LMFDB - Embedded newform 245.4.l.d.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(68,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("245.68");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			68.3
Character	$\chi$	$=$	245.68
Dual form			245.4.l.d.227.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25845 - 4.69658i) q^{2} +(-2.23302 - 0.598336i) q^{3} +(-13.5460 + 7.82078i) q^{4} +(3.35008 - 10.6666i) q^{5} +11.2405i q^{6} +(26.2728 + 26.2728i) q^{8} +(-18.7543 - 10.8278i) q^{9} +O(q^{10})$	\(q+(-1.25845 - 4.69658i) q^{2} +(-2.23302 - 0.598336i) q^{3} +(-13.5460 + 7.82078i) q^{4} +(3.35008 - 10.6666i) q^{5} +11.2405i q^{6} +(26.2728 + 26.2728i) q^{8} +(-18.7543 - 10.8278i) q^{9} +(-54.3126 - 2.31057i) q^{10} +(18.2655 + 31.6368i) q^{11} +(34.9279 - 9.35891i) q^{12} +(-43.0940 + 43.0940i) q^{13} +(-13.8630 + 21.8143i) q^{15} +(27.7631 - 48.0870i) q^{16} +(2.81676 - 10.5123i) q^{17} +(-27.2524 + 101.707i) q^{18} +(-61.3794 + 106.312i) q^{19} +(38.0412 + 170.690i) q^{20} +(125.599 - 125.599i) q^{22} +(172.388 - 46.1912i) q^{23} +(-42.9477 - 74.3875i) q^{24} +(-102.554 - 71.4682i) q^{25} +(256.626 + 148.163i) q^{26} +(79.5366 + 79.5366i) q^{27} -230.609i q^{29} +(119.899 + 37.6567i) q^{30} +(-118.740 + 68.5546i) q^{31} +(26.3311 + 7.05539i) q^{32} +(-21.8579 - 81.5746i) q^{33} -52.9166 q^{34} +338.728 q^{36} +(60.0123 + 223.969i) q^{37} +(576.547 + 154.485i) q^{38} +(122.014 - 70.4450i) q^{39} +(368.258 - 192.226i) q^{40} -227.230i q^{41} +(151.453 + 151.453i) q^{43} +(-494.850 - 285.702i) q^{44} +(-178.325 + 163.771i) q^{45} +(-433.882 - 751.505i) q^{46} +(-324.950 + 87.0700i) q^{47} +(-90.7677 + 90.7677i) q^{48} +(-206.598 + 571.592i) q^{50} +(-12.5798 + 21.7888i) q^{51} +(246.722 - 920.779i) q^{52} +(-49.9612 + 186.458i) q^{53} +(273.458 - 473.642i) q^{54} +(398.649 - 88.8457i) q^{55} +(200.672 - 200.672i) q^{57} +(-1083.07 + 290.208i) q^{58} +(-3.99297 - 6.91603i) q^{59} +(17.1834 - 403.916i) q^{60} +(-135.243 - 78.0826i) q^{61} +(471.400 + 471.400i) q^{62} -576.754i q^{64} +(315.299 + 604.036i) q^{65} +(-355.615 + 205.314i) q^{66} +(-533.618 - 142.983i) q^{67} +(44.0586 + 164.429i) q^{68} -412.584 q^{69} +271.564 q^{71} +(-208.251 - 777.204i) q^{72} +(861.772 + 230.911i) q^{73} +(976.366 - 563.705i) q^{74} +(186.243 + 220.952i) q^{75} -1920.14i q^{76} +(-484.399 - 484.399i) q^{78} +(777.999 + 449.178i) q^{79} +(-419.918 - 457.234i) q^{80} +(162.334 + 281.170i) q^{81} +(-1067.21 + 285.957i) q^{82} +(-614.022 + 614.022i) q^{83} +(-102.694 - 65.2624i) q^{85} +(520.715 - 901.905i) q^{86} +(-137.981 + 514.954i) q^{87} +(-351.301 + 1311.07i) q^{88} +(-537.160 + 930.388i) q^{89} +(993.577 + 631.419i) q^{90} +(-1973.92 + 1973.92i) q^{92} +(306.168 - 82.0373i) q^{93} +(817.863 + 1416.58i) q^{94} +(928.367 + 1010.87i) q^{95} +(-54.5763 - 31.5097i) q^{96} +(174.230 + 174.230i) q^{97} -791.103i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q+O(q^{10}) $ 144 * q	$ 144 q + 32 q^{11} + 1152 q^{16} + 64 q^{18} + 1152 q^{22} - 768 q^{23} - 288 q^{25} + 2512 q^{30} - 1840 q^{32} - 9280 q^{36} - 864 q^{37} + 1216 q^{43} + 3552 q^{46} - 4960 q^{50} - 1056 q^{51} + 1384 q^{53} + 15744 q^{57} - 5296 q^{58} - 9104 q^{60} - 736 q^{65} - 1856 q^{67} - 13632 q^{71} + 8528 q^{72} - 10816 q^{78} + 12616 q^{81} + 11200 q^{85} - 8672 q^{86} + 10080 q^{88} + 21248 q^{92} - 416 q^{93} - 5888 q^{95}+O(q^{100}) $ 144 * q + 32 * q^11 + 1152 * q^16 + 64 * q^18 + 1152 * q^22 - 768 * q^23 - 288 * q^25 + 2512 * q^30 - 1840 * q^32 - 9280 * q^36 - 864 * q^37 + 1216 * q^43 + 3552 * q^46 - 4960 * q^50 - 1056 * q^51 + 1384 * q^53 + 15744 * q^57 - 5296 * q^58 - 9104 * q^60 - 736 * q^65 - 1856 * q^67 - 13632 * q^71 + 8528 * q^72 - 10816 * q^78 + 12616 * q^81 + 11200 * q^85 - 8672 * q^86 + 10080 * q^88 + 21248 * q^92 - 416 * q^93 - 5888 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.25845	−	4.69658i	−0.444928	−	1.66049i	−0.716128	−	0.697969i	$-0.754087\pi$
$2$	−1.25845	−	4.69658i	−0.444928	−	1.66049i	0.271200	−	0.962523i	$-0.412580\pi$
$3$	−2.23302	−	0.598336i	−0.429745	−	0.115150i	0.0374615	−	0.999298i	$-0.488073\pi$
$3$	−2.23302	−	0.598336i	−0.429745	−	0.115150i	−0.467206	+	0.884148i	$0.654740\pi$
$4$	−13.5460	+	7.82078i	−1.69325	+	0.977598i
$5$	3.35008	−	10.6666i	0.299640	−	0.954052i
$5$	3.35008	−	10.6666i	0.299640	−	0.954052i
$6$			11.2405i			0.764822i
$7$		0			0
$7$		0			0
$8$	26.2728	+	26.2728i	1.16110	+	1.16110i
$9$	−18.7543	−	10.8278i	−0.694604	−	0.401030i
$10$	−54.3126	−	2.31057i	−1.71751	−	0.0730665i
$11$	18.2655	+	31.6368i	0.500661	+	0.867170i	1.00000		0.000762948i	$0.000242854\pi$
$11$	18.2655	+	31.6368i	0.500661	+	0.867170i	−0.499339	+	0.866407i	$0.666424\pi$
$12$	34.9279	−	9.35891i	0.840236	−	0.225140i
$13$	−43.0940	+	43.0940i	−0.919394	+	0.919394i	−0.996985	−	0.0775917i	$-0.975277\pi$
$13$	−43.0940	+	43.0940i	−0.919394	+	0.919394i	0.0775917	+	0.996985i	$0.475277\pi$
$14$		0			0
$15$	−13.8630	+	21.8143i	−0.238628	+	0.375496i
$16$	27.7631	−	48.0870i	0.433798	−	0.751360i
$17$	2.81676	−	10.5123i	0.0401862	−	0.149977i	−0.942918	−	0.333026i	$-0.891930\pi$
$17$	2.81676	−	10.5123i	0.0401862	−	0.149977i	0.983104	+	0.183049i	$0.0585969\pi$
$18$	−27.2524	+	101.707i	−0.356859	+	1.33181i
$19$	−61.3794	+	106.312i	−0.741126	+	1.28367i	0.210856	+	0.977517i	$0.432375\pi$
$19$	−61.3794	+	106.312i	−0.741126	+	1.28367i	−0.951983	+	0.306152i	$0.900959\pi$
$20$	38.0412	+	170.690i	0.425314	+	1.90838i
$21$		0			0
$22$	125.599	−	125.599i	1.21717	−	1.21717i
$23$	172.388	−	46.1912i	1.56284	−	0.418762i	0.629280	−	0.777178i	$-0.283350\pi$
$23$	172.388	−	46.1912i	1.56284	−	0.418762i	0.933562	+	0.358416i	$0.116683\pi$
$24$	−42.9477	−	74.3875i	−0.365277	−	0.632679i
$25$	−102.554	−	71.4682i	−0.820431	−	0.571745i
$26$	256.626	+	148.163i	1.93571	+	1.11758i
$27$	79.5366	+	79.5366i	0.566919	+	0.566919i
$28$		0			0
$29$		−	230.609i		−	1.47665i	−0.674443	−	0.738326i	$-0.735616\pi$
$29$		−	230.609i		−	1.47665i	0.674443	−	0.738326i	$-0.264384\pi$
$30$	119.899	+	37.6567i	0.729680	+	0.229172i
$31$	−118.740	+	68.5546i	−0.687946	+	0.397186i	−0.802842	−	0.596192i	$-0.796680\pi$
$31$	−118.740	+	68.5546i	−0.687946	+	0.397186i	0.114896	+	0.993378i	$0.463347\pi$
$32$	26.3311	+	7.05539i	0.145460	+	0.0389759i
$33$	−21.8579	−	81.5746i	−0.115302	−	0.430313i
$34$	−52.9166			−0.266915
$35$		0			0
$36$	338.728			1.56818
$37$	60.0123	+	223.969i	0.266648	+	0.995142i	0.961234	+	0.275733i	$0.0889207\pi$
$37$	60.0123	+	223.969i	0.266648	+	0.995142i	−0.694587	+	0.719409i	$0.744413\pi$
$38$	576.547	+	154.485i	2.46127	+	0.659495i
$39$	122.014	−	70.4450i	0.500973	−	0.289237i
$40$	368.258	−	192.226i	1.45567	−	0.759839i
$41$		−	227.230i		−	0.865547i	−0.901503	−	0.432774i	$-0.857535\pi$
$41$		−	227.230i		−	0.865547i	0.901503	−	0.432774i	$-0.142465\pi$
$42$		0			0
$43$	151.453	+	151.453i	0.537124	+	0.537124i	0.922683	−	0.385559i	$-0.125992\pi$
$43$	151.453	+	151.453i	0.537124	+	0.537124i	−0.385559	+	0.922683i	$0.625992\pi$
$44$	−494.850	−	285.702i	−1.69549	−	0.978890i
$45$	−178.325	+	163.771i	−0.590735	+	0.542524i
$46$	−433.882	−	751.505i	−1.39070	−	2.40877i
$47$	−324.950	+	87.0700i	−1.00849	+	0.270223i	−0.724996	−	0.688753i	$-0.758159\pi$
$47$	−324.950	+	87.0700i	−1.00849	+	0.270223i	−0.283489	+	0.958976i	$0.591492\pi$
$48$	−90.7677	+	90.7677i	−0.272941	+	0.272941i
$49$		0			0
$50$	−206.598	+	571.592i	−0.584346	+	1.61671i
$51$	−12.5798	+	21.7888i	−0.0345396	+	0.0598244i
$52$	246.722	−	920.779i	0.657965	−	2.45556i
$53$	−49.9612	+	186.458i	−0.129485	+	0.483244i	−0.999960	−	0.00896868i	$-0.997145\pi$
$53$	−49.9612	+	186.458i	−0.129485	+	0.483244i	0.870475	+	0.492213i	$0.163812\pi$
$54$	273.458	−	473.642i	0.689127	−	1.19360i
$55$	398.649	−	88.8457i	0.977343	−	0.217817i
$56$		0			0
$57$	200.672	−	200.672i	0.466310	−	0.466310i
$58$	−1083.07	+	290.208i	−2.45197	+	0.657004i
$59$	−3.99297	−	6.91603i	−0.00881086	−	0.0152609i	0.861586	−	0.507611i	$-0.169471\pi$
$59$	−3.99297	−	6.91603i	−0.00881086	−	0.0152609i	−0.870397	+	0.492350i	$0.836138\pi$
$60$	17.1834	−	403.916i	0.0369728	−	0.869090i
$61$	−135.243	−	78.0826i	−0.283870	−	0.163893i	0.351304	−	0.936261i	$-0.385738\pi$
$61$	−135.243	−	78.0826i	−0.283870	−	0.163893i	−0.635174	+	0.772369i	$0.719072\pi$
$62$	471.400	+	471.400i	0.965611	+	0.965611i
$63$		0			0
$64$		−	576.754i		−	1.12647i
$65$	315.299	+	604.036i	0.601662	+	1.15264i
$66$	−355.615	+	205.314i	−0.663230	+	0.382916i
$67$	−533.618	−	142.983i	−0.973013	−	0.260718i	−0.262913	−	0.964819i	$-0.584683\pi$
$67$	−533.618	−	142.983i	−0.973013	−	0.260718i	−0.710099	+	0.704102i	$0.751350\pi$
