LMFDB - Embedded newform 525.2.bf.g.32.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(32,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("525.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bf (of order $12$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			32.11
Character	$\chi$	$=$	525.32
Dual form			525.2.bf.g.443.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.364909 + 0.0977772i) q^{2} +(-1.71744 + 0.224513i) q^{3} +(-1.60845 - 0.928640i) q^{4} +(-0.648661 - 0.0859992i) q^{6} +(2.42547 + 1.05692i) q^{7} +(-1.03040 - 1.03040i) q^{8} +(2.89919 - 0.771175i) q^{9} +O(q^{10})$	\(q+(0.364909 + 0.0977772i) q^{2} +(-1.71744 + 0.224513i) q^{3} +(-1.60845 - 0.928640i) q^{4} +(-0.648661 - 0.0859992i) q^{6} +(2.42547 + 1.05692i) q^{7} +(-1.03040 - 1.03040i) q^{8} +(2.89919 - 0.771175i) q^{9} +(-4.25545 - 2.45689i) q^{11} +(2.97091 + 1.23376i) q^{12} +(-0.902810 + 0.902810i) q^{13} +(0.781736 + 0.622835i) q^{14} +(1.58203 + 2.74015i) q^{16} +(1.36373 + 5.08951i) q^{17} +(1.13334 + 0.00206519i) q^{18} +(-3.40819 + 1.96772i) q^{19} +(-4.40289 - 1.27064i) q^{21} +(-1.31263 - 1.31263i) q^{22} +(-1.65075 + 6.16067i) q^{23} +(2.00099 + 1.53832i) q^{24} +(-0.417718 + 0.241170i) q^{26} +(-4.80604 + 1.97535i) q^{27} +(-2.91977 - 3.95239i) q^{28} -7.51143 q^{29} +(0.312262 - 0.540853i) q^{31} +(1.06368 + 3.96971i) q^{32} +(7.86008 + 3.26414i) q^{33} +1.99055i q^{34} +(-5.37935 - 1.45190i) q^{36} +(0.330451 - 1.23326i) q^{37} +(-1.43608 + 0.384796i) q^{38} +(1.34783 - 1.75321i) q^{39} +6.30525i q^{41} +(-1.48242 - 0.894170i) q^{42} +(-5.75709 + 5.75709i) q^{43} +(4.56313 + 7.90357i) q^{44} +(-1.20475 + 2.08668i) q^{46} +(1.25681 + 0.336762i) q^{47} +(-3.33223 - 4.35085i) q^{48} +(4.76586 + 5.12705i) q^{49} +(-3.48478 - 8.43474i) q^{51} +(2.29051 - 0.613741i) q^{52} +(1.98663 - 0.532317i) q^{53} +(-1.94691 + 0.250904i) q^{54} +(-1.41017 - 3.58827i) q^{56} +(5.41157 - 4.14462i) q^{57} +(-2.74099 - 0.734446i) q^{58} +(4.69053 - 8.12423i) q^{59} +(4.29939 + 7.44677i) q^{61} +(0.166830 - 0.166830i) q^{62} +(7.84697 + 1.19373i) q^{63} -4.77552i q^{64} +(2.54906 + 1.95965i) q^{66} +(-8.83552 + 2.36747i) q^{67} +(2.53283 - 9.45264i) q^{68} +(1.45190 - 10.9512i) q^{69} -7.08463i q^{71} +(-3.78196 - 2.19271i) q^{72} +(-2.12683 - 7.93742i) q^{73} +(0.241170 - 0.417718i) q^{74} +7.30921 q^{76} +(-7.72477 - 10.4568i) q^{77} +(0.663259 - 0.507977i) q^{78} +(-3.24024 + 1.87075i) q^{79} +(7.81058 - 4.47156i) q^{81} +(-0.616509 + 2.30084i) q^{82} +(1.66497 + 1.66497i) q^{83} +(5.90188 + 6.13246i) q^{84} +(-2.66373 + 1.53790i) q^{86} +(12.9004 - 1.68642i) q^{87} +(1.85325 + 6.91642i) q^{88} +(-5.30346 - 9.18587i) q^{89} +(-3.14394 + 1.23555i) q^{91} +(8.37620 - 8.37620i) q^{92} +(-0.414861 + 0.998988i) q^{93} +(0.425695 + 0.245775i) q^{94} +(-2.71806 - 6.57892i) q^{96} +(7.27861 + 7.27861i) q^{97} +(1.23780 + 2.33690i) q^{98} +(-14.2320 - 3.84127i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{6}+O(q^{10}) $ 80 * q + 16 * q^6	$ 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) $ 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.364909	+	0.0977772i	0.258030	+	0.0691389i	0.385515	−	0.922702i	$-0.374024\pi$
$2$	0.364909	+	0.0977772i	0.258030	+	0.0691389i	−0.127485	+	0.991840i	$0.540690\pi$
$3$	−1.71744	+	0.224513i	−0.991563	+	0.129623i
$3$	−1.71744	+	0.224513i	−0.991563	+	0.129623i
$4$	−1.60845	−	0.928640i	−0.804226	−	0.464320i
$5$		0			0
$5$		0			0
$6$	−0.648661	−	0.0859992i	−0.264815	−	0.0351090i
$7$	2.42547	+	1.05692i	0.916743	+	0.399477i
$7$	2.42547	+	1.05692i	0.916743	+	0.399477i
$8$	−1.03040	−	1.03040i	−0.364303	−	0.364303i
$9$	2.89919	−	0.771175i	0.966396	−	0.257058i
$10$		0			0
$11$	−4.25545	−	2.45689i	−1.28307	−	0.740779i	−0.305659	−	0.952141i	$-0.598877\pi$
$11$	−4.25545	−	2.45689i	−1.28307	−	0.740779i	−0.977408	+	0.211362i	$0.932210\pi$
$12$	2.97091	+	1.23376i	0.857628	+	0.356157i
$13$	−0.902810	+	0.902810i	−0.250394	+	0.250394i	−0.821132	−	0.570738i	$-0.806657\pi$
$13$	−0.902810	+	0.902810i	−0.250394	+	0.250394i	0.570738	+	0.821132i	$0.306657\pi$
$14$	0.781736	+	0.622835i	0.208928	+	0.166460i
$15$		0			0
$16$	1.58203	+	2.74015i	0.395507	+	0.685038i
$17$	1.36373	+	5.08951i	0.330753	+	1.23439i	0.908401	+	0.418101i	$0.137304\pi$
$17$	1.36373	+	5.08951i	0.330753	+	1.23439i	−0.577648	+	0.816286i	$0.696029\pi$
$18$	1.13334	+	0.00206519i	0.267132	+	0.000486771i
$19$	−3.40819	+	1.96772i	−0.781892	+	0.451425i	−0.837100	−	0.547050i	$-0.815751\pi$
$19$	−3.40819	+	1.96772i	−0.781892	+	0.451425i	0.0552086	+	0.998475i	$0.482418\pi$
$20$		0			0
$21$	−4.40289	−	1.27064i	−0.960790	−	0.277276i
$22$	−1.31263	−	1.31263i	−0.279853	−	0.279853i
$23$	−1.65075	+	6.16067i	−0.344205	+	1.28459i	0.549334	+	0.835603i	$0.314882\pi$
$23$	−1.65075	+	6.16067i	−0.344205	+	1.28459i	−0.893539	+	0.448986i	$0.851785\pi$
$24$	2.00099	+	1.53832i	0.408451	+	0.314007i
$25$		0			0
$26$	−0.417718	+	0.241170i	−0.0819212	+	0.0472972i
$27$	−4.80604	+	1.97535i	−0.924922	+	0.380157i
$28$	−2.91977	−	3.95239i	−0.551784	−	0.746932i
$29$	−7.51143			−1.39484			−0.697418	−	0.716664i	$-0.745668\pi$
$29$	−7.51143			−1.39484			−0.697418	+	0.716664i	$0.745668\pi$
$30$		0			0
$31$	0.312262	−	0.540853i	0.0560838	−	0.0971400i	−0.836620	−	0.547783i	$-0.815472\pi$
$31$	0.312262	−	0.540853i	0.0560838	−	0.0971400i	0.892704	+	0.450643i	$0.148805\pi$
$32$	1.06368	+	3.96971i	0.188034	+	0.701752i
$33$	7.86008	+	3.26414i	1.36826	+	0.568215i
$34$			1.99055i			0.341377i
$35$		0			0
$36$	−5.37935	−	1.45190i	−0.896558	−	0.241984i
$37$	0.330451	−	1.23326i	0.0543259	−	0.202747i	−0.933429	−	0.358763i	$-0.883199\pi$
$37$	0.330451	−	1.23326i	0.0543259	−	0.202747i	0.987754	+	0.156016i	$0.0498652\pi$
$38$	−1.43608	+	0.384796i	−0.232962	+	0.0624221i
$39$	1.34783	−	1.75321i	0.215825	−	0.280739i
$40$		0			0
$41$			6.30525i			0.984714i	0.870393	+	0.492357i	$0.163865\pi$
$41$			6.30525i			0.984714i	−0.870393	+	0.492357i	$0.836135\pi$
$42$	−1.48242	−	0.894170i	−0.228742	−	0.137973i
$43$	−5.75709	+	5.75709i	−0.877947	+	0.877947i	−0.993322	−	0.115375i	$-0.963193\pi$
$43$	−5.75709	+	5.75709i	−0.877947	+	0.877947i	0.115375	+	0.993322i	$0.463193\pi$
$44$	4.56313	+	7.90357i	0.687917	+	1.19151i
$45$		0			0
$46$	−1.20475	+	2.08668i	−0.177630	+	0.307664i
$47$	1.25681	+	0.336762i	0.183325	+	0.0491218i	0.349314	−	0.937006i	$-0.386415\pi$
$47$	1.25681	+	0.336762i	0.183325	+	0.0491218i	−0.165988	+	0.986128i	$0.553081\pi$
$48$	−3.33223	−	4.35085i	−0.480966	−	0.627992i
$49$	4.76586	+	5.12705i	0.680837	+	0.732435i
$50$		0			0
$51$	−3.48478	−	8.43474i	−0.487967	−	1.18110i
$52$	2.29051	−	0.613741i	0.317637	−	0.0851105i
$53$	1.98663	−	0.532317i	0.272885	−	0.0731193i	−0.119781	−	0.992800i	$-0.538219\pi$
$53$	1.98663	−	0.532317i	0.272885	−	0.0731193i	0.392666	+	0.919681i	$0.371553\pi$
$54$	−1.94691	+	0.250904i	−0.264941	+	0.0341437i
$55$		0			0
$56$	−1.41017	−	3.58827i	−0.188442	−	0.479503i
$57$	5.41157	−	4.14462i	0.716780	−	0.548968i
$58$	−2.74099	−	0.734446i	−0.359910	−	0.0964375i
$59$	4.69053	−	8.12423i	0.610654	−	1.05768i	−0.380476	−	0.924791i	$-0.624240\pi$
$59$	4.69053	−	8.12423i	0.610654	−	1.05768i	0.991130	−	0.132894i	$-0.0424269\pi$
$60$		0			0
$61$	4.29939	+	7.44677i	0.550481	+	0.953461i	0.998240	+	0.0593064i	$0.0188889\pi$
$61$	4.29939	+	7.44677i	0.550481	+	0.953461i	−0.447759	+	0.894154i	$0.647778\pi$
$62$	0.166830	−	0.166830i	0.0211875	−	0.0211875i
$63$	7.84697	+	1.19373i	0.988626	+	0.150396i
$64$		−	4.77552i		−	0.596940i
$65$		0			0
$66$	2.54906	+	1.95965i	0.313767	+	0.241217i
$67$	−8.83552	+	2.36747i	−1.07943	+	0.289233i	−0.754363	−	0.656458i	$-0.772054\pi$
$67$	−8.83552	+	2.36747i	−1.07943	+	0.289233i	−0.325068	+	0.945691i	$0.605387\pi$
$68$	2.53283	−	9.45264i	0.307151	−	1.14630i
$69$	1.45190	−	10.9512i	0.174789	−	1.31837i
$70$		0			0
$71$		−	7.08463i		−	0.840791i	−0.907341	−	0.420395i	$-0.861891\pi$
$71$		−	7.08463i		−	0.840791i	0.907341	−	0.420395i	$-0.138109\pi$
$72$	−3.78196	−	2.19271i	−0.445708	−	0.258414i
$73$	−2.12683	−	7.93742i	−0.248926	−	0.929005i	−0.971369	−	0.237575i	$-0.923648\pi$
$73$	−2.12683	−	7.93742i	−0.248926	−	0.929005i	0.722443	−	0.691430i	$-0.243019\pi$
$74$	0.241170	−	0.417718i	0.0280354	−	0.0485587i
$75$		0			0
$76$	7.30921			0.838424
$77$	−7.72477	−	10.4568i	−0.880319	−	1.19166i
$78$	0.663259	−	0.507977i	0.0750993	−	0.0575171i
