LMFDB - Embedded newform 289.3.e.r.249.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,3,Mod(40,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([15]))

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

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

chi := DirichletCharacter("289.40");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, 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:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			249.3
Character	$\chi$	$=$	289.249
Dual form			289.3.e.r.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.74407 - 1.13663i) q^{2} +(-0.848504 - 4.26572i) q^{3} +(3.40954 + 3.40954i) q^{4} +(5.61992 + 3.75511i) q^{5} +(-2.52019 + 12.6698i) q^{6} +(-2.34806 + 1.56892i) q^{7} +(-0.934102 - 2.25512i) q^{8} +(-9.16146 + 3.79480i) q^{9} +O(q^{10})$	\(q+(-2.74407 - 1.13663i) q^{2} +(-0.848504 - 4.26572i) q^{3} +(3.40954 + 3.40954i) q^{4} +(5.61992 + 3.75511i) q^{5} +(-2.52019 + 12.6698i) q^{6} +(-2.34806 + 1.56892i) q^{7} +(-0.934102 - 2.25512i) q^{8} +(-9.16146 + 3.79480i) q^{9} +(-11.1533 - 16.6920i) q^{10} +(-2.98487 - 0.593727i) q^{11} +(11.6511 - 17.4371i) q^{12} +(11.5039 - 11.5039i) q^{13} +(8.22652 - 1.63636i) q^{14} +(11.2497 - 27.1592i) q^{15} -12.0373i q^{16} +29.4529 q^{18} +(3.45602 + 1.43153i) q^{19} +(6.35814 + 31.9645i) q^{20} +(8.68492 + 8.68492i) q^{21} +(7.51583 + 5.02191i) q^{22} +(6.80324 - 34.2022i) q^{23} +(-8.82712 + 5.89809i) q^{24} +(7.91555 + 19.1098i) q^{25} +(-44.6432 + 18.4918i) q^{26} +(2.21406 + 3.31358i) q^{27} +(-13.3551 - 2.65650i) q^{28} +(18.6583 - 27.9241i) q^{29} +(-61.7399 + 61.7399i) q^{30} +(-37.6850 + 7.49600i) q^{31} +(-17.4184 + 42.0517i) q^{32} +13.2364i q^{33} -19.0874 q^{35} +(-44.1749 - 18.2978i) q^{36} +(-6.19239 - 31.1313i) q^{37} +(-7.85642 - 7.85642i) q^{38} +(-58.8336 - 39.3113i) q^{39} +(3.21865 - 16.1813i) q^{40} +(0.486907 - 0.325341i) q^{41} +(-13.9605 - 33.7035i) q^{42} +(11.8865 - 4.92353i) q^{43} +(-8.15269 - 12.2014i) q^{44} +(-65.7365 - 13.0758i) q^{45} +(-57.5437 + 86.1203i) q^{46} +(10.7320 - 10.7320i) q^{47} +(-51.3479 + 10.2137i) q^{48} +(-15.6996 + 37.9022i) q^{49} -61.4357i q^{50} +78.4462 q^{52} +(86.0309 + 35.6352i) q^{53} +(-2.30922 - 11.6092i) q^{54} +(-14.5452 - 14.5452i) q^{55} +(5.73144 + 3.82963i) q^{56} +(3.17405 - 15.9570i) q^{57} +(-82.9389 + 55.4180i) q^{58} +(-19.5605 - 47.2233i) q^{59} +(130.957 - 54.2441i) q^{60} +(-41.5737 - 62.2194i) q^{61} +(111.930 + 22.2643i) q^{62} +(15.5579 - 23.2840i) q^{63} +(61.5477 - 61.5477i) q^{64} +(107.850 - 21.4526i) q^{65} +(15.0449 - 36.3215i) q^{66} +59.7204i q^{67} -151.669 q^{69} +(52.3770 + 21.6953i) q^{70} +(-7.49194 - 37.6645i) q^{71} +(17.1155 + 17.1155i) q^{72} +(-12.6260 - 8.43645i) q^{73} +(-18.3924 + 92.4646i) q^{74} +(74.8007 - 49.9803i) q^{75} +(6.90257 + 16.6643i) q^{76} +(7.94017 - 3.28892i) q^{77} +(116.761 + 174.745i) q^{78} +(-33.7242 - 6.70816i) q^{79} +(45.2015 - 67.6489i) q^{80} +(-50.8507 + 50.8507i) q^{81} +(-1.70590 + 0.339324i) q^{82} +(55.8282 - 134.781i) q^{83} +59.2232i q^{84} -38.2134 q^{86} +(-134.948 - 55.8973i) q^{87} +(1.44925 + 7.28585i) q^{88} +(77.4719 + 77.4719i) q^{89} +(165.523 + 110.599i) q^{90} +(-8.96313 + 45.0607i) q^{91} +(139.810 - 93.4178i) q^{92} +(63.9516 + 154.393i) q^{93} +(-41.6475 + 17.2510i) q^{94} +(14.0470 + 21.0228i) q^{95} +(194.160 + 38.6209i) q^{96} +(-71.2255 + 106.596i) q^{97} +(86.1616 - 86.1616i) q^{98} +(29.5988 - 5.88757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q + 288 q^{18} + 384 q^{35} + 1920 q^{52} - 1152 q^{69} - 6240 q^{86}+O(q^{100}) $ 96 * q + 288 * q^18 + 384 * q^35 + 1920 * q^52 - 1152 * q^69 - 6240 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{16}\right)$

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 $

$2$	−2.74407	−	1.13663i	−1.37203	−	0.568314i	−0.429694	−	0.902975i	$-0.641378\pi$
$2$	−2.74407	−	1.13663i	−1.37203	−	0.568314i	−0.942339	+	0.334660i	$0.891378\pi$
$3$	−0.848504	−	4.26572i	−0.282835	−	1.42191i	−0.817055	−	0.576560i	$-0.804395\pi$
$3$	−0.848504	−	4.26572i	−0.282835	−	1.42191i	0.534220	−	0.845345i	$-0.320605\pi$
$4$	3.40954	+	3.40954i	0.852385	+	0.852385i
$5$	5.61992	+	3.75511i	1.12398	+	0.751022i	0.971442	−	0.237275i	$-0.0762543\pi$
$5$	5.61992	+	3.75511i	1.12398	+	0.751022i	0.152541	+	0.988297i	$0.451254\pi$
$6$	−2.52019	+	12.6698i	−0.420031	+	2.11164i
$7$	−2.34806	+	1.56892i	−0.335437	+	0.224132i	−0.711869	−	0.702312i	$-0.752151\pi$
$7$	−2.34806	+	1.56892i	−0.335437	+	0.224132i	0.376432	+	0.926444i	$0.377151\pi$
$8$	−0.934102	−	2.25512i	−0.116763	−	0.281890i
$9$	−9.16146	+	3.79480i	−1.01794	+	0.421644i
$10$	−11.1533	−	16.6920i	−1.11533	−	1.66920i
$11$	−2.98487	−	0.593727i	−0.271352	−	0.0539752i	0.0575388	−	0.998343i	$-0.481675\pi$
$11$	−2.98487	−	0.593727i	−0.271352	−	0.0539752i	−0.328891	+	0.944368i	$0.606675\pi$
$12$	11.6511	−	17.4371i	0.970927	−	1.45309i
$13$	11.5039	−	11.5039i	0.884917	−	0.884917i	−0.109112	−	0.994029i	$-0.534801\pi$
$13$	11.5039	−	11.5039i	0.884917	−	0.884917i	0.994029	+	0.109112i	$0.0348008\pi$
$14$	8.22652	−	1.63636i	0.587608	−	0.116883i
$15$	11.2497	−	27.1592i	0.749981	−	1.81061i
$16$		−	12.0373i		−	0.752334i
$17$		0			0
$17$		0			0
$18$	29.4529			1.63627
$19$	3.45602	+	1.43153i	0.181896	+	0.0753436i	0.471773	−	0.881720i	$-0.343614\pi$
$19$	3.45602	+	1.43153i	0.181896	+	0.0753436i	−0.289877	+	0.957064i	$0.593614\pi$
$20$	6.35814	+	31.9645i	0.317907	+	1.59823i
$21$	8.68492	+	8.68492i	0.413568	+	0.413568i
$22$	7.51583	+	5.02191i	0.341628	+	0.228269i
$23$	6.80324	−	34.2022i	0.295793	−	1.48705i	−0.491720	−	0.870754i	$-0.663632\pi$
$23$	6.80324	−	34.2022i	0.295793	−	1.48705i	0.787513	−	0.616298i	$-0.211368\pi$
$24$	−8.82712	+	5.89809i	−0.367797	+	0.245754i
$25$	7.91555	+	19.1098i	0.316622	+	0.764393i
$26$	−44.6432	+	18.4918i	−1.71705	+	0.711224i
$27$	2.21406	+	3.31358i	0.0820022	+	0.122725i
$28$	−13.3551	−	2.65650i	−0.476968	−	0.0948749i
$29$	18.6583	−	27.9241i	0.643390	−	0.962901i	−0.356204	−	0.934408i	$-0.615929\pi$
$29$	18.6583	−	27.9241i	0.643390	−	0.962901i	0.999594	−	0.0284925i	$-0.00907068\pi$
$30$	−61.7399	+	61.7399i	−2.05800	+	2.05800i
$31$	−37.6850	+	7.49600i	−1.21564	+	0.241807i	−0.760932	−	0.648832i	$-0.775258\pi$
$31$	−37.6850	+	7.49600i	−1.21564	+	0.241807i	−0.454712	+	0.890638i	$0.650258\pi$
$32$	−17.4184	+	42.0517i	−0.544325	+	1.31412i
$33$			13.2364i			0.401102i
$34$		0			0
$35$	−19.0874			−0.545354
$36$	−44.1749	−	18.2978i	−1.22708	−	0.508273i
$37$	−6.19239	−	31.1313i	−0.167362	−	0.841385i	−0.969659	−	0.244461i	$-0.921389\pi$
$37$	−6.19239	−	31.1313i	−0.167362	−	0.841385i	0.802297	−	0.596925i	$-0.203611\pi$
$38$	−7.85642	−	7.85642i	−0.206748	−	0.206748i
$39$	−58.8336	−	39.3113i	−1.50855	−	1.00798i
$40$	3.21865	−	16.1813i	0.0804663	−	0.404532i
$41$	0.486907	−	0.325341i	0.0118758	−	0.00793514i	−0.549618	−	0.835416i	$-0.685227\pi$
$41$	0.486907	−	0.325341i	0.0118758	−	0.00793514i	0.561494	+	0.827481i	$0.310227\pi$
$42$	−13.9605	−	33.7035i	−0.332392	−	0.802465i
$43$	11.8865	−	4.92353i	0.276429	−	0.114501i	−0.240162	−	0.970733i	$-0.577201\pi$
$43$	11.8865	−	4.92353i	0.276429	−	0.114501i	0.516591	+	0.856232i	$0.327201\pi$
$44$	−8.15269	−	12.2014i	−0.185288	−	0.277304i
$45$	−65.7365	−	13.0758i	−1.46081	−	0.290574i
$46$	−57.5437	+	86.1203i	−1.25095	+	1.87218i
$47$	10.7320	−	10.7320i	0.228340	−	0.228340i	−0.583659	−	0.811999i	$-0.698379\pi$
$47$	10.7320	−	10.7320i	0.228340	−	0.228340i	0.811999	+	0.583659i	$0.198379\pi$
$48$	−51.3479	+	10.2137i	−1.06975	+	0.212786i
$49$	−15.6996	+	37.9022i	−0.320400	+	0.773515i
$50$		−	61.4357i		−	1.22871i
$51$		0			0
$52$	78.4462			1.50858
$53$	86.0309	+	35.6352i	1.62322	+	0.672361i	0.994448	−	0.105226i	$-0.0335565\pi$
$53$	86.0309	+	35.6352i	1.62322	+	0.672361i	0.628775	+	0.777587i	$0.283556\pi$
$54$	−2.30922	−	11.6092i	−0.0427633	−	0.214986i
$55$	−14.5452	−	14.5452i	−0.264458	−	0.264458i
$56$	5.73144	+	3.82963i	0.102347	+	0.0683862i
$57$	3.17405	−	15.9570i	0.0556852	−	0.279948i
$58$	−82.9389	+	55.4180i	−1.42998	+	0.955483i
$59$	−19.5605	−	47.2233i	−0.331534	−	0.800395i	−0.998471	−	0.0552801i	$-0.982395\pi$
$59$	−19.5605	−	47.2233i	−0.331534	−	0.800395i	0.666937	−	0.745114i	$-0.267605\pi$
$60$	130.957	−	54.2441i	2.18261	−	0.904068i
$61$	−41.5737	−	62.2194i	−0.681535	−	1.01999i	−0.997462	−	0.0712060i	$-0.977315\pi$
$61$	−41.5737	−	62.2194i	−0.681535	−	1.01999i	0.315926	−	0.948784i	$-0.397685\pi$
$62$	111.930	+	22.2643i	1.80533	+	0.359101i
$63$	15.5579	−	23.2840i	0.246951	−	0.369588i
$64$	61.5477	−	61.5477i	0.961683	−	0.961683i
$65$	107.850	−	21.4526i	1.65922	−	0.330040i
$66$	15.0449	−	36.3215i	0.227952	−	0.550326i
$67$			59.7204i			0.891349i	0.895195	+	0.445675i	$0.147036\pi$
$67$			59.7204i			0.891349i	−0.895195	+	0.445675i	$0.852964\pi$
$68$		0			0
$69$	−151.669			−2.19811
$70$	52.3770	+	21.6953i	0.748243	+	0.309933i
$71$	−7.49194	−	37.6645i	−0.105520	−	0.530486i	−0.996998	−	0.0774225i	$-0.975331\pi$
