LMFDB - Embedded newform 684.3.m.a.653.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(353,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 4]))

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

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

chi := DirichletCharacter("684.353");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.m (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			653.12
Character	$\chi$	$=$	684.653
Dual form			684.3.m.a.353.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70356 + 2.46939i) q^{3} +9.28650i q^{5} +(-2.28067 - 3.95023i) q^{7} +(-3.19575 - 8.41351i) q^{9} +O(q^{10})$	\(q+(-1.70356 + 2.46939i) q^{3} +9.28650i q^{5} +(-2.28067 - 3.95023i) q^{7} +(-3.19575 - 8.41351i) q^{9} +(-1.10584 + 0.638454i) q^{11} +(-3.30958 - 5.73235i) q^{13} +(-22.9320 - 15.8201i) q^{15} +(-11.0966 + 6.40664i) q^{17} +(-18.7585 - 3.01961i) q^{19} +(13.6399 + 1.09762i) q^{21} +(16.3480 - 9.43853i) q^{23} -61.2390 q^{25} +(26.2204 + 6.44140i) q^{27} +7.10485i q^{29} +(7.90302 - 13.6884i) q^{31} +(0.307269 - 3.81838i) q^{33} +(36.6838 - 21.1794i) q^{35} -16.9760 q^{37} +(19.7935 + 1.59280i) q^{39} +17.6906i q^{41} +(20.8849 - 36.1738i) q^{43} +(78.1321 - 29.6773i) q^{45} +22.7792i q^{47} +(14.0971 - 24.4169i) q^{49} +(3.08332 - 38.3160i) q^{51} +(5.86723 + 3.38745i) q^{53} +(-5.92901 - 10.2693i) q^{55} +(39.4129 - 41.1779i) q^{57} -82.7526i q^{59} +47.4838 q^{61} +(-25.9469 + 31.8124i) q^{63} +(53.2335 - 30.7344i) q^{65} +(21.3601 + 36.9968i) q^{67} +(-4.54247 + 56.4487i) q^{69} +(-21.4678 + 12.3945i) q^{71} +(-39.6934 - 68.7509i) q^{73} +(104.325 - 151.223i) q^{75} +(5.04409 + 2.91221i) q^{77} +(-54.2353 + 93.9382i) q^{79} +(-60.5744 + 53.7749i) q^{81} +(34.7029 - 20.0357i) q^{83} +(-59.4952 - 103.049i) q^{85} +(-17.5446 - 12.1036i) q^{87} +(-49.2445 - 28.4313i) q^{89} +(-15.0961 + 26.1472i) q^{91} +(20.3387 + 42.8347i) q^{93} +(28.0416 - 174.201i) q^{95} +(-86.8612 + 150.448i) q^{97} +(8.90562 + 7.26362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9	$ 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−1.70356	+	2.46939i	−0.567854	+	0.823129i
$3$	−1.70356	+	2.46939i	−0.567854	+	0.823129i
$4$		0			0
$5$			9.28650i			1.85730i	0.370958	+	0.928650i	$0.379029\pi$
$5$			9.28650i			1.85730i	−0.370958	+	0.928650i	$0.620971\pi$
$6$		0			0
$7$	−2.28067	−	3.95023i	−0.325810	−	0.564319i	0.655866	−	0.754877i	$-0.272304\pi$
$7$	−2.28067	−	3.95023i	−0.325810	−	0.564319i	−0.981676	+	0.190558i	$0.938970\pi$
$8$		0			0
$9$	−3.19575	−	8.41351i	−0.355083	−	0.934835i
$10$		0			0
$11$	−1.10584	+	0.638454i	−0.100531	+	0.0580413i	−0.549422	−	0.835545i	$-0.685152\pi$
$11$	−1.10584	+	0.638454i	−0.100531	+	0.0580413i	0.448892	+	0.893586i	$0.351819\pi$
$12$		0			0
$13$	−3.30958	−	5.73235i	−0.254583	−	0.440950i	0.710199	−	0.704001i	$-0.248605\pi$
$13$	−3.30958	−	5.73235i	−0.254583	−	0.440950i	−0.964782	+	0.263050i	$0.915271\pi$
$14$		0			0
$15$	−22.9320	−	15.8201i	−1.52880	−	1.05468i
$16$		0			0
$17$	−11.0966	+	6.40664i	−0.652743	+	0.376861i	−0.789506	−	0.613743i	$-0.789663\pi$
$17$	−11.0966	+	6.40664i	−0.652743	+	0.376861i	0.136764	+	0.990604i	$0.456330\pi$
$18$		0			0
$19$	−18.7585	−	3.01961i	−0.987290	−	0.158927i
$19$	−18.7585	−	3.01961i	−0.987290	−	0.158927i
$20$		0			0
$21$	13.6399	+	1.09762i	0.649520	+	0.0522674i
$22$		0			0
$23$	16.3480	−	9.43853i	0.710783	−	0.410371i	−0.100568	−	0.994930i	$-0.532066\pi$
$23$	16.3480	−	9.43853i	0.710783	−	0.410371i	0.811351	+	0.584559i	$0.198733\pi$
$24$		0			0
$25$	−61.2390			−2.44956
$26$		0			0
$27$	26.2204	+	6.44140i	0.971125	+	0.238570i
$28$		0			0
$29$			7.10485i			0.244995i	0.992469	+	0.122497i	$0.0390903\pi$
$29$			7.10485i			0.244995i	−0.992469	+	0.122497i	$0.960910\pi$
$30$		0			0
$31$	7.90302	−	13.6884i	0.254936	−	0.441562i	−0.709942	−	0.704260i	$-0.751279\pi$
$31$	7.90302	−	13.6884i	0.254936	−	0.441562i	0.964878	+	0.262698i	$0.0846123\pi$
$32$		0			0
$33$	0.307269	−	3.81838i	0.00931117	−	0.115709i
$34$		0			0
$35$	36.6838	−	21.1794i	1.04811	−	0.605126i
$36$		0			0
$37$	−16.9760			−0.458810			−0.229405	−	0.973331i	$-0.573678\pi$
$37$	−16.9760			−0.458810			−0.229405	+	0.973331i	$0.573678\pi$
$38$		0			0
$39$	19.7935	+	1.59280i	0.507525	+	0.0408410i
$40$		0			0
$41$			17.6906i			0.431477i	0.976451	+	0.215739i	$0.0692159\pi$
$41$			17.6906i			0.431477i	−0.976451	+	0.215739i	$0.930784\pi$
$42$		0			0
$43$	20.8849	−	36.1738i	0.485696	−	0.841251i	−0.514169	−	0.857689i	$-0.671899\pi$
$43$	20.8849	−	36.1738i	0.485696	−	0.841251i	0.999865	+	0.0164385i	$0.00523277\pi$
$44$		0			0
$45$	78.1321	−	29.6773i	1.73627	−	0.659496i
$46$		0			0
$47$			22.7792i			0.484665i	0.970193	+	0.242332i	$0.0779124\pi$
$47$			22.7792i			0.484665i	−0.970193	+	0.242332i	$0.922088\pi$
$48$		0			0
$49$	14.0971	−	24.4169i	0.287696	−	0.498304i
$50$		0			0
$51$	3.08332	−	38.3160i	0.0604572	−	0.751294i
$52$		0			0
$53$	5.86723	+	3.38745i	0.110702	+	0.0639141i	0.554329	−	0.832298i	$-0.312975\pi$
$53$	5.86723	+	3.38745i	0.110702	+	0.0639141i	−0.443626	+	0.896212i	$0.646308\pi$
$54$		0			0
$55$	−5.92901	−	10.2693i	−0.107800	−	0.186715i
$56$		0			0
$57$	39.4129	−	41.1779i	0.691454	−	0.722420i
$58$		0			0
$59$		−	82.7526i		−	1.40259i	−0.712873	−	0.701293i	$-0.752606\pi$
$59$		−	82.7526i		−	1.40259i	0.712873	−	0.701293i	$-0.247394\pi$
$60$		0			0
$61$	47.4838			0.778423			0.389211	−	0.921148i	$-0.372748\pi$
$61$	47.4838			0.778423			0.389211	+	0.921148i	$0.372748\pi$
$62$		0			0
$63$	−25.9469	+	31.8124i	−0.411855	+	0.504959i
$64$		0			0
$65$	53.2335	−	30.7344i	0.818977	−	0.472836i
$66$		0			0
$67$	21.3601	+	36.9968i	0.318807	+	0.552190i	0.980239	−	0.197815i	$-0.0633844\pi$
$67$	21.3601	+	36.9968i	0.318807	+	0.552190i	−0.661432	+	0.750005i	$0.730051\pi$
$68$		0			0
$69$	−4.54247	+	56.4487i	−0.0658330	+	0.818097i
$70$		0			0
$71$	−21.4678	+	12.3945i	−0.302364	+	0.174570i	−0.643504	−	0.765442i	$-0.722520\pi$
$71$	−21.4678	+	12.3945i	−0.302364	+	0.174570i	0.341140	+	0.940012i	$0.389187\pi$
$72$		0			0
$73$	−39.6934	−	68.7509i	−0.543745	−	0.941793i	−0.998685	−	0.0512713i	$-0.983673\pi$
$73$	−39.6934	−	68.7509i	−0.543745	−	0.941793i	0.454940	−	0.890522i	$-0.349661\pi$
$74$		0			0
$75$	104.325	−	151.223i	1.39099	−	2.01631i
$76$		0			0
$77$	5.04409	+	2.91221i	0.0655076	+	0.0378209i
$78$		0			0
$79$	−54.2353	+	93.9382i	−0.686522	+	1.18909i	0.286434	+	0.958100i	$0.407530\pi$
$79$	−54.2353	+	93.9382i	−0.686522	+	1.18909i	−0.972956	+	0.230991i	$0.925803\pi$
$80$		0			0
$81$	−60.5744	+	53.7749i	−0.747832	+	0.663888i
$82$		0			0
$83$	34.7029	−	20.0357i	0.418107	−	0.241394i	−0.276160	−	0.961112i	$-0.589062\pi$
