	+	0.287471i	$0.0928144\pi$
$487$			279.996i			0.574941i	−0.957789	+	0.287471i	$0.907186\pi$
$488$		0			0
$489$	−329.506	+	190.240i	−0.673836	+	0.389040i
$490$		0			0
$491$	198.108	+	343.133i	0.403478	+	0.698845i	0.994143	−	0.108072i	$-0.0344677\pi$
$491$	198.108	+	343.133i	0.403478	+	0.698845i	−0.590665	+	0.806917i	$0.701134\pi$
$492$		0			0
$493$			160.751i			0.326066i
$494$		0			0
$495$	115.947			0.234236
$496$		0			0
$497$	157.451	−	90.9043i	0.316803	−	0.182906i
$498$		0			0
$499$	17.5780	+	30.4460i	0.0352265	+	0.0610141i	0.883101	−	0.469183i	$-0.155451\pi$
$499$	17.5780	+	30.4460i	0.0352265	+	0.0610141i	−0.847875	+	0.530197i	$0.822118\pi$
$500$		0			0
$501$	229.539			0.458161
$502$		0			0
$503$	108.671	−	188.223i	0.216045	−	0.374202i	−0.737550	−	0.675292i	$-0.764017\pi$
$503$	108.671	−	188.223i	0.216045	−	0.374202i	0.953595	+	0.301091i	$0.0973508\pi$
$504$		0			0
$505$	61.3984			0.121581
$506$		0			0
$507$	−237.923	−	137.365i	−0.469277	−	0.270937i
$508$		0			0
$509$	242.699	+	140.122i	0.476816	+	0.275290i	0.719088	−	0.694919i	$-0.244560\pi$
$509$	242.699	+	140.122i	0.476816	+	0.275290i	−0.242273	+	0.970208i	$0.577893\pi$
$510$		0			0
$511$	−105.149	−	182.124i	−0.205772	−	0.356407i
$512$		0			0
$513$	−32.6873	−	93.1587i	−0.0637179	−	0.181596i
$514$		0			0
$515$	−1061.08	+	612.618i	−2.06036	+	1.18955i
$516$		0			0
$517$	−0.838547	+	1.45241i	−0.00162195	+	0.00280930i
$518$		0			0
$519$	−93.9224	+	162.678i	−0.180968	+	0.313446i
$520$		0			0
$521$		−	838.025i		−	1.60849i	−0.594296	−	0.804246i	$-0.702569\pi$
$521$		−	838.025i		−	1.60849i	0.594296	−	0.804246i	$-0.297431\pi$
$522$		0			0
$523$	−405.533	−	234.135i	−0.775397	−	0.447676i	0.0593992	−	0.998234i	$-0.481082\pi$
$523$	−405.533	−	234.135i	−0.775397	−	0.447676i	−0.834797	+	0.550558i	$0.814415\pi$
$524$		0			0
$525$		−	293.610i		−	0.559256i
$526$		0			0
$527$	−121.412	+	70.0973i	−0.230383	+	0.133012i
$528$		0			0
$529$	256.197	+	443.747i	0.484305	+	0.838841i
$530$		0			0
$531$			63.4743i			0.119537i
$532$		0			0
$533$	151.238			0.283748
$534$		0			0
$535$	−1420.52	+	820.135i	−2.65517	+	1.53296i
$536$		0			0
$537$	232.811	+	403.240i	0.433540	+	0.750913i
$538$		0			0
$539$	169.468			0.314411
$540$		0			0
$541$	68.5763	−	118.778i	0.126758	−	0.219552i	−0.795661	−	0.605743i	$-0.792876\pi$
$541$	68.5763	−	118.778i	0.126758	−	0.219552i	0.922419	+	0.386191i	$0.126209\pi$
$542$		0			0
$543$	218.800			0.402946
$544$		0			0
$545$	−1057.07	−	610.298i	−1.93957	−	1.11981i
$546$		0			0
$547$	405.394	+	234.054i	0.741122	+	0.427887i	0.822477	−	0.568798i	$-0.192592\pi$
$547$	405.394	+	234.054i	0.741122	+	0.427887i	−0.0813553	+	0.996685i	$0.525925\pi$
$548$		0			0
$549$	51.3803	+	88.9933i	0.0935888	+	0.162101i
$550$		0			0
$551$	−680.514	−	128.156i	−1.23505	−	0.232588i
$552$		0			0
$553$	210.108	−	121.306i	0.379942	−	0.219360i
$554$		0			0
$555$	342.584	−	593.373i	0.617269	−	1.06914i
$556$		0			0
$557$	−500.314	+	866.569i	−0.898230	+	1.55578i	−0.0684744	+	0.997653i	$0.521813\pi$
$557$	−500.314	+	866.569i	−0.898230	+	1.55578i	−0.829756	+	0.558127i	$0.811520\pi$
$558$		0			0
$559$		−	188.845i		−	0.337826i
$560$		0			0
$561$	29.0113	+	16.7497i	0.0517135	+	0.0298568i
$562$		0			0