$71$	−7.49194	−	37.6645i	−0.105520	−	0.530486i	0.891478	−	0.453064i	$-0.149669\pi$
$72$	17.1155	+	17.1155i	0.237715	+	0.237715i
$73$	−12.6260	−	8.43645i	−0.172959	−	0.115568i	0.466077	−	0.884744i	$-0.345667\pi$
$73$	−12.6260	−	8.43645i	−0.172959	−	0.115568i	−0.639037	+	0.769176i	$0.720667\pi$
$74$	−18.3924	+	92.4646i	−0.248545	+	1.24952i
$75$	74.8007	−	49.9803i	0.997343	−	0.666403i
$76$	6.90257	+	16.6643i	0.0908233	+	0.219267i
$77$	7.94017	−	3.28892i	0.103119	−	0.0427133i
$78$	116.761	+	174.745i	1.49693	+	2.24032i
$79$	−33.7242	−	6.70816i	−0.426889	−	0.0849135i	−0.0230300	−	0.999735i	$-0.507331\pi$
$79$	−33.7242	−	6.70816i	−0.426889	−	0.0849135i	−0.403859	+	0.914821i	$0.632331\pi$
$80$	45.2015	−	67.6489i	0.565019	−	0.845611i
$81$	−50.8507	+	50.8507i	−0.627787	+	0.627787i
$82$	−1.70590	+	0.339324i	−0.0208036	+	0.00413810i
$83$	55.8282	−	134.781i	0.672629	−	1.62387i	−0.104496	−	0.994525i	$-0.533323\pi$
$83$	55.8282	−	134.781i	0.672629	−	1.62387i	0.777126	−	0.629345i	$-0.216677\pi$
$84$			59.2232i			0.705038i
$85$		0			0
$86$	−38.2134			−0.444342
$87$	−134.948	−	55.8973i	−1.55113	−	0.642497i
$88$	1.44925	+	7.28585i	0.0164687	+	0.0827937i
$89$	77.4719	+	77.4719i	0.870471	+	0.870471i	0.992524	−	0.122053i	$-0.0389477\pi$
$89$	77.4719	+	77.4719i	0.870471	+	0.870471i	−0.122053	+	0.992524i	$0.538948\pi$
$90$	165.523	+	110.599i	1.83914	+	1.22888i
$91$	−8.96313	+	45.0607i	−0.0984959	+	0.495172i
$92$	139.810	−	93.4178i	1.51967	−	1.01541i
$93$	63.9516	+	154.393i	0.687652	+	1.66014i
$94$	−41.6475	+	17.2510i	−0.443059	+	0.183521i
$95$	14.0470	+	21.0228i	0.147863	+	0.221293i
$96$	194.160	+	38.6209i	2.02250	+	0.402301i
$97$	−71.2255	+	106.596i	−0.734284	+	1.09893i	0.256900	+	0.966438i	$0.417299\pi$
$97$	−71.2255	+	106.596i	−0.734284	+	1.09893i	−0.991184	+	0.132495i	$0.957701\pi$
$98$	86.1616	−	86.1616i	0.879200	−	0.879200i
$99$	29.5988	−	5.88757i	0.298978	−	0.0594704i
$100$	−38.1674	+	92.1441i	−0.381674	+	0.921441i
$101$		−	67.7756i		−	0.671046i	−0.942032	−	0.335523i	$-0.891087\pi$
$101$		−	67.7756i		−	0.671046i	0.942032	−	0.335523i	$-0.108913\pi$
$102$		0			0
$103$	17.3018			0.167978			0.0839892	−	0.996467i	$-0.473234\pi$
$103$	17.3018			0.167978			0.0839892	+	0.996467i	$0.473234\pi$
$104$	−36.6886	−	15.1969i	−0.352775	−	0.146124i
$105$	16.1957	+	81.4214i	0.154245	+	0.775442i
$106$	−195.570	−	195.570i	−1.84500	−	1.84500i
$107$	61.7612	+	41.2675i	0.577208	+	0.385678i	0.809633	−	0.586936i	$-0.199666\pi$
$107$	61.7612	+	41.2675i	0.577208	+	0.385678i	−0.232425	+	0.972614i	$0.574666\pi$
$108$	−3.74884	+	18.8467i	−0.0347115	+	0.174506i
$109$	97.8124	−	65.3562i	0.897362	−	0.599598i	−0.0190572	−	0.999818i	$-0.506066\pi$
$109$	97.8124	−	65.3562i	0.897362	−	0.599598i	0.916419	+	0.400220i	$0.131066\pi$
$110$	23.3805	+	56.4455i	0.212550	+	0.513141i
$111$	−127.543	+	52.8300i	−1.14903	+	0.475946i
$112$	18.8857	+	28.2644i	0.168622	+	0.252361i
$113$	−16.0436	−	3.19127i	−0.141979	−	0.0282413i	0.123589	−	0.992333i	$-0.460559\pi$
$113$	−16.0436	−	3.19127i	−0.141979	−	0.0282413i	−0.265568	+	0.964092i	$0.585559\pi$
$114$	−26.8470	+	40.1794i	−0.235500	+	0.352451i
$115$	166.667	−	166.667i	1.44928	−	1.44928i
$116$	158.825	−	31.5922i	1.36918	−	0.272346i
$117$	−61.7376	+	149.048i	−0.527672	+	1.27391i
$118$			151.817i			1.28658i
$119$		0			0
$120$	−71.7557			−0.597964
$121$	−103.232	−	42.7603i	−0.853161	−	0.353391i
$122$	43.3605	+	217.988i	0.355414	+	1.78679i
$123$	−1.80095	−	1.80095i	−0.0146419	−	0.0146419i
$124$	−154.046	−	102.930i	−1.24231	−	0.830084i
$125$	5.69072	−	28.6092i	0.0455258	−	0.228873i
$126$	−69.1572	+	46.2094i	−0.548867	+	0.366741i
$127$	−85.6726	−	206.832i	−0.674587	−	1.62860i	−0.773724	−	0.633523i	$-0.781608\pi$
$127$	−85.6726	−	206.832i	−0.674587	−	1.62860i	0.0991366	−	0.995074i	$-0.468392\pi$
$128$	−70.6408	+	29.2604i	−0.551882	+	0.228597i
$129$	−31.0881	−	46.5266i	−0.240993	−	0.360671i
$130$	−320.330	−	63.7176i	−2.46408	−	0.490135i
$131$	−19.3991	+	29.0328i	−0.148085	+	0.221624i	−0.898095	−	0.439802i	$-0.855049\pi$
$131$	−19.3991	+	29.0328i	−0.148085	+	0.221624i	0.750010	+	0.661426i	$0.230049\pi$
$132$	−45.1300	+	45.1300i	−0.341894	+	0.341894i
$133$	−10.3609	+	2.06091i	−0.0779015	+	0.0154956i
$134$	67.8799	−	163.877i	0.506567	−	1.22296i
$135$			26.9361i			0.199526i
$136$		0			0
$137$	147.093			1.07367			0.536836	−	0.843687i	$-0.319620\pi$
$137$	147.093			1.07367			0.536836	+	0.843687i	$0.319620\pi$
$138$	416.191	+	172.392i	3.01587	+	1.24922i
$139$	−41.8081	−	210.183i	−0.300778	−	1.51211i	−0.775144	−	0.631784i	$-0.782323\pi$
$139$	−41.8081	−	210.183i	−0.300778	−	1.51211i	0.474367	−	0.880327i	$-0.342677\pi$
$140$	−65.0792	−	65.0792i	−0.464852	−	0.464852i
$141$	−54.8857	−	36.6734i	−0.389260	−	0.260095i
$142$	−22.2522	+	111.869i	−0.156706	+	0.787813i
$143$	−41.1679	+	27.5075i	−0.287887	+	0.192360i
$144$	45.6793	+	110.280i	0.317217	+	0.765830i
$145$	209.716	−	86.8673i	1.44632	−	0.599085i
$146$	25.0576	+	37.5013i	0.171627	+	0.256858i
$147$	175.001	+	34.8099i	1.19049	+	0.236802i
$148$	85.0301	−	127.256i	0.574527	−	0.859841i
$149$	−21.6711	+	21.6711i	−0.145444	+	0.145444i	−0.776079	−	0.630636i	$-0.782794\pi$
$149$	−21.6711	+	21.6711i	−0.145444	+	0.145444i	0.630636	+	0.776079i	$0.282794\pi$
$150$	−262.067	+	52.1284i	−1.74711	+	0.347523i
$151$	−54.5103	+	131.600i	−0.360995	+	0.871520i	0.634160	+	0.773202i	$0.281346\pi$
$151$	−54.5103	+	131.600i	−0.360995	+	0.871520i	−0.995155	+	0.0983178i	$0.968654\pi$
$152$		−	9.13094i		−	0.0600720i
$153$		0			0
$154$	−25.5266			−0.165757
$155$	−239.935	−	99.3842i	−1.54797	−	0.641189i
$156$	−66.5619	−	334.629i	−0.426679	−	2.14506i
$157$	140.674	+	140.674i	0.896015	+	0.896015i	0.995081	−	0.0990662i	$-0.0315855\pi$
$157$	140.674	+	140.674i	0.896015	+	0.896015i	−0.0990662	+	0.995081i	$0.531586\pi$
$158$	84.9168	+	56.7396i	0.537448	+	0.359111i
$159$	79.0119	−	397.220i	0.496930	−	2.49824i
$160$	−255.799	+	170.919i	−1.59874	+	1.06825i
$161$	37.6862	+	90.9826i	0.234076	+	0.565109i
$162$	197.336	−	81.7393i	1.21812	−	0.504564i
$163$	5.79818	+	8.67759i	0.0355717	+	0.0532367i	0.848829	−	0.528667i	$-0.177308\pi$
$163$	5.79818	+	8.67759i	0.0355717	+	0.0532367i	−0.813258	+	0.581904i	$0.802308\pi$
$164$	2.76939	+	0.550866i	0.0168865	+	0.00335894i
$165$	−49.7041	+	74.3874i	−0.301237	+	0.450833i
$166$	−306.393	+	306.393i	−1.84574	+	1.84574i
$167$	−100.280	+	19.9468i	−0.600476	+	0.119442i	−0.485963	−	0.873979i	$-0.661531\pi$
$167$	−100.280	+	19.9468i	−0.600476	+	0.119442i	−0.114514	+	0.993422i	$0.536531\pi$
$168$	11.4730	−	27.6982i	0.0682914	−	0.164870i
$169$		−	95.6804i		−	0.566156i
$170$		0			0
$171$	−37.0945			−0.216927
$172$	57.3143	+	23.7404i	0.333223	+	0.138025i
$173$	34.3828	+	172.854i	0.198745	+	0.999158i	0.943387	+	0.331694i	$0.107620\pi$
$173$	34.3828	+	172.854i	0.198745	+	0.999158i	−0.744642	+	0.667464i	$0.767380\pi$
$174$	306.772	+	306.772i	1.76305	+	1.76305i
$175$	−48.5681	−	32.4521i	−0.277532	−	0.185441i
$176$	−7.14690	+	35.9299i	−0.0406074	+	0.204147i
$177$	−184.844	+	123.509i	−1.04432	+	0.697790i
$178$	−124.531	−	300.645i	−0.699613	−	1.68902i
$179$	64.3011	−	26.6344i	0.359224	−	0.148795i	−0.195770	−	0.980650i	$-0.562721\pi$
$179$	64.3011	−	26.6344i	0.359224	−	0.148795i	0.554994	+	0.831854i	$0.312721\pi$
$180$	−179.549	−	268.714i	−0.997494	−	1.49285i
$181$	−10.3701	−	2.06275i	−0.0572935	−	0.0113964i	0.166360	−	0.986065i	$-0.446799\pi$
$181$	−10.3701	−	2.06275i	−0.0572935	−	0.0113964i	−0.223654	+	0.974669i	$0.571799\pi$
$182$	75.8127	−	113.462i	0.416553	−	0.623416i
$183$	−230.135	+	230.135i	−1.25757	+	1.25757i
$184$	−83.4851	+	16.6062i	−0.453723	+	0.0902512i
$185$	82.1005	−	198.208i	0.443787	−	1.07140i
$186$		−	496.354i		−	2.66857i
$187$		0			0
$188$	73.1822			0.389267
$189$	−10.3975	−	4.30678i	−0.0550132	−	0.0227872i
$190$	−14.6507	−	73.6541i	−0.0771091	−	0.387653i
$191$	−78.9144	−	78.9144i	−0.413165	−	0.413165i	0.469675	−	0.882839i	$-0.344371\pi$
$191$	−78.9144	−	78.9144i	−0.413165	−	0.413165i	−0.882839	+	0.469675i	$0.844371\pi$
$192$	−314.768	−	210.322i	−1.63942	−	1.09542i
$193$	−43.1149	+	216.753i	−0.223393	+	1.12307i	0.692428	+	0.721487i	$0.256541\pi$
$193$	−43.1149	+	216.753i	−0.223393	+	1.12307i	−0.915821	+	0.401587i	$0.868459\pi$
$194$	316.608	−	211.551i	1.63200	−	1.09047i
$195$	−183.022	−	441.853i	−0.938572	−	2.26591i
$196$	−182.758	+	75.7007i	−0.932437	+	0.386228i
$197$	−62.5706	−	93.6435i	−0.317617	−	0.475348i	0.637968	−	0.770063i	$-0.279775\pi$
$197$	−62.5706	−	93.6435i	−0.317617	−	0.475348i	−0.955585	+	0.294715i	$0.904775\pi$
$198$	−87.9131	−	17.4870i	−0.444005	−	0.0883182i
$199$	7.73344	−	11.5739i	0.0388615	−	0.0581604i	−0.811530	−	0.584311i	$-0.801365\pi$
$199$	7.73344	−	11.5739i	0.0388615	−	0.0581604i	0.850392	+	0.526150i	$0.176365\pi$
$200$	35.7011	−	35.7011i	0.178505	−	0.178505i
$201$	254.750	−	50.6730i	1.26741	−	0.252104i
$202$	−77.0358	+	185.981i	−0.381365	+	0.920697i
$203$			94.8410i			0.467197i
$204$		0			0