$83$	34.7029	−	20.0357i	0.418107	−	0.241394i	0.694267	+	0.719717i	$0.255729\pi$
$84$		0			0
$85$	−59.4952	−	103.049i	−0.699944	−	1.21234i
$86$		0			0
$87$	−17.5446	−	12.1036i	−0.201662	−	0.139121i
$88$		0			0
$89$	−49.2445	−	28.4313i	−0.553309	−	0.319453i	0.197147	−	0.980374i	$-0.436832\pi$
$89$	−49.2445	−	28.4313i	−0.553309	−	0.319453i	−0.750455	+	0.660921i	$0.770166\pi$
$90$		0			0
$91$	−15.0961	+	26.1472i	−0.165891	+	0.287332i
$92$		0			0
$93$	20.3387	+	42.8347i	0.218696	+	0.460588i
$94$		0			0
$95$	28.0416	−	174.201i	0.295175	−	1.83369i
$96$		0			0
$97$	−86.8612	+	150.448i	−0.895477	+	1.55101i	−0.0622629	+	0.998060i	$0.519832\pi$
$97$	−86.8612	+	150.448i	−0.895477	+	1.55101i	−0.833214	+	0.552951i	$0.813502\pi$
$98$		0			0
$99$	8.90562	+	7.26362i	0.0899557	+	0.0733699i
$100$		0			0
$101$		−	88.8592i		−	0.879794i	−0.898048	−	0.439897i	$-0.855015\pi$
$101$		−	88.8592i		−	0.879794i	0.898048	−	0.439897i	$-0.144985\pi$
$102$		0			0
$103$	43.5924	−	75.5043i	0.423227	−	0.733051i	−0.573026	−	0.819537i	$-0.694231\pi$
$103$	43.5924	−	75.5043i	0.423227	−	0.733051i	0.996253	+	0.0864862i	$0.0275639\pi$
$104$		0			0
$105$	−10.1930	+	126.667i	−0.0970763	+	1.20635i
$106$		0			0
$107$		−	85.1392i		−	0.795693i	−0.917452	−	0.397847i	$-0.869758\pi$
$107$		−	85.1392i		−	0.795693i	0.917452	−	0.397847i	$-0.130242\pi$
$108$		0			0
$109$	−103.317	−	178.950i	−0.947861	−	1.64174i	−0.749919	−	0.661529i	$-0.769908\pi$
$109$	−103.317	−	178.950i	−0.947861	−	1.64174i	−0.197941	−	0.980214i	$-0.563426\pi$
$110$		0			0
$111$	28.9196	−	41.9203i	0.260537	−	0.377660i
$112$		0			0
$113$	−180.905	−	104.445i	−1.60093	−	0.924296i	−0.991302	−	0.131605i	$-0.957987\pi$
$113$	−180.905	−	104.445i	−1.60093	−	0.924296i	−0.609625	−	0.792690i	$-0.708680\pi$
$114$		0			0
$115$	87.6509	+	151.816i	0.762181	+	1.32014i
$116$		0			0
$117$	−37.6526	+	46.1643i	−0.321817	+	0.394567i
$118$		0			0
$119$	50.6154	+	29.2228i	0.425340	+	0.245570i
$120$		0			0
$121$	−59.6848	+	103.377i	−0.493262	+	0.854356i
$122$		0			0
$123$	−43.6849	−	30.1370i	−0.355162	−	0.245016i
$124$		0			0
$125$		−	336.534i		−	2.69227i
$126$		0			0
$127$	56.4818	−	97.8294i	0.444739	−	0.770310i	−0.553295	−	0.832985i	$-0.686630\pi$
$127$	56.4818	−	97.8294i	0.444739	−	0.770310i	0.998034	+	0.0626751i	$0.0199632\pi$
$128$		0			0
$129$	53.7483	+	113.197i	0.416653	+	0.877499i
$130$		0			0
$131$		−	8.51243i		−	0.0649803i	−0.999472	−	0.0324902i	$-0.989656\pi$
$131$		−	8.51243i		−	0.0649803i	0.999472	−	0.0324902i	$-0.0103438\pi$
$132$		0			0
$133$	30.8538	+	80.9873i	0.231983	+	0.608927i
$134$		0			0
$135$	−59.8181	+	243.495i	−0.443097	+	1.80367i
$136$		0			0
$137$			214.194i			1.56346i	0.623618	+	0.781729i	$0.285662\pi$
$137$			214.194i			1.56346i	−0.623618	+	0.781729i	$0.714338\pi$
$138$		0			0
$139$	25.7715	+	44.6376i	0.185407	+	0.321134i	0.943713	−	0.330764i	$-0.107306\pi$
$139$	25.7715	+	44.6376i	0.185407	+	0.321134i	−0.758307	+	0.651898i	$0.773973\pi$
$140$		0			0
$141$	−56.2508	−	38.8059i	−0.398942	−	0.275219i
$142$		0			0
$143$	7.31969	+	4.22603i	0.0511867	+	0.0295526i
$144$		0			0
$145$	−65.9792			−0.455029
$146$		0			0
$147$	36.2795	+	76.4069i	0.246799	+	0.519775i
$148$		0			0
$149$			143.809i			0.965164i	0.875851	+	0.482582i	$0.160301\pi$
$149$			143.809i			0.965164i	−0.875851	+	0.482582i	$0.839699\pi$
$150$		0			0
$151$	109.749	+	190.090i	0.726813	+	1.25888i	0.958223	+	0.286021i	$0.0923326\pi$
$151$	109.749	+	190.090i	0.726813	+	1.25888i	−0.231411	+	0.972856i	$0.574334\pi$
$152$		0			0
$153$	89.3644	+	72.8876i	0.584081	+	0.476389i
$154$		0			0
$155$	127.118	+	73.3913i	0.820113	+	0.473493i
$156$		0			0
$157$	−31.4750			−0.200477			−0.100239	−	0.994963i	$-0.531961\pi$
$157$	−31.4750			−0.200477			−0.100239	+	0.994963i	$0.531961\pi$
$158$		0			0
$159$	−18.3601	+	8.71774i	−0.115472	+	0.0548286i
$160$		0			0
$161$	−74.5688	−	43.0523i	−0.463160	−	0.267406i
$162$		0			0
$163$	−27.3667			−0.167894			−0.0839469	−	0.996470i	$-0.526753\pi$
$163$	−27.3667			−0.167894			−0.0839469	+	0.996470i	$0.526753\pi$
$164$		0			0
$165$	35.4594	+	2.85345i	0.214906	+	0.0172936i
$166$		0			0
$167$	200.623	−	115.830i	1.20134	−	0.693592i	0.240485	−	0.970653i	$-0.422694\pi$
$167$	200.623	−	115.830i	1.20134	−	0.693592i	0.960852	+	0.277061i	$0.0893603\pi$
$168$		0			0
$169$	62.5934	−	108.415i	0.370375	−	0.641509i
$170$		0			0
$171$	34.5420	+	167.475i	0.202000	+	0.979386i
$172$		0			0
$173$	−103.634	−	59.8331i	−0.599041	−	0.345856i	0.169623	−	0.985509i	$-0.445745\pi$
$173$	−103.634	−	59.8331i	−0.599041	−	0.345856i	−0.768664	+	0.639653i	$0.779078\pi$
$174$		0			0
$175$	139.666	+	241.908i	0.798091	+	1.38233i
$176$		0			0
$177$	204.348	+	140.974i	1.15451	+	0.796465i
$178$		0			0
$179$		−	182.887i		−	1.02171i	−0.859666	−	0.510856i	$-0.829328\pi$
$179$		−	182.887i		−	1.02171i	0.859666	−	0.510856i	$-0.170672\pi$
$180$		0			0
$181$	77.9550	−	135.022i	0.430691	−	0.745978i	−0.566242	−	0.824239i	$-0.691603\pi$
$181$	77.9550	−	135.022i	0.430691	−	0.745978i	0.996933	+	0.0782606i	$0.0249366\pi$
$182$		0			0
$183$	−80.8916	+	117.256i	−0.442031	+	0.640743i
$184$		0			0
$185$		−	157.647i		−	0.852148i
$186$		0			0
$187$	8.18069	−	14.1694i	0.0437470	−	0.0757721i
$188$		0			0
$189$	−34.3550	−	118.267i	−0.181772	−	0.625753i
$190$		0			0
$191$	−292.923	+	169.119i	−1.53363	+	0.885440i	−0.534436	+	0.845209i	$0.679476\pi$
$191$	−292.923	+	169.119i	−1.53363	+	0.885440i	−0.999190	+	0.0402304i	$0.987191\pi$
$192$		0			0
$193$	−213.007			−1.10366			−0.551832	−	0.833955i	$-0.686071\pi$
$193$	−213.007			−1.10366			−0.551832	+	0.833955i	$0.686071\pi$
$194$		0			0
$195$	−14.7915	+	183.812i	−0.0758539	+	0.942626i
$196$		0			0
$197$		−	7.74954i		−	0.0393378i	−0.999807	−	0.0196689i	$-0.993739\pi$
$197$		−	7.74954i		−	0.0393378i	0.999807	−	0.0196689i	$-0.00626120\pi$
$198$		0			0
$199$	−149.979	+	259.771i	−0.753662	+	1.30538i	0.192375	+	0.981321i	$0.438381\pi$
$199$	−149.979	+	259.771i	−0.753662	+	1.30538i	−0.946037	+	0.324059i	$0.894952\pi$
$200$		0			0
$201$	−127.748	−	10.2800i	−0.635560	−	0.0511441i
$202$		0			0
$203$	28.0658	−	16.2038i	0.138255	−	0.0798217i
$204$		0			0
$205$	−164.283			−0.801383
$206$		0			0
$207$	−131.655	−	107.381i	−0.636016	−	0.518749i
$208$		0			0
$209$	22.6717	−	8.63726i	0.108477	−	0.0413266i
$210$		0			0
$211$	−368.255			−1.74528			−0.872641	−	0.488362i	$-0.837595\pi$
$211$	−368.255			−1.74528			−0.872641	+	0.488362i	$0.837595\pi$
$212$		0			0
$213$	5.96508	−	74.1272i	0.0280050	−	0.348015i
$214$		0			0
$215$	335.928	+	193.948i	1.56245	+	0.902083i
$216$		0			0
$217$	−72.0966			−0.332243