$563$			718.352i			1.27594i	0.770063	+	0.637968i	$0.220225\pi$
$563$			718.352i			1.27594i	−0.770063	+	0.637968i	$0.779775\pi$
$564$		0			0
$565$	−410.049	+	236.742i	−0.725750	+	0.419012i
$566$		0			0
$567$	14.4795	+	25.0791i	0.0255370	+	0.0442313i
$568$		0			0
$569$			246.682i			0.433536i	0.976223	+	0.216768i	$0.0695515\pi$
$569$			246.682i			0.433536i	−0.976223	+	0.216768i	$0.930449\pi$
$570$		0			0
$571$	−414.146			−0.725299			−0.362650	−	0.931926i	$-0.618128\pi$
$571$	−414.146			−0.725299			−0.362650	+	0.931926i	$0.618128\pi$
$572$		0			0
$573$	−146.934	+	84.8324i	−0.256429	+	0.148050i
$574$		0			0
$575$	−107.340	−	185.919i	−0.186679	−	0.323338i
$576$		0			0
$577$	−107.641			−0.186553			−0.0932767	−	0.995640i	$-0.529734\pi$
$577$	−107.641			−0.186553			−0.0932767	+	0.995640i	$0.529734\pi$
$578$		0			0
$579$	−174.212	+	301.744i	−0.300884	+	0.521147i
$580$		0			0
$581$	−96.1663			−0.165519
$582$		0			0
$583$	28.7364	+	16.5910i	0.0492906	+	0.0284579i
$584$		0			0
$585$	73.7914	+	42.6035i	0.126139	+	0.0728265i
$586$		0			0
$587$	−447.052	−	774.318i	−0.761589	−	1.31911i	−0.942031	−	0.335525i	$-0.891086\pi$
$587$	−447.052	−	774.318i	−0.761589	−	1.31911i	0.180443	−	0.983585i	$-0.442247\pi$
$588$		0			0
$589$	−199.952	−	569.864i	−0.339478	−	0.967511i
$590$		0			0
$591$	−253.266	+	146.223i	−0.428538	+	0.247416i
$592$		0			0
$593$	−340.116	+	589.099i	−0.573552	+	0.993421i	0.422645	+	0.906295i	$0.361102\pi$
$593$	−340.116	+	589.099i	−0.573552	+	0.993421i	−0.996197	+	0.0871261i	$0.972232\pi$
$594$		0			0
$595$	62.5423	−	108.326i	0.105113	−	0.182061i
$596$		0			0
$597$			105.823i			0.177258i
$598$		0			0
$599$	−134.482	−	77.6430i	−0.224510	−	0.129621i	0.383527	−	0.923530i	$-0.374709\pi$
$599$	−134.482	−	77.6430i	−0.224510	−	0.129621i	−0.608037	+	0.793909i	$0.708043\pi$
$600$		0			0
$601$		−	476.554i		−	0.792934i	−0.918049	−	0.396467i	$-0.870236\pi$
$601$		−	476.554i		−	0.792934i	0.918049	−	0.396467i	$-0.129764\pi$
$602$		0			0
$603$	293.768	−	169.607i	0.487177	−	0.281272i
$604$		0			0
$605$	448.496	+	776.817i	0.741315	+	1.28400i
$606$		0			0
$607$		−	1134.80i		−	1.86953i	−0.355271	−	0.934763i	$-0.615611\pi$
$607$		−	1134.80i		−	1.86953i	0.355271	−	0.934763i	$-0.384389\pi$
$608$		0			0
$609$	203.119			0.333530
$610$		0			0
$611$	−1.06734	+	0.616232i	−0.00174688	+	0.00100856i
$612$		0			0
$613$	−196.630	−	340.573i	−0.320766	−	0.555583i	0.659880	−	0.751371i	$-0.270607\pi$
$613$	−196.630	−	340.573i	−0.320766	−	0.555583i	−0.980646	+	0.195788i	$0.937274\pi$
$614$		0			0
$615$	716.462			1.16498
$616$		0			0
$617$	−456.528	+	790.730i	−0.739916	+	1.28157i	0.212617	+	0.977136i	$0.431801\pi$
$617$	−456.528	+	790.730i	−0.739916	+	1.28157i	−0.952533	+	0.304436i	$0.901532\pi$
$618$		0			0
$619$	−907.656			−1.46633			−0.733163	−	0.680053i	$-0.761957\pi$
$619$	−907.656			−1.46633			−0.733163	+	0.680053i	$0.761957\pi$
$620$		0			0
$621$	18.3373	+	10.5871i	0.0295287	+	0.0170484i
$622$		0			0
$623$	−75.1437	−	43.3843i	−0.120616	−	0.0696377i
$624$		0			0
$625$	−416.710	−	721.762i	−0.666735	−	1.15482i
$626$		0			0
$627$	−94.0362	+	109.462i	−0.149978	+	0.174580i
$628$		0			0
$629$	171.438	−	98.9795i	0.272556	−	0.157360i
$630$		0			0
$631$	130.245	−	225.591i	0.206410	−	0.357513i	−0.744171	−	0.667989i	$-0.767155\pi$
