LMFDB - Embedded newform 912.3.z.e.847.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,3,Mod(463,912)]

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([3, 0, 0, 2]))

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

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

chi := DirichletCharacter("912.463");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	912.z (of order $6$, degree $2$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 28 x^{14} - 348 x^{13} - 348 x^{12} + 2078 x^{11} + 15746 x^{10} - 116662 x^{9} + \cdots + 14339668675 $ x^16 - 28x^14 - 348x^13 - 348x^12 + 2078x^11 + 15746x^10 - 116662x^9 + 1437888x^8 + 6662192x^7 + 22843584x^6 + 245977140x^5 + 970849640x^4 + 765826994x^3 + 7368705162x^2 - 410399010x + 14339668675
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			847.1
Root			$-5.13124 - 3.34935i$ of defining polynomial
Character	$\chi$	$=$	912.847
Dual form			912.3.z.e.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(-4.96624 + 8.60179i) q^{5} -5.53823i q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(-4.96624 + 8.60179i) q^{5} -5.53823i q^{7} +(1.50000 + 2.59808i) q^{9} -15.2797i q^{11} +(8.32019 + 14.4110i) q^{13} +(14.8987 - 8.60179i) q^{15} +(9.95916 - 17.2498i) q^{17} +(4.37821 - 18.4887i) q^{19} +(-4.79624 + 8.30734i) q^{21} +(-19.9422 + 11.5136i) q^{23} +(-36.8272 - 63.7865i) q^{25} -5.19615i q^{27} +(10.7087 + 18.5480i) q^{29} +24.1676i q^{31} +(-13.2326 + 22.9196i) q^{33} +(47.6386 + 27.5042i) q^{35} +27.5783 q^{37} -28.8220i q^{39} +(-32.6077 + 56.4782i) q^{41} +(68.3188 + 39.4439i) q^{43} -29.7975 q^{45} +(-34.7033 + 20.0360i) q^{47} +18.3281 q^{49} +(-29.8775 + 17.2498i) q^{51} +(38.3501 + 66.4244i) q^{53} +(131.433 + 75.8828i) q^{55} +(-22.5790 + 23.9414i) q^{57} +(29.1176 + 16.8111i) q^{59} +(-38.5217 - 66.7215i) q^{61} +(14.3887 - 8.30734i) q^{63} -165.280 q^{65} +(-31.2130 + 18.0208i) q^{67} +39.8844 q^{69} +(-69.7967 - 40.2972i) q^{71} +(18.8505 - 32.6499i) q^{73} +127.573i q^{75} -84.6225 q^{77} +(54.8446 + 31.6645i) q^{79} +(-4.50000 + 7.79423i) q^{81} +25.1850i q^{83} +(98.9192 + 171.333i) q^{85} -37.0959i q^{87} +(50.9074 + 88.1742i) q^{89} +(79.8114 - 46.0791i) q^{91} +(20.9298 - 36.2514i) q^{93} +(137.292 + 129.480i) q^{95} +(50.1089 - 86.7912i) q^{97} +(39.6979 - 22.9196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{3} + 2 q^{5} + 24 q^{9}+O(q^{10}) $ 16 * q - 24 * q^3 + 2 * q^5 + 24 * q^9	$ 16 q - 24 q^{3} + 2 q^{5} + 24 q^{9} - 8 q^{13} - 6 q^{15} + 8 q^{17} - 12 q^{19} + 6 q^{21} + 6 q^{23} - 120 q^{25} + 24 q^{29} - 6 q^{33} + 18 q^{35} + 136 q^{37} - 68 q^{41} + 114 q^{43} + 12 q^{45} - 132 q^{47} - 264 q^{49} - 24 q^{51} + 94 q^{53} + 180 q^{55} + 6 q^{57} + 114 q^{59} + 44 q^{61} - 18 q^{63} - 412 q^{65} + 30 q^{67} - 12 q^{69} - 12 q^{71} + 104 q^{73} + 20 q^{77} - 66 q^{79} - 72 q^{81} + 140 q^{85} + 66 q^{89} + 102 q^{91} + 6 q^{93} + 90 q^{95} + 240 q^{97} + 18 q^{99}+O(q^{100}) $ 16 * q - 24 * q^3 + 2 * q^5 + 24 * q^9 - 8 * q^13 - 6 * q^15 + 8 * q^17 - 12 * q^19 + 6 * q^21 + 6 * q^23 - 120 * q^25 + 24 * q^29 - 6 * q^33 + 18 * q^35 + 136 * q^37 - 68 * q^41 + 114 * q^43 + 12 * q^45 - 132 * q^47 - 264 * q^49 - 24 * q^51 + 94 * q^53 + 180 * q^55 + 6 * q^57 + 114 * q^59 + 44 * q^61 - 18 * q^63 - 412 * q^65 + 30 * q^67 - 12 * q^69 - 12 * q^71 + 104 * q^73 + 20 * q^77 - 66 * q^79 - 72 * q^81 + 140 * q^85 + 66 * q^89 + 102 * q^91 + 6 * q^93 + 90 * q^95 + 240 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$-1$

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
$5$	−4.96624	+	8.60179i	−0.993249	+	1.72036i	−0.396162	+	0.918181i	$0.629658\pi$
$5$	−4.96624	+	8.60179i	−0.993249	+	1.72036i	−0.597087	+	0.802177i	$0.703675\pi$
$6$		0			0
$7$		−	5.53823i		−	0.791175i	−0.918428	−	0.395588i	$-0.870541\pi$
$7$		−	5.53823i		−	0.791175i	0.918428	−	0.395588i	$-0.129459\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$		0			0
$11$		−	15.2797i		−	1.38906i	−0.719461	−	0.694532i	$-0.755611\pi$
$11$		−	15.2797i		−	1.38906i	0.719461	−	0.694532i	$-0.244389\pi$
$12$		0			0
$13$	8.32019	+	14.4110i	0.640015	+	1.10854i	0.985429	+	0.170088i	$0.0544052\pi$
$13$	8.32019	+	14.4110i	0.640015	+	1.10854i	−0.345414	+	0.938450i	$0.612261\pi$
$14$		0			0
$15$	14.8987	−	8.60179i	0.993249	−	0.573452i
$16$		0			0
$17$	9.95916	−	17.2498i	0.585833	−	1.01469i	−0.408938	−	0.912562i	$-0.634101\pi$
$17$	9.95916	−	17.2498i	0.585833	−	1.01469i	0.994771	−	0.102130i	$-0.0325658\pi$
$18$		0			0
$19$	4.37821	−	18.4887i	0.230432	−	0.973088i
$19$	4.37821	−	18.4887i	0.230432	−	0.973088i
$20$		0			0
$21$	−4.79624	+	8.30734i	−0.228393	+	0.395588i
$22$		0			0
$23$	−19.9422	+	11.5136i	−0.867051	+	0.500592i	−0.866367	−	0.499407i	$-0.833551\pi$
$23$	−19.9422	+	11.5136i	−0.867051	+	0.500592i	−0.000684134		1.00000i	$0.500218\pi$
$24$		0			0
$25$	−36.8272	−	63.7865i	−1.47309	−	2.55146i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	10.7087	+	18.5480i	0.369264	+	0.639585i	0.989451	−	0.144870i	$-0.0462763\pi$
$29$	10.7087	+	18.5480i	0.369264	+	0.639585i	−0.620186	+	0.784455i	$0.712943\pi$
$30$		0			0
$31$			24.1676i			0.779600i	0.920900	+	0.389800i	$0.127456\pi$
$31$			24.1676i			0.779600i	−0.920900	+	0.389800i	$0.872544\pi$
$32$		0			0
$33$	−13.2326	+	22.9196i	−0.400988	+	0.694532i
$34$		0			0
$35$	47.6386	+	27.5042i	1.36110	+	0.785834i
$36$		0			0
$37$	27.5783			0.745360			0.372680	−	0.927960i	$-0.378439\pi$
$37$	27.5783			0.745360			0.372680	+	0.927960i	$0.378439\pi$
$38$		0			0
$39$		−	28.8220i		−	0.739026i
$40$		0			0
$41$	−32.6077	+	56.4782i	−0.795310	+	1.37752i	0.127332	+	0.991860i	$0.459359\pi$
$41$	−32.6077	+	56.4782i	−0.795310	+	1.37752i	−0.922642	+	0.385657i	$0.873975\pi$
$42$		0			0
$43$	68.3188	+	39.4439i	1.58881	+	0.917299i	0.993504	+	0.113799i	$0.0363020\pi$
$43$	68.3188	+	39.4439i	1.58881	+	0.917299i	0.595305	+	0.803500i	$0.297031\pi$
$44$		0			0
$45$	−29.7975			−0.662166
$46$		0			0
$47$	−34.7033	+	20.0360i	−0.738369	+	0.426297i	−0.821476	−	0.570243i	$-0.806849\pi$
$47$	−34.7033	+	20.0360i	−0.738369	+	0.426297i	0.0831071	+	0.996541i	$0.473516\pi$
$48$		0			0
$49$	18.3281			0.374042
$50$		0			0
$51$	−29.8775	+	17.2498i	−0.585833	+	0.338231i
$52$		0			0
$53$	38.3501	+	66.4244i	0.723587	+	1.25329i	0.959553	+	0.281529i	$0.0908414\pi$
$53$	38.3501	+	66.4244i	0.723587	+	1.25329i	−0.235965	+	0.971761i	$0.575825\pi$
$54$		0			0
$55$	131.433	+	75.8828i	2.38969	+	1.37969i
$56$		0			0
$57$	−22.5790	+	23.9414i	−0.396123	+	0.420024i
$58$		0			0
$59$	29.1176	+	16.8111i	0.493519	+	0.284933i	0.726033	−	0.687660i	$-0.241362\pi$
