LMFDB - Embedded newform 684.3.m.a.353.12

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			353.12
Character	$\chi$	$=$	684.353
Dual form			684.3.m.a.653.12

$q$-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 $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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	$-0.620971\pi$
$5$		−	9.28650i		−	1.85730i	0.370958	−	0.928650i	$-0.379029\pi$
$6$		0			0
$7$	−2.28067	+	3.95023i	−0.325810	+	0.564319i	−0.981676	−	0.190558i	$-0.938970\pi$
$7$	−2.28067	+	3.95023i	−0.325810	+	0.564319i	0.655866	+	0.754877i	$0.272304\pi$
$8$		0			0
$9$	−3.19575	+	8.41351i	−0.355083	+	0.934835i
$10$		0			0
$11$	−1.10584	−	0.638454i	−0.100531	−	0.0580413i	0.448892	−	0.893586i	$-0.351819\pi$
$11$	−1.10584	−	0.638454i	−0.100531	−	0.0580413i	−0.549422	+	0.835545i	$0.685152\pi$
$12$		0			0
$13$	−3.30958	+	5.73235i	−0.254583	+	0.440950i	−0.964782	−	0.263050i	$-0.915271\pi$
$13$	−3.30958	+	5.73235i	−0.254583	+	0.440950i	0.710199	+	0.704001i	$0.248605\pi$
$14$		0			0
$15$	−22.9320	+	15.8201i	−1.52880	+	1.05468i
$16$		0			0
$17$	−11.0966	−	6.40664i	−0.652743	−	0.376861i	0.136764	−	0.990604i	$-0.456330\pi$
$17$	−11.0966	−	6.40664i	−0.652743	−	0.376861i	−0.789506	+	0.613743i	$0.789663\pi$
$18$		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	0.811351	−	0.584559i	$-0.198733\pi$
$23$	16.3480	+	9.43853i	0.710783	+	0.410371i	−0.100568	+	0.994930i	$0.532066\pi$
$24$		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	$-0.960910\pi$
$29$		−	7.10485i		−	0.244995i	0.992469	−	0.122497i	$-0.0390903\pi$
$30$		0			0
$31$	7.90302	+	13.6884i	0.254936	+	0.441562i	0.964878	−	0.262698i	$-0.0846123\pi$
$31$	7.90302	+	13.6884i	0.254936	+	0.441562i	−0.709942	+	0.704260i	$0.751279\pi$
$32$		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	$-0.930784\pi$
$41$		−	17.6906i		−	0.431477i	0.976451	−	0.215739i	$-0.0692159\pi$
$42$		0			0
$43$	20.8849	+	36.1738i	0.485696	+	0.841251i	0.999865	−	0.0164385i	$-0.00523277\pi$
$43$	20.8849	+	36.1738i	0.485696	+	0.841251i	−0.514169	+	0.857689i	$0.671899\pi$
$44$		0			0
$45$	78.1321	+	29.6773i	1.73627	+	0.659496i
$46$		0			0
$47$		−	22.7792i		−	0.484665i	−0.970193	−	0.242332i	$-0.922088\pi$
$47$		−	22.7792i		−	0.484665i	0.970193	−	0.242332i	$-0.0779124\pi$
$48$		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	−0.443626	−	0.896212i	$-0.646308\pi$
$53$	5.86723	−	3.38745i	0.110702	−	0.0639141i	0.554329	+	0.832298i	$0.312975\pi$
$54$		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	$0.247394\pi$
$59$			82.7526i			1.40259i	−0.712873	+	0.701293i	$0.752606\pi$
$60$		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	−0.661432	−	0.750005i	$-0.730051\pi$
$67$	21.3601	−	36.9968i	0.318807	−	0.552190i	0.980239	+	0.197815i	$0.0633844\pi$
$68$		0			0
$69$	−4.54247	−	56.4487i	−0.0658330	−	0.818097i
$70$		0			0
$71$	−21.4678	−	12.3945i	−0.302364	−	0.174570i	0.341140	−	0.940012i	$-0.389187\pi$
$71$	−21.4678	−	12.3945i	−0.302364	−	0.174570i	−0.643504	+	0.765442i	$0.722520\pi$
$72$		0			0
$73$	−39.6934	+	68.7509i	−0.543745	+	0.941793i	0.454940	+	0.890522i	$0.349661\pi$
$73$	−39.6934	+	68.7509i	−0.543745	+	0.941793i	−0.998685	+	0.0512713i	$0.983673\pi$
$74$		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	−0.972956	−	0.230991i	$-0.925803\pi$
$79$	−54.2353	−	93.9382i	−0.686522	−	1.18909i	0.286434	−	0.958100i	$-0.407530\pi$
$80$		0			0
$81$	−60.5744	−	53.7749i	−0.747832	−	0.663888i