$631$	130.245	−	225.591i	0.206410	−	0.357513i	0.950581	+	0.310476i	$0.100489\pi$
$632$		0			0
$633$	−79.5224	+	137.737i	−0.125628	+	0.217594i
$634$		0			0
$635$			1378.98i			2.17163i
$636$		0			0
$637$	107.853	+	62.2692i	0.169315	+	0.0977539i
$638$		0			0
$639$			169.510i			0.265274i
$640$		0			0
$641$	−349.389	+	201.720i	−0.545068	+	0.314695i	−0.747131	−	0.664677i	$-0.768569\pi$
$641$	−349.389	+	201.720i	−0.545068	+	0.314695i	0.202062	+	0.979373i	$0.435236\pi$
$642$		0			0
$643$	−445.655	−	771.896i	−0.693086	−	1.20046i	−0.970822	−	0.239803i	$-0.922917\pi$
$643$	−445.655	−	771.896i	−0.693086	−	1.20046i	0.277735	−	0.960658i	$-0.410416\pi$
$644$		0			0
$645$		−	894.618i		−	1.38700i
$646$		0			0
$647$	−580.419			−0.897092			−0.448546	−	0.893760i	$-0.648058\pi$
$647$	−580.419			−0.897092			−0.448546	+	0.893760i	$0.648058\pi$
$648$		0			0
$649$	80.3493	−	46.3897i	0.123805	−	0.0714787i
$650$		0			0
$651$	88.5727	+	153.412i	0.136056	+	0.235657i
$652$		0			0
$653$	−232.065			−0.355383			−0.177691	−	0.984086i	$-0.556863\pi$
$653$	−232.065			−0.355383			−0.177691	+	0.984086i	$0.556863\pi$
$654$		0			0
$655$	304.863	−	528.038i	0.465439	−	0.806164i
$656$		0			0
$657$	196.073			0.298437
$658$		0			0
$659$	484.667	+	279.822i	0.735458	+	0.424617i	0.820416	−	0.571768i	$-0.193742\pi$
$659$	484.667	+	279.822i	0.735458	+	0.424617i	−0.0849577	+	0.996385i	$0.527076\pi$
$660$		0			0
$661$	590.216	+	340.761i	0.892914	+	0.515524i	0.874895	−	0.484314i	$-0.160931\pi$
$661$	590.216	+	340.761i	0.892914	+	0.515524i	0.0180195	+	0.999838i	$0.494264\pi$
$662$		0			0
$663$	12.3090	+	21.3198i	0.0185656	+	0.0321566i
$664$		0			0
$665$	408.723	+	351.125i	0.614621	+	0.528008i
$666$		0			0
$667$	128.619	−	74.2583i	0.192832	−	0.111332i
$668$		0			0
$669$	218.573	−	378.579i	0.326715	−	0.565887i
$670$		0			0
$671$	75.1017	−	130.080i	0.111925	−	0.193860i
$672$		0			0
$673$		−	1041.65i		−	1.54777i	−0.633329	−	0.773883i	$-0.718312\pi$
$673$		−	1041.65i		−	1.54777i	0.633329	−	0.773883i	$-0.281688\pi$
$674$		0			0
$675$	237.073	+	136.874i	0.351220	+	0.202777i
$676$		0			0
$677$			958.389i			1.41564i	0.706392	+	0.707821i	$0.250322\pi$
$677$			958.389i			1.41564i	−0.706392	+	0.707821i	$0.749678\pi$
$678$		0			0
$679$	371.115	−	214.263i	0.546561	−	0.315557i
$680$		0			0
$681$	−11.2849	−	19.5460i	−0.0165711	−	0.0287020i
$682$		0			0
$683$		−	374.317i		−	0.548048i	−0.961723	−	0.274024i	$-0.911645\pi$
$683$		−	374.317i		−	0.548048i	0.961723	−	0.274024i	$-0.0883548\pi$
$684$		0			0
$685$	−2285.49			−3.33648
$686$		0			0
$687$	−218.732	+	126.285i	−0.318387	+	0.183821i
$688$		0			0
$689$	12.1924	+	21.1178i	0.0176957	+	0.0306499i
$690$		0			0
$691$	486.123			0.703506			0.351753	−	0.936093i	$-0.385586\pi$
$691$	486.123			0.703506			0.351753	+	0.936093i	$0.385586\pi$
$692$		0			0
$693$	21.1644	−	36.6578i	0.0305402	−	0.0528972i
$694$		0			0
$695$	242.321			0.348664
$696$		0			0
$697$	179.267	+	103.500i	0.257199	+	0.148494i
$698$		0			0
$699$	−417.034	−	240.775i	−0.596615	−	0.344456i
$700$		0			0
$701$	113.884	+	197.252i	0.162459	+	0.281387i	0.935750	−	0.352664i	$-0.114724\pi$
$701$	113.884	+	197.252i	0.162459	+	0.281387i	−0.773291	+	0.634051i	$0.781391\pi$
$702$		0			0