$59$	29.1176	+	16.8111i	0.493519	+	0.284933i	−0.232514	+	0.972593i	$0.574695\pi$
$60$		0			0
$61$	−38.5217	−	66.7215i	−0.631503	−	1.09379i	−0.987245	−	0.159211i	$-0.949105\pi$
$61$	−38.5217	−	66.7215i	−0.631503	−	1.09379i	0.355742	−	0.934584i	$-0.384228\pi$
$62$		0			0
$63$	14.3887	−	8.30734i	0.228393	−	0.131863i
$64$		0			0
$65$	−165.280			−2.54278
$66$		0			0
$67$	−31.2130	+	18.0208i	−0.465866	+	0.268968i	−0.714508	−	0.699628i	$-0.753349\pi$
$67$	−31.2130	+	18.0208i	−0.465866	+	0.268968i	0.248642	+	0.968596i	$0.420016\pi$
$68$		0			0
$69$	39.8844			0.578034
$70$		0			0
$71$	−69.7967	−	40.2972i	−0.983053	−	0.567566i	−0.0798622	−	0.996806i	$-0.525448\pi$
$71$	−69.7967	−	40.2972i	−0.983053	−	0.567566i	−0.903190	+	0.429240i	$0.858781\pi$
$72$		0			0
$73$	18.8505	−	32.6499i	0.258225	−	0.447259i	−0.707541	−	0.706672i	$-0.750196\pi$
$73$	18.8505	−	32.6499i	0.258225	−	0.447259i	0.965767	+	0.259413i	$0.0835290\pi$
$74$		0			0
$75$			127.573i			1.70097i
$76$		0			0
$77$	−84.6225			−1.09899
$78$		0			0
$79$	54.8446	+	31.6645i	0.694235	+	0.400817i	0.805197	−	0.593008i	$-0.202060\pi$
$79$	54.8446	+	31.6645i	0.694235	+	0.400817i	−0.110962	+	0.993825i	$0.535393\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			25.1850i			0.303434i	0.988424	+	0.151717i	$0.0484802\pi$
$83$			25.1850i			0.303434i	−0.988424	+	0.151717i	$0.951520\pi$
$84$		0			0
$85$	98.9192	+	171.333i	1.16376	+	2.01568i
$86$		0			0
$87$		−	37.0959i		−	0.426390i
$88$		0			0
$89$	50.9074	+	88.1742i	0.571993	+	0.990722i	0.996361	+	0.0852316i	$0.0271630\pi$
$89$	50.9074	+	88.1742i	0.571993	+	0.990722i	−0.424368	+	0.905490i	$0.639504\pi$
$90$		0			0
$91$	79.8114	−	46.0791i	0.877048	−	0.506364i
$92$		0			0
$93$	20.9298	−	36.2514i	0.225051	−	0.389800i
$94$		0			0
$95$	137.292	+	129.480i	1.44518	+	1.36294i
$96$		0			0
$97$	50.1089	−	86.7912i	0.516587	−	0.894755i	−0.483227	−	0.875495i	$-0.660536\pi$
$97$	50.1089	−	86.7912i	0.516587	−	0.894755i	0.999815	−	0.0192601i	$-0.00613107\pi$
$98$		0			0
$99$	39.6979	−	22.9196i	0.400988	−	0.231511i
$100$		0			0
$101$	33.4393	+	57.9186i	0.331083	+	0.573452i	0.982724	−	0.185075i	$-0.0592528\pi$
$101$	33.4393	+	57.9186i	0.331083	+	0.573452i	−0.651642	+	0.758527i	$0.725919\pi$
$102$		0			0
$103$			18.4094i			0.178732i	0.995999	+	0.0893660i	$0.0284841\pi$
$103$			18.4094i			0.178732i	−0.995999	+	0.0893660i	$0.971516\pi$
$104$		0			0
$105$	−47.6386	−	82.5125i	−0.453701	−	0.785834i
$106$		0			0
$107$			92.2305i			0.861967i	0.902360	+	0.430984i	$0.141833\pi$
$107$			92.2305i			0.861967i	−0.902360	+	0.430984i	$0.858167\pi$
$108$		0			0
$109$	−52.8820	+	91.5943i	−0.485156	+	0.840314i	−0.999855	−	0.0170567i	$-0.994570\pi$
$109$	−52.8820	+	91.5943i	−0.485156	+	0.840314i	0.514699	+	0.857371i	$0.327904\pi$
$110$		0			0
$111$	−41.3675	−	23.8835i	−0.372680	−	0.215167i
$112$		0			0
$113$	89.2313			0.789657			0.394829	−	0.918755i	$-0.370804\pi$
$113$	89.2313			0.789657			0.394829	+	0.918755i	$0.370804\pi$
$114$		0			0
$115$		−	228.718i		−	1.98885i
$116$		0			0
$117$	−24.9606	+	43.2330i	−0.213338	+	0.369513i
$118$		0			0
$119$	−95.5331	−	55.1561i	−0.802799	−	0.463496i
$120$		0			0
$121$	−112.470			−0.929501
$122$		0			0
$123$	97.8231	−	56.4782i	0.795310	−	0.459172i
$124$		0			0
$125$	483.258			3.86607
$126$		0			0
$127$	−158.106	+	91.2826i	−1.24493	+	0.718761i	−0.970094	−	0.242730i	$-0.921957\pi$
$127$	−158.106	+	91.2826i	−1.24493	+	0.718761i	−0.274836	+	0.961491i	$0.588624\pi$
$128$		0			0
$129$	−68.3188	−	118.332i	−0.529603	−	0.917299i
$130$		0			0
$131$	32.2769	+	18.6351i	0.246389	+	0.142253i	0.618110	−	0.786092i	$-0.287899\pi$
$131$	32.2769	+	18.6351i	0.246389	+	0.142253i	−0.371721	+	0.928345i	$0.621232\pi$
$132$		0			0
$133$	−102.394	−	24.2475i	−0.769883	−	0.182312i
$134$		0			0
$135$	44.6962	+	25.8054i	0.331083	+	0.191151i
$136$		0			0
$137$	55.1262	+	95.4814i	0.402381	+	0.696945i	0.994013	−	0.109264i	$-0.0348493\pi$
$137$	55.1262	+	95.4814i	0.402381	+	0.696945i	−0.591632	+	0.806208i	$0.701516\pi$
$138$		0			0
$139$	177.291	−	102.359i	1.27547	−	0.736395i	0.299461	−	0.954109i	$-0.403193\pi$
$139$	177.291	−	102.359i	1.27547	−	0.736395i	0.976013	+	0.217714i	$0.0698600\pi$
$140$		0			0
$141$	69.4067			0.492246
$142$		0			0
$143$	220.196	−	127.130i	1.53983	−	0.889022i
$144$		0			0
$145$	−212.727			−1.46709
$146$		0			0
$147$	−27.4921	−	15.8726i	−0.187021	−	0.107977i
$148$		0			0
$149$	−25.6865	+	44.4903i	−0.172393	+	0.298593i	−0.939256	−	0.343218i	$-0.888483\pi$
$149$	−25.6865	+	44.4903i	−0.172393	+	0.298593i	0.766863	+	0.641811i	$0.221816\pi$
$150$		0			0
$151$		−	84.2823i		−	0.558161i	−0.960268	−	0.279081i	$-0.909970\pi$
$151$		−	84.2823i		−	0.558161i	0.960268	−	0.279081i	$-0.0900296\pi$
$152$		0			0
$153$	59.7549			0.390555
$154$		0			0
$155$	−207.885	−	120.022i	−1.34119	−	0.774337i
$156$		0			0
$157$	2.14482	−	3.71494i	0.0136613	−	0.0236621i	−0.859114	−	0.511784i	$-0.828985\pi$
$157$	2.14482	−	3.71494i	0.0136613	−	0.0236621i	0.872775	+	0.488122i	$0.162318\pi$
$158$		0			0
$159$		−	132.849i		−	0.835527i
$160$		0			0
$161$	63.7650	+	110.444i	0.396056	+	0.685989i
$162$		0			0
$163$			185.054i			1.13530i	0.823270	+	0.567650i	$0.192147\pi$
$163$			185.054i			1.13530i	−0.823270	+	0.567650i	$0.807853\pi$
$164$		0			0
$165$	−131.433	−	227.648i	−0.796563	−	1.37969i
$166$		0			0
$167$	198.294	−	114.485i	1.18739	−	0.685541i	0.229679	−	0.973267i	$-0.426233\pi$
$167$	198.294	−	114.485i	1.18739	−	0.685541i	0.957713	+	0.287726i	$0.0928992\pi$
$168$		0			0
$169$	−53.9512	+	93.4463i	−0.319238	+	0.552937i
$170$		0			0
$171$	54.6023	−	16.3581i	0.319312	−	0.0956613i
$172$		0			0
$173$	103.244	−	178.824i	0.596787	−	1.03367i	−0.396505	−	0.918033i	$-0.629777\pi$
$173$	103.244	−	178.824i	0.596787	−	1.03367i	0.993292	−	0.115633i	$-0.0368897\pi$
$174$		0			0
$175$	−353.264	+	203.957i	−2.01865	+	1.16547i
$176$		0			0
$177$	−29.1176	−	50.4332i	−0.164506	−	0.284933i
$178$		0			0
$179$			331.131i			1.84989i	0.380099	+	0.924946i	$0.375890\pi$
$179$			331.131i			1.84989i	−0.380099	+	0.924946i	$0.624110\pi$
$180$		0			0
$181$	80.4664	+	139.372i	0.444566	+	0.770010i	0.998022	−	0.0628679i	$-0.0200247\pi$
$181$	80.4664	+	139.372i	0.444566	+	0.770010i	−0.553456	+	0.832878i	$0.686691\pi$
$182$		0			0
$183$			133.443i			0.729196i
$184$		0			0
$185$	−136.961	+	237.223i	−0.740328	+	1.28229i
$186$		0			0
$187$	−263.571	−	152.173i	−1.40947	−	0.813760i
$188$		0			0
$189$	−28.7775			−0.152262
$190$		0			0
$191$			125.655i			0.657882i	0.944350	+	0.328941i	$0.106692\pi$
$191$			125.655i			0.657882i	−0.944350	+	0.328941i	$0.893308\pi$