$79$	−3.24024	+	1.87075i	−0.364555	+	0.210476i	−0.671077	−	0.741388i	$-0.734168\pi$
$79$	−3.24024	+	1.87075i	−0.364555	+	0.210476i	0.306522	+	0.951864i	$0.400835\pi$
$80$		0			0
$81$	7.81058	−	4.47156i	0.867842	−	0.496841i
$82$	−0.616509	+	2.30084i	−0.0680820	+	0.254086i
$83$	1.66497	+	1.66497i	0.182754	+	0.182754i	0.792555	−	0.609801i	$-0.208750\pi$
$83$	1.66497	+	1.66497i	0.182754	+	0.182754i	−0.609801	+	0.792555i	$0.708750\pi$
$84$	5.90188	+	6.13246i	0.643948	+	0.669107i
$85$		0			0
$86$	−2.66373	+	1.53790i	−0.287237	+	0.165836i
$87$	12.9004	−	1.68642i	1.38307	−	0.180803i
$88$	1.85325	+	6.91642i	0.197557	+	0.737293i
$89$	−5.30346	−	9.18587i	−0.562166	−	0.973700i	−0.997307	−	0.0733379i	$-0.976635\pi$
$89$	−5.30346	−	9.18587i	−0.562166	−	0.973700i	0.435141	−	0.900362i	$-0.356698\pi$
$90$		0			0
$91$	−3.14394	+	1.23555i	−0.329574	+	0.129521i
$92$	8.37620	−	8.37620i	0.873279	−	0.873279i
$93$	−0.414861	+	0.998988i	−0.0430191	+	0.103590i
$94$	0.425695	+	0.245775i	0.0439071	+	0.0253498i
$95$		0			0
$96$	−2.71806	−	6.57892i	−0.277411	−	0.671458i
$97$	7.27861	+	7.27861i	0.739030	+	0.739030i	0.972390	−	0.233360i	$-0.0749721\pi$
$97$	7.27861	+	7.27861i	0.739030	+	0.739030i	−0.233360	+	0.972390i	$0.574972\pi$
$98$	1.23780	+	2.33690i	0.125036	+	0.236062i
$99$	−14.2320	−	3.84127i	−1.43037	−	0.386062i
$100$		0			0
$101$	14.3369	+	8.27744i	1.42658	+	0.823636i	0.996849	−	0.0793211i	$-0.0252752\pi$
$101$	14.3369	+	8.27744i	1.42658	+	0.823636i	0.429730	+	0.902957i	$0.358609\pi$
$102$	−0.446905	−	3.41865i	−0.0442502	−	0.338496i
$103$	−3.10729	−	0.832596i	−0.306171	−	0.0820381i	0.102463	−	0.994737i	$-0.467328\pi$
$103$	−3.10729	−	0.832596i	−0.306171	−	0.0820381i	−0.408633	+	0.912699i	$0.633994\pi$
$104$	1.86052			0.182439
$105$		0			0
$106$	0.776989			0.0754679
$107$	−15.7704	−	4.22568i	−1.52459	−	0.408512i	−0.603338	−	0.797486i	$-0.706163\pi$
$107$	−15.7704	−	4.22568i	−1.52459	−	0.408512i	−0.921249	+	0.388974i	$0.872830\pi$
$108$	9.56467	+	1.28582i	0.920361	+	0.123728i
$109$	−6.38608	−	3.68700i	−0.611675	−	0.353151i	0.161946	−	0.986800i	$-0.448223\pi$
$109$	−6.38608	−	3.68700i	−0.611675	−	0.353151i	−0.773621	+	0.633649i	$0.781556\pi$
$110$		0			0
$111$	−0.290646	+	2.19224i	−0.0275869	+	0.208078i
$112$	0.941057	+	8.31824i	0.0889216	+	0.785999i
$113$	2.99343	+	2.99343i	0.281599	+	0.281599i	0.833746	−	0.552148i	$-0.186192\pi$
$113$	2.99343	+	2.99343i	0.281599	+	0.281599i	−0.552148	+	0.833746i	$0.686192\pi$
$114$	2.37998	−	0.983281i	0.222906	−	0.0920927i
$115$		0			0
$116$	12.0818	+	6.97541i	1.12176	+	0.647651i
$117$	−1.92119	+	3.31364i	−0.177614	+	0.306346i
$118$	2.50598	−	2.50598i	0.230694	−	0.230694i
$119$	−2.07149	+	13.7858i	−0.189893	+	1.26374i
$120$		0			0
$121$	6.57258	+	11.3840i	0.597507	+	1.03491i
$122$	0.840765	+	3.13778i	0.0761193	+	0.284081i
$123$	−1.41561	−	10.8289i	−0.127641	−	0.976406i
$124$	−1.00452	+	0.579957i	−0.0902082	+	0.0520817i
$125$		0			0
$126$	2.74671	+	1.20286i	0.244697	+	0.107159i
$127$	−6.28791	−	6.28791i	−0.557962	−	0.557962i	0.370765	−	0.928727i	$-0.379096\pi$
$127$	−6.28791	−	6.28791i	−0.557962	−	0.557962i	−0.928727	+	0.370765i	$0.879096\pi$
$128$	2.59430	−	9.68205i	0.229306	−	0.855780i
$129$	8.59490	−	11.1800i	0.756738	−	0.984342i
$130$		0			0
$131$	10.6718	−	6.16135i	0.932397	−	0.538320i	0.0448282	−	0.998995i	$-0.485726\pi$
$131$	10.6718	−	6.16135i	0.932397	−	0.538320i	0.887569	+	0.460675i	$0.152393\pi$
$132$	−9.61134	−	12.5494i	−0.836560	−	1.09229i
$133$	−10.3462	+	1.17048i	−0.897128	+	0.101494i
$134$	−3.45565			−0.298523
$135$		0			0
$136$	3.83906	−	6.64944i	0.329196	−	0.570185i
$137$	−1.46782	−	5.47798i	−0.125404	−	0.468015i	0.874449	−	0.485117i	$-0.161223\pi$
$137$	−1.46782	−	5.47798i	−0.125404	−	0.468015i	−0.999854	+	0.0171015i	$0.994556\pi$
$138$	1.60059	−	3.85423i	0.136251	−	0.328094i
$139$			15.6849i			1.33038i	0.746675	+	0.665189i	$0.231649\pi$
$139$			15.6849i			1.33038i	−0.746675	+	0.665189i	$0.768351\pi$
$140$		0			0
$141$	−2.23411	−	0.296197i	−0.188146	−	0.0249443i
$142$	0.692715	−	2.58525i	0.0581313	−	0.216949i
$143$	6.05996	−	1.62376i	0.506760	−	0.135786i
$144$	6.69973	+	6.72419i	0.558311	+	0.560349i
$145$		0			0
$146$		−	3.10439i		−	0.256921i
$147$	−9.33616	−	7.73539i	−0.770033	−	0.638004i
$148$	−1.67677	+	1.67677i	−0.137830	+	0.137830i
$149$	1.38483	+	2.39859i	0.113449	+	0.196500i	0.917159	−	0.398522i	$-0.130477\pi$
$149$	1.38483	+	2.39859i	0.113449	+	0.196500i	−0.803709	+	0.595022i	$0.797143\pi$
$150$		0			0
$151$	0.179141	−	0.310281i	0.0145783	−	0.0252503i	−0.858644	−	0.512572i	$-0.828693\pi$
$151$	0.179141	−	0.310281i	0.0145783	−	0.0252503i	0.873223	+	0.487322i	$0.162026\pi$
$152$	5.53935	+	1.48426i	0.449301	+	0.120390i
$153$	7.87861	+	13.7038i	0.636948	+	1.10788i
$154$	−1.79641	−	4.57108i	−0.144759	−	0.368348i
$155$		0			0
$156$	−3.79602	+	1.56831i	−0.303925	+	0.125565i
$157$	−20.9972	+	5.62619i	−1.67576	+	0.449019i	−0.966655	−	0.256083i	$-0.917568\pi$
$157$	−20.9972	+	5.62619i	−1.67576	+	0.449019i	−0.709106	+	0.705102i	$0.750901\pi$
$158$	−1.36531	+	0.365834i	−0.108618	+	0.0291042i
$159$	−3.29241	+	1.36025i	−0.261105	+	0.107875i
$160$		0			0
$161$	−10.5152	+	13.1979i	−0.828711	+	1.04014i
$162$	3.28737	−	0.868020i	0.258280	−	0.0681981i
$163$	8.68658	+	2.32756i	0.680386	+	0.182309i	0.582429	−	0.812882i	$-0.302103\pi$
$163$	8.68658	+	2.32756i	0.680386	+	0.182309i	0.0979571	+	0.995191i	$0.468769\pi$
$164$	5.85531	−	10.1417i	0.457223	−	0.791933i
$165$		0			0
$166$	0.444767	+	0.770359i	0.0345206	+	0.0597915i
$167$	−5.51835	+	5.51835i	−0.427023	+	0.427023i	−0.887613	−	0.460590i	$-0.847638\pi$
$167$	−5.51835	+	5.51835i	−0.427023	+	0.427023i	0.460590	+	0.887613i	$0.347638\pi$
$168$	3.22749	+	5.84603i	0.249006	+	0.451031i
$169$			11.3699i			0.874605i
$170$		0			0
$171$	−8.36352	+	8.33309i	−0.639574	+	0.637247i
$172$	14.6063	−	3.91374i	1.11372	−	0.298420i
$173$	−2.91879	+	10.8931i	−0.221911	+	0.828184i	0.761707	+	0.647921i	$0.224361\pi$
$173$	−2.91879	+	10.8931i	−0.221911	+	0.828184i	−0.983619	+	0.180263i	$0.942305\pi$
$174$	4.87237	+	0.645977i	0.369374	+	0.0489714i
$175$		0			0
$176$		−	15.5474i		−	1.17193i
$177$	−6.23169	+	15.0059i	−0.468403	+	1.12792i
$178$	−1.03712	−	3.87057i	−0.0777351	−	0.290111i
$179$	6.11995	−	10.6001i	0.457427	−	0.792286i	−0.541397	−	0.840767i	$-0.682105\pi$
$179$	6.11995	−	10.6001i	0.457427	−	0.792286i	0.998824	+	0.0484806i	$0.0154379\pi$
$180$		0			0
$181$	−18.7187			−1.39135			−0.695675	−	0.718357i	$-0.744895\pi$
$181$	−18.7187			−1.39135			−0.695675	+	0.718357i	$0.744895\pi$
$182$	−1.26806	+	0.143458i	−0.0939949	+	0.0106338i
$183$	−9.05584	−	11.8241i	−0.669427	−	0.874062i
$184$	8.04892	−	4.64705i	0.593374	−	0.342585i
$185$		0			0
$186$	−0.249065	+	0.323976i	−0.0182623	+	0.0237551i
$187$	6.70105	−	25.0087i	0.490030	−	1.82882i
$188$	−1.70879	−	1.70879i	−0.124627	−	0.124627i
$189$	−13.7447	−	0.288408i	−0.999780	−	0.0209786i
$190$		0			0
$191$	−11.8166	+	6.82234i	−0.855022	+	0.493647i	−0.862342	−	0.506326i	$-0.831003\pi$
$191$	−11.8166	+	6.82234i	−0.855022	+	0.493647i	0.00732041	+	0.999973i	$0.497670\pi$
$192$	1.07217	+	8.20166i	0.0773771	+	0.591904i
$193$	−0.0168175	−	0.0627638i	−0.00121055	−	0.00451784i	0.965318	−	0.261077i	$-0.0840777\pi$
$193$	−0.0168175	−	0.0627638i	−0.00121055	−	0.00451784i	−0.966528	+	0.256559i	$0.917411\pi$
$194$	1.94435	+	3.36771i	0.139596	+	0.241788i
$195$		0			0
$196$	−2.90447	−	12.6724i	−0.207462	−	0.905170i
$197$	16.3046	−	16.3046i	1.16165	−	1.16165i	0.177539	−	0.984114i	$-0.443186\pi$
$197$	16.3046	−	16.3046i	1.16165	−	1.16165i	0.984114	−	0.177539i	$-0.0568137\pi$
$198$	−4.81782	−	2.79329i	−0.342387	−	0.198510i
$199$	−12.1826	−	7.03362i	−0.863600	−	0.498600i	0.00161591	−	0.999999i	$-0.499486\pi$
$199$	−12.1826	−	7.03362i	−0.863600	−	0.498600i	−0.865216	+	0.501399i	$0.832819\pi$
$200$		0			0
$201$	14.6429	−	6.04968i	1.03283	−	0.426711i
$202$	4.42234	+	4.42234i	0.311155	+	0.311155i
$203$	−18.2188	−	7.93895i	−1.27871	−	0.557205i
$204$	−2.22773	+	16.8030i	−0.155972	+	1.17644i
$205$		0			0
$206$	−1.05247	−	0.607644i	−0.0733291	−	0.0423366i
$207$	−0.0348662	+	19.1340i	−0.00242337	+	1.32990i
$208$	−3.90210	−	1.04557i	−0.270562	−	0.0724969i
$209$	19.3378			1.33763
$210$		0			0
$211$	1.27038			0.0874566			0.0437283	−	0.999043i	$-0.486076\pi$
$211$	1.27038			0.0874566			0.0437283	+	0.999043i	$0.486076\pi$
