LMFDB - Embedded newform 552.2.q.a.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	552.169
Dual form			552.2.q.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 + 0.909632i) q^{3} +(-1.96611 - 2.26901i) q^{5} +(3.59431 + 2.30992i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.415415 + 0.909632i) q^{3} +(-1.96611 - 2.26901i) q^{5} +(3.59431 + 2.30992i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.492758 - 3.42721i) q^{11} +(2.61277 - 1.67912i) q^{13} +(1.24721 - 2.73102i) q^{15} +(-0.416498 + 0.122295i) q^{17} +(5.69457 + 1.67208i) q^{19} +(-0.608049 + 4.22908i) q^{21} +(1.75587 + 4.46284i) q^{23} +(-0.571250 + 3.97313i) q^{25} +(-0.959493 - 0.281733i) q^{27} +(5.56565 - 1.63422i) q^{29} +(2.51732 - 5.51216i) q^{31} +(2.91280 - 1.87194i) q^{33} +(-1.82556 - 12.6971i) q^{35} +(-2.84815 + 3.28694i) q^{37} +(2.61277 + 1.67912i) q^{39} +(4.31465 + 4.97937i) q^{41} +(-3.59967 - 7.88219i) q^{43} +3.00233 q^{45} -2.34432 q^{47} +(4.67542 + 10.2377i) q^{49} +(-0.284263 - 0.328057i) q^{51} +(2.29721 + 1.47633i) q^{53} +(-6.80755 + 7.85634i) q^{55} +(0.844636 + 5.87457i) q^{57} +(3.95904 - 2.54432i) q^{59} +(-4.40845 + 9.65315i) q^{61} +(-4.09950 + 1.20372i) q^{63} +(-8.94693 - 2.62706i) q^{65} +(1.72555 - 12.0015i) q^{67} +(-3.33012 + 3.45113i) q^{69} +(-0.995876 + 6.92647i) q^{71} +(-8.86701 - 2.60359i) q^{73} +(-3.85139 + 1.13087i) q^{75} +(6.14546 - 13.4567i) q^{77} +(-1.94315 + 1.24879i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-11.7385 + 13.5470i) q^{83} +(1.09637 + 0.704593i) q^{85} +(3.79859 + 4.38381i) q^{87} +(-3.49733 - 7.65808i) q^{89} +13.2697 q^{91} +6.05976 q^{93} +(-7.40219 - 16.2085i) q^{95} +(-11.6577 - 13.4537i) q^{97} +(2.91280 + 1.87194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$3$	0.415415	+	0.909632i	0.239840	+	0.525176i
$4$		0			0
$5$	−1.96611	−	2.26901i	−0.879270	−	1.01473i	−0.999758	−	0.0220171i	$-0.992991\pi$
$5$	−1.96611	−	2.26901i	−0.879270	−	1.01473i	0.120487	−	0.992715i	$-0.461554\pi$
$6$		0			0
$7$	3.59431	+	2.30992i	1.35852	+	0.873069i	0.998213	−	0.0597640i	$-0.0190348\pi$
$7$	3.59431	+	2.30992i	1.35852	+	0.873069i	0.360309	+	0.932833i	$0.382671\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−0.492758	−	3.42721i	−0.148572	−	1.03334i	−0.918559	−	0.395283i	$-0.870647\pi$
$11$	−0.492758	−	3.42721i	−0.148572	−	1.03334i	0.769987	−	0.638059i	$-0.220263\pi$
$12$		0			0
$13$	2.61277	−	1.67912i	0.724651	−	0.465705i	−0.125601	−	0.992081i	$-0.540086\pi$
$13$	2.61277	−	1.67912i	0.724651	−	0.465705i	0.850252	+	0.526376i	$0.176449\pi$
$14$		0			0
$15$	1.24721	−	2.73102i	0.322029	−	0.705145i
$16$		0			0
$17$	−0.416498	+	0.122295i	−0.101016	+	0.0296608i	−0.331850	−	0.943332i	$-0.607673\pi$
$17$	−0.416498	+	0.122295i	−0.101016	+	0.0296608i	0.230834	+	0.972993i	$0.425855\pi$
$18$		0			0
$19$	5.69457	+	1.67208i	1.30642	+	0.383601i	0.859576	−	0.511008i	$-0.170728\pi$
$19$	5.69457	+	1.67208i	1.30642	+	0.383601i	0.446849	+	0.894609i	$0.352546\pi$
$20$		0			0
$21$	−0.608049	+	4.22908i	−0.132687	+	0.922860i
$22$		0			0
$23$	1.75587	+	4.46284i	0.366124	+	0.930566i
$23$	1.75587	+	4.46284i	0.366124	+	0.930566i
$24$		0			0
$25$	−0.571250	+	3.97313i	−0.114250	+	0.794626i
$26$		0			0
$27$	−0.959493	−	0.281733i	−0.184655	−	0.0542195i
$28$		0			0
$29$	5.56565	−	1.63422i	1.03352	−	0.303467i	0.279376	−	0.960182i	$-0.409872\pi$
$29$	5.56565	−	1.63422i	1.03352	−	0.303467i	0.754139	+	0.656714i	$0.228054\pi$
$30$		0			0
$31$	2.51732	−	5.51216i	0.452124	−	0.990012i	−0.537089	−	0.843526i	$-0.680476\pi$
$31$	2.51732	−	5.51216i	0.452124	−	0.990012i	0.989213	−	0.146487i	$-0.0467966\pi$
$32$		0			0
$33$	2.91280	−	1.87194i	0.507053	−	0.325863i
$34$		0			0
$35$	−1.82556	−	12.6971i	−0.308577	−	2.14620i
$36$		0			0
$37$	−2.84815	+	3.28694i	−0.468233	+	0.540370i	−0.939919	−	0.341396i	$-0.889100\pi$
$37$	−2.84815	+	3.28694i	−0.468233	+	0.540370i	0.471686	+	0.881767i	$0.343646\pi$
$38$		0			0
$39$	2.61277	+	1.67912i	0.418378	+	0.268875i
$40$		0			0
$41$	4.31465	+	4.97937i	0.673835	+	0.777647i	0.984971	−	0.172718i	$-0.0552550\pi$
$41$	4.31465	+	4.97937i	0.673835	+	0.777647i	−0.311136	+	0.950365i	$0.600710\pi$
$42$		0			0
$43$	−3.59967	−	7.88219i	−0.548945	−	1.20202i	−0.957273	−	0.289187i	$-0.906615\pi$
$43$	−3.59967	−	7.88219i	−0.548945	−	1.20202i	0.408327	−	0.912836i	$-0.366112\pi$
$44$		0			0
$45$	3.00233			0.447561
$46$		0			0
$47$	−2.34432			−0.341955			−0.170977	−	0.985275i	$-0.554692\pi$
$47$	−2.34432			−0.341955			−0.170977	+	0.985275i	$0.554692\pi$
$48$		0			0
$49$	4.67542	+	10.2377i	0.667917	+	1.46253i
$50$		0			0
$51$	−0.284263	−	0.328057i	−0.0398047	−	0.0459371i
$52$		0			0
$53$	2.29721	+	1.47633i	0.315546	+	0.202789i	0.688821	−	0.724932i	$-0.258129\pi$
$53$	2.29721	+	1.47633i	0.315546	+	0.202789i	−0.373275	+	0.927721i	$0.621765\pi$
$54$		0			0
$55$	−6.80755	+	7.85634i	−0.917930	+	1.05935i
$56$		0			0
$57$	0.844636	+	5.87457i	0.111875	+	0.778106i
$58$		0			0
$59$	3.95904	−	2.54432i	0.515423	−	0.331242i	−0.256936	−	0.966428i	$-0.582713\pi$
$59$	3.95904	−	2.54432i	0.515423	−	0.331242i	0.772359	+	0.635186i	$0.219077\pi$
$60$		0			0
$61$	−4.40845	+	9.65315i	−0.564444	+	1.23596i	0.385260	+	0.922808i	$0.374112\pi$
$61$	−4.40845	+	9.65315i	−0.564444	+	1.23596i	−0.949703	+	0.313151i	$0.898615\pi$
$62$		0			0
$63$	−4.09950	+	1.20372i	−0.516488	+	0.151655i
$64$		0			0
$65$	−8.94693	−	2.62706i	−1.10973	−	0.325846i
$66$		0			0
$67$	1.72555	−	12.0015i	0.210810	−	1.46621i	−0.559653	−	0.828727i	$-0.689066\pi$
$67$	1.72555	−	12.0015i	0.210810	−	1.46621i	0.770462	−	0.637485i	$-0.220025\pi$
$68$		0			0
$69$	−3.33012	+	3.45113i	−0.400900	+	0.415467i
$70$		0			0
$71$	−0.995876	+	6.92647i	−0.118189	+	0.822020i	0.841359	+	0.540476i	$0.181756\pi$
$71$	−0.995876	+	6.92647i	−0.118189	+	0.822020i	−0.959548	+	0.281544i	$0.909153\pi$
$72$		0			0
$73$	−8.86701	−	2.60359i	−1.03781	−	0.304727i	−0.281925	−	0.959437i	$-0.590973\pi$
$73$	−8.86701	−	2.60359i	−1.03781	−	0.304727i	−0.755881	+	0.654710i	$0.772791\pi$
$74$		0			0
$75$	−3.85139	+	1.13087i	−0.444720	+	0.130582i
$76$		0			0
$77$	6.14546	−	13.4567i	0.700340	−	1.53353i
$78$		0			0
$79$	−1.94315	+	1.24879i	−0.218622	+	0.140500i	−0.645368	−	0.763872i	$-0.723296\pi$
$79$	−1.94315	+	1.24879i	−0.218622	+	0.140500i	0.426747	+	0.904371i	$0.359660\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	−11.7385	+	13.5470i	−1.28847	+	1.48697i	−0.508641	+	0.860979i	$0.669852\pi$
$83$	−11.7385	+	13.5470i	−1.28847	+	1.48697i	−0.779828	+	0.625994i	$0.784694\pi$
$84$		0			0
$85$	1.09637	+	0.704593i	0.118918	+	0.0764238i
$86$		0			0
$87$	3.79859	+	4.38381i	0.407252	+	0.469994i
