LMFDB - Embedded newform 912.3.be.e.145.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("912.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.8502001097$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.3
Root			$0.403374 + 1.68443i$ of defining polynomial
Character	$\chi$	$=$	912.145
Dual form			912.3.be.e.673.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(4.17458 + 7.23058i) q^{5} -4.32088 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(4.17458 + 7.23058i) q^{5} -4.32088 q^{7} +(1.50000 - 2.59808i) q^{9} +16.6044 q^{11} +(2.07976 + 1.20075i) q^{13} +(12.5237 + 7.23058i) q^{15} +(2.60803 + 4.51724i) q^{17} +(-6.76940 - 17.7532i) q^{19} +(-6.48133 + 3.74200i) q^{21} +(17.8729 - 30.9568i) q^{23} +(-22.3542 + 38.7186i) q^{25} -5.19615i q^{27} +(35.7867 + 20.6615i) q^{29} +36.8485i q^{31} +(24.9066 - 14.3799i) q^{33} +(-18.0379 - 31.2425i) q^{35} +0.393159i q^{37} +4.15951 q^{39} +(-31.8133 + 18.3674i) q^{41} +(28.8159 + 49.9107i) q^{43} +25.0475 q^{45} +(-27.9536 + 48.4170i) q^{47} -30.3300 q^{49} +(7.82409 + 4.51724i) q^{51} +(77.2086 + 44.5764i) q^{53} +(69.3165 + 120.060i) q^{55} +(-25.5288 - 20.7673i) q^{57} +(45.3269 - 26.1695i) q^{59} +(27.1555 - 47.0347i) q^{61} +(-6.48133 + 11.2260i) q^{63} +20.0505i q^{65} +(-85.8161 - 49.5459i) q^{67} -61.9135i q^{69} +(-69.5525 + 40.1562i) q^{71} +(14.7553 + 25.5569i) q^{73} +77.4373i q^{75} -71.7458 q^{77} +(-55.3483 + 31.9554i) q^{79} +(-4.50000 - 7.79423i) q^{81} -61.9528 q^{83} +(-21.7749 + 37.7152i) q^{85} +71.5735 q^{87} +(0.168059 + 0.0970291i) q^{89} +(-8.98639 - 5.18830i) q^{91} +(31.9117 + 55.2727i) q^{93} +(100.106 - 123.059i) q^{95} +(91.0094 - 52.5443i) q^{97} +(24.9066 - 43.1396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9}+O(q^{10}) $ 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9	$ 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9} + 20 q^{11} + 21 q^{13} + 12 q^{15} - 2 q^{17} + 10 q^{19} - 15 q^{21} + 2 q^{23} - 5 q^{25} + 114 q^{29} + 30 q^{33} - 32 q^{35} + 42 q^{39} + 48 q^{41} + 21 q^{43} + 24 q^{45} - 46 q^{47} - 240 q^{49} - 6 q^{51} - 18 q^{53} + 140 q^{55} - 3 q^{57} + 144 q^{59} + 19 q^{61} - 15 q^{63} - 201 q^{67} - 204 q^{71} + 51 q^{73} - 220 q^{77} - 153 q^{79} - 27 q^{81} - 52 q^{83} - 92 q^{85} + 228 q^{87} + 216 q^{89} + 57 q^{91} - 15 q^{93} + 248 q^{95} + 12 q^{97} + 30 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9 + 20 * q^11 + 21 * q^13 + 12 * q^15 - 2 * q^17 + 10 * q^19 - 15 * q^21 + 2 * q^23 - 5 * q^25 + 114 * q^29 + 30 * q^33 - 32 * q^35 + 42 * q^39 + 48 * q^41 + 21 * q^43 + 24 * q^45 - 46 * q^47 - 240 * q^49 - 6 * q^51 - 18 * q^53 + 140 * q^55 - 3 * q^57 + 144 * q^59 + 19 * q^61 - 15 * q^63 - 201 * q^67 - 204 * q^71 + 51 * q^73 - 220 * q^77 - 153 * q^79 - 27 * q^81 - 52 * q^83 - 92 * q^85 + 228 * q^87 + 216 * q^89 + 57 * q^91 - 15 * q^93 + 248 * q^95 + 12 * q^97 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$		0			0
$5$	4.17458	+	7.23058i	0.834916	+	1.44612i	0.894099	+	0.447870i	$0.147817\pi$
$5$	4.17458	+	7.23058i	0.834916	+	1.44612i	−0.0591831	+	0.998247i	$0.518850\pi$
$6$		0			0
$7$	−4.32088			−0.617269			−0.308635	−	0.951181i	$-0.599872\pi$
$7$	−4.32088			−0.617269			−0.308635	+	0.951181i	$0.599872\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$		0			0
$11$	16.6044			1.50949			0.754746	−	0.656017i	$-0.227760\pi$
$11$	16.6044			1.50949			0.754746	+	0.656017i	$0.227760\pi$
$12$		0			0
$13$	2.07976	+	1.20075i	0.159981	+	0.0923653i	0.577853	−	0.816141i	$-0.303891\pi$
$13$	2.07976	+	1.20075i	0.159981	+	0.0923653i	−0.417872	+	0.908506i	$0.637224\pi$
$14$		0			0
$15$	12.5237	+	7.23058i	0.834916	+	0.482039i
$16$		0			0
$17$	2.60803	+	4.51724i	0.153414	+	0.265720i	0.932480	−	0.361221i	$-0.117640\pi$
$17$	2.60803	+	4.51724i	0.153414	+	0.265720i	−0.779067	+	0.626941i	$0.784307\pi$
$18$		0			0
$19$	−6.76940	−	17.7532i	−0.356284	−	0.934378i
$19$	−6.76940	−	17.7532i	−0.356284	−	0.934378i
$20$		0			0
$21$	−6.48133	+	3.74200i	−0.308635	+	0.178190i
$22$		0			0
$23$	17.8729	−	30.9568i	0.777082	−	1.34595i	−0.156534	−	0.987673i	$-0.550032\pi$
$23$	17.8729	−	30.9568i	0.777082	−	1.34595i	0.933617	−	0.358274i	$-0.116635\pi$
$24$		0			0
$25$	−22.3542	+	38.7186i	−0.894169	+	1.54875i
$26$		0			0
$27$		−	5.19615i		−	0.192450i
$28$		0			0
$29$	35.7867	+	20.6615i	1.23403	+	0.712465i	0.967867	−	0.251464i	$-0.0809120\pi$
$29$	35.7867	+	20.6615i	1.23403	+	0.712465i	0.266159	+	0.963929i	$0.414245\pi$
$30$		0			0
$31$			36.8485i			1.18866i	0.804221	+	0.594330i	$0.202583\pi$
$31$			36.8485i			1.18866i	−0.804221	+	0.594330i	$0.797417\pi$
$32$		0			0
$33$	24.9066	−	14.3799i	0.754746	−	0.435753i
$34$		0			0
$35$	−18.0379	−	31.2425i	−0.515368	−	0.892643i
$36$		0			0
$37$			0.393159i			0.0106259i	0.999986	+	0.00531296i	$0.00169117\pi$
$37$			0.393159i			0.0106259i	−0.999986	+	0.00531296i	$0.998309\pi$
$38$		0			0
$39$	4.15951			0.106654
$40$		0			0
$41$	−31.8133	+	18.3674i	−0.775933	+	0.447985i	−0.834987	−	0.550269i	$-0.814525\pi$
$41$	−31.8133	+	18.3674i	−0.775933	+	0.447985i	0.0590538	+	0.998255i	$0.481192\pi$
$42$		0			0
$43$	28.8159	+	49.9107i	0.670138	+	1.16071i	0.977865	+	0.209239i	$0.0670986\pi$
$43$	28.8159	+	49.9107i	0.670138	+	1.16071i	−0.307726	+	0.951475i	$0.599568\pi$
$44$		0			0
$45$	25.0475			0.556611
$46$		0			0
$47$	−27.9536	+	48.4170i	−0.594757	+	1.03015i	0.398824	+	0.917027i	$0.369418\pi$
$47$	−27.9536	+	48.4170i	−0.594757	+	1.03015i	−0.993581	+	0.113122i	$0.963915\pi$
$48$		0			0
$49$	−30.3300			−0.618979
$50$		0			0
$51$	7.82409	+	4.51724i	0.153414	+	0.0885734i
$52$		0			0
$53$	77.2086	+	44.5764i	1.45677	+	0.841064i	0.998851	−	0.0479320i	$-0.0152631\pi$
$53$	77.2086	+	44.5764i	1.45677	+	0.841064i	0.457915	+	0.888996i	$0.348596\pi$
$54$		0			0
$55$	69.3165	+	120.060i	1.26030	+	2.18290i
$56$		0			0
$57$	−25.5288	−	20.7673i	−0.447874	−	0.364338i
$58$		0			0
$59$	45.3269	−	26.1695i	0.768252	−	0.443551i	−0.0639986	−	0.997950i	$-0.520385\pi$
$59$	45.3269	−	26.1695i	0.768252	−	0.443551i	0.832251	+	0.554399i	$0.187052\pi$
$60$		0			0
$61$	27.1555	−	47.0347i	0.445172	−	0.771061i	−0.552892	−	0.833253i	$-0.686476\pi$
$61$	27.1555	−	47.0347i	0.445172	−	0.771061i	0.998064	+	0.0621920i	$0.0198091\pi$
$62$		0			0
$63$	−6.48133	+	11.2260i	−0.102878	+	0.178190i
$64$		0			0
$65$			20.0505i			0.308469i
$66$		0			0
$67$	−85.8161	−	49.5459i	−1.28084	−	0.739491i	−0.303835	−	0.952725i	$-0.598267\pi$
$67$	−85.8161	−	49.5459i	−1.28084	−	0.739491i	−0.977001	+	0.213233i	$0.931601\pi$
$68$		0			0