$212$	−3.68973	−	0.988661i	−0.253412	−	0.0679015i
$213$	1.59059	+	12.1674i	0.108986	+	0.833697i
$214$	−5.34161	−	3.08398i	−0.365145	−	0.210816i
$215$		0			0
$216$	6.98757	+	2.91675i	0.475444	+	0.198460i
$217$	1.32902	−	0.981791i	0.0902197	−	0.0666483i
$218$	−1.96983	−	1.96983i	−0.133414	−	0.133414i
$219$	5.43475	+	13.1545i	0.367246	+	0.888901i
$220$		0			0
$221$	−5.82604	−	3.36367i	−0.391902	−	0.226265i
$222$	−0.320411	+	0.771550i	−0.0215045	+	0.0517831i
$223$	0.208893	−	0.208893i	0.0139885	−	0.0139885i	−0.700078	−	0.714066i	$-0.746851\pi$
$223$	0.208893	−	0.208893i	0.0139885	−	0.0139885i	0.714066	+	0.700078i	$0.246851\pi$
$224$	−1.61572	+	10.7526i	−0.107955	+	0.718442i
$225$		0			0
$226$	0.799642	+	1.38502i	0.0531914	+	0.0921302i
$227$	6.05264	+	22.5887i	0.401728	+	1.49927i	0.810012	+	0.586413i	$0.199460\pi$
$227$	6.05264	+	22.5887i	0.401728	+	1.49927i	−0.408285	+	0.912855i	$0.633873\pi$
$228$	−12.5531	+	1.64101i	−0.831350	+	0.108679i
$229$	22.9301	−	13.2387i	1.51526	−	0.874838i	0.515424	−	0.856935i	$-0.327634\pi$
$229$	22.9301	−	13.2387i	1.51526	−	0.874838i	0.999840	−	0.0179026i	$-0.00569889\pi$
$230$		0			0
$231$	15.6145	+	16.2245i	1.02736	+	1.06750i
$232$	7.73980	+	7.73980i	0.508143	+	0.508143i
$233$	−0.781293	+	2.91583i	−0.0511842	+	0.191022i	−0.986784	−	0.162040i	$-0.948193\pi$
$233$	−0.781293	+	2.91583i	−0.0511842	+	0.191022i	0.935600	+	0.353062i	$0.114859\pi$
$234$	−1.02506	+	1.02133i	−0.0670102	+	0.0667664i
$235$		0			0
$236$	−15.0890	+	8.71162i	−0.982209	+	0.567078i
$237$	5.14490	−	3.94038i	0.334197	−	0.255955i
$238$	−2.10384	+	4.82803i	−0.136372	+	0.312955i
$239$	−26.1079			−1.68878			−0.844391	−	0.535728i	$-0.820037\pi$
$239$	−26.1079			−1.68878			−0.844391	+	0.535728i	$0.820037\pi$
$240$		0			0
$241$	9.64512	−	16.7058i	0.621297	−	1.07612i	−0.367948	−	0.929847i	$-0.619939\pi$
$241$	9.64512	−	16.7058i	0.621297	−	1.07612i	0.989245	−	0.146271i	$-0.0467273\pi$
$242$	1.28530	+	4.79679i	0.0826219	+	0.308349i
$243$	−12.4103	+	9.43321i	−0.796118	+	0.605141i
$244$		−	15.9704i		−	1.02240i
$245$		0			0
$246$	0.542246	−	4.08997i	0.0345724	−	0.260767i
$247$	1.30047	−	4.85342i	0.0827469	−	0.308816i
$248$	−0.879052	+	0.235541i	−0.0558199	+	0.0149569i
$249$	−3.23329	−	2.48568i	−0.204901	−	0.157523i
$250$		0			0
$251$		−	21.6028i		−	1.36356i	−0.731559	−	0.681779i	$-0.761207\pi$
$251$		−	21.6028i		−	1.36356i	0.731559	−	0.681779i	$-0.238793\pi$
$252$	−11.5129	−	9.20708i	−0.725247	−	0.579991i
$253$	22.1608	−	22.1608i	1.39323	−	1.39323i
$254$	−1.67970	−	2.90933i	−0.105394	−	0.182548i
$255$		0			0
$256$	−2.88215	+	4.99204i	−0.180135	+	0.312002i
$257$	15.5985	+	4.17961i	0.973009	+	0.260717i	0.710098	−	0.704103i	$-0.248651\pi$
$257$	15.5985	+	4.17961i	0.973009	+	0.260717i	0.262911	+	0.964820i	$0.415317\pi$
$258$	4.22950	−	3.23929i	0.263317	−	0.201670i
$259$	2.10495	−	2.64198i	0.130796	−	0.164165i
$260$		0			0
$261$	−21.7770	+	5.79263i	−1.34796	+	0.358555i
$262$	4.49667	−	1.20488i	0.277805	−	0.0744377i
$263$	4.71964	−	1.26462i	0.291025	−	0.0779800i	−0.110353	−	0.993892i	$-0.535198\pi$
$263$	4.71964	−	1.26462i	0.291025	−	0.0779800i	0.401378	+	0.915912i	$0.368531\pi$
$264$	−4.73567	−	11.4624i	−0.291460	−	0.705464i
$265$		0			0
$266$	−3.88987	−	0.584500i	−0.238503	−	0.0358380i
$267$	11.1707	+	14.5855i	0.683637	+	0.892616i
$268$	16.4100	+	4.39706i	1.00240	+	0.268593i
$269$	−2.17887	+	3.77392i	−0.132848	+	0.230100i	−0.924773	−	0.380518i	$-0.875746\pi$
$269$	−2.17887	+	3.77392i	−0.132848	+	0.230100i	0.791925	+	0.610618i	$0.209079\pi$
$270$		0			0
$271$	−10.4694	−	18.1335i	−0.635970	−	1.10153i	−0.986309	−	0.164909i	$-0.947267\pi$
$271$	−10.4694	−	18.1335i	−0.635970	−	1.10153i	0.350339	−	0.936623i	$-0.386066\pi$
$272$	−11.7886	+	11.7886i	−0.714786	+	0.714786i
$273$	5.12212	−	2.82783i	0.310005	−	0.171148i
$274$		−	2.14248i		−	0.129432i
$275$		0			0
$276$	−12.5050	+	16.2662i	−0.752715	+	0.979109i
$277$	6.47192	−	1.73414i	0.388860	−	0.104195i	−0.0590916	−	0.998253i	$-0.518820\pi$
$277$	6.47192	−	1.73414i	0.388860	−	0.104195i	0.447951	+	0.894058i	$0.352154\pi$
$278$	−1.53363	+	5.72357i	−0.0919808	+	0.343277i
$279$	0.488212	−	1.80884i	0.0292285	−	0.108293i
$280$		0			0
$281$		−	2.67341i		−	0.159482i	−0.996816	−	0.0797412i	$-0.974591\pi$
$281$		−	2.67341i		−	0.159482i	0.996816	−	0.0797412i	$-0.0254094\pi$
$282$	−0.786285	−	0.326530i	−0.0468226	−	0.0194446i
$283$	5.16900	+	19.2910i	0.307265	+	1.14673i	0.930978	+	0.365075i	$0.118957\pi$
$283$	5.16900	+	19.2910i	0.307265	+	1.14673i	−0.623713	+	0.781654i	$0.714377\pi$
$284$	−6.57907	+	11.3953i	−0.390396	+	0.676186i
$285$		0			0
$286$	2.37010			0.140147
$287$	−6.66411	+	15.2932i	−0.393370	+	0.902730i
$288$	6.14515	+	10.6886i	0.362106	+	0.629834i
$289$	−9.32089	+	5.38142i	−0.548288	+	0.316554i
$290$		0			0
$291$	−14.1347	−	10.8664i	−0.828591	−	0.637000i
$292$	−3.95011	+	14.7420i	−0.231163	+	0.862711i
$293$	5.08802	+	5.08802i	0.297245	+	0.297245i	0.839934	−	0.542689i	$-0.182594\pi$
$293$	5.08802	+	5.08802i	0.297245	+	0.297245i	−0.542689	+	0.839934i	$0.682594\pi$
$294$	−2.65051	−	3.73558i	−0.154581	−	0.217863i
$295$		0			0
$296$	−1.61126	+	0.930259i	−0.0936523	+	0.0540702i
$297$	25.3051	+	3.40187i	1.46835	+	0.197396i
$298$	0.270809	+	1.01067i	0.0156875	+	0.0585467i
$299$	−4.07161	−	7.05223i	−0.235467	−	0.407841i
$300$		0			0
$301$	−20.0484	+	7.87891i	−1.15557	+	0.454133i
$302$	0.0957085	−	0.0957085i	0.00550740	−	0.00550740i
$303$	−26.4812	−	10.9972i	−1.52131	−	0.631770i
$304$	−10.7837	−	6.22596i	−0.618487	−	0.357083i
$305$		0			0
$306$	1.53506	+	5.77098i	0.0877537	+	0.329905i
$307$	7.78824	+	7.78824i	0.444498	+	0.444498i	0.893521	−	0.449022i	$-0.148228\pi$
$307$	7.78824	+	7.78824i	0.444498	+	0.444498i	−0.449022	+	0.893521i	$0.648228\pi$
$308$	2.71434	+	23.9927i	0.154664	+	1.36711i
$309$	5.52351	+	0.732304i	0.314221	+	0.0416593i
$310$		0			0
$311$	−5.80289	−	3.35030i	−0.329052	−	0.189978i	0.326368	−	0.945243i	$-0.394175\pi$
$311$	−5.80289	−	3.35030i	−0.329052	−	0.189978i	−0.655420	+	0.755265i	$0.727508\pi$
$312$	−3.19532	+	0.417711i	−0.180900	+	0.0236482i
$313$	−1.76847	−	0.473860i	−0.0999597	−	0.0267841i	0.208492	−	0.978024i	$-0.433144\pi$
$313$	−1.76847	−	0.473860i	−0.0999597	−	0.0267841i	−0.308452	+	0.951240i	$0.599811\pi$
$314$	−8.21220			−0.463441
$315$		0			0
$316$	6.94902			0.390913
$317$	9.50906	+	2.54794i	0.534082	+	0.143107i	0.515773	−	0.856726i	$-0.327505\pi$
$317$	9.50906	+	2.54794i	0.534082	+	0.143107i	0.0183094	+	0.999832i	$0.494172\pi$
$318$	−1.33443	+	0.174444i	−0.0748312	+	0.00978236i
$319$	31.9645	+	18.4547i	1.78967	+	1.03327i
$320$		0			0
$321$	28.0335	+	3.71667i	1.56468	+	0.207444i
$322$	−5.12753	+	3.78788i	−0.285746	+	0.211090i
$323$	−14.6626	−	14.6626i	−0.815846	−	0.815846i
$324$	−16.7154	−	0.0609183i	−0.928634	−	0.00338435i
$325$		0			0
$326$	2.94223	+	1.69870i	0.162955	+	0.0940822i
$327$	11.7955	+	4.89844i	0.652291	+	0.270884i
$328$	6.49695	−	6.49695i	0.358734	−	0.358734i
$329$	2.69244	+	2.14515i	0.148439	+	0.118266i
$330$		0			0
$331$	−2.02148	−	3.50131i	−0.111111	−	0.192449i	0.805108	−	0.593129i	$-0.202107\pi$
$331$	−2.02148	−	3.50131i	−0.111111	−	0.192449i	−0.916218	+	0.400679i	$0.868774\pi$
$332$	−1.13187	−	4.22418i	−0.0621192	−	0.231832i
$333$	0.00697961	−	3.83029i	0.000382480	−	0.209899i
$334$	−2.55326	+	1.47413i	−0.139708	+	0.0806607i
$335$		0			0
$336$	−3.48376	−	14.0748i	−0.190055	−	0.767842i
$337$	−19.6955	−	19.6955i	−1.07288	−	1.07288i	−0.997127	−	0.0757532i	$-0.975864\pi$
$337$	−19.6955	−	19.6955i	−1.07288	−	1.07288i	−0.0757532	−	0.997127i	$-0.524136\pi$
$338$	−1.11171	+	4.14897i	−0.0604692	+	0.225674i
$339$	−5.81310	−	4.46897i	−0.315724	−	0.242721i
$340$		0			0
$341$	−2.65763	+	1.53438i	−0.143919	+	0.0830914i
$342$	−3.86671	+	2.22306i	−0.209088	+	0.120209i
$343$	6.14061	+	17.4726i	0.331562	+	0.943433i
$344$	11.8642			0.639677
$345$		0			0
$346$	−2.13018	+	3.68959i	−0.114519	+	0.198353i
$347$	1.53192	+	5.71721i	0.0822379	+	0.306916i	0.994777	−	0.102074i	$-0.0325478\pi$
$347$	1.53192	+	5.71721i	0.0822379	+	0.306916i	−0.912539	+	0.408990i	$0.865881\pi$
$348$	−22.3158	−	9.26732i	−1.19625	−	0.496781i
$349$		−	1.61208i		−	0.0862925i	−0.999069	−	0.0431462i	$-0.986262\pi$
$349$		−	1.61208i		−	0.0862925i	0.999069	−	0.0431462i	$-0.0137381\pi$
$350$		0			0
$351$	2.55557	−	6.12230i	0.136406	−	0.326784i
$352$	5.22668	−	19.5062i	0.278583	−	1.03969i