$703$	282.339	+	804.666i	0.401620	+	1.14462i
$704$		0			0
$705$	−5.05635	+	2.91928i	−0.00717213	+	0.00414083i
$706$		0			0
$707$	11.2074	−	19.4117i	0.0158520	−	0.0274565i
$708$		0			0
$709$	111.698	−	193.467i	0.157543	−	0.272873i	−0.776439	−	0.630192i	$-0.782976\pi$
$709$	111.698	−	193.467i	0.157543	−	0.272873i	0.933982	+	0.357320i	$0.116309\pi$
$710$		0			0
$711$			226.200i			0.318144i
$712$		0			0
$713$	112.172	+	64.7625i	0.157324	+	0.0908309i
$714$		0			0
$715$		−	124.546i		−	0.174190i
$716$		0			0
$717$	44.0143	−	25.4117i	0.0613868	−	0.0354417i
$718$		0			0
$719$	594.075	+	1028.97i	0.826252	+	1.43111i	0.900958	+	0.433905i	$0.142865\pi$
$719$	594.075	+	1028.97i	0.826252	+	1.43111i	−0.0747062	+	0.997206i	$0.523802\pi$
$720$		0			0
$721$			447.297i			0.620385i
$722$		0			0
$723$	−558.499			−0.772475
$724$		0			0
$725$	1662.85	−	960.045i	2.29358	−	1.32420i
$726$		0			0
$727$	180.837	+	313.218i	0.248744	+	0.430837i	0.963177	−	0.268866i	$-0.0866490\pi$
$727$	180.837	+	313.218i	0.248744	+	0.430837i	−0.714434	+	0.699703i	$0.753316\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	129.237	−	223.844i	0.176794	−	0.306216i
$732$		0			0
$733$	−848.339			−1.15735			−0.578676	−	0.815557i	$-0.696430\pi$
$733$	−848.339			−1.15735			−0.578676	+	0.815557i	$0.696430\pi$
$734$		0			0
$735$	510.936	+	294.989i	0.695151	+	0.401346i
$736$		0			0
$737$	−429.396	−	247.912i	−0.582626	−	0.336379i
$738$		0			0
$739$	498.956	+	864.217i	0.675177	+	1.16944i	0.976417	+	0.215893i	$0.0692662\pi$
$739$	498.956	+	864.217i	0.675177	+	1.16944i	−0.301240	+	0.953548i	$0.597400\pi$
$740$		0			0
$741$	−100.068	+	35.1114i	−0.135044	+	0.0473839i
$742$		0			0
$743$	200.807	−	115.936i	0.270266	−	0.156038i	−0.358743	−	0.933437i	$-0.616794\pi$
$743$	200.807	−	115.936i	0.270266	−	0.156038i	0.629008	+	0.777399i	$0.283461\pi$
$744$		0			0
$745$	−866.702	+	1501.17i	−1.16336	+	2.01500i
$746$		0			0
$747$	44.8306	−	77.6489i	0.0600142	−	0.103948i
$748$		0			0
$749$			598.815i			0.799485i
$750$		0			0
$751$	−704.906	−	406.977i	−0.938623	−	0.541914i	−0.0490944	−	0.998794i	$-0.515634\pi$
$751$	−704.906	−	406.977i	−0.938623	−	0.541914i	−0.889528	+	0.456880i	$0.848967\pi$
$752$		0			0
$753$		−	417.652i		−	0.554651i
$754$		0			0
$755$	338.887	−	195.657i	0.448857	−	0.259148i
$756$		0			0
$757$	−148.315	−	256.889i	−0.195924	−	0.339351i	0.751279	−	0.659985i	$-0.229437\pi$
$757$	−148.315	−	256.889i	−0.195924	−	0.339351i	−0.947203	+	0.320634i	$0.896104\pi$
$758$		0			0
$759$		−	30.9499i		−	0.0407772i
$760$		0			0
$761$	−234.320			−0.307911			−0.153956	−	0.988078i	$-0.549201\pi$
$761$	−234.320			−0.307911			−0.153956	+	0.988078i	$0.549201\pi$
$762$		0			0
$763$	−385.904	+	222.802i	−0.505772	+	0.292008i
$764$		0			0
$765$	58.3116	+	100.999i	0.0762244	+	0.132024i
$766$		0			0
$767$	68.1817			0.0888940
$768$		0			0
$769$	583.147	−	1010.04i	0.758318	−	1.31345i	−0.185389	−	0.982665i	$-0.559355\pi$
$769$	583.147	−	1010.04i	0.758318	−	1.31345i	0.943708	−	0.330781i	$-0.107312\pi$
$770$		0			0
$771$	−93.6673			−0.121488
$772$		0			0
$773$	51.3920	+	29.6712i	0.0664838	+	0.0383845i	0.532873	−	0.846195i	$-0.321112\pi$
$773$	51.3920	+	29.6712i	0.0664838	+	0.0383845i	−0.466390	+	0.884579i	$0.654446\pi$
$774$		0			0