$68$	44.0586	+	164.429i	0.0785719	+	0.293234i
$69$	−412.584			−0.719844
$70$		0			0
$71$	271.564			0.453925			0.226963	−	0.973903i	$-0.427120\pi$
$71$	271.564			0.453925			0.226963	+	0.973903i	$0.427120\pi$
$72$	−208.251	−	777.204i	−0.340870	−	1.27214i
$73$	861.772	+	230.911i	1.38168	+	0.370221i	0.871732	−	0.489983i	$-0.162997\pi$
$73$	861.772	+	230.911i	1.38168	+	0.370221i	0.509950	+	0.860204i	$0.329664\pi$
$74$	976.366	−	563.705i	1.53379	−	0.885533i
$75$	186.243	+	220.952i	0.286740	+	0.340177i
$76$		−	1920.14i		−	2.89809i
$77$		0			0
$78$	−484.399	−	484.399i	−0.703172	−	0.703172i
$79$	777.999	+	449.178i	1.10800	+	0.639702i	0.938310	−	0.345796i	$-0.112391\pi$
$79$	777.999	+	449.178i	1.10800	+	0.639702i	0.169687	+	0.985498i	$0.445724\pi$
$80$	−419.918	−	457.234i	−0.586853	−	0.639003i
$81$	162.334	+	281.170i	0.222680	+	0.385693i
$82$	−1067.21	+	285.957i	−1.43723	+	0.385106i
$83$	−614.022	+	614.022i	−0.812021	+	0.812021i	−0.984937	−	0.172916i	$-0.944681\pi$
$83$	−614.022	+	614.022i	−0.812021	+	0.812021i	0.172916	+	0.984937i	$0.444681\pi$
$84$		0			0
$85$	−102.694	−	65.2624i	−0.131044	−	0.0832789i
$86$	520.715	−	901.905i	0.652909	−	1.13087i
$87$	−137.981	+	514.954i	−0.170036	+	0.634584i
$88$	−351.301	+	1311.07i	−0.425555	+	1.58819i
$89$	−537.160	+	930.388i	−0.639762	+	1.10810i	0.345723	+	0.938337i	$0.387634\pi$
$89$	−537.160	+	930.388i	−0.639762	+	1.10810i	−0.985485	+	0.169763i	$0.945700\pi$
$90$	993.577	+	631.419i	1.16369	+	0.739527i
$91$		0			0
$92$	−1973.92	+	1973.92i	−2.23690	+	2.23690i
$93$	306.168	−	82.0373i	0.341377	−	0.0914718i
$94$	817.863	+	1416.58i	0.897406	+	1.55435i
$95$	928.367	+	1010.87i	1.00262	+	1.09171i
$96$	−54.5763	−	31.5097i	−0.0580226	−	0.0334994i
$97$	174.230	+	174.230i	0.182375	+	0.182375i	0.792390	−	0.610015i	$-0.208837\pi$
$97$	174.230	+	174.230i	0.182375	+	0.182375i	−0.610015	+	0.792390i	$0.708837\pi$
$98$		0			0
$99$		−	791.103i		−	0.803119i
$100$	1948.13	+	166.055i	1.94813	+	0.166055i
$101$	−1429.75	+	825.464i	−1.40857	+	0.813236i	−0.995250	−	0.0973525i	$-0.968963\pi$
$101$	−1429.75	+	825.464i	−1.40857	+	0.813236i	−0.413315	+	0.910588i	$0.635629\pi$
$102$	118.164	+	31.6619i	0.114706	+	0.0307353i
$103$	169.747	+	633.505i	0.162385	+	0.606030i	0.998359	+	0.0572611i	$0.0182368\pi$
$103$	169.747	+	633.505i	0.162385	+	0.606030i	−0.835974	+	0.548769i	$0.815097\pi$
$104$	−2264.39			−2.13502
$105$		0			0
$106$	938.587			0.860035
$107$	208.704	+	778.895i	0.188563	+	0.703726i	0.993840	+	0.110827i	$0.0353499\pi$
$107$	208.704	+	778.895i	0.188563	+	0.703726i	−0.805277	+	0.592899i	$0.797983\pi$
$108$	−1699.44	−	455.364i	−1.51415	−	0.405717i
$109$	−1568.83	+	905.763i	−1.37859	+	0.795930i	−0.991990	−	0.126316i	$-0.959685\pi$
$109$	−1568.83	+	905.763i	−1.37859	+	0.795930i	−0.386602	+	0.922247i	$0.626351\pi$
$110$	−918.950	−	1760.48i	−0.796531	−	1.52596i
$111$		−	536.035i		−	0.458362i
$112$		0			0
$113$	−253.074	−	253.074i	−0.210683	−	0.210683i	0.593875	−	0.804558i	$-0.297598\pi$
$113$	−253.074	−	253.074i	−0.210683	−	0.210683i	−0.804558	+	0.593875i	$0.797598\pi$
$114$	−1195.01	−	689.937i	−0.981777	−	0.566829i
$115$	84.8093	−	1993.54i	0.0687697	−	1.61651i
$116$	1803.54	+	3123.82i	1.44357	+	2.50034i
$117$	1274.81	−	341.585i	1.00732	−	0.269910i
$118$	−27.4568	+	27.4568i	−0.0214203	+	0.0214203i
$119$		0			0
$120$	−937.342	+	208.902i	−0.713060	+	0.158917i
$121$	−1.75964	+	3.04779i	−0.00132205	+	0.00228985i
$122$	−196.525	+	733.443i	−0.145841	+	0.544285i
$123$	−135.960	+	507.410i	−0.0996676	+	0.371965i
$124$	1072.30	−	1857.28i	0.776576	−	1.34507i
$125$	−1105.89	+	854.480i	−0.791309	+	0.611416i
$126$		0			0
$127$	−499.840	+	499.840i	−0.349241	+	0.349241i	−0.859827	−	0.510586i	$-0.829429\pi$
$127$	−499.840	+	499.840i	−0.349241	+	0.349241i	0.510586	+	0.859827i	$0.329429\pi$
$128$	−2498.12	+	669.370i	−1.72504	+	0.462223i
$129$	−247.577	−	428.817i	−0.168976	−	0.292676i
$130$	2440.12	−	2240.97i	1.64625	−	1.51190i
$131$	−358.241	−	206.830i	−0.238929	−	0.137945i	0.375756	−	0.926719i	$-0.377383\pi$
$131$	−358.241	−	206.830i	−0.238929	−	0.137945i	−0.614684	+	0.788773i	$0.710717\pi$
$132$	934.064	+	934.064i	0.615908	+	0.615908i
$133$		0			0
$134$			2686.12i			1.73168i
$135$	1114.84	−	581.933i	0.710743	−	0.370999i
$136$	350.191	−	202.183i	0.220799	−	0.127478i
$137$	−117.922	−	31.5972i	−0.0735385	−	0.0197046i	0.221862	−	0.975078i	$-0.428786\pi$
$137$	−117.922	−	31.5972i	−0.0735385	−	0.0197046i	−0.295401	+	0.955373i	$0.595453\pi$
$138$	519.214	+	1937.73i	0.320279	+	1.19530i
$139$	−0.984410			−0.000600695			−0.000300347	−	1.00000i	$-0.500096\pi$
$139$	−0.984410			−0.000600695			−0.000300347		1.00000i	$0.500096\pi$
$140$		0			0
$141$	777.717			0.464508
$142$	−341.748	−	1275.42i	−0.201964	−	0.753740i
$143$	−2150.49	−	576.222i	−1.25757	−	0.336966i
$144$	−1041.35	+	601.226i	−0.602635	+	0.347932i
$145$	−2459.82	−	772.558i	−1.40880	−	0.442465i
$146$		−	4337.97i		−	2.45899i
$147$		0			0
$148$	−2564.54	−	2564.54i	−1.42435	−	1.42435i
$149$	−823.016	−	475.169i	−0.452511	−	0.261257i	0.256379	−	0.966576i	$-0.417470\pi$
$149$	−823.016	−	475.169i	−0.452511	−	0.261257i	−0.708890	+	0.705319i	$0.750804\pi$
$150$	803.340	−	1152.76i	0.437283	−	0.627484i
$151$	−553.685	−	959.010i	−0.298399	−	0.516842i	0.677371	−	0.735642i	$-0.263119\pi$
$151$	−553.685	−	959.010i	−0.298399	−	0.516842i	−0.975770	+	0.218800i	$0.929786\pi$
$152$	−4405.72	+	1180.51i	−2.35100	+	0.629947i
$153$	−166.652	+	166.652i	−0.0880587	+	0.0880587i
$154$		0			0
$155$	333.457	+	1496.22i	0.172800	+	0.775350i
$156$	−1101.87	+	1908.50i	−0.565515	+	0.979500i
$157$	−259.436	+	968.229i	−0.131881	+	0.492185i	−0.999991	−	0.00418557i	$-0.998668\pi$
$157$	−259.436	+	968.229i	−0.131881	+	0.492185i	0.868111	+	0.496371i	$0.165334\pi$
$158$	1130.53	−	4219.20i	0.569243	−	2.12444i
$159$	223.129	−	386.470i	0.111291	−	0.192762i
$160$	163.468	−	257.228i	0.0807707	−	0.127098i
$161$		0			0
$162$	1116.25	−	1116.25i	0.541364	−	0.541364i
$163$	386.018	−	103.433i	0.185492	−	0.0497025i	−0.164877	−	0.986314i	$-0.552723\pi$
$163$	386.018	−	103.433i	0.185492	−	0.0497025i	0.350369	+	0.936612i	$0.386056\pi$
$164$	1777.12	+	3078.06i	0.846157	+	1.46559i
$165$	−943.352	−	40.1321i	−0.445090	−	0.0189350i
$166$	3656.52	+	2111.09i	1.70964	+	0.987064i
$167$	−389.010	−	389.010i	−0.180254	−	0.180254i	0.611212	−	0.791467i	$-0.290682\pi$
$167$	−389.010	−	389.010i	−0.180254	−	0.180254i	−0.791467	+	0.611212i	$0.790682\pi$
$168$		0			0
$169$		−	1517.18i		−	0.690569i
$170$	−177.275	+	564.442i	−0.0799787	+	0.254651i
$171$	2302.26	−	1329.21i	1.02958	−	0.594428i
$172$	−3236.06	−	867.099i	−1.43458	−	0.384393i
$173$	378.517	+	1412.64i	0.166347	+	0.620817i	0.997865	+	0.0653178i	$0.0208061\pi$
$173$	378.517	+	1412.64i	0.166347	+	0.620817i	−0.831517	+	0.555499i	$0.812527\pi$
$174$	2592.16			1.12938
$175$		0			0
$176$	2028.43			0.868742
$177$	4.77828	+	17.8328i	0.00202914	+	0.00757284i
$178$	5045.63	+	1351.97i	2.12464	+	0.569295i
$179$	951.912	−	549.587i	0.397482	−	0.229486i	−0.287915	−	0.957656i	$-0.592962\pi$
$179$	951.912	−	549.587i	0.397482	−	0.229486i	0.685397	+	0.728170i	$0.259629\pi$
$180$	1134.77	−	3613.08i	0.469891	−	1.49613i
$181$			2558.15i			1.05053i	0.850940	+	0.525264i	$0.176033\pi$
$181$			2558.15i			1.05053i	−0.850940	+	0.525264i	$0.823967\pi$
$182$		0			0
$183$	255.281	+	255.281i	0.103120	+	0.103120i
$184$	5742.68	+	3315.54i	2.30085	+	1.32839i
$185$	2590.04	+	110.186i	1.02932	+	0.0437892i
$186$	−770.590	−	1334.70i	−0.303776	−	0.526156i
$187$	384.026	−	102.899i	0.150175	−	0.0402393i
$188$	3720.81	−	3720.81i	1.44345	−	1.44345i
$189$		0			0
$190$	3579.32	−	5632.27i	1.36669	−	2.15057i
$191$	414.077	−	717.203i	0.156867	−	0.271701i	−0.776870	−	0.629661i	$-0.783194\pi$
$191$	414.077	−	717.203i	0.156867	−	0.271701i	0.933737	+	0.357959i	$0.116527\pi$
$192$	−345.093	+	1287.90i	−0.129713	+	0.484096i
$193$	−417.195	+	1556.99i	−0.155598	+	0.580699i	0.843456	+	0.537199i	$0.180517\pi$
$193$	−417.195	+	1556.99i	−0.155598	+	0.580699i	−0.999053	+	0.0434999i	$0.986149\pi$
$194$	599.026	−	1037.54i	0.221689	−	0.383976i
$195$	−342.653	−	1537.48i	−0.125835	−	0.564621i
$196$		0			0
$197$	−2246.52	+	2246.52i	−0.812477	+	0.812477i	−0.985005	−	0.172527i	$-0.944807\pi$
$197$	−2246.52	+	2246.52i	−0.812477	+	0.812477i	0.172527	+	0.985005i	$0.444807\pi$
$198$	−3715.48	+	995.560i	−1.33357	+	0.357330i
$199$	−1934.14	−	3350.03i	−0.688982	−	1.19335i	−0.972167	−	0.234287i	$-0.924724\pi$
$199$	−1934.14	−	3350.03i	−0.688982	−	1.19335i	0.283185	−	0.959065i	$-0.408609\pi$