$205$	3.95807			0.0193077
$206$	−47.4772	−	19.6657i	−0.230472	−	0.0954645i
$207$	67.4629	+	339.159i	0.325908	+	1.63845i
$208$	−138.477	−	138.477i	−0.665753	−	0.665753i
$209$	−9.46582	−	6.32486i	−0.0452910	−	0.0302625i
$210$	48.1038	−	241.834i	0.229066	−	1.15159i
$211$	−135.480	+	90.5252i	−0.642087	+	0.429029i	−0.833530	−	0.552475i	$-0.813684\pi$
$211$	−135.480	+	90.5252i	−0.642087	+	0.429029i	0.191442	+	0.981504i	$0.438684\pi$
$212$	171.826	+	414.825i	0.810501	+	1.95672i
$213$	−154.309	+	63.9170i	−0.724457	+	0.300080i
$214$	−122.571	−	183.440i	−0.572761	−	0.857198i
$215$	85.2893	+	16.9651i	0.396695	+	0.0789075i
$216$	5.40436	−	8.08820i	0.0250202	−	0.0374454i
$217$	76.7259	−	76.7259i	0.353576	−	0.353576i
$218$	−342.689	+	68.1652i	−1.57197	+	0.312684i
$219$	−25.2743	+	61.0174i	−0.115408	+	0.278618i
$220$		−	99.1850i		−	0.450841i
$221$		0			0
$222$	410.034			1.84700
$223$	263.986	+	109.347i	1.18380	+	0.490344i	0.885730	−	0.464201i	$-0.153659\pi$
$223$	263.986	+	109.347i	1.18380	+	0.490344i	0.298066	+	0.954545i	$0.403659\pi$
$224$	−25.0765	−	126.068i	−0.111949	−	0.562804i
$225$	−145.036	−	145.036i	−0.644604	−	0.644604i
$226$	40.3974	+	26.9927i	0.178749	+	0.119437i
$227$	−18.7574	+	94.3000i	−0.0826319	+	0.415419i	0.917223	+	0.398375i	$0.130426\pi$
$227$	−18.7574	+	94.3000i	−0.0826319	+	0.415419i	−0.999855	+	0.0170441i	$0.994574\pi$
$228$	65.2283	−	43.5841i	0.286089	−	0.191158i
$229$	109.401	+	264.116i	0.477732	+	1.15335i	0.960670	+	0.277693i	$0.0895696\pi$
$229$	109.401	+	264.116i	0.477732	+	1.15335i	−0.482938	+	0.875655i	$0.660430\pi$
$230$	−646.782	+	267.906i	−2.81210	+	1.16481i
$231$	−20.7669	−	31.0798i	−0.0898999	−	0.134545i
$232$	−80.4011	−	15.9928i	−0.346556	−	0.0689343i
$233$	77.8929	−	116.575i	0.334304	−	0.500322i	−0.625793	−	0.779989i	$-0.715224\pi$
$233$	77.8929	−	116.575i	0.334304	−	0.500322i	0.960097	+	0.279668i	$0.0902244\pi$
$234$	338.824	−	338.824i	1.44797	−	1.44797i
$235$	100.613	−	20.0131i	0.428139	−	0.0851621i
$236$	94.3173	−	227.702i	0.399650	−	0.964839i
$237$			149.550i			0.631012i
$238$		0			0
$239$	94.0682			0.393591			0.196795	−	0.980445i	$-0.436947\pi$
$239$	94.0682			0.393591			0.196795	+	0.980445i	$0.436947\pi$
$240$	−326.925	−	135.417i	−1.36219	−	0.564236i
$241$	17.6070	+	88.5165i	0.0730582	+	0.367288i	0.999968	−	0.00799568i	$-0.00254513\pi$
$241$	17.6070	+	88.5165i	0.0730582	+	0.367288i	−0.926910	+	0.375284i	$0.877545\pi$
$242$	234.674	+	234.674i	0.969728	+	0.969728i
$243$	289.884	+	193.694i	1.19294	+	0.797096i
$244$	70.3924	−	353.887i	0.288493	−	1.45035i
$245$	−230.558	+	154.054i	−0.941052	+	0.628791i
$246$	2.89492	+	6.98895i	0.0117680	+	0.0284104i
$247$	56.2260	−	23.2896i	0.227635	−	0.0942897i
$248$	52.1060	+	77.9822i	0.210105	+	0.314444i
$249$	−622.309	−	123.785i	−2.49923	−	0.497128i
$250$	−48.1337	+	72.0372i	−0.192535	+	0.288149i
$251$	36.7555	−	36.7555i	0.146436	−	0.146436i	−0.630088	−	0.776524i	$-0.716981\pi$
$251$	36.7555	−	36.7555i	0.146436	−	0.146436i	0.776524	+	0.630088i	$0.216981\pi$
$252$	132.433	−	26.3426i	0.525529	−	0.104534i
$253$	−40.6136	+	98.0498i	−0.160528	+	0.387549i
$254$			664.938i			2.61787i
$255$		0			0
$256$	−121.065			−0.472911
$257$	−189.819	−	78.6257i	−0.738596	−	0.305936i	−0.0185169	−	0.999829i	$-0.505894\pi$
$257$	−189.819	−	78.6257i	−0.738596	−	0.305936i	−0.720079	+	0.693892i	$0.755894\pi$
$258$	32.4242	+	163.008i	0.125675	+	0.631813i
$259$	63.3827	+	63.3827i	0.244721	+	0.244721i
$260$	440.861	+	294.574i	1.69562	+	1.13298i
$261$	−64.9708	+	326.630i	−0.248930	+	1.25146i
$262$	86.2319	−	57.6183i	0.329129	−	0.219917i
$263$	79.3675	+	191.610i	0.301777	+	0.728555i	0.999921	+	0.0125970i	$0.00400987\pi$
$263$	79.3675	+	191.610i	0.301777	+	0.728555i	−0.698143	+	0.715958i	$0.745990\pi$
$264$	29.8497	−	12.3641i	0.113067	−	0.0468338i
$265$	349.673	+	523.322i	1.31952	+	1.97480i
$266$	30.7735	+	6.12122i	0.115690	+	0.0230121i
$267$	264.738	−	396.208i	0.991528	−	1.48393i
$268$	−203.619	+	203.619i	−0.759773	+	0.759773i
$269$	167.418	−	33.3015i	0.622372	−	0.123797i	0.126176	−	0.992008i	$-0.459730\pi$
$269$	167.418	−	33.3015i	0.622372	−	0.123797i	0.496196	+	0.868211i	$0.334730\pi$
$270$	30.6163	−	73.9143i	0.113394	−	0.273757i
$271$			347.614i			1.28271i	0.767245	+	0.641354i	$0.221627\pi$
$271$			347.614i			1.28271i	−0.767245	+	0.641354i	$0.778373\pi$
$272$		0			0
$273$	199.821			0.731946
$274$	−403.633	−	167.190i	−1.47311	−	0.610183i
$275$	−12.2809	−	61.7400i	−0.0446577	−	0.224509i
$276$	−517.123	−	517.123i	−1.87363	−	1.87363i
$277$	45.9538	+	30.7053i	0.165898	+	0.110850i	0.635748	−	0.771897i	$-0.280692\pi$
$277$	45.9538	+	30.7053i	0.165898	+	0.110850i	−0.469850	+	0.882746i	$0.655692\pi$
$278$	−124.177	+	624.277i	−0.446678	+	2.24560i
$279$	316.803	−	211.681i	1.13550	−	0.758714i
$280$	17.8296	+	43.0444i	0.0636771	+	0.153730i
$281$	58.1156	−	24.0723i	0.206817	−	0.0856665i	−0.276870	−	0.960907i	$-0.589297\pi$
$281$	58.1156	−	24.0723i	0.206817	−	0.0856665i	0.483687	+	0.875241i	$0.339297\pi$
$282$	108.926	+	163.019i	0.386262	+	0.578082i
$283$	354.515	+	70.5174i	1.25270	+	0.249178i	0.776477	−	0.630146i	$-0.217005\pi$
$283$	354.515	+	70.5174i	1.25270	+	0.249178i	0.476225	+	0.879323i	$0.342005\pi$
$284$	102.875	−	153.963i	0.362235	−	0.542123i
$285$	77.7584	−	77.7584i	0.272836	−	0.272836i
$286$	144.233	−	28.6898i	0.504312	−	0.100314i
$287$	−0.632852	+	1.52784i	−0.00220506	+	0.00532349i
$288$		−	451.355i		−	1.56720i
$289$		0			0
$290$	−674.211			−2.32487
$291$	515.145	+	213.380i	1.77026	+	0.733265i
$292$	−14.2846	−	71.8134i	−0.0489198	−	0.245936i
$293$	199.577	+	199.577i	0.681151	+	0.681151i	0.960260	−	0.279108i	$-0.0900388\pi$
$293$	199.577	+	199.577i	0.681151	+	0.681151i	−0.279108	+	0.960260i	$0.590039\pi$
$294$	−440.649	−	294.432i	−1.49881	−	1.00147i
$295$	67.4000	−	338.843i	0.228475	−	1.14862i
$296$	−64.4205	+	43.0444i	−0.217637	+	0.145420i
$297$	−4.64132	−	11.2051i	−0.0156273	−	0.0377277i
$298$	84.0988	−	34.8349i	0.282211	−	0.116896i
$299$	−315.195	−	471.723i	−1.05417	−	1.57767i
$300$	425.446	+	84.6264i	1.41815	+	0.282088i
$301$	−20.1855	+	30.2097i	−0.0670614	+	0.100364i
$302$	299.160	−	299.160i	0.990595	−	0.990595i
$303$	−289.112	+	57.5079i	−0.954164	+	0.189795i
$304$	17.2318	−	41.6013i	0.0566836	−	0.136846i
$305$		−	505.781i		−	1.65830i
$306$		0			0
$307$	12.8007			0.0416960			0.0208480	−	0.999783i	$-0.493363\pi$
$307$	12.8007			0.0416960			0.0208480	+	0.999783i	$0.493363\pi$
$308$	38.2860	+	15.8586i	0.124305	+	0.0514889i
$309$	−14.6806	−	73.8044i	−0.0475101	−	0.238849i
$310$	545.434	+	545.434i	1.75946	+	1.75946i
$311$	311.082	+	207.859i	1.00026	+	0.668356i	0.943961	−	0.330058i	$-0.107068\pi$
$311$	311.082	+	207.859i	1.00026	+	0.668356i	0.0563041	+	0.998414i	$0.482068\pi$
$312$	−33.6953	+	169.398i	−0.107998	+	0.542941i
$313$	267.916	−	179.016i	0.855962	−	0.571935i	−0.0483391	−	0.998831i	$-0.515393\pi$
$313$	267.916	−	179.016i	0.855962	−	0.571935i	0.904301	+	0.426896i	$0.140393\pi$
$314$	−226.125	−	545.914i	−0.720143	−	1.73858i
$315$	174.868	−	72.4328i	0.555137	−	0.229945i
$316$	−92.1123	−	137.856i	−0.291495	−	0.436253i
$317$	363.088	+	72.2228i	1.14539	+	0.227832i	0.731072	−	0.682300i	$-0.239020\pi$
$317$	363.088	+	72.2228i	1.14539	+	0.227832i	0.414318	+	0.910132i	$0.364020\pi$
$318$	−668.305	+	1000.19i	−2.10159	+	3.14525i
$319$	−72.2719	+	72.2719i	−0.226558	+	0.226558i
$320$	577.011	−	114.775i	1.80316	−	0.358671i
$321$	123.631	−	298.471i	0.385143	−	0.929818i
$322$		−	292.497i		−	0.908377i
$323$		0			0
$324$	−346.755			−1.07023
$325$	310.898	+	128.778i	0.956609	+	0.396240i
$326$	−6.04738	−	30.4022i	−0.0185503	−	0.0932584i
$327$	−361.785	−	361.785i	−1.10638	−	1.10638i
$328$	−1.18850	−	0.794133i	−0.00362349	−	0.00242114i
$329$	−8.36168	+	42.0370i	−0.0254154	+	0.127772i
$330$	220.942	−	147.629i	0.669521	−	0.447360i
$331$	179.824	+	434.132i	0.543274	+	1.31158i	0.922401	+	0.386234i	$0.126224\pi$
$331$	179.824	+	434.132i	0.543274	+	1.31158i	−0.379127	+	0.925345i	$0.623776\pi$
$332$	649.891	−	269.194i	1.95750	−	0.810824i
$333$	174.868	+	261.709i	0.525130	+	0.785912i
$334$	297.846	+	59.2452i	0.891754	+	0.177381i
$335$	−224.257	+	335.624i	−0.669423	+	1.00186i
$336$	104.543	−	104.543i	0.311141	−	0.311141i
$337$	−515.160	+	102.472i	−1.52867	+	0.304071i	−0.886585	−	0.462566i	$-0.846929\pi$
$337$	−515.160	+	102.472i	−1.52867	+	0.304071i	−0.642081	+	0.766637i	$0.721929\pi$
$338$	−108.753	+	262.553i	−0.321755	+	0.776785i
$339$			71.1452i			0.209868i
$340$		0			0
$341$	116.935			0.342919
$342$	101.790	+	42.1627i	0.297631	+	0.123283i
$343$	−49.5978	−	249.345i	−0.144600	−	0.726953i
$344$	−22.2063	−	22.2063i	−0.0645533	−	0.0645533i
$345$	−852.370	−	569.535i	−2.47064	−	1.65083i
$346$	102.122	−	513.404i	0.295151	−	1.48383i
$347$	−36.8263	+	24.6066i	−0.106128	+	0.0709123i	−0.607502	−	0.794319i	$-0.707828\pi$
$347$	−36.8263	+	24.6066i	−0.106128	+	0.0709123i	0.501374	+	0.865231i	$0.332828\pi$
$348$	−269.527	−	650.695i	−0.774502	−	1.86981i