$192$		0			0
$193$	12.7392	−	22.0650i	0.0660064	−	0.114326i	−0.831134	−	0.556073i	$-0.812308\pi$
$193$	12.7392	−	22.0650i	0.0660064	−	0.114326i	0.897140	+	0.441746i	$0.145641\pi$
$194$		0			0
$195$	247.921	+	143.137i	1.27139	+	0.734036i
$196$		0			0
$197$	−303.164			−1.53891			−0.769453	−	0.638704i	$-0.779471\pi$
$197$	−303.164			−1.53891			−0.769453	+	0.638704i	$0.779471\pi$
$198$		0			0
$199$	−4.20818	+	2.42959i	−0.0211466	+	0.0122090i	−0.510536	−	0.859856i	$-0.670553\pi$
$199$	−4.20818	+	2.42959i	−0.0211466	+	0.0122090i	0.489389	+	0.872065i	$0.337220\pi$
$200$		0			0
$201$	62.4260			0.310577
$202$		0			0
$203$	102.723	−	59.3070i	0.506023	−	0.292153i
$204$		0			0
$205$	−323.876	−	560.969i	−1.57988	−	2.73643i
$206$		0			0
$207$	−59.8265	−	34.5409i	−0.289017	−	0.166864i
$208$		0			0
$209$	−282.502	−	66.8978i	−1.35168	−	0.320085i
$210$		0			0
$211$	−7.20931	−	4.16230i	−0.0341673	−	0.0197265i	0.482819	−	0.875720i	$-0.339613\pi$
$211$	−7.20931	−	4.16230i	−0.0341673	−	0.0197265i	−0.516986	+	0.855994i	$0.672946\pi$
$212$		0			0
$213$	69.7967	+	120.891i	0.327684	+	0.567566i
$214$		0			0
$215$	−678.575	+	391.776i	−3.15616	+	1.82221i
$216$		0			0
$217$	133.846			0.616800
$218$		0			0
$219$	−56.5514	+	32.6499i	−0.258225	+	0.149086i
$220$		0			0
$221$	331.448			1.49977
$222$		0			0
$223$	237.337	+	137.026i	1.06429	+	0.614468i	0.926616	−	0.376010i	$-0.122704\pi$
$223$	237.337	+	137.026i	1.06429	+	0.614468i	0.137674	+	0.990478i	$0.456037\pi$
$224$		0			0
$225$	110.481	−	191.360i	0.491029	−	0.850487i
$226$		0			0
$227$		−	321.101i		−	1.41454i	−0.706943	−	0.707270i	$-0.749926\pi$
$227$		−	321.101i		−	1.41454i	0.706943	−	0.707270i	$-0.250074\pi$
$228$		0			0
$229$	−69.1286			−0.301871			−0.150936	−	0.988544i	$-0.548229\pi$
$229$	−69.1286			−0.301871			−0.150936	+	0.988544i	$0.548229\pi$
$230$		0			0
$231$	126.934	+	73.2852i	0.549497	+	0.317252i
$232$		0			0
$233$	23.1980	−	40.1800i	0.0995620	−	0.172446i	−0.811941	−	0.583739i	$-0.801589\pi$
$233$	23.1980	−	40.1800i	0.0995620	−	0.172446i	0.911503	+	0.411292i	$0.134922\pi$
$234$		0			0
$235$		−	398.014i		−	1.69368i
$236$		0			0
$237$	−54.8446	−	94.9936i	−0.231412	−	0.400817i
$238$		0			0
$239$		−	106.850i		−	0.447070i	−0.974696	−	0.223535i	$-0.928240\pi$
$239$		−	106.850i		−	0.447070i	0.974696	−	0.223535i	$-0.0717597\pi$
$240$		0			0
$241$	122.793	+	212.683i	0.509513	+	0.882502i	0.999939	+	0.0110195i	$0.00350768\pi$
$241$	122.793	+	212.683i	0.509513	+	0.882502i	−0.490426	+	0.871483i	$0.663159\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$		0			0
$245$	−91.0216	+	157.654i	−0.371517	+	0.643486i
$246$		0			0
$247$	302.868	−	90.7350i	1.22619	−	0.367348i
$248$		0			0
$249$	21.8108	−	37.7775i	0.0875938	−	0.151717i
$250$		0			0
$251$	2.58823	−	1.49432i	0.0103117	−	0.00595346i	−0.494835	−	0.868987i	$-0.664772\pi$
$251$	2.58823	−	1.49432i	0.0103117	−	0.00595346i	0.505147	+	0.863033i	$0.331438\pi$
$252$		0			0
$253$	175.925	+	304.711i	0.695355	+	1.20439i
$254$		0			0
$255$		−	342.666i		−	1.34379i
$256$		0			0
$257$	153.504	+	265.876i	0.597290	+	1.03454i	0.993219	+	0.116256i	$0.0370892\pi$
$257$	153.504	+	265.876i	0.597290	+	1.03454i	−0.395929	+	0.918281i	$0.629578\pi$
$258$		0			0
$259$		−	152.735i		−	0.589710i
$260$		0			0
$261$	−32.1260	+	55.6439i	−0.123088	+	0.213195i
$262$		0			0
$263$	−183.735	−	106.079i	−0.698612	−	0.403344i	0.108218	−	0.994127i	$-0.465485\pi$
$263$	−183.735	−	106.079i	−0.698612	−	0.403344i	−0.806830	+	0.590783i	$0.798819\pi$
$264$		0			0
$265$	−761.824			−2.87481
$266$		0			0
$267$		−	176.348i		−	0.660481i
$268$		0			0
$269$	123.327	−	213.608i	0.458464	−	0.794082i	−0.540416	−	0.841398i	$-0.681733\pi$
$269$	123.327	−	213.608i	0.458464	−	0.794082i	0.998880	+	0.0473155i	$0.0150666\pi$
$270$		0			0
$271$	−277.954	−	160.477i	−1.02566	−	0.592165i	−0.109922	−	0.993940i	$-0.535060\pi$
$271$	−277.954	−	160.477i	−1.02566	−	0.592165i	−0.915739	+	0.401775i	$0.868393\pi$
$272$		0			0
$273$	−159.623			−0.584699
$274$		0			0
$275$	−974.639	+	562.708i	−3.54414	+	2.04621i
$276$		0			0
$277$	176.704			0.637921			0.318961	−	0.947768i	$-0.396666\pi$
$277$	176.704			0.637921			0.318961	+	0.947768i	$0.396666\pi$
$278$		0			0
$279$	−62.7893	+	36.2514i	−0.225051	+	0.129933i
$280$		0			0
$281$	−93.6596	−	162.223i	−0.333308	−	0.577307i	0.649850	−	0.760062i	$-0.274832\pi$
$281$	−93.6596	−	162.223i	−0.333308	−	0.577307i	−0.983158	+	0.182756i	$0.941498\pi$
$282$		0			0
$283$	83.5959	+	48.2641i	0.295392	+	0.170545i	0.640371	−	0.768066i	$-0.278781\pi$
$283$	83.5959	+	48.2641i	0.295392	+	0.170545i	−0.344979	+	0.938610i	$0.612114\pi$
$284$		0			0
$285$	−93.8058	−	313.118i	−0.329143	−	1.09866i
$286$		0			0
$287$	312.789	+	180.589i	1.08986	+	0.629229i
$288$		0			0
$289$	−53.8696	−	93.3049i	−0.186400	−	0.322854i
$290$		0			0
$291$	−150.327	+	86.7912i	−0.516587	+	0.298252i
$292$		0			0
$293$	−52.3978			−0.178832			−0.0894160	−	0.995994i	$-0.528500\pi$
$293$	−52.3978			−0.178832			−0.0894160	+	0.995994i	$0.528500\pi$
$294$		0			0
$295$	−289.210	+	166.976i	−0.980373	+	0.566019i
$296$		0			0
$297$	−79.3957			−0.267326
$298$		0			0
$299$	−331.846	−	191.591i	−1.10985	−	0.640773i
$300$		0			0
$301$	218.449	−	378.365i	0.725744	−	1.25703i
$302$		0			0
$303$		−	115.837i		−	0.382301i
$304$		0			0
$305$	765.232			2.50896
$306$		0			0
$307$	−130.391	−	75.2815i	−0.424728	−	0.245217i	0.272370	−	0.962192i	$-0.412192\pi$
$307$	−130.391	−	75.2815i	−0.424728	−	0.245217i	−0.697098	+	0.716976i	$0.745526\pi$
$308$		0			0
$309$	15.9430	−	27.6141i	0.0515955	−	0.0893660i
$310$		0			0
$311$		−	268.126i		−	0.862142i	−0.902318	−	0.431071i	$-0.858136\pi$
$311$		−	268.126i		−	0.862142i	0.902318	−	0.431071i	$-0.141864\pi$
$312$		0			0
$313$	225.600	+	390.751i	0.720768	+	1.24841i	0.960692	+	0.277615i	$0.0895439\pi$
$313$	225.600	+	390.751i	0.720768	+	1.24841i	−0.239925	+	0.970791i	$0.577123\pi$
$314$		0			0
$315$			165.025i			0.523889i
$316$		0			0
$317$	−38.6657	−	66.9710i	−0.121974	−	0.211265i	0.798572	−	0.601899i	$-0.205589\pi$
$317$	−38.6657	−	66.9710i	−0.121974	−	0.211265i	−0.920546	+	0.390634i	$0.872256\pi$
$318$		0			0
$319$	283.407	−	163.625i	0.888425	−	0.512932i
$320$		0			0
$321$	79.8739	−	138.346i	0.248828	−	0.430984i
$322$		0			0
$323$	−275.322	−	259.655i	−0.852390	−	0.803885i
$324$		0			0
$325$	612.818	−	1061.43i	1.88559	−	3.26595i
$326$		0			0
$327$	158.646	−	91.5943i	0.485156	−	0.280105i
$328$		0			0
$329$	110.964	+	192.195i	0.337276	+	0.584179i
$330$		0			0
$331$		−	84.8460i		−	0.256332i	−0.991753	−	0.128166i	$-0.959091\pi$
$331$		−	84.8460i		−	0.256332i	0.991753	−	0.128166i	$-0.0409091\pi$