$200$	−816.708	−	4572.04i	−0.288750	−	1.61646i
$201$	1106.03	+	638.566i	0.388126	+	0.224084i
$202$	5676.12	+	5676.12i	1.97708	+	1.97708i
$203$		0			0
$204$		−	393.535i		−	0.135063i
$205$	−2423.78	−	761.241i	−0.825777	−	0.259353i
$206$	2761.69	−	1594.46i	0.934059	−	0.539279i
$207$	−3733.17	−	1000.30i	−1.25349	−	0.335872i
$208$	875.840	+	3268.68i	0.291964	+	1.08963i
$209$	−4484.51			−1.48421
$210$		0			0
$211$	−4515.36			−1.47322			−0.736612	−	0.676316i	$-0.763575\pi$
$211$	−4515.36			−1.47322			−0.736612	+	0.676316i	$0.763575\pi$
$212$	−781.471	−	2916.49i	−0.253168	−	0.944837i
$213$	−606.408	−	162.486i	−0.195072	−	0.0522694i
$214$	3395.50	−	1960.39i	1.08463	−	0.626214i
$215$	2122.87	−	1108.11i	0.673388	−	0.351500i
$216$			4179.29i			1.31650i
$217$		0			0
$218$	6228.28	+	6228.28i	1.93501	+	1.93501i
$219$	−1786.19	−	1031.26i	−0.551140	−	0.318201i
$220$	−4705.26	+	4321.25i	−1.44195	+	1.32427i
$221$	331.631	+	574.402i	0.100941	+	0.174835i
$222$	−2517.53	+	674.570i	−0.761106	+	0.203938i
$223$	361.498	−	361.498i	0.108555	−	0.108555i	−0.650743	−	0.759298i	$-0.725543\pi$
$223$	361.498	−	361.498i	0.108555	−	0.108555i	0.759298	+	0.650743i	$0.225543\pi$
$224$		0			0
$225$	1149.48	+	2450.77i	0.340588	+	0.726154i
$226$	−870.102	+	1507.06i	−0.256099	+	0.443576i
$227$	910.081	−	3396.47i	0.266098	−	0.993090i	−0.695477	−	0.718548i	$-0.744807\pi$
$227$	910.081	−	3396.47i	0.266098	−	0.993090i	0.961575	−	0.274542i	$-0.0885263\pi$
$228$	−1148.89	+	4287.71i	−0.333715	+	1.24544i
$229$	1104.92	−	1913.78i	0.318844	−	0.552254i	−0.661403	−	0.750031i	$-0.730039\pi$
$229$	1104.92	−	1913.78i	0.318844	−	0.552254i	0.980247	+	0.197777i	$0.0633721\pi$
$230$	−9469.56	+	2110.45i	−2.71480	+	0.605039i
$231$		0			0
$232$	6058.72	−	6058.72i	1.71455	−	1.71455i
$233$	3033.83	−	812.912i	0.853016	−	0.228565i	0.194286	−	0.980945i	$-0.437761\pi$
$233$	3033.83	−	812.912i	0.853016	−	0.228565i	0.658729	+	0.752380i	$0.271094\pi$
$234$	−3208.56	−	5557.39i	−0.896368	−	1.55255i
$235$	−159.865	+	3757.81i	−0.0443763	+	1.04312i
$236$	108.178	+	62.4563i	0.0298380	+	0.0172270i
$237$	−1468.53	−	1468.53i	−0.402495	−	0.402495i
$238$		0			0
$239$		−	749.777i		−	0.202925i	−0.994839	−	0.101462i	$-0.967648\pi$
$239$		−	749.777i		−	0.202925i	0.994839	−	0.101462i	$-0.0323522\pi$
$240$	664.106	+	1272.26i	0.178616	+	0.342185i
$241$	−5107.45	+	2948.79i	−1.36514	+	0.788167i	−0.990303	−	0.138922i	$-0.955636\pi$
$241$	−5107.45	+	2948.79i	−1.36514	+	0.788167i	−0.374841	+	0.927089i	$0.622303\pi$
$242$	16.5286	+	4.42883i	0.00439050	+	0.00117643i
$243$	−980.295	−	3658.51i	−0.258790	−	0.965817i
$244$	2442.67			0.640885
$245$		0			0
$246$	2554.19			0.661989
$247$	−1936.33	−	7226.50i	−0.498810	−	1.86158i
$248$	−4920.74	−	1318.51i	−1.25995	−	0.337603i
$249$	1738.52	−	1003.73i	0.442466	−	0.255458i
$250$	5404.84	+	4118.58i	1.36733	+	1.04193i
$251$			3068.86i			0.771732i	0.922555	+	0.385866i	$0.126097\pi$
$251$			3068.86i			0.771732i	−0.922555	+	0.385866i	$0.873903\pi$
$252$		0			0
$253$	4610.10	+	4610.10i	1.14559	+	1.14559i
$254$	2976.56	+	1718.52i	0.735299	+	0.424525i
$255$	190.270	+	207.178i	0.0467261	+	0.0508784i
$256$	3980.49	+	6894.41i	0.971799	+	1.68320i
$257$	2292.27	−	614.211i	0.556373	−	0.149080i	0.0303332	−	0.999540i	$-0.490343\pi$
$257$	2292.27	−	614.211i	0.556373	−	0.149080i	0.526039	+	0.850460i	$0.323676\pi$
$258$	−1702.41	+	1702.41i	−0.410804	+	0.410804i
$259$		0			0
$260$	−8995.07	−	5716.38i	−2.14558	−	1.36352i
$261$	−2496.99	+	4324.90i	−0.592182	+	1.02569i
$262$	−520.569	+	1942.79i	−0.122751	+	0.458115i
$263$	−851.578	+	3178.13i	−0.199660	+	0.745141i	0.791351	+	0.611362i	$0.209378\pi$
$263$	−851.578	+	3178.13i	−0.199660	+	0.745141i	−0.991011	+	0.133779i	$0.957289\pi$
$264$	1568.92	−	2717.46i	0.365760	−	0.633515i
$265$	1821.50	+	1157.57i	0.422241	+	0.268335i
$266$		0			0
$267$	1756.17	−	1756.17i	0.402532	−	0.402532i
$268$	8346.63	−	2236.47i	1.90243	−	0.509755i
$269$	−3434.83	−	5949.30i	−0.778532	−	1.34846i	−0.932788	−	0.360426i	$-0.882631\pi$
$269$	−3434.83	−	5949.30i	−0.778532	−	1.34846i	0.154256	−	0.988031i	$-0.450702\pi$
$270$	−4136.06	−	4503.61i	−0.932269	−	1.01512i
$271$	6114.10	+	3529.98i	1.37050	+	0.791258i	0.990991	−	0.133931i	$-0.0427601\pi$
$271$	6114.10	+	3529.98i	1.37050	+	0.791258i	0.379508	+	0.925189i	$0.376093\pi$
$272$	−427.303	−	427.303i	−0.0952539	−	0.0952539i
$273$		0			0
$274$			593.595i			0.130877i
$275$	387.825	−	4549.89i	0.0850425	−	0.997703i
$276$	5588.86	−	3226.73i	1.21888	−	0.703718i
$277$	1038.63	+	278.299i	0.225289	+	0.0603660i	0.369697	−	0.929152i	$-0.379461\pi$
$277$	1038.63	+	278.299i	0.225289	+	0.0603660i	−0.144409	+	0.989518i	$0.546128\pi$
$278$	1.23883	+	4.62336i	0.000267266	+	0.000997449i
$279$	2969.18			0.637134
$280$		0			0
$281$	−1015.21			−0.215524			−0.107762	−	0.994177i	$-0.534369\pi$
$281$	−1015.21			−0.215524			−0.107762	+	0.994177i	$0.534369\pi$
$282$	−978.714	−	3652.61i	−0.206672	−	0.771311i
$283$	6163.08	+	1651.39i	1.29455	+	0.346873i	0.839386	−	0.543536i	$-0.182915\pi$
$283$	6163.08	+	1651.39i	1.29455	+	0.346873i	0.455162	+	0.890409i	$0.349581\pi$
$284$	−3678.60	+	2123.84i	−0.768609	+	0.443757i
$285$	−1468.23	−	2812.76i	−0.305158	−	0.584609i
$286$			10825.1i			2.23812i
$287$		0			0
$288$	−417.427	−	417.427i	−0.0854066	−	0.0854066i
$289$	4152.21	+	2397.28i	0.845147	+	0.487946i
$290$	−532.837	+	12524.9i	−0.107894	+	2.53617i
$291$	−284.811	−	493.307i	−0.0573743	−	0.0993752i
$292$	−13479.5	+	3611.81i	−2.70146	+	0.723854i
$293$	6725.58	−	6725.58i	1.34100	−	1.34100i	0.445930	−	0.895068i	$-0.352873\pi$
$293$	6725.58	−	6725.58i	1.34100	−	1.34100i	0.895068	−	0.445930i	$-0.147127\pi$
$294$		0			0
$295$	−87.1475	+	19.4223i	−0.0171997	+	0.00383325i
$296$	−4307.59	+	7460.97i	−0.845857	+	1.46507i
$297$	−1063.51	+	3969.06i	−0.207781	+	0.775449i
$298$	−1195.95	+	4463.34i	−0.232481	+	0.867632i
$299$	−5438.32	+	9419.44i	−1.05186	+	1.82187i
$300$	−4250.86	−	1536.44i	−0.818079	−	0.295688i
$301$		0			0
$302$	−3807.29	+	3807.29i	−0.725446	+	0.725446i
$303$	3686.56	−	987.810i	0.698968	−	0.187288i
$304$	3408.16	+	5903.11i	0.642998	+	1.11371i
$305$	−1285.95	+	1181.00i	−0.241421	+	0.221718i
$306$	992.415	+	572.971i	0.185401	+	0.107041i
$307$	−6263.08	−	6263.08i	−1.16434	−	1.16434i	−0.983515	−	0.180827i	$-0.942123\pi$
$307$	−6263.08	−	6263.08i	−1.16434	−	1.16434i	−0.180827	−	0.983515i	$-0.557877\pi$
$308$		0			0
$309$		−	1516.20i		−	0.279137i
$310$	6607.48	−	3449.02i	1.21058	−	0.631907i
$311$	−2418.09	+	1396.08i	−0.440891	+	0.254549i	−0.703976	−	0.710224i	$-0.748594\pi$
$311$	−2418.09	+	1396.08i	−0.440891	+	0.254549i	0.263084	+	0.964773i	$0.415260\pi$
$312$	5056.44	+	1354.87i	0.917514	+	0.245847i
$313$	−748.278	−	2792.61i	−0.135128	−	0.504306i	−0.999997	−	0.00230827i	$-0.999265\pi$
$313$	−748.278	−	2792.61i	−0.135128	−	0.504306i	0.864869	−	0.501998i	$-0.167401\pi$
$314$	4873.85			0.875947
$315$		0			0
$316$	−14051.7			−2.50149
$317$	1548.41	+	5778.73i	0.274344	+	1.02387i	0.956279	+	0.292455i	$0.0944721\pi$
$317$	1548.41	+	5778.73i	0.274344	+	1.02387i	−0.681935	+	0.731413i	$0.738861\pi$
$318$	−2095.88	−	561.591i	−0.369596	−	0.0990328i
$319$	7295.73	−	4212.19i	1.28051	−	0.739302i
$320$	−6152.02	−	1932.17i	−1.07471	−	0.337537i
$321$		−	1864.16i		−	0.324135i
$322$		0			0
$323$	944.695	+	944.695i	0.162738	+	0.162738i
$324$	−4397.94	−	2539.15i	−0.754105	−	0.435383i
$325$	7499.30	−	1339.61i	1.27996	−	0.228640i
$326$	−971.564	−	1682.80i	−0.165061	−	0.285894i
$327$	4045.18	−	1083.90i	0.684094	−	0.183302i
$328$	5969.97	−	5969.97i	1.00499	−	1.00499i
$329$		0			0
$330$	998.673	+	4481.03i	0.166591	+	0.747493i
$331$	−2452.08	+	4247.13i	−0.407186	+	0.705267i	−0.994573	−	0.104039i	$-0.966823\pi$
$331$	−2452.08	+	4247.13i	−0.407186	+	0.705267i	0.587387	+	0.809306i	$0.300157\pi$
$332$	3515.41	−	13119.7i	0.581124	−	2.16878i
$333$	1299.60	−	4850.19i	0.213867	−	0.798164i
$334$	−1337.47	+	2316.57i	−0.219111	+	0.379511i
$335$	−3312.81	+	5212.90i	−0.540292	+	0.850183i
$336$		0			0
$337$	976.895	−	976.895i	0.157908	−	0.157908i	−0.623731	−	0.781639i	$-0.714384\pi$
$337$	976.895	−	976.895i	0.157908	−	0.157908i	0.781639	+	0.623731i	$0.214384\pi$
$338$	−7125.56	+	1909.29i	−1.14668	+	0.307253i
$339$	413.696	+	716.542i	0.0662798	+	0.114800i
$340$	1901.50	+	80.8937i	0.303304	+	0.0129032i
$341$	−4337.70	−	2504.37i	−0.688855	−	0.397711i
$342$	−9140.00	−	9140.00i	−1.44513	−	1.44513i
$343$		0			0
$344$			7958.16i			1.24731i
$345$	−1382.19	+	4400.88i	−0.215694	+	0.686769i
$346$	6158.26	−	3555.47i	0.956849	−	0.552437i
$347$	−488.028	−	130.767i	−0.0755006	−	0.0202303i	0.220871	−	0.975303i	$-0.429110\pi$
