LMFDB - Embedded newform 648.3.h.a.485.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [648,3,Mod(485,648)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(648, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("648.485");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	648.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.6567211305$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			485.9
Character	$\chi$	$=$	648.485
Dual form			648.3.h.a.485.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49306 - 1.33070i) q^{2} +(0.458456 + 3.97364i) q^{4} +3.06253 q^{5} +1.44096 q^{7} +(4.60324 - 6.54295i) q^{8} +O(q^{10})$	\(q+(-1.49306 - 1.33070i) q^{2} +(0.458456 + 3.97364i) q^{4} +3.06253 q^{5} +1.44096 q^{7} +(4.60324 - 6.54295i) q^{8} +(-4.57254 - 4.07532i) q^{10} -17.6558 q^{11} +9.23764i q^{13} +(-2.15144 - 1.91749i) q^{14} +(-15.5796 + 3.64348i) q^{16} +4.69563i q^{17} +16.8874i q^{19} +(1.40404 + 12.1694i) q^{20} +(26.3612 + 23.4947i) q^{22} -39.0706i q^{23} -15.6209 q^{25} +(12.2926 - 13.7924i) q^{26} +(0.660616 + 5.72585i) q^{28} +15.2070 q^{29} -48.7030 q^{31} +(28.1097 + 15.2919i) q^{32} +(6.24849 - 7.01085i) q^{34} +4.41298 q^{35} -14.1853i q^{37} +(22.4721 - 25.2139i) q^{38} +(14.0975 - 20.0380i) q^{40} -10.1435i q^{41} -22.3460i q^{43} +(-8.09442 - 70.1579i) q^{44} +(-51.9914 + 58.3347i) q^{46} -42.5709i q^{47} -46.9236 q^{49} +(23.3229 + 20.7868i) q^{50} +(-36.7071 + 4.23505i) q^{52} -71.2201 q^{53} -54.0715 q^{55} +(6.63307 - 9.42812i) q^{56} +(-22.7050 - 20.2360i) q^{58} -69.9985 q^{59} +103.643i q^{61} +(72.7166 + 64.8093i) q^{62} +(-21.6204 - 60.2375i) q^{64} +28.2906i q^{65} -12.1430i q^{67} +(-18.6587 + 2.15274i) q^{68} +(-6.58884 - 5.87237i) q^{70} +112.880i q^{71} +84.0137 q^{73} +(-18.8764 + 21.1795i) q^{74} +(-67.1044 + 7.74212i) q^{76} -25.4413 q^{77} +45.9651 q^{79} +(-47.7131 + 11.1583i) q^{80} +(-13.4981 + 15.1449i) q^{82} -51.5768 q^{83} +14.3805i q^{85} +(-29.7359 + 33.3639i) q^{86} +(-81.2740 + 115.521i) q^{88} -105.051i q^{89} +13.3111i q^{91} +(155.253 - 17.9121i) q^{92} +(-56.6492 + 63.5609i) q^{94} +51.7181i q^{95} -38.8643 q^{97} +(70.0598 + 62.4415i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{4} + 4 q^{7}+O(q^{10}) $ 44 * q + 2 * q^4 + 4 * q^7	$ 44 q + 2 q^{4} + 4 q^{7} + 4 q^{10} + 2 q^{16} - 14 q^{22} + 144 q^{25} + 28 q^{28} + 4 q^{31} - 18 q^{34} + 112 q^{40} + 72 q^{46} + 144 q^{49} + 84 q^{52} + 92 q^{55} + 76 q^{58} + 2 q^{64} + 8 q^{70} - 8 q^{73} + 126 q^{76} + 4 q^{79} + 186 q^{82} + 154 q^{88} + 372 q^{94} + 4 q^{97}+O(q^{100}) $ 44 * q + 2 * q^4 + 4 * q^7 + 4 * q^10 + 2 * q^16 - 14 * q^22 + 144 * q^25 + 28 * q^28 + 4 * q^31 - 18 * q^34 + 112 * q^40 + 72 * q^46 + 144 * q^49 + 84 * q^52 + 92 * q^55 + 76 * q^58 + 2 * q^64 + 8 * q^70 - 8 * q^73 + 126 * q^76 + 4 * q^79 + 186 * q^82 + 154 * q^88 + 372 * q^94 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.49306	−	1.33070i	−0.746530	−	0.665352i
$2$	−1.49306	−	1.33070i	−0.746530	−	0.665352i
$3$		0			0
$3$		0			0
$4$	0.458456	+	3.97364i	0.114614	+	0.993410i
$5$	3.06253			0.612506			0.306253	−	0.951950i	$-0.400925\pi$
$5$	3.06253			0.612506			0.306253	+	0.951950i	$0.400925\pi$
$6$		0			0
$7$	1.44096			0.205851			0.102926	−	0.994689i	$-0.467180\pi$
$7$	1.44096			0.205851			0.102926	+	0.994689i	$0.467180\pi$
$8$	4.60324	−	6.54295i	0.575404	−	0.817869i
$9$		0			0
$10$	−4.57254	−	4.07532i	−0.457254	−	0.407532i
$11$	−17.6558			−1.60508			−0.802538	−	0.596601i	$-0.796517\pi$
$11$	−17.6558			−1.60508			−0.802538	+	0.596601i	$0.796517\pi$
$12$		0			0
$13$			9.23764i			0.710588i	0.934755	+	0.355294i	$0.115619\pi$
$13$			9.23764i			0.710588i	−0.934755	+	0.355294i	$0.884381\pi$
$14$	−2.15144	−	1.91749i	−0.153674	−	0.136963i
$15$		0			0
$16$	−15.5796	+	3.64348i	−0.973727	+	0.227717i
$17$			4.69563i			0.276213i	0.990417	+	0.138107i	$0.0441017\pi$
$17$			4.69563i			0.276213i	−0.990417	+	0.138107i	$0.955898\pi$
$18$		0			0
$19$			16.8874i			0.888810i	0.895826	+	0.444405i	$0.146585\pi$
$19$			16.8874i			0.888810i	−0.895826	+	0.444405i	$0.853415\pi$
$20$	1.40404	+	12.1694i	0.0702018	+	0.608470i
$21$		0			0
$22$	26.3612	+	23.4947i	1.19824	+	1.06794i
$23$		−	39.0706i		−	1.69872i	−0.527813	−	0.849361i	$-0.676988\pi$
$23$		−	39.0706i		−	1.69872i	0.527813	−	0.849361i	$-0.323012\pi$
$24$		0			0
$25$	−15.6209			−0.624836
$26$	12.2926	−	13.7924i	0.472791	−	0.530475i
$27$		0			0
$28$	0.660616	+	5.72585i	0.0235934	+	0.204495i
$29$	15.2070			0.524379			0.262190	−	0.965016i	$-0.415555\pi$
$29$	15.2070			0.524379			0.262190	+	0.965016i	$0.415555\pi$
$30$		0			0
$31$	−48.7030			−1.57107			−0.785533	−	0.618820i	$-0.787611\pi$
$31$	−48.7030			−1.57107			−0.785533	+	0.618820i	$0.787611\pi$
$32$	28.1097	+	15.2919i	0.878429	+	0.477873i
$33$		0			0
$34$	6.24849	−	7.01085i	0.183779	−	0.206202i
$35$	4.41298			0.126085
$36$		0			0
$37$		−	14.1853i		−	0.383386i	−0.981455	−	0.191693i	$-0.938602\pi$
$37$		−	14.1853i		−	0.383386i	0.981455	−	0.191693i	$-0.0613977\pi$
$38$	22.4721	−	25.2139i	0.591371	−	0.663523i
$39$		0			0
$40$	14.0975	−	20.0380i	0.352439	−	0.500950i
$41$		−	10.1435i		−	0.247404i	−0.992319	−	0.123702i	$-0.960523\pi$
$41$		−	10.1435i		−	0.247404i	0.992319	−	0.123702i	$-0.0394766\pi$
$42$		0			0
$43$		−	22.3460i		−	0.519675i	−0.965652	−	0.259837i	$-0.916331\pi$
$43$		−	22.3460i		−	0.519675i	0.965652	−	0.259837i	$-0.0836689\pi$
$44$	−8.09442	−	70.1579i	−0.183964	−	1.59450i
$45$		0			0
$46$	−51.9914	+	58.3347i	−1.13025	+	1.26815i
$47$		−	42.5709i		−	0.905763i	−0.891571	−	0.452882i	$-0.850396\pi$
$47$		−	42.5709i		−	0.905763i	0.891571	−	0.452882i	$-0.149604\pi$
$48$		0			0
$49$	−46.9236			−0.957625
$50$	23.3229	+	20.7868i	0.466459	+	0.415736i
$51$		0			0
$52$	−36.7071	+	4.23505i	−0.705905	+	0.0814433i
$53$	−71.2201			−1.34378			−0.671888	−	0.740653i	$-0.734516\pi$
$53$	−71.2201			−1.34378			−0.671888	+	0.740653i	$0.734516\pi$
$54$		0			0
$55$	−54.0715			−0.983119
$56$	6.63307	−	9.42812i	0.118448	−	0.168359i
$57$		0			0
$58$	−22.7050	−	20.2360i	−0.391465	−	0.348897i
$59$	−69.9985			−1.18642			−0.593208	−	0.805049i	$-0.702139\pi$
$59$	−69.9985			−1.18642			−0.593208	+	0.805049i	$0.702139\pi$
$60$		0			0
$61$			103.643i			1.69907i	0.527534	+	0.849534i	$0.323117\pi$
$61$			103.643i			1.69907i	−0.527534	+	0.849534i	$0.676883\pi$
$62$	72.7166	+	64.8093i	1.17285	+	1.04531i
$63$		0			0
$64$	−21.6204	−	60.2375i	−0.337819	−	0.941211i
$65$			28.2906i			0.435239i
$66$		0			0
$67$		−	12.1430i		−	0.181239i	−0.995886	−	0.0906197i	$-0.971115\pi$
$67$		−	12.1430i		−	0.181239i	0.995886	−	0.0906197i	$-0.0288848\pi$
$68$	−18.6587	+	2.15274i	−0.274393	+	0.0316579i
$69$		0			0
$70$	−6.58884	−	5.87237i	−0.0941263	−	0.0838910i