$353$	−2.89722	+	0.776309i	−0.154204	+	0.0413188i	−0.335095	−	0.942184i	$-0.608768\pi$
$353$	−2.89722	+	0.776309i	−0.154204	+	0.0413188i	0.180891	+	0.983503i	$0.442102\pi$
$354$	−3.74124	+	4.86649i	−0.198845	+	0.258651i
$355$		0			0
$356$			19.7000i			1.04410i
$357$	0.462555	−	24.1414i	0.0244810	−	1.27770i
$358$	3.26967	−	3.26967i	0.172808	−	0.172808i
$359$	13.8455	+	23.9812i	0.730740	+	1.26568i	0.956567	+	0.291512i	$0.0941582\pi$
$359$	13.8455	+	23.9812i	0.730740	+	1.26568i	−0.225827	+	0.974167i	$0.572508\pi$
$360$		0			0
$361$	−1.75618	+	3.04179i	−0.0924303	+	0.160094i
$362$	−6.83063	−	1.83026i	−0.359010	−	0.0961964i
$363$	−13.8439	−	18.0757i	−0.726614	−	0.948731i
$364$	6.20425	+	0.932266i	0.325191	+	0.0488640i
$365$		0			0
$366$	−2.14843	−	5.20017i	−0.112300	−	0.271817i
$367$	−31.1992	+	8.35980i	−1.62859	+	0.436378i	−0.953508	−	0.301369i	$-0.902556\pi$
$367$	−31.1992	+	8.35980i	−1.62859	+	0.436378i	−0.675077	+	0.737747i	$0.735890\pi$
$368$	−19.4927	+	5.22305i	−1.01613	+	0.272271i
$369$	4.86245	+	18.2801i	0.253129	+	0.951623i
$370$		0			0
$371$	5.38114	+	0.808583i	0.279375	+	0.0419795i
$372$	1.59499	−	1.22157i	0.0826961	−	0.0633354i
$373$	24.4708	+	6.55694i	1.26705	+	0.339505i	0.828900	−	0.559396i	$-0.188967\pi$
$373$	24.4708	+	6.55694i	1.26705	+	0.339505i	0.438151	+	0.898902i	$0.355634\pi$
$374$	4.89055	−	8.47069i	0.252885	−	0.438009i
$375$		0			0
$376$	−0.948025	−	1.64203i	−0.0488906	−	0.0846811i
$377$	6.78139	−	6.78139i	0.349259	−	0.349259i
$378$	−4.98737	−	1.44916i	−0.256523	−	0.0745368i
$379$			1.55582i			0.0799171i	0.999201	+	0.0399585i	$0.0127226\pi$
$379$			1.55582i			0.0799171i	−0.999201	+	0.0399585i	$0.987277\pi$
$380$		0			0
$381$	12.2108	+	9.38738i	0.625579	+	0.480930i
$382$	−4.97907	+	1.33414i	−0.254751	+	0.0682604i
$383$	5.86499	−	21.8884i	0.299687	−	1.11845i	−0.637736	−	0.770255i	$-0.720129\pi$
$383$	5.86499	−	21.8884i	0.299687	−	1.11845i	0.937423	−	0.348192i	$-0.113204\pi$
$384$	−2.28180	+	17.2108i	−0.116442	+	0.878284i
$385$		0			0
$386$		−	0.0245475i		−	0.00124943i
$387$	−12.2511	+	21.1306i	−0.622761	+	1.07413i
$388$	−4.94808	−	18.4665i	−0.251201	−	0.937494i
$389$	5.19425	−	8.99670i	0.263359	−	0.456151i	−0.703774	−	0.710424i	$-0.748503\pi$
$389$	5.19425	−	8.99670i	0.263359	−	0.456151i	0.967132	+	0.254274i	$0.0818364\pi$
$390$		0			0
$391$	−33.6060			−1.69953
$392$	0.372170	−	10.1937i	0.0187974	−	0.514859i
$393$	−16.9448	+	12.9777i	−0.854752	+	0.654638i
$394$	7.54391	−	4.35548i	0.380057	−	0.219426i
$395$		0			0
$396$	19.3244	+	19.3950i	0.971088	+	0.974633i
$397$	1.06444	−	3.97255i	0.0534228	−	0.199377i	−0.934056	−	0.357125i	$-0.883757\pi$
$397$	1.06444	−	3.97255i	0.0534228	−	0.199377i	0.987479	+	0.157749i	$0.0504236\pi$
$398$	−3.75781	−	3.75781i	−0.188362	−	0.188362i
$399$	17.5061	−	4.33309i	0.876403	−	0.216926i
$400$		0			0
$401$	21.5285	−	12.4295i	1.07508	−	0.620699i	0.145517	−	0.989356i	$-0.453515\pi$
$401$	21.5285	−	12.4295i	1.07508	−	0.620699i	0.929566	+	0.368656i	$0.120182\pi$
$402$	5.93486	−	0.775839i	0.296004	−	0.0386954i
$403$	0.206374	+	0.770200i	0.0102802	+	0.0383664i
$404$	−15.3735	−	26.6277i	−0.764862	−	1.32478i
$405$		0			0
$406$	−5.87195	−	4.67838i	−0.291420	−	0.232184i
$407$	−4.43620	+	4.43620i	−0.219894	+	0.219894i
$408$	−5.10045	+	12.2819i	−0.252510	+	0.608046i
$409$	16.6176	+	9.59418i	0.821688	+	0.474402i	0.850998	−	0.525169i	$-0.175998\pi$
$409$	16.6176	+	9.59418i	0.821688	+	0.474402i	−0.0293105	+	0.999570i	$0.509331\pi$
$410$		0			0
$411$	3.75077	+	9.07854i	0.185012	+	0.447811i
$412$	4.22475	+	4.22475i	0.208138	+	0.208138i
$413$	19.9634	−	14.7476i	0.982334	−	0.725683i
$414$	−1.88359	+	6.97875i	−0.0925733	+	0.342987i
$415$		0			0
$416$	−4.54419	−	2.62359i	−0.222797	−	0.128632i
$417$	−3.52147	−	26.9379i	−0.172447	−	1.31915i
$418$	7.05655	+	1.89080i	0.345147	+	0.0924820i
$419$	0.812376			0.0396872			0.0198436	−	0.999803i	$-0.493683\pi$
$419$	0.812376			0.0396872			0.0198436	+	0.999803i	$0.493683\pi$
$420$		0			0
$421$	2.86820			0.139788			0.0698938	−	0.997554i	$-0.477734\pi$
$421$	2.86820			0.139788			0.0698938	+	0.997554i	$0.477734\pi$
$422$	0.463574	+	0.124214i	0.0225664	+	0.00604665i
$423$	3.90344	+	0.00711290i	0.189792	+	0.000345841i
$424$	−2.59553	−	1.49853i	−0.126050	−	0.0727752i
$425$		0			0
$426$	−0.609273	+	4.59553i	−0.0295194	+	0.222654i
$427$	2.55746	+	22.6060i	0.123764	+	1.09398i
$428$	21.4419	+	21.4419i	1.03643	+	1.03643i
$429$	−10.0431	+	4.14925i	−0.484883	+	0.200328i
$430$		0			0
$431$	−10.4584	−	6.03814i	−0.503762	−	0.290847i	0.226504	−	0.974010i	$-0.427270\pi$
$431$	−10.4584	−	6.03814i	−0.503762	−	0.290847i	−0.730266	+	0.683163i	$0.760604\pi$
$432$	−13.0160	−	10.0442i	−0.626235	−	0.483252i
$433$	−26.7814	+	26.7814i	−1.28703	+	1.28703i	−0.350449	+	0.936582i	$0.613971\pi$
$433$	−26.7814	+	26.7814i	−1.28703	+	1.28703i	−0.936582	+	0.350449i	$0.886029\pi$
$434$	0.580968	−	0.228317i	0.0278874	−	0.0109596i
$435$		0			0
$436$	6.84780	+	11.8607i	0.327950	+	0.568026i
$437$	−6.49641	−	24.2449i	−0.310765	−	1.15979i
$438$	0.696978	+	5.33160i	0.0333029	+	0.254754i
$439$	0.619844	−	0.357867i	0.0295835	−	0.0170801i	−0.485135	−	0.874439i	$-0.661230\pi$
$439$	0.619844	−	0.357867i	0.0295835	−	0.0170801i	0.514719	+	0.857359i	$0.327896\pi$
$440$		0			0
$441$	17.7710	+	11.1890i	0.846237	+	0.532807i
$442$	−1.79709	−	1.79709i	−0.0854788	−	0.0854788i
$443$	−2.22111	+	8.28928i	−0.105528	+	0.393836i	−0.998405	−	0.0564658i	$-0.982017\pi$
$443$	−2.22111	+	8.28928i	−0.105528	+	0.393836i	0.892877	+	0.450301i	$0.148683\pi$
$444$	2.50329	−	3.25621i	0.118801	−	0.154533i
$445$		0			0
$446$	0.0966519	−	0.0558020i	0.00457660	−	0.00264230i
$447$	−2.91687	−	3.80852i	−0.137963	−	0.180137i
$448$	5.04732	−	11.5829i	0.238464	−	0.547241i
$449$	12.1704			0.574357			0.287178	−	0.957877i	$-0.407283\pi$
$449$	12.1704			0.574357			0.287178	+	0.957877i	$0.407283\pi$
$450$		0			0
$451$	15.4913	−	26.8317i	0.729455	−	1.26345i
$452$	−2.03497	−	7.59462i	−0.0957170	−	0.357221i
$453$	−0.238001	+	0.573108i	−0.0111823	+	0.0269269i
$454$			8.83465i			0.414631i
$455$		0			0
$456$	−9.84673	−	1.30547i	−0.461115	−	0.0611345i
$457$	2.69597	−	10.0615i	0.126112	−	0.470656i	−0.873765	−	0.486349i	$-0.838329\pi$
$457$	2.69597	−	10.0615i	0.126112	−	0.470656i	0.999877	+	0.0156922i	$0.00499518\pi$
$458$	9.66185	−	2.58888i	0.451469	−	0.120971i
$459$	−16.6077	−	21.7665i	−0.775181	−	1.01597i
$460$		0			0
$461$			28.3412i			1.31998i	0.751273	+	0.659992i	$0.229440\pi$
$461$			28.3412i			1.31998i	−0.751273	+	0.659992i	$0.770560\pi$
$462$	4.11149	+	7.44723i	0.191284	+	0.346476i
$463$	6.48454	−	6.48454i	0.301362	−	0.301362i	−0.540185	−	0.841547i	$-0.681646\pi$
$463$	6.48454	−	6.48454i	0.301362	−	0.301362i	0.841547	+	0.540185i	$0.181646\pi$
$464$	−11.8833	−	20.5824i	−0.551667	−	0.955516i
$465$		0			0
$466$	−0.570202	+	0.987620i	−0.0264141	+	0.0457506i
$467$	−21.5849	−	5.78366i	−0.998830	−	0.267636i	−0.277875	−	0.960617i	$-0.589630\pi$
$467$	−21.5849	−	5.78366i	−0.998830	−	0.267636i	−0.720955	+	0.692982i	$0.756297\pi$
$468$	6.16732	−	3.54574i	0.285085	−	0.163902i
$469$	−23.9326	−	3.59616i	−1.10510	−	0.166055i
$470$		0			0
$471$	34.7983	−	14.3768i	1.60342	−	0.662448i
$472$	−13.2044	+	3.53810i	−0.607780	+	0.162854i
$473$	38.6435	−	10.3545i	1.77683	−	0.476100i
$474$	2.26270	−	0.934827i	0.103929	−	0.0429380i
$475$		0			0
$476$	16.1340	−	20.2502i	0.739499	−	0.928165i
$477$	5.34911	−	3.07533i	0.244919	−	0.140810i
$478$	−9.52703	−	2.55276i	−0.435756	−	0.116760i
$479$	−16.0883	+	27.8657i	−0.735092	+	1.27322i	0.219592	+	0.975592i	$0.429527\pi$
$479$	−16.0883	+	27.8657i	−0.735092	+	1.27322i	−0.954683	+	0.297624i	$0.903806\pi$
$480$		0			0
$481$	0.815066	+	1.41173i	0.0371638	+	0.0643696i
$482$	5.15305	−	5.15305i	0.234715	−	0.234715i
$483$	15.0960	−	25.0273i	0.686894	−	1.13878i
$484$		−	24.4142i		−	1.10974i
$485$		0			0
$486$	−5.45097	+	2.22883i	−0.247261	+	0.101102i
$487$	32.5054	−	8.70979i	1.47296	−	0.394678i	0.569014	−	0.822328i	$-0.307325\pi$
$487$	32.5054	−	8.70979i	1.47296	−	0.394678i	0.903945	+	0.427649i	$0.140658\pi$
$488$	3.24307	−	12.1033i	0.146807	−	0.547890i
$489$	−15.4412	−	2.04719i	−0.698277	−	0.0925772i
$490$		0			0
$491$			21.8890i			0.987839i	0.869508	+	0.493919i	$0.164436\pi$
$491$			21.8890i			0.987839i	−0.869508	+	0.493919i	$0.835564\pi$
$492$	−7.77918	+	18.7323i	−0.350713	+	0.844518i
$493$	−10.2436	−	38.2295i	−0.461346	−	1.72177i
