LMFDB - Embedded newform 252.4.bm.a.173.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(173,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.173");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.bm (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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.16
Character	$\chi$	$=$	252.173
Dual form			252.4.bm.a.185.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.64863 + 4.47043i) q^{3} -7.63023 q^{5} +(-0.685930 + 18.5076i) q^{7} +(-12.9695 + 23.6810i) q^{9} +O(q^{10})$	\(q+(2.64863 + 4.47043i) q^{3} -7.63023 q^{5} +(-0.685930 + 18.5076i) q^{7} +(-12.9695 + 23.6810i) q^{9} -33.1281i q^{11} +(-31.2793 + 18.0591i) q^{13} +(-20.2097 - 34.1104i) q^{15} +(-24.8660 - 43.0692i) q^{17} +(-16.5348 - 9.54640i) q^{19} +(-84.5535 + 45.9532i) q^{21} +41.0939i q^{23} -66.7796 q^{25} +(-140.216 + 4.74292i) q^{27} +(70.5972 + 40.7593i) q^{29} +(-185.203 - 106.927i) q^{31} +(148.097 - 87.7442i) q^{33} +(5.23380 - 141.217i) q^{35} +(-94.2188 + 163.192i) q^{37} +(-163.580 - 92.0002i) q^{39} +(101.721 + 176.186i) q^{41} +(116.716 - 202.159i) q^{43} +(98.9605 - 180.692i) q^{45} +(-145.633 - 252.244i) q^{47} +(-342.059 - 25.3898i) q^{49} +(126.677 - 225.236i) q^{51} +(-3.42470 + 1.97725i) q^{53} +252.775i q^{55} +(-1.11816 - 99.2028i) q^{57} +(-278.792 + 482.882i) q^{59} +(160.458 - 92.6404i) q^{61} +(-429.382 - 256.278i) q^{63} +(238.669 - 137.795i) q^{65} +(-261.260 + 452.516i) q^{67} +(-183.707 + 108.842i) q^{69} +876.821i q^{71} +(-765.387 + 441.896i) q^{73} +(-176.874 - 298.534i) q^{75} +(613.121 + 22.7236i) q^{77} +(408.120 + 706.885i) q^{79} +(-392.583 - 614.263i) q^{81} +(276.079 - 478.183i) q^{83} +(189.733 + 328.628i) q^{85} +(4.77410 + 423.557i) q^{87} +(225.239 - 390.125i) q^{89} +(-312.775 - 591.291i) q^{91} +(-12.5243 - 1111.15i) q^{93} +(126.165 + 72.8412i) q^{95} +(337.678 + 194.959i) q^{97} +(784.509 + 429.656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 - 30 * q^9	$ 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	2.64863	+	4.47043i	0.509729	+	0.860335i
$3$	2.64863	+	4.47043i	0.509729	+	0.860335i
$4$		0			0
$5$	−7.63023			−0.682469			−0.341234	−	0.939978i	$-0.610845\pi$
$5$	−7.63023			−0.682469			−0.341234	+	0.939978i	$0.610845\pi$
$6$		0			0
$7$	−0.685930	+	18.5076i	−0.0370367	+	0.999314i
$7$	−0.685930	+	18.5076i	−0.0370367	+	0.999314i
$8$		0			0
$9$	−12.9695	+	23.6810i	−0.480353	+	0.877075i
$10$		0			0
$11$		−	33.1281i		−	0.908046i	−0.890990	−	0.454023i	$-0.849988\pi$
$11$		−	33.1281i		−	0.908046i	0.890990	−	0.454023i	$-0.150012\pi$
$12$		0			0
$13$	−31.2793	+	18.0591i	−0.667333	+	0.385285i	−0.795065	−	0.606524i	$-0.792563\pi$
$13$	−31.2793	+	18.0591i	−0.667333	+	0.385285i	0.127732	+	0.991809i	$0.459230\pi$
$14$		0			0
$15$	−20.2097	−	34.1104i	−0.347874	−	0.587152i
$16$		0			0
$17$	−24.8660	−	43.0692i	−0.354758	−	0.614459i	0.632318	−	0.774709i	$-0.282104\pi$
$17$	−24.8660	−	43.0692i	−0.354758	−	0.614459i	−0.987077	+	0.160249i	$0.948770\pi$
$18$		0			0
$19$	−16.5348	−	9.54640i	−0.199650	−	0.115268i	0.396842	−	0.917887i	$-0.370106\pi$
$19$	−16.5348	−	9.54640i	−0.199650	−	0.115268i	−0.596492	+	0.802619i	$0.703439\pi$
$20$		0			0
$21$	−84.5535	+	45.9532i	−0.878623	+	0.477515i
$22$		0			0
$23$			41.0939i			0.372551i	0.982498	+	0.186275i	$0.0596416\pi$
$23$			41.0939i			0.372551i	−0.982498	+	0.186275i	$0.940358\pi$
$24$		0			0
$25$	−66.7796			−0.534237
$26$		0			0
$27$	−140.216	+	4.74292i	−0.999428	+	0.0338065i
$28$		0			0
$29$	70.5972	+	40.7593i	0.452054	+	0.260994i	0.708697	−	0.705513i	$-0.249283\pi$
$29$	70.5972	+	40.7593i	0.452054	+	0.260994i	−0.256643	+	0.966506i	$0.582616\pi$
$30$		0			0
$31$	−185.203	−	106.927i	−1.07302	−	0.619506i	−0.144012	−	0.989576i	$-0.546000\pi$
$31$	−185.203	−	106.927i	−1.07302	−	0.619506i	−0.929004	+	0.370070i	$0.879334\pi$
$32$		0			0
$33$	148.097	−	87.7442i	0.781224	−	0.462857i
$34$		0			0
$35$	5.23380	−	141.217i	0.0252764	−	0.682000i
$36$		0			0
$37$	−94.2188	+	163.192i	−0.418634	+	0.725096i	−0.995802	−	0.0915294i	$-0.970824\pi$
$37$	−94.2188	+	163.192i	−0.418634	+	0.725096i	0.577168	+	0.816625i	$0.304158\pi$
$38$		0			0
$39$	−163.580	−	92.0002i	−0.671633	−	0.377739i
$40$		0			0
$41$	101.721	+	176.186i	0.387468	+	0.671114i	0.992108	−	0.125385i	$-0.0400166\pi$
$41$	101.721	+	176.186i	0.387468	+	0.671114i	−0.604641	+	0.796498i	$0.706683\pi$
$42$		0			0
$43$	116.716	−	202.159i	0.413932	−	0.716951i	−0.581384	−	0.813629i	$-0.697489\pi$
$43$	116.716	−	202.159i	0.413932	−	0.716951i	0.995316	+	0.0966784i	$0.0308218\pi$
$44$		0			0
$45$	98.9605	−	180.692i	0.327826	−	0.598576i
$46$		0			0
$47$	−145.633	−	252.244i	−0.451974	−	0.782842i	0.546534	−	0.837437i	$-0.315947\pi$
$47$	−145.633	−	252.244i	−0.451974	−	0.782842i	−0.998509	+	0.0545944i	$0.982613\pi$
$48$		0			0
$49$	−342.059	−	25.3898i	−0.997257	−	0.0740226i
$50$		0			0
$51$	126.677	−	225.236i	0.347810	−	0.618419i
$52$		0			0
$53$	−3.42470	+	1.97725i	−0.00887582	+	0.00512446i	−0.504431	−	0.863452i	$-0.668298\pi$
$53$	−3.42470	+	1.97725i	−0.00887582	+	0.00512446i	0.495556	+	0.868576i	$0.334965\pi$
$54$		0			0
$55$			252.775i			0.619713i
$56$		0			0
$57$	−1.11816	−	99.2028i	−0.00259831	−	0.230522i
$58$		0			0
$59$	−278.792	+	482.882i	−0.615180	+	1.06552i	0.375173	+	0.926955i	$0.377583\pi$
$59$	−278.792	+	482.882i	−0.615180	+	1.06552i	−0.990353	+	0.138568i	$0.955750\pi$
$60$		0			0
$61$	160.458	−	92.6404i	0.336795	−	0.194449i	−0.322059	−	0.946720i	$-0.604375\pi$
$61$	160.458	−	92.6404i	0.336795	−	0.194449i	0.658854	+	0.752271i	$0.271041\pi$
$62$		0			0
$63$	−429.382	−	256.278i	−0.858683	−	0.512507i
$64$		0			0
$65$	238.669	−	137.795i	0.455434	−	0.262945i
$66$		0			0
$67$	−261.260	+	452.516i	−0.476388	+	0.825128i	−0.999634	−	0.0270537i	$-0.991388\pi$
$67$	−261.260	+	452.516i	−0.476388	+	0.825128i	0.523246	+	0.852182i	$0.324721\pi$
$68$		0			0
$69$	−183.707	+	108.842i	−0.320518	+	0.189900i
$70$		0			0
$71$			876.821i			1.46563i	0.680429	+	0.732814i	$0.261793\pi$
$71$			876.821i			1.46563i	−0.680429	+	0.732814i	$0.738207\pi$
$72$		0			0
$73$	−765.387	+	441.896i	−1.22715	+	0.708494i	−0.966432	−	0.256922i	$-0.917292\pi$
$73$	−765.387	+	441.896i	−1.22715	+	0.708494i	−0.260715	+	0.965416i	$0.583958\pi$
$74$		0			0
$75$	−176.874	−	298.534i	−0.272316	−	0.459622i
$76$		0			0
$77$	613.121	+	22.7236i	0.907423	+	0.0336310i
$78$		0			0
$79$	408.120	+	706.885i	0.581229	+	1.00672i	0.995334	+	0.0964894i	$0.0307614\pi$
$79$	408.120	+	706.885i	0.581229	+	1.00672i	−0.414105	+	0.910229i	$0.635905\pi$
$80$		0			0
$81$	−392.583	−	614.263i	−0.538523	−	0.842611i
$82$		0			0