$332$		0			0
$333$	41.3675	+	71.6506i	0.124227	+	0.215167i
$334$		0			0
$335$		−	357.984i		−	1.06861i
$336$		0			0
$337$	141.465	−	245.025i	0.419778	−	0.727078i	−0.576139	−	0.817352i	$-0.695441\pi$
$337$	141.465	−	245.025i	0.419778	−	0.727078i	0.995917	+	0.0902745i	$0.0287745\pi$
$338$		0			0
$339$	−133.847	−	77.2765i	−0.394829	−	0.227954i
$340$		0			0
$341$	369.274			1.08291
$342$		0			0
$343$		−	372.878i		−	1.08711i
$344$		0			0
$345$	−198.075	+	343.077i	−0.574132	+	0.994426i
$346$		0			0
$347$	133.026	+	76.8024i	0.383359	+	0.221333i	0.679279	−	0.733880i	$-0.262293\pi$
$347$	133.026	+	76.8024i	0.383359	+	0.221333i	−0.295919	+	0.955213i	$0.595626\pi$
$348$		0			0
$349$	327.842			0.939376			0.469688	−	0.882832i	$-0.344366\pi$
$349$	327.842			0.939376			0.469688	+	0.882832i	$0.344366\pi$
$350$		0			0
$351$	74.8817	−	43.2330i	0.213338	−	0.123171i
$352$		0			0
$353$	−255.079			−0.722603			−0.361302	−	0.932449i	$-0.617668\pi$
$353$	−255.079			−0.722603			−0.361302	+	0.932449i	$0.617668\pi$
$354$		0			0
$355$	693.255	−	400.251i	1.95283	−	1.12747i
$356$		0			0
$357$	95.5331	+	165.468i	0.267600	+	0.463496i
$358$		0			0
$359$	−18.6759	−	10.7825i	−0.0520221	−	0.0300349i	0.473763	−	0.880652i	$-0.342895\pi$
$359$	−18.6759	−	10.7825i	−0.0520221	−	0.0300349i	−0.525785	+	0.850617i	$0.676229\pi$
$360$		0			0
$361$	−322.662	−	161.895i	−0.893802	−	0.448462i
$362$		0			0
$363$	168.704	+	97.4015i	0.464750	+	0.268324i
$364$		0			0
$365$	187.232	+	324.295i	0.512964	+	0.888480i
$366$		0			0
$367$	−10.2452	+	5.91506i	−0.0279160	+	0.0161173i	−0.513893	−	0.857854i	$-0.671797\pi$
$367$	−10.2452	+	5.91506i	−0.0279160	+	0.0161173i	0.485977	+	0.873972i	$0.338464\pi$
$368$		0			0
$369$	−195.646			−0.530207
$370$		0			0
$371$	367.873	−	212.392i	0.991572	−	0.572484i
$372$		0			0
$373$	309.726			0.830364			0.415182	−	0.909738i	$-0.363718\pi$
$373$	309.726			0.830364			0.415182	+	0.909738i	$0.363718\pi$
$374$		0			0
$375$	−724.888	−	418.514i	−1.93303	−	1.11604i
$376$		0			0
$377$	−178.196	+	308.645i	−0.472669	+	0.818688i
$378$		0			0
$379$			513.733i			1.35550i	0.735294	+	0.677748i	$0.237044\pi$
$379$			513.733i			1.35550i	−0.735294	+	0.677748i	$0.762956\pi$
$380$		0			0
$381$	316.212			0.829953
$382$		0			0
$383$	58.9458	+	34.0324i	0.153906	+	0.0888574i	0.574975	−	0.818171i	$-0.305012\pi$
$383$	58.9458	+	34.0324i	0.153906	+	0.0888574i	−0.421069	+	0.907028i	$0.638345\pi$
$384$		0			0
$385$	420.256	−	727.905i	1.09157	−	1.89066i
$386$		0			0
$387$			236.663i			0.611533i
$388$		0			0
$389$	375.720	+	650.766i	0.965862	+	1.67292i	0.707282	+	0.706932i	$0.249921\pi$
$389$	375.720	+	650.766i	0.965862	+	1.67292i	0.258580	+	0.965990i	$0.416745\pi$
$390$		0			0
$391$			458.664i			1.17305i
$392$		0			0
$393$	−32.2769	−	55.9053i	−0.0821296	−	0.142253i
$394$		0			0
$395$	−544.743	+	314.508i	−1.37910	+	0.796222i
$396$		0			0
$397$	214.820	−	372.079i	0.541108	−	0.937227i	−0.457732	−	0.889090i	$-0.651338\pi$
$397$	214.820	−	372.079i	0.541108	−	0.937227i	0.998841	−	0.0481372i	$-0.0153285\pi$
$398$		0			0
$399$	132.593	+	125.048i	0.332313	+	0.313402i
$400$		0			0
$401$	95.5950	−	165.575i	0.238391	−	0.412906i	−0.721861	−	0.692038i	$-0.756713\pi$
$401$	95.5950	−	165.575i	0.238391	−	0.412906i	0.960253	+	0.279132i	$0.0900465\pi$
$402$		0			0
$403$	−348.279	+	201.079i	−0.864217	+	0.498956i
$404$		0			0
$405$	−44.6962	−	77.4161i	−0.110361	−	0.191151i
$406$		0			0
$407$		−	421.389i		−	1.03535i
$408$		0			0
$409$	−79.2825	−	137.321i	−0.193845	−	0.335749i	0.752677	−	0.658390i	$-0.228762\pi$
$409$	−79.2825	−	137.321i	−0.193845	−	0.335749i	−0.946521	+	0.322642i	$0.895429\pi$
$410$		0			0
$411$		−	190.963i		−	0.464630i
$412$		0			0
$413$	93.1034	−	161.260i	0.225432	−	0.390460i
$414$		0			0
$415$	−216.636	−	125.075i	−0.522014	−	0.301385i
$416$		0			0
$417$	−354.582			−0.850315
$418$		0			0
$419$			274.458i			0.655031i	0.944846	+	0.327515i	$0.106211\pi$
$419$			274.458i			0.655031i	−0.944846	+	0.327515i	$0.893789\pi$
$420$		0			0
$421$	−250.513	+	433.901i	−0.595043	+	1.03064i	0.398498	+	0.917169i	$0.369532\pi$
$421$	−250.513	+	433.901i	−0.595043	+	1.03064i	−0.993541	+	0.113475i	$0.963802\pi$
$422$		0			0
$423$	−104.110	−	60.1079i	−0.246123	−	0.142099i
$424$		0			0
$425$	−1467.07			−3.45193
$426$		0			0
$427$	−369.519	+	213.342i	−0.865383	+	0.499629i
$428$		0			0
$429$	−440.392			−1.02655
$430$		0			0
$431$	−162.011	+	93.5372i	−0.375896	+	0.217024i	−0.676031	−	0.736873i	$-0.736302\pi$
$431$	−162.011	+	93.5372i	−0.375896	+	0.217024i	0.300135	+	0.953897i	$0.402968\pi$
$432$		0			0
$433$	−206.414	−	357.519i	−0.476706	−	0.825680i	0.522937	−	0.852371i	$-0.324836\pi$
$433$	−206.414	−	357.519i	−0.476706	−	0.825680i	−0.999644	+	0.0266915i	$0.991503\pi$
$434$		0			0
$435$	319.091	+	184.227i	0.733543	+	0.423511i
$436$		0			0
$437$	125.561	+	419.114i	0.287324	+	0.959070i
$438$		0			0
$439$	408.630	+	235.923i	0.930820	+	0.537409i	0.887071	−	0.461633i	$-0.152736\pi$
$439$	408.630	+	235.923i	0.930820	+	0.537409i	0.0437493	+	0.999043i	$0.486070\pi$
$440$		0			0
$441$	27.4921	+	47.6177i	0.0623403	+	0.107977i
$442$		0			0
$443$	−46.3555	+	26.7634i	−0.104640	+	0.0604139i	−0.551407	−	0.834237i	$-0.685909\pi$
$443$	−46.3555	+	26.7634i	−0.104640	+	0.0604139i	0.446767	+	0.894650i	$0.352575\pi$
$444$		0			0
$445$	−1011.27			−2.27253
$446$		0			0
$447$	77.0595	−	44.4903i	0.172393	−	0.0995309i
$448$		0			0
$449$	405.284			0.902638			0.451319	−	0.892363i	$-0.350954\pi$
$449$	405.284			0.902638			0.451319	+	0.892363i	$0.350954\pi$
$450$		0			0
$451$	862.971	+	498.236i	1.91346	+	1.10474i
$452$		0			0
$453$	−72.9906	+	126.423i	−0.161127	+	0.279081i
$454$		0			0
$455$			915.360i			2.01178i
$456$		0			0
$457$	−778.986			−1.70456			−0.852282	−	0.523082i	$-0.824782\pi$
$457$	−778.986			−1.70456			−0.852282	+	0.523082i	$0.824782\pi$
$458$		0			0
$459$	−89.6324	−	51.7493i	−0.195278	−	0.112744i
$460$		0			0
$461$	−215.224	+	372.779i	−0.466863	+	0.808631i	−0.999283	−	0.0378495i	$-0.987949\pi$
$461$	−215.224	+	372.779i	−0.466863	+	0.808631i	0.532420	+	0.846480i	$0.321283\pi$
$462$		0			0
$463$		−	406.216i		−	0.877357i	−0.898644	−	0.438678i	$-0.855447\pi$
$463$		−	406.216i		−	0.877357i	0.898644	−	0.438678i	$-0.144553\pi$
$464$		0			0
$465$	207.885	+	360.067i	0.447064	+	0.774337i
$466$		0			0
$467$		−	32.6869i		−	0.0699934i	−0.999387	−	0.0349967i	$-0.988858\pi$
$467$		−	32.6869i		−	0.0699934i	0.999387	−	0.0349967i	$-0.0111421\pi$
$468$		0			0
$469$	99.8035	+	172.865i	0.212801	+	0.368582i
$470$		0			0
$471$	−6.43447	+	3.71494i	−0.0136613	+	0.00788735i