$775$	1450.21	+	837.278i	1.87124	+	1.08036i
$776$		0			0
$777$	−125.067	−	216.623i	−0.160962	−	0.278794i
$778$		0			0
$779$	−581.071	+	676.389i	−0.745919	+	0.868278i
$780$		0			0
$781$	214.576	−	123.885i	0.274745	−	0.158624i
$782$		0			0
$783$	−94.6898	+	164.008i	−0.120932	+	0.209460i
$784$		0			0
$785$	−1266.06	+	2192.88i	−1.61281	+	2.79347i
$786$		0			0
$787$		−	1249.88i		−	1.58816i	−0.607815	−	0.794079i	$-0.707954\pi$
$787$		−	1249.88i		−	1.58816i	0.607815	−	0.794079i	$-0.292046\pi$
$788$		0			0
$789$	−208.892	−	120.604i	−0.264755	−	0.152856i
$790$		0			0
$791$			172.855i			0.218527i
$792$		0			0
$793$	95.5932	−	55.1907i	0.120546	−	0.0695974i
$794$		0			0
$795$	57.7591	+	100.042i	0.0726530	+	0.125839i
$796$		0			0
$797$		−	542.952i		−	0.681245i	−0.940200	−	0.340623i	$-0.889362\pi$
$797$		−	542.952i		−	0.681245i	0.940200	−	0.340623i	$-0.110638\pi$
$798$		0			0
$799$	−1.68688			−0.00211124
$800$		0			0
$801$	70.0607	−	40.4496i	0.0874665	−	0.0504988i
$802$		0			0
$803$	−143.299	−	248.201i	−0.178454	−	0.309092i
$804$		0			0
$805$	−115.565			−0.143559
$806$		0			0
$807$	367.620	−	636.736i	0.455538	−	0.789016i
$808$		0			0
$809$	146.014			0.180487			0.0902437	−	0.995920i	$-0.471235\pi$
$809$	146.014			0.180487			0.0902437	+	0.995920i	$0.471235\pi$
$810$		0			0
$811$	301.348	+	173.984i	0.371576	+	0.214530i	0.674147	−	0.738597i	$-0.264511\pi$
$811$	301.348	+	173.984i	0.371576	+	0.214530i	−0.302571	+	0.953127i	$0.597845\pi$
$812$		0			0
$813$	−179.556	−	103.667i	−0.220856	−	0.127511i
$814$		0			0
$815$	968.066	+	1676.74i	1.18781	+	2.05735i
$816$		0			0
$817$	844.580	+	725.561i	1.03376	+	0.888079i
$818$		0			0
$819$	26.9391	−	15.5533i	0.0328926	−	0.0189906i
$820$		0			0
$821$	654.271	−	1133.23i	0.796919	−	1.38030i	−0.124694	−	0.992195i	$-0.539795\pi$
$821$	654.271	−	1133.23i	0.796919	−	1.38030i	0.921613	−	0.388109i	$-0.126872\pi$
$822$		0			0
$823$	−460.157	+	797.015i	−0.559121	+	0.968426i	0.438449	+	0.898756i	$0.355528\pi$
$823$	−460.157	+	797.015i	−0.559121	+	0.968426i	−0.997570	+	0.0696699i	$0.977805\pi$
$824$		0			0
$825$		−	400.134i		−	0.485011i
$826$		0			0
$827$	−1066.20	−	615.569i	−1.28924	−	0.744340i	−0.310717	−	0.950502i	$-0.600569\pi$
$827$	−1066.20	−	615.569i	−1.28924	−	0.744340i	−0.978518	+	0.206162i	$0.933903\pi$
$828$		0			0
$829$			1435.20i			1.73124i	0.500702	+	0.865620i	$0.333075\pi$
$829$			1435.20i			1.73124i	−0.500702	+	0.865620i	$0.666925\pi$
$830$		0			0
$831$	506.927	−	292.675i	0.610021	−	0.352196i
$832$		0			0
$833$	85.2282	+	147.620i	0.102315	+	0.177214i
$834$		0			0
$835$		−	1168.04i		−	1.39885i
$836$		0			0
$837$	−165.163			−0.197327
$838$		0			0
$839$	526.457	−	303.950i	0.627481	−	0.362276i	−0.152295	−	0.988335i	$-0.548666\pi$
$839$	526.457	−	303.950i	0.627481	−	0.362276i	0.779776	+	0.626059i	$0.215333\pi$
$840$		0			0
$841$	243.660	+	422.031i	0.289726	+	0.501821i
$842$		0			0
$843$	−6.27424			−0.00744275
$844$		0			0
$845$	−699.002	+	1210.71i	−0.827222	+	1.43279i
$846$		0			0
$847$	327.465			0.386618
$848$		0			0
$849$	603.688	+	348.540i	0.711058	+	0.410530i
$850$		0			0
$851$	−158.390	−	91.4466i	−0.186122	−	0.107458i
$852$		0			0
$853$	−28.7065	−	49.7211i	−0.0336536	−	0.0582897i	0.848708	−	0.528862i	$-0.177381\pi$