$494$	0.949107	−	1.64390i	0.0427023	−	0.0739626i
$495$		0			0
$496$	1.97602			0.0887261
$497$	7.48786	−	17.1836i	0.335876	−	0.770789i
$498$	−0.936816	−	1.22319i	−0.0419797	−	0.0548124i
$499$	34.0854	−	19.6792i	1.52587	−	0.880963i	0.526344	−	0.850272i	$-0.323562\pi$
$499$	34.0854	−	19.6792i	1.52587	−	0.880963i	0.999529	−	0.0306913i	$-0.00977089\pi$
$500$		0			0
$501$	8.23848	−	10.7164i	0.368068	−	0.478772i
$502$	2.11226	−	7.88307i	0.0942748	−	0.351838i
$503$	3.98778	+	3.98778i	0.177806	+	0.177806i	0.790399	−	0.612593i	$-0.209873\pi$
$503$	3.98778	+	3.98778i	0.177806	+	0.177806i	−0.612593	+	0.790399i	$0.709873\pi$
$504$	−6.85553	−	9.31558i	−0.305369	−	0.414949i
$505$		0			0
$506$	10.2535	−	5.91985i	0.455823	−	0.263169i
$507$	−2.55269	−	19.5270i	−0.113369	−	0.867227i
$508$	4.27460	+	15.9530i	0.189655	+	0.707801i
$509$	20.4148	+	35.3594i	0.904869	+	1.56728i	0.821093	+	0.570794i	$0.193365\pi$
$509$	20.4148	+	35.3594i	0.904869	+	1.56728i	0.0837760	+	0.996485i	$0.473302\pi$
$510$		0			0
$511$	3.23062	−	21.4999i	0.142914	−	0.951099i
$512$	−15.7153	+	15.7153i	−0.694526	+	0.694526i
$513$	12.4929	−	16.1893i	0.551576	−	0.714775i
$514$	5.28338	+	3.05036i	0.233040	+	0.134546i
$515$		0			0
$516$	−24.2067	+	10.0009i	−1.06564	+	0.440265i
$517$	−4.52092	−	4.52092i	−0.198830	−	0.198830i
$518$	1.02644	−	0.758268i	0.0450993	−	0.0333164i
$519$	2.56720	−	19.3635i	0.112687	−	0.849961i
$520$		0			0
$521$	22.2289	+	12.8338i	0.973865	+	0.562261i	0.900412	−	0.435038i	$-0.143265\pi$
$521$	22.2289	+	12.8338i	0.973865	+	0.562261i	0.0734524	+	0.997299i	$0.476598\pi$
$522$	−8.51303	−	0.0155125i	−0.372605	−	0.000678966i
$523$	19.3432	+	5.18300i	0.845819	+	0.226637i	0.655603	−	0.755106i	$-0.272414\pi$
$523$	19.3432	+	5.18300i	0.845819	+	0.226637i	0.190216	+	0.981742i	$0.439081\pi$
$524$	−22.8867			−0.999811
$525$		0			0
$526$	1.84589			0.0804847
$527$	3.17851	+	0.851680i	0.138458	+	0.0370998i
$528$	3.49061	+	26.7018i	0.151909	+	1.16205i
$529$	−15.3104	−	8.83944i	−0.665668	−	0.384323i
$530$		0			0
$531$	7.33351	−	27.1709i	0.318247	−	1.17912i
$532$	17.7283	+	7.72522i	0.768619	+	0.334931i
$533$	−5.69244	−	5.69244i	−0.246567	−	0.246567i
$534$	2.65018	+	6.41461i	0.114684	+	0.277587i
$535$		0			0
$536$	11.5436	+	6.66471i	0.498608	+	0.287871i
$537$	−8.13078	+	19.5790i	−0.350869	+	0.844895i
$538$	−1.16409	+	1.16409i	−0.0501876	+	0.0501876i
$539$	−7.68431	−	33.5271i	−0.330987	−	1.44411i
$540$		0			0
$541$	2.26699	+	3.92655i	0.0974656	+	0.168815i	0.910635	−	0.413212i	$-0.135593\pi$
$541$	2.26699	+	3.92655i	0.0974656	+	0.168815i	−0.813169	+	0.582027i	$0.802260\pi$
$542$	−2.04733	−	7.64075i	−0.0879405	−	0.328199i
$543$	32.1482	−	4.20260i	1.37961	−	0.180351i
$544$	−18.7533	+	10.8272i	−0.804040	+	0.464213i
$545$		0			0
$546$	2.14561	−	0.531077i	0.0918235	−	0.0227280i
$547$	1.90396	+	1.90396i	0.0814073	+	0.0814073i	0.746638	−	0.665231i	$-0.231667\pi$
$547$	1.90396	+	1.90396i	0.0814073	+	0.0814073i	−0.665231	+	0.746638i	$0.731667\pi$
$548$	−2.72615	+	10.1741i	−0.116455	+	0.434618i
$549$	18.2075	+	18.2740i	0.777078	+	0.779915i
$550$		0			0
$551$	25.6003	−	14.7804i	1.09061	−	0.629665i
$552$	−12.7802	+	9.78810i	−0.543961	+	0.416609i
$553$	−9.83634	+	1.11280i	−0.418284	+	0.0473212i
$554$	2.53122			0.107541
$555$		0			0
$556$	14.5657	−	25.2284i	0.617721	−	1.06992i
$557$	−1.30017	−	4.85232i	−0.0550902	−	0.205599i	0.932895	−	0.360149i	$-0.117274\pi$
$557$	−1.30017	−	4.85232i	−0.0550902	−	0.205599i	−0.987985	+	0.154549i	$0.950607\pi$
$558$	0.355017	−	0.612327i	0.0150291	−	0.0259219i
$559$		−	10.3951i		−	0.439666i
$560$		0			0
$561$	−5.89387	+	44.4553i	−0.248839	+	1.87691i
$562$	0.261399	−	0.975553i	0.0110264	−	0.0411512i
$563$	−31.9530	+	8.56178i	−1.34666	+	0.360836i	−0.858900	−	0.512143i	$-0.828852\pi$
$563$	−31.9530	+	8.56178i	−1.34666	+	0.360836i	−0.487758	+	0.872979i	$0.662185\pi$
$564$	3.31840	+	2.55110i	0.139730	+	0.107421i
$565$		0			0
$566$			7.54486i			0.317134i
$567$	23.6704	−	2.59055i	0.994064	−	0.108793i
$568$	−7.30003	+	7.30003i	−0.306302	+	0.306302i
$569$	−5.68011	−	9.83823i	−0.238122	−	0.412440i	0.722053	−	0.691838i	$-0.243199\pi$
$569$	−5.68011	−	9.83823i	−0.238122	−	0.412440i	−0.960176	+	0.279397i	$0.909865\pi$
$570$		0			0
$571$	−10.6527	+	18.4509i	−0.445800	+	0.772148i	−0.998108	−	0.0614926i	$-0.980414\pi$
$571$	−10.6527	+	18.4509i	−0.445800	+	0.772148i	0.552308	+	0.833640i	$0.313747\pi$
$572$	−11.2551	−	3.01578i	−0.470597	−	0.126096i
$573$	18.7626	−	14.3699i	0.783820	−	0.600313i
$574$	−3.92712	+	4.92904i	−0.163915	+	0.205734i
$575$		0			0
$576$	−3.68276	−	13.8451i	−0.153449	−	0.576880i
$577$	10.7663	−	2.88482i	0.448206	−	0.120096i	−0.0276537	−	0.999618i	$-0.508804\pi$
$577$	10.7663	−	2.88482i	0.448206	−	0.120096i	0.475860	+	0.879521i	$0.342137\pi$
$578$	−3.92746	+	1.05236i	−0.163361	+	0.0437724i
$579$	0.0429744	+	0.104017i	0.00178595	+	0.00432281i
$580$		0			0
$581$	2.27861	+	5.79808i	0.0945327	+	0.240545i
$582$	−4.09540	−	5.34731i	−0.169760	−	0.221653i
$583$	−9.76186	−	2.61568i	−0.404295	−	0.108330i
$584$	−5.98726	+	10.3702i	−0.247755	+	0.429123i
$585$		0			0
$586$	1.35917	+	2.35416i	0.0561469	+	0.0972493i
$587$	22.7106	−	22.7106i	0.937365	−	0.937365i	−0.0607860	−	0.998151i	$-0.519361\pi$
$587$	22.7106	−	22.7106i	0.937365	−	0.937365i	0.998151	+	0.0607860i	$0.0193607\pi$
$588$	7.83337	+	21.1119i	0.323043	+	0.870641i
$589$			2.45777i			0.101271i
$590$		0			0
$591$	−24.3415	+	31.6627i	−1.00128	+	1.30243i
$592$	3.90210	−	1.04557i	0.160375	−	0.0429725i
$593$	−4.47634	+	16.7059i	−0.183821	+	0.686030i	0.811059	+	0.584965i	$0.198892\pi$
$593$	−4.47634	+	16.7059i	−0.183821	+	0.686030i	−0.994880	+	0.101065i	$0.967775\pi$
$594$	8.90143	+	3.71563i	0.365230	+	0.152454i
$595$		0			0
$596$		−	5.14402i		−	0.210707i
$597$	22.5020	+	9.34465i	0.920944	+	0.382451i
$598$	−0.796220	−	2.97153i	−0.0325599	−	0.121515i
$599$	2.75073	−	4.76440i	0.112392	−	0.194668i	−0.804342	−	0.594166i	$-0.797482\pi$
$599$	2.75073	−	4.76440i	0.112392	−	0.194668i	0.916734	+	0.399498i	$0.130815\pi$
$600$		0			0
$601$	−14.8519			−0.605822			−0.302911	−	0.953019i	$-0.597958\pi$
$601$	−14.8519			−0.605822			−0.302911	+	0.953019i	$0.597958\pi$
$602$	−8.08623	+	0.914811i	−0.329570	+	0.0372849i
$603$	−23.7901	+	13.6775i	−0.968808	+	0.556990i
$604$	−0.576279	+	0.332715i	−0.0234484	+	0.0135380i
$605$		0			0
$606$	−8.58797	−	6.60222i	−0.348863	−	0.268197i
$607$	−8.41250	+	31.3959i	−0.341453	+	1.27432i	0.555249	+	0.831684i	$0.312623\pi$
$607$	−8.41250	+	31.3959i	−0.341453	+	1.27432i	−0.896702	+	0.442635i	$0.854044\pi$
$608$	−11.4365	−	11.4365i	−0.463811	−	0.463811i
$609$	33.0720	+	9.54429i	1.34015	+	0.386754i
$610$		0			0
$611$	−1.43870	+	0.830632i	−0.0582034	+	0.0336038i
$612$	0.0534970	−	29.3582i	0.00216249	−	1.18674i
$613$	−6.31362	−	23.5628i	−0.255005	−	0.951691i	−0.968088	−	0.250611i	$-0.919368\pi$
$613$	−6.31362	−	23.5628i	−0.255005	−	0.951691i	0.713083	−	0.701080i	$-0.247298\pi$
$614$	2.08049	+	3.60351i	0.0839617	+	0.145426i
$615$		0			0
$616$	−2.81506	+	18.7343i	−0.113422	+	0.754827i
$617$	−25.6386	+	25.6386i	−1.03217	+	1.03217i	−0.0327046	+	0.999465i	$0.510412\pi$
$617$	−25.6386	+	25.6386i	−1.03217	+	1.03217i	−0.999465	+	0.0327046i	$0.989588\pi$
$618$	1.94398	+	0.807298i	0.0781982	+	0.0324743i
$619$	−16.4024	−	9.46994i	−0.659268	−	0.380629i	0.132730	−	0.991152i	$-0.457626\pi$
$619$	−16.4024	−	9.46994i	−0.659268	−	0.380629i	−0.791998	+	0.610523i	$0.790959\pi$
$620$		0			0
$621$	−4.23595	−	32.8692i	−0.169983	−	1.31900i
$622$	−1.78995	−	1.78995i	−0.0717703	−	0.0717703i
$623$	−3.15473	−	27.8854i	−0.126392	−	1.11721i
$624$	6.93637	+	0.919620i	0.277677	+	0.0368143i
$625$		0			0
$626$	−0.598998	−	0.345832i	−0.0239408	−	0.0138222i
$627$	−33.2115	+	4.34160i	−1.32634	+	0.173387i
$628$	38.9977	+	10.4494i	1.55618	+	0.416977i
$629$	6.72734			0.268236
$630$		0			0
$631$	31.7330			1.26327			0.631635	−	0.775266i	$-0.282384\pi$
$631$	31.7330			1.26327			0.631635	+	0.775266i	$0.282384\pi$
$632$	5.26638	+	1.41112i	0.209485	+	0.0561315i
$633$	−2.18180	+	0.285217i	−0.0867188	+	0.0113364i
$634$	3.22081	+	1.85954i	0.127915	+	0.0738517i
$635$		0			0
$636$	6.55886	+	0.869570i	0.260076	+	0.0344807i
$637$	−8.93141	−	0.326085i	−0.353875	−	0.0129199i
$638$	9.85970	+	9.85970i	0.390349	+	0.390349i
$639$	−5.46349	−	20.5397i	−0.216132	−	0.812537i
$640$		0			0