$82$		0			0
$83$	34.7029	+	20.0357i	0.418107	+	0.241394i	0.694267	−	0.719717i	$-0.255729\pi$
$83$	34.7029	+	20.0357i	0.418107	+	0.241394i	−0.276160	+	0.961112i	$0.589062\pi$
$84$		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	−0.750455	−	0.660921i	$-0.770166\pi$
$89$	−49.2445	+	28.4313i	−0.553309	+	0.319453i	0.197147	+	0.980374i	$0.436832\pi$
$90$		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	−0.833214	−	0.552951i	$-0.813502\pi$
$97$	−86.8612	−	150.448i	−0.895477	−	1.55101i	−0.0622629	−	0.998060i	$-0.519832\pi$
$98$		0			0
$99$	8.90562	−	7.26362i	0.0899557	−	0.0733699i
$100$		0			0
$101$			88.8592i			0.879794i	0.898048	+	0.439897i	$0.144985\pi$
$101$			88.8592i			0.879794i	−0.898048	+	0.439897i	$0.855015\pi$
$102$		0			0
$103$	43.5924	+	75.5043i	0.423227	+	0.733051i	0.996253	−	0.0864862i	$-0.0275639\pi$
$103$	43.5924	+	75.5043i	0.423227	+	0.733051i	−0.573026	+	0.819537i	$0.694231\pi$
$104$		0			0
$105$	−10.1930	−	126.667i	−0.0970763	−	1.20635i
$106$		0			0
$107$			85.1392i			0.795693i	0.917452	+	0.397847i	$0.130242\pi$
$107$			85.1392i			0.795693i	−0.917452	+	0.397847i	$0.869758\pi$
$108$		0			0
$109$	−103.317	+	178.950i	−0.947861	+	1.64174i	−0.197941	+	0.980214i	$0.563426\pi$
$109$	−103.317	+	178.950i	−0.947861	+	1.64174i	−0.749919	+	0.661529i	$0.769908\pi$
$110$		0			0
$111$	28.9196	+	41.9203i	0.260537	+	0.377660i
$112$		0			0
$113$	−180.905	+	104.445i	−1.60093	+	0.924296i	−0.609625	+	0.792690i	$0.708680\pi$
$113$	−180.905	+	104.445i	−1.60093	+	0.924296i	−0.991302	+	0.131605i	$0.957987\pi$
$114$		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	0.998034	−	0.0626751i	$-0.0199632\pi$
$127$	56.4818	+	97.8294i	0.444739	+	0.770310i	−0.553295	+	0.832985i	$0.686630\pi$
$128$		0			0
$129$	53.7483	−	113.197i	0.416653	−	0.877499i
$130$		0			0
$131$			8.51243i			0.0649803i	0.999472	+	0.0324902i	$0.0103438\pi$
$131$			8.51243i			0.0649803i	−0.999472	+	0.0324902i	$0.989656\pi$
$132$		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	$-0.714338\pi$
$137$		−	214.194i		−	1.56346i	0.623618	−	0.781729i	$-0.285662\pi$
$138$		0			0
$139$	25.7715	−	44.6376i	0.185407	−	0.321134i	−0.758307	−	0.651898i	$-0.773973\pi$
$139$	25.7715	−	44.6376i	0.185407	−	0.321134i	0.943713	+	0.330764i	$0.107306\pi$
$140$		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	$-0.839699\pi$
$149$		−	143.809i		−	0.965164i	0.875851	−	0.482582i	$-0.160301\pi$
$150$		0			0
$151$	109.749	−	190.090i	0.726813	−	1.25888i	−0.231411	−	0.972856i	$-0.574334\pi$
$151$	109.749	−	190.090i	0.726813	−	1.25888i	0.958223	−	0.286021i	$-0.0923326\pi$
$152$		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	0.960852	−	0.277061i	$-0.0893603\pi$
$167$	200.623	+	115.830i	1.20134	+	0.693592i	0.240485	+	0.970653i	$0.422694\pi$
$168$		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	−0.768664	−	0.639653i	$-0.779078\pi$
$173$	−103.634	+	59.8331i	−0.599041	+	0.345856i	0.169623	+	0.985509i	$0.445745\pi$
$174$		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	$0.170672\pi$
$179$			182.887i			1.02171i	−0.859666	+	0.510856i	$0.829328\pi$
$180$		0			0
$181$	77.9550	+	135.022i	0.430691	+	0.745978i	0.996933	−	0.0782606i	$-0.0249366\pi$
$181$	77.9550	+	135.022i	0.430691	+	0.745978i	−0.566242	+	0.824239i	$0.691603\pi$
$182$		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	−0.999190	−	0.0402304i	$-0.987191\pi$