$853$	−28.7065	−	49.7211i	−0.0336536	−	0.0582897i	−0.882362	+	0.470572i	$0.844048\pi$
$854$		0			0
$855$	−474.052	+	166.334i	−0.554446	+	0.194543i
$856$		0			0
$857$	−1101.22	+	635.789i	−1.28497	+	0.741877i	−0.977752	−	0.209762i	$-0.932731\pi$
$857$	−1101.22	+	635.789i	−1.28497	+	0.741877i	−0.307217	+	0.951640i	$0.599398\pi$
$858$		0			0
$859$	277.465	−	480.583i	0.323009	−	0.559468i	−0.658099	−	0.752932i	$-0.728639\pi$
$859$	277.465	−	480.583i	0.323009	−	0.559468i	0.981107	+	0.193464i	$0.0619723\pi$
$860$		0			0
$861$	130.780	−	226.517i	0.151893	−	0.263086i
$862$		0			0
$863$			707.318i			0.819604i	0.912175	+	0.409802i	$0.134402\pi$
$863$			707.318i			0.819604i	−0.912175	+	0.409802i	$0.865598\pi$
$864$		0			0
$865$	827.813	+	477.938i	0.957009	+	0.552530i
$866$		0			0
$867$		−	466.868i		−	0.538487i
$868$		0			0
$869$	286.337	−	165.317i	0.329502	−	0.190238i
$870$		0			0
$871$	−182.185	−	315.554i	−0.209168	−	0.362289i
$872$		0			0
$873$			399.539i			0.457662i
$874$		0			0
$875$	−785.081			−0.897236
$876$		0			0
$877$	−593.208	+	342.489i	−0.676405	+	0.390523i	−0.798499	−	0.601996i	$-0.794372\pi$
$877$	−593.208	+	342.489i	−0.676405	+	0.390523i	0.122094	+	0.992519i	$0.461039\pi$
$878$		0			0
$879$	−155.416	−	269.188i	−0.176810	−	0.306243i
$880$		0			0
$881$	−0.0346557			−3.93368e−5			−1.96684e−5	−	1.00000i	$-0.500006\pi$
$881$	−0.0346557			−3.93368e−5			−1.96684e−5		1.00000i	$0.500006\pi$
$882$		0			0
$883$	843.829	−	1461.56i	0.955639	−	1.65522i	0.222741	−	0.974878i	$-0.428500\pi$
$883$	843.829	−	1461.56i	0.955639	−	1.65522i	0.732899	−	0.680338i	$-0.238167\pi$
$884$		0			0
$885$	322.998			0.364970
$886$		0			0
$887$	666.456	+	384.778i	0.751359	+	0.433798i	0.826185	−	0.563399i	$-0.190507\pi$
$887$	666.456	+	384.778i	0.751359	+	0.433798i	−0.0748255	+	0.997197i	$0.523840\pi$
$888$		0			0
$889$	435.980	+	251.713i	0.490416	+	0.283142i
$890$		0			0
$891$	19.7327	+	34.1781i	0.0221467	+	0.0383593i
$892$		0			0
$893$	1.34484	−	7.14116i	0.00150598	−	0.00799682i
$894$		0			0
$895$	2051.95	−	1184.69i	2.29268	−	1.32368i
$896$		0			0
$897$	11.3722	−	19.6973i	0.0126781	−	0.0219590i
$898$		0			0
$899$	−579.230	+	1003.26i	−0.644305	+	1.11597i
$900$		0			0
$901$			33.3755i			0.0370428i
$902$		0			0
$903$	−282.843	−	163.299i	−0.313226	−	0.180841i
$904$		0			0
$905$		−	1113.39i		−	1.23027i
$906$		0			0
$907$	136.419	−	78.7613i	0.150406	−	0.0868371i	−0.422908	−	0.906173i	$-0.638991\pi$
$907$	136.419	−	78.7613i	0.150406	−	0.0868371i	0.573314	+	0.819335i	$0.305657\pi$
$908$		0			0
$909$	10.4493	+	18.0987i	0.0114953	+	0.0199105i
$910$		0			0
$911$		−	477.594i		−	0.524253i	−0.965034	−	0.262126i	$-0.915576\pi$
$911$		−	477.594i		−	0.524253i	0.965034	−	0.262126i	$-0.0844238\pi$
$912$		0			0
$913$	−131.056			−0.143545
$914$		0			0
$915$	452.855	−	261.456i	0.494924	−	0.285744i
$916$		0			0
$917$	−111.296	−	192.771i	−0.121370	−	0.210219i
$918$		0			0
$919$	943.460			1.02662			0.513308	−	0.858204i	$-0.328420\pi$
$919$	943.460			1.02662			0.513308	+	0.858204i	$0.328420\pi$
$920$		0			0
$921$	−98.8255	+	171.171i	−0.107302	+	0.185853i
$922$		0			0
$923$	182.082			0.197272
$924$		0			0
$925$	−2047.74	−	1182.26i	−2.21377	−	1.27812i
$926$		0			0
$927$	−361.167	−	208.520i	−0.389609	−	0.224941i