$69$		−	61.9135i		−	0.897298i
$70$		0			0
$71$	−69.5525	+	40.1562i	−0.979613	+	0.565580i	−0.902153	−	0.431416i	$-0.858014\pi$
$71$	−69.5525	+	40.1562i	−0.979613	+	0.565580i	−0.0774599	+	0.996995i	$0.524681\pi$
$72$		0			0
$73$	14.7553	+	25.5569i	0.202127	+	0.350094i	0.949214	−	0.314633i	$-0.101881\pi$
$73$	14.7553	+	25.5569i	0.202127	+	0.350094i	−0.747087	+	0.664727i	$0.768548\pi$
$74$		0			0
$75$			77.4373i			1.03250i
$76$		0			0
$77$	−71.7458			−0.931764
$78$		0			0
$79$	−55.3483	+	31.9554i	−0.700612	+	0.404498i	−0.807575	−	0.589765i	$-0.799221\pi$
$79$	−55.3483	+	31.9554i	−0.700612	+	0.404498i	0.106963	+	0.994263i	$0.465887\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−61.9528			−0.746419			−0.373210	−	0.927747i	$-0.621743\pi$
$83$	−61.9528			−0.746419			−0.373210	+	0.927747i	$0.621743\pi$
$84$		0			0
$85$	−21.7749	+	37.7152i	−0.256175	+	0.443708i
$86$		0			0
$87$	71.5735			0.822684
$88$		0			0
$89$	0.168059	+	0.0970291i	0.00188831	+	0.00109021i	0.500944	−	0.865480i	$-0.332986\pi$
$89$	0.168059	+	0.0970291i	0.00188831	+	0.00109021i	−0.499056	+	0.866570i	$0.666320\pi$
$90$		0			0
$91$	−8.98639	−	5.18830i	−0.0987515	−	0.0570142i
$92$		0			0
$93$	31.9117	+	55.2727i	0.343137	+	0.594330i
$94$		0			0
$95$	100.106	−	123.059i	1.05375	−	1.29536i
$96$		0			0
$97$	91.0094	−	52.5443i	0.938242	−	0.541694i	0.0488329	−	0.998807i	$-0.484450\pi$
$97$	91.0094	−	52.5443i	0.938242	−	0.541694i	0.889409	+	0.457113i	$0.151116\pi$
$98$		0			0
$99$	24.9066	−	43.1396i	0.251582	−	0.435753i
$100$		0			0
$101$	16.0610	−	27.8184i	0.159019	−	0.275430i	−0.775496	−	0.631353i	$-0.782500\pi$
$101$	16.0610	−	27.8184i	0.159019	−	0.275430i	0.934515	+	0.355923i	$0.115833\pi$
$102$		0			0
$103$			41.8663i			0.406469i	0.979130	+	0.203234i	$0.0651453\pi$
$103$			41.8663i			0.406469i	−0.979130	+	0.203234i	$0.934855\pi$
$104$		0			0
$105$	−54.1136	−	31.2425i	−0.515368	−	0.297548i
$106$		0			0
$107$			35.7022i			0.333666i	0.985985	+	0.166833i	$0.0533540\pi$
$107$			35.7022i			0.333666i	−0.985985	+	0.166833i	$0.946646\pi$
$108$		0			0
$109$	99.0684	−	57.1972i	0.908885	−	0.524745i	0.0288125	−	0.999585i	$-0.490827\pi$
$109$	99.0684	−	57.1972i	0.908885	−	0.524745i	0.880072	+	0.474840i	$0.157494\pi$
$110$		0			0
$111$	0.340485	+	0.589738i	0.00306744	+	0.00531296i
$112$		0			0
$113$		−	76.2121i		−	0.674443i	−0.941425	−	0.337222i	$-0.890513\pi$
$113$		−	76.2121i		−	0.674443i	0.941425	−	0.337222i	$-0.109487\pi$
$114$		0			0
$115$	298.447			2.59519
$116$		0			0
$117$	6.23927	−	3.60225i	0.0533271	−	0.0307884i
$118$		0			0
$119$	−11.2690	−	19.5185i	−0.0946975	−	0.164021i
$120$		0			0
$121$	154.707			1.27857
$122$		0			0
$123$	−31.8133	+	55.1022i	−0.258644	+	0.447985i
$124$		0			0
$125$	−164.549			−1.31639
$126$		0			0
$127$	94.0779	+	54.3159i	0.740771	+	0.427684i	0.822349	−	0.568983i	$-0.192663\pi$
$127$	94.0779	+	54.3159i	0.740771	+	0.427684i	−0.0815789	+	0.996667i	$0.525996\pi$
$128$		0			0
$129$	86.4478	+	49.9107i	0.670138	+	0.386905i
$130$		0			0
$131$	−64.3941	−	111.534i	−0.491558	−	0.851403i	0.508395	−	0.861124i	$-0.330239\pi$
$131$	−64.3941	−	111.534i	−0.491558	−	0.851403i	−0.999953	+	0.00972086i	$0.996906\pi$
$132$		0			0
$133$	29.2498	+	76.7094i	0.219923	+	0.576763i
$134$		0			0
$135$	37.5712	−	21.6917i	0.278305	−	0.160680i
$136$		0			0
$137$	61.9054	−	107.223i	0.451864	−	0.782652i	−0.546638	−	0.837369i	$-0.684092\pi$
$137$	61.9054	−	107.223i	0.451864	−	0.782652i	0.998502	+	0.0547174i	$0.0174258\pi$
$138$		0			0
$139$	10.3083	−	17.8546i	0.0741607	−	0.128450i	−0.826560	−	0.562848i	$-0.809706\pi$
$139$	10.3083	−	17.8546i	0.0741607	−	0.128450i	0.900721	+	0.434398i	$0.143039\pi$
$140$		0			0
$141$			96.8340i			0.686766i
$142$		0			0
$143$	34.5332	+	19.9377i	0.241491	+	0.139425i
$144$		0			0
$145$			345.012i			2.37939i
$146$		0			0
$147$	−45.4949	+	26.2665i	−0.309489	+	0.178684i
$148$		0			0
$149$	106.807	+	184.996i	0.716827	+	1.24158i	0.962251	+	0.272165i	$0.0877398\pi$
$149$	106.807	+	184.996i	0.716827	+	1.24158i	−0.245423	+	0.969416i	$0.578927\pi$
$150$		0			0
$151$		−	250.524i		−	1.65910i	−0.558432	−	0.829550i	$-0.688597\pi$
$151$		−	250.524i		−	1.65910i	0.558432	−	0.829550i	$-0.311403\pi$
$152$		0			0
$153$	15.6482			0.102276
$154$		0			0
$155$	−266.436	+	153.827i	−1.71894	+	0.992431i
$156$		0			0
$157$	−124.466	−	215.581i	−0.792774	−	1.37313i	−0.924243	−	0.381805i	$-0.875303\pi$
$157$	−124.466	−	215.581i	−0.792774	−	1.37313i	0.131469	−	0.991320i	$-0.458031\pi$
$158$		0			0
$159$	154.417			0.971177
$160$		0			0
$161$	−77.2267	+	133.761i	−0.479669	+	0.830811i
$162$		0			0
$163$	−30.2648			−0.185674			−0.0928370	−	0.995681i	$-0.529594\pi$
$163$	−30.2648			−0.185674			−0.0928370	+	0.995681i	$0.529594\pi$
$164$		0			0
$165$	207.949	+	120.060i	1.26030	+	0.727634i
$166$		0			0
$167$	113.985	+	65.8094i	0.682546	+	0.394068i	0.800814	−	0.598914i	$-0.204401\pi$
$167$	113.985	+	65.8094i	0.682546	+	0.394068i	−0.118268	+	0.992982i	$0.537734\pi$
$168$		0			0
$169$	−81.6164	−	141.364i	−0.482937	−	0.836472i
$170$		0			0
$171$	−56.2782	−	9.04234i	−0.329112	−	0.0528792i
$172$		0			0
$173$	−164.875	+	95.1905i	−0.953033	+	0.550234i	−0.894022	−	0.448023i	$-0.852128\pi$
$173$	−164.875	+	95.1905i	−0.953033	+	0.550234i	−0.0590113	+	0.998257i	$0.518795\pi$
$174$		0			0
$175$	96.5900	−	167.299i	0.551943	−	0.955993i
$176$		0			0
$177$	45.3269	−	78.5085i	0.256084	−	0.443551i
$178$		0			0
$179$			0.765561i			0.00427688i	0.999998	+	0.00213844i	$0.000680686\pi$
$179$			0.765561i			0.00427688i	−0.999998	+	0.00213844i	$0.999319\pi$
$180$		0			0
$181$	212.331	+	122.589i	1.17310	+	0.677288i	0.954408	−	0.298506i	$-0.0964884\pi$
$181$	212.331	+	122.589i	1.17310	+	0.677288i	0.218690	+	0.975794i	$0.429822\pi$
$182$		0			0
$183$		−	94.0694i		−	0.514041i
$184$		0			0
$185$	−2.84277	+	1.64127i	−0.0153663	+	0.00887174i
$186$		0			0
$187$	43.3049	+	75.0062i	0.231577	+	0.401103i
$188$		0			0
$189$			22.4520i			0.118794i
$190$		0			0
$191$	2.33983			0.0122504			0.00612521	−	0.999981i	$-0.498050\pi$
$191$	2.33983			0.0122504			0.00612521	+	0.999981i	$0.498050\pi$
$192$		0			0
$193$	−196.862	+	113.658i	−1.02001	+	0.588903i	−0.914107	−	0.405473i	$-0.867107\pi$
$193$	−196.862	+	113.658i	−1.02001	+	0.588903i	−0.105903	+	0.994376i	$0.533773\pi$
$194$		0			0
$195$	17.3642	+	30.0757i	0.0890473	+	0.154234i
$196$		0			0
$197$	−253.748			−1.28806			−0.644031	−	0.764999i	$-0.722739\pi$
$197$	−253.748			−1.28806			−0.644031	+	0.764999i	$0.722739\pi$
$198$		0			0
$199$	121.762	−	210.897i	0.611867	−	1.05978i	−0.379059	−	0.925373i	$-0.623752\pi$