$472$		0			0
$473$	602.691	−	1043.89i	1.27419	−	2.20696i
$474$		0			0
$475$	−1340.57	+	401.615i	−2.82224	+	0.845504i
$476$		0			0
$477$	−115.050	+	199.273i	−0.241196	+	0.417763i
$478$		0			0
$479$	84.8216	−	48.9718i	0.177081	−	0.102238i	−0.408840	−	0.912606i	$-0.634066\pi$
$479$	84.8216	−	48.9718i	0.177081	−	0.102238i	0.585920	+	0.810369i	$0.300733\pi$
$480$		0			0
$481$	229.457	+	397.431i	0.477041	+	0.826260i
$482$		0			0
$483$		−	220.889i		−	0.457326i
$484$		0			0
$485$	497.706	+	862.053i	1.02620	+	1.77743i
$486$		0			0
$487$		−	188.426i		−	0.386911i	−0.981109	−	0.193456i	$-0.938030\pi$
$487$		−	188.426i		−	0.386911i	0.981109	−	0.193456i	$-0.0619696\pi$
$488$		0			0
$489$	160.261	−	277.581i	0.327733	−	0.567650i
$490$		0			0
$491$	345.544	+	199.500i	0.703755	+	0.406313i	0.808744	−	0.588160i	$-0.200148\pi$
$491$	345.544	+	199.500i	0.703755	+	0.406313i	−0.104990	+	0.994473i	$0.533481\pi$
$492$		0			0
$493$	426.597			0.865309
$494$		0			0
$495$			455.297i			0.919791i
$496$		0			0
$497$	−223.175	+	386.550i	−0.449044	+	0.777767i
$498$		0			0
$499$	694.954	+	401.232i	1.39269	+	0.804072i	0.993613	−	0.112843i	$-0.0359958\pi$
$499$	694.954	+	401.232i	1.39269	+	0.804072i	0.399081	+	0.916916i	$0.369329\pi$
$500$		0			0
$501$	−396.589			−0.791594
$502$		0			0
$503$	556.294	−	321.176i	1.10595	−	0.638521i	0.168174	−	0.985757i	$-0.446213\pi$
$503$	556.294	−	321.176i	1.10595	−	0.638521i	0.937778	+	0.347236i	$0.112880\pi$
$504$		0			0
$505$	−664.272			−1.31539
$506$		0			0
$507$	161.854	−	93.4463i	0.319238	−	0.184312i
$508$		0			0
$509$	−12.4565	−	21.5754i	−0.0244726	−	0.0423877i	0.853530	−	0.521044i	$-0.174457\pi$
$509$	−12.4565	−	21.5754i	−0.0244726	−	0.0423877i	−0.878002	+	0.478656i	$0.841124\pi$
$510$		0			0
$511$	−180.823	−	104.398i	−0.353860	−	0.204301i
$512$		0			0
$513$	−96.0700	−	22.7499i	−0.187271	−	0.0443467i
$514$		0			0
$515$	−158.354	−	91.4255i	−0.307483	−	0.177525i
$516$		0			0
$517$	306.144	+	530.257i	0.592155	+	1.02564i
$518$		0			0
$519$	−309.733	+	178.824i	−0.596787	+	0.344555i
$520$		0			0
$521$	−256.306			−0.491950			−0.245975	−	0.969276i	$-0.579108\pi$
$521$	−256.306			−0.491950			−0.245975	+	0.969276i	$0.579108\pi$
$522$		0			0
$523$	−364.950	+	210.704i	−0.697801	+	0.402875i	−0.806528	−	0.591196i	$-0.798656\pi$
$523$	−364.950	+	210.704i	−0.697801	+	0.402875i	0.108727	+	0.994072i	$0.465323\pi$
$524$		0			0
$525$	706.528			1.34577
$526$		0			0
$527$	416.885	+	240.689i	0.791054	+	0.456715i
$528$		0			0
$529$	0.627088	−	1.08615i	0.00118542	−	0.00205321i
$530$		0			0
$531$			100.866i			0.189955i
$532$		0			0
$533$	−1085.21			−2.03604
$534$		0			0
$535$	−793.347	−	458.039i	−1.48289	−	0.856148i
$536$		0			0
$537$	286.768	−	496.696i	0.534018	−	0.924946i
$538$		0			0
$539$		−	280.048i		−	0.519569i
$540$		0			0
$541$	39.0926	+	67.7105i	0.0722600	+	0.125158i	0.899891	−	0.436114i	$-0.143646\pi$
$541$	39.0926	+	67.7105i	0.0722600	+	0.125158i	−0.827631	+	0.561272i	$0.810312\pi$
$542$		0			0
$543$		−	278.744i		−	0.513340i
$544$		0			0
$545$	−525.250	−	909.759i	−0.963761	−	1.66928i
$546$		0			0
$547$	731.151	−	422.130i	1.33666	−	0.771719i	0.350346	−	0.936620i	$-0.386064\pi$
$547$	731.151	−	422.130i	1.33666	−	0.771719i	0.986310	+	0.164902i	$0.0527308\pi$
$548$		0			0
$549$	115.565	−	200.164i	0.210501	−	0.364598i
$550$		0			0
$551$	389.812	−	116.782i	0.707463	−	0.211946i
$552$		0			0
$553$	175.365	−	303.742i	0.317116	−	0.549261i
$554$		0			0
$555$	410.882	−	237.223i	0.740328	−	0.427428i
$556$		0			0
$557$	−163.151	−	282.587i	−0.292911	−	0.507337i	0.681586	−	0.731738i	$-0.261291\pi$
$557$	−163.151	−	282.587i	−0.292911	−	0.507337i	−0.974497	+	0.224401i	$0.927957\pi$
$558$		0			0
$559$			1312.72i			2.34834i
$560$		0			0
$561$	263.571	+	456.519i	0.469824	+	0.813760i
$562$		0			0
$563$		−	1022.89i		−	1.81686i	−0.418042	−	0.908428i	$-0.637283\pi$
$563$		−	1022.89i		−	1.81686i	0.418042	−	0.908428i	$-0.362717\pi$
$564$		0			0
$565$	−443.144	+	767.548i	−0.784326	+	1.35849i
$566$		0			0
$567$	43.1662	+	24.9220i	0.0761309	+	0.0439542i
$568$		0			0
$569$	−135.217			−0.237639			−0.118819	−	0.992916i	$-0.537911\pi$
$569$	−135.217			−0.237639			−0.118819	+	0.992916i	$0.537911\pi$
$570$		0			0
$571$		−	69.7774i		−	0.122202i	−0.998132	−	0.0611010i	$-0.980539\pi$
$571$		−	69.7774i		−	0.122202i	0.998132	−	0.0611010i	$-0.0194612\pi$
$572$		0			0
$573$	108.821	−	188.483i	0.189914	−	0.328941i
$574$		0			0
$575$	1468.83	+	848.028i	2.55448	+	1.47483i
$576$		0			0
$577$	450.850			0.781369			0.390685	−	0.920525i	$-0.372238\pi$
$577$	450.850			0.781369			0.390685	+	0.920525i	$0.372238\pi$
$578$		0			0
$579$	−38.2177	+	22.0650i	−0.0660064	+	0.0381088i
$580$		0			0
$581$	139.480			0.240069
$582$		0			0
$583$	1014.95	−	585.979i	1.74090	−	1.00511i
$584$		0			0
$585$	−247.921	−	429.411i	−0.423796	−	0.734036i
$586$		0			0
$587$	380.682	+	219.787i	0.648521	+	0.374424i	0.787890	−	0.615817i	$-0.211174\pi$
$587$	380.682	+	219.787i	0.648521	+	0.374424i	−0.139368	+	0.990241i	$0.544507\pi$
$588$		0			0
$589$	446.827	+	105.811i	0.758620	+	0.179645i
$590$		0			0
$591$	454.747	+	262.548i	0.769453	+	0.444244i
$592$		0			0
$593$	−44.8581	−	77.6964i	−0.0756460	−	0.131023i	0.825721	−	0.564079i	$-0.190769\pi$
$593$	−44.8581	−	77.6964i	−0.0756460	−	0.131023i	−0.901367	+	0.433056i	$0.857435\pi$
$594$		0			0
$595$	948.881	−	547.837i	1.59476	−	0.920734i
$596$		0			0
$597$	8.41636			0.0140978
$598$		0			0
$599$	−212.320	+	122.583i	−0.354458	+	0.204646i	−0.666647	−	0.745374i	$-0.732271\pi$
$599$	−212.320	+	122.583i	−0.354458	+	0.204646i	0.312189	+	0.950020i	$0.398938\pi$
$600$		0			0
$601$	446.406			0.742773			0.371386	−	0.928478i	$-0.378883\pi$
$601$	446.406			0.742773			0.371386	+	0.928478i	$0.378883\pi$
$602$		0			0
$603$	−93.6391	−	54.0625i	−0.155289	−	0.0896560i
$604$		0			0
$605$	558.551	−	967.439i	0.923225	−	1.59907i
$606$		0			0
$607$		−	695.984i		−	1.14660i	−0.819347	−	0.573298i	$-0.805664\pi$
$607$		−	695.984i		−	1.14660i	0.819347	−	0.573298i	$-0.194336\pi$
$608$		0			0
$609$	−205.446			−0.337349
$610$		0			0
$611$	−577.477	−	333.406i	−0.945134	−	0.545673i
$612$		0			0
$613$	−122.742	+	212.596i	−0.200232	+	0.346812i	−0.948603	−	0.316468i	$-0.897503\pi$
$613$	−122.742	+	212.596i	−0.200232	+	0.346812i	0.748371	+	0.663280i	$0.230836\pi$
$614$		0			0
$615$			1121.94i			1.82429i
$616$		0			0
$617$	152.250	+	263.704i	0.246758	+	0.427398i	0.962624	−	0.270840i	$-0.0873013\pi$
$617$	152.250	+	263.704i	0.246758	+	0.427398i	−0.715866	+	0.698237i	$0.753968\pi$
$618$		0			0
$619$		−	10.8870i		−	0.0175880i	−0.999961	−	0.00879400i	$-0.997201\pi$