$191$	−292.923	−	169.119i	−1.53363	−	0.885440i	−0.534436	−	0.845209i	$-0.679476\pi$
$192$		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	$0.00626120\pi$
$197$			7.74954i			0.0393378i	−0.999807	+	0.0196689i	$0.993739\pi$
$198$		0			0
$199$	−149.979	−	259.771i	−0.753662	−	1.30538i	−0.946037	−	0.324059i	$-0.894952\pi$
$199$	−149.979	−	259.771i	−0.753662	−	1.30538i	0.192375	−	0.981321i	$-0.438381\pi$
$200$		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	0.985088	−	0.172052i	$-0.0550397\pi$
$223$	76.6100	+	132.692i	0.343543	+	0.595033i	−0.641545	+	0.767085i	$0.721706\pi$
$224$		0			0
$225$	195.705	−	515.235i	0.869798	−	2.28993i
$226$		0			0
$227$	119.451	+	68.9649i	0.526214	+	0.303810i	0.739474	−	0.673186i	$-0.235075\pi$
$227$	119.451	+	68.9649i	0.526214	+	0.303810i	−0.213259	+	0.976996i	$0.568408\pi$
$228$		0			0
$229$	−84.2944	−	146.002i	−0.368098	−	0.637564i	0.621170	−	0.783676i	$-0.286657\pi$
$229$	−84.2944	−	146.002i	−0.368098	−	0.637564i	−0.989268	+	0.146112i	$0.953324\pi$
$230$		0			0
$231$	−15.7843	−	7.49468i	−0.0683302	−	0.0324445i
$232$		0			0
$233$	−257.617	−	148.735i	−1.10565	−	0.638348i	−0.167952	−	0.985795i	$-0.553715\pi$
$233$	−257.617	−	148.735i	−1.10565	−	0.638348i	−0.937700	+	0.347447i	$0.887049\pi$
$234$		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	−0.951993	−	0.306119i	$-0.900969\pi$
$239$	−277.929	+	160.462i	−1.16288	+	0.671391i	−0.210889	+	0.977510i	$0.567636\pi$
$240$		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	0.299104	−	0.954220i	$-0.403312\pi$
$251$	320.034	−	184.772i	1.27504	−	0.736142i	0.975931	+	0.218078i	$0.0699788\pi$
$252$		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	0.776847	−	0.629689i	$-0.216818\pi$
$257$	159.326	+	91.9868i	0.619945	+	0.357925i	−0.156903	+	0.987614i	$0.550151\pi$
$258$		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	−0.751887	−	0.659292i	$-0.770856\pi$
$263$	−146.456	+	84.5564i	−0.556867	+	0.321507i	0.195020	+	0.980799i	$0.437523\pi$
$264$		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	0.500939	−	0.865483i	$-0.332988\pi$
$269$	0.505277	+	0.291722i	0.00187835	+	0.00108447i	−0.499061	+	0.866567i	$0.666321\pi$
$270$		0			0
$271$	−173.903	+	301.208i	−0.641707	+	1.11147i	0.343344	+	0.939210i	$0.388440\pi$
$271$	−173.903	+	301.208i	−0.641707	+	1.11147i	−0.985052	+	0.172260i	$0.944893\pi$
$272$		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	−0.995762	−	0.0919678i	$-0.970684\pi$
$277$	−115.851	+	200.660i	−0.418235	+	0.724404i	0.577527	+	0.816371i	$0.304018\pi$
$278$		0			0
$279$	−140.424	+	22.7473i	−0.503311	+	0.0815317i
$280$		0			0
$281$		−	501.455i		−	1.78454i	−0.451505	−	0.892268i	$-0.649113\pi$
$281$		−	501.455i		−	1.78454i	0.451505	−	0.892268i	$-0.350887\pi$
$282$		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	−0.610884	−	0.791720i	$-0.709186\pi$
$293$	−67.5883	+	39.0221i	−0.230677	+	0.133181i	0.380207	+	0.924901i	$0.375853\pi$
$294$		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	−0.886655	−	0.462431i	$-0.846977\pi$
$307$	−13.1550	+	22.7852i	−0.0428503	+	0.0742188i	0.843805	+	0.536650i	$0.180311\pi$
$308$		0			0
$309$	112.187	−	236.273i	0.363064	−	0.764637i
$310$		0			0
$311$	−339.125	+	195.794i	−1.09043	+	0.629562i	−0.933692	−	0.358078i	$-0.883432\pi$
$311$	−339.125	+	195.794i	−1.09043	+	0.629562i	−0.156741	+	0.987640i	$0.550099\pi$
$312$		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	$0.0287064\pi$