$349$	321.915	−	133.341i	0.922392	−	0.382067i	0.129605	−	0.991566i	$-0.458629\pi$
$349$	321.915	−	133.341i	0.922392	−	0.382067i	0.792787	+	0.609499i	$0.208629\pi$
$350$	96.3879	+	144.255i	0.275394	+	0.412156i
$351$	63.5895	+	12.6487i	0.181167	+	0.0360363i
$352$	76.9589	−	115.177i	0.218633	−	0.327208i
$353$	−38.3872	+	38.3872i	−0.108746	+	0.108746i	−0.759386	−	0.650640i	$-0.774501\pi$
$353$	−38.3872	+	38.3872i	−0.108746	+	0.108746i	0.650640	+	0.759386i	$0.274501\pi$
$354$	647.607	−	128.817i	1.82940	−	0.363890i
$355$	99.3303	−	239.805i	0.279804	−	0.675506i
$356$			528.287i			1.48395i
$357$		0			0
$358$	−206.720			−0.577429
$359$	−39.7163	−	16.4510i	−0.110630	−	0.0458245i	0.326682	−	0.945134i	$-0.394069\pi$
$359$	−39.7163	−	16.4510i	−0.110630	−	0.0458245i	−0.437312	+	0.899310i	$0.644069\pi$
$360$	31.9171	+	160.458i	0.0886586	+	0.445717i
$361$	−245.371	−	245.371i	−0.679697	−	0.679697i
$362$	26.1117	+	17.4473i	0.0721318	+	0.0481970i
$363$	−94.8101	+	476.643i	−0.261185	+	1.31307i
$364$	−184.196	+	123.076i	−0.506034	+	0.338121i
$365$	−39.2775	−	94.8243i	−0.107610	−	0.259793i
$366$	893.083	−	369.927i	2.44012	−	1.01073i
$367$	133.331	+	199.544i	0.363299	+	0.543715i	0.967420	−	0.253177i	$-0.0814756\pi$
$367$	133.331	+	199.544i	0.363299	+	0.543715i	−0.604121	+	0.796893i	$0.706476\pi$
$368$	−411.704	−	81.8929i	−1.11876	−	0.222535i
$369$	−3.22617	+	4.82831i	−0.00874302	+	0.0130849i
$370$	−450.578	+	450.578i	−1.21778	+	1.21778i
$371$	−257.915	+	51.3024i	−0.695187	+	0.138281i
$372$	−308.363	+	744.455i	−0.828933	+	2.00122i
$373$		−	502.321i		−	1.34671i	−0.739321	−	0.673353i	$-0.764854\pi$
$373$		−	502.321i		−	1.34671i	0.739321	−	0.673353i	$-0.235146\pi$
$374$		0			0
$375$	−126.867			−0.338313
$376$	−34.2267	−	14.1772i	−0.0910284	−	0.0377052i
$377$	−106.593	−	535.880i	−0.282741	−	1.42143i
$378$	23.6362	+	23.6362i	0.0625296	+	0.0625296i
$379$	244.780	+	163.557i	0.645858	+	0.431548i	0.834886	−	0.550423i	$-0.185534\pi$
$379$	244.780	+	163.557i	0.645858	+	0.431548i	−0.189028	+	0.981972i	$0.560534\pi$
$380$	−23.7843	+	119.572i	−0.0625903	+	0.314663i
$381$	−809.592	+	540.952i	−2.12491	+	1.41982i
$382$	126.850	+	306.243i	0.332068	+	0.801683i
$383$	−481.937	+	199.625i	−1.25832	+	0.521213i	−0.909394	−	0.415937i	$-0.863454\pi$
$383$	−481.937	+	199.625i	−1.25832	+	0.521213i	−0.348927	+	0.937150i	$0.613454\pi$
$384$	184.756	+	276.506i	0.481134	+	0.720068i
$385$	56.9734	+	11.3327i	0.147983	+	0.0294356i
$386$	364.678	−	545.779i	0.944762	−	1.41394i
$387$	−90.2135	+	90.2135i	−0.233110	+	0.233110i
$388$	−606.291	+	120.599i	−1.56261	+	0.310822i
$389$	−238.706	+	576.287i	−0.613640	+	1.48146i	0.245335	+	0.969438i	$0.421102\pi$
$389$	−238.706	+	576.287i	−0.613640	+	1.48146i	−0.858974	+	0.512019i	$0.828898\pi$
$390$			1420.50i			3.64231i
$391$		0			0
$392$	100.139			0.255457
$393$	140.306	+	58.1166i	0.357012	+	0.147879i
$394$	65.2598	+	328.083i	0.165634	+	0.832699i
$395$	−164.337	−	164.337i	−0.416044	−	0.416044i
$396$	120.992	+	80.8445i	0.305536	+	0.204153i
$397$	71.6836	−	360.378i	0.180563	−	0.907752i	−0.779164	−	0.626820i	$-0.784356\pi$
$397$	71.6836	−	360.378i	0.180563	−	0.907752i	0.959727	−	0.280933i	$-0.0906438\pi$
$398$	−34.3763	+	22.9695i	−0.0863726	+	0.0577124i
$399$	17.5825	+	42.4480i	0.0440665	+	0.106386i
$400$	230.032	−	95.2822i	0.575079	−	0.238206i
$401$	407.115	+	609.291i	1.01525	+	1.51943i	0.845524	+	0.533937i	$0.179288\pi$
$401$	407.115	+	609.291i	1.01525	+	1.51943i	0.169725	+	0.985491i	$0.445712\pi$
$402$	−756.648	−	150.507i	−1.88221	−	0.374394i
$403$	−347.291	+	519.758i	−0.861765	+	1.28972i
$404$	231.084	−	231.084i	0.571990	−	0.571990i
$405$	−476.727	+	94.8269i	−1.17710	+	0.234141i
$406$	107.799	−	260.250i	0.265515	−	0.641009i
$407$			96.5993i			0.237345i
$408$		0			0
$409$	−730.857			−1.78694			−0.893469	−	0.449126i	$-0.851736\pi$
$409$	−730.857			−1.78694			−0.893469	+	0.449126i	$0.851736\pi$
$410$	−10.8612	−	4.49886i	−0.0264907	−	0.0109728i
$411$	−124.809	−	627.457i	−0.303671	−	1.52666i
$412$	58.9911	+	58.9911i	0.143182	+	0.143182i
$413$	120.019	+	80.1942i	0.290603	+	0.194175i
$414$	200.375	−	1007.35i	0.483998	−	2.43322i
$415$	819.869	−	547.819i	1.97559	−	1.32004i
$416$	283.380	+	684.140i	0.681202	+	1.64457i
$417$	−861.109	+	356.683i	−2.06501	+	0.855355i
$418$	18.7858	+	28.1149i	0.0449421	+	0.0672606i
$419$	−626.945	−	124.707i	−1.49629	−	0.297630i	−0.621993	−	0.783023i	$-0.713677\pi$
$419$	−626.945	−	124.707i	−1.49629	−	0.297630i	−0.874296	+	0.485392i	$0.838677\pi$
$420$	−222.390	+	332.829i	−0.529499	+	0.792451i
$421$	238.674	−	238.674i	0.566921	−	0.566921i	−0.364344	−	0.931265i	$-0.618707\pi$
$421$	238.674	−	238.674i	0.566921	−	0.566921i	0.931265	+	0.364344i	$0.118707\pi$
$422$	474.661	−	94.4159i	1.12479	−	0.223734i
$423$	−57.5948	+	139.046i	−0.136158	+	0.328715i
$424$		−	227.297i		−	0.536078i
$425$		0			0
$426$	496.084			1.16452
$427$	195.235	+	80.8690i	0.457225	+	0.189389i
$428$	69.8741	+	351.281i	0.163257	+	0.820749i
$429$	152.270	+	152.270i	0.354942	+	0.354942i
$430$	−214.756	−	143.496i	−0.499434	−	0.333711i
$431$	−2.97367	+	14.9497i	−0.00689947	+	0.0346860i	−0.984082	−	0.177717i	$-0.943129\pi$
$431$	−2.97367	+	14.9497i	−0.00689947	+	0.0346860i	0.977182	+	0.212403i	$0.0681289\pi$
$432$	39.8866	−	26.6514i	0.0923302	−	0.0616931i
$433$	−146.767	−	354.328i	−0.338954	−	0.818309i	−0.997817	−	0.0660448i	$-0.978962\pi$
$433$	−146.767	−	354.328i	−0.338954	−	0.818309i	0.658862	−	0.752264i	$-0.271038\pi$
$434$	−297.750	+	123.332i	−0.686059	+	0.284175i
$435$	−548.496	−	820.883i	−1.26091	−	1.88709i
$436$	556.330	+	110.661i	1.27599	+	0.253809i
$437$	72.4736	−	108.464i	0.165843	−	0.248202i
$438$	138.708	−	138.708i	0.316686	−	0.316686i
$439$	329.200	−	65.4819i	0.749885	−	0.149161i	0.194671	−	0.980869i	$-0.437636\pi$
$439$	329.200	−	65.4819i	0.749885	−	0.149161i	0.555214	+	0.831707i	$0.312636\pi$
$440$	−19.2145	+	46.3879i	−0.0436694	+	0.105427i
$441$		−	406.817i		−	0.922487i
$442$		0			0
$443$	708.195			1.59863			0.799317	−	0.600909i	$-0.205195\pi$
$443$	708.195			1.59863			0.799317	+	0.600909i	$0.205195\pi$
$444$	−614.988	−	254.736i	−1.38511	−	0.573731i
$445$	144.470	+	726.301i	0.324652	+	1.63214i
$446$	−600.109	−	600.109i	−1.34554	−	1.34554i
$447$	110.831	+	74.0547i	0.247943	+	0.165670i
$448$	−47.9541	+	241.081i	−0.107040	+	0.538128i
$449$	152.896	−	102.162i	0.340526	−	0.227532i	−0.373534	−	0.927616i	$-0.621854\pi$
$449$	152.896	−	102.162i	0.340526	−	0.227532i	0.714061	+	0.700084i	$0.246854\pi$
$450$	233.136	+	562.840i	0.518080	+	1.25076i
$451$	−1.64652	+	0.682010i	−0.00365082	+	0.00151222i
$452$	−43.8205	−	65.5820i	−0.0969480	−	0.145093i
$453$	607.618	+	120.863i	1.34132	+	0.266805i
$454$	158.656	−	237.445i	0.349462	−	0.523007i
$455$	−219.580	+	219.580i	−0.482593	+	0.482593i
$456$	−38.9500	+	7.74763i	−0.0854166	+	0.0169904i
$457$	315.280	−	761.154i	0.689891	−	1.66554i	−0.0551091	−	0.998480i	$-0.517551\pi$
$457$	315.280	−	761.154i	0.689891	−	1.66554i	0.745000	−	0.667064i	$-0.232449\pi$
$458$		−	849.101i		−	1.85393i
$459$		0			0
$460$	1136.51			2.47068
$461$	−255.913	−	106.003i	−0.555126	−	0.229941i	0.0874419	−	0.996170i	$-0.472131\pi$
$461$	−255.913	−	106.003i	−0.555126	−	0.229941i	−0.642568	+	0.766229i	$0.722131\pi$
$462$	21.6594	+	108.889i	0.0468819	+	0.235691i
$463$	−187.237	−	187.237i	−0.404401	−	0.404401i	0.475380	−	0.879781i	$-0.342311\pi$
$463$	−187.237	−	187.237i	−0.404401	−	0.404401i	−0.879781	+	0.475380i	$0.842311\pi$
$464$	−336.132	−	224.596i	−0.724423	−	0.484044i
$465$	−220.359	+	1107.82i	−0.473891	+	2.38241i
$466$	−346.246	+	231.354i	−0.743016	+	0.496467i
$467$	−248.069	−	598.890i	−0.531196	−	1.28242i	−0.930732	−	0.365703i	$-0.880829\pi$
$467$	−248.069	−	598.890i	−0.531196	−	1.28242i	0.399536	−	0.916718i	$-0.369171\pi$
$468$	−718.681	+	297.687i	−1.53564	+	0.636084i
$469$	−93.6968	−	140.227i	−0.199780	−	0.298992i
$470$	−298.835	−	59.4420i	−0.635819	−	0.126472i
$471$	480.714	−	719.439i	1.02062	−	1.52747i
$472$	−88.2228	+	88.2228i	−0.186913	+	0.186913i
$473$	−38.4028	+	7.63878i	−0.0811898	+	0.0161496i
$474$	169.983	−	410.374i	0.358613	−	0.865769i
$475$			77.3753i			0.162895i
$476$		0			0
$477$	−923.396			−1.93584
$478$	−258.129	−	106.921i	−0.540019	−	0.223683i
$479$	150.459	+	756.406i	0.314110	+	1.57914i	0.738881	+	0.673836i	$0.235355\pi$
$479$	150.459	+	756.406i	0.314110	+	1.57914i	−0.424771	+	0.905301i	$0.639645\pi$
$480$	946.140	+	946.140i	1.97112	+	1.97112i
$481$	−429.368	−	286.895i	−0.892658	−	0.596455i
$482$	52.2956	−	262.908i	0.108497	−	0.545452i
$483$	356.129	−	237.958i	0.737327	−	0.492666i
$484$	−206.182	−	497.768i	−0.425997	−	1.02845i
$485$	−800.563	+	331.604i	−1.65065	+	0.683720i
$486$	−575.302	−	861.000i	−1.18375	−	1.77161i
$487$	585.504	+	116.464i	1.20227	+	0.239146i	0.755285	−	0.655397i	$-0.227499\pi$
$487$	585.504	+	116.464i	1.20227	+	0.239146i	0.446982	+	0.894543i	$0.352499\pi$
$488$	−101.478	+	151.873i	−0.207947	+	0.311215i