$88$		0			0
$89$	−3.49733	−	7.65808i	−0.370716	−	0.811755i	−0.999418	−	0.0341088i	$-0.989141\pi$
$89$	−3.49733	−	7.65808i	−0.370716	−	0.811755i	0.628702	−	0.777646i	$-0.283587\pi$
$90$		0			0
$91$	13.2697			1.39105
$92$		0			0
$93$	6.05976			0.628368
$94$		0			0
$95$	−7.40219	−	16.2085i	−0.759448	−	1.66296i
$96$		0			0
$97$	−11.6577	−	13.4537i	−1.18366	−	1.36602i	−0.915338	−	0.402687i	$-0.868076\pi$
$97$	−11.6577	−	13.4537i	−1.18366	−	1.36602i	−0.268322	−	0.963329i	$-0.586469\pi$
$98$		0			0
$99$	2.91280	+	1.87194i	0.292747	+	0.188137i
$100$		0			0
$101$	−5.30265	+	6.11959i	−0.527634	+	0.608922i	−0.955526	−	0.294908i	$-0.904711\pi$
$101$	−5.30265	+	6.11959i	−0.527634	+	0.608922i	0.427892	+	0.903830i	$0.359256\pi$
$102$		0			0
$103$	0.776172	+	5.39839i	0.0764785	+	0.531920i	0.991660	+	0.128879i	$0.0411377\pi$
$103$	0.776172	+	5.39839i	0.0764785	+	0.531920i	−0.915182	+	0.403041i	$0.867953\pi$
$104$		0			0
$105$	10.7913	−	6.93515i	1.05312	−	0.676801i
$106$		0			0
$107$	6.97950	−	15.2830i	0.674733	−	1.47746i	−0.193395	−	0.981121i	$-0.561950\pi$
$107$	6.97950	−	15.2830i	0.674733	−	1.47746i	0.868129	−	0.496339i	$-0.165323\pi$
$108$		0			0
$109$	−13.1980	+	3.87528i	−1.26414	+	0.371185i	−0.844033	−	0.536290i	$-0.819825\pi$
$109$	−13.1980	+	3.87528i	−1.26414	+	0.371185i	−0.420106	+	0.907475i	$0.638007\pi$
$110$		0			0
$111$	−4.17307	−	1.22533i	−0.396091	−	0.116303i
$112$		0			0
$113$	0.971307	−	6.75559i	0.0913729	−	0.635513i	−0.891745	−	0.452539i	$-0.850518\pi$
$113$	0.971307	−	6.75559i	0.0913729	−	0.635513i	0.983118	−	0.182974i	$-0.0585724\pi$
$114$		0			0
$115$	6.67399	−	12.7585i	0.622353	−	1.18974i
$116$		0			0
$117$	−0.442002	+	3.07419i	−0.0408631	+	0.284209i
$118$		0			0
$119$	−1.77951	−	0.522513i	−0.163128	−	0.0478986i
$120$		0			0
$121$	−0.948526	+	0.278512i	−0.0862296	+	0.0253193i
$122$		0			0
$123$	−2.73702	+	5.99325i	−0.246789	+	0.540393i
$124$		0			0
$125$	−2.49040	+	1.60048i	−0.222748	+	0.143151i
$126$		0			0
$127$	1.60062	+	11.1326i	0.142032	+	0.987858i	0.928793	+	0.370599i	$0.120848\pi$
$127$	1.60062	+	11.1326i	0.142032	+	0.987858i	−0.786760	+	0.617258i	$0.788243\pi$
$128$		0			0
$129$	5.67453	−	6.54876i	0.499615	−	0.576586i
$130$		0			0
$131$	−9.09530	−	5.84520i	−0.794660	−	0.510697i	0.0792091	−	0.996858i	$-0.474761\pi$
$131$	−9.09530	−	5.84520i	−0.794660	−	0.510697i	−0.873869	+	0.486161i	$0.838397\pi$
$132$		0			0
$133$	16.6057	+	19.1640i	1.43990	+	1.66173i
$134$		0			0
$135$	1.24721	+	2.73102i	0.107343	+	0.235048i
$136$		0			0
$137$	−11.9556			−1.02144			−0.510720	−	0.859747i	$-0.670621\pi$
$137$	−11.9556			−1.02144			−0.510720	+	0.859747i	$0.670621\pi$
$138$		0			0
$139$	17.2434			1.46257			0.731283	−	0.682074i	$-0.238922\pi$
$139$	17.2434			1.46257			0.731283	+	0.682074i	$0.238922\pi$
$140$		0			0
$141$	−0.973867	−	2.13247i	−0.0820144	−	0.179586i
$142$		0			0
$143$	−7.04217	−	8.12710i	−0.588896	−	0.679622i
$144$		0			0
$145$	−14.6507	−	9.41545i	−1.21668	−	0.781911i
$146$		0			0
$147$	−7.37034	+	8.50582i	−0.607895	+	0.701548i
$148$		0			0
$149$	1.43162	+	9.95715i	0.117283	+	0.815721i	0.960526	+	0.278189i	$0.0897342\pi$
$149$	1.43162	+	9.95715i	0.117283	+	0.815721i	−0.843243	+	0.537532i	$0.819357\pi$
$150$		0			0
$151$	−9.83043	+	6.31764i	−0.799989	+	0.514122i	−0.875612	−	0.483015i	$-0.839542\pi$
$151$	−9.83043	+	6.31764i	−0.799989	+	0.514122i	0.0756230	+	0.997136i	$0.475905\pi$
$152$		0			0
$153$	0.180324	−	0.394854i	0.0145783	−	0.0319221i
$154$		0			0
$155$	−17.4565	+	5.12568i	−1.40214	+	0.411704i
$156$		0			0
$157$	−3.89725	−	1.14434i	−0.311034	−	0.0913279i	0.122490	−	0.992470i	$-0.460912\pi$
$157$	−3.89725	−	1.14434i	−0.311034	−	0.0913279i	−0.433524	+	0.901142i	$0.642730\pi$
$158$		0			0
$159$	−0.388619	+	2.70290i	−0.0308195	+	0.214354i
$160$		0			0
$161$	−3.99766	+	20.0968i	−0.315060	+	1.58385i
$162$		0			0
$163$	−1.65136	+	11.4855i	−0.129344	+	0.899610i	0.817043	+	0.576577i	$0.195612\pi$
$163$	−1.65136	+	11.4855i	−0.129344	+	0.899610i	−0.946387	+	0.323034i	$0.895297\pi$
$164$		0			0
$165$	−9.97433	−	2.92873i	−0.776501	−	0.228001i
$166$		0			0
$167$	−8.82333	+	2.59076i	−0.682770	+	0.200479i	−0.604682	−	0.796467i	$-0.706700\pi$
$167$	−8.82333	+	2.59076i	−0.682770	+	0.200479i	−0.0780881	+	0.996946i	$0.524882\pi$
$168$		0			0
$169$	−1.39330	+	3.05090i	−0.107177	+	0.234685i
$170$		0			0
$171$	−4.99282	+	3.20869i	−0.381811	+	0.245375i
$172$		0			0
$173$	−1.90699	−	13.2634i	−0.144986	−	1.00840i	−0.924273	−	0.381732i	$-0.875328\pi$
$173$	−1.90699	−	13.2634i	−0.144986	−	1.00840i	0.779287	−	0.626667i	$-0.215581\pi$
$174$		0			0
$175$	−11.2309	+	12.9611i	−0.848974	+	0.979768i
$176$		0			0
$177$	3.95904	+	2.54432i	0.297580	+	0.191243i
$178$		0			0
$179$	−1.92517	−	2.22176i	−0.143894	−	0.166062i	0.679228	−	0.733928i	$-0.262315\pi$
$179$	−1.92517	−	2.22176i	−0.143894	−	0.166062i	−0.823121	+	0.567865i	$0.807769\pi$
$180$		0			0
$181$	−1.48908	−	3.26064i	−0.110683	−	0.242361i	0.846183	−	0.532893i	$-0.178895\pi$
$181$	−1.48908	−	3.26064i	−0.110683	−	0.242361i	−0.956865	+	0.290532i	$0.906168\pi$
$182$		0			0
$183$	−10.6121			−0.784473
$184$		0			0
$185$	13.0579			0.960034
$186$		0			0
$187$	0.624363	+	1.36716i	0.0456579	+	0.0999769i
$188$		0			0
$189$	−2.79794	−	3.22899i	−0.203520	−	0.234874i
$190$		0			0
$191$	18.2304	+	11.7160i	1.31911	+	0.847739i	0.995153	−	0.0983338i	$-0.0313513\pi$
$191$	18.2304	+	11.7160i	1.31911	+	0.847739i	0.323954	+	0.946073i	$0.394988\pi$
$192$		0			0
$193$	−11.8105	+	13.6300i	−0.850135	+	0.981109i	−0.999971	−	0.00760240i	$-0.997580\pi$
$193$	−11.8105	+	13.6300i	−0.850135	+	0.981109i	0.149836	+	0.988711i	$0.452126\pi$
$194$		0			0
$195$	−1.32704	−	9.22973i	−0.0950310	−	0.660955i
$196$		0			0
$197$	−1.67837	+	1.07862i	−0.119579	+	0.0768488i	−0.599063	−	0.800702i	$-0.704460\pi$
$197$	−1.67837	+	1.07862i	−0.119579	+	0.0768488i	0.479484	+	0.877551i	$0.340824\pi$
$198$		0			0
$199$	9.13984	−	20.0135i	0.647906	−	1.41872i	−0.245469	−	0.969404i	$-0.578942\pi$
$199$	9.13984	−	20.0135i	0.647906	−	1.41872i	0.893375	−	0.449312i	$-0.148331\pi$
$200$		0			0
$201$	11.6337	−	3.41597i	0.820581	−	0.240944i
$202$		0			0
$203$	23.7796	+	6.98232i	1.66900	+	0.490063i
$204$		0			0
$205$	2.81517	−	19.5800i	0.196620	−	1.36752i
$206$		0			0
$207$	−4.52264	−	1.59554i	−0.314345	−	0.110898i
$208$		0			0
$209$	2.92451	−	20.3404i	0.202293	−	1.40698i
$210$		0			0
$211$	13.8116	+	4.05546i	0.950831	+	0.279189i	0.720133	−	0.693836i	$-0.244081\pi$
$211$	13.8116	+	4.05546i	0.950831	+	0.279189i	0.230698	+	0.973025i	$0.425899\pi$
$212$		0			0
$213$	−6.71424	+	1.97148i	−0.460052	+	0.135083i