$347$	−488.028	−	130.767i	−0.0755006	−	0.0202303i	−0.296372	+	0.955073i	$0.595777\pi$
$348$	−2158.25	−	8054.68i	−0.332454	−	1.24074i
$349$	2840.46			0.435663			0.217831	−	0.975986i	$-0.430102\pi$
$349$	2840.46			0.435663			0.217831	+	0.975986i	$0.430102\pi$
$350$		0			0
$351$	−6855.09			−1.04244
$352$	257.741	+	961.902i	0.0390274	+	0.145652i
$353$	−5760.09	−	1543.41i	−0.868494	−	0.232712i	−0.203058	−	0.979167i	$-0.565088\pi$
$353$	−5760.09	−	1543.41i	−0.868494	−	0.232712i	−0.665437	+	0.746454i	$0.731755\pi$
$354$	77.7399	−	44.8831i	0.0116718	−	0.00673873i
$355$	909.761	−	2896.67i	0.136014	−	0.433068i
$356$		−	16804.0i		−	2.50172i
$357$		0			0
$358$	−3779.11	−	3779.11i	−0.557911	−	0.557911i
$359$	−11042.3	−	6375.27i	−1.62337	−	0.937253i	−0.986010	−	0.166688i	$-0.946693\pi$
$359$	−11042.3	−	6375.27i	−1.62337	−	0.937253i	−0.637361	−	0.770566i	$-0.719974\pi$
$360$	−8987.80	−	382.359i	−1.31583	−	0.0559781i
$361$	−4105.36	−	7110.70i	−0.598537	−	1.03670i
$362$	12014.5	−	3219.29i	1.74439	−	0.467409i
$363$	5.75292	−	5.75292i	0.000831819	−	0.000831819i
$364$		0			0
$365$	5350.05	−	8418.63i	0.767217	−	1.20726i
$366$	877.690	−	1520.20i	0.125349	−	0.217110i
$367$	−2672.89	+	9975.37i	−0.380174	+	1.41883i	0.465462	+	0.885068i	$0.345888\pi$
$367$	−2672.89	+	9975.37i	−0.380174	+	1.41883i	−0.845636	+	0.533760i	$0.820778\pi$
$368$	2564.82	−	9572.03i	0.363316	−	1.35592i
$369$	−2460.41	+	4261.55i	−0.347110	+	0.601213i
$370$	−2741.93	−	12303.0i	−0.385260	−	1.72866i
$371$		0			0
$372$	−3505.75	+	3505.75i	−0.488614	+	0.488614i
$373$	−5556.25	+	1488.79i	−0.771292	+	0.206667i	−0.622942	−	0.782268i	$-0.714063\pi$
$373$	−5556.25	+	1488.79i	−0.771292	+	0.206667i	−0.148350	+	0.988935i	$0.547396\pi$
$374$	−966.550	−	1674.11i	−0.133634	−	0.231461i
$375$	2980.74	−	1246.38i	0.410466	−	0.171634i
$376$	−10824.9	−	6249.76i	−1.48471	−	0.857198i
$377$	9937.84	+	9937.84i	1.35763	+	1.35763i
$378$		0			0
$379$		−	3568.88i		−	0.483697i	−0.970314	−	0.241849i	$-0.922246\pi$
$379$		−	3568.88i		−	0.483697i	0.970314	−	0.241849i	$-0.0777538\pi$
$380$	−20481.4	−	6432.63i	−2.76493	−	0.868386i
$381$	1415.22	−	817.080i	0.190300	−	0.109869i
$382$	−3889.50	−	1042.19i	−0.520953	−	0.139589i
$383$	−396.266	−	1478.88i	−0.0528675	−	0.197304i	0.934441	−	0.356118i	$-0.115900\pi$
$383$	−396.266	−	1478.88i	−0.0528675	−	0.197304i	−0.987309	+	0.158814i	$0.949233\pi$
$384$	5978.87			0.794552
$385$		0			0
$386$	7837.56			1.03348
$387$	−1200.49	−	4480.29i	−0.157686	−	0.588491i
$388$	−3722.73	−	997.503i	−0.487096	−	0.130517i
$389$	1821.15	−	1051.44i	0.237368	−	0.137044i	−0.376599	−	0.926377i	$-0.622906\pi$
$389$	1821.15	−	1051.44i	0.237368	−	0.137044i	0.613966	+	0.789332i	$0.289573\pi$
$390$	−6789.68	+	3544.13i	−0.881562	+	0.460164i
$391$		−	1942.30i		−	0.251219i
$392$		0			0
$393$	676.205	+	676.205i	0.0867939	+	0.0867939i
$394$	13378.1	+	7723.85i	1.71061	+	0.987619i
$395$	7397.58	−	6793.85i	0.942310	−	0.865406i
$396$	6187.04	+	10716.3i	0.785128	+	1.35988i
$397$	−10416.5	+	2791.08i	−1.31684	+	0.352848i	−0.847795	−	0.530324i	$-0.822070\pi$
$397$	−10416.5	+	2791.08i	−1.31684	+	0.352848i	−0.469050	+	0.883172i	$0.655404\pi$
$398$	−13299.7	+	13299.7i	−1.67501	+	1.67501i
$399$		0			0
$400$	−6283.90	+	2947.34i	−0.785488	+	0.368417i
$401$	−504.934	+	874.571i	−0.0628807	+	0.108913i	−0.895752	−	0.444554i	$-0.853362\pi$
$401$	−504.934	+	874.571i	−0.0628807	+	0.108913i	0.832871	+	0.553467i	$0.186695\pi$
$402$	1607.20	−	5998.16i	0.199403	−	0.744181i
$403$	2162.69	−	8071.27i	0.267323	−	0.997664i
$404$	12911.6	−	22363.5i	1.59003	−	2.75402i
$405$	3542.97	−	789.609i	0.434695	−	0.0968790i
$406$		0			0
$407$	−5989.51	+	5989.51i	−0.729457	+	0.729457i
$408$	−902.957	+	241.947i	−0.109566	+	0.0293582i
$409$	5132.87	+	8890.38i	0.620547	+	1.07482i	0.989384	+	0.145325i	$0.0464229\pi$
$409$	5132.87	+	8890.38i	0.620547	+	1.07482i	−0.368837	+	0.929494i	$0.620244\pi$
$410$	−525.031	+	12341.5i	−0.0632426	+	1.48659i
$411$	244.417	+	141.114i	0.0293338	+	0.0169359i
$412$	−7253.90	−	7253.90i	−0.867413	−	0.867413i
$413$		0			0
$414$			18791.9i			2.23085i
$415$	4492.52	+	8606.57i	0.531396	+	1.01802i
$416$	−1438.76	+	830.666i	−0.169569	+	0.0979008i
$417$	2.19821	+	0.589008i	0.000258146	+	6.91699e-5i
$418$	5643.51	+	21061.9i	0.660367	+	2.46452i
$419$	−5463.78			−0.637047			−0.318524	−	0.947915i	$-0.603187\pi$
$419$	−5463.78			−0.637047			−0.318524	+	0.947915i	$0.603187\pi$
$420$		0			0
$421$	854.085			0.0988731			0.0494365	−	0.998777i	$-0.484257\pi$
$421$	854.085			0.0988731			0.0494365	+	0.998777i	$0.484257\pi$
$422$	5682.33	+	21206.8i	0.655478	+	2.44628i
$423$	7036.99	+	1885.56i	0.808865	+	0.216735i
$424$	−6211.38	+	3586.14i	−0.711441	+	0.410751i
$425$	−1040.16	+	876.769i	−0.118719	+	0.100069i
$426$			3052.52i			0.347172i
$427$		0			0
$428$	−8918.68	−	8918.68i	−1.00724	−	1.00724i
$429$	4457.32	+	2573.43i	0.501635	+	0.289619i
$430$	−7875.85	−	8575.73i	−0.883272	−	0.961764i
$431$	580.093	+	1004.75i	0.0648309	+	0.112290i	0.896619	−	0.442803i	$-0.146016\pi$
$431$	580.093	+	1004.75i	0.0648309	+	0.112290i	−0.831788	+	0.555093i	$0.812683\pi$
$432$	6032.86	−	1616.50i	0.671889	−	0.180032i
$433$	3549.00	−	3549.00i	0.393889	−	0.393889i	−0.482182	−	0.876071i	$-0.660156\pi$
$433$	3549.00	−	3549.00i	0.393889	−	0.393889i	0.876071	+	0.482182i	$0.160156\pi$
$434$		0			0
$435$	5030.57	+	3196.93i	0.554477	+	0.352371i
$436$	14167.6	−	24538.9i	1.55620	−	2.69542i
$437$	−5670.38	+	21162.1i	−0.620712	+	2.31653i
$438$	−2595.56	+	9686.78i	−0.283153	+	1.05674i
$439$	−273.361	+	473.476i	−0.0297194	+	0.0514756i	−0.880503	−	0.474041i	$-0.842795\pi$
$439$	−273.361	+	473.476i	−0.0297194	+	0.0514756i	0.850783	+	0.525517i	$0.176128\pi$
$440$	12807.8	+	8139.40i	1.38770	+	0.881888i
$441$		0			0
$442$	2280.39	−	2280.39i	0.245400	−	0.245400i
$443$	17151.9	−	4595.84i	1.83953	−	0.492900i	0.840709	−	0.541487i	$-0.182138\pi$
$443$	17151.9	−	4595.84i	1.83953	−	0.492900i	0.998819	+	0.0485867i	$0.0154717\pi$
$444$	4192.21	+	7261.12i	0.448094	+	0.776121i
$445$	8124.57	+	8846.56i	0.865487	+	0.942398i
$446$	−2152.73	−	1242.88i	−0.228553	−	0.131955i
$447$	1553.50	+	1553.50i	0.164381	+	0.164381i
$448$		0			0
$449$		−	17447.1i		−	1.83380i	−0.399112	−	0.916902i	$-0.630682\pi$
$449$		−	17447.1i		−	1.83380i	0.399112	−	0.916902i	$-0.369318\pi$
$450$	10063.7	−	8482.81i	1.05424	−	0.888630i
$451$	7188.85	−	4150.49i	0.750576	−	0.433345i
$452$	5407.37	+	1448.90i	0.562702	+	0.150776i
$453$	662.579	+	2472.78i	0.0687212	+	0.256471i
$454$	−17097.1			−1.76741
$455$		0			0
$456$	10544.4			1.08287
$457$	2396.82	+	8945.04i	0.245336	+	0.915605i	0.973214	+	0.229899i	$0.0738396\pi$
$457$	2396.82	+	8945.04i	0.245336	+	0.915605i	−0.727879	+	0.685706i	$0.759494\pi$
$458$	−10378.7	−	2780.97i	−1.05888	−	0.283725i
$459$	1060.15	−	612.077i	0.107807	−	0.0622425i
$460$	14442.2	+	27667.8i	1.46385	+	2.80439i
$461$			11684.1i			1.18044i	0.807243	+	0.590219i	$0.200959\pi$
$461$			11684.1i			1.18044i	−0.807243	+	0.590219i	$0.799041\pi$
$462$		0			0
$463$	−9508.03	−	9508.03i	−0.954375	−	0.954375i	0.0446288	−	0.999004i	$-0.485789\pi$
$463$	−9508.03	−	9508.03i	−0.954375	−	0.954375i	−0.999004	+	0.0446288i	$0.985789\pi$
$464$	−11089.3	−	6402.40i	−1.10950	−	0.640569i
$465$	150.625	−	3540.61i	0.0150216	−	0.353100i
$466$	−7635.81	−	13225.6i	−0.759061	−	1.31473i
$467$	12964.9	−	3473.93i	1.28467	−	0.344228i	0.449039	−	0.893512i	$-0.351766\pi$
$467$	12964.9	−	3473.93i	1.28467	−	0.344228i	0.835635	+	0.549285i	$0.185100\pi$
$468$	−14597.1	+	14597.1i	−1.44178	+	1.44178i
$469$		0			0
$470$	17850.0	−	3978.18i	1.75183	−	0.390425i
$471$	1158.65	−	2006.84i	0.113350	−	0.196328i
$472$	76.7968	−	286.609i	0.00748911	−	0.0279497i
$473$	−2025.12	+	7557.85i	−0.196861	+	0.734694i
$474$	−5049.00	+	8745.13i	−0.489258	+	0.847420i
$475$	13892.6	−	6516.06i	1.34197	−	0.629426i
$476$		0			0
$477$	2955.92	−	2955.92i	0.283736	−	0.283736i
$478$	−3521.39	+	943.554i	−0.336955	+	0.0902869i
$479$	361.137	+	625.508i	0.0344484	+	0.0596664i	0.882736	−	0.469870i	$-0.155699\pi$
$479$	361.137	+	625.508i	0.0344484	+	0.0596664i	−0.848287	+	0.529536i	$0.822366\pi$
$480$	−518.937	+	476.585i	−0.0493461	+	0.0453189i
$481$	−12237.9	−	7065.54i	−1.16008	−	0.669773i
$482$	20276.7	+	20276.7i	1.91614	+	1.91614i
$483$		0			0
$484$		−	55.0472i		−	0.00516972i
$485$	2442.13	−	1274.76i	0.228642	−	0.119348i
$486$	−15948.8	+	9208.07i	−1.48859	+	0.859438i
$487$	−13917.9	−	3729.30i	−1.29504	−	0.347004i	−0.455465	−	0.890254i	$-0.650527\pi$
$487$	−13917.9	−	3729.30i	−1.29504	−	0.347004i	−0.839571	+	0.543250i	$0.817193\pi$