$199$	121.762	−	210.897i	0.611867	−	1.05978i	0.990926	−	0.134412i	$-0.0429145\pi$
$200$		0			0
$201$	−171.632			−0.853891
$202$		0			0
$203$	−154.630	−	89.2759i	−0.761726	−	0.439783i
$204$		0			0
$205$	−265.614	−	153.352i	−1.29568	−	0.748060i
$206$		0			0
$207$	−53.6187	−	92.8703i	−0.259027	−	0.448649i
$208$		0			0
$209$	−112.402	−	294.781i	−0.537809	−	1.41044i
$210$		0			0
$211$	−258.747	+	149.388i	−1.22629	+	0.707999i	−0.966252	−	0.257599i	$-0.917069\pi$
$211$	−258.747	+	149.388i	−1.22629	+	0.707999i	−0.260039	+	0.965598i	$0.583735\pi$
$212$		0			0
$213$	−69.5525	+	120.469i	−0.326538	+	0.565580i
$214$		0			0
$215$	−240.589	+	416.712i	−1.11902	+	1.93820i
$216$		0			0
$217$		−	159.218i		−	0.733723i
$218$		0			0
$219$	44.2658	+	25.5569i	0.202127	+	0.116698i
$220$		0			0
$221$			12.5264i			0.0566803i
$222$		0			0
$223$	117.466	−	67.8189i	0.526752	−	0.304120i	−0.212941	−	0.977065i	$-0.568304\pi$
$223$	117.466	−	67.8189i	0.526752	−	0.304120i	0.739693	+	0.672945i	$0.234971\pi$
$224$		0			0
$225$	67.0627	+	116.156i	0.298056	+	0.516249i
$226$		0			0
$227$			81.4669i			0.358885i	0.983768	+	0.179443i	$0.0574294\pi$
$227$			81.4669i			0.358885i	−0.983768	+	0.179443i	$0.942571\pi$
$228$		0			0
$229$	350.832			1.53202			0.766008	−	0.642831i	$-0.222240\pi$
$229$	350.832			1.53202			0.766008	+	0.642831i	$0.222240\pi$
$230$		0			0
$231$	−107.619	+	62.1337i	−0.465882	+	0.268977i
$232$		0			0
$233$	−192.369	−	333.192i	−0.825616	−	1.43001i	−0.901448	−	0.432888i	$-0.857495\pi$
$233$	−192.369	−	333.192i	−0.825616	−	1.43001i	0.0758317	−	0.997121i	$-0.475839\pi$
$234$		0			0
$235$	−466.778			−1.98629
$236$		0			0
$237$	−55.3483	+	95.8661i	−0.233537	+	0.404498i
$238$		0			0
$239$	119.840			0.501423			0.250711	−	0.968062i	$-0.419335\pi$
$239$	119.840			0.501423			0.250711	+	0.968062i	$0.419335\pi$
$240$		0			0
$241$	285.201	+	164.661i	1.18341	+	0.683241i	0.956800	−	0.290746i	$-0.0939033\pi$
$241$	285.201	+	164.661i	1.18341	+	0.683241i	0.226607	+	0.973986i	$0.427237\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−126.615	−	219.303i	−0.516795	−	0.895115i
$246$		0			0
$247$	7.23839	−	45.0506i	0.0293052	−	0.182391i
$248$		0			0
$249$	−92.9292	+	53.6527i	−0.373210	+	0.215473i
$250$		0			0
$251$	21.9983	−	38.1023i	0.0876428	−	0.151802i	−0.818871	−	0.573977i	$-0.805400\pi$
$251$	21.9983	−	38.1023i	0.0876428	−	0.151802i	0.906514	+	0.422175i	$0.138733\pi$
$252$		0			0
$253$	296.769	−	514.019i	1.17300	−	2.03170i
$254$		0			0
$255$			75.4303i			0.295805i
$256$		0			0
$257$	−183.130	−	105.730i	−0.712570	−	0.411402i	0.0994419	−	0.995043i	$-0.468294\pi$
$257$	−183.130	−	105.730i	−0.712570	−	0.411402i	−0.812012	+	0.583641i	$0.801628\pi$
$258$		0			0
$259$		−	1.69879i		−	0.00655905i
$260$		0			0
$261$	107.360	−	61.9845i	0.411342	−	0.237488i
$262$		0			0
$263$	−239.650	−	415.086i	−0.911217	−	1.57827i	−0.812347	−	0.583174i	$-0.801810\pi$
$263$	−239.650	−	415.086i	−0.911217	−	1.57827i	−0.0988702	−	0.995100i	$-0.531523\pi$
$264$		0			0
$265$			744.351i			2.80887i
$266$		0			0
$267$	0.336119			0.00125887
$268$		0			0
$269$	168.125	−	97.0669i	0.624999	−	0.360843i	−0.153814	−	0.988100i	$-0.549156\pi$
$269$	168.125	−	97.0669i	0.624999	−	0.360843i	0.778813	+	0.627256i	$0.215822\pi$
$270$		0			0
$271$	−230.655	−	399.505i	−0.851124	−	1.47419i	−0.880195	−	0.474612i	$-0.842588\pi$
$271$	−230.655	−	399.505i	−0.851124	−	1.47419i	0.0290713	−	0.999577i	$-0.490745\pi$
$272$		0			0
$273$	−17.9728			−0.0658344
$274$		0			0
$275$	−371.179	+	642.901i	−1.34974	+	2.33782i
$276$		0			0
$277$	−321.736			−1.16150			−0.580750	−	0.814082i	$-0.697241\pi$
$277$	−321.736			−1.16150			−0.580750	+	0.814082i	$0.697241\pi$
$278$		0			0
$279$	95.7351	+	55.2727i	0.343137	+	0.198110i
$280$		0			0
$281$	−326.416	−	188.457i	−1.16162	−	0.670664i	−0.209931	−	0.977716i	$-0.567324\pi$
$281$	−326.416	−	188.457i	−1.16162	−	0.670664i	−0.951693	+	0.307052i	$0.900657\pi$
$282$		0			0
$283$	149.632	+	259.170i	0.528735	+	0.915795i	0.999439	+	0.0335040i	$0.0106667\pi$
$283$	149.632	+	259.170i	0.528735	+	0.915795i	−0.470704	+	0.882291i	$0.656000\pi$
$284$		0			0
$285$	43.5876	−	271.283i	0.152939	−	0.951870i
$286$		0			0
$287$	137.461	−	79.3634i	0.478960	−	0.276528i
$288$		0			0
$289$	130.896	−	226.719i	0.452929	−	0.784495i
$290$		0			0
$291$	91.0094	−	157.633i	0.312747	−	0.541694i
$292$		0			0
$293$		−	413.521i		−	1.41133i	−0.708544	−	0.705667i	$-0.750648\pi$
$293$		−	413.521i		−	1.41133i	0.708544	−	0.705667i	$-0.249352\pi$
$294$		0			0
$295$	378.441	+	218.493i	1.28285	+	0.740655i
$296$		0			0
$297$		−	86.2791i		−	0.290502i
$298$		0			0
$299$	74.3426	−	42.9217i	0.248637	−	0.143551i
$300$		0			0
$301$	−124.510	−	215.658i	−0.413656	−	0.716473i
$302$		0			0
$303$		−	55.6368i		−	0.183620i
$304$		0			0
$305$	453.451			1.48673
$306$		0			0
$307$	−331.226	+	191.233i	−1.07891	+	0.622909i	−0.930602	−	0.366032i	$-0.880716\pi$
$307$	−331.226	+	191.233i	−1.07891	+	0.622909i	−0.148308	+	0.988941i	$0.547383\pi$
$308$		0			0
$309$	36.2572	+	62.7994i	0.117337	+	0.203234i
$310$		0			0
$311$	146.591			0.471353			0.235676	−	0.971832i	$-0.424269\pi$
$311$	146.591			0.471353			0.235676	+	0.971832i	$0.424269\pi$
$312$		0			0
$313$	−49.4120	+	85.5841i	−0.157866	+	0.273432i	−0.934099	−	0.357014i	$-0.883795\pi$
$313$	−49.4120	+	85.5841i	−0.157866	+	0.273432i	0.776233	+	0.630446i	$0.217128\pi$
$314$		0			0
$315$	−108.227			−0.343579
$316$		0			0
$317$	−45.8278	−	26.4587i	−0.144567	−	0.0834660i	0.425972	−	0.904737i	$-0.359932\pi$
$317$	−45.8278	−	26.4587i	−0.144567	−	0.0834660i	−0.570539	+	0.821271i	$0.693266\pi$
$318$		0			0
$319$	594.218	+	343.072i	1.86275	+	1.07546i
$320$		0			0
$321$	30.9190	+	53.5534i	0.0963210	+	0.166833i
$322$		0			0
$323$	62.5406	−	76.8799i	0.193624	−	0.238018i
$324$		0			0
$325$	−92.9827	+	53.6836i	−0.286101	+	0.165180i
$326$		0			0
$327$	99.0684	−	171.592i	0.302962	−	0.524745i
$328$		0			0
$329$	120.784	−	209.204i	0.367125	−	0.635880i
$330$		0			0
$331$			98.3079i			0.297003i	0.988912	+	0.148501i	$0.0474450\pi$
$331$			98.3079i			0.297003i	−0.988912	+	0.148501i	$0.952555\pi$
$332$		0			0
$333$	1.02146	+	0.589738i	0.00306744	+	0.00177099i
$334$		0			0
$335$		−	827.333i		−	2.46965i
$336$		0			0
$337$	191.485	−	110.554i	0.568204	−	0.328052i	−0.188228	−	0.982125i	$-0.560274\pi$
$337$	191.485	−	110.554i	0.568204	−	0.328052i	0.756432	+	0.654073i	$0.226941\pi$
$338$		0			0
$339$	−66.0016	−	114.318i	−0.194695	−	0.337222i
$340$		0			0
$341$			611.847i			1.79427i
$342$		0			0
$343$	342.776			0.999346