$619$		−	10.8870i		−	0.0175880i	0.999961	−	0.00879400i	$-0.00279925\pi$
$620$		0			0
$621$	59.8265	+	103.623i	0.0963390	+	0.166864i
$622$		0			0
$623$	488.329	−	281.937i	0.783834	−	0.452547i
$624$		0			0
$625$	−1479.30	+	2562.22i	−2.36688	+	4.09956i
$626$		0			0
$627$	365.817	+	345.000i	0.583441	+	0.550240i
$628$		0			0
$629$	274.657	−	475.719i	0.436656	−	0.756311i
$630$		0			0
$631$	429.951	−	248.232i	0.681381	−	0.393395i	−0.118994	−	0.992895i	$-0.537967\pi$
$631$	429.951	−	248.232i	0.681381	−	0.393395i	0.800375	+	0.599500i	$0.204634\pi$
$632$		0			0
$633$	7.20931	+	12.4869i	0.0113891	+	0.0197265i
$634$		0			0
$635$		−	1813.33i		−	2.85563i
$636$		0			0
$637$	152.493	+	264.126i	0.239393	+	0.414640i
$638$		0			0
$639$		−	241.783i		−	0.378377i
$640$		0			0
$641$	−25.7155	+	44.5405i	−0.0401177	+	0.0694859i	−0.885387	−	0.464855i	$-0.846107\pi$
$641$	−25.7155	+	44.5405i	−0.0401177	+	0.0694859i	0.845269	+	0.534340i	$0.179440\pi$
$642$		0			0
$643$	−105.889	−	61.1353i	−0.164680	−	0.0950782i	0.415395	−	0.909641i	$-0.363643\pi$
$643$	−105.889	−	61.1353i	−0.164680	−	0.0950782i	−0.580075	+	0.814563i	$0.696977\pi$
$644$		0			0
$645$	1357.15			2.10411
$646$		0			0
$647$			96.1355i			0.148587i	0.997236	+	0.0742933i	$0.0236701\pi$
$647$			96.1355i			0.148587i	−0.997236	+	0.0742933i	$0.976330\pi$
$648$		0			0
$649$	256.868	−	444.908i	0.395790	−	0.685529i
$650$		0			0
$651$	−200.768	−	115.914i	−0.308400	−	0.178055i
$652$		0			0
$653$	−390.987			−0.598755			−0.299378	−	0.954135i	$-0.596779\pi$
$653$	−390.987			−0.598755			−0.299378	+	0.954135i	$0.596779\pi$
$654$		0			0
$655$	−320.590	+	185.093i	−0.489451	+	0.282585i
$656$		0			0
$657$	113.103			0.172150
$658$		0			0
$659$	−568.111	+	327.999i	−0.862080	+	0.497722i	−0.864708	−	0.502274i	$-0.832497\pi$
$659$	−568.111	+	327.999i	−0.862080	+	0.497722i	0.00262796	+	0.999997i	$0.499163\pi$
$660$		0			0
$661$	337.465	+	584.507i	0.510537	+	0.884277i	0.999925	+	0.0122104i	$0.00388680\pi$
$661$	337.465	+	584.507i	0.510537	+	0.884277i	−0.489388	+	0.872066i	$0.662780\pi$
$662$		0			0
$663$	−497.173	−	287.043i	−0.749883	−	0.432945i
$664$		0			0
$665$	717.088	−	760.356i	1.07833	−	1.14339i
$666$		0			0
$667$	−427.108	−	246.591i	−0.640342	−	0.369702i
$668$		0			0
$669$	−237.337	−	411.079i	−0.354763	−	0.614468i
$670$		0			0
$671$	−1019.48	+	588.600i	−1.51935	+	0.877198i
$672$		0			0
$673$	−421.053			−0.625635			−0.312818	−	0.949813i	$-0.601273\pi$
$673$	−421.053			−0.625635			−0.312818	+	0.949813i	$0.601273\pi$
$674$		0			0
$675$	−331.444	+	191.360i	−0.491029	+	0.283496i
$676$		0			0
$677$	−579.107			−0.855401			−0.427701	−	0.903920i	$-0.640676\pi$
$677$	−579.107			−0.855401			−0.427701	+	0.903920i	$0.640676\pi$
$678$		0			0
$679$	−480.669	−	277.515i	−0.707908	−	0.408711i
$680$		0			0
$681$	−278.081	+	481.651i	−0.408343	+	0.707270i
$682$		0			0
$683$			616.151i			0.902125i	0.892492	+	0.451062i	$0.148955\pi$
$683$			616.151i			0.902125i	−0.892492	+	0.451062i	$0.851045\pi$
$684$		0			0
$685$	−1095.08			−1.59866
$686$		0			0
$687$	103.693	+	59.8671i	0.150936	+	0.0871428i
$688$		0			0
$689$	−638.161	+	1105.33i	−0.926213	+	1.60425i
$690$		0			0
$691$		−	826.446i		−	1.19601i	−0.801491	−	0.598007i	$-0.795960\pi$
$691$		−	826.446i		−	1.19601i	0.801491	−	0.598007i	$-0.204040\pi$
$692$		0			0
$693$	−126.934	−	219.856i	−0.183166	−	0.317252i
$694$		0			0
$695$			2033.36i			2.92569i
$696$		0			0
$697$	649.491	+	1124.95i	0.931837	+	1.61399i
$698$		0			0
$699$	−69.5939	+	40.1800i	−0.0995620	+	0.0574822i
$700$		0			0
$701$	−300.208	+	519.975i	−0.428256	+	0.741762i	−0.996718	−	0.0809476i	$-0.974205\pi$
$701$	−300.208	+	519.975i	−0.428256	+	0.741762i	0.568462	+	0.822710i	$0.307539\pi$
$702$		0			0
$703$	120.744	−	509.887i	0.171755	−	0.725301i
$704$		0			0
$705$	−344.690	+	597.021i	−0.488923	+	0.846839i
$706$		0			0
$707$	320.766	−	185.195i	0.453701	−	0.261944i
$708$		0			0
$709$	278.235	+	481.917i	0.392433	+	0.679714i	0.992770	−	0.120033i	$-0.0383001\pi$
$709$	278.235	+	481.917i	0.392433	+	0.679714i	−0.600337	+	0.799747i	$0.704967\pi$
$710$		0			0
$711$			189.987i			0.267211i
$712$		0			0
$713$	−278.257	−	481.955i	−0.390262	−	0.675953i
$714$		0			0
$715$			2525.44i			3.53208i
$716$		0			0
$717$	−92.5346	+	160.275i	−0.129058	+	0.223535i
$718$		0			0
$719$	645.885	+	372.902i	0.898310	+	0.518639i	0.876651	−	0.481126i	$-0.159772\pi$
$719$	645.885	+	372.902i	0.898310	+	0.518639i	0.0216584	+	0.999765i	$0.493105\pi$
$720$		0			0
$721$	101.955			0.141408
$722$		0			0
$723$		−	425.366i		−	0.588335i
$724$		0			0
$725$	788.740	−	1366.14i	1.08792	−	1.88433i
$726$		0			0
$727$	−1195.48	−	690.212i	−1.64441	−	0.949398i	−0.979241	−	0.202702i	$-0.935028\pi$
$727$	−1195.48	−	690.212i	−1.64441	−	0.949398i	−0.665165	−	0.746696i	$-0.731639\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	1360.79	−	785.655i	1.86155	−	1.07477i
$732$		0			0
$733$	124.235			0.169489			0.0847443	−	0.996403i	$-0.472993\pi$
$733$	124.235			0.169489			0.0847443	+	0.996403i	$0.472993\pi$
$734$		0			0
$735$	273.065	−	157.654i	0.371517	−	0.214495i
$736$		0			0
$737$	275.353	+	476.926i	0.373614	+	0.647118i
$738$		0			0
$739$	388.623	+	224.372i	0.525878	+	0.303616i	0.739336	−	0.673337i	$-0.235140\pi$
$739$	388.623	+	224.372i	0.525878	+	0.303616i	−0.213459	+	0.976952i	$0.568473\pi$
$740$		0			0
$741$	−532.881	−	126.189i	−0.719137	−	0.170295i
$742$		0			0
$743$	520.651	+	300.598i	0.700741	+	0.404573i	0.807623	−	0.589699i	$-0.200753\pi$
$743$	520.651	+	300.598i	0.700741	+	0.404573i	−0.106882	+	0.994272i	$0.534087\pi$
$744$		0			0
$745$	−255.131	−	441.900i	−0.342457	−	0.593154i
$746$		0			0
$747$	−65.4325	+	37.7775i	−0.0875938	+	0.0505723i
$748$		0			0
$749$	510.793			0.681967
$750$		0			0
$751$	−1032.77	+	596.268i	−1.37519	+	0.793966i	−0.991576	−	0.129528i	$-0.958654\pi$
$751$	−1032.77	+	596.268i	−1.37519	+	0.793966i	−0.383614	+	0.923494i	$0.625321\pi$
$752$		0			0
$753$	−5.17647			−0.00687446
$754$		0			0
$755$	724.979	+	418.567i	0.960237	+	0.554393i
$756$		0			0
$757$	404.057	−	699.847i	0.533761	−	0.924501i	−0.465461	−	0.885068i	$-0.654112\pi$
$757$	404.057	−	699.847i	0.533761	−	0.924501i	0.999222	−	0.0394329i	$-0.0125551\pi$
$758$		0			0
$759$		−	609.422i		−	0.802927i
$760$		0			0
$761$	1173.69			1.54229			0.771147	−	0.636657i	$-0.219683\pi$
$761$	1173.69			1.54229			0.771147	+	0.636657i	$0.219683\pi$
$762$		0			0
$763$	507.270	+	292.872i	0.664836	+	0.383843i
$764$		0			0
$765$	−296.758	+	513.999i	−0.387918	+	0.671894i
$766$		0			0
$767$			559.485i			0.729446i
$768$		0			0