$214$		0			0
$215$	−10.8074	+	23.6649i	−0.737059	+	1.61393i
$216$		0			0
$217$	21.7807	−	13.9976i	1.47857	−	0.950218i
$218$		0			0
$219$	−1.31518	−	9.14729i	−0.0888717	−	0.618116i
$220$		0			0
$221$	−0.882864	+	1.01888i	−0.0593878	+	0.0685372i
$222$		0			0
$223$	−9.30748	−	5.98156i	−0.623275	−	0.400555i	0.190539	−	0.981680i	$-0.438976\pi$
$223$	−9.30748	−	5.98156i	−0.623275	−	0.400555i	−0.813814	+	0.581125i	$0.802613\pi$
$224$		0			0
$225$	−2.62860	−	3.03357i	−0.175240	−	0.202238i
$226$		0			0
$227$	8.34649	+	18.2763i	0.553976	+	1.21304i	0.954900	+	0.296927i	$0.0959619\pi$
$227$	8.34649	+	18.2763i	0.553976	+	1.21304i	−0.400924	+	0.916111i	$0.631311\pi$
$228$		0			0
$229$	16.6898			1.10290			0.551448	−	0.834209i	$-0.314075\pi$
$229$	16.6898			1.10290			0.551448	+	0.834209i	$0.314075\pi$
$230$		0			0
$231$	14.7935			0.973344
$232$		0			0
$233$	10.7652	+	23.5725i	0.705251	+	1.54428i	0.833486	+	0.552540i	$0.186341\pi$
$233$	10.7652	+	23.5725i	0.705251	+	1.54428i	−0.128235	+	0.991744i	$0.540931\pi$
$234$		0			0
$235$	4.60919	+	5.31929i	0.300670	+	0.346992i
$236$		0			0
$237$	−1.94315	−	1.24879i	−0.126221	−	0.0811174i
$238$		0			0
$239$	16.9797	−	19.5956i	1.09833	−	1.26754i	0.137466	−	0.990506i	$-0.456104\pi$
$239$	16.9797	−	19.5956i	1.09833	−	1.26754i	0.960861	−	0.277031i	$-0.0893503\pi$
$240$		0			0
$241$	−2.14905	−	14.9470i	−0.138432	−	0.962819i	−0.934081	−	0.357060i	$-0.883779\pi$
$241$	−2.14905	−	14.9470i	−0.138432	−	0.962819i	0.795649	−	0.605758i	$-0.207130\pi$
$242$		0			0
$243$	0.841254	−	0.540641i	0.0539664	−	0.0346821i
$244$		0			0
$245$	14.0371	−	30.7371i	0.896801	−	1.96372i
$246$		0			0
$247$	17.6862	−	5.19314i	1.12535	−	0.330432i
$248$		0			0
$249$	−17.1991	−	5.05011i	−1.08995	−	0.320038i
$250$		0			0
$251$	1.56673	−	10.8968i	0.0988910	−	0.687802i	−0.878713	−	0.477350i	$-0.841597\pi$
$251$	1.56673	−	10.8968i	0.0988910	−	0.687802i	0.977604	−	0.210452i	$-0.0674935\pi$
$252$		0			0
$253$	14.4299	−	8.21684i	0.907197	−	0.516588i
$254$		0			0
$255$	−0.185473	+	1.28999i	−0.0116147	+	0.0807823i
$256$		0			0
$257$	15.1503	+	4.44854i	0.945052	+	0.277492i	0.717726	−	0.696326i	$-0.245183\pi$
$257$	15.1503	+	4.44854i	0.945052	+	0.277492i	0.227327	+	0.973819i	$0.427001\pi$
$258$		0			0
$259$	−17.8297	+	5.23528i	−1.10789	+	0.325305i
$260$		0			0
$261$	−2.40966	+	5.27642i	−0.149154	+	0.326602i
$262$		0			0
$263$	−6.23104	+	4.00444i	−0.384222	+	0.246925i	−0.718466	−	0.695562i	$-0.755155\pi$
$263$	−6.23104	+	4.00444i	−0.384222	+	0.246925i	0.334244	+	0.942487i	$0.391519\pi$
$264$		0			0
$265$	−1.16676	−	8.11501i	−0.0716736	−	0.498501i
$266$		0			0
$267$	5.51319	−	6.36256i	0.337402	−	0.389383i
$268$		0			0
$269$	−8.91889	−	5.73182i	−0.543794	−	0.349475i	0.239727	−	0.970840i	$-0.422942\pi$
$269$	−8.91889	−	5.73182i	−0.543794	−	0.349475i	−0.783521	+	0.621365i	$0.786578\pi$
$270$		0			0
$271$	20.3709	+	23.5093i	1.23744	+	1.42809i	0.866309	+	0.499508i	$0.166486\pi$
$271$	20.3709	+	23.5093i	1.23744	+	1.42809i	0.371135	+	0.928579i	$0.378969\pi$
$272$		0			0
$273$	5.51245	+	12.0706i	0.333629	+	0.730545i
$274$		0			0
$275$	13.8982			0.838095
$276$		0			0
$277$	−17.5445			−1.05415			−0.527073	−	0.849820i	$-0.676710\pi$
$277$	−17.5445			−1.05415			−0.527073	+	0.849820i	$0.676710\pi$
$278$		0			0
$279$	2.51732	+	5.51216i	0.150708	+	0.330004i
$280$		0			0
$281$	13.3782	+	15.4393i	0.798078	+	0.921031i	0.998274	−	0.0587248i	$-0.0187034\pi$
$281$	13.3782	+	15.4393i	0.798078	+	0.921031i	−0.200196	+	0.979756i	$0.564158\pi$
$282$		0			0
$283$	−20.4682	−	13.1541i	−1.21671	−	0.781930i	−0.234939	−	0.972010i	$-0.575489\pi$
$283$	−20.4682	−	13.1541i	−1.21671	−	0.781930i	−0.981769	+	0.190080i	$0.939125\pi$
$284$		0			0
$285$	11.6688	−	13.4665i	0.691201	−	0.797688i
$286$		0			0
$287$	4.00623	+	27.8639i	0.236480	+	1.64475i
$288$		0			0
$289$	−14.1428	+	9.08902i	−0.831929	+	0.534648i
$290$		0			0
$291$	7.39513	−	16.1931i	0.433510	−	0.949255i
$292$		0			0
$293$	−20.2277	+	5.93938i	−1.18171	+	0.346982i	−0.812834	−	0.582495i	$-0.802077\pi$
$293$	−20.2277	+	5.93938i	−1.18171	+	0.346982i	−0.368879	+	0.929477i	$0.620258\pi$
$294$		0			0
$295$	−13.5570	−	3.98069i	−0.789318	−	0.231765i
$296$		0			0
$297$	−0.492758	+	3.42721i	−0.0285927	+	0.198867i
$298$		0			0
$299$	12.0813	+	8.71203i	0.698682	+	0.503830i
$300$		0			0
$301$	5.26890	−	36.6460i	0.303694	−	2.11224i
$302$		0			0
$303$	−7.76938	−	2.28129i	−0.446339	−	0.131057i
$304$		0			0
$305$	30.5706	−	8.97633i	1.75047	−	0.513983i
$306$		0			0
$307$	−0.594692	+	1.30219i	−0.0339409	+	0.0743201i	−0.925843	−	0.377908i	$-0.876644\pi$
$307$	−0.594692	+	1.30219i	−0.0339409	+	0.0743201i	0.891902	+	0.452228i	$0.149371\pi$
$308$		0			0
$309$	−4.58812	+	2.94860i	−0.261009	+	0.167740i
$310$		0			0
$311$	1.42290	+	9.89651i	0.0806855	+	0.561180i	0.989561	+	0.144113i	$0.0460328\pi$
$311$	1.42290	+	9.89651i	0.0806855	+	0.561180i	−0.908876	+	0.417067i	$0.863058\pi$
$312$		0			0
$313$	2.24139	−	2.58670i	0.126691	−	0.146209i	−0.688860	−	0.724894i	$-0.741889\pi$
$313$	2.24139	−	2.58670i	0.126691	−	0.146209i	0.815551	+	0.578685i	$0.196434\pi$
$314$		0			0
$315$	10.7913	+	6.93515i	0.608021	+	0.390752i
$316$		0			0
$317$	13.1071	+	15.1264i	0.736167	+	0.849582i	0.993152	−	0.116834i	$-0.0372744\pi$
$317$	13.1071	+	15.1264i	0.736167	+	0.849582i	−0.256985	+	0.966416i	$0.582729\pi$
$318$		0			0
$319$	−8.34334	−	18.2694i	−0.467137	−	1.02289i
$320$		0			0
$321$	16.8013			0.937755
$322$		0			0
$323$	−2.57626			−0.143347
$324$		0			0
$325$	5.17883	+	11.3401i	0.287270	+	0.629033i
$326$		0			0
$327$	−9.00773	−	10.3955i	−0.498128	−	0.574871i
$328$		0			0
$329$	−8.42622	−	5.41520i	−0.464553	−	0.298550i
$330$		0			0
$331$	−4.45852	+	5.14541i	−0.245063	+	0.282817i	−0.864934	−	0.501886i	$-0.832640\pi$
$331$	−4.45852	+	5.14541i	−0.245063	+	0.282817i	0.619871	+	0.784704i	$0.287185\pi$
$332$		0			0
$333$	−0.618963	−	4.30498i	−0.0339189	−	0.235911i
$334$		0			0
$335$	−30.6241	+	19.6809i	−1.67317	+	1.07528i
$336$		0			0
$337$	−13.9423	+	30.5294i	−0.759486	+	1.66304i	−0.0109579	+	0.999940i	$0.503488\pi$
$337$	−13.9423	+	30.5294i	−0.759486	+	1.66304i	−0.748528	+	0.663103i	$0.769239\pi$
$338$		0			0
$339$	6.54860	−	1.92284i	0.355671	−	0.104434i
$340$		0			0
$341$	−20.1317	−	5.91121i	−1.09019	−	0.320110i
$342$		0			0
$343$	−2.58714	+	17.9939i	−0.139692	+	0.971581i
$344$		0			0
$345$	14.3780	+	0.770797i	0.774087	+	0.0414983i
$346$		0			0
$347$	−0.113053	+	0.786298i	−0.00606898	+	0.0422107i	−0.992631	−	0.121177i	$-0.961333\pi$
$347$	−0.113053	+	0.786298i	−0.00606898	+	0.0422107i	0.986562	+	0.163388i	$0.0522422\pi$
$348$		0			0