$218$		0			0
$219$	237.393	+	19.1032i	1.08399	+	0.0872292i
$220$		0			0
$221$	73.4502	+	42.4065i	0.332354	+	0.191885i
$222$		0			0
$223$	76.6100	−	132.692i	0.343543	−	0.595033i	−0.641545	−	0.767085i	$-0.721706\pi$
$223$	76.6100	−	132.692i	0.343543	−	0.595033i	0.985088	+	0.172052i	$0.0550397\pi$
$224$		0			0
$225$	195.705	+	515.235i	0.869798	+	2.28993i
$226$		0			0
$227$	119.451	−	68.9649i	0.526214	−	0.303810i	−0.213259	−	0.976996i	$-0.568408\pi$
$227$	119.451	−	68.9649i	0.526214	−	0.303810i	0.739474	+	0.673186i	$0.235075\pi$
$228$		0			0
$229$	−84.2944	+	146.002i	−0.368098	+	0.637564i	−0.989268	−	0.146112i	$-0.953324\pi$
$229$	−84.2944	+	146.002i	−0.368098	+	0.637564i	0.621170	+	0.783676i	$0.286657\pi$
$230$		0			0
$231$	−15.7843	+	7.49468i	−0.0683302	+	0.0324445i
$232$		0			0
$233$	−257.617	+	148.735i	−1.10565	+	0.638348i	−0.937700	−	0.347447i	$-0.887049\pi$
$233$	−257.617	+	148.735i	−1.10565	+	0.638348i	−0.167952	+	0.985795i	$0.553715\pi$
$234$		0			0
$235$	−211.539			−0.900167
$236$		0			0
$237$	−139.577	−	293.957i	−0.588931	−	1.24033i
$238$		0			0
$239$	−277.929	−	160.462i	−1.16288	−	0.671391i	−0.210889	−	0.977510i	$-0.567636\pi$
$239$	−277.929	−	160.462i	−1.16288	−	0.671391i	−0.951993	+	0.306119i	$0.900969\pi$
$240$		0			0
$241$	−393.874			−1.63433			−0.817167	−	0.576402i	$-0.804456\pi$
$241$	−393.874			−1.63433			−0.817167	+	0.576402i	$0.804456\pi$
$242$		0			0
$243$	−29.5990	−	241.191i	−0.121806	−	0.992554i
$244$		0			0
$245$	226.747	+	130.913i	0.925500	+	0.534338i
$246$		0			0
$247$	44.7732	+	117.524i	0.181268	+	0.475806i
$248$		0			0
$249$	−9.64259	+	119.827i	−0.0387252	+	0.481233i
$250$		0			0
$251$	320.034	+	184.772i	1.27504	+	0.736142i	0.975931	−	0.218078i	$-0.0699788\pi$
$251$	320.034	+	184.772i	1.27504	+	0.736142i	0.299104	+	0.954220i	$0.403312\pi$
$252$		0			0
$253$	−12.0521	+	20.8749i	−0.0476369	+	0.0825096i
$254$		0			0
$255$	355.821	+	28.6332i	1.39538	+	0.112287i
$256$		0			0
$257$	159.326	−	91.9868i	0.619945	−	0.357925i	−0.156903	−	0.987614i	$-0.550151\pi$
$257$	159.326	−	91.9868i	0.619945	−	0.357925i	0.776847	+	0.629689i	$0.216818\pi$
$258$		0			0
$259$	38.7166	+	67.0591i	0.149485	+	0.258915i
$260$		0			0
$261$	59.7767	−	22.7053i	0.229030	−	0.0869935i
$262$		0			0
$263$	−146.456	−	84.5564i	−0.556867	−	0.321507i	0.195020	−	0.980799i	$-0.437523\pi$
$263$	−146.456	−	84.5564i	−0.556867	−	0.321507i	−0.751887	+	0.659292i	$0.770856\pi$
$264$		0			0
$265$	−31.4575	+	54.4860i	−0.118708	+	0.205608i
$266$		0			0
$267$	154.099	−	73.1692i	0.577150	−	0.274042i
$268$		0			0
$269$	0.505277	−	0.291722i	0.00187835	−	0.00108447i	−0.499061	−	0.866567i	$-0.666321\pi$
$269$	0.505277	−	0.291722i	0.00187835	−	0.00108447i	0.500939	+	0.865483i	$0.332988\pi$
$270$		0			0
$271$	−173.903	−	301.208i	−0.641707	−	1.11147i	−0.985052	−	0.172260i	$-0.944893\pi$
$271$	−173.903	−	301.208i	−0.641707	−	1.11147i	0.343344	−	0.939210i	$-0.388440\pi$
$272$		0			0
$273$	−38.8504	−	81.8215i	−0.142309	−	0.299712i
$274$		0			0
$275$	67.7203	−	39.0983i	0.246256	−	0.142176i
$276$		0			0
$277$	−115.851	−	200.660i	−0.418235	−	0.724404i	0.577527	−	0.816371i	$-0.304018\pi$
$277$	−115.851	−	200.660i	−0.418235	−	0.724404i	−0.995762	+	0.0919678i	$0.970684\pi$
$278$		0			0
$279$	−140.424	−	22.7473i	−0.503311	−	0.0815317i
$280$		0			0
$281$			501.455i			1.78454i	0.451505	+	0.892268i	$0.350887\pi$
$281$			501.455i			1.78454i	−0.451505	+	0.892268i	$0.649113\pi$
$282$		0			0
$283$	−46.8874			−0.165680			−0.0828399	−	0.996563i	$-0.526399\pi$
$283$	−46.8874			−0.165680			−0.0828399	+	0.996563i	$0.526399\pi$
$284$		0			0
$285$	382.399	+	366.008i	1.34175	+	1.28424i
$286$		0			0
$287$	69.8819	−	40.3463i	0.243491	−	0.140580i
$288$		0			0
$289$	−62.4099	+	108.097i	−0.215951	+	0.374039i
$290$		0			0
$291$	−223.541	−	470.792i	−0.768182	−	1.61784i
$292$		0			0
$293$	−67.5883	−	39.0221i	−0.230677	−	0.133181i	0.380207	−	0.924901i	$-0.375853\pi$
$293$	−67.5883	−	39.0221i	−0.230677	−	0.133181i	−0.610884	+	0.791720i	$0.709186\pi$
$294$		0			0
$295$	768.482			2.60502
$296$		0			0
$297$	−33.1080	+	9.61739i	−0.111475	+	0.0323818i
$298$		0			0
$299$	−108.210	−	62.4750i	−0.361906	−	0.208947i
$300$		0			0
$301$	−190.526			−0.632978
$302$		0			0
$303$	219.428	+	151.377i	0.724184	+	0.499595i
$304$		0			0
$305$			440.958i			1.44576i
$306$		0			0
$307$	−13.1550	−	22.7852i	−0.0428503	−	0.0742188i	0.843805	−	0.536650i	$-0.180311\pi$
$307$	−13.1550	−	22.7852i	−0.0428503	−	0.0742188i	−0.886655	+	0.462431i	$0.846977\pi$
$308$		0			0
$309$	112.187	+	236.273i	0.363064	+	0.764637i
$310$		0			0
$311$	−339.125	−	195.794i	−1.09043	−	0.629562i	−0.156741	−	0.987640i	$-0.550099\pi$
$311$	−339.125	−	195.794i	−1.09043	−	0.629562i	−0.933692	+	0.358078i	$0.883432\pi$
$312$		0			0
$313$	−93.3871			−0.298361			−0.149181	−	0.988810i	$-0.547664\pi$
$313$	−93.3871			−0.298361			−0.149181	+	0.988810i	$0.547664\pi$
$314$		0			0
$315$	−295.426	−	240.956i	−0.937859	−	0.764939i
$316$		0			0
$317$		−	57.0992i		−	0.180124i	−0.995936	−	0.0900618i	$-0.971294\pi$
$317$		−	57.0992i		−	0.180124i	0.995936	−	0.0900618i	$-0.0287064\pi$
$318$		0			0
$319$	−4.53612	−	7.85679i	−0.0142198	−	0.0246294i
$320$		0			0
$321$	210.242	+	145.040i	0.654958	+	0.451838i
$322$		0			0
$323$	227.502	−	86.6715i	0.704340	−	0.268333i
$324$		0			0
$325$	202.675	+	351.044i	0.623616	+	1.08013i
$326$		0			0
$327$	617.904	+	49.7232i	1.88961	+	0.152059i
$328$		0			0
$329$	89.9833	−	51.9519i	0.273505	−	0.157908i
$330$		0			0
$331$	−5.97582	−	10.3504i	−0.0180538	−	0.0312702i	0.856857	−	0.515554i	$-0.172414\pi$
$331$	−5.97582	−	10.3504i	−0.0180538	−	0.0312702i	−0.874911	+	0.484283i	$0.839080\pi$
$332$		0			0
$333$	54.2510	+	142.828i	0.162916	+	0.428912i
$334$		0			0
$335$	−343.570	+	198.360i	−1.02558	+	0.592121i
$336$		0			0
$337$	−100.450			−0.298071			−0.149035	−	0.988832i	$-0.547617\pi$
$337$	−100.450			−0.298071			−0.149035	+	0.988832i	$0.547617\pi$
$338$		0			0
$339$	566.099	−	268.795i	1.66991	−	0.792905i
$340$		0			0
$341$			20.1829i			0.0591873i
$342$		0			0
$343$	−352.109			−1.02656
$344$		0			0
$345$	−524.211	−	42.1837i	−1.51945	−	0.122272i
$346$		0			0
$347$		−	151.374i		−	0.436236i	−0.975922	−	0.218118i	$-0.930008\pi$
$347$		−	151.374i		−	0.436236i	0.975922	−	0.218118i	$-0.0699917\pi$
$348$		0			0
$349$	−219.737	−	380.596i	−0.629619	−	1.09053i	−0.987628	−	0.156814i	$-0.949878\pi$
$349$	−219.737	−	380.596i	−0.629619	−	1.09053i	0.358009	−	0.933718i	$-0.383456\pi$
$350$		0			0
$351$	−49.8539	−	171.623i	−0.142034	−	0.488954i
$352$		0			0
$353$	524.353	−	302.736i	1.48542	−	0.857608i	0.485558	−	0.874204i	$-0.338616\pi$