$83$	276.079	−	478.183i	0.365104	−	0.632378i	−0.623689	−	0.781672i	$-0.714367\pi$
$83$	276.079	−	478.183i	0.365104	−	0.632378i	0.988793	+	0.149295i	$0.0477002\pi$
$84$		0			0
$85$	189.733	+	328.628i	0.242111	+	0.419349i
$86$		0			0
$87$	4.77410	+	423.557i	0.00588319	+	0.521954i
$88$		0			0
$89$	225.239	−	390.125i	0.268261	−	0.464642i	−0.700152	−	0.713994i	$-0.746884\pi$
$89$	225.239	−	390.125i	0.268261	−	0.464642i	0.968413	+	0.249352i	$0.0802176\pi$
$90$		0			0
$91$	−312.775	−	591.291i	−0.360305	−	0.681145i
$92$		0			0
$93$	−12.5243	−	1111.15i	−0.0139646	−	1.23893i
$94$		0			0
$95$	126.165	+	72.8412i	0.136255	+	0.0786668i
$96$		0			0
$97$	337.678	+	194.959i	0.353464	+	0.204073i	0.666210	−	0.745764i	$-0.267915\pi$
$97$	337.678	+	194.959i	0.353464	+	0.204073i	−0.312746	+	0.949837i	$0.601249\pi$
$98$		0			0
$99$	784.509	+	429.656i	0.796425	+	0.436182i
$100$		0			0
$101$	1185.50			1.16794			0.583968	−	0.811777i	$-0.301499\pi$
$101$	1185.50			1.16794			0.583968	+	0.811777i	$0.301499\pi$
$102$		0			0
$103$			151.620i			0.145044i	0.997367	+	0.0725220i	$0.0231047\pi$
$103$			151.620i			0.145044i	−0.997367	+	0.0725220i	$0.976895\pi$
$104$		0			0
$105$	645.163	−	350.634i	0.599633	−	0.325889i
$106$		0			0
$107$	1653.68	+	954.753i	1.49409	+	0.862611i	0.999977	−	0.00678805i	$-0.00216072\pi$
$107$	1653.68	+	954.753i	1.49409	+	0.862611i	0.494110	+	0.869399i	$0.335494\pi$
$108$		0			0
$109$	741.751	+	1284.75i	0.651806	+	1.12896i	0.982684	+	0.185288i	$0.0593219\pi$
$109$	741.751	+	1284.75i	0.651806	+	1.12896i	−0.330878	+	0.943674i	$0.607345\pi$
$110$		0			0
$111$	−979.088	+	11.0358i	−0.837216	+	0.00943665i
$112$		0			0
$113$	989.731	−	571.421i	0.823947	−	0.475706i	−0.0278286	−	0.999613i	$-0.508859\pi$
$113$	989.731	−	571.421i	0.823947	−	0.475706i	0.851776	+	0.523907i	$0.175526\pi$
$114$		0			0
$115$		−	313.556i		−	0.254254i
$116$		0			0
$117$	−21.9809	−	974.946i	−0.0173687	−	0.770374i
$118$		0			0
$119$	814.161	−	430.666i	0.627177	−	0.331757i
$120$		0			0
$121$	233.527			0.175452
$122$		0			0
$123$	−518.207	+	921.389i	−0.379879	+	0.675438i
$124$		0			0
$125$	1463.32			1.04707
$126$		0			0
$127$	384.631			0.268744			0.134372	−	0.990931i	$-0.457098\pi$
$127$	384.631			0.268744			0.134372	+	0.990931i	$0.457098\pi$
$128$		0			0
$129$	1212.87	−	13.6709i	0.827811	−	0.00933064i
$130$		0			0
$131$	−1547.72			−1.03225			−0.516124	−	0.856514i	$-0.672626\pi$
$131$	−1547.72			−1.03225			−0.516124	+	0.856514i	$0.672626\pi$
$132$		0			0
$133$	188.022	−	299.471i	0.122583	−	0.195244i
$134$		0			0
$135$	1069.88	−	36.1896i	0.682078	−	0.0230719i
$136$		0			0
$137$		−	2225.43i		−	1.38782i	−0.720062	−	0.693909i	$-0.755887\pi$
$137$		−	2225.43i		−	1.38782i	0.720062	−	0.693909i	$-0.244113\pi$
$138$		0			0
$139$	−2563.53	+	1480.05i	−1.56429	+	0.903140i	−0.567470	+	0.823394i	$0.692078\pi$
$139$	−2563.53	+	1480.05i	−1.56429	+	0.903140i	−0.996815	+	0.0797465i	$0.974589\pi$
$140$		0			0
$141$	741.912	−	1319.14i	0.443122	−	0.787887i
$142$		0			0
$143$	598.266	+	1036.23i	0.349856	+	0.605969i
$144$		0			0
$145$	−538.673	−	311.003i	−0.308513	−	0.178120i
$146$		0			0
$147$	−792.484	−	1596.40i	−0.444646	−	0.895706i
$148$		0			0
$149$			2075.33i			1.14106i	0.821277	+	0.570530i	$0.193262\pi$
$149$			2075.33i			1.14106i	−0.821277	+	0.570530i	$0.806738\pi$
$150$		0			0
$151$	−1263.80			−0.681103			−0.340551	−	0.940226i	$-0.610614\pi$
$151$	−1263.80			−0.681103			−0.340551	+	0.940226i	$0.610614\pi$
$152$		0			0
$153$	1342.42	−	30.2660i	0.709336	−	0.0159926i
$154$		0			0
$155$	1413.14	+	815.879i	0.732299	+	0.422793i
$156$		0			0
$157$	−735.383	−	424.574i	−0.373821	−	0.215826i	0.301305	−	0.953528i	$-0.402578\pi$
$157$	−735.383	−	424.574i	−0.373821	−	0.215826i	−0.675127	+	0.737702i	$0.735911\pi$
$158$		0			0
$159$	−17.9099	−	10.0729i	−0.00893301	−	0.00502409i
$160$		0			0
$161$	−760.547	−	28.1875i	−0.372295	−	0.0137980i
$162$		0			0
$163$	−742.237	+	1285.59i	−0.356665	+	0.617763i	−0.987402	−	0.158235i	$-0.949420\pi$
$163$	−742.237	+	1285.59i	−0.356665	+	0.617763i	0.630736	+	0.775997i	$0.282753\pi$
$164$		0			0
$165$	−1130.01	+	669.508i	−0.533161	+	0.315886i
$166$		0			0
$167$	1210.05	+	2095.87i	0.560698	+	0.971157i	0.997436	+	0.0715685i	$0.0228005\pi$
$167$	1210.05	+	2095.87i	0.560698	+	0.971157i	−0.436738	+	0.899589i	$0.643866\pi$
$168$		0			0
$169$	−446.235	+	772.902i	−0.203111	+	0.351799i
$170$		0			0
$171$	440.518	−	267.750i	0.197001	−	0.119739i
$172$		0			0
$173$	−854.013	−	1479.19i	−0.375315	−	0.650064i	0.615059	−	0.788481i	$-0.289132\pi$
$173$	−854.013	−	1479.19i	−0.375315	−	0.650064i	−0.990374	+	0.138417i	$0.955799\pi$
$174$		0			0
$175$	45.8061	−	1235.93i	0.0197864	−	0.533870i
$176$		0			0
$177$	−2897.11	+	32.6546i	−1.23028	+	0.0138671i
$178$		0			0
$179$	−1566.10	+	904.190i	−0.653945	+	0.377555i	−0.789966	−	0.613151i	$-0.789902\pi$
$179$	−1566.10	+	904.190i	−0.653945	+	0.377555i	0.136021	+	0.990706i	$0.456568\pi$
$180$		0			0
$181$			3860.36i			1.58530i	0.609679	+	0.792648i	$0.291298\pi$
$181$			3860.36i			1.58530i	−0.609679	+	0.792648i	$0.708702\pi$
$182$		0			0
$183$	839.136	+	471.946i	0.338966	+	0.190641i
$184$		0			0
$185$	718.911	−	1245.19i	0.285705	−	0.494855i
$186$		0			0
$187$	−1426.80	+	823.764i	−0.557957	+	0.322137i
$188$		0			0
$189$	8.39835	−	2598.31i	0.00323222	−	0.999995i
$190$		0			0
$191$	−143.765	+	83.0025i	−0.0544630	+	0.0314442i	−0.526984	−	0.849875i	$-0.676677\pi$
$191$	−143.765	+	83.0025i	−0.0544630	+	0.0314442i	0.472521	+	0.881319i	$0.343344\pi$
$192$		0			0
$193$	2018.82	−	3496.70i	0.752943	−	1.30413i	−0.193448	−	0.981111i	$-0.561967\pi$
$193$	2018.82	−	3496.70i	0.752943	−	1.30413i	0.946391	−	0.323024i	$-0.104700\pi$
$194$		0			0
$195$	1248.15	+	701.983i	0.458369	+	0.257795i
$196$		0			0
$197$		−	1924.98i		−	0.696189i	−0.937459	−	0.348094i	$-0.886829\pi$
$197$		−	1924.98i		−	0.696189i	0.937459	−	0.348094i	$-0.113171\pi$
$198$		0			0
$199$	−612.539	+	353.650i	−0.218200	+	0.125978i	−0.605116	−	0.796137i	$-0.706873\pi$
$199$	−612.539	+	353.650i	−0.218200	+	0.125978i	0.386917	+	0.922115i	$0.373540\pi$
$200$		0			0
$201$	−2714.92	+	30.6011i	−0.952715	+	0.0107385i
$202$		0			0
$203$	−802.780	+	1278.62i	−0.277557	+	0.442078i
$204$		0			0
$205$	−776.156	−	1344.34i	−0.264434	−	0.458014i
$206$		0			0
$207$	−973.145	−	532.968i	−0.326755	−	0.178956i
$208$		0			0
$209$	−316.254	+	547.768i	−0.104669	+	0.181292i
$210$		0			0
$211$	−1223.50	−	2119.16i	−0.399190	−	0.691417i	0.594437	−	0.804142i	$-0.297375\pi$
$211$	−1223.50	−	2119.16i	−0.399190	−	0.691417i	−0.993626	+	0.112726i	$0.964042\pi$
$212$		0			0
$213$	−3919.77	+	2322.38i	−1.26093	+	0.747073i
$214$		0			0
