LMFDB - Embedded newform 387.3.j.f.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,3,Mod(37,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("387.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	387.j (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:	$10.5449862307$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	387.37
Dual form			387.3.j.f.136.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.98399i q^{2} -11.8722 q^{4} +(-4.48413 - 2.58892i) q^{5} +(-4.28862 + 2.47604i) q^{7} +31.3628i q^{8} +O(q^{10})$	\(q-3.98399i q^{2} -11.8722 q^{4} +(-4.48413 - 2.58892i) q^{5} +(-4.28862 + 2.47604i) q^{7} +31.3628i q^{8} +(-10.3142 + 17.8648i) q^{10} +12.2169 q^{11} +(-3.29424 - 5.70580i) q^{13} +(9.86452 + 17.0858i) q^{14} +77.4603 q^{16} +(4.47754 + 7.75533i) q^{17} +(-19.2431 - 11.1100i) q^{19} +(53.2365 + 30.7361i) q^{20} -48.6722i q^{22} +(-1.43160 + 2.47960i) q^{23} +(0.904965 + 1.56745i) q^{25} +(-22.7319 + 13.1242i) q^{26} +(50.9154 - 29.3960i) q^{28} +(-25.7572 + 14.8709i) q^{29} +(-22.4879 + 38.9502i) q^{31} -183.150i q^{32} +(30.8972 - 17.8385i) q^{34} +25.6410 q^{35} +(30.8831 + 17.8303i) q^{37} +(-44.2621 + 76.6643i) q^{38} +(81.1956 - 140.635i) q^{40} +73.5446 q^{41} +(42.8615 - 3.44802i) q^{43} -145.042 q^{44} +(9.87869 + 5.70347i) q^{46} +22.4754 q^{47} +(-12.2385 + 21.1977i) q^{49} +(6.24469 - 3.60537i) q^{50} +(39.1099 + 67.7404i) q^{52} +(-45.1133 + 78.1386i) q^{53} +(-54.7824 - 31.6286i) q^{55} +(-77.6555 - 134.503i) q^{56} +(59.2456 + 102.616i) q^{58} +78.3888 q^{59} +(-37.9469 + 21.9087i) q^{61} +(155.177 + 89.5917i) q^{62} -419.828 q^{64} +34.1141i q^{65} +(-59.8966 + 103.744i) q^{67} +(-53.1582 - 92.0728i) q^{68} -102.154i q^{70} +(-37.1638 + 21.4565i) q^{71} +(29.4029 - 16.9758i) q^{73} +(71.0360 - 123.038i) q^{74} +(228.458 + 131.900i) q^{76} +(-52.3939 + 30.2496i) q^{77} +(-42.8246 - 74.1745i) q^{79} +(-347.342 - 200.538i) q^{80} -293.001i q^{82} +(23.3608 - 40.4621i) q^{83} -46.3679i q^{85} +(-13.7369 - 170.760i) q^{86} +383.158i q^{88} +(-12.0185 - 6.93889i) q^{89} +(28.2555 + 16.3133i) q^{91} +(16.9962 - 29.4383i) q^{92} -89.5419i q^{94} +(57.5257 + 99.6374i) q^{95} -101.805 q^{97} +(84.4513 + 48.7580i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 84 q^{4} - 30 q^{7}+O(q^{10}) $ 28 * q - 84 * q^4 - 30 * q^7	$ 28 q - 84 q^{4} - 30 q^{7} + 4 q^{10} - 34 q^{13} + 164 q^{16} - 78 q^{19} + 112 q^{25} + 342 q^{28} - 74 q^{31} + 192 q^{34} - 222 q^{37} + 104 q^{40} + 104 q^{43} + 150 q^{46} + 112 q^{49} - 64 q^{52} - 450 q^{55} + 346 q^{58} - 198 q^{61} - 1264 q^{64} - 26 q^{67} + 342 q^{73} + 282 q^{76} - 48 q^{79} + 684 q^{91} - 480 q^{97}+O(q^{100}) $ 28 * q - 84 * q^4 - 30 * q^7 + 4 * q^10 - 34 * q^13 + 164 * q^16 - 78 * q^19 + 112 * q^25 + 342 * q^28 - 74 * q^31 + 192 * q^34 - 222 * q^37 + 104 * q^40 + 104 * q^43 + 150 * q^46 + 112 * q^49 - 64 * q^52 - 450 * q^55 + 346 * q^58 - 198 * q^61 - 1264 * q^64 - 26 * q^67 + 342 * q^73 + 282 * q^76 - 48 * q^79 + 684 * q^91 - 480 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$		−	3.98399i		−	1.99200i	−0.0893727	−	0.995998i	$-0.528486\pi$
$2$		−	3.98399i		−	1.99200i	0.0893727	−	0.995998i	$-0.471514\pi$
$3$		0			0
$3$		0			0
$4$	−11.8722			−2.96805
$5$	−4.48413	−	2.58892i	−0.896827	−	0.517783i	−0.0206573	−	0.999787i	$-0.506576\pi$
$5$	−4.48413	−	2.58892i	−0.896827	−	0.517783i	−0.876169	+	0.482004i	$0.839909\pi$
$6$		0			0
$7$	−4.28862	+	2.47604i	−0.612661	+	0.353720i	−0.774006	−	0.633178i	$-0.781750\pi$
$7$	−4.28862	+	2.47604i	−0.612661	+	0.353720i	0.161345	+	0.986898i	$0.448417\pi$
$8$			31.3628i			3.92035i
$9$		0			0
$10$	−10.3142	+	17.8648i	−1.03142	+	1.78648i
$11$	12.2169			1.11063			0.555316	−	0.831640i	$-0.312597\pi$
$11$	12.2169			1.11063			0.555316	+	0.831640i	$0.312597\pi$
$12$		0			0
$13$	−3.29424	−	5.70580i	−0.253403	−	0.438907i	0.711057	−	0.703134i	$-0.248217\pi$
$13$	−3.29424	−	5.70580i	−0.253403	−	0.438907i	−0.964461	+	0.264227i	$0.914883\pi$
$14$	9.86452	+	17.0858i	0.704608	+	1.22042i
$15$		0			0
$16$	77.4603			4.84127
$17$	4.47754	+	7.75533i	0.263385	+	0.456196i	0.967139	−	0.254248i	$-0.0818278\pi$
$17$	4.47754	+	7.75533i	0.263385	+	0.456196i	−0.703754	+	0.710443i	$0.748494\pi$
$18$		0			0
$19$	−19.2431	−	11.1100i	−1.01279	−	0.584737i	−0.100785	−	0.994908i	$-0.532135\pi$
$19$	−19.2431	−	11.1100i	−1.01279	−	0.584737i	−0.912008	+	0.410172i	$0.865469\pi$
$20$	53.2365	+	30.7361i	2.66183	+	1.53681i
$21$		0			0
$22$		−	48.6722i		−	2.21237i
$23$	−1.43160	+	2.47960i	−0.0622433	+	0.107809i	−0.895468	−	0.445126i	$-0.853159\pi$
$23$	−1.43160	+	2.47960i	−0.0622433	+	0.107809i	0.833225	+	0.552935i	$0.186492\pi$
$24$		0			0
$25$	0.904965	+	1.56745i	0.0361986	+	0.0626978i
$26$	−22.7319	+	13.1242i	−0.874302	+	0.504779i
$27$		0			0
$28$	50.9154	−	29.3960i	1.81841	−	1.04986i
$29$	−25.7572	+	14.8709i	−0.888179	+	0.512790i	−0.873346	−	0.487100i	$-0.838055\pi$
$29$	−25.7572	+	14.8709i	−0.888179	+	0.512790i	−0.0148324	+	0.999890i	$0.504721\pi$
$30$		0			0
$31$	−22.4879	+	38.9502i	−0.725416	+	1.25646i	0.233386	+	0.972384i	$0.425019\pi$
$31$	−22.4879	+	38.9502i	−0.725416	+	1.25646i	−0.958802	+	0.284074i	$0.908314\pi$
$32$		−	183.150i		−	5.72345i
$33$		0			0
$34$	30.8972	−	17.8385i	0.908740	−	0.524661i
$35$	25.6410			0.732600
$36$		0			0
$37$	30.8831	+	17.8303i	0.834677	+	0.481901i	0.855451	−	0.517883i	$-0.173280\pi$
$37$	30.8831	+	17.8303i	0.834677	+	0.481901i	−0.0207742	+	0.999784i	$0.506613\pi$
$38$	−44.2621	+	76.6643i	−1.16479	+	2.01748i
$39$		0			0
$40$	81.1956	−	140.635i	2.02989	−	3.51587i
$41$	73.5446			1.79377			0.896886	−	0.442263i	$-0.145824\pi$
$41$	73.5446			1.79377			0.896886	+	0.442263i	$0.145824\pi$
$42$		0			0
$43$	42.8615	−	3.44802i	0.996780	−	0.0801865i
$43$	42.8615	−	3.44802i	0.996780	−	0.0801865i
$44$	−145.042			−3.29641
$45$		0			0
$46$	9.87869	+	5.70347i	0.214754	+	0.123988i
$47$	22.4754			0.478200			0.239100	−	0.970995i	$-0.423148\pi$
$47$	22.4754			0.478200			0.239100	+	0.970995i	$0.423148\pi$
$48$		0			0
$49$	−12.2385	+	21.1977i	−0.249765	+	0.432605i
$50$	6.24469	−	3.60537i	0.124894	−	0.0721075i
$51$		0			0
$52$	39.1099	+	67.7404i	0.752114	+	1.30270i
$53$	−45.1133	+	78.1386i	−0.851195	+	1.47431i	0.0289356	+	0.999581i	$0.490788\pi$
$53$	−45.1133	+	78.1386i	−0.851195	+	1.47431i	−0.880131	+	0.474732i	$0.842545\pi$
$54$		0			0
$55$	−54.7824	−	31.6286i	−0.996044	−	0.575066i
$56$	−77.6555	−	134.503i	−1.38670	−	2.40184i
$57$		0			0
$58$	59.2456	+	102.616i	1.02148	+	1.76925i
$59$	78.3888			1.32862			0.664312	−	0.747455i	$-0.268725\pi$
$59$	78.3888			1.32862			0.664312	+	0.747455i	$0.268725\pi$
$60$		0			0
$61$	−37.9469	+	21.9087i	−0.622081	+	0.359159i	−0.777679	−	0.628662i	$-0.783603\pi$
$61$	−37.9469	+	21.9087i	−0.622081	+	0.359159i	0.155598	+	0.987820i	$0.450270\pi$
$62$	155.177	+	89.5917i	2.50286	+	1.44503i
$63$		0			0
$64$	−419.828			−6.55981
$65$			34.1141i			0.524832i
$66$		0			0
$67$	−59.8966	+	103.744i	−0.893979	+	1.54842i	−0.0589162	+	0.998263i	$0.518764\pi$
$67$	−59.8966	+	103.744i	−0.893979	+	1.54842i	−0.835063	+	0.550154i	$0.814569\pi$
$68$	−53.1582	−	92.0728i	−0.781739	−	1.35401i