$353$	524.353	−	302.736i	1.48542	−	0.857608i	0.999862	+	0.0165964i	$0.00528304\pi$
$354$		0			0
$355$	−115.101	−	199.361i	−0.324229	−	0.561580i
$356$		0			0
$357$	−158.389	+	75.2062i	−0.443667	+	0.210662i
$358$		0			0
$359$	−84.9553	+	49.0490i	−0.236644	+	0.136627i	−0.613633	−	0.789591i	$-0.710293\pi$
$359$	−84.9553	+	49.0490i	−0.236644	+	0.136627i	0.376989	+	0.926218i	$0.376959\pi$
$360$		0			0
$361$	342.764	+	113.287i	0.949484	+	0.313814i
$362$		0			0
$363$	−153.601	−	323.494i	−0.423144	−	0.891168i
$364$		0			0
$365$	638.455	−	368.612i	1.74919	−	1.00990i
$366$		0			0
$367$	−324.259			−0.883539			−0.441769	−	0.897129i	$-0.645649\pi$
$367$	−324.259			−0.883539			−0.441769	+	0.897129i	$0.645649\pi$
$368$		0			0
$369$	148.840	−	56.5346i	0.403360	−	0.153210i
$370$		0			0
$371$		−	30.9026i		−	0.0832954i
$372$		0			0
$373$	−79.8812	+	138.358i	−0.214159	+	0.370934i	−0.953012	−	0.302933i	$-0.902034\pi$
$373$	−79.8812	+	138.358i	−0.214159	+	0.370934i	0.738853	+	0.673866i	$0.235368\pi$
$374$		0			0
$375$	831.032	+	573.306i	2.21609	+	1.52882i
$376$		0			0
$377$	40.7275	−	23.5140i	0.108030	−	0.0623714i
$378$		0			0
$379$	366.244			0.966343			0.483171	−	0.875526i	$-0.339485\pi$
$379$	366.244			0.966343			0.483171	+	0.875526i	$0.339485\pi$
$380$		0			0
$381$	145.358	+	306.134i	0.381518	+	0.803501i
$382$		0			0
$383$		−	124.052i		−	0.323895i	−0.986799	−	0.161948i	$-0.948222\pi$
$383$		−	124.052i		−	0.323895i	0.986799	−	0.161948i	$-0.0517775\pi$
$384$		0			0
$385$	−27.0442	+	46.8419i	−0.0702446	+	0.121667i
$386$		0			0
$387$	−371.092	−	60.1134i	−0.958893	−	0.155332i
$388$		0			0
$389$			415.200i			1.06735i	0.845689	+	0.533676i	$0.179190\pi$
$389$			415.200i			1.06735i	−0.845689	+	0.533676i	$0.820810\pi$
$390$		0			0
$391$	−120.938	+	209.472i	−0.309306	+	0.535733i
$392$		0			0
$393$	21.0205	+	14.5014i	0.0534872	+	0.0368994i
$394$		0			0
$395$	−872.357	−	503.656i	−2.20850	−	1.27508i
$396$		0			0
$397$	247.236	+	428.225i	0.622760	+	1.07865i	0.988969	+	0.148120i	$0.0473220\pi$
$397$	247.236	+	428.225i	0.622760	+	1.07865i	−0.366209	+	0.930532i	$0.619345\pi$
$398$		0			0
$399$	−252.550	−	61.7769i	−0.632958	−	0.154829i
$400$		0			0
$401$			299.577i			0.747075i	0.927615	+	0.373538i	$0.121855\pi$
$401$			299.577i			0.747075i	−0.927615	+	0.373538i	$0.878145\pi$
$402$		0			0
$403$	−104.623			−0.259609
$404$		0			0
$405$	−499.381	−	562.524i	−1.23304	−	1.38895i
$406$		0			0
$407$	18.7726	−	10.8384i	0.0461244	−	0.0266299i
$408$		0			0
$409$	80.2674	+	139.027i	0.196253	+	0.339920i	0.947310	−	0.320317i	$-0.103789\pi$
$409$	80.2674	+	139.027i	0.196253	+	0.339920i	−0.751058	+	0.660237i	$0.770456\pi$
$410$		0			0
$411$	−528.928	−	364.893i	−1.28693	−	0.887817i
$412$		0			0
$413$	−326.892	+	188.731i	−0.791506	+	0.456976i
$414$		0			0
$415$	186.062	+	322.268i	0.448342	+	0.776550i
$416$		0			0
$417$	−154.131	−	12.4030i	−0.369619	−	0.0297435i
$418$		0			0
$419$	442.295	+	255.359i	1.05560	+	0.609449i	0.924211	−	0.381882i	$-0.124724\pi$
$419$	442.295	+	255.359i	1.05560	+	0.609449i	0.131386	+	0.991331i	$0.458057\pi$
$420$		0			0
$421$	−176.079	+	304.978i	−0.418241	+	0.724414i	−0.995763	−	0.0919610i	$-0.970686\pi$
$421$	−176.079	+	304.978i	−0.418241	+	0.724414i	0.577522	+	0.816375i	$0.304020\pi$
$422$		0			0
$423$	191.653	−	72.7967i	0.453081	−	0.172096i
$424$		0			0
$425$	679.547	−	392.336i	1.59893	−	0.923144i
$426$		0			0
$427$	−108.295	−	187.572i	−0.253618	−	0.439279i
$428$		0			0
$429$	−22.9052	+	10.8759i	−0.0533922	+	0.0253516i
$430$		0			0
$431$	−561.436	−	324.145i	−1.30264	−	0.752077i	−0.321780	−	0.946815i	$-0.604281\pi$
$431$	−561.436	−	324.145i	−1.30264	−	0.752077i	−0.980855	+	0.194738i	$0.937614\pi$
$432$		0			0
$433$	270.752	−	468.956i	0.625293	−	1.08304i	−0.363191	−	0.931715i	$-0.618313\pi$
$433$	270.752	−	468.956i	0.625293	−	1.08304i	0.988484	−	0.151325i	$-0.0483539\pi$
$434$		0			0
$435$	112.400	−	162.928i	0.258390	−	0.374547i
$436$		0			0
$437$	−335.165	+	127.688i	−0.766968	+	0.292192i
$438$		0			0
$439$	230.430	−	399.117i	0.524898	−	0.909151i	−0.474681	−	0.880158i	$-0.657437\pi$
$439$	230.430	−	399.117i	0.524898	−	0.909151i	0.999580	−	0.0289930i	$-0.00923004\pi$
$440$		0			0
$441$	−250.483	−	40.5759i	−0.567988	−	0.0920088i
$442$		0			0
$443$			798.745i			1.80304i	0.432740	+	0.901519i	$0.357547\pi$
$443$			798.745i			1.80304i	−0.432740	+	0.901519i	$0.642453\pi$
$444$		0			0
$445$	264.027	−	457.309i	0.593320	−	1.02766i
$446$		0			0
$447$	−355.121	−	244.988i	−0.794455	−	0.548072i
$448$		0			0
$449$		−	751.768i		−	1.67432i	−0.546962	−	0.837158i	$-0.684216\pi$
$449$		−	751.768i		−	1.67432i	0.546962	−	0.837158i	$-0.315784\pi$
$450$		0			0
$451$	−11.2946	−	19.5629i	−0.0250435	−	0.0433766i
$452$		0			0
$453$	−656.371	−	52.8187i	−1.44894	−	0.116598i
$454$		0			0
$455$	−242.816	−	140.190i	−0.533661	−	0.308109i
$456$		0			0
$457$	−341.536	−	591.557i	−0.747343	−	1.29444i	−0.949092	−	0.314999i	$-0.897996\pi$
$457$	−341.536	−	591.557i	−0.747343	−	1.29444i	0.201749	−	0.979437i	$-0.435338\pi$
$458$		0			0
$459$	−332.225	+	96.5067i	−0.723803	+	0.210254i
$460$		0			0
$461$	−495.618	−	286.145i	−1.07509	−	0.620706i	−0.145525	−	0.989355i	$-0.546487\pi$
$461$	−495.618	−	286.145i	−1.07509	−	0.620706i	−0.929569	+	0.368649i	$0.879820\pi$
$462$		0			0
$463$	221.398	−	383.473i	0.478182	−	0.828236i	−0.521505	−	0.853248i	$-0.674629\pi$
$463$	221.398	−	383.473i	0.478182	−	0.828236i	0.999687	+	0.0250123i	$0.00796250\pi$
$464$		0			0
$465$	−397.784	+	188.876i	−0.855450	+	0.406184i
$466$		0			0
$467$		−	246.829i		−	0.528542i	−0.964449	−	0.264271i	$-0.914869\pi$
$467$		−	246.829i		−	0.528542i	0.964449	−	0.264271i	$-0.0851313\pi$
$468$		0			0
$469$	97.4306	−	168.755i	0.207741	−	0.359818i
$470$		0			0
$471$	53.6196	−	77.7239i	0.113842	−	0.165019i
$472$		0			0
$473$			53.3363i			0.112762i
$474$		0			0
$475$	1148.75	+	184.918i	2.41843	+	0.389301i
$476$		0			0
$477$	9.75013	−	60.1895i	0.0204405	−	0.126183i
$478$		0			0
$479$		−	208.455i		−	0.435188i	−0.976039	−	0.217594i	$-0.930179\pi$
$479$		−	208.455i		−	0.435188i	0.976039	−	0.217594i	$-0.0698209\pi$
$480$		0			0
$481$	56.1833	+	97.3123i	0.116805	+	0.202312i
$482$		0			0
$483$	233.345	−	110.797i	0.483117	−	0.229393i
$484$		0			0
$485$	−1397.14	−	806.637i	−2.88069	−	1.66317i
$486$		0			0
$487$	467.236			0.959416			0.479708	−	0.877428i	$-0.340743\pi$
$487$	467.236			0.959416			0.479708	+	0.877428i	$0.340743\pi$
$488$		0			0
$489$	46.6208	−	67.5789i	0.0953391	−	0.138198i
$490$		0			0
$491$			263.317i			0.536287i	0.963379	+	0.268143i	$0.0864101\pi$
$491$			263.317i			0.536287i	−0.963379	+	0.268143i	$0.913590\pi$