$349$	−15.6436	−	4.59337i	−0.837382	−	0.245878i	−0.165197	−	0.986261i	$-0.552826\pi$
$349$	−15.6436	−	4.59337i	−0.837382	−	0.245878i	−0.672185	+	0.740383i	$0.734644\pi$
$350$		0			0
$351$	−2.98000	+	0.875006i	−0.159060	+	0.0467043i
$352$		0			0
$353$	3.22196	−	7.05512i	0.171488	−	0.375506i	−0.804301	−	0.594223i	$-0.797460\pi$
$353$	3.22196	−	7.05512i	0.171488	−	0.375506i	0.975788	+	0.218717i	$0.0701871\pi$
$354$		0			0
$355$	17.6742	−	11.3585i	0.938050	−	0.602848i
$356$		0			0
$357$	−0.263943	−	1.83576i	−0.0139693	−	0.0971589i
$358$		0			0
$359$	−2.73280	+	3.15382i	−0.144232	+	0.166452i	−0.823269	−	0.567652i	$-0.807852\pi$
$359$	−2.73280	+	3.15382i	−0.144232	+	0.166452i	0.679037	+	0.734104i	$0.262398\pi$
$360$		0			0
$361$	13.6485	+	8.77136i	0.718342	+	0.461651i
$362$		0			0
$363$	−0.647376	−	0.747111i	−0.0339784	−	0.0392132i
$364$		0			0
$365$	11.5259	+	25.2383i	0.603295	+	1.32103i
$366$		0			0
$367$	5.84151			0.304924			0.152462	−	0.988309i	$-0.451280\pi$
$367$	5.84151			0.304924			0.152462	+	0.988309i	$0.451280\pi$
$368$		0			0
$369$	−6.58865			−0.342991
$370$		0			0
$371$	4.84668	+	10.6128i	0.251627	+	0.550987i
$372$		0			0
$373$	16.9686	+	19.5828i	0.878600	+	1.01396i	0.999773	+	0.0213265i	$0.00678896\pi$
$373$	16.9686	+	19.5828i	0.878600	+	1.01396i	−0.121173	+	0.992631i	$0.538666\pi$
$374$		0			0
$375$	−2.49040	−	1.60048i	−0.128604	−	0.0826486i
$376$		0			0
$377$	11.7977	−	13.6153i	0.607612	−	0.701221i
$378$		0			0
$379$	−4.53871	−	31.5674i	−0.233138	−	1.62151i	−0.684392	−	0.729115i	$-0.739932\pi$
$379$	−4.53871	−	31.5674i	−0.233138	−	1.62151i	0.451254	−	0.892396i	$-0.350977\pi$
$380$		0			0
$381$	−9.46164	+	6.08062i	−0.484734	+	0.311520i
$382$		0			0
$383$	4.01922	−	8.80087i	0.205373	−	0.449703i	−0.778717	−	0.627375i	$-0.784129\pi$
$383$	4.01922	−	8.80087i	0.205373	−	0.449703i	0.984090	+	0.177672i	$0.0568565\pi$
$384$		0			0
$385$	−42.6160	+	12.5132i	−2.17191	+	0.637731i
$386$		0			0
$387$	8.31425	+	2.44128i	0.422637	+	0.124097i
$388$		0			0
$389$	3.85451	−	26.8087i	0.195431	−	1.35926i	−0.621904	−	0.783094i	$-0.713641\pi$
$389$	3.85451	−	26.8087i	0.195431	−	1.35926i	0.817335	−	0.576162i	$-0.195450\pi$
$390$		0			0
$391$	−1.27710	−	1.64403i	−0.0645856	−	0.0831421i
$392$		0			0
$393$	1.53865	−	10.7016i	0.0776147	−	0.539822i
$394$		0			0
$395$	6.65395	+	1.95378i	0.334797	+	0.0983052i
$396$		0			0
$397$	29.8086	−	8.75258i	1.49605	−	0.439279i	0.571583	−	0.820545i	$-0.306330\pi$
$397$	29.8086	−	8.75258i	1.49605	−	0.439279i	0.924466	+	0.381265i	$0.124511\pi$
$398$		0			0
$399$	−10.5339	+	23.0661i	−0.527356	+	1.15475i
$400$		0			0
$401$	−6.64421	+	4.26998i	−0.331796	+	0.213232i	−0.695922	−	0.718117i	$-0.745004\pi$
$401$	−6.64421	+	4.26998i	−0.331796	+	0.213232i	0.364126	+	0.931350i	$0.381368\pi$
$402$		0			0
$403$	−2.67843	−	18.6289i	−0.133422	−	0.927970i
$404$		0			0
$405$	−1.96611	+	2.26901i	−0.0976967	+	0.112748i
$406$		0			0
$407$	12.6685	+	8.14154i	0.627954	+	0.403561i
$408$		0			0
$409$	−5.94867	−	6.86513i	−0.294143	−	0.339459i	0.589372	−	0.807861i	$-0.299375\pi$
$409$	−5.94867	−	6.86513i	−0.294143	−	0.339459i	−0.883515	+	0.468403i	$0.844830\pi$
$410$		0			0
$411$	−4.96656	−	10.8752i	−0.244982	−	0.536436i
$412$		0			0
$413$	20.1072			0.989411
$414$		0			0
$415$	53.8174			2.64179
$416$		0			0
$417$	7.16316	+	15.6851i	0.350782	+	0.768105i
$418$		0			0
$419$	−7.15793	−	8.26069i	−0.349688	−	0.403561i	0.553471	−	0.832869i	$-0.313303\pi$
$419$	−7.15793	−	8.26069i	−0.349688	−	0.403561i	−0.903158	+	0.429307i	$0.858758\pi$
$420$		0			0
$421$	−13.1050	−	8.42208i	−0.638699	−	0.410467i	0.180822	−	0.983516i	$-0.442124\pi$
$421$	−13.1050	−	8.42208i	−0.638699	−	0.410467i	−0.819521	+	0.573049i	$0.805761\pi$
$422$		0			0
$423$	1.53520	−	1.77172i	0.0746442	−	0.0861440i
$424$		0			0
$425$	−0.247969	−	1.72466i	−0.0120282	−	0.0836583i
$426$		0			0
$427$	−38.1434	+	24.5132i	−1.84589	+	1.18628i
$428$		0			0
$429$	4.46724	−	9.78190i	0.215681	−	0.472275i
$430$		0			0
$431$	−0.714025	+	0.209657i	−0.0343934	+	0.0100988i	−0.298884	−	0.954289i	$-0.596614\pi$
$431$	−0.714025	+	0.209657i	−0.0343934	+	0.0100988i	0.264491	+	0.964388i	$0.414796\pi$
$432$		0			0
$433$	0.927558	+	0.272356i	0.0445756	+	0.0130886i	0.303944	−	0.952690i	$-0.401696\pi$
$433$	0.927558	+	0.272356i	0.0445756	+	0.0130886i	−0.259369	+	0.965778i	$0.583514\pi$
$434$		0			0
$435$	2.47846	−	17.2381i	0.118833	−	0.826503i
$436$		0			0
$437$	2.53673	+	28.3499i	0.121348	+	1.35616i
$438$		0			0
$439$	2.73442	−	19.0183i	0.130507	−	0.907693i	−0.814389	−	0.580320i	$-0.802927\pi$
$439$	2.73442	−	19.0183i	0.130507	−	0.907693i	0.944895	−	0.327373i	$-0.106163\pi$
$440$		0			0
$441$	−10.7989	−	3.17085i	−0.514234	−	0.150993i
$442$		0			0
$443$	0.170222	−	0.0499816i	0.00808748	−	0.00237470i	−0.277686	−	0.960672i	$-0.589568\pi$
$443$	0.170222	−	0.0499816i	0.00808748	−	0.00237470i	0.285774	+	0.958297i	$0.407749\pi$
$444$		0			0
$445$	−10.5001	+	22.9921i	−0.497754	+	1.08993i
$446$		0			0
$447$	−8.46262	+	5.43860i	−0.400268	+	0.257237i
$448$		0			0
$449$	−0.552327	−	3.84152i	−0.0260659	−	0.181293i	0.972629	−	0.232363i	$-0.0746458\pi$
$449$	−0.552327	−	3.84152i	−0.0260659	−	0.181293i	−0.998695	+	0.0510706i	$0.983737\pi$
$450$		0			0
$451$	14.9393	−	17.2408i	0.703462	−	0.811839i
$452$		0			0
$453$	−9.83043	−	6.31764i	−0.461874	−	0.296828i
$454$		0			0
$455$	−26.0897	−	30.1092i	−1.22311	−	1.41154i
$456$		0			0
$457$	−7.73760	−	16.9430i	−0.361950	−	0.792559i	−0.999750	−	0.0223573i	$-0.992883\pi$
$457$	−7.73760	−	16.9430i	−0.361950	−	0.792559i	0.637801	−	0.770202i	$-0.279844\pi$
$458$		0			0
$459$	0.434081			0.0202612
$460$		0			0
$461$	−28.9689			−1.34921			−0.674607	−	0.738177i	$-0.735687\pi$
$461$	−28.9689			−1.34921			−0.674607	+	0.738177i	$0.735687\pi$
$462$		0			0
$463$	3.80413	+	8.32988i	0.176793	+	0.387122i	0.977196	−	0.212340i	$-0.0681084\pi$
$463$	3.80413	+	8.32988i	0.176793	+	0.387122i	−0.800403	+	0.599462i	$0.795381\pi$
$464$		0			0
$465$	−11.9142	−	13.7497i	−0.552506	−	0.637625i
$466$		0			0
$467$	−27.8985	−	17.9293i	−1.29099	−	0.829669i	−0.298789	−	0.954319i	$-0.596583\pi$
$467$	−27.8985	−	17.9293i	−1.29099	−	0.829669i	−0.992201	+	0.124650i	$0.960219\pi$
$468$		0			0
$469$	33.9246	−	39.1511i	1.56649	−	1.80783i
$470$		0			0
$471$	−0.578052	−	4.02044i	−0.0266352	−	0.185252i
$472$		0			0
$473$	−25.2401	+	16.2208i	−1.16054	+	0.745835i
$474$		0			0
$475$	−9.89640	+	21.6701i	−0.454078	+	0.994292i
$476$		0			0
$477$	−2.62009	+	0.769327i	−0.119965	+	0.0352250i
$478$		0			0
$479$	0.635490	+	0.186597i	0.0290363	+	0.00852582i	0.296218	−	0.955120i	$-0.404274\pi$