$71$			112.880i			1.58985i	0.606705	+	0.794927i	$0.292491\pi$
$71$			112.880i			1.58985i	−0.606705	+	0.794927i	$0.707509\pi$
$72$		0			0
$73$	84.0137			1.15087			0.575436	−	0.817847i	$-0.304832\pi$
$73$	84.0137			1.15087			0.575436	+	0.817847i	$0.304832\pi$
$74$	−18.8764	+	21.1795i	−0.255086	+	0.286209i
$75$		0			0
$76$	−67.1044	+	7.74212i	−0.882953	+	0.101870i
$77$	−25.4413			−0.330407
$78$		0			0
$79$	45.9651			0.581837			0.290918	−	0.956748i	$-0.406039\pi$
$79$	45.9651			0.581837			0.290918	+	0.956748i	$0.406039\pi$
$80$	−47.7131	+	11.1583i	−0.596414	+	0.139478i
$81$		0			0
$82$	−13.4981	+	15.1449i	−0.164610	+	0.184694i
$83$	−51.5768			−0.621408			−0.310704	−	0.950507i	$-0.600565\pi$
$83$	−51.5768			−0.621408			−0.310704	+	0.950507i	$0.600565\pi$
$84$		0			0
$85$			14.3805i			0.169182i
$86$	−29.7359	+	33.3639i	−0.345766	+	0.387953i
$87$		0			0
$88$	−81.2740	+	115.521i	−0.923568	+	1.31274i
$89$		−	105.051i		−	1.18035i	−0.807275	−	0.590176i	$-0.799058\pi$
$89$		−	105.051i		−	1.18035i	0.807275	−	0.590176i	$-0.200942\pi$
$90$		0			0
$91$			13.3111i			0.146275i
$92$	155.253	−	17.9121i	1.68753	−	0.194697i
$93$		0			0
$94$	−56.6492	+	63.5609i	−0.602651	+	0.676179i
$95$			51.7181i			0.544401i
$96$		0			0
$97$	−38.8643			−0.400663			−0.200331	−	0.979728i	$-0.564202\pi$
$97$	−38.8643			−0.400663			−0.200331	+	0.979728i	$0.564202\pi$
$98$	70.0598	+	62.4415i	0.714896	+	0.637158i
$99$		0			0
$100$	−7.16150	−	62.0719i	−0.0716150	−	0.620719i
$101$	−113.144			−1.12024			−0.560118	−	0.828413i	$-0.689244\pi$
$101$	−113.144			−1.12024			−0.560118	+	0.828413i	$0.689244\pi$
$102$		0			0
$103$	30.4098			0.295241			0.147621	−	0.989044i	$-0.452839\pi$
$103$	30.4098			0.295241			0.147621	+	0.989044i	$0.452839\pi$
$104$	60.4414	+	42.5230i	0.581168	+	0.408875i
$105$		0			0
$106$	106.336	+	94.7729i	1.00317	+	0.894084i
$107$	−32.1820			−0.300767			−0.150383	−	0.988628i	$-0.548051\pi$
$107$	−32.1820			−0.300767			−0.150383	+	0.988628i	$0.548051\pi$
$108$		0			0
$109$			111.285i			1.02096i	0.859890	+	0.510480i	$0.170532\pi$
$109$			111.285i			1.02096i	−0.859890	+	0.510480i	$0.829468\pi$
$110$	80.7320	+	71.9532i	0.733928	+	0.654120i
$111$		0			0
$112$	−22.4496	+	5.25010i	−0.200443	+	0.0468759i
$113$			104.060i			0.920884i	0.887690	+	0.460442i	$0.152309\pi$
$113$			104.060i			0.920884i	−0.887690	+	0.460442i	$0.847691\pi$
$114$		0			0
$115$		−	119.655i		−	1.04048i
$116$	6.97174	+	60.4271i	0.0601012	+	0.520924i
$117$		0			0
$118$	104.512	+	93.1473i	0.885695	+	0.789384i
$119$			6.76620i			0.0568589i
$120$		0			0
$121$	190.728			1.57627
$122$	137.918	−	154.745i	1.13048	−	1.26841i
$123$		0			0
$124$	−22.3282	−	193.528i	−0.180066	−	1.56071i
$125$	−124.403			−0.995222
$126$		0			0
$127$	−215.952			−1.70041			−0.850203	−	0.526455i	$-0.823521\pi$
$127$	−215.952			−1.70041			−0.850203	+	0.526455i	$0.823521\pi$
$128$	−47.8776	+	118.709i	−0.374044	+	0.927411i
$129$		0			0
$130$	37.6463	−	42.2395i	0.289587	−	0.324919i
$131$	−69.3808			−0.529625			−0.264812	−	0.964300i	$-0.585310\pi$
$131$	−69.3808			−0.529625			−0.264812	+	0.964300i	$0.585310\pi$
$132$		0			0
$133$			24.3340i			0.182963i
$134$	−16.1588	+	18.1303i	−0.120588	+	0.135301i
$135$		0			0
$136$	30.7233	+	21.6151i	0.225906	+	0.158934i
$137$			86.2214i			0.629354i	0.949199	+	0.314677i	$0.101896\pi$
$137$			86.2214i			0.629354i	−0.949199	+	0.314677i	$0.898104\pi$
$138$		0			0
$139$		−	12.9183i		−	0.0929373i	−0.998920	−	0.0464686i	$-0.985203\pi$
$139$		−	12.9183i		−	0.0929373i	0.998920	−	0.0464686i	$-0.0147968\pi$
$140$	2.02316	+	17.5356i	0.0144511	+	0.125254i
$141$		0			0
$142$	150.209	−	168.536i	1.05781	−	1.18687i
$143$		−	163.098i		−	1.14055i
$144$		0			0
$145$	46.5719			0.321185
$146$	−125.438	−	111.797i	−0.859161	−	0.765735i
$147$		0			0
$148$	56.3671	−	6.50332i	0.380859	−	0.0439413i
$149$	−89.1486			−0.598313			−0.299156	−	0.954204i	$-0.596705\pi$
$149$	−89.1486			−0.598313			−0.299156	+	0.954204i	$0.596705\pi$
$150$		0			0
$151$	−225.047			−1.49038			−0.745189	−	0.666854i	$-0.767641\pi$
$151$	−225.047			−1.49038			−0.745189	+	0.666854i	$0.767641\pi$
$152$	110.493	+	77.7366i	0.726930	+	0.511425i
$153$		0			0
$154$	37.9854	+	33.8549i	0.246659	+	0.219837i
$155$	−149.155			−0.962287
$156$		0			0
$157$			161.672i			1.02976i	0.857263	+	0.514878i	$0.172163\pi$
$157$			161.672i			1.02976i	−0.857263	+	0.514878i	$0.827837\pi$
$158$	−68.6287	−	61.1659i	−0.434359	−	0.387126i
$159$		0			0
$160$	86.0869	+	46.8321i	0.538043	+	0.292700i
$161$		−	56.2991i		−	0.349684i
$162$		0			0
$163$		−	181.252i		−	1.11197i	−0.831191	−	0.555987i	$-0.812340\pi$
$163$		−	181.252i		−	1.11197i	0.831191	−	0.555987i	$-0.187660\pi$
$164$	40.3068	−	4.65037i	0.245773	−	0.0283559i
$165$		0			0
$166$	77.0073	+	68.6335i	0.463899	+	0.413455i
$167$		−	8.83241i		−	0.0528887i	−0.999650	−	0.0264443i	$-0.991582\pi$
$167$		−	8.83241i		−	0.0528887i	0.999650	−	0.0264443i	$-0.00841847\pi$
$168$		0			0
$169$	83.6660			0.495065
$170$	19.1362	−	21.4709i	0.112566	−	0.126300i
$171$		0			0
$172$	88.7950	−	10.2447i	0.516250	−	0.0595620i
$173$	51.2824			0.296430			0.148215	−	0.988955i	$-0.452647\pi$
$173$	51.2824			0.296430			0.148215	+	0.988955i	$0.452647\pi$
$174$		0			0
$175$	−22.5091			−0.128623
$176$	275.071	−	64.3286i	1.56291	−	0.365504i
$177$		0			0
$178$	−139.792	+	156.848i	−0.785349	+	0.881168i
$179$	−11.7809			−0.0658149			−0.0329074	−	0.999458i	$-0.510477\pi$
$179$	−11.7809			−0.0658149			−0.0329074	+	0.999458i	$0.510477\pi$
$180$		0			0
$181$		−	215.066i		−	1.18821i	−0.804387	−	0.594105i	$-0.797506\pi$
$181$		−	215.066i		−	1.18821i	0.804387	−	0.594105i	$-0.202494\pi$
$182$	17.7131	−	19.8742i	0.0973246	−	0.109199i
$183$		0			0
$184$	−255.637	−	179.851i	−1.38933	−	0.977452i
$185$		−	43.4428i		−	0.234826i
$186$		0			0
$187$		−	82.9052i		−	0.443343i
$188$	169.161	−	19.5169i	0.899794	−	0.103813i
$189$		0			0
$190$	68.8215	−	77.2183i	0.362218	−	0.406412i
$191$			64.2197i			0.336229i	0.985767	+	0.168114i	$0.0537678\pi$
$191$			64.2197i			0.336229i	−0.985767	+	0.168114i	$0.946232\pi$
$192$		0			0
$193$	201.268			1.04284			0.521421	−	0.853300i	$-0.325402\pi$
$193$	201.268			1.04284			0.521421	+	0.853300i	$0.325402\pi$
$194$	58.0267	+	51.7168i	0.299107	+	0.266582i
$195$		0			0
$196$	−21.5124	−	186.458i	−0.109757	−	0.951315i
$197$	159.855			0.811448			0.405724	−	0.913996i	$-0.367019\pi$
$197$	159.855			0.811448			0.405724	+	0.913996i	$0.367019\pi$
$198$		0			0
$199$	252.515			1.26892			0.634461	−	0.772955i	$-0.281222\pi$
$199$	252.515			1.26892			0.634461	+	0.772955i	$0.281222\pi$
$200$	−71.9067	+	102.207i	−0.359534	+	0.511034i
$201$		0			0
$202$	168.931	+	150.561i	0.836290	+	0.745352i
$203$	21.9127			0.107944
$204$		0			0
$205$		−	31.0649i		−	0.151536i
$206$	−45.4037	−	40.4665i	−0.220406	−	0.196439i