$488$	−1501.76	−	5604.65i	−0.139307	−	0.519899i
$489$	−923.873			−0.0854376
$490$		0			0
$491$	12781.9			1.17482			0.587412	−	0.809288i	$-0.300147\pi$
$491$	12781.9			1.17482			0.587412	+	0.809288i	$0.300147\pi$
$492$	−2126.63	−	7936.69i	−0.194870	−	0.727264i
$493$	−2424.23	−	649.570i	−0.221464	−	0.0593411i
$494$	−31503.1	+	18188.3i	−2.86921	+	1.65654i
$495$	−8438.40	−	2650.26i	−0.766218	−	0.240647i
$496$			7613.14i			0.689194i
$497$		0			0
$498$	−6901.94	−	6901.94i	−0.621051	−	0.621051i
$499$	−5582.37	−	3222.98i	−0.500804	−	0.289139i	0.228242	−	0.973605i	$-0.426702\pi$
$499$	−5582.37	−	3222.98i	−0.500804	−	0.289139i	−0.729045	+	0.684465i	$0.760036\pi$
$500$	8297.65	−	20223.7i	0.742165	−	1.80886i
$501$	635.909	+	1101.43i	0.0567072	+	0.0982197i
$502$	14413.1	−	3861.99i	1.28145	−	0.343365i
$503$	7078.21	−	7078.21i	0.627439	−	0.627439i	−0.319984	−	0.947423i	$-0.603678\pi$
$503$	7078.21	−	7078.21i	0.627439	−	0.627439i	0.947423	+	0.319984i	$0.103678\pi$
$504$		0			0
$505$	4015.15	+	18015.9i	0.353806	+	1.58752i
$506$	15850.2	−	27453.3i	1.39254	−	2.41195i
$507$	−907.784	+	3387.89i	−0.0795189	+	0.296769i
$508$	2861.69	−	10680.0i	0.249935	−	0.932769i
$509$	−3180.96	+	5509.58i	−0.277001	+	0.479780i	−0.970638	−	0.240545i	$-0.922674\pi$
$509$	−3180.96	+	5509.58i	−0.277001	+	0.479780i	0.693637	+	0.720325i	$0.256007\pi$
$510$	733.585	−	1154.34i	0.0636935	−	0.100226i
$511$		0			0
$512$	12740.9	−	12740.9i	1.09975	−	1.09975i
$513$	−13337.6	+	3573.80i	−1.14790	+	0.307578i
$514$	−5769.39	−	9992.87i	−0.495091	−	0.857523i
$515$	7326.03	+	311.664i	0.626842	+	0.0266671i
$516$	6707.36	+	3872.50i	0.572239	+	0.330382i
$517$	−8690.00	−	8690.00i	−0.739238	−	0.739238i
$518$		0			0
$519$		−	3380.94i		−	0.285948i
$520$	−7585.91	+	24153.5i	−0.639739	+	2.03692i
$521$	−15522.6	+	8961.96i	−1.30529	+	0.753609i	−0.981306	−	0.192453i	$-0.938356\pi$
$521$	−15522.6	+	8961.96i	−1.30529	+	0.753609i	−0.323984	+	0.946063i	$0.605022\pi$
$522$	23454.6	+	6284.64i	1.96663	+	0.526956i
$523$	−207.555	−	774.607i	−0.0173533	−	0.0647633i	0.956706	−	0.291055i	$-0.0940063\pi$
$523$	−207.555	−	774.607i	−0.0173533	−	0.0647633i	−0.974060	+	0.226292i	$0.927340\pi$
$524$	6470.30			0.539421
$525$		0			0
$526$	15998.0			1.32613
$527$	386.204	+	1441.33i	0.0319228	+	0.119137i
$528$	−4529.52	−	1213.68i	−0.373337	−	0.100035i
$529$	17047.0	−	9842.12i	1.40109	−	0.808919i
$530$	3144.34	−	10011.6i	0.257701	−	0.820518i
$531$			172.940i			0.0141337i
$532$		0			0
$533$	9792.26	+	9792.26i	0.795779	+	0.795779i
$534$	−10458.1	−	6037.96i	−0.847499	−	0.489304i
$535$	9007.36	+	383.191i	0.727892	+	0.0309660i
$536$	−10263.1	−	17776.2i	−0.827047	−	1.43249i
$537$	−2454.48	+	657.675i	−0.197241	+	0.0528506i
$538$	−23618.8	+	23618.8i	−1.89271	+	1.89271i
$539$		0			0
$540$	−10550.5	+	16601.8i	−0.840777	+	1.32301i
$541$	−6653.89	+	11524.9i	−0.528785	+	0.915883i	0.470651	+	0.882319i	$0.344019\pi$
$541$	−6653.89	+	11524.9i	−0.528785	+	0.915883i	−0.999437	+	0.0335638i	$0.989314\pi$
$542$	8884.56	−	33157.6i	0.704105	−	2.62775i
$543$	1530.63	−	5712.39i	0.120968	−	0.451459i
$544$	148.337	−	256.927i	0.0116910	−	0.0202493i
$545$	4405.74	+	19768.5i	0.346277	+	1.55374i
$546$		0			0
$547$	−9565.99	+	9565.99i	−0.747737	+	0.747737i	−0.974054	−	0.226317i	$-0.927331\pi$
$547$	−9565.99	+	9565.99i	−0.747737	+	0.747737i	0.226317	+	0.974054i	$0.427331\pi$
$548$	1844.49	−	494.229i	0.143782	−	0.0385263i
$549$	1690.93	+	2928.77i	0.131452	+	0.227681i
$550$	−21857.0	+	3904.33i	−1.69452	+	0.302693i
$551$	24516.5	+	14154.6i	1.89553	+	1.09439i
$552$	−10839.7	−	10839.7i	−0.835813	−	0.835813i
$553$		0			0
$554$		−	5228.22i		−	0.400949i
$555$	−5717.68	−	1795.76i	−0.437301	−	0.137344i
$556$	13.3348	−	7.69886i	0.00101713	−	0.000587238i
$557$	3765.15	+	1008.87i	0.286418	+	0.0767454i	0.399167	−	0.916878i	$-0.369299\pi$
$557$	3765.15	+	1008.87i	0.286418	+	0.0767454i	−0.112750	+	0.993623i	$0.535966\pi$
$558$	−3736.55	−	13945.0i	−0.283478	−	1.05796i
$559$	−13053.4			−0.987656
$560$		0			0
$561$	−919.105			−0.0691705
$562$	1277.59	+	4768.02i	0.0958927	+	0.357877i
$563$	5439.57	+	1457.53i	0.407195	+	0.109108i	0.456602	−	0.889671i	$-0.349066\pi$
$563$	5439.57	+	1457.53i	0.407195	+	0.109108i	−0.0494069	+	0.998779i	$0.515733\pi$
$564$	−10534.9	+	6082.35i	−0.786527	+	0.454102i
$565$	−3547.26	+	1851.63i	−0.264132	+	0.137873i
$566$		−	31023.6i		−	2.30392i
$567$		0			0
$568$	7134.73	+	7134.73i	0.527054	+	0.527054i
$569$	−13159.6	−	7597.67i	−0.969556	−	0.559773i	−0.0704549	−	0.997515i	$-0.522445\pi$
$569$	−13159.6	−	7597.67i	−0.969556	−	0.559773i	−0.899101	+	0.437742i	$0.855778\pi$
$570$	−11362.7	+	10435.3i	−0.834965	+	0.766822i
$571$	−1769.71	−	3065.22i	−0.129702	−	0.224651i	0.793859	−	0.608102i	$-0.208069\pi$
$571$	−1769.71	−	3065.22i	−0.129702	−	0.224651i	−0.923561	+	0.383451i	$0.874735\pi$
$572$	33637.1	−	9013.02i	2.45880	−	0.658835i
$573$	−1353.77	+	1353.77i	−0.0986991	+	0.0986991i
$574$		0			0
$575$	−20980.3	−	7583.16i	−1.52163	−	0.549982i
$576$	−6244.98	+	10816.6i	−0.451749	+	0.782452i
$577$	3929.45	−	14664.9i	0.283509	−	1.05807i	−0.666412	−	0.745584i	$-0.732171\pi$
$577$	3929.45	−	14664.9i	0.283509	−	1.05807i	0.949922	−	0.312488i	$-0.101162\pi$
$578$	6033.69	−	22518.0i	0.434201	−	1.62046i
$579$	1863.21	−	3227.18i	0.133735	−	0.231635i
$580$	39362.7	−	8772.63i	2.81801	−	0.628040i
$581$		0			0
$582$	−1958.44	+	1958.44i	−0.139484	+	0.139484i
$583$	−6811.50	+	1825.14i	−0.483883	+	0.129656i
$584$	16574.5	+	28707.8i	1.17441	+	2.03414i
$585$	627.166	−	14742.3i	0.0443250	−	1.04191i
$586$	−40051.0	−	23123.4i	−2.82336	−	1.63007i
$587$	−982.935	−	982.935i	−0.0691143	−	0.0691143i	0.671705	−	0.740819i	$-0.265562\pi$
$587$	−982.935	−	982.935i	−0.0691143	−	0.0691143i	−0.740819	+	0.671705i	$0.765562\pi$
$588$		0			0
$589$		−	16831.4i		−	1.17746i
$590$	200.889	+	384.853i	0.0140177	+	0.0268545i
$591$	6360.70	−	3672.35i	0.442715	−	0.255601i
$592$	12436.1	+	3332.25i	0.863381	+	0.231342i
$593$	−5564.66	−	20767.6i	−0.385351	−	1.43815i	−0.837613	−	0.546264i	$-0.816050\pi$
$593$	−5564.66	−	20767.6i	−0.385351	−	1.43815i	0.452262	−	0.891885i	$-0.350617\pi$
$594$	19979.4			1.38008
$595$		0			0
$596$	14864.8			1.02162
$597$	2314.53	+	8637.94i	0.158672	+	0.592173i
$598$	51083.0	+	13687.7i	3.49321	+	0.936003i
$599$	−16394.6	+	9465.44i	−1.11831	+	0.645655i	−0.940968	−	0.338495i	$-0.890082\pi$
$599$	−16394.6	+	9465.44i	−1.11831	+	0.645655i	−0.177339	+	0.984150i	$0.556749\pi$
$600$	−911.890	+	10698.1i	−0.0620462	+	0.727915i
$601$		−	17782.5i		−	1.20693i	−0.797389	−	0.603465i	$-0.793786\pi$
$601$		−	17782.5i		−	1.20693i	0.797389	−	0.603465i	$-0.206214\pi$
$602$		0			0
$603$	8459.46	+	8459.46i	0.571303	+	0.571303i
$604$	15000.4	+	8660.50i	1.01053	+	0.583428i
$605$	26.6147	+	28.9798i	0.00178850	+	0.00194743i
$606$	−9278.66	−	16071.1i	−0.621980	−	1.07730i
$607$	6434.59	−	1724.14i	0.430267	−	0.115290i	−0.0371845	−	0.999308i	$-0.511839\pi$
$607$	6434.59	−	1724.14i	0.430267	−	0.115290i	0.467451	+	0.884019i	$0.345172\pi$
$608$	−2366.26	+	2366.26i	−0.157836	+	0.157836i
$609$		0			0
$610$	7164.98	+	4553.36i	0.475577	+	0.302230i
$611$	10251.2	−	17755.6i	0.678754	−	1.17564i
$612$	954.116	−	3560.81i	0.0630193	−	0.235191i
$613$	294.255	−	1098.17i	0.0193880	−	0.0723570i	−0.955554	−	0.294816i	$-0.904742\pi$
$613$	294.255	−	1098.17i	0.0193880	−	0.0723570i	0.974942	+	0.222459i	$0.0714083\pi$
$614$	−21533.3	+	37296.8i	−1.41533	+	2.45143i
$615$	4956.88	+	3150.10i	0.325009	+	0.206544i
$616$		0			0
$617$	17773.8	−	17773.8i	1.15972	−	1.15972i	0.175179	−	0.984537i	$-0.443950\pi$
$617$	17773.8	−	17773.8i	1.15972	−	1.15972i	0.984537	−	0.175179i	$-0.0560505\pi$
$618$	−7120.94	+	1908.05i	−0.463505	+	0.124196i
$619$	−5945.74	−	10298.3i	−0.386074	−	0.668699i	0.605844	−	0.795584i	$-0.292836\pi$
$619$	−5945.74	−	10298.3i	−0.386074	−	0.668699i	−0.991918	+	0.126884i	$0.959502\pi$
$620$	−16218.6	−	17659.9i	−1.05057	−	1.14393i
$621$	17385.0	+	10037.3i	1.12341	+	0.648601i
$622$	9599.85	+	9599.85i	0.618841	+	0.618841i
$623$		0			0
$624$		−	7823.08i		−	0.501881i
$625$	5409.60	+	14658.7i	0.346215	+	0.938155i
$626$	−12174.1	+	7028.70i	−0.777274	+	0.448759i
$627$	10014.0	+	2683.24i	0.637832	+	0.170907i
$628$	−4057.99	−	15144.6i	−0.257853	−	0.962319i
$629$	2523.47			0.159964
$630$		0			0
$631$	−23901.0			−1.50790			−0.753949	−	0.656933i	$-0.771853\pi$
$631$	−23901.0			−1.50790			−0.753949	+	0.656933i	$0.771853\pi$
$632$	8639.04	+	32241.3i	0.543738	+	2.02926i
$633$	10082.9	+	2701.70i	0.633110	+	0.169641i
$634$	25191.7	−	14544.4i	1.57806	−	0.911094i
$635$	3657.10	+	7006.11i	0.228547	+	0.437841i