$479$	0.635490	+	0.186597i	0.0290363	+	0.00852582i	−0.267182	+	0.963646i	$0.586093\pi$
$480$		0			0
$481$	−1.92238	+	13.3704i	−0.0876528	+	0.609639i
$482$		0			0
$483$	−19.9413	+	4.71209i	−0.907362	+	0.214407i
$484$		0			0
$485$	−7.60628	+	52.9029i	−0.345383	+	2.40219i
$486$		0			0
$487$	26.3058	+	7.72408i	1.19203	+	0.350012i	0.816800	−	0.576920i	$-0.195746\pi$
$487$	26.3058	+	7.72408i	1.19203	+	0.350012i	0.375230	+	0.926932i	$0.377564\pi$
$488$		0			0
$489$	−11.1335	+	3.26910i	−0.503476	+	0.147834i
$490$		0			0
$491$	−13.6974	+	29.9931i	−0.618155	+	1.35357i	0.298698	+	0.954348i	$0.403448\pi$
$491$	−13.6974	+	29.9931i	−0.618155	+	1.35357i	−0.916853	+	0.399224i	$0.869280\pi$
$492$		0			0
$493$	−2.11822	+	1.36130i	−0.0954000	+	0.0613099i
$494$		0			0
$495$	−1.47942	−	10.2896i	−0.0664951	−	0.462484i
$496$		0			0
$497$	−19.5791	+	22.5955i	−0.878242	+	1.01355i
$498$		0			0
$499$	−20.9911	−	13.4901i	−0.939690	−	0.603902i	−0.0213828	−	0.999771i	$-0.506807\pi$
$499$	−20.9911	−	13.4901i	−0.939690	−	0.603902i	−0.918307	+	0.395870i	$0.870443\pi$
$500$		0			0
$501$	−6.02199	−	6.94974i	−0.269043	−	0.310492i
$502$		0			0
$503$	16.3322	+	35.7625i	0.728216	+	1.59457i	0.802020	+	0.597297i	$0.203759\pi$
$503$	16.3322	+	35.7625i	0.728216	+	1.59457i	−0.0738046	+	0.997273i	$0.523514\pi$
$504$		0			0
$505$	24.3110			1.08183
$506$		0			0
$507$	−3.35399			−0.148956
$508$		0			0
$509$	−5.96691	−	13.0657i	−0.264479	−	0.579127i	0.730073	−	0.683369i	$-0.239486\pi$
$509$	−5.96691	−	13.0657i	−0.264479	−	0.579127i	−0.994552	+	0.104241i	$0.966759\pi$
$510$		0			0
$511$	−25.8567	−	29.8402i	−1.14383	−	1.32005i
$512$		0			0
$513$	−4.99282	−	3.20869i	−0.220439	−	0.141667i
$514$		0			0
$515$	10.7230	−	12.3750i	0.472511	−	0.545306i
$516$		0			0
$517$	1.15518	+	8.03448i	0.0508049	+	0.353356i
$518$		0			0
$519$	11.2726	−	7.24449i	0.494814	−	0.317998i
$520$		0			0
$521$	4.17290	−	9.13737i	0.182818	−	0.400315i	−0.795928	−	0.605391i	$-0.793017\pi$
$521$	4.17290	−	9.13737i	0.182818	−	0.400315i	0.978746	+	0.205076i	$0.0657440\pi$
$522$		0			0
$523$	−22.9072	+	6.72617i	−1.00166	+	0.294115i	−0.741138	−	0.671352i	$-0.765714\pi$
$523$	−22.9072	+	6.72617i	−1.00166	+	0.294115i	−0.260525	+	0.965467i	$0.583896\pi$
$524$		0			0
$525$	−16.4553	−	4.83172i	−0.718169	−	0.210873i
$526$		0			0
$527$	−0.374349	+	2.60366i	−0.0163069	+	0.113417i
$528$		0			0
$529$	−16.8338	+	15.6723i	−0.731906	+	0.681406i
$530$		0			0
$531$	−0.669751	+	4.65822i	−0.0290647	+	0.202149i
$532$		0			0
$533$	19.6342	+	5.76511i	0.850449	+	0.249714i
$534$		0			0
$535$	−48.3996	+	14.2114i	−2.09250	+	0.614413i
$536$		0			0
$537$	1.22124	−	2.67415i	0.0527005	−	0.115398i
$538$		0			0
$539$	32.7830	−	21.0684i	1.41206	−	0.907479i
$540$		0			0
$541$	5.85061	+	40.6919i	0.251538	+	1.74948i	0.588991	+	0.808140i	$0.299525\pi$
$541$	5.85061	+	40.6919i	0.251538	+	1.74948i	−0.337453	+	0.941342i	$0.609566\pi$
$542$		0			0
$543$	2.34739	−	2.70903i	0.100736	−	0.116256i
$544$		0			0
$545$	34.7417	+	22.3272i	1.48817	+	0.956391i
$546$		0			0
$547$	−1.45033	−	1.67377i	−0.0620116	−	0.0715652i	0.723896	−	0.689909i	$-0.242349\pi$
$547$	−1.45033	−	1.67377i	−0.0620116	−	0.0715652i	−0.785908	+	0.618344i	$0.787804\pi$
$548$		0			0
$549$	−4.40845	−	9.65315i	−0.188148	−	0.411986i
$550$		0			0
$551$	34.4265			1.46662
$552$		0			0
$553$	−9.86889			−0.419668
$554$		0			0
$555$	5.42444	+	11.8779i	0.230255	+	0.504187i
$556$		0			0
$557$	−18.3979	−	21.2323i	−0.779542	−	0.899639i	0.217534	−	0.976053i	$-0.430199\pi$
$557$	−18.3979	−	21.2323i	−0.779542	−	0.899639i	−0.997076	+	0.0764133i	$0.975653\pi$
$558$		0			0
$559$	−22.6403	−	14.5500i	−0.957582	−	0.615400i
$560$		0			0
$561$	−0.984246	+	1.13588i	−0.0415549	+	0.0479569i
$562$		0			0
$563$	−3.94129	−	27.4123i	−0.166106	−	1.15529i	−0.886839	−	0.462078i	$-0.847104\pi$
$563$	−3.94129	−	27.4123i	−0.166106	−	1.15529i	0.720733	−	0.693212i	$-0.243805\pi$
$564$		0			0
$565$	−17.2382	+	11.0783i	−0.725216	+	0.466068i
$566$		0			0
$567$	1.77489	−	3.88646i	0.0745383	−	0.163216i
$568$		0			0
$569$	26.8218	−	7.87560i	1.12443	−	0.330162i	0.333914	−	0.942604i	$-0.391631\pi$
$569$	26.8218	−	7.87560i	1.12443	−	0.330162i	0.790516	+	0.612441i	$0.209812\pi$
$570$		0			0
$571$	−0.377169	−	0.110747i	−0.0157840	−	0.00463461i	0.273831	−	0.961778i	$-0.411709\pi$
$571$	−0.377169	−	0.110747i	−0.0157840	−	0.00463461i	−0.289615	+	0.957143i	$0.593527\pi$
$572$		0			0
$573$	−3.08404	+	21.4500i	−0.128838	+	0.896086i
$574$		0			0
$575$	−18.7345	+	4.42691i	−0.781281	+	0.184615i
$576$		0			0
$577$	2.81712	−	19.5935i	0.117278	−	0.815688i	−0.843253	−	0.537516i	$-0.819363\pi$
$577$	2.81712	−	19.5935i	0.117278	−	0.815688i	0.960531	−	0.278171i	$-0.0897283\pi$
$578$		0			0
$579$	−17.3045	−	5.08107i	−0.719151	−	0.211162i
$580$		0			0
$581$	−73.4843	+	21.5769i	−3.04864	+	0.895162i
$582$		0			0
$583$	3.92771	−	8.60049i	0.162669	−	0.356196i
$584$		0			0
$585$	7.84439	−	5.04128i	0.324326	−	0.208431i
$586$		0			0
$587$	−4.77867	−	33.2364i	−0.197237	−	1.37181i	−0.812257	−	0.583300i	$-0.801761\pi$
$587$	−4.77867	−	33.2364i	−0.197237	−	1.37181i	0.615020	−	0.788511i	$-0.289148\pi$
$588$		0			0
$589$	23.5518	−	27.1802i	0.970435	−	1.11994i
$590$		0			0
$591$	−1.67837	−	1.07862i	−0.0690390	−	0.0443687i
$592$		0			0
$593$	4.29457	+	4.95620i	0.176357	+	0.203527i	0.837045	−	0.547133i	$-0.184281\pi$
$593$	4.29457	+	4.95620i	0.176357	+	0.203527i	−0.660688	+	0.750660i	$0.729736\pi$
$594$		0			0
$595$	2.31313	+	5.06505i	0.0948291	+	0.207647i
$596$		0			0
$597$	22.0017			0.900470
$598$		0			0
$599$	20.1044			0.821443			0.410722	−	0.911761i	$-0.365277\pi$
$599$	20.1044			0.821443			0.410722	+	0.911761i	$0.365277\pi$
$600$		0			0
$601$	−10.3779	−	22.7244i	−0.423323	−	0.926947i	−0.994363	−	0.106026i	$-0.966187\pi$
$601$	−10.3779	−	22.7244i	−0.423323	−	0.926947i	0.571041	−	0.820922i	$-0.306540\pi$
$602$		0			0
$603$	7.94011	+	9.16337i	0.323346	+	0.373161i
$604$		0			0
$605$	2.49685	+	1.60463i	0.101511	+	0.0652374i
$606$		0			0
$607$	2.25560	−	2.60310i	0.0915519	−	0.105656i	−0.708125	−	0.706087i	$-0.750459\pi$
$607$	2.25560	−	2.60310i	0.0915519	−	0.105656i	0.799677	+	0.600431i	$0.205004\pi$
$608$		0			0
$609$	3.52706	+	24.5312i	0.142924	+	0.994056i
$610$		0			0
$611$	−6.12517	+	3.93641i	−0.247798	+	0.159250i
$612$		0			0
$613$	8.31170	−	18.2001i	0.335706	−	0.735095i	−0.664216	−	0.747541i	$-0.731235\pi$
$613$	8.31170	−	18.2001i	0.335706	−	0.735095i	0.999923	+	0.0124460i	$0.00396179\pi$
$614$		0			0
$615$	18.9800	−	5.57304i	0.765348	−	0.224727i
$616$		0			0
$617$	−39.4705	−	11.5896i	−1.58902	−	0.466579i	−0.636557	−	0.771230i	$-0.719642\pi$