$317$			57.0992i			0.180124i	−0.995936	+	0.0900618i	$0.971294\pi$
$318$		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	−0.874911	−	0.484283i	$-0.839080\pi$
$331$	−5.97582	+	10.3504i	−0.0180538	+	0.0312702i	0.856857	+	0.515554i	$0.172414\pi$
$332$		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	$0.0699917\pi$
$347$			151.374i			0.436236i	−0.975922	+	0.218118i	$0.930008\pi$
$348$		0			0
$349$	−219.737	+	380.596i	−0.629619	+	1.09053i	0.358009	+	0.933718i	$0.383456\pi$
$349$	−219.737	+	380.596i	−0.629619	+	1.09053i	−0.987628	+	0.156814i	$0.949878\pi$
$350$		0			0
$351$	−49.8539	+	171.623i	−0.142034	+	0.488954i
$352$		0			0
$353$	524.353	+	302.736i	1.48542	+	0.857608i	0.999862	−	0.0165964i	$-0.00528304\pi$
$353$	524.353	+	302.736i	1.48542	+	0.857608i	0.485558	+	0.874204i	$0.338616\pi$
$354$		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	0.376989	−	0.926218i	$-0.376959\pi$
$359$	−84.9553	−	49.0490i	−0.236644	−	0.136627i	−0.613633	+	0.789591i	$0.710293\pi$
$360$		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	0.738853	−	0.673866i	$-0.235368\pi$
$373$	−79.8812	−	138.358i	−0.214159	−	0.370934i	−0.953012	+	0.302933i	$0.902034\pi$
$374$		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	$0.0517775\pi$
$383$			124.052i			0.323895i	−0.986799	+	0.161948i	$0.948222\pi$
$384$		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	$-0.820810\pi$
$389$		−	415.200i		−	1.06735i	0.845689	−	0.533676i	$-0.179190\pi$
$390$		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	−0.366209	−	0.930532i	$-0.619345\pi$
$397$	247.236	−	428.225i	0.622760	−	1.07865i	0.988969	−	0.148120i	$-0.0473220\pi$
$398$		0			0
$399$	−252.550	+	61.7769i	−0.632958	+	0.154829i
$400$		0			0
$401$		−	299.577i		−	0.747075i	−0.927615	−	0.373538i	$-0.878145\pi$
$401$		−	299.577i		−	0.747075i	0.927615	−	0.373538i	$-0.121855\pi$
$402$		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	−0.751058	−	0.660237i	$-0.770456\pi$
$409$	80.2674	−	139.027i	0.196253	−	0.339920i	0.947310	+	0.320317i	$0.103789\pi$
$410$		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	0.131386	−	0.991331i	$-0.458057\pi$
$419$	442.295	−	255.359i	1.05560	−	0.609449i	0.924211	+	0.381882i	$0.124724\pi$
$420$		0			0
$421$	−176.079	−	304.978i	−0.418241	−	0.724414i	0.577522	−	0.816375i	$-0.304020\pi$
$421$	−176.079	−	304.978i	−0.418241	−	0.724414i	−0.995763	+	0.0919610i	$0.970686\pi$
$422$		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	−0.980855	−	0.194738i	$-0.937614\pi$
$431$	−561.436	+	324.145i	−1.30264	+	0.752077i	−0.321780	+	0.946815i	$0.604281\pi$
$432$		0			0
$433$	270.752	+	468.956i	0.625293	+	1.08304i	0.988484	+	0.151325i	$0.0483539\pi$
$433$	270.752	+	468.956i	0.625293	+	1.08304i	−0.363191	+	0.931715i	$0.618313\pi$
$434$		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	0.999580	+	0.0289930i	$0.00923004\pi$
$439$	230.430	+	399.117i	0.524898	+	0.909151i	−0.474681	+	0.880158i	$0.657437\pi$
$440$		0			0
$441$	−250.483	+	40.5759i	−0.567988	+	0.0920088i
$442$		0			0
$443$		−	798.745i		−	1.80304i	−0.432740	−	0.901519i	$-0.642453\pi$
$443$		−	798.745i		−	1.80304i	0.432740	−	0.901519i	$-0.357547\pi$
$444$		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	$0.315784\pi$
$449$			751.768i			1.67432i	−0.546962	+	0.837158i	$0.684216\pi$
$450$		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	0.201749	+	0.979437i	$0.435338\pi$
$457$	−341.536	+	591.557i	−0.747343	+	1.29444i	−0.949092	+	0.314999i	$0.897996\pi$