$69$		0			0
$70$		−	102.154i		−	1.45934i
$71$	−37.1638	+	21.4565i	−0.523434	+	0.302205i	−0.738339	−	0.674430i	$-0.764389\pi$
$71$	−37.1638	+	21.4565i	−0.523434	+	0.302205i	0.214904	+	0.976635i	$0.431056\pi$
$72$		0			0
$73$	29.4029	−	16.9758i	0.402780	−	0.232545i	−0.284903	−	0.958556i	$-0.591961\pi$
$73$	29.4029	−	16.9758i	0.402780	−	0.232545i	0.687683	+	0.726011i	$0.258628\pi$
$74$	71.0360	−	123.038i	0.959945	−	1.66267i
$75$		0			0
$76$	228.458	+	131.900i	3.00602	+	1.73553i
$77$	−52.3939	+	30.2496i	−0.680440	+	0.392852i
$78$		0			0
$79$	−42.8246	−	74.1745i	−0.542084	−	0.938917i	−0.998784	−	0.0492965i	$-0.984302\pi$
$79$	−42.8246	−	74.1745i	−0.542084	−	0.938917i	0.456700	−	0.889621i	$-0.349031\pi$
$80$	−347.342	−	200.538i	−4.34178	−	2.50673i
$81$		0			0
$82$		−	293.001i		−	3.57319i
$83$	23.3608	−	40.4621i	0.281455	−	0.487495i	−0.690288	−	0.723535i	$-0.742516\pi$
$83$	23.3608	−	40.4621i	0.281455	−	0.487495i	0.971743	+	0.236040i	$0.0758496\pi$
$84$		0			0
$85$		−	46.3679i		−	0.545505i
$86$	−13.7369	−	170.760i	−0.159731	−	1.98558i
$87$		0			0
$88$			383.158i			4.35406i
$89$	−12.0185	−	6.93889i	−0.135040	−	0.0779651i	0.430958	−	0.902372i	$-0.358176\pi$
$89$	−12.0185	−	6.93889i	−0.135040	−	0.0779651i	−0.565998	+	0.824407i	$0.691509\pi$
$90$		0			0
$91$	28.2555	+	16.3133i	0.310500	+	0.179268i
$92$	16.9962	−	29.4383i	0.184741	−	0.319981i
$93$		0			0
$94$		−	89.5419i		−	0.952573i
$95$	57.5257	+	99.6374i	0.605533	+	1.04881i
$96$		0			0
$97$	−101.805			−1.04954			−0.524768	−	0.851245i	$-0.675848\pi$
$97$	−101.805			−1.04954			−0.524768	+	0.851245i	$0.675848\pi$
$98$	84.4513	+	48.7580i	0.861748	+	0.497530i
$99$		0			0
$100$	−10.7439	−	18.6090i	−0.107439	−	0.186090i
$101$	66.7773	+	115.662i	0.661161	+	1.14516i	0.980311	+	0.197460i	$0.0632694\pi$
$101$	66.7773	+	115.662i	0.661161	+	1.14516i	−0.319150	+	0.947704i	$0.603397\pi$
$102$		0			0
$103$	−11.6746	−	20.2209i	−0.113345	−	0.196320i	0.803772	−	0.594938i	$-0.202823\pi$
$103$	−11.6746	−	20.2209i	−0.113345	−	0.196320i	−0.917117	+	0.398618i	$0.869490\pi$
$104$	178.950	−	103.317i	1.72067	−	0.993429i
$105$		0			0
$106$	311.304	+	179.731i	2.93683	+	1.69558i
$107$	−63.7037			−0.595362			−0.297681	−	0.954665i	$-0.596213\pi$
$107$	−63.7037			−0.595362			−0.297681	+	0.954665i	$0.596213\pi$
$108$		0			0
$109$	−36.9763	+	64.0448i	−0.339232	+	0.587567i	−0.984288	−	0.176568i	$-0.943500\pi$
$109$	−36.9763	+	64.0448i	−0.339232	+	0.587567i	0.645057	+	0.764135i	$0.276834\pi$
$110$	−126.008	+	218.253i	−1.14553	+	1.98412i
$111$		0			0
$112$	−332.198	+	191.795i	−2.96606	+	1.71245i
$113$			47.5095i			0.420438i	0.977654	+	0.210219i	$0.0674177\pi$
$113$			47.5095i			0.420438i	−0.977654	+	0.210219i	$0.932582\pi$
$114$		0			0
$115$	12.8389	−	7.41256i	0.111643	−	0.0644570i
$116$	305.794	−	176.551i	2.63616	−	1.52199i
$117$		0			0
$118$		−	312.300i		−	2.64661i
$119$	−38.4050	−	22.1731i	−0.322731	−	0.186329i
$120$		0			0
$121$	28.2538			0.233503
$122$	87.2840	+	151.180i	0.715443	+	1.23918i
$123$		0			0
$124$	266.981	−	462.425i	2.15307	−	3.72923i
$125$			120.074i			0.960594i
$126$		0			0
$127$	−120.755			−0.950824			−0.475412	−	0.879763i	$-0.657701\pi$
$127$	−120.755			−0.950824			−0.475412	+	0.879763i	$0.657701\pi$
$128$			939.991i			7.34368i
$129$		0			0
$130$	135.910			1.04546
$131$			19.9778i			0.152502i	0.997089	+	0.0762510i	$0.0242950\pi$
$131$			19.9778i			0.152502i	−0.997089	+	0.0762510i	$0.975705\pi$
$132$		0			0
$133$	110.035			0.827332
$134$	413.315	+	238.628i	3.08444	+	1.78080i
$135$		0			0
$136$	−243.229	+	140.428i	−1.78845	+	1.03256i
$137$		−	9.01764i		−	0.0658222i	−0.999458	−	0.0329111i	$-0.989522\pi$
$137$		−	9.01764i		−	0.0658222i	0.999458	−	0.0329111i	$-0.0104778\pi$
$138$		0			0
$139$	−71.0810	+	123.116i	−0.511374	+	0.885726i	0.488539	+	0.872542i	$0.337530\pi$
$139$	−71.0810	+	123.116i	−0.511374	+	0.885726i	−0.999913	+	0.0131839i	$0.995803\pi$
$140$	−304.415			−2.17439
$141$		0			0
$142$	85.4827	+	148.060i	0.601991	+	1.04268i
$143$	−40.2456	−	69.7074i	−0.281438	−	0.487464i
$144$		0			0
$145$	153.998			1.06206
$146$	−67.6314	−	117.141i	−0.463229	−	0.802336i
$147$		0			0
$148$	−366.650	−	211.685i	−2.47736	−	1.43031i
$149$	−124.411	−	71.8287i	−0.834973	−	0.482072i	0.0205796	−	0.999788i	$-0.493449\pi$
$149$	−124.411	−	71.8287i	−0.834973	−	0.482072i	−0.855552	+	0.517717i	$0.826782\pi$
$150$		0			0
$151$		−	93.4744i		−	0.619036i	−0.950894	−	0.309518i	$-0.899832\pi$
$151$		−	93.4744i		−	0.619036i	0.950894	−	0.309518i	$-0.100168\pi$
$152$	348.441	−	603.517i	2.29237	−	3.97050i
$153$		0			0
$154$	120.514	+	208.737i	0.782561	+	1.35543i
$155$	201.678	−	116.439i	1.30115	−	0.751217i
$156$		0			0
$157$	26.3916	−	15.2372i	0.168100	−	0.0970524i	−0.413590	−	0.910463i	$-0.635725\pi$
$157$	26.3916	−	15.2372i	0.168100	−	0.0970524i	0.581689	+	0.813411i	$0.302392\pi$
$158$	−295.511	+	170.613i	−1.87032	+	1.07983i
$159$		0			0
$160$	−474.161	+	821.270i	−2.96350	+	5.13294i
$161$		−	14.1787i		−	0.0880667i
$162$		0			0
$163$	−157.324	+	90.8311i	−0.965178	+	0.557246i	−0.897763	−	0.440479i	$-0.854809\pi$
$163$	−157.324	+	90.8311i	−0.965178	+	0.557246i	−0.0674152	+	0.997725i	$0.521475\pi$
$164$	−873.136			−5.32400
$165$		0			0
$166$	−161.201	−	93.0692i	−0.971088	−	0.560658i
$167$	46.5866	−	80.6903i	0.278961	−	0.483175i	−0.692165	−	0.721739i	$-0.743343\pi$
$167$	46.5866	−	80.6903i	0.278961	−	0.483175i	0.971127	+	0.238563i	$0.0766765\pi$
$168$		0			0
$169$	62.7959	−	108.766i	0.371574	−	0.643584i
$170$	−184.729			−1.08664
$171$		0			0
$172$	−508.861	+	40.9356i	−2.95849	+	0.237997i
$173$	263.027			1.52039			0.760194	−	0.649696i	$-0.225104\pi$
$173$	263.027			1.52039			0.760194	+	0.649696i	$0.225104\pi$
$174$		0			0
$175$	−7.76211	−	4.48145i	−0.0443549	−	0.0256083i
$176$	946.329			5.37687
$177$		0			0
$178$	−27.6445	+	47.8817i	−0.155306	+	0.268998i
$179$	−131.668	+	76.0186i	−0.735576	+	0.424685i	−0.820459	−	0.571706i	$-0.806282\pi$
$179$	−131.668	+	76.0186i	−0.735576	+	0.424685i	0.0848824	+	0.996391i	$0.472949\pi$
$180$		0			0
$181$	104.609	+	181.189i	0.577952	+	1.00104i	0.995714	+	0.0924861i	$0.0294814\pi$
$181$	104.609	+	181.189i	0.577952	+	1.00104i	−0.417762	+	0.908557i	$0.637185\pi$
$182$	64.9922	−	112.570i	0.357100	−	0.618516i
$183$		0			0
$184$	−77.7670	−	44.8988i	−0.422647	−	0.244015i
$185$	−92.3225	−	159.907i	−0.499040	−	0.864363i
$186$		0			0
$187$	54.7019	+	94.7464i	0.292523	+	0.506665i
$188$	−266.833			−1.41932
$189$		0			0
$190$	396.955	−	229.182i	2.08924	−	1.20622i
$191$	−40.4124	−	23.3321i	−0.211583	−	0.122158i	0.390464	−	0.920618i	$-0.372315\pi$
$191$	−40.4124	−	23.3321i	−0.211583	−	0.122158i	−0.602047	+	0.798461i	$0.705648\pi$
$192$		0			0
$193$	−60.4673			−0.313302			−0.156651	−	0.987654i	$-0.550070\pi$
$193$	−60.4673			−0.313302			−0.156651	+	0.987654i	$0.550070\pi$
$194$			405.590i			2.09067i
$195$		0			0
$196$	145.298	−	251.663i	0.741314	−	1.28399i
$197$	−66.6666	−	115.470i	−0.338409	−	0.586142i	0.645725	−	0.763570i	$-0.276555\pi$
$197$	−66.6666	−	115.470i	−0.338409	−	0.586142i	−0.984134	+	0.177429i	$0.943222\pi$
$198$		0			0
$199$			242.666i			1.21943i	0.792621	+	0.609714i	$0.208716\pi$