$617$	−39.4705	−	11.5896i	−1.58902	−	0.466579i	−0.952464	+	0.304651i	$0.901460\pi$
$618$		0			0
$619$	−4.66732	+	32.4619i	−0.187595	+	1.30475i	0.650615	+	0.759408i	$0.274511\pi$
$619$	−4.66732	+	32.4619i	−0.187595	+	1.30475i	−0.838211	+	0.545347i	$0.816398\pi$
$620$		0			0
$621$	−0.427420	−	4.77675i	−0.0171518	−	0.191684i
$622$		0			0
$623$	5.11910	−	35.6041i	0.205092	−	1.42645i
$624$		0			0
$625$	27.7849	+	8.15837i	1.11139	+	0.326335i
$626$		0			0
$627$	19.7172	−	5.78949i	0.787428	−	0.231210i
$628$		0			0
$629$	0.784273	−	1.71732i	0.0312710	−	0.0684740i
$630$		0			0
$631$	−0.549082	+	0.352874i	−0.0218586	+	0.0140477i	−0.551525	−	0.834159i	$-0.685954\pi$
$631$	−0.549082	+	0.352874i	−0.0218586	+	0.0140477i	0.529666	+	0.848206i	$0.322317\pi$
$632$		0			0
$633$	2.04858	+	14.2482i	0.0814238	+	0.566315i
$634$		0			0
$635$	22.1129	−	25.5197i	0.877526	−	1.01272i
$636$		0			0
$637$	29.4062	+	18.8982i	1.16512	+	0.748775i
$638$		0			0
$639$	−4.58251	−	5.28850i	−0.181281	−	0.209210i
$640$		0			0
$641$	−2.72452	−	5.96587i	−0.107612	−	0.235638i	0.848164	−	0.529735i	$-0.177708\pi$
$641$	−2.72452	−	5.96587i	−0.107612	−	0.235638i	−0.955776	+	0.294097i	$0.904981\pi$
$642$		0			0
$643$	24.7900			0.977623			0.488812	−	0.872389i	$-0.337430\pi$
$643$	24.7900			0.977623			0.488812	+	0.872389i	$0.337430\pi$
$644$		0			0
$645$	−26.0159			−1.02438
$646$		0			0
$647$	−6.60462	−	14.4621i	−0.259654	−	0.568564i	0.734241	−	0.678889i	$-0.237538\pi$
$647$	−6.60462	−	14.4621i	−0.259654	−	0.568564i	−0.993896	+	0.110325i	$0.964811\pi$
$648$		0			0
$649$	−10.6708	−	12.3147i	−0.418864	−	0.483395i
$650$		0			0
$651$	21.7807	+	13.9976i	0.853652	+	0.548609i
$652$		0			0
$653$	−27.2586	+	31.4581i	−1.06671	+	1.23105i	−0.0948534	+	0.995491i	$0.530238\pi$
$653$	−27.2586	+	31.4581i	−1.06671	+	1.23105i	−0.971860	+	0.235561i	$0.924307\pi$
$654$		0			0
$655$	4.61954	+	32.1296i	0.180500	+	1.25541i
$656$		0			0
$657$	7.77432	−	4.99625i	0.303305	−	0.194922i
$658$		0			0
$659$	−7.72300	+	16.9110i	−0.300845	+	0.658759i	−0.998326	−	0.0578446i	$-0.981577\pi$
$659$	−7.72300	+	16.9110i	−0.300845	+	0.658759i	0.697480	+	0.716604i	$0.254304\pi$
$660$		0			0
$661$	−24.2858	+	7.13097i	−0.944610	+	0.277362i	−0.717541	−	0.696516i	$-0.754732\pi$
$661$	−24.2858	+	7.13097i	−0.944610	+	0.277362i	−0.227069	+	0.973879i	$0.572914\pi$
$662$		0			0
$663$	−1.29356	−	0.379823i	−0.0502377	−	0.0147511i
$664$		0			0
$665$	10.8347	−	75.3570i	0.420151	−	2.92222i
$666$		0			0
$667$	17.0658	+	21.9691i	0.660792	+	0.850647i
$668$		0			0
$669$	1.57455	−	10.9512i	0.0608755	−	0.423398i
$670$		0			0
$671$	35.2557	+	10.3520i	1.36103	+	0.399634i
$672$		0			0
$673$	−24.4694	+	7.18485i	−0.943224	+	0.276956i	−0.716963	−	0.697111i	$-0.754468\pi$
$673$	−24.4694	+	7.18485i	−0.943224	+	0.276956i	−0.226261	+	0.974067i	$0.572650\pi$
$674$		0			0
$675$	1.66747	−	3.65125i	0.0641809	−	0.140537i
$676$		0			0
$677$	−37.3613	+	24.0107i	−1.43591	+	0.922804i	−0.436175	+	0.899862i	$0.643667\pi$
$677$	−37.3613	+	24.0107i	−1.43591	+	0.922804i	−0.999737	+	0.0229422i	$0.992697\pi$
$678$		0			0
$679$	−10.8244	−	75.2852i	−0.415401	−	2.88918i
$680$		0			0
$681$	−13.1574	+	15.1845i	−0.504193	+	0.581870i
$682$		0			0
$683$	−1.25934	−	0.809327i	−0.0481872	−	0.0309680i	0.516325	−	0.856392i	$-0.327299\pi$
$683$	−1.25934	−	0.809327i	−0.0481872	−	0.0309680i	−0.564513	+	0.825424i	$0.690936\pi$
$684$		0			0
$685$	23.5061	+	27.1275i	0.898122	+	1.03649i
$686$		0			0
$687$	6.93321	+	15.1816i	0.264519	+	0.579215i
$688$		0			0
$689$	8.48101			0.323101
$690$		0			0
$691$	−4.38233			−0.166712			−0.0833559	−	0.996520i	$-0.526564\pi$
$691$	−4.38233			−0.166712			−0.0833559	+	0.996520i	$0.526564\pi$
$692$		0			0
$693$	6.14546	+	13.4567i	0.233447	+	0.511177i
$694$		0			0
$695$	−33.9024	−	39.1254i	−1.28599	−	1.48411i
$696$		0			0
$697$	−2.40599	−	1.54624i	−0.0911335	−	0.0585679i
$698$		0			0
$699$	−16.9703	+	19.5847i	−0.641874	+	0.740762i
$700$		0			0
$701$	1.52301	+	10.5928i	0.0575234	+	0.400084i	0.998158	+	0.0606640i	$0.0193218\pi$
$701$	1.52301	+	10.5928i	0.0575234	+	0.400084i	−0.940635	+	0.339420i	$0.889769\pi$
$702$		0			0
$703$	−21.7150	+	13.9554i	−0.818998	+	0.526338i
$704$		0			0
$705$	−2.92387	+	6.40238i	−0.110119	+	0.241128i
$706$		0			0
$707$	−33.1952	+	9.74698i	−1.24843	+	0.366573i
$708$		0			0
$709$	41.9642	+	12.3218i	1.57600	+	0.462755i	0.948740	−	0.316056i	$-0.102359\pi$
$709$	41.9642	+	12.3218i	1.57600	+	0.462755i	0.627258	+	0.778811i	$0.284177\pi$
$710$		0			0
$711$	0.328723	−	2.28632i	0.0123281	−	0.0857436i
$712$		0			0
$713$	29.0199	+	1.55574i	1.08681	+	0.0582630i
$714$		0			0
$715$	−4.59479	+	31.9575i	−0.171836	+	1.19514i
$716$		0			0
$717$	24.8785	+	7.30498i	0.929103	+	0.272809i
$718$		0			0
$719$	3.10295	−	0.911109i	0.115721	−	0.0339786i	−0.223360	−	0.974736i	$-0.571702\pi$
$719$	3.10295	−	0.911109i	0.115721	−	0.0339786i	0.339080	+	0.940757i	$0.389884\pi$
$720$		0			0
$721$	−9.68007	+	21.1964i	−0.360505	+	0.789395i
$722$		0			0
$723$	12.7035	−	8.16404i	0.472448	−	0.303624i
$724$		0			0
$725$	3.31360	+	23.0466i	0.123064	+	0.855929i
$726$		0			0
$727$	−17.9934	+	20.7655i	−0.667339	+	0.770151i	−0.983958	−	0.178402i	$-0.942907\pi$
$727$	−17.9934	+	20.7655i	−0.667339	+	0.770151i	0.316618	+	0.948553i	$0.397453\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	2.46321	+	2.84269i	0.0911050	+	0.105141i
$732$		0			0
$733$	−11.6462	−	25.5016i	−0.430162	−	0.941924i	−0.993300	−	0.115561i	$-0.963133\pi$
$733$	−11.6462	−	25.5016i	−0.430162	−	0.941924i	0.563138	−	0.826363i	$-0.309594\pi$
$734$		0			0
$735$	33.7907			1.24639
$736$		0			0
$737$	−41.9818			−1.54642
$738$		0			0
$739$	4.64476	+	10.1706i	0.170860	+	0.374132i	0.975619	−	0.219470i	$-0.0704327\pi$
$739$	4.64476	+	10.1706i	0.170860	+	0.374132i	−0.804759	+	0.593602i	$0.797705\pi$
$740$		0			0
$741$	12.0710	+	13.9306i	0.443438	+	0.511755i
$742$		0			0
$743$	−22.2309	−	14.2869i	−0.815571	−	0.524136i	0.0650917	−	0.997879i	$-0.479266\pi$
$743$	−22.2309	−	14.2869i	−0.815571	−	0.524136i	−0.880663	+	0.473744i	$0.842902\pi$
$744$		0			0
$745$	19.7781	−	22.8252i	0.724615	−	0.836250i
$746$		0			0
$747$	−2.55102	−	17.7427i	−0.0933370	−	0.649173i
$748$		0			0
$749$	60.3890	−	38.8096i	2.20656	−	1.41807i
$750$		0			0
$751$	0.961378	−	2.10512i	0.0350812	−	0.0768171i	−0.891280	−	0.453453i	$-0.850192\pi$
$751$	0.961378	−	2.10512i	0.0350812	−	0.0768171i	0.926361	+	0.376636i	$0.122919\pi$
$752$		0			0
$753$	10.5630	−	3.10156i	0.384935	−	0.113027i
$754$		0			0
$755$	33.6625	+	9.88419i	1.22510	+	0.359723i
$756$		0			0
$757$	3.10744	−	21.6127i	0.112942	−	0.785528i	−0.852090	−	0.523396i	$-0.824665\pi$