$769$	−15.1714	−	26.2777i	−0.0197288	−	0.0341713i	0.855992	−	0.516988i	$-0.172947\pi$
$769$	−15.1714	−	26.2777i	−0.0197288	−	0.0341713i	−0.875721	+	0.482817i	$0.839614\pi$
$770$		0			0
$771$		−	531.752i		−	0.689691i
$772$		0			0
$773$	−238.887	−	413.765i	−0.309039	−	0.535272i	0.669113	−	0.743160i	$-0.266674\pi$
$773$	−238.887	−	413.765i	−0.309039	−	0.535272i	−0.978152	+	0.207889i	$0.933341\pi$
$774$		0			0
$775$	1541.57	−	890.024i	1.98912	−	1.14842i
$776$		0			0
$777$	−132.272	+	229.102i	−0.170235	+	0.294855i
$778$		0			0
$779$	901.444	+	850.147i	1.15718	+	1.09133i
$780$		0			0
$781$	−615.729	+	1066.47i	−0.788385	+	1.36552i
$782$		0			0
$783$	96.3780	−	55.6439i	0.123088	−	0.0710650i
$784$		0			0
$785$	21.3034	+	36.8986i	0.0271381	+	0.0470046i
$786$		0			0
$787$			1073.96i			1.36462i	0.731062	+	0.682311i	$0.239025\pi$
$787$			1073.96i			1.36462i	−0.731062	+	0.682311i	$0.760975\pi$
$788$		0			0
$789$	183.735	+	318.238i	0.232871	+	0.403344i
$790$		0			0
$791$		−	494.183i		−	0.624757i
$792$		0			0
$793$	641.015	−	1110.27i	0.808342	−	1.40009i
$794$		0			0
$795$	1142.74	+	659.759i	1.43740	+	0.829886i
$796$		0			0
$797$	−1410.02			−1.76916			−0.884579	−	0.466390i	$-0.845554\pi$
$797$	−1410.02			−1.76916			−0.884579	+	0.466390i	$0.845554\pi$
$798$		0			0
$799$			798.166i			0.998956i
$800$		0			0
$801$	−152.722	+	264.523i	−0.190664	+	0.330241i
$802$		0			0
$803$	−498.882	−	288.029i	−0.621272	−	0.358692i
$804$		0			0
$805$	−1266.69			−1.57353
$806$		0			0
$807$	−369.980	+	213.608i	−0.458464	+	0.264694i
$808$		0			0
$809$	−615.804			−0.761191			−0.380596	−	0.924742i	$-0.624281\pi$
$809$	−615.804			−0.761191			−0.380596	+	0.924742i	$0.624281\pi$
$810$		0			0
$811$	324.928	−	187.597i	0.400651	−	0.231316i	−0.286114	−	0.958196i	$-0.592364\pi$
$811$	324.928	−	187.597i	0.400651	−	0.231316i	0.686765	+	0.726880i	$0.259030\pi$
$812$		0			0
$813$	277.954	+	481.431i	0.341887	+	0.592165i
$814$		0			0
$815$	−1591.79	−	919.023i	−1.95312	−	1.12764i
$816$		0			0
$817$	1028.38	−	1090.43i	1.25873	−	1.33468i
$818$		0			0
$819$	239.434	+	138.237i	0.292349	+	0.168788i
$820$		0			0
$821$	−645.099	−	1117.34i	−0.785747	−	1.36095i	−0.928552	−	0.371203i	$-0.878945\pi$
$821$	−645.099	−	1117.34i	−0.785747	−	1.36095i	0.142804	−	0.989751i	$-0.454388\pi$
$822$		0			0
$823$	1072.46	−	619.184i	1.30311	−	0.752350i	0.322172	−	0.946681i	$-0.395587\pi$
$823$	1072.46	−	619.184i	1.30311	−	0.752350i	0.980936	+	0.194332i	$0.0622538\pi$
$824$		0			0
$825$	1949.28			2.36276
$826$		0			0
$827$	−796.943	+	460.115i	−0.963655	+	0.556366i	−0.897296	−	0.441429i	$-0.854472\pi$
$827$	−796.943	+	460.115i	−0.963655	+	0.556366i	−0.0663588	+	0.997796i	$0.521138\pi$
$828$		0			0
$829$	−993.068			−1.19791			−0.598955	−	0.800782i	$-0.704417\pi$
$829$	−993.068			−1.19791			−0.598955	+	0.800782i	$0.704417\pi$
$830$		0			0
$831$	−265.056	−	153.030i	−0.318961	−	0.184152i
$832$		0			0
$833$	182.532	−	316.155i	0.219126	−	0.379538i
$834$		0			0
$835$			2274.25i			2.72365i
$836$		0			0
$837$	125.579			0.150034
$838$		0			0
$839$	958.296	+	553.272i	1.14219	+	0.659443i	0.946972	−	0.321317i	$-0.104126\pi$
$839$	958.296	+	553.272i	1.14219	+	0.659443i	0.195217	+	0.980760i	$0.437459\pi$
$840$		0			0
$841$	191.149	−	331.080i	0.227288	−	0.393674i
$842$		0			0
$843$			324.446i			0.384871i
$844$		0			0
$845$	−535.870	−	928.154i	−0.634166	−	1.09841i
$846$		0			0
$847$			622.882i			0.735398i
$848$		0			0
$849$	−83.5959	−	144.792i	−0.0984640	−	0.170545i
$850$		0			0
$851$	−549.972	+	317.526i	−0.646265	+	0.373121i
$852$		0			0
$853$	−342.429	+	593.104i	−0.401441	+	0.695316i	−0.993900	−	0.110285i	$-0.964824\pi$
$853$	−342.429	+	593.104i	−0.401441	+	0.695316i	0.592459	+	0.805600i	$0.298157\pi$
$854$		0			0
$855$	−130.460	+	550.916i	−0.152584	+	0.644346i
$856$		0			0
$857$	216.772	−	375.461i	0.252943	−	0.438110i	−0.711392	−	0.702796i	$-0.751935\pi$
$857$	216.772	−	375.461i	0.252943	−	0.438110i	0.964335	+	0.264685i	$0.0852681\pi$
$858$		0			0
$859$	−999.482	+	577.051i	−1.16354	+	0.671771i	−0.952150	−	0.305631i	$-0.901133\pi$
$859$	−999.482	+	577.051i	−1.16354	+	0.671771i	−0.211391	+	0.977402i	$0.567799\pi$
$860$		0			0
$861$	−312.789	−	541.766i	−0.363286	−	0.629229i
$862$		0			0
$863$			327.184i			0.379124i	0.981869	+	0.189562i	$0.0607069\pi$
$863$			327.184i			0.379124i	−0.981869	+	0.189562i	$0.939293\pi$
$864$		0			0
$865$	1025.47	+	1776.17i	1.18552	+	2.05337i
$866$		0			0
$867$			186.610i			0.215236i
$868$		0			0
$869$	483.825	−	838.009i	0.556760	−	0.964337i
$870$		0			0
$871$	−519.397	−	299.874i	−0.596322	−	0.344287i
$872$		0			0
$873$	300.654			0.344391
$874$		0			0
$875$		−	2676.39i		−	3.05874i
$876$		0			0
$877$	557.327	−	965.318i	0.635492	−	1.10070i	−0.350919	−	0.936406i	$-0.614131\pi$
$877$	557.327	−	965.318i	0.635492	−	1.10070i	0.986411	−	0.164299i	$-0.0525361\pi$
$878$		0			0
$879$	78.5966	+	45.3778i	0.0894160	+	0.0516243i
$880$		0			0
$881$	−966.073			−1.09656			−0.548282	−	0.836294i	$-0.684718\pi$
$881$	−966.073			−1.09656			−0.548282	+	0.836294i	$0.684718\pi$
$882$		0			0
$883$	−1063.98	+	614.290i	−1.20496	+	0.695685i	−0.961655	−	0.274264i	$-0.911566\pi$
$883$	−1063.98	+	614.290i	−1.20496	+	0.695685i	−0.243308	+	0.969949i	$0.578233\pi$
$884$		0			0
$885$	578.420			0.653582
$886$		0			0
$887$	523.920	−	302.486i	0.590666	−	0.341021i	−0.174695	−	0.984623i	$-0.555894\pi$
$887$	523.920	−	302.486i	0.590666	−	0.341021i	0.765361	+	0.643602i	$0.222561\pi$
$888$		0			0
$889$	505.544	+	875.627i	0.568665	+	0.984957i
$890$		0			0
$891$	119.094	+	68.7587i	0.133663	+	0.0771703i
$892$		0			0
$893$	218.500	+	729.341i	0.244681	+	0.816731i
$894$		0			0
$895$	−2848.31	−	1644.48i	−3.18247	−	1.83740i
$896$		0			0
$897$	331.846	+	574.774i	0.369951	+	0.640773i
$898$		0			0
$899$	−448.260	+	258.803i	−0.498620	+	0.287879i
$900$		0			0
$901$	1527.74			1.69560
$902$		0			0
$903$	−655.347	+	378.365i	−0.725744	+	0.419009i
$904$		0			0
$905$	−1598.46			−1.76626
$906$		0			0
$907$	1385.70	+	800.033i	1.52778	+	0.882065i	0.999455	+	0.0330234i	$0.0105136\pi$
$907$	1385.70	+	800.033i	1.52778	+	0.882065i	0.528326	+	0.849041i	$0.322820\pi$
$908$		0			0
$909$	−100.318	+	173.756i	−0.110361	+	0.191151i
$910$		0			0
$911$			95.8088i			0.105169i	0.998616	+	0.0525844i	$0.0167459\pi$
$911$			95.8088i			0.105169i	−0.998616	+	0.0525844i	$0.983254\pi$
$912$		0			0
$913$	384.820			0.421489
$914$		0			0
$915$	−1147.85	−	662.710i	−1.25448	−	0.724274i
$916$		0			0
$917$	103.205	−	178.757i	0.112547	−	0.194937i
$918$		0			0
$919$			120.294i			0.130897i	0.997856	+	0.0654484i	$0.0208478\pi$
$919$			120.294i			0.130897i	−0.997856	+	0.0654484i	$0.979152\pi$