$199$			242.666i			1.21943i	−0.792621	+	0.609714i	$0.791284\pi$
$200$	−49.1595	+	28.3822i	−0.245797	+	0.141911i
$201$		0			0
$202$	460.795	−	266.040i	2.28116	−	1.31703i
$203$	73.6419	−	127.552i	0.362768	−	0.628333i
$204$		0			0
$205$	−329.784	−	190.401i	−1.60870	−	0.928784i
$206$	−80.5600	+	46.5114i	−0.391068	+	0.225783i
$207$		0			0
$208$	−255.173	−	441.973i	−1.22679	−	2.12487i
$209$	−235.092	−	135.730i	−1.12484	−	0.649427i
$210$		0			0
$211$			24.3126i			0.115226i	0.998339	+	0.0576129i	$0.0183489\pi$
$211$			24.3126i			0.115226i	−0.998339	+	0.0576129i	$0.981651\pi$
$212$	535.595	−	927.677i	2.52639	−	4.37583i
$213$		0			0
$214$			253.795i			1.18596i
$215$	−201.123	−	95.5035i	−0.935458	−	0.444202i
$216$		0			0
$217$		−	222.724i		−	1.02638i
$218$	255.154	+	147.313i	1.17043	+	0.675749i
$219$		0			0
$220$	650.388	+	375.502i	2.95631	+	1.70683i
$221$	29.5002	−	51.0959i	0.133485	−	0.231203i
$222$		0			0
$223$			43.9155i			0.196930i	0.995140	+	0.0984652i	$0.0313933\pi$
$223$			43.9155i			0.196930i	−0.995140	+	0.0984652i	$0.968607\pi$
$224$	453.487	+	785.463i	2.02450	+	3.50653i
$225$		0			0
$226$	189.278			0.837511
$227$	−55.2702	−	31.9103i	−0.243481	−	0.140574i	0.373294	−	0.927713i	$-0.378228\pi$
$227$	−55.2702	−	31.9103i	−0.243481	−	0.140574i	−0.616776	+	0.787139i	$0.711561\pi$
$228$		0			0
$229$	67.6718	+	117.211i	0.295510	+	0.511838i	0.975103	−	0.221751i	$-0.0711771\pi$
$229$	67.6718	+	117.211i	0.295510	+	0.511838i	−0.679593	+	0.733589i	$0.737844\pi$
$230$	−29.5316	−	51.1502i	−0.128398	−	0.222392i
$231$		0			0
$232$	−466.393	−	807.817i	−2.01032	−	3.48197i
$233$	117.773	−	67.9964i	0.505464	−	0.291830i	−0.225503	−	0.974242i	$-0.572403\pi$
$233$	117.773	−	67.9964i	0.505464	−	0.291830i	0.730967	+	0.682413i	$0.239069\pi$
$234$		0			0
$235$	−100.783	−	58.1869i	−0.428863	−	0.247604i
$236$	−930.648			−3.94342
$237$		0			0
$238$	−88.3375	+	153.005i	−0.371166	+	0.642879i
$239$	−41.2275	+	71.4082i	−0.172500	+	0.298779i	−0.939293	−	0.343115i	$-0.888518\pi$
$239$	−41.2275	+	71.4082i	−0.172500	+	0.298779i	0.766793	+	0.641894i	$0.221851\pi$
$240$		0			0
$241$	−265.259	+	153.148i	−1.10066	+	0.635467i	−0.936395	−	0.350949i	$-0.885859\pi$
$241$	−265.259	+	153.148i	−1.10066	+	0.635467i	−0.164267	+	0.986416i	$0.552526\pi$
$242$		−	112.563i		−	0.465137i
$243$		0			0
$244$	450.514	−	260.104i	1.84637	−	1.06600i
$245$	109.758	−	63.3687i	0.447991	−	0.258648i
$246$		0			0
$247$			146.396i			0.592697i
$248$	−1221.59	−	705.283i	−4.92575	−	2.84389i
$249$		0			0
$250$	478.375			1.91350
$251$	−64.2543	−	111.292i	−0.255993	−	0.443393i	0.709172	−	0.705036i	$-0.249069\pi$
$251$	−64.2543	−	111.292i	−0.255993	−	0.443393i	−0.965165	+	0.261643i	$0.915736\pi$
$252$		0			0
$253$	−17.4897	+	30.2931i	−0.0691293	+	0.119736i
$254$			481.086i			1.89404i
$255$		0			0
$256$	2065.61			8.06877
$257$		−	171.029i		−	0.665483i	−0.943018	−	0.332741i	$-0.892026\pi$
$257$		−	171.029i		−	0.665483i	0.943018	−	0.332741i	$-0.107974\pi$
$258$		0			0
$259$	−176.594			−0.681832
$260$		−	405.009i		−	1.55773i
$261$		0			0
$262$	79.5912			0.303783
$263$	−172.396	−	99.5327i	−0.655497	−	0.378451i	0.135062	−	0.990837i	$-0.456877\pi$
$263$	−172.396	−	99.5327i	−0.655497	−	0.378451i	−0.790559	+	0.612386i	$0.790210\pi$
$264$		0			0
$265$	404.588	−	233.589i	1.52675	−	0.881469i
$266$		−	438.379i		−	1.64804i
$267$		0			0
$268$	711.104	−	1231.67i	2.65337	−	4.59578i
$269$	−120.208			−0.446870			−0.223435	−	0.974719i	$-0.571727\pi$
$269$	−120.208			−0.446870			−0.223435	+	0.974719i	$0.571727\pi$
$270$		0			0
$271$	219.428	+	380.061i	0.809698	+	1.40244i	0.913073	+	0.407796i	$0.133702\pi$
$271$	219.428	+	380.061i	0.809698	+	1.40244i	−0.103375	+	0.994642i	$0.532964\pi$
$272$	346.832	+	600.730i	1.27512	+	2.20857i
$273$		0			0
$274$	−35.9262			−0.131118
$275$	11.0559	+	19.1494i	0.0402033	+	0.0696342i
$276$		0			0
$277$	−230.531	−	133.097i	−0.832241	−	0.480495i	0.0223784	−	0.999750i	$-0.492876\pi$
$277$	−230.531	−	133.097i	−0.832241	−	0.480495i	−0.854619	+	0.519255i	$0.826209\pi$
$278$	490.493	+	283.186i	1.76436	+	1.01866i
$279$		0			0
$280$			804.174i			2.87205i
$281$	154.257	−	267.182i	0.548959	−	0.950824i	−0.449388	−	0.893337i	$-0.648358\pi$
$281$	154.257	−	267.182i	0.548959	−	0.950824i	0.998346	−	0.0574873i	$-0.0183089\pi$
$282$		0			0
$283$	−226.635	−	392.544i	−0.800832	−	1.38708i	−0.919069	−	0.394096i	$-0.871058\pi$
$283$	−226.635	−	392.544i	−0.800832	−	1.38708i	0.118237	−	0.992985i	$-0.462276\pi$
$284$	441.216	−	254.736i	1.55358	−	0.896959i
$285$		0			0
$286$	−277.714	+	160.338i	−0.971028	+	0.560623i
$287$	−315.405	+	182.099i	−1.09897	+	0.634492i
$288$		0			0
$289$	104.403	−	180.832i	0.361257	−	0.625715i
$290$		−	613.528i		−	2.11561i
$291$		0			0
$292$	−349.078	+	201.540i	−1.19547	+	0.690206i
$293$	191.302			0.652908			0.326454	−	0.945213i	$-0.394146\pi$
$293$	191.302			0.652908			0.326454	+	0.945213i	$0.394146\pi$
$294$		0			0
$295$	−351.506	−	202.942i	−1.19155	−	0.687939i
$296$	−559.209	+	968.579i	−1.88922	+	3.27223i
$297$		0			0
$298$	−286.165	+	495.652i	−0.960285	+	1.66326i
$299$	18.8641			0.0630906
$300$		0			0
$301$	−175.280	+	120.914i	−0.582324	+	0.401708i
$302$	−372.401			−1.23312
$303$		0			0
$304$	−1490.58	−	860.584i	−4.90321	−	2.83087i
$305$	226.879			0.743865
$306$		0			0
$307$	−64.7667	+	112.179i	−0.210967	+	0.365405i	−0.952017	−	0.306044i	$-0.900994\pi$
$307$	−64.7667	+	112.179i	−0.210967	+	0.365405i	0.741051	+	0.671449i	$0.234328\pi$
$308$	622.031	−	359.130i	2.01958	−	1.16601i
$309$		0			0
$310$	−463.890	−	803.482i	−1.49642	−	2.59188i
$311$	−263.467	+	456.339i	−0.847162	+	1.46733i	0.0365680	+	0.999331i	$0.488357\pi$
$311$	−263.467	+	456.339i	−0.847162	+	1.46733i	−0.883730	+	0.467997i	$0.844976\pi$
$312$		0			0
$313$	−39.8307	−	22.9962i	−0.127254	−	0.0734704i	0.435021	−	0.900420i	$-0.356741\pi$
$313$	−39.8307	−	22.9962i	−0.127254	−	0.0734704i	−0.562276	+	0.826950i	$0.690074\pi$
$314$	−60.7050	−	105.144i	−0.193328	−	0.334854i
$315$		0			0
$316$	508.423	+	880.614i	1.60893	+	2.78675i
$317$	−421.969			−1.33113			−0.665567	−	0.746338i	$-0.731810\pi$
$317$	−421.969			−1.33113			−0.665567	+	0.746338i	$0.731810\pi$
$318$		0			0
$319$	−314.674	+	181.677i	−0.986439	+	0.569521i
$320$	1882.57	+	1086.90i	5.88302	+	3.39656i
$321$		0			0
$322$	−56.4880			−0.175429
$323$		−	198.982i		−	0.616043i
$324$		0			0
$325$	5.96235	−	10.3271i	0.0183457	−	0.0317757i
$326$	361.870	+	626.778i	1.11003	+	1.92263i
$327$		0			0
$328$			2306.56i			7.03221i
$329$	−96.3886	+	55.6500i	−0.292974	+	0.169149i
$330$		0			0
$331$	130.559	−	75.3785i	0.394439	−	0.227730i	−0.289642	−	0.957135i	$-0.593536\pi$
$331$	130.559	−	75.3785i	0.394439	−	0.227730i	0.684082	+	0.729405i	$0.260203\pi$
$332$	−277.344	+	480.374i	−0.835373	+	1.44691i
$333$		0			0
$334$	−321.470	−	185.601i	−0.962484	−	0.555690i
$335$	537.169	−	310.134i	1.60349	−	0.925775i
$336$		0			0
$337$	124.545	+	215.719i	0.369570	+	0.640115i	0.989498	−	0.144544i	$-0.0461716\pi$
$337$	124.545	+	215.719i	0.369570	+	0.640115i	−0.619928	+	0.784659i	$0.712838\pi$
$338$	−433.322	−	250.179i	−1.28202	−	0.740173i
$339$		0			0