$757$	3.10744	−	21.6127i	0.112942	−	0.785528i	0.965032	−	0.262133i	$-0.0844259\pi$
$758$		0			0
$759$	13.4687	+	9.71246i	0.488882	+	0.352540i
$760$		0			0
$761$	1.98647	−	13.8162i	0.0720095	−	0.500837i	−0.921616	−	0.388104i	$-0.873130\pi$
$761$	1.98647	−	13.8162i	0.0720095	−	0.500837i	0.993625	−	0.112734i	$-0.0359606\pi$
$762$		0			0
$763$	−56.3893	−	16.5574i	−2.04143	−	0.599418i
$764$		0			0
$765$	−1.25046	+	0.367169i	−0.0452106	+	0.0132750i
$766$		0			0
$767$	6.07182	−	13.2954i	0.219241	−	0.480070i
$768$		0			0
$769$	−2.95648	+	1.90002i	−0.106613	+	0.0685163i	−0.592861	−	0.805305i	$-0.702002\pi$
$769$	−2.95648	+	1.90002i	−0.106613	+	0.0685163i	0.486248	+	0.873821i	$0.338365\pi$
$770$		0			0
$771$	2.24714	+	15.6292i	0.0809289	+	0.562873i
$772$		0			0
$773$	−3.01120	+	3.47511i	−0.108305	+	0.124991i	−0.807314	−	0.590122i	$-0.799079\pi$
$773$	−3.01120	+	3.47511i	−0.108305	+	0.124991i	0.699009	+	0.715113i	$0.253625\pi$
$774$		0			0
$775$	20.4625	+	13.1504i	0.735034	+	0.472378i
$776$		0			0
$777$	−12.1689	−	14.0437i	−0.436557	−	0.503814i
$778$		0			0
$779$	16.2442	+	35.5698i	0.582009	+	1.27442i
$780$		0			0
$781$	24.2292			0.866988
$782$		0			0
$783$	−5.80061			−0.207297
$784$		0			0
$785$	5.06591	+	11.0928i	0.180810	+	0.395918i
$786$		0			0
$787$	16.3193	+	18.8334i	0.581719	+	0.671339i	0.967973	−	0.251053i	$-0.0807769\pi$
$787$	16.3193	+	18.8334i	0.581719	+	0.671339i	−0.386255	+	0.922392i	$0.626231\pi$
$788$		0			0
$789$	−6.23104	−	4.00444i	−0.221831	−	0.142562i
$790$		0			0
$791$	19.0961	−	22.0380i	0.678978	−	0.783583i
$792$		0			0
$793$	4.69059	+	32.6238i	0.166568	+	1.15850i
$794$		0			0
$795$	6.89698	−	4.43242i	0.244611	−	0.157202i
$796$		0			0
$797$	−2.32185	+	5.08415i	−0.0822442	+	0.180090i	−0.946286	−	0.323330i	$-0.895198\pi$
$797$	−2.32185	+	5.08415i	−0.0822442	+	0.180090i	0.864042	+	0.503420i	$0.167925\pi$
$798$		0			0
$799$	0.976405	−	0.286698i	0.0345427	−	0.0101427i
$800$		0			0
$801$	8.07786	+	2.37187i	0.285417	+	0.0838060i
$802$		0			0
$803$	−4.55375	+	31.6720i	−0.160698	+	1.11768i
$804$		0			0
$805$	53.4596	−	30.4416i	1.88420	−	1.07293i
$806$		0			0
$807$	1.50881	−	10.4940i	0.0531126	−	0.369406i
$808$		0			0
$809$	−2.80269	−	0.822944i	−0.0985373	−	0.0289332i	0.232092	−	0.972694i	$-0.425443\pi$
$809$	−2.80269	−	0.822944i	−0.0985373	−	0.0289332i	−0.330630	+	0.943761i	$0.607261\pi$
$810$		0			0
$811$	−5.55883	+	1.63222i	−0.195197	+	0.0573150i	−0.377870	−	0.925859i	$-0.623343\pi$
$811$	−5.55883	+	1.63222i	−0.195197	+	0.0573150i	0.182673	+	0.983174i	$0.441525\pi$
$812$		0			0
$813$	−12.9224	+	28.2961i	−0.453209	+	0.992389i
$814$		0			0
$815$	29.3074	−	18.8347i	1.02659	−	0.659751i
$816$		0			0
$817$	−7.31898	−	50.9046i	−0.256059	−	1.78093i
$818$		0			0
$819$	−8.68983	+	10.0286i	−0.303647	+	0.350428i
$820$		0			0
$821$	−16.6962	−	10.7300i	−0.582702	−	0.374480i	0.215831	−	0.976431i	$-0.430754\pi$
$821$	−16.6962	−	10.7300i	−0.582702	−	0.374480i	−0.798533	+	0.601951i	$0.794390\pi$
$822$		0			0
$823$	15.8106	+	18.2464i	0.551123	+	0.636030i	0.961144	−	0.276046i	$-0.0890243\pi$
$823$	15.8106	+	18.2464i	0.551123	+	0.636030i	−0.410021	+	0.912076i	$0.634479\pi$
$824$		0			0
$825$	5.77353	+	12.6423i	0.201009	+	0.440147i
$826$		0			0
$827$	−14.0159			−0.487381			−0.243691	−	0.969853i	$-0.578358\pi$
$827$	−14.0159			−0.487381			−0.243691	+	0.969853i	$0.578358\pi$
$828$		0			0
$829$	45.1797			1.56916			0.784578	−	0.620030i	$-0.212880\pi$
$829$	45.1797			1.56916			0.784578	+	0.620030i	$0.212880\pi$
$830$		0			0
$831$	−7.28824	−	15.9590i	−0.252826	−	0.553612i
$832$		0			0
$833$	−3.19932	−	3.69222i	−0.110850	−	0.127928i
$834$		0			0
$835$	23.2261	+	14.9265i	0.803772	+	0.516553i
$836$		0			0
$837$	−3.96830	+	4.57966i	−0.137165	+	0.158296i
$838$		0			0
$839$	−1.65031	−	11.4782i	−0.0569752	−	0.396271i	−0.998276	−	0.0587011i	$-0.981304\pi$
$839$	−1.65031	−	11.4782i	−0.0569752	−	0.396271i	0.941300	−	0.337570i	$-0.109605\pi$
$840$		0			0
$841$	3.90942	−	2.51243i	0.134807	−	0.0866355i
$842$		0			0
$843$	−8.48656	+	18.5830i	−0.292293	+	0.640032i
$844$		0			0
$845$	9.66189	−	2.83699i	0.332379	−	0.0975954i
$846$		0			0
$847$	−4.05264	−	1.18996i	−0.139250	−	0.0408876i
$848$		0			0
$849$	3.46260	−	24.0829i	0.118836	−	0.826524i
$850$		0			0
$851$	−19.6701	−	6.93939i	−0.674282	−	0.237879i
$852$		0			0
$853$	0.378190	−	2.63037i	0.0129490	−	0.0900621i	−0.982322	−	0.187199i	$-0.940059\pi$
$853$	0.378190	−	2.63037i	0.0129490	−	0.0900621i	0.995271	+	0.0971364i	$0.0309683\pi$
$854$		0			0
$855$	17.0970	+	5.02013i	0.584705	+	0.171685i
$856$		0			0
$857$	21.7664	−	6.39119i	0.743526	−	0.218319i	0.112037	−	0.993704i	$-0.464262\pi$
$857$	21.7664	−	6.39119i	0.743526	−	0.218319i	0.631489	+	0.775385i	$0.282444\pi$
$858$		0			0
$859$	1.20931	−	2.64803i	0.0412613	−	0.0903495i	−0.887879	−	0.460077i	$-0.847822\pi$
$859$	1.20931	−	2.64803i	0.0412613	−	0.0903495i	0.929140	+	0.369728i	$0.120549\pi$
$860$		0			0
$861$	−23.6817	+	15.2193i	−0.807069	+	0.518672i
$862$		0			0
$863$	−1.06041	−	7.37532i	−0.0360968	−	0.251059i	0.963781	−	0.266695i	$-0.0859317\pi$
$863$	−1.06041	−	7.37532i	−0.0360968	−	0.251059i	−0.999878	+	0.0156363i	$0.995023\pi$
$864$		0			0
$865$	−26.3455	+	30.4043i	−0.895773	+	1.03378i
$866$		0			0
$867$	−14.1428	−	9.08902i	−0.480315	−	0.308679i
$868$		0			0
$869$	5.23736	+	6.04423i	0.177665	+	0.205037i
$870$		0			0
$871$	−15.6435	−	34.2545i	−0.530059	−	1.16067i
$872$		0			0
$873$	17.8018			0.602500
$874$		0			0
$875$	−12.6483			−0.427589
$876$		0			0
$877$	−4.89815	−	10.7255i	−0.165399	−	0.362173i	0.808725	−	0.588186i	$-0.200158\pi$
$877$	−4.89815	−	10.7255i	−0.165399	−	0.362173i	−0.974124	+	0.226014i	$0.927431\pi$
$878$		0			0
$879$	−13.8055	−	15.9324i	−0.465649	−	0.537388i
$880$		0			0
$881$	8.82103	+	5.66893i	0.297188	+	0.190991i	0.680734	−	0.732531i	$-0.261661\pi$
$881$	8.82103	+	5.66893i	0.297188	+	0.190991i	−0.383546	+	0.923522i	$0.625297\pi$
$882$		0			0
$883$	−5.71672	+	6.59744i	−0.192383	+	0.222022i	−0.843743	−	0.536747i	$-0.819653\pi$
$883$	−5.71672	+	6.59744i	−0.192383	+	0.222022i	0.651361	+	0.758768i	$0.274199\pi$
$884$		0			0
$885$	−2.01081	−	13.9855i	−0.0675927	−	0.470118i
$886$		0			0
$887$	36.2516	−	23.2975i	1.21721	−	0.782254i	0.235360	−	0.971908i	$-0.424373\pi$
$887$	36.2516	−	23.2975i	1.21721	−	0.782254i	0.981851	+	0.189654i	$0.0607367\pi$
$888$		0			0
$889$	−19.9623	+	43.7113i	−0.669513	+	1.46603i
$890$		0			0
$891$	−3.32220	+	0.975485i	−0.111298	+	0.0326800i
$892$		0			0
$893$	−13.3499	−	3.91989i	−0.446738	−	0.131174i
$894$		0			0
$895$	−1.25611	+	8.73645i	−0.0419872	+	0.292027i
$896$		0			0
$897$	−2.90597	+	14.6087i	−0.0970276	+	0.487770i