$492$		0			0
$493$	−45.5182	−	78.8398i	−0.0923290	−	0.159919i
$494$		0			0
$495$	−67.4536	+	82.7020i	−0.136270	+	0.167075i
$496$		0			0
$497$	97.9220	+	56.5353i	0.197026	+	0.113753i
$498$		0			0
$499$	−891.558			−1.78669			−0.893345	−	0.449372i	$-0.851648\pi$
$499$	−891.558			−1.78669			−0.893345	+	0.449372i	$0.851648\pi$
$500$		0			0
$501$	−55.7454	+	692.740i	−0.111268	+	1.38271i
$502$		0			0
$503$	−383.876	−	221.631i	−0.763174	−	0.440619i	0.0672604	−	0.997735i	$-0.478574\pi$
$503$	−383.876	−	221.631i	−0.763174	−	0.440619i	−0.830434	+	0.557117i	$0.811908\pi$
$504$		0			0
$505$	825.191			1.63404
$506$		0			0
$507$	161.087	+	339.259i	0.317725	+	0.669150i
$508$		0			0
$509$	306.042	−	176.693i	0.601261	−	0.347138i	−0.168276	−	0.985740i	$-0.553820\pi$
$509$	306.042	−	176.693i	0.601261	−	0.347138i	0.769538	+	0.638602i	$0.220487\pi$
$510$		0			0
$511$	−181.055	+	313.596i	−0.354315	+	0.613691i
$512$		0			0
$513$	−472.405	−	200.007i	−0.920867	−	0.389876i
$514$		0			0
$515$	701.170	+	404.821i	1.36150	+	0.786060i
$516$		0			0
$517$	−14.5435	−	25.1901i	−0.0281306	−	0.0487236i
$518$		0			0
$519$	324.298	−	153.983i	0.624852	−	0.296692i
$520$		0			0
$521$			530.816i			1.01884i	0.860518	+	0.509420i	$0.170140\pi$
$521$			530.816i			1.01884i	−0.860518	+	0.509420i	$0.829860\pi$
$522$		0			0
$523$	518.783	−	898.559i	0.991938	−	1.71809i	0.386221	−	0.922406i	$-0.373780\pi$
$523$	518.783	−	898.559i	0.991938	−	1.71809i	0.605717	−	0.795680i	$-0.292887\pi$
$524$		0			0
$525$	−835.295	−	67.2169i	−1.59104	−	0.128032i
$526$		0			0
$527$			202.527i			0.384302i
$528$		0			0
$529$	−86.3284	+	149.525i	−0.163192	+	0.282656i
$530$		0			0
$531$	−696.240	+	264.457i	−1.31119	+	0.498035i
$532$		0			0
$533$	101.409	−	58.5483i	0.190260	−	0.109847i
$534$		0			0
$535$	790.645			1.47784
$536$		0			0
$537$	451.618	+	311.559i	0.841001	+	0.580184i
$538$		0			0
$539$			36.0014i			0.0667930i
$540$		0			0
$541$	−427.224	+	739.974i	−0.789693	+	1.36779i	0.136462	+	0.990645i	$0.456427\pi$
$541$	−427.224	+	739.974i	−0.789693	+	1.36779i	−0.926155	+	0.377143i	$0.876906\pi$
$542$		0			0
$543$	200.621	+	422.520i	0.369467	+	0.778121i
$544$		0			0
$545$	1661.82	−	959.451i	3.04921	−	1.76046i
$546$		0			0
$547$	−412.287			−0.753724			−0.376862	−	0.926269i	$-0.622997\pi$
$547$	−412.287			−0.753724			−0.376862	+	0.926269i	$0.622997\pi$
$548$		0			0
$549$	−151.746	−	399.506i	−0.276405	−	0.727697i
$550$		0			0
$551$	21.4539	−	133.276i	0.0389363	−	0.241881i
$552$		0			0
$553$	494.770			0.894703
$554$		0			0
$555$	389.292	+	268.562i	0.701428	+	0.483896i
$556$		0			0
$557$	863.794	+	498.712i	1.55080	+	0.895353i	0.998077	+	0.0619859i	$0.0197434\pi$
$557$	863.794	+	498.712i	1.55080	+	0.895353i	0.552720	+	0.833367i	$0.313590\pi$
$558$		0			0
$559$	−276.481			−0.494600
$560$		0			0
$561$	21.0534	+	44.3397i	0.0375283	+	0.0790369i
$562$		0			0
$563$	−305.679	−	176.484i	−0.542947	−	0.313470i	0.203326	−	0.979111i	$-0.434825\pi$
$563$	−305.679	−	176.484i	−0.542947	−	0.313470i	−0.746272	+	0.665641i	$0.768158\pi$
$564$		0			0
$565$	969.932	−	1679.97i	1.71669	−	2.97340i
$566$		0			0
$567$	350.574	+	116.640i	0.618296	+	0.205714i
$568$		0			0
$569$	276.835	−	159.831i	0.486529	−	0.280897i	−0.236605	−	0.971606i	$-0.576035\pi$
$569$	276.835	−	159.831i	0.486529	−	0.280897i	0.723133	+	0.690709i	$0.242701\pi$
$570$		0			0
$571$	352.313	−	610.224i	0.617010	−	1.06869i	−0.373018	−	0.927824i	$-0.621677\pi$
$571$	352.313	−	610.224i	0.617010	−	1.06869i	0.990028	−	0.140869i	$-0.0449897\pi$
$572$		0			0
$573$	81.3918	−	1011.44i	0.142045	−	1.76517i
$574$		0			0
$575$	−1001.14	+	578.006i	−1.74111	+	1.00523i
$576$		0			0
$577$	322.338			0.558644			0.279322	−	0.960197i	$-0.409890\pi$
$577$	322.338			0.558644			0.279322	+	0.960197i	$0.409890\pi$
$578$		0			0
$579$	362.871	−	525.997i	0.626720	−	0.908458i
$580$		0			0
$581$	−158.292	−	91.3897i	−0.272447	−	0.157297i
$582$		0			0
$583$	−8.65093			−0.0148386
$584$		0			0
$585$	−428.705	−	349.661i	−0.732829	−	0.597711i
$586$		0			0
$587$	974.121	+	562.409i	1.65949	+	0.958107i	0.972950	+	0.231016i	$0.0742050\pi$
$587$	974.121	+	562.409i	1.65949	+	0.958107i	0.686541	+	0.727091i	$0.259128\pi$
$588$		0			0
$589$	−189.583	+	232.911i	−0.321872	+	0.395434i
$590$		0			0
$591$	19.1366	+	13.2018i	0.0323801	+	0.0223381i
$592$		0			0
$593$	686.343	+	396.261i	1.15741	+	0.668230i	0.950682	−	0.310168i	$-0.100385\pi$
$593$	686.343	+	396.261i	1.15741	+	0.668230i	0.206727	+	0.978399i	$0.433719\pi$
$594$		0			0
$595$	−271.378	+	470.040i	−0.456097	+	0.789983i
$596$		0			0
$597$	−385.976	−	812.891i	−0.646527	−	1.36163i
$598$		0			0
$599$	−695.903	+	401.780i	−1.16177	+	0.670750i	−0.951728	−	0.306941i	$-0.900695\pi$
$599$	−695.903	+	401.780i	−1.16177	+	0.670750i	−0.210045	+	0.977692i	$0.567361\pi$
$600$		0			0
$601$	3.87039	+	6.70371i	0.00643992	+	0.0111543i	0.869227	−	0.494412i	$-0.164617\pi$
$601$	3.87039	+	6.70371i	0.00643992	+	0.0111543i	−0.862787	+	0.505567i	$0.831283\pi$
$602$		0			0
$603$	243.011	−	297.946i	0.403004	−	0.494106i
$604$		0			0
$605$	−960.010	−	554.262i	−1.58679	−	0.916136i
$606$		0			0
$607$	111.655	−	193.392i	0.183945	−	0.318602i	−0.759275	−	0.650769i	$-0.774446\pi$
$607$	111.655	−	193.392i	0.183945	−	0.318602i	0.943221	+	0.332167i	$0.107780\pi$
$608$		0			0
$609$	−7.79839	+	96.9095i	−0.0128052	+	0.159129i
$610$		0			0
$611$	130.579	−	75.3896i	0.213713	−	0.123387i
$612$		0			0
$613$	188.469	+	326.438i	0.307454	+	0.532525i	0.977805	−	0.209519i	$-0.0671898\pi$
$613$	188.469	+	326.438i	0.307454	+	0.532525i	−0.670351	+	0.742044i	$0.733856\pi$
$614$		0			0
$615$	279.867	−	405.679i	0.455068	−	0.659641i
$616$		0			0
$617$	−404.809	+	233.717i	−0.656093	+	0.378795i	−0.790787	−	0.612092i	$-0.790328\pi$
$617$	−404.809	+	233.717i	−0.656093	+	0.378795i	0.134694	+	0.990887i	$0.456995\pi$
$618$		0			0
$619$	481.347	+	833.718i	0.777621	+	1.34688i	0.933310	+	0.359073i	$0.116907\pi$
$619$	481.347	+	833.718i	0.777621	+	1.34688i	−0.155689	+	0.987806i	$0.549760\pi$
$620$		0			0
$621$	489.448	−	142.178i	0.788162	−	0.228950i
$622$		0			0
$623$			259.370i			0.416324i
$624$		0			0
$625$	1594.24			2.55079
$626$		0			0
$627$	−17.2939	+	70.6994i	−0.0275820	+	0.112758i
$628$		0			0
$629$	188.376	−	108.759i	0.299485	−	0.172908i
$630$		0			0
$631$	132.578	−	229.632i	0.210108	−	0.363917i	−0.741640	−	0.670798i	$-0.765952\pi$
$631$	132.578	−	229.632i	0.210108	−	0.363917i	0.951748	+	0.306880i	$0.0992852\pi$
$632$		0			0
$633$	627.345	−	909.363i	0.991066	−	1.43659i
$634$		0			0
$635$	908.492	+	524.518i	1.43070	+	0.826013i
$636$		0			0
$637$	−186.622			−0.292970