$340$			550.489i			1.61908i
$341$	−274.734	+	475.853i	−0.805670	+	1.39546i
$342$		0			0
$343$		−	363.863i		−	1.06083i
$344$	108.139	+	1344.26i	0.314359	+	3.90772i
$345$		0			0
$346$		−	1047.90i		−	3.02861i
$347$	146.228	+	84.4246i	0.421406	+	0.243299i	0.695679	−	0.718353i	$-0.255104\pi$
$347$	146.228	+	84.4246i	0.421406	+	0.243299i	−0.274273	+	0.961652i	$0.588437\pi$
$348$		0			0
$349$	501.339	+	289.448i	1.43650	+	0.829365i	0.997605	−	0.0691723i	$-0.0220358\pi$
$349$	501.339	+	289.448i	1.43650	+	0.829365i	0.438897	+	0.898537i	$0.355369\pi$
$350$	−17.8541	+	30.9242i	−0.0510117	+	0.0883548i
$351$		0			0
$352$		−	2237.54i		−	6.35664i
$353$	−203.815	−	353.018i	−0.577380	−	1.00005i	−0.995779	−	0.0917884i	$-0.970742\pi$
$353$	−203.815	−	353.018i	−0.577380	−	1.00005i	0.418398	−	0.908264i	$-0.362592\pi$
$354$		0			0
$355$	222.197			0.625906
$356$	142.686	+	82.3799i	0.400804	+	0.231404i
$357$		0			0
$358$	302.858	+	524.565i	0.845971	+	1.46527i
$359$	127.964	+	221.640i	0.356446	+	0.617382i	0.987364	−	0.158467i	$-0.0506551\pi$
$359$	127.964	+	221.640i	0.356446	+	0.617382i	−0.630918	+	0.775849i	$0.717322\pi$
$360$		0			0
$361$	66.3641	+	114.946i	0.183834	+	0.318410i
$362$	721.855	−	416.763i	1.99407	−	1.15128i
$363$		0			0
$364$	−335.455	−	193.675i	−0.921581	−	0.532075i
$365$	−175.796			−0.481632
$366$		0			0
$367$	−207.111	+	358.726i	−0.564334	+	0.977455i	0.432778	+	0.901501i	$0.357534\pi$
$367$	−207.111	+	358.726i	−0.564334	+	0.977455i	−0.997111	+	0.0759541i	$0.975800\pi$
$368$	−110.892	+	192.070i	−0.301337	+	0.521930i
$369$		0			0
$370$	−637.069	+	367.812i	−1.72181	+	0.994087i
$371$		−	446.809i		−	1.20434i
$372$		0			0
$373$	297.922	−	172.006i	0.798719	−	0.461141i	−0.0443038	−	0.999018i	$-0.514107\pi$
$373$	297.922	−	172.006i	0.798719	−	0.461141i	0.843023	+	0.537877i	$0.180774\pi$
$374$	377.469	−	217.932i	1.00928	−	0.582706i
$375$		0			0
$376$			704.892i			1.87471i
$377$	169.701	+	97.9768i	0.450135	+	0.259885i
$378$		0			0
$379$	431.976			1.13978			0.569890	−	0.821721i	$-0.306986\pi$
$379$	431.976			1.13978			0.569890	+	0.821721i	$0.306986\pi$
$380$	−682.956	−	1182.92i	−1.79725	−	3.11293i
$381$		0			0
$382$	−92.9551	+	161.003i	−0.243338	+	0.421474i
$383$		−	398.062i		−	1.03933i	−0.854371	−	0.519663i	$-0.826057\pi$
$383$		−	398.062i		−	1.03933i	0.854371	−	0.519663i	$-0.173943\pi$
$384$		0			0
$385$	313.255			0.813649
$386$			240.901i			0.624097i
$387$		0			0
$388$	1208.65			3.11508
$389$		−	366.310i		−	0.941670i	−0.882221	−	0.470835i	$-0.843953\pi$
$389$		−	366.310i		−	0.941670i	0.882221	−	0.470835i	$-0.156047\pi$
$390$		0			0
$391$	−25.6401			−0.0655757
$392$	−664.818	−	383.833i	−1.69596	−	0.979165i
$393$		0			0
$394$	−460.031	+	265.599i	−1.16759	+	0.674109i
$395$			443.477i			1.12273i
$396$		0			0
$397$	135.348	−	234.430i	0.340928	−	0.590505i	−0.643677	−	0.765297i	$-0.722592\pi$
$397$	135.348	−	234.430i	0.340928	−	0.590505i	0.984605	+	0.174792i	$0.0559254\pi$
$398$	966.781			2.42910
$399$		0			0
$400$	70.0989	+	121.415i	0.175247	+	0.303537i
$401$	138.306	+	239.553i	0.344903	+	0.597390i	0.985336	−	0.170624i	$-0.0545784\pi$
$401$	138.306	+	239.553i	0.344903	+	0.597390i	−0.640433	+	0.768014i	$0.721245\pi$
$402$		0			0
$403$	296.323			0.735292
$404$	−792.793	−	1373.16i	−1.96236	−	3.39891i
$405$		0			0
$406$	−508.164	−	293.389i	−1.25164	−	0.722633i
$407$	377.297	+	217.832i	0.927019	+	0.535215i
$408$		0			0
$409$		−	353.309i		−	0.863835i	−0.901913	−	0.431918i	$-0.857837\pi$
$409$		−	353.309i		−	0.863835i	0.901913	−	0.431918i	$-0.142163\pi$
$410$	−758.555	+	1313.86i	−1.85014	+	3.20453i
$411$		0			0
$412$	138.603	+	240.067i	0.336414	+	0.582687i
$413$	−336.180	+	194.094i	−0.813995	+	0.469960i
$414$		0			0
$415$	−209.506	+	120.958i	−0.504833	+	0.291466i
$416$	−1045.02	+	603.342i	−2.51206	+	1.45034i
$417$		0			0
$418$	−540.748	+	936.604i	−1.29366	+	2.24068i
$419$			308.520i			0.736324i	0.929762	+	0.368162i	$0.120013\pi$
$419$			308.520i			0.736324i	−0.929762	+	0.368162i	$0.879987\pi$
$420$		0			0
$421$	397.445	−	229.465i	0.944049	−	0.545047i	0.0528216	−	0.998604i	$-0.483179\pi$
$421$	397.445	−	229.465i	0.944049	−	0.545047i	0.891227	+	0.453557i	$0.149845\pi$
$422$	96.8614			0.229529
$423$		0			0
$424$	−2450.64	−	1414.88i	−5.77982	−	3.33698i
$425$	−8.10403	+	14.0366i	−0.0190683	+	0.0330273i
$426$		0			0
$427$	108.493	−	187.916i	0.254083	−	0.440085i
$428$	756.303			1.76706
$429$		0			0
$430$	−380.485	+	801.274i	−0.884850	+	1.86343i
$431$	235.768			0.547026			0.273513	−	0.961868i	$-0.411814\pi$
$431$	235.768			0.547026			0.273513	+	0.961868i	$0.411814\pi$
$432$		0			0
$433$	492.977	+	284.621i	1.13852	+	0.657322i	0.946063	−	0.323984i	$-0.105022\pi$
$433$	492.977	+	284.621i	1.13852	+	0.657322i	0.192453	+	0.981306i	$0.438356\pi$
$434$	−887.329			−2.04454
$435$		0			0
$436$	438.990	−	760.353i	1.00686	−	1.74393i
$437$	55.0966	−	31.8100i	0.126079	−	0.0727918i
$438$		0			0
$439$	−23.7227	−	41.0890i	−0.0540381	−	0.0935967i	0.837741	−	0.546068i	$-0.183876\pi$
$439$	−23.7227	−	41.0890i	−0.0540381	−	0.0935967i	−0.891779	+	0.452471i	$0.850543\pi$
$440$	991.963	−	1718.13i	2.25446	−	3.90484i
$441$		0			0
$442$	−203.566	−	117.529i	−0.460556	−	0.265902i
$443$	165.629	+	286.877i	0.373879	+	0.647578i	0.990159	−	0.139950i	$-0.0446941\pi$
$443$	165.629	+	286.877i	0.373879	+	0.647578i	−0.616279	+	0.787528i	$0.711361\pi$
$444$		0			0
$445$	35.9284	+	62.2298i	0.0807380	+	0.139842i
$446$	174.959			0.392285
$447$		0			0
$448$	1800.48	−	1039.51i	4.01894	−	2.32034i
$449$	26.0156	+	15.0201i	0.0579413	+	0.0334524i	0.528691	−	0.848814i	$-0.322683\pi$
$449$	26.0156	+	15.0201i	0.0579413	+	0.0334524i	−0.470750	+	0.882267i	$0.656016\pi$
$450$		0			0
$451$	898.491			1.99222
$452$		−	564.042i		−	1.24788i
$453$		0			0
$454$	−127.130	+	220.196i	−0.280023	+	0.485014i
$455$	−84.4677	−	146.302i	−0.185643	−	0.321544i
$456$		0			0
$457$		−	90.2426i		−	0.197467i	−0.995114	−	0.0987337i	$-0.968521\pi$
$457$		−	90.2426i		−	0.197467i	0.995114	−	0.0987337i	$-0.0314792\pi$
$458$	466.968	−	269.604i	1.01958	−	0.588655i
$459$		0			0
$460$	−152.426	+	88.0034i	−0.331362	+	0.191312i
$461$	−61.6884	+	106.847i	−0.133814	+	0.231773i	−0.925144	−	0.379617i	$-0.876056\pi$
$461$	−61.6884	+	106.847i	−0.133814	+	0.231773i	0.791330	+	0.611390i	$0.209389\pi$
$462$		0			0
$463$	−550.232	−	317.677i	−1.18841	−	0.686127i	−0.230462	−	0.973081i	$-0.574024\pi$
$463$	−550.232	−	317.677i	−1.18841	−	0.686127i	−0.957944	+	0.286954i	$0.907357\pi$
$464$	−1995.16	+	1151.91i	−4.29991	+	2.48256i
$465$		0			0
$466$	−270.897	−	469.207i	−0.581324	−	1.00688i
$467$	−104.695	−	60.4456i	−0.224186	−	0.129434i	0.383701	−	0.923457i	$-0.374649\pi$
$467$	−104.695	−	60.4456i	−0.224186	−	0.129434i	−0.607887	+	0.794024i	$0.707983\pi$
$468$		0			0
$469$		−	593.225i		−	1.26487i
$470$	−231.816	+	401.518i	−0.493226	+	0.854293i
$471$		0			0
$472$			2458.49i			5.20867i
$473$	523.637	−	42.1243i	1.10706	−	0.0890576i
$474$		0			0
$475$		−	40.2166i		−	0.0846666i
$476$	455.951	+	263.244i	0.957881	+	0.553033i
$477$		0			0
$478$	284.490	+	164.250i	0.595167	+	0.343620i
$479$	−277.076	+	479.910i	−0.578448	+	1.00190i	0.417210	+	0.908810i	$0.363008\pi$