$344$		0			0
$345$	447.671	−	258.463i	1.29760	−	0.749168i
$346$		0			0
$347$	−97.8671	−	169.511i	−0.282038	−	0.488504i	0.689849	−	0.723954i	$-0.257677\pi$
$347$	−97.8671	−	169.511i	−0.282038	−	0.488504i	−0.971887	+	0.235450i	$0.924344\pi$
$348$		0			0
$349$	−266.366			−0.763228			−0.381614	−	0.924322i	$-0.624632\pi$
$349$	−266.366			−0.763228			−0.381614	+	0.924322i	$0.624632\pi$
$350$		0			0
$351$	6.23927	−	10.8067i	0.0177757	−	0.0307884i
$352$		0			0
$353$	−321.881			−0.911843			−0.455922	−	0.890020i	$-0.650690\pi$
$353$	−321.881			−0.911843			−0.455922	+	0.890020i	$0.650690\pi$
$354$		0			0
$355$	−580.705	−	335.270i	−1.63579	−	0.944423i
$356$		0			0
$357$	−33.8070	−	19.5185i	−0.0946975	−	0.0546736i
$358$		0			0
$359$	−30.1395	−	52.2032i	−0.0839541	−	0.145413i	0.820991	−	0.570941i	$-0.193422\pi$
$359$	−30.1395	−	52.2032i	−0.0839541	−	0.145413i	−0.904945	+	0.425528i	$0.860088\pi$
$360$		0			0
$361$	−269.350	+	240.357i	−0.746123	+	0.665808i
$362$		0			0
$363$	232.060	−	133.980i	0.639284	−	0.369091i
$364$		0			0
$365$	−123.194	+	213.378i	−0.337518	+	0.584598i
$366$		0			0
$367$	−15.0994	+	26.1530i	−0.0411429	+	0.0712615i	−0.885864	−	0.463946i	$-0.846433\pi$
$367$	−15.0994	+	26.1530i	−0.0411429	+	0.0712615i	0.844721	+	0.535207i	$0.179767\pi$
$368$		0			0
$369$			110.204i			0.298657i
$370$		0			0
$371$	−333.609	−	192.609i	−0.899217	−	0.519163i
$372$		0			0
$373$			65.1134i			0.174567i	0.996184	+	0.0872834i	$0.0278186\pi$
$373$			65.1134i			0.174567i	−0.996184	+	0.0872834i	$0.972181\pi$
$374$		0			0
$375$	−246.823	+	142.504i	−0.658196	+	0.380009i
$376$		0			0
$377$	49.6185	+	85.9418i	0.131614	+	0.227962i
$378$		0			0
$379$		−	639.802i		−	1.68813i	−0.536240	−	0.844066i	$-0.680156\pi$
$379$		−	639.802i		−	1.68813i	0.536240	−	0.844066i	$-0.319844\pi$
$380$		0			0
$381$	188.156			0.493847
$382$		0			0
$383$	−196.461	+	113.427i	−0.512954	+	0.296154i	−0.734047	−	0.679099i	$-0.762371\pi$
$383$	−196.461	+	113.427i	−0.512954	+	0.296154i	0.221093	+	0.975253i	$0.429037\pi$
$384$		0			0
$385$	−299.508	−	518.764i	−0.777944	−	1.34744i
$386$		0			0
$387$	172.896			0.446759
$388$		0			0
$389$	−216.426	+	374.861i	−0.556366	+	0.963653i	0.441430	+	0.897296i	$0.354471\pi$
$389$	−216.426	+	374.861i	−0.556366	+	0.963653i	−0.997796	+	0.0663579i	$0.978862\pi$
$390$		0			0
$391$	186.452			0.476860
$392$		0			0
$393$	−193.182	−	111.534i	−0.491558	−	0.283801i
$394$		0			0
$395$	−462.112	−	266.800i	−1.16990	−	0.675444i
$396$		0			0
$397$	50.8986	+	88.1589i	0.128208	+	0.222063i	0.922982	−	0.384842i	$-0.125744\pi$
$397$	50.8986	+	88.1589i	0.128208	+	0.222063i	−0.794774	+	0.606905i	$0.792411\pi$
$398$		0			0
$399$	110.307	+	89.7331i	0.276459	+	0.224895i
$400$		0			0
$401$	610.643	−	352.555i	1.52280	−	0.879189i	0.523163	−	0.852232i	$-0.324752\pi$
$401$	610.643	−	352.555i	1.52280	−	0.879189i	0.999637	−	0.0269566i	$-0.00858160\pi$
$402$		0			0
$403$	−44.2457	+	76.6358i	−0.109791	+	0.190163i
$404$		0			0
$405$	37.5712	−	65.0752i	0.0927684	−	0.160680i
$406$		0			0
$407$			6.52817i			0.0160397i
$408$		0			0
$409$	−307.581	−	177.582i	−0.752031	−	0.434185i	0.0743962	−	0.997229i	$-0.476297\pi$
$409$	−307.581	−	177.582i	−0.752031	−	0.434185i	−0.826427	+	0.563043i	$0.809630\pi$
$410$		0			0
$411$		−	214.447i		−	0.521768i
$412$		0			0
$413$	−195.852	+	113.075i	−0.474218	+	0.273790i
$414$		0			0
$415$	−258.627	−	447.955i	−0.623197	−	1.07941i
$416$		0			0
$417$		−	35.7091i		−	0.0856334i
$418$		0			0
$419$	−57.2788			−0.136704			−0.0683518	−	0.997661i	$-0.521774\pi$
$419$	−57.2788			−0.136704			−0.0683518	+	0.997661i	$0.521774\pi$
$420$		0			0
$421$	−231.641	+	133.738i	−0.550217	+	0.317668i	−0.749209	−	0.662333i	$-0.769566\pi$
$421$	−231.641	+	133.738i	−0.550217	+	0.317668i	0.198993	+	0.980001i	$0.436233\pi$
$422$		0			0
$423$	83.8607	+	145.251i	0.198252	+	0.343383i
$424$		0			0
$425$	−233.202			−0.548711
$426$		0			0
$427$	−117.336	+	203.232i	−0.274791	+	0.475952i
$428$		0			0
$429$	69.0663			0.160994
$430$		0			0
$431$	361.360	+	208.631i	0.838423	+	0.484064i	0.856728	−	0.515769i	$-0.172494\pi$
$431$	361.360	+	208.631i	0.838423	+	0.484064i	−0.0183051	+	0.999832i	$0.505827\pi$
$432$		0			0
$433$	648.116	+	374.190i	1.49680	+	0.864180i	0.999993	−	0.00367944i	$-0.00117121\pi$
$433$	648.116	+	374.190i	1.49680	+	0.864180i	0.496810	+	0.867859i	$0.334505\pi$
$434$		0			0
$435$	298.789	+	517.518i	0.686872	+	1.18970i
$436$		0			0
$437$	−670.570	−	107.742i	−1.53448	−	0.246549i
$438$		0			0
$439$	−168.933	+	97.5337i	−0.384814	+	0.222172i	−0.679911	−	0.733295i	$-0.737981\pi$
$439$	−168.933	+	97.5337i	−0.384814	+	0.222172i	0.295097	+	0.955467i	$0.404648\pi$
$440$		0			0
$441$	−45.4949	+	78.7995i	−0.103163	+	0.178684i
$442$		0			0
$443$	259.836	−	450.049i	0.586537	−	1.01591i	−0.408145	−	0.912917i	$-0.633824\pi$
$443$	259.836	−	450.049i	0.586537	−	1.01591i	0.994682	−	0.102994i	$-0.0328423\pi$
$444$		0			0
$445$			1.62022i			0.00364095i
$446$		0			0
$447$	320.422	+	184.996i	0.716827	+	0.413860i
$448$		0			0
$449$			313.860i			0.699019i	0.936933	+	0.349510i	$0.113652\pi$
$449$			313.860i			0.699019i	−0.936933	+	0.349510i	$0.886348\pi$
$450$		0			0
$451$	−528.241	+	304.980i	−1.17127	+	0.676231i
$452$		0			0
$453$	−216.960	−	375.786i	−0.478941	−	0.829550i
$454$		0			0
$455$		−	86.6358i		−	0.190408i
$456$		0			0
$457$	−456.575			−0.999070			−0.499535	−	0.866294i	$-0.666496\pi$
$457$	−456.575			−0.999070			−0.499535	+	0.866294i	$0.666496\pi$
$458$		0			0
$459$	23.4723	−	13.5517i	0.0511379	−	0.0295245i
$460$		0			0
$461$	−237.358	−	411.116i	−0.514876	−	0.891792i	−0.999851	−	0.0172635i	$-0.994505\pi$
$461$	−237.358	−	411.116i	−0.514876	−	0.891792i	0.484975	−	0.874528i	$-0.338829\pi$
$462$		0			0
$463$	−767.681			−1.65806			−0.829029	−	0.559206i	$-0.811106\pi$
$463$	−767.681			−1.65806			−0.829029	+	0.559206i	$0.811106\pi$
$464$		0			0
$465$	−266.436	+	461.480i	−0.572980	+	0.992431i
$466$		0			0
$467$	646.178			1.38368			0.691839	−	0.722051i	$-0.256801\pi$
$467$	646.178			1.38368			0.691839	+	0.722051i	$0.256801\pi$
$468$		0			0
$469$	370.801	+	214.082i	0.790621	+	0.456465i
$470$		0			0
$471$	−373.397	−	215.581i	−0.792774	−	0.457708i
$472$		0			0
$473$	478.472	+	828.738i	1.01157	+	1.75209i
$474$		0			0
$475$	838.704	+	134.756i	1.76569	+	0.283698i
$476$		0			0
$477$	231.626	−	133.729i	0.485589	−	0.280355i
$478$		0			0
$479$	105.687	−	183.055i	0.220640	−	0.382160i	−0.734362	−	0.678758i	$-0.762519\pi$
$479$	105.687	−	183.055i	0.220640	−	0.382160i	0.955003	+	0.296597i	$0.0958520\pi$
$480$		0			0