$641$	−35.2877	−	20.3734i	−1.39378	−	0.804700i	−0.400050	−	0.916493i	$-0.631007\pi$
$641$	−35.2877	−	20.3734i	−1.39378	−	0.804700i	−0.993731	+	0.111793i	$0.964340\pi$
$642$	9.86628	+	4.09728i	0.389391	+	0.161707i
$643$	−4.17354	+	4.17354i	−0.164588	+	0.164588i	−0.784596	−	0.620008i	$-0.787130\pi$
$643$	−4.17354	+	4.17354i	−0.164588	+	0.164588i	0.620008	+	0.784596i	$0.287130\pi$
$644$	29.1692	−	11.4633i	1.14943	−	0.451718i
$645$		0			0
$646$	−3.91684	−	6.78417i	−0.154106	−	0.266919i
$647$	−0.0772225	−	0.288198i	−0.00303593	−	0.0113302i	0.964391	−	0.264480i	$-0.0852002\pi$
$647$	−0.0772225	−	0.288198i	−0.00303593	−	0.0113302i	−0.967427	+	0.253149i	$0.918534\pi$
$648$	−12.6556	−	3.44053i	−0.497158	−	0.135157i
$649$	−39.9206	+	23.0482i	−1.56702	+	0.904720i
$650$		0			0
$651$	−2.06208	+	1.98455i	−0.0808194	+	0.0777805i
$652$	−11.8105	−	11.8105i	−0.462534	−	0.462534i
$653$	4.56206	−	17.0258i	0.178527	−	0.666272i	−0.817397	−	0.576075i	$-0.804584\pi$
$653$	4.56206	−	17.0258i	0.178527	−	0.666272i	0.995924	−	0.0901973i	$-0.0287498\pi$
$654$	3.82532	+	2.94082i	0.149582	+	0.114995i
$655$		0			0
$656$	−17.2773	+	9.97507i	−0.674566	+	0.389461i
$657$	−12.2872	−	21.3719i	−0.479370	−	0.833798i
$658$	0.772750	+	1.04605i	0.0301249	+	0.0407791i
$659$	34.3342			1.33747			0.668734	−	0.743501i	$-0.266836\pi$
$659$	34.3342			1.33747			0.668734	+	0.743501i	$0.266836\pi$
$660$		0			0
$661$	−11.0032	+	19.0580i	−0.427973	+	0.741271i	−0.996693	−	0.0812602i	$-0.974106\pi$
$661$	−11.0032	+	19.0580i	−0.427973	+	0.741271i	0.568720	+	0.822531i	$0.307439\pi$
$662$	−0.395310	−	1.47532i	−0.0153641	−	0.0573398i
$663$	10.7611	+	4.46887i	0.417925	+	0.173556i
$664$		−	3.43118i		−	0.133156i
$665$		0			0
$666$	0.377062	−	1.39703i	0.0146109	−	0.0541337i
$667$	12.3995	−	46.2754i	0.480109	−	1.79179i
$668$	14.0006	−	3.75144i	0.541698	−	0.145148i
$669$	−0.311861	+	0.405660i	−0.0120573	+	0.0156837i
$670$		0			0
$671$		−	42.2525i		−	1.63114i
$672$	0.360783	−	18.8298i	0.0139175	−	0.726374i
$673$	−14.2780	+	14.2780i	−0.550378	+	0.550378i	−0.926550	−	0.376172i	$-0.877240\pi$
$673$	−14.2780	+	14.2780i	−0.550378	+	0.550378i	0.376172	+	0.926550i	$0.377240\pi$
$674$	−5.26129	−	9.11282i	−0.202657	−	0.351013i
$675$		0			0
$676$	10.5585	−	18.2879i	0.406097	−	0.703380i
$677$	5.30712	+	1.42204i	0.203969	+	0.0546534i	0.359357	−	0.933200i	$-0.382996\pi$
$677$	5.30712	+	1.42204i	0.203969	+	0.0546534i	−0.155388	+	0.987854i	$0.549663\pi$
$678$	−1.68429	−	2.19916i	−0.0646849	−	0.0844582i
$679$	9.96120	+	25.3469i	0.382276	+	0.972727i
$680$		0			0
$681$	−15.4665	−	37.4359i	−0.592678	−	1.43455i
$682$	−1.11982	+	0.300055i	−0.0428801	+	0.0114897i
$683$	−9.69914	+	2.59888i	−0.371127	+	0.0994433i	−0.439562	−	0.898212i	$-0.644866\pi$
$683$	−9.69914	+	2.59888i	−0.371127	+	0.0994433i	0.0684345	+	0.997656i	$0.478200\pi$
$684$	21.1908	−	5.63668i	0.810249	−	0.215524i
$685$		0			0
$686$	0.532342	+	6.97634i	0.0203249	+	0.266358i
$687$	−36.4088	+	27.8848i	−1.38908	+	1.06387i
$688$	−24.8831	−	6.66742i	−0.948661	−	0.254193i
$689$	−1.31297	+	2.27413i	−0.0500202	+	0.0866375i
$690$		0			0
$691$	20.4398	+	35.4027i	0.777566	+	1.34678i	0.933341	+	0.358991i	$0.116879\pi$
$691$	20.4398	+	35.4027i	0.777566	+	1.34678i	−0.155775	+	0.987793i	$0.549788\pi$
$692$	14.8105	−	14.8105i	0.563009	−	0.563009i
$693$	−30.4596	−	24.3590i	−1.15706	−	0.925321i
$694$			2.23605i			0.0848793i
$695$		0			0
$696$	−15.0303	−	11.5549i	−0.569723	−	0.437989i
$697$	−32.0906	+	8.59865i	−1.21552	+	0.325697i
$698$	0.157624	−	0.588262i	0.00596617	−	0.0222660i
$699$	0.687181	−	5.18316i	0.0259916	−	0.196045i
$700$		0			0
$701$			21.0222i			0.793996i	0.917819	+	0.396998i	$0.129948\pi$
$701$			21.0222i			0.793996i	−0.917819	+	0.396998i	$0.870052\pi$
$702$	1.53117	−	1.98421i	0.0577904	−	0.0748892i
$703$	1.30047	+	4.85342i	0.0490481	+	0.183050i
$704$	−11.7329	+	20.3220i	−0.442201	+	0.765914i
$705$		0			0
$706$	−1.13313			−0.0426459
$707$	26.0253	+	35.2297i	0.978784	+	1.32495i
$708$	23.9585	−	18.3494i	0.900416	−	0.689611i
$709$	−35.0447	+	20.2331i	−1.31613	+	0.759870i	−0.983104	−	0.183047i	$-0.941404\pi$
$709$	−35.0447	+	20.2331i	−1.31613	+	0.759870i	−0.333029	+	0.942917i	$0.608071\pi$
$710$		0			0
$711$	−7.95138	+	7.92245i	−0.298200	+	0.297115i
$712$	−4.00044	+	14.9299i	−0.149923	+	0.559520i
$713$	2.81655	+	2.81655i	0.105481	+	0.105481i
$714$	2.52927	−	8.76418i	0.0946554	−	0.327991i
$715$		0			0
$716$	−19.6873	+	11.3665i	−0.735749	+	0.424785i
$717$	44.8388	−	5.86158i	1.67453	−	0.218905i
$718$	2.70756	+	10.1047i	0.101045	+	0.377106i
$719$	16.7113	+	28.9448i	0.623226	+	1.07946i	0.988881	+	0.148709i	$0.0475117\pi$
$719$	16.7113	+	28.9448i	0.623226	+	1.07946i	−0.365655	+	0.930751i	$0.619155\pi$
$720$		0			0
$721$	−6.65667	−	5.30359i	−0.247907	−	0.197516i
$722$	−0.938262	+	0.938262i	−0.0349185	+	0.0349185i
$723$	−12.8142	+	30.8567i	−0.476566	+	1.14757i
$724$	30.1081	+	17.3829i	1.11896	+	0.646032i
$725$		0			0
$726$	−3.28436	−	7.94962i	−0.121894	−	0.295038i
$727$	13.5236	+	13.5236i	0.501562	+	0.501562i	0.911923	−	0.410361i	$-0.134597\pi$
$727$	13.5236	+	13.5236i	0.501562	+	0.501562i	−0.410361	+	0.911923i	$0.634597\pi$
$728$	4.51264	+	1.96641i	0.167249	+	0.0728800i
$729$	19.1960	−	18.9872i	0.710962	−	0.703231i
$730$		0			0
$731$	−37.1518	−	21.4496i	−1.37411	−	0.793343i
$732$	3.58556	+	27.4281i	0.132526	+	1.01377i
$733$	−16.7373	−	4.48473i	−0.618204	−	0.165647i	−0.0638931	−	0.997957i	$-0.520352\pi$
$733$	−16.7373	−	4.48473i	−0.618204	−	0.165647i	−0.554311	+	0.832309i	$0.687018\pi$
$734$	−12.2023			−0.450394
$735$		0			0
$736$	−26.2119			−0.966185
$737$	43.4157	+	11.6332i	1.59924	+	0.428515i
$738$	−0.0130216	+	7.14601i	−0.000479330	+	0.263048i
$739$	11.5630	+	6.67588i	0.425351	+	0.245576i	0.697364	−	0.716717i	$-0.254356\pi$
$739$	11.5630	+	6.67588i	0.425351	+	0.245576i	−0.272013	+	0.962293i	$0.587689\pi$
$740$		0			0
$741$	−1.14382	+	8.62742i	−0.0420192	+	0.316936i
$742$	1.88457	+	0.821212i	0.0691847	+	0.0301476i
$743$	−1.50716	−	1.50716i	−0.0552925	−	0.0552925i	0.678920	−	0.734212i	$-0.262448\pi$
$743$	−1.50716	−	1.50716i	−0.0552925	−	0.0552925i	−0.734212	+	0.678920i	$0.762448\pi$
$744$	1.45684	−	0.601887i	0.0534102	−	0.0220662i
$745$		0			0
$746$	8.28851	+	4.78537i	0.303464	+	0.175205i
$747$	6.11104	+	3.54308i	0.223591	+	0.129634i
$748$	−34.0024	+	34.0024i	−1.24325	+	1.24325i
$749$	−33.7846	−	26.9173i	−1.23446	−	0.983537i
$750$		0			0
$751$	17.2167	+	29.8203i	0.628248	+	1.08816i	0.987903	+	0.155072i	$0.0495610\pi$
$751$	17.2167	+	29.8203i	0.628248	+	1.08816i	−0.359655	+	0.933085i	$0.617106\pi$
$752$	1.06553	+	3.97663i	0.0388560	+	0.145013i
$753$	4.85012	+	37.1015i	0.176748	+	1.35205i
$754$	3.13766	−	1.81153i	0.114267	−	0.0659719i
$755$		0			0
$756$	21.8399	+	13.2278i	0.794308	+	0.481090i
$757$	20.6600	+	20.6600i	0.750901	+	0.750901i	0.974647	−	0.223746i	$-0.0718287\pi$
$757$	20.6600	+	20.6600i	0.750901	+	0.750901i	−0.223746	+	0.974647i	$0.571829\pi$
$758$	−0.152124	+	0.567733i	−0.00552538	+	0.0206210i
$759$	−33.0843	+	43.0351i	−1.20089	+	1.56208i
$760$		0			0
$761$	−21.2834	+	12.2880i	−0.771521	+	0.445438i	−0.833417	−	0.552645i	$-0.813619\pi$
$761$	−21.2834	+	12.2880i	−0.771521	+	0.445438i	0.0618959	+	0.998083i	$0.480285\pi$
$762$	3.53797	+	4.61948i	0.128167	+	0.167346i
$763$	−11.5924	−	15.6923i	−0.419674	−	0.568099i
$764$	25.3420			0.916841
$765$		0			0
$766$	4.28038	−	7.41383i	0.154656	−	0.267873i
$767$	3.09998	+	11.5693i	0.111934	+	0.417743i
$768$	3.82914	−	9.22060i	0.138172	−	0.332720i
$769$		−	17.7006i		−	0.638302i	−0.947704	−	0.319151i	$-0.896602\pi$
$769$		−	17.7006i		−	0.638302i	0.947704	−	0.319151i	$-0.103398\pi$
$770$		0			0
$771$	−27.7279	−	3.67615i	−0.998595	−	0.132393i
$772$	−0.0312349	+	0.116570i	−0.00112417	+	0.00419545i
$773$	−19.9199	+	5.33751i	−0.716467	+	0.191977i	−0.598595	−	0.801052i	$-0.704274\pi$
$773$	−19.9199	+	5.33751i	−0.716467	+	0.191977i	−0.117872	+	0.993029i	$0.537607\pi$
$774$	−6.53665	+	6.51287i	−0.234955	+	0.234100i
$775$		0			0
$776$		−	14.9998i		−	0.538462i
$777$	−3.02197	+	5.01004i	−0.108413	+	0.179734i
$778$	2.77510	−	2.77510i	0.0994922	−	0.0994922i
$779$	−12.4069	−	21.4895i	−0.444525	−	0.769940i
$780$		0			0
$781$	−17.4061	+	30.1483i	−0.622840	+	1.07879i
$782$	−12.2631	−	3.28590i	−0.438529	−	0.117503i
$783$	36.1002	−	14.8377i	1.29012	−	0.530257i
$784$	−6.50917	+	21.1703i	−0.232470	+	0.756082i