$207$		0			0
$208$	−33.6571	−	143.919i	−0.161813	−	0.691919i
$209$		−	298.161i		−	1.42661i
$210$		0			0
$211$		−	345.001i		−	1.63508i	−0.575873	−	0.817539i	$-0.695338\pi$
$211$		−	345.001i		−	1.63508i	0.575873	−	0.817539i	$-0.304662\pi$
$212$	−32.6513	−	283.003i	−0.154016	−	1.33492i
$213$		0			0
$214$	48.0497	+	42.8247i	0.224531	+	0.200116i
$215$		−	68.4353i		−	0.318304i
$216$		0			0
$217$	−70.1791			−0.323406
$218$	148.087	−	166.155i	0.679297	−	0.762177i
$219$		0			0
$220$	−24.7894	−	214.861i	−0.112679	−	0.976640i
$221$	−43.3765			−0.196274
$222$		0			0
$223$	80.9474			0.362993			0.181496	−	0.983392i	$-0.441906\pi$
$223$	80.9474			0.362993			0.181496	+	0.983392i	$0.441906\pi$
$224$	40.5049	+	22.0351i	0.180826	+	0.0983708i
$225$		0			0
$226$	138.473	−	155.368i	0.612712	−	0.687468i
$227$	165.633			0.729659			0.364829	−	0.931074i	$-0.381127\pi$
$227$	165.633			0.729659			0.364829	+	0.931074i	$0.381127\pi$
$228$		0			0
$229$		−	10.0886i		−	0.0440549i	−0.999757	−	0.0220274i	$-0.992988\pi$
$229$		−	10.0886i		−	0.0440549i	0.999757	−	0.0220274i	$-0.00701212\pi$
$230$	−159.225	+	178.652i	−0.692284	+	0.776748i
$231$		0			0
$232$	70.0014	−	99.4986i	0.301730	−	0.428873i
$233$			219.759i			0.943170i	0.881821	+	0.471585i	$0.156318\pi$
$233$			219.759i			0.943170i	−0.881821	+	0.471585i	$0.843682\pi$
$234$		0			0
$235$		−	130.375i		−	0.554785i
$236$	−32.0912	−	278.149i	−0.135980	−	1.17860i
$237$		0			0
$238$	9.00381	−	10.1023i	0.0378311	−	0.0424468i
$239$			46.5130i			0.194615i	0.995254	+	0.0973076i	$0.0310231\pi$
$239$			46.5130i			0.194615i	−0.995254	+	0.0973076i	$0.968977\pi$
$240$		0			0
$241$	473.803			1.96599			0.982995	−	0.183634i	$-0.0587862\pi$
$241$	473.803			1.96599			0.982995	+	0.183634i	$0.0587862\pi$
$242$	−284.769	−	253.803i	−1.17673	−	1.04877i
$243$		0			0
$244$	−411.841	+	47.5158i	−1.68787	+	0.194737i
$245$	−143.705			−0.586551
$246$		0			0
$247$	−156.000			−0.631577
$248$	−224.192	+	318.662i	−0.903998	+	1.28493i
$249$		0			0
$250$	185.741	+	165.543i	0.742963	+	0.662173i
$251$	−151.118			−0.602065			−0.301033	−	0.953614i	$-0.597331\pi$
$251$	−151.118			−0.602065			−0.301033	+	0.953614i	$0.597331\pi$
$252$		0			0
$253$			689.824i			2.72658i
$254$	322.429	+	287.368i	1.26940	+	1.13137i
$255$		0			0
$256$	229.450	−	113.528i	0.896290	−	0.443469i
$257$		−	300.498i		−	1.16925i	−0.811303	−	0.584626i	$-0.801241\pi$
$257$		−	300.498i		−	1.16925i	0.811303	−	0.584626i	$-0.198759\pi$
$258$		0			0
$259$		−	20.4404i		−	0.0789204i
$260$	−112.417	+	12.9700i	−0.432371	+	0.0498845i
$261$		0			0
$262$	103.590	+	92.3253i	0.395381	+	0.352387i
$263$			49.2004i			0.187074i	0.995616	+	0.0935369i	$0.0298173\pi$
$263$			49.2004i			0.187074i	−0.995616	+	0.0935369i	$0.970183\pi$
$264$		0			0
$265$	−218.114			−0.823071
$266$	32.3814	−	36.3322i	0.121734	−	0.136587i
$267$		0			0
$268$	48.2521	−	5.56705i	0.180045	−	0.0207726i
$269$	−151.922			−0.564767			−0.282383	−	0.959302i	$-0.591125\pi$
$269$	−151.922			−0.564767			−0.282383	+	0.959302i	$0.591125\pi$
$270$		0			0
$271$	114.040			0.420811			0.210405	−	0.977614i	$-0.432522\pi$
$271$	114.040			0.420811			0.210405	+	0.977614i	$0.432522\pi$
$272$	−17.1084	−	73.1562i	−0.0628986	−	0.268956i
$273$		0			0
$274$	114.735	−	128.734i	0.418742	−	0.469831i
$275$	275.800			1.00291
$276$		0			0
$277$			131.081i			0.473217i	0.971605	+	0.236608i	$0.0760359\pi$
$277$			131.081i			0.473217i	−0.971605	+	0.236608i	$0.923964\pi$
$278$	−17.1904	+	19.2878i	−0.0618360	+	0.0693805i
$279$		0			0
$280$	20.3140	−	28.8739i	0.0725499	−	0.103121i
$281$		−	174.139i		−	0.619711i	−0.950784	−	0.309856i	$-0.899719\pi$
$281$		−	174.139i		−	0.619711i	0.950784	−	0.309856i	$-0.100281\pi$
$282$		0			0
$283$		−	118.115i		−	0.417369i	−0.977983	−	0.208685i	$-0.933082\pi$
$283$		−	118.115i		−	0.417369i	0.977983	−	0.208685i	$-0.0669182\pi$
$284$	−448.543	+	51.7503i	−1.57938	+	0.182220i
$285$		0			0
$286$	−217.035	+	243.515i	−0.758865	+	0.851453i
$287$		−	14.6164i		−	0.0509283i
$288$		0			0
$289$	266.951			0.923706
$290$	−69.5346	−	61.9734i	−0.239775	−	0.213701i
$291$		0			0
$292$	38.5166	+	333.840i	0.131906	+	1.14329i
$293$	−32.7323			−0.111714			−0.0558571	−	0.998439i	$-0.517789\pi$
$293$	−32.7323			−0.111714			−0.0558571	+	0.998439i	$0.517789\pi$
$294$		0			0
$295$	−214.373			−0.726687
$296$	−92.8135	−	65.2981i	−0.313559	−	0.220602i
$297$		0			0
$298$	133.104	+	118.630i	0.446658	+	0.398088i
$299$	360.920			1.20709
$300$		0			0
$301$		−	32.1997i		−	0.106976i
$302$	336.009	+	299.471i	1.11261	+	0.991625i
$303$		0			0
$304$	−61.5288	−	263.099i	−0.202397	−	0.865458i
$305$			317.410i			1.04069i
$306$		0			0
$307$		−	309.352i		−	1.00766i	−0.863802	−	0.503831i	$-0.831923\pi$
$307$		−	309.352i		−	1.00766i	0.863802	−	0.503831i	$-0.168077\pi$
$308$	−11.6637	−	101.095i	−0.0378692	−	0.328229i
$309$		0			0
$310$	222.697	+	198.480i	0.718376	+	0.640260i
$311$		−	126.641i		−	0.407206i	−0.979054	−	0.203603i	$-0.934735\pi$
$311$		−	126.641i		−	0.407206i	0.979054	−	0.203603i	$-0.0652651\pi$
$312$		0			0
$313$	197.265			0.630241			0.315120	−	0.949052i	$-0.397955\pi$
$313$	197.265			0.630241			0.315120	+	0.949052i	$0.397955\pi$
$314$	215.137	−	241.386i	0.685150	−	0.768744i
$315$		0			0
$316$	21.0730	+	182.649i	0.0666866	+	0.578003i
$317$	191.400			0.603785			0.301892	−	0.953342i	$-0.402382\pi$
$317$	191.400			0.603785			0.301892	+	0.953342i	$0.402382\pi$
$318$		0			0
$319$	−268.492			−0.841668
$320$	−66.2133	−	184.479i	−0.206917	−	0.576497i
$321$		0			0
$322$	−74.9174	+	84.0580i	−0.232663	+	0.261050i
$323$	−79.2969			−0.245501
$324$		0			0
$325$		−	144.300i		−	0.444001i
$326$	−241.192	+	270.620i	−0.739854	+	0.830122i
$327$		0			0
$328$	−66.3687	−	46.6931i	−0.202344	−	0.142357i
$329$		−	61.3429i		−	0.186452i
$330$		0			0
$331$			375.392i			1.13411i	0.823679	+	0.567057i	$0.191918\pi$
$331$			375.392i			1.13411i	−0.823679	+	0.567057i	$0.808082\pi$
$332$	−23.6457	−	204.948i	−0.0712220	−	0.617313i
$333$		0			0
$334$	−11.7533	+	13.1873i	−0.0351896	+	0.0394830i
$335$		−	37.1884i		−	0.111010i
$336$		0			0
$337$	23.3081			0.0691635			0.0345818	−	0.999402i	$-0.488990\pi$
$337$	23.3081			0.0691635			0.0345818	+	0.999402i	$0.488990\pi$
$338$	−124.918	−	111.335i	−0.369581	−	0.329392i
$339$		0			0
$340$	−57.1429	+	6.59283i	−0.168067	+	0.0193907i
$341$	859.893			2.52168
$342$		0			0
$343$	−138.222			−0.402980
$344$	−146.209	−	102.864i	−0.425026	−	0.299023i
$345$		0			0
$346$	−76.5677	−	68.2417i	−0.221294	−	0.197230i
$347$	66.9756			0.193013			0.0965067	−	0.995332i	$-0.469233\pi$
$347$	66.9756			0.193013			0.0965067	+	0.995332i	$0.469233\pi$
$348$		0			0
$349$		−	346.531i		−	0.992925i	−0.868058	−	0.496463i	$-0.834632\pi$
$349$		−	346.531i		−	0.992925i	0.868058	−	0.496463i	$-0.165368\pi$