$458$		0			0
$459$	−332.225	−	96.5067i	−0.723803	−	0.210254i
$460$		0			0
$461$	−495.618	+	286.145i	−1.07509	+	0.620706i	−0.929569	−	0.368649i	$-0.879820\pi$
$461$	−495.618	+	286.145i	−1.07509	+	0.620706i	−0.145525	+	0.989355i	$0.546487\pi$
$462$		0			0
$463$	221.398	+	383.473i	0.478182	+	0.828236i	0.999687	−	0.0250123i	$-0.00796250\pi$
$463$	221.398	+	383.473i	0.478182	+	0.828236i	−0.521505	+	0.853248i	$0.674629\pi$
$464$		0			0
$465$	−397.784	−	188.876i	−0.855450	−	0.406184i
$466$		0			0
$467$			246.829i			0.528542i	0.964449	+	0.264271i	$0.0851313\pi$
$467$			246.829i			0.528542i	−0.964449	+	0.264271i	$0.914869\pi$
$468$		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	$0.0698209\pi$
$479$			208.455i			0.435188i	−0.976039	+	0.217594i	$0.930179\pi$
$480$		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	$-0.913590\pi$
$491$		−	263.317i		−	0.536287i	0.963379	−	0.268143i	$-0.0864101\pi$
$492$		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	−0.830434	−	0.557117i	$-0.811908\pi$
$503$	−383.876	+	221.631i	−0.763174	+	0.440619i	0.0672604	+	0.997735i	$0.478574\pi$
$504$		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	0.769538	−	0.638602i	$-0.220487\pi$
$509$	306.042	+	176.693i	0.601261	+	0.347138i	−0.168276	+	0.985740i	$0.553820\pi$
$510$		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	$-0.829860\pi$
$521$		−	530.816i		−	1.01884i	0.860518	−	0.509420i	$-0.170140\pi$
$522$		0			0
$523$	518.783	+	898.559i	0.991938	+	1.71809i	0.605717	+	0.795680i	$0.292887\pi$
$523$	518.783	+	898.559i	0.991938	+	1.71809i	0.386221	+	0.922406i	$0.373780\pi$
$524$		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	−0.926155	−	0.377143i	$-0.876906\pi$
$541$	−427.224	−	739.974i	−0.789693	−	1.36779i	0.136462	−	0.990645i	$-0.456427\pi$
$542$		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	0.552720	−	0.833367i	$-0.313590\pi$
$557$	863.794	−	498.712i	1.55080	−	0.895353i	0.998077	−	0.0619859i	$-0.0197434\pi$
$558$		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	−0.746272	−	0.665641i	$-0.768158\pi$
$563$	−305.679	+	176.484i	−0.542947	+	0.313470i	0.203326	+	0.979111i	$0.434825\pi$
$564$		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	0.723133	−	0.690709i	$-0.242701\pi$
$569$	276.835	+	159.831i	0.486529	+	0.280897i	−0.236605	+	0.971606i	$0.576035\pi$
$570$		0			0
$571$	352.313	+	610.224i	0.617010	+	1.06869i	0.990028	+	0.140869i	$0.0449897\pi$
$571$	352.313	+	610.224i	0.617010	+	1.06869i	−0.373018	+	0.927824i	$0.621677\pi$
$572$		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	0.686541	−	0.727091i	$-0.259128\pi$
$587$	974.121	−	562.409i	1.65949	−	0.958107i	0.972950	−	0.231016i	$-0.0742050\pi$
$588$		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	0.206727	−	0.978399i	$-0.433719\pi$
$593$	686.343	−	396.261i	1.15741	−	0.668230i	0.950682	+	0.310168i	$0.100385\pi$
$594$		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	−0.210045	−	0.977692i	$-0.567361\pi$
$599$	−695.903	−	401.780i	−1.16177	−	0.670750i	−0.951728	+	0.306941i	$0.900695\pi$
$600$		0			0
$601$	3.87039	−	6.70371i	0.00643992	−	0.0111543i	−0.862787	−	0.505567i	$-0.831283\pi$
$601$	3.87039	−	6.70371i	0.00643992	−	0.0111543i	0.869227	+	0.494412i	$0.164617\pi$
$602$		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	0.943221	−	0.332167i	$-0.107780\pi$
$607$	111.655	+	193.392i	0.183945	+	0.318602i	−0.759275	+	0.650769i	$0.774446\pi$