$481$	−0.472085	+	0.817675i	−0.000981465	+	0.00169995i
$482$		0			0
$483$			267.521i			0.553874i
$484$		0			0
$485$	759.852	+	438.701i	1.56671	+	0.904538i
$486$		0			0
$487$			765.091i			1.57103i	0.618843	+	0.785515i	$0.287602\pi$
$487$			765.091i			1.57103i	−0.618843	+	0.785515i	$0.712398\pi$
$488$		0			0
$489$	−45.3973	+	26.2101i	−0.0928370	+	0.0535994i
$490$		0			0
$491$	−428.533	−	742.240i	−0.872775	−	1.51169i	−0.859114	−	0.511784i	$-0.828985\pi$
$491$	−428.533	−	742.240i	−0.872775	−	1.51169i	−0.0136609	−	0.999907i	$-0.504349\pi$
$492$		0			0
$493$			215.543i			0.437207i
$494$		0			0
$495$	415.899			0.840200
$496$		0			0
$497$	300.528	−	173.510i	0.604685	−	0.349115i
$498$		0			0
$499$	132.721	+	229.880i	0.265974	+	0.460681i	0.967818	−	0.251649i	$-0.0809730\pi$
$499$	132.721	+	229.880i	0.265974	+	0.460681i	−0.701844	+	0.712331i	$0.747640\pi$
$500$		0			0
$501$	227.970			0.455031
$502$		0			0
$503$	−163.343	+	282.918i	−0.324737	+	0.562461i	−0.981459	−	0.191672i	$-0.938609\pi$
$503$	−163.343	+	282.918i	−0.324737	+	0.562461i	0.656722	+	0.754133i	$0.271942\pi$
$504$		0			0
$505$	268.191			0.531071
$506$		0			0
$507$	−244.849	−	141.364i	−0.482937	−	0.278824i
$508$		0			0
$509$	−839.279	−	484.558i	−1.64888	−	0.951980i	−0.977519	−	0.210848i	$-0.932378\pi$
$509$	−839.279	−	484.558i	−1.64888	−	0.951980i	−0.671359	−	0.741132i	$-0.734289\pi$
$510$		0			0
$511$	−63.7558	−	110.428i	−0.124767	−	0.216102i
$512$		0			0
$513$	−92.2482	+	35.1748i	−0.179821	+	0.0685669i
$514$		0			0
$515$	−302.718	+	174.774i	−0.587801	+	0.339367i
$516$		0			0
$517$	−464.153	+	803.937i	−0.897782	+	1.55500i
$518$		0			0
$519$	−164.875	+	285.571i	−0.317678	+	0.550234i
$520$		0			0
$521$			566.386i			1.08711i	0.839373	+	0.543557i	$0.182923\pi$
$521$			566.386i			1.08711i	−0.839373	+	0.543557i	$0.817077\pi$
$522$		0			0
$523$	339.304	+	195.897i	0.648764	+	0.374564i	0.787983	−	0.615697i	$-0.211126\pi$
$523$	339.304	+	195.897i	0.648764	+	0.374564i	−0.139218	+	0.990262i	$0.544459\pi$
$524$		0			0
$525$		−	334.598i		−	0.637329i
$526$		0			0
$527$	−166.453	+	96.1019i	−0.315851	+	0.182357i
$528$		0			0
$529$	−374.381	−	648.447i	−0.707714	−	1.22580i
$530$		0			0
$531$		−	157.017i		−	0.295700i
$532$		0			0
$533$	−88.2185			−0.165513
$534$		0			0
$535$	−258.148	+	149.042i	−0.482520	+	0.278583i
$536$		0			0
$537$	0.662995	+	1.14834i	0.00123463	+	0.00213844i
$538$		0			0
$539$	−503.611			−0.934344
$540$		0			0
$541$	439.598	−	761.406i	0.812565	−	1.40740i	−0.0984975	−	0.995137i	$-0.531404\pi$
$541$	439.598	−	761.406i	0.812565	−	1.40740i	0.911063	−	0.412267i	$-0.135263\pi$
$542$		0			0
$543$	424.661			0.782065
$544$		0			0
$545$	827.138	+	477.548i	1.51768	+	0.876236i
$546$		0			0
$547$	−101.726	−	58.7317i	−0.185971	−	0.107370i	0.404124	−	0.914704i	$-0.367576\pi$
$547$	−101.726	−	58.7317i	−0.185971	−	0.107370i	−0.590095	+	0.807334i	$0.700910\pi$
$548$		0			0
$549$	−81.4665	−	141.104i	−0.148391	−	0.257020i
$550$		0			0
$551$	124.552	−	775.194i	0.226047	−	1.40689i
$552$		0			0
$553$	239.154	−	138.075i	0.432466	−	0.249684i
$554$		0			0
$555$	−2.84277	+	4.92382i	−0.00512210	+	0.00887174i
$556$		0			0
$557$	−191.046	+	330.901i	−0.342990	+	0.594077i	−0.984987	−	0.172631i	$-0.944773\pi$
$557$	−191.046	+	330.901i	−0.342990	+	0.594077i	0.641996	+	0.766708i	$0.278107\pi$
$558$		0			0
$559$			138.403i			0.247590i
$560$		0			0
$561$	129.915	+	75.0062i	0.231577	+	0.133701i
$562$		0			0
$563$			383.086i			0.680437i	0.940346	+	0.340219i	$0.110501\pi$
$563$			383.086i			0.680437i	−0.940346	+	0.340219i	$0.889499\pi$
$564$		0			0
$565$	551.058	−	318.153i	0.975323	−	0.563103i
$566$		0			0
$567$	19.4440	+	33.6780i	0.0342927	+	0.0593968i
$568$		0			0
$569$		−	572.419i		−	1.00601i	−0.864284	−	0.503004i	$-0.832228\pi$
$569$		−	572.419i		−	1.00601i	0.864284	−	0.503004i	$-0.167772\pi$
$570$		0			0
$571$	418.114			0.732249			0.366125	−	0.930566i	$-0.380684\pi$
$571$	418.114			0.732249			0.366125	+	0.930566i	$0.380684\pi$
$572$		0			0
$573$	3.50974	−	2.02635i	0.00612521	−	0.00353639i
$574$		0			0
$575$	799.069	+	1384.03i	1.38969	+	2.40701i
$576$		0			0
$577$	−438.427			−0.759840			−0.379920	−	0.925019i	$-0.624048\pi$
$577$	−438.427			−0.759840			−0.379920	+	0.925019i	$0.624048\pi$
$578$		0			0
$579$	−196.862	+	340.975i	−0.340003	+	0.588903i
$580$		0			0
$581$	267.691			0.460742
$582$		0			0
$583$	1282.00	+	740.165i	2.19898	+	1.26958i
$584$		0			0
$585$	52.0927	+	30.0757i	0.0890473	+	0.0514115i
$586$		0			0
$587$	284.117	+	492.104i	0.484015	+	0.838338i	0.999831	−	0.0183610i	$-0.00584480\pi$
$587$	284.117	+	492.104i	0.484015	+	0.838338i	−0.515817	+	0.856699i	$0.672511\pi$
$588$		0			0
$589$	654.177	−	249.442i	1.11066	−	0.423501i
$590$		0			0
$591$	−380.622	+	219.752i	−0.644031	+	0.371831i
$592$		0			0
$593$	251.988	−	436.457i	0.424938	−	0.736014i	−0.571477	−	0.820618i	$-0.693629\pi$
$593$	251.988	−	436.457i	0.424938	−	0.736014i	0.996415	+	0.0846040i	$0.0269625\pi$
$594$		0			0
$595$	94.0867	−	162.963i	0.158129	−	0.273887i
$596$		0			0
$597$		−	421.794i		−	0.706523i
$598$		0			0
$599$	565.070	+	326.244i	0.943356	+	0.544647i	0.891011	−	0.453982i	$-0.149997\pi$
$599$	565.070	+	326.244i	0.943356	+	0.544647i	0.0523455	+	0.998629i	$0.483330\pi$
$600$		0			0
$601$			516.381i			0.859203i	0.903018	+	0.429602i	$0.141346\pi$
$601$			516.381i			0.859203i	−0.903018	+	0.429602i	$0.858654\pi$
$602$		0			0
$603$	−257.448	+	148.638i	−0.426946	+	0.246497i
$604$		0			0
$605$	645.836	+	1118.62i	1.06750	+	1.84896i
$606$		0			0
$607$			638.130i			1.05129i	0.850706	+	0.525643i	$0.176175\pi$
$607$			638.130i			1.05129i	−0.850706	+	0.525643i	$0.823825\pi$
$608$		0			0
$609$	−309.261			−0.507817
$610$		0			0
$611$	−116.273	+	67.1304i	−0.190300	+	0.109870i
$612$		0			0
$613$	−29.8401	−	51.6846i	−0.0486788	−	0.0843142i	0.840659	−	0.541564i	$-0.182168\pi$
$613$	−29.8401	−	51.6846i	−0.0486788	−	0.0843142i	−0.889338	+	0.457250i	$0.848834\pi$
$614$		0			0
$615$	−531.228			−0.863785
$616$		0			0
$617$	287.486	−	497.940i	0.465941	−	0.807034i	−0.533302	−	0.845925i	$-0.679049\pi$
$617$	287.486	−	497.940i	0.465941	−	0.807034i	0.999243	+	0.0388907i	$0.0123824\pi$
$618$		0			0
$619$	890.221			1.43816			0.719080	−	0.694928i	$-0.244564\pi$
$619$	890.221			1.43816			0.719080	+	0.694928i	$0.244564\pi$
$620$		0			0
$621$	−160.856	−	92.8703i	−0.259027	−	0.149550i
$622$		0			0
$623$	−0.726165	−	0.419251i	−0.00116559	−	0.000672956i
$624$		0			0
$625$	−128.067	−	221.819i	−0.204907	−	0.354910i
$626$		0			0
$627$	−423.891	−	344.829i	−0.676062	−	0.549966i