$350$	33.6074	+	29.9529i	0.0960212	+	0.0855797i
$351$		0			0
$352$	−496.301	−	269.992i	−1.40994	−	0.767023i
$353$			588.364i			1.66675i	0.552705	+	0.833377i	$0.313596\pi$
$353$			588.364i			1.66675i	−0.552705	+	0.833377i	$0.686404\pi$
$354$		0			0
$355$			345.697i			0.973796i
$356$	417.436	−	48.1614i	1.17257	−	0.135285i
$357$		0			0
$358$	17.5895	+	15.6768i	0.0491328	+	0.0437901i
$359$			325.201i			0.905854i	0.891548	+	0.452927i	$0.149620\pi$
$359$			325.201i			0.905854i	−0.891548	+	0.452927i	$0.850380\pi$
$360$		0			0
$361$	75.8162			0.210017
$362$	−286.189	+	321.107i	−0.790578	+	0.887035i
$363$		0			0
$364$	−52.8934	+	6.10253i	−0.145311	+	0.0167652i
$365$	257.295			0.704917
$366$		0			0
$367$	−205.397			−0.559664			−0.279832	−	0.960049i	$-0.590279\pi$
$367$	−205.397			−0.559664			−0.279832	+	0.960049i	$0.590279\pi$
$368$	142.353	+	608.706i	0.386828	+	1.65409i
$369$		0			0
$370$	−57.8095	+	64.8627i	−0.156242	+	0.175305i
$371$	−102.625			−0.276618
$372$		0			0
$373$			380.451i			1.01998i	0.860182	+	0.509988i	$0.170350\pi$
$373$			380.451i			1.01998i	−0.860182	+	0.509988i	$0.829650\pi$
$374$	−110.322	+	123.782i	−0.294979	+	0.330969i
$375$		0			0
$376$	−278.539	−	195.964i	−0.740796	−	0.521180i
$377$			140.477i			0.372617i
$378$		0			0
$379$		−	122.536i		−	0.323315i	−0.986847	−	0.161658i	$-0.948316\pi$
$379$		−	122.536i		−	0.323315i	0.986847	−	0.161658i	$-0.0516840\pi$
$380$	−205.509	+	23.7105i	−0.540814	+	0.0623960i
$381$		0			0
$382$	85.4574	−	95.8839i	0.223710	−	0.251005i
$383$			162.192i			0.423477i	0.977326	+	0.211738i	$0.0679125\pi$
$383$			162.192i			0.423477i	−0.977326	+	0.211738i	$0.932087\pi$
$384$		0			0
$385$	−77.9148			−0.202376
$386$	−300.506	−	267.829i	−0.778513	−	0.693857i
$387$		0			0
$388$	−17.8176	−	154.433i	−0.0459215	−	0.398022i
$389$	−258.066			−0.663408			−0.331704	−	0.943383i	$-0.607624\pi$
$389$	−258.066			−0.663408			−0.331704	+	0.943383i	$0.607624\pi$
$390$		0			0
$391$	183.461			0.469210
$392$	−216.001	+	307.019i	−0.551022	+	0.783212i
$393$		0			0
$394$	−238.673	−	212.720i	−0.605770	−	0.539898i
$395$	140.770			0.356379
$396$		0			0
$397$			214.037i			0.539137i	0.962981	+	0.269568i	$0.0868810\pi$
$397$			214.037i			0.539137i	−0.962981	+	0.269568i	$0.913119\pi$
$398$	−377.021	−	336.023i	−0.947288	−	0.844279i
$399$		0			0
$400$	243.368	−	56.9144i	0.608420	−	0.142286i
$401$			270.214i			0.673850i	0.941531	+	0.336925i	$0.109387\pi$
$401$			270.214i			0.673850i	−0.941531	+	0.336925i	$0.890613\pi$
$402$		0			0
$403$		−	449.901i		−	1.11638i
$404$	−51.8715	−	449.593i	−0.128395	−	1.11285i
$405$		0			0
$406$	−32.7169	−	29.1592i	−0.0805835	−	0.0718208i
$407$			250.453i			0.615363i
$408$		0			0
$409$	11.6548			0.0284958			0.0142479	−	0.999898i	$-0.495465\pi$
$409$	11.6548			0.0284958			0.0142479	+	0.999898i	$0.495465\pi$
$410$	−41.3382	+	46.3818i	−0.100825	+	0.113126i
$411$		0			0
$412$	13.9416	+	120.838i	0.0338388	+	0.293296i
$413$	−100.865			−0.244225
$414$		0			0
$415$	−157.956			−0.380616
$416$	−141.262	+	259.667i	−0.339571	+	0.624201i
$417$		0			0
$418$	−396.764	+	445.172i	−0.949196	+	1.06500i
$419$	−272.082			−0.649361			−0.324681	−	0.945824i	$-0.605257\pi$
$419$	−272.082			−0.649361			−0.324681	+	0.945824i	$0.605257\pi$
$420$		0			0
$421$			501.154i			1.19039i	0.803582	+	0.595195i	$0.202925\pi$
$421$			501.154i			1.19039i	−0.803582	+	0.595195i	$0.797075\pi$
$422$	−459.095	+	515.108i	−1.08790	+	1.22063i
$423$		0			0
$424$	−327.843	+	465.990i	−0.773215	+	1.09903i
$425$		−	73.3499i		−	0.172588i
$426$		0			0
$427$			149.345i			0.349755i
$428$	−14.7540	−	127.880i	−0.0344721	−	0.298785i
$429$		0			0
$430$	−91.0671	+	102.178i	−0.211784	+	0.237623i
$431$		−	701.705i		−	1.62809i	−0.580805	−	0.814043i	$-0.697262\pi$
$431$		−	701.705i		−	1.62809i	0.580805	−	0.814043i	$-0.302738\pi$
$432$		0			0
$433$	−387.204			−0.894236			−0.447118	−	0.894475i	$-0.647550\pi$
$433$	−387.204			−0.894236			−0.447118	+	0.894475i	$0.647550\pi$
$434$	104.782	+	93.3875i	0.241432	+	0.215179i
$435$		0			0
$436$	−442.205	+	51.0191i	−1.01423	+	0.117016i
$437$	659.800			1.50984
$438$		0			0
$439$	−324.269			−0.738653			−0.369327	−	0.929300i	$-0.620412\pi$
$439$	−324.269			−0.738653			−0.369327	+	0.929300i	$0.620412\pi$
$440$	−248.904	+	353.787i	−0.565691	+	0.804062i
$441$		0			0
$442$	64.7637	+	57.7213i	0.146524	+	0.130591i
$443$	10.1018			0.0228032			0.0114016	−	0.999935i	$-0.496371\pi$
$443$	10.1018			0.0228032			0.0114016	+	0.999935i	$0.496371\pi$
$444$		0			0
$445$		−	321.723i		−	0.722973i
$446$	−120.859	−	107.717i	−0.270985	−	0.241518i
$447$		0			0
$448$	−31.1542	−	86.7997i	−0.0695406	−	0.193749i
$449$		−	71.1875i		−	0.158547i	−0.996853	−	0.0792734i	$-0.974740\pi$
$449$		−	71.1875i		−	0.158547i	0.996853	−	0.0792734i	$-0.0252600\pi$
$450$		0			0
$451$			179.093i			0.397102i
$452$	−413.497	+	47.7069i	−0.914816	+	0.105546i
$453$		0			0
$454$	−247.299	−	220.408i	−0.544712	−	0.485480i
$455$			40.7655i			0.0895946i
$456$		0			0
$457$	−334.849			−0.732711			−0.366355	−	0.930475i	$-0.619395\pi$
$457$	−334.849			−0.732711			−0.366355	+	0.930475i	$0.619395\pi$
$458$	−13.4249	+	15.0628i	−0.0293120	+	0.0328883i
$459$		0			0
$460$	475.466	−	54.8565i	1.03362	−	0.119253i
$461$	811.172			1.75959			0.879796	−	0.475351i	$-0.157679\pi$
$461$	811.172			1.75959			0.879796	+	0.475351i	$0.157679\pi$
$462$		0			0
$463$	−102.320			−0.220995			−0.110497	−	0.993876i	$-0.535244\pi$
$463$	−102.320			−0.220995			−0.110497	+	0.993876i	$0.535244\pi$
$464$	−236.919	+	55.4064i	−0.510602	+	0.119410i
$465$		0			0
$466$	292.433	−	328.113i	0.627540	−	0.704104i
$467$	211.289			0.452439			0.226220	−	0.974076i	$-0.427363\pi$
$467$	211.289			0.452439			0.226220	+	0.974076i	$0.427363\pi$
$468$		0			0
$469$		−	17.4976i		−	0.0373084i
$470$	−173.490	+	194.657i	−0.369127	+	0.414164i
$471$		0			0
$472$	−322.220	+	457.997i	−0.682669	+	0.970333i
$473$			394.537i			0.834117i
$474$		0			0
$475$		−	263.796i		−	0.555361i
$476$	−26.8865	+	3.10201i	−0.0564842	+	0.00651682i
$477$		0			0
$478$	61.8950	−	69.4467i	0.129488	−	0.145286i
$479$		−	462.267i		−	0.965066i	−0.875878	−	0.482533i	$-0.839717\pi$
$479$		−	462.267i		−	0.965066i	0.875878	−	0.482533i	$-0.160283\pi$
$480$		0			0
$481$	131.038			0.272429
$482$	−707.417	−	630.492i	−1.46767	−	1.30807i
$483$		0			0
$484$	87.4406	+	757.886i	0.180662	+	1.56588i
$485$	−119.023			−0.245408
$486$		0			0
$487$	−581.940			−1.19495			−0.597474	−	0.801888i	$-0.703829\pi$
$487$	−581.940			−1.19495			−0.597474	+	0.801888i	$0.703829\pi$
$488$	678.132	+	477.094i	1.38961	+	0.977651i
$489$		0			0
$490$	214.560	+	191.229i	0.437878	+	0.390263i
$491$	578.179			1.17755			0.588777	−	0.808296i	$-0.299610\pi$
$491$	578.179			1.17755			0.588777	+	0.808296i	$0.299610\pi$