$215$	−890.572	+	1542.52i	−0.282495	+	0.489297i
$216$		0			0
$217$	2106.00	−	3354.31i	0.658822	−	1.04933i
$218$		0			0
$219$	−4002.69	−	2251.19i	−1.23505	−	0.694618i
$220$		0			0
$221$	1555.58	+	898.117i	0.473484	+	0.273366i
$222$		0			0
$223$	3829.91	+	2211.20i	1.15009	+	0.664003i	0.948908	−	0.315551i	$-0.102189\pi$
$223$	3829.91	+	2211.20i	1.15009	+	0.664003i	0.201179	+	0.979555i	$0.435523\pi$
$224$		0			0
$225$	866.099	−	1581.41i	0.256622	−	0.468566i
$226$		0			0
$227$	−5530.23			−1.61698			−0.808489	−	0.588511i	$-0.799714\pi$
$227$	−5530.23			−1.61698			−0.808489	+	0.588511i	$0.799714\pi$
$228$		0			0
$229$			2892.29i			0.834620i	0.908764	+	0.417310i	$0.137027\pi$
$229$			2892.29i			0.834620i	−0.908764	+	0.417310i	$0.862973\pi$
$230$		0			0
$231$	1522.35	+	2801.10i	0.433606	+	0.797831i
$232$		0			0
$233$	−4553.37	−	2628.89i	−1.28026	−	0.739159i	−0.303365	−	0.952874i	$-0.598110\pi$
$233$	−4553.37	−	2628.89i	−1.28026	−	0.739159i	−0.976896	+	0.213715i	$0.931444\pi$
$234$		0			0
$235$	1111.22	+	1924.68i	0.308458	+	0.534265i
$236$		0			0
$237$	−2079.12	+	3696.75i	−0.569846	+	1.01321i
$238$		0			0
$239$	4731.59	−	2731.79i	1.28059	−	0.739349i	0.303634	−	0.952789i	$-0.401800\pi$
$239$	4731.59	−	2731.79i	1.28059	−	0.739349i	0.976956	+	0.213439i	$0.0684665\pi$
$240$		0			0
$241$		−	1694.23i		−	0.452843i	−0.974029	−	0.226422i	$-0.927297\pi$
$241$		−	1694.23i		−	0.452843i	0.974029	−	0.226422i	$-0.0727027\pi$
$242$		0			0
$243$	1706.22	−	3381.97i	0.450427	−	0.892813i
$244$		0			0
$245$	2609.99	+	193.730i	0.680596	+	0.0505181i
$246$		0			0
$247$	689.599			0.177644
$248$		0			0
$249$	2868.91	−	32.3369i	0.730161	−	0.00822998i
$250$		0			0
$251$	−7893.44			−1.98498			−0.992489	−	0.122333i	$-0.960962\pi$
$251$	−7893.44			−1.98498			−0.992489	+	0.122333i	$0.960962\pi$
$252$		0			0
$253$	1361.36			0.338293
$254$		0			0
$255$	−966.575	+	1718.60i	−0.237370	+	0.422051i
$256$		0			0
$257$	−1086.17			−0.263632			−0.131816	−	0.991274i	$-0.542081\pi$
$257$	−1086.17			−0.263632			−0.131816	+	0.991274i	$0.542081\pi$
$258$		0			0
$259$	−2955.65	−	1855.70i	−0.709094	−	0.445202i
$260$		0			0
$261$	−1880.84	+	1143.19i	−0.446057	+	0.271117i
$262$		0			0
$263$		−	7911.04i		−	1.85481i	−0.374056	−	0.927406i	$-0.622033\pi$
$263$		−	7911.04i		−	1.85481i	0.374056	−	0.927406i	$-0.377967\pi$
$264$		0			0
$265$	26.1312	−	15.0869i	0.00605747	−	0.00349728i
$266$		0			0
$267$	2340.60	−	26.3820i	0.536488	−	0.00604701i
$268$		0			0
$269$	−2223.37	−	3850.99i	−0.503945	−	0.872858i	−0.999990	−	0.00456087i	$-0.998548\pi$
$269$	−2223.37	−	3850.99i	−0.503945	−	0.872858i	0.496045	−	0.868297i	$-0.334785\pi$
$270$		0			0
$271$	−4658.97	−	2689.86i	−1.04432	−	0.602941i	−0.123270	−	0.992373i	$-0.539338\pi$
$271$	−4658.97	−	2689.86i	−1.04432	−	0.602941i	−0.921055	+	0.389432i	$0.872671\pi$
$272$		0			0
$273$	1814.90	−	2964.35i	0.402355	−	0.657182i
$274$		0			0
$275$			2212.28i			0.485112i
$276$		0			0
$277$	819.545			0.177768			0.0888839	−	0.996042i	$-0.471670\pi$
$277$	819.545			0.177768			0.0888839	+	0.996042i	$0.471670\pi$
$278$		0			0
$279$	4934.14	−	2999.01i	1.05878	−	0.643534i
$280$		0			0
$281$	3331.83	+	1923.63i	0.707332	+	0.408378i	0.810072	−	0.586330i	$-0.199428\pi$
$281$	3331.83	+	1923.63i	0.707332	+	0.408378i	−0.102741	+	0.994708i	$0.532761\pi$
$282$		0			0
$283$	118.520	+	68.4277i	0.0248950	+	0.0143732i	0.512396	−	0.858749i	$-0.328758\pi$
$283$	118.520	+	68.4277i	0.0248950	+	0.0143732i	−0.487501	+	0.873123i	$0.662091\pi$
$284$		0			0
$285$	8.53182	+	756.940i	0.00177327	+	0.157324i
$286$		0			0
$287$	−3330.55	+	1761.76i	−0.685004	+	0.362346i
$288$		0			0
$289$	1219.86	−	2112.87i	0.248293	−	0.430056i
$290$		0			0
$291$	22.8353	+	2025.94i	0.00460010	+	0.408120i
$292$		0			0
$293$	2891.21	+	5007.72i	0.576472	+	0.998479i	0.995880	+	0.0906808i	$0.0289043\pi$
$293$	2891.21	+	5007.72i	0.576472	+	0.998479i	−0.419408	+	0.907798i	$0.637762\pi$
$294$		0			0
$295$	2127.25	−	3684.50i	0.419841	−	0.727186i
$296$		0			0
$297$	157.124	+	4645.09i	0.0306979	+	0.907527i
$298$		0			0
$299$	−742.120	−	1285.39i	−0.143538	−	0.248615i
$300$		0			0
$301$	3661.40	+	2298.80i	0.701128	+	0.440201i
$302$		0			0
$303$	3139.95	+	5299.69i	0.595331	+	1.00482i
$304$		0			0
$305$	−1224.33	+	706.867i	−0.229852	+	0.132705i
$306$		0			0
$307$		−	6205.35i		−	1.15361i	−0.816882	−	0.576804i	$-0.804299\pi$
$307$		−	6205.35i		−	1.15361i	0.816882	−	0.576804i	$-0.195701\pi$
$308$		0			0
$309$	−677.805	+	401.584i	−0.124786	+	0.0739331i
$310$		0			0
$311$	−5082.04	+	8802.35i	−0.926611	+	1.60494i	−0.137662	+	0.990479i	$0.543959\pi$
$311$	−5082.04	+	8802.35i	−0.926611	+	1.60494i	−0.788949	+	0.614458i	$0.789375\pi$
$312$		0			0
$313$	−5920.67	+	3418.30i	−1.06919	+	0.617296i	−0.927960	−	0.372681i	$-0.878439\pi$
$313$	−5920.67	+	3418.30i	−1.06919	+	0.617296i	−0.141229	+	0.989977i	$0.545105\pi$
$314$		0			0
$315$	3276.28	+	1955.46i	0.586024	+	0.349770i
$316$		0			0
$317$	2331.97	−	1346.36i	0.413174	−	0.238546i	−0.278978	−	0.960297i	$-0.589996\pi$
$317$	2331.97	−	1346.36i	0.413174	−	0.238546i	0.692153	+	0.721751i	$0.256662\pi$
$318$		0			0
$319$	1350.28	−	2338.75i	0.236994	−	0.410486i
$320$		0			0
$321$	111.829	+	9921.45i	0.0194446	+	1.72511i
$322$		0			0
$323$			949.523i			0.163569i
$324$		0			0
$325$	2088.82	−	1205.98i	0.356514	−	0.205833i
$326$		0			0
$327$	−3778.77	+	6718.78i	−0.639041	+	1.13624i
$328$		0			0
$329$	4768.32	−	2522.29i	0.799045	−	0.422670i
$330$		0			0
$331$	767.448	+	1329.26i	0.127440	+	0.220733i	0.922684	−	0.385557i	$-0.125991\pi$
$331$	767.448	+	1329.26i	0.127440	+	0.220733i	−0.795244	+	0.606290i	$0.792657\pi$
$332$		0			0
$333$	−2642.58	−	4347.72i	−0.434872	−	0.715476i
$334$		0			0
$335$	1993.47	−	3452.80i	0.325120	−	0.563124i
$336$		0			0
$337$	4864.18	+	8425.00i	0.786257	+	1.36184i	0.928245	+	0.371968i	$0.121317\pi$
$337$	4864.18	+	8425.00i	0.786257	+	1.36184i	−0.141989	+	0.989868i	$0.545350\pi$
$338$		0			0
$339$	5175.93	+	2911.04i	0.829256	+	0.466389i
$340$		0			0
$341$	−3542.30	+	6135.44i	−0.562540	+	0.974348i
$342$		0			0
$343$	704.531	−	6313.26i	0.110907	−	0.993831i
$344$		0			0
$345$	1401.73	−	830.493i	0.218744	−	0.129601i
$346$		0			0
$347$	−2118.71	−	1223.24i	−0.327777	−	0.189242i	0.327077	−	0.944998i	$-0.393936\pi$
$347$	−2118.71	−	1223.24i	−0.327777	−	0.189242i	−0.654854	+	0.755756i	$0.727270\pi$
$348$		0			0
$349$	5463.17	+	3154.16i	0.837927	+	0.483778i	0.856559	−	0.516049i	$-0.172598\pi$
$349$	5463.17	+	3154.16i	0.837927	+	0.483778i	−0.0186318	+	0.999826i	$0.505931\pi$
$350$		0			0
$351$	4300.21	−	2680.53i	0.653926	−	0.407625i
$352$		0			0
$353$	−3385.36			−0.510438			−0.255219	−	0.966883i	$-0.582148\pi$