$608$		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	−0.670351	−	0.742044i	$-0.733856\pi$
$613$	188.469	−	326.438i	0.307454	−	0.532525i	0.977805	+	0.209519i	$0.0671898\pi$
$614$		0			0
$615$	279.867	+	405.679i	0.455068	+	0.659641i
$616$		0			0
$617$	−404.809	−	233.717i	−0.656093	−	0.378795i	0.134694	−	0.990887i	$-0.456995\pi$
$617$	−404.809	−	233.717i	−0.656093	−	0.378795i	−0.790787	+	0.612092i	$0.790328\pi$
$618$		0			0
$619$	481.347	−	833.718i	0.777621	−	1.34688i	−0.155689	−	0.987806i	$-0.549760\pi$
$619$	481.347	−	833.718i	0.777621	−	1.34688i	0.933310	−	0.359073i	$-0.116907\pi$
$620$		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	0.951748	−	0.306880i	$-0.0992852\pi$
$631$	132.578	+	229.632i	0.210108	+	0.363917i	−0.741640	+	0.670798i	$0.765952\pi$
$632$		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	−0.516960	−	0.856009i	$-0.672936\pi$
$641$	−21.8673	+	12.6251i	−0.0341143	+	0.0196959i	0.482846	+	0.875705i	$0.339603\pi$
$642$		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	$-0.753152\pi$
$647$		−	905.889i		−	1.40014i	0.714075	−	0.700069i	$-0.246848\pi$
$648$		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	0.426339	−	0.904564i	$-0.359803\pi$
$653$	929.143	−	536.441i	1.42288	−	0.821502i	0.996544	+	0.0830615i	$0.0264698\pi$
$654$		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	$-0.712111\pi$
$659$		−	1036.04i		−	1.57214i	0.618135	−	0.786072i	$-0.287889\pi$
$660$		0			0
$661$	47.1772	−	81.7133i	0.0713725	−	0.123621i	−0.828131	−	0.560535i	$-0.810595\pi$
$661$	47.1772	−	81.7133i	0.0713725	−	0.123621i	0.899503	+	0.436914i	$0.143929\pi$
$662$		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	−0.958570	−	0.284858i	$-0.908053\pi$
$673$	−156.533	+	271.123i	−0.232590	+	0.402858i	0.725979	+	0.687716i	$0.241387\pi$
$674$		0			0
$675$	−1605.71	+	394.465i	−2.37883	+	0.584393i
$676$		0			0
$677$	−523.760	−	302.393i	−0.773649	−	0.446666i	0.0605259	−	0.998167i	$-0.480722\pi$
$677$	−523.760	−	302.393i	−0.773649	−	0.446666i	−0.834175	+	0.551500i	$0.814056\pi$
$678$		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	$-0.993595\pi$
$683$		−	27.4860i		−	0.0402430i	0.999798	−	0.0201215i	$-0.00640531\pi$
$684$		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	−0.864313	−	0.502954i	$-0.832247\pi$
$691$	2.35922	−	4.08630i	0.00341422	−	0.00591360i	0.867727	+	0.497040i	$0.165580\pi$
$692$		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	0.440624	−	0.897692i	$-0.354757\pi$
$701$	−81.6577	−	47.1451i	−0.116487	−	0.0672541i	−0.557112	+	0.830438i	$0.688090\pi$
$702$		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	−0.349419	−	0.936966i	$-0.613621\pi$
$719$	−960.272	−	554.413i	−1.33557	−	0.771089i	−0.986146	+	0.165877i	$0.946954\pi$
$720$		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	0.970871	−	0.239604i	$-0.0770175\pi$
$727$	202.057	+	349.973i	0.277933	+	0.481393i	−0.692938	+	0.720997i	$0.743684\pi$
$728$		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	−0.937362	−	0.348358i	$-0.886739\pi$
$733$	−564.680	−	978.054i	−0.770368	−	1.33432i	0.166994	−	0.985958i	$-0.446594\pi$
$734$		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	−0.562181	−	0.827014i	$-0.690038\pi$
$739$	321.557	−	556.953i	0.435124	−	0.753658i	0.997306	+	0.0733563i	$0.0233710\pi$
$740$		0			0
$741$	−366.486	+	89.6471i	−0.494584	+	0.120981i
$742$		0			0
$743$			1205.28i			1.62219i	0.584917	+	0.811093i	$0.301127\pi$