$928$		0			0
$929$	−916.038	−	1586.62i	−0.986047	−	1.70788i	−0.637188	−	0.770708i	$-0.719903\pi$
$929$	−916.038	−	1586.62i	−0.986047	−	1.70788i	−0.348859	−	0.937175i	$-0.613431\pi$
$930$		0			0
$931$	−692.873	+	243.114i	−0.744225	+	0.261132i
$932$		0			0
$933$	674.884	−	389.644i	0.723348	−	0.417625i
$934$		0			0
$935$	85.2332	−	147.628i	0.0911585	−	0.157891i
$936$		0			0
$937$	−363.820	+	630.155i	−0.388282	+	0.672524i	−0.992219	−	0.124508i	$-0.960265\pi$
$937$	−363.820	+	630.155i	−0.388282	+	0.672524i	0.603936	+	0.797032i	$0.293598\pi$
$938$		0			0
$939$		−	286.419i		−	0.305026i
$940$		0			0
$941$	−1016.64	−	586.958i	−1.08038	−	0.623760i	−0.149384	−	0.988779i	$-0.547729\pi$
$941$	−1016.64	−	586.958i	−1.08038	−	0.623760i	−0.931000	+	0.365020i	$0.881062\pi$
$942$		0			0
$943$		−	191.246i		−	0.202806i
$944$		0			0
$945$	127.619	−	73.6808i	0.135046	−	0.0779691i
$946$		0			0
$947$	−472.820	−	818.949i	−0.499282	−	0.864782i	0.500717	−	0.865611i	$-0.333070\pi$
$947$	−472.820	−	818.949i	−0.499282	−	0.864782i	−1.00000		0.000828630i	$0.999736\pi$
$948$		0			0
$949$		−	210.615i		−	0.221933i
$950$		0			0
$951$	−821.165			−0.863476
$952$		0			0
$953$	808.936	−	467.039i	0.848831	−	0.490073i	−0.0114252	−	0.999935i	$-0.503637\pi$
$953$	808.936	−	467.039i	0.848831	−	0.490073i	0.860256	+	0.509862i	$0.170304\pi$
$954$		0			0
$955$	431.682	+	747.695i	0.452023	+	0.782927i
$956$		0			0
$957$	276.813			0.289251
$958$		0			0
$959$	−417.182	+	722.581i	−0.435018	+	0.753474i
$960$		0			0
$961$	−49.3219			−0.0513235
$962$		0			0
$963$	−483.509	−	279.154i	−0.502086	−	0.289880i
$964$		0			0
$965$	1535.47	+	886.503i	1.59116	+	0.918656i
$966$		0			0
$967$	−9.39696	−	16.2760i	−0.00971764	−	0.0168314i	0.861126	−	0.508392i	$-0.169760\pi$
$967$	−9.39696	−	16.2760i	−0.00971764	−	0.0168314i	−0.870843	+	0.491561i	$0.836427\pi$
$968$		0			0
$969$	−142.642	−	26.8627i	−0.147205	−	0.0277221i
$970$		0			0
$971$	120.918	−	69.8119i	0.124529	−	0.0718969i	−0.436441	−	0.899733i	$-0.643761\pi$
$971$	120.918	−	69.8119i	0.124529	−	0.0718969i	0.560971	+	0.827836i	$0.310428\pi$
$972$		0			0
$973$	44.2322	−	76.6124i	0.0454596	−	0.0787384i
$974$		0			0
$975$	147.025	−	254.655i	0.150795	−	0.261185i
$976$		0			0
$977$		−	763.183i		−	0.781150i	−0.920571	−	0.390575i	$-0.872276\pi$
$977$		−	763.183i		−	0.781150i	0.920571	−	0.390575i	$-0.127724\pi$
$978$		0			0
$979$	−102.407	−	59.1245i	−0.104603	−	0.0603927i
$980$		0			0
$981$		−	415.461i		−	0.423508i
$982$		0			0
$983$	−678.340	+	391.640i	−0.690072	+	0.398413i	−0.803639	−	0.595117i	$-0.797106\pi$
$983$	−678.340	+	391.640i	−0.690072	+	0.398413i	0.113567	+	0.993530i	$0.463772\pi$
$984$		0			0
$985$	744.077	+	1288.78i	0.755408	+	1.30841i
$986$		0			0
$987$			2.13149i			0.00215956i
$988$		0			0
$989$	−238.802			−0.241458
$990$		0			0
$991$	119.437	−	68.9569i	0.120522	−	0.0695831i	−0.438527	−	0.898718i	$-0.644500\pi$
$991$	119.437	−	68.9569i	0.120522	−	0.0695831i	0.559049	+	0.829135i	$0.311166\pi$
$992$		0			0
$993$	−194.836	−	337.465i	−0.196209	−	0.339844i
$994$		0			0
$995$	538.497			0.541203
$996$		0			0
$997$	615.424	−	1065.95i	0.617276	−	1.06915i	−0.372704	−	0.927950i	$-0.621569\pi$
$997$	615.424	−	1065.95i	0.617276	−	1.06915i	0.989981	−	0.141204i	$-0.0450973\pi$