$353$	−3385.36			−0.510438			−0.255219	+	0.966883i	$0.582148\pi$
$354$		0			0
$355$		−	6690.35i		−	1.00024i
$356$		0			0
$357$	4081.68	+	2498.98i	0.605113	+	0.370476i
$358$		0			0
$359$	−5447.71	−	3145.24i	−0.800889	−	0.462394i	0.0428929	−	0.999080i	$-0.486343\pi$
$359$	−5447.71	−	3145.24i	−0.800889	−	0.462394i	−0.843782	+	0.536686i	$0.819676\pi$
$360$		0			0
$361$	−3247.23	−	5624.37i	−0.473427	−	0.819999i
$362$		0			0
$363$	618.526	+	1043.97i	0.0894331	+	0.150948i
$364$		0			0
$365$	5840.08	−	3371.77i	0.837489	−	0.483525i
$366$		0			0
$367$		−	9920.77i		−	1.41106i	−0.708679	−	0.705531i	$-0.750709\pi$
$367$		−	9920.77i		−	1.41106i	0.708679	−	0.705531i	$-0.249291\pi$
$368$		0			0
$369$	−5491.55	+	123.811i	−0.774738	+	0.0174671i
$370$		0			0
$371$	−34.2450	−	64.7390i	−0.00479221	−	0.00905952i
$372$		0			0
$373$	5838.36			0.810453			0.405226	−	0.914216i	$-0.367193\pi$
$373$	5838.36			0.810453			0.405226	+	0.914216i	$0.367193\pi$
$374$		0			0
$375$	3875.80	+	6541.68i	0.533721	+	0.900830i
$376$		0			0
$377$	−2944.31			−0.402228
$378$		0			0
$379$	9842.81			1.33401			0.667007	−	0.745051i	$-0.267575\pi$
$379$	9842.81			1.33401			0.667007	+	0.745051i	$0.267575\pi$
$380$		0			0
$381$	1018.75	+	1719.47i	0.136987	+	0.231210i
$382$		0			0
$383$	506.592			0.0675866			0.0337933	−	0.999429i	$-0.489241\pi$
$383$	506.592			0.0675866			0.0337933	+	0.999429i	$0.489241\pi$
$384$		0			0
$385$	−4678.25	−	173.386i	−0.619288	−	0.0229521i
$386$		0			0
$387$	3273.57	+	5385.86i	0.429987	+	0.707439i
$388$		0			0
$389$		−	2974.04i		−	0.387635i	−0.981038	−	0.193817i	$-0.937913\pi$
$389$		−	2974.04i		−	0.387635i	0.981038	−	0.193817i	$-0.0620869\pi$
$390$		0			0
$391$	1769.88	−	1021.84i	0.228917	−	0.132165i
$392$		0			0
$393$	−4099.33	−	6918.96i	−0.526167	−	0.888079i
$394$		0			0
$395$	−3114.05	−	5393.70i	−0.396671	−	0.687054i
$396$		0			0
$397$	2024.50	+	1168.85i	0.255936	+	0.147765i	0.622479	−	0.782636i	$-0.286125\pi$
$397$	2024.50	+	1168.85i	0.255936	+	0.147765i	−0.366543	+	0.930401i	$0.619459\pi$
$398$		0			0
$399$	1836.77	+	47.3517i	0.230460	+	0.00594123i
$400$		0			0
$401$		−	8202.43i		−	1.02147i	−0.859738	−	0.510735i	$-0.829373\pi$
$401$		−	8202.43i		−	1.02147i	0.859738	−	0.510735i	$-0.170627\pi$
$402$		0			0
$403$	7724.05			0.954745
$404$		0			0
$405$	2995.50	+	4686.97i	0.367525	+	0.575056i
$406$		0			0
$407$	5406.24	+	3121.29i	0.658421	+	0.380139i
$408$		0			0
$409$	10385.4	+	5996.03i	1.25557	+	0.724901i	0.972209	−	0.234113i	$-0.0752187\pi$
$409$	10385.4	+	5996.03i	1.25557	+	0.724901i	0.283356	+	0.959015i	$0.408552\pi$
$410$		0			0
$411$	9948.63	−	5894.34i	1.19399	−	0.707412i
$412$		0			0
$413$	−8745.73	−	5490.98i	−1.04201	−	0.654221i
$414$		0			0
$415$	−2106.55	+	3648.64i	−0.249172	+	0.431578i
$416$		0			0
$417$	−13406.3	−	7539.97i	−1.57436	−	0.885452i
$418$		0			0
$419$	3319.61	+	5749.73i	0.387049	+	0.670389i	0.992051	−	0.125835i	$-0.0401611\pi$
$419$	3319.61	+	5749.73i	0.387049	+	0.670389i	−0.605002	+	0.796224i	$0.706828\pi$
$420$		0			0
$421$	−8330.92	+	14429.6i	−0.964428	+	1.67044i	−0.253285	+	0.967392i	$0.581511\pi$
$421$	−8330.92	+	14429.6i	−0.964428	+	1.67044i	−0.711143	+	0.703047i	$0.751822\pi$
$422$		0			0
$423$	7862.20	−	177.259i	0.903719	−	0.0203751i
$424$		0			0
$425$	1660.54	+	2876.14i	0.189525	+	0.328267i
$426$		0			0
$427$	1604.48	+	3033.23i	0.181842	+	0.343766i
$428$		0			0
$429$	−3047.80	+	5419.09i	−0.343005	+	0.609874i
$430$		0			0
$431$	−3574.71	+	2063.86i	−0.399507	+	0.230656i	−0.686271	−	0.727346i	$-0.740754\pi$
$431$	−3574.71	+	2063.86i	−0.399507	+	0.230656i	0.286764	+	0.958001i	$0.407420\pi$
$432$		0			0
$433$		−	5426.63i		−	0.602280i	−0.953580	−	0.301140i	$-0.902633\pi$
$433$		−	5426.63i		−	0.602280i	0.953580	−	0.301140i	$-0.0973672\pi$
$434$		0			0
$435$	−36.4275	−	3231.83i	−0.00401509	−	0.356217i
$436$		0			0
$437$	392.298	−	679.480i	0.0429432	−	0.0743798i
$438$		0			0
$439$	7040.55	−	4064.86i	0.765437	−	0.441925i	−0.0658073	−	0.997832i	$-0.520962\pi$
$439$	7040.55	−	4064.86i	0.765437	−	0.441925i	0.831245	+	0.555907i	$0.187629\pi$
$440$		0			0
$441$	5037.60	−	7771.02i	0.543958	−	0.839112i
$442$		0			0
$443$	6822.24	−	3938.82i	0.731680	−	0.422436i	−0.0873565	−	0.996177i	$-0.527842\pi$
$443$	6822.24	−	3938.82i	0.731680	−	0.422436i	0.819036	+	0.573742i	$0.194509\pi$
$444$		0			0
$445$	−1718.62	+	2976.74i	−0.183080	+	0.317104i
$446$		0			0
$447$	−9277.63	+	5496.79i	−0.981693	+	0.581631i
$448$		0			0
$449$			9872.10i			1.03762i	0.854888	+	0.518812i	$0.173625\pi$
$449$			9872.10i			1.03762i	−0.854888	+	0.518812i	$0.826375\pi$
$450$		0			0
$451$	5836.72	−	3369.83i	0.609402	−	0.351838i
$452$		0			0
$453$	−3347.34	−	5649.73i	−0.347178	−	0.585977i
$454$		0			0
$455$	2386.55	+	4511.69i	0.245897	+	0.464860i
$456$		0			0
$457$	1927.49	+	3338.51i	0.197296	+	0.341726i	0.947651	−	0.319309i	$-0.103451\pi$
$457$	1927.49	+	3338.51i	0.197296	+	0.341726i	−0.750355	+	0.661035i	$0.770117\pi$
$458$		0			0
$459$	3690.88	+	5921.05i	0.375328	+	0.602115i
$460$		0			0
$461$	−2144.75	+	3714.82i	−0.216684	+	0.375307i	−0.953792	−	0.300468i	$-0.902857\pi$
$461$	−2144.75	+	3714.82i	−0.216684	+	0.375307i	0.737109	+	0.675774i	$0.236191\pi$
$462$		0			0
$463$	−6924.87	−	11994.2i	−0.695088	−	1.20393i	−0.970151	−	0.242502i	$-0.922032\pi$
$463$	−6924.87	−	11994.2i	−0.695088	−	1.20393i	0.275063	−	0.961426i	$-0.411301\pi$
$464$		0			0
$465$	95.5631	+	8478.32i	0.00953039	+	0.845533i
$466$		0			0
$467$	2406.59	−	4168.33i	0.238466	−	0.413035i	−0.721808	−	0.692093i	$-0.756689\pi$
$467$	2406.59	−	4168.33i	0.238466	−	0.413035i	0.960274	+	0.279058i	$0.0900222\pi$
$468$		0			0
$469$	−8195.75	−	5145.68i	−0.806918	−	0.506621i
$470$		0			0
$471$	−49.7299	−	4412.02i	−0.00486504	−	0.431624i
$472$		0			0
$473$	−6697.14	−	3866.59i	−0.651025	−	0.375869i
$474$		0			0
$475$	1104.19	+	637.504i	0.106660	+	0.0615804i
$476$		0			0
$477$	−2.40664	−	106.744i	−0.000231011	−	0.0102463i
$478$		0			0
$479$	−15047.2			−1.43533			−0.717666	−	0.696387i	$-0.754790\pi$
$479$	−15047.2			−1.43533			−0.717666	+	0.696387i	$0.754790\pi$
$480$		0			0
$481$		−	6806.04i		−	0.645174i
$482$		0			0
$483$	−1888.40	−	3474.63i	−0.177899	−	0.327332i
$484$		0			0
$485$	−2576.56	−	1487.58i	−0.241228	−	0.139273i
$486$		0			0
$487$	8651.87	+	14985.5i	0.805038	+	1.39437i	0.916265	+	0.400572i	$0.131189\pi$
$487$	8651.87	+	14985.5i	0.805038	+	1.39437i	−0.111227	+	0.993795i	$0.535478\pi$
$488$		0			0
$489$	−7713.06	+	86.9375i	−0.713286	+	0.00803977i
$490$		0			0
$491$	−4937.70	+	2850.78i	−0.453840	+	0.262025i	−0.709451	−	0.704755i	$-0.751057\pi$