$636$			6980.17i			0.435191i
$637$		0			0
$638$	−28964.2	−	28964.2i	−1.79734	−	1.79734i
$639$	−5092.99	−	2940.44i	−0.315298	−	0.182038i
$640$	−1229.00	+	28889.0i	−0.0759068	+	1.78428i
$641$	1037.29	+	1796.64i	0.0639165	+	0.110707i	0.896213	−	0.443624i	$-0.146308\pi$
$641$	1037.29	+	1796.64i	0.0639165	+	0.110707i	−0.832296	+	0.554331i	$0.812974\pi$
$642$	−8755.20	+	2345.95i	−0.538225	+	0.144217i
$643$	12479.8	−	12479.8i	0.765406	−	0.765406i	−0.211888	−	0.977294i	$-0.567961\pi$
$643$	12479.8	−	12479.8i	0.765406	−	0.765406i	0.977294	+	0.211888i	$0.0679613\pi$
$644$		0			0
$645$	−5403.43	+	1204.24i	−0.329860	+	0.0735149i
$646$	3247.99	−	5625.69i	0.197818	−	0.342631i
$647$	2305.64	−	8604.76i	0.140099	−	0.522856i	−0.859826	−	0.510588i	$-0.829428\pi$
$647$	2305.64	−	8604.76i	0.140099	−	0.522856i	0.999925	−	0.0122689i	$-0.00390540\pi$
$648$	−3122.16	+	11652.1i	−0.189275	+	0.706383i
$649$	145.868	−	252.650i	0.00882250	−	0.0152810i
$650$	−15729.0	−	33535.3i	−0.949144	−	2.02363i
$651$		0			0
$652$	−4420.07	+	4420.07i	−0.265496	+	0.265496i
$653$	12957.8	−	3472.02i	0.776533	−	0.208071i	0.151277	−	0.988491i	$-0.451661\pi$
$653$	12957.8	−	3472.02i	0.776533	−	0.208071i	0.625256	+	0.780420i	$0.284995\pi$
$654$	−10181.3	−	17634.5i	−0.608745	−	1.05438i
$655$	−3406.32	+	3128.32i	−0.203200	+	0.186616i
$656$	−10926.8	−	6308.61i	−0.650337	−	0.375472i
$657$	−13661.7	−	13661.7i	−0.811252	−	0.811252i
$658$		0			0
$659$			15987.7i			0.945057i	0.881315	+	0.472529i	$0.156659\pi$
$659$			15987.7i			0.945057i	−0.881315	+	0.472529i	$0.843341\pi$
$660$	13092.5	−	6834.12i	0.772159	−	0.403057i
$661$	−3731.25	+	2154.24i	−0.219559	+	0.126763i	−0.605746	−	0.795658i	$-0.707125\pi$
$661$	−3731.25	+	2154.24i	−0.219559	+	0.126763i	0.386187	+	0.922421i	$0.373792\pi$
$662$	23032.8	+	6171.62i	1.35226	+	0.362337i
$663$	−396.854	−	1481.08i	−0.0232466	−	0.0867577i
$664$	−32264.1			−1.88568
$665$		0			0
$666$	−24414.8			−1.42050
$667$	−10652.1	−	39754.1i	−0.618367	−	2.30778i
$668$	8311.89	+	2227.16i	0.481432	+	0.128999i
$669$	−1023.53	+	590.935i	−0.0591508	+	0.0341508i
$670$	28651.8	+	8998.72i	1.65211	+	0.518882i
$671$		−	5704.88i		−	0.328218i
$672$		0			0
$673$	10710.4	+	10710.4i	0.613456	+	0.613456i	0.943845	−	0.330389i	$-0.107180\pi$
$673$	10710.4	+	10710.4i	0.613456	+	0.613456i	−0.330389	+	0.943845i	$0.607180\pi$
$674$	−5817.44	−	3358.70i	−0.332462	−	0.191947i
$675$	−2472.45	−	13841.1i	−0.140985	−	0.789252i
$676$	11865.5	+	20551.7i	0.675099	+	1.16931i
$677$	−7960.66	+	2133.05i	−0.451924	+	0.121093i	−0.477600	−	0.878578i	$-0.658493\pi$
$677$	−7960.66	+	2133.05i	−0.451924	+	0.121093i	0.0256753	+	0.999670i	$0.491826\pi$
$678$	2844.68	−	2844.68i	0.161135	−	0.161135i
$679$		0			0
$680$	−983.441	−	4412.69i	−0.0554607	−	0.248851i
$681$	−4064.46	+	7039.85i	−0.228708	+	0.396134i
$682$	−6303.23	+	23524.0i	−0.353905	+	1.32079i
$683$	−4457.78	+	16636.7i	−0.249740	+	0.932042i	0.721202	+	0.692725i	$0.243590\pi$
$683$	−4457.78	+	16636.7i	−0.249740	+	0.932042i	−0.970942	+	0.239317i	$0.923077\pi$
$684$	−20790.9	+	36010.9i	−1.16222	+	2.01303i
$685$	−732.084	+	1151.98i	−0.0408343	+	0.0642553i
$686$		0			0
$687$	−3612.39	+	3612.39i	−0.200613	+	0.200613i
$688$	11487.7	−	3078.12i	0.636576	−	0.170570i
$689$	−5882.18	−	10188.2i	−0.325244	−	0.563339i
$690$	22408.5	+	953.302i	1.23634	+	0.0525965i
$691$	−20554.2	−	11867.0i	−1.13157	−	0.653315i	−0.187244	−	0.982313i	$-0.559955\pi$
$691$	−20554.2	−	11867.0i	−1.13157	−	0.653315i	−0.944330	+	0.328999i	$0.893289\pi$
$692$	−16175.4	−	16175.4i	−0.888577	−	0.888577i
$693$		0			0
$694$			2456.62i			0.134369i
$695$	−3.29786	+	10.5003i	−0.000179993	+	0.000573094i
$696$	−17154.4	+	9904.10i	−0.934247	+	0.539388i
$697$	−2388.72	−	640.054i	−0.129812	−	0.0347830i
$698$	−3574.56	−	13340.4i	−0.193838	−	0.723415i
$699$	−7260.99			−0.392898
$700$		0			0
$701$	−2641.08			−0.142300			−0.0711501	−	0.997466i	$-0.522667\pi$
$701$	−2641.08			−0.142300			−0.0711501	+	0.997466i	$0.522667\pi$
$702$	8626.76	+	32195.5i	0.463812	+	1.73097i
$703$	−27494.2	−	7367.04i	−1.47505	−	0.395239i
$704$	18246.7	−	10534.7i	0.976842	−	0.563980i
$705$	2605.41	−	8295.61i	0.139185	−	0.443164i
$706$			28995.0i			1.54567i
$707$		0			0
$708$	−204.193	−	204.193i	−0.0108390	−	0.0108390i
$709$	−15418.5	−	8901.89i	−0.816721	−	0.471534i	0.0325634	−	0.999470i	$-0.489633\pi$
$709$	−15418.5	−	8901.89i	−0.816721	−	0.471534i	−0.849284	+	0.527936i	$0.822966\pi$
$710$	−14749.3	−	627.467i	−0.779624	−	0.0331668i
$711$	−9727.23	−	16848.1i	−0.513080	−	0.888680i
$712$	−38556.5	+	10331.2i	−2.02945	+	0.543789i
$713$	−17302.7	+	17302.7i	−0.908825	+	0.908825i
$714$		0			0
$715$	−13350.7	+	21008.1i	−0.698303	+	1.09882i
$716$	−8596.40	+	14889.4i	−0.448691	+	0.777155i
$717$	−448.619	+	1674.27i	−0.0233668	+	0.0872060i
$718$	−16045.9	+	59884.0i	−0.834020	+	3.11260i
$719$	13918.8	−	24108.0i	0.721950	−	1.25045i	−0.238267	−	0.971200i	$-0.576579\pi$
$719$	13918.8	−	24108.0i	0.721950	−	1.25045i	0.960217	−	0.279254i	$-0.0900873\pi$
$720$	2924.43	+	13121.9i	0.151371	+	0.679200i
$721$		0			0
$722$	−28229.6	+	28229.6i	−1.45512	+	1.45512i
$723$	13169.4	−	3528.73i	0.677421	−	0.181514i
$724$	−20006.7	−	34652.6i	−1.02699	−	1.77880i
$725$	−16481.2	+	23649.8i	−0.844269	+	1.21149i
$726$	−34.2588	−	19.7793i	−0.00175133	−	0.00101113i
$727$	16901.8	+	16901.8i	0.862246	+	0.862246i	0.991599	−	0.129353i	$-0.0412899\pi$
$727$	16901.8	+	16901.8i	0.862246	+	0.862246i	−0.129353	+	0.991599i	$0.541290\pi$
$728$		0			0
$729$		−	9.93984i		−	0.000504996i
$730$	−46271.5	−	14532.6i	−2.34601	−	0.736814i
$731$	2018.72	−	1165.51i	0.102141	−	0.0589712i
$732$	−5454.53	−	1461.54i	−0.275417	−	0.0737977i
$733$	5266.14	+	19653.5i	0.265360	+	0.990338i	0.962029	+	0.272946i	$0.0879979\pi$
$733$	5266.14	+	19653.5i	0.265360	+	0.990338i	−0.696669	+	0.717393i	$0.745335\pi$
$734$	50213.8			2.52510
$735$		0			0
$736$	4865.06			0.243653
$737$	−5223.31	−	19493.6i	−0.261062	−	0.974298i
$738$	23111.0	+	6192.58i	1.15275	+	0.308878i
$739$	7600.10	−	4387.92i	0.378314	−	0.218420i	−0.298770	−	0.954325i	$-0.596576\pi$
$739$	7600.10	−	4387.92i	0.378314	−	0.218420i	0.677085	+	0.735905i	$0.263243\pi$
$740$	−35946.4	+	18763.6i	−1.78570	+	0.932112i
$741$			17295.5i			0.857444i
$742$		0			0
$743$	24208.9	+	24208.9i	1.19534	+	1.19534i	0.975546	+	0.219795i	$0.0705388\pi$
$743$	24208.9	+	24208.9i	1.19534	+	1.19534i	0.219795	+	0.975546i	$0.429461\pi$
$744$	10199.2	+	5888.52i	0.502582	+	0.290166i
$745$	−7825.62	+	7186.96i	−0.384844	+	0.353436i
$746$	13984.5	+	24221.8i	0.686338	+	1.18877i
$747$	18164.1	−	4867.05i	0.889677	−	0.238388i
$748$	−4397.26	+	4397.26i	−0.214946	+	0.214946i
$749$		0			0
$750$	−9604.81	−	12430.8i	−0.467624	−	0.605210i
$751$	19242.6	−	33329.2i	0.934983	−	1.61944i	0.160320	−	0.987065i	$-0.448748\pi$
$751$	19242.6	−	33329.2i	0.934983	−	1.61944i	0.774664	−	0.632373i	$-0.217919\pi$
$752$	−4834.66	+	18043.2i	−0.234444	+	0.874957i
$753$	1836.21	−	6852.82i	0.0888648	−	0.331648i
$754$	34167.6	−	59180.1i	1.65028	−	2.85837i
$755$	−12084.3	+	2693.19i	−0.582507	+	0.129821i
$756$		0			0
$757$	4414.65	−	4414.65i	0.211959	−	0.211959i	−0.593140	−	0.805099i	$-0.702112\pi$
$757$	4414.65	−	4414.65i	0.211959	−	0.211959i	0.805099	+	0.593140i	$0.202112\pi$
$758$	−16761.6	+	4491.25i	−0.803176	+	0.215210i
$759$	−7536.06	−	13052.8i	−0.360398	−	0.624227i
$760$	−2167.47	+	50949.0i	−0.103451	+	2.43173i
$761$	−17427.5	−	10061.8i	−0.830152	−	0.479289i	0.0237526	−	0.999718i	$-0.492439\pi$
$761$	−17427.5	−	10061.8i	−0.830152	−	0.479289i	−0.853905	+	0.520429i	$0.825772\pi$
$762$	−5618.47	−	5618.47i	−0.267107	−	0.267107i
$763$		0			0
$764$			12953.6i			0.613411i
$765$	1219.31	+	2335.91i	0.0576267	+	0.110399i
$766$	−6447.02	+	3722.19i	−0.304100	+	0.175572i
$767$	470.112	+	125.966i	0.0221314	+	0.00593008i
$768$	−4763.34	−	17777.0i	−0.223805	−	0.835251i
$769$	−18145.5			−0.850900			−0.425450	−	0.904982i	$-0.639884\pi$
$769$	−18145.5			−0.850900			−0.425450	+	0.904982i	$0.639884\pi$
$770$		0			0
$771$	−5486.19			−0.256265
$772$	−6525.59	−	24353.8i	−0.304224	−	1.13538i
$773$	−37766.6	−	10119.5i	−1.75727	−	0.470860i	−0.771118	−	0.636692i	$-0.780302\pi$
$773$	−37766.6	−	10119.5i	−1.75727	−	0.470860i	−0.986154	+	0.165832i	$0.946969\pi$
$774$	−19531.3	+	11276.4i	−0.907026	+	0.523672i
$775$	17076.7	+	1455.59i	0.791502	+	0.0674663i
$776$			9155.00i			0.423512i
$777$		0			0
$778$	−7230.01	−	7230.01i	−0.333173	−	0.333173i
$779$	24157.4	+	13947.3i	1.11108	+	0.641480i
$780$	16665.9	+	18146.9i	0.765043	+	0.833028i
$781$	4960.26	+	8591.42i	0.227263	+	0.393630i