$920$		0			0
$921$	130.391	+	225.844i	0.141576	+	0.245217i
$922$		0			0
$923$		−	1341.12i		−	1.45300i
$924$		0			0
$925$	−1015.63	−	1759.12i	−1.09798	−	1.90176i
$926$		0			0
$927$	−47.8290	+	27.6141i	−0.0515955	+	0.0297887i
$928$		0			0
$929$	−843.606	+	1461.17i	−0.908080	+	1.57284i	−0.0913503	+	0.995819i	$0.529118\pi$
$929$	−843.606	+	1461.17i	−0.908080	+	1.57284i	−0.816729	+	0.577021i	$0.804215\pi$
$930$		0			0
$931$	80.2442	−	338.862i	0.0861914	−	0.363976i
$932$		0			0
$933$	−232.204	+	402.189i	−0.248879	+	0.431071i
$934$		0			0
$935$	2617.92	−	1511.46i	2.79991	−	1.61653i
$936$		0			0
$937$	−10.8515	−	18.7954i	−0.0115811	−	0.0200591i	0.860177	−	0.509996i	$-0.170353\pi$
$937$	−10.8515	−	18.7954i	−0.0115811	−	0.0200591i	−0.871758	+	0.489937i	$0.837020\pi$
$938$		0			0
$939$		−	781.502i		−	0.832271i
$940$		0			0
$941$	−176.538	−	305.773i	−0.187607	−	0.324945i	0.756845	−	0.653595i	$-0.226740\pi$
$941$	−176.538	−	305.773i	−0.187607	−	0.324945i	−0.944452	+	0.328650i	$0.893406\pi$
$942$		0			0
$943$		−	1501.73i		−	1.59250i
$944$		0			0
$945$	142.916	−	247.538i	0.151234	−	0.261945i
$946$		0			0
$947$	113.914	+	65.7683i	0.120289	+	0.0694491i	0.558937	−	0.829210i	$-0.311209\pi$
$947$	113.914	+	65.7683i	0.120289	+	0.0694491i	−0.438648	+	0.898659i	$0.644543\pi$
$948$		0			0
$949$	627.358			0.661072
$950$		0			0
$951$			133.942i			0.140843i
$952$		0			0
$953$	−499.790	+	865.662i	−0.524439	+	0.908355i	0.475156	+	0.879901i	$0.342392\pi$
$953$	−499.790	+	865.662i	−0.524439	+	0.908355i	−0.999595	+	0.0284532i	$0.990942\pi$
$954$		0			0
$955$	−1080.86	−	624.036i	−1.13179	−	0.653441i
$956$		0			0
$957$	−566.815			−0.592283
$958$		0			0
$959$	528.798	−	305.301i	0.551405	−	0.318354i
$960$		0			0
$961$	376.927			0.392224
$962$		0			0
$963$	−239.622	+	138.346i	−0.248828	+	0.143661i
$964$		0			0
$965$	126.532	+	219.160i	0.131122	+	0.227109i
$966$		0			0
$967$	−1231.03	−	710.735i	−1.27304	−	0.734990i	−0.297481	−	0.954728i	$-0.596146\pi$
$967$	−1231.03	−	710.735i	−1.27304	−	0.734990i	−0.975559	+	0.219738i	$0.929480\pi$
$968$		0			0
$969$	188.115	+	627.918i	0.194134	+	0.648006i
$970$		0			0
$971$	−1495.57	−	863.467i	−1.54023	−	0.889255i	−0.998823	−	0.0484973i	$-0.984557\pi$
$971$	−1495.57	−	863.467i	−1.54023	−	0.889255i	−0.541412	−	0.840758i	$-0.682110\pi$
$972$		0			0
$973$	−566.887	−	981.876i	−0.582617	−	1.00912i
$974$		0			0
$975$	−1838.45	+	1061.43i	−1.88559	+	1.08865i
$976$		0			0
$977$	1678.16			1.71767			0.858833	−	0.512255i	$-0.171190\pi$
$977$	1678.16			1.71767			0.858833	+	0.512255i	$0.171190\pi$
$978$		0			0
$979$	1347.28	−	777.850i	1.37618	−	0.794536i
$980$		0			0
$981$	−317.292			−0.323437
$982$		0			0
$983$	−985.110	−	568.754i	−1.00215	−	0.578590i	−0.0932640	−	0.995641i	$-0.529730\pi$
$983$	−985.110	−	568.754i	−1.00215	−	0.578590i	−0.908883	+	0.417052i	$0.863063\pi$
$984$		0			0
$985$	1505.59	−	2607.76i	1.52852	−	2.64747i
$986$		0			0
$987$		−	384.390i		−	0.389453i
$988$		0			0
$989$	−1816.57			−1.83677
$990$		0			0
$991$	565.674	+	326.592i	0.570811	+	0.329558i	0.757473	−	0.652866i	$-0.226434\pi$
$991$	565.674	+	326.592i	0.570811	+	0.329558i	−0.186662	+	0.982424i	$0.559767\pi$
$992$		0			0
$993$	−73.4788	+	127.269i	−0.0739968	+	0.128166i
$994$		0			0
$995$		−	48.2638i		−	0.0485063i
$996$		0			0
$997$	−14.0882	−	24.4015i	−0.0141306	−	0.0244749i	0.858874	−	0.512188i	$-0.171165\pi$
$997$	−14.0882	−	24.4015i	−0.0141306	−	0.0244749i	−0.873004	+	0.487713i	$0.837831\pi$
$998$		0			0
$999$		−	143.301i		−	0.143445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.z.e.847.1	yes	16
4.3	odd	2		912.3.z.f.847.1	yes	16
19.7	even	3		912.3.z.f.463.1	yes	16
76.7	odd	6	inner	912.3.z.e.463.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.3.z.e.463.1	✓	16	76.7	odd	6	inner
912.3.z.e.847.1	yes	16	1.1	even	1	trivial
912.3.z.f.463.1	yes	16	19.7	even	3
912.3.z.f.847.1	yes	16	4.3	odd	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	912.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-4.96624 + 8.60179i) q^{5} -5.53823i q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-4.96624 + 8.60179i) q^{5} -5.53823i q^{7} +(1.50000 + 2.59808i) q^{9} -15.2797i q^{11} +(8.32019 + 14.4110i) q^{13} +(14.8987 - 8.60179i) q^{15} +(9.95916 - 17.2498i) q^{17} +(4.37821 - 18.4887i) q^{19} +(-4.79624 + 8.30734i) q^{21} +(-19.9422 + 11.5136i) q^{23} +(-36.8272 - 63.7865i) q^{25} -5.19615i q^{27} +(10.7087 + 18.5480i) q^{29} +24.1676i q^{31} +(-13.2326 + 22.9196i) q^{33} +(47.6386 + 27.5042i) q^{35} +27.5783 q^{37} -28.8220i q^{39} +(-32.6077 + 56.4782i) q^{41} +(68.3188 + 39.4439i) q^{43} -29.7975 q^{45} +(-34.7033 + 20.0360i) q^{47} +18.3281 q^{49} +(-29.8775 + 17.2498i) q^{51} +(38.3501 + 66.4244i) q^{53} +(131.433 + 75.8828i) q^{55} +(-22.5790 + 23.9414i) q^{57} +(29.1176 + 16.8111i) q^{59} +(-38.5217 - 66.7215i) q^{61} +(14.3887 - 8.30734i) q^{63} -165.280 q^{65} +(-31.2130 + 18.0208i) q^{67} +39.8844 q^{69} +(-69.7967 - 40.2972i) q^{71} +(18.8505 - 32.6499i) q^{73} +127.573i q^{75} -84.6225 q^{77} +(54.8446 + 31.6645i) q^{79} +(-4.50000 + 7.79423i) q^{81} +25.1850i q^{83} +(98.9192 + 171.333i) q^{85} -37.0959i q^{87} +(50.9074 + 88.1742i) q^{89} +(79.8114 - 46.0791i) q^{91} +(20.9298 - 36.2514i) q^{93} +(137.292 + 129.480i) q^{95} +(50.1089 - 86.7912i) q^{97} +(39.6979 - 22.9196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{3} + 2 q^{5} + 24 q^{9}+O(q^{10}) \) 16 * q - 24 * q^3 + 2 * q^5 + 24 * q^9	\( 16 q - 24 q^{3} + 2 q^{5} + 24 q^{9} - 8 q^{13} - 6 q^{15} + 8 q^{17} - 12 q^{19} + 6 q^{21} + 6 q^{23} - 120 q^{25} + 24 q^{29} - 6 q^{33} + 18 q^{35} + 136 q^{37} - 68 q^{41} + 114 q^{43} + 12 q^{45} - 132 q^{47} - 264 q^{49} - 24 q^{51} + 94 q^{53} + 180 q^{55} + 6 q^{57} + 114 q^{59} + 44 q^{61} - 18 q^{63} - 412 q^{65} + 30 q^{67} - 12 q^{69} - 12 q^{71} + 104 q^{73} + 20 q^{77} - 66 q^{79} - 72 q^{81} + 140 q^{85} + 66 q^{89} + 102 q^{91} + 6 q^{93} + 90 q^{95} + 240 q^{97} + 18 q^{99}+O(q^{100}) \) 16 * q - 24 * q^3 + 2 * q^5 + 24 * q^9 - 8 * q^13 - 6 * q^15 + 8 * q^17 - 12 * q^19 + 6 * q^21 + 6 * q^23 - 120 * q^25 + 24 * q^29 - 6 * q^33 + 18 * q^35 + 136 * q^37 - 68 * q^41 + 114 * q^43 + 12 * q^45 - 132 * q^47 - 264 * q^49 - 24 * q^51 + 94 * q^53 + 180 * q^55 + 6 * q^57 + 114 * q^59 + 44 * q^61 - 18 * q^63 - 412 * q^65 + 30 * q^67 - 12 * q^69 - 12 * q^71 + 104 * q^73 + 20 * q^77 - 66 * q^79 - 72 * q^81 + 140 * q^85 + 66 * q^89 + 102 * q^91 + 6 * q^93 + 90 * q^95 + 240 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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