$491$	−4937.70	+	2850.78i	−0.453840	+	0.262025i	0.255611	+	0.966780i	$0.417723\pi$
$492$		0			0
$493$		−	4054.09i		−	0.370359i
$494$		0			0
$495$	−5985.98	−	3278.37i	−0.543535	−	0.297681i
$496$		0			0
$497$	−16227.8	−	601.438i	−1.46462	−	0.0542820i
$498$		0			0
$499$	−6689.83			−0.600156			−0.300078	−	0.953915i	$-0.597013\pi$
$499$	−6689.83			−0.600156			−0.300078	+	0.953915i	$0.597013\pi$
$500$		0			0
$501$	−6164.47	+	10960.6i	−0.549717	+	0.977415i
$502$		0			0
$503$	5850.48			0.518608			0.259304	−	0.965796i	$-0.416507\pi$
$503$	5850.48			0.518608			0.259304	+	0.965796i	$0.416507\pi$
$504$		0			0
$505$	−9045.63			−0.797079
$506$		0			0
$507$	−4637.12	+	52.2671i	−0.406196	+	0.00457843i
$508$		0			0
$509$	18243.3			1.58865			0.794323	−	0.607496i	$-0.207826\pi$
$509$	18243.3			1.58865			0.794323	+	0.607496i	$0.207826\pi$
$510$		0			0
$511$	−7653.42	−	14468.5i	−0.662558	−	1.25255i
$512$		0			0
$513$	2363.73	+	1260.13i	0.203433	+	0.108453i
$514$		0			0
$515$		−	1156.89i		−	0.0989879i
$516$		0			0
$517$	−8356.38	+	4824.56i	−0.710857	+	0.410413i
$518$		0			0
$519$	4350.67	−	7735.65i	0.367964	−	0.654253i
$520$		0			0
$521$	2531.39	+	4384.50i	0.212864	+	0.368692i	0.952610	−	0.304195i	$-0.0983875\pi$
$521$	2531.39	+	4384.50i	0.212864	+	0.368692i	−0.739746	+	0.672887i	$0.765054\pi$
$522$		0			0
$523$	−11709.1	−	6760.27i	−0.978977	−	0.565212i	−0.0770156	−	0.997030i	$-0.524539\pi$
$523$	−11709.1	−	6760.27i	−0.978977	−	0.565212i	−0.901961	+	0.431817i	$0.857872\pi$
$524$		0			0
$525$	5646.45	−	3068.74i	0.469393	−	0.255106i
$526$		0			0
$527$			10635.4i			0.879099i
$528$		0			0
$529$	10478.3			0.861206
$530$		0			0
$531$	−7819.34	−	12864.8i	−0.639041	−	1.05139i
$532$		0			0
$533$	−6363.54	−	3673.99i	−0.517140	−	0.298571i
$534$		0			0
$535$	−12618.0	−	7284.98i	−1.01967	−	0.588705i
$536$		0			0
$537$	−8190.15	−	4606.29i	−0.658158	−	0.370161i
$538$		0			0
$539$	−841.115	+	11331.8i	−0.0672159	+	0.905555i
$540$		0			0
$541$	−9993.70	+	17309.6i	−0.794201	+	1.37560i	0.129144	+	0.991626i	$0.458777\pi$
$541$	−9993.70	+	17309.6i	−0.794201	+	1.37560i	−0.923345	+	0.383971i	$0.874556\pi$
$542$		0			0
$543$	−17257.5	+	10224.7i	−1.36389	+	0.808071i
$544$		0			0
$545$	−5659.73	−	9802.95i	−0.444837	−	0.770481i
$546$		0			0
$547$	−4022.26	+	6966.76i	−0.314405	+	0.544565i	−0.979311	−	0.202362i	$-0.935138\pi$
$547$	−4022.26	+	6966.76i	−0.314405	+	0.544565i	0.664906	+	0.746927i	$0.268472\pi$
$548$		0			0
$549$	112.758	+	5001.31i	0.00876578	+	0.388799i
$550$		0			0
$551$	−778.209	−	1347.90i	−0.0601685	−	0.104215i
$552$		0			0
$553$	−13362.7	+	7068.43i	−1.02755	+	0.543545i
$554$		0			0
$555$	7470.67	−	84.2054i	0.571373	−	0.00644021i
$556$		0			0
$557$	6301.22	−	3638.01i	0.479338	−	0.276746i	−0.240803	−	0.970574i	$-0.577411\pi$
$557$	6301.22	−	3638.01i	0.479338	−	0.276746i	0.720140	+	0.693828i	$0.244077\pi$
$558$		0			0
$559$			8431.18i			0.637927i
$560$		0			0
$561$	−7461.65	−	4196.57i	−0.561553	−	0.315828i
$562$		0			0
$563$	−8557.81	+	14822.6i	−0.640619	+	1.10958i	0.344676	+	0.938722i	$0.387989\pi$
$563$	−8557.81	+	14822.6i	−0.640619	+	1.10958i	−0.985295	+	0.170863i	$0.945344\pi$
$564$		0			0
$565$	−7551.87	+	4360.08i	−0.562318	+	0.324654i
$566$		0			0
$567$	11637.8	−	6844.41i	0.861978	−	0.506946i
$568$		0			0
$569$	21667.6	−	12509.8i	1.59640	−	0.921682i	0.604226	−	0.796813i	$-0.293482\pi$
$569$	21667.6	−	12509.8i	1.59640	−	0.921682i	0.992173	−	0.124869i	$-0.0398509\pi$
$570$		0			0
$571$	−1779.90	+	3082.87i	−0.130449	+	0.225944i	−0.923850	−	0.382755i	$-0.874975\pi$
$571$	−1779.90	+	3082.87i	−0.130449	+	0.225944i	0.793401	+	0.608700i	$0.208309\pi$
$572$		0			0
$573$	−751.836	−	422.847i	−0.0548140	−	0.0308284i
$574$		0			0
$575$		−	2744.23i		−	0.199030i
$576$		0			0
$577$	12827.3	−	7405.82i	0.925486	−	0.534330i	0.0401049	−	0.999195i	$-0.487231\pi$
$577$	12827.3	−	7405.82i	0.925486	−	0.534330i	0.885381	+	0.464866i	$0.153897\pi$
$578$		0			0
$579$	20978.9	−	236.463i	1.50579	−	0.0169725i
$580$		0			0
$581$	8660.62	+	5437.54i	0.618422	+	0.388274i
$582$		0			0
$583$	65.5026	+	113.454i	0.00465324	+	0.00805965i
$584$		0			0
$585$	167.720	+	7439.06i	0.0118536	+	0.525756i
$586$		0			0
$587$	3803.77	−	6588.33i	0.267459	−	0.463253i	−0.700746	−	0.713411i	$-0.747149\pi$
$587$	3803.77	−	6588.33i	0.267459	−	0.463253i	0.968205	+	0.250158i	$0.0804826\pi$
$588$		0			0
$589$	2041.54	+	3536.05i	0.142818	+	0.247369i
$590$		0			0
$591$	8605.50	−	5098.56i	0.598956	−	0.354868i
$592$		0			0
$593$	3331.78	−	5770.81i	0.230725	−	0.399627i	−0.727297	−	0.686323i	$-0.759224\pi$
$593$	3331.78	−	5770.81i	0.230725	−	0.399627i	0.958022	+	0.286696i	$0.0925570\pi$
$594$		0			0
$595$	−6212.24	+	3286.08i	−0.428029	+	0.226414i
$596$		0			0
$597$	−3203.36	−	1801.63i	−0.219606	−	0.123510i
$598$		0			0
$599$	−3755.39	−	2168.17i	−0.256162	−	0.147895i	0.366421	−	0.930449i	$-0.380583\pi$
$599$	−3755.39	−	2168.17i	−0.256162	−	0.147895i	−0.622583	+	0.782554i	$0.713917\pi$
$600$		0			0
$601$	−10824.8	−	6249.70i	−0.734696	−	0.424177i	0.0854415	−	0.996343i	$-0.472770\pi$
$601$	−10824.8	−	6249.70i	−0.734696	−	0.424177i	−0.820138	+	0.572166i	$0.806103\pi$
$602$		0			0
$603$	−7327.62	−	12055.8i	−0.494865	−	0.814180i
$604$		0			0
$605$	−1781.86			−0.119741
$606$		0			0
$607$			1753.45i			0.117249i	0.998280	+	0.0586247i	$0.0186715\pi$
$607$			1753.45i			0.117249i	−0.998280	+	0.0586247i	$0.981328\pi$
$608$		0			0
$609$	−7842.27	−	202.173i	−0.521814	−	0.0134523i
$610$		0			0
$611$	9110.62	+	5260.02i	0.603235	+	0.348278i
$612$		0			0
$613$	7827.70	+	13558.0i	0.515755	+	0.893314i	0.999833	+	0.0182890i	$0.00582188\pi$
$613$	7827.70	+	13558.0i	0.515755	+	0.893314i	−0.484078	+	0.875025i	$0.660845\pi$
$614$		0			0
$615$	3954.04	−	7030.41i	0.259255	−	0.460965i
$616$		0			0
$617$	11532.0	−	6658.01i	0.752449	−	0.434427i	−0.0741291	−	0.997249i	$-0.523618\pi$
$617$	11532.0	−	6658.01i	0.752449	−	0.434427i	0.826578	+	0.562822i	$0.190284\pi$
$618$		0			0
$619$		−	8544.40i		−	0.554812i	−0.960753	−	0.277406i	$-0.910525\pi$
$619$		−	8544.40i		−	0.554812i	0.960753	−	0.277406i	$-0.0894747\pi$
$620$		0			0
$621$	−194.905	−	5762.01i	−0.0125946	−	0.372338i
$622$		0			0
$623$	7065.76	+	4436.21i	0.454388	+	0.285286i
$624$		0			0
$625$	−2818.04			−0.180355
$626$		0			0
$627$	−3286.40	+	37.0426i	−0.209324	+	0.00235939i
$628$		0			0
$629$	9371.38			0.594056
$630$		0			0
$631$	−19234.9			−1.21352			−0.606759	−	0.794886i	$-0.707531\pi$
$631$	−19234.9			−1.21352			−0.606759	+	0.794886i	$0.707531\pi$
$632$		0			0
$633$	6232.96	−	11082.4i	0.391371	−	0.695872i
$634$		0			0
$635$	−2934.82			−0.183409
$636$		0			0
$637$	11157.9	−	5383.12i	0.694022	−	0.334830i
$638$		0			0