$785$		0			0
$786$	−7.45224	+	3.07887i	−0.265813	+	0.109820i
$787$	−36.9690	+	9.90582i	−1.31780	+	0.353104i	−0.848154	−	0.529749i	$-0.822286\pi$
$787$	−36.9690	+	9.90582i	−1.31780	+	0.353104i	−0.469649	+	0.882853i	$0.655619\pi$
$788$	−41.3662	+	11.0840i	−1.47361	+	0.394853i
$789$	−7.82176	+	3.23153i	−0.278462	+	0.115046i
$790$		0			0
$791$	4.09669	+	10.4243i	0.145662	+	0.370646i
$792$	10.7067	+	18.6228i	0.380446	+	0.661733i
$793$	−10.6045	−	2.84148i	−0.376578	−	0.100904i
$794$	0.776850	−	1.34554i	0.0275694	−	0.0477515i
$795$		0			0
$796$	13.0634	+	22.6265i	0.463020	+	0.801974i
$797$	−32.4675	+	32.4675i	−1.15006	+	1.15006i	−0.163516	+	0.986541i	$0.552284\pi$
$797$	−32.4675	+	32.4675i	−1.15006	+	1.15006i	−0.986541	+	0.163516i	$0.947716\pi$
$798$	6.81183	+	0.130517i	0.241136	+	0.00462024i
$799$			6.85582i			0.242541i
$800$		0			0
$801$	−22.4597	−	22.5417i	−0.793573	−	0.796470i
$802$	9.07128	−	2.43064i	0.320318	−	0.0858289i
$803$	−10.4507	+	39.0027i	−0.368798	+	1.37637i
$804$	−29.1704	−	3.86740i	−1.02876	−	0.136393i
$805$		0			0
$806$			0.301232i			0.0106104i
$807$	2.89478	−	6.97065i	0.101901	−	0.245379i
$808$	−6.24374	−	23.3020i	−0.219654	−	0.819760i
$809$	−17.1189	+	29.6507i	−0.601867	+	1.04246i	0.390672	+	0.920530i	$0.372243\pi$
$809$	−17.1189	+	29.6507i	−0.601867	+	1.04246i	−0.992538	+	0.121934i	$0.961091\pi$
$810$		0			0
$811$	43.4051			1.52416			0.762079	−	0.647484i	$-0.224179\pi$
$811$	43.4051			1.52416			0.762079	+	0.647484i	$0.224179\pi$
$812$	21.9316	+	29.6881i	0.769648	+	1.04185i
$813$	22.0517	+	28.7927i	0.773388	+	1.00980i
$814$	−2.05257	+	1.18505i	−0.0719426	+	0.0415361i
$815$		0			0
$816$	17.5994	−	22.8928i	0.616103	−	0.801409i
$817$	8.29290	−	30.9495i	0.290132	−	1.08279i
$818$	5.12583	+	5.12583i	0.179220	+	0.179220i
$819$	−8.16204	+	6.00661i	−0.285205	+	0.209888i
$820$		0			0
$821$	7.00660	−	4.04526i	0.244532	−	0.141181i	−0.372726	−	0.927941i	$-0.621577\pi$
$821$	7.00660	−	4.04526i	0.244532	−	0.141181i	0.617258	+	0.786761i	$0.288244\pi$
$822$	0.481016	+	3.67958i	0.0167774	+	0.128340i
$823$	0.936129	+	3.49368i	0.0326314	+	0.121782i	0.980320	−	0.197413i	$-0.0632541\pi$
$823$	0.936129	+	3.49368i	0.0326314	+	0.121782i	−0.947689	+	0.319195i	$0.896587\pi$
$824$	2.34385	+	4.05968i	0.0816520	+	0.141425i
$825$		0			0
$826$	8.72680	−	3.42958i	0.303644	−	0.119330i
$827$	−14.8183	+	14.8183i	−0.515283	+	0.515283i	−0.916140	−	0.400857i	$-0.868712\pi$
$827$	−14.8183	+	14.8183i	−0.515283	+	0.515283i	0.400857	+	0.916140i	$0.368712\pi$
$828$	17.8247	−	30.7437i	0.619450	−	1.06842i
$829$	−13.5213	−	7.80652i	−0.469614	−	0.271132i	0.246464	−	0.969152i	$-0.420731\pi$
$829$	−13.5213	−	7.80652i	−0.469614	−	0.271132i	−0.716078	+	0.698020i	$0.754065\pi$
$830$		0			0
$831$	−10.7258	+	4.43132i	−0.372073	+	0.153721i
$832$	4.31139	+	4.31139i	0.149470	+	0.149470i
$833$	−19.5948	+	31.2478i	−0.678919	+	1.08267i
$834$	1.34889	−	10.1742i	0.0467083	−	0.352304i
$835$		0			0
$836$	−31.1040	−	17.9579i	−1.07575	−	0.621087i
$837$	−0.432365	+	3.21618i	−0.0149447	+	0.111168i
$838$	0.296444	+	0.0794318i	0.0102405	+	0.00274393i
$839$	−27.0215			−0.932885			−0.466442	−	0.884552i	$-0.654464\pi$
$839$	−27.0215			−0.932885			−0.466442	+	0.884552i	$0.654464\pi$
$840$		0			0
$841$	27.4215			0.945569
$842$	1.04663	+	0.280444i	0.0360693	+	0.00966475i
$843$	0.600216	+	4.59142i	0.0206725	+	0.158137i
$844$	−2.04335	−	1.17973i	−0.0703349	−	0.0406079i
$845$		0			0
$846$	1.42371	+	0.384263i	0.0489480	+	0.0132112i
$847$	3.90965	+	34.5584i	0.134337	+	1.18744i
$848$	4.60153	+	4.60153i	0.158017	+	0.158017i
$849$	−13.2085	−	31.9705i	−0.453315	−	1.09723i
$850$		0			0
$851$	7.05223	+	4.07161i	0.241747	+	0.139573i
$852$	8.74076	−	21.0478i	0.299453	−	0.721086i
$853$	6.24530	−	6.24530i	0.213835	−	0.213835i	−0.592059	−	0.805894i	$-0.701685\pi$
$853$	6.24530	−	6.24530i	0.213835	−	0.213835i	0.805894	+	0.592059i	$0.201685\pi$
$854$	−1.27711	+	8.49922i	−0.0437019	+	0.290837i
$855$		0			0
$856$	11.8958	+	20.6041i	0.406589	+	0.704233i
$857$	−9.79444	−	36.5533i	−0.334572	−	1.24864i	−0.904333	−	0.426828i	$-0.859631\pi$
$857$	−9.79444	−	36.5533i	−0.334572	−	1.24864i	0.569761	−	0.821810i	$-0.307036\pi$
$858$	−4.07051	+	0.532120i	−0.138965	+	0.0181663i
$859$	39.7344	−	22.9407i	1.35572	−	0.782726i	0.366677	−	0.930348i	$-0.380495\pi$
$859$	39.7344	−	22.9407i	1.35572	−	0.782726i	0.989044	+	0.147623i	$0.0471621\pi$
$860$		0			0
$861$	8.01167	−	27.7613i	0.273037	−	0.946104i
$862$	−3.22596	−	3.22596i	−0.109877	−	0.109877i
$863$	7.39902	−	27.6135i	0.251866	−	0.939975i	−0.717942	−	0.696103i	$-0.754916\pi$
$863$	7.39902	−	27.6135i	0.251866	−	0.939975i	0.969807	−	0.243872i	$-0.0784177\pi$
$864$	−12.9537	−	16.9774i	−0.440692	−	0.577583i
$865$		0			0
$866$	−12.3914	+	7.15417i	−0.421076	+	0.243109i
$867$	14.7999	−	11.3349i	0.502629	−	0.384954i
$868$	−3.04939	+	0.344984i	−0.103503	+	0.0117095i
$869$	18.3849			0.623665
$870$		0			0
$871$	5.83942	−	10.1142i	0.197861	−	0.342706i
$872$	2.78114	+	10.3793i	0.0941812	+	0.351489i
$873$	26.7151	+	15.4890i	0.904170	+	0.524222i
$874$		−	9.48240i		−	0.320747i
$875$		0			0
$876$	3.47429	−	26.2054i	0.117385	−	0.885397i
$877$	−5.36097	+	20.0074i	−0.181027	+	0.675602i	0.814419	+	0.580277i	$0.197056\pi$
$877$	−5.36097	+	20.0074i	−0.181027	+	0.675602i	−0.995446	+	0.0953252i	$0.969611\pi$
$878$	0.261178	−	0.0699824i	0.00881433	−	0.00236179i
$879$	−9.88068	−	7.59602i	−0.333267	−	0.256208i
$880$		0			0
$881$		−	20.9173i		−	0.704723i	−0.935864	−	0.352361i	$-0.885379\pi$
$881$		−	20.9173i		−	0.704723i	0.935864	−	0.352361i	$-0.114621\pi$
$882$	5.39077	+	5.82055i	0.181517	+	0.195988i
$883$	−7.30469	+	7.30469i	−0.245822	+	0.245822i	−0.819254	−	0.573431i	$-0.805612\pi$
$883$	−7.30469	+	7.30469i	−0.245822	+	0.245822i	0.573431	+	0.819254i	$0.305612\pi$
$884$	6.24728	+	10.8206i	0.210119	+	0.363936i
$885$		0			0
$886$	−1.62100	+	2.80766i	−0.0544587	+	0.0943253i
$887$	17.6020	+	4.71644i	0.591017	+	0.158363i	0.541918	−	0.840431i	$-0.317698\pi$
$887$	17.6020	+	4.71644i	0.591017	+	0.158363i	0.0490991	+	0.998794i	$0.484365\pi$
$888$	2.55838	−	1.95941i	0.0858535	−	0.0657535i
$889$	−8.60538	−	21.8970i	−0.288615	−	0.734401i
$890$		0			0
$891$	−44.2237	−	0.161170i	−1.48155	−	0.00539941i
$892$	−0.529981	+	0.142008i	−0.0177451	+	0.00475478i
$893$	−4.94611	+	1.32531i	−0.165515	+	0.0443497i
$894$	−0.692007	−	1.67497i	−0.0231442	−	0.0560193i
$895$		0			0
$896$	16.5255	−	20.7416i	0.552079	−	0.692929i
$897$	8.57605	+	11.1976i	0.286346	+	0.373878i
$898$	4.44109	+	1.18999i	0.148201	+	0.0397104i
$899$	−2.34553	+	4.06258i	−0.0782278	+	0.135494i
$900$		0			0
$901$	5.41846	+	9.38504i	0.180515	+	0.312661i
$902$	8.27643	−	8.27643i	0.275575	−	0.275575i
$903$	32.6630	−	18.0327i	1.08696	−	0.600090i
$904$		−	6.16889i		−	0.205174i
$905$		0			0
$906$	−0.142886	+	0.185861i	−0.00474706	+	0.00617483i
$907$	51.4317	−	13.7811i	1.70776	−	0.457594i	0.732888	−	0.680349i	$-0.238172\pi$
$907$	51.4317	−	13.7811i	1.70776	−	0.457594i	0.974874	+	0.222756i	$0.0715052\pi$
$908$	11.2414	−	41.9536i	0.373060	−	1.39228i
$909$	47.9489	+	12.9415i	1.59036	+	0.429244i
$910$		0			0
$911$			30.2060i			1.00077i	0.865804	+	0.500384i	$0.166808\pi$
$911$			30.2060i			1.00077i	−0.865804	+	0.500384i	$0.833192\pi$
$912$	19.9181	+	8.27163i	0.659555	+	0.273901i
$913$	−2.99456	−	11.1758i	−0.0991054	−	0.369866i
$914$	1.96757	−	3.40793i	0.0650813	−	0.112724i
$915$		0			0
$916$	−49.1760			−1.62482
$917$	32.3961	−	3.66504i	1.06982	−	0.121030i
$918$	−3.93204	−	9.56666i	−0.129777	−	0.315747i
$919$	15.0778	−	8.70517i	0.497371	−	0.287157i	−0.230256	−	0.973130i	$-0.573957\pi$
$919$	15.0778	−	8.70517i	0.497371	−	0.287157i	0.727627	+	0.685973i	$0.240623\pi$
$920$		0			0
$921$	−15.1244	−	11.6273i	−0.498365	−	0.383131i
$922$	−2.77113	+	10.3420i	−0.0912622	+	0.340595i
$923$	6.39607	+	6.39607i	0.210529	+	0.210529i
$924$	−10.0484	−	40.5967i	−0.330568	−	1.33553i
$925$		0			0
$926$	3.00031	−	1.73223i	0.0985963	−	0.0569246i
$927$	−9.65070	−	0.0175856i	−0.316971	−	0.000577588i
$928$	−7.98975	−	29.8182i	−0.262277	−	0.978829i
$929$	5.76695	+	9.98866i	0.189208	+	0.327717i	0.944986	−	0.327110i	$-0.106075\pi$
$929$	5.76695	+	9.98866i	0.189208	+	0.327717i	−0.755779	+	0.654827i	$0.772741\pi$
$930$		0			0
$931$	−26.3315	−	8.09607i	−0.862980	−	0.265338i
$932$	3.96443	−	3.96443i	0.129859	−	0.129859i
$933$	10.7183	+	4.45111i	0.350901	+	0.145723i