$898$		0			0
$899$	5.00242	−	34.7926i	0.166840	−	1.16040i
$900$		0			0
$901$	−1.13733	−	0.333950i	−0.0378900	−	0.0111255i
$902$		0			0
$903$	35.5232	−	10.4305i	1.18214	−	0.347107i
$904$		0			0
$905$	−4.47072	+	9.78951i	−0.148612	+	0.325414i
$906$		0			0
$907$	43.3199	−	27.8400i	1.43841	−	0.924412i	0.438745	−	0.898611i	$-0.355423\pi$
$907$	43.3199	−	27.8400i	1.43841	−	0.924412i	0.999667	−	0.0258001i	$-0.00821332\pi$
$908$		0			0
$909$	−1.15238	−	8.01496i	−0.0382219	−	0.265839i
$910$		0			0
$911$	−1.89126	+	2.18263i	−0.0626603	+	0.0723139i	−0.786214	−	0.617954i	$-0.787962\pi$
$911$	−1.89126	+	2.18263i	−0.0626603	+	0.0723139i	0.723554	+	0.690268i	$0.242507\pi$
$912$		0			0
$913$	52.2125	+	33.5549i	1.72798	+	1.11051i
$914$		0			0
$915$	20.8646	+	24.0791i	0.689763	+	0.796029i
$916$		0			0
$917$	−19.1894	−	42.0189i	−0.633689	−	1.38759i
$918$		0			0
$919$	−39.4323			−1.30075			−0.650376	−	0.759612i	$-0.725389\pi$
$919$	−39.4323			−1.30075			−0.650376	+	0.759612i	$0.725389\pi$
$920$		0			0
$921$	−1.43156			−0.0471715
$922$		0			0
$923$	9.02840	+	19.7694i	0.297173	+	0.650719i
$924$		0			0
$925$	−11.4324	−	13.1937i	−0.375896	−	0.433807i
$926$		0			0
$927$	−4.58812	−	2.94860i	−0.150694	−	0.0968449i
$928$		0			0
$929$	−27.9478	+	32.2535i	−0.916937	+	1.05820i	0.0811699	+	0.996700i	$0.474134\pi$
$929$	−27.9478	+	32.2535i	−0.916937	+	1.05820i	−0.998107	+	0.0615016i	$0.980411\pi$
$930$		0			0
$931$	9.50622	+	66.1172i	0.311554	+	2.16690i
$932$		0			0
$933$	−8.41109	+	5.40548i	−0.275367	+	0.176967i
$934$		0			0
$935$	1.87454	−	4.10468i	0.0613041	−	0.134237i
$936$		0			0
$937$	21.6484	−	6.35655i	0.707223	−	0.207659i	0.0917097	−	0.995786i	$-0.470767\pi$
$937$	21.6484	−	6.35655i	0.707223	−	0.207659i	0.615514	+	0.788126i	$0.288949\pi$
$938$		0			0
$939$	3.28405	+	0.964286i	0.107171	+	0.0314683i
$940$		0			0
$941$	8.65630	−	60.2059i	0.282187	−	1.96266i	0.0117071	−	0.999931i	$-0.496273\pi$
$941$	8.65630	−	60.2059i	0.282187	−	1.96266i	0.270480	−	0.962725i	$-0.412817\pi$
$942$		0			0
$943$	−14.6462	+	27.9987i	−0.476944	+	0.911763i
$944$		0			0
$945$	−1.82556	+	12.6971i	−0.0593856	+	0.413036i
$946$		0			0
$947$	6.49608	+	1.90742i	0.211094	+	0.0619829i	0.385570	−	0.922679i	$-0.374005\pi$
$947$	6.49608	+	1.90742i	0.211094	+	0.0619829i	−0.174476	+	0.984661i	$0.555823\pi$
$948$		0			0
$949$	−27.5392	+	8.08623i	−0.893960	+	0.262490i
$950$		0			0
$951$	−8.31456	+	18.2063i	−0.269618	+	0.590381i
$952$		0			0
$953$	36.9596	−	23.7525i	1.19724	−	0.769418i	0.218762	−	0.975778i	$-0.429798\pi$
$953$	36.9596	−	23.7525i	1.19724	−	0.769418i	0.978476	+	0.206360i	$0.0661618\pi$
$954$		0			0
$955$	−9.25931	−	64.3999i	−0.299624	−	2.08393i
$956$		0			0
$957$	13.1525	−	15.1787i	0.425158	−	0.490659i
$958$		0			0
$959$	−42.9723	−	27.6166i	−1.38765	−	0.891787i
$960$		0			0
$961$	−3.74629	−	4.32345i	−0.120848	−	0.139466i
$962$		0			0
$963$	6.97950	+	15.2830i	0.224911	+	0.492487i
$964$		0			0
$965$	54.1472			1.74306
$966$		0			0
$967$	46.1512			1.48412			0.742061	−	0.670333i	$-0.233849\pi$
$967$	46.1512			1.48412			0.742061	+	0.670333i	$0.233849\pi$
$968$		0			0
$969$	−1.07022	−	2.34345i	−0.0343804	−	0.0752825i
$970$		0			0
$971$	13.0184	+	15.0240i	0.417781	+	0.482144i	0.925159	−	0.379579i	$-0.123931\pi$
$971$	13.0184	+	15.0240i	0.417781	+	0.482144i	−0.507379	+	0.861723i	$0.669386\pi$
$972$		0			0
$973$	61.9781	+	39.8309i	1.98693	+	1.27692i
$974$		0			0
$975$	−8.16391	+	9.42166i	−0.261455	+	0.301735i
$976$		0			0
$977$	2.61041	+	18.1558i	0.0835145	+	0.580856i	0.988012	+	0.154377i	$0.0493371\pi$
$977$	2.61041	+	18.1558i	0.0835145	+	0.580856i	−0.904497	+	0.426479i	$0.859754\pi$
$978$		0			0
$979$	−24.5225	+	15.7597i	−0.783743	+	0.503681i
$980$		0			0
$981$	5.71411	−	12.5122i	0.182437	−	0.399482i
$982$		0			0
$983$	−14.1134	+	4.14406i	−0.450147	+	0.132175i	−0.498945	−	0.866634i	$-0.666279\pi$
$983$	−14.1134	+	4.14406i	−0.450147	+	0.132175i	0.0487982	+	0.998809i	$0.484461\pi$
$984$		0			0
$985$	5.74727	+	1.68755i	0.183123	+	0.0537698i
$986$		0			0
$987$	1.42546	−	9.91432i	0.0453730	−	0.315576i
$988$		0			0
$989$	28.8564	−	29.9049i	0.917579	−	0.950919i
$990$		0			0
$991$	−0.414961	+	2.88611i	−0.0131817	+	0.0916804i	−0.995350	−	0.0963219i	$-0.969292\pi$
$991$	−0.414961	+	2.88611i	−0.0131817	+	0.0916804i	0.982169	+	0.188002i	$0.0602013\pi$
$992$		0			0
$993$	−6.53257	−	1.91814i	−0.207305	−	0.0608702i
$994$		0			0
$995$	−63.3806	+	18.6102i	−2.00930	+	0.589984i
$996$		0			0
$997$	−1.61590	+	3.53832i	−0.0511759	+	0.112060i	−0.933493	−	0.358596i	$-0.883255\pi$
$997$	−1.61590	+	3.53832i	−0.0511759	+	0.112060i	0.882317	+	0.470656i	$0.155983\pi$
$998$		0			0
$999$	3.65882	−	2.35138i	0.115760	−	0.0743944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.169.1	yes	30
23.3	even	11	inner	552.2.q.a.49.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.49.1	✓	30	23.3	even	11	inner
552.2.q.a.169.1	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{3} +(-1.96611 - 2.26901i) q^{5} +(3.59431 + 2.30992i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.415415 + 0.909632i) q^{3} +(-1.96611 - 2.26901i) q^{5} +(3.59431 + 2.30992i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-0.492758 - 3.42721i) q^{11} +(2.61277 - 1.67912i) q^{13} +(1.24721 - 2.73102i) q^{15} +(-0.416498 + 0.122295i) q^{17} +(5.69457 + 1.67208i) q^{19} +(-0.608049 + 4.22908i) q^{21} +(1.75587 + 4.46284i) q^{23} +(-0.571250 + 3.97313i) q^{25} +(-0.959493 - 0.281733i) q^{27} +(5.56565 - 1.63422i) q^{29} +(2.51732 - 5.51216i) q^{31} +(2.91280 - 1.87194i) q^{33} +(-1.82556 - 12.6971i) q^{35} +(-2.84815 + 3.28694i) q^{37} +(2.61277 + 1.67912i) q^{39} +(4.31465 + 4.97937i) q^{41} +(-3.59967 - 7.88219i) q^{43} +3.00233 q^{45} -2.34432 q^{47} +(4.67542 + 10.2377i) q^{49} +(-0.284263 - 0.328057i) q^{51} +(2.29721 + 1.47633i) q^{53} +(-6.80755 + 7.85634i) q^{55} +(0.844636 + 5.87457i) q^{57} +(3.95904 - 2.54432i) q^{59} +(-4.40845 + 9.65315i) q^{61} +(-4.09950 + 1.20372i) q^{63} +(-8.94693 - 2.62706i) q^{65} +(1.72555 - 12.0015i) q^{67} +(-3.33012 + 3.45113i) q^{69} +(-0.995876 + 6.92647i) q^{71} +(-8.86701 - 2.60359i) q^{73} +(-3.85139 + 1.13087i) q^{75} +(6.14546 - 13.4567i) q^{77} +(-1.94315 + 1.24879i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(-11.7385 + 13.5470i) q^{83} +(1.09637 + 0.704593i) q^{85} +(3.79859 + 4.38381i) q^{87} +(-3.49733 - 7.65808i) q^{89} +13.2697 q^{91} +6.05976 q^{93} +(-7.40219 - 16.2085i) q^{95} +(-11.6577 - 13.4537i) q^{97} +(2.91280 + 1.87194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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