$639$	−20764.0	−	11372.0i	−1.28547	−	0.704018i
$640$		0			0
$641$		−	28728.7i		−	1.77022i	−0.465378	−	0.885112i	$-0.654081\pi$
$641$		−	28728.7i		−	1.77022i	0.465378	−	0.885112i	$-0.345919\pi$
$642$		0			0
$643$	6380.38	−	3683.71i	0.391318	−	0.225928i	−0.291413	−	0.956597i	$-0.594125\pi$
$643$	6380.38	−	3683.71i	0.391318	−	0.225928i	0.682731	+	0.730670i	$0.260792\pi$
$644$		0			0
$645$	−9254.51	+	104.312i	−0.564955	+	0.00636787i
$646$		0			0
$647$	−5411.29	−	9372.64i	−0.328810	−	0.569515i	0.653466	−	0.756956i	$-0.273314\pi$
$647$	−5411.29	−	9372.64i	−0.328810	−	0.569515i	−0.982276	+	0.187440i	$0.939981\pi$
$648$		0			0
$649$	15997.0	+	9235.86i	0.967544	+	0.558612i
$650$		0			0
$651$	20573.2	+	530.376i	1.23860	+	0.0319310i
$652$		0			0
$653$			7320.32i			0.438693i	0.975647	+	0.219346i	$0.0703924\pi$
$653$			7320.32i			0.438693i	−0.975647	+	0.219346i	$0.929608\pi$
$654$		0			0
$655$	11809.4			0.704477
$656$		0			0
$657$	−537.860	−	23856.3i	−0.0319390	−	1.41663i
$658$		0			0
$659$	27887.5	+	16100.9i	1.64847	+	0.951746i	0.977679	+	0.210102i	$0.0673797\pi$
$659$	27887.5	+	16100.9i	1.64847	+	0.951746i	0.670794	+	0.741644i	$0.265954\pi$
$660$		0			0
$661$	5301.45	+	3060.79i	0.311955	+	0.180107i	0.647801	−	0.761810i	$-0.275689\pi$
$661$	5301.45	+	3060.79i	0.311955	+	0.180107i	−0.335846	+	0.941917i	$0.609022\pi$
$662$		0			0
$663$	105.196	+	9332.91i	0.00616208	+	0.546697i
$664$		0			0
$665$	−1434.65	+	2285.04i	−0.0836593	+	0.133248i
$666$		0			0
$667$	−1674.96	+	2901.11i	−0.0972333	+	0.168413i
$668$		0			0
$669$	258.995	+	22978.0i	0.0149676	+	1.32792i
$670$		0			0
$671$	−3069.00	−	5315.67i	−0.176569	−	0.305826i
$672$		0			0
$673$	−16153.0	+	27977.8i	−0.925189	+	1.60247i	−0.133932	+	0.990990i	$0.542760\pi$
$673$	−16153.0	+	27977.8i	−0.925189	+	1.60247i	−0.791257	+	0.611484i	$0.790573\pi$
$674$		0			0
$675$	9363.56	−	316.730i	0.533931	−	0.0180607i
$676$		0			0
$677$	9120.61	+	15797.4i	0.517775	+	0.896812i	0.999787	+	0.0206474i	$0.00657274\pi$
$677$	9120.61	+	15797.4i	0.517775	+	0.896812i	−0.482012	+	0.876164i	$0.660094\pi$
$678$		0			0
$679$	−3839.83	+	6115.87i	−0.217024	+	0.345664i
$680$		0			0
$681$	−14647.5	−	24722.5i	−0.824221	−	1.39114i
$682$		0			0
$683$	13821.6	−	7979.89i	0.774331	−	0.447060i	−0.0600866	−	0.998193i	$-0.519138\pi$
$683$	13821.6	−	7979.89i	0.774331	−	0.447060i	0.834417	+	0.551133i	$0.185804\pi$
$684$		0			0
$685$			16980.5i			0.947143i
$686$		0			0
$687$	−12929.8	+	7660.61i	−0.718053	+	0.425430i
$688$		0			0
$689$	71.4149	−	123.694i	0.00394875	−	0.00683944i
$690$		0			0
$691$	−2575.40	+	1486.91i	−0.141784	+	0.0818591i	−0.569214	−	0.822189i	$-0.692752\pi$
$691$	−2575.40	+	1486.91i	−0.141784	+	0.0818591i	0.427430	+	0.904048i	$0.359419\pi$
$692$		0			0
$693$	−8490.00	+	14224.6i	−0.465380	+	0.779724i
$694$		0			0
$695$	19560.3	−	11293.2i	1.06758	−	0.616365i
$696$		0			0
$697$	5058.80	−	8762.09i	0.274915	−	0.476166i
$698$		0			0
$699$	−307.919	−	27318.5i	−0.0166618	−	1.47822i
$700$		0			0
$701$			9817.01i			0.528935i	0.964395	+	0.264467i	$0.0851962\pi$
$701$			9817.01i			0.528935i	−0.964395	+	0.264467i	$0.914804\pi$
$702$		0			0
$703$	3115.79	−	1798.90i	0.167161	−	0.0965104i
$704$		0			0
$705$	−5660.96	+	10065.4i	−0.302417	+	0.537708i
$706$		0			0
$707$	−813.168	+	21940.7i	−0.0432565	+	1.16713i
$708$		0			0
$709$	3405.38	+	5898.29i	0.180383	+	0.312433i	0.942011	−	0.335582i	$-0.108933\pi$
$709$	3405.38	+	5898.29i	0.180383	+	0.312433i	−0.761628	+	0.648015i	$0.775600\pi$
$710$		0			0
$711$	−22032.9	+	496.749i	−1.16216	+	0.0262019i
$712$		0			0
$713$	4394.05	−	7610.72i	0.230797	−	0.399752i
$714$		0			0
$715$	−4564.90	−	7906.65i	−0.238766	−	0.413555i
$716$		0			0
$717$	24744.5	+	13916.8i	1.28884	+	0.724869i
$718$		0			0
$719$	−1857.32	+	3216.97i	−0.0963371	+	0.166861i	−0.910166	−	0.414244i	$-0.864046\pi$
$719$	−1857.32	+	3216.97i	−0.0963371	+	0.166861i	0.813829	+	0.581105i	$0.197379\pi$
$720$		0			0
$721$	−2806.11	−	104.000i	−0.144944	−	0.00537195i
$722$		0			0
$723$	7573.96	−	4487.40i	0.389597	−	0.230827i
$724$		0			0
$725$	−4714.45	−	2721.89i	−0.241504	−	0.139432i
$726$		0			0
$727$	14636.7	+	8450.51i	0.746693	+	0.431103i	0.824498	−	0.565865i	$-0.191458\pi$
$727$	14636.7	+	8450.51i	0.746693	+	0.431103i	−0.0778050	+	0.996969i	$0.524791\pi$
$728$		0			0
$729$	19638.0	−	1330.07i	0.997714	−	0.0675744i
$730$		0			0
$731$	−11609.1			−0.587383
$732$		0			0
$733$			6735.08i			0.339380i	0.985497	+	0.169690i	$0.0542767\pi$
$733$			6735.08i			0.339380i	−0.985497	+	0.169690i	$0.945723\pi$
$734$		0			0
$735$	6046.84	+	12180.9i	0.303457	+	0.611291i
$736$		0			0
$737$	14991.0	+	8655.05i	0.749254	+	0.432582i
$738$		0			0
$739$	3782.96	+	6552.27i	0.188306	+	0.326156i	0.944686	−	0.327977i	$-0.106367\pi$
$739$	3782.96	+	6552.27i	0.188306	+	0.326156i	−0.756379	+	0.654133i	$0.773034\pi$
$740$		0			0
$741$	1826.49	+	3082.80i	0.0905504	+	0.152834i
$742$		0			0
$743$	−20284.4	+	11711.2i	−1.00157	+	0.578254i	−0.908711	−	0.417425i	$-0.862932\pi$
$743$	−20284.4	+	11711.2i	−1.00157	+	0.578254i	−0.0928546	+	0.995680i	$0.529599\pi$
$744$		0			0
$745$		−	15835.3i		−	0.778737i
$746$		0			0
$747$	7743.25	+	12739.6i	0.379265	+	0.623988i
$748$		0			0
$749$	−18804.4	+	29950.7i	−0.917356	+	1.46111i
$750$		0			0
$751$	21214.0			1.03077			0.515387	−	0.856958i	$-0.327648\pi$
$751$	21214.0			1.03077			0.515387	+	0.856958i	$0.327648\pi$
$752$		0			0
$753$	−20906.8	−	35287.1i	−1.01180	−	1.70775i
$754$		0			0
$755$	9643.08			0.464831
$756$		0			0
$757$	−18800.3			−0.902653			−0.451326	−	0.892359i	$-0.649049\pi$
$757$	−18800.3			−0.902653			−0.451326	+	0.892359i	$0.649049\pi$
$758$		0			0
$759$	3605.75	+	6085.88i	0.172438	+	0.291045i
$760$		0			0
$761$	16073.2			0.765642			0.382821	−	0.923822i	$-0.374953\pi$
$761$	16073.2			0.765642			0.382821	+	0.923822i	$0.374953\pi$
$762$		0			0
$763$	−24286.4	+	12846.8i	−1.15233	+	0.609546i
$764$		0			0
$765$	−10243.0	+	230.936i	−0.484100	+	0.0109144i
$766$		0			0
$767$		−	20139.0i		−	0.948078i
$768$		0			0
$769$	−266.994	+	154.149i	−0.0125202	+	0.00722854i	−0.506247	−	0.862389i	$-0.668968\pi$
$769$	−266.994	+	154.149i	−0.0125202	+	0.00722854i	0.493727	+	0.869617i	$0.335634\pi$
$770$		0			0
$771$	−2876.87	−	4855.66i	−0.134381	−	0.226812i
$772$		0			0
$773$	17304.3	+	29971.9i	0.805165	+	1.39459i	0.916180	+	0.400768i	$0.131256\pi$
$773$	17304.3	+	29971.9i	0.805165	+	1.39459i	−0.111015	+	0.993819i	$0.535410\pi$
$774$		0			0
$775$	12367.8	+	7140.55i	0.573244	+	0.330963i
$776$		0			0
$777$	467.341	−	18128.1i	0.0215775	−	0.836991i
$778$		0			0
$779$		−	3884.28i		−	0.178651i
$780$		0			0
$781$	29047.5			1.33086
$782$		0			0