$934$	−7.31102	−	4.22102i	−0.239224	−	0.138116i
$935$		0			0
$936$	5.39399	−	1.43479i	0.176308	−	0.0468974i
$937$	−18.3531	−	18.3531i	−0.599569	−	0.599569i	0.340628	−	0.940198i	$-0.389360\pi$
$937$	−18.3531	−	18.3531i	−0.599569	−	0.599569i	−0.940198	+	0.340628i	$0.889360\pi$
$938$	−8.38159	−	3.65233i	−0.273669	−	0.119253i
$939$	3.14362	+	0.416780i	0.102588	+	0.0136011i
$940$		0			0
$941$	−16.6711	−	9.62509i	−0.543464	−	0.313769i	0.203018	−	0.979175i	$-0.434925\pi$
$941$	−16.6711	−	9.62509i	−0.543464	−	0.313769i	−0.746482	+	0.665406i	$0.768258\pi$
$942$	14.1039	−	1.84375i	0.459531	−	0.0600725i
$943$	−38.8446	−	10.4084i	−1.26495	−	0.338943i
$944$	29.6822			0.966072
$945$		0			0
$946$	15.1138			0.491392
$947$	−21.4189	−	5.73918i	−0.696021	−	0.186498i	−0.106573	−	0.994305i	$-0.533988\pi$
$947$	−21.4189	−	5.73918i	−0.696021	−	0.186498i	−0.589448	+	0.807807i	$0.700655\pi$
$948$	−11.9345	+	1.56015i	−0.387615	+	0.0506713i
$949$	9.08610	+	5.24586i	0.294947	+	0.170288i
$950$		0			0
$951$	−16.9033	−	2.24103i	−0.548126	−	0.0726703i
$952$	16.3394	−	12.0705i	0.529564	−	0.391207i
$953$	−6.88889	−	6.88889i	−0.223153	−	0.223153i	0.586672	−	0.809825i	$-0.300438\pi$
$953$	−6.88889	−	6.88889i	−0.223153	−	0.223153i	−0.809825	+	0.586672i	$0.800438\pi$
$954$	2.25264	−	0.599195i	0.0729318	−	0.0193997i
$955$		0			0
$956$	41.9934	+	24.2449i	1.35816	+	0.784135i
$957$	−59.0404	−	24.5184i	−1.90850	−	0.792567i
$958$	−8.59539	+	8.59539i	−0.277704	+	0.277704i
$959$	2.22960	−	14.8381i	0.0719976	−	0.479146i
$960$		0			0
$961$	15.3050	+	26.5090i	0.493709	+	0.855129i
$962$	0.159390	+	0.594850i	0.00513893	+	0.0191787i
$963$	−48.9802	−	0.0892524i	−1.57837	−	0.00287612i
$964$	−31.0274	+	17.9137i	−0.999327	+	0.576961i
$965$		0			0
$966$	7.95579	−	7.65665i	0.255973	−	0.246349i
$967$	−7.87363	−	7.87363i	−0.253199	−	0.253199i	0.569082	−	0.822281i	$-0.307299\pi$
$967$	−7.87363	−	7.87363i	−0.253199	−	0.253199i	−0.822281	+	0.569082i	$0.807299\pi$
$968$	4.95775	−	18.5026i	0.159348	−	0.594695i
$969$	28.4740	+	21.8901i	0.914716	+	0.703211i
$970$		0			0
$971$	7.17395	−	4.14188i	0.230223	−	0.132919i	−0.380452	−	0.924801i	$-0.624232\pi$
$971$	7.17395	−	4.14188i	0.230223	−	0.132919i	0.610675	+	0.791881i	$0.290898\pi$
$972$	28.7214	−	3.64821i	0.921238	−	0.117016i
$973$	−16.5776	+	38.0434i	−0.531455	+	1.21961i
$974$	12.7131			0.407355
$975$		0			0
$976$	−13.6035	+	23.5620i	−0.435438	+	0.754200i
$977$	−12.7015	−	47.4027i	−0.406358	−	1.51655i	−0.801538	−	0.597944i	$-0.795984\pi$
$977$	−12.7015	−	47.4027i	−0.406358	−	1.51655i	0.395180	−	0.918604i	$-0.370682\pi$
$978$	−5.43448	−	2.25684i	−0.173776	−	0.0721658i
$979$			52.1200i			1.66576i
$980$		0			0
$981$	−21.3578	−	5.76453i	−0.681901	−	0.184047i
$982$	−2.14025	+	7.98752i	−0.0682981	+	0.254892i
$983$	27.1932	−	7.28639i	0.867327	−	0.232400i	0.202396	−	0.979304i	$-0.435127\pi$
$983$	27.1932	−	7.28639i	0.867327	−	0.232400i	0.664932	+	0.746904i	$0.268461\pi$
$984$	−9.69946	+	12.6168i	−0.309207	+	0.402208i
$985$		0			0
$986$		−	14.9519i		−	0.476165i
$987$	−5.10572	−	3.07968i	−0.162517	−	0.0980274i
$988$	−6.59882	+	6.59882i	−0.209937	+	0.209937i
$989$	−25.9640	−	44.9710i	−0.825608	−	1.43000i
$990$		0			0
$991$	29.9213	−	51.8252i	0.950481	−	1.64628i	0.206096	−	0.978532i	$-0.433924\pi$
$991$	29.9213	−	51.8252i	0.950481	−	1.64628i	0.744385	−	0.667750i	$-0.232743\pi$
$992$	2.47917	+	0.664293i	0.0787139	+	0.0210913i
$993$	4.25786	+	5.55944i	0.135119	+	0.176423i
$994$	4.41255	−	5.53831i	0.139958	−	0.175665i
$995$		0			0
$996$	2.89230	+	7.00065i	0.0916459	+	0.221824i
$997$	−13.2381	+	3.54714i	−0.419255	+	0.112339i	−0.462278	−	0.886735i	$-0.652968\pi$
$997$	−13.2381	+	3.54714i	−0.419255	+	0.112339i	0.0430233	+	0.999074i	$0.486301\pi$
$998$	14.3623	−	3.84836i	0.454630	−	0.121818i
$999$	0.847964	+	6.57986i	0.0268284	+	0.208177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bf.g.32.11	yes	80
3.2	odd	2	inner	525.2.bf.g.32.9	✓	80
5.2	odd	4	inner	525.2.bf.g.368.9	yes	80
5.3	odd	4	inner	525.2.bf.g.368.12	yes	80
5.4	even	2	inner	525.2.bf.g.32.10	yes	80
7.2	even	3	inner	525.2.bf.g.107.10	yes	80
15.2	even	4	inner	525.2.bf.g.368.11	yes	80
15.8	even	4	inner	525.2.bf.g.368.10	yes	80
15.14	odd	2	inner	525.2.bf.g.32.12	yes	80
21.2	odd	6	inner	525.2.bf.g.107.12	yes	80
35.2	odd	12	inner	525.2.bf.g.443.12	yes	80
35.9	even	6	inner	525.2.bf.g.107.11	yes	80
35.23	odd	12	inner	525.2.bf.g.443.9	yes	80
105.2	even	12	inner	525.2.bf.g.443.10	yes	80
105.23	even	12	inner	525.2.bf.g.443.11	yes	80
105.44	odd	6	inner	525.2.bf.g.107.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bf.g.32.9	✓	80	3.2	odd	2	inner
525.2.bf.g.32.10	yes	80	5.4	even	2	inner
525.2.bf.g.32.11	yes	80	1.1	even	1	trivial
525.2.bf.g.32.12	yes	80	15.14	odd	2	inner
525.2.bf.g.107.9	yes	80	105.44	odd	6	inner
525.2.bf.g.107.10	yes	80	7.2	even	3	inner
525.2.bf.g.107.11	yes	80	35.9	even	6	inner
525.2.bf.g.107.12	yes	80	21.2	odd	6	inner
525.2.bf.g.368.9	yes	80	5.2	odd	4	inner
525.2.bf.g.368.10	yes	80	15.8	even	4	inner
525.2.bf.g.368.11	yes	80	15.2	even	4	inner
525.2.bf.g.368.12	yes	80	5.3	odd	4	inner
525.2.bf.g.443.9	yes	80	35.23	odd	12	inner
525.2.bf.g.443.10	yes	80	105.2	even	12	inner
525.2.bf.g.443.11	yes	80	105.23	even	12	inner
525.2.bf.g.443.12	yes	80	35.2	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.364909 + 0.0977772i) q^{2} +(-1.71744 + 0.224513i) q^{3} +(-1.60845 - 0.928640i) q^{4} +(-0.648661 - 0.0859992i) q^{6} +(2.42547 + 1.05692i) q^{7} +(-1.03040 - 1.03040i) q^{8} +(2.89919 - 0.771175i) q^{9} +O(q^{10})\)	\(q+(0.364909 + 0.0977772i) q^{2} +(-1.71744 + 0.224513i) q^{3} +(-1.60845 - 0.928640i) q^{4} +(-0.648661 - 0.0859992i) q^{6} +(2.42547 + 1.05692i) q^{7} +(-1.03040 - 1.03040i) q^{8} +(2.89919 - 0.771175i) q^{9} +(-4.25545 - 2.45689i) q^{11} +(2.97091 + 1.23376i) q^{12} +(-0.902810 + 0.902810i) q^{13} +(0.781736 + 0.622835i) q^{14} +(1.58203 + 2.74015i) q^{16} +(1.36373 + 5.08951i) q^{17} +(1.13334 + 0.00206519i) q^{18} +(-3.40819 + 1.96772i) q^{19} +(-4.40289 - 1.27064i) q^{21} +(-1.31263 - 1.31263i) q^{22} +(-1.65075 + 6.16067i) q^{23} +(2.00099 + 1.53832i) q^{24} +(-0.417718 + 0.241170i) q^{26} +(-4.80604 + 1.97535i) q^{27} +(-2.91977 - 3.95239i) q^{28} -7.51143 q^{29} +(0.312262 - 0.540853i) q^{31} +(1.06368 + 3.96971i) q^{32} +(7.86008 + 3.26414i) q^{33} +1.99055i q^{34} +(-5.37935 - 1.45190i) q^{36} +(0.330451 - 1.23326i) q^{37} +(-1.43608 + 0.384796i) q^{38} +(1.34783 - 1.75321i) q^{39} +6.30525i q^{41} +(-1.48242 - 0.894170i) q^{42} +(-5.75709 + 5.75709i) q^{43} +(4.56313 + 7.90357i) q^{44} +(-1.20475 + 2.08668i) q^{46} +(1.25681 + 0.336762i) q^{47} +(-3.33223 - 4.35085i) q^{48} +(4.76586 + 5.12705i) q^{49} +(-3.48478 - 8.43474i) q^{51} +(2.29051 - 0.613741i) q^{52} +(1.98663 - 0.532317i) q^{53} +(-1.94691 + 0.250904i) q^{54} +(-1.41017 - 3.58827i) q^{56} +(5.41157 - 4.14462i) q^{57} +(-2.74099 - 0.734446i) q^{58} +(4.69053 - 8.12423i) q^{59} +(4.29939 + 7.44677i) q^{61} +(0.166830 - 0.166830i) q^{62} +(7.84697 + 1.19373i) q^{63} -4.77552i q^{64} +(2.54906 + 1.95965i) q^{66} +(-8.83552 + 2.36747i) q^{67} +(2.53283 - 9.45264i) q^{68} +(1.45190 - 10.9512i) q^{69} -7.08463i q^{71} +(-3.78196 - 2.19271i) q^{72} +(-2.12683 - 7.93742i) q^{73} +(0.241170 - 0.417718i) q^{74} +7.30921 q^{76} +(-7.72477 - 10.4568i) q^{77} +(0.663259 - 0.507977i) q^{78} +(-3.24024 + 1.87075i) q^{79} +(7.81058 - 4.47156i) q^{81} +(-0.616509 + 2.30084i) q^{82} +(1.66497 + 1.66497i) q^{83} +(5.90188 + 6.13246i) q^{84} +(-2.66373 + 1.53790i) q^{86} +(12.9004 - 1.68642i) q^{87} +(1.85325 + 6.91642i) q^{88} +(-5.30346 - 9.18587i) q^{89} +(-3.14394 + 1.23555i) q^{91} +(8.37620 - 8.37620i) q^{92} +(-0.414861 + 0.998988i) q^{93} +(0.425695 + 0.245775i) q^{94} +(-2.71806 - 6.57892i) q^{96} +(7.27861 + 7.27861i) q^{97} +(1.23780 + 2.33690i) q^{98} +(-14.2320 - 3.84127i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{6}+O(q^{10}) \) 80 * q + 16 * q^6	\( 80 q + 16 q^{6} + 72 q^{16} + 44 q^{21} + 72 q^{31} - 240 q^{36} - 92 q^{51} - 24 q^{61} - 216 q^{66} - 208 q^{76} - 20 q^{81} - 40 q^{91} - 156 q^{96}+O(q^{100}) \) 80 * q + 16 * q^6 + 72 * q^16 + 44 * q^21 + 72 * q^31 - 240 * q^36 - 92 * q^51 - 24 * q^61 - 216 * q^66 - 208 * q^76 - 20 * q^81 - 40 * q^91 - 156 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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