$489$	32.0964	−	32.0964i	0.0656367	−	0.0656367i
$490$	807.767	−	160.675i	1.64850	−	0.327908i
$491$	−196.111	+	473.454i	−0.399411	+	0.964264i	0.588395	+	0.808574i	$0.299760\pi$
$491$	−196.111	+	473.454i	−0.399411	+	0.964264i	−0.987806	+	0.155690i	$0.950240\pi$
$492$		−	12.2809i		−	0.0249611i
$493$		0			0
$494$	−180.759			−0.365909
$495$	188.451	+	78.0591i	0.380710	+	0.157695i
$496$	90.2320	+	453.627i	0.181919	+	0.914570i
$497$	76.6843	+	76.6843i	0.154294	+	0.154294i
$498$	1566.96	+	1047.01i	3.14650	+	2.10243i
$499$	−92.1730	+	463.385i	−0.184715	+	0.928628i	0.771559	+	0.636158i	$0.219477\pi$
$499$	−92.1730	+	463.385i	−0.184715	+	0.928628i	−0.956275	+	0.292470i	$0.905523\pi$
$500$	116.947	−	78.1414i	0.233894	−	0.156283i
$501$	170.175	+	410.839i	0.339671	+	0.820038i
$502$	−142.637	+	59.0820i	−0.284137	+	0.117693i
$503$	60.0234	+	89.8313i	0.119331	+	0.178591i	0.886326	−	0.463062i	$-0.153249\pi$
$503$	60.0234	+	89.8313i	0.119331	+	0.178591i	−0.766995	+	0.641653i	$0.778249\pi$
$504$	−67.0411	−	13.3353i	−0.133018	−	0.0264589i
$505$	254.505	−	380.894i	0.503970	−	0.754245i
$506$	222.892	−	222.892i	0.440499	−	0.440499i
$507$	−408.145	+	81.1852i	−0.805020	+	0.160129i
$508$	413.097	−	997.306i	0.813184	−	1.96320i
$509$			193.751i			0.380650i	0.981721	+	0.190325i	$0.0609542\pi$
$509$			193.751i			0.380650i	−0.981721	+	0.190325i	$0.939046\pi$
$510$		0			0
$511$	42.8828			0.0839195
$512$	614.774	+	254.648i	1.20073	+	0.497359i
$513$	2.90835	+	14.6213i	0.00566930	+	0.0285015i
$514$	431.508	+	431.508i	0.839510	+	0.839510i
$515$	97.2345	+	64.9700i	0.188805	+	0.126155i
$516$	52.6383	−	264.630i	0.102012	−	0.512850i
$517$	−38.4054	+	25.6617i	−0.0742851	+	0.0496357i
$518$	−101.884	−	245.969i	−0.196687	−	0.474843i
$519$	708.173	−	293.335i	1.36450	−	0.565193i
$520$	−149.121	−	223.175i	−0.286771	−	0.429183i
$521$	36.0440	+	7.16959i	0.0691823	+	0.0137612i	0.229560	−	0.973294i	$-0.426271\pi$
$521$	36.0440	+	7.16959i	0.0691823	+	0.0137612i	−0.160378	+	0.987056i	$0.551271\pi$
$522$	549.541	−	822.447i	1.05276	−	1.57557i
$523$	−550.511	+	550.511i	−1.05260	+	1.05260i	−0.0540647	+	0.998537i	$0.517218\pi$
$523$	−550.511	+	550.511i	−1.05260	+	1.05260i	−0.998537	+	0.0540647i	$0.982782\pi$
$524$	−165.130	+	32.8465i	−0.315134	+	0.0626841i
$525$	−97.2214	+	234.713i	−0.185184	+	0.447073i
$526$		−	616.002i		−	1.17111i
$527$		0			0
$528$	159.331			0.301763
$529$	−634.774	−	262.932i	−1.19995	−	0.497036i
$530$	−364.701	−	1833.48i	−0.688116	−	3.45939i
$531$	358.406	+	358.406i	0.674964	+	0.674964i
$532$	−42.3527	−	28.2991i	−0.0796103	−	0.0531939i
$533$	1.85864	−	9.34404i	0.00348714	−	0.0175310i
$534$	−1176.80	+	786.313i	−2.20375	+	1.47250i
$535$	192.129	+	463.840i	0.359120	+	0.866991i
$536$	134.677	−	55.7850i	0.251263	−	0.104076i
$537$	−168.174	−	251.691i	−0.313174	−	0.468698i
$538$	−497.257	−	98.9106i	−0.924270	−	0.183849i
$539$	69.3649	−	103.812i	0.128692	−	0.192601i
$540$	−91.8396	+	91.8396i	−0.170073	+	0.170073i
$541$	−48.4556	+	9.63841i	−0.0895667	+	0.0178159i	−0.239670	−	0.970854i	$-0.577039\pi$
$541$	−48.4556	+	9.63841i	−0.0895667	+	0.0178159i	0.150104	+	0.988670i	$0.452039\pi$
$542$	395.108	−	953.875i	0.728981	−	1.75992i
$543$			45.9863i			0.0846893i
$544$		0			0
$545$	795.118			1.45893
$546$	−548.323	−	227.123i	−1.00425	−	0.415976i
$547$	−183.186	−	920.938i	−0.334892	−	1.68362i	−0.670735	−	0.741698i	$-0.734021\pi$
$547$	−183.186	−	920.938i	−0.334892	−	1.68362i	0.335843	−	0.941918i	$-0.390979\pi$
$548$	501.519	+	501.519i	0.915181	+	0.915181i
$549$	616.985	+	412.256i	1.12383	+	0.750922i
$550$	−36.4760	+	183.377i	−0.0663201	+	0.333413i
$551$	104.458	−	69.7963i	0.189578	−	0.126672i
$552$	141.675	+	342.033i	0.256657	+	0.619625i
$553$	89.7111	−	37.1596i	0.162226	−	0.0671963i
$554$	−91.1996	−	136.490i	−0.164620	−	0.246372i
$555$	−915.163	−	182.037i	−1.64894	−	0.327995i
$556$	574.083	−	859.175i	1.03252	−	1.54528i
$557$	365.407	−	365.407i	0.656027	−	0.656027i	−0.298410	−	0.954438i	$-0.596456\pi$
$557$	365.407	−	365.407i	0.656027	−	0.656027i	0.954438	+	0.298410i	$0.0964564\pi$
$558$	−1109.93	+	220.779i	−1.98913	+	0.395662i
$559$	80.1010	−	193.381i	0.143293	−	0.345941i
$560$			229.761i			0.410288i
$561$		0			0
$562$	−186.834			−0.332445
$563$	259.271	+	107.393i	0.460517	+	0.190752i	0.600866	−	0.799350i	$-0.294823\pi$
$563$	259.271	+	107.393i	0.460517	+	0.190752i	−0.140349	+	0.990102i	$0.544823\pi$
$564$	−62.0954	−	312.175i	−0.110098	−	0.553501i
$565$	−78.1801	−	78.1801i	−0.138372	−	0.138372i
$566$	−892.659	−	596.456i	−1.57714	−	1.05381i
$567$	39.6197	−	199.182i	0.0698760	−	0.351290i
$568$	−77.9399	+	52.0778i	−0.137218	+	0.0916862i
$569$	30.3056	+	73.1641i	0.0532611	+	0.128584i	0.948270	−	0.317464i	$-0.102831\pi$
$569$	30.3056	+	73.1641i	0.0532611	+	0.128584i	−0.895009	+	0.446048i	$0.852831\pi$
$570$	−301.756	+	124.992i	−0.529397	+	0.219284i
$571$	222.718	+	333.320i	0.390048	+	0.583748i	0.973581	−	0.228341i	$-0.0733301\pi$
$571$	222.718	+	333.320i	0.390048	+	0.583748i	−0.583533	+	0.812089i	$0.698330\pi$
$572$	−234.152	−	46.5756i	−0.409356	−	0.0814259i
$573$	−269.667	+	403.586i	−0.470624	+	0.704338i
$574$	3.47318	−	3.47318i	0.00605083	−	0.00605083i
$575$	707.450	−	140.720i	1.23035	−	0.244731i
$576$	−330.305	+	797.428i	−0.573447	+	1.38442i
$577$			333.536i			0.578052i	0.957321	+	0.289026i	$0.0933314\pi$
$577$			333.536i			0.578052i	−0.957321	+	0.289026i	$0.906669\pi$
$578$		0			0
$579$	961.191			1.66009
$580$	1011.21	+	418.858i	1.74347	+	0.722170i
$581$	80.3735	+	404.065i	0.138336	+	0.695464i
$582$	−1171.06	−	1171.06i	−2.01213	−	2.01213i
$583$	−235.633	−	157.445i	−0.404174	−	0.270060i
$584$	−7.23121	+	36.3538i	−0.0123822	+	0.0622496i
$585$	−906.651	+	605.805i	−1.54983	+	1.03556i
$586$	−320.808	−	774.499i	−0.547454	−	1.32167i
$587$	797.038	−	330.144i	1.35782	−	0.562426i	0.419358	−	0.907821i	$-0.362255\pi$
$587$	797.038	−	330.144i	1.35782	−	0.562426i	0.938457	+	0.345395i	$0.112255\pi$
$588$	477.988	+	715.360i	0.812905	+	1.21660i
$589$	−140.971	−	28.0408i	−0.239339	−	0.0476075i
$590$	−570.089	+	853.198i	−0.966252	+	1.44610i
$591$	−346.365	+	346.365i	−0.586066	+	0.586066i
$592$	−374.738	+	74.5399i	−0.633003	+	0.125912i
$593$	−109.829	+	265.150i	−0.185208	+	0.447133i	−0.989026	−	0.147744i	$-0.952799\pi$
$593$	−109.829	+	265.150i	−0.185208	+	0.447133i	0.803817	+	0.594876i	$0.202799\pi$
$594$			36.0231i			0.0606449i
$595$		0			0
$596$	−147.777			−0.247948
$597$	−55.9329	−	23.1682i	−0.0936899	−	0.0388076i
$598$	328.742	+	1652.70i	0.549736	+	2.76371i
$599$	−161.433	−	161.433i	−0.269505	−	0.269505i	0.559396	−	0.828901i	$-0.311033\pi$
$599$	−161.433	−	161.433i	−0.269505	−	0.269505i	−0.828901	+	0.559396i	$0.811033\pi$
$600$	−182.583	−	121.998i	−0.304305	−	0.203330i
$601$	48.3592	−	243.118i	0.0804646	−	0.404523i	−0.919471	−	0.393158i	$-0.871382\pi$
$601$	48.3592	−	243.118i	0.0804646	−	0.404523i	0.999935	−	0.0113647i	$-0.00361756\pi$
$602$	89.7275	−	59.9540i	0.149049	−	0.0995913i
$603$	−226.627	−	547.126i	−0.375832	−	0.907340i
$604$	−634.549	+	262.839i	−1.05058	+	0.435164i
$605$	−419.589	−	627.959i	−0.693535	−	1.03795i
$606$	858.706	+	170.807i	1.41701	+	0.281860i
$607$	−335.005	+	501.370i	−0.551903	+	0.825981i	−0.997603	−	0.0692016i	$-0.977955\pi$
$607$	−335.005	+	501.370i	−0.551903	+	0.825981i	0.445700	+	0.895182i	$0.352955\pi$
$608$	−120.397	+	120.397i	−0.198021	+	0.198021i
$609$	404.565	−	80.4729i	0.664310	−	0.132139i
$610$	−574.886	+	1387.90i	−0.942436	+	2.27524i
$611$		−	246.920i		−	0.404124i
$612$		0			0
$613$	−766.730			−1.25078			−0.625392	−	0.780311i	$-0.715061\pi$
$613$	−766.730			−1.25078			−0.625392	+	0.780311i	$0.715061\pi$
$614$	−35.1259	−	14.5496i	−0.0572082	−	0.0236964i
$615$	−3.35844	−	16.8840i	−0.00546087	−	0.0274537i
$616$	−14.8339	−	14.8339i	−0.0240809	−	0.0240809i
$617$	−343.791	−	229.714i	−0.557198	−	0.372308i	0.244856	−	0.969559i	$-0.421259\pi$
$617$	−343.791	−	229.714i	−0.557198	−	0.372308i	−0.802054	+	0.597252i	$0.796259\pi$
$618$	−43.6037	+	219.211i	−0.0705561	+	0.354710i
$619$	−58.1507	+	38.8551i	−0.0939430	+	0.0627707i	−0.601655	−	0.798756i	$-0.705492\pi$
$619$	−58.1507	+	38.8551i	−0.0939430	+	0.0627707i	0.507712	+	0.861527i	$0.330492\pi$
$620$	−479.213	−	1156.92i	−0.772924	−	1.86600i
$621$	128.394	−	53.1827i	0.206754	−	0.0856404i
$622$	−617.372	−	923.963i	−0.992560	−	1.48547i
$623$	−303.456	−	60.3612i	−0.487089	−	0.0968880i
$624$	−473.204	+	708.200i	−0.758340	+	1.13494i
$625$	505.063	−	505.063i	0.808100	−	0.808100i
$626$	−938.654	+	186.710i	−1.49945	+	0.298258i
$627$	−18.9483	+	45.7452i	−0.0302205	+	0.0729588i
$628$			959.269i			1.52750i
$629$		0			0
$630$	−562.179			−0.892348
$631$	−15.8903	−	6.58198i	−0.0251827	−	0.0104310i	0.370057	−	0.929009i	$-0.379338\pi$
$631$	−15.8903	−	6.58198i	−0.0251827	−	0.0104310i	−0.395239	+	0.918578i	$0.629338\pi$
$632$	16.3741	+	82.3184i	0.0259084	+	0.130251i
$633$	501.110	+	501.110i	0.791643	+	0.791643i
$634$	−914.248	−	610.881i	−1.44203	−	0.963535i