$783$	−10092.2	−	5380.27i	−0.460619	−	0.245562i
$784$		0			0
$785$	5611.14	+	3239.59i	0.255121	+	0.147294i
$786$		0			0
$787$	−28303.8	−	16341.2i	−1.28198	−	0.740154i	−0.304774	−	0.952425i	$-0.598581\pi$
$787$	−28303.8	−	16341.2i	−1.28198	−	0.740154i	−0.977211	+	0.212271i	$0.931914\pi$
$788$		0			0
$789$	35365.8	−	20953.4i	1.59576	−	0.945452i
$790$		0			0
$791$	9896.72	+	18709.4i	0.444863	+	0.841000i
$792$		0			0
$793$	−3346.01	+	5795.46i	−0.149836	+	0.259524i
$794$		0			0
$795$	136.657	+	76.8584i	0.00609650	+	0.00342879i
$796$		0			0
$797$	−16978.3	−	29407.3i	−0.754583	−	1.30698i	−0.945581	−	0.325386i	$-0.894506\pi$
$797$	−16978.3	−	29407.3i	−0.754583	−	1.30698i	0.190998	−	0.981590i	$-0.438827\pi$
$798$		0			0
$799$	−7242.63	+	12544.6i	−0.320683	+	0.555440i
$800$		0			0
$801$	6317.32	+	10393.6i	0.278666	+	0.458477i
$802$		0			0
$803$	14639.2	+	25355.8i	0.643345	+	1.11431i
$804$		0			0
$805$	5803.15	+	215.077i	0.254080	+	0.00941673i
$806$		0			0
$807$	11326.7	−	20139.2i	0.494075	−	0.878482i
$808$		0			0
$809$	24445.8	−	14113.8i	1.06238	−	0.613367i	0.136292	−	0.990669i	$-0.456481\pi$
$809$	24445.8	−	14113.8i	1.06238	−	0.613367i	0.926090	+	0.377302i	$0.123148\pi$
$810$		0			0
$811$		−	12847.3i		−	0.556262i	−0.960543	−	0.278131i	$-0.910285\pi$
$811$		−	12847.3i		−	0.556262i	0.960543	−	0.278131i	$-0.0897150\pi$
$812$		0			0
$813$	−315.060	−	27952.0i	−0.0135912	−	1.20581i
$814$		0			0
$815$	5663.44	−	9809.36i	0.243413	−	0.421604i
$816$		0			0
$817$	−3859.77	+	2228.44i	−0.165283	+	0.0954263i
$818$		0			0
$819$	18058.9	+	261.931i	0.770489	+	0.0111753i
$820$		0			0
$821$	−8865.61	+	5118.56i	−0.376872	+	0.217587i	−0.676456	−	0.736483i	$-0.736485\pi$
$821$	−8865.61	+	5118.56i	−0.376872	+	0.217587i	0.299584	+	0.954070i	$0.403152\pi$
$822$		0			0
$823$	−9885.36	+	17122.0i	−0.418690	+	0.725193i	−0.995808	−	0.0914681i	$-0.970844\pi$
$823$	−9885.36	+	17122.0i	−0.418690	+	0.725193i	0.577118	+	0.816661i	$0.304177\pi$
$824$		0			0
$825$	−9889.86	+	5859.52i	−0.417358	+	0.247275i
$826$		0			0
$827$			2392.65i			0.100605i	0.998734	+	0.0503027i	$0.0160186\pi$
$827$			2392.65i			0.100605i	−0.998734	+	0.0503027i	$0.983981\pi$
$828$		0			0
$829$	37971.8	−	21923.0i	1.59085	−	0.918477i	0.597687	−	0.801730i	$-0.296087\pi$
$829$	37971.8	−	21923.0i	1.59085	−	0.918477i	0.993162	−	0.116747i	$-0.0372467\pi$
$830$		0			0
$831$	2170.67	+	3663.72i	0.0906134	+	0.152940i
$832$		0			0
$833$	7412.12	+	15363.5i	0.308301	+	0.639034i
$834$		0			0
$835$	−9232.97	−	15992.0i	−0.382659	−	0.662784i
$836$		0			0
$837$	26475.6	+	14114.5i	1.09335	+	0.582877i
$838$		0			0
$839$	14280.3	−	24734.3i	0.587619	−	1.01779i	−0.406925	−	0.913462i	$-0.633399\pi$
$839$	14280.3	−	24734.3i	0.587619	−	1.01779i	0.994543	−	0.104324i	$-0.0332678\pi$
$840$		0			0
$841$	−8871.85	−	15366.5i	−0.363765	−	0.630059i
$842$		0			0
$843$	225.313	+	19989.7i	0.00920546	+	0.816705i
$844$		0			0
$845$	3404.88	−	5897.42i	0.138617	−	0.240092i
$846$		0			0
$847$	−160.183	+	4322.01i	−0.00649817	+	0.175332i
$848$		0			0
$849$	8.01487	+	711.076i	0.000323992	+	0.0287445i
$850$		0			0
$851$	−6706.18	−	3871.81i	−0.270135	−	0.155962i
$852$		0			0
$853$	−6904.41	−	3986.26i	−0.277143	−	0.160008i	0.354987	−	0.934871i	$-0.384485\pi$
$853$	−6904.41	−	3986.26i	−0.277143	−	0.160008i	−0.632129	+	0.774863i	$0.717819\pi$
$854$		0			0
$855$	−3361.25	+	2042.99i	−0.134447	+	0.0817181i
$856$		0			0
$857$	−44239.4			−1.76335			−0.881674	−	0.471860i	$-0.843583\pi$
$857$	−44239.4			−1.76335			−0.881674	+	0.471860i	$0.843583\pi$
$858$		0			0
$859$			30106.1i			1.19582i	0.801564	+	0.597909i	$0.204001\pi$
$859$			30106.1i			1.19582i	−0.801564	+	0.597909i	$0.795999\pi$
$860$		0			0
$861$	−16697.2	−	10222.7i	−0.660905	−	0.404634i
$862$		0			0
$863$	−28410.6	−	16402.9i	−1.12063	−	0.646998i	−0.179071	−	0.983836i	$-0.557309\pi$
$863$	−28410.6	−	16402.9i	−1.12063	−	0.646998i	−0.941563	+	0.336838i	$0.890643\pi$
$864$		0			0
$865$	6516.32	+	11286.6i	0.256140	+	0.443648i
$866$		0			0
$867$	12676.4	−	142.882i	0.496555	−	0.00559690i
$868$		0			0
$869$	23417.8	−	13520.3i	0.914147	−	0.527783i
$870$		0			0
$871$		−	18872.5i		−	0.734180i
$872$		0			0
$873$	−8996.35	+	5468.05i	−0.348775	+	0.211988i
$874$		0			0
$875$	−1003.74	+	27082.5i	−0.0387800	+	1.04635i
$876$		0			0
$877$	−11450.8			−0.440897			−0.220448	−	0.975399i	$-0.570752\pi$
$877$	−11450.8			−0.440897			−0.220448	+	0.975399i	$0.570752\pi$
$878$		0			0
$879$	−14728.9	+	26188.6i	−0.565182	+	1.00491i
$880$		0			0
$881$	12917.8			0.493996			0.246998	−	0.969016i	$-0.420556\pi$
$881$	12917.8			0.493996			0.246998	+	0.969016i	$0.420556\pi$
$882$		0			0
$883$	−37086.7			−1.41344			−0.706719	−	0.707494i	$-0.749825\pi$
$883$	−37086.7			−1.41344			−0.706719	+	0.707494i	$0.749825\pi$
$884$		0			0
$885$	22105.6	−	249.162i	0.839629	−	0.00946384i
$886$		0			0
$887$	−42000.5			−1.58990			−0.794949	−	0.606676i	$-0.792503\pi$
$887$	−42000.5			−1.58990			−0.794949	+	0.606676i	$0.792503\pi$
$888$		0			0
$889$	−263.830	+	7118.58i	−0.00995340	+	0.268560i
$890$		0			0
$891$	−20349.4	+	13005.5i	−0.765130	+	0.489003i
$892$		0			0
$893$			5561.09i			0.208393i
$894$		0			0
$895$	11949.7	−	6899.18i	0.446297	−	0.257670i
$896$		0			0
$897$	3780.64	−	6722.11i	0.140727	−	0.250217i
$898$		0			0
$899$	−8716.56	−	15097.5i	−0.323374	−	0.560101i
$900$		0			0
$901$	170.317	+	98.3326i	0.00629754	+	0.00363589i
$902$		0			0
$903$	−578.932	+	22456.7i	−0.0213352	+	0.827589i
$904$		0			0
$905$		−	29455.5i		−	1.08191i
$906$		0			0
$907$	22380.3			0.819322			0.409661	−	0.912238i	$-0.365647\pi$
$907$	22380.3			0.819322			0.409661	+	0.912238i	$0.365647\pi$
$908$		0			0
$909$	−15375.3	+	28073.8i	−0.561021	+	1.02437i
$910$		0			0
$911$	−30660.0	−	17701.6i	−1.11505	−	0.643775i	−0.174918	−	0.984583i	$-0.555966\pi$
$911$	−30660.0	−	17701.6i	−1.11505	−	0.643775i	−0.940133	+	0.340808i	$0.889299\pi$
$912$		0			0
$913$	−15841.3	−	9145.98i	−0.574228	−	0.331531i
$914$		0			0
$915$	−6402.80	−	3601.05i	−0.231333	−	0.130106i
$916$		0			0
$917$	1061.62	−	28644.4i	0.0382311	−	1.03154i
$918$		0			0
$919$	−21.9845	+	38.0783i	−0.000789121	+	0.00136680i	−0.866420	−	0.499316i	$-0.833585\pi$
$919$	−21.9845	+	38.0783i	−0.000789121	+	0.00136680i	0.865631	+	0.500683i	$0.166918\pi$
$920$		0			0
$921$	27740.6	−	16435.7i	0.992490	−	0.588028i
$922$		0			0
$923$	−15834.6	−	27426.4i	−0.564684	−	0.978062i
$924$		0			0
$925$	6291.89	−	10897.9i	0.223650	−	0.387373i
$926$		0			0
$927$	−3590.51	−	1966.43i	−0.127214	−	0.0696722i
$928$		0			0
$929$	16722.9	+	28964.9i	0.590592	+	1.02293i	0.994153	+	0.107982i	$0.0344389\pi$
$929$	16722.9	+	28964.9i	0.590592	+	1.02293i	−0.403561	+	0.914953i	$0.632228\pi$