$743$			1205.28i			1.62219i	−0.584917	+	0.811093i	$0.698873\pi$
$744$		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	−0.936686	−	0.350171i	$-0.886123\pi$
$751$	−123.979	+	214.738i	−0.165086	+	0.285937i	0.771600	+	0.636108i	$0.219457\pi$
$752$		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	−0.995400	−	0.0958047i	$-0.969458\pi$
$757$	−313.951	+	543.779i	−0.414731	+	0.718335i	0.580669	+	0.814139i	$0.302791\pi$
$758$		0			0
$759$	−31.0167	+	65.3231i	−0.0408652	+	0.0860647i
$760$		0			0
$761$	856.714	−	494.624i	1.12577	−	0.649966i	0.182905	−	0.983131i	$-0.441450\pi$
$761$	856.714	−	494.624i	1.12577	−	0.649966i	0.942869	+	0.333165i	$0.108117\pi$
$762$		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	−0.983284	−	0.182077i	$-0.941718\pi$
$769$	−256.815	+	444.816i	−0.333959	+	0.578434i	0.649325	+	0.760511i	$0.275051\pi$
$770$		0			0
$771$	−44.2704	−	550.142i	−0.0574195	−	0.713544i
$772$		0			0
$773$	464.596	−	268.235i	0.601030	−	0.347005i	−0.168417	−	0.985716i	$-0.553865\pi$
$773$	464.596	−	268.235i	0.601030	−	0.347005i	0.769447	+	0.638711i	$0.220532\pi$
$774$		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	0.901839	−	0.432072i	$-0.142217\pi$
$787$	60.3896	+	104.598i	0.0767339	+	0.132907i	−0.825105	+	0.564979i	$0.808884\pi$
$788$		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	−0.132507	−	0.991182i	$-0.542303\pi$
$797$	525.724	−	303.527i	0.659629	−	0.380837i	0.792136	+	0.610345i	$0.208969\pi$
$798$		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	$-0.971593\pi$
$809$		−	144.203i		−	0.178248i	0.996021	−	0.0891241i	$-0.0284068\pi$
$810$		0			0
$811$	−487.189	−	843.837i	−0.600727	−	1.04049i	−0.992711	−	0.120518i	$-0.961545\pi$
$811$	−487.189	−	843.837i	−0.600727	−	1.04049i	0.391984	−	0.919972i	$-0.371789\pi$
$812$		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	$-0.677705\pi$
$821$		−	1392.69i		−	1.69634i	0.529726	−	0.848169i	$-0.322295\pi$
$822$		0			0
$823$	−327.037	+	566.445i	−0.397372	+	0.688268i	−0.993401	−	0.114695i	$-0.963411\pi$
$823$	−327.037	+	566.445i	−0.397372	+	0.688268i	0.596029	+	0.802963i	$0.296744\pi$
$824$		0			0
$825$	−18.8168	−	233.834i	−0.0228083	−	0.283435i
$826$		0			0
$827$	−966.498	+	558.008i	−1.16868	+	0.674737i	−0.953369	−	0.301808i	$-0.902410\pi$
$827$	−966.498	+	558.008i	−1.16868	+	0.674737i	−0.215310	+	0.976546i	$0.569076\pi$
$828$		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	−0.232656	−	0.972559i	$-0.574741\pi$
$839$	413.860	−	238.942i	0.493278	−	0.284794i	0.725933	+	0.687765i	$0.241408\pi$
$840$		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	0.999809	+	0.0195570i	$0.00622558\pi$
$853$	440.866	+	763.602i	0.516841	+	0.895195i	−0.482968	+	0.875638i	$0.660441\pi$
$854$		0			0
$855$	−1555.26	−	320.774i	−1.81901	−	0.375174i
$856$		0			0
$857$	727.761	−	420.173i	0.849197	−	0.490284i	−0.0111831	−	0.999937i	$-0.503560\pi$
$857$	727.761	−	420.173i	0.849197	−	0.490284i	0.860380	+	0.509654i	$0.170226\pi$
$858$		0			0
$859$	578.204	−	1001.48i	0.673113	−	1.16587i	−0.303904	−	0.952703i	$-0.598290\pi$
$859$	578.204	−	1001.48i	0.673113	−	1.16587i	0.977017	−	0.213163i	$-0.0683765\pi$
$860$		0			0
$861$	−19.4174	−	241.298i	−0.0225522	−	0.280253i
$862$		0			0
$863$		−	267.381i		−	0.309828i	−0.987928	−	0.154914i	$-0.950490\pi$
$863$		−	267.381i		−	0.309828i	0.987928	−	0.154914i	$-0.0495100\pi$
$864$		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	$0.174871\pi$