$782$	−9122.19	+	2444.28i	−0.417147	+	0.111774i
$783$	18341.8	−	18341.8i	0.837143	−	0.837143i
$784$		0			0
$785$	9458.61	+	6010.96i	0.430054	+	0.273300i
$786$	2324.88	−	4026.82i	0.105504	−	0.182738i
$787$	145.841	−	544.285i	0.00660566	−	0.0246527i	−0.962544	−	0.271124i	$-0.912605\pi$
$787$	145.841	−	544.285i	0.00660566	−	0.0246527i	0.969150	+	0.246472i	$0.0792712\pi$
$788$	12861.8	−	48000.9i	0.581451	−	2.17000i
$789$	3803.18	−	6587.30i	0.171606	−	0.297230i
$790$	−41217.3	−	26193.6i	−1.85626	−	1.17966i
$791$		0			0
$792$	20784.5	−	20784.5i	0.932504	−	0.932504i
$793$	9193.05	−	2463.27i	0.411671	−	0.110307i
$794$	26217.1	+	45409.4i	1.17180	+	2.02962i
$795$	−3374.84	−	3674.74i	−0.150557	−	0.163937i
$796$	52399.7	+	30253.0i	2.33324	+	1.34710i
$797$	−20102.6	−	20102.6i	−0.893438	−	0.893438i	0.101407	−	0.994845i	$-0.467666\pi$
$797$	−20102.6	−	20102.6i	−0.893438	−	0.893438i	−0.994845	+	0.101407i	$0.967666\pi$
$798$		0			0
$799$			3661.23i			0.162109i
$800$	−2196.12	−	2605.39i	−0.0970556	−	0.115143i
$801$	20148.1	−	11632.5i	0.888762	−	0.513127i
$802$	4742.92	+	1270.86i	0.208826	+	0.0559548i
$803$	8435.43	+	31481.5i	0.370710	+	1.38351i
$804$	−19976.3			−0.876258
$805$		0			0
$806$	−40629.0			−1.77555
$807$	4110.36	+	15340.1i	0.179296	+	0.669141i
$808$	−59250.6	−	15876.2i	−2.57974	−	0.691239i
$809$	−35867.8	+	20708.3i	−1.55877	+	0.899955i	−0.561393	+	0.827549i	$0.689734\pi$
$809$	−35867.8	+	20708.3i	−1.55877	+	0.899955i	−0.997375	+	0.0724063i	$0.976932\pi$
$810$	−8167.10	−	15646.2i	−0.354275	−	0.678704i
$811$			23291.9i			1.00850i	0.863559	+	0.504248i	$0.168230\pi$
$811$			23291.9i			1.00850i	−0.863559	+	0.504248i	$0.831770\pi$
$812$		0			0
$813$	−11540.8	−	11540.8i	−0.497852	−	0.497852i
$814$	35667.7	+	20592.8i	1.53581	+	0.886703i
$815$	189.908	−	4464.02i	0.00816220	−	0.191862i
$816$	698.506	+	1209.85i	0.0299664	+	0.0519034i
$817$	−25397.4	+	6805.20i	−1.08757	+	0.291412i
$818$	35295.0	−	35295.0i	1.50863	−	1.50863i
$819$		0			0
$820$	38786.1	−	8644.12i	1.65179	−	0.368129i
$821$	−20285.0	+	35134.7i	−0.862304	+	1.49355i	0.00739561	+	0.999973i	$0.497646\pi$
$821$	−20285.0	+	35134.7i	−0.862304	+	1.49355i	−0.869700	+	0.493582i	$0.835687\pi$
$822$	355.169	−	1325.51i	0.0150705	−	0.0562438i
$823$	374.613	−	1398.07i	0.0158666	−	0.0592148i	−0.957539	−	0.288305i	$-0.906908\pi$
$823$	374.613	−	1398.07i	0.0158666	−	0.0592148i	0.973405	+	0.229090i	$0.0735750\pi$
$824$	−12184.2	+	21103.7i	−0.515117	+	0.892210i
$825$	−3588.38	+	9927.94i	−0.151432	+	0.418965i
$826$		0			0
$827$	7402.23	−	7402.23i	0.311246	−	0.311246i	−0.534146	−	0.845392i	$-0.679367\pi$
$827$	7402.23	−	7402.23i	0.311246	−	0.311246i	0.845392	+	0.534146i	$0.179367\pi$
$828$	58392.6	−	15646.2i	2.45082	−	0.656696i
$829$	18615.2	+	32242.5i	0.779894	+	1.35082i	0.932002	+	0.362453i	$0.118061\pi$
$829$	18615.2	+	32242.5i	0.779894	+	1.35082i	−0.152108	+	0.988364i	$0.548606\pi$
$830$	34767.9	−	31930.4i	1.45399	−	1.33533i
$831$	−2152.76	−	1242.89i	−0.0898656	−	0.0518839i
$832$	24854.6	+	24854.6i	1.03567	+	1.03567i
$833$		0			0
$834$		−	11.0653i		−	0.000459424i
$835$	−5452.64	+	2846.21i	−0.225984	+	0.117961i
$836$	60747.2	−	35072.4i	2.51314	−	1.45096i
$837$	−14896.8	−	3991.58i	−0.615182	−	0.164838i
$838$	6875.86	+	25661.1i	0.283440	+	1.05781i
$839$	−22615.9			−0.930615			−0.465308	−	0.885149i	$-0.654056\pi$
$839$	−22615.9			−0.930615			−0.465308	+	0.885149i	$0.654056\pi$
$840$		0			0
$841$	−28791.3			−1.18050
$842$	−1074.82	−	4011.28i	−0.0439914	−	0.164178i
$843$	2266.98	+	607.437i	0.0926205	+	0.0248176i
$844$	61165.0	−	35313.6i	2.49453	−	1.44022i
$845$	−16183.2	−	5082.68i	−0.658839	−	0.206922i
$846$		−	35422.7i		−	1.43955i
$847$		0			0
$848$	7579.12	+	7579.12i	0.306920	+	0.306920i
$849$	−12774.2	−	7375.19i	−0.516383	−	0.298134i
$850$	5426.81	+	3781.85i	0.218986	+	0.152608i
$851$	20690.8	+	35837.5i	0.833456	+	1.44359i
$852$	9485.17	−	2541.54i	0.381404	−	0.102197i
$853$	7541.07	−	7541.07i	0.302698	−	0.302698i	−0.539371	−	0.842068i	$-0.681338\pi$
$853$	7541.07	−	7541.07i	0.302698	−	0.302698i	0.842068	+	0.539371i	$0.181338\pi$
$854$		0			0
$855$	−6465.42	−	29010.3i	−0.258612	−	1.16039i
$856$	−14980.5	+	25947.0i	−0.598157	+	1.03604i
$857$	−2477.71	+	9246.93i	−0.0987595	+	0.368575i	−0.997563	−	0.0697771i	$-0.977771\pi$
$857$	−2477.71	+	9246.93i	−0.0987595	+	0.368575i	0.898803	+	0.438353i	$0.144438\pi$
$858$	6477.05	−	24172.7i	0.257719	−	0.961820i
$859$	−10993.0	+	19040.4i	−0.436642	+	0.756286i	−0.997428	−	0.0716744i	$-0.977166\pi$
$859$	−10993.0	+	19040.4i	−0.436642	+	0.756286i	0.560786	+	0.827961i	$0.310499\pi$
$860$	−20090.1	+	31613.0i	−0.796588	+	1.25348i
$861$		0			0
$862$	3988.88	−	3988.88i	0.157612	−	0.157612i
$863$	6160.92	−	1650.81i	0.243013	−	0.0651151i	−0.135257	−	0.990811i	$-0.543186\pi$
$863$	6160.92	−	1650.81i	0.243013	−	0.0651151i	0.378270	+	0.925695i	$0.376519\pi$
$864$	1533.12	+	2655.44i	0.0603679	+	0.104560i
$865$	16336.2	+	694.975i	0.642136	+	0.0273178i
$866$	−21134.4	−	12201.9i	−0.829302	−	0.478798i
$867$	−7837.59	−	7837.59i	−0.307011	−	0.307011i
$868$		0			0
$869$			32817.9i			1.28110i
$870$	8683.96	−	27649.6i	0.338407	−	1.07748i
$871$	29157.4	−	16834.0i	1.13428	−	0.654879i
$872$	−65014.3	−	17420.5i	−2.52484	−	0.676530i
$873$	−1381.03	−	5154.09i	−0.0535406	−	0.199816i
$874$	106526.			4.12275
$875$		0			0
$876$	32261.0			1.24429
$877$	1710.62	+	6384.13i	0.0658650	+	0.245812i	0.991007	−	0.133810i	$-0.0427210\pi$
$877$	1710.62	+	6384.13i	0.0658650	+	0.245812i	−0.925142	+	0.379621i	$0.876054\pi$
$878$	2567.73	+	688.021i	0.0986978	+	0.0264460i
$879$	−19042.5	+	10994.2i	−0.730703	+	0.421871i
$880$	6795.40	−	21636.5i	0.260310	−	0.828825i
$881$			26453.1i			1.01161i	0.862648	+	0.505805i	$0.168805\pi$
$881$			26453.1i			1.01161i	−0.862648	+	0.505805i	$0.831195\pi$
$882$		0			0
$883$	−5892.09	−	5892.09i	−0.224558	−	0.224558i	0.585857	−	0.810415i	$-0.300758\pi$
$883$	−5892.09	−	5892.09i	−0.224558	−	0.224558i	−0.810415	+	0.585857i	$0.800758\pi$
$884$	−8984.55	−	5187.23i	−0.341836	−	0.197359i
$885$	206.223	+	8.77315i	0.00783290	+	0.000333227i
$886$	−43169.4	−	74771.7i	−1.63691	−	2.83522i
$887$	14938.5	−	4002.77i	0.565486	−	0.151522i	0.0352607	−	0.999378i	$-0.488774\pi$
$887$	14938.5	−	4002.77i	0.565486	−	0.151522i	0.530226	+	0.847856i	$0.322107\pi$
$888$	14083.1	−	14083.1i	0.532205	−	0.532205i
$889$		0			0
$890$	31324.2	−	49290.6i	1.17977	−	1.85643i
$891$	−5930.22	+	10271.4i	−0.222974	+	0.386202i
$892$	−2069.65	+	7724.04i	−0.0776873	+	0.289933i
$893$	10688.6	−	39890.5i	0.400538	−	1.49483i
$894$	5341.15	−	9251.15i	0.199815	−	0.346090i
$895$	−2673.25	−	11994.9i	−0.0998402	−	0.447982i
$896$		0			0
$897$	17779.9	−	17779.9i	0.661820	−	0.661820i
$898$	−81941.6	+	21956.2i	−3.04502	+	0.815910i
$899$	15809.3	+	27382.5i	0.586506	+	1.01586i
$900$	−34737.9	−	24208.2i	−1.28659	−	0.896602i
$901$	1819.37	+	1050.41i	0.0672719	+	0.0388395i
$902$	−28539.9	−	28539.9i	−1.05352	−	1.05352i
$903$		0			0
$904$		−	13297.9i		−	0.489249i
$905$	27286.8	+	8570.00i	1.00226	+	0.314781i
$906$	10779.8	−	6223.71i	0.395292	−	0.228222i
$907$	−13751.7	−	3684.77i	−0.503439	−	0.134896i	−0.00184344	−	0.999998i	$-0.500587\pi$
$907$	−13751.7	−	3684.77i	−0.503439	−	0.134896i	−0.501596	+	0.865102i	$0.667253\pi$
$908$	14235.1	+	53126.1i	0.520273	+	1.94169i
$909$	35751.9			1.30453
$910$		0			0
$911$	2046.69			0.0744346			0.0372173	−	0.999307i	$-0.488151\pi$
$911$	2046.69			0.0744346			0.0372173	+	0.999307i	$0.488151\pi$
$912$	−4078.45	−	15221.0i	−0.148082	−	0.552650i
$913$	−30641.2	−	8210.28i	−1.11071	−	0.297613i
$914$	38994.9	−	22513.7i	1.41120	−	0.814756i
$915$	3578.20	−	1867.77i	0.129280	−	0.0674827i
$916$			34565.4i			1.24680i
$917$		0			0
$918$	−4208.81	−	4208.81i	−0.151320	−	0.151320i
$919$	1559.32	+	900.276i	0.0559710	+	0.0323149i	0.527724	−	0.849416i	$-0.323045\pi$
$919$	1559.32	+	900.276i	0.0559710	+	0.0323149i	−0.471753	+	0.881731i	$0.656379\pi$
$920$	54604.0	−	50147.7i	1.95678	−	1.79709i
$921$	10238.2	+	17733.0i	0.366296	+	0.634444i
$922$	54875.2	−	14703.8i	1.96011	−	0.525209i
$923$	−11702.8	+	11702.8i	−0.417336	+	0.417336i
$924$		0			0
$925$	9852.15	−	27257.9i	0.350202	−	0.968900i
$926$	−32689.9	+	56620.6i	−1.16010	+	2.00936i
$927$	3675.98	−	13718.9i	0.130243	−	0.486073i
$928$	1627.03	−	6072.17i	0.0575539	−	0.214794i
$929$	3181.03	−	5509.70i	0.112342	−	0.194583i	−0.804372	−	0.594126i	$-0.797498\pi$
$929$	3181.03	−	5509.70i	0.112342	−	0.194583i	0.916714	+	0.399543i	$0.130831\pi$
$930$	−16818.3	+	3748.24i	−0.593004	+	0.132161i
$931$		0			0
$932$	−34738.6	+	34738.6i	−1.22092	+	1.22092i