$479$	−277.076	+	479.910i	−0.578448	+	1.00190i	−0.995658	+	0.0930905i	$0.970325\pi$
$480$		0			0
$481$		−	234.950i		−	0.488461i
$482$	610.139	+	1056.79i	1.26585	+	2.19251i
$483$		0			0
$484$	−335.435			−0.693048
$485$	456.507	+	263.565i	0.941252	+	0.543432i
$486$		0			0
$487$	−115.269	−	199.652i	−0.236692	−	0.409963i	0.723071	−	0.690774i	$-0.242730\pi$
$487$	−115.269	−	199.652i	−0.236692	−	0.409963i	−0.959763	+	0.280811i	$0.909397\pi$
$488$	−687.117	−	1190.12i	−1.40803	−	2.43877i
$489$		0			0
$490$	−252.461	−	437.275i	−0.515226	−	0.892397i
$491$	−809.002	+	467.077i	−1.64766	+	0.951278i	−0.669664	+	0.742665i	$0.733562\pi$
$491$	−809.002	+	467.077i	−1.64766	+	0.951278i	−0.977998	+	0.208613i	$0.933105\pi$
$492$		0			0
$493$	−230.658	−	133.170i	−0.467865	−	0.270122i
$494$	583.241			1.18065
$495$		0			0
$496$	−1741.92	+	3017.10i	−3.51194	+	6.08285i
$497$	106.254	−	184.038i	0.213792	−	0.370298i
$498$		0			0
$499$	−301.092	+	173.836i	−0.603391	+	0.348368i	−0.770374	−	0.637592i	$-0.779931\pi$
$499$	−301.092	+	173.836i	−0.603391	+	0.348368i	0.166983	+	0.985960i	$0.446597\pi$
$500$		−	1425.55i		−	2.85109i
$501$		0			0
$502$	−443.385	+	255.989i	−0.883238	+	0.509938i
$503$	−183.679	+	106.047i	−0.365166	+	0.210829i	−0.671345	−	0.741145i	$-0.734283\pi$
$503$	−183.679	+	106.047i	−0.365166	+	0.210829i	0.306178	+	0.951974i	$0.400950\pi$
$504$		0			0
$505$		−	691.523i		−	1.36935i
$506$	120.687	+	69.6789i	0.238513	+	0.137705i
$507$		0			0
$508$	1433.62			2.82209
$509$	481.480	+	833.948i	0.945933	+	1.63840i	0.753871	+	0.657022i	$0.228184\pi$
$509$	481.480	+	833.948i	0.945933	+	1.63840i	0.192062	+	0.981383i	$0.438483\pi$
$510$		0			0
$511$	−84.0654	+	145.606i	−0.164512	+	0.284942i
$512$		−	4469.39i		−	8.72929i
$513$		0			0
$514$	−681.378			−1.32564
$515$			120.898i			0.234753i
$516$		0			0
$517$	274.581			0.531104
$518$			703.551i			1.35821i
$519$		0			0
$520$	−1069.91			−2.05752
$521$	369.566	+	213.369i	0.709340	+	0.409537i	0.810817	−	0.585300i	$-0.199023\pi$
$521$	369.566	+	213.369i	0.709340	+	0.409537i	−0.101477	+	0.994838i	$0.532357\pi$
$522$		0			0
$523$	−889.482	+	513.543i	−1.70073	+	0.981917i	−0.755709	+	0.654908i	$0.772708\pi$
$523$	−889.482	+	513.543i	−1.70073	+	0.981917i	−0.945021	+	0.327009i	$0.893959\pi$
$524$		−	237.180i		−	0.452633i
$525$		0			0
$526$	−396.538	+	686.823i	−0.753874	+	1.30575i
$527$	−402.762			−0.764254
$528$		0			0
$529$	260.401	+	451.028i	0.492252	+	0.852605i
$530$	−930.618	−	1611.88i	−1.75588	−	3.04128i
$531$		0			0
$532$	−1306.36			−2.45556
$533$	−242.274	−	419.631i	−0.454548	−	0.787299i
$534$		0			0
$535$	285.656	+	164.923i	0.533936	+	0.308268i
$536$	−3253.70	−	1878.52i	−6.07034	−	3.50471i
$537$		0			0
$538$			478.907i			0.890163i
$539$	−149.517	+	258.971i	−0.277397	+	0.480465i
$540$		0			0
$541$	69.0772	+	119.645i	0.127684	+	0.221156i	0.922779	−	0.385330i	$-0.125912\pi$
$541$	69.0772	+	119.645i	0.127684	+	0.221156i	−0.795095	+	0.606485i	$0.792579\pi$
$542$	1514.16	−	874.200i	2.79365	−	1.61292i
$543$		0			0
$544$	1420.39	−	820.063i	2.61101	−	1.50747i
$545$	331.613	−	191.457i	0.608464	−	0.351297i
$546$		0			0
$547$	−2.01982	+	3.49843i	−0.00369254	+	0.00639567i	−0.867866	−	0.496799i	$-0.834509\pi$
$547$	−2.01982	+	3.49843i	−0.00369254	+	0.00639567i	0.864173	+	0.503194i	$0.167842\pi$
$548$			107.059i			0.195364i
$549$		0			0
$550$	76.2911	−	44.0467i	0.138711	−	0.0800848i
$551$	660.863			1.19939
$552$		0			0
$553$	367.318	+	212.071i	0.664227	+	0.383492i
$554$	−530.257	+	918.433i	−0.957143	+	1.65782i
$555$		0			0
$556$	843.888	−	1461.66i	1.51778	−	2.62888i
$557$	7.20953			0.0129435			0.00647175	−	0.999979i	$-0.497940\pi$
$557$	7.20953			0.0129435			0.00647175	+	0.999979i	$0.497940\pi$
$558$		0			0
$559$	−160.870	−	233.201i	−0.287782	−	0.417175i
$560$	1986.16			3.54672
$561$		0			0
$562$	−1064.45	−	614.560i	−1.89404	−	1.09352i
$563$	495.134			0.879457			0.439729	−	0.898131i	$-0.355075\pi$
$563$	495.134			0.879457			0.439729	+	0.898131i	$0.355075\pi$
$564$		0			0
$565$	122.998	−	213.039i	0.217696	−	0.377060i
$566$	−1563.89	+	902.914i	−2.76306	+	1.59525i
$567$		0			0
$568$	−672.937	−	1165.56i	−1.18475	−	2.05204i
$569$	162.743	−	281.878i	0.286015	−	0.495393i	−0.686840	−	0.726809i	$-0.741003\pi$
$569$	162.743	−	281.878i	0.286015	−	0.495393i	0.972855	+	0.231416i	$0.0743359\pi$
$570$		0			0
$571$	−438.400	−	253.110i	−0.767776	−	0.443276i	0.0643049	−	0.997930i	$-0.479517\pi$
$571$	−438.400	−	253.110i	−0.767776	−	0.443276i	−0.832081	+	0.554655i	$0.812850\pi$
$572$	477.804	+	827.580i	0.835321	+	1.44682i
$573$		0			0
$574$	725.482	+	1256.57i	1.26391	+	2.18915i
$575$	−5.18217			−0.00901247
$576$		0			0
$577$	290.129	−	167.506i	0.502823	−	0.290305i	−0.227056	−	0.973882i	$-0.572910\pi$
$577$	290.129	−	167.506i	0.502823	−	0.290305i	0.729878	+	0.683577i	$0.239577\pi$
$578$	−720.433	−	415.942i	−1.24642	−	0.719623i
$579$		0			0
$580$	−1828.30			−3.15224
$581$			231.369i			0.398225i
$582$		0			0
$583$	−551.147	+	954.615i	−0.945364	+	1.63742i
$584$	532.408	+	922.158i	0.911658	+	1.57904i
$585$		0			0
$586$		−	762.146i		−	1.30059i
$587$	573.170	−	330.920i	0.976440	−	0.563748i	0.0752463	−	0.997165i	$-0.476026\pi$
$587$	573.170	−	330.920i	0.976440	−	0.563748i	0.901193	+	0.433417i	$0.142692\pi$
$588$		0			0
$589$	865.473	−	499.681i	1.46939	−	0.848355i
$590$	−808.519	+	1400.40i	−1.37037	+	2.37355i
$591$		0			0
$592$	2392.21	+	1381.14i	4.04090	+	2.33301i
$593$	109.004	−	62.9338i	0.183819	−	0.106128i	−0.405267	−	0.914198i	$-0.632821\pi$
$593$	109.004	−	62.9338i	0.183819	−	0.106128i	0.589086	+	0.808071i	$0.299488\pi$
$594$		0			0
$595$	114.809	+	198.854i	0.192956	+	0.334209i
$596$	1477.03	+	852.765i	2.47824	+	1.43081i
$597$		0			0
$598$		−	75.1544i		−	0.125676i
$599$	271.490	−	470.235i	0.453240	−	0.785034i	−0.545346	−	0.838211i	$-0.683602\pi$
$599$	271.490	−	470.235i	0.453240	−	0.785034i	0.998585	+	0.0531774i	$0.0169349\pi$
$600$		0			0
$601$		−	700.068i		−	1.16484i	−0.812888	−	0.582420i	$-0.802106\pi$
$601$		−	700.068i		−	1.16484i	0.812888	−	0.582420i	$-0.197894\pi$
$602$	481.721	+	698.313i	0.800201	+	1.15999i
$603$		0			0
$604$			1109.75i			1.83733i
$605$	−126.694	−	73.1468i	−0.209411	−	0.120904i
$606$		0			0
$607$	291.972	+	168.570i	0.481008	+	0.277710i	0.720836	−	0.693105i	$-0.243758\pi$
$607$	291.972	+	168.570i	0.481008	+	0.277710i	−0.239828	+	0.970815i	$0.577091\pi$
$608$	−2034.80	+	3524.38i	−3.34671	+	5.79667i
$609$		0			0
$610$		−	903.883i		−	1.48178i
$611$	−74.0395	−	128.240i	−0.121178	−	0.209886i
$612$		0			0
$613$	−899.953			−1.46811			−0.734056	−	0.679089i	$-0.762375\pi$
$613$	−899.953			−1.46811			−0.734056	+	0.679089i	$0.762375\pi$
$614$	446.921	+	258.030i	0.727885	+	0.420245i
$615$		0			0
$616$	−948.713	−	1643.22i	−1.54012	−	2.66756i
$617$	−177.601	−	307.613i	−0.287846	−	0.498563i	0.685450	−	0.728120i	$-0.259606\pi$
$617$	−177.601	−	307.613i	−0.287846	−	0.498563i	−0.973295	+	0.229557i	$0.926272\pi$
$618$		0			0
$619$	303.427	+	525.551i	0.490189	+	0.849033i	0.999936	−	0.0112915i	$-0.00359427\pi$
$619$	303.427	+	525.551i	0.490189	+	0.849033i	−0.509747	+	0.860324i	$0.670261\pi$