$628$		0			0
$629$	−1.77599	+	1.02537i	−0.00282352	+	0.00163016i
$630$		0			0
$631$	36.0129	−	62.3761i	0.0570727	−	0.0988528i	−0.836077	−	0.548611i	$-0.815157\pi$
$631$	36.0129	−	62.3761i	0.0570727	−	0.0988528i	0.893150	+	0.449759i	$0.148490\pi$
$632$		0			0
$633$	−258.747	+	448.164i	−0.408764	+	0.707999i
$634$		0			0
$635$			906.984i			1.42832i
$636$		0			0
$637$	−63.0789	−	36.4186i	−0.0990250	−	0.0571721i
$638$		0			0
$639$			240.937i			0.377053i
$640$		0			0
$641$	99.5649	−	57.4838i	0.155327	−	0.0896784i	−0.420322	−	0.907375i	$-0.638083\pi$
$641$	99.5649	−	57.4838i	0.155327	−	0.0896784i	0.575649	+	0.817697i	$0.304749\pi$
$642$		0			0
$643$	−559.144	−	968.466i	−0.869587	−	1.50617i	−0.862419	−	0.506194i	$-0.831052\pi$
$643$	−559.144	−	968.466i	−0.869587	−	1.50617i	−0.00716749	−	0.999974i	$-0.502282\pi$
$644$		0			0
$645$			833.424i			1.29213i
$646$		0			0
$647$	−404.148			−0.624650			−0.312325	−	0.949975i	$-0.601108\pi$
$647$	−404.148			−0.624650			−0.312325	+	0.949975i	$0.601108\pi$
$648$		0			0
$649$	752.627	−	434.529i	1.15967	−	0.669536i
$650$		0			0
$651$	−137.887	−	238.827i	−0.211808	−	0.366862i
$652$		0			0
$653$	886.509			1.35759			0.678797	−	0.734326i	$-0.262502\pi$
$653$	886.509			1.35759			0.678797	+	0.734326i	$0.262502\pi$
$654$		0			0
$655$	537.636	−	931.214i	0.820819	−	1.42170i
$656$		0			0
$657$	88.5316			0.134751
$658$		0			0
$659$	369.935	+	213.582i	0.561358	+	0.324100i	0.753690	−	0.657230i	$-0.228272\pi$
$659$	369.935	+	213.582i	0.561358	+	0.324100i	−0.192333	+	0.981330i	$0.561605\pi$
$660$		0			0
$661$	883.600	+	510.146i	1.33676	+	0.771780i	0.986326	−	0.164807i	$-0.0527001\pi$
$661$	883.600	+	510.146i	1.33676	+	0.771780i	0.350436	+	0.936587i	$0.386033\pi$
$662$		0			0
$663$	10.8481	+	18.7895i	0.0163622	+	0.0283402i
$664$		0			0
$665$	−432.548	+	531.723i	−0.650448	+	0.799583i
$666$		0			0
$667$	1279.23	−	738.561i	1.91788	−	1.10729i
$668$		0			0
$669$	117.466	−	203.457i	0.175584	−	0.304120i
$670$		0			0
$671$	450.901	−	780.984i	0.671984	−	1.16391i
$672$		0			0
$673$		−	588.064i		−	0.873796i	−0.899511	−	0.436898i	$-0.856077\pi$
$673$		−	588.064i		−	0.873796i	0.899511	−	0.436898i	$-0.143923\pi$
$674$		0			0
$675$	201.188	+	116.156i	0.298056	+	0.172083i
$676$		0			0
$677$		−	542.465i		−	0.801277i	−0.916236	−	0.400639i	$-0.868788\pi$
$677$		−	542.465i		−	0.801277i	0.916236	−	0.400639i	$-0.131212\pi$
$678$		0			0
$679$	−393.241	+	227.038i	−0.579148	+	0.334371i
$680$		0			0
$681$	70.5524	+	122.200i	0.103601	+	0.179443i
$682$		0			0
$683$			413.293i			0.605115i	0.953131	+	0.302557i	$0.0978404\pi$
$683$			413.293i			0.605115i	−0.953131	+	0.302557i	$0.902160\pi$
$684$		0			0
$685$	1033.72			1.50907
$686$		0			0
$687$	526.247	−	303.829i	0.766008	−	0.442255i
$688$		0			0
$689$	107.050	+	185.416i	0.155370	+	0.269109i
$690$		0			0
$691$	−603.532			−0.873418			−0.436709	−	0.899603i	$-0.643856\pi$
$691$	−603.532			−0.873418			−0.436709	+	0.899603i	$0.643856\pi$
$692$		0			0
$693$	−107.619	+	186.401i	−0.155294	+	0.268977i
$694$		0			0
$695$	172.132			0.247672
$696$		0			0
$697$	−165.940	−	95.8055i	−0.238077	−	0.137454i
$698$		0			0
$699$	−577.106	−	333.192i	−0.825616	−	0.476670i
$700$		0			0
$701$	−52.4325	−	90.8157i	−0.0747967	−	0.129552i	0.826201	−	0.563375i	$-0.190497\pi$
$701$	−52.4325	−	90.8157i	−0.0747967	−	0.129552i	−0.900998	+	0.433824i	$0.857164\pi$
$702$		0			0
$703$	6.97982	−	2.66145i	0.00992861	−	0.00378584i
$704$		0			0
$705$	−700.167	+	404.241i	−0.993144	+	0.573392i
$706$		0			0
$707$	−69.3975	+	120.200i	−0.0981578	+	0.170014i
$708$		0			0
$709$	90.4971	−	156.746i	0.127641	−	0.221080i	−0.795121	−	0.606450i	$-0.792593\pi$
$709$	90.4971	−	156.746i	0.127641	−	0.221080i	0.922762	+	0.385370i	$0.125926\pi$
$710$		0			0
$711$			191.732i			0.269666i
$712$		0			0
$713$	1140.71	+	658.589i	1.59987	+	0.923687i
$714$		0			0
$715$			332.927i			0.465632i
$716$		0			0
$717$	179.760	−	103.785i	0.250711	−	0.144748i
$718$		0			0
$719$	180.222	+	312.153i	0.250656	+	0.434149i	0.963707	−	0.266964i	$-0.0860204\pi$
$719$	180.222	+	312.153i	0.250656	+	0.434149i	−0.713051	+	0.701113i	$0.752687\pi$
$720$		0			0
$721$		−	180.899i		−	0.250901i
$722$		0			0
$723$	570.402			0.788938
$724$		0			0
$725$	−1599.97	+	923.743i	−2.20685	+	1.27413i
$726$		0			0
$727$	−28.4856	−	49.3385i	−0.0391824	−	0.0678659i	0.845769	−	0.533549i	$-0.179142\pi$
$727$	−28.4856	−	49.3385i	−0.0391824	−	0.0678659i	−0.884952	+	0.465683i	$0.845809\pi$
$728$		0			0
$729$	−27.0000			−0.0370370
$730$		0			0
$731$	−150.306	+	260.337i	−0.205617	+	0.356139i
$732$		0			0
$733$	−758.964			−1.03542			−0.517710	−	0.855556i	$-0.673216\pi$
$733$	−758.964			−1.03542			−0.517710	+	0.855556i	$0.673216\pi$
$734$		0			0
$735$	−379.844	−	219.303i	−0.516795	−	0.298372i
$736$		0			0
$737$	−1424.93	−	822.681i	−1.93341	−	1.11626i
$738$		0			0
$739$	−142.050	−	246.038i	−0.192220	−	0.332934i	0.753766	−	0.657143i	$-0.228235\pi$
$739$	−142.050	−	246.038i	−0.192220	−	0.332934i	−0.945986	+	0.324209i	$0.894902\pi$
$740$		0			0
$741$	−28.1574	−	73.8446i	−0.0379992	−	0.0996553i
$742$		0			0
$743$	−303.643	+	175.308i	−0.408672	+	0.235947i	−0.690219	−	0.723601i	$-0.742486\pi$
$743$	−303.643	+	175.308i	−0.408672	+	0.235947i	0.281547	+	0.959547i	$0.409152\pi$
$744$		0			0
$745$	−891.751	+	1544.56i	−1.19698	+	2.07323i
$746$		0			0
$747$	−92.9292	+	160.958i	−0.124403	+	0.215473i
$748$		0			0
$749$		−	154.265i		−	0.205962i
$750$		0			0
$751$	−715.761	−	413.245i	−0.953077	−	0.550259i	−0.0590415	−	0.998256i	$-0.518804\pi$
$751$	−715.761	−	413.245i	−0.953077	−	0.550259i	−0.894035	+	0.447996i	$0.852138\pi$
$752$		0			0
$753$		−	76.2045i		−	0.101201i
$754$		0			0
$755$	1811.44	−	1045.83i	2.39925	−	1.38521i
$756$		0			0
$757$	391.567	+	678.213i	0.517261	+	0.895923i	0.999799	+	0.0200475i	$0.00638173\pi$
$757$	391.567	+	678.213i	0.517261	+	0.895923i	−0.482538	+	0.875875i	$0.660285\pi$
$758$		0			0
$759$		−	1028.04i		−	1.35446i
$760$		0			0
$761$	−342.458			−0.450011			−0.225005	−	0.974358i	$-0.572240\pi$
$761$	−342.458			−0.450011			−0.225005	+	0.974358i	$0.572240\pi$
$762$		0			0
$763$	−428.063	+	247.142i	−0.561027	+	0.323909i
$764$		0			0
$765$	65.3246	+	113.146i	0.0853916	+	0.147903i
$766$		0			0
$767$	125.692			0.163875
$768$		0			0
$769$	−356.160	+	616.887i	−0.463146	+	0.802193i	−0.999116	−	0.0420443i	$-0.986613\pi$
$769$	−356.160	+	616.887i	−0.463146	+	0.802193i	0.535969	+	0.844237i	$0.319946\pi$
$770$		0			0
$771$	−366.261			−0.475047
$772$		0			0
$773$	95.3607	+	55.0565i	0.123364	+	0.0712245i	0.560412	−	0.828214i	$-0.310643\pi$