$635$	295.203	−	1484.09i	0.464887	−	2.33715i
$636$	1623.73	−	1084.94i	2.55304	−	1.70588i
$637$	255.417	+	616.632i	0.400969	+	0.968024i
$638$	280.465	−	116.172i	0.439600	−	0.182088i
$639$	211.566	+	316.632i	0.331090	+	0.495511i
$640$	−506.872	−	100.823i	−0.791987	−	0.157536i
$641$	−316.138	+	473.133i	−0.493194	+	0.738117i	−0.991673	−	0.128785i	$-0.958892\pi$
$641$	−316.138	+	473.133i	−0.493194	+	0.738117i	0.498478	+	0.866902i	$0.333892\pi$
$642$	−678.503	+	678.503i	−1.05686	+	1.05686i
$643$	1137.07	−	226.177i	1.76838	−	0.351752i	0.799763	−	0.600316i	$-0.204959\pi$
$643$	1137.07	−	226.177i	1.76838	−	0.351752i	0.968616	+	0.248564i	$0.0799586\pi$
$644$	−181.716	+	438.702i	−0.282168	+	0.681214i
$645$		−	378.215i		−	0.586380i
$646$		0			0
$647$	306.699			0.474032			0.237016	−	0.971506i	$-0.423831\pi$
$647$	306.699			0.474032			0.237016	+	0.971506i	$0.423831\pi$
$648$	162.174	+	67.1749i	0.250269	+	0.103665i
$649$	30.3478	+	152.569i	0.0467609	+	0.235083i
$650$	−706.751	−	706.751i	−1.08731	−	1.08731i
$651$	−392.393	−	262.189i	−0.602754	−	0.402748i
$652$	−9.81746	+	49.3557i	−0.0150575	+	0.0756990i
$653$	−1071.24	+	715.783i	−1.64050	+	1.09614i	−0.729281	+	0.684214i	$0.760145\pi$
$653$	−1071.24	+	715.783i	−1.64050	+	1.09614i	−0.911215	+	0.411931i	$0.864855\pi$
$654$	581.546	+	1403.98i	0.889215	+	2.14675i
$655$	−218.043	+	90.3162i	−0.332889	+	0.137887i
$656$	−3.91624	−	5.86107i	−0.00596988	−	0.00893455i
$657$	147.688	+	29.3769i	0.224791	+	0.0447137i
$658$	70.7254	−	105.848i	0.107485	−	0.160863i
$659$	−341.600	+	341.600i	−0.518361	+	0.518361i	−0.917075	−	0.398714i	$-0.869457\pi$
$659$	−341.600	+	341.600i	−0.518361	+	0.518361i	0.398714	+	0.917075i	$0.369457\pi$
$660$	−423.095	+	84.1588i	−0.641053	+	0.127513i
$661$	−316.461	+	764.004i	−0.478761	+	1.15583i	0.481430	+	0.876485i	$0.340118\pi$
$661$	−316.461	+	764.004i	−0.478761	+	1.15583i	−0.960190	+	0.279346i	$0.909882\pi$
$662$		−	1395.68i		−	2.10828i
$663$		0			0
$664$	−356.098			−0.536292
$665$	−65.9664	−	27.3242i	−0.0991975	−	0.0410890i
$666$	−182.384	−	916.906i	−0.273850	−	1.37674i
$667$	−828.129	−	828.129i	−1.24157	−	1.24157i
$668$	−409.917	−	273.898i	−0.613648	−	0.410026i
$669$	242.449	−	1218.87i	0.362405	−	1.82193i
$670$	996.854	−	666.077i	1.48784	−	0.994145i
$671$	87.1506	+	210.400i	0.129882	+	0.313562i
$672$	−516.493	+	213.939i	−0.768591	+	0.318361i
$673$	559.330	+	837.097i	0.831100	+	1.24383i	0.967423	+	0.253164i	$0.0814713\pi$
$673$	559.330	+	837.097i	0.831100	+	1.24383i	−0.136324	+	0.990664i	$0.543529\pi$
$674$	1530.11	+	304.357i	2.27019	+	0.451568i
$675$	−45.7964	+	68.5391i	−0.0678465	+	0.101539i
$676$	326.226	−	326.226i	0.482583	−	0.482583i
$677$	−861.404	+	171.344i	−1.27238	+	0.253093i	−0.784672	−	0.619912i	$-0.787168\pi$
$677$	−861.404	+	171.344i	−1.27238	+	0.253093i	−0.487712	+	0.873004i	$0.662168\pi$
$678$	80.8657	−	195.227i	0.119271	−	0.287945i
$679$		−	362.042i		−	0.533199i
$680$		0			0
$681$	418.173			0.614057
$682$	−320.878	−	132.912i	−0.470495	−	0.194886i
$683$	141.982	+	713.791i	0.207880	+	1.04508i	0.933934	+	0.357445i	$0.116352\pi$
$683$	141.982	+	713.791i	0.207880	+	1.04508i	−0.726054	+	0.687637i	$0.758648\pi$
$684$	−126.475	−	126.475i	−0.184905	−	0.184905i
$685$	826.651	+	552.350i	1.20679	+	0.806351i
$686$	−147.313	+	740.593i	−0.214742	+	1.07958i
$687$	1033.82	−	690.776i	1.50483	−	1.00550i
$688$	−59.2662	−	143.081i	−0.0861428	−	0.207967i
$689$	1399.64	−	579.748i	2.03140	−	0.841434i
$690$	1691.61	+	2531.67i	2.45161	+	3.66909i
$691$	35.1947	+	7.00065i	0.0509329	+	0.0101312i	0.220491	−	0.975389i	$-0.429234\pi$
$691$	35.1947	+	7.00065i	0.0509329	+	0.0101312i	−0.169558	+	0.985520i	$0.554234\pi$
$692$	−472.124	+	706.583i	−0.682260	+	1.02107i
$693$	−60.2627	+	60.2627i	−0.0869591	+	0.0869591i
$694$	129.022	−	25.6641i	0.185911	−	0.0369800i
$695$	554.304	−	1338.21i	0.797560	−	1.92548i
$696$			356.538i			0.512267i
$697$		0			0
$698$	−1034.91			−1.48269
$699$	−563.368	−	233.355i	−0.805963	−	0.333841i
$700$	−54.9479	−	276.242i	−0.0784970	−	0.394631i
$701$	717.719	+	717.719i	1.02385	+	1.02385i	0.999709	+	0.0241418i	$0.00768531\pi$
$701$	717.719	+	717.719i	1.02385	+	1.02385i	0.0241418	+	0.999709i	$0.492315\pi$
$702$	−160.117	−	106.987i	−0.228087	−	0.152403i
$703$	23.1643	−	116.455i	0.0329506	−	0.165654i
$704$	−220.254	+	147.169i	−0.312861	+	0.209047i
$705$	−170.740	−	412.204i	−0.242185	−	0.584686i
$706$	148.969	−	61.7050i	0.211004	−	0.0874008i
$707$	106.335	+	159.141i	0.150403	+	0.225094i
$708$	−1051.34	−	209.125i	−1.48494	−	0.295374i
$709$	−164.383	+	246.016i	−0.231852	+	0.346991i	−0.929093	−	0.369846i	$-0.879411\pi$
$709$	−164.383	+	246.016i	−0.231852	+	0.346991i	0.697241	+	0.716836i	$0.254411\pi$
$710$	−545.138	+	545.138i	−0.767800	+	0.767800i
$711$	334.419	−	66.5201i	0.470350	−	0.0935585i
$712$	102.342	−	247.075i	0.143739	−	0.347016i
$713$			1339.91i			1.87925i
$714$		0			0
$715$	−334.654			−0.468047
$716$	310.048	+	128.426i	0.433028	+	0.179366i
$717$	−79.8172	−	401.268i	−0.111321	−	0.559649i
$718$	90.2853	+	90.2853i	0.125746	+	0.125746i
$719$	973.315	+	650.348i	1.35371	+	0.904518i	0.999530	−	0.0306606i	$-0.00976111\pi$
$719$	973.315	+	650.348i	1.35371	+	0.904518i	0.354177	+	0.935178i	$0.384761\pi$
$720$	−157.398	+	791.293i	−0.218608	+	1.09902i
$721$	−40.6256	+	27.1452i	−0.0563462	+	0.0376493i
$722$	394.418	+	952.209i	0.546285	+	1.31885i
$723$	362.647	−	150.213i	0.501586	−	0.207764i
$724$	−28.3244	−	42.3904i	−0.0391220	−	0.0585503i
$725$	681.316	+	135.522i	0.939746	+	0.186927i
$726$	801.931	−	1200.17i	1.10459	−	1.65313i
$727$	347.839	−	347.839i	0.478458	−	0.478458i	−0.426180	−	0.904638i	$-0.640141\pi$
$727$	347.839	−	347.839i	0.478458	−	0.478458i	0.904638	+	0.426180i	$0.140141\pi$
$728$	109.990	−	21.8783i	0.151085	−	0.0300527i
$729$	332.595	−	802.956i	0.456235	−	1.10145i
$730$			304.848i			0.417600i
$731$		0			0
$732$	−1569.31			−2.14386
$733$	740.491	+	306.722i	1.01022	+	0.418447i	0.825535	−	0.564351i	$-0.190874\pi$
$733$	740.491	+	306.722i	1.01022	+	0.418447i	0.184685	+	0.982798i	$0.440874\pi$
$734$	−139.061	−	699.108i	−0.189457	−	0.952463i
$735$	852.778	+	852.778i	1.16024	+	1.16024i
$736$	1319.76	+	881.836i	1.79315	+	1.19815i
$737$	35.4576	−	178.258i	0.0481108	−	0.241869i
$738$	14.3408	−	9.58224i	0.0194320	−	0.0129841i
$739$	−280.208	−	676.483i	−0.379172	−	0.915403i	−0.992121	−	0.125281i	$-0.960017\pi$
$739$	−280.208	−	676.483i	−0.379172	−	0.915403i	0.612949	−	0.790123i	$-0.289983\pi$
$740$	955.724	−	395.874i	1.29152	−	0.534965i
$741$	−147.055	−	220.083i	−0.198454	−	0.297008i
$742$	766.046	+	152.376i	1.03241	+	0.205359i
$743$	459.923	−	688.324i	0.619008	−	0.926412i	−0.380990	−	0.924579i	$-0.624417\pi$
$743$	459.923	−	688.324i	0.619008	−	0.926412i	0.999998	−	0.00183243i	$-0.000583280\pi$
$744$	288.438	−	288.438i	0.387685	−	0.387685i
$745$	−203.167	+	40.4124i	−0.272707	+	0.0542449i
$746$	−570.953	+	1378.40i	−0.765352	+	1.84772i
$747$			1446.65i			1.93661i
$748$		0			0
$749$	−209.765			−0.280060
$750$	348.132	+	144.201i	0.464176	+	0.192268i
$751$	98.0808	+	493.085i	0.130600	+	0.656572i	0.989512	+	0.144449i	$0.0461408\pi$
$751$	98.0808	+	493.085i	0.130600	+	0.656572i	−0.858912	+	0.512123i	$0.828859\pi$
$752$	−129.184	−	129.184i	−0.171788	−	0.171788i
$753$	−187.975	−	125.601i	−0.249635	−	0.166801i
$754$	−316.598	+	1591.65i	−0.419892	+	2.11094i
$755$	−800.514	+	534.886i	−1.06028	+	0.708459i
$756$	−20.7665	−	50.1348i	−0.0274690	−	0.0663159i
$757$	−428.340	+	177.424i	−0.565839	+	0.234378i	−0.647218	−	0.762305i	$-0.724068\pi$
$757$	−428.340	+	177.424i	−0.565839	+	0.234378i	0.0813788	+	0.996683i	$0.474068\pi$
$758$	−485.789	−	727.035i	−0.640883	−	0.959149i
$759$	452.713	+	90.0503i	0.596460	+	0.118643i
$760$	34.2877	−	51.3151i	0.0451154	−	0.0675199i
$761$	321.374	−	321.374i	0.422305	−	0.422305i	−0.463692	−	0.885997i	$-0.653476\pi$
$761$	321.374	−	321.374i	0.422305	−	0.422305i	0.885997	+	0.463692i	$0.153476\pi$
$762$	2836.44	−	564.202i	3.72236	−	0.740423i
$763$	−127.131	+	306.921i	−0.166619	+	0.402255i
$764$		−	538.124i		−	0.704351i
$765$		0			0
$766$	1549.36			2.02267
$767$	−768.276	−	318.230i	−1.00166	−	0.414902i
$768$	102.724	+	516.429i	0.133755	+	0.672434i
$769$	−372.600	−	372.600i	−0.484525	−	0.484525i	0.422048	−	0.906573i	$-0.361311\pi$
$769$	−372.600	−	372.600i	−0.484525	−	0.484525i	−0.906573	+	0.422048i	$0.861311\pi$
$770$	−143.458	−	95.8552i	−0.186308	−	0.124487i
$771$	−174.333	+	876.429i	−0.226112	+	1.13674i
$772$	−886.031	+	592.027i	−1.14771	+	0.766874i
$773$	47.9441	+	115.747i	0.0620234	+	0.149738i	0.951853	−	0.306556i	$-0.0991767\pi$
$773$	47.9441	+	115.747i	0.0620234	+	0.149738i	−0.889829	+	0.456294i	$0.849177\pi$
$774$	350.091	−	145.012i	0.452314	−	0.187354i
$775$	−441.545	−	660.818i	−0.569735	−	0.852669i
$776$	306.920	+	61.0502i	0.395516	+	0.0786729i
$777$	216.592	−	324.153i	0.278754	−	0.417185i
$778$	1310.05	−	1310.05i	1.68387	−	1.68387i
$779$	2.14849	−	0.427362i	0.00275802	−	0.000548603i