$933$	6234.96	−	1670.65i	0.218782	−	0.0586224i
$934$	−32631.2	−	56518.9i	−1.14317	−	1.98004i
$935$	188.928	−	4440.98i	0.00660814	−	0.155332i
$936$	42467.2	+	24518.4i	1.48299	+	0.856207i
$937$	−1779.41	−	1779.41i	−0.0620391	−	0.0620391i	0.675406	−	0.737446i	$-0.263968\pi$
$937$	−1779.41	−	1779.41i	−0.0620391	−	0.0620391i	−0.737446	+	0.675406i	$0.763968\pi$
$938$		0			0
$939$			6683.68i			0.232283i
$940$	−27223.5	−	52153.6i	−0.944609	−	1.80964i
$941$	16502.1	−	9527.52i	0.571684	−	0.330062i	−0.186138	−	0.982524i	$-0.559597\pi$
$941$	16502.1	−	9527.52i	0.571684	−	0.330062i	0.757822	+	0.652462i	$0.226264\pi$
$942$	−10883.4	−	2916.20i	−0.376434	−	0.100865i
$943$	−10496.1	−	39171.8i	−0.362459	−	1.35271i
$944$	−443.428			−0.0152885
$945$		0			0
$946$	38044.6			1.30754
$947$	2857.93	+	10666.0i	0.0980679	+	0.365995i	0.997467	−	0.0711345i	$-0.0226620\pi$
$947$	2857.93	+	10666.0i	0.0980679	+	0.365995i	−0.899399	+	0.437129i	$0.855995\pi$
$948$	31377.7	+	8407.64i	1.07500	+	0.288046i
$949$	−47088.0	+	27186.3i	−1.61069	+	0.929931i
$950$	−48086.3	−	57047.8i	−1.64224	−	1.94829i
$951$		−	13830.5i		−	0.471593i
$952$		0			0
$953$	−7680.65	−	7680.65i	−0.261071	−	0.261071i	0.564418	−	0.825489i	$-0.309101\pi$
$953$	−7680.65	−	7680.65i	−0.261071	−	0.261071i	−0.825489	+	0.564418i	$0.809101\pi$
$954$	−17602.6	−	10162.8i	−0.597384	−	0.344900i
$955$	−6262.94	−	6819.50i	−0.212214	−	0.231072i
$956$	5863.85	+	10156.5i	0.198379	+	0.343602i
$957$	−18811.8	+	5040.61i	−0.635423	+	0.170261i
$958$	2483.28	−	2483.28i	0.0837485	−	0.0837485i
$959$		0			0
$960$	12581.5	+	7995.55i	0.422985	+	0.268808i
$961$	−5496.04	+	9519.42i	−0.184487	+	0.319540i
$962$	−17783.2	+	66367.8i	−0.596001	+	2.22431i
$963$	4519.62	−	16867.5i	0.151239	−	0.564430i
$964$	46123.7	−	79888.6i	1.54102	−	2.66913i
$965$	15210.2	+	9666.12i	0.507393	+	0.322449i
$966$		0			0
$967$	10778.0	−	10778.0i	0.358426	−	0.358426i	−0.504806	−	0.863233i	$-0.668436\pi$
$967$	10778.0	−	10778.0i	0.358426	−	0.358426i	0.863233	+	0.504806i	$0.168436\pi$
$968$	−126.305	+	33.8432i	−0.00419378	+	0.00112372i
$969$	−1544.28	−	2674.77i	−0.0511965	−	0.0886749i
$970$	−9060.31	−	9865.45i	−0.299906	−	0.326557i
$971$	36782.8	+	21236.5i	1.21567	+	0.701867i	0.963989	−	0.265943i	$-0.0856834\pi$
$971$	36782.8	+	21236.5i	1.21567	+	0.701867i	0.251681	+	0.967810i	$0.419017\pi$
$972$	41891.5	+	41891.5i	1.38238	+	1.38238i
$973$		0			0
$974$			70059.9i			2.30479i
$975$	−17547.6	−	1495.73i	−0.576383	−	0.0491299i
$976$	−7509.52	+	4335.62i	−0.246285	+	0.142193i
$977$	11969.2	+	3207.13i	0.391943	+	0.105021i	0.449408	−	0.893327i	$-0.351635\pi$
$977$	11969.2	+	3207.13i	0.391943	+	0.105021i	−0.0574648	+	0.998348i	$0.518302\pi$
$978$	1162.64	+	4339.05i	0.0380135	+	0.141868i
$979$	−39246.0			−1.28121
$980$		0			0
$981$	39229.7			1.27677
$982$	−16085.3	−	60031.2i	−0.522712	−	1.95079i
$983$	−39023.8	−	10456.4i	−1.26619	−	0.339275i	−0.437620	−	0.899160i	$-0.644179\pi$
$983$	−39023.8	−	10456.4i	−1.26619	−	0.339275i	−0.828570	+	0.559885i	$0.810845\pi$
$984$	−16903.1	+	9759.02i	−0.547613	+	0.316165i
$985$	16436.8	+	31488.8i	0.531695	+	1.01860i
$986$			12203.0i			0.394142i
$987$		0			0
$988$	82746.5	+	82746.5i	2.66449	+	2.66449i
$989$	33104.4	+	19112.8i	1.06437	+	0.614512i
$990$	−1827.90	+	42966.8i	−0.0586812	+	1.37937i
$991$	9159.67	+	15865.0i	0.293609	+	0.508546i	0.974660	−	0.223690i	$-0.0718103\pi$
$991$	9159.67	+	15865.0i	0.293609	+	0.508546i	−0.681051	+	0.732236i	$0.738477\pi$
$992$	−3610.23	+	967.358i	−0.115549	+	0.0309614i
$993$	8016.76	−	8016.76i	0.256198	−	0.256198i
$994$		0			0
$995$	−42213.0	+	9407.88i	−1.34497	+	0.299748i
$996$	−15700.0	+	27193.1i	−0.499470	+	0.865107i
$997$	2575.08	−	9610.32i	0.0817989	−	0.305278i	−0.912890	−	0.408206i	$-0.866155\pi$
$997$	2575.08	−	9610.32i	0.0817989	−	0.305278i	0.994689	+	0.102928i	$0.0328212\pi$
$998$	−8111.89	+	30274.0i	−0.257292	+	0.960227i
$999$	−13040.6	+	22586.9i	−0.412998	+	0.715333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.l.d.68.3		144
5.2	odd	4	inner	245.4.l.d.117.33		144
7.2	even	3		245.4.f.b.48.4	yes	72
7.3	odd	6	inner	245.4.l.d.178.33		144
7.4	even	3	inner	245.4.l.d.178.34		144
7.5	odd	6		245.4.f.b.48.3	✓	72
7.6	odd	2	inner	245.4.l.d.68.4		144
35.2	odd	12		245.4.f.b.97.3	yes	72
35.12	even	12		245.4.f.b.97.4	yes	72
35.17	even	12	inner	245.4.l.d.227.3		144
35.27	even	4	inner	245.4.l.d.117.34		144
35.32	odd	12	inner	245.4.l.d.227.4		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.4.f.b.48.3	✓	72	7.5	odd	6
245.4.f.b.48.4	yes	72	7.2	even	3
245.4.f.b.97.3	yes	72	35.2	odd	12
245.4.f.b.97.4	yes	72	35.12	even	12
245.4.l.d.68.3		144	1.1	even	1	trivial
245.4.l.d.68.4		144	7.6	odd	2	inner
245.4.l.d.117.33		144	5.2	odd	4	inner
245.4.l.d.117.34		144	35.27	even	4	inner
245.4.l.d.178.33		144	7.3	odd	6	inner
245.4.l.d.178.34		144	7.4	even	3	inner
245.4.l.d.227.3		144	35.17	even	12	inner
245.4.l.d.227.4		144	35.32	odd	12	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.25845 - 4.69658i) q^{2} +(-2.23302 - 0.598336i) q^{3} +(-13.5460 + 7.82078i) q^{4} +(3.35008 - 10.6666i) q^{5} +11.2405i q^{6} +(26.2728 + 26.2728i) q^{8} +(-18.7543 - 10.8278i) q^{9} +O(q^{10})\)	\(q+(-1.25845 - 4.69658i) q^{2} +(-2.23302 - 0.598336i) q^{3} +(-13.5460 + 7.82078i) q^{4} +(3.35008 - 10.6666i) q^{5} +11.2405i q^{6} +(26.2728 + 26.2728i) q^{8} +(-18.7543 - 10.8278i) q^{9} +(-54.3126 - 2.31057i) q^{10} +(18.2655 + 31.6368i) q^{11} +(34.9279 - 9.35891i) q^{12} +(-43.0940 + 43.0940i) q^{13} +(-13.8630 + 21.8143i) q^{15} +(27.7631 - 48.0870i) q^{16} +(2.81676 - 10.5123i) q^{17} +(-27.2524 + 101.707i) q^{18} +(-61.3794 + 106.312i) q^{19} +(38.0412 + 170.690i) q^{20} +(125.599 - 125.599i) q^{22} +(172.388 - 46.1912i) q^{23} +(-42.9477 - 74.3875i) q^{24} +(-102.554 - 71.4682i) q^{25} +(256.626 + 148.163i) q^{26} +(79.5366 + 79.5366i) q^{27} -230.609i q^{29} +(119.899 + 37.6567i) q^{30} +(-118.740 + 68.5546i) q^{31} +(26.3311 + 7.05539i) q^{32} +(-21.8579 - 81.5746i) q^{33} -52.9166 q^{34} +338.728 q^{36} +(60.0123 + 223.969i) q^{37} +(576.547 + 154.485i) q^{38} +(122.014 - 70.4450i) q^{39} +(368.258 - 192.226i) q^{40} -227.230i q^{41} +(151.453 + 151.453i) q^{43} +(-494.850 - 285.702i) q^{44} +(-178.325 + 163.771i) q^{45} +(-433.882 - 751.505i) q^{46} +(-324.950 + 87.0700i) q^{47} +(-90.7677 + 90.7677i) q^{48} +(-206.598 + 571.592i) q^{50} +(-12.5798 + 21.7888i) q^{51} +(246.722 - 920.779i) q^{52} +(-49.9612 + 186.458i) q^{53} +(273.458 - 473.642i) q^{54} +(398.649 - 88.8457i) q^{55} +(200.672 - 200.672i) q^{57} +(-1083.07 + 290.208i) q^{58} +(-3.99297 - 6.91603i) q^{59} +(17.1834 - 403.916i) q^{60} +(-135.243 - 78.0826i) q^{61} +(471.400 + 471.400i) q^{62} -576.754i q^{64} +(315.299 + 604.036i) q^{65} +(-355.615 + 205.314i) q^{66} +(-533.618 - 142.983i) q^{67} +(44.0586 + 164.429i) q^{68} -412.584 q^{69} +271.564 q^{71} +(-208.251 - 777.204i) q^{72} +(861.772 + 230.911i) q^{73} +(976.366 - 563.705i) q^{74} +(186.243 + 220.952i) q^{75} -1920.14i q^{76} +(-484.399 - 484.399i) q^{78} +(777.999 + 449.178i) q^{79} +(-419.918 - 457.234i) q^{80} +(162.334 + 281.170i) q^{81} +(-1067.21 + 285.957i) q^{82} +(-614.022 + 614.022i) q^{83} +(-102.694 - 65.2624i) q^{85} +(520.715 - 901.905i) q^{86} +(-137.981 + 514.954i) q^{87} +(-351.301 + 1311.07i) q^{88} +(-537.160 + 930.388i) q^{89} +(993.577 + 631.419i) q^{90} +(-1973.92 + 1973.92i) q^{92} +(306.168 - 82.0373i) q^{93} +(817.863 + 1416.58i) q^{94} +(928.367 + 1010.87i) q^{95} +(-54.5763 - 31.5097i) q^{96} +(174.230 + 174.230i) q^{97} -791.103i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q+O(q^{10}) \) 144 * q	\( 144 q + 32 q^{11} + 1152 q^{16} + 64 q^{18} + 1152 q^{22} - 768 q^{23} - 288 q^{25} + 2512 q^{30} - 1840 q^{32} - 9280 q^{36} - 864 q^{37} + 1216 q^{43} + 3552 q^{46} - 4960 q^{50} - 1056 q^{51} + 1384 q^{53} + 15744 q^{57} - 5296 q^{58} - 9104 q^{60} - 736 q^{65} - 1856 q^{67} - 13632 q^{71} + 8528 q^{72} - 10816 q^{78} + 12616 q^{81} + 11200 q^{85} - 8672 q^{86} + 10080 q^{88} + 21248 q^{92} - 416 q^{93} - 5888 q^{95}+O(q^{100}) \) 144 * q + 32 * q^11 + 1152 * q^16 + 64 * q^18 + 1152 * q^22 - 768 * q^23 - 288 * q^25 + 2512 * q^30 - 1840 * q^32 - 9280 * q^36 - 864 * q^37 + 1216 * q^43 + 3552 * q^46 - 4960 * q^50 - 1056 * q^51 + 1384 * q^53 + 15744 * q^57 - 5296 * q^58 - 9104 * q^60 - 736 * q^65 - 1856 * q^67 - 13632 * q^71 + 8528 * q^72 - 10816 * q^78 + 12616 * q^81 + 11200 * q^85 - 8672 * q^86 + 10080 * q^88 + 21248 * q^92 - 416 * q^93 - 5888 * q^95

Introduction

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