$620$	−2394.36	+	1382.38i	−3.86186	+	2.22965i
$621$		0			0
$622$	1818.05	+	1049.65i	2.92291	+	1.68754i
$623$	68.7239			0.110311
$624$		0			0
$625$	333.486	−	577.615i	0.533578	−	0.924184i
$626$	−91.6169	+	158.685i	−0.146353	+	0.253490i
$627$		0			0
$628$	−313.327	+	180.899i	−0.498928	+	0.288056i
$629$			319.344i			0.507701i
$630$		0			0
$631$	−671.565	+	387.728i	−1.06429	+	0.614466i	−0.926615	−	0.376011i	$-0.877295\pi$
$631$	−671.565	+	387.728i	−1.06429	+	0.614466i	−0.137672	+	0.990478i	$0.543962\pi$
$632$	2326.32	−	1343.10i	3.68088	−	2.12516i
$633$		0			0
$634$			1681.12i			2.65161i
$635$	541.480	+	312.624i	0.852724	+	0.492321i
$636$		0			0
$637$	161.266			0.253165
$638$	723.801	+	1253.66i	1.13448	+	1.96498i
$639$		0			0
$640$	2433.56	−	4215.05i	3.80243	−	6.58601i
$641$		−	11.6170i		−	0.0181232i	−0.999959	−	0.00906161i	$-0.997116\pi$
$641$		−	11.6170i		−	0.0181232i	0.999959	−	0.00906161i	$-0.00288444\pi$
$642$		0			0
$643$	−724.354			−1.12652			−0.563261	−	0.826279i	$-0.690454\pi$
$643$	−724.354			−1.12652			−0.563261	+	0.826279i	$0.690454\pi$
$644$			168.333i			0.261386i
$645$		0			0
$646$	−792.742			−1.22716
$647$			793.608i			1.22660i	0.789851	+	0.613298i	$0.210158\pi$
$647$			793.608i			1.22660i	−0.789851	+	0.613298i	$0.789842\pi$
$648$		0			0
$649$	957.672			1.47561
$650$	−41.1431	−	23.7540i	−0.0632970	−	0.0365445i
$651$		0			0
$652$	1867.78	−	1078.36i	2.86470	−	1.65393i
$653$		−	403.095i		−	0.617297i	−0.951176	−	0.308648i	$-0.900123\pi$
$653$		−	403.095i		−	0.617297i	0.951176	−	0.308648i	$-0.0998766\pi$
$654$		0			0
$655$	51.7207	−	89.5829i	0.0789629	−	0.136768i
$656$	5696.79			8.68413
$657$		0			0
$658$	221.709	+	384.011i	0.336944	+	0.583604i
$659$	−198.765	−	344.271i	−0.301616	−	0.522415i	0.674886	−	0.737922i	$-0.264193\pi$
$659$	−198.765	−	344.271i	−0.301616	−	0.522415i	−0.976502	+	0.215507i	$0.930860\pi$
$660$		0			0
$661$	567.625			0.858736			0.429368	−	0.903130i	$-0.358736\pi$
$661$	567.625			0.858736			0.429368	+	0.903130i	$0.358736\pi$
$662$	−300.308	−	520.148i	−0.453637	−	0.785722i
$663$		0			0
$664$	1269.00	+	732.660i	1.91115	+	1.10340i
$665$	−493.412	−	284.872i	−0.741973	−	0.428378i
$666$		0			0
$667$		−	85.1565i		−	0.127671i
$668$	−553.085	+	957.971i	−0.827971	+	1.43409i
$669$		0			0
$670$	−1235.57	−	2140.08i	−1.84414	−	3.19414i
$671$	−463.596	+	267.657i	−0.690903	+	0.398893i
$672$		0			0
$673$	1021.09	−	589.529i	1.51723	−	0.875971i	0.517432	−	0.855725i	$-0.326888\pi$
$673$	1021.09	−	589.529i	1.51723	−	0.875971i	0.999795	−	0.0202467i	$-0.00644517\pi$
$674$	859.421	−	496.187i	1.27511	−	0.736183i
$675$		0			0
$676$	−745.526	+	1291.29i	−1.10285	+	1.91019i
$677$			822.031i			1.21423i	0.794615	+	0.607113i	$0.207673\pi$
$677$			822.031i			1.21423i	−0.794615	+	0.607113i	$0.792327\pi$
$678$		0			0
$679$	436.603	−	252.073i	0.643009	−	0.371242i
$680$	1454.23			2.13857
$681$		0			0
$682$	1895.79	+	1094.54i	2.77976	+	1.60489i
$683$	−189.807	+	328.755i	−0.277902	+	0.481340i	−0.970863	−	0.239635i	$-0.922972\pi$
$683$	−189.807	+	328.755i	−0.277902	+	0.481340i	0.692961	+	0.720975i	$0.256306\pi$
$684$		0			0
$685$	−23.3459	+	40.4363i	−0.0340816	+	0.0590311i
$686$	−1449.63			−2.11316
$687$		0			0
$688$	3320.07	−	267.085i	4.82568	−	0.388204i
$689$	594.457			0.862783
$690$		0			0
$691$	−795.331	−	459.185i	−1.15099	−	0.664522i	−0.201859	−	0.979415i	$-0.564698\pi$
$691$	−795.331	−	459.185i	−1.15099	−	0.664522i	−0.949127	+	0.314893i	$0.898032\pi$
$692$	−3122.71			−4.51259
$693$		0			0
$694$	336.347	−	582.570i	0.484650	−	0.839439i
$695$	637.473	−	368.045i	0.917228	−	0.529562i
$696$		0			0
$697$	329.299	+	570.362i	0.472452	+	0.818311i
$698$	1153.16	−	1997.33i	1.65209	−	2.86151i
$699$		0			0
$700$	92.1533	+	53.2047i	0.131648	+	0.0760068i
$701$	−178.978	−	309.998i	−0.255318	−	0.442223i	0.709664	−	0.704540i	$-0.248847\pi$
$701$	−178.978	−	309.998i	−0.255318	−	0.442223i	−0.964982	+	0.262317i	$0.915513\pi$
$702$		0			0
$703$	−396.190	−	686.221i	−0.563570	−	0.976133i
$704$	−5129.02			−7.28554
$705$		0			0
$706$	−1406.42	+	811.999i	−1.99210	+	1.15014i
$707$	−572.765	−	330.686i	−0.810135	−	0.467731i
$708$		0			0
$709$	−799.354			−1.12744			−0.563719	−	0.825967i	$-0.690630\pi$
$709$	−799.354			−1.12744			−0.563719	+	0.825967i	$0.690630\pi$
$710$		−	885.230i		−	1.24680i
$711$		0			0
$712$	217.623	−	376.934i	0.305650	−	0.529402i
$713$	−64.3872	−	111.522i	−0.0903046	−	0.156412i
$714$		0			0
$715$			416.770i			0.582895i
$716$	1563.19	−	902.509i	2.18323	−	1.26049i
$717$		0			0
$718$	883.013	−	509.808i	1.22982	−	0.710039i
$719$	−48.0059	+	83.1487i	−0.0667676	+	0.115645i	−0.897477	−	0.441062i	$-0.854602\pi$
$719$	−48.0059	+	83.1487i	−0.0667676	+	0.115645i	0.830709	+	0.556707i	$0.187935\pi$
$720$		0			0
$721$	100.136	+	57.8133i	0.138884	+	0.0801849i
$722$	457.944	−	264.394i	0.634271	−	0.366197i
$723$		0			0
$724$	−1241.94	−	2151.11i	−1.71539	−	2.97115i
$725$	−46.6187	−	26.9153i	−0.0643016	−	0.0371246i
$726$		0			0
$727$		−	505.455i		−	0.695261i	−0.937632	−	0.347631i	$-0.886986\pi$
$727$		−	505.455i		−	0.695261i	0.937632	−	0.347631i	$-0.113014\pi$
$728$	−511.632	+	886.173i	−0.702791	+	1.21727i
$729$		0			0
$730$			700.368i			0.959409i
$731$	218.655	+	316.967i	0.299117	+	0.433607i
$732$		0			0
$733$			969.169i			1.32220i	0.750300	+	0.661098i	$0.229909\pi$
$733$			969.169i			1.32220i	−0.750300	+	0.661098i	$0.770091\pi$
$734$	1429.16	+	825.127i	1.94709	+	1.12415i
$735$		0			0
$736$	454.139	+	262.197i	0.617036	+	0.356246i
$737$	−731.754	+	1267.43i	−0.992882	+	1.71972i
$738$		0			0
$739$			899.723i			1.21749i	0.793367	+	0.608743i	$0.208326\pi$
$739$			899.723i			1.21749i	−0.793367	+	0.608743i	$0.791674\pi$
$740$	1096.07	+	1898.45i	1.48118	+	2.56547i
$741$		0			0
$742$	−1780.09			−2.39904
$743$	66.7854	+	38.5586i	0.0898861	+	0.0518958i	0.544269	−	0.838911i	$-0.316807\pi$
$743$	66.7854	+	38.5586i	0.0898861	+	0.0518958i	−0.454383	+	0.890806i	$0.650140\pi$
$744$		0			0
$745$	371.917	+	644.179i	0.499217	+	0.864669i
$746$	−685.269	−	1186.92i	−0.918591	−	1.59105i
$747$		0			0
$748$	−649.432	−	1124.85i	−0.868224	−	1.50381i
$749$	273.201	−	157.733i	0.364755	−	0.210591i
$750$		0			0
$751$	481.345	+	277.905i	0.640938	+	0.370046i	0.784976	−	0.619526i	$-0.212675\pi$
$751$	481.345	+	277.905i	0.640938	+	0.370046i	−0.144037	+	0.989572i	$0.546009\pi$
$752$	1740.95			2.31510
$753$		0			0
$754$	390.339	−	676.087i	0.517691	−	0.896667i
$755$	−241.997	+	419.152i	−0.320526	+	0.555168i
$756$		0			0
$757$	−362.925	+	209.535i	−0.479425	+	0.276796i	−0.720177	−	0.693790i	$-0.755939\pi$
$757$	−362.925	+	209.535i	−0.479425	+	0.276796i	0.240752	+	0.970587i	$0.422606\pi$
$758$		−	1720.99i		−	2.27044i
$759$		0			0
$760$	−3124.91	+	1804.17i	−4.11172	+	2.37390i
$761$	−820.494	+	473.713i	−1.07818	+	0.622487i	−0.930405	−	0.366534i	$-0.880544\pi$
$761$	−820.494	+	473.713i	−1.07818	+	0.622487i	−0.147775	+	0.989021i	$0.547211\pi$
$762$		0			0
$763$		−	366.219i		−	0.479972i
$764$	479.785	+	277.004i	0.627990	+	0.362570i
$765$		0			0
$766$	−1585.88			−2.07034
$767$	−258.232	−	447.271i	−0.336678	−	0.583143i
$768$		0			0