$780$	882.497	−	2130.54i	1.13141	−	2.73146i
$781$			116.872i			0.149644i
$782$		0			0
$783$	133.839			0.170931
$784$	456.242	+	188.982i	0.581942	+	0.241048i
$785$	262.331	+	1318.83i	0.334179	+	1.68003i
$786$	−318.951	−	318.951i	−0.405790	−	0.405790i
$787$	−171.158	−	114.364i	−0.217482	−	0.145317i	0.442058	−	0.896987i	$-0.354249\pi$
$787$	−171.158	−	114.364i	−0.217482	−	0.145317i	−0.659539	+	0.751670i	$0.729249\pi$
$788$	105.944	−	532.618i	0.134447	−	0.675911i
$789$	750.010	−	501.141i	0.950583	−	0.635159i
$790$	264.162	+	637.743i	0.334382	+	0.807270i
$791$	42.6782	−	17.6779i	0.0539547	−	0.0223488i
$792$	−40.9255	−	61.2494i	−0.0516736	−	0.0773351i
$793$	−1194.03	−	237.507i	−1.50571	−	0.299504i
$794$	−606.320	+	907.422i	−0.763627	+	1.14285i
$795$	1935.64	−	1935.64i	2.43477	−	2.43477i
$796$	65.8292	−	13.0942i	0.0827000	−	0.0164501i
$797$	−172.430	+	416.283i	−0.216349	+	0.522312i	−0.994375	−	0.105920i	$-0.966221\pi$
$797$	−172.430	+	416.283i	−0.216349	+	0.522312i	0.778026	+	0.628232i	$0.216221\pi$
$798$		−	136.465i		−	0.171008i
$799$		0			0
$800$	−941.478			−1.17685
$801$	−1003.75	−	415.765i	−1.25312	−	0.519058i
$802$	−424.613	−	2134.67i	−0.529442	−	2.66169i
$803$	32.6781	+	32.6781i	0.0406950	+	0.0406950i
$804$	1041.35	+	695.810i	1.29521	+	0.865435i
$805$	−129.856	+	652.831i	−0.161312	+	0.810970i
$806$	1543.76	−	1031.51i	1.91534	−	1.27979i
$807$	−284.109	−	685.901i	−0.352056	−	0.849939i
$808$	−152.842	+	63.3094i	−0.189161	+	0.0783532i
$809$	112.468	+	168.320i	0.139021	+	0.208060i	0.894447	−	0.447175i	$-0.147570\pi$
$809$	112.468	+	168.320i	0.139021	+	0.208060i	−0.755426	+	0.655235i	$0.772570\pi$
$810$	1415.95	+	281.651i	1.74809	+	0.347717i
$811$	−67.2145	+	100.594i	−0.0828785	+	0.124037i	−0.870593	−	0.492004i	$-0.836264\pi$
$811$	−67.2145	+	100.594i	−0.0828785	+	0.124037i	0.787714	+	0.616041i	$0.211264\pi$
$812$	−323.364	+	323.364i	−0.398232	+	0.398232i
$813$	1482.82	−	294.952i	1.82389	−	0.362794i
$814$	109.798	−	265.075i	0.134886	−	0.325645i
$815$			70.5401i			0.0865523i
$816$		0			0
$817$	48.1280			0.0589082
$818$	2005.52	+	830.714i	2.45174	+	1.01554i
$819$	−88.8810	−	446.835i	−0.108524	−	0.545586i
$820$	13.4952	+	13.4952i	0.0164576	+	0.0164576i
$821$	−1329.58	−	888.396i	−1.61946	−	1.08209i	−0.935939	−	0.352162i	$-0.885447\pi$
$821$	−1329.58	−	888.396i	−1.61946	−	1.08209i	−0.683524	−	0.729928i	$-0.739553\pi$
$822$	−370.702	+	1863.64i	−0.450975	+	2.26721i
$823$	−477.629	+	319.142i	−0.580352	+	0.387779i	−0.810815	−	0.585302i	$-0.800976\pi$
$823$	−477.629	+	319.142i	−0.580352	+	0.387779i	0.230463	+	0.973081i	$0.425976\pi$
$824$	−16.1616	−	39.0176i	−0.0196136	−	0.0473515i
$825$	−252.945	+	104.773i	−0.306600	+	0.126998i
$826$	−238.189	−	356.475i	−0.288364	−	0.431568i
$827$	−190.852	−	37.9628i	−0.230776	−	0.0459042i	0.0783475	−	0.996926i	$-0.475036\pi$
$827$	−190.852	−	37.9628i	−0.230776	−	0.0459042i	−0.309123	+	0.951022i	$0.600036\pi$
$828$	−926.358	+	1386.39i	−1.11879	+	1.67439i
$829$	158.394	−	158.394i	0.191066	−	0.191066i	−0.605091	−	0.796157i	$-0.706863\pi$
$829$	158.394	−	158.394i	0.191066	−	0.191066i	0.796157	+	0.605091i	$0.206863\pi$
$830$	−2872.44	+	571.364i	−3.46077	+	0.688390i
$831$	91.9883	−	222.079i	0.110696	−	0.267244i
$832$		−	1416.08i		−	1.70202i
$833$		0			0
$834$	2768.35			3.31937
$835$	−638.466	−	264.461i	−0.764629	−	0.316720i
$836$	−10.7092	−	53.8390i	−0.0128101	−	0.0644007i
$837$	−108.275	−	108.275i	−0.129361	−	0.129361i
$838$	1578.63	+	1054.81i	1.88381	+	1.25872i
$839$	−81.7732	+	411.101i	−0.0974650	+	0.489990i	0.900961	+	0.433901i	$0.142863\pi$
$839$	−81.7732	+	411.101i	−0.0974650	+	0.489990i	−0.998426	+	0.0560892i	$0.982137\pi$
$840$	168.487	−	112.579i	0.200579	−	0.134023i
$841$	−109.787	−	265.050i	−0.130544	−	0.315161i
$842$	−926.219	+	383.653i	−1.10002	+	0.455644i
$843$	−151.997	−	227.479i	−0.180305	−	0.269845i
$844$	−770.575	−	153.277i	−0.913004	−	0.181608i
$845$	359.290	−	537.716i	0.425196	−	0.636350i
$846$	316.088	−	316.088i	0.373626	−	0.373626i
$847$	309.484	−	61.5602i	0.365388	−	0.0726802i
$848$	428.953	−	1035.58i	0.505840	−	1.22121i
$849$		−	1572.09i		−	1.85170i
$850$		0			0
$851$	−1106.89			−1.30069
$852$	−744.051	−	308.196i	−0.873299	−	0.361732i
$853$	−319.537	−	1606.42i	−0.374603	−	1.88326i	−0.461664	−	0.887055i	$-0.652748\pi$
$853$	−319.537	−	1606.42i	−0.374603	−	1.88326i	0.0870612	−	0.996203i	$-0.472252\pi$
$854$	−443.819	−	443.819i	−0.519695	−	0.519695i
$855$	−208.468	−	139.294i	−0.243822	−	0.162917i
$856$	35.3720	−	177.827i	0.0413225	−	0.207742i
$857$	353.795	−	236.398i	0.412829	−	0.275844i	−0.331764	−	0.943363i	$-0.607644\pi$
$857$	353.795	−	236.398i	0.412829	−	0.275844i	0.744593	+	0.667519i	$0.232644\pi$
$858$	−244.765	−	590.914i	−0.285274	−	0.688711i
$859$	−1306.43	+	541.143i	−1.52088	+	0.629969i	−0.977767	−	0.209692i	$-0.932754\pi$
$859$	−1306.43	+	541.143i	−1.52088	+	0.629969i	−0.543111	+	0.839661i	$0.682754\pi$
$860$	232.954	+	348.641i	0.270877	+	0.405396i
$861$	7.05431	+	1.40319i	0.00819316	+	0.00162972i
$862$	25.1522	−	37.6429i	0.0291789	−	0.0436692i
$863$	−728.647	+	728.647i	−0.844319	+	0.844319i	−0.989417	−	0.145099i	$-0.953650\pi$
$863$	−728.647	+	728.647i	−0.844319	+	0.844319i	0.145099	+	0.989417i	$0.453650\pi$
$864$	−177.907	+	35.3879i	−0.205911	+	0.0409582i
$865$	−455.858	+	1100.54i	−0.527003	+	1.27230i
$866$			1139.12i			1.31538i
$867$		0			0
$868$	523.200			0.602765
$869$	96.6795	+	40.0460i	0.111254	+	0.0460828i
$870$	572.070	+	2875.99i	0.657552	+	3.30574i
$871$	687.019	+	687.019i	0.788770	+	0.788770i
$872$	−238.753	−	159.530i	−0.273799	−	0.182947i
$873$	248.017	−	1246.87i	0.284097	−	1.42825i
$874$	−322.156	+	215.258i	−0.368599	+	0.246290i
$875$	31.5235	+	76.1044i	0.0360268	+	0.0869764i
$876$	−294.215	+	121.868i	−0.335862	+	0.139119i
$877$	−341.988	−	511.822i	−0.389953	−	0.583605i	0.583608	−	0.812036i	$-0.301641\pi$
$877$	−341.988	−	511.822i	−0.389953	−	0.583605i	−0.973560	+	0.228430i	$0.926641\pi$
$878$	−977.774	−	194.491i	−1.11364	−	0.221516i
$879$	681.998	−	1020.68i	0.775880	−	1.16119i
$880$	−175.086	+	175.086i	−0.198961	+	0.198961i
$881$	1226.98	−	244.062i	1.39271	−	0.277028i	0.558974	−	0.829185i	$-0.311195\pi$
$881$	1226.98	−	244.062i	1.39271	−	0.277028i	0.833740	+	0.552158i	$0.186195\pi$
$882$	−462.400	+	1116.33i	−0.524263	+	1.26568i
$883$			1616.61i			1.83081i	0.402532	+	0.915406i	$0.368130\pi$
$883$			1616.61i			1.83081i	−0.402532	+	0.915406i	$0.631870\pi$
$884$		0			0
$885$	−1502.60			−1.69785
$886$	−1943.33	−	804.955i	−2.19338	−	0.908527i
$887$	93.9141	+	472.138i	0.105878	+	0.532287i	0.996924	+	0.0783730i	$0.0249725\pi$
$887$	93.9141	+	472.138i	0.105878	+	0.532287i	−0.891046	+	0.453914i	$0.850027\pi$
$888$	238.276	+	238.276i	0.268329	+	0.268329i
$889$	525.668	+	351.240i	0.591302	+	0.395096i
$890$	429.099	−	2157.23i	0.482134	−	2.42385i
$891$	181.974	−	121.591i	0.204236	−	0.136466i
$892$	527.250	+	1272.89i	0.591088	+	1.42701i
$893$	52.4530	−	21.7268i	0.0587380	−	0.0243301i
$894$	−219.954	−	329.184i	−0.246033	−	0.368215i
$895$	461.382	+	91.7746i	0.515510	+	0.102541i
$896$	119.962	−	179.535i	0.133886	−	0.200374i
$897$	−1744.79	+	1744.79i	−1.94514	+	1.94514i
$898$	−535.678	+	106.553i	−0.596523	+	0.118656i
$899$	−493.818	+	1192.18i	−0.549297	+	1.32612i
$900$		−	989.012i		−	1.09890i
$901$		0			0
$902$	5.29334			0.00586845
$903$	145.993	+	60.4725i	0.161676	+	0.0669684i
$904$	7.78965	+	39.1612i	0.00861687	+	0.0433199i
$905$	−50.5334	−	50.5334i	−0.0558381	−	0.0558381i
$906$	−1529.97	−	1022.29i	−1.68871	−	1.12836i
$907$	−14.5535	+	73.1656i	−0.0160458	+	0.0806677i	−0.987978	−	0.154591i	$-0.950594\pi$
$907$	−14.5535	+	73.1656i	−0.0160458	+	0.0806677i	0.971933	+	0.235259i	$0.0755939\pi$
$908$	−385.474	+	257.565i	−0.424531	+	0.283662i
$909$	257.195	+	620.924i	0.282943	+	0.683084i
$910$	852.122	−	352.961i	0.936398	−	0.387869i
$911$	187.315	+	280.337i	0.205615	+	0.307725i	0.919917	−	0.392113i	$-0.128256\pi$
$911$	187.315	+	280.337i	0.205615	+	0.307725i	−0.714302	+	0.699838i	$0.753256\pi$
$912$	−192.080	−	38.2072i	−0.210614	−	0.0418938i
$913$	−246.663	+	369.158i	−0.270168	+	0.404335i
$914$	−1730.30	+	1730.30i	−1.89311	+	1.89311i
$915$	−2157.52	+	429.157i	−2.35795	+	0.469024i
$916$	−527.510	+	1273.52i	−0.575884	+	1.39031i
$917$		−	98.6064i		−	0.107532i
$918$		0			0
$919$	−1030.62			−1.12146			−0.560728	−	0.828000i	$-0.689478\pi$
$919$	−1030.62			−1.12146			−0.560728	+	0.828000i	$0.689478\pi$
$920$	−531.537	−	220.170i	−0.577758	−	0.239315i
$921$	−10.8614	−	54.6040i	−0.0117931	−	0.0592877i
$922$	581.756	+	581.756i	0.630972	+	0.630972i
$923$	−519.476	−	347.103i	−0.562813	−	0.376060i
$924$	35.1624	−	176.773i	0.0380546	−	0.191313i
$925$	545.897	−	364.757i	0.590159	−	0.394332i
$926$	300.972	+	726.611i	0.325024	+	0.784677i
$927$	−158.509	+	65.6567i	−0.170992	+	0.0708271i
$928$	849.260	+	1271.01i	0.915151	+	1.36962i
$929$	188.411	+	37.4772i	0.202810	+	0.0403415i	0.295450	−	0.955358i	$-0.404530\pi$