$638$		0			0
$639$	172.887	+	141.010i	0.270558	+	0.220673i
$640$		0			0
$641$	−21.8673	−	12.6251i	−0.0341143	−	0.0196959i	0.482846	−	0.875705i	$-0.339603\pi$
$641$	−21.8673	−	12.6251i	−0.0341143	−	0.0196959i	−0.516960	+	0.856009i	$0.672936\pi$
$642$		0			0
$643$	−335.777			−0.522204			−0.261102	−	0.965311i	$-0.584086\pi$
$643$	−335.777			−0.522204			−0.261102	+	0.965311i	$0.584086\pi$
$644$		0			0
$645$	−1051.21	+	499.133i	−1.62978	+	0.773850i
$646$		0			0
$647$			905.889i			1.40014i	0.714075	+	0.700069i	$0.246848\pi$
$647$			905.889i			1.40014i	−0.714075	+	0.700069i	$0.753152\pi$
$648$		0			0
$649$	52.8338	+	91.5108i	0.0814080	+	0.141003i
$650$		0			0
$651$	122.821	−	178.035i	0.188665	−	0.273479i
$652$		0			0
$653$	929.143	+	536.441i	1.42288	+	0.821502i	0.996544	−	0.0830615i	$-0.0264698\pi$
$653$	929.143	+	536.441i	1.42288	+	0.821502i	0.426339	+	0.904564i	$0.359803\pi$
$654$		0			0
$655$	79.0506			0.120688
$656$		0			0
$657$	−451.587	+	553.671i	−0.687346	+	0.842726i
$658$		0			0
$659$			1036.04i			1.57214i	0.618135	+	0.786072i	$0.287889\pi$
$659$			1036.04i			1.57214i	−0.618135	+	0.786072i	$0.712111\pi$
$660$		0			0
$661$	47.1772	+	81.7133i	0.0713725	+	0.123621i	0.899503	−	0.436914i	$-0.143929\pi$
$661$	47.1772	+	81.7133i	0.0713725	+	0.123621i	−0.828131	+	0.560535i	$0.810595\pi$
$662$		0			0
$663$	−229.845	+	109.135i	−0.346674	+	0.164608i
$664$		0			0
$665$	−752.088	+	286.524i	−1.13096	+	0.430862i
$666$		0			0
$667$	67.0593	+	116.150i	0.100539	+	0.174138i
$668$		0			0
$669$	197.159	+	415.230i	0.294707	+	0.620672i
$670$		0			0
$671$	−52.5093	+	30.3162i	−0.0782553	+	0.0451807i
$672$		0			0
$673$	−156.533	−	271.123i	−0.232590	−	0.402858i	0.725979	−	0.687716i	$-0.241387\pi$
$673$	−156.533	−	271.123i	−0.232590	−	0.402858i	−0.958570	+	0.284858i	$0.908053\pi$
$674$		0			0
$675$	−1605.71	−	394.465i	−2.37883	−	0.584393i
$676$		0			0
$677$	−523.760	+	302.393i	−0.773649	+	0.446666i	−0.834175	−	0.551500i	$-0.814056\pi$
$677$	−523.760	+	302.393i	−0.773649	+	0.446666i	0.0605259	+	0.998167i	$0.480722\pi$
$678$		0			0
$679$	792.407			1.16702
$680$		0			0
$681$	−33.1907	+	412.456i	−0.0487382	+	0.605662i
$682$		0			0
$683$			27.4860i			0.0402430i	0.999798	+	0.0201215i	$0.00640531\pi$
$683$			27.4860i			0.0402430i	−0.999798	+	0.0201215i	$0.993595\pi$
$684$		0			0
$685$	−1989.11			−2.90381
$686$		0			0
$687$	−216.935	−	456.879i	−0.315772	−	0.665035i
$688$		0			0
$689$		−	44.8441i		−	0.0650857i
$690$		0			0
$691$	2.35922	+	4.08630i	0.00341422	+	0.00591360i	0.867727	−	0.497040i	$-0.165580\pi$
$691$	2.35922	+	4.08630i	0.00341422	+	0.00591360i	−0.864313	+	0.502954i	$0.832247\pi$
$692$		0			0
$693$	8.38224	−	51.7452i	0.0120956	−	0.0746684i
$694$		0			0
$695$	−414.527	+	239.327i	−0.596442	+	0.344356i
$696$		0			0
$697$	−113.337	−	196.306i	−0.162607	−	0.281644i
$698$		0			0
$699$	71.5817	−	889.536i	0.102406	−	1.27258i
$700$		0			0
$701$	−81.6577	+	47.1451i	−0.116487	+	0.0672541i	−0.557112	−	0.830438i	$-0.688090\pi$
$701$	−81.6577	+	47.1451i	−0.116487	+	0.0672541i	0.440624	+	0.897692i	$0.354757\pi$
$702$		0			0
$703$	318.444	+	51.2609i	0.452979	+	0.0729173i
$704$		0			0
$705$	360.370	−	522.373i	0.511164	−	0.740954i
$706$		0			0
$707$	−351.014	+	202.658i	−0.496484	+	0.286645i
$708$		0			0
$709$	−866.770			−1.22252			−0.611262	−	0.791428i	$-0.709338\pi$
$709$	−866.770			−1.22252			−0.611262	+	0.791428i	$0.709338\pi$
$710$		0			0
$711$	963.673	+	156.106i	1.35538	+	0.219558i
$712$		0			0
$713$		−	298.371i		−	0.418473i
$714$		0			0
$715$	−39.2450	+	67.9743i	−0.0548881	+	0.0950689i
$716$		0			0
$717$	869.713	−	412.957i	1.21299	−	0.575951i
$718$		0			0
$719$	−960.272	+	554.413i	−1.33557	+	0.771089i	−0.986146	−	0.165877i	$-0.946954\pi$
$719$	−960.272	+	554.413i	−1.33557	+	0.771089i	−0.349419	+	0.936966i	$0.613621\pi$
$720$		0			0
$721$	−397.679			−0.551566
$722$		0			0
$723$	670.990	−	972.628i	0.928063	−	1.34527i
$724$		0			0
$725$		−	435.094i		−	0.600130i
$726$		0			0
$727$	202.057	−	349.973i	0.277933	−	0.481393i	−0.692938	−	0.720997i	$-0.743684\pi$
$727$	202.057	−	349.973i	0.277933	−	0.481393i	0.970871	+	0.239604i	$0.0770175\pi$
$728$		0			0
$729$	646.017	+	337.792i	0.886168	+	0.463363i
$730$		0			0
$731$			535.209i			0.732160i
$732$		0			0
$733$	−564.680	+	978.054i	−0.770368	+	1.33432i	0.166994	+	0.985958i	$0.446594\pi$
$733$	−564.680	+	978.054i	−0.770368	+	1.33432i	−0.937362	+	0.348358i	$0.886739\pi$
$734$		0			0
$735$	−709.553	+	336.909i	−0.965378	+	0.458380i
$736$		0			0
$737$	−47.2415	−	27.2749i	−0.0640997	−	0.0370080i
$738$		0			0
$739$	321.557	+	556.953i	0.435124	+	0.753658i	0.997306	−	0.0733563i	$-0.0233710\pi$
$739$	321.557	+	556.953i	0.435124	+	0.753658i	−0.562181	+	0.827014i	$0.690038\pi$
$740$		0			0
$741$	−366.486	−	89.6471i	−0.494584	−	0.120981i
$742$		0			0
$743$		−	1205.28i		−	1.62219i	−0.584917	−	0.811093i	$-0.698873\pi$
$743$		−	1205.28i		−	1.62219i	0.584917	−	0.811093i	$-0.301127\pi$
$744$		0			0
$745$	−1335.49			−1.79260
$746$		0			0
$747$	−279.473	−	227.944i	−0.374127	−	0.305146i
$748$		0			0
$749$	−336.320	+	194.174i	−0.449025	+	0.259245i
$750$		0			0
$751$	−123.979	−	214.738i	−0.165086	−	0.285937i	0.771600	−	0.636108i	$-0.219457\pi$
$751$	−123.979	−	214.738i	−0.165086	−	0.285937i	−0.936686	+	0.350171i	$0.886123\pi$
$752$		0			0
$753$	−1001.47	+	475.518i	−1.32997	+	0.631498i
$754$		0			0
$755$	−1765.27	+	1019.18i	−2.33811	+	1.34991i
$756$		0			0
$757$	−313.951	−	543.779i	−0.414731	−	0.718335i	0.580669	−	0.814139i	$-0.302791\pi$
$757$	−313.951	−	543.779i	−0.414731	−	0.718335i	−0.995400	+	0.0958047i	$0.969458\pi$
$758$		0			0
$759$	−31.0167	−	65.3231i	−0.0408652	−	0.0860647i
$760$		0			0
$761$	856.714	+	494.624i	1.12577	+	0.649966i	0.942869	−	0.333165i	$-0.108117\pi$
$761$	856.714	+	494.624i	1.12577	+	0.649966i	0.182905	+	0.983131i	$0.441450\pi$
$762$		0			0
$763$	−471.263	+	816.251i	−0.617645	+	1.06979i
$764$		0			0
$765$	−676.870	+	829.882i	−0.884798	+	1.08481i
$766$		0			0
$767$	−474.367	+	273.876i	−0.618471	+	0.357074i
$768$		0			0
$769$	−256.815	−	444.816i	−0.333959	−	0.578434i	0.649325	−	0.760511i	$-0.275051\pi$
$769$	−256.815	−	444.816i	−0.333959	−	0.578434i	−0.983284	+	0.182077i	$0.941718\pi$
$770$		0			0
$771$	−44.2704	+	550.142i	−0.0574195	+	0.713544i
$772$		0			0
$773$	464.596	+	268.235i	0.601030	+	0.347005i	0.769447	−	0.638711i	$-0.220532\pi$
$773$	464.596	+	268.235i	0.601030	+	0.347005i	−0.168417	+	0.985716i	$0.553865\pi$
$774$		0			0
$775$	−483.973	+	838.266i	−0.624481	+	1.08163i
$776$		0			0
$777$	−231.551	−	18.6331i	−0.298006	−	0.0239808i
$778$		0			0
$779$	53.4187	−	331.849i	0.0685734	−	0.425993i