$769$	−266.595	+	461.756i	−0.346678	+	0.600463i	−0.985657	−	0.168761i	$-0.946024\pi$
$769$	−266.595	+	461.756i	−0.346678	+	0.600463i	0.638980	+	0.769224i	$0.279357\pi$
$770$		−	1248.01i		−	1.62079i
$771$		0			0
$772$	717.880			0.929897
$773$		−	625.734i		−	0.809487i	−0.914430	−	0.404744i	$-0.867361\pi$
$773$		−	625.734i		−	0.809487i	0.914430	−	0.404744i	$-0.132639\pi$
$774$		0			0
$775$	−81.4031			−0.105036
$776$		−	3192.89i		−	4.11455i
$777$		0			0
$778$	−1459.38			−1.87580
$779$	−1415.22	−	817.080i	−1.81672	−	1.04888i
$780$		0			0
$781$	−454.028	+	262.133i	−0.581342	+	0.335638i
$782$			102.150i			0.130627i
$783$		0			0
$784$	−947.996	+	1641.98i	−1.20918	+	2.09436i
$785$	−157.792			−0.201008
$786$		0			0
$787$	−129.531	−	224.354i	−0.164588	−	0.285075i	0.771921	−	0.635719i	$-0.219296\pi$
$787$	−129.531	−	224.354i	−0.164588	−	0.285075i	−0.936509	+	0.350643i	$0.885963\pi$
$788$	791.479	+	1370.88i	1.00441	+	1.73970i
$789$		0			0
$790$	1766.81			2.23647
$791$	−117.635	−	203.750i	−0.148717	−	0.257586i
$792$		0			0
$793$	250.013	+	144.345i	0.315275	+	0.182024i
$794$	−933.969	−	539.227i	−1.17628	−	0.679127i
$795$		0			0
$796$		−	2880.98i		−	3.61933i
$797$	−287.556	+	498.062i	−0.360798	+	0.624920i	−0.988092	−	0.153862i	$-0.950829\pi$
$797$	−287.556	+	498.062i	−0.360798	+	0.624920i	0.627294	+	0.778782i	$0.284162\pi$
$798$		0			0
$799$	100.635	+	174.304i	0.125951	+	0.218153i
$800$	287.078	−	165.745i	0.358848	−	0.207181i
$801$		0			0
$802$	954.379	−	551.011i	1.19000	−	0.687046i
$803$	359.214	−	207.392i	0.447340	−	0.258272i
$804$		0			0
$805$	−36.7075	+	63.5793i	−0.0455994	+	0.0789805i
$806$		−	1180.55i		−	1.46470i
$807$		0			0
$808$	−3627.47	+	2094.32i	−4.48944	+	2.59198i
$809$	1110.48			1.37266			0.686328	−	0.727292i	$-0.259221\pi$
$809$	1110.48			1.37266			0.686328	+	0.727292i	$0.259221\pi$
$810$		0			0
$811$	−442.230	−	255.321i	−0.545290	−	0.314823i	0.201930	−	0.979400i	$-0.435279\pi$
$811$	−442.230	−	255.321i	−0.545290	−	0.314823i	−0.747220	+	0.664577i	$0.768612\pi$
$812$	−874.292	+	1514.32i	−1.07671	+	1.86492i
$813$		0			0
$814$	867.843	−	1503.15i	1.06615	−	1.84662i
$815$	940.616			1.15413
$816$		0			0
$817$	−863.095	−	409.841i	−1.05642	−	0.501641i
$818$	−1407.58			−1.72076
$819$		0			0
$820$	3915.26	+	2260.48i	4.77471	+	2.75668i
$821$	798.445			0.972527			0.486263	−	0.873812i	$-0.338360\pi$
$821$	798.445			0.972527			0.486263	+	0.873812i	$0.338360\pi$
$822$		0			0
$823$	79.9364	−	138.454i	0.0971280	−	0.168231i	−0.813367	−	0.581751i	$-0.802368\pi$
$823$	79.9364	−	138.454i	0.0971280	−	0.168231i	0.910495	+	0.413521i	$0.135701\pi$
$824$	634.185	−	366.147i	0.769642	−	0.444353i
$825$		0			0
$826$	773.268	+	1339.34i	0.936160	+	1.62148i
$827$	−624.898	+	1082.36i	−0.755620	+	1.30877i	0.189445	+	0.981891i	$0.439331\pi$
$827$	−624.898	+	1082.36i	−0.755620	+	1.30877i	−0.945065	+	0.326882i	$0.894002\pi$
$828$		0			0
$829$	225.574	+	130.235i	0.272104	+	0.157099i	0.629843	−	0.776722i	$-0.283119\pi$
$829$	225.574	+	130.235i	0.272104	+	0.157099i	−0.357740	+	0.933821i	$0.616452\pi$
$830$	481.897	+	834.669i	0.580598	+	1.00563i
$831$		0			0
$832$	1383.02	+	2395.45i	1.66228	+	2.87915i
$833$	−219.193			−0.263137
$834$		0			0
$835$	−417.801	+	241.217i	−0.500360	+	0.288883i
$836$	2791.06	+	1611.42i	3.33858	+	1.92753i
$837$		0			0
$838$	1229.14			1.46675
$839$		−	1250.66i		−	1.49066i	−0.666698	−	0.745328i	$-0.732293\pi$
$839$		−	1250.66i		−	1.49066i	0.666698	−	0.745328i	$-0.267707\pi$
$840$		0			0
$841$	21.7884	−	37.7385i	0.0259077	−	0.0448734i
$842$	−914.186	−	1583.42i	−1.08573	−	1.88054i
$843$		0			0
$844$		−	288.645i		−	0.341996i
$845$	−563.171	+	325.147i	−0.666474	+	0.384789i
$846$		0			0
$847$	−121.170	+	69.9576i	−0.143058	+	0.0825945i
$848$	−3494.49	+	6052.64i	−4.12087	+	7.13755i
$849$		0			0
$850$	55.9217	+	32.2864i	0.0657902	+	0.0379840i
$851$	−88.4241	+	51.0517i	−0.103906	+	0.0599902i
$852$		0			0
$853$	−549.802	−	952.285i	−0.644551	−	1.11640i	−0.984405	−	0.175917i	$-0.943711\pi$
$853$	−549.802	−	952.285i	−0.644551	−	1.11640i	0.339854	−	0.940478i	$-0.389622\pi$
$854$	−748.656	−	432.237i	−0.876647	−	0.506132i
$855$		0			0
$856$		−	1997.93i		−	2.33403i
$857$	338.878	−	586.954i	0.395423	−	0.684893i	−0.597732	−	0.801696i	$-0.703931\pi$
$857$	338.878	−	586.954i	0.395423	−	0.684893i	0.993155	+	0.116803i	$0.0372646\pi$
$858$		0			0
$859$			249.914i			0.290936i	0.989363	+	0.145468i	$0.0464687\pi$
$859$			249.914i			0.290936i	−0.989363	+	0.145468i	$0.953531\pi$
$860$	2387.78	+	1133.84i	2.77649	+	1.31841i
$861$		0			0
$862$		−	939.298i		−	1.08967i
$863$	−87.5968	−	50.5740i	−0.101503	−	0.0586026i	0.448389	−	0.893838i	$-0.351998\pi$
$863$	−87.5968	−	50.5740i	−0.101503	−	0.0586026i	−0.549892	+	0.835236i	$0.685331\pi$
$864$		0			0
$865$	−1179.45	−	680.955i	−1.36352	−	0.787231i
$866$	1133.93	−	1964.02i	1.30938	−	2.26792i
$867$		0			0
$868$			2644.22i			3.04634i
$869$	−523.186	−	906.186i	−0.602056	−	1.04279i
$870$		0			0
$871$	789.256			0.906149
$872$	−2008.62	−	1159.68i	−2.30347	−	1.32991i
$873$		0			0
$874$	−126.731	−	219.504i	−0.145001	−	0.251149i
$875$	−297.308	−	514.953i	−0.339781	−	0.588518i
$876$		0			0
$877$	302.403	+	523.778i	0.344816	+	0.597238i	0.985320	−	0.170716i	$-0.0546081\pi$
$877$	302.403	+	523.778i	0.344816	+	0.597238i	−0.640505	+	0.767954i	$0.721275\pi$
$878$	−163.698	+	94.5112i	−0.186444	+	0.107644i
$879$		0			0
$880$	−4243.46	−	2449.97i	−4.82212	−	2.78405i
$881$	−1131.47			−1.28430			−0.642152	−	0.766578i	$-0.721958\pi$
$881$	−1131.47			−1.28430			−0.642152	+	0.766578i	$0.721958\pi$
$882$		0			0
$883$	−28.9408	+	50.1269i	−0.0327755	+	0.0567688i	−0.881948	−	0.471347i	$-0.843768\pi$
$883$	−28.9408	+	50.1269i	−0.0327755	+	0.0567688i	0.849172	+	0.528116i	$0.177101\pi$
$884$	−350.232	+	606.620i	−0.396190	+	0.686222i
$885$		0			0
$886$	1142.92	−	659.863i	1.28997	−	0.744766i
$887$		−	113.329i		−	0.127767i	−0.997957	−	0.0638834i	$-0.979651\pi$
$887$		−	113.329i		−	0.127767i	0.997957	−	0.0638834i	$-0.0203486\pi$
$888$		0			0
$889$	517.871	−	298.993i	0.582532	−	0.336325i
$890$	247.923	−	143.139i	0.278565	−	0.160830i
$891$		0			0
$892$		−	521.373i		−	0.584499i
$893$	−432.496	−	249.702i	−0.484318	−	0.279621i
$894$		0			0
$895$	787.223			0.879579
$896$	−2327.45	−	4031.27i	−2.59760	−	4.49918i
$897$		0			0
$898$	59.8401	−	103.646i	0.0666371	−	0.115419i
$899$		−	1337.66i		−	1.48795i
$900$		0			0
$901$	−807.987			−0.896767
$902$		−	3579.58i		−	3.96849i
$903$		0			0
$904$	−1490.03			−1.64826
$905$		−	1083.30i		−	1.19702i
$906$		0			0
$907$	−1263.04			−1.39254			−0.696272	−	0.717778i	$-0.745159\pi$
$907$	−1263.04			−1.39254			−0.696272	+	0.717778i	$0.745159\pi$
$908$	656.179	+	378.845i	0.722664	+	0.417230i
$909$		0			0
$910$	−582.868	+	336.519i	−0.640514	+	0.369801i
$911$		−	1560.99i		−	1.71349i	−0.515736	−	0.856747i	$-0.672482\pi$
$911$		−	1560.99i		−	1.71349i	0.515736	−	0.856747i	$-0.327518\pi$
$912$		0			0
$913$	285.398	−	494.323i	0.312593	−	0.541427i
$914$	−359.526			−0.393355
$915$		0			0
$916$	−803.413	−	1391.55i	−0.877088	−	1.51916i
$917$	−49.4657	−	85.6771i	−0.0539429	−	0.0934319i
$918$		0			0
$919$	−1133.83			−1.23376			−0.616881	−	0.787057i	$-0.711604\pi$