$492$		0			0
$493$			71.4064i			0.144841i
$494$	232.917	+	207.589i	0.471491	+	0.420221i
$495$		0			0
$496$	758.776	−	177.448i	1.52979	−	0.357759i
$497$			162.655i			0.327273i
$498$		0			0
$499$		−	798.964i		−	1.60113i	−0.599246	−	0.800565i	$-0.704533\pi$
$499$		−	798.964i		−	1.60113i	0.599246	−	0.800565i	$-0.295467\pi$
$500$	−57.0332	−	494.332i	−0.114066	−	0.988664i
$501$		0			0
$502$	225.629	+	201.094i	0.449460	+	0.400585i
$503$			252.819i			0.502622i	0.967906	+	0.251311i	$0.0808616\pi$
$503$			252.819i			0.502622i	−0.967906	+	0.251311i	$0.919138\pi$
$504$		0			0
$505$	−346.507			−0.686152
$506$	917.951	−	1029.95i	1.81413	−	2.03547i
$507$		0			0
$508$	−99.0043	−	858.114i	−0.194890	−	1.68920i
$509$	−461.382			−0.906448			−0.453224	−	0.891397i	$-0.649726\pi$
$509$	−461.382			−0.906448			−0.453224	+	0.891397i	$0.649726\pi$
$510$		0			0
$511$	121.060			0.236909
$512$	−493.655	−	135.826i	−0.964170	−	0.265285i
$513$		0			0
$514$	−399.873	+	448.661i	−0.777963	+	0.872881i
$515$	93.1311			0.180837
$516$		0			0
$517$			751.624i			1.45382i
$518$	−27.2001	+	30.5187i	−0.0525098	+	0.0589164i
$519$		0			0
$520$	185.104	+	130.228i	0.355969	+	0.250439i
$521$		−	765.575i		−	1.46943i	−0.678374	−	0.734717i	$-0.737315\pi$
$521$		−	765.575i		−	1.46943i	0.678374	−	0.734717i	$-0.262685\pi$
$522$		0			0
$523$			1007.67i			1.92671i	0.268222	+	0.963357i	$0.413564\pi$
$523$			1007.67i			1.92671i	−0.268222	+	0.963357i	$0.586436\pi$
$524$	−31.8080	−	275.694i	−0.0607024	−	0.526134i
$525$		0			0
$526$	65.4711	−	73.4591i	0.124470	−	0.139656i
$527$		−	228.691i		−	0.433949i
$528$		0			0
$529$	−997.512			−1.88566
$530$	325.657	+	290.245i	0.614447	+	0.547632i
$531$		0			0
$532$	−96.6947	+	11.1561i	−0.181757	+	0.0209701i
$533$	93.7024			0.175802
$534$		0			0
$535$	−98.5584			−0.184221
$536$	−79.4513	−	55.8973i	−0.148230	−	0.104286i
$537$		0			0
$538$	226.829	+	202.163i	0.421615	+	0.375769i
$539$	828.476			1.53706
$540$		0			0
$541$		−	367.842i		−	0.679930i	−0.940438	−	0.339965i	$-0.889585\pi$
$541$		−	367.842i		−	0.679930i	0.940438	−	0.339965i	$-0.110415\pi$
$542$	−170.268	−	151.753i	−0.314148	−	0.279987i
$543$		0			0
$544$	−71.8053	+	131.993i	−0.131995	+	0.242634i
$545$			340.813i			0.625344i
$546$		0			0
$547$			674.370i			1.23285i	0.787413	+	0.616426i	$0.211420\pi$
$547$			674.370i			1.23285i	−0.787413	+	0.616426i	$0.788580\pi$
$548$	−342.613	+	39.5287i	−0.625206	+	0.0721327i
$549$		0			0
$550$	−411.786	−	367.008i	−0.748702	−	0.667288i
$551$			256.806i			0.466073i
$552$		0			0
$553$	66.2338			0.119772
$554$	174.430	−	195.712i	0.314856	−	0.353271i
$555$		0			0
$556$	51.3326	−	5.92246i	0.0923248	−	0.0106519i
$557$	−552.503			−0.991927			−0.495963	−	0.868344i	$-0.665185\pi$
$557$	−552.503			−0.991927			−0.495963	+	0.868344i	$0.665185\pi$
$558$		0			0
$559$	206.424			0.369274
$560$	−68.7526	+	16.0786i	−0.122773	+	0.0287118i
$561$		0			0
$562$	−231.727	+	260.000i	−0.412326	+	0.462633i
$563$	144.946			0.257453			0.128726	−	0.991680i	$-0.458911\pi$
$563$	144.946			0.257453			0.128726	+	0.991680i	$0.458911\pi$
$564$		0			0
$565$			318.687i			0.564047i
$566$	−157.177	+	176.353i	−0.277697	+	0.311578i
$567$		0			0
$568$	738.566	+	519.612i	1.30029	+	0.914809i
$569$		−	624.449i		−	1.09745i	−0.836003	−	0.548725i	$-0.815114\pi$
$569$		−	624.449i		−	1.09745i	0.836003	−	0.548725i	$-0.184886\pi$
$570$		0			0
$571$			522.294i			0.914700i	0.889287	+	0.457350i	$0.151201\pi$
$571$			522.294i			0.914700i	−0.889287	+	0.457350i	$0.848799\pi$
$572$	648.094	−	74.7734i	1.13303	−	0.130723i
$573$		0			0
$574$	−19.4501	+	21.8232i	−0.0338853	+	0.0380195i
$575$			610.318i			1.06142i
$576$		0			0
$577$	17.0045			0.0294706			0.0147353	−	0.999891i	$-0.495309\pi$
$577$	17.0045			0.0294706			0.0147353	+	0.999891i	$0.495309\pi$
$578$	−398.574	−	355.233i	−0.689574	−	0.614590i
$579$		0			0
$580$	21.3512	+	185.060i	0.0368123	+	0.319069i
$581$	−74.3201			−0.127918
$582$		0			0
$583$	1257.45			2.15686
$584$	386.735	−	549.698i	0.662217	−	0.941263i
$585$		0			0
$586$	48.8712	+	43.5569i	0.0833980	+	0.0743292i
$587$	−122.224			−0.208218			−0.104109	−	0.994566i	$-0.533199\pi$
$587$	−122.224			−0.208218			−0.104109	+	0.994566i	$0.533199\pi$
$588$		0			0
$589$		−	822.467i		−	1.39638i
$590$	320.071	+	285.266i	0.542493	+	0.483502i
$591$		0			0
$592$	51.6837	+	221.001i	0.0873035	+	0.373313i
$593$		−	811.371i		−	1.36825i	−0.729366	−	0.684124i	$-0.760185\pi$
$593$		−	811.371i		−	1.36825i	0.729366	−	0.684124i	$-0.239815\pi$
$594$		0			0
$595$			20.7217i			0.0348264i
$596$	−40.8707	−	354.244i	−0.0685750	−	0.594370i
$597$		0			0
$598$	−538.875	−	480.278i	−0.901129	−	0.803140i
$599$			1003.26i			1.67489i	0.546518	+	0.837447i	$0.315953\pi$
$599$			1003.26i			1.67489i	−0.546518	+	0.837447i	$0.684047\pi$
$600$		0			0
$601$	408.811			0.680218			0.340109	−	0.940386i	$-0.389536\pi$
$601$	408.811			0.680218			0.340109	+	0.940386i	$0.389536\pi$
$602$	−42.8482	+	48.0760i	−0.0711764	+	0.0798605i
$603$		0			0
$604$	−103.174	−	894.256i	−0.170818	−	1.48056i
$605$	584.112			0.965474
$606$		0			0
$607$	635.975			1.04774			0.523868	−	0.851800i	$-0.324489\pi$
$607$	635.975			1.04774			0.523868	+	0.851800i	$0.324489\pi$
$608$	−258.241	+	474.700i	−0.424739	+	0.780756i
$609$		0			0
$610$	422.379	−	473.913i	0.692425	−	0.776906i
$611$	393.254			0.643624
$612$		0			0
$613$		−	1029.22i		−	1.67899i	−0.543367	−	0.839495i	$-0.682851\pi$
$613$		−	1029.22i		−	1.67899i	0.543367	−	0.839495i	$-0.317149\pi$
$614$	−411.656	+	461.882i	−0.670450	+	0.752250i
$615$		0			0
$616$	−117.112	+	166.461i	−0.190118	+	0.270230i
$617$		−	532.843i		−	0.863603i	−0.901969	−	0.431801i	$-0.857878\pi$
$617$		−	532.843i		−	0.863603i	0.901969	−	0.431801i	$-0.142122\pi$
$618$		0			0
$619$		−	89.0355i		−	0.143838i	−0.997410	−	0.0719188i	$-0.977088\pi$
$619$		−	89.0355i		−	0.143838i	0.997410	−	0.0719188i	$-0.0229123\pi$
$620$	−68.3808	−	592.687i	−0.110292	−	0.955946i
$621$		0			0
$622$	−168.522	+	189.083i	−0.270935	+	0.303991i
$623$		−	151.375i		−	0.242977i
$624$		0			0
$625$	9.53535			0.0152566
$626$	−294.529	−	262.502i	−0.470494	−	0.419332i
$627$		0			0
$628$	−642.425	+	74.1194i	−1.02297	+	0.118024i
$629$	66.6087			0.105896
$630$		0			0
$631$	8.45150			0.0133938			0.00669691	−	0.999978i	$-0.497868\pi$
$631$	8.45150			0.0133938			0.00669691	+	0.999978i	$0.497868\pi$
$632$	211.588	−	300.748i	0.334792	−	0.475866i
$633$		0			0
$634$	−285.771	−	254.696i	−0.450744	−	0.401729i
$635$	−661.358			−1.04151
$636$		0			0
$637$		−	433.464i		−	0.680477i
$638$	400.875	+	357.283i	0.628331	+	0.560005i
$639$		0			0
$640$	−146.627	+	363.549i	−0.229104	+	0.568045i
$641$		−	621.134i		−	0.969008i	−0.874789	−	0.484504i	$-0.839000\pi$
$641$		−	621.134i		−	0.969008i	0.874789	−	0.484504i	$-0.161000\pi$