$930$		0			0
$931$	5413.51	+	3685.25i	0.190570	+	0.129730i
$932$		0			0
$933$	−52810.8	+	595.254i	−1.85310	+	0.0208872i
$934$		0			0
$935$	10886.8	−	6285.51i	0.380788	−	0.219848i
$936$		0			0
$937$		−	41213.4i		−	1.43691i	−0.695575	−	0.718453i	$-0.744850\pi$
$937$		−	41213.4i		−	1.43691i	0.695575	−	0.718453i	$-0.255150\pi$
$938$		0			0
$939$	−30962.9	−	17414.1i	−1.07608	−	0.605207i
$940$		0			0
$941$	7781.55	−	13478.0i	0.269576	−	0.466920i	−0.699176	−	0.714949i	$-0.746450\pi$
$941$	7781.55	−	13478.0i	0.269576	−	0.466920i	0.968752	+	0.248030i	$0.0797831\pi$
$942$		0			0
$943$	−7240.17	+	4180.11i	−0.250024	+	0.144351i
$944$		0			0
$945$	−64.0814	+	19825.7i	−0.00220589	+	0.682465i
$946$		0			0
$947$	−23054.1	+	13310.3i	−0.791085	+	0.456733i	−0.840344	−	0.542053i	$-0.817647\pi$
$947$	−23054.1	+	13310.3i	−0.791085	+	0.456733i	0.0492595	+	0.998786i	$0.484314\pi$
$948$		0			0
$949$	15960.5	−	27644.5i	0.545944	−	0.945603i
$950$		0			0
$951$	12195.3	+	6858.89i	0.415837	+	0.233874i
$952$		0			0
$953$			10595.3i			0.360142i	0.983654	+	0.180071i	$0.0576327\pi$
$953$			10595.3i			0.360142i	−0.983654	+	0.180071i	$0.942367\pi$
$954$		0			0
$955$	1096.96	−	633.328i	0.0371693	−	0.0214597i
$956$		0			0
$957$	14031.6	−	158.157i	0.473959	−	0.00534221i
$958$		0			0
$959$	41187.2	+	1526.49i	1.38687	+	0.0514003i
$960$		0			0
$961$	7971.32	+	13806.7i	0.267575	+	0.463453i
$962$		0			0
$963$	−44057.0	+	26778.2i	−1.47426	+	0.896069i
$964$		0			0
$965$	−15404.1	+	26680.6i	−0.513860	+	0.890031i
$966$		0			0
$967$	14982.9	+	25951.1i	0.498259	+	0.863009i	0.999998	−	0.00200949i	$-0.000639640\pi$
$967$	14982.9	+	25951.1i	0.498259	+	0.863009i	−0.501739	+	0.865019i	$0.667306\pi$
$968$		0			0
$969$	−4244.78	+	2514.93i	−0.140724	+	0.0833760i
$970$		0			0
$971$	10567.9	−	18304.1i	0.349268	−	0.604950i	−0.636851	−	0.770987i	$-0.719764\pi$
$971$	10567.9	−	18304.1i	0.349268	−	0.604950i	0.986120	+	0.166036i	$0.0530969\pi$
$972$		0			0
$973$	−25633.8	−	48459.9i	−0.844585	−	1.59666i
$974$		0			0
$975$	10923.8	+	6143.74i	0.358811	+	0.201802i
$976$		0			0
$977$	−38224.9	−	22069.2i	−1.25171	−	0.722677i	−0.280263	−	0.959923i	$-0.590422\pi$
$977$	−38224.9	−	22069.2i	−1.25171	−	0.722677i	−0.971449	+	0.237247i	$0.923755\pi$
$978$		0			0
$979$	−12924.1	−	7461.74i	−0.421916	−	0.243594i
$980$		0			0
$981$	−40044.4	+	902.833i	−1.30328	+	0.0293835i
$982$		0			0
$983$	−28627.9			−0.928879			−0.464440	−	0.885605i	$-0.653744\pi$
$983$	−28627.9			−0.928879			−0.464440	+	0.885605i	$0.653744\pi$
$984$		0			0
$985$			14688.0i			0.475127i
$986$		0			0
$987$	23905.2	+	14635.8i	0.770934	+	0.471999i
$988$		0			0
$989$	8307.48	+	4796.32i	0.267100	+	0.154211i
$990$		0			0
$991$	19984.7	+	34614.6i	0.640601	+	1.10955i	0.985299	+	0.170840i	$0.0546481\pi$
$991$	19984.7	+	34614.6i	0.640601	+	1.10955i	−0.344698	+	0.938714i	$0.612019\pi$
$992$		0			0
$993$	−3909.68	+	6951.54i	−0.124944	+	0.222155i
$994$		0			0
$995$	4673.81	−	2698.43i	0.148914	−	0.0859758i
$996$		0			0
$997$		−	38496.9i		−	1.22288i	−0.791291	−	0.611439i	$-0.790591\pi$
$997$		−	38496.9i		−	1.22288i	0.791291	−	0.611439i	$-0.209409\pi$
$998$		0			0
$999$	12437.0	−	23328.9i	0.393882	−	0.738834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.bm.a.173.16	yes	48
3.2	odd	2		756.4.bm.a.89.18		48
7.3	odd	6		252.4.w.a.101.8	yes	48
9.4	even	3		756.4.w.a.341.18		48
9.5	odd	6		252.4.w.a.5.8	✓	48
21.17	even	6		756.4.w.a.521.18		48
63.31	odd	6		756.4.bm.a.17.18		48
63.59	even	6	inner	252.4.bm.a.185.16	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.8	✓	48	9.5	odd	6
252.4.w.a.101.8	yes	48	7.3	odd	6
252.4.bm.a.173.16	yes	48	1.1	even	1	trivial
252.4.bm.a.185.16	yes	48	63.59	even	6	inner
756.4.w.a.341.18		48	9.4	even	3
756.4.w.a.521.18		48	21.17	even	6
756.4.bm.a.17.18		48	63.31	odd	6
756.4.bm.a.89.18		48	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.64863 + 4.47043i) q^{3} -7.63023 q^{5} +(-0.685930 + 18.5076i) q^{7} +(-12.9695 + 23.6810i) q^{9} +O(q^{10})\)	\(q+(2.64863 + 4.47043i) q^{3} -7.63023 q^{5} +(-0.685930 + 18.5076i) q^{7} +(-12.9695 + 23.6810i) q^{9} -33.1281i q^{11} +(-31.2793 + 18.0591i) q^{13} +(-20.2097 - 34.1104i) q^{15} +(-24.8660 - 43.0692i) q^{17} +(-16.5348 - 9.54640i) q^{19} +(-84.5535 + 45.9532i) q^{21} +41.0939i q^{23} -66.7796 q^{25} +(-140.216 + 4.74292i) q^{27} +(70.5972 + 40.7593i) q^{29} +(-185.203 - 106.927i) q^{31} +(148.097 - 87.7442i) q^{33} +(5.23380 - 141.217i) q^{35} +(-94.2188 + 163.192i) q^{37} +(-163.580 - 92.0002i) q^{39} +(101.721 + 176.186i) q^{41} +(116.716 - 202.159i) q^{43} +(98.9605 - 180.692i) q^{45} +(-145.633 - 252.244i) q^{47} +(-342.059 - 25.3898i) q^{49} +(126.677 - 225.236i) q^{51} +(-3.42470 + 1.97725i) q^{53} +252.775i q^{55} +(-1.11816 - 99.2028i) q^{57} +(-278.792 + 482.882i) q^{59} +(160.458 - 92.6404i) q^{61} +(-429.382 - 256.278i) q^{63} +(238.669 - 137.795i) q^{65} +(-261.260 + 452.516i) q^{67} +(-183.707 + 108.842i) q^{69} +876.821i q^{71} +(-765.387 + 441.896i) q^{73} +(-176.874 - 298.534i) q^{75} +(613.121 + 22.7236i) q^{77} +(408.120 + 706.885i) q^{79} +(-392.583 - 614.263i) q^{81} +(276.079 - 478.183i) q^{83} +(189.733 + 328.628i) q^{85} +(4.77410 + 423.557i) q^{87} +(225.239 - 390.125i) q^{89} +(-312.775 - 591.291i) q^{91} +(-12.5243 - 1111.15i) q^{93} +(126.165 + 72.8412i) q^{95} +(337.678 + 194.959i) q^{97} +(784.509 + 429.656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} - 30 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 - 30 * q^9	\( 48 q + 6 q^{7} - 30 q^{9} + 36 q^{13} + 66 q^{15} + 72 q^{17} + 126 q^{21} + 1200 q^{25} + 396 q^{27} + 42 q^{29} - 90 q^{31} + 108 q^{33} - 390 q^{35} + 84 q^{37} + 1014 q^{39} + 618 q^{41} - 42 q^{43} - 1014 q^{45} + 198 q^{47} - 276 q^{49} + 408 q^{51} + 1620 q^{53} + 492 q^{57} + 750 q^{59} - 1314 q^{61} + 1542 q^{63} + 564 q^{65} + 294 q^{67} + 924 q^{69} - 1410 q^{75} - 2448 q^{77} - 804 q^{79} - 666 q^{81} - 360 q^{85} + 1788 q^{87} - 1722 q^{89} + 540 q^{91} + 1128 q^{93} - 2946 q^{95} + 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 - 30 * q^9 + 36 * q^13 + 66 * q^15 + 72 * q^17 + 126 * q^21 + 1200 * q^25 + 396 * q^27 + 42 * q^29 - 90 * q^31 + 108 * q^33 - 390 * q^35 + 84 * q^37 + 1014 * q^39 + 618 * q^41 - 42 * q^43 - 1014 * q^45 + 198 * q^47 - 276 * q^49 + 408 * q^51 + 1620 * q^53 + 492 * q^57 + 750 * q^59 - 1314 * q^61 + 1542 * q^63 + 564 * q^65 + 294 * q^67 + 924 * q^69 - 1410 * q^75 - 2448 * q^77 - 804 * q^79 - 666 * q^81 - 360 * q^85 + 1788 * q^87 - 1722 * q^89 + 540 * q^91 + 1128 * q^93 - 2946 * q^95 + 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more