$919$	−1133.83			−1.23376			−0.616881	+	0.787057i	$0.711604\pi$
$920$	232.478	+	402.665i	0.252694	+	0.437679i
$921$		0			0
$922$	425.680	+	245.766i	0.461691	+	0.266558i
$923$	244.853	+	141.366i	0.265280	+	0.153159i
$924$		0			0
$925$			64.5433i			0.0697766i
$926$	−1265.62	+	2192.12i	−1.36676	+	2.36730i
$927$		0			0
$928$	2723.61	+	4717.44i	2.93493	+	5.08344i
$929$	−672.669	+	388.366i	−0.724079	+	0.418047i	−0.816252	−	0.577696i	$-0.803952\pi$
$929$	−672.669	+	388.366i	−0.724079	+	0.418047i	0.0921733	+	0.995743i	$0.470619\pi$
$930$		0			0
$931$	471.012	−	271.939i	0.505920	−	0.292093i
$932$	−1398.23	+	807.266i	−1.50024	+	0.866166i
$933$		0			0
$934$	−240.815	+	417.103i	−0.257832	+	0.446578i
$935$		−	566.474i		−	0.605855i
$936$		0			0
$937$	1254.56	−	724.321i	1.33891	−	0.773022i	0.352267	−	0.935900i	$-0.385411\pi$
$937$	1254.56	−	724.321i	1.33891	−	0.773022i	0.986646	+	0.162878i	$0.0520777\pi$
$938$	−2363.40			−2.51962
$939$		0			0
$940$	1196.51	+	690.807i	1.27289	+	0.734901i
$941$	−626.118	+	1084.47i	−0.665376	+	1.15246i	0.313808	+	0.949487i	$0.398395\pi$
$941$	−626.118	+	1084.47i	−0.665376	+	1.15246i	−0.979183	+	0.202978i	$0.934938\pi$
$942$		0			0
$943$	−105.286	+	182.361i	−0.111650	+	0.193384i
$944$	6072.02			6.43223
$945$		0			0
$946$	−167.823	−	2086.17i	−0.177403	−	2.20525i
$947$	963.802			1.01774			0.508871	−	0.860843i	$-0.330063\pi$
$947$	963.802			1.01774			0.508871	+	0.860843i	$0.330063\pi$
$948$		0			0
$949$	−193.721	−	111.845i	−0.204132	−	0.117855i
$950$	−160.223			−0.168656
$951$		0			0
$952$	695.411	−	1204.49i	0.730474	−	1.26522i
$953$	−15.8161	+	9.13141i	−0.0165961	+	0.00958176i	−0.508275	−	0.861195i	$-0.669717\pi$
$953$	−15.8161	+	9.13141i	−0.0165961	+	0.00958176i	0.491679	+	0.870777i	$0.336383\pi$
$954$		0			0
$955$	120.810	+	209.249i	0.126502	+	0.219109i
$956$	489.462	−	847.772i	0.511989	−	0.886791i
$957$		0			0
$958$	1911.96	+	1103.87i	1.99578	+	1.15227i
$959$	22.3280	+	38.6733i	0.0232826	+	0.0403267i
$960$		0			0
$961$	−530.912	−	919.566i	−0.552458	−	0.956885i
$962$	−936.039			−0.973013
$963$		0			0
$964$	3149.21	−	1818.20i	3.26682	−	1.88610i
$965$	271.144	+	156.545i	0.280978	+	0.162223i
$966$		0			0
$967$	618.894			0.640014			0.320007	−	0.947415i	$-0.396315\pi$
$967$	618.894			0.640014			0.320007	+	0.947415i	$0.396315\pi$
$968$			886.119i			0.915412i
$969$		0			0
$970$	1050.04	−	1818.72i	1.08251	−	1.87497i
$971$	−100.570	−	174.192i	−0.103574	−	0.179395i	0.809581	−	0.587008i	$-0.199694\pi$
$971$	−100.570	−	174.192i	−0.103574	−	0.179395i	−0.913155	+	0.407613i	$0.866361\pi$
$972$		0			0
$973$		−	703.997i		−	0.723533i
$974$	−795.412	+	459.231i	−0.816645	+	0.471490i
$975$		0			0
$976$	−2939.38	+	1697.05i	−3.01166	+	1.73878i
$977$	249.561	−	432.252i	0.255436	−	0.442428i	−0.709578	−	0.704627i	$-0.751114\pi$
$977$	249.561	−	432.252i	0.255436	−	0.442428i	0.965014	+	0.262199i	$0.0844476\pi$
$978$		0			0
$979$	−146.830	−	84.7721i	−0.149979	−	0.0865905i
$980$	−1303.07	+	752.326i	−1.32966	+	0.767680i
$981$		0			0
$982$	1860.83	+	3223.06i	1.89494	+	3.28214i
$983$	−427.591	−	246.870i	−0.434985	−	0.251139i	0.266483	−	0.963840i	$-0.414138\pi$
$983$	−427.591	−	246.870i	−0.434985	−	0.251139i	−0.701468	+	0.712701i	$0.747472\pi$
$984$		0			0
$985$			690.376i			0.700890i
$986$	−530.549	+	918.938i	−0.538082	+	0.931986i
$987$		0			0
$988$		−	1738.04i		−	1.75915i
$989$	−52.8107	+	111.215i	−0.0533981	+	0.112452i
$990$		0			0
$991$			407.540i			0.411241i	0.978632	+	0.205620i	$0.0659212\pi$
$991$			407.540i			0.411241i	−0.978632	+	0.205620i	$0.934079\pi$
$992$	7133.74	+	4118.67i	7.19127	+	4.15188i
$993$		0			0
$994$	−733.206	−	423.317i	−0.737632	−	0.425872i
$995$	628.243	−	1088.15i	0.631400	−	1.09362i
$996$		0			0
$997$			864.932i			0.867535i	0.901025	+	0.433767i	$0.142816\pi$
$997$			864.932i			0.867535i	−0.901025	+	0.433767i	$0.857184\pi$
$998$	692.560	+	1199.55i	0.693948	+	1.20195i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.3.j.f.37.1	✓	28
3.2	odd	2	inner	387.3.j.f.37.14	yes	28
43.7	odd	6	inner	387.3.j.f.136.14	yes	28
129.50	even	6	inner	387.3.j.f.136.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.3.j.f.37.1	✓	28	1.1	even	1	trivial
387.3.j.f.37.14	yes	28	3.2	odd	2	inner
387.3.j.f.136.1	yes	28	129.50	even	6	inner
387.3.j.f.136.14	yes	28	43.7	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	387.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.98399i q^{2} -11.8722 q^{4} +(-4.48413 - 2.58892i) q^{5} +(-4.28862 + 2.47604i) q^{7} +31.3628i q^{8} +O(q^{10})\)	\(q-3.98399i q^{2} -11.8722 q^{4} +(-4.48413 - 2.58892i) q^{5} +(-4.28862 + 2.47604i) q^{7} +31.3628i q^{8} +(-10.3142 + 17.8648i) q^{10} +12.2169 q^{11} +(-3.29424 - 5.70580i) q^{13} +(9.86452 + 17.0858i) q^{14} +77.4603 q^{16} +(4.47754 + 7.75533i) q^{17} +(-19.2431 - 11.1100i) q^{19} +(53.2365 + 30.7361i) q^{20} -48.6722i q^{22} +(-1.43160 + 2.47960i) q^{23} +(0.904965 + 1.56745i) q^{25} +(-22.7319 + 13.1242i) q^{26} +(50.9154 - 29.3960i) q^{28} +(-25.7572 + 14.8709i) q^{29} +(-22.4879 + 38.9502i) q^{31} -183.150i q^{32} +(30.8972 - 17.8385i) q^{34} +25.6410 q^{35} +(30.8831 + 17.8303i) q^{37} +(-44.2621 + 76.6643i) q^{38} +(81.1956 - 140.635i) q^{40} +73.5446 q^{41} +(42.8615 - 3.44802i) q^{43} -145.042 q^{44} +(9.87869 + 5.70347i) q^{46} +22.4754 q^{47} +(-12.2385 + 21.1977i) q^{49} +(6.24469 - 3.60537i) q^{50} +(39.1099 + 67.7404i) q^{52} +(-45.1133 + 78.1386i) q^{53} +(-54.7824 - 31.6286i) q^{55} +(-77.6555 - 134.503i) q^{56} +(59.2456 + 102.616i) q^{58} +78.3888 q^{59} +(-37.9469 + 21.9087i) q^{61} +(155.177 + 89.5917i) q^{62} -419.828 q^{64} +34.1141i q^{65} +(-59.8966 + 103.744i) q^{67} +(-53.1582 - 92.0728i) q^{68} -102.154i q^{70} +(-37.1638 + 21.4565i) q^{71} +(29.4029 - 16.9758i) q^{73} +(71.0360 - 123.038i) q^{74} +(228.458 + 131.900i) q^{76} +(-52.3939 + 30.2496i) q^{77} +(-42.8246 - 74.1745i) q^{79} +(-347.342 - 200.538i) q^{80} -293.001i q^{82} +(23.3608 - 40.4621i) q^{83} -46.3679i q^{85} +(-13.7369 - 170.760i) q^{86} +383.158i q^{88} +(-12.0185 - 6.93889i) q^{89} +(28.2555 + 16.3133i) q^{91} +(16.9962 - 29.4383i) q^{92} -89.5419i q^{94} +(57.5257 + 99.6374i) q^{95} -101.805 q^{97} +(84.4513 + 48.7580i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 84 q^{4} - 30 q^{7}+O(q^{10}) \) 28 * q - 84 * q^4 - 30 * q^7	\( 28 q - 84 q^{4} - 30 q^{7} + 4 q^{10} - 34 q^{13} + 164 q^{16} - 78 q^{19} + 112 q^{25} + 342 q^{28} - 74 q^{31} + 192 q^{34} - 222 q^{37} + 104 q^{40} + 104 q^{43} + 150 q^{46} + 112 q^{49} - 64 q^{52} - 450 q^{55} + 346 q^{58} - 198 q^{61} - 1264 q^{64} - 26 q^{67} + 342 q^{73} + 282 q^{76} - 48 q^{79} + 684 q^{91} - 480 q^{97}+O(q^{100}) \) 28 * q - 84 * q^4 - 30 * q^7 + 4 * q^10 - 34 * q^13 + 164 * q^16 - 78 * q^19 + 112 * q^25 + 342 * q^28 - 74 * q^31 + 192 * q^34 - 222 * q^37 + 104 * q^40 + 104 * q^43 + 150 * q^46 + 112 * q^49 - 64 * q^52 - 450 * q^55 + 346 * q^58 - 198 * q^61 - 1264 * q^64 - 26 * q^67 + 342 * q^73 + 282 * q^76 - 48 * q^79 + 684 * q^91 - 480 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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