$642$		0			0
$643$			931.443i			1.44859i	0.689490	+	0.724295i	$0.257835\pi$
$643$			931.443i			1.44859i	−0.689490	+	0.724295i	$0.742165\pi$
$644$	223.712	−	25.8107i	0.347380	−	0.0400787i
$645$		0			0
$646$	118.395	+	105.521i	0.183274	+	0.163345i
$647$		−	168.057i		−	0.259749i	−0.991530	−	0.129874i	$-0.958543\pi$
$647$		−	168.057i		−	0.259749i	0.991530	−	0.129874i	$-0.0414574\pi$
$648$		0			0
$649$	1235.88			1.90429
$650$	−192.021	+	215.449i	−0.295417	+	0.331460i
$651$		0			0
$652$	720.229	−	83.0959i	1.10465	−	0.127448i
$653$	121.170			0.185559			0.0927796	−	0.995687i	$-0.470425\pi$
$653$	121.170			0.185559			0.0927796	+	0.995687i	$0.470425\pi$
$654$		0			0
$655$	−212.481			−0.324398
$656$	36.9578	+	158.033i	0.0563381	+	0.240904i
$657$		0			0
$658$	−81.6292	+	91.5886i	−0.124056	+	0.139192i
$659$	163.245			0.247716			0.123858	−	0.992300i	$-0.460473\pi$
$659$	163.245			0.247716			0.123858	+	0.992300i	$0.460473\pi$
$660$		0			0
$661$		−	238.641i		−	0.361030i	−0.983572	−	0.180515i	$-0.942224\pi$
$661$		−	238.641i		−	0.361030i	0.983572	−	0.180515i	$-0.0577765\pi$
$662$	499.535	−	560.482i	0.754585	−	0.846650i
$663$		0			0
$664$	−237.420	+	337.465i	−0.357561	+	0.508230i
$665$			74.5237i			0.112066i
$666$		0			0
$667$		−	594.146i		−	0.890774i
$668$	35.0968	−	4.04927i	0.0525401	−	0.00606178i
$669$		0			0
$670$	−49.4868	+	55.5246i	−0.0738609	+	0.0828725i
$671$		−	1829.91i		−	2.72713i
$672$		0			0
$673$	−190.214			−0.282636			−0.141318	−	0.989964i	$-0.545134\pi$
$673$	−190.214			−0.282636			−0.141318	+	0.989964i	$0.545134\pi$
$674$	−34.8004	−	31.0162i	−0.0516327	−	0.0460181i
$675$		0			0
$676$	38.3572	+	332.459i	0.0567414	+	0.491803i
$677$	−1256.32			−1.85571			−0.927857	−	0.372937i	$-0.878351\pi$
$677$	−1256.32			−1.85571			−0.927857	+	0.372937i	$0.878351\pi$
$678$		0			0
$679$	−56.0018			−0.0824769
$680$	94.0909	+	66.1968i	0.138369	+	0.0973483i
$681$		0			0
$682$	−1283.87	−	1144.26i	−1.88251	−	1.67780i
$683$	−415.707			−0.608648			−0.304324	−	0.952569i	$-0.598431\pi$
$683$	−415.707			−0.608648			−0.304324	+	0.952569i	$0.598431\pi$
$684$		0			0
$685$			264.056i			0.385483i
$686$	206.374	+	183.932i	0.300836	+	0.268123i
$687$		0			0
$688$	81.4172	+	348.143i	0.118339	+	0.506021i
$689$		−	657.906i		−	0.954871i
$690$		0			0
$691$		−	609.942i		−	0.882695i	−0.897336	−	0.441348i	$-0.854501\pi$
$691$		−	609.942i		−	0.882695i	0.897336	−	0.441348i	$-0.145499\pi$
$692$	23.5107	+	203.778i	0.0339750	+	0.294477i
$693$		0			0
$694$	−99.9986	−	89.1247i	−0.144090	−	0.128422i
$695$		−	39.5626i		−	0.0569247i
$696$		0			0
$697$	47.6303			0.0683362
$698$	−461.130	+	517.391i	−0.660644	+	0.741248i
$699$		0			0
$700$	−10.3194	−	89.4430i	−0.0147420	−	0.127776i
$701$	−922.743			−1.31632			−0.658162	−	0.752877i	$-0.728666\pi$
$701$	−922.743			−1.31632			−0.658162	+	0.752877i	$0.728666\pi$
$702$		0			0
$703$	239.552			0.340757
$704$	381.727	+	1063.54i	0.542226	+	1.51071i
$705$		0			0
$706$	782.939	−	878.463i	1.10898	−	1.24428i
$707$	−163.036			−0.230602
$708$		0			0
$709$			261.447i			0.368755i	0.982856	+	0.184377i	$0.0590268\pi$
$709$			261.447i			0.368755i	−0.982856	+	0.184377i	$0.940973\pi$
$710$	460.021	−	516.147i	0.647917	−	0.726968i
$711$		0			0
$712$	−687.346	−	483.576i	−0.965373	−	0.679180i
$713$			1902.86i			2.66880i
$714$		0			0
$715$		−	499.493i		−	0.698592i
$716$	−5.40101	−	46.8129i	−0.00754331	−	0.0653812i
$717$		0			0
$718$	432.747	−	485.545i	0.602711	−	0.676247i
$719$			995.870i			1.38508i	0.721381	+	0.692538i	$0.243508\pi$
$719$			995.870i			1.38508i	−0.721381	+	0.692538i	$0.756492\pi$
$720$		0			0
$721$	43.8193			0.0607757
$722$	−113.198	−	100.889i	−0.156784	−	0.139735i
$723$		0			0
$724$	854.596	−	98.5983i	1.18038	−	0.136186i
$725$	−237.547			−0.327651
$726$		0			0
$727$	818.322			1.12561			0.562807	−	0.826588i	$-0.309721\pi$
$727$	818.322			1.12561			0.562807	+	0.826588i	$0.309721\pi$
$728$	87.0936	+	61.2739i	0.119634	+	0.0841675i
$729$		0			0
$730$	−384.156	−	342.383i	−0.526241	−	0.469018i
$731$	104.928			0.143541
$732$		0			0
$733$		−	657.950i		−	0.897613i	−0.893629	−	0.448807i	$-0.851849\pi$
$733$		−	657.950i		−	0.897613i	0.893629	−	0.448807i	$-0.148151\pi$
$734$	306.670	+	273.322i	0.417806	+	0.372373i
$735$		0			0
$736$	597.466	−	1098.26i	0.811774	−	1.49221i
$737$			214.396i			0.290903i
$738$		0			0
$739$			971.543i			1.31467i	0.753597	+	0.657336i	$0.228317\pi$
$739$			971.543i			1.31467i	−0.753597	+	0.657336i	$0.771683\pi$
$740$	172.626	−	19.9166i	0.233279	−	0.0269143i
$741$		0			0
$742$	153.226	+	136.564i	0.206504	+	0.184048i
$743$			899.657i			1.21084i	0.795905	+	0.605422i	$0.206996\pi$
$743$			899.657i			1.21084i	−0.795905	+	0.605422i	$0.793004\pi$
$744$		0			0
$745$	−273.020			−0.366470
$746$	506.267	−	568.036i	0.678643	−	0.761442i
$747$		0			0
$748$	329.435	−	38.0084i	0.440422	−	0.0508133i
$749$	−46.3730			−0.0619132
$750$		0			0
$751$	797.369			1.06174			0.530871	−	0.847453i	$-0.321865\pi$
$751$	797.369			1.06174			0.530871	+	0.847453i	$0.321865\pi$
$752$	155.106	+	663.239i	0.206258	+	0.881966i
$753$		0			0
$754$	186.933	−	209.740i	0.247922	−	0.278170i
$755$	−689.213			−0.912865
$756$		0			0
$757$		−	577.348i		−	0.762680i	−0.924435	−	0.381340i	$-0.875463\pi$
$757$		−	577.348i		−	0.762680i	0.924435	−	0.381340i	$-0.124537\pi$
$758$	−163.060	+	182.954i	−0.215118	+	0.241365i
$759$		0			0
$760$	338.389	+	238.071i	0.445249	+	0.313251i
$761$			689.287i			0.905765i	0.891570	+	0.452882i	$0.149604\pi$
$761$			689.287i			0.905765i	−0.891570	+	0.452882i	$0.850396\pi$
$762$		0			0
$763$			160.357i			0.210166i
$764$	−255.186	+	29.4419i	−0.334013	+	0.0385365i
$765$		0			0
$766$	215.829	−	242.162i	0.281761	−	0.316138i
$767$		−	646.621i		−	0.843052i
$768$		0			0
$769$	−1505.38			−1.95759			−0.978793	−	0.204850i	$-0.934329\pi$
$769$	−1505.38			−1.95759			−0.978793	+	0.204850i	$0.934329\pi$
$770$	116.332	+	103.682i	0.151080	+	0.134651i
$771$		0			0
$772$	92.2727	+	799.768i	0.119524	+	1.03597i
$773$	584.466			0.756101			0.378051	−	0.925785i	$-0.376595\pi$
$773$	584.466			0.756101			0.378051	+	0.925785i	$0.376595\pi$
$774$		0			0
$775$	760.786			0.981659
$776$	−178.901	+	254.287i	−0.230543	+	0.327690i
$777$		0			0
$778$	385.308	+	343.409i	0.495254	+	0.441400i
$779$	171.298			0.219895
$780$		0			0
$781$		−	1992.98i		−	2.55184i
$782$	−273.918	−	244.132i	−0.350279	−	0.312189i
$783$		0			0
$784$	731.053	−	170.965i	0.932466	−	0.218068i
$785$			495.125i			0.630732i
$786$		0			0
$787$			257.351i			0.327003i	0.986543	+	0.163501i	$0.0522788\pi$
$787$			257.351i			0.327003i	−0.986543	+	0.163501i	$0.947721\pi$
$788$	73.2866	+	635.207i	0.0930033	+	0.806100i
$789$		0			0
$790$	−210.177	−	187.323i	−0.266047	−	0.237117i
$791$			149.946i			0.189565i
$792$		0			0