$881$			920.034i			1.04431i	−0.852852	+	0.522153i	$0.825129\pi$
$882$		0			0
$883$	261.135	+	452.299i	0.295736	+	0.512230i	0.975156	−	0.221520i	$-0.0711018\pi$
$883$	261.135	+	452.299i	0.295736	+	0.512230i	−0.679420	+	0.733750i	$0.737768\pi$
$884$		0			0
$885$	−1309.16	−	1897.68i	−1.47927	−	2.14427i
$886$		0			0
$887$	−239.539	−	138.298i	−0.270055	−	0.155917i	0.358857	−	0.933392i	$-0.383166\pi$
$887$	−239.539	−	138.298i	−0.270055	−	0.155917i	−0.628913	+	0.777476i	$0.716500\pi$
$888$		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	0.944933	−	0.327265i	$-0.106127\pi$
$907$	171.465	+	296.986i	0.189046	+	0.327438i	−0.755886	+	0.654703i	$0.772794\pi$
$908$		0			0
$909$	−747.618	−	283.972i	−0.822462	−	0.312400i
$910$		0			0
$911$	−629.426	−	363.399i	−0.690918	−	0.398901i	0.113038	−	0.993591i	$-0.463942\pi$
$911$	−629.426	−	363.399i	−0.690918	−	0.398901i	−0.803956	+	0.594689i	$0.797275\pi$
$912$		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	−0.0125930	−	0.999921i	$-0.504009\pi$
$929$	786.926	−	454.332i	0.847067	−	0.489055i	0.859660	+	0.510866i	$0.170675\pi$
$930$		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	0.844944	−	0.534855i	$-0.179634\pi$
$937$	−38.1604	−	66.0958i	−0.0407262	−	0.0705398i	−0.885670	+	0.464315i	$0.846300\pi$
$938$		0			0
$939$	159.091	+	230.609i	0.169426	+	0.245590i
$940$		0			0
$941$	−755.091	−	435.952i	−0.802434	−	0.463286i	0.0418872	−	0.999122i	$-0.486663\pi$
$941$	−755.091	−	435.952i	−0.802434	−	0.463286i	−0.844322	+	0.535837i	$0.819996\pi$
$942$		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	−0.342815	−	0.939403i	$-0.611380\pi$
$947$	283.460	−	163.656i	0.299324	−	0.172815i	0.642139	+	0.766588i	$0.278047\pi$
$948$		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	0.545447	−	0.838145i	$-0.316360\pi$
$953$	87.9770	+	50.7935i	0.0923158	+	0.0532986i	−0.453131	+	0.891444i	$0.649693\pi$
$954$		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	1.00000		0.000663529i	$-0.000211208\pi$
$971$	1455.94	+	840.588i	1.49943	+	0.865693i	0.499425	+	0.866357i	$0.333545\pi$
$972$		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	−0.270614	−	0.962688i	$-0.587227\pi$
$977$	417.952	−	241.305i	0.427792	−	0.246986i	0.698405	+	0.715702i	$0.253893\pi$
$978$		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	−0.347787	−	0.937574i	$-0.613067\pi$
$983$	285.347	−	164.745i	0.290282	−	0.167594i	0.638069	+	0.769979i	$0.279733\pi$
$984$		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	−0.792834	−	0.609438i	$-0.791395\pi$
$991$	130.189	−	225.494i	0.131371	−	0.227542i	0.924205	+	0.381896i	$0.124729\pi$
$992$		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.353.12	✓	80
3.2	odd	2		2052.3.m.a.1493.40		80
9.4	even	3		2052.3.be.a.125.1		80
9.5	odd	6		684.3.be.a.581.38	yes	80
19.7	even	3		684.3.be.a.425.38	yes	80
57.26	odd	6		2052.3.be.a.197.1		80
171.121	even	3		2052.3.m.a.881.1		80
171.140	odd	6	inner	684.3.m.a.653.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.m.a.353.12	✓	80	1.1	even	1	trivial
684.3.m.a.653.12	yes	80	171.140	odd	6	inner
684.3.be.a.425.38	yes	80	19.7	even	3
684.3.be.a.581.38	yes	80	9.5	odd	6
2052.3.m.a.881.1		80	171.121	even	3
2052.3.m.a.1493.40		80	3.2	odd	2
2052.3.be.a.125.1		80	9.4	even	3
2052.3.be.a.197.1		80	57.26	odd	6

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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