$998$		0			0
$999$	233.215			0.233448

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.j.145.1		20
4.3	odd	2		456.3.w.a.145.1	✓	20
12.11	even	2		1368.3.bv.c.145.10		20
19.8	odd	6	inner	912.3.be.j.673.1		20
76.27	even	6		456.3.w.a.217.1	yes	20
228.179	odd	6		1368.3.bv.c.217.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.3.w.a.145.1	✓	20	4.3	odd	2
456.3.w.a.217.1	yes	20	76.27	even	6
912.3.be.j.145.1		20	1.1	even	1	trivial
912.3.be.j.673.1		20	19.8	odd	6	inner
1368.3.bv.c.145.10		20	12.11	even	2
1368.3.bv.c.217.10		20	228.179	odd	6

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.be (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(-4.40690 - 7.63297i) q^{5} -3.21766 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(-4.40690 - 7.63297i) q^{5} -3.21766 q^{7} +(1.50000 - 2.59808i) q^{9} -4.38505 q^{11} +(-2.79075 - 1.61124i) q^{13} +(-13.2207 - 7.63297i) q^{15} +(-2.20532 - 3.81972i) q^{17} +(17.9284 - 6.29067i) q^{19} +(-4.82648 + 2.78657i) q^{21} +(-2.03748 + 3.52902i) q^{23} +(-26.3415 + 45.6248i) q^{25} -5.19615i q^{27} +(-31.5633 - 18.2231i) q^{29} -31.7856i q^{31} +(-6.57758 + 3.79757i) q^{33} +(14.1799 + 24.5603i) q^{35} +44.8822i q^{37} -5.58151 q^{39} +(-40.6444 + 23.4660i) q^{41} +(29.3011 + 50.7510i) q^{43} -26.4414 q^{45} +(0.191229 - 0.331218i) q^{47} -38.6467 q^{49} +(-6.61595 - 3.81972i) q^{51} +(-6.55327 - 3.78353i) q^{53} +(19.3245 + 33.4710i) q^{55} +(21.4447 - 24.9625i) q^{57} +(-18.3235 + 10.5791i) q^{59} +(-17.1268 + 29.6644i) q^{61} +(-4.82648 + 8.35972i) q^{63} +28.4023i q^{65} +(97.9226 + 56.5356i) q^{67} +7.05804i q^{69} +(-48.9334 + 28.2517i) q^{71} +(32.6789 + 56.6015i) q^{73} +91.2495i q^{75} +14.1096 q^{77} +(-65.2985 + 37.7001i) q^{79} +(-4.50000 - 7.79423i) q^{81} +29.8871 q^{83} +(-19.4372 + 33.6662i) q^{85} -63.1265 q^{87} +(23.3536 + 13.4832i) q^{89} +(8.97969 + 5.18443i) q^{91} +(-27.5271 - 47.6783i) q^{93} +(-127.025 - 109.125i) q^{95} +(-115.337 + 66.5899i) q^{97} +(-6.57758 + 11.3927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9}+O(q^{10}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9	\( 20 q + 30 q^{3} - 20 q^{7} + 30 q^{9} + 8 q^{11} + 18 q^{13} + 8 q^{17} - 28 q^{19} - 30 q^{21} + 8 q^{23} - 58 q^{25} + 108 q^{29} + 12 q^{33} - 20 q^{35} + 36 q^{39} - 36 q^{41} + 2 q^{43} + 296 q^{49} + 24 q^{51} - 72 q^{53} - 216 q^{55} - 30 q^{57} - 72 q^{59} - 26 q^{61} - 30 q^{63} - 138 q^{67} + 204 q^{71} + 218 q^{73} - 8 q^{77} + 78 q^{79} - 90 q^{81} + 112 q^{83} + 224 q^{85} + 216 q^{87} - 432 q^{89} + 330 q^{91} - 126 q^{93} - 220 q^{95} + 132 q^{97} + 12 q^{99}+O(q^{100}) \) 20 * q + 30 * q^3 - 20 * q^7 + 30 * q^9 + 8 * q^11 + 18 * q^13 + 8 * q^17 - 28 * q^19 - 30 * q^21 + 8 * q^23 - 58 * q^25 + 108 * q^29 + 12 * q^33 - 20 * q^35 + 36 * q^39 - 36 * q^41 + 2 * q^43 + 296 * q^49 + 24 * q^51 - 72 * q^53 - 216 * q^55 - 30 * q^57 - 72 * q^59 - 26 * q^61 - 30 * q^63 - 138 * q^67 + 204 * q^71 + 218 * q^73 - 8 * q^77 + 78 * q^79 - 90 * q^81 + 112 * q^83 + 224 * q^85 + 216 * q^87 - 432 * q^89 + 330 * q^91 - 126 * q^93 - 220 * q^95 + 132 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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