$793$	−957.418			−1.20734
$794$	284.820	−	319.570i	0.358716	−	0.402482i
$795$		0			0
$796$	115.767	+	1003.41i	0.145436	+	1.26056i
$797$	893.657			1.12128			0.560638	−	0.828061i	$-0.310556\pi$
$797$	893.657			1.12128			0.560638	+	0.828061i	$0.310556\pi$
$798$		0			0
$799$	199.897			0.250184
$800$	−439.099	−	238.874i	−0.548874	−	0.298593i
$801$		0			0
$802$	359.575	−	403.446i	0.448348	−	0.503049i
$803$	−1483.33			−1.84724
$804$		0			0
$805$		−	172.418i		−	0.214184i
$806$	−598.685	+	671.729i	−0.742785	+	0.833411i
$807$		0			0
$808$	−520.828	+	740.295i	−0.644589	+	0.916207i
$809$			1243.52i			1.53711i	0.639784	+	0.768554i	$0.279024\pi$
$809$			1243.52i			1.53711i	−0.639784	+	0.768554i	$0.720976\pi$
$810$		0			0
$811$			257.659i			0.317705i	0.987302	+	0.158852i	$0.0507794\pi$
$811$			257.659i			0.317705i	−0.987302	+	0.158852i	$0.949221\pi$
$812$	10.0460	+	87.0730i	0.0123719	+	0.107233i
$813$		0			0
$814$	333.278	−	373.941i	0.409433	−	0.459387i
$815$		−	555.089i		−	0.681091i
$816$		0			0
$817$	377.366			0.461892
$818$	−17.4013	−	15.5090i	−0.0212729	−	0.0189597i
$819$		0			0
$820$	123.441	−	14.2419i	0.150538	−	0.0173682i
$821$	−997.784			−1.21533			−0.607664	−	0.794194i	$-0.707893\pi$
$821$	−997.784			−1.21533			−0.607664	+	0.794194i	$0.707893\pi$
$822$		0			0
$823$	−318.613			−0.387137			−0.193568	−	0.981087i	$-0.562006\pi$
$823$	−318.613			−0.387137			−0.193568	+	0.981087i	$0.562006\pi$
$824$	139.984	−	198.970i	0.169883	−	0.241469i
$825$		0			0
$826$	150.597	+	134.221i	0.182321	+	0.162496i
$827$	−279.151			−0.337547			−0.168773	−	0.985655i	$-0.553981\pi$
$827$	−279.151			−0.337547			−0.168773	+	0.985655i	$0.553981\pi$
$828$		0			0
$829$			444.345i			0.536001i	0.963419	+	0.268000i	$0.0863628\pi$
$829$			444.345i			0.536001i	−0.963419	+	0.268000i	$0.913637\pi$
$830$	235.837	+	210.192i	0.284141	+	0.253244i
$831$		0			0
$832$	556.452	−	199.722i	0.668813	−	0.240050i
$833$		−	220.336i		−	0.264509i
$834$		0			0
$835$		−	27.0495i		−	0.0323946i
$836$	1184.78	−	136.694i	1.41721	−	0.163509i
$837$		0			0
$838$	406.235	+	362.061i	0.484768	+	0.432054i
$839$			113.742i			0.135569i	0.997700	+	0.0677845i	$0.0215930\pi$
$839$			113.742i			0.135569i	−0.997700	+	0.0677845i	$0.978407\pi$
$840$		0			0
$841$	−609.747			−0.725027
$842$	666.887	−	748.253i	0.792028	−	0.888661i
$843$		0			0
$844$	1370.91	−	158.168i	1.62430	−	0.187403i
$845$	256.230			0.303230
$846$		0			0
$847$	274.832			0.324477
$848$	1109.58	−	259.489i	1.30847	−	0.306001i
$849$		0			0
$850$	−97.6070	+	109.516i	−0.114832	+	0.128842i
$851$	−554.227			−0.651265
$852$		0			0
$853$			733.694i			0.860133i	0.902797	+	0.430067i	$0.141510\pi$
$853$			733.694i			0.860133i	−0.902797	+	0.430067i	$0.858490\pi$
$854$	198.735	−	222.982i	0.232710	−	0.261103i
$855$		0			0
$856$	−148.141	+	210.565i	−0.173062	+	0.245988i
$857$		−	956.875i		−	1.11654i	−0.829659	−	0.558270i	$-0.811465\pi$
$857$		−	956.875i		−	1.11654i	0.829659	−	0.558270i	$-0.188535\pi$
$858$		0			0
$859$			825.873i			0.961435i	0.876876	+	0.480717i	$0.159624\pi$
$859$			825.873i			0.961435i	−0.876876	+	0.480717i	$0.840376\pi$
$860$	271.937	−	31.3746i	0.316206	−	0.0364821i
$861$		0			0
$862$	−933.762	+	1047.69i	−1.08325	+	1.21542i
$863$		−	945.401i		−	1.09548i	−0.836648	−	0.547741i	$-0.815488\pi$
$863$		−	945.401i		−	1.09548i	0.836648	−	0.547741i	$-0.184512\pi$
$864$		0			0
$865$	157.054			0.181565
$866$	578.119	+	515.254i	0.667574	+	0.594981i
$867$		0			0
$868$	−32.1740	−	278.866i	−0.0370668	−	0.321275i
$869$	−811.552			−0.933892
$870$		0			0
$871$	112.173			0.128787
$872$	728.130	+	512.269i	0.835011	+	0.587465i
$873$		0			0
$874$	−985.121	−	877.999i	−1.12714	−	1.00458i
$875$	−179.259			−0.204868
$876$		0			0
$877$		−	847.547i		−	0.966416i	−0.875506	−	0.483208i	$-0.839472\pi$
$877$		−	847.547i		−	0.966416i	0.875506	−	0.483208i	$-0.160528\pi$
$878$	484.153	+	431.506i	0.551427	+	0.491464i
$879$		0			0
$880$	842.415	−	197.008i	0.957290	−	0.223873i
$881$			716.539i			0.813324i	0.913579	+	0.406662i	$0.133307\pi$
$881$			716.539i			0.813324i	−0.913579	+	0.406662i	$0.866693\pi$
$882$		0			0
$883$		−	915.122i		−	1.03638i	−0.855266	−	0.518189i	$-0.826606\pi$
$883$		−	915.122i		−	1.03638i	0.855266	−	0.518189i	$-0.173394\pi$
$884$	−19.8862	−	172.363i	−0.0224957	−	0.194980i
$885$		0			0
$886$	−15.0826	−	13.4425i	−0.0170233	−	0.0151722i
$887$			57.1916i			0.0644776i	0.999480	+	0.0322388i	$0.0102637\pi$
$887$			57.1916i			0.0644776i	−0.999480	+	0.0322388i	$0.989736\pi$
$888$		0			0
$889$	−311.177			−0.350031
$890$	−428.118	+	480.352i	−0.481031	+	0.539721i
$891$		0			0
$892$	37.1108	+	321.656i	0.0416041	+	0.360601i
$893$	718.911			0.805051
$894$		0			0
$895$	−36.0793			−0.0403120
$896$	−68.9897	+	171.054i	−0.0769974	+	0.190909i
$897$		0			0
$898$	−94.7294	+	106.287i	−0.105489	+	0.118360i
$899$	−740.627			−0.823834
$900$		0			0
$901$		−	334.423i		−	0.371169i
$902$	238.319	−	267.396i	0.264212	−	0.296448i
$903$		0			0
$904$	680.859	+	479.012i	0.753163	+	0.529881i
$905$		−	658.647i		−	0.727786i
$906$		0			0
$907$			1539.82i			1.69770i	0.528631	+	0.848852i	$0.322706\pi$
$907$			1539.82i			1.69770i	−0.528631	+	0.848852i	$0.677294\pi$
$908$	75.9352	+	658.164i	0.0836291	+	0.724850i
$909$		0			0
$910$	54.2468	−	60.8654i	0.0596119	−	0.0668850i
$911$			888.075i			0.974835i	0.873169	+	0.487418i	$0.162061\pi$
$911$			888.075i			0.974835i	−0.873169	+	0.487418i	$0.837939\pi$
$912$		0			0
$913$	910.632			0.997406
$914$	499.949	+	445.585i	0.546991	+	0.487511i
$915$		0			0
$916$	40.0883	−	4.62516i	0.0437646	−	0.00504931i
$917$	−99.9749			−0.109024
$918$		0			0
$919$	1135.32			1.23539			0.617695	−	0.786418i	$-0.288067\pi$
$919$	1135.32			1.23539			0.617695	+	0.786418i	$0.288067\pi$
$920$	−782.896	−	550.800i	−0.850974	−	0.598695i
$921$		0			0
$922$	−1211.13	−	1079.43i	−1.31359	−	1.17075i
$923$	−1042.74			−1.12973
$924$		0			0
$925$			221.587i			0.239553i
$926$	152.771	+	136.158i	0.164979	+	0.147039i
$927$		0			0
$928$	427.464	+	232.545i	0.460630	+	0.250587i
$929$		−	1215.41i		−	1.30830i	−0.756367	−	0.654148i	$-0.773027\pi$
$929$		−	1215.41i		−	1.30830i	0.756367	−	0.654148i	$-0.226973\pi$
$930$		0			0
$931$		−	792.418i		−	0.851147i
$932$	−873.241	+	100.750i	−0.936954	+	0.108100i
$933$		0			0
$934$	−315.467	−	281.163i	−0.337759	−	0.301031i
$935$		−	253.900i		−	0.271551i
$936$		0			0
$937$	−551.201			−0.588262			−0.294131	−	0.955765i	$-0.595030\pi$
$937$	−551.201			−0.588262			−0.294131	+	0.955765i	$0.595030\pi$
$938$	−23.2841	+	26.1250i	−0.0248232	+	0.0278518i
$939$		0			0
$940$	518.062	−	59.7710i	0.551129	−	0.0635862i
$941$	−1369.24			−1.45509			−0.727543	−	0.686062i	$-0.759338\pi$
$941$	−1369.24			−1.45509			−0.727543	+	0.686062i	$0.759338\pi$
$942$		0			0