$780$		0			0
$781$	15.8266	−	27.4125i	0.0202645	−	0.0350992i
$782$		0			0
$783$	−45.7652	+	186.292i	−0.0584485	+	0.237921i
$784$		0			0
$785$		−	292.292i		−	0.372347i
$786$		0			0
$787$	60.3896	−	104.598i	0.0767339	−	0.132907i	−0.825105	−	0.564979i	$-0.808884\pi$
$787$	60.3896	−	104.598i	0.0767339	−	0.132907i	0.901839	+	0.432072i	$0.142217\pi$
$788$		0			0
$789$	458.300	−	217.610i	0.580861	−	0.275804i
$790$		0			0
$791$			952.821i			1.20458i
$792$		0			0
$793$	−157.151	−	272.194i	−0.198173	−	0.343246i
$794$		0			0
$795$	−80.9573	−	170.501i	−0.101833	−	0.214467i
$796$		0			0
$797$	525.724	+	303.527i	0.659629	+	0.380837i	0.792136	−	0.610345i	$-0.208969\pi$
$797$	525.724	+	303.527i	0.659629	+	0.380837i	−0.132507	+	0.991182i	$0.542303\pi$
$798$		0			0
$799$	−145.938	−	252.773i	−0.182651	−	0.316361i
$800$		0			0
$801$	−81.8342	+	505.178i	−0.102165	+	0.630685i
$802$		0			0
$803$	87.7886	+	50.6848i	0.109326	+	0.0631193i
$804$		0			0
$805$	399.805	−	692.483i	0.496652	−	0.860227i
$806$		0			0
$807$	−0.140397	+	1.74469i	−0.000173974	+	0.00216195i
$808$		0			0
$809$			144.203i			0.178248i	0.996021	+	0.0891241i	$0.0284068\pi$
$809$			144.203i			0.178248i	−0.996021	+	0.0891241i	$0.971593\pi$
$810$		0			0
$811$	−487.189	+	843.837i	−0.600727	+	1.04049i	0.391984	+	0.919972i	$0.371789\pi$
$811$	−487.189	+	843.837i	−0.600727	+	1.04049i	−0.992711	+	0.120518i	$0.961545\pi$
$812$		0			0
$813$	1040.05	+	83.6940i	1.27928	+	0.102945i
$814$		0			0
$815$		−	254.141i		−	0.311829i
$816$		0			0
$817$	−501.001	+	615.502i	−0.613221	+	0.753368i
$818$		0			0
$819$	268.233	+	43.4513i	0.327513	+	0.0530540i
$820$		0			0
$821$			1392.69i			1.69634i	0.529726	+	0.848169i	$0.322295\pi$
$821$			1392.69i			1.69634i	−0.529726	+	0.848169i	$0.677705\pi$
$822$		0			0
$823$	−327.037	−	566.445i	−0.397372	−	0.688268i	0.596029	−	0.802963i	$-0.296744\pi$
$823$	−327.037	−	566.445i	−0.397372	−	0.688268i	−0.993401	+	0.114695i	$0.963411\pi$
$824$		0			0
$825$	−18.8168	+	233.834i	−0.0228083	+	0.283435i
$826$		0			0
$827$	−966.498	−	558.008i	−1.16868	−	0.674737i	−0.215310	−	0.976546i	$-0.569076\pi$
$827$	−966.498	−	558.008i	−1.16868	−	0.674737i	−0.953369	+	0.301808i	$0.902410\pi$
$828$		0			0
$829$	−42.5592			−0.0513380			−0.0256690	−	0.999670i	$-0.508172\pi$
$829$	−42.5592			−0.0513380			−0.0256690	+	0.999670i	$0.508172\pi$
$830$		0			0
$831$	692.866	+	55.7555i	0.833774	+	0.0670945i
$832$		0			0
$833$			361.260i			0.433686i
$834$		0			0
$835$	1075.65	+	1863.09i	1.28821	+	2.23124i
$836$		0			0
$837$	295.393	−	308.009i	0.352918	−	0.367992i
$838$		0			0
$839$	413.860	+	238.942i	0.493278	+	0.284794i	0.725933	−	0.687765i	$-0.241408\pi$
$839$	413.860	+	238.942i	0.493278	+	0.284794i	−0.232656	+	0.972559i	$0.574741\pi$
$840$		0			0
$841$	790.521			0.939978
$842$		0			0
$843$	−1238.29	−	854.260i	−1.46890	−	1.01336i
$844$		0			0
$845$	1006.80	+	581.274i	1.19147	+	0.687898i
$846$		0			0
$847$	544.484			0.642839
$848$		0			0
$849$	79.8756	−	115.783i	0.0940820	−	0.136376i
$850$		0			0
$851$	−277.523	+	160.228i	−0.326114	+	0.188282i
$852$		0			0
$853$	440.866	−	763.602i	0.516841	−	0.895195i	−0.482968	−	0.875638i	$-0.660441\pi$
$853$	440.866	−	763.602i	0.516841	−	0.895195i	0.999809	−	0.0195570i	$-0.00622558\pi$
$854$		0			0
$855$	−1555.26	+	320.774i	−1.81901	+	0.375174i
$856$		0			0
$857$	727.761	+	420.173i	0.849197	+	0.490284i	0.860380	−	0.509654i	$-0.170226\pi$
$857$	727.761	+	420.173i	0.849197	+	0.490284i	−0.0111831	+	0.999937i	$0.503560\pi$
$858$		0			0
$859$	578.204	+	1001.48i	0.673113	+	1.16587i	0.977017	+	0.213163i	$0.0683765\pi$
$859$	578.204	+	1001.48i	0.673113	+	1.16587i	−0.303904	+	0.952703i	$0.598290\pi$
$860$		0			0
$861$	−19.4174	+	241.298i	−0.0225522	+	0.280253i
$862$		0			0
$863$			267.381i			0.309828i	0.987928	+	0.154914i	$0.0495100\pi$
$863$			267.381i			0.309828i	−0.987928	+	0.154914i	$0.950490\pi$
$864$		0			0
$865$	555.640	−	962.397i	0.642359	−	1.11260i
$866$		0			0
$867$	−160.615	−	338.265i	−0.185253	−	0.390155i
$868$		0			0
$869$		−	138.507i		−	0.159387i
$870$		0			0
$871$	141.386	−	244.887i	0.162326	−	0.281156i
$872$		0			0
$873$	1543.38	+	250.014i	1.76791	+	0.286385i
$874$		0			0
$875$	−1329.39	+	767.522i	−1.51930	+	0.877168i
$876$		0			0
$877$	1435.34			1.63665			0.818326	−	0.574754i	$-0.194902\pi$
$877$	1435.34			1.63665			0.818326	+	0.574754i	$0.194902\pi$
$878$		0			0
$879$	211.502	−	100.425i	0.240616	−	0.114249i
$880$		0			0
$881$		−	920.034i		−	1.04431i	−0.852852	−	0.522153i	$-0.825129\pi$
$881$		−	920.034i		−	1.04431i	0.852852	−	0.522153i	$-0.174871\pi$
$882$		0			0
$883$	261.135	−	452.299i	0.295736	−	0.512230i	−0.679420	−	0.733750i	$-0.737768\pi$
$883$	261.135	−	452.299i	0.295736	−	0.512230i	0.975156	+	0.221520i	$0.0711018\pi$
$884$		0			0
$885$	−1309.16	+	1897.68i	−1.47927	+	2.14427i
$886$		0			0
$887$	−239.539	+	138.298i	−0.270055	+	0.155917i	−0.628913	−	0.777476i	$-0.716500\pi$
$887$	−239.539	+	138.298i	−0.270055	+	0.155917i	0.358857	+	0.933392i	$0.383166\pi$
$888$		0			0
$889$	−515.265			−0.579601
$890$		0			0
$891$	32.6524	−	98.1402i	0.0366470	−	0.110146i
$892$		0			0
$893$	68.7845	−	427.305i	0.0770263	−	0.478505i
$894$		0			0
$895$	1698.38			1.89763
$896$		0			0
$897$	338.617	−	160.782i	0.377500	−	0.179244i
$898$		0			0
$899$	97.2542	+	56.1497i	0.108180	+	0.0624580i
$900$		0			0
$901$	−86.8086			−0.0963470
$902$		0			0
$903$	324.574	−	470.484i	0.359439	−	0.521023i
$904$		0			0
$905$	1253.88	+	723.929i	1.38551	+	0.799922i
$906$		0			0
$907$	171.465	−	296.986i	0.189046	−	0.327438i	−0.755886	−	0.654703i	$-0.772794\pi$
$907$	171.465	−	296.986i	0.189046	−	0.327438i	0.944933	+	0.327265i	$0.106127\pi$
$908$		0			0
$909$	−747.618	+	283.972i	−0.822462	+	0.312400i
$910$		0			0
$911$	−629.426	+	363.399i	−0.690918	+	0.398901i	−0.803956	−	0.594689i	$-0.797275\pi$
$911$	−629.426	+	363.399i	−0.690918	+	0.398901i	0.113038	+	0.993591i	$0.463942\pi$
$912$		0			0
$913$	−25.5838	+	44.3124i	−0.0280217	+	0.0485350i
$914$		0			0
$915$	−1088.90	−	751.200i	−1.19005	−	0.820983i
$916$		0			0
$917$	−33.6261	+	19.4140i	−0.0366696	+	0.0211712i
$918$		0			0
$919$	−851.166			−0.926188			−0.463094	−	0.886309i	$-0.653261\pi$
$919$	−851.166			−0.926188			−0.463094	+	0.886309i	$0.653261\pi$
$920$		0			0
$921$	78.6759	+	6.33111i	0.0854244	+	0.00687417i
$922$		0			0
$923$	142.099	+	82.0408i	0.153953	+	0.0888850i
$924$		0			0
$925$	1039.59			1.12388
$926$		0			0
$927$	−774.566	−	125.473i	−0.835563	−	0.135353i
$928$		0			0
$929$	786.926	+	454.332i	0.847067	+	0.489055i	0.859660	−	0.510866i	$-0.170675\pi$
$929$	786.926	+	454.332i	0.847067	+	0.489055i	−0.0125930	+	0.999921i	$0.504009\pi$