$773$	95.3607	+	55.0565i	0.123364	+	0.0712245i	−0.437048	+	0.899438i	$0.643976\pi$
$774$		0			0
$775$	−1426.72	−	823.719i	−1.84093	−	1.06286i
$776$		0			0
$777$	−1.47120	−	2.54819i	−0.00189343	−	0.00327952i
$778$		0			0
$779$	541.436	+	440.450i	0.695040	+	0.565405i
$780$		0			0
$781$	−1154.88	+	666.770i	−1.47872	+	0.853739i
$782$		0			0
$783$	107.360	−	185.953i	0.137114	−	0.237488i
$784$		0			0
$785$	1039.18	−	1799.92i	1.32380	−	2.29289i
$786$		0			0
$787$		−	194.657i		−	0.247341i	−0.992323	−	0.123670i	$-0.960533\pi$
$787$		−	194.657i		−	0.247341i	0.992323	−	0.123670i	$-0.0394666\pi$
$788$		0			0
$789$	−718.950	−	415.086i	−0.911217	−	0.526092i
$790$		0			0
$791$			329.304i			0.416313i
$792$		0			0
$793$	112.954	−	65.2139i	0.142438	−	0.0822369i
$794$		0			0
$795$	644.627	+	1116.53i	0.810851	+	1.40444i
$796$		0			0
$797$			1022.36i			1.28277i	0.767221	+	0.641383i	$0.221639\pi$
$797$			1022.36i			1.28277i	−0.767221	+	0.641383i	$0.778361\pi$
$798$		0			0
$799$	−291.615			−0.364975
$800$		0			0
$801$	0.504178	−	0.291087i	0.000629435	−	0.000363405i
$802$		0			0
$803$	245.003	+	424.357i	0.305109	+	0.528465i
$804$		0			0
$805$	−1289.56			−1.60193
$806$		0			0
$807$	168.125	−	291.201i	0.208333	−	0.360843i
$808$		0			0
$809$	240.528			0.297316			0.148658	−	0.988889i	$-0.452505\pi$
$809$	240.528			0.297316			0.148658	+	0.988889i	$0.452505\pi$
$810$		0			0
$811$	−1021.37	−	589.690i	−1.25940	−	0.727114i	−0.286441	−	0.958098i	$-0.592472\pi$
$811$	−1021.37	−	589.690i	−1.25940	−	0.727114i	−0.972958	+	0.230984i	$0.925806\pi$
$812$		0			0
$813$	−691.964	−	399.505i	−0.851124	−	0.491396i
$814$		0			0
$815$	−126.343	−	218.833i	−0.155022	−	0.268506i
$816$		0			0
$817$	691.006	−	849.440i	0.845785	−	1.03971i
$818$		0			0
$819$	−26.9592	+	15.5649i	−0.0329172	+	0.0190047i
$820$		0			0
$821$	467.189	−	809.195i	0.569049	−	0.985621i	−0.427612	−	0.903962i	$-0.640645\pi$
$821$	467.189	−	809.195i	0.569049	−	0.985621i	0.996660	−	0.0816586i	$-0.0260217\pi$
$822$		0			0
$823$	454.944	−	787.985i	0.552787	−	0.957455i	−0.445285	−	0.895389i	$-0.646898\pi$
$823$	454.944	−	787.985i	0.552787	−	0.957455i	0.998072	−	0.0620660i	$-0.0197689\pi$
$824$		0			0
$825$			1285.80i			1.55855i
$826$		0			0
$827$	−1044.24	−	602.891i	−1.26268	−	0.729010i	−0.289090	−	0.957302i	$-0.593353\pi$
$827$	−1044.24	−	602.891i	−1.26268	−	0.729010i	−0.973593	+	0.228292i	$0.926686\pi$
$828$		0			0
$829$			815.444i			0.983648i	0.870695	+	0.491824i	$0.163670\pi$
$829$			815.444i			0.983648i	−0.870695	+	0.491824i	$0.836330\pi$
$830$		0			0
$831$	−482.604	+	278.631i	−0.580750	+	0.335296i
$832$		0			0
$833$	−79.1015	−	137.008i	−0.0949598	−	0.164475i
$834$		0			0
$835$			1098.91i			1.31605i
$836$		0			0
$837$	191.470			0.228758
$838$		0			0
$839$	868.893	−	501.656i	1.03563	−	0.597921i	0.117037	−	0.993128i	$-0.462660\pi$
$839$	868.893	−	501.656i	1.03563	−	0.597921i	0.918592	+	0.395206i	$0.129327\pi$
$840$		0			0
$841$	433.294	+	750.488i	0.515213	+	0.892375i
$842$		0			0
$843$	−652.833			−0.774416
$844$		0			0
$845$	681.428	−	1180.27i	0.806424	−	1.39677i
$846$		0			0
$847$	−668.470			−0.789221
$848$		0			0
$849$	448.896	+	259.170i	0.528735	+	0.305265i
$850$		0			0
$851$	12.1709	+	7.02688i	0.0143019	+	0.00825721i
$852$		0			0
$853$	−222.206	−	384.873i	−0.260500	−	0.451199i	0.705875	−	0.708336i	$-0.250554\pi$
$853$	−222.206	−	384.873i	−0.260500	−	0.451199i	−0.966375	+	0.257137i	$0.917221\pi$
$854$		0			0
$855$	−169.556	−	444.672i	−0.198312	−	0.520084i
$856$		0			0
$857$	764.709	−	441.505i	0.892310	−	0.515175i	0.0176124	−	0.999845i	$-0.494394\pi$
$857$	764.709	−	441.505i	0.892310	−	0.515175i	0.874697	+	0.484670i	$0.161060\pi$
$858$		0			0
$859$	−428.701	+	742.532i	−0.499070	+	0.864415i	−0.999999	−	0.00107335i	$-0.999658\pi$
$859$	−428.701	+	742.532i	−0.499070	+	0.864415i	0.500929	+	0.865488i	$0.332992\pi$
$860$		0			0
$861$	137.461	−	238.090i	0.159653	−	0.276528i
$862$		0			0
$863$		−	755.301i		−	0.875204i	−0.899169	−	0.437602i	$-0.855828\pi$
$863$		−	755.301i		−	0.875204i	0.899169	−	0.437602i	$-0.144172\pi$
$864$		0			0
$865$	−1376.57	−	794.760i	−1.59140	−	0.918798i
$866$		0			0
$867$		−	453.438i		−	0.522997i
$868$		0			0
$869$	−919.027	+	530.601i	−1.05757	+	0.610588i
$870$		0			0
$871$	−118.984	−	206.087i	−0.136607	−	0.236610i
$872$		0			0
$873$		−	315.266i		−	0.361129i
$874$		0			0
$875$	710.997			0.812568
$876$		0			0
$877$	971.688	−	561.004i	1.10797	−	0.639686i	0.169666	−	0.985502i	$-0.445731\pi$
$877$	971.688	−	561.004i	1.10797	−	0.639686i	0.938302	+	0.345816i	$0.112398\pi$
$878$		0			0
$879$	−358.119	−	620.281i	−0.407417	−	0.705667i
$880$		0			0
$881$	120.766			0.137078			0.0685392	−	0.997648i	$-0.478166\pi$
$881$	120.766			0.137078			0.0685392	+	0.997648i	$0.478166\pi$
$882$		0			0
$883$	480.728	−	832.646i	0.544426	−	0.942974i	−0.454216	−	0.890891i	$-0.650081\pi$
$883$	480.728	−	832.646i	0.544426	−	0.942974i	0.998643	−	0.0520827i	$-0.0165859\pi$
$884$		0			0
$885$	756.883			0.855235
$886$		0			0
$887$	497.208	+	287.063i	0.560550	+	0.323634i	0.753366	−	0.657601i	$-0.228429\pi$
$887$	497.208	+	287.063i	0.560550	+	0.323634i	−0.192816	+	0.981235i	$0.561762\pi$
$888$		0			0
$889$	−406.500	−	234.693i	−0.457255	−	0.263996i
$890$		0			0
$891$	−74.7199	−	129.419i	−0.0838607	−	0.145251i
$892$		0			0
$893$	1048.78	+	168.511i	1.17445	+	0.188702i
$894$		0			0
$895$	−5.53545	+	3.19589i	−0.00618486	+	0.00357083i
$896$		0			0
$897$	74.3426	−	128.765i	0.0828791	−	0.143551i
$898$		0			0
$899$	−761.344	+	1318.69i	−0.846879	+	1.46684i
$900$		0			0
$901$			465.026i			0.516123i
$902$		0			0
$903$	−373.531	−	215.658i	−0.413656	−	0.238824i
$904$		0			0
$905$			2047.03i			2.26191i
$906$		0			0
$907$	−55.3197	+	31.9388i	−0.0609919	+	0.0352137i	−0.530186	−	0.847881i	$-0.677878\pi$
$907$	−55.3197	+	31.9388i	−0.0609919	+	0.0352137i	0.469194	+	0.883095i	$0.344545\pi$
$908$		0			0
$909$	−48.1829	−	83.4552i	−0.0530065	−	0.0918099i
$910$		0			0
$911$			1512.86i			1.66066i	0.557271	+	0.830331i	$0.311848\pi$
$911$			1512.86i			1.66066i	−0.557271	+	0.830331i	$0.688152\pi$
$912$		0			0
$913$	−1028.69			−1.12671
$914$		0			0
$915$	680.177	−	392.700i	0.743363	−	0.429181i
$916$		0			0
$917$	278.239	+	481.925i	0.303424	+	0.525545i
$918$		0			0
$919$	1288.32			1.40187			0.700935	−	0.713225i	$-0.252766\pi$
$919$	1288.32			1.40187			0.700935	+	0.713225i	$0.252766\pi$
$920$		0			0
$921$	−331.226	+	573.699i	−0.359637	+	0.622909i
$922$		0			0
$923$	−192.870			−0.208960
$924$		0			0