$943$	−396.314			−0.420270
$944$	1090.55	−	255.038i	1.15525	−	0.270167i
$945$		0			0
$946$	525.012	−	589.068i	0.554981	−	0.622693i
$947$	924.838			0.976597			0.488299	−	0.872677i	$-0.337618\pi$
$947$	924.838			0.976597			0.488299	+	0.872677i	$0.337618\pi$
$948$		0			0
$949$			776.089i			0.817796i
$950$	−351.035	+	393.864i	−0.369510	+	0.414593i
$951$		0			0
$952$	44.2709	+	31.1464i	0.0465031	+	0.0327168i
$953$		−	279.545i		−	0.293331i	−0.989186	−	0.146666i	$-0.953146\pi$
$953$		−	279.545i		−	0.293331i	0.989186	−	0.146666i	$-0.0468541\pi$
$954$		0			0
$955$			196.675i			0.205942i
$956$	−184.826	+	21.3242i	−0.193333	+	0.0223056i
$957$		0			0
$958$	−615.140	+	690.192i	−0.642109	+	0.720451i
$959$			124.242i			0.129553i
$960$		0			0
$961$	1410.99			1.46825
$962$	−195.648	−	174.373i	−0.203376	−	0.181261i
$963$		0			0
$964$	217.218	+	1882.72i	0.225330	+	1.95303i
$965$	616.391			0.638747
$966$		0			0
$967$	2.56721			0.00265482			0.00132741	−	0.999999i	$-0.499577\pi$
$967$	2.56721			0.00265482			0.00132741	+	0.999999i	$0.499577\pi$
$968$	877.968	−	1247.93i	0.906992	−	1.28918i
$969$		0			0
$970$	177.709	+	158.384i	0.183205	+	0.163283i
$971$	−1053.61			−1.08508			−0.542540	−	0.840030i	$-0.682537\pi$
$971$	−1053.61			−1.08508			−0.542540	+	0.840030i	$0.682537\pi$
$972$		0			0
$973$		−	18.6147i		−	0.0191313i
$974$	868.871	+	774.390i	0.892065	+	0.795061i
$975$		0			0
$976$	−377.621	−	1614.72i	−0.386907	−	1.65443i
$977$			788.865i			0.807436i	0.914884	+	0.403718i	$0.132282\pi$
$977$			788.865i			0.807436i	−0.914884	+	0.403718i	$0.867718\pi$
$978$		0			0
$979$			1854.77i			1.89455i
$980$	−65.8824	−	571.032i	−0.0672270	−	0.582686i
$981$		0			0
$982$	−863.256	−	769.385i	−0.879079	−	0.783488i
$983$			544.960i			0.554385i	0.960814	+	0.277192i	$0.0894039\pi$
$983$			544.960i			0.554385i	−0.960814	+	0.277192i	$0.910596\pi$
$984$		0			0
$985$	489.561			0.497017
$986$	95.0207	−	106.614i	0.0963699	−	0.108128i
$987$		0			0
$988$	−71.5189	−	619.886i	−0.0723876	−	0.627415i
$989$	−873.072			−0.882782
$990$		0			0
$991$	830.022			0.837560			0.418780	−	0.908088i	$-0.362458\pi$
$991$	830.022			0.837560			0.418780	+	0.908088i	$0.362458\pi$
$992$	−1369.03	−	744.764i	−1.38007	−	0.750770i
$993$		0			0
$994$	216.445	−	242.854i	0.217752	−	0.244319i
$995$	773.336			0.777222
$996$		0			0
$997$		−	1282.56i		−	1.28642i	−0.765690	−	0.643210i	$-0.777602\pi$
$997$		−	1282.56i		−	1.28642i	0.765690	−	0.643210i	$-0.222398\pi$
$998$	−1063.18	+	1192.90i	−1.06531	+	1.19529i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.3.h.a.485.9		44
3.2	odd	2	inner	648.3.h.a.485.36		44
4.3	odd	2		2592.3.h.a.1457.29		44
8.3	odd	2		2592.3.h.a.1457.15		44
8.5	even	2	inner	648.3.h.a.485.35		44
9.2	odd	6		216.3.j.a.125.12		44
9.4	even	3		216.3.j.a.197.20		44
9.5	odd	6		72.3.j.a.29.3	yes	44
9.7	even	3		72.3.j.a.5.11	yes	44
12.11	even	2		2592.3.h.a.1457.16		44
24.5	odd	2	inner	648.3.h.a.485.10		44
24.11	even	2		2592.3.h.a.1457.30		44
36.7	odd	6		288.3.n.a.113.13		44
36.11	even	6		864.3.n.a.17.15		44
36.23	even	6		288.3.n.a.209.10		44
36.31	odd	6		864.3.n.a.305.8		44
72.5	odd	6		72.3.j.a.29.11	yes	44
72.11	even	6		864.3.n.a.17.8		44
72.13	even	6		216.3.j.a.197.12		44
72.29	odd	6		216.3.j.a.125.20		44
72.43	odd	6		288.3.n.a.113.10		44
72.59	even	6		288.3.n.a.209.13		44
72.61	even	6		72.3.j.a.5.3	✓	44
72.67	odd	6		864.3.n.a.305.15		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.3	✓	44	72.61	even	6
72.3.j.a.5.11	yes	44	9.7	even	3
72.3.j.a.29.3	yes	44	9.5	odd	6
72.3.j.a.29.11	yes	44	72.5	odd	6
216.3.j.a.125.12		44	9.2	odd	6
216.3.j.a.125.20		44	72.29	odd	6
216.3.j.a.197.12		44	72.13	even	6
216.3.j.a.197.20		44	9.4	even	3
288.3.n.a.113.10		44	72.43	odd	6
288.3.n.a.113.13		44	36.7	odd	6
288.3.n.a.209.10		44	36.23	even	6
288.3.n.a.209.13		44	72.59	even	6
648.3.h.a.485.9		44	1.1	even	1	trivial
648.3.h.a.485.10		44	24.5	odd	2	inner
648.3.h.a.485.35		44	8.5	even	2	inner
648.3.h.a.485.36		44	3.2	odd	2	inner
864.3.n.a.17.8		44	72.11	even	6
864.3.n.a.17.15		44	36.11	even	6
864.3.n.a.305.8		44	36.31	odd	6
864.3.n.a.305.15		44	72.67	odd	6
2592.3.h.a.1457.15		44	8.3	odd	2
2592.3.h.a.1457.16		44	12.11	even	2
2592.3.h.a.1457.29		44	4.3	odd	2
2592.3.h.a.1457.30		44	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	648.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49306 - 1.33070i) q^{2} +(0.458456 + 3.97364i) q^{4} +3.06253 q^{5} +1.44096 q^{7} +(4.60324 - 6.54295i) q^{8} +O(q^{10})\)	\(q+(-1.49306 - 1.33070i) q^{2} +(0.458456 + 3.97364i) q^{4} +3.06253 q^{5} +1.44096 q^{7} +(4.60324 - 6.54295i) q^{8} +(-4.57254 - 4.07532i) q^{10} -17.6558 q^{11} +9.23764i q^{13} +(-2.15144 - 1.91749i) q^{14} +(-15.5796 + 3.64348i) q^{16} +4.69563i q^{17} +16.8874i q^{19} +(1.40404 + 12.1694i) q^{20} +(26.3612 + 23.4947i) q^{22} -39.0706i q^{23} -15.6209 q^{25} +(12.2926 - 13.7924i) q^{26} +(0.660616 + 5.72585i) q^{28} +15.2070 q^{29} -48.7030 q^{31} +(28.1097 + 15.2919i) q^{32} +(6.24849 - 7.01085i) q^{34} +4.41298 q^{35} -14.1853i q^{37} +(22.4721 - 25.2139i) q^{38} +(14.0975 - 20.0380i) q^{40} -10.1435i q^{41} -22.3460i q^{43} +(-8.09442 - 70.1579i) q^{44} +(-51.9914 + 58.3347i) q^{46} -42.5709i q^{47} -46.9236 q^{49} +(23.3229 + 20.7868i) q^{50} +(-36.7071 + 4.23505i) q^{52} -71.2201 q^{53} -54.0715 q^{55} +(6.63307 - 9.42812i) q^{56} +(-22.7050 - 20.2360i) q^{58} -69.9985 q^{59} +103.643i q^{61} +(72.7166 + 64.8093i) q^{62} +(-21.6204 - 60.2375i) q^{64} +28.2906i q^{65} -12.1430i q^{67} +(-18.6587 + 2.15274i) q^{68} +(-6.58884 - 5.87237i) q^{70} +112.880i q^{71} +84.0137 q^{73} +(-18.8764 + 21.1795i) q^{74} +(-67.1044 + 7.74212i) q^{76} -25.4413 q^{77} +45.9651 q^{79} +(-47.7131 + 11.1583i) q^{80} +(-13.4981 + 15.1449i) q^{82} -51.5768 q^{83} +14.3805i q^{85} +(-29.7359 + 33.3639i) q^{86} +(-81.2740 + 115.521i) q^{88} -105.051i q^{89} +13.3111i q^{91} +(155.253 - 17.9121i) q^{92} +(-56.6492 + 63.5609i) q^{94} +51.7181i q^{95} -38.8643 q^{97} +(70.0598 + 62.4415i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{4} + 4 q^{7}+O(q^{10}) \) 44 * q + 2 * q^4 + 4 * q^7	\( 44 q + 2 q^{4} + 4 q^{7} + 4 q^{10} + 2 q^{16} - 14 q^{22} + 144 q^{25} + 28 q^{28} + 4 q^{31} - 18 q^{34} + 112 q^{40} + 72 q^{46} + 144 q^{49} + 84 q^{52} + 92 q^{55} + 76 q^{58} + 2 q^{64} + 8 q^{70} - 8 q^{73} + 126 q^{76} + 4 q^{79} + 186 q^{82} + 154 q^{88} + 372 q^{94} + 4 q^{97}+O(q^{100}) \) 44 * q + 2 * q^4 + 4 * q^7 + 4 * q^10 + 2 * q^16 - 14 * q^22 + 144 * q^25 + 28 * q^28 + 4 * q^31 - 18 * q^34 + 112 * q^40 + 72 * q^46 + 144 * q^49 + 84 * q^52 + 92 * q^55 + 76 * q^58 + 2 * q^64 + 8 * q^70 - 8 * q^73 + 126 * q^76 + 4 * q^79 + 186 * q^82 + 154 * q^88 + 372 * q^94 + 4 * q^97

Introduction

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