$929$	188.411	+	37.4772i	0.202810	+	0.0403415i	−0.0926397	+	0.995700i	$0.529530\pi$
$930$	1863.86	−	2789.47i	2.00415	−	2.99943i
$931$	−108.516	+	108.516i	−0.116559	+	0.116559i
$932$	663.046	−	131.888i	0.711422	−	0.141511i
$933$	622.711	−	1503.36i	0.667429	−	1.61132i
$934$			1925.36i			2.06141i
$935$		0			0
$936$	393.790			0.420716
$937$	−99.6749	−	41.2867i	−0.106377	−	0.0440626i	0.328860	−	0.944379i	$-0.393335\pi$
$937$	−99.6749	−	41.2867i	−0.106377	−	0.0440626i	−0.435237	+	0.900316i	$0.643335\pi$
$938$	97.7238	+	491.291i	0.104183	+	0.523764i
$939$	−990.958	−	990.958i	−1.05533	−	1.05533i
$940$	411.278	+	274.807i	0.437530	+	0.292348i
$941$	−11.7986	+	59.3153i	−0.0125383	+	0.0630344i	−0.986548	−	0.163472i	$-0.947731\pi$
$941$	−11.7986	+	59.3153i	−0.0125383	+	0.0630344i	0.974010	+	0.226507i	$0.0727305\pi$
$942$	−2136.85	+	1427.79i	−2.26841	+	1.51571i
$943$	−7.81483	−	18.8667i	−0.00828720	−	0.0200071i
$944$	−568.443	+	235.457i	−0.602164	+	0.249424i
$945$	−42.2606	−	63.2475i	−0.0447202	−	0.0669286i
$946$	114.062	+	22.6884i	0.120573	+	0.0239835i
$947$	−1010.51	+	1512.33i	−1.06706	+	1.59697i	−0.301667	+	0.953413i	$0.597543\pi$
$947$	−1010.51	+	1512.33i	−1.06706	+	1.59697i	−0.765396	+	0.643559i	$0.777457\pi$
$948$	−509.896	+	509.896i	−0.537865	+	0.537865i
$949$	−242.301	+	48.1967i	−0.255323	+	0.0507868i
$950$	87.9470	−	212.323i	0.0925757	−	0.223498i
$951$		−	1610.11i		−	1.69307i
$952$		0			0
$953$	1182.89			1.24122			0.620612	−	0.784118i	$-0.286884\pi$
$953$	1182.89			1.24122			0.620612	+	0.784118i	$0.286884\pi$
$954$	2533.86	+	1049.56i	2.65604	+	1.10017i
$955$	−147.160	−	739.825i	−0.154095	−	0.774686i
$956$	320.729	+	320.729i	0.335491	+	0.335491i
$957$	369.614	+	246.968i	0.386222	+	0.258065i
$958$	446.885	−	2246.64i	0.466477	−	2.34514i
$959$	−345.383	+	230.778i	−0.360149	+	0.240644i
$960$	−979.193	−	2363.98i	−1.01999	−	2.46248i
$961$	476.118	−	197.214i	0.495440	−	0.205218i
$962$	852.122	+	1275.29i	0.885781	+	1.32567i
$963$	−722.425	−	143.699i	−0.750182	−	0.149220i
$964$	−241.769	+	361.833i	−0.250797	+	0.375345i
$965$	−1056.23	+	1056.23i	−1.09454	+	1.09454i
$966$	−1247.71	+	248.185i	−1.29163	+	0.256920i
$967$	597.009	−	1441.31i	0.617383	−	1.49049i	−0.237349	−	0.971425i	$-0.576278\pi$
$967$	597.009	−	1441.31i	0.617383	−	1.49049i	0.854732	−	0.519070i	$-0.173722\pi$
$968$			272.744i			0.281761i
$969$		0			0
$970$	2573.71			2.65331
$971$	−233.317	−	96.6433i	−0.240286	−	0.0995296i	0.259291	−	0.965799i	$-0.416511\pi$
$971$	−233.317	−	96.6433i	−0.240286	−	0.0995296i	−0.499577	+	0.866270i	$0.666511\pi$
$972$	327.963	+	1648.78i	0.337410	+	1.69628i
$973$	427.930	+	427.930i	0.439805	+	0.439805i
$974$	−1474.28	−	985.086i	−1.51364	−	1.01138i
$975$	285.533	−	1435.47i	0.292854	−	1.47228i
$976$	−748.956	+	500.436i	−0.767373	+	0.512742i
$977$	−139.293	−	336.283i	−0.142572	−	0.344199i	0.836423	−	0.548085i	$-0.184643\pi$
$977$	−139.293	−	336.283i	−0.142572	−	0.344199i	−0.978995	+	0.203886i	$0.934643\pi$
$978$	−124.556	+	51.5928i	−0.127358	+	0.0527534i
$979$	−185.246	−	277.241i	−0.189220	−	0.283188i
$980$	−1311.35	−	260.843i	−1.33811	−	0.266167i
$981$	−648.091	+	969.936i	−0.660643	+	0.988722i
$982$	1076.28	−	1076.28i	1.09601	−	1.09601i
$983$	−708.993	+	141.028i	−0.721255	+	0.143466i	−0.542051	−	0.840346i	$-0.682352\pi$
$983$	−708.993	+	141.028i	−0.721255	+	0.143466i	−0.179204	+	0.983812i	$0.557352\pi$
$984$	−2.37910	+	5.74365i	−0.00241778	+	0.00583704i
$985$		−	761.228i		−	0.772820i
$986$		0			0
$987$	186.413			0.188868
$988$	271.111	+	112.298i	0.274404	+	0.113662i
$989$	−87.5292	−	440.039i	−0.0885027	−	0.444933i
$990$	−428.399	−	428.399i	−0.432726	−	0.432726i
$991$	−1494.24	−	998.417i	−1.50781	−	1.00748i	−0.988216	−	0.153069i	$-0.951084\pi$
$991$	−1494.24	−	998.417i	−1.50781	−	1.00748i	−0.519591	−	0.854415i	$-0.673916\pi$
$992$	341.192	−	1715.29i	0.343943	−	1.72912i
$993$	1699.30	−	1135.44i	1.71128	−	1.14344i
$994$	−123.265	−	297.588i	−0.124009	−	0.299385i
$995$	86.9226	−	36.0045i	0.0873594	−	0.0361855i
$996$	−1699.74	−	2543.84i	−1.70656	−	2.55405i
$997$	−1699.87	−	338.126i	−1.70499	−	0.339144i	−0.756029	−	0.654538i	$-0.772863\pi$
$997$	−1699.87	−	338.126i	−1.70499	−	0.339144i	−0.948961	+	0.315394i	$0.897863\pi$
$998$	779.626	−	1166.79i	0.781188	−	1.16913i
$999$	89.4454	−	89.4454i	0.0895350	−	0.0895350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.r.249.3	yes	96
17.2	even	8	inner	289.3.e.r.214.9	yes	96
17.3	odd	16	inner	289.3.e.r.65.4	yes	96
17.4	even	4	inner	289.3.e.r.40.9	✓	96
17.5	odd	16	inner	289.3.e.r.224.10	yes	96
17.6	odd	16	inner	289.3.e.r.158.3	yes	96
17.7	odd	16	inner	289.3.e.r.131.9	yes	96
17.8	even	8	inner	289.3.e.r.75.3	yes	96
17.9	even	8	inner	289.3.e.r.75.4	yes	96
17.10	odd	16	inner	289.3.e.r.131.10	yes	96
17.11	odd	16	inner	289.3.e.r.158.4	yes	96
17.12	odd	16	inner	289.3.e.r.224.9	yes	96
17.13	even	4	inner	289.3.e.r.40.10	yes	96
17.14	odd	16	inner	289.3.e.r.65.3	yes	96
17.15	even	8	inner	289.3.e.r.214.10	yes	96
17.16	even	2	inner	289.3.e.r.249.4	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.3.e.r.40.9	✓	96	17.4	even	4	inner
289.3.e.r.40.10	yes	96	17.13	even	4	inner
289.3.e.r.65.3	yes	96	17.14	odd	16	inner
289.3.e.r.65.4	yes	96	17.3	odd	16	inner
289.3.e.r.75.3	yes	96	17.8	even	8	inner
289.3.e.r.75.4	yes	96	17.9	even	8	inner
289.3.e.r.131.9	yes	96	17.7	odd	16	inner
289.3.e.r.131.10	yes	96	17.10	odd	16	inner
289.3.e.r.158.3	yes	96	17.6	odd	16	inner
289.3.e.r.158.4	yes	96	17.11	odd	16	inner
289.3.e.r.214.9	yes	96	17.2	even	8	inner
289.3.e.r.214.10	yes	96	17.15	even	8	inner
289.3.e.r.224.9	yes	96	17.12	odd	16	inner
289.3.e.r.224.10	yes	96	17.5	odd	16	inner
289.3.e.r.249.3	yes	96	1.1	even	1	trivial
289.3.e.r.249.4	yes	96	17.16	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.74407 - 1.13663i) q^{2} +(-0.848504 - 4.26572i) q^{3} +(3.40954 + 3.40954i) q^{4} +(5.61992 + 3.75511i) q^{5} +(-2.52019 + 12.6698i) q^{6} +(-2.34806 + 1.56892i) q^{7} +(-0.934102 - 2.25512i) q^{8} +(-9.16146 + 3.79480i) q^{9} +O(q^{10})\)	\(q+(-2.74407 - 1.13663i) q^{2} +(-0.848504 - 4.26572i) q^{3} +(3.40954 + 3.40954i) q^{4} +(5.61992 + 3.75511i) q^{5} +(-2.52019 + 12.6698i) q^{6} +(-2.34806 + 1.56892i) q^{7} +(-0.934102 - 2.25512i) q^{8} +(-9.16146 + 3.79480i) q^{9} +(-11.1533 - 16.6920i) q^{10} +(-2.98487 - 0.593727i) q^{11} +(11.6511 - 17.4371i) q^{12} +(11.5039 - 11.5039i) q^{13} +(8.22652 - 1.63636i) q^{14} +(11.2497 - 27.1592i) q^{15} -12.0373i q^{16} +29.4529 q^{18} +(3.45602 + 1.43153i) q^{19} +(6.35814 + 31.9645i) q^{20} +(8.68492 + 8.68492i) q^{21} +(7.51583 + 5.02191i) q^{22} +(6.80324 - 34.2022i) q^{23} +(-8.82712 + 5.89809i) q^{24} +(7.91555 + 19.1098i) q^{25} +(-44.6432 + 18.4918i) q^{26} +(2.21406 + 3.31358i) q^{27} +(-13.3551 - 2.65650i) q^{28} +(18.6583 - 27.9241i) q^{29} +(-61.7399 + 61.7399i) q^{30} +(-37.6850 + 7.49600i) q^{31} +(-17.4184 + 42.0517i) q^{32} +13.2364i q^{33} -19.0874 q^{35} +(-44.1749 - 18.2978i) q^{36} +(-6.19239 - 31.1313i) q^{37} +(-7.85642 - 7.85642i) q^{38} +(-58.8336 - 39.3113i) q^{39} +(3.21865 - 16.1813i) q^{40} +(0.486907 - 0.325341i) q^{41} +(-13.9605 - 33.7035i) q^{42} +(11.8865 - 4.92353i) q^{43} +(-8.15269 - 12.2014i) q^{44} +(-65.7365 - 13.0758i) q^{45} +(-57.5437 + 86.1203i) q^{46} +(10.7320 - 10.7320i) q^{47} +(-51.3479 + 10.2137i) q^{48} +(-15.6996 + 37.9022i) q^{49} -61.4357i q^{50} +78.4462 q^{52} +(86.0309 + 35.6352i) q^{53} +(-2.30922 - 11.6092i) q^{54} +(-14.5452 - 14.5452i) q^{55} +(5.73144 + 3.82963i) q^{56} +(3.17405 - 15.9570i) q^{57} +(-82.9389 + 55.4180i) q^{58} +(-19.5605 - 47.2233i) q^{59} +(130.957 - 54.2441i) q^{60} +(-41.5737 - 62.2194i) q^{61} +(111.930 + 22.2643i) q^{62} +(15.5579 - 23.2840i) q^{63} +(61.5477 - 61.5477i) q^{64} +(107.850 - 21.4526i) q^{65} +(15.0449 - 36.3215i) q^{66} +59.7204i q^{67} -151.669 q^{69} +(52.3770 + 21.6953i) q^{70} +(-7.49194 - 37.6645i) q^{71} +(17.1155 + 17.1155i) q^{72} +(-12.6260 - 8.43645i) q^{73} +(-18.3924 + 92.4646i) q^{74} +(74.8007 - 49.9803i) q^{75} +(6.90257 + 16.6643i) q^{76} +(7.94017 - 3.28892i) q^{77} +(116.761 + 174.745i) q^{78} +(-33.7242 - 6.70816i) q^{79} +(45.2015 - 67.6489i) q^{80} +(-50.8507 + 50.8507i) q^{81} +(-1.70590 + 0.339324i) q^{82} +(55.8282 - 134.781i) q^{83} +59.2232i q^{84} -38.2134 q^{86} +(-134.948 - 55.8973i) q^{87} +(1.44925 + 7.28585i) q^{88} +(77.4719 + 77.4719i) q^{89} +(165.523 + 110.599i) q^{90} +(-8.96313 + 45.0607i) q^{91} +(139.810 - 93.4178i) q^{92} +(63.9516 + 154.393i) q^{93} +(-41.6475 + 17.2510i) q^{94} +(14.0470 + 21.0228i) q^{95} +(194.160 + 38.6209i) q^{96} +(-71.2255 + 106.596i) q^{97} +(86.1616 - 86.1616i) q^{98} +(29.5988 - 5.88757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q + 288 q^{18} + 384 q^{35} + 1920 q^{52} - 1152 q^{69} - 6240 q^{86}+O(q^{100}) \) 96 * q + 288 * q^18 + 384 * q^35 + 1920 * q^52 - 1152 * q^69 - 6240 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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