$925$	−15.2226	−	8.78876i	−0.0164568	−	0.00950136i
$926$		0			0
$927$	108.772	+	62.7994i	0.117337	+	0.0677448i
$928$		0			0
$929$	110.780	+	191.877i	0.119247	+	0.206542i	0.919469	−	0.393161i	$-0.128619\pi$
$929$	110.780	+	191.877i	0.119247	+	0.206542i	−0.800222	+	0.599703i	$0.795285\pi$
$930$		0			0
$931$	205.316	+	538.453i	0.220532	+	0.578360i
$932$		0			0
$933$	219.886	−	126.951i	0.235676	−	0.136068i
$934$		0			0
$935$	−361.559	+	626.239i	−0.386694	+	0.669774i
$936$		0			0
$937$	−74.9437	+	129.806i	−0.0799826	+	0.138534i	−0.903242	−	0.429131i	$-0.858820\pi$
$937$	−74.9437	+	129.806i	−0.0799826	+	0.138534i	0.823260	+	0.567665i	$0.192153\pi$
$938$		0			0
$939$			171.168i			0.182288i
$940$		0			0
$941$	−1039.33	−	600.060i	−1.10450	−	0.637683i	−0.167101	−	0.985940i	$-0.553440\pi$
$941$	−1039.33	−	600.060i	−1.10450	−	0.637683i	−0.937399	+	0.348257i	$0.886774\pi$
$942$		0			0
$943$			1313.11i			1.39249i
$944$		0			0
$945$	−162.341	+	93.7275i	−0.171789	+	0.0991826i
$946$		0			0
$947$	566.016	+	980.368i	0.597693	+	1.03524i	0.993161	+	0.116755i	$0.0372493\pi$
$947$	566.016	+	980.368i	0.597693	+	1.03524i	−0.395467	+	0.918480i	$0.629417\pi$
$948$		0			0
$949$			70.8694i			0.0746780i
$950$		0			0
$951$	−91.6557			−0.0963782
$952$		0			0
$953$	1503.54	−	868.069i	1.57769	−	0.910880i	0.582510	−	0.812823i	$-0.302071\pi$
$953$	1503.54	−	868.069i	1.57769	−	0.910880i	0.995181	−	0.0980569i	$-0.0312627\pi$
$954$		0			0
$955$	9.76780	+	16.9183i	0.0102281	+	0.0177155i
$956$		0			0
$957$	1188.44			1.24184
$958$		0			0
$959$	−267.486	+	463.300i	−0.278922	+	0.483107i
$960$		0			0
$961$	−396.809			−0.412912
$962$		0			0
$963$	92.7571	+	53.5534i	0.0963210	+	0.0556110i
$964$		0			0
$965$	−1643.63	−	948.951i	−1.70325	−	0.983369i
$966$		0			0
$967$	−50.5381	−	87.5346i	−0.0522628	−	0.0905218i	0.838710	−	0.544578i	$-0.183310\pi$
$967$	−50.5381	−	87.5346i	−0.0522628	−	0.0905218i	−0.890973	+	0.454056i	$0.849977\pi$
$968$		0			0
$969$	27.2310	−	169.482i	0.0281021	−	0.174904i
$970$		0			0
$971$	305.437	−	176.344i	0.314560	−	0.181611i	−0.334405	−	0.942429i	$-0.608535\pi$
$971$	305.437	−	176.344i	0.314560	−	0.181611i	0.648965	+	0.760818i	$0.275202\pi$
$972$		0			0
$973$	−44.5411	+	77.1475i	−0.0457771	+	0.0792882i
$974$		0			0
$975$	−92.9827	+	161.051i	−0.0953669	+	0.165180i
$976$		0			0
$977$		−	844.451i		−	0.864331i	−0.901794	−	0.432166i	$-0.857750\pi$
$977$		−	844.451i		−	0.864331i	0.901794	−	0.432166i	$-0.142250\pi$
$978$		0			0
$979$	2.79053	+	1.61111i	0.00285039	+	0.00164567i
$980$		0			0
$981$		−	343.183i		−	0.349830i
$982$		0			0
$983$	−629.880	+	363.661i	−0.640773	+	0.369950i	−0.784912	−	0.619607i	$-0.787292\pi$
$983$	−629.880	+	363.661i	−0.640773	+	0.369950i	0.144139	+	0.989557i	$0.453959\pi$
$984$		0			0
$985$	−1059.29	−	1834.75i	−1.07542	−	1.86269i
$986$		0			0
$987$		−	418.409i		−	0.423920i
$988$		0			0
$989$	2060.10			2.08301
$990$		0			0
$991$	−1050.59	+	606.560i	−1.06013	+	0.612068i	−0.925469	−	0.378823i	$-0.876329\pi$
$991$	−1050.59	+	606.560i	−1.06013	+	0.612068i	−0.134664	+	0.990891i	$0.542996\pi$
$992$		0			0
$993$	85.1372	+	147.462i	0.0857373	+	0.148501i
$994$		0			0
$995$	2033.21			2.04343
$996$		0			0
$997$	178.069	−	308.424i	0.178604	−	0.309352i	−0.762798	−	0.646636i	$-0.776175\pi$
$997$	178.069	−	308.424i	0.178604	−	0.309352i	0.941403	+	0.337285i	$0.109508\pi$
$998$		0			0
$999$	2.04291			0.00204496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.3.be.e.145.3		6
4.3	odd	2		228.3.l.d.145.3	✓	6
12.11	even	2		684.3.y.f.145.1		6
19.8	odd	6	inner	912.3.be.e.673.3		6
76.27	even	6		228.3.l.d.217.3	yes	6
228.179	odd	6		684.3.y.f.217.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.l.d.145.3	✓	6	4.3	odd	2
228.3.l.d.217.3	yes	6	76.27	even	6
684.3.y.f.145.1		6	12.11	even	2
684.3.y.f.217.1		6	228.179	odd	6
912.3.be.e.145.3		6	1.1	even	1	trivial
912.3.be.e.673.3		6	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(4.17458 + 7.23058i) q^{5} -4.32088 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(4.17458 + 7.23058i) q^{5} -4.32088 q^{7} +(1.50000 - 2.59808i) q^{9} +16.6044 q^{11} +(2.07976 + 1.20075i) q^{13} +(12.5237 + 7.23058i) q^{15} +(2.60803 + 4.51724i) q^{17} +(-6.76940 - 17.7532i) q^{19} +(-6.48133 + 3.74200i) q^{21} +(17.8729 - 30.9568i) q^{23} +(-22.3542 + 38.7186i) q^{25} -5.19615i q^{27} +(35.7867 + 20.6615i) q^{29} +36.8485i q^{31} +(24.9066 - 14.3799i) q^{33} +(-18.0379 - 31.2425i) q^{35} +0.393159i q^{37} +4.15951 q^{39} +(-31.8133 + 18.3674i) q^{41} +(28.8159 + 49.9107i) q^{43} +25.0475 q^{45} +(-27.9536 + 48.4170i) q^{47} -30.3300 q^{49} +(7.82409 + 4.51724i) q^{51} +(77.2086 + 44.5764i) q^{53} +(69.3165 + 120.060i) q^{55} +(-25.5288 - 20.7673i) q^{57} +(45.3269 - 26.1695i) q^{59} +(27.1555 - 47.0347i) q^{61} +(-6.48133 + 11.2260i) q^{63} +20.0505i q^{65} +(-85.8161 - 49.5459i) q^{67} -61.9135i q^{69} +(-69.5525 + 40.1562i) q^{71} +(14.7553 + 25.5569i) q^{73} +77.4373i q^{75} -71.7458 q^{77} +(-55.3483 + 31.9554i) q^{79} +(-4.50000 - 7.79423i) q^{81} -61.9528 q^{83} +(-21.7749 + 37.7152i) q^{85} +71.5735 q^{87} +(0.168059 + 0.0970291i) q^{89} +(-8.98639 - 5.18830i) q^{91} +(31.9117 + 55.2727i) q^{93} +(100.106 - 123.059i) q^{95} +(91.0094 - 52.5443i) q^{97} +(24.9066 - 43.1396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9}+O(q^{10}) \) 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9	\( 6 q + 9 q^{3} + 4 q^{5} - 10 q^{7} + 9 q^{9} + 20 q^{11} + 21 q^{13} + 12 q^{15} - 2 q^{17} + 10 q^{19} - 15 q^{21} + 2 q^{23} - 5 q^{25} + 114 q^{29} + 30 q^{33} - 32 q^{35} + 42 q^{39} + 48 q^{41} + 21 q^{43} + 24 q^{45} - 46 q^{47} - 240 q^{49} - 6 q^{51} - 18 q^{53} + 140 q^{55} - 3 q^{57} + 144 q^{59} + 19 q^{61} - 15 q^{63} - 201 q^{67} - 204 q^{71} + 51 q^{73} - 220 q^{77} - 153 q^{79} - 27 q^{81} - 52 q^{83} - 92 q^{85} + 228 q^{87} + 216 q^{89} + 57 q^{91} - 15 q^{93} + 248 q^{95} + 12 q^{97} + 30 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 + 4 * q^5 - 10 * q^7 + 9 * q^9 + 20 * q^11 + 21 * q^13 + 12 * q^15 - 2 * q^17 + 10 * q^19 - 15 * q^21 + 2 * q^23 - 5 * q^25 + 114 * q^29 + 30 * q^33 - 32 * q^35 + 42 * q^39 + 48 * q^41 + 21 * q^43 + 24 * q^45 - 46 * q^47 - 240 * q^49 - 6 * q^51 - 18 * q^53 + 140 * q^55 - 3 * q^57 + 144 * q^59 + 19 * q^61 - 15 * q^63 - 201 * q^67 - 204 * q^71 + 51 * q^73 - 220 * q^77 - 153 * q^79 - 27 * q^81 - 52 * q^83 - 92 * q^85 + 228 * q^87 + 216 * q^89 + 57 * q^91 - 15 * q^93 + 248 * q^95 + 12 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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