$930$		0			0
$931$	−338.170	+	415.457i	−0.363233	+	0.446248i
$932$		0			0
$933$	1061.21	−	503.883i	1.13742	−	0.540068i
$934$		0			0
$935$	131.584	+	75.9700i	0.140731	+	0.0812513i
$936$		0			0
$937$	−38.1604	+	66.0958i	−0.0407262	+	0.0705398i	−0.885670	−	0.464315i	$-0.846300\pi$
$937$	−38.1604	+	66.0958i	−0.0407262	+	0.0705398i	0.844944	+	0.534855i	$0.179634\pi$
$938$		0			0
$939$	159.091	−	230.609i	0.169426	−	0.245590i
$940$		0			0
$941$	−755.091	+	435.952i	−0.802434	+	0.463286i	−0.844322	−	0.535837i	$-0.819996\pi$
$941$	−755.091	+	435.952i	−0.802434	+	0.463286i	0.0418872	+	0.999122i	$0.486663\pi$
$942$		0			0
$943$	166.973	+	289.206i	0.177066	+	0.306687i
$944$		0			0
$945$	1098.29	−	319.037i	1.16221	−	0.337605i
$946$		0			0
$947$	283.460	+	163.656i	0.299324	+	0.172815i	0.642139	−	0.766588i	$-0.278047\pi$
$947$	283.460	+	163.656i	0.299324	+	0.172815i	−0.342815	+	0.939403i	$0.611380\pi$
$948$		0			0
$949$	−262.736	+	455.073i	−0.276856	+	0.479529i
$950$		0			0
$951$	141.000	+	97.2720i	0.148265	+	0.102284i
$952$		0			0
$953$	87.9770	−	50.7935i	0.0923158	−	0.0532986i	−0.453131	−	0.891444i	$-0.649693\pi$
$953$	87.9770	−	50.7935i	0.0923158	−	0.0532986i	0.545447	+	0.838145i	$0.316360\pi$
$954$		0			0
$955$	−1570.52	−	2720.22i	−1.64453	−	2.84840i
$956$		0			0
$957$	27.1290	+	2.18310i	0.0283480	+	0.00228119i
$958$		0			0
$959$	846.116	−	488.505i	0.882290	−	0.509390i
$960$		0			0
$961$	355.585	+	615.891i	0.370015	+	0.640885i
$962$		0			0
$963$	−716.320	+	272.083i	−0.743842	+	0.282537i
$964$		0			0
$965$		−	1978.09i		−	2.04984i
$966$		0			0
$967$	645.605			0.667637			0.333819	−	0.942637i	$-0.391663\pi$
$967$	645.605			0.667637			0.333819	+	0.942637i	$0.391663\pi$
$968$		0			0
$969$	−173.538	+	709.440i	−0.179090	+	0.732137i
$970$		0			0
$971$	1455.94	−	840.588i	1.49943	−	0.865693i	0.499425	−	0.866357i	$-0.333545\pi$
$971$	1455.94	−	840.588i	1.49943	−	0.865693i	1.00000		0.000663529i	$0.000211208\pi$
$972$		0			0
$973$	117.553	−	203.607i	0.120815	−	0.209257i
$974$		0			0
$975$	−1212.13	−	97.5414i	−1.24321	−	0.100042i
$976$		0			0
$977$	417.952	+	241.305i	0.427792	+	0.246986i	0.698405	−	0.715702i	$-0.253893\pi$
$977$	417.952	+	241.305i	0.427792	+	0.246986i	−0.270614	+	0.962688i	$0.587227\pi$
$978$		0			0
$979$	72.6084			0.0741659
$980$		0			0
$981$	−1175.42	+	1441.14i	−1.19819	+	1.46905i
$982$		0			0
$983$	285.347	+	164.745i	0.290282	+	0.167594i	0.638069	−	0.769979i	$-0.279733\pi$
$983$	285.347	+	164.745i	0.290282	+	0.167594i	−0.347787	+	0.937574i	$0.613067\pi$
$984$		0			0
$985$	71.9661			0.0730620
$986$		0			0
$987$	−25.0029	+	310.707i	−0.0253322	+	0.314799i
$988$		0			0
$989$		−	788.492i		−	0.797262i
$990$		0			0
$991$	130.189	+	225.494i	0.131371	+	0.227542i	0.924205	−	0.381896i	$-0.124729\pi$
$991$	130.189	+	225.494i	0.131371	+	0.227542i	−0.792834	+	0.609438i	$0.791395\pi$
$992$		0			0
$993$	35.7394	+	2.87598i	0.0359913	+	0.00289625i
$994$		0			0
$995$	−2412.36	−	1392.78i	−2.42448	−	1.39978i
$996$		0			0
$997$	1452.05			1.45642			0.728210	−	0.685354i	$-0.240353\pi$
$997$	1452.05			1.45642			0.728210	+	0.685354i	$0.240353\pi$
$998$		0			0
$999$	−445.117	−	109.349i	−0.445562	−	0.109459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.m.a.653.12	yes	80
3.2	odd	2		2052.3.m.a.881.1		80
9.2	odd	6		684.3.be.a.425.38	yes	80
9.7	even	3		2052.3.be.a.197.1		80
19.11	even	3		684.3.be.a.581.38	yes	80
57.11	odd	6		2052.3.be.a.125.1		80
171.11	odd	6	inner	684.3.m.a.353.12	✓	80
171.106	even	3		2052.3.m.a.1493.40		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.12	✓	80	171.11	odd	6	inner
684.3.m.a.653.12	yes	80	1.1	even	1	trivial
684.3.be.a.425.38	yes	80	9.2	odd	6
684.3.be.a.581.38	yes	80	19.11	even	3
2052.3.m.a.881.1		80	3.2	odd	2
2052.3.m.a.1493.40		80	171.106	even	3
2052.3.be.a.125.1		80	57.11	odd	6
2052.3.be.a.197.1		80	9.7	even	3

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70356 + 2.46939i) q^{3} +9.28650i q^{5} +(-2.28067 - 3.95023i) q^{7} +(-3.19575 - 8.41351i) q^{9} +O(q^{10})\)	\(q+(-1.70356 + 2.46939i) q^{3} +9.28650i q^{5} +(-2.28067 - 3.95023i) q^{7} +(-3.19575 - 8.41351i) q^{9} +(-1.10584 + 0.638454i) q^{11} +(-3.30958 - 5.73235i) q^{13} +(-22.9320 - 15.8201i) q^{15} +(-11.0966 + 6.40664i) q^{17} +(-18.7585 - 3.01961i) q^{19} +(13.6399 + 1.09762i) q^{21} +(16.3480 - 9.43853i) q^{23} -61.2390 q^{25} +(26.2204 + 6.44140i) q^{27} +7.10485i q^{29} +(7.90302 - 13.6884i) q^{31} +(0.307269 - 3.81838i) q^{33} +(36.6838 - 21.1794i) q^{35} -16.9760 q^{37} +(19.7935 + 1.59280i) q^{39} +17.6906i q^{41} +(20.8849 - 36.1738i) q^{43} +(78.1321 - 29.6773i) q^{45} +22.7792i q^{47} +(14.0971 - 24.4169i) q^{49} +(3.08332 - 38.3160i) q^{51} +(5.86723 + 3.38745i) q^{53} +(-5.92901 - 10.2693i) q^{55} +(39.4129 - 41.1779i) q^{57} -82.7526i q^{59} +47.4838 q^{61} +(-25.9469 + 31.8124i) q^{63} +(53.2335 - 30.7344i) q^{65} +(21.3601 + 36.9968i) q^{67} +(-4.54247 + 56.4487i) q^{69} +(-21.4678 + 12.3945i) q^{71} +(-39.6934 - 68.7509i) q^{73} +(104.325 - 151.223i) q^{75} +(5.04409 + 2.91221i) q^{77} +(-54.2353 + 93.9382i) q^{79} +(-60.5744 + 53.7749i) q^{81} +(34.7029 - 20.0357i) q^{83} +(-59.4952 - 103.049i) q^{85} +(-17.5446 - 12.1036i) q^{87} +(-49.2445 - 28.4313i) q^{89} +(-15.0961 + 26.1472i) q^{91} +(20.3387 + 42.8347i) q^{93} +(28.0416 - 174.201i) q^{95} +(-86.8612 + 150.448i) q^{97} +(8.90562 + 7.26362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9	\( 80 q - 2 q^{3} + q^{7} - 2 q^{9} + 18 q^{11} - 5 q^{13} - 2 q^{15} - 9 q^{17} + 20 q^{19} - 30 q^{21} + 72 q^{23} - 400 q^{25} + 25 q^{27} - 8 q^{31} - 64 q^{33} + 22 q^{37} + 39 q^{39} - 44 q^{43} - 196 q^{45} - 267 q^{49} - 47 q^{51} - 36 q^{53} + 84 q^{57} - 14 q^{61} - 260 q^{63} - 144 q^{65} - 77 q^{67} + 44 q^{69} - 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} - 17 q^{79} - 254 q^{81} - 171 q^{83} - 244 q^{87} + 216 q^{89} + 122 q^{91} + 292 q^{93} - 288 q^{95} - 8 q^{97} + 172 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + q^7 - 2 * q^9 + 18 * q^11 - 5 * q^13 - 2 * q^15 - 9 * q^17 + 20 * q^19 - 30 * q^21 + 72 * q^23 - 400 * q^25 + 25 * q^27 - 8 * q^31 - 64 * q^33 + 22 * q^37 + 39 * q^39 - 44 * q^43 - 196 * q^45 - 267 * q^49 - 47 * q^51 - 36 * q^53 + 84 * q^57 - 14 * q^61 - 260 * q^63 - 144 * q^65 - 77 * q^67 + 44 * q^69 - 135 * q^71 + 43 * q^73 + 69 * q^75 + 216 * q^77 - 17 * q^79 - 254 * q^81 - 171 * q^83 - 244 * q^87 + 216 * q^89 + 122 * q^91 + 292 * q^93 - 288 * q^95 - 8